SuiteSparse/0000755001170100242450000000000010712416123011744 5ustar davisfacSuiteSparse/AMD/0000755001170100242450000000000010620447137012354 5ustar davisfacSuiteSparse/AMD/Doc/0000755001170100242450000000000010711427507013061 5ustar davisfacSuiteSparse/AMD/Doc/Makefile0000644001170100242450000000200010423447623014512 0ustar davisfac#------------------------------------------------------------------------------ # AMD Makefile for compiling on Unix systems (for GNU or original make) #------------------------------------------------------------------------------ default: dist include ../../UFconfig/UFconfig.mk #------------------------------------------------------------------------------ # Remove all but the files in the original distribution #------------------------------------------------------------------------------ clean: - $(RM) $(CLEAN) purge: distclean distclean: clean - $(RM) *.aux *.bbl *.blg *.log *.toc #------------------------------------------------------------------------------ # Create the User Guide and Quick Start Guide #------------------------------------------------------------------------------ AMD_UserGuide.pdf: AMD_UserGuide.tex AMD_UserGuide.bib pdflatex AMD_UserGuide bibtex AMD_UserGuide pdflatex AMD_UserGuide pdflatex AMD_UserGuide dist: AMD_UserGuide.pdf - $(RM) *.aux *.bbl *.blg *.log *.toc SuiteSparse/AMD/Doc/AMD_UserGuide.bib0000644001170100242450000000470310250413605016110 0ustar davisfac@string{SIREV = "{SIAM} Review"} @string{SIMAX = "{SIAM} J. Matrix Anal. Applic."} @string{SIAMJSC = "{SIAM} J. Sci. Comput."} @string{TOMS = "{ACM} Trans. Math. Softw."} @article{schu:01, author = {J. Schulze}, title = {Towards a tighter coupling of bottom-up and top-down sparse matrix ordering methods}, journal = {BIT}, volume = {41}, number = {4}, pages = "800--841", year = {2001} } @article{GeorgeLiu89, author={George, A. and Liu, J. W. H.}, year={1989}, title={The Evolution of the Minimum Degree Ordering Algorithm}, journal=SIREV, volume={31}, number={1}, pages={1--19}} @article{AmestoyDavisDuff96, author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.}, title={An approximate minimum degree ordering algorithm}, journal=SIMAX, year={1996} ,volume={17} ,number={4} ,pages={886-905} } @article{AmestoyDavisDuff04, author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.}, title={Algorithm 837: An approximate minimum degree ordering algorithm}, journal=TOMS, year={2004} ,volume={30} ,number={3} ,pages={381-388} } @misc{hsl:2002, author = {HSL}, title = "{HSL} 2002: {A} collection of {F}ortran codes for large scale scientific computation", note = {{\tt www.cse.clrc.ac.uk/nag/hsl}}, year = 2002} @article{RothbergEisenstat98, author={Rothberg, E. and Eisenstat, S. C.}, title={Node selection strategies for bottom-up sparse matrix orderings}, journal=SIMAX, year={1998} ,volume={19} ,number={3} ,pages={682-695} } @article{KarypisKumar98e, author={Karypis, G. and Kumar, V.}, title={A fast and high quality multilevel scheme for partitioning irregular graphs}, journal=SIAMJSC, year={1998} ,volume={20} ,pages={359-392} } @article{Chaco, author={B. Hendrickson and E. Rothberg}, title={Improving the runtime and quality of nested dissection ordering}, journal=SIAMJSC, year={1999} ,volume={20} ,pages={468--489} } @article{PellegriniRomanAmestoy00, author={Pellegrini, F. and Roman, J. and Amestoy, P.}, title={Hybridizing nested dissection and halo approximate minimum degree for efficient sparse matrix ordering}, journal={Concurrency: Practice and Experience}, year={2000} ,volume={12} ,pages={68-84} } @article{DavisGilbertLarimoreNg04, author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.}, title={A column approximate minimum degree ordering algorithm}, journal=TOMS, year={2004} ,volume={30} ,pages={353-376} } SuiteSparse/AMD/Doc/AMD_UserGuide.pdf0000644001170100242450000053112110617112147016130 0ustar davisfac%PDF-1.4 3 0 obj << /Length 3445 /Filter /FlateDecode >> stream xڕr`V,XKhmQJK*"!eA+׿d0y9X89HǾa0Z< 󭵣woz{>Xe_qn<^1^]178=.WpGU>s04x$RI2ljލMe-j%?5y3x@_ FJ#iH?ClO@&=E5wM})v$rL묨; 88)L(=_&hb?NPo,(XLGF&"FƤa6ٲe>Q'Q(]gN@|kҼ TE ro0lKyC+ jQ[og7@\hG([r'"z dS=A1}Q/Nj`I5xvTc5o;Wm=md;б;^n|bYSDdGV_`jad7F_r sSm^][=mcjŃq|[ɖ8 <"q{37qebp'ISDZhSjZD6-:8d$K@9kF[-fxD Pjr$?4 ˙8D1hz >AHt;t+ZV)ﲬIL]e$6/zMIYy'BX? 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0000159817 00000 n 0000159551 00000 n 0000167455 00000 n 0000167151 00000 n 0000172527 00000 n 0000172331 00000 n 0000173219 00000 n 0000173302 00000 n 0000173355 00000 n trailer << /Size 150 /Root 148 0 R /Info 149 0 R /ID [ ] >> startxref 173559 %%EOF SuiteSparse/AMD/Doc/AMD_UserGuide.tex0000644001170100242450000014675310617112144016171 0ustar davisfac\documentclass[11pt]{article} \newcommand{\m}[1]{{\bf{#1}}} % for matrices and vectors \newcommand{\tr}{^{\sf T}} % transpose \topmargin 0in \textheight 9in \oddsidemargin 0pt \evensidemargin 0pt \textwidth 6.5in %------------------------------------------------------------------------------ \begin{document} %------------------------------------------------------------------------------ \title{AMD Version 2.2 User Guide} \author{Patrick R. Amestoy\thanks{ENSEEIHT-IRIT, 2 rue Camichel 31017 Toulouse, France. email: amestoy@enseeiht.fr. http://www.enseeiht.fr/$\sim$amestoy.} \and Timothy A. Davis\thanks{ Dept.~of Computer and Information Science and Engineering, Univ.~of Florida, Gainesville, FL, USA. email: davis@cise.ufl.edu. http://www.cise.ufl.edu/$\sim$davis. This work was supported by the National Science Foundation, under grants ASC-9111263, DMS-9223088, and CCR-0203270. Portions of the work were done while on sabbatical at Stanford University and Lawrence Berkeley National Laboratory (with funding from Stanford University and the SciDAC program). } \and Iain S. Duff\thanks{Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, England. email: i.s.duff@rl.ac.uk. http://www.numerical.rl.ac.uk/people/isd/isd.html. This work was supported by the EPSRC under grant GR/R46441. }} \date{May 31, 2007} \maketitle %------------------------------------------------------------------------------ \begin{abstract} AMD is a set of routines that implements the approximate minimum degree ordering algorithm to permute sparse matrices prior to numerical factorization. There are versions written in both C and Fortran 77. A MATLAB interface is included. \end{abstract} %------------------------------------------------------------------------------ Technical report TR-04-002 (revised), CISE Department, University of Florida, Gainesville, FL, 2007. AMD Version 2.2, Copyright\copyright 2007 by Timothy A. Davis, Patrick R. Amestoy, and Iain S. Duff. All Rights Reserved. AMD is available under alternate licences; contact T. Davis for details. {\bf AMD License:} Your use or distribution of AMD or any modified version of AMD implies that you agree to this License. This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Permission is hereby granted to use or copy this program under the terms of the GNU LGPL, provided that the Copyright, this License, and the Availability of the original version is retained on all copies. User documentation of any code that uses this code or any modified version of this code must cite the Copyright, this License, the Availability note, and "Used by permission." Permission to modify the code and to distribute modified code is granted, provided the Copyright, this License, and the Availability note are retained, and a notice that the code was modified is included. {\bf Availability:} http://www.cise.ufl.edu/research/sparse/amd {\bf Acknowledgments:} This work was supported by the National Science Foundation, under grants ASC-9111263 and DMS-9223088 and CCR-0203270. The conversion to C, the addition of the elimination tree post-ordering, and the handling of dense rows and columns were done while Davis was on sabbatical at Stanford University and Lawrence Berkeley National Laboratory. %------------------------------------------------------------------------------ \newpage \section{Overview} %------------------------------------------------------------------------------ AMD is a set of routines for preordering a sparse matrix prior to numerical factorization. It uses an approximate minimum degree ordering algorithm \cite{AmestoyDavisDuff96,AmestoyDavisDuff04} to find a permutation matrix $\m{P}$ so that the Cholesky factorization $\m{PAP}\tr=\m{LL}\tr$ has fewer (often much fewer) nonzero entries than the Cholesky factorization of $\m{A}$. The algorithm is typically much faster than other ordering methods and minimum degree ordering algorithms that compute an exact degree \cite{GeorgeLiu89}. Some methods, such as approximate deficiency \cite{RothbergEisenstat98} and graph-partitioning based methods \cite{Chaco,KarypisKumar98e,PellegriniRomanAmestoy00,schu:01} can produce better orderings, depending on the matrix. The algorithm starts with an undirected graph representation of a symmetric sparse matrix $\m{A}$. Node $i$ in the graph corresponds to row and column $i$ of the matrix, and there is an edge $(i,j)$ in the graph if $a_{ij}$ is nonzero. The degree of a node is initialized to the number of off-diagonal nonzeros in row $i$, which is the size of the set of nodes adjacent to $i$ in the graph. The selection of a pivot $a_{ii}$ from the diagonal of $\m{A}$ and the first step of Gaussian elimination corresponds to one step of graph elimination. Numerical fill-in causes new nonzero entries in the matrix (fill-in refers to nonzeros in $\m{L}$ that are not in $\m{A}$). Node $i$ is eliminated and edges are added to its neighbors so that they form a clique (or {\em element}). To reduce fill-in, node $i$ is selected as the node of least degree in the graph. This process repeats until the graph is eliminated. The clique is represented implicitly. Rather than listing all the new edges in the graph, a single list of nodes is kept which represents the clique. This list corresponds to the nonzero pattern of the first column of $\m{L}$. As the elimination proceeds, some of these cliques become subsets of subsequent cliques, and are removed. This graph can be stored in place, that is using the same amount of memory as the original graph. The most costly part of the minimum degree algorithm is the recomputation of the degrees of nodes adjacent to the current pivot element. Rather than keep track of the exact degree, the approximate minimum degree algorithm finds an upper bound on the degree that is easier to compute. For nodes of least degree, this bound tends to be tight. Using the approximate degree instead of the exact degree leads to a substantial savings in run time, particularly for very irregularly structured matrices. It has no effect on the quality of the ordering. In the C version of AMD, the elimination phase is followed by an elimination tree post-ordering. This has no effect on fill-in, but reorganizes the ordering so that the subsequent numerical factorization is more efficient. It also includes a pre-processing phase in which nodes of very high degree are removed (without causing fill-in), and placed last in the permutation $\m{P}$. This reduces the run time substantially if the matrix has a few rows with many nonzero entries, and has little effect on the quality of the ordering. The C version operates on the symmetric nonzero pattern of $\m{A}+\m{A}\tr$, so it can be given an unsymmetric matrix, or either the lower or upper triangular part of a symmetric matrix. The two Fortran versions of AMD are essentially identical to two versions of the AMD algorithm discussed in an earlier paper \cite{AmestoyDavisDuff96} (approximate minimum external degree, both with and without aggressive absorption). For a discussion of the long history of the minimum degree algorithm, see \cite{GeorgeLiu89}. %------------------------------------------------------------------------------ \section{Availability} %------------------------------------------------------------------------------ In addition to appearing as a Collected Algorithm of the ACM, \newline AMD is available at http://www.cise.ufl.edu/research/sparse. The Fortran version is available as the routine {\tt MC47} in HSL (formerly the Harwell Subroutine Library) \cite{hsl:2002}. %------------------------------------------------------------------------------ \section{Using AMD in MATLAB} %------------------------------------------------------------------------------ The MATLAB function {\tt amd} is now a built-in function in MATLAB 7.3 (R2006b). The built-in {\tt amd} and the {\tt amd2} function provided here differ in how the optional parameters are passed (the 2nd input parameter). To use AMD2 in MATLAB, you must first compile the AMD2 mexFunction. Just type {\tt make} in the Unix system shell, while in the {\tt AMD/MATLAB} directory. You can also type {\tt amd\_make} in MATLAB, while in the {\tt AMD/MATLAB} directory. Place the {\tt AMD/MATLAB} directory in your MATLAB path. This can be done on any system with MATLAB, including Windows. See Section~\ref{Install} for more details on how to install AMD. The MATLAB statement {\tt p=amd(A)} finds a permutation vector {\tt p} such that the Cholesky factorization {\tt chol(A(p,p))} is typically sparser than {\tt chol(A)}. If {\tt A} is unsymmetric, {\tt amd(A)} is identical to {\tt amd(A+A')} (ignoring numerical cancellation). If {\tt A} is not symmetric positive definite, but has substantial diagonal entries and a mostly symmetric nonzero pattern, then this ordering is also suitable for LU factorization. A partial pivoting threshold may be required to prevent pivots from being selected off the diagonal, such as the statement {\tt [L,U,P] = lu (A (p,p), 0.1)}. Type {\tt help lu} for more details. The statement {\tt [L,U,P,Q] = lu (A (p,p))} in MATLAB 6.5 is not suitable, however, because it uses UMFPACK Version 4.0 and thus does not attempt to select pivots from the diagonal. UMFPACK Version 4.1 in MATLAB 7.0 and later uses several strategies, including a symmetric pivoting strategy, and will give you better results if you want to factorize an unsymmetric matrix of this type. Refer to the UMFPACK User Guide for more details, at http://www.cise.ufl.edu/research/sparse/umfpack. The AMD mexFunction is much faster than the built-in MATLAB symmetric minimum degree ordering methods, SYMAMD and SYMMMD. Its ordering quality is comparable to SYMAMD, and better than SYMMMD \cite{DavisGilbertLarimoreNg04}. An optional input argument can be used to modify the control parameters for AMD (aggressive absorption, dense row/column handling, and printing of statistics). An optional output argument provides statistics on the ordering, including an analysis of the fill-in and the floating-point operation count for a subsequent factorization. For more details (once AMD is installed), type {\tt help amd} in the MATLAB command window. %------------------------------------------------------------------------------ \section{Using AMD in a C program} \label{Cversion} %------------------------------------------------------------------------------ The C-callable AMD library consists of seven user-callable routines and one include file. There are two versions of each of the routines, with {\tt int} and {\tt long} integers. The routines with prefix {\tt amd\_l\_} use {\tt long} integer arguments; the others use {\tt int} integer arguments. If you compile AMD in the standard ILP32 mode (32-bit {\tt int}'s, {\tt long}'s, and pointers) then the versions are essentially identical. You will be able to solve problems using up to 2GB of memory. If you compile AMD in the standard LP64 mode, the size of an {\tt int} remains 32-bits, but the size of a {\tt long} and a pointer both get promoted to 64-bits. The following routines are fully described in Section~\ref{Primary}: \begin{itemize} \item {\tt amd\_order} ({\tt long} version: {\tt amd\_l\_order}) {\footnotesize \begin{verbatim} #include "amd.h" int n, Ap [n+1], Ai [nz], P [n] ; double Control [AMD_CONTROL], Info [AMD_INFO] ; int result = amd_order (n, Ap, Ai, P, Control, Info) ; \end{verbatim} } Computes the approximate minimum degree ordering of an $n$-by-$n$ matrix $\m{A}$. Returns a permutation vector {\tt P} of size {\tt n}, where {\tt P[k] = i} if row and column {\tt i} are the {\tt k}th row and column in the permuted matrix. This routine allocates its own memory of size $1.2e+9n$ integers, where $e$ is the number of nonzeros in $\m{A}+\m{A}\tr$. It computes statistics about the matrix $\m{A}$, such as the symmetry of its nonzero pattern, the number of nonzeros in $\m{L}$, and the number of floating-point operations required for Cholesky and LU factorizations (which are returned in the {\tt Info} array). The user's input matrix is not modified. It returns {\tt AMD\_OK} if successful, {\tt AMD\_OK\_BUT\_JUMBLED} if successful (but the matrix had unsorted and/or duplicate row indices), {\tt AMD\_INVALID} if the matrix is invalid, {\tt AMD\_OUT\_OF\_MEMORY} if out of memory. \item {\tt amd\_defaults} ({\tt long} version: {\tt amd\_l\_defaults}) {\footnotesize \begin{verbatim} #include "amd.h" double Control [AMD_CONTROL] ; amd_defaults (Control) ; \end{verbatim} } Sets the default control parameters in the {\tt Control} array. These can then be modified as desired before passing the array to the other AMD routines. \item {\tt amd\_control} ({\tt long} version: {\tt amd\_l\_control}) {\footnotesize \begin{verbatim} #include "amd.h" double Control [AMD_CONTROL] ; amd_control (Control) ; \end{verbatim} } Prints a description of the control parameters, and their values. \item {\tt amd\_info} ({\tt long} version: {\tt amd\_l\_info}) {\footnotesize \begin{verbatim} #include "amd.h" double Info [AMD_INFO] ; amd_info (Info) ; \end{verbatim} } Prints a description of the statistics computed by AMD, and their values. \item {\tt amd\_valid} ({\tt long} version: {\tt amd\_valid}) {\footnotesize \begin{verbatim} #include "amd.h" int n, Ap [n+1], Ai [nz] ; int result = amd_valid (n, n, Ap, Ai) ; \end{verbatim} } Returns {\tt AMD\_OK} or {\tt AMD\_OK\_BUT\_JUMBLED} if the matrix is valid as input to {\tt amd\_order}; the latter is returned if the matrix has unsorted and/or duplicate row indices in one or more columns. Returns {\tt AMD\_INVALID} if the matrix cannot be passed to {\tt amd\_order}. For {\tt amd\_order}, the matrix must also be square. The first two arguments are the number of rows and the number of columns of the matrix. For its use in AMD, these must both equal {\tt n}. \item {\tt amd\_2} ({\tt long} version: {\tt amd\_l2}) AMD ordering kernel. It is faster than {\tt amd\_order}, and can be called by the user, but it is difficult to use. It does not check its inputs for errors. It does not require the columns of its input matrix to be sorted, but it destroys the matrix on output. Additional workspace must be passed. Refer to the source file {\tt AMD/Source/amd\_2.c} for a description. \end{itemize} The nonzero pattern of the matrix $\m{A}$ is represented in compressed column form. For an $n$-by-$n$ matrix $\m{A}$ with {\tt nz} nonzero entries, the representation consists of two arrays: {\tt Ap} of size {\tt n+1} and {\tt Ai} of size {\tt nz}. The row indices of entries in column {\tt j} are stored in {\tt Ai[Ap[j]} $\ldots$ {\tt Ap[j+1]-1]}. For {\tt amd\_order}, if duplicate row indices are present, or if the row indices in any given column are not sorted in ascending order, then {\tt amd\_order} creates an internal copy of the matrix with sorted rows and no duplicate entries, and orders the copy. This adds slightly to the time and memory usage of {\tt amd\_order}, but is not an error condition. The matrix is 0-based, and thus row indices must be in the range {\tt 0} to {\tt n-1}. The first entry {\tt Ap[0]} must be zero. The total number of entries in the matrix is thus {\tt nz = Ap[n]}. The matrix must be square, but it does not need to be symmetric. The {\tt amd\_order} routine constructs the nonzero pattern of $\m{B} = \m{A}+\m{A}\tr$ (without forming $\m{A}\tr$ explicitly if $\m{A}$ has sorted columns and no duplicate entries), and then orders the matrix $\m{B}$. Thus, either the lower triangular part of $\m{A}$, the upper triangular part, or any combination may be passed. The transpose $\m{A}\tr$ may also be passed to {\tt amd\_order}. The diagonal entries may be present, but are ignored. %------------------------------------------------------------------------------ \subsection{Control parameters} \label{control_param} %------------------------------------------------------------------------------ Control parameters are set in an optional {\tt Control} array. It is optional in the sense that if a {\tt NULL} pointer is passed for the {\tt Control} input argument, then default control parameters are used. % \begin{itemize} \item {\tt Control[AMD\_DENSE]} (or {\tt Control(1)} in MATLAB): controls the threshold for ``dense'' rows/columns. A dense row/column in $\m{A}+\m{A}\tr$ can cause AMD to spend significant time in ordering the matrix. If {\tt Control[AMD\_DENSE]} $\ge 0$, rows/columns with more than {\tt Control[AMD\_DENSE]} $\sqrt{n}$ entries are ignored during the ordering, and placed last in the output order. The default value of {\tt Control[AMD\_DENSE]} is 10. If negative, no rows/columns are treated as ``dense.'' Rows/columns with 16 or fewer off-diagonal entries are never considered ``dense.'' % \item {\tt Control[AMD\_AGGRESSIVE]} (or {\tt Control(2)} in MATLAB): controls whether or not to use aggressive absorption, in which a prior element is absorbed into the current element if it is a subset of the current element, even if it is not adjacent to the current pivot element (refer to \cite{AmestoyDavisDuff96,AmestoyDavisDuff04} for more details). The default value is nonzero, which means that aggressive absorption will be performed. This nearly always leads to a better ordering (because the approximate degrees are more accurate) and a lower execution time. There are cases where it can lead to a slightly worse ordering, however. To turn it off, set {\tt Control[AMD\_AGGRESSIVE]} to 0. % \end{itemize} Statistics are returned in the {\tt Info} array (if {\tt Info} is {\tt NULL}, then no statistics are returned). Refer to {\tt amd.h} file, for more details (14 different statistics are returned, so the list is not included here). %------------------------------------------------------------------------------ \subsection{Sample C program} %------------------------------------------------------------------------------ The following program, {\tt amd\_demo.c}, illustrates the basic use of AMD. See Section~\ref{Synopsis} for a short description of each calling sequence. {\footnotesize \begin{verbatim} #include #include "amd.h" int n = 5 ; int Ap [ ] = { 0, 2, 6, 10, 12, 14} ; int Ai [ ] = { 0,1, 0,1,2,4, 1,2,3,4, 2,3, 1,4 } ; int P [5] ; int main (void) { int k ; (void) amd_order (n, Ap, Ai, P, (double *) NULL, (double *) NULL) ; for (k = 0 ; k < n ; k++) printf ("P [%d] = %d\n", k, P [k]) ; return (0) ; } \end{verbatim} } The {\tt Ap} and {\tt Ai} arrays represent the binary matrix \[ \m{A} = \left[ \begin{array}{rrrrr} 1 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 0 & 1 & 1 & 0 \\ 0 & 1 & 1 & 0 & 1 \\ \end{array} \right]. \] The diagonal entries are ignored. % AMD constructs the pattern of $\m{A}+\m{A}\tr$, and returns a permutation vector of $(0, 3, 1, 4, 2)$. % Since the matrix is unsymmetric but with a mostly symmetric nonzero pattern, this would be a suitable permutation for an LU factorization of a matrix with this nonzero pattern and whose diagonal entries are not too small. The program uses default control settings and does not return any statistics about the ordering, factorization, or solution ({\tt Control} and {\tt Info} are both {\tt (double *) NULL}). It also ignores the status value returned by {\tt amd\_order}. More example programs are included with the AMD package. The {\tt amd\_demo.c} program provides a more detailed demo of AMD. Another example is the AMD mexFunction, {\tt amd\_mex.c}. %------------------------------------------------------------------------------ \subsection{A note about zero-sized arrays} %------------------------------------------------------------------------------ AMD uses several user-provided arrays of size {\tt n} or {\tt nz}. Either {\tt n} or {\tt nz} can be zero. If you attempt to {\tt malloc} an array of size zero, however, {\tt malloc} will return a null pointer which AMD will report as invalid. If you {\tt malloc} an array of size {\tt n} or {\tt nz} to pass to AMD, make sure that you handle the {\tt n} = 0 and {\tt nz = 0} cases correctly. %------------------------------------------------------------------------------ \section{Synopsis of C-callable routines} \label{Synopsis} %------------------------------------------------------------------------------ The matrix $\m{A}$ is {\tt n}-by-{\tt n} with {\tt nz} entries. {\footnotesize \begin{verbatim} #include "amd.h" int n, status, Ap [n+1], Ai [nz], P [n] ; double Control [AMD_CONTROL], Info [AMD_INFO] ; amd_defaults (Control) ; status = amd_order (n, Ap, Ai, P, Control, Info) ; amd_control (Control) ; amd_info (Info) ; status = amd_valid (n, n, Ap, Ai) ; \end{verbatim} } The {\tt amd\_l\_*} routines are identical, except that all {\tt int} arguments become {\tt long}: {\footnotesize \begin{verbatim} #include "amd.h" long n, status, Ap [n+1], Ai [nz], P [n] ; double Control [AMD_CONTROL], Info [AMD_INFO] ; amd_l_defaults (Control) ; status = amd_l_order (n, Ap, Ai, P, Control, Info) ; amd_l_control (Control) ; amd_l_info (Info) ; status = amd_l_valid (n, n, Ap, Ai) ; \end{verbatim} } %------------------------------------------------------------------------------ \section{Using AMD in a Fortran program} %------------------------------------------------------------------------------ Two Fortran versions of AMD are provided. The {\tt AMD} routine computes the approximate minimum degree ordering, using aggressive absorption. The {\tt AMDBAR} routine is identical, except that it does not perform aggressive absorption. The {\tt AMD} routine is essentially identical to the HSL routine {\tt MC47B/BD}. Note that earlier versions of the Fortran {\tt AMD} and {\tt AMDBAR} routines included an {\tt IOVFLO} argument, which is no longer present. In contrast to the C version, the Fortran routines require a symmetric nonzero pattern, with no diagonal entries present although the {\tt MC47A/AD} wrapper in HSL allows duplicates, ignores out-of-range entries, and only uses entries from the upper triangular part of the matrix. Although we have an experimental Fortran code for treating ``dense'' rows, the Fortran codes in this release do not treat ``dense'' rows and columns of $\m{A}$ differently, and thus their run time can be high if there are a few dense rows and columns in the matrix. They do not perform a post-ordering of the elimination tree, compute statistics on the ordering, or check the validity of their input arguments. These facilities are provided by {\tt MC47A/AD} and other subroutines from HSL. Only one {\tt integer} version of each Fortran routine is provided. Both Fortran routines overwrite the user's input matrix, in contrast to the C version. % The C version does not return the elimination or assembly tree. The Fortran version returns an assembly tree; refer to the User Guide for details. The following is the syntax of the {\tt AMD} Fortran routine. The {\tt AMDBAR} routine is identical except for the routine name. {\footnotesize \begin{verbatim} INTEGER N, IWLEN, PFREE, NCMPA, IW (IWLEN), PE (N), DEGREE (N), NV (N), $ NEXT (N), LAST (N), HEAD (N), ELEN (N), W (N), LEN (N) CALL AMD (N, PE, IW, LEN, IWLEN, PFREE, NV, NEXT, $ LAST, HEAD, ELEN, DEGREE, NCMPA, W) CALL AMDBAR (N, PE, IW, LEN, IWLEN, PFREE, NV, NEXT, $ LAST, HEAD, ELEN, DEGREE, NCMPA, W) \end{verbatim} } The input matrix is provided to {\tt AMD} and {\tt AMDBAR} in three arrays, {\tt PE}, of size {\tt N}, {\tt LEN}, of size {\tt N}, and {\tt IW}, of size {\tt IWLEN}. The size of {\tt IW} must be at least {\tt NZ+N}. The recommended size is {\tt 1.2*NZ + N}. On input, the indices of nonzero entries in row {\tt I} are stored in {\tt IW}. {\tt PE(I)} is the index in {\tt IW} of the start of row {\tt I}. {\tt LEN(I)} is the number of entries in row {\tt I}. The matrix is 1-based, with row and column indices in the range 1 to {\tt N}. Row {\tt I} is contained in {\tt IW (PE(I)} $\ldots \:$ {\tt PE(I) + LEN(I) - 1)}. The diagonal entries must not be present. The indices within each row must not contain any duplicates, but they need not be sorted. The rows themselves need not be in any particular order, and there may be empty space between the rows. If {\tt LEN(I)} is zero, then there are no off-diagonal entries in row {\tt I}, and {\tt PE(I)} is ignored. The integer {\tt PFREE} defines what part of {\tt IW} contains the user's input matrix, which is held in {\tt IW(1}~$\ldots~\:${\tt PFREE-1)}. The contents of {\tt IW} and {\tt LEN} are undefined on output, and {\tt PE} is modified to contain information about the ordering. As the algorithm proceeds, it modifies the {\tt IW} array, placing the pattern of the partially eliminated matrix in {\tt IW(PFREE} $\ldots \:${\tt IWLEN)}. If this space is exhausted, the space is compressed. The number of compressions performed on the {\tt IW} array is returned in the scalar {\tt NCMPA}. The value of {\tt PFREE} on output is the length of {\tt IW} required for no compressions to be needed. The output permutation is returned in the array {\tt LAST}, of size {\tt N}. If {\tt I=LAST(K)}, then {\tt I} is the {\tt K}th row in the permuted matrix. The inverse permutation is returned in the array {\tt ELEN}, where {\tt K=ELEN(I)} if {\tt I} is the {\tt K}th row in the permuted matrix. On output, the {\tt PE} and {\tt NV} arrays hold the assembly tree, a supernodal elimination tree that represents the relationship between columns of the Cholesky factor $\m{L}$. If {\tt NV(I)} $> 0$, then {\tt I} is a node in the assembly tree, and the parent of {\tt I} is {\tt -PE(I)}. If {\tt I} is a root of the tree, then {\tt PE(I)} is zero. The value of {\tt NV(I)} is the number of entries in the corresponding column of $\m{L}$, including the diagonal. If {\tt NV(I)} is zero, then {\tt I} is a non-principal node that is not in the assembly tree. Node {\tt -PE(I)} is the parent of node {\tt I} in a subtree, the root of which is a node in the assembly tree. All nodes in one subtree belong to the same supernode in the assembly tree. The other size {\tt N} arrays ({\tt DEGREE}, {\tt HEAD}, {\tt NEXT}, and {\tt W}) are used as workspace, and are not defined on input or output. If you want to use a simpler user-interface and compute the elimination tree post-ordering, you should be able to call the C routines {\tt amd\_order} or {\tt amd\_l\_order} from a Fortran program. Just be sure to take into account the 0-based indexing in the {\tt P}, {\tt Ap}, and {\tt Ai} arguments to {\tt amd\_order} and {\tt amd\_l\_order}. A sample interface is provided in the files {\tt AMD/Demo/amd\_f77cross.f} and {\tt AMD/Demo/amd\_f77wrapper.c}. To compile the {\tt amd\_f77cross} program, type {\tt make cross} in the {\tt AMD/Demo} directory. The Fortran-to-C calling conventions are highly non-portable, so this example is not guaranteed to work with your compiler C and Fortran compilers. The output of {\tt amd\_f77cross} is in {\tt amd\_f77cross.out}. %------------------------------------------------------------------------------ \section{Sample Fortran main program} %------------------------------------------------------------------------------ The following program illustrates the basic usage of the Fortran version of AMD. The {\tt AP} and {\tt AI} arrays represent the binary matrix \[ \m{A} = \left[ \begin{array}{rrrrr} 1 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 0 & 1 \\ 0 & 1 & 1 & 1 & 1 \\ 0 & 0 & 1 & 1 & 0 \\ 0 & 1 & 1 & 0 & 1 \\ \end{array} \right] \] in a conventional 1-based column-oriented form, except that the diagonal entries are not present. The matrix has the same as nonzero pattern of $\m{A}+\m{A}\tr$ in the C program, in Section~\ref{Cversion}. The output permutation is $(4, 1, 3, 5, 2)$. It differs from the permutation returned by the C routine {\tt amd\_order} because a post-order of the elimination tree has not yet been performed. {\footnotesize \begin{verbatim} INTEGER N, NZ, J, K, P, IWLEN, PFREE, NCMPA PARAMETER (N = 5, NZ = 10, IWLEN = 17) INTEGER AP (N+1), AI (NZ), LAST (N), PE (N), LEN (N), ELEN (N), $ IW (IWLEN), DEGREE (N), NV (N), NEXT (N), HEAD (N), W (N) DATA AP / 1, 2, 5, 8, 9, 11/ DATA AI / 2, 1,3,5, 2,4,5, 3, 2,3 / C load the matrix into the AMD workspace DO 10 J = 1,N PE (J) = AP (J) LEN (J) = AP (J+1) - AP (J) 10 CONTINUE DO 20 P = 1,NZ IW (P) = AI (P) 20 CONTINUE PFREE = NZ + 1 C order the matrix (destroys the copy of A in IW, PE, and LEN) CALL AMD (N, PE, IW, LEN, IWLEN, PFREE, NV, NEXT, LAST, HEAD, $ ELEN, DEGREE, NCMPA, W) DO 60 K = 1, N PRINT 50, K, LAST (K) 50 FORMAT ('P (',I2,') = ', I2) 60 CONTINUE END \end{verbatim} } The {\tt Demo} directory contains an example of how the C version may be called from a Fortran program, but this is highly non-portable. For this reason, it is placed in the {\tt Demo} directory, not in the primary {\tt Source} directory. %------------------------------------------------------------------------------ \section{Installation} \label{Install} %------------------------------------------------------------------------------ The following discussion assumes you have the {\tt make} program, either in Unix, or in Windows with Cygwin. System-dependent configurations are in the {\tt ../UFconfig/UFconfig.mk} file. You can edit that file to customize the compilation. The default settings will work on most systems. Sample configuration files are provided for Linux, Sun Solaris, SGI IRIX, IBM AIX, and the DEC/Compaq Alpha. To compile and install the C-callable AMD library, go to the {\tt AMD} directory and type {\tt make}. The library will be placed in {\tt AMD/Lib/libamd.a}. Three demo programs of the AMD ordering routine will be compiled and tested in the {\tt AMD/Demo} directory. The outputs of these demo programs will then be compared with output files in the distribution. To compile and install the Fortran-callable AMD library, go to the {\tt AMD} directory and type {\tt make fortran}. The library will be placed in {\tt AMD/Lib/libamdf77.a}. A demo program will be compiled and tested in the {\tt AMD/Demo} directory. The output will be compared with an output file in the distribution. Typing {\tt make clean} will remove all but the final compiled libraries and demo programs. Typing {\tt make purge} or {\tt make distclean} removes all files not in the original distribution. If you compile AMD and then later change the {\tt ../UFconfig/UFconfig.mk} file then you should type {\tt make purge} and then {\tt make} to recompile. When you compile your program that uses the C-callable AMD library, you need to add the {\tt AMD/Lib/libamd.a} library and you need to tell your compiler to look in the {\tt AMD/Include} directory for include files. To compile a Fortran program that calls the Fortran AMD library, you need to add the {\tt AMD/Lib/libamdf77.a} library. See {\tt AMD/Demo/Makefile} for an example. If all you want to use is the AMD2 mexFunction in MATLAB, you can skip the use of the {\tt make} command entirely. Simply type {\tt amd\_make} in MATLAB while in the {\tt AMD/MATLAB} directory. This works on any system with MATLAB, including Windows. Alternately, type {\tt make} in the {\tt AMD/MATLAB} directory, or just use the built-in {\tt amd} in MATLAB 7.3 or later. If you have MATLAB 7.2 or earlier, you must first edit UFconfig/UFconfig.h to remove the "-largeArrayDims" option from the MEX command, prior to {\tt make mex} or {\tt make} in the MATLAB directory (or just use {\tt amd\_make.m} inside MATLAB. If you are including AMD as a subset of a larger library and do not want to link the C standard I/O library, or if you simply do not need to use them, you can safely remove the {\tt amd\_control.c} and {\tt amd\_info.c} files. Similarly, if you use default parameters (or define your own {\tt Control} array), then you can exclude the {\tt amd\_defaults.c} file. Each of these files contains the user-callable routines of the same name. None of these auxiliary routines are directly called by {\tt amd\_order}. The {\tt amd\_dump.c} file contains debugging routines that are neither used nor compiled unless debugging is enabled. The {\tt amd\_internal.h} file must be edited to enable debugging; refer to the instructions in that file. The bare minimum files required to use just {\tt amd\_order} are {\tt amd.h} and {\tt amd\_internal.h} in the {\tt Include} directory, and {\tt amd\_1.c}, {\tt amd\_2.c}, {\tt amd\_aat.c}, {\tt amd\_global.c}, {\tt and\_order.c}, {\tt amd\_postorder.c}, {\tt amd\_post\_tree.c}, {\tt amd\_preprocess.c}, and {\tt amd\_valid.c} in the {\tt Source} directory. %------------------------------------------------------------------------------ \newpage \section{The AMD routines} \label{Primary} %------------------------------------------------------------------------------ The file {\tt AMD/Include/amd.h} listed below describes each user-callable routine in the C version of AMD, and gives details on their use. {\footnotesize \begin{verbatim} /* ========================================================================= */ /* === AMD: approximate minimum degree ordering =========================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD Version 2.2, Copyright (c) 2007 by Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ /* AMD finds a symmetric ordering P of a matrix A so that the Cholesky * factorization of P*A*P' has fewer nonzeros and takes less work than the * Cholesky factorization of A. If A is not symmetric, then it performs its * ordering on the matrix A+A'. Two sets of user-callable routines are * provided, one for int integers and the other for UF_long integers. * * The method is based on the approximate minimum degree algorithm, discussed * in Amestoy, Davis, and Duff, "An approximate degree ordering algorithm", * SIAM Journal of Matrix Analysis and Applications, vol. 17, no. 4, pp. * 886-905, 1996. This package can perform both the AMD ordering (with * aggressive absorption), and the AMDBAR ordering (without aggressive * absorption) discussed in the above paper. This package differs from the * Fortran codes discussed in the paper: * * (1) it can ignore "dense" rows and columns, leading to faster run times * (2) it computes the ordering of A+A' if A is not symmetric * (3) it is followed by a depth-first post-ordering of the assembly tree * (or supernodal elimination tree) * * For historical reasons, the Fortran versions, amd.f and amdbar.f, have * been left (nearly) unchanged. They compute the identical ordering as * described in the above paper. */ #ifndef AMD_H #define AMD_H /* make it easy for C++ programs to include AMD */ #ifdef __cplusplus extern "C" { #endif /* get the definition of size_t: */ #include /* define UF_long */ #include "UFconfig.h" int amd_order /* returns AMD_OK, AMD_OK_BUT_JUMBLED, * AMD_INVALID, or AMD_OUT_OF_MEMORY */ ( int n, /* A is n-by-n. n must be >= 0. */ const int Ap [ ], /* column pointers for A, of size n+1 */ const int Ai [ ], /* row indices of A, of size nz = Ap [n] */ int P [ ], /* output permutation, of size n */ double Control [ ], /* input Control settings, of size AMD_CONTROL */ double Info [ ] /* output Info statistics, of size AMD_INFO */ ) ; UF_long amd_l_order /* see above for description of arguments */ ( UF_long n, const UF_long Ap [ ], const UF_long Ai [ ], UF_long P [ ], double Control [ ], double Info [ ] ) ; /* Input arguments (not modified): * * n: the matrix A is n-by-n. * Ap: an int/UF_long array of size n+1, containing column pointers of A. * Ai: an int/UF_long array of size nz, containing the row indices of A, * where nz = Ap [n]. * Control: a double array of size AMD_CONTROL, containing control * parameters. Defaults are used if Control is NULL. * * Output arguments (not defined on input): * * P: an int/UF_long array of size n, containing the output permutation. If * row i is the kth pivot row, then P [k] = i. In MATLAB notation, * the reordered matrix is A (P,P). * Info: a double array of size AMD_INFO, containing statistical * information. Ignored if Info is NULL. * * On input, the matrix A is stored in column-oriented form. The row indices * of nonzero entries in column j are stored in Ai [Ap [j] ... Ap [j+1]-1]. * * If the row indices appear in ascending order in each column, and there * are no duplicate entries, then amd_order is slightly more efficient in * terms of time and memory usage. If this condition does not hold, a copy * of the matrix is created (where these conditions do hold), and the copy is * ordered. This feature is new to v2.0 (v1.2 and earlier required this * condition to hold for the input matrix). * * Row indices must be in the range 0 to * n-1. Ap [0] must be zero, and thus nz = Ap [n] is the number of nonzeros * in A. The array Ap is of size n+1, and the array Ai is of size nz = Ap [n]. * The matrix does not need to be symmetric, and the diagonal does not need to * be present (if diagonal entries are present, they are ignored except for * the output statistic Info [AMD_NZDIAG]). The arrays Ai and Ap are not * modified. This form of the Ap and Ai arrays to represent the nonzero * pattern of the matrix A is the same as that used internally by MATLAB. * If you wish to use a more flexible input structure, please see the * umfpack_*_triplet_to_col routines in the UMFPACK package, at * http://www.cise.ufl.edu/research/sparse/umfpack. * * Restrictions: n >= 0. Ap [0] = 0. Ap [j] <= Ap [j+1] for all j in the * range 0 to n-1. nz = Ap [n] >= 0. Ai [0..nz-1] must be in the range 0 * to n-1. Finally, Ai, Ap, and P must not be NULL. If any of these * restrictions are not met, AMD returns AMD_INVALID. * * AMD returns: * * AMD_OK if the matrix is valid and sufficient memory can be allocated to * perform the ordering. * * AMD_OUT_OF_MEMORY if not enough memory can be allocated. * * AMD_INVALID if the input arguments n, Ap, Ai are invalid, or if P is * NULL. * * AMD_OK_BUT_JUMBLED if the matrix had unsorted columns, and/or duplicate * entries, but was otherwise valid. * * The AMD routine first forms the pattern of the matrix A+A', and then * computes a fill-reducing ordering, P. If P [k] = i, then row/column i of * the original is the kth pivotal row. In MATLAB notation, the permuted * matrix is A (P,P), except that 0-based indexing is used instead of the * 1-based indexing in MATLAB. * * The Control array is used to set various parameters for AMD. If a NULL * pointer is passed, default values are used. The Control array is not * modified. * * Control [AMD_DENSE]: controls the threshold for "dense" rows/columns. * A dense row/column in A+A' can cause AMD to spend a lot of time in * ordering the matrix. If Control [AMD_DENSE] >= 0, rows/columns * with more than Control [AMD_DENSE] * sqrt (n) entries are ignored * during the ordering, and placed last in the output order. The * default value of Control [AMD_DENSE] is 10. If negative, no * rows/columns are treated as "dense". Rows/columns with 16 or * fewer off-diagonal entries are never considered "dense". * * Control [AMD_AGGRESSIVE]: controls whether or not to use aggressive * absorption, in which a prior element is absorbed into the current * element if is a subset of the current element, even if it is not * adjacent to the current pivot element (refer to Amestoy, Davis, * & Duff, 1996, for more details). The default value is nonzero, * which means to perform aggressive absorption. This nearly always * leads to a better ordering (because the approximate degrees are * more accurate) and a lower execution time. There are cases where * it can lead to a slightly worse ordering, however. To turn it off, * set Control [AMD_AGGRESSIVE] to 0. * * Control [2..4] are not used in the current version, but may be used in * future versions. * * The Info array provides statistics about the ordering on output. If it is * not present, the statistics are not returned. This is not an error * condition. * * Info [AMD_STATUS]: the return value of AMD, either AMD_OK, * AMD_OK_BUT_JUMBLED, AMD_OUT_OF_MEMORY, or AMD_INVALID. * * Info [AMD_N]: n, the size of the input matrix * * Info [AMD_NZ]: the number of nonzeros in A, nz = Ap [n] * * Info [AMD_SYMMETRY]: the symmetry of the matrix A. It is the number * of "matched" off-diagonal entries divided by the total number of * off-diagonal entries. An entry A(i,j) is matched if A(j,i) is also * an entry, for any pair (i,j) for which i != j. In MATLAB notation, * S = spones (A) ; * B = tril (S, -1) + triu (S, 1) ; * symmetry = nnz (B & B') / nnz (B) ; * * Info [AMD_NZDIAG]: the number of entries on the diagonal of A. * * Info [AMD_NZ_A_PLUS_AT]: the number of nonzeros in A+A', excluding the * diagonal. If A is perfectly symmetric (Info [AMD_SYMMETRY] = 1) * with a fully nonzero diagonal, then Info [AMD_NZ_A_PLUS_AT] = nz-n * (the smallest possible value). If A is perfectly unsymmetric * (Info [AMD_SYMMETRY] = 0, for an upper triangular matrix, for * example) with no diagonal, then Info [AMD_NZ_A_PLUS_AT] = 2*nz * (the largest possible value). * * Info [AMD_NDENSE]: the number of "dense" rows/columns of A+A' that were * removed from A prior to ordering. These are placed last in the * output order P. * * Info [AMD_MEMORY]: the amount of memory used by AMD, in bytes. In the * current version, this is 1.2 * Info [AMD_NZ_A_PLUS_AT] + 9*n * times the size of an integer. This is at most 2.4nz + 9n. This * excludes the size of the input arguments Ai, Ap, and P, which have * a total size of nz + 2*n + 1 integers. * * Info [AMD_NCMPA]: the number of garbage collections performed. * * Info [AMD_LNZ]: the number of nonzeros in L (excluding the diagonal). * This is a slight upper bound because mass elimination is combined * with the approximate degree update. It is a rough upper bound if * there are many "dense" rows/columns. The rest of the statistics, * below, are also slight or rough upper bounds, for the same reasons. * The post-ordering of the assembly tree might also not exactly * correspond to a true elimination tree postordering. * * Info [AMD_NDIV]: the number of divide operations for a subsequent LDL' * or LU factorization of the permuted matrix A (P,P). * * Info [AMD_NMULTSUBS_LDL]: the number of multiply-subtract pairs for a * subsequent LDL' factorization of A (P,P). * * Info [AMD_NMULTSUBS_LU]: the number of multiply-subtract pairs for a * subsequent LU factorization of A (P,P), assuming that no numerical * pivoting is required. * * Info [AMD_DMAX]: the maximum number of nonzeros in any column of L, * including the diagonal. * * Info [14..19] are not used in the current version, but may be used in * future versions. */ /* ------------------------------------------------------------------------- */ /* direct interface to AMD */ /* ------------------------------------------------------------------------- */ /* amd_2 is the primary AMD ordering routine. It is not meant to be * user-callable because of its restrictive inputs and because it destroys * the user's input matrix. It does not check its inputs for errors, either. * However, if you can work with these restrictions it can be faster than * amd_order and use less memory (assuming that you can create your own copy * of the matrix for AMD to destroy). Refer to AMD/Source/amd_2.c for a * description of each parameter. */ void amd_2 ( int n, int Pe [ ], int Iw [ ], int Len [ ], int iwlen, int pfree, int Nv [ ], int Next [ ], int Last [ ], int Head [ ], int Elen [ ], int Degree [ ], int W [ ], double Control [ ], double Info [ ] ) ; void amd_l2 ( UF_long n, UF_long Pe [ ], UF_long Iw [ ], UF_long Len [ ], UF_long iwlen, UF_long pfree, UF_long Nv [ ], UF_long Next [ ], UF_long Last [ ], UF_long Head [ ], UF_long Elen [ ], UF_long Degree [ ], UF_long W [ ], double Control [ ], double Info [ ] ) ; /* ------------------------------------------------------------------------- */ /* amd_valid */ /* ------------------------------------------------------------------------- */ /* Returns AMD_OK or AMD_OK_BUT_JUMBLED if the matrix is valid as input to * amd_order; the latter is returned if the matrix has unsorted and/or * duplicate row indices in one or more columns. Returns AMD_INVALID if the * matrix cannot be passed to amd_order. For amd_order, the matrix must also * be square. The first two arguments are the number of rows and the number * of columns of the matrix. For its use in AMD, these must both equal n. * * NOTE: this routine returned TRUE/FALSE in v1.2 and earlier. */ int amd_valid ( int n_row, /* # of rows */ int n_col, /* # of columns */ const int Ap [ ], /* column pointers, of size n_col+1 */ const int Ai [ ] /* row indices, of size Ap [n_col] */ ) ; UF_long amd_l_valid ( UF_long n_row, UF_long n_col, const UF_long Ap [ ], const UF_long Ai [ ] ) ; /* ------------------------------------------------------------------------- */ /* AMD memory manager and printf routines */ /* ------------------------------------------------------------------------- */ /* The user can redefine these to change the malloc, free, and printf routines * that AMD uses. */ #ifndef EXTERN #define EXTERN extern #endif EXTERN void *(*amd_malloc) (size_t) ; /* pointer to malloc */ EXTERN void (*amd_free) (void *) ; /* pointer to free */ EXTERN void *(*amd_realloc) (void *, size_t) ; /* pointer to realloc */ EXTERN void *(*amd_calloc) (size_t, size_t) ; /* pointer to calloc */ EXTERN int (*amd_printf) (const char *, ...) ; /* pointer to printf */ /* ------------------------------------------------------------------------- */ /* AMD Control and Info arrays */ /* ------------------------------------------------------------------------- */ /* amd_defaults: sets the default control settings */ void amd_defaults (double Control [ ]) ; void amd_l_defaults (double Control [ ]) ; /* amd_control: prints the control settings */ void amd_control (double Control [ ]) ; void amd_l_control (double Control [ ]) ; /* amd_info: prints the statistics */ void amd_info (double Info [ ]) ; void amd_l_info (double Info [ ]) ; #define AMD_CONTROL 5 /* size of Control array */ #define AMD_INFO 20 /* size of Info array */ /* contents of Control */ #define AMD_DENSE 0 /* "dense" if degree > Control [0] * sqrt (n) */ #define AMD_AGGRESSIVE 1 /* do aggressive absorption if Control [1] != 0 */ /* default Control settings */ #define AMD_DEFAULT_DENSE 10.0 /* default "dense" degree 10*sqrt(n) */ #define AMD_DEFAULT_AGGRESSIVE 1 /* do aggressive absorption by default */ /* contents of Info */ #define AMD_STATUS 0 /* return value of amd_order and amd_l_order */ #define AMD_N 1 /* A is n-by-n */ #define AMD_NZ 2 /* number of nonzeros in A */ #define AMD_SYMMETRY 3 /* symmetry of pattern (1 is sym., 0 is unsym.) */ #define AMD_NZDIAG 4 /* # of entries on diagonal */ #define AMD_NZ_A_PLUS_AT 5 /* nz in A+A' */ #define AMD_NDENSE 6 /* number of "dense" rows/columns in A */ #define AMD_MEMORY 7 /* amount of memory used by AMD */ #define AMD_NCMPA 8 /* number of garbage collections in AMD */ #define AMD_LNZ 9 /* approx. nz in L, excluding the diagonal */ #define AMD_NDIV 10 /* number of fl. point divides for LU and LDL' */ #define AMD_NMULTSUBS_LDL 11 /* number of fl. point (*,-) pairs for LDL' */ #define AMD_NMULTSUBS_LU 12 /* number of fl. point (*,-) pairs for LU */ #define AMD_DMAX 13 /* max nz. in any column of L, incl. diagonal */ /* ------------------------------------------------------------------------- */ /* return values of AMD */ /* ------------------------------------------------------------------------- */ #define AMD_OK 0 /* success */ #define AMD_OUT_OF_MEMORY -1 /* malloc failed, or problem too large */ #define AMD_INVALID -2 /* input arguments are not valid */ #define AMD_OK_BUT_JUMBLED 1 /* input matrix is OK for amd_order, but * columns were not sorted, and/or duplicate entries were present. AMD had * to do extra work before ordering the matrix. This is a warning, not an * error. */ /* ========================================================================== */ /* === AMD version ========================================================== */ /* ========================================================================== */ /* AMD Version 1.2 and later include the following definitions. * As an example, to test if the version you are using is 1.2 or later: * * #ifdef AMD_VERSION * if (AMD_VERSION >= AMD_VERSION_CODE (1,2)) ... * #endif * * This also works during compile-time: * * #if defined(AMD_VERSION) && (AMD_VERSION >= AMD_VERSION_CODE (1,2)) * printf ("This is version 1.2 or later\n") ; * #else * printf ("This is an early version\n") ; * #endif * * Versions 1.1 and earlier of AMD do not include a #define'd version number. */ #define AMD_DATE "May 31, 2007" #define AMD_VERSION_CODE(main,sub) ((main) * 1000 + (sub)) #define AMD_MAIN_VERSION 2 #define AMD_SUB_VERSION 2 #define AMD_SUBSUB_VERSION 0 #define AMD_VERSION AMD_VERSION_CODE(AMD_MAIN_VERSION,AMD_SUB_VERSION) #ifdef __cplusplus } #endif #endif #endif \end{verbatim} } %------------------------------------------------------------------------------ \newpage % References %------------------------------------------------------------------------------ \bibliographystyle{plain} \bibliography{AMD_UserGuide} \end{document} SuiteSparse/AMD/Doc/License0000644001170100242450000000342710616377407014403 0ustar davisfacAMD, Copyright (c) by Timothy A. Davis, Patrick R. Amestoy, and Iain S. Duff. All Rights Reserved. AMD is available under alternate licenses, contact T. Davis for details. AMD License: Your use or distribution of AMD or any modified version of AMD implies that you agree to this License. This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Permission is hereby granted to use or copy this program under the terms of the GNU LGPL, provided that the Copyright, this License, and the Availability of the original version is retained on all copies. User documentation of any code that uses this code or any modified version of this code must cite the Copyright, this License, the Availability note, and "Used by permission." Permission to modify the code and to distribute modified code is granted, provided the Copyright, this License, and the Availability note are retained, and a notice that the code was modified is included. Availability: http://www.cise.ufl.edu/research/sparse/amd ------------------------------------------------------------------------------- SuiteSparse/AMD/Doc/ChangeLog0000644001170100242450000001122010620613776014633 0ustar davisfacMay 31, 2007: version 2.2.0 * port to 64-bit MATLAB * Makefile moved from Source/ to Lib/ * minor changes to printing routines (amd_control.c, amd_info.c) Dec 12, 2006, version 2.0.4 * minor MATLAB code cleanup Nov 29, 2006, version 2.0.3 * changed MATLAB function name to amd2, so as not to conflict with the now built-in version of AMD in MATLAB (which is the same thing as the AMD here...). Sept 28, 2006, version 2.0.2 * #define SIZE_T_MAX not done if already defined (Mac OSX). Aug 31, 2006: * trivial change to comments in amd.m Apr 30, 2006: AMD Version 2.0: * long integer redefined as UF_long, controlled by UFconfig.h. * amd_order no longer requires its input to have sorted columns. It can also tolerate duplicate entries in each column. If these conditions hold, but the matrix is otherwise valid, amd_order returns AMD_OK_BUT_JUMBLED (a warning, not an error). * amd_preprocess no longer deemed user-callable, since it is no longer needed (it was used to ensure the input matrix had sorted columns with no duplicate entries). It still exists, with additional parameters, and is called by amd_order if necessary. amd_wpreprocess and amd_preprocess_valid removed. Fortran interface routine amdpreproc removed. * Integer overflow computations modified, to extend the size of problem that the "int" version can solve when used in an LP64 compilation. * amd_demo2.c simplified (it tests AMD with a jumbled matrix). * amd_valid returned TRUE/FALSE in v1.2. It now returns AMD_OK, AMD_OK_BUT_JUMBLED, or AMD_INVALID. Only in the latter case is the matrix unsuitable as input to amd_order. * amd_internal.h include file moved from AMD/Source to AMD/Include. Nov 15, 2005: * minor editting of comments; version number (1.2) unchanged. Aug. 30, 2005: AMD Version 1.2 * AMD v1.2 is upward compatible with v1.1 and v1.0, except that v1.2 no longer includes the compile-time redefinition of malloc and free. * Makefile modified to use UFconfig.mk. "Make" directory removed. * License changed to GNU LGPL. * Easier inclusion in C++ programs. * option to allow compile-time redefinition of malloc and free (added to v1.1) removed for v1.2. Replaced with a run-time redefinition. AMD includes function pointers for malloc, free, calloc, realloc, and printf, so that all those routines can be redefined at compile time. These function pointers are global variables, and so are not technically thread-safe, unless you use defaults and don't need to change them (the common case) or if you change them in one thread before using them in other threads. * added #define'd version number * minor modification to AMD_2 to ensure all lines can be tested, without conditional compilation. * moved the prototype for AMD_2 from amd_internal.h to amd.h * moved the prototype for AMD_valid from amd_internal.h to amd.h * MATLAB mexFunction uses libamd.a (compiled with cc) instead of compiling each AMD source file with the mex command * long demo (amd_l_demo.c) added. Jan. 21, 2004: AMD Version 1.1 * No bugs found or fixed - new features added, only * amd_preprocess added, to allow for more general input of the matrix A. * ME=0 added to amd*.f, unused DEXT variable removed from amdbar.f, to avoid spurious compiler warnings (this was not a bug). * amd_demo2.c and amd_demo2.out added, to test/demo amd_preprocess. * option to allow compile-time redefinition of malloc, free, printf added * amd_demo.c shortened slightly (removed printing of PAP') * User Guide modified (more details added) * linewidth reduced from 80 to 79 columns Oct. 7, 2003: AMD version 1.0.1. * MATLAB mexFunction modified, to remove call to mexCallMATLAB function. This function can take a long time to call, particularly if you are ordering many small matrices. May 6, 2003: AMD Version 1.0 released. * converted to C (compare amd.f and amdbar.f with amd_2.c) * dense rows/column removed prior to ordering * elimination tree post-ordering added * demos, user guide written * statistics added (nz in L, flop count, symmetry of A) * computes the pattern of A+A' if A is unsymmetric * user's input matrix no longer overwritten * degree lists initialized differently * IOVFLO argument removed from Fortran versions (amd.f and amdbar.f) * parameters added (dense row/column detection, aggressive absorption) * MATLAB mexFunction added Jan, 1996: * amdbar.f posted at http://www.netlib.org (with a restricted License) * amd.f appears as MC47B/BD in the Harwell Subroutine Library (without the IOVFLO argument) SuiteSparse/AMD/Doc/lesser.txt0000644001170100242450000006350010263214067015120 0ustar davisfac GNU LESSER GENERAL PUBLIC LICENSE Version 2.1, February 1999 Copyright (C) 1991, 1999 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. 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SuiteSparse/AMD/Lib/0000755001170100242450000000000010711435721013057 5ustar davisfacSuiteSparse/AMD/Lib/Makefile0000644001170100242450000000611110617345350014521 0ustar davisfac#------------------------------------------------------------------------------- # AMD Makefile for compiling on Unix systems (for original Make ONLY) #------------------------------------------------------------------------------- # This is a very ugly Makefile, and is only provided for those who do not # have GNU make. Note that it is not used if you have GNU make. It ignores # dependency checking and just compiles everything. default: everything include ../../UFconfig/UFconfig.mk C = $(CC) $(CFLAGS) $(CONFIG) -I../Include -I../../UFconfig everything: $(C) -DDINT -c ../Source/amd_aat.c -o amd_i_aat.o $(C) -DDINT -c ../Source/amd_1.c -o amd_i_1.o $(C) -DDINT -c ../Source/amd_2.c -o amd_i_2.o $(C) -DDINT -c ../Source/amd_dump.c -o amd_i_dump.o $(C) -DDINT -c ../Source/amd_postorder.c -o amd_i_postorder.o $(C) -DDINT -c ../Source/amd_post_tree.c -o amd_i_post_tree.o $(C) -DDINT -c ../Source/amd_defaults.c -o amd_i_defaults.o $(C) -DDINT -c ../Source/amd_order.c -o amd_i_order.o $(C) -DDINT -c ../Source/amd_control.c -o amd_i_control.o $(C) -DDINT -c ../Source/amd_info.c -o amd_i_info.o $(C) -DDINT -c ../Source/amd_valid.c -o amd_i_valid.o $(C) -DDINT -c ../Source/amd_preprocess.c -o amd_i_preprocess.o $(C) -DDLONG -c ../Source/amd_aat.c -o amd_l_aat.o $(C) -DDLONG -c ../Source/amd_1.c -o ../Source/amd_l_1.o $(C) -DDLONG -c ../Source/amd_2.c -o amd_l_2.o $(C) -DDLONG -c ../Source/amd_dump.c -o amd_l_dump.o $(C) -DDLONG -c ../Source/amd_postorder.c -o amd_l_postorder.o $(C) -DDLONG -c ../Source/amd_post_tree.c -o amd_l_post_tree.o $(C) -DDLONG -c ../Source/amd_defaults.c -o amd_l_defaults.o $(C) -DDLONG -c ../Source/amd_order.c -o amd_l_order.o $(C) -DDLONG -c ../Source/amd_control.c -o amd_l_control.o $(C) -DDLONG -c ../Source/amd_info.c -o amd_l_info.o $(C) -DDLONG -c ../Source/amd_valid.c -o amd_l_valid.o $(C) -DDLONG -c ../Source/amd_preprocess.c -o amd_l_preprocess.o $(C) -c ../Source/amd_global.c $(AR) ../Lib/libamd.a amd_i_aat.o amd_i_1.o amd_i_2.o amd_i_dump.o \ amd_i_postorder.o amd_i_post_tree.o amd_i_defaults.o amd_i_order.o \ amd_i_control.o amd_i_info.o amd_i_valid.o amd_l_aat.o amd_l_1.o \ amd_l_2.o amd_l_dump.o amd_l_postorder.o amd_l_post_tree.o \ amd_l_defaults.o amd_l_order.o amd_l_control.o amd_l_info.o \ amd_l_valid.o amd_i_preprocess.o amd_l_preprocess.o amd_global.o - $(RANLIB) ../Lib/libamd.a #------------------------------------------------------------------------------- # compile the Fortran versions and the libamdf77.a library #------------------------------------------------------------------------------- fortran: $(F77) $(F77FLAGS) -c ../Source/amd.f -o amd.o $(F77) $(F77FLAGS) -c ../Source/amdbar.f -o amdbar.o $(AR) ../Lib/libamdf77.a amd.o amdbar.o - $(RANLIB) ../Lib/libamdf77.a #------------------------------------------------------------------------------- # Remove all but the files in the original distribution #------------------------------------------------------------------------------- clean: - $(RM) $(CLEAN) purge: distclean distclean: clean - $(RM) ../Lib/libamd.a ../Lib/libamdf77.a SuiteSparse/AMD/Lib/libamd.def0000644001170100242450000000021010423471333014757 0ustar davisfacLIBRARY libamd.dll EXPORTS amd_order amd_defaults amd_control amd_info amd_2 amd_l_order amd_l_defaults amd_l_control amd_l_info amd_l2 SuiteSparse/AMD/Lib/GNUmakefile0000644001170100242450000000512410617345323015136 0ustar davisfac#------------------------------------------------------------------------------- # AMD Makefile for compiling on Unix systems (for GNU make only) #------------------------------------------------------------------------------- default: ../Lib/libamd.a include ../../UFconfig/UFconfig.mk C = $(CC) $(CFLAGS) $(CONFIG) -I../Include -I../../UFconfig #------------------------------------------------------------------------------- # source files #------------------------------------------------------------------------------- AMD = amd_aat amd_1 amd_2 amd_dump amd_postorder amd_post_tree amd_defaults \ amd_order amd_control amd_info amd_valid amd_preprocess UFCONFIG = ../../UFconfig/UFconfig.h INC = ../Include/amd.h ../Include/amd_internal.h $(UFCONFIG) #------------------------------------------------------------------------------- # object files for each version #------------------------------------------------------------------------------- AMDI = $(addsuffix .o, $(subst amd_,amd_i_,$(AMD))) AMDL = $(addsuffix .o, $(subst amd_,amd_l_,$(AMD))) #------------------------------------------------------------------------------- # compile each int and long routine (with no real/complex version) #------------------------------------------------------------------------------- amd_global.o: ../Source/amd_global.c $(INC) $(C) -c $< -o $@ amd_i_%.o: ../Source/amd_%.c $(INC) $(C) -DDINT -c $< -o $@ amd_l_%.o: ../Source/amd_%.c $(INC) $(C) -DDLONG -c $< -o $@ #------------------------------------------------------------------------------- # Create the libamd.a library (C versions only) #------------------------------------------------------------------------------- ../Lib/libamd.a: amd_global.o $(AMDI) $(AMDL) $(AR) ../Lib/libamd.a $^ - $(RANLIB) ../Lib/libamd.a #------------------------------------------------------------------------------- # compile the Fortran versions and the libamdf77.a library #------------------------------------------------------------------------------- fortran: ../Lib/libamdf77.a AMDF77 = amd.o amdbar.o amd.o: ../Source/amd.f $(F77) $(F77FLAGS) -c ../Source/amd.f -o amd.o amdbar.o: ../Source/amdbar.f $(F77) $(F77FLAGS) -c ../Source/amdbar.f -o amdbar.o ../Lib/libamdf77.a: $(AMDF77) $(AR) ../Lib/libamdf77.a $^ - $(RANLIB) ../Lib/libamdf77.a #------------------------------------------------------------------------------- # Remove all but the files in the original distribution #------------------------------------------------------------------------------- clean: - $(RM) $(CLEAN) purge: distclean distclean: clean - $(RM) ../Lib/libamd.a ../Lib/libamdf77.a SuiteSparse/AMD/Demo/0000755001170100242450000000000010711435721013235 5ustar davisfacSuiteSparse/AMD/Demo/amd_l_demo.out0000644001170100242450000001664410616431751016064 0ustar davisfacAMD version 2.2, date: May 31, 2007 AMD demo, with the 24-by-24 Harwell/Boeing matrix, can_24: AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 Input matrix: 24-by-24, with 160 entries. Note that for a symmetric matrix such as this one, only the strictly lower or upper triangular parts would need to be passed to AMD, since AMD computes the ordering of A+A'. The diagonal entries are also not needed, since AMD ignores them. Column: 0, number of entries: 9, with row indices in Ai [0 ... 8]: row indices: 0 5 6 12 13 17 18 19 21 Column: 1, number of entries: 6, with row indices in Ai [9 ... 14]: row indices: 1 8 9 13 14 17 Column: 2, number of entries: 6, with row indices in Ai [15 ... 20]: row indices: 2 6 11 20 21 22 Column: 3, number of entries: 6, with row indices in Ai [21 ... 26]: row indices: 3 7 10 15 18 19 Column: 4, number of entries: 6, with row indices in Ai [27 ... 32]: row indices: 4 7 9 14 15 16 Column: 5, number of entries: 6, with row indices in Ai [33 ... 38]: row indices: 0 5 6 12 13 17 Column: 6, number of entries: 9, with row indices in Ai [39 ... 47]: row indices: 0 2 5 6 11 12 19 21 23 Column: 7, number of entries: 9, with row indices in Ai [48 ... 56]: row indices: 3 4 7 9 14 15 16 17 18 Column: 8, number of entries: 4, with row indices in Ai [57 ... 60]: row indices: 1 8 9 14 Column: 9, number of entries: 9, with row indices in Ai [61 ... 69]: row indices: 1 4 7 8 9 13 14 17 18 Column: 10, number of entries: 6, with row indices in Ai [70 ... 75]: row indices: 3 10 18 19 20 21 Column: 11, number of entries: 6, with row indices in Ai [76 ... 81]: row indices: 2 6 11 12 21 23 Column: 12, number of entries: 6, with row indices in Ai [82 ... 87]: row indices: 0 5 6 11 12 23 Column: 13, number of entries: 6, with row indices in Ai [88 ... 93]: row indices: 0 1 5 9 13 17 Column: 14, number of entries: 6, with row indices in Ai [94 ... 99]: row indices: 1 4 7 8 9 14 Column: 15, number of entries: 6, with row indices in Ai [100 ... 105]: row indices: 3 4 7 15 16 18 Column: 16, number of entries: 4, with row indices in Ai [106 ... 109]: row indices: 4 7 15 16 Column: 17, number of entries: 9, with row indices in Ai [110 ... 118]: row indices: 0 1 5 7 9 13 17 18 19 Column: 18, number of entries: 9, with row indices in Ai [119 ... 127]: row indices: 0 3 7 9 10 15 17 18 19 Column: 19, number of entries: 9, with row indices in Ai [128 ... 136]: row indices: 0 3 6 10 17 18 19 20 21 Column: 20, number of entries: 6, with row indices in Ai [137 ... 142]: row indices: 2 10 19 20 21 22 Column: 21, number of entries: 9, with row indices in Ai [143 ... 151]: row indices: 0 2 6 10 11 19 20 21 22 Column: 22, number of entries: 4, with row indices in Ai [152 ... 155]: row indices: 2 20 21 22 Column: 23, number of entries: 4, with row indices in Ai [156 ... 159]: row indices: 6 11 12 23 Plot of input matrix pattern: 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 0: X . . . . X X . . . . . X X . . . X X X . X . . 1: . X . . . . . . X X . . . X X . . X . . . . . . 2: . . X . . . X . . . . X . . . . . . . . X X X . 3: . . . X . . . X . . X . . . . X . . X X . . . . 4: . . . . X . . X . X . . . . X X X . . . . . . . 5: X . . . . X X . . . . . X X . . . X . . . . . . 6: X . X . . X X . . . . X X . . . . . . X . X . X 7: . . . X X . . X . X . . . . X X X X X . . . . . 8: . X . . . . . . X X . . . . X . . . . . . . . . 9: . X . . X . . X X X . . . X X . . X X . . . . . 10: . . . X . . . . . . X . . . . . . . X X X X . . 11: . . X . . . X . . . . X X . . . . . . . . X . X 12: X . . . . X X . . . . X X . . . . . . . . . . X 13: X X . . . X . . . X . . . X . . . X . . . . . . 14: . X . . X . . X X X . . . . X . . . . . . . . . 15: . . . X X . . X . . . . . . . X X . X . . . . . 16: . . . . X . . X . . . . . . . X X . . . . . . . 17: X X . . . X . X . X . . . X . . . X X X . . . . 18: X . . X . . . X . X X . . . . X . X X X . . . . 19: X . . X . . X . . . X . . . . . . X X X X X . . 20: . . X . . . . . . . X . . . . . . . . X X X X . 21: X . X . . . X . . . X X . . . . . . . X X X X . 22: . . X . . . . . . . . . . . . . . . . . X X X . 23: . . . . . . X . . . . X X . . . . . . . . . . X return value from amd_l_order: 0 (should be 0) AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 24 nz, number of nonzeros in A: 160 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 136 # dense rows/columns of A+A': 0 memory used, in bytes: 3032 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 97 nonzeros in L (including diagonal): 121 # divide operations for LDL' or LU: 97 # multiply-subtract operations for LDL': 275 # multiply-subtract operations for LU: 453 max nz. in any column of L (incl. diagonal): 8 chol flop count for real A, sqrt counted as 1 flop: 671 LDL' flop count for real A: 647 LDL' flop count for complex A: 3073 LU flop count for real A (with no pivoting): 1003 LU flop count for complex A (with no pivoting): 4497 Permutation vector: 22 20 10 23 12 5 16 8 14 4 15 7 1 9 13 17 0 2 3 6 11 18 21 19 Inverse permutation vector: 16 12 17 18 9 5 19 11 7 13 2 20 4 14 8 10 6 15 21 23 1 22 0 3 Plot of permuted matrix pattern: 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 0: X X . . . . . . . . . . . . . . . X . . . . X . 1: X X X . . . . . . . . . . . . . . X . . . . X X 2: . X X . . . . . . . . . . . . . . . X . . X X X 3: . . . X X . . . . . . . . . . . . . . X X . . . 4: . . . X X X . . . . . . . . . . X . . X X . . . 5: . . . . X X . . . . . . . . X X X . . X . . . . 6: . . . . . . X . . X X X . . . . . . . . . . . . 7: . . . . . . . X X . . . X X . . . . . . . . . . 8: . . . . . . . X X X . X X X . . . . . . . . . . 9: . . . . . . X . X X X X . X . . . . . . . . . . 10: . . . . . . X . . X X X . . . . . . X . . X . . 11: . . . . . . X . X X X X . X . X . . X . . X . . 12: . . . . . . . X X . . . X X X X . . . . . . . . 13: . . . . . . . X X X . X X X X X . . . . . X . . 14: . . . . . X . . . . . . X X X X X . . . . . . . 15: . . . . . X . . . . . X X X X X X . . . . X . X 16: . . . . X X . . . . . . . . X X X . . X . X X X 17: X X . . . . . . . . . . . . . . . X . X X . X . 18: . . X . . . . . . . X X . . . . . . X . . X . X 19: . . . X X X . . . . . . . . . . X X . X X . X X 20: . . . X X . . . . . . . . . . . . X . X X . X . 21: . . X . . . . . . . X X . X . X X . X . . X . X 22: X X X . . . . . . . . . . . . . X X . X X . X X 23: . X X . . . . . . . . . . . . X X . X X . X X X SuiteSparse/AMD/Demo/amd_f77simple.f0000644001170100242450000000272010616376325016053 0ustar davisfacC ---------------------------------------------------------------------- C AMD, Copyright (c) by Timothy A. Davis, Patrick R. C Amestoy, and Iain S. Duff. See ../README.txt for C License. email: davis at cise.ufl.edu CISE Department, Univ. of C Florida. web: http://www.cise.ufl.edu/research/sparse/amd C ---------------------------------------------------------------------- C This program provides an example of how to call the Fortran version C of AMD. It uses the same matrix as the amd_simple.c demo (in C). C Note that the diagonal entries are not present, and the matrix is C symmetric. INTEGER N, NZ, J, K, P, IWLEN, PFREE, NCMPA PARAMETER (N = 5, NZ = 10, IWLEN = 17) INTEGER AP (N+1), AI (NZ), LAST (N), PE (N), LEN (N), ELEN (N), $ IW (IWLEN), DEGREE (N), NV (N), NEXT (N), HEAD (N), W (N) DATA AP / 1, 2, 5, 8, 9, 11/ DATA AI / 2, 1,3,5, 2,4,5, 3, 2,3 / C load the matrix into the AMD workspace DO 10 J = 1,N PE (J) = AP (J) LEN (J) = AP (J+1) - AP (J) 10 CONTINUE DO 20 P = 1,NZ IW (P) = AI (P) 20 CONTINUE PFREE = NZ + 1 C order the matrix (destroys the copy of A in IW, PE, and LEN) CALL AMD (N, PE, IW, LEN, IWLEN, PFREE, NV, NEXT, LAST, HEAD, $ ELEN, DEGREE, NCMPA, W) DO 60 K = 1, N PRINT 50, K, LAST (K) 50 FORMAT ('P (',I2,') = ', I2) 60 CONTINUE END SuiteSparse/AMD/Demo/Makefile0000644001170100242450000000552410617111726014704 0ustar davisfac#----------------------------------------------------------------------------- # compile the AMD demo (for both GNU make or original make) #----------------------------------------------------------------------------- default: amd_simple amd_demo amd_demo2 amd_l_demo include ../../UFconfig/UFconfig.mk C = $(CC) $(CFLAGS) -I../Include -I../../UFconfig INC = ../Include/amd.h ../../UFconfig/UFconfig.h library: ( cd ../Lib ; $(MAKE) ) f77lib: ( cd ../Lib ; $(MAKE) fortran ) #------------------------------------------------------------------------------ # Create the demo program, run it, and compare the output #------------------------------------------------------------------------------ dist: amd_demo: amd_demo.c library $(INC) $(C) -o amd_demo amd_demo.c ../Lib/libamd.a $(LIB) ./amd_demo > my_amd_demo.out - diff amd_demo.out my_amd_demo.out amd_l_demo: amd_l_demo.c library $(INC) $(C) -o amd_l_demo amd_l_demo.c ../Lib/libamd.a $(LIB) ./amd_l_demo > my_amd_l_demo.out - diff amd_l_demo.out my_amd_l_demo.out amd_demo2: amd_demo2.c library $(INC) $(C) -o amd_demo2 amd_demo2.c ../Lib/libamd.a $(LIB) ./amd_demo2 > my_amd_demo2.out - diff amd_demo2.out my_amd_demo2.out amd_simple: amd_simple.c library $(INC) $(C) -o amd_simple amd_simple.c ../Lib/libamd.a $(LIB) ./amd_simple > my_amd_simple.out - diff amd_simple.out my_amd_simple.out #------------------------------------------------------------------------------ # compile the Fortran demo #------------------------------------------------------------------------------ fortran: amd_f77demo amd_f77simple cross: amd_f77cross amd_f77demo: amd_f77demo.f f77lib $(F77) $(F77FLAGS) -o amd_f77demo amd_f77demo.f ../Lib/libamdf77.a \ $(F77LIB) ./amd_f77demo > my_amd_f77demo.out - diff amd_f77demo.out my_amd_f77demo.out amd_f77simple: amd_f77simple.f f77lib $(F77) $(F77FLAGS) -o amd_f77simple amd_f77simple.f \ ../Lib/libamdf77.a $(F77LIB) ./amd_f77simple > my_amd_f77simple.out - diff amd_f77simple.out my_amd_f77simple.out amd_f77wrapper.o: amd_f77wrapper.c $(C) -DDINT -c amd_f77wrapper.c amd_f77cross: amd_f77cross.f amd_f77wrapper.o ../Lib/libamd.a $(F77) $(F77FLAGS) -o amd_f77cross amd_f77cross.f amd_f77wrapper.o \ ../Lib/libamd.a $(F77LIB) ./amd_f77cross > my_amd_f77cross.out - diff amd_f77cross.out my_amd_f77cross.out #------------------------------------------------------------------------------ # Remove all but the files in the original distribution #------------------------------------------------------------------------------ clean: - $(RM) $(CLEAN) purge: distclean distclean: clean - $(RM) amd_demo my_amd_demo.out - $(RM) amd_l_demo my_amd_l_demo.out - $(RM) amd_demo2 my_amd_demo2.out - $(RM) amd_simple my_amd_simple.out - $(RM) amd_f77demo my_amd_f77demo.out - $(RM) amd_f77simple my_amd_f77simple.out - $(RM) amd_f77cross my_amd_f77cross.out SuiteSparse/AMD/Demo/amd_f77cross.out0000644001170100242450000000374410250414043016264 0ustar davisfacInput matrix: 5-by- 5 with 14 entries Column: 1 number of entries: 2 with row indices in AI ( 1 ... 2) row indices: 1 2 Column: 2 number of entries: 4 with row indices in AI ( 3 ... 6) row indices: 1 2 3 5 Column: 3 number of entries: 4 with row indices in AI ( 7 ... 10) row indices: 2 3 4 5 Column: 4 number of entries: 2 with row indices in AI ( 11 ... 12) row indices: 3 4 Column: 5 number of entries: 2 with row indices in AI ( 13 ... 14) row indices: 2 5 amd: approximate minimum degree ordering, results: status: OK n, dimension of A: 5 nz, number of nonzeros in A: 14 symmetry of A: 0.8889 number of nonzeros on diagonal: 5 nonzeros in pattern of A+A' (excl. diagonal): 10 # dense rows/columns of A+A': 0 memory used, in bytes: 228 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 5 nonzeros in L (including diagonal): 10 # divide operations for LDL' or LU: 5 # multiply-subtract operations for LDL': 6 # multiply-subtract operations for LU: 7 max nz. in any column of L (incl. diagonal): 3 chol flop count for real A, sqrt counted as 1 flop: 22 LDL' flop count for real A: 17 LDL' flop count for complex A: 93 LU flop count for real A (with no pivoting): 19 LU flop count for complex A (with no pivoting): 101 PERM ( 1) = 1 PERM ( 2) = 4 PERM ( 3) = 3 PERM ( 4) = 5 PERM ( 5) = 2 SuiteSparse/AMD/Demo/amd_demo2.out0000644001170100242450000002140210616431751015617 0ustar davisfacAMD demo, with a jumbled version of the 24-by-24 Harwell/Boeing matrix, can_24: AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 Jumbled input matrix: 24-by-24, with 116 entries. Note that for a symmetric matrix such as this one, only the strictly lower or upper triangular parts would need to be passed to AMD, since AMD computes the ordering of A+A'. The diagonal entries are also not needed, since AMD ignores them. This version of the matrix has jumbled columns and duplicate row indices. Column: 0, number of entries: 9, with row indices in Ai [0 ... 8]: row indices: 0 17 18 21 5 12 5 0 13 Column: 1, number of entries: 5, with row indices in Ai [9 ... 13]: row indices: 14 1 8 13 17 Column: 2, number of entries: 6, with row indices in Ai [14 ... 19]: row indices: 2 20 11 6 11 22 Column: 3, number of entries: 8, with row indices in Ai [20 ... 27]: row indices: 3 3 10 7 18 18 15 19 Column: 4, number of entries: 5, with row indices in Ai [28 ... 32]: row indices: 7 9 15 14 16 Column: 5, number of entries: 4, with row indices in Ai [33 ... 36]: row indices: 5 13 6 17 Column: 6, number of entries: 7, with row indices in Ai [37 ... 43]: row indices: 5 0 11 6 12 6 23 Column: 7, number of entries: 9, with row indices in Ai [44 ... 52]: row indices: 3 4 9 7 14 16 15 17 18 Column: 8, number of entries: 5, with row indices in Ai [53 ... 57]: row indices: 1 9 14 14 14 Column: 9, number of entries: 5, with row indices in Ai [58 ... 62]: row indices: 7 13 8 1 17 Column: 10, number of entries: 0, with row indices in Ai [63 ... 62]: row indices: Column: 11, number of entries: 3, with row indices in Ai [63 ... 65]: row indices: 2 12 23 Column: 12, number of entries: 3, with row indices in Ai [66 ... 68]: row indices: 5 11 12 Column: 13, number of entries: 3, with row indices in Ai [69 ... 71]: row indices: 0 13 17 Column: 14, number of entries: 3, with row indices in Ai [72 ... 74]: row indices: 1 9 14 Column: 15, number of entries: 3, with row indices in Ai [75 ... 77]: row indices: 3 15 16 Column: 16, number of entries: 4, with row indices in Ai [78 ... 81]: row indices: 16 4 4 15 Column: 17, number of entries: 4, with row indices in Ai [82 ... 85]: row indices: 13 17 19 17 Column: 18, number of entries: 5, with row indices in Ai [86 ... 90]: row indices: 15 17 19 9 10 Column: 19, number of entries: 6, with row indices in Ai [91 ... 96]: row indices: 17 19 20 0 6 10 Column: 20, number of entries: 4, with row indices in Ai [97 ... 100]: row indices: 22 10 20 21 Column: 21, number of entries: 11, with row indices in Ai [101 ... 111]: row indices: 6 2 10 19 20 11 21 22 22 22 22 Column: 22, number of entries: 0, with row indices in Ai [112 ... 111]: row indices: Column: 23, number of entries: 4, with row indices in Ai [112 ... 115]: row indices: 12 11 12 23 Plot of (jumbled) input matrix pattern: 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 0: X . . . . . X . . . . . . X . . . . . X . . . . 1: . X . . . . . . X X . . . . X . . . . . . . . . 2: . . X . . . . . . . . X . . . . . . . . . X . . 3: . . . X . . . X . . . . . . . X . . . . . . . . 4: . . . . . . . X . . . . . . . . X . . . . . . . 5: X . . . . X X . . . . . X . . . . . . . . . . . 6: . . X . . X X . . . . . . . . . . . . X . X . . 7: . . . X X . . X . X . . . . . . . . . . . . . . 8: . X . . . . . . . X . . . . . . . . . . . . . . 9: . . . . X . . X X . . . . . X . . . X . . . . . 10: . . . X . . . . . . . . . . . . . . X X X X . . 11: . . X . . . X . . . . . X . . . . . . . . X . X 12: X . . . . . X . . . . X X . . . . . . . . . . X 13: X X . . . X . . . X . . . X . . . X . . . . . . 14: . X . . X . . X X . . . . . X . . . . . . . . . 15: . . . X X . . X . . . . . . . X X . X . . . . . 16: . . . . X . . X . . . . . . . X X . . . . . . . 17: X X . . . X . X . X . . . X . . . X X X . . . . 18: X . . X . . . X . . . . . . . . . . . . . . . . 19: . . . X . . . . . . . . . . . . . X X X . X . . 20: . . X . . . . . . . . . . . . . . . . X X X . . 21: X . . . . . . . . . . . . . . . . . . . X X . . 22: . . X . . . . . . . . . . . . . . . . . X X . . 23: . . . . . . X . . . . X . . . . . . . . . . . X Plot of symmetric matrix to be ordered by amd_order: 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 0: X . . . . X X . . . . . X X . . . X X X . X . . 1: . X . . . . . . X X . . . X X . . X . . . . . . 2: . . X . . . X . . . . X . . . . . . . . X X X . 3: . . . X . . . X . . X . . . . X . . X X . . . . 4: . . . . X . . X . X . . . . X X X . . . . . . . 5: X . . . . X X . . . . . X X . . . X . . . . . . 6: X . X . . X X . . . . X X . . . . . . X . X . X 7: . . . X X . . X . X . . . . X X X X X . . . . . 8: . X . . . . . . X X . . . . X . . . . . . . . . 9: . X . . X . . X X X . . . X X . . X X . . . . . 10: . . . X . . . . . . X . . . . . . . X X X X . . 11: . . X . . . X . . . . X X . . . . . . . . X . X 12: X . . . . X X . . . . X X . . . . . . . . . . X 13: X X . . . X . . . X . . . X . . . X . . . . . . 14: . X . . X . . X X X . . . . X . . . . . . . . . 15: . . . X X . . X . . . . . . . X X . X . . . . . 16: . . . . X . . X . . . . . . . X X . . . . . . . 17: X X . . . X . X . X . . . X . . . X X X . . . . 18: X . . X . . . X . X X . . . . X . X X X . . . . 19: X . . X . . X . . . X . . . . . . X X X X X . . 20: . . X . . . . . . . X . . . . . . . . X X X X . 21: X . X . . . X . . . X X . . . . . . . X X X X . 22: . . X . . . . . . . . . . . . . . . . . X X X . 23: . . . . . . X . . . . X X . . . . . . . . . . X return value from amd_order: 1 (should be 1) AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 24 nz, number of nonzeros in A: 102 symmetry of A: 0.4000 number of nonzeros on diagonal: 17 nonzeros in pattern of A+A' (excl. diagonal): 136 # dense rows/columns of A+A': 0 memory used, in bytes: 2080 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 97 nonzeros in L (including diagonal): 121 # divide operations for LDL' or LU: 97 # multiply-subtract operations for LDL': 275 # multiply-subtract operations for LU: 453 max nz. in any column of L (incl. diagonal): 8 chol flop count for real A, sqrt counted as 1 flop: 671 LDL' flop count for real A: 647 LDL' flop count for complex A: 3073 LU flop count for real A (with no pivoting): 1003 LU flop count for complex A (with no pivoting): 4497 Permutation vector: 22 20 10 23 12 5 16 8 14 4 15 7 1 9 13 17 0 2 3 6 11 18 21 19 Inverse permutation vector: 16 12 17 18 9 5 19 11 7 13 2 20 4 14 8 10 6 15 21 23 1 22 0 3 Plot of (symmetrized) permuted matrix pattern: 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 0: X X . . . . . . . . . . . . . . . X . . . . X . 1: X X X . . . . . . . . . . . . . . X . . . . X X 2: . X X . . . . . . . . . . . . . . . X . . X X X 3: . . . X X . . . . . . . . . . . . . . X X . . . 4: . . . X X X . . . . . . . . . . X . . X X . . . 5: . . . . X X . . . . . . . . X X X . . X . . . . 6: . . . . . . X . . X X X . . . . . . . . . . . . 7: . . . . . . . X X . . . X X . . . . . . . . . . 8: . . . . . . . X X X . X X X . . . . . . . . . . 9: . . . . . . X . X X X X . X . . . . . . . . . . 10: . . . . . . X . . X X X . . . . . . X . . X . . 11: . . . . . . X . X X X X . X . X . . X . . X . . 12: . . . . . . . X X . . . X X X X . . . . . . . . 13: . . . . . . . X X X . X X X X X . . . . . X . . 14: . . . . . X . . . . . . X X X X X . . . . . . . 15: . . . . . X . . . . . X X X X X X . . . . X . X 16: . . . . X X . . . . . . . . X X X . . X . X X X 17: X X . . . . . . . . . . . . . . . X . X X . X . 18: . . X . . . . . . . X X . . . . . . X . . X . X 19: . . . X X X . . . . . . . . . . X X . X X . X X 20: . . . X X . . . . . . . . . . . . X . X X . X . 21: . . X . . . . . . . X X . X . X X . X . . X . X 22: X X X . . . . . . . . . . . . . X X . X X . X X 23: . X X . . . . . . . . . . . . X X . X X . X X X SuiteSparse/AMD/Demo/amd_f77cross.f0000644001170100242450000000415510616376310015711 0ustar davisfacC ====================================================================== C === AMD_cross ======================================================== C ====================================================================== C ---------------------------------------------------------------------- C AMD, Copyright (c) by Timothy A. Davis, Patrick R. C Amestoy, and Iain S. Duff. See ../README.txt for C License. email: davis at cise.ufl.edu CISE Department, Univ. of C Florida. web: http://www.cise.ufl.edu/research/sparse/amd C ---------------------------------------------------------------------- C This program provides an example of how to call the C version of AMD C from a Fortran program. It is HIGHLY non-portable. C The amd_order routine returns PERM (1) < 0 if an error occurs. C (-1: out of memory, -2: invalid matrix) C Note that the input matrix is 0-based. From Fortran, column j of the C matrix is in AI (AP (I)+1 ... AP (I+1)). The row indices in this C set are in the range 0 to N-1. To demonstrate this translation, C the input matrix is printed in 1-based form. This program uses C the same 5-by-5 test matrix as amd_simple.c. INTEGER N, NZ, K, P PARAMETER (N = 5, NZ = 14) INTEGER AP (N+1), AI (NZ), PERM (N) DATA AP / 0, 2, 6, 10, 12, 14 / DATA AI / 0,1, 0,1,2,4, 1,2,3,4, 2,3, 1,4 / DOUBLE PRECISION CONTROL (5), INFO (20) C print the input matrix PRINT 10, N, N, NZ 10 FORMAT ('Input matrix:', I2, '-by-', I2, ' with',I3,' entries') DO 40 J = 1, N PRINT 20, J, AP (J+1) - AP (J), AP (J)+1, AP (J+1) 20 FORMAT ( /, 'Column: ', I2, ' number of entries: ', I2, $ ' with row indices in AI (', I3, ' ... ', I3, ')') PRINT 30, ((AI (P) + 1), P = AP (J) + 1, AP (J+1)) 30 FORMAT (' row indices: ', 24I3) 40 CONTINUE CALL AMDDEFAULTS (CONTROL) CALL AMDORDER (N, AP, AI, PERM, CONTROL, INFO) CALL AMDINFO (INFO) DO 60 K = 1, N PRINT 50, K, PERM (K) + 1 50 FORMAT ('PERM (',I2,') = ', I2) 60 CONTINUE END SuiteSparse/AMD/Demo/amd_simple.c0000644001170100242450000000145310616376360015525 0ustar davisfac/* ------------------------------------------------------------------------- */ /* AMD Copyright (c) by Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ #include #include "amd.h" int n = 5 ; int Ap [ ] = { 0, 2, 6, 10, 12, 14} ; int Ai [ ] = { 0,1, 0,1,2,4, 1,2,3,4, 2,3, 1,4 } ; int P [5] ; int main (void) { int k ; (void) amd_order (n, Ap, Ai, P, (double *) NULL, (double *) NULL) ; for (k = 0 ; k < n ; k++) printf ("P [%d] = %d\n", k, P [k]) ; return (0) ; } SuiteSparse/AMD/Demo/amd_f77demo.out0000644001170100242450000002723210250414043016055 0ustar davisfacAMD Fortran 77 demo, with the 24-by-24 Harwell/Boeing matrix, can_24: Input matrix: 24-by-24 with 136 entries Note that the Fortran version of AMD requires that no diagonal entries be present. Column: 1 number of entries: 8 with row indices in AI ( 1 ... 8) row indices: 6 7 13 14 18 19 20 22 Column: 2 number of entries: 5 with row indices in AI ( 9 ... 13) row indices: 9 10 14 15 18 Column: 3 number of entries: 5 with row indices in AI ( 14 ... 18) row indices: 7 12 21 22 23 Column: 4 number of entries: 5 with row indices in AI ( 19 ... 23) row indices: 8 11 16 19 20 Column: 5 number of entries: 5 with row indices in AI ( 24 ... 28) row indices: 8 10 15 16 17 Column: 6 number of entries: 5 with row indices in AI ( 29 ... 33) row indices: 1 7 13 14 18 Column: 7 number of entries: 8 with row indices in AI ( 34 ... 41) row indices: 1 3 6 12 13 20 22 24 Column: 8 number of entries: 8 with row indices in AI ( 42 ... 49) row indices: 4 5 10 15 16 17 18 19 Column: 9 number of entries: 3 with row indices in AI ( 50 ... 52) row indices: 2 10 15 Column: 10 number of entries: 8 with row indices in AI ( 53 ... 60) row indices: 2 5 8 9 14 15 18 19 Column: 11 number of entries: 5 with row indices in AI ( 61 ... 65) row indices: 4 19 20 21 22 Column: 12 number of entries: 5 with row indices in AI ( 66 ... 70) row indices: 3 7 13 22 24 Column: 13 number of entries: 5 with row indices in AI ( 71 ... 75) row indices: 1 6 7 12 24 Column: 14 number of entries: 5 with row indices in AI ( 76 ... 80) row indices: 1 2 6 10 18 Column: 15 number of entries: 5 with row indices in AI ( 81 ... 85) row indices: 2 5 8 9 10 Column: 16 number of entries: 5 with row indices in AI ( 86 ... 90) row indices: 4 5 8 17 19 Column: 17 number of entries: 3 with row indices in AI ( 91 ... 93) row indices: 5 8 16 Column: 18 number of entries: 8 with row indices in AI ( 94 ... 101) row indices: 1 2 6 8 10 14 19 20 Column: 19 number of entries: 8 with row indices in AI (102 ... 109) row indices: 1 4 8 10 11 16 18 20 Column: 20 number of entries: 8 with row indices in AI (110 ... 117) row indices: 1 4 7 11 18 19 21 22 Column: 21 number of entries: 5 with row indices in AI (118 ... 122) row indices: 3 11 20 22 23 Column: 22 number of entries: 8 with row indices in AI (123 ... 130) row indices: 1 3 7 11 12 20 21 23 Column: 23 number of entries: 3 with row indices in AI (131 ... 133) row indices: 3 21 22 Column: 24 number of entries: 3 with row indices in AI (134 ... 136) row indices: 7 12 13 Plot of input matrix pattern: 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 1: X . . . . X X . . . . . X X . . . X X X . X . . 2: . X . . . . . . X X . . . X X . . X . . . . . . 3: . . X . . . X . . . . X . . . . . . . . X X X . 4: . . . X . . . X . . X . . . . X . . X X . . . . 5: . . . . X . . X . X . . . . X X X . . . . . . . 6: X . . . . X X . . . . . X X . . . X . . . . . . 7: X . X . . X X . . . . X X . . . . . . X . X . X 8: . . . X X . . X . X . . . . X X X X X . . . . . 9: . X . . . . . . X X . . . . X . . . . . . . . . 10: . X . . X . . X X X . . . X X . . X X . . . . . 11: . . . X . . . . . . X . . . . . . . X X X X . . 12: . . X . . . X . . . . X X . . . . . . . . X . X 13: X . . . . X X . . . . X X . . . . . . . . . . X 14: X X . . . X . . . X . . . X . . . X . . . . . . 15: . X . . X . . X X X . . . . X . . . . . . . . . 16: . . . X X . . X . . . . . . . X X . X . . . . . 17: . . . . X . . X . . . . . . . X X . . . . . . . 18: X X . . . X . X . X . . . X . . . X X X . . . . 19: X . . X . . . X . X X . . . . X . X X X . . . . 20: X . . X . . X . . . X . . . . . . X X X X X . . 21: . . X . . . . . . . X . . . . . . . . X X X X . 22: X . X . . . X . . . X X . . . . . . . X X X X . 23: . . X . . . . . . . . . . . . . . . . . X X X . 24: . . . . . . X . . . . X X . . . . . . . . . . X ------------------------------------------ ordering the matrix with AMD ------------------------------------------ Permutation vector: 24 23 17 9 15 5 21 13 6 11 16 8 2 10 14 18 1 3 4 19 7 12 22 20 Inverse permutation vector: 17 13 18 19 6 9 21 12 4 14 10 22 8 15 5 11 3 16 20 24 7 23 2 1 Plot of permuted matrix pattern: 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 1: X . . . . . . X . . . . . . . . . . . . X X . . 2: . X . . . . X . . . . . . . . . . X . . . . X . 3: . . X . . X . . . . X X . . . . . . . . . . . . 4: . . . X X . . . . . . . X X . . . . . . . . . . 5: . . . X X X . . . . . X X X . . . . . . . . . . 6: . . X . X X . . . . X X . X . . . . . . . . . . 7: . X . . . . X . . X . . . . . . . X . . . . X X 8: X . . . . . . X X . . . . . . . X . . . X X . . 9: . . . . . . . X X . . . . . X X X . . . X . . . 10: . . . . . . X . . X . . . . . . . . X X . . X X 11: . . X . . X . . . . X X . . . . . . X X . . . . 12: . . X . X X . . . . X X . X . X . . X X . . . . 13: . . . X X . . . . . . . X X X X . . . . . . . . 14: . . . X X X . . . . . X X X X X . . . X . . . . 15: . . . . . . . . X . . . X X X X X . . . . . . . 16: . . . . . . . . X . . X X X X X X . . X . . . X 17: . . . . . . . X X . . . . . X X X . . X X . X X 18: . X . . . . X . . . . . . . . . . X . . X X X . 19: . . . . . . . . . X X X . . . . . . X X . . . X 20: . . . . . . . . . X X X . X . X X . X X . . . X 21: X . . . . . . X X . . . . . . . X X . . X X X X 22: X . . . . . . X . . . . . . . . . X . . X X X . 23: . X . . . . X . . X . . . . . . X X . . X X X X 24: . . . . . . X . . X . . . . . X X . X X X . X X New column: 1 old column: 24 number of entries: 3 new row indices: 21 22 8 New column: 2 old column: 23 number of entries: 3 new row indices: 18 7 23 New column: 3 old column: 17 number of entries: 3 new row indices: 6 12 11 New column: 4 old column: 9 number of entries: 3 new row indices: 13 14 5 New column: 5 old column: 15 number of entries: 5 new row indices: 13 6 12 4 14 New column: 6 old column: 5 number of entries: 5 new row indices: 12 14 5 11 3 New column: 7 old column: 21 number of entries: 5 new row indices: 18 10 24 23 2 New column: 8 old column: 13 number of entries: 5 new row indices: 17 9 21 22 1 New column: 9 old column: 6 number of entries: 5 new row indices: 17 21 8 15 16 New column: 10 old column: 11 number of entries: 5 new row indices: 19 20 24 7 23 New column: 11 old column: 16 number of entries: 5 new row indices: 19 6 12 3 20 New column: 12 old column: 8 number of entries: 8 new row indices: 19 6 14 5 11 3 16 20 New column: 13 old column: 2 number of entries: 5 new row indices: 4 14 15 5 16 New column: 14 old column: 10 number of entries: 8 new row indices: 13 6 12 4 15 5 16 20 New column: 15 old column: 14 number of entries: 5 new row indices: 17 13 9 14 16 New column: 16 old column: 18 number of entries: 8 new row indices: 17 13 9 12 14 15 20 24 New column: 17 old column: 1 number of entries: 8 new row indices: 9 21 8 15 16 20 24 23 New column: 18 old column: 3 number of entries: 5 new row indices: 21 22 7 23 2 New column: 19 old column: 4 number of entries: 5 new row indices: 12 10 11 20 24 New column: 20 old column: 19 number of entries: 8 new row indices: 17 19 12 14 10 11 16 24 New column: 21 old column: 7 number of entries: 8 new row indices: 17 18 9 22 8 24 23 1 New column: 22 old column: 12 number of entries: 5 new row indices: 18 21 8 23 1 New column: 23 old column: 22 number of entries: 8 new row indices: 17 18 21 10 22 24 7 2 New column: 24 old column: 20 number of entries: 8 new row indices: 17 19 21 10 16 20 7 23 ------------------------------------------ ordering the matrix with AMDBAR ------------------------------------------ Permutation vector: 24 23 17 9 15 5 21 13 6 11 16 8 2 10 14 18 1 3 4 19 7 12 22 20 Inverse permutation vector: 17 13 18 19 6 9 21 12 4 14 10 22 8 15 5 11 3 16 20 24 7 23 2 1 Plot of permuted matrix pattern: 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 1: X . . . . . . X . . . . . . . . . . . . X X . . 2: . X . . . . X . . . . . . . . . . X . . . . X . 3: . . X . . X . . . . X X . . . . . . . . . . . . 4: . . . X X . . . . . . . X X . . . . . . . . . . 5: . . . X X X . . . . . X X X . . . . . . . . . . 6: . . X . X X . . . . X X . X . . . . . . . . . . 7: . X . . . . X . . X . . . . . . . X . . . . X X 8: X . . . . . . X X . . . . . . . X . . . X X . . 9: . . . . . . . X X . . . . . X X X . . . X . . . 10: . . . . . . X . . X . . . . . . . . X X . . X X 11: . . X . . X . . . . X X . . . . . . X X . . . . 12: . . X . X X . . . . X X . X . X . . X X . . . . 13: . . . X X . . . . . . . X X X X . . . . . . . . 14: . . . X X X . . . . . X X X X X . . . X . . . . 15: . . . . . . . . X . . . X X X X X . . . . . . . 16: . . . . . . . . X . . X X X X X X . . X . . . X 17: . . . . . . . X X . . . . . X X X . . X X . X X 18: . X . . . . X . . . . . . . . . . X . . X X X . 19: . . . . . . . . . X X X . . . . . . X X . . . X 20: . . . . . . . . . X X X . X . X X . X X . . . X 21: X . . . . . . X X . . . . . . . X X . . X X X X 22: X . . . . . . X . . . . . . . . . X . . X X X . 23: . X . . . . X . . X . . . . . . X X . . X X X X 24: . . . . . . X . . X . . . . . X X . X X X . X X New column: 1 old column: 24 number of entries: 3 new row indices: 21 22 8 New column: 2 old column: 23 number of entries: 3 new row indices: 18 7 23 New column: 3 old column: 17 number of entries: 3 new row indices: 6 12 11 New column: 4 old column: 9 number of entries: 3 new row indices: 13 14 5 New column: 5 old column: 15 number of entries: 5 new row indices: 13 6 12 4 14 New column: 6 old column: 5 number of entries: 5 new row indices: 12 14 5 11 3 New column: 7 old column: 21 number of entries: 5 new row indices: 18 10 24 23 2 New column: 8 old column: 13 number of entries: 5 new row indices: 17 9 21 22 1 New column: 9 old column: 6 number of entries: 5 new row indices: 17 21 8 15 16 New column: 10 old column: 11 number of entries: 5 new row indices: 19 20 24 7 23 New column: 11 old column: 16 number of entries: 5 new row indices: 19 6 12 3 20 New column: 12 old column: 8 number of entries: 8 new row indices: 19 6 14 5 11 3 16 20 New column: 13 old column: 2 number of entries: 5 new row indices: 4 14 15 5 16 New column: 14 old column: 10 number of entries: 8 new row indices: 13 6 12 4 15 5 16 20 New column: 15 old column: 14 number of entries: 5 new row indices: 17 13 9 14 16 New column: 16 old column: 18 number of entries: 8 new row indices: 17 13 9 12 14 15 20 24 New column: 17 old column: 1 number of entries: 8 new row indices: 9 21 8 15 16 20 24 23 New column: 18 old column: 3 number of entries: 5 new row indices: 21 22 7 23 2 New column: 19 old column: 4 number of entries: 5 new row indices: 12 10 11 20 24 New column: 20 old column: 19 number of entries: 8 new row indices: 17 19 12 14 10 11 16 24 New column: 21 old column: 7 number of entries: 8 new row indices: 17 18 9 22 8 24 23 1 New column: 22 old column: 12 number of entries: 5 new row indices: 18 21 8 23 1 New column: 23 old column: 22 number of entries: 8 new row indices: 17 18 21 10 22 24 7 2 New column: 24 old column: 20 number of entries: 8 new row indices: 17 19 21 10 16 20 7 23 SuiteSparse/AMD/Demo/amd_l_demo.c0000644001170100242450000001306710616376347015504 0ustar davisfac/* ========================================================================= */ /* === AMD demo main program (UF_long integer version) ===================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD Copyright (c) by Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ /* A simple C main program that illustrates the use of the ANSI C interface * to AMD. */ #include "amd.h" #include #include #include "UFconfig.h" int main (void) { /* The symmetric can_24 Harwell/Boeing matrix, including upper and lower * triangular parts, and the diagonal entries. Note that this matrix is * 0-based, with row and column indices in the range 0 to n-1. */ UF_long n = 24, nz, Ap [ ] = { 0, 9, 15, 21, 27, 33, 39, 48, 57, 61, 70, 76, 82, 88, 94, 100, 106, 110, 119, 128, 137, 143, 152, 156, 160 }, Ai [ ] = { /* column 0: */ 0, 5, 6, 12, 13, 17, 18, 19, 21, /* column 1: */ 1, 8, 9, 13, 14, 17, /* column 2: */ 2, 6, 11, 20, 21, 22, /* column 3: */ 3, 7, 10, 15, 18, 19, /* column 4: */ 4, 7, 9, 14, 15, 16, /* column 5: */ 0, 5, 6, 12, 13, 17, /* column 6: */ 0, 2, 5, 6, 11, 12, 19, 21, 23, /* column 7: */ 3, 4, 7, 9, 14, 15, 16, 17, 18, /* column 8: */ 1, 8, 9, 14, /* column 9: */ 1, 4, 7, 8, 9, 13, 14, 17, 18, /* column 10: */ 3, 10, 18, 19, 20, 21, /* column 11: */ 2, 6, 11, 12, 21, 23, /* column 12: */ 0, 5, 6, 11, 12, 23, /* column 13: */ 0, 1, 5, 9, 13, 17, /* column 14: */ 1, 4, 7, 8, 9, 14, /* column 15: */ 3, 4, 7, 15, 16, 18, /* column 16: */ 4, 7, 15, 16, /* column 17: */ 0, 1, 5, 7, 9, 13, 17, 18, 19, /* column 18: */ 0, 3, 7, 9, 10, 15, 17, 18, 19, /* column 19: */ 0, 3, 6, 10, 17, 18, 19, 20, 21, /* column 20: */ 2, 10, 19, 20, 21, 22, /* column 21: */ 0, 2, 6, 10, 11, 19, 20, 21, 22, /* column 22: */ 2, 20, 21, 22, /* column 23: */ 6, 11, 12, 23 } ; UF_long P [24], Pinv [24], i, j, k, jnew, p, inew, result ; double Control [AMD_CONTROL], Info [AMD_INFO] ; char A [24][24] ; /* here is an example of how to use AMD_VERSION. This code will work in * any version of AMD. */ #if defined(AMD_VERSION) && (AMD_VERSION >= AMD_VERSION_CODE(1,2)) printf ("AMD version %d.%d, date: %s\n", AMD_MAIN_VERSION, AMD_SUB_VERSION, AMD_DATE) ; #else printf ("AMD version: 1.1 or earlier\n") ; #endif printf ("AMD demo, with the 24-by-24 Harwell/Boeing matrix, can_24:\n") ; /* get the default parameters, and print them */ amd_l_defaults (Control) ; amd_l_control (Control) ; /* print the input matrix */ nz = Ap [n] ; printf ("\nInput matrix: %ld-by-%ld, with %ld entries.\n" " Note that for a symmetric matrix such as this one, only the\n" " strictly lower or upper triangular parts would need to be\n" " passed to AMD, since AMD computes the ordering of A+A'. The\n" " diagonal entries are also not needed, since AMD ignores them.\n" , n, n, nz) ; for (j = 0 ; j < n ; j++) { printf ("\nColumn: %ld, number of entries: %ld, with row indices in" " Ai [%ld ... %ld]:\n row indices:", j, Ap [j+1] - Ap [j], Ap [j], Ap [j+1]-1) ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; printf (" %ld", i) ; } printf ("\n") ; } /* print a character plot of the input matrix. This is only reasonable * because the matrix is small. */ printf ("\nPlot of input matrix pattern:\n") ; for (j = 0 ; j < n ; j++) { for (i = 0 ; i < n ; i++) A [i][j] = '.' ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; A [i][j] = 'X' ; } } printf (" ") ; for (j = 0 ; j < n ; j++) printf (" %1ld", j % 10) ; printf ("\n") ; for (i = 0 ; i < n ; i++) { printf ("%2ld: ", i) ; for (j = 0 ; j < n ; j++) { printf (" %c", A [i][j]) ; } printf ("\n") ; } /* order the matrix */ result = amd_l_order (n, Ap, Ai, P, Control, Info) ; printf ("return value from amd_l_order: %ld (should be %d)\n", result, AMD_OK) ; /* print the statistics */ amd_l_info (Info) ; if (result != AMD_OK) { printf ("AMD failed\n") ; exit (1) ; } /* print the permutation vector, P, and compute the inverse permutation */ printf ("Permutation vector:\n") ; for (k = 0 ; k < n ; k++) { /* row/column j is the kth row/column in the permuted matrix */ j = P [k] ; Pinv [j] = k ; printf (" %2ld", j) ; } printf ("\n\n") ; printf ("Inverse permutation vector:\n") ; for (j = 0 ; j < n ; j++) { k = Pinv [j] ; printf (" %2ld", k) ; } printf ("\n\n") ; /* print a character plot of the permuted matrix. */ printf ("\nPlot of permuted matrix pattern:\n") ; for (jnew = 0 ; jnew < n ; jnew++) { j = P [jnew] ; for (inew = 0 ; inew < n ; inew++) A [inew][jnew] = '.' ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { inew = Pinv [Ai [p]] ; A [inew][jnew] = 'X' ; } } printf (" ") ; for (j = 0 ; j < n ; j++) printf (" %1ld", j % 10) ; printf ("\n") ; for (i = 0 ; i < n ; i++) { printf ("%2ld: ", i) ; for (j = 0 ; j < n ; j++) { printf (" %c", A [i][j]) ; } printf ("\n") ; } return (0) ; } SuiteSparse/AMD/Demo/amd_simple.out0000644001170100242450000000006210425660213016074 0ustar davisfacP [0] = 0 P [1] = 3 P [2] = 2 P [3] = 4 P [4] = 1 SuiteSparse/AMD/Demo/amd_f77wrapper.c0000644001170100242450000000636710616376335016253 0ustar davisfac/* ========================================================================= */ /* === amd_f77wrapper ====================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD Copyright (c) by Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ /* Fortran interface for the C-callable AMD library (int version only). This * is HIGHLY non-portable. You will need to modify this depending on how your * Fortran and C compilers behave. Two examples are provided. * * To avoid using I/O, and to avoid the extra porting step of a Fortran * function, the status code is returned as the first entry in P (P [0] in C * and P (1) in Fortran) if an error occurs. The error codes are negative * (-1: out of memory, -2: invalid matrix). * * For some C and Fortran compilers, the Fortran compiler appends a single "_" * after each routine name. C doesn't do this, so the translation is made * here. Some Fortran compilers don't append an underscore (xlf on IBM AIX, * for * example). * * Tested with the following compilers: * Solaris with cc and f77 from Sun WorkShop 6 update 1. * SGI Irix with MIPSpro cc and f77 compilers version 7.4 * Linux with GNU gcc or Intel's icc, and GNU g77 Intel's ifc Fortran compiler. * (any combination). Note that with g77, a call to amd_order in Fortran * gets translated to a call to amd_order__, with two underscores ("_"). * Thus, the Fortran names do not include an underscore. */ #include "amd.h" #include /* ------------------------------------------------------------------------- */ /* Linux, Solaris, SGI */ /* ------------------------------------------------------------------------- */ void amdorder_ (int *n, const int *Ap, const int *Ai, int *P, double *Control, double *Info) { int result = amd_order (*n, Ap, Ai, P, Control, Info) ; if (result != AMD_OK && P) P [0] = result ; } void amddefaults_ (double *Control) { amd_defaults (Control) ; } void amdcontrol_ (double *Control) { fflush (stdout) ; amd_control (Control) ; fflush (stdout) ; } void amdinfo_ (double *Info) { fflush (stdout) ; amd_info (Info) ; fflush (stdout) ; } /* ------------------------------------------------------------------------- */ /* IBM AIX. Probably Windows, Compaq Alpha, and HP Unix as well. */ /* ------------------------------------------------------------------------- */ void amdorder (int *n, const int *Ap, const int *Ai, int *P, double *Control, double *Info) { int result = amd_order (*n, Ap, Ai, P, Control, Info) ; if (result != AMD_OK && P) P [0] = result ; } void amddefaults (double *Control) { amd_defaults (Control) ; } void amdcontrol (double *Control) { fflush (stdout) ; amd_control (Control) ; fflush (stdout) ; } void amdinfo (double *Info) { fflush (stdout) ; amd_info (Info) ; fflush (stdout) ; } SuiteSparse/AMD/Demo/amd_f77demo.f0000644001170100242450000001437510616376317015520 0ustar davisfacC ====================================================================== C === Fortran AMD demo main program ==================================== C ====================================================================== C ---------------------------------------------------------------------- C AMD, Copyright (c) by Timothy A. Davis, Patrick R. C Amestoy, and Iain S. Duff. See ../README.txt for C License. email: davis at cise.ufl.edu CISE Department, Univ. of C Florida. web: http://www.cise.ufl.edu/research/sparse/amd C ---------------------------------------------------------------------- C A simple Fortran 77 main program that illustrates the use of the C Fortran version of AMD (both the AMD and AMDBAR routines). Note C that aggressive absorption has no effect on this particular matrix. C AP and AI contain the symmetric can_24 Harwell/Boeing matrix, C including upper and lower triangular parts, but excluding the C diagonal entries. Note that this matrix is 1-based, with row C and column indices in the range 1 to N. INTEGER N, NZ, IWLEN, PFREE, I, J, K, JNEW, P, INEW, $ METHOD, NCMPA PARAMETER (N = 24, NZ = 136, IWLEN = 200) INTEGER PE (N), DEGREE (N), NV (N), NEXT (N), PERM (N), W (N), $ HEAD (N), PINV (N), LEN (N), AP (N+1), AI (NZ), IW (IWLEN) CHARACTER A (24,24) DATA AP $ / 1, 9, 14, 19, 24, 29, 34, 42, 50, 53, 61, 66, 71, $ 76, 81, 86, 91, 94, 102, 110, 118, 123, 131, 134, 137 / DATA AI / $ 6, 7, 13, 14, 18, 19, 20, 22, $ 9, 10, 14, 15, 18, $ 7, 12, 21, 22, 23, $ 8, 11, 16, 19, 20, $ 8, 10, 15, 16, 17, $ 1, 7, 13, 14, 18, $ 1, 3, 6, 12, 13, 20, 22, 24, $ 4, 5, 10, 15, 16, 17, 18, 19, $ 2, 10, 15, $ 2, 5, 8, 9, 14, 15, 18, 19, $ 4, 19, 20, 21, 22, $ 3, 7, 13, 22, 24, $ 1, 6, 7, 12, 24, $ 1, 2, 6, 10, 18, $ 2, 5, 8, 9, 10, $ 4, 5, 8, 17, 19, $ 5, 8, 16, $ 1, 2, 6, 8, 10, 14, 19, 20, $ 1, 4, 8, 10, 11, 16, 18, 20, $ 1, 4, 7, 11, 18, 19, 21, 22, $ 3, 11, 20, 22, 23, $ 1, 3, 7, 11, 12, 20, 21, 23, $ 3, 21, 22, $ 7, 12, 13 / C print the input matrix PRINT 11, N, N, NZ 11 FORMAT ('AMD Fortran 77 demo, with the 24-by-24', $ ' Harwell/Boeing matrix, can_24:' $ /, 'Input matrix: ', I2, '-by-', I2,' with ',I3,' entries', $ /, 'Note that the Fortran version of AMD requires that' $ /, 'no diagonal entries be present.') DO 20 J = 1, N PRINT 21, J, AP (J+1) - AP (J), AP (J), AP (J+1)-1 21 FORMAT ( /, 'Column: ', I2, ' number of entries: ', I2, $ ' with row indices in AI (', I3, ' ... ', I3, ')') PRINT 10, ((AI (P)), P = AP (J), AP (J+1) - 1) 10 FORMAT (' row indices: ', 24I3) 20 CONTINUE C print a character plot of the input matrix. This is only C reasonable because the matrix is small. PRINT 31 31 FORMAT ('Plot of input matrix pattern:') DO 50 J = 1,N DO 30 I = 1,N A (I, J) = '.' 30 CONTINUE C add the diagonal entry to the plot A (J, J) = 'X' DO 40 P = AP (J), AP (J+1) - 1 I = AI (P) A (I, J) = 'X' 40 CONTINUE 50 CONTINUE PRINT 60, ((MOD (J, 10)), J = 1,N) 60 FORMAT (' ', 24I2) DO 80 I = 1,N PRINT 70, I, (A (I, J), J = 1,N) 70 FORMAT (' ', I2, ': ', 24A2) 80 CONTINUE DO 190 METHOD = 1,2 C load the matrix into AMD's workspace DO 90 J = 1,N PE (J) = AP (J) LEN (J) = AP (J+1) - AP (J) 90 CONTINUE DO 100 P = 1,NZ IW (P) = AI (P) 100 CONTINUE PFREE = NZ + 1 C order the matrix using AMD or AMDBAR IF (METHOD .EQ. 1) THEN PRINT 101 101 FORMAT (/, '------------------------------------------', $ /, 'ordering the matrix with AMD', $ /, '------------------------------------------') CALL AMD (N, PE, IW, LEN, IWLEN, PFREE, NV, NEXT, $ PERM, HEAD, PINV, DEGREE, NCMPA, W) ELSE PRINT 102 102 FORMAT (/, '------------------------------------------', $ /, 'ordering the matrix with AMDBAR', $ /, '------------------------------------------') CALL AMDBAR (N, PE, IW, LEN, IWLEN, PFREE, NV, NEXT, $ PERM, HEAD, PINV, DEGREE, NCMPA, W) ENDIF C print the permutation vector, PERM, and its inverse, PINV. C row/column J = PERM (K) is the Kth row/column in the C permuted matrix. PRINT 110, (PERM (K), K = 1,N) 110 FORMAT (/, 'Permutation vector: ', /, 24I3) PRINT 120, (PINV (J), J = 1,N) 120 FORMAT (/, 'Inverse permutation vector: ', /, 24I3) C print a character plot of the permuted matrix. PRINT 121 121 FORMAT ('Plot of permuted matrix pattern:') DO 150 JNEW = 1,N J = PERM (JNEW) DO 130 INEW = 1,N A (INEW, JNEW) = '.' 130 CONTINUE C add the diagonal entry to the plot A (JNEW, JNEW) = 'X' DO 140 P = AP (J), AP (J+1) - 1 INEW = PINV (AI (P)) A (INEW, JNEW) = 'X' 140 CONTINUE 150 CONTINUE PRINT 60, ((MOD (J, 10)), J = 1,N) DO 160 I = 1,N PRINT 70, I, (A (I, J), J = 1,N) 160 CONTINUE C print the permuted matrix, PERM*A*PERM' DO 180 JNEW = 1,N J = PERM (JNEW) PRINT 171, JNEW, J, AP (J+1) - AP (J) 171 FORMAT (/, 'New column: ', I2, ' old column: ', I2, $ ' number of entries: ', I2) PRINT 170, (PINV (AI (P)), P = AP (J), AP (J+1) - 1) 170 FORMAT (' new row indices: ', 24I3) 180 CONTINUE 190 CONTINUE END SuiteSparse/AMD/Demo/amd_demo.out0000644001170100242450000001664210616431751015547 0ustar davisfacAMD version 2.2, date: May 31, 2007 AMD demo, with the 24-by-24 Harwell/Boeing matrix, can_24: AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 Input matrix: 24-by-24, with 160 entries. Note that for a symmetric matrix such as this one, only the strictly lower or upper triangular parts would need to be passed to AMD, since AMD computes the ordering of A+A'. The diagonal entries are also not needed, since AMD ignores them. Column: 0, number of entries: 9, with row indices in Ai [0 ... 8]: row indices: 0 5 6 12 13 17 18 19 21 Column: 1, number of entries: 6, with row indices in Ai [9 ... 14]: row indices: 1 8 9 13 14 17 Column: 2, number of entries: 6, with row indices in Ai [15 ... 20]: row indices: 2 6 11 20 21 22 Column: 3, number of entries: 6, with row indices in Ai [21 ... 26]: row indices: 3 7 10 15 18 19 Column: 4, number of entries: 6, with row indices in Ai [27 ... 32]: row indices: 4 7 9 14 15 16 Column: 5, number of entries: 6, with row indices in Ai [33 ... 38]: row indices: 0 5 6 12 13 17 Column: 6, number of entries: 9, with row indices in Ai [39 ... 47]: row indices: 0 2 5 6 11 12 19 21 23 Column: 7, number of entries: 9, with row indices in Ai [48 ... 56]: row indices: 3 4 7 9 14 15 16 17 18 Column: 8, number of entries: 4, with row indices in Ai [57 ... 60]: row indices: 1 8 9 14 Column: 9, number of entries: 9, with row indices in Ai [61 ... 69]: row indices: 1 4 7 8 9 13 14 17 18 Column: 10, number of entries: 6, with row indices in Ai [70 ... 75]: row indices: 3 10 18 19 20 21 Column: 11, number of entries: 6, with row indices in Ai [76 ... 81]: row indices: 2 6 11 12 21 23 Column: 12, number of entries: 6, with row indices in Ai [82 ... 87]: row indices: 0 5 6 11 12 23 Column: 13, number of entries: 6, with row indices in Ai [88 ... 93]: row indices: 0 1 5 9 13 17 Column: 14, number of entries: 6, with row indices in Ai [94 ... 99]: row indices: 1 4 7 8 9 14 Column: 15, number of entries: 6, with row indices in Ai [100 ... 105]: row indices: 3 4 7 15 16 18 Column: 16, number of entries: 4, with row indices in Ai [106 ... 109]: row indices: 4 7 15 16 Column: 17, number of entries: 9, with row indices in Ai [110 ... 118]: row indices: 0 1 5 7 9 13 17 18 19 Column: 18, number of entries: 9, with row indices in Ai [119 ... 127]: row indices: 0 3 7 9 10 15 17 18 19 Column: 19, number of entries: 9, with row indices in Ai [128 ... 136]: row indices: 0 3 6 10 17 18 19 20 21 Column: 20, number of entries: 6, with row indices in Ai [137 ... 142]: row indices: 2 10 19 20 21 22 Column: 21, number of entries: 9, with row indices in Ai [143 ... 151]: row indices: 0 2 6 10 11 19 20 21 22 Column: 22, number of entries: 4, with row indices in Ai [152 ... 155]: row indices: 2 20 21 22 Column: 23, number of entries: 4, with row indices in Ai [156 ... 159]: row indices: 6 11 12 23 Plot of input matrix pattern: 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 0: X . . . . X X . . . . . X X . . . X X X . X . . 1: . X . . . . . . X X . . . X X . . X . . . . . . 2: . . X . . . X . . . . X . . . . . . . . X X X . 3: . . . X . . . X . . X . . . . X . . X X . . . . 4: . . . . X . . X . X . . . . X X X . . . . . . . 5: X . . . . X X . . . . . X X . . . X . . . . . . 6: X . X . . X X . . . . X X . . . . . . X . X . X 7: . . . X X . . X . X . . . . X X X X X . . . . . 8: . X . . . . . . X X . . . . X . . . . . . . . . 9: . X . . X . . X X X . . . X X . . X X . . . . . 10: . . . X . . . . . . X . . . . . . . X X X X . . 11: . . X . . . X . . . . X X . . . . . . . . X . X 12: X . . . . X X . . . . X X . . . . . . . . . . X 13: X X . . . X . . . X . . . X . . . X . . . . . . 14: . X . . X . . X X X . . . . X . . . . . . . . . 15: . . . X X . . X . . . . . . . X X . X . . . . . 16: . . . . X . . X . . . . . . . X X . . . . . . . 17: X X . . . X . X . X . . . X . . . X X X . . . . 18: X . . X . . . X . X X . . . . X . X X X . . . . 19: X . . X . . X . . . X . . . . . . X X X X X . . 20: . . X . . . . . . . X . . . . . . . . X X X X . 21: X . X . . . X . . . X X . . . . . . . X X X X . 22: . . X . . . . . . . . . . . . . . . . . X X X . 23: . . . . . . X . . . . X X . . . . . . . . . . X return value from amd_order: 0 (should be 0) AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 24 nz, number of nonzeros in A: 160 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 136 # dense rows/columns of A+A': 0 memory used, in bytes: 1516 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 97 nonzeros in L (including diagonal): 121 # divide operations for LDL' or LU: 97 # multiply-subtract operations for LDL': 275 # multiply-subtract operations for LU: 453 max nz. in any column of L (incl. diagonal): 8 chol flop count for real A, sqrt counted as 1 flop: 671 LDL' flop count for real A: 647 LDL' flop count for complex A: 3073 LU flop count for real A (with no pivoting): 1003 LU flop count for complex A (with no pivoting): 4497 Permutation vector: 22 20 10 23 12 5 16 8 14 4 15 7 1 9 13 17 0 2 3 6 11 18 21 19 Inverse permutation vector: 16 12 17 18 9 5 19 11 7 13 2 20 4 14 8 10 6 15 21 23 1 22 0 3 Plot of permuted matrix pattern: 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 0: X X . . . . . . . . . . . . . . . X . . . . X . 1: X X X . . . . . . . . . . . . . . X . . . . X X 2: . X X . . . . . . . . . . . . . . . X . . X X X 3: . . . X X . . . . . . . . . . . . . . X X . . . 4: . . . X X X . . . . . . . . . . X . . X X . . . 5: . . . . X X . . . . . . . . X X X . . X . . . . 6: . . . . . . X . . X X X . . . . . . . . . . . . 7: . . . . . . . X X . . . X X . . . . . . . . . . 8: . . . . . . . X X X . X X X . . . . . . . . . . 9: . . . . . . X . X X X X . X . . . . . . . . . . 10: . . . . . . X . . X X X . . . . . . X . . X . . 11: . . . . . . X . X X X X . X . X . . X . . X . . 12: . . . . . . . X X . . . X X X X . . . . . . . . 13: . . . . . . . X X X . X X X X X . . . . . X . . 14: . . . . . X . . . . . . X X X X X . . . . . . . 15: . . . . . X . . . . . X X X X X X . . . . X . X 16: . . . . X X . . . . . . . . X X X . . X . X X X 17: X X . . . . . . . . . . . . . . . X . X X . X . 18: . . X . . . . . . . X X . . . . . . X . . X . X 19: . . . X X X . . . . . . . . . . X X . X X . X X 20: . . . X X . . . . . . . . . . . . X . X X . X . 21: . . X . . . . . . . X X . X . X X . X . . X . X 22: X X X . . . . . . . . . . . . . X X . X X . X X 23: . X X . . . . . . . . . . . . X X . X X . X X X SuiteSparse/AMD/Demo/amd_f77simple.out0000644001170100242450000000007410250414043016415 0ustar davisfacP ( 1) = 4 P ( 2) = 1 P ( 3) = 3 P ( 4) = 5 P ( 5) = 2 SuiteSparse/AMD/Demo/amd_demo.c0000644001170100242450000001300010616376270015147 0ustar davisfac/* ========================================================================= */ /* === AMD demo main program =============================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD Copyright (c) by Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ /* A simple C main program that illustrates the use of the ANSI C interface * to AMD. */ #include "amd.h" #include #include int main (void) { /* The symmetric can_24 Harwell/Boeing matrix, including upper and lower * triangular parts, and the diagonal entries. Note that this matrix is * 0-based, with row and column indices in the range 0 to n-1. */ int n = 24, nz, Ap [ ] = { 0, 9, 15, 21, 27, 33, 39, 48, 57, 61, 70, 76, 82, 88, 94, 100, 106, 110, 119, 128, 137, 143, 152, 156, 160 }, Ai [ ] = { /* column 0: */ 0, 5, 6, 12, 13, 17, 18, 19, 21, /* column 1: */ 1, 8, 9, 13, 14, 17, /* column 2: */ 2, 6, 11, 20, 21, 22, /* column 3: */ 3, 7, 10, 15, 18, 19, /* column 4: */ 4, 7, 9, 14, 15, 16, /* column 5: */ 0, 5, 6, 12, 13, 17, /* column 6: */ 0, 2, 5, 6, 11, 12, 19, 21, 23, /* column 7: */ 3, 4, 7, 9, 14, 15, 16, 17, 18, /* column 8: */ 1, 8, 9, 14, /* column 9: */ 1, 4, 7, 8, 9, 13, 14, 17, 18, /* column 10: */ 3, 10, 18, 19, 20, 21, /* column 11: */ 2, 6, 11, 12, 21, 23, /* column 12: */ 0, 5, 6, 11, 12, 23, /* column 13: */ 0, 1, 5, 9, 13, 17, /* column 14: */ 1, 4, 7, 8, 9, 14, /* column 15: */ 3, 4, 7, 15, 16, 18, /* column 16: */ 4, 7, 15, 16, /* column 17: */ 0, 1, 5, 7, 9, 13, 17, 18, 19, /* column 18: */ 0, 3, 7, 9, 10, 15, 17, 18, 19, /* column 19: */ 0, 3, 6, 10, 17, 18, 19, 20, 21, /* column 20: */ 2, 10, 19, 20, 21, 22, /* column 21: */ 0, 2, 6, 10, 11, 19, 20, 21, 22, /* column 22: */ 2, 20, 21, 22, /* column 23: */ 6, 11, 12, 23 } ; int P [24], Pinv [24], i, j, k, jnew, p, inew, result ; double Control [AMD_CONTROL], Info [AMD_INFO] ; char A [24][24] ; /* here is an example of how to use AMD_VERSION. This code will work in * any version of AMD. */ #if defined(AMD_VERSION) && (AMD_VERSION >= AMD_VERSION_CODE(1,2)) printf ("AMD version %d.%d, date: %s\n", AMD_MAIN_VERSION, AMD_SUB_VERSION, AMD_DATE) ; #else printf ("AMD version: 1.1 or earlier\n") ; #endif printf ("AMD demo, with the 24-by-24 Harwell/Boeing matrix, can_24:\n") ; /* get the default parameters, and print them */ amd_defaults (Control) ; amd_control (Control) ; /* print the input matrix */ nz = Ap [n] ; printf ("\nInput matrix: %d-by-%d, with %d entries.\n" " Note that for a symmetric matrix such as this one, only the\n" " strictly lower or upper triangular parts would need to be\n" " passed to AMD, since AMD computes the ordering of A+A'. The\n" " diagonal entries are also not needed, since AMD ignores them.\n" , n, n, nz) ; for (j = 0 ; j < n ; j++) { printf ("\nColumn: %d, number of entries: %d, with row indices in" " Ai [%d ... %d]:\n row indices:", j, Ap [j+1] - Ap [j], Ap [j], Ap [j+1]-1) ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; printf (" %d", i) ; } printf ("\n") ; } /* print a character plot of the input matrix. This is only reasonable * because the matrix is small. */ printf ("\nPlot of input matrix pattern:\n") ; for (j = 0 ; j < n ; j++) { for (i = 0 ; i < n ; i++) A [i][j] = '.' ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; A [i][j] = 'X' ; } } printf (" ") ; for (j = 0 ; j < n ; j++) printf (" %1d", j % 10) ; printf ("\n") ; for (i = 0 ; i < n ; i++) { printf ("%2d: ", i) ; for (j = 0 ; j < n ; j++) { printf (" %c", A [i][j]) ; } printf ("\n") ; } /* order the matrix */ result = amd_order (n, Ap, Ai, P, Control, Info) ; printf ("return value from amd_order: %d (should be %d)\n", result, AMD_OK) ; /* print the statistics */ amd_info (Info) ; if (result != AMD_OK) { printf ("AMD failed\n") ; exit (1) ; } /* print the permutation vector, P, and compute the inverse permutation */ printf ("Permutation vector:\n") ; for (k = 0 ; k < n ; k++) { /* row/column j is the kth row/column in the permuted matrix */ j = P [k] ; Pinv [j] = k ; printf (" %2d", j) ; } printf ("\n\n") ; printf ("Inverse permutation vector:\n") ; for (j = 0 ; j < n ; j++) { k = Pinv [j] ; printf (" %2d", k) ; } printf ("\n\n") ; /* print a character plot of the permuted matrix. */ printf ("\nPlot of permuted matrix pattern:\n") ; for (jnew = 0 ; jnew < n ; jnew++) { j = P [jnew] ; for (inew = 0 ; inew < n ; inew++) A [inew][jnew] = '.' ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { inew = Pinv [Ai [p]] ; A [inew][jnew] = 'X' ; } } printf (" ") ; for (j = 0 ; j < n ; j++) printf (" %1d", j % 10) ; printf ("\n") ; for (i = 0 ; i < n ; i++) { printf ("%2d: ", i) ; for (j = 0 ; j < n ; j++) { printf (" %c", A [i][j]) ; } printf ("\n") ; } return (0) ; } SuiteSparse/AMD/Demo/amd_demo2.c0000644001170100242450000001413610616376252015244 0ustar davisfac/* ========================================================================= */ /* === AMD demo main program (jumbled matrix version) ====================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD Copyright (c) by Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ /* A simple C main program that illustrates the use of the ANSI C interface * to AMD. * * Identical to amd_demo.c, except that it operates on an input matrix that has * unsorted columns and duplicate entries. */ #include "amd.h" #include #include int main (void) { /* The symmetric can_24 Harwell/Boeing matrix (jumbled, and not symmetric). * Since AMD operates on A+A', only A(i,j) or A(j,i) need to be specified, * or both. The diagonal entries are optional (some are missing). * There are many duplicate entries, which must be removed. */ int n = 24, nz, Ap [ ] = { 0, 9, 14, 20, 28, 33, 37, 44, 53, 58, 63, 63, 66, 69, 72, 75, 78, 82, 86, 91, 97, 101, 112, 112, 116 }, Ai [ ] = { /* column 0: */ 0, 17, 18, 21, 5, 12, 5, 0, 13, /* column 1: */ 14, 1, 8, 13, 17, /* column 2: */ 2, 20, 11, 6, 11, 22, /* column 3: */ 3, 3, 10, 7, 18, 18, 15, 19, /* column 4: */ 7, 9, 15, 14, 16, /* column 5: */ 5, 13, 6, 17, /* column 6: */ 5, 0, 11, 6, 12, 6, 23, /* column 7: */ 3, 4, 9, 7, 14, 16, 15, 17, 18, /* column 8: */ 1, 9, 14, 14, 14, /* column 9: */ 7, 13, 8, 1, 17, /* column 10: */ /* column 11: */ 2, 12, 23, /* column 12: */ 5, 11, 12, /* column 13: */ 0, 13, 17, /* column 14: */ 1, 9, 14, /* column 15: */ 3, 15, 16, /* column 16: */ 16, 4, 4, 15, /* column 17: */ 13, 17, 19, 17, /* column 18: */ 15, 17, 19, 9, 10, /* column 19: */ 17, 19, 20, 0, 6, 10, /* column 20: */ 22, 10, 20, 21, /* column 21: */ 6, 2, 10, 19, 20, 11, 21, 22, 22, 22, 22, /* column 22: */ /* column 23: */ 12, 11, 12, 23 } ; int P [24], Pinv [24], i, j, k, jnew, p, inew, result ; double Control [AMD_CONTROL], Info [AMD_INFO] ; char A [24][24] ; printf ("AMD demo, with a jumbled version of the 24-by-24\n") ; printf ("Harwell/Boeing matrix, can_24:\n") ; /* get the default parameters, and print them */ amd_defaults (Control) ; amd_control (Control) ; /* print the input matrix */ nz = Ap [n] ; printf ("\nJumbled input matrix: %d-by-%d, with %d entries.\n" " Note that for a symmetric matrix such as this one, only the\n" " strictly lower or upper triangular parts would need to be\n" " passed to AMD, since AMD computes the ordering of A+A'. The\n" " diagonal entries are also not needed, since AMD ignores them.\n" " This version of the matrix has jumbled columns and duplicate\n" " row indices.\n", n, n, nz) ; for (j = 0 ; j < n ; j++) { printf ("\nColumn: %d, number of entries: %d, with row indices in" " Ai [%d ... %d]:\n row indices:", j, Ap [j+1] - Ap [j], Ap [j], Ap [j+1]-1) ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; printf (" %d", i) ; } printf ("\n") ; } /* print a character plot of the input matrix. This is only reasonable * because the matrix is small. */ printf ("\nPlot of (jumbled) input matrix pattern:\n") ; for (j = 0 ; j < n ; j++) { for (i = 0 ; i < n ; i++) A [i][j] = '.' ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; A [i][j] = 'X' ; } } printf (" ") ; for (j = 0 ; j < n ; j++) printf (" %1d", j % 10) ; printf ("\n") ; for (i = 0 ; i < n ; i++) { printf ("%2d: ", i) ; for (j = 0 ; j < n ; j++) { printf (" %c", A [i][j]) ; } printf ("\n") ; } /* print a character plot of the matrix A+A'. */ printf ("\nPlot of symmetric matrix to be ordered by amd_order:\n") ; for (j = 0 ; j < n ; j++) { for (i = 0 ; i < n ; i++) A [i][j] = '.' ; } for (j = 0 ; j < n ; j++) { A [j][j] = 'X' ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; A [i][j] = 'X' ; A [j][i] = 'X' ; } } printf (" ") ; for (j = 0 ; j < n ; j++) printf (" %1d", j % 10) ; printf ("\n") ; for (i = 0 ; i < n ; i++) { printf ("%2d: ", i) ; for (j = 0 ; j < n ; j++) { printf (" %c", A [i][j]) ; } printf ("\n") ; } /* order the matrix */ result = amd_order (n, Ap, Ai, P, Control, Info) ; printf ("return value from amd_order: %d (should be %d)\n", result, AMD_OK_BUT_JUMBLED) ; /* print the statistics */ amd_info (Info) ; if (result != AMD_OK_BUT_JUMBLED) { printf ("AMD failed\n") ; exit (1) ; } /* print the permutation vector, P, and compute the inverse permutation */ printf ("Permutation vector:\n") ; for (k = 0 ; k < n ; k++) { /* row/column j is the kth row/column in the permuted matrix */ j = P [k] ; Pinv [j] = k ; printf (" %2d", j) ; } printf ("\n\n") ; printf ("Inverse permutation vector:\n") ; for (j = 0 ; j < n ; j++) { k = Pinv [j] ; printf (" %2d", k) ; } printf ("\n\n") ; /* print a character plot of the permuted matrix. */ printf ("\nPlot of (symmetrized) permuted matrix pattern:\n") ; for (j = 0 ; j < n ; j++) { for (i = 0 ; i < n ; i++) A [i][j] = '.' ; } for (jnew = 0 ; jnew < n ; jnew++) { j = P [jnew] ; A [jnew][jnew] = 'X' ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { inew = Pinv [Ai [p]] ; A [inew][jnew] = 'X' ; A [jnew][inew] = 'X' ; } } printf (" ") ; for (j = 0 ; j < n ; j++) printf (" %1d", j % 10) ; printf ("\n") ; for (i = 0 ; i < n ; i++) { printf ("%2d: ", i) ; for (j = 0 ; j < n ; j++) { printf (" %c", A [i][j]) ; } printf ("\n") ; } return (0) ; } SuiteSparse/AMD/Makefile0000644001170100242450000000326310617136643014023 0ustar davisfac#------------------------------------------------------------------------------ # AMD Makefile (for GNU Make or original make) #------------------------------------------------------------------------------ default: demo include ../UFconfig/UFconfig.mk # Compile all C code, including the C-callable routines. # Do not compile the FORTRAN versions, or MATLAB interface. demo: ( cd Lib ; $(MAKE) ) ( cd Demo ; $(MAKE) ) # Compile all C code, including the C-callable routine and the mexFunctions. # Do not compile the FORTRAN versions. all: ( cd Lib ; $(MAKE) ) ( cd Demo ; $(MAKE) ) ( cd MATLAB ; $(MAKE) ) # compile just the C-callable libraries (not mexFunctions or Demos) library: ( cd Lib ; $(MAKE) ) # compile the FORTRAN libraries and demo programs (not compiled by "make all") fortran: ( cd Lib ; $(MAKE) fortran ) ( cd Demo ; $(MAKE) fortran ) # compile a FORTRAN demo program that calls the C version of AMD # (not compiled by "make all") cross: ( cd Demo ; $(MAKE) cross ) # remove object files, but keep the compiled programs and library archives clean: ( cd Lib ; $(MAKE) clean ) ( cd Demo ; $(MAKE) clean ) ( cd MATLAB ; $(MAKE) clean ) ( cd Doc ; $(MAKE) clean ) # clean, and then remove compiled programs and library archives purge: ( cd Lib ; $(MAKE) purge ) ( cd Demo ; $(MAKE) purge ) ( cd MATLAB ; $(MAKE) purge ) ( cd Doc ; $(MAKE) purge ) distclean: purge # create PDF documents for the original distribution doc: ( cd Doc ; $(MAKE) ) # get ready for distribution dist: purge ( cd Demo ; $(MAKE) dist ) ( cd Doc ; $(MAKE) ) ccode: library lib: library # compile the MATLAB mexFunction mex: ( cd MATLAB ; $(MAKE) ) SuiteSparse/AMD/MATLAB/0000755001170100242450000000000010711653375013320 5ustar davisfacSuiteSparse/AMD/MATLAB/Makefile0000644001170100242450000000210310616365605014754 0ustar davisfac#------------------------------------------------------------------------------ # Makefile for the AMD MATLAB mexFunction #------------------------------------------------------------------------------ default: amd2 include ../../UFconfig/UFconfig.mk AMD = ../Lib/libamd.a I = -I../Include -I../../UFconfig INC = ../Include/amd.h ../Include/amd_internal.h ../../UFconfig/UFconfig.h SRC = ../Source/amd_1.c ../Source/amd_2.c ../Source/amd_aat.c \ ../Source/amd_control.c ../Source/amd_defaults.c ../Source/amd_dump.c \ ../Source/amd_global.c ../Source/amd_info.c ../Source/amd_order.c \ ../Source/amd_postorder.c ../Source/amd_post_tree.c \ ../Source/amd_preprocess.c ../Source/amd_valid.c amd2: $(SRC) $(INC) amd_mex.c $(MEX) -DDLONG $(I) -output amd2 amd_mex.c $(SRC) #------------------------------------------------------------------------------ # Remove all but the files in the original distribution #------------------------------------------------------------------------------ clean: - $(RM) $(CLEAN) purge: distclean distclean: clean - $(RM) amd2.mex* SuiteSparse/AMD/MATLAB/Contents.m0000644001170100242450000000114410620366115015263 0ustar davisfac%Contents of the AMD sparse matrix ordering package: % % amd2 - p = amd2 (A), the approximate minimum degree ordering of A % amd_demo - a demo of amd2, using the can_24 matrix % amd_make - to compile amd2 for use in MATLAB % amd_install - compile and install amd2 for use in MATLAB % % See also: amd, amd2, colamd, symamd, colmmd, symmmd, umfpack % % Note that amd2 and the built-in amd function in MATLAB 7.3 and later are one % and the same. % % Example: % p = amd2 (A) ; % Copyright 1994-2007, Tim Davis, University of Florida, % Patrick R. Amestoy, and Iain S. Duff. help Contents SuiteSparse/AMD/MATLAB/amd_mex.c0000644001170100242450000001364310616377050015102 0ustar davisfac/* ========================================================================= */ /* === AMD mexFunction ===================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ /* * Usage: * p = amd (A) * p = amd (A, Control) * [p, Info] = amd (A) * [p, Info] = amd (A, Control) * Control = amd ; % return the default Control settings for AMD * amd ; % print the default Control settings for AMD * * Given a square matrix A, compute a permutation P suitable for a Cholesky * factorization of the matrix B (P,P), where B = spones (A) + spones (A'). * The method used is the approximate minimum degree ordering method. See * amd.m and amd.h for more information. * * The input matrix need not have sorted columns, and can have duplicate * entries. */ #include "amd.h" #include "mex.h" #include "matrix.h" #include "UFconfig.h" void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { UF_long i, m, n, *Ap, *Ai, *P, nc, result, spumoni, full ; double *Pout, *InfoOut, Control [AMD_CONTROL], Info [AMD_INFO], *ControlIn ; mxArray *A ; /* --------------------------------------------------------------------- */ /* get control parameters */ /* --------------------------------------------------------------------- */ amd_malloc = mxMalloc ; amd_free = mxFree ; amd_calloc = mxCalloc ; amd_realloc = mxRealloc ; amd_printf = mexPrintf ; spumoni = 0 ; if (nargin == 0) { /* get the default control parameters, and return */ pargout [0] = mxCreateDoubleMatrix (AMD_CONTROL, 1, mxREAL) ; amd_l_defaults (mxGetPr (pargout [0])) ; if (nargout == 0) { amd_l_control (mxGetPr (pargout [0])) ; } return ; } amd_l_defaults (Control) ; if (nargin > 1) { ControlIn = mxGetPr (pargin [1]) ; nc = mxGetM (pargin [1]) * mxGetN (pargin [1]) ; Control [AMD_DENSE] = (nc > 0) ? ControlIn [AMD_DENSE] : AMD_DEFAULT_DENSE ; Control [AMD_AGGRESSIVE] = (nc > 1) ? ControlIn [AMD_AGGRESSIVE] : AMD_DEFAULT_AGGRESSIVE ; spumoni = (nc > 2) ? (ControlIn [2] != 0) : 0 ; } if (spumoni > 0) { amd_l_control (Control) ; } /* --------------------------------------------------------------------- */ /* get inputs */ /* --------------------------------------------------------------------- */ if (nargout > 2 || nargin > 2) { mexErrMsgTxt ("Usage: p = amd (A)\nor [p, Info] = amd (A, Control)") ; } A = (mxArray *) pargin [0] ; n = mxGetN (A) ; m = mxGetM (A) ; if (spumoni > 0) { mexPrintf (" input matrix A is %d-by-%d\n", m, n) ; } if (mxGetNumberOfDimensions (A) != 2) { mexErrMsgTxt ("amd: A must be 2-dimensional") ; } if (m != n) { mexErrMsgTxt ("amd: A must be square") ; } /* --------------------------------------------------------------------- */ /* allocate workspace for output permutation */ /* --------------------------------------------------------------------- */ P = mxMalloc ((n+1) * sizeof (UF_long)) ; /* --------------------------------------------------------------------- */ /* if A is full, convert to a sparse matrix */ /* --------------------------------------------------------------------- */ full = !mxIsSparse (A) ; if (full) { if (spumoni > 0) { mexPrintf ( " input matrix A is full (sparse copy of A will be created)\n"); } mexCallMATLAB (1, &A, 1, (mxArray **) pargin, "sparse") ; } Ap = (UF_long *) mxGetJc (A) ; Ai = (UF_long *) mxGetIr (A) ; if (spumoni > 0) { mexPrintf (" input matrix A has %d nonzero entries\n", Ap [n]) ; } /* --------------------------------------------------------------------- */ /* order the matrix */ /* --------------------------------------------------------------------- */ result = amd_l_order (n, Ap, Ai, P, Control, Info) ; /* --------------------------------------------------------------------- */ /* if A is full, free the sparse copy of A */ /* --------------------------------------------------------------------- */ if (full) { mxDestroyArray (A) ; } /* --------------------------------------------------------------------- */ /* print results (including return value) */ /* --------------------------------------------------------------------- */ if (spumoni > 0) { amd_l_info (Info) ; } /* --------------------------------------------------------------------- */ /* check error conditions */ /* --------------------------------------------------------------------- */ if (result == AMD_OUT_OF_MEMORY) { mexErrMsgTxt ("amd: out of memory") ; } else if (result == AMD_INVALID) { mexErrMsgTxt ("amd: input matrix A is corrupted") ; } /* --------------------------------------------------------------------- */ /* copy the outputs to MATLAB */ /* --------------------------------------------------------------------- */ /* output permutation, P */ pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ; Pout = mxGetPr (pargout [0]) ; for (i = 0 ; i < n ; i++) { Pout [i] = P [i] + 1 ; /* change to 1-based indexing for MATLAB */ } mxFree (P) ; /* Info */ if (nargout > 1) { pargout [1] = mxCreateDoubleMatrix (AMD_INFO, 1, mxREAL) ; InfoOut = mxGetPr (pargout [1]) ; for (i = 0 ; i < AMD_INFO ; i++) { InfoOut [i] = Info [i] ; } } } SuiteSparse/AMD/MATLAB/amd2.m0000644001170100242450000001000710620366010014301 0ustar davisfacfunction [p, Info] = amd2 (A, Control) %#ok %AMD2 p = amd2 (A), the approximate minimum degree ordering of A % P = AMD2 (S) returns the approximate minimum degree permutation vector for % the sparse matrix C = S+S'. The Cholesky factorization of C (P,P), or % S (P,P), tends to be sparser than that of C or S. AMD tends to be faster % than SYMMMD and SYMAMD, and tends to return better orderings than SYMMMD. % S must be square. If S is full, amd(S) is equivalent to amd(sparse(S)). % % Note that the built-in AMD routine in MATLAB is identical to AMD2, % except that AMD in MATLAB allows for a struct input to set the parameters. % % Usage: P = amd2 (S) ; % finds the ordering % [P, Info] = amd2 (S, Control) ; % optional parameters & statistics % Control = amd2 ; % returns default parameters % amd2 ; % prints default parameters. % % Control (1); If S is n-by-n, then rows/columns with more than % max (16, (Control (1))* sqrt(n)) entries in S+S' are considered % "dense", and ignored during ordering. They are placed last in the % output permutation. The default is 10.0 if Control is not present. % Control (2): If nonzero, then aggressive absorption is performed. % This is the default if Control is not present. % Control (3): If nonzero, print statistics about the ordering. % % Info (1): status (0: ok, -1: out of memory, -2: matrix invalid) % Info (2): n = size (A,1) % Info (3): nnz (A) % Info (4): the symmetry of the matrix S (0.0 means purely unsymmetric, % 1.0 means purely symmetric). Computed as: % B = tril (S, -1) + triu (S, 1) ; symmetry = nnz (B & B') / nnz (B); % Info (5): nnz (diag (S)) % Info (6): nnz in S+S', excluding the diagonal (= nnz (B+B')) % Info (7): number "dense" rows/columns in S+S' % Info (8): the amount of memory used by AMD, in bytes % Info (9): the number of memory compactions performed by AMD % % The following statistics are slight upper bounds because of the % approximate degree in AMD. The bounds are looser if "dense" rows/columns % are ignored during ordering (Info (7) > 0). The statistics are for a % subsequent factorization of the matrix C (P,P). The LU factorization % statistics assume no pivoting. % % Info (10): the number of nonzeros in L, excluding the diagonal % Info (11): the number of divide operations for LL', LDL', or LU % Info (12): the number of multiply-subtract pairs for LL' or LDL' % Info (13): the number of multiply-subtract pairs for LU % Info (14): the max # of nonzeros in any column of L (incl. diagonal) % Info (15:20): unused, reserved for future use % % An assembly tree post-ordering is performed, which is typically the same % as an elimination tree post-ordering. It is not always identical because % of the approximate degree update used, and because "dense" rows/columns % do not take part in the post-order. It well-suited for a subsequent % "chol", however. If you require a precise elimination tree post-ordering, % then see the example below: % % Example: % % P = amd2 (S) ; % C = spones (S) + spones (S') ; % skip this if S already symmetric % [ignore, Q] = etree (C (P,P)) ; % P = P (Q) ; % % See also AMD, COLMMD, COLAMD, COLPERM, SYMAMD, SYMMMD, SYMRCM. % -------------------------------------------------------------------------- % Copyright 1994-2007, Tim Davis, University of Florida % Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. % email: davis at cise.ufl.edu CISE Department, Univ. of Florida. % web: http://www.cise.ufl.edu/research/sparse/amd % -------------------------------------------------------------------------- % % Acknowledgements: This work was supported by the National Science % Foundation, under grants ASC-9111263, DMS-9223088, and CCR-0203270. error ('amd2 mexFunction not found') ; SuiteSparse/AMD/MATLAB/can_240000644001170100242450000000240010301472250014267 0ustar davisfac 1 1 1 6 1 1 7 1 1 13 1 1 14 1 1 18 1 1 19 1 1 20 1 1 22 1 1 2 2 1 9 2 1 10 2 1 14 2 1 15 2 1 18 2 1 3 3 1 7 3 1 12 3 1 21 3 1 22 3 1 23 3 1 4 4 1 8 4 1 11 4 1 16 4 1 19 4 1 20 4 1 5 5 1 8 5 1 10 5 1 15 5 1 16 5 1 17 5 1 1 6 1 6 6 1 7 6 1 13 6 1 14 6 1 18 6 1 1 7 1 3 7 1 6 7 1 7 7 1 12 7 1 13 7 1 20 7 1 22 7 1 24 7 1 4 8 1 5 8 1 8 8 1 10 8 1 15 8 1 16 8 1 17 8 1 18 8 1 19 8 1 2 9 1 9 9 1 10 9 1 15 9 1 2 10 1 5 10 1 8 10 1 9 10 1 10 10 1 14 10 1 15 10 1 18 10 1 19 10 1 4 11 1 11 11 1 19 11 1 20 11 1 21 11 1 22 11 1 3 12 1 7 12 1 12 12 1 13 12 1 22 12 1 24 12 1 1 13 1 6 13 1 7 13 1 12 13 1 13 13 1 24 13 1 1 14 1 2 14 1 6 14 1 10 14 1 14 14 1 18 14 1 2 15 1 5 15 1 8 15 1 9 15 1 10 15 1 15 15 1 4 16 1 5 16 1 8 16 1 16 16 1 17 16 1 19 16 1 5 17 1 8 17 1 16 17 1 17 17 1 1 18 1 2 18 1 6 18 1 8 18 1 10 18 1 14 18 1 18 18 1 19 18 1 20 18 1 1 19 1 4 19 1 8 19 1 10 19 1 11 19 1 16 19 1 18 19 1 19 19 1 20 19 1 1 20 1 4 20 1 7 20 1 11 20 1 18 20 1 19 20 1 20 20 1 21 20 1 22 20 1 3 21 1 11 21 1 20 21 1 21 21 1 22 21 1 23 21 1 1 22 1 3 22 1 7 22 1 11 22 1 12 22 1 20 22 1 21 22 1 22 22 1 23 22 1 3 23 1 21 23 1 22 23 1 23 23 1 7 24 1 12 24 1 13 24 1 24 24 1 SuiteSparse/AMD/MATLAB/amd_install.m0000644001170100242450000000110510620366052015752 0ustar davisfacfunction amd_install %AMD_INSTALL compile and install amd2 for use in MATLAB % Your current directory must be AMD/MATLAB for this function to work. % % Example: % amd_install % % See also amd, amd2. % Copyright 1994-2007, Tim Davis, University of Florida, % Patrick R. Amestoy, and Iain S. Duff. % This orders the same matrix as the ANSI C demo, amd_demo.c. It includes an amd_make addpath (pwd) fprintf ('\nThe following path has been added. You may wish to add it\n') ; fprintf ('permanently, using the MATLAB pathtool command.\n') ; fprintf ('%s\n\n', pwd) ; amd_demo SuiteSparse/AMD/MATLAB/amd_demo.m.out0000644001170100242450000001355610620423605016051 0ustar davisfacamd_demo AMD2 p = amd2 (A), the approximate minimum degree ordering of A P = AMD2 (S) returns the approximate minimum degree permutation vector for the sparse matrix C = S+S'. The Cholesky factorization of C (P,P), or S (P,P), tends to be sparser than that of C or S. AMD tends to be faster than SYMMMD and SYMAMD, and tends to return better orderings than SYMMMD. S must be square. If S is full, amd(S) is equivalent to amd(sparse(S)). Note that the built-in AMD routine in MATLAB is identical to AMD2, except that AMD in MATLAB allows for a struct input to set the parameters. Usage: P = amd2 (S) ; % finds the ordering [P, Info] = amd2 (S, Control) ; % optional parameters & statistics Control = amd2 ; % returns default parameters amd2 ; % prints default parameters. Control (1); If S is n-by-n, then rows/columns with more than max (16, (Control (1))* sqrt(n)) entries in S+S' are considered "dense", and ignored during ordering. They are placed last in the output permutation. The default is 10.0 if Control is not present. Control (2): If nonzero, then aggressive absorption is performed. This is the default if Control is not present. Control (3): If nonzero, print statistics about the ordering. Info (1): status (0: ok, -1: out of memory, -2: matrix invalid) Info (2): n = size (A,1) Info (3): nnz (A) Info (4): the symmetry of the matrix S (0.0 means purely unsymmetric, 1.0 means purely symmetric). Computed as: B = tril (S, -1) + triu (S, 1) ; symmetry = nnz (B & B') / nnz (B); Info (5): nnz (diag (S)) Info (6): nnz in S+S', excluding the diagonal (= nnz (B+B')) Info (7): number "dense" rows/columns in S+S' Info (8): the amount of memory used by AMD, in bytes Info (9): the number of memory compactions performed by AMD The following statistics are slight upper bounds because of the approximate degree in AMD. The bounds are looser if "dense" rows/columns are ignored during ordering (Info (7) > 0). The statistics are for a subsequent factorization of the matrix C (P,P). The LU factorization statistics assume no pivoting. Info (10): the number of nonzeros in L, excluding the diagonal Info (11): the number of divide operations for LL', LDL', or LU Info (12): the number of multiply-subtract pairs for LL' or LDL' Info (13): the number of multiply-subtract pairs for LU Info (14): the max # of nonzeros in any column of L (incl. diagonal) Info (15:20): unused, reserved for future use An assembly tree post-ordering is performed, which is typically the same as an elimination tree post-ordering. It is not always identical because of the approximate degree update used, and because "dense" rows/columns do not take part in the post-order. It well-suited for a subsequent "chol", however. If you require a precise elimination tree post-ordering, then see the example below: Example: P = amd2 (S) ; C = spones (S) + spones (S') ; % skip this if S already symmetric [ignore, Q] = etree (C (P,P)) ; P = P (Q) ; See also AMD, COLMMD, COLAMD, COLPERM, SYMAMD, SYMMMD, SYMRCM. If the next step fails, then you have not yet compiled the AMD mexFunction. AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 input matrix A is 24-by-24 input matrix A has 160 nonzero entries AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 24 nz, number of nonzeros in A: 160 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 136 # dense rows/columns of A+A': 0 memory used, in bytes: 1516 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 97 nonzeros in L (including diagonal): 121 # divide operations for LDL' or LU: 97 # multiply-subtract operations for LDL': 275 # multiply-subtract operations for LU: 453 max nz. in any column of L (incl. diagonal): 8 chol flop count for real A, sqrt counted as 1 flop: 671 LDL' flop count for real A: 647 LDL' flop count for complex A: 3073 LU flop count for real A (with no pivoting): 1003 LU flop count for complex A (with no pivoting): 4497 Permutation vector: 23 21 11 24 13 6 17 9 15 5 16 8 2 10 14 18 1 3 4 7 12 19 22 20 Analyze A(p,p) with MATLAB's symbfact routine: number of nonzeros in L (including diagonal): 120 floating point operation count for chol (A (p,p)): 656 Results from AMD's approximate analysis: number of nonzeros in L (including diagonal): 121 floating point operation count for chol (A (p,p)): 671 Note that the nonzero and flop counts from AMD are slight upper bounds. This is due to the approximate minimum degree method used, in conjunction with "mass elimination". See the discussion about mass elimination in amd.h and amd_2.c for more details. diary off SuiteSparse/AMD/MATLAB/amd_demo.m0000644001170100242450000000460110620664020015230 0ustar davisfacfunction amd_demo %AMD_DEMO a demo of amd2, using the can_24 matrix % % A demo of AMD for MATLAB. % % Example: % amd_demo % % See also: amd, amd2, amd_make % Copyright 1994-2007, Tim Davis, University of Florida, % Patrick R. Amestoy, and Iain S. Duff. % This orders the same matrix as the ANSI C demo, amd_demo.c. It includes an % additional analysis of the matrix via MATLAB's symbfact routine. % First, print the help information for AMD help amd2 % Get the Harwell/Boeing can_24 matrix. load can_24 A = spconvert (can_24) ; n = size (A,1) ; figure (1) clf hold off subplot (2,2,1) ; spy (A) title ('HB/can24 matrix') ; % order the matrix. Note that the Info argument is optional. fprintf ('\nIf the next step fails, then you have\n') ; fprintf ('not yet compiled the AMD mexFunction.\n') ; [p, Info] = amd2 (A) ; %#ok % order again, but this time print some statistics [p, Info] = amd2 (A, [10 1 1]) ; fprintf ('Permutation vector:\n') ; fprintf (' %2d', p) ; fprintf ('\n\n') ; subplot (2,2,2) ; spy (A (p,p)) ; title ('Permuted matrix') ; % The amd_demo.c program stops here. fprintf ('Analyze A(p,p) with MATLAB''s symbfact routine:\n') ; [cn, height, parent, post, R] = symbfact (A (p,p)) ; subplot (2,2,3) ; spy (R') ; title ('Cholesky factor, L') ; subplot (2,2,4) ; treeplot (parent) ; title ('elimination tree') ; % results from symbfact lnz = sum (cn) ; % number of nonzeros in L, incl. diagonal cn = cn - 1 ; % get the count of off-diagonal entries fl = n + sum (cn.^2 + 2*cn) ; % flop count for chol (A (p,p) fprintf ('number of nonzeros in L (including diagonal): %d\n', lnz) ; fprintf ('floating point operation count for chol (A (p,p)): %d\n', fl) ; % approximations from amd: lnz2 = n + Info (10) ; fl2 = n + Info (11) + 2 * Info (12) ; fprintf ('\nResults from AMD''s approximate analysis:\n') ; fprintf ('number of nonzeros in L (including diagonal): %d\n', lnz2) ; fprintf ('floating point operation count for chol (A (p,p)): %d\n\n', fl2) ; if (lnz2 ~= lnz | fl ~= fl2) %#ok fprintf ('Note that the nonzero and flop counts from AMD are slight\n') ; fprintf ('upper bounds. This is due to the approximate minimum degree\n'); fprintf ('method used, in conjunction with "mass elimination".\n') ; fprintf ('See the discussion about mass elimination in amd.h and\n') ; fprintf ('amd_2.c for more details.\n') ; end SuiteSparse/AMD/MATLAB/amd_make.m0000644001170100242450000000163610620366073015235 0ustar davisfacfunction amd_make %AMD_MAKE to compile amd2 for use in MATLAB % % Example: % amd_make % % See also amd, amd2. % Copyright 1994-2007, Tim Davis, University of Florida, % Patrick R. Amestoy, and Iain S. Duff. details = 0 ; % 1 if details of each command are to be printed d = '' ; if (~isempty (strfind (computer, '64'))) d = '-largeArrayDims' ; end i = sprintf ('-I..%sInclude -I..%s..%sUFconfig', filesep, filesep, filesep) ; cmd = sprintf ('mex -O %s -DDLONG -output amd2 %s amd_mex.c', d, i) ; files = {'amd_order', 'amd_dump', 'amd_postorder', 'amd_post_tree', ... 'amd_aat', 'amd_2', 'amd_1', 'amd_defaults', 'amd_control', ... 'amd_info', 'amd_valid', 'amd_global', 'amd_preprocess' } ; for i = 1 : length (files) cmd = sprintf ('%s ..%sSource%s%s.c', cmd, filesep, filesep, files {i}) ; end if (details) fprintf ('%s\n', cmd) ; end eval (cmd) ; fprintf ('AMD successfully compiled.\n') ; SuiteSparse/AMD/Include/0000755001170100242450000000000010661134516013736 5ustar davisfacSuiteSparse/AMD/Include/amd.h0000644001170100242450000004161510616646472014670 0ustar davisfac/* ========================================================================= */ /* === AMD: approximate minimum degree ordering =========================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD Version 2.2, Copyright (c) 2007 by Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ /* AMD finds a symmetric ordering P of a matrix A so that the Cholesky * factorization of P*A*P' has fewer nonzeros and takes less work than the * Cholesky factorization of A. If A is not symmetric, then it performs its * ordering on the matrix A+A'. Two sets of user-callable routines are * provided, one for int integers and the other for UF_long integers. * * The method is based on the approximate minimum degree algorithm, discussed * in Amestoy, Davis, and Duff, "An approximate degree ordering algorithm", * SIAM Journal of Matrix Analysis and Applications, vol. 17, no. 4, pp. * 886-905, 1996. This package can perform both the AMD ordering (with * aggressive absorption), and the AMDBAR ordering (without aggressive * absorption) discussed in the above paper. This package differs from the * Fortran codes discussed in the paper: * * (1) it can ignore "dense" rows and columns, leading to faster run times * (2) it computes the ordering of A+A' if A is not symmetric * (3) it is followed by a depth-first post-ordering of the assembly tree * (or supernodal elimination tree) * * For historical reasons, the Fortran versions, amd.f and amdbar.f, have * been left (nearly) unchanged. They compute the identical ordering as * described in the above paper. */ #ifndef AMD_H #define AMD_H /* make it easy for C++ programs to include AMD */ #ifdef __cplusplus extern "C" { #endif /* get the definition of size_t: */ #include /* define UF_long */ #include "UFconfig.h" int amd_order /* returns AMD_OK, AMD_OK_BUT_JUMBLED, * AMD_INVALID, or AMD_OUT_OF_MEMORY */ ( int n, /* A is n-by-n. n must be >= 0. */ const int Ap [ ], /* column pointers for A, of size n+1 */ const int Ai [ ], /* row indices of A, of size nz = Ap [n] */ int P [ ], /* output permutation, of size n */ double Control [ ], /* input Control settings, of size AMD_CONTROL */ double Info [ ] /* output Info statistics, of size AMD_INFO */ ) ; UF_long amd_l_order /* see above for description of arguments */ ( UF_long n, const UF_long Ap [ ], const UF_long Ai [ ], UF_long P [ ], double Control [ ], double Info [ ] ) ; /* Input arguments (not modified): * * n: the matrix A is n-by-n. * Ap: an int/UF_long array of size n+1, containing column pointers of A. * Ai: an int/UF_long array of size nz, containing the row indices of A, * where nz = Ap [n]. * Control: a double array of size AMD_CONTROL, containing control * parameters. Defaults are used if Control is NULL. * * Output arguments (not defined on input): * * P: an int/UF_long array of size n, containing the output permutation. If * row i is the kth pivot row, then P [k] = i. In MATLAB notation, * the reordered matrix is A (P,P). * Info: a double array of size AMD_INFO, containing statistical * information. Ignored if Info is NULL. * * On input, the matrix A is stored in column-oriented form. The row indices * of nonzero entries in column j are stored in Ai [Ap [j] ... Ap [j+1]-1]. * * If the row indices appear in ascending order in each column, and there * are no duplicate entries, then amd_order is slightly more efficient in * terms of time and memory usage. If this condition does not hold, a copy * of the matrix is created (where these conditions do hold), and the copy is * ordered. This feature is new to v2.0 (v1.2 and earlier required this * condition to hold for the input matrix). * * Row indices must be in the range 0 to * n-1. Ap [0] must be zero, and thus nz = Ap [n] is the number of nonzeros * in A. The array Ap is of size n+1, and the array Ai is of size nz = Ap [n]. * The matrix does not need to be symmetric, and the diagonal does not need to * be present (if diagonal entries are present, they are ignored except for * the output statistic Info [AMD_NZDIAG]). The arrays Ai and Ap are not * modified. This form of the Ap and Ai arrays to represent the nonzero * pattern of the matrix A is the same as that used internally by MATLAB. * If you wish to use a more flexible input structure, please see the * umfpack_*_triplet_to_col routines in the UMFPACK package, at * http://www.cise.ufl.edu/research/sparse/umfpack. * * Restrictions: n >= 0. Ap [0] = 0. Ap [j] <= Ap [j+1] for all j in the * range 0 to n-1. nz = Ap [n] >= 0. Ai [0..nz-1] must be in the range 0 * to n-1. Finally, Ai, Ap, and P must not be NULL. If any of these * restrictions are not met, AMD returns AMD_INVALID. * * AMD returns: * * AMD_OK if the matrix is valid and sufficient memory can be allocated to * perform the ordering. * * AMD_OUT_OF_MEMORY if not enough memory can be allocated. * * AMD_INVALID if the input arguments n, Ap, Ai are invalid, or if P is * NULL. * * AMD_OK_BUT_JUMBLED if the matrix had unsorted columns, and/or duplicate * entries, but was otherwise valid. * * The AMD routine first forms the pattern of the matrix A+A', and then * computes a fill-reducing ordering, P. If P [k] = i, then row/column i of * the original is the kth pivotal row. In MATLAB notation, the permuted * matrix is A (P,P), except that 0-based indexing is used instead of the * 1-based indexing in MATLAB. * * The Control array is used to set various parameters for AMD. If a NULL * pointer is passed, default values are used. The Control array is not * modified. * * Control [AMD_DENSE]: controls the threshold for "dense" rows/columns. * A dense row/column in A+A' can cause AMD to spend a lot of time in * ordering the matrix. If Control [AMD_DENSE] >= 0, rows/columns * with more than Control [AMD_DENSE] * sqrt (n) entries are ignored * during the ordering, and placed last in the output order. The * default value of Control [AMD_DENSE] is 10. If negative, no * rows/columns are treated as "dense". Rows/columns with 16 or * fewer off-diagonal entries are never considered "dense". * * Control [AMD_AGGRESSIVE]: controls whether or not to use aggressive * absorption, in which a prior element is absorbed into the current * element if is a subset of the current element, even if it is not * adjacent to the current pivot element (refer to Amestoy, Davis, * & Duff, 1996, for more details). The default value is nonzero, * which means to perform aggressive absorption. This nearly always * leads to a better ordering (because the approximate degrees are * more accurate) and a lower execution time. There are cases where * it can lead to a slightly worse ordering, however. To turn it off, * set Control [AMD_AGGRESSIVE] to 0. * * Control [2..4] are not used in the current version, but may be used in * future versions. * * The Info array provides statistics about the ordering on output. If it is * not present, the statistics are not returned. This is not an error * condition. * * Info [AMD_STATUS]: the return value of AMD, either AMD_OK, * AMD_OK_BUT_JUMBLED, AMD_OUT_OF_MEMORY, or AMD_INVALID. * * Info [AMD_N]: n, the size of the input matrix * * Info [AMD_NZ]: the number of nonzeros in A, nz = Ap [n] * * Info [AMD_SYMMETRY]: the symmetry of the matrix A. It is the number * of "matched" off-diagonal entries divided by the total number of * off-diagonal entries. An entry A(i,j) is matched if A(j,i) is also * an entry, for any pair (i,j) for which i != j. In MATLAB notation, * S = spones (A) ; * B = tril (S, -1) + triu (S, 1) ; * symmetry = nnz (B & B') / nnz (B) ; * * Info [AMD_NZDIAG]: the number of entries on the diagonal of A. * * Info [AMD_NZ_A_PLUS_AT]: the number of nonzeros in A+A', excluding the * diagonal. If A is perfectly symmetric (Info [AMD_SYMMETRY] = 1) * with a fully nonzero diagonal, then Info [AMD_NZ_A_PLUS_AT] = nz-n * (the smallest possible value). If A is perfectly unsymmetric * (Info [AMD_SYMMETRY] = 0, for an upper triangular matrix, for * example) with no diagonal, then Info [AMD_NZ_A_PLUS_AT] = 2*nz * (the largest possible value). * * Info [AMD_NDENSE]: the number of "dense" rows/columns of A+A' that were * removed from A prior to ordering. These are placed last in the * output order P. * * Info [AMD_MEMORY]: the amount of memory used by AMD, in bytes. In the * current version, this is 1.2 * Info [AMD_NZ_A_PLUS_AT] + 9*n * times the size of an integer. This is at most 2.4nz + 9n. This * excludes the size of the input arguments Ai, Ap, and P, which have * a total size of nz + 2*n + 1 integers. * * Info [AMD_NCMPA]: the number of garbage collections performed. * * Info [AMD_LNZ]: the number of nonzeros in L (excluding the diagonal). * This is a slight upper bound because mass elimination is combined * with the approximate degree update. It is a rough upper bound if * there are many "dense" rows/columns. The rest of the statistics, * below, are also slight or rough upper bounds, for the same reasons. * The post-ordering of the assembly tree might also not exactly * correspond to a true elimination tree postordering. * * Info [AMD_NDIV]: the number of divide operations for a subsequent LDL' * or LU factorization of the permuted matrix A (P,P). * * Info [AMD_NMULTSUBS_LDL]: the number of multiply-subtract pairs for a * subsequent LDL' factorization of A (P,P). * * Info [AMD_NMULTSUBS_LU]: the number of multiply-subtract pairs for a * subsequent LU factorization of A (P,P), assuming that no numerical * pivoting is required. * * Info [AMD_DMAX]: the maximum number of nonzeros in any column of L, * including the diagonal. * * Info [14..19] are not used in the current version, but may be used in * future versions. */ /* ------------------------------------------------------------------------- */ /* direct interface to AMD */ /* ------------------------------------------------------------------------- */ /* amd_2 is the primary AMD ordering routine. It is not meant to be * user-callable because of its restrictive inputs and because it destroys * the user's input matrix. It does not check its inputs for errors, either. * However, if you can work with these restrictions it can be faster than * amd_order and use less memory (assuming that you can create your own copy * of the matrix for AMD to destroy). Refer to AMD/Source/amd_2.c for a * description of each parameter. */ void amd_2 ( int n, int Pe [ ], int Iw [ ], int Len [ ], int iwlen, int pfree, int Nv [ ], int Next [ ], int Last [ ], int Head [ ], int Elen [ ], int Degree [ ], int W [ ], double Control [ ], double Info [ ] ) ; void amd_l2 ( UF_long n, UF_long Pe [ ], UF_long Iw [ ], UF_long Len [ ], UF_long iwlen, UF_long pfree, UF_long Nv [ ], UF_long Next [ ], UF_long Last [ ], UF_long Head [ ], UF_long Elen [ ], UF_long Degree [ ], UF_long W [ ], double Control [ ], double Info [ ] ) ; /* ------------------------------------------------------------------------- */ /* amd_valid */ /* ------------------------------------------------------------------------- */ /* Returns AMD_OK or AMD_OK_BUT_JUMBLED if the matrix is valid as input to * amd_order; the latter is returned if the matrix has unsorted and/or * duplicate row indices in one or more columns. Returns AMD_INVALID if the * matrix cannot be passed to amd_order. For amd_order, the matrix must also * be square. The first two arguments are the number of rows and the number * of columns of the matrix. For its use in AMD, these must both equal n. * * NOTE: this routine returned TRUE/FALSE in v1.2 and earlier. */ int amd_valid ( int n_row, /* # of rows */ int n_col, /* # of columns */ const int Ap [ ], /* column pointers, of size n_col+1 */ const int Ai [ ] /* row indices, of size Ap [n_col] */ ) ; UF_long amd_l_valid ( UF_long n_row, UF_long n_col, const UF_long Ap [ ], const UF_long Ai [ ] ) ; /* ------------------------------------------------------------------------- */ /* AMD memory manager and printf routines */ /* ------------------------------------------------------------------------- */ /* The user can redefine these to change the malloc, free, and printf routines * that AMD uses. */ #ifndef EXTERN #define EXTERN extern #endif EXTERN void *(*amd_malloc) (size_t) ; /* pointer to malloc */ EXTERN void (*amd_free) (void *) ; /* pointer to free */ EXTERN void *(*amd_realloc) (void *, size_t) ; /* pointer to realloc */ EXTERN void *(*amd_calloc) (size_t, size_t) ; /* pointer to calloc */ EXTERN int (*amd_printf) (const char *, ...) ; /* pointer to printf */ /* ------------------------------------------------------------------------- */ /* AMD Control and Info arrays */ /* ------------------------------------------------------------------------- */ /* amd_defaults: sets the default control settings */ void amd_defaults (double Control [ ]) ; void amd_l_defaults (double Control [ ]) ; /* amd_control: prints the control settings */ void amd_control (double Control [ ]) ; void amd_l_control (double Control [ ]) ; /* amd_info: prints the statistics */ void amd_info (double Info [ ]) ; void amd_l_info (double Info [ ]) ; #define AMD_CONTROL 5 /* size of Control array */ #define AMD_INFO 20 /* size of Info array */ /* contents of Control */ #define AMD_DENSE 0 /* "dense" if degree > Control [0] * sqrt (n) */ #define AMD_AGGRESSIVE 1 /* do aggressive absorption if Control [1] != 0 */ /* default Control settings */ #define AMD_DEFAULT_DENSE 10.0 /* default "dense" degree 10*sqrt(n) */ #define AMD_DEFAULT_AGGRESSIVE 1 /* do aggressive absorption by default */ /* contents of Info */ #define AMD_STATUS 0 /* return value of amd_order and amd_l_order */ #define AMD_N 1 /* A is n-by-n */ #define AMD_NZ 2 /* number of nonzeros in A */ #define AMD_SYMMETRY 3 /* symmetry of pattern (1 is sym., 0 is unsym.) */ #define AMD_NZDIAG 4 /* # of entries on diagonal */ #define AMD_NZ_A_PLUS_AT 5 /* nz in A+A' */ #define AMD_NDENSE 6 /* number of "dense" rows/columns in A */ #define AMD_MEMORY 7 /* amount of memory used by AMD */ #define AMD_NCMPA 8 /* number of garbage collections in AMD */ #define AMD_LNZ 9 /* approx. nz in L, excluding the diagonal */ #define AMD_NDIV 10 /* number of fl. point divides for LU and LDL' */ #define AMD_NMULTSUBS_LDL 11 /* number of fl. point (*,-) pairs for LDL' */ #define AMD_NMULTSUBS_LU 12 /* number of fl. point (*,-) pairs for LU */ #define AMD_DMAX 13 /* max nz. in any column of L, incl. diagonal */ /* ------------------------------------------------------------------------- */ /* return values of AMD */ /* ------------------------------------------------------------------------- */ #define AMD_OK 0 /* success */ #define AMD_OUT_OF_MEMORY -1 /* malloc failed, or problem too large */ #define AMD_INVALID -2 /* input arguments are not valid */ #define AMD_OK_BUT_JUMBLED 1 /* input matrix is OK for amd_order, but * columns were not sorted, and/or duplicate entries were present. AMD had * to do extra work before ordering the matrix. This is a warning, not an * error. */ /* ========================================================================== */ /* === AMD version ========================================================== */ /* ========================================================================== */ /* AMD Version 1.2 and later include the following definitions. * As an example, to test if the version you are using is 1.2 or later: * * #ifdef AMD_VERSION * if (AMD_VERSION >= AMD_VERSION_CODE (1,2)) ... * #endif * * This also works during compile-time: * * #if defined(AMD_VERSION) && (AMD_VERSION >= AMD_VERSION_CODE (1,2)) * printf ("This is version 1.2 or later\n") ; * #else * printf ("This is an early version\n") ; * #endif * * Versions 1.1 and earlier of AMD do not include a #define'd version number. */ #define AMD_DATE "May 31, 2007" #define AMD_VERSION_CODE(main,sub) ((main) * 1000 + (sub)) #define AMD_MAIN_VERSION 2 #define AMD_SUB_VERSION 2 #define AMD_SUBSUB_VERSION 0 #define AMD_VERSION AMD_VERSION_CODE(AMD_MAIN_VERSION,AMD_SUB_VERSION) #ifdef __cplusplus } #endif #endif SuiteSparse/AMD/Include/amd_internal.h0000644001170100242450000002204410636070275016551 0ustar davisfac/* ========================================================================= */ /* === amd_internal.h ====================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ /* This file is for internal use in AMD itself, and does not normally need to * be included in user code (it is included in UMFPACK, however). All others * should use amd.h instead. * * The following compile-time definitions affect how AMD is compiled. * * -DNPRINT * * Disable all printing. stdio.h will not be included. Printing can * be re-enabled at run-time by setting the global pointer amd_printf * to printf (or mexPrintf for a MATLAB mexFunction). * * -DNMALLOC * * No memory manager is defined at compile-time. You MUST define the * function pointers amd_malloc, amd_free, amd_realloc, and * amd_calloc at run-time for AMD to work properly. */ /* ========================================================================= */ /* === NDEBUG ============================================================== */ /* ========================================================================= */ /* * Turning on debugging takes some work (see below). If you do not edit this * file, then debugging is always turned off, regardless of whether or not * -DNDEBUG is specified in your compiler options. * * If AMD is being compiled as a mexFunction, then MATLAB_MEX_FILE is defined, * and mxAssert is used instead of assert. If debugging is not enabled, no * MATLAB include files or functions are used. Thus, the AMD library libamd.a * can be safely used in either a stand-alone C program or in another * mexFunction, without any change. */ /* AMD will be exceedingly slow when running in debug mode. The next three lines ensure that debugging is turned off. */ #ifndef NDEBUG #define NDEBUG #endif /* To enable debugging, uncomment the following line: #undef NDEBUG */ /* ------------------------------------------------------------------------- */ /* ANSI include files */ /* ------------------------------------------------------------------------- */ /* from stdlib.h: size_t, malloc, free, realloc, and calloc */ #include #if !defined(NPRINT) || !defined(NDEBUG) /* from stdio.h: printf. Not included if NPRINT is defined at compile time. * fopen and fscanf are used when debugging. */ #include #endif /* from limits.h: INT_MAX and LONG_MAX */ #include /* from math.h: sqrt */ #include /* ------------------------------------------------------------------------- */ /* MATLAB include files (only if being used in or via MATLAB) */ /* ------------------------------------------------------------------------- */ #ifdef MATLAB_MEX_FILE #include "matrix.h" #include "mex.h" #endif /* ------------------------------------------------------------------------- */ /* basic definitions */ /* ------------------------------------------------------------------------- */ #ifdef FLIP #undef FLIP #endif #ifdef MAX #undef MAX #endif #ifdef MIN #undef MIN #endif #ifdef EMPTY #undef EMPTY #endif #ifdef GLOBAL #undef GLOBAL #endif #ifdef PRIVATE #undef PRIVATE #endif /* FLIP is a "negation about -1", and is used to mark an integer i that is * normally non-negative. FLIP (EMPTY) is EMPTY. FLIP of a number > EMPTY * is negative, and FLIP of a number < EMTPY is positive. FLIP (FLIP (i)) = i * for all integers i. UNFLIP (i) is >= EMPTY. */ #define EMPTY (-1) #define FLIP(i) (-(i)-2) #define UNFLIP(i) ((i < EMPTY) ? FLIP (i) : (i)) /* for integer MAX/MIN, or for doubles when we don't care how NaN's behave: */ #define MAX(a,b) (((a) > (b)) ? (a) : (b)) #define MIN(a,b) (((a) < (b)) ? (a) : (b)) /* logical expression of p implies q: */ #define IMPLIES(p,q) (!(p) || (q)) /* Note that the IBM RS 6000 xlc predefines TRUE and FALSE in . */ /* The Compaq Alpha also predefines TRUE and FALSE. */ #ifdef TRUE #undef TRUE #endif #ifdef FALSE #undef FALSE #endif #define TRUE (1) #define FALSE (0) #define PRIVATE static #define GLOBAL #define EMPTY (-1) /* Note that Linux's gcc 2.96 defines NULL as ((void *) 0), but other */ /* compilers (even gcc 2.95.2 on Solaris) define NULL as 0 or (0). We */ /* need to use the ANSI standard value of 0. */ #ifdef NULL #undef NULL #endif #define NULL 0 /* largest value of size_t */ #ifndef SIZE_T_MAX #define SIZE_T_MAX ((size_t) (-1)) #endif /* ------------------------------------------------------------------------- */ /* integer type for AMD: int or UF_long */ /* ------------------------------------------------------------------------- */ /* define UF_long */ #include "UFconfig.h" #if defined (DLONG) || defined (ZLONG) #define Int UF_long #define ID UF_long_id #define Int_MAX UF_long_max #define AMD_order amd_l_order #define AMD_defaults amd_l_defaults #define AMD_control amd_l_control #define AMD_info amd_l_info #define AMD_1 amd_l1 #define AMD_2 amd_l2 #define AMD_valid amd_l_valid #define AMD_aat amd_l_aat #define AMD_postorder amd_l_postorder #define AMD_post_tree amd_l_post_tree #define AMD_dump amd_l_dump #define AMD_debug amd_l_debug #define AMD_debug_init amd_l_debug_init #define AMD_preprocess amd_l_preprocess #else #define Int int #define ID "%d" #define Int_MAX INT_MAX #define AMD_order amd_order #define AMD_defaults amd_defaults #define AMD_control amd_control #define AMD_info amd_info #define AMD_1 amd_1 #define AMD_2 amd_2 #define AMD_valid amd_valid #define AMD_aat amd_aat #define AMD_postorder amd_postorder #define AMD_post_tree amd_post_tree #define AMD_dump amd_dump #define AMD_debug amd_debug #define AMD_debug_init amd_debug_init #define AMD_preprocess amd_preprocess #endif /* ========================================================================= */ /* === PRINTF macro ======================================================== */ /* ========================================================================= */ /* All output goes through the PRINTF macro. */ #define PRINTF(params) { if (amd_printf != NULL) (void) amd_printf params ; } /* ------------------------------------------------------------------------- */ /* AMD routine definitions (user-callable) */ /* ------------------------------------------------------------------------- */ #include "amd.h" /* ------------------------------------------------------------------------- */ /* AMD routine definitions (not user-callable) */ /* ------------------------------------------------------------------------- */ GLOBAL size_t AMD_aat ( Int n, const Int Ap [ ], const Int Ai [ ], Int Len [ ], Int Tp [ ], double Info [ ] ) ; GLOBAL void AMD_1 ( Int n, const Int Ap [ ], const Int Ai [ ], Int P [ ], Int Pinv [ ], Int Len [ ], Int slen, Int S [ ], double Control [ ], double Info [ ] ) ; GLOBAL void AMD_postorder ( Int nn, Int Parent [ ], Int Npiv [ ], Int Fsize [ ], Int Order [ ], Int Child [ ], Int Sibling [ ], Int Stack [ ] ) ; GLOBAL Int AMD_post_tree ( Int root, Int k, Int Child [ ], const Int Sibling [ ], Int Order [ ], Int Stack [ ] #ifndef NDEBUG , Int nn #endif ) ; GLOBAL void AMD_preprocess ( Int n, const Int Ap [ ], const Int Ai [ ], Int Rp [ ], Int Ri [ ], Int W [ ], Int Flag [ ] ) ; /* ------------------------------------------------------------------------- */ /* debugging definitions */ /* ------------------------------------------------------------------------- */ #ifndef NDEBUG /* from assert.h: assert macro */ #include #ifndef EXTERN #define EXTERN extern #endif EXTERN Int AMD_debug ; GLOBAL void AMD_debug_init ( char *s ) ; GLOBAL void AMD_dump ( Int n, Int Pe [ ], Int Iw [ ], Int Len [ ], Int iwlen, Int pfree, Int Nv [ ], Int Next [ ], Int Last [ ], Int Head [ ], Int Elen [ ], Int Degree [ ], Int W [ ], Int nel ) ; #ifdef ASSERT #undef ASSERT #endif /* Use mxAssert if AMD is compiled into a mexFunction */ #ifdef MATLAB_MEX_FILE #define ASSERT(expression) (mxAssert ((expression), "")) #else #define ASSERT(expression) (assert (expression)) #endif #define AMD_DEBUG0(params) { PRINTF (params) ; } #define AMD_DEBUG1(params) { if (AMD_debug >= 1) PRINTF (params) ; } #define AMD_DEBUG2(params) { if (AMD_debug >= 2) PRINTF (params) ; } #define AMD_DEBUG3(params) { if (AMD_debug >= 3) PRINTF (params) ; } #define AMD_DEBUG4(params) { if (AMD_debug >= 4) PRINTF (params) ; } #else /* no debugging */ #define ASSERT(expression) #define AMD_DEBUG0(params) #define AMD_DEBUG1(params) #define AMD_DEBUG2(params) #define AMD_DEBUG3(params) #define AMD_DEBUG4(params) #endif SuiteSparse/AMD/Source/0000755001170100242450000000000010672324407013615 5ustar davisfacSuiteSparse/AMD/Source/amd.f0000644001170100242450000014662110250413605014526 0ustar davisfacC----------------------------------------------------------------------- C AMD: approximate minimum degree, with aggressive absorption C----------------------------------------------------------------------- SUBROUTINE AMD $ (N, PE, IW, LEN, IWLEN, PFREE, NV, NEXT, $ LAST, HEAD, ELEN, DEGREE, NCMPA, W) INTEGER N, IWLEN, PFREE, NCMPA, IW (IWLEN), PE (N), $ DEGREE (N), NV (N), NEXT (N), LAST (N), HEAD (N), $ ELEN (N), W (N), LEN (N) C Given a representation of the nonzero pattern of a symmetric matrix, C A, (excluding the diagonal) perform an approximate minimum C (UMFPACK/MA38-style) degree ordering to compute a pivot order C such that the introduction of nonzeros (fill-in) in the Cholesky C factors A = LL^T are kept low. At each step, the pivot C selected is the one with the minimum UMFPACK/MA38-style C upper-bound on the external degree. C C Aggresive absorption is used to tighten the bound on the degree. C ********************************************************************** C ***** CAUTION: ARGUMENTS ARE NOT CHECKED FOR ERRORS ON INPUT. ****** C ********************************************************************** C References: C C [1] Timothy A. Davis and Iain Duff, "An unsymmetric-pattern C multifrontal method for sparse LU factorization", SIAM J. C Matrix Analysis and Applications, vol. 18, no. 1, pp. C 140-158. Discusses UMFPACK / MA38, which first introduced C the approximate minimum degree used by this routine. C C [2] Patrick Amestoy, Timothy A. Davis, and Iain S. Duff, "An C approximate degree ordering algorithm," SIAM J. Matrix C Analysis and Applications, vol. 17, no. 4, pp. 886-905, C 1996. Discusses AMD, AMDBAR, and MC47B. C C [3] Alan George and Joseph Liu, "The evolution of the minimum C degree ordering algorithm," SIAM Review, vol. 31, no. 1, C pp. 1-19, 1989. We list below the features mentioned in C that paper that this code includes: C C mass elimination: C Yes. MA27 relied on supervariable detection for mass C elimination. C indistinguishable nodes: C Yes (we call these "supervariables"). This was also in C the MA27 code - although we modified the method of C detecting them (the previous hash was the true degree, C which we no longer keep track of). A supervariable is C a set of rows with identical nonzero pattern. All C variables in a supervariable are eliminated together. C Each supervariable has as its numerical name that of C one of its variables (its principal variable). C quotient graph representation: C Yes. We use the term "element" for the cliques formed C during elimination. This was also in the MA27 code. C The algorithm can operate in place, but it will work C more efficiently if given some "elbow room." C element absorption: C Yes. This was also in the MA27 code. C external degree: C Yes. The MA27 code was based on the true degree. C incomplete degree update and multiple elimination: C No. This was not in MA27, either. Our method of C degree update within MC47B/BD is element-based, not C variable-based. It is thus not well-suited for use C with incomplete degree update or multiple elimination. C----------------------------------------------------------------------- C Authors, and Copyright (C) 1995 by: C Timothy A. Davis, Patrick Amestoy, Iain S. Duff, & John K. Reid. C C Acknowledgements: C This work (and the UMFPACK package) was supported by the C National Science Foundation (ASC-9111263 and DMS-9223088). C The UMFPACK/MA38 approximate degree update algorithm, the C unsymmetric analog which forms the basis of MC47B/BD, was C developed while Tim Davis was supported by CERFACS (Toulouse, C France) in a post-doctoral position. C C Date: September, 1995 C----------------------------------------------------------------------- C----------------------------------------------------------------------- C INPUT ARGUMENTS (unaltered): C----------------------------------------------------------------------- C n: The matrix order. C C Restriction: 1 .le. n .lt. (iovflo/2)-2, where iovflo is C the largest positive integer that your computer can represent. C iwlen: The length of iw (1..iwlen). On input, the matrix is C stored in iw (1..pfree-1). However, iw (1..iwlen) should be C slightly larger than what is required to hold the matrix, at C least iwlen .ge. pfree + n is recommended. Otherwise, C excessive compressions will take place. C *** We do not recommend running this algorithm with *** C *** iwlen .lt. pfree + n. *** C *** Better performance will be obtained if *** C *** iwlen .ge. pfree + n *** C *** or better yet *** C *** iwlen .gt. 1.2 * pfree *** C *** (where pfree is its value on input). *** C The algorithm will not run at all if iwlen .lt. pfree-1. C C Restriction: iwlen .ge. pfree-1 C----------------------------------------------------------------------- C INPUT/OUPUT ARGUMENTS: C----------------------------------------------------------------------- C pe: On input, pe (i) is the index in iw of the start of row i, or C zero if row i has no off-diagonal non-zeros. C C During execution, it is used for both supervariables and C elements: C C * Principal supervariable i: index into iw of the C description of supervariable i. A supervariable C represents one or more rows of the matrix C with identical nonzero pattern. C * Non-principal supervariable i: if i has been absorbed C into another supervariable j, then pe (i) = -j. C That is, j has the same pattern as i. C Note that j might later be absorbed into another C supervariable j2, in which case pe (i) is still -j, C and pe (j) = -j2. C * Unabsorbed element e: the index into iw of the description C of element e, if e has not yet been absorbed by a C subsequent element. Element e is created when C the supervariable of the same name is selected as C the pivot. C * Absorbed element e: if element e is absorbed into element C e2, then pe (e) = -e2. This occurs when the pattern of C e (that is, Le) is found to be a subset of the pattern C of e2 (that is, Le2). If element e is "null" (it has C no nonzeros outside its pivot block), then pe (e) = 0. C C On output, pe holds the assembly tree/forest, which implicitly C represents a pivot order with identical fill-in as the actual C order (via a depth-first search of the tree). C C On output: C If nv (i) .gt. 0, then i represents a node in the assembly tree, C and the parent of i is -pe (i), or zero if i is a root. C If nv (i) = 0, then (i,-pe (i)) represents an edge in a C subtree, the root of which is a node in the assembly tree. C pfree: On input the tail end of the array, iw (pfree..iwlen), C is empty, and the matrix is stored in iw (1..pfree-1). C During execution, additional data is placed in iw, and pfree C is modified so that iw (pfree..iwlen) is always the unused part C of iw. On output, pfree is set equal to the size of iw that C would have been needed for no compressions to occur. If C ncmpa is zero, then pfree (on output) is less than or equal to C iwlen, and the space iw (pfree+1 ... iwlen) was not used. C Otherwise, pfree (on output) is greater than iwlen, and all the C memory in iw was used. C----------------------------------------------------------------------- C INPUT/MODIFIED (undefined on output): C----------------------------------------------------------------------- C len: On input, len (i) holds the number of entries in row i of the C matrix, excluding the diagonal. The contents of len (1..n) C are undefined on output. C iw: On input, iw (1..pfree-1) holds the description of each row i C in the matrix. The matrix must be symmetric, and both upper C and lower triangular parts must be present. The diagonal must C not be present. Row i is held as follows: C C len (i): the length of the row i data structure C iw (pe (i) ... pe (i) + len (i) - 1): C the list of column indices for nonzeros C in row i (simple supervariables), excluding C the diagonal. All supervariables start with C one row/column each (supervariable i is just C row i). C if len (i) is zero on input, then pe (i) is ignored C on input. C C Note that the rows need not be in any particular order, C and there may be empty space between the rows. C C During execution, the supervariable i experiences fill-in. C This is represented by placing in i a list of the elements C that cause fill-in in supervariable i: C C len (i): the length of supervariable i C iw (pe (i) ... pe (i) + elen (i) - 1): C the list of elements that contain i. This list C is kept short by removing absorbed elements. C iw (pe (i) + elen (i) ... pe (i) + len (i) - 1): C the list of supervariables in i. This list C is kept short by removing nonprincipal C variables, and any entry j that is also C contained in at least one of the elements C (j in Le) in the list for i (e in row i). C C When supervariable i is selected as pivot, we create an C element e of the same name (e=i): C C len (e): the length of element e C iw (pe (e) ... pe (e) + len (e) - 1): C the list of supervariables in element e. C C An element represents the fill-in that occurs when supervariable C i is selected as pivot (which represents the selection of row i C and all non-principal variables whose principal variable is i). C We use the term Le to denote the set of all supervariables C in element e. Absorbed supervariables and elements are pruned C from these lists when computationally convenient. C C CAUTION: THE INPUT MATRIX IS OVERWRITTEN DURING COMPUTATION. C The contents of iw are undefined on output. C----------------------------------------------------------------------- C OUTPUT (need not be set on input): C----------------------------------------------------------------------- C nv: During execution, abs (nv (i)) is equal to the number of rows C that are represented by the principal supervariable i. If i is C a nonprincipal variable, then nv (i) = 0. Initially, C nv (i) = 1 for all i. nv (i) .lt. 0 signifies that i is a C principal variable in the pattern Lme of the current pivot C element me. On output, nv (e) holds the true degree of element C e at the time it was created (including the diagonal part). C ncmpa: The number of times iw was compressed. If this is C excessive, then the execution took longer than what could have C been. To reduce ncmpa, try increasing iwlen to be 10% or 20% C larger than the value of pfree on input (or at least C iwlen .ge. pfree + n). The fastest performance will be C obtained when ncmpa is returned as zero. If iwlen is set to C the value returned by pfree on *output*, then no compressions C will occur. C elen: See the description of iw above. At the start of execution, C elen (i) is set to zero. During execution, elen (i) is the C number of elements in the list for supervariable i. When e C becomes an element, elen (e) = -nel is set, where nel is the C current step of factorization. elen (i) = 0 is done when i C becomes nonprincipal. C C For variables, elen (i) .ge. 0 holds until just before the C permutation vectors are computed. For elements, C elen (e) .lt. 0 holds. C C On output elen (1..n) holds the inverse permutation (the same C as the 'INVP' argument in Sparspak). That is, if k = elen (i), C then row i is the kth pivot row. Row i of A appears as the C (elen(i))-th row in the permuted matrix, PAP^T. C last: In a degree list, last (i) is the supervariable preceding i, C or zero if i is the head of the list. In a hash bucket, C last (i) is the hash key for i. last (head (hash)) is also C used as the head of a hash bucket if head (hash) contains a C degree list (see head, below). C C On output, last (1..n) holds the permutation (the same as the C 'PERM' argument in Sparspak). That is, if i = last (k), then C row i is the kth pivot row. Row last (k) of A is the k-th row C in the permuted matrix, PAP^T. C----------------------------------------------------------------------- C LOCAL (not input or output - used only during execution): C----------------------------------------------------------------------- C degree: If i is a supervariable, then degree (i) holds the C current approximation of the external degree of row i (an upper C bound). The external degree is the number of nonzeros in row i, C minus abs (nv (i)) (the diagonal part). The bound is equal to C the external degree if elen (i) is less than or equal to two. C C We also use the term "external degree" for elements e to refer C to |Le \ Lme|. If e is an element, then degree (e) holds |Le|, C which is the degree of the off-diagonal part of the element e C (not including the diagonal part). C head: head is used for degree lists. head (deg) is the first C supervariable in a degree list (all supervariables i in a C degree list deg have the same approximate degree, namely, C deg = degree (i)). If the list deg is empty then C head (deg) = 0. C C During supervariable detection head (hash) also serves as a C pointer to a hash bucket. C If head (hash) .gt. 0, there is a degree list of degree hash. C The hash bucket head pointer is last (head (hash)). C If head (hash) = 0, then the degree list and hash bucket are C both empty. C If head (hash) .lt. 0, then the degree list is empty, and C -head (hash) is the head of the hash bucket. C After supervariable detection is complete, all hash buckets C are empty, and the (last (head (hash)) = 0) condition is C restored for the non-empty degree lists. C next: next (i) is the supervariable following i in a link list, or C zero if i is the last in the list. Used for two kinds of C lists: degree lists and hash buckets (a supervariable can be C in only one kind of list at a time). C w: The flag array w determines the status of elements and C variables, and the external degree of elements. C C for elements: C if w (e) = 0, then the element e is absorbed C if w (e) .ge. wflg, then w (e) - wflg is the size of C the set |Le \ Lme|, in terms of nonzeros (the C sum of abs (nv (i)) for each principal variable i that C is both in the pattern of element e and NOT in the C pattern of the current pivot element, me). C if wflg .gt. w (e) .gt. 0, then e is not absorbed and has C not yet been seen in the scan of the element lists in C the computation of |Le\Lme| in loop 150 below. C C for variables: C during supervariable detection, if w (j) .ne. wflg then j is C not in the pattern of variable i C C The w array is initialized by setting w (i) = 1 for all i, C and by setting wflg = 2. It is reinitialized if wflg becomes C too large (to ensure that wflg+n does not cause integer C overflow). C----------------------------------------------------------------------- C LOCAL INTEGERS: C----------------------------------------------------------------------- INTEGER DEG, DEGME, DEXT, DMAX, E, ELENME, ELN, HASH, HMOD, I, $ ILAST, INEXT, J, JLAST, JNEXT, K, KNT1, KNT2, KNT3, $ LENJ, LN, MAXMEM, ME, MEM, MINDEG, NEL, NEWMEM, $ NLEFT, NVI, NVJ, NVPIV, SLENME, WE, WFLG, WNVI, X C deg: the degree of a variable or element C degme: size, |Lme|, of the current element, me (= degree (me)) C dext: external degree, |Le \ Lme|, of some element e C dmax: largest |Le| seen so far C e: an element C elenme: the length, elen (me), of element list of pivotal var. C eln: the length, elen (...), of an element list C hash: the computed value of the hash function C hmod: the hash function is computed modulo hmod = max (1,n-1) C i: a supervariable C ilast: the entry in a link list preceding i C inext: the entry in a link list following i C j: a supervariable C jlast: the entry in a link list preceding j C jnext: the entry in a link list, or path, following j C k: the pivot order of an element or variable C knt1: loop counter used during element construction C knt2: loop counter used during element construction C knt3: loop counter used during compression C lenj: len (j) C ln: length of a supervariable list C maxmem: amount of memory needed for no compressions C me: current supervariable being eliminated, and the C current element created by eliminating that C supervariable C mem: memory in use assuming no compressions have occurred C mindeg: current minimum degree C nel: number of pivots selected so far C newmem: amount of new memory needed for current pivot element C nleft: n - nel, the number of nonpivotal rows/columns remaining C nvi: the number of variables in a supervariable i (= nv (i)) C nvj: the number of variables in a supervariable j (= nv (j)) C nvpiv: number of pivots in current element C slenme: number of variables in variable list of pivotal variable C we: w (e) C wflg: used for flagging the w array. See description of iw. C wnvi: wflg - nv (i) C x: either a supervariable or an element C----------------------------------------------------------------------- C LOCAL POINTERS: C----------------------------------------------------------------------- INTEGER P, P1, P2, P3, PDST, PEND, PJ, PME, PME1, PME2, PN, PSRC C Any parameter (pe (...) or pfree) or local variable C starting with "p" (for Pointer) is an index into iw, C and all indices into iw use variables starting with C "p." The only exception to this rule is the iwlen C input argument. C p: pointer into lots of things C p1: pe (i) for some variable i (start of element list) C p2: pe (i) + elen (i) - 1 for some var. i (end of el. list) C p3: index of first supervariable in clean list C pdst: destination pointer, for compression C pend: end of memory to compress C pj: pointer into an element or variable C pme: pointer into the current element (pme1...pme2) C pme1: the current element, me, is stored in iw (pme1...pme2) C pme2: the end of the current element C pn: pointer into a "clean" variable, also used to compress C psrc: source pointer, for compression C----------------------------------------------------------------------- C FUNCTIONS CALLED: C----------------------------------------------------------------------- INTRINSIC MAX, MIN, MOD C======================================================================= C INITIALIZATIONS C======================================================================= WFLG = 2 MINDEG = 1 NCMPA = 0 NEL = 0 HMOD = MAX (1, N-1) DMAX = 0 MEM = PFREE - 1 MAXMEM = MEM ME = 0 DO 10 I = 1, N LAST (I) = 0 HEAD (I) = 0 NV (I) = 1 W (I) = 1 ELEN (I) = 0 DEGREE (I) = LEN (I) 10 CONTINUE C ---------------------------------------------------------------- C initialize degree lists and eliminate rows with no off-diag. nz. C ---------------------------------------------------------------- DO 20 I = 1, N DEG = DEGREE (I) IF (DEG .GT. 0) THEN C ---------------------------------------------------------- C place i in the degree list corresponding to its degree C ---------------------------------------------------------- INEXT = HEAD (DEG) IF (INEXT .NE. 0) LAST (INEXT) = I NEXT (I) = INEXT HEAD (DEG) = I ELSE C ---------------------------------------------------------- C we have a variable that can be eliminated at once because C there is no off-diagonal non-zero in its row. C ---------------------------------------------------------- NEL = NEL + 1 ELEN (I) = -NEL PE (I) = 0 W (I) = 0 ENDIF 20 CONTINUE C======================================================================= C WHILE (selecting pivots) DO C======================================================================= 30 CONTINUE IF (NEL .LT. N) THEN C======================================================================= C GET PIVOT OF MINIMUM DEGREE C======================================================================= C ------------------------------------------------------------- C find next supervariable for elimination C ------------------------------------------------------------- DO 40 DEG = MINDEG, N ME = HEAD (DEG) IF (ME .GT. 0) GOTO 50 40 CONTINUE 50 CONTINUE MINDEG = DEG C ------------------------------------------------------------- C remove chosen variable from link list C ------------------------------------------------------------- INEXT = NEXT (ME) IF (INEXT .NE. 0) LAST (INEXT) = 0 HEAD (DEG) = INEXT C ------------------------------------------------------------- C me represents the elimination of pivots nel+1 to nel+nv(me). C place me itself as the first in this set. It will be moved C to the nel+nv(me) position when the permutation vectors are C computed. C ------------------------------------------------------------- ELENME = ELEN (ME) ELEN (ME) = - (NEL + 1) NVPIV = NV (ME) NEL = NEL + NVPIV C======================================================================= C CONSTRUCT NEW ELEMENT C======================================================================= C ------------------------------------------------------------- C At this point, me is the pivotal supervariable. It will be C converted into the current element. Scan list of the C pivotal supervariable, me, setting tree pointers and C constructing new list of supervariables for the new element, C me. p is a pointer to the current position in the old list. C ------------------------------------------------------------- C flag the variable "me" as being in Lme by negating nv (me) NV (ME) = -NVPIV DEGME = 0 IF (ELENME .EQ. 0) THEN C ---------------------------------------------------------- C construct the new element in place C ---------------------------------------------------------- PME1 = PE (ME) PME2 = PME1 - 1 DO 60 P = PME1, PME1 + LEN (ME) - 1 I = IW (P) NVI = NV (I) IF (NVI .GT. 0) THEN C ---------------------------------------------------- C i is a principal variable not yet placed in Lme. C store i in new list C ---------------------------------------------------- DEGME = DEGME + NVI C flag i as being in Lme by negating nv (i) NV (I) = -NVI PME2 = PME2 + 1 IW (PME2) = I C ---------------------------------------------------- C remove variable i from degree list. C ---------------------------------------------------- ILAST = LAST (I) INEXT = NEXT (I) IF (INEXT .NE. 0) LAST (INEXT) = ILAST IF (ILAST .NE. 0) THEN NEXT (ILAST) = INEXT ELSE C i is at the head of the degree list HEAD (DEGREE (I)) = INEXT ENDIF ENDIF 60 CONTINUE C this element takes no new memory in iw: NEWMEM = 0 ELSE C ---------------------------------------------------------- C construct the new element in empty space, iw (pfree ...) C ---------------------------------------------------------- P = PE (ME) PME1 = PFREE SLENME = LEN (ME) - ELENME DO 120 KNT1 = 1, ELENME + 1 IF (KNT1 .GT. ELENME) THEN C search the supervariables in me. E = ME PJ = P LN = SLENME ELSE C search the elements in me. E = IW (P) P = P + 1 PJ = PE (E) LN = LEN (E) ENDIF C ------------------------------------------------------- C search for different supervariables and add them to the C new list, compressing when necessary. this loop is C executed once for each element in the list and once for C all the supervariables in the list. C ------------------------------------------------------- DO 110 KNT2 = 1, LN I = IW (PJ) PJ = PJ + 1 NVI = NV (I) IF (NVI .GT. 0) THEN C ------------------------------------------------- C compress iw, if necessary C ------------------------------------------------- IF (PFREE .GT. IWLEN) THEN C prepare for compressing iw by adjusting C pointers and lengths so that the lists being C searched in the inner and outer loops contain C only the remaining entries. PE (ME) = P LEN (ME) = LEN (ME) - KNT1 IF (LEN (ME) .EQ. 0) THEN C nothing left of supervariable me PE (ME) = 0 ENDIF PE (E) = PJ LEN (E) = LN - KNT2 IF (LEN (E) .EQ. 0) THEN C nothing left of element e PE (E) = 0 ENDIF NCMPA = NCMPA + 1 C store first item in pe C set first entry to -item DO 70 J = 1, N PN = PE (J) IF (PN .GT. 0) THEN PE (J) = IW (PN) IW (PN) = -J ENDIF 70 CONTINUE C psrc/pdst point to source/destination PDST = 1 PSRC = 1 PEND = PME1 - 1 C while loop: 80 CONTINUE IF (PSRC .LE. PEND) THEN C search for next negative entry J = -IW (PSRC) PSRC = PSRC + 1 IF (J .GT. 0) THEN IW (PDST) = PE (J) PE (J) = PDST PDST = PDST + 1 C copy from source to destination LENJ = LEN (J) DO 90 KNT3 = 0, LENJ - 2 IW (PDST + KNT3) = IW (PSRC + KNT3) 90 CONTINUE PDST = PDST + LENJ - 1 PSRC = PSRC + LENJ - 1 ENDIF GOTO 80 ENDIF C move the new partially-constructed element P1 = PDST DO 100 PSRC = PME1, PFREE - 1 IW (PDST) = IW (PSRC) PDST = PDST + 1 100 CONTINUE PME1 = P1 PFREE = PDST PJ = PE (E) P = PE (ME) ENDIF C ------------------------------------------------- C i is a principal variable not yet placed in Lme C store i in new list C ------------------------------------------------- DEGME = DEGME + NVI C flag i as being in Lme by negating nv (i) NV (I) = -NVI IW (PFREE) = I PFREE = PFREE + 1 C ------------------------------------------------- C remove variable i from degree link list C ------------------------------------------------- ILAST = LAST (I) INEXT = NEXT (I) IF (INEXT .NE. 0) LAST (INEXT) = ILAST IF (ILAST .NE. 0) THEN NEXT (ILAST) = INEXT ELSE C i is at the head of the degree list HEAD (DEGREE (I)) = INEXT ENDIF ENDIF 110 CONTINUE IF (E .NE. ME) THEN C set tree pointer and flag to indicate element e is C absorbed into new element me (the parent of e is me) PE (E) = -ME W (E) = 0 ENDIF 120 CONTINUE PME2 = PFREE - 1 C this element takes newmem new memory in iw (possibly zero) NEWMEM = PFREE - PME1 MEM = MEM + NEWMEM MAXMEM = MAX (MAXMEM, MEM) ENDIF C ------------------------------------------------------------- C me has now been converted into an element in iw (pme1..pme2) C ------------------------------------------------------------- C degme holds the external degree of new element DEGREE (ME) = DEGME PE (ME) = PME1 LEN (ME) = PME2 - PME1 + 1 C ------------------------------------------------------------- C make sure that wflg is not too large. With the current C value of wflg, wflg+n must not cause integer overflow C ------------------------------------------------------------- IF (WFLG + N .LE. WFLG) THEN DO 130 X = 1, N IF (W (X) .NE. 0) W (X) = 1 130 CONTINUE WFLG = 2 ENDIF C======================================================================= C COMPUTE (w (e) - wflg) = |Le\Lme| FOR ALL ELEMENTS C======================================================================= C ------------------------------------------------------------- C Scan 1: compute the external degrees of previous elements C with respect to the current element. That is: C (w (e) - wflg) = |Le \ Lme| C for each element e that appears in any supervariable in Lme. C The notation Le refers to the pattern (list of C supervariables) of a previous element e, where e is not yet C absorbed, stored in iw (pe (e) + 1 ... pe (e) + iw (pe (e))). C The notation Lme refers to the pattern of the current element C (stored in iw (pme1..pme2)). If (w (e) - wflg) becomes C zero, then the element e will be absorbed in scan 2. C ------------------------------------------------------------- DO 150 PME = PME1, PME2 I = IW (PME) ELN = ELEN (I) IF (ELN .GT. 0) THEN C note that nv (i) has been negated to denote i in Lme: NVI = -NV (I) WNVI = WFLG - NVI DO 140 P = PE (I), PE (I) + ELN - 1 E = IW (P) WE = W (E) IF (WE .GE. WFLG) THEN C unabsorbed element e has been seen in this loop WE = WE - NVI ELSE IF (WE .NE. 0) THEN C e is an unabsorbed element C this is the first we have seen e in all of Scan 1 WE = DEGREE (E) + WNVI ENDIF W (E) = WE 140 CONTINUE ENDIF 150 CONTINUE C======================================================================= C DEGREE UPDATE AND ELEMENT ABSORPTION C======================================================================= C ------------------------------------------------------------- C Scan 2: for each i in Lme, sum up the degree of Lme (which C is degme), plus the sum of the external degrees of each Le C for the elements e appearing within i, plus the C supervariables in i. Place i in hash list. C ------------------------------------------------------------- DO 180 PME = PME1, PME2 I = IW (PME) P1 = PE (I) P2 = P1 + ELEN (I) - 1 PN = P1 HASH = 0 DEG = 0 C ---------------------------------------------------------- C scan the element list associated with supervariable i C ---------------------------------------------------------- DO 160 P = P1, P2 E = IW (P) C dext = | Le \ Lme | DEXT = W (E) - WFLG IF (DEXT .GT. 0) THEN DEG = DEG + DEXT IW (PN) = E PN = PN + 1 HASH = HASH + E ELSE IF (DEXT .EQ. 0) THEN C aggressive absorption: e is not adjacent to me, but C the |Le \ Lme| is 0, so absorb it into me PE (E) = -ME W (E) = 0 ELSE C element e has already been absorbed, due to C regular absorption, in do loop 120 above. Ignore it. CONTINUE ENDIF 160 CONTINUE C count the number of elements in i (including me): ELEN (I) = PN - P1 + 1 C ---------------------------------------------------------- C scan the supervariables in the list associated with i C ---------------------------------------------------------- P3 = PN DO 170 P = P2 + 1, P1 + LEN (I) - 1 J = IW (P) NVJ = NV (J) IF (NVJ .GT. 0) THEN C j is unabsorbed, and not in Lme. C add to degree and add to new list DEG = DEG + NVJ IW (PN) = J PN = PN + 1 HASH = HASH + J ENDIF 170 CONTINUE C ---------------------------------------------------------- C update the degree and check for mass elimination C ---------------------------------------------------------- IF (DEG .EQ. 0) THEN C ------------------------------------------------------- C mass elimination C ------------------------------------------------------- C There is nothing left of this node except for an C edge to the current pivot element. elen (i) is 1, C and there are no variables adjacent to node i. C Absorb i into the current pivot element, me. PE (I) = -ME NVI = -NV (I) DEGME = DEGME - NVI NVPIV = NVPIV + NVI NEL = NEL + NVI NV (I) = 0 ELEN (I) = 0 ELSE C ------------------------------------------------------- C update the upper-bound degree of i C ------------------------------------------------------- C the following degree does not yet include the size C of the current element, which is added later: DEGREE (I) = MIN (DEGREE (I), DEG) C ------------------------------------------------------- C add me to the list for i C ------------------------------------------------------- C move first supervariable to end of list IW (PN) = IW (P3) C move first element to end of element part of list IW (P3) = IW (P1) C add new element to front of list. IW (P1) = ME C store the new length of the list in len (i) LEN (I) = PN - P1 + 1 C ------------------------------------------------------- C place in hash bucket. Save hash key of i in last (i). C ------------------------------------------------------- HASH = MOD (HASH, HMOD) + 1 J = HEAD (HASH) IF (J .LE. 0) THEN C the degree list is empty, hash head is -j NEXT (I) = -J HEAD (HASH) = -I ELSE C degree list is not empty C use last (head (hash)) as hash head NEXT (I) = LAST (J) LAST (J) = I ENDIF LAST (I) = HASH ENDIF 180 CONTINUE DEGREE (ME) = DEGME C ------------------------------------------------------------- C Clear the counter array, w (...), by incrementing wflg. C ------------------------------------------------------------- DMAX = MAX (DMAX, DEGME) WFLG = WFLG + DMAX C make sure that wflg+n does not cause integer overflow IF (WFLG + N .LE. WFLG) THEN DO 190 X = 1, N IF (W (X) .NE. 0) W (X) = 1 190 CONTINUE WFLG = 2 ENDIF C at this point, w (1..n) .lt. wflg holds C======================================================================= C SUPERVARIABLE DETECTION C======================================================================= DO 250 PME = PME1, PME2 I = IW (PME) IF (NV (I) .LT. 0) THEN C i is a principal variable in Lme C ------------------------------------------------------- C examine all hash buckets with 2 or more variables. We C do this by examing all unique hash keys for super- C variables in the pattern Lme of the current element, me C ------------------------------------------------------- HASH = LAST (I) C let i = head of hash bucket, and empty the hash bucket J = HEAD (HASH) IF (J .EQ. 0) GOTO 250 IF (J .LT. 0) THEN C degree list is empty I = -J HEAD (HASH) = 0 ELSE C degree list is not empty, restore last () of head I = LAST (J) LAST (J) = 0 ENDIF IF (I .EQ. 0) GOTO 250 C while loop: 200 CONTINUE IF (NEXT (I) .NE. 0) THEN C ---------------------------------------------------- C this bucket has one or more variables following i. C scan all of them to see if i can absorb any entries C that follow i in hash bucket. Scatter i into w. C ---------------------------------------------------- LN = LEN (I) ELN = ELEN (I) C do not flag the first element in the list (me) DO 210 P = PE (I) + 1, PE (I) + LN - 1 W (IW (P)) = WFLG 210 CONTINUE C ---------------------------------------------------- C scan every other entry j following i in bucket C ---------------------------------------------------- JLAST = I J = NEXT (I) C while loop: 220 CONTINUE IF (J .NE. 0) THEN C ------------------------------------------------- C check if j and i have identical nonzero pattern C ------------------------------------------------- IF (LEN (J) .NE. LN) THEN C i and j do not have same size data structure GOTO 240 ENDIF IF (ELEN (J) .NE. ELN) THEN C i and j do not have same number of adjacent el GOTO 240 ENDIF C do not flag the first element in the list (me) DO 230 P = PE (J) + 1, PE (J) + LN - 1 IF (W (IW (P)) .NE. WFLG) THEN C an entry (iw(p)) is in j but not in i GOTO 240 ENDIF 230 CONTINUE C ------------------------------------------------- C found it! j can be absorbed into i C ------------------------------------------------- PE (J) = -I C both nv (i) and nv (j) are negated since they C are in Lme, and the absolute values of each C are the number of variables in i and j: NV (I) = NV (I) + NV (J) NV (J) = 0 ELEN (J) = 0 C delete j from hash bucket J = NEXT (J) NEXT (JLAST) = J GOTO 220 C ------------------------------------------------- 240 CONTINUE C j cannot be absorbed into i C ------------------------------------------------- JLAST = J J = NEXT (J) GOTO 220 ENDIF C ---------------------------------------------------- C no more variables can be absorbed into i C go to next i in bucket and clear flag array C ---------------------------------------------------- WFLG = WFLG + 1 I = NEXT (I) IF (I .NE. 0) GOTO 200 ENDIF ENDIF 250 CONTINUE C======================================================================= C RESTORE DEGREE LISTS AND REMOVE NONPRINCIPAL SUPERVAR. FROM ELEMENT C======================================================================= P = PME1 NLEFT = N - NEL DO 260 PME = PME1, PME2 I = IW (PME) NVI = -NV (I) IF (NVI .GT. 0) THEN C i is a principal variable in Lme C restore nv (i) to signify that i is principal NV (I) = NVI C ------------------------------------------------------- C compute the external degree (add size of current elem) C ------------------------------------------------------- DEG = MIN (DEGREE (I) + DEGME - NVI, NLEFT - NVI) C ------------------------------------------------------- C place the supervariable at the head of the degree list C ------------------------------------------------------- INEXT = HEAD (DEG) IF (INEXT .NE. 0) LAST (INEXT) = I NEXT (I) = INEXT LAST (I) = 0 HEAD (DEG) = I C ------------------------------------------------------- C save the new degree, and find the minimum degree C ------------------------------------------------------- MINDEG = MIN (MINDEG, DEG) DEGREE (I) = DEG C ------------------------------------------------------- C place the supervariable in the element pattern C ------------------------------------------------------- IW (P) = I P = P + 1 ENDIF 260 CONTINUE C======================================================================= C FINALIZE THE NEW ELEMENT C======================================================================= NV (ME) = NVPIV + DEGME C nv (me) is now the degree of pivot (including diagonal part) C save the length of the list for the new element me LEN (ME) = P - PME1 IF (LEN (ME) .EQ. 0) THEN C there is nothing left of the current pivot element PE (ME) = 0 W (ME) = 0 ENDIF IF (NEWMEM .NE. 0) THEN C element was not constructed in place: deallocate part C of it (final size is less than or equal to newmem, C since newly nonprincipal variables have been removed). PFREE = P MEM = MEM - NEWMEM + LEN (ME) ENDIF C======================================================================= C END WHILE (selecting pivots) GOTO 30 ENDIF C======================================================================= C======================================================================= C COMPUTE THE PERMUTATION VECTORS C======================================================================= C ---------------------------------------------------------------- C The time taken by the following code is O(n). At this C point, elen (e) = -k has been done for all elements e, C and elen (i) = 0 has been done for all nonprincipal C variables i. At this point, there are no principal C supervariables left, and all elements are absorbed. C ---------------------------------------------------------------- C ---------------------------------------------------------------- C compute the ordering of unordered nonprincipal variables C ---------------------------------------------------------------- DO 290 I = 1, N IF (ELEN (I) .EQ. 0) THEN C ---------------------------------------------------------- C i is an un-ordered row. Traverse the tree from i until C reaching an element, e. The element, e, was the C principal supervariable of i and all nodes in the path C from i to when e was selected as pivot. C ---------------------------------------------------------- J = -PE (I) C while (j is a variable) do: 270 CONTINUE IF (ELEN (J) .GE. 0) THEN J = -PE (J) GOTO 270 ENDIF E = J C ---------------------------------------------------------- C get the current pivot ordering of e C ---------------------------------------------------------- K = -ELEN (E) C ---------------------------------------------------------- C traverse the path again from i to e, and compress the C path (all nodes point to e). Path compression allows C this code to compute in O(n) time. Order the unordered C nodes in the path, and place the element e at the end. C ---------------------------------------------------------- J = I C while (j is a variable) do: 280 CONTINUE IF (ELEN (J) .GE. 0) THEN JNEXT = -PE (J) PE (J) = -E IF (ELEN (J) .EQ. 0) THEN C j is an unordered row ELEN (J) = K K = K + 1 ENDIF J = JNEXT GOTO 280 ENDIF C leave elen (e) negative, so we know it is an element ELEN (E) = -K ENDIF 290 CONTINUE C ---------------------------------------------------------------- C reset the inverse permutation (elen (1..n)) to be positive, C and compute the permutation (last (1..n)). C ---------------------------------------------------------------- DO 300 I = 1, N K = ABS (ELEN (I)) LAST (K) = I ELEN (I) = K 300 CONTINUE C======================================================================= C RETURN THE MEMORY USAGE IN IW C======================================================================= C If maxmem is less than or equal to iwlen, then no compressions C occurred, and iw (maxmem+1 ... iwlen) was unused. Otherwise C compressions did occur, and iwlen would have had to have been C greater than or equal to maxmem for no compressions to occur. C Return the value of maxmem in the pfree argument. PFREE = MAXMEM RETURN END SuiteSparse/AMD/Source/amd_post_tree.c0000644001170100242450000000730710616426533016616 0ustar davisfac/* ========================================================================= */ /* === AMD_post_tree ======================================================= */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ /* Post-ordering of a supernodal elimination tree. */ #include "amd_internal.h" GLOBAL Int AMD_post_tree ( Int root, /* root of the tree */ Int k, /* start numbering at k */ Int Child [ ], /* input argument of size nn, undefined on * output. Child [i] is the head of a link * list of all nodes that are children of node * i in the tree. */ const Int Sibling [ ], /* input argument of size nn, not modified. * If f is a node in the link list of the * children of node i, then Sibling [f] is the * next child of node i. */ Int Order [ ], /* output order, of size nn. Order [i] = k * if node i is the kth node of the reordered * tree. */ Int Stack [ ] /* workspace of size nn */ #ifndef NDEBUG , Int nn /* nodes are in the range 0..nn-1. */ #endif ) { Int f, head, h, i ; #if 0 /* --------------------------------------------------------------------- */ /* recursive version (Stack [ ] is not used): */ /* --------------------------------------------------------------------- */ /* this is simple, but can caouse stack overflow if nn is large */ i = root ; for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) { k = AMD_post_tree (f, k, Child, Sibling, Order, Stack, nn) ; } Order [i] = k++ ; return (k) ; #endif /* --------------------------------------------------------------------- */ /* non-recursive version, using an explicit stack */ /* --------------------------------------------------------------------- */ /* push root on the stack */ head = 0 ; Stack [0] = root ; while (head >= 0) { /* get head of stack */ ASSERT (head < nn) ; i = Stack [head] ; AMD_DEBUG1 (("head of stack "ID" \n", i)) ; ASSERT (i >= 0 && i < nn) ; if (Child [i] != EMPTY) { /* the children of i are not yet ordered */ /* push each child onto the stack in reverse order */ /* so that small ones at the head of the list get popped first */ /* and the biggest one at the end of the list gets popped last */ for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) { head++ ; ASSERT (head < nn) ; ASSERT (f >= 0 && f < nn) ; } h = head ; ASSERT (head < nn) ; for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) { ASSERT (h > 0) ; Stack [h--] = f ; AMD_DEBUG1 (("push "ID" on stack\n", f)) ; ASSERT (f >= 0 && f < nn) ; } ASSERT (Stack [h] == i) ; /* delete child list so that i gets ordered next time we see it */ Child [i] = EMPTY ; } else { /* the children of i (if there were any) are already ordered */ /* remove i from the stack and order it. Front i is kth front */ head-- ; AMD_DEBUG1 (("pop "ID" order "ID"\n", i, k)) ; Order [i] = k++ ; ASSERT (k <= nn) ; } #ifndef NDEBUG AMD_DEBUG1 (("\nStack:")) ; for (h = head ; h >= 0 ; h--) { Int j = Stack [h] ; AMD_DEBUG1 ((" "ID, j)) ; ASSERT (j >= 0 && j < nn) ; } AMD_DEBUG1 (("\n\n")) ; ASSERT (head < nn) ; #endif } return (k) ; } SuiteSparse/AMD/Source/amd_defaults.c0000644001170100242450000000246510616426300016411 0ustar davisfac/* ========================================================================= */ /* === AMD_defaults ======================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ /* User-callable. Sets default control parameters for AMD. See amd.h * for details. */ #include "amd_internal.h" /* ========================================================================= */ /* === AMD defaults ======================================================== */ /* ========================================================================= */ GLOBAL void AMD_defaults ( double Control [ ] ) { Int i ; if (Control != (double *) NULL) { for (i = 0 ; i < AMD_CONTROL ; i++) { Control [i] = 0 ; } Control [AMD_DENSE] = AMD_DEFAULT_DENSE ; Control [AMD_AGGRESSIVE] = AMD_DEFAULT_AGGRESSIVE ; } } SuiteSparse/AMD/Source/amd_aat.c0000644001170100242450000001147710616426273015363 0ustar davisfac/* ========================================================================= */ /* === AMD_aat ============================================================= */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ /* AMD_aat: compute the symmetry of the pattern of A, and count the number of * nonzeros each column of A+A' (excluding the diagonal). Assumes the input * matrix has no errors, with sorted columns and no duplicates * (AMD_valid (n, n, Ap, Ai) must be AMD_OK, but this condition is not * checked). */ #include "amd_internal.h" GLOBAL size_t AMD_aat /* returns nz in A+A' */ ( Int n, const Int Ap [ ], const Int Ai [ ], Int Len [ ], /* Len [j]: length of column j of A+A', excl diagonal*/ Int Tp [ ], /* workspace of size n */ double Info [ ] ) { Int p1, p2, p, i, j, pj, pj2, k, nzdiag, nzboth, nz ; double sym ; size_t nzaat ; #ifndef NDEBUG AMD_debug_init ("AMD AAT") ; for (k = 0 ; k < n ; k++) Tp [k] = EMPTY ; ASSERT (AMD_valid (n, n, Ap, Ai) == AMD_OK) ; #endif if (Info != (double *) NULL) { /* clear the Info array, if it exists */ for (i = 0 ; i < AMD_INFO ; i++) { Info [i] = EMPTY ; } Info [AMD_STATUS] = AMD_OK ; } for (k = 0 ; k < n ; k++) { Len [k] = 0 ; } nzdiag = 0 ; nzboth = 0 ; nz = Ap [n] ; for (k = 0 ; k < n ; k++) { p1 = Ap [k] ; p2 = Ap [k+1] ; AMD_DEBUG2 (("\nAAT Column: "ID" p1: "ID" p2: "ID"\n", k, p1, p2)) ; /* construct A+A' */ for (p = p1 ; p < p2 ; ) { /* scan the upper triangular part of A */ j = Ai [p] ; if (j < k) { /* entry A (j,k) is in the strictly upper triangular part, * add both A (j,k) and A (k,j) to the matrix A+A' */ Len [j]++ ; Len [k]++ ; AMD_DEBUG3 ((" upper ("ID","ID") ("ID","ID")\n", j,k, k,j)); p++ ; } else if (j == k) { /* skip the diagonal */ p++ ; nzdiag++ ; break ; } else /* j > k */ { /* first entry below the diagonal */ break ; } /* scan lower triangular part of A, in column j until reaching * row k. Start where last scan left off. */ ASSERT (Tp [j] != EMPTY) ; ASSERT (Ap [j] <= Tp [j] && Tp [j] <= Ap [j+1]) ; pj2 = Ap [j+1] ; for (pj = Tp [j] ; pj < pj2 ; ) { i = Ai [pj] ; if (i < k) { /* A (i,j) is only in the lower part, not in upper. * add both A (i,j) and A (j,i) to the matrix A+A' */ Len [i]++ ; Len [j]++ ; AMD_DEBUG3 ((" lower ("ID","ID") ("ID","ID")\n", i,j, j,i)) ; pj++ ; } else if (i == k) { /* entry A (k,j) in lower part and A (j,k) in upper */ pj++ ; nzboth++ ; break ; } else /* i > k */ { /* consider this entry later, when k advances to i */ break ; } } Tp [j] = pj ; } /* Tp [k] points to the entry just below the diagonal in column k */ Tp [k] = p ; } /* clean up, for remaining mismatched entries */ for (j = 0 ; j < n ; j++) { for (pj = Tp [j] ; pj < Ap [j+1] ; pj++) { i = Ai [pj] ; /* A (i,j) is only in the lower part, not in upper. * add both A (i,j) and A (j,i) to the matrix A+A' */ Len [i]++ ; Len [j]++ ; AMD_DEBUG3 ((" lower cleanup ("ID","ID") ("ID","ID")\n", i,j, j,i)) ; } } /* --------------------------------------------------------------------- */ /* compute the symmetry of the nonzero pattern of A */ /* --------------------------------------------------------------------- */ /* Given a matrix A, the symmetry of A is: * B = tril (spones (A), -1) + triu (spones (A), 1) ; * sym = nnz (B & B') / nnz (B) ; * or 1 if nnz (B) is zero. */ if (nz == nzdiag) { sym = 1 ; } else { sym = (2 * (double) nzboth) / ((double) (nz - nzdiag)) ; } nzaat = 0 ; for (k = 0 ; k < n ; k++) { nzaat += Len [k] ; } AMD_DEBUG1 (("AMD nz in A+A', excluding diagonal (nzaat) = %g\n", (double) nzaat)) ; AMD_DEBUG1 ((" nzboth: "ID" nz: "ID" nzdiag: "ID" symmetry: %g\n", nzboth, nz, nzdiag, sym)) ; if (Info != (double *) NULL) { Info [AMD_STATUS] = AMD_OK ; Info [AMD_N] = n ; Info [AMD_NZ] = nz ; Info [AMD_SYMMETRY] = sym ; /* symmetry of pattern of A */ Info [AMD_NZDIAG] = nzdiag ; /* nonzeros on diagonal of A */ Info [AMD_NZ_A_PLUS_AT] = nzaat ; /* nonzeros in A+A' */ } return (nzaat) ; } SuiteSparse/AMD/Source/amd_postorder.c0000644001170100242450000001272510616426531016631 0ustar davisfac/* ========================================================================= */ /* === AMD_postorder ======================================================= */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ /* Perform a postordering (via depth-first search) of an assembly tree. */ #include "amd_internal.h" GLOBAL void AMD_postorder ( /* inputs, not modified on output: */ Int nn, /* nodes are in the range 0..nn-1 */ Int Parent [ ], /* Parent [j] is the parent of j, or EMPTY if root */ Int Nv [ ], /* Nv [j] > 0 number of pivots represented by node j, * or zero if j is not a node. */ Int Fsize [ ], /* Fsize [j]: size of node j */ /* output, not defined on input: */ Int Order [ ], /* output post-order */ /* workspaces of size nn: */ Int Child [ ], Int Sibling [ ], Int Stack [ ] ) { Int i, j, k, parent, frsize, f, fprev, maxfrsize, bigfprev, bigf, fnext ; for (j = 0 ; j < nn ; j++) { Child [j] = EMPTY ; Sibling [j] = EMPTY ; } /* --------------------------------------------------------------------- */ /* place the children in link lists - bigger elements tend to be last */ /* --------------------------------------------------------------------- */ for (j = nn-1 ; j >= 0 ; j--) { if (Nv [j] > 0) { /* this is an element */ parent = Parent [j] ; if (parent != EMPTY) { /* place the element in link list of the children its parent */ /* bigger elements will tend to be at the end of the list */ Sibling [j] = Child [parent] ; Child [parent] = j ; } } } #ifndef NDEBUG { Int nels, ff, nchild ; AMD_DEBUG1 (("\n\n================================ AMD_postorder:\n")); nels = 0 ; for (j = 0 ; j < nn ; j++) { if (Nv [j] > 0) { AMD_DEBUG1 (( ""ID" : nels "ID" npiv "ID" size "ID " parent "ID" maxfr "ID"\n", j, nels, Nv [j], Fsize [j], Parent [j], Fsize [j])) ; /* this is an element */ /* dump the link list of children */ nchild = 0 ; AMD_DEBUG1 ((" Children: ")) ; for (ff = Child [j] ; ff != EMPTY ; ff = Sibling [ff]) { AMD_DEBUG1 ((ID" ", ff)) ; ASSERT (Parent [ff] == j) ; nchild++ ; ASSERT (nchild < nn) ; } AMD_DEBUG1 (("\n")) ; parent = Parent [j] ; if (parent != EMPTY) { ASSERT (Nv [parent] > 0) ; } nels++ ; } } } AMD_DEBUG1 (("\n\nGo through the children of each node, and put\n" "the biggest child last in each list:\n")) ; #endif /* --------------------------------------------------------------------- */ /* place the largest child last in the list of children for each node */ /* --------------------------------------------------------------------- */ for (i = 0 ; i < nn ; i++) { if (Nv [i] > 0 && Child [i] != EMPTY) { #ifndef NDEBUG Int nchild ; AMD_DEBUG1 (("Before partial sort, element "ID"\n", i)) ; nchild = 0 ; for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) { ASSERT (f >= 0 && f < nn) ; AMD_DEBUG1 ((" f: "ID" size: "ID"\n", f, Fsize [f])) ; nchild++ ; ASSERT (nchild <= nn) ; } #endif /* find the biggest element in the child list */ fprev = EMPTY ; maxfrsize = EMPTY ; bigfprev = EMPTY ; bigf = EMPTY ; for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) { ASSERT (f >= 0 && f < nn) ; frsize = Fsize [f] ; if (frsize >= maxfrsize) { /* this is the biggest seen so far */ maxfrsize = frsize ; bigfprev = fprev ; bigf = f ; } fprev = f ; } ASSERT (bigf != EMPTY) ; fnext = Sibling [bigf] ; AMD_DEBUG1 (("bigf "ID" maxfrsize "ID" bigfprev "ID" fnext "ID " fprev " ID"\n", bigf, maxfrsize, bigfprev, fnext, fprev)) ; if (fnext != EMPTY) { /* if fnext is EMPTY then bigf is already at the end of list */ if (bigfprev == EMPTY) { /* delete bigf from the element of the list */ Child [i] = fnext ; } else { /* delete bigf from the middle of the list */ Sibling [bigfprev] = fnext ; } /* put bigf at the end of the list */ Sibling [bigf] = EMPTY ; ASSERT (Child [i] != EMPTY) ; ASSERT (fprev != bigf) ; ASSERT (fprev != EMPTY) ; Sibling [fprev] = bigf ; } #ifndef NDEBUG AMD_DEBUG1 (("After partial sort, element "ID"\n", i)) ; for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) { ASSERT (f >= 0 && f < nn) ; AMD_DEBUG1 ((" "ID" "ID"\n", f, Fsize [f])) ; ASSERT (Nv [f] > 0) ; nchild-- ; } ASSERT (nchild == 0) ; #endif } } /* --------------------------------------------------------------------- */ /* postorder the assembly tree */ /* --------------------------------------------------------------------- */ for (i = 0 ; i < nn ; i++) { Order [i] = EMPTY ; } k = 0 ; for (i = 0 ; i < nn ; i++) { if (Parent [i] == EMPTY && Nv [i] > 0) { AMD_DEBUG1 (("Root of assembly tree "ID"\n", i)) ; k = AMD_post_tree (i, k, Child, Sibling, Order, Stack #ifndef NDEBUG , nn #endif ) ; } } } SuiteSparse/AMD/Source/amd_global.c0000644001170100242450000000627510616377251016057 0ustar davisfac/* ========================================================================= */ /* === amd_global ========================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ #include #ifdef MATLAB_MEX_FILE #include "mex.h" #include "matrix.h" #endif #ifndef NULL #define NULL 0 #endif /* ========================================================================= */ /* === Default AMD memory manager ========================================== */ /* ========================================================================= */ /* The user can redefine these global pointers at run-time to change the memory * manager used by AMD. AMD only uses malloc and free; realloc and calloc are * include for completeness, in case another package wants to use the same * memory manager as AMD. * * If compiling as a MATLAB mexFunction, the default memory manager is mxMalloc. * You can also compile AMD as a standard ANSI-C library and link a mexFunction * against it, and then redefine these pointers at run-time, in your * mexFunction. * * If -DNMALLOC is defined at compile-time, no memory manager is specified at * compile-time. You must then define these functions at run-time, before * calling AMD, for AMD to work properly. */ #ifndef NMALLOC #ifdef MATLAB_MEX_FILE /* MATLAB mexFunction: */ void *(*amd_malloc) (size_t) = mxMalloc ; void (*amd_free) (void *) = mxFree ; void *(*amd_realloc) (void *, size_t) = mxRealloc ; void *(*amd_calloc) (size_t, size_t) = mxCalloc ; #else /* standard ANSI-C: */ void *(*amd_malloc) (size_t) = malloc ; void (*amd_free) (void *) = free ; void *(*amd_realloc) (void *, size_t) = realloc ; void *(*amd_calloc) (size_t, size_t) = calloc ; #endif #else /* no memory manager defined at compile-time; you MUST define one at run-time */ void *(*amd_malloc) (size_t) = NULL ; void (*amd_free) (void *) = NULL ; void *(*amd_realloc) (void *, size_t) = NULL ; void *(*amd_calloc) (size_t, size_t) = NULL ; #endif /* ========================================================================= */ /* === Default AMD printf routine ========================================== */ /* ========================================================================= */ /* The user can redefine this global pointer at run-time to change the printf * routine used by AMD. If NULL, no printing occurs. * * If -DNPRINT is defined at compile-time, stdio.h is not included. Printing * can then be enabled at run-time by setting amd_printf to a non-NULL function. */ #ifndef NPRINT #ifdef MATLAB_MEX_FILE int (*amd_printf) (const char *, ...) = mexPrintf ; #else #include int (*amd_printf) (const char *, ...) = printf ; #endif #else int (*amd_printf) (const char *, ...) = NULL ; #endif SuiteSparse/AMD/Source/amd_valid.c0000644001170100242450000000576410616426546015722 0ustar davisfac/* ========================================================================= */ /* === AMD_valid =========================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ /* Check if a column-form matrix is valid or not. The matrix A is * n_row-by-n_col. The row indices of entries in column j are in * Ai [Ap [j] ... Ap [j+1]-1]. Required conditions are: * * n_row >= 0 * n_col >= 0 * nz = Ap [n_col] >= 0 number of entries in the matrix * Ap [0] == 0 * Ap [j] <= Ap [j+1] for all j in the range 0 to n_col. * Ai [0 ... nz-1] must be in the range 0 to n_row-1. * * If any of the above conditions hold, AMD_INVALID is returned. If the * following condition holds, AMD_OK_BUT_JUMBLED is returned (a warning, * not an error): * * row indices in Ai [Ap [j] ... Ap [j+1]-1] are not sorted in ascending * order, and/or duplicate entries exist. * * Otherwise, AMD_OK is returned. * * In v1.2 and earlier, this function returned TRUE if the matrix was valid * (now returns AMD_OK), or FALSE otherwise (now returns AMD_INVALID or * AMD_OK_BUT_JUMBLED). */ #include "amd_internal.h" GLOBAL Int AMD_valid ( /* inputs, not modified on output: */ Int n_row, /* A is n_row-by-n_col */ Int n_col, const Int Ap [ ], /* column pointers of A, of size n_col+1 */ const Int Ai [ ] /* row indices of A, of size nz = Ap [n_col] */ ) { Int nz, j, p1, p2, ilast, i, p, result = AMD_OK ; if (n_row < 0 || n_col < 0 || Ap == NULL || Ai == NULL) { return (AMD_INVALID) ; } nz = Ap [n_col] ; if (Ap [0] != 0 || nz < 0) { /* column pointers must start at Ap [0] = 0, and Ap [n] must be >= 0 */ AMD_DEBUG0 (("column 0 pointer bad or nz < 0\n")) ; return (AMD_INVALID) ; } for (j = 0 ; j < n_col ; j++) { p1 = Ap [j] ; p2 = Ap [j+1] ; AMD_DEBUG2 (("\nColumn: "ID" p1: "ID" p2: "ID"\n", j, p1, p2)) ; if (p1 > p2) { /* column pointers must be ascending */ AMD_DEBUG0 (("column "ID" pointer bad\n", j)) ; return (AMD_INVALID) ; } ilast = EMPTY ; for (p = p1 ; p < p2 ; p++) { i = Ai [p] ; AMD_DEBUG3 (("row: "ID"\n", i)) ; if (i < 0 || i >= n_row) { /* row index out of range */ AMD_DEBUG0 (("index out of range, col "ID" row "ID"\n", j, i)); return (AMD_INVALID) ; } if (i <= ilast) { /* row index unsorted, or duplicate entry present */ AMD_DEBUG1 (("index unsorted/dupl col "ID" row "ID"\n", j, i)); result = AMD_OK_BUT_JUMBLED ; } ilast = i ; } } return (result) ; } SuiteSparse/AMD/Source/amd_preprocess.c0000644001170100242450000000746010616426536017002 0ustar davisfac/* ========================================================================= */ /* === AMD_preprocess ====================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ /* Sorts, removes duplicate entries, and transposes from the nonzero pattern of * a column-form matrix A, to obtain the matrix R. The input matrix can have * duplicate entries and/or unsorted columns (AMD_valid (n,Ap,Ai) must not be * AMD_INVALID). * * This input condition is NOT checked. This routine is not user-callable. */ #include "amd_internal.h" /* ========================================================================= */ /* === AMD_preprocess ====================================================== */ /* ========================================================================= */ /* AMD_preprocess does not check its input for errors or allocate workspace. * On input, the condition (AMD_valid (n,n,Ap,Ai) != AMD_INVALID) must hold. */ GLOBAL void AMD_preprocess ( Int n, /* input matrix: A is n-by-n */ const Int Ap [ ], /* size n+1 */ const Int Ai [ ], /* size nz = Ap [n] */ /* output matrix R: */ Int Rp [ ], /* size n+1 */ Int Ri [ ], /* size nz (or less, if duplicates present) */ Int W [ ], /* workspace of size n */ Int Flag [ ] /* workspace of size n */ ) { /* --------------------------------------------------------------------- */ /* local variables */ /* --------------------------------------------------------------------- */ Int i, j, p, p2 ; ASSERT (AMD_valid (n, n, Ap, Ai) != AMD_INVALID) ; /* --------------------------------------------------------------------- */ /* count the entries in each row of A (excluding duplicates) */ /* --------------------------------------------------------------------- */ for (i = 0 ; i < n ; i++) { W [i] = 0 ; /* # of nonzeros in row i (excl duplicates) */ Flag [i] = EMPTY ; /* Flag [i] = j if i appears in column j */ } for (j = 0 ; j < n ; j++) { p2 = Ap [j+1] ; for (p = Ap [j] ; p < p2 ; p++) { i = Ai [p] ; if (Flag [i] != j) { /* row index i has not yet appeared in column j */ W [i]++ ; /* one more entry in row i */ Flag [i] = j ; /* flag row index i as appearing in col j*/ } } } /* --------------------------------------------------------------------- */ /* compute the row pointers for R */ /* --------------------------------------------------------------------- */ Rp [0] = 0 ; for (i = 0 ; i < n ; i++) { Rp [i+1] = Rp [i] + W [i] ; } for (i = 0 ; i < n ; i++) { W [i] = Rp [i] ; Flag [i] = EMPTY ; } /* --------------------------------------------------------------------- */ /* construct the row form matrix R */ /* --------------------------------------------------------------------- */ /* R = row form of pattern of A */ for (j = 0 ; j < n ; j++) { p2 = Ap [j+1] ; for (p = Ap [j] ; p < p2 ; p++) { i = Ai [p] ; if (Flag [i] != j) { /* row index i has not yet appeared in column j */ Ri [W [i]++] = j ; /* put col j in row i */ Flag [i] = j ; /* flag row index i as appearing in col j*/ } } } #ifndef NDEBUG ASSERT (AMD_valid (n, n, Rp, Ri) == AMD_OK) ; for (j = 0 ; j < n ; j++) { ASSERT (W [j] == Rp [j+1]) ; } #endif } SuiteSparse/AMD/Source/amd_1.c0000644001170100242450000001323610616426266014753 0ustar davisfac/* ========================================================================= */ /* === AMD_1 =============================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ /* AMD_1: Construct A+A' for a sparse matrix A and perform the AMD ordering. * * The n-by-n sparse matrix A can be unsymmetric. It is stored in MATLAB-style * compressed-column form, with sorted row indices in each column, and no * duplicate entries. Diagonal entries may be present, but they are ignored. * Row indices of column j of A are stored in Ai [Ap [j] ... Ap [j+1]-1]. * Ap [0] must be zero, and nz = Ap [n] is the number of entries in A. The * size of the matrix, n, must be greater than or equal to zero. * * This routine must be preceded by a call to AMD_aat, which computes the * number of entries in each row/column in A+A', excluding the diagonal. * Len [j], on input, is the number of entries in row/column j of A+A'. This * routine constructs the matrix A+A' and then calls AMD_2. No error checking * is performed (this was done in AMD_valid). */ #include "amd_internal.h" GLOBAL void AMD_1 ( Int n, /* n > 0 */ const Int Ap [ ], /* input of size n+1, not modified */ const Int Ai [ ], /* input of size nz = Ap [n], not modified */ Int P [ ], /* size n output permutation */ Int Pinv [ ], /* size n output inverse permutation */ Int Len [ ], /* size n input, undefined on output */ Int slen, /* slen >= sum (Len [0..n-1]) + 7n, * ideally slen = 1.2 * sum (Len) + 8n */ Int S [ ], /* size slen workspace */ double Control [ ], /* input array of size AMD_CONTROL */ double Info [ ] /* output array of size AMD_INFO */ ) { Int i, j, k, p, pfree, iwlen, pj, p1, p2, pj2, *Iw, *Pe, *Nv, *Head, *Elen, *Degree, *s, *W, *Sp, *Tp ; /* --------------------------------------------------------------------- */ /* construct the matrix for AMD_2 */ /* --------------------------------------------------------------------- */ ASSERT (n > 0) ; iwlen = slen - 6*n ; s = S ; Pe = s ; s += n ; Nv = s ; s += n ; Head = s ; s += n ; Elen = s ; s += n ; Degree = s ; s += n ; W = s ; s += n ; Iw = s ; s += iwlen ; ASSERT (AMD_valid (n, n, Ap, Ai) == AMD_OK) ; /* construct the pointers for A+A' */ Sp = Nv ; /* use Nv and W as workspace for Sp and Tp [ */ Tp = W ; pfree = 0 ; for (j = 0 ; j < n ; j++) { Pe [j] = pfree ; Sp [j] = pfree ; pfree += Len [j] ; } /* Note that this restriction on iwlen is slightly more restrictive than * what is strictly required in AMD_2. AMD_2 can operate with no elbow * room at all, but it will be very slow. For better performance, at * least size-n elbow room is enforced. */ ASSERT (iwlen >= pfree + n) ; #ifndef NDEBUG for (p = 0 ; p < iwlen ; p++) Iw [p] = EMPTY ; #endif for (k = 0 ; k < n ; k++) { AMD_DEBUG1 (("Construct row/column k= "ID" of A+A'\n", k)) ; p1 = Ap [k] ; p2 = Ap [k+1] ; /* construct A+A' */ for (p = p1 ; p < p2 ; ) { /* scan the upper triangular part of A */ j = Ai [p] ; ASSERT (j >= 0 && j < n) ; if (j < k) { /* entry A (j,k) in the strictly upper triangular part */ ASSERT (Sp [j] < (j == n-1 ? pfree : Pe [j+1])) ; ASSERT (Sp [k] < (k == n-1 ? pfree : Pe [k+1])) ; Iw [Sp [j]++] = k ; Iw [Sp [k]++] = j ; p++ ; } else if (j == k) { /* skip the diagonal */ p++ ; break ; } else /* j > k */ { /* first entry below the diagonal */ break ; } /* scan lower triangular part of A, in column j until reaching * row k. Start where last scan left off. */ ASSERT (Ap [j] <= Tp [j] && Tp [j] <= Ap [j+1]) ; pj2 = Ap [j+1] ; for (pj = Tp [j] ; pj < pj2 ; ) { i = Ai [pj] ; ASSERT (i >= 0 && i < n) ; if (i < k) { /* A (i,j) is only in the lower part, not in upper */ ASSERT (Sp [i] < (i == n-1 ? pfree : Pe [i+1])) ; ASSERT (Sp [j] < (j == n-1 ? pfree : Pe [j+1])) ; Iw [Sp [i]++] = j ; Iw [Sp [j]++] = i ; pj++ ; } else if (i == k) { /* entry A (k,j) in lower part and A (j,k) in upper */ pj++ ; break ; } else /* i > k */ { /* consider this entry later, when k advances to i */ break ; } } Tp [j] = pj ; } Tp [k] = p ; } /* clean up, for remaining mismatched entries */ for (j = 0 ; j < n ; j++) { for (pj = Tp [j] ; pj < Ap [j+1] ; pj++) { i = Ai [pj] ; ASSERT (i >= 0 && i < n) ; /* A (i,j) is only in the lower part, not in upper */ ASSERT (Sp [i] < (i == n-1 ? pfree : Pe [i+1])) ; ASSERT (Sp [j] < (j == n-1 ? pfree : Pe [j+1])) ; Iw [Sp [i]++] = j ; Iw [Sp [j]++] = i ; } } #ifndef NDEBUG for (j = 0 ; j < n-1 ; j++) ASSERT (Sp [j] == Pe [j+1]) ; ASSERT (Sp [n-1] == pfree) ; #endif /* Tp and Sp no longer needed ] */ /* --------------------------------------------------------------------- */ /* order the matrix */ /* --------------------------------------------------------------------- */ AMD_2 (n, Pe, Iw, Len, iwlen, pfree, Nv, Pinv, P, Head, Elen, Degree, W, Control, Info) ; } SuiteSparse/AMD/Source/amd_2.c0000644001170100242450000017646710616426270014767 0ustar davisfac/* ========================================================================= */ /* === AMD_2 =============================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ /* AMD_2: performs the AMD ordering on a symmetric sparse matrix A, followed * by a postordering (via depth-first search) of the assembly tree using the * AMD_postorder routine. */ #include "amd_internal.h" /* ========================================================================= */ /* === clear_flag ========================================================== */ /* ========================================================================= */ static Int clear_flag (Int wflg, Int wbig, Int W [ ], Int n) { Int x ; if (wflg < 2 || wflg >= wbig) { for (x = 0 ; x < n ; x++) { if (W [x] != 0) W [x] = 1 ; } wflg = 2 ; } /* at this point, W [0..n-1] < wflg holds */ return (wflg) ; } /* ========================================================================= */ /* === AMD_2 =============================================================== */ /* ========================================================================= */ GLOBAL void AMD_2 ( Int n, /* A is n-by-n, where n > 0 */ Int Pe [ ], /* Pe [0..n-1]: index in Iw of row i on input */ Int Iw [ ], /* workspace of size iwlen. Iw [0..pfree-1] * holds the matrix on input */ Int Len [ ], /* Len [0..n-1]: length for row/column i on input */ Int iwlen, /* length of Iw. iwlen >= pfree + n */ Int pfree, /* Iw [pfree ... iwlen-1] is empty on input */ /* 7 size-n workspaces, not defined on input: */ Int Nv [ ], /* the size of each supernode on output */ Int Next [ ], /* the output inverse permutation */ Int Last [ ], /* the output permutation */ Int Head [ ], Int Elen [ ], /* the size columns of L for each supernode */ Int Degree [ ], Int W [ ], /* control parameters and output statistics */ double Control [ ], /* array of size AMD_CONTROL */ double Info [ ] /* array of size AMD_INFO */ ) { /* * Given a representation of the nonzero pattern of a symmetric matrix, A, * (excluding the diagonal) perform an approximate minimum (UMFPACK/MA38-style) * degree ordering to compute a pivot order such that the introduction of * nonzeros (fill-in) in the Cholesky factors A = LL' is kept low. At each * step, the pivot selected is the one with the minimum UMFAPACK/MA38-style * upper-bound on the external degree. This routine can optionally perform * aggresive absorption (as done by MC47B in the Harwell Subroutine * Library). * * The approximate degree algorithm implemented here is the symmetric analog of * the degree update algorithm in MA38 and UMFPACK (the Unsymmetric-pattern * MultiFrontal PACKage, both by Davis and Duff). The routine is based on the * MA27 minimum degree ordering algorithm by Iain Duff and John Reid. * * This routine is a translation of the original AMDBAR and MC47B routines, * in Fortran, with the following modifications: * * (1) dense rows/columns are removed prior to ordering the matrix, and placed * last in the output order. The presence of a dense row/column can * increase the ordering time by up to O(n^2), unless they are removed * prior to ordering. * * (2) the minimum degree ordering is followed by a postordering (depth-first * search) of the assembly tree. Note that mass elimination (discussed * below) combined with the approximate degree update can lead to the mass * elimination of nodes with lower exact degree than the current pivot * element. No additional fill-in is caused in the representation of the * Schur complement. The mass-eliminated nodes merge with the current * pivot element. They are ordered prior to the current pivot element. * Because they can have lower exact degree than the current element, the * merger of two or more of these nodes in the current pivot element can * lead to a single element that is not a "fundamental supernode". The * diagonal block can have zeros in it. Thus, the assembly tree used here * is not guaranteed to be the precise supernodal elemination tree (with * "funadmental" supernodes), and the postordering performed by this * routine is not guaranteed to be a precise postordering of the * elimination tree. * * (3) input parameters are added, to control aggressive absorption and the * detection of "dense" rows/columns of A. * * (4) additional statistical information is returned, such as the number of * nonzeros in L, and the flop counts for subsequent LDL' and LU * factorizations. These are slight upper bounds, because of the mass * elimination issue discussed above. * * (5) additional routines are added to interface this routine to MATLAB * to provide a simple C-callable user-interface, to check inputs for * errors, compute the symmetry of the pattern of A and the number of * nonzeros in each row/column of A+A', to compute the pattern of A+A', * to perform the assembly tree postordering, and to provide debugging * ouput. Many of these functions are also provided by the Fortran * Harwell Subroutine Library routine MC47A. * * (6) both int and UF_long versions are provided. In the descriptions below * and integer is and int or UF_long depending on which version is * being used. ********************************************************************** ***** CAUTION: ARGUMENTS ARE NOT CHECKED FOR ERRORS ON INPUT. ****** ********************************************************************** ** If you want error checking, a more versatile input format, and a ** ** simpler user interface, use amd_order or amd_l_order instead. ** ** This routine is not meant to be user-callable. ** ********************************************************************** * ---------------------------------------------------------------------------- * References: * ---------------------------------------------------------------------------- * * [1] Timothy A. Davis and Iain Duff, "An unsymmetric-pattern multifrontal * method for sparse LU factorization", SIAM J. Matrix Analysis and * Applications, vol. 18, no. 1, pp. 140-158. Discusses UMFPACK / MA38, * which first introduced the approximate minimum degree used by this * routine. * * [2] Patrick Amestoy, Timothy A. Davis, and Iain S. Duff, "An approximate * minimum degree ordering algorithm," SIAM J. Matrix Analysis and * Applications, vol. 17, no. 4, pp. 886-905, 1996. Discusses AMDBAR and * MC47B, which are the Fortran versions of this routine. * * [3] Alan George and Joseph Liu, "The evolution of the minimum degree * ordering algorithm," SIAM Review, vol. 31, no. 1, pp. 1-19, 1989. * We list below the features mentioned in that paper that this code * includes: * * mass elimination: * Yes. MA27 relied on supervariable detection for mass elimination. * * indistinguishable nodes: * Yes (we call these "supervariables"). This was also in the MA27 * code - although we modified the method of detecting them (the * previous hash was the true degree, which we no longer keep track * of). A supervariable is a set of rows with identical nonzero * pattern. All variables in a supervariable are eliminated together. * Each supervariable has as its numerical name that of one of its * variables (its principal variable). * * quotient graph representation: * Yes. We use the term "element" for the cliques formed during * elimination. This was also in the MA27 code. The algorithm can * operate in place, but it will work more efficiently if given some * "elbow room." * * element absorption: * Yes. This was also in the MA27 code. * * external degree: * Yes. The MA27 code was based on the true degree. * * incomplete degree update and multiple elimination: * No. This was not in MA27, either. Our method of degree update * within MC47B is element-based, not variable-based. It is thus * not well-suited for use with incomplete degree update or multiple * elimination. * * Authors, and Copyright (C) 2004 by: * Timothy A. Davis, Patrick Amestoy, Iain S. Duff, John K. Reid. * * Acknowledgements: This work (and the UMFPACK package) was supported by the * National Science Foundation (ASC-9111263, DMS-9223088, and CCR-0203270). * The UMFPACK/MA38 approximate degree update algorithm, the unsymmetric analog * which forms the basis of AMD, was developed while Tim Davis was supported by * CERFACS (Toulouse, France) in a post-doctoral position. This C version, and * the etree postorder, were written while Tim Davis was on sabbatical at * Stanford University and Lawrence Berkeley National Laboratory. * ---------------------------------------------------------------------------- * INPUT ARGUMENTS (unaltered): * ---------------------------------------------------------------------------- * n: The matrix order. Restriction: n >= 1. * * iwlen: The size of the Iw array. On input, the matrix is stored in * Iw [0..pfree-1]. However, Iw [0..iwlen-1] should be slightly larger * than what is required to hold the matrix, at least iwlen >= pfree + n. * Otherwise, excessive compressions will take place. The recommended * value of iwlen is 1.2 * pfree + n, which is the value used in the * user-callable interface to this routine (amd_order.c). The algorithm * will not run at all if iwlen < pfree. Restriction: iwlen >= pfree + n. * Note that this is slightly more restrictive than the actual minimum * (iwlen >= pfree), but AMD_2 will be very slow with no elbow room. * Thus, this routine enforces a bare minimum elbow room of size n. * * pfree: On input the tail end of the array, Iw [pfree..iwlen-1], is empty, * and the matrix is stored in Iw [0..pfree-1]. During execution, * additional data is placed in Iw, and pfree is modified so that * Iw [pfree..iwlen-1] is always the unused part of Iw. * * Control: A double array of size AMD_CONTROL containing input parameters * that affect how the ordering is computed. If NULL, then default * settings are used. * * Control [AMD_DENSE] is used to determine whether or not a given input * row is "dense". A row is "dense" if the number of entries in the row * exceeds Control [AMD_DENSE] times sqrt (n), except that rows with 16 or * fewer entries are never considered "dense". To turn off the detection * of dense rows, set Control [AMD_DENSE] to a negative number, or to a * number larger than sqrt (n). The default value of Control [AMD_DENSE] * is AMD_DEFAULT_DENSE, which is defined in amd.h as 10. * * Control [AMD_AGGRESSIVE] is used to determine whether or not aggressive * absorption is to be performed. If nonzero, then aggressive absorption * is performed (this is the default). * ---------------------------------------------------------------------------- * INPUT/OUPUT ARGUMENTS: * ---------------------------------------------------------------------------- * * Pe: An integer array of size n. On input, Pe [i] is the index in Iw of * the start of row i. Pe [i] is ignored if row i has no off-diagonal * entries. Thus Pe [i] must be in the range 0 to pfree-1 for non-empty * rows. * * During execution, it is used for both supervariables and elements: * * Principal supervariable i: index into Iw of the description of * supervariable i. A supervariable represents one or more rows of * the matrix with identical nonzero pattern. In this case, * Pe [i] >= 0. * * Non-principal supervariable i: if i has been absorbed into another * supervariable j, then Pe [i] = FLIP (j), where FLIP (j) is defined * as (-(j)-2). Row j has the same pattern as row i. Note that j * might later be absorbed into another supervariable j2, in which * case Pe [i] is still FLIP (j), and Pe [j] = FLIP (j2) which is * < EMPTY, where EMPTY is defined as (-1) in amd_internal.h. * * Unabsorbed element e: the index into Iw of the description of element * e, if e has not yet been absorbed by a subsequent element. Element * e is created when the supervariable of the same name is selected as * the pivot. In this case, Pe [i] >= 0. * * Absorbed element e: if element e is absorbed into element e2, then * Pe [e] = FLIP (e2). This occurs when the pattern of e (which we * refer to as Le) is found to be a subset of the pattern of e2 (that * is, Le2). In this case, Pe [i] < EMPTY. If element e is "null" * (it has no nonzeros outside its pivot block), then Pe [e] = EMPTY, * and e is the root of an assembly subtree (or the whole tree if * there is just one such root). * * Dense variable i: if i is "dense", then Pe [i] = EMPTY. * * On output, Pe holds the assembly tree/forest, which implicitly * represents a pivot order with identical fill-in as the actual order * (via a depth-first search of the tree), as follows. If Nv [i] > 0, * then i represents a node in the assembly tree, and the parent of i is * Pe [i], or EMPTY if i is a root. If Nv [i] = 0, then (i, Pe [i]) * represents an edge in a subtree, the root of which is a node in the * assembly tree. Note that i refers to a row/column in the original * matrix, not the permuted matrix. * * Info: A double array of size AMD_INFO. If present, (that is, not NULL), * then statistics about the ordering are returned in the Info array. * See amd.h for a description. * ---------------------------------------------------------------------------- * INPUT/MODIFIED (undefined on output): * ---------------------------------------------------------------------------- * * Len: An integer array of size n. On input, Len [i] holds the number of * entries in row i of the matrix, excluding the diagonal. The contents * of Len are undefined on output. * * Iw: An integer array of size iwlen. On input, Iw [0..pfree-1] holds the * description of each row i in the matrix. The matrix must be symmetric, * and both upper and lower triangular parts must be present. The * diagonal must not be present. Row i is held as follows: * * Len [i]: the length of the row i data structure in the Iw array. * Iw [Pe [i] ... Pe [i] + Len [i] - 1]: * the list of column indices for nonzeros in row i (simple * supervariables), excluding the diagonal. All supervariables * start with one row/column each (supervariable i is just row i). * If Len [i] is zero on input, then Pe [i] is ignored on input. * * Note that the rows need not be in any particular order, and there * may be empty space between the rows. * * During execution, the supervariable i experiences fill-in. This is * represented by placing in i a list of the elements that cause fill-in * in supervariable i: * * Len [i]: the length of supervariable i in the Iw array. * Iw [Pe [i] ... Pe [i] + Elen [i] - 1]: * the list of elements that contain i. This list is kept short * by removing absorbed elements. * Iw [Pe [i] + Elen [i] ... Pe [i] + Len [i] - 1]: * the list of supervariables in i. This list is kept short by * removing nonprincipal variables, and any entry j that is also * contained in at least one of the elements (j in Le) in the list * for i (e in row i). * * When supervariable i is selected as pivot, we create an element e of * the same name (e=i): * * Len [e]: the length of element e in the Iw array. * Iw [Pe [e] ... Pe [e] + Len [e] - 1]: * the list of supervariables in element e. * * An element represents the fill-in that occurs when supervariable i is * selected as pivot (which represents the selection of row i and all * non-principal variables whose principal variable is i). We use the * term Le to denote the set of all supervariables in element e. Absorbed * supervariables and elements are pruned from these lists when * computationally convenient. * * CAUTION: THE INPUT MATRIX IS OVERWRITTEN DURING COMPUTATION. * The contents of Iw are undefined on output. * ---------------------------------------------------------------------------- * OUTPUT (need not be set on input): * ---------------------------------------------------------------------------- * * Nv: An integer array of size n. During execution, ABS (Nv [i]) is equal to * the number of rows that are represented by the principal supervariable * i. If i is a nonprincipal or dense variable, then Nv [i] = 0. * Initially, Nv [i] = 1 for all i. Nv [i] < 0 signifies that i is a * principal variable in the pattern Lme of the current pivot element me. * After element me is constructed, Nv [i] is set back to a positive * value. * * On output, Nv [i] holds the number of pivots represented by super * row/column i of the original matrix, or Nv [i] = 0 for non-principal * rows/columns. Note that i refers to a row/column in the original * matrix, not the permuted matrix. * * Elen: An integer array of size n. See the description of Iw above. At the * start of execution, Elen [i] is set to zero for all rows i. During * execution, Elen [i] is the number of elements in the list for * supervariable i. When e becomes an element, Elen [e] = FLIP (esize) is * set, where esize is the size of the element (the number of pivots, plus * the number of nonpivotal entries). Thus Elen [e] < EMPTY. * Elen (i) = EMPTY set when variable i becomes nonprincipal. * * For variables, Elen (i) >= EMPTY holds until just before the * postordering and permutation vectors are computed. For elements, * Elen [e] < EMPTY holds. * * On output, Elen [i] is the degree of the row/column in the Cholesky * factorization of the permuted matrix, corresponding to the original row * i, if i is a super row/column. It is equal to EMPTY if i is * non-principal. Note that i refers to a row/column in the original * matrix, not the permuted matrix. * * Note that the contents of Elen on output differ from the Fortran * version (Elen holds the inverse permutation in the Fortran version, * which is instead returned in the Next array in this C version, * described below). * * Last: In a degree list, Last [i] is the supervariable preceding i, or EMPTY * if i is the head of the list. In a hash bucket, Last [i] is the hash * key for i. * * Last [Head [hash]] is also used as the head of a hash bucket if * Head [hash] contains a degree list (see the description of Head, * below). * * On output, Last [0..n-1] holds the permutation. That is, if * i = Last [k], then row i is the kth pivot row (where k ranges from 0 to * n-1). Row Last [k] of A is the kth row in the permuted matrix, PAP'. * * Next: Next [i] is the supervariable following i in a link list, or EMPTY if * i is the last in the list. Used for two kinds of lists: degree lists * and hash buckets (a supervariable can be in only one kind of list at a * time). * * On output Next [0..n-1] holds the inverse permutation. That is, if * k = Next [i], then row i is the kth pivot row. Row i of A appears as * the (Next[i])-th row in the permuted matrix, PAP'. * * Note that the contents of Next on output differ from the Fortran * version (Next is undefined on output in the Fortran version). * ---------------------------------------------------------------------------- * LOCAL WORKSPACE (not input or output - used only during execution): * ---------------------------------------------------------------------------- * * Degree: An integer array of size n. If i is a supervariable, then * Degree [i] holds the current approximation of the external degree of * row i (an upper bound). The external degree is the number of nonzeros * in row i, minus ABS (Nv [i]), the diagonal part. The bound is equal to * the exact external degree if Elen [i] is less than or equal to two. * * We also use the term "external degree" for elements e to refer to * |Le \ Lme|. If e is an element, then Degree [e] is |Le|, which is the * degree of the off-diagonal part of the element e (not including the * diagonal part). * * Head: An integer array of size n. Head is used for degree lists. * Head [deg] is the first supervariable in a degree list. All * supervariables i in a degree list Head [deg] have the same approximate * degree, namely, deg = Degree [i]. If the list Head [deg] is empty then * Head [deg] = EMPTY. * * During supervariable detection Head [hash] also serves as a pointer to * a hash bucket. If Head [hash] >= 0, there is a degree list of degree * hash. The hash bucket head pointer is Last [Head [hash]]. If * Head [hash] = EMPTY, then the degree list and hash bucket are both * empty. If Head [hash] < EMPTY, then the degree list is empty, and * FLIP (Head [hash]) is the head of the hash bucket. After supervariable * detection is complete, all hash buckets are empty, and the * (Last [Head [hash]] = EMPTY) condition is restored for the non-empty * degree lists. * * W: An integer array of size n. The flag array W determines the status of * elements and variables, and the external degree of elements. * * for elements: * if W [e] = 0, then the element e is absorbed. * if W [e] >= wflg, then W [e] - wflg is the size of the set * |Le \ Lme|, in terms of nonzeros (the sum of ABS (Nv [i]) for * each principal variable i that is both in the pattern of * element e and NOT in the pattern of the current pivot element, * me). * if wflg > W [e] > 0, then e is not absorbed and has not yet been * seen in the scan of the element lists in the computation of * |Le\Lme| in Scan 1 below. * * for variables: * during supervariable detection, if W [j] != wflg then j is * not in the pattern of variable i. * * The W array is initialized by setting W [i] = 1 for all i, and by * setting wflg = 2. It is reinitialized if wflg becomes too large (to * ensure that wflg+n does not cause integer overflow). * ---------------------------------------------------------------------------- * LOCAL INTEGERS: * ---------------------------------------------------------------------------- */ Int deg, degme, dext, lemax, e, elenme, eln, i, ilast, inext, j, jlast, jnext, k, knt1, knt2, knt3, lenj, ln, me, mindeg, nel, nleft, nvi, nvj, nvpiv, slenme, wbig, we, wflg, wnvi, ok, ndense, ncmpa, dense, aggressive ; unsigned Int hash ; /* unsigned, so that hash % n is well defined.*/ /* * deg: the degree of a variable or element * degme: size, |Lme|, of the current element, me (= Degree [me]) * dext: external degree, |Le \ Lme|, of some element e * lemax: largest |Le| seen so far (called dmax in Fortran version) * e: an element * elenme: the length, Elen [me], of element list of pivotal variable * eln: the length, Elen [...], of an element list * hash: the computed value of the hash function * i: a supervariable * ilast: the entry in a link list preceding i * inext: the entry in a link list following i * j: a supervariable * jlast: the entry in a link list preceding j * jnext: the entry in a link list, or path, following j * k: the pivot order of an element or variable * knt1: loop counter used during element construction * knt2: loop counter used during element construction * knt3: loop counter used during compression * lenj: Len [j] * ln: length of a supervariable list * me: current supervariable being eliminated, and the current * element created by eliminating that supervariable * mindeg: current minimum degree * nel: number of pivots selected so far * nleft: n - nel, the number of nonpivotal rows/columns remaining * nvi: the number of variables in a supervariable i (= Nv [i]) * nvj: the number of variables in a supervariable j (= Nv [j]) * nvpiv: number of pivots in current element * slenme: number of variables in variable list of pivotal variable * wbig: = INT_MAX - n for the int version, UF_long_max - n for the * UF_long version. wflg is not allowed to be >= wbig. * we: W [e] * wflg: used for flagging the W array. See description of Iw. * wnvi: wflg - Nv [i] * x: either a supervariable or an element * * ok: true if supervariable j can be absorbed into i * ndense: number of "dense" rows/columns * dense: rows/columns with initial degree > dense are considered "dense" * aggressive: true if aggressive absorption is being performed * ncmpa: number of garbage collections * ---------------------------------------------------------------------------- * LOCAL DOUBLES, used for statistical output only (except for alpha): * ---------------------------------------------------------------------------- */ double f, r, ndiv, s, nms_lu, nms_ldl, dmax, alpha, lnz, lnzme ; /* * f: nvpiv * r: degme + nvpiv * ndiv: number of divisions for LU or LDL' factorizations * s: number of multiply-subtract pairs for LU factorization, for the * current element me * nms_lu number of multiply-subtract pairs for LU factorization * nms_ldl number of multiply-subtract pairs for LDL' factorization * dmax: the largest number of entries in any column of L, including the * diagonal * alpha: "dense" degree ratio * lnz: the number of nonzeros in L (excluding the diagonal) * lnzme: the number of nonzeros in L (excl. the diagonal) for the * current element me * ---------------------------------------------------------------------------- * LOCAL "POINTERS" (indices into the Iw array) * ---------------------------------------------------------------------------- */ Int p, p1, p2, p3, p4, pdst, pend, pj, pme, pme1, pme2, pn, psrc ; /* * Any parameter (Pe [...] or pfree) or local variable starting with "p" (for * Pointer) is an index into Iw, and all indices into Iw use variables starting * with "p." The only exception to this rule is the iwlen input argument. * * p: pointer into lots of things * p1: Pe [i] for some variable i (start of element list) * p2: Pe [i] + Elen [i] - 1 for some variable i * p3: index of first supervariable in clean list * p4: * pdst: destination pointer, for compression * pend: end of memory to compress * pj: pointer into an element or variable * pme: pointer into the current element (pme1...pme2) * pme1: the current element, me, is stored in Iw [pme1...pme2] * pme2: the end of the current element * pn: pointer into a "clean" variable, also used to compress * psrc: source pointer, for compression */ /* ========================================================================= */ /* INITIALIZATIONS */ /* ========================================================================= */ /* Note that this restriction on iwlen is slightly more restrictive than * what is actually required in AMD_2. AMD_2 can operate with no elbow * room at all, but it will be slow. For better performance, at least * size-n elbow room is enforced. */ ASSERT (iwlen >= pfree + n) ; ASSERT (n > 0) ; /* initialize output statistics */ lnz = 0 ; ndiv = 0 ; nms_lu = 0 ; nms_ldl = 0 ; dmax = 1 ; me = EMPTY ; mindeg = 0 ; ncmpa = 0 ; nel = 0 ; lemax = 0 ; /* get control parameters */ if (Control != (double *) NULL) { alpha = Control [AMD_DENSE] ; aggressive = (Control [AMD_AGGRESSIVE] != 0) ; } else { alpha = AMD_DEFAULT_DENSE ; aggressive = AMD_DEFAULT_AGGRESSIVE ; } /* Note: if alpha is NaN, this is undefined: */ if (alpha < 0) { /* only remove completely dense rows/columns */ dense = n-2 ; } else { dense = alpha * sqrt ((double) n) ; } dense = MAX (16, dense) ; dense = MIN (n, dense) ; AMD_DEBUG1 (("\n\nAMD (debug), alpha %g, aggr. "ID"\n", alpha, aggressive)) ; for (i = 0 ; i < n ; i++) { Last [i] = EMPTY ; Head [i] = EMPTY ; Next [i] = EMPTY ; /* if separate Hhead array is used for hash buckets: * Hhead [i] = EMPTY ; */ Nv [i] = 1 ; W [i] = 1 ; Elen [i] = 0 ; Degree [i] = Len [i] ; } #ifndef NDEBUG AMD_DEBUG1 (("\n======Nel "ID" initial\n", nel)) ; AMD_dump (n, Pe, Iw, Len, iwlen, pfree, Nv, Next, Last, Head, Elen, Degree, W, -1) ; #endif /* initialize wflg */ wbig = Int_MAX - n ; wflg = clear_flag (0, wbig, W, n) ; /* --------------------------------------------------------------------- */ /* initialize degree lists and eliminate dense and empty rows */ /* --------------------------------------------------------------------- */ ndense = 0 ; for (i = 0 ; i < n ; i++) { deg = Degree [i] ; ASSERT (deg >= 0 && deg < n) ; if (deg == 0) { /* ------------------------------------------------------------- * we have a variable that can be eliminated at once because * there is no off-diagonal non-zero in its row. Note that * Nv [i] = 1 for an empty variable i. It is treated just * the same as an eliminated element i. * ------------------------------------------------------------- */ Elen [i] = FLIP (1) ; nel++ ; Pe [i] = EMPTY ; W [i] = 0 ; } else if (deg > dense) { /* ------------------------------------------------------------- * Dense variables are not treated as elements, but as unordered, * non-principal variables that have no parent. They do not take * part in the postorder, since Nv [i] = 0. Note that the Fortran * version does not have this option. * ------------------------------------------------------------- */ AMD_DEBUG1 (("Dense node "ID" degree "ID"\n", i, deg)) ; ndense++ ; Nv [i] = 0 ; /* do not postorder this node */ Elen [i] = EMPTY ; nel++ ; Pe [i] = EMPTY ; } else { /* ------------------------------------------------------------- * place i in the degree list corresponding to its degree * ------------------------------------------------------------- */ inext = Head [deg] ; ASSERT (inext >= EMPTY && inext < n) ; if (inext != EMPTY) Last [inext] = i ; Next [i] = inext ; Head [deg] = i ; } } /* ========================================================================= */ /* WHILE (selecting pivots) DO */ /* ========================================================================= */ while (nel < n) { #ifndef NDEBUG AMD_DEBUG1 (("\n======Nel "ID"\n", nel)) ; if (AMD_debug >= 2) { AMD_dump (n, Pe, Iw, Len, iwlen, pfree, Nv, Next, Last, Head, Elen, Degree, W, nel) ; } #endif /* ========================================================================= */ /* GET PIVOT OF MINIMUM DEGREE */ /* ========================================================================= */ /* ----------------------------------------------------------------- */ /* find next supervariable for elimination */ /* ----------------------------------------------------------------- */ ASSERT (mindeg >= 0 && mindeg < n) ; for (deg = mindeg ; deg < n ; deg++) { me = Head [deg] ; if (me != EMPTY) break ; } mindeg = deg ; ASSERT (me >= 0 && me < n) ; AMD_DEBUG1 (("=================me: "ID"\n", me)) ; /* ----------------------------------------------------------------- */ /* remove chosen variable from link list */ /* ----------------------------------------------------------------- */ inext = Next [me] ; ASSERT (inext >= EMPTY && inext < n) ; if (inext != EMPTY) Last [inext] = EMPTY ; Head [deg] = inext ; /* ----------------------------------------------------------------- */ /* me represents the elimination of pivots nel to nel+Nv[me]-1. */ /* place me itself as the first in this set. */ /* ----------------------------------------------------------------- */ elenme = Elen [me] ; nvpiv = Nv [me] ; ASSERT (nvpiv > 0) ; nel += nvpiv ; /* ========================================================================= */ /* CONSTRUCT NEW ELEMENT */ /* ========================================================================= */ /* ----------------------------------------------------------------- * At this point, me is the pivotal supervariable. It will be * converted into the current element. Scan list of the pivotal * supervariable, me, setting tree pointers and constructing new list * of supervariables for the new element, me. p is a pointer to the * current position in the old list. * ----------------------------------------------------------------- */ /* flag the variable "me" as being in Lme by negating Nv [me] */ Nv [me] = -nvpiv ; degme = 0 ; ASSERT (Pe [me] >= 0 && Pe [me] < iwlen) ; if (elenme == 0) { /* ------------------------------------------------------------- */ /* construct the new element in place */ /* ------------------------------------------------------------- */ pme1 = Pe [me] ; pme2 = pme1 - 1 ; for (p = pme1 ; p <= pme1 + Len [me] - 1 ; p++) { i = Iw [p] ; ASSERT (i >= 0 && i < n && Nv [i] >= 0) ; nvi = Nv [i] ; if (nvi > 0) { /* ----------------------------------------------------- */ /* i is a principal variable not yet placed in Lme. */ /* store i in new list */ /* ----------------------------------------------------- */ /* flag i as being in Lme by negating Nv [i] */ degme += nvi ; Nv [i] = -nvi ; Iw [++pme2] = i ; /* ----------------------------------------------------- */ /* remove variable i from degree list. */ /* ----------------------------------------------------- */ ilast = Last [i] ; inext = Next [i] ; ASSERT (ilast >= EMPTY && ilast < n) ; ASSERT (inext >= EMPTY && inext < n) ; if (inext != EMPTY) Last [inext] = ilast ; if (ilast != EMPTY) { Next [ilast] = inext ; } else { /* i is at the head of the degree list */ ASSERT (Degree [i] >= 0 && Degree [i] < n) ; Head [Degree [i]] = inext ; } } } } else { /* ------------------------------------------------------------- */ /* construct the new element in empty space, Iw [pfree ...] */ /* ------------------------------------------------------------- */ p = Pe [me] ; pme1 = pfree ; slenme = Len [me] - elenme ; for (knt1 = 1 ; knt1 <= elenme + 1 ; knt1++) { if (knt1 > elenme) { /* search the supervariables in me. */ e = me ; pj = p ; ln = slenme ; AMD_DEBUG2 (("Search sv: "ID" "ID" "ID"\n", me,pj,ln)) ; } else { /* search the elements in me. */ e = Iw [p++] ; ASSERT (e >= 0 && e < n) ; pj = Pe [e] ; ln = Len [e] ; AMD_DEBUG2 (("Search element e "ID" in me "ID"\n", e,me)) ; ASSERT (Elen [e] < EMPTY && W [e] > 0 && pj >= 0) ; } ASSERT (ln >= 0 && (ln == 0 || (pj >= 0 && pj < iwlen))) ; /* --------------------------------------------------------- * search for different supervariables and add them to the * new list, compressing when necessary. this loop is * executed once for each element in the list and once for * all the supervariables in the list. * --------------------------------------------------------- */ for (knt2 = 1 ; knt2 <= ln ; knt2++) { i = Iw [pj++] ; ASSERT (i >= 0 && i < n && (i == me || Elen [i] >= EMPTY)); nvi = Nv [i] ; AMD_DEBUG2 ((": "ID" "ID" "ID" "ID"\n", i, Elen [i], Nv [i], wflg)) ; if (nvi > 0) { /* ------------------------------------------------- */ /* compress Iw, if necessary */ /* ------------------------------------------------- */ if (pfree >= iwlen) { AMD_DEBUG1 (("GARBAGE COLLECTION\n")) ; /* prepare for compressing Iw by adjusting pointers * and lengths so that the lists being searched in * the inner and outer loops contain only the * remaining entries. */ Pe [me] = p ; Len [me] -= knt1 ; /* check if nothing left of supervariable me */ if (Len [me] == 0) Pe [me] = EMPTY ; Pe [e] = pj ; Len [e] = ln - knt2 ; /* nothing left of element e */ if (Len [e] == 0) Pe [e] = EMPTY ; ncmpa++ ; /* one more garbage collection */ /* store first entry of each object in Pe */ /* FLIP the first entry in each object */ for (j = 0 ; j < n ; j++) { pn = Pe [j] ; if (pn >= 0) { ASSERT (pn >= 0 && pn < iwlen) ; Pe [j] = Iw [pn] ; Iw [pn] = FLIP (j) ; } } /* psrc/pdst point to source/destination */ psrc = 0 ; pdst = 0 ; pend = pme1 - 1 ; while (psrc <= pend) { /* search for next FLIP'd entry */ j = FLIP (Iw [psrc++]) ; if (j >= 0) { AMD_DEBUG2 (("Got object j: "ID"\n", j)) ; Iw [pdst] = Pe [j] ; Pe [j] = pdst++ ; lenj = Len [j] ; /* copy from source to destination */ for (knt3 = 0 ; knt3 <= lenj - 2 ; knt3++) { Iw [pdst++] = Iw [psrc++] ; } } } /* move the new partially-constructed element */ p1 = pdst ; for (psrc = pme1 ; psrc <= pfree-1 ; psrc++) { Iw [pdst++] = Iw [psrc] ; } pme1 = p1 ; pfree = pdst ; pj = Pe [e] ; p = Pe [me] ; } /* ------------------------------------------------- */ /* i is a principal variable not yet placed in Lme */ /* store i in new list */ /* ------------------------------------------------- */ /* flag i as being in Lme by negating Nv [i] */ degme += nvi ; Nv [i] = -nvi ; Iw [pfree++] = i ; AMD_DEBUG2 ((" s: "ID" nv "ID"\n", i, Nv [i])); /* ------------------------------------------------- */ /* remove variable i from degree link list */ /* ------------------------------------------------- */ ilast = Last [i] ; inext = Next [i] ; ASSERT (ilast >= EMPTY && ilast < n) ; ASSERT (inext >= EMPTY && inext < n) ; if (inext != EMPTY) Last [inext] = ilast ; if (ilast != EMPTY) { Next [ilast] = inext ; } else { /* i is at the head of the degree list */ ASSERT (Degree [i] >= 0 && Degree [i] < n) ; Head [Degree [i]] = inext ; } } } if (e != me) { /* set tree pointer and flag to indicate element e is * absorbed into new element me (the parent of e is me) */ AMD_DEBUG1 ((" Element "ID" => "ID"\n", e, me)) ; Pe [e] = FLIP (me) ; W [e] = 0 ; } } pme2 = pfree - 1 ; } /* ----------------------------------------------------------------- */ /* me has now been converted into an element in Iw [pme1..pme2] */ /* ----------------------------------------------------------------- */ /* degme holds the external degree of new element */ Degree [me] = degme ; Pe [me] = pme1 ; Len [me] = pme2 - pme1 + 1 ; ASSERT (Pe [me] >= 0 && Pe [me] < iwlen) ; Elen [me] = FLIP (nvpiv + degme) ; /* FLIP (Elen (me)) is now the degree of pivot (including * diagonal part). */ #ifndef NDEBUG AMD_DEBUG2 (("New element structure: length= "ID"\n", pme2-pme1+1)) ; for (pme = pme1 ; pme <= pme2 ; pme++) AMD_DEBUG3 ((" "ID"", Iw[pme])); AMD_DEBUG3 (("\n")) ; #endif /* ----------------------------------------------------------------- */ /* make sure that wflg is not too large. */ /* ----------------------------------------------------------------- */ /* With the current value of wflg, wflg+n must not cause integer * overflow */ wflg = clear_flag (wflg, wbig, W, n) ; /* ========================================================================= */ /* COMPUTE (W [e] - wflg) = |Le\Lme| FOR ALL ELEMENTS */ /* ========================================================================= */ /* ----------------------------------------------------------------- * Scan 1: compute the external degrees of previous elements with * respect to the current element. That is: * (W [e] - wflg) = |Le \ Lme| * for each element e that appears in any supervariable in Lme. The * notation Le refers to the pattern (list of supervariables) of a * previous element e, where e is not yet absorbed, stored in * Iw [Pe [e] + 1 ... Pe [e] + Len [e]]. The notation Lme * refers to the pattern of the current element (stored in * Iw [pme1..pme2]). If aggressive absorption is enabled, and * (W [e] - wflg) becomes zero, then the element e will be absorbed * in Scan 2. * ----------------------------------------------------------------- */ AMD_DEBUG2 (("me: ")) ; for (pme = pme1 ; pme <= pme2 ; pme++) { i = Iw [pme] ; ASSERT (i >= 0 && i < n) ; eln = Elen [i] ; AMD_DEBUG3 ((""ID" Elen "ID": \n", i, eln)) ; if (eln > 0) { /* note that Nv [i] has been negated to denote i in Lme: */ nvi = -Nv [i] ; ASSERT (nvi > 0 && Pe [i] >= 0 && Pe [i] < iwlen) ; wnvi = wflg - nvi ; for (p = Pe [i] ; p <= Pe [i] + eln - 1 ; p++) { e = Iw [p] ; ASSERT (e >= 0 && e < n) ; we = W [e] ; AMD_DEBUG4 ((" e "ID" we "ID" ", e, we)) ; if (we >= wflg) { /* unabsorbed element e has been seen in this loop */ AMD_DEBUG4 ((" unabsorbed, first time seen")) ; we -= nvi ; } else if (we != 0) { /* e is an unabsorbed element */ /* this is the first we have seen e in all of Scan 1 */ AMD_DEBUG4 ((" unabsorbed")) ; we = Degree [e] + wnvi ; } AMD_DEBUG4 (("\n")) ; W [e] = we ; } } } AMD_DEBUG2 (("\n")) ; /* ========================================================================= */ /* DEGREE UPDATE AND ELEMENT ABSORPTION */ /* ========================================================================= */ /* ----------------------------------------------------------------- * Scan 2: for each i in Lme, sum up the degree of Lme (which is * degme), plus the sum of the external degrees of each Le for the * elements e appearing within i, plus the supervariables in i. * Place i in hash list. * ----------------------------------------------------------------- */ for (pme = pme1 ; pme <= pme2 ; pme++) { i = Iw [pme] ; ASSERT (i >= 0 && i < n && Nv [i] < 0 && Elen [i] >= 0) ; AMD_DEBUG2 (("Updating: i "ID" "ID" "ID"\n", i, Elen[i], Len [i])); p1 = Pe [i] ; p2 = p1 + Elen [i] - 1 ; pn = p1 ; hash = 0 ; deg = 0 ; ASSERT (p1 >= 0 && p1 < iwlen && p2 >= -1 && p2 < iwlen) ; /* ------------------------------------------------------------- */ /* scan the element list associated with supervariable i */ /* ------------------------------------------------------------- */ /* UMFPACK/MA38-style approximate degree: */ if (aggressive) { for (p = p1 ; p <= p2 ; p++) { e = Iw [p] ; ASSERT (e >= 0 && e < n) ; we = W [e] ; if (we != 0) { /* e is an unabsorbed element */ /* dext = | Le \ Lme | */ dext = we - wflg ; if (dext > 0) { deg += dext ; Iw [pn++] = e ; hash += e ; AMD_DEBUG4 ((" e: "ID" hash = "ID"\n",e,hash)) ; } else { /* external degree of e is zero, absorb e into me*/ AMD_DEBUG1 ((" Element "ID" =>"ID" (aggressive)\n", e, me)) ; ASSERT (dext == 0) ; Pe [e] = FLIP (me) ; W [e] = 0 ; } } } } else { for (p = p1 ; p <= p2 ; p++) { e = Iw [p] ; ASSERT (e >= 0 && e < n) ; we = W [e] ; if (we != 0) { /* e is an unabsorbed element */ dext = we - wflg ; ASSERT (dext >= 0) ; deg += dext ; Iw [pn++] = e ; hash += e ; AMD_DEBUG4 ((" e: "ID" hash = "ID"\n",e,hash)) ; } } } /* count the number of elements in i (including me): */ Elen [i] = pn - p1 + 1 ; /* ------------------------------------------------------------- */ /* scan the supervariables in the list associated with i */ /* ------------------------------------------------------------- */ /* The bulk of the AMD run time is typically spent in this loop, * particularly if the matrix has many dense rows that are not * removed prior to ordering. */ p3 = pn ; p4 = p1 + Len [i] ; for (p = p2 + 1 ; p < p4 ; p++) { j = Iw [p] ; ASSERT (j >= 0 && j < n) ; nvj = Nv [j] ; if (nvj > 0) { /* j is unabsorbed, and not in Lme. */ /* add to degree and add to new list */ deg += nvj ; Iw [pn++] = j ; hash += j ; AMD_DEBUG4 ((" s: "ID" hash "ID" Nv[j]= "ID"\n", j, hash, nvj)) ; } } /* ------------------------------------------------------------- */ /* update the degree and check for mass elimination */ /* ------------------------------------------------------------- */ /* with aggressive absorption, deg==0 is identical to the * Elen [i] == 1 && p3 == pn test, below. */ ASSERT (IMPLIES (aggressive, (deg==0) == (Elen[i]==1 && p3==pn))) ; if (Elen [i] == 1 && p3 == pn) { /* --------------------------------------------------------- */ /* mass elimination */ /* --------------------------------------------------------- */ /* There is nothing left of this node except for an edge to * the current pivot element. Elen [i] is 1, and there are * no variables adjacent to node i. Absorb i into the * current pivot element, me. Note that if there are two or * more mass eliminations, fillin due to mass elimination is * possible within the nvpiv-by-nvpiv pivot block. It is this * step that causes AMD's analysis to be an upper bound. * * The reason is that the selected pivot has a lower * approximate degree than the true degree of the two mass * eliminated nodes. There is no edge between the two mass * eliminated nodes. They are merged with the current pivot * anyway. * * No fillin occurs in the Schur complement, in any case, * and this effect does not decrease the quality of the * ordering itself, just the quality of the nonzero and * flop count analysis. It also means that the post-ordering * is not an exact elimination tree post-ordering. */ AMD_DEBUG1 ((" MASS i "ID" => parent e "ID"\n", i, me)) ; Pe [i] = FLIP (me) ; nvi = -Nv [i] ; degme -= nvi ; nvpiv += nvi ; nel += nvi ; Nv [i] = 0 ; Elen [i] = EMPTY ; } else { /* --------------------------------------------------------- */ /* update the upper-bound degree of i */ /* --------------------------------------------------------- */ /* the following degree does not yet include the size * of the current element, which is added later: */ Degree [i] = MIN (Degree [i], deg) ; /* --------------------------------------------------------- */ /* add me to the list for i */ /* --------------------------------------------------------- */ /* move first supervariable to end of list */ Iw [pn] = Iw [p3] ; /* move first element to end of element part of list */ Iw [p3] = Iw [p1] ; /* add new element, me, to front of list. */ Iw [p1] = me ; /* store the new length of the list in Len [i] */ Len [i] = pn - p1 + 1 ; /* --------------------------------------------------------- */ /* place in hash bucket. Save hash key of i in Last [i]. */ /* --------------------------------------------------------- */ /* NOTE: this can fail if hash is negative, because the ANSI C * standard does not define a % b when a and/or b are negative. * That's why hash is defined as an unsigned Int, to avoid this * problem. */ hash = hash % n ; ASSERT (((Int) hash) >= 0 && ((Int) hash) < n) ; /* if the Hhead array is not used: */ j = Head [hash] ; if (j <= EMPTY) { /* degree list is empty, hash head is FLIP (j) */ Next [i] = FLIP (j) ; Head [hash] = FLIP (i) ; } else { /* degree list is not empty, use Last [Head [hash]] as * hash head. */ Next [i] = Last [j] ; Last [j] = i ; } /* if a separate Hhead array is used: * Next [i] = Hhead [hash] ; Hhead [hash] = i ; */ Last [i] = hash ; } } Degree [me] = degme ; /* ----------------------------------------------------------------- */ /* Clear the counter array, W [...], by incrementing wflg. */ /* ----------------------------------------------------------------- */ /* make sure that wflg+n does not cause integer overflow */ lemax = MAX (lemax, degme) ; wflg += lemax ; wflg = clear_flag (wflg, wbig, W, n) ; /* at this point, W [0..n-1] < wflg holds */ /* ========================================================================= */ /* SUPERVARIABLE DETECTION */ /* ========================================================================= */ AMD_DEBUG1 (("Detecting supervariables:\n")) ; for (pme = pme1 ; pme <= pme2 ; pme++) { i = Iw [pme] ; ASSERT (i >= 0 && i < n) ; AMD_DEBUG2 (("Consider i "ID" nv "ID"\n", i, Nv [i])) ; if (Nv [i] < 0) { /* i is a principal variable in Lme */ /* --------------------------------------------------------- * examine all hash buckets with 2 or more variables. We do * this by examing all unique hash keys for supervariables in * the pattern Lme of the current element, me * --------------------------------------------------------- */ /* let i = head of hash bucket, and empty the hash bucket */ ASSERT (Last [i] >= 0 && Last [i] < n) ; hash = Last [i] ; /* if Hhead array is not used: */ j = Head [hash] ; if (j == EMPTY) { /* hash bucket and degree list are both empty */ i = EMPTY ; } else if (j < EMPTY) { /* degree list is empty */ i = FLIP (j) ; Head [hash] = EMPTY ; } else { /* degree list is not empty, restore Last [j] of head j */ i = Last [j] ; Last [j] = EMPTY ; } /* if separate Hhead array is used: * i = Hhead [hash] ; Hhead [hash] = EMPTY ; */ ASSERT (i >= EMPTY && i < n) ; AMD_DEBUG2 (("----i "ID" hash "ID"\n", i, hash)) ; while (i != EMPTY && Next [i] != EMPTY) { /* ----------------------------------------------------- * this bucket has one or more variables following i. * scan all of them to see if i can absorb any entries * that follow i in hash bucket. Scatter i into w. * ----------------------------------------------------- */ ln = Len [i] ; eln = Elen [i] ; ASSERT (ln >= 0 && eln >= 0) ; ASSERT (Pe [i] >= 0 && Pe [i] < iwlen) ; /* do not flag the first element in the list (me) */ for (p = Pe [i] + 1 ; p <= Pe [i] + ln - 1 ; p++) { ASSERT (Iw [p] >= 0 && Iw [p] < n) ; W [Iw [p]] = wflg ; } /* ----------------------------------------------------- */ /* scan every other entry j following i in bucket */ /* ----------------------------------------------------- */ jlast = i ; j = Next [i] ; ASSERT (j >= EMPTY && j < n) ; while (j != EMPTY) { /* ------------------------------------------------- */ /* check if j and i have identical nonzero pattern */ /* ------------------------------------------------- */ AMD_DEBUG3 (("compare i "ID" and j "ID"\n", i,j)) ; /* check if i and j have the same Len and Elen */ ASSERT (Len [j] >= 0 && Elen [j] >= 0) ; ASSERT (Pe [j] >= 0 && Pe [j] < iwlen) ; ok = (Len [j] == ln) && (Elen [j] == eln) ; /* skip the first element in the list (me) */ for (p = Pe [j] + 1 ; ok && p <= Pe [j] + ln - 1 ; p++) { ASSERT (Iw [p] >= 0 && Iw [p] < n) ; if (W [Iw [p]] != wflg) ok = 0 ; } if (ok) { /* --------------------------------------------- */ /* found it! j can be absorbed into i */ /* --------------------------------------------- */ AMD_DEBUG1 (("found it! j "ID" => i "ID"\n", j,i)); Pe [j] = FLIP (i) ; /* both Nv [i] and Nv [j] are negated since they */ /* are in Lme, and the absolute values of each */ /* are the number of variables in i and j: */ Nv [i] += Nv [j] ; Nv [j] = 0 ; Elen [j] = EMPTY ; /* delete j from hash bucket */ ASSERT (j != Next [j]) ; j = Next [j] ; Next [jlast] = j ; } else { /* j cannot be absorbed into i */ jlast = j ; ASSERT (j != Next [j]) ; j = Next [j] ; } ASSERT (j >= EMPTY && j < n) ; } /* ----------------------------------------------------- * no more variables can be absorbed into i * go to next i in bucket and clear flag array * ----------------------------------------------------- */ wflg++ ; i = Next [i] ; ASSERT (i >= EMPTY && i < n) ; } } } AMD_DEBUG2 (("detect done\n")) ; /* ========================================================================= */ /* RESTORE DEGREE LISTS AND REMOVE NONPRINCIPAL SUPERVARIABLES FROM ELEMENT */ /* ========================================================================= */ p = pme1 ; nleft = n - nel ; for (pme = pme1 ; pme <= pme2 ; pme++) { i = Iw [pme] ; ASSERT (i >= 0 && i < n) ; nvi = -Nv [i] ; AMD_DEBUG3 (("Restore i "ID" "ID"\n", i, nvi)) ; if (nvi > 0) { /* i is a principal variable in Lme */ /* restore Nv [i] to signify that i is principal */ Nv [i] = nvi ; /* --------------------------------------------------------- */ /* compute the external degree (add size of current element) */ /* --------------------------------------------------------- */ deg = Degree [i] + degme - nvi ; deg = MIN (deg, nleft - nvi) ; ASSERT (IMPLIES (aggressive, deg > 0) && deg >= 0 && deg < n) ; /* --------------------------------------------------------- */ /* place the supervariable at the head of the degree list */ /* --------------------------------------------------------- */ inext = Head [deg] ; ASSERT (inext >= EMPTY && inext < n) ; if (inext != EMPTY) Last [inext] = i ; Next [i] = inext ; Last [i] = EMPTY ; Head [deg] = i ; /* --------------------------------------------------------- */ /* save the new degree, and find the minimum degree */ /* --------------------------------------------------------- */ mindeg = MIN (mindeg, deg) ; Degree [i] = deg ; /* --------------------------------------------------------- */ /* place the supervariable in the element pattern */ /* --------------------------------------------------------- */ Iw [p++] = i ; } } AMD_DEBUG2 (("restore done\n")) ; /* ========================================================================= */ /* FINALIZE THE NEW ELEMENT */ /* ========================================================================= */ AMD_DEBUG2 (("ME = "ID" DONE\n", me)) ; Nv [me] = nvpiv ; /* save the length of the list for the new element me */ Len [me] = p - pme1 ; if (Len [me] == 0) { /* there is nothing left of the current pivot element */ /* it is a root of the assembly tree */ Pe [me] = EMPTY ; W [me] = 0 ; } if (elenme != 0) { /* element was not constructed in place: deallocate part of */ /* it since newly nonprincipal variables may have been removed */ pfree = p ; } /* The new element has nvpiv pivots and the size of the contribution * block for a multifrontal method is degme-by-degme, not including * the "dense" rows/columns. If the "dense" rows/columns are included, * the frontal matrix is no larger than * (degme+ndense)-by-(degme+ndense). */ if (Info != (double *) NULL) { f = nvpiv ; r = degme + ndense ; dmax = MAX (dmax, f + r) ; /* number of nonzeros in L (excluding the diagonal) */ lnzme = f*r + (f-1)*f/2 ; lnz += lnzme ; /* number of divide operations for LDL' and for LU */ ndiv += lnzme ; /* number of multiply-subtract pairs for LU */ s = f*r*r + r*(f-1)*f + (f-1)*f*(2*f-1)/6 ; nms_lu += s ; /* number of multiply-subtract pairs for LDL' */ nms_ldl += (s + lnzme)/2 ; } #ifndef NDEBUG AMD_DEBUG2 (("finalize done nel "ID" n "ID"\n ::::\n", nel, n)) ; for (pme = Pe [me] ; pme <= Pe [me] + Len [me] - 1 ; pme++) { AMD_DEBUG3 ((" "ID"", Iw [pme])) ; } AMD_DEBUG3 (("\n")) ; #endif } /* ========================================================================= */ /* DONE SELECTING PIVOTS */ /* ========================================================================= */ if (Info != (double *) NULL) { /* count the work to factorize the ndense-by-ndense submatrix */ f = ndense ; dmax = MAX (dmax, (double) ndense) ; /* number of nonzeros in L (excluding the diagonal) */ lnzme = (f-1)*f/2 ; lnz += lnzme ; /* number of divide operations for LDL' and for LU */ ndiv += lnzme ; /* number of multiply-subtract pairs for LU */ s = (f-1)*f*(2*f-1)/6 ; nms_lu += s ; /* number of multiply-subtract pairs for LDL' */ nms_ldl += (s + lnzme)/2 ; /* number of nz's in L (excl. diagonal) */ Info [AMD_LNZ] = lnz ; /* number of divide ops for LU and LDL' */ Info [AMD_NDIV] = ndiv ; /* number of multiply-subtract pairs for LDL' */ Info [AMD_NMULTSUBS_LDL] = nms_ldl ; /* number of multiply-subtract pairs for LU */ Info [AMD_NMULTSUBS_LU] = nms_lu ; /* number of "dense" rows/columns */ Info [AMD_NDENSE] = ndense ; /* largest front is dmax-by-dmax */ Info [AMD_DMAX] = dmax ; /* number of garbage collections in AMD */ Info [AMD_NCMPA] = ncmpa ; /* successful ordering */ Info [AMD_STATUS] = AMD_OK ; } /* ========================================================================= */ /* POST-ORDERING */ /* ========================================================================= */ /* ------------------------------------------------------------------------- * Variables at this point: * * Pe: holds the elimination tree. The parent of j is FLIP (Pe [j]), * or EMPTY if j is a root. The tree holds both elements and * non-principal (unordered) variables absorbed into them. * Dense variables are non-principal and unordered. * * Elen: holds the size of each element, including the diagonal part. * FLIP (Elen [e]) > 0 if e is an element. For unordered * variables i, Elen [i] is EMPTY. * * Nv: Nv [e] > 0 is the number of pivots represented by the element e. * For unordered variables i, Nv [i] is zero. * * Contents no longer needed: * W, Iw, Len, Degree, Head, Next, Last. * * The matrix itself has been destroyed. * * n: the size of the matrix. * No other scalars needed (pfree, iwlen, etc.) * ------------------------------------------------------------------------- */ /* restore Pe */ for (i = 0 ; i < n ; i++) { Pe [i] = FLIP (Pe [i]) ; } /* restore Elen, for output information, and for postordering */ for (i = 0 ; i < n ; i++) { Elen [i] = FLIP (Elen [i]) ; } /* Now the parent of j is Pe [j], or EMPTY if j is a root. Elen [e] > 0 * is the size of element e. Elen [i] is EMPTY for unordered variable i. */ #ifndef NDEBUG AMD_DEBUG2 (("\nTree:\n")) ; for (i = 0 ; i < n ; i++) { AMD_DEBUG2 ((" "ID" parent: "ID" ", i, Pe [i])) ; ASSERT (Pe [i] >= EMPTY && Pe [i] < n) ; if (Nv [i] > 0) { /* this is an element */ e = i ; AMD_DEBUG2 ((" element, size is "ID"\n", Elen [i])) ; ASSERT (Elen [e] > 0) ; } AMD_DEBUG2 (("\n")) ; } AMD_DEBUG2 (("\nelements:\n")) ; for (e = 0 ; e < n ; e++) { if (Nv [e] > 0) { AMD_DEBUG3 (("Element e= "ID" size "ID" nv "ID" \n", e, Elen [e], Nv [e])) ; } } AMD_DEBUG2 (("\nvariables:\n")) ; for (i = 0 ; i < n ; i++) { Int cnt ; if (Nv [i] == 0) { AMD_DEBUG3 (("i unordered: "ID"\n", i)) ; j = Pe [i] ; cnt = 0 ; AMD_DEBUG3 ((" j: "ID"\n", j)) ; if (j == EMPTY) { AMD_DEBUG3 ((" i is a dense variable\n")) ; } else { ASSERT (j >= 0 && j < n) ; while (Nv [j] == 0) { AMD_DEBUG3 ((" j : "ID"\n", j)) ; j = Pe [j] ; AMD_DEBUG3 ((" j:: "ID"\n", j)) ; cnt++ ; if (cnt > n) break ; } e = j ; AMD_DEBUG3 ((" got to e: "ID"\n", e)) ; } } } #endif /* ========================================================================= */ /* compress the paths of the variables */ /* ========================================================================= */ for (i = 0 ; i < n ; i++) { if (Nv [i] == 0) { /* ------------------------------------------------------------- * i is an un-ordered row. Traverse the tree from i until * reaching an element, e. The element, e, was the principal * supervariable of i and all nodes in the path from i to when e * was selected as pivot. * ------------------------------------------------------------- */ AMD_DEBUG1 (("Path compression, i unordered: "ID"\n", i)) ; j = Pe [i] ; ASSERT (j >= EMPTY && j < n) ; AMD_DEBUG3 ((" j: "ID"\n", j)) ; if (j == EMPTY) { /* Skip a dense variable. It has no parent. */ AMD_DEBUG3 ((" i is a dense variable\n")) ; continue ; } /* while (j is a variable) */ while (Nv [j] == 0) { AMD_DEBUG3 ((" j : "ID"\n", j)) ; j = Pe [j] ; AMD_DEBUG3 ((" j:: "ID"\n", j)) ; ASSERT (j >= 0 && j < n) ; } /* got to an element e */ e = j ; AMD_DEBUG3 (("got to e: "ID"\n", e)) ; /* ------------------------------------------------------------- * traverse the path again from i to e, and compress the path * (all nodes point to e). Path compression allows this code to * compute in O(n) time. * ------------------------------------------------------------- */ j = i ; /* while (j is a variable) */ while (Nv [j] == 0) { jnext = Pe [j] ; AMD_DEBUG3 (("j "ID" jnext "ID"\n", j, jnext)) ; Pe [j] = e ; j = jnext ; ASSERT (j >= 0 && j < n) ; } } } /* ========================================================================= */ /* postorder the assembly tree */ /* ========================================================================= */ AMD_postorder (n, Pe, Nv, Elen, W, /* output order */ Head, Next, Last) ; /* workspace */ /* ========================================================================= */ /* compute output permutation and inverse permutation */ /* ========================================================================= */ /* W [e] = k means that element e is the kth element in the new * order. e is in the range 0 to n-1, and k is in the range 0 to * the number of elements. Use Head for inverse order. */ for (k = 0 ; k < n ; k++) { Head [k] = EMPTY ; Next [k] = EMPTY ; } for (e = 0 ; e < n ; e++) { k = W [e] ; ASSERT ((k == EMPTY) == (Nv [e] == 0)) ; if (k != EMPTY) { ASSERT (k >= 0 && k < n) ; Head [k] = e ; } } /* construct output inverse permutation in Next, * and permutation in Last */ nel = 0 ; for (k = 0 ; k < n ; k++) { e = Head [k] ; if (e == EMPTY) break ; ASSERT (e >= 0 && e < n && Nv [e] > 0) ; Next [e] = nel ; nel += Nv [e] ; } ASSERT (nel == n - ndense) ; /* order non-principal variables (dense, & those merged into supervar's) */ for (i = 0 ; i < n ; i++) { if (Nv [i] == 0) { e = Pe [i] ; ASSERT (e >= EMPTY && e < n) ; if (e != EMPTY) { /* This is an unordered variable that was merged * into element e via supernode detection or mass * elimination of i when e became the pivot element. * Place i in order just before e. */ ASSERT (Next [i] == EMPTY && Nv [e] > 0) ; Next [i] = Next [e] ; Next [e]++ ; } else { /* This is a dense unordered variable, with no parent. * Place it last in the output order. */ Next [i] = nel++ ; } } } ASSERT (nel == n) ; AMD_DEBUG2 (("\n\nPerm:\n")) ; for (i = 0 ; i < n ; i++) { k = Next [i] ; ASSERT (k >= 0 && k < n) ; Last [k] = i ; AMD_DEBUG2 ((" perm ["ID"] = "ID"\n", k, i)) ; } } SuiteSparse/AMD/Source/amd_order.c0000644001170100242450000001351410616426526015724 0ustar davisfac/* ========================================================================= */ /* === AMD_order =========================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ /* User-callable AMD minimum degree ordering routine. See amd.h for * documentation. */ #include "amd_internal.h" /* ========================================================================= */ /* === AMD_order =========================================================== */ /* ========================================================================= */ GLOBAL Int AMD_order ( Int n, const Int Ap [ ], const Int Ai [ ], Int P [ ], double Control [ ], double Info [ ] ) { Int *Len, *S, nz, i, *Pinv, info, status, *Rp, *Ri, *Cp, *Ci, ok ; size_t nzaat, slen ; double mem = 0 ; #ifndef NDEBUG AMD_debug_init ("amd") ; #endif /* clear the Info array, if it exists */ info = Info != (double *) NULL ; if (info) { for (i = 0 ; i < AMD_INFO ; i++) { Info [i] = EMPTY ; } Info [AMD_N] = n ; Info [AMD_STATUS] = AMD_OK ; } /* make sure inputs exist and n is >= 0 */ if (Ai == (Int *) NULL || Ap == (Int *) NULL || P == (Int *) NULL || n < 0) { if (info) Info [AMD_STATUS] = AMD_INVALID ; return (AMD_INVALID) ; /* arguments are invalid */ } if (n == 0) { return (AMD_OK) ; /* n is 0 so there's nothing to do */ } nz = Ap [n] ; if (info) { Info [AMD_NZ] = nz ; } if (nz < 0) { if (info) Info [AMD_STATUS] = AMD_INVALID ; return (AMD_INVALID) ; } /* check if n or nz will cause size_t overflow */ if (((size_t) n) >= SIZE_T_MAX / sizeof (Int) || ((size_t) nz) >= SIZE_T_MAX / sizeof (Int)) { if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ; return (AMD_OUT_OF_MEMORY) ; /* problem too large */ } /* check the input matrix: AMD_OK, AMD_INVALID, or AMD_OK_BUT_JUMBLED */ status = AMD_valid (n, n, Ap, Ai) ; if (status == AMD_INVALID) { if (info) Info [AMD_STATUS] = AMD_INVALID ; return (AMD_INVALID) ; /* matrix is invalid */ } /* allocate two size-n integer workspaces */ Len = amd_malloc (n * sizeof (Int)) ; Pinv = amd_malloc (n * sizeof (Int)) ; mem += n ; mem += n ; if (!Len || !Pinv) { /* :: out of memory :: */ amd_free (Len) ; amd_free (Pinv) ; if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ; return (AMD_OUT_OF_MEMORY) ; } if (status == AMD_OK_BUT_JUMBLED) { /* sort the input matrix and remove duplicate entries */ AMD_DEBUG1 (("Matrix is jumbled\n")) ; Rp = amd_malloc ((n+1) * sizeof (Int)) ; Ri = amd_malloc (MAX (nz,1) * sizeof (Int)) ; mem += (n+1) ; mem += MAX (nz,1) ; if (!Rp || !Ri) { /* :: out of memory :: */ amd_free (Rp) ; amd_free (Ri) ; amd_free (Len) ; amd_free (Pinv) ; if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ; return (AMD_OUT_OF_MEMORY) ; } /* use Len and Pinv as workspace to create R = A' */ AMD_preprocess (n, Ap, Ai, Rp, Ri, Len, Pinv) ; Cp = Rp ; Ci = Ri ; } else { /* order the input matrix as-is. No need to compute R = A' first */ Rp = NULL ; Ri = NULL ; Cp = (Int *) Ap ; Ci = (Int *) Ai ; } /* --------------------------------------------------------------------- */ /* determine the symmetry and count off-diagonal nonzeros in A+A' */ /* --------------------------------------------------------------------- */ nzaat = AMD_aat (n, Cp, Ci, Len, P, Info) ; AMD_DEBUG1 (("nzaat: %g\n", (double) nzaat)) ; ASSERT ((MAX (nz-n, 0) <= nzaat) && (nzaat <= 2 * (size_t) nz)) ; /* --------------------------------------------------------------------- */ /* allocate workspace for matrix, elbow room, and 6 size-n vectors */ /* --------------------------------------------------------------------- */ S = NULL ; slen = nzaat ; /* space for matrix */ ok = ((slen + nzaat/5) >= slen) ; /* check for size_t overflow */ slen += nzaat/5 ; /* add elbow room */ for (i = 0 ; ok && i < 7 ; i++) { ok = ((slen + n) > slen) ; /* check for size_t overflow */ slen += n ; /* size-n elbow room, 6 size-n work */ } mem += slen ; ok = ok && (slen < SIZE_T_MAX / sizeof (Int)) ; /* check for overflow */ ok = ok && (slen < Int_MAX) ; /* S[i] for Int i must be OK */ if (ok) { S = amd_malloc (slen * sizeof (Int)) ; } AMD_DEBUG1 (("slen %g\n", (double) slen)) ; if (!S) { /* :: out of memory :: (or problem too large) */ amd_free (Rp) ; amd_free (Ri) ; amd_free (Len) ; amd_free (Pinv) ; if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ; return (AMD_OUT_OF_MEMORY) ; } if (info) { /* memory usage, in bytes. */ Info [AMD_MEMORY] = mem * sizeof (Int) ; } /* --------------------------------------------------------------------- */ /* order the matrix */ /* --------------------------------------------------------------------- */ AMD_1 (n, Cp, Ci, P, Pinv, Len, slen, S, Control, Info) ; /* --------------------------------------------------------------------- */ /* free the workspace */ /* --------------------------------------------------------------------- */ amd_free (Rp) ; amd_free (Ri) ; amd_free (Len) ; amd_free (Pinv) ; amd_free (S) ; if (info) Info [AMD_STATUS] = status ; return (status) ; /* successful ordering */ } SuiteSparse/AMD/Source/amd_dump.c0000644001170100242450000001174410616402631015550 0ustar davisfac/* ========================================================================= */ /* === AMD_dump ============================================================ */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ /* Debugging routines for AMD. Not used if NDEBUG is not defined at compile- * time (the default). See comments in amd_internal.h on how to enable * debugging. Not user-callable. */ #include "amd_internal.h" #ifndef NDEBUG /* This global variable is present only when debugging */ GLOBAL Int AMD_debug = -999 ; /* default is no debug printing */ /* ========================================================================= */ /* === AMD_debug_init ====================================================== */ /* ========================================================================= */ /* Sets the debug print level, by reading the file debug.amd (if it exists) */ GLOBAL void AMD_debug_init ( char *s ) { FILE *f ; f = fopen ("debug.amd", "r") ; if (f == (FILE *) NULL) { AMD_debug = -999 ; } else { fscanf (f, ID, &AMD_debug) ; fclose (f) ; } if (AMD_debug >= 0) { printf ("%s: AMD_debug_init, D= "ID"\n", s, AMD_debug) ; } } /* ========================================================================= */ /* === AMD_dump ============================================================ */ /* ========================================================================= */ /* Dump AMD's data structure, except for the hash buckets. This routine * cannot be called when the hash buckets are non-empty. */ GLOBAL void AMD_dump ( Int n, /* A is n-by-n */ Int Pe [ ], /* pe [0..n-1]: index in iw of start of row i */ Int Iw [ ], /* workspace of size iwlen, iwlen [0..pfree-1] * holds the matrix on input */ Int Len [ ], /* len [0..n-1]: length for row i */ Int iwlen, /* length of iw */ Int pfree, /* iw [pfree ... iwlen-1] is empty on input */ Int Nv [ ], /* nv [0..n-1] */ Int Next [ ], /* next [0..n-1] */ Int Last [ ], /* last [0..n-1] */ Int Head [ ], /* head [0..n-1] */ Int Elen [ ], /* size n */ Int Degree [ ], /* size n */ Int W [ ], /* size n */ Int nel ) { Int i, pe, elen, nv, len, e, p, k, j, deg, w, cnt, ilast ; if (AMD_debug < 0) return ; ASSERT (pfree <= iwlen) ; AMD_DEBUG3 (("\nAMD dump, pfree: "ID"\n", pfree)) ; for (i = 0 ; i < n ; i++) { pe = Pe [i] ; elen = Elen [i] ; nv = Nv [i] ; len = Len [i] ; w = W [i] ; if (elen >= EMPTY) { if (nv == 0) { AMD_DEBUG3 (("\nI "ID": nonprincipal: ", i)) ; ASSERT (elen == EMPTY) ; if (pe == EMPTY) { AMD_DEBUG3 ((" dense node\n")) ; ASSERT (w == 1) ; } else { ASSERT (pe < EMPTY) ; AMD_DEBUG3 ((" i "ID" -> parent "ID"\n", i, FLIP (Pe[i]))); } } else { AMD_DEBUG3 (("\nI "ID": active principal supervariable:\n",i)); AMD_DEBUG3 ((" nv(i): "ID" Flag: %d\n", nv, (nv < 0))) ; ASSERT (elen >= 0) ; ASSERT (nv > 0 && pe >= 0) ; p = pe ; AMD_DEBUG3 ((" e/s: ")) ; if (elen == 0) AMD_DEBUG3 ((" : ")) ; ASSERT (pe + len <= pfree) ; for (k = 0 ; k < len ; k++) { j = Iw [p] ; AMD_DEBUG3 ((" "ID"", j)) ; ASSERT (j >= 0 && j < n) ; if (k == elen-1) AMD_DEBUG3 ((" : ")) ; p++ ; } AMD_DEBUG3 (("\n")) ; } } else { e = i ; if (w == 0) { AMD_DEBUG3 (("\nE "ID": absorbed element: w "ID"\n", e, w)) ; ASSERT (nv > 0 && pe < 0) ; AMD_DEBUG3 ((" e "ID" -> parent "ID"\n", e, FLIP (Pe [e]))) ; } else { AMD_DEBUG3 (("\nE "ID": unabsorbed element: w "ID"\n", e, w)) ; ASSERT (nv > 0 && pe >= 0) ; p = pe ; AMD_DEBUG3 ((" : ")) ; ASSERT (pe + len <= pfree) ; for (k = 0 ; k < len ; k++) { j = Iw [p] ; AMD_DEBUG3 ((" "ID"", j)) ; ASSERT (j >= 0 && j < n) ; p++ ; } AMD_DEBUG3 (("\n")) ; } } } /* this routine cannot be called when the hash buckets are non-empty */ AMD_DEBUG3 (("\nDegree lists:\n")) ; if (nel >= 0) { cnt = 0 ; for (deg = 0 ; deg < n ; deg++) { if (Head [deg] == EMPTY) continue ; ilast = EMPTY ; AMD_DEBUG3 ((ID": \n", deg)) ; for (i = Head [deg] ; i != EMPTY ; i = Next [i]) { AMD_DEBUG3 ((" "ID" : next "ID" last "ID" deg "ID"\n", i, Next [i], Last [i], Degree [i])) ; ASSERT (i >= 0 && i < n && ilast == Last [i] && deg == Degree [i]) ; cnt += Nv [i] ; ilast = i ; } AMD_DEBUG3 (("\n")) ; } ASSERT (cnt == n - nel) ; } } #endif SuiteSparse/AMD/Source/amd_info.c0000644001170100242450000001023510616426641015537 0ustar davisfac/* ========================================================================= */ /* === AMD_info ============================================================ */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ /* User-callable. Prints the output statistics for AMD. See amd.h * for details. If the Info array is not present, nothing is printed. */ #include "amd_internal.h" #define PRI(format,x) { if (x >= 0) { PRINTF ((format, x)) ; }} GLOBAL void AMD_info ( double Info [ ] ) { double n, ndiv, nmultsubs_ldl, nmultsubs_lu, lnz, lnzd ; PRINTF (("\nAMD version %d.%d.%d, %s, results:\n", AMD_MAIN_VERSION, AMD_SUB_VERSION, AMD_SUBSUB_VERSION, AMD_DATE)) ; if (!Info) { return ; } n = Info [AMD_N] ; ndiv = Info [AMD_NDIV] ; nmultsubs_ldl = Info [AMD_NMULTSUBS_LDL] ; nmultsubs_lu = Info [AMD_NMULTSUBS_LU] ; lnz = Info [AMD_LNZ] ; lnzd = (n >= 0 && lnz >= 0) ? (n + lnz) : (-1) ; /* AMD return status */ PRINTF ((" status: ")) ; if (Info [AMD_STATUS] == AMD_OK) { PRINTF (("OK\n")) ; } else if (Info [AMD_STATUS] == AMD_OUT_OF_MEMORY) { PRINTF (("out of memory\n")) ; } else if (Info [AMD_STATUS] == AMD_INVALID) { PRINTF (("invalid matrix\n")) ; } else if (Info [AMD_STATUS] == AMD_OK_BUT_JUMBLED) { PRINTF (("OK, but jumbled\n")) ; } else { PRINTF (("unknown\n")) ; } /* statistics about the input matrix */ PRI (" n, dimension of A: %.20g\n", n); PRI (" nz, number of nonzeros in A: %.20g\n", Info [AMD_NZ]) ; PRI (" symmetry of A: %.4f\n", Info [AMD_SYMMETRY]) ; PRI (" number of nonzeros on diagonal: %.20g\n", Info [AMD_NZDIAG]) ; PRI (" nonzeros in pattern of A+A' (excl. diagonal): %.20g\n", Info [AMD_NZ_A_PLUS_AT]) ; PRI (" # dense rows/columns of A+A': %.20g\n", Info [AMD_NDENSE]) ; /* statistics about AMD's behavior */ PRI (" memory used, in bytes: %.20g\n", Info [AMD_MEMORY]) ; PRI (" # of memory compactions: %.20g\n", Info [AMD_NCMPA]) ; /* statistics about the ordering quality */ PRINTF (("\n" " The following approximate statistics are for a subsequent\n" " factorization of A(P,P) + A(P,P)'. They are slight upper\n" " bounds if there are no dense rows/columns in A+A', and become\n" " looser if dense rows/columns exist.\n\n")) ; PRI (" nonzeros in L (excluding diagonal): %.20g\n", lnz) ; PRI (" nonzeros in L (including diagonal): %.20g\n", lnzd) ; PRI (" # divide operations for LDL' or LU: %.20g\n", ndiv) ; PRI (" # multiply-subtract operations for LDL': %.20g\n", nmultsubs_ldl) ; PRI (" # multiply-subtract operations for LU: %.20g\n", nmultsubs_lu) ; PRI (" max nz. in any column of L (incl. diagonal): %.20g\n", Info [AMD_DMAX]) ; /* total flop counts for various factorizations */ if (n >= 0 && ndiv >= 0 && nmultsubs_ldl >= 0 && nmultsubs_lu >= 0) { PRINTF (("\n" " chol flop count for real A, sqrt counted as 1 flop: %.20g\n" " LDL' flop count for real A: %.20g\n" " LDL' flop count for complex A: %.20g\n" " LU flop count for real A (with no pivoting): %.20g\n" " LU flop count for complex A (with no pivoting): %.20g\n\n", n + ndiv + 2*nmultsubs_ldl, ndiv + 2*nmultsubs_ldl, 9*ndiv + 8*nmultsubs_ldl, ndiv + 2*nmultsubs_lu, 9*ndiv + 8*nmultsubs_lu)) ; } } SuiteSparse/AMD/Source/amdbar.f0000644001170100242450000014607210250413605015213 0ustar davisfacC----------------------------------------------------------------------- C AMDBAR: approximate minimum degree, without aggressive absorption C----------------------------------------------------------------------- SUBROUTINE AMDBAR $ (N, PE, IW, LEN, IWLEN, PFREE, NV, NEXT, $ LAST, HEAD, ELEN, DEGREE, NCMPA, W) INTEGER N, IWLEN, PFREE, NCMPA, IW (IWLEN), PE (N), $ DEGREE (N), NV (N), NEXT (N), LAST (N), HEAD (N), $ ELEN (N), W (N), LEN (N) C Given a representation of the nonzero pattern of a symmetric matrix, C A, (excluding the diagonal) perform an approximate minimum C (UMFPACK/MA38-style) degree ordering to compute a pivot order C such that the introduction of nonzeros (fill-in) in the Cholesky C factors A = LL^T are kept low. At each step, the pivot C selected is the one with the minimum UMFPACK/MA38-style C upper-bound on the external degree. C C This routine does not do aggresive absorption (as done by AMD). C ********************************************************************** C ***** CAUTION: ARGUMENTS ARE NOT CHECKED FOR ERRORS ON INPUT. ****** C ********************************************************************** C References: C C [1] Timothy A. Davis and Iain Duff, "An unsymmetric-pattern C multifrontal method for sparse LU factorization", SIAM J. C Matrix Analysis and Applications, vol. 18, no. 1, pp. C 140-158. Discusses UMFPACK / MA38, which first introduced C the approximate minimum degree used by this routine. C C [2] Patrick Amestoy, Timothy A. Davis, and Iain S. Duff, "An C approximate degree ordering algorithm," SIAM J. Matrix C Analysis and Applications, vol. 17, no. 4, pp. 886-905, C 1996. Discusses AMD, AMDBAR, and MC47B. C C [3] Alan George and Joseph Liu, "The evolution of the minimum C degree ordering algorithm," SIAM Review, vol. 31, no. 1, C pp. 1-19, 1989. We list below the features mentioned in C that paper that this code includes: C C mass elimination: C Yes. MA27 relied on supervariable detection for mass C elimination. C indistinguishable nodes: C Yes (we call these "supervariables"). This was also in C the MA27 code - although we modified the method of C detecting them (the previous hash was the true degree, C which we no longer keep track of). A supervariable is C a set of rows with identical nonzero pattern. All C variables in a supervariable are eliminated together. C Each supervariable has as its numerical name that of C one of its variables (its principal variable). C quotient graph representation: C Yes. We use the term "element" for the cliques formed C during elimination. This was also in the MA27 code. C The algorithm can operate in place, but it will work C more efficiently if given some "elbow room." C element absorption: C Yes. This was also in the MA27 code. C external degree: C Yes. The MA27 code was based on the true degree. C incomplete degree update and multiple elimination: C No. This was not in MA27, either. Our method of C degree update within MC47B/BD is element-based, not C variable-based. It is thus not well-suited for use C with incomplete degree update or multiple elimination. C----------------------------------------------------------------------- C Authors, and Copyright (C) 1995 by: C Timothy A. Davis, Patrick Amestoy, Iain S. Duff, & John K. Reid. C C Acknowledgements: C This work (and the UMFPACK package) was supported by the C National Science Foundation (ASC-9111263 and DMS-9223088). C The UMFPACK/MA38 approximate degree update algorithm, the C unsymmetric analog which forms the basis of MC47B/BD, was C developed while Tim Davis was supported by CERFACS (Toulouse, C France) in a post-doctoral position. C C Date: September, 1995 C----------------------------------------------------------------------- C----------------------------------------------------------------------- C INPUT ARGUMENTS (unaltered): C----------------------------------------------------------------------- C n: The matrix order. C C Restriction: 1 .le. n .lt. (iovflo/2)-2, where iovflo is C the largest positive integer that your computer can represent. C iwlen: The length of iw (1..iwlen). On input, the matrix is C stored in iw (1..pfree-1). However, iw (1..iwlen) should be C slightly larger than what is required to hold the matrix, at C least iwlen .ge. pfree + n is recommended. Otherwise, C excessive compressions will take place. C *** We do not recommend running this algorithm with *** C *** iwlen .lt. pfree + n. *** C *** Better performance will be obtained if *** C *** iwlen .ge. pfree + n *** C *** or better yet *** C *** iwlen .gt. 1.2 * pfree *** C *** (where pfree is its value on input). *** C The algorithm will not run at all if iwlen .lt. pfree-1. C C Restriction: iwlen .ge. pfree-1 C----------------------------------------------------------------------- C INPUT/OUPUT ARGUMENTS: C----------------------------------------------------------------------- C pe: On input, pe (i) is the index in iw of the start of row i, or C zero if row i has no off-diagonal non-zeros. C C During execution, it is used for both supervariables and C elements: C C * Principal supervariable i: index into iw of the C description of supervariable i. A supervariable C represents one or more rows of the matrix C with identical nonzero pattern. C * Non-principal supervariable i: if i has been absorbed C into another supervariable j, then pe (i) = -j. C That is, j has the same pattern as i. C Note that j might later be absorbed into another C supervariable j2, in which case pe (i) is still -j, C and pe (j) = -j2. C * Unabsorbed element e: the index into iw of the description C of element e, if e has not yet been absorbed by a C subsequent element. Element e is created when C the supervariable of the same name is selected as C the pivot. C * Absorbed element e: if element e is absorbed into element C e2, then pe (e) = -e2. This occurs when the pattern of C e (that is, Le) is found to be a subset of the pattern C of e2 (that is, Le2). If element e is "null" (it has C no nonzeros outside its pivot block), then pe (e) = 0. C C On output, pe holds the assembly tree/forest, which implicitly C represents a pivot order with identical fill-in as the actual C order (via a depth-first search of the tree). C C On output: C If nv (i) .gt. 0, then i represents a node in the assembly tree, C and the parent of i is -pe (i), or zero if i is a root. C If nv (i) = 0, then (i,-pe (i)) represents an edge in a C subtree, the root of which is a node in the assembly tree. C pfree: On input the tail end of the array, iw (pfree..iwlen), C is empty, and the matrix is stored in iw (1..pfree-1). C During execution, additional data is placed in iw, and pfree C is modified so that iw (pfree..iwlen) is always the unused part C of iw. On output, pfree is set equal to the size of iw that C would have been needed for no compressions to occur. If C ncmpa is zero, then pfree (on output) is less than or equal to C iwlen, and the space iw (pfree+1 ... iwlen) was not used. C Otherwise, pfree (on output) is greater than iwlen, and all the C memory in iw was used. C----------------------------------------------------------------------- C INPUT/MODIFIED (undefined on output): C----------------------------------------------------------------------- C len: On input, len (i) holds the number of entries in row i of the C matrix, excluding the diagonal. The contents of len (1..n) C are undefined on output. C iw: On input, iw (1..pfree-1) holds the description of each row i C in the matrix. The matrix must be symmetric, and both upper C and lower triangular parts must be present. The diagonal must C not be present. Row i is held as follows: C C len (i): the length of the row i data structure C iw (pe (i) ... pe (i) + len (i) - 1): C the list of column indices for nonzeros C in row i (simple supervariables), excluding C the diagonal. All supervariables start with C one row/column each (supervariable i is just C row i). C if len (i) is zero on input, then pe (i) is ignored C on input. C C Note that the rows need not be in any particular order, C and there may be empty space between the rows. C C During execution, the supervariable i experiences fill-in. C This is represented by placing in i a list of the elements C that cause fill-in in supervariable i: C C len (i): the length of supervariable i C iw (pe (i) ... pe (i) + elen (i) - 1): C the list of elements that contain i. This list C is kept short by removing absorbed elements. C iw (pe (i) + elen (i) ... pe (i) + len (i) - 1): C the list of supervariables in i. This list C is kept short by removing nonprincipal C variables, and any entry j that is also C contained in at least one of the elements C (j in Le) in the list for i (e in row i). C C When supervariable i is selected as pivot, we create an C element e of the same name (e=i): C C len (e): the length of element e C iw (pe (e) ... pe (e) + len (e) - 1): C the list of supervariables in element e. C C An element represents the fill-in that occurs when supervariable C i is selected as pivot (which represents the selection of row i C and all non-principal variables whose principal variable is i). C We use the term Le to denote the set of all supervariables C in element e. Absorbed supervariables and elements are pruned C from these lists when computationally convenient. C C CAUTION: THE INPUT MATRIX IS OVERWRITTEN DURING COMPUTATION. C The contents of iw are undefined on output. C----------------------------------------------------------------------- C OUTPUT (need not be set on input): C----------------------------------------------------------------------- C nv: During execution, abs (nv (i)) is equal to the number of rows C that are represented by the principal supervariable i. If i is C a nonprincipal variable, then nv (i) = 0. Initially, C nv (i) = 1 for all i. nv (i) .lt. 0 signifies that i is a C principal variable in the pattern Lme of the current pivot C element me. On output, nv (e) holds the true degree of element C e at the time it was created (including the diagonal part). C ncmpa: The number of times iw was compressed. If this is C excessive, then the execution took longer than what could have C been. To reduce ncmpa, try increasing iwlen to be 10% or 20% C larger than the value of pfree on input (or at least C iwlen .ge. pfree + n). The fastest performance will be C obtained when ncmpa is returned as zero. If iwlen is set to C the value returned by pfree on *output*, then no compressions C will occur. C elen: See the description of iw above. At the start of execution, C elen (i) is set to zero. During execution, elen (i) is the C number of elements in the list for supervariable i. When e C becomes an element, elen (e) = -nel is set, where nel is the C current step of factorization. elen (i) = 0 is done when i C becomes nonprincipal. C C For variables, elen (i) .ge. 0 holds until just before the C permutation vectors are computed. For elements, C elen (e) .lt. 0 holds. C C On output elen (1..n) holds the inverse permutation (the same C as the 'INVP' argument in Sparspak). That is, if k = elen (i), C then row i is the kth pivot row. Row i of A appears as the C (elen(i))-th row in the permuted matrix, PAP^T. C last: In a degree list, last (i) is the supervariable preceding i, C or zero if i is the head of the list. In a hash bucket, C last (i) is the hash key for i. last (head (hash)) is also C used as the head of a hash bucket if head (hash) contains a C degree list (see head, below). C C On output, last (1..n) holds the permutation (the same as the C 'PERM' argument in Sparspak). That is, if i = last (k), then C row i is the kth pivot row. Row last (k) of A is the k-th row C in the permuted matrix, PAP^T. C----------------------------------------------------------------------- C LOCAL (not input or output - used only during execution): C----------------------------------------------------------------------- C degree: If i is a supervariable, then degree (i) holds the C current approximation of the external degree of row i (an upper C bound). The external degree is the number of nonzeros in row i, C minus abs (nv (i)) (the diagonal part). The bound is equal to C the external degree if elen (i) is less than or equal to two. C C We also use the term "external degree" for elements e to refer C to |Le \ Lme|. If e is an element, then degree (e) holds |Le|, C which is the degree of the off-diagonal part of the element e C (not including the diagonal part). C head: head is used for degree lists. head (deg) is the first C supervariable in a degree list (all supervariables i in a C degree list deg have the same approximate degree, namely, C deg = degree (i)). If the list deg is empty then C head (deg) = 0. C C During supervariable detection head (hash) also serves as a C pointer to a hash bucket. C If head (hash) .gt. 0, there is a degree list of degree hash. C The hash bucket head pointer is last (head (hash)). C If head (hash) = 0, then the degree list and hash bucket are C both empty. C If head (hash) .lt. 0, then the degree list is empty, and C -head (hash) is the head of the hash bucket. C After supervariable detection is complete, all hash buckets C are empty, and the (last (head (hash)) = 0) condition is C restored for the non-empty degree lists. C next: next (i) is the supervariable following i in a link list, or C zero if i is the last in the list. Used for two kinds of C lists: degree lists and hash buckets (a supervariable can be C in only one kind of list at a time). C w: The flag array w determines the status of elements and C variables, and the external degree of elements. C C for elements: C if w (e) = 0, then the element e is absorbed C if w (e) .ge. wflg, then w (e) - wflg is the size of C the set |Le \ Lme|, in terms of nonzeros (the C sum of abs (nv (i)) for each principal variable i that C is both in the pattern of element e and NOT in the C pattern of the current pivot element, me). C if wflg .gt. w (e) .gt. 0, then e is not absorbed and has C not yet been seen in the scan of the element lists in C the computation of |Le\Lme| in loop 150 below. C C for variables: C during supervariable detection, if w (j) .ne. wflg then j is C not in the pattern of variable i C C The w array is initialized by setting w (i) = 1 for all i, C and by setting wflg = 2. It is reinitialized if wflg becomes C too large (to ensure that wflg+n does not cause integer C overflow). C----------------------------------------------------------------------- C LOCAL INTEGERS: C----------------------------------------------------------------------- INTEGER DEG, DEGME, DMAX, E, ELENME, ELN, HASH, HMOD, I, $ ILAST, INEXT, J, JLAST, JNEXT, K, KNT1, KNT2, KNT3, $ LENJ, LN, MAXMEM, ME, MEM, MINDEG, NEL, NEWMEM, $ NLEFT, NVI, NVJ, NVPIV, SLENME, WE, WFLG, WNVI, X C deg: the degree of a variable or element C degme: size, |Lme|, of the current element, me (= degree (me)) C dext: external degree, |Le \ Lme|, of some element e C dmax: largest |Le| seen so far C e: an element C elenme: the length, elen (me), of element list of pivotal var. C eln: the length, elen (...), of an element list C hash: the computed value of the hash function C hmod: the hash function is computed modulo hmod = max (1,n-1) C i: a supervariable C ilast: the entry in a link list preceding i C inext: the entry in a link list following i C j: a supervariable C jlast: the entry in a link list preceding j C jnext: the entry in a link list, or path, following j C k: the pivot order of an element or variable C knt1: loop counter used during element construction C knt2: loop counter used during element construction C knt3: loop counter used during compression C lenj: len (j) C ln: length of a supervariable list C maxmem: amount of memory needed for no compressions C me: current supervariable being eliminated, and the C current element created by eliminating that C supervariable C mem: memory in use assuming no compressions have occurred C mindeg: current minimum degree C nel: number of pivots selected so far C newmem: amount of new memory needed for current pivot element C nleft: n - nel, the number of nonpivotal rows/columns remaining C nvi: the number of variables in a supervariable i (= nv (i)) C nvj: the number of variables in a supervariable j (= nv (j)) C nvpiv: number of pivots in current element C slenme: number of variables in variable list of pivotal variable C we: w (e) C wflg: used for flagging the w array. See description of iw. C wnvi: wflg - nv (i) C x: either a supervariable or an element C----------------------------------------------------------------------- C LOCAL POINTERS: C----------------------------------------------------------------------- INTEGER P, P1, P2, P3, PDST, PEND, PJ, PME, PME1, PME2, PN, PSRC C Any parameter (pe (...) or pfree) or local variable C starting with "p" (for Pointer) is an index into iw, C and all indices into iw use variables starting with C "p." The only exception to this rule is the iwlen C input argument. C p: pointer into lots of things C p1: pe (i) for some variable i (start of element list) C p2: pe (i) + elen (i) - 1 for some var. i (end of el. list) C p3: index of first supervariable in clean list C pdst: destination pointer, for compression C pend: end of memory to compress C pj: pointer into an element or variable C pme: pointer into the current element (pme1...pme2) C pme1: the current element, me, is stored in iw (pme1...pme2) C pme2: the end of the current element C pn: pointer into a "clean" variable, also used to compress C psrc: source pointer, for compression C----------------------------------------------------------------------- C FUNCTIONS CALLED: C----------------------------------------------------------------------- INTRINSIC MAX, MIN, MOD C======================================================================= C INITIALIZATIONS C======================================================================= WFLG = 2 MINDEG = 1 NCMPA = 0 NEL = 0 HMOD = MAX (1, N-1) DMAX = 0 MEM = PFREE - 1 MAXMEM = MEM ME = 0 DO 10 I = 1, N LAST (I) = 0 HEAD (I) = 0 NV (I) = 1 W (I) = 1 ELEN (I) = 0 DEGREE (I) = LEN (I) 10 CONTINUE C ---------------------------------------------------------------- C initialize degree lists and eliminate rows with no off-diag. nz. C ---------------------------------------------------------------- DO 20 I = 1, N DEG = DEGREE (I) IF (DEG .GT. 0) THEN C ---------------------------------------------------------- C place i in the degree list corresponding to its degree C ---------------------------------------------------------- INEXT = HEAD (DEG) IF (INEXT .NE. 0) LAST (INEXT) = I NEXT (I) = INEXT HEAD (DEG) = I ELSE C ---------------------------------------------------------- C we have a variable that can be eliminated at once because C there is no off-diagonal non-zero in its row. C ---------------------------------------------------------- NEL = NEL + 1 ELEN (I) = -NEL PE (I) = 0 W (I) = 0 ENDIF 20 CONTINUE C======================================================================= C WHILE (selecting pivots) DO C======================================================================= 30 CONTINUE IF (NEL .LT. N) THEN C======================================================================= C GET PIVOT OF MINIMUM DEGREE C======================================================================= C ------------------------------------------------------------- C find next supervariable for elimination C ------------------------------------------------------------- DO 40 DEG = MINDEG, N ME = HEAD (DEG) IF (ME .GT. 0) GOTO 50 40 CONTINUE 50 CONTINUE MINDEG = DEG C ------------------------------------------------------------- C remove chosen variable from link list C ------------------------------------------------------------- INEXT = NEXT (ME) IF (INEXT .NE. 0) LAST (INEXT) = 0 HEAD (DEG) = INEXT C ------------------------------------------------------------- C me represents the elimination of pivots nel+1 to nel+nv(me). C place me itself as the first in this set. It will be moved C to the nel+nv(me) position when the permutation vectors are C computed. C ------------------------------------------------------------- ELENME = ELEN (ME) ELEN (ME) = - (NEL + 1) NVPIV = NV (ME) NEL = NEL + NVPIV C======================================================================= C CONSTRUCT NEW ELEMENT C======================================================================= C ------------------------------------------------------------- C At this point, me is the pivotal supervariable. It will be C converted into the current element. Scan list of the C pivotal supervariable, me, setting tree pointers and C constructing new list of supervariables for the new element, C me. p is a pointer to the current position in the old list. C ------------------------------------------------------------- C flag the variable "me" as being in Lme by negating nv (me) NV (ME) = -NVPIV DEGME = 0 IF (ELENME .EQ. 0) THEN C ---------------------------------------------------------- C construct the new element in place C ---------------------------------------------------------- PME1 = PE (ME) PME2 = PME1 - 1 DO 60 P = PME1, PME1 + LEN (ME) - 1 I = IW (P) NVI = NV (I) IF (NVI .GT. 0) THEN C ---------------------------------------------------- C i is a principal variable not yet placed in Lme. C store i in new list C ---------------------------------------------------- DEGME = DEGME + NVI C flag i as being in Lme by negating nv (i) NV (I) = -NVI PME2 = PME2 + 1 IW (PME2) = I C ---------------------------------------------------- C remove variable i from degree list. C ---------------------------------------------------- ILAST = LAST (I) INEXT = NEXT (I) IF (INEXT .NE. 0) LAST (INEXT) = ILAST IF (ILAST .NE. 0) THEN NEXT (ILAST) = INEXT ELSE C i is at the head of the degree list HEAD (DEGREE (I)) = INEXT ENDIF ENDIF 60 CONTINUE C this element takes no new memory in iw: NEWMEM = 0 ELSE C ---------------------------------------------------------- C construct the new element in empty space, iw (pfree ...) C ---------------------------------------------------------- P = PE (ME) PME1 = PFREE SLENME = LEN (ME) - ELENME DO 120 KNT1 = 1, ELENME + 1 IF (KNT1 .GT. ELENME) THEN C search the supervariables in me. E = ME PJ = P LN = SLENME ELSE C search the elements in me. E = IW (P) P = P + 1 PJ = PE (E) LN = LEN (E) ENDIF C ------------------------------------------------------- C search for different supervariables and add them to the C new list, compressing when necessary. this loop is C executed once for each element in the list and once for C all the supervariables in the list. C ------------------------------------------------------- DO 110 KNT2 = 1, LN I = IW (PJ) PJ = PJ + 1 NVI = NV (I) IF (NVI .GT. 0) THEN C ------------------------------------------------- C compress iw, if necessary C ------------------------------------------------- IF (PFREE .GT. IWLEN) THEN C prepare for compressing iw by adjusting C pointers and lengths so that the lists being C searched in the inner and outer loops contain C only the remaining entries. PE (ME) = P LEN (ME) = LEN (ME) - KNT1 IF (LEN (ME) .EQ. 0) THEN C nothing left of supervariable me PE (ME) = 0 ENDIF PE (E) = PJ LEN (E) = LN - KNT2 IF (LEN (E) .EQ. 0) THEN C nothing left of element e PE (E) = 0 ENDIF NCMPA = NCMPA + 1 C store first item in pe C set first entry to -item DO 70 J = 1, N PN = PE (J) IF (PN .GT. 0) THEN PE (J) = IW (PN) IW (PN) = -J ENDIF 70 CONTINUE C psrc/pdst point to source/destination PDST = 1 PSRC = 1 PEND = PME1 - 1 C while loop: 80 CONTINUE IF (PSRC .LE. PEND) THEN C search for next negative entry J = -IW (PSRC) PSRC = PSRC + 1 IF (J .GT. 0) THEN IW (PDST) = PE (J) PE (J) = PDST PDST = PDST + 1 C copy from source to destination LENJ = LEN (J) DO 90 KNT3 = 0, LENJ - 2 IW (PDST + KNT3) = IW (PSRC + KNT3) 90 CONTINUE PDST = PDST + LENJ - 1 PSRC = PSRC + LENJ - 1 ENDIF GOTO 80 ENDIF C move the new partially-constructed element P1 = PDST DO 100 PSRC = PME1, PFREE - 1 IW (PDST) = IW (PSRC) PDST = PDST + 1 100 CONTINUE PME1 = P1 PFREE = PDST PJ = PE (E) P = PE (ME) ENDIF C ------------------------------------------------- C i is a principal variable not yet placed in Lme C store i in new list C ------------------------------------------------- DEGME = DEGME + NVI C flag i as being in Lme by negating nv (i) NV (I) = -NVI IW (PFREE) = I PFREE = PFREE + 1 C ------------------------------------------------- C remove variable i from degree link list C ------------------------------------------------- ILAST = LAST (I) INEXT = NEXT (I) IF (INEXT .NE. 0) LAST (INEXT) = ILAST IF (ILAST .NE. 0) THEN NEXT (ILAST) = INEXT ELSE C i is at the head of the degree list HEAD (DEGREE (I)) = INEXT ENDIF ENDIF 110 CONTINUE IF (E .NE. ME) THEN C set tree pointer and flag to indicate element e is C absorbed into new element me (the parent of e is me) PE (E) = -ME W (E) = 0 ENDIF 120 CONTINUE PME2 = PFREE - 1 C this element takes newmem new memory in iw (possibly zero) NEWMEM = PFREE - PME1 MEM = MEM + NEWMEM MAXMEM = MAX (MAXMEM, MEM) ENDIF C ------------------------------------------------------------- C me has now been converted into an element in iw (pme1..pme2) C ------------------------------------------------------------- C degme holds the external degree of new element DEGREE (ME) = DEGME PE (ME) = PME1 LEN (ME) = PME2 - PME1 + 1 C ------------------------------------------------------------- C make sure that wflg is not too large. With the current C value of wflg, wflg+n must not cause integer overflow C ------------------------------------------------------------- IF (WFLG + N .LE. WFLG) THEN DO 130 X = 1, N IF (W (X) .NE. 0) W (X) = 1 130 CONTINUE WFLG = 2 ENDIF C======================================================================= C COMPUTE (w (e) - wflg) = |Le\Lme| FOR ALL ELEMENTS C======================================================================= C ------------------------------------------------------------- C Scan 1: compute the external degrees of previous elements C with respect to the current element. That is: C (w (e) - wflg) = |Le \ Lme| C for each element e that appears in any supervariable in Lme. C The notation Le refers to the pattern (list of C supervariables) of a previous element e, where e is not yet C absorbed, stored in iw (pe (e) + 1 ... pe (e) + iw (pe (e))). C The notation Lme refers to the pattern of the current element C (stored in iw (pme1..pme2)). If (w (e) - wflg) becomes C zero, then the element e will be absorbed in scan 2. C ------------------------------------------------------------- DO 150 PME = PME1, PME2 I = IW (PME) ELN = ELEN (I) IF (ELN .GT. 0) THEN C note that nv (i) has been negated to denote i in Lme: NVI = -NV (I) WNVI = WFLG - NVI DO 140 P = PE (I), PE (I) + ELN - 1 E = IW (P) WE = W (E) IF (WE .GE. WFLG) THEN C unabsorbed element e has been seen in this loop WE = WE - NVI ELSE IF (WE .NE. 0) THEN C e is an unabsorbed element C this is the first we have seen e in all of Scan 1 WE = DEGREE (E) + WNVI ENDIF W (E) = WE 140 CONTINUE ENDIF 150 CONTINUE C======================================================================= C DEGREE UPDATE AND ELEMENT ABSORPTION C======================================================================= C ------------------------------------------------------------- C Scan 2: for each i in Lme, sum up the degree of Lme (which C is degme), plus the sum of the external degrees of each Le C for the elements e appearing within i, plus the C supervariables in i. Place i in hash list. C ------------------------------------------------------------- DO 180 PME = PME1, PME2 I = IW (PME) P1 = PE (I) P2 = P1 + ELEN (I) - 1 PN = P1 HASH = 0 DEG = 0 C ---------------------------------------------------------- C scan the element list associated with supervariable i C ---------------------------------------------------------- C UMFPACK/MA38-style approximate degree: DO 160 P = P1, P2 E = IW (P) WE = W (E) IF (WE .NE. 0) THEN C e is an unabsorbed element DEG = DEG + WE - WFLG IW (PN) = E PN = PN + 1 HASH = HASH + E ENDIF 160 CONTINUE C count the number of elements in i (including me): ELEN (I) = PN - P1 + 1 C ---------------------------------------------------------- C scan the supervariables in the list associated with i C ---------------------------------------------------------- P3 = PN DO 170 P = P2 + 1, P1 + LEN (I) - 1 J = IW (P) NVJ = NV (J) IF (NVJ .GT. 0) THEN C j is unabsorbed, and not in Lme. C add to degree and add to new list DEG = DEG + NVJ IW (PN) = J PN = PN + 1 HASH = HASH + J ENDIF 170 CONTINUE C ---------------------------------------------------------- C update the degree and check for mass elimination C ---------------------------------------------------------- IF (ELEN (I) .EQ. 1 .AND. P3 .EQ. PN) THEN C ------------------------------------------------------- C mass elimination C ------------------------------------------------------- C There is nothing left of this node except for an C edge to the current pivot element. elen (i) is 1, C and there are no variables adjacent to node i. C Absorb i into the current pivot element, me. PE (I) = -ME NVI = -NV (I) DEGME = DEGME - NVI NVPIV = NVPIV + NVI NEL = NEL + NVI NV (I) = 0 ELEN (I) = 0 ELSE C ------------------------------------------------------- C update the upper-bound degree of i C ------------------------------------------------------- C the following degree does not yet include the size C of the current element, which is added later: DEGREE (I) = MIN (DEGREE (I), DEG) C ------------------------------------------------------- C add me to the list for i C ------------------------------------------------------- C move first supervariable to end of list IW (PN) = IW (P3) C move first element to end of element part of list IW (P3) = IW (P1) C add new element to front of list. IW (P1) = ME C store the new length of the list in len (i) LEN (I) = PN - P1 + 1 C ------------------------------------------------------- C place in hash bucket. Save hash key of i in last (i). C ------------------------------------------------------- HASH = MOD (HASH, HMOD) + 1 J = HEAD (HASH) IF (J .LE. 0) THEN C the degree list is empty, hash head is -j NEXT (I) = -J HEAD (HASH) = -I ELSE C degree list is not empty C use last (head (hash)) as hash head NEXT (I) = LAST (J) LAST (J) = I ENDIF LAST (I) = HASH ENDIF 180 CONTINUE DEGREE (ME) = DEGME C ------------------------------------------------------------- C Clear the counter array, w (...), by incrementing wflg. C ------------------------------------------------------------- DMAX = MAX (DMAX, DEGME) WFLG = WFLG + DMAX C make sure that wflg+n does not cause integer overflow IF (WFLG + N .LE. WFLG) THEN DO 190 X = 1, N IF (W (X) .NE. 0) W (X) = 1 190 CONTINUE WFLG = 2 ENDIF C at this point, w (1..n) .lt. wflg holds C======================================================================= C SUPERVARIABLE DETECTION C======================================================================= DO 250 PME = PME1, PME2 I = IW (PME) IF (NV (I) .LT. 0) THEN C i is a principal variable in Lme C ------------------------------------------------------- C examine all hash buckets with 2 or more variables. We C do this by examing all unique hash keys for super- C variables in the pattern Lme of the current element, me C ------------------------------------------------------- HASH = LAST (I) C let i = head of hash bucket, and empty the hash bucket J = HEAD (HASH) IF (J .EQ. 0) GOTO 250 IF (J .LT. 0) THEN C degree list is empty I = -J HEAD (HASH) = 0 ELSE C degree list is not empty, restore last () of head I = LAST (J) LAST (J) = 0 ENDIF IF (I .EQ. 0) GOTO 250 C while loop: 200 CONTINUE IF (NEXT (I) .NE. 0) THEN C ---------------------------------------------------- C this bucket has one or more variables following i. C scan all of them to see if i can absorb any entries C that follow i in hash bucket. Scatter i into w. C ---------------------------------------------------- LN = LEN (I) ELN = ELEN (I) C do not flag the first element in the list (me) DO 210 P = PE (I) + 1, PE (I) + LN - 1 W (IW (P)) = WFLG 210 CONTINUE C ---------------------------------------------------- C scan every other entry j following i in bucket C ---------------------------------------------------- JLAST = I J = NEXT (I) C while loop: 220 CONTINUE IF (J .NE. 0) THEN C ------------------------------------------------- C check if j and i have identical nonzero pattern C ------------------------------------------------- IF (LEN (J) .NE. LN) THEN C i and j do not have same size data structure GOTO 240 ENDIF IF (ELEN (J) .NE. ELN) THEN C i and j do not have same number of adjacent el GOTO 240 ENDIF C do not flag the first element in the list (me) DO 230 P = PE (J) + 1, PE (J) + LN - 1 IF (W (IW (P)) .NE. WFLG) THEN C an entry (iw(p)) is in j but not in i GOTO 240 ENDIF 230 CONTINUE C ------------------------------------------------- C found it! j can be absorbed into i C ------------------------------------------------- PE (J) = -I C both nv (i) and nv (j) are negated since they C are in Lme, and the absolute values of each C are the number of variables in i and j: NV (I) = NV (I) + NV (J) NV (J) = 0 ELEN (J) = 0 C delete j from hash bucket J = NEXT (J) NEXT (JLAST) = J GOTO 220 C ------------------------------------------------- 240 CONTINUE C j cannot be absorbed into i C ------------------------------------------------- JLAST = J J = NEXT (J) GOTO 220 ENDIF C ---------------------------------------------------- C no more variables can be absorbed into i C go to next i in bucket and clear flag array C ---------------------------------------------------- WFLG = WFLG + 1 I = NEXT (I) IF (I .NE. 0) GOTO 200 ENDIF ENDIF 250 CONTINUE C======================================================================= C RESTORE DEGREE LISTS AND REMOVE NONPRINCIPAL SUPERVAR. FROM ELEMENT C======================================================================= P = PME1 NLEFT = N - NEL DO 260 PME = PME1, PME2 I = IW (PME) NVI = -NV (I) IF (NVI .GT. 0) THEN C i is a principal variable in Lme C restore nv (i) to signify that i is principal NV (I) = NVI C ------------------------------------------------------- C compute the external degree (add size of current elem) C ------------------------------------------------------- DEG = MAX (1, MIN (DEGREE (I) + DEGME-NVI, NLEFT-NVI)) C ------------------------------------------------------- C place the supervariable at the head of the degree list C ------------------------------------------------------- INEXT = HEAD (DEG) IF (INEXT .NE. 0) LAST (INEXT) = I NEXT (I) = INEXT LAST (I) = 0 HEAD (DEG) = I C ------------------------------------------------------- C save the new degree, and find the minimum degree C ------------------------------------------------------- MINDEG = MIN (MINDEG, DEG) DEGREE (I) = DEG C ------------------------------------------------------- C place the supervariable in the element pattern C ------------------------------------------------------- IW (P) = I P = P + 1 ENDIF 260 CONTINUE C======================================================================= C FINALIZE THE NEW ELEMENT C======================================================================= NV (ME) = NVPIV + DEGME C nv (me) is now the degree of pivot (including diagonal part) C save the length of the list for the new element me LEN (ME) = P - PME1 IF (LEN (ME) .EQ. 0) THEN C there is nothing left of the current pivot element PE (ME) = 0 W (ME) = 0 ENDIF IF (NEWMEM .NE. 0) THEN C element was not constructed in place: deallocate part C of it (final size is less than or equal to newmem, C since newly nonprincipal variables have been removed). PFREE = P MEM = MEM - NEWMEM + LEN (ME) ENDIF C======================================================================= C END WHILE (selecting pivots) GOTO 30 ENDIF C======================================================================= C======================================================================= C COMPUTE THE PERMUTATION VECTORS C======================================================================= C ---------------------------------------------------------------- C The time taken by the following code is O(n). At this C point, elen (e) = -k has been done for all elements e, C and elen (i) = 0 has been done for all nonprincipal C variables i. At this point, there are no principal C supervariables left, and all elements are absorbed. C ---------------------------------------------------------------- C ---------------------------------------------------------------- C compute the ordering of unordered nonprincipal variables C ---------------------------------------------------------------- DO 290 I = 1, N IF (ELEN (I) .EQ. 0) THEN C ---------------------------------------------------------- C i is an un-ordered row. Traverse the tree from i until C reaching an element, e. The element, e, was the C principal supervariable of i and all nodes in the path C from i to when e was selected as pivot. C ---------------------------------------------------------- J = -PE (I) C while (j is a variable) do: 270 CONTINUE IF (ELEN (J) .GE. 0) THEN J = -PE (J) GOTO 270 ENDIF E = J C ---------------------------------------------------------- C get the current pivot ordering of e C ---------------------------------------------------------- K = -ELEN (E) C ---------------------------------------------------------- C traverse the path again from i to e, and compress the C path (all nodes point to e). Path compression allows C this code to compute in O(n) time. Order the unordered C nodes in the path, and place the element e at the end. C ---------------------------------------------------------- J = I C while (j is a variable) do: 280 CONTINUE IF (ELEN (J) .GE. 0) THEN JNEXT = -PE (J) PE (J) = -E IF (ELEN (J) .EQ. 0) THEN C j is an unordered row ELEN (J) = K K = K + 1 ENDIF J = JNEXT GOTO 280 ENDIF C leave elen (e) negative, so we know it is an element ELEN (E) = -K ENDIF 290 CONTINUE C ---------------------------------------------------------------- C reset the inverse permutation (elen (1..n)) to be positive, C and compute the permutation (last (1..n)). C ---------------------------------------------------------------- DO 300 I = 1, N K = ABS (ELEN (I)) LAST (K) = I ELEN (I) = K 300 CONTINUE C======================================================================= C RETURN THE MEMORY USAGE IN IW C======================================================================= C If maxmem is less than or equal to iwlen, then no compressions C occurred, and iw (maxmem+1 ... iwlen) was unused. Otherwise C compressions did occur, and iwlen would have had to have been C greater than or equal to maxmem for no compressions to occur. C Return the value of maxmem in the pfree argument. PFREE = MAXMEM RETURN END SuiteSparse/AMD/Source/amd_control.c0000644001170100242450000000351210616431707016263 0ustar davisfac/* ========================================================================= */ /* === AMD_control ========================================================= */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* AMD, Copyright (c) Timothy A. Davis, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/amd */ /* ------------------------------------------------------------------------- */ /* User-callable. Prints the control parameters for AMD. See amd.h * for details. If the Control array is not present, the defaults are * printed instead. */ #include "amd_internal.h" GLOBAL void AMD_control ( double Control [ ] ) { double alpha ; Int aggressive ; if (Control != (double *) NULL) { alpha = Control [AMD_DENSE] ; aggressive = Control [AMD_AGGRESSIVE] != 0 ; } else { alpha = AMD_DEFAULT_DENSE ; aggressive = AMD_DEFAULT_AGGRESSIVE ; } PRINTF (("\nAMD version %d.%d.%d, %s: approximate minimum degree ordering\n" " dense row parameter: %g\n", AMD_MAIN_VERSION, AMD_SUB_VERSION, AMD_SUBSUB_VERSION, AMD_DATE, alpha)) ; if (alpha < 0) { PRINTF ((" no rows treated as dense\n")) ; } else { PRINTF (( " (rows with more than max (%g * sqrt (n), 16) entries are\n" " considered \"dense\", and placed last in output permutation)\n", alpha)) ; } if (aggressive) { PRINTF ((" aggressive absorption: yes\n")) ; } else { PRINTF ((" aggressive absorption: no\n")) ; } PRINTF ((" size of AMD integer: %d\n\n", sizeof (Int))) ; } SuiteSparse/AMD/README.txt0000644001170100242450000002151010617112024014037 0ustar davisfacAMD Version 2.2, Copyright (c) 2007 by Timothy A. Davis, Patrick R. Amestoy, and Iain S. Duff. All Rights Reserved. AMD is available under alternate licences; contact T. Davis for details. AMD: a set of routines for permuting sparse matrices prior to factorization. Includes a version in C, a version in Fortran, and a MATLAB mexFunction. Requires UFconfig, in the ../UFconfig directory relative to this directory. Quick start (Unix, or Windows with Cygwin): To compile, test, and install AMD, you may wish to first configure the installation by editting the ../UFconfig/UFconfig.mk file. Next, cd to this directory (AMD) and type "make" (or "make lib" if you do not have MATLAB). To compile and run a demo program for the Fortran version, type "make fortran". When done, type "make clean" to remove unused *.o files (keeps the compiled libraries and demo programs). See the User Guide (Doc/AMD_UserGuide.pdf), or ../UFconfig/UFconfig.mk for more details. Quick start (for MATLAB users); To compile, test, and install the AMD mexFunction, cd to the AMD/MATLAB directory and type amd_make at the MATLAB prompt. If you have MATLAB 7.2 or earlier and use "make mex", you must first edit UFconfig/UFconfig.h to remove the "-largeArrayDims" option from the MEX command (or just use amd_make.m inside MATLAB). ------------------------------------------------------------------------------- AMD License: Your use or distribution of AMD or any modified version of AMD implies that you agree to this License. This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Permission is hereby granted to use or copy this program under the terms of the GNU LGPL, provided that the Copyright, this License, and the Availability of the original version is retained on all copies. User documentation of any code that uses this code or any modified version of this code must cite the Copyright, this License, the Availability note, and "Used by permission." Permission to modify the code and to distribute modified code is granted, provided the Copyright, this License, and the Availability note are retained, and a notice that the code was modified is included. Availability: http://www.cise.ufl.edu/research/sparse/amd ------------------------------------------------------------------------------- This is the AMD README file. It is a terse overview of AMD. Refer to the User Guide (Doc/AMD_UserGuide.pdf) for how to install and use AMD. Description: AMD is a set of routines for pre-ordering sparse matrices prior to Cholesky or LU factorization, using the approximate minimum degree ordering algorithm. Written in ANSI/ISO C with a MATLAB interface, and in Fortran 77. Authors: Timothy A. Davis (davis at cise.ufl.edu), University of Florida. Patrick R. Amestory, ENSEEIHT, Toulouse, France. Iain S. Duff, Rutherford Appleton Laboratory, UK. Acknowledgements: This work was supported by the National Science Foundation, under grants DMS-9504974, DMS-9803599, and CCR-0203270. Portions of this work were done while on sabbatical at Stanford University and Lawrence Berkeley National Laboratory (with funding from the SciDAC program). I would like to thank Gene Golub, Esmond Ng, and Horst Simon for making this sabbatical possible. ------------------------------------------------------------------------------- Files and directories in the AMD distribution: ------------------------------------------------------------------------------- --------------------------------------------------------------------------- Subdirectories of the AMD directory: --------------------------------------------------------------------------- Doc documentation Source primary source code Include include file for use in your code that calls AMD Demo demo programs. also serves as test of the AMD installation. MATLAB AMD mexFunction for MATLAB, and supporting m-files Lib where the compiled C-callable and Fortran-callable AMD libraries placed. --------------------------------------------------------------------------- Files in the AMD directory: --------------------------------------------------------------------------- Makefile top-level Makefile for GNU make or original make. Windows users would require Cygwin to use "make" README.txt this file --------------------------------------------------------------------------- Doc directory: documentation --------------------------------------------------------------------------- ChangeLog change log License the AMD License Makefile for creating the documentation AMD_UserGuide.bib AMD User Guide (references) AMD_UserGuide.tex AMD User Guide (LaTeX) AMD_UserGuide.pdf AMD User Guide (PDF) lesser.txt the GNU LGPL license --------------------------------------------------------------------------- Source directory: --------------------------------------------------------------------------- amd_order.c user-callable, primary AMD ordering routine amd_control.c user-callable, prints the control parameters amd_defaults.c user-callable, sets default control parameters amd_info.c user-callable, prints the statistics from AMD amd_1.c non-user-callable, construct A+A' amd_2.c user-callable, primary ordering kernel (a C version of amd.f and amdbar.f, with post-ordering added) amd_aat.c non-user-callable, computes nnz (A+A') amd_dump.c non-user-callable, debugging routines amd_postorder.c non-user-callable, postorder amd_post_tree.c non-user-callable, postorder just one tree amd_valid.c non-user-callable, verifies a matrix amd_preprocess.c non-user-callable, computes A', removes duplic amd.f user-callable Fortran 77 version amdbar.f user-callable Fortran 77 version --------------------------------------------------------------------------- Include directory: --------------------------------------------------------------------------- amd.h include file for C programs that use AMD amd_internal.h non-user-callable, include file for AMD --------------------------------------------------------------------------- Demo directory: --------------------------------------------------------------------------- Makefile for GNU make or original make amd_demo.c C demo program for AMD amd_demo.out output of amd_demo.c amd_demo2.c C demo program for AMD, jumbled matrix amd_demo2.out output of amd_demo2.c amd_l_demo.c C demo program for AMD (UF_long version) amd_l_demo.out output of amd_l_demo.c amd_simple.c simple C demo program for AMD amd_simple.out output of amd_simple.c amd_f77demo.f Fortran 77 demo program for AMD amd_f77demo.out output of amd_f77demo.f amd_f77simple.c simple Fortran 77 demo program for AMD amd_f77simple.out output of amd_f77simple.f amd_f77cross.f Fortran 77 demo, calls the C version of AMD amd_f77cross.out output of amd_f77cross.f amd_f77wrapper.c Fortran-callable wrapper for C version of AMD --------------------------------------------------------------------------- MATLAB directory: --------------------------------------------------------------------------- GNUmakefile a nice Makefile, for GNU make Makefile an ugly Unix Makefile (for older make's) Contents.m for "help amd2" listing of toolbox contents amd2.m MATLAB help file for AMD amd_make.m MATLAB m-file for compiling AMD mexFunction amd_install.m compile and install the AMD mexFunction amd_mex.c AMD mexFunction for MATLAB amd_demo.m MATLAB demo for AMD amd_demo.m.out diary output of amd_demo.m can_24.mat input file for AMD demo --------------------------------------------------------------------------- Lib directory: libamd.a and libamdf77.a libraries placed here --------------------------------------------------------------------------- GNUmakefile a nice Makefile, for GNU make Makefile an ugly Unix Makefile (for older make's) libamd.def AMD definitions for Windows SuiteSparse/BTF/0000755001170100242450000000000010620160773012364 5ustar davisfacSuiteSparse/BTF/Doc/0000755001170100242450000000000010711427547013077 5ustar davisfacSuiteSparse/BTF/Doc/ChangeLog0000644001170100242450000000203410711427514014642 0ustar davisfacNov 1, 2007: version 1.0.1 * trivial change to BTF/MATLAB/btf.c mexFunction: unused variable removed. May 31, 2007: version 1.0 released * the C application program interface has been modified (see below) * maxtrans function renamed to btf_maxtrans * strongcomp function renamed to btf_strongcomp * full statement coverage tests (KLU/Tcov) * maxwork parameter added to btf_maxtrans and btf_order * btf_maxtrans modified; now returns Q[i] = -1 if row i is unmatched; code to complete the permutation moved to btf_order. This also changes the maxtrans mexFunction. * btf_install added for easy MATLAB installation * illustrative recursive version of maxtrans removed (see the recursive version of cs_maxtrans in CSparse instead) * MAXTRANS_* macros renamed BTF_* * no bug fixes in this release Dec 12, 2006: version 0.11 * minor MATLAB cleanup Apr 30, 2006: * minor editing of comments. dmperm.c moved to MATLAB directory, since it requires MATLAB. Version number not changed. SuiteSparse/BTF/Doc/lesser.txt0000644001170100242450000006350010275714132015133 0ustar davisfac GNU LESSER GENERAL PUBLIC LICENSE Version 2.1, February 1999 Copyright (C) 1991, 1999 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. [This is the first released version of the Lesser GPL. It also counts as the successor of the GNU Library Public License, version 2, hence the version number 2.1.] Preamble The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public Licenses are intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users. 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SuiteSparse/BTF/Lib/0000755001170100242450000000000010711435722013072 5ustar davisfacSuiteSparse/BTF/Lib/Makefile0000644001170100242450000000221710616443561014540 0ustar davisfacdefault: all ccode: all include ../../UFconfig/UFconfig.mk # for testing only: # TEST = -DTESTING C = $(CC) $(CFLAGS) INC = ../Include/btf.h ../Include/btf_internal.h I = -I../Include -I../../UFconfig all: library library: libbtf.a OBJ = btf_order.o btf_maxtrans.o btf_strongcomp.o \ btf_l_order.o btf_l_maxtrans.o btf_l_strongcomp.o libbtf.a: $(OBJ) $(AR) libbtf.a $(OBJ) $(RANLIB) libbtf.a $(OBJ): $(INC) #------------------------------------------------------------------------------- btf_order.o: ../Source/btf_order.c $(C) -c $(I) $< -o $@ btf_maxtrans.o: ../Source/btf_maxtrans.c $(C) -c $(I) $< -o $@ btf_strongcomp.o: ../Source/btf_strongcomp.c $(C) -c $(I) $< -o $@ #------------------------------------------------------------------------------- btf_l_order.o: ../Source/btf_order.c $(C) -c $(I) -DDLONG $< -o $@ btf_l_maxtrans.o: ../Source/btf_maxtrans.c $(C) -c $(I) -DDLONG $< -o $@ btf_l_strongcomp.o: ../Source/btf_strongcomp.c $(C) -c $(I) -DDLONG $< -o $@ #------------------------------------------------------------------------------- purge: distclean distclean: clean - $(RM) libbtf.a clean: - $(RM) $(CLEAN) SuiteSparse/BTF/Makefile0000644001170100242450000000036610616404675014040 0ustar davisfacdefault: library include ../UFconfig/UFconfig.mk library: ( cd Lib ; $(MAKE) ) clean: ( cd Lib ; $(MAKE) clean ) distclean: ( cd Lib ; $(MAKE) distclean ) ( cd MATLAB ; $(MAKE) distclean ) mex: ( cd MATLAB ; $(MAKE) ) purge: distclean SuiteSparse/BTF/MATLAB/0000755001170100242450000000000010711653376013333 5ustar davisfacSuiteSparse/BTF/MATLAB/drawbtf.m0000644001170100242450000000077610620365500015140 0ustar davisfacfunction drawbtf (A, p, q, r) %DRAWBTF plot the BTF form of a matrix % % A(p,q) is in BTF form, r the block boundaries % % Example: % [p,q,r] = dmperm (A) % drawbtf (A, p, q, r) % % See also btf, maxtrans, strongcomp, dmperm. % Copyright 2004-2007, Tim Davis, University of Florida nblocks = length (r) - 1 ; hold off spy (A (p,abs(q))) hold on for k = 1:nblocks k1 = r (k) ; k2 = r (k+1) ; nk = k2 - k1 ; if (nk > 1) plot ([k1 k2 k2 k1 k1]-.5, [k1 k1 k2 k2 k1]-.5, 'r') ; end end SuiteSparse/BTF/MATLAB/Test/0000755001170100242450000000000010711445542014244 5ustar davisfacSuiteSparse/BTF/MATLAB/Test/test1.m0000644001170100242450000000642710711445424015472 0ustar davisfacfunction test1 (nmat) %TEST1 test for BTF % Requires CSparse and UFget % Example: % test1 % See also btf, maxtrans, strongcomp, dmperm, UFget, % test1, test2, test3, test4, test5. % Copyright 2007, Timothy A. Davis, University of Florida index = UFget ; % f = find (index.sprank < min (index.nrows, index.ncols)) ; f = 1:length (index.nrows) ; % too much time: skip = [1514 1297 1876 1301] ; f = setdiff (f, skip) ; [ignore i] = sort (index.nnz (f)) ; f = f (i) ; if (nargin < 1) nmat = 1000 ; end nmat = min (nmat, length (f)) ; f = f (1:nmat) ; T0 = zeros (nmat,1) ; T1 = zeros (nmat,1) ; Anz = zeros (nmat,1) ; figure (1) ; MN = zeros (nmat, 2) ; Nzdiag = zeros (nmat,1) ; % warmup p = maxtrans (sparse (1)) ; %#ok p = cs_dmperm (sparse (1)) ; %#ok a = cs_transpose (sparse (1)) ; %#ok h = waitbar (0, 'BTF test 1 of 6') ; try for k = 1:nmat Prob = UFget (f (k), index) ; A = Prob.A ; clear Prob t = 0 ; waitbar (k/nmat, h) ; r = full (sum (spones (A), 2)) ; c = full (sum (spones (A))) ; m2 = length (find (r > 0)) ; n2 = length (find (c > 0)) ; if (m2 < n2) tic A = cs_transpose (A) ; t = toc ; end Nzdiag (k) = nnz (diag (A)) ; [m n] = size (A) ; Anz (k) = nnz (A) ; MN (k,:) = [m n] ; tic q = maxtrans (A) ; t0 = toc ; s0 = sum (q > 0) ; T0 (k) = max (1e-9, t0) ; tic p = cs_dmperm (A) ; t1 = toc ; s1 = sum (p > 0) ; T1 (k) = max (1e-9, t1) ; fprintf (... '%4d maxtrans %10.6f %10.6f cs_dmperm %10.6f m/n %8.2f', ... f(k), t, t0, t1, m/n) ; if (t1 ~= 0) fprintf (' rel: %8.4f', t0 / t1) ; end fprintf ('\n') ; if (s0 ~= s1) error ('!') ; end if (s0 == n & m == n) %#ok B = A (:, q) ; subplot (2,2,1) ; cspy (B) ; if (nnz (diag (B)) ~= n) error ('?') end clear B else cspy (0) ; end maxnz = nnz (A) ; zfree = find (MN (1:k,1) == MN (1:k,2) & Nzdiag (1:k) == MN(1:k,1)) ; square = find (MN (1:k,1) == MN (1:k,2) & Nzdiag (1:k) ~= MN(1:k,1)) ; tall = find (MN (1:k,1) > MN (1:k,2)) ; squat = find (MN (1:k,1) < MN (1:k,2)) ; subplot (2,2,2) ; loglog (Anz (square), T0 (square) ./ T1 (square), ... 'o', [1 maxnz], [1 1], 'r-') ; title ('square') ; subplot (2,2,3) ; loglog (Anz (tall), T0 (tall) ./ T1 (tall), ... 'o', [1 maxnz], [1 1], 'r-') ; title ('tall') ; subplot (2,2,4) ; title ('square, intially zero-free') ; loglog (Anz (zfree), T0 (zfree) ./ T1 (zfree), ... 'o', [1 maxnz], [1 1], 'r-') ; title ('square, zero-free diag') ; drawnow end catch % out-of-memory is OK, other errors are not disp (lasterr) ; if (isempty (strfind (lasterr, 'Out of memory'))) error (lasterr) ; %#ok else fprintf ('test terminated early, but otherwise OK\n') ; end end close (h) ; SuiteSparse/BTF/MATLAB/Test/test2.m0000644001170100242450000000436610711445435015475 0ustar davisfacfunction test2 (nmat) %TEST2 test for BTF % Requires CSparse and UFget % Example: % test2 % See also btf, maxtrans, strongcomp, dmperm, UFget, % test1, test2, test3, test4, test5. % Copyright 2007, Timothy A. Davis, University of Florida index = UFget ; f = find (index.nrows == index.ncols) ; % too much time: skip = [1514 1297 1876 1301] ; f = setdiff (f, skip) ; [ignore i] = sort (index.nnz (f)) ; f = f (i) ; if (nargin < 1) nmat = 1000 ; end nmat = min (nmat, length (f)) ; f = f (1:nmat) ; T0 = zeros (nmat,1) ; T1 = zeros (nmat,1) ; Anz = zeros (nmat,1) ; figure (1) ; clf MN = zeros (nmat, 2) ; Nzdiag = zeros (nmat,1) ; % warmup p = maxtrans (sparse (1)) ; %#ok p = btf (sparse (1)) ; %#ok p = cs_dmperm (sparse (1)) ; %#ok a = cs_transpose (sparse (1)) ; %#ok h = waitbar (0, 'BTF test 2 of 6') ; try for k = 1:nmat Prob = UFget (f (k), index) ; A = Prob.A ; waitbar (k/nmat, h) ; Nzdiag (k) = nnz (diag (A)) ; [m n] = size (A) ; Anz (k) = nnz (A) ; MN (k,:) = [m n] ; tic [p,q,r] = btf (A) ; t0 = toc ; s0 = sum (q > 0) ; T0 (k) = max (1e-9, t0) ; tic [p2,q2,r2] = cs_dmperm (A) ; t1 = toc ; s1 = sum (dmperm (A) > 0) ; T1 (k) = max (1e-9, t1) ; fprintf ('%4d btf %10.6f cs_dmperm %10.6f', f(k), t0, t1) ; if (t1 ~= 0) fprintf (' rel: %8.4f', t0 / t1) ; end fprintf ('\n') ; if (s0 ~= s1) error ('!') ; end C = A (p, abs (q)) ; subplot (1,2,1) ; cspy (C) ; z = find (q < 0) ; zd = nnz (diag (C (z,z))) ; if (zd > 0) error ('?') ; end minnz = Anz (1) ; maxnz = nnz (A) ; subplot (1,2,2) ; loglog (Anz (1:k), T0 (1:k) ./ T1 (1:k), ... 'o', [minnz maxnz], [1 1], 'r-') ; drawnow clear C A Prob end catch % out-of-memory is OK, other errors are not disp (lasterr) ; if (isempty (strfind (lasterr, 'Out of memory'))) error (lasterr) ; %#ok else fprintf ('test terminated early, but otherwise OK\n') ; end end close (h) ; SuiteSparse/BTF/MATLAB/Test/test3.m0000644001170100242450000003770210711445507015476 0ustar davisfacfunction test3 (nmat) %TEST3 test for BTF % Requires UFget % Example: % test3 % See also btf, maxtrans, strongcomp, dmperm, UFget, % test1, test2, test3, test4, test5. % Copyright 2007, Timothy A. Davis, Univ. of Florida doplot = 1 ; dopause = 0 ; dostrong = 1 ; index = UFget ; f = find (index.nrows == index.ncols) ; [ignore i] = sort (index.nnz (f)) ; f = f (i) ; clear i figure (1) % short test set: seg faults, lots of blocks, lots of work, and so on: nasty = [ % --- various test matrices (no seg fault, quick run time) -(1:8)' % generated matrices 904 % vanHeukelum/cage3 (5-by-5) 819 % Simon/raefsky6 (permuted triangular matrix) % % --- older seg faults: 264 % HB/west0156, causes older strongcomp_recursive to fail 824 % TOKAMAK/utm300 (300-by-300), causes older code to fail 868 % Pothen/bodyy4 % % --- seg faults in old MATLAB dmperm 290 % Averous/epb3 983 % Sanghavi/ecl32 885 % Pothen/tandem_dual 879 % Pothen/onera_dual 955 % Schenk_IBMSDS/2D_54019_highK 957 % Schenk_IBMSDS/3D_51448_3D 958 % Schenk_IBMSDS/ibm_matrix_2 912 % vanHeukelum/cage11 924 % Andrews/Andrews 960 % Schenk_IBMSDS/matrix-new_3 862 % Kim/kim1 544 % Hamm/scircuit 897 % Norris/torso2 801 % Ronis/xenon1 53 % HB/bcsstk31 958 % Schenk_IBMSDS/matrix_9 844 % Cunningham/qa8fk 845 % Cunningham/qa8fk 821 % Simon/venkat25 822 % Simon/venkat50 820 % Simon/venkat01 812 % Simon/bbmat 804 % Rothberg/cfd1 54 % HB/bcsstk32 913 % vanHeukelum/cage12 846 % Boeing/bcsstk39 972 % Schenk_IBMSDS/para-10 974 % Schenk_IBMSDS/para-5 975 % Schenk_IBMSDS/para-6 976 % Schenk_IBMSDS/para-7 977 % Schenk_IBMSDS/para-8 978 % Schenk_IBMSDS/para-9 961 % Schenk_ISEI/barrier2-10 962 % Schenk_ISEI/barrier2-11 963 % Schenk_ISEI/barrier2-12 964 % Schenk_ISEI/barrier2-1 965 % Schenk_ISEI/barrier2-2 966 % Schenk_ISEI/barrier2-3 967 % Schenk_ISEI/barrier2-4 968 % Schenk_ISEI/barrier2-9 851 % Chen/pkustk05 979 % Kamvar/Stanford 374 % Bova/rma10 % % --- lots of time: 395 % DRIVCAV/cavity16 396 % DRIVCAV/cavity17 397 % DRIVCAV/cavity18 398 % DRIVCAV/cavity19 399 % DRIVCAV/cavity20 400 % DRIVCAV/cavity21 401 % DRIVCAV/cavity22 402 % DRIVCAV/cavity23 403 % DRIVCAV/cavity24 404 % DRIVCAV/cavity25 405 % DRIVCAV/cavity26 1109 % Sandia/mult_dcop_01 1110 % Sandia/mult_dcop_02 1111 % Sandia/mult_dcop_03 376 % Brethour/coater2 284 % ATandT/onetone2 588 % Hollinger/mark3jac100 589 % Hollinger/mark3jac100sc 452 % Grund/bayer01 920 % Hohn/sinc12 590 % Hollinger/mark3jac120 591 % Hollinger/mark3jac120sc 809 % Shyy/shyy161 448 % Graham/graham1 283 % ATandT/onetone1 445 % Garon/garon2 541 % Hamm/bcircuit 592 % Hollinger/mark3jac140 593 % Hollinger/mark3jac140sc 435 % FIDAP/ex40 912 % Hohn/sinc15 894 % Norris/lung2 542 % Hamm/hcircuit 752 % Mulvey/finan512 753 % Mulvey/pfinan512 564 % Hollinger/g7jac180 565 % Hollinger/g7jac180sc 566 % Hollinger/g7jac200 567 % Hollinger/g7jac200sc 748 % Mallya/lhr34 749 % Mallya/lhr34c 922 % Hohn/sinc18 447 % Goodwin/rim 807 % Rothberg/struct3 286 % ATandT/twotone 982 % Tromble/language 953 % Schenk_IBMNA/c-73 890 % Norris/heart1 750 % Mallya/lhr71 751 % Mallya/lhr71c 925 % FEMLAB/ns3Da 827 % Vavasis/av41092 931 % FEMLAB/sme3Db 1297 % GHS_index/boyd2 1301 % GHS_indef/cont-300 % % --- lots of time, and seg faults: 285 % ATandT/pre2 % --- huge matrix, turn off plotting 940 % Shenk/af_shell1, memory leak in plot, after call to btf, once. % ---- ]' ; % maxtrans_recursive causes a seg fault on these matrices, because of % stack overflow (this is expected) skip_list_maxtrans_recursive = 285 ; % p = dmperm (A) in MATLAB 7.4 causes a seg fault on these matrices: skip_list_dmperm = [285 1301 1231 1251 1232 1241] ; % [p,q,r] = dmperm (A) in MATLAB 7.4 causes a seg fault on these matrices: skip_list_dmperm_btf = ... [ 285 879 885 290 955 957 958 924 960 897 959 844 845 ... 821 822 820 804 913 846 972 974:978 961:968 979 940 ... 1422 1513 1412 1510 1301 1231 1251 1434 1213 1232 1241 1357 1579 1431 1281] ; % length(skip_list_dmperm_btf) % time intensive skip_costly = [1514 1297 1876 1301] ; % strongcomp (recursive) causes a seg fault on these matrices because of % stack overflow (this is expected). skip_list_strongcomp_recursive = ... [983 285 879 885 290 955 957 958 912 924 960 862 544 897 801 53 959 844 845 ... 821 822 820 812 804 54 913 846 972 974:978 961:968 851 374 940] ; skip_list_strongcomp_recursive = ... [ skip_list_strongcomp_recursive 592 593 752 753 807 286 982 855 566 567 ] ; % matrices with the largest # of nonzeros in the set (untested) toobig = [ 928 853 852 356 761 368 973 895 805 849 932 ... 803 854 936 802 850 537 856 898 857 859 971 937 ... 914 858 980 896 806 538 863 369 938 860 941 942 ... 943 944 945 946 947 948 915 939 916 ] ; f = [ -(1:8) f ] ; % f = nasty ; h = waitbar (0, 'BTF test 3 of 6') ; if (nargin < 1) nmat = 1000 ; end nmat = min (nmat, length (f)) ; f = f (1:nmat) ; try for matnum = 1:nmat waitbar (matnum/nmat, h) ; j = f (matnum) ; if (any (j == toobig) | any (j == skip_costly)) %#ok fprintf ('\n%4d: %3d %s/%s too big\n', ... matnum, j, index.Group{j}, index.Name{j}) ; continue ; end rand ('state', 0) ; % clear all unused variables. % nothing here is left that is proportional to the matrix size clear A p1 p2 p3 q3 r3 match1 match2 match4 pa ra sa qa B C pb rb pc rc clear jumble B11 B12 B13 B21 B22 B23 B31 B32 B33 pjumble qjumble ans clear c kbad kgood % whos % pause if (j > 0) Problem = UFget (j, index) ; name = Problem.name ; A = Problem.A ; clear Problem else % construct the jth test matrix j = -j ; if (j == 1 | j == 2) %#ok B11 = UFget ('Grund/b1_ss') ; % 7-by-7 diagonal block B11 = B11.A ; B12 = sparse (zeros (7,2)) ; B12 (3,2) = 1 ; B13 = sparse (ones (7,5)) ; B21 = sparse (zeros (2,7)) ; B22 = sparse (ones (2,2)) ; % 2-by-2 diagonal block B23 = sparse (ones (2,5)) ; B31 = sparse (zeros (5,7)) ; B32 = sparse (zeros (5,2)) ; B33 = UFget ('vanHeukelum/cage3') ; % 5-by-5 diagonal block B33 = B33.A ; A = [ B11 B12 B13 ; B21 B22 B23 ; B31 B32 B33 ] ; name = '(j=1 test matrix)' ; end if (j == 2) pjumble = [ 10 7 11 1 13 12 8 2 5 14 9 6 4 3 ] ; qjumble = [ 3 14 2 11 1 8 5 7 10 12 4 13 9 6 ] ; A = A (pjumble, qjumble) ; name = '(j=2 test matrix)' ; elseif (j == 3) A = sparse (1) ; elseif (j == 4) A = sparse (0) ; elseif (j == 5) A = sparse (ones (2)) ; elseif (j == 6) A = sparse (2,2) ; elseif (j == 7) A = speye (2) ; elseif (j == 8) A = sparse (2,2) ; A (2,1) = 1 ; end if (j > 2) full (A) end end [m n] = size (A) ; if (m ~= n) continue ; end fprintf ('\n%4d: ', matnum) ; fprintf (' =========================== Matrix: %3d %s\n', j, name) ; fprintf ('n: %d nz: %d\n', n, nnz (A)) ; if (nnz (A) > 6e6) doplot = 0 ; end %----------------------------------------------------------------------- % now try maxtrans tic match1 = maxtrans (A) ; t = toc ; s1 = sum (match1 > 0) ; fprintf ('n-sprank: %d\n', n-s1) ; fprintf ('maxtrans: %8.2f seconds\n', t) ; singular = s1 < n ; if (doplot) % figure (1) clf subplot (2,4,1) spy (A) title (name) ; end p1 = match1 ; if (any (p1 <= 0)) % complete the permutation badrow = find (p1 <= 0) ; badcol = ones (1,n) ; badcol (p1 (p1 > 0)) = 0 ; badcol = find (badcol) ; p1 (badrow) = badcol ; % construct the older form of match1 match1 (badrow) = -p1 (badrow) ; end if (any (sort (p1) ~= 1:n)) error ('!!') ; end B = A (:,p1) ; if (doplot) subplot (2,4,2) hold off spy (B) hold on badcol = find (match1 < 0) ; Junk = sparse (badcol, badcol, ones (length (badcol), 1), n, n) ; % if (~isempty (A)) % spy (Junk, 'ro') ; % end title ('maxtrans') ; end d = nnz (diag (B)) ; if (d ~= s1) error ('bad sprank') ; end clear B %----------------------------------------------------------------------- % try p = dmperm(A) skip_dmperm = any (j == skip_list_dmperm) ; if (~skip_dmperm) tic match4 = dmperm (A) ; t = toc ; fprintf ('p=dmperm(A): %8.2f seconds\n', t) ; s4 = sum (match4 > 0) ; singular4 = (s4 < n) ; if (doplot) if (~singular4) subplot (2,4,3) spy (A (match4,:)) title ('dmperm') ; end end if (singular ~= singular4) error ('s4?') ; end if (s1 ~= s4) error ('bad sprank') ; end else fprintf ('p=dmperm(A): skip\n') ; end %----------------------------------------------------------------------- nblocks = -1 ; skip_dmperm_btf = any (j == skip_list_dmperm_btf) ; if (~skip_dmperm_btf) % get btf form tic [pa,qa,ra,sa] = dmperm (A) ; t = toc ; fprintf ('[p,q,r,s]=dmperm(A): %8.2f seconds\n', t) ; nblocks = length (ra) - 1 ; fprintf ('nblocks: %d\n', nblocks) ; if (~singular4) checkbtf (A, pa, qa, ra) ; if (doplot) subplot (2,4,4) drawbtf (A, pa, qa, ra) title ('dmperm blocks') end end else fprintf ('[p,q,r,s]=dmperm(A): skip\n') ; end jumble = randperm (n) ; %----------------------------------------------------------------------- % try strongcomp, non-recursive version %------------------------------------------------------------------- % try strongcomp on original matrix B = A (:,p1) ; tic ; [pb,rb] = strongcomp (B) ; t = toc ; fprintf ('strongcomp %8.2f seconds\n', t) ; if (~singular & ~skip_dmperm_btf & (length (rb) ~= nblocks+1)) %#ok error ('BTF:invalid (rb)') ; end checkbtf (B, pb, pb, rb) ; if (doplot) subplot (2,4,5) drawbtf (B, pb, pb, rb) ; title ('strongcomp') ; end %------------------------------------------------------------------- % try btf on original matrix tic ; [pw,qw,rw] = btf (A) ; t = toc ; fprintf ('btf %8.2f seconds nblocks %d\n', ... t, length (rw)-1) ; if (any (pw ~= pb)) error ('pw') ; end if (any (rw ~= rb)) error ('rw') ; end if (any (abs (qw) ~= p1 (pw))) error ('qw') ; end c = diag (A (pw,abs (qw))) ; if (~singular & ~skip_dmperm_btf & (length (rw) ~= nblocks+1)) %#ok error ('BTF:invalid (rw)') ; end checkbtf (A, pw, abs (qw), rw) ; kbad = find (qw < 0) ; kgood = find (qw > 0) ; if (any (c (kbad) ~= 0)) error ('kbad') ; end if (any (c (kgood) == 0)) %#ok error ('kgood') ; end if (doplot) subplot (2,4,6) drawbtf (A, pw, abs (qw), rw) ; if (n < 500) for k = kbad plot ([k (k+1) (k+1) k k]-.5, ... [k k (k+1) (k+1) k]-.5, 'r') ; end end title ('btf') ; end %------------------------------------------------------------------- % try [p,q,r] = strongcomp (A, qin) form tic [pz,qz,rz] = strongcomp (A, match1) ; t = toc ; fprintf ('[p,q,r]=strongcomp(A,qin)%8.2f seconds\n', t) ; if (any (pz ~= pb)) error ('pz') ; end if (any (rz ~= rb)) error ('rz') ; end if (any (abs (qz) ~= p1 (pz))) error ('qz') ; end c = diag (A (pz,abs (qz))) ; if (~singular & ~skip_dmperm_btf & (length (rz) ~= nblocks+1)) %#ok error ('BTF:invalid (rz)') ; end checkbtf (A, pz, abs (qz), rz) ; kbad = find (qz < 0) ; kgood = find (qz > 0) ; if (any (c (kbad) ~= 0)) error ('kbad') ; end if (any (c (kgood) == 0)) %#ok error ('kgood') ; end if (doplot) subplot (2,4,7) drawbtf (A, pz, abs (qz), rz) ; if (n < 500) for k = kbad plot ([k (k+1) (k+1) k k]-.5, ... [k k (k+1) (k+1) k]-.5, 'r') ; end end title ('strongcomp(A,qin)') ; end %------------------------------------------------------------------- % try strongcomp again, on a randomly jumbled matrix C = sparse (B (jumble, jumble)) ; tic ; [pc,rc] = strongcomp (C) ; t = toc ; fprintf ('strongcomp (rand) %8.2f seconds\n', t) ; if (~singular & ~skip_dmperm_btf & (length (rc) ~= nblocks+1)) %#ok error ('BTF:invalid (rc)') ; end checkbtf (C, pc, pc, rc) ; if (doplot) subplot (2,4,8) drawbtf (C, pc, pc, rc) ; title ('strongcomp(rand)') ; end if (length (rc) ~= length (rb)) error ('strongcomp random mismatch') ; end %----------------------------------------------------------------------- if (doplot) drawnow end if (matnum ~= nmat & dopause) %#ok input ('Hit enter: ') ; end end catch % out-of-memory is OK, other errors are not disp (lasterr) ; if (isempty (strfind (lasterr, 'Out of memory'))) error (lasterr) ; %#ok else fprintf ('test terminated early, but otherwise OK\n') ; end end close (h) ; SuiteSparse/BTF/MATLAB/Test/test4.m0000644001170100242450000000407310711445477015500 0ustar davisfacfunction test4 (nmat) %TEST4 test for BTF % Requires UFget % Example: % test4 % See also btf, maxtrans, strongcomp, dmperm, UFget, % test1, test2, test3, test4, test5. % Copyright 2007, Timothy A. Davis, University of Florida index = UFget ; f = find (index.nrows == index.ncols) ; [ignore i] = sort (index.nnz (f)) ; f = f (i) ; % time intensive skip_costly = [1514 1297 1876 1301] ; f = setdiff (f, skip_costly) ; if (nargin < 1) nmat = 1000 ; end nmat = min (nmat, length (f)) ; f = f (1:nmat) ; h = waitbar (0, 'BTF test 4 of 6') ; try for k = 1:nmat Prob = UFget (f (k), index) ; A = Prob.A ; waitbar (k/nmat, h) ; for tr = [1 -1] if (tr == -1) AT = A' ; [m n] = size (A) ; if (m == n) if (nnz (spones (AT) - spones (A)) == 0) fprintf ('skip transpose\n') ; continue ; end end A = AT ; end tic [p1,q1,r1,work1] = btf (A) ; t1 = toc ; n1 = length (r1) - 1 ; tic [p2,q2,r2,work2] = btf (A, 10) ; t2 = toc ; n2 = length (r2) - 1 ; fprintf (... '%4d %4d : %10.4f %8d %8g : %10.4f %8d %8g :', ... k, f(k), t1, n1, work1, t2, n2, work2) ; if (t2 ~= 0) fprintf (' rel %8.4f %8.4f' , t1 / t2, n2 / (max (1, n1))) ; end fprintf ('\n') ; if (n1 ~= n2 | work1 ~= work2) %#ok disp (Prob) ; fprintf ('^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n') ; end end end catch % out-of-memory is OK, other errors are not disp (lasterr) ; if (isempty (strfind (lasterr, 'Out of memory'))) error (lasterr) ; %#ok else fprintf ('test terminated early, but otherwise OK\n') ; end end close (h) ; SuiteSparse/BTF/MATLAB/Test/test5.m0000644001170100242450000000371410711445520015467 0ustar davisfacfunction test5 (nmat) %TEST5 test for BTF % Requires UFget % Example: % test5 % See also btf, maxtrans, strongcomp, dmperm, UFget, % test1, test2, test3, test4, test5. % Copyright 2007, Timothy A. Davis, University of Florida index = UFget ; [ignore f] = sort (index.nnz) ; % time intensive skip_costly = [1514 1297 1876 1301] ; f = setdiff (f, skip_costly) ; if (nargin < 1) nmat = 1000 ; end nmat = min (nmat, length (f)) ; f = f (1:nmat) ; h = waitbar (0, 'BTF test 5 of 6') ; try for k = 1:nmat i = f(k) ; Prob = UFget (i, index) ; A = Prob.A ; waitbar (k/nmat, h) ; for tr = [1 -1] if (tr == -1) AT = A' ; [m n] = size (A) ; if (m == n) if (nnz (spones (AT) - spones (A)) == 0) fprintf ('skip test with transpose\n') ; continue ; end end A = AT ; end tic q1 = maxtrans (A) ; t1 = toc ; r1 = sum (q1 > 0) ; tic q2 = maxtrans (A, 10) ; t2 = toc ; r2 = sum (q2 > 0) ; fprintf (... '%4d %4d : %10.4f %8d : %10.4f %8d', k, f(k), t1, r1, t2, r2) ; fprintf (' rel sprank %8.4f', r2 / (max (1, r1))) ; if (t2 ~= 0) fprintf (': rel time %8.4f', t1 / t2) ; end fprintf ('\n') ; if (r1 ~= r2) disp (Prob) ; fprintf ('^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n') ; end end end catch % out-of-memory is OK, other errors are not disp (lasterr) ; if (isempty (strfind (lasterr, 'Out of memory'))) error (lasterr) ; %#ok else fprintf ('test terminated early, but otherwise OK\n') ; end end close (h) ; SuiteSparse/BTF/MATLAB/Test/btf_test.m0000644001170100242450000000052110710446670016234 0ustar davisfacfunction btf_test (nmat) %BTF_TEST test for BTF % Requires CSparse (or CXSparse) and UFget % Example: % btf_test % See also btf, maxtrans, strongcomp, dmperm, UFget, % test1, test2, test3, test4, test5, test6. if (nargin < 1) nmat = 800 ; end test1 (nmat) ; test2 (nmat) ; test3 (nmat) ; test4 (nmat) ; test5 (nmat) ; test6 ; SuiteSparse/BTF/MATLAB/Test/checkbtf.m0000644001170100242450000000152710620664675016211 0ustar davisfacfunction checkbtf (A, p, q, r) %CHECKBTF ensure A(p,q) is in BTF form % % A(p,q) is in BTF form, r the block boundaries % % Example: % [p,q,r] = dmperm (A) % checkbtf (A, p, q, r) % % See also drawbtf, maxtrans, strongcomp. % Copyright 2007, Timothy A. Davis, University of Florida [m n] = size (A) ; if (m ~= n) error ('A must be square') ; end if (any (sort (p) ~= 1:n)) error ('p not a permutation') ; end if (any (sort (q) ~= 1:n)) error ('q not a permutation') ; end nblocks = length (r) - 1 ; if (r (1) ~= 1) error ('r(1) not one') ; end if (r (end) ~= n+1) error ('r(end) not n+1') ; end if (nblocks < 1 | nblocks > n) %#ok error ('nblocks wrong') ; end nblocks = length (r) - 1 ; rdiff = r (2:(nblocks+1)) - r (1:nblocks) ; if (any (rdiff < 1) | any (rdiff > n)) %#ok error ('r bad') end SuiteSparse/BTF/MATLAB/Test/test6.m0000644001170100242450000000774110711445541015477 0ustar davisfacfunction test6 %TEST6 test for BTF % Requires UFget % Example: % test6 % See also btf, maxtrans, strongcomp, dmperm, UFget, % test1, test2, test3, test4, test5. % Copyright 2007, Timothy A. Davis, University of Florida quick2 = [ ... 1522 -272 1463 1521 460 1507 -838 1533 -1533 -1456 -1512 734 211 ... -385 -735 394 -397 1109 -744 ... -734 -375 -1200 -1536 -837 519 -519 520 -520 189 -189 454 385 ... 387 -387 384 -384 386 -386 388 -388 525 -525 526 -526 735 ... 1508 209 210 1243 -1243 1534 -840 1234 -1234 390 -390 392 -392 ... -394 1472 1242 -1242 389 -389 391 -391 393 -393 1215 -1215 1216 ... -1216 736 -736 737 -737 455 -455 -224 -839 1426 -1426 -1473 396 ... -396 398 -398 400 -400 402 -402 404 -404 -1531 395 -395 397 ... 399 -399 401 -401 403 -403 405 -405 -738 -739 1459 -1459 1111 ... 1110 376 -376 284 -284 -740 -742 -741 -743 1293 -1293 452 920 ... -745 -446 1462 -1461 448 -448 283 -283 1502 -1502 1292 -1292 1503 ... -1503 1291 -1291 445 -445 -746 -747 1300 -1300 435 -435 -1343 -1345 ... -1344 1305 -1305 921 -1513 1307 -1307 1369 -1369 1374 -1374 1377 ... -1377 748 -748 -749 1510 922 -922 ] ; index = UFget ; nmat = length (quick2) ; dopause = 0 ; h = waitbar (0, 'BTF test 6 of 6') ; try for k = 1:nmat waitbar (k/nmat, h) ; i = quick2 (k) ; Prob = UFget (abs (i), index) ; disp (Prob) ; if (i < 0) fprintf ('transposed\n') ; A = Prob.A' ; [m n] = size (A) ; if (m == n) if (nnz (spones (A) - spones (Prob.A)) == 0) fprintf ('skip...\n') ; continue ; end end else A = Prob.A ; end tic [p1,q1,r1,work1] = btf (A) ; t1 = toc ; n1 = length (r1) - 1 ; m1 = nnz (diag (A (p1, abs (q1)))) ; limit = work1/nnz(A) ; fprintf ('full search: %g * nnz(A)\n', limit) ; works = linspace(0,limit,9) ; works (1) = eps ; nw = length (works) ; T2 = zeros (nw, 1) ; N2 = zeros (nw, 1) ; M2 = zeros (nw, 1) ; T2 (end) = t1 ; N2 (end) = n1 ; M2 (end) = m1 ; fprintf ('full time %10.4f blocks %8d nnz(diag) %8d\n\n', t1, n1, m1) ; subplot (3,4,4) ; drawbtf (A, p1, abs (q1), r1) ; title (Prob.name, 'Interpreter', 'none') ; for j = 1:nw-1 maxwork = works (j) ; tic [p2,q2,r2,work2] = btf (A, maxwork) ; t2 = toc ; n2 = length (r2) - 1 ; m2 = nnz (diag (A (p2, abs (q2)))) ; T2 (j) = t2 ; N2 (j) = n2 ; M2 (j) = m2 ; fprintf ('%9.1f %10.4f blocks %8d nnz(diag) %8d\n', ... maxwork, t2, n2, m2) ; subplot (3,4,4+j) ; drawbtf (A, p2, abs (q2), r2) ; title (sprintf ('%g', maxwork)) ; ss = [1:j nw] ; subplot (3,4,1) ; plot (works(ss), T2(ss), 'o-') ; title ('time vs work') ; axis ([0 limit 0 max(0.1,max(T2))]) ; subplot (3,4,2) ; plot (works(ss), N2(ss), 'o-') ; title ('blocks vs work') ; axis ([0 limit 0 n1]) ; subplot (3,4,3) ; plot (works(ss), M2(ss), 'o-') ; title ('nnz(diag) vs work') ; axis ([0 limit 0 m1]) ; drawnow end fprintf ('full time %10.4f blocks %8d nnz(diag) %8d\n', t1, n1, m1) ; if (dopause) input ('hit enter: ') ; end end catch % out-of-memory is OK, other errors are not disp (lasterr) ; if (isempty (strfind (lasterr, 'Out of memory'))) error (lasterr) ; %#ok else fprintf ('test terminated early, but otherwise OK\n') ; end end close (h) ; SuiteSparse/BTF/MATLAB/strongcomp.c0000644001170100242450000001243210616144521015663 0ustar davisfac/* ========================================================================== */ /* === stongcomp mexFunction ================================================ */ /* ========================================================================== */ /* STRONGCOMP: Find a symmetric permutation to upper block triangular form of * a sparse square matrix. * * Usage: * * [p,r] = strongcomp (A) ; * * [p,q,r] = strongcomp (A,qin) ; * * In the first usage, the permuted matrix is C = A (p,p). In the second usage, * the matrix A (:,qin) is symmetrically permuted to upper block triangular * form, where qin is an input column permutation, and the final permuted * matrix is C = A (p,q). This second usage is equivalent to * * [p,r] = strongcomp (A (:,qin)) ; * q = qin (p) ; * * That is, if qin is not present it is assumed to be qin = 1:n. * * C is the permuted matrix, with a number of blocks equal to length(r)-1. * The kth block is from row/col r(k) to row/col r(k+1)-1 of C. * r(1) is one and the last entry in r is equal to n+1. * The diagonal of A (or A (:,qin)) is ignored. * * strongcomp is normally proceeded by a maximum transversal: * * [p,q,r] = strongcomp (A, maxtrans (A)) * * if the matrix has full structural rank. This is identical to * * [p,q,r] = btf (A) * * (except that btf handles the case when A is structurally rank-deficient). * It essentially the same as * * [p,q,r] = dmperm (A) * * except that p, q, and r will differ between btf and dmperm. Both return an * upper block triangular form with a zero-free diagonal. The number and sizes * of the blocks will be identical, but the order of the blocks, and the * ordering within the blocks, can be different. For structurally rank * deficient matrices, dmpmerm returns the maximum matching as a zero-free * diagonal that is above the main diagonal; btf always returns the matching as * the main diagonal (which will thus contain zeros). * * Copyright (c) 2004-2007. Tim Davis, University of Florida, * with support from Sandia National Laboratories. All Rights Reserved. * * See also maxtrans, btf, dmperm */ /* ========================================================================== */ #include "mex.h" #include "btf.h" void mexFunction ( int nargout, mxArray *pargout[], int nargin, const mxArray *pargin[] ) { UF_long b, n, i, k, j, *Ap, *Ai, *P, *R, nblocks, *Work, *Q, jj ; double *Px, *Rx, *Qx ; /* ---------------------------------------------------------------------- */ /* get inputs and allocate workspace */ /* ---------------------------------------------------------------------- */ if (!((nargin == 1 && nargout <= 2) || (nargin == 2 && nargout <= 3))) { mexErrMsgTxt ("Usage: [p,r] = strongcomp (A)" " or [p,q,r] = strongcomp (A,qin)") ; } n = mxGetM (pargin [0]) ; if (!mxIsSparse (pargin [0]) || n != mxGetN (pargin [0])) { mexErrMsgTxt ("strongcomp: A must be sparse, square, and non-empty") ; } /* get sparse matrix A */ Ap = (UF_long *) mxGetJc (pargin [0]) ; Ai = (UF_long *) mxGetIr (pargin [0]) ; /* get output arrays */ P = mxMalloc (n * sizeof (UF_long)) ; R = mxMalloc ((n+1) * sizeof (UF_long)) ; /* get workspace of size 4n (recursive code only needs 2n) */ Work = mxMalloc (4*n * sizeof (UF_long)) ; /* get the input column permutation Q */ if (nargin == 2) { if (mxGetNumberOfElements (pargin [1]) != n) { mexErrMsgTxt ("strongcomp: qin must be a permutation vector of size n") ; } Qx = mxGetPr (pargin [1]) ; Q = mxMalloc (n * sizeof (UF_long)) ; /* connvert Qin to 0-based and check validity */ for (i = 0 ; i < n ; i++) { Work [i] = 0 ; } for (k = 0 ; k < n ; k++) { j = Qx [k] - 1 ; /* convert to 0-based */ jj = BTF_UNFLIP (j) ; if (jj < 0 || jj >= n || Work [jj] == 1) { mexErrMsgTxt ("strongcomp: qin must be a permutation vector of size n") ; } Work [jj] = 1 ; Q [k] = j ; } } else { /* no input column permutation */ Q = (UF_long *) NULL ; } /* ---------------------------------------------------------------------- */ /* find the strongly-connected components of A */ /* ---------------------------------------------------------------------- */ nblocks = btf_l_strongcomp (n, Ap, Ai, Q, P, R, Work) ; /* ---------------------------------------------------------------------- */ /* create outputs and free workspace */ /* ---------------------------------------------------------------------- */ /* create P */ pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ; Px = mxGetPr (pargout [0]) ; for (k = 0 ; k < n ; k++) { Px [k] = P [k] + 1 ; /* convert to 1-based */ } /* create Q */ if (nargin == 2 && nargout > 1) { pargout [1] = mxCreateDoubleMatrix (1, n, mxREAL) ; Qx = mxGetPr (pargout [1]) ; for (k = 0 ; k < n ; k++) { Qx [k] = Q [k] + 1 ; /* convert to 1-based */ } } /* create R */ if (nargout == nargin + 1) { pargout [nargin] = mxCreateDoubleMatrix (1, nblocks+1, mxREAL) ; Rx = mxGetPr (pargout [nargin]) ; for (b = 0 ; b <= nblocks ; b++) { Rx [b] = R [b] + 1 ; /* convert to 1-based */ } } mxFree (P) ; mxFree (R) ; mxFree (Work) ; if (nargin == 2) { mxFree (Q) ; } } SuiteSparse/BTF/MATLAB/strongcomp.m0000644001170100242450000000332410620366436015703 0ustar davisfacfunction [p,q,r] = strongcomp (A, qin) %#ok %STRONGCOMP symmetric permutation to upper block triangular form % The matrix must be sparse and square. % % Example: % [p,r] = strongcomp (A) ; % [p,q,r] = strongcomp (A,qin) ; % % In the first usage, the permuted matrix is C = A (p,p). In the second usage, % the matrix A (:,qin) is symmetrically permuted to upper block triangular % form, where qin is an input column permutation, and the final permuted % matrix is C = A (p,q). This second usage is equivalent to % % [p,r] = strongcomp (A (:,qin)) ; % q = qin (p) ; % % That is, if qin is not present it is assumed to be qin = 1:n. % % C is the permuted matrix, with a number of blocks equal to length(r)-1. % The kth block is from row/col r(k) to row/col r(k+1)-1 of C. % r(1) is one and the last entry in r is equal to n+1. % The diagonal of A (or A (:,qin)) is ignored. % % strongcomp is normally proceeded by a maximum transversal. % Assuming A is square and structurally nonsingular, % % [p,q,r] = strongcomp (A, maxtrans (A)) % % is essentially identical to % % [p,q,r] = dmperm (A) % % except that p, q, and r will differ. Both return an upper block triangular % form with a zero-free diagonal. The number and sizes of the blocks will be % identical, but the order of the blocks, and the ordering within the blocks, % can be different. If the matrix is structurally singular, both strongcomp % and maxtrans return a vector q containing negative entries. abs(q) is a % permutation of 1:n, and find(q<0) gives a list of the indices of the % diagonal of A(p,q) that are zero. % % See also btf, maxtrans, dmperm % Copyright 2004-2007, Tim Davis, University of Florida error ('strongcomp mexFunction not found') ; SuiteSparse/BTF/MATLAB/Makefile0000644001170100242450000000176010616443621014771 0ustar davisfac include ../../UFconfig/UFconfig.mk I = -I../Include -I../../UFconfig MX = $(MEX) $(I) -DDLONG all: maxtrans.mexglx strongcomp.mexglx btf.mexglx recursive: strongcomp_recursive.mexglx maxtrans.mexglx: ../Source/btf_maxtrans.c ../Include/btf.h maxtrans.c \ ../Include/btf_internal.h $(MX) maxtrans.c ../Source/btf_maxtrans.c strongcomp.mexglx: ../Source/btf_strongcomp.c ../Include/btf.h \ strongcomp.c ../Include/btf_internal.h $(MX) strongcomp.c ../Source/btf_strongcomp.c strongcomp_recursive.mexglx: ../Source/btf_strongcomp.c ../Include/btf.h \ strongcomp.c ../Include/btf_internal.h $(MX) -DRECURSIVE -output strongcomp_recursive \ ../Source/btf_strongcomp.c strongcomp.c btf.mexglx: ../Source/btf_strongcomp.c ../Include/btf.h btf.c \ ../Include/btf_internal.h \ ../Source/btf_maxtrans.c ../Source/btf_order.c $(MX) btf.c ../Source/btf_maxtrans.c \ ../Source/btf_strongcomp.c ../Source/btf_order.c distclean: purge purge: clean - $(RM) *.o *.mex* clean: - $(RM) $(CLEAN) SuiteSparse/BTF/MATLAB/btf.c0000644001170100242450000001052010634323167014244 0ustar davisfac/* ========================================================================== */ /* === btf mexFunction ====================================================== */ /* ========================================================================== */ /* BTF: Permute a square matrix to upper block triangular form with a zero-free * diagonal, or with a maximum number of nonzeros along the diagonal if a * zero-free permutation does not exist. * * Usage: * * [p,q,r] = btf (A) ; * [p,q,r] = btf (A, maxwork) ; * * If the matrix has structural full rank, this is essentially identical to * * [p,q,r] = dmperm (A) * * except that p, q, and r will differ in trivial ways. Both return an upper * block triangular form with a zero-free diagonal, if the matrix is * structurally non-singular. The number and sizes of the blocks will be * identical, but the order of the blocks, and the ordering within the blocks, * can be different. * * If the matrix is structurally singular, q will contain negative entries. * The permuted matrix is C = A(p,abs(q)), and find(q<0) gives a list of * indices of the diagonal of C that are equal to zero. This differs from * dmperm, which does not place the maximum matching along the main diagonal * of C=A(p,q), but places it above the diagonal instead. * * See maxtrans, or btf.m, for a description of maxwork. * * An optional fourth output [p,q,r,work] = btf (...) returns the amount of * work performed, or -1 if the maximum work limit is reached (in which case * the maximum matching might not have been found). * * Copyright (c) 2004-2007. Tim Davis, University of Florida, * with support from Sandia National Laboratories. All Rights Reserved. * * See also maxtrans, strongcomp, dmperm */ /* ========================================================================== */ #include "mex.h" #include "btf.h" void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double work, maxwork ; UF_long b, n, k, *Ap, *Ai, *P, *R, nblocks, *Work, *Q, nmatch ; double *Px, *Rx, *Qx, *w ; /* ---------------------------------------------------------------------- */ /* get inputs and allocate workspace */ /* ---------------------------------------------------------------------- */ if (nargin < 1 || nargin > 2 || nargout > 4) { mexErrMsgTxt ("Usage: [p,q,r] = btf (A)") ; } n = mxGetM (pargin [0]) ; if (!mxIsSparse (pargin [0]) || n != mxGetN (pargin [0])) { mexErrMsgTxt ("btf: A must be sparse, square, and non-empty") ; } /* get sparse matrix A */ Ap = (UF_long *) mxGetJc (pargin [0]) ; Ai = (UF_long *) mxGetIr (pargin [0]) ; /* get output arrays */ Q = mxMalloc (n * sizeof (UF_long)) ; P = mxMalloc (n * sizeof (UF_long)) ; R = mxMalloc ((n+1) * sizeof (UF_long)) ; /* get workspace */ Work = mxMalloc (5*n * sizeof (UF_long)) ; maxwork = 0 ; if (nargin > 1) { maxwork = mxGetScalar (pargin [1]) ; } work = 0 ; /* ---------------------------------------------------------------------- */ /* find the permutation to BTF */ /* ---------------------------------------------------------------------- */ nblocks = btf_l_order (n, Ap, Ai, maxwork, &work, P, Q, R, &nmatch, Work) ; /* ---------------------------------------------------------------------- */ /* create outputs and free workspace */ /* ---------------------------------------------------------------------- */ /* create P */ pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ; Px = mxGetPr (pargout [0]) ; for (k = 0 ; k < n ; k++) { Px [k] = P [k] + 1 ; /* convert to 1-based */ } /* create Q */ if (nargout > 1) { pargout [1] = mxCreateDoubleMatrix (1, n, mxREAL) ; Qx = mxGetPr (pargout [1]) ; for (k = 0 ; k < n ; k++) { Qx [k] = Q [k] + 1 ; /* convert to 1-based */ } } /* create R */ if (nargout > 2) { pargout [2] = mxCreateDoubleMatrix (1, nblocks+1, mxREAL) ; Rx = mxGetPr (pargout [2]) ; for (b = 0 ; b <= nblocks ; b++) { Rx [b] = R [b] + 1 ; /* convert to 1-based */ } } /* create work output */ if (nargout > 3) { pargout [3] = mxCreateDoubleMatrix (1, 1, mxREAL) ; w = mxGetPr (pargout [3]) ; w [0] = work ; } mxFree (P) ; mxFree (R) ; mxFree (Work) ; mxFree (Q) ; } SuiteSparse/BTF/MATLAB/btf.m0000644001170100242450000000332210620366273014260 0ustar davisfacfunction [p,q,r] = btf (A) %#ok %BTF permute a square sparse matrix into upper block triangular form % with a zero-free diagonal, or with a maximum number of nonzeros along the % diagonal if a zero-free permutation does not exist. % % Example: % [p,q,r] = btf (A) ; % [p,q,r] = btf (A,maxwork) ; % % If the matrix has structural full rank, this is essentially identical to % % [p,q,r] = dmperm (A) % % except that p, q, and r will differ in trivial ways. Both return an upper % block triangular form with a zero-free diagonal, if the matrix is % structurally non-singular. The number and sizes of the blocks will be % identical, but the order of the blocks, and the ordering within the blocks, % can be different. % % If the matrix is structurally singular, the q from btf will contain negative % entries. The permuted matrix is C = A(p,abs(q)), and find(q<0) gives a list % of indices of the diagonal of C that are equal to zero. This differs from % dmperm, which does not place the maximum matching along the main diagonal % of C=A(p,q), but places it above the diagonal instead. % % The second input limits the maximum amount of work the function does to % be maxwork*nnz(A), or no limit at all if maxwork <= 0. If the function % terminates early as a result, a maximum matching may not be found, and the % diagonal of A(p,abs(q)) might not have the maximum number of nonzeros % possible. Also, the number of blocks (length(r)-1) may be larger than % what btf(A) or dmperm(A) would compute. % % See also maxtrans, strongcomp, dmperm, sprank % Copyright 2004-2007, Tim Davis, University of Florida % with support from Sandia National Laboratories. All Rights Reserved. error ('btf mexFunction not found') ; SuiteSparse/BTF/MATLAB/maxtrans.c0000644001170100242450000000602610620707602015327 0ustar davisfac/* ========================================================================== */ /* === maxtrans mexFunction ================================================= */ /* ========================================================================== */ #define MIN(a,b) (((a) < (b)) ? (a) : (b)) /* MAXTRANS: Find a column permutation for a zero-free diagonal. * * Usage: * * q = maxtrans (A) ; * q = maxtrans (A,maxwork) ; * * A (:,q) has a zero-free diagonal if sprank(A) == n. * If the matrix is structurally singular, q will contain zeros. Similar * to p = dmperm (A), except that dmperm returns a row permutation. * * An optional second output [q,work] = maxtrans (...) returns the amount of * work performed, or -1 if the maximum work limit is reached (in which case * the maximum matching might not have been found). * * Copyright (c) 2004-2007. Tim Davis, University of Florida, * with support from Sandia National Laboratories. All Rights Reserved. */ /* ========================================================================== */ #include "mex.h" #include "btf.h" void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double maxwork, work ; UF_long nrow, ncol, i, *Ap, *Ai, *Match, nmatch, *Work ; double *Matchx, *w ; /* ---------------------------------------------------------------------- */ /* get inputs and allocate workspace */ /* ---------------------------------------------------------------------- */ if (nargin < 1 || nargin > 2 || nargout > 2) { mexErrMsgTxt ("Usage: q = maxtrans (A)") ; } nrow = mxGetM (pargin [0]) ; ncol = mxGetN (pargin [0]) ; if (!mxIsSparse (pargin [0])) { mexErrMsgTxt ("maxtrans: A must be sparse, and non-empty") ; } /* get sparse matrix A */ Ap = (UF_long *) mxGetJc (pargin [0]) ; Ai = (UF_long *) mxGetIr (pargin [0]) ; /* get output array */ Match = mxMalloc (nrow * sizeof (UF_long)) ; /* get workspace of size 5n (recursive version needs only 2n) */ Work = mxMalloc (5*ncol * sizeof (UF_long)) ; maxwork = 0 ; if (nargin > 1) { maxwork = mxGetScalar (pargin [1]) ; } work = 0 ; /* ---------------------------------------------------------------------- */ /* perform the maximum transversal */ /* ---------------------------------------------------------------------- */ nmatch = btf_l_maxtrans (nrow, ncol, Ap, Ai, maxwork, &work, Match, Work) ; /* ---------------------------------------------------------------------- */ /* create outputs and free workspace */ /* ---------------------------------------------------------------------- */ pargout [0] = mxCreateDoubleMatrix (1, nrow, mxREAL) ; Matchx = mxGetPr (pargout [0]) ; for (i = 0 ; i < nrow ; i++) { Matchx [i] = Match [i] + 1 ; /* convert to 1-based */ } if (nargout > 1) { pargout [1] = mxCreateDoubleMatrix (1, 1, mxREAL) ; w = mxGetPr (pargout [1]) ; w [0] = work ; } mxFree (Work) ; mxFree (Match) ; } SuiteSparse/BTF/MATLAB/maxtrans.m0000644001170100242450000000235510620366412015342 0ustar davisfacfunction q = maxtrans (A) %#ok %MAXTRANS permute the columns of a sparse matrix so it has a zero-free diagonal % (if it exists). If no zero-free diagonal exists, then a maximum matching is % found. Note that this differs from p=dmperm(A), which returns a row % permutation. % % Example: % q = maxtrans (A) % q = maxtrans (A,maxwork) % % If row i and column j are matched, then q(i) = j. Otherwise, if row is % unmatched, then q(i) = 0. This is similar to dmperm, except that % p = dmperm(A) returns p(j)=i if row i and column j are matched, or p(j)=0 if % column j is unmatched. % % If A is structurally nonsingular, then A(:,maxtrans(A)) has a zero-free % diagonal, as does A (dmperm(A),:). % % The second input limits the maximum amount of work the function does % (excluding the O(nnz(A)) cheap match phase) to be maxwork*nnz(A), or no limit % at all if maxwork <= 0. If the function terminates early as a result, a % maximum matching may not be found. An optional second output % [q,work] = maxtrans (...) returns the amount of work performed, or -1 if the % maximum work limit is reached. % % See also: btf, strongcomp, dmperm, sprank % Copyright 2004-2007, Tim Davis, University of Florida error ('maxtrans mexfunction not found') ; SuiteSparse/BTF/MATLAB/btf_demo.m0000644001170100242450000000150110620366517015262 0ustar davisfac%BTF_DEMO demo for BTF % % Example: % btf_demo % % See also btf, dmperm, strongcomp, maxtrans % Copyright 2004-2007, Tim Davis, University of Florida load west0479 ; A = west0479 ; figure (1) clf subplot (2,3,1) ; spy (A) title ('west0479') ; subplot (2,3,2) ; [p, q, r] = btf (A) ; % spy (A (p, abs(q))) ; drawbtf (A, p, q, r) ; title ('btf') ; fprintf ('\nbtf_demo: n %d nnz(A) %d # of blocks %d\n', ... size (A,1), nnz (A), length (r) - 1) ; subplot (2,3,3) ; [p, q, r, s] = dmperm (A) ; drawbtf (A, p, q, r) ; title ('dmperm btf') subplot (2,3,4) ; [p, r] = strongcomp (A) ; % spy (A (p, abs(q))) ; drawbtf (A, p, p, r) ; title ('strongly conn. comp.') ; subplot (2,3,5) ; q = maxtrans (A) ; spy (A (:,q)) title ('max transversal') ; subplot (2,3,6) ; p = dmperm (A) ; spy (A (p,:)) title ('dmperm maxtrans') ; SuiteSparse/BTF/MATLAB/Contents.m0000644001170100242450000000116210620366573015305 0ustar davisfac% BTF ordering toolbox: % % Primary functions: % % btf - permute a square sparse matrix into upper block triangular form % maxtrans - permute the columns of a sparse matrix so it has a zero-free diagonal % strongcomp - symmetric permutation to upper block triangular form % % Other: % btf_install - compile and install BTF for use in MATLAB. % btf_demo - demo for BTF % drawbtf - plot the BTF form of a matrix % btf_make - compile BTF for use in MATLAB % % Example: % q = maxtrans (A) % [p,q,r] = btf (A) % [p,r] = strongcomp (A) % Copyright 2004-2007, Tim Davis, University of Florida SuiteSparse/BTF/MATLAB/btf_make.m0000644001170100242450000000157010620366573015263 0ustar davisfacfunction btf_make %BTF_MAKE compile BTF for use in MATLAB % Your current working directory must be BTF/MATLAB for this function to work. % % Example: % btf_make % % See also btf, maxtrans, stroncomp, dmperm. % Copyright 2004-2007, Tim Davis, University of Florida details = 0 ; % if 1, print details of each command mexcmd = 'mex -O -DDLONG -I../Include -I../../UFconfig ' ; if (~isempty (strfind (computer, '64'))) mexcmd = [mexcmd '-largeArrayDims '] ; end s = [mexcmd 'maxtrans.c ../Source/btf_maxtrans.c'] ; if (details) fprintf ('%s\n', s) ; end eval (s) ; s = [mexcmd 'strongcomp.c ../Source/btf_strongcomp.c'] ; if (details) fprintf ('%s\n', s) ; end eval (s) ; s = [mexcmd 'btf.c ../Source/btf_maxtrans.c ../Source/btf_strongcomp.c ../Source/btf_order.c'] ; if (details) fprintf ('%s\n', s) ; end eval (s) ; fprintf ('BTF successfully compiled.\n') ; SuiteSparse/BTF/MATLAB/btf_install.m0000644001170100242450000000074210620366505016007 0ustar davisfacfunction btf_install %BTF_INSTALL compile and install BTF for use in MATLAB. % Your current working directory must be BTF/MATLAB for this function to work. % % Example: % btf_install % % See also btf, maxtrans, stroncomp, dmperm. % Copyright 2004-2007, Tim Davis, University of Florida btf_make addpath (pwd) ; fprintf ('BTF has been compiled and installed. The path:\n') ; disp (pwd) ; fprintf ('has been added to your path. Use pathtool to add it permanently.\n'); btf_demo SuiteSparse/BTF/Include/0000755001170100242450000000000010711427556013755 5ustar davisfacSuiteSparse/BTF/Include/btf.h0000644001170100242450000002714110711427247014703 0ustar davisfac/* ========================================================================== */ /* === BTF package ========================================================== */ /* ========================================================================== */ /* BTF_MAXTRANS: find a column permutation Q to give A*Q a zero-free diagonal * BTF_STRONGCOMP: find a symmetric permutation P to put P*A*P' into block * upper triangular form. * BTF_ORDER: do both of the above (btf_maxtrans then btf_strongcomp). * * Copyright (c) 2004-2007. Tim Davis, University of Florida, * with support from Sandia National Laboratories. All Rights Reserved. */ /* ========================================================================== */ /* === BTF_MAXTRANS ========================================================= */ /* ========================================================================== */ /* BTF_MAXTRANS: finds a permutation of the columns of a matrix so that it has a * zero-free diagonal. The input is an m-by-n sparse matrix in compressed * column form. The array Ap of size n+1 gives the starting and ending * positions of the columns in the array Ai. Ap[0] must be zero. The array Ai * contains the row indices of the nonzeros of the matrix A, and is of size * Ap[n]. The row indices of column j are located in Ai[Ap[j] ... Ap[j+1]-1]. * Row indices must be in the range 0 to m-1. Duplicate entries may be present * in any given column. The input matrix is not checked for validity (row * indices out of the range 0 to m-1 will lead to an undeterminate result - * possibly a core dump, for example). Row indices in any given column need * not be in sorted order. However, if they are sorted and the matrix already * has a zero-free diagonal, then the identity permutation is returned. * * The output of btf_maxtrans is an array Match of size n. If row i is matched * with column j, then A(i,j) is nonzero, and then Match[i] = j. If the matrix * is structurally nonsingular, all entries in the Match array are unique, and * Match can be viewed as a column permutation if A is square. That is, column * k of the original matrix becomes column Match[k] of the permuted matrix. In * MATLAB, this can be expressed as (for non-structurally singular matrices): * * Match = maxtrans (A) ; * B = A (:, Match) ; * * except of course here the A matrix and Match vector are all 0-based (rows * and columns in the range 0 to n-1), not 1-based (rows/cols in range 1 to n). * The MATLAB dmperm routine returns a row permutation. See the maxtrans * mexFunction for more details. * * If row i is not matched to any column, then Match[i] is == -1. The * btf_maxtrans routine returns the number of nonzeros on diagonal of the * permuted matrix. * * In the MATLAB mexFunction interface to btf_maxtrans, 1 is added to the Match * array to obtain a 1-based permutation. Thus, in MATLAB where A is m-by-n: * * q = maxtrans (A) ; % has entries in the range 0:n * q % a column permutation (only if sprank(A)==n) * B = A (:, q) ; % permuted matrix (only if sprank(A)==n) * sum (q > 0) ; % same as "sprank (A)" * * This behaviour differs from p = dmperm (A) in MATLAB, which returns the * matching as p(j)=i if row i and column j are matched, and p(j)=0 if column j * is unmatched. * * p = dmperm (A) ; % has entries in the range 0:m * p % a row permutation (only if sprank(A)==m) * B = A (p, :) ; % permuted matrix (only if sprank(A)==m) * sum (p > 0) ; % definition of sprank (A) * * This algorithm is based on the paper "On Algorithms for obtaining a maximum * transversal" by Iain Duff, ACM Trans. Mathematical Software, vol 7, no. 1, * pp. 315-330, and "Algorithm 575: Permutations for a zero-free diagonal", * same issue, pp. 387-390. Algorithm 575 is MC21A in the Harwell Subroutine * Library. This code is not merely a translation of the Fortran code into C. * It is a completely new implementation of the basic underlying method (depth * first search over a subgraph with nodes corresponding to columns matched so * far, and cheap matching). This code was written with minimal observation of * the MC21A/B code itself. See comments below for a comparison between the * maxtrans and MC21A/B codes. * * This routine operates on a column-form matrix and produces a column * permutation. MC21A uses a row-form matrix and produces a row permutation. * The difference is merely one of convention in the comments and interpretation * of the inputs and outputs. If you want a row permutation, simply pass a * compressed-row sparse matrix to this routine and you will get a row * permutation (just like MC21A). Similarly, you can pass a column-oriented * matrix to MC21A and it will happily return a column permutation. */ #ifndef _BTF_H #define _BTF_H /* make it easy for C++ programs to include BTF */ #ifdef __cplusplus extern "C" { #endif #include "UFconfig.h" int btf_maxtrans /* returns # of columns matched */ ( /* --- input, not modified: --- */ int nrow, /* A is nrow-by-ncol in compressed column form */ int ncol, int Ap [ ], /* size ncol+1 */ int Ai [ ], /* size nz = Ap [ncol] */ double maxwork, /* maximum amount of work to do is maxwork*nnz(A); no limit * if <= 0 */ /* --- output, not defined on input --- */ double *work, /* work = -1 if maxwork > 0 and the total work performed * reached the maximum of maxwork*nnz(A). * Otherwise, work = the total work performed. */ int Match [ ], /* size nrow. Match [i] = j if column j matched to row i * (see above for the singular-matrix case) */ /* --- workspace, not defined on input or output --- */ int Work [ ] /* size 5*ncol */ ) ; /* long integer version (all "int" parameters become "UF_long") */ UF_long btf_l_maxtrans (UF_long, UF_long, UF_long *, UF_long *, double, double *, UF_long *, UF_long *) ; /* ========================================================================== */ /* === BTF_STRONGCOMP ======================================================= */ /* ========================================================================== */ /* BTF_STRONGCOMP finds the strongly connected components of a graph, returning * a symmetric permutation. The matrix A must be square, and is provided on * input in compressed-column form (see BTF_MAXTRANS, above). The diagonal of * the input matrix A (or A*Q if Q is provided on input) is ignored. * * If Q is not NULL on input, then the strongly connected components of A*Q are * found. Q may be flagged on input, where Q[k] < 0 denotes a flagged column k. * The permutation is j = BTF_UNFLIP (Q [k]). On output, Q is modified (the * flags are preserved) so that P*A*Q is in block upper triangular form. * * If Q is NULL, then the permutation P is returned so that P*A*P' is in upper * block triangular form. * * The vector R gives the block boundaries, where block b is in rows/columns * R[b] to R[b+1]-1 of the permuted matrix, and where b ranges from 1 to the * number of strongly connected components found. */ int btf_strongcomp /* return # of strongly connected components */ ( /* input, not modified: */ int n, /* A is n-by-n in compressed column form */ int Ap [ ], /* size n+1 */ int Ai [ ], /* size nz = Ap [n] */ /* optional input, modified (if present) on output: */ int Q [ ], /* size n, input column permutation */ /* output, not defined on input */ int P [ ], /* size n. P [k] = j if row and column j are kth row/col * in permuted matrix. */ int R [ ], /* size n+1. block b is in rows/cols R[b] ... R[b+1]-1 */ /* workspace, not defined on input or output */ int Work [ ] /* size 4n */ ) ; UF_long btf_l_strongcomp (UF_long, UF_long *, UF_long *, UF_long *, UF_long *, UF_long *, UF_long *) ; /* ========================================================================== */ /* === BTF_ORDER ============================================================ */ /* ========================================================================== */ /* BTF_ORDER permutes a square matrix into upper block triangular form. It * does this by first finding a maximum matching (or perhaps a limited matching * if the work is limited), via the btf_maxtrans function. If a complete * matching is not found, BTF_ORDER completes the permutation, but flags the * columns of P*A*Q to denote which columns are not matched. If the matrix is * structurally rank deficient, some of the entries on the diagonal of the * permuted matrix will be zero. BTF_ORDER then calls btf_strongcomp to find * the strongly-connected components. * * On output, P and Q are the row and column permutations, where i = P[k] if * row i of A is the kth row of P*A*Q, and j = BTF_UNFLIP(Q[k]) if column j of * A is the kth column of P*A*Q. If Q[k] < 0, then the (k,k)th entry in P*A*Q * is structurally zero. * * The vector R gives the block boundaries, where block b is in rows/columns * R[b] to R[b+1]-1 of the permuted matrix, and where b ranges from 1 to the * number of strongly connected components found. */ int btf_order /* returns number of blocks found */ ( /* --- input, not modified: --- */ int n, /* A is n-by-n in compressed column form */ int Ap [ ], /* size n+1 */ int Ai [ ], /* size nz = Ap [n] */ double maxwork, /* do at most maxwork*nnz(A) work in the maximum * transversal; no limit if <= 0 */ /* --- output, not defined on input --- */ double *work, /* return value from btf_maxtrans */ int P [ ], /* size n, row permutation */ int Q [ ], /* size n, column permutation */ int R [ ], /* size n+1. block b is in rows/cols R[b] ... R[b+1]-1 */ int *nmatch, /* # nonzeros on diagonal of P*A*Q */ /* --- workspace, not defined on input or output --- */ int Work [ ] /* size 5n */ ) ; UF_long btf_l_order (UF_long, UF_long *, UF_long *, double , double *, UF_long *, UF_long *, UF_long *, UF_long *, UF_long *) ; /* ========================================================================== */ /* === BTF marking of singular columns ====================================== */ /* ========================================================================== */ /* BTF_FLIP is a "negation about -1", and is used to mark an integer j * that is normally non-negative. BTF_FLIP (-1) is -1. BTF_FLIP of * a number > -1 is negative, and BTF_FLIP of a number < -1 is positive. * BTF_FLIP (BTF_FLIP (j)) = j for all integers j. UNFLIP (j) acts * like an "absolute value" operation, and is always >= -1. You can test * whether or not an integer j is "flipped" with the BTF_ISFLIPPED (j) * macro. */ #define BTF_FLIP(j) (-(j)-2) #define BTF_ISFLIPPED(j) ((j) < -1) #define BTF_UNFLIP(j) ((BTF_ISFLIPPED (j)) ? BTF_FLIP (j) : (j)) /* ========================================================================== */ /* === BTF version ========================================================== */ /* ========================================================================== */ /* All versions of BTF include these definitions. * As an example, to test if the version you are using is 1.2 or later: * * if (BTF_VERSION >= BTF_VERSION_CODE (1,2)) ... * * This also works during compile-time: * * #if (BTF >= BTF_VERSION_CODE (1,2)) * printf ("This is version 1.2 or later\n") ; * #else * printf ("This is an early version\n") ; * #endif */ #define BTF_DATE "Nov 1, 2007" #define BTF_VERSION_CODE(main,sub) ((main) * 1000 + (sub)) #define BTF_MAIN_VERSION 1 #define BTF_SUB_VERSION 0 #define BTF_SUBSUB_VERSION 1 #define BTF_VERSION BTF_VERSION_CODE(BTF_MAIN_VERSION,BTF_SUB_VERSION) #ifdef __cplusplus } #endif #endif SuiteSparse/BTF/Include/btf_internal.h0000644001170100242450000000257610616443513016602 0ustar davisfac/* ========================================================================== */ /* === btf_internal include file ============================================ */ /* ========================================================================== */ #ifndef _BTF_INTERNAL_H #define _BTF_INTERNAL_H /* * Copyright (c) 2004-2007. Tim Davis, University of Florida, * with support from Sandia National Laboratories. All Rights Reserved. */ /* Not to be included in any user program. */ #ifdef DLONG #define Int UF_long #define Int_id UF_long_id #define BTF(name) btf_l_ ## name #else #define Int int #define Int_id "%d" #define BTF(name) btf_ ## name #endif /* ========================================================================== */ /* make sure debugging and printing is turned off */ #ifndef NDEBUG #define NDEBUG #endif #ifndef NPRINT #define NPRINT #endif /* To enable debugging and assertions, uncomment this line: #undef NDEBUG */ /* To enable diagnostic printing, uncomment this line: #undef NPRINT */ /* ========================================================================== */ #include #include #define ASSERT(a) assert(a) #undef TRUE #undef FALSE #undef PRINTF #undef MIN #ifndef NPRINT #define PRINTF(s) { printf s ; } ; #else #define PRINTF(s) #endif #define TRUE 1 #define FALSE 0 #define EMPTY (-1) #define MIN(a,b) (((a) < (b)) ? (a) : (b)) #endif SuiteSparse/BTF/Source/0000755001170100242450000000000010664634152013631 5ustar davisfacSuiteSparse/BTF/Source/btf_maxtrans.c0000644001170100242450000003424710620341747016474 0ustar davisfac/* ========================================================================== */ /* === BTF_MAXTRANS ========================================================= */ /* ========================================================================== */ /* Finds a column permutation that maximizes the number of entries on the * diagonal of a sparse matrix. See btf.h for more information. * * This function is identical to cs_maxtrans in CSparse, with the following * exceptions: * * (1) cs_maxtrans finds both jmatch and imatch, where jmatch [i] = j and * imatch [j] = i if row i is matched to column j. This function returns * just jmatch (the Match array). The MATLAB interface to cs_maxtrans * (the single-output cs_dmperm) returns imatch, not jmatch to the MATLAB * caller. * * (2) cs_maxtrans includes a pre-pass that counts the number of non-empty * rows and columns (m2 and n2, respectively), and computes the matching * using the transpose of A if m2 < n2. cs_maxtrans also returns quickly * if the diagonal of the matrix is already zero-free. This pre-pass * allows cs_maxtrans to be much faster than maxtrans, if the use of the * transpose is warranted. * * However, for square structurally non-singular matrices with one or more * zeros on the diagonal, the pre-pass is a waste of time, and for these * matrices, maxtrans can be twice as fast as cs_maxtrans. Since the * maxtrans function is intended primarily for square matrices that are * typically structurally nonsingular, the pre-pass is not included here. * If this maxtrans function is used on a matrix with many more columns * than rows, consider passing the transpose to this function, or use * cs_maxtrans instead. * * (3) cs_maxtrans can operate as a randomized algorithm, to help avoid * rare cases of excessive run-time. * * (4) this maxtrans function includes an option that limits the total work * performed. If this limit is reached, the maximum transveral might not * be found. * * Thus, for general usage, cs_maxtrans is preferred. For square matrices that * are typically structurally non-singular, maxtrans is preferred. A partial * maxtrans can still be very useful when solving a sparse linear system. * * Copyright (c) 2004-2007. Tim Davis, University of Florida, * with support from Sandia National Laboratories. All Rights Reserved. */ #include "btf.h" #include "btf_internal.h" /* ========================================================================== */ /* === augment ============================================================== */ /* ========================================================================== */ /* Perform a depth-first-search starting at column k, to find an augmenting * path. An augmenting path is a sequence of row/column pairs (i1,k), (i2,j1), * (i3,j2), ..., (i(s+1), js), such that all of the following properties hold: * * * column k is not matched to any row * * entries in the path are nonzero * * the pairs (i1,j1), (i2,j2), (i3,j3) ..., (is,js) have been * previously matched to each other * * (i(s+1), js) is nonzero, and row i(s+1) is not matched to any column * * Once this path is found, the matching can be changed to the set of pairs * path. An augmenting path is a sequence of row/column pairs * * (i1,k), (i2,j1), (i3,j2), ..., (i(s+1), js) * * Once a row is matched with a column it remains matched with some column, but * not necessarily the column it was first matched with. * * In the worst case, this function can examine every nonzero in A. Since it * is called n times by maxtrans, the total time of maxtrans can be as high as * O(n*nnz(A)). To limit this work, pass a value of maxwork > 0. Then at * most O((maxwork+1)*nnz(A)) work will be performed; the maximum matching might * not be found, however. * * This routine is very similar to the dfs routine in klu_kernel.c, in the * KLU sparse LU factorization package. It is essentially identical to the * cs_augment routine in CSparse, and its recursive version (augment function * in cs_maxtransr_mex.c), except that this routine allows for the search to be * terminated early if too much work is being performed. * * The algorithm is based on the paper "On Algorithms for obtaining a maximum * transversal" by Iain Duff, ACM Trans. Mathematical Software, vol 7, no. 1, * pp. 315-330, and "Algorithm 575: Permutations for a zero-free diagonal", * same issue, pp. 387-390. The code here is a new implementation of that * algorithm, with different data structures and control flow. After writing * this code, I carefully compared my algorithm with MC21A/B (ACM Algorithm 575) * Some of the comparisons are partial because I didn't dig deeply into all of * the details of MC21A/B, such as how the stack is maintained. The following * arguments are essentially identical between this code and MC21A: * * maxtrans MC21A,B * -------- ------- * n N identical * k JORD identical * Ap IP column / row pointers * Ai ICN row / column indices * Ap[n] LICN length of index array (# of nonzeros in A) * Match IPERM output column / row permutation * nmatch NUMNZ # of nonzeros on diagonal of permuted matrix * Flag CV mark a node as visited by the depth-first-search * * The following are different, but analogous: * * Cheap ARP indicates what part of the a column / row has * already been matched. * * The following arguments are very different: * * - LENR # of entries in each row/column (unused in maxtrans) * Pstack OUT Pstack keeps track of where we are in the depth- * first-search scan of column j. I think that OUT * plays a similar role in MC21B, but I'm unsure. * Istack PR keeps track of the rows in the path. PR is a link * list, though, whereas Istack is a stack. Maxtrans * does not use any link lists. * Jstack OUT? PR? the stack for nodes in the path (unsure) * * The following control structures are roughly comparable: * * maxtrans MC21B * -------- ----- * for (k = 0 ; k < n ; k++) DO 100 JORD=1,N * while (head >= 0) DO 70 K=1,JORD * for (p = Cheap [j] ; ...) DO 20 II=IN1,IN2 * for (p = head ; ...) DO 90 K=1,JORD */ static Int augment ( Int k, /* which stage of the main loop we're in */ Int Ap [ ], /* column pointers, size n+1 */ Int Ai [ ], /* row indices, size nz = Ap [n] */ Int Match [ ], /* size n, Match [i] = j if col j matched to i */ Int Cheap [ ], /* rows Ai [Ap [j] .. Cheap [j]-1] alread matched */ Int Flag [ ], /* Flag [j] = k if j already visited this stage */ Int Istack [ ], /* size n. Row index stack. */ Int Jstack [ ], /* size n. Column index stack. */ Int Pstack [ ], /* size n. Keeps track of position in adjacency list */ double *work, /* work performed by the depth-first-search */ double maxwork /* maximum work allowed */ ) { /* local variables, but "global" to all DFS levels: */ Int found ; /* true if match found. */ Int head ; /* top of stack */ /* variables that are purely local to any one DFS level: */ Int j2 ; /* the next DFS goes to node j2 */ Int pend ; /* one past the end of the adjacency list for node j */ Int pstart ; Int quick ; /* variables that need to be pushed then popped from the stack: */ Int i ; /* the row tentatively matched to i if DFS successful */ Int j ; /* the DFS is at the current node j */ Int p ; /* current index into the adj. list for node j */ /* the variables i, j, and p are stacked in Istack, Jstack, and Pstack */ quick = (maxwork > 0) ; /* start a DFS to find a match for column k */ found = FALSE ; i = EMPTY ; head = 0 ; Jstack [0] = k ; ASSERT (Flag [k] != k) ; while (head >= 0) { j = Jstack [head] ; pend = Ap [j+1] ; if (Flag [j] != k) /* a node is not yet visited */ { /* -------------------------------------------------------------- */ /* prework for node j */ /* -------------------------------------------------------------- */ /* first time that j has been visited */ Flag [j] = k ; /* cheap assignment: find the next unmatched row in col j. This * loop takes at most O(nnz(A)) time for the sum total of all * calls to augment. */ for (p = Cheap [j] ; p < pend && !found ; p++) { i = Ai [p] ; found = (Match [i] == EMPTY) ; } Cheap [j] = p ; /* -------------------------------------------------------------- */ /* prepare for DFS */ if (found) { /* end of augmenting path, column j matched with row i */ Istack [head] = i ; break ; } /* set Pstack [head] to the first entry in column j to scan */ Pstack [head] = Ap [j] ; } /* ------------------------------------------------------------------ */ /* quick return if too much work done */ /* ------------------------------------------------------------------ */ if (quick && *work > maxwork) { /* too much work has been performed; abort the search */ return (EMPTY) ; } /* ------------------------------------------------------------------ */ /* DFS for nodes adjacent to j */ /* ------------------------------------------------------------------ */ /* If cheap assignment not made, continue the depth-first search. All * rows in column j are already matched. Add the adjacent nodes to the * stack by iterating through until finding another non-visited node. * * It is the following loop that can force maxtrans to take * O(n*nnz(A)) time. */ pstart = Pstack [head] ; for (p = pstart ; p < pend ; p++) { i = Ai [p] ; j2 = Match [i] ; ASSERT (j2 != EMPTY) ; if (Flag [j2] != k) { /* Node j2 is not yet visited, start a depth-first search on * node j2. Keep track of where we left off in the scan of adj * list of node j so we can restart j where we left off. */ Pstack [head] = p + 1 ; /* Push j2 onto the stack and immediately break so we can * recurse on node j2. Also keep track of row i which (if this * search for an augmenting path works) will be matched with the * current node j. */ Istack [head] = i ; Jstack [++head] = j2 ; break ; } } /* ------------------------------------------------------------------ */ /* determine how much work was just performed */ /* ------------------------------------------------------------------ */ *work += (p - pstart + 1) ; /* ------------------------------------------------------------------ */ /* node j is done, but the postwork is postponed - see below */ /* ------------------------------------------------------------------ */ if (p == pend) { /* If all adjacent nodes of j are already visited, pop j from * stack and continue. We failed to find a match. */ head-- ; } } /* postwork for all nodes j in the stack */ /* unwind the path and make the corresponding matches */ if (found) { for (p = head ; p >= 0 ; p--) { j = Jstack [p] ; i = Istack [p] ; /* -------------------------------------------------------------- */ /* postwork for node j */ /* -------------------------------------------------------------- */ /* if found, match row i with column j */ Match [i] = j ; } } return (found) ; } /* ========================================================================== */ /* === maxtrans ============================================================= */ /* ========================================================================== */ Int BTF(maxtrans) /* returns # of columns in the matching */ ( /* --- input --- */ Int nrow, /* A is nrow-by-ncol in compressed column form */ Int ncol, Int Ap [ ], /* size ncol+1 */ Int Ai [ ], /* size nz = Ap [ncol] */ double maxwork, /* do at most maxwork*nnz(A) work; no limit if <= 0. This * work limit excludes the O(nnz(A)) cheap-match phase. */ /* --- output --- */ double *work, /* work = -1 if maxwork > 0 and the total work performed * reached the maximum of maxwork*nnz(A)). * Otherwise, work = the total work performed. */ Int Match [ ], /* size nrow. Match [i] = j if column j matched to row i */ /* --- workspace --- */ Int Work [ ] /* size 5*ncol */ ) { Int *Cheap, *Flag, *Istack, *Jstack, *Pstack ; Int i, j, k, nmatch, work_limit_reached, result ; /* ---------------------------------------------------------------------- */ /* get workspace and initialize */ /* ---------------------------------------------------------------------- */ Cheap = Work ; Work += ncol ; Flag = Work ; Work += ncol ; /* stack for non-recursive depth-first search in augment function */ Istack = Work ; Work += ncol ; Jstack = Work ; Work += ncol ; Pstack = Work ; /* in column j, rows Ai [Ap [j] .. Cheap [j]-1] are known to be matched */ for (j = 0 ; j < ncol ; j++) { Cheap [j] = Ap [j] ; Flag [j] = EMPTY ; } /* all rows and columns are currently unmatched */ for (i = 0 ; i < nrow ; i++) { Match [i] = EMPTY ; } if (maxwork > 0) { maxwork *= Ap [ncol] ; } *work = 0 ; /* ---------------------------------------------------------------------- */ /* find a matching row for each column k */ /* ---------------------------------------------------------------------- */ nmatch = 0 ; work_limit_reached = FALSE ; for (k = 0 ; k < ncol ; k++) { /* find an augmenting path to match some row i to column k */ result = augment (k, Ap, Ai, Match, Cheap, Flag, Istack, Jstack, Pstack, work, maxwork) ; if (result == TRUE) { /* we found it. Match [i] = k for some row i has been done. */ nmatch++ ; } else if (result == EMPTY) { /* augment gave up because of too much work, and no match found */ work_limit_reached = TRUE ; } } /* ---------------------------------------------------------------------- */ /* return the Match, and the # of matches made */ /* ---------------------------------------------------------------------- */ /* At this point, row i is matched to j = Match [i] if j >= 0. i is an * unmatched row if Match [i] == EMPTY. */ if (work_limit_reached) { /* return -1 if the work limit of maxwork*nnz(A) was reached */ *work = EMPTY ; } return (nmatch) ; } SuiteSparse/BTF/Source/btf_order.c0000644001170100242450000001116510620341601015731 0ustar davisfac/* ========================================================================== */ /* === BTF_ORDER ============================================================ */ /* ========================================================================== */ /* Find a permutation P and Q to permute a square sparse matrix into upper block * triangular form. A(P,Q) will contain a zero-free diagonal if A has * structural full-rank. Otherwise, the number of nonzeros on the diagonal of * A(P,Q) will be maximized, and will equal the structural rank of A. * * Q[k] will be "flipped" if a zero-free diagonal was not found. Q[k] will be * negative, and j = BTF_UNFLIP (Q [k]) gives the corresponding permutation. * * R defines the block boundaries of A(P,Q). The kth block consists of rows * and columns R[k] to R[k+1]-1. * * If maxwork > 0 on input, then the work performed in btf_maxtrans is limited * to maxwork*nnz(A) (excluding the "cheap match" phase, which can take another * nnz(A) work). On output, the work parameter gives the actual work performed, * or -1 if the limit was reached. In the latter case, the diagonal of A(P,Q) * might not be zero-free, and the number of nonzeros on the diagonal of A(P,Q) * might not be equal to the structural rank. * * See btf.h for more details. * * Copyright (c) 2004-2007. Tim Davis, University of Florida, * with support from Sandia National Laboratories. All Rights Reserved. */ #include "btf.h" #include "btf_internal.h" /* This function only operates on square matrices (either structurally full- * rank, or structurally rank deficient). */ Int BTF(order) /* returns number of blocks found */ ( /* input, not modified: */ Int n, /* A is n-by-n in compressed column form */ Int Ap [ ], /* size n+1 */ Int Ai [ ], /* size nz = Ap [n] */ double maxwork, /* do at most maxwork*nnz(A) work in the maximum * transversal; no limit if <= 0 */ /* output, not defined on input */ double *work, /* work performed in maxtrans, or -1 if limit reached */ Int P [ ], /* size n, row permutation */ Int Q [ ], /* size n, column permutation */ Int R [ ], /* size n+1. block b is in rows/cols R[b] ... R[b+1]-1 */ Int *nmatch, /* # nonzeros on diagonal of P*A*Q */ /* workspace, not defined on input or output */ Int Work [ ] /* size 5n */ ) { Int *Flag ; Int nblocks, i, j, nbadcol ; /* ---------------------------------------------------------------------- */ /* compute the maximum matching */ /* ---------------------------------------------------------------------- */ /* if maxwork > 0, then a maximum matching might not be found */ *nmatch = BTF(maxtrans) (n, n, Ap, Ai, maxwork, work, Q, Work) ; /* ---------------------------------------------------------------------- */ /* complete permutation if the matrix is structurally singular */ /* ---------------------------------------------------------------------- */ /* Since the matrix is square, ensure BTF_UNFLIP(Q[0..n-1]) is a * permutation of the columns of A so that A has as many nonzeros on the * diagonal as possible. */ if (*nmatch < n) { /* get a size-n work array */ Flag = Work + n ; for (j = 0 ; j < n ; j++) { Flag [j] = 0 ; } /* flag all matched columns */ for (i = 0 ; i < n ; i++) { j = Q [i] ; if (j != EMPTY) { /* row i and column j are matched to each other */ Flag [j] = 1 ; } } /* make a list of all unmatched columns, in Work [0..nbadcol-1] */ nbadcol = 0 ; for (j = n-1 ; j >= 0 ; j--) { if (!Flag [j]) { /* j is matched to nobody */ Work [nbadcol++] = j ; } } ASSERT (*nmatch + nbadcol == n) ; /* make an assignment for each unmatched row */ for (i = 0 ; i < n ; i++) { if (Q [i] == EMPTY && nbadcol > 0) { /* get an unmatched column j */ j = Work [--nbadcol] ; /* assign j to row i and flag the entry by "flipping" it */ Q [i] = BTF_FLIP (j) ; } } } /* The permutation of a square matrix can be recovered as follows: Row i is * matched with column j, where j = BTF_UNFLIP (Q [i]) and where j * will always be in the valid range 0 to n-1. The entry A(i,j) is zero * if BTF_ISFLIPPED (Q [i]) is true, and nonzero otherwise. nmatch * is the number of entries in the Q array that are non-negative. */ /* ---------------------------------------------------------------------- */ /* find the strongly connected components */ /* ---------------------------------------------------------------------- */ nblocks = BTF(strongcomp) (n, Ap, Ai, Q, P, R, Work) ; return (nblocks) ; } SuiteSparse/BTF/Source/btf_strongcomp.c0000644001170100242450000005312110616145037017021 0ustar davisfac/* ========================================================================== */ /* === BTF_STRONGCOMP ======================================================= */ /* ========================================================================== */ /* Finds the strongly connected components of a graph, or equivalently, permutes * the matrix into upper block triangular form. See btf.h for more details. * Input matrix and Q are not checked on input. * * Copyright (c) 2004-2007. Tim Davis, University of Florida, * with support from Sandia National Laboratories. All Rights Reserved. */ #include "btf.h" #include "btf_internal.h" #define UNVISITED (-2) /* Flag [j] = UNVISITED if node j not visited yet */ #define UNASSIGNED (-1) /* Flag [j] = UNASSIGNED if node j has been visited, * but not yet assigned to a strongly-connected * component (aka block). Flag [j] = k (k in the * range 0 to nblocks-1) if node j has been visited * (and completed, with its postwork done) and * assigned to component k. */ /* This file contains two versions of the depth-first-search, a recursive one * and a non-recursive one. By default, the non-recursive one is used. */ #ifndef RECURSIVE /* ========================================================================== */ /* === dfs: non-recursive version (default) ================================= */ /* ========================================================================== */ /* Perform a depth-first-search of a graph, stored in an adjacency-list form. * The row indices of column j (equivalently, the out-adjacency list of node j) * are stored in Ai [Ap[j] ... Ap[j+1]-1]. Self-edge (diagonal entries) are * ignored. Ap[0] must be zero, and thus nz = Ap[n] is the number of entries * in the matrix (or edges in the graph). The row indices in each column need * not be in any particular order. If an input column permutation is given, * node j (in the permuted matrix A*Q) is located in * Ai [Ap[Q[j]] ... Ap[Q[j]+1]-1]. This Q can be the same as the Match array * output from the maxtrans routine, for a square matrix that is structurally * full rank. * * The algorithm is from the paper by Robert E. Tarjan, "Depth-first search and * linear graph algorithms," SIAM Journal on Computing, vol. 1, no. 2, * pp. 146-160, 1972. The time taken by strongcomp is O(nnz(A)). * * See also MC13A/B in the Harwell subroutine library (Iain S. Duff and John * K. Reid, "Algorithm 529: permutations to block triangular form," ACM Trans. * on Mathematical Software, vol. 4, no. 2, pp. 189-192, 1978, and "An * implementation of Tarjan's algorithm for the block triangular form of a * matrix," same journal, pp. 137-147. This code is implements the same * algorithm as MC13A/B, except that the data structures are very different. * Also, unlike MC13A/B, the output permutation preserves the natural ordering * within each block. */ static void dfs ( /* inputs, not modified on output: */ Int j, /* start the DFS at node j */ Int Ap [ ], /* size n+1, column pointers for the matrix A */ Int Ai [ ], /* row indices, size nz = Ap [n] */ Int Q [ ], /* input column permutation */ /* inputs, modified on output (each array is of size n): */ Int Time [ ], /* Time [j] = "time" that node j was first visited */ Int Flag [ ], /* Flag [j]: see above */ Int Low [ ], /* Low [j]: see definition below */ Int *p_nblocks, /* number of blocks (aka strongly-connected-comp.)*/ Int *p_timestamp, /* current "time" */ /* workspace, not defined on input or output: */ Int Cstack [ ], /* size n, output stack to hold nodes of components */ Int Jstack [ ], /* size n, stack for the variable j */ Int Pstack [ ] /* size n, stack for the variable p */ ) { /* ---------------------------------------------------------------------- */ /* local variables, and initializations */ /* ---------------------------------------------------------------------- */ /* local variables, but "global" to all DFS levels: */ Int chead ; /* top of Cstack */ Int jhead ; /* top of Jstack and Pstack */ /* variables that are purely local to any one DFS level: */ Int i ; /* edge (j,i) considered; i can be next node to traverse */ Int parent ; /* parent of node j in the DFS tree */ Int pend ; /* one past the end of the adjacency list for node j */ Int jj ; /* column j of A*Q is column jj of the input matrix A */ /* variables that need to be pushed then popped from the stack: */ Int p ; /* current index into the adj. list for node j */ /* the variables j and p are stacked in Jstack and Pstack */ /* local copies of variables in the calling routine */ Int nblocks = *p_nblocks ; Int timestamp = *p_timestamp ; /* ---------------------------------------------------------------------- */ /* start a DFS at node j (same as the recursive call dfs (EMPTY, j)) */ /* ---------------------------------------------------------------------- */ chead = 0 ; /* component stack is empty */ jhead = 0 ; /* Jstack and Pstack are empty */ Jstack [0] = j ; /* put the first node j on the Jstack */ ASSERT (Flag [j] == UNVISITED) ; while (jhead >= 0) { j = Jstack [jhead] ; /* grab the node j from the top of Jstack */ /* determine which column jj of the A is column j of A*Q */ jj = (Q == (Int *) NULL) ? (j) : (BTF_UNFLIP (Q [j])) ; pend = Ap [jj+1] ; /* j's row index list ends at Ai [pend-1] */ if (Flag [j] == UNVISITED) { /* -------------------------------------------------------------- */ /* prework at node j */ /* -------------------------------------------------------------- */ /* node j is being visited for the first time */ Cstack [++chead] = j ; /* push j onto the stack */ timestamp++ ; /* get a timestamp */ Time [j] = timestamp ; /* give the timestamp to node j */ Low [j] = timestamp ; Flag [j] = UNASSIGNED ; /* flag node j as visited */ /* -------------------------------------------------------------- */ /* set Pstack [jhead] to the first entry in column j to scan */ /* -------------------------------------------------------------- */ Pstack [jhead] = Ap [jj] ; } /* ------------------------------------------------------------------ */ /* DFS rooted at node j (start it, or continue where left off) */ /* ------------------------------------------------------------------ */ for (p = Pstack [jhead] ; p < pend ; p++) { i = Ai [p] ; /* examine the edge from node j to node i */ if (Flag [i] == UNVISITED) { /* Node i has not been visited - start a DFS at node i. * Keep track of where we left off in the scan of adjacency list * of node j so we can restart j where we left off. */ Pstack [jhead] = p + 1 ; /* Push i onto the stack and immediately break * so we can recurse on node i. */ Jstack [++jhead] = i ; ASSERT (Time [i] == EMPTY) ; ASSERT (Low [i] == EMPTY) ; /* break here to do what the recursive call dfs (j,i) does */ break ; } else if (Flag [i] == UNASSIGNED) { /* Node i has been visited, but still unassigned to a block * this is a back or cross edge if Time [i] < Time [j]. * Note that i might equal j, in which case this code does * nothing. */ ASSERT (Time [i] > 0) ; ASSERT (Low [i] > 0) ; Low [j] = MIN (Low [j], Time [i]) ; } } if (p == pend) { /* If all adjacent nodes of j are already visited, pop j from * Jstack and do the post work for node j. This also pops p * from the Pstack. */ jhead-- ; /* -------------------------------------------------------------- */ /* postwork at node j */ /* -------------------------------------------------------------- */ /* determine if node j is the head of a component */ if (Low [j] == Time [j]) { /* pop all nodes in this SCC from Cstack */ while (TRUE) { ASSERT (chead >= 0) ; /* stack not empty (j in it) */ i = Cstack [chead--] ; /* pop a node from the Cstack */ ASSERT (i >= 0) ; ASSERT (Flag [i] == UNASSIGNED) ; Flag [i] = nblocks ; /* assign i to current block */ if (i == j) break ; /* current block ends at j */ } nblocks++ ; /* one more block has been found */ } /* update Low [parent], if the parent exists */ if (jhead >= 0) { parent = Jstack [jhead] ; Low [parent] = MIN (Low [parent], Low [j]) ; } } } /* ---------------------------------------------------------------------- */ /* cleanup: update timestamp and nblocks */ /* ---------------------------------------------------------------------- */ *p_timestamp = timestamp ; *p_nblocks = nblocks ; } #else /* ========================================================================== */ /* === dfs: recursive version (only for illustration) ======================= */ /* ========================================================================== */ /* The following is a recursive version of dfs, which computes identical results * as the non-recursive dfs. It is included here because it is easier to read. * Compare the comments in the code below with the identical comments in the * non-recursive code above, and that will help you see the correlation between * the two routines. * * This routine can cause stack overflow, and is thus not recommended for heavy * usage, particularly for large matrices. To help in delaying stack overflow, * global variables are used, reducing the amount of information each call to * dfs places on the call/return stack (the integers i, j, p, parent, and the * return address). Note that this means the recursive code is not thread-safe. * To try this version, compile the code with -DRECURSIVE or include the * following line at the top of this file: #define RECURSIVE */ static Int /* for recursive illustration only, not for production use */ chead, timestamp, nblocks, n, *Ap, *Ai, *Flag, *Cstack, *Time, *Low, *P, *R, *Q ; static void dfs ( Int parent, /* came from parent node */ Int j /* at node j in the DFS */ ) { Int p ; /* current index into the adj. list for node j */ Int i ; /* edge (j,i) considered; i can be next node to traverse */ Int jj ; /* column j of A*Q is column jj of the input matrix A */ /* ---------------------------------------------------------------------- */ /* prework at node j */ /* ---------------------------------------------------------------------- */ /* node j is being visited for the first time */ Cstack [++chead] = j ; /* push j onto the stack */ timestamp++ ; /* get a timestamp */ Time [j] = timestamp ; /* give the timestamp to node j */ Low [j] = timestamp ; Flag [j] = UNASSIGNED ; /* flag node j as visited */ /* ---------------------------------------------------------------------- */ /* DFS rooted at node j */ /* ---------------------------------------------------------------------- */ /* determine which column jj of the A is column j of A*Q */ jj = (Q == (Int *) NULL) ? (j) : (BTF_UNFLIP (Q [j])) ; for (p = Ap [jj] ; p < Ap [jj+1] ; p++) { i = Ai [p] ; /* examine the edge from node j to node i */ if (Flag [i] == UNVISITED) { /* Node i has not been visited - start a DFS at node i. */ dfs (j, i) ; } else if (Flag [i] == UNASSIGNED) { /* Node i has been visited, but still unassigned to a block * this is a back or cross edge if Time [i] < Time [j]. * Note that i might equal j, in which case this code does * nothing. */ Low [j] = MIN (Low [j], Time [i]) ; } } /* ---------------------------------------------------------------------- */ /* postwork at node j */ /* ---------------------------------------------------------------------- */ /* determine if node j is the head of a component */ if (Low [j] == Time [j]) { /* pop all nodes in this strongly connected component from Cstack */ while (TRUE) { i = Cstack [chead--] ; /* pop a node from the Cstack */ Flag [i] = nblocks ; /* assign node i to current block */ if (i == j) break ; /* current block ends at node j */ } nblocks++ ; /* one more block has been found */ } /* update Low [parent] */ if (parent != EMPTY) { /* Note that this could be done with Low[j] = MIN(Low[j],Low[i]) just * after the dfs (j,i) statement above, and then parent would not have * to be an input argument. Putting it here places all the postwork * for node j in one place, thus making the non-recursive DFS easier. */ Low [parent] = MIN (Low [parent], Low [j]) ; } } #endif /* ========================================================================== */ /* === btf_strongcomp ======================================================= */ /* ========================================================================== */ #ifndef RECURSIVE Int BTF(strongcomp) /* return # of strongly connected components */ ( /* input, not modified: */ Int n, /* A is n-by-n in compressed column form */ Int Ap [ ], /* size n+1 */ Int Ai [ ], /* size nz = Ap [n] */ /* optional input, modified (if present) on output: */ Int Q [ ], /* size n, input column permutation. The permutation Q can * include a flag which indicates an unmatched row. * jold = BTF_UNFLIP (Q [jnew]) is the permutation; * this function ingnores these flags. On output, it is * modified according to the permutation P. */ /* output, not defined on input: */ Int P [ ], /* size n. P [k] = j if row and column j are kth row/col * in permuted matrix. */ Int R [ ], /* size n+1. kth block is in rows/cols R[k] ... R[k+1]-1 * of the permuted matrix. */ /* workspace, not defined on input or output: */ Int Work [ ] /* size 4n */ ) #else Int BTF(strongcomp) /* recursive version - same as above except for Work size */ ( Int n_in, Int Ap_in [ ], Int Ai_in [ ], Int Q_in [ ], Int P_in [ ], Int R_in [ ], Int Work [ ] /* size 2n */ ) #endif { Int j, k, b ; #ifndef RECURSIVE Int timestamp, nblocks, *Flag, *Cstack, *Time, *Low, *Jstack, *Pstack ; #else n = n_in ; Ap = Ap_in ; Ai = Ai_in ; Q = Q_in ; P = P_in ; R = R_in ; chead = EMPTY ; #endif /* ---------------------------------------------------------------------- */ /* get and initialize workspace */ /* ---------------------------------------------------------------------- */ /* timestamp is incremented each time a new node is visited. * * Time [j] is the timestamp given to node j. * * Low [j] is the lowest timestamp of any node reachable from j via either * a path to any descendent of j in the DFS tree, or via a single edge to * an either an ancestor (a back edge) or another node that's neither an * ancestor nor a descendant (a cross edge). If Low [j] is equal to * the timestamp of node j (Time [j]), then node j is the "head" of a * strongly connected component (SCC). That is, it is the first node * visited in its strongly connected component, and the DFS subtree rooted * at node j spans all the nodes of the strongly connected component. * * The term "block" and "component" are used interchangebly in this code; * "block" being a matrix term and "component" being a graph term for the * same thing. * * When a node is visited, it is placed on the Cstack (for "component" * stack). When node j is found to be an SCC head, all the nodes from the * top of the stack to node j itself form the nodes in the SCC. This Cstack * is used for both the recursive and non-recursive versions. */ Time = Work ; Work += n ; Flag = Work ; Work += n ; Low = P ; /* use output array P as workspace for Low */ Cstack = R ; /* use output array R as workspace for Cstack */ #ifndef RECURSIVE /* stack for non-recursive dfs */ Jstack = Work ; Work += n ; /* stack for j */ Pstack = Work ; /* stack for p */ #endif for (j = 0 ; j < n ; j++) { Flag [j] = UNVISITED ; Low [j] = EMPTY ; Time [j] = EMPTY ; #ifndef NDEBUG Cstack [j] = EMPTY ; #ifndef RECURSIVE Jstack [j] = EMPTY ; Pstack [j] = EMPTY ; #endif #endif } timestamp = 0 ; /* each node given a timestamp when it is visited */ nblocks = 0 ; /* number of blocks found so far */ /* ---------------------------------------------------------------------- */ /* find the connected components via a depth-first-search */ /* ---------------------------------------------------------------------- */ for (j = 0 ; j < n ; j++) { /* node j is unvisited or assigned to a block. Cstack is empty. */ ASSERT (Flag [j] == UNVISITED || (Flag [j] >= 0 && Flag [j] < nblocks)); if (Flag [j] == UNVISITED) { #ifndef RECURSIVE /* non-recursive dfs (default) */ dfs (j, Ap, Ai, Q, Time, Flag, Low, &nblocks, ×tamp, Cstack, Jstack, Pstack) ; #else /* recursive dfs (for illustration only) */ ASSERT (chead == EMPTY) ; dfs (EMPTY, j) ; ASSERT (chead == EMPTY) ; #endif } } ASSERT (timestamp == n) ; /* ---------------------------------------------------------------------- */ /* construct the block boundary array, R */ /* ---------------------------------------------------------------------- */ for (b = 0 ; b < nblocks ; b++) { R [b] = 0 ; } for (j = 0 ; j < n ; j++) { /* node j has been assigned to block b = Flag [j] */ ASSERT (Time [j] > 0 && Time [j] <= n) ; ASSERT (Low [j] > 0 && Low [j] <= n) ; ASSERT (Flag [j] >= 0 && Flag [j] < nblocks) ; R [Flag [j]]++ ; } /* R [b] is now the number of nodes in block b. Compute cumulative sum * of R, using Time [0 ... nblocks-1] as workspace. */ Time [0] = 0 ; for (b = 1 ; b < nblocks ; b++) { Time [b] = Time [b-1] + R [b-1] ; } for (b = 0 ; b < nblocks ; b++) { R [b] = Time [b] ; } R [nblocks] = n ; /* ---------------------------------------------------------------------- */ /* construct the permutation, preserving the natural order */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG for (k = 0 ; k < n ; k++) { P [k] = EMPTY ; } #endif for (j = 0 ; j < n ; j++) { /* place column j in the permutation */ P [Time [Flag [j]]++] = j ; } #ifndef NDEBUG for (k = 0 ; k < n ; k++) { ASSERT (P [k] != EMPTY) ; } #endif /* Now block b consists of the nodes k1 to k2-1 in the permuted matrix, * where k1 = R [b] and k2 = R [b+1]. Row and column j of the original * matrix becomes row and column P [k] of the permuted matrix. The set of * of rows/columns (nodes) in block b is given by P [k1 ... k2-1], and this * set is sorted in ascending order. Thus, if the matrix consists of just * one block, P is the identity permutation. */ /* ---------------------------------------------------------------------- */ /* if Q is present on input, set Q = Q*P' */ /* ---------------------------------------------------------------------- */ if (Q != (Int *) NULL) { /* We found a symmetric permutation P for the matrix A*Q. The overall * permutation is thus P*(A*Q)*P'. Set Q=Q*P' so that the final * permutation is P*A*Q. Use Time as workspace. Note that this * preserves the negative values of Q if the matrix is structurally * singular. */ for (k = 0 ; k < n ; k++) { Time [k] = Q [P [k]] ; } for (k = 0 ; k < n ; k++) { Q [k] = Time [k] ; } } /* ---------------------------------------------------------------------- */ /* how to traverse the permuted matrix */ /* ---------------------------------------------------------------------- */ /* If Q is not present, the following code can be used to traverse the * permuted matrix P*A*P' * * // compute the inverse of P * for (knew = 0 ; knew < n ; knew++) * { * // row and column kold in the old matrix is row/column knew * // in the permuted matrix P*A*P' * kold = P [knew] ; * Pinv [kold] = knew ; * } * for (b = 0 ; b < nblocks ; b++) * { * // traverse block b of the permuted matrix P*A*P' * k1 = R [b] ; * k2 = R [b+1] ; * nk = k2 - k1 ; * for (jnew = k1 ; jnew < k2 ; jnew++) * { * jold = P [jnew] ; * for (p = Ap [jold] ; p < Ap [jold+1] ; p++) * { * iold = Ai [p] ; * inew = Pinv [iold] ; * // Entry in the old matrix is A (iold, jold), and its * // position in the new matrix P*A*P' is (inew, jnew). * // Let B be the bth diagonal block of the permuted * // matrix. If inew >= k1, then this entry is in row/ * // column (inew-k1, jnew-k1) of the nk-by-nk matrix B. * // Otherwise, the entry is in the upper block triangular * // part, not in any diagonal block. * } * } * } * * If Q is present replace the above statement * jold = P [jnew] ; * with * jold = Q [jnew] ; * or * jold = BTF_UNFLIP (Q [jnew]) ; * * then entry A (iold,jold) in the old (unpermuted) matrix is at (inew,jnew) * in the permuted matrix P*A*Q. Everything else remains the same as the * above (simply replace P*A*P' with P*A*Q in the above comments). */ /* ---------------------------------------------------------------------- */ /* return # of blocks / # of strongly connected components */ /* ---------------------------------------------------------------------- */ return (nblocks) ; } SuiteSparse/BTF/README.txt0000644001170100242450000001010610620160773014060 0ustar davisfacBTF Version 1.0, May 31, 2007, by Timothy A. Davis Copyright (C) 2004-2007, University of Florida BTF is also available under other licenses; contact the author for details. http://www.cise.ufl.edu/research/sparse BTF is a software package for permuting a matrix into block upper triangular form. It includes a maximum transversal algorithm, which finds a permutation of a square or rectangular matrix so that it has a zero-free diagonal (if one exists); otherwise, it finds a maximal matching which maximizes the number of nonzeros on the diagonal. The package also includes a method for finding the strongly connected components of a graph. These two methods together give the permutation to block upper triangular form. Requires UFconfig, in the ../UFconfig directory relative to this directory. KLU relies on this package to permute To compile the libbtf.a library, type "make". The compiled library is located in BTF/Lib/libbtf.a. Compile code that uses BTF with -IBTF/Include. Type "make clean" to remove all but the compiled library, and "make distclean" to remove all files not in the original distribution. This package does not include a statement coverage test (Tcov directory) or demo program (Demo directory). See the KLU package for both. The BTF package does include a MATLAB interface, a MATLAB test suite (in the MATLAB/Test directory), and a MATLAB demo. See BTF/Include/btf.h for documentation on how to use the C-callable functions. Use "help btf", "help maxtrans" and "help strongcomp" in MATLAB, for details on how to use the MATLAB-callable functions. Additional details on the use of BTF are given in the KLU User Guide, normally in ../KLU/Doc/KLU_UserGuide.pdf relative to this directory. -------------------------------------------------------------------------------- BTF is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This Module is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA -------------------------------------------------------------------------------- A full text of the license is in Doc/lesser.txt. -------------------------------------------------------------------------------- Files and directories in the BTF package: Doc documentation and license Include include files Lib compiled BTF library Makefile Makefile for C and MATLAB versions MATLAB MATLAB interface README.txt this file Source BTF source code ./Doc: ChangeLog changes in BTF lesser.txt license ./Include: btf.h primary user include file btf_internal.h internal include file, not for user programs ./Lib: Makefile Makefile for C library ./MATLAB: btf.c btf mexFunction btf_install.m compile and install BTF for use in MATLAB btf.m btf help Contents.m contents of MATLAB interface Makefile Makefile for MATLAB functions maxtrans.c maxtrans mexFunction maxtrans.m maxtrans help strongcomp.c strongcomp mexFunction strongcomp.m strongcomp help Test MATLAB test directory ./MATLAB/Test: checkbtf.m check a BTF ordering drawbtf.m plot a BTF ordering test1.m compare maxtrans and cs_dmperm test2.m compare btf and cs_dmperm test3.m extensive test (maxtrans, strongcomp, and btf) test4b.m test btf maxwork option test4.m test btf maxwork option test5.m test maxtrans maxwork option ./Source: btf_maxtrans.c btf_maxtrans C function btf_order.c btf_order C function btf_strongcomp.c btf_strongcomp C function SuiteSparse/KLU/0000755001170100242450000000000010710765365012414 5ustar davisfacSuiteSparse/KLU/Doc/0000755001170100242450000000000010711442214013103 5ustar davisfacSuiteSparse/KLU/Doc/Makefile0000644001170100242450000000266610620343272014560 0ustar davisfac#------------------------------------------------------------------------------ # KLU Makefile for creating the user guide #------------------------------------------------------------------------------ default: dist include ../../UFconfig/UFconfig.mk #------------------------------------------------------------------------------ # Remove all but the files in the original distribution #------------------------------------------------------------------------------ clean: - $(RM) $(CLEAN) purge: distclean distclean: clean - $(RM) *.aux *.bbl *.blg *.log *.toc #------------------------------------------------------------------------------ # Create the User Guide and Quick Start Guide #------------------------------------------------------------------------------ KLU_UserGuide.pdf: KLU_UserGuide.tex KLU_UserGuide.bib \ ../Include/klu.h ../../BTF/Include/btf.h echo '\begin{verbatim}' > klu_h.tex expand -8 ../Include/klu.h >> klu_h.tex echo '\end{verbatim}' >> klu_h.tex echo '\begin{verbatim}' > btf_h.tex expand -8 ../../BTF/Include/btf.h >> btf_h.tex echo '\end{verbatim}' >> btf_h.tex echo '\begin{verbatim}' > klu_simple_c.tex expand -8 ../Demo/klu_simple.c >> klu_simple_c.tex echo '\end{verbatim}' >> klu_simple_c.tex pdflatex KLU_UserGuide bibtex KLU_UserGuide pdflatex KLU_UserGuide pdflatex KLU_UserGuide dist: KLU_UserGuide.pdf - $(RM) *.aux *.bbl *.blg *.log *.toc - $(RM) klu_simple_c.tex klu_h.tex btf_h.tex SuiteSparse/KLU/Doc/KLU_UserGuide.bib0000644001170100242450000001210710620156075016177 0ustar davisfac%------------------------------------------------------------------------------- @string{TOMS = "{ACM} Trans. Math. Software"} @string{SIAMJSSC = "{SIAM} J. Sci. Statist. Comput."} @string{SIMAX = "{SIAM} J. Matrix Anal. Appl."} @string{SICOMP= "{SIAM} J. Comput."} @string{SIAMJSC = "{SIAM} J. Sci. Comput."} @techreport{NagelPederson, author={Nagel, L. W and Pederson, D. O.}, title={{SPICE} (Simulation Program with Integrated Circuit Emphasis)}, number={Memorandum No. ERL-M382}, address={University of California, Berkeley}, year={1973}} @incollection{Kundert86, author={Kundert, K. S.}, year={1986}, title={Sparse Matrix Techniques and Their Applications to Circuit Simulation}, editor={Ruehli, A. E.}, booktitle={Circuit Analysis, Simulation and Design}, publisher={New York: North-Holland}} @techreport{KundertSangiovanniVincentelli85, author={Kundert, K. S. and Sangiovanni-Vincentelli, A.}, month={Oct.}, year={1985}, title={User's Guide: Sparse1.2}, institution={Dept.~of EE and CS, UC Berkeley}, keywords={ 31 Sparse1.2 software package direct methods}} @phdthesis{Quarles:M89/42, Author = {Thomas L. Quarles}, Title = {Analysis of Performance and Convergence Issues for Circuit Simulation}, School = {EECS Department, University of California, Berkeley}, Year = {1989}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1989/1216.html}, Number = {UCB/ERL M89/42}} @book{Davis06book, author={T. A. Davis}, title={Direct Methods for Sparse Linear Systems}, publisher={SIAM}, year={2006}, address={Philadelphia, PA}} @article{GilbertPeierls88, author={Gilbert, J. R. and Peierls, T.}, year={1988}, title={Sparse Partial Pivoting in Time Proportional to Arithmetic Operations}, journal=SIAMJSSC, volume={9}, pages={862-874}} @article{Duff78a, author={Duff, I. S. and Reid, J. K.}, year={1978}, title={An Implementation of {Tarjan}'s Algorithm for the Block Triangularization of a Matrix}, journal=TOMS, volume={4}, pages={137-147}} @article{Duff81, author={Duff, I. S.}, year={1981}, title={On Algorithms for Obtaining a Maximum Transversal}, journal=TOMS, volume={7}, pages={315-330}} @article{AmestoyDavisDuff96, author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.}, title={An approximate minimum degree ordering algorithm}, journal=SIMAX, year={1996}, volume={17}, pages={886--905}} @article{AmestoyDavisDuff03, author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.}, title={Algorithm 837: {AMD}, an approximate minimum degree ordering algorithm}, journal=TOMS, year={2004}, volume={30}, pages={381-388}} @article{Tarjan72, author={Tarjan, R. E.}, title={Depth first search and linear graph algorithms}, journal=SICOMP, year={1972}, volume={1}, pages={146--160}} @article{DavisGilbertLarimoreNg00, author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.}, title={A column approximate minimum degree ordering algorithm}, journal=TOMS, year={2004}, volume={30}, pages={353-376}} @article{DavisGilbertLarimoreNg00_algo, author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.}, title={Algorithm 836: {COLAMD}, a column approximate minimum degree ordering algorithm}, journal=TOMS, year={2004}, volume={30}, pages={377-380}} @article{ChenDavisHagerRajamanickam06, author={Chen, Y. and Davis, T. A. and Hager, W. W. and Rajamanickam, S.}, title={Algorithm 8xx: {CHOLMOD}, supernodal sparse {Cholesky} factorization and update/downdate}, journal=TOMS, note={(submitted)}, year={2006}} @article{KarypisKumar98e, author={Karypis, G. and Kumar, V.}, title={A fast and high quality multilevel scheme for partitioning irregular graphs}, journal=SIAMJSC, year={1998}, volume={20}} @article{ACM679a, author={Dongarra, J. J. and {Du Croz}, J. and Duff, I. S. and Hammarling, S.}, title={A set of level-3 basic linear algebra subprograms}, journal=TOMS, year={1990}, volume={16}, pages={1--17}} @article{SuperLU99, author={Demmel, J. W. and Eisenstat, S. C. and Gilbert, J. R. and Li, X. S. and Liu, J. W. H.}, title={A supernodal approach to sparse partial pivoting}, journal=SIMAX, year={1999}, volume={20}, pages={720-755} } @article{Davis03, author={Davis, T. A.}, title={A column pre-ordering strategy for the unsymmetric-pattern multifrontal method}, journal=TOMS, year={2004}, volume={30}, pages={165--195}} @article{Davis03_algo, author={Davis, T. A.}, title={Algorithm 832: {UMFPACK V4.3}, an unsymmetric-pattern multifrontal method}, journal=TOMS, year={2002}, volume={30}, pages={196--199}} @article{Hager84, author={Hager, W. W.}, title={Condition estimates}, journal=SIAMJSSC, year={1984},volume={5}, pages={311-316}} @article{HighamTisseur00, author={Higham, N. J. and Tisseur, F.}, title={A block algorithm for matrix 1-norm estimation with an application to 1-norm pseudospectra}, journal=SIMAX, year={2000},volume={21},pages={1185--1201} } @techreport{Palamadai05, author={Palamadai, E.}, title={{KLU} - a high performance sparse linear system solver for circuit simulation problems}, note={M.S. 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davisfac\documentclass[11pt]{article} \newcommand{\m}[1]{{\bf{#1}}} % for matrices and vectors \newcommand{\tr}{^{\sf T}} % transpose \topmargin 0in \textheight 9in \oddsidemargin 0pt \evensidemargin 0pt \textwidth 6.5in %------------------------------------------------------------------------------ \begin{document} %------------------------------------------------------------------------------ \title{User Guide for KLU Version 1.0.1 and BTF Version 1.0.1} \author{ Timothy A. Davis\thanks{ Dept.~of Computer and Information Science and Engineering, Univ.~of Florida, Gainesville, FL, USA. email: davis@cise.ufl.edu. http://www.cise.ufl.edu/$\sim$davis. This work was supported by Sandia National Labs, and the National Science Foundation. Portions of the work were done while on sabbatical at Stanford University and Lawrence Berkeley National Laboratory (with funding from Stanford University and the SciDAC program). } \and Eka Palamadai} \date{Nov 1, 2007} \maketitle %------------------------------------------------------------------------------ \begin{abstract} KLU is a set of routines for solving sparse linear systems of equations. It is particularly well-suited to matrices arising in SPICE-like circuit simulation applications. It relies on a permutation to block triangular form (BTF), several methods for finding a fill-reducing ordering (variants of approximate minimum degree, and nested dissection), and a sparse left-looking LU factorization method to factorize each block. A MATLAB interface is included. \end{abstract} %------------------------------------------------------------------------------ \newpage \tableofcontents \newpage %------------------------------------------------------------------------------ \section{License and Copyright} %------------------------------------------------------------------------------ KLU Version 1.0.1, Copyright\copyright 2007 University of Florida. All Rights Reserved. KLU is available under alternate licenses; contact T. Davis for details. {\bf KLU License:} Your use or distribution of KLU or any modified version of KLU implies that you agree to this License. This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Permission is hereby granted to use or copy this program under the terms of the GNU LGPL, provided that the Copyright, this License, and the Availability of the original version is retained on all copies. User documentation of any code that uses this code or any modified version of this code must cite the Copyright, this License, the Availability note, and "Used by permission." Permission to modify the code and to distribute modified code is granted, provided the Copyright, this License, and the Availability note are retained, and a notice that the code was modified is included. {\bf Availability:} {\tt http://www.cise.ufl.edu/research/sparse/klu} {\tt http://www.cise.ufl.edu/research/sparse/btf} {\bf Acknowledgments:} This work was supported by Sandia National Laboratories (Mike Heroux) and the National Science Foundation under grants 0203270 and 0620286. %------------------------------------------------------------------------------ \newpage \section{Overview} %------------------------------------------------------------------------------ KLU is a set of routines for solving sparse linear systems of equations. It first permutes the matrix into upper block triangular form, via the BTF package. This is done by first finding a permutation for a zero-free diagonal (a maximum transversal) \cite{Duff81}. If there is no such permutation, then the matrix is structurally rank-deficient, and is numerically singular. Next, Tarjan's method \cite{Duff78a,Tarjan72} is used to find the strongly-connected components of the graph. The block triangular form is essentially unique; any method will lead to the same number and sizes of blocks, although the ordering of the blocks may vary (consider a diagonal matrix, for example). Assuming the matrix has full structural rank, the permuted matrix has the following form: \[ PAQ = \left[ \begin{array}{ccc} A_{11} & \cdots & A_{1k} \\ & \ddots & \vdots \\ & & A_{kk} \\ \end{array} \right], \] where each diagonal block is square with a zero-free diagonal. Next, each diagonal block is factorized with a sparse left-looking method \cite{GilbertPeierls88}. The kernel of this factorization method is an efficient method for solving $Lx=b$ when $L$, $x$, and $b$ are all sparse. This kernel is used to compute each column of $L$ and $U$, one column at a time. The total work performed by this method is always proportional to the number of floating-point operations, something that is not true of any other sparse LU factorization method. Prior to factorizing each diagonal block, the blocks are ordered to reduce fill-in. By default, the symmetric approximate minimum degree (AMD) ordering is used on $A_{ii}+A_{ii}^T$ \cite{AmestoyDavisDuff96,AmestoyDavisDuff03}. Another ordering option is to find a column ordering via COLAMD \cite{DavisGilbertLarimoreNg00_algo,DavisGilbertLarimoreNg00}. Alternatively, a permutation can be provided by the user, or a pointer to a user-provided ordering function can be passed, which is then used to order each block. Only the diagonal blocks need to be factorized. Consider a linear system where the matrix is permuted into three blocks, for example: \[ \left[ \begin{array}{ccc} A_{11} & A_{12} & A_{13} \\ & A_{22} & A_{23} \\ & & A_{33} \\ \end{array} \right] \left[ \begin{array}{c} x_{1} \\ x_{2} \\ x_{3} \\ \end{array} \right] = \left[ \begin{array}{c} b_{1} \\ b_{2} \\ b_{3} \\ \end{array} \right]. \] The non-singular system $A_{33} x_{3} = b_{3}$ can first be solved for $x_{3}$. After a block back substitution, the resulting system becomes \[ \left[ \begin{array}{cc} A_{11} & A_{12} \\ & A_{22} \\ \end{array} \right] \left[ \begin{array}{c} x_{1} \\ x_{2} \\ \end{array} \right] = \left[ \begin{array}{c} b_{1} - A_{13} x_{3}\\ b_{2} - A_{23} x_{3}\\ \end{array} \right] = \left[ \begin{array}{c} b'_{1} \\ b'_{2} \\ \end{array} \right] \] and the $A_{22} x_{2} = b'_{2}$ system can be solved for $x_{2}$. The primary advantage of this method is that no fill-in occurs in the off-diagonal blocks ($A_{12}$, $A_{13}$, and $A_{23}$). This is particular critical for sparse linear systems arising in SPICE-like circuit simulation \cite{Kundert86,KundertSangiovanniVincentelli85,NagelPederson,Quarles:M89/42}. Circuit matrices are typically permutable into block triangular form, with many singletons (1-by-1 blocks). They also often have a handful of rows and columns with many nonzero entries, due to voltage and current sources. These rows and columns are pushed into the upper block triangular form, and related to the singleton blocks (for example, $A_{33}$ in the above system is 1-by-1, and the column in $A_{13}$ and $A_{23}$ has many nonzero entries). Since these nearly-dense rows and columns do not appear in the LU factorization of the diagonal blocks, they cause no fill-in. The structural rank of a matrix is based solely on the pattern of its entries, not their numerical values. With random entries, the two ranks are equal with probability one. The structural rank of any matrix is an upper bound on the numerical rank. The maximum transversal algorithm in the BTF package is useful in determining if a matrix is structurally rank deficient, and if so, it reveals a (non-unique) set of rows and columns that contribute to that rank deficiency. This is useful in determining what parts of a circuit are poorly formulated (such as dangling components). When ordered and factorized with KLU, very little fill-in occurs in the resulting LU factors, which means that there is little scope for use of the BLAS \cite{ACM679a}. Sparse LU factorization methods that use the BLAS (such as SuperLU \cite{SuperLU99} amd UMFPACK \cite{Davis03_algo,Davis03}) are slower than KLU when applied to sparse matrices arising in circuit simulation. Both KLU and SuperLU are based on Gilbert and Peierl's left-looking method \cite{GilbertPeierls88}. SuperLU uses supernodes, but KLU does not; thus the name {\em KLU} refers to a ``Clark Kent'' LU factorization algorithm (what SuperLU was before it became Super). For details of the permutation to block triangular form, left-looking sparse LU factorization, and approximate minimum degree, refer to \cite{Davis06book}. Concise versions of these methods can be found in the CSparse package. KLU is also the topic of a Master's thesis by Palamadai \cite{Palamadai05}; a copy of the thesis can be found in the {\tt KLU/Doc} directory. It includes a description of an earlier version of KLU; some of the function names and parameter lists have changed in this version. The descriptions of the methods used still applies to the current version of KLU, however. %------------------------------------------------------------------------------ \section{Availability} %------------------------------------------------------------------------------ KLU and its required ordering packages (BTF, COLAMD, AMD, and UFconfig) are available at \newline {\tt http://www.cise.ufl.edu/research/sparse.} In addition, KLU can make use of any user-provided ordering function. One such function is included, which provides KLU with an interface to the ordering methods used in CHOLMOD \cite{ChenDavisHagerRajamanickam06}, such as METIS, a nested dissection method \cite{KarypisKumar98e}. After permutation to block triangular form, circuit matrices have very good node separators, and are thus excellent candidates for nested dissection. The METIS ordering takes much more time to compute than the AMD ordering, but if the ordering is reused many times (typical in circuit simulation) the better-quality ordering can pay off in lower total simulation time. To use KLU, you must obtain the KLU, BTF, UFconfig, AMD, and COLAMD packages in the SuiteSparse suite of sparse matrix libraries. See {\tt http://www.cise.ufl.edu/research/sparse} for each of these packages. They are also all contained within the single {\tt SuiteSparse.zip} or {\tt SuiteSparse.tar.gz} distribution. %------------------------------------------------------------------------------ \section{Using KLU and BTF in MATLAB} %------------------------------------------------------------------------------ KLU has a single MATLAB interface which provides several options for factorizing a matrix and/or using the factors to solve a linear system. The following is a synopsis of its use. For more details, type {\tt help klu} in MATLAB. {\footnotesize \begin{verbatim} LU = klu (A) factorizes R\A(p,q) into L*U+F, returning a struct x = klu (A,'\',b) x = A\b x = klu (b,'/',A) x = b/A x = klu (LU,'\',b) x = A\b, where LU = klu(A) x = klu (b,'/',LU) x = b/A, where LU = klu(A) \end{verbatim} } With a single input {\tt klu(A)} returns a MATLAB struct containing the LU factors. The factorization is in the form \verb'L*U + F = R \ A(p,q)' where {\tt L*U} is the LU factorization of just the diagonal blocks of the block triangular form, {\tt F} is a sparse matrix containing the entries in the off-diagonal blocks, {\tt R} is a diagonal matrix containing the row scale factors, and {\tt p} and {\tt q} are permutation vectors. The {\tt LU} struct also contains a vector {\tt r} which describes the block boundaries (the same as the third output parameter of {\tt dmperm}). The {\tt k}th block consists of rows and columns {\tt r(k)} to {\tt r(k+1)-1} in the permuted matrix {\tt A(p,q)} and the factors {\tt L} and {\tt U}. An optional final input argument ({\tt klu(A,opts)} for example) provides a way of modifying KLU's user-definable parameters, including a partial pivoting tolerance and ordering options. A second output argument ({\tt [LU,info] = klu ( ... )}) provides statistics on the factorization. The BTF package includes three user-callable MATLAB functions which replicate most of features of the MATLAB built-in {\tt dmperm} function, and provide an additional option which can significantly limit the worst-case time taken by {\tt dmperm}. For more details, type {\tt help btf}, {\tt help maxtrans}, and {\tt help strongcomp} in MATLAB. Additional information about how these functions work can be found in \cite{Davis06book}. {\footnotesize \begin{verbatim} [p,q,r] = btf (A) similar to [p,q,r] = dmperm (A) q = maxtrans (A) similar to q = dmperm (A') [p,r] = strongcomp (A) similar to [p,q,r] = dmperm (A + speye(n)) \end{verbatim} } Both {\tt btf} and {\tt maxtrans} include a second option input, {\tt maxwork}, which limits the total work performed in the maximum transversal to {\tt maxwork * nnz(A)}. The worst-case time taken by the algorithm is $O$ ({\tt n * nnz(A)}), where the matrix {\tt A} is {\tt n}-by-{\tt n}, but this worst-case time is rarely reached in practice. To use the KLU and BTF functions in MATLAB, you must first compile and install them. In the {\tt BTF/MATLAB} directory, type {\tt btf\_install}, and then type {\tt klu\_install} in the {\tt KLU/MATLAB} directory. Alternatively, if you have the entire SuiteSparse, simply run the {\tt SuiteSparse\_install} function in the {\tt SuiteSparse} directory. To use METIS 4.0.1 with KLU (and CHOLMOD, another part of SuiteSparse) you must first download it from {\tt http://glaros.dtc.umn.edu/gkhome/views/metis} and place the {\tt metis-4.0} directory in the {\tt SuiteSparse} directory, alongside the {\tt KLU} and {\tt BTF} directories. After running the installation scripts, type {\tt pathtool} and save your path for future MATLAB sessions. If you cannot save your path because of file permissions, edit your {\tt startup.m} by adding {\tt addpath} commands (type {\tt doc startup} and {\tt doc addpath} for more information). %------------------------------------------------------------------------------ \section{Using KLU and BTF in a C program} \label{Cversion} %------------------------------------------------------------------------------ KLU and BTF include the following C-callable functions. Each function is available in two or four versions: with {\tt int} or {\tt long} integers, and (for functions that deal with numerical values), with {\tt double} or complex {\tt double} values. The {\tt long} integer is actually a {\tt UF\_long}, which is typically a {\tt long}, defined with a {\tt \#define} statement. It becomes an {\tt \_\_int64} on Microsoft Windows 64, however. The usage of real and complex, and {\tt int} and {\tt UF\_long}, must not be mixed, except that some functions can be used for both real and complex cases. %------------------------------------------------------------------------------ \subsection{KLU Common object} %------------------------------------------------------------------------------ The {\tt klu\_common} object ({\tt klu\_l\_common} for the {\tt UF\_long} version) contains user-definable parameters and statistics returned from KLU functions. This object appears in every KLU function as the last parameter. Details are given in the {\tt klu.h} include file, which also appears below in Section~\ref{klu_include}. Primary parameters and statistics are summarized below. The defaults are chosen specifically for circuit simulation matrices. \begin{itemize} \item {\tt tol}: partial pivoting tolerance. If the diagonal entry has a magnitude greater than or equal to {\tt tol} times the largest magnitude of entries in the pivot column, then the diagonal entry is chosen. Default value: 0.001. \item {\tt ordering}: which fill-reducing ordering to use: 0 for AMD, 1 for COLAMD, 2 for a user-provided permutation {\tt P} and {\tt Q} (or a natural ordering if {\tt P} and {\tt Q} are NULL), or 3 for the {\tt user\_order} function. Default: 0 (AMD). \item {\tt scale}: whether or not the matrix should be scaled. If {\tt scale < 0}, then no scaling is performed and the input matrix is not checked for errors. If {\tt scale >= 0}, the input matrix is check for errors. If {\tt scale=0}, then no scaling is performed. If {\tt scale=1}, then each row of {\tt A} is divided by the sum of the absolute values in that row. If {\tt scale=2}, then each row of {\tt A} is divided by the maximum absolute value in that row. Default: 2. \item {\tt btf}: if nonzero, then BTF is used to permute the input matrix into block upper triangular form. This step is skipped if {\tt Common.btf} is zero. Default: 1. \item {\tt maxwork}: sets an upper limit on the amount of work performed in {\tt btf\_maxtrans} to \newline {\tt maxwork*nnz(A)}. If the limit is reached, a partial zero-free diagonal might be found. This has no effect on whether or not the matrix can be factorized, since the matrix can be factorized with no BTF pre-ordering at all. This option provides a tradeoff between the effectiveness of the BTF ordering and the cost to compute it. A partial result can result in fewer, and larger, blocks in the BTF form, resulting to more work required to factorize the matrix. No limit is enforced if {\tt maxwork <= 0}. Default: 0. \item {\tt user\_order}: a pointer to a function that can be provided by the application that uses KLU, to redefine the fill-reducing ordering used by KLU for each diagonal block. The {\tt int} and {\tt UF\_long} prototypes must be as follows: {\footnotesize \begin{verbatim} int my_ordering_function (int n, int Ap [ ], int Ai [ ], int Perm [ ], klu_common *Common) ; UF_long my_long_ordering_function (UF_long n, UF_long Ap [ ], UF_long Ai [ ], UF_long Perm [ ], klu_l_common *Common); \end{verbatim} } The function should return 0 if an error occurred, and either -1 or a positive (nonzero) value if no error occurred. If greater than zero, then the return value is interpreted by KLU as an estimate of the number of nonzeros in $L$ or $U$ (whichever is greater), when the permuted matrix is factorized. Only an estimate is possible, since partial pivoting with row interchanges is performed during numerical factorization. The input matrix is provided to the function in the parameters {\tt n}, {\tt Ap}, and {\tt Ai}, in compressed-column form. The matrix {\tt A} is {\tt n}-by-{\tt n}. The {\tt Ap} array is of size {\tt n+1}; the {\tt j}th column of {\tt A} has row indices {\tt Ai[Ap[j] ... Ap[j+1]-1]}. The {\tt Ai} array is of size {\tt Ap[n]}. The first column pointer {\tt Ap[0]} is zero. The row indices might not appear sorted in each column, but no duplicates will appear. The output permutation is to be passed back in the {\tt Perm} array, where {\tt Perm[k]=j} means that row and column {\tt j} of {\tt A} will appear as the {\tt k}th row and column of the permuted matrix factorized by KLU. The {\tt Perm} array is already allocated when it is passed to the user function. The user function may use, and optionally modify, the contents of the {\tt klu\_common Common} object. In particular, prior to calling KLU, the user application can set both {\tt Common.user\_order} and {\tt Common.user\_data}. The latter is a {\tt void *} pointer that KLU does not use, except to pass to the user ordering function pointed to by {\tt Common.user\_order}. This is a mechanism for passing additional arguments to the user function. An example user function is provided in the {\tt KLU/User} directory, which provides an interface to the ordering method in CHOLMOD. \end{itemize} %------------------------------------------------------------------------------ \subsection{KLU Symbolic object} %------------------------------------------------------------------------------ KLU performs its sparse LU factorization in two steps. The first is purely symbolic, and does not depend on the numerical values. This analysis returns a {\tt klu\_symbolic} object ({\tt klu\_l\_symbolic} in the {\tt UF\_long} version). The {\tt Symbolic} object contains a pre-ordering which combines the block triangular form with the fill-reducing ordering, and an estimate of the number of nonzeros in the factors of each block. Its size is thus modest, only proportional to {\tt n}, the dimension of {\tt A}. It can be reused multiple times for the factorization of a sequence of matrices with identical nonzero pattern. Note: a {\em nonzero} in this sense is an entry present in the data structure of {\tt A}; such entries may in fact be numerically zero. %------------------------------------------------------------------------------ \subsection{KLU Numeric object} %------------------------------------------------------------------------------ The {\tt Numeric} object contains the numeric sparse LU factorization, including the final pivot permutations. To solve a linear system, both the {\tt Symbolic} and {\tt Numeric} objects are required. %------------------------------------------------------------------------------ \subsection{A sparse matrix in KLU} %------------------------------------------------------------------------------ % From here on, only the {\tt int} version is described. In the {\tt UF\_long} % version, the function names change slightly ({\tt klu\_factor} becomes % {\tt klu\_l\_factor}, and the {\tt int}/complex version {\tt klu\_z\_factor} % becomes {\tt klu\_zl\_factor}, for example). For more details on the % {\tt UF\_long} version, refer to Section~\ref{klu_include}. The input matrix provided to KLU is in sparse compressed-column form, which is the same data structure used internally in MATLAB, except that the version used here allows for the row indices to appear in any ordering, and this version also allows explicit zero entries to appear in the data structure. The same data structure is used in CSparse, which is fully documented in \cite{Davis06book}. If you wish to use a simpler input data structure, consider creating a triplet matrix in CSparse (or CXSparse if you use the long and/or complex versions of KLU), and then convert this data structure into a sparse compressed-column data structure, using the CSparse {\tt cs\_compress} and {\tt cs\_dupl} functions. Similar functions are available in CHOLMOD {\tt cholmod\_triplet\_to\_sparse}. The matrix is described with four parameters: \begin{itemize} \item {\tt n}: an integer scalar. The matrix is {\tt n}-by-{\tt n}. Note that KLU only operates on square matrices. \item {\tt Ap}: an integer array of size {\tt n+1}. The first entry is {\tt Ap[0]=0}, and the last entry {\tt nz=Ap[n]} is equal to the number of entries in the matrix. \item {\tt Ai}: an integer array of size {\tt nz = Ap[n]}. The row indices of entries in column {\tt j} of {\tt A} are located in {\tt Ai [Ap [j] ... Ap [j+1]-1]}. The matrix is zero-based; row and column indices are in the range 0 to {\tt n-1}. \item {\tt Ax}: a {\tt double} array of size {\tt nz} for the real case, or {\tt 2*nz} for the complex case. For the complex case, the real and imaginary parts are interleaved, compatible with Fortran and the ANSI C99 Complex data type. KLU does not rely on the ANSI C99 data type, however, for portability reasons. The numerical values in column {\tt j} of a real matrix are located in {\tt Ax [Ap [j] ... Ap [j+1]-1]}. For a complex matrix, they appear in {\tt Ax [2*Ap [j] ... 2*Ap [j+1]-1]}, as real/imaginary pairs (the real part appears first, followed by the imaginary part). \end{itemize} %------------------------------------------------------------------------------- \subsection{{\tt klu\_defaults}: set default parameters} %------------------------------------------------------------------------------- This function sets the default parameters for KLU and clears the statistics. It may be used for either the real or complex cases. A value of 0 is returned if an error occurs, 1 otherwise. This function {\bf must} be called before any other KLU function can be called. {\footnotesize \begin{verbatim} #include "klu.h" int ok ; klu_common Common ; ok = klu_defaults (&Common) ; /* real or complex */ #include "klu.h" UF_long ok ; klu_l_common Common ; ok = klu_l_defaults (&Common) ; /* real or complex */ \end{verbatim} } %------------------------------------------------------------------------------- \subsection{{\tt klu\_analyze}: order and analyze a matrix} %------------------------------------------------------------------------------- The following usage returns a {\tt Symbolic} object that contains the fill-reducing ordering needed to factorize the matrix {\tt A}. A NULL pointer is returned if a failure occurs. The error status for this function, and all others, is returned in {\tt Common.status}. These functions may be used for both real and complex cases. The AMD ordering is used if {\tt Common.ordering = 0}, COLAMD is used if it is 1, the natural ordering is used if it is 2, and the user-provided {\tt Common.user\_ordering} is used if it is 3. {\footnotesize \begin{verbatim} #include "klu.h" int n, Ap [n+1], Ai [nz] ; klu_symbolic *Symbolic ; klu_common Common ; Symbolic = klu_analyze (n, Ap, Ai, &Common) ; /* real or complex */ #include "klu.h" UF_long n, Ap [n+1], Ai [nz] ; klu_l_symbolic *Symbolic ; klu_l_common Common ; Symbolic = klu_l_analyze (n, Ap, Ai, &Common) ; /* real or complex */ \end{verbatim} } %------------------------------------------------------------------------------- \subsection{{\tt klu\_analyze\_given}: order and analyze a matrix} %------------------------------------------------------------------------------- In this routine, the fill-reducing ordering is provided by the user ({\tt Common.ordering} is ignored). Instead, the row permutation {\tt P} and column permutation {\tt Q} are used. These are integer arrays of size {\tt n}. If NULL, a natural ordering is used (so to provide just a column ordering, pass {\tt Q} as non-NULL and {\tt P} as NULL). A NULL pointer is returned if an error occurs. These functions may be used for both real and complex cases. {\footnotesize \begin{verbatim} #include "klu.h" int n, Ap [n+1], Ai [nz], P [n], Q [n] ; klu_symbolic *Symbolic ; klu_common Common ; Symbolic = klu_analyze_given (n, Ap, Ai, P, Q, &Common) ; /* real or complex */ #include "klu.h" UF_long n, Ap [n+1], Ai [nz], P [n], Q [n] ; klu_l_symbolic *Symbolic ; klu_l_common Common ; Symbolic = klu_l_analyze_given (n, Ap, Ai, P, Q, &Common) ; /* real or complex */ \end{verbatim} } %------------------------------------------------------------------------------- \subsection{{\tt klu\_factor}: numerical factorization} %------------------------------------------------------------------------------- The {\tt klu\_factor} function factorizes a matrix, using a sparse left-looking method with threshold partial pivoting. The inputs {\tt Ap} and {\tt Ai} must be unchanged from the previous call to {\tt klu\_analyze} that created the {\tt Symbolic} object. A NULL pointer is returned if an error occurs. {\footnotesize \begin{verbatim} #include "klu.h" int Ap [n+1], Ai [nz] ; double Ax [nz], Az [2*nz] ; klu_symbolic *Symbolic ; klu_numeric *Numeric ; klu_common Common ; Numeric = klu_factor (Ap, Ai, Ax, Symbolic, &Common) ; /* real */ Numeric = klu_z_factor (Ap, Ai, Az, Symbolic, &Common) ; /* complex */ #include "klu.h" UF_long Ap [n+1], Ai [nz] ; double Ax [nz], Az [2*nz] ; klu_l_symbolic *Symbolic ; klu_l_numeric *Numeric ; klu_l_common Common ; Numeric = klu_l_factor (Ap, Ai, Ax, Symbolic, &Common) ; /* real */ Numeric = klu_zl_factor (Ap, Ai, Az, Symbolic, &Common) ; /* complex */ \end{verbatim} } %------------------------------------------------------------------------------- \subsection{{\tt klu\_solve}: solve a linear system} %------------------------------------------------------------------------------- Solves the linear system $Ax=b$, using the {\tt Symbolic} and {\tt Numeric} objects. The right-hand side {\tt B} is overwritten with the solution on output. The array {\tt B} is stored in column major order, with a leading dimension of {\tt ldim}, and {\tt nrhs} columns. Thus, the real entry $b_{ij}$ is stored in {\tt B [i+j*ldim]}, where {\tt ldim >= n} must hold. A complex entry $b_{ij}$ is stored in {\tt B [2*(i+j*ldim)]} and {\tt B [2*(i+j*ldim)+1]} (for the real and imaginary parts, respectively). Returns 1 if successful, 0 if an error occurs. {\footnotesize \begin{verbatim} #include "klu.h" int ldim, nrhs, ok ; double B [ldim*nrhs], Bz [2*ldim*nrhs] ; klu_symbolic *Symbolic ; klu_numeric *Numeric ; klu_common Common ; ok = klu_solve (Symbolic, Numeric, ldim, nrhs, B, &Common) ; /* real */ ok = klu_z_solve (Symbolic, Numeric, ldim, nrhs, Bz, &Common) ; /* complex */ #include "klu.h" UF_long ldim, nrhs, ok ; double B [ldim*nrhs], Bz [2*ldim*nrhs] ; klu_symbolic *Symbolic ; klu_numeric *Numeric ; klu_common Common ; ok = klu_l_solve (Symbolic, Numeric, ldim, nrhs, B, &Common) ; /* real */ ok = klu_zl_solve (Symbolic, Numeric, ldim, nrhs, Bz, &Common) ; /* complex */ \end{verbatim} } %------------------------------------------------------------------------------- \subsection{{\tt klu\_tsolve}: solve a transposed linear system} %------------------------------------------------------------------------------- Solves the linear system $A^Tx=b$ or $A^Hx=b$. The {\tt conj\_solve} input is 0 for $A^Tx=b$, or nonzero for $A^Hx=b$. Otherwise, the function is identical to {\tt klu\_solve}. {\footnotesize \begin{verbatim} #include "klu.h" int ldim, nrhs, ok ; double B [ldim*nrhs], Bz [2*ldim*nrhs] ; klu_symbolic *Symbolic ; klu_numeric *Numeric ; klu_common Common ; ok = klu_tsolve (Symbolic, Numeric, ldim, nrhs, B, &Common) ; /* real */ ok = klu_z_tsolve (Symbolic, Numeric, ldim, nrhs, Bz, conj_solve, &Common) ; /* complex */ #include "klu.h" UF_long ldim, nrhs, ok ; double B [ldim*nrhs], Bz [2*ldim*nrhs] ; klu_symbolic *Symbolic ; klu_numeric *Numeric ; klu_common Common ; ok = klu_l_tsolve (Symbolic, Numeric, ldim, nrhs, B, &Common) ; /* real */ ok = klu_zl_tsolve (Symbolic, Numeric, ldim, nrhs, Bz, conj_solve, &Common) ; /* complex */ \end{verbatim} } %------------------------------------------------------------------------------- \subsection{{\tt klu\_refactor}: numerical refactorization} %------------------------------------------------------------------------------- The {\tt klu\_refactor} function takes as input the {\tt Numeric} object created by {\tt klu\_factor} (or as modified by a previous call to {\tt klu\_refactor}). It factorizes a new matrix with the same nonzero pattern as that given to the call to {\tt klu\_factor} which created it. The same pivot order is used. Since this can lead to numeric instability, the use of {\tt klu\_rcond}, {\tt klu\_rgrowth}, or {\tt klu\_condest} is recommended to check the accuracy of the resulting factorization. The inputs {\tt Ap} and {\tt Ai} must be unmodified since the call to {\tt klu\_factor} that first created the {\tt Numeric} object. This is function is much faster than {\tt klu\_factor}, and requires no dynamic memory allocation. {\footnotesize \begin{verbatim} #include "klu.h" int ok, Ap [n+1], Ai [nz] ; double Ax [nz], Az [2*nz] ; klu_symbolic *Symbolic ; klu_numeric *Numeric ; klu_common Common ; ok = klu_refactor (Ap, Ai, Ax, Symbolic, Numeric, &Common) ; /* real */ ok = klu_z_refactor (Ap, Ai, Az, Symbolic, Numeric, &Common) ; /* complex */ #include "klu.h" UF_long ok, Ap [n+1], Ai [nz] ; double Ax [nz], Az [2*nz] ; klu_l_symbolic *Symbolic ; klu_l_numeric *Numeric ; klu_l_common Common ; ok = klu_l_refactor (Ap, Ai, Ax, Symbolic, Numeric, &Common) ; /* real */ ok = klu_zl_refactor (Ap, Ai, Az, Symbolic, Numeric, &Common) ; /* complex */ \end{verbatim} } %------------------------------------------------------------------------------- \subsection{{\tt klu\_free\_symbolic}: destroy the {\tt Symbolic} object} %------------------------------------------------------------------------------- It is the user's responsibility to destroy the {\tt Symbolic} object when it is no longer needed, or else a memory leak will occur. It is safe to pass a NULL {\tt Symbolic} pointer. These functions may be used for both real and complex cases. {\footnotesize \begin{verbatim} #include "klu.h" klu_symbolic *Symbolic ; klu_common Common ; klu_free_symbolic (&Symbolic, &Common) ; /* real or complex */ #include "klu.h" klu_l_symbolic *Symbolic ; klu_l_common Common ; klu_l_free_symbolic (&Symbolic, &Common) ; /* real or complex */ \end{verbatim} } %------------------------------------------------------------------------------- \subsection{{\tt klu\_free\_numeric}: destroy the {\tt Numeric} object} %------------------------------------------------------------------------------- It is the user's responsibility to destroy the {\tt Numeric} object when it is no longer needed, or else a memory leak will occur. It is safe to pass a NULL {\tt Numeric} pointer. {\footnotesize \begin{verbatim} #include "klu.h" klu_numeric *Numeric ; klu_common Common ; klu_free_numeric (&Numeric, &Common) ; /* real */ klu_z_free_numeric (&Numeric, &Common) ; /* complex */ #include "klu.h" klu_l_numeric *Numeric ; klu_l_common Common ; klu_l_free_numeric (&Numeric, &Common) ; /* real */ klu_zl_free_numeric (&Numeric, &Common) ; /* complex */ \end{verbatim} } %------------------------------------------------------------------------------- \subsection{{\tt klu\_sort}: sort the columns of L and U} %------------------------------------------------------------------------------- The {\tt klu\_factor} function creates a {\tt Numeric} object with factors {\tt L} and {\tt U} stored in a compressed-column form (not the same data structure as {\tt A}, but similar). The columns typically contain lists of row indices in unsorted order. This function sorts these indices, for two purposes: (1) to return {\tt L} and {\tt U} to MATLAB, which expects its sparse matrices to have sorted columns, and (2) to slightly improve the performance of subsequent calls to {\tt klu\_solve} and {\tt klu\_tsolve}. Except within a MATLAB mexFunction (see {\tt KLU/MATLAB/klu\_mex.c}, the use of this function is optional. {\footnotesize \begin{verbatim} #include "klu.h" int ok ; klu_symbolic *Symbolic ; klu_numeric *Numeric ; klu_common Common ; ok = klu_sort (Symbolic, Numeric, &Common) ; /* real */ ok = klu_z_sort (Symbolic, Numeric, &Common) ; /* complex */ #include "klu.h" UF_long ok ; klu_l_symbolic *Symbolic ; klu_l_numeric *Numeric ; klu_l_common Common ; ok = klu_l_sort (Symbolic, Numeric, &Common) ; /* real */ ok = klu_zl_sort (Symbolic, Numeric, &Common) ; /* complex */ \end{verbatim} } %------------------------------------------------------------------------------- \subsection{{\tt klu\_flops}: determine the flop count} %------------------------------------------------------------------------------- This function determines the number of floating-point operations performed when the matrix was factorized by {\tt klu\_factor} or {\tt klu\_refactor}. The result is returned in {\tt Common.flops}. {\footnotesize \begin{verbatim} #include "klu.h" int ok ; klu_symbolic *Symbolic ; klu_numeric *Numeric ; klu_common Common ; ok = klu_flops (Symbolic, Numeric, &Common) ; /* real */ ok = klu_z_flops (Symbolic, Numeric, &Common) ; /* complex */ #include "klu.h" UF_long ok ; klu_l_symbolic *Symbolic ; klu_l_numeric *Numeric ; klu_l_common Common ; ok = klu_l_flops (Symbolic, Numeric, &Common) ; /* real */ ok = klu_zl_flops (Symbolic, Numeric, &Common) ; /* complex */ \end{verbatim} } %------------------------------------------------------------------------------- \subsection{{\tt klu\_rgrowth}: determine the pivot growth} %------------------------------------------------------------------------------- Computes the reciprocal pivot growth, $\mbox{\em rgrowth} = \min_j (( \max_i |c_{ij}| ) / ( \max_i |u_{ij}| ))$, where $c_{ij}$ is a scaled entry in a diagonal block of the block triangular form. In MATLAB notation: \begin{verbatim} rgrowth = min (max (abs (R\A(p,q) - F)) ./ max (abs (U))) \end{verbatim} where the factorization is \verb'L*U + F = R \ A(p,q)'. This function returns 0 if an error occurred, 1 otherwise. If {\tt rgrowth} is very small, an inaccurate factorization may have been performed. The inputs {\tt Ap}, {\tt Ai}, and {\tt Ax} ({\tt Az} in the complex case) must be unchanged since the last call to {\tt klu\_factor} or {\tt klu\_refactor}. The result is returned in {\tt Common.rgrowth}. {\footnotesize \begin{verbatim} #include "klu.h" int ok, Ap [n+1], Ai [nz] ; double Ax [nz], Az [2*nz] ; klu_symbolic *Symbolic ; klu_numeric *Numeric ; klu_common Common ; ok = klu_rgrowth (Ap, Ai, Ax, Symbolic, Numeric, &Common) ; /* real */ ok = klu_z_rgrowth (Ap, Ai, Az, Symbolic, Numeric, &Common) ; /* complex */ #include "klu.h" UF_long ok, Ap [n+1], Ai [nz] ; double Ax [nz], Az [2*nz] ; klu_l_symbolic *Symbolic ; klu_l_numeric *Numeric ; klu_l_common Common ; ok = klu_l_rgrowth (Ap, Ai, Ax, Symbolic, Numeric, &Common) ; /* real */ ok = klu_zl_rgrowth (Ap, Ai, Az, Symbolic, Numeric, &Common) ; /* complex */ \end{verbatim} } %------------------------------------------------------------------------------- \subsection{{\tt klu\_condest}: accurate condition number estimation} %------------------------------------------------------------------------------- This function is essentially the same as the MATLAB {\tt condest} function. It computes an estimate of the 1-norm condition number, using Hager's method \cite{Hager84} and the generalization by Higham and Tisseur \cite{HighamTisseur00}. The inputs {\tt Ap}, and {\tt Ax} ({\tt Az} in the complex case) must be unchanged since the last call to {\tt klu\_factor} or {\tt klu\_refactor}. The result is returned in {\tt Common.condest}. {\footnotesize \begin{verbatim} #include "klu.h" int ok, Ap [n+1] ; double Ax [nz], Az [2*nz] ; klu_symbolic *Symbolic ; klu_numeric *Numeric ; klu_common Common ; ok = klu_condest (Ap, Ax, Symbolic, Numeric, &Common) ; /* real */ ok = klu_z_condest (Ap, Az, Symbolic, Numeric, &Common) ; /* complex */ #include "klu.h" UF_long ok, Ap [n+1] ; double Ax [nz], Az [2*nz] ; klu_l_symbolic *Symbolic ; klu_l_numeric *Numeric ; klu_l_common Common ; ok = klu_l_condest (Ap, Ax, Symbolic, Numeric, &Common) ; /* real */ ok = klu_zl_condest (Ap, Az, Symbolic, Numeric, &Common) ; /* complex */ \end{verbatim} } %------------------------------------------------------------------------------- \subsection{{\tt klu\_rcond}: cheap reciprocal condition number estimation} %------------------------------------------------------------------------------- This function returns the smallest diagonal entry of {\tt U} divided by the largest, which is a very crude estimate of the reciprocal of the condition number of the matrix {\tt A}. It is very cheap to compute, however. In MATLAB notation, {\tt rcond = min(abs(diag(U))) / max(abs(diag(U)))}. If the matrix is singular, {\tt rcond} will be zero. The result is returned in {\tt Common.rcond}. {\footnotesize \begin{verbatim} #include "klu.h" int ok ; klu_symbolic *Symbolic ; klu_numeric *Numeric ; klu_common Common ; ok = klu_rcond (Symbolic, Numeric, &Common) ; /* real */ ok = klu_z_rcond (Symbolic, Numeric, &Common) ; /* complex */ #include "klu.h" UF_long ok ; klu_l_symbolic *Symbolic ; klu_l_numeric *Numeric ; klu_l_common Common ; ok = klu_l_rcond (Symbolic, Numeric, &Common) ; /* real */ ok = klu_zl_rcond (Symbolic, Numeric, &Common) ; /* complex */ \end{verbatim} } %------------------------------------------------------------------------------- \subsection{{\tt klu\_scale}: scale and check a sparse matrix} %------------------------------------------------------------------------------- This function computes the row scaling factors of a matrix and checks to see if it is a valid sparse matrix. It can perform two kinds of scaling, computing either the largest magnitude in each row, or the sum of the magnitudes of the entries each row. KLU calls this function itself, depending upon the {\tt Common.scale} parameter, where {\tt scale < 0} means no scaling, {\tt scale=1} means the sum, and {\tt scale=2} means the maximum. That is, in MATLAB notation, {\tt Rs = sum(abs(A'))} or {\tt Rs = max(abs(A'))}. KLU then divides each row of {\tt A} by its corresponding scale factor. The function returns 0 if the matrix is invalid, or 1 otherwise. A valid sparse matrix must meet the following conditions: \begin{enumerate} \item {\tt n > 0}. Note that KLU does not handle empty (0-by-0) matrices. \item {\tt Ap}, {\tt Ai}, and {\tt Ax} ({\tt Az} for the complex case) must not be NULL. \item {\tt Ap[0]=0}, and {\tt Ap [j] <= Ap [j+1]} for all {\tt j} in the range 0 to {\tt n-1}. \item The row indices in each column, {\tt Ai [Ap [j] ... Ap [j+1]-1]}, must be in the range 0 to {\tt n-1}, and no duplicates can appear. If the workspace {\tt W} is NULL on input, the check for duplicate entries is skipped. \end{enumerate} {\footnotesize \begin{verbatim} #include "klu.h" int scale, ok, n, Ap [n+1], Ai [nz], W [n] ; double Ax [nz], Az [2*nz], Rs [n] ; klu_common Common ; ok = klu_scale (scale, n, Ap, Ai, Ax, Symbolic, Numeric, &Common) ; /* real */ ok = klu_z_scale (scale, n, Ap, Ai, Az, Symbolic, Numeric, &Common) ; /* complex */ #include "klu.h" UF_long scale, ok, n, Ap [n+1], Ai [nz], W [n] ; double Ax [nz], Az [2*nz], Rs [n] ; klu_l_common Common ; ok = klu_l_scale (scale, n, Ap, Ai, Ax, Symbolic, Numeric, &Common) ; /* real */ ok = klu_zl_scale (scale, n, Ap, Ai, Az, Symbolic, Numeric, &Common) ; /* complex */ \end{verbatim} } %------------------------------------------------------------------------------- \subsection{{\tt klu\_extract}: extract the LU factorization} %------------------------------------------------------------------------------- This function extracts the LU factorization into a set of data structures suitable for passing back to MATLAB, with matrices in conventional compressed-column form. The {\tt klu\_sort} function should be called first if the row indices should be returned sorted. The factorization is returned in caller-provided arrays; if any of them are NULL, that part of the factorization is not extracted (this is not an error). Returns 1 if successful, 0 otherwise. The sizes of {\tt Li}, {\tt Lx}, and {\tt Lz} are {\tt Numeric->lnz}, {\tt Ui}, {\tt Ux}, and {\tt Uz} are of size {\tt Numeric->unz}, and {\tt Fi}, {\tt Fx}, and {\tt Fz} are of size {\tt Numeric->nzoff}. Note that in the complex versions, the real and imaginary parts are returned in separate arrays, to be compatible with how MATLAB stores complex matrices. This function is not required to solve a linear system with KLU. KLU does not itself make use of the extracted LU factorization returned by this function. It is only provided to simplify the MATLAB interface to KLU, and it may be of use to the end user who wishes to examine the contents of the LU factors. {\footnotesize \begin{verbatim} #include "klu.h" int ok, Lp [n+1], Li [lnz], Up [n+1], Ui [unz], Fp [n+1], Fi [nzoff], P [n], Q [n], R [n] ; double Lx [lnz], Lz [lnz], Ux [unz], Uz [unz], Fx [nzoff], Fz [nzoff], Rs [n] ; klu_symbolic *Symbolic ; klu_numeric *Numeric ; klu_common Common ; ok = klu_extract (Numeric, Symbolic, Lp, Li, Lx, Up, Ui, Ux, Fp, Fi, Fx, P, Q, Rs, R, &Common) ; /* real */ ok = klu_z_extract (Numeric, Symbolic, Lp, Li, Lx, Lz, Up, Ui, Ux, Uz, Fp, Fi, Fx, Fz, P, Q, Rs, R, &Common) ; /* complex */ #include "klu.h" UF_long ok, Lp [n+1], Li [lnz], Up [n+1], Ui [unz], Fp [n+1], Fi [nzoff], P [n], Q [n], R [n] ; double Lx [lnz], Lz [lnz], Ux [unz], Uz [unz], Fx [nzoff], Fz [nzoff], Rs [n] ; klu_l_symbolic *Symbolic ; klu_l_numeric *Numeric ; klu_l_common Common ; ok = klu_l_extract (Numeric, Symbolic, Lp, Li, Lx, Up, Ui, Ux, Fp, Fi, Fx, P, Q, Rs, R, &Common) ; /* real */ ok = klu_zl_extract (Numeric, Symbolic, Lp, Li, Lx, Lz, Up, Ui, Ux, Uz, Fp, Fi, Fx, Fz, P, Q, Rs, R, &Common) ; /* complex */ \end{verbatim} } %------------------------------------------------------------------------------- \subsection{{\tt klu\_malloc}, {\tt klu\_free}, {\tt klu\_realloc}: memory management} %------------------------------------------------------------------------------- KLU uses a set of wrapper routines for {\tt malloc}, {\tt free}, and {\tt realloc}. By default, these wrapper routines call the ANSI C versions of these functions. However, pointers to functions in {\tt Common} can be modified after calling {\tt klu\_defaults} to allow the use of other memory management functions (such as the MATLAB {\tt mxMalloc}, {\tt mxFree}, and {\tt mxRealloc}. These wrapper functions keep track of the current and peak memory usage of KLU. They can be called by the user. {\tt klu\_malloc} is essentially the same as {\tt p = malloc (n * sizeof (size))}, {\tt klu\_free} is essentially the same as {\tt free(p)} except that {\tt klu\_free} returns NULL which can then be assigned to {\tt p}. {\tt klu\_realloc} is similar to {\tt realloc}, except that if the reallocation fails, {\tt p} is returned unchanged. Failure conditions are returned in {\tt Common.status}. {\footnotesize \begin{verbatim} #include "klu.h" size_t n, nnew, nold, size ; void *p ; klu_common Common ; p = klu_malloc (n, size, &Common) ; p = klu_free (p, n, size, &Common) ; p = klu_realloc (nnew, nold, size, p, &Common) ; #include "klu.h" size_t n, nnew, nold, size ; void *p ; klu_l_common Common ; p = klu_l_malloc (n, size, &Common) ; p = klu_l_free (p, n, size, &Common) ; p = klu_l_realloc (nnew, nold, size, p, &Common) ; \end{verbatim} } %------------------------------------------------------------------------------- \subsection{{\tt btf\_maxtrans}: maximum transversal} %------------------------------------------------------------------------------- The BTF package includes three user-callable functions (each with {\tt int} and {\tt UF\_long} versions). They do not need to be called directly by an application that uses KLU. KLU will call these functions to perform the permutation into upper block triangular form. The {\tt btf\_maxtrans} function finds a column permutation {\tt Q} that gives {\tt A*Q} a zero-free diagonal, if one exists. If row {\tt i} is matched to column {\tt j}, then {\tt Match[i]=j}. If the matrix is structurally singular, there will be some unmatched rows. If row {\tt i} is unmatched, then {\tt Match[i]=-1}. If the matrix is square and structurally non-singular, then {\tt Q=Match} is the column permutation. The {\tt btf\_maxtrans} function can accept as input a rectangular matrix; it operates on the bipartite graph of {\tt A}. It returns the number of columns matched. Unlike the KLU user-callable functions, the BTF functions do not check its inputs at all; a segmentation fault will occur if any input pointers are NULL, for example. The function can require up to $O$({\tt n*nnz(A)}) time (excluding the {\em cheap match} phase, which takes another $O$({\tt nnz(A)}) time. If {\tt maxwork > 0} on input, the work is limited to $O$({\tt maxwork*nnz(A)}) (excluding the cheap match), but the maximum transversal might not be found if the limit is reached. The {\tt Work} array is workspace required by the methods; its contents are undefined on input and output. {\footnotesize \begin{verbatim} int nrow, ncol, Ap [ncol+1], Ai [nz], Match [nrow], Work [5*ncol], nmatch ; double maxwork, work ; nmatch = btf_maxtrans (nrow, ncol, Ap, Ai, maxwork, &work, Match, Work) ; UF_long nrow, ncol, Ap [ncol+1], Ai [nz], Match [nrow], Work [5*ncol], nmatch ; double maxwork, work ; nmatch = btf_l_maxtrans (nrow, ncol, Ap, Ai, maxwork, &work, Match, Work) ; \end{verbatim} } %------------------------------------------------------------------------------- \subsection{{\tt btf\_strongcomp}: strongly connected components} %------------------------------------------------------------------------------- The {\tt btf\_strongcomp} function finds the strongly connected components of a directed graph, returning a symmetric permutation {\tt P}. The matrix {\tt A} must be square. The diagonal of {\tt A} (or {\tt A*Q} if a column permutation is given on input) is ignored. If {\tt Q} is NULL on input, the matrix {\tt P*A*P'} is in upper block triangular form. Otherwise, {\tt Q} is modified on output so that {\tt P*A*Q} is in upper block triangular form. The vector {\tt R} gives the block boundaries, where the {\tt k}th block consists of rows and columns {\tt R[k]} through {\tt R[k+1]-1} in the permuted matrix. The function returns the number of strongly connected components found (the diagonal blocks in the block triangular form). {\footnotesize \begin{verbatim} int n, Ap [n+1], Ai [nz], Q [n], P [n], R [n+1], Work [4*n], ncomp ; ncomp = btf_strongcomp (n, Ap, Ai, Q, P, R, Work) ; UF_long n, Ap [n+1], Ai [nz], Q [n], P [n], R [n+1], Work [4*n], ncomp ; ncomp = btf_l_strongcomp (n, Ap, Ai, Q, P, R, Work) ; \end{verbatim} } %------------------------------------------------------------------------------- \subsection{{\tt btf\_order}: permutation to block triangular form} %------------------------------------------------------------------------------- The {\tt btf\_order} function combines the above two functions, first finding a maximum transversal and then permuting the resulting matrix into upper block triangular form. Unlike {\tt dmperm} in MATLAB, it always reveals the maximum matching along the diagonal, even if the matrix is structurally singular. On output, {\tt P} and {\tt Q} are the row and column permutations, where {\tt i = P[k]} if row {\tt i} of {\tt A} is the {\tt k}th row of {\tt P*A*Q}, and {\tt j = BTF\_UNFLIP(Q[k])} if column {\tt j} of {\tt A} is the {\tt k}th column of {\tt P*A*Q}. If {\tt Q[k] < 0}, then the {\tt (k,k)}th entry in {\tt P*A*Q} is structurally zero. The vector {\tt R}, and the return value, are the same as {\tt btf\_strongcomp}. {\footnotesize \begin{verbatim} int n, Ap [n+1], Ai [nz], P [n], Q [n], R [n+1], nfound, Work [5*n], ncomp, nfound ; double maxwork, work ; ncomp = btf_order (n, Ap, Ai, maxwork, &work, P, Q, R, &nfound, Work) ; UF_long n, Ap [n+1], Ai [nz], P [n], Q [n], R [n+1], nfound, Work [5*n], ncomp, nfound ; double maxwork, work ; ncomp = btf_l_order (n, Ap, Ai, maxwork, &work, P, Q, R, &nfound, Work) ; \end{verbatim} } %------------------------------------------------------------------------------ \subsection{Sample C programs that use KLU} %------------------------------------------------------------------------------ Here is a simple main program, {\tt klu\_simple.c}, that illustrates the basic usage of KLU. It uses KLU, and indirectly makes use of BTF and AMD. COLAMD is required to compile the demo, but it is not called by this example. It uses statically defined global variables for the sparse matrix {\tt A}, which would not be typical of a complete application. It just makes for a simpler example. {\footnotesize \input{klu_simple_c.tex} } The {\tt Ap}, {\tt Ai}, and {\tt Ax} arrays represent the matrix \[ A = \left[ \begin{array}{ccccc} 2 & 3 & 0 & 0 & 0 \\ 3 & 0 & 4 & 0 & 6 \\ 0 & -1 & -3 & 2 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 4 & 2 & 0 & 1 \\ \end{array} \right]. \] The solution to $Ax=b$ is $x = [1 \, 2 \, 3 \, 4 \, 5]^T$. The program uses default control settings (no scaling, permutation to block triangular form, and the AMD ordering). It ignores the error codes in the return values and {\tt Common.status}. The block triangular form found by {\tt btf\_order} for this matrix is given below \[ PAQ = \left[ \begin{array}{c|ccc|c} 2 & 0 & 0 & -1 & -3 \\ \hline & 2 & 0 & 3 & 0 \\ & 3 & 6 & 0 & 4 \\ & 0 & 1 & 4 & 1 \\ \hline & & & & 1 \\ \end{array} \right]. \] This ordering is not modified by the AMD ordering because the 3-by-3 matrix $A_{22} + A_{22}^T$ happens to be a dense matrix. No partial pivoting happens to occur during LU factorization; all pivots are selected along the diagonal of each block. The matrix contains two singletons, which are the original entries $a_{34}=2$ and $a_{43}=1$, and one 3-by-3 diagonal block (in which a single fill-in entry occurs during factorization: the $u_{23}$ entry of this 3-by-3 matrix). For a more complete program that uses KLU, see {\tt KLU/Demo/kludemo.c} for an {\tt int} version, and {\tt KLU/Demo/kluldemo.c} for a version that uses {\tt UF\_long} instead. The top-level main routine uses CHOLMOD to read in a compressed-column sparse matrix from a Matrix Market file, because KLU does not include such a function. Otherwise, no CHOLMOD functions are used. Unlike {\tt klu\_simple.c}, CHOLMOD is required to run the {\tt kludemo.c} and {\tt kluldemo.c} programs. %------------------------------------------------------------------------------ \section{Installation} \label{Install} %------------------------------------------------------------------------------ Installation of the C-callable interface requires the {\tt make} utility, in Linux/Unix. Alternatively, you can use the Cygwin {\tt make} in Windows. The MATLAB installation in any platform, including Windows is simple; just type {\tt klu\_install} to compile and install KLU, BTF, AMD, and COLAMD. For {\tt make}, system-dependent configurations are in the {\tt ../UFconfig/UFconfig.mk} file. You can edit that file to customize the compilation. The default settings will work on most systems. Sample configuration files are provided for Linux, Sun Solaris, SGI IRIX, IBM AIX, and the DEC/Compaq Alpha. To compile and install the C-callable KLU, BTF, AMD, and COLAMD libraries, go to the {\tt KLU} directory and type {\tt make}. The KLU and BTF libraries are placed in {\tt KLU/Lib/libklu.a} and {\tt BTF/Lib/libbtf.a}. Two KLU demo programs will be compiled and tested in the {\tt KLU/Demo} directory. You can compare the output of {\tt make} with the results in the KLU distribution, {\tt kludemo.out}. Typing {\tt make clean} will remove all but the final compiled libraries and demo programs. Typing {\tt make purge} or {\tt make distclean} removes all files not in the original distribution. If you compile KLU or BTF and then later change the {\tt ../UFconfig/UFconfig.mk} file then you should type {\tt make purge} and then {\tt make} to recompile. When you compile your program that uses the C-callable KLU library, you need to add the {\tt KLU/Lib/libklu.a}, {\tt BTF/Lib/libbtf.a}, {\tt AMD/Lib/libamd.a}, and {\tt COLAMD/Lib/libamd.a} libraries, a nd you need to tell your compiler to look in the {\tt KLU/Include} and {\tt BTF/Include} directory for include files. If all you want to use is the KLU mexFunction in MATLAB, you can skip the use of the {\tt make} command entirely. Simply type {\tt klu\_install} in the MATLAB command window while in the {\tt KLU/MATLAB} directory. This works on any system with MATLAB, including Windows. Alternately, type {\tt make} in the {\tt KLU/MATLAB} directory. If you have MATLAB 7.2 or earlier, you must first edit UFconfig/UFconfig.h to remove the {\tt -largeArrayDims} option from the {\tt MEX} command, prior to {\tt make mex} or {\tt make} in the MATLAB directory (or just use {\tt klu\_install.m} inside MATLAB, which handles this case). %------------------------------------------------------------------------------ \newpage \section{The KLU routines} \label{klu_include} %------------------------------------------------------------------------------ The file {\tt KLU/Include/klu.h} listed below describes each user-callable routine in the C version of KLU, and gives details on their use. {\footnotesize \input{klu_h.tex} } %------------------------------------------------------------------------------ \newpage \section{The BTF routines} \label{btf_include} %------------------------------------------------------------------------------ The file {\tt BTF/Include/btf.h} listed below describes each user-callable routine in the C version of BTF, and gives details on their use. {\footnotesize \input{btf_h.tex} } %------------------------------------------------------------------------------ \newpage % References %------------------------------------------------------------------------------ \bibliographystyle{plain} \bibliography{KLU_UserGuide} \end{document} SuiteSparse/KLU/Doc/palamadai_e.pdf0000644001170100242450000121113410426213540016017 0ustar davisfac%PDF-1.3 %쏢 63 0 obj <> stream xT=o0+4iR"Q:hNE|Ht(4xG޽{זmI\b͵9VϗvST[^-U m4w}?AY`ܝ)\OnjR0\ꂎ {JZ0AhC 90}2 ȺҘ>ԦɎIҲĖS0 WbWr(++HP~ 1s5KJ$3UێaDBMry> stream xEN0 y avv& oOB98?<!YapBfL 7?`^J=R y=BUG?O {L&g<QCy[a{JW/w39ĴmQ[6jS/sܡK\t*W뷺> stream x}n {2)n.?6RII唷`2@v 锻م]8fV~-{z7 G5(!nȁn4og~1 qL{]D@B,0-Q"h[yV-w P + Kb@ a r$;*B%L wZ!V5m"n+!3!M4x:4պۃ7JB4~]_9߶0~_Fc{H4Բ\~"6C6`!t"endstream endobj 76 0 obj 308 endobj 79 0 obj <> stream xWKsF +3fߏc;2_NQ&GJK vE'Xygf8% ۈiV&7qVJxVa;lfm"~cTE4m}.N珩;D\Da<@\\-V=W9?Ŧ"rS3*^Wӌ0[+'D{g4P" F,OgQ҃)7uwy]ߋg f M~h;QH0QĶ-ɶ=]WQ>N-릪|E@|`uY@Ԗ6}׷y#4Tyh3O6|(X٦ODh!ĝ U|_zD3mmzX=UEr$,BGۢYjmBv^3.;@ ɲPQ F*c1|Xdendstream endobj 80 0 obj 1213 endobj 83 0 obj <> stream x\Ks6WGnbȏZtzdef#Q%I} @QډC#1Yb"H?9[ > >ElM?]K4 HDFH20gt1x=}3cWRH4 )2'b$ N6_L'7S:fFFFFDy2{0t am~~SO~ VH I`X̮:?\\'"!K?=Z? 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00000 n 82 1 0000326244 00000 n 117 1 0000326637 00000 n 157 1 0000326983 00000 n 588 10 0000327193 00000 n 0000327323 00000 n 0000327383 00000 n 0000327509 00000 n 0000327639 00000 n 0000327700 00000 n 0000327830 00000 n 0000327889 00000 n 0000328019 00000 n 0000328078 00000 n trailer <<08B18604ABD4C44591BD54ED57A7B366>]/Prev 314067 >> startxref 331883 %%EOF SuiteSparse/KLU/Doc/ChangeLog0000644001170100242450000000321010711427761014663 0ustar davisfacNov 1, 2007, version 1.0.1 * minor lint cleanup May 31, 2007, version 1.0 * Overview: this is the first clean release of KLU. Only one bug was fixed since in the last pre-1.0 version (see below). This release adds a 64-bit version, a better Demo, a 100% statement coverage test, new parameters and statistics in the KLU Common object, reduced memory usage, a method for limiting worst-case work in the BTF ordering, and a completely redesigned MATLAB interface. * scaling default changed from no scaling, to max row scaling * C-callable API modified for klu_malloc, klu_free, klu_realloc, klu_rcond, klu_rgrowth, klu_condest. API of other user-callable KLU functions not modified. * user ordering function prototype modified (final argument is now klu_common, not Common->user_data) * User Guide added. * KLU Demo completely rewritten. Now depends on CHOLMOD to read in its matrices, in Matrix Market format. * port to 64-bit version * reduction in memory usage, particularly when the BTF form results in many small diagonal blocks * new Common parameter (maxwork) and statistics (work, memusage, mempeak) * Makefile and object files (*.o) now placed in KLU/Lib, not KLU/Source * added klu_install.m, klu_demo.m, klu_make.m to KLU/MATLAB. * klu mexFunction now returns a struct for LU, not a lengthy list of matrices. MATLAB interface completely rewritten. * Tcov tests completely rewritten * bug fix in complex klu_z_refactor, when both btf and scaling are in use * bug fix in klu_rgrowth, when the matrix is scaled Dec 12, 2006: version 0.11 * minor MATLAB cleanup SuiteSparse/KLU/Doc/lesser.txt0000644001170100242450000006350010275713647015165 0ustar davisfac GNU LESSER GENERAL PUBLIC LICENSE Version 2.1, February 1999 Copyright (C) 1991, 1999 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. [This is the first released version of the Lesser GPL. It also counts as the successor of the GNU Library Public License, version 2, hence the version number 2.1.] Preamble The licenses for most software are designed to take away your freedom to share and change it. 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SuiteSparse/KLU/Lib/0000755001170100242450000000000010711435723013113 5ustar davisfacSuiteSparse/KLU/Lib/Makefile0000644001170100242450000001430010617112702014543 0ustar davisfacdefault: all ccode: all include ../../UFconfig/UFconfig.mk # for testing only: # TEST = -DTESTING C = $(CC) $(CFLAGS) INC = ../Include/klu.h ../Include/klu_internal.h ../Include/klu_version.h \ ../../UFconfig/UFconfig.h Makefile I = -I../../AMD/Include -I../../COLAMD/Include -I../../BTF/Include \ -I../Include -I../../UFconfig all: library library: libklu.a KLU_D = klu_d.o klu_d_kernel.o klu_d_dump.o \ klu_d_factor.o klu_d_free_numeric.o klu_d_solve.o \ klu_d_scale.o klu_d_refactor.o \ klu_d_tsolve.o klu_d_diagnostics.o klu_d_sort.o klu_d_extract.o KLU_Z = klu_z.o klu_z_kernel.o klu_z_dump.o \ klu_z_factor.o klu_z_free_numeric.o klu_z_solve.o \ klu_z_scale.o klu_z_refactor.o \ klu_z_tsolve.o klu_z_diagnostics.o klu_z_sort.o klu_z_extract.o KLU_L = klu_l.o klu_l_kernel.o klu_l_dump.o \ klu_l_factor.o klu_l_free_numeric.o klu_l_solve.o \ klu_l_scale.o klu_l_refactor.o \ klu_l_tsolve.o klu_l_diagnostics.o klu_l_sort.o klu_l_extract.o KLU_ZL = klu_zl.o klu_zl_kernel.o klu_zl_dump.o \ klu_zl_factor.o klu_zl_free_numeric.o klu_zl_solve.o \ klu_zl_scale.o klu_zl_refactor.o \ klu_zl_tsolve.o klu_zl_diagnostics.o klu_zl_sort.o klu_zl_extract.o COMMON = \ klu_free_symbolic.o klu_defaults.o klu_analyze_given.o \ klu_analyze.o klu_memory.o \ klu_l_free_symbolic.o klu_l_defaults.o klu_l_analyze_given.o \ klu_l_analyze.o klu_l_memory.o OBJ = $(COMMON) $(KLU_D) $(KLU_Z) $(KLU_L) $(KLU_ZL) libklu.a: $(OBJ) $(AR) libklu.a $(OBJ) $(RANLIB) libklu.a $(OBJ): $(INC) #------------------------------------------------------------------------------- klu_d.o: ../Source/klu.c $(C) -c $(I) $< -o $@ klu_z.o: ../Source/klu.c $(C) -c -DCOMPLEX $(I) $< -o $@ klu_d_kernel.o: ../Source/klu_kernel.c $(C) -c $(I) $< -o $@ klu_z_kernel.o: ../Source/klu_kernel.c $(C) -c -DCOMPLEX $(I) $< -o $@ klu_d_sort.o: ../Source/klu_sort.c $(C) -c $(I) $< -o $@ klu_z_sort.o: ../Source/klu_sort.c $(C) -c -DCOMPLEX $(I) $< -o $@ klu_d_diagnostics.o: ../Source/klu_diagnostics.c $(C) -c $(I) $< -o $@ klu_z_diagnostics.o: ../Source/klu_diagnostics.c $(C) -c -DCOMPLEX $(I) $< -o $@ klu_d_dump.o: ../Source/klu_dump.c $(C) -c $(I) $< -o $@ klu_z_dump.o: ../Source/klu_dump.c $(C) -c -DCOMPLEX $(I) $< -o $@ klu_d_factor.o: ../Source/klu_factor.c $(C) -c $(I) $< -o $@ klu_z_factor.o: ../Source/klu_factor.c $(C) -c -DCOMPLEX $(I) $< -o $@ klu_d_free_numeric.o: ../Source/klu_free_numeric.c $(C) -c $(I) $< -o $@ klu_z_free_numeric.o: ../Source/klu_free_numeric.c $(C) -c -DCOMPLEX $(I) $< -o $@ klu_d_extract.o: ../Source/klu_extract.c $(C) -c $(I) $< -o $@ klu_z_extract.o: ../Source/klu_extract.c $(C) -c -DCOMPLEX $(I) $< -o $@ klu_d_refactor.o: ../Source/klu_refactor.c $(C) -c $(I) $< -o $@ klu_z_refactor.o: ../Source/klu_refactor.c $(C) -c -DCOMPLEX $(I) $< -o $@ klu_d_scale.o: ../Source/klu_scale.c $(C) -c $(I) $< -o $@ klu_z_scale.o: ../Source/klu_scale.c $(C) -c -DCOMPLEX $(I) $< -o $@ klu_d_solve.o: ../Source/klu_solve.c $(C) -c $(I) $< -o $@ klu_z_solve.o: ../Source/klu_solve.c $(C) -c -DCOMPLEX $(I) $< -o $@ klu_d_tsolve.o: ../Source/klu_tsolve.c $(C) -c $(I) $< -o $@ klu_z_tsolve.o: ../Source/klu_tsolve.c $(C) -c -DCOMPLEX $(I) $< -o $@ #------------------------------------------------------------------------------- klu_analyze.o: ../Source/klu_analyze.c $(C) -c $(I) $< -o $@ klu_analyze_given.o: ../Source/klu_analyze_given.c $(C) -c $(I) $< -o $@ klu_defaults.o: ../Source/klu_defaults.c $(C) -c $(I) $< -o $@ klu_free_symbolic.o: ../Source/klu_free_symbolic.c $(C) -c $(I) $< -o $@ klu_memory.o: ../Source/klu_memory.c $(C) -c $(I) $< -o $@ #------------------------------------------------------------------------------- purge: distclean distclean: clean - $(RM) libklu.a clean: - $(RM) $(CLEAN) #------------------------------------------------------------------------------- klu_l.o: ../Source/klu.c $(C) -c -DDLONG $(I) $< -o $@ klu_zl.o: ../Source/klu.c $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@ klu_l_kernel.o: ../Source/klu_kernel.c $(C) -c -DDLONG $(I) $< -o $@ klu_zl_kernel.o: ../Source/klu_kernel.c $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@ klu_l_sort.o: ../Source/klu_sort.c $(C) -c -DDLONG $(I) $< -o $@ klu_zl_sort.o: ../Source/klu_sort.c $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@ klu_l_diagnostics.o: ../Source/klu_diagnostics.c $(C) -c -DDLONG $(I) $< -o $@ klu_zl_diagnostics.o: ../Source/klu_diagnostics.c $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@ klu_l_dump.o: ../Source/klu_dump.c $(C) -c -DDLONG $(I) $< -o $@ klu_zl_dump.o: ../Source/klu_dump.c $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@ klu_l_factor.o: ../Source/klu_factor.c $(C) -c -DDLONG $(I) $< -o $@ klu_zl_factor.o: ../Source/klu_factor.c $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@ klu_l_free_numeric.o: ../Source/klu_free_numeric.c $(C) -c -DDLONG $(I) $< -o $@ klu_zl_free_numeric.o: ../Source/klu_free_numeric.c $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@ klu_l_extract.o: ../Source/klu_extract.c $(C) -c -DDLONG $(I) $< -o $@ klu_zl_extract.o: ../Source/klu_extract.c $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@ klu_l_refactor.o: ../Source/klu_refactor.c $(C) -c -DDLONG $(I) $< -o $@ klu_zl_refactor.o: ../Source/klu_refactor.c $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@ klu_l_scale.o: ../Source/klu_scale.c $(C) -c -DDLONG $(I) $< -o $@ klu_zl_scale.o: ../Source/klu_scale.c $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@ klu_l_solve.o: ../Source/klu_solve.c $(C) -c -DDLONG $(I) $< -o $@ klu_zl_solve.o: ../Source/klu_solve.c $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@ klu_l_tsolve.o: ../Source/klu_tsolve.c $(C) -c -DDLONG $(I) $< -o $@ klu_zl_tsolve.o: ../Source/klu_tsolve.c $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@ #------------------------------------------------------------------------------- klu_l_analyze.o: ../Source/klu_analyze.c $(C) -c -DDLONG $(I) $< -o $@ klu_l_analyze_given.o: ../Source/klu_analyze_given.c $(C) -c -DDLONG $(I) $< -o $@ klu_l_defaults.o: ../Source/klu_defaults.c $(C) -c -DDLONG $(I) $< -o $@ klu_l_free_symbolic.o: ../Source/klu_free_symbolic.c $(C) -c -DDLONG $(I) $< -o $@ klu_l_memory.o: ../Source/klu_memory.c $(C) -c -DDLONG $(I) $< -o $@ #------------------------------------------------------------------------------- SuiteSparse/KLU/Demo/0000755001170100242450000000000010711435723013271 5ustar davisfacSuiteSparse/KLU/Demo/klu_simple.c0000644001170100242450000000142110620342701015567 0ustar davisfac/* klu_simple: a simple KLU demo */ #include #include "klu.h" int n = 5 ; int Ap [ ] = {0, 2, 5, 9, 10, 12} ; int Ai [ ] = { 0, 1, 0, 2, 4, 1, 2, 3, 4, 2, 1, 4} ; double Ax [ ] = {2., 3., 3., -1., 4., 4., -3., 1., 2., 2., 6., 1.} ; double b [ ] = {8., 45., -3., 3., 19.} ; int main (void) { klu_symbolic *Symbolic ; klu_numeric *Numeric ; klu_common Common ; int i ; klu_defaults (&Common) ; Symbolic = klu_analyze (n, Ap, Ai, &Common) ; Numeric = klu_factor (Ap, Ai, Ax, Symbolic, &Common) ; klu_solve (Symbolic, Numeric, 5, 1, b, &Common) ; klu_free_symbolic (&Symbolic, &Common) ; klu_free_numeric (&Numeric, &Common) ; for (i = 0 ; i < n ; i++) printf ("x [%d] = %g\n", i, b [i]) ; return (0) ; } SuiteSparse/KLU/Demo/Makefile0000644001170100242450000000330710710765233014735 0ustar davisfac# KLU Demo Makefile. The klu_simple demo is stand-alone. The other demos # require CHOLMOD. default: all include ../../UFconfig/UFconfig.mk LIB = ../Lib/libklu.a ../../BTF/Lib/libbtf.a \ ../../AMD/Lib/libamd.a ../../COLAMD/Lib/libcolamd.a CHOLMOD = ../../CHOLMOD/Lib/libcholmod.a I = -I../../UFconfig -I../../AMD/Include -I../../COLAMD/Include \ -I../../BTF/Include -I../Include -I../../CHOLMOD/Include all: $(LIB) klu_simple $(CHOLMOD) kludemo kluldemo - ./klu_simple - ./kludemo < ../Matrix/1c.mtx - ./kludemo < ../Matrix/arrowc.mtx - ./kludemo < ../Matrix/arrow.mtx - ./kludemo < ../Matrix/impcol_a.mtx - ./kludemo < ../Matrix/w156.mtx - ./kludemo < ../Matrix/ctina.mtx - ./kluldemo < ../Matrix/1c.mtx - ./kluldemo < ../Matrix/arrowc.mtx - ./kluldemo < ../Matrix/arrow.mtx - ./kluldemo < ../Matrix/impcol_a.mtx - ./kluldemo < ../Matrix/w156.mtx - ./kluldemo < ../Matrix/ctina.mtx ../Lib/libklu.a: ( cd ../Lib ; $(MAKE) ) ../../BTF/Lib/libbtf.a: ( cd ../../BTF ; $(MAKE) library ) ../../AMD/Lib/libamd.a: ( cd ../../AMD ; $(MAKE) library ) ../../COLAMD/Lib/libcolamd.a: ( cd ../../COLAMD ; $(MAKE) library ) ../../CHOLMOD/Lib/libcholmod.a: ( cd ../../CHOLMOD ; $(MAKE) library ) # ( cd ../../CAMD ; $(MAKE) ) # ( cd ../../CCOLAMD ; $(MAKE) ) # ( cd ../../metis-4.0 ; $(MAKE) ) purge: distclean distclean: clean - $(RM) kludemo kluldemo klu_simple clean: - $(RM) $(CLEAN) kludemo: kludemo.c Makefile $(LIB) $(CC) $(CFLAGS) $(I) kludemo.c -o kludemo $(LIB) $(CHOLMOD) -lm kluldemo: kludemo.c Makefile $(LIB) $(CC) $(CFLAGS) $(I) kluldemo.c -o kluldemo $(LIB) $(CHOLMOD) -lm klu_simple: klu_simple.c Makefile $(LIB) $(CC) $(CFLAGS) $(I) klu_simple.c -o klu_simple $(LIB) -lm - ./klu_simple SuiteSparse/KLU/Demo/kludemo.out0000644001170100242450000000467110711432712015465 0ustar davisfac./klu_simple x [0] = 1 x [1] = 2 x [2] = 3 x [3] = 4 x [4] = 5 ./kludemo < ../Matrix/1c.mtx KLU: Nov 1, 2007, version: 1.0.1 n 1 nnz(A) 1 nnz(L+U+F) 1 resid 0 recip growth 1 condest 1 rcond 1 flops 0 peak memory usage: 492 bytes ./kludemo < ../Matrix/arrowc.mtx KLU: Nov 1, 2007, version: 1.0.1 n 100 nnz(A) 298 nnz(L+U+F) 298 resid 1.68007e-14 recip growth 0.019999 condest 295.99 rcond 0.019999 flops 297 peak memory usage: 32244 bytes ./kludemo < ../Matrix/arrow.mtx KLU: Nov 1, 2007, version: 1.0.1 n 100 nnz(A) 298 nnz(L+U+F) 298 resid 1.77636e-15 recip growth 0.0204082 condest 303 rcond 0.0204082 flops 297 peak memory usage: 20412 bytes ./kludemo < ../Matrix/impcol_a.mtx KLU: Nov 1, 2007, version: 1.0.1 n 207 nnz(A) 572 nnz(L+U+F) 615 resid 6.98492e-10 recip growth 0.00957447 condest 4.35093e+07 rcond 4.5277e-05 flops 259 peak memory usage: 34276 bytes ./kludemo < ../Matrix/w156.mtx KLU: Nov 1, 2007, version: 1.0.1 n 156 nnz(A) 362 nnz(L+U+F) 396 resid 6.23816e-08 recip growth 0.00889922 condest 1.79787e+09 rcond 0.000124785 flops 175 peak memory usage: 39516 bytes ./kludemo < ../Matrix/ctina.mtx KLU: Nov 1, 2007, version: 1.0.1 n 11 nnz(A) 36 nnz(L+U+F) 45 resid 4.44089e-16 recip growth 1 condest 56 rcond 1 flops 73 peak memory usage: 4268 bytes ./kluldemo < ../Matrix/1c.mtx KLU: Nov 1, 2007, version: 1.0.1 n 1 nnz(A) 1 nnz(L+U+F) 1 resid 0 recip growth 1 condest 1 rcond 1 flops 0 peak memory usage: 600 bytes ./kluldemo < ../Matrix/arrowc.mtx KLU: Nov 1, 2007, version: 1.0.1 n 100 nnz(A) 298 nnz(L+U+F) 298 resid 1.68007e-14 recip growth 0.019999 condest 295.99 rcond 0.019999 flops 297 peak memory usage: 39000 bytes ./kluldemo < ../Matrix/arrow.mtx KLU: Nov 1, 2007, version: 1.0.1 n 100 nnz(A) 298 nnz(L+U+F) 298 resid 1.77636e-15 recip growth 0.0204082 condest 303 rcond 0.0204082 flops 297 peak memory usage: 29584 bytes ./kluldemo < ../Matrix/impcol_a.mtx KLU: Nov 1, 2007, version: 1.0.1 n 207 nnz(A) 572 nnz(L+U+F) 615 resid 6.98492e-10 recip growth 0.00957447 condest 4.35093e+07 rcond 4.5277e-05 flops 259 peak memory usage: 44800 bytes ./kluldemo < ../Matrix/w156.mtx KLU: Nov 1, 2007, version: 1.0.1 n 156 nnz(A) 362 nnz(L+U+F) 396 resid 6.23816e-08 recip growth 0.00889922 condest 1.79787e+09 rcond 0.000124785 flops 175 peak memory usage: 47480 bytes ./kluldemo < ../Matrix/ctina.mtx KLU: Nov 1, 2007, version: 1.0.1 n 11 nnz(A) 36 nnz(L+U+F) 45 resid 4.44089e-16 recip growth 1 condest 56 rcond 1 flops 73 peak memory usage: 5144 bytes SuiteSparse/KLU/Demo/kluldemo.c0000644001170100242450000002363010620326237015253 0ustar davisfac/* ========================================================================== */ /* === KLU DEMO (long integer version) ====================================== */ /* ========================================================================== */ /* Read in a Matrix Market matrix (using CHOLMOD) and solve a linear system. * UF_long is normally a "long", but it becomes "_int64" on Windows 64. */ #include #include #include "klu.h" /* for handling complex matrices */ #define REAL(X,i) (X [2*(i)]) #define IMAG(X,i) (X [2*(i)+1]) #define CABS(X,i) (sqrt (REAL (X,i) * REAL (X,i) + IMAG (X,i) * IMAG (X,i))) #define MAX(a,b) (((a) > (b)) ? (a) : (b)) /* ========================================================================== */ /* === klu_l_backslash ====================================================== */ /* ========================================================================== */ static UF_long klu_l_backslash /* return 1 if successful, 0 otherwise */ ( /* --- input ---- */ UF_long n, /* A is n-by-n */ UF_long *Ap, /* size n+1, column pointers */ UF_long *Ai, /* size nz = Ap [n], row indices */ double *Ax, /* size nz, numerical values */ UF_long isreal, /* nonzero if A is real, 0 otherwise */ double *B, /* size n, right-hand-side */ /* --- output ---- */ double *X, /* size n, solution to Ax=b */ double *R, /* size n, residual r = b-A*x */ /* --- scalar output --- */ UF_long *lunz, /* nnz (L+U+F) */ double *rnorm, /* norm (b-A*x,1) / norm (A,1) */ /* --- workspace - */ klu_l_common *Common /* default parameters and statistics */ ) { double anorm = 0, asum ; klu_l_symbolic *Symbolic ; klu_l_numeric *Numeric ; UF_long i, j, p ; if (!Ap || !Ai || !Ax || !B || !X || !B) return (0) ; /* ---------------------------------------------------------------------- */ /* symbolic ordering and analysis */ /* ---------------------------------------------------------------------- */ Symbolic = klu_l_analyze (n, Ap, Ai, Common) ; if (!Symbolic) return (0) ; if (isreal) { /* ------------------------------------------------------------------ */ /* factorization */ /* ------------------------------------------------------------------ */ Numeric = klu_l_factor (Ap, Ai, Ax, Symbolic, Common) ; if (!Numeric) { klu_l_free_symbolic (&Symbolic, Common) ; return (0) ; } /* ------------------------------------------------------------------ */ /* statistics (not required to solve Ax=b) */ /* ------------------------------------------------------------------ */ klu_l_rgrowth (Ap, Ai, Ax, Symbolic, Numeric, Common) ; klu_l_condest (Ap, Ax, Symbolic, Numeric, Common) ; klu_l_rcond (Symbolic, Numeric, Common) ; klu_l_flops (Symbolic, Numeric, Common) ; *lunz = Numeric->lnz + Numeric->unz - n + ((Numeric->Offp) ? (Numeric->Offp [n]) : 0) ; /* ------------------------------------------------------------------ */ /* solve Ax=b */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < n ; i++) { X [i] = B [i] ; } klu_l_solve (Symbolic, Numeric, n, 1, X, Common) ; /* ------------------------------------------------------------------ */ /* compute residual, rnorm = norm(b-Ax,1) / norm(A,1) */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < n ; i++) { R [i] = B [i] ; } for (j = 0 ; j < n ; j++) { asum = 0 ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { /* R (i) -= A (i,j) * X (j) */ R [Ai [p]] -= Ax [p] * X [j] ; asum += fabs (Ax [p]) ; } anorm = MAX (anorm, asum) ; } *rnorm = 0 ; for (i = 0 ; i < n ; i++) { *rnorm = MAX (*rnorm, fabs (R [i])) ; } /* ------------------------------------------------------------------ */ /* free numeric factorization */ /* ------------------------------------------------------------------ */ klu_l_free_numeric (&Numeric, Common) ; } else { /* ------------------------------------------------------------------ */ /* statistics (not required to solve Ax=b) */ /* ------------------------------------------------------------------ */ Numeric = klu_zl_factor (Ap, Ai, Ax, Symbolic, Common) ; if (!Numeric) { klu_l_free_symbolic (&Symbolic, Common) ; return (0) ; } /* ------------------------------------------------------------------ */ /* statistics */ /* ------------------------------------------------------------------ */ klu_zl_rgrowth (Ap, Ai, Ax, Symbolic, Numeric, Common) ; klu_zl_condest (Ap, Ax, Symbolic, Numeric, Common) ; klu_zl_rcond (Symbolic, Numeric, Common) ; klu_zl_flops (Symbolic, Numeric, Common) ; *lunz = Numeric->lnz + Numeric->unz - n + ((Numeric->Offp) ? (Numeric->Offp [n]) : 0) ; /* ------------------------------------------------------------------ */ /* solve Ax=b */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < 2*n ; i++) { X [i] = B [i] ; } klu_zl_solve (Symbolic, Numeric, n, 1, X, Common) ; /* ------------------------------------------------------------------ */ /* compute residual, rnorm = norm(b-Ax,1) / norm(A,1) */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < 2*n ; i++) { R [i] = B [i] ; } for (j = 0 ; j < n ; j++) { asum = 0 ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { /* R (i) -= A (i,j) * X (j) */ i = Ai [p] ; REAL (R,i) -= REAL(Ax,p) * REAL(X,j) - IMAG(Ax,p) * IMAG(X,j) ; IMAG (R,i) -= IMAG(Ax,p) * REAL(X,j) + REAL(Ax,p) * IMAG(X,j) ; asum += CABS (Ax, p) ; } anorm = MAX (anorm, asum) ; } *rnorm = 0 ; for (i = 0 ; i < n ; i++) { *rnorm = MAX (*rnorm, CABS (R, i)) ; } /* ------------------------------------------------------------------ */ /* free numeric factorization */ /* ------------------------------------------------------------------ */ klu_zl_free_numeric (&Numeric, Common) ; } /* ---------------------------------------------------------------------- */ /* free symbolic analysis, and residual */ /* ---------------------------------------------------------------------- */ klu_l_free_symbolic (&Symbolic, Common) ; return (1) ; } /* ========================================================================== */ /* === klu_l_demo =========================================================== */ /* ========================================================================== */ /* Given a sparse matrix A, set up a right-hand-side and solve X = A\b */ static void klu_l_demo (UF_long n, UF_long *Ap, UF_long *Ai, double *Ax, UF_long isreal) { double rnorm ; klu_l_common Common ; double *B, *X, *R ; UF_long i, lunz ; printf ("KLU: %s, version: %d.%d.%d\n", KLU_DATE, KLU_MAIN_VERSION, KLU_SUB_VERSION, KLU_SUBSUB_VERSION) ; /* ---------------------------------------------------------------------- */ /* set defaults */ /* ---------------------------------------------------------------------- */ klu_l_defaults (&Common) ; /* ---------------------------------------------------------------------- */ /* create a right-hand-side */ /* ---------------------------------------------------------------------- */ if (isreal) { /* B = 1 + (1:n)/n */ B = klu_l_malloc (n, sizeof (double), &Common) ; X = klu_l_malloc (n, sizeof (double), &Common) ; R = klu_l_malloc (n, sizeof (double), &Common) ; if (B) { for (i = 0 ; i < n ; i++) { B [i] = 1 + ((double) i+1) / ((double) n) ; } } } else { /* real (B) = 1 + (1:n)/n, imag(B) = (n:-1:1)/n */ B = klu_l_malloc (n, 2 * sizeof (double), &Common) ; X = klu_l_malloc (n, 2 * sizeof (double), &Common) ; R = klu_l_malloc (n, 2 * sizeof (double), &Common) ; if (B) { for (i = 0 ; i < n ; i++) { REAL (B, i) = 1 + ((double) i+1) / ((double) n) ; IMAG (B, i) = ((double) n-i) / ((double) n) ; } } } /* ---------------------------------------------------------------------- */ /* X = A\b using KLU and print statistics */ /* ---------------------------------------------------------------------- */ if (!klu_l_backslash (n, Ap, Ai, Ax, isreal, B, X, R, &lunz, &rnorm, &Common)) { printf ("KLU failed\n") ; } else { printf ("n %d nnz(A) %d nnz(L+U+F) %d resid %g\n" "recip growth %g condest %g rcond %g flops %g\n", n, Ap [n], lunz, rnorm, Common.rgrowth, Common.condest, Common.rcond, Common.flops) ; } /* ---------------------------------------------------------------------- */ /* free the problem */ /* ---------------------------------------------------------------------- */ if (isreal) { klu_l_free (B, n, sizeof (double), &Common) ; klu_l_free (X, n, sizeof (double), &Common) ; klu_l_free (R, n, sizeof (double), &Common) ; } else { klu_l_free (B, 2*n, sizeof (double), &Common) ; klu_l_free (X, 2*n, sizeof (double), &Common) ; klu_l_free (R, 2*n, sizeof (double), &Common) ; } printf ("peak memory usage: %g bytes\n\n", (double) (Common.mempeak)) ; } /* ========================================================================== */ /* === main ================================================================= */ /* ========================================================================== */ /* Read in a sparse matrix in Matrix Market format using CHOLMOD, and then * solve Ax=b with KLU. Note that CHOLMOD is only used to read the matrix. */ #include "cholmod.h" int main (void) { cholmod_sparse *A ; cholmod_common ch ; cholmod_l_start (&ch) ; A = cholmod_l_read_sparse (stdin, &ch) ; if (A) { if (A->nrow != A->ncol || A->stype != 0 || (!(A->xtype == CHOLMOD_REAL || A->xtype == CHOLMOD_COMPLEX))) { printf ("invalid matrix\n") ; } else { klu_l_demo (A->nrow, A->p, A->i, A->x, A->xtype == CHOLMOD_REAL) ; } cholmod_l_free_sparse (&A, &ch) ; } cholmod_l_finish (&ch) ; return (0) ; } SuiteSparse/KLU/Demo/kludemo.c0000644001170100242450000002331410620325770015077 0ustar davisfac/* ========================================================================== */ /* === KLU DEMO ============================================================= */ /* ========================================================================== */ /* Read in a Matrix Market matrix (using CHOLMOD) and solve a linear system. */ #include #include #include "klu.h" /* for handling complex matrices */ #define REAL(X,i) (X [2*(i)]) #define IMAG(X,i) (X [2*(i)+1]) #define CABS(X,i) (sqrt (REAL (X,i) * REAL (X,i) + IMAG (X,i) * IMAG (X,i))) #define MAX(a,b) (((a) > (b)) ? (a) : (b)) /* ========================================================================== */ /* === klu_backslash ======================================================== */ /* ========================================================================== */ static int klu_backslash /* return 1 if successful, 0 otherwise */ ( /* --- input ---- */ int n, /* A is n-by-n */ int *Ap, /* size n+1, column pointers */ int *Ai, /* size nz = Ap [n], row indices */ double *Ax, /* size nz, numerical values */ int isreal, /* nonzero if A is real, 0 otherwise */ double *B, /* size n, right-hand-side */ /* --- output ---- */ double *X, /* size n, solution to Ax=b */ double *R, /* size n, residual r = b-A*x */ /* --- scalar output --- */ int *lunz, /* nnz (L+U+F) */ double *rnorm, /* norm (b-A*x,1) / norm (A,1) */ /* --- workspace - */ klu_common *Common /* default parameters and statistics */ ) { double anorm = 0, asum ; klu_symbolic *Symbolic ; klu_numeric *Numeric ; int i, j, p ; if (!Ap || !Ai || !Ax || !B || !X || !B) return (0) ; /* ---------------------------------------------------------------------- */ /* symbolic ordering and analysis */ /* ---------------------------------------------------------------------- */ Symbolic = klu_analyze (n, Ap, Ai, Common) ; if (!Symbolic) return (0) ; if (isreal) { /* ------------------------------------------------------------------ */ /* factorization */ /* ------------------------------------------------------------------ */ Numeric = klu_factor (Ap, Ai, Ax, Symbolic, Common) ; if (!Numeric) { klu_free_symbolic (&Symbolic, Common) ; return (0) ; } /* ------------------------------------------------------------------ */ /* statistics (not required to solve Ax=b) */ /* ------------------------------------------------------------------ */ klu_rgrowth (Ap, Ai, Ax, Symbolic, Numeric, Common) ; klu_condest (Ap, Ax, Symbolic, Numeric, Common) ; klu_rcond (Symbolic, Numeric, Common) ; klu_flops (Symbolic, Numeric, Common) ; *lunz = Numeric->lnz + Numeric->unz - n + ((Numeric->Offp) ? (Numeric->Offp [n]) : 0) ; /* ------------------------------------------------------------------ */ /* solve Ax=b */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < n ; i++) { X [i] = B [i] ; } klu_solve (Symbolic, Numeric, n, 1, X, Common) ; /* ------------------------------------------------------------------ */ /* compute residual, rnorm = norm(b-Ax,1) / norm(A,1) */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < n ; i++) { R [i] = B [i] ; } for (j = 0 ; j < n ; j++) { asum = 0 ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { /* R (i) -= A (i,j) * X (j) */ R [Ai [p]] -= Ax [p] * X [j] ; asum += fabs (Ax [p]) ; } anorm = MAX (anorm, asum) ; } *rnorm = 0 ; for (i = 0 ; i < n ; i++) { *rnorm = MAX (*rnorm, fabs (R [i])) ; } /* ------------------------------------------------------------------ */ /* free numeric factorization */ /* ------------------------------------------------------------------ */ klu_free_numeric (&Numeric, Common) ; } else { /* ------------------------------------------------------------------ */ /* statistics (not required to solve Ax=b) */ /* ------------------------------------------------------------------ */ Numeric = klu_z_factor (Ap, Ai, Ax, Symbolic, Common) ; if (!Numeric) { klu_free_symbolic (&Symbolic, Common) ; return (0) ; } /* ------------------------------------------------------------------ */ /* statistics */ /* ------------------------------------------------------------------ */ klu_z_rgrowth (Ap, Ai, Ax, Symbolic, Numeric, Common) ; klu_z_condest (Ap, Ax, Symbolic, Numeric, Common) ; klu_z_rcond (Symbolic, Numeric, Common) ; klu_z_flops (Symbolic, Numeric, Common) ; *lunz = Numeric->lnz + Numeric->unz - n + ((Numeric->Offp) ? (Numeric->Offp [n]) : 0) ; /* ------------------------------------------------------------------ */ /* solve Ax=b */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < 2*n ; i++) { X [i] = B [i] ; } klu_z_solve (Symbolic, Numeric, n, 1, X, Common) ; /* ------------------------------------------------------------------ */ /* compute residual, rnorm = norm(b-Ax,1) / norm(A,1) */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < 2*n ; i++) { R [i] = B [i] ; } for (j = 0 ; j < n ; j++) { asum = 0 ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { /* R (i) -= A (i,j) * X (j) */ i = Ai [p] ; REAL (R,i) -= REAL(Ax,p) * REAL(X,j) - IMAG(Ax,p) * IMAG(X,j) ; IMAG (R,i) -= IMAG(Ax,p) * REAL(X,j) + REAL(Ax,p) * IMAG(X,j) ; asum += CABS (Ax, p) ; } anorm = MAX (anorm, asum) ; } *rnorm = 0 ; for (i = 0 ; i < n ; i++) { *rnorm = MAX (*rnorm, CABS (R, i)) ; } /* ------------------------------------------------------------------ */ /* free numeric factorization */ /* ------------------------------------------------------------------ */ klu_z_free_numeric (&Numeric, Common) ; } /* ---------------------------------------------------------------------- */ /* free symbolic analysis, and residual */ /* ---------------------------------------------------------------------- */ klu_free_symbolic (&Symbolic, Common) ; return (1) ; } /* ========================================================================== */ /* === klu_demo ============================================================= */ /* ========================================================================== */ /* Given a sparse matrix A, set up a right-hand-side and solve X = A\b */ static void klu_demo (int n, int *Ap, int *Ai, double *Ax, int isreal) { double rnorm ; klu_common Common ; double *B, *X, *R ; int i, lunz ; printf ("KLU: %s, version: %d.%d.%d\n", KLU_DATE, KLU_MAIN_VERSION, KLU_SUB_VERSION, KLU_SUBSUB_VERSION) ; /* ---------------------------------------------------------------------- */ /* set defaults */ /* ---------------------------------------------------------------------- */ klu_defaults (&Common) ; /* ---------------------------------------------------------------------- */ /* create a right-hand-side */ /* ---------------------------------------------------------------------- */ if (isreal) { /* B = 1 + (1:n)/n */ B = klu_malloc (n, sizeof (double), &Common) ; X = klu_malloc (n, sizeof (double), &Common) ; R = klu_malloc (n, sizeof (double), &Common) ; if (B) { for (i = 0 ; i < n ; i++) { B [i] = 1 + ((double) i+1) / ((double) n) ; } } } else { /* real (B) = 1 + (1:n)/n, imag(B) = (n:-1:1)/n */ B = klu_malloc (n, 2 * sizeof (double), &Common) ; X = klu_malloc (n, 2 * sizeof (double), &Common) ; R = klu_malloc (n, 2 * sizeof (double), &Common) ; if (B) { for (i = 0 ; i < n ; i++) { REAL (B, i) = 1 + ((double) i+1) / ((double) n) ; IMAG (B, i) = ((double) n-i) / ((double) n) ; } } } /* ---------------------------------------------------------------------- */ /* X = A\b using KLU and print statistics */ /* ---------------------------------------------------------------------- */ if (!klu_backslash (n, Ap, Ai, Ax, isreal, B, X, R, &lunz, &rnorm, &Common)) { printf ("KLU failed\n") ; } else { printf ("n %d nnz(A) %d nnz(L+U+F) %d resid %g\n" "recip growth %g condest %g rcond %g flops %g\n", n, Ap [n], lunz, rnorm, Common.rgrowth, Common.condest, Common.rcond, Common.flops) ; } /* ---------------------------------------------------------------------- */ /* free the problem */ /* ---------------------------------------------------------------------- */ if (isreal) { klu_free (B, n, sizeof (double), &Common) ; klu_free (X, n, sizeof (double), &Common) ; klu_free (R, n, sizeof (double), &Common) ; } else { klu_free (B, 2*n, sizeof (double), &Common) ; klu_free (X, 2*n, sizeof (double), &Common) ; klu_free (R, 2*n, sizeof (double), &Common) ; } printf ("peak memory usage: %g bytes\n\n", (double) (Common.mempeak)) ; } /* ========================================================================== */ /* === main ================================================================= */ /* ========================================================================== */ /* Read in a sparse matrix in Matrix Market format using CHOLMOD, and then * solve Ax=b with KLU. Note that CHOLMOD is only used to read the matrix. */ #include "cholmod.h" int main (void) { cholmod_sparse *A ; cholmod_common ch ; cholmod_start (&ch) ; A = cholmod_read_sparse (stdin, &ch) ; if (A) { if (A->nrow != A->ncol || A->stype != 0 || (!(A->xtype == CHOLMOD_REAL || A->xtype == CHOLMOD_COMPLEX))) { printf ("invalid matrix\n") ; } else { klu_demo (A->nrow, A->p, A->i, A->x, A->xtype == CHOLMOD_REAL) ; } cholmod_free_sparse (&A, &ch) ; } cholmod_finish (&ch) ; return (0) ; } SuiteSparse/KLU/Tcov/0000755001170100242450000000000010711175713013320 5ustar davisfacSuiteSparse/KLU/Tcov/vklultests0000755001170100242450000000135210620325360015461 0ustar davisfac#!/bin/csh # 57 unique statements: valgrind ./klultest < ../Matrix/impcol_a.mtx # 20: valgrind ./klultest < ../Matrix/GD99_cc.mtx # 17: valgrind ./klultest < ../Matrix/two.mtx # 10: valgrind ./klultest < ../Matrix/w156.mtx # 3, xsize memgrow in klu_kernel valgrind ./klultest < ../Matrix/arrow.mtx # 3, xsize memgrow in klu_kernel, 1 in klu_z_condest, valgrind ./klultest < ../Matrix/arrowc.mtx # 2 in klu_z_kernel (if pivot == 0 and halt_if_singular, and in complex divide) valgrind ./klultest < ../Matrix/onec.mtx # 1 in klu_kernel (if pivot == 0 and halt if singular) valgrind ./klultest < ../Matrix/one.mtx # 1 in klu_z_condest: valgrind ./klultest < ../Matrix/1c.mtx # 1 in klu_z_condest: valgrind ./klultest < ../Matrix/ctina.mtx SuiteSparse/KLU/Tcov/Makefile0000644001170100242450000003102310710765317014763 0ustar davisfac# If the libraries (AMD, COLAMD, CAMD, CCOLAMD, metis, and CHOLMOD) are not # yet built, use "make libs" first. Then "make" to compile and run all tests. default: all include ../../UFconfig/UFconfig.mk # CFLAGS = -Wall -W -Wshadow -Wmissing-prototypes -Wstrict-prototypes \ # -Wredundant-decls -Wnested-externs -Wdisabled-optimization \ # -pedantic -ansi -O3 -pg # for statement coverage, picky tests CFLAGS = -Wall -W -Werror -Wshadow -Wmissing-prototypes -Wstrict-prototypes \ -Wredundant-decls -Wnested-externs -Wdisabled-optimization \ -ansi -g -ftest-coverage -fprofile-arcs -fexceptions C = $(CC) $(CFLAGS) LIB = ../../AMD/Lib/libamd.a ../../COLAMD/Lib/libcolamd.a \ ../../CHOLMOD/Lib/libcholmod.a \ ../../CAMD/Lib/libcamd.a ../../CCOLAMD/Lib/libccolamd.a \ ../../metis-4.0/libmetis.a \ -lm I = -I../../UFconfig -I../../AMD/Include -I../../COLAMD/Include \ -I../../BTF/Include -I../../CHOLMOD/Include -I../../CAMD/Include \ -I../../CCOLAMD/Include -I../../metis-4.0/Lib -I../Include -I../User PRETTY = grep -v "^\#" | indent -bl -nce -ss -bli0 -i4 -sob all: purge libs klutest klultest - ./klultests > klultests.out - ./klutests > klutests.out - ./coverage valgrind: purge klutest klultest - ./vklutests > klutests.out - ./vklultests > klultests.out - ./coverage libs: ( cd ../../AMD ; $(MAKE) library ) ( cd ../../COLAMD ; $(MAKE) library ) ( cd ../../CAMD ; $(MAKE) library ) ( cd ../../CCOLAMD ; $(MAKE) library ) ( cd ../../metis-4.0 ; $(MAKE) ) ( cd ../../CHOLMOD ; $(MAKE) library ) purge: distclean distclean: clean - $(RM) klutest klultest *.c.gcov *.out *.a cov_*.c *.gcda *.gcno clean: - $(RM) $(CLEAN) INC = \ ../Include/klu.h \ ../Include/klu_internal.h \ ../Include/klu_version.h BTFOBJ = \ cov_btf_order.o \ cov_btf_maxtrans.o \ cov_btf_strongcomp.o \ BTFLOBJ = \ cov_btf_l_order.o \ cov_btf_l_maxtrans.o \ cov_btf_l_strongcomp.o KLUOBJ = \ cov_klu_analyze.o \ cov_klu_analyze_given.o \ cov_klu_defaults.o \ cov_klu_free_symbolic.o \ cov_klu_memory.o \ cov_klu_d.o \ cov_klu_d_diagnostics.o \ cov_klu_d_dump.o \ cov_klu_d_factor.o \ cov_klu_d_free_numeric.o \ cov_klu_d_kernel.o \ cov_klu_d_extract.o \ cov_klu_d_refactor.o \ cov_klu_d_scale.o \ cov_klu_d_solve.o \ cov_klu_d_tsolve.o \ cov_klu_z.o \ cov_klu_z_diagnostics.o \ cov_klu_z_dump.o \ cov_klu_z_factor.o \ cov_klu_z_free_numeric.o \ cov_klu_z_kernel.o \ cov_klu_z_extract.o \ cov_klu_z_refactor.o \ cov_klu_z_scale.o \ cov_klu_z_solve.o \ cov_klu_z_tsolve.o KLULOBJ = \ cov_klu_l_analyze.o \ cov_klu_l_analyze_given.o \ cov_klu_l_defaults.o \ cov_klu_l_free_symbolic.o \ cov_klu_l_memory.o \ cov_klu_l.o \ cov_klu_l_diagnostics.o \ cov_klu_l_dump.o \ cov_klu_l_factor.o \ cov_klu_l_free_numeric.o \ cov_klu_l_kernel.o \ cov_klu_l_extract.o \ cov_klu_l_refactor.o \ cov_klu_l_scale.o \ cov_klu_l_solve.o \ cov_klu_l_tsolve.o \ cov_klu_zl.o \ cov_klu_zl_diagnostics.o \ cov_klu_zl_dump.o \ cov_klu_zl_factor.o \ cov_klu_zl_free_numeric.o \ cov_klu_zl_kernel.o \ cov_klu_zl_extract.o \ cov_klu_zl_refactor.o \ cov_klu_zl_scale.o \ cov_klu_zl_solve.o \ cov_klu_zl_tsolve.o KLUCHOLMODOBJ = cov_klu_cholmod.o KLUCHOLMODLOBJ = cov_klu_l_cholmod.o OBJ = $(BTFOBJ) $(KLUOBJ) $(KLUCHOLMODOBJ) LOBJ = $(BTFLOBJ) $(KLULOBJ) $(KLUCHOLMODLOBJ) $(OBJ): $(INC) $(LOBJ): $(INC) klutest: $(OBJ) klutest.c $(C) $(I) klutest.c -o klutest $(OBJ) $(LIB) klultest: $(LOBJ) klutest.c $(C) -DDLONG $(I) klutest.c -o klultest $(LOBJ) $(LIB) .c.o: $(C) -c $(I) $*.c #------------------------------------------------------------------------------- cov_klu_d.o: ../Source/klu.c $(C) -E $(I) $< | $(PRETTY) > cov_klu_d.c $(C) -c $(I) cov_klu_d.c cov_klu_z.o: ../Source/klu.c $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z.c $(C) -c $(I) cov_klu_z.c cov_klu_d_kernel.o: ../Source/klu_kernel.c $(C) -E $(I) $< | $(PRETTY) > cov_klu_d_kernel.c $(C) -c $(I) cov_klu_d_kernel.c cov_klu_z_kernel.o: ../Source/klu_kernel.c $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z_kernel.c $(C) -c $(I) cov_klu_z_kernel.c cov_klu_d_diagnostics.o: ../Source/klu_diagnostics.c $(C) -E $(I) $< | $(PRETTY) > cov_klu_d_diagnostics.c $(C) -c $(I) cov_klu_d_diagnostics.c cov_klu_z_diagnostics.o: ../Source/klu_diagnostics.c $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z_diagnostics.c $(C) -c $(I) cov_klu_z_diagnostics.c cov_klu_d_dump.o: ../Source/klu_dump.c $(C) -E $(I) $< | $(PRETTY) > cov_klu_d_dump.c $(C) -c $(I) cov_klu_d_dump.c cov_klu_z_dump.o: ../Source/klu_dump.c $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z_dump.c $(C) -c $(I) cov_klu_z_dump.c cov_klu_d_factor.o: ../Source/klu_factor.c $(C) -E $(I) $< | $(PRETTY) > cov_klu_d_factor.c $(C) -c $(I) cov_klu_d_factor.c cov_klu_z_factor.o: ../Source/klu_factor.c $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z_factor.c $(C) -c $(I) cov_klu_z_factor.c cov_klu_d_free_numeric.o: ../Source/klu_free_numeric.c $(C) -E $(I) $< | $(PRETTY) > cov_klu_d_free_numeric.c $(C) -c $(I) cov_klu_d_free_numeric.c cov_klu_z_free_numeric.o: ../Source/klu_free_numeric.c $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z_free_numeric.c $(C) -c $(I) cov_klu_z_free_numeric.c cov_klu_d_extract.o: ../Source/klu_extract.c $(C) -E $(I) $< | $(PRETTY) > cov_klu_d_extract.c $(C) -c $(I) cov_klu_d_extract.c cov_klu_z_extract.o: ../Source/klu_extract.c $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z_extract.c $(C) -c $(I) cov_klu_z_extract.c cov_klu_d_refactor.o: ../Source/klu_refactor.c $(C) -E $(I) $< | $(PRETTY) > cov_klu_d_refactor.c $(C) -c $(I) cov_klu_d_refactor.c cov_klu_z_refactor.o: ../Source/klu_refactor.c $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z_refactor.c $(C) -c $(I) cov_klu_z_refactor.c cov_klu_d_scale.o: ../Source/klu_scale.c $(C) -E $(I) $< | $(PRETTY) > cov_klu_d_scale.c $(C) -c $(I) cov_klu_d_scale.c cov_klu_z_scale.o: ../Source/klu_scale.c $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z_scale.c $(C) -c $(I) cov_klu_z_scale.c cov_klu_d_solve.o: ../Source/klu_solve.c $(C) -E $(I) $< | $(PRETTY) > cov_klu_d_solve.c $(C) -c $(I) cov_klu_d_solve.c cov_klu_z_solve.o: ../Source/klu_solve.c $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z_solve.c $(C) -c $(I) cov_klu_z_solve.c cov_klu_d_tsolve.o: ../Source/klu_tsolve.c $(C) -E $(I) $< | $(PRETTY) > cov_klu_d_tsolve.c $(C) -c $(I) cov_klu_d_tsolve.c cov_klu_z_tsolve.o: ../Source/klu_tsolve.c $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z_tsolve.c $(C) -c $(I) cov_klu_z_tsolve.c #------------------------------------------------------------------------------- cov_klu_analyze.o: ../Source/klu_analyze.c $(C) -E $(I) $< | $(PRETTY) > cov_klu_analyze.c $(C) -c $(I) cov_klu_analyze.c cov_klu_analyze_given.o: ../Source/klu_analyze_given.c $(C) -E $(I) $< | $(PRETTY) > cov_klu_analyze_given.c $(C) -c $(I) cov_klu_analyze_given.c cov_klu_defaults.o: ../Source/klu_defaults.c $(C) -E $(I) $< | $(PRETTY) > cov_klu_defaults.c $(C) -c $(I) cov_klu_defaults.c cov_klu_free_symbolic.o: ../Source/klu_free_symbolic.c $(C) -E $(I) $< | $(PRETTY) > cov_klu_free_symbolic.c $(C) -c $(I) cov_klu_free_symbolic.c cov_klu_memory.o: ../Source/klu_memory.c $(C) -E $(I) $< | $(PRETTY) > cov_klu_memory.c $(C) -c $(I) cov_klu_memory.c #------------------------------------------------------------------------------- cov_btf_order.o: ../../BTF/Source/btf_order.c $(C) -E $(I) $< | $(PRETTY) > cov_btf_order.c $(C) -c $(I) cov_btf_order.c cov_btf_maxtrans.o: ../../BTF/Source/btf_maxtrans.c $(C) -E $(I) $< | $(PRETTY) > cov_btf_maxtrans.c $(C) -c $(I) cov_btf_maxtrans.c cov_btf_strongcomp.o: ../../BTF/Source/btf_strongcomp.c $(C) -E $(I) $< | $(PRETTY) > cov_btf_strongcomp.c $(C) -c $(I) cov_btf_strongcomp.c #------------------------------------------------------------------------------- cov_klu_cholmod.o: ../User/klu_cholmod.c $(C) -E $(I) $< | $(PRETTY) > cov_klu_cholmod.c $(C) -c $(I) cov_klu_cholmod.c #------------------------------------------------------------------------------- cov_klu_l.o: ../Source/klu.c $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l.c $(C) -c $(I) cov_klu_l.c cov_klu_zl.o: ../Source/klu.c $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl.c $(C) -c $(I) cov_klu_zl.c cov_klu_l_kernel.o: ../Source/klu_kernel.c $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_kernel.c $(C) -c $(I) cov_klu_l_kernel.c cov_klu_zl_kernel.o: ../Source/klu_kernel.c $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl_kernel.c $(C) -c $(I) cov_klu_zl_kernel.c cov_klu_l_diagnostics.o: ../Source/klu_diagnostics.c $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_diagnostics.c $(C) -c $(I) cov_klu_l_diagnostics.c cov_klu_zl_diagnostics.o: ../Source/klu_diagnostics.c $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl_diagnostics.c $(C) -c $(I) cov_klu_zl_diagnostics.c cov_klu_l_dump.o: ../Source/klu_dump.c $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_dump.c $(C) -c $(I) cov_klu_l_dump.c cov_klu_zl_dump.o: ../Source/klu_dump.c $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl_dump.c $(C) -c $(I) cov_klu_zl_dump.c cov_klu_l_factor.o: ../Source/klu_factor.c $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_factor.c $(C) -c $(I) cov_klu_l_factor.c cov_klu_zl_factor.o: ../Source/klu_factor.c $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl_factor.c $(C) -c $(I) cov_klu_zl_factor.c cov_klu_l_free_numeric.o: ../Source/klu_free_numeric.c $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_free_numeric.c $(C) -c $(I) cov_klu_l_free_numeric.c cov_klu_zl_free_numeric.o: ../Source/klu_free_numeric.c $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl_free_numeric.c $(C) -c $(I) cov_klu_zl_free_numeric.c cov_klu_l_extract.o: ../Source/klu_extract.c $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_extract.c $(C) -c $(I) cov_klu_l_extract.c cov_klu_zl_extract.o: ../Source/klu_extract.c $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl_extract.c $(C) -c $(I) cov_klu_zl_extract.c cov_klu_l_refactor.o: ../Source/klu_refactor.c $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_refactor.c $(C) -c $(I) cov_klu_l_refactor.c cov_klu_zl_refactor.o: ../Source/klu_refactor.c $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl_refactor.c $(C) -c $(I) cov_klu_zl_refactor.c cov_klu_l_scale.o: ../Source/klu_scale.c $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_scale.c $(C) -c $(I) cov_klu_l_scale.c cov_klu_zl_scale.o: ../Source/klu_scale.c $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl_scale.c $(C) -c $(I) cov_klu_zl_scale.c cov_klu_l_solve.o: ../Source/klu_solve.c $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_solve.c $(C) -c $(I) cov_klu_l_solve.c cov_klu_zl_solve.o: ../Source/klu_solve.c $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl_solve.c $(C) -c $(I) cov_klu_zl_solve.c cov_klu_l_tsolve.o: ../Source/klu_tsolve.c $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_tsolve.c $(C) -c $(I) cov_klu_l_tsolve.c cov_klu_zl_tsolve.o: ../Source/klu_tsolve.c $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl_tsolve.c $(C) -c $(I) cov_klu_zl_tsolve.c #------------------------------------------------------------------------------- cov_klu_l_analyze.o: ../Source/klu_analyze.c $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_analyze.c $(C) -c $(I) cov_klu_l_analyze.c cov_klu_l_analyze_given.o: ../Source/klu_analyze_given.c $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_analyze_given.c $(C) -c $(I) cov_klu_l_analyze_given.c cov_klu_l_defaults.o: ../Source/klu_defaults.c $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_defaults.c $(C) -c $(I) cov_klu_l_defaults.c cov_klu_l_free_symbolic.o: ../Source/klu_free_symbolic.c $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_free_symbolic.c $(C) -c $(I) cov_klu_l_free_symbolic.c cov_klu_l_memory.o: ../Source/klu_memory.c $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_memory.c $(C) -c $(I) cov_klu_l_memory.c #------------------------------------------------------------------------------- cov_btf_l_order.o: ../../BTF/Source/btf_order.c $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_btf_l_order.c $(C) -c $(I) cov_btf_l_order.c cov_btf_l_maxtrans.o: ../../BTF/Source/btf_maxtrans.c $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_btf_l_maxtrans.c $(C) -c $(I) cov_btf_l_maxtrans.c cov_btf_l_strongcomp.o: ../../BTF/Source/btf_strongcomp.c $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_btf_l_strongcomp.c $(C) -c $(I) cov_btf_l_strongcomp.c #------------------------------------------------------------------------------- cov_klu_l_cholmod.o: ../User/klu_l_cholmod.c $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_cholmod.c $(C) -c $(I) cov_klu_l_cholmod.c SuiteSparse/KLU/Tcov/klultests0000755001170100242450000000122010620325707015272 0ustar davisfac#!/bin/csh # 57 unique statements: ./klultest < ../Matrix/impcol_a.mtx # 20: ./klultest < ../Matrix/GD99_cc.mtx # 17: ./klultest < ../Matrix/two.mtx # 10: ./klultest < ../Matrix/w156.mtx # 3, xsize memgrow in klu_kernel ./klultest < ../Matrix/arrow.mtx # 3, xsize memgrow in klu_kernel, 1 in klu_z_condest, ./klultest < ../Matrix/arrowc.mtx # 2 in klu_z_kernel (if pivot == 0 and halt_if_singular, and in complex divide) ./klultest < ../Matrix/onec.mtx # 1 in klu_kernel (if pivot == 0 and halt if singular) ./klultest < ../Matrix/one.mtx # 1 in klu_z_condest: ./klultest < ../Matrix/1c.mtx # 1 in klu_z_condest: ./klultest < ../Matrix/ctina.mtx SuiteSparse/KLU/Tcov/klutest.c0000644001170100242450000011210510620326154015153 0ustar davisfac/* ========================================================================== */ /* === KLU test ============================================================= */ /* ========================================================================== */ /* Exhaustive test for KLU and BTF (int, long, real, and complex versions) */ #include #include "cholmod.h" #include "klu_cholmod.h" #include "klu_internal.h" #define ID Int_id #define NRHS 6 #define HALT { fprintf (stderr, "Test failure: %d\n", __LINE__) ; abort () ; } #define OK(a) { if (!(a)) HALT ; } #define FAIL(a) { if (a) HALT ; } #define MAX(a,b) (((a) > (b)) ? (a) : (b)) #ifdef DLONG #define klu_z_scale klu_zl_scale #define klu_z_solve klu_zl_solve #define klu_z_tsolve klu_zl_tsolve #define klu_z_free_numeric klu_zl_free_numeric #define klu_z_factor klu_zl_factor #define klu_z_refactor klu_zl_refactor #define klu_z_lsolve klu_zl_lsolve #define klu_z_ltsolve klu_zl_ltsolve #define klu_z_usolve klu_zl_usolve #define klu_z_utsolve klu_zl_utsolve #define klu_z_defaults klu_zl_defaults #define klu_z_rgrowth klu_zl_rgrowth #define klu_z_rcond klu_zl_rcond #define klu_z_extract klu_zl_extract #define klu_z_condest klu_zl_condest #define klu_z_flops klu_zl_flops #define klu_scale klu_l_scale #define klu_solve klu_l_solve #define klu_tsolve klu_l_tsolve #define klu_free_numeric klu_l_free_numeric #define klu_factor klu_l_factor #define klu_refactor klu_l_refactor #define klu_lsolve klu_l_lsolve #define klu_ltsolve klu_l_ltsolve #define klu_usolve klu_l_usolve #define klu_utsolve klu_l_utsolve #define klu_defaults klu_l_defaults #define klu_rgrowth klu_l_rgrowth #define klu_rcond klu_l_rcond #define klu_extract klu_l_extract #define klu_condest klu_l_condest #define klu_flops klu_l_flops #define klu_analyze klu_l_analyze #define klu_analyze_given klu_l_analyze_given #define klu_malloc klu_l_malloc #define klu_free klu_l_free #define klu_realloc klu_l_realloc #define klu_free_symbolic klu_l_free_symbolic #define klu_free_numeric klu_l_free_numeric #define klu_defaults klu_l_defaults #define klu_cholmod klu_l_cholmod #endif #ifdef DLONG #define CHOLMOD_print_sparse cholmod_l_print_sparse #define CHOLMOD_print_dense cholmod_l_print_dense #define CHOLMOD_copy_sparse cholmod_l_copy_sparse #define CHOLMOD_copy_dense cholmod_l_copy_dense #define CHOLMOD_transpose cholmod_l_transpose #define CHOLMOD_sdmult cholmod_l_sdmult #define CHOLMOD_norm_dense cholmod_l_norm_dense #define CHOLMOD_norm_sparse cholmod_l_norm_sparse #define CHOLMOD_free_sparse cholmod_l_free_sparse #define CHOLMOD_free_dense cholmod_l_free_dense #define CHOLMOD_start cholmod_l_start #define CHOLMOD_read_sparse cholmod_l_read_sparse #define CHOLMOD_allocate_dense cholmod_l_allocate_dense #define CHOLMOD_finish cholmod_l_finish #else #define CHOLMOD_print_sparse cholmod_print_sparse #define CHOLMOD_print_dense cholmod_print_dense #define CHOLMOD_copy_sparse cholmod_copy_sparse #define CHOLMOD_copy_dense cholmod_copy_dense #define CHOLMOD_transpose cholmod_transpose #define CHOLMOD_sdmult cholmod_sdmult #define CHOLMOD_norm_dense cholmod_norm_dense #define CHOLMOD_norm_sparse cholmod_norm_sparse #define CHOLMOD_free_sparse cholmod_free_sparse #define CHOLMOD_free_dense cholmod_free_dense #define CHOLMOD_start cholmod_start #define CHOLMOD_read_sparse cholmod_read_sparse #define CHOLMOD_allocate_dense cholmod_allocate_dense #define CHOLMOD_finish cholmod_finish #endif /* ========================================================================== */ /* === random numbers ======================================================= */ /* ========================================================================== */ #define MY_RAND_MAX 32767 static unsigned long next = 1 ; static Int my_rand (void) { next = next * 1103515245 + 12345 ; return ((unsigned)(next/65536) % (MY_RAND_MAX+1)) ; } static void my_srand (unsigned seed) { next = seed ; } /* ========================================================================== */ /* === memory management ==================================================== */ /* ========================================================================== */ void *my_malloc (size_t size) ; void *my_calloc (size_t n, size_t size) ; void *my_realloc (void *p, size_t size) ; Int my_tries = -1 ; void *my_malloc (size_t size) { if (my_tries == 0) return (NULL) ; /* pretend to fail */ if (my_tries > 0) my_tries-- ; return (malloc (size)) ; } void *my_calloc (size_t n, size_t size) { if (my_tries == 0) return (NULL) ; /* pretend to fail */ if (my_tries > 0) my_tries-- ; return (calloc (n, size)) ; } void *my_realloc (void *p, size_t size) { if (my_tries == 0) return (NULL) ; /* pretend to fail */ if (my_tries > 0) my_tries-- ; return (realloc (p, size)) ; } static void normal_memory_handler (KLU_common *Common) { Common->malloc_memory = malloc ; Common->calloc_memory = calloc ; Common->realloc_memory = realloc ; Common->free_memory = free ; my_tries = -1 ; } static void test_memory_handler (KLU_common *Common) { Common->malloc_memory = my_malloc ; Common->calloc_memory = my_calloc ; Common->realloc_memory = my_realloc ; Common->free_memory = free ; my_tries = -1 ; } /* ========================================================================== */ /* === print_sparse ========================================================= */ /* ========================================================================== */ /* print a sparse matrix */ static void print_sparse (Int n, Int isreal, Int *Ap, Int *Ai, double *Ax, double *Az) { double ax, az ; Int i, j, p ; for (j = 0 ; j < n ; j++) { printf ("column "ID":\n", j) ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; if (isreal) { ax = Ax [p] ; az = 0 ; } else if (Az) { /* split complex */ ax = Ax [p] ; az = Az [p] ; } else { /* merged complex */ ax = Ax [2*p ] ; az = Ax [2*p+1] ; } printf (" row "ID" : %g", i, ax) ; if (!isreal) { printf (" + (%g)i", az) ; } printf ("\n") ; } } fflush (stdout) ; } /* ========================================================================== */ /* === print_int ============================================================ */ /* ========================================================================== */ /* print an Int vector */ static void print_int (Int n, Int *P) { Int j ; for (j = 0 ; j < n ; j++) { printf (" "ID" : "ID"\n", j, P [j]) ; } fflush (stdout) ; } /* ========================================================================== */ /* === print_double ========================================================= */ /* ========================================================================== */ /* print a double vector */ static void print_double (Int n, double *X) { Int j ; for (j = 0 ; j < n ; j++) { printf (" "ID" : %g\n", j, X [j]) ; } fflush (stdout) ; } /* ========================================================================== */ /* === ludump =============================================================== */ /* ========================================================================== */ /* extract and print the LU factors */ static void ludump (KLU_symbolic *Symbolic, KLU_numeric *Numeric, Int isreal, cholmod_common *ch, KLU_common *Common) { Int *Lp, *Li, *Up, *Ui, *Fp, *Fi, *P, *Q, *R ; double *Lx, *Ux, *Fx, *Lz, *Uz, *Fz, *Rs ; Int n, lnz, unz, fnz, nb, result ; if (Symbolic == NULL || Numeric == NULL) { return ; } n = Symbolic->n ; lnz = Numeric->lnz ; unz = Numeric->unz ; fnz = Numeric->Offp [n] ; nb = Symbolic->nblocks ; printf ("n "ID" lnz "ID" unz "ID" fnz "ID" nblocks "ID" isreal "ID"\n", n, lnz, unz, fnz, nb, isreal) ; fflush (stdout) ; Lp = malloc ((n+1) * sizeof (Int)) ; Li = malloc (lnz * sizeof (Int)) ; Lx = malloc (lnz * sizeof (double)) ; Lz = malloc (lnz * sizeof (double)) ; Up = malloc ((n+1) * sizeof (Int)) ; Ui = malloc (unz * sizeof (Int)) ; Ux = malloc (unz * sizeof (double)) ; Uz = malloc (unz * sizeof (double)) ; Fp = malloc ((n+1) * sizeof (Int)) ; Fi = malloc (fnz * sizeof (Int)) ; Fx = malloc (fnz * sizeof (double)) ; Fz = malloc (fnz * sizeof (double)) ; P = malloc (n * sizeof (Int)) ; Q = malloc (n * sizeof (Int)) ; Rs = malloc (n * sizeof (double)) ; R = malloc ((nb+1) * sizeof (double)) ; if (isreal) { result = klu_extract (Numeric, Symbolic, Lp, Li, Lx, Up, Ui, Ux, Fp, Fi, Fx, P, Q, Rs, R, Common) ; } else { result = klu_z_extract (Numeric, Symbolic, Lp, Li, Lx, Lz, Up, Ui, Ux, Uz, Fp, Fi, Fx, Fz, P, Q, Rs, R, Common) ; } if (my_tries != 0) OK (result) ; if (ch->print >= 5) { printf ("------ L:\n") ; print_sparse (n, isreal, Lp, Li, Lx, Lz) ; printf ("------ U:\n") ; print_sparse (n, isreal, Up, Ui, Ux, Uz) ; printf ("------ F:\n") ; print_sparse (n, isreal, Fp, Fi, Fx, Fz) ; printf ("------ P:\n") ; print_int (n, P) ; printf ("------ Q:\n") ; print_int (n, Q) ; printf ("------ Rs:\n") ; print_double (n, Rs) ; printf ("------ R:\n") ; print_int (nb+1, R) ; } free (Lp) ; free (Li) ; free (Lx) ; free (Lz) ; free (Up) ; free (Ui) ; free (Ux) ; free (Uz) ; free (Fp) ; free (Fi) ; free (Fx) ; free (Fz) ; free (P) ; free (Q) ; free (Rs) ; free (R) ; } /* ========================================================================== */ /* === randperm ============================================================= */ /* ========================================================================== */ /* return a random permutation vector */ static Int *randperm (Int n, Int seed) { Int *p, k, j, t ; p = malloc (n * sizeof (Int)) ; for (k = 0 ; k < n ; k++) { p [k] = k ; } my_srand (seed) ; /* get new random number seed */ for (k = 0 ; k < n ; k++) { j = k + (my_rand ( ) % (n-k)) ; /* j = my_rand in range k to n-1 */ t = p [j] ; /* swap p[k] and p[j] */ p [j] = p [k] ; p [k] = t ; } return (p) ; } /* ========================================================================== */ /* === do_1_solve =========================================================== */ /* ========================================================================== */ static double do_1_solve (cholmod_sparse *A, cholmod_dense *B, cholmod_dense *Xknown, Int *Puser, Int *Quser, KLU_common *Common, cholmod_common *ch, Int *nan) { Int *Ai, *Ap ; double *Ax, *Bx, *Xknownx, *Xx, *Ax2, *Axx ; KLU_symbolic *Symbolic = NULL ; KLU_numeric *Numeric = NULL ; cholmod_dense *X = NULL, *R = NULL ; cholmod_sparse *AT = NULL, *A2 = NULL, *AT2 = NULL ; double one [2], minusone [2], rnorm, anorm, bnorm, xnorm, relresid, relerr, err = 0. ; Int i, j, nrhs2, isreal, n, nrhs, transpose, step, k, save, tries ; printf ("\ndo_1_solve: btf "ID" maxwork %g scale "ID" ordering "ID" user: " ID" P,Q: %d halt: "ID"\n", Common->btf, Common->maxwork, Common->scale, Common->ordering, Common->user_data ? (*((Int *) Common->user_data)) : -1, (Puser != NULL || Quser != NULL), Common->halt_if_singular) ; fflush (stdout) ; fflush (stderr) ; CHOLMOD_print_sparse (A, "A", ch) ; CHOLMOD_print_dense (B, "B", ch) ; Ap = A->p ; Ai = A->i ; Ax = A->x ; n = A->nrow ; isreal = (A->xtype == CHOLMOD_REAL) ; Bx = B->x ; Xknownx = Xknown->x ; nrhs = B->ncol ; one [0] = 1 ; one [1] = 0 ; minusone [0] = -1 ; minusone [1] = 0 ; /* ---------------------------------------------------------------------- */ /* symbolic analysis */ /* ---------------------------------------------------------------------- */ Symbolic = NULL ; my_tries = 0 ; for (tries = 0 ; Symbolic == NULL && my_tries == 0 ; tries++) { my_tries = tries ; if (Puser != NULL || Quser != NULL) { Symbolic = klu_analyze_given (n, Ap, Ai, Puser, Quser, Common) ; } else { Symbolic = klu_analyze (n, Ap, Ai, Common) ; } } printf ("sym try "ID" btf "ID" ordering "ID"\n", tries, Common->btf, Common->ordering) ; if (Symbolic == NULL) { printf ("Symbolic is null\n") ; return (998) ; } my_tries = -1 ; /* create a modified version of A */ A2 = CHOLMOD_copy_sparse (A, ch) ; Ax2 = A2->x ; my_srand (42) ; for (k = 0 ; k < Ap [n] * (isreal ? 1:2) ; k++) { Ax2 [k] = Ax [k] * (1 + 1e-4 * ((double) my_rand ( )) / ((double) MY_RAND_MAX)) ; } AT = isreal ? NULL : CHOLMOD_transpose (A, 1, ch) ; AT2 = isreal ? NULL : CHOLMOD_transpose (A2, 1, ch) ; /* ---------------------------------------------------------------------- */ /* factorize then solve */ /* ---------------------------------------------------------------------- */ for (step = 1 ; step <= 3 ; step++) { printf ("step: "ID"\n", step) ; fflush (stdout) ; /* ------------------------------------------------------------------ */ /* factorization or refactorization */ /* ------------------------------------------------------------------ */ /* step 1: factor step 2: refactor with same A step 3: refactor with modified A, and scaling forced on and solve each time */ if (step == 1) { /* numeric factorization */ Numeric = NULL ; my_tries = 0 ; for (tries = 0 ; Numeric == NULL && my_tries == 0 ; tries++) { my_tries = tries ; if (isreal) { Numeric = klu_factor (Ap, Ai, Ax, Symbolic, Common) ; } else { Numeric = klu_z_factor (Ap, Ai, Ax, Symbolic, Common) ; } } printf ("num try "ID" btf "ID"\n", tries, Common->btf) ; my_tries = -1 ; if (Common->status == KLU_OK || (Common->status == KLU_SINGULAR && !Common->halt_if_singular)) { OK (Numeric) ; } else { FAIL (Numeric) ; } if (Common->status < KLU_OK) { printf ("factor failed: "ID"\n", Common->status) ; } } else if (step == 2) { /* numeric refactorization with same values, same scaling */ if (isreal) { klu_refactor (Ap, Ai, Ax, Symbolic, Numeric, Common) ; } else { klu_z_refactor (Ap, Ai, Ax, Symbolic, Numeric, Common) ; } } else { /* numeric refactorization with different values */ save = Common->scale ; if (Common->scale == 0) { Common->scale = 1 ; } for (tries = 0 ; tries <= 1 ; tries++) { my_tries = tries ; if (isreal) { klu_refactor (Ap, Ai, Ax2, Symbolic, Numeric, Common) ; } else { klu_z_refactor (Ap, Ai, Ax2, Symbolic, Numeric, Common) ; } } my_tries = -1 ; Common->scale = save ; } if (Common->status == KLU_SINGULAR) { printf ("# singular column : "ID"\n", Common->singular_col) ; } /* ------------------------------------------------------------------ */ /* diagnostics */ /* ------------------------------------------------------------------ */ Axx = (step == 3) ? Ax2 : Ax ; if (isreal) { klu_rgrowth (Ap, Ai, Axx, Symbolic, Numeric, Common) ; klu_condest (Ap, Axx, Symbolic, Numeric, Common) ; klu_rcond (Symbolic, Numeric, Common) ; klu_flops (Symbolic, Numeric, Common) ; } else { klu_z_rgrowth (Ap, Ai, Axx, Symbolic, Numeric, Common) ; klu_z_condest (Ap, Axx, Symbolic, Numeric, Common) ; klu_z_rcond (Symbolic, Numeric, Common) ; klu_z_flops (Symbolic, Numeric, Common) ; } printf ("growth %g condest %g rcond %g flops %g\n", Common->rgrowth, Common->condest, Common->rcond, Common->flops) ; ludump (Symbolic, Numeric, isreal, ch, Common) ; if (Numeric == NULL || Common->status < KLU_OK) { continue ; } /* ------------------------------------------------------------------ */ /* solve */ /* ------------------------------------------------------------------ */ /* forward/backsolve to solve A*X=B or A'*X=B */ for (transpose = (isreal ? 0 : -1) ; transpose <= 1 ; transpose++) { for (nrhs2 = 1 ; nrhs2 <= nrhs ; nrhs2++) { /* mangle B so that it has only nrhs2 columns */ B->ncol = nrhs2 ; X = CHOLMOD_copy_dense (B, ch) ; CHOLMOD_print_dense (X, "X before solve", ch) ; Xx = X->x ; if (isreal) { if (transpose) { /* solve A'x=b */ klu_tsolve (Symbolic, Numeric, n, nrhs2, Xx, Common) ; } else { /* solve A*x=b */ klu_solve (Symbolic, Numeric, n, nrhs2, Xx, Common) ; } } else { if (transpose) { /* solve A'x=b (if 1) or A.'x=b (if -1) */ klu_z_tsolve (Symbolic, Numeric, n, nrhs2, Xx, (transpose == 1), Common) ; } else { /* solve A*x=b */ klu_z_solve (Symbolic, Numeric, n, nrhs2, Xx, Common) ; } } CHOLMOD_print_dense (X, "X", ch) ; /* compute the residual, R = B-A*X, B-A'*X, or B-A.'*X */ R = CHOLMOD_copy_dense (B, ch) ; if (transpose == -1) { /* R = B-A.'*X (use A.' explicitly) */ CHOLMOD_sdmult ((step == 3) ? AT2 : AT, 0, minusone, one, X, R, ch) ; } else { /* R = B-A*X or B-A'*X */ CHOLMOD_sdmult ((step == 3) ? A2 :A, transpose, minusone, one, X, R, ch) ; } CHOLMOD_print_dense (R, "R", ch) ; /* compute the norms of R, A, X, and B */ rnorm = CHOLMOD_norm_dense (R, 1, ch) ; anorm = CHOLMOD_norm_sparse ((step == 3) ? A2 : A, 1, ch) ; xnorm = CHOLMOD_norm_dense (X, 1, ch) ; bnorm = CHOLMOD_norm_dense (B, 1, ch) ; CHOLMOD_free_dense (&R, ch) ; /* relative residual = norm (r) / (norm (A) * norm (x)) */ relresid = rnorm ; if (anorm > 0) { relresid /= anorm ; } if (xnorm > 0) { relresid /= xnorm ; } if (SCALAR_IS_NAN (relresid)) { *nan = TRUE ; } else { err = MAX (err, relresid) ; } /* relative error = norm (x - xknown) / norm (xknown) */ /* overwrite X with X - Xknown */ if (transpose || step == 3) { /* not computed */ relerr = -1 ; } else { for (j = 0 ; j < nrhs2 ; j++) { for (i = 0 ; i < n ; i++) { if (isreal) { Xx [i+j*n] -= Xknownx [i+j*n] ; } else { Xx [2*(i+j*n) ] -= Xknownx [2*(i+j*n) ] ; Xx [2*(i+j*n)+1] -= Xknownx [2*(i+j*n)+1] ; } } } relerr = CHOLMOD_norm_dense (X, 1, ch) ; xnorm = CHOLMOD_norm_dense (Xknown, 1, ch) ; if (xnorm > 0) { relerr /= xnorm ; } if (SCALAR_IS_NAN (relerr)) { *nan = TRUE ; } else { err = MAX (relerr, err) ; } } CHOLMOD_free_dense (&X, ch) ; printf (ID" "ID" relresid %10.3g relerr %10.3g %g\n", transpose, nrhs2, relresid, relerr, err) ; B->ncol = nrhs ; /* restore B */ } } } /* ---------------------------------------------------------------------- */ /* free factorization and temporary matrices, and return */ /* ---------------------------------------------------------------------- */ klu_free_symbolic (&Symbolic, Common) ; if (isreal) { klu_free_numeric (&Numeric, Common) ; } else { klu_z_free_numeric (&Numeric, Common) ; } CHOLMOD_free_sparse (&A2, ch) ; CHOLMOD_free_sparse (&AT, ch) ; CHOLMOD_free_sparse (&AT2, ch) ; fflush (stdout) ; fflush (stderr) ; return (err) ; } /* ========================================================================== */ /* === do_solves ============================================================ */ /* ========================================================================== */ /* test KLU with many options */ static double do_solves (cholmod_sparse *A, cholmod_dense *B, cholmod_dense *X, Int *Puser, Int *Quser, KLU_common *Common, cholmod_common *ch, Int *nan) { double err, maxerr = 0 ; Int n = A->nrow, sflag ; *nan = FALSE ; /* ---------------------------------------------------------------------- */ /* test KLU with the system A*X=B and default options */ /* ---------------------------------------------------------------------- */ maxerr = do_1_solve (A, B, X, NULL, NULL, Common, ch, nan) ; /* ---------------------------------------------------------------------- */ /* test with non-default options */ /* ---------------------------------------------------------------------- */ Common->user_order = klu_cholmod ; for (Common->btf = 0 ; Common->btf <= 2 ; Common->btf++) { Common->maxwork = (Common->btf == 2) ? 0.001 : 0 ; for (Common->halt_if_singular = 0 ; Common->halt_if_singular <= 1 ; Common->halt_if_singular++) { for (Common->scale = 0 ; Common->scale <= 2 ; Common->scale++) { fprintf (stderr, ".") ; fflush (stderr) ; /* orderings: 0: AMD, 1: COLAMD, 2: natural, 3: user function */ for (Common->ordering = 0 ; Common->ordering <= 3 ; Common->ordering++) { err = do_1_solve (A, B, X, NULL, NULL, Common, ch, nan) ; maxerr = MAX (maxerr, err) ; } /* user-ordering, unsymmetric case */ Common->ordering = 3 ; Common->user_data = &sflag ; sflag = 0 ; err = do_1_solve (A, B, X, NULL, NULL, Common, ch, nan) ; maxerr = MAX (maxerr, err) ; Common->user_data = NULL ; /* Puser and Quser, but only for small matrices */ Common->ordering = 2 ; if (n < 200) { err = do_1_solve (A, B, X, Puser, Quser, Common, ch, nan) ; maxerr = MAX (maxerr, err) ; } } } } /* restore defaults */ Common->btf = TRUE ; Common->maxwork = 0 ; Common->ordering = 0 ; Common->scale = -1 ; Common->halt_if_singular = TRUE ; Common->user_order = NULL ; my_tries = -1 ; return (maxerr) ; } /* ========================================================================== */ /* === main ================================================================= */ /* ========================================================================== */ int main (void) { KLU_common Common ; cholmod_sparse *A, *A2 ; cholmod_dense *X, *B ; cholmod_common ch ; Int *Ap, *Ai, *Puser, *Quser, *Gunk ; double *Ax, *Bx, *Xx, *A2x ; double one [2], zero [2], xsave, maxerr ; Int n, i, j, nz, save, isreal, k, nan ; KLU_symbolic *Symbolic, *Symbolic2 ; KLU_numeric *Numeric ; one [0] = 1 ; one [1] = 0 ; zero [0] = 0 ; zero [1] = 0 ; printf ("klu test: -------------------------------------------------\n") ; OK (klu_defaults (&Common)) ; CHOLMOD_start (&ch) ; ch.print = 0 ; normal_memory_handler (&Common) ; /* ---------------------------------------------------------------------- */ /* read in a sparse matrix from stdin */ /* ---------------------------------------------------------------------- */ A = CHOLMOD_read_sparse (stdin, &ch) ; if (A->nrow != A->ncol || A->stype != 0) { fprintf (stderr, "error: only square unsymmetric matrices handled\n") ; CHOLMOD_free_sparse (&A, &ch) ; return (0) ; } if (!(A->xtype == CHOLMOD_REAL || A->xtype == CHOLMOD_COMPLEX)) { fprintf (stderr, "error: only real or complex matrices hanlded\n") ; CHOLMOD_free_sparse (&A, &ch) ; return (0) ; } n = A->nrow ; Ap = A->p ; Ai = A->i ; Ax = A->x ; nz = Ap [n] ; isreal = (A->xtype == CHOLMOD_REAL) ; /* ---------------------------------------------------------------------- */ /* construct random permutations */ /* ---------------------------------------------------------------------- */ Puser = randperm (n, n) ; Quser = randperm (n, n) ; /* ---------------------------------------------------------------------- */ /* select known solution to Ax=b */ /* ---------------------------------------------------------------------- */ X = CHOLMOD_allocate_dense (n, NRHS, n, A->xtype, &ch) ; Xx = X->x ; for (j = 0 ; j < NRHS ; j++) { for (i = 0 ; i < n ; i++) { if (isreal) { Xx [i] = 1 + ((double) i) / ((double) n) + j * 100; } else { Xx [2*i ] = 1 + ((double) i) / ((double) n) + j * 100 ; Xx [2*i+1] = - ((double) i+1) / ((double) n + j) ; if (j == NRHS-1) { Xx [2*i+1] = 0 ; /* zero imaginary part */ } else if (j == NRHS-2) { Xx [2*i] = 0 ; /* zero real part */ } } } Xx += isreal ? n : 2*n ; } /* B = A*X */ B = CHOLMOD_allocate_dense (n, NRHS, n, A->xtype, &ch) ; CHOLMOD_sdmult (A, 0, one, zero, X, B, &ch) ; Bx = B->x ; /* ---------------------------------------------------------------------- */ /* test KLU */ /* ---------------------------------------------------------------------- */ test_memory_handler (&Common) ; maxerr = do_solves (A, B, X, Puser, Quser, &Common, &ch, &nan) ; /* ---------------------------------------------------------------------- */ /* basic error checking */ /* ---------------------------------------------------------------------- */ FAIL (klu_defaults (NULL)) ; FAIL (klu_extract (NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL)) ; FAIL (klu_extract (NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, &Common)) ; FAIL (klu_z_extract (NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL)) ; FAIL (klu_z_extract (NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, &Common)) ; FAIL (klu_analyze (0, NULL, NULL, NULL)) ; FAIL (klu_analyze (0, NULL, NULL, &Common)) ; FAIL (klu_analyze_given (0, NULL, NULL, NULL, NULL, NULL)) ; FAIL (klu_analyze_given (0, NULL, NULL, NULL, NULL, &Common)) ; FAIL (klu_cholmod (0, NULL, NULL, NULL, NULL)) ; FAIL (klu_factor (NULL, NULL, NULL, NULL, NULL)) ; FAIL (klu_factor (NULL, NULL, NULL, NULL, &Common)) ; FAIL (klu_z_factor (NULL, NULL, NULL, NULL, NULL)) ; FAIL (klu_z_factor (NULL, NULL, NULL, NULL, &Common)) ; FAIL (klu_refactor (NULL, NULL, NULL, NULL, NULL, NULL)) ; FAIL (klu_refactor (NULL, NULL, NULL, NULL, NULL, &Common)) ; FAIL (klu_z_refactor (NULL, NULL, NULL, NULL, NULL, NULL)) ; FAIL (klu_z_refactor (NULL, NULL, NULL, NULL, NULL, &Common)) ; FAIL (klu_rgrowth (NULL, NULL, NULL, NULL, NULL, NULL)) ; FAIL (klu_rgrowth (NULL, NULL, NULL, NULL, NULL, &Common)) ; FAIL (klu_z_rgrowth (NULL, NULL, NULL, NULL, NULL, NULL)) ; FAIL (klu_z_rgrowth (NULL, NULL, NULL, NULL, NULL, &Common)) ; FAIL (klu_condest (NULL, NULL, NULL, NULL, NULL)) ; FAIL (klu_condest (NULL, NULL, NULL, NULL, &Common)) ; FAIL (klu_z_condest (NULL, NULL, NULL, NULL, NULL)) ; FAIL (klu_z_condest (NULL, NULL, NULL, NULL, &Common)) ; FAIL (klu_flops (NULL, NULL, NULL)) ; FAIL (klu_flops (NULL, NULL, &Common)) ; FAIL (klu_z_flops (NULL, NULL, NULL)) ; FAIL (klu_z_flops (NULL, NULL, &Common)) ; FAIL (klu_rcond (NULL, NULL, NULL)) ; FAIL (klu_rcond (NULL, NULL, &Common)) ; FAIL (klu_z_rcond (NULL, NULL, NULL)) ; FAIL (klu_z_rcond (NULL, NULL, &Common)) ; FAIL (klu_free_symbolic (NULL, NULL)) ; OK (klu_free_symbolic (NULL, &Common)) ; FAIL (klu_free_numeric (NULL, NULL)) ; OK (klu_free_numeric (NULL, &Common)) ; FAIL (klu_z_free_numeric (NULL, NULL)) ; OK (klu_z_free_numeric (NULL, &Common)) ; FAIL (klu_scale (0, 0, NULL, NULL, NULL, NULL, NULL, NULL)) ; FAIL (klu_scale (0, 0, NULL, NULL, NULL, NULL, NULL, &Common)) ; OK (klu_scale (-1, 0, NULL, NULL, NULL, NULL, NULL, &Common)) ; FAIL (klu_z_scale (0, 0, NULL, NULL, NULL, NULL, NULL, NULL)) ; FAIL (klu_z_scale (0, 0, NULL, NULL, NULL, NULL, NULL, &Common)) ; OK (klu_z_scale (-1, 0, NULL, NULL, NULL, NULL, NULL, &Common)) ; FAIL (klu_solve (NULL, NULL, 0, 0, NULL, NULL)) ; FAIL (klu_solve (NULL, NULL, 0, 0, NULL, &Common)) ; FAIL (klu_z_solve (NULL, NULL, 0, 0, NULL, NULL)) ; FAIL (klu_z_solve (NULL, NULL, 0, 0, NULL, &Common)) ; FAIL (klu_tsolve (NULL, NULL, 0, 0, NULL, NULL)) ; FAIL (klu_tsolve (NULL, NULL, 0, 0, NULL, &Common)) ; FAIL (klu_z_tsolve (NULL, NULL, 0, 0, NULL, 0, NULL)) ; FAIL (klu_z_tsolve (NULL, NULL, 0, 0, NULL, 0, &Common)) ; FAIL (klu_malloc (0, 0, NULL)) ; FAIL (klu_malloc (0, 0, &Common)) ; FAIL (klu_malloc (Int_MAX, 1, &Common)) ; FAIL (klu_realloc (0, 0, 0, NULL, NULL)) ; FAIL (klu_realloc (0, 0, 0, NULL, &Common)) ; FAIL (klu_realloc (Int_MAX, 1, 0, NULL, &Common)) ; Gunk = (Int *) klu_realloc (1, 0, sizeof (Int), NULL, &Common) ; OK (Gunk) ; OK (klu_realloc (Int_MAX, 1, sizeof (Int), Gunk, &Common)) ; OK (Common.status == KLU_TOO_LARGE) ; klu_free (Gunk, 1, sizeof (Int), &Common) ; /* ---------------------------------------------------------------------- */ /* mangle the matrix, and other error checking */ /* ---------------------------------------------------------------------- */ printf ("\nerror handling:\n") ; Symbolic = klu_analyze (n, Ap, Ai, &Common) ; OK (Symbolic) ; Xx = X->x ; if (nz > 0) { /* ------------------------------------------------------------------ */ /* row index out of bounds */ /* ------------------------------------------------------------------ */ save = Ai [0] ; Ai [0] = -1 ; FAIL (klu_analyze (n, Ap, Ai, &Common)) ; if (isreal) { FAIL (klu_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ; } else { FAIL (klu_z_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ; } Ai [0] = save ; /* ------------------------------------------------------------------ */ /* row index out of bounds */ /* ------------------------------------------------------------------ */ save = Ai [0] ; Ai [0] = Int_MAX ; FAIL (klu_analyze (n, Ap, Ai, &Common)) ; if (isreal) { FAIL (klu_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ; } else { FAIL (klu_z_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ; } Ai [0] = save ; /* ------------------------------------------------------------------ */ /* column pointers mangled */ /* ------------------------------------------------------------------ */ save = Ap [n] ; Ap [n] = -1 ; FAIL (klu_analyze (n, Ap, Ai, &Common)) ; if (isreal) { FAIL (klu_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ; } else { FAIL (klu_z_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ; } Ap [n] = save ; /* ------------------------------------------------------------------ */ /* column pointers mangled */ /* ------------------------------------------------------------------ */ save = Ap [n] ; Ap [n] = Ap [n-1] - 1 ; FAIL (klu_analyze (n, Ap, Ai, &Common)) ; if (isreal) { FAIL (klu_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ; } else { FAIL (klu_z_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ; } Ap [n] = save ; /* ------------------------------------------------------------------ */ /* duplicates */ /* ------------------------------------------------------------------ */ if (n > 1 && Ap [1] - Ap [0] > 1) { save = Ai [1] ; Ai [1] = Ai [0] ; FAIL (klu_analyze (n, Ap, Ai, &Common)) ; if (isreal) { FAIL (klu_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ; } else { FAIL (klu_z_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ; } Ai [1] = save ; } /* ------------------------------------------------------------------ */ /* invalid ordering */ /* ------------------------------------------------------------------ */ save = Common.ordering ; Common.ordering = 42 ; FAIL (klu_analyze (n, Ap, Ai, &Common)) ; Common.ordering = save ; /* ------------------------------------------------------------------ */ /* invalid ordering (klu_cholmod, with NULL user_ordering) */ /* ------------------------------------------------------------------ */ save = Common.ordering ; Common.user_order = NULL ; Common.ordering = 3 ; FAIL (klu_analyze (n, Ap, Ai, &Common)) ; Common.ordering = save ; } /* ---------------------------------------------------------------------- */ /* tests with valid symbolic factorization */ /* ---------------------------------------------------------------------- */ Common.halt_if_singular = FALSE ; Common.scale = 0 ; Numeric = NULL ; if (nz > 0) { /* ------------------------------------------------------------------ */ /* Int overflow */ /* ------------------------------------------------------------------ */ if (n == 100) { Common.ordering = 2 ; Symbolic2 = klu_analyze (n, Ap, Ai, &Common) ; OK (Symbolic2) ; Common.memgrow = Int_MAX ; if (isreal) { Numeric = klu_factor (Ap, Ai, Ax, Symbolic2, &Common) ; } else { Numeric = klu_z_factor (Ap, Ai, Ax, Symbolic2, &Common) ; } Common.memgrow = 1.2 ; Common.ordering = 0 ; klu_free_symbolic (&Symbolic2, &Common) ; klu_free_numeric (&Numeric, &Common) ; } /* ------------------------------------------------------------------ */ /* Int overflow again */ /* ------------------------------------------------------------------ */ Common.initmem = Int_MAX ; Common.initmem_amd = Int_MAX ; if (isreal) { Numeric = klu_factor (Ap, Ai, Ax, Symbolic, &Common) ; } else { Numeric = klu_z_factor (Ap, Ai, Ax, Symbolic, &Common) ; } Common.initmem = 10 ; Common.initmem_amd = 1.2 ; klu_free_numeric (&Numeric, &Common) ; /* ------------------------------------------------------------------ */ /* mangle the matrix */ /* ------------------------------------------------------------------ */ save = Ai [0] ; Ai [0] = -1 ; if (isreal) { Numeric = klu_factor (Ap, Ai, Ax, Symbolic, &Common) ; } else { Numeric = klu_z_factor (Ap, Ai, Ax, Symbolic, &Common) ; } FAIL (Numeric) ; Ai [0] = save ; /* ------------------------------------------------------------------ */ /* nan and inf handling */ /* ------------------------------------------------------------------ */ xsave = Ax [0] ; Ax [0] = one [0] / zero [0] ; if (isreal) { Numeric = klu_factor (Ap, Ai, Ax, Symbolic, &Common) ; klu_rcond (Symbolic, Numeric, &Common) ; klu_condest (Ap, Ax, Symbolic, Numeric, &Common) ; } else { Numeric = klu_z_factor (Ap, Ai, Ax, Symbolic, &Common) ; klu_z_rcond (Symbolic, Numeric, &Common) ; klu_z_condest (Ap, Ax, Symbolic, Numeric, &Common) ; } printf ("Nan case: rcond %g condest %g\n", Common.rcond, Common.condest) ; OK (Numeric) ; Ax [0] = xsave ; /* ------------------------------------------------------------------ */ /* mangle the matrix again */ /* ------------------------------------------------------------------ */ save = Ai [0] ; Ai [0] = -1 ; if (isreal) { FAIL (klu_refactor (Ap, Ai, Ax, Symbolic, Numeric, &Common)) ; } else { FAIL (klu_z_refactor (Ap, Ai, Ax, Symbolic, Numeric, &Common)) ; } Ai [0] = save ; /* ------------------------------------------------------------------ */ /* all zero */ /* ------------------------------------------------------------------ */ A2 = CHOLMOD_copy_sparse (A, &ch) ; A2x = A2->x ; for (k = 0 ; k < nz * (isreal ? 1:2) ; k++) { A2x [k] = 0 ; } for (Common.halt_if_singular = 0 ; Common.halt_if_singular <= 1 ; Common.halt_if_singular++) { for (Common.scale = -1 ; Common.scale <= 2 ; Common.scale++) { if (isreal) { klu_refactor (Ap, Ai, A2x, Symbolic, Numeric, &Common) ; klu_condest (Ap, A2x, Symbolic, Numeric, &Common) ; } else { klu_z_refactor (Ap, Ai, A2x, Symbolic, Numeric, &Common) ; klu_z_condest (Ap, A2x, Symbolic, Numeric, &Common) ; } OK (Common.status = KLU_SINGULAR) ; } } CHOLMOD_free_sparse (&A2, &ch) ; /* ------------------------------------------------------------------ */ /* all one, or all 1i for complex case */ /* ------------------------------------------------------------------ */ A2 = CHOLMOD_copy_sparse (A, &ch) ; A2x = A2->x ; for (k = 0 ; k < nz ; k++) { if (isreal) { A2x [k] = 1 ; } else { A2x [2*k ] = 0 ; A2x [2*k+1] = 1 ; } } Common.halt_if_singular = 0 ; Common.scale = 0 ; if (isreal) { klu_refactor (Ap, Ai, A2x, Symbolic, Numeric, &Common) ; klu_condest (Ap, A2x, Symbolic, Numeric, &Common) ; } else { klu_z_refactor (Ap, Ai, A2x, Symbolic, Numeric, &Common) ; klu_z_condest (Ap, A2x, Symbolic, Numeric, &Common) ; } OK (Common.status = KLU_SINGULAR) ; CHOLMOD_free_sparse (&A2, &ch) ; } klu_free_symbolic (&Symbolic, &Common) ; if (isreal) { klu_free_numeric (&Numeric, &Common) ; } else { klu_z_free_numeric (&Numeric, &Common) ; } /* ---------------------------------------------------------------------- */ /* free problem and quit */ /* ---------------------------------------------------------------------- */ CHOLMOD_free_dense (&X, &ch) ; CHOLMOD_free_dense (&B, &ch) ; CHOLMOD_free_sparse (&A, &ch) ; free (Puser) ; free (Quser) ; CHOLMOD_finish (&ch) ; fprintf (stderr, " maxerr %10.3e", maxerr) ; printf (" maxerr %10.3e", maxerr) ; if (maxerr < 1e-8) { fprintf (stderr, " test passed") ; printf (" test passed") ; } else { fprintf (stderr, " test FAILED") ; printf (" test FAILED") ; } if (nan) { fprintf (stderr, " *") ; printf (" *") ; } fprintf (stderr, "\n") ; printf ("\n-----------------------------------------------------------\n") ; return (0) ; } SuiteSparse/KLU/Tcov/coverage0000755001170100242450000000014610614771343015045 0ustar davisfac#!/bin/csh gcov cov*.c >& /dev/null echo -n 'statements not covered: ' grep "#####" *.c.gcov | wc -l SuiteSparse/KLU/Tcov/README.txt0000644001170100242450000000035510614773140015021 0ustar davisfacTest suite for KLU To compile and run the test suite, first type "make" in the Linux/Unix shell. The libraries must be compiled first (if they aren't use "make libs"). "make clean" or "make distclean" will remove all unnecessary files. SuiteSparse/KLU/Tcov/vklutests0000755001170100242450000000134010620325362015304 0ustar davisfac#!/bin/csh # 57 unique statements: valgrind ./klutest < ../Matrix/impcol_a.mtx # 20: valgrind ./klutest < ../Matrix/GD99_cc.mtx # 17: valgrind ./klutest < ../Matrix/two.mtx # 10: valgrind ./klutest < ../Matrix/w156.mtx # 3, xsize memgrow in klu_kernel valgrind ./klutest < ../Matrix/arrow.mtx # 3, xsize memgrow in klu_kernel, 1 in klu_z_condest, valgrind ./klutest < ../Matrix/arrowc.mtx # 2 in klu_z_kernel (if pivot == 0 and halt_if_singular, and in complex divide) valgrind ./klutest < ../Matrix/onec.mtx # 1 in klu_kernel (if pivot == 0 and halt if singular) valgrind ./klutest < ../Matrix/one.mtx # 1 in klu_z_condest: valgrind ./klutest < ../Matrix/1c.mtx # 1 in klu_z_condest: valgrind ./klutest < ../Matrix/ctina.mtx SuiteSparse/KLU/Tcov/klutests0000755001170100242450000000120610620325354015120 0ustar davisfac#!/bin/csh # 57 unique statements: ./klutest < ../Matrix/impcol_a.mtx # 20: ./klutest < ../Matrix/GD99_cc.mtx # 17: ./klutest < ../Matrix/two.mtx # 10: ./klutest < ../Matrix/w156.mtx # 3, xsize memgrow in klu_kernel ./klutest < ../Matrix/arrow.mtx # 3, xsize memgrow in klu_kernel, 1 in klu_z_condest, ./klutest < ../Matrix/arrowc.mtx # 2 in klu_z_kernel (if pivot == 0 and halt_if_singular, and in complex divide) ./klutest < ../Matrix/onec.mtx # 1 in klu_kernel (if pivot == 0 and halt if singular) ./klutest < ../Matrix/one.mtx # 1 in klu_z_condest: ./klutest < ../Matrix/1c.mtx # 1 in klu_z_condest: ./klutest < ../Matrix/ctina.mtx SuiteSparse/KLU/User/0000755001170100242450000000000010620123411013306 5ustar davisfacSuiteSparse/KLU/User/klu_l_cholmod.c0000644001170100242450000000633710616733361016316 0ustar davisfac/* ========================================================================== */ /* === klu_cholmod ========================================================== */ /* ========================================================================== */ /* klu_l_cholmod: user-defined ordering function to interface KLU to CHOLMOD. * * This routine is an example of a user-provided ordering function for KLU. * Its return value is klu_l_cholmod's estimate of max (nnz(L),nnz(U)): * 0 if error, * -1 if OK, but estimate of max (nnz(L),nnz(U)) not computed * > 0 if OK and estimate computed. * * This function can be assigned to KLU's Common->user_order function pointer. */ #include "klu_cholmod.h" #include "cholmod.h" #define TRUE 1 #define FALSE 0 UF_long klu_l_cholmod ( /* inputs */ UF_long n, /* A is n-by-n */ UF_long Ap [ ], /* column pointers */ UF_long Ai [ ], /* row indices */ /* outputs */ UF_long Perm [ ], /* fill-reducing permutation */ /* user-defined */ klu_l_common *Common /* user-defined data is in Common->user_data */ ) { double one [2] = {1,0}, zero [2] = {0,0}, lnz = 0 ; cholmod_sparse Amatrix, *A, *AT, *S ; cholmod_factor *L ; cholmod_common cm ; UF_long *P ; UF_long k, symmetric ; if (Ap == NULL || Ai == NULL || Perm == NULL || n < 0) { /* invalid inputs */ return (0) ; } /* start CHOLMOD */ cholmod_l_start (&cm) ; cm.supernodal = CHOLMOD_SIMPLICIAL ; cm.print = 0 ; /* use KLU memory management routines for CHOLMOD */ cm.malloc_memory = Common->malloc_memory ; cm.realloc_memory = Common->realloc_memory ; cm.calloc_memory = Common->calloc_memory ; cm.free_memory = Common->free_memory ; /* construct a CHOLMOD version of the input matrix A */ A = &Amatrix ; A->nrow = n ; /* A is n-by-n */ A->ncol = n ; A->nzmax = Ap [n] ; /* with nzmax entries */ A->packed = TRUE ; /* there is no A->nz array */ A->stype = 0 ; /* A is unsymmetric */ A->itype = CHOLMOD_INT ; A->xtype = CHOLMOD_PATTERN ; A->dtype = CHOLMOD_DOUBLE ; A->nz = NULL ; A->p = Ap ; /* column pointers */ A->i = Ai ; /* row indices */ A->x = NULL ; /* no numerical values */ A->z = NULL ; A->sorted = FALSE ; /* columns of A are not sorted */ /* get the user_data; default is symmetric if user_data is NULL */ symmetric = (Common->user_data == NULL) ? TRUE : (((UF_long *) (Common->user_data)) [0] != 0) ; /* AT = pattern of A' */ AT = cholmod_l_transpose (A, 0, &cm) ; if (symmetric) { /* S = the symmetric pattern of A+A' */ S = cholmod_l_add (A, AT, one, zero, FALSE, FALSE, &cm) ; cholmod_l_free_sparse (&AT, &cm) ; if (S != NULL) { S->stype = 1 ; } } else { /* S = A'. CHOLMOD will order S*S', which is A'*A */ S = AT ; } /* order and analyze S or S*S' */ L = cholmod_l_analyze (S, &cm) ; /* copy the permutation from L to the output */ if (L != NULL) { P = L->Perm ; for (k = 0 ; k < n ; k++) { Perm [k] = P [k] ; } lnz = cm.lnz ; } cholmod_l_free_sparse (&S, &cm) ; cholmod_l_free_factor (&L, &cm) ; cholmod_l_finish (&cm) ; return (lnz) ; } SuiteSparse/KLU/User/Makefile0000644001170100242450000000104510615511420014753 0ustar davisfacdefault: all include ../../UFconfig/UFconfig.mk all: libklu_cholmod.a I = -I../../CHOLMOD/Include -I../../UFconfig -I../Include -I../../AMD/Include \ -I../../BTF/Include -I../../COLAMD libklu_cholmod.a: library klu_cholmod.c klu_cholmod.h $(CC) $(CFLAGS) $(I) -c klu_cholmod.c $(AR) libklu_cholmod.a klu_cholmod.o $(RANLIB) libklu_cholmod.a distclean: purge purge: clean - $(RM) *.o *.a clean: - $(RM) $(CLEAN) library: ( cd ../../AMD ; $(MAKE) library ) ( cd ../../COLAMD ; $(MAKE) library ) ( cd ../../CHOLMOD/Lib ; $(MAKE) ) SuiteSparse/KLU/User/klu_cholmod.c0000644001170100242450000000625010616230755015774 0ustar davisfac/* ========================================================================== */ /* === klu_cholmod ========================================================== */ /* ========================================================================== */ /* klu_cholmod: user-defined ordering function to interface KLU to CHOLMOD. * * This routine is an example of a user-provided ordering function for KLU. * Its return value is klu_cholmod's estimate of max (nnz(L),nnz(U)): * 0 if error, * -1 if OK, but estimate of max (nnz(L),nnz(U)) not computed * > 0 if OK and estimate computed. * * This function can be assigned to KLU's Common->user_order function pointer. */ #include "klu_cholmod.h" #include "cholmod.h" #define TRUE 1 #define FALSE 0 int klu_cholmod ( /* inputs */ int n, /* A is n-by-n */ int Ap [ ], /* column pointers */ int Ai [ ], /* row indices */ /* outputs */ int Perm [ ], /* fill-reducing permutation */ /* user-defined */ klu_common *Common /* user-defined data is in Common->user_data */ ) { double one [2] = {1,0}, zero [2] = {0,0}, lnz = 0 ; cholmod_sparse Amatrix, *A, *AT, *S ; cholmod_factor *L ; cholmod_common cm ; int *P ; int k, symmetric ; if (Ap == NULL || Ai == NULL || Perm == NULL || n < 0) { /* invalid inputs */ return (0) ; } /* start CHOLMOD */ cholmod_start (&cm) ; cm.supernodal = CHOLMOD_SIMPLICIAL ; cm.print = 0 ; /* use KLU memory management routines for CHOLMOD */ cm.malloc_memory = Common->malloc_memory ; cm.realloc_memory = Common->realloc_memory ; cm.calloc_memory = Common->calloc_memory ; cm.free_memory = Common->free_memory ; /* construct a CHOLMOD version of the input matrix A */ A = &Amatrix ; A->nrow = n ; /* A is n-by-n */ A->ncol = n ; A->nzmax = Ap [n] ; /* with nzmax entries */ A->packed = TRUE ; /* there is no A->nz array */ A->stype = 0 ; /* A is unsymmetric */ A->itype = CHOLMOD_INT ; A->xtype = CHOLMOD_PATTERN ; A->dtype = CHOLMOD_DOUBLE ; A->nz = NULL ; A->p = Ap ; /* column pointers */ A->i = Ai ; /* row indices */ A->x = NULL ; /* no numerical values */ A->z = NULL ; A->sorted = FALSE ; /* columns of A are not sorted */ /* get the user_data; default is symmetric if user_data is NULL */ symmetric = (Common->user_data == NULL) ? TRUE : (((int *) (Common->user_data)) [0] != 0) ; /* AT = pattern of A' */ AT = cholmod_transpose (A, 0, &cm) ; if (symmetric) { /* S = the symmetric pattern of A+A' */ S = cholmod_add (A, AT, one, zero, FALSE, FALSE, &cm) ; cholmod_free_sparse (&AT, &cm) ; if (S != NULL) { S->stype = 1 ; } } else { /* S = A'. CHOLMOD will order S*S', which is A'*A */ S = AT ; } /* order and analyze S or S*S' */ L = cholmod_analyze (S, &cm) ; /* copy the permutation from L to the output */ if (L != NULL) { P = L->Perm ; for (k = 0 ; k < n ; k++) { Perm [k] = P [k] ; } lnz = cm.lnz ; } cholmod_free_sparse (&S, &cm) ; cholmod_free_factor (&L, &cm) ; cholmod_finish (&cm) ; return (lnz) ; } SuiteSparse/KLU/User/klu_cholmod.h0000644001170100242450000000034210616223645015775 0ustar davisfac#include "klu.h" #include "UFconfig.h" int klu_cholmod (int n, int Ap [ ], int Ai [ ], int Perm [ ], klu_common *) ; UF_long klu_l_cholmod (UF_long n, UF_long Ap [ ], UF_long Ai [ ], UF_long Perm [ ], klu_l_common *) ; SuiteSparse/KLU/User/README.txt0000644001170100242450000000016410615514712015021 0ustar davisfacThis directory contains a sample user-ordering function, klu_cholmod. Its use (and the use of CHOLMOD) is optional. SuiteSparse/KLU/Makefile0000644001170100242450000000071710710742743014054 0ustar davisfacdefault: library include ../UFconfig/UFconfig.mk library: ( cd Lib ; $(MAKE) ) ( cd Demo ; $(MAKE) ) clean: ( cd Demo ; $(MAKE) clean ) ( cd Lib ; $(MAKE) clean ) ( cd Tcov ; $(MAKE) clean ) distclean: ( cd Demo ; $(MAKE) distclean ) ( cd Lib ; $(MAKE) distclean ) ( cd Tcov ; $(MAKE) distclean ) ( cd User ; $(MAKE) distclean ) ( cd MATLAB ; $(MAKE) distclean ) mex: ( cd MATLAB ; $(MAKE) ) purge: distclean cov: library ( cd Tcov ; $(MAKE) ) SuiteSparse/KLU/MATLAB/0000755001170100242450000000000010712165101013334 5ustar davisfacSuiteSparse/KLU/MATLAB/klu_make.m0000644001170100242450000002474610621026431015320 0ustar davisfacfunction klu_make (with_cholmod) %KLU_MAKE compiles the KLU mexFunctions % % Example: % klu_make % compiles KLU without CHOLMOD % klu_make (1) % with CHOLMOD, CCAMD, CCOLAMD, and METIS % % KLU relies on AMD, COLAMD, and BTF for its ordering options, and can % optionally use CHOLMOD, CCOLAMD, CAMD, and METIS as well. By default, % CHOLMOD, CCOLAMD, CAMD, and METIS are not used. % % See http://www-users.cs.umn.edu/~karypis/metis for a copy of METIS 4.0.1. % % You must type the klu_make command while in the KLU/MATLAB directory. % % See also klu % Copyright 2004-2007 Timothy A. Davis, Univ. of Florida % http://www.cise.ufl.edu/research/sparse if (nargin < 1) with_cholmod = 0 ; end details = 0 ; % if 1, print details of each command % modify this if your copy of METIS is not in SuiteSparse/metis-4.0: metis_path = '../../metis-4.0' ; d = '' ; if (~isempty (strfind (computer, '64'))) % 64-bit MATLAB d = '-largeArrayDims' ; end fprintf ('Compiling KLU ') ; kk = 0 ; include = '-I. -I../../AMD/Include -I../../COLAMD/Include -I../Include -I../../UFconfig -I../../BTF/Include' ; if (with_cholmod) include = [include ' -I../../CCOLAMD/Include -I../../CAMD/Include -I../../CHOLMOD/Include -I../../UFconfig -I' metis_path '/Lib -I../User'] ; end % do not attempt to compile CHOLMOD with large file support (not needed) include = [include ' -DNLARGEFILE'] ; % fix the METIS 4.0.1 rename.h file if (with_cholmod) fprintf ('with CHOLMOD, CCAMD, CCOLAMD, and METIS\n') ; f = fopen ('rename.h', 'w') ; if (f == -1) error ('unable to create rename.h in current directory') ; end fprintf (f, '/* do not edit this file; generated by klu_make */\n') ; fprintf (f, '#undef log2\n') ; fprintf (f, '#include "%s/Lib/rename.h"\n', metis_path) ; fprintf (f, '#undef log2\n') ; fprintf (f, '#define log2 METIS__log2\n') ; fprintf (f, '#include "mex.h"\n') ; fprintf (f, '#define malloc mxMalloc\n') ; fprintf (f, '#define free mxFree\n') ; fprintf (f, '#define calloc mxCalloc\n') ; fprintf (f, '#define realloc mxRealloc\n') ; fclose (f) ; include = ['-DNSUPERNODAL -DNMODIFY -DNMATRIXOPS -DNCHECK ' include] ; else fprintf ('without CHOLMOD, CCAMD, CCOLAMD, and METIS\n') ; include = ['-DNCHOLMOD ' include] ; end include = strrep (include, '/', filesep) ; amd_src = { ... '../../AMD/Source/amd_1', ... '../../AMD/Source/amd_2', ... '../../AMD/Source/amd_aat', ... '../../AMD/Source/amd_control', ... '../../AMD/Source/amd_defaults', ... '../../AMD/Source/amd_dump', ... '../../AMD/Source/amd_global', ... '../../AMD/Source/amd_info', ... '../../AMD/Source/amd_order', ... '../../AMD/Source/amd_postorder', ... '../../AMD/Source/amd_post_tree', ... '../../AMD/Source/amd_preprocess', ... '../../AMD/Source/amd_valid' } ; camd_src = { ... '../../CAMD/Source/camd_1', ... '../../CAMD/Source/camd_2', ... '../../CAMD/Source/camd_aat', ... '../../CAMD/Source/camd_control', ... '../../CAMD/Source/camd_defaults', ... '../../CAMD/Source/camd_dump', ... '../../CAMD/Source/camd_global', ... '../../CAMD/Source/camd_info', ... '../../CAMD/Source/camd_order', ... '../../CAMD/Source/camd_postorder', ... '../../CAMD/Source/camd_preprocess', ... '../../CAMD/Source/camd_valid' } ; colamd_src = { '../../COLAMD/Source/colamd', ... '../../COLAMD/Source/colamd_global' } ; ccolamd_src = { '../../CCOLAMD/Source/ccolamd', ... '../../CCOLAMD/Source/ccolamd_global' } ; metis_src = { 'Lib/balance', ... 'Lib/bucketsort', ... 'Lib/ccgraph', ... 'Lib/coarsen', ... 'Lib/compress', ... 'Lib/debug', ... 'Lib/estmem', ... 'Lib/fm', ... 'Lib/fortran', ... 'Lib/frename', ... 'Lib/graph', ... 'Lib/initpart', ... 'Lib/kmetis', ... 'Lib/kvmetis', ... 'Lib/kwayfm', ... 'Lib/kwayrefine', ... 'Lib/kwayvolfm', ... 'Lib/kwayvolrefine', ... 'Lib/match', ... 'Lib/mbalance2', ... 'Lib/mbalance', ... 'Lib/mcoarsen', ... 'Lib/memory', ... 'Lib/mesh', ... 'Lib/meshpart', ... 'Lib/mfm2', ... 'Lib/mfm', ... 'Lib/mincover', ... 'Lib/minitpart2', ... 'Lib/minitpart', ... 'Lib/mkmetis', ... 'Lib/mkwayfmh', ... 'Lib/mkwayrefine', ... 'Lib/mmatch', ... 'Lib/mmd', ... 'Lib/mpmetis', ... 'Lib/mrefine2', ... 'Lib/mrefine', ... 'Lib/mutil', ... 'Lib/myqsort', ... 'Lib/ometis', ... 'Lib/parmetis', ... 'Lib/pmetis', ... 'Lib/pqueue', ... 'Lib/refine', ... 'Lib/separator', ... 'Lib/sfm', ... 'Lib/srefine', ... 'Lib/stat', ... 'Lib/subdomains', ... 'Lib/timing', ... 'Lib/util' } ; for i = 1:length (metis_src) metis_src {i} = [metis_path '/' metis_src{i}] ; end cholmod_src = { '../../CHOLMOD/Core/cholmod_aat', ... '../../CHOLMOD/Core/cholmod_add', ... '../../CHOLMOD/Core/cholmod_band', ... '../../CHOLMOD/Core/cholmod_change_factor', ... '../../CHOLMOD/Core/cholmod_common', ... '../../CHOLMOD/Core/cholmod_complex', ... '../../CHOLMOD/Core/cholmod_copy', ... '../../CHOLMOD/Core/cholmod_dense', ... '../../CHOLMOD/Core/cholmod_error', ... '../../CHOLMOD/Core/cholmod_factor', ... '../../CHOLMOD/Core/cholmod_memory', ... '../../CHOLMOD/Core/cholmod_sparse', ... '../../CHOLMOD/Core/cholmod_transpose', ... '../../CHOLMOD/Core/cholmod_triplet', ... '../../CHOLMOD/Cholesky/cholmod_amd', ... '../../CHOLMOD/Cholesky/cholmod_analyze', ... '../../CHOLMOD/Cholesky/cholmod_colamd', ... '../../CHOLMOD/Cholesky/cholmod_etree', ... '../../CHOLMOD/Cholesky/cholmod_postorder', ... '../../CHOLMOD/Cholesky/cholmod_rowcolcounts', ... '../../CHOLMOD/Partition/cholmod_ccolamd', ... '../../CHOLMOD/Partition/cholmod_csymamd', ... '../../CHOLMOD/Partition/cholmod_camd', ... '../../CHOLMOD/Partition/cholmod_metis', ... '../../CHOLMOD/Partition/cholmod_nesdis' } ; btf_src = { '../../BTF/Source/btf_maxtrans', ... '../../BTF/Source/btf_order', ... '../../BTF/Source/btf_strongcomp' } ; klu_src = { '../Source/klu_free_symbolic', ... '../Source/klu_defaults', ... '../Source/klu_analyze_given', ... '../Source/klu_analyze', ... '../Source/klu_memory' } ; if (with_cholmod) klu_src = [klu_src { '../User/klu_l_cholmod' }] ; %#ok end klu_zlsrc = { '../Source/klu', ... '../Source/klu_kernel', ... '../Source/klu_dump', ... '../Source/klu_factor', ... '../Source/klu_free_numeric', ... '../Source/klu_solve', ... '../Source/klu_scale', ... '../Source/klu_refactor', ... '../Source/klu_tsolve', ... '../Source/klu_diagnostics', ... '../Source/klu_sort', ... '../Source/klu_extract', ... } ; klu_lobj = { 'klu_l', ... 'klu_l_kernel', ... 'klu_l_dump', ... 'klu_l_factor', ... 'klu_l_free_numeric', ... 'klu_l_solve', ... 'klu_l_scale', ... 'klu_l_refactor', ... 'klu_l_tsolve', ... 'klu_l_diagnostics', ... 'klu_l_sort', ... 'klu_l_extract', ... } ; klu_zlobj = { 'klu_zl', ... 'klu_zl_kernel', ... 'klu_zl_dump', ... 'klu_zl_factor', ... 'klu_zl_free_numeric', ... 'klu_zl_solve', ... 'klu_zl_scale', ... 'klu_zl_refactor', ... 'klu_zl_tsolve', ... 'klu_zl_diagnostics', ... 'klu_zl_sort', ... 'klu_zl_extract', ... } ; try % ispc does not appear in MATLAB 5.3 pc = ispc ; catch % if ispc fails, assume we are on a Windows PC if it's not unix pc = ~isunix ; end if (pc) % Windows does not have drand48 and srand48, required by METIS. Use % drand48 and srand48 in CHOLMOD/MATLAB/Windows/rand48.c instead. obj_extension = '.obj' ; cholmod_src = [cholmod_src {'../../CHOLMOD/MATLAB/Windows/rand48'}] ; include = [include ' -I../../CHOLMOD/MATLAB/Windows'] ; else obj_extension = '.o' ; end % compile each library source file obj = ' ' ; source = [amd_src btf_src klu_src colamd_src] ; if (with_cholmod) source = [metis_src ccolamd_src camd_src cholmod_src source] ; end for f = source fs = strrep (f {1}, '/', filesep) ; slash = strfind (fs, filesep) ; if (isempty (slash)) slash = 1 ; else slash = slash (end) + 1 ; end o = fs (slash:end) ; obj = [obj ' ' o obj_extension] ; %#ok s = sprintf ('mex %s -DDLONG -O %s -c %s.c', d, include, fs) ; kk = do_cmd (s, kk, details) ; end for k = 1:length(klu_zlsrc) ff = strrep (klu_zlsrc {k}, '/', filesep) ; slash = strfind (ff, filesep) ; if (isempty (slash)) slash = 1 ; else slash = slash (end) + 1 ; end o = ff (slash:end) ; s = sprintf ('mex %s -DDLONG -O %s -c %s.c', d, include, ff) ; kk = do_cmd (s, kk, details) ; lobj = klu_lobj {k} ; obj = [obj ' ' lobj obj_extension] ; %#ok mvfile ([o obj_extension], [lobj obj_extension]) ; s = sprintf ('mex %s -DDLONG -DCOMPLEX -O %s -c %s.c', d, include, ff) ; kk = do_cmd (s, kk, details) ; zlobj = klu_zlobj {k} ; obj = [obj ' ' zlobj obj_extension] ; %#ok mvfile ([o obj_extension], [zlobj obj_extension]) ; end % compile the KLU mexFunction s = sprintf ('mex %s -DDLONG -O %s -output klu klu_mex.c', d, include) ; s = [s obj] ; %#ok kk = do_cmd (s, kk, details) ; % clean up s = ['delete ' obj] ; do_cmd (s, kk, details) ; fprintf ('\nKLU successfully compiled\n') ; %------------------------------------------------------------------------------- function rmfile (file) % rmfile: delete a file, but only if it exists if (length (dir (file)) > 0) %#ok delete (file) ; end %------------------------------------------------------------------------------- function cpfile (src, dst) % cpfile: copy the src file to the filename dst, overwriting dst if it exists rmfile (dst) if (length (dir (src)) == 0) %#ok fprintf ('File does not exist: %s\n', src) ; error ('File does not exist') ; end copyfile (src, dst) ; %------------------------------------------------------------------------------- function mvfile (src, dst) % mvfile: move the src file to the filename dst, overwriting dst if it exists cpfile (src, dst) ; rmfile (src) ; %------------------------------------------------------------------------------- function kk = do_cmd (s, kk, details) %DO_CMD: evaluate a command, and either print it or print a "." if (details) fprintf ('%s\n', s) ; else if (mod (kk, 60) == 0) fprintf ('\n') ; end kk = kk + 1 ; fprintf ('.') ; end eval (s) ; SuiteSparse/KLU/MATLAB/Test/0000755001170100242450000000000010711446037014264 5ustar davisfacSuiteSparse/KLU/MATLAB/Test/klu_test.m0000644001170100242450000000043610710510521016264 0ustar davisfacfunction klu_test (nmat) %klu_test KLU test % Example: % klu_test % % See also klu % Copyright 2004-2007 Timothy A. Davis, Univ. of Florida % http://www.cise.ufl.edu/research/sparse if (nargin < 1) nmat = 500 ; end test1 (nmat) ; test2 (nmat) ; test3 ; test4 (nmat) ; test5 ; SuiteSparse/KLU/MATLAB/Test/test1.m0000644001170100242450000000455310711446035015507 0ustar davisfacfunction test1 (nmat) %test1: KLU test % Example: % test1 % % See also klu % Copyright 2004-2007 Timothy A. Davis, Univ. of Florida % http://www.cise.ufl.edu/research/sparse clear functions rand ('state', 0) ; index = UFget ; f = find (index.nrows == index.ncols & index.isReal) ; [ignore i] = sort (index.nnz (f)) ; f = f (i) ; h = waitbar (0, 'KLU test 1 of 5') ; if (nargin < 1) nmat = 500 ; end nmat = min (nmat, length (f)) ; % just use the first 100 matrices nmat = min (nmat, 100) ; f = f (1:nmat) ; % f = 274 % f = 101 ; % MATLAB condest is poor nmat = length (f) ; conds_klu = ones (1,nmat) ; conds_matlab = ones (1,nmat) ; figure (1) clf try for k = 1:nmat waitbar (k/nmat, h) ; i = f (k) ; try c = -1 ; blocks = 0 ; rho = 0 ; c2 = 0 ; r1 = 0 ; r2 = 0 ; err = 0 ; Prob = UFget (i,index) ; A = Prob.A ; c = condest (A) ; % klu (A) % [L,U,p,q,R,F,r,info] = klu (A) ; [LU, info, c2] = klu (A) ; L = LU.L ; U = LU.U ; p = LU.p ; q = LU.q ; R = LU.R ; F = LU.F ; r = LU.r ; blocks = length (r) - 1 ; n = size (A,1) ; b = rand (n,1) ; x = klu (LU,'\',b) ; err = norm (A*x-b,1) / norm (A,1) ; % info rho = lu_normest (R\A(p,q) - F, L, U) ; r1 = info.rcond ; r2 = full (min (abs (diag (U))) / max (abs (diag (U)))) ; if (r1 ~= r2) fprintf ('!\n') ; pause end conds_klu (k) = c2 ; conds_matlab (k) = c ; catch disp (lasterr) ; end fprintf (... 'blocks %6d err %8.2e condest %8.2e %8.2e rcond %8.2e %8.2e err %8.2e\n', ... blocks, rho, c2, c, r1, r2, err) ; end k = nmat ; plot (1:k, log10 (conds_klu (1:k) ./ conds_matlab (1:k)), 'o') ; drawnow catch % out-of-memory is OK, other errors are not disp (lasterr) ; if (isempty (strfind (lasterr, 'Out of memory'))) error (lasterr) ; %#ok else fprintf ('test terminated early, but otherwise OK\n') ; end end close (h) ; SuiteSparse/KLU/MATLAB/Test/test2.m0000644001170100242450000001162210711445567015514 0ustar davisfacfunction test2 (nmat) %test2: KLU test % Example: % test2 % See also klu % Copyright 2004-2007 Timothy A. Davis, Univ. of Florida % http://www.cise.ufl.edu/research/sparse clear functions rand ('state', 0) ; % warning ('off', 'MATLAB:singularMatrix') ; % warning ('off', 'MATLAB:nearlySingularMatrix') ; % warning ('off', 'MATLAB:divideByZero') ; index = UFget ; f = find (index.nrows == index.ncols) ; [ignore i] = sort (index.nnz (f)) ; f = f (i) ; if (nargin < 1) nmat = 500 ; end nmat = min (nmat, length (f)) ; f = f (1:nmat) ; if (~isempty (strfind (computer, '64'))) is64 = 1 ; else is64 = 0 ; end Tklu = 1e-6 * ones (2*nmat,1) ; Tmatlab = zeros (2*nmat,1) ; Tcsparse = zeros (2*nmat,1) ; LUnz = zeros (2*nmat, 1) ; k = 0 ; h = waitbar (0, 'KLU test 2 of 5') ; figure (1) clf try for kk = 1:nmat Prob = UFget (f (kk), index) ; waitbar (kk/nmat, h) ; disp (Prob) ; if (isfield (Prob, 'kind')) if (~isempty (strfind (Prob.kind, 'subsequent'))) fprintf ('skip ...\n') ; continue end end A = Prob.A ; for do_complex = 0:1 k = k + 1 ; if (do_complex) A = sprand (A) + 1i * sprand (A) ; end try [L,U,p,q] = lu (A, 'vector') ; catch % older version of MATLAB, which doesn't have 'vector' option [L,U,P,Q] = lu (A) ; [p ignore1 ignore2] = find (P') ; [q ignore1 ignore2] = find (Q) ; clear ignore1 ignore2 P Q end LU.L = L ; LU.U = U ; if (is64) LU.p = int64 (p) ; LU.q = int64 (q) ; else LU.p = int32 (p) ; LU.q = int32 (q) ; end C = A (p,q) ; LUnz (k) = nnz (L) + nnz (U) ; n = size (A,1) ; do_klu = (nnz (diag (U)) == n) ; if (do_klu) fprintf ('klu...\n') ; err = 0 ; erc = 0 ; er2 = 0 ; for nrhs = 10:-1:1 b = rand (n,nrhs) ; tic ; x = klu (LU,'\',b) ; Tklu (k) = max (1e-6, toc) ; tic ; y = U \ (L \ b (p,:)) ; y (q,:) = y ; Tmatlab (k) = max (1e-6, toc) ; if (nrhs == 1 & isreal (U) & isreal (L) & isreal (b)) %#ok tic ; z = cs_usolve (U, cs_lsolve (L, b (p))) ; z (q) = z ; Tcsparse (k) = max (1e-6, toc) ; erc = norm (A*z-b,1) / norm (A,1) ; end err = max (err, norm (A*x-b,1) / norm (A,1)) ; er2 = max (er2, norm (A*y-b,1) / norm (A,1)) ; if (err > 100*er2) fprintf ('error %g %g\n', err, er2) ; error ('?') ; end end fprintf ('klu... with randomized scaling for L\n') ; er3 = 0 ; er4 = 0 ; D = spdiags (rand (n,1), 0, n, n) ; LU.L = D * L ; A2 = D * A (p,q) ; if (is64) LU.p = int64 (1:n) ; LU.q = int64 (1:n) ; else LU.p = int32 (1:n) ; LU.q = int32 (1:n) ; end for nrhs = 1:10 b = rand (n,nrhs) ; x = klu (LU,'\',b) ; y = U \ (LU.L \ b) ; er3 = max (er3, norm (A2*x-b,1) / norm (A,1)) ; er4 = max (er4, norm (A2*y-b,1) / norm (A,1)) ; if (er3 > 1e3*er4) fprintf ('error %g %g\n', er3, er4) ; error ('?') ; end end else err = Inf ; er2 = Inf ; er3 = Inf ; er4 = Inf ; erc = Inf ; end lumax = max (LUnz (1:k)) ; loglog (... LUnz (1:k), Tmatlab (1:k) ./ Tklu (1:k), 'o', ... LUnz (1:k), Tcsparse (1:k) ./ Tklu (1:k), 'x', ... [20 lumax], [1 1], 'r-') ; axis ([20 lumax .1 20]) ; drawnow fprintf ('err %g %g %g\n', err, er2, erc) ; end end catch % out-of-memory is OK, other errors are not disp (lasterr) ; if (isempty (strfind (lasterr, 'Out of memory'))) error (lasterr) ; %#ok else fprintf ('test terminated early, but otherwise OK\n') ; end end close (h) ; SuiteSparse/KLU/MATLAB/Test/test3.m0000644001170100242450000000310210710414316015472 0ustar davisfacfunction test3 %test3: KLU test % Example: % test3 % See also klu % Copyright 2004-2007 Timothy A. Davis, Univ. of Florida % http://www.cise.ufl.edu/research/sparse h = waitbar (1/12, 'KLU test 3 of 5') ; rand ('state', 0) ; load west0479 A = west0479 ; % A = sparse (rand (4)) ; % A (3:4, 1:2) = 0 ; n = size (A,1) ; b = rand (n,1) ; spparms ('spumoni',2) x = A\b ; spparms ('spumoni',0) fprintf ('MATLAB resid %g\n', norm (A*x-b,1)) ; [LU,info,cond_estimate] = klu (A) ; fprintf ('\nLU = \n') ; disp (LU) ; fprintf ('\ninfo = \n') ; disp (info) ; fprintf ('KLU condest %g\n', cond_estimate) ; matlab_condest = condest (A) ; matlab_cond = cond (full (A)) ; fprintf ('MATLAB condest %g cond %g\n', matlab_condest, matlab_cond) ; for nrhs = 1:10 waitbar (nrhs/12, h) ; b = rand (n,nrhs) ; x = klu (LU,'\',b) ; fprintf ('nrhs: %d resid: %g\n', ... nrhs, norm (A*x-b,1) / norm (A,1)) ; end [x,info,cond_estimate] = klu (A, '\', b) ; fprintf ('\ninfo = \n') ; disp (info) ; fprintf ('KLU cond_estimate %g\n', cond_estimate) ; waitbar (11/12, h) ; [x,info] = klu (A, '\', b, struct ('ordering',1)) ; fprintf ('\ninfo = \n') ; disp (info) ; [x,info,cond_estimate] = klu (A, '\', b, struct ('ordering',2)) ; fprintf ('\ninfo = \n') ; disp (info) ; try [x,info,cond_estimate] = klu (A, '\', b, struct ('ordering',3)) ; fprintf ('\ninfo = \n') ; disp (info) ; [x,info,cond_estimate] = klu (A, '\', b, struct ('ordering',4)) ; fprintf ('\ninfo = \n') ; disp (info) ; catch fprintf ('KLU test with CHOLMOD skipped (CHOLMOD not installed)\n') ; end close (h) ; SuiteSparse/KLU/MATLAB/Test/test4.m0000644001170100242450000001363610711445573015522 0ustar davisfacfunction test4 (nmat) %test4: KLU test % Example: % test4 % See also klu % Copyright 2004-2007 Timothy A. Davis, Univ. of Florida % http://www.cise.ufl.edu/research/sparse % rand ('state', 0) ; % warning ('off', 'MATLAB:singularMatrix') ; % warning ('off', 'MATLAB:nearlySingularMatrix') ; % warning ('off', 'KLU:rcond') ; % warning ('off', 'MATLAB:Axes:NegativeDataInLogAxis') ; index = UFget ; f = find (index.nrows == index.ncols & index.isReal & index.amd_lnz > 0) ; [ignore i] = sort (index.amd_lnz (f)) ; f = f (i) ; % f = f (1:100) ; if (nargin < 1) nmat = 500 ; end nmat = min (nmat, length (f)) ; f = f (1:nmat) ; if (1) Tlu = -ones (nmat,1) ; Tklu = -ones (nmat,1) ; Tklu2 = -ones (nmat,1) ; LUnz = -ones (nmat,1) ; k = 0 ; end if (~isempty (strfind (computer, '64'))) is64 = 1 ; else is64 = 0 ; end % 589: Sieber h = waitbar (0, 'KLU test 4 of 5') ; figure (1) clf try for kk = 1:nmat Prob = UFget (f (kk), index) ; waitbar (kk/nmat, h) ; disp (Prob) ; if (isfield (Prob, 'kind')) if (~isempty (strfind (Prob.kind, 'subsequent'))) fprintf ('skip ...\n') ; continue end if (~isempty (strfind (Prob.kind, 'random'))) fprintf ('skip ...\n') ; continue end end k = k + 1 ; A = Prob.A ; n = size (A,1) ; err1 = 0 ; err2 = 0 ; err4 = 0 ; terr1 = 0 ; terr2 = 0 ; terr4 = 0 ; for do_imag = 0:1 if (do_imag) A = sprand (A) + 1i * sprand (A) ; end % compare with UMFPACK try tic [L,U,p,q,R1] = lu (A, 'vector') ; t1 = max (1e-6, toc) ; catch % older version of MATLAB, which doesn't have 'vector' option tic [L,U,P,Q] = lu (A) ; t1 = max (1e-6, toc) ; [p ignore1 ignore2] = find (P') ; [q ignore1 ignore2] = find (Q) ; clear ignore1 ignore2 P Q R1 = speye (n) ; end if (Tlu (k) == -1) Tlu (k) = t1 ; LUnz (k) = nnz (L) + nnz (U) ; end % note that the scaling R1 and R2 are different with KLU and UMFPACK % UMFPACK: L*U-P*(R1\A)*Q % KLU: L*U-R2\(P*A*Q) % % R1 and R2 are related, via P, where R2 = P*R*P', or equivalently % R2 = R1 (p,p). rcond = min (abs (diag (U))) / max (abs (diag (U))) ; if (rcond < 1e-15) fprintf ('skip...\n') ; break ; end F.L = L ; F.U = U ; if (is64) F.p = int64(p) ; F.q = int64(q) ; else F.p = int32(p) ; F.q = int32(q) ; end F.R = R1(p,p) ; b = rand (n,1) ; x = klu (F, '\', b) ; y = klu (b', '/', F) ; fprintf ('solve with klu %g\n', ... norm (A*x-b,1)/norm(A,1)) ; fprintf ('solve with klu %g transpose\n', ... norm (y*A-b',1)/norm(A,1)) ; for nrhs = 1:10 for do_b_imag = 0:1 b = rand (n, nrhs) ; if (do_b_imag) b = b + 1i * rand (n, nrhs) ; end % KLU backslash tic ; x = klu (A,'\',b) ; t2 = max (1e-6, toc) ; % KLU slash xt = klu (b','/',A) ; % KLU backslash with precomputed LU tic LU = klu (A) ; z = klu (LU,'\',b) ; t4 = max (1e-6, toc) ; % KLU slash with precomputed LU zt = klu (b','/',LU) ; % UMFPACK tic rb = R1 \ b ; y = U \ (L \ rb (p,:)) ; y (q,:) = y ; t3 = max (1e-6, toc) ; yt = (L' \ (U' \ b (q,:))) ; yt (p,:) = yt ; yt = R1 \ yt ; yt = yt' ; if (Tklu (k) == -1) Tlu (k) = Tlu (k) + t3 ; Tklu (k) = t2 ; Tklu2 (k) = t4 ; end err1 = max (err1, norm (A*x-b,1) / norm (A,1)) ; err2 = max (err2, norm (A*y-b,1) / norm (A,1)) ; err4 = max (err4, norm (A*z-b,1) / norm (A,1)) ; terr1 = max (terr1, norm (xt*A-b',1) / norm (A,1)) ; terr2 = max (terr2, norm (yt*A-b',1) / norm (A,1)) ; terr4 = max (terr4, norm (zt*A-b',1) / norm (A,1)) ; end end end fprintf ('err %g %g %g\n', err1, err2, err4) ; if (err1 > 1e4*err2 | err4 > 1e4*err2) %#ok fprintf ('warning: KLU inaccurate!\n') end fprintf ('terr %g %g %g\n', terr1, terr2, terr4) ; if (terr1 > 1e4*terr2 | terr4 > 1e4*terr2) %#ok fprintf ('warning: KLU T inaccurate!\n') end lunzmax = max (LUnz (1:k)) ; loglog ( ... LUnz (1:k), Tklu (1:k) ./ Tlu (1:k), 'o', ... LUnz (1:k), Tklu2 (1:k) ./ Tlu (1:k), 'x', ... [10 lunzmax], [1 1], 'r-') ; drawnow end catch % out-of-memory is OK, other errors are not disp (lasterr) ; if (isempty (strfind (lasterr, 'Out of memory'))) error (lasterr) ; %#ok else fprintf ('test terminated early, but otherwise OK\n') ; end end close (h) ; SuiteSparse/KLU/MATLAB/Test/test5.m0000644001170100242450000001163010711445576015516 0ustar davisfacfunction test5 %test5: KLU test % Example: % test5 % % test circuit matrices in the UF sparse matrix collection. % % See also klu % Copyright 2004-2007 Timothy A. Davis, Univ. of Florida % http://www.cise.ufl.edu/research/sparse do_diary = 0 ; if (do_diary) diary off s = date ; t = clock ; s = sprintf ('diary test5_%s_%d-%d-%d.txt\n', s, t (4), t(5), fix(t(6))); eval (s) ; end % ATandT frequency-domain circuits, exclude these: freq = [ 283 284 285 286 ] ; % sorted in order of MATLAB 7.3 x=A\b time on storm % (AMD Opteron, 64-bit, 8GB mem, 2 cores) circ = [ 1195 % Rajat/rajat11 n: 135 nz 665 1198 % Rajat/rajat14 n: 180 nz 1475 1189 % Rajat/rajat05 n: 301 nz 1250 1169 % Sandia/oscil_trans_01 n: 430 nz 1614 1112 % Sandia/oscil_dcop_01 n: 430 nz 1544 1346 % Rajat/rajat19 n: 1157 nz 3699 1199 % Hamrle/Hamrle1 n: 32 nz 98 1106 % Sandia/fpga_trans_01 n: 1220 nz 7382 1188 % Rajat/rajat04 n: 1041 nz 8725 1055 % Sandia/fpga_dcop_01 n: 1220 nz 5892 1108 % Sandia/init_adder1 n: 1813 nz 11156 1196 % Rajat/rajat12 n: 1879 nz 12818 1053 % Sandia/adder_trans_01 n: 1814 nz 14579 539 % Hamm/add20 n: 2395 nz 13151 371 % Bomhof/circuit_2 n: 4510 nz 21199 540 % Hamm/add32 n: 4960 nz 19848 1186 % Rajat/rajat02 n: 1960 nz 11187 466 % Grund/meg4 n: 5860 nz 25258 465 % Grund/meg1 n: 2904 nz 58142 370 % Bomhof/circuit_1 n: 2624 nz 35823 1200 % Hamrle/Hamrle2 n: 5952 nz 22162 1197 % Rajat/rajat13 n: 7598 nz 48762 1187 % Rajat/rajat03 n: 7602 nz 32653 372 % Bomhof/circuit_3 n: 12127 nz 48137 1185 % Rajat/rajat01 n: 6833 nz 43250 1183 % IBM_Austin/coupled n: 11341 nz 97193 1376 % Rajat/rajat27 n: 20640 nz 97353 543 % Hamm/memplus n: 17758 nz 99147 1109 % Sandia/mult_dcop_01 n: 25187 nz 193276 1371 % Rajat/rajat22 n: 39899 nz 195429 1375 % Rajat/rajat26 n: 51032 nz 247528 1414 % IBM_EDA/ckt11752_tr_0 n: 49702 nz 332807 541 % Hamm/bcircuit n: 68902 nz 375558 1413 % IBM_EDA/ckt11752_dc_1 n: 49702 nz 333029 542 % Hamm/hcircuit n: 105676 nz 513072 1316 % Rajat/rajat15 n: 37261 nz 443573 1190 % Rajat/rajat06 n: 10922 nz 46983 1191 % Rajat/rajat07 n: 14842 nz 63913 1372 % Rajat/rajat23 n: 110355 nz 555441 373 % Bomhof/circuit_4 n: 80209 nz 307604 544 % Hamm/scircuit n: 170998 nz 958936 1412 % AMD/G2_circuit n: 150102 nz 726674 is this solid state device? 1415 % Sandia/ASIC_100k n: 99340 nz 940621 1416 % Sandia/ASIC_100ks n: 99190 nz 578890 1420 % Sandia/ASIC_680ks n: 682712 nz 1693767 1192 % Rajat/rajat08 n: 19362 nz 83443 1193 % Rajat/rajat09 n: 24482 nz 105573 1323 % IBM_EDA/trans4 n: 116835 nz 749800 1320 % IBM_EDA/dc1 n: 116835 nz 766396 1194 % Rajat/rajat10 n: 30202 nz 130303 1418 % Sandia/ASIC_320ks n: 321671 nz 1316085 1417 % Sandia/ASIC_320k n: 321821 nz 1931828 1343 % Rajat/rajat16 n: 94294 nz 476766 1345 % Rajat/rajat18 n: 94294 nz 479151 1344 % Rajat/rajat17 n: 94294 nz 479246 1377 % Rajat/rajat28 n: 87190 nz 606489 1369 % Rajat/rajat20 n: 86916 nz 604299 1374 % Rajat/rajat25 n: 87190 nz 606489 1370 % Rajat/rajat21 n: 411676 nz 1876011 1419 1396 1201 1397 1421 1398 1373 % Rajat/rajat24 n: 358172 nz 1946979 ]' ; fprintf ('Running KLU on %d circuits.\n', length (circ)) ; index = UFget ; opts_noscale.scale = -1 ; opts_sum.scale = 1 ; opts_max.scale = 2 ; % default scaling h = waitbar (0, 'KLU test 5 of 5') ; nmat = length (circ) ; try for kk = 1:nmat k = circ (kk) ; Prob = UFget (k, index) ; waitbar (kk/nmat, h) ; A = Prob.A ; n = size (A,1) ; b = rand (n,1) ; fprintf ('\n%d : %s n: %d nz %d\n', k, Prob.name, n, nnz (A)) ; try tic ; x2 = klu (A, '\', b, opts_noscale) ; t2 = toc ; e2 = norm (A*x2-b) ; catch t2 = 0 ; e2 = 0 ; end fprintf ('KLU no scale: err %8.2e t: %8.4f\n', e2, t2) ; try tic ; x4 = klu (A, '\', b, opts_max) ; t4 = toc ; e4 = norm (A*x4-b) ; catch t4 = 0 ; e4 = 0 ; end fprintf ('KLU max scale: err %8.2e t: %8.4f\n', e4, t4) ; try tic ; x3 = klu (A, '\', b, opts_sum) ; t3 = toc ; e3 = norm (A*x3-b) ; catch t3 = 0 ; e3 = 0 ; end fprintf ('KLU sum scale: err %8.2e t: %8.4f\n', e3, t3) ; tic x1 = A\b ; t1 = toc ; e1 = norm (A*x1-b) ; fprintf ('matlab: err %8.2e t: %8.4f\n', e1, t1) ; fprintf (' speedup %8.2f\n', t1 / t4) ; clear Prob if (do_diary) diary off diary on end end catch % out-of-memory is OK, other errors are not disp (lasterr) ; if (isempty (strfind (lasterr, 'Out of memory'))) error (lasterr) ; %#ok else fprintf ('test terminated early, but otherwise OK\n') ; end end close (h) ; SuiteSparse/KLU/MATLAB/Makefile0000644001170100242450000003520310617133712015006 0ustar davisfac#=============================================================================== # KLU/MATLAB/Makefile #=============================================================================== default: all include ../../UFconfig/UFconfig.mk # with CHOLMOD and supporting functions (CAMD, CCOLAMD, METIS) I = -I. -I../../AMD/Include -I../../COLAMD/Include \ -I../Include -I../../UFconfig -I../../BTF/Include -I../User \ -I../../CCOLAMD/Include -I../../CAMD/Include \ -I$(METIS_PATH)/Lib -I../../CHOLMOD/Include all: klu MX = $(MEX) -DDLONG -DNLARGEFILE $(I) distclean: purge purge: clean - $(RM) *.mex* rename.h clean: - $(RM) $(CLEAN) #=============================================================================== AMD_INC = ../../AMD/Include/amd.h ../../AMD/Include/amd_internal.h AMD = \ amd_1.o \ amd_2.o \ amd_aat.o \ amd_control.o \ amd_defaults.o \ amd_dump.o \ amd_global.o \ amd_info.o \ amd_order.o \ amd_postorder.o \ amd_post_tree.o \ amd_preprocess.o \ amd_valid.o $(AMD): $(AMD_INC) amd_1.o: ../../AMD/Source/amd_1.c $(MX) -c $< amd_2.o: ../../AMD/Source/amd_2.c $(MX) -c $< amd_aat.o: ../../AMD/Source/amd_aat.c $(MX) -c $< amd_control.o: ../../AMD/Source/amd_control.c $(MX) -c $< amd_defaults.o: ../../AMD/Source/amd_defaults.c $(MX) -c $< amd_dump.o: ../../AMD/Source/amd_dump.c $(MX) -c $< amd_global.o: ../../AMD/Source/amd_global.c $(MX) -c $< amd_info.o: ../../AMD/Source/amd_info.c $(MX) -c $< amd_order.o: ../../AMD/Source/amd_order.c $(MX) -c $< amd_postorder.o: ../../AMD/Source/amd_postorder.c $(MX) -c $< amd_post_tree.o: ../../AMD/Source/amd_post_tree.c $(MX) -c $< amd_preprocess.o: ../../AMD/Source/amd_preprocess.c $(MX) -c $< amd_valid.o: ../../AMD/Source/amd_valid.c $(MX) -c $< #=============================================================================== CAMD_INC = ../../CAMD/Include/camd.h ../../CAMD/Include/camd_internal.h CAMD = \ camd_1.o \ camd_2.o \ camd_aat.o \ camd_control.o \ camd_defaults.o \ camd_dump.o \ camd_global.o \ camd_info.o \ camd_order.o \ camd_postorder.o \ camd_preprocess.o \ camd_valid.o $(CAMD): $(CAMD_INC) camd_1.o: ../../CAMD/Source/camd_1.c $(MX) -c $< camd_2.o: ../../CAMD/Source/camd_2.c $(MX) -c $< camd_aat.o: ../../CAMD/Source/camd_aat.c $(MX) -c $< camd_control.o: ../../CAMD/Source/camd_control.c $(MX) -c $< camd_defaults.o: ../../CAMD/Source/camd_defaults.c $(MX) -c $< camd_dump.o: ../../CAMD/Source/camd_dump.c $(MX) -c $< camd_global.o: ../../CAMD/Source/camd_global.c $(MX) -c $< camd_info.o: ../../CAMD/Source/camd_info.c $(MX) -c $< camd_order.o: ../../CAMD/Source/camd_order.c $(MX) -c $< camd_postorder.o: ../../CAMD/Source/camd_postorder.c $(MX) -c $< camd_post_tree.o: ../../CAMD/Source/camd_post_tree.c $(MX) -c $< camd_preprocess.o: ../../CAMD/Source/camd_preprocess.c $(MX) -c $< camd_valid.o: ../../CAMD/Source/camd_valid.c $(MX) -c $< #=============================================================================== COLAMD_INC = ../../COLAMD/Include/colamd.h COLAMD = colamd.o colamd_global.o $(COLAMD): $(COLAMD_INC) colamd.o: ../../COLAMD/Source/colamd.c $(MX) -c $< colamd_global.o: ../../COLAMD/Source/colamd_global.c $(MX) -c $< #=============================================================================== CCOLAMD_INC = ../../CCOLAMD/Include/ccolamd.h CCOLAMD = ccolamd.o ccolamd_global.o $(CCOLAMD): $(CCOLAMD_INC) ccolamd.o: ../../CCOLAMD/Source/ccolamd.c $(MX) -c $< ccolamd_global.o: ../../CCOLAMD/Source/ccolamd_global.c $(MX) -c $< #=============================================================================== # patch METIS 4.0.1 rename.h: $(METIS_PATH)/Lib/rename.h echo '/* do not edit this file; generated by KLU/MATLAB/Makefile */' > rename.h echo '#undef log2' >> rename.h echo '#include "$(METIS_PATH)/Lib/rename.h"' >> rename.h echo '#undef log2' >> rename.h echo '#define log2 METIS__log2' >> rename.h echo '#include "mex.h"' >> rename.h echo '#define malloc mxMalloc' >> rename.h echo '#define free mxFree' >> rename.h echo '#define calloc mxCalloc' >> rename.h echo '#define realloc mxRealloc' >> rename.h METIS_INC = rename.h \ $(METIS_PATH)/Lib/defs.h \ $(METIS_PATH)/Lib/macros.h \ $(METIS_PATH)/Lib/metis.h \ $(METIS_PATH)/Lib/proto.h \ $(METIS_PATH)/Lib/rename.h \ $(METIS_PATH)/Lib/struct.h METIS = \ balance.o \ bucketsort.o \ ccgraph.o \ coarsen.o \ compress.o \ debug.o \ estmem.o \ fm.o \ fortran.o \ frename.o \ graph.o \ initpart.o \ kmetis.o \ kvmetis.o \ kwayfm.o \ kwayrefine.o \ kwayvolfm.o \ kwayvolrefine.o \ match.o \ mbalance2.o \ mbalance.o \ mcoarsen.o \ memory.o \ mesh.o \ meshpart.o \ mfm2.o \ mfm.o \ mincover.o \ minitpart2.o \ minitpart.o \ mkmetis.o \ mkwayfmh.o \ mkwayrefine.o \ mmatch.o \ mmd.o \ mpmetis.o \ mrefine2.o \ mrefine.o \ mutil.o \ myqsort.o \ ometis.o \ parmetis.o \ pmetis.o \ pqueue.o \ refine.o \ separator.o \ sfm.o \ srefine.o \ stat.o \ subdomains.o \ timing.o \ util.o $(METIS): $(METIS_INC) balance.o: $(METIS_PATH)/Lib/balance.c $(MX) -c $< bucketsort.o: $(METIS_PATH)/Lib/bucketsort.c $(MX) -c $< ccgraph.o: $(METIS_PATH)/Lib/ccgraph.c $(MX) -c $< coarsen.o: $(METIS_PATH)/Lib/coarsen.c $(MX) -c $< compress.o: $(METIS_PATH)/Lib/compress.c $(MX) -c $< debug.o: $(METIS_PATH)/Lib/debug.c $(MX) -c $< estmem.o: $(METIS_PATH)/Lib/estmem.c $(MX) -c $< fm.o: $(METIS_PATH)/Lib/fm.c $(MX) -c $< fortran.o: $(METIS_PATH)/Lib/fortran.c $(MX) -c $< frename.o: $(METIS_PATH)/Lib/frename.c $(MX) -c $< graph.o: $(METIS_PATH)/Lib/graph.c $(MX) -c $< initpart.o: $(METIS_PATH)/Lib/initpart.c $(MX) -c $< kmetis.o: $(METIS_PATH)/Lib/kmetis.c $(MX) -c $< kvmetis.o: $(METIS_PATH)/Lib/kvmetis.c $(MX) -c $< kwayfm.o: $(METIS_PATH)/Lib/kwayfm.c $(MX) -c $< kwayrefine.o: $(METIS_PATH)/Lib/kwayrefine.c $(MX) -c $< kwayvolfm.o: $(METIS_PATH)/Lib/kwayvolfm.c $(MX) -c $< kwayvolrefine.o: $(METIS_PATH)/Lib/kwayvolrefine.c $(MX) -c $< match.o: $(METIS_PATH)/Lib/match.c $(MX) -c $< mbalance2.o: $(METIS_PATH)/Lib/mbalance2.c $(MX) -c $< mbalance.o: $(METIS_PATH)/Lib/mbalance.c $(MX) -c $< mcoarsen.o: $(METIS_PATH)/Lib/mcoarsen.c $(MX) -c $< memory.o: $(METIS_PATH)/Lib/memory.c $(MX) -c $< mesh.o: $(METIS_PATH)/Lib/mesh.c $(MX) -c $< meshpart.o: $(METIS_PATH)/Lib/meshpart.c $(MX) -c $< mfm2.o: $(METIS_PATH)/Lib/mfm2.c $(MX) -c $< mfm.o: $(METIS_PATH)/Lib/mfm.c $(MX) -c $< mincover.o: $(METIS_PATH)/Lib/mincover.c $(MX) -c $< minitpart2.o: $(METIS_PATH)/Lib/minitpart2.c $(MX) -c $< minitpart.o: $(METIS_PATH)/Lib/minitpart.c $(MX) -c $< mkmetis.o: $(METIS_PATH)/Lib/mkmetis.c $(MX) -c $< mkwayfmh.o: $(METIS_PATH)/Lib/mkwayfmh.c $(MX) -c $< mkwayrefine.o: $(METIS_PATH)/Lib/mkwayrefine.c $(MX) -c $< mmatch.o: $(METIS_PATH)/Lib/mmatch.c $(MX) -c $< mmd.o: $(METIS_PATH)/Lib/mmd.c $(MX) -c $< mpmetis.o: $(METIS_PATH)/Lib/mpmetis.c $(MX) -c $< mrefine2.o: $(METIS_PATH)/Lib/mrefine2.c $(MX) -c $< mrefine.o: $(METIS_PATH)/Lib/mrefine.c $(MX) -c $< mutil.o: $(METIS_PATH)/Lib/mutil.c $(MX) -c $< myqsort.o: $(METIS_PATH)/Lib/myqsort.c $(MX) -c $< ometis.o: $(METIS_PATH)/Lib/ometis.c $(MX) -c $< parmetis.o: $(METIS_PATH)/Lib/parmetis.c $(MX) -c $< pmetis.o: $(METIS_PATH)/Lib/pmetis.c $(MX) -c $< pqueue.o: $(METIS_PATH)/Lib/pqueue.c $(MX) -c $< refine.o: $(METIS_PATH)/Lib/refine.c $(MX) -c $< separator.o: $(METIS_PATH)/Lib/separator.c $(MX) -c $< sfm.o: $(METIS_PATH)/Lib/sfm.c $(MX) -c $< srefine.o: $(METIS_PATH)/Lib/srefine.c $(MX) -c $< stat.o: $(METIS_PATH)/Lib/stat.c $(MX) -c $< subdomains.o: $(METIS_PATH)/Lib/subdomains.c $(MX) -c $< timing.o: $(METIS_PATH)/Lib/timing.c $(MX) -c $< util.o: $(METIS_PATH)/Lib/util.c $(MX) -c $< #=============================================================================== CHOLMOD_INC = \ ../../CHOLMOD/Include/cholmod_blas.h \ ../../CHOLMOD/Include/cholmod_cholesky.h \ ../../CHOLMOD/Include/cholmod_complexity.h \ ../../CHOLMOD/Include/cholmod_config.h \ ../../CHOLMOD/Include/cholmod_core.h \ ../../CHOLMOD/Include/cholmod.h \ ../../CHOLMOD/Include/cholmod_internal.h \ ../../CHOLMOD/Include/cholmod_io64.h \ ../../CHOLMOD/Include/cholmod_partition.h \ ../../CHOLMOD/Include/cholmod_template.h CHOLMOD = \ cholmod_amd.o \ cholmod_analyze.o \ cholmod_colamd.o \ cholmod_etree.o \ cholmod_postorder.o \ cholmod_rowcolcounts.o \ cholmod_aat.o \ cholmod_add.o \ cholmod_band.o \ cholmod_change_factor.o \ cholmod_common.o \ cholmod_complex.o \ cholmod_copy.o \ cholmod_dense.o \ cholmod_error.o \ cholmod_factor.o \ cholmod_memory.o \ cholmod_sparse.o \ cholmod_transpose.o \ cholmod_triplet.o \ cholmod_camd.o \ cholmod_ccolamd.o \ cholmod_csymamd.o \ cholmod_metis.o \ cholmod_nesdis.o $(CHOLMOD): $(CHOLMOD_INC) CH = -DNSUPERNODAL -DNMODIFY -DNMATRIXOPS -DNCHECK cholmod_amd.o: ../../CHOLMOD/Cholesky/cholmod_amd.c $(MX) $(CH) -c $< cholmod_analyze.o: ../../CHOLMOD/Cholesky/cholmod_analyze.c $(MX) $(CH) -c $< cholmod_colamd.o: ../../CHOLMOD/Cholesky/cholmod_colamd.c $(MX) $(CH) -c $< cholmod_etree.o: ../../CHOLMOD/Cholesky/cholmod_etree.c $(MX) $(CH) -c $< cholmod_postorder.o: ../../CHOLMOD/Cholesky/cholmod_postorder.c $(MX) $(CH) -c $< cholmod_rowcolcounts.o: ../../CHOLMOD/Cholesky/cholmod_rowcolcounts.c $(MX) $(CH) -c $< cholmod_aat.o: ../../CHOLMOD/Core/cholmod_aat.c $(MX) $(CH) -c $< cholmod_add.o: ../../CHOLMOD/Core/cholmod_add.c $(MX) $(CH) -c $< cholmod_band.o: ../../CHOLMOD/Core/cholmod_band.c $(MX) $(CH) -c $< cholmod_change_factor.o: ../../CHOLMOD/Core/cholmod_change_factor.c \ ../../CHOLMOD/Core/t_cholmod_change_factor.c $(MX) $(CH) -c $< cholmod_common.o: ../../CHOLMOD/Core/cholmod_common.c $(MX) $(CH) -c $< cholmod_complex.o: ../../CHOLMOD/Core/cholmod_complex.c $(MX) $(CH) -c $< cholmod_copy.o: ../../CHOLMOD/Core/cholmod_copy.c $(MX) $(CH) -c $< cholmod_dense.o: ../../CHOLMOD/Core/cholmod_dense.c \ ../../CHOLMOD/Core/t_cholmod_dense.c $(MX) $(CH) -c $< cholmod_error.o: ../../CHOLMOD/Core/cholmod_error.c $(MX) $(CH) -c $< cholmod_factor.o: ../../CHOLMOD/Core/cholmod_factor.c $(MX) $(CH) -c $< cholmod_memory.o: ../../CHOLMOD/Core/cholmod_memory.c $(MX) $(CH) -c $< cholmod_sparse.o: ../../CHOLMOD/Core/cholmod_sparse.c $(MX) $(CH) -c $< cholmod_transpose.o: ../../CHOLMOD/Core/cholmod_transpose.c \ ../../CHOLMOD/Core/t_cholmod_transpose.c $(MX) $(CH) -c $< cholmod_triplet.o: ../../CHOLMOD/Core/cholmod_triplet.c \ ../../CHOLMOD/Core/t_cholmod_triplet.c $(MX) $(CH) -c $< cholmod_camd.o: ../../CHOLMOD/Partition/cholmod_camd.c $(MX) $(CH) -c $< cholmod_ccolamd.o: ../../CHOLMOD/Partition/cholmod_ccolamd.c $(MX) $(CH) -c $< cholmod_csymamd.o: ../../CHOLMOD/Partition/cholmod_csymamd.c $(MX) $(CH) -c $< cholmod_metis.o: ../../CHOLMOD/Partition/cholmod_metis.c $(MX) $(CH) -c $< cholmod_nesdis.o: ../../CHOLMOD/Partition/cholmod_nesdis.c $(MX) $(CH) -c $< #=============================================================================== BTF_INC = ../../BTF/Include/btf.h ../../BTF/Include/btf_internal.h BTF = btf_maxtrans.o btf_order.o btf_strongcomp.o $(BTF): $(BTF_INC) btf_maxtrans.o: ../../BTF/Source/btf_maxtrans.c $(MX) -c $< btf_order.o: ../../BTF/Source/btf_order.c $(MX) -c $< btf_strongcomp.o: ../../BTF/Source/btf_strongcomp.c $(MX) -c $< #=============================================================================== KLU_INC = ../Include/klu.h ../Include/klu_internal.h ../Include/klu_version.h \ ../User/klu_cholmod.h KLU_L = klu_l.o klu_l_kernel.o klu_l_dump.o \ klu_l_factor.o klu_l_free_numeric.o klu_l_solve.o \ klu_l_scale.o klu_l_refactor.o \ klu_l_tsolve.o klu_l_diagnostics.o klu_l_sort.o klu_l_extract.o KLU_ZL = klu_zl.o klu_zl_kernel.o klu_zl_dump.o \ klu_zl_factor.o klu_zl_free_numeric.o klu_zl_solve.o \ klu_zl_scale.o klu_zl_refactor.o \ klu_zl_tsolve.o klu_zl_diagnostics.o klu_zl_sort.o klu_zl_extract.o COMMON = klu_free_symbolic.o klu_defaults.o klu_analyze_given.o \ klu_analyze.o klu_memory.o USER = klu_l_cholmod.o KLU = $(COMMON) $(KLU_L) $(KLU_ZL) $(USER) $(KLU): $(KLU_INC) #------------------------------------------------------------------------------- klu_l.o: ../Source/klu.c $(MX) -c $< $(MV) klu.o $@ klu_zl.o: ../Source/klu.c $(MX) -c -DCOMPLEX $< $(MV) klu.o $@ klu_l_kernel.o: ../Source/klu_kernel.c $(MX) -c $< $(MV) klu_kernel.o $@ klu_zl_kernel.o: ../Source/klu_kernel.c $(MX) -c -DCOMPLEX $< $(MV) klu_kernel.o $@ klu_l_sort.o: ../Source/klu_sort.c $(MX) -c $< $(MV) klu_sort.o $@ klu_zl_sort.o: ../Source/klu_sort.c $(MX) -c -DCOMPLEX $< $(MV) klu_sort.o $@ klu_l_diagnostics.o: ../Source/klu_diagnostics.c $(MX) -c $< $(MV) klu_diagnostics.o $@ klu_zl_diagnostics.o: ../Source/klu_diagnostics.c $(MX) -c -DCOMPLEX $< $(MV) klu_diagnostics.o $@ klu_l_dump.o: ../Source/klu_dump.c $(MX) -c $< $(MV) klu_dump.o $@ klu_zl_dump.o: ../Source/klu_dump.c $(MX) -c -DCOMPLEX $< $(MV) klu_dump.o $@ klu_l_factor.o: ../Source/klu_factor.c $(MX) -c $< $(MV) klu_factor.o $@ klu_zl_factor.o: ../Source/klu_factor.c $(MX) -c -DCOMPLEX $< $(MV) klu_factor.o $@ klu_l_free_numeric.o: ../Source/klu_free_numeric.c $(MX) -c $< $(MV) klu_free_numeric.o $@ klu_zl_free_numeric.o: ../Source/klu_free_numeric.c $(MX) -c -DCOMPLEX $< $(MV) klu_free_numeric.o $@ klu_l_extract.o: ../Source/klu_extract.c $(MX) -c $< $(MV) klu_extract.o $@ klu_zl_extract.o: ../Source/klu_extract.c $(MX) -c -DCOMPLEX $< $(MV) klu_extract.o $@ klu_l_refactor.o: ../Source/klu_refactor.c $(MX) -c $< $(MV) klu_refactor.o $@ klu_zl_refactor.o: ../Source/klu_refactor.c $(MX) -c -DCOMPLEX $< $(MV) klu_refactor.o $@ klu_l_scale.o: ../Source/klu_scale.c $(MX) -c $< $(MV) klu_scale.o $@ klu_zl_scale.o: ../Source/klu_scale.c $(MX) -c -DCOMPLEX $< $(MV) klu_scale.o $@ klu_l_solve.o: ../Source/klu_solve.c $(MX) -c $< $(MV) klu_solve.o $@ klu_zl_solve.o: ../Source/klu_solve.c $(MX) -c -DCOMPLEX $< $(MV) klu_solve.o $@ klu_l_tsolve.o: ../Source/klu_tsolve.c $(MX) -c $< $(MV) klu_tsolve.o $@ klu_zl_tsolve.o: ../Source/klu_tsolve.c $(MX) -c -DCOMPLEX $< $(MV) klu_tsolve.o $@ #------------------------------------------------------------------------------- klu_analyze.o: ../Source/klu_analyze.c $(MX) -c $< klu_analyze_given.o: ../Source/klu_analyze_given.c $(MX) -c $< klu_defaults.o: ../Source/klu_defaults.c $(MX) -c $< klu_free_symbolic.o: ../Source/klu_free_symbolic.c $(MX) -c $< klu_memory.o: ../Source/klu_memory.c $(MX) -c $< #------------------------------------------------------------------------------- klu_l_cholmod.o: ../User/klu_l_cholmod.c $(MX) $(CH) -c $< #=============================================================================== OBJ = $(AMD) $(CAMD) $(COLAMD) $(CCOLAMD) $(METIS) $(CHOLMOD) $(KLU) $(BTF) klu: klu_mex.c $(OBJ) $(MX) -output klu klu_mex.c $(OBJ) SuiteSparse/KLU/MATLAB/klu_demo.m.out0000644001170100242450000000325310711435170016127 0ustar davisfacklu_demo MATLAB condest: 1.42443e+12 KLU condest: 1.42443e+12 cond: 3.25816e+11 KLU with scaling, AMD ordering and condition number estimate: resid: 3.88932e-13 KLU condest: 1.42443e+12 rgrowth: 1.85769e-05 noffdiag: 12 nrealloc: 0 rcond: 7.1253e-09 rgrowth: 1.8577e-05 flops: 31592 nblocks: 166 ordering: 0 scale: 1 lnz: 1923 unz: 1892 offnz: 450 tol: 1.0000e-03 memory: 136748 KLU with COLAMD ordering resid: 1.00707e-11 noffdiag: 14 nrealloc: 0 rcond: 9.1888e-10 rgrowth: 4.3963e-08 flops: 42513 nblocks: 166 ordering: 1 scale: 2 lnz: 1956 unz: 2490 offnz: 450 tol: 1.0000e-03 memory: 397692 KLU with natural ordering (lots of fillin) resid: 3.13025e-13 noffdiag: 437 nrealloc: 0 rcond: 6.4525e-08 rgrowth: 1.7654e-04 flops: 328911 nblocks: 2 ordering: 2 scale: 2 lnz: 7846 unz: 7332 offnz: 40 tol: 1.0000e-03 memory: 453556 KLU with CHOLMOD(A'*A) ordering resid: 1.7568e-13 noffdiag: 24 nrealloc: 0 rcond: 4.1814e-09 rgrowth: 1.0676e-04 flops: 36747 nblocks: 166 ordering: 3 scale: 2 lnz: 2020 unz: 2227 offnz: 450 tol: 1.0000e-03 memory: 191132 KLU with CHOLMOD(A+A') ordering resid: 5.1045e-13 noffdiag: 13 nrealloc: 0 rcond: 3.9046e-11 rgrowth: 2.4378e-06 flops: 31925 nblocks: 166 ordering: 4 scale: 2 lnz: 2000 unz: 1878 offnz: 450 tol: 1.0000e-03 memory: 136044 diary off SuiteSparse/KLU/MATLAB/klu.m0000644001170100242450000000717010620376517014327 0ustar davisfacfunction [LU_or_x,info,c] = klu (A,operation,b,opts) %#ok %KLU sparse left-looking LU factorization, using a block triangular form. % % Example: % LU = klu (A) factorizes R\A(p,q) into L*U+F, returning a struct % x = klu (A,'\',b) x = A\b, using KLU % x = klu (b,'/',A) x = b/A, using KLU % x = klu (LU,'\',b) x = A\b, where LU = klu(A) % x = klu (b,'/',LU) x = b/A, where LU = klu(A) % % KLU(A) factorizes a square sparse matrix, L*U+F = R\A(p,q), where L and U % are the factors of the diagonal blocks of the block, F are the entries % above the diagonal blocks. r corresponds to the 3rd output of dmperm; it % specifies where the block boundaries are. The kth block consists of % rows/columns r(k) to r(k+1)-1 of A(p,q). % % Note that the use of the scale factor R differs between KLU and UMFPACK % (and the LU function, which is based on UMFPACK). In LU, the factorization % is L*U = P*(R1\A)*Q; in KLU it is L*U+F = R2\(P*A*Q). R1 and R2 are related % via R2 = P*R1*P', or equivalently R2 = R1(p,p). % % The LU output is a struct containing members L, U, p, q, R, F, and r. % % opts is an optional input struct which appears as the last input argument. % Entries not present are set to their defaults: % % opts.tol 0.001 partial pivoting tolerance; valid range 0 to 1. % opts.btf 1 use block triangular form (BTF) if nonzero % opts.ordering 0 how each block is ordered: % 0: AMD, 1: COLAMD, 2: natural, % 3: CHOLMOD's ordering of (A'*A), % 4: CHOLMOD's ordering of (A+A') % opts.scale -1 1: R = diag(sum(abs(A)')), row-sum % 2: R = diag(max(abs(A)')), max in each row % otherwise: none (R=I) % opts.maxwork 0 if > 0, limit work in BTF ordering to % opts.maxwork*nnz(A); no limit if <= 0. % % The CHOLMOD ordering is to try AMD (for A+A') or COLAMD (for A'*A) % first. If the fill-in with AMD or COLAMD is high, METIS is tried (on % A+A' or A'*A), and the best ordering found is selected. CHOLMOD, METIS, % CAMD, and CCOLAMD are required. If not available, only ordering options % 0, 1, and 2 may be used (AMD and COLAMD are always required by KLU). % % Two optional outputs, [LU,info,c] = klu (A) or [x,info,c] = klu (A,'\',b) % provide statistics about the factorization: % % info.noffdiag number of off-diagonal pivots chosen (after preordering) % info.nrealloc number of memory reallocations of L and U % info.rcond a very cheap estimate of 1/(condition number) % info.rgrowth reciprocal pivot growth % info.flops flop count % info.nblocks # of blocks in BTF form (1 if not computed) % info.ordering AMD, COLAMD, natural, cholmod(AA'), cholmod(A+A') % info.scale scaling (<=0: none, 1: sum, 2: max) % info.lnz nnz(L), including diagonal % info.unz nnz(U), including diagonal % info.offnz nnz(F) % info.tol pivot tolerance used % info.memory peak memory usage in bytes % c the same as MATLAB's condest % % info and c are relevant only if the matrix is factorized (LU = klu (A), % x = klu (A,'/',b), or x = klu (b,'/',A) usages). % % See also BTF, LU, DMPERM, CONDEST, CHOLMOD, AMD, COLAMD, CAMD, CCOLAMD. % Copyright 2004-2007 Timothy A. Davis, Univ. of Florida % http://www.cise.ufl.edu/research/sparse error ('klu mexFunction not found') ; SuiteSparse/KLU/MATLAB/klu_install.m0000644001170100242450000000312610620376415016047 0ustar davisfacfunction klu_install (with_cholmod) %KLU_INSTALL compiles and installs the KLU, BTF, AMD, and COLAMD mexFunctions % % Example: % klu_install % compiles KLU without CHOLMOD % klu_install (1) % with CHOLMOD, CCAMD, CCOLAMD, and METIS % % KLU relies on AMD, COLAMD, and BTF for its ordering options, and can % optionally use CHOLMOD, CCOLAMD, CAMD, and METIS as well. By default, % CHOLMOD, CCOLAMD, CAMD, and METIS are not used. % % See http://www-users.cs.umn.edu/~karypis/metis for a copy of METIS 4.0.1. % % You must type the klu_install command while in the KLU/MATLAB directory. % % See also klu, btf % Copyright 2004-2007 Timothy A. Davis, Univ. of Florida if (nargin < 1) with_cholmod = 0 ; end % compile KLU and add to the path klu_make (with_cholmod) ; klu_path = pwd ; addpath (klu_path) fprintf ('\nNow compiling the AMD, COLAMD, and BTF mexFunctions:\n') ; % compile BTF and add to the path cd ../../BTF/MATLAB btf_make btf_path = pwd ; addpath (btf_path) % compile AMD and add to the path cd ../../AMD/MATLAB amd_make amd_path = pwd ; addpath (amd_path) % compile COLAMD and add to the path cd ../../COLAMD/MATLAB colamd_make colamd_path = pwd ; addpath (colamd_path) cd (klu_path) fprintf ('\nThe following paths have been added. You may wish to add them\n') ; fprintf ('permanently, using the MATLAB pathtool command.\n') ; fprintf ('%s\n', klu_path) ; fprintf ('%s\n', amd_path) ; fprintf ('%s\n', colamd_path) ; fprintf ('%s\n', btf_path) ; fprintf ('\nTo try your new mexFunctions, cut-and-paste this command:\n') ; fprintf ('klu_demo, btf_demo, amd_demo, colamd_demo\n') ; SuiteSparse/KLU/MATLAB/Contents.m0000644001170100242450000000072210620376375015327 0ustar davisfac% KLU: a "Clark Kent" LU factorization algorithm % % klu - sparse left-looking LU factorization, using a block triangular form. % klu_install - compiles and installs the KLU, BTF, AMD, and COLAMD mexFunctions % klu_demo - KLU demo % klu_make - compiles the KLU mexFunctions % % Example: % % LU = klu (A) ; % x = klu (A, '\', b) ; % x = klu (LU, '\', b) ; % % Copyright 2004-2007 Timothy A. Davis, Univ. of Florida % KLU Version 1.0. SuiteSparse/KLU/MATLAB/Makefile_no_CHOLMOD0000644001170100242450000001346610617133736016664 0ustar davisfac#=============================================================================== # KLU/MATLAB/Makefile_no_CHOLMOD #=============================================================================== # Makefile for klu mexFunction, without the use of CHOLMOD. Ordering options # 3 and 4 for klu will not be available. See "help klu" in MATLAB for more # details. Usage: # # make -f Makefile_no_CHOLMOD default: all include ../../UFconfig/UFconfig.mk # without CHOLMOD I = -I. -I../../AMD/Include -I../../AMD/Source -I../../COLAMD/Include \ -I../Include -I../../UFconfig -I../../BTF/Include all: klu MX = $(MEX) -DDLONG -D_FILE_OFFSET_BITS=64 -D_LARGEFILE64_SOURCE $(I) distclean: purge purge: clean - $(RM) *.mex* rename.h clean: - $(RM) $(CLEAN) #=============================================================================== AMD_INC = ../../AMD/Include/amd.h ../../AMD/Include/amd_internal.h AMD = \ amd_1.o \ amd_2.o \ amd_aat.o \ amd_control.o \ amd_defaults.o \ amd_dump.o \ amd_global.o \ amd_info.o \ amd_order.o \ amd_postorder.o \ amd_post_tree.o \ amd_preprocess.o \ amd_valid.o $(AMD): $(AMD_INC) amd_1.o: ../../AMD/Source/amd_1.c $(MX) -c $< amd_2.o: ../../AMD/Source/amd_2.c $(MX) -c $< amd_aat.o: ../../AMD/Source/amd_aat.c $(MX) -c $< amd_control.o: ../../AMD/Source/amd_control.c $(MX) -c $< amd_defaults.o: ../../AMD/Source/amd_defaults.c $(MX) -c $< amd_dump.o: ../../AMD/Source/amd_dump.c $(MX) -c $< amd_global.o: ../../AMD/Source/amd_global.c $(MX) -c $< amd_info.o: ../../AMD/Source/amd_info.c $(MX) -c $< amd_order.o: ../../AMD/Source/amd_order.c $(MX) -c $< amd_postorder.o: ../../AMD/Source/amd_postorder.c $(MX) -c $< amd_post_tree.o: ../../AMD/Source/amd_post_tree.c $(MX) -c $< amd_preprocess.o: ../../AMD/Source/amd_preprocess.c $(MX) -c $< amd_valid.o: ../../AMD/Source/amd_valid.c $(MX) -c $< #=============================================================================== COLAMD_INC = ../../COLAMD/Include/colamd.h COLAMD = colamd.o colamd_global.o $(COLAMD): $(COLAMD_INC) colamd.o: ../../COLAMD/Source/colamd.c $(MX) -c $< colamd_global.o: ../../COLAMD/Source/colamd_global.c $(MX) -c $< #=============================================================================== BTF_INC = ../../BTF/Include/btf.h ../../BTF/Include/btf_internal.h BTF = btf_maxtrans.o btf_order.o btf_strongcomp.o $(BTF): $(BTF_INC) btf_maxtrans.o: ../../BTF/Source/btf_maxtrans.c $(MX) -c $< btf_order.o: ../../BTF/Source/btf_order.c $(MX) -c $< btf_strongcomp.o: ../../BTF/Source/btf_strongcomp.c $(MX) -c $< #=============================================================================== KLU_INC = ../Include/klu.h ../Include/klu_internal.h ../Include/klu_version.h KLU_L = klu_l.o klu_l_kernel.o klu_l_dump.o \ klu_l_factor.o klu_l_free_numeric.o klu_l_solve.o \ klu_l_scale.o klu_l_refactor.o \ klu_l_tsolve.o klu_l_diagnostics.o klu_l_sort.o klu_l_extract.o KLU_ZL = klu_zl.o klu_zl_kernel.o klu_zl_dump.o \ klu_zl_factor.o klu_zl_free_numeric.o klu_zl_solve.o \ klu_zl_scale.o klu_zl_refactor.o \ klu_zl_tsolve.o klu_zl_diagnostics.o klu_zl_sort.o klu_zl_extract.o COMMON = klu_free_symbolic.o klu_defaults.o klu_analyze_given.o \ klu_analyze.o klu_memory.o KLU = $(COMMON) $(KLU_L) $(KLU_ZL) $(KLU): $(KLU_INC) #------------------------------------------------------------------------------- klu_l.o: ../Source/klu.c $(MX) -c $< $(MV) klu.o $@ klu_zl.o: ../Source/klu.c $(MX) -c -DCOMPLEX $< $(MV) klu.o $@ klu_l_kernel.o: ../Source/klu_kernel.c $(MX) -c $< $(MV) klu_kernel.o $@ klu_zl_kernel.o: ../Source/klu_kernel.c $(MX) -c -DCOMPLEX $< $(MV) klu_kernel.o $@ klu_l_sort.o: ../Source/klu_sort.c $(MX) -c $< $(MV) klu_sort.o $@ klu_zl_sort.o: ../Source/klu_sort.c $(MX) -c -DCOMPLEX $< $(MV) klu_sort.o $@ klu_l_diagnostics.o: ../Source/klu_diagnostics.c $(MX) -c $< $(MV) klu_diagnostics.o $@ klu_zl_diagnostics.o: ../Source/klu_diagnostics.c $(MX) -c -DCOMPLEX $< $(MV) klu_diagnostics.o $@ klu_l_dump.o: ../Source/klu_dump.c $(MX) -c $< $(MV) klu_dump.o $@ klu_zl_dump.o: ../Source/klu_dump.c $(MX) -c -DCOMPLEX $< $(MV) klu_dump.o $@ klu_l_factor.o: ../Source/klu_factor.c $(MX) -c $< $(MV) klu_factor.o $@ klu_zl_factor.o: ../Source/klu_factor.c $(MX) -c -DCOMPLEX $< $(MV) klu_factor.o $@ klu_l_free_numeric.o: ../Source/klu_free_numeric.c $(MX) -c $< $(MV) klu_free_numeric.o $@ klu_zl_free_numeric.o: ../Source/klu_free_numeric.c $(MX) -c -DCOMPLEX $< $(MV) klu_free_numeric.o $@ klu_l_extract.o: ../Source/klu_extract.c $(MX) -c $< $(MV) klu_extract.o $@ klu_zl_extract.o: ../Source/klu_extract.c $(MX) -c -DCOMPLEX $< $(MV) klu_extract.o $@ klu_l_refactor.o: ../Source/klu_refactor.c $(MX) -c $< $(MV) klu_refactor.o $@ klu_zl_refactor.o: ../Source/klu_refactor.c $(MX) -c -DCOMPLEX $< $(MV) klu_refactor.o $@ klu_l_scale.o: ../Source/klu_scale.c $(MX) -c $< $(MV) klu_scale.o $@ klu_zl_scale.o: ../Source/klu_scale.c $(MX) -c -DCOMPLEX $< $(MV) klu_scale.o $@ klu_l_solve.o: ../Source/klu_solve.c $(MX) -c $< $(MV) klu_solve.o $@ klu_zl_solve.o: ../Source/klu_solve.c $(MX) -c -DCOMPLEX $< $(MV) klu_solve.o $@ klu_l_tsolve.o: ../Source/klu_tsolve.c $(MX) -c $< $(MV) klu_tsolve.o $@ klu_zl_tsolve.o: ../Source/klu_tsolve.c $(MX) -c -DCOMPLEX $< $(MV) klu_tsolve.o $@ #------------------------------------------------------------------------------- klu_analyze.o: ../Source/klu_analyze.c $(MX) -c $< klu_analyze_given.o: ../Source/klu_analyze_given.c $(MX) -c $< klu_defaults.o: ../Source/klu_defaults.c $(MX) -c $< klu_free_symbolic.o: ../Source/klu_free_symbolic.c $(MX) -c $< klu_memory.o: ../Source/klu_memory.c $(MX) -c $< #=============================================================================== OBJ = $(AMD) $(COLAMD) $(KLU) $(BTF) klu: klu_mex.c $(OBJ) $(MX) -DNCHOLMOD -output klu klu_mex.c $(OBJ) SuiteSparse/KLU/MATLAB/klu_demo.m0000644001170100242450000000366010620376407015331 0ustar davisfacfunction klu_demo % KLU demo % % Example: % klu_demo % % See also klu, btf % Copyright 2004-2007 Timothy A. Davis, Univ. of Florida load west0479 A = west0479 ; n = size (A,1) ; b = rand (n,1) ; clf subplot (2,2,1) ; spy (A) title ('west0479') ; subplot (2,2,2) ; [p, q, r] = btf (A) ; drawbtf (A, p, q, r) ; title ('BTF form') ; [x,info,c] = klu (A, '\', b) ; matlab_condest = condest (A) ; matlab_cond = cond (full (A)) ; fprintf ('MATLAB condest: %g KLU condest: %g cond: %g\n', ... matlab_condest, c, matlab_cond) ; fprintf ('\nKLU with scaling, AMD ordering and condition number estimate:\n') ; [LU,info] = klu (A, struct ('ordering',0, 'scale', 1)) ; x = klu (LU, '\', b) ; resid = norm (A*x-b,1) / norm (A,1) ; rgrowth = full (min (max (abs ((LU.R \ A (LU.p,LU.q)) - LU.F)) ./ ... max (abs (LU.U)))) ; fprintf ('resid: %g KLU condest: %g rgrowth: %g\n', resid, c, rgrowth) ; disp (info) ; subplot (2,2,3) ; spy (LU.L + LU.U + LU.F) ; title ('KLU+AMD factors') ; fprintf ('\nKLU with COLAMD ordering\n') ; [LU,info] = klu (A, struct ('ordering',1)) ; x = klu (LU, '\', b) ; resid = norm (A*x-b,1) / norm (A,1) ; fprintf ('resid: %g\n', resid) ; disp (info) ; subplot (2,2,4) ; spy (LU.L + LU.U + LU.F) ; title ('KLU+COLAMD factors') ; fprintf ('\nKLU with natural ordering (lots of fillin)\n') ; [x,info] = klu (A, '\', b, struct ('ordering',2)) ; resid = norm (A*x-b,1) / norm (A,1) ; fprintf ('resid: %g\n', resid) ; disp (info) ; try fprintf ('\nKLU with CHOLMOD(A''*A) ordering\n') ; [x,info] = klu (A, '\', b, struct ('ordering',3)) ; resid = norm (A*x-b,1) / norm (A,1) ; fprintf ('resid: %g\n', resid) ; disp (info) ; fprintf ('\nKLU with CHOLMOD(A+A'') ordering\n') ; [x,info] = klu (A, '\', b, struct ('ordering',4)) ; resid = norm (A*x-b,1) / norm (A,1) ; fprintf ('resid: %g\n', resid) ; disp (info) ; catch fprintf ('KLU test with CHOLMOD skipped (CHOLMOD not installed)\n') ; end SuiteSparse/KLU/MATLAB/klu_mex.c0000644001170100242450000013715410634325173015171 0ustar davisfac/* ========================================================================== */ /* === klu mexFunction ====================================================== */ /* ========================================================================== */ /* KLU: a MATLAB interface to a "Clark Kent" sparse LU factorization algorithm. 3 or 4 input arguments: factorize and solve, returning the solution: x = klu (A, '\', b) x = klu (A, '\', b, opts) x = klu (b, '/', A) x = klu (b, '/', A, opts) A can be the LU struct, instead: x = klu (LU, '\', b) x = klu (LU, '\', b, opts) x = klu (b, '/', LU) x = klu (b, '/', LU, opts) where LU is a struct containing members: L, U, p, q, R, F, and r. Only L and U are required. The factorization is L*U+F = R\A(p,q), where r defines the block boundaries of the BTF form, and F contains the entries in the upper block triangular part. with 1 or 2 input arguments: factorize, returning the LU struct: LU = klu (A) LU = klu (A, opts) 2nd optional output: info, which is only meaningful if A was factorized. A must be square. b can be a matrix, but it cannot be sparse. Obscure options, mainly for testing: opts.memgrow 1.2 when L and U need to grow, inc. by this ratio. valid range: 1 or more. opts.imemamd 1.2 initial size of L and U with AMD or other symmetric ordering is 1.2*nnz(L)+n; valid range 1 or more. opts.imem 10 initial size of L and U is 10*nnz(A)+n if a symmetric ordering not used; valid range 1 or more */ /* ========================================================================== */ #include "klu.h" #include #ifndef NCHOLMOD #include "klu_cholmod.h" #endif #include "mex.h" #define MAX(a,b) (((a) > (b)) ? (a) : (b)) #define MIN(a,b) (((a) < (b)) ? (a) : (b)) #define ABS(x) (((x) < 0) ? -(x) : (x)) #define STRING_MATCH(s1,s2) (strcmp ((s1), (s2)) == 0) /* Complex division. This uses ACM Algo 116, by R. L. Smith, 1962. */ /* Note that c cannot be the same variable as a or b */ #define DIV(cx,cz,ax,az,bx,bz) \ { \ double r, den ; \ if (ABS (bx) >= ABS (bz)) \ { \ r = bz / bx ; \ den = bx + r * bz ; \ cx = (ax + az * r) / den ; \ cz = (az - ax * r) / den ; \ } \ else \ { \ r = bx / bz ; \ den = r * bx + bz ; \ cx = (ax * r + az) / den ; \ cz = (az * r - ax) / den ; \ } \ } /* complex multiply/subtract, c -= a*b */ /* Note that c cannot be the same variable as a or b */ #define MULT_SUB(cx,cz,ax,az,bx,bz) \ { \ cx -= ax * bx - az * bz ; \ cz -= az * bx + ax * bz ; \ } /* complex multiply/subtract, c -= a*conj(b) */ /* Note that c cannot be the same variable as a or b */ #define MULT_SUB_CONJ(cx,cz,ax,az,bx,bz) \ { \ cx -= ax * bx + az * bz ; \ cz -= az * bx - ax * bz ; \ } /* ========================================================================== */ /* === klu mexFunction ====================================================== */ /* ========================================================================== */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double ukk, lkk, rs, s, lik, uik, x [4], offik, z, ukkz, lkkz, sz, wx, wz ; double *X, *B, *Xz, *Xx, *Bx, *Bz, *A, *Ax, *Az, *Lx, *Ux, *Rs, *Offx, *Wx, *Uz, *Lz, *Offz, *Wz, *W, *Xi, *Bi ; UF_long *Ap, *Ai, *Lp, *Li, *Up, *Ui, *P, *Q, *R, *Rp, *Ri, *Offp, *Offi ; char *operator ; mxArray *L_matlab, *U_matlab, *p_matlab, *q_matlab, *R_matlab, *F_matlab, *r_matlab, *field ; const mxArray *A_matlab = NULL, *LU_matlab, *B_matlab = NULL, *opts_matlab ; klu_l_symbolic *Symbolic ; klu_l_numeric *Numeric ; klu_l_common Common ; UF_long n = 0, k, nrhs = 0, do_solve, do_factorize, symmetric, A_complex = 0, B_complex, nz, do_transpose = 0, p, pend, nblocks, R1 [2], chunk, nr, i, j, block, k1, k2, nk, bn = 0, ordering ; int mx_int ; static const char *fnames [ ] = { "noffdiag", /* # of off-diagonal pivots */ "nrealloc", /* # of memory reallocations */ "rcond", /* cheap reciprocal number estimate */ "rgrowth", /* reciprocal pivot growth */ "flops", /* flop count */ "nblocks", /* # of blocks in BTF form (1 if not computed) */ "ordering", /* AMD, COLAMD, natural, cholmod(AA'), cholmod(A+A') */ "scale", /* scaling (<=0: none, 1: sum, 2: max */ "lnz", /* nnz(L), including diagonal */ "unz", /* nnz(U), including diagonal */ "offnz", /* nnz(F), including diagonal */ "tol", /* pivot tolerance used */ "memory" /* peak memory usage */ }, *LUnames [ ] = { "L", "U", "p", "q", "R", "F", "r" } ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if (nargin < 1 || nargin > 4 || nargout > 3) { mexErrMsgTxt ( "Usage: x = klu(A,'\',b), x = klu(A,'/',b) or LU = klu(A)") ; } /* return the solution x, or just do LU factorization */ do_solve = (nargin > 2) ; /* determine size of the MATLAB integer */ if (sizeof (UF_long) == sizeof (INT32_T)) { mx_int = mxINT32_CLASS ; } else { mx_int = mxINT64_CLASS ; } if (do_solve) { /* ------------------------------------------------------------------ */ /* slash or backslash */ /* ------------------------------------------------------------------ */ /* usage, where opts is the optional 4th input argument: x = klu (A, '\', b) x = klu (LU, '\', b) x = klu (b, '/', A) x = klu (b, '/', LU) */ /* determine the operator, slash (/) or backslash (\) */ if (!mxIsChar (pargin [1])) { mexErrMsgTxt ("invalid operator") ; } operator = mxArrayToString (pargin [1]) ; if (STRING_MATCH (operator, "\\")) { do_transpose = 0 ; A_matlab = pargin [0] ; B_matlab = pargin [2] ; nrhs = mxGetN (B_matlab) ; bn = mxGetM (B_matlab) ; } else if (STRING_MATCH (operator, "/")) { do_transpose = 1 ; A_matlab = pargin [2] ; B_matlab = pargin [0] ; nrhs = mxGetM (B_matlab) ; bn = mxGetN (B_matlab) ; } else { mexErrMsgTxt ("invalid operator") ; } if (mxIsSparse (B_matlab)) { mexErrMsgTxt ("B cannot be sparse") ; } opts_matlab = (nargin > 3) ? pargin [3] : NULL ; /* determine if the factorization needs to be performed */ do_factorize = !mxIsStruct (A_matlab) ; if (do_factorize) { LU_matlab = NULL ; } else { LU_matlab = A_matlab ; A_matlab = NULL ; } } else { /* ------------------------------------------------------------------ */ /* factorize A and return LU factorization */ /* ------------------------------------------------------------------ */ /* usage, where opts in the optional 2nd input argument: LU = klu (A) */ LU_matlab = NULL ; A_matlab = pargin [0] ; B_matlab = NULL ; opts_matlab = (nargin > 1) ? pargin [1] : NULL ; do_factorize = 1 ; if (mxIsStruct (A_matlab)) { mexErrMsgTxt ("invalid input, A must be a sparse matrix") ; } } /* ---------------------------------------------------------------------- */ /* get options and set Common defaults */ /* ---------------------------------------------------------------------- */ klu_l_defaults (&Common) ; /* memory management routines */ Common.malloc_memory = mxMalloc ; Common.calloc_memory = mxCalloc ; Common.free_memory = mxFree ; Common.realloc_memory = mxRealloc ; /* factorization options */ if (opts_matlab != NULL && mxIsStruct (opts_matlab)) { if ((field = mxGetField (opts_matlab, 0, "tol")) != NULL) { Common.tol = mxGetScalar (field) ; } if ((field = mxGetField (opts_matlab, 0, "memgrow")) != NULL) { Common.memgrow = mxGetScalar (field) ; } if ((field = mxGetField (opts_matlab, 0, "imemamd")) != NULL) { Common.initmem_amd = mxGetScalar (field) ; } if ((field = mxGetField (opts_matlab, 0, "imem")) != NULL) { Common.initmem = mxGetScalar (field) ; } if ((field = mxGetField (opts_matlab, 0, "btf")) != NULL) { Common.btf = mxGetScalar (field) ; } if ((field = mxGetField (opts_matlab, 0, "ordering")) != NULL) { Common.ordering = mxGetScalar (field) ; } if ((field = mxGetField (opts_matlab, 0, "scale")) != NULL) { Common.scale = mxGetScalar (field) ; } if ((field = mxGetField (opts_matlab, 0, "maxwork")) != NULL) { Common.maxwork = mxGetScalar (field) ; } } if (Common.ordering < 0 || Common.ordering > 4) { mexErrMsgTxt ("invalid ordering option") ; } ordering = Common.ordering ; #ifndef NCHOLMOD /* ordering option 3,4 becomes KLU option 3, with symmetric 0 or 1 */ symmetric = (Common.ordering == 4) ; if (symmetric) Common.ordering = 3 ; Common.user_order = klu_l_cholmod ; Common.user_data = &symmetric ; #else /* CHOLMOD, METIS, CAMD, CCOLAMD, not available */ if (Common.ordering > 2) { mexErrMsgTxt ("invalid ordering option") ; } #endif if (Common.scale < 1 || Common.scale > 2) { Common.scale = -1 ; /* no scaling, and no error checking either */ } /* ---------------------------------------------------------------------- */ /* factorize, if needed */ /* ---------------------------------------------------------------------- */ if (do_factorize) { /* get input matrix A to factorize */ n = mxGetN (A_matlab) ; if (!mxIsSparse (A_matlab) || n != mxGetM (A_matlab) || n == 0) { mexErrMsgTxt ("A must be sparse, square, and non-empty") ; } Ap = (UF_long *) mxGetJc (A_matlab) ; Ai = (UF_long *) mxGetIr (A_matlab) ; Ax = mxGetPr (A_matlab) ; Az = mxGetPi (A_matlab) ; nz = Ap [n] ; A_complex = mxIsComplex (A_matlab) ; if (do_solve && (n != bn || nrhs == 0)) { mexErrMsgTxt ("B must be non-empty with same number of rows as A") ; } /* ------------------------------------------------------------------ */ /* analyze */ /* ------------------------------------------------------------------ */ Symbolic = klu_l_analyze (n, Ap, Ai, &Common) ; if (Symbolic == (klu_l_symbolic *) NULL) { mexErrMsgTxt ("klu symbolic analysis failed") ; } /* ------------------------------------------------------------------ */ /* factorize */ /* ------------------------------------------------------------------ */ if (A_complex) { /* A is complex */ A = mxMalloc (nz * 2 * sizeof (double)) ; for (k = 0 ; k < nz ; k++) { A [2*k ] = Ax [k] ; /* real part */ A [2*k+1] = Az [k] ; /* imaginary part */ } Numeric = klu_zl_factor (Ap, Ai, A, Symbolic, &Common) ; if (nargout > 1) { /* flops and rgrowth, if requested */ klu_zl_flops (Symbolic, Numeric, &Common) ; klu_zl_rgrowth (Ap, Ai, A, Symbolic, Numeric, &Common) ; } mxFree (A) ; } else { /* A is real */ Numeric = klu_l_factor (Ap, Ai, Ax, Symbolic, &Common) ; if (nargout > 1) { /* flops, if requested */ klu_l_flops (Symbolic, Numeric, &Common) ; klu_l_rgrowth (Ap, Ai, Ax, Symbolic, Numeric, &Common) ; } } if (Common.status != KLU_OK) { mexErrMsgTxt ("klu numeric factorization failed") ; } /* ------------------------------------------------------------------ */ /* compute cheap condition number estimate */ /* ------------------------------------------------------------------ */ if (A_complex) { klu_zl_rcond (Symbolic, Numeric, &Common) ; } else { klu_l_rcond (Symbolic, Numeric, &Common) ; } /* ------------------------------------------------------------------ */ /* return info, if requested */ /* ------------------------------------------------------------------ */ #define INFO(i,x) \ mxSetFieldByNumber (pargout [1], 0, i, mxCreateScalarDouble (x)) if (nargout > 1) { pargout [1] = mxCreateStructMatrix (1, 1, 13, fnames) ; INFO (0, Common.noffdiag) ; INFO (1, Common.nrealloc) ; INFO (2, Common.rcond) ; INFO (3, Common.rgrowth) ; INFO (4, Common.flops) ; INFO (5, Symbolic->nblocks) ; INFO (6, ordering) ; INFO (7, Common.scale) ; INFO (8, Numeric->lnz) ; INFO (9, Numeric->unz) ; INFO (10, Numeric->nzoff) ; INFO (11, Common.tol) ; INFO (12, Common.mempeak) ; } if (nargout > 2) { /* this is done separately, since it's costly */ klu_l_condest (Ap, Ax, Symbolic, Numeric, &Common) ; pargout [2] = mxCreateDoubleMatrix (1, 1, mxREAL) ; Wx = mxGetPr (pargout [2]) ; Wx [0] = Common.condest ; } } else { /* create an empty "info" and "condest" output */ if (nargout > 1) { pargout [1] = mxCreateDoubleMatrix (0, 0, mxREAL) ; } if (nargout > 2) { pargout [2] = mxCreateDoubleMatrix (0, 0, mxREAL) ; } } /* ---------------------------------------------------------------------- */ /* solve, or return LU factorization */ /* ---------------------------------------------------------------------- */ if (do_solve) { /* ------------------------------------------------------------------ */ /* solve, x = klu ( ... ) usage */ /* ------------------------------------------------------------------ */ B_complex = mxIsComplex (B_matlab) ; if (do_factorize) { /* -------------------------------------------------------------- */ /* solve using KLU factors computed above */ /* -------------------------------------------------------------- */ /* klu (A,'\',b) or klu (b,'/',A) usage */ /* create X */ if (do_transpose) { pargout [0] = mxCreateDoubleMatrix (nrhs, n, (A_complex || B_complex) ? mxCOMPLEX : mxREAL) ; } else { pargout [0] = mxCreateDoubleMatrix (n, nrhs, (A_complex || B_complex) ? mxCOMPLEX : mxREAL) ; } if (A_complex) { /* ---------------------------------------------------------- */ /* A is complex, but B might be real */ /* ---------------------------------------------------------- */ X = mxMalloc (n * nrhs * 2 * sizeof (double)) ; Bx = mxGetPr (B_matlab) ; Bz = mxGetPi (B_matlab) ; if (do_transpose) { /* X = B', merge and transpose B */ for (j = 0 ; j < nrhs ; j++) { for (i = 0 ; i < n ; i++) { X [2*(i+j*n) ] = Bx [j+i*nrhs] ; /* real */ X [2*(i+j*n)+1] = Bz ? (-Bz [j+i*nrhs]) : 0 ; } } /* solve A'x=b (complex conjugate) */ klu_zl_tsolve (Symbolic, Numeric, n, nrhs, X, 1, &Common) ; /* split and transpose the solution */ Xx = mxGetPr (pargout [0]) ; Xz = mxGetPi (pargout [0]) ; for (j = 0 ; j < nrhs ; j++) { for (i = 0 ; i < n ; i++) { Xx [j+i*nrhs] = X [2*(i+j*n) ] ; /* real part */ Xz [j+i*nrhs] = -X [2*(i+j*n)+1] ; /* imag part */ } } } else { /* X = B, but create merged X from a split B */ for (k = 0 ; k < n*nrhs ; k++) { X [2*k ] = Bx [k] ; /* real part */ X [2*k+1] = Bz ? (Bz [k]) : 0 ; /* imaginary part */ } /* solve Ax=b */ klu_zl_solve (Symbolic, Numeric, n, nrhs, X, &Common) ; /* split the solution into real and imaginary parts */ Xx = mxGetPr (pargout [0]) ; Xz = mxGetPi (pargout [0]) ; for (k = 0 ; k < n*nrhs ; k++) { Xx [k] = X [2*k ] ; /* real part */ Xz [k] = X [2*k+1] ; /* imaginary part */ } } mxFree (X) ; } else { if (do_transpose) { /* solve in chunks of 4 columns at a time */ W = mxMalloc (n * MAX (nrhs,4) * sizeof (double)) ; X = mxGetPr (pargout [0]) ; B = mxGetPr (B_matlab) ; Xi = mxGetPi (pargout [0]) ; Bi = mxGetPi (B_matlab) ; for (chunk = 0 ; chunk < nrhs ; chunk += 4) { /* A is real: real(X) = real(b) / real(A) */ UF_long chunksize = MIN (nrhs - chunk, 4) ; for (j = 0 ; j < chunksize ; j++) { for (i = 0 ; i < n ; i++) { W [i+j*n] = B [i*nrhs+j] ; } } klu_l_tsolve (Symbolic, Numeric, n, chunksize, W, &Common) ; for (j = 0 ; j < chunksize ; j++) { for (i = 0 ; i < n ; i++) { X [i*nrhs+j] = W [i+j*n] ; } } X += 4 ; B += 4 ; if (B_complex) { /* B is complex: imag(X) = imag(B) / real(A) */ for (j = 0 ; j < chunksize ; j++) { for (i = 0 ; i < n ; i++) { W [i+j*n] = Bi [i*nrhs+j] ; } } klu_l_tsolve (Symbolic, Numeric, n, chunksize, W, &Common) ; for (j = 0 ; j < chunksize ; j++) { for (i = 0 ; i < n ; i++) { Xi [i*nrhs+j] = W [i+j*n] ; } } Xi += 4 ; Bi += 4 ; } } mxFree (W) ; } else { /* A is real: real(X) = real(A) \ real(b) */ X = mxGetPr (pargout [0]) ; B = mxGetPr (B_matlab) ; for (k = 0 ; k < n*nrhs ; k++) { X [k] = B [k] ; } klu_l_solve (Symbolic, Numeric, n, nrhs, X, &Common) ; if (B_complex) { /* B is complex: imag(X) = real(A) \ imag(B) */ X = mxGetPi (pargout [0]) ; B = mxGetPi (B_matlab) ; for (k = 0 ; k < n*nrhs ; k++) { X [k] = B [k] ; } klu_l_solve (Symbolic, Numeric, n, nrhs, X, &Common) ; } } } /* -------------------------------------------------------------- */ /* free Symbolic and Numeric objects */ /* -------------------------------------------------------------- */ klu_l_free_symbolic (&Symbolic, &Common) ; if (A_complex) { klu_zl_free_numeric (&Numeric, &Common) ; } else { klu_l_free_numeric (&Numeric, &Common) ; } } else { /* -------------------------------------------------------------- */ /* solve using LU struct given on input */ /* -------------------------------------------------------------- */ /* the factorization is L*U+F = R\A(p,q), where L*U is block diagonal, and F contains the entries in the upper block triangular part */ L_matlab = mxGetField (LU_matlab, 0, "L") ; U_matlab = mxGetField (LU_matlab, 0, "U") ; p_matlab = mxGetField (LU_matlab, 0, "p") ; q_matlab = mxGetField (LU_matlab, 0, "q") ; R_matlab = mxGetField (LU_matlab, 0, "R") ; F_matlab = mxGetField (LU_matlab, 0, "F") ; r_matlab = mxGetField (LU_matlab, 0, "r") ; if (!L_matlab || !U_matlab || !mxIsSparse (L_matlab) || !mxIsSparse (U_matlab)) { mexErrMsgTxt ("invalid LU struct") ; } n = mxGetM (L_matlab) ; if (n != mxGetN (L_matlab) || n != mxGetM (U_matlab) || n != mxGetN (U_matlab) /* ... */ ) { mexErrMsgTxt ("invalid LU struct") ; } if (n != bn || nrhs == 0) { mexErrMsgTxt ( "B must be non-empty with same number of rows as L and U") ; } /* get L */ if (!mxIsSparse (L_matlab) || n != mxGetM (L_matlab) || n != mxGetN (L_matlab)) { mexErrMsgTxt ("LU.L must be sparse and same size as A") ; } Lp = (UF_long *) mxGetJc (L_matlab) ; Li = (UF_long *) mxGetIr (L_matlab) ; Lx = mxGetPr (L_matlab) ; Lz = mxGetPi (L_matlab) ; /* get U */ if (!mxIsSparse (U_matlab) || n != mxGetM (U_matlab) || n != mxGetN (U_matlab)) { mexErrMsgTxt ("LU.U must be sparse and same size as A") ; } Up = (UF_long *) mxGetJc (U_matlab) ; Ui = (UF_long *) mxGetIr (U_matlab) ; Ux = mxGetPr (U_matlab) ; Uz = mxGetPi (U_matlab) ; /* get p */ if (p_matlab) { if (mxGetNumberOfElements (p_matlab) != n || mxIsSparse (p_matlab) || mxGetClassID (p_matlab) != mx_int) { mexErrMsgTxt ("P invalid") ; } P = (UF_long *) mxGetData (p_matlab) ; for (k = 0 ; k < n ; k++) { if (P [k] < 1 || P [k] > n) mexErrMsgTxt ("P invalid") ; } } else { /* no P, use identity instead */ P = NULL ; } /* get q */ if (q_matlab) { if (mxGetNumberOfElements (q_matlab) != n || mxIsSparse (q_matlab) || mxGetClassID (q_matlab) != mx_int) { mexErrMsgTxt ("Q invalid") ; } Q = (UF_long *) mxGetData (q_matlab) ; for (k = 0 ; k < n ; k++) { if (Q [k] < 1 || Q [k] > n) mexErrMsgTxt ("Q invalid.") ; } } else { /* no Q, use identity instead */ Q = NULL ; } /* get r */ R1 [0] = 1 ; R1 [1] = n+1 ; if (r_matlab) { nblocks = mxGetNumberOfElements (r_matlab) - 1 ; if (nblocks < 1 || nblocks > n || mxIsSparse (r_matlab) || mxGetClassID (r_matlab) != mx_int) { mexErrMsgTxt ("r invalid") ; } R = (UF_long *) mxGetData (r_matlab) ; if (R [0] != 1) mexErrMsgTxt ("r invalid") ; for (k = 1 ; k <= nblocks ; k++) { if (R [k] <= R [k-1] || R [k] > n+1) { mexErrMsgTxt ("rinvalid") ; } } if (R [nblocks] != n+1) mexErrMsgTxt ("r invalid") ; } else { /* no r */ nblocks = 1 ; R = R1 ; } /* get R, scale factors */ if (R_matlab) { /* ensure R is sparse, real, and has the right size */ if (!mxIsSparse (R_matlab) || n != mxGetM (R_matlab) || n != mxGetN (R_matlab)) { mexErrMsgTxt ("LU.R must be sparse and same size as A") ; } Rp = (UF_long *) mxGetJc (R_matlab) ; Rs = mxGetPr (R_matlab) ; if (Rp [n] != n) { mexErrMsgTxt ("LU.R invalid, must be diagonal") ; } } else { /* no scale factors */ Rs = NULL ; } /* get F, off diagonal entries */ if (F_matlab) { if (!mxIsSparse (F_matlab) || n != mxGetM (F_matlab) || n != mxGetN (F_matlab)) { mexErrMsgTxt ("LU.F must be sparse and same size as A") ; } Offp = (UF_long *) mxGetJc (F_matlab) ; Offi = (UF_long *) mxGetIr (F_matlab) ; Offx = mxGetPr (F_matlab) ; Offz = mxGetPi (F_matlab) ; } else { /* no off-diagonal entries */ Offp = NULL ; Offi = NULL ; Offx = NULL ; Offz = NULL ; } /* -------------------------------------------------------------- */ /* solve */ /* -------------------------------------------------------------- */ if (mxIsComplex (L_matlab) || mxIsComplex (U_matlab) || (F_matlab && mxIsComplex (F_matlab)) || B_complex) { /* ========================================================== */ /* === complex case ========================================= */ /* ========================================================== */ /* create X */ if (do_transpose) { pargout [0] = mxCreateDoubleMatrix (nrhs, n, mxCOMPLEX) ; } else { pargout [0] = mxCreateDoubleMatrix (n, nrhs, mxCOMPLEX) ; } Xx = mxGetPr (pargout [0]) ; Xz = mxGetPi (pargout [0]) ; Bx = mxGetPr (B_matlab) ; Bz = mxGetPi (B_matlab) ; /* get workspace */ Wx = mxMalloc (n * sizeof (double)) ; Wz = mxMalloc (n * sizeof (double)) ; /* ---------------------------------------------------------- */ /* do just one row/column of the right-hand-side at a time */ /* ---------------------------------------------------------- */ if (do_transpose) { for (chunk = 0 ; chunk < nrhs ; chunk++) { /* -------------------------------------------------- */ /* transpose and permute right hand side, W = Q'*B' */ /* -------------------------------------------------- */ for (k = 0 ; k < n ; k++) { i = Q ? (Q [k] - 1) : k ; Wx [k] = Bx [i*nrhs] ; Wz [k] = Bz ? (-Bz [i*nrhs]) : 0 ; } /* -------------------------------------------------- */ /* solve W = (L*U + Off)'\W */ /* -------------------------------------------------- */ for (block = 0 ; block < nblocks ; block++) { /* ---------------------------------------------- */ /* block of size nk, rows/columns k1 to k2-1 */ /* ---------------------------------------------- */ k1 = R [block] - 1 ; /* R is 1-based */ k2 = R [block+1] - 1 ; nk = k2 - k1 ; /* ---------------------------------------------- */ /* block back-substitution for off-diagonal-block */ /* ---------------------------------------------- */ if (block > 0 && Offp != NULL) { for (k = k1 ; k < k2 ; k++) { pend = Offp [k+1] ; for (p = Offp [k] ; p < pend ; p++) { i = Offi [p] ; /* W [k] -= W [i] * conj(Off [p]) ; */ z = Offz ? Offz [p] : 0 ; MULT_SUB_CONJ (Wx [k], Wz [k], Wx [i], Wz [i], Offx [p], z) ; } } } /* solve the block system */ if (nk == 1) { /* W [k1] /= conj (L(k1,k1)) ; */ p = Lp [k1] ; s = Lx [p] ; sz = Lz ? (-Lz [p]) : 0 ; DIV (wx, wz, Wx [k1], Wz [k1], s, sz) ; Wx [k1] = wx ; Wz [k1] = wz ; /* W [k1] /= conj (U(k1,k1)) ; */ p = Up [k1] ; s = Ux [p] ; sz = Uz ? (-Uz [p]) : 0 ; DIV (wx, wz, Wx [k1], Wz [k1], s, sz) ; Wx [k1] = wx ; Wz [k1] = wz ; } else { /* ------------------------------------------ */ /* W = U'\W and then W=L'\W */ /* ------------------------------------------ */ /* W = U'\W */ for (k = k1 ; k < k2 ; k++) { pend = Up [k+1] - 1 ; /* w = W [k] */ wx = Wx [k] ; wz = Wz [k] ; for (p = Up [k] ; p < pend ; p++) { i = Ui [p] ; /* w -= W [i] * conj(U [p]) */ z = Uz ? Uz [p] : 0 ; MULT_SUB_CONJ (wx, wz, Wx [i], Wz [i], Ux [p], z) ; } /* W [k] = w / conj(ukk) ; */ ukk = Ux [pend] ; ukkz = Uz ? (-Uz [pend]) : 0 ; DIV (Wx [k], Wz [k], wx, wz, ukk, ukkz) ; } /* W = L'\W */ for (k = k2-1 ; k >= k1 ; k--) { p = Lp [k] ; pend = Lp [k+1] ; /* w = W [k] */ wx = Wx [k] ; wz = Wz [k] ; lkk = Lx [p] ; lkkz = Lz ? (-Lz [p]) : 0 ; for (p++ ; p < pend ; p++) { i = Li [p] ; /* w -= W [i] * conj (Lx [p]) ; */ z = Lz ? Lz [p] : 0 ; MULT_SUB_CONJ (wx, wz, Wx [i], Wz [i], Lx [p], z) ; } /* W [k] = w / conj(lkk) ; */ DIV (Wx [k], Wz [k], wx, wz, lkk, lkkz) ; } } } /* -------------------------------------------------- */ /* scale, permute, and tranpose: X = (P*(R\W))' */ /* -------------------------------------------------- */ if (Rs == NULL) { /* no scaling */ for (k = 0 ; k < n ; k++) { i = P ? (P [k] - 1) : k ; Xx [i*nrhs] = Wx [k] ; Xz [i*nrhs] = Wz ? (-Wz [k]) : 0 ; } } else { /* with scaling */ for (k = 0 ; k < n ; k++) { i = P ? (P [k] - 1) : k ; rs = Rs [k] ; Xx [i*nrhs] = Wx [k] / rs ; Xz [i*nrhs] = Wz ? (-Wz [k] / rs) : 0 ; } } /* -------------------------------------------------- */ /* go to the next row of B and X */ /* -------------------------------------------------- */ Xx++ ; Xz++ ; Bx++ ; if (Bz) Bz++ ; } } else { for (chunk = 0 ; chunk < nrhs ; chunk++) { /* -------------------------------------------------- */ /* scale and permute the right hand side, W = P*(R\B) */ /* -------------------------------------------------- */ if (Rs == NULL) { /* no scaling */ for (k = 0 ; k < n ; k++) { i = P ? (P [k] - 1) : k ; Wx [k] = Bx [i] ; Wz [k] = Bz ? Bz [i] : 0 ; } } else { /* with scaling */ for (k = 0 ; k < n ; k++) { i = P ? (P [k] - 1) : k ; rs = Rs [k] ; Wx [k] = Bx [i] / rs ; Wz [k] = Bz ? (Bz [i] / rs) : 0 ; } } /* -------------------------------------------------- */ /* solve W = (L*U + Off)\W */ /* -------------------------------------------------- */ for (block = nblocks-1 ; block >= 0 ; block--) { /* ---------------------------------------------- */ /* block of size nk, rows/columns k1 to k2-1 */ /* ---------------------------------------------- */ k1 = R [block] - 1 ; /* R is 1-based */ k2 = R [block+1] - 1 ; nk = k2 - k1 ; /* solve the block system */ if (nk == 1) { /* W [k1] /= L(k1,k1) ; */ p = Lp [k1] ; s = Lx [p] ; sz = Lz ? Lz [p] : 0 ; DIV (wx, wz, Wx [k1], Wz [k1], s, sz) ; Wx [k1] = wx ; Wz [k1] = wz ; /* W [k1] /= U(k1,k1) ; */ p = Up [k1] ; s = Ux [p] ; sz = Uz ? Uz [p] : 0 ; DIV (wx, wz, Wx [k1], Wz [k1], s, sz) ; Wx [k1] = wx ; Wz [k1] = wz ; } else { /* ------------------------------------------ */ /* W = L\W and then W=U\W */ /* ------------------------------------------ */ /* W = L\W */ for (k = k1 ; k < k2 ; k++) { p = Lp [k] ; pend = Lp [k+1] ; lkk = Lx [p] ; lkkz = Lz ? Lz [p] : 0 ; /* w = W [k] / lkk ; */ DIV (wx, wz, Wx [k], Wz [k], lkk, lkkz) ; Wx [k] = wx ; Wz [k] = wz ; for (p++ ; p < pend ; p++) { i = Li [p] ; /* W [i] -= Lx [p] * w ; */ z = Lz ? Lz [p] : 0 ; MULT_SUB (Wx [i], Wz [i], Lx [p], z, wx, wz) ; } } /* W = U\W */ for (k = k2-1 ; k >= k1 ; k--) { pend = Up [k+1] - 1 ; ukk = Ux [pend] ; ukkz = Uz ? Uz [pend] : 0 ; /* w = W [k] / ukk ; */ DIV (wx, wz, Wx [k], Wz [k], ukk, ukkz) ; Wx [k] = wx ; Wz [k] = wz ; for (p = Up [k] ; p < pend ; p++) { i = Ui [p] ; /* W [i] -= U [p] * w ; */ z = Uz ? Uz [p] : 0 ; MULT_SUB (Wx [i], Wz [i], Ux [p], z, wx, wz) ; } } } /* ---------------------------------------------- */ /* block back-substitution for off-diagonal-block */ /* ---------------------------------------------- */ if (block > 0 && Offp != NULL) { for (k = k1 ; k < k2 ; k++) { pend = Offp [k+1] ; wx = Wx [k] ; wz = Wz [k] ; for (p = Offp [k] ; p < pend ; p++) { i = Offi [p] ; /* W [Offi [p]] -= Offx [p] * w ; */ z = Offz ? Offz [p] : 0 ; MULT_SUB (Wx [i], Wz [i], Offx [p], z, wx, wz) ; } } } } /* -------------------------------------------------- */ /* permute the result, X = Q*W */ /* -------------------------------------------------- */ for (k = 0 ; k < n ; k++) { i = Q ? (Q [k] - 1) : k ; Xx [i] = Wx [k] ; Xz [i] = Wz [k] ; } /* -------------------------------------------------- */ /* go to the next column of B and X */ /* -------------------------------------------------- */ Xx += n ; Xz += n ; Bx += n ; if (Bz) Bz += n ; } } /* free workspace */ mxFree (Wx) ; mxFree (Wz) ; } else { /* ========================================================== */ /* === real case ============================================ */ /* ========================================================== */ /* create X */ if (do_transpose) { pargout [0] = mxCreateDoubleMatrix (nrhs, n, mxREAL) ; } else { pargout [0] = mxCreateDoubleMatrix (n, nrhs, mxREAL) ; } Xx = mxGetPr (pargout [0]) ; Bx = mxGetPr (B_matlab) ; if (do_transpose) { /* ------------------------------------------------------ */ /* solve in chunks of one row at a time */ /* ------------------------------------------------------ */ /* get workspace */ Wx = mxMalloc (n * sizeof (double)) ; for (chunk = 0 ; chunk < nrhs ; chunk++) { /* -------------------------------------------------- */ /* transpose and permute right hand side, W = Q'*B' */ /* -------------------------------------------------- */ for (k = 0 ; k < n ; k++) { i = Q ? (Q [k] - 1) : k ; Wx [k] = Bx [i*nrhs] ; } /* -------------------------------------------------- */ /* solve W = (L*U + Off)'\W */ /* -------------------------------------------------- */ for (block = 0 ; block < nblocks ; block++) { /* ---------------------------------------------- */ /* block of size nk, rows/columns k1 to k2-1 */ /* ---------------------------------------------- */ k1 = R [block] - 1 ; /* R is 1-based */ k2 = R [block+1] - 1 ; nk = k2 - k1 ; /* ---------------------------------------------- */ /* block back-substitution for off-diagonal-block */ /* ---------------------------------------------- */ if (block > 0 && Offp != NULL) { for (k = k1 ; k < k2 ; k++) { pend = Offp [k+1] ; for (p = Offp [k] ; p < pend ; p++) { Wx [k] -= Wx [Offi [p]] * Offx [p] ; } } } /* solve the block system */ if (nk == 1) { Wx [k1] /= Lx [Lp [k1]] ; Wx [k1] /= Ux [Up [k1]] ; } else { /* ------------------------------------------ */ /* W = U'\W and then W=L'\W */ /* ------------------------------------------ */ /* W = U'\W */ for (k = k1 ; k < k2 ; k++) { pend = Up [k+1] - 1 ; for (p = Up [k] ; p < pend ; p++) { Wx [k] -= Wx [Ui [p]] * Ux [p] ; } Wx [k] /= Ux [pend] ; } /* W = L'\W */ for (k = k2-1 ; k >= k1 ; k--) { p = Lp [k] ; pend = Lp [k+1] ; lkk = Lx [p] ; for (p++ ; p < pend ; p++) { Wx [k] -= Wx [Li [p]] * Lx [p] ; } Wx [k] /= lkk ; } } } /* -------------------------------------------------- */ /* scale, permute, and tranpose: X = (P*(R\W))' */ /* -------------------------------------------------- */ if (Rs == NULL) { /* no scaling */ for (k = 0 ; k < n ; k++) { i = P ? (P [k] - 1) : k ; Xx [i*nrhs] = Wx [k] ; } } else { /* with scaling */ for (k = 0 ; k < n ; k++) { i = P ? (P [k] - 1) : k ; rs = Rs [k] ; Xx [i*nrhs] = Wx [k] / rs ; } } /* -------------------------------------------------- */ /* go to the next row of B and X */ /* -------------------------------------------------- */ Xx++ ; Bx++ ; } } else { /* ------------------------------------------------------ */ /* solve in chunks of 4 columns at a time */ /* ------------------------------------------------------ */ /* get workspace */ Wx = mxMalloc (n * MAX (4, nrhs) * sizeof (double)) ; for (chunk = 0 ; chunk < nrhs ; chunk += 4) { /* -------------------------------------------------- */ /* get the size of the current chunk */ /* -------------------------------------------------- */ nr = MIN (nrhs - chunk, 4) ; /* -------------------------------------------------- */ /* scale and permute the right hand side, W = P*(R\B) */ /* -------------------------------------------------- */ if (Rs == NULL) { /* no scaling */ switch (nr) { case 1: for (k = 0 ; k < n ; k++) { i = P ? (P [k] - 1) : k ; Wx [k] = Bx [i] ; } break ; case 2: for (k = 0 ; k < n ; k++) { i = P ? (P [k] - 1) : k ; Wx [2*k ] = Bx [i ] ; Wx [2*k + 1] = Bx [i + n ] ; } break ; case 3: for (k = 0 ; k < n ; k++) { i = P ? (P [k] - 1) : k ; Wx [3*k ] = Bx [i ] ; Wx [3*k + 1] = Bx [i + n ] ; Wx [3*k + 2] = Bx [i + n*2] ; } break ; case 4: for (k = 0 ; k < n ; k++) { i = P ? (P [k] - 1) : k ; Wx [4*k ] = Bx [i ] ; Wx [4*k + 1] = Bx [i + n ] ; Wx [4*k + 2] = Bx [i + n*2] ; Wx [4*k + 3] = Bx [i + n*3] ; } break ; } } else { switch (nr) { case 1: for (k = 0 ; k < n ; k++) { i = P ? (P [k] - 1) : k ; rs = Rs [k] ; Wx [k] = Bx [i] / rs ; } break ; case 2: for (k = 0 ; k < n ; k++) { i = P ? (P [k] - 1) : k ; rs = Rs [k] ; Wx [2*k ] = Bx [i ] / rs ; Wx [2*k + 1] = Bx [i + n ] / rs ; } break ; case 3: for (k = 0 ; k < n ; k++) { i = P ? (P [k] - 1) : k ; rs = Rs [k] ; Wx [3*k ] = Bx [i ] / rs ; Wx [3*k + 1] = Bx [i + n ] / rs ; Wx [3*k + 2] = Bx [i + n*2] / rs ; } break ; case 4: for (k = 0 ; k < n ; k++) { i = P ? (P [k] - 1) : k ; rs = Rs [k] ; Wx [4*k ] = Bx [i ] / rs ; Wx [4*k + 1] = Bx [i + n ] / rs ; Wx [4*k + 2] = Bx [i + n*2] / rs ; Wx [4*k + 3] = Bx [i + n*3] / rs ; } break ; } } /* -------------------------------------------------- */ /* solve W = (L*U + Off)\W */ /* -------------------------------------------------- */ for (block = nblocks-1 ; block >= 0 ; block--) { /* ---------------------------------------------- */ /* block of size nk is rows/columns k1 to k2-1 */ /* ---------------------------------------------- */ k1 = R [block] - 1 ; /* R is 1-based */ k2 = R [block+1] - 1 ; nk = k2 - k1 ; /* solve the block system */ if (nk == 1) { /* this is not done if L comes from KLU, since in that case, L is unit lower triangular */ s = Lx [Lp [k1]] ; if (s != 1.0) switch (nr) { case 1: Wx [k1] /= s ; break ; case 2: Wx [2*k1] /= s ; Wx [2*k1 + 1] /= s ; break ; case 3: Wx [3*k1] /= s ; Wx [3*k1 + 1] /= s ; Wx [3*k1 + 2] /= s ; break ; case 4: Wx [4*k1] /= s ; Wx [4*k1 + 1] /= s ; Wx [4*k1 + 2] /= s ; Wx [4*k1 + 3] /= s ; break ; } s = Ux [Up [k1]] ; if (s != 1.0) switch (nr) { case 1: Wx [k1] /= s ; break ; case 2: Wx [2*k1] /= s ; Wx [2*k1 + 1] /= s ; break ; case 3: Wx [3*k1] /= s ; Wx [3*k1 + 1] /= s ; Wx [3*k1 + 2] /= s ; break ; case 4: Wx [4*k1] /= s ; Wx [4*k1 + 1] /= s ; Wx [4*k1 + 2] /= s ; Wx [4*k1 + 3] /= s ; break ; } } else { /* ------------------------------------------ */ /* W = L\W and then W=U\W */ /* ------------------------------------------ */ switch (nr) { case 1: /* W = L\W */ for (k = k1 ; k < k2 ; k++) { p = Lp [k] ; pend = Lp [k+1] ; lkk = Lx [p++] ; x [0] = Wx [k] / lkk ; Wx [k] = x [0] ; for ( ; p < pend ; p++) { Wx [Li [p]] -= Lx [p] * x [0] ; } } /* W = U\W */ for (k = k2-1 ; k >= k1 ; k--) { pend = Up [k+1] - 1 ; ukk = Ux [pend] ; x [0] = Wx [k] / ukk ; Wx [k] = x [0] ; for (p = Up [k] ; p < pend ; p++) { Wx [Ui [p]] -= Ux [p] * x [0] ; } } break ; case 2: /* W = L\W */ for (k = k1 ; k < k2 ; k++) { p = Lp [k] ; pend = Lp [k+1] ; lkk = Lx [p++] ; x [0] = Wx [2*k ] / lkk ; x [1] = Wx [2*k + 1] / lkk ; Wx [2*k ] = x [0] ; Wx [2*k + 1] = x [1] ; for ( ; p < pend ; p++) { i = Li [p] ; lik = Lx [p] ; Wx [2*i ] -= lik * x [0] ; Wx [2*i + 1] -= lik * x [1] ; } } /* W = U\W */ for (k = k2-1 ; k >= k1 ; k--) { pend = Up [k+1] - 1 ; ukk = Ux [pend] ; x [0] = Wx [2*k ] / ukk ; x [1] = Wx [2*k + 1] / ukk ; Wx [2*k ] = x [0] ; Wx [2*k + 1] = x [1] ; for (p = Up [k] ; p < pend ; p++) { i = Ui [p] ; uik = Ux [p] ; Wx [2*i ] -= uik * x [0] ; Wx [2*i + 1] -= uik * x [1] ; } } break ; case 3: /* W = L\W */ for (k = k1 ; k < k2 ; k++) { p = Lp [k] ; pend = Lp [k+1] ; lkk = Lx [p++] ; x [0] = Wx [3*k ] / lkk ; x [1] = Wx [3*k + 1] / lkk ; x [2] = Wx [3*k + 2] / lkk ; Wx [3*k ] = x [0] ; Wx [3*k + 1] = x [1] ; Wx [3*k + 2] = x [2] ; for ( ; p < pend ; p++) { i = Li [p] ; lik = Lx [p] ; Wx [3*i ] -= lik * x [0] ; Wx [3*i + 1] -= lik * x [1] ; Wx [3*i + 2] -= lik * x [2] ; } } /* W = U\W */ for (k = k2-1 ; k >= k1 ; k--) { pend = Up [k+1] - 1 ; ukk = Ux [pend] ; x [0] = Wx [3*k ] / ukk ; x [1] = Wx [3*k + 1] / ukk ; x [2] = Wx [3*k + 2] / ukk ; Wx [3*k ] = x [0] ; Wx [3*k + 1] = x [1] ; Wx [3*k + 2] = x [2] ; for (p = Up [k] ; p < pend ; p++) { i = Ui [p] ; uik = Ux [p] ; Wx [3*i ] -= uik * x [0] ; Wx [3*i + 1] -= uik * x [1] ; Wx [3*i + 2] -= uik * x [2] ; } } break ; case 4: /* W = L\W */ for (k = k1 ; k < k2 ; k++) { p = Lp [k] ; pend = Lp [k+1] ; lkk = Lx [p++] ; x [0] = Wx [4*k ] / lkk ; x [1] = Wx [4*k + 1] / lkk ; x [2] = Wx [4*k + 2] / lkk ; x [3] = Wx [4*k + 3] / lkk ; Wx [4*k ] = x [0] ; Wx [4*k + 1] = x [1] ; Wx [4*k + 2] = x [2] ; Wx [4*k + 3] = x [3] ; for ( ; p < pend ; p++) { i = Li [p] ; lik = Lx [p] ; Wx [4*i ] -= lik * x [0] ; Wx [4*i + 1] -= lik * x [1] ; Wx [4*i + 2] -= lik * x [2] ; Wx [4*i + 3] -= lik * x [3] ; } } /* Wx = U\Wx */ for (k = k2-1 ; k >= k1 ; k--) { pend = Up [k+1] - 1 ; ukk = Ux [pend] ; x [0] = Wx [4*k ] / ukk ; x [1] = Wx [4*k + 1] / ukk ; x [2] = Wx [4*k + 2] / ukk ; x [3] = Wx [4*k + 3] / ukk ; Wx [4*k ] = x [0] ; Wx [4*k + 1] = x [1] ; Wx [4*k + 2] = x [2] ; Wx [4*k + 3] = x [3] ; for (p = Up [k] ; p < pend ; p++) { i = Ui [p] ; uik = Ux [p] ; Wx [4*i ] -= uik * x [0] ; Wx [4*i + 1] -= uik * x [1] ; Wx [4*i + 2] -= uik * x [2] ; Wx [4*i + 3] -= uik * x [3] ; } } break ; } } /* ---------------------------------------------- */ /* block back-substitution for off-diagonal-block */ /* ---------------------------------------------- */ if (block > 0 && Offp != NULL) { switch (nr) { case 1: for (k = k1 ; k < k2 ; k++) { pend = Offp [k+1] ; x [0] = Wx [k] ; for (p = Offp [k] ; p < pend ; p++) { Wx [Offi [p]] -= Offx[p] * x[0]; } } break ; case 2: for (k = k1 ; k < k2 ; k++) { pend = Offp [k+1] ; x [0] = Wx [2*k ] ; x [1] = Wx [2*k + 1] ; for (p = Offp [k] ; p < pend ; p++) { i = Offi [p] ; offik = Offx [p] ; Wx [2*i ] -= offik * x [0] ; Wx [2*i + 1] -= offik * x [1] ; } } break ; case 3: for (k = k1 ; k < k2 ; k++) { pend = Offp [k+1] ; x [0] = Wx [3*k ] ; x [1] = Wx [3*k + 1] ; x [2] = Wx [3*k + 2] ; for (p = Offp [k] ; p < pend ; p++) { i = Offi [p] ; offik = Offx [p] ; Wx [3*i ] -= offik * x [0] ; Wx [3*i + 1] -= offik * x [1] ; Wx [3*i + 2] -= offik * x [2] ; } } break ; case 4: for (k = k1 ; k < k2 ; k++) { pend = Offp [k+1] ; x [0] = Wx [4*k ] ; x [1] = Wx [4*k + 1] ; x [2] = Wx [4*k + 2] ; x [3] = Wx [4*k + 3] ; for (p = Offp [k] ; p < pend ; p++) { i = Offi [p] ; offik = Offx [p] ; Wx [4*i ] -= offik * x [0] ; Wx [4*i + 1] -= offik * x [1] ; Wx [4*i + 2] -= offik * x [2] ; Wx [4*i + 3] -= offik * x [3] ; } } break ; } } } /* -------------------------------------------------- */ /* permute the result, X = Q*W */ /* -------------------------------------------------- */ switch (nr) { case 1: for (k = 0 ; k < n ; k++) { i = Q ? (Q [k] - 1) : k ; Xx [i] = Wx [k] ; } break ; case 2: for (k = 0 ; k < n ; k++) { i = Q ? (Q [k] - 1) : k ; Xx [i ] = Wx [2*k ] ; Xx [i + n ] = Wx [2*k + 1] ; } break ; case 3: for (k = 0 ; k < n ; k++) { i = Q ? (Q [k] - 1) : k ; Xx [i ] = Wx [3*k ] ; Xx [i + n ] = Wx [3*k + 1] ; Xx [i + n*2] = Wx [3*k + 2] ; } break ; case 4: for (k = 0 ; k < n ; k++) { i = Q ? (Q [k] - 1) : k ; Xx [i ] = Wx [4*k ] ; Xx [i + n ] = Wx [4*k + 1] ; Xx [i + n*2] = Wx [4*k + 2] ; Xx [i + n*3] = Wx [4*k + 3] ; } break ; } /* -------------------------------------------------- */ /* go to the next chunk of B and X */ /* -------------------------------------------------- */ Xx += n*4 ; Bx += n*4 ; } } /* free workspace */ mxFree (Wx) ; } } } else { /* ------------------------------------------------------------------ */ /* LU = klu (A) usage; extract factorization */ /* ------------------------------------------------------------------ */ /* sort the row indices in each column of L and U */ if (A_complex) { klu_zl_sort (Symbolic, Numeric, &Common) ; } else { klu_l_sort (Symbolic, Numeric, &Common) ; } /* L */ L_matlab = mxCreateSparse (n, n, Numeric->lnz, A_complex ? mxCOMPLEX: mxREAL) ; Lp = (UF_long *) mxGetJc (L_matlab) ; Li = (UF_long *) mxGetIr (L_matlab) ; Lx = mxGetPr (L_matlab) ; Lz = mxGetPi (L_matlab) ; /* U */ U_matlab = mxCreateSparse (n, n, Numeric->unz, A_complex ? mxCOMPLEX: mxREAL) ; Up = (UF_long *) mxGetJc (U_matlab) ; Ui = (UF_long *) mxGetIr (U_matlab) ; Ux = mxGetPr (U_matlab) ; Uz = mxGetPi (U_matlab) ; /* p */ p_matlab = mxCreateNumericMatrix (1, n, mx_int, mxREAL) ; P = (UF_long *) mxGetData (p_matlab) ; /* q */ q_matlab = mxCreateNumericMatrix (1, n, mx_int, mxREAL) ; Q = (UF_long *) mxGetData (q_matlab) ; /* R, as a sparse diagonal matrix */ R_matlab = mxCreateSparse (n, n, n+1, mxREAL) ; Rp = (UF_long *) mxGetJc (R_matlab) ; Ri = (UF_long *) mxGetIr (R_matlab) ; Rs = mxGetPr (R_matlab) ; for (k = 0 ; k <= n ; k++) { Rp [k] = k ; Ri [k] = k ; } /* F, off diagonal blocks */ F_matlab = mxCreateSparse (n, n, Numeric->nzoff, A_complex ? mxCOMPLEX: mxREAL) ; Offp = (UF_long *) mxGetJc (F_matlab) ; Offi = (UF_long *) mxGetIr (F_matlab) ; Offx = mxGetPr (F_matlab) ; Offz = mxGetPi (F_matlab) ; /* r, block boundaries */ nblocks = Symbolic->nblocks ; r_matlab = mxCreateNumericMatrix (1, nblocks+1, mx_int, mxREAL) ; R = (UF_long *) mxGetData (r_matlab) ; /* extract the LU factorization from KLU Numeric and Symbolic objects */ if (A_complex) { klu_zl_extract (Numeric, Symbolic, Lp, Li, Lx, Lz, Up, Ui, Ux, Uz, Offp, Offi, Offx, Offz, P, Q, Rs, R, &Common) ; } else { klu_l_extract (Numeric, Symbolic, Lp, Li, Lx, Up, Ui, Ux, Offp, Offi, Offx, P, Q, Rs, R, &Common) ; } /* fix p and q for 1-based indexing */ for (k = 0 ; k < n ; k++) { P [k]++ ; Q [k]++ ; } /* fix r for 1-based indexing */ for (k = 0 ; k <= nblocks ; k++) { R [k]++ ; } /* create output LU struct */ pargout [0] = mxCreateStructMatrix (1, 1, 7, LUnames) ; mxSetFieldByNumber (pargout [0], 0, 0, L_matlab) ; mxSetFieldByNumber (pargout [0], 0, 1, U_matlab) ; mxSetFieldByNumber (pargout [0], 0, 2, p_matlab) ; mxSetFieldByNumber (pargout [0], 0, 3, q_matlab) ; mxSetFieldByNumber (pargout [0], 0, 4, R_matlab) ; mxSetFieldByNumber (pargout [0], 0, 5, F_matlab) ; mxSetFieldByNumber (pargout [0], 0, 6, r_matlab) ; /* ------------------------------------------------------------------ */ /* free Symbolic and Numeric objects */ /* ------------------------------------------------------------------ */ klu_l_free_symbolic (&Symbolic, &Common) ; klu_l_free_numeric (&Numeric, &Common) ; } } SuiteSparse/KLU/Matrix/0000755001170100242450000000000010615726227013656 5ustar davisfacSuiteSparse/KLU/Matrix/GD99_cc.mtx0000644001170100242450000000311010614651617015523 0ustar davisfac%%MatrixMarket matrix coordinate complex general % imaginary part is Pajek/GD99_c, real part is zero 105 105 149 6 1 0 1 5 2 0 1 7 2 0 1 4 3 0 1 8 3 0 1 5 4 0 1 1 5 0 1 24 6 0 1 6 7 0 1 7 8 0 1 26 9 0 1 105 10 0 1 94 11 0 1 40 12 0 1 26 13 0 1 16 14 0 1 26 15 0 1 26 16 0 1 16 17 0 1 16 19 0 1 16 20 0 1 57 21 0 1 15 22 0 1 31 22 0 1 13 23 0 1 15 24 0 1 13 25 0 1 9 26 0 1 16 26 0 1 57 26 0 1 24 27 0 1 85 28 0 1 85 29 0 1 32 30 0 1 86 30 0 1 22 31 0 1 45 31 0 1 57 31 0 1 22 32 0 1 85 32 0 1 54 33 0 1 88 33 0 1 91 33 0 1 91 34 0 1 92 34 0 1 95 35 0 1 50 36 0 1 98 37 0 1 98 38 0 1 38 39 0 1 38 40 0 1 102 41 0 1 101 42 0 1 103 43 0 1 100 44 0 1 104 44 0 1 31 45 0 1 93 45 0 1 28 46 0 1 50 47 0 1 87 47 0 1 100 47 0 1 53 48 0 1 99 48 0 1 87 49 0 1 89 49 0 1 45 50 0 1 94 50 0 1 31 51 0 1 104 51 0 1 48 52 0 1 90 52 0 1 91 52 0 1 89 53 0 1 87 54 0 1 90 54 0 1 93 54 0 1 99 55 0 1 29 56 0 1 18 57 0 1 21 57 0 1 26 57 0 1 31 57 0 1 95 58 0 1 45 59 0 1 103 59 0 1 59 60 0 1 102 61 0 1 61 62 0 1 61 63 0 1 53 64 0 1 64 65 0 1 65 66 0 1 64 67 0 1 91 67 0 1 92 67 0 1 88 68 0 1 97 69 0 1 96 70 0 1 97 70 0 1 96 71 0 1 92 72 0 1 48 73 0 1 64 73 0 1 98 73 0 1 40 74 0 1 86 75 0 1 96 76 0 1 86 77 0 1 82 78 0 1 78 79 0 1 82 79 0 1 81 80 0 1 84 80 0 1 78 81 0 1 33 82 0 1 82 83 0 1 83 84 0 1 32 85 0 1 30 86 0 1 47 87 0 1 54 87 0 1 33 88 0 1 97 88 0 1 49 89 0 1 99 89 0 1 52 90 0 1 55 90 0 1 33 91 0 1 67 91 0 1 34 92 0 1 50 93 0 1 50 94 0 1 95 94 0 1 94 95 0 1 70 96 0 1 88 97 0 1 73 98 0 1 55 99 0 1 89 99 0 1 47 100 0 1 101 100 0 1 100 101 0 1 102 101 0 1 101 102 0 1 59 103 0 1 105 103 0 1 105 104 0 1 104 105 0 1 SuiteSparse/KLU/Matrix/onec.mtx0000644001170100242450000000012710614241571015325 0ustar davisfac%%MatrixMarket matrix coordinate complex general 2 2 4 1 1 0 0 1 2 0 0 2 1 0 0 2 2 0 0 SuiteSparse/KLU/Matrix/impcol_a.mtx0000644001170100242450000001636610557446060016206 0ustar davisfac%%MatrixMarket matrix coordinate real general %------------------------------------------------------------------------------- % UF Sparse Matrix Collection, Tim Davis % http://www.cise.ufl.edu/research/sparse/matrices/HB/impcol_a % name: HB/impcol_a % [UNSYMMETRIC MATRIX - HEAT EXCHANGER NETWORK (CHEM ENG) ,1982] % id: 171 % date: 1982 % author: D. Bogle % ed: I. Duff, R. Grimes, J. Lewis % fields: title A name id date author ed kind % kind: chemical process simulation problem %------------------------------------------------------------------------------- 207 207 572 5 1 -1 6 1 -1 8 1 -1 11 1 .0662129 12 1 .1634 1 2 1 2 2 1 11 2 -.579712 12 2 -.422521 3 3 1 4 3 1 10 3 -1 11 3 17.8775 12 3 44.1179 5 4 -1 65 4 1 66 4 .5 1 5 -1 62 5 -1 3 6 -1 64 6 -1 6 7 680 7 8 1 9 9 1 8 10 1 14 10 -1 17 10 .00297937 18 10 .0247819 12 11 1 17 11 -.220568 18 11 -.808841 10 12 1 16 12 -1 17 12 .804429 18 12 6.69112 11 13 .0708967 12 13 -.0706236 13 14 -1 17 14 -.0323714 18 14 -.00352409 23 14 -1 24 14 -1 17 15 -.779432 18 15 -.191159 19 15 1 20 15 1 15 16 -1 17 16 -7.57491 18 16 -.824638 21 16 1 22 16 1 13 17 1 31 17 -1 33 17 -150 17 18 1 33 18 -234 15 19 1 32 19 -1 14 20 1 34 20 -1 36 20 -126.8 16 21 1 17 22 .104857 18 22 -.0908757 23 23 -1 26 23 -1 29 23 -.0311679 30 23 -.103571 19 24 -1 29 24 -.757389 30 24 -.625946 21 25 -1 28 25 -1 29 25 -10.7841 30 25 -35.8356 24 26 580 25 27 1 27 28 1 26 29 1 31 29 -1 33 29 -142.6 28 30 1 29 31 -.0979613 30 31 .0483804 31 32 1 33 32 145.6 33 33 580 32 34 1 34 35 -1 36 35 -161 38 35 1 35 36 -1 40 36 1 34 37 -1 36 37 -152.2 203 37 1 205 38 1 34 39 -1 36 39 -136.3 197 39 1 199 40 1 34 41 -1 36 41 -108.6 98 41 1 100 42 1 34 43 -1 36 43 -120.7 67 43 1 69 44 1 34 45 1 36 45 128 95 45 1 96 45 .2 36 46 680 92 46 -1 35 47 1 94 47 -1 38 48 -1 41 48 1.65272 42 48 2.82163 47 48 -1 41 49 -.607865 42 49 -.263986 43 49 -1 40 50 -1 41 50 36.3599 42 50 62.0759 45 50 -1 37 51 1 39 52 1 41 53 .559606 42 53 -.677581 47 54 1 48 54 .7 53 54 -1 44 55 -1 49 55 -1 46 56 -1 51 56 -1 47 57 -1 48 57 -1 203 57 -1 206 57 .478232 207 57 1.21868 43 58 1 44 58 1 206 58 -.330881 207 58 -.280695 45 59 1 46 59 1 205 59 -1 206 59 21.9987 207 59 56.0594 48 60 68 53 61 1 54 61 .6 59 61 -1 50 62 -1 55 62 -1 52 63 -1 57 63 -1 53 64 -1 54 64 -1 197 64 -1 200 64 .27161 201 64 .629158 49 65 1 50 65 1 200 65 -.561642 201 65 -.382811 51 66 1 52 66 1 199 66 -1 200 66 24.7165 201 66 57.2534 54 67 159 59 68 1 60 68 .2 65 68 -1 56 69 -1 61 69 -1 58 70 -1 63 70 -1 59 71 -1 60 71 -1 98 71 -1 101 71 .244371 102 71 1.02444 55 72 1 56 72 1 101 72 -.272351 102 72 -.432602 57 73 1 58 73 1 100 73 -1 101 73 11.7298 102 73 49.1733 60 74 207 65 75 -1 66 75 -1 67 75 -1 71 75 .232813 72 75 .061436 61 76 1 62 76 1 71 76 -.573583 72 76 -.869891 63 77 1 64 77 1 69 77 -1 71 77 47.4938 72 77 12.5329 66 78 411 68 79 -1 71 79 -.341668 72 79 -.40286 74 79 1 70 80 -1 71 80 -34.1668 72 80 -40.286 76 80 1 68 81 1 70 82 1 71 83 -.0459958 72 83 .0938315 73 84 -1 77 84 .179968 78 84 .0328426 83 84 -1 84 84 -1 77 85 -.53763 78 85 -.943234 79 85 1 80 85 1 75 86 -1 77 86 36.7135 78 86 6.69988 81 86 1 82 86 1 74 87 -1 77 87 -.311136 78 87 -.186857 164 87 1 76 88 -1 77 88 -31.1136 78 88 -18.6857 166 88 1 73 89 1 109 89 -1 111 89 -201 75 90 1 77 91 -.012899 78 91 .026314 83 92 1 84 92 .4 89 92 -1 80 93 -1 85 93 -1 82 94 -1 87 94 -1 83 95 -1 131 95 -1 134 95 .0222685 135 95 .0916503 79 96 -1 134 96 -.852598 135 96 -.686678 81 97 -1 133 97 -1 134 97 6.30198 135 97 25.937 84 98 487 89 99 1 90 99 .1 95 99 -1 86 100 -1 91 100 -1 88 101 -1 93 101 -1 89 102 -1 90 102 -1 104 102 -1 107 102 .306796 108 102 1.72865 85 103 1 86 103 1 107 103 -.953179 108 103 -.478015 87 104 1 88 104 1 106 104 -1 107 104 14.7262 108 104 82.9751 90 105 535 95 106 -1 96 106 -1 122 106 1 123 106 .6 91 107 1 92 107 1 119 107 -1 93 108 1 94 108 1 121 108 -1 96 109 680 97 110 -1 101 110 -.312836 102 110 -.082762 103 110 1 99 111 -1 101 111 -31.2836 102 111 -8.2762 105 111 1 97 112 1 99 113 1 101 114 .409192 102 114 -.852483 104 115 1 109 115 -1 111 115 -273.9 106 116 1 107 117 .147934 108 117 -.0810126 109 118 -1 111 118 -176.9 131 118 1 110 119 -1 133 119 1 109 120 -1 111 120 -209.1 125 120 1 127 121 1 109 122 -1 111 122 -193 113 122 1 111 123 -54 117 123 1 115 124 1 109 125 1 111 125 197 161 125 1 162 125 .6 111 126 680 158 126 -1 110 127 1 160 127 -1 113 128 -1 116 128 .250032 117 128 .597517 122 128 -1 116 129 -.585577 117 129 -.406865 118 129 -1 115 130 -1 116 130 13.5017 117 130 32.2659 120 130 -1 112 131 1 202 131 -1 206 131 -.419796 207 131 -.122705 114 132 1 204 132 -1 206 132 -41.9796 207 132 -12.2705 116 133 .239041 117 133 -.242126 122 134 -1 123 134 -1 125 134 -1 128 134 .158767 129 134 .340658 118 135 1 119 135 1 128 135 -.588216 129 135 -.353609 120 136 1 121 136 1 127 136 -1 128 136 14.4478 129 136 30.9999 123 137 145 124 138 -1 128 138 -.307616 129 138 -.130446 190 138 1 128 139 -.411784 129 139 -.646391 194 139 1 126 140 -1 128 140 -30.7616 129 140 -13.0446 192 140 1 124 141 1 196 141 -1 200 141 -.562373 201 141 -.225697 126 142 1 198 142 -1 200 142 -56.2373 201 142 -22.5697 128 143 .10564 129 143 -.116088 130 144 -1 134 144 -.276727 135 144 -.171445 140 144 -1 141 144 -1 134 145 -.147402 135 145 -.313322 136 145 1 137 145 1 132 146 -1 134 146 -28.7796 135 146 -17.8303 138 146 1 139 146 1 130 147 1 154 147 -1 156 147 -193.6 132 148 1 155 148 -1 134 149 .087773 135 149 -.0322558 140 150 -1 143 150 -1 146 150 -.0323781 147 150 -.0683179 136 151 -1 146 151 -.60537 147 151 -.349597 138 152 -1 145 152 -1 146 152 -12.1741 147 152 -25.6875 141 153 480 142 154 1 144 155 1 143 156 1 149 156 -1 152 156 -.00472003 153 156 -.0317473 147 157 1 152 157 -.934841 153 157 -.792495 145 158 1 151 158 -1 152 158 -1.77473 153 158 -11.937 146 159 -.0203625 147 159 .0218773 148 160 1 150 161 1 149 162 1 154 162 -1 156 162 -198 153 163 1 156 163 -376 151 164 1 152 165 -.0366465 153 165 .00813435 154 166 1 156 166 197.2 155 167 1 161 168 -1 162 168 -1 163 168 -1 167 168 .0165562 168 168 .00408216 157 169 1 158 169 1 167 169 -.832633 168 169 -.729721 159 170 1 160 170 1 165 170 -1 167 170 7.21849 168 170 1.77982 161 171 -1 191 171 -1 194 171 .00193333 195 171 .0781847 157 172 -1 194 172 -.995803 195 172 -.705952 159 173 -1 193 173 -1 194 173 .471732 195 173 19.0771 162 174 680 164 175 -1 167 175 -.0379488 168 175 -.16853 170 175 1 167 176 -.167367 168 176 -.270279 174 176 1 166 177 -1 167 177 -3.79488 168 177 -16.853 172 177 1 163 178 1 185 178 -1 188 178 .0406846 189 178 .100421 165 179 1 187 179 -1 188 179 17.7385 189 179 43.7834 167 180 -.0235888 168 180 .102847 169 181 -1 173 181 .123883 174 181 .0243372 191 181 1 171 182 -1 173 182 30.2273 174 182 5.93828 193 182 1 170 183 -1 173 183 -.242234 174 183 -.211144 176 183 1 173 184 -.3775 174 184 -.0788991 180 184 1 172 185 -1 173 185 -24.2234 174 185 -21.1144 178 185 1 169 186 1 181 186 -1 183 186 -281.7 171 187 1 182 187 -1 173 188 -.0173768 174 188 .0423995 175 189 -1 179 189 .0149554 180 189 .00262203 181 189 1 183 189 291 179 190 -.825997 180 190 -.904947 183 190 680 177 191 -1 179 191 10.1696 180 191 1.78298 182 191 1 175 192 1 177 193 1 179 194 -.00696415 180 194 .0362189 181 195 -1 183 195 -296 185 195 1 187 196 1 184 197 1 188 198 1 186 199 1 188 200 .0382256 189 200 -.0306734 194 201 .00264546 195 201 -.000781169 196 202 1 198 203 1 200 204 .229712 201 204 -.25243 202 205 1 204 206 1 206 207 .27097 207 207 -.589066 SuiteSparse/KLU/Matrix/two.mtx0000644001170100242450000000007210614235637015217 0ustar davisfac%%MatrixMarket matrix coordinate real general 2 2 1 1 1 3 SuiteSparse/KLU/Matrix/w156.mtx0000644001170100242450000002616710614162203015111 0ustar davisfac%%MatrixMarket matrix coordinate complex general % complex matrix with the same real part, and same pattern, as HB/west0156 156 156 362 147 1 1 -89.00615831818635 148 2 1 19.968263502718298 149 2 -.1632648 -21.370801333956592 59 3 -1.16206 -56.926762937042156 134 3 -.8122999 -63.520075069490886 149 3 1 -84.64919515773938 52 4 1 -98.51526079522304 53 5 1 57.75659925548426 54 5 -.2166122 -96.44247397535688 54 6 1 75.58829308886945 59 6 -.1 -29.491646321365707 118 7 1 44.42795357432983 119 8 1 93.69016787815801 120 8 -.2113848 -68.86640328523129 59 9 1 -67.40889160696356 105 9 .699017 -37.32052633277537 120 9 1 -94.12369035075191 150 10 1.009263 -28.474976610167545 151 10 11.46533 -94.56192034360119 150 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========================================================================== */ /* === klu include file ===================================================== */ /* ========================================================================== */ /* Include file for user programs that call klu_* routines */ #ifndef _KLU_H #define _KLU_H /* make it easy for C++ programs to include KLU */ #ifdef __cplusplus extern "C" { #endif #include "amd.h" #include "colamd.h" #include "btf.h" /* -------------------------------------------------------------------------- */ /* Symbolic object - contains the pre-ordering computed by klu_analyze */ /* -------------------------------------------------------------------------- */ typedef struct { /* A (P,Q) is in upper block triangular form. The kth block goes from * row/col index R [k] to R [k+1]-1. The estimated number of nonzeros * in the L factor of the kth block is Lnz [k]. */ /* only computed if the AMD ordering is chosen: */ double symmetry ; /* symmetry of largest block */ double est_flops ; /* est. factorization flop count */ double lnz, unz ; /* estimated nz in L and U, including diagonals */ double *Lnz ; /* size n, but only Lnz [0..nblocks-1] is used */ /* computed for all orderings: */ int n, /* input matrix A is n-by-n */ nz, /* # entries in input matrix */ *P, /* size n */ *Q, /* size n */ *R, /* size n+1, but only R [0..nblocks] is used */ nzoff, /* nz in off-diagonal blocks */ nblocks, /* number of blocks */ maxblock, /* size of largest block */ ordering, /* ordering used (AMD, COLAMD, or GIVEN) */ do_btf ; /* whether or not BTF preordering was requested */ /* only computed if BTF preordering requested */ int structural_rank ; /* 0 to n-1 if the matrix is structurally rank * deficient. -1 if not computed. n if the matrix has * full structural rank */ } klu_symbolic ; typedef struct /* 64-bit version (otherwise same as above) */ { double symmetry, est_flops, lnz, unz ; double *Lnz ; UF_long n, nz, *P, *Q, *R, nzoff, nblocks, maxblock, ordering, do_btf, structural_rank ; } klu_l_symbolic ; /* -------------------------------------------------------------------------- */ /* Numeric object - contains the factors computed by klu_factor */ /* -------------------------------------------------------------------------- */ typedef struct { /* LU factors of each block, the pivot row permutation, and the * entries in the off-diagonal blocks */ int n ; /* A is n-by-n */ int nblocks ; /* number of diagonal blocks */ int lnz ; /* actual nz in L, including diagonal */ int unz ; /* actual nz in U, including diagonal */ int max_lnz_block ; /* max actual nz in L in any one block, incl. diag */ int max_unz_block ; /* max actual nz in U in any one block, incl. diag */ int *Pnum ; /* size n. final pivot permutation */ int *Pinv ; /* size n. inverse of final pivot permutation */ /* LU factors of each block */ int *Lip ; /* size n. pointers into LUbx[block] for L */ int *Uip ; /* size n. pointers into LUbx[block] for U */ int *Llen ; /* size n. Llen [k] = # of entries in kth column of L */ int *Ulen ; /* size n. Ulen [k] = # of entries in kth column of U */ void **LUbx ; /* L and U indices and entries (excl. diagonal of U) */ size_t *LUsize ; /* size of each LUbx [block], in sizeof (Unit) */ void *Udiag ; /* diagonal of U */ /* scale factors; can be NULL if no scaling */ double *Rs ; /* size n. Rs [i] is scale factor for row i */ /* permanent workspace for factorization and solve */ size_t worksize ; /* size (in bytes) of Work */ void *Work ; /* workspace */ void *Xwork ; /* alias into Numeric->Work */ int *Iwork ; /* alias into Numeric->Work */ /* off-diagonal entries in a conventional compressed-column sparse matrix */ int *Offp ; /* size n+1, column pointers */ int *Offi ; /* size nzoff, row indices */ void *Offx ; /* size nzoff, numerical values */ int nzoff ; } klu_numeric ; typedef struct /* 64-bit version (otherwise same as above) */ { UF_long n, nblocks, lnz, unz, max_lnz_block, max_unz_block, *Pnum, *Pinv, *Lip, *Uip, *Llen, *Ulen ; void **LUbx ; size_t *LUsize ; void *Udiag ; double *Rs ; size_t worksize ; void *Work, *Xwork ; UF_long *Iwork ; UF_long *Offp, *Offi ; void *Offx ; UF_long nzoff ; } klu_l_numeric ; /* -------------------------------------------------------------------------- */ /* KLU control parameters and statistics */ /* -------------------------------------------------------------------------- */ /* Common->status values */ #define KLU_OK 0 #define KLU_SINGULAR (1) /* status > 0 is a warning, not an error */ #define KLU_OUT_OF_MEMORY (-2) #define KLU_INVALID (-3) #define KLU_TOO_LARGE (-4) /* integer overflow has occured */ typedef struct klu_common_struct { /* ---------------------------------------------------------------------- */ /* parameters */ /* ---------------------------------------------------------------------- */ double tol ; /* pivot tolerance for diagonal preference */ double memgrow ; /* realloc memory growth size for LU factors */ double initmem_amd ; /* init. memory size with AMD: c*nnz(L) + n */ double initmem ; /* init. memory size: c*nnz(A) + n */ double maxwork ; /* maxwork for BTF, <= 0 if no limit */ int btf ; /* use BTF pre-ordering, or not */ int ordering ; /* 0: AMD, 1: COLAMD, 2: user P and Q, * 3: user function */ int scale ; /* row scaling: -1: none (and no error check), * 0: none, 1: sum, 2: max */ /* memory management routines */ void *(*malloc_memory) (size_t) ; /* pointer to malloc */ void *(*realloc_memory) (void *, size_t) ; /* pointer to realloc */ void (*free_memory) (void *) ; /* pointer to free */ void *(*calloc_memory) (size_t, size_t) ; /* pointer to calloc */ /* pointer to user ordering function */ int (*user_order) (int, int *, int *, int *, struct klu_common_struct *) ; /* pointer to user data, passed unchanged as the last parameter to the * user ordering function (optional, the user function need not use this * information). */ void *user_data ; int halt_if_singular ; /* how to handle a singular matrix: * FALSE: keep going. Return a Numeric object with a zero U(k,k). A * divide-by-zero may occur when computing L(:,k). The Numeric object * can be passed to klu_solve (a divide-by-zero will occur). It can * also be safely passed to klu_refactor. * TRUE: stop quickly. klu_factor will free the partially-constructed * Numeric object. klu_refactor will not free it, but will leave the * numerical values only partially defined. This is the default. */ /* ---------------------------------------------------------------------- */ /* statistics */ /* ---------------------------------------------------------------------- */ int status ; /* KLU_OK if OK, < 0 if error */ int nrealloc ; /* # of reallocations of L and U */ int structural_rank ; /* 0 to n-1 if the matrix is structurally rank * deficient (as determined by maxtrans). -1 if not computed. n if the * matrix has full structural rank. This is computed by klu_analyze * if a BTF preordering is requested. */ int numerical_rank ; /* First k for which a zero U(k,k) was found, * if the matrix was singular (in the range 0 to n-1). n if the matrix * has full rank. This is not a true rank-estimation. It just reports * where the first zero pivot was found. -1 if not computed. * Computed by klu_factor and klu_refactor. */ int singular_col ; /* n if the matrix is not singular. If in the * range 0 to n-1, this is the column index of the original matrix A that * corresponds to the column of U that contains a zero diagonal entry. * -1 if not computed. Computed by klu_factor and klu_refactor. */ int noffdiag ; /* # of off-diagonal pivots, -1 if not computed */ double flops ; /* actual factorization flop count, from klu_flops */ double rcond ; /* crude reciprocal condition est., from klu_rcond */ double condest ; /* accurate condition est., from klu_condest */ double rgrowth ; /* reciprocal pivot rgrowth, from klu_rgrowth */ double work ; /* actual work done in BTF, in klu_analyze */ size_t memusage ; /* current memory usage, in bytes */ size_t mempeak ; /* peak memory usage, in bytes */ } klu_common ; typedef struct klu_l_common_struct /* 64-bit version (otherwise same as above)*/ { double tol, memgrow, initmem_amd, initmem, maxwork ; UF_long btf, ordering, scale ; void *(*malloc_memory) (size_t) ; void *(*realloc_memory) (void *, size_t) ; void (*free_memory) (void *) ; void *(*calloc_memory) (size_t, size_t) ; UF_long (*user_order) (UF_long, UF_long *, UF_long *, UF_long *, struct klu_l_common_struct *) ; void *user_data ; UF_long halt_if_singular ; UF_long status, nrealloc, structural_rank, numerical_rank, singular_col, noffdiag ; double flops, rcond, condest, rgrowth, work ; size_t memusage, mempeak ; } klu_l_common ; /* -------------------------------------------------------------------------- */ /* klu_defaults: sets default control parameters */ /* -------------------------------------------------------------------------- */ int klu_defaults ( klu_common *Common ) ; UF_long klu_l_defaults (klu_l_common *Common) ; /* -------------------------------------------------------------------------- */ /* klu_analyze: orders and analyzes a matrix */ /* -------------------------------------------------------------------------- */ /* Order the matrix with BTF (or not), then order each block with AMD, COLAMD, * a natural ordering, or with a user-provided ordering function */ klu_symbolic *klu_analyze ( /* inputs, not modified */ int n, /* A is n-by-n */ int Ap [ ], /* size n+1, column pointers */ int Ai [ ], /* size nz, row indices */ klu_common *Common ) ; klu_l_symbolic *klu_l_analyze (UF_long, UF_long *, UF_long *, klu_l_common *Common) ; /* -------------------------------------------------------------------------- */ /* klu_analyze_given: analyzes a matrix using given P and Q */ /* -------------------------------------------------------------------------- */ /* Order the matrix with BTF (or not), then use natural or given ordering * P and Q on the blocks. P and Q are interpretted as identity * if NULL. */ klu_symbolic *klu_analyze_given ( /* inputs, not modified */ int n, /* A is n-by-n */ int Ap [ ], /* size n+1, column pointers */ int Ai [ ], /* size nz, row indices */ int P [ ], /* size n, user's row permutation (may be NULL) */ int Q [ ], /* size n, user's column permutation (may be NULL) */ klu_common *Common ) ; klu_l_symbolic *klu_l_analyze_given (UF_long, UF_long *, UF_long *, UF_long *, UF_long *, klu_l_common *) ; /* -------------------------------------------------------------------------- */ /* klu_factor: factors a matrix using the klu_analyze results */ /* -------------------------------------------------------------------------- */ klu_numeric *klu_factor /* returns KLU_OK if OK, < 0 if error */ ( /* inputs, not modified */ int Ap [ ], /* size n+1, column pointers */ int Ai [ ], /* size nz, row indices */ double Ax [ ], /* size nz, numerical values */ klu_symbolic *Symbolic, klu_common *Common ) ; klu_numeric *klu_z_factor /* returns KLU_OK if OK, < 0 if error */ ( /* inputs, not modified */ int Ap [ ], /* size n+1, column pointers */ int Ai [ ], /* size nz, row indices */ double Ax [ ], /* size 2*nz, numerical values (real,imag pairs) */ klu_symbolic *Symbolic, klu_common *Common ) ; /* long / real version */ klu_l_numeric *klu_l_factor (UF_long *, UF_long *, double *, klu_l_symbolic *, klu_l_common *) ; /* long / complex version */ klu_l_numeric *klu_zl_factor (UF_long *, UF_long *, double *, klu_l_symbolic *, klu_l_common *) ; /* -------------------------------------------------------------------------- */ /* klu_solve: solves Ax=b using the Symbolic and Numeric objects */ /* -------------------------------------------------------------------------- */ int klu_solve ( /* inputs, not modified */ klu_symbolic *Symbolic, klu_numeric *Numeric, int ldim, /* leading dimension of B */ int nrhs, /* number of right-hand-sides */ /* right-hand-side on input, overwritten with solution to Ax=b on output */ double B [ ], /* size ldim*nrhs */ klu_common *Common ) ; int klu_z_solve ( /* inputs, not modified */ klu_symbolic *Symbolic, klu_numeric *Numeric, int ldim, /* leading dimension of B */ int nrhs, /* number of right-hand-sides */ /* right-hand-side on input, overwritten with solution to Ax=b on output */ double B [ ], /* size 2*ldim*nrhs */ klu_common *Common ) ; UF_long klu_l_solve (klu_l_symbolic *, klu_l_numeric *, UF_long, UF_long, double *, klu_l_common *) ; UF_long klu_zl_solve (klu_l_symbolic *, klu_l_numeric *, UF_long, UF_long, double *, klu_l_common *) ; /* -------------------------------------------------------------------------- */ /* klu_tsolve: solves A'x=b using the Symbolic and Numeric objects */ /* -------------------------------------------------------------------------- */ int klu_tsolve ( /* inputs, not modified */ klu_symbolic *Symbolic, klu_numeric *Numeric, int ldim, /* leading dimension of B */ int nrhs, /* number of right-hand-sides */ /* right-hand-side on input, overwritten with solution to Ax=b on output */ double B [ ], /* size ldim*nrhs */ klu_common *Common ) ; int klu_z_tsolve ( /* inputs, not modified */ klu_symbolic *Symbolic, klu_numeric *Numeric, int ldim, /* leading dimension of B */ int nrhs, /* number of right-hand-sides */ /* right-hand-side on input, overwritten with solution to Ax=b on output */ double B [ ], /* size 2*ldim*nrhs */ int conj_solve, /* TRUE: conjugate solve, FALSE: solve A.'x=b */ klu_common *Common ) ; UF_long klu_l_tsolve (klu_l_symbolic *, klu_l_numeric *, UF_long, UF_long, double *, klu_l_common *) ; UF_long klu_zl_tsolve (klu_l_symbolic *, klu_l_numeric *, UF_long, UF_long, double *, UF_long, klu_l_common * ) ; /* -------------------------------------------------------------------------- */ /* klu_refactor: refactorizes matrix with same ordering as klu_factor */ /* -------------------------------------------------------------------------- */ int klu_refactor /* return TRUE if successful, FALSE otherwise */ ( /* inputs, not modified */ int Ap [ ], /* size n+1, column pointers */ int Ai [ ], /* size nz, row indices */ double Ax [ ], /* size nz, numerical values */ klu_symbolic *Symbolic, /* input, and numerical values modified on output */ klu_numeric *Numeric, klu_common *Common ) ; int klu_z_refactor /* return TRUE if successful, FALSE otherwise */ ( /* inputs, not modified */ int Ap [ ], /* size n+1, column pointers */ int Ai [ ], /* size nz, row indices */ double Ax [ ], /* size 2*nz, numerical values */ klu_symbolic *Symbolic, /* input, and numerical values modified on output */ klu_numeric *Numeric, klu_common *Common ) ; UF_long klu_l_refactor (UF_long *, UF_long *, double *, klu_l_symbolic *, klu_l_numeric *, klu_l_common *) ; UF_long klu_zl_refactor (UF_long *, UF_long *, double *, klu_l_symbolic *, klu_l_numeric *, klu_l_common *) ; /* -------------------------------------------------------------------------- */ /* klu_free_symbolic: destroys the Symbolic object */ /* -------------------------------------------------------------------------- */ int klu_free_symbolic ( klu_symbolic **Symbolic, klu_common *Common ) ; UF_long klu_l_free_symbolic (klu_l_symbolic **, klu_l_common *) ; /* -------------------------------------------------------------------------- */ /* klu_free_numeric: destroys the Numeric object */ /* -------------------------------------------------------------------------- */ /* Note that klu_free_numeric and klu_z_free_numeric are identical; each can * free both kinds of Numeric objects (real and complex) */ int klu_free_numeric ( klu_numeric **Numeric, klu_common *Common ) ; int klu_z_free_numeric ( klu_numeric **Numeric, klu_common *Common ) ; UF_long klu_l_free_numeric (klu_l_numeric **, klu_l_common *) ; UF_long klu_zl_free_numeric (klu_l_numeric **, klu_l_common *) ; /* -------------------------------------------------------------------------- */ /* klu_sort: sorts the columns of the LU factorization */ /* -------------------------------------------------------------------------- */ /* this is not needed except for the MATLAB interface */ int klu_sort ( /* inputs, not modified */ klu_symbolic *Symbolic, /* input/output */ klu_numeric *Numeric, klu_common *Common ) ; int klu_z_sort ( /* inputs, not modified */ klu_symbolic *Symbolic, /* input/output */ klu_numeric *Numeric, klu_common *Common ) ; UF_long klu_l_sort (klu_l_symbolic *, klu_l_numeric *, klu_l_common *) ; UF_long klu_zl_sort (klu_l_symbolic *, klu_l_numeric *, klu_l_common *) ; /* -------------------------------------------------------------------------- */ /* klu_flops: determines # of flops performed in numeric factorzation */ /* -------------------------------------------------------------------------- */ int klu_flops ( /* inputs, not modified */ klu_symbolic *Symbolic, klu_numeric *Numeric, /* input/output */ klu_common *Common ) ; int klu_z_flops ( /* inputs, not modified */ klu_symbolic *Symbolic, klu_numeric *Numeric, /* input/output */ klu_common *Common ) ; UF_long klu_l_flops (klu_l_symbolic *, klu_l_numeric *, klu_l_common *) ; UF_long klu_zl_flops (klu_l_symbolic *, klu_l_numeric *, klu_l_common *) ; /* -------------------------------------------------------------------------- */ /* klu_rgrowth : compute the reciprocal pivot growth */ /* -------------------------------------------------------------------------- */ /* Pivot growth is computed after the input matrix is permuted, scaled, and * off-diagonal entries pruned. This is because the LU factorization of each * block takes as input the scaled diagonal blocks of the BTF form. The * reciprocal pivot growth in column j of an LU factorization of a matrix C * is the largest entry in C divided by the largest entry in U; then the overall * reciprocal pivot growth is the smallest such value for all columns j. Note * that the off-diagonal entries are not scaled, since they do not take part in * the LU factorization of the diagonal blocks. * * In MATLAB notation: * * rgrowth = min (max (abs ((R \ A(p,q)) - F)) ./ max (abs (U))) */ int klu_rgrowth ( int Ap [ ], int Ai [ ], double Ax [ ], klu_symbolic *Symbolic, klu_numeric *Numeric, klu_common *Common /* Common->rgrowth = reciprocal pivot growth */ ) ; int klu_z_rgrowth ( int Ap [ ], int Ai [ ], double Ax [ ], klu_symbolic *Symbolic, klu_numeric *Numeric, klu_common *Common /* Common->rgrowth = reciprocal pivot growth */ ) ; UF_long klu_l_rgrowth (UF_long *, UF_long *, double *, klu_l_symbolic *, klu_l_numeric *, klu_l_common *) ; UF_long klu_zl_rgrowth (UF_long *, UF_long *, double *, klu_l_symbolic *, klu_l_numeric *, klu_l_common *) ; /* -------------------------------------------------------------------------- */ /* klu_condest */ /* -------------------------------------------------------------------------- */ /* Computes a reasonably accurate estimate of the 1-norm condition number, using * Hager's method, as modified by Higham and Tisseur (same method as used in * MATLAB's condest */ int klu_condest ( int Ap [ ], /* size n+1, column pointers, not modified */ double Ax [ ], /* size nz = Ap[n], numerical values, not modified*/ klu_symbolic *Symbolic, /* symbolic analysis, not modified */ klu_numeric *Numeric, /* numeric factorization, not modified */ klu_common *Common /* result returned in Common->condest */ ) ; int klu_z_condest ( int Ap [ ], double Ax [ ], /* size 2*nz */ klu_symbolic *Symbolic, klu_numeric *Numeric, klu_common *Common /* result returned in Common->condest */ ) ; UF_long klu_l_condest (UF_long *, double *, klu_l_symbolic *, klu_l_numeric *, klu_l_common *) ; UF_long klu_zl_condest (UF_long *, double *, klu_l_symbolic *, klu_l_numeric *, klu_l_common *) ; /* -------------------------------------------------------------------------- */ /* klu_rcond: compute min(abs(diag(U))) / max(abs(diag(U))) */ /* -------------------------------------------------------------------------- */ int klu_rcond ( klu_symbolic *Symbolic, /* input, not modified */ klu_numeric *Numeric, /* input, not modified */ klu_common *Common /* result in Common->rcond */ ) ; int klu_z_rcond ( klu_symbolic *Symbolic, /* input, not modified */ klu_numeric *Numeric, /* input, not modified */ klu_common *Common /* result in Common->rcond */ ) ; UF_long klu_l_rcond (klu_l_symbolic *, klu_l_numeric *, klu_l_common *) ; UF_long klu_zl_rcond (klu_l_symbolic *, klu_l_numeric *, klu_l_common *) ; /* -------------------------------------------------------------------------- */ /* klu_scale */ /* -------------------------------------------------------------------------- */ int klu_scale /* return TRUE if successful, FALSE otherwise */ ( /* inputs, not modified */ int scale, /* <0: none, no error check; 0: none, 1: sum, 2: max */ int n, int Ap [ ], /* size n+1, column pointers */ int Ai [ ], /* size nz, row indices */ double Ax [ ], /* outputs, not defined on input */ double Rs [ ], /* workspace, not defined on input or output */ int W [ ], /* size n, can be NULL */ klu_common *Common ) ; int klu_z_scale /* return TRUE if successful, FALSE otherwise */ ( /* inputs, not modified */ int scale, /* <0: none, no error check; 0: none, 1: sum, 2: max */ int n, int Ap [ ], /* size n+1, column pointers */ int Ai [ ], /* size nz, row indices */ double Ax [ ], /* outputs, not defined on input */ double Rs [ ], /* workspace, not defined on input or output */ int W [ ], /* size n, can be NULL */ klu_common *Common ) ; UF_long klu_l_scale (UF_long, UF_long, UF_long *, UF_long *, double *, double *, UF_long *, klu_l_common *) ; UF_long klu_zl_scale (UF_long, UF_long, UF_long *, UF_long *, double *, double *, UF_long *, klu_l_common *) ; /* -------------------------------------------------------------------------- */ /* klu_extract */ /* -------------------------------------------------------------------------- */ int klu_extract /* returns TRUE if successful, FALSE otherwise */ ( /* inputs: */ klu_numeric *Numeric, klu_symbolic *Symbolic, /* outputs, either allocated on input, or ignored otherwise */ /* L */ int *Lp, /* size n+1 */ int *Li, /* size Numeric->lnz */ double *Lx, /* size Numeric->lnz */ /* U */ int *Up, /* size n+1 */ int *Ui, /* size Numeric->unz */ double *Ux, /* size Numeric->unz */ /* F */ int *Fp, /* size n+1 */ int *Fi, /* size Numeric->nzoff */ double *Fx, /* size Numeric->nzoff */ /* P, row permutation */ int *P, /* size n */ /* Q, column permutation */ int *Q, /* size n */ /* Rs, scale factors */ double *Rs, /* size n */ /* R, block boundaries */ int *R, /* size Symbolic->nblocks+1 (nblocks is at most n) */ klu_common *Common ) ; int klu_z_extract /* returns TRUE if successful, FALSE otherwise */ ( /* inputs: */ klu_numeric *Numeric, klu_symbolic *Symbolic, /* outputs, all of which must be allocated on input */ /* L */ int *Lp, /* size n+1 */ int *Li, /* size nnz(L) */ double *Lx, /* size nnz(L) */ double *Lz, /* size nnz(L) for the complex case, ignored if real */ /* U */ int *Up, /* size n+1 */ int *Ui, /* size nnz(U) */ double *Ux, /* size nnz(U) */ double *Uz, /* size nnz(U) for the complex case, ignored if real */ /* F */ int *Fp, /* size n+1 */ int *Fi, /* size nnz(F) */ double *Fx, /* size nnz(F) */ double *Fz, /* size nnz(F) for the complex case, ignored if real */ /* P, row permutation */ int *P, /* size n */ /* Q, column permutation */ int *Q, /* size n */ /* Rs, scale factors */ double *Rs, /* size n */ /* R, block boundaries */ int *R, /* size Symbolic->nblocks+1 (nblocks is at most n) */ klu_common *Common ) ; UF_long klu_l_extract (klu_l_numeric *, klu_l_symbolic *, UF_long *, UF_long *, double *, UF_long *, UF_long *, double *, UF_long *, UF_long *, double *, UF_long *, UF_long *, double *, UF_long *, klu_l_common *) ; UF_long klu_zl_extract (klu_l_numeric *, klu_l_symbolic *, UF_long *, UF_long *, double *, double *, UF_long *, UF_long *, double *, double *, UF_long *, UF_long *, double *, double *, UF_long *, UF_long *, double *, UF_long *, klu_l_common *) ; /* -------------------------------------------------------------------------- */ /* KLU memory management routines */ /* -------------------------------------------------------------------------- */ void *klu_malloc /* returns pointer to the newly malloc'd block */ ( /* ---- input ---- */ size_t n, /* number of items */ size_t size, /* size of each item */ /* --------------- */ klu_common *Common ) ; void *klu_free /* always returns NULL */ ( /* ---- in/out --- */ void *p, /* block of memory to free */ size_t n, /* number of items */ size_t size, /* size of each item */ /* --------------- */ klu_common *Common ) ; void *klu_realloc /* returns pointer to reallocated block */ ( /* ---- input ---- */ size_t nnew, /* requested # of items in reallocated block */ size_t nold, /* current size of block, in # of items */ size_t size, /* size of each item */ /* ---- in/out --- */ void *p, /* block of memory to realloc */ /* --------------- */ klu_common *Common ) ; void *klu_l_malloc (size_t, size_t, klu_l_common *) ; void *klu_l_free (void *, size_t, size_t, klu_l_common *) ; void *klu_l_realloc (size_t, size_t, size_t, void *, klu_l_common *) ; /* ========================================================================== */ /* === KLU version ========================================================== */ /* ========================================================================== */ /* All versions of KLU include these definitions. * As an example, to test if the version you are using is 1.2 or later: * * if (KLU_VERSION >= KLU_VERSION_CODE (1,2)) ... * * This also works during compile-time: * * #if (KLU >= KLU_VERSION_CODE (1,2)) * printf ("This is version 1.2 or later\n") ; * #else * printf ("This is an early version\n") ; * #endif */ #define KLU_DATE "Nov 1, 2007" #define KLU_VERSION_CODE(main,sub) ((main) * 1000 + (sub)) #define KLU_MAIN_VERSION 1 #define KLU_SUB_VERSION 0 #define KLU_SUBSUB_VERSION 1 #define KLU_VERSION KLU_VERSION_CODE(KLU_MAIN_VERSION,KLU_SUB_VERSION) #ifdef __cplusplus } #endif #endif SuiteSparse/KLU/Include/klu_internal.h0000644001170100242450000001430510616717326016641 0ustar davisfac/* ========================================================================== */ /* === KLU/Include/klu_internal.h =========================================== */ /* ========================================================================== */ /* For internal use in KLU routines only, not for user programs */ #ifndef _KLU_INTERNAL_H #define _KLU_INTERNAL_H #include "klu.h" #include "btf.h" #include "klu_version.h" /* ========================================================================== */ /* make sure debugging and printing is turned off */ #ifndef NDEBUG #define NDEBUG #endif #ifndef NPRINT #define NPRINT #endif /* To enable debugging and assertions, uncomment this line: #undef NDEBUG */ /* To enable diagnostic printing, uncomment this line: #undef NPRINT */ /* ========================================================================== */ #include #include #include #include #include #undef ASSERT #ifndef NDEBUG #define ASSERT(a) assert(a) #else #define ASSERT(a) #endif #define SCALAR_IS_NAN(x) ((x) != (x)) /* true if an integer (stored in double x) would overflow (or if x is NaN) */ #define INT_OVERFLOW(x) ((!((x) * (1.0+1e-8) <= (double) INT_MAX)) \ || SCALAR_IS_NAN (x)) #undef TRUE #undef FALSE #undef MAX #undef MIN #undef PRINTF #undef FLIP #ifndef NPRINT #define PRINTF(s) { printf s ; } ; #else #define PRINTF(s) #endif #define TRUE 1 #define FALSE 0 #define MAX(a,b) (((a) > (b)) ? (a) : (b)) #define MIN(a,b) (((a) < (b)) ? (a) : (b)) /* FLIP is a "negation about -1", and is used to mark an integer i that is * normally non-negative. FLIP (EMPTY) is EMPTY. FLIP of a number > EMPTY * is negative, and FLIP of a number < EMTPY is positive. FLIP (FLIP (i)) = i * for all integers i. UNFLIP (i) is >= EMPTY. */ #define EMPTY (-1) #define FLIP(i) (-(i)-2) #define UNFLIP(i) (((i) < EMPTY) ? FLIP (i) : (i)) size_t KLU_kernel /* final size of LU on output */ ( /* input, not modified */ Int n, /* A is n-by-n */ Int Ap [ ], /* size n+1, column pointers for A */ Int Ai [ ], /* size nz = Ap [n], row indices for A */ Entry Ax [ ], /* size nz, values of A */ Int Q [ ], /* size n, optional input permutation */ size_t lusize, /* initial size of LU */ /* output, not defined on input */ Int Pinv [ ], /* size n */ Int P [ ], /* size n */ Unit **p_LU, /* size lusize on input, size Uxp[n] on output*/ Entry Udiag [ ], /* size n, diagonal of U */ Int Llen [ ], /* size n, column length of L */ Int Ulen [ ], /* size n, column length of U */ Int Lip [ ], /* size n+1 */ Int Uip [ ], /* size n+1 */ Int *lnz, /* size of L */ Int *unz, /* size of U */ /* workspace, not defined on input */ Entry X [ ], /* size n, zero on output */ /* workspace, not defined on input or output */ Int Stack [ ], /* size n */ Int Flag [ ], /* size n */ Int adj_pos [ ], /* size n */ /* workspace for pruning only */ Int Lpend [ ], /* size n workspace */ /* inputs, not modified on output */ Int k1, /* the block of A is from k1 to k2-1 */ Int PSinv [ ], /* inverse of P from symbolic factorization */ double Rs [ ], /* scale factors for A */ /* inputs, modified on output */ Int Offp [ ], /* off-diagonal matrix (modified by this routine) */ Int Offi [ ], Entry Offx [ ], KLU_common *Common /* the control input/output structure */ ) ; size_t KLU_kernel_factor /* 0 if failure, size of LU if OK */ ( /* inputs, not modified */ Int n, /* A is n-by-n. n must be > 0. */ Int Ap [ ], /* size n+1, column pointers for A */ Int Ai [ ], /* size nz = Ap [n], row indices for A */ Entry Ax [ ], /* size nz, values of A */ Int Q [ ], /* size n, optional column permutation */ double Lsize, /* initial size of L and U */ /* outputs, not defined on input */ Unit **p_LU, /* row indices and values of L and U */ Entry Udiag [ ], /* size n, diagonal of U */ Int Llen [ ], /* size n, column length of L */ Int Ulen [ ], /* size n, column length of U */ Int Lip [ ], /* size n+1, column pointers of L */ Int Uip [ ], /* size n+1, column pointers of U */ Int P [ ], /* row permutation, size n */ Int *lnz, /* size of L */ Int *unz, /* size of U */ /* workspace, undefined on input */ Entry *X, /* size n entries. Zero on output */ Int *Work, /* size 5n Int's */ /* inputs, not modified on output */ Int k1, /* the block of A is from k1 to k2-1 */ Int PSinv [ ], /* inverse of P from symbolic factorization */ double Rs [ ], /* scale factors for A */ /* inputs, modified on output */ Int Offp [ ], /* off-diagonal matrix (modified by this routine) */ Int Offi [ ], Entry Offx [ ], KLU_common *Common /* the control input/output structure */ ) ; void KLU_lsolve ( /* inputs, not modified: */ Int n, Int Lp [ ], Int Li [ ], Unit LU [ ], Int nrhs, /* right-hand-side on input, solution to Lx=b on output */ Entry X [ ] ) ; void KLU_ltsolve ( /* inputs, not modified: */ Int n, Int Lp [ ], Int Li [ ], Unit LU [ ], Int nrhs, #ifdef COMPLEX Int conj_solve, #endif /* right-hand-side on input, solution to L'x=b on output */ Entry X [ ] ) ; void KLU_usolve ( /* inputs, not modified: */ Int n, Int Up [ ], Int Ui [ ], Unit LU [ ], Entry Udiag [ ], Int nrhs, /* right-hand-side on input, solution to Ux=b on output */ Entry X [ ] ) ; void KLU_utsolve ( /* inputs, not modified: */ Int n, Int Up [ ], Int Ui [ ], Unit LU [ ], Entry Udiag [ ], Int nrhs, #ifdef COMPLEX Int conj_solve, #endif /* right-hand-side on input, solution to U'x=b on output */ Entry X [ ] ) ; Int KLU_valid ( Int n, Int Ap [ ], Int Ai [ ], Entry Ax [ ] ) ; Int KLU_valid_LU ( Int n, Int flag_test_start_ptr, Int Xip [ ], Int Xlen [ ], Unit LU [ ] ); size_t KLU_add_size_t (size_t a, size_t b, Int *ok) ; size_t KLU_mult_size_t (size_t a, size_t k, Int *ok) ; KLU_symbolic *KLU_alloc_symbolic (Int n, Int *Ap, Int *Ai, KLU_common *Common) ; #endif SuiteSparse/KLU/Include/klu_version.h0000644001170100242450000004441310620326133016500 0ustar davisfac#ifndef _KLU_VERSION_H #define _KLU_VERSION_H #ifdef DLONG #define Int UF_long #define Int_id UF_long_id #define Int_MAX UF_long_max #else #define Int int #define Int_id "%d" #define Int_MAX INT_MAX #endif #define NPRINT #define BYTES(type,n) (sizeof (type) * (n)) #define CEILING(b,u) (((b)+(u)-1) / (u)) #define UNITS(type,n) (CEILING (BYTES (type,n), sizeof (Unit))) #define DUNITS(type,n) (ceil (BYTES (type, (double) n) / sizeof (Unit))) #define GET_I_POINTER(LU, Xip, Xi, k) \ { \ Xi = (Int *) (LU + Xip [k]) ; \ } #define GET_X_POINTER(LU, Xip, Xlen, Xx, k) \ { \ Xx = (Entry *) (LU + Xip [k] + UNITS (Int, Xlen [k])) ; \ } #define GET_POINTER(LU, Xip, Xlen, Xi, Xx, k, xlen) \ { \ Unit *xp = LU + Xip [k] ; \ xlen = Xlen [k] ; \ Xi = (Int *) xp ; \ Xx = (Entry *) (xp + UNITS (Int, xlen)) ; \ } /* function names */ #ifdef COMPLEX #ifdef DLONG #define KLU_scale klu_zl_scale #define KLU_solve klu_zl_solve #define KLU_tsolve klu_zl_tsolve #define KLU_free_numeric klu_zl_free_numeric #define KLU_factor klu_zl_factor #define KLU_refactor klu_zl_refactor #define KLU_kernel_factor klu_zl_kernel_factor #define KLU_lsolve klu_zl_lsolve #define KLU_ltsolve klu_zl_ltsolve #define KLU_usolve klu_zl_usolve #define KLU_utsolve klu_zl_utsolve #define KLU_kernel klu_zl_kernel #define KLU_valid klu_zl_valid #define KLU_valid_LU klu_zl_valid_LU #define KLU_sort klu_zl_sort #define KLU_rgrowth klu_zl_rgrowth #define KLU_rcond klu_zl_rcond #define KLU_extract klu_zl_extract #define KLU_condest klu_zl_condest #define KLU_flops klu_zl_flops #else #define KLU_scale klu_z_scale #define KLU_solve klu_z_solve #define KLU_tsolve klu_z_tsolve #define KLU_free_numeric klu_z_free_numeric #define KLU_factor klu_z_factor #define KLU_refactor klu_z_refactor #define KLU_kernel_factor klu_z_kernel_factor #define KLU_lsolve klu_z_lsolve #define KLU_ltsolve klu_z_ltsolve #define KLU_usolve klu_z_usolve #define KLU_utsolve klu_z_utsolve #define KLU_kernel klu_z_kernel #define KLU_valid klu_z_valid #define KLU_valid_LU klu_z_valid_LU #define KLU_sort klu_z_sort #define KLU_rgrowth klu_z_rgrowth #define KLU_rcond klu_z_rcond #define KLU_extract klu_z_extract #define KLU_condest klu_z_condest #define KLU_flops klu_z_flops #endif #else #ifdef DLONG #define KLU_scale klu_l_scale #define KLU_solve klu_l_solve #define KLU_tsolve klu_l_tsolve #define KLU_free_numeric klu_l_free_numeric #define KLU_factor klu_l_factor #define KLU_refactor klu_l_refactor #define KLU_kernel_factor klu_l_kernel_factor #define KLU_lsolve klu_l_lsolve #define KLU_ltsolve klu_l_ltsolve #define KLU_usolve klu_l_usolve #define KLU_utsolve klu_l_utsolve #define KLU_kernel klu_l_kernel #define KLU_valid klu_l_valid #define KLU_valid_LU klu_l_valid_LU #define KLU_sort klu_l_sort #define KLU_rgrowth klu_l_rgrowth #define KLU_rcond klu_l_rcond #define KLU_extract klu_l_extract #define KLU_condest klu_l_condest #define KLU_flops klu_l_flops #else #define KLU_scale klu_scale #define KLU_solve klu_solve #define KLU_tsolve klu_tsolve #define KLU_free_numeric klu_free_numeric #define KLU_factor klu_factor #define KLU_refactor klu_refactor #define KLU_kernel_factor klu_kernel_factor #define KLU_lsolve klu_lsolve #define KLU_ltsolve klu_ltsolve #define KLU_usolve klu_usolve #define KLU_utsolve klu_utsolve #define KLU_kernel klu_kernel #define KLU_valid klu_valid #define KLU_valid_LU klu_valid_LU #define KLU_sort klu_sort #define KLU_rgrowth klu_rgrowth #define KLU_rcond klu_rcond #define KLU_extract klu_extract #define KLU_condest klu_condest #define KLU_flops klu_flops #endif #endif #ifdef DLONG #define KLU_analyze klu_l_analyze #define KLU_analyze_given klu_l_analyze_given #define KLU_alloc_symbolic klu_l_alloc_symbolic #define KLU_free_symbolic klu_l_free_symbolic #define KLU_defaults klu_l_defaults #define KLU_free klu_l_free #define KLU_malloc klu_l_malloc #define KLU_realloc klu_l_realloc #define KLU_add_size_t klu_l_add_size_t #define KLU_mult_size_t klu_l_mult_size_t #define KLU_symbolic klu_l_symbolic #define KLU_numeric klu_l_numeric #define KLU_common klu_l_common #define BTF_order btf_l_order #define BTF_strongcomp btf_l_strongcomp #define AMD_order amd_l_order #define COLAMD colamd_l #define COLAMD_recommended colamd_l_recommended #else #define KLU_analyze klu_analyze #define KLU_analyze_given klu_analyze_given #define KLU_alloc_symbolic klu_alloc_symbolic #define KLU_free_symbolic klu_free_symbolic #define KLU_defaults klu_defaults #define KLU_free klu_free #define KLU_malloc klu_malloc #define KLU_realloc klu_realloc #define KLU_add_size_t klu_add_size_t #define KLU_mult_size_t klu_mult_size_t #define KLU_symbolic klu_symbolic #define KLU_numeric klu_numeric #define KLU_common klu_common #define BTF_order btf_order #define BTF_strongcomp btf_strongcomp #define AMD_order amd_order #define COLAMD colamd #define COLAMD_recommended colamd_recommended #endif /* -------------------------------------------------------------------------- */ /* Numerical relop macros for correctly handling the NaN case */ /* -------------------------------------------------------------------------- */ /* SCALAR_IS_NAN(x): True if x is NaN. False otherwise. The commonly-existing isnan(x) function could be used, but it's not in Kernighan & Ritchie 2nd edition (ANSI C). It may appear in , but I'm not certain about portability. The expression x != x is true if and only if x is NaN, according to the IEEE 754 floating-point standard. SCALAR_IS_ZERO(x): True if x is zero. False if x is nonzero, NaN, or +/- Inf. This is (x == 0) if the compiler is IEEE 754 compliant. SCALAR_IS_NONZERO(x): True if x is nonzero, NaN, or +/- Inf. False if x zero. This is (x != 0) if the compiler is IEEE 754 compliant. SCALAR_IS_LTZERO(x): True if x is < zero or -Inf. False if x is >= 0, NaN, or +Inf. This is (x < 0) if the compiler is IEEE 754 compliant. */ /* These all work properly, according to the IEEE 754 standard ... except on */ /* a PC with windows. Works fine in Linux on the same PC... */ #define SCALAR_IS_NAN(x) ((x) != (x)) #define SCALAR_IS_ZERO(x) ((x) == 0.) #define SCALAR_IS_NONZERO(x) ((x) != 0.) #define SCALAR_IS_LTZERO(x) ((x) < 0.) /* scalar absolute value macro. If x is NaN, the result is NaN: */ #define SCALAR_ABS(x) ((SCALAR_IS_LTZERO (x)) ? -(x) : (x)) /* print a scalar (avoid printing "-0" for negative zero). */ #ifdef NPRINT #define PRINT_SCALAR(a) #else #define PRINT_SCALAR(a) \ { \ if (SCALAR_IS_NONZERO (a)) \ { \ PRINTF ((" (%g)", (a))) ; \ } \ else \ { \ PRINTF ((" (0)")) ; \ } \ } #endif /* -------------------------------------------------------------------------- */ /* Real floating-point arithmetic */ /* -------------------------------------------------------------------------- */ #ifndef COMPLEX typedef double Unit ; #define Entry double #define SPLIT(s) (1) #define REAL(c) (c) #define IMAG(c) (0.) #define ASSIGN(c,s1,s2,p,split) { (c) = (s1)[p] ; } #define CLEAR(c) { (c) = 0. ; } #define CLEAR_AND_INCREMENT(p) { *p++ = 0. ; } #define IS_NAN(a) SCALAR_IS_NAN (a) #define IS_ZERO(a) SCALAR_IS_ZERO (a) #define IS_NONZERO(a) SCALAR_IS_NONZERO (a) #define SCALE_DIV(c,s) { (c) /= (s) ; } #define SCALE_DIV_ASSIGN(a,c,s) { a = c / s ; } #define SCALE(c,s) { (c) *= (s) ; } #define ASSEMBLE(c,a) { (c) += (a) ; } #define ASSEMBLE_AND_INCREMENT(c,p) { (c) += *p++ ; } #define DECREMENT(c,a) { (c) -= (a) ; } #define MULT(c,a,b) { (c) = (a) * (b) ; } #define MULT_CONJ(c,a,b) { (c) = (a) * (b) ; } #define MULT_SUB(c,a,b) { (c) -= (a) * (b) ; } #define MULT_SUB_CONJ(c,a,b) { (c) -= (a) * (b) ; } #define DIV(c,a,b) { (c) = (a) / (b) ; } #define RECIPROCAL(c) { (c) = 1.0 / (c) ; } #define DIV_CONJ(c,a,b) { (c) = (a) / (b) ; } #define APPROX_ABS(s,a) { (s) = SCALAR_ABS (a) ; } #define ABS(s,a) { (s) = SCALAR_ABS (a) ; } #define PRINT_ENTRY(a) PRINT_SCALAR (a) #define CONJ(a,x) a = x /* for flop counts */ #define MULTSUB_FLOPS 2. /* c -= a*b */ #define DIV_FLOPS 1. /* c = a/b */ #define ABS_FLOPS 0. /* c = abs (a) */ #define ASSEMBLE_FLOPS 1. /* c += a */ #define DECREMENT_FLOPS 1. /* c -= a */ #define MULT_FLOPS 1. /* c = a*b */ #define SCALE_FLOPS 1. /* c = a/s */ #else /* -------------------------------------------------------------------------- */ /* Complex floating-point arithmetic */ /* -------------------------------------------------------------------------- */ /* Note: An alternative to this Double_Complex type would be to use a struct { double r ; double i ; }. The problem with that method (used by the Sun Performance Library, for example) is that ANSI C provides no guarantee about the layout of a struct. It is possible that the sizeof the struct above would be greater than 2 * sizeof (double). This would mean that the complex BLAS could not be used. The method used here avoids that possibility. ANSI C *does* guarantee that an array of structs has the same size as n times the size of one struct. The ANSI C99 version of the C language includes a "double _Complex" type. It should be possible in that case to do the following: #define Entry double _Complex and remove the Double_Complex struct. The macros, below, could then be replaced with instrinsic operators. Note that the #define Real and #define Imag should also be removed (they only appear in this file). For the MULT, MULT_SUB, MULT_SUB_CONJ, and MULT_CONJ macros, the output argument c cannot be the same as any input argument. */ typedef struct { double component [2] ; /* real and imaginary parts */ } Double_Complex ; typedef Double_Complex Unit ; #define Entry Double_Complex #define Real component [0] #define Imag component [1] /* for flop counts */ #define MULTSUB_FLOPS 8. /* c -= a*b */ #define DIV_FLOPS 9. /* c = a/b */ #define ABS_FLOPS 6. /* c = abs (a), count sqrt as one flop */ #define ASSEMBLE_FLOPS 2. /* c += a */ #define DECREMENT_FLOPS 2. /* c -= a */ #define MULT_FLOPS 6. /* c = a*b */ #define SCALE_FLOPS 2. /* c = a/s or c = a*s */ /* -------------------------------------------------------------------------- */ /* real part of c */ #define REAL(c) ((c).Real) /* -------------------------------------------------------------------------- */ /* imag part of c */ #define IMAG(c) ((c).Imag) /* -------------------------------------------------------------------------- */ /* Return TRUE if a complex number is in split form, FALSE if in packed form */ #define SPLIT(sz) ((sz) != (double *) NULL) /* c = (s1) + (s2)*i, if s2 is null, then X is in "packed" format (compatible * with Entry and ANSI C99 double _Complex type). */ /*#define ASSIGN(c,s1,s2,p,split) \ { \ if (split) \ { \ (c).Real = (s1)[p] ; \ (c).Imag = (s2)[p] ; \ } \ else \ { \ (c) = ((Entry *)(s1))[p] ; \ } \ }*/ /* -------------------------------------------------------------------------- */ #define CONJ(a, x) \ { \ a.Real = x.Real ; \ a.Imag = -x.Imag ; \ } /* c = 0 */ #define CLEAR(c) \ { \ (c).Real = 0. ; \ (c).Imag = 0. ; \ } /* -------------------------------------------------------------------------- */ /* *p++ = 0 */ #define CLEAR_AND_INCREMENT(p) \ { \ p->Real = 0. ; \ p->Imag = 0. ; \ p++ ; \ } /* -------------------------------------------------------------------------- */ /* True if a == 0 */ #define IS_ZERO(a) \ (SCALAR_IS_ZERO ((a).Real) && SCALAR_IS_ZERO ((a).Imag)) /* -------------------------------------------------------------------------- */ /* True if a is NaN */ #define IS_NAN(a) \ (SCALAR_IS_NAN ((a).Real) || SCALAR_IS_NAN ((a).Imag)) /* -------------------------------------------------------------------------- */ /* True if a != 0 */ #define IS_NONZERO(a) \ (SCALAR_IS_NONZERO ((a).Real) || SCALAR_IS_NONZERO ((a).Imag)) /* -------------------------------------------------------------------------- */ /* a = c/s */ #define SCALE_DIV_ASSIGN(a,c,s) \ { \ a.Real = c.Real / s ; \ a.Imag = c.Imag / s ; \ } /* c /= s */ #define SCALE_DIV(c,s) \ { \ (c).Real /= (s) ; \ (c).Imag /= (s) ; \ } /* -------------------------------------------------------------------------- */ /* c *= s */ #define SCALE(c,s) \ { \ (c).Real *= (s) ; \ (c).Imag *= (s) ; \ } /* -------------------------------------------------------------------------- */ /* c += a */ #define ASSEMBLE(c,a) \ { \ (c).Real += (a).Real ; \ (c).Imag += (a).Imag ; \ } /* -------------------------------------------------------------------------- */ /* c += *p++ */ #define ASSEMBLE_AND_INCREMENT(c,p) \ { \ (c).Real += p->Real ; \ (c).Imag += p->Imag ; \ p++ ; \ } /* -------------------------------------------------------------------------- */ /* c -= a */ #define DECREMENT(c,a) \ { \ (c).Real -= (a).Real ; \ (c).Imag -= (a).Imag ; \ } /* -------------------------------------------------------------------------- */ /* c = a*b, assert because c cannot be the same as a or b */ #define MULT(c,a,b) \ { \ ASSERT (&(c) != &(a) && &(c) != &(b)) ; \ (c).Real = (a).Real * (b).Real - (a).Imag * (b).Imag ; \ (c).Imag = (a).Imag * (b).Real + (a).Real * (b).Imag ; \ } /* -------------------------------------------------------------------------- */ /* c = a*conjugate(b), assert because c cannot be the same as a or b */ #define MULT_CONJ(c,a,b) \ { \ ASSERT (&(c) != &(a) && &(c) != &(b)) ; \ (c).Real = (a).Real * (b).Real + (a).Imag * (b).Imag ; \ (c).Imag = (a).Imag * (b).Real - (a).Real * (b).Imag ; \ } /* -------------------------------------------------------------------------- */ /* c -= a*b, assert because c cannot be the same as a or b */ #define MULT_SUB(c,a,b) \ { \ ASSERT (&(c) != &(a) && &(c) != &(b)) ; \ (c).Real -= (a).Real * (b).Real - (a).Imag * (b).Imag ; \ (c).Imag -= (a).Imag * (b).Real + (a).Real * (b).Imag ; \ } /* -------------------------------------------------------------------------- */ /* c -= a*conjugate(b), assert because c cannot be the same as a or b */ #define MULT_SUB_CONJ(c,a,b) \ { \ ASSERT (&(c) != &(a) && &(c) != &(b)) ; \ (c).Real -= (a).Real * (b).Real + (a).Imag * (b).Imag ; \ (c).Imag -= (a).Imag * (b).Real - (a).Real * (b).Imag ; \ } /* -------------------------------------------------------------------------- */ /* c = a/b, be careful to avoid underflow and overflow */ #ifdef MATHWORKS #define DIV(c,a,b) \ { \ (void) utDivideComplex ((a).Real, (a).Imag, (b).Real, (b).Imag, \ &((c).Real), &((c).Imag)) ; \ } #else /* This uses ACM Algo 116, by R. L. Smith, 1962. */ /* c can be the same variable as a or b. */ /* Ignore NaN case for double relop br>=bi. */ #define DIV(c,a,b) \ { \ double r, den, ar, ai, br, bi ; \ br = (b).Real ; \ bi = (b).Imag ; \ ar = (a).Real ; \ ai = (a).Imag ; \ if (SCALAR_ABS (br) >= SCALAR_ABS (bi)) \ { \ r = bi / br ; \ den = br + r * bi ; \ (c).Real = (ar + ai * r) / den ; \ (c).Imag = (ai - ar * r) / den ; \ } \ else \ { \ r = br / bi ; \ den = r * br + bi ; \ (c).Real = (ar * r + ai) / den ; \ (c).Imag = (ai * r - ar) / den ; \ } \ } #endif /* -------------------------------------------------------------------------- */ /* c = 1/c, be careful to avoid underflow and overflow */ /* Not used if MATHWORKS is defined. */ /* This uses ACM Algo 116, by R. L. Smith, 1962. */ /* Ignore NaN case for double relop cr>=ci. */ #define RECIPROCAL(c) \ { \ double r, den, cr, ci ; \ cr = (c).Real ; \ ci = (c).Imag ; \ if (SCALAR_ABS (cr) >= SCALAR_ABS (ci)) \ { \ r = ci / cr ; \ den = cr + r * ci ; \ (c).Real = 1.0 / den ; \ (c).Imag = - r / den ; \ } \ else \ { \ r = cr / ci ; \ den = r * cr + ci ; \ (c).Real = r / den ; \ (c).Imag = - 1.0 / den ; \ } \ } /* -------------------------------------------------------------------------- */ /* c = a/conjugate(b), be careful to avoid underflow and overflow */ #ifdef MATHWORKS #define DIV_CONJ(c,a,b) \ { \ (void) utDivideComplex ((a).Real, (a).Imag, (b).Real, (-(b).Imag), \ &((c).Real), &((c).Imag)) ; \ } #else /* This uses ACM Algo 116, by R. L. Smith, 1962. */ /* c can be the same variable as a or b. */ /* Ignore NaN case for double relop br>=bi. */ #define DIV_CONJ(c,a,b) \ { \ double r, den, ar, ai, br, bi ; \ br = (b).Real ; \ bi = (b).Imag ; \ ar = (a).Real ; \ ai = (a).Imag ; \ if (SCALAR_ABS (br) >= SCALAR_ABS (bi)) \ { \ r = (-bi) / br ; \ den = br - r * bi ; \ (c).Real = (ar + ai * r) / den ; \ (c).Imag = (ai - ar * r) / den ; \ } \ else \ { \ r = br / (-bi) ; \ den = r * br - bi; \ (c).Real = (ar * r + ai) / den ; \ (c).Imag = (ai * r - ar) / den ; \ } \ } #endif /* -------------------------------------------------------------------------- */ /* approximate absolute value, s = |r|+|i| */ #define APPROX_ABS(s,a) \ { \ (s) = SCALAR_ABS ((a).Real) + SCALAR_ABS ((a).Imag) ; \ } /* -------------------------------------------------------------------------- */ /* exact absolute value, s = sqrt (a.real^2 + amag^2) */ #ifdef MATHWORKS #define ABS(s,a) \ { \ (s) = utFdlibm_hypot ((a).Real, (a).Imag) ; \ } #else /* Ignore NaN case for the double relops ar>=ai and ar+ai==ar. */ #define ABS(s,a) \ { \ double r, ar, ai ; \ ar = SCALAR_ABS ((a).Real) ; \ ai = SCALAR_ABS ((a).Imag) ; \ if (ar >= ai) \ { \ if (ar + ai == ar) \ { \ (s) = ar ; \ } \ else \ { \ r = ai / ar ; \ (s) = ar * sqrt (1.0 + r*r) ; \ } \ } \ else \ { \ if (ai + ar == ai) \ { \ (s) = ai ; \ } \ else \ { \ r = ar / ai ; \ (s) = ai * sqrt (1.0 + r*r) ; \ } \ } \ } #endif /* -------------------------------------------------------------------------- */ /* print an entry (avoid printing "-0" for negative zero). */ #ifdef NPRINT #define PRINT_ENTRY(a) #else #define PRINT_ENTRY(a) \ { \ if (SCALAR_IS_NONZERO ((a).Real)) \ { \ PRINTF ((" (%g", (a).Real)) ; \ } \ else \ { \ PRINTF ((" (0")) ; \ } \ if (SCALAR_IS_LTZERO ((a).Imag)) \ { \ PRINTF ((" - %gi)", -(a).Imag)) ; \ } \ else if (SCALAR_IS_ZERO ((a).Imag)) \ { \ PRINTF ((" + 0i)")) ; \ } \ else \ { \ PRINTF ((" + %gi)", (a).Imag)) ; \ } \ } #endif /* -------------------------------------------------------------------------- */ #endif /* #ifndef COMPLEX */ #endif SuiteSparse/KLU/Source/0000755001170100242450000000000010660617102013641 5ustar davisfacSuiteSparse/KLU/Source/klu_tsolve.c0000644001170100242450000002433210616200241016171 0ustar davisfac/* ========================================================================== */ /* === KLU_tsolve =========================================================== */ /* ========================================================================== */ /* Solve A'x=b using the symbolic and numeric objects from KLU_analyze * (or KLU_analyze_given) and KLU_factor. Note that no iterative refinement is * performed. Uses Numeric->Xwork as workspace (undefined on input and output), * of size 4n Entry's (note that columns 2 to 4 of Xwork overlap with * Numeric->Iwork). */ #include "klu_internal.h" Int KLU_tsolve ( /* inputs, not modified */ KLU_symbolic *Symbolic, KLU_numeric *Numeric, Int d, /* leading dimension of B */ Int nrhs, /* number of right-hand-sides */ /* right-hand-side on input, overwritten with solution to Ax=b on output */ double B [ ], /* size n*nrhs, in column-oriented form, with * leading dimension d. */ #ifdef COMPLEX Int conj_solve, /* TRUE for conjugate transpose solve, FALSE for * array transpose solve. Used for the complex * case only. */ #endif /* --------------- */ KLU_common *Common ) { Entry x [4], offik, s ; double rs, *Rs ; Entry *Offx, *X, *Bz, *Udiag ; Int *Q, *R, *Pnum, *Offp, *Offi, *Lip, *Uip, *Llen, *Ulen ; Unit **LUbx ; Int k1, k2, nk, k, block, pend, n, p, nblocks, chunk, nr, i ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ if (Common == NULL) { return (FALSE) ; } if (Numeric == NULL || Symbolic == NULL || d < Symbolic->n || nrhs < 0 || B == NULL) { Common->status = KLU_INVALID ; return (FALSE) ; } Common->status = KLU_OK ; /* ---------------------------------------------------------------------- */ /* get the contents of the Symbolic object */ /* ---------------------------------------------------------------------- */ Bz = (Entry *) B ; n = Symbolic->n ; nblocks = Symbolic->nblocks ; Q = Symbolic->Q ; R = Symbolic->R ; /* ---------------------------------------------------------------------- */ /* get the contents of the Numeric object */ /* ---------------------------------------------------------------------- */ ASSERT (nblocks == Numeric->nblocks) ; Pnum = Numeric->Pnum ; Offp = Numeric->Offp ; Offi = Numeric->Offi ; Offx = (Entry *) Numeric->Offx ; Lip = Numeric->Lip ; Llen = Numeric->Llen ; Uip = Numeric->Uip ; Ulen = Numeric->Ulen ; LUbx = (Unit **) Numeric->LUbx ; Udiag = Numeric->Udiag ; Rs = Numeric->Rs ; X = (Entry *) Numeric->Xwork ; ASSERT (KLU_valid (n, Offp, Offi, Offx)) ; /* ---------------------------------------------------------------------- */ /* solve in chunks of 4 columns at a time */ /* ---------------------------------------------------------------------- */ for (chunk = 0 ; chunk < nrhs ; chunk += 4) { /* ------------------------------------------------------------------ */ /* get the size of the current chunk */ /* ------------------------------------------------------------------ */ nr = MIN (nrhs - chunk, 4) ; /* ------------------------------------------------------------------ */ /* permute the right hand side, X = Q'*B */ /* ------------------------------------------------------------------ */ switch (nr) { case 1: for (k = 0 ; k < n ; k++) { X [k] = Bz [Q [k]] ; } break ; case 2: for (k = 0 ; k < n ; k++) { i = Q [k] ; X [2*k ] = Bz [i ] ; X [2*k + 1] = Bz [i + d ] ; } break ; case 3: for (k = 0 ; k < n ; k++) { i = Q [k] ; X [3*k ] = Bz [i ] ; X [3*k + 1] = Bz [i + d ] ; X [3*k + 2] = Bz [i + d*2] ; } break ; case 4: for (k = 0 ; k < n ; k++) { i = Q [k] ; X [4*k ] = Bz [i ] ; X [4*k + 1] = Bz [i + d ] ; X [4*k + 2] = Bz [i + d*2] ; X [4*k + 3] = Bz [i + d*3] ; } break ; } /* ------------------------------------------------------------------ */ /* solve X = (L*U + Off)'\X */ /* ------------------------------------------------------------------ */ for (block = 0 ; block < nblocks ; block++) { /* -------------------------------------------------------------- */ /* the block of size nk is from rows/columns k1 to k2-1 */ /* -------------------------------------------------------------- */ k1 = R [block] ; k2 = R [block+1] ; nk = k2 - k1 ; PRINTF (("tsolve %d, k1 %d k2-1 %d nk %d\n", block, k1,k2-1,nk)) ; /* -------------------------------------------------------------- */ /* block back-substitution for the off-diagonal-block entries */ /* -------------------------------------------------------------- */ if (block > 0) { switch (nr) { case 1: for (k = k1 ; k < k2 ; k++) { pend = Offp [k+1] ; for (p = Offp [k] ; p < pend ; p++) { #ifdef COMPLEX if (conj_solve) { MULT_SUB_CONJ (X [k], X [Offi [p]], Offx [p]) ; } else #endif { MULT_SUB (X [k], Offx [p], X [Offi [p]]) ; } } } break ; case 2: for (k = k1 ; k < k2 ; k++) { pend = Offp [k+1] ; x [0] = X [2*k ] ; x [1] = X [2*k + 1] ; for (p = Offp [k] ; p < pend ; p++) { i = Offi [p] ; #ifdef COMPLEX if (conj_solve) { CONJ (offik, Offx [p]) ; } else #endif { offik = Offx [p] ; } MULT_SUB (x [0], offik, X [2*i]) ; MULT_SUB (x [1], offik, X [2*i + 1]) ; } X [2*k ] = x [0] ; X [2*k + 1] = x [1] ; } break ; case 3: for (k = k1 ; k < k2 ; k++) { pend = Offp [k+1] ; x [0] = X [3*k ] ; x [1] = X [3*k + 1] ; x [2] = X [3*k + 2] ; for (p = Offp [k] ; p < pend ; p++) { i = Offi [p] ; #ifdef COMPLEX if (conj_solve) { CONJ (offik, Offx [p]) ; } else #endif { offik = Offx [p] ; } MULT_SUB (x [0], offik, X [3*i]) ; MULT_SUB (x [1], offik, X [3*i + 1]) ; MULT_SUB (x [2], offik, X [3*i + 2]) ; } X [3*k ] = x [0] ; X [3*k + 1] = x [1] ; X [3*k + 2] = x [2] ; } break ; case 4: for (k = k1 ; k < k2 ; k++) { pend = Offp [k+1] ; x [0] = X [4*k ] ; x [1] = X [4*k + 1] ; x [2] = X [4*k + 2] ; x [3] = X [4*k + 3] ; for (p = Offp [k] ; p < pend ; p++) { i = Offi [p] ; #ifdef COMPLEX if (conj_solve) { CONJ(offik, Offx [p]) ; } else #endif { offik = Offx [p] ; } MULT_SUB (x [0], offik, X [4*i]) ; MULT_SUB (x [1], offik, X [4*i + 1]) ; MULT_SUB (x [2], offik, X [4*i + 2]) ; MULT_SUB (x [3], offik, X [4*i + 3]) ; } X [4*k ] = x [0] ; X [4*k + 1] = x [1] ; X [4*k + 2] = x [2] ; X [4*k + 3] = x [3] ; } break ; } } /* -------------------------------------------------------------- */ /* solve the block system */ /* -------------------------------------------------------------- */ if (nk == 1) { #ifdef COMPLEX if (conj_solve) { CONJ (s, Udiag [k1]) ; } else #endif { s = Udiag [k1] ; } switch (nr) { case 1: DIV (X [k1], X [k1], s) ; break ; case 2: DIV (X [2*k1], X [2*k1], s) ; DIV (X [2*k1 + 1], X [2*k1 + 1], s) ; break ; case 3: DIV (X [3*k1], X [3*k1], s) ; DIV (X [3*k1 + 1], X [3*k1 + 1], s) ; DIV (X [3*k1 + 2], X [3*k1 + 2], s) ; break ; case 4: DIV (X [4*k1], X [4*k1], s) ; DIV (X [4*k1 + 1], X [4*k1 + 1], s) ; DIV (X [4*k1 + 2], X [4*k1 + 2], s) ; DIV (X [4*k1 + 3], X [4*k1 + 3], s) ; break ; } } else { KLU_utsolve (nk, Uip + k1, Ulen + k1, LUbx [block], Udiag + k1, nr, #ifdef COMPLEX conj_solve, #endif X + nr*k1) ; KLU_ltsolve (nk, Lip + k1, Llen + k1, LUbx [block], nr, #ifdef COMPLEX conj_solve, #endif X + nr*k1) ; } } /* ------------------------------------------------------------------ */ /* scale and permute the result, Bz = P'(R\X) */ /* ------------------------------------------------------------------ */ if (Rs == NULL) { /* no scaling */ switch (nr) { case 1: for (k = 0 ; k < n ; k++) { Bz [Pnum [k]] = X [k] ; } break ; case 2: for (k = 0 ; k < n ; k++) { i = Pnum [k] ; Bz [i ] = X [2*k ] ; Bz [i + d ] = X [2*k + 1] ; } break ; case 3: for (k = 0 ; k < n ; k++) { i = Pnum [k] ; Bz [i ] = X [3*k ] ; Bz [i + d ] = X [3*k + 1] ; Bz [i + d*2] = X [3*k + 2] ; } break ; case 4: for (k = 0 ; k < n ; k++) { i = Pnum [k] ; Bz [i ] = X [4*k ] ; Bz [i + d ] = X [4*k + 1] ; Bz [i + d*2] = X [4*k + 2] ; Bz [i + d*3] = X [4*k + 3] ; } break ; } } else { switch (nr) { case 1: for (k = 0 ; k < n ; k++) { SCALE_DIV_ASSIGN (Bz [Pnum [k]], X [k], Rs [k]) ; } break ; case 2: for (k = 0 ; k < n ; k++) { i = Pnum [k] ; rs = Rs [k] ; SCALE_DIV_ASSIGN (Bz [i], X [2*k], rs) ; SCALE_DIV_ASSIGN (Bz [i + d], X [2*k + 1], rs) ; } break ; case 3: for (k = 0 ; k < n ; k++) { i = Pnum [k] ; rs = Rs [k] ; SCALE_DIV_ASSIGN (Bz [i], X [3*k], rs) ; SCALE_DIV_ASSIGN (Bz [i + d], X [3*k + 1], rs) ; SCALE_DIV_ASSIGN (Bz [i + d*2], X [3*k + 2], rs) ; } break ; case 4: for (k = 0 ; k < n ; k++) { i = Pnum [k] ; rs = Rs [k] ; SCALE_DIV_ASSIGN (Bz [i], X [4*k], rs) ; SCALE_DIV_ASSIGN (Bz [i + d], X [4*k + 1], rs) ; SCALE_DIV_ASSIGN (Bz [i + d*2], X [4*k + 2], rs) ; SCALE_DIV_ASSIGN (Bz [i + d*3], X [4*k + 3], rs) ; } break ; } } /* ------------------------------------------------------------------ */ /* go to the next chunk of B */ /* ------------------------------------------------------------------ */ Bz += d*4 ; } return (TRUE) ; } SuiteSparse/KLU/Source/klu_sort.c0000644001170100242450000000757710616721417015675 0ustar davisfac/* ========================================================================== */ /* === KLU_sort ============================================================= */ /* ========================================================================== */ /* sorts the columns of L and U so that the row indices appear in strictly * increasing order. */ #include "klu_internal.h" /* ========================================================================== */ /* === sort ================================================================= */ /* ========================================================================== */ /* Sort L or U using a double-transpose */ static void sort (Int n, Int *Xip, Int *Xlen, Unit *LU, Int *Tp, Int *Tj, Entry *Tx, Int *W) { Int *Xi ; Entry *Xx ; Int p, i, j, len, nz, tp, xlen, pend ; ASSERT (KLU_valid_LU (n, FALSE, Xip, Xlen, LU)) ; /* count the number of entries in each row of L or U */ for (i = 0 ; i < n ; i++) { W [i] = 0 ; } for (j = 0 ; j < n ; j++) { GET_POINTER (LU, Xip, Xlen, Xi, Xx, j, len) ; for (p = 0 ; p < len ; p++) { W [Xi [p]]++ ; } } /* construct the row pointers for T */ nz = 0 ; for (i = 0 ; i < n ; i++) { Tp [i] = nz ; nz += W [i] ; } Tp [n] = nz ; for (i = 0 ; i < n ; i++) { W [i] = Tp [i] ; } /* transpose the matrix into Tp, Ti, Tx */ for (j = 0 ; j < n ; j++) { GET_POINTER (LU, Xip, Xlen, Xi, Xx, j, len) ; for (p = 0 ; p < len ; p++) { tp = W [Xi [p]]++ ; Tj [tp] = j ; Tx [tp] = Xx [p] ; } } /* transpose the matrix back into Xip, Xlen, Xi, Xx */ for (j = 0 ; j < n ; j++) { W [j] = 0 ; } for (i = 0 ; i < n ; i++) { pend = Tp [i+1] ; for (p = Tp [i] ; p < pend ; p++) { j = Tj [p] ; GET_POINTER (LU, Xip, Xlen, Xi, Xx, j, len) ; xlen = W [j]++ ; Xi [xlen] = i ; Xx [xlen] = Tx [p] ; } } ASSERT (KLU_valid_LU (n, FALSE, Xip, Xlen, LU)) ; } /* ========================================================================== */ /* === KLU_sort ============================================================= */ /* ========================================================================== */ Int KLU_sort ( KLU_symbolic *Symbolic, KLU_numeric *Numeric, KLU_common *Common ) { Int *R, *W, *Tp, *Ti, *Lip, *Uip, *Llen, *Ulen ; Entry *Tx ; Unit **LUbx ; Int n, nk, nz, block, nblocks, maxblock, k1 ; size_t m1 ; if (Common == NULL) { return (FALSE) ; } Common->status = KLU_OK ; n = Symbolic->n ; R = Symbolic->R ; nblocks = Symbolic->nblocks ; maxblock = Symbolic->maxblock ; Lip = Numeric->Lip ; Llen = Numeric->Llen ; Uip = Numeric->Uip ; Ulen = Numeric->Ulen ; LUbx = (Unit **) Numeric->LUbx ; m1 = ((size_t) maxblock) + 1 ; /* allocate workspace */ nz = MAX (Numeric->max_lnz_block, Numeric->max_unz_block) ; W = KLU_malloc (maxblock, sizeof (Int), Common) ; Tp = KLU_malloc (m1, sizeof (Int), Common) ; Ti = KLU_malloc (nz, sizeof (Int), Common) ; Tx = KLU_malloc (nz, sizeof (Entry), Common) ; PRINTF (("\n======================= Start sort:\n")) ; if (Common->status == KLU_OK) { /* sort each block of L and U */ for (block = 0 ; block < nblocks ; block++) { k1 = R [block] ; nk = R [block+1] - k1 ; if (nk > 1) { PRINTF (("\n-------------------block: %d nk %d\n", block, nk)) ; sort (nk, Lip + k1, Llen + k1, LUbx [block], Tp, Ti, Tx, W) ; sort (nk, Uip + k1, Ulen + k1, LUbx [block], Tp, Ti, Tx, W) ; } } } PRINTF (("\n======================= sort done.\n")) ; /* free workspace */ KLU_free (W, maxblock, sizeof (Int), Common) ; KLU_free (Tp, m1, sizeof (Int), Common) ; KLU_free (Ti, nz, sizeof (Int), Common) ; KLU_free (Tx, nz, sizeof (Entry), Common) ; return (Common->status == KLU_OK) ; } SuiteSparse/KLU/Source/klu_diagnostics.c0000644001170100242450000003416510634325142017201 0ustar davisfac/* ========================================================================== */ /* === KLU_diagnostics ====================================================== */ /* ========================================================================== */ /* Linear algebraic diagnostics: * KLU_rgrowth: reciprocal pivot growth, takes O(|A|+|U|) time * KLU_condest: condition number estimator, takes about O(|A|+5*(|L|+|U|)) time * KLU_flops: compute # flops required to factorize A into L*U * KLU_rcond: compute a really cheap estimate of the reciprocal of the * condition number, min(abs(diag(U))) / max(abs(diag(U))). * Takes O(n) time. */ #include "klu_internal.h" /* ========================================================================== */ /* === KLU_rgrowth ========================================================== */ /* ========================================================================== */ /* Compute the reciprocal pivot growth factor. In MATLAB notation: * * rgrowth = min (max (abs ((R \ A (p,q)) - F))) ./ max (abs (U))) */ Int KLU_rgrowth /* return TRUE if successful, FALSE otherwise */ ( Int *Ap, Int *Ai, double *Ax, KLU_symbolic *Symbolic, KLU_numeric *Numeric, KLU_common *Common ) { double temp, max_ai, max_ui, min_block_rgrowth ; Entry aik ; Int *Q, *Ui, *Uip, *Ulen, *Pinv ; Unit *LU ; Entry *Aentry, *Ux, *Ukk ; double *Rs ; Int i, newrow, oldrow, k1, k2, nk, j, oldcol, k, pend, len ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ if (Common == NULL) { return (FALSE) ; } if (Symbolic == NULL || Ap == NULL || Ai == NULL || Ax == NULL) { Common->status = KLU_INVALID ; return (FALSE) ; } if (Numeric == NULL) { /* treat this as a singular matrix */ Common->rgrowth = 0 ; Common->status = KLU_SINGULAR ; return (TRUE) ; } Common->status = KLU_OK ; /* ---------------------------------------------------------------------- */ /* compute the reciprocal pivot growth */ /* ---------------------------------------------------------------------- */ Aentry = (Entry *) Ax ; Pinv = Numeric->Pinv ; Rs = Numeric->Rs ; Q = Symbolic->Q ; Common->rgrowth = 1 ; for (i = 0 ; i < Symbolic->nblocks ; i++) { k1 = Symbolic->R[i] ; k2 = Symbolic->R[i+1] ; nk = k2 - k1 ; if (nk == 1) { continue ; /* skip singleton blocks */ } LU = (Unit *) Numeric->LUbx[i] ; Uip = Numeric->Uip + k1 ; Ulen = Numeric->Ulen + k1 ; Ukk = ((Entry *) Numeric->Udiag) + k1 ; min_block_rgrowth = 1 ; for (j = 0 ; j < nk ; j++) { max_ai = 0 ; max_ui = 0 ; oldcol = Q[j + k1] ; pend = Ap [oldcol + 1] ; for (k = Ap [oldcol] ; k < pend ; k++) { oldrow = Ai [k] ; newrow = Pinv [oldrow] ; if (newrow < k1) { continue ; /* skip entry outside the block */ } ASSERT (newrow < k2) ; if (Rs != NULL) { /* aik = Aentry [k] / Rs [oldrow] */ SCALE_DIV_ASSIGN (aik, Aentry [k], Rs [newrow]) ; } else { aik = Aentry [k] ; } /* temp = ABS (aik) */ ABS (temp, aik) ; if (temp > max_ai) { max_ai = temp ; } } GET_POINTER (LU, Uip, Ulen, Ui, Ux, j, len) ; for (k = 0 ; k < len ; k++) { /* temp = ABS (Ux [k]) */ ABS (temp, Ux [k]) ; if (temp > max_ui) { max_ui = temp ; } } /* consider the diagonal element */ ABS (temp, Ukk [j]) ; if (temp > max_ui) { max_ui = temp ; } /* if max_ui is 0, skip the column */ if (SCALAR_IS_ZERO (max_ui)) { continue ; } temp = max_ai / max_ui ; if (temp < min_block_rgrowth) { min_block_rgrowth = temp ; } } if (min_block_rgrowth < Common->rgrowth) { Common->rgrowth = min_block_rgrowth ; } } return (TRUE) ; } /* ========================================================================== */ /* === KLU_condest ========================================================== */ /* ========================================================================== */ /* Estimate the condition number. Uses Higham and Tisseur's algorithm * (A block algorithm for matrix 1-norm estimation, with applications to * 1-norm pseudospectra, SIAM J. Matrix Anal. Appl., 21(4):1185-1201, 2000. */ Int KLU_condest /* return TRUE if successful, FALSE otherwise */ ( Int Ap [ ], double Ax [ ], KLU_symbolic *Symbolic, KLU_numeric *Numeric, KLU_common *Common ) { double xj, Xmax, csum, anorm, ainv_norm, est_old, est_new, abs_value ; Entry *Udiag, *Aentry, *X, *S ; Int *R ; Int nblocks, i, j, jmax, jnew, pend, n ; #ifndef COMPLEX Int unchanged ; #endif /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ if (Common == NULL) { return (FALSE) ; } if (Symbolic == NULL || Ap == NULL || Ax == NULL) { Common->status = KLU_INVALID ; return (FALSE) ; } abs_value = 0 ; if (Numeric == NULL) { /* treat this as a singular matrix */ Common->condest = 1 / abs_value ; Common->status = KLU_SINGULAR ; return (TRUE) ; } Common->status = KLU_OK ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ n = Symbolic->n ; nblocks = Symbolic->nblocks ; R = Symbolic->R ; Udiag = Numeric->Udiag ; /* ---------------------------------------------------------------------- */ /* check if diagonal of U has a zero on it */ /* ---------------------------------------------------------------------- */ for (i = 0 ; i < n ; i++) { ABS (abs_value, Udiag [i]) ; if (SCALAR_IS_ZERO (abs_value)) { Common->condest = 1 / abs_value ; Common->status = KLU_SINGULAR ; return (TRUE) ; } } /* ---------------------------------------------------------------------- */ /* compute 1-norm (maximum column sum) of the matrix */ /* ---------------------------------------------------------------------- */ anorm = 0.0 ; Aentry = (Entry *) Ax ; for (i = 0 ; i < n ; i++) { pend = Ap [i + 1] ; csum = 0.0 ; for (j = Ap [i] ; j < pend ; j++) { ABS (abs_value, Aentry [j]) ; csum += abs_value ; } if (csum > anorm) { anorm = csum ; } } /* ---------------------------------------------------------------------- */ /* compute estimate of 1-norm of inv (A) */ /* ---------------------------------------------------------------------- */ /* get workspace (size 2*n Entry's) */ X = Numeric->Xwork ; /* size n space used in KLU_solve, tsolve */ X += n ; /* X is size n */ S = X + n ; /* S is size n */ for (i = 0 ; i < n ; i++) { CLEAR (S [i]) ; CLEAR (X [i]) ; REAL (X [i]) = 1.0 / ((double) n) ; } jmax = 0 ; ainv_norm = 0.0 ; for (i = 0 ; i < 5 ; i++) { if (i > 0) { /* X [jmax] is the largest entry in X */ for (j = 0 ; j < n ; j++) { /* X [j] = 0 ;*/ CLEAR (X [j]) ; } REAL (X [jmax]) = 1 ; } KLU_solve (Symbolic, Numeric, n, 1, (double *) X, Common) ; est_old = ainv_norm ; ainv_norm = 0.0 ; for (j = 0 ; j < n ; j++) { /* ainv_norm += ABS (X [j]) ;*/ ABS (abs_value, X [j]) ; ainv_norm += abs_value ; } #ifndef COMPLEX unchanged = TRUE ; for (j = 0 ; j < n ; j++) { double s = (X [j] >= 0) ? 1 : -1 ; if (s != (Int) REAL (S [j])) { S [j] = s ; unchanged = FALSE ; } } if (i > 0 && (ainv_norm <= est_old || unchanged)) { break ; } #else for (j = 0 ; j < n ; j++) { if (IS_NONZERO (X [j])) { ABS (abs_value, X [j]) ; SCALE_DIV_ASSIGN (S [j], X [j], abs_value) ; } else { CLEAR (S [j]) ; REAL (S [j]) = 1 ; } } if (i > 0 && ainv_norm <= est_old) { break ; } #endif for (j = 0 ; j < n ; j++) { X [j] = S [j] ; } #ifndef COMPLEX /* do a transpose solve */ KLU_tsolve (Symbolic, Numeric, n, 1, X, Common) ; #else /* do a conjugate transpose solve */ KLU_tsolve (Symbolic, Numeric, n, 1, (double *) X, 1, Common) ; #endif /* jnew = the position of the largest entry in X */ jnew = 0 ; Xmax = 0 ; for (j = 0 ; j < n ; j++) { /* xj = ABS (X [j]) ;*/ ABS (xj, X [j]) ; if (xj > Xmax) { Xmax = xj ; jnew = j ; } } if (i > 0 && jnew == jmax) { /* the position of the largest entry did not change * from the previous iteration */ break ; } jmax = jnew ; } /* ---------------------------------------------------------------------- */ /* compute another estimate of norm(inv(A),1), and take the largest one */ /* ---------------------------------------------------------------------- */ for (j = 0 ; j < n ; j++) { CLEAR (X [j]) ; if (j % 2) { REAL (X [j]) = 1 + ((double) j) / ((double) (n-1)) ; } else { REAL (X [j]) = -1 - ((double) j) / ((double) (n-1)) ; } } KLU_solve (Symbolic, Numeric, n, 1, (double *) X, Common) ; est_new = 0.0 ; for (j = 0 ; j < n ; j++) { /* est_new += ABS (X [j]) ;*/ ABS (abs_value, X [j]) ; est_new += abs_value ; } est_new = 2 * est_new / (3 * n) ; ainv_norm = MAX (est_new, ainv_norm) ; /* ---------------------------------------------------------------------- */ /* compute estimate of condition number */ /* ---------------------------------------------------------------------- */ Common->condest = ainv_norm * anorm ; return (TRUE) ; } /* ========================================================================== */ /* === KLU_flops ============================================================ */ /* ========================================================================== */ /* Compute the flop count for the LU factorization (in Common->flops) */ Int KLU_flops /* return TRUE if successful, FALSE otherwise */ ( KLU_symbolic *Symbolic, KLU_numeric *Numeric, KLU_common *Common ) { double flops = 0 ; Int *R, *Ui, *Uip, *Llen, *Ulen ; Unit **LUbx ; Unit *LU ; Int k, ulen, p, n, nk, block, nblocks, k1 ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ if (Common == NULL) { return (FALSE) ; } Common->flops = EMPTY ; if (Numeric == NULL || Symbolic == NULL) { Common->status = KLU_INVALID ; return (FALSE) ; } Common->status = KLU_OK ; /* ---------------------------------------------------------------------- */ /* get the contents of the Symbolic object */ /* ---------------------------------------------------------------------- */ n = Symbolic->n ; R = Symbolic->R ; nblocks = Symbolic->nblocks ; /* ---------------------------------------------------------------------- */ /* get the contents of the Numeric object */ /* ---------------------------------------------------------------------- */ LUbx = (Unit **) Numeric->LUbx ; /* ---------------------------------------------------------------------- */ /* compute the flop count */ /* ---------------------------------------------------------------------- */ for (block = 0 ; block < nblocks ; block++) { k1 = R [block] ; nk = R [block+1] - k1 ; if (nk > 1) { Llen = Numeric->Llen + k1 ; Uip = Numeric->Uip + k1 ; Ulen = Numeric->Ulen + k1 ; LU = LUbx [block] ; for (k = 0 ; k < nk ; k++) { /* compute kth column of U, and update kth column of A */ GET_I_POINTER (LU, Uip, Ui, k) ; ulen = Ulen [k] ; for (p = 0 ; p < ulen ; p++) { flops += 2 * Llen [Ui [p]] ; } /* gather and divide by pivot to get kth column of L */ flops += Llen [k] ; } } } Common->flops = flops ; return (TRUE) ; } /* ========================================================================== */ /* === KLU_rcond ============================================================ */ /* ========================================================================== */ /* Compute a really cheap estimate of the reciprocal of the condition number, * condition number, min(abs(diag(U))) / max(abs(diag(U))). If U has a zero * pivot, or a NaN pivot, rcond will be zero. Takes O(n) time. */ Int KLU_rcond /* return TRUE if successful, FALSE otherwise */ ( KLU_symbolic *Symbolic, /* input, not modified */ KLU_numeric *Numeric, /* input, not modified */ KLU_common *Common /* result in Common->rcond */ ) { double ukk, umin = 0, umax = 0 ; Entry *Udiag ; Int j, n ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ if (Common == NULL) { return (FALSE) ; } if (Symbolic == NULL) { Common->status = KLU_INVALID ; return (FALSE) ; } if (Numeric == NULL) { Common->rcond = 0 ; Common->status = KLU_SINGULAR ; return (TRUE) ; } Common->status = KLU_OK ; /* ---------------------------------------------------------------------- */ /* compute rcond */ /* ---------------------------------------------------------------------- */ n = Symbolic->n ; Udiag = Numeric->Udiag ; for (j = 0 ; j < n ; j++) { /* get the magnitude of the pivot */ ABS (ukk, Udiag [j]) ; if (SCALAR_IS_NAN (ukk) || SCALAR_IS_ZERO (ukk)) { /* if NaN, or zero, the rcond is zero */ Common->rcond = 0 ; Common->status = KLU_SINGULAR ; return (TRUE) ; } if (j == 0) { /* first pivot entry */ umin = ukk ; umax = ukk ; } else { /* subsequent pivots */ umin = MIN (umin, ukk) ; umax = MAX (umax, ukk) ; } } Common->rcond = umin / umax ; if (SCALAR_IS_NAN (Common->rcond) || SCALAR_IS_ZERO (Common->rcond)) { /* this can occur if umin or umax are Inf or NaN */ Common->rcond = 0 ; Common->status = KLU_SINGULAR ; } return (TRUE) ; } SuiteSparse/KLU/Source/klu.c0000644001170100242450000004616410616721046014617 0ustar davisfac/* ========================================================================== */ /* === klu ================================================================== */ /* ========================================================================== */ /* KLU: factorizes P*A into L*U, using the Gilbert-Peierls algorithm [1], with * optional symmetric pruning by Eisenstat and Liu [2]. The code is by Tim * Davis. This algorithm is what appears as the default sparse LU routine in * MATLAB version 6.0, and still appears in MATLAB 6.5 as [L,U,P] = lu (A). * Note that no column ordering is provided (see COLAMD or AMD for suitable * orderings). SuperLU is based on this algorithm, except that it adds the * use of dense matrix operations on "supernodes" (adjacent columns with * identical). This code doesn't use supernodes, thus its name ("Kent" LU, * as in "Clark Kent", in contrast with Super-LU...). This algorithm is slower * than SuperLU and UMFPACK for large matrices with lots of nonzeros in their * factors (such as for most finite-element problems). However, for matrices * with very sparse LU factors, this algorithm is typically faster than both * SuperLU and UMFPACK, since in this case there is little chance to exploit * dense matrix kernels (the BLAS). * * Only one block of A is factorized, in the BTF form. The input n is the * size of the block; k1 is the first row and column in the block. * * NOTE: no error checking is done on the inputs. This version is not meant to * be called directly by the user. Use klu_factor instead. * * No fill-reducing ordering is provided. The ordering quality of * klu_kernel_factor is the responsibility of the caller. The input A must * pre-permuted to reduce fill-in, or fill-reducing input permutation Q must * be provided. * * The input matrix A must be in compressed-column form, with either sorted * or unsorted row indices. Row indices for column j of A is in * Ai [Ap [j] ... Ap [j+1]-1] and the same range of indices in Ax holds the * numerical values. No duplicate entries are allowed. * * Copyright 2004-2007, Tim Davis. All rights reserved. See the README * file for details on permitted use. Note that no code from The MathWorks, * Inc, or from SuperLU, or from any other source appears here. The code is * written from scratch, from the algorithmic description in Gilbert & Peierls' * and Eisenstat & Liu's journal papers [1,2]. * * If an input permutation Q is provided, the factorization L*U = A (P,Q) * is computed, where P is determined by partial pivoting, and Q is the input * ordering. If the pivot tolerance is less than 1, the "diagonal" entry that * KLU attempts to choose is the diagonal of A (Q,Q). In other words, the * input permutation is applied symmetrically to the input matrix. The output * permutation P includes both the partial pivoting ordering and the input * permutation. If Q is NULL, then it is assumed to be the identity * permutation. Q is not modified. * * [1] Gilbert, J. R. and Peierls, T., "Sparse Partial Pivoting in Time * Proportional to Arithmetic Operations," SIAM J. Sci. Stat. Comp., * vol 9, pp. 862-874, 1988. * [2] Eisenstat, S. C. and Liu, J. W. H., "Exploiting Structural Symmetry in * Unsymmetric Sparse Symbolic Factorization," SIAM J. Matrix Analysis & * Applic., vol 13, pp. 202-211, 1992. */ /* ========================================================================== */ #include "klu_internal.h" size_t KLU_kernel_factor /* 0 if failure, size of LU if OK */ ( /* inputs, not modified */ Int n, /* A is n-by-n. n must be > 0. */ Int Ap [ ], /* size n+1, column pointers for A */ Int Ai [ ], /* size nz = Ap [n], row indices for A */ Entry Ax [ ], /* size nz, values of A */ Int Q [ ], /* size n, optional column permutation */ double Lsize, /* estimate of number of nonzeros in L */ /* outputs, not defined on input */ Unit **p_LU, /* row indices and values of L and U */ Entry Udiag [ ], /* size n, diagonal of U */ Int Llen [ ], /* size n, column length of L */ Int Ulen [ ], /* size n, column length of U */ Int Lip [ ], /* size n, column pointers for L */ Int Uip [ ], /* size n, column pointers for U */ Int P [ ], /* row permutation, size n */ Int *lnz, /* size of L */ Int *unz, /* size of U */ /* workspace, undefined on input */ Entry *X, /* size n double's, zero on output */ Int *Work, /* size 5n Int's */ /* inputs, not modified on output */ Int k1, /* the block of A is from k1 to k2-1 */ Int PSinv [ ], /* inverse of P from symbolic factorization */ double Rs [ ], /* scale factors for A */ /* inputs, modified on output */ Int Offp [ ], /* off-diagonal matrix (modified by this routine) */ Int Offi [ ], Entry Offx [ ], /* --------------- */ KLU_common *Common ) { double maxlnz, dunits ; Unit *LU ; Int *Pinv, *Lpend, *Stack, *Flag, *Ap_pos, *W ; Int lsize, usize, anz, ok ; size_t lusize ; ASSERT (Common != NULL) ; /* ---------------------------------------------------------------------- */ /* get control parameters, or use defaults */ /* ---------------------------------------------------------------------- */ n = MAX (1, n) ; anz = Ap [n+k1] - Ap [k1] ; if (Lsize <= 0) { Lsize = -Lsize ; Lsize = MAX (Lsize, 1.0) ; lsize = Lsize * anz + n ; } else { lsize = Lsize ; } usize = lsize ; lsize = MAX (n+1, lsize) ; usize = MAX (n+1, usize) ; maxlnz = (((double) n) * ((double) n) + ((double) n)) / 2. ; maxlnz = MIN (maxlnz, ((double) INT_MAX)) ; lsize = MIN (maxlnz, lsize) ; usize = MIN (maxlnz, usize) ; PRINTF (("Welcome to klu: n %d anz %d k1 %d lsize %d usize %d maxlnz %g\n", n, anz, k1, lsize, usize, maxlnz)) ; /* ---------------------------------------------------------------------- */ /* allocate workspace and outputs */ /* ---------------------------------------------------------------------- */ /* return arguments are not yet assigned */ *p_LU = (Unit *) NULL ; /* these computations are safe from size_t overflow */ W = Work ; Pinv = (Int *) W ; W += n ; Stack = (Int *) W ; W += n ; Flag = (Int *) W ; W += n ; Lpend = (Int *) W ; W += n ; Ap_pos = (Int *) W ; W += n ; dunits = DUNITS (Int, lsize) + DUNITS (Entry, lsize) + DUNITS (Int, usize) + DUNITS (Entry, usize) ; lusize = (size_t) dunits ; ok = !INT_OVERFLOW (dunits) ; LU = ok ? KLU_malloc (lusize, sizeof (Unit), Common) : NULL ; if (LU == NULL) { /* out of memory, or problem too large */ Common->status = KLU_OUT_OF_MEMORY ; lusize = 0 ; return (lusize) ; } /* ---------------------------------------------------------------------- */ /* factorize */ /* ---------------------------------------------------------------------- */ /* with pruning, and non-recursive depth-first-search */ lusize = KLU_kernel (n, Ap, Ai, Ax, Q, lusize, Pinv, P, &LU, Udiag, Llen, Ulen, Lip, Uip, lnz, unz, X, Stack, Flag, Ap_pos, Lpend, k1, PSinv, Rs, Offp, Offi, Offx, Common) ; /* ---------------------------------------------------------------------- */ /* return LU factors, or return nothing if an error occurred */ /* ---------------------------------------------------------------------- */ if (Common->status < KLU_OK) { LU = KLU_free (LU, lusize, sizeof (Unit), Common) ; lusize = 0 ; } *p_LU = LU ; PRINTF ((" in klu noffdiag %d\n", Common->noffdiag)) ; return (lusize) ; } /* ========================================================================== */ /* === KLU_lsolve =========================================================== */ /* ========================================================================== */ /* Solve Lx=b. Assumes L is unit lower triangular and where the unit diagonal * entry is NOT stored. Overwrites B with the solution X. B is n-by-nrhs * and is stored in ROW form with row dimension nrhs. nrhs must be in the * range 1 to 4. */ void KLU_lsolve ( /* inputs, not modified: */ Int n, Int Lip [ ], Int Llen [ ], Unit LU [ ], Int nrhs, /* right-hand-side on input, solution to Lx=b on output */ Entry X [ ] ) { Entry x [4], lik ; Int *Li ; Entry *Lx ; Int k, p, len, i ; switch (nrhs) { case 1: for (k = 0 ; k < n ; k++) { x [0] = X [k] ; GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ; /* unit diagonal of L is not stored*/ for (p = 0 ; p < len ; p++) { /* X [Li [p]] -= Lx [p] * x [0] ; */ MULT_SUB (X [Li [p]], Lx [p], x [0]) ; } } break ; case 2: for (k = 0 ; k < n ; k++) { x [0] = X [2*k ] ; x [1] = X [2*k + 1] ; GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ; for (p = 0 ; p < len ; p++) { i = Li [p] ; lik = Lx [p] ; MULT_SUB (X [2*i], lik, x [0]) ; MULT_SUB (X [2*i + 1], lik, x [1]) ; } } break ; case 3: for (k = 0 ; k < n ; k++) { x [0] = X [3*k ] ; x [1] = X [3*k + 1] ; x [2] = X [3*k + 2] ; GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ; for (p = 0 ; p < len ; p++) { i = Li [p] ; lik = Lx [p] ; MULT_SUB (X [3*i], lik, x [0]) ; MULT_SUB (X [3*i + 1], lik, x [1]) ; MULT_SUB (X [3*i + 2], lik, x [2]) ; } } break ; case 4: for (k = 0 ; k < n ; k++) { x [0] = X [4*k ] ; x [1] = X [4*k + 1] ; x [2] = X [4*k + 2] ; x [3] = X [4*k + 3] ; GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ; for (p = 0 ; p < len ; p++) { i = Li [p] ; lik = Lx [p] ; MULT_SUB (X [4*i], lik, x [0]) ; MULT_SUB (X [4*i + 1], lik, x [1]) ; MULT_SUB (X [4*i + 2], lik, x [2]) ; MULT_SUB (X [4*i + 3], lik, x [3]) ; } } break ; } } /* ========================================================================== */ /* === KLU_usolve =========================================================== */ /* ========================================================================== */ /* Solve Ux=b. Assumes U is non-unit upper triangular and where the diagonal * entry is NOT stored. Overwrites B with the solution X. B is n-by-nrhs * and is stored in ROW form with row dimension nrhs. nrhs must be in the * range 1 to 4. */ void KLU_usolve ( /* inputs, not modified: */ Int n, Int Uip [ ], Int Ulen [ ], Unit LU [ ], Entry Udiag [ ], Int nrhs, /* right-hand-side on input, solution to Ux=b on output */ Entry X [ ] ) { Entry x [4], uik, ukk ; Int *Ui ; Entry *Ux ; Int k, p, len, i ; switch (nrhs) { case 1: for (k = n-1 ; k >= 0 ; k--) { GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ; /* x [0] = X [k] / Udiag [k] ; */ DIV (x [0], X [k], Udiag [k]) ; X [k] = x [0] ; for (p = 0 ; p < len ; p++) { /* X [Ui [p]] -= Ux [p] * x [0] ; */ MULT_SUB (X [Ui [p]], Ux [p], x [0]) ; } } break ; case 2: for (k = n-1 ; k >= 0 ; k--) { GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ; ukk = Udiag [k] ; /* x [0] = X [2*k ] / ukk ; x [1] = X [2*k + 1] / ukk ; */ DIV (x [0], X [2*k], ukk) ; DIV (x [1], X [2*k + 1], ukk) ; X [2*k ] = x [0] ; X [2*k + 1] = x [1] ; for (p = 0 ; p < len ; p++) { i = Ui [p] ; uik = Ux [p] ; /* X [2*i ] -= uik * x [0] ; X [2*i + 1] -= uik * x [1] ; */ MULT_SUB (X [2*i], uik, x [0]) ; MULT_SUB (X [2*i + 1], uik, x [1]) ; } } break ; case 3: for (k = n-1 ; k >= 0 ; k--) { GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ; ukk = Udiag [k] ; DIV (x [0], X [3*k], ukk) ; DIV (x [1], X [3*k + 1], ukk) ; DIV (x [2], X [3*k + 2], ukk) ; X [3*k ] = x [0] ; X [3*k + 1] = x [1] ; X [3*k + 2] = x [2] ; for (p = 0 ; p < len ; p++) { i = Ui [p] ; uik = Ux [p] ; MULT_SUB (X [3*i], uik, x [0]) ; MULT_SUB (X [3*i + 1], uik, x [1]) ; MULT_SUB (X [3*i + 2], uik, x [2]) ; } } break ; case 4: for (k = n-1 ; k >= 0 ; k--) { GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ; ukk = Udiag [k] ; DIV (x [0], X [4*k], ukk) ; DIV (x [1], X [4*k + 1], ukk) ; DIV (x [2], X [4*k + 2], ukk) ; DIV (x [3], X [4*k + 3], ukk) ; X [4*k ] = x [0] ; X [4*k + 1] = x [1] ; X [4*k + 2] = x [2] ; X [4*k + 3] = x [3] ; for (p = 0 ; p < len ; p++) { i = Ui [p] ; uik = Ux [p] ; MULT_SUB (X [4*i], uik, x [0]) ; MULT_SUB (X [4*i + 1], uik, x [1]) ; MULT_SUB (X [4*i + 2], uik, x [2]) ; MULT_SUB (X [4*i + 3], uik, x [3]) ; } } break ; } } /* ========================================================================== */ /* === KLU_ltsolve ========================================================== */ /* ========================================================================== */ /* Solve L'x=b. Assumes L is unit lower triangular and where the unit diagonal * entry is NOT stored. Overwrites B with the solution X. B is n-by-nrhs * and is stored in ROW form with row dimension nrhs. nrhs must in the * range 1 to 4. */ void KLU_ltsolve ( /* inputs, not modified: */ Int n, Int Lip [ ], Int Llen [ ], Unit LU [ ], Int nrhs, #ifdef COMPLEX Int conj_solve, #endif /* right-hand-side on input, solution to L'x=b on output */ Entry X [ ] ) { Entry x [4], lik ; Int *Li ; Entry *Lx ; Int k, p, len, i ; switch (nrhs) { case 1: for (k = n-1 ; k >= 0 ; k--) { GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ; x [0] = X [k] ; for (p = 0 ; p < len ; p++) { #ifdef COMPLEX if (conj_solve) { /* x [0] -= CONJ (Lx [p]) * X [Li [p]] ; */ MULT_SUB_CONJ (x [0], X [Li [p]], Lx [p]) ; } else #endif { /*x [0] -= Lx [p] * X [Li [p]] ;*/ MULT_SUB (x [0], Lx [p], X [Li [p]]) ; } } X [k] = x [0] ; } break ; case 2: for (k = n-1 ; k >= 0 ; k--) { x [0] = X [2*k ] ; x [1] = X [2*k + 1] ; GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ; for (p = 0 ; p < len ; p++) { i = Li [p] ; #ifdef COMPLEX if (conj_solve) { CONJ (lik, Lx [p]) ; } else #endif { lik = Lx [p] ; } MULT_SUB (x [0], lik, X [2*i]) ; MULT_SUB (x [1], lik, X [2*i + 1]) ; } X [2*k ] = x [0] ; X [2*k + 1] = x [1] ; } break ; case 3: for (k = n-1 ; k >= 0 ; k--) { x [0] = X [3*k ] ; x [1] = X [3*k + 1] ; x [2] = X [3*k + 2] ; GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ; for (p = 0 ; p < len ; p++) { i = Li [p] ; #ifdef COMPLEX if (conj_solve) { CONJ (lik, Lx [p]) ; } else #endif { lik = Lx [p] ; } MULT_SUB (x [0], lik, X [3*i]) ; MULT_SUB (x [1], lik, X [3*i + 1]) ; MULT_SUB (x [2], lik, X [3*i + 2]) ; } X [3*k ] = x [0] ; X [3*k + 1] = x [1] ; X [3*k + 2] = x [2] ; } break ; case 4: for (k = n-1 ; k >= 0 ; k--) { x [0] = X [4*k ] ; x [1] = X [4*k + 1] ; x [2] = X [4*k + 2] ; x [3] = X [4*k + 3] ; GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ; for (p = 0 ; p < len ; p++) { i = Li [p] ; #ifdef COMPLEX if (conj_solve) { CONJ (lik, Lx [p]) ; } else #endif { lik = Lx [p] ; } MULT_SUB (x [0], lik, X [4*i]) ; MULT_SUB (x [1], lik, X [4*i + 1]) ; MULT_SUB (x [2], lik, X [4*i + 2]) ; MULT_SUB (x [3], lik, X [4*i + 3]) ; } X [4*k ] = x [0] ; X [4*k + 1] = x [1] ; X [4*k + 2] = x [2] ; X [4*k + 3] = x [3] ; } break ; } } /* ========================================================================== */ /* === KLU_utsolve ========================================================== */ /* ========================================================================== */ /* Solve U'x=b. Assumes U is non-unit upper triangular and where the diagonal * entry is stored (and appears last in each column of U). Overwrites B * with the solution X. B is n-by-nrhs and is stored in ROW form with row * dimension nrhs. nrhs must be in the range 1 to 4. */ void KLU_utsolve ( /* inputs, not modified: */ Int n, Int Uip [ ], Int Ulen [ ], Unit LU [ ], Entry Udiag [ ], Int nrhs, #ifdef COMPLEX Int conj_solve, #endif /* right-hand-side on input, solution to Ux=b on output */ Entry X [ ] ) { Entry x [4], uik, ukk ; Int k, p, len, i ; Int *Ui ; Entry *Ux ; switch (nrhs) { case 1: for (k = 0 ; k < n ; k++) { GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ; x [0] = X [k] ; for (p = 0 ; p < len ; p++) { #ifdef COMPLEX if (conj_solve) { /* x [0] -= CONJ (Ux [p]) * X [Ui [p]] ; */ MULT_SUB_CONJ (x [0], X [Ui [p]], Ux [p]) ; } else #endif { /* x [0] -= Ux [p] * X [Ui [p]] ; */ MULT_SUB (x [0], Ux [p], X [Ui [p]]) ; } } #ifdef COMPLEX if (conj_solve) { CONJ (ukk, Udiag [k]) ; } else #endif { ukk = Udiag [k] ; } DIV (X [k], x [0], ukk) ; } break ; case 2: for (k = 0 ; k < n ; k++) { GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ; x [0] = X [2*k ] ; x [1] = X [2*k + 1] ; for (p = 0 ; p < len ; p++) { i = Ui [p] ; #ifdef COMPLEX if (conj_solve) { CONJ (uik, Ux [p]) ; } else #endif { uik = Ux [p] ; } MULT_SUB (x [0], uik, X [2*i]) ; MULT_SUB (x [1], uik, X [2*i + 1]) ; } #ifdef COMPLEX if (conj_solve) { CONJ (ukk, Udiag [k]) ; } else #endif { ukk = Udiag [k] ; } DIV (X [2*k], x [0], ukk) ; DIV (X [2*k + 1], x [1], ukk) ; } break ; case 3: for (k = 0 ; k < n ; k++) { GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ; x [0] = X [3*k ] ; x [1] = X [3*k + 1] ; x [2] = X [3*k + 2] ; for (p = 0 ; p < len ; p++) { i = Ui [p] ; #ifdef COMPLEX if (conj_solve) { CONJ (uik, Ux [p]) ; } else #endif { uik = Ux [p] ; } MULT_SUB (x [0], uik, X [3*i]) ; MULT_SUB (x [1], uik, X [3*i + 1]) ; MULT_SUB (x [2], uik, X [3*i + 2]) ; } #ifdef COMPLEX if (conj_solve) { CONJ (ukk, Udiag [k]) ; } else #endif { ukk = Udiag [k] ; } DIV (X [3*k], x [0], ukk) ; DIV (X [3*k + 1], x [1], ukk) ; DIV (X [3*k + 2], x [2], ukk) ; } break ; case 4: for (k = 0 ; k < n ; k++) { GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ; x [0] = X [4*k ] ; x [1] = X [4*k + 1] ; x [2] = X [4*k + 2] ; x [3] = X [4*k + 3] ; for (p = 0 ; p < len ; p++) { i = Ui [p] ; #ifdef COMPLEX if (conj_solve) { CONJ (uik, Ux [p]) ; } else #endif { uik = Ux [p] ; } MULT_SUB (x [0], uik, X [4*i]) ; MULT_SUB (x [1], uik, X [4*i + 1]) ; MULT_SUB (x [2], uik, X [4*i + 2]) ; MULT_SUB (x [3], uik, X [4*i + 3]) ; } #ifdef COMPLEX if (conj_solve) { CONJ (ukk, Udiag [k]) ; } else #endif { ukk = Udiag [k] ; } DIV (X [4*k], x [0], ukk) ; DIV (X [4*k + 1], x [1], ukk) ; DIV (X [4*k + 2], x [2], ukk) ; DIV (X [4*k + 3], x [3], ukk) ; } break ; } } SuiteSparse/KLU/Source/klu_extract.c0000644001170100242450000001472110620223666016343 0ustar davisfac/* ========================================================================== */ /* === KLU_extract ========================================================== */ /* ========================================================================== */ /* Extract KLU factorization into conventional compressed-column matrices. * If any output array is NULL, that part of the LU factorization is not * extracted (this is not an error condition). * * nnz(L) = Numeric->lnz, nnz(U) = Numeric->unz, and nnz(F) = Numeric->Offp [n] */ #include "klu_internal.h" Int KLU_extract /* returns TRUE if successful, FALSE otherwise */ ( /* inputs: */ KLU_numeric *Numeric, KLU_symbolic *Symbolic, /* outputs, all of which must be allocated on input */ /* L */ Int *Lp, /* size n+1 */ Int *Li, /* size nnz(L) */ double *Lx, /* size nnz(L) */ #ifdef COMPLEX double *Lz, /* size nnz(L) for the complex case, ignored if real */ #endif /* U */ Int *Up, /* size n+1 */ Int *Ui, /* size nnz(U) */ double *Ux, /* size nnz(U) */ #ifdef COMPLEX double *Uz, /* size nnz(U) for the complex case, ignored if real */ #endif /* F */ Int *Fp, /* size n+1 */ Int *Fi, /* size nnz(F) */ double *Fx, /* size nnz(F) */ #ifdef COMPLEX double *Fz, /* size nnz(F) for the complex case, ignored if real */ #endif /* P, row permutation */ Int *P, /* size n */ /* Q, column permutation */ Int *Q, /* size n */ /* Rs, scale factors */ double *Rs, /* size n */ /* R, block boundaries */ Int *R, /* size nblocks+1 */ KLU_common *Common ) { Int *Lip, *Llen, *Uip, *Ulen, *Li2, *Ui2 ; Unit *LU ; Entry *Lx2, *Ux2, *Ukk ; Int i, k, block, nblocks, n, nz, k1, k2, nk, len, kk, p ; if (Common == NULL) { return (FALSE) ; } if (Symbolic == NULL || Numeric == NULL) { Common->status = KLU_INVALID ; return (FALSE) ; } Common->status = KLU_OK ; n = Symbolic->n ; nblocks = Symbolic->nblocks ; /* ---------------------------------------------------------------------- */ /* extract scale factors */ /* ---------------------------------------------------------------------- */ if (Rs != NULL) { if (Numeric->Rs != NULL) { for (i = 0 ; i < n ; i++) { Rs [i] = Numeric->Rs [i] ; } } else { /* no scaling */ for (i = 0 ; i < n ; i++) { Rs [i] = 1 ; } } } /* ---------------------------------------------------------------------- */ /* extract block boundaries */ /* ---------------------------------------------------------------------- */ if (R != NULL) { for (block = 0 ; block <= nblocks ; block++) { R [block] = Symbolic->R [block] ; } } /* ---------------------------------------------------------------------- */ /* extract final row permutation */ /* ---------------------------------------------------------------------- */ if (P != NULL) { for (k = 0 ; k < n ; k++) { P [k] = Numeric->Pnum [k] ; } } /* ---------------------------------------------------------------------- */ /* extract column permutation */ /* ---------------------------------------------------------------------- */ if (Q != NULL) { for (k = 0 ; k < n ; k++) { Q [k] = Symbolic->Q [k] ; } } /* ---------------------------------------------------------------------- */ /* extract each block of L */ /* ---------------------------------------------------------------------- */ if (Lp != NULL && Li != NULL && Lx != NULL #ifdef COMPLEX && Lz != NULL #endif ) { nz = 0 ; for (block = 0 ; block < nblocks ; block++) { k1 = Symbolic->R [block] ; k2 = Symbolic->R [block+1] ; nk = k2 - k1 ; if (nk == 1) { /* singleton block */ Lp [k1] = nz ; Li [nz] = k1 ; Lx [nz] = 1 ; #ifdef COMPLEX Lz [nz] = 0 ; #endif nz++ ; } else { /* non-singleton block */ LU = Numeric->LUbx [block] ; Lip = Numeric->Lip + k1 ; Llen = Numeric->Llen + k1 ; for (kk = 0 ; kk < nk ; kk++) { Lp [k1+kk] = nz ; /* add the unit diagonal entry */ Li [nz] = k1 + kk ; Lx [nz] = 1 ; #ifdef COMPLEX Lz [nz] = 0 ; #endif nz++ ; GET_POINTER (LU, Lip, Llen, Li2, Lx2, kk, len) ; for (p = 0 ; p < len ; p++) { Li [nz] = k1 + Li2 [p] ; Lx [nz] = REAL (Lx2 [p]) ; #ifdef COMPLEX Lz [nz] = IMAG (Lx2 [p]) ; #endif nz++ ; } } } } Lp [n] = nz ; ASSERT (nz == Numeric->lnz) ; } /* ---------------------------------------------------------------------- */ /* extract each block of U */ /* ---------------------------------------------------------------------- */ if (Up != NULL && Ui != NULL && Ux != NULL #ifdef COMPLEX && Uz != NULL #endif ) { nz = 0 ; for (block = 0 ; block < nblocks ; block++) { k1 = Symbolic->R [block] ; k2 = Symbolic->R [block+1] ; nk = k2 - k1 ; Ukk = ((Entry *) Numeric->Udiag) + k1 ; if (nk == 1) { /* singleton block */ Up [k1] = nz ; Ui [nz] = k1 ; Ux [nz] = REAL (Ukk [0]) ; #ifdef COMPLEX Uz [nz] = IMAG (Ukk [0]) ; #endif nz++ ; } else { /* non-singleton block */ LU = Numeric->LUbx [block] ; Uip = Numeric->Uip + k1 ; Ulen = Numeric->Ulen + k1 ; for (kk = 0 ; kk < nk ; kk++) { Up [k1+kk] = nz ; GET_POINTER (LU, Uip, Ulen, Ui2, Ux2, kk, len) ; for (p = 0 ; p < len ; p++) { Ui [nz] = k1 + Ui2 [p] ; Ux [nz] = REAL (Ux2 [p]) ; #ifdef COMPLEX Uz [nz] = IMAG (Ux2 [p]) ; #endif nz++ ; } /* add the diagonal entry */ Ui [nz] = k1 + kk ; Ux [nz] = REAL (Ukk [kk]) ; #ifdef COMPLEX Uz [nz] = IMAG (Ukk [kk]) ; #endif nz++ ; } } } Up [n] = nz ; ASSERT (nz == Numeric->unz) ; } /* ---------------------------------------------------------------------- */ /* extract the off-diagonal blocks, F */ /* ---------------------------------------------------------------------- */ if (Fp != NULL && Fi != NULL && Fx != NULL #ifdef COMPLEX && Fz != NULL #endif ) { for (k = 0 ; k <= n ; k++) { Fp [k] = Numeric->Offp [k] ; } nz = Fp [n] ; for (k = 0 ; k < nz ; k++) { Fi [k] = Numeric->Offi [k] ; } for (k = 0 ; k < nz ; k++) { Fx [k] = REAL (((Entry *) Numeric->Offx) [k]) ; #ifdef COMPLEX Fz [k] = IMAG (((Entry *) Numeric->Offx) [k]) ; #endif } } return (TRUE) ; } SuiteSparse/KLU/Source/klu_refactor.c0000644001170100242450000003103110616721351016466 0ustar davisfac/* ========================================================================== */ /* === KLU_refactor ========================================================= */ /* ========================================================================== */ /* Factor the matrix, after ordering and analyzing it with KLU_analyze, and * factoring it once with KLU_factor. This routine cannot do any numerical * pivoting. The pattern of the input matrix (Ap, Ai) must be identical to * the pattern given to KLU_factor. */ #include "klu_internal.h" /* ========================================================================== */ /* === KLU_refactor ========================================================= */ /* ========================================================================== */ Int KLU_refactor /* returns TRUE if successful, FALSE otherwise */ ( /* inputs, not modified */ Int Ap [ ], /* size n+1, column pointers */ Int Ai [ ], /* size nz, row indices */ double Ax [ ], KLU_symbolic *Symbolic, /* input/output */ KLU_numeric *Numeric, KLU_common *Common ) { Entry ukk, ujk, s ; Entry *Offx, *Lx, *Ux, *X, *Az, *Udiag ; double *Rs ; Int *P, *Q, *R, *Pnum, *Offp, *Offi, *Ui, *Li, *Pinv, *Lip, *Uip, *Llen, *Ulen ; Unit **LUbx ; Unit *LU ; Int k1, k2, nk, k, block, oldcol, pend, oldrow, n, p, newrow, scale, nblocks, poff, i, j, up, ulen, llen, maxblock, nzoff ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ if (Common == NULL) { return (FALSE) ; } Common->status = KLU_OK ; if (Numeric == NULL) { /* invalid Numeric object */ Common->status = KLU_INVALID ; return (FALSE) ; } Common->numerical_rank = EMPTY ; Common->singular_col = EMPTY ; Az = (Entry *) Ax ; /* ---------------------------------------------------------------------- */ /* get the contents of the Symbolic object */ /* ---------------------------------------------------------------------- */ n = Symbolic->n ; P = Symbolic->P ; Q = Symbolic->Q ; R = Symbolic->R ; nblocks = Symbolic->nblocks ; maxblock = Symbolic->maxblock ; /* ---------------------------------------------------------------------- */ /* get the contents of the Numeric object */ /* ---------------------------------------------------------------------- */ Pnum = Numeric->Pnum ; Offp = Numeric->Offp ; Offi = Numeric->Offi ; Offx = (Entry *) Numeric->Offx ; LUbx = (Unit **) Numeric->LUbx ; scale = Common->scale ; if (scale > 0) { /* factorization was not scaled, but refactorization is scaled */ if (Numeric->Rs == NULL) { Numeric->Rs = KLU_malloc (n, sizeof (double), Common) ; if (Common->status < KLU_OK) { Common->status = KLU_OUT_OF_MEMORY ; return (FALSE) ; } } } else { /* no scaling for refactorization; ensure Numeric->Rs is freed. This * does nothing if Numeric->Rs is already NULL. */ Numeric->Rs = KLU_free (Numeric->Rs, n, sizeof (double), Common) ; } Rs = Numeric->Rs ; Pinv = Numeric->Pinv ; X = (Entry *) Numeric->Xwork ; Common->nrealloc = 0 ; Udiag = Numeric->Udiag ; nzoff = Symbolic->nzoff ; /* ---------------------------------------------------------------------- */ /* check the input matrix compute the row scale factors, Rs */ /* ---------------------------------------------------------------------- */ /* do no scale, or check the input matrix, if scale < 0 */ if (scale >= 0) { /* check for out-of-range indices, but do not check for duplicates */ if (!KLU_scale (scale, n, Ap, Ai, Ax, Rs, NULL, Common)) { return (FALSE) ; } } /* ---------------------------------------------------------------------- */ /* clear workspace X */ /* ---------------------------------------------------------------------- */ for (k = 0 ; k < maxblock ; k++) { /* X [k] = 0 */ CLEAR (X [k]) ; } poff = 0 ; /* ---------------------------------------------------------------------- */ /* factor each block */ /* ---------------------------------------------------------------------- */ if (scale <= 0) { /* ------------------------------------------------------------------ */ /* no scaling */ /* ------------------------------------------------------------------ */ for (block = 0 ; block < nblocks ; block++) { /* -------------------------------------------------------------- */ /* the block is from rows/columns k1 to k2-1 */ /* -------------------------------------------------------------- */ k1 = R [block] ; k2 = R [block+1] ; nk = k2 - k1 ; if (nk == 1) { /* ---------------------------------------------------------- */ /* singleton case */ /* ---------------------------------------------------------- */ oldcol = Q [k1] ; pend = Ap [oldcol+1] ; CLEAR (s) ; for (p = Ap [oldcol] ; p < pend ; p++) { newrow = Pinv [Ai [p]] - k1 ; if (newrow < 0 && poff < nzoff) { /* entry in off-diagonal block */ Offx [poff] = Az [p] ; poff++ ; } else { /* singleton */ s = Az [p] ; } } Udiag [k1] = s ; } else { /* ---------------------------------------------------------- */ /* construct and factor the kth block */ /* ---------------------------------------------------------- */ Lip = Numeric->Lip + k1 ; Llen = Numeric->Llen + k1 ; Uip = Numeric->Uip + k1 ; Ulen = Numeric->Ulen + k1 ; LU = LUbx [block] ; for (k = 0 ; k < nk ; k++) { /* ------------------------------------------------------ */ /* scatter kth column of the block into workspace X */ /* ------------------------------------------------------ */ oldcol = Q [k+k1] ; pend = Ap [oldcol+1] ; for (p = Ap [oldcol] ; p < pend ; p++) { newrow = Pinv [Ai [p]] - k1 ; if (newrow < 0 && poff < nzoff) { /* entry in off-diagonal block */ Offx [poff] = Az [p] ; poff++ ; } else { /* (newrow,k) is an entry in the block */ X [newrow] = Az [p] ; } } /* ------------------------------------------------------ */ /* compute kth column of U, and update kth column of A */ /* ------------------------------------------------------ */ GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, ulen) ; for (up = 0 ; up < ulen ; up++) { j = Ui [up] ; ujk = X [j] ; /* X [j] = 0 */ CLEAR (X [j]) ; Ux [up] = ujk ; GET_POINTER (LU, Lip, Llen, Li, Lx, j, llen) ; for (p = 0 ; p < llen ; p++) { /* X [Li [p]] -= Lx [p] * ujk */ MULT_SUB (X [Li [p]], Lx [p], ujk) ; } } /* get the diagonal entry of U */ ukk = X [k] ; /* X [k] = 0 */ CLEAR (X [k]) ; /* singular case */ if (IS_ZERO (ukk)) { /* matrix is numerically singular */ Common->status = KLU_SINGULAR ; if (Common->numerical_rank == EMPTY) { Common->numerical_rank = k+k1 ; Common->singular_col = Q [k+k1] ; } if (Common->halt_if_singular) { /* do not continue the factorization */ return (FALSE) ; } } Udiag [k+k1] = ukk ; /* gather and divide by pivot to get kth column of L */ GET_POINTER (LU, Lip, Llen, Li, Lx, k, llen) ; for (p = 0 ; p < llen ; p++) { i = Li [p] ; DIV (Lx [p], X [i], ukk) ; CLEAR (X [i]) ; } } } } } else { /* ------------------------------------------------------------------ */ /* scaling */ /* ------------------------------------------------------------------ */ for (block = 0 ; block < nblocks ; block++) { /* -------------------------------------------------------------- */ /* the block is from rows/columns k1 to k2-1 */ /* -------------------------------------------------------------- */ k1 = R [block] ; k2 = R [block+1] ; nk = k2 - k1 ; if (nk == 1) { /* ---------------------------------------------------------- */ /* singleton case */ /* ---------------------------------------------------------- */ oldcol = Q [k1] ; pend = Ap [oldcol+1] ; CLEAR (s) ; for (p = Ap [oldcol] ; p < pend ; p++) { oldrow = Ai [p] ; newrow = Pinv [oldrow] - k1 ; if (newrow < 0 && poff < nzoff) { /* entry in off-diagonal block */ /* Offx [poff] = Az [p] / Rs [oldrow] */ SCALE_DIV_ASSIGN (Offx [poff], Az [p], Rs [oldrow]) ; poff++ ; } else { /* singleton */ /* s = Az [p] / Rs [oldrow] */ SCALE_DIV_ASSIGN (s, Az [p], Rs [oldrow]) ; } } Udiag [k1] = s ; } else { /* ---------------------------------------------------------- */ /* construct and factor the kth block */ /* ---------------------------------------------------------- */ Lip = Numeric->Lip + k1 ; Llen = Numeric->Llen + k1 ; Uip = Numeric->Uip + k1 ; Ulen = Numeric->Ulen + k1 ; LU = LUbx [block] ; for (k = 0 ; k < nk ; k++) { /* ------------------------------------------------------ */ /* scatter kth column of the block into workspace X */ /* ------------------------------------------------------ */ oldcol = Q [k+k1] ; pend = Ap [oldcol+1] ; for (p = Ap [oldcol] ; p < pend ; p++) { oldrow = Ai [p] ; newrow = Pinv [oldrow] - k1 ; if (newrow < 0 && poff < nzoff) { /* entry in off-diagonal part */ /* Offx [poff] = Az [p] / Rs [oldrow] */ SCALE_DIV_ASSIGN (Offx [poff], Az [p], Rs [oldrow]); poff++ ; } else { /* (newrow,k) is an entry in the block */ /* X [newrow] = Az [p] / Rs [oldrow] */ SCALE_DIV_ASSIGN (X [newrow], Az [p], Rs [oldrow]) ; } } /* ------------------------------------------------------ */ /* compute kth column of U, and update kth column of A */ /* ------------------------------------------------------ */ GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, ulen) ; for (up = 0 ; up < ulen ; up++) { j = Ui [up] ; ujk = X [j] ; /* X [j] = 0 */ CLEAR (X [j]) ; Ux [up] = ujk ; GET_POINTER (LU, Lip, Llen, Li, Lx, j, llen) ; for (p = 0 ; p < llen ; p++) { /* X [Li [p]] -= Lx [p] * ujk */ MULT_SUB (X [Li [p]], Lx [p], ujk) ; } } /* get the diagonal entry of U */ ukk = X [k] ; /* X [k] = 0 */ CLEAR (X [k]) ; /* singular case */ if (IS_ZERO (ukk)) { /* matrix is numerically singular */ Common->status = KLU_SINGULAR ; if (Common->numerical_rank == EMPTY) { Common->numerical_rank = k+k1 ; Common->singular_col = Q [k+k1] ; } if (Common->halt_if_singular) { /* do not continue the factorization */ return (FALSE) ; } } Udiag [k+k1] = ukk ; /* gather and divide by pivot to get kth column of L */ GET_POINTER (LU, Lip, Llen, Li, Lx, k, llen) ; for (p = 0 ; p < llen ; p++) { i = Li [p] ; DIV (Lx [p], X [i], ukk) ; CLEAR (X [i]) ; } } } } } /* ---------------------------------------------------------------------- */ /* permute scale factors Rs according to pivotal row order */ /* ---------------------------------------------------------------------- */ if (scale > 0) { for (k = 0 ; k < n ; k++) { REAL (X [k]) = Rs [Pnum [k]] ; } for (k = 0 ; k < n ; k++) { Rs [k] = REAL (X [k]) ; } } #ifndef NDEBUG ASSERT (Offp [n] == poff) ; ASSERT (Symbolic->nzoff == poff) ; PRINTF (("\n------------------- Off diagonal entries, new:\n")) ; ASSERT (KLU_valid (n, Offp, Offi, Offx)) ; if (Common->status == KLU_OK) { PRINTF (("\n ########### KLU_BTF_REFACTOR done, nblocks %d\n",nblocks)); for (block = 0 ; block < nblocks ; block++) { k1 = R [block] ; k2 = R [block+1] ; nk = k2 - k1 ; PRINTF (( "\n================KLU_refactor output: k1 %d k2 %d nk %d\n", k1, k2, nk)) ; if (nk == 1) { PRINTF (("singleton ")) ; PRINT_ENTRY (Udiag [k1]) ; } else { Lip = Numeric->Lip + k1 ; Llen = Numeric->Llen + k1 ; LU = (Unit *) Numeric->LUbx [block] ; PRINTF (("\n---- L block %d\n", block)) ; ASSERT (KLU_valid_LU (nk, TRUE, Lip, Llen, LU)) ; Uip = Numeric->Uip + k1 ; Ulen = Numeric->Ulen + k1 ; PRINTF (("\n---- U block %d\n", block)) ; ASSERT (KLU_valid_LU (nk, FALSE, Uip, Ulen, LU)) ; } } } #endif return (TRUE) ; } SuiteSparse/KLU/Source/klu_solve.c0000644001170100242450000002202210616200177016007 0ustar davisfac/* ========================================================================== */ /* === KLU_solve ============================================================ */ /* ========================================================================== */ /* Solve Ax=b using the symbolic and numeric objects from KLU_analyze * (or KLU_analyze_given) and KLU_factor. Note that no iterative refinement is * performed. Uses Numeric->Xwork as workspace (undefined on input and output), * of size 4n Entry's (note that columns 2 to 4 of Xwork overlap with * Numeric->Iwork). */ #include "klu_internal.h" Int KLU_solve ( /* inputs, not modified */ KLU_symbolic *Symbolic, KLU_numeric *Numeric, Int d, /* leading dimension of B */ Int nrhs, /* number of right-hand-sides */ /* right-hand-side on input, overwritten with solution to Ax=b on output */ double B [ ], /* size n*nrhs, in column-oriented form, with * leading dimension d. */ /* --------------- */ KLU_common *Common ) { Entry x [4], offik, s ; double rs, *Rs ; Entry *Offx, *X, *Bz, *Udiag ; Int *Q, *R, *Pnum, *Offp, *Offi, *Lip, *Uip, *Llen, *Ulen ; Unit **LUbx ; Int k1, k2, nk, k, block, pend, n, p, nblocks, chunk, nr, i ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ if (Common == NULL) { return (FALSE) ; } if (Numeric == NULL || Symbolic == NULL || d < Symbolic->n || nrhs < 0 || B == NULL) { Common->status = KLU_INVALID ; return (FALSE) ; } Common->status = KLU_OK ; /* ---------------------------------------------------------------------- */ /* get the contents of the Symbolic object */ /* ---------------------------------------------------------------------- */ Bz = (Entry *) B ; n = Symbolic->n ; nblocks = Symbolic->nblocks ; Q = Symbolic->Q ; R = Symbolic->R ; /* ---------------------------------------------------------------------- */ /* get the contents of the Numeric object */ /* ---------------------------------------------------------------------- */ ASSERT (nblocks == Numeric->nblocks) ; Pnum = Numeric->Pnum ; Offp = Numeric->Offp ; Offi = Numeric->Offi ; Offx = (Entry *) Numeric->Offx ; Lip = Numeric->Lip ; Llen = Numeric->Llen ; Uip = Numeric->Uip ; Ulen = Numeric->Ulen ; LUbx = (Unit **) Numeric->LUbx ; Udiag = Numeric->Udiag ; Rs = Numeric->Rs ; X = (Entry *) Numeric->Xwork ; ASSERT (KLU_valid (n, Offp, Offi, Offx)) ; /* ---------------------------------------------------------------------- */ /* solve in chunks of 4 columns at a time */ /* ---------------------------------------------------------------------- */ for (chunk = 0 ; chunk < nrhs ; chunk += 4) { /* ------------------------------------------------------------------ */ /* get the size of the current chunk */ /* ------------------------------------------------------------------ */ nr = MIN (nrhs - chunk, 4) ; /* ------------------------------------------------------------------ */ /* scale and permute the right hand side, X = P*(R\B) */ /* ------------------------------------------------------------------ */ if (Rs == NULL) { /* no scaling */ switch (nr) { case 1: for (k = 0 ; k < n ; k++) { X [k] = Bz [Pnum [k]] ; } break ; case 2: for (k = 0 ; k < n ; k++) { i = Pnum [k] ; X [2*k ] = Bz [i ] ; X [2*k + 1] = Bz [i + d ] ; } break ; case 3: for (k = 0 ; k < n ; k++) { i = Pnum [k] ; X [3*k ] = Bz [i ] ; X [3*k + 1] = Bz [i + d ] ; X [3*k + 2] = Bz [i + d*2] ; } break ; case 4: for (k = 0 ; k < n ; k++) { i = Pnum [k] ; X [4*k ] = Bz [i ] ; X [4*k + 1] = Bz [i + d ] ; X [4*k + 2] = Bz [i + d*2] ; X [4*k + 3] = Bz [i + d*3] ; } break ; } } else { switch (nr) { case 1: for (k = 0 ; k < n ; k++) { SCALE_DIV_ASSIGN (X [k], Bz [Pnum [k]], Rs [k]) ; } break ; case 2: for (k = 0 ; k < n ; k++) { i = Pnum [k] ; rs = Rs [k] ; SCALE_DIV_ASSIGN (X [2*k], Bz [i], rs) ; SCALE_DIV_ASSIGN (X [2*k + 1], Bz [i + d], rs) ; } break ; case 3: for (k = 0 ; k < n ; k++) { i = Pnum [k] ; rs = Rs [k] ; SCALE_DIV_ASSIGN (X [3*k], Bz [i], rs) ; SCALE_DIV_ASSIGN (X [3*k + 1], Bz [i + d], rs) ; SCALE_DIV_ASSIGN (X [3*k + 2], Bz [i + d*2], rs) ; } break ; case 4: for (k = 0 ; k < n ; k++) { i = Pnum [k] ; rs = Rs [k] ; SCALE_DIV_ASSIGN (X [4*k], Bz [i], rs) ; SCALE_DIV_ASSIGN (X [4*k + 1], Bz [i + d], rs) ; SCALE_DIV_ASSIGN (X [4*k + 2], Bz [i + d*2], rs) ; SCALE_DIV_ASSIGN (X [4*k + 3], Bz [i + d*3], rs) ; } break ; } } /* ------------------------------------------------------------------ */ /* solve X = (L*U + Off)\X */ /* ------------------------------------------------------------------ */ for (block = nblocks-1 ; block >= 0 ; block--) { /* -------------------------------------------------------------- */ /* the block of size nk is from rows/columns k1 to k2-1 */ /* -------------------------------------------------------------- */ k1 = R [block] ; k2 = R [block+1] ; nk = k2 - k1 ; PRINTF (("solve %d, k1 %d k2-1 %d nk %d\n", block, k1,k2-1,nk)) ; /* solve the block system */ if (nk == 1) { s = Udiag [k1] ; switch (nr) { case 1: DIV (X [k1], X [k1], s) ; break ; case 2: DIV (X [2*k1], X [2*k1], s) ; DIV (X [2*k1 + 1], X [2*k1 + 1], s) ; break ; case 3: DIV (X [3*k1], X [3*k1], s) ; DIV (X [3*k1 + 1], X [3*k1 + 1], s) ; DIV (X [3*k1 + 2], X [3*k1 + 2], s) ; break ; case 4: DIV (X [4*k1], X [4*k1], s) ; DIV (X [4*k1 + 1], X [4*k1 + 1], s) ; DIV (X [4*k1 + 2], X [4*k1 + 2], s) ; DIV (X [4*k1 + 3], X [4*k1 + 3], s) ; break ; } } else { KLU_lsolve (nk, Lip + k1, Llen + k1, LUbx [block], nr, X + nr*k1) ; KLU_usolve (nk, Uip + k1, Ulen + k1, LUbx [block], Udiag + k1, nr, X + nr*k1) ; } /* -------------------------------------------------------------- */ /* block back-substitution for the off-diagonal-block entries */ /* -------------------------------------------------------------- */ if (block > 0) { switch (nr) { case 1: for (k = k1 ; k < k2 ; k++) { pend = Offp [k+1] ; x [0] = X [k] ; for (p = Offp [k] ; p < pend ; p++) { MULT_SUB (X [Offi [p]], Offx [p], x [0]) ; } } break ; case 2: for (k = k1 ; k < k2 ; k++) { pend = Offp [k+1] ; x [0] = X [2*k ] ; x [1] = X [2*k + 1] ; for (p = Offp [k] ; p < pend ; p++) { i = Offi [p] ; offik = Offx [p] ; MULT_SUB (X [2*i], offik, x [0]) ; MULT_SUB (X [2*i + 1], offik, x [1]) ; } } break ; case 3: for (k = k1 ; k < k2 ; k++) { pend = Offp [k+1] ; x [0] = X [3*k ] ; x [1] = X [3*k + 1] ; x [2] = X [3*k + 2] ; for (p = Offp [k] ; p < pend ; p++) { i = Offi [p] ; offik = Offx [p] ; MULT_SUB (X [3*i], offik, x [0]) ; MULT_SUB (X [3*i + 1], offik, x [1]) ; MULT_SUB (X [3*i + 2], offik, x [2]) ; } } break ; case 4: for (k = k1 ; k < k2 ; k++) { pend = Offp [k+1] ; x [0] = X [4*k ] ; x [1] = X [4*k + 1] ; x [2] = X [4*k + 2] ; x [3] = X [4*k + 3] ; for (p = Offp [k] ; p < pend ; p++) { i = Offi [p] ; offik = Offx [p] ; MULT_SUB (X [4*i], offik, x [0]) ; MULT_SUB (X [4*i + 1], offik, x [1]) ; MULT_SUB (X [4*i + 2], offik, x [2]) ; MULT_SUB (X [4*i + 3], offik, x [3]) ; } } break ; } } } /* ------------------------------------------------------------------ */ /* permute the result, Bz = Q*X */ /* ------------------------------------------------------------------ */ switch (nr) { case 1: for (k = 0 ; k < n ; k++) { Bz [Q [k]] = X [k] ; } break ; case 2: for (k = 0 ; k < n ; k++) { i = Q [k] ; Bz [i ] = X [2*k ] ; Bz [i + d ] = X [2*k + 1] ; } break ; case 3: for (k = 0 ; k < n ; k++) { i = Q [k] ; Bz [i ] = X [3*k ] ; Bz [i + d ] = X [3*k + 1] ; Bz [i + d*2] = X [3*k + 2] ; } break ; case 4: for (k = 0 ; k < n ; k++) { i = Q [k] ; Bz [i ] = X [4*k ] ; Bz [i + d ] = X [4*k + 1] ; Bz [i + d*2] = X [4*k + 2] ; Bz [i + d*3] = X [4*k + 3] ; } break ; } /* ------------------------------------------------------------------ */ /* go to the next chunk of B */ /* ------------------------------------------------------------------ */ Bz += d*4 ; } return (TRUE) ; } SuiteSparse/KLU/Source/klu_free_symbolic.c0000644001170100242450000000170710616721454017516 0ustar davisfac/* ========================================================================== */ /* === KLU_free_symbolic ==================================================== */ /* ========================================================================== */ /* Free the KLU Symbolic object. */ #include "klu_internal.h" Int KLU_free_symbolic ( KLU_symbolic **SymbolicHandle, KLU_common *Common ) { KLU_symbolic *Symbolic ; Int n ; if (Common == NULL) { return (FALSE) ; } if (SymbolicHandle == NULL || *SymbolicHandle == NULL) { return (TRUE) ; } Symbolic = *SymbolicHandle ; n = Symbolic->n ; KLU_free (Symbolic->P, n, sizeof (Int), Common) ; KLU_free (Symbolic->Q, n, sizeof (Int), Common) ; KLU_free (Symbolic->R, n+1, sizeof (Int), Common) ; KLU_free (Symbolic->Lnz, n, sizeof (double), Common) ; KLU_free (Symbolic, 1, sizeof (KLU_symbolic), Common) ; *SymbolicHandle = NULL ; return (TRUE) ; } SuiteSparse/KLU/Source/klu_free_numeric.c0000644001170100242450000000361710617236422017336 0ustar davisfac/* ========================================================================== */ /* === KLU_free_numeric ===================================================== */ /* ========================================================================== */ /* Free the KLU Numeric object. */ #include "klu_internal.h" Int KLU_free_numeric ( KLU_numeric **NumericHandle, KLU_common *Common ) { KLU_numeric *Numeric ; Unit **LUbx ; size_t *LUsize ; Int block, n, nzoff, nblocks ; if (Common == NULL) { return (FALSE) ; } if (NumericHandle == NULL || *NumericHandle == NULL) { return (TRUE) ; } Numeric = *NumericHandle ; n = Numeric->n ; nzoff = Numeric->nzoff ; nblocks = Numeric->nblocks ; LUsize = Numeric->LUsize ; LUbx = (Unit **) Numeric->LUbx ; if (LUbx != NULL) { for (block = 0 ; block < nblocks ; block++) { KLU_free (LUbx [block], LUsize ? LUsize [block] : 0, sizeof (Unit), Common) ; } } KLU_free (Numeric->Pnum, n, sizeof (Int), Common) ; KLU_free (Numeric->Offp, n+1, sizeof (Int), Common) ; KLU_free (Numeric->Offi, nzoff+1, sizeof (Int), Common) ; KLU_free (Numeric->Offx, nzoff+1, sizeof (Entry), Common) ; KLU_free (Numeric->Lip, n, sizeof (Int), Common) ; KLU_free (Numeric->Llen, n, sizeof (Int), Common) ; KLU_free (Numeric->Uip, n, sizeof (Int), Common) ; KLU_free (Numeric->Ulen, n, sizeof (Int), Common) ; KLU_free (Numeric->LUsize, nblocks, sizeof (size_t), Common) ; KLU_free (Numeric->LUbx, nblocks, sizeof (Unit *), Common) ; KLU_free (Numeric->Udiag, n, sizeof (Entry), Common) ; KLU_free (Numeric->Rs, n, sizeof (double), Common) ; KLU_free (Numeric->Pinv, n, sizeof (Int), Common) ; KLU_free (Numeric->Work, Numeric->worksize, 1, Common) ; KLU_free (Numeric, 1, sizeof (KLU_numeric), Common) ; *NumericHandle = NULL ; return (TRUE) ; } SuiteSparse/KLU/Source/klu_kernel.c0000644001170100242450000007154610634325116016157 0ustar davisfac/* ========================================================================== */ /* === KLU_kernel =========================================================== */ /* ========================================================================== */ /* Sparse left-looking LU factorization, with partial pivoting. Based on * Gilbert & Peierl's method, with a non-recursive DFS and with Eisenstat & * Liu's symmetric pruning. No user-callable routines are in this file. */ #include "klu_internal.h" /* ========================================================================== */ /* === dfs ================================================================== */ /* ========================================================================== */ /* Does a depth-first-search, starting at node j. */ static Int dfs ( /* input, not modified on output: */ Int j, /* node at which to start the DFS */ Int k, /* mark value, for the Flag array */ Int Pinv [ ], /* Pinv [i] = k if row i is kth pivot row, or EMPTY if * row i is not yet pivotal. */ Int Llen [ ], /* size n, Llen [k] = # nonzeros in column k of L */ Int Lip [ ], /* size n, Lip [k] is position in LU of column k of L */ /* workspace, not defined on input or output */ Int Stack [ ], /* size n */ /* input/output: */ Int Flag [ ], /* Flag [i] == k means i is marked */ Int Lpend [ ], /* for symmetric pruning */ Int top, /* top of stack on input*/ Unit LU [], Int *Lik, /* Li row index array of the kth column */ Int *plength, /* other, not defined on input or output */ Int Ap_pos [ ] /* keeps track of position in adj list during DFS */ ) { Int i, pos, jnew, head, l_length ; Int *Li ; l_length = *plength ; head = 0 ; Stack [0] = j ; ASSERT (Flag [j] != k) ; while (head >= 0) { j = Stack [head] ; jnew = Pinv [j] ; ASSERT (jnew >= 0 && jnew < k) ; /* j is pivotal */ if (Flag [j] != k) /* a node is not yet visited */ { /* first time that j has been visited */ Flag [j] = k ; PRINTF (("[ start dfs at %d : new %d\n", j, jnew)) ; /* set Ap_pos [head] to one past the last entry in col j to scan */ Ap_pos [head] = (Lpend [jnew] == EMPTY) ? Llen [jnew] : Lpend [jnew] ; } /* add the adjacent nodes to the recursive stack by iterating through * until finding another non-visited pivotal node */ Li = (Int *) (LU + Lip [jnew]) ; for (pos = --Ap_pos [head] ; pos >= 0 ; --pos) { i = Li [pos] ; if (Flag [i] != k) { /* node i is not yet visited */ if (Pinv [i] >= 0) { /* keep track of where we left off in the scan of the * adjacency list of node j so we can restart j where we * left off. */ Ap_pos [head] = pos ; /* node i is pivotal; push it onto the recursive stack * and immediately break so we can recurse on node i. */ Stack [++head] = i ; break ; } else { /* node i is not pivotal (no outgoing edges). */ /* Flag as visited and store directly into L, * and continue with current node j. */ Flag [i] = k ; Lik [l_length] = i ; l_length++ ; } } } if (pos == -1) { /* if all adjacent nodes of j are already visited, pop j from * recursive stack and push j onto output stack */ head-- ; Stack[--top] = j ; PRINTF ((" end dfs at %d ] head : %d\n", j, head)) ; } } *plength = l_length ; return (top) ; } /* ========================================================================== */ /* === lsolve_symbolic ====================================================== */ /* ========================================================================== */ /* Finds the pattern of x, for the solution of Lx=b */ static Int lsolve_symbolic ( /* input, not modified on output: */ Int n, /* L is n-by-n, where n >= 0 */ Int k, /* also used as the mark value, for the Flag array */ Int Ap [ ], Int Ai [ ], Int Q [ ], Int Pinv [ ], /* Pinv [i] = k if i is kth pivot row, or EMPTY if row i * is not yet pivotal. */ /* workspace, not defined on input or output */ Int Stack [ ], /* size n */ /* workspace, defined on input and output */ Int Flag [ ], /* size n. Initially, all of Flag [0..n-1] < k. After * lsolve_symbolic is done, Flag [i] == k if i is in * the pattern of the output, and Flag [0..n-1] <= k. */ /* other */ Int Lpend [ ], /* for symmetric pruning */ Int Ap_pos [ ], /* workspace used in dfs */ Unit LU [ ], /* LU factors (pattern and values) */ Int lup, /* pointer to free space in LU */ Int Llen [ ], /* size n, Llen [k] = # nonzeros in column k of L */ Int Lip [ ], /* size n, Lip [k] is position in LU of column k of L */ /* ---- the following are only used in the BTF case --- */ Int k1, /* the block of A is from k1 to k2-1 */ Int PSinv [ ] /* inverse of P from symbolic factorization */ ) { Int *Lik ; Int i, p, pend, oldcol, kglobal, top, l_length ; top = n ; l_length = 0 ; Lik = (Int *) (LU + lup); /* ---------------------------------------------------------------------- */ /* BTF factorization of A (k1:k2-1, k1:k2-1) */ /* ---------------------------------------------------------------------- */ kglobal = k + k1 ; /* column k of the block is col kglobal of A */ oldcol = Q [kglobal] ; /* Q must be present for BTF case */ pend = Ap [oldcol+1] ; for (p = Ap [oldcol] ; p < pend ; p++) { i = PSinv [Ai [p]] - k1 ; if (i < 0) continue ; /* skip entry outside the block */ /* (i,k) is an entry in the block. start a DFS at node i */ PRINTF (("\n ===== DFS at node %d in b, inew: %d\n", i, Pinv [i])) ; if (Flag [i] != k) { if (Pinv [i] >= 0) { top = dfs (i, k, Pinv, Llen, Lip, Stack, Flag, Lpend, top, LU, Lik, &l_length, Ap_pos) ; } else { /* i is not pivotal, and not flagged. Flag and put in L */ Flag [i] = k ; Lik [l_length] = i ; l_length++; } } } /* If Llen [k] is zero, the matrix is structurally singular */ Llen [k] = l_length ; return (top) ; } /* ========================================================================== */ /* === construct_column ===================================================== */ /* ========================================================================== */ /* Construct the kth column of A, and the off-diagonal part, if requested. * Scatter the numerical values into the workspace X, and construct the * corresponding column of the off-diagonal matrix. */ static void construct_column ( /* inputs, not modified on output */ Int k, /* the column of A (or the column of the block) to get */ Int Ap [ ], Int Ai [ ], Entry Ax [ ], Int Q [ ], /* column pre-ordering */ /* zero on input, modified on output */ Entry X [ ], /* ---- the following are only used in the BTF case --- */ /* inputs, not modified on output */ Int k1, /* the block of A is from k1 to k2-1 */ Int PSinv [ ], /* inverse of P from symbolic factorization */ double Rs [ ], /* scale factors for A */ Int scale, /* 0: no scaling, nonzero: scale the rows with Rs */ /* inputs, modified on output */ Int Offp [ ], /* off-diagonal matrix (modified by this routine) */ Int Offi [ ], Entry Offx [ ] ) { Entry aik ; Int i, p, pend, oldcol, kglobal, poff, oldrow ; /* ---------------------------------------------------------------------- */ /* Scale and scatter the column into X. */ /* ---------------------------------------------------------------------- */ kglobal = k + k1 ; /* column k of the block is col kglobal of A */ poff = Offp [kglobal] ; /* start of off-diagonal column */ oldcol = Q [kglobal] ; pend = Ap [oldcol+1] ; if (scale <= 0) { /* no scaling */ for (p = Ap [oldcol] ; p < pend ; p++) { oldrow = Ai [p] ; i = PSinv [oldrow] - k1 ; aik = Ax [p] ; if (i < 0) { /* this is an entry in the off-diagonal part */ Offi [poff] = oldrow ; Offx [poff] = aik ; poff++ ; } else { /* (i,k) is an entry in the block. scatter into X */ X [i] = aik ; } } } else { /* row scaling */ for (p = Ap [oldcol] ; p < pend ; p++) { oldrow = Ai [p] ; i = PSinv [oldrow] - k1 ; aik = Ax [p] ; SCALE_DIV (aik, Rs [oldrow]) ; if (i < 0) { /* this is an entry in the off-diagonal part */ Offi [poff] = oldrow ; Offx [poff] = aik ; poff++ ; } else { /* (i,k) is an entry in the block. scatter into X */ X [i] = aik ; } } } Offp [kglobal+1] = poff ; /* start of the next col of off-diag part */ } /* ========================================================================== */ /* === lsolve_numeric ======================================================= */ /* ========================================================================== */ /* Computes the numerical values of x, for the solution of Lx=b. Note that x * may include explicit zeros if numerical cancelation occurs. L is assumed * to be unit-diagonal, with possibly unsorted columns (but the first entry in * the column must always be the diagonal entry). */ static void lsolve_numeric ( /* input, not modified on output: */ Int Pinv [ ], /* Pinv [i] = k if i is kth pivot row, or EMPTY if row i * is not yet pivotal. */ Unit *LU, /* LU factors (pattern and values) */ Int Stack [ ], /* stack for dfs */ Int Lip [ ], /* size n, Lip [k] is position in LU of column k of L */ Int top, /* top of stack on input */ Int n, /* A is n-by-n */ Int Llen [ ], /* size n, Llen [k] = # nonzeros in column k of L */ /* output, must be zero on input: */ Entry X [ ] /* size n, initially zero. On output, * X [Ui [up1..up-1]] and X [Li [lp1..lp-1]] * contains the solution. */ ) { Entry xj ; Entry *Lx ; Int *Li ; Int p, s, j, jnew, len ; /* solve Lx=b */ for (s = top ; s < n ; s++) { /* forward solve with column j of L */ j = Stack [s] ; jnew = Pinv [j] ; ASSERT (jnew >= 0) ; xj = X [j] ; GET_POINTER (LU, Lip, Llen, Li, Lx, jnew, len) ; ASSERT (Lip [jnew] <= Lip [jnew+1]) ; for (p = 0 ; p < len ; p++) { /*X [Li [p]] -= Lx [p] * xj ; */ MULT_SUB (X [Li [p]], Lx [p], xj) ; } } } /* ========================================================================== */ /* === lpivot =============================================================== */ /* ========================================================================== */ /* Find a pivot via partial pivoting, and scale the column of L. */ static Int lpivot ( Int diagrow, Int *p_pivrow, Entry *p_pivot, double *p_abs_pivot, double tol, Entry X [ ], Unit *LU, /* LU factors (pattern and values) */ Int Lip [ ], Int Llen [ ], Int k, Int n, Int Pinv [ ], /* Pinv [i] = k if row i is kth pivot row, or EMPTY if * row i is not yet pivotal. */ Int *p_firstrow, KLU_common *Common ) { Entry x, pivot, *Lx ; double abs_pivot, xabs ; Int p, i, ppivrow, pdiag, pivrow, *Li, last_row_index, firstrow, len ; pivrow = EMPTY ; if (Llen [k] == 0) { /* matrix is structurally singular */ if (Common->halt_if_singular) { return (FALSE) ; } for (firstrow = *p_firstrow ; firstrow < n ; firstrow++) { PRINTF (("check %d\n", firstrow)) ; if (Pinv [firstrow] < 0) { /* found the lowest-numbered non-pivotal row. Pick it. */ pivrow = firstrow ; PRINTF (("Got pivotal row: %d\n", pivrow)) ; break ; } } ASSERT (pivrow >= 0 && pivrow < n) ; CLEAR (pivot) ; *p_pivrow = pivrow ; *p_pivot = pivot ; *p_abs_pivot = 0 ; *p_firstrow = firstrow ; return (FALSE) ; } pdiag = EMPTY ; ppivrow = EMPTY ; abs_pivot = EMPTY ; i = Llen [k] - 1 ; GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ; last_row_index = Li [i] ; /* decrement the length by 1 */ Llen [k] = i ; GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ; /* look in Li [0 ..Llen [k] - 1 ] for a pivot row */ for (p = 0 ; p < len ; p++) { /* gather the entry from X and store in L */ i = Li [p] ; x = X [i] ; CLEAR (X [i]) ; Lx [p] = x ; /* xabs = ABS (x) ; */ ABS (xabs, x) ; /* find the diagonal */ if (i == diagrow) { pdiag = p ; } /* find the partial-pivoting choice */ if (xabs > abs_pivot) { abs_pivot = xabs ; ppivrow = p ; } } /* xabs = ABS (X [last_row_index]) ;*/ ABS (xabs, X [last_row_index]) ; if (xabs > abs_pivot) { abs_pivot = xabs ; ppivrow = EMPTY ; } /* compare the diagonal with the largest entry */ if (last_row_index == diagrow) { if (xabs >= tol * abs_pivot) { abs_pivot = xabs ; ppivrow = EMPTY ; } } else if (pdiag != EMPTY) { /* xabs = ABS (Lx [pdiag]) ;*/ ABS (xabs, Lx [pdiag]) ; if (xabs >= tol * abs_pivot) { /* the diagonal is large enough */ abs_pivot = xabs ; ppivrow = pdiag ; } } if (ppivrow != EMPTY) { pivrow = Li [ppivrow] ; pivot = Lx [ppivrow] ; /* overwrite the ppivrow values with last index values */ Li [ppivrow] = last_row_index ; Lx [ppivrow] = X [last_row_index] ; } else { pivrow = last_row_index ; pivot = X [last_row_index] ; } CLEAR (X [last_row_index]) ; *p_pivrow = pivrow ; *p_pivot = pivot ; *p_abs_pivot = abs_pivot ; ASSERT (pivrow >= 0 && pivrow < n) ; if (IS_ZERO (pivot) && Common->halt_if_singular) { /* numerically singular case */ return (FALSE) ; } /* divide L by the pivot value */ for (p = 0 ; p < Llen [k] ; p++) { /* Lx [p] /= pivot ; */ DIV (Lx [p], Lx [p], pivot) ; } return (TRUE) ; } /* ========================================================================== */ /* === prune ================================================================ */ /* ========================================================================== */ /* Prune the columns of L to reduce work in subsequent depth-first searches */ static void prune ( /* input/output: */ Int Lpend [ ], /* Lpend [j] marks symmetric pruning point for L(:,j) */ /* input: */ Int Pinv [ ], /* Pinv [i] = k if row i is kth pivot row, or EMPTY if * row i is not yet pivotal. */ Int k, /* prune using column k of U */ Int pivrow, /* current pivot row */ /* input/output: */ Unit *LU, /* LU factors (pattern and values) */ /* input */ Int Uip [ ], /* size n, column pointers for U */ Int Lip [ ], /* size n, column pointers for L */ Int Ulen [ ], /* size n, column length of U */ Int Llen [ ] /* size n, column length of L */ ) { Entry x ; Entry *Lx, *Ux ; Int *Li, *Ui ; Int p, i, j, p2, phead, ptail, llen, ulen ; /* check to see if any column of L can be pruned */ GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, ulen) ; for (p = 0 ; p < ulen ; p++) { j = Ui [p] ; ASSERT (j < k) ; PRINTF (("%d is pruned: %d. Lpend[j] %d Lip[j+1] %d\n", j, Lpend [j] != EMPTY, Lpend [j], Lip [j+1])) ; if (Lpend [j] == EMPTY) { /* scan column j of L for the pivot row */ GET_POINTER (LU, Lip, Llen, Li, Lx, j, llen) ; for (p2 = 0 ; p2 < llen ; p2++) { if (pivrow == Li [p2]) { /* found it! This column can be pruned */ #ifndef NDEBUG PRINTF (("==== PRUNE: col j %d of L\n", j)) ; { Int p3 ; for (p3 = 0 ; p3 < Llen [j] ; p3++) { PRINTF (("before: %i pivotal: %d\n", Li [p3], Pinv [Li [p3]] >= 0)) ; } } #endif /* partition column j of L. The unit diagonal of L * is not stored in the column of L. */ phead = 0 ; ptail = Llen [j] ; while (phead < ptail) { i = Li [phead] ; if (Pinv [i] >= 0) { /* leave at the head */ phead++ ; } else { /* swap with the tail */ ptail-- ; Li [phead] = Li [ptail] ; Li [ptail] = i ; x = Lx [phead] ; Lx [phead] = Lx [ptail] ; Lx [ptail] = x ; } } /* set Lpend to one past the last entry in the * first part of the column of L. Entries in * Li [0 ... Lpend [j]-1] are the only part of * column j of L that needs to be scanned in the DFS. * Lpend [j] was EMPTY; setting it >= 0 also flags * column j as pruned. */ Lpend [j] = ptail ; #ifndef NDEBUG { Int p3 ; for (p3 = 0 ; p3 < Llen [j] ; p3++) { if (p3 == Lpend [j]) PRINTF (("----\n")) ; PRINTF (("after: %i pivotal: %d\n", Li [p3], Pinv [Li [p3]] >= 0)) ; } } #endif break ; } } } } } /* ========================================================================== */ /* === KLU_kernel =========================================================== */ /* ========================================================================== */ size_t KLU_kernel /* final size of LU on output */ ( /* input, not modified */ Int n, /* A is n-by-n */ Int Ap [ ], /* size n+1, column pointers for A */ Int Ai [ ], /* size nz = Ap [n], row indices for A */ Entry Ax [ ], /* size nz, values of A */ Int Q [ ], /* size n, optional input permutation */ size_t lusize, /* initial size of LU on input */ /* output, not defined on input */ Int Pinv [ ], /* size n, inverse row permutation, where Pinv [i] = k if * row i is the kth pivot row */ Int P [ ], /* size n, row permutation, where P [k] = i if row i is the * kth pivot row. */ Unit **p_LU, /* LU array, size lusize on input */ Entry Udiag [ ], /* size n, diagonal of U */ Int Llen [ ], /* size n, column length of L */ Int Ulen [ ], /* size n, column length of U */ Int Lip [ ], /* size n, column pointers for L */ Int Uip [ ], /* size n, column pointers for U */ Int *lnz, /* size of L*/ Int *unz, /* size of U*/ /* workspace, not defined on input */ Entry X [ ], /* size n, undefined on input, zero on output */ /* workspace, not defined on input or output */ Int Stack [ ], /* size n */ Int Flag [ ], /* size n */ Int Ap_pos [ ], /* size n */ /* other workspace: */ Int Lpend [ ], /* size n workspace, for pruning only */ /* inputs, not modified on output */ Int k1, /* the block of A is from k1 to k2-1 */ Int PSinv [ ], /* inverse of P from symbolic factorization */ double Rs [ ], /* scale factors for A */ /* inputs, modified on output */ Int Offp [ ], /* off-diagonal matrix (modified by this routine) */ Int Offi [ ], Entry Offx [ ], /* --------------- */ KLU_common *Common ) { Entry pivot ; double abs_pivot, xsize, nunits, tol, memgrow ; Entry *Ux ; Int *Li, *Ui ; Unit *LU ; /* LU factors (pattern and values) */ Int k, p, i, j, pivrow = 0, kbar, diagrow, firstrow, lup, top, scale, len ; size_t newlusize ; #ifndef NDEBUG Entry *Lx ; #endif ASSERT (Common != NULL) ; scale = Common->scale ; tol = Common->tol ; memgrow = Common->memgrow ; *lnz = 0 ; *unz = 0 ; CLEAR (pivot) ; /* ---------------------------------------------------------------------- */ /* get initial Li, Lx, Ui, and Ux */ /* ---------------------------------------------------------------------- */ PRINTF (("input: lusize %d \n", lusize)) ; ASSERT (lusize > 0) ; LU = *p_LU ; /* ---------------------------------------------------------------------- */ /* initializations */ /* ---------------------------------------------------------------------- */ firstrow = 0 ; lup = 0 ; for (k = 0 ; k < n ; k++) { /* X [k] = 0 ; */ CLEAR (X [k]) ; Flag [k] = EMPTY ; Lpend [k] = EMPTY ; /* flag k as not pruned */ } /* ---------------------------------------------------------------------- */ /* mark all rows as non-pivotal and determine initial diagonal mapping */ /* ---------------------------------------------------------------------- */ /* PSinv does the symmetric permutation, so don't do it here */ for (k = 0 ; k < n ; k++) { P [k] = k ; Pinv [k] = FLIP (k) ; /* mark all rows as non-pivotal */ } /* initialize the construction of the off-diagonal matrix */ Offp [0] = 0 ; /* P [k] = row means that UNFLIP (Pinv [row]) = k, and visa versa. * If row is pivotal, then Pinv [row] >= 0. A row is initially "flipped" * (Pinv [k] < EMPTY), and then marked "unflipped" when it becomes * pivotal. */ #ifndef NDEBUG for (k = 0 ; k < n ; k++) { PRINTF (("Initial P [%d] = %d\n", k, P [k])) ; } #endif /* ---------------------------------------------------------------------- */ /* factorize */ /* ---------------------------------------------------------------------- */ for (k = 0 ; k < n ; k++) { PRINTF (("\n\n==================================== k: %d\n", k)) ; /* ------------------------------------------------------------------ */ /* determine if LU factors have grown too big */ /* ------------------------------------------------------------------ */ /* (n - k) entries for L and k entries for U */ nunits = DUNITS (Int, n - k) + DUNITS (Int, k) + DUNITS (Entry, n - k) + DUNITS (Entry, k) ; /* LU can grow by at most 'nunits' entries if the column is dense */ PRINTF (("lup %d lusize %g lup+nunits: %g\n", lup, (double) lusize, lup+nunits)); xsize = ((double) lup) + nunits ; if (xsize > (double) lusize) { /* check here how much to grow */ xsize = (memgrow * ((double) lusize) + 4*n + 1) ; if (INT_OVERFLOW (xsize)) { PRINTF (("Matrix is too large (Int overflow)\n")) ; Common->status = KLU_TOO_LARGE ; return (lusize) ; } newlusize = memgrow * lusize + 2*n + 1 ; /* Future work: retry mechanism in case of malloc failure */ LU = KLU_realloc (newlusize, lusize, sizeof (Unit), LU, Common) ; Common->nrealloc++ ; *p_LU = LU ; if (Common->status == KLU_OUT_OF_MEMORY) { PRINTF (("Matrix is too large (LU)\n")) ; return (lusize) ; } lusize = newlusize ; PRINTF (("inc LU to %d done\n", lusize)) ; } /* ------------------------------------------------------------------ */ /* start the kth column of L and U */ /* ------------------------------------------------------------------ */ Lip [k] = lup ; /* ------------------------------------------------------------------ */ /* compute the nonzero pattern of the kth column of L and U */ /* ------------------------------------------------------------------ */ #ifndef NDEBUG for (i = 0 ; i < n ; i++) { ASSERT (Flag [i] < k) ; /* ASSERT (X [i] == 0) ; */ ASSERT (IS_ZERO (X [i])) ; } #endif top = lsolve_symbolic (n, k, Ap, Ai, Q, Pinv, Stack, Flag, Lpend, Ap_pos, LU, lup, Llen, Lip, k1, PSinv) ; #ifndef NDEBUG PRINTF (("--- in U:\n")) ; for (p = top ; p < n ; p++) { PRINTF (("pattern of X for U: %d : %d pivot row: %d\n", p, Stack [p], Pinv [Stack [p]])) ; ASSERT (Flag [Stack [p]] == k) ; } PRINTF (("--- in L:\n")) ; Li = (Int *) (LU + Lip [k]); for (p = 0 ; p < Llen [k] ; p++) { PRINTF (("pattern of X in L: %d : %d pivot row: %d\n", p, Li [p], Pinv [Li [p]])) ; ASSERT (Flag [Li [p]] == k) ; } p = 0 ; for (i = 0 ; i < n ; i++) { ASSERT (Flag [i] <= k) ; if (Flag [i] == k) p++ ; } #endif /* ------------------------------------------------------------------ */ /* get the column of the matrix to factorize and scatter into X */ /* ------------------------------------------------------------------ */ construct_column (k, Ap, Ai, Ax, Q, X, k1, PSinv, Rs, scale, Offp, Offi, Offx) ; /* ------------------------------------------------------------------ */ /* compute the numerical values of the kth column (s = L \ A (:,k)) */ /* ------------------------------------------------------------------ */ lsolve_numeric (Pinv, LU, Stack, Lip, top, n, Llen, X) ; #ifndef NDEBUG for (p = top ; p < n ; p++) { PRINTF (("X for U %d : ", Stack [p])) ; PRINT_ENTRY (X [Stack [p]]) ; } Li = (Int *) (LU + Lip [k]) ; for (p = 0 ; p < Llen [k] ; p++) { PRINTF (("X for L %d : ", Li [p])) ; PRINT_ENTRY (X [Li [p]]) ; } #endif /* ------------------------------------------------------------------ */ /* partial pivoting with diagonal preference */ /* ------------------------------------------------------------------ */ /* determine what the "diagonal" is */ diagrow = P [k] ; /* might already be pivotal */ PRINTF (("k %d, diagrow = %d, UNFLIP (diagrow) = %d\n", k, diagrow, UNFLIP (diagrow))) ; /* find a pivot and scale the pivot column */ if (!lpivot (diagrow, &pivrow, &pivot, &abs_pivot, tol, X, LU, Lip, Llen, k, n, Pinv, &firstrow, Common)) { /* matrix is structurally or numerically singular */ Common->status = KLU_SINGULAR ; if (Common->numerical_rank == EMPTY) { Common->numerical_rank = k+k1 ; Common->singular_col = Q [k+k1] ; } if (Common->halt_if_singular) { /* do not continue the factorization */ return (lusize) ; } } /* we now have a valid pivot row, even if the column has NaN's or * has no entries on or below the diagonal at all. */ PRINTF (("\nk %d : Pivot row %d : ", k, pivrow)) ; PRINT_ENTRY (pivot) ; ASSERT (pivrow >= 0 && pivrow < n) ; ASSERT (Pinv [pivrow] < 0) ; /* set the Uip pointer */ Uip [k] = Lip [k] + UNITS (Int, Llen [k]) + UNITS (Entry, Llen [k]) ; /* move the lup pointer to the position where indices of U * should be stored */ lup += UNITS (Int, Llen [k]) + UNITS (Entry, Llen [k]) ; Ulen [k] = n - top ; /* extract Stack [top..n-1] to Ui and the values to Ux and clear X */ GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ; for (p = top, i = 0 ; p < n ; p++, i++) { j = Stack [p] ; Ui [i] = Pinv [j] ; Ux [i] = X [j] ; CLEAR (X [j]) ; } /* position the lu index at the starting point for next column */ lup += UNITS (Int, Ulen [k]) + UNITS (Entry, Ulen [k]) ; /* U(k,k) = pivot */ Udiag [k] = pivot ; /* ------------------------------------------------------------------ */ /* log the pivot permutation */ /* ------------------------------------------------------------------ */ ASSERT (UNFLIP (Pinv [diagrow]) < n) ; ASSERT (P [UNFLIP (Pinv [diagrow])] == diagrow) ; if (pivrow != diagrow) { /* an off-diagonal pivot has been chosen */ Common->noffdiag++ ; PRINTF ((">>>>>>>>>>>>>>>>> pivrow %d k %d off-diagonal\n", pivrow, k)) ; if (Pinv [diagrow] < 0) { /* the former diagonal row index, diagrow, has not yet been * chosen as a pivot row. Log this diagrow as the "diagonal" * entry in the column kbar for which the chosen pivot row, * pivrow, was originally logged as the "diagonal" */ kbar = FLIP (Pinv [pivrow]) ; P [kbar] = diagrow ; Pinv [diagrow] = FLIP (kbar) ; } } P [k] = pivrow ; Pinv [pivrow] = k ; #ifndef NDEBUG for (i = 0 ; i < n ; i++) { ASSERT (IS_ZERO (X [i])) ;} GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ; for (p = 0 ; p < len ; p++) { PRINTF (("Column %d of U: %d : ", k, Ui [p])) ; PRINT_ENTRY (Ux [p]) ; } GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ; for (p = 0 ; p < len ; p++) { PRINTF (("Column %d of L: %d : ", k, Li [p])) ; PRINT_ENTRY (Lx [p]) ; } #endif /* ------------------------------------------------------------------ */ /* symmetric pruning */ /* ------------------------------------------------------------------ */ prune (Lpend, Pinv, k, pivrow, LU, Uip, Lip, Ulen, Llen) ; *lnz += Llen [k] + 1 ; /* 1 added to lnz for diagonal */ *unz += Ulen [k] + 1 ; /* 1 added to unz for diagonal */ } /* ---------------------------------------------------------------------- */ /* finalize column pointers for L and U, and put L in the pivotal order */ /* ---------------------------------------------------------------------- */ for (p = 0 ; p < n ; p++) { Li = (Int *) (LU + Lip [p]) ; for (i = 0 ; i < Llen [p] ; i++) { Li [i] = Pinv [Li [i]] ; } } #ifndef NDEBUG for (i = 0 ; i < n ; i++) { PRINTF (("P [%d] = %d Pinv [%d] = %d\n", i, P [i], i, Pinv [i])) ; } for (i = 0 ; i < n ; i++) { ASSERT (Pinv [i] >= 0 && Pinv [i] < n) ; ASSERT (P [i] >= 0 && P [i] < n) ; ASSERT (P [Pinv [i]] == i) ; ASSERT (IS_ZERO (X [i])) ; } #endif /* ---------------------------------------------------------------------- */ /* shrink the LU factors to just the required size */ /* ---------------------------------------------------------------------- */ newlusize = lup ; ASSERT ((size_t) newlusize <= lusize) ; /* this cannot fail, since the block is descreasing in size */ LU = KLU_realloc (newlusize, lusize, sizeof (Unit), LU, Common) ; *p_LU = LU ; return (newlusize) ; } SuiteSparse/KLU/Source/klu_memory.c0000644001170100242450000001520310616721573016202 0ustar davisfac/* ========================================================================== */ /* === KLU_memory =========================================================== */ /* ========================================================================== */ /* KLU memory management routines: * * KLU_malloc malloc wrapper * KLU_free free wrapper * KLU_realloc realloc wrapper */ #include "klu_internal.h" /* ========================================================================== */ /* === KLU_add_size_t ======================================================= */ /* ========================================================================== */ /* Safely compute a+b, and check for size_t overflow */ size_t KLU_add_size_t (size_t a, size_t b, Int *ok) { (*ok) = (*ok) && ((a + b) >= MAX (a,b)) ; return ((*ok) ? (a + b) : ((size_t) -1)) ; } /* ========================================================================== */ /* === KLU_mult_size_t ====================================================== */ /* ========================================================================== */ /* Safely compute a*k, where k should be small, and check for size_t overflow */ size_t KLU_mult_size_t (size_t a, size_t k, Int *ok) { size_t i, s = 0 ; for (i = 0 ; i < k ; i++) { s = KLU_add_size_t (s, a, ok) ; } return ((*ok) ? s : ((size_t) -1)) ; } /* ========================================================================== */ /* === KLU_malloc =========================================================== */ /* ========================================================================== */ /* Wrapper around malloc routine (mxMalloc for a mexFunction). Allocates * space of size MAX(1,n)*size, where size is normally a sizeof (...). * * This routine and KLU_realloc do not set Common->status to KLU_OK on success, * so that a sequence of KLU_malloc's or KLU_realloc's can be used. If any of * them fails, the Common->status will hold the most recent error status. * * Usage, for a pointer to Int: * * p = KLU_malloc (n, sizeof (Int), Common) * * Uses a pointer to the malloc routine (or its equivalent) defined in Common. */ void *KLU_malloc /* returns pointer to the newly malloc'd block */ ( /* ---- input ---- */ size_t n, /* number of items */ size_t size, /* size of each item */ /* --------------- */ KLU_common *Common ) { void *p ; size_t s ; Int ok = TRUE ; if (Common == NULL) { p = NULL ; } else if (size == 0) { /* size must be > 0 */ Common->status = KLU_INVALID ; p = NULL ; } else if (n >= INT_MAX) { /* object is too big to allocate; p[i] where i is an Int will not * be enough. */ Common->status = KLU_TOO_LARGE ; p = NULL ; } else { /* call malloc, or its equivalent */ s = KLU_mult_size_t (MAX (1,n), size, &ok) ; p = ok ? ((Common->malloc_memory) (s)) : NULL ; if (p == NULL) { /* failure: out of memory */ Common->status = KLU_OUT_OF_MEMORY ; } else { Common->memusage += s ; Common->mempeak = MAX (Common->mempeak, Common->memusage) ; } } return (p) ; } /* ========================================================================== */ /* === KLU_free ============================================================= */ /* ========================================================================== */ /* Wrapper around free routine (mxFree for a mexFunction). Returns NULL, * which can be assigned to the pointer being freed, as in: * * p = KLU_free (p, n, sizeof (int), Common) ; */ void *KLU_free /* always returns NULL */ ( /* ---- in/out --- */ void *p, /* block of memory to free */ /* ---- input --- */ size_t n, /* size of block to free, in # of items */ size_t size, /* size of each item */ /* --------------- */ KLU_common *Common ) { size_t s ; Int ok = TRUE ; if (p != NULL && Common != NULL) { /* only free the object if the pointer is not NULL */ /* call free, or its equivalent */ (Common->free_memory) (p) ; s = KLU_mult_size_t (MAX (1,n), size, &ok) ; Common->memusage -= s ; } /* return NULL, and the caller should assign this to p. This avoids * freeing the same pointer twice. */ return (NULL) ; } /* ========================================================================== */ /* === KLU_realloc ========================================================== */ /* ========================================================================== */ /* Wrapper around realloc routine (mxRealloc for a mexFunction). Given a * pointer p to a block allocated by KLU_malloc, it changes the size of the * block pointed to by p to be MAX(1,nnew)*size in size. It may return a * pointer different than p. This should be used as (for a pointer to Int): * * p = KLU_realloc (nnew, nold, sizeof (Int), p, Common) ; * * If p is NULL, this is the same as p = KLU_malloc (...). * A size of nnew=0 is treated as nnew=1. * * If the realloc fails, p is returned unchanged and Common->status is set * to KLU_OUT_OF_MEMORY. If successful, Common->status is not modified, * and p is returned (possibly changed) and pointing to a large block of memory. * * Uses a pointer to the realloc routine (or its equivalent) defined in Common. */ void *KLU_realloc /* returns pointer to reallocated block */ ( /* ---- input ---- */ size_t nnew, /* requested # of items in reallocated block */ size_t nold, /* old # of items */ size_t size, /* size of each item */ /* ---- in/out --- */ void *p, /* block of memory to realloc */ /* --------------- */ KLU_common *Common ) { void *pnew ; size_t snew, sold ; Int ok = TRUE ; if (Common == NULL) { p = NULL ; } else if (size == 0) { /* size must be > 0 */ Common->status = KLU_INVALID ; p = NULL ; } else if (p == NULL) { /* A fresh object is being allocated. */ p = KLU_malloc (nnew, size, Common) ; } else if (nnew >= INT_MAX) { /* failure: nnew is too big. Do not change p */ Common->status = KLU_TOO_LARGE ; } else { /* The object exists, and is changing to some other nonzero size. */ /* call realloc, or its equivalent */ snew = KLU_mult_size_t (MAX (1,nnew), size, &ok) ; sold = KLU_mult_size_t (MAX (1,nold), size, &ok) ; pnew = ok ? ((Common->realloc_memory) (p, snew)) : NULL ; if (pnew == NULL) { /* Do not change p, since it still points to allocated memory */ Common->status = KLU_OUT_OF_MEMORY ; } else { /* success: return the new p and change the size of the block */ Common->memusage += (snew - sold) ; Common->mempeak = MAX (Common->mempeak, Common->memusage) ; p = pnew ; } } return (p) ; } SuiteSparse/KLU/Source/klu_defaults.c0000644001170100242450000000362610620445504016477 0ustar davisfac/* ========================================================================== */ /* === KLU_defaults ========================================================= */ /* ========================================================================== */ /* Sets default parameters for KLU */ #include "klu_internal.h" Int KLU_defaults ( KLU_common *Common ) { if (Common == NULL) { return (FALSE) ; } /* parameters */ Common->tol = 0.001 ; /* pivot tolerance for diagonal */ Common->memgrow = 1.2; /* realloc size ratio increase for LU factors */ Common->initmem_amd = 1.2 ; /* init. mem with AMD: c*nnz(L) + n */ Common->initmem = 10 ; /* init. mem otherwise: c*nnz(A) + n */ Common->btf = TRUE ; /* use BTF pre-ordering, or not */ Common->maxwork = 0 ; /* no limit to work done by btf_order */ Common->ordering = 0 ; /* 0: AMD, 1: COLAMD, 2: user-provided P and Q, * 3: user-provided function */ Common->scale = 2 ; /* scale: -1: none, and do not check for errors * in the input matrix in KLU_refactor. * 0: none, but check for errors, * 1: sum, 2: max */ Common->halt_if_singular = TRUE ; /* quick halt if matrix is singular */ /* memory management routines */ Common->malloc_memory = malloc ; Common->calloc_memory = calloc ; Common->free_memory = free ; Common->realloc_memory = realloc ; /* user ordering function and optional argument */ Common->user_order = NULL ; Common->user_data = NULL ; /* statistics */ Common->status = KLU_OK ; Common->nrealloc = 0 ; Common->structural_rank = EMPTY ; Common->numerical_rank = EMPTY ; Common->noffdiag = EMPTY ; Common->flops = EMPTY ; Common->rcond = EMPTY ; Common->condest = EMPTY ; Common->rgrowth = EMPTY ; Common->work = 0 ; /* work done by btf_order */ Common->memusage = 0 ; Common->mempeak = 0 ; return (TRUE) ; } SuiteSparse/KLU/Source/klu_factor.c0000644001170100242450000003766110620333242016147 0ustar davisfac/* ========================================================================== */ /* === KLU_factor =========================================================== */ /* ========================================================================== */ /* Factor the matrix, after ordering and analyzing it with KLU_analyze * or KLU_analyze_given. */ #include "klu_internal.h" /* ========================================================================== */ /* === KLU_factor2 ========================================================== */ /* ========================================================================== */ static void factor2 ( /* inputs, not modified */ Int Ap [ ], /* size n+1, column pointers */ Int Ai [ ], /* size nz, row indices */ Entry Ax [ ], KLU_symbolic *Symbolic, /* inputs, modified on output: */ KLU_numeric *Numeric, KLU_common *Common ) { double lsize ; double *Lnz, *Rs ; Int *P, *Q, *R, *Pnum, *Offp, *Offi, *Pblock, *Pinv, *Iwork, *Lip, *Uip, *Llen, *Ulen ; Entry *Offx, *X, s, *Udiag ; Unit **LUbx ; Int k1, k2, nk, k, block, oldcol, pend, oldrow, n, lnz, unz, p, newrow, nblocks, poff, nzoff, lnz_block, unz_block, scale, max_lnz_block, max_unz_block ; /* ---------------------------------------------------------------------- */ /* initializations */ /* ---------------------------------------------------------------------- */ /* get the contents of the Symbolic object */ n = Symbolic->n ; P = Symbolic->P ; Q = Symbolic->Q ; R = Symbolic->R ; Lnz = Symbolic->Lnz ; nblocks = Symbolic->nblocks ; nzoff = Symbolic->nzoff ; Pnum = Numeric->Pnum ; Offp = Numeric->Offp ; Offi = Numeric->Offi ; Offx = (Entry *) Numeric->Offx ; Lip = Numeric->Lip ; Uip = Numeric->Uip ; Llen = Numeric->Llen ; Ulen = Numeric->Ulen ; LUbx = (Unit **) Numeric->LUbx ; Udiag = Numeric->Udiag ; Rs = Numeric->Rs ; Pinv = Numeric->Pinv ; X = (Entry *) Numeric->Xwork ; /* X is of size n */ Iwork = Numeric->Iwork ; /* 5*maxblock for KLU_factor */ /* 1*maxblock for Pblock */ Pblock = Iwork + 5*((size_t) Symbolic->maxblock) ; Common->nrealloc = 0 ; scale = Common->scale ; max_lnz_block = 1 ; max_unz_block = 1 ; /* compute the inverse of P from symbolic analysis. Will be updated to * become the inverse of the numerical factorization when the factorization * is done, for use in KLU_refactor */ #ifndef NDEBUG for (k = 0 ; k < n ; k++) { Pinv [k] = EMPTY ; } #endif for (k = 0 ; k < n ; k++) { ASSERT (P [k] >= 0 && P [k] < n) ; Pinv [P [k]] = k ; } #ifndef NDEBUG for (k = 0 ; k < n ; k++) ASSERT (Pinv [k] != EMPTY) ; #endif lnz = 0 ; unz = 0 ; Common->noffdiag = 0 ; Offp [0] = 0 ; /* ---------------------------------------------------------------------- */ /* optionally check input matrix and compute scale factors */ /* ---------------------------------------------------------------------- */ if (scale >= 0) { /* use Pnum as workspace. NOTE: scale factors are not yet permuted * according to the final pivot row ordering, so Rs [oldrow] is the * scale factor for A (oldrow,:), for the user's matrix A. Pnum is * used as workspace in KLU_scale. When the factorization is done, * the scale factors are permuted according to the final pivot row * permutation, so that Rs [k] is the scale factor for the kth row of * A(p,q) where p and q are the final row and column permutations. */ KLU_scale (scale, n, Ap, Ai, (double *) Ax, Rs, Pnum, Common) ; if (Common->status < KLU_OK) { /* matrix is invalid */ return ; } } #ifndef NDEBUG if (scale > 0) { for (k = 0 ; k < n ; k++) PRINTF (("Rs [%d] %g\n", k, Rs [k])) ; } #endif /* ---------------------------------------------------------------------- */ /* factor each block using klu */ /* ---------------------------------------------------------------------- */ for (block = 0 ; block < nblocks ; block++) { /* ------------------------------------------------------------------ */ /* the block is from rows/columns k1 to k2-1 */ /* ------------------------------------------------------------------ */ k1 = R [block] ; k2 = R [block+1] ; nk = k2 - k1 ; PRINTF (("FACTOR BLOCK %d, k1 %d k2-1 %d nk %d\n", block, k1,k2-1,nk)) ; if (nk == 1) { /* -------------------------------------------------------------- */ /* singleton case */ /* -------------------------------------------------------------- */ poff = Offp [k1] ; oldcol = Q [k1] ; pend = Ap [oldcol+1] ; CLEAR (s) ; if (scale <= 0) { /* no scaling */ for (p = Ap [oldcol] ; p < pend ; p++) { oldrow = Ai [p] ; newrow = Pinv [oldrow] ; if (newrow < k1) { Offi [poff] = oldrow ; Offx [poff] = Ax [p] ; poff++ ; } else { ASSERT (newrow == k1) ; PRINTF (("singleton block %d", block)) ; PRINT_ENTRY (Ax [p]) ; s = Ax [p] ; } } } else { /* row scaling. NOTE: scale factors are not yet permuted * according to the pivot row permutation, so Rs [oldrow] is * used below. When the factorization is done, the scale * factors are permuted, so that Rs [newrow] will be used in * klu_solve, klu_tsolve, and klu_rgrowth */ for (p = Ap [oldcol] ; p < pend ; p++) { oldrow = Ai [p] ; newrow = Pinv [oldrow] ; if (newrow < k1) { Offi [poff] = oldrow ; /* Offx [poff] = Ax [p] / Rs [oldrow] ; */ SCALE_DIV_ASSIGN (Offx [poff], Ax [p], Rs [oldrow]) ; poff++ ; } else { ASSERT (newrow == k1) ; PRINTF (("singleton block %d ", block)) ; PRINT_ENTRY (Ax[p]) ; SCALE_DIV_ASSIGN (s, Ax [p], Rs [oldrow]) ; } } } Udiag [k1] = s ; if (IS_ZERO (s)) { /* singular singleton */ Common->status = KLU_SINGULAR ; Common->numerical_rank = k1 ; Common->singular_col = oldcol ; if (Common->halt_if_singular) { return ; } } Offp [k1+1] = poff ; Pnum [k1] = P [k1] ; lnz++ ; unz++ ; } else { /* -------------------------------------------------------------- */ /* construct and factorize the kth block */ /* -------------------------------------------------------------- */ if (Lnz [block] < 0) { /* COLAMD was used - no estimate of fill-in */ /* use 10 times the nnz in A, plus n */ lsize = -(Common->initmem) ; } else { lsize = Common->initmem_amd * Lnz [block] + nk ; } /* allocates 1 arrays: LUbx [block] */ Numeric->LUsize [block] = KLU_kernel_factor (nk, Ap, Ai, Ax, Q, lsize, &LUbx [block], Udiag + k1, Llen + k1, Ulen + k1, Lip + k1, Uip + k1, Pblock, &lnz_block, &unz_block, X, Iwork, k1, Pinv, Rs, Offp, Offi, Offx, Common) ; if (Common->status < KLU_OK || (Common->status == KLU_SINGULAR && Common->halt_if_singular)) { /* out of memory, invalid inputs, or singular */ return ; } PRINTF (("\n----------------------- L %d:\n", block)) ; ASSERT (KLU_valid_LU (nk, TRUE, Lip+k1, Llen+k1, LUbx [block])) ; PRINTF (("\n----------------------- U %d:\n", block)) ; ASSERT (KLU_valid_LU (nk, FALSE, Uip+k1, Ulen+k1, LUbx [block])) ; /* -------------------------------------------------------------- */ /* get statistics */ /* -------------------------------------------------------------- */ lnz += lnz_block ; unz += unz_block ; max_lnz_block = MAX (max_lnz_block, lnz_block) ; max_unz_block = MAX (max_unz_block, unz_block) ; if (Lnz [block] == EMPTY) { /* revise estimate for subsequent factorization */ Lnz [block] = MAX (lnz_block, unz_block) ; } /* -------------------------------------------------------------- */ /* combine the klu row ordering with the symbolic pre-ordering */ /* -------------------------------------------------------------- */ PRINTF (("Pnum, 1-based:\n")) ; for (k = 0 ; k < nk ; k++) { ASSERT (k + k1 < n) ; ASSERT (Pblock [k] + k1 < n) ; Pnum [k + k1] = P [Pblock [k] + k1] ; PRINTF (("Pnum (%d + %d + 1 = %d) = %d + 1 = %d\n", k, k1, k+k1+1, Pnum [k+k1], Pnum [k+k1]+1)) ; } /* the local pivot row permutation Pblock is no longer needed */ } } ASSERT (nzoff == Offp [n]) ; PRINTF (("\n------------------- Off diagonal entries:\n")) ; ASSERT (KLU_valid (n, Offp, Offi, Offx)) ; Numeric->lnz = lnz ; Numeric->unz = unz ; Numeric->max_lnz_block = max_lnz_block ; Numeric->max_unz_block = max_unz_block ; /* compute the inverse of Pnum */ #ifndef NDEBUG for (k = 0 ; k < n ; k++) { Pinv [k] = EMPTY ; } #endif for (k = 0 ; k < n ; k++) { ASSERT (Pnum [k] >= 0 && Pnum [k] < n) ; Pinv [Pnum [k]] = k ; } #ifndef NDEBUG for (k = 0 ; k < n ; k++) ASSERT (Pinv [k] != EMPTY) ; #endif /* permute scale factors Rs according to pivotal row order */ if (scale > 0) { for (k = 0 ; k < n ; k++) { REAL (X [k]) = Rs [Pnum [k]] ; } for (k = 0 ; k < n ; k++) { Rs [k] = REAL (X [k]) ; } } PRINTF (("\n------------------- Off diagonal entries, old:\n")) ; ASSERT (KLU_valid (n, Offp, Offi, Offx)) ; /* apply the pivot row permutations to the off-diagonal entries */ for (p = 0 ; p < nzoff ; p++) { ASSERT (Offi [p] >= 0 && Offi [p] < n) ; Offi [p] = Pinv [Offi [p]] ; } PRINTF (("\n------------------- Off diagonal entries, new:\n")) ; ASSERT (KLU_valid (n, Offp, Offi, Offx)) ; #ifndef NDEBUG { PRINTF (("\n ############# KLU_BTF_FACTOR done, nblocks %d\n",nblocks)); Entry ss, *Udiag = Numeric->Udiag ; for (block = 0 ; block < nblocks && Common->status == KLU_OK ; block++) { k1 = R [block] ; k2 = R [block+1] ; nk = k2 - k1 ; PRINTF (("\n======================KLU_factor output: k1 %d k2 %d nk %d\n",k1,k2,nk)) ; if (nk == 1) { PRINTF (("singleton ")) ; /* ENTRY_PRINT (singleton [block]) ; */ ss = Udiag [k1] ; PRINT_ENTRY (ss) ; } else { Int *Lip, *Uip, *Llen, *Ulen ; Unit *LU ; Lip = Numeric->Lip + k1 ; Llen = Numeric->Llen + k1 ; LU = (Unit *) Numeric->LUbx [block] ; PRINTF (("\n---- L block %d\n", block)); ASSERT (KLU_valid_LU (nk, TRUE, Lip, Llen, LU)) ; Uip = Numeric->Uip + k1 ; Ulen = Numeric->Ulen + k1 ; PRINTF (("\n---- U block %d\n", block)) ; ASSERT (KLU_valid_LU (nk, FALSE, Uip, Ulen, LU)) ; } } } #endif } /* ========================================================================== */ /* === KLU_factor =========================================================== */ /* ========================================================================== */ KLU_numeric *KLU_factor /* returns NULL if error, or a valid KLU_numeric object if successful */ ( /* --- inputs --- */ Int Ap [ ], /* size n+1, column pointers */ Int Ai [ ], /* size nz, row indices */ double Ax [ ], KLU_symbolic *Symbolic, /* -------------- */ KLU_common *Common ) { Int n, nzoff, nblocks, maxblock, k, ok = TRUE ; Int *R ; KLU_numeric *Numeric ; size_t n1, nzoff1, s, b6, n3 ; if (Common == NULL) { return (NULL) ; } Common->status = KLU_OK ; Common->numerical_rank = EMPTY ; Common->singular_col = EMPTY ; /* ---------------------------------------------------------------------- */ /* get the contents of the Symbolic object */ /* ---------------------------------------------------------------------- */ /* check for a valid Symbolic object */ if (Symbolic == NULL) { Common->status = KLU_INVALID ; return (NULL) ; } n = Symbolic->n ; nzoff = Symbolic->nzoff ; nblocks = Symbolic->nblocks ; maxblock = Symbolic->maxblock ; R = Symbolic->R ; PRINTF (("KLU_factor: n %d nzoff %d nblocks %d maxblock %d\n", n, nzoff, nblocks, maxblock)) ; /* ---------------------------------------------------------------------- */ /* get control parameters and make sure they are in the proper range */ /* ---------------------------------------------------------------------- */ Common->initmem_amd = MAX (1.0, Common->initmem_amd) ; Common->initmem = MAX (1.0, Common->initmem) ; Common->tol = MIN (Common->tol, 1.0) ; Common->tol = MAX (0.0, Common->tol) ; Common->memgrow = MAX (1.0, Common->memgrow) ; /* ---------------------------------------------------------------------- */ /* allocate the Numeric object */ /* ---------------------------------------------------------------------- */ /* this will not cause size_t overflow (already checked by KLU_symbolic) */ n1 = ((size_t) n) + 1 ; nzoff1 = ((size_t) nzoff) + 1 ; Numeric = KLU_malloc (sizeof (KLU_numeric), 1, Common) ; if (Common->status < KLU_OK) { /* out of memory */ Common->status = KLU_OUT_OF_MEMORY ; return (NULL) ; } Numeric->n = n ; Numeric->nblocks = nblocks ; Numeric->nzoff = nzoff ; Numeric->Pnum = KLU_malloc (n, sizeof (Int), Common) ; Numeric->Offp = KLU_malloc (n1, sizeof (Int), Common) ; Numeric->Offi = KLU_malloc (nzoff1, sizeof (Int), Common) ; Numeric->Offx = KLU_malloc (nzoff1, sizeof (Entry), Common) ; Numeric->Lip = KLU_malloc (n, sizeof (Int), Common) ; Numeric->Uip = KLU_malloc (n, sizeof (Int), Common) ; Numeric->Llen = KLU_malloc (n, sizeof (Int), Common) ; Numeric->Ulen = KLU_malloc (n, sizeof (Int), Common) ; Numeric->LUsize = KLU_malloc (nblocks, sizeof (size_t), Common) ; Numeric->LUbx = KLU_malloc (nblocks, sizeof (Unit *), Common) ; if (Numeric->LUbx != NULL) { for (k = 0 ; k < nblocks ; k++) { Numeric->LUbx [k] = NULL ; } } Numeric->Udiag = KLU_malloc (n, sizeof (Entry), Common) ; if (Common->scale > 0) { Numeric->Rs = KLU_malloc (n, sizeof (double), Common) ; } else { /* no scaling */ Numeric->Rs = NULL ; } Numeric->Pinv = KLU_malloc (n, sizeof (Int), Common) ; /* allocate permanent workspace for factorization and solve. Note that the * solver will use an Xwork of size 4n, whereas the factorization codes use * an Xwork of size n and integer space (Iwork) of size 6n. KLU_condest * uses an Xwork of size 2n. Total size is: * * n*sizeof(Entry) + max (6*maxblock*sizeof(Int), 3*n*sizeof(Entry)) */ s = KLU_mult_size_t (n, sizeof (Entry), &ok) ; n3 = KLU_mult_size_t (n, 3 * sizeof (Entry), &ok) ; b6 = KLU_mult_size_t (maxblock, 6 * sizeof (Int), &ok) ; Numeric->worksize = KLU_add_size_t (s, MAX (n3, b6), &ok) ; Numeric->Work = KLU_malloc (Numeric->worksize, 1, Common) ; Numeric->Xwork = Numeric->Work ; Numeric->Iwork = (Int *) ((Entry *) Numeric->Xwork + n) ; if (!ok || Common->status < KLU_OK) { /* out of memory or problem too large */ Common->status = ok ? KLU_OUT_OF_MEMORY : KLU_TOO_LARGE ; KLU_free_numeric (&Numeric, Common) ; return (NULL) ; } /* ---------------------------------------------------------------------- */ /* factorize the blocks */ /* ---------------------------------------------------------------------- */ factor2 (Ap, Ai, (Entry *) Ax, Symbolic, Numeric, Common) ; /* ---------------------------------------------------------------------- */ /* return or free the Numeric object */ /* ---------------------------------------------------------------------- */ if (Common->status < KLU_OK) { /* out of memory or inputs invalid */ KLU_free_numeric (&Numeric, Common) ; } else if (Common->status == KLU_SINGULAR) { if (Common->halt_if_singular) { /* Matrix is singular, and the Numeric object is only partially * defined because we halted early. This is the default case for * a singular matrix. */ KLU_free_numeric (&Numeric, Common) ; } } else if (Common->status == KLU_OK) { /* successful non-singular factorization */ Common->numerical_rank = n ; Common->singular_col = n ; } return (Numeric) ; } SuiteSparse/KLU/Source/klu_analyze_given.c0000644001170100242450000002367410616720575017541 0ustar davisfac/* ========================================================================== */ /* === klu_analyze_given ==================================================== */ /* ========================================================================== */ /* Given an input permutation P and Q, create the Symbolic object. BTF can * be done to modify the user's P and Q (does not perform the max transversal; * just finds the strongly-connected components). */ #include "klu_internal.h" /* ========================================================================== */ /* === klu_alloc_symbolic =================================================== */ /* ========================================================================== */ /* Allocate Symbolic object, and check input matrix. Not user callable. */ KLU_symbolic *KLU_alloc_symbolic ( Int n, Int *Ap, Int *Ai, KLU_common *Common ) { KLU_symbolic *Symbolic ; Int *P, *Q, *R ; double *Lnz ; Int nz, i, j, p, pend ; if (Common == NULL) { return (NULL) ; } Common->status = KLU_OK ; /* A is n-by-n, with n > 0. Ap [0] = 0 and nz = Ap [n] >= 0 required. * Ap [j] <= Ap [j+1] must hold for all j = 0 to n-1. Row indices in Ai * must be in the range 0 to n-1, and no duplicate entries can be present. * The list of row indices in each column of A need not be sorted. */ if (n <= 0 || Ap == NULL || Ai == NULL) { /* Ap and Ai must be present, and n must be > 0 */ Common->status = KLU_INVALID ; return (NULL) ; } nz = Ap [n] ; if (Ap [0] != 0 || nz < 0) { /* nz must be >= 0 and Ap [0] must equal zero */ Common->status = KLU_INVALID ; return (NULL) ; } for (j = 0 ; j < n ; j++) { if (Ap [j] > Ap [j+1]) { /* column pointers must be non-decreasing */ Common->status = KLU_INVALID ; return (NULL) ; } } P = KLU_malloc (n, sizeof (Int), Common) ; if (Common->status < KLU_OK) { /* out of memory */ Common->status = KLU_OUT_OF_MEMORY ; return (NULL) ; } for (i = 0 ; i < n ; i++) { P [i] = EMPTY ; } for (j = 0 ; j < n ; j++) { pend = Ap [j+1] ; for (p = Ap [j] ; p < pend ; p++) { i = Ai [p] ; if (i < 0 || i >= n || P [i] == j) { /* row index out of range, or duplicate entry */ KLU_free (P, n, sizeof (Int), Common) ; Common->status = KLU_INVALID ; return (NULL) ; } /* flag row i as appearing in column j */ P [i] = j ; } } /* ---------------------------------------------------------------------- */ /* allocate the Symbolic object */ /* ---------------------------------------------------------------------- */ Symbolic = KLU_malloc (sizeof (KLU_symbolic), 1, Common) ; if (Common->status < KLU_OK) { /* out of memory */ KLU_free (P, n, sizeof (Int), Common) ; Common->status = KLU_OUT_OF_MEMORY ; return (NULL) ; } Q = KLU_malloc (n, sizeof (Int), Common) ; R = KLU_malloc (n+1, sizeof (Int), Common) ; Lnz = KLU_malloc (n, sizeof (double), Common) ; Symbolic->n = n ; Symbolic->nz = nz ; Symbolic->P = P ; Symbolic->Q = Q ; Symbolic->R = R ; Symbolic->Lnz = Lnz ; if (Common->status < KLU_OK) { /* out of memory */ KLU_free_symbolic (&Symbolic, Common) ; Common->status = KLU_OUT_OF_MEMORY ; return (NULL) ; } return (Symbolic) ; } /* ========================================================================== */ /* === KLU_analyze_given ==================================================== */ /* ========================================================================== */ KLU_symbolic *KLU_analyze_given /* returns NULL if error, or a valid KLU_symbolic object if successful */ ( /* inputs, not modified */ Int n, /* A is n-by-n */ Int Ap [ ], /* size n+1, column pointers */ Int Ai [ ], /* size nz, row indices */ Int Puser [ ], /* size n, user's row permutation (may be NULL) */ Int Quser [ ], /* size n, user's column permutation (may be NULL) */ /* -------------------- */ KLU_common *Common ) { KLU_symbolic *Symbolic ; double *Lnz ; Int nblocks, nz, block, maxblock, *P, *Q, *R, nzoff, p, pend, do_btf, k ; /* ---------------------------------------------------------------------- */ /* determine if input matrix is valid, and get # of nonzeros */ /* ---------------------------------------------------------------------- */ Symbolic = KLU_alloc_symbolic (n, Ap, Ai, Common) ; if (Symbolic == NULL) { return (NULL) ; } P = Symbolic->P ; Q = Symbolic->Q ; R = Symbolic->R ; Lnz = Symbolic->Lnz ; nz = Symbolic->nz ; /* ---------------------------------------------------------------------- */ /* Q = Quser, or identity if Quser is NULL */ /* ---------------------------------------------------------------------- */ if (Quser == (Int *) NULL) { for (k = 0 ; k < n ; k++) { Q [k] = k ; } } else { for (k = 0 ; k < n ; k++) { Q [k] = Quser [k] ; } } /* ---------------------------------------------------------------------- */ /* get the control parameters for BTF and ordering method */ /* ---------------------------------------------------------------------- */ do_btf = Common->btf ; do_btf = (do_btf) ? TRUE : FALSE ; Symbolic->ordering = 2 ; Symbolic->do_btf = do_btf ; /* ---------------------------------------------------------------------- */ /* find the block triangular form, if requested */ /* ---------------------------------------------------------------------- */ if (do_btf) { /* ------------------------------------------------------------------ */ /* get workspace for BTF_strongcomp */ /* ------------------------------------------------------------------ */ Int *Pinv, *Work, *Bi, k1, k2, nk, oldcol ; Work = KLU_malloc (4*n, sizeof (Int), Common) ; Pinv = KLU_malloc (n, sizeof (Int), Common) ; if (Puser != (Int *) NULL) { Bi = KLU_malloc (nz+1, sizeof (Int), Common) ; } else { Bi = Ai ; } if (Common->status < KLU_OK) { /* out of memory */ KLU_free (Work, 4*n, sizeof (Int), Common) ; KLU_free (Pinv, n, sizeof (Int), Common) ; if (Puser != (Int *) NULL) { KLU_free (Bi, nz+1, sizeof (Int), Common) ; } KLU_free_symbolic (&Symbolic, Common) ; Common->status = KLU_OUT_OF_MEMORY ; return (NULL) ; } /* ------------------------------------------------------------------ */ /* B = Puser * A */ /* ------------------------------------------------------------------ */ if (Puser != (Int *) NULL) { for (k = 0 ; k < n ; k++) { Pinv [Puser [k]] = k ; } for (p = 0 ; p < nz ; p++) { Bi [p] = Pinv [Ai [p]] ; } } /* ------------------------------------------------------------------ */ /* find the strongly-connected components */ /* ------------------------------------------------------------------ */ /* modifies Q, and determines P and R */ nblocks = BTF_strongcomp (n, Ap, Bi, Q, P, R, Work) ; /* ------------------------------------------------------------------ */ /* P = P * Puser */ /* ------------------------------------------------------------------ */ if (Puser != (Int *) NULL) { for (k = 0 ; k < n ; k++) { Work [k] = Puser [P [k]] ; } for (k = 0 ; k < n ; k++) { P [k] = Work [k] ; } } /* ------------------------------------------------------------------ */ /* Pinv = inverse of P */ /* ------------------------------------------------------------------ */ for (k = 0 ; k < n ; k++) { Pinv [P [k]] = k ; } /* ------------------------------------------------------------------ */ /* analyze each block */ /* ------------------------------------------------------------------ */ nzoff = 0 ; /* nz in off-diagonal part */ maxblock = 1 ; /* size of the largest block */ for (block = 0 ; block < nblocks ; block++) { /* -------------------------------------------------------------- */ /* the block is from rows/columns k1 to k2-1 */ /* -------------------------------------------------------------- */ k1 = R [block] ; k2 = R [block+1] ; nk = k2 - k1 ; PRINTF (("BLOCK %d, k1 %d k2-1 %d nk %d\n", block, k1, k2-1, nk)) ; maxblock = MAX (maxblock, nk) ; /* -------------------------------------------------------------- */ /* scan the kth block, C */ /* -------------------------------------------------------------- */ for (k = k1 ; k < k2 ; k++) { oldcol = Q [k] ; pend = Ap [oldcol+1] ; for (p = Ap [oldcol] ; p < pend ; p++) { if (Pinv [Ai [p]] < k1) { nzoff++ ; } } } /* fill-in not estimated */ Lnz [block] = EMPTY ; } /* ------------------------------------------------------------------ */ /* free all workspace */ /* ------------------------------------------------------------------ */ KLU_free (Work, 4*n, sizeof (Int), Common) ; KLU_free (Pinv, n, sizeof (Int), Common) ; if (Puser != (Int *) NULL) { KLU_free (Bi, nz+1, sizeof (Int), Common) ; } } else { /* ------------------------------------------------------------------ */ /* BTF not requested */ /* ------------------------------------------------------------------ */ nzoff = 0 ; nblocks = 1 ; maxblock = n ; R [0] = 0 ; R [1] = n ; Lnz [0] = EMPTY ; /* ------------------------------------------------------------------ */ /* P = Puser, or identity if Puser is NULL */ /* ------------------------------------------------------------------ */ for (k = 0 ; k < n ; k++) { P [k] = (Puser == NULL) ? k : Puser [k] ; } } /* ---------------------------------------------------------------------- */ /* return the symbolic object */ /* ---------------------------------------------------------------------- */ Symbolic->nblocks = nblocks ; Symbolic->maxblock = maxblock ; Symbolic->lnz = EMPTY ; Symbolic->unz = EMPTY ; Symbolic->nzoff = nzoff ; return (Symbolic) ; } SuiteSparse/KLU/Source/klu_dump.c0000644001170100242450000000746510616177425015653 0ustar davisfac/* ========================================================================== */ /* === KLU_dump ============================================================= */ /* ========================================================================== */ /* Debug routines for klu. Only used when NDEBUG is not defined at * compile-time. */ #include "klu_internal.h" #ifndef NDEBUG /* ========================================================================== */ /* === KLU_valid ============================================================ */ /* ========================================================================== */ /* Check if a column-form matrix is valid or not. The matrix A is * n-by-n. The row indices of entries in column j are in * Ai [Ap [j] ... Ap [j+1]-1]. Required conditions are: * * n >= 0 * nz = Ap [n_col] >= 0 number of entries in the matrix * Ap [0] == 0 * Ap [j] <= Ap [j+1] for all j in the range 0 to n_col. * row indices in Ai [Ap [j] ... Ap [j+1]-1] * must be in the range 0 to n_row-1, * and no duplicate entries can exist (duplicates not checked here). * * Not user-callable. Only used when debugging. */ Int KLU_valid (Int n, Int Ap [ ], Int Ai [ ], Entry Ax [ ]) { Int nz, j, p1, p2, i, p ; PRINTF (("\ncolumn oriented matrix, n = %d\n", n)) ; if (n <= 0) { PRINTF (("n must be >= 0: %d\n", n)) ; return (FALSE) ; } nz = Ap [n] ; if (Ap [0] != 0 || nz < 0) { /* column pointers must start at Ap [0] = 0, and Ap [n] must be >= 0 */ PRINTF (("column 0 pointer bad or nz < 0\n")) ; return (FALSE) ; } for (j = 0 ; j < n ; j++) { p1 = Ap [j] ; p2 = Ap [j+1] ; PRINTF (("\nColumn: %d p1: %d p2: %d\n", j, p1, p2)) ; if (p1 > p2) { /* column pointers must be ascending */ PRINTF (("column %d pointer bad\n", j)) ; return (FALSE) ; } for (p = p1 ; p < p2 ; p++) { i = Ai [p] ; PRINTF (("row: %d", i)) ; if (i < 0 || i >= n) { /* row index out of range */ PRINTF (("index out of range, col %d row %d\n", j, i)) ; return (FALSE) ; } if (Ax != (Entry *) NULL) { PRINT_ENTRY (Ax [p]) ; } PRINTF (("\n")) ; } } return (TRUE) ; } /* ========================================================================== */ /* === KLU_valid_LU ========================================================= */ /* ========================================================================== */ /* This function does the same validity tests as KLU_valid but for the * LU factor storage format. The flag flag_test_start_ptr is used to * test if Xip [0] = 0. This is not applicable for U. So when calling this * function for U, the flag should be set to false. Only used when debugging. */ Int KLU_valid_LU (Int n, Int flag_test_start_ptr, Int Xip [ ], Int Xlen [ ], Unit LU [ ]) { Int *Xi ; Entry *Xx ; Int j, p1, p2, i, p, len ; PRINTF (("\ncolumn oriented matrix, n = %d\n", n)) ; if (n <= 0) { PRINTF (("n must be >= 0: %d\n", n)) ; return (FALSE) ; } if (flag_test_start_ptr && Xip [0] != 0) { /* column pointers must start at Xip [0] = 0*/ PRINTF (("column 0 pointer bad\n")) ; return (FALSE) ; } for (j = 0 ; j < n ; j++) { p1 = Xip [j] ; p2 = Xip [j+1] ; PRINTF (("\nColumn: %d p1: %d p2: %d\n", j, p1, p2)) ; if (p1 > p2) { /* column pointers must be ascending */ PRINTF (("column %d pointer bad\n", j)) ; return (FALSE) ; } GET_POINTER (LU, Xip, Xlen, Xi, Xx, j, len) ; for (p = 0 ; p < len ; p++) { i = Xi [p] ; PRINTF (("row: %d", i)) ; if (i < 0 || i >= n) { /* row index out of range */ PRINTF (("index out of range, col %d row %d\n", j, i)) ; return (FALSE) ; } if (Xx != (Entry *) NULL) { PRINT_ENTRY (Xx [p]) ; } PRINTF (("\n")) ; } } return (TRUE) ; } #endif SuiteSparse/KLU/Source/klu_analyze.c0000644001170100242450000003545310616723523016343 0ustar davisfac/* ========================================================================== */ /* === klu_analyze ========================================================== */ /* ========================================================================== */ /* Order the matrix using BTF (or not), and then AMD, COLAMD, the natural * ordering, or the user-provided-function on the blocks. Does not support * using a given ordering (use klu_analyze_given for that case). */ #include "klu_internal.h" /* ========================================================================== */ /* === analyze_worker ======================================================= */ /* ========================================================================== */ static Int analyze_worker /* returns KLU_OK or < 0 if error */ ( /* inputs, not modified */ Int n, /* A is n-by-n */ Int Ap [ ], /* size n+1, column pointers */ Int Ai [ ], /* size nz, row indices */ Int nblocks, /* # of blocks */ Int Pbtf [ ], /* BTF row permutation */ Int Qbtf [ ], /* BTF col permutation */ Int R [ ], /* size n+1, but only Rbtf [0..nblocks] is used */ Int ordering, /* what ordering to use (0, 1, or 3 for this routine) */ /* output only, not defined on input */ Int P [ ], /* size n */ Int Q [ ], /* size n */ double Lnz [ ], /* size n, but only Lnz [0..nblocks-1] is used */ /* workspace, not defined on input or output */ Int Pblk [ ], /* size maxblock */ Int Cp [ ], /* size maxblock+1 */ Int Ci [ ], /* size MAX (nz+1, Cilen) */ Int Cilen, /* nz+1, or COLAMD_recommend(nz,n,n) for COLAMD */ Int Pinv [ ], /* size maxblock */ /* input/output */ KLU_symbolic *Symbolic, KLU_common *Common ) { double amd_Info [AMD_INFO], lnz, lnz1, flops, flops1 ; Int k1, k2, nk, k, block, oldcol, pend, newcol, result, pc, p, newrow, maxnz, nzoff, cstats [COLAMD_STATS], ok, err = KLU_INVALID ; /* ---------------------------------------------------------------------- */ /* initializations */ /* ---------------------------------------------------------------------- */ /* compute the inverse of Pbtf */ #ifndef NDEBUG for (k = 0 ; k < n ; k++) { P [k] = EMPTY ; Q [k] = EMPTY ; Pinv [k] = EMPTY ; } #endif for (k = 0 ; k < n ; k++) { ASSERT (Pbtf [k] >= 0 && Pbtf [k] < n) ; Pinv [Pbtf [k]] = k ; } #ifndef NDEBUG for (k = 0 ; k < n ; k++) ASSERT (Pinv [k] != EMPTY) ; #endif nzoff = 0 ; lnz = 0 ; maxnz = 0 ; flops = 0 ; Symbolic->symmetry = EMPTY ; /* only computed by AMD */ /* ---------------------------------------------------------------------- */ /* order each block */ /* ---------------------------------------------------------------------- */ for (block = 0 ; block < nblocks ; block++) { /* ------------------------------------------------------------------ */ /* the block is from rows/columns k1 to k2-1 */ /* ------------------------------------------------------------------ */ k1 = R [block] ; k2 = R [block+1] ; nk = k2 - k1 ; PRINTF (("BLOCK %d, k1 %d k2-1 %d nk %d\n", block, k1, k2-1, nk)) ; /* ------------------------------------------------------------------ */ /* construct the kth block, C */ /* ------------------------------------------------------------------ */ Lnz [block] = EMPTY ; pc = 0 ; for (k = k1 ; k < k2 ; k++) { newcol = k-k1 ; Cp [newcol] = pc ; oldcol = Qbtf [k] ; pend = Ap [oldcol+1] ; for (p = Ap [oldcol] ; p < pend ; p++) { newrow = Pinv [Ai [p]] ; if (newrow < k1) { nzoff++ ; } else { /* (newrow,newcol) is an entry in the block */ ASSERT (newrow < k2) ; newrow -= k1 ; Ci [pc++] = newrow ; } } } Cp [nk] = pc ; maxnz = MAX (maxnz, pc) ; ASSERT (KLU_valid (nk, Cp, Ci, NULL)) ; /* ------------------------------------------------------------------ */ /* order the block C */ /* ------------------------------------------------------------------ */ if (nk <= 3) { /* -------------------------------------------------------------- */ /* use natural ordering for tiny blocks (3-by-3 or less) */ /* -------------------------------------------------------------- */ for (k = 0 ; k < nk ; k++) { Pblk [k] = k ; } lnz1 = nk * (nk + 1) / 2 ; flops1 = nk * (nk - 1) / 2 + (nk-1)*nk*(2*nk-1) / 6 ; ok = TRUE ; } else if (ordering == 0) { /* -------------------------------------------------------------- */ /* order the block with AMD (C+C') */ /* -------------------------------------------------------------- */ result = AMD_order (nk, Cp, Ci, Pblk, NULL, amd_Info) ; ok = (result >= AMD_OK) ; if (result == AMD_OUT_OF_MEMORY) { err = KLU_OUT_OF_MEMORY ; } /* account for memory usage in AMD */ Common->mempeak = MAX (Common->mempeak, Common->memusage + amd_Info [AMD_MEMORY]) ; /* get the ordering statistics from AMD */ lnz1 = (Int) (amd_Info [AMD_LNZ]) + nk ; flops1 = 2 * amd_Info [AMD_NMULTSUBS_LU] + amd_Info [AMD_NDIV] ; if (pc == maxnz) { /* get the symmetry of the biggest block */ Symbolic->symmetry = amd_Info [AMD_SYMMETRY] ; } } else if (ordering == 1) { /* -------------------------------------------------------------- */ /* order the block with COLAMD (C) */ /* -------------------------------------------------------------- */ /* order (and destroy) Ci, returning column permutation in Cp. * COLAMD "cannot" fail since the matrix has already been checked, * and Ci allocated. */ ok = COLAMD (nk, nk, Cilen, Ci, Cp, NULL, cstats) ; lnz1 = EMPTY ; flops1 = EMPTY ; /* copy the permutation from Cp to Pblk */ for (k = 0 ; k < nk ; k++) { Pblk [k] = Cp [k] ; } } else { /* -------------------------------------------------------------- */ /* pass the block to the user-provided ordering function */ /* -------------------------------------------------------------- */ lnz1 = (Common->user_order) (nk, Cp, Ci, Pblk, Common) ; flops1 = EMPTY ; ok = (lnz1 != 0) ; } if (!ok) { return (err) ; /* ordering method failed */ } /* ------------------------------------------------------------------ */ /* keep track of nnz(L) and flops statistics */ /* ------------------------------------------------------------------ */ Lnz [block] = lnz1 ; lnz = (lnz == EMPTY || lnz1 == EMPTY) ? EMPTY : (lnz + lnz1) ; flops = (flops == EMPTY || flops1 == EMPTY) ? EMPTY : (flops + flops1) ; /* ------------------------------------------------------------------ */ /* combine the preordering with the BTF ordering */ /* ------------------------------------------------------------------ */ PRINTF (("Pblk, 1-based:\n")) ; for (k = 0 ; k < nk ; k++) { ASSERT (k + k1 < n) ; ASSERT (Pblk [k] + k1 < n) ; Q [k + k1] = Qbtf [Pblk [k] + k1] ; } for (k = 0 ; k < nk ; k++) { ASSERT (k + k1 < n) ; ASSERT (Pblk [k] + k1 < n) ; P [k + k1] = Pbtf [Pblk [k] + k1] ; } } PRINTF (("nzoff %d Ap[n] %d\n", nzoff, Ap [n])) ; ASSERT (nzoff >= 0 && nzoff <= Ap [n]) ; /* return estimates of # of nonzeros in L including diagonal */ Symbolic->lnz = lnz ; /* EMPTY if COLAMD used */ Symbolic->unz = lnz ; Symbolic->nzoff = nzoff ; Symbolic->est_flops = flops ; /* EMPTY if COLAMD or user-ordering used */ return (KLU_OK) ; } /* ========================================================================== */ /* === order_and_analyze ==================================================== */ /* ========================================================================== */ /* Orders the matrix with or with BTF, then orders each block with AMD, COLAMD, * or the user ordering function. Does not handle the natural or given * ordering cases. */ static KLU_symbolic *order_and_analyze /* returns NULL if error, or a valid KLU_symbolic object if successful */ ( /* inputs, not modified */ Int n, /* A is n-by-n */ Int Ap [ ], /* size n+1, column pointers */ Int Ai [ ], /* size nz, row indices */ /* --------------------- */ KLU_common *Common ) { double work ; KLU_symbolic *Symbolic ; double *Lnz ; Int *Qbtf, *Cp, *Ci, *Pinv, *Pblk, *Pbtf, *P, *Q, *R ; Int nblocks, nz, block, maxblock, k1, k2, nk, do_btf, ordering, k, Cilen, *Work ; /* ---------------------------------------------------------------------- */ /* allocate the Symbolic object, and check input matrix */ /* ---------------------------------------------------------------------- */ Symbolic = KLU_alloc_symbolic (n, Ap, Ai, Common) ; if (Symbolic == NULL) { return (NULL) ; } P = Symbolic->P ; Q = Symbolic->Q ; R = Symbolic->R ; Lnz = Symbolic->Lnz ; nz = Symbolic->nz ; ordering = Common->ordering ; if (ordering == 1) { /* COLAMD */ Cilen = COLAMD_recommended (nz, n, n) ; } else if (ordering == 0 || (ordering == 3 && Common->user_order != NULL)) { /* AMD or user ordering function */ Cilen = nz+1 ; } else { /* invalid ordering */ Common->status = KLU_INVALID ; KLU_free_symbolic (&Symbolic, Common) ; return (NULL) ; } /* AMD memory management routines */ amd_malloc = Common->malloc_memory ; amd_free = Common->free_memory ; amd_calloc = Common->calloc_memory ; amd_realloc = Common->realloc_memory ; /* ---------------------------------------------------------------------- */ /* allocate workspace for BTF permutation */ /* ---------------------------------------------------------------------- */ Pbtf = KLU_malloc (n, sizeof (Int), Common) ; Qbtf = KLU_malloc (n, sizeof (Int), Common) ; if (Common->status < KLU_OK) { KLU_free (Pbtf, n, sizeof (Int), Common) ; KLU_free (Qbtf, n, sizeof (Int), Common) ; KLU_free_symbolic (&Symbolic, Common) ; return (NULL) ; } /* ---------------------------------------------------------------------- */ /* get the common parameters for BTF and ordering method */ /* ---------------------------------------------------------------------- */ do_btf = Common->btf ; do_btf = (do_btf) ? TRUE : FALSE ; Symbolic->ordering = ordering ; Symbolic->do_btf = do_btf ; Symbolic->structural_rank = EMPTY ; /* ---------------------------------------------------------------------- */ /* find the block triangular form (if requested) */ /* ---------------------------------------------------------------------- */ Common->work = 0 ; if (do_btf) { Work = KLU_malloc (5*n, sizeof (Int), Common) ; if (Common->status < KLU_OK) { /* out of memory */ KLU_free (Pbtf, n, sizeof (Int), Common) ; KLU_free (Qbtf, n, sizeof (Int), Common) ; KLU_free_symbolic (&Symbolic, Common) ; return (NULL) ; } nblocks = BTF_order (n, Ap, Ai, Common->maxwork, &work, Pbtf, Qbtf, R, &(Symbolic->structural_rank), Work) ; Common->structural_rank = Symbolic->structural_rank ; Common->work += work ; KLU_free (Work, 5*n, sizeof (Int), Common) ; /* unflip Qbtf if the matrix does not have full structural rank */ if (Symbolic->structural_rank < n) { for (k = 0 ; k < n ; k++) { Qbtf [k] = BTF_UNFLIP (Qbtf [k]) ; } } /* find the size of the largest block */ maxblock = 1 ; for (block = 0 ; block < nblocks ; block++) { k1 = R [block] ; k2 = R [block+1] ; nk = k2 - k1 ; PRINTF (("block %d size %d\n", block, nk)) ; maxblock = MAX (maxblock, nk) ; } } else { /* BTF not requested */ nblocks = 1 ; maxblock = n ; R [0] = 0 ; R [1] = n ; for (k = 0 ; k < n ; k++) { Pbtf [k] = k ; Qbtf [k] = k ; } } Symbolic->nblocks = nblocks ; PRINTF (("maxblock size %d\n", maxblock)) ; Symbolic->maxblock = maxblock ; /* ---------------------------------------------------------------------- */ /* allocate more workspace, for analyze_worker */ /* ---------------------------------------------------------------------- */ Pblk = KLU_malloc (maxblock, sizeof (Int), Common) ; Cp = KLU_malloc (maxblock + 1, sizeof (Int), Common) ; Ci = KLU_malloc (MAX (Cilen, nz+1), sizeof (Int), Common) ; Pinv = KLU_malloc (n, sizeof (Int), Common) ; /* ---------------------------------------------------------------------- */ /* order each block of the BTF ordering, and a fill-reducing ordering */ /* ---------------------------------------------------------------------- */ if (Common->status == KLU_OK) { PRINTF (("calling analyze_worker\n")) ; Common->status = analyze_worker (n, Ap, Ai, nblocks, Pbtf, Qbtf, R, ordering, P, Q, Lnz, Pblk, Cp, Ci, Cilen, Pinv, Symbolic, Common) ; PRINTF (("analyze_worker done\n")) ; } /* ---------------------------------------------------------------------- */ /* free all workspace */ /* ---------------------------------------------------------------------- */ KLU_free (Pblk, maxblock, sizeof (Int), Common) ; KLU_free (Cp, maxblock+1, sizeof (Int), Common) ; KLU_free (Ci, MAX (Cilen, nz+1), sizeof (Int), Common) ; KLU_free (Pinv, n, sizeof (Int), Common) ; KLU_free (Pbtf, n, sizeof (Int), Common) ; KLU_free (Qbtf, n, sizeof (Int), Common) ; /* ---------------------------------------------------------------------- */ /* return the symbolic object */ /* ---------------------------------------------------------------------- */ if (Common->status < KLU_OK) { KLU_free_symbolic (&Symbolic, Common) ; } return (Symbolic) ; } /* ========================================================================== */ /* === KLU_analyze ========================================================== */ /* ========================================================================== */ KLU_symbolic *KLU_analyze /* returns NULL if error, or a valid KLU_symbolic object if successful */ ( /* inputs, not modified */ Int n, /* A is n-by-n */ Int Ap [ ], /* size n+1, column pointers */ Int Ai [ ], /* size nz, row indices */ /* -------------------- */ KLU_common *Common ) { /* ---------------------------------------------------------------------- */ /* get the control parameters for BTF and ordering method */ /* ---------------------------------------------------------------------- */ if (Common == NULL) { return (NULL) ; } Common->status = KLU_OK ; Common->structural_rank = EMPTY ; /* ---------------------------------------------------------------------- */ /* order and analyze */ /* ---------------------------------------------------------------------- */ if (Common->ordering == 2) { /* natural ordering */ return (KLU_analyze_given (n, Ap, Ai, NULL, NULL, Common)) ; } else { /* order with P and Q */ return (order_and_analyze (n, Ap, Ai, Common)) ; } } SuiteSparse/KLU/Source/klu_scale.c0000644001170100242450000000755310616200156015757 0ustar davisfac/* ========================================================================== */ /* === KLU_scale ============================================================ */ /* ========================================================================== */ /* Scale a matrix and check to see if it is valid. Can be called by the user. * This is called by KLU_factor and KLU_refactor. Returns TRUE if the input * matrix is valid, FALSE otherwise. If the W input argument is non-NULL, * then the input matrix is checked for duplicate entries. * * scaling methods: * <0: no scaling, do not compute Rs, and do not check input matrix. * 0: no scaling * 1: the scale factor for row i is sum (abs (A (i,:))) * 2 or more: the scale factor for row i is max (abs (A (i,:))) */ #include "klu_internal.h" Int KLU_scale /* return TRUE if successful, FALSE otherwise */ ( /* inputs, not modified */ Int scale, /* 0: none, 1: sum, 2: max */ Int n, Int Ap [ ], /* size n+1, column pointers */ Int Ai [ ], /* size nz, row indices */ double Ax [ ], /* outputs, not defined on input */ double Rs [ ], /* size n, can be NULL if scale <= 0 */ /* workspace, not defined on input or output */ Int W [ ], /* size n, can be NULL */ /* --------------- */ KLU_common *Common ) { double a ; Entry *Az ; Int row, col, p, pend, check_duplicates ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ if (Common == NULL) { return (FALSE) ; } Common->status = KLU_OK ; if (scale < 0) { /* return without checking anything and without computing the * scale factors */ return (TRUE) ; } Az = (Entry *) Ax ; if (n <= 0 || Ap == NULL || Ai == NULL || Az == NULL || (scale > 0 && Rs == NULL)) { /* Ap, Ai, Ax and Rs must be present, and n must be > 0 */ Common->status = KLU_INVALID ; return (FALSE) ; } if (Ap [0] != 0 || Ap [n] < 0) { /* nz = Ap [n] must be >= 0 and Ap [0] must equal zero */ Common->status = KLU_INVALID ; return (FALSE) ; } for (col = 0 ; col < n ; col++) { if (Ap [col] > Ap [col+1]) { /* column pointers must be non-decreasing */ Common->status = KLU_INVALID ; return (FALSE) ; } } /* ---------------------------------------------------------------------- */ /* scale */ /* ---------------------------------------------------------------------- */ if (scale > 0) { /* initialize row sum or row max */ for (row = 0 ; row < n ; row++) { Rs [row] = 0 ; } } /* check for duplicates only if W is present */ check_duplicates = (W != (Int *) NULL) ; if (check_duplicates) { for (row = 0 ; row < n ; row++) { W [row] = EMPTY ; } } for (col = 0 ; col < n ; col++) { pend = Ap [col+1] ; for (p = Ap [col] ; p < pend ; p++) { row = Ai [p] ; if (row < 0 || row >= n) { /* row index out of range, or duplicate entry */ Common->status = KLU_INVALID ; return (FALSE) ; } if (check_duplicates) { if (W [row] == col) { /* duplicate entry */ Common->status = KLU_INVALID ; return (FALSE) ; } /* flag row i as appearing in column col */ W [row] = col ; } /* a = ABS (Az [p]) ;*/ ABS (a, Az [p]) ; if (scale == 1) { /* accumulate the abs. row sum */ Rs [row] += a ; } else if (scale > 1) { /* find the max abs. value in the row */ Rs [row] = MAX (Rs [row], a) ; } } } if (scale > 0) { /* do not scale empty rows */ for (row = 0 ; row < n ; row++) { /* matrix is singular */ PRINTF (("Rs [%d] = %g\n", row, Rs [row])) ; if (Rs [row] == 0.0) { PRINTF (("Row %d of A is all zero\n", row)) ; Rs [row] = 1.0 ; } } } return (TRUE) ; } SuiteSparse/KLU/README.txt0000644001170100242450000001202710620334700014075 0ustar davisfacKLU Version 1.0, May 31, 2007, by Timothy A. Davis and Ekanathan Palamadai. Copyright (C) 2004-2007, University of Florida KLU is also available under other licenses; contact authors for details. http://www.cise.ufl.edu/research/sparse Requires the AMD, COLAMD, and BTF libraries, in ../AMD, ../COLAMD, and ../BTF, respectively. Requires the ../UFconfig/UFconfig.mk configuration file. Optionally uses CHOLMOD (KLU/User example ordering). The Tcov tests and the Demo both require CHOLMOD. To compile the libklu.a library, type "make". The compiled library is located in KLU/Lib/libklu.a. Compile code that uses KLU with -IKLU/Include. Type "make clean" to remove all but the compiled library, and "make distclean" to remove all files not in the original distribution. -------------------------------------------------------------------------------- KLU is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This Module is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA -------------------------------------------------------------------------------- A full text of the license is in Doc/lesser.txt. Files in this distribution: Demo example programs that use KLU (requires CHOLMOD) Doc documentation Include include files Lib compiled library Makefile top-level Makefile MATLAB MATLAB interface Matrix test matrices README.txt this file Source source code Tcov exhaustive test of KLU and BTF User example user ordering function (interface to CHOLMOD) ./Demo: kludemo.c KLU demo (int version) kludemo.out output of "make" in this directory kluldemo.c KLU demo (UF_long version) Makefile Makefile for compiling the demo ./Doc: ChangeLog KLU_UserGuide.bib Bibiography KLU_UserGuide.pdf PDF version of KLU User Guide KLU_UserGuide.tex TEX source of KLU User Guide lesser.txt license (LGPL) Makefile Makefile for creating the User Guide palamadai_e.pdf Eka Palamadai's MS thesis ./Include: klu.h user include file klu_internal.h internal include file, not needed by the user klu_version.h internal include file, not needed by the user ./Lib: Makefile Makefile for compiling the KLU C-callable library ./MATLAB: Contents.m list of MATLAB functions in KLU klu_demo.m MATLAB demo klu_demo.m.out output of MATLAB demo klu_install.m compiles and installs KLU for use in MATLAB, runs demo klu.m MATLAB help for KLU klu_make.m compiles KLU for use in MATLAB klu_mex.c MATLAB mexFunction interface for KLU Makefile Makefile for KLU mexFunction, with CHOLMOD Makefile_no_CHOLMOD Makefile for KLU mexFunction, without CHOLMOD Test MATLAB tests ./MATLAB/Test: KLU tests, requires UFget test1.m test2.m test3.m test4.m test5.m ./Matrix: test matrices for programs in ./Demo and ./Tcov 1c.mtx arrowc.mtx arrow.mtx ctina.mtx GD99_cc.mtx impcol_a.mtx onec.mtx one.mtx two.mtx w156.mtx ./Source: klu_analyze.c klu_analyze and supporting functions klu_analyze_given.c klu_analyze_given and supporting functions klu.c kernel factor/solve functions, not user-callable klu_defaults.c klu_defaults function klu_diagnostics.c klu_rcond, klu_condest, klu_rgrowth, kluflops klu_dump.c debugging functions klu_extract.c klu_extract klu_factor.c klu_factor and supporting functions klu_free_numeric.c klu_free_numeric function klu_free_symbolic.c klu_free_symbolic function klu_kernel.c kernel factor functions, not user-callable klu_memory.c klu_malloc, klu_free, klu_realloc, and supporing func. klu_refactor.c klu_refactor function klu_scale.c klu_scale function klu_solve.c klu_solve function klu_sort.c klu_sort and supporting functions klu_tsolve.c klu_tsovle function ./Tcov: exhaustive test suite; requires Linux/Unix coverage determine statement coverage klultests KLU UF_long tests klutest.c KLU test program klutests KLU int tests Makefile Makefile for compiling and running the tests README.txt README file for Tcov vklutests KLU int tests, using valgrind vklultests KLU UF_long tests, using valgrind ./User: klu_cholmod.c sample KLU user ordering function (int version) klu_cholmod.h include file for klu_cholmod and klu_l_cholmod klu_l_cholmod.c sample KLU user ordering function (UF_long version) Makefile Makefile for compiling the user ordering functions README.txt README for User directory SuiteSparse/LDL/0000755001170100242450000000000010617142432012362 5ustar davisfacSuiteSparse/LDL/Doc/0000755001170100242450000000000010711442313013063 5ustar davisfacSuiteSparse/LDL/Doc/Makefile0000644001170100242450000000174310617140256014536 0ustar davisfac#------------------------------------------------------------------------------- # Makefile for the LDL documentation #------------------------------------------------------------------------------- default: ldl_userguide.pdf include ../../UFconfig/UFconfig.mk #------------------------------------------------------------------------------- # clean-up: #------------------------------------------------------------------------------- distclean: purge purge: clean - $(RM) *.dvi *.aux *.log *.bak *.bbl *.blg *.ps clean: - $(RM) $(CLEAN) #------------------------------------------------------------------------------- # user guide: #------------------------------------------------------------------------------- ldl_userguide.pdf: ldl_userguide.tex ldl.bib latex ldl_userguide - bibtex ldl_userguide latex ldl_userguide latex ldl_userguide dvips ldl_userguide -o ldl_userguide.ps pdflatex ldl_userguide pdflatex ldl_userguide - $(RM) *.dvi *.aux *.log *.bak *.bbl *.blg *.ps SuiteSparse/LDL/Doc/ldl.bib0000644001170100242450000000705510617141160014324 0ustar davisfac@string{TOMS = "{ACM} Trans. Math. Softw."} @string{SIMAX = "{SIAM} J. Matrix Anal. Applic."} @string{SIAMJSC = "{SIAM} J. Sci. Comput."} @string{SIAMJSSC = "{SIAM} J. Sci. Statist. Comput."} @article{AmestoyDavisDuff96, author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.}, title={An approximate minimum degree ordering algorithm}, journal=SIMAX, year={1996} ,volume={17} ,number={4} ,pages={886-905} } @article{AmestoyDavisDuff03, author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.}, title={Algorithm 837: {AMD}, an approximate minimum degree ordering algorithm}, journal=TOMS, year={2004} ,volume={30} ,number={3} ,pages={381-388}} @article{Davis05, author={Davis, T. A}, title={Algorithm 849: a concise sparse Cholesky factorization package}, journal=TOMS, year={2005}, volume={31}, number={4}, pages={587--591} } @article{GeorgeLiu79, author={George, A. and Liu, J. W. H.}, month={Jun.}, year={1979}, title={The Design of a User Interface for a Sparse Matrix Package}, journal=TOMS, annote={f}, volume={5}, number={2}, pages={139-162}, keywords={software user interface SPARSPAK}} @book{GeorgeLiu, author={George, A. and Liu, J. W. H.}, year={1981}, title={Computer Solution of Large Sparse Positive Definite Systems}, address={Englewood Cliffs, New Jersey}, publisher={Prentice-Hall}, keywords={ positive definite systems}, annote={sh} } @article{GilbertMolerSchreiber, author={Gilbert, J. R. and Moler, C. and Schreiber, R.}, title={Sparse matrices in {MATLAB}: design and implementation}, journal=SIMAX, year={1992} ,volume={13} ,number={1} ,pages={333-356} ,annote={f} } @article{GilbertNgPeyton94, author={Gilbert, J. R. and Ng, E. G. and Peyton, B. W.}, title={An efficient algorithm to compute row and column counts for sparse {C}holesky factorization}, journal=SIMAX, year={1994} ,volume={15} ,number={4} ,pages={1075-1091} ,annote={f} } @article{GilbertPeierls88, author={Gilbert, J. R. and Peierls, T.}, year={1988}, title={Sparse Partial Pivoting in Time Proportional to Arithmetic Operations}, journal=SIAMJSSC, annote={f}, volume={9}, pages={862-874}, keywords={316 partial pivoting, graph algorithms}} @article{Liu86c, author={Liu, J. W. H.}, month={Jun.}, year={1986}, title={A Compact Row Storage Scheme for {C}holesky Factors Using Elimination Trees}, journal=TOMS, volume={12}, number={2}, pages={127-148}, annote={f. previously Report CS-84-02, Dept. Computer Science, York University (1984)}} @article{Liu90a, author={Liu, J. W. H.}, title={The Role of Elimination Trees in Sparse Factorization}, journal=SIMAX, year={1990} ,volume={11} ,number={1} ,pages={134-172} ,annote={f} } @article{Liu91, author={Liu, J. W. H.}, title={A generalized envelope method for sparse factorization by rows}, journal=TOMS, year={1991} ,volume={17} ,number={1} ,pages={112-129} ,annote={f} } @article{NgPeyton93, author={Ng, E. G. and Peyton, B. W.}, title={A supernodal {Cholesky} factorization algorithm for shared-memory multiprocessors}, journal=SIAMJSC, year={1993} ,volume={14} ,pages={761-769} ,annote={f} } @article{RothbergGupta91, author={Rothberg, E. and Gupta, A.}, title={Efficient sparse matrix factorization on high-performance workstations - {E}xploiting the memory hierarchy}, journal=TOMS, year={1991} ,volume={17} ,number={3} ,pages={313-334} ,annote={f} } @techreport{Stewart03, author={Stewart, G. W.}, title={Building an old-fashioned sparse solver}, institution={Univ. 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0000115781 00000 n 0000115419 00000 n 0000120242 00000 n 0000120104 00000 n 0000123623 00000 n 0000123365 00000 n 0000138315 00000 n 0000137922 00000 n 0000144700 00000 n 0000144478 00000 n 0000145207 00000 n 0000145275 00000 n 0000145328 00000 n trailer << /Size 134 /Root 132 0 R /Info 133 0 R /ID [<3562457E942F67F6A0C8C929B4A39ECD> <3562457E942F67F6A0C8C929B4A39ECD>] >> startxref 145532 %%EOF SuiteSparse/LDL/Doc/ldl_userguide.tex0000644001170100242450000007077010711442272016453 0ustar davisfac\documentclass[12pt]{article} \newcommand{\m}[1]{{\bf{#1}}} % for matrices and vectors \newcommand{\tr}{^{\sf T}} % transpose \topmargin 0in \textheight 9in \oddsidemargin 0pt \evensidemargin 0pt \textwidth 6.5in %------------------------------------------------------------------------------- \begin{document} %------------------------------------------------------------------------------- \title{User Guide for LDL, a concise sparse Cholesky package} \author{Timothy A. Davis\thanks{ Dept.~of Computer and Information Science and Engineering, Univ.~of Florida, Gainesville, FL, USA. email: davis@cise.ufl.edu. http://www.cise.ufl.edu/$\sim$davis. This work was supported by the National Science Foundation, under grant CCR-0203270. Portions of the work were done while on sabbatical at Stanford University and Lawrence Berkeley National Laboratory (with funding from Stanford University and the SciDAC program). }} \date{Nov 1, 2007} \maketitle %------------------------------------------------------------------------------- \begin{abstract} The {\tt LDL} software package is a set of short, concise routines for factorizing symmetric positive-definite sparse matrices, with some applicability to symmetric indefinite matrices. Its primary purpose is to illustrate much of the basic theory of sparse matrix algorithms in as concise a code as possible, including an elegant method of sparse symmetric factorization that computes the factorization row-by-row but stores it column-by-column. The entire symbolic and numeric factorization consists of less than 50 lines of code. The package is written in C, and includes a MATLAB interface. \end{abstract} %------------------------------------------------------------------------------- %------------------------------------------------------------------------------- \section{Overview} %------------------------------------------------------------------------------- {\tt LDL} is a set of short, concise routines that compute the $\m{LDL}\tr$ factorization of a sparse symmetric matrix $\m{A}$. Its primary purpose is to illustrate much of the basic theory of sparse matrix algorithms in as compact a code as possible, including an elegant method of sparse symmetric factorization (related to \cite{Liu86c,Liu91}). The lower triangular factor $\m{L}$ is computed row-by-row, in contrast to the conventional column-by-column method. Although it does not achieve the same level of performance as methods based on dense matrix kernels (such as \cite{NgPeyton93,RothbergGupta91}), its performance is competitive with column-by-column methods that do not use dense kernels \cite{GeorgeLiu79, GeorgeLiu, GilbertMolerSchreiber}. Section~\ref{Algorithm} gives a brief description of the algorithm used in the symbolic and numeric factorization. A more detailed tutorial-level discussion may be found in \cite{Stewart03}. Details of the concise implementation of this method are given in Section~\ref{Implementation}. Sections~\ref{MATLAB}~and~\ref{C} give an overview of how to use the package in MATLAB and in a stand-alone C program. %------------------------------------------------------------------------------- \section{Algorithm} \label{Algorithm} %------------------------------------------------------------------------------- The underlying numerical algorithm is described below. The $k$th step solves a lower triangular system of dimension $k-1$ to compute the $k$th row of $\m{L}$ and the $d_{kk}$ entry of the diagonal matrix $\m{D}$. Colon notation is used for submatrices. For example, $\m{L}_{k,1:k-1}$ refers to the first $k-1$ columns of the $k$th row of $\m{L}$. Similarly, $\m{L}_{1:k-1,1:k-1}$ refers to the leading $(k-1)$-by-$(k-1)$ submatrix of $\m{L}$. %--------------- \vspace{-0.2in} \begin{tabbing} \hspace{2em} \= \hspace{2em} \= \hspace{2em} \= \\ {\bf Algorithm~1 ($\m{LDL}\tr$ factorization of a $n$-by-$n$ symmetric matrix $\m{A}$)} \\ \> {\bf for} $k = 1$ {\bf to} $n$ \\ \>\> (step 1) Solve $\m{L}_{1:k-1,1:k-1}\m{y} = \m{A}_{1:k-1,k}$ for $\m{y}$ \\ \>\> (step 2) $\m{L}_{k,1:k-1} = (\m{D}_{1:k-1,1:k-1}^{-1} \m{y})\tr$ \\ \>\> (step 3) $l_{kk} = 1$ \\ \>\> (step 4) $d_{kk} = a_{kk} - \m{L}_{k,1:k-1}\m{y}$ \\ \> {\bf end for} \end{tabbing} %--------------- The algorithm computes an $\m{LDL}\tr$ factorization without numerical pivoting. It can thus factorize any symmetric positive definite matrix, and any symmetric indefinite matrix whose leading minors are all well-conditioned. When $\m{A}$ and $\m{L}$ are sparse, step 1 of Algorithm~1 requires a triangular solve of the form $\m{Lx}=\m{b}$, where all three terms in the equation are sparse. This is the most costly step of the Algorithm. Steps 2 through 4 are fairly straightforward. Let ${\cal X}$ and ${\cal B}$ refer to the set of indices of nonzero entries in $\m{x}$ and $\m{b}$, respectively, in the lower triangular system $\m{Lx}=\m{b}$. To compute $\m{x}$ efficiently the nonzero pattern ${\cal X}$ must be found first. In the general case when $\m{L}$ is arbitrary \cite{GilbertPeierls88}, the nonzero pattern ${\cal X}$ is the set of nodes reachable via paths in the graph $G_L$ from all nodes in the set ${\cal B}$, and where the graph $G_L$ has $n$ nodes and a directed edge $(j,i)$ if and only if $l_{ij}$ is nonzero. To compute the numerical solution to $\m{Lx}=\m{b}$ by accessing the columns of $\m{L}$ one at a time, ${\cal X}$ can be traversed in any topological order of the subgraph of $G_L$ consisting of nodes in ${\cal X}$. That is, $x_j$ must be computed before $x_i$ if there is a path from $j$ to $i$ in $G_L$. The natural order ($1, 2, \ldots, n$) is one such ordering, but that requires a costly sort of ${\cal X}$. With a graph traversal and topological sort, the solution of $\m{Lx}=\m{b}$ can be computed using Algorithm~2 below. The computation of ${\cal X}$ and $\m{x}$ both take time proportional to the floating-point operation count. %--------------- \vspace{-0.2in} \begin{tabbing} \hspace{2em} \= \hspace{2em} \= \hspace{2em} \= \\ {\bf Algorithm~2 (Solve $\m{Lx}=\m{b}$, where $\m{L}$ is lower triangular with unit diagonal)} \\ \> ${\cal X} = \mbox{Reach}_{G_L} ({\cal B})$ \\ \> $\m{x} = \m{b}$ \\ \> {\bf for} $i \in {\cal X}$ in any topological order \\ \>\> $\m{x}_{i+1:n} = \m{x}_{i+1:n} - \m{L}_{i+1:n,i} x_i$ \\ \> {\bf end for} \end{tabbing} %--------------- The general result also governs the pattern of $\m{y}$ in Algorithm~1. However, in this case $\m{L}$ arises from a sparse Cholesky factorization, and is governed by the elimination tree \cite{Liu90a}. A general graph traversal is not required. In the elimination tree, the parent of node $i$ is the smallest $j > i$ such that $l_{ji}$ is nonzero. Node $i$ has no parent if column $i$ of $\m{L}$ is completely zero below the diagonal; $i$ is a root of the elimination tree in this case. The nonzero pattern of $\m{x}$ is the union of all the nodes on the paths from any node $i$ (where $b_i$ is nonzero) to the root of the elimination tree \cite[Thm 2.4]{Liu86c}. It is referred to here as a tree, but in general it can be a forest. Rather than a general topological sort of the subgraph of $G_L$ consisting nodes reachable from nodes in ${\cal B}$, a simpler tree traversal can be used. First, select any nonzero entry $b_i$ and follow the path from $i$ to the root of tree. Nodes along this path are marked and placed in a stack, with $i$ at the top of the stack and the root at the bottom. Repeat for every other nonzero entry in $b_i$, in arbitrary order, but stop just before reaching a marked node (the result can be empty if $i$ is already in the stack). The stack now contains ${\cal X}$, a topological ordering of the nonzero pattern of $\m{x}$, which can be used in Algorithm~2 to solve $\m{Lx}=\m{b}$. The time to compute ${\cal X}$ using an elimination tree traversal is much faster than the general graph traversal, taking time proportional to the size of ${\cal X}$ rather than the number of floating-point operations required to compute $\m{x}$. In the $k$th step of the factorization, the set ${\cal X}$ becomes the nonzero pattern of row $k$ of $\m{L}$. This step requires the elimination tree of $\m{L}_{1:k-1,1:k-1}$, and must construct the elimination tree of $\m{L}_{1:k,1:k}$ for step $k+1$. Recall that the parent of $i$ in the tree is the smallest $j$ such that $i < j$ and $l_{ji} \ne 0$. Thus, if any node $i$ already has a parent $j$, then $j$ will remain the parent of $i$ in the elimination trees of all other larger leading submatrices of $\m{L}$, and in the elimination tree of $\m{L}$ itself. If $l_{ki} \ne 0$ and $i$ does not have a parent in the elimination tree of $\m{L}_{1:k-1,1:k-1}$, then the parent of $i$ is $k$ in the elimination tree of $\m{L}_{1:k,1:k}$. Node $k$ becomes the parent of any node $i \in {\cal X}$ that does not yet have a parent. Since Algorithm~2 traverses $\m{L}$ in column order, $\m{L}$ is stored in a conventional sparse column representation. Each column $j$ is stored as a list of nonzero values and their corresponding row indices. When row $k$ is computed, the new entries can be placed at the end of each list. As a by-product of computing $\m{L}$ one row at a time, the columns of $\m{L}$ are computed in a sorted manner. This is a convenient form of the output. MATLAB requires the columns of its sparse matrices to be sorted, for example. Sorted columns improve the speed of Algorithm~2, since the memory access pattern is more regular. The conventional column-by-column algorithm \cite{GeorgeLiu79,GeorgeLiu} does not produce columns of $\m{L}$ with sorted row indices. A simple symbolic pre-analysis can be obtained by repeating the subtree traversals. All that is required to compute the nonzero pattern of the $k$th row of $\m{L}$ is the partially constructed elimination tree and the nonzero pattern of the $k$th column of $\m{A}$. This is computed in time proportional to the size of this set, using the elimination tree traversal. Once constructed, the number of nonzeros in each column of $\m{L}$ is incremented, for each entry in ${\cal X}$, and then ${\cal X}$ is discarded. The set ${\cal X}$ need not be constructed in topological order, so no stack is required. The run time of the symbolic analysis algorithm is thus proportional to the number of nonzeros in $\m{L}$. This is more costly than the optimal algorithm \cite{GilbertNgPeyton94}, which takes time essentially proportional to the number of nonzeros in $\m{A}$. The memory requirements are just the matrix $\m{A}$ and a few size-$n$ integer arrays. The result of the algorithm is the elimination tree, a count of the number of nonzeros in each column of $\m{L}$, and the cumulative sum of the column counts. %------------------------------------------------------------------------------- \section{Implementation} \label{Implementation} %------------------------------------------------------------------------------- Because of its simplicity, the implementation of this algorithm leads to a very short, concise code. The symbolic analysis routine {\tt ldl\_symbolic} shown in Figure~\ref{ldlsymbolic} consists of only 18 lines of executable C code. This includes 5 lines of code to allow for a sparsity-preserving ordering $\m{P}$ so that either $\m{A}$ or $\m{PAP}\tr$ can be analyzed, 3 lines of code to compute the cumulative sum of the column counts, and one line of code to speed up a {\tt for} loop. An additional line of code allows for a more general form of the input sparse matrix $\m{A}$. The {\tt n}-by-{\tt n} sparse matrix $\m{A}$ is provided in compressed column form as an {\tt int} array {\tt Ap} of length {\tt n+1}, an {\tt int} array {\tt Ai} of length {\tt nz}, and a {\tt double} array {\tt Ax} also of length {\tt nz}, where {\tt nz} is the number of entries in the matrix. The numerical values of entries in column $j$ are stored in {\tt Ax[Ap[j]} $\ldots$ {\tt Ap[j+1]-1]} and the corresponding row indices are in {\tt Ai[Ap[j]} $\ldots$ {\tt Ap[j+1]-1]}. With {\tt Ap[0] = 0}, the number of entries in the matrix is {\tt nz = Ap[n]}. If no fill-reducing ordering {\tt P} is provided, only entries in the upper triangular part of $\m{A}$ are considered. If {\tt P} is provided and row/column {\tt i} of the matrix $\m{A}$ is the {\tt k}-th row/column of $\m{PAP}\tr$, then {\tt P[k]=i}. Only entries in the upper triangular part of $\m{PAP}\tr$ are considered. These entries may be in the lower triangular part of $\m{A}$, so to ensure that the correct matrix is factorized, all entries of $\m{A}$ should be provided when using the permutation input {\tt P}. The outputs of {\tt ldl\_symbolic} are three size-{\tt n} arrays: {\tt Parent} holds the elimination tree, {\tt Lnz} holds the counts of the number of entries in each column of $\m{L}$, and {\tt Lp} holds the cumulative sum of {\tt Lnz}. The size-{\tt n} array {\tt Flag} is used as workspace. None of the output or workspace arrays need to be initialized. \begin{figure} \caption{{\tt ldl\_symbolic:} finding the elimination tree and column counts} \label{ldlsymbolic} {\scriptsize \begin{verbatim} void ldl_symbolic ( int n, /* A and L are n-by-n, where n >= 0 */ int Ap [ ], /* input of size n+1, not modified */ int Ai [ ], /* input of size nz=Ap[n], not modified */ int Lp [ ], /* output of size n+1, not defined on input */ int Parent [ ], /* output of size n, not defined on input */ int Lnz [ ], /* output of size n, not defined on input */ int Flag [ ], /* workspace of size n, not defn. on input or output */ int P [ ], /* optional input of size n */ int Pinv [ ] /* optional output of size n (used if P is not NULL) */ ) { int i, k, p, kk, p2 ; if (P) { /* If P is present then compute Pinv, the inverse of P */ for (k = 0 ; k < n ; k++) { Pinv [P [k]] = k ; } } for (k = 0 ; k < n ; k++) { /* L(k,:) pattern: all nodes reachable in etree from nz in A(0:k-1,k) */ Parent [k] = -1 ; /* parent of k is not yet known */ Flag [k] = k ; /* mark node k as visited */ Lnz [k] = 0 ; /* count of nonzeros in column k of L */ kk = (P) ? (P [k]) : (k) ; /* kth original, or permuted, column */ p2 = Ap [kk+1] ; for (p = Ap [kk] ; p < p2 ; p++) { /* A (i,k) is nonzero (original or permuted A) */ i = (Pinv) ? (Pinv [Ai [p]]) : (Ai [p]) ; if (i < k) { /* follow path from i to root of etree, stop at flagged node */ for ( ; Flag [i] != k ; i = Parent [i]) { /* find parent of i if not yet determined */ if (Parent [i] == -1) Parent [i] = k ; Lnz [i]++ ; /* L (k,i) is nonzero */ Flag [i] = k ; /* mark i as visited */ } } } } /* construct Lp index array from Lnz column counts */ Lp [0] = 0 ; for (k = 0 ; k < n ; k++) { Lp [k+1] = Lp [k] + Lnz [k] ; } } \end{verbatim} } \end{figure} The {\tt ldl\_numeric} numeric factorization routine shown in Figure~\ref{ldlnumeric} consists of only 31 lines of executable code. It includes this same subtree traversal algorithm as {\tt ldl\_symbolic}, except that each path is placed on a stack that holds nonzero pattern of the $k$th row of $\m{L}$. This traversal is followed by a sparse forward solve using this pattern, and all of the nonzero entries in the resulting $k$th row of $\m{L}$ are appended to their respective columns in the data structure of $\m{L}$. \begin{figure} \caption{{\tt ldl\_numeric:} numeric factorization} \label{ldlnumeric} {\scriptsize \begin{verbatim} int ldl_numeric /* returns n if successful, k if D (k,k) is zero */ ( int n, /* A and L are n-by-n, where n >= 0 */ int Ap [ ], /* input of size n+1, not modified */ int Ai [ ], /* input of size nz=Ap[n], not modified */ double Ax [ ], /* input of size nz=Ap[n], not modified */ int Lp [ ], /* input of size n+1, not modified */ int Parent [ ], /* input of size n, not modified */ int Lnz [ ], /* output of size n, not defn. on input */ int Li [ ], /* output of size lnz=Lp[n], not defined on input */ double Lx [ ], /* output of size lnz=Lp[n], not defined on input */ double D [ ], /* output of size n, not defined on input */ double Y [ ], /* workspace of size n, not defn. on input or output */ int Pattern [ ], /* workspace of size n, not defn. on input or output */ int Flag [ ], /* workspace of size n, not defn. on input or output */ int P [ ], /* optional input of size n */ int Pinv [ ] /* optional input of size n */ ) { double yi, l_ki ; int i, k, p, kk, p2, len, top ; for (k = 0 ; k < n ; k++) { /* compute nonzero Pattern of kth row of L, in topological order */ Y [k] = 0.0 ; /* Y(0:k) is now all zero */ top = n ; /* stack for pattern is empty */ Flag [k] = k ; /* mark node k as visited */ Lnz [k] = 0 ; /* count of nonzeros in column k of L */ kk = (P) ? (P [k]) : (k) ; /* kth original, or permuted, column */ p2 = Ap [kk+1] ; for (p = Ap [kk] ; p < p2 ; p++) { i = (Pinv) ? (Pinv [Ai [p]]) : (Ai [p]) ; /* get A(i,k) */ if (i <= k) { Y [i] += Ax [p] ; /* scatter A(i,k) into Y (sum duplicates) */ for (len = 0 ; Flag [i] != k ; i = Parent [i]) { Pattern [len++] = i ; /* L(k,i) is nonzero */ Flag [i] = k ; /* mark i as visited */ } while (len > 0) Pattern [--top] = Pattern [--len] ; } } /* compute numerical values kth row of L (a sparse triangular solve) */ D [k] = Y [k] ; /* get D(k,k) and clear Y(k) */ Y [k] = 0.0 ; for ( ; top < n ; top++) { i = Pattern [top] ; /* Pattern [top:n-1] is pattern of L(:,k) */ yi = Y [i] ; /* get and clear Y(i) */ Y [i] = 0.0 ; p2 = Lp [i] + Lnz [i] ; for (p = Lp [i] ; p < p2 ; p++) { Y [Li [p]] -= Lx [p] * yi ; } l_ki = yi / D [i] ; /* the nonzero entry L(k,i) */ D [k] -= l_ki * yi ; Li [p] = k ; /* store L(k,i) in column form of L */ Lx [p] = l_ki ; Lnz [i]++ ; /* increment count of nonzeros in col i */ } if (D [k] == 0.0) return (k) ; /* failure, D(k,k) is zero */ } return (n) ; /* success, diagonal of D is all nonzero */ } \end{verbatim} } \end{figure} After the matrix is factorized, the {\tt ldl\_lsolve}, {\tt ldl\_dsolve}, and {\tt ldl\_ltsolve} routines shown in Figure~\ref{ldlsolve} are provided to solve $\m{Lx}=\m{b}$, $\m{Dx}=\m{b}$, and $\m{L}\tr\m{x}=\m{b}$, respectively. Together, they solve $\m{Ax}=\m{b}$, and consist of only 10 lines of executable code. If a fill-reducing permutation is used, {\tt ldl\_perm} and {\tt ldl\_permt} must be used to permute $\m{b}$ and $\m{x}$ accordingly. \begin{figure} \caption{Solve routines} \label{ldlsolve} {\scriptsize \begin{verbatim} void ldl_lsolve ( int n, /* L is n-by-n, where n >= 0 */ double X [ ], /* size n. right-hand-side on input, soln. on output */ int Lp [ ], /* input of size n+1, not modified */ int Li [ ], /* input of size lnz=Lp[n], not modified */ double Lx [ ] /* input of size lnz=Lp[n], not modified */ ) { int j, p, p2 ; for (j = 0 ; j < n ; j++) { p2 = Lp [j+1] ; for (p = Lp [j] ; p < p2 ; p++) { X [Li [p]] -= Lx [p] * X [j] ; } } } void ldl_dsolve ( int n, /* D is n-by-n, where n >= 0 */ double X [ ], /* size n. right-hand-side on input, soln. on output */ double D [ ] /* input of size n, not modified */ ) { int j ; for (j = 0 ; j < n ; j++) { X [j] /= D [j] ; } } void ldl_ltsolve ( int n, /* L is n-by-n, where n >= 0 */ double X [ ], /* size n. right-hand-side on input, soln. on output */ int Lp [ ], /* input of size n+1, not modified */ int Li [ ], /* input of size lnz=Lp[n], not modified */ double Lx [ ] /* input of size lnz=Lp[n], not modified */ ) { int j, p, p2 ; for (j = n-1 ; j >= 0 ; j--) { p2 = Lp [j+1] ; for (p = Lp [j] ; p < p2 ; p++) { X [j] -= Lx [p] * X [Li [p]] ; } } } \end{verbatim} } \end{figure} In addition to appearing as a Collected Algorithm of the ACM \cite{Davis05}, {\tt LDL} is available at http://www.cise.ufl.edu/research/sparse. %------------------------------------------------------------------------------- \section{Using LDL in MATLAB} \label{MATLAB} %------------------------------------------------------------------------------- The simplest way to use {\tt LDL} is within MATLAB. Once the {\tt ldlsparse} mexFunction is compiled and installed, the MATLAB statement {\tt [L, D, Parent, fl] = ldlsparse (A)} returns the sparse factorization {\tt A = (L+I)*D*(L+I)'}, where {\tt L} is lower triangular, {\tt D} is a diagonal matrix, and {\tt I} is the {\tt n}-by-{\tt n} identity matrix ({\tt ldlsparse} does not return the unit diagonal of {\tt L}). The elimination tree is returned in {\tt Parent}. If no zero on the diagonal of {\tt D} is encountered, {\tt fl} is the floating-point operation count. Otherwise, {\tt D(-fl,-fl)} is the first zero entry encountered. Let {\tt d=-fl}. The function returns the factorization of {\tt A (1:d,1:d)}, where rows {\tt d+1} to {\tt n} of {\tt L} and {\tt D} are all zero. If a sparsity preserving permutation {\tt P} is passed, {\tt [L, D, Parent, fl] = ldlsparse (A,P)} operates on {\tt A(P,P)} without forming it explicitly. The statement {\tt x = ldlsparse (A, [ ], b)} is roughly equivalent to {\tt x = A}$\backslash${\tt b}, when {\tt A} is sparse, real, and symmetric. The $\m{LDL}\tr$ factorization of {\tt A} is performed. If {\tt P} is provided, {\tt x = ldlsparse (A, P, b)} still performs {\tt x = A}$\backslash${\tt b}, except that {\tt A(P,P)} is factorized instead. %------------------------------------------------------------------------------- \section{Using LDL in a C program} \label{C} %------------------------------------------------------------------------------- The C-callable {\tt LDL} library consists of nine user-callable routines and one include file. \begin{itemize} \item {\tt ldl\_symbolic}: given the nonzero pattern of a sparse symmetric matrix $\m{A}$ and an optional permutation $\m{P}$, analyzes either $\m{A}$ or $\m{PAP}\tr$, and returns the elimination tree, the number of nonzeros in each column of $\m{L}$, and the {\tt Lp} array for the sparse matrix data structure for $\m{L}$. Duplicate entries are allowed in the columns of $\m{A}$, and the row indices in each column need not be sorted. Providing a sparsity-preserving ordering is critical for obtaining good performance. A minimum degree ordering (such as AMD \cite{AmestoyDavisDuff96,AmestoyDavisDuff03}) or a graph-partitioning based ordering are appropriate. \item {\tt ldl\_numeric}: given {\tt Lp} and the elimination tree computed by {\tt ldl\_symbolic}, and an optional permutation $\m{P}$, returns the numerical factorization of $\m{A}$ or $\m{PAP}\tr$. Duplicate entries are allowed in the columns of $\m{A}$ (any duplicate entries are summed), and the row indices in each column need not be sorted. The data structure for $\m{L}$ is the same as $\m{A}$, except that no duplicates appear, and each column has sorted row indices. \item {\tt ldl\_lsolve}: given the factor $\m{L}$ computed by {\tt ldl\_numeric}, solves the linear system $\m{Lx}=\m{b}$, where $\m{x}$ and $\m{b}$ are full $n$-by-1 vectors. \item {\tt ldl\_dsolve}: given the factor $\m{D}$ computed by {\tt ldl\_numeric}, solves the linear system $\m{Dx}=\m{b}$. \item {\tt ldl\_ltsolve}: given the factor $\m{L}$ computed by {\tt ldl\_numeric}, solves the linear system $\m{L}\tr\m{x}=\m{b}$. \item {\tt ldl\_perm}: given a vector $\m{b}$ and a permutation $\m{P}$, returns $\m{x}=\m{Pb}$. \item {\tt ldl\_permt}: given a vector $\m{b}$ and a permutation $\m{P}$, returns $\m{x}=\m{P}\tr\m{b}$. \item {\tt ldl\_valid\_perm}: Except for checking if the diagonal of $\m{D}$ is zero, none of the above routines check their inputs for errors. This routine checks the validity of a permutation $\m{P}$. \item {\tt ldl\_valid\_matrix}: checks if a matrix $\m{A}$ is valid as input to {\tt ldl\_symbolic} and {\tt ldl\_numeric}. \end{itemize} Note that the primary input to the {\tt ldl\_symbolic} and {\tt ldl\_numeric} is the sparse matrix $\m{A}$. It is provided in column-oriented form, and only the upper triangular part is accessed. This is slightly different than the primary output: the matrix $\m{L}$, which is lower triangular in column-oriented form. If you wish to factorize a symmetric matrix $\m{A}$ for which only the lower triangular part is supplied, you would need to transpose $\m{A}$ before passing it {\tt ldl\_symbolic} and {\tt ldl\_numeric}. An additional set of routines is available for use in a 64-bit environment. Each routine name changes uniformly; {\tt ldl\_symbolic} becomes {\tt ldl\_l\_symbolic}, and each {\tt int} parameter becomes type {\tt UF\_long}. The {\tt UF\_long} type is {\tt long}, except for Microsoft Windows 64, where it becomes {\tt \_\_int64}. \begin{figure} \caption{Example of use} \label{ldlsimple} {\scriptsize \begin{verbatim} #include #include "ldl.h" #define N 10 /* A is 10-by-10 */ #define ANZ 19 /* # of nonzeros on diagonal and upper triangular part of A */ #define LNZ 13 /* # of nonzeros below the diagonal of L */ int main (void) { /* only the upper triangular part of A is required */ int Ap [N+1] = {0, 1, 2, 3, 4, 6, 7, 9, 11, 15, ANZ}, Ai [ANZ] = {0, 1, 2, 3, 1,4, 5, 4,6, 4,7, 0,4,7,8, 1,4,6,9 } ; double Ax [ANZ] = {1.7, 1., 1.5, 1.1, .02,2.6, 1.2, .16,1.3, .09,1.6, .13,.52,.11,1.4, .01,.53,.56,3.1}, b [N] = {.287, .22, .45, .44, 2.486, .72, 1.55, 1.424, 1.621, 3.759}; double Lx [LNZ], D [N], Y [N] ; int Li [LNZ], Lp [N+1], Parent [N], Lnz [N], Flag [N], Pattern [N], d, i ; /* factorize A into LDL' (P and Pinv not used) */ ldl_symbolic (N, Ap, Ai, Lp, Parent, Lnz, Flag, NULL, NULL) ; printf ("Nonzeros in L, excluding diagonal: %d\n", Lp [N]) ; d = ldl_numeric (N, Ap, Ai, Ax, Lp, Parent, Lnz, Li, Lx, D, Y, Pattern, Flag, NULL, NULL) ; if (d == N) { /* solve Ax=b, overwriting b with the solution x */ ldl_lsolve (N, b, Lp, Li, Lx) ; ldl_dsolve (N, b, D) ; ldl_ltsolve (N, b, Lp, Li, Lx) ; for (i = 0 ; i < N ; i++) printf ("x [%d] = %g\n", i, b [i]) ; } else { printf ("ldl_numeric failed, D (%d,%d) is zero\n", d, d) ; } return (0) ; } \end{verbatim} } \end{figure} The program in Figure~\ref{ldlsimple} illustrates the basic usage of the {\tt LDL} routines. It analyzes and factorizes the sparse symmetric positive-definite matrix {\small \[ \m{A} = \left[ \begin{array}{cccccccccc} 1.7 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & .13 & 0 \\ 0 & 1. & 0 & 0 & .02 & 0 & 0 & 0 & 0 & .01 \\ 0 & 0 & 1.5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1.1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & .02 & 0 & 0 & 2.6 & 0 & .16 & .09 & .52 & .53 \\ 0 & 0 & 0 & 0 & 0 & 1.2 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & .16 & 0 & 1.3 & 0 & 0 & .56 \\ 0 & 0 & 0 & 0 & .09 & 0 & 0 & 1.6 & .11 & 0 \\ .13 & 0 & 0 & 0 & .52 & 0 & 0 & .11 & 1.4 & 0 \\ 0 & .01 & 0 & 0 & .53 & 0 & .56 & 0 & 0 & 3.1 \\ \end{array} \right] \] } and then solves a system $\m{Ax}=\m{b}$ whose true solution is $x_i = i/10$. Note that {\tt Li} and {\tt Lx} are statically allocated. Normally they would be allocated after their size, {\tt Lp[n]}, is determined by {\tt ldl\_symbolic}. More example programs are included with the {\tt LDL} package. \section{Acknowledgments} I would like to thank Pete Stewart for his comments on an earlier draft of this software and its accompanying paper. \newpage \bibliographystyle{plain} \bibliography{ldl} \end{document} SuiteSparse/LDL/Doc/ChangeLog0000644001170100242450000000174710620620364014651 0ustar davisfacMay 31, 2007: version 2.0.0 * C-callable 64-bit version added * ported to 64-bit MATLAB * subdirectories added (Source/, Include/, Lib/, Demo/, Doc/, MATLAB/) Dec 12, 2006: version 1.3.4 * minor MATLAB cleanup Sept 11, 2006: version 1.3.1 * The ldl m-file renamed to ldlsparse, to avoid name conflict with the new MATLAB ldl function (in MATLAB 7.3). Apr 30, 2006: version 1.3 * requires AMD v2.0. ldlmain.c demo program modified, since AMD can now handle jumbled matrices. Minor change to Makefile. Aug 30, 2005: * Makefile changed to use ../UFconfig/UFconfig.mk. License changed to GNU LGPL. July 4, 2005: * user guide added. Since no changes to the code were made, the version number (1.1) and code release date (Apr 22, 2005) were left unchanged. Apr. 22, 2005: LDL v1.1 released. * No real changes were made. The code was revised so that each routine fits on a single page in the documentation. Dec 31, 2003: LDL v1.0 released. SuiteSparse/LDL/Doc/lesser.txt0000644001170100242450000006350010301451045015122 0ustar davisfac GNU LESSER GENERAL PUBLIC LICENSE Version 2.1, February 1999 Copyright (C) 1991, 1999 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. [This is the first released version of the Lesser GPL. It also counts as the successor of the GNU Library Public License, version 2, hence the version number 2.1.] Preamble The licenses for most software are designed to take away your freedom to share and change it. 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SuiteSparse/LDL/Lib/0000755001170100242450000000000010711435723013073 5ustar davisfacSuiteSparse/LDL/Lib/Makefile0000644001170100242450000000136110617137600014532 0ustar davisfac#------------------------------------------------------------------------------- # Makefile for the LDL library #------------------------------------------------------------------------------- default: all include ../../UFconfig/UFconfig.mk I = -I../../UFconfig -I../Include C = $(CC) $(CFLAGS) $(I) all: libldl.a #------------------------------------------------------------------------------- # the ldl library: #------------------------------------------------------------------------------- libldl.a: ../Source/ldl.c ../Include/ldl.h $(C) -c ../Source/ldl.c -o ldl.o $(C) -DLDL_LONG -c ../Source/ldl.c -o ldll.o $(AR) libldl.a ldl.o ldll.o - $(RANLIB) libldl.a distclean: purge purge: clean - $(RM) libldl.a clean: - $(RM) $(CLEAN) SuiteSparse/LDL/Demo/0000755001170100242450000000000010711435723013251 5ustar davisfacSuiteSparse/LDL/Demo/Makefile0000644001170100242450000000465610617137440014724 0ustar davisfac#------------------------------------------------------------------------------- # LDL Demo Makefile #------------------------------------------------------------------------------- default: all include ../../UFconfig/UFconfig.mk I = -I../../UFconfig -I../Include C = $(CC) $(CFLAGS) $(I) all: ldlsimple ldllsimple ldlmain ldllmain ldlamd ldllamd library: ( cd ../../AMD ; $(MAKE) library ) ( cd ../Lib ; $(MAKE) ) #------------------------------------------------------------------------------- # stand-alone C programs: #------------------------------------------------------------------------------- ldlmain: ldlmain.c library $(C) ldlmain.c ../Lib/libldl.a -o ldlmain -lm - ./ldlmain > my_ldlmain.out - diff ldlmain.out my_ldlmain.out ldllmain: ldlmain.c library $(C) -DLDL_LONG ldlmain.c ../Lib/libldl.a -o ldllmain -lm - ./ldllmain > my_ldllmain.out - diff ldlmain.out my_ldllmain.out ldlsimple: ldlsimple.c library $(C) ldlsimple.c ../Lib/libldl.a -o ldlsimple -lm - ./ldlsimple > my_ldlsimple.out - diff ldlsimple.out my_ldlsimple.out ldllsimple: ldlsimple.c library $(C) $(I) -DLDL_LONG ldlsimple.c ../Lib/libldl.a -o ldllsimple -lm - ./ldllsimple > my_ldllsimple.out - diff ldlsimple.out my_ldllsimple.out ldlamd: ldlmain.c library - $(C) -I../../AMD/Include -DUSE_AMD \ ldlmain.c ../../AMD/Lib/libamd.a ../Lib/libldl.a -o ldlamd -lm - ./ldlamd > my_ldlamd.out - diff ldlamd.out my_ldlamd.out ldllamd: ldlmain.c library - $(C) -DLDL_LONG $(I) -I../../AMD/Include -DUSE_AMD \ ldlmain.c ../../AMD/Lib/libamd.a ../Lib/libldl.a -o ldllamd -lm - ./ldllamd > my_ldllamd.out - diff ldllamd.out my_ldllamd.out run: - ./ldlsimple > my_ldlsimple.out - diff ldlsimple.out my_ldlsimple.out - ./ldllsimple > my_ldllsimple.out - diff ldlsimple.out my_ldllsimple.out - ./ldlmain > my_ldlmain.out - diff ldlmain.out my_ldlmain.out - ./ldllmain > my_ldllmain.out - diff ldlmain.out my_ldllmain.out - ./ldlamd > my_ldlamd.out - diff ldlamd.out my_ldlamd.out - ./ldllamd > my_ldllamd.out - diff ldllamd.out my_ldllamd.out #------------------------------------------------------------------------------- # clean-up: #------------------------------------------------------------------------------- distclean: purge purge: clean - $(RM) ldlmain ldllmain ldlsimple ldllsimple ldlamd ldllamd - $(RM) my_ldlmain.out my_ldlamd.out my_ldlsimple.out my_ldllamd.out - $(RM) my_ldllsimple.out my_ldllmain.out clean: - $(RM) $(CLEAN) SuiteSparse/LDL/Demo/ldlsimple.out0000644001170100242450000000023410711433076015765 0ustar davisfacNonzeros in L, excluding diagonal: 13 x [0] = 0.1 x [1] = 0.2 x [2] = 0.3 x [3] = 0.4 x [4] = 0.5 x [5] = 0.6 x [6] = 0.7 x [7] = 0.8 x [8] = 0.9 x [9] = 1 SuiteSparse/LDL/Demo/ldlsimple.c0000644001170100242450000000571010616417061015404 0ustar davisfac/* ========================================================================== */ /* === ldlsimple.c: a simple LDL main program ============================== */ /* ========================================================================== */ /* LDLSIMPLE: this is a very simple main program that illustrates the basic * usage of the LDL routines. The output of this program is in ldlsimple.out. * This program factorizes the matrix * * A =[ ... * 1.7 0 0 0 0 0 0 0 .13 0 * 0 1. 0 0 .02 0 0 0 0 .01 * 0 0 1.5 0 0 0 0 0 0 0 * 0 0 0 1.1 0 0 0 0 0 0 * 0 .02 0 0 2.6 0 .16 .09 .52 .53 * 0 0 0 0 0 1.2 0 0 0 0 * 0 0 0 0 .16 0 1.3 0 0 .56 * 0 0 0 0 .09 0 0 1.6 .11 0 * .13 0 0 0 .52 0 0 .11 1.4 0 * 0 .01 0 0 .53 0 .56 0 0 3.1 ] ; * * and then solves a system Ax=b whose true solution is * x = [.1 .2 .3 .4 .5 .6 .7 .8 .9 1]' ; * * Note that Li and Lx are statically allocated, with length 13. This is just * enough to hold the factor L, but normally this size is not known until after * ldl_symbolic has analyzed the matrix. The size of Li and Lx must be greater * than or equal to lnz = Lp [N], which is 13 for this matrix L. * * LDL Version 1.3, Copyright (c) 2006 by Timothy A Davis, * University of Florida. All Rights Reserved. See README for the License. */ #include #include "ldl.h" #define N 10 /* A is 10-by-10 */ #define ANZ 19 /* # of nonzeros on diagonal and upper triangular part of A */ #define LNZ 13 /* # of nonzeros below the diagonal of L */ int main (void) { /* only the upper triangular part of A is required */ int Ap [N+1] = {0, 1, 2, 3, 4, 6, 7, 9, 11, 15, ANZ}, Ai [ANZ] = {0, 1, 2, 3, 1,4, 5, 4,6, 4,7, 0,4,7,8, 1,4,6,9 } ; double Ax [ANZ] = {1.7, 1., 1.5, 1.1, .02,2.6, 1.2, .16,1.3, .09,1.6, .13,.52,.11,1.4, .01,.53,.56,3.1}, b [N] = {.287, .22, .45, .44, 2.486, .72, 1.55, 1.424, 1.621, 3.759}; double Lx [LNZ], D [N], Y [N] ; int Li [LNZ], Lp [N+1], Parent [N], Lnz [N], Flag [N], Pattern [N], d, i ; /* factorize A into LDL' (P and Pinv not used) */ ldl_symbolic (N, Ap, Ai, Lp, Parent, Lnz, Flag, NULL, NULL) ; printf ("Nonzeros in L, excluding diagonal: %d\n", Lp [N]) ; d = ldl_numeric (N, Ap, Ai, Ax, Lp, Parent, Lnz, Li, Lx, D, Y, Pattern, Flag, NULL, NULL) ; if (d == N) { /* solve Ax=b, overwriting b with the solution x */ ldl_lsolve (N, b, Lp, Li, Lx) ; ldl_dsolve (N, b, D) ; ldl_ltsolve (N, b, Lp, Li, Lx) ; for (i = 0 ; i < N ; i++) printf ("x [%d] = %g\n", i, b [i]) ; } else { printf ("ldl_numeric failed, D (%d,%d) is zero\n", d, d) ; } return (0) ; } SuiteSparse/LDL/Demo/ldllsimple.c0000644001170100242450000000600210616417067015561 0ustar davisfac/* ========================================================================== */ /* === ldllsimple.c: a simple LDL main program (long integer version) ====== */ /* ========================================================================== */ /* LDLSIMPLE: this is a very simple main program that illustrates the basic * usage of the LDL routines. The output of this program is in ldlsimple.out. * This program factorizes the matrix * * A =[ ... * 1.7 0 0 0 0 0 0 0 .13 0 * 0 1. 0 0 .02 0 0 0 0 .01 * 0 0 1.5 0 0 0 0 0 0 0 * 0 0 0 1.1 0 0 0 0 0 0 * 0 .02 0 0 2.6 0 .16 .09 .52 .53 * 0 0 0 0 0 1.2 0 0 0 0 * 0 0 0 0 .16 0 1.3 0 0 .56 * 0 0 0 0 .09 0 0 1.6 .11 0 * .13 0 0 0 .52 0 0 .11 1.4 0 * 0 .01 0 0 .53 0 .56 0 0 3.1 ] ; * * and then solves a system Ax=b whose true solution is * x = [.1 .2 .3 .4 .5 .6 .7 .8 .9 1]' ; * * Note that Li and Lx are statically allocated, with length 13. This is just * enough to hold the factor L, but normally this size is not known until after * ldl_symbolic has analyzed the matrix. The size of Li and Lx must be greater * than or equal to lnz = Lp [N], which is 13 for this matrix L. * * LDL Version 1.3, Copyright (c) 2006 by Timothy A Davis, * University of Florida. All Rights Reserved. See README for the License. */ #ifndef LDL_LONG #define LDL_LONG #endif #include #include "ldl.h" #define N 10 /* A is 10-by-10 */ #define ANZ 19 /* # of nonzeros on diagonal and upper triangular part of A */ #define LNZ 13 /* # of nonzeros below the diagonal of L */ int main (void) { /* only the upper triangular part of A is required */ UF_long Ap[N+1] = {0, 1, 2, 3, 4, 6, 7, 9, 11, 15, ANZ}, Ai [ANZ] = {0, 1, 2, 3, 1,4, 5, 4,6, 4,7, 0,4,7,8, 1,4,6,9 } ; double Ax [ANZ] = {1.7, 1., 1.5, 1.1, .02,2.6, 1.2, .16,1.3, .09,1.6, .13,.52,.11,1.4, .01,.53,.56,3.1}, b [N] = {.287, .22, .45, .44, 2.486, .72, 1.55, 1.424, 1.621, 3.759}; double Lx [LNZ], D [N], Y [N] ; UF_long Li [LNZ], Lp [N+1], Parent [N], Lnz [N], Flag [N], Pattern [N], d, i ; /* factorize A into LDL' (P and Pinv not used) */ ldl_l_symbolic (N, Ap, Ai, Lp, Parent, Lnz, Flag, NULL, NULL) ; printf ("Nonzeros in L, excluding diagonal: %d\n", Lp [N]) ; d = ldl_l_numeric (N, Ap, Ai, Ax, Lp, Parent, Lnz, Li, Lx, D, Y, Pattern, Flag, NULL, NULL) ; if (d == N) { /* solve Ax=b, overwriting b with the solution x */ ldl_l_lsolve (N, b, Lp, Li, Lx) ; ldl_l_dsolve (N, b, D) ; ldl_l_ltsolve (N, b, Lp, Li, Lx) ; for (i = 0 ; i < N ; i++) printf ("x [%d] = %g\n", i, b [i]) ; } else { printf ("ldl_l_numeric failed, D (%d,%d) is zero\n", d, d) ; } return (0) ; } SuiteSparse/LDL/Demo/ldlmain.out0000644001170100242450000002446210711433076015431 0ustar davisfac -------------------------------------------------------- Input matrix: name: Dense/0 n: 0 entries: 0 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 -------------------------------------------------------- Input matrix: name: Dense/0 n: 0 entries: 0 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 -------------------------------------------------------- Input matrix: name: Dense/1 n: 1 entries: 1 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 -------------------------------------------------------- Input matrix: name: Dense/1 n: 1 entries: 2 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 8.32667e-17 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 8.32667e-17 -------------------------------------------------------- Input matrix: name: Dense/2 n: 2 entries: 4 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 5.55112e-17 Factorize A=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 5.55112e-17 -------------------------------------------------------- Input matrix: name: Dense/2 n: 2 entries: 5 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 1.11022e-16 Factorize A=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 1.11022e-16 -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.11022e-16 Factorize A=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.11022e-16 -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 11 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.38778e-16 Factorize A=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.38778e-16 -------------------------------------------------------- Input matrix: name: HB/can_24 n: 24 entries: 160 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 96 Flop count: 632 Ax=b not solved since D(1,1) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 146 Flop count: 1360 Ax=b not solved since D(5,5) is zero. -------------------------------------------------------- Input matrix: name: HB/can_24 n: 24 entries: 188 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 96 Flop count: 632 Ax=b not solved since D(1,1) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 146 Flop count: 1360 Ax=b not solved since D(5,5) is zero. -------------------------------------------------------- Input matrix: name: FIDAP/ex5 n: 27 entries: 279 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 126 Flop count: 954 relative maxnorm of residual: 2.59625e-10 Factorize A=LDL' and solve Ax=b Nz in L: 276 Flop count: 4206 relative maxnorm of residual: 2.72848e-10 -------------------------------------------------------- Input matrix: name: FIDAP/ex5 n: 27 entries: 325 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 126 Flop count: 954 relative maxnorm of residual: 3.27418e-10 Factorize A=LDL' and solve Ax=b Nz in L: 276 Flop count: 4206 relative maxnorm of residual: 2.32376e-10 -------------------------------------------------------- Input matrix: name: HB/bcsstk01 n: 48 entries: 400 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 441 Flop count: 5961 relative maxnorm of residual: 2.38712e-13 Factorize A=LDL' and solve Ax=b Nz in L: 829 Flop count: 20103 relative maxnorm of residual: 2.27374e-13 -------------------------------------------------------- Input matrix: name: HB/bcsstk01 n: 48 entries: 472 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 441 Flop count: 5961 relative maxnorm of residual: 2.27374e-13 Factorize A=LDL' and solve Ax=b Nz in L: 829 Flop count: 20103 relative maxnorm of residual: 3.83693e-13 -------------------------------------------------------- Input matrix: name: HB/bcsstm01 n: 48 entries: 24 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. -------------------------------------------------------- Input matrix: name: HB/bcsstm01 n: 48 entries: 26 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. -------------------------------------------------------- Input matrix: name: Pothen/mesh1e1 n: 48 entries: 306 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 288 Flop count: 2630 relative maxnorm of residual: 5.96745e-16 Factorize A=LDL' and solve Ax=b Nz in L: 511 Flop count: 7383 relative maxnorm of residual: 6.93889e-16 -------------------------------------------------------- Input matrix: name: Pothen/mesh1e1 n: 48 entries: 359 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 288 Flop count: 2630 relative maxnorm of residual: 5.55112e-16 Factorize A=LDL' and solve Ax=b Nz in L: 511 Flop count: 7383 relative maxnorm of residual: 5.55112e-16 -------------------------------------------------------- Input matrix: name: Bai/bfwb62 n: 62 entries: 342 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 226 Flop count: 1472 relative maxnorm of residual: 5.55112e-16 Factorize A=LDL' and solve Ax=b Nz in L: 662 Flop count: 11350 relative maxnorm of residual: 1.11022e-15 -------------------------------------------------------- Input matrix: name: Bai/bfwb62 n: 62 entries: 407 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 226 Flop count: 1472 relative maxnorm of residual: 5.68434e-14 Factorize A=LDL' and solve Ax=b Nz in L: 662 Flop count: 11350 relative maxnorm of residual: 2.15827e-12 -------------------------------------------------------- Input matrix: name: HB/bcsstk02 n: 66 entries: 4356 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 7.50219e-13 Factorize A=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 7.50219e-13 -------------------------------------------------------- Input matrix: name: HB/bcsstk02 n: 66 entries: 5175 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 8.59759e-13 Factorize A=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 8.59759e-13 -------------------------------------------------------- Input matrix: name: HB/bcsstm02 n: 66 entries: 66 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 -------------------------------------------------------- Input matrix: name: HB/bcsstm02 n: 66 entries: 72 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 -------------------------------------------------------- Input matrix: name: Dense/0 n: 0 entries: 0 (invalid matrix, Ap [0] = 99) -------------------------------------------------------- ldlmain: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/2 n: 2 entries: 4 (invalid perm, P[1]=99) -------------------------------------------------------- ldlmain: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 (invalid perm) -------------------------------------------------------- ldlmain: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ap) -------------------------------------------------------- ldlmain: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ai) -------------------------------------------------------- ldlmain: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ai) -------------------------------------------------------- ldlmain: invalid matrix and/or permutation Largest residual during all tests: 3.27418e-10 ldlmain: all tests passed SuiteSparse/LDL/Demo/ldlamd.out0000644001170100242450000014043710711433076015247 0ustar davisfac -------------------------------------------------------- Input matrix: name: Dense/0 n: 0 entries: 0 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 -------------------------------------------------------- Input matrix: name: Dense/0 n: 0 entries: 0 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 -------------------------------------------------------- Input matrix: name: Dense/1 n: 1 entries: 1 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 1 nz, number of nonzeros in A: 1 symmetry of A: 1.0000 number of nonzeros on diagonal: 1 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 36 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 1 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 1 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 -------------------------------------------------------- Input matrix: name: Dense/1 n: 1 entries: 2 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 1 nz, number of nonzeros in A: 1 symmetry of A: 1.0000 number of nonzeros on diagonal: 1 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 52 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 1 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 1 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 8.32667e-17 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 8.32667e-17 -------------------------------------------------------- Input matrix: name: Dense/2 n: 2 entries: 4 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 2 nz, number of nonzeros in A: 4 symmetry of A: 1.0000 number of nonzeros on diagonal: 2 nonzeros in pattern of A+A' (excl. diagonal): 2 # dense rows/columns of A+A': 0 memory used, in bytes: 80 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 1 nonzeros in L (including diagonal): 3 # divide operations for LDL' or LU: 1 # multiply-subtract operations for LDL': 1 # multiply-subtract operations for LU: 1 max nz. in any column of L (incl. diagonal): 2 chol flop count for real A, sqrt counted as 1 flop: 5 LDL' flop count for real A: 3 LDL' flop count for complex A: 17 LU flop count for real A (with no pivoting): 3 LU flop count for complex A (with no pivoting): 17 Factorize PAP'=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 5.55112e-17 Factorize A=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 5.55112e-17 -------------------------------------------------------- Input matrix: name: Dense/2 n: 2 entries: 5 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 2 nz, number of nonzeros in A: 4 symmetry of A: 1.0000 number of nonzeros on diagonal: 2 nonzeros in pattern of A+A' (excl. diagonal): 2 # dense rows/columns of A+A': 0 memory used, in bytes: 112 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 1 nonzeros in L (including diagonal): 3 # divide operations for LDL' or LU: 1 # multiply-subtract operations for LDL': 1 # multiply-subtract operations for LU: 1 max nz. in any column of L (incl. diagonal): 2 chol flop count for real A, sqrt counted as 1 flop: 5 LDL' flop count for real A: 3 LDL' flop count for complex A: 17 LU flop count for real A (with no pivoting): 3 LU flop count for complex A (with no pivoting): 17 Factorize PAP'=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 1.11022e-16 Factorize A=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 1.11022e-16 -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 3 nz, number of nonzeros in A: 9 symmetry of A: 1.0000 number of nonzeros on diagonal: 3 nonzeros in pattern of A+A' (excl. diagonal): 6 # dense rows/columns of A+A': 0 memory used, in bytes: 136 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 3 nonzeros in L (including diagonal): 6 # divide operations for LDL' or LU: 3 # multiply-subtract operations for LDL': 4 # multiply-subtract operations for LU: 5 max nz. in any column of L (incl. diagonal): 3 chol flop count for real A, sqrt counted as 1 flop: 14 LDL' flop count for real A: 11 LDL' flop count for complex A: 59 LU flop count for real A (with no pivoting): 13 LU flop count for complex A (with no pivoting): 67 Factorize PAP'=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.11022e-16 Factorize A=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.11022e-16 -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 11 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 3 nz, number of nonzeros in A: 9 symmetry of A: 1.0000 number of nonzeros on diagonal: 3 nonzeros in pattern of A+A' (excl. diagonal): 6 # dense rows/columns of A+A': 0 memory used, in bytes: 196 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 3 nonzeros in L (including diagonal): 6 # divide operations for LDL' or LU: 3 # multiply-subtract operations for LDL': 4 # multiply-subtract operations for LU: 5 max nz. in any column of L (incl. diagonal): 3 chol flop count for real A, sqrt counted as 1 flop: 14 LDL' flop count for real A: 11 LDL' flop count for complex A: 59 LU flop count for real A (with no pivoting): 13 LU flop count for complex A (with no pivoting): 67 Factorize PAP'=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.38778e-16 Factorize A=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.38778e-16 -------------------------------------------------------- Input matrix: name: HB/can_24 n: 24 entries: 160 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 24 nz, number of nonzeros in A: 160 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 136 # dense rows/columns of A+A': 0 memory used, in bytes: 1516 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 97 nonzeros in L (including diagonal): 121 # divide operations for LDL' or LU: 97 # multiply-subtract operations for LDL': 275 # multiply-subtract operations for LU: 453 max nz. in any column of L (incl. diagonal): 8 chol flop count for real A, sqrt counted as 1 flop: 671 LDL' flop count for real A: 647 LDL' flop count for complex A: 3073 LU flop count for real A (with no pivoting): 1003 LU flop count for complex A (with no pivoting): 4497 Factorize PAP'=LDL' and solve Ax=b Nz in L: 96 Flop count: 632 Ax=b not solved since D(1,1) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 146 Flop count: 1360 Ax=b not solved since D(5,5) is zero. -------------------------------------------------------- Input matrix: name: HB/can_24 n: 24 entries: 188 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 24 nz, number of nonzeros in A: 160 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 136 # dense rows/columns of A+A': 0 memory used, in bytes: 2368 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 97 nonzeros in L (including diagonal): 121 # divide operations for LDL' or LU: 97 # multiply-subtract operations for LDL': 275 # multiply-subtract operations for LU: 453 max nz. in any column of L (incl. diagonal): 8 chol flop count for real A, sqrt counted as 1 flop: 671 LDL' flop count for real A: 647 LDL' flop count for complex A: 3073 LU flop count for real A (with no pivoting): 1003 LU flop count for complex A (with no pivoting): 4497 Factorize PAP'=LDL' and solve Ax=b Nz in L: 96 Flop count: 632 Ax=b not solved since D(1,1) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 146 Flop count: 1360 Ax=b not solved since D(5,5) is zero. -------------------------------------------------------- Input matrix: name: FIDAP/ex5 n: 27 entries: 279 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 27 nz, number of nonzeros in A: 279 symmetry of A: 1.0000 number of nonzeros on diagonal: 27 nonzeros in pattern of A+A' (excl. diagonal): 252 # dense rows/columns of A+A': 0 memory used, in bytes: 2180 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 126 nonzeros in L (including diagonal): 153 # divide operations for LDL' or LU: 126 # multiply-subtract operations for LDL': 414 # multiply-subtract operations for LU: 702 max nz. in any column of L (incl. diagonal): 9 chol flop count for real A, sqrt counted as 1 flop: 981 LDL' flop count for real A: 954 LDL' flop count for complex A: 4446 LU flop count for real A (with no pivoting): 1530 LU flop count for complex A (with no pivoting): 6750 Factorize PAP'=LDL' and solve Ax=b Nz in L: 126 Flop count: 954 relative maxnorm of residual: 2.59625e-10 Factorize A=LDL' and solve Ax=b Nz in L: 276 Flop count: 4206 relative maxnorm of residual: 2.72848e-10 -------------------------------------------------------- Input matrix: name: FIDAP/ex5 n: 27 entries: 325 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 27 nz, number of nonzeros in A: 279 symmetry of A: 1.0000 number of nonzeros on diagonal: 27 nonzeros in pattern of A+A' (excl. diagonal): 252 # dense rows/columns of A+A': 0 memory used, in bytes: 3592 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 126 nonzeros in L (including diagonal): 153 # divide operations for LDL' or LU: 126 # multiply-subtract operations for LDL': 414 # multiply-subtract operations for LU: 702 max nz. in any column of L (incl. diagonal): 9 chol flop count for real A, sqrt counted as 1 flop: 981 LDL' flop count for real A: 954 LDL' flop count for complex A: 4446 LU flop count for real A (with no pivoting): 1530 LU flop count for complex A (with no pivoting): 6750 Factorize PAP'=LDL' and solve Ax=b Nz in L: 126 Flop count: 954 relative maxnorm of residual: 3.27418e-10 Factorize A=LDL' and solve Ax=b Nz in L: 276 Flop count: 4206 relative maxnorm of residual: 2.32376e-10 -------------------------------------------------------- Input matrix: name: HB/bcsstk01 n: 48 entries: 400 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 48 nz, number of nonzeros in A: 400 symmetry of A: 1.0000 number of nonzeros on diagonal: 48 nonzeros in pattern of A+A' (excl. diagonal): 352 # dense rows/columns of A+A': 0 memory used, in bytes: 3416 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 441 nonzeros in L (including diagonal): 489 # divide operations for LDL' or LU: 441 # multiply-subtract operations for LDL': 2760 # multiply-subtract operations for LU: 5079 max nz. in any column of L (incl. diagonal): 20 chol flop count for real A, sqrt counted as 1 flop: 6009 LDL' flop count for real A: 5961 LDL' flop count for complex A: 26049 LU flop count for real A (with no pivoting): 10599 LU flop count for complex A (with no pivoting): 44601 Factorize PAP'=LDL' and solve Ax=b Nz in L: 441 Flop count: 5961 relative maxnorm of residual: 2.38712e-13 Factorize A=LDL' and solve Ax=b Nz in L: 829 Flop count: 20103 relative maxnorm of residual: 2.27374e-13 -------------------------------------------------------- Input matrix: name: HB/bcsstk01 n: 48 entries: 472 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 48 nz, number of nonzeros in A: 400 symmetry of A: 1.0000 number of nonzeros on diagonal: 48 nonzeros in pattern of A+A' (excl. diagonal): 352 # dense rows/columns of A+A': 0 memory used, in bytes: 5500 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 441 nonzeros in L (including diagonal): 489 # divide operations for LDL' or LU: 441 # multiply-subtract operations for LDL': 2760 # multiply-subtract operations for LU: 5079 max nz. in any column of L (incl. diagonal): 20 chol flop count for real A, sqrt counted as 1 flop: 6009 LDL' flop count for real A: 5961 LDL' flop count for complex A: 26049 LU flop count for real A (with no pivoting): 10599 LU flop count for complex A (with no pivoting): 44601 Factorize PAP'=LDL' and solve Ax=b Nz in L: 441 Flop count: 5961 relative maxnorm of residual: 2.27374e-13 Factorize A=LDL' and solve Ax=b Nz in L: 829 Flop count: 20103 relative maxnorm of residual: 3.83693e-13 -------------------------------------------------------- Input matrix: name: HB/bcsstm01 n: 48 entries: 24 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 48 nz, number of nonzeros in A: 24 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 1728 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 48 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 48 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. -------------------------------------------------------- Input matrix: name: HB/bcsstm01 n: 48 entries: 26 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 48 nz, number of nonzeros in A: 24 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 2028 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 48 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 48 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. -------------------------------------------------------- Input matrix: name: Pothen/mesh1e1 n: 48 entries: 306 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 48 nz, number of nonzeros in A: 306 symmetry of A: 1.0000 number of nonzeros on diagonal: 48 nonzeros in pattern of A+A' (excl. diagonal): 258 # dense rows/columns of A+A': 0 memory used, in bytes: 2964 # of memory compactions: 1 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 288 nonzeros in L (including diagonal): 336 # divide operations for LDL' or LU: 288 # multiply-subtract operations for LDL': 1171 # multiply-subtract operations for LU: 2054 max nz. in any column of L (incl. diagonal): 13 chol flop count for real A, sqrt counted as 1 flop: 2678 LDL' flop count for real A: 2630 LDL' flop count for complex A: 11960 LU flop count for real A (with no pivoting): 4396 LU flop count for complex A (with no pivoting): 19024 Factorize PAP'=LDL' and solve Ax=b Nz in L: 288 Flop count: 2630 relative maxnorm of residual: 5.96745e-16 Factorize A=LDL' and solve Ax=b Nz in L: 511 Flop count: 7383 relative maxnorm of residual: 6.93889e-16 -------------------------------------------------------- Input matrix: name: Pothen/mesh1e1 n: 48 entries: 359 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 48 nz, number of nonzeros in A: 306 symmetry of A: 1.0000 number of nonzeros on diagonal: 48 nonzeros in pattern of A+A' (excl. diagonal): 258 # dense rows/columns of A+A': 0 memory used, in bytes: 4596 # of memory compactions: 1 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 288 nonzeros in L (including diagonal): 336 # divide operations for LDL' or LU: 288 # multiply-subtract operations for LDL': 1171 # multiply-subtract operations for LU: 2054 max nz. in any column of L (incl. diagonal): 13 chol flop count for real A, sqrt counted as 1 flop: 2678 LDL' flop count for real A: 2630 LDL' flop count for complex A: 11960 LU flop count for real A (with no pivoting): 4396 LU flop count for complex A (with no pivoting): 19024 Factorize PAP'=LDL' and solve Ax=b Nz in L: 288 Flop count: 2630 relative maxnorm of residual: 5.55112e-16 Factorize A=LDL' and solve Ax=b Nz in L: 511 Flop count: 7383 relative maxnorm of residual: 5.55112e-16 -------------------------------------------------------- Input matrix: name: Bai/bfwb62 n: 62 entries: 342 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 62 nz, number of nonzeros in A: 342 symmetry of A: 1.0000 number of nonzeros on diagonal: 62 nonzeros in pattern of A+A' (excl. diagonal): 280 # dense rows/columns of A+A': 0 memory used, in bytes: 3576 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 226 nonzeros in L (including diagonal): 288 # divide operations for LDL' or LU: 226 # multiply-subtract operations for LDL': 623 # multiply-subtract operations for LU: 1020 max nz. in any column of L (incl. diagonal): 9 chol flop count for real A, sqrt counted as 1 flop: 1534 LDL' flop count for real A: 1472 LDL' flop count for complex A: 7018 LU flop count for real A (with no pivoting): 2266 LU flop count for complex A (with no pivoting): 10194 Factorize PAP'=LDL' and solve Ax=b Nz in L: 226 Flop count: 1472 relative maxnorm of residual: 5.55112e-16 Factorize A=LDL' and solve Ax=b Nz in L: 662 Flop count: 11350 relative maxnorm of residual: 1.11022e-15 -------------------------------------------------------- Input matrix: name: Bai/bfwb62 n: 62 entries: 407 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 62 nz, number of nonzeros in A: 342 symmetry of A: 1.0000 number of nonzeros on diagonal: 62 nonzeros in pattern of A+A' (excl. diagonal): 280 # dense rows/columns of A+A': 0 memory used, in bytes: 5456 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 226 nonzeros in L (including diagonal): 288 # divide operations for LDL' or LU: 226 # multiply-subtract operations for LDL': 623 # multiply-subtract operations for LU: 1020 max nz. in any column of L (incl. diagonal): 9 chol flop count for real A, sqrt counted as 1 flop: 1534 LDL' flop count for real A: 1472 LDL' flop count for complex A: 7018 LU flop count for real A (with no pivoting): 2266 LU flop count for complex A (with no pivoting): 10194 Factorize PAP'=LDL' and solve Ax=b Nz in L: 226 Flop count: 1472 relative maxnorm of residual: 5.68434e-14 Factorize A=LDL' and solve Ax=b Nz in L: 662 Flop count: 11350 relative maxnorm of residual: 2.15827e-12 -------------------------------------------------------- Input matrix: name: HB/bcsstk02 n: 66 entries: 4356 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 66 nz, number of nonzeros in A: 4356 symmetry of A: 1.0000 number of nonzeros on diagonal: 66 nonzeros in pattern of A+A' (excl. diagonal): 4290 # dense rows/columns of A+A': 0 memory used, in bytes: 22968 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 2145 nonzeros in L (including diagonal): 2211 # divide operations for LDL' or LU: 2145 # multiply-subtract operations for LDL': 47905 # multiply-subtract operations for LU: 93665 max nz. in any column of L (incl. diagonal): 66 chol flop count for real A, sqrt counted as 1 flop: 98021 LDL' flop count for real A: 97955 LDL' flop count for complex A: 402545 LU flop count for real A (with no pivoting): 189475 LU flop count for complex A (with no pivoting): 768625 Factorize PAP'=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 7.50219e-13 Factorize A=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 7.50219e-13 -------------------------------------------------------- Input matrix: name: HB/bcsstk02 n: 66 entries: 5175 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 66 nz, number of nonzeros in A: 4356 symmetry of A: 1.0000 number of nonzeros on diagonal: 66 nonzeros in pattern of A+A' (excl. diagonal): 4290 # dense rows/columns of A+A': 0 memory used, in bytes: 43936 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 2145 nonzeros in L (including diagonal): 2211 # divide operations for LDL' or LU: 2145 # multiply-subtract operations for LDL': 47905 # multiply-subtract operations for LU: 93665 max nz. in any column of L (incl. diagonal): 66 chol flop count for real A, sqrt counted as 1 flop: 98021 LDL' flop count for real A: 97955 LDL' flop count for complex A: 402545 LU flop count for real A (with no pivoting): 189475 LU flop count for complex A (with no pivoting): 768625 Factorize PAP'=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 8.59759e-13 Factorize A=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 8.59759e-13 -------------------------------------------------------- Input matrix: name: HB/bcsstm02 n: 66 entries: 66 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 66 nz, number of nonzeros in A: 66 symmetry of A: 1.0000 number of nonzeros on diagonal: 66 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 2376 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 66 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 66 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 -------------------------------------------------------- Input matrix: name: HB/bcsstm02 n: 66 entries: 72 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 66 nz, number of nonzeros in A: 66 symmetry of A: 1.0000 number of nonzeros on diagonal: 66 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 2932 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 66 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 66 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 -------------------------------------------------------- Input matrix: name: Dense/0 n: 0 entries: 0 (invalid matrix, Ap [0] = 99) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/2 n: 2 entries: 4 (invalid perm, P[1]=99) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 (invalid perm) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ap) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ai) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ai) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation Largest residual during all tests: 3.27418e-10 ldlamd: all tests passed SuiteSparse/LDL/Demo/ldlmain.c0000644001170100242450000002762110617137675015057 0ustar davisfac/* ========================================================================== */ /* === ldlmain.c: LDL main program, for demo and testing ==================== */ /* ========================================================================== */ /* LDLMAIN: this main program has two purposes. It provides an example of how * to use the LDL routines, and it tests the package. The output of this * program is in ldlmain.out (without AMD) and ldlamd.out (with AMD). If you * did not download and install AMD, then the compilation of this program will * not work with USE_AMD defined. Compare your output with ldlmain.out and * ldlamd.out. * * The program reads in a set of matrices, in the Matrix/ subdirectory. * The format of the files is as follows: * * one line with the matrix description * one line with 2 integers: n jumbled * n+1 lines, containing the Ap array of size n+1 (column pointers) * nz lines, containing the Ai array of size nz (row indices) * nz lines, containing the Ax array of size nz (numerical values) * n lines, containing the P permutation array of size n * * The Ap, Ai, Ax, and P data structures are described in ldl.c. * The jumbled flag is 1 if the matrix could contain unsorted columns and/or * duplicate entries, and 0 otherwise. * * Once the matrix is read in, it is checked to see if it is valid. Some * matrices are invalid by design, to test the error-checking routines. If * valid, the matrix factorized twice (A and P*A*P'). A linear * system Ax=b is set up and solved, and the residual computed. * If any system is not solved accurately, this test will fail. * * This program can also be compiled as a MATLAB mexFunction, with the command * "mex ldlmain.c ldl.c". You can then run the program in MATLAB, with the * command "ldlmain". * * LDL Copyright (c) by Timothy A Davis, * University of Florida. All Rights Reserved. See README for the License. */ #ifdef MATLAB_MEX_FILE #ifndef LDL_LONG #define LDL_LONG #endif #endif #include #include #include "ldl.h" #define NMATRICES 30 /* number of test matrices in Matrix/ directory */ #define LEN 200 /* string length */ #ifdef USE_AMD /* get AMD include file, if using AMD */ #include "amd.h" #define PROGRAM "ldlamd" #else #define PROGRAM "ldlmain" #endif #ifdef MATLAB_MEX_FILE #include "mex.h" #define EXIT_ERROR mexErrMsgTxt ("failure") ; #define EXIT_OK #else #define EXIT_ERROR exit (EXIT_FAILURE) ; #define EXIT_OK exit (EXIT_SUCCESS) ; #endif /* -------------------------------------------------------------------------- */ /* ALLOC_MEMORY: allocate a block of memory */ /* -------------------------------------------------------------------------- */ #define ALLOC_MEMORY(p,type,size) \ p = (type *) malloc ((((size) <= 0) ? 1 : (size)) * sizeof (type)) ; \ if (p == (type *) NULL) \ { \ printf (PROGRAM ": out of memory\n") ; \ EXIT_ERROR ; \ } /* -------------------------------------------------------------------------- */ /* FREE_MEMORY: free a block of memory */ /* -------------------------------------------------------------------------- */ #define FREE_MEMORY(p,type) \ if (p != (type *) NULL) \ { \ free (p) ; \ p = (type *) NULL ; \ } /* -------------------------------------------------------------------------- */ /* stand-alone main program, or MATLAB mexFunction */ /* -------------------------------------------------------------------------- */ #ifdef MATLAB_MEX_FILE void mexFunction ( int nargout, mxArray *pargout[ ], int nargin, const mxArray *pargin[ ] ) #else int main (void) #endif { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ #ifdef USE_AMD double Info [AMD_INFO] ; #endif double r, rnorm, flops, maxrnorm = 0. ; double *Ax, *Lx, *B, *D, *X, *Y ; LDL_int matrix, *Ai, *Ap, *Li, *Lp, *P, *Pinv, *Perm, *PermInv, n, i, j, p, nz, *Flag, *Pattern, *Lnz, *Parent, trial, lnz, d, jumbled ; FILE *f ; char s [LEN] ; /* ---------------------------------------------------------------------- */ /* check the error-checking routines with null matrices */ /* ---------------------------------------------------------------------- */ i = 1 ; n = -1 ; if (LDL_valid_perm (n, (LDL_int *) NULL, &i) || !LDL_valid_perm (0, (LDL_int *) NULL, &i) || LDL_valid_matrix (n, (LDL_int *) NULL, (LDL_int *) NULL) || LDL_valid_matrix (0, &i, &i)) { printf (PROGRAM ": ldl error-checking routine failed\n") ; EXIT_ERROR ; } /* ---------------------------------------------------------------------- */ /* read in a factorize a set of matrices */ /* ---------------------------------------------------------------------- */ for (matrix = 1 ; matrix <= NMATRICES ; matrix++) { /* ------------------------------------------------------------------ */ /* read in the matrix and the permutation */ /* ------------------------------------------------------------------ */ sprintf (s, "../Matrix/A%02d", (int) matrix) ; if ((f = fopen (s, "r")) == (FILE *) NULL) { printf (PROGRAM ": could not open file: %s\n", s) ; EXIT_ERROR ; } fgets (s, LEN, f) ; printf ("\n\n--------------------------------------------------------"); printf ("\nInput matrix: %s", s) ; printf ("--------------------------------------------------------\n\n"); fscanf (f, LDL_ID " " LDL_ID, &n, &jumbled) ; n = (n < 0) ? (0) : (n) ; ALLOC_MEMORY (P, LDL_int, n) ; ALLOC_MEMORY (Ap, LDL_int, n+1) ; for (j = 0 ; j <= n ; j++) { fscanf (f, LDL_ID, &Ap [j]) ; } nz = Ap [n] ; ALLOC_MEMORY (Ai, LDL_int, nz) ; ALLOC_MEMORY (Ax, double, nz) ; for (p = 0 ; p < nz ; p++) { fscanf (f, LDL_ID , &Ai [p]) ; } for (p = 0 ; p < nz ; p++) { fscanf (f, "%lg", &Ax [p]) ; } for (j = 0 ; j < n ; j++) { fscanf (f, LDL_ID , &P [j]) ; } fclose (f) ; /* ------------------------------------------------------------------ */ /* check the matrix A and the permutation P */ /* ------------------------------------------------------------------ */ ALLOC_MEMORY (Flag, LDL_int, n) ; /* To test the error-checking routines, some of the input matrices * are not valid. So this error is expected to occur. */ if (!LDL_valid_matrix (n, Ap, Ai) || !LDL_valid_perm (n, P, Flag)) { printf (PROGRAM ": invalid matrix and/or permutation\n") ; FREE_MEMORY (P, LDL_int) ; FREE_MEMORY (Ap, LDL_int) ; FREE_MEMORY (Ai, LDL_int) ; FREE_MEMORY (Ax, double) ; FREE_MEMORY (Flag, LDL_int) ; continue ; } /* ------------------------------------------------------------------ */ /* get the AMD permutation, if available */ /* ------------------------------------------------------------------ */ #ifdef USE_AMD /* recompute the permutation with AMD */ /* Assume that AMD produces a valid permutation P. */ #ifdef LDL_LONG if (amd_l_order (n, Ap, Ai, P, (double *) NULL, Info) < AMD_OK) { printf (PROGRAM ": call to AMD failed\n") ; EXIT_ERROR ; } amd_l_control ((double *) NULL) ; amd_l_info (Info) ; #else if (amd_order (n, Ap, Ai, P, (double *) NULL, Info) < AMD_OK) { printf (PROGRAM ": call to AMD failed\n") ; EXIT_ERROR ; } amd_control ((double *) NULL) ; amd_info (Info) ; #endif #endif /* ------------------------------------------------------------------ */ /* allocate workspace and the first part of LDL factorization */ /* ------------------------------------------------------------------ */ ALLOC_MEMORY (Pinv, LDL_int, n) ; ALLOC_MEMORY (Y, double, n) ; ALLOC_MEMORY (Pattern, LDL_int, n) ; ALLOC_MEMORY (Lnz, LDL_int, n) ; ALLOC_MEMORY (Lp, LDL_int, n+1) ; ALLOC_MEMORY (Parent, LDL_int, n) ; ALLOC_MEMORY (D, double, n) ; ALLOC_MEMORY (B, double, n) ; ALLOC_MEMORY (X, double, n) ; /* ------------------------------------------------------------------ */ /* factorize twice, with and without permutation */ /* ------------------------------------------------------------------ */ for (trial = 1 ; trial <= 2 ; trial++) { if (trial == 1) { printf ("Factorize PAP'=LDL' and solve Ax=b\n") ; Perm = P ; PermInv = Pinv ; } else { printf ("Factorize A=LDL' and solve Ax=b\n") ; Perm = (LDL_int *) NULL ; PermInv = (LDL_int *) NULL ; } /* -------------------------------------------------------------- */ /* symbolic factorization to get Lp, Parent, Lnz, and Pinv */ /* -------------------------------------------------------------- */ LDL_symbolic (n, Ap, Ai, Lp, Parent, Lnz, Flag, Perm, PermInv) ; lnz = Lp [n] ; /* find # of nonzeros in L, and flop count for LDL_numeric */ flops = 0 ; for (j = 0 ; j < n ; j++) { flops += ((double) Lnz [j]) * (Lnz [j] + 2) ; } printf ("Nz in L: "LDL_ID" Flop count: %g\n", lnz, flops) ; /* -------------------------------------------------------------- */ /* allocate remainder of L, of size lnz */ /* -------------------------------------------------------------- */ ALLOC_MEMORY (Li, LDL_int, lnz) ; ALLOC_MEMORY (Lx, double, lnz) ; /* -------------------------------------------------------------- */ /* numeric factorization to get Li, Lx, and D */ /* -------------------------------------------------------------- */ d = LDL_numeric (n, Ap, Ai, Ax, Lp, Parent, Lnz, Li, Lx, D, Y, Flag, Pattern, Perm, PermInv) ; /* -------------------------------------------------------------- */ /* solve, or report singular case */ /* -------------------------------------------------------------- */ if (d != n) { printf ("Ax=b not solved since D("LDL_ID","LDL_ID") is zero.\n", d, d) ; } else { /* construct the right-hand-side, B */ for (i = 0 ; i < n ; i++) { B [i] = 1 + ((double) i) / 100 ; } /* solve Ax=b */ if (trial == 1) { /* the factorization is LDL' = PAP' */ LDL_perm (n, Y, B, P) ; /* y = Pb */ LDL_lsolve (n, Y, Lp, Li, Lx) ; /* y = L\y */ LDL_dsolve (n, Y, D) ; /* y = D\y */ LDL_ltsolve (n, Y, Lp, Li, Lx) ; /* y = L'\y */ LDL_permt (n, X, Y, P) ; /* x = P'y */ } else { /* the factorization is LDL' = A */ for (i = 0 ; i < n ; i++) /* x = b */ { X [i] = B [i] ; } LDL_lsolve (n, X, Lp, Li, Lx) ; /* x = L\x */ LDL_dsolve (n, X, D) ; /* x = D\x */ LDL_ltsolve (n, X, Lp, Li, Lx) ; /* x = L'\x */ } /* compute the residual y = Ax-b */ /* note that this code can tolerate a jumbled matrix */ for (i = 0 ; i < n ; i++) { Y [i] = -B [i] ; } for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { Y [Ai [p]] += Ax [p] * X [j] ; } } /* rnorm = norm (y, inf) */ rnorm = 0 ; for (i = 0 ; i < n ; i++) { r = (Y [i] > 0) ? (Y [i]) : (-Y [i]) ; rnorm = (r > rnorm) ? (r) : (rnorm) ; } maxrnorm = (rnorm > maxrnorm) ? (rnorm) : (maxrnorm) ; printf ("relative maxnorm of residual: %g\n", rnorm) ; } /* -------------------------------------------------------------- */ /* free the size-lnz part of L */ /* -------------------------------------------------------------- */ FREE_MEMORY (Li, LDL_int) ; FREE_MEMORY (Lx, double) ; } /* free everything */ FREE_MEMORY (P, LDL_int) ; FREE_MEMORY (Ap, LDL_int) ; FREE_MEMORY (Ai, LDL_int) ; FREE_MEMORY (Ax, double) ; FREE_MEMORY (Pinv, LDL_int) ; FREE_MEMORY (Y, double) ; FREE_MEMORY (Flag, LDL_int) ; FREE_MEMORY (Pattern, LDL_int) ; FREE_MEMORY (Lnz, LDL_int) ; FREE_MEMORY (Lp, LDL_int) ; FREE_MEMORY (Parent, LDL_int) ; FREE_MEMORY (D, double) ; FREE_MEMORY (B, double) ; FREE_MEMORY (X, double) ; } printf ("\nLargest residual during all tests: %g\n", maxrnorm) ; if (maxrnorm < 1e-8) { printf ("\n" PROGRAM ": all tests passed\n") ; EXIT_OK ; } else { printf ("\n" PROGRAM ": one more tests failed (residual too high)\n") ; EXIT_ERROR ; } } SuiteSparse/LDL/Demo/ldllamd.out0000644001170100242450000014044310711433076015420 0ustar davisfac -------------------------------------------------------- Input matrix: name: Dense/0 n: 0 entries: 0 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 -------------------------------------------------------- Input matrix: name: Dense/0 n: 0 entries: 0 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 -------------------------------------------------------- Input matrix: name: Dense/1 n: 1 entries: 1 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 1 nz, number of nonzeros in A: 1 symmetry of A: 1.0000 number of nonzeros on diagonal: 1 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 72 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 1 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 1 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 -------------------------------------------------------- Input matrix: name: Dense/1 n: 1 entries: 2 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 1 nz, number of nonzeros in A: 1 symmetry of A: 1.0000 number of nonzeros on diagonal: 1 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 104 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 1 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 1 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 8.32667e-17 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 8.32667e-17 -------------------------------------------------------- Input matrix: name: Dense/2 n: 2 entries: 4 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 2 nz, number of nonzeros in A: 4 symmetry of A: 1.0000 number of nonzeros on diagonal: 2 nonzeros in pattern of A+A' (excl. diagonal): 2 # dense rows/columns of A+A': 0 memory used, in bytes: 160 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 1 nonzeros in L (including diagonal): 3 # divide operations for LDL' or LU: 1 # multiply-subtract operations for LDL': 1 # multiply-subtract operations for LU: 1 max nz. in any column of L (incl. diagonal): 2 chol flop count for real A, sqrt counted as 1 flop: 5 LDL' flop count for real A: 3 LDL' flop count for complex A: 17 LU flop count for real A (with no pivoting): 3 LU flop count for complex A (with no pivoting): 17 Factorize PAP'=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 5.55112e-17 Factorize A=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 5.55112e-17 -------------------------------------------------------- Input matrix: name: Dense/2 n: 2 entries: 5 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 2 nz, number of nonzeros in A: 4 symmetry of A: 1.0000 number of nonzeros on diagonal: 2 nonzeros in pattern of A+A' (excl. diagonal): 2 # dense rows/columns of A+A': 0 memory used, in bytes: 224 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 1 nonzeros in L (including diagonal): 3 # divide operations for LDL' or LU: 1 # multiply-subtract operations for LDL': 1 # multiply-subtract operations for LU: 1 max nz. in any column of L (incl. diagonal): 2 chol flop count for real A, sqrt counted as 1 flop: 5 LDL' flop count for real A: 3 LDL' flop count for complex A: 17 LU flop count for real A (with no pivoting): 3 LU flop count for complex A (with no pivoting): 17 Factorize PAP'=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 1.11022e-16 Factorize A=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 1.11022e-16 -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 3 nz, number of nonzeros in A: 9 symmetry of A: 1.0000 number of nonzeros on diagonal: 3 nonzeros in pattern of A+A' (excl. diagonal): 6 # dense rows/columns of A+A': 0 memory used, in bytes: 272 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 3 nonzeros in L (including diagonal): 6 # divide operations for LDL' or LU: 3 # multiply-subtract operations for LDL': 4 # multiply-subtract operations for LU: 5 max nz. in any column of L (incl. diagonal): 3 chol flop count for real A, sqrt counted as 1 flop: 14 LDL' flop count for real A: 11 LDL' flop count for complex A: 59 LU flop count for real A (with no pivoting): 13 LU flop count for complex A (with no pivoting): 67 Factorize PAP'=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.11022e-16 Factorize A=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.11022e-16 -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 11 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 3 nz, number of nonzeros in A: 9 symmetry of A: 1.0000 number of nonzeros on diagonal: 3 nonzeros in pattern of A+A' (excl. diagonal): 6 # dense rows/columns of A+A': 0 memory used, in bytes: 392 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 3 nonzeros in L (including diagonal): 6 # divide operations for LDL' or LU: 3 # multiply-subtract operations for LDL': 4 # multiply-subtract operations for LU: 5 max nz. in any column of L (incl. diagonal): 3 chol flop count for real A, sqrt counted as 1 flop: 14 LDL' flop count for real A: 11 LDL' flop count for complex A: 59 LU flop count for real A (with no pivoting): 13 LU flop count for complex A (with no pivoting): 67 Factorize PAP'=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.38778e-16 Factorize A=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.38778e-16 -------------------------------------------------------- Input matrix: name: HB/can_24 n: 24 entries: 160 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 24 nz, number of nonzeros in A: 160 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 136 # dense rows/columns of A+A': 0 memory used, in bytes: 3032 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 97 nonzeros in L (including diagonal): 121 # divide operations for LDL' or LU: 97 # multiply-subtract operations for LDL': 275 # multiply-subtract operations for LU: 453 max nz. in any column of L (incl. diagonal): 8 chol flop count for real A, sqrt counted as 1 flop: 671 LDL' flop count for real A: 647 LDL' flop count for complex A: 3073 LU flop count for real A (with no pivoting): 1003 LU flop count for complex A (with no pivoting): 4497 Factorize PAP'=LDL' and solve Ax=b Nz in L: 96 Flop count: 632 Ax=b not solved since D(1,1) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 146 Flop count: 1360 Ax=b not solved since D(5,5) is zero. -------------------------------------------------------- Input matrix: name: HB/can_24 n: 24 entries: 188 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 24 nz, number of nonzeros in A: 160 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 136 # dense rows/columns of A+A': 0 memory used, in bytes: 4736 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 97 nonzeros in L (including diagonal): 121 # divide operations for LDL' or LU: 97 # multiply-subtract operations for LDL': 275 # multiply-subtract operations for LU: 453 max nz. in any column of L (incl. diagonal): 8 chol flop count for real A, sqrt counted as 1 flop: 671 LDL' flop count for real A: 647 LDL' flop count for complex A: 3073 LU flop count for real A (with no pivoting): 1003 LU flop count for complex A (with no pivoting): 4497 Factorize PAP'=LDL' and solve Ax=b Nz in L: 96 Flop count: 632 Ax=b not solved since D(1,1) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 146 Flop count: 1360 Ax=b not solved since D(5,5) is zero. -------------------------------------------------------- Input matrix: name: FIDAP/ex5 n: 27 entries: 279 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 27 nz, number of nonzeros in A: 279 symmetry of A: 1.0000 number of nonzeros on diagonal: 27 nonzeros in pattern of A+A' (excl. diagonal): 252 # dense rows/columns of A+A': 0 memory used, in bytes: 4360 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 126 nonzeros in L (including diagonal): 153 # divide operations for LDL' or LU: 126 # multiply-subtract operations for LDL': 414 # multiply-subtract operations for LU: 702 max nz. in any column of L (incl. diagonal): 9 chol flop count for real A, sqrt counted as 1 flop: 981 LDL' flop count for real A: 954 LDL' flop count for complex A: 4446 LU flop count for real A (with no pivoting): 1530 LU flop count for complex A (with no pivoting): 6750 Factorize PAP'=LDL' and solve Ax=b Nz in L: 126 Flop count: 954 relative maxnorm of residual: 2.59625e-10 Factorize A=LDL' and solve Ax=b Nz in L: 276 Flop count: 4206 relative maxnorm of residual: 2.72848e-10 -------------------------------------------------------- Input matrix: name: FIDAP/ex5 n: 27 entries: 325 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 27 nz, number of nonzeros in A: 279 symmetry of A: 1.0000 number of nonzeros on diagonal: 27 nonzeros in pattern of A+A' (excl. diagonal): 252 # dense rows/columns of A+A': 0 memory used, in bytes: 7184 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 126 nonzeros in L (including diagonal): 153 # divide operations for LDL' or LU: 126 # multiply-subtract operations for LDL': 414 # multiply-subtract operations for LU: 702 max nz. in any column of L (incl. diagonal): 9 chol flop count for real A, sqrt counted as 1 flop: 981 LDL' flop count for real A: 954 LDL' flop count for complex A: 4446 LU flop count for real A (with no pivoting): 1530 LU flop count for complex A (with no pivoting): 6750 Factorize PAP'=LDL' and solve Ax=b Nz in L: 126 Flop count: 954 relative maxnorm of residual: 3.27418e-10 Factorize A=LDL' and solve Ax=b Nz in L: 276 Flop count: 4206 relative maxnorm of residual: 2.32376e-10 -------------------------------------------------------- Input matrix: name: HB/bcsstk01 n: 48 entries: 400 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 48 nz, number of nonzeros in A: 400 symmetry of A: 1.0000 number of nonzeros on diagonal: 48 nonzeros in pattern of A+A' (excl. diagonal): 352 # dense rows/columns of A+A': 0 memory used, in bytes: 6832 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 441 nonzeros in L (including diagonal): 489 # divide operations for LDL' or LU: 441 # multiply-subtract operations for LDL': 2760 # multiply-subtract operations for LU: 5079 max nz. in any column of L (incl. diagonal): 20 chol flop count for real A, sqrt counted as 1 flop: 6009 LDL' flop count for real A: 5961 LDL' flop count for complex A: 26049 LU flop count for real A (with no pivoting): 10599 LU flop count for complex A (with no pivoting): 44601 Factorize PAP'=LDL' and solve Ax=b Nz in L: 441 Flop count: 5961 relative maxnorm of residual: 2.38712e-13 Factorize A=LDL' and solve Ax=b Nz in L: 829 Flop count: 20103 relative maxnorm of residual: 2.27374e-13 -------------------------------------------------------- Input matrix: name: HB/bcsstk01 n: 48 entries: 472 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 48 nz, number of nonzeros in A: 400 symmetry of A: 1.0000 number of nonzeros on diagonal: 48 nonzeros in pattern of A+A' (excl. diagonal): 352 # dense rows/columns of A+A': 0 memory used, in bytes: 11000 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 441 nonzeros in L (including diagonal): 489 # divide operations for LDL' or LU: 441 # multiply-subtract operations for LDL': 2760 # multiply-subtract operations for LU: 5079 max nz. in any column of L (incl. diagonal): 20 chol flop count for real A, sqrt counted as 1 flop: 6009 LDL' flop count for real A: 5961 LDL' flop count for complex A: 26049 LU flop count for real A (with no pivoting): 10599 LU flop count for complex A (with no pivoting): 44601 Factorize PAP'=LDL' and solve Ax=b Nz in L: 441 Flop count: 5961 relative maxnorm of residual: 2.27374e-13 Factorize A=LDL' and solve Ax=b Nz in L: 829 Flop count: 20103 relative maxnorm of residual: 3.83693e-13 -------------------------------------------------------- Input matrix: name: HB/bcsstm01 n: 48 entries: 24 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 48 nz, number of nonzeros in A: 24 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 3456 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 48 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 48 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. -------------------------------------------------------- Input matrix: name: HB/bcsstm01 n: 48 entries: 26 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 48 nz, number of nonzeros in A: 24 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 4056 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 48 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 48 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. -------------------------------------------------------- Input matrix: name: Pothen/mesh1e1 n: 48 entries: 306 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 48 nz, number of nonzeros in A: 306 symmetry of A: 1.0000 number of nonzeros on diagonal: 48 nonzeros in pattern of A+A' (excl. diagonal): 258 # dense rows/columns of A+A': 0 memory used, in bytes: 5928 # of memory compactions: 1 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 288 nonzeros in L (including diagonal): 336 # divide operations for LDL' or LU: 288 # multiply-subtract operations for LDL': 1171 # multiply-subtract operations for LU: 2054 max nz. in any column of L (incl. diagonal): 13 chol flop count for real A, sqrt counted as 1 flop: 2678 LDL' flop count for real A: 2630 LDL' flop count for complex A: 11960 LU flop count for real A (with no pivoting): 4396 LU flop count for complex A (with no pivoting): 19024 Factorize PAP'=LDL' and solve Ax=b Nz in L: 288 Flop count: 2630 relative maxnorm of residual: 5.96745e-16 Factorize A=LDL' and solve Ax=b Nz in L: 511 Flop count: 7383 relative maxnorm of residual: 6.93889e-16 -------------------------------------------------------- Input matrix: name: Pothen/mesh1e1 n: 48 entries: 359 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 48 nz, number of nonzeros in A: 306 symmetry of A: 1.0000 number of nonzeros on diagonal: 48 nonzeros in pattern of A+A' (excl. diagonal): 258 # dense rows/columns of A+A': 0 memory used, in bytes: 9192 # of memory compactions: 1 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 288 nonzeros in L (including diagonal): 336 # divide operations for LDL' or LU: 288 # multiply-subtract operations for LDL': 1171 # multiply-subtract operations for LU: 2054 max nz. in any column of L (incl. diagonal): 13 chol flop count for real A, sqrt counted as 1 flop: 2678 LDL' flop count for real A: 2630 LDL' flop count for complex A: 11960 LU flop count for real A (with no pivoting): 4396 LU flop count for complex A (with no pivoting): 19024 Factorize PAP'=LDL' and solve Ax=b Nz in L: 288 Flop count: 2630 relative maxnorm of residual: 5.55112e-16 Factorize A=LDL' and solve Ax=b Nz in L: 511 Flop count: 7383 relative maxnorm of residual: 5.55112e-16 -------------------------------------------------------- Input matrix: name: Bai/bfwb62 n: 62 entries: 342 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 62 nz, number of nonzeros in A: 342 symmetry of A: 1.0000 number of nonzeros on diagonal: 62 nonzeros in pattern of A+A' (excl. diagonal): 280 # dense rows/columns of A+A': 0 memory used, in bytes: 7152 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 226 nonzeros in L (including diagonal): 288 # divide operations for LDL' or LU: 226 # multiply-subtract operations for LDL': 623 # multiply-subtract operations for LU: 1020 max nz. in any column of L (incl. diagonal): 9 chol flop count for real A, sqrt counted as 1 flop: 1534 LDL' flop count for real A: 1472 LDL' flop count for complex A: 7018 LU flop count for real A (with no pivoting): 2266 LU flop count for complex A (with no pivoting): 10194 Factorize PAP'=LDL' and solve Ax=b Nz in L: 226 Flop count: 1472 relative maxnorm of residual: 5.55112e-16 Factorize A=LDL' and solve Ax=b Nz in L: 662 Flop count: 11350 relative maxnorm of residual: 1.11022e-15 -------------------------------------------------------- Input matrix: name: Bai/bfwb62 n: 62 entries: 407 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 62 nz, number of nonzeros in A: 342 symmetry of A: 1.0000 number of nonzeros on diagonal: 62 nonzeros in pattern of A+A' (excl. diagonal): 280 # dense rows/columns of A+A': 0 memory used, in bytes: 10912 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 226 nonzeros in L (including diagonal): 288 # divide operations for LDL' or LU: 226 # multiply-subtract operations for LDL': 623 # multiply-subtract operations for LU: 1020 max nz. in any column of L (incl. diagonal): 9 chol flop count for real A, sqrt counted as 1 flop: 1534 LDL' flop count for real A: 1472 LDL' flop count for complex A: 7018 LU flop count for real A (with no pivoting): 2266 LU flop count for complex A (with no pivoting): 10194 Factorize PAP'=LDL' and solve Ax=b Nz in L: 226 Flop count: 1472 relative maxnorm of residual: 5.68434e-14 Factorize A=LDL' and solve Ax=b Nz in L: 662 Flop count: 11350 relative maxnorm of residual: 2.15827e-12 -------------------------------------------------------- Input matrix: name: HB/bcsstk02 n: 66 entries: 4356 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 66 nz, number of nonzeros in A: 4356 symmetry of A: 1.0000 number of nonzeros on diagonal: 66 nonzeros in pattern of A+A' (excl. diagonal): 4290 # dense rows/columns of A+A': 0 memory used, in bytes: 45936 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 2145 nonzeros in L (including diagonal): 2211 # divide operations for LDL' or LU: 2145 # multiply-subtract operations for LDL': 47905 # multiply-subtract operations for LU: 93665 max nz. in any column of L (incl. diagonal): 66 chol flop count for real A, sqrt counted as 1 flop: 98021 LDL' flop count for real A: 97955 LDL' flop count for complex A: 402545 LU flop count for real A (with no pivoting): 189475 LU flop count for complex A (with no pivoting): 768625 Factorize PAP'=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 7.50219e-13 Factorize A=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 7.50219e-13 -------------------------------------------------------- Input matrix: name: HB/bcsstk02 n: 66 entries: 5175 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 66 nz, number of nonzeros in A: 4356 symmetry of A: 1.0000 number of nonzeros on diagonal: 66 nonzeros in pattern of A+A' (excl. diagonal): 4290 # dense rows/columns of A+A': 0 memory used, in bytes: 87872 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 2145 nonzeros in L (including diagonal): 2211 # divide operations for LDL' or LU: 2145 # multiply-subtract operations for LDL': 47905 # multiply-subtract operations for LU: 93665 max nz. in any column of L (incl. diagonal): 66 chol flop count for real A, sqrt counted as 1 flop: 98021 LDL' flop count for real A: 97955 LDL' flop count for complex A: 402545 LU flop count for real A (with no pivoting): 189475 LU flop count for complex A (with no pivoting): 768625 Factorize PAP'=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 8.59759e-13 Factorize A=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 8.59759e-13 -------------------------------------------------------- Input matrix: name: HB/bcsstm02 n: 66 entries: 66 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 66 nz, number of nonzeros in A: 66 symmetry of A: 1.0000 number of nonzeros on diagonal: 66 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 4752 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 66 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 66 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 -------------------------------------------------------- Input matrix: name: HB/bcsstm02 n: 66 entries: 72 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 66 nz, number of nonzeros in A: 66 symmetry of A: 1.0000 number of nonzeros on diagonal: 66 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 5864 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 66 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 66 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 -------------------------------------------------------- Input matrix: name: Dense/0 n: 0 entries: 0 (invalid matrix, Ap [0] = 99) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/2 n: 2 entries: 4 (invalid perm, P[1]=99) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 (invalid perm) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ap) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ai) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ai) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation Largest residual during all tests: 3.27418e-10 ldlamd: all tests passed SuiteSparse/LDL/Makefile0000644001170100242450000000241510617136676014041 0ustar davisfac#------------------------------------------------------------------------------ # LDL Makefile #------------------------------------------------------------------------------ default: demo include ../UFconfig/UFconfig.mk # Compile all C code, including the C-callable routine. demo: ( cd Lib ; $(MAKE) ) ( cd Demo ; $(MAKE) ) # Compile all C code, including the C-callable routine and the mexFunctions. all: ( cd Lib ; $(MAKE) ) ( cd Demo ; $(MAKE) ) ( cd MATLAB ; $(MAKE) ) # compile just the C-callable libraries (not mexFunctions or Demos) library: ( cd Lib ; $(MAKE) ) # remove object files, but keep the compiled programs and library archives clean: ( cd Lib ; $(MAKE) clean ) ( cd Demo ; $(MAKE) clean ) ( cd MATLAB ; $(MAKE) clean ) ( cd Doc ; $(MAKE) clean ) # clean, and then remove compiled programs and library archives purge: ( cd Lib ; $(MAKE) purge ) ( cd Demo ; $(MAKE) purge ) ( cd MATLAB ; $(MAKE) purge ) ( cd Doc ; $(MAKE) purge ) distclean: purge # create PDF documents for the original distribution doc: ( cd Doc ; $(MAKE) ) # get ready for distribution dist: purge ( cd Demo ; $(MAKE) dist ) ( cd Doc ; $(MAKE) ) ccode: library lib: library # compile the MATLAB mexFunction mex: ( cd MATLAB ; $(MAKE) ) SuiteSparse/LDL/MATLAB/0000755001170100242450000000000010711653377013334 5ustar davisfacSuiteSparse/LDL/MATLAB/ldlmain2.out0000644001170100242450000016535510711435406015575 0ustar davisfacldlmain2 LDLMAIN2 compiles and runs a longer test program for LDL Example: ldlmain2 See also ldlsparse. LDL successfully compiled. -------------------------------------------------------- Input matrix: name: Dense/0 n: 0 entries: 0 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 -------------------------------------------------------- Input matrix: name: Dense/0 n: 0 entries: 0 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 -------------------------------------------------------- Input matrix: name: Dense/1 n: 1 entries: 1 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 -------------------------------------------------------- Input matrix: name: Dense/1 n: 1 entries: 2 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 8.32667e-17 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 8.32667e-17 -------------------------------------------------------- Input matrix: name: Dense/2 n: 2 entries: 4 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 5.55112e-17 Factorize A=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 5.55112e-17 -------------------------------------------------------- Input matrix: name: Dense/2 n: 2 entries: 5 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 1.11022e-16 Factorize A=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 1.11022e-16 -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.11022e-16 Factorize A=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.11022e-16 -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 11 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.38778e-16 Factorize A=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.38778e-16 -------------------------------------------------------- Input matrix: name: HB/can_24 n: 24 entries: 160 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 96 Flop count: 632 Ax=b not solved since D(1,1) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 146 Flop count: 1360 Ax=b not solved since D(5,5) is zero. -------------------------------------------------------- Input matrix: name: HB/can_24 n: 24 entries: 188 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 96 Flop count: 632 Ax=b not solved since D(1,1) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 146 Flop count: 1360 Ax=b not solved since D(5,5) is zero. -------------------------------------------------------- Input matrix: name: FIDAP/ex5 n: 27 entries: 279 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 126 Flop count: 954 relative maxnorm of residual: 2.59625e-10 Factorize A=LDL' and solve Ax=b Nz in L: 276 Flop count: 4206 relative maxnorm of residual: 2.72848e-10 -------------------------------------------------------- Input matrix: name: FIDAP/ex5 n: 27 entries: 325 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 126 Flop count: 954 relative maxnorm of residual: 3.27418e-10 Factorize A=LDL' and solve Ax=b Nz in L: 276 Flop count: 4206 relative maxnorm of residual: 2.32376e-10 -------------------------------------------------------- Input matrix: name: HB/bcsstk01 n: 48 entries: 400 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 441 Flop count: 5961 relative maxnorm of residual: 2.38712e-13 Factorize A=LDL' and solve Ax=b Nz in L: 829 Flop count: 20103 relative maxnorm of residual: 2.27374e-13 -------------------------------------------------------- Input matrix: name: HB/bcsstk01 n: 48 entries: 472 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 441 Flop count: 5961 relative maxnorm of residual: 2.27374e-13 Factorize A=LDL' and solve Ax=b Nz in L: 829 Flop count: 20103 relative maxnorm of residual: 3.83693e-13 -------------------------------------------------------- Input matrix: name: HB/bcsstm01 n: 48 entries: 24 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. -------------------------------------------------------- Input matrix: name: HB/bcsstm01 n: 48 entries: 26 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. -------------------------------------------------------- Input matrix: name: Pothen/mesh1e1 n: 48 entries: 306 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 288 Flop count: 2630 relative maxnorm of residual: 5.96745e-16 Factorize A=LDL' and solve Ax=b Nz in L: 511 Flop count: 7383 relative maxnorm of residual: 6.93889e-16 -------------------------------------------------------- Input matrix: name: Pothen/mesh1e1 n: 48 entries: 359 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 288 Flop count: 2630 relative maxnorm of residual: 5.55112e-16 Factorize A=LDL' and solve Ax=b Nz in L: 511 Flop count: 7383 relative maxnorm of residual: 5.55112e-16 -------------------------------------------------------- Input matrix: name: Bai/bfwb62 n: 62 entries: 342 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 226 Flop count: 1472 relative maxnorm of residual: 5.55112e-16 Factorize A=LDL' and solve Ax=b Nz in L: 662 Flop count: 11350 relative maxnorm of residual: 1.11022e-15 -------------------------------------------------------- Input matrix: name: Bai/bfwb62 n: 62 entries: 407 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 226 Flop count: 1472 relative maxnorm of residual: 5.68434e-14 Factorize A=LDL' and solve Ax=b Nz in L: 662 Flop count: 11350 relative maxnorm of residual: 2.15827e-12 -------------------------------------------------------- Input matrix: name: HB/bcsstk02 n: 66 entries: 4356 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 7.50219e-13 Factorize A=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 7.50219e-13 -------------------------------------------------------- Input matrix: name: HB/bcsstk02 n: 66 entries: 5175 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 8.59759e-13 Factorize A=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 8.59759e-13 -------------------------------------------------------- Input matrix: name: HB/bcsstm02 n: 66 entries: 66 -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 -------------------------------------------------------- Input matrix: name: HB/bcsstm02 n: 66 entries: 72 (jumbled version) -------------------------------------------------------- Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 -------------------------------------------------------- Input matrix: name: Dense/0 n: 0 entries: 0 (invalid matrix, Ap [0] = 99) -------------------------------------------------------- ldlmain: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/2 n: 2 entries: 4 (invalid perm, P[1]=99) -------------------------------------------------------- ldlmain: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 (invalid perm) -------------------------------------------------------- ldlmain: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ap) -------------------------------------------------------- ldlmain: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ai) -------------------------------------------------------- ldlmain: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ai) -------------------------------------------------------- ldlmain: invalid matrix and/or permutation Largest residual during all tests: 3.27418e-10 ldlmain: all tests passed -------------------------------------------------------- Input matrix: name: Dense/0 n: 0 entries: 0 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 -------------------------------------------------------- Input matrix: name: Dense/0 n: 0 entries: 0 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 -------------------------------------------------------- Input matrix: name: Dense/1 n: 1 entries: 1 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 1 nz, number of nonzeros in A: 1 symmetry of A: 1.0000 number of nonzeros on diagonal: 1 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 36 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 1 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 1 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 -------------------------------------------------------- Input matrix: name: Dense/1 n: 1 entries: 2 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 1 nz, number of nonzeros in A: 1 symmetry of A: 1.0000 number of nonzeros on diagonal: 1 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 52 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 1 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 1 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 8.32667e-17 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 8.32667e-17 -------------------------------------------------------- Input matrix: name: Dense/2 n: 2 entries: 4 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 2 nz, number of nonzeros in A: 4 symmetry of A: 1.0000 number of nonzeros on diagonal: 2 nonzeros in pattern of A+A' (excl. diagonal): 2 # dense rows/columns of A+A': 0 memory used, in bytes: 80 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 1 nonzeros in L (including diagonal): 3 # divide operations for LDL' or LU: 1 # multiply-subtract operations for LDL': 1 # multiply-subtract operations for LU: 1 max nz. in any column of L (incl. diagonal): 2 chol flop count for real A, sqrt counted as 1 flop: 5 LDL' flop count for real A: 3 LDL' flop count for complex A: 17 LU flop count for real A (with no pivoting): 3 LU flop count for complex A (with no pivoting): 17 Factorize PAP'=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 5.55112e-17 Factorize A=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 5.55112e-17 -------------------------------------------------------- Input matrix: name: Dense/2 n: 2 entries: 5 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 2 nz, number of nonzeros in A: 4 symmetry of A: 1.0000 number of nonzeros on diagonal: 2 nonzeros in pattern of A+A' (excl. diagonal): 2 # dense rows/columns of A+A': 0 memory used, in bytes: 112 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 1 nonzeros in L (including diagonal): 3 # divide operations for LDL' or LU: 1 # multiply-subtract operations for LDL': 1 # multiply-subtract operations for LU: 1 max nz. in any column of L (incl. diagonal): 2 chol flop count for real A, sqrt counted as 1 flop: 5 LDL' flop count for real A: 3 LDL' flop count for complex A: 17 LU flop count for real A (with no pivoting): 3 LU flop count for complex A (with no pivoting): 17 Factorize PAP'=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 1.11022e-16 Factorize A=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 1.11022e-16 -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 3 nz, number of nonzeros in A: 9 symmetry of A: 1.0000 number of nonzeros on diagonal: 3 nonzeros in pattern of A+A' (excl. diagonal): 6 # dense rows/columns of A+A': 0 memory used, in bytes: 136 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 3 nonzeros in L (including diagonal): 6 # divide operations for LDL' or LU: 3 # multiply-subtract operations for LDL': 4 # multiply-subtract operations for LU: 5 max nz. in any column of L (incl. diagonal): 3 chol flop count for real A, sqrt counted as 1 flop: 14 LDL' flop count for real A: 11 LDL' flop count for complex A: 59 LU flop count for real A (with no pivoting): 13 LU flop count for complex A (with no pivoting): 67 Factorize PAP'=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.11022e-16 Factorize A=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.11022e-16 -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 11 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 3 nz, number of nonzeros in A: 9 symmetry of A: 1.0000 number of nonzeros on diagonal: 3 nonzeros in pattern of A+A' (excl. diagonal): 6 # dense rows/columns of A+A': 0 memory used, in bytes: 196 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 3 nonzeros in L (including diagonal): 6 # divide operations for LDL' or LU: 3 # multiply-subtract operations for LDL': 4 # multiply-subtract operations for LU: 5 max nz. in any column of L (incl. diagonal): 3 chol flop count for real A, sqrt counted as 1 flop: 14 LDL' flop count for real A: 11 LDL' flop count for complex A: 59 LU flop count for real A (with no pivoting): 13 LU flop count for complex A (with no pivoting): 67 Factorize PAP'=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.38778e-16 Factorize A=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.38778e-16 -------------------------------------------------------- Input matrix: name: HB/can_24 n: 24 entries: 160 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 24 nz, number of nonzeros in A: 160 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 136 # dense rows/columns of A+A': 0 memory used, in bytes: 1516 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 97 nonzeros in L (including diagonal): 121 # divide operations for LDL' or LU: 97 # multiply-subtract operations for LDL': 275 # multiply-subtract operations for LU: 453 max nz. in any column of L (incl. diagonal): 8 chol flop count for real A, sqrt counted as 1 flop: 671 LDL' flop count for real A: 647 LDL' flop count for complex A: 3073 LU flop count for real A (with no pivoting): 1003 LU flop count for complex A (with no pivoting): 4497 Factorize PAP'=LDL' and solve Ax=b Nz in L: 96 Flop count: 632 Ax=b not solved since D(1,1) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 146 Flop count: 1360 Ax=b not solved since D(5,5) is zero. -------------------------------------------------------- Input matrix: name: HB/can_24 n: 24 entries: 188 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 24 nz, number of nonzeros in A: 160 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 136 # dense rows/columns of A+A': 0 memory used, in bytes: 2368 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 97 nonzeros in L (including diagonal): 121 # divide operations for LDL' or LU: 97 # multiply-subtract operations for LDL': 275 # multiply-subtract operations for LU: 453 max nz. in any column of L (incl. diagonal): 8 chol flop count for real A, sqrt counted as 1 flop: 671 LDL' flop count for real A: 647 LDL' flop count for complex A: 3073 LU flop count for real A (with no pivoting): 1003 LU flop count for complex A (with no pivoting): 4497 Factorize PAP'=LDL' and solve Ax=b Nz in L: 96 Flop count: 632 Ax=b not solved since D(1,1) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 146 Flop count: 1360 Ax=b not solved since D(5,5) is zero. -------------------------------------------------------- Input matrix: name: FIDAP/ex5 n: 27 entries: 279 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 27 nz, number of nonzeros in A: 279 symmetry of A: 1.0000 number of nonzeros on diagonal: 27 nonzeros in pattern of A+A' (excl. diagonal): 252 # dense rows/columns of A+A': 0 memory used, in bytes: 2180 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 126 nonzeros in L (including diagonal): 153 # divide operations for LDL' or LU: 126 # multiply-subtract operations for LDL': 414 # multiply-subtract operations for LU: 702 max nz. in any column of L (incl. diagonal): 9 chol flop count for real A, sqrt counted as 1 flop: 981 LDL' flop count for real A: 954 LDL' flop count for complex A: 4446 LU flop count for real A (with no pivoting): 1530 LU flop count for complex A (with no pivoting): 6750 Factorize PAP'=LDL' and solve Ax=b Nz in L: 126 Flop count: 954 relative maxnorm of residual: 2.59625e-10 Factorize A=LDL' and solve Ax=b Nz in L: 276 Flop count: 4206 relative maxnorm of residual: 2.72848e-10 -------------------------------------------------------- Input matrix: name: FIDAP/ex5 n: 27 entries: 325 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 27 nz, number of nonzeros in A: 279 symmetry of A: 1.0000 number of nonzeros on diagonal: 27 nonzeros in pattern of A+A' (excl. diagonal): 252 # dense rows/columns of A+A': 0 memory used, in bytes: 3592 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 126 nonzeros in L (including diagonal): 153 # divide operations for LDL' or LU: 126 # multiply-subtract operations for LDL': 414 # multiply-subtract operations for LU: 702 max nz. in any column of L (incl. diagonal): 9 chol flop count for real A, sqrt counted as 1 flop: 981 LDL' flop count for real A: 954 LDL' flop count for complex A: 4446 LU flop count for real A (with no pivoting): 1530 LU flop count for complex A (with no pivoting): 6750 Factorize PAP'=LDL' and solve Ax=b Nz in L: 126 Flop count: 954 relative maxnorm of residual: 3.27418e-10 Factorize A=LDL' and solve Ax=b Nz in L: 276 Flop count: 4206 relative maxnorm of residual: 2.32376e-10 -------------------------------------------------------- Input matrix: name: HB/bcsstk01 n: 48 entries: 400 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 48 nz, number of nonzeros in A: 400 symmetry of A: 1.0000 number of nonzeros on diagonal: 48 nonzeros in pattern of A+A' (excl. diagonal): 352 # dense rows/columns of A+A': 0 memory used, in bytes: 3416 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 441 nonzeros in L (including diagonal): 489 # divide operations for LDL' or LU: 441 # multiply-subtract operations for LDL': 2760 # multiply-subtract operations for LU: 5079 max nz. in any column of L (incl. diagonal): 20 chol flop count for real A, sqrt counted as 1 flop: 6009 LDL' flop count for real A: 5961 LDL' flop count for complex A: 26049 LU flop count for real A (with no pivoting): 10599 LU flop count for complex A (with no pivoting): 44601 Factorize PAP'=LDL' and solve Ax=b Nz in L: 441 Flop count: 5961 relative maxnorm of residual: 2.38712e-13 Factorize A=LDL' and solve Ax=b Nz in L: 829 Flop count: 20103 relative maxnorm of residual: 2.27374e-13 -------------------------------------------------------- Input matrix: name: HB/bcsstk01 n: 48 entries: 472 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 48 nz, number of nonzeros in A: 400 symmetry of A: 1.0000 number of nonzeros on diagonal: 48 nonzeros in pattern of A+A' (excl. diagonal): 352 # dense rows/columns of A+A': 0 memory used, in bytes: 5500 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 441 nonzeros in L (including diagonal): 489 # divide operations for LDL' or LU: 441 # multiply-subtract operations for LDL': 2760 # multiply-subtract operations for LU: 5079 max nz. in any column of L (incl. diagonal): 20 chol flop count for real A, sqrt counted as 1 flop: 6009 LDL' flop count for real A: 5961 LDL' flop count for complex A: 26049 LU flop count for real A (with no pivoting): 10599 LU flop count for complex A (with no pivoting): 44601 Factorize PAP'=LDL' and solve Ax=b Nz in L: 441 Flop count: 5961 relative maxnorm of residual: 2.27374e-13 Factorize A=LDL' and solve Ax=b Nz in L: 829 Flop count: 20103 relative maxnorm of residual: 3.83693e-13 -------------------------------------------------------- Input matrix: name: HB/bcsstm01 n: 48 entries: 24 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 48 nz, number of nonzeros in A: 24 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 1728 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 48 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 48 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. -------------------------------------------------------- Input matrix: name: HB/bcsstm01 n: 48 entries: 26 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 48 nz, number of nonzeros in A: 24 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 2028 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 48 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 48 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. -------------------------------------------------------- Input matrix: name: Pothen/mesh1e1 n: 48 entries: 306 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 48 nz, number of nonzeros in A: 306 symmetry of A: 1.0000 number of nonzeros on diagonal: 48 nonzeros in pattern of A+A' (excl. diagonal): 258 # dense rows/columns of A+A': 0 memory used, in bytes: 2964 # of memory compactions: 1 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 288 nonzeros in L (including diagonal): 336 # divide operations for LDL' or LU: 288 # multiply-subtract operations for LDL': 1171 # multiply-subtract operations for LU: 2054 max nz. in any column of L (incl. diagonal): 13 chol flop count for real A, sqrt counted as 1 flop: 2678 LDL' flop count for real A: 2630 LDL' flop count for complex A: 11960 LU flop count for real A (with no pivoting): 4396 LU flop count for complex A (with no pivoting): 19024 Factorize PAP'=LDL' and solve Ax=b Nz in L: 288 Flop count: 2630 relative maxnorm of residual: 5.96745e-16 Factorize A=LDL' and solve Ax=b Nz in L: 511 Flop count: 7383 relative maxnorm of residual: 6.93889e-16 -------------------------------------------------------- Input matrix: name: Pothen/mesh1e1 n: 48 entries: 359 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 48 nz, number of nonzeros in A: 306 symmetry of A: 1.0000 number of nonzeros on diagonal: 48 nonzeros in pattern of A+A' (excl. diagonal): 258 # dense rows/columns of A+A': 0 memory used, in bytes: 4596 # of memory compactions: 1 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 288 nonzeros in L (including diagonal): 336 # divide operations for LDL' or LU: 288 # multiply-subtract operations for LDL': 1171 # multiply-subtract operations for LU: 2054 max nz. in any column of L (incl. diagonal): 13 chol flop count for real A, sqrt counted as 1 flop: 2678 LDL' flop count for real A: 2630 LDL' flop count for complex A: 11960 LU flop count for real A (with no pivoting): 4396 LU flop count for complex A (with no pivoting): 19024 Factorize PAP'=LDL' and solve Ax=b Nz in L: 288 Flop count: 2630 relative maxnorm of residual: 5.55112e-16 Factorize A=LDL' and solve Ax=b Nz in L: 511 Flop count: 7383 relative maxnorm of residual: 5.55112e-16 -------------------------------------------------------- Input matrix: name: Bai/bfwb62 n: 62 entries: 342 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 62 nz, number of nonzeros in A: 342 symmetry of A: 1.0000 number of nonzeros on diagonal: 62 nonzeros in pattern of A+A' (excl. diagonal): 280 # dense rows/columns of A+A': 0 memory used, in bytes: 3576 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 226 nonzeros in L (including diagonal): 288 # divide operations for LDL' or LU: 226 # multiply-subtract operations for LDL': 623 # multiply-subtract operations for LU: 1020 max nz. in any column of L (incl. diagonal): 9 chol flop count for real A, sqrt counted as 1 flop: 1534 LDL' flop count for real A: 1472 LDL' flop count for complex A: 7018 LU flop count for real A (with no pivoting): 2266 LU flop count for complex A (with no pivoting): 10194 Factorize PAP'=LDL' and solve Ax=b Nz in L: 226 Flop count: 1472 relative maxnorm of residual: 5.55112e-16 Factorize A=LDL' and solve Ax=b Nz in L: 662 Flop count: 11350 relative maxnorm of residual: 1.11022e-15 -------------------------------------------------------- Input matrix: name: Bai/bfwb62 n: 62 entries: 407 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 62 nz, number of nonzeros in A: 342 symmetry of A: 1.0000 number of nonzeros on diagonal: 62 nonzeros in pattern of A+A' (excl. diagonal): 280 # dense rows/columns of A+A': 0 memory used, in bytes: 5456 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 226 nonzeros in L (including diagonal): 288 # divide operations for LDL' or LU: 226 # multiply-subtract operations for LDL': 623 # multiply-subtract operations for LU: 1020 max nz. in any column of L (incl. diagonal): 9 chol flop count for real A, sqrt counted as 1 flop: 1534 LDL' flop count for real A: 1472 LDL' flop count for complex A: 7018 LU flop count for real A (with no pivoting): 2266 LU flop count for complex A (with no pivoting): 10194 Factorize PAP'=LDL' and solve Ax=b Nz in L: 226 Flop count: 1472 relative maxnorm of residual: 5.68434e-14 Factorize A=LDL' and solve Ax=b Nz in L: 662 Flop count: 11350 relative maxnorm of residual: 2.15827e-12 -------------------------------------------------------- Input matrix: name: HB/bcsstk02 n: 66 entries: 4356 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 66 nz, number of nonzeros in A: 4356 symmetry of A: 1.0000 number of nonzeros on diagonal: 66 nonzeros in pattern of A+A' (excl. diagonal): 4290 # dense rows/columns of A+A': 0 memory used, in bytes: 22968 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 2145 nonzeros in L (including diagonal): 2211 # divide operations for LDL' or LU: 2145 # multiply-subtract operations for LDL': 47905 # multiply-subtract operations for LU: 93665 max nz. in any column of L (incl. diagonal): 66 chol flop count for real A, sqrt counted as 1 flop: 98021 LDL' flop count for real A: 97955 LDL' flop count for complex A: 402545 LU flop count for real A (with no pivoting): 189475 LU flop count for complex A (with no pivoting): 768625 Factorize PAP'=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 7.50219e-13 Factorize A=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 7.50219e-13 -------------------------------------------------------- Input matrix: name: HB/bcsstk02 n: 66 entries: 5175 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 66 nz, number of nonzeros in A: 4356 symmetry of A: 1.0000 number of nonzeros on diagonal: 66 nonzeros in pattern of A+A' (excl. diagonal): 4290 # dense rows/columns of A+A': 0 memory used, in bytes: 43936 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 2145 nonzeros in L (including diagonal): 2211 # divide operations for LDL' or LU: 2145 # multiply-subtract operations for LDL': 47905 # multiply-subtract operations for LU: 93665 max nz. in any column of L (incl. diagonal): 66 chol flop count for real A, sqrt counted as 1 flop: 98021 LDL' flop count for real A: 97955 LDL' flop count for complex A: 402545 LU flop count for real A (with no pivoting): 189475 LU flop count for complex A (with no pivoting): 768625 Factorize PAP'=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 8.59759e-13 Factorize A=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 8.59759e-13 -------------------------------------------------------- Input matrix: name: HB/bcsstm02 n: 66 entries: 66 -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 66 nz, number of nonzeros in A: 66 symmetry of A: 1.0000 number of nonzeros on diagonal: 66 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 2376 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 66 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 66 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 -------------------------------------------------------- Input matrix: name: HB/bcsstm02 n: 66 entries: 72 (jumbled version) -------------------------------------------------------- AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD version 2.2.0, May 31, 2007, results: status: OK, but jumbled n, dimension of A: 66 nz, number of nonzeros in A: 66 symmetry of A: 1.0000 number of nonzeros on diagonal: 66 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 2932 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 66 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 66 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 -------------------------------------------------------- Input matrix: name: Dense/0 n: 0 entries: 0 (invalid matrix, Ap [0] = 99) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/2 n: 2 entries: 4 (invalid perm, P[1]=99) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 (invalid perm) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ap) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ai) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation -------------------------------------------------------- Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ai) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation Largest residual during all tests: 3.27418e-10 ldlamd: all tests passed diary off SuiteSparse/LDL/MATLAB/Makefile0000644001170100242450000000133510617142011014755 0ustar davisfac#------------------------------------------------------------------------------- # Makefile for the LDL mexFunction #------------------------------------------------------------------------------- default: mex include ../../UFconfig/UFconfig.mk I = -I../../UFconfig -I../Include MX = $(MEX) $(I) -DLDL_LONG mex: ldlmex.c ../Source/ldl.c ../Include/ldl.h ldlsymbolmex.c - $(MX) -output ldlsparse ../Source/ldl.c ldlmex.c - $(MX) -output ldlsymbol ../Source/ldl.c ldlsymbolmex.c #------------------------------------------------------------------------------- # clean-up: #------------------------------------------------------------------------------- distclean: purge purge: clean - $(RM) *.mex* clean: - $(RM) $(CLEAN) SuiteSparse/LDL/MATLAB/ldl_install.m0000644001170100242450000000073510620377143016011 0ustar davisfacfunction ldl_install %LDL_INSTALL compile and install the LDL package for use in MATLAB. % Your current working directory must be LDL for this function to work. % % Example: % ldl_install % % See also ldlsparse, ldlsymbol % Copyright 2006-2007 by Timothy A. Davis, Univ. of Florida ldl_make addpath (pwd) ; fprintf ('LDL has been compiled and installed. The path:\n') ; disp (pwd) ; fprintf ('has been added to your path. Use pathtool to add it permanently.\n'); ldldemo SuiteSparse/LDL/MATLAB/ldlmain2.m0000644001170100242450000000206310707707603015212 0ustar davisfacfunction ldlmain2 %LDLMAIN2 compiles and runs a longer test program for LDL % % Example: % ldlmain2 % % See also ldlsparse. % Copyright 2006-2007 by Timothy A. Davis, Univ. of Florida help ldlmain2 detail = 0 ; ldl_make d = '' ; if (~isempty (strfind (computer, '64'))) d = '-largeArrayDims' ; end mx = sprintf ('mex -O %s -DLDL_LONG -DDLONG -I../../UFconfig -I../Include', d) ; % compile ldlmain without AMD cmd = sprintf ('%s ../Demo/ldlmain.c ../Source/ldl.c', mx) ; if (detail) fprintf ('%s\n', cmd) ; end eval (cmd) ; ldlmain % compile ldlamd (ldlmain with AMD) cmd = sprintf ('%s -I../../AMD/Include', mx) ; files = {'amd_order', 'amd_dump', 'amd_postorder', 'amd_post_tree', ... 'amd_aat', 'amd_2', 'amd_1', 'amd_defaults', 'amd_control', ... 'amd_info', 'amd_valid', 'amd_global', 'amd_preprocess' } ; for i = 1 : length (files) cmd = sprintf ('%s ../../AMD/Source/%s.c', cmd, files {i}) ; end cmd = [cmd ' -DUSE_AMD -output ldlamd ../Demo/ldlmain.c ../Source/ldl.c'] ; if (detail) fprintf ('%s\n', cmd) ; end eval (cmd) ; ldlamd SuiteSparse/LDL/MATLAB/ldlmex.c0000644001170100242450000002511310634323125014754 0ustar davisfac/* ========================================================================== */ /* === ldlmex.c: LDL mexFunction =========================================== */ /* ========================================================================== */ /* MATLAB interface for numerical LDL' factorization using the LDL sparse matrix * package. * * MATLAB calling syntax is: * * [L, D, Parent, flops] = ldl (A) * [L, D, Parent, flops] = ldl (A, P) * [x, flops] = ldl (A, [ ], b) * [x, flops] = ldl (A, P, b) * * The factorization is L*D*L' = A or L*D*L' = A(P,P). A must be sparse, * square, and real. L is lower triangular with unit diagonal, but the diagonal * is not returned. D is diagonal sparse matrix. Let n = size (A,1). If P is * not present or empty, the factorization is: * * (L + speye (n)) * D * (L + speye (n))' = A * * otherwise, the factorization is * * (L + speye (n)) * D * (L + speye (n))' = A(P,P) * * P is a permutation of 1:n, an output of AMD, SYMAMD, or SYMRCM, for example. * Only the diagonal and upper triangular part of A or A(P,P) is accessed; the * lower triangular part is ignored. * * The elimination tree is returned in the Parent array. * * In the x = ldl (A, P, b) usage, the LDL' factorization is not returned. * Instead, the system A*x=b is solved for x, where b is a dense n-by-m matrix, * using P as the fill-reducing ordering for the LDL' factorization of A(P,P). * If P is not present or equal to [ ], it is assumed to be the identity * permutation. * * If no zero entry on the diagonal of D is encountered, then the flops argument * is the floating point count. * * If any entry on the diagonal of D is zero, then the LDL' factorization is * terminated at that point. If there is no flops output argument, an error * message is printed and no outputs are returned. Otherwise, flops is * negative, d = -flops, and D (d,d) is the first zero entry on the diagonal of * D. A partial factorization is returned. Let B = A if P is not present or * empty, or B = A(P,P) otherwise. Then the factorization is * * LDL = (L + speye (n)) * D * (L + speye (n))' * LDL (1:d, 1:d) = B (1:d,1:d) * * That is, the LDL' factorization of B (1:d,1:d) is in the first d rows and * columns of L and D. The rest of L and D are zero. * * LDL Copyright (c) by Timothy A Davis, * University of Florida. All Rights Reserved. See README for the License. */ #ifndef LDL_LONG #define LDL_LONG #endif #include "ldl.h" #include "mex.h" /* ========================================================================== */ /* === LDL mexFunction ====================================================== */ /* ========================================================================== */ void mexFunction ( int nargout, mxArray *pargout[ ], int nargin, const mxArray *pargin[ ] ) { UF_long i, n, *Pattern, *Flag, *Li, *Lp, *Ap, *Ai, *Lnz, *Parent, do_chol, nrhs = 0, lnz, do_solve, *P, *Pinv, nn, k, j, permute, *Dp = NULL, *Di, d, do_flops, psrc, pdst ; double *Y, *D, *Lx, *Ax, flops, *X = NULL, *B = NULL, *p ; /* ---------------------------------------------------------------------- */ /* get inputs and allocate workspace */ /* ---------------------------------------------------------------------- */ do_chol = (nargin > 0) && (nargin <= 2) && (nargout <= 4) ; do_solve = (nargin == 3) && (nargout <= 2) ; if (!(do_chol || do_solve)) { mexErrMsgTxt ("Usage:\n" " [L, D, etree, flopcount] = ldl (A) ;\n" " [L, D, etree, flopcount] = ldl (A, P) ;\n" " [x, flopcount] = ldl (A, [ ], b) ;\n" " [x, flopcount] = ldl (A, P, b) ;\n" "The etree and flopcount arguments are optional.") ; } n = mxGetM (pargin [0]) ; if (!mxIsSparse (pargin [0]) || n != mxGetN (pargin [0]) || mxIsComplex (pargin [0])) { mexErrMsgTxt ("ldl: A must be sparse, square, and real") ; } if (do_solve) { if (mxIsSparse (pargin [2]) || n != mxGetM (pargin [2]) || !mxIsDouble (pargin [2]) || mxIsComplex (pargin [2])) { mexErrMsgTxt ( "ldl: b must be dense, real, and with proper dimension") ; } } nn = (n == 0) ? 1 : n ; /* get sparse matrix A */ Ap = (UF_long *) mxGetJc (pargin [0]) ; Ai = (UF_long *) mxGetIr (pargin [0]) ; Ax = mxGetPr (pargin [0]) ; /* get fill-reducing ordering, if present */ permute = ((nargin > 1) && !mxIsEmpty (pargin [1])) ; if (permute) { if (mxGetM (pargin [1]) * mxGetN (pargin [1]) != n || mxIsSparse (pargin [1])) { mexErrMsgTxt ("ldl: invalid input permutation\n") ; } P = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ; Pinv = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ; p = mxGetPr (pargin [1]) ; for (k = 0 ; k < n ; k++) { P [k] = p [k] - 1 ; /* convert to 0-based */ } } else { P = (UF_long *) NULL ; Pinv = (UF_long *) NULL ; } /* allocate first part of L */ Lp = (UF_long *) mxMalloc ((n+1) * sizeof (UF_long)) ; Parent = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ; /* get workspace */ Y = (double *) mxMalloc (nn * sizeof (double)) ; Flag = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ; Pattern = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ; Lnz = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ; /* make sure the input P is valid */ if (permute && !ldl_l_valid_perm (n, P, Flag)) { mexErrMsgTxt ("ldl: invalid input permutation\n") ; } /* note that we assume that the input matrix is valid */ /* ---------------------------------------------------------------------- */ /* symbolic factorization to get Lp, Parent, Lnz, and optionally Pinv */ /* ---------------------------------------------------------------------- */ ldl_l_symbolic (n, Ap, Ai, Lp, Parent, Lnz, Flag, P, Pinv) ; lnz = Lp [n] ; /* ---------------------------------------------------------------------- */ /* create outputs */ /* ---------------------------------------------------------------------- */ if (do_chol) { /* create the output matrix L, using the Lp array from ldl_l_symbolic */ pargout [0] = mxCreateSparse (n, n, lnz+1, mxREAL) ; mxFree (mxGetJc (pargout [0])) ; mxSetJc (pargout [0], (void *) Lp) ; /* Lp is not mxFree'd */ Li = (UF_long *) mxGetIr (pargout [0]) ; Lx = mxGetPr (pargout [0]) ; /* create sparse diagonal matrix D */ if (nargout > 1) { pargout [1] = mxCreateSparse (n, n, nn, mxREAL) ; Dp = (UF_long *) mxGetJc (pargout [1]) ; Di = (UF_long *) mxGetIr (pargout [1]) ; for (j = 0 ; j < n ; j++) { Dp [j] = j ; Di [j] = j ; } Dp [n] = n ; D = mxGetPr (pargout [1]) ; } else { D = (double *) mxMalloc (nn * sizeof (double)) ; } /* return elimination tree (add 1 to change from 0-based to 1-based) */ if (nargout > 2) { pargout [2] = mxCreateDoubleMatrix (1, n, mxREAL) ; p = mxGetPr (pargout [2]) ; for (i = 0 ; i < n ; i++) { p [i] = Parent [i] + 1 ; } } do_flops = (nargout == 4) ? (3) : (-1) ; } else { /* create L and D as temporary matrices */ Li = (UF_long *) mxMalloc ((lnz+1) * sizeof (UF_long)) ; Lx = (double *) mxMalloc ((lnz+1) * sizeof (double)) ; D = (double *) mxMalloc (nn * sizeof (double)) ; /* create solution x */ nrhs = mxGetN (pargin [2]) ; pargout [0] = mxCreateDoubleMatrix (n, nrhs, mxREAL) ; X = mxGetPr (pargout [0]) ; B = mxGetPr (pargin [2]) ; do_flops = (nargout == 2) ? (1) : (-1) ; } if (do_flops >= 0) { /* find flop count for ldl_l_numeric */ flops = 0 ; for (k = 0 ; k < n ; k++) { flops += ((double) Lnz [k]) * (Lnz [k] + 2) ; } if (do_solve) { /* add flop count for solve */ for (k = 0 ; k < n ; k++) { flops += 4 * ((double) Lnz [k]) + 1 ; } } pargout [do_flops] = mxCreateDoubleMatrix (1, 1, mxREAL) ; p = mxGetPr (pargout [do_flops]) ; p [0] = flops ; } /* ---------------------------------------------------------------------- */ /* numeric factorization to get Li, Lx, and D */ /* ---------------------------------------------------------------------- */ d = ldl_l_numeric (n, Ap, Ai, Ax, Lp, Parent, Lnz, Li, Lx, D, Y, Flag, Pattern, P, Pinv) ; /* ---------------------------------------------------------------------- */ /* singular case : truncate the factorization */ /* ---------------------------------------------------------------------- */ if (d != n) { /* D [d] is zero: report error, or clean up */ if (do_chol && do_flops < 0) { mexErrMsgTxt ("ldl: zero pivot encountered\n") ; } else { /* L and D are incomplete, compact them */ if (do_chol) { for (k = d ; k < n ; k++) { Dp [k] = d ; } Dp [n] = d ; } for (k = d ; k < n ; k++) { D [k] = 0 ; } pdst = 0 ; for (k = 0 ; k < d ; k++) { for (psrc = Lp [k] ; psrc < Lp [k] + Lnz [k] ; psrc++) { Li [pdst] = Li [psrc] ; Lx [pdst] = Lx [psrc] ; pdst++ ; } } for (k = 0 ; k < d ; k++) { Lp [k+1] = Lp [k] + Lnz [k] ; } for (k = d ; k <= n ; k++) { Lp [k] = pdst ; } if (do_flops >= 0) { /* return -d instead of the flop count (convert to 1-based) */ p = mxGetPr (pargout [do_flops]) ; p [0] = -(1+d) ; } } } /* ---------------------------------------------------------------------- */ /* solve Ax=b, if requested */ /* ---------------------------------------------------------------------- */ if (do_solve) { if (permute) { for (j = 0 ; j < nrhs ; j++) { ldl_l_perm (n, Y, B, P) ; /* y = Pb */ ldl_l_lsolve (n, Y, Lp, Li, Lx) ; /* y = L\y */ ldl_l_dsolve (n, Y, D) ; /* y = D\y */ ldl_l_ltsolve (n, Y, Lp, Li, Lx) ; /* y = L'\y */ ldl_l_permt (n, X, Y, P) ; /* x = P'y */ X += n ; B += n ; } } else { for (j = 0 ; j < nrhs ; j++) { for (k = 0 ; k < n ; k++) /* x = b */ { X [k] = B [k] ; } ldl_l_lsolve (n, X, Lp, Li, Lx) ; /* x = L\x */ ldl_l_dsolve (n, X, D) ; /* x = D\x */ ldl_l_ltsolve (n, X, Lp, Li, Lx) ; /* x = L'\x */ X += n ; B += n ; } } /* free the matrix L */ mxFree (Lp) ; mxFree (Li) ; mxFree (Lx) ; mxFree (D) ; } /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ if (do_chol && nargout < 2) { mxFree (D) ; } if (permute) { mxFree (P) ; mxFree (Pinv) ; } mxFree (Parent) ; mxFree (Y) ; mxFree (Flag) ; mxFree (Pattern) ; mxFree (Lnz) ; } SuiteSparse/LDL/MATLAB/ldlsparse.m0000644001170100242450000000320710620377467015507 0ustar davisfacfunction [arg1, arg2, arg3, arg4] = ldlsparse (A, P, b) %#ok %LDLSPARSE LDL' factorization of a real, sparse, symmetric matrix % % Example: % [L, D, Parent, fl] = ldlsparse (A) % [L, D, Parent, fl] = ldlsparse (A, P) % [x, fl] = ldlsparse (A, [ ], b) % [x, fl] = ldlsparse (A, P, b) % % Let I = speye (size (A,1)). The factorization is (L+I)*D*(L+I)' = A or A(P,P). % A must be sparse, square, and real. Only the diagonal and upper triangular % part of A or A(P,P) are accessed. L is lower triangular with unit diagonal, % but the diagonal is not returned. D is a diagonal sparse matrix. P is either % a permutation of 1:n, or an empty vector, where n = size (A,1). If not % present, or empty, then P=1:n is assumed. Parent is the elimination tree of % A or A(P,P). If positive, fl is the floating point operation count, or % negative if any entry on the diagonal of D is zero. % % In the x = ldlsparse (A, P, b) usage, the LDL' factorization is not returned. % Instead, the system A*x=b is solved for x, where both b and x are dense. % % If a zero entry on the diagonal of D is encountered, the LDL' factorization is % terminated at that point. If there is no fl output argument, an error occurs. % Otherwise, fl is negative, and let d=-fl. D(d,d) is the first zero entry on % the diagonal of D. A partial factorization is returned. Let B = A, or A(P,P) % if P is present. Let F = (L+I)*D*(L+I)'. Then F (1:d,1:d) = B (1:d,1:d). % Rows d+1 to n of L and D are all zero. % % See also chol, ldl, ldlsymbol, symbfact, etree % Copyright 2006-2007 by Timothy A. Davis, Univ. of Florida error ('ldlsparse mexFunction not found') ; SuiteSparse/LDL/MATLAB/ldl_make.m0000644001170100242450000000107310620377606015260 0ustar davisfacfunction ldl_make %LDL_MAKE compile LDL % % Example: % ldl_make % compiles ldlsparse and ldlsymbol % % See also ldlsparse, ldlsymbol % Copyright 2006-2007 by Timothy A. Davis, Univ. of Florida d = '' ; if (~isempty (strfind (computer, '64'))) d = '-largeArrayDims' ; end eval (sprintf ('mex -O %s -DLDL_LONG -I../../UFconfig -I../Include -output ldlsparse ../Source/ldl.c ldlmex.c', d)) ; eval (sprintf ('mex -O %s -DLDL_LONG -I../../UFconfig -I../Include -output ldlsymbol ../Source/ldl.c ldlsymbolmex.c', d)) ; fprintf ('LDL successfully compiled.\n') ; SuiteSparse/LDL/MATLAB/ldlrow.m0000644001170100242450000000361710620377512015015 0ustar davisfacfunction [L, D] = ldlrow (A) %LDLROW an m-file description of the algorithm used by LDL % % Example: % [L, D] = ldlrow (A) % % Compute the L*D*L' factorization of A, by rows. Returns % full L and D matrices. This routine serves as an outline % of the numerical factorization performed by ldl.c. % % Here is a diagram of how L is computed. "a" means an % entry that is accessed at the kth step, and "c" means an % entry that is computed. A "-" means neither accessed nor % computed. A "1" means the value of the entry is L (the % unit diagonal of L), and it is accessed at the kth step. % A "." means the value is zero. % % The L matrix % % 1 . . . . . . . % a 1 . . . . . . % a a 1 . . . . . % a a a 1 . . . . % c c c c c . . . <- kth row of L % - - - - - - . . % - - - - - - - . % - - - - - - - - % % The A matrix: % % the kth column of A % v % - - - - a - - - % - - - - a - - - % - - - - a - - - % - - - - a - - - % - - - - a - - - <- kth row of A % - - - - - - - - % - - - - - - - - % - - - - - - - - % % The D matrix: % % the kth column of D % v % a . . . . . . . % . a . . . . . . % . . a . . . . . % . . . a . . . . % . . . . c . . . <- kth row of D % . . . . . . . . % . . . . . . . . % . . . . . . . . % % See also ldlsparse. % Copyright 2006-2007 by Timothy A. Davis, Univ. of Florida [m n] = size (A) ; L = zeros (n, n) ; D = zeros (n, 1) ; A = full (A) ; L (1, 1) = 1 ; D (1) = A (1,1) ; for k = 2:n % note the sparse triangular solve. For the sparse % case, the pattern of y is the same as the pattern of % the kth row of L. y = L (1:k-1, 1:k-1) \ A (1:k-1, k) ; % scale row k of L L (k, 1:k-1) = (y ./ D (1:k-1))' ; L (k, k) = 1 ; % compute the diagonal D (k) = A (k,k) - L (k, 1:k-1) * y ; end D = diag (D) ; SuiteSparse/LDL/MATLAB/Contents.m0000644001170100242450000000241310620377626015306 0ustar davisfac% LDL package: simple sparse LDL factorization % % Primary routines: % % ldlsparse - LDL' factorization of a real, sparse, symmetric matrix % ldlsymbol - symbolic Cholesky factorization % % Helper routines: % % ldldemo - demo program for LDL % ldlrow - an m-file description of the algorithm used by LDL % ldltest - test program for LDL % ldlmain2 - compiles and runs a longer test program for LDL % ldl_install - compile and install the LDL package for use in MATLAB. % ldl_make - compile LDL % % Example: % % [L, D, Parent, fl] = ldlsparse (A) % Copyright 2006-2007 by Timothy A. Davis, Univ. of Florida % LDL License: GNU Lesser General Public License as published by the % Free Software Foundation; either version 2.1 of the License, or % (at your option) any later version. % % Availability: % % http://www.cise.ufl.edu/research/sparse/ldl % % Acknowledgements: % % This work was supported by the National Science Foundation, under % grant CCR-0203270. % % Portions of this work were done while on sabbatical at Stanford University % and Lawrence Berkeley National Laboratory (with funding from the SciDAC % program). I would like to thank Gene Golub, Esmond Ng, and Horst Simon % for making this sabbatical possible. SuiteSparse/LDL/MATLAB/ldldemo.m0000644001170100242450000000531210620377476015135 0ustar davisfacfunction ldldemo %LDLDEMO demo program for LDL % % Example: % ldldemo % % See also ldlsparse. % Copyright 2006-2007 by Timothy A. Davis, Univ. of Florida % compile the LDLSPARSE and LDLSYMBOL mexFunctions help ldlsparse fprintf ('\nTesting ldlsparse and ldlsymbol:\n') ; % create a small random symmetric positive definite sparse matrix n = 100 ; d = 0.03 ; rand ('state', 0) ; randn ('state', 0) ; A = sprandn (n, n, d) ; A = speye (n) + A*A' ; b = randn (n, 1) ; figure (1) clf subplot (2,2,1) ; spy (A) ; title ('original matrix') ; % permute for sparsity p = symamd (A) ; C = A (p,p) ; subplot (2,2,2) ; spy (C) ; title ('permuted matrix') ; drawnow % factorize, without using ldlsparse's internal permutation [L, D, Parent, fl] = ldlsparse (C) ; L = L + speye (n) ; err = norm (L*D*L' - C, 1) ; fprintf ('norm (LDL''-PAP'') = %g\n', err) ; % solve Ax=b x = L' \ (D \ (L \ (b (p)))) ; x (p) = x ; resid = norm (A*x-b) ; fprintf ('residual %g for ldlsparse, flops %10.1f\n', resid, fl) ; % solve Ax=b with one call to ldlsparse x = ldlsparse (C, [ ], b (p)) ; x (p) = x ; resid = norm (A*x-b) ; fprintf ('residual %g for ldlsparse solve\n', resid) ; subplot (2,2,3) ; spy (L + D + L') ; title ('L+D+L''') ; subplot (2,2,4) ; treeplot (Parent) title ('elimination tree') ; % try ldlrow (this will be slow) [L, D] = ldlrow (C) ; x = L' \ (D \ (L \ (b (p)))) ; x (p) = x ; resid = norm (A*x-b) ; fprintf ('residual %g for ldlrow.m\n', resid) ; % factorize, using ldlsparse's internal permutation [L, D, Parent, fl] = ldlsparse (A, p) ; L = L + speye (n) ; err = norm (L*D*L' - C, 1) ; fprintf ('norm (LDL''-PAP'') = %g\n', err) ; % solve Ax=b x = L' \ (D \ (L \ (b (p)))) ; x (p) = x ; resid = norm (A*x-b) ; fprintf ('residual %g for ldlsparse, flops %10.1f\n', resid, fl) ; % solve Ax=b with one call to ldlsparse x = ldlsparse (A, p, b) ; resid = norm (A*x-b) ; fprintf ('residual %g for ldlsparse solve\n\n', resid) ; % compare ldlsymbol and symbfact [Lnz, Parent, fl] = ldlsymbol (A) ; fprintf ('Original matrix: nz in L: %5d flop count: %g\n', sum (Lnz), fl) ; Lnz2 = symbfact (A) - 1 ; Parent2 = etree (A) ; fl2 = sum (Lnz2 .* (Lnz2 + 2)) ; if (any (Lnz ~= Lnz2)) error ('Lnz mismatch') ; end if (any (Parent ~= Parent2)) error ('Parent mismatch') ; end if (fl ~= fl2) error ('fl mismatch') ; end [Lnz, Parent, fl] = ldlsymbol (A, p) ; fprintf ('Permuted matrix: nz in L: %5d flop count: %g\n', sum (Lnz), fl) ; Lnz2 = symbfact (A (p,p)) - 1 ; Parent2 = etree (A (p,p)) ; fl2 = sum (Lnz2 .* (Lnz2 + 2)) ; if (any (Lnz ~= Lnz2)) error ('Lnz mismatch') ; end if (any (Parent ~= Parent2)) error ('Parent mismatch') ; end if (fl ~= fl2) error ('fl mismatch') ; end fprintf ('\nldldemo: all tests passed\n') ; SuiteSparse/LDL/MATLAB/ldltest.out0000644001170100242450000000333210711435406015530 0ustar davisfacldltest LDLSPARSE LDL' factorization of a real, sparse, symmetric matrix Example: [L, D, Parent, fl] = ldlsparse (A) [L, D, Parent, fl] = ldlsparse (A, P) [x, fl] = ldlsparse (A, [ ], b) [x, fl] = ldlsparse (A, P, b) Let I = speye (size (A,1)). The factorization is (L+I)*D*(L+I)' = A or A(P,P). A must be sparse, square, and real. Only the diagonal and upper triangular part of A or A(P,P) are accessed. L is lower triangular with unit diagonal, but the diagonal is not returned. D is a diagonal sparse matrix. P is either a permutation of 1:n, or an empty vector, where n = size (A,1). If not present, or empty, then P=1:n is assumed. Parent is the elimination tree of A or A(P,P). If positive, fl is the floating point operation count, or negative if any entry on the diagonal of D is zero. In the x = ldlsparse (A, P, b) usage, the LDL' factorization is not returned. Instead, the system A*x=b is solved for x, where both b and x are dense. If a zero entry on the diagonal of D is encountered, the LDL' factorization is terminated at that point. If there is no fl output argument, an error occurs. Otherwise, fl is negative, and let d=-fl. D(d,d) is the first zero entry on the diagonal of D. A partial factorization is returned. Let B = A, or A(P,P) if P is present. Let F = (L+I)*D*(L+I)'. Then F (1:d,1:d) = B (1:d,1:d). Rows d+1 to n of L and D are all zero. See also chol, ldl, ldlsymbol, symbfact, etree err: 4.44089e-16 fl: 61 err: 4.44089e-16 err: 4.44089e-16 err: 0 err: 5.68989e-16 err: 5.68989e-16 fl: 123 err: 4.57967e-16 fl: 57 err: 4.57967e-16 err: 4.57967e-16 err: 0 err: 6.36644e-16 err: 6.36644e-16 fl: 119 ldl: all tests passed diary off SuiteSparse/LDL/MATLAB/ldltest.m0000644001170100242450000000730010707707627015170 0ustar davisfacfunction ldltest %LDLTEST test program for LDL % % Example: % ldltest % See also ldlsparse. % Copyright 2006-2007 by Timothy A. Davis, Univ. of Florida help ldlsparse A = sparse ([ ]) ; [L, D, Parent, fl] = ldlsparse (A) ; %#ok [L, D, Parent, fl] = ldlsparse (A, [ ]) ; %#ok try [L, D, Parent, fl] = ldlsparse (A, [1 2]) ; fprintf ('L = ') ; disp (L) fprintf ('D = ') ; disp (D) fprintf ('Parent = ') ; disp (Parent) fprintf ('fl = %g\n', fl) ; ok = 0 ; catch ok = 1 ; end if (~ok) error ('?') ; end try ldlsparse ok = 0 ; catch ok = 1 ; end if (~ok) error ('?') end try [L, D, Parent, fl] = ldlsparse (1) ; %#ok ok = 0 ; catch ok = 1 ; end if (~ok) error ('?') end try x = ldlsparse (1,2) ; %#ok ok = 0 ; catch ok = 1 ; end if (~ok) error ('?') end A =[ ... 1.7 0 0 0 0 0 0 0 .13 0 0 1.0 0 0 .02 0 0 0 0 .01 0 0 1.5 0 0 0 0 0 0 0 0 0 0 1.1 0 0 0 0 0 0 0 .02 0 0 2.6 0 .16 .09 .52 .53 0 0 0 0 0 1.2 0 0 0 0 0 0 0 0 .16 0 1.3 0 0 .56 0 0 0 0 .09 0 0 1.6 .11 0 .13 0 0 0 .52 0 0 .11 1.4 0 0 .01 0 0 .53 0 .56 0 0 3.1 ] ; A = sparse (A) ; b = [ ... .98 .64 .05 .58 .20 .44 .42 .37 .30 .51 .78 .84 .33 .68 .01 .43 .46 .76 .22 .56 .97 .57 .79 .99 .76 .05 .78 .52 .60 .43 ] ; P = [3 10 2 5 8 6 9 7 1 4] ; I = speye (10) ; [L, D, Parent, fl] = ldlsparse (A) ; err = norm ((L+I)*D*(L+I)'-A, 1) ; fprintf ('err: %g fl: %g\n', err, fl) ; if (err > 1e-14) error ('?') ; end ; Parent2 = etree (A) ; if (any (Parent2 ~= Parent)) error ('?') ; end [L, D, Parent] = ldlsparse (A) ; %#ok err = norm ((L+I)*D*(L+I)'-A, 1) ; fprintf ('err: %g\n', err) ; if (err > 1e-14) error ('?') ; end ; [L, D] = ldlsparse (A) ; err = norm ((L+I)*D*(L+I)'-A, 1) ; fprintf ('err: %g\n', err) ; if (err > 1e-14) error ('?') ; end ; L2 = ldlsparse (A) ; err = norm (L - L2, 1) ; fprintf ('err: %g\n', err) ; if (err > 1e-14) error ('?') ; end ; x = ldlsparse (A, [ ], b) ; err = norm (A*x-b, 1) ; fprintf ('err: %g\n', err) ; if (err > 1e-14) error ('?') ; end ; [x, fl] = ldlsparse (A, [ ], b) ; err = norm (A*x-b, 1) ; fprintf ('err: %g fl: %g\n', err, fl) ; if (err > 1e-14) error ('?') ; end ; [L, D, Parent, fl] = ldlsparse (A, P) ; err = norm ((L+I)*D*(L+I)'-A(P,P), 1) ; fprintf ('err: %g fl: %g\n', err, fl) ; if (err > 1e-14) error ('?') ; end ; Parent2 = etree (A (P,P)) ; if (any (Parent2 ~= Parent)) error ('?') ; end figure (1) clf subplot (2,2,1), spy (A), title ('original matrix') ; subplot (2,2,2), spy (A (P,P)), title ('permuted matrix') ; subplot (2,2,3), spy (L+D+L'), title ('L+D+L''') ; subplot (2,2,4), treeplot (Parent), title ('elimination tree') ; [L, D, Parent] = ldlsparse (A, P) ; err = norm ((L+I)*D*(L+I)'-A(P,P), 1) ; fprintf ('err: %g\n', err) ; if (err > 1e-14) error ('?') ; end ; [L, D] = ldlsparse (A, P) ; err = norm ((L+I)*D*(L+I)'-A(P,P), 1) ; fprintf ('err: %g\n', err) ; if (err > 1e-14) error ('?') ; end ; L2 = ldlsparse (A, P) ; err = norm (L - L2, 1) ; fprintf ('err: %g\n', err) ; if (err > 1e-14) error ('?') ; end ; x = ldlsparse (A, P, b) ; err = norm (A*x-b, 1) ; fprintf ('err: %g\n', err) ; if (err > 1e-14) error ('?') ; end ; [x, fl] = ldlsparse (A, P, b) ; err = norm (A*x-b, 1) ; fprintf ('err: %g fl: %g\n', err, fl) ; if (err > 1e-14) error ('?') ; end ; fprintf ('\nldl: all tests passed\n') ; SuiteSparse/LDL/MATLAB/ldlsymbol.m0000644001170100242450000000231110620377474015510 0ustar davisfacfunction [Lnz, Parent, fl] = ldlsymbol (A, P) %#ok %LDLSYMBOL symbolic Cholesky factorization % % Example: % [Lnz, Parent, fl] = ldlsymbol (A) % [Lnz, Parent, fl] = ldlsymbol (A, P) % % P is a permutation of 1:n, an output of AMD, SYMAMD, or SYMRCM, for example. % Only the diagonal and upper triangular part of A or A(P,P) is accessed; the % lower triangular part is ignored. If P is not provided, then P = 1:n is % assumed. % % The elimination tree is returned in the Parent array. The number of nonzeros % in each column of L is returned in Lnz. fl is the floating point operation % count for a subsequent LDL' factorization. This mexFunction replicates the % following MATLAB computations, using ldl_symbolic: % % Lnz = symbfact (A) - 1 ; % Parent = etree (A) ; % fl = sum (Lnz .* (Lnz + 2)) ; % % or, if P is provided, % % Lnz = symbfact (A (P,P)) - 1 ; % Parent = etree (A (P,P)) ; % fl = sum (Lnz .* (Lnz + 2)) ; % % Note that this routine is not required by LDL, since LDL does its own % symbolic factorization. % % See also ldlsparse, symbfact, etree % Copyright 2006-2007 by Timothy A. Davis, Univ. of Florida error ('ldlsymbol mexFunction not found') ; SuiteSparse/LDL/MATLAB/ldldemo.out0000644001170100242450000000365510711435406015505 0ustar davisfacldldemo LDLSPARSE LDL' factorization of a real, sparse, symmetric matrix Example: [L, D, Parent, fl] = ldlsparse (A) [L, D, Parent, fl] = ldlsparse (A, P) [x, fl] = ldlsparse (A, [ ], b) [x, fl] = ldlsparse (A, P, b) Let I = speye (size (A,1)). The factorization is (L+I)*D*(L+I)' = A or A(P,P). A must be sparse, square, and real. Only the diagonal and upper triangular part of A or A(P,P) are accessed. L is lower triangular with unit diagonal, but the diagonal is not returned. D is a diagonal sparse matrix. P is either a permutation of 1:n, or an empty vector, where n = size (A,1). If not present, or empty, then P=1:n is assumed. Parent is the elimination tree of A or A(P,P). If positive, fl is the floating point operation count, or negative if any entry on the diagonal of D is zero. In the x = ldlsparse (A, P, b) usage, the LDL' factorization is not returned. Instead, the system A*x=b is solved for x, where both b and x are dense. If a zero entry on the diagonal of D is encountered, the LDL' factorization is terminated at that point. If there is no fl output argument, an error occurs. Otherwise, fl is negative, and let d=-fl. D(d,d) is the first zero entry on the diagonal of D. A partial factorization is returned. Let B = A, or A(P,P) if P is present. Let F = (L+I)*D*(L+I)'. Then F (1:d,1:d) = B (1:d,1:d). Rows d+1 to n of L and D are all zero. See also chol, ldl, ldlsymbol, symbfact, etree Testing ldlsparse and ldlsymbol: norm (LDL'-PAP') = 6.51562e-15 residual 3.55986e-15 for ldlsparse, flops 14813.0 residual 3.86691e-15 for ldlsparse solve residual 3.64202e-15 for ldlrow.m norm (LDL'-PAP') = 6.63575e-15 residual 2.96267e-15 for ldlsparse, flops 14813.0 residual 3.53833e-15 for ldlsparse solve Original matrix: nz in L: 2206 flop count: 81044 Permuted matrix: nz in L: 893 flop count: 14813 ldldemo: all tests passed diary off SuiteSparse/LDL/MATLAB/ldlsymbolmex.c0000644001170100242450000001244010620716421016201 0ustar davisfac/* ========================================================================== */ /* === ldlsymbolmex.c: LDLSYMBOL mexFunction =============================== */ /* ========================================================================== */ /* MATLAB interface for symbolic LDL' factorization using the LDL sparse matrix * package. This mexFunction is not required by the LDL mexFunction. * * MATLAB calling syntax is: * * [Lnz, Parent, flopcount] = ldlsymbol (A) * [Lnz, Parent, flopcount] = ldlsymbol (A, P) * * P is a permutation of 1:n, an output of AMD, SYMAMD, or SYMRCM, for example. * Only the diagonal and upper triangular part of A or A(P,P) is accessed; the * lower triangular part is ignored. * * The elimination tree is returned in the Parent array. The number of nonzeros * in each column of L is returned in Lnz. This mexFunction replicates the * following MATLAB computations, using ldl_l_symbolic: * * Lnz = symbfact (A) - 1 ; * Parent = etree (A) ; * flopcount = sum (Lnz .* (Lnz + 2)) ; * * or, if P is provided, * * B = A (P,P) ; * Lnz = symbfact (B) - 1 ; * Parent = etree (B) ; * flopcount = sum (Lnz .* (Lnz + 2)) ; * * This code is faster than the above MATLAB statements, typically by a factor * of 4 to 40 (median speedup of 9) in MATLAB 6.5 on a Pentium 4 Linux laptop * (excluding the B=A(P,P) time), on a wide range of symmetric sparse matrices. * * LDL Version 1.3, Copyright (c) 2006 by Timothy A Davis, * University of Florida. All Rights Reserved. See README for the License. */ #ifndef LDL_LONG #define LDL_LONG #endif #include "ldl.h" #include "mex.h" /* ========================================================================== */ /* === LDLSYMBOL mexFunction ================================================ */ /* ========================================================================== */ void mexFunction ( int nargout, mxArray *pargout[ ], int nargin, const mxArray *pargin[ ] ) { UF_long i, n, *Pattern, *Flag, *Lp, *Ap, *Ai, *Lnz, *Parent, *P, *Pinv, nn, k, j, permute ; double flops, *p ; /* ---------------------------------------------------------------------- */ /* get inputs and allocate workspace */ /* ---------------------------------------------------------------------- */ if (nargin == 0 || nargin > 2) { mexErrMsgTxt ("Usage:\n" " [Lnz, Parent, flopcount] = ldl (A) ;\n" " [Lnz, Parent, flopcount] = ldl (A, P) ;\n") ; } n = mxGetM (pargin [0]) ; if (!mxIsSparse (pargin [0]) || n != mxGetN (pargin [0]) || mxIsComplex (pargin [0])) { mexErrMsgTxt ("ldlsymbol: A must be sparse, square, and real") ; } nn = (n == 0) ? 1 : n ; /* get sparse matrix A */ Ap = (UF_long *) mxGetJc (pargin [0]) ; Ai = (UF_long *) mxGetIr (pargin [0]) ; /* get fill-reducing ordering, if present */ permute = ((nargin > 1) && !mxIsEmpty (pargin [1])) ; if (permute) { if (mxGetM (pargin [1]) * mxGetN (pargin [1]) != n || mxIsSparse (pargin [1])) { mexErrMsgTxt ("ldlsymbol: invalid input permutation\n") ; } P = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ; Pinv = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ; p = mxGetPr (pargin [1]) ; for (k = 0 ; k < n ; k++) { P [k] = p [k] - 1 ; /* convert to 0-based */ } } else { P = (UF_long *) NULL ; Pinv = (UF_long *) NULL ; } /* allocate first part of L */ Lp = (UF_long *) mxMalloc ((n+1) * sizeof (UF_long)) ; Parent = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ; /* get workspace */ Flag = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ; Pattern = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ; Lnz = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ; /* make sure the input P is valid */ if (permute && !ldl_l_valid_perm (n, P, Flag)) { mexErrMsgTxt ("ldlsymbol: invalid input permutation\n") ; } /* note that we assume that the input matrix is valid */ /* ---------------------------------------------------------------------- */ /* symbolic factorization to get Lp, Parent, Lnz, and optionally Pinv */ /* ---------------------------------------------------------------------- */ ldl_l_symbolic (n, Ap, Ai, Lp, Parent, Lnz, Flag, P, Pinv) ; /* ---------------------------------------------------------------------- */ /* create outputs */ /* ---------------------------------------------------------------------- */ /* create the output Lnz vector */ pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ; p = mxGetPr (pargout [0]) ; for (j = 0 ; j < n ; j++) { p [j] = Lnz [j] ; } /* return elimination tree (add 1 to change from 0-based to 1-based) */ if (nargout > 1) { pargout [1] = mxCreateDoubleMatrix (1, n, mxREAL) ; p = mxGetPr (pargout [1]) ; for (i = 0 ; i < n ; i++) { p [i] = Parent [i] + 1 ; } } if (nargout > 2) { /* find flop count for ldl_l_numeric */ flops = 0 ; for (k = 0 ; k < n ; k++) { flops += ((double) Lnz [k]) * (Lnz [k] + 2) ; } pargout [2] = mxCreateDoubleMatrix (1, 1, mxREAL) ; p = mxGetPr (pargout [2]) ; p [0] = flops ; } if (permute) { mxFree (P) ; mxFree (Pinv) ; } mxFree (Lp) ; mxFree (Parent) ; mxFree (Flag) ; mxFree (Pattern) ; mxFree (Lnz) ; } SuiteSparse/LDL/Matrix/0000755001170100242450000000000010232253701013621 5ustar davisfacSuiteSparse/LDL/Matrix/A010000644001170100242450000000004510232253701014064 0ustar davisfacname: Dense/0 n: 0 entries: 0 0 0 0 SuiteSparse/LDL/Matrix/A020000644001170100242450000000007010232253701014063 0ustar davisfacname: Dense/0 n: 0 entries: 0 (jumbled version) 0 1 0 SuiteSparse/LDL/Matrix/A030000644001170100242450000000006310232253701014066 0ustar davisfacname: Dense/1 n: 1 entries: 1 1 0 0 1 0 1.90275 0 SuiteSparse/LDL/Matrix/A040000644001170100242450000000012110232253701014062 0ustar davisfacname: Dense/1 n: 1 entries: 2 (jumbled version) 1 1 0 2 0 0 1.90275 0.606843 0 SuiteSparse/LDL/Matrix/A050000644001170100242450000000012710232253701014071 0ustar davisfacname: Dense/2 n: 2 entries: 4 2 0 0 2 4 0 1 0 1 1.78915 0.389047 0.389047 1.67505 0 1 SuiteSparse/LDL/Matrix/A060000644001170100242450000000016510232253701014074 0ustar davisfacname: Dense/2 n: 2 entries: 5 (jumbled version) 2 1 0 3 5 0 1 0 1 0 1.78915 0.389047 0.738207 1.67505 0.389047 0 1 SuiteSparse/LDL/Matrix/A070000644001170100242450000000022110232253701014066 0ustar davisfacname: Dense/3 n: 3 entries: 9 3 0 0 3 6 9 0 1 2 0 1 2 0 1 2 1.92648 0.776267 0.405764 0.776267 1.68063 0.250703 0.405764 0.250703 1.44517 0 1 2 SuiteSparse/LDL/Matrix/A080000644001170100242450000000027410232253701014077 0ustar davisfacname: Dense/3 n: 3 entries: 11 (jumbled version) 3 1 0 4 7 11 2 0 1 2 1 0 2 0 2 0 1 0.262576 1.92648 0.776267 0.405764 1.68063 0.776267 0.250703 0.262576 1.44517 0.405764 0.250703 0 1 2 SuiteSparse/LDL/Matrix/A090000644001170100242450000000162410232253701014100 0ustar davisfacname: HB/can_24 n: 24 entries: 160 24 0 0 9 15 21 27 33 39 48 57 61 70 76 82 88 94 100 106 110 119 128 137 143 152 156 160 0 5 6 12 13 17 18 19 21 1 8 9 13 14 17 2 6 11 20 21 22 3 7 10 15 18 19 4 7 9 14 15 16 0 5 6 12 13 17 0 2 5 6 11 12 19 21 23 3 4 7 9 14 15 16 17 18 1 8 9 14 1 4 7 8 9 13 14 17 18 3 10 18 19 20 21 2 6 11 12 21 23 0 5 6 11 12 23 0 1 5 9 13 17 1 4 7 8 9 14 3 4 7 15 16 18 4 7 15 16 0 1 5 7 9 13 17 18 19 0 3 7 9 10 15 17 18 19 0 3 6 10 17 18 19 20 21 2 10 19 20 21 22 0 2 6 10 11 19 20 21 22 2 20 21 22 6 11 12 23 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 22 20 10 23 12 5 16 8 14 4 15 7 1 9 13 17 0 2 3 6 11 18 21 19 SuiteSparse/LDL/Matrix/A100000644001170100242450000000236310232253701014071 0ustar davisfacname: HB/can_24 n: 24 entries: 188 (jumbled version) 24 1 0 10 16 23 30 37 44 54 67 71 81 89 95 102 108 114 123 128 141 152 161 168 179 183 188 12 6 13 5 17 21 19 0 21 18 14 17 9 8 1 13 2 21 22 21 11 6 20 15 10 18 3 7 19 10 16 9 14 15 7 7 4 6 17 12 0 5 17 13 21 0 6 11 23 6 2 12 5 19 17 15 15 14 7 3 18 16 4 4 9 18 17 8 1 9 14 18 8 14 9 13 17 17 1 7 4 20 20 21 3 19 18 3 10 12 23 11 21 6 2 11 23 5 12 0 23 6 5 0 9 17 13 1 7 1 4 9 14 8 7 15 7 18 15 18 16 4 3 16 4 7 16 15 17 7 5 17 9 0 13 1 19 5 18 7 9 15 0 19 9 7 18 3 7 17 15 10 21 10 3 6 18 19 17 20 0 19 21 2 10 22 10 20 21 19 10 22 11 20 0 0 2 2 6 20 2 21 22 6 12 23 11 12 1 1 1 1 1 0.435191 1 1 1 1 1 1 1 1 1 1 1 0.445161 1 1 1 1 1 1 1 1 1 1 1 0.00496365 1 1 1 1 1 0.215083 1 1 1 1 1 1 0.0801502 1 1 1 1 1 1 0.869867 1 1 1 1 0.436428 1 0.332466 1 1 1 0.367454 1 0.215083 1 1 1 1 1 1 1 1 1 1 1 1 1 0.409378 1 1 1 1 0.132225 1 1 1 1 1 0.00496365 1 1 1 1 1 1 1 1 1 1 1 1 0.483444 1 1 1 1 1 1 1 1 1 1 1 1 1 0.332466 0.23788 1 0.467118 1 1 1 1 1 0.645831 1 1 1 1 1 0.436428 1 0.13701 0.409378 1 1 1 1 0.0801502 1 1 1 1 1 1 1 0.367454 1 1 1 1 0.467118 1 1 1 1 1 1 1 1 1 1 1 1 1 0.132225 1 1 1 1 1 1 1 1 1 1 0.435191 1 0.445161 1 1 1 1 1 1 0.483444 1 1 1 22 20 10 23 12 5 16 8 14 4 15 7 1 9 13 17 0 2 3 6 11 18 21 19 SuiteSparse/LDL/Matrix/A110000644001170100242450000000626510232253701014077 0ustar davisfacname: FIDAP/ex5 n: 27 entries: 279 27 0 0 6 18 27 42 51 66 75 87 93 99 111 120 135 144 159 168 180 186 192 204 213 228 237 252 261 273 279 0 1 9 10 18 19 0 1 2 3 9 10 11 12 18 19 20 21 1 2 3 10 11 12 19 20 21 1 2 3 4 5 10 11 12 13 14 19 20 21 22 23 3 4 5 12 13 14 21 22 23 3 4 5 6 7 12 13 14 15 16 21 22 23 24 25 5 6 7 14 15 16 23 24 25 5 6 7 8 14 15 16 17 23 24 25 26 7 8 16 17 25 26 0 1 9 10 18 19 0 1 2 3 9 10 11 12 18 19 20 21 1 2 3 10 11 12 19 20 21 1 2 3 4 5 10 11 12 13 14 19 20 21 22 23 3 4 5 12 13 14 21 22 23 3 4 5 6 7 12 13 14 15 16 21 22 23 24 25 5 6 7 14 15 16 23 24 25 5 6 7 8 14 15 16 17 23 24 25 26 7 8 16 17 25 26 0 1 9 10 18 19 0 1 2 3 9 10 11 12 18 19 20 21 1 2 3 10 11 12 19 20 21 1 2 3 4 5 10 11 12 13 14 19 20 21 22 23 3 4 5 12 13 14 21 22 23 3 4 5 6 7 12 13 14 15 16 21 22 23 24 25 5 6 7 14 15 16 23 24 25 5 6 7 8 14 15 16 17 23 24 25 26 7 8 16 17 25 26 1.03704e+06 259259 -1.18519e+06 -296297 148148 37037.1 259259 296298 259259 -18518.6 -296297 -148149 -296297 -74074 37037.1 -148148 37037.1 92592.6 259259 1.03704e+06 259259 -296297 -1.18519e+06 -296297 37037.1 148148 37037.1 -18518.6 259259 296298 259259 -18518.6 -74074 -296297 -148149 -296297 -74074 92592.6 37037.1 -148148 37037.1 92592.6 259259 1.03704e+06 259259 -296297 -1.18519e+06 -296297 37037.1 148148 37037.1 -18518.6 259259 296298 259259 -18518.6 -74074 -296297 -148149 -296297 -74074 92592.6 37037.1 -148148 37037.1 92592.6 259259 1.03704e+06 259259 -296297 -1.18519e+06 -296297 37037.1 148148 37037.1 -18518.6 259259 296298 259259 -74074 -296297 -148149 -296297 92592.6 37037.1 -148148 37037.1 259259 1.03704e+06 -296297 -1.18519e+06 37037.1 148148 -1.18519e+06 -296297 2.37038e+06 592592 -1.18519e+06 -296297 -296297 -148149 -296297 -74074 592592 296300 592592 148148 -296297 -148149 -296297 -74074 -296297 -1.18519e+06 -296297 592592 2.37038e+06 592592 -296297 -1.18519e+06 -296297 -74074 -296297 -148149 -296297 -74074 148148 592592 296300 592592 148148 -74074 -296297 -148149 -296297 -74074 -296297 -1.18519e+06 -296297 592592 2.37038e+06 592592 -296297 -1.18519e+06 -296297 -74074 -296297 -148149 -296297 -74074 148148 592592 296300 592592 148148 -74074 -296297 -148149 -296297 -74074 -296297 -1.18519e+06 -296297 592592 2.37038e+06 592592 -296297 -1.18519e+06 -296297 -74074 -296297 -148149 -296297 148148 592592 296300 592592 -74074 -296297 -148149 -296297 -296297 -1.18519e+06 592592 2.37038e+06 -296297 -1.18519e+06 148148 37037.1 -1.18519e+06 -296297 1.03704e+06 259259 37037.1 -148148 37037.1 92592.6 -296297 -148149 -296297 -74074 259259 296298 259259 -18518.6 37037.1 148148 37037.1 -296297 -1.18519e+06 -296297 259259 1.03704e+06 259259 92592.6 37037.1 -148148 37037.1 92592.6 -74074 -296297 -148149 -296297 -74074 -18518.6 259259 296298 259259 -18518.6 37037.1 148148 37037.1 -296297 -1.18519e+06 -296297 259259 1.03704e+06 259259 92592.6 37037.1 -148148 37037.1 92592.6 -74074 -296297 -148149 -296297 -74074 -18518.6 259259 296298 259259 -18518.6 37037.1 148148 37037.1 -296297 -1.18519e+06 -296297 259259 1.03704e+06 259259 92592.6 37037.1 -148148 37037.1 -74074 -296297 -148149 -296297 -18518.6 259259 296298 259259 37037.1 148148 -296297 -1.18519e+06 259259 1.03704e+06 8 17 26 0 9 18 1 2 10 11 20 19 3 4 12 13 22 21 5 6 7 14 15 16 24 25 23 SuiteSparse/LDL/Matrix/A120000644001170100242450000000734010232253701014073 0ustar davisfacname: FIDAP/ex5 n: 27 entries: 325 (jumbled version) 27 1 0 6 19 31 47 57 76 87 101 109 115 127 139 158 168 186 196 211 217 223 236 247 265 275 293 303 318 325 19 9 10 18 1 0 0 2 12 9 12 3 1 11 21 19 10 18 20 21 1 20 12 2 3 11 12 21 10 11 19 22 20 23 19 21 13 19 10 14 11 3 2 12 4 1 5 13 5 22 4 23 21 14 22 3 12 13 14 7 23 15 4 7 3 24 21 25 16 12 5 6 12 14 6 22 5 16 25 5 23 23 6 14 15 24 7 5 26 24 25 17 8 5 14 16 8 15 23 7 6 25 17 16 26 7 25 8 7 9 1 0 10 19 18 18 9 10 11 19 2 1 21 3 12 20 0 11 12 10 21 19 21 20 1 2 2 20 3 5 2 20 22 12 4 14 2 11 1 5 1 19 13 23 12 3 10 21 14 23 23 5 22 21 13 4 12 3 4 6 24 22 3 16 15 16 21 12 23 21 13 5 25 7 14 5 5 7 16 14 23 6 25 15 25 24 6 14 5 7 26 15 24 26 24 25 17 8 23 14 16 16 8 17 25 26 7 18 1 10 9 19 0 1 12 11 18 3 21 0 19 9 2 10 3 20 11 19 21 20 3 10 2 20 11 1 12 22 11 13 4 14 20 19 11 2 23 1 3 10 21 5 12 2 14 12 3 23 13 21 4 4 14 5 22 6 15 13 23 3 5 24 22 14 16 6 7 25 25 21 4 13 12 7 15 5 24 14 6 16 25 23 16 5 8 6 26 14 23 17 23 15 24 15 7 8 25 16 16 7 25 16 26 17 8 37037.1 -1.18519e+06 -296297 148148 259259 1.03704e+06 259259 259259 -74074 -296297 0.440353 -18518.6 296298 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0.49806 -296297 0.280408 -1.18519e+06 -1.18519e+06 -296297 0.22728 0.33095 -296297 -296297 0.904949 -296297 148148 -296297 592592 0.440353 -74074 -74074 -74074 592592 -74074 296300 -148149 148148 -148149 592592 0.166548 -296297 -296297 -1.18519e+06 -296297 2.37038e+06 -1.18519e+06 592592 -296297 -296297 -296297 -296297 -296297 -74074 0.411059 592592 148148 -74074 148148 -148149 0.238296 592592 -148149 -74074 -74074 296300 0.0651008 -296297 -296297 592592 592592 -296297 -1.18519e+06 -296297 2.37038e+06 0.34257 -1.18519e+06 -296297 0.411059 -74074 -148149 0.610887 592592 0.257604 -296297 -296297 -148149 592592 -296297 -74074 148148 296300 592592 -1.18519e+06 2.37038e+06 -296297 -1.18519e+06 -296297 1.03704e+06 37037.1 -296297 -1.18519e+06 259259 148148 -148148 -74074 -296297 259259 0.293848 -18518.6 37037.1 296298 -296297 37037.1 -148149 92592.6 259259 0.49806 259259 259259 0.0136264 37037.1 -296297 148148 1.03704e+06 -1.18519e+06 37037.1 -296297 259259 0.520633 -296297 37037.1 0.238296 259259 -18518.6 -296297 0.483351 -18518.6 92592.6 -148148 -74074 296298 92592.6 -148149 37037.1 -74074 -296297 37037.1 259259 -1.18519e+06 259259 0.0325172 148148 -296297 37037.1 1.03704e+06 37037.1 -296297 -296297 296298 92592.6 -148148 259259 259259 -148149 -74074 0.333923 92592.6 -18518.6 0.127177 -18518.6 37037.1 0.166548 -74074 37037.1 -1.18519e+06 37037.1 1.03704e+06 -296297 148148 0.257604 259259 259259 -296297 92592.6 37037.1 37037.1 259259 -74074 -18518.6 -296297 0.127177 -296297 259259 0.34257 -148148 0.255077 296298 -148149 0.610887 37037.1 259259 -296297 1.03704e+06 -1.18519e+06 148148 8 17 26 0 9 18 1 2 10 11 20 19 3 4 12 13 22 21 5 6 7 14 15 16 24 25 23 SuiteSparse/LDL/Matrix/A130000644001170100242450000001262510232253701014076 0ustar davisfacname: HB/bcsstk01 n: 48 entries: 400 48 0 0 8 16 24 32 40 48 56 64 72 80 88 96 107 119 131 142 154 166 174 182 190 198 206 214 221 226 231 238 243 248 256 264 272 280 288 296 304 312 320 328 336 344 354 363 372 382 391 400 0 4 5 6 10 18 24 29 1 3 5 7 9 19 23 25 2 3 4 8 20 22 26 27 1 2 3 7 9 21 26 27 0 2 4 6 10 20 22 28 0 1 5 11 19 23 24 29 0 4 6 10 11 12 30 35 1 3 7 9 11 13 17 31 2 8 9 10 14 16 32 33 1 3 7 8 9 15 32 33 0 4 6 8 10 14 16 34 5 6 7 11 13 17 30 35 6 12 16 17 18 22 36 41 42 46 47 7 11 13 14 15 17 19 21 37 43 44 45 8 10 13 14 15 16 20 38 39 43 44 45 9 13 14 15 19 21 38 39 43 44 45 8 10 12 14 16 17 18 22 40 42 46 47 7 11 12 13 16 17 23 36 41 42 46 47 0 12 16 18 22 23 42 47 1 5 13 15 19 21 23 43 2 4 14 20 21 22 44 45 3 13 15 19 20 21 44 45 2 4 12 16 18 20 22 46 1 5 17 18 19 23 42 47 0 5 24 28 29 30 34 1 25 27 31 33 2 3 26 27 32 2 3 25 26 27 31 33 4 24 28 30 34 0 5 24 29 35 6 11 24 28 30 34 35 36 7 25 27 31 33 35 37 41 8 9 26 32 33 34 38 40 8 9 25 27 31 32 33 39 10 24 28 30 32 34 38 40 6 11 29 30 31 35 37 41 12 17 30 36 40 41 42 46 13 31 35 37 39 41 43 45 14 15 32 34 38 39 40 44 14 15 33 37 38 39 43 45 16 32 34 36 38 40 42 46 12 17 31 35 36 37 41 47 12 16 17 18 23 36 40 42 46 47 13 14 15 19 37 39 43 44 45 13 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SuiteSparse/LDL/Matrix/A170000644001170100242450000000743710232253701014107 0ustar davisfacname: Pothen/mesh1e1 n: 48 entries: 306 48 0 0 5 12 16 22 26 32 36 42 49 54 61 68 73 79 84 90 96 103 109 117 123 131 138 144 150 158 164 171 178 184 190 197 204 211 218 224 232 238 245 251 258 266 272 279 287 294 301 306 0 1 7 44 47 0 1 2 41 42 45 47 1 2 3 45 2 3 4 36 43 45 3 4 5 43 4 5 6 40 43 46 5 6 7 46 0 6 7 34 44 46 8 9 14 17 22 29 30 8 9 10 20 22 9 10 11 20 23 24 26 10 11 12 26 33 35 37 11 12 13 18 33 12 13 14 15 16 18 8 13 14 15 17 13 14 15 16 17 19 13 15 16 18 19 21 8 14 15 17 19 30 39 12 13 16 18 21 33 15 16 17 19 21 39 41 42 9 10 20 22 23 27 16 18 19 21 33 36 42 45 8 9 20 22 27 29 32 10 20 23 24 25 27 10 23 24 25 26 28 23 24 25 27 28 34 40 46 10 11 24 26 28 37 20 22 23 25 27 32 34 24 25 26 28 37 38 40 8 22 29 30 31 32 8 17 29 30 31 39 29 30 31 32 39 41 44 22 27 29 31 32 34 44 11 12 18 21 33 35 36 7 25 27 32 34 44 46 11 33 35 36 37 38 3 21 33 35 36 38 43 45 11 26 28 35 37 38 28 35 36 37 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0ustar davisfacname: Dense/2 n: 2 entries: 4 (invalid perm, P[1]=99) 2 0 0 2 4 0 1 0 1 1.78915 0.389047 0.389047 1.67505 0 99 SuiteSparse/LDL/Matrix/A270000644001170100242450000000024010232253701014071 0ustar davisfacname: Dense/3 n: 3 entries: 9 (invalid perm) 3 0 0 3 6 9 0 1 2 0 1 2 0 1 2 1.92648 0.776267 0.405764 0.776267 1.68063 0.250703 0.405764 0.250703 1.44517 0 1 1 SuiteSparse/LDL/Matrix/A280000644001170100242450000000023610232253701014077 0ustar davisfacname: Dense/3 n: 3 entries: 9 (invalid Ap) 3 0 0 3 2 9 0 1 2 0 1 2 0 1 2 1.92648 0.776267 0.405764 0.776267 1.68063 0.250703 0.405764 0.250703 1.44517 0 1 2 SuiteSparse/LDL/Matrix/A290000644001170100242450000000023610232253701014100 0ustar davisfacname: Dense/3 n: 3 entries: 9 (invalid Ai) 3 0 0 3 6 9 0 1 3 0 1 2 0 1 2 1.92648 0.776267 0.405764 0.776267 1.68063 0.250703 0.405764 0.250703 1.44517 0 1 2 SuiteSparse/LDL/Matrix/A300000644001170100242450000000023710232253701014071 0ustar davisfacname: Dense/3 n: 3 entries: 9 (invalid Ai) 3 0 0 3 6 9 0 -1 2 0 1 2 0 1 2 1.92648 0.776267 0.405764 0.776267 1.68063 0.250703 0.405764 0.250703 1.44517 0 1 2 SuiteSparse/LDL/Include/0000755001170100242450000000000010617162634013753 5ustar davisfacSuiteSparse/LDL/Include/ldl.h0000644001170100242450000000753510711427321014701 0ustar davisfac/* ========================================================================== */ /* === ldl.h: include file for the LDL package ============================= */ /* ========================================================================== */ /* LDL Copyright (c) Timothy A Davis, * University of Florida. All Rights Reserved. See README for the License. */ #include "UFconfig.h" #ifdef LDL_LONG #define LDL_int UF_long #define LDL_ID UF_long_id #define LDL_symbolic ldl_l_symbolic #define LDL_numeric ldl_l_numeric #define LDL_lsolve ldl_l_lsolve #define LDL_dsolve ldl_l_dsolve #define LDL_ltsolve ldl_l_ltsolve #define LDL_perm ldl_l_perm #define LDL_permt ldl_l_permt #define LDL_valid_perm ldl_l_valid_perm #define LDL_valid_matrix ldl_l_valid_matrix #else #define LDL_int int #define LDL_ID "%d" #define LDL_symbolic ldl_symbolic #define LDL_numeric ldl_numeric #define LDL_lsolve ldl_lsolve #define LDL_dsolve ldl_dsolve #define LDL_ltsolve ldl_ltsolve #define LDL_perm ldl_perm #define LDL_permt ldl_permt #define LDL_valid_perm ldl_valid_perm #define LDL_valid_matrix ldl_valid_matrix #endif /* ========================================================================== */ /* === int version ========================================================== */ /* ========================================================================== */ void ldl_symbolic (int n, int Ap [ ], int Ai [ ], int Lp [ ], int Parent [ ], int Lnz [ ], int Flag [ ], int P [ ], int Pinv [ ]) ; int ldl_numeric (int n, int Ap [ ], int Ai [ ], double Ax [ ], int Lp [ ], int Parent [ ], int Lnz [ ], int Li [ ], double Lx [ ], double D [ ], double Y [ ], int Pattern [ ], int Flag [ ], int P [ ], int Pinv [ ]) ; void ldl_lsolve (int n, double X [ ], int Lp [ ], int Li [ ], double Lx [ ]) ; void ldl_dsolve (int n, double X [ ], double D [ ]) ; void ldl_ltsolve (int n, double X [ ], int Lp [ ], int Li [ ], double Lx [ ]) ; void ldl_perm (int n, double X [ ], double B [ ], int P [ ]) ; void ldl_permt (int n, double X [ ], double B [ ], int P [ ]) ; int ldl_valid_perm (int n, int P [ ], int Flag [ ]) ; int ldl_valid_matrix ( int n, int Ap [ ], int Ai [ ]) ; /* ========================================================================== */ /* === long version ========================================================= */ /* ========================================================================== */ void ldl_l_symbolic (UF_long n, UF_long Ap [ ], UF_long Ai [ ], UF_long Lp [ ], UF_long Parent [ ], UF_long Lnz [ ], UF_long Flag [ ], UF_long P [ ], UF_long Pinv [ ]) ; UF_long ldl_l_numeric (UF_long n, UF_long Ap [ ], UF_long Ai [ ], double Ax [ ], UF_long Lp [ ], UF_long Parent [ ], UF_long Lnz [ ], UF_long Li [ ], double Lx [ ], double D [ ], double Y [ ], UF_long Pattern [ ], UF_long Flag [ ], UF_long P [ ], UF_long Pinv [ ]) ; void ldl_l_lsolve (UF_long n, double X [ ], UF_long Lp [ ], UF_long Li [ ], double Lx [ ]) ; void ldl_l_dsolve (UF_long n, double X [ ], double D [ ]) ; void ldl_l_ltsolve (UF_long n, double X [ ], UF_long Lp [ ], UF_long Li [ ], double Lx [ ]) ; void ldl_l_perm (UF_long n, double X [ ], double B [ ], UF_long P [ ]) ; void ldl_l_permt (UF_long n, double X [ ], double B [ ], UF_long P [ ]) ; UF_long ldl_l_valid_perm (UF_long n, UF_long P [ ], UF_long Flag [ ]) ; UF_long ldl_l_valid_matrix ( UF_long n, UF_long Ap [ ], UF_long Ai [ ]) ; /* ========================================================================== */ /* === LDL version ========================================================== */ /* ========================================================================== */ #define LDL_DATE "Nov 1, 2007" #define LDL_VERSION_CODE(main,sub) ((main) * 1000 + (sub)) #define LDL_MAIN_VERSION 2 #define LDL_SUB_VERSION 0 #define LDL_SUBSUB_VERSION 1 #define LDL_VERSION LDL_VERSION_CODE(LDL_MAIN_VERSION,LDL_SUB_VERSION) SuiteSparse/LDL/Source/0000755001170100242450000000000010661335241013623 5ustar davisfacSuiteSparse/LDL/Source/ldl.c0000644001170100242450000005060710616416710014553 0ustar davisfac/* ========================================================================== */ /* === ldl.c: sparse LDL' factorization and solve package =================== */ /* ========================================================================== */ /* LDL: a simple set of routines for sparse LDL' factorization. These routines * are not terrifically fast (they do not use dense matrix kernels), but the * code is very short. The purpose is to illustrate the algorithms in a very * concise manner, primarily for educational purposes. Although the code is * very concise, this package is slightly faster than the built-in sparse * Cholesky factorization in MATLAB 7.0 (chol), when using the same input * permutation. * * The routines compute the LDL' factorization of a real sparse symmetric * matrix A (or PAP' if a permutation P is supplied), and solve upper * and lower triangular systems with the resulting L and D factors. If A is * positive definite then the factorization will be accurate. A can be * indefinite (with negative values on the diagonal D), but in this case no * guarantee of accuracy is provided, since no numeric pivoting is performed. * * The n-by-n sparse matrix A is in compressed-column form. The nonzero values * in column j are stored in Ax [Ap [j] ... Ap [j+1]-1], with corresponding row * indices in Ai [Ap [j] ... Ap [j+1]-1]. Ap [0] = 0 is required, and thus * nz = Ap [n] is the number of nonzeros in A. Ap is an int array of size n+1. * The int array Ai and the double array Ax are of size nz. This data structure * is identical to the one used by MATLAB, except for the following * generalizations. The row indices in each column of A need not be in any * particular order, although they must be in the range 0 to n-1. Duplicate * entries can be present; any duplicates are summed. That is, if row index i * appears twice in a column j, then the value of A (i,j) is the sum of the two * entries. The data structure used here for the input matrix A is more * flexible than MATLAB's, which requires sorted columns with no duplicate * entries. * * Only the diagonal and upper triangular part of A (or PAP' if a permutation * P is provided) is accessed. The lower triangular parts of the matrix A or * PAP' can be present, but they are ignored. * * The optional input permutation is provided as an array P of length n. If * P [k] = j, the row and column j of A is the kth row and column of PAP'. * If P is present then the factorization is LDL' = PAP' or L*D*L' = A(P,P) in * 0-based MATLAB notation. If P is not present (a null pointer) then no * permutation is performed, and the factorization is LDL' = A. * * The lower triangular matrix L is stored in the same compressed-column * form (an int Lp array of size n+1, an int Li array of size Lp [n], and a * double array Lx of the same size as Li). It has a unit diagonal, which is * not stored. The row indices in each column of L are always returned in * ascending order, with no duplicate entries. This format is compatible with * MATLAB, except that it would be more convenient for MATLAB to include the * unit diagonal of L. Doing so here would add additional complexity to the * code, and is thus omitted in the interest of keeping this code short and * readable. * * The elimination tree is held in the Parent [0..n-1] array. It is normally * not required by the user, but it is required by ldl_numeric. The diagonal * matrix D is held as an array D [0..n-1] of size n. * * -------------------- * C-callable routines: * -------------------- * * ldl_symbolic: Given the pattern of A, computes the Lp and Parent arrays * required by ldl_numeric. Takes time proportional to the number of * nonzeros in L. Computes the inverse Pinv of P if P is provided. * Also returns Lnz, the count of nonzeros in each column of L below * the diagonal (this is not required by ldl_numeric). * ldl_numeric: Given the pattern and numerical values of A, the Lp array, * the Parent array, and P and Pinv if applicable, computes the * pattern and numerical values of L and D. * ldl_lsolve: Solves Lx=b for a dense vector b. * ldl_dsolve: Solves Dx=b for a dense vector b. * ldl_ltsolve: Solves L'x=b for a dense vector b. * ldl_perm: Computes x=Pb for a dense vector b. * ldl_permt: Computes x=P'b for a dense vector b. * ldl_valid_perm: checks the validity of a permutation vector * ldl_valid_matrix: checks the validity of the sparse matrix A * * ---------------------------- * Limitations of this package: * ---------------------------- * * In the interest of keeping this code simple and readable, ldl_symbolic and * ldl_numeric assume their inputs are valid. You can check your own inputs * prior to calling these routines with the ldl_valid_perm and ldl_valid_matrix * routines. Except for the two ldl_valid_* routines, no routine checks to see * if the array arguments are present (non-NULL). Like all C routines, no * routine can determine if the arrays are long enough and don't overlap. * * The ldl_numeric does check the numerical factorization, however. It returns * n if the factorization is successful. If D (k,k) is zero, then k is * returned, and L is only partially computed. * * No pivoting to control fill-in is performed, which is often critical for * obtaining good performance. I recommend that you compute the permutation P * using AMD or SYMAMD (approximate minimum degree ordering routines), or an * appropriate graph-partitioning based ordering. See the ldldemo.m routine for * an example in MATLAB, and the ldlmain.c stand-alone C program for examples of * how to find P. Routines for manipulating compressed-column matrices are * available in UMFPACK. AMD, SYMAMD, UMFPACK, and this LDL package are all * available at http://www.cise.ufl.edu/research/sparse. * * ------------------------- * Possible simplifications: * ------------------------- * * These routines could be made even simpler with a few additional assumptions. * If no input permutation were performed, the caller would have to permute the * matrix first, but the computation of Pinv, and the use of P and Pinv could be * removed. If only the diagonal and upper triangular part of A or PAP' are * present, then the tests in the "if (i < k)" statement in ldl_symbolic and * "if (i <= k)" in ldl_numeric, are always true, and could be removed (i can * equal k in ldl_symbolic, but then the body of the if statement would * correctly do no work since Flag [k] == k). If we could assume that no * duplicate entries are present, then the statement Y [i] += Ax [p] could be * replaced with Y [i] = Ax [p] in ldl_numeric. * * -------------------------- * Description of the method: * -------------------------- * * LDL computes the symbolic factorization by finding the pattern of L one row * at a time. It does this based on the following theory. Consider a sparse * system Lx=b, where L, x, and b, are all sparse, and where L comes from a * Cholesky (or LDL') factorization. The elimination tree (etree) of L is * defined as follows. The parent of node j is the smallest k > j such that * L (k,j) is nonzero. Node j has no parent if column j of L is completely zero * below the diagonal (j is a root of the etree in this case). The nonzero * pattern of x is the union of the paths from each node i to the root, for * each nonzero b (i). To compute the numerical solution to Lx=b, we can * traverse the columns of L corresponding to nonzero values of x. This * traversal does not need to be done in the order 0 to n-1. It can be done in * any "topological" order, such that x (i) is computed before x (j) if i is a * descendant of j in the elimination tree. * * The row-form of the LDL' factorization is shown in the MATLAB function * ldlrow.m in this LDL package. Note that row k of L is found via a sparse * triangular solve of L (1:k-1, 1:k-1) \ A (1:k-1, k), to use 1-based MATLAB * notation. Thus, we can start with the nonzero pattern of the kth column of * A (above the diagonal), follow the paths up to the root of the etree of the * (k-1)-by-(k-1) leading submatrix of L, and obtain the pattern of the kth row * of L. Note that we only need the leading (k-1)-by-(k-1) submatrix of L to * do this. The elimination tree can be constructed as we go. * * The symbolic factorization does the same thing, except that it discards the * pattern of L as it is computed. It simply counts the number of nonzeros in * each column of L and then constructs the Lp index array when it's done. The * symbolic factorization does not need to do this in topological order. * Compare ldl_symbolic with the first part of ldl_numeric, and note that the * while (len > 0) loop is not present in ldl_symbolic. * * LDL Version 1.3, Copyright (c) 2006 by Timothy A Davis, * University of Florida. All Rights Reserved. Developed while on sabbatical * at Stanford University and Lawrence Berkeley National Laboratory. Refer to * the README file for the License. Available at * http://www.cise.ufl.edu/research/sparse. */ #include "ldl.h" /* ========================================================================== */ /* === ldl_symbolic ========================================================= */ /* ========================================================================== */ /* The input to this routine is a sparse matrix A, stored in column form, and * an optional permutation P. The output is the elimination tree * and the number of nonzeros in each column of L. Parent [i] = k if k is the * parent of i in the tree. The Parent array is required by ldl_numeric. * Lnz [k] gives the number of nonzeros in the kth column of L, excluding the * diagonal. * * One workspace vector (Flag) of size n is required. * * If P is NULL, then it is ignored. The factorization will be LDL' = A. * Pinv is not computed. In this case, neither P nor Pinv are required by * ldl_numeric. * * If P is not NULL, then it is assumed to be a valid permutation. If * row and column j of A is the kth pivot, the P [k] = j. The factorization * will be LDL' = PAP', or A (p,p) in MATLAB notation. The inverse permutation * Pinv is computed, where Pinv [j] = k if P [k] = j. In this case, both P * and Pinv are required as inputs to ldl_numeric. * * The floating-point operation count of the subsequent call to ldl_numeric * is not returned, but could be computed after ldl_symbolic is done. It is * the sum of (Lnz [k]) * (Lnz [k] + 2) for k = 0 to n-1. */ void LDL_symbolic ( LDL_int n, /* A and L are n-by-n, where n >= 0 */ LDL_int Ap [ ], /* input of size n+1, not modified */ LDL_int Ai [ ], /* input of size nz=Ap[n], not modified */ LDL_int Lp [ ], /* output of size n+1, not defined on input */ LDL_int Parent [ ], /* output of size n, not defined on input */ LDL_int Lnz [ ], /* output of size n, not defined on input */ LDL_int Flag [ ], /* workspace of size n, not defn. on input or output */ LDL_int P [ ], /* optional input of size n */ LDL_int Pinv [ ] /* optional output of size n (used if P is not NULL) */ ) { LDL_int i, k, p, kk, p2 ; if (P) { /* If P is present then compute Pinv, the inverse of P */ for (k = 0 ; k < n ; k++) { Pinv [P [k]] = k ; } } for (k = 0 ; k < n ; k++) { /* L(k,:) pattern: all nodes reachable in etree from nz in A(0:k-1,k) */ Parent [k] = -1 ; /* parent of k is not yet known */ Flag [k] = k ; /* mark node k as visited */ Lnz [k] = 0 ; /* count of nonzeros in column k of L */ kk = (P) ? (P [k]) : (k) ; /* kth original, or permuted, column */ p2 = Ap [kk+1] ; for (p = Ap [kk] ; p < p2 ; p++) { /* A (i,k) is nonzero (original or permuted A) */ i = (Pinv) ? (Pinv [Ai [p]]) : (Ai [p]) ; if (i < k) { /* follow path from i to root of etree, stop at flagged node */ for ( ; Flag [i] != k ; i = Parent [i]) { /* find parent of i if not yet determined */ if (Parent [i] == -1) Parent [i] = k ; Lnz [i]++ ; /* L (k,i) is nonzero */ Flag [i] = k ; /* mark i as visited */ } } } } /* construct Lp index array from Lnz column counts */ Lp [0] = 0 ; for (k = 0 ; k < n ; k++) { Lp [k+1] = Lp [k] + Lnz [k] ; } } /* ========================================================================== */ /* === ldl_numeric ========================================================== */ /* ========================================================================== */ /* Given a sparse matrix A (the arguments n, Ap, Ai, and Ax) and its symbolic * analysis (Lp and Parent, and optionally P and Pinv), compute the numeric LDL' * factorization of A or PAP'. The outputs of this routine are arguments Li, * Lx, and D. It also requires three size-n workspaces (Y, Pattern, and Flag). */ LDL_int LDL_numeric /* returns n if successful, k if D (k,k) is zero */ ( LDL_int n, /* A and L are n-by-n, where n >= 0 */ LDL_int Ap [ ], /* input of size n+1, not modified */ LDL_int Ai [ ], /* input of size nz=Ap[n], not modified */ double Ax [ ], /* input of size nz=Ap[n], not modified */ LDL_int Lp [ ], /* input of size n+1, not modified */ LDL_int Parent [ ], /* input of size n, not modified */ LDL_int Lnz [ ], /* output of size n, not defn. on input */ LDL_int Li [ ], /* output of size lnz=Lp[n], not defined on input */ double Lx [ ], /* output of size lnz=Lp[n], not defined on input */ double D [ ], /* output of size n, not defined on input */ double Y [ ], /* workspace of size n, not defn. on input or output */ LDL_int Pattern [ ],/* workspace of size n, not defn. on input or output */ LDL_int Flag [ ], /* workspace of size n, not defn. on input or output */ LDL_int P [ ], /* optional input of size n */ LDL_int Pinv [ ] /* optional input of size n */ ) { double yi, l_ki ; LDL_int i, k, p, kk, p2, len, top ; for (k = 0 ; k < n ; k++) { /* compute nonzero Pattern of kth row of L, in topological order */ Y [k] = 0.0 ; /* Y(0:k) is now all zero */ top = n ; /* stack for pattern is empty */ Flag [k] = k ; /* mark node k as visited */ Lnz [k] = 0 ; /* count of nonzeros in column k of L */ kk = (P) ? (P [k]) : (k) ; /* kth original, or permuted, column */ p2 = Ap [kk+1] ; for (p = Ap [kk] ; p < p2 ; p++) { i = (Pinv) ? (Pinv [Ai [p]]) : (Ai [p]) ; /* get A(i,k) */ if (i <= k) { Y [i] += Ax [p] ; /* scatter A(i,k) into Y (sum duplicates) */ for (len = 0 ; Flag [i] != k ; i = Parent [i]) { Pattern [len++] = i ; /* L(k,i) is nonzero */ Flag [i] = k ; /* mark i as visited */ } while (len > 0) Pattern [--top] = Pattern [--len] ; } } /* compute numerical values kth row of L (a sparse triangular solve) */ D [k] = Y [k] ; /* get D(k,k) and clear Y(k) */ Y [k] = 0.0 ; for ( ; top < n ; top++) { i = Pattern [top] ; /* Pattern [top:n-1] is pattern of L(:,k) */ yi = Y [i] ; /* get and clear Y(i) */ Y [i] = 0.0 ; p2 = Lp [i] + Lnz [i] ; for (p = Lp [i] ; p < p2 ; p++) { Y [Li [p]] -= Lx [p] * yi ; } l_ki = yi / D [i] ; /* the nonzero entry L(k,i) */ D [k] -= l_ki * yi ; Li [p] = k ; /* store L(k,i) in column form of L */ Lx [p] = l_ki ; Lnz [i]++ ; /* increment count of nonzeros in col i */ } if (D [k] == 0.0) return (k) ; /* failure, D(k,k) is zero */ } return (n) ; /* success, diagonal of D is all nonzero */ } /* ========================================================================== */ /* === ldl_lsolve: solve Lx=b ============================================== */ /* ========================================================================== */ void LDL_lsolve ( LDL_int n, /* L is n-by-n, where n >= 0 */ double X [ ], /* size n. right-hand-side on input, soln. on output */ LDL_int Lp [ ], /* input of size n+1, not modified */ LDL_int Li [ ], /* input of size lnz=Lp[n], not modified */ double Lx [ ] /* input of size lnz=Lp[n], not modified */ ) { LDL_int j, p, p2 ; for (j = 0 ; j < n ; j++) { p2 = Lp [j+1] ; for (p = Lp [j] ; p < p2 ; p++) { X [Li [p]] -= Lx [p] * X [j] ; } } } /* ========================================================================== */ /* === ldl_dsolve: solve Dx=b ============================================== */ /* ========================================================================== */ void LDL_dsolve ( LDL_int n, /* D is n-by-n, where n >= 0 */ double X [ ], /* size n. right-hand-side on input, soln. on output */ double D [ ] /* input of size n, not modified */ ) { LDL_int j ; for (j = 0 ; j < n ; j++) { X [j] /= D [j] ; } } /* ========================================================================== */ /* === ldl_ltsolve: solve L'x=b ============================================ */ /* ========================================================================== */ void LDL_ltsolve ( LDL_int n, /* L is n-by-n, where n >= 0 */ double X [ ], /* size n. right-hand-side on input, soln. on output */ LDL_int Lp [ ], /* input of size n+1, not modified */ LDL_int Li [ ], /* input of size lnz=Lp[n], not modified */ double Lx [ ] /* input of size lnz=Lp[n], not modified */ ) { int j, p, p2 ; for (j = n-1 ; j >= 0 ; j--) { p2 = Lp [j+1] ; for (p = Lp [j] ; p < p2 ; p++) { X [j] -= Lx [p] * X [Li [p]] ; } } } /* ========================================================================== */ /* === ldl_perm: permute a vector, x=Pb ===================================== */ /* ========================================================================== */ void LDL_perm ( LDL_int n, /* size of X, B, and P */ double X [ ], /* output of size n. */ double B [ ], /* input of size n. */ LDL_int P [ ] /* input permutation array of size n. */ ) { LDL_int j ; for (j = 0 ; j < n ; j++) { X [j] = B [P [j]] ; } } /* ========================================================================== */ /* === ldl_permt: permute a vector, x=P'b =================================== */ /* ========================================================================== */ void LDL_permt ( LDL_int n, /* size of X, B, and P */ double X [ ], /* output of size n. */ double B [ ], /* input of size n. */ LDL_int P [ ] /* input permutation array of size n. */ ) { LDL_int j ; for (j = 0 ; j < n ; j++) { X [P [j]] = B [j] ; } } /* ========================================================================== */ /* === ldl_valid_perm: check if a permutation vector is valid =============== */ /* ========================================================================== */ LDL_int LDL_valid_perm /* returns 1 if valid, 0 otherwise */ ( LDL_int n, LDL_int P [ ], /* input of size n, a permutation of 0:n-1 */ LDL_int Flag [ ] /* workspace of size n */ ) { LDL_int j, k ; if (n < 0 || !Flag) { return (0) ; /* n must be >= 0, and Flag must be present */ } if (!P) { return (1) ; /* If NULL, P is assumed to be the identity perm. */ } for (j = 0 ; j < n ; j++) { Flag [j] = 0 ; /* clear the Flag array */ } for (k = 0 ; k < n ; k++) { j = P [k] ; if (j < 0 || j >= n || Flag [j] != 0) { return (0) ; /* P is not valid */ } Flag [j] = 1 ; } return (1) ; /* P is valid */ } /* ========================================================================== */ /* === ldl_valid_matrix: check if a sparse matrix is valid ================== */ /* ========================================================================== */ /* This routine checks to see if a sparse matrix A is valid for input to * ldl_symbolic and ldl_numeric. It returns 1 if the matrix is valid, 0 * otherwise. A is in sparse column form. The numerical values in column j * are stored in Ax [Ap [j] ... Ap [j+1]-1], with row indices in * Ai [Ap [j] ... Ap [j+1]-1]. The Ax array is not checked. */ LDL_int LDL_valid_matrix ( LDL_int n, LDL_int Ap [ ], LDL_int Ai [ ] ) { LDL_int j, p ; if (n < 0 || !Ap || !Ai || Ap [0] != 0) { return (0) ; /* n must be >= 0, and Ap and Ai must be present */ } for (j = 0 ; j < n ; j++) { if (Ap [j] > Ap [j+1]) { return (0) ; /* Ap must be monotonically nondecreasing */ } } for (p = 0 ; p < Ap [n] ; p++) { if (Ai [p] < 0 || Ai [p] >= n) { return (0) ; /* row indices must be in the range 0 to n-1 */ } } return (1) ; /* matrix is valid */ } SuiteSparse/LDL/README.txt0000644001170100242450000001323710617136555014077 0ustar davisfacLDL Version 2.0: a sparse LDL' factorization and solve package. Written in C, with both a C and MATLAB mexFunction interface. These routines are not terrifically fast (they do not use dense matrix kernels), but the code is very short and concise. The purpose is to illustrate the algorithms in a very concise and readable manner, primarily for educational purposes. Although the code is very concise, this package is slightly faster than the built-in sparse Cholesky factorization in MATLAB 6.5 (chol), when using the same input permutation. Requires UFconfig, in the ../UFconfig directory relative to this directory. Quick start (Unix, or Windows with Cygwin): To compile, test, and install LDL, you may wish to first obtain a copy of AMD v2.0 from http://www.cise.ufl.edu/research/sparse, and place it in the ../AMD directory, relative to this directory. Next, type "make", which will compile the LDL library and three demo main programs (one of which requires AMD). It will also compile the LDL MATLAB mexFunction (if you have MATLAB). Typing "make clean" will remove non-essential files. AMD v2.0 or later is required. Its use is optional. Quick start (for MATLAB users); To compile, test, and install the LDL mexFunctions (ldlsparse and ldlsymbol), start MATLAB in this directory and type ldl_install. This works on any system supported by MATLAB. -------------------------------------------------------------------------------- LDL Copyright (c) 2005 by Timothy A. Davis. All Rights Reserved. LDL License: Your use or distribution of LDL or any modified version of LDL implies that you agree to this License. This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Permission is hereby granted to use or copy this program under the terms of the GNU LGPL, provided that the Copyright, this License, and the Availability of the original version is retained on all copies. User documentation of any code that uses this code or any modified version of this code must cite the Copyright, this License, the Availability note, and "Used by permission." Permission to modify the code and to distribute modified code is granted, provided the Copyright, this License, and the Availability note are retained, and a notice that the code was modified is included. Availability: http://www.cise.ufl.edu/research/sparse/ldl Acknowledgements: This work was supported by the National Science Foundation, under grant CCR-0203270. Portions of this work were done while on sabbatical at Stanford University and Lawrence Berkeley National Laboratory (with funding from the SciDAC program). I would like to thank Gene Golub, Esmond Ng, and Horst Simon for making this sabbatical possible. I would like to thank Pete Stewart for his comments on a draft of this software and paper. -------------------------------------------------------------------------------- Files and directories in this distribution: -------------------------------------------------------------------------------- Documentation, and compiling: README.txt this file Makefile for compiling LDL ChangeLog changes since V1.0 (Dec 31, 2003) License license lesser.txt the GNU LGPL license ldl_userguide.pdf user guide in PDF ldl_userguide.ps user guide in postscript ldl_userguide.tex user guide in Latex ldl.bib bibliography for user guide The LDL library itself: ldl.c the C-callable routines ldl.h include file for any code that calls LDL A simple C main program that demonstrates how to use LDL: ldlsimple.c a stand-alone C program, uses the basic features of LDL ldlsimple.out output of ldlsimple ldllsimple.c long integer version of ldlsimple.c Demo C program, for testing LDL and providing an example of its use ldlmain.c a stand-alone C main program that uses and tests LDL Matrix a directory containing matrices used by ldlmain.c ldlmain.out output of ldlmain ldlamd.out output of ldlamd (ldlmain.c compiled with AMD) ldllamd.out output of ldllamd (ldlmain.c compiled with AMD, long) MATLAB-related, not required for use in a regular C program Contents.m a list of the MATLAB-callable routines ldl.m MATLAB help file for the LDL mexFunction ldldemo.m MATLAB demo of how to use the LDL mexFunction ldldemo.out diary output of ldldemo ldltest.m to test the LDL mexFunction ldltest.out diary output of ldltest ldlmex.c the LDL mexFunction for MATLAB ldlrow.m the numerical algorithm that LDL is based on ldlmain2.m compiles and runs ldlmain.c as a MATLAB mexFunction ldlmain2.out output of ldlmain2.m ldlsymbolmex.c symbolic factorization using LDL (see SYMBFACT, ETREE) ldlsymbol.m help file for the LDLSYMBOL mexFunction ldl_install.m compile, install, and test LDL functions ldl_make.m compile LDL (ldlsparse and ldlsymbol) ldlsparse.m help for ldlsparse See ldl.c for a description of how to use the code from a C program. Type "help ldl" in MATLAB for information on how to use LDL in a MATLAB program. SuiteSparse/CAMD/0000755001170100242450000000000010617112467012460 5ustar davisfacSuiteSparse/CAMD/Doc/0000755001170100242450000000000010621174211013153 5ustar davisfacSuiteSparse/CAMD/Doc/Makefile0000644001170100242450000000205710425640053014623 0ustar davisfac#------------------------------------------------------------------------------ # CAMD Makefile for compiling on Unix systems (for GNU or original make) #------------------------------------------------------------------------------ default: dist include ../../UFconfig/UFconfig.mk #------------------------------------------------------------------------------ # Remove all but the files in the original distribution #------------------------------------------------------------------------------ clean: - $(RM) $(CLEAN) - $(RM) camd_temp purge: distclean distclean: clean - $(RM) *.aux *.bbl *.blg *.log *.toc #------------------------------------------------------------------------------ # Create the User Guide and Quick Start Guide #------------------------------------------------------------------------------ CAMD_UserGuide.pdf: CAMD_UserGuide.tex CAMD_UserGuide.bib pdflatex CAMD_UserGuide bibtex CAMD_UserGuide pdflatex CAMD_UserGuide pdflatex CAMD_UserGuide dist: CAMD_UserGuide.pdf - $(RM) *.aux *.bbl *.blg *.log *.toc - $(RM) camd_temp SuiteSparse/CAMD/Doc/cdiff0000755001170100242450000000010510423445532014157 0ustar davisfac# echo diff $1 $2 sed -f camd.sed < $1 > camd_temp diff camd_temp $2 SuiteSparse/CAMD/Doc/docdiff0000755001170100242450000000411710616401241014502 0ustar davisfac./cdiff ../Demo/camd_demo2.c ../../AMD/Demo/amd_demo2.c ./cdiff ../Demo/camd_demo.c ../../AMD/Demo/amd_demo.c ./cdiff ../Demo/camd_l_demo.c ../../AMD/Demo/amd_l_demo.c ./cdiff ../Demo/camd_simple.c ../../AMD/Demo/amd_simple.c ./cdiff ../Demo/Makefile ../../AMD/Demo/Makefile ./cdiff ../Doc/CAMD_UserGuide.bib ../../AMD/Doc/AMD_UserGuide.bib ./cdiff ../Doc/CAMD_UserGuide.tex ../../AMD/Doc/AMD_UserGuide.tex ./cdiff ../Doc/lesser.txt ../../AMD/Doc/lesser.txt ./cdiff ../Doc/License ../../AMD/Doc/License ./cdiff ../Doc/Makefile ../../AMD/Doc/Makefile ./cdiff ../Include/camd.h ../../AMD/Include/amd.h ./cdiff ../Include/camd_internal.h ../../AMD/Include/amd_internal.h ./cdiff ../Lib/libcamd.def ../../AMD/Lib/libamd.def ./cdiff ../MATLAB/camd_demo.m ../../AMD/MATLAB/amd_demo.m ./cdiff ../MATLAB/camd.m ../../AMD/MATLAB/amd2.m ./cdiff ../MATLAB/camd_make.m ../../AMD/MATLAB/amd_make.m ./cdiff ../MATLAB/camd_mex.c ../../AMD/MATLAB/amd_mex.c ./cdiff ../MATLAB/can_24 ../../AMD/MATLAB/can_24 ./cdiff ../MATLAB/Contents.m ../../AMD/MATLAB/Contents.m ./cdiff ../MATLAB/Makefile ../../AMD/MATLAB/Makefile ./cdiff ../Source/camd_1.c ../../AMD/Source/amd_1.c ./cdiff ../Source/camd_2.c ../../AMD/Source/amd_2.c ./cdiff ../Source/camd_aat.c ../../AMD/Source/amd_aat.c ./cdiff ../Source/camd_control.c ../../AMD/Source/amd_control.c ./cdiff ../Source/camd_defaults.c ../../AMD/Source/amd_defaults.c ./cdiff ../Source/camd_dump.c ../../AMD/Source/amd_dump.c ./cdiff ../Source/camd_global.c ../../AMD/Source/amd_global.c ./cdiff ../Source/camd_info.c ../../AMD/Source/amd_info.c ./cdiff ../Source/camd_order.c ../../AMD/Source/amd_order.c ./cdiff ../Source/camd_postorder.c ../../AMD/Source/amd_postorder.c # ./cdiff ../Source/camd_post_tree.c ../../AMD/Source/amd_post_tree.c ./cdiff ../Source/camd_preprocess.c ../../AMD/Source/amd_preprocess.c ./cdiff ../Source/camd_valid.c ../../AMD/Source/amd_valid.c ./cdiff ../Source/GNUmakefile ../../AMD/Source/GNUmakefile ./cdiff ../Source/Makefile ../../AMD/Source/Makefile ./cdiff ../Makefile ../../AMD/Makefile ./cdiff ../README.txt ../../AMD/README.txt SuiteSparse/CAMD/Doc/camd.sed0000644001170100242450000000003210423445544014561 0ustar davisfacs/CAMD/AMD/g s/camd/amd/g SuiteSparse/CAMD/Doc/License0000644001170100242450000000345310616400731014470 0ustar davisfacCAMD, Copyright (c) by Timothy A. Davis, Yanqing Chen, Patrick R. Amestoy, and Iain S. Duff. All Rights Reserved. CAMD is available under alternate licenses, contact T. Davis for details. CAMD License: Your use or distribution of CAMD or any modified version of CAMD implies that you agree to this License. This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Permission is hereby granted to use or copy this program under the terms of the GNU LGPL, provided that the Copyright, this License, and the Availability of the original version is retained on all copies. User documentation of any code that uses this code or any modified version of this code must cite the Copyright, this License, the Availability note, and "Used by permission." Permission to modify the code and to distribute modified code is granted, provided the Copyright, this License, and the Availability note are retained, and a notice that the code was modified is included. Availability: http://www.cise.ufl.edu/research/sparse/camd ------------------------------------------------------------------------------- SuiteSparse/CAMD/Doc/CAMD_UserGuide.bib0000644001170100242450000000470310325005010016304 0ustar davisfac@string{SIREV = "{SIAM} Review"} @string{SIMAX = "{SIAM} J. Matrix Anal. Applic."} @string{SIAMJSC = "{SIAM} J. Sci. Comput."} @string{TOMS = "{ACM} Trans. Math. Softw."} @article{schu:01, author = {J. Schulze}, title = {Towards a tighter coupling of bottom-up and top-down sparse matrix ordering methods}, journal = {BIT}, volume = {41}, number = {4}, pages = "800--841", year = {2001} } @article{GeorgeLiu89, author={George, A. and Liu, J. W. H.}, year={1989}, title={The Evolution of the Minimum Degree Ordering Algorithm}, journal=SIREV, volume={31}, number={1}, pages={1--19}} @article{AmestoyDavisDuff96, author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.}, title={An approximate minimum degree ordering algorithm}, journal=SIMAX, year={1996} ,volume={17} ,number={4} ,pages={886-905} } @article{AmestoyDavisDuff04, author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.}, title={Algorithm 837: An approximate minimum degree ordering algorithm}, journal=TOMS, year={2004} ,volume={30} ,number={3} ,pages={381-388} } @misc{hsl:2002, author = {HSL}, title = "{HSL} 2002: {A} collection of {F}ortran codes for large scale scientific computation", note = {{\tt www.cse.clrc.ac.uk/nag/hsl}}, year = 2002} @article{RothbergEisenstat98, author={Rothberg, E. and Eisenstat, S. 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G.}, title={A column approximate minimum degree ordering algorithm}, journal=TOMS, year={2004} ,volume={30} ,pages={353-376} } SuiteSparse/CAMD/Doc/CAMD_UserGuide.pdf0000644001170100242450000051110310617112546016337 0ustar davisfac%PDF-1.4 3 0 obj << /Length 3643 /Filter /FlateDecode >> stream xڕrP]5 Sbe*-Rk(R!qz&X@hޠ?<\p"W<,'*H+FkbԸĵ?$]S?O?{CnLcȨ~ƓMSSz"y 49źFVMGS-Ƶ ]'f?2-*>m>8mSf q5'DH˜p XHNL&:$hN g0HDgvM?OUq'0K񆆨#79%n%c2@VeRY*עV;֡ͦa?uLe]T(- M.(u٣w-DpYLP'8[ Yv5)HWnRg2XF8Znꆩ!q<zѻeSvE]F;%]BD#wxVHѢq` g+qRW7ΌgDZ< W +Xy㝨Na(QDQ Tyn%- 3Xt{!@ lY@/񵏶_yE" s#|h똝motzb:@_FCI< ^yLaE:b"^s)e>=!\Z"*F!{P`ʚhヸnnD00n',bJQɀ"F2H!Jhb$A1EQʒ^ vws~  ήaetNHhM;( EV s CZ#~pתJ,yI~KYޥEٺ}ZJ&& ?rE^Kk ~XB4B!0&.Vq艣2 .S_i%VuMNq+ג}+O$ `떇 ZRǛG '19!֓u*dݦDL[^Gؒ^06qM.04^HX%`vrJ%La$@i̠ѧȠ]%r)Vh$;;AкYВ{\)C⤄0&o]c R$;TƎ]VC} b](zc~]p󓭫eCnK\ȧ3TOLcv_TPn(~u^EEx\-V H(<1 >{4ӟ-ڳW̠6{qps\H'3# }uyx{Zs@<RzŹp^c^ y:Lӥ<u\Z[_׍Ӈvl3U@|xM ˛>2?ք\ikŁH<zqnDlҲgds"f\Fv=]wX)pG=E)3 qSf9_5EQ1S l6/-c\ҍSwC9C{\99! n~=f*J\z_ߘ ؾ&ҘI<In6,r6.Dk7u@"|\َ)ik=i:5xl~:M{,e)I>1 $Nmȏ QEJjwԡ gX挔ՕZ}WKbM'3@+ o 9w)T3v4 '癗F90;=Í%]oNLR(be|K^:~=J{D$`Wg}Ny6JC,Շ~d"X2,M'wO@Gtri:T 2%ZA|)DƖ 6<5yjo4!]i7 b j ܛm6eO@0 x)SI,88*Y8㰼 ĹBP쿒2w<4P'̧`tru[bJ ~i}IbYLV螰!5iva6s^ا!]|tE1re;۽m#?/SAu7G2 CC}xr>k_5HO'nGM"X"endstream endobj 2 0 obj << /Type /Page /Contents 3 0 R /Resources 1 0 R /MediaBox [0 0 595.2756 841.8898] /Parent 31 0 R >> endobj 1 0 obj << /Font << /F16 6 0 R /F17 9 0 R /F24 12 0 R /F29 15 0 R /F8 18 0 R /F30 21 0 R /F25 24 0 R /F26 27 0 R /F28 30 0 R >> /ProcSet [ /PDF /Text ] >> endobj 34 0 obj << /Length 379 /Filter /FlateDecode >> stream xmRN0+rt$;rmNHmdV{< @7fɦ]>QMQ*>f%Ue/+Bv ,)-U\P*59Ѕπ^͟Gi1ʢ$ghb&w $fcUF8O ]x?;r 7EBa;|֣Ce߹~bpN|p%[/q]4N -¹@u~z%A! kr纛ni{qH_s2Y)SZ*JJ֤5J_>]}ƺendstream endobj 33 0 obj << /Type /Page /Contents 34 0 R /Resources 32 0 R /MediaBox [0 0 595.2756 841.8898] /Parent 31 0 R >> endobj 32 0 obj << /Font << /F8 18 0 R >> /ProcSet [ /PDF /Text ] >> endobj 37 0 obj << /Length 4289 /Filter /FlateDecode >> stream xڕ[K6Wm9#>j+ʖMNNđhKBRǿ~`5"h4~?|ܨ<5yooJ tyؼIJ)m|5*ixM>ުÇۇcuǛfa>5MnWFJF|,[g_ NRNC; 1-q󞚁Atf֡M'zqN=ou E;tf/@c&{Z*7U< d2kfIs1JpVgh urЈ4MZ$:6@$2km@.P]B,+I.'?4G:ɹ늢jphLiY%$pQ( ] 9f~:p"pnym ֦>7)XRlA;%D5׈SE1ǁ; Rd Y2'|[;7ܾh݊Mp;ĭ|kދЇk;Tou}*{ kd">! 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\newcommand{\m}[1]{{\bf{#1}}} % for matrices and vectors \newcommand{\tr}{^{\sf T}} % transpose \topmargin 0in \textheight 9in \oddsidemargin 0pt \evensidemargin 0pt \textwidth 6.5in %------------------------------------------------------------------------------ \begin{document} %------------------------------------------------------------------------------ \title{CAMD Version 2.2 User Guide} \author{Patrick R. Amestoy\thanks{ENSEEIHT-IRIT, 2 rue Camichel 31017 Toulouse, France. email: amestoy@enseeiht.fr. http://www.enseeiht.fr/$\sim$amestoy.} \and Yanqing (Morris) Chen \and Timothy A. Davis\thanks{ Dept.~of Computer and Information Science and Engineering, Univ.~of Florida, Gainesville, FL, USA. email: davis@cise.ufl.edu. http://www.cise.ufl.edu/$\sim$davis. This work was supported by the National Science Foundation, under grants ASC-9111263, DMS-9223088, and CCR-0203270. Portions of the work were done while on sabbatical at Stanford University and Lawrence Berkeley National Laboratory (with funding from Stanford University and the SciDAC program). Ordering constraints added with support from Sandia National Laboratory (Dept. of Energy). } \and Iain S. Duff\thanks{Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, England. email: i.s.duff@rl.ac.uk. http://www.numerical.rl.ac.uk/people/isd/isd.html. This work was supported by the EPSRC under grant GR/R46441. }} \date{May 31, 2007} \maketitle %------------------------------------------------------------------------------ \begin{abstract} CAMD is a set of ANSI C routines that implements the approximate minimum degree ordering algorithm to permute sparse matrices prior to numerical factorization. Ordering constraints can be optionally provided. A MATLAB interface is included. \end{abstract} %------------------------------------------------------------------------------ CAMD Version 2.2, Copyright\copyright 2007 by Timothy A. Davis, Yanqing (Morris) Chen, Patrick R. Amestoy, and Iain S. Duff. All Rights Reserved. CAMD is available under alternate licences; contact T. Davis for details. {\bf CAMD License:} Your use or distribution of CAMD or any modified version of CAMD implies that you agree to this License. This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Permission is hereby granted to use or copy this program under the terms of the GNU LGPL, provided that the Copyright, this License, and the Availability of the original version is retained on all copies. User documentation of any code that uses this code or any modified version of this code must cite the Copyright, this License, the Availability note, and "Used by permission." Permission to modify the code and to distribute modified code is granted, provided the Copyright, this License, and the Availability note are retained, and a notice that the code was modified is included. {\bf Availability:} http://www.cise.ufl.edu/research/sparse/camd {\bf Acknowledgments:} This work was supported by the National Science Foundation, under grants ASC-9111263 and DMS-9223088 and CCR-0203270, and by Sandia National Labs (a grant from DOE). The conversion to C, the addition of the elimination tree post-ordering, and the handling of dense rows and columns were done while Davis was on sabbatical at Stanford University and Lawrence Berkeley National Laboratory. The ordering constraints were added by Chen and Davis. %------------------------------------------------------------------------------ \newpage \section{Overview} %------------------------------------------------------------------------------ CAMD is a set of routines for preordering a sparse matrix prior to numerical factorization. It uses an approximate minimum degree ordering algorithm \cite{AmestoyDavisDuff96,AmestoyDavisDuff04} to find a permutation matrix $\m{P}$ so that the Cholesky factorization $\m{PAP}\tr=\m{LL}\tr$ has fewer (often much fewer) nonzero entries than the Cholesky factorization of $\m{A}$. The algorithm is typically much faster than other ordering methods and minimum degree ordering algorithms that compute an exact degree \cite{GeorgeLiu89}. Some methods, such as approximate deficiency \cite{RothbergEisenstat98} and graph-partitioning based methods \cite{Chaco,KarypisKumar98e,PellegriniRomanAmestoy00,schu:01} can produce better orderings, depending on the matrix. The algorithm starts with an undirected graph representation of a symmetric sparse matrix $\m{A}$. Node $i$ in the graph corresponds to row and column $i$ of the matrix, and there is an edge $(i,j)$ in the graph if $a_{ij}$ is nonzero. The degree of a node is initialized to the number of off-diagonal nonzeros in row $i$, which is the size of the set of nodes adjacent to $i$ in the graph. The selection of a pivot $a_{ii}$ from the diagonal of $\m{A}$ and the first step of Gaussian elimination corresponds to one step of graph elimination. Numerical fill-in causes new nonzero entries in the matrix (fill-in refers to nonzeros in $\m{L}$ that are not in $\m{A}$). Node $i$ is eliminated and edges are added to its neighbors so that they form a clique (or {\em element}). To reduce fill-in, node $i$ is selected as the node of least degree in the graph. This process repeats until the graph is eliminated. The clique is represented implicitly. Rather than listing all the new edges in the graph, a single list of nodes is kept which represents the clique. This list corresponds to the nonzero pattern of the first column of $\m{L}$. As the elimination proceeds, some of these cliques become subsets of subsequent cliques, and are removed. This graph can be stored in place, that is using the same amount of memory as the original graph. The most costly part of the minimum degree algorithm is the recomputation of the degrees of nodes adjacent to the current pivot element. Rather than keep track of the exact degree, the approximate minimum degree algorithm finds an upper bound on the degree that is easier to compute. For nodes of least degree, this bound tends to be tight. Using the approximate degree instead of the exact degree leads to a substantial savings in run time, particularly for very irregularly structured matrices. It has no effect on the quality of the ordering. The elimination phase is followed by an elimination tree post-ordering. This has no effect on fill-in, but reorganizes the ordering so that the subsequent numerical factorization is more efficient. It also includes a pre-processing phase in which nodes of very high degree are removed (without causing fill-in), and placed last in the permutation $\m{P}$ (subject to the constraints). This reduces the run time substantially if the matrix has a few rows with many nonzero entries, and has little effect on the quality of the ordering. CAMD operates on the symmetric nonzero pattern of $\m{A}+\m{A}\tr$, so it can be given an unsymmetric matrix, or either the lower or upper triangular part of a symmetric matrix. CAMD has the ability to order the matrix with constraints. Each node $i$ in the graph (row/column $i$ in the matrix) has a constraint, {\tt C[i]}, which is in the range {\tt 0} to {\tt n-1}. All nodes with {\tt C[i] = 0} are ordered first, followed by all nodes with constraint {\tt 1}, and so on. That is, {\tt C[P[k]]} is monotonically non-decreasing as {\tt k} varies from {\tt 0} to {\tt n-1}. If {\tt C} is NULL, no constraints are used (the ordering will be similar to AMD's ordering, except that the postordering is different). The optional {\tt C} parameter is also provided in the MATLAB interface, ({\tt p = camd (A,Control,C)}). For a discussion of the long history of the minimum degree algorithm, see \cite{GeorgeLiu89}. %------------------------------------------------------------------------------ \section{Availability} %------------------------------------------------------------------------------ CAMD is available at http://www.cise.ufl.edu/research/sparse. The Fortran version is available as the routine {\tt MC47} in HSL (formerly the Harwell Subroutine Library) \cite{hsl:2002}. {\tt MC47} does not include ordering constraints. %------------------------------------------------------------------------------ \section{Using CAMD in MATLAB} %------------------------------------------------------------------------------ To use CAMD in MATLAB, you must first compile the CAMD mexFunction. Just type {\tt make} in the Unix system shell, while in the {\tt CAMD} directory. You can also type {\tt camd\_make} in MATLAB, while in the {\tt CAMD/MATLAB} directory. Place the {\tt CAMD/MATLAB} directory in your MATLAB path. This can be done on any system with MATLAB, including Windows. See Section~\ref{Install} for more details on how to install CAMD. The MATLAB statement {\tt p=camd(A)} finds a permutation vector {\tt p} such that the Cholesky factorization {\tt chol(A(p,p))} is typically sparser than {\tt chol(A)}. If {\tt A} is unsymmetric, {\tt camd(A)} is identical to {\tt camd(A+A')} (ignoring numerical cancellation). If {\tt A} is not symmetric positive definite, but has substantial diagonal entries and a mostly symmetric nonzero pattern, then this ordering is also suitable for LU factorization. A partial pivoting threshold may be required to prevent pivots from being selected off the diagonal, such as the statement {\tt [L,U,P] = lu (A (p,p), 0.1)}. Type {\tt help lu} for more details. The statement {\tt [L,U,P,Q] = lu (A (p,p))} in MATLAB 6.5 is not suitable, however, because it uses UMFPACK Version 4.0 and thus does not attempt to select pivots from the diagonal. UMFPACK Version 4.1 in MATLAB 7.0 and later uses several strategies, including a symmetric pivoting strategy, and will give you better results if you want to factorize an unsymmetric matrix of this type. Refer to the UMFPACK User Guide for more details, at http://www.cise.ufl.edu/research/sparse/umfpack. The CAMD mexFunction is much faster than the built-in MATLAB symmetric minimum degree ordering methods, SYMAMD and SYMMMD. Its ordering quality is essentially identical to AMD, comparable to SYMAMD, and better than SYMMMD \cite{DavisGilbertLarimoreNg04}. An optional input argument can be used to modify the control parameters for CAMD (aggressive absorption, dense row/column handling, and printing of statistics). An optional output argument provides statistics on the ordering, including an analysis of the fill-in and the floating-point operation count for a subsequent factorization. For more details (once CAMD is installed), type {\tt help camd} in the MATLAB command window. %------------------------------------------------------------------------------ \section{Using CAMD in a C program} \label{Cversion} %------------------------------------------------------------------------------ The C-callable CAMD library consists of seven user-callable routines and one include file. There are two versions of each of the routines, with {\tt int} and {\tt long} integers. The routines with prefix {\tt camd\_l\_} use {\tt long} integer arguments; the others use {\tt int} integer arguments. If you compile CAMD in the standard ILP32 mode (32-bit {\tt int}'s, {\tt long}'s, and pointers) then the versions are essentially identical. You will be able to solve problems using up to 2GB of memory. If you compile CAMD in the standard LP64 mode, the size of an {\tt int} remains 32-bits, but the size of a {\tt long} and a pointer both get promoted to 64-bits. The following routines are fully described in Section~\ref{Primary}: \begin{itemize} \item {\tt camd\_order} ({\tt long} version: {\tt camd\_l\_order}) {\footnotesize \begin{verbatim} #include "camd.h" int n, Ap [n+1], Ai [nz], P [n], C [n] ; double Control [CAMD_CONTROL], Info [CAMD_INFO] ; int result = camd_order (n, Ap, Ai, P, Control, Info, C) ; \end{verbatim} } Computes the approximate minimum degree ordering of an $n$-by-$n$ matrix $\m{A}$. Returns a permutation vector {\tt P} of size {\tt n}, where {\tt P[k] = i} if row and column {\tt i} are the {\tt k}th row and column in the permuted matrix. This routine allocates its own memory of size $1.2e+9n$ integers, where $e$ is the number of nonzeros in $\m{A}+\m{A}\tr$. It computes statistics about the matrix $\m{A}$, such as the symmetry of its nonzero pattern, the number of nonzeros in $\m{L}$, and the number of floating-point operations required for Cholesky and LU factorizations (which are returned in the {\tt Info} array). The user's input matrix is not modified. It returns {\tt CAMD\_OK} if successful, {\tt CAMD\_OK\_BUT\_JUMBLED} if successful (but the matrix had unsorted and/or duplicate row indices), {\tt CAMD\_INVALID} if the matrix is invalid, {\tt CAMD\_OUT\_OF\_MEMORY} if out of memory. The array {\tt C} provides the ordering constraints. On input, {\tt C} may be null (to denote no constraints); otherwise, it must be an array size {\tt n}, with entries in the range {\tt 0} to {\tt n-1}. On output, {\tt C[P[0..n-1]]} is monotonically non-descreasing. \item {\tt camd\_defaults} ({\tt long} version: {\tt camd\_l\_defaults}) {\footnotesize \begin{verbatim} #include "camd.h" double Control [CAMD_CONTROL] ; camd_defaults (Control) ; \end{verbatim} } Sets the default control parameters in the {\tt Control} array. These can then be modified as desired before passing the array to the other CAMD routines. \item {\tt camd\_control} ({\tt long} version: {\tt camd\_l\_control}) {\footnotesize \begin{verbatim} #include "camd.h" double Control [CAMD_CONTROL] ; camd_control (Control) ; \end{verbatim} } Prints a description of the control parameters, and their values. \item {\tt camd\_info} ({\tt long} version: {\tt camd\_l\_info}) {\footnotesize \begin{verbatim} #include "camd.h" double Info [CAMD_INFO] ; camd_info (Info) ; \end{verbatim} } Prints a description of the statistics computed by CAMD, and their values. \item {\tt camd\_valid} ({\tt long} version: {\tt camd\_valid}) {\footnotesize \begin{verbatim} #include "camd.h" int n, Ap [n+1], Ai [nz] ; int result = camd_valid (n, n, Ap, Ai) ; \end{verbatim} } Returns {\tt CAMD\_OK} or {\tt CAMD\_OK\_BUT\_JUMBLED} if the matrix is valid as input to {\tt camd\_order}; the latter is returned if the matrix has unsorted and/or duplicate row indices in one or more columns. Returns {\tt CAMD\_INVALID} if the matrix cannot be passed to {\tt camd\_order}. For {\tt camd\_order}, the matrix must also be square. The first two arguments are the number of rows and the number of columns of the matrix. For its use in CAMD, these must both equal {\tt n}. \item {\tt camd\_2} ({\tt long} version: {\tt camd\_l2}) CAMD ordering kernel. It is faster than {\tt camd\_order}, and can be called by the user, but it is difficult to use. It does not check its inputs for errors. It does not require the columns of its input matrix to be sorted, but it destroys the matrix on output. Additional workspace must be passed. Refer to the source file {\tt CAMD/Source/camd\_2.c} for a description. \end{itemize} The nonzero pattern of the matrix $\m{A}$ is represented in compressed column form. For an $n$-by-$n$ matrix $\m{A}$ with {\tt nz} nonzero entries, the representation consists of two arrays: {\tt Ap} of size {\tt n+1} and {\tt Ai} of size {\tt nz}. The row indices of entries in column {\tt j} are stored in {\tt Ai[Ap[j]} $\ldots$ {\tt Ap[j+1]-1]}. For {\tt camd\_order}, if duplicate row indices are present, or if the row indices in any given column are not sorted in ascending order, then {\tt camd\_order} creates an internal copy of the matrix with sorted rows and no duplicate entries, and orders the copy. This adds slightly to the time and memory usage of {\tt camd\_order}, but is not an error condition. The matrix is 0-based, and thus row indices must be in the range {\tt 0} to {\tt n-1}. The first entry {\tt Ap[0]} must be zero. The total number of entries in the matrix is thus {\tt nz = Ap[n]}. The matrix must be square, but it does not need to be symmetric. The {\tt camd\_order} routine constructs the nonzero pattern of $\m{B} = \m{A}+\m{A}\tr$ (without forming $\m{A}\tr$ explicitly if $\m{A}$ has sorted columns and no duplicate entries), and then orders the matrix $\m{B}$. Thus, either the lower triangular part of $\m{A}$, the upper triangular part, or any combination may be passed. The transpose $\m{A}\tr$ may also be passed to {\tt camd\_order}. The diagonal entries may be present, but are ignored. %------------------------------------------------------------------------------ \subsection{Control parameters} \label{control_param} %------------------------------------------------------------------------------ Control parameters are set in an optional {\tt Control} array. It is optional in the sense that if a {\tt NULL} pointer is passed for the {\tt Control} input argument, then default control parameters are used. % \begin{itemize} \item {\tt Control[CAMD\_DENSE]} (or {\tt Control(1)} in MATLAB): controls the threshold for ``dense'' rows/columns. A dense row/column in $\m{A}+\m{A}\tr$ can cause CAMD to spend significant time in ordering the matrix. If {\tt Control[CAMD\_DENSE]} $\ge 0$, rows/columns with more than {\tt Control[CAMD\_DENSE]} $\sqrt{n}$ entries are ignored during the ordering, and placed last in the output order. The default value of {\tt Control[CAMD\_DENSE]} is 10. If negative, no rows/columns are treated as ``dense.'' Rows/columns with 16 or fewer off-diagonal entries are never considered ``dense.'' % \item {\tt Control[CAMD\_AGGRESSIVE]} (or {\tt Control(2)} in MATLAB): controls whether or not to use aggressive absorption, in which a prior element is absorbed into the current element if it is a subset of the current element, even if it is not adjacent to the current pivot element (refer to \cite{AmestoyDavisDuff96,AmestoyDavisDuff04} for more details). The default value is nonzero, which means that aggressive absorption will be performed. This nearly always leads to a better ordering (because the approximate degrees are more accurate) and a lower execution time. There are cases where it can lead to a slightly worse ordering, however. To turn it off, set {\tt Control[CAMD\_AGGRESSIVE]} to 0. % \end{itemize} Statistics are returned in the {\tt Info} array (if {\tt Info} is {\tt NULL}, then no statistics are returned). Refer to {\tt camd.h} file, for more details (14 different statistics are returned, so the list is not included here). %------------------------------------------------------------------------------ \subsection{Sample C program} %------------------------------------------------------------------------------ The following program, {\tt camd\_demo.c}, illustrates the basic use of CAMD. See Section~\ref{Synopsis} for a short description of each calling sequence. {\footnotesize \begin{verbatim} #include #include "camd.h" int n = 5 ; int Ap [ ] = { 0, 2, 6, 10, 12, 14} ; int Ai [ ] = { 0,1, 0,1,2,4, 1,2,3,4, 2,3, 1,4 } ; int C [ ] = { 2, 0, 0, 0, 1 } ; int P [5] ; int main (void) { int k ; (void) camd_order (n, Ap, Ai, P, (double *) NULL, (double *) NULL, C) ; for (k = 0 ; k < n ; k++) printf ("P [%d] = %d\n", k, P [k]) ; return (0) ; } \end{verbatim} } The {\tt Ap} and {\tt Ai} arrays represent the binary matrix \[ \m{A} = \left[ \begin{array}{rrrrr} 1 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 0 & 1 & 1 & 0 \\ 0 & 1 & 1 & 0 & 1 \\ \end{array} \right]. \] The diagonal entries are ignored. % CAMD constructs the pattern of $\m{A}+\m{A}\tr$, and returns a permutation vector of $(3, 2, 1, 4, 0)$. Note that nodes 1, 2, and 3 appear first (they are in the constraint set 0), node 4 appears next (since {\tt C[4] = 1}), and node 0 appears last. % Since the matrix is unsymmetric but with a mostly symmetric nonzero pattern, this would be a suitable permutation for an LU factorization of a matrix with this nonzero pattern and whose diagonal entries are not too small. The program uses default control settings and does not return any statistics about the ordering, factorization, or solution ({\tt Control} and {\tt Info} are both {\tt (double *) NULL}). It also ignores the status value returned by {\tt camd\_order}. More example programs are included with the CAMD package. The {\tt camd\_demo.c} program provides a more detailed demo of CAMD. Another example is the CAMD mexFunction, {\tt camd\_mex.c}. %------------------------------------------------------------------------------ \subsection{A note about zero-sized arrays} %------------------------------------------------------------------------------ CAMD uses several user-provided arrays of size {\tt n} or {\tt nz}. Either {\tt n} or {\tt nz} can be zero. If you attempt to {\tt malloc} an array of size zero, however, {\tt malloc} will return a null pointer which CAMD will report as invalid. If you {\tt malloc} an array of size {\tt n} or {\tt nz} to pass to CAMD, make sure that you handle the {\tt n} = 0 and {\tt nz = 0} cases correctly. %------------------------------------------------------------------------------ \section{Synopsis of C-callable routines} \label{Synopsis} %------------------------------------------------------------------------------ The matrix $\m{A}$ is {\tt n}-by-{\tt n} with {\tt nz} entries. {\footnotesize \begin{verbatim} #include "camd.h" int n, status, Ap [n+1], Ai [nz], P [n], C [n] ; double Control [CAMD_CONTROL], Info [CAMD_INFO] ; camd_defaults (Control) ; status = camd_order (n, Ap, Ai, P, Control, Info, C) ; camd_control (Control) ; camd_info (Info) ; status = camd_valid (n, n, Ap, Ai) ; \end{verbatim} } The {\tt camd\_l\_*} routines are identical, except that all {\tt int} arguments become {\tt long}: {\footnotesize \begin{verbatim} #include "camd.h" long n, status, Ap [n+1], Ai [nz], P [n], C [n] ; double Control [CAMD_CONTROL], Info [CAMD_INFO] ; camd_l_defaults (Control) ; status = camd_l_order (n, Ap, Ai, P, Control, Info, C) ; camd_l_control (Control) ; camd_l_info (Info) ; status = camd_l_valid (n, n, Ap, Ai) ; \end{verbatim} } %------------------------------------------------------------------------------ \section{Installation} \label{Install} %------------------------------------------------------------------------------ The following discussion assumes you have the {\tt make} program, either in Unix, or in Windows with Cygwin. System-dependent configurations are in the {\tt ../UFconfig/UFconfig.mk} file. You can edit that file to customize the compilation. The default settings will work on most systems. Sample configuration files are provided for Linux, Sun Solaris, SGI IRIX, IBM AIX, and the DEC/Compaq Alpha. To compile and install the C-callable CAMD library, go to the {\tt CAMD} directory and type {\tt make}. The library will be placed in {\tt CAMD/Lib/libcamd.a}. Three demo programs of the CAMD ordering routine will be compiled and tested in the {\tt CAMD/Demo} directory. The outputs of these demo programs will then be compared with output files in the distribution. Typing {\tt make clean} will remove all but the final compiled libraries and demo programs. Typing {\tt make purge} or {\tt make distclean} removes all files not in the original distribution. If you compile CAMD and then later change the {\tt ../UFconfig/UFconfig.mk} file then you should type {\tt make purge} and then {\tt make} to recompile. When you compile your program that uses the C-callable CAMD library, you need to add the {\tt CAMD/Lib/libcamd.a} library and you need to tell your compiler to look in the {\tt CAMD/Include} directory for include files. See {\tt CAMD/Demo/Makefile} for an example. If all you want to use is the CAMD mexFunction in MATLAB, you can skip the use of the {\tt make} command entirely. Simply type {\tt camd\_make} in MATLAB while in the {\tt CAMD/MATLAB} directory. This works on any system with MATLAB, including Windows. Alternately, type {\tt make} in the {\tt CAMD/MATLAB} directory. If you have MATLAB 7.2 or earlier, you must first edit UFconfig/UFconfig.h to remove the "-largeArrayDims" option from the MEX command, prior to {\tt make mex} or {\tt make} in the MATLAB directory (or just use {\tt camd\_make.m} inside MATLAB. If you are including CAMD as a subset of a larger library and do not want to link the C standard I/O library, or if you simply do not need to use them, you can safely remove the {\tt camd\_control.c} and {\tt camd\_info.c} files. Similarly, if you use default parameters (or define your own {\tt Control} array), then you can exclude the {\tt camd\_defaults.c} file. Each of these files contains the user-callable routines of the same name. None of these auxiliary routines are directly called by {\tt camd\_order}. The {\tt camd\_dump.c} file contains debugging routines that are neither used nor compiled unless debugging is enabled. The {\tt camd\_internal.h} file must be edited to enable debugging; refer to the instructions in that file. The bare minimum files required to use just {\tt camd\_order} are {\tt camd.h} and {\tt camd\_internal.h} in the {\tt Include} directory, and {\tt camd\_1.c}, {\tt camd\_2.c}, {\tt camd\_aat.c}, {\tt camd\_global.c}, {\tt and\_order.c}, {\tt camd\_postorder.c}, {\tt camd\_preprocess.c}, and {\tt camd\_valid.c} in the {\tt Source} directory. %------------------------------------------------------------------------------ \newpage \section{The CAMD routines} \label{Primary} %------------------------------------------------------------------------------ The file {\tt CAMD/Include/camd.h} listed below describes each user-callable routine in CAMD, and gives details on their use. {\footnotesize \begin{verbatim} /* ========================================================================= */ /* === CAMD: approximate minimum degree ordering ========================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* CAMD Version 2.2, Copyright (c) 2007 by Timothy A. Davis, Yanqing Chen, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/camd */ /* ------------------------------------------------------------------------- */ /* CAMD finds a symmetric ordering P of a matrix A so that the Cholesky * factorization of P*A*P' has fewer nonzeros and takes less work than the * Cholesky factorization of A. If A is not symmetric, then it performs its * ordering on the matrix A+A'. Two sets of user-callable routines are * provided, one for int integers and the other for UF_long integers. * * The method is based on the approximate minimum degree algorithm, discussed * in Amestoy, Davis, and Duff, "An approximate degree ordering algorithm", * SIAM Journal of Matrix Analysis and Applications, vol. 17, no. 4, pp. * 886-905, 1996. */ #ifndef CAMD_H #define CAMD_H /* make it easy for C++ programs to include CAMD */ #ifdef __cplusplus extern "C" { #endif /* get the definition of size_t: */ #include /* define UF_long */ #include "UFconfig.h" int camd_order /* returns CAMD_OK, CAMD_OK_BUT_JUMBLED, * CAMD_INVALID, or CAMD_OUT_OF_MEMORY */ ( int n, /* A is n-by-n. n must be >= 0. */ const int Ap [ ], /* column pointers for A, of size n+1 */ const int Ai [ ], /* row indices of A, of size nz = Ap [n] */ int P [ ], /* output permutation, of size n */ double Control [ ], /* input Control settings, of size CAMD_CONTROL */ double Info [ ], /* output Info statistics, of size CAMD_INFO */ const int C [ ] /* Constraint set of A, of size n; can be NULL */ ) ; UF_long camd_l_order /* see above for description of arguments */ ( UF_long n, const UF_long Ap [ ], const UF_long Ai [ ], UF_long P [ ], double Control [ ], double Info [ ], const UF_long C [ ] ) ; /* Input arguments (not modified): * * n: the matrix A is n-by-n. * Ap: an int/UF_long array of size n+1, containing column pointers of A. * Ai: an int/UF_long array of size nz, containing the row indices of A, * where nz = Ap [n]. * Control: a double array of size CAMD_CONTROL, containing control * parameters. Defaults are used if Control is NULL. * * Output arguments (not defined on input): * * P: an int/UF_long array of size n, containing the output permutation. If * row i is the kth pivot row, then P [k] = i. In MATLAB notation, * the reordered matrix is A (P,P). * Info: a double array of size CAMD_INFO, containing statistical * information. Ignored if Info is NULL. * * On input, the matrix A is stored in column-oriented form. The row indices * of nonzero entries in column j are stored in Ai [Ap [j] ... Ap [j+1]-1]. * * If the row indices appear in ascending order in each column, and there * are no duplicate entries, then camd_order is slightly more efficient in * terms of time and memory usage. If this condition does not hold, a copy * of the matrix is created (where these conditions do hold), and the copy is * ordered. * * Row indices must be in the range 0 to * n-1. Ap [0] must be zero, and thus nz = Ap [n] is the number of nonzeros * in A. The array Ap is of size n+1, and the array Ai is of size nz = Ap [n]. * The matrix does not need to be symmetric, and the diagonal does not need to * be present (if diagonal entries are present, they are ignored except for * the output statistic Info [CAMD_NZDIAG]). The arrays Ai and Ap are not * modified. This form of the Ap and Ai arrays to represent the nonzero * pattern of the matrix A is the same as that used internally by MATLAB. * If you wish to use a more flexible input structure, please see the * umfpack_*_triplet_to_col routines in the UMFPACK package, at * http://www.cise.ufl.edu/research/sparse/umfpack. * * Restrictions: n >= 0. Ap [0] = 0. Ap [j] <= Ap [j+1] for all j in the * range 0 to n-1. nz = Ap [n] >= 0. Ai [0..nz-1] must be in the range 0 * to n-1. Finally, Ai, Ap, and P must not be NULL. If any of these * restrictions are not met, CAMD returns CAMD_INVALID. * * CAMD returns: * * CAMD_OK if the matrix is valid and sufficient memory can be allocated to * perform the ordering. * * CAMD_OUT_OF_MEMORY if not enough memory can be allocated. * * CAMD_INVALID if the input arguments n, Ap, Ai are invalid, or if P is * NULL. * * CAMD_OK_BUT_JUMBLED if the matrix had unsorted columns, and/or duplicate * entries, but was otherwise valid. * * The CAMD routine first forms the pattern of the matrix A+A', and then * computes a fill-reducing ordering, P. If P [k] = i, then row/column i of * the original is the kth pivotal row. In MATLAB notation, the permuted * matrix is A (P,P), except that 0-based indexing is used instead of the * 1-based indexing in MATLAB. * * The Control array is used to set various parameters for CAMD. If a NULL * pointer is passed, default values are used. The Control array is not * modified. * * Control [CAMD_DENSE]: controls the threshold for "dense" rows/columns. * A dense row/column in A+A' can cause CAMD to spend a lot of time in * ordering the matrix. If Control [CAMD_DENSE] >= 0, rows/columns * with more than Control [CAMD_DENSE] * sqrt (n) entries are ignored * during the ordering, and placed last in the output order. The * default value of Control [CAMD_DENSE] is 10. If negative, no * rows/columns are treated as "dense". Rows/columns with 16 or * fewer off-diagonal entries are never considered "dense". * * Control [CAMD_AGGRESSIVE]: controls whether or not to use aggressive * absorption, in which a prior element is absorbed into the current * element if is a subset of the current element, even if it is not * adjacent to the current pivot element (refer to Amestoy, Davis, * & Duff, 1996, for more details). The default value is nonzero, * which means to perform aggressive absorption. This nearly always * leads to a better ordering (because the approximate degrees are * more accurate) and a lower execution time. There are cases where * it can lead to a slightly worse ordering, however. To turn it off, * set Control [CAMD_AGGRESSIVE] to 0. * * Control [2..4] are not used in the current version, but may be used in * future versions. * * The Info array provides statistics about the ordering on output. If it is * not present, the statistics are not returned. This is not an error * condition. * * Info [CAMD_STATUS]: the return value of CAMD, either CAMD_OK, * CAMD_OK_BUT_JUMBLED, CAMD_OUT_OF_MEMORY, or CAMD_INVALID. * * Info [CAMD_N]: n, the size of the input matrix * * Info [CAMD_NZ]: the number of nonzeros in A, nz = Ap [n] * * Info [CAMD_SYMMETRY]: the symmetry of the matrix A. It is the number * of "matched" off-diagonal entries divided by the total number of * off-diagonal entries. An entry A(i,j) is matched if A(j,i) is also * an entry, for any pair (i,j) for which i != j. In MATLAB notation, * S = spones (A) ; * B = tril (S, -1) + triu (S, 1) ; * symmetry = nnz (B & B') / nnz (B) ; * * Info [CAMD_NZDIAG]: the number of entries on the diagonal of A. * * Info [CAMD_NZ_A_PLUS_AT]: the number of nonzeros in A+A', excluding the * diagonal. If A is perfectly symmetric (Info [CAMD_SYMMETRY] = 1) * with a fully nonzero diagonal, then Info [CAMD_NZ_A_PLUS_AT] = nz-n * (the smallest possible value). If A is perfectly unsymmetric * (Info [CAMD_SYMMETRY] = 0, for an upper triangular matrix, for * example) with no diagonal, then Info [CAMD_NZ_A_PLUS_AT] = 2*nz * (the largest possible value). * * Info [CAMD_NDENSE]: the number of "dense" rows/columns of A+A' that were * removed from A prior to ordering. These are placed last in the * output order P. * * Info [CAMD_MEMORY]: the amount of memory used by CAMD, in bytes. In the * current version, this is 1.2 * Info [CAMD_NZ_A_PLUS_AT] + 9*n * times the size of an integer. This is at most 2.4nz + 9n. This * excludes the size of the input arguments Ai, Ap, and P, which have * a total size of nz + 2*n + 1 integers. * * Info [CAMD_NCMPA]: the number of garbage collections performed. * * Info [CAMD_LNZ]: the number of nonzeros in L (excluding the diagonal). * This is a slight upper bound because mass elimination is combined * with the approximate degree update. It is a rough upper bound if * there are many "dense" rows/columns. The rest of the statistics, * below, are also slight or rough upper bounds, for the same reasons. * The post-ordering of the assembly tree might also not exactly * correspond to a true elimination tree postordering. * * Info [CAMD_NDIV]: the number of divide operations for a subsequent LDL' * or LU factorization of the permuted matrix A (P,P). * * Info [CAMD_NMULTSUBS_LDL]: the number of multiply-subtract pairs for a * subsequent LDL' factorization of A (P,P). * * Info [CAMD_NMULTSUBS_LU]: the number of multiply-subtract pairs for a * subsequent LU factorization of A (P,P), assuming that no numerical * pivoting is required. * * Info [CAMD_DMAX]: the maximum number of nonzeros in any column of L, * including the diagonal. * * Info [14..19] are not used in the current version, but may be used in * future versions. */ /* ------------------------------------------------------------------------- */ /* direct interface to CAMD */ /* ------------------------------------------------------------------------- */ /* camd_2 is the primary CAMD ordering routine. It is not meant to be * user-callable because of its restrictive inputs and because it destroys * the user's input matrix. It does not check its inputs for errors, either. * However, if you can work with these restrictions it can be faster than * camd_order and use less memory (assuming that you can create your own copy * of the matrix for CAMD to destroy). Refer to CAMD/Source/camd_2.c for a * description of each parameter. */ void camd_2 ( int n, int Pe [ ], int Iw [ ], int Len [ ], int iwlen, int pfree, int Nv [ ], int Next [ ], int Last [ ], int Head [ ], int Elen [ ], int Degree [ ], int W [ ], double Control [ ], double Info [ ], const int C [ ], int BucketSet [ ] ) ; void camd_l2 ( UF_long n, UF_long Pe [ ], UF_long Iw [ ], UF_long Len [ ], UF_long iwlen, UF_long pfree, UF_long Nv [ ], UF_long Next [ ], UF_long Last [ ], UF_long Head [ ], UF_long Elen [ ], UF_long Degree [ ], UF_long W [ ], double Control [ ], double Info [ ], const UF_long C [ ], UF_long BucketSet [ ] ) ; /* ------------------------------------------------------------------------- */ /* camd_valid */ /* ------------------------------------------------------------------------- */ /* Returns CAMD_OK or CAMD_OK_BUT_JUMBLED if the matrix is valid as input to * camd_order; the latter is returned if the matrix has unsorted and/or * duplicate row indices in one or more columns. Returns CAMD_INVALID if the * matrix cannot be passed to camd_order. For camd_order, the matrix must also * be square. The first two arguments are the number of rows and the number * of columns of the matrix. For its use in CAMD, these must both equal n. */ int camd_valid ( int n_row, /* # of rows */ int n_col, /* # of columns */ const int Ap [ ], /* column pointers, of size n_col+1 */ const int Ai [ ] /* row indices, of size Ap [n_col] */ ) ; UF_long camd_l_valid ( UF_long n_row, UF_long n_col, const UF_long Ap [ ], const UF_long Ai [ ] ) ; /* ------------------------------------------------------------------------- */ /* camd_cvalid */ /* ------------------------------------------------------------------------- */ /* Returns TRUE if the constraint set is valid as input to camd_order, * FALSE otherwise. */ int camd_cvalid ( int n, const int C [ ] ) ; UF_long camd_l_cvalid ( UF_long n, const UF_long C [ ] ) ; /* ------------------------------------------------------------------------- */ /* CAMD memory manager and printf routines */ /* ------------------------------------------------------------------------- */ /* The user can redefine these to change the malloc, free, and printf routines * that CAMD uses. */ #ifndef EXTERN #define EXTERN extern #endif EXTERN void *(*camd_malloc) (size_t) ; /* pointer to malloc */ EXTERN void (*camd_free) (void *) ; /* pointer to free */ EXTERN void *(*camd_realloc) (void *, size_t) ; /* pointer to realloc */ EXTERN void *(*camd_calloc) (size_t, size_t) ; /* pointer to calloc */ EXTERN int (*camd_printf) (const char *, ...) ; /* pointer to printf */ /* ------------------------------------------------------------------------- */ /* CAMD Control and Info arrays */ /* ------------------------------------------------------------------------- */ /* camd_defaults: sets the default control settings */ void camd_defaults (double Control [ ]) ; void camd_l_defaults (double Control [ ]) ; /* camd_control: prints the control settings */ void camd_control (double Control [ ]) ; void camd_l_control (double Control [ ]) ; /* camd_info: prints the statistics */ void camd_info (double Info [ ]) ; void camd_l_info (double Info [ ]) ; #define CAMD_CONTROL 5 /* size of Control array */ #define CAMD_INFO 20 /* size of Info array */ /* contents of Control */ #define CAMD_DENSE 0 /* "dense" if degree > Control [0] * sqrt (n) */ #define CAMD_AGGRESSIVE 1 /* do aggressive absorption if Control [1] != 0 */ /* default Control settings */ #define CAMD_DEFAULT_DENSE 10.0 /* default "dense" degree 10*sqrt(n) */ #define CAMD_DEFAULT_AGGRESSIVE 1 /* do aggressive absorption by default */ /* contents of Info */ #define CAMD_STATUS 0 /* return value of camd_order and camd_l_order */ #define CAMD_N 1 /* A is n-by-n */ #define CAMD_NZ 2 /* number of nonzeros in A */ #define CAMD_SYMMETRY 3 /* symmetry of pattern (1 is sym., 0 is unsym.) */ #define CAMD_NZDIAG 4 /* # of entries on diagonal */ #define CAMD_NZ_A_PLUS_AT 5 /* nz in A+A' */ #define CAMD_NDENSE 6 /* number of "dense" rows/columns in A */ #define CAMD_MEMORY 7 /* amount of memory used by CAMD */ #define CAMD_NCMPA 8 /* number of garbage collections in CAMD */ #define CAMD_LNZ 9 /* approx. nz in L, excluding the diagonal */ #define CAMD_NDIV 10 /* number of fl. point divides for LU and LDL' */ #define CAMD_NMULTSUBS_LDL 11 /* number of fl. point (*,-) pairs for LDL' */ #define CAMD_NMULTSUBS_LU 12 /* number of fl. point (*,-) pairs for LU */ #define CAMD_DMAX 13 /* max nz. in any column of L, incl. diagonal */ /* ------------------------------------------------------------------------- */ /* return values of CAMD */ /* ------------------------------------------------------------------------- */ #define CAMD_OK 0 /* success */ #define CAMD_OUT_OF_MEMORY -1 /* malloc failed, or problem too large */ #define CAMD_INVALID -2 /* input arguments are not valid */ #define CAMD_OK_BUT_JUMBLED 1 /* input matrix is OK for camd_order, but * columns were not sorted, and/or duplicate entries were present. CAMD had * to do extra work before ordering the matrix. This is a warning, not an * error. */ /* ========================================================================== */ /* === CAMD version ========================================================= */ /* ========================================================================== */ /* * As an example, to test if the version you are using is 1.2 or later: * * if (CAMD_VERSION >= CAMD_VERSION_CODE (1,2)) ... * * This also works during compile-time: * * #if (CAMD_VERSION >= CAMD_VERSION_CODE (1,2)) * printf ("This is version 1.2 or later\n") ; * #else * printf ("This is an early version\n") ; * #endif */ #define CAMD_DATE "May 31, 2007" #define CAMD_VERSION_CODE(main,sub) ((main) * 1000 + (sub)) #define CAMD_MAIN_VERSION 2 #define CAMD_SUB_VERSION 2 #define CAMD_SUBSUB_VERSION 0 #define CAMD_VERSION CAMD_VERSION_CODE(CAMD_MAIN_VERSION,CAMD_SUB_VERSION) #ifdef __cplusplus } #endif #endif \end{verbatim} } %------------------------------------------------------------------------------ \newpage % References %------------------------------------------------------------------------------ \bibliographystyle{plain} \bibliography{CAMD_UserGuide} \end{document} SuiteSparse/CAMD/Doc/ChangeLog0000644001170100242450000000346210620614362014737 0ustar davisfacMay 31, 2007: version 2.2.0 * port to 64-bit MATLAB * Makefile moved from Source/ to Lib/ Dec 12, 2006, v2.1.3 * minor MATLAB cleanup Sept 28, 2006, v2.1.2 * #define SIZE_T_MAX not done if already defined (Mac OSX). Aug 31, 2006: v2.1.1 * trivial change to comments in camd.m June 27, 2006: CAMD Version 2.1 * bug fix. Ordering constraints not always met if dense and/or empty nodes are present in the matrix. Apr. 30, 2006: CAMD Version 2.0 * CAMD released, based on AMD v2.0. To compare the two codes, type the command ./docdiff in this directory (the "CAMD" and "camd" strings are replaced with "AMD" and "amd" when the two packages are compared, to make more evident the substantive differences between the packages). Primary differences with AMD v2.0: CAMD adds the ability to order the matrix with constraints. Each node i in the graph (row/column i in the matrix) has a constraint, C[i], which is in the range 0 to n-1. All nodes with C[i] = 0 are ordered first, followed by all nodes with constraint 1, and so on. That is, C[P[k]] is monotonically non-decreasing as k varies from 0 to n-1. camd_order has an additional C parameter; if NULL, no constraints are used (the ordering will be similar to AMD's ordering). The optional C parameter is also added to the MATLAB interface, p = camd (A,Control,C). Since the C parameter is optional, CAMD can replace AMD in any application that uses AMD. Just pass C = NULL (or omit C in the MATLAB interface). There is no Fortran version of CAMD, however. The postordering is different, and there is no camd_post_tree.c file. A new routine, camd_cvalid, has been added to check the validity of C. CAMD requires more workspace than AMD (n+1 integers). All user-visible names AMD* and amd* replaced with CAMD* and camd*. 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You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Also add information on how to contact you by electronic and paper mail. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the library, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the library `Frob' (a library for tweaking knobs) written by James Random Hacker. , 1 April 1990 Ty Coon, President of Vice That's all there is to it! SuiteSparse/CAMD/Lib/0000755001170100242450000000000010711435721013162 5ustar davisfacSuiteSparse/CAMD/Lib/Makefile0000644001170100242450000000504510621147006014622 0ustar davisfac#------------------------------------------------------------------------------- # CAMD Makefile for compiling on Unix systems (for original Make ONLY) #------------------------------------------------------------------------------- # This is a very ugly Makefile, and is only provided for those who do not # have GNU make. Note that it is not used if you have GNU make. It ignores # dependency checking and just compiles everything. default: everything include ../../UFconfig/UFconfig.mk C = $(CC) $(CFLAGS) $(CONFIG) -I../Include -I../../UFconfig everything: $(C) -DDINT -c ../Source/camd_aat.c -o camd_i_aat.o $(C) -DDINT -c ../Source/camd_1.c -o camd_i_1.o $(C) -DDINT -c ../Source/camd_2.c -o camd_i_2.o $(C) -DDINT -c ../Source/camd_dump.c -o camd_i_dump.o $(C) -DDINT -c ../Source/camd_postorder.c -o camd_i_postorder.o $(C) -DDINT -c ../Source/camd_defaults.c -o camd_i_defaults.o $(C) -DDINT -c ../Source/camd_order.c -o camd_i_order.o $(C) -DDINT -c ../Source/camd_control.c -o camd_i_control.o $(C) -DDINT -c ../Source/camd_info.c -o camd_i_info.o $(C) -DDINT -c ../Source/camd_valid.c -o camd_i_valid.o $(C) -DDINT -c ../Source/camd_preprocess.c -o camd_i_preprocess.o $(C) -DDLONG -c ../Source/camd_aat.c -o camd_l_aat.o $(C) -DDLONG -c ../Source/camd_1.c -o camd_l_1.o $(C) -DDLONG -c ../Source/camd_2.c -o camd_l_2.o $(C) -DDLONG -c ../Source/camd_dump.c -o camd_l_dump.o $(C) -DDLONG -c ../Source/camd_postorder.c -o camd_l_postorder.o $(C) -DDLONG -c ../Source/camd_defaults.c -o camd_l_defaults.o $(C) -DDLONG -c ../Source/camd_order.c -o camd_l_order.o $(C) -DDLONG -c ../Source/camd_control.c -o camd_l_control.o $(C) -DDLONG -c ../Source/camd_info.c -o camd_l_info.o $(C) -DDLONG -c ../Source/camd_valid.c -o camd_l_valid.o $(C) -DDLONG -c ../Source/camd_preprocess.c -o camd_l_preprocess.o $(C) -c ../Source/camd_global.c $(AR) libcamd.a camd_i_aat.o camd_i_1.o camd_i_2.o camd_i_dump.o \ camd_i_postorder.o camd_i_defaults.o camd_i_order.o \ camd_i_control.o camd_i_info.o camd_i_valid.o camd_l_aat.o \ camd_l_1.o camd_l_2.o camd_l_dump.o camd_l_postorder.o \ camd_l_defaults.o camd_l_order.o camd_l_control.o camd_l_info.o \ camd_l_valid.o camd_i_preprocess.o camd_l_preprocess.o camd_global.o - $(RANLIB) libcamd.a #------------------------------------------------------------------------------- # Remove all but the files in the original distribution #------------------------------------------------------------------------------- clean: - $(RM) $(CLEAN) purge: distclean distclean: clean - $(RM) libcamd.a SuiteSparse/CAMD/Lib/libcamd.def0000644001170100242450000000022310423471324015231 0ustar davisfacLIBRARY libcamd.dll EXPORTS camd_order camd_defaults camd_control camd_info camd_2 camd_l_order camd_l_defaults camd_l_control camd_l_info camd_l2 SuiteSparse/CAMD/Lib/GNUmakefile0000644001170100242450000000405210617112305015230 0ustar davisfac#------------------------------------------------------------------------------- # CAMD Makefile for compiling on Unix systems (for GNU make only) #------------------------------------------------------------------------------- default: libcamd.a include ../../UFconfig/UFconfig.mk C = $(CC) $(CFLAGS) $(CONFIG) -I../Include -I../../UFconfig #------------------------------------------------------------------------------- # source files #------------------------------------------------------------------------------- CAMD = camd_aat camd_1 camd_2 camd_dump camd_postorder camd_defaults \ camd_order camd_control camd_info camd_valid camd_preprocess UFCONFIG = ../../UFconfig/UFconfig.h INC = ../Include/camd.h ../Include/camd_internal.h $(UFCONFIG) #------------------------------------------------------------------------------- # object files for each version #------------------------------------------------------------------------------- CAMDI = $(addsuffix .o, $(subst camd_,camd_i_,$(CAMD))) CAMDL = $(addsuffix .o, $(subst camd_,camd_l_,$(CAMD))) #------------------------------------------------------------------------------- # compile each int and long routine (with no real/complex version) #------------------------------------------------------------------------------- camd_global.o: ../Source/camd_global.c $(INC) $(C) -c $< -o $@ camd_i_%.o: ../Source/camd_%.c $(INC) $(C) -DDINT -c $< -o $@ camd_l_%.o: ../Source/camd_%.c $(INC) $(C) -DDLONG -c $< -o $@ #------------------------------------------------------------------------------- # Create the libcamd.a library (C versions only) #------------------------------------------------------------------------------- libcamd.a: camd_global.o $(CAMDI) $(CAMDL) $(AR) libcamd.a $^ - $(RANLIB) libcamd.a #------------------------------------------------------------------------------- # Remove all but the files in the original distribution #------------------------------------------------------------------------------- clean: - $(RM) $(CLEAN) purge: distclean distclean: clean - $(RM) libcamd.a SuiteSparse/CAMD/Demo/0000755001170100242450000000000010711435721013340 5ustar davisfacSuiteSparse/CAMD/Demo/Makefile0000644001170100242450000000346010617112412014775 0ustar davisfac#----------------------------------------------------------------------------- # compile the CAMD demo (for both GNU make or original make) #----------------------------------------------------------------------------- default: camd_simple camd_demo camd_demo2 camd_l_demo include ../../UFconfig/UFconfig.mk C = $(CC) $(CFLAGS) $(CONFIG) -I../Include -I../../UFconfig UFCONFIG = ../../UFconfig/UFconfig.h INC = ../Include/camd.h $(UFCONFIG) library: ( cd ../Lib ; $(MAKE) ) #------------------------------------------------------------------------------ # Create the demo program, run it, and compare the output #------------------------------------------------------------------------------ dist: camd_demo: camd_demo.c library $(INC) $(C) -o camd_demo camd_demo.c ../Lib/libcamd.a $(LIB) ./camd_demo > my_camd_demo.out - diff camd_demo.out my_camd_demo.out camd_l_demo: camd_l_demo.c library $(INC) $(C) -o camd_l_demo camd_l_demo.c ../Lib/libcamd.a $(LIB) ./camd_l_demo > my_camd_l_demo.out - diff camd_l_demo.out my_camd_l_demo.out camd_demo2: camd_demo2.c library $(INC) $(C) -o camd_demo2 camd_demo2.c ../Lib/libcamd.a $(LIB) ./camd_demo2 > my_camd_demo2.out - diff camd_demo2.out my_camd_demo2.out camd_simple: camd_simple.c library $(INC) $(C) -o camd_simple camd_simple.c ../Lib/libcamd.a $(LIB) ./camd_simple > my_camd_simple.out - diff camd_simple.out my_camd_simple.out #------------------------------------------------------------------------------ # Remove all but the files in the original distribution #------------------------------------------------------------------------------ clean: - $(RM) $(CLEAN) purge: distclean distclean: clean - $(RM) camd_demo my_camd_demo.out - $(RM) camd_l_demo my_camd_l_demo.out - $(RM) camd_demo2 my_camd_demo2.out - $(RM) camd_simple my_camd_simple.out SuiteSparse/CAMD/Demo/camd_simple.c0000644001170100242450000000153410616400305015756 0ustar davisfac/* ------------------------------------------------------------------------- */ /* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/camd */ /* ------------------------------------------------------------------------- */ #include #include "camd.h" int n = 5 ; int Ap [ ] = { 0, 2, 6, 10, 12, 14} ; int Ai [ ] = { 0,1, 0,1,2,4, 1,2,3,4, 2,3, 1,4 } ; int C [ ] = { 2, 0, 0, 0, 1 } ; int P [5] ; int main (void) { int k ; (void) camd_order (n, Ap, Ai, P, (double *) NULL, (double *) NULL, C) ; for (k = 0 ; k < n ; k++) printf ("P [%d] = %d\n", k, P [k]) ; return (0) ; } SuiteSparse/CAMD/Demo/camd_l_demo.out0000644001170100242450000001664010616403262016322 0ustar davisfacCAMD version 2.2, date: May 31, 2007 CAMD demo, with the 24-by-24 Harwell/Boeing matrix, can_24: camd version 2.2, May 31, 2007: approximate minimum degree ordering: dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes Input matrix: 24-by-24, with 160 entries. Note that for a symmetric matrix such as this one, only the strictly lower or upper triangular parts would need to be passed to CAMD, since CAMD computes the ordering of A+A'. The diagonal entries are also not needed, since CAMD ignores them. Column: 0, number of entries: 9, with row indices in Ai [0 ... 8]: row indices: 0 5 6 12 13 17 18 19 21 Column: 1, number of entries: 6, with row indices in Ai [9 ... 14]: row indices: 1 8 9 13 14 17 Column: 2, number of entries: 6, with row indices in Ai [15 ... 20]: row indices: 2 6 11 20 21 22 Column: 3, number of entries: 6, with row indices in Ai [21 ... 26]: row indices: 3 7 10 15 18 19 Column: 4, number of entries: 6, with row indices in Ai [27 ... 32]: row indices: 4 7 9 14 15 16 Column: 5, number of entries: 6, with row indices in Ai [33 ... 38]: row indices: 0 5 6 12 13 17 Column: 6, number of entries: 9, with row indices in Ai [39 ... 47]: row indices: 0 2 5 6 11 12 19 21 23 Column: 7, number of entries: 9, with row indices in Ai [48 ... 56]: row indices: 3 4 7 9 14 15 16 17 18 Column: 8, number of entries: 4, with row indices in Ai [57 ... 60]: row indices: 1 8 9 14 Column: 9, number of entries: 9, with row indices in Ai [61 ... 69]: row indices: 1 4 7 8 9 13 14 17 18 Column: 10, number of entries: 6, with row indices in Ai [70 ... 75]: row indices: 3 10 18 19 20 21 Column: 11, number of entries: 6, with row indices in Ai [76 ... 81]: row indices: 2 6 11 12 21 23 Column: 12, number of entries: 6, with row indices in Ai [82 ... 87]: row indices: 0 5 6 11 12 23 Column: 13, number of entries: 6, with row indices in Ai [88 ... 93]: row indices: 0 1 5 9 13 17 Column: 14, number of entries: 6, with row indices in Ai [94 ... 99]: row indices: 1 4 7 8 9 14 Column: 15, number of entries: 6, with row indices in Ai [100 ... 105]: row indices: 3 4 7 15 16 18 Column: 16, number of entries: 4, with row indices in Ai [106 ... 109]: row indices: 4 7 15 16 Column: 17, number of entries: 9, with row indices in Ai [110 ... 118]: row indices: 0 1 5 7 9 13 17 18 19 Column: 18, number of entries: 9, with row indices in Ai [119 ... 127]: row indices: 0 3 7 9 10 15 17 18 19 Column: 19, number of entries: 9, with row indices in Ai [128 ... 136]: row indices: 0 3 6 10 17 18 19 20 21 Column: 20, number of entries: 6, with row indices in Ai [137 ... 142]: row indices: 2 10 19 20 21 22 Column: 21, number of entries: 9, with row indices in Ai [143 ... 151]: row indices: 0 2 6 10 11 19 20 21 22 Column: 22, number of entries: 4, with row indices in Ai [152 ... 155]: row indices: 2 20 21 22 Column: 23, number of entries: 4, with row indices in Ai [156 ... 159]: row indices: 6 11 12 23 Plot of input matrix pattern: 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 0: X . . . . X X . . . . . X X . . . X X X . X . . 1: . X . . . . . . X X . . . X X . . X . . . . . . 2: . . X . . . X . . . . X . . . . . . . . X X X . 3: . . . X . . . X . . X . . . . X . . X X . . . . 4: . . . . X . . X . X . . . . X X X . . . . . . . 5: X . . . . X X . . . . . X X . . . X . . . . . . 6: X . X . . X X . . . . X X . . . . . . X . X . X 7: . . . X X . . X . X . . . . X X X X X . . . . . 8: . X . . . . . . X X . . . . X . . . . . . . . . 9: . X . . X . . X X X . . . X X . . X X . . . . . 10: . . . X . . . . . . X . . . . . . . X X X X . . 11: . . X . . . X . . . . X X . . . . . . . . X . X 12: X . . . . X X . . . . X X . . . . . . . . . . X 13: X X . . . X . . . X . . . X . . . X . . . . . . 14: . X . . X . . X X X . . . . X . . . . . . . . . 15: . . . X X . . X . . . . . . . X X . X . . . . . 16: . . . . X . . X . . . . . . . X X . . . . . . . 17: X X . . . X . X . X . . . X . . . X X X . . . . 18: X . . X . . . X . X X . . . . X . X X X . . . . 19: X . . X . . X . . . X . . . . . . X X X X X . . 20: . . X . . . . . . . X . . . . . . . . X X X X . 21: X . X . . . X . . . X X . . . . . . . X X X X . 22: . . X . . . . . . . . . . . . . . . . . X X X . 23: . . . . . . X . . . . X X . . . . . . . . . . X return value from camd_l_order: 0 (should be 0) camd: approximate minimum degree ordering, results: status: OK n, dimension of A: 24 nz, number of nonzeros in A: 160 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 136 # dense rows/columns of A+A': 0 memory used, in bytes: 3288 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 135 nonzeros in L (including diagonal): 159 # divide operations for LDL' or LU: 135 # multiply-subtract operations for LDL': 541 # multiply-subtract operations for LU: 947 max nz. in any column of L (incl. diagonal): 12 chol flop count for real A, sqrt counted as 1 flop: 1241 LDL' flop count for real A: 1217 LDL' flop count for complex A: 5543 LU flop count for real A (with no pivoting): 2029 LU flop count for complex A (with no pivoting): 8791 Permutation vector: 23 3 1 5 0 22 4 8 9 7 6 21 17 19 10 14 2 11 20 15 12 13 18 16 Inverse permutation vector: 4 2 16 1 6 3 10 9 7 8 14 17 20 21 15 19 23 12 22 13 18 11 5 0 Plot of permuted matrix pattern: 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 0: X . . . . . . . . . X . . . . . . X . . X . . . 1: . X . . . . . . . X . . . X X . . . . X . . X . 2: . . X . . . . X X . . . X . . X . . . . . X . . 3: . . . X X . . . . . X . X . . . . . . . X X . . 4: . . . X X . . . . . X X X X . . . . . . X X X . 5: . . . . . X . . . . . X . . . . X . X . . . . . 6: . . . . . . X . X X . . . . . X . . . X . . . X 7: . . X . . . . X X . . . . . . X . . . . . . . . 8: . . X . . . X X X X . . X . . X . . . . . X X . 9: . X . . . . X . X X . . X . . X . . . X . . X X 10: X . . X X . . . . . X X . X . . X X . . X . . . 11: . . . . X X . . . . X X . X X . X X X . . . . . 12: . . X X X . . . X X . . X X . . . . . . . X X . 13: . X . . X . . . . . X X X X X . . . X . . . X . 14: . X . . . . . . . . . X . X X . . . X . . . X . 15: . . X . . . X X X X . . . . . X . . . . . . . . 16: . . . . . X . . . . X X . . . . X X X . . . . . 17: X . . . . . . . . . X X . . . . X X . . X . . . 18: . . . . . X . . . . . X . X X . X . X . . . . . 19: . X . . . . X . . X . . . . . . . . . X . . X X 20: X . . X X . . . . . X . . . . . . X . . X . . . 21: . . X X X . . . X . . . X . . . . . . . . X . . 22: . X . . X . . . X X . . X X X . . . . X . . X . 23: . . . . . . X . . X . . . . . . . . . X . . . X SuiteSparse/CAMD/Demo/camd_demo2.out0000644001170100242450000002153610616403262016071 0ustar davisfacCAMD demo, with a jumbled version of the 24-by-24 Harwell/Boeing matrix, can_24: camd version 2.2, May 31, 2007: approximate minimum degree ordering: dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes Jumbled input matrix: 24-by-24, with 116 entries. Note that for a symmetric matrix such as this one, only the strictly lower or upper triangular parts would need to be passed to CAMD, since CAMD computes the ordering of A+A'. The diagonal entries are also not needed, since CAMD ignores them. This version of the matrix has jumbled columns and duplicate row indices. Column: 0, number of entries: 9, with row indices in Ai [0 ... 8]: row indices: 0 17 18 21 5 12 5 0 13 Column: 1, number of entries: 5, with row indices in Ai [9 ... 13]: row indices: 14 1 8 13 17 Column: 2, number of entries: 6, with row indices in Ai [14 ... 19]: row indices: 2 20 11 6 11 22 Column: 3, number of entries: 8, with row indices in Ai [20 ... 27]: row indices: 3 3 10 7 18 18 15 19 Column: 4, number of entries: 5, with row indices in Ai [28 ... 32]: row indices: 7 9 15 14 16 Column: 5, number of entries: 4, with row indices in Ai [33 ... 36]: row indices: 5 13 6 17 Column: 6, number of entries: 7, with row indices in Ai [37 ... 43]: row indices: 5 0 11 6 12 6 23 Column: 7, number of entries: 9, with row indices in Ai [44 ... 52]: row indices: 3 4 9 7 14 16 15 17 18 Column: 8, number of entries: 5, with row indices in Ai [53 ... 57]: row indices: 1 9 14 14 14 Column: 9, number of entries: 5, with row indices in Ai [58 ... 62]: row indices: 7 13 8 1 17 Column: 10, number of entries: 0, with row indices in Ai [63 ... 62]: row indices: Column: 11, number of entries: 3, with row indices in Ai [63 ... 65]: row indices: 2 12 23 Column: 12, number of entries: 3, with row indices in Ai [66 ... 68]: row indices: 5 11 12 Column: 13, number of entries: 3, with row indices in Ai [69 ... 71]: row indices: 0 13 17 Column: 14, number of entries: 3, with row indices in Ai [72 ... 74]: row indices: 1 9 14 Column: 15, number of entries: 3, with row indices in Ai [75 ... 77]: row indices: 3 15 16 Column: 16, number of entries: 4, with row indices in Ai [78 ... 81]: row indices: 16 4 4 15 Column: 17, number of entries: 4, with row indices in Ai [82 ... 85]: row indices: 13 17 19 17 Column: 18, number of entries: 5, with row indices in Ai [86 ... 90]: row indices: 15 17 19 9 10 Column: 19, number of entries: 6, with row indices in Ai [91 ... 96]: row indices: 17 19 20 0 6 10 Column: 20, number of entries: 4, with row indices in Ai [97 ... 100]: row indices: 22 10 20 21 Column: 21, number of entries: 11, with row indices in Ai [101 ... 111]: row indices: 6 2 10 19 20 11 21 22 22 22 22 Column: 22, number of entries: 0, with row indices in Ai [112 ... 111]: row indices: Column: 23, number of entries: 4, with row indices in Ai [112 ... 115]: row indices: 12 11 12 23 Plot of (jumbled) input matrix pattern: 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 0: X . . . . . X . . . . . . X . . . . . X . . . . 1: . X . . . . . . X X . . . . X . . . . . . . . . 2: . . X . . . . . . . . X . . . . . . . . . X . . 3: . . . X . . . X . . . . . . . X . . . . . . . . 4: . . . . . . . X . . . . . . . . X . . . . . . . 5: X . . . . X X . . . . . X . . . . . . . . . . . 6: . . X . . X X . . . . . . . . . . . . X . X . . 7: . . . X X . . X . X . . . . . . . . . . . . . . 8: . X . . . . . . . X . . . . . . . . . . . . . . 9: . . . . X . . X X . . . . . X . . . X . . . . . 10: . . . X . . . . . . . . . . . . . . X X X X . . 11: . . X . . . X . . . . . X . . . . . . . . X . X 12: X . . . . . X . . . . X X . . . . . . . . . . X 13: X X . . . X . . . X . . . X . . . X . . . . . . 14: . X . . X . . X X . . . . . X . . . . . . . . . 15: . . . X X . . X . . . . . . . X X . X . . . . . 16: . . . . X . . X . . . . . . . X X . . . . . . . 17: X X . . . X . X . X . . . X . . . X X X . . . . 18: X . . X . . . X . . . . . . . . . . . . . . . . 19: . . . X . . . . . . . . . . . . . X X X . X . . 20: . . X . . . . . . . . . . . . . . . . X X X . . 21: X . . . . . . . . . . . . . . . . . . . X X . . 22: . . X . . . . . . . . . . . . . . . . . X X . . 23: . . . . . . X . . . . X . . . . . . . . . . . X Plot of symmetric matrix to be ordered by camd_order: 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 0: X . . . . X X . . . . . X X . . . X X X . X . . 1: . X . . . . . . X X . . . X X . . X . . . . . . 2: . . X . . . X . . . . X . . . . . . . . X X X . 3: . . . X . . . X . . X . . . . X . . X X . . . . 4: . . . . X . . X . X . . . . X X X . . . . . . . 5: X . . . . X X . . . . . X X . . . X . . . . . . 6: X . X . . X X . . . . X X . . . . . . X . X . X 7: . . . X X . . X . X . . . . X X X X X . . . . . 8: . X . . . . . . X X . . . . X . . . . . . . . . 9: . X . . X . . X X X . . . X X . . X X . . . . . 10: . . . X . . . . . . X . . . . . . . X X X X . . 11: . . X . . . X . . . . X X . . . . . . . . X . X 12: X . . . . X X . . . . X X . . . . . . . . . . X 13: X X . . . X . . . X . . . X . . . X . . . . . . 14: . X . . X . . X X X . . . . X . . . . . . . . . 15: . . . X X . . X . . . . . . . X X . X . . . . . 16: . . . . X . . X . . . . . . . X X . . . . . . . 17: X X . . . X . X . X . . . X . . . X X X . . . . 18: X . . X . . . X . X X . . . . X . X X X . . . . 19: X . . X . . X . . . X . . . . . . X X X X X . . 20: . . X . . . . . . . X . . . . . . . . X X X X . 21: X . X . . . X . . . X X . . . . . . . X X X X . 22: . . X . . . . . . . . . . . . . . . . . X X X . 23: . . . . . . X . . . . X X . . . . . . . . . . X return value from camd_order: 1 (should be 1) camd: approximate minimum degree ordering, results: status: OK, but jumbled n, dimension of A: 24 nz, number of nonzeros in A: 102 symmetry of A: 0.4000 number of nonzeros on diagonal: 17 nonzeros in pattern of A+A' (excl. diagonal): 136 # dense rows/columns of A+A': 0 memory used, in bytes: 2208 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 140 nonzeros in L (including diagonal): 164 # divide operations for LDL' or LU: 140 # multiply-subtract operations for LDL': 593 # multiply-subtract operations for LU: 1046 max nz. in any column of L (incl. diagonal): 13 chol flop count for real A, sqrt counted as 1 flop: 1350 LDL' flop count for real A: 1326 LDL' flop count for complex A: 6004 LU flop count for real A (with no pivoting): 2232 LU flop count for complex A (with no pivoting): 9628 Permutation vector: 23 3 1 5 4 8 9 7 17 22 21 6 10 14 0 2 11 15 20 13 16 12 18 19 Permuted constraints: 0 0 0 1 1 2 2 2 2 2 2 2 3 3 3 4 4 4 4 5 5 5 8 10 Inverse permutation vector: 14 2 15 1 4 3 11 7 5 6 12 16 21 19 13 17 20 8 22 23 18 10 9 0 Plot of (symmetrized) permuted matrix pattern: 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 0: X . . . . . . . . . . X . . . . X . . . . X . . 1: . X . . . . . X . . . . X . . . . X . . . . X X 2: . . X . . X X . X . . . . X . . . . . X . . . . 3: . . . X . . . . X . . X . . X . . . . X . X . . 4: . . . . X . X X . . . . . X . . . X . . X . . . 5: . . X . . X X . . . . . . X . . . . . . . . . . 6: . . X . X X X X X . . . . X . . . . . X . . X . 7: . X . . X . X X X . . . . X . . . X . . X . X . 8: . . X X . . X X X . . . . . X . . . . X . . X X 9: . . . . . . . . . X X . . . . X . . X . . . . . 10: . . . . . . . . . X X X X . X X X . X . . . . X 11: X . . X . . . . . . X X . . X X X . . . . X . X 12: . X . . . . . . . . X . X . . . . . X . . . X X 13: . . X . X X X X . . . . . X . . . . . . . . . . 14: . . . X . . . . X . X X . . X . . . . X . X X X 15: . . . . . . . . . X X X . . . X X . X . . . . . 16: X . . . . . . . . . X X . . . X X . . . . X . . 17: . X . . X . . X . . . . . . . . . X . . X . X . 18: . . . . . . . . . X X . X . . X . . X . . . . X 19: . . X X . . X . X . . . . . X . . . . X . . . . 20: . . . . X . . X . . . . . . . . . X . . X . . . 21: X . . X . . . . . . . X . . X . X . . . . X . . 22: . X . . . . X X X . . . X . X . . X . . . . X X 23: . X . . . . . . X . X X X . X . . . X . . . X X SuiteSparse/CAMD/Demo/camd_l_demo.c0000644001170100242450000001274210616400300015722 0ustar davisfac/* ========================================================================= */ /* === CAMD demo main program (UF_long integer version) ==================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/camd */ /* ------------------------------------------------------------------------- */ /* A simple C main program that illustrates the use of the ANSI C interface * to CAMD. */ #include "camd.h" #include #include /* define UF_long */ #include "UFconfig.h" int main (void) { /* The symmetric can_24 Harwell/Boeing matrix, including upper and lower * triangular parts, and the diagonal entries. Note that this matrix is * 0-based, with row and column indices in the range 0 to n-1. */ UF_long n = 24, nz, Ap [ ] = { 0, 9, 15, 21, 27, 33, 39, 48, 57, 61, 70, 76, 82, 88, 94, 100, 106, 110, 119, 128, 137, 143, 152, 156, 160 }, Ai [ ] = { /* column 0: */ 0, 5, 6, 12, 13, 17, 18, 19, 21, /* column 1: */ 1, 8, 9, 13, 14, 17, /* column 2: */ 2, 6, 11, 20, 21, 22, /* column 3: */ 3, 7, 10, 15, 18, 19, /* column 4: */ 4, 7, 9, 14, 15, 16, /* column 5: */ 0, 5, 6, 12, 13, 17, /* column 6: */ 0, 2, 5, 6, 11, 12, 19, 21, 23, /* column 7: */ 3, 4, 7, 9, 14, 15, 16, 17, 18, /* column 8: */ 1, 8, 9, 14, /* column 9: */ 1, 4, 7, 8, 9, 13, 14, 17, 18, /* column 10: */ 3, 10, 18, 19, 20, 21, /* column 11: */ 2, 6, 11, 12, 21, 23, /* column 12: */ 0, 5, 6, 11, 12, 23, /* column 13: */ 0, 1, 5, 9, 13, 17, /* column 14: */ 1, 4, 7, 8, 9, 14, /* column 15: */ 3, 4, 7, 15, 16, 18, /* column 16: */ 4, 7, 15, 16, /* column 17: */ 0, 1, 5, 7, 9, 13, 17, 18, 19, /* column 18: */ 0, 3, 7, 9, 10, 15, 17, 18, 19, /* column 19: */ 0, 3, 6, 10, 17, 18, 19, 20, 21, /* column 20: */ 2, 10, 19, 20, 21, 22, /* column 21: */ 0, 2, 6, 10, 11, 19, 20, 21, 22, /* column 22: */ 2, 20, 21, 22, /* column 23: */ 6, 11, 12, 23 } ; UF_long P [24], Pinv [24], i, j, k, jnew, p, inew, result ; double Control [CAMD_CONTROL], Info [CAMD_INFO] ; char A [24][24] ; UF_long C [ ] = { 0, 0, 4, 0, 1, 0, 2, 2, 1, 1, 3, 4, 5, 5, 3, 4, 5, 2, 5, 3, 4, 2, 1, 0 }; printf ("CAMD version %d.%d, date: %s\n", CAMD_MAIN_VERSION, CAMD_SUB_VERSION, CAMD_DATE) ; printf ("CAMD demo, with the 24-by-24 Harwell/Boeing matrix, can_24:\n") ; /* get the default parameters, and print them */ camd_l_defaults (Control) ; camd_l_control (Control) ; /* print the input matrix */ nz = Ap [n] ; printf ("\nInput matrix: %ld-by-%ld, with %ld entries.\n" " Note that for a symmetric matrix such as this one, only the\n" " strictly lower or upper triangular parts would need to be\n" " passed to CAMD, since CAMD computes the ordering of A+A'. The\n" " diagonal entries are also not needed, since CAMD ignores them.\n" , n, n, nz) ; for (j = 0 ; j < n ; j++) { printf ("\nColumn: %ld, number of entries: %ld, with row indices in" " Ai [%ld ... %ld]:\n row indices:", j, Ap [j+1] - Ap [j], Ap [j], Ap [j+1]-1) ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; printf (" %ld", i) ; } printf ("\n") ; } /* print a character plot of the input matrix. This is only reasonable * because the matrix is small. */ printf ("\nPlot of input matrix pattern:\n") ; for (j = 0 ; j < n ; j++) { for (i = 0 ; i < n ; i++) A [i][j] = '.' ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; A [i][j] = 'X' ; } } printf (" ") ; for (j = 0 ; j < n ; j++) printf (" %1ld", j % 10) ; printf ("\n") ; for (i = 0 ; i < n ; i++) { printf ("%2ld: ", i) ; for (j = 0 ; j < n ; j++) { printf (" %c", A [i][j]) ; } printf ("\n") ; } /* order the matrix */ result = camd_l_order (n, Ap, Ai, P, Control, Info, C) ; printf ("return value from camd_l_order: %ld (should be %d)\n", result, CAMD_OK) ; /* print the statistics */ camd_l_info (Info) ; if (result != CAMD_OK) { printf ("CAMD failed\n") ; exit (1) ; } /* print the permutation vector, P, and compute the inverse permutation */ printf ("Permutation vector:\n") ; for (k = 0 ; k < n ; k++) { /* row/column j is the kth row/column in the permuted matrix */ j = P [k] ; Pinv [j] = k ; printf (" %2ld", j) ; } printf ("\n\n") ; printf ("Inverse permutation vector:\n") ; for (j = 0 ; j < n ; j++) { k = Pinv [j] ; printf (" %2ld", k) ; } printf ("\n\n") ; /* print a character plot of the permuted matrix. */ printf ("\nPlot of permuted matrix pattern:\n") ; for (jnew = 0 ; jnew < n ; jnew++) { j = P [jnew] ; for (inew = 0 ; inew < n ; inew++) A [inew][jnew] = '.' ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { inew = Pinv [Ai [p]] ; A [inew][jnew] = 'X' ; } } printf (" ") ; for (j = 0 ; j < n ; j++) printf (" %1ld", j % 10) ; printf ("\n") ; for (i = 0 ; i < n ; i++) { printf ("%2ld: ", i) ; for (j = 0 ; j < n ; j++) { printf (" %c", A [i][j]) ; } printf ("\n") ; } return (0) ; } SuiteSparse/CAMD/Demo/camd_demo.out0000644001170100242450000001663610616403262016014 0ustar davisfacCAMD version 2.2, date: May 31, 2007 CAMD demo, with the 24-by-24 Harwell/Boeing matrix, can_24: camd version 2.2, May 31, 2007: approximate minimum degree ordering: dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes Input matrix: 24-by-24, with 160 entries. Note that for a symmetric matrix such as this one, only the strictly lower or upper triangular parts would need to be passed to CAMD, since CAMD computes the ordering of A+A'. The diagonal entries are also not needed, since CAMD ignores them. Column: 0, number of entries: 9, with row indices in Ai [0 ... 8]: row indices: 0 5 6 12 13 17 18 19 21 Column: 1, number of entries: 6, with row indices in Ai [9 ... 14]: row indices: 1 8 9 13 14 17 Column: 2, number of entries: 6, with row indices in Ai [15 ... 20]: row indices: 2 6 11 20 21 22 Column: 3, number of entries: 6, with row indices in Ai [21 ... 26]: row indices: 3 7 10 15 18 19 Column: 4, number of entries: 6, with row indices in Ai [27 ... 32]: row indices: 4 7 9 14 15 16 Column: 5, number of entries: 6, with row indices in Ai [33 ... 38]: row indices: 0 5 6 12 13 17 Column: 6, number of entries: 9, with row indices in Ai [39 ... 47]: row indices: 0 2 5 6 11 12 19 21 23 Column: 7, number of entries: 9, with row indices in Ai [48 ... 56]: row indices: 3 4 7 9 14 15 16 17 18 Column: 8, number of entries: 4, with row indices in Ai [57 ... 60]: row indices: 1 8 9 14 Column: 9, number of entries: 9, with row indices in Ai [61 ... 69]: row indices: 1 4 7 8 9 13 14 17 18 Column: 10, number of entries: 6, with row indices in Ai [70 ... 75]: row indices: 3 10 18 19 20 21 Column: 11, number of entries: 6, with row indices in Ai [76 ... 81]: row indices: 2 6 11 12 21 23 Column: 12, number of entries: 6, with row indices in Ai [82 ... 87]: row indices: 0 5 6 11 12 23 Column: 13, number of entries: 6, with row indices in Ai [88 ... 93]: row indices: 0 1 5 9 13 17 Column: 14, number of entries: 6, with row indices in Ai [94 ... 99]: row indices: 1 4 7 8 9 14 Column: 15, number of entries: 6, with row indices in Ai [100 ... 105]: row indices: 3 4 7 15 16 18 Column: 16, number of entries: 4, with row indices in Ai [106 ... 109]: row indices: 4 7 15 16 Column: 17, number of entries: 9, with row indices in Ai [110 ... 118]: row indices: 0 1 5 7 9 13 17 18 19 Column: 18, number of entries: 9, with row indices in Ai [119 ... 127]: row indices: 0 3 7 9 10 15 17 18 19 Column: 19, number of entries: 9, with row indices in Ai [128 ... 136]: row indices: 0 3 6 10 17 18 19 20 21 Column: 20, number of entries: 6, with row indices in Ai [137 ... 142]: row indices: 2 10 19 20 21 22 Column: 21, number of entries: 9, with row indices in Ai [143 ... 151]: row indices: 0 2 6 10 11 19 20 21 22 Column: 22, number of entries: 4, with row indices in Ai [152 ... 155]: row indices: 2 20 21 22 Column: 23, number of entries: 4, with row indices in Ai [156 ... 159]: row indices: 6 11 12 23 Plot of input matrix pattern: 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 0: X . . . . X X . . . . . X X . . . X X X . X . . 1: . X . . . . . . X X . . . X X . . X . . . . . . 2: . . X . . . X . . . . X . . . . . . . . X X X . 3: . . . X . . . X . . X . . . . X . . X X . . . . 4: . . . . X . . X . X . . . . X X X . . . . . . . 5: X . . . . X X . . . . . X X . . . X . . . . . . 6: X . X . . X X . . . . X X . . . . . . X . X . X 7: . . . X X . . X . X . . . . X X X X X . . . . . 8: . X . . . . . . X X . . . . X . . . . . . . . . 9: . X . . X . . X X X . . . X X . . X X . . . . . 10: . . . X . . . . . . X . . . . . . . X X X X . . 11: . . X . . . X . . . . X X . . . . . . . . X . X 12: X . . . . X X . . . . X X . . . . . . . . . . X 13: X X . . . X . . . X . . . X . . . X . . . . . . 14: . X . . X . . X X X . . . . X . . . . . . . . . 15: . . . X X . . X . . . . . . . X X . X . . . . . 16: . . . . X . . X . . . . . . . X X . . . . . . . 17: X X . . . X . X . X . . . X . . . X X X . . . . 18: X . . X . . . X . X X . . . . X . X X X . . . . 19: X . . X . . X . . . X . . . . . . X X X X X . . 20: . . X . . . . . . . X . . . . . . . . X X X X . 21: X . X . . . X . . . X X . . . . . . . X X X X . 22: . . X . . . . . . . . . . . . . . . . . X X X . 23: . . . . . . X . . . . X X . . . . . . . . . . X return value from camd_order: 0 (should be 0) camd: approximate minimum degree ordering, results: status: OK n, dimension of A: 24 nz, number of nonzeros in A: 160 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 136 # dense rows/columns of A+A': 0 memory used, in bytes: 1644 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 135 nonzeros in L (including diagonal): 159 # divide operations for LDL' or LU: 135 # multiply-subtract operations for LDL': 541 # multiply-subtract operations for LU: 947 max nz. in any column of L (incl. diagonal): 12 chol flop count for real A, sqrt counted as 1 flop: 1241 LDL' flop count for real A: 1217 LDL' flop count for complex A: 5543 LU flop count for real A (with no pivoting): 2029 LU flop count for complex A (with no pivoting): 8791 Permutation vector: 23 3 1 5 0 22 4 8 9 7 6 21 17 19 10 14 2 11 20 15 12 13 18 16 Inverse permutation vector: 4 2 16 1 6 3 10 9 7 8 14 17 20 21 15 19 23 12 22 13 18 11 5 0 Plot of permuted matrix pattern: 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 0: X . . . . . . . . . X . . . . . . X . . X . . . 1: . X . . . . . . . X . . . X X . . . . X . . X . 2: . . X . . . . X X . . . X . . X . . . . . X . . 3: . . . X X . . . . . X . X . . . . . . . X X . . 4: . . . X X . . . . . X X X X . . . . . . X X X . 5: . . . . . X . . . . . X . . . . X . X . . . . . 6: . . . . . . X . X X . . . . . X . . . X . . . X 7: . . X . . . . X X . . . . . . X . . . . . . . . 8: . . X . . . X X X X . . X . . X . . . . . X X . 9: . X . . . . X . X X . . X . . X . . . X . . X X 10: X . . X X . . . . . X X . X . . X X . . X . . . 11: . . . . X X . . . . X X . X X . X X X . . . . . 12: . . X X X . . . X X . . X X . . . . . . . X X . 13: . X . . X . . . . . X X X X X . . . X . . . X . 14: . X . . . . . . . . . X . X X . . . X . . . X . 15: . . X . . . X X X X . . . . . X . . . . . . . . 16: . . . . . X . . . . X X . . . . X X X . . . . . 17: X . . . . . . . . . X X . . . . X X . . X . . . 18: . . . . . X . . . . . X . X X . X . X . . . . . 19: . X . . . . X . . X . . . . . . . . . X . . X X 20: X . . X X . . . . . X . . . . . . X . . X . . . 21: . . X X X . . . X . . . X . . . . . . . . X . . 22: . X . . X . . . X X . . X X X . . . . X . . X . 23: . . . . . . X . . X . . . . . . . . . X . . . X SuiteSparse/CAMD/Demo/camd_demo2.c0000644001170100242450000001463010616400254015477 0ustar davisfac/* ========================================================================= */ /* === CAMD demo main program (jumbled matrix version) ===================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/camd */ /* ------------------------------------------------------------------------- */ /* A simple C main program that illustrates the use of the ANSI C interface * to CAMD. * * Identical to camd_demo.c, except that it operates on an input matrix that has * unsorted columns and duplicate entries. */ #include "camd.h" #include #include int main (void) { /* The symmetric can_24 Harwell/Boeing matrix (jumbled, and not symmetric). * Since CAMD operates on A+A', only A(i,j) or A(j,i) need to be specified, * or both. The diagonal entries are optional (some are missing). * There are many duplicate entries, which must be removed. */ int n = 24, nz, Ap [ ] = { 0, 9, 14, 20, 28, 33, 37, 44, 53, 58, 63, 63, 66, 69, 72, 75, 78, 82, 86, 91, 97, 101, 112, 112, 116 }, Ai [ ] = { /* column 0: */ 0, 17, 18, 21, 5, 12, 5, 0, 13, /* column 1: */ 14, 1, 8, 13, 17, /* column 2: */ 2, 20, 11, 6, 11, 22, /* column 3: */ 3, 3, 10, 7, 18, 18, 15, 19, /* column 4: */ 7, 9, 15, 14, 16, /* column 5: */ 5, 13, 6, 17, /* column 6: */ 5, 0, 11, 6, 12, 6, 23, /* column 7: */ 3, 4, 9, 7, 14, 16, 15, 17, 18, /* column 8: */ 1, 9, 14, 14, 14, /* column 9: */ 7, 13, 8, 1, 17, /* column 10: */ /* column 11: */ 2, 12, 23, /* column 12: */ 5, 11, 12, /* column 13: */ 0, 13, 17, /* column 14: */ 1, 9, 14, /* column 15: */ 3, 15, 16, /* column 16: */ 16, 4, 4, 15, /* column 17: */ 13, 17, 19, 17, /* column 18: */ 15, 17, 19, 9, 10, /* column 19: */ 17, 19, 20, 0, 6, 10, /* column 20: */ 22, 10, 20, 21, /* column 21: */ 6, 2, 10, 19, 20, 11, 21, 22, 22, 22, 22, /* column 22: */ /* column 23: */ 12, 11, 12, 23 } ; int P [24], Pinv [24], i, j, k, jnew, p, inew, result ; double Control [CAMD_CONTROL], Info [CAMD_INFO] ; char A [24][24] ; int C [ ] = { 3, 0, 4, 0, 1, 1, 2, 2, 2, 2, 3, 4, 5, 5, 3, 4, 5, 2, 8, 10, 4, 2, 2, 0 } ; printf ("CAMD demo, with a jumbled version of the 24-by-24\n") ; printf ("Harwell/Boeing matrix, can_24:\n") ; /* get the default parameters, and print them */ camd_defaults (Control) ; camd_control (Control) ; /* print the input matrix */ nz = Ap [n] ; printf ("\nJumbled input matrix: %d-by-%d, with %d entries.\n" " Note that for a symmetric matrix such as this one, only the\n" " strictly lower or upper triangular parts would need to be\n" " passed to CAMD, since CAMD computes the ordering of A+A'. The\n" " diagonal entries are also not needed, since CAMD ignores them.\n" " This version of the matrix has jumbled columns and duplicate\n" " row indices.\n", n, n, nz) ; for (j = 0 ; j < n ; j++) { printf ("\nColumn: %d, number of entries: %d, with row indices in" " Ai [%d ... %d]:\n row indices:", j, Ap [j+1] - Ap [j], Ap [j], Ap [j+1]-1) ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; printf (" %d", i) ; } printf ("\n") ; } /* print a character plot of the input matrix. This is only reasonable * because the matrix is small. */ printf ("\nPlot of (jumbled) input matrix pattern:\n") ; for (j = 0 ; j < n ; j++) { for (i = 0 ; i < n ; i++) A [i][j] = '.' ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; A [i][j] = 'X' ; } } printf (" ") ; for (j = 0 ; j < n ; j++) printf (" %1d", j % 10) ; printf ("\n") ; for (i = 0 ; i < n ; i++) { printf ("%2d: ", i) ; for (j = 0 ; j < n ; j++) { printf (" %c", A [i][j]) ; } printf ("\n") ; } /* print a character plot of the matrix A+A'. */ printf ("\nPlot of symmetric matrix to be ordered by camd_order:\n") ; for (j = 0 ; j < n ; j++) { for (i = 0 ; i < n ; i++) A [i][j] = '.' ; } for (j = 0 ; j < n ; j++) { A [j][j] = 'X' ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; A [i][j] = 'X' ; A [j][i] = 'X' ; } } printf (" ") ; for (j = 0 ; j < n ; j++) printf (" %1d", j % 10) ; printf ("\n") ; for (i = 0 ; i < n ; i++) { printf ("%2d: ", i) ; for (j = 0 ; j < n ; j++) { printf (" %c", A [i][j]) ; } printf ("\n") ; } /* order the matrix */ result = camd_order (n, Ap, Ai, P, Control, Info, C) ; printf ("return value from camd_order: %d (should be %d)\n", result, CAMD_OK_BUT_JUMBLED) ; /* print the statistics */ camd_info (Info) ; if (result != CAMD_OK_BUT_JUMBLED) { printf ("CAMD failed\n") ; exit (1) ; } /* print the permutation vector, P, and compute the inverse permutation */ printf ("Permutation vector:\n") ; for (k = 0 ; k < n ; k++) { /* row/column j is the kth row/column in the permuted matrix */ j = P [k] ; Pinv [j] = k ; printf (" %2d", j) ; } printf ("\nPermuted constraints:\n") ; for (k = 0 ; k < n ; k++) { /* row/column j is the kth row/column in the permuted matrix */ printf (" %2d", C [P [k]]) ; } printf ("\n\n") ; printf ("Inverse permutation vector:\n") ; for (j = 0 ; j < n ; j++) { k = Pinv [j] ; printf (" %2d", k) ; } printf ("\n\n") ; /* print a character plot of the permuted matrix. */ printf ("\nPlot of (symmetrized) permuted matrix pattern:\n") ; for (j = 0 ; j < n ; j++) { for (i = 0 ; i < n ; i++) A [i][j] = '.' ; } for (jnew = 0 ; jnew < n ; jnew++) { j = P [jnew] ; A [jnew][jnew] = 'X' ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { inew = Pinv [Ai [p]] ; A [inew][jnew] = 'X' ; A [jnew][inew] = 'X' ; } } printf (" ") ; for (j = 0 ; j < n ; j++) printf (" %1d", j % 10) ; printf ("\n") ; for (i = 0 ; i < n ; i++) { printf ("%2d: ", i) ; for (j = 0 ; j < n ; j++) { printf (" %c", A [i][j]) ; } printf ("\n") ; } return (0) ; } SuiteSparse/CAMD/Demo/camd_demo.c0000644001170100242450000001262710616400272015421 0ustar davisfac/* ========================================================================= */ /* === CAMD demo main program ============================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/camd */ /* ------------------------------------------------------------------------- */ /* A simple C main program that illustrates the use of the ANSI C interface * to CAMD. */ #include "camd.h" #include #include int main (void) { /* The symmetric can_24 Harwell/Boeing matrix, including upper and lower * triangular parts, and the diagonal entries. Note that this matrix is * 0-based, with row and column indices in the range 0 to n-1. */ int n = 24, nz, Ap [ ] = { 0, 9, 15, 21, 27, 33, 39, 48, 57, 61, 70, 76, 82, 88, 94, 100, 106, 110, 119, 128, 137, 143, 152, 156, 160 }, Ai [ ] = { /* column 0: */ 0, 5, 6, 12, 13, 17, 18, 19, 21, /* column 1: */ 1, 8, 9, 13, 14, 17, /* column 2: */ 2, 6, 11, 20, 21, 22, /* column 3: */ 3, 7, 10, 15, 18, 19, /* column 4: */ 4, 7, 9, 14, 15, 16, /* column 5: */ 0, 5, 6, 12, 13, 17, /* column 6: */ 0, 2, 5, 6, 11, 12, 19, 21, 23, /* column 7: */ 3, 4, 7, 9, 14, 15, 16, 17, 18, /* column 8: */ 1, 8, 9, 14, /* column 9: */ 1, 4, 7, 8, 9, 13, 14, 17, 18, /* column 10: */ 3, 10, 18, 19, 20, 21, /* column 11: */ 2, 6, 11, 12, 21, 23, /* column 12: */ 0, 5, 6, 11, 12, 23, /* column 13: */ 0, 1, 5, 9, 13, 17, /* column 14: */ 1, 4, 7, 8, 9, 14, /* column 15: */ 3, 4, 7, 15, 16, 18, /* column 16: */ 4, 7, 15, 16, /* column 17: */ 0, 1, 5, 7, 9, 13, 17, 18, 19, /* column 18: */ 0, 3, 7, 9, 10, 15, 17, 18, 19, /* column 19: */ 0, 3, 6, 10, 17, 18, 19, 20, 21, /* column 20: */ 2, 10, 19, 20, 21, 22, /* column 21: */ 0, 2, 6, 10, 11, 19, 20, 21, 22, /* column 22: */ 2, 20, 21, 22, /* column 23: */ 6, 11, 12, 23 } ; int P [24], Pinv [24], i, j, k, jnew, p, inew, result ; double Control [CAMD_CONTROL], Info [CAMD_INFO] ; char A [24][24] ; int C [ ] = { 0, 0, 4, 0, 1, 0, 2, 2, 1, 1, 3, 4, 5, 5, 3, 4, 5, 2, 5, 3, 4, 2, 1, 0 } ; printf ("CAMD version %d.%d, date: %s\n", CAMD_MAIN_VERSION, CAMD_SUB_VERSION, CAMD_DATE) ; printf ("CAMD demo, with the 24-by-24 Harwell/Boeing matrix, can_24:\n") ; /* get the default parameters, and print them */ camd_defaults (Control) ; camd_control (Control) ; /* print the input matrix */ nz = Ap [n] ; printf ("\nInput matrix: %d-by-%d, with %d entries.\n" " Note that for a symmetric matrix such as this one, only the\n" " strictly lower or upper triangular parts would need to be\n" " passed to CAMD, since CAMD computes the ordering of A+A'. The\n" " diagonal entries are also not needed, since CAMD ignores them.\n" , n, n, nz) ; for (j = 0 ; j < n ; j++) { printf ("\nColumn: %d, number of entries: %d, with row indices in" " Ai [%d ... %d]:\n row indices:", j, Ap [j+1] - Ap [j], Ap [j], Ap [j+1]-1) ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; printf (" %d", i) ; } printf ("\n") ; } /* print a character plot of the input matrix. This is only reasonable * because the matrix is small. */ printf ("\nPlot of input matrix pattern:\n") ; for (j = 0 ; j < n ; j++) { for (i = 0 ; i < n ; i++) A [i][j] = '.' ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; A [i][j] = 'X' ; } } printf (" ") ; for (j = 0 ; j < n ; j++) printf (" %1d", j % 10) ; printf ("\n") ; for (i = 0 ; i < n ; i++) { printf ("%2d: ", i) ; for (j = 0 ; j < n ; j++) { printf (" %c", A [i][j]) ; } printf ("\n") ; } /* order the matrix */ result = camd_order (n, Ap, Ai, P, Control, Info, C) ; printf ("return value from camd_order: %d (should be %d)\n", result, CAMD_OK) ; /* print the statistics */ camd_info (Info) ; if (result != CAMD_OK) { printf ("CAMD failed\n") ; exit (1) ; } /* print the permutation vector, P, and compute the inverse permutation */ printf ("Permutation vector:\n") ; for (k = 0 ; k < n ; k++) { /* row/column j is the kth row/column in the permuted matrix */ j = P [k] ; Pinv [j] = k ; printf (" %2d", j) ; } printf ("\n\n") ; printf ("Inverse permutation vector:\n") ; for (j = 0 ; j < n ; j++) { k = Pinv [j] ; printf (" %2d", k) ; } printf ("\n\n") ; /* print a character plot of the permuted matrix. */ printf ("\nPlot of permuted matrix pattern:\n") ; for (jnew = 0 ; jnew < n ; jnew++) { j = P [jnew] ; for (inew = 0 ; inew < n ; inew++) A [inew][jnew] = '.' ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { inew = Pinv [Ai [p]] ; A [inew][jnew] = 'X' ; } } printf (" ") ; for (j = 0 ; j < n ; j++) printf (" %1d", j % 10) ; printf ("\n") ; for (i = 0 ; i < n ; i++) { printf ("%2d: ", i) ; for (j = 0 ; j < n ; j++) { printf (" %c", A [i][j]) ; } printf ("\n") ; } return (0) ; } SuiteSparse/CAMD/Demo/camd_simple.out0000644001170100242450000000006210616403262016343 0ustar davisfacP [0] = 3 P [1] = 2 P [2] = 1 P [3] = 4 P [4] = 0 SuiteSparse/CAMD/Makefile0000644001170100242450000000264610617112221014114 0ustar davisfac#------------------------------------------------------------------------------ # CAMD Makefile (for GNU Make or original make) #------------------------------------------------------------------------------ default: demo include ../UFconfig/UFconfig.mk # Compile all C code, including the C-callable routine and the mexFunctions. # Do not compile the FORTRAN versions, or MATLAB interface. demo: ( cd Lib ; $(MAKE) ) ( cd Demo ; $(MAKE) ) # Compile all C code, including the C-callable routine and the mexFunctions. # Do not compile the FORTRAN versions. all: ( cd Lib ; $(MAKE) ) ( cd Demo ; $(MAKE) ) ( cd MATLAB ; $(MAKE) ) # compile just the C-callable libraries (not mexFunctions or Demos) library: ( cd Lib ; $(MAKE) ) # remove object files, but keep the compiled programs and library archives clean: ( cd Lib ; $(MAKE) clean ) ( cd Demo ; $(MAKE) clean ) ( cd MATLAB ; $(MAKE) clean ) ( cd Doc ; $(MAKE) clean ) # clean, and then remove compiled programs and library archives purge: ( cd Lib ; $(MAKE) purge ) ( cd Demo ; $(MAKE) purge ) ( cd MATLAB ; $(MAKE) purge ) ( cd Doc ; $(MAKE) purge ) distclean: purge # create PDF documents for the original distribution doc: ( cd Doc ; $(MAKE) ) # get ready for distribution dist: purge ( cd Demo ; $(MAKE) dist ) ( cd Doc ; $(MAKE) ) ccode: library lib: library # compile the MATLAB mexFunction mex: ( cd MATLAB ; $(MAKE) ) SuiteSparse/CAMD/MATLAB/0000755001170100242450000000000010711653375013423 5ustar davisfacSuiteSparse/CAMD/MATLAB/camd_make.m0000644001170100242450000000164610620367253015505 0ustar davisfacfunction camd_make %CAMD_MAKE to compile camd for use in MATLAB % % Example: % camd_make % % See also camd. % Copyright 1994-2007, Tim Davis, University of Florida, % Patrick R. Amestoy, Iain S. Duff, and Yanqing Chen. details = 0 ; % 1 if details of each command are to be printed d = '' ; if (~isempty (strfind (computer, '64'))) d = '-largeArrayDims' ; end i = sprintf ('-I..%sInclude -I..%s..%sUFconfig', filesep, filesep, filesep) ; cmd = sprintf ('mex -O %s -DDLONG -output camd %s camd_mex.c', d, i) ; files = {'camd_order', 'camd_dump', 'camd_postorder', ... 'camd_aat', 'camd_2', 'camd_1', 'camd_defaults', 'camd_control', ... 'camd_info', 'camd_valid', 'camd_global', 'camd_preprocess' } ; for i = 1 : length (files) cmd = sprintf ('%s ..%sSource%s%s.c', cmd, filesep, filesep, files {i}) ; end if (details) fprintf ('%s\n', cmd) ; end eval (cmd) ; fprintf ('CAMD successfully compiled.\n') ; SuiteSparse/CAMD/MATLAB/Makefile0000644001170100242450000000207410616366211015060 0ustar davisfac#------------------------------------------------------------------------------ # Makefile for the CAMD MATLAB mexFunction #------------------------------------------------------------------------------ default: camd include ../../UFconfig/UFconfig.mk CAMD = ../Lib/libcamd.a I = -I../Include -I../../UFconfig INC = ../Include/camd.h ../Include/camd_internal.h ../../UFconfig/UFconfig.h SRC = ../Source/camd_1.c ../Source/camd_2.c ../Source/camd_aat.c \ ../Source/camd_control.c ../Source/camd_defaults.c ../Source/camd_dump.c \ ../Source/camd_global.c ../Source/camd_info.c ../Source/camd_order.c \ ../Source/camd_postorder.c \ ../Source/camd_preprocess.c ../Source/camd_valid.c camd: $(SRC) $(INC) camd_mex.c $(MEX) -DDLONG $(I) -output camd camd_mex.c $(SRC) #------------------------------------------------------------------------------ # Remove all but the files in the original distribution #------------------------------------------------------------------------------ clean: - $(RM) $(CLEAN) purge: distclean distclean: clean - $(RM) camd.mex* SuiteSparse/CAMD/MATLAB/Contents.m0000644001170100242450000000071310620367267015400 0ustar davisfac%Contents of the CAMD sparse matrix ordering package: % % camd - p = camd (A), the approximate minimum degree ordering of A % camd_demo - a demo of camd, using the can_24 matrix % camd_make - to compile camd for use in MATLAB % % Example: % p = camd(A) % % See also: camd, amd, colamd, symamd, colmmd, symmmd, umfpack % Copyright 1994-2007, Tim Davis, University of Florida, % Patrick R. Amestoy, Iain S. Duff, and Yanqing Chen. help Contents SuiteSparse/CAMD/MATLAB/camd.m0000644001170100242450000001024310620367237014503 0ustar davisfacfunction [p, Info] = camd (A, Control, C) %#ok %CAMD p = camd (A), the approximate minimum degree ordering of A % P = CAMD (S) returns the approximate minimum degree permutation vector for % the sparse matrix C = S+S'. The Cholesky factorization of C (P,P), or % S (P,P), tends to be sparser than that of C or S. CAMD tends to be faster % than SYMMMD and SYMAMD, and tends to return better orderings than SYMMMD. % S must be square. If S is full, camd(S) is equivalent to camd(sparse(S)). % % Usage: P = camd (S) ; % finds the ordering % [P, Info] = camd (S,Control,C) ; % optional parameters & statistics % Control = camd ; % returns default parameters % camd ; % prints default parameters. % % Control (1); If S is n-by-n, then rows/columns with more than % max (16, (Control (1))* sqrt(n)) entries in S+S' are considered % "dense", and ignored during ordering. They are placed last in the % output permutation. The default is 10.0 if Control is not present. % Control (2): If nonzero, then aggressive absorption is performed. % This is the default if Control is not present. % Control (3): If nonzero, print statistics about the ordering. % % Info (1): status (0: ok, -1: out of memory, -2: matrix invalid) % Info (2): n = size (A,1) % Info (3): nnz (A) % Info (4): the symmetry of the matrix S (0.0 means purely unsymmetric, % 1.0 means purely symmetric). Computed as: % B = tril (S, -1) + triu (S, 1) ; symmetry = nnz (B & B') / nnz (B); % Info (5): nnz (diag (S)) % Info (6): nnz in S+S', excluding the diagonal (= nnz (B+B')) % Info (7): number "dense" rows/columns in S+S' % Info (8): the amount of memory used by CAMD, in bytes % Info (9): the number of memory compactions performed by CAMD % % The following statistics are slight upper bounds because of the % approximate degree in CAMD. The bounds are looser if "dense" rows/columns % are ignored during ordering (Info (7) > 0). The statistics are for a % subsequent factorization of the matrix C (P,P). The LU factorization % statistics assume no pivoting. % % Info (10): the number of nonzeros in L, excluding the diagonal % Info (11): the number of divide operations for LL', LDL', or LU % Info (12): the number of multiply-subtract pairs for LL' or LDL' % Info (13): the number of multiply-subtract pairs for LU % Info (14): the max # of nonzeros in any column of L (incl. diagonal) % Info (15:20): unused, reserved for future use % % An assembly tree post-ordering is performed, which is typically the same % as an elimination tree post-ordering. It is not always identical because % of the approximate degree update used, and because "dense" rows/columns % do not take part in the post-order. It well-suited for a subsequent % "chol", however. If you require a precise elimination tree post-ordering, % then do the following: % % Example: % P = camd (S) ; % C = spones (S) + spones (S') ; % skip this if S already symmetric % [ignore, Q] = etree (C (P,P)) ; % P = P (Q) ; % % CAMD has the ability to order the matrix with constraints. Each % node i in the graph (row/column i in the matrix) has a constraint, % C(i), which is in the range 1 to n. All nodes with C(i) = 1 are % ordered first, followed by all nodes with constraint 2, and so on. % That is, C(P) is monotonically non-decreasing. If C is not provided, % no constraints are used (the ordering will be similar to AMD's ordering, % except that the postordering is different). % % See also AMD, COLMMD, COLAMD, COLPERM, SYMAMD, SYMMMD, SYMRCM. % Copyright 1994-2007, Tim Davis, University of Florida, % Patrick R. Amestoy, Iain S. Duff, and Yanqing Chen. % % Acknowledgements: This work was supported by the National Science % Foundation, under grants ASC-9111263, DMS-9223088, and CCR-0203270, % and by Sandia National Laboratories. % help camd error ('camd mexFunction not found! Type "camd_make" in MATLAB to compile camd'); SuiteSparse/CAMD/MATLAB/can_240000644001170100242450000000240010325005010014362 0ustar davisfac 1 1 1 6 1 1 7 1 1 13 1 1 14 1 1 18 1 1 19 1 1 20 1 1 22 1 1 2 2 1 9 2 1 10 2 1 14 2 1 15 2 1 18 2 1 3 3 1 7 3 1 12 3 1 21 3 1 22 3 1 23 3 1 4 4 1 8 4 1 11 4 1 16 4 1 19 4 1 20 4 1 5 5 1 8 5 1 10 5 1 15 5 1 16 5 1 17 5 1 1 6 1 6 6 1 7 6 1 13 6 1 14 6 1 18 6 1 1 7 1 3 7 1 6 7 1 7 7 1 12 7 1 13 7 1 20 7 1 22 7 1 24 7 1 4 8 1 5 8 1 8 8 1 10 8 1 15 8 1 16 8 1 17 8 1 18 8 1 19 8 1 2 9 1 9 9 1 10 9 1 15 9 1 2 10 1 5 10 1 8 10 1 9 10 1 10 10 1 14 10 1 15 10 1 18 10 1 19 10 1 4 11 1 11 11 1 19 11 1 20 11 1 21 11 1 22 11 1 3 12 1 7 12 1 12 12 1 13 12 1 22 12 1 24 12 1 1 13 1 6 13 1 7 13 1 12 13 1 13 13 1 24 13 1 1 14 1 2 14 1 6 14 1 10 14 1 14 14 1 18 14 1 2 15 1 5 15 1 8 15 1 9 15 1 10 15 1 15 15 1 4 16 1 5 16 1 8 16 1 16 16 1 17 16 1 19 16 1 5 17 1 8 17 1 16 17 1 17 17 1 1 18 1 2 18 1 6 18 1 8 18 1 10 18 1 14 18 1 18 18 1 19 18 1 20 18 1 1 19 1 4 19 1 8 19 1 10 19 1 11 19 1 16 19 1 18 19 1 19 19 1 20 19 1 1 20 1 4 20 1 7 20 1 11 20 1 18 20 1 19 20 1 20 20 1 21 20 1 22 20 1 3 21 1 11 21 1 20 21 1 21 21 1 22 21 1 23 21 1 1 22 1 3 22 1 7 22 1 11 22 1 12 22 1 20 22 1 21 22 1 22 22 1 23 22 1 3 23 1 21 23 1 22 23 1 23 23 1 7 24 1 12 24 1 13 24 1 24 24 1 SuiteSparse/CAMD/MATLAB/camd_mex.c0000644001170100242450000001456210616401062015340 0ustar davisfac/* ========================================================================= */ /* === CAMD mexFunction ===================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/camd */ /* ------------------------------------------------------------------------- */ /* * Usage: * p = camd (A) * p = camd (A, Control) * [p, Info] = camd (A) * [p, Info] = camd (A, Control, C) * Control = camd ; % return the default Control settings for CAMD * camd ; % print the default Control settings for CAMD * * Given a square matrix A, compute a permutation P suitable for a Cholesky * factorization of the matrix B (P,P), where B = spones (A) + spones (A'). * The method used is the approximate minimum degree ordering method. See * camd.m and camd.h for more information. * * The input matrix need not have sorted columns, and can have duplicate * entries. */ #include "camd.h" #include "mex.h" #include "matrix.h" #include "UFconfig.h" void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { UF_long i, m, n, *Ap, *Ai, *P, nc, result, spumoni, full, *C, Clen ; double *Pout, *InfoOut, Control [CAMD_CONTROL], Info [CAMD_INFO], *ControlIn, *Cin ; mxArray *A ; /* --------------------------------------------------------------------- */ /* get control parameters */ /* --------------------------------------------------------------------- */ camd_malloc = mxMalloc ; camd_free = mxFree ; camd_calloc = mxCalloc ; camd_realloc = mxRealloc ; camd_printf = mexPrintf ; spumoni = 0 ; if (nargin == 0) { /* get the default control parameters, and return */ pargout [0] = mxCreateDoubleMatrix (CAMD_CONTROL, 1, mxREAL) ; camd_l_defaults (mxGetPr (pargout [0])) ; if (nargout == 0) { camd_l_control (mxGetPr (pargout [0])) ; } return ; } camd_l_defaults (Control) ; if (nargin > 1) { ControlIn = mxGetPr (pargin [1]) ; nc = mxGetM (pargin [1]) * mxGetN (pargin [1]) ; Control [CAMD_DENSE] = (nc > 0) ? ControlIn [CAMD_DENSE] : CAMD_DEFAULT_DENSE ; Control [CAMD_AGGRESSIVE] = (nc > 1) ? ControlIn [CAMD_AGGRESSIVE] : CAMD_DEFAULT_AGGRESSIVE ; spumoni = (nc > 2) ? (ControlIn [2] != 0) : 0 ; } if (spumoni > 0) { camd_l_control (Control) ; } /* --------------------------------------------------------------------- */ /* get inputs */ /* --------------------------------------------------------------------- */ if (nargout > 2 || nargin > 3) { mexErrMsgTxt ("Usage: p = camd (A)\n" "or [p, Info] = camd (A, Control, C)") ; } Clen = 0 ; C = NULL ; if (nargin > 2) { Cin = mxGetPr (pargin [2]) ; Clen = mxGetNumberOfElements (pargin [2]) ; if (Clen != 0) { C = (UF_long *) mxCalloc (Clen, sizeof (UF_long)) ; for (i = 0 ; i < Clen ; i++) { /* convert c from 1-based to 0-based */ C [i] = (UF_long) Cin [i] - 1 ; } } } A = (mxArray *) pargin [0] ; n = mxGetN (A) ; m = mxGetM (A) ; if (spumoni > 0) { mexPrintf (" input matrix A is %d-by-%d\n", m, n) ; } if (mxGetNumberOfDimensions (A) != 2) { mexErrMsgTxt ("camd: A must be 2-dimensional") ; } if (m != n) { mexErrMsgTxt ("camd: A must be square") ; } /* --------------------------------------------------------------------- */ /* allocate workspace for output permutation */ /* --------------------------------------------------------------------- */ P = mxMalloc ((n+1) * sizeof (UF_long)) ; /* --------------------------------------------------------------------- */ /* if A is full, convert to a sparse matrix */ /* --------------------------------------------------------------------- */ full = !mxIsSparse (A) ; if (full) { if (spumoni > 0) { mexPrintf ( " input matrix A is full (sparse copy of A will be created)\n"); } mexCallMATLAB (1, &A, 1, (mxArray **) pargin, "sparse") ; } Ap = (UF_long *) mxGetJc (A) ; Ai = (UF_long *) mxGetIr (A) ; if (spumoni > 0) { mexPrintf (" input matrix A has %d nonzero entries\n", Ap [n]) ; } /* --------------------------------------------------------------------- */ /* order the matrix */ /* --------------------------------------------------------------------- */ result = camd_l_order (n, Ap, Ai, P, Control, Info, C) ; /* --------------------------------------------------------------------- */ /* if A is full, free the sparse copy of A */ /* --------------------------------------------------------------------- */ if (full) { mxDestroyArray (A) ; } /* --------------------------------------------------------------------- */ /* print results (including return value) */ /* --------------------------------------------------------------------- */ if (spumoni > 0) { camd_l_info (Info) ; } /* --------------------------------------------------------------------- */ /* check error conditions */ /* --------------------------------------------------------------------- */ if (result == CAMD_OUT_OF_MEMORY) { mexErrMsgTxt ("camd: out of memory") ; } else if (result == CAMD_INVALID) { mexErrMsgTxt ("camd: input matrix A is corrupted") ; } /* --------------------------------------------------------------------- */ /* copy the outputs to MATLAB */ /* --------------------------------------------------------------------- */ /* output permutation, P */ pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ; Pout = mxGetPr (pargout [0]) ; for (i = 0 ; i < n ; i++) { Pout [i] = P [i] + 1 ; /* change to 1-based indexing for MATLAB */ } mxFree (P) ; if (nargin > 2) mxFree (C) ; /* Info */ if (nargout > 1) { pargout [1] = mxCreateDoubleMatrix (CAMD_INFO, 1, mxREAL) ; InfoOut = mxGetPr (pargout [1]) ; for (i = 0 ; i < CAMD_INFO ; i++) { InfoOut [i] = Info [i] ; } } } SuiteSparse/CAMD/MATLAB/camd_demo.m0000644001170100242450000000635410620664032015510 0ustar davisfacfunction camd_demo %CAMD_DEMO a demo of camd, using the can_24 matrix % % A demo of CAMD for MATLAB. % % Example: % camd_demo % % See also: camd, camd_make % Copyright 1994-2007, Tim Davis, University of Florida, % Patrick R. Amestoy, Iain S. Duff, and Yanqing Chen. % This orders the same matrix as the ANSI C demo, camd_demo.c. It includes an % additional analysis of the matrix via MATLAB's symbfact routine. % First, print the help information for CAMD help camd % Get the Harwell/Boeing can_24 matrix. load can_24 A = spconvert (can_24) ; n = size (A,1) ; rand ('state', 0) ; C = irand (6, n) ; figure (1) clf hold off subplot (2,2,1) ; spy (A) title ('HB/can24 matrix') ; % print the details during CAMD ordering and SYMBFACT % spparms ('spumoni', 1) ; % order the matrix. Note that the Info argument is optional. fprintf ('\nIf the next step fails, then you have\n') ; fprintf ('not yet compiled the CAMD mexFunction.\n') ; [p, Info] = camd (A) ; %#ok % order again, but this time print some statistics [p, camd_Info] = camd (A, [10 1 1], C) ; fprintf ('Permutation vector:\n') ; fprintf (' %2d', p) ; fprintf ('\n\n') ; fprintf ('Corresponding constraint sets:\n') ; if (any (sort (C (p)) ~= C (p))) error ('Error!') ; end for j = 1:n fprintf (' %2d', C (p (j))) ; end fprintf ('\n\n\n') ; subplot (2,2,2) ; spy (A (p,p)) ; title ('Permuted matrix') ; % The camd_demo.c program stops here. fprintf ('Analyze A(p,p) with MATLAB symbfact routine:\n') ; [cn, height, parent, post, R] = symbfact (A(p,p)) ; subplot (2,2,3) ; spy (R') ; title ('Cholesky factor L') ; subplot (2,2,4) ; treeplot (parent) ; title ('etree') ; % results from symbfact lnz = sum (cn) ; % number of nonzeros in L, incl. diagonal cn = cn - 1 ; % get the count of off-diagonal entries fl = n + sum (cn.^2 + 2*cn) ; % flop count for chol (A (p,p) fprintf ('number of nonzeros in L (including diagonal): %d\n', lnz) ; fprintf ('floating point operation count for chol (A (p,p)): %d\n', fl) ; % approximations from camd: lnz2 = n + camd_Info (10) ; fl2 = n + camd_Info (11) + 2 * camd_Info (12) ; fprintf ('\nResults from CAMD''s approximate analysis:\n') ; fprintf ('number of nonzeros in L (including diagonal): %d\n', lnz2) ; fprintf ('floating point operation count for chol (A (p,p)): %d\n\n', fl2) ; fprintf ('\nNote that the ordering quality is not as good as p=amd(A).\n') ; fprintf ('This is only because the ordering constraints, C, have been\n') ; fprintf ('randomly selected.\n') ; if (lnz2 ~= lnz | fl ~= fl2) %#ok fprintf ('Note that the nonzero and flop counts from CAMD are slight\n') ; fprintf ('upper bounds. This is due to the approximate minimum degree\n'); fprintf ('method used, in conjunction with "mass elimination".\n') ; fprintf ('See the discussion about mass elimination in camd.h and\n') ; fprintf ('camd_2.c for more details.\n') ; end % turn off diagnostic output in MATLAB's sparse matrix routines % spparms ('spumoni', 0) ; %------------------------------------------------------------------------------- function i = irand (n,s) % irand: return a random vector of size s, with values between 1 and n if (nargin == 1) s = 1 ; end i = min (n, 1 + floor (rand (1,s) * n)) ; SuiteSparse/CAMD/MATLAB/camd_demo.m.out0000644001170100242450000001427010620423703016310 0ustar davisfaccamd_demo CAMD p = camd (A), the approximate minimum degree ordering of A P = CAMD (S) returns the approximate minimum degree permutation vector for the sparse matrix C = S+S'. The Cholesky factorization of C (P,P), or S (P,P), tends to be sparser than that of C or S. CAMD tends to be faster than SYMMMD and SYMAMD, and tends to return better orderings than SYMMMD. S must be square. If S is full, camd(S) is equivalent to camd(sparse(S)). Usage: P = camd (S) ; % finds the ordering [P, Info] = camd (S,Control,C) ; % optional parameters & statistics Control = camd ; % returns default parameters camd ; % prints default parameters. Control (1); If S is n-by-n, then rows/columns with more than max (16, (Control (1))* sqrt(n)) entries in S+S' are considered "dense", and ignored during ordering. They are placed last in the output permutation. The default is 10.0 if Control is not present. Control (2): If nonzero, then aggressive absorption is performed. This is the default if Control is not present. Control (3): If nonzero, print statistics about the ordering. Info (1): status (0: ok, -1: out of memory, -2: matrix invalid) Info (2): n = size (A,1) Info (3): nnz (A) Info (4): the symmetry of the matrix S (0.0 means purely unsymmetric, 1.0 means purely symmetric). Computed as: B = tril (S, -1) + triu (S, 1) ; symmetry = nnz (B & B') / nnz (B); Info (5): nnz (diag (S)) Info (6): nnz in S+S', excluding the diagonal (= nnz (B+B')) Info (7): number "dense" rows/columns in S+S' Info (8): the amount of memory used by CAMD, in bytes Info (9): the number of memory compactions performed by CAMD The following statistics are slight upper bounds because of the approximate degree in CAMD. The bounds are looser if "dense" rows/columns are ignored during ordering (Info (7) > 0). The statistics are for a subsequent factorization of the matrix C (P,P). The LU factorization statistics assume no pivoting. Info (10): the number of nonzeros in L, excluding the diagonal Info (11): the number of divide operations for LL', LDL', or LU Info (12): the number of multiply-subtract pairs for LL' or LDL' Info (13): the number of multiply-subtract pairs for LU Info (14): the max # of nonzeros in any column of L (incl. diagonal) Info (15:20): unused, reserved for future use An assembly tree post-ordering is performed, which is typically the same as an elimination tree post-ordering. It is not always identical because of the approximate degree update used, and because "dense" rows/columns do not take part in the post-order. It well-suited for a subsequent "chol", however. If you require a precise elimination tree post-ordering, then do the following: Example: P = camd (S) ; C = spones (S) + spones (S') ; % skip this if S already symmetric [ignore, Q] = etree (C (P,P)) ; P = P (Q) ; CAMD has the ability to order the matrix with constraints. Each node i in the graph (row/column i in the matrix) has a constraint, C(i), which is in the range 1 to n. All nodes with C(i) = 1 are ordered first, followed by all nodes with constraint 2, and so on. That is, C(P) is monotonically non-decreasing. If C is not provided, no constraints are used (the ordering will be similar to AMD's ordering, except that the postordering is different). See also AMD, COLMMD, COLAMD, COLPERM, SYMAMD, SYMMMD, SYMRCM. If the next step fails, then you have not yet compiled the CAMD mexFunction. camd version 2.2, May 31, 2007: approximate minimum degree ordering: dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes input matrix A is 24-by-24 input matrix A has 160 nonzero entries camd: approximate minimum degree ordering, results: status: OK n, dimension of A: 24 nz, number of nonzeros in A: 160 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 136 # dense rows/columns of A+A': 0 memory used, in bytes: 1644 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 149 nonzeros in L (including diagonal): 173 # divide operations for LDL' or LU: 149 # multiply-subtract operations for LDL': 631 # multiply-subtract operations for LU: 1113 max nz. in any column of L (incl. diagonal): 12 chol flop count for real A, sqrt counted as 1 flop: 1435 LDL' flop count for real A: 1411 LDL' flop count for complex A: 6389 LU flop count for real A (with no pivoting): 2375 LU flop count for complex A (with no pivoting): 10245 Permutation vector: 24 21 8 2 15 10 16 4 19 22 7 3 11 6 9 23 12 14 20 1 5 13 18 17 Corresponding constraint sets: 1 1 1 2 2 3 3 3 3 3 3 4 4 5 5 5 5 5 6 6 6 6 6 6 Analyze A(p,p) with MATLAB symbfact routine: number of nonzeros in L (including diagonal): 173 floating point operation count for chol (A (p,p)): 1435 Results from CAMD's approximate analysis: number of nonzeros in L (including diagonal): 173 floating point operation count for chol (A (p,p)): 1435 Note that the ordering quality is not as good as p=amd(A). This is only because the ordering constraints, C, have been randomly selected. diary off SuiteSparse/CAMD/Include/0000755001170100242450000000000010616401025014031 5ustar davisfacSuiteSparse/CAMD/Include/camd_internal.h0000644001170100242450000002205510616401024017005 0ustar davisfac/* ========================================================================= */ /* === camd_internal.h ===================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/camd */ /* ------------------------------------------------------------------------- */ /* This file is for internal use in CAMD itself, and does not normally need to * be included in user code (it is included in UMFPACK, however). All others * should use camd.h instead. * * The following compile-time definitions affect how CAMD is compiled. * * -DNPRINT * * Disable all printing. stdio.h will not be included. Printing can * be re-enabled at run-time by setting the global pointer camd_printf * to printf (or mexPrintf for a MATLAB mexFunction). * * -DNMALLOC * * No memory manager is defined at compile-time. You MUST define the * function pointers camd_malloc, camd_free, camd_realloc, and * camd_calloc at run-time for CAMD to work properly. */ /* ========================================================================= */ /* === NDEBUG ============================================================== */ /* ========================================================================= */ /* * Turning on debugging takes some work (see below). If you do not edit this * file, then debugging is always turned off, regardless of whether or not * -DNDEBUG is specified in your compiler options. * * If CAMD is being compiled as a mexFunction, then MATLAB_MEX_FILE is defined, * and mxAssert is used instead of assert. If debugging is not enabled, no * MATLAB include files or functions are used. Thus, the CAMD library libcamd.a * can be safely used in either a stand-alone C program or in another * mexFunction, without any change. */ /* CAMD will be exceedingly slow when running in debug mode. The next three lines ensure that debugging is turned off. */ #ifndef NDEBUG #define NDEBUG #endif /* To enable debugging, uncomment the following line: #undef NDEBUG */ /* ------------------------------------------------------------------------- */ /* ANSI include files */ /* ------------------------------------------------------------------------- */ /* from stdlib.h: size_t, malloc, free, realloc, and calloc */ #include #if !defined(NPRINT) || !defined(NDEBUG) /* from stdio.h: printf. Not included if NPRINT is defined at compile time. * fopen and fscanf are used when debugging. */ #include #endif /* from limits.h: INT_MAX and LONG_MAX */ #include /* from math.h: sqrt */ #include /* ------------------------------------------------------------------------- */ /* MATLAB include files (only if being used in or via MATLAB) */ /* ------------------------------------------------------------------------- */ #ifdef MATLAB_MEX_FILE #include "matrix.h" #include "mex.h" #endif /* ------------------------------------------------------------------------- */ /* basic definitions */ /* ------------------------------------------------------------------------- */ #ifdef FLIP #undef FLIP #endif #ifdef MAX #undef MAX #endif #ifdef MIN #undef MIN #endif #ifdef EMPTY #undef EMPTY #endif #ifdef GLOBAL #undef GLOBAL #endif #ifdef PRIVATE #undef PRIVATE #endif /* FLIP is a "negation about -1", and is used to mark an integer i that is * normally non-negative. FLIP (EMPTY) is EMPTY. FLIP of a number > EMPTY * is negative, and FLIP of a number < EMTPY is positive. FLIP (FLIP (i)) = i * for all integers i. UNFLIP (i) is >= EMPTY. */ #define EMPTY (-1) #define FLIP(i) (-(i)-2) #define UNFLIP(i) ((i < EMPTY) ? FLIP (i) : (i)) /* for integer MAX/MIN, or for doubles when we don't care how NaN's behave: */ #define MAX(a,b) (((a) > (b)) ? (a) : (b)) #define MIN(a,b) (((a) < (b)) ? (a) : (b)) /* logical expression of p implies q: */ #define IMPLIES(p,q) (!(p) || (q)) /* Note that the IBM RS 6000 xlc predefines TRUE and FALSE in . */ /* The Compaq Alpha also predefines TRUE and FALSE. */ #ifdef TRUE #undef TRUE #endif #ifdef FALSE #undef FALSE #endif #define TRUE (1) #define FALSE (0) #define PRIVATE static #define GLOBAL #define EMPTY (-1) /* Note that Linux's gcc 2.96 defines NULL as ((void *) 0), but other */ /* compilers (even gcc 2.95.2 on Solaris) define NULL as 0 or (0). We */ /* need to use the ANSI standard value of 0. */ #ifdef NULL #undef NULL #endif #define NULL 0 /* largest value of size_t */ #ifndef SIZE_T_MAX #define SIZE_T_MAX ((size_t) (-1)) #endif /* ------------------------------------------------------------------------- */ /* integer type for CAMD: int or UF_long */ /* ------------------------------------------------------------------------- */ /* define UF_long */ #include "UFconfig.h" #if defined (DLONG) || defined (ZLONG) #define Int UF_long #define ID UF_long_id #define Int_MAX UF_long_max #define CAMD_order camd_l_order #define CAMD_defaults camd_l_defaults #define CAMD_control camd_l_control #define CAMD_info camd_l_info #define CAMD_1 camd_l1 #define CAMD_2 camd_l2 #define CAMD_valid camd_l_valid #define CAMD_cvalid camd_l_cvalid #define CAMD_aat camd_l_aat #define CAMD_postorder camd_l_postorder #define CAMD_post_tree camd_l_post_tree #define CAMD_dump camd_l_dump #define CAMD_debug camd_l_debug #define CAMD_debug_init camd_l_debug_init #define CAMD_preprocess camd_l_preprocess #else #define Int int #define ID "%d" #define Int_MAX INT_MAX #define CAMD_order camd_order #define CAMD_defaults camd_defaults #define CAMD_control camd_control #define CAMD_info camd_info #define CAMD_1 camd_1 #define CAMD_2 camd_2 #define CAMD_valid camd_valid #define CAMD_cvalid camd_cvalid #define CAMD_aat camd_aat #define CAMD_postorder camd_postorder #define CAMD_post_tree camd_post_tree #define CAMD_dump camd_dump #define CAMD_debug camd_debug #define CAMD_debug_init camd_debug_init #define CAMD_preprocess camd_preprocess #endif /* ========================================================================= */ /* === PRINTF macro ======================================================== */ /* ========================================================================= */ /* All output goes through the PRINTF macro. */ #define PRINTF(params) { if (camd_printf != NULL) (void) camd_printf params ; } /* ------------------------------------------------------------------------- */ /* CAMD routine definitions (user-callable) */ /* ------------------------------------------------------------------------- */ #include "camd.h" /* ------------------------------------------------------------------------- */ /* CAMD routine definitions (not user-callable) */ /* ------------------------------------------------------------------------- */ GLOBAL size_t CAMD_aat ( Int n, const Int Ap [ ], const Int Ai [ ], Int Len [ ], Int Tp [ ], double Info [ ] ) ; GLOBAL void CAMD_1 ( Int n, const Int Ap [ ], const Int Ai [ ], Int P [ ], Int Pinv [ ], Int Len [ ], Int slen, Int S [ ], double Control [ ], double Info [ ], const Int C [ ] ) ; GLOBAL Int CAMD_postorder ( Int j, Int k, Int n, Int head [], Int next [], Int post [], Int stack [] ) ; GLOBAL void CAMD_preprocess ( Int n, const Int Ap [ ], const Int Ai [ ], Int Rp [ ], Int Ri [ ], Int W [ ], Int Flag [ ] ) ; /* ------------------------------------------------------------------------- */ /* debugging definitions */ /* ------------------------------------------------------------------------- */ #ifndef NDEBUG /* from assert.h: assert macro */ #include #ifndef EXTERN #define EXTERN extern #endif EXTERN Int CAMD_debug ; GLOBAL void CAMD_debug_init ( char *s ) ; GLOBAL void CAMD_dump ( Int n, Int Pe [ ], Int Iw [ ], Int Len [ ], Int iwlen, Int pfree, Int Nv [ ], Int Next [ ], Int Last [ ], Int Head [ ], Int Elen [ ], Int Degree [ ], Int W [ ], Int nel, Int BucketSet [], const Int C [], Int Curc ) ; #ifdef ASSERT #undef ASSERT #endif /* Use mxAssert if CAMD is compiled into a mexFunction */ #ifdef MATLAB_MEX_FILE #define ASSERT(expression) (mxAssert ((expression), "")) #else #define ASSERT(expression) (assert (expression)) #endif #define CAMD_DEBUG0(params) { PRINTF (params) ; } #define CAMD_DEBUG1(params) { if (CAMD_debug >= 1) PRINTF (params) ; } #define CAMD_DEBUG2(params) { if (CAMD_debug >= 2) PRINTF (params) ; } #define CAMD_DEBUG3(params) { if (CAMD_debug >= 3) PRINTF (params) ; } #define CAMD_DEBUG4(params) { if (CAMD_debug >= 4) PRINTF (params) ; } #else /* no debugging */ #define ASSERT(expression) #define CAMD_DEBUG0(params) #define CAMD_DEBUG1(params) #define CAMD_DEBUG2(params) #define CAMD_DEBUG3(params) #define CAMD_DEBUG4(params) #endif SuiteSparse/CAMD/Include/camd.h0000644001170100242450000004111710616400757015125 0ustar davisfac/* ========================================================================= */ /* === CAMD: approximate minimum degree ordering ========================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* CAMD Version 2.2, Copyright (c) 2007 by Timothy A. Davis, Yanqing Chen, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/camd */ /* ------------------------------------------------------------------------- */ /* CAMD finds a symmetric ordering P of a matrix A so that the Cholesky * factorization of P*A*P' has fewer nonzeros and takes less work than the * Cholesky factorization of A. If A is not symmetric, then it performs its * ordering on the matrix A+A'. Two sets of user-callable routines are * provided, one for int integers and the other for UF_long integers. * * The method is based on the approximate minimum degree algorithm, discussed * in Amestoy, Davis, and Duff, "An approximate degree ordering algorithm", * SIAM Journal of Matrix Analysis and Applications, vol. 17, no. 4, pp. * 886-905, 1996. */ #ifndef CAMD_H #define CAMD_H /* make it easy for C++ programs to include CAMD */ #ifdef __cplusplus extern "C" { #endif /* get the definition of size_t: */ #include /* define UF_long */ #include "UFconfig.h" int camd_order /* returns CAMD_OK, CAMD_OK_BUT_JUMBLED, * CAMD_INVALID, or CAMD_OUT_OF_MEMORY */ ( int n, /* A is n-by-n. n must be >= 0. */ const int Ap [ ], /* column pointers for A, of size n+1 */ const int Ai [ ], /* row indices of A, of size nz = Ap [n] */ int P [ ], /* output permutation, of size n */ double Control [ ], /* input Control settings, of size CAMD_CONTROL */ double Info [ ], /* output Info statistics, of size CAMD_INFO */ const int C [ ] /* Constraint set of A, of size n; can be NULL */ ) ; UF_long camd_l_order /* see above for description of arguments */ ( UF_long n, const UF_long Ap [ ], const UF_long Ai [ ], UF_long P [ ], double Control [ ], double Info [ ], const UF_long C [ ] ) ; /* Input arguments (not modified): * * n: the matrix A is n-by-n. * Ap: an int/UF_long array of size n+1, containing column pointers of A. * Ai: an int/UF_long array of size nz, containing the row indices of A, * where nz = Ap [n]. * Control: a double array of size CAMD_CONTROL, containing control * parameters. Defaults are used if Control is NULL. * * Output arguments (not defined on input): * * P: an int/UF_long array of size n, containing the output permutation. If * row i is the kth pivot row, then P [k] = i. In MATLAB notation, * the reordered matrix is A (P,P). * Info: a double array of size CAMD_INFO, containing statistical * information. Ignored if Info is NULL. * * On input, the matrix A is stored in column-oriented form. The row indices * of nonzero entries in column j are stored in Ai [Ap [j] ... Ap [j+1]-1]. * * If the row indices appear in ascending order in each column, and there * are no duplicate entries, then camd_order is slightly more efficient in * terms of time and memory usage. If this condition does not hold, a copy * of the matrix is created (where these conditions do hold), and the copy is * ordered. * * Row indices must be in the range 0 to * n-1. Ap [0] must be zero, and thus nz = Ap [n] is the number of nonzeros * in A. The array Ap is of size n+1, and the array Ai is of size nz = Ap [n]. * The matrix does not need to be symmetric, and the diagonal does not need to * be present (if diagonal entries are present, they are ignored except for * the output statistic Info [CAMD_NZDIAG]). The arrays Ai and Ap are not * modified. This form of the Ap and Ai arrays to represent the nonzero * pattern of the matrix A is the same as that used internally by MATLAB. * If you wish to use a more flexible input structure, please see the * umfpack_*_triplet_to_col routines in the UMFPACK package, at * http://www.cise.ufl.edu/research/sparse/umfpack. * * Restrictions: n >= 0. Ap [0] = 0. Ap [j] <= Ap [j+1] for all j in the * range 0 to n-1. nz = Ap [n] >= 0. Ai [0..nz-1] must be in the range 0 * to n-1. Finally, Ai, Ap, and P must not be NULL. If any of these * restrictions are not met, CAMD returns CAMD_INVALID. * * CAMD returns: * * CAMD_OK if the matrix is valid and sufficient memory can be allocated to * perform the ordering. * * CAMD_OUT_OF_MEMORY if not enough memory can be allocated. * * CAMD_INVALID if the input arguments n, Ap, Ai are invalid, or if P is * NULL. * * CAMD_OK_BUT_JUMBLED if the matrix had unsorted columns, and/or duplicate * entries, but was otherwise valid. * * The CAMD routine first forms the pattern of the matrix A+A', and then * computes a fill-reducing ordering, P. If P [k] = i, then row/column i of * the original is the kth pivotal row. In MATLAB notation, the permuted * matrix is A (P,P), except that 0-based indexing is used instead of the * 1-based indexing in MATLAB. * * The Control array is used to set various parameters for CAMD. If a NULL * pointer is passed, default values are used. The Control array is not * modified. * * Control [CAMD_DENSE]: controls the threshold for "dense" rows/columns. * A dense row/column in A+A' can cause CAMD to spend a lot of time in * ordering the matrix. If Control [CAMD_DENSE] >= 0, rows/columns * with more than Control [CAMD_DENSE] * sqrt (n) entries are ignored * during the ordering, and placed last in the output order. The * default value of Control [CAMD_DENSE] is 10. If negative, no * rows/columns are treated as "dense". Rows/columns with 16 or * fewer off-diagonal entries are never considered "dense". * * Control [CAMD_AGGRESSIVE]: controls whether or not to use aggressive * absorption, in which a prior element is absorbed into the current * element if is a subset of the current element, even if it is not * adjacent to the current pivot element (refer to Amestoy, Davis, * & Duff, 1996, for more details). The default value is nonzero, * which means to perform aggressive absorption. This nearly always * leads to a better ordering (because the approximate degrees are * more accurate) and a lower execution time. There are cases where * it can lead to a slightly worse ordering, however. To turn it off, * set Control [CAMD_AGGRESSIVE] to 0. * * Control [2..4] are not used in the current version, but may be used in * future versions. * * The Info array provides statistics about the ordering on output. If it is * not present, the statistics are not returned. This is not an error * condition. * * Info [CAMD_STATUS]: the return value of CAMD, either CAMD_OK, * CAMD_OK_BUT_JUMBLED, CAMD_OUT_OF_MEMORY, or CAMD_INVALID. * * Info [CAMD_N]: n, the size of the input matrix * * Info [CAMD_NZ]: the number of nonzeros in A, nz = Ap [n] * * Info [CAMD_SYMMETRY]: the symmetry of the matrix A. It is the number * of "matched" off-diagonal entries divided by the total number of * off-diagonal entries. An entry A(i,j) is matched if A(j,i) is also * an entry, for any pair (i,j) for which i != j. In MATLAB notation, * S = spones (A) ; * B = tril (S, -1) + triu (S, 1) ; * symmetry = nnz (B & B') / nnz (B) ; * * Info [CAMD_NZDIAG]: the number of entries on the diagonal of A. * * Info [CAMD_NZ_A_PLUS_AT]: the number of nonzeros in A+A', excluding the * diagonal. If A is perfectly symmetric (Info [CAMD_SYMMETRY] = 1) * with a fully nonzero diagonal, then Info [CAMD_NZ_A_PLUS_AT] = nz-n * (the smallest possible value). If A is perfectly unsymmetric * (Info [CAMD_SYMMETRY] = 0, for an upper triangular matrix, for * example) with no diagonal, then Info [CAMD_NZ_A_PLUS_AT] = 2*nz * (the largest possible value). * * Info [CAMD_NDENSE]: the number of "dense" rows/columns of A+A' that were * removed from A prior to ordering. These are placed last in the * output order P. * * Info [CAMD_MEMORY]: the amount of memory used by CAMD, in bytes. In the * current version, this is 1.2 * Info [CAMD_NZ_A_PLUS_AT] + 9*n * times the size of an integer. This is at most 2.4nz + 9n. This * excludes the size of the input arguments Ai, Ap, and P, which have * a total size of nz + 2*n + 1 integers. * * Info [CAMD_NCMPA]: the number of garbage collections performed. * * Info [CAMD_LNZ]: the number of nonzeros in L (excluding the diagonal). * This is a slight upper bound because mass elimination is combined * with the approximate degree update. It is a rough upper bound if * there are many "dense" rows/columns. The rest of the statistics, * below, are also slight or rough upper bounds, for the same reasons. * The post-ordering of the assembly tree might also not exactly * correspond to a true elimination tree postordering. * * Info [CAMD_NDIV]: the number of divide operations for a subsequent LDL' * or LU factorization of the permuted matrix A (P,P). * * Info [CAMD_NMULTSUBS_LDL]: the number of multiply-subtract pairs for a * subsequent LDL' factorization of A (P,P). * * Info [CAMD_NMULTSUBS_LU]: the number of multiply-subtract pairs for a * subsequent LU factorization of A (P,P), assuming that no numerical * pivoting is required. * * Info [CAMD_DMAX]: the maximum number of nonzeros in any column of L, * including the diagonal. * * Info [14..19] are not used in the current version, but may be used in * future versions. */ /* ------------------------------------------------------------------------- */ /* direct interface to CAMD */ /* ------------------------------------------------------------------------- */ /* camd_2 is the primary CAMD ordering routine. It is not meant to be * user-callable because of its restrictive inputs and because it destroys * the user's input matrix. It does not check its inputs for errors, either. * However, if you can work with these restrictions it can be faster than * camd_order and use less memory (assuming that you can create your own copy * of the matrix for CAMD to destroy). Refer to CAMD/Source/camd_2.c for a * description of each parameter. */ void camd_2 ( int n, int Pe [ ], int Iw [ ], int Len [ ], int iwlen, int pfree, int Nv [ ], int Next [ ], int Last [ ], int Head [ ], int Elen [ ], int Degree [ ], int W [ ], double Control [ ], double Info [ ], const int C [ ], int BucketSet [ ] ) ; void camd_l2 ( UF_long n, UF_long Pe [ ], UF_long Iw [ ], UF_long Len [ ], UF_long iwlen, UF_long pfree, UF_long Nv [ ], UF_long Next [ ], UF_long Last [ ], UF_long Head [ ], UF_long Elen [ ], UF_long Degree [ ], UF_long W [ ], double Control [ ], double Info [ ], const UF_long C [ ], UF_long BucketSet [ ] ) ; /* ------------------------------------------------------------------------- */ /* camd_valid */ /* ------------------------------------------------------------------------- */ /* Returns CAMD_OK or CAMD_OK_BUT_JUMBLED if the matrix is valid as input to * camd_order; the latter is returned if the matrix has unsorted and/or * duplicate row indices in one or more columns. Returns CAMD_INVALID if the * matrix cannot be passed to camd_order. For camd_order, the matrix must also * be square. The first two arguments are the number of rows and the number * of columns of the matrix. For its use in CAMD, these must both equal n. */ int camd_valid ( int n_row, /* # of rows */ int n_col, /* # of columns */ const int Ap [ ], /* column pointers, of size n_col+1 */ const int Ai [ ] /* row indices, of size Ap [n_col] */ ) ; UF_long camd_l_valid ( UF_long n_row, UF_long n_col, const UF_long Ap [ ], const UF_long Ai [ ] ) ; /* ------------------------------------------------------------------------- */ /* camd_cvalid */ /* ------------------------------------------------------------------------- */ /* Returns TRUE if the constraint set is valid as input to camd_order, * FALSE otherwise. */ int camd_cvalid ( int n, const int C [ ] ) ; UF_long camd_l_cvalid ( UF_long n, const UF_long C [ ] ) ; /* ------------------------------------------------------------------------- */ /* CAMD memory manager and printf routines */ /* ------------------------------------------------------------------------- */ /* The user can redefine these to change the malloc, free, and printf routines * that CAMD uses. */ #ifndef EXTERN #define EXTERN extern #endif EXTERN void *(*camd_malloc) (size_t) ; /* pointer to malloc */ EXTERN void (*camd_free) (void *) ; /* pointer to free */ EXTERN void *(*camd_realloc) (void *, size_t) ; /* pointer to realloc */ EXTERN void *(*camd_calloc) (size_t, size_t) ; /* pointer to calloc */ EXTERN int (*camd_printf) (const char *, ...) ; /* pointer to printf */ /* ------------------------------------------------------------------------- */ /* CAMD Control and Info arrays */ /* ------------------------------------------------------------------------- */ /* camd_defaults: sets the default control settings */ void camd_defaults (double Control [ ]) ; void camd_l_defaults (double Control [ ]) ; /* camd_control: prints the control settings */ void camd_control (double Control [ ]) ; void camd_l_control (double Control [ ]) ; /* camd_info: prints the statistics */ void camd_info (double Info [ ]) ; void camd_l_info (double Info [ ]) ; #define CAMD_CONTROL 5 /* size of Control array */ #define CAMD_INFO 20 /* size of Info array */ /* contents of Control */ #define CAMD_DENSE 0 /* "dense" if degree > Control [0] * sqrt (n) */ #define CAMD_AGGRESSIVE 1 /* do aggressive absorption if Control [1] != 0 */ /* default Control settings */ #define CAMD_DEFAULT_DENSE 10.0 /* default "dense" degree 10*sqrt(n) */ #define CAMD_DEFAULT_AGGRESSIVE 1 /* do aggressive absorption by default */ /* contents of Info */ #define CAMD_STATUS 0 /* return value of camd_order and camd_l_order */ #define CAMD_N 1 /* A is n-by-n */ #define CAMD_NZ 2 /* number of nonzeros in A */ #define CAMD_SYMMETRY 3 /* symmetry of pattern (1 is sym., 0 is unsym.) */ #define CAMD_NZDIAG 4 /* # of entries on diagonal */ #define CAMD_NZ_A_PLUS_AT 5 /* nz in A+A' */ #define CAMD_NDENSE 6 /* number of "dense" rows/columns in A */ #define CAMD_MEMORY 7 /* amount of memory used by CAMD */ #define CAMD_NCMPA 8 /* number of garbage collections in CAMD */ #define CAMD_LNZ 9 /* approx. nz in L, excluding the diagonal */ #define CAMD_NDIV 10 /* number of fl. point divides for LU and LDL' */ #define CAMD_NMULTSUBS_LDL 11 /* number of fl. point (*,-) pairs for LDL' */ #define CAMD_NMULTSUBS_LU 12 /* number of fl. point (*,-) pairs for LU */ #define CAMD_DMAX 13 /* max nz. in any column of L, incl. diagonal */ /* ------------------------------------------------------------------------- */ /* return values of CAMD */ /* ------------------------------------------------------------------------- */ #define CAMD_OK 0 /* success */ #define CAMD_OUT_OF_MEMORY -1 /* malloc failed, or problem too large */ #define CAMD_INVALID -2 /* input arguments are not valid */ #define CAMD_OK_BUT_JUMBLED 1 /* input matrix is OK for camd_order, but * columns were not sorted, and/or duplicate entries were present. CAMD had * to do extra work before ordering the matrix. This is a warning, not an * error. */ /* ========================================================================== */ /* === CAMD version ========================================================= */ /* ========================================================================== */ /* * As an example, to test if the version you are using is 1.2 or later: * * if (CAMD_VERSION >= CAMD_VERSION_CODE (1,2)) ... * * This also works during compile-time: * * #if (CAMD_VERSION >= CAMD_VERSION_CODE (1,2)) * printf ("This is version 1.2 or later\n") ; * #else * printf ("This is an early version\n") ; * #endif */ #define CAMD_DATE "May 31, 2007" #define CAMD_VERSION_CODE(main,sub) ((main) * 1000 + (sub)) #define CAMD_MAIN_VERSION 2 #define CAMD_SUB_VERSION 2 #define CAMD_SUBSUB_VERSION 0 #define CAMD_VERSION CAMD_VERSION_CODE(CAMD_MAIN_VERSION,CAMD_SUB_VERSION) #ifdef __cplusplus } #endif #endif SuiteSparse/CAMD/Source/0000755001170100242450000000000010617112500013704 5ustar davisfacSuiteSparse/CAMD/Source/camd_preprocess.c0000644001170100242450000000751010616401145017231 0ustar davisfac/* ========================================================================= */ /* === CAMD_preprocess ===================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/camd */ /* ------------------------------------------------------------------------- */ /* Sorts, removes duplicate entries, and transposes from the nonzero pattern of * a column-form matrix A, to obtain the matrix R. The input matrix can have * duplicate entries and/or unsorted columns (CAMD_valid (n,Ap,Ai) must not be * CAMD_INVALID). * * This input condition is NOT checked. This routine is not user-callable. */ #include "camd_internal.h" /* ========================================================================= */ /* === CAMD_preprocess ===================================================== */ /* ========================================================================= */ /* CAMD_preprocess does not check its input for errors or allocate workspace. * On input, the condition (CAMD_valid (n,n,Ap,Ai) != CAMD_INVALID) must hold. */ GLOBAL void CAMD_preprocess ( Int n, /* input matrix: A is n-by-n */ const Int Ap [ ], /* size n+1 */ const Int Ai [ ], /* size nz = Ap [n] */ /* output matrix R: */ Int Rp [ ], /* size n+1 */ Int Ri [ ], /* size nz (or less, if duplicates present) */ Int W [ ], /* workspace of size n */ Int Flag [ ] /* workspace of size n */ ) { /* --------------------------------------------------------------------- */ /* local variables */ /* --------------------------------------------------------------------- */ Int i, j, p, p2 ; ASSERT (CAMD_valid (n, n, Ap, Ai) != CAMD_INVALID) ; /* --------------------------------------------------------------------- */ /* count the entries in each row of A (excluding duplicates) */ /* --------------------------------------------------------------------- */ for (i = 0 ; i < n ; i++) { W [i] = 0 ; /* # of nonzeros in row i (excl duplicates) */ Flag [i] = EMPTY ; /* Flag [i] = j if i appears in column j */ } for (j = 0 ; j < n ; j++) { p2 = Ap [j+1] ; for (p = Ap [j] ; p < p2 ; p++) { i = Ai [p] ; if (Flag [i] != j) { /* row index i has not yet appeared in column j */ W [i]++ ; /* one more entry in row i */ Flag [i] = j ; /* flag row index i as appearing in col j*/ } } } /* --------------------------------------------------------------------- */ /* compute the row pointers for R */ /* --------------------------------------------------------------------- */ Rp [0] = 0 ; for (i = 0 ; i < n ; i++) { Rp [i+1] = Rp [i] + W [i] ; } for (i = 0 ; i < n ; i++) { W [i] = Rp [i] ; Flag [i] = EMPTY ; } /* --------------------------------------------------------------------- */ /* construct the row form matrix R */ /* --------------------------------------------------------------------- */ /* R = row form of pattern of A */ for (j = 0 ; j < n ; j++) { p2 = Ap [j+1] ; for (p = Ap [j] ; p < p2 ; p++) { i = Ai [p] ; if (Flag [i] != j) { /* row index i has not yet appeared in column j */ Ri [W [i]++] = j ; /* put col j in row i */ Flag [i] = j ; /* flag row index i as appearing in col j*/ } } } #ifndef NDEBUG ASSERT (CAMD_valid (n, n, Rp, Ri) == CAMD_OK) ; for (j = 0 ; j < n ; j++) { ASSERT (W [j] == Rp [j+1]) ; } #endif } SuiteSparse/CAMD/Source/camd_control.c0000644001170100242450000000342010616401111016511 0ustar davisfac/* ========================================================================= */ /* === CAMD_control ======================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/camd */ /* ------------------------------------------------------------------------- */ /* User-callable. Prints the control parameters for CAMD. See camd.h * for details. If the Control array is not present, the defaults are * printed instead. */ #include "camd_internal.h" GLOBAL void CAMD_control ( double Control [ ] ) { double alpha ; Int aggressive ; if (Control != (double *) NULL) { alpha = Control [CAMD_DENSE] ; aggressive = Control [CAMD_AGGRESSIVE] != 0 ; } else { alpha = CAMD_DEFAULT_DENSE ; aggressive = CAMD_DEFAULT_AGGRESSIVE ; } PRINTF (("\ncamd version %d.%d, %s: approximate minimum degree ordering:\n" " dense row parameter: %g\n", CAMD_MAIN_VERSION, CAMD_SUB_VERSION, CAMD_DATE, alpha)) ; if (alpha < 0) { PRINTF ((" no rows treated as dense\n")) ; } else { PRINTF (( " (rows with more than max (%g * sqrt (n), 16) entries are\n" " considered \"dense\", and placed last in output permutation)\n", alpha)) ; } if (aggressive) { PRINTF ((" aggressive absorption: yes\n\n")) ; } else { PRINTF ((" aggressive absorption: no\n\n")) ; } } SuiteSparse/CAMD/Source/camd_postorder.c0000644001170100242450000000370510616401142017064 0ustar davisfac/* ========================================================================= */ /* === CAMD_postorder ====================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/camd */ /* ------------------------------------------------------------------------- */ /* Perform a postordering (via depth-first search) of an assembly tree. */ #include "camd_internal.h" GLOBAL Int CAMD_postorder ( Int j, /* start at node j, a root of the assembly tree */ Int k, /* on input, next node is the kth node */ Int n, /* normal nodes 0 to n-1, place-holder node n */ Int head [], /* head of link list of children of each node */ Int next [], /* next[i] is the next child after i in link list */ Int post [], /* postordering, post [k] = p if p is the kth node */ Int stack [] /* recursion stack */ ) { int i, p, top = 0 ; stack [0] = j ; /* place j on the stack, maybe place-holder node n */ while (top >= 0) /* while (stack is not empty) */ { p = stack [top] ; /* p = top of stack */ i = head [p] ; /* i = youngest child of p */ if (i == -1) { top-- ; /* p has no unordered children left */ if (p != n) { /* node p is the kth postordered node. Do not postorder the * place-holder node n, which is the root of a subtree * containing all dense and empty nodes. */ post [k++] = p ; } } else { head [p] = next [i] ; /* remove i from children of p */ stack [++top] = i ; /* start dfs on child node i */ } } return (k) ; } SuiteSparse/CAMD/Source/camd_1.c0000644001170100242450000001373210616401100015176 0ustar davisfac/* ========================================================================= */ /* === CAMD_1 ============================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/camd */ /* ------------------------------------------------------------------------- */ /* CAMD_1: Construct A+A' for a sparse matrix A and perform the CAMD ordering. * * The n-by-n sparse matrix A can be unsymmetric. It is stored in MATLAB-style * compressed-column form, with sorted row indices in each column, and no * duplicate entries. Diagonal entries may be present, but they are ignored. * Row indices of column j of A are stored in Ai [Ap [j] ... Ap [j+1]-1]. * Ap [0] must be zero, and nz = Ap [n] is the number of entries in A. The * size of the matrix, n, must be greater than or equal to zero. * * This routine must be preceded by a call to CAMD_aat, which computes the * number of entries in each row/column in A+A', excluding the diagonal. * Len [j], on input, is the number of entries in row/column j of A+A'. This * routine constructs the matrix A+A' and then calls CAMD_2. No error checking * is performed (this was done in CAMD_valid). */ #include "camd_internal.h" GLOBAL void CAMD_1 ( Int n, /* n > 0 */ const Int Ap [ ], /* input of size n+1, not modified */ const Int Ai [ ], /* input of size nz = Ap [n], not modified */ Int P [ ], /* size n output permutation */ Int Pinv [ ], /* size n output inverse permutation */ Int Len [ ], /* size n input, undefined on output */ Int slen, /* slen >= sum (Len [0..n-1]) + 7n+2, * ideally slen = 1.2 * sum (Len) + 8n+2 */ Int S [ ], /* size slen workspace */ double Control [ ], /* input array of size CAMD_CONTROL */ double Info [ ], /* output array of size CAMD_INFO */ const Int C [ ] /* Constraint set of size n */ ) { Int i, j, k, p, pfree, iwlen, pj, p1, p2, pj2, *Iw, *Pe, *Nv, *Head, *Elen, *Degree, *s, *W, *Sp, *Tp, *BucketSet ; /* --------------------------------------------------------------------- */ /* construct the matrix for CAMD_2 */ /* --------------------------------------------------------------------- */ ASSERT (n > 0) ; iwlen = slen - (7*n+2) ; /* allocate 7*n+2 workspace from S */ s = S ; Pe = s ; s += n ; Nv = s ; s += n ; Head = s ; s += n+1 ; /* NOTE: was size n in AMD; size n+1 in CAMD */ Elen = s ; s += n ; Degree = s ; s += n ; W = s ; s += n+1 ; /* NOTE: was size n in AMD; size n+1 in CAMD */ BucketSet = s ; s += n ; Iw = s ; s += iwlen ; ASSERT (CAMD_valid (n, n, Ap, Ai) == CAMD_OK) ; ASSERT (CAMD_cvalid (n, C)) ; /* construct the pointers for A+A' */ Sp = Nv ; /* use Nv and W as workspace for Sp and Tp [ */ Tp = W ; pfree = 0 ; for (j = 0 ; j < n ; j++) { Pe [j] = pfree ; Sp [j] = pfree ; pfree += Len [j] ; } /* Note that this restriction on iwlen is slightly more restrictive than * what is strictly required in CAMD_2. CAMD_2 can operate with no elbow * room at all, but it will be very slow. For better performance, at * least size-n elbow room is enforced. */ ASSERT (iwlen >= pfree + n) ; #ifndef NDEBUG for (p = 0 ; p < iwlen ; p++) Iw [p] = EMPTY ; #endif for (k = 0 ; k < n ; k++) { CAMD_DEBUG1 (("Construct row/column k= "ID" of A+A'\n", k)) ; p1 = Ap [k] ; p2 = Ap [k+1] ; /* construct A+A' */ for (p = p1 ; p < p2 ; ) { /* scan the upper triangular part of A */ j = Ai [p] ; ASSERT (j >= 0 && j < n) ; if (j < k) { /* entry A (j,k) in the strictly upper triangular part */ ASSERT (Sp [j] < (j == n-1 ? pfree : Pe [j+1])) ; ASSERT (Sp [k] < (k == n-1 ? pfree : Pe [k+1])) ; Iw [Sp [j]++] = k ; Iw [Sp [k]++] = j ; p++ ; } else if (j == k) { /* skip the diagonal */ p++ ; break ; } else /* j > k */ { /* first entry below the diagonal */ break ; } /* scan lower triangular part of A, in column j until reaching * row k. Start where last scan left off. */ ASSERT (Ap [j] <= Tp [j] && Tp [j] <= Ap [j+1]) ; pj2 = Ap [j+1] ; for (pj = Tp [j] ; pj < pj2 ; ) { i = Ai [pj] ; ASSERT (i >= 0 && i < n) ; if (i < k) { /* A (i,j) is only in the lower part, not in upper */ ASSERT (Sp [i] < (i == n-1 ? pfree : Pe [i+1])) ; ASSERT (Sp [j] < (j == n-1 ? pfree : Pe [j+1])) ; Iw [Sp [i]++] = j ; Iw [Sp [j]++] = i ; pj++ ; } else if (i == k) { /* entry A (k,j) in lower part and A (j,k) in upper */ pj++ ; break ; } else /* i > k */ { /* consider this entry later, when k advances to i */ break ; } } Tp [j] = pj ; } Tp [k] = p ; } /* clean up, for remaining mismatched entries */ for (j = 0 ; j < n ; j++) { for (pj = Tp [j] ; pj < Ap [j+1] ; pj++) { i = Ai [pj] ; ASSERT (i >= 0 && i < n) ; /* A (i,j) is only in the lower part, not in upper */ ASSERT (Sp [i] < (i == n-1 ? pfree : Pe [i+1])) ; ASSERT (Sp [j] < (j == n-1 ? pfree : Pe [j+1])) ; Iw [Sp [i]++] = j ; Iw [Sp [j]++] = i ; } } #ifndef NDEBUG for (j = 0 ; j < n-1 ; j++) ASSERT (Sp [j] == Pe [j+1]) ; ASSERT (Sp [n-1] == pfree) ; #endif /* Tp and Sp no longer needed ] */ /* --------------------------------------------------------------------- */ /* order the matrix */ /* --------------------------------------------------------------------- */ CAMD_2 (n, Pe, Iw, Len, iwlen, pfree, Nv, Pinv, P, Head, Elen, Degree, W, Control, Info, C, BucketSet) ; } SuiteSparse/CAMD/Source/camd_2.c0000644001170100242450000021204710616401104015203 0ustar davisfac/* ========================================================================= */ /* === CAMD_2 ============================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/camd */ /* ------------------------------------------------------------------------- */ /* CAMD_2: performs the CAMD ordering on a symmetric sparse matrix A, followed * by a postordering (via depth-first search) of the assembly tree using the * CAMD_postorder routine. */ /* ========================================================================= */ /* === Macros and definitions ============================================== */ /* ========================================================================= */ /* True if node i is in the current Constraint Set */ #define IsInCurrentSet(C,i,curC) ((C == NULL) ? 1 : (C [i] == curC)) /* True if i and j are in the same Constraint Set */ #define InSameConstraintSet(C,i,j) ((C == NULL) ? 1 : (C [i] == C [j])) #include "camd_internal.h" /* ========================================================================= */ /* === clear_flag ========================================================== */ /* ========================================================================= */ static Int clear_flag (Int wflg, Int wbig, Int W [ ], Int n) { Int x ; if (wflg < 2 || wflg >= wbig) { for (x = 0 ; x < n ; x++) { if (W [x] != 0) W [x] = 1 ; } wflg = 2 ; } /* at this point, W [0..n-1] < wflg holds */ return (wflg) ; } /* ========================================================================= */ /* === CAMD_2 ============================================================== */ /* ========================================================================= */ GLOBAL void CAMD_2 ( Int n, /* A is n-by-n, where n > 0 */ Int Pe [ ], /* Pe [0..n-1]: index in Iw of row i on input */ Int Iw [ ], /* workspace of size iwlen. Iw [0..pfree-1] * holds the matrix on input */ Int Len [ ], /* Len [0..n-1]: length for row/column i on input */ Int iwlen, /* length of Iw. iwlen >= pfree + n */ Int pfree, /* Iw [pfree ... iwlen-1] is empty on input */ /* 7 size-n or size-n+1 workspaces, not defined on input: */ Int Nv [ ], /* size n, the size of each supernode on output */ Int Next [ ], /* size n, the output inverse permutation */ Int Last [ ], /* size n, the output permutation */ Int Head [ ], /* size n+1 (Note: it was size n in AMD) */ Int Elen [ ], /* size n, the size columns of L for each supernode */ Int Degree [ ], /* size n */ Int W [ ], /* size n+1 (Note: it was size n in AMD) */ /* control parameters and output statistics */ double Control [ ], /* array of size CAMD_CONTROL */ double Info [ ], /* array of size CAMD_INFO */ /* input, not modified: */ const Int C [ ], /* size n, C [i] is the constraint set of node i */ /* size-n workspace, not defined on input or output: */ Int BucketSet [ ] /* size n */ ) { /* * Given a representation of the nonzero pattern of a symmetric matrix, A, * (excluding the diagonal) perform an approximate minimum (UMFPACK/MA38-style) * degree ordering to compute a pivot order such that the introduction of * nonzeros (fill-in) in the Cholesky factors A = LL' is kept low. At each * step, the pivot selected is the one with the minimum UMFAPACK/MA38-style * upper-bound on the external degree. This routine can optionally perform * aggresive absorption (as done by MC47B in the Harwell Subroutine * Library). * * The approximate degree algorithm implemented here is the symmetric analog of * the degree update algorithm in MA38 and UMFPACK (the Unsymmetric-pattern * MultiFrontal PACKage, both by Davis and Duff). The routine is based on the * MA27 minimum degree ordering algorithm by Iain Duff and John Reid. * * This routine is a translation of the original AMDBAR and MC47B routines, * in Fortran, with the following modifications: * * (1) dense rows/columns are removed prior to ordering the matrix, and placed * last in the output order. The presence of a dense row/column can * increase the ordering time by up to O(n^2), unless they are removed * prior to ordering. * * (2) the minimum degree ordering is followed by a postordering (depth-first * search) of the assembly tree. Note that mass elimination (discussed * below) combined with the approximate degree update can lead to the mass * elimination of nodes with lower exact degree than the current pivot * element. No additional fill-in is caused in the representation of the * Schur complement. The mass-eliminated nodes merge with the current * pivot element. They are ordered prior to the current pivot element. * Because they can have lower exact degree than the current element, the * merger of two or more of these nodes in the current pivot element can * lead to a single element that is not a "fundamental supernode". The * diagonal block can have zeros in it. Thus, the assembly tree used here * is not guaranteed to be the precise supernodal elemination tree (with * "funadmental" supernodes), and the postordering performed by this * routine is not guaranteed to be a precise postordering of the * elimination tree. * * (3) input parameters are added, to control aggressive absorption and the * detection of "dense" rows/columns of A. * * (4) additional statistical information is returned, such as the number of * nonzeros in L, and the flop counts for subsequent LDL' and LU * factorizations. These are slight upper bounds, because of the mass * elimination issue discussed above. * * (5) additional routines are added to interface this routine to MATLAB * to provide a simple C-callable user-interface, to check inputs for * errors, compute the symmetry of the pattern of A and the number of * nonzeros in each row/column of A+A', to compute the pattern of A+A', * to perform the assembly tree postordering, and to provide debugging * ouput. Many of these functions are also provided by the Fortran * Harwell Subroutine Library routine MC47A. * * (6) both "int" and "long" versions are provided. In the descriptions below * and integer is and "int" or "long", depending on which version is * being used. ********************************************************************** ***** CAUTION: ARGUMENTS ARE NOT CHECKED FOR ERRORS ON INPUT. ****** ********************************************************************** ** If you want error checking, a more versatile input format, and a ** ** simpler user interface, use camd_order or camd_l_order instead. ** ** This routine is not meant to be user-callable. ** ********************************************************************** * ---------------------------------------------------------------------------- * References: * ---------------------------------------------------------------------------- * * [1] Timothy A. Davis and Iain Duff, "An unsymmetric-pattern multifrontal * method for sparse LU factorization", SIAM J. Matrix Analysis and * Applications, vol. 18, no. 1, pp. 140-158. Discusses UMFPACK / MA38, * which first introduced the approximate minimum degree used by this * routine. * * [2] Patrick Amestoy, Timothy A. Davis, and Iain S. Duff, "An approximate * minimum degree ordering algorithm," SIAM J. Matrix Analysis and * Applications, vol. 17, no. 4, pp. 886-905, 1996. Discusses AMDBAR and * MC47B, which are the Fortran versions of this routine. * * [3] Alan George and Joseph Liu, "The evolution of the minimum degree * ordering algorithm," SIAM Review, vol. 31, no. 1, pp. 1-19, 1989. * We list below the features mentioned in that paper that this code * includes: * * mass elimination: * Yes. MA27 relied on supervariable detection for mass elimination. * * indistinguishable nodes: * Yes (we call these "supervariables"). This was also in the MA27 * code - although we modified the method of detecting them (the * previous hash was the true degree, which we no longer keep track * of). A supervariable is a set of rows with identical nonzero * pattern. All variables in a supervariable are eliminated together. * Each supervariable has as its numerical name that of one of its * variables (its principal variable). * * quotient graph representation: * Yes. We use the term "element" for the cliques formed during * elimination. This was also in the MA27 code. The algorithm can * operate in place, but it will work more efficiently if given some * "elbow room." * * element absorption: * Yes. This was also in the MA27 code. * * external degree: * Yes. The MA27 code was based on the true degree. * * incomplete degree update and multiple elimination: * No. This was not in MA27, either. Our method of degree update * within MC47B is element-based, not variable-based. It is thus * not well-suited for use with incomplete degree update or multiple * elimination. * * AMD Authors, and Copyright (C) 2004 by: * Timothy A. Davis, Patrick Amestoy, Iain S. Duff, John K. Reid. * Modifications for CAMD authored by Davis and Yanqing "Morris" Chen. * * Acknowledgements: This work (and the UMFPACK package) was supported by the * National Science Foundation (ASC-9111263, DMS-9223088, and CCR-0203270). * The UMFPACK/MA38 approximate degree update algorithm, the unsymmetric analog * which forms the basis of CAMD, was developed while Tim Davis was supported by * CERFACS (Toulouse, France) in a post-doctoral position. This C version, and * the etree postorder, were written while Tim Davis was on sabbatical at * Stanford University and Lawrence Berkeley National Laboratory. * Ordering constraints were added with support from Sandia National Labs (DOE). * ---------------------------------------------------------------------------- * INPUT ARGUMENTS (unaltered): * ---------------------------------------------------------------------------- * n: The matrix order. Restriction: n >= 1. * * iwlen: The size of the Iw array. On input, the matrix is stored in * Iw [0..pfree-1]. However, Iw [0..iwlen-1] should be slightly larger * than what is required to hold the matrix, at least iwlen >= pfree + n. * Otherwise, excessive compressions will take place. The recommended * value of iwlen is 1.2 * pfree + n, which is the value used in the * user-callable interface to this routine (camd_order.c). The algorithm * will not run at all if iwlen < pfree. Restriction: iwlen >= pfree + n. * Note that this is slightly more restrictive than the actual minimum * (iwlen >= pfree), but CAMD_2 will be very slow with no elbow room. * Thus, this routine enforces a bare minimum elbow room of size n. * * pfree: On input the tail end of the array, Iw [pfree..iwlen-1], is empty, * and the matrix is stored in Iw [0..pfree-1]. During execution, * additional data is placed in Iw, and pfree is modified so that * Iw [pfree..iwlen-1] is always the unused part of Iw. * * Control: A double array of size CAMD_CONTROL containing input parameters * that affect how the ordering is computed. If NULL, then default * settings are used. * * Control [CAMD_DENSE] is used to determine whether or not a given input * row is "dense". A row is "dense" if the number of entries in the row * exceeds Control [CAMD_DENSE] times sqrt (n), except that rows with 16 or * fewer entries are never considered "dense". To turn off the detection * of dense rows, set Control [CAMD_DENSE] to a negative number, or to a * number larger than sqrt (n). The default value of Control [CAMD_DENSE] * is CAMD_DEFAULT_DENSE, which is defined in camd.h as 10. * * Control [CAMD_AGGRESSIVE] is used to determine whether or not aggressive * absorption is to be performed. If nonzero, then aggressive absorption * is performed (this is the default). * * C: defines the ordering constraints. s = C [j] gives the constraint set s * that contains the row/column j (Restriction: 0 <= s < n). * In the output row permutation, all rows in set 0 appear first, followed * by all rows in set 1, and so on. If NULL, all rows are treated as if * they were in a single constraint set, and you will obtain a similar * ordering as AMD (slightly different because of the different * postordering used). * ---------------------------------------------------------------------------- * INPUT/OUPUT ARGUMENTS: * ---------------------------------------------------------------------------- * * Pe: An integer array of size n. On input, Pe [i] is the index in Iw of * the start of row i. Pe [i] is ignored if row i has no off-diagonal * entries. Thus Pe [i] must be in the range 0 to pfree-1 for non-empty * rows. * * During execution, it is used for both supervariables and elements: * * Principal supervariable i: index into Iw of the description of * supervariable i. A supervariable represents one or more rows of * the matrix with identical nonzero pattern. In this case, * Pe [i] >= 0. * * Non-principal supervariable i: if i has been absorbed into another * supervariable j, then Pe [i] = FLIP (j), where FLIP (j) is defined * as (-(j)-2). Row j has the same pattern as row i. Note that j * might later be absorbed into another supervariable j2, in which * case Pe [i] is still FLIP (j), and Pe [j] = FLIP (j2) which is * < EMPTY, where EMPTY is defined as (-1) in camd_internal.h. * * Unabsorbed element e: the index into Iw of the description of element * e, if e has not yet been absorbed by a subsequent element. Element * e is created when the supervariable of the same name is selected as * the pivot. In this case, Pe [i] >= 0. * * Absorbed element e: if element e is absorbed into element e2, then * Pe [e] = FLIP (e2). This occurs when the pattern of e (which we * refer to as Le) is found to be a subset of the pattern of e2 (that * is, Le2). In this case, Pe [i] < EMPTY. If element e is "null" * (it has no nonzeros outside its pivot block), then Pe [e] = EMPTY, * and e is the root of an assembly subtree (or the whole tree if * there is just one such root). * * Dense or empty variable i: if i is "dense" or empty (with zero degree), * then Pe [i] = FLIP (n). * * On output, Pe holds the assembly tree/forest, which implicitly * represents a pivot order with identical fill-in as the actual order * (via a depth-first search of the tree), as follows. If Nv [i] > 0, * then i represents a node in the assembly tree, and the parent of i is * Pe [i], or EMPTY if i is a root. If Nv [i] = 0, then (i, Pe [i]) * represents an edge in a subtree, the root of which is a node in the * assembly tree. Note that i refers to a row/column in the original * matrix, not the permuted matrix. * * Info: A double array of size CAMD_INFO. If present, (that is, not NULL), * then statistics about the ordering are returned in the Info array. * See camd.h for a description. * ---------------------------------------------------------------------------- * INPUT/MODIFIED (undefined on output): * ---------------------------------------------------------------------------- * * Len: An integer array of size n. On input, Len [i] holds the number of * entries in row i of the matrix, excluding the diagonal. The contents * of Len are undefined on output. Len also works as a temporary * workspace in post ordering with dense nodes detected. * * Iw: An integer array of size iwlen. On input, Iw [0..pfree-1] holds the * description of each row i in the matrix. The matrix must be symmetric, * and both upper and lower triangular parts must be present. The * diagonal must not be present. Row i is held as follows: * * Len [i]: the length of the row i data structure in the Iw array. * Iw [Pe [i] ... Pe [i] + Len [i] - 1]: * the list of column indices for nonzeros in row i (simple * supervariables), excluding the diagonal. All supervariables * start with one row/column each (supervariable i is just row i). * If Len [i] is zero on input, then Pe [i] is ignored on input. * * Note that the rows need not be in any particular order, and there * may be empty space between the rows. * * During execution, the supervariable i experiences fill-in. This is * represented by placing in i a list of the elements that cause fill-in * in supervariable i: * * Len [i]: the length of supervariable i in the Iw array. * Iw [Pe [i] ... Pe [i] + Elen [i] - 1]: * the list of elements that contain i. This list is kept short * by removing absorbed elements. * Iw [Pe [i] + Elen [i] ... Pe [i] + Len [i] - 1]: * the list of supervariables in i. This list is kept short by * removing nonprincipal variables, and any entry j that is also * contained in at least one of the elements (j in Le) in the list * for i (e in row i). * * When supervariable i is selected as pivot, we create an element e of * the same name (e=i): * * Len [e]: the length of element e in the Iw array. * Iw [Pe [e] ... Pe [e] + Len [e] - 1]: * the list of supervariables in element e. * * An element represents the fill-in that occurs when supervariable i is * selected as pivot (which represents the selection of row i and all * non-principal variables whose principal variable is i). We use the * term Le to denote the set of all supervariables in element e. Absorbed * supervariables and elements are pruned from these lists when * computationally convenient. * * CAUTION: THE INPUT MATRIX IS OVERWRITTEN DURING COMPUTATION. * The contents of Iw are undefined on output. * ---------------------------------------------------------------------------- * OUTPUT (need not be set on input): * ---------------------------------------------------------------------------- * * * Nv: An integer array of size n. During execution, ABS (Nv [i]) is equal to * the number of rows that are represented by the principal supervariable * i. If i is a nonprincipal or dense variable, then Nv [i] = 0. * Initially, Nv [i] = 1 for all i. Nv [i] < 0 signifies that i is a * principal variable in the pattern Lme of the current pivot element me. * After element me is constructed, Nv [i] is set back to a positive * value. * * On output, Nv [i] holds the number of pivots represented by super * row/column i of the original matrix, or Nv [i] = 0 for non-principal * rows/columns. Note that i refers to a row/column in the original * matrix, not the permuted matrix. * * Nv also works as a temporary workspace in initializing the BucketSet * array. * * Elen: An integer array of size n. See the description of Iw above. At the * start of execution, Elen [i] is set to zero for all rows i. During * execution, Elen [i] is the number of elements in the list for * supervariable i. When e becomes an element, Elen [e] = FLIP (esize) is * set, where esize is the size of the element (the number of pivots, plus * the number of nonpivotal entries). Thus Elen [e] < EMPTY. * Elen (i) = EMPTY set when variable i becomes nonprincipal. * * For variables, Elen (i) >= EMPTY holds until just before the * postordering and permutation vectors are computed. For elements, * Elen [e] < EMPTY holds. * * On output, Elen [i] is the degree of the row/column in the Cholesky * factorization of the permuted matrix, corresponding to the original row * i, if i is a super row/column. It is equal to EMPTY if i is * non-principal. Note that i refers to a row/column in the original * matrix, not the permuted matrix. * * Note that the contents of Elen on output differ from the Fortran * version (Elen holds the inverse permutation in the Fortran version, * which is instead returned in the Next array in this C version, * described below). * * Last: In a degree list, Last [i] is the supervariable preceding i, or EMPTY * if i is the head of the list. In a hash bucket, Last [i] is the hash * key for i. * * Last [Head [hash]] is also used as the head of a hash bucket if * Head [hash] contains a degree list (see the description of Head, * below). * * On output, Last [0..n-1] holds the permutation. That is, if * i = Last [k], then row i is the kth pivot row (where k ranges from 0 to * n-1). Row Last [k] of A is the kth row in the permuted matrix, PAP'. * * Next: Next [i] is the supervariable following i in a link list, or EMPTY if * i is the last in the list. Used for two kinds of lists: degree lists * and hash buckets (a supervariable can be in only one kind of list at a * time). * * On output Next [0..n-1] holds the inverse permutation. That is, if * k = Next [i], then row i is the kth pivot row. Row i of A appears as * the (Next[i])-th row in the permuted matrix, PAP'. * * Note that the contents of Next on output differ from the Fortran * version (Next is undefined on output in the Fortran version). * ---------------------------------------------------------------------------- * LOCAL WORKSPACE (not input or output - used only during execution): * ---------------------------------------------------------------------------- * * Degree: An integer array of size n. If i is a supervariable, then * Degree [i] holds the current approximation of the external degree of * row i (an upper bound). The external degree is the number of nonzeros * in row i, minus ABS (Nv [i]), the diagonal part. The bound is equal to * the exact external degree if Elen [i] is less than or equal to two. * * We also use the term "external degree" for elements e to refer to * |Le \ Lme|. If e is an element, then Degree [e] is |Le|, which is the * degree of the off-diagonal part of the element e (not including the * diagonal part). * * Head: An integer array of size n. Head is used for degree lists. * Head [deg] is the first supervariable in a degree list. All * supervariables i in a degree list Head [deg] have the same approximate * degree, namely, deg = Degree [i]. If the list Head [deg] is empty then * Head [deg] = EMPTY. * * During supervariable detection Head [hash] also serves as a pointer to * a hash bucket. If Head [hash] >= 0, there is a degree list of degree * hash. The hash bucket head pointer is Last [Head [hash]]. If * Head [hash] = EMPTY, then the degree list and hash bucket are both * empty. If Head [hash] < EMPTY, then the degree list is empty, and * FLIP (Head [hash]) is the head of the hash bucket. After supervariable * detection is complete, all hash buckets are empty, and the * (Last [Head [hash]] = EMPTY) condition is restored for the non-empty * degree lists. * * Head also workes as a temporary workspace in post ordering with dense * nodes detected. * * W: An integer array of size n. The flag array W determines the status of * elements and variables, and the external degree of elements. * * for elements: * if W [e] = 0, then the element e is absorbed. * if W [e] >= wflg, then W [e] - wflg is the size of the set * |Le \ Lme|, in terms of nonzeros (the sum of ABS (Nv [i]) for * each principal variable i that is both in the pattern of * element e and NOT in the pattern of the current pivot element, * me). * if wflg > W [e] > 0, then e is not absorbed and has not yet been * seen in the scan of the element lists in the computation of * |Le\Lme| in Scan 1 below. * * for variables: * during supervariable detection, if W [j] != wflg then j is * not in the pattern of variable i. * * The W array is initialized by setting W [i] = 1 for all i, and by * setting wflg = 2. It is reinitialized if wflg becomes too large (to * ensure that wflg+n does not cause integer overflow). * * BucketSet: An integer array of size n. * During execution it stores the rows that sorted in the ascending order * based on C []. For instance: if C[]={0,2,1,0,1,0,2,1}, the * Bucketset will be {0,3,5,2,4,7,1,6}. * The elements in Bucketset are then modified, to maintain the order of * roots (Pe[i]=-1) in each Constraint Set. * ---------------------------------------------------------------------------- * LOCAL INTEGERS: * ---------------------------------------------------------------------------- */ Int deg, degme, dext, lemax, e, elenme, eln, i, ilast, inext, j, jlast, k, knt1, knt2, knt3, lenj, ln, me, mindeg, nel, nleft, nvi, nvj, nvpiv, slenme, wbig, we, wflg, wnvi, ok, ndense, ncmpa, nnull, dense, aggressive ; unsigned Int hash ; /* unsigned, so that hash % n is well defined.*/ /* * deg: the degree of a variable or element * degme: size, |Lme|, of the current element, me (= Degree [me]) * dext: external degree, |Le \ Lme|, of some element e * lemax: largest |Le| seen so far (called dmax in Fortran version) * e: an element * elenme: the length, Elen [me], of element list of pivotal variable * eln: the length, Elen [...], of an element list * hash: the computed value of the hash function * i: a supervariable * ilast: the entry in a link list preceding i * inext: the entry in a link list following i * j: a supervariable * jlast: the entry in a link list preceding j * k: the pivot order of an element or variable * knt1: loop counter used during element construction * knt2: loop counter used during element construction * knt3: loop counter used during compression * lenj: Len [j] * ln: length of a supervariable list * me: current supervariable being eliminated, and the current * element created by eliminating that supervariable * mindeg: current minimum degree * nel: number of pivots selected so far * nleft: n - nel, the number of nonpivotal rows/columns remaining * nvi: the number of variables in a supervariable i (= Nv [i]) * nvj: the number of variables in a supervariable j (= Nv [j]) * nvpiv: number of pivots in current element * slenme: number of variables in variable list of pivotal variable * wbig: = INT_MAX - n for the "int" version, LONG_MAX - n for the * "long" version. wflg is not allowed to be >= wbig. * we: W [e] * wflg: used for flagging the W array. See description of Iw. * wnvi: wflg - Nv [i] * x: either a supervariable or an element * * ok: true if supervariable j can be absorbed into i * ndense: number of "dense" rows/columns * nnull: number of empty rows/columns * dense: rows/columns with initial degree > dense are considered "dense" * aggressive: true if aggressive absorption is being performed * ncmpa: number of garbage collections * ---------------------------------------------------------------------------- * LOCAL DOUBLES, used for statistical output only (except for alpha): * ---------------------------------------------------------------------------- */ double f, r, ndiv, s, nms_lu, nms_ldl, dmax, alpha, lnz, lnzme ; /* * f: nvpiv * r: degme + nvpiv * ndiv: number of divisions for LU or LDL' factorizations * s: number of multiply-subtract pairs for LU factorization, for the * current element me * nms_lu number of multiply-subtract pairs for LU factorization * nms_ldl number of multiply-subtract pairs for LDL' factorization * dmax: the largest number of entries in any column of L, including the * diagonal * alpha: "dense" degree ratio * lnz: the number of nonzeros in L (excluding the diagonal) * lnzme: the number of nonzeros in L (excl. the diagonal) for the * current element me * ---------------------------------------------------------------------------- * LOCAL "POINTERS" (indices into the Iw array) * ---------------------------------------------------------------------------- */ Int p, p1, p2, p3, p4, pdst, pend, pj, pme, pme1, pme2, pn, psrc ; /* * Any parameter (Pe [...] or pfree) or local variable starting with "p" (for * Pointer) is an index into Iw, and all indices into Iw use variables starting * with "p." The only exception to this rule is the iwlen input argument. * * p: pointer into lots of things * p1: Pe [i] for some variable i (start of element list) * p2: Pe [i] + Elen [i] - 1 for some variable i * p3: index of first supervariable in clean list * p4: * pdst: destination pointer, for compression * pend: end of memory to compress * pj: pointer into an element or variable * pme: pointer into the current element (pme1...pme2) * pme1: the current element, me, is stored in Iw [pme1...pme2] * pme2: the end of the current element * pn: pointer into a "clean" variable, also used to compress * psrc: source pointer, for compression */ Int curC, pBucket, pBucket2, degreeListCounter, c, cmax = 0, ndense_or_null ; Int *Bucket, *Perm ; /* * curC: the current Constraint Set being ordered * pBucket: pointer into Bucketset[] when building the degreelist for each * Constraint Set * pBucket2: pointer into Bucketset[] to tell the post ordering where to stop * degreeListCounter: number of elements remaining in the * degreelist of current Constraint Set * Bucket: used to construct BucketSet * Perm: permutation */ /* ========================================================================= */ /* INITIALIZATIONS */ /* ========================================================================= */ /* Note that this restriction on iwlen is slightly more restrictive than * what is actually required in CAMD_2. CAMD_2 can operate with no elbow * room at all, but it will be slow. For better performance, at least * size-n elbow room is enforced. */ ASSERT (iwlen >= pfree + n) ; ASSERT (n > 0) ; /* initialize output statistics */ lnz = 0 ; ndiv = 0 ; nms_lu = 0 ; nms_ldl = 0 ; dmax = 1 ; me = EMPTY ; mindeg = 0 ; ncmpa = 0 ; nel = 0 ; lemax = 0 ; curC = 0 ; /* camd work initBucketSet using CountingSort * BucketSort the index Array BucketSet According to Contrains Array C, Using * Nv[] as a temporary workspace * Input: Index Array from 0 to n.(index of rows) * Output: Index Array sorted according to C. worked as a bucket set. * * All the value in C must be 0 <= C[i] <= n-1 * For instance: if C[]={0,2,1,0,1,0,2,1}, the output Bucketset should be * {0,3,5,2,4,7,1,6} */ /* CountingSort BucketSet[] based on C[], It is O(n) linear time */ if (C == NULL) { /* store everything in bucket without changing order */ for (j = 0 ; j < n ; j++) { BucketSet [j] = j ; } } else { Bucket = Nv ; for (i = 0 ; i < n ; i++) { Bucket [i] = 0 ; } cmax = C [0] ; for (j = 0 ; j < n ; j++) { c = C [j] ; CAMD_DEBUG1 (("C [%d] = "ID"\n", j, c)) ; Bucket [c]++ ; cmax = MAX (cmax, c) ; ASSERT (c >= 0 && c < n) ; } CAMD_DEBUG1 (("Max constraint set: "ID"\n", cmax)) ; for (i = 1 ; i < n ; i++) { Bucket [i] += Bucket [i-1] ; } for (j = n-1 ; j >= 0 ; j--) { BucketSet [--Bucket [C [j]]] = j ; } #ifndef NDEBUG CAMD_DEBUG3 (("\nConstraint Set "ID" :", C [BucketSet [0]])); for (i = 0 ; i < n ; i++) { CAMD_DEBUG3 ((ID" ", BucketSet [i])) ; if (i == n-1) { CAMD_DEBUG3 (("\n")) ; break ; } if (C [BucketSet [i+1]] != C [BucketSet [i]]) { CAMD_DEBUG3 (("\nConstraint Set "ID" :", C [BucketSet [i+1]])) ; } } #endif } /* get control parameters */ if (Control != (double *) NULL) { alpha = Control [CAMD_DENSE] ; aggressive = (Control [CAMD_AGGRESSIVE] != 0) ; } else { alpha = CAMD_DEFAULT_DENSE ; aggressive = CAMD_DEFAULT_AGGRESSIVE ; } /* Note: if alpha is NaN, this is undefined: */ if (alpha < 0) { /* only remove completely dense rows/columns */ dense = n-2 ; } else { dense = alpha * sqrt ((double) n) ; } dense = MAX (16, dense) ; dense = MIN (n, dense) ; CAMD_DEBUG1 (("\n\nCAMD (debug), alpha %g, aggr. "ID"\n", alpha, aggressive)) ; for (i = 0 ; i < n ; i++) { Last [i] = EMPTY ; Head [i] = EMPTY ; Next [i] = EMPTY ; /* if separate Hhead array is used for hash buckets: * Hhead [i] = EMPTY ; */ Nv [i] = 1 ; W [i] = 1 ; Elen [i] = 0 ; Degree [i] = Len [i] ; } Head [n] = EMPTY ; /* initialize wflg */ wbig = Int_MAX - n ; wflg = clear_flag (0, wbig, W, n) ; /* --------------------------------------------------------------------- */ /* eliminate dense and empty rows */ /* --------------------------------------------------------------------- */ ndense = 0 ; nnull = 0 ; for (j = 0 ; j < n ; j++) { i = BucketSet [j] ; deg = Degree [i] ; ASSERT (deg >= 0 && deg < n) ; if (deg > dense || deg == 0) { /* ------------------------------------------------------------- * Dense or empty variables are treated as non-principal variables * represented by node n. That is, i is absorbed into n, just like * j is absorbed into i in supervariable detection (see "found it!" * comment, below). * ------------------------------------------------------------- */ if (deg > dense) { CAMD_DEBUG1 (("Dense node "ID" degree "ID" bucket "ID"\n", i, deg, j)) ; ndense++ ; } else { CAMD_DEBUG1 (("Empty node "ID" degree "ID" bucket "ID"\n", i, deg, j)) ; nnull++ ; } Pe [i] = FLIP (n) ; Nv [i] = 0 ; /* do not postorder this node */ Elen [i] = EMPTY ; nel++ ; } } ndense_or_null = ndense + nnull ; pBucket = 0 ; degreeListCounter = 0 ; pBucket2 = 0 ; /* ========================================================================= */ /* WHILE (selecting pivots) DO */ /* ========================================================================= */ while (nel < n) { /* ------------------------------------------------------------------ */ /* if empty, fill the degree list with next non-empty constraint set */ /* ------------------------------------------------------------------ */ while (degreeListCounter == 0) { mindeg = n ; /* determine the new constraint set */ curC = (C == NULL) ? 0 : C [BucketSet [pBucket]] ; for ( ; pBucket < n ; pBucket++) { /* add i to the degree list, unless it's dead or not in curC */ i = BucketSet [pBucket] ; if (!IsInCurrentSet (C, i, curC)) break ; deg = Degree [i] ; ASSERT (deg >= 0 && deg < n) ; if (Pe [i] >= 0) { /* ------------------------------------------------------ * place i in the degree list corresponding to its degree * ------------------------------------------------------ */ inext = Head [deg] ; ASSERT (inext >= EMPTY && inext < n) ; if (inext != EMPTY) Last [inext] = i ; Next [i] = inext ; Head [deg] = i ; degreeListCounter++ ; Last [i] = EMPTY ; mindeg = MIN (mindeg, deg) ; } } } #ifndef NDEBUG CAMD_DEBUG1 (("\n======Nel "ID"\n", nel)) ; if (CAMD_debug >= 2) { CAMD_dump (n, Pe, Iw, Len, iwlen, pfree, Nv, Next, Last, Head, Elen, Degree, W, nel, BucketSet, C, curC) ; } #endif /* ========================================================================= */ /* GET PIVOT OF MINIMUM DEGREE */ /* ========================================================================= */ /* ----------------------------------------------------------------- */ /* find next supervariable for elimination */ /* ----------------------------------------------------------------- */ ASSERT (mindeg >= 0 && mindeg < n) ; for (deg = mindeg ; deg < n ; deg++) { me = Head [deg] ; if (me != EMPTY) break ; } mindeg = deg ; ASSERT (me >= 0 && me < n) ; CAMD_DEBUG1 (("=================me: "ID"\n", me)) ; /* ----------------------------------------------------------------- */ /* remove chosen variable from link list */ /* ----------------------------------------------------------------- */ inext = Next [me] ; ASSERT (inext >= EMPTY && inext < n) ; if (inext != EMPTY) Last [inext] = EMPTY ; Head [deg] = inext ; degreeListCounter-- ; /* ----------------------------------------------------------------- */ /* me represents the elimination of pivots nel to nel+Nv[me]-1. */ /* place me itself as the first in this set. */ /* ----------------------------------------------------------------- */ elenme = Elen [me] ; nvpiv = Nv [me] ; ASSERT (nvpiv > 0) ; nel += nvpiv ; CAMD_DEBUG1 (("nvpiv is initially "ID"\n", nvpiv)) ; /* ========================================================================= */ /* CONSTRUCT NEW ELEMENT */ /* ========================================================================= */ /* ----------------------------------------------------------------- * At this point, me is the pivotal supervariable. It will be * converted into the current element. Scan list of the pivotal * supervariable, me, setting tree pointers and constructing new list * of supervariables for the new element, me. p is a pointer to the * current position in the old list. * ----------------------------------------------------------------- */ /* flag the variable "me" as being in Lme by negating Nv [me] */ Nv [me] = -nvpiv ; degme = 0 ; ASSERT (Pe [me] >= 0 && Pe [me] < iwlen) ; if (elenme == 0) { /* ------------------------------------------------------------- */ /* construct the new element in place */ /* ------------------------------------------------------------- */ pme1 = Pe [me] ; pme2 = pme1 - 1 ; for (p = pme1 ; p <= pme1 + Len [me] - 1 ; p++) { i = Iw [p] ; ASSERT (i >= 0 && i < n && Nv [i] >= 0) ; nvi = Nv [i] ; if (nvi > 0) { /* ----------------------------------------------------- */ /* i is a principal variable not yet placed in Lme. */ /* store i in new list */ /* ----------------------------------------------------- */ /* flag i as being in Lme by negating Nv [i] */ degme += nvi ; Nv [i] = -nvi ; Iw [++pme2] = i ; /* ----------------------------------------------------- */ /* remove variable i from degree list. */ /* ----------------------------------------------------- */ if (IsInCurrentSet (C, i, curC)) { ilast = Last [i] ; inext = Next [i] ; ASSERT (ilast >= EMPTY && ilast < n) ; ASSERT (inext >= EMPTY && inext < n) ; if (inext != EMPTY) Last [inext] = ilast ; if (ilast != EMPTY) { Next [ilast] = inext ; } else { /* i is at the head of the degree list */ ASSERT (Degree [i] >= 0 && Degree [i] < n) ; Head [Degree [i]] = inext ; } degreeListCounter-- ; } } } } else { /* ------------------------------------------------------------- */ /* construct the new element in empty space, Iw [pfree ...] */ /* ------------------------------------------------------------- */ p = Pe [me] ; pme1 = pfree ; slenme = Len [me] - elenme ; for (knt1 = 1 ; knt1 <= elenme + 1 ; knt1++) { if (knt1 > elenme) { /* search the supervariables in me. */ e = me ; pj = p ; ln = slenme ; CAMD_DEBUG2 (("Search sv: "ID" "ID" "ID"\n", me,pj,ln)) ; } else { /* search the elements in me. */ e = Iw [p++] ; ASSERT (e >= 0 && e < n) ; pj = Pe [e] ; ln = Len [e] ; CAMD_DEBUG2 (("Search element e "ID" in me "ID"\n", e,me)) ; ASSERT (Elen [e] < EMPTY && W [e] > 0 && pj >= 0) ; } ASSERT (ln >= 0 && (ln == 0 || (pj >= 0 && pj < iwlen))) ; /* --------------------------------------------------------- * search for different supervariables and add them to the * new list, compressing when necessary. this loop is * executed once for each element in the list and once for * all the supervariables in the list. * --------------------------------------------------------- */ for (knt2 = 1 ; knt2 <= ln ; knt2++) { i = Iw [pj++] ; ASSERT (i >= 0 && i < n && (i == me || Elen [i] >= EMPTY)); nvi = Nv [i] ; CAMD_DEBUG2 ((": "ID" "ID" "ID" "ID"\n", i, Elen [i], Nv [i], wflg)) ; if (nvi > 0) { /* ------------------------------------------------- */ /* compress Iw, if necessary */ /* ------------------------------------------------- */ if (pfree >= iwlen) { CAMD_DEBUG1 (("GARBAGE COLLECTION\n")) ; /* prepare for compressing Iw by adjusting pointers * and lengths so that the lists being searched in * the inner and outer loops contain only the * remaining entries. */ Pe [me] = p ; Len [me] -= knt1 ; /* check if nothing left of supervariable me */ if (Len [me] == 0) Pe [me] = EMPTY ; Pe [e] = pj ; Len [e] = ln - knt2 ; /* nothing left of element e */ if (Len [e] == 0) Pe [e] = EMPTY ; ncmpa++ ; /* one more garbage collection */ /* store first entry of each object in Pe */ /* FLIP the first entry in each object */ for (j = 0 ; j < n ; j++) { pn = Pe [j] ; if (pn >= 0) { ASSERT (pn >= 0 && pn < iwlen) ; Pe [j] = Iw [pn] ; Iw [pn] = FLIP (j) ; } } /* psrc/pdst point to source/destination */ psrc = 0 ; pdst = 0 ; pend = pme1 - 1 ; while (psrc <= pend) { /* search for next FLIP'd entry */ j = FLIP (Iw [psrc++]) ; if (j >= 0) { CAMD_DEBUG2 (("Got object j: "ID"\n", j)) ; Iw [pdst] = Pe [j] ; Pe [j] = pdst++ ; lenj = Len [j] ; /* copy from source to destination */ for (knt3 = 0 ; knt3 <= lenj - 2 ; knt3++) { Iw [pdst++] = Iw [psrc++] ; } } } /* move the new partially-constructed element */ p1 = pdst ; for (psrc = pme1 ; psrc <= pfree-1 ; psrc++) { Iw [pdst++] = Iw [psrc] ; } pme1 = p1 ; pfree = pdst ; pj = Pe [e] ; p = Pe [me] ; } /* ------------------------------------------------- */ /* i is a principal variable not yet placed in Lme */ /* store i in new list */ /* ------------------------------------------------- */ /* flag i as being in Lme by negating Nv [i] */ degme += nvi ; Nv [i] = -nvi ; Iw [pfree++] = i ; CAMD_DEBUG2 ((" s: "ID" nv "ID"\n", i, Nv [i])); /* ------------------------------------------------- */ /* remove variable i from degree link list */ /* ------------------------------------------------- */ if (IsInCurrentSet (C, i, curC)) { ilast = Last [i] ; inext = Next [i] ; ASSERT (ilast >= EMPTY && ilast < n) ; ASSERT (inext >= EMPTY && inext < n) ; if (inext != EMPTY) Last [inext] = ilast ; if (ilast != EMPTY) { Next [ilast] = inext ; } else { /* i is at the head of the degree list */ ASSERT (Degree [i] >= 0 && Degree [i] < n) ; Head [Degree [i]] = inext ; } degreeListCounter-- ; } } } if (e != me) { if (IsInCurrentSet (C, e, curC)) { /* absorb element here if in same bucket */ /* set tree pointer and flag to indicate element e is * absorbed into new element me (the parent of e is me) */ CAMD_DEBUG1 ((" Element "ID" => "ID"\n", e, me)) ; Pe [e] = FLIP (me) ; W [e] = 0 ; } else { /* make element a root; kill it if not in same bucket */ CAMD_DEBUG1 (("2 Element "ID" => "ID"\n", e, me)) ; Pe [e] = EMPTY ; W [e] = 0 ; } } } pme2 = pfree - 1 ; } /* ----------------------------------------------------------------- */ /* me has now been converted into an element in Iw [pme1..pme2] */ /* ----------------------------------------------------------------- */ /* degme holds the external degree of new element */ Degree [me] = degme ; Pe [me] = pme1 ; Len [me] = pme2 - pme1 + 1 ; ASSERT (Pe [me] >= 0 && Pe [me] < iwlen) ; Elen [me] = FLIP (nvpiv + degme) ; /* FLIP (Elen (me)) is now the degree of pivot (including * diagonal part). */ #ifndef NDEBUG CAMD_DEBUG2 (("New element structure: length= "ID"\n", pme2-pme1+1)) ; for (pme = pme1 ; pme <= pme2 ; pme++) CAMD_DEBUG3 ((" "ID"", Iw[pme])); CAMD_DEBUG3 (("\n")) ; #endif /* ----------------------------------------------------------------- */ /* make sure that wflg is not too large. */ /* ----------------------------------------------------------------- */ /* With the current value of wflg, wflg+n must not cause integer * overflow */ wflg = clear_flag (wflg, wbig, W, n) ; /* ========================================================================= */ /* COMPUTE (W [e] - wflg) = |Le\Lme| FOR ALL ELEMENTS */ /* ========================================================================= */ /* ----------------------------------------------------------------- * Scan 1: compute the external degrees of previous elements with * respect to the current element. That is: * (W [e] - wflg) = |Le \ Lme| * for each element e that appears in any supervariable in Lme. The * notation Le refers to the pattern (list of supervariables) of a * previous element e, where e is not yet absorbed, stored in * Iw [Pe [e] + 1 ... Pe [e] + Len [e]]. The notation Lme * refers to the pattern of the current element (stored in * Iw [pme1..pme2]). If aggressive absorption is enabled, and * (W [e] - wflg) becomes zero, then the element e will be absorbed * in Scan 2. * ----------------------------------------------------------------- */ CAMD_DEBUG2 (("me: ")) ; for (pme = pme1 ; pme <= pme2 ; pme++) { i = Iw [pme] ; ASSERT (i >= 0 && i < n) ; eln = Elen [i] ; CAMD_DEBUG3 ((""ID" Elen "ID": \n", i, eln)) ; if (eln > 0) { /* note that Nv [i] has been negated to denote i in Lme: */ nvi = -Nv [i] ; ASSERT (nvi > 0 && Pe [i] >= 0 && Pe [i] < iwlen) ; wnvi = wflg - nvi ; for (p = Pe [i] ; p <= Pe [i] + eln - 1 ; p++) { e = Iw [p] ; ASSERT (e >= 0 && e < n) ; we = W [e] ; CAMD_DEBUG4 ((" e "ID" we "ID" ", e, we)) ; if (we >= wflg) { /* unabsorbed element e has been seen in this loop */ CAMD_DEBUG4 ((" unabsorbed, first time seen")) ; we -= nvi ; } else if (we != 0) { /* e is an unabsorbed element */ /* this is the first we have seen e in all of Scan 1 */ CAMD_DEBUG4 ((" unabsorbed")) ; we = Degree [e] + wnvi ; } CAMD_DEBUG4 (("\n")) ; W [e] = we ; } } } CAMD_DEBUG2 (("\n")) ; /* ========================================================================= */ /* DEGREE UPDATE AND ELEMENT ABSORPTION */ /* ========================================================================= */ /* ----------------------------------------------------------------- * Scan 2: for each i in Lme, sum up the degree of Lme (which is * degme), plus the sum of the external degrees of each Le for the * elements e appearing within i, plus the supervariables in i. * Place i in hash list. * ----------------------------------------------------------------- */ for (pme = pme1 ; pme <= pme2 ; pme++) { i = Iw [pme] ; ASSERT (i >= 0 && i < n && Nv [i] < 0 && Elen [i] >= 0) ; CAMD_DEBUG2 (("Updating: i "ID" "ID" "ID"\n", i, Elen[i], Len [i])); p1 = Pe [i] ; p2 = p1 + Elen [i] - 1 ; pn = p1 ; hash = 0 ; deg = 0 ; ASSERT (p1 >= 0 && p1 < iwlen && p2 >= -1 && p2 < iwlen) ; /* ------------------------------------------------------------- */ /* scan the element list associated with supervariable i */ /* ------------------------------------------------------------- */ /* UMFPACK/MA38-style approximate degree: */ if (aggressive) { for (p = p1 ; p <= p2 ; p++) { e = Iw [p] ; ASSERT (e >= 0 && e < n) ; we = W [e] ; if (we != 0) { /* e is an unabsorbed element */ /* dext = | Le \ Lme | */ dext = we - wflg ; if (dext > 0) { deg += dext ; Iw [pn++] = e ; hash += e ; CAMD_DEBUG4 ((" e: "ID" hash = "ID"\n",e,hash)) ; } else { if (IsInCurrentSet (C, e, curC)) { /* external degree of e is zero and if * C[e] = curC; absorb e into me */ CAMD_DEBUG1 ((" Element "ID" =>"ID" (aggr)\n", e, me)) ; ASSERT (dext == 0) ; Pe [e] = FLIP (me) ; W [e] = 0 ; } else { /* make element a root; kill it if not in same * bucket */ CAMD_DEBUG1 (("2 Element "ID" =>"ID" (aggr)\n", e, me)) ; ASSERT (dext == 0) ; Pe [e] = EMPTY ; W [e] = 0 ; } } } } } else { for (p = p1 ; p <= p2 ; p++) { e = Iw [p] ; ASSERT (e >= 0 && e < n) ; we = W [e] ; if (we != 0) { /* e is an unabsorbed element */ dext = we - wflg ; ASSERT (dext >= 0) ; deg += dext ; Iw [pn++] = e ; hash += e ; CAMD_DEBUG4 ((" e: "ID" hash = "ID"\n",e,hash)) ; } } } /* count the number of elements in i (including me): */ Elen [i] = pn - p1 + 1 ; /* ------------------------------------------------------------- */ /* scan the supervariables in the list associated with i */ /* ------------------------------------------------------------- */ /* The bulk of the CAMD run time is typically spent in this loop, * particularly if the matrix has many dense rows that are not * removed prior to ordering. */ p3 = pn ; p4 = p1 + Len [i] ; for (p = p2 + 1 ; p < p4 ; p++) { j = Iw [p] ; ASSERT (j >= 0 && j < n) ; nvj = Nv [j] ; if (nvj > 0) { /* j is unabsorbed, and not in Lme. */ /* add to degree and add to new list */ deg += nvj ; Iw [pn++] = j ; hash += j ; CAMD_DEBUG4 ((" s: "ID" hash "ID" Nv[j]= "ID"\n", j, hash, nvj)) ; } } /* ------------------------------------------------------------- */ /* update the degree and check for mass elimination */ /* ------------------------------------------------------------- */ /* with aggressive absorption, deg==0 is identical to the * Elen [i] == 1 && p3 == pn test, below. */ ASSERT (IMPLIES (aggressive, (deg==0) == (Elen[i]==1 && p3==pn))) ; if (Elen [i] == 1 && p3 == pn && IsInCurrentSet (C, i, curC)) { /* --------------------------------------------------------- */ /* mass elimination */ /* --------------------------------------------------------- */ /* There is nothing left of this node except for an edge to * the current pivot element. Elen [i] is 1, and there are * no variables adjacent to node i. Absorb i into the * current pivot element, me. Note that if there are two or * more mass eliminations, fillin due to mass elimination is * possible within the nvpiv-by-nvpiv pivot block. It is this * step that causes CAMD's analysis to be an upper bound. * * The reason is that the selected pivot has a lower * approximate degree than the true degree of the two mass * eliminated nodes. There is no edge between the two mass * eliminated nodes. They are merged with the current pivot * anyway. * * No fillin occurs in the Schur complement, in any case, * and this effect does not decrease the quality of the * ordering itself, just the quality of the nonzero and * flop count analysis. It also means that the post-ordering * is not an exact elimination tree post-ordering. */ CAMD_DEBUG1 ((" MASS i "ID" => parent e "ID"\n", i, me)) ; Pe [i] = FLIP (me) ; nvi = -Nv [i] ; degme -= nvi ; nvpiv += nvi ; nel += nvi ; Nv [i] = 0 ; Elen [i] = EMPTY ; } else { /* --------------------------------------------------------- */ /* update the upper-bound degree of i */ /* --------------------------------------------------------- */ /* the following degree does not yet include the size * of the current element, which is added later: */ Degree [i] = MIN (Degree [i], deg) ; /* --------------------------------------------------------- */ /* add me to the list for i */ /* --------------------------------------------------------- */ /* move first supervariable to end of list */ Iw [pn] = Iw [p3] ; /* move first element to end of element part of list */ Iw [p3] = Iw [p1] ; /* add new element, me, to front of list. */ Iw [p1] = me ; /* store the new length of the list in Len [i] */ Len [i] = pn - p1 + 1 ; /* --------------------------------------------------------- */ /* place in hash bucket. Save hash key of i in Last [i]. */ /* --------------------------------------------------------- */ /* NOTE: this can fail if hash is negative, because the ANSI C * standard does not define a % b when a and/or b are negative. * That's why hash is defined as an unsigned Int, to avoid this * problem. */ hash = hash % n ; ASSERT (((Int) hash) >= 0 && ((Int) hash) < n) ; /* if the Hhead array is not used: */ j = Head [hash] ; if (j <= EMPTY) { /* degree list is empty, hash head is FLIP (j) */ Next [i] = FLIP (j) ; Head [hash] = FLIP (i) ; } else { /* degree list is not empty, use Last [Head [hash]] as * hash head. */ Next [i] = Last [j] ; Last [j] = i ; } /* if a separate Hhead array is used: * Next [i] = Hhead [hash] ; Hhead [hash] = i ; */ CAMD_DEBUG4 ((" s: "ID" hash "ID" \n", i, hash)) ; Last [i] = hash ; } } Degree [me] = degme ; /* ----------------------------------------------------------------- */ /* Clear the counter array, W [...], by incrementing wflg. */ /* ----------------------------------------------------------------- */ /* make sure that wflg+n does not cause integer overflow */ lemax = MAX (lemax, degme) ; wflg += lemax ; wflg = clear_flag (wflg, wbig, W, n) ; /* at this point, W [0..n-1] < wflg holds */ /* ========================================================================= */ /* SUPERVARIABLE DETECTION */ /* ========================================================================= */ CAMD_DEBUG1 (("Detecting supervariables:\n")) ; for (pme = pme1 ; pme <= pme2 ; pme++) { i = Iw [pme] ; ASSERT (i >= 0 && i < n) ; CAMD_DEBUG2 (("Consider i "ID" nv "ID"\n", i, Nv [i])) ; if (Nv [i] < 0) { /* i is a principal variable in Lme */ /* --------------------------------------------------------- * examine all hash buckets with 2 or more variables. We do * this by examing all unique hash keys for supervariables in * the pattern Lme of the current element, me * --------------------------------------------------------- */ CAMD_DEBUG2 (("Last: "ID"\n", Last [i])) ; /* let i = head of hash bucket, and empty the hash bucket */ ASSERT (Last [i] >= 0 && Last [i] < n) ; hash = Last [i] ; /* if Hhead array is not used: */ j = Head [hash] ; if (j == EMPTY) { /* hash bucket and degree list are both empty */ i = EMPTY ; } else if (j < EMPTY) { /* degree list is empty */ i = FLIP (j) ; Head [hash] = EMPTY ; } else { /* degree list is not empty, restore Last [j] of head j */ i = Last [j] ; Last [j] = EMPTY ; } /* if separate Hhead array is used: * i = Hhead [hash] ; Hhead [hash] = EMPTY ; */ ASSERT (i >= EMPTY && i < n) ; CAMD_DEBUG2 (("----i "ID" hash "ID"\n", i, hash)) ; while (i != EMPTY && Next [i] != EMPTY) { /* ----------------------------------------------------- * this bucket has one or more variables following i. * scan all of them to see if i can absorb any entries * that follow i in hash bucket. Scatter i into w. * ----------------------------------------------------- */ ln = Len [i] ; eln = Elen [i] ; ASSERT (ln >= 0 && eln >= 0) ; ASSERT (Pe [i] >= 0 && Pe [i] < iwlen) ; /* do not flag the first element in the list (me) */ for (p = Pe [i] + 1 ; p <= Pe [i] + ln - 1 ; p++) { ASSERT (Iw [p] >= 0 && Iw [p] < n) ; W [Iw [p]] = wflg ; } /* ----------------------------------------------------- */ /* scan every other entry j following i in bucket */ /* ----------------------------------------------------- */ jlast = i ; j = Next [i] ; ASSERT (j >= EMPTY && j < n) ; while (j != EMPTY) { /* ------------------------------------------------- */ /* check if j and i have identical nonzero pattern */ /* ------------------------------------------------- */ CAMD_DEBUG3 (("compare i "ID" and j "ID"\n", i,j)) ; /* check if i and j have the same Len and Elen */ /* and are in the same bucket */ ASSERT (Len [j] >= 0 && Elen [j] >= 0) ; ASSERT (Pe [j] >= 0 && Pe [j] < iwlen) ; ok = (Len [j] == ln) && (Elen [j] == eln) ; ok = ok && InSameConstraintSet (C,i,j) ; /* skip the first element in the list (me) */ for (p = Pe [j] + 1 ; ok && p <= Pe [j] + ln - 1 ; p++) { ASSERT (Iw [p] >= 0 && Iw [p] < n) ; if (W [Iw [p]] != wflg) ok = 0 ; } if (ok) { /* --------------------------------------------- */ /* found it! j can be absorbed into i */ /* --------------------------------------------- */ CAMD_DEBUG1 (("found it! j "ID" => i "ID"\n", j,i)); Pe [j] = FLIP (i) ; /* both Nv [i] and Nv [j] are negated since they */ /* are in Lme, and the absolute values of each */ /* are the number of variables in i and j: */ Nv [i] += Nv [j] ; Nv [j] = 0 ; Elen [j] = EMPTY ; /* delete j from hash bucket */ ASSERT (j != Next [j]) ; j = Next [j] ; Next [jlast] = j ; } else { /* j cannot be absorbed into i */ jlast = j ; ASSERT (j != Next [j]) ; j = Next [j] ; } ASSERT (j >= EMPTY && j < n) ; } /* ----------------------------------------------------- * no more variables can be absorbed into i * go to next i in bucket and clear flag array * ----------------------------------------------------- */ wflg++ ; i = Next [i] ; ASSERT (i >= EMPTY && i < n) ; } } } CAMD_DEBUG2 (("detect done\n")) ; /* ========================================================================= */ /* RESTORE DEGREE LISTS AND REMOVE NONPRINCIPAL SUPERVARIABLES FROM ELEMENT */ /* ========================================================================= */ p = pme1 ; nleft = n - nel ; for (pme = pme1 ; pme <= pme2 ; pme++) { i = Iw [pme] ; ASSERT (i >= 0 && i < n) ; nvi = -Nv [i] ; CAMD_DEBUG3 (("Restore i "ID" "ID"\n", i, nvi)) ; if (nvi > 0) { /* i is a principal variable in Lme */ /* restore Nv [i] to signify that i is principal */ Nv [i] = nvi ; /* --------------------------------------------------------- */ /* compute the external degree (add size of current element) */ /* --------------------------------------------------------- */ deg = Degree [i] + degme - nvi ; deg = MIN (deg, nleft - nvi) ; ASSERT (deg >= 0 && deg < n) ; /* --------------------------------------------------------- */ /* place the supervariable at the head of the degree list */ /* --------------------------------------------------------- */ if (IsInCurrentSet (C, i, curC)) { inext = Head [deg] ; ASSERT (inext >= EMPTY && inext < n) ; if (inext != EMPTY) Last [inext] = i ; Next [i] = inext ; Last [i] = EMPTY ; Head [deg] = i ; degreeListCounter++ ; } /* --------------------------------------------------------- */ /* save the new degree, and find the minimum degree */ /* --------------------------------------------------------- */ mindeg = MIN (mindeg, deg) ; Degree [i] = deg ; /* --------------------------------------------------------- */ /* place the supervariable in the element pattern */ /* --------------------------------------------------------- */ Iw [p++] = i ; } } CAMD_DEBUG2 (("restore done\n")) ; /* ========================================================================= */ /* FINALIZE THE NEW ELEMENT */ /* ========================================================================= */ CAMD_DEBUG2 (("ME = "ID" DONE\n", me)) ; Nv [me] = nvpiv ; /* save the length of the list for the new element me */ Len [me] = p - pme1 ; if (Len [me] == 0) { /* there is nothing left of the current pivot element */ /* it is a root of the assembly tree */ Pe [me] = EMPTY ; W [me] = 0 ; } if (elenme != 0) { /* element was not constructed in place: deallocate part of */ /* it since newly nonprincipal variables may have been removed */ pfree = p ; } /* Store the element back into BucketSet. This is the way to maintain * the order of roots (Pe[i]=-1) in each Constraint Set. */ BucketSet [pBucket2++] = me ; /* The new element has nvpiv pivots and the size of the contribution * block for a multifrontal method is degme-by-degme, not including * the "dense" rows/columns. If the "dense" rows/columns are included, * the frontal matrix is no larger than * (degme+ndense)-by-(degme+ndense). */ if (Info != (double *) NULL) { f = nvpiv ; r = degme + ndense ; dmax = MAX (dmax, f + r) ; /* number of nonzeros in L (excluding the diagonal) */ lnzme = f*r + (f-1)*f/2 ; lnz += lnzme ; /* number of divide operations for LDL' and for LU */ ndiv += lnzme ; /* number of multiply-subtract pairs for LU */ s = f*r*r + r*(f-1)*f + (f-1)*f*(2*f-1)/6 ; nms_lu += s ; /* number of multiply-subtract pairs for LDL' */ nms_ldl += (s + lnzme)/2 ; } #ifndef NDEBUG CAMD_DEBUG2 (("finalize done nel "ID" n "ID"\n ::::\n", nel, n)) ; for (pme = Pe [me] ; pme <= Pe [me] + Len [me] - 1 ; pme++) { CAMD_DEBUG3 ((" "ID"", Iw [pme])) ; } CAMD_DEBUG3 (("\n")) ; #endif } /* ========================================================================= */ /* DONE SELECTING PIVOTS */ /* ========================================================================= */ if (Info != (double *) NULL) { /* count the work to factorize the ndense-by-ndense submatrix */ f = ndense ; dmax = MAX (dmax, (double) ndense) ; /* number of nonzeros in L (excluding the diagonal) */ lnzme = (f-1)*f/2 ; lnz += lnzme ; /* number of divide operations for LDL' and for LU */ ndiv += lnzme ; /* number of multiply-subtract pairs for LU */ s = (f-1)*f*(2*f-1)/6 ; nms_lu += s ; /* number of multiply-subtract pairs for LDL' */ nms_ldl += (s + lnzme)/2 ; /* number of nz's in L (excl. diagonal) */ Info [CAMD_LNZ] = lnz ; /* number of divide ops for LU and LDL' */ Info [CAMD_NDIV] = ndiv ; /* number of multiply-subtract pairs for LDL' */ Info [CAMD_NMULTSUBS_LDL] = nms_ldl ; /* number of multiply-subtract pairs for LU */ Info [CAMD_NMULTSUBS_LU] = nms_lu ; /* number of "dense" rows/columns */ Info [CAMD_NDENSE] = ndense ; /* largest front is dmax-by-dmax */ Info [CAMD_DMAX] = dmax ; /* number of garbage collections in CAMD */ Info [CAMD_NCMPA] = ncmpa ; /* successful ordering */ Info [CAMD_STATUS] = CAMD_OK ; } /* ========================================================================= */ /* POST-ORDERING */ /* ========================================================================= */ /* ------------------------------------------------------------------------- * Variables at this point: * * Pe: holds the elimination tree. The parent of j is FLIP (Pe [j]), * or EMPTY if j is a root. The tree holds both elements and * non-principal (unordered) variables absorbed into them. * Dense and empty variables are non-principal and unordered. They are * all represented by the fictitious node n (that is, Pe [i] = FLIP (n) * and Elen [i] = EMPTY if i is a dense or empty node). * * Elen: holds the size of each element, including the diagonal part. * FLIP (Elen [e]) > 0 if e is an element. For unordered * variables i, Elen [i] is EMPTY. * * Nv: Nv [e] > 0 is the number of pivots represented by the element e. * For unordered variables i, Nv [i] is zero. * * BucketSet: BucketSet [0.....pBucket2] holds all * the elements that removed during the elimination, in eliminated order. * * * Contents no longer needed: * W, Iw, Len, Degree, Head, Next, Last. * * The matrix itself has been destroyed. * * n: the size of the matrix. * ndense: the number of "dense" nodes. * nnull: the number of empty nodes (zero degree) * No other scalars needed (pfree, iwlen, etc.) * ------------------------------------------------------------------------- */ /* restore Pe */ for (i = 0 ; i < n ; i++) { Pe [i] = FLIP (Pe [i]) ; } /* restore Elen, for output information only */ for (i = 0 ; i < n ; i++) { Elen [i] = FLIP (Elen [i]) ; } /* Now, Pe [j] is the parent of j, or EMPTY if j is a root. * Pe [j] = n if j is a dense/empty node */ /* place all variables in the list of children of their parents */ for (j = n-1 ; j >= 0 ; j--) { if (Nv [j] > 0) continue ; /* skip if j is an element */ ASSERT (Pe [j] >= 0 && Pe [j] <= n) ; Next [j] = Head [Pe [j]] ; /* place j in list of its parent */ Head [Pe [j]] = j ; } /* place all elements in the list of children of their parents */ for (e = n-1 ; e >= 0 ; e--) { if (Nv [e] <= 0) continue ; /* skip if e is a variable */ if (Pe [e] == EMPTY) continue ; /* skip if e is a root */ Next [e] = Head [Pe [e]] ; /* place e in list of its parent */ Head [Pe [e]] = e ; } /* determine where to put the postordering permutation */ if (C != NULL && ndense_or_null > 0) { /* Perm needs to be computed in a temporary workspace, and then * transformed and copied into the output permutation, in Last */ Perm = Degree ; } else { /* the postorder computes the permutation directly, in Last */ Perm = Last ; } /* postorder the elements and their descendants (both elements and * variables), but not (yet) the dense/empty nodes */ for (k = 0 , i = 0 ; i < pBucket2 ; i++) { j = BucketSet [i] ; ASSERT (j >= 0 && j < n) ; if (Pe [j] == EMPTY) { k = CAMD_postorder (j, k, n, Head, Next, Perm, W) ; } } /* Perm [0..k-1] now contains a list of the nonempty/nondense nodes, * ordered via minimum degree and following the constraints. */ CAMD_DEBUG1 (("before dense/empty, k = "ID"\n", k)) ; fflush (stdout) ; ASSERT (k + ndense_or_null == n) ; if (ndense_or_null > 0) { if (C == NULL) { /* postorder the dense/empty nodes (the parent of all these is n) */ CAMD_postorder (n, k, n, Head, Next, Perm, W) ; } else { /* dense (or empty) nodes exist, AND C also exists. The dense/empty * nodes are a link list whose head is Head[n], and Next[i] gives the * next node after i in the list. They need to be sorted by their * constraints, and then merged with Perm [0..k-1].*/ /* count how many dense/empty nodes are in each constraint set */ Bucket = W ; /* use W as workspace (it has size n+1) */ /* count the number of dense/empty nodes in each constraint set */ for (c = 0 ; c <= cmax ; c++) { Bucket [c] = 0 ; } i = 0 ; for (j = Head [n] ; j != EMPTY ; j = Next [j]) { CAMD_DEBUG1 (("Dense/empty node: "ID" : "ID" "ID"\n", j, Pe [j], Elen [j])) ; fflush (stdout) ; ASSERT (Pe [j] == n && Elen [j] == EMPTY) ; i++ ; Bucket [C [j]]++ ; } ASSERT (i == ndense_or_null) ; /* find the cumulative sum of Bucket */ knt1 = 0 ; for (c = 0 ; c <= cmax ; c++) { i = Bucket [c] ; Bucket [c] = knt1 ; knt1 += i ; } CAMD_DEBUG1 (("knt1 "ID" dense/empty "ID"\n", knt1, ndense_or_null)); ASSERT (knt1 == ndense_or_null) ; /* place dense/empty nodes in BucketSet, in constraint order, * ties in natural order */ for (j = Head [n] ; j != EMPTY ; j = Next [j]) { BucketSet [Bucket [C [j]]++] = j ; } #ifndef NDEBUG /* each set is in monotonically increasing order of constraints */ for (i = 1 ; i < k ; i++) { ASSERT (C [Perm [i]] >= C [Perm [i-1]]) ; } for (i = 1 ; i < ndense_or_null ; i++) { /* in order of constraints, with ties in natural order */ ASSERT ( (C [BucketSet [i]] > C [BucketSet [i-1]]) || (C [BucketSet [i]] == C [BucketSet [i-1]] && (BucketSet [i] > BucketSet [i-1]))) ; } #endif /* merge Perm [0..k-1] and BucketSet [0..ndense+nnull] */ p1 = 0 ; p2 = 0 ; p3 = 0 ; while (p1 < k && p2 < ndense_or_null) { /* place the dense/empty nodes at the end of each constraint * set, after the non-dense/non-empty nodes in the same set */ if (C [Perm [p1]] <= C [BucketSet [p2]]) { /* non-dense/non-empty node */ Last [p3++] = Perm [p1++] ; } else { /* dense/empty node */ Last [p3++] = BucketSet [p2++] ; } } /* wrap up; either Perm[0..k-1] or BucketSet[ ] is used up */ while (p1 < k) { Last [p3++] = Perm [p1++] ; } while (p2 < ndense_or_null) { Last [p3++] = BucketSet [p2++] ; } } } #ifndef NDEBUG CAMD_DEBUG1 (("\nFinal constrained ordering:\n")) ; i = 0 ; CAMD_DEBUG1 (("Last ["ID"] = "ID", C["ID"] = "ID"\n", i, Last [i], Last [i], C [Last [i]])) ; for (i = 1 ; i < n ; i++) { CAMD_DEBUG1 (("Last ["ID"] = "ID", C["ID"] = "ID"\n", i, Last [i], Last [i], C [Last [i]])) ; /* This is the critical assertion. It states that the permutation * satisfies the constraints. */ ASSERT (C [Last [i]] >= C [Last [i-1]]) ; } #endif } SuiteSparse/CAMD/Source/camd_aat.c0000644001170100242450000001154510616401106015611 0ustar davisfac/* ========================================================================= */ /* === CAMD_aat ============================================================ */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/camd */ /* ------------------------------------------------------------------------- */ /* CAMD_aat: compute the symmetry of the pattern of A, and count the number of * nonzeros each column of A+A' (excluding the diagonal). Assumes the input * matrix has no errors, with sorted columns and no duplicates * (CAMD_valid (n, n, Ap, Ai) must be CAMD_OK, but this condition is not * checked). */ #include "camd_internal.h" GLOBAL size_t CAMD_aat /* returns nz in A+A' */ ( Int n, const Int Ap [ ], const Int Ai [ ], Int Len [ ], /* Len [j]: length of column j of A+A', excl diagonal*/ Int Tp [ ], /* workspace of size n */ double Info [ ] ) { Int p1, p2, p, i, j, pj, pj2, k, nzdiag, nzboth, nz ; double sym ; size_t nzaat ; #ifndef NDEBUG CAMD_debug_init ("CAMD AAT") ; for (k = 0 ; k < n ; k++) Tp [k] = EMPTY ; ASSERT (CAMD_valid (n, n, Ap, Ai) == CAMD_OK) ; #endif if (Info != (double *) NULL) { /* clear the Info array, if it exists */ for (i = 0 ; i < CAMD_INFO ; i++) { Info [i] = EMPTY ; } Info [CAMD_STATUS] = CAMD_OK ; } for (k = 0 ; k < n ; k++) { Len [k] = 0 ; } nzdiag = 0 ; nzboth = 0 ; nz = Ap [n] ; for (k = 0 ; k < n ; k++) { p1 = Ap [k] ; p2 = Ap [k+1] ; CAMD_DEBUG2 (("\nAAT Column: "ID" p1: "ID" p2: "ID"\n", k, p1, p2)) ; /* construct A+A' */ for (p = p1 ; p < p2 ; ) { /* scan the upper triangular part of A */ j = Ai [p] ; if (j < k) { /* entry A (j,k) is in the strictly upper triangular part, * add both A (j,k) and A (k,j) to the matrix A+A' */ Len [j]++ ; Len [k]++ ; CAMD_DEBUG3 ((" upper ("ID","ID") ("ID","ID")\n", j,k, k,j)); p++ ; } else if (j == k) { /* skip the diagonal */ p++ ; nzdiag++ ; break ; } else /* j > k */ { /* first entry below the diagonal */ break ; } /* scan lower triangular part of A, in column j until reaching * row k. Start where last scan left off. */ ASSERT (Tp [j] != EMPTY) ; ASSERT (Ap [j] <= Tp [j] && Tp [j] <= Ap [j+1]) ; pj2 = Ap [j+1] ; for (pj = Tp [j] ; pj < pj2 ; ) { i = Ai [pj] ; if (i < k) { /* A (i,j) is only in the lower part, not in upper. * add both A (i,j) and A (j,i) to the matrix A+A' */ Len [i]++ ; Len [j]++ ; CAMD_DEBUG3 ((" lower ("ID","ID") ("ID","ID")\n", i,j, j,i)) ; pj++ ; } else if (i == k) { /* entry A (k,j) in lower part and A (j,k) in upper */ pj++ ; nzboth++ ; break ; } else /* i > k */ { /* consider this entry later, when k advances to i */ break ; } } Tp [j] = pj ; } /* Tp [k] points to the entry just below the diagonal in column k */ Tp [k] = p ; } /* clean up, for remaining mismatched entries */ for (j = 0 ; j < n ; j++) { for (pj = Tp [j] ; pj < Ap [j+1] ; pj++) { i = Ai [pj] ; /* A (i,j) is only in the lower part, not in upper. * add both A (i,j) and A (j,i) to the matrix A+A' */ Len [i]++ ; Len [j]++ ; CAMD_DEBUG3 ((" lower cleanup ("ID","ID") ("ID","ID")\n", i,j, j,i)) ; } } /* --------------------------------------------------------------------- */ /* compute the symmetry of the nonzero pattern of A */ /* --------------------------------------------------------------------- */ /* Given a matrix A, the symmetry of A is: * B = tril (spones (A), -1) + triu (spones (A), 1) ; * sym = nnz (B & B') / nnz (B) ; * or 1 if nnz (B) is zero. */ if (nz == nzdiag) { sym = 1 ; } else { sym = (2 * (double) nzboth) / ((double) (nz - nzdiag)) ; } nzaat = 0 ; for (k = 0 ; k < n ; k++) { nzaat += Len [k] ; } CAMD_DEBUG1 (("CAMD nz in A+A', excluding diagonal (nzaat) = %g\n", (double) nzaat)) ; CAMD_DEBUG1 ((" nzboth: "ID" nz: "ID" nzdiag: "ID" symmetry: %g\n", nzboth, nz, nzdiag, sym)) ; if (Info != (double *) NULL) { Info [CAMD_STATUS] = CAMD_OK ; Info [CAMD_N] = n ; Info [CAMD_NZ] = nz ; Info [CAMD_SYMMETRY] = sym ; /* symmetry of pattern of A */ Info [CAMD_NZDIAG] = nzdiag ; /* nonzeros on diagonal of A */ Info [CAMD_NZ_A_PLUS_AT] = nzaat ; /* nonzeros in A+A' */ } return (nzaat) ; } SuiteSparse/CAMD/Source/camd_valid.c0000644001170100242450000000645510616401152016150 0ustar davisfac/* ========================================================================= */ /* === CAMD_valid ========================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/camd */ /* ------------------------------------------------------------------------- */ /* Check if a column-form matrix is valid or not. The matrix A is * n_row-by-n_col. The row indices of entries in column j are in * Ai [Ap [j] ... Ap [j+1]-1]. Required conditions are: * * n_row >= 0 * n_col >= 0 * nz = Ap [n_col] >= 0 number of entries in the matrix * Ap [0] == 0 * Ap [j] <= Ap [j+1] for all j in the range 0 to n_col. * Ai [0 ... nz-1] must be in the range 0 to n_row-1. * * If any of the above conditions hold, CAMD_INVALID is returned. If the * following condition holds, CAMD_OK_BUT_JUMBLED is returned (a warning, * not an error): * * row indices in Ai [Ap [j] ... Ap [j+1]-1] are not sorted in ascending * order, and/or duplicate entries exist. * * Otherwise, CAMD_OK is returned. */ #include "camd_internal.h" GLOBAL Int CAMD_valid ( /* inputs, not modified on output: */ Int n_row, /* A is n_row-by-n_col */ Int n_col, const Int Ap [ ], /* column pointers of A, of size n_col+1 */ const Int Ai [ ] /* row indices of A, of size nz = Ap [n_col] */ ) { Int nz, j, p1, p2, ilast, i, p, result = CAMD_OK ; if (n_row < 0 || n_col < 0 || Ap == NULL || Ai == NULL) { return (CAMD_INVALID) ; } nz = Ap [n_col] ; if (Ap [0] != 0 || nz < 0) { /* column pointers must start at Ap [0] = 0, and Ap [n] must be >= 0 */ CAMD_DEBUG0 (("column 0 pointer bad or nz < 0\n")) ; return (CAMD_INVALID) ; } for (j = 0 ; j < n_col ; j++) { p1 = Ap [j] ; p2 = Ap [j+1] ; CAMD_DEBUG2 (("\nColumn: "ID" p1: "ID" p2: "ID"\n", j, p1, p2)) ; if (p1 > p2) { /* column pointers must be ascending */ CAMD_DEBUG0 (("column "ID" pointer bad\n", j)) ; return (CAMD_INVALID) ; } ilast = EMPTY ; for (p = p1 ; p < p2 ; p++) { i = Ai [p] ; CAMD_DEBUG3 (("row: "ID"\n", i)) ; if (i < 0 || i >= n_row) { /* row index out of range */ CAMD_DEBUG0 (("index out of range, col "ID" row "ID"\n", j, i)); return (CAMD_INVALID) ; } if (i <= ilast) { /* row index unsorted, or duplicate entry present */ CAMD_DEBUG1 (("index unsorted/dupl col "ID" row "ID"\n", j, i)); result = CAMD_OK_BUT_JUMBLED ; } ilast = i ; } } return (result) ; } GLOBAL Int CAMD_cvalid /* return TRUE if the Constraint set is valid, * FALSE otherwise */ ( /* inputs, not modified on output: */ Int n, /* the length of constraint set */ const Int C [ ] /* constraint set */ ) { Int i ; if (C != NULL) { for (i = 0 ; i < n ; i++) { if (C [i] < 0 || C [i] > n - 1) { CAMD_DEBUG0 (("C["ID"] = "ID" invalid\n", i, C [i])) ; return (FALSE) ; } } } return (TRUE) ; } SuiteSparse/CAMD/Source/camd_global.c0000644001170100242450000000634110616401124016302 0ustar davisfac/* ========================================================================= */ /* === camd_global ========================================================= */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/camd */ /* ------------------------------------------------------------------------- */ #include #ifdef MATLAB_MEX_FILE #include "mex.h" #include "matrix.h" #endif #ifndef NULL #define NULL 0 #endif /* ========================================================================= */ /* === Default CAMD memory manager ========================================= */ /* ========================================================================= */ /* The user can redefine these global pointers at run-time to change the memory * manager used by CAMD. CAMD only uses malloc and free; realloc and calloc are * include for completeness, in case another package wants to use the same * memory manager as CAMD. * * If compiling as a MATLAB mexFunction, the default memory manager is mxMalloc. * You can also compile CAMD as a standard ANSI-C library and link a mexFunction * against it, and then redefine these pointers at run-time, in your * mexFunction. * * If -DNMALLOC is defined at compile-time, no memory manager is specified at * compile-time. You must then define these functions at run-time, before * calling CAMD, for CAMD to work properly. */ #ifndef NMALLOC #ifdef MATLAB_MEX_FILE /* MATLAB mexFunction: */ void *(*camd_malloc) (size_t) = mxMalloc ; void (*camd_free) (void *) = mxFree ; void *(*camd_realloc) (void *, size_t) = mxRealloc ; void *(*camd_calloc) (size_t, size_t) = mxCalloc ; #else /* standard ANSI-C: */ void *(*camd_malloc) (size_t) = malloc ; void (*camd_free) (void *) = free ; void *(*camd_realloc) (void *, size_t) = realloc ; void *(*camd_calloc) (size_t, size_t) = calloc ; #endif #else /* no memory manager defined at compile-time; you MUST define one at run-time */ void *(*camd_malloc) (size_t) = NULL ; void (*camd_free) (void *) = NULL ; void *(*camd_realloc) (void *, size_t) = NULL ; void *(*camd_calloc) (size_t, size_t) = NULL ; #endif /* ========================================================================= */ /* === Default CAMD printf routine ========================================= */ /* ========================================================================= */ /* The user can redefine this global pointer at run-time to change the printf * routine used by CAMD. If NULL, no printing occurs. * * If -DNPRINT is defined at compile-time, stdio.h is not included. Printing * can then be enabled at run-time by setting camd_printf to a non-NULL function. */ #ifndef NPRINT #ifdef MATLAB_MEX_FILE int (*camd_printf) (const char *, ...) = mexPrintf ; #else #include int (*camd_printf) (const char *, ...) = printf ; #endif #else int (*camd_printf) (const char *, ...) = NULL ; #endif SuiteSparse/CAMD/Source/camd_order.c0000644001170100242450000001367610616401137016172 0ustar davisfac/* ========================================================================= */ /* === CAMD_order ========================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/camd */ /* ------------------------------------------------------------------------- */ /* User-callable CAMD minimum degree ordering routine. See camd.h for * documentation. */ #include "camd_internal.h" /* ========================================================================= */ /* === CAMD_order ========================================================== */ /* ========================================================================= */ GLOBAL Int CAMD_order ( Int n, const Int Ap [ ], const Int Ai [ ], Int P [ ], double Control [ ], double Info [ ], const Int C [ ] ) { Int *Len, *S, nz, i, *Pinv, info, status, *Rp, *Ri, *Cp, *Ci, ok ; size_t nzaat, slen ; double mem = 0 ; #ifndef NDEBUG CAMD_debug_init ("camd") ; #endif /* clear the Info array, if it exists */ info = Info != (double *) NULL ; if (info) { for (i = 0 ; i < CAMD_INFO ; i++) { Info [i] = EMPTY ; } Info [CAMD_N] = n ; Info [CAMD_STATUS] = CAMD_OK ; } /* make sure inputs exist and n is >= 0 */ if (Ai == (Int *) NULL || Ap == (Int *) NULL || P == (Int *) NULL || n < 0) { if (info) Info [CAMD_STATUS] = CAMD_INVALID ; return (CAMD_INVALID) ; /* arguments are invalid */ } if (n == 0) { return (CAMD_OK) ; /* n is 0 so there's nothing to do */ } nz = Ap [n] ; if (info) { Info [CAMD_NZ] = nz ; } if (nz < 0) { if (info) Info [CAMD_STATUS] = CAMD_INVALID ; return (CAMD_INVALID) ; } /* check if n or nz will cause size_t overflow */ if ((size_t) n >= SIZE_T_MAX / sizeof (Int) || (size_t) nz >= SIZE_T_MAX / sizeof (Int)) { if (info) Info [CAMD_STATUS] = CAMD_OUT_OF_MEMORY ; return (CAMD_OUT_OF_MEMORY) ; /* problem too large */ } /* check the input matrix: CAMD_OK, CAMD_INVALID, or CAMD_OK_BUT_JUMBLED */ status = CAMD_valid (n, n, Ap, Ai) ; if (status == CAMD_INVALID) { if (info) Info [CAMD_STATUS] = CAMD_INVALID ; return (CAMD_INVALID) ; /* matrix is invalid */ } /* allocate two size-n integer workspaces */ Len = camd_malloc (n * sizeof (Int)) ; Pinv = camd_malloc (n * sizeof (Int)) ; mem += n ; mem += n ; if (!Len || !Pinv) { /* :: out of memory :: */ camd_free (Len) ; camd_free (Pinv) ; if (info) Info [CAMD_STATUS] = CAMD_OUT_OF_MEMORY ; return (CAMD_OUT_OF_MEMORY) ; } if (status == CAMD_OK_BUT_JUMBLED) { /* sort the input matrix and remove duplicate entries */ CAMD_DEBUG1 (("Matrix is jumbled\n")) ; Rp = camd_malloc ((n+1) * sizeof (Int)) ; Ri = camd_malloc (MAX (nz,1) * sizeof (Int)) ; mem += (n+1) ; mem += MAX (nz,1) ; if (!Rp || !Ri) { /* :: out of memory :: */ camd_free (Rp) ; camd_free (Ri) ; camd_free (Len) ; camd_free (Pinv) ; if (info) Info [CAMD_STATUS] = CAMD_OUT_OF_MEMORY ; return (CAMD_OUT_OF_MEMORY) ; } /* use Len and Pinv as workspace to create R = A' */ CAMD_preprocess (n, Ap, Ai, Rp, Ri, Len, Pinv) ; Cp = Rp ; Ci = Ri ; } else { /* order the input matrix as-is. No need to compute R = A' first */ Rp = NULL ; Ri = NULL ; Cp = (Int *) Ap ; Ci = (Int *) Ai ; } /* --------------------------------------------------------------------- */ /* determine the symmetry and count off-diagonal nonzeros in A+A' */ /* --------------------------------------------------------------------- */ nzaat = CAMD_aat (n, Cp, Ci, Len, P, Info) ; CAMD_DEBUG1 (("nzaat: %g\n", (double) nzaat)) ; ASSERT ((MAX (nz-n, 0) <= nzaat) && (nzaat <= 2 * (size_t) nz)) ; /* --------------------------------------------------------------------- */ /* allocate workspace for matrix, elbow room, and 7 size-n vectors */ /* --------------------------------------------------------------------- */ S = NULL ; slen = nzaat ; /* space for matrix */ ok = ((slen + nzaat/5) >= slen) ; /* check for size_t overflow */ slen += nzaat/5 ; /* add elbow room */ for (i = 0 ; ok && i < 8 ; i++) { ok = ((slen + n+1) > slen) ; /* check for size_t overflow */ slen += (n+1) ; /* size-n elbow room, 7 size-(n+1) workspace */ } mem += slen ; ok = ok && (slen < SIZE_T_MAX / sizeof (Int)) ; /* check for overflow */ ok = ok && (slen < Int_MAX) ; /* S[i] for Int i must be OK */ if (ok) { S = camd_malloc (slen * sizeof (Int)) ; } CAMD_DEBUG1 (("slen %g\n", (double) slen)) ; if (!S) { /* :: out of memory :: (or problem too large) */ camd_free (Rp) ; camd_free (Ri) ; camd_free (Len) ; camd_free (Pinv) ; if (info) Info [CAMD_STATUS] = CAMD_OUT_OF_MEMORY ; return (CAMD_OUT_OF_MEMORY) ; } if (info) { /* memory usage, in bytes. */ Info [CAMD_MEMORY] = mem * sizeof (Int) ; } /* --------------------------------------------------------------------- */ /* order the matrix */ /* --------------------------------------------------------------------- */ CAMD_1 (n, Cp, Ci, P, Pinv, Len, slen, S, Control, Info, C) ; /* --------------------------------------------------------------------- */ /* free the workspace */ /* --------------------------------------------------------------------- */ camd_free (Rp) ; camd_free (Ri) ; camd_free (Len) ; camd_free (Pinv) ; camd_free (S) ; if (info) Info [CAMD_STATUS] = status ; return (status) ; /* successful ordering */ } SuiteSparse/CAMD/Source/camd_defaults.c0000644001170100242450000000251210616401114016644 0ustar davisfac/* ========================================================================= */ /* === CAMD_defaults ======================================================= */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/camd */ /* ------------------------------------------------------------------------- */ /* User-callable. Sets default control parameters for CAMD. See camd.h * for details. */ #include "camd_internal.h" /* ========================================================================= */ /* === CAMD defaults ======================================================= */ /* ========================================================================= */ GLOBAL void CAMD_defaults ( double Control [ ] ) { Int i ; if (Control != (double *) NULL) { for (i = 0 ; i < CAMD_CONTROL ; i++) { Control [i] = 0 ; } Control [CAMD_DENSE] = CAMD_DEFAULT_DENSE ; Control [CAMD_AGGRESSIVE] = CAMD_DEFAULT_AGGRESSIVE ; } } SuiteSparse/CAMD/Source/camd_dump.c0000644001170100242450000001255510616402635016023 0ustar davisfac/* ========================================================================= */ /* === CAMD_dump =========================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/camd */ /* ------------------------------------------------------------------------- */ /* Debugging routines for CAMD. Not used if NDEBUG is not defined at compile- * time (the default). See comments in camd_internal.h on how to enable * debugging. Not user-callable. */ #include "camd_internal.h" #ifndef NDEBUG /* This global variable is present only when debugging */ GLOBAL Int CAMD_debug = -999 ; /* default is no debug printing */ /* ========================================================================= */ /* === CAMD_debug_init ===================================================== */ /* ========================================================================= */ /* Sets the debug print level, by reading the file debug.camd (if it exists) */ GLOBAL void CAMD_debug_init ( char *s ) { FILE *f ; f = fopen ("debug.camd", "r") ; if (f == (FILE *) NULL) { CAMD_debug = -999 ; } else { fscanf (f, ID, &CAMD_debug) ; fclose (f) ; } if (CAMD_debug >= 0) { printf ("%s: CAMD_debug_init, D= "ID"\n", s, CAMD_debug) ; } } /* ========================================================================= */ /* === CAMD_dump =========================================================== */ /* ========================================================================= */ /* Dump CAMD's data structure, except for the hash buckets. This routine * cannot be called when the hash buckets are non-empty. */ GLOBAL void CAMD_dump ( Int n, /* A is n-by-n */ Int Pe [ ], /* pe [0..n-1]: index in iw of start of row i */ Int Iw [ ], /* workspace of size iwlen, iwlen [0..pfree-1] * holds the matrix on input */ Int Len [ ], /* len [0..n-1]: length for row i */ Int iwlen, /* length of iw */ Int pfree, /* iw [pfree ... iwlen-1] is empty on input */ Int Nv [ ], /* nv [0..n-1] */ Int Next [ ], /* next [0..n-1] */ Int Last [ ], /* last [0..n-1] */ Int Head [ ], /* head [0..n-1] */ Int Elen [ ], /* size n */ Int Degree [ ], /* size n */ Int W [ ], /* size n */ Int nel, Int BucketSet [ ], const Int C [ ], Int CurC ) { Int i, pe, elen, nv, len, e, p, k, j, deg, w, cnt, ilast ; if (CAMD_debug < 0) return ; ASSERT (pfree <= iwlen) ; CAMD_DEBUG3 (("\nCAMD dump, pfree: "ID"\n", pfree)) ; for (i = 0 ; i < n ; i++) { pe = Pe [i] ; elen = Elen [i] ; nv = Nv [i] ; len = Len [i] ; w = W [i] ; if (elen >= EMPTY) { if (nv == 0) { CAMD_DEBUG4 (("\nI "ID": nonprincipal: ", i)) ; ASSERT (elen == EMPTY) ; if (pe == FLIP(n)) { CAMD_DEBUG4 ((" dense node\n")) ; ASSERT (w == 1) ; } else { ASSERT (pe < EMPTY) ; CAMD_DEBUG4 ((" i "ID" -> parent "ID"\n", i, FLIP (Pe[i]))); } } else { CAMD_DEBUG4 (("\nI "ID": active principal supervariable:\n",i)); CAMD_DEBUG4 ((" nv(i): "ID" Flag: %d\n", nv, (nv < 0))) ; ASSERT (elen >= 0) ; ASSERT (nv > 0 && pe >= 0) ; p = pe ; CAMD_DEBUG4 ((" e/s: ")) ; if (elen == 0) CAMD_DEBUG4 ((" : ")) ; ASSERT (pe + len <= pfree) ; for (k = 0 ; k < len ; k++) { j = Iw [p] ; CAMD_DEBUG4 ((" "ID"", j)) ; ASSERT (j >= 0 && j < n) ; if (k == elen-1) CAMD_DEBUG4 ((" : ")) ; p++ ; } CAMD_DEBUG4 (("\n")) ; } } else { e = i ; if (w == 0) { CAMD_DEBUG4 (("\nE "ID": absorbed element: w "ID"\n", e, w)) ; ASSERT (nv > 0 && pe < 0) ; CAMD_DEBUG4 ((" e "ID" -> parent "ID"\n", e, FLIP (Pe [e]))) ; } else { CAMD_DEBUG4 (("\nE "ID": unabsorbed element: w "ID"\n", e, w)) ; ASSERT (nv > 0 && pe >= 0) ; p = pe ; CAMD_DEBUG4 ((" : ")) ; ASSERT (pe + len <= pfree) ; for (k = 0 ; k < len ; k++) { j = Iw [p] ; CAMD_DEBUG4 ((" "ID"", j)) ; ASSERT (j >= 0 && j < n) ; p++ ; } CAMD_DEBUG4 (("\n")) ; } } CAMD_DEBUG4 (("C[i] is :"ID"\n", (C == NULL) ? 0 : C [i])); } /* this routine cannot be called when the hash buckets are non-empty */ CAMD_DEBUG4 (("\nDegree lists:\n")) ; if (nel >= 0) { cnt = 0 ; for (deg = 0 ; deg < n ; deg++) { if (Head [deg] == EMPTY) continue ; ilast = EMPTY ; CAMD_DEBUG4 ((ID": \n", deg)) ; for (i = Head [deg] ; i != EMPTY ; i = Next [i]) { CAMD_DEBUG4 ((" "ID" : next "ID" last "ID" deg "ID"\n", i, Next [i], Last [i], Degree [i])) ; ASSERT (i >= 0 && i < n && ilast == Last [i] && deg == Degree [i]) ; cnt += Nv [i] ; ilast = i ; } CAMD_DEBUG4 (("\n")) ; } } CAMD_DEBUG4(("\nCurrent C[i] is "ID". current Buckets are:\n", CurC)) ; for (i = 0 ; i < n ; i++) { if ((C == NULL) ? 1 : (C [BucketSet [i]] <= CurC)) CAMD_DEBUG4((ID",",BucketSet [i])); } CAMD_DEBUG4 (("\n")) ; } #endif SuiteSparse/CAMD/Source/camd_info.c0000644001170100242450000001020610616401134015771 0ustar davisfac/* ========================================================================= */ /* === CAMD_info =========================================================== */ /* ========================================================================= */ /* ------------------------------------------------------------------------- */ /* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */ /* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */ /* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */ /* web: http://www.cise.ufl.edu/research/sparse/camd */ /* ------------------------------------------------------------------------- */ /* User-callable. Prints the output statistics for CAMD. See camd.h * for details. If the Info array is not present, nothing is printed. */ #include "camd_internal.h" #define PRI(format,x) { if (x >= 0) { PRINTF ((format, x)) ; }} GLOBAL void CAMD_info ( double Info [ ] ) { double n, ndiv, nmultsubs_ldl, nmultsubs_lu, lnz, lnzd ; if (!Info) { return ; } n = Info [CAMD_N] ; ndiv = Info [CAMD_NDIV] ; nmultsubs_ldl = Info [CAMD_NMULTSUBS_LDL] ; nmultsubs_lu = Info [CAMD_NMULTSUBS_LU] ; lnz = Info [CAMD_LNZ] ; lnzd = (n >= 0 && lnz >= 0) ? (n + lnz) : (-1) ; /* CAMD return status */ PRINTF (( "\ncamd: approximate minimum degree ordering, results:\n" " status: ")) ; if (Info [CAMD_STATUS] == CAMD_OK) { PRINTF (("OK\n")) ; } else if (Info [CAMD_STATUS] == CAMD_OUT_OF_MEMORY) { PRINTF (("out of memory\n")) ; } else if (Info [CAMD_STATUS] == CAMD_INVALID) { PRINTF (("invalid matrix\n")) ; } else if (Info [CAMD_STATUS] == CAMD_OK_BUT_JUMBLED) { PRINTF (("OK, but jumbled\n")) ; } else { PRINTF (("unknown\n")) ; } /* statistics about the input matrix */ PRI (" n, dimension of A: %.20g\n", n); PRI (" nz, number of nonzeros in A: %.20g\n", Info [CAMD_NZ]) ; PRI (" symmetry of A: %.4f\n", Info [CAMD_SYMMETRY]) ; PRI (" number of nonzeros on diagonal: %.20g\n", Info [CAMD_NZDIAG]) ; PRI (" nonzeros in pattern of A+A' (excl. diagonal): %.20g\n", Info [CAMD_NZ_A_PLUS_AT]) ; PRI (" # dense rows/columns of A+A': %.20g\n", Info [CAMD_NDENSE]) ; /* statistics about CAMD's behavior */ PRI (" memory used, in bytes: %.20g\n", Info [CAMD_MEMORY]) ; PRI (" # of memory compactions: %.20g\n", Info [CAMD_NCMPA]) ; /* statistics about the ordering quality */ PRINTF (("\n" " The following approximate statistics are for a subsequent\n" " factorization of A(P,P) + A(P,P)'. They are slight upper\n" " bounds if there are no dense rows/columns in A+A', and become\n" " looser if dense rows/columns exist.\n\n")) ; PRI (" nonzeros in L (excluding diagonal): %.20g\n", lnz) ; PRI (" nonzeros in L (including diagonal): %.20g\n", lnzd) ; PRI (" # divide operations for LDL' or LU: %.20g\n", ndiv) ; PRI (" # multiply-subtract operations for LDL': %.20g\n", nmultsubs_ldl) ; PRI (" # multiply-subtract operations for LU: %.20g\n", nmultsubs_lu) ; PRI (" max nz. in any column of L (incl. diagonal): %.20g\n", Info [CAMD_DMAX]) ; /* total flop counts for various factorizations */ if (n >= 0 && ndiv >= 0 && nmultsubs_ldl >= 0 && nmultsubs_lu >= 0) { PRINTF (("\n" " chol flop count for real A, sqrt counted as 1 flop: %.20g\n" " LDL' flop count for real A: %.20g\n" " LDL' flop count for complex A: %.20g\n" " LU flop count for real A (with no pivoting): %.20g\n" " LU flop count for complex A (with no pivoting): %.20g\n\n", n + ndiv + 2*nmultsubs_ldl, ndiv + 2*nmultsubs_ldl, 9*ndiv + 8*nmultsubs_ldl, ndiv + 2*nmultsubs_lu, 9*ndiv + 8*nmultsubs_lu)) ; } } SuiteSparse/CAMD/README.txt0000644001170100242450000002056410617112467014165 0ustar davisfacCAMD Version 2.2, Copyright (c) 2007 by Timothy A. Davis, Yanqing Chen, Patrick R. Amestoy, and Iain S. Duff. All Rights Reserved. CAMD is available under alternate licences; contact T. Davis for details. CAMD: a set of routines for permuting sparse matrices prior to factorization. Includes a version in C, a version in Fortran, and a MATLAB mexFunction. Requires UFconfig, in the ../UFconfig directory relative to this directory. Quick start (Unix, or Windows with Cygwin): To compile, test, and install CAMD, you may wish to first configure the installation by editting the ../UFconfig/UFconfig.mk file. Next, cd to this directory (CAMD) and type "make" (or "make lib" if you do not have MATLAB). When done, type "make clean" to remove unused *.o files (keeps the compiled libraries and demo programs). See the User Guide (Doc/CAMD_UserGuide.pdf), or ../UFconfig/UFconfig.mk for more details. Quick start (for MATLAB users); To compile, test, and install the CAMD mexFunction, cd to the CAMD/MATLAB directory and type camd_make at the MATLAB prompt. If you have MATLAB 7.2 or earlier and use "make mex", you must first edit UFconfig/UFconfig.h to remove the "-largeArrayDims" option from the MEX command (or just use camd_make.m inside MATLAB). ------------------------------------------------------------------------------- CAMD License: Your use or distribution of CAMD or any modified version of CAMD implies that you agree to this License. This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Permission is hereby granted to use or copy this program under the terms of the GNU LGPL, provided that the Copyright, this License, and the Availability of the original version is retained on all copies. User documentation of any code that uses this code or any modified version of this code must cite the Copyright, this License, the Availability note, and "Used by permission." Permission to modify the code and to distribute modified code is granted, provided the Copyright, this License, and the Availability note are retained, and a notice that the code was modified is included. Availability: http://www.cise.ufl.edu/research/sparse/camd ------------------------------------------------------------------------------- This is the CAMD README file. It is a terse overview of CAMD. Refer to the User Guide (Doc/CAMD_UserGuide.pdf) for how to install and use CAMD. Description: CAMD is a set of routines for pre-ordering sparse matrices prior to Cholesky or LU factorization, using the approximate minimum degree ordering algorithm with optional ordering constraints. Written in ANSI/ISO C with a MATLAB interface. Authors: Timothy A. Davis (davis at cise.ufl.edu), University of Florida. Patrick R. Amestory, ENSEEIHT, Toulouse, France. Iain S. Duff, Rutherford Appleton Laboratory, UK. Acknowledgements: This work was supported by the National Science Foundation, under grants DMS-9504974, DMS-9803599, and CCR-0203270. Portions of this work were done while on sabbatical at Stanford University and Lawrence Berkeley National Laboratory (with funding from the SciDAC program). I would like to thank Gene Golub, Esmond Ng, and Horst Simon for making this sabbatical possible. ------------------------------------------------------------------------------- Files and directories in the CAMD distribution: ------------------------------------------------------------------------------- --------------------------------------------------------------------------- Subdirectories of the CAMD directory: --------------------------------------------------------------------------- Doc documentation Source primary source code Include include file for use in your code that calls CAMD Demo demo programs. also serves as test of the CAMD installation. MATLAB CAMD mexFunction for MATLAB, and supporting m-files Lib where the compiled C-callable and Fortran-callable CAMD libraries placed. --------------------------------------------------------------------------- Files in the CAMD directory: --------------------------------------------------------------------------- Makefile top-level Makefile for GNU make or original make. Windows users would require Cygwin to use "make" README.txt this file --------------------------------------------------------------------------- Doc directory: documentation --------------------------------------------------------------------------- ChangeLog change log License the CAMD License Makefile for creating the documentation CAMD_UserGuide.bib CAMD User Guide (references) CAMD_UserGuide.tex CAMD User Guide (LaTeX) CAMD_UserGuide.pdf CAMD User Guide (PDF) lesser.txt the GNU LGPL license docdiff tools for comparing CAMD with AMD cdiff camd.sed --------------------------------------------------------------------------- Source directory: --------------------------------------------------------------------------- camd_order.c user-callable, primary CAMD ordering routine camd_control.c user-callable, prints the control parameters camd_defaults.c user-callable, sets default control parameters camd_info.c user-callable, prints the statistics from CAMD camd_1.c non-user-callable, construct A+A' camd_2.c user-callable, primary ordering kernel (a C version of camd.f and camdbar.f, with post-ordering added) camd_aat.c non-user-callable, computes nnz (A+A') camd_dump.c non-user-callable, debugging routines camd_postorder.c non-user-callable, postorder camd_valid.c non-user-callable, verifies a matrix camd_preprocess.c non-user-callable, computes A', removes duplic --------------------------------------------------------------------------- Include directory: --------------------------------------------------------------------------- camd.h include file for C programs that use CAMD camd_internal.h non-user-callable, include file for CAMD --------------------------------------------------------------------------- Demo directory: --------------------------------------------------------------------------- Makefile for GNU make or original make camd_demo.c C demo program for CAMD camd_demo.out output of camd_demo.c camd_demo2.c C demo program for CAMD, jumbled matrix camd_demo2.out output of camd_demo2.c camd_l_demo.c C demo program for CAMD ("long" version) camd_l_demo.out output of camd_l_demo.c camd_simple.c simple C demo program for CAMD camd_simple.out output of camd_simple.c --------------------------------------------------------------------------- MATLAB directory: --------------------------------------------------------------------------- GNUmakefile a nice Makefile, for GNU make Makefile an ugly Unix Makefile (for older make's) Contents.m for "help camd" listing of toolbox contents camd.m MATLAB help file for CAMD camd_make.m MATLAB m-file for compiling CAMD mexFunction camd_install.m compile and install CAMD mexFunctions camd_mex.c CAMD mexFunction for MATLAB camd_demo.m MATLAB demo for CAMD camd_demo.m.out diary output of camd_demo.m can_24.mat input file for CAMD demo --------------------------------------------------------------------------- Lib directory: libcamd.a library placed here --------------------------------------------------------------------------- GNUmakefile a nice Makefile, for GNU make Makefile an ugly Unix Makefile (for older make's) libcamd.def CAMD definitions for Windows SuiteSparse/RBio/0000755001170100242450000000000010711661157012607 5ustar davisfacSuiteSparse/RBio/Doc/0000755001170100242450000000000010711430326013304 5ustar davisfacSuiteSparse/RBio/Doc/dodiff0000755001170100242450000000072210617637234014502 0ustar davisfac # complex vs real diff ../RBcread_64.f ../RBrread_64.f diff ../RBcread_32.f ../RBrread_32.f # 32 vs 64 bit diff ../RBcread_32.f ../RBcread_64.f diff ../RBcsplit_32.f ../RBcsplit_64.f diff ../RBraw_mex_32.f ../RBraw_mex_64.f diff ../RBread_32.f ../RBread_64.f diff ../RBread_mex_32.f ../RBread_mex_64.f diff ../RBrread_32.f ../RBrread_64.f diff ../RBtype_mex_32.f ../RBtype_mex_64.f diff ../RBwrite_32.f ../RBwrite_64.f diff ../RBwrite_mex_32.f ../RBwrite_mex_64.f SuiteSparse/RBio/Doc/License.txt0000644001170100242450000000163010621162160015425 0ustar davisfacRBio toolbox. Copyright (C) 2006-2007, Timothy A. Davis RBio is also available under other licenses; contact authors for details. http://www.cise.ufl.edu/research/sparse -------------------------------------------------------------------------------- RBio is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. RBio is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. SuiteSparse/RBio/Doc/gpl.txt0000644001170100242450000004313310532557055014645 0ustar davisfac GNU GENERAL PUBLIC LICENSE Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users. This General Public License applies to most of the Free Software Foundation's software and to any other program whose authors commit to using it. (Some other Free Software Foundation software is covered by the GNU Library General Public License instead.) You can apply it to your programs, too. 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If the Program specifies a version number of this License which applies to it and "any later version", you have the option of following the terms and conditions either of that version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of this License, you may choose any version ever published by the Free Software Foundation. 10. If you wish to incorporate parts of the Program into other free programs whose distribution conditions are different, write to the author to ask for permission. For software which is copyrighted by the Free Software Foundation, write to the Free Software Foundation; we sometimes make exceptions for this. Our decision will be guided by the two goals of preserving the free status of all derivatives of our free software and of promoting the sharing and reuse of software generally. NO WARRANTY 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. END OF TERMS AND CONDITIONS How to Apply These Terms to Your New Programs If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms. To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively convey the exclusion of warranty; and each file should have at least the "copyright" line and a pointer to where the full notice is found. Copyright (C) This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Also add information on how to contact you by electronic and paper mail. If the program is interactive, make it output a short notice like this when it starts in an interactive mode: Gnomovision version 69, Copyright (C) year name of author Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the program `Gnomovision' (which makes passes at compilers) written by James Hacker. , 1 April 1989 Ty Coon, President of Vice This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Library General Public License instead of this License. SuiteSparse/RBio/Doc/ChangeLog0000644001170100242450000000040710711430001015045 0ustar davisfacNov 1, 2007: version 1.1.1 * minor lint cleanup May 31, 2007: version 1.1 * port to 64-bit MATLAB. Tested on Linux 32-bit and 64-bit. Not tested on Windows, since I do not have a Fortran compiler on that platform. Dec 1, 2006: version 1.0 released SuiteSparse/RBio/Test/0000755001170100242450000000000010711435016013517 5ustar davisfacSuiteSparse/RBio/Test/lap_25.rb0000644001170100242450000000117410524711202015125 0ustar davisfacHB/lap_25; 1980; I. Duff; ed: I. Duff et al. |1177 5 1 4 0 psa 25 25 97 0 (26I3) (26I3) 1 5 10 15 20 23 27 32 37 42 45 49 54 59 64 67 71 76 81 86 89 91 93 95 97 98 1 2 6 7 2 3 6 7 8 3 4 7 8 9 4 5 8 9 10 5 9 10 6 7 11 12 7 8 11 12 13 8 9 12 13 14 9 10 13 14 15 10 14 15 11 12 16 17 12 13 16 17 18 13 14 17 18 19 14 15 18 19 20 15 19 20 16 17 21 22 17 18 21 22 23 18 19 22 23 24 19 20 23 24 25 20 24 25 21 22 22 23 23 24 24 25 25 SuiteSparse/RBio/Test/west0479.rb0000644001170100242450000011504410524630002015351 0ustar davisfacHB/west0479; 1983; A. Westerberg; ed: I. Duff et al. |267 508 30 96 382 rua 479 479 1910 0 (16I5) (20I4) (5E15.7) 1 4 7 10 12 14 19 24 27 30 33 37 40 43 46 48 50 55 58 61 64 67 70 73 76 78 80 82 84 86 88 90 92 96 102 104 106 109 113 116 119 122 125 128 130 132 137 142 145 148 151 155 158 161 164 166 168 173 176 179 182 185 188 191 193 195 197 199 201 203 205 207 209 213 219 221 223 226 230 233 236 238 239 246 248 249 257 261 296 304 306 307 321 335 349 353 382 387 389 390 401 412 423 431 440 444 447 448 460 472 484 492 508 514 517 518 530 542 554 563 572 581 590 599 608 617 626 635 644 653 662 671 680 689 698 707 716 725 734 743 752 761 770 778 786 794 802 810 818 821 824 827 830 833 836 839 842 845 848 851 854 857 860 863 866 869 872 876 880 884 891 901 903 905 912 917 923 926 928 930 932 934 936 938 940 942 944 947 950 953 956 959 962 965 968 971 974 977 980 984 988 992 997 1005 1007 1009 1015 1018 1022 1023 1025 1027 1029 1031 1033 1035 1037 1039 1041 1049 1052 1055 1058 1059 1066 1073 1080 1088 1094 1095 1098 1099 1105 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LAPLACIAN ON A 5 BY 5 GRID. LAP 25 6 2 4 0 0 PSE 25 16 64 0 (16I5) (16I5) (16I5) 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 1 2 6 7 6 7 11 12 11 12 16 17 16 17 21 22 2 3 7 8 7 8 12 13 12 13 17 18 17 18 22 23 3 4 8 9 8 9 13 14 13 14 18 19 18 19 23 24 4 5 9 10 9 10 14 15 14 15 19 20 19 20 24 25 SuiteSparse/RBio/Test/farm.rb0000644001170100242450000000107010527062631014773 0ustar davisfacMeszaros/farm; 2004; ; ed: C. Meszaros |1710 6 1 2 3 ira 7 17 41 0 (26I3) (40I2) (20I4) 1 2 3 4 5 6 9 13 15 18 21 24 28 32 36 40 41 42 1 2 3 6 7 1 2 3 1 2 3 4 1 2 1 2 4 1 2 5 1 2 4 1 2 3 6 1 2 4 6 1 2 3 7 1 2 4 7 3 4 1 1 1 1 1 4 1 20 4 1 15 40 2 1 2 1 35 1 1 1 1 1 50 250 2 30 1 250 2 15 1 125 1 20 1 125 1 10 1 1 1 SuiteSparse/RBio/Test/bcsstk01.rb0000644001170100242450000001305610524626645015517 0ustar davisfacHB/bcsstk01; 1982; J. Lewis; ed: I. 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davisfacfunction testRB1 %testRB1: test the RBio toolbox. % % Example: % testRB1 % % See also UFget, RBread, RBreade, testRB2. % Copyright 2006, Timothy A. Davis files = { 'bcsstk01.rb' 'farm.rb' 'lap_25.pse' 'lap_25.rb' 'west0479.rb' 'west0479.rua' } ; for k = 1:length(files) file = files {k} ; fprintf ('%s : ', file) ; if (file (end) == 'e') [A Z] = RBreade (file) ; else [A Z] = RBread (file) ; end fprintf ('%s\n', RBtype (A)) ; RBwrite ('temp.rb', A, Z) ; [A2 Z2] = RBread ('temp.rb') ; if (~isequal (A, A2)) fprintf ('test failed: %s (A differs)\n', file) ; error ('!') ; end if (~isequal (Z, Z2)) fprintf ('test failed: %s (Z differs)\n', file) ; error ('!') ; end end load west0479 C = west0479 ; RBwrite ('mywest', C, 'WEST0479 chemical eng. problem', 'west0479') ; A = RBread ('mywest') ; if (~isequal (A, C)) error ('test failed: west0479 (MATLAB version)') ; end fprintf ('west0479 (MATLAB matrix) : %s\n', RBtype (A)) ; if (~strcmp (RBtype (A), 'rua')) error ('test failed: RBtype(A)\n') ; end if (~strcmp (RBtype (spones (A)), 'pua')) error ('test failed: RBtype(spones(A))\n') ; end if (~strcmp (RBtype (2*spones (A)), 'iua')) error ('test failed: RBtype(2*spones(A))\n') ; end C = A+A' ; if (~strcmp (RBtype (C), 'rsa')) error ('test failed: RBtype(A+A'')\n') ; end delete ('mywest') ; delete ('temp.rb') ; fprintf ('testRB1: all tests passed\n') ; SuiteSparse/RBio/Test/testRB2.m0000644001170100242450000000273310617665762015211 0ustar davisfacfunction testRB2 %testRB2: test the RBio toolbox. UFget is required. % Note that UFget requires the Nov 25, 2006, revision of the UF_Index.mat file, % or later, to access all the Problems used by this test. % % Example: % testRB2 % % See also UFget, RBread, RBreade, testRB1. % Copyright 2006, Timothy A. Davis Problem = UFget ('Meszaros/farm') ; disp (Problem) ; A = RBread ('farm.rb') ; if (~isequal (A, Problem.A)) error ('test failure: farm.rb') ; end fprintf ('mtype: %s\n', RBtype (A)) ; Problem = UFget ('HB/bcsstk01') ; disp (Problem) ; A = RBread ('bcsstk01.rb') ; if (~isequal (A, Problem.A)) error ('test failure: bcsstk01.rb') ; end fprintf ('mtype: %s\n', RBtype (A)) ; Problem = UFget ('HB/lap_25') ; disp (Problem) ; A = RBread ('lap_25.rb') ; if (~isequal (A, Problem.A)) error ('test failure: lap_25.rb') ; end A = RBreade ('lap_25.pse') ; if (~isequal (A, Problem.A)) error ('test failure: lap_25.pse') ; end fprintf ('mtype: %s\n', RBtype (A)) ; Problem = UFget ('HB/west0479') ; disp (Problem) ; [A Z] = RBread ('west0479.rb') ; if (~isequal (A, Problem.A)) error ('test failure: west0479.rb') ; end if (~isequal (Z, Problem.Zeros)) error ('test failure: west0479.rb') ; end [A Z] = RBread ('west0479.rua') ; if (~isequal (A, Problem.A)) error ('test failure: west0479.rua') ; end if (~isequal (Z, Problem.Zeros)) error ('test failure: west0479.rua') ; end fprintf ('mtype: %s\n', RBtype (A)) ; fprintf ('testRB2: all tests passed\n') ; SuiteSparse/RBio/RBwrite_mex_32.f0000644001170100242450000002461710634267663015533 0ustar davisfacc======================================================================= c=== RBio/RBwrite_mex_32 =============================================== c======================================================================= c RBio: a MATLAB toolbox for reading and writing sparse matrices in c Rutherford/Boeing format. c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida c----------------------------------------------------------------------- c RBwrite mexFunction: write a sparse matrix to a Rutherford/Boeing file c----------------------------------------------------------------------- c c mtype = RBwrite (filename, A, Z, title, key) c c A: a sparse matrix (no explicit zero entries) c Z: binary pattern of explicit zero entries to include in the c Rutherford/Boeing file. This always has the same size as A, c and is always sparse. Not used if [ ], or if nnz(Z) is 0. c title: title of Rutherford/Boeing file, up to 72 characters c key: the name of the matrix, up to 8 characters c c Z is optional. RBwrite (filename, A) uses a default c title and key, and does not include any explicit zeros. c RBwrite (filname, A, 'title...', 'key') uses the given title and c key, with no Z matrix. c c A must be sparse. Z must be empty, or sparse. c c mtype is a 3-character string with the file-type used c mtype(1): r: 0 (real), p: 1 (pattern), c: 2 (complex), c i: 3 (ineger) c mtype(2): r: -1 (rectangular), u: 0 (unsymmetric), s: 1 symmetric, c h: 2 (Hermitian), z: 3 (skew symmetric) c mtype(3): a: assembled matrix c----------------------------------------------------------------------- subroutine mexfunction (nargout, pargout, nargin, pargin) integer*4 $ pargout (*), pargin (*) integer*4 nargout, nargin c ---------------------------------------------------------------- c MATLAB functions c ---------------------------------------------------------------- integer*4 mxIsChar, mxClassIDFromClassName, $ mxIsClass, mxIsSparse, mxIsComplex integer*4 $ mxGetM, mxGetN, mxGetJc, mxGetIr, mxGetPr, mxGetPi, $ mxGetString, mxGetData, mxCreateNumericMatrix, $ mxCreateString c ---------------------------------------------------------------- c local variables c ---------------------------------------------------------------- integer*4 $ nrow, ncol, nnz, mkind, cp, info, zmin, zmax, $ skind, wmat, cpmat, ww, kmin, kmax, task, $ Ap, Ai, Ax, Az, Zp, Zi, Zx, Zz, znz, zrow, zcol, i, $ mzkind, szkind, totcrd, ptrcrd, indcrd, valcrd, nw, one, $ w, valn, valn2, indn, nnz2, ptrn, i1, ititle, vals integer*4 iclass, cmplex, wcmplex character title*72, key*8, mtype*3, ptrfmt*20, indfmt*20, $ valfmt*20, filename*1024, fmt2*20, ztype*3 double precision t logical doZ, l1, is_int c ---------------------------------------------------------------- c check inputs c ---------------------------------------------------------------- if (nargin .lt. 2 .or. nargin .gt. 5. .or. nargout .gt. 2 .or. $ mxIsChar (pargin (1)) .ne. 1) then call mexErrMsgTxt $ ('[m s] = RBwrite (filename, A, Z, title, key)') endif c ---------------------------------------------------------------- c get filename c ---------------------------------------------------------------- if (mxGetString (pargin (1), filename, 1024) .ne. 0) then call mexErrMsgTxt ('filename too long') endif close (unit = 7) open (unit = 7, file = filename, err = 998) c ---------------------------------------------------------------- c get A c ---------------------------------------------------------------- if (mxIsClass (pargin (2), 'double') .ne. 1 .or. $ mxIsSparse (pargin (2)) .ne. 1) then call mexErrMsgTxt ('A must be sparse and double') endif cmplex = mxIsComplex (pargin (2)) Ap = mxGetJc (pargin (2)) Ai = mxGetIr (pargin (2)) Ax = mxGetPr (pargin (2)) Az = mxGetPi (pargin (2)) nrow = mxGetM (pargin (2)) ncol = mxGetN (pargin (2)) c ---------------------------------------------------------------- c get title and key c ---------------------------------------------------------------- do 5 i = 1, 72 title (i:i) = ' ' 5 continue key = ' ' ititle = 99 do 15 i = 3, nargin if (mxIsChar (pargin (i)) .eq. 1) then if (ititle .eq. 99) then c get the title, up to 72 characters long i1 = mxGetString (pargin (i), title, 72) ititle = i else c get the key, up to 8 characters long i1 = mxGetString (pargin (i), key, 8) endif endif 15 continue c place a marker in the title, so we know that the c Rutherford/Boeing file was generated by the RBwrite mexFunction. title (72:72) = '|' c ---------------------------------------------------------------- c get Z, if present c ---------------------------------------------------------------- if (nargin .ge. 3 .and. ititle .gt. 3) then zrow = mxGetM (pargin (3)) zcol = mxGetN (pargin (3)) if (zrow .eq. 0 .or. zcol .eq. 0) then c -------------------------------------------------------- c Z matrix is empty c -------------------------------------------------------- doZ = .false. else c -------------------------------------------------------- c get the Z matrix c -------------------------------------------------------- if (mxIsClass (pargin (3), 'double') .ne. 1 .or. $ mxIsSparse (pargin (3)) .ne. 1 .or. $ mxIsComplex (pargin (3)) .ne. 0 .or. $ zrow .ne. nrow .or. zcol .ne. ncol) then call mexErrMsgTxt $ ('Z must be sparse, double, real, and same size as A') endif Zp = mxGetJc (pargin (3)) Zi = mxGetIr (pargin (3)) Zx = mxGetPr (pargin (3)) Zz = mxGetPi (pargin (3)) doZ = .true. endif else c ------------------------------------------------------------ c no Z matrix is present c ------------------------------------------------------------ doZ = .false. endif c ---------------------------------------------------------------- c get workspace c ---------------------------------------------------------------- iclass = mxClassIDFromClassName ('int32') nw = max (nrow, ncol) + 1 one = 1 wcomplex = 0 wmat = mxCreateNumericMatrix (nw, one, iclass, wcmplex) cpmat = mxCreateNumericMatrix (nw, one, iclass, wcmplex) w = mxGetData (wmat) cp = mxGetData (cpmat) c ---------------------------------------------------------------- c determine the matrix type (RSA, RUA, etc) c ---------------------------------------------------------------- c find the symmetry of A (mkind, skind), and nnz(A) call RBkind (nrow, ncol, %val(Ap), %val(Ai), %val(Ax), $ %val(Az), cmplex, mkind, skind, mtype, nnz, %val(cp), $ kmin, kmax) if (doZ) then c find the symmetry of Z and find nnz(Z) call RBkind (nrow, ncol, %val(Zp), %val(Zi), %val(Zx), $ %val(Zz), 0, mzkind, szkind, ztype, znz, %val(cp), $ zmin, zmax) if (znz .eq. 0) then c ignore the Z matrix doZ = .false. elseif (szkind .le. 0) then c if Z is unsymmetric, then A+Z is unsymmetric too skind = szkind endif endif pargout (1) = mxCreateString (mtype) c ---------------------------------------------------------------- c determine the required precision c ---------------------------------------------------------------- indfmt = ' ' valfmt = ' ' is_int = mkind .eq. 3 ww = 1 if (mkind .ne. 1) then call RBformat (nnz, %val (Ax), ww, valfmt, valn, is_int, $ kmin, kmax) if (cmplex .eq. 1) then call RBformat (nnz, %val (Az), ww, valfmt, valn, is_int, $ kmin, kmax) endif endif c ---------------------------------------------------------------- c determine the number of entries in the matrix A+Z c ---------------------------------------------------------------- task = 1 call RBwrite (task, nrow, ncol, skind, cmplex, doZ, %val(Ap), $ %val(Ai), %val(Ax), %val(Az), %val(Zp), %val(Zi), mkind, $ indfmt, indn, valfmt, valn, nnz2, %val(w), %val(cp)) if (nnz2 .eq. 0) then call mexErrMsgTxt ('empty matrices not handled') endif c determine pointer format. ncol+1 integers, largest is nnz2+1 call RBiformat (1, nnz2+1, ptrfmt, ptrn, i) call RBcards (ncol+1, ptrn, ptrcrd) c determine row index format. nnz2 integers, largest is nrow call RBiformat (1, nrow, indfmt, indn, i) call RBcards (nnz2, indn, indcrd) c determine how many lines for the numerical values if (mkind .eq. 0 .or. mkind .eq. 3) then c real or integer vals = 1 elseif (mkind .eq. 1) then c pattern vals = 0 else c complex vals = 2 endif call RBcards (vals*nnz2, valn, valcrd) c ---------------------------------------------------------------- c determine total number of cards c ---------------------------------------------------------------- totcrd = ptrcrd + indcrd + valcrd c ---------------------------------------------------------------- c write the header c ---------------------------------------------------------------- write (unit = 7, fmt = 10, err = 999) $ title, key, $ totcrd, ptrcrd, indcrd, valcrd, $ mtype, nrow, ncol, nnz2, 0, $ ptrfmt, indfmt, valfmt 10 format (a72, a8 / 4i14 / a3, 11x, 4i14 / 2a16, a20) c ---------------------------------------------------------------- c write the pointers c ---------------------------------------------------------------- call RBiflush (ptrfmt, %val (cp), ncol+1) c ---------------------------------------------------------------- c write the row indices c ---------------------------------------------------------------- task = 2 call RBwrite (task, nrow, ncol, skind, cmplex, doZ, %val(Ap), $ %val(Ai), %val(Ax), %val(Az), %val(Zp), %val(Zi), mkind, $ indfmt, indn, valfmt, valn, nnz2, %val(w), %val(cp)) c ---------------------------------------------------------------- c write the numerical values c ---------------------------------------------------------------- if (mkind .ne. 1) then task = 3 call RBwrite(task, nrow, ncol, skind, cmplex, doZ, %val(Ap), $ %val(Ai), %val(Ax), %val(Az), %val(Zp), %val(Zi), mkind, $ indfmt, indn, valfmt, valn, nnz2, %val(w), %val(cp)) endif c ---------------------------------------------------------------- c free workspace and return c ---------------------------------------------------------------- close (unit = 7) call mxDestroyArray (%val (cpmat)) return 998 call mexErrMsgTxt ('error openning file') 999 call mexErrMsgTxt ('error writing file') end SuiteSparse/RBio/RBwrite_mex_64.f0000644001170100242450000002461710617641041015523 0ustar davisfacc======================================================================= c=== RBio/RBwrite_mex_64 =============================================== c======================================================================= c RBio: a MATLAB toolbox for reading and writing sparse matrices in c Rutherford/Boeing format. c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida c----------------------------------------------------------------------- c RBwrite mexFunction: write a sparse matrix to a Rutherford/Boeing file c----------------------------------------------------------------------- c c mtype = RBwrite (filename, A, Z, title, key) c c A: a sparse matrix (no explicit zero entries) c Z: binary pattern of explicit zero entries to include in the c Rutherford/Boeing file. This always has the same size as A, c and is always sparse. Not used if [ ], or if nnz(Z) is 0. c title: title of Rutherford/Boeing file, up to 72 characters c key: the name of the matrix, up to 8 characters c c Z is optional. RBwrite (filename, A) uses a default c title and key, and does not include any explicit zeros. c RBwrite (filname, A, 'title...', 'key') uses the given title and c key, with no Z matrix. c c A must be sparse. Z must be empty, or sparse. c c mtype is a 3-character string with the file-type used c mtype(1): r: 0 (real), p: 1 (pattern), c: 2 (complex), c i: 3 (ineger) c mtype(2): r: -1 (rectangular), u: 0 (unsymmetric), s: 1 symmetric, c h: 2 (Hermitian), z: 3 (skew symmetric) c mtype(3): a: assembled matrix c----------------------------------------------------------------------- subroutine mexfunction (nargout, pargout, nargin, pargin) integer*8 $ pargout (*), pargin (*) integer*4 nargout, nargin c ---------------------------------------------------------------- c MATLAB functions c ---------------------------------------------------------------- integer*4 mxIsChar, mxClassIDFromClassName, $ mxIsClass, mxIsSparse, mxIsComplex integer*8 $ mxGetM, mxGetN, mxGetJc, mxGetIr, mxGetPr, mxGetPi, $ mxGetString, mxGetData, mxCreateNumericMatrix, $ mxCreateString c ---------------------------------------------------------------- c local variables c ---------------------------------------------------------------- integer*8 $ nrow, ncol, nnz, mkind, cp, info, zmin, zmax, $ skind, wmat, cpmat, ww, kmin, kmax, task, $ Ap, Ai, Ax, Az, Zp, Zi, Zx, Zz, znz, zrow, zcol, i, $ mzkind, szkind, totcrd, ptrcrd, indcrd, valcrd, nw, one, $ w, valn, valn2, indn, nnz2, ptrn, i1, ititle, vals integer*4 iclass, cmplex, wcmplex character title*72, key*8, mtype*3, ptrfmt*20, indfmt*20, $ valfmt*20, filename*1024, fmt2*20, ztype*3 double precision t logical doZ, l1, is_int c ---------------------------------------------------------------- c check inputs c ---------------------------------------------------------------- if (nargin .lt. 2 .or. nargin .gt. 5. .or. nargout .gt. 2 .or. $ mxIsChar (pargin (1)) .ne. 1) then call mexErrMsgTxt $ ('[m s] = RBwrite (filename, A, Z, title, key)') endif c ---------------------------------------------------------------- c get filename c ---------------------------------------------------------------- if (mxGetString (pargin (1), filename, 1024) .ne. 0) then call mexErrMsgTxt ('filename too long') endif close (unit = 7) open (unit = 7, file = filename, err = 998) c ---------------------------------------------------------------- c get A c ---------------------------------------------------------------- if (mxIsClass (pargin (2), 'double') .ne. 1 .or. $ mxIsSparse (pargin (2)) .ne. 1) then call mexErrMsgTxt ('A must be sparse and double') endif cmplex = mxIsComplex (pargin (2)) Ap = mxGetJc (pargin (2)) Ai = mxGetIr (pargin (2)) Ax = mxGetPr (pargin (2)) Az = mxGetPi (pargin (2)) nrow = mxGetM (pargin (2)) ncol = mxGetN (pargin (2)) c ---------------------------------------------------------------- c get title and key c ---------------------------------------------------------------- do 5 i = 1, 72 title (i:i) = ' ' 5 continue key = ' ' ititle = 99 do 15 i = 3, nargin if (mxIsChar (pargin (i)) .eq. 1) then if (ititle .eq. 99) then c get the title, up to 72 characters long i1 = mxGetString (pargin (i), title, 72) ititle = i else c get the key, up to 8 characters long i1 = mxGetString (pargin (i), key, 8) endif endif 15 continue c place a marker in the title, so we know that the c Rutherford/Boeing file was generated by the RBwrite mexFunction. title (72:72) = '|' c ---------------------------------------------------------------- c get Z, if present c ---------------------------------------------------------------- if (nargin .ge. 3 .and. ititle .gt. 3) then zrow = mxGetM (pargin (3)) zcol = mxGetN (pargin (3)) if (zrow .eq. 0 .or. zcol .eq. 0) then c -------------------------------------------------------- c Z matrix is empty c -------------------------------------------------------- doZ = .false. else c -------------------------------------------------------- c get the Z matrix c -------------------------------------------------------- if (mxIsClass (pargin (3), 'double') .ne. 1 .or. $ mxIsSparse (pargin (3)) .ne. 1 .or. $ mxIsComplex (pargin (3)) .ne. 0 .or. $ zrow .ne. nrow .or. zcol .ne. ncol) then call mexErrMsgTxt $ ('Z must be sparse, double, real, and same size as A') endif Zp = mxGetJc (pargin (3)) Zi = mxGetIr (pargin (3)) Zx = mxGetPr (pargin (3)) Zz = mxGetPi (pargin (3)) doZ = .true. endif else c ------------------------------------------------------------ c no Z matrix is present c ------------------------------------------------------------ doZ = .false. endif c ---------------------------------------------------------------- c get workspace c ---------------------------------------------------------------- iclass = mxClassIDFromClassName ('int64') nw = max (nrow, ncol) + 1 one = 1 wcomplex = 0 wmat = mxCreateNumericMatrix (nw, one, iclass, wcmplex) cpmat = mxCreateNumericMatrix (nw, one, iclass, wcmplex) w = mxGetData (wmat) cp = mxGetData (cpmat) c ---------------------------------------------------------------- c determine the matrix type (RSA, RUA, etc) c ---------------------------------------------------------------- c find the symmetry of A (mkind, skind), and nnz(A) call RBkind (nrow, ncol, %val(Ap), %val(Ai), %val(Ax), $ %val(Az), cmplex, mkind, skind, mtype, nnz, %val(cp), $ kmin, kmax) if (doZ) then c find the symmetry of Z and find nnz(Z) call RBkind (nrow, ncol, %val(Zp), %val(Zi), %val(Zx), $ %val(Zz), 0, mzkind, szkind, ztype, znz, %val(cp), $ zmin, zmax) if (znz .eq. 0) then c ignore the Z matrix doZ = .false. elseif (szkind .le. 0) then c if Z is unsymmetric, then A+Z is unsymmetric too skind = szkind endif endif pargout (1) = mxCreateString (mtype) c ---------------------------------------------------------------- c determine the required precision c ---------------------------------------------------------------- indfmt = ' ' valfmt = ' ' is_int = mkind .eq. 3 ww = 1 if (mkind .ne. 1) then call RBformat (nnz, %val (Ax), ww, valfmt, valn, is_int, $ kmin, kmax) if (cmplex .eq. 1) then call RBformat (nnz, %val (Az), ww, valfmt, valn, is_int, $ kmin, kmax) endif endif c ---------------------------------------------------------------- c determine the number of entries in the matrix A+Z c ---------------------------------------------------------------- task = 1 call RBwrite (task, nrow, ncol, skind, cmplex, doZ, %val(Ap), $ %val(Ai), %val(Ax), %val(Az), %val(Zp), %val(Zi), mkind, $ indfmt, indn, valfmt, valn, nnz2, %val(w), %val(cp)) if (nnz2 .eq. 0) then call mexErrMsgTxt ('empty matrices not handled') endif c determine pointer format. ncol+1 integers, largest is nnz2+1 call RBiformat (1, nnz2+1, ptrfmt, ptrn, i) call RBcards (ncol+1, ptrn, ptrcrd) c determine row index format. nnz2 integers, largest is nrow call RBiformat (1, nrow, indfmt, indn, i) call RBcards (nnz2, indn, indcrd) c determine how many lines for the numerical values if (mkind .eq. 0 .or. mkind .eq. 3) then c real or integer vals = 1 elseif (mkind .eq. 1) then c pattern vals = 0 else c complex vals = 2 endif call RBcards (vals*nnz2, valn, valcrd) c ---------------------------------------------------------------- c determine total number of cards c ---------------------------------------------------------------- totcrd = ptrcrd + indcrd + valcrd c ---------------------------------------------------------------- c write the header c ---------------------------------------------------------------- write (unit = 7, fmt = 10, err = 999) $ title, key, $ totcrd, ptrcrd, indcrd, valcrd, $ mtype, nrow, ncol, nnz2, 0, $ ptrfmt, indfmt, valfmt 10 format (a72, a8 / 4i14 / a3, 11x, 4i14 / 2a16, a20) c ---------------------------------------------------------------- c write the pointers c ---------------------------------------------------------------- call RBiflush (ptrfmt, %val (cp), ncol+1) c ---------------------------------------------------------------- c write the row indices c ---------------------------------------------------------------- task = 2 call RBwrite (task, nrow, ncol, skind, cmplex, doZ, %val(Ap), $ %val(Ai), %val(Ax), %val(Az), %val(Zp), %val(Zi), mkind, $ indfmt, indn, valfmt, valn, nnz2, %val(w), %val(cp)) c ---------------------------------------------------------------- c write the numerical values c ---------------------------------------------------------------- if (mkind .ne. 1) then task = 3 call RBwrite(task, nrow, ncol, skind, cmplex, doZ, %val(Ap), $ %val(Ai), %val(Ax), %val(Az), %val(Zp), %val(Zi), mkind, $ indfmt, indn, valfmt, valn, nnz2, %val(w), %val(cp)) endif c ---------------------------------------------------------------- c free workspace and return c ---------------------------------------------------------------- close (unit = 7) call mxDestroyArray (%val (cpmat)) return 998 call mexErrMsgTxt ('error openning file') 999 call mexErrMsgTxt ('error writing file') end SuiteSparse/RBio/Contents.m0000644001170100242450000000171710620377774014600 0ustar davisfac% RBio: MATLAB toolbox for reading/writing sparse matrices in the Rutherford/ % Boeing format, and for reading/writing problems in the UF Sparse Matrix % Collection from/to a set of files in a directory. % % RBread - read a sparse matrix from a Rutherford/Boeing file % RBreade - read a symmetric finite-element matrix from a R/B file % RBtype - determine the Rutherford/Boeing type of a sparse matrix % RBwrite - write a sparse matrix to a Rutherford/Boeing file % RBraw - read the raw contents of a Rutherford/Boeing file % RBfix - read a possibly corrupted matrix from a R/B file % RBinstall - install the RBio toolbox for use in MATLAB % RBmake - compile the RBio toolbox for use in MATLAB % % Example: % % load west0479 % C = west0479 ; % RBwrite ('mywest', C, 'WEST0479 chemical eng. problem', 'west0479') % A = RBread ('mywest') ; % norm (A-C,1) % % See also UFget, mread, mwrite. % Copyright 2007, Timothy A. Davis SuiteSparse/RBio/RBraw_mex_32.f0000644001170100242450000001531310617641067015156 0ustar davisfacc======================================================================= c=== RBio/RBraw_mex_32 ================================================= c======================================================================= c RBio: a MATLAB toolbox for reading and writing sparse matrices in c Rutherford/Boeing format. c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida c----------------------------------------------------------------------- c RBraw mexFunction: read the raw contents of a Rutherford/Boeing file c----------------------------------------------------------------------- c c [mtype Ap Ai Ax title key nrow] = RBraw (filename) c c mtype: Rutherford/Boeing matrix type (psa, rua, rsa, rse, ...) c Ap: column pointers (1-based) c Ai: row indices (1-based) c Ax: numerical values (real, complex, or integer). Empty for p*a c matrices. A complex matrix is read in as a single double array c Ax, where the kth entry has real value Ax(2*k-1) and imaginary c value Ax(2*k). c title: a string containing the title from the first line of the file c key: a string containing the 8-char key, from 1st line of the file c nrow: number of rows in the matrix c c This function works for both assembled and unassembled (finite- c element) matrices. It is also useful for checking the contents of a c Rutherford/Boeing file in detail, in case the file has invalid column c pointers, unsorted columns, duplicate entries, entries in the upper c triangular part of the file for a symmetric matrix, etc. c c Example: c c load west0479 c RBwrite ('mywest', west0479, [ ], 'My west0479 file', 'west0479') ; c [mtype Ap Ai Ax title key nrow] = RBraw ('mywest') ; c c See also RBfix, RBread, RBreade. c----------------------------------------------------------------------- subroutine mexfunction (nargout, pargout, nargin, pargin) integer*4 $ pargout (*), pargin (*) integer*4 nargout, nargin c ---------------------------------------------------------------- c MATLAB functions c ---------------------------------------------------------------- integer*4 mxIsChar, mxClassIDFromClassName integer*4 $ mxGetString, mxCreateString, mxCreateDoubleScalar, $ mxCreateNumericMatrix, mxGetData c ---------------------------------------------------------------- c local variables c ---------------------------------------------------------------- integer*4 $ nrow, ncol, nnz, mkind, info, skind, k, nelnz, one, zero integer*4 iclass, cmplex, wcmplex character title*72, key*8, mtype*3, ptrfmt*16, indfmt*16, $ valfmt*20, filename*1024 double precision x c ---------------------------------------------------------------- c check inputs c ---------------------------------------------------------------- if (nargin .ne. 1 .or. nargout .gt. 7 .or. $ mxIsChar (pargin (1)) .ne. 1) then call mexErrMsgTxt $ ('Usage: [mtype Ap Ai Ax title key nrow] = RBraw (filename)') endif c ---------------------------------------------------------------- c get filename and open file c ---------------------------------------------------------------- if (mxGetString (pargin (1), filename, 1024) .ne. 0) then call mexErrMsgTxt ('filename too long') endif close (unit = 7) open (unit = 7, file = filename, status = 'OLD', err = 998) c ---------------------------------------------------------------- c read the header and determine the matrix type c ---------------------------------------------------------------- call RBheader (title, key, mtype, nrow, ncol, nnz, $ ptrfmt, indfmt, valfmt, $ mkind, cmplex, skind, nelnz, info) call RBerr (info) c ---------------------------------------------------------------- c return the matrix type to MATLAB c ---------------------------------------------------------------- pargout (1) = mxCreateString (mtype) c ---------------------------------------------------------------- c read in the column pointers c ---------------------------------------------------------------- iclass = mxClassIDFromClassName ('int32') one = 1 zero = 0 wcmplex = 0 if (nargout .ge. 2) then pargout (2) = mxCreateNumericMatrix $ (ncol+1, one, iclass, wcmplex) call RBiread (ptrfmt, ncol+1, $ %val(mxGetData (pargout (2))), info) call RBerr (info) endif c ---------------------------------------------------------------- c read in the row indices c ---------------------------------------------------------------- if (nargout .ge. 3) then pargout (3) = mxCreateNumericMatrix $ (nnz, one, iclass, wcmplex) call RBiread (indfmt, nnz, $ %val(mxGetData (pargout (3))), info) if (info .lt. 0) then info = -93 endif call RBerr (info) endif c ---------------------------------------------------------------- c read in the numerical values c ---------------------------------------------------------------- if (nelnz .eq. 0) then k = nnz else k = nelnz endif if (nargout .ge. 4) then if (mkind .eq. 1) then c pattern-only: create an empty numerical array pargout (4) = mxCreateNumericMatrix (zero, zero, $ mxClassIDFromClassName ('double'), wcmplex) elseif (mkind .eq. 3) then c read in the numerical values (integer) pargout (4) = mxCreateNumericMatrix $ (k, one, iclass, wcmplex) call RBiread (valfmt, k, $ %val(mxGetData (pargout (4))), info) call RBerr (info) else c read in the numerical values (real or complex) if (cmplex .eq. 1) then k = 2*k endif pargout (4) = mxCreateNumericMatrix (k, one, $ mxClassIDFromClassName ('double'), wcmplex) call RBxread (valfmt, k, $ %val(mxGetData (pargout (4))), info) call RBerr (info) endif endif c ---------------------------------------------------------------- c return the title c ---------------------------------------------------------------- if (nargout .ge. 5) then pargout (5) = mxCreateString (title) endif c ---------------------------------------------------------------- c return the key c ---------------------------------------------------------------- if (nargout .ge. 6) then pargout (6) = mxCreateString (key) endif c ---------------------------------------------------------------- c return the number of rows c ---------------------------------------------------------------- if (nargout .ge. 7) then x = nrow pargout (7) = mxCreateDoubleScalar (x) endif c ---------------------------------------------------------------- c close file c ---------------------------------------------------------------- close (unit = 7) return c ---------------------------------------------------------------- c error return c ---------------------------------------------------------------- 998 call mexErrMsgTxt ('error opening file') end SuiteSparse/RBio/RBraw_mex_64.f0000644001170100242450000001531310617640747015167 0ustar davisfacc======================================================================= c=== RBio/RBraw_mex_64 ================================================= c======================================================================= c RBio: a MATLAB toolbox for reading and writing sparse matrices in c Rutherford/Boeing format. c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida c----------------------------------------------------------------------- c RBraw mexFunction: read the raw contents of a Rutherford/Boeing file c----------------------------------------------------------------------- c c [mtype Ap Ai Ax title key nrow] = RBraw (filename) c c mtype: Rutherford/Boeing matrix type (psa, rua, rsa, rse, ...) c Ap: column pointers (1-based) c Ai: row indices (1-based) c Ax: numerical values (real, complex, or integer). Empty for p*a c matrices. A complex matrix is read in as a single double array c Ax, where the kth entry has real value Ax(2*k-1) and imaginary c value Ax(2*k). c title: a string containing the title from the first line of the file c key: a string containing the 8-char key, from 1st line of the file c nrow: number of rows in the matrix c c This function works for both assembled and unassembled (finite- c element) matrices. It is also useful for checking the contents of a c Rutherford/Boeing file in detail, in case the file has invalid column c pointers, unsorted columns, duplicate entries, entries in the upper c triangular part of the file for a symmetric matrix, etc. c c Example: c c load west0479 c RBwrite ('mywest', west0479, [ ], 'My west0479 file', 'west0479') ; c [mtype Ap Ai Ax title key nrow] = RBraw ('mywest') ; c c See also RBfix, RBread, RBreade. c----------------------------------------------------------------------- subroutine mexfunction (nargout, pargout, nargin, pargin) integer*8 $ pargout (*), pargin (*) integer*4 nargout, nargin c ---------------------------------------------------------------- c MATLAB functions c ---------------------------------------------------------------- integer*4 mxIsChar, mxClassIDFromClassName integer*8 $ mxGetString, mxCreateString, mxCreateDoubleScalar, $ mxCreateNumericMatrix, mxGetData c ---------------------------------------------------------------- c local variables c ---------------------------------------------------------------- integer*8 $ nrow, ncol, nnz, mkind, info, skind, k, nelnz, one, zero integer*4 iclass, cmplex, wcmplex character title*72, key*8, mtype*3, ptrfmt*16, indfmt*16, $ valfmt*20, filename*1024 double precision x c ---------------------------------------------------------------- c check inputs c ---------------------------------------------------------------- if (nargin .ne. 1 .or. nargout .gt. 7 .or. $ mxIsChar (pargin (1)) .ne. 1) then call mexErrMsgTxt $ ('Usage: [mtype Ap Ai Ax title key nrow] = RBraw (filename)') endif c ---------------------------------------------------------------- c get filename and open file c ---------------------------------------------------------------- if (mxGetString (pargin (1), filename, 1024) .ne. 0) then call mexErrMsgTxt ('filename too long') endif close (unit = 7) open (unit = 7, file = filename, status = 'OLD', err = 998) c ---------------------------------------------------------------- c read the header and determine the matrix type c ---------------------------------------------------------------- call RBheader (title, key, mtype, nrow, ncol, nnz, $ ptrfmt, indfmt, valfmt, $ mkind, cmplex, skind, nelnz, info) call RBerr (info) c ---------------------------------------------------------------- c return the matrix type to MATLAB c ---------------------------------------------------------------- pargout (1) = mxCreateString (mtype) c ---------------------------------------------------------------- c read in the column pointers c ---------------------------------------------------------------- iclass = mxClassIDFromClassName ('int64') one = 1 zero = 0 wcmplex = 0 if (nargout .ge. 2) then pargout (2) = mxCreateNumericMatrix $ (ncol+1, one, iclass, wcmplex) call RBiread (ptrfmt, ncol+1, $ %val(mxGetData (pargout (2))), info) call RBerr (info) endif c ---------------------------------------------------------------- c read in the row indices c ---------------------------------------------------------------- if (nargout .ge. 3) then pargout (3) = mxCreateNumericMatrix $ (nnz, one, iclass, wcmplex) call RBiread (indfmt, nnz, $ %val(mxGetData (pargout (3))), info) if (info .lt. 0) then info = -93 endif call RBerr (info) endif c ---------------------------------------------------------------- c read in the numerical values c ---------------------------------------------------------------- if (nelnz .eq. 0) then k = nnz else k = nelnz endif if (nargout .ge. 4) then if (mkind .eq. 1) then c pattern-only: create an empty numerical array pargout (4) = mxCreateNumericMatrix (zero, zero, $ mxClassIDFromClassName ('double'), wcmplex) elseif (mkind .eq. 3) then c read in the numerical values (integer) pargout (4) = mxCreateNumericMatrix $ (k, one, iclass, wcmplex) call RBiread (valfmt, k, $ %val(mxGetData (pargout (4))), info) call RBerr (info) else c read in the numerical values (real or complex) if (cmplex .eq. 1) then k = 2*k endif pargout (4) = mxCreateNumericMatrix (k, one, $ mxClassIDFromClassName ('double'), wcmplex) call RBxread (valfmt, k, $ %val(mxGetData (pargout (4))), info) call RBerr (info) endif endif c ---------------------------------------------------------------- c return the title c ---------------------------------------------------------------- if (nargout .ge. 5) then pargout (5) = mxCreateString (title) endif c ---------------------------------------------------------------- c return the key c ---------------------------------------------------------------- if (nargout .ge. 6) then pargout (6) = mxCreateString (key) endif c ---------------------------------------------------------------- c return the number of rows c ---------------------------------------------------------------- if (nargout .ge. 7) then x = nrow pargout (7) = mxCreateDoubleScalar (x) endif c ---------------------------------------------------------------- c close file c ---------------------------------------------------------------- close (unit = 7) return c ---------------------------------------------------------------- c error return c ---------------------------------------------------------------- 998 call mexErrMsgTxt ('error opening file') end SuiteSparse/RBio/RBread_mex_32.f0000644001170100242450000001734710617641117015305 0ustar davisfacc======================================================================= c=== RBio/RBread_mex_32 ================================================ c======================================================================= c RBio: a MATLAB toolbox for reading and writing sparse matrices in c Rutherford/Boeing format. c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida c----------------------------------------------------------------------- c RBread mexFunction: read a sparse matrix from a Rutherford/Boeing file c----------------------------------------------------------------------- c c [A Z title key mtype] = RBread (filename) c c A: a sparse matrix (no explicit zero entries) c Z: binary pattern of explicit zero entries in Rutherford/Boeing file. c This always has the same size as A, and is always sparse. c c title: the 72-character title string in the file c key: the 8-character matrix name in the file c mtype: see RBwrite.m for a description. c c----------------------------------------------------------------------- subroutine mexfunction (nargout, pargout, nargin, pargin) integer*4 $ pargout (*), pargin (*) integer*4 nargout, nargin c ---------------------------------------------------------------- c MATLAB functions c ---------------------------------------------------------------- integer*4 mxIsChar, mxClassIDFromClassName integer*4 $ mxGetM, mxGetN, mxCreateSparse, mxGetJc, mxGetData, $ mxGetIr, mxGetPr, mxGetPi, mxGetString, mxCreateString, $ mxCreateNumericMatrix c ---------------------------------------------------------------- c local variables c ---------------------------------------------------------------- integer*4 $ nrow, ncol, nnz, mkind, w, cp, $ skind, wmat, cpmat, Zmat, nw, $ Ap, Ai, Ax, Az, Cmat, Cx, nzeros, info, Zp, Zi, Zx, i, $ nnz2, nnz1, nelnz, one integer*4 iclass, cmplex, wcmplex character title*72, key*8, mtype*3, ptrfmt*16, indfmt*16, $ valfmt*20, filename*1024 c ---------------------------------------------------------------- c check inputs c ---------------------------------------------------------------- if (nargin .ne. 1 .or. nargout .gt. 5 .or. $ mxIsChar (pargin (1)) .ne. 1) then call mexErrMsgTxt $ ('Usage: [A Z title key mtype] = RBread (filename)') endif c ---------------------------------------------------------------- c get filename and open file c ---------------------------------------------------------------- if (mxGetString (pargin (1), filename, 1024) .ne. 0) then call mexErrMsgTxt ('filename too long') endif close (unit = 7) open (unit = 7, file = filename, status = 'OLD', err = 998) rewind (unit = 7) c ---------------------------------------------------------------- c read the header and determine the matrix type c ---------------------------------------------------------------- call RBheader (title, key, mtype, nrow, ncol, nnz, $ ptrfmt, indfmt, valfmt, mkind, cmplex, skind, nelnz, info) if (nelnz .ne. 0) then c finite-element matrices not supported info = -5 endif call RBerr (info) c ---------------------------------------------------------------- c allocate result A c ---------------------------------------------------------------- if (skind .gt. 0) then c allocate enough space for upper triangular part (S,H,Z) nnz1 = 2 * nnz else nnz1 = nnz endif nnz1 = max (nnz1, 1) pargout (1) = mxCreateSparse (nrow, ncol, nnz1, cmplex) Ap = mxGetJc (pargout (1)) Ai = mxGetIr (pargout (1)) Ax = mxGetPr (pargout (1)) Az = mxGetPi (pargout (1)) c ---------------------------------------------------------------- c allocate workspace c ---------------------------------------------------------------- iclass = mxClassIDFromClassName ('int32') nw = max (nrow,ncol) + 1 wcmplex = 0 one = 1 wmat = mxCreateNumericMatrix (nw, one, iclass, wcmplex) cpmat = mxCreateNumericMatrix (ncol+1, one, iclass, wcmplex) w = mxGetData (wmat) cp = mxGetData (cpmat) c ---------------------------------------------------------------- c read in the sparse matrix c ---------------------------------------------------------------- if (mkind .eq. 2) then c complex matrices Cmat = mxCreateNumericMatrix (2 * nnz1, one, $ mxClassIDFromClassName ('double'), wcmplex) Cx = mxGetData (Cmat) call RBcread (nrow, ncol, nnz, ptrfmt, indfmt, valfmt, $ mkind, skind, %val (Ap), %val (Ai), %val (Cx), nzeros, $ %val (w), %val (cp), info, nw, nnz1) else c real, pattern, and integer matrices call RBrread (nrow, ncol, nnz, ptrfmt, indfmt, valfmt, $ mkind, skind, %val (Ap), %val (Ai), %val (Ax), nzeros, $ %val (w), %val (cp), info, nw, nnz1) endif call RBerr (info) close (unit = 7) c ---------------------------------------------------------------- c extract or discard explicit zero entries c ---------------------------------------------------------------- if (nargout .ge. 2) then c ------------------------------------------------------------ c extract explicit zeros from A and store them in Z c ------------------------------------------------------------ pargout (2) = mxCreateSparse $ (nrow, ncol, max (nzeros,1), wcmplex) Zp = mxGetJc (pargout (2)) Zi = mxGetIr (pargout (2)) Zx = mxGetPr (pargout (2)) if (mkind .eq. 2) then c complex matrices call RBczeros (nrow, ncol, %val (cp), $ %val (Ap), %val (Ai), %val (Cx), $ %val (Zp), %val (Zi), %val (Zx)) else c real, pattern-only, and integer matrices call RBrzeros (nrow, ncol, %val (cp), $ %val (Ap), %val (Ai), %val (Ax), $ %val (Zp), %val (Zi), %val (Zx)) endif c convert Z to zero-based call RBmangle (ncol, %val (Zp), %val (Zi), i) else c ------------------------------------------------------------ c discard explicit zero entries from A (do not keep them) c ------------------------------------------------------------ if (mkind .eq. 2) then c complex matrices call RBcprune (nrow, ncol, $ %val (Ap), %val (Ai), %val (Cx)) else c real, pattern-only, and integer matrices call RBrprune (nrow, ncol, $ %val (Ap), %val (Ai), %val (Ax)) endif endif c ---------------------------------------------------------------- c convert A to final MATLAB form (zero-based, split complex) c ---------------------------------------------------------------- call RBmangle (ncol, %val (Ap), %val (Ai), nnz2) if (mkind .eq. 2) then c convert Fortran-style complex values to MATLAB-style call RBcsplit (%val (Cx), %val (Ax), %val (Az), nnz2) call mxDestroyArray (%val (Cmat)) endif c ---------------------------------------------------------------- c return title c ---------------------------------------------------------------- if (nargout .ge. 3) then pargout (3) = mxCreateString (title) endif c ---------------------------------------------------------------- c return key c ---------------------------------------------------------------- if (nargout .ge. 4) then pargout (4) = mxCreateString (key) endif c ---------------------------------------------------------------- c return the matrix type to MATLAB c ---------------------------------------------------------------- if (nargout .ge. 5) then pargout (5) = mxCreateString (mtype) endif c ---------------------------------------------------------------- c free workspace and return c ---------------------------------------------------------------- call mxDestroyArray (%val (wmat)) call mxDestroyArray (%val (cpmat)) return c ---------------------------------------------------------------- c error return c ---------------------------------------------------------------- 998 call mexErrMsgTxt ('error opening file') end SuiteSparse/RBio/RBread_mex_64.f0000644001170100242450000001734710617640777015325 0ustar davisfacc======================================================================= c=== RBio/RBread_mex_64 ================================================ c======================================================================= c RBio: a MATLAB toolbox for reading and writing sparse matrices in c Rutherford/Boeing format. c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida c----------------------------------------------------------------------- c RBread mexFunction: read a sparse matrix from a Rutherford/Boeing file c----------------------------------------------------------------------- c c [A Z title key mtype] = RBread (filename) c c A: a sparse matrix (no explicit zero entries) c Z: binary pattern of explicit zero entries in Rutherford/Boeing file. c This always has the same size as A, and is always sparse. c c title: the 72-character title string in the file c key: the 8-character matrix name in the file c mtype: see RBwrite.m for a description. c c----------------------------------------------------------------------- subroutine mexfunction (nargout, pargout, nargin, pargin) integer*8 $ pargout (*), pargin (*) integer*4 nargout, nargin c ---------------------------------------------------------------- c MATLAB functions c ---------------------------------------------------------------- integer*4 mxIsChar, mxClassIDFromClassName integer*8 $ mxGetM, mxGetN, mxCreateSparse, mxGetJc, mxGetData, $ mxGetIr, mxGetPr, mxGetPi, mxGetString, mxCreateString, $ mxCreateNumericMatrix c ---------------------------------------------------------------- c local variables c ---------------------------------------------------------------- integer*8 $ nrow, ncol, nnz, mkind, w, cp, $ skind, wmat, cpmat, Zmat, nw, $ Ap, Ai, Ax, Az, Cmat, Cx, nzeros, info, Zp, Zi, Zx, i, $ nnz2, nnz1, nelnz, one integer*4 iclass, cmplex, wcmplex character title*72, key*8, mtype*3, ptrfmt*16, indfmt*16, $ valfmt*20, filename*1024 c ---------------------------------------------------------------- c check inputs c ---------------------------------------------------------------- if (nargin .ne. 1 .or. nargout .gt. 5 .or. $ mxIsChar (pargin (1)) .ne. 1) then call mexErrMsgTxt $ ('Usage: [A Z title key mtype] = RBread (filename)') endif c ---------------------------------------------------------------- c get filename and open file c ---------------------------------------------------------------- if (mxGetString (pargin (1), filename, 1024) .ne. 0) then call mexErrMsgTxt ('filename too long') endif close (unit = 7) open (unit = 7, file = filename, status = 'OLD', err = 998) rewind (unit = 7) c ---------------------------------------------------------------- c read the header and determine the matrix type c ---------------------------------------------------------------- call RBheader (title, key, mtype, nrow, ncol, nnz, $ ptrfmt, indfmt, valfmt, mkind, cmplex, skind, nelnz, info) if (nelnz .ne. 0) then c finite-element matrices not supported info = -5 endif call RBerr (info) c ---------------------------------------------------------------- c allocate result A c ---------------------------------------------------------------- if (skind .gt. 0) then c allocate enough space for upper triangular part (S,H,Z) nnz1 = 2 * nnz else nnz1 = nnz endif nnz1 = max (nnz1, 1) pargout (1) = mxCreateSparse (nrow, ncol, nnz1, cmplex) Ap = mxGetJc (pargout (1)) Ai = mxGetIr (pargout (1)) Ax = mxGetPr (pargout (1)) Az = mxGetPi (pargout (1)) c ---------------------------------------------------------------- c allocate workspace c ---------------------------------------------------------------- iclass = mxClassIDFromClassName ('int64') nw = max (nrow,ncol) + 1 wcmplex = 0 one = 1 wmat = mxCreateNumericMatrix (nw, one, iclass, wcmplex) cpmat = mxCreateNumericMatrix (ncol+1, one, iclass, wcmplex) w = mxGetData (wmat) cp = mxGetData (cpmat) c ---------------------------------------------------------------- c read in the sparse matrix c ---------------------------------------------------------------- if (mkind .eq. 2) then c complex matrices Cmat = mxCreateNumericMatrix (2 * nnz1, one, $ mxClassIDFromClassName ('double'), wcmplex) Cx = mxGetData (Cmat) call RBcread (nrow, ncol, nnz, ptrfmt, indfmt, valfmt, $ mkind, skind, %val (Ap), %val (Ai), %val (Cx), nzeros, $ %val (w), %val (cp), info, nw, nnz1) else c real, pattern, and integer matrices call RBrread (nrow, ncol, nnz, ptrfmt, indfmt, valfmt, $ mkind, skind, %val (Ap), %val (Ai), %val (Ax), nzeros, $ %val (w), %val (cp), info, nw, nnz1) endif call RBerr (info) close (unit = 7) c ---------------------------------------------------------------- c extract or discard explicit zero entries c ---------------------------------------------------------------- if (nargout .ge. 2) then c ------------------------------------------------------------ c extract explicit zeros from A and store them in Z c ------------------------------------------------------------ pargout (2) = mxCreateSparse $ (nrow, ncol, max (nzeros,1), wcmplex) Zp = mxGetJc (pargout (2)) Zi = mxGetIr (pargout (2)) Zx = mxGetPr (pargout (2)) if (mkind .eq. 2) then c complex matrices call RBczeros (nrow, ncol, %val (cp), $ %val (Ap), %val (Ai), %val (Cx), $ %val (Zp), %val (Zi), %val (Zx)) else c real, pattern-only, and integer matrices call RBrzeros (nrow, ncol, %val (cp), $ %val (Ap), %val (Ai), %val (Ax), $ %val (Zp), %val (Zi), %val (Zx)) endif c convert Z to zero-based call RBmangle (ncol, %val (Zp), %val (Zi), i) else c ------------------------------------------------------------ c discard explicit zero entries from A (do not keep them) c ------------------------------------------------------------ if (mkind .eq. 2) then c complex matrices call RBcprune (nrow, ncol, $ %val (Ap), %val (Ai), %val (Cx)) else c real, pattern-only, and integer matrices call RBrprune (nrow, ncol, $ %val (Ap), %val (Ai), %val (Ax)) endif endif c ---------------------------------------------------------------- c convert A to final MATLAB form (zero-based, split complex) c ---------------------------------------------------------------- call RBmangle (ncol, %val (Ap), %val (Ai), nnz2) if (mkind .eq. 2) then c convert Fortran-style complex values to MATLAB-style call RBcsplit (%val (Cx), %val (Ax), %val (Az), nnz2) call mxDestroyArray (%val (Cmat)) endif c ---------------------------------------------------------------- c return title c ---------------------------------------------------------------- if (nargout .ge. 3) then pargout (3) = mxCreateString (title) endif c ---------------------------------------------------------------- c return key c ---------------------------------------------------------------- if (nargout .ge. 4) then pargout (4) = mxCreateString (key) endif c ---------------------------------------------------------------- c return the matrix type to MATLAB c ---------------------------------------------------------------- if (nargout .ge. 5) then pargout (5) = mxCreateString (mtype) endif c ---------------------------------------------------------------- c free workspace and return c ---------------------------------------------------------------- call mxDestroyArray (%val (wmat)) call mxDestroyArray (%val (cpmat)) return c ---------------------------------------------------------------- c error return c ---------------------------------------------------------------- 998 call mexErrMsgTxt ('error opening file') end SuiteSparse/RBio/RBread_32.f0000644001170100242450000003031310617641102014412 0ustar davisfacc======================================================================= c=== RBio/RBread_32 ==================================================== c======================================================================= c RBio: a MATLAB toolbox for reading and writing sparse matrices in c Rutherford/Boeing format. c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida c----------------------------------------------------------------------- c RBheader: read Rutherford/Boeing header lines c----------------------------------------------------------------------- c c Rutherford/Boeing file type is a 3-character string: c c (1) R: real, C: complex, P: pattern only, I: integer c mkind: R: 0, P: 1, C: 2, I: 3 c c (2) S: symmetric, U: unsymmetric, H: Hermitian, Z: skew symmetric, c R: rectangular c skind: R: -1, U: 0, S: 1, H: 2, Z: 3 c c (3) A: assembled, E: element form c nelnz = 0 for A, number of elements for E c c pattern matrices are given numerical values of 1 (except PZA). c PZA matrices have +1 in the lower triangular part and -1 in c the upper triangular part. c c The matrix is nrow-by-ncol with nnz entries. c For symmetric matrices, Ai and Ax are of size 2*nnz (the upper c triangular part is constructed). To skip this construction, c pass skind = 0 to RBpattern. c----------------------------------------------------------------------- subroutine RBheader (title, key, mtype, nrow, ncol, nnz, $ ptrfmt, indfmt, valfmt, mkind, cmplex, skind, nelnz, info) integer*4 $ nrow, ncol, nnz, totcrd, ptrcrd, nelnz, $ indcrd, valcrd, mkind, skind, info integer*4 cmplex character title*72, key*8, mtype*3, ptrfmt*16, indfmt*16, $ valfmt*20, rhstyp*3 logical fem c ---------------------------------------------------------------- c read header lines 1-4 c ---------------------------------------------------------------- read (7, 10, err = 91, end = 91) $ title, key, $ totcrd, ptrcrd, indcrd, valcrd, $ mtype, nrow, ncol, nnz, nelnz, $ ptrfmt, indfmt, valfmt 10 format (a72, a8 / 4i14 / a3, 11x, 4i14 / 2a16, a20) if (nrow .lt. 0 .or. ncol .lt. 0 .or. nnz .lt. 0) then c error: invalid matrix dimensions info = -6 return endif c ---------------------------------------------------------------- c skip the Harwell/Boeing header line 5, if present c ---------------------------------------------------------------- read (7, 20, err = 91, end = 91) rhstyp 20 format (a3) if ((rhstyp (1:1) .eq. 'F' .or. rhstyp (1:1) .eq. 'f' .or. $ rhstyp (1:1) .eq. 'M' .or. rhstyp (1:1) .eq. 'm')) then c This is the 5th line Harwell/Boeing format. Ignore it. call mexErrMsgTxt ('Harwell/Boeing RHS ignored') else c Backspace one record, since we just read in one row of c the column pointers. backspace (unit = 7) endif c ---------------------------------------------------------------- c determine if real, pattern, integer, or complex c ---------------------------------------------------------------- if (mtype (1:1) .eq. 'R' .or. mtype (1:1) .eq. 'r') then c real mkind = 0 cmplex = 0 elseif (mtype (1:1) .eq. 'P' .or. mtype (1:1) .eq. 'p') then c pattern mkind = 1 cmplex = 0 elseif (mtype (1:1) .eq. 'C' .or. mtype (1:1) .eq. 'c') then c complex mkind = 2 cmplex = 1 elseif (mtype (1:1) .eq. 'I' .or. mtype (1:1) .eq. 'i') then c integer mkind = 3 cmplex = 0 else c error: invalid matrix type info = -5 return endif c ---------------------------------------------------------------- c determine if the upper part must be constructed c ---------------------------------------------------------------- if (mtype (2:2) .eq. 'R' .or. mtype (2:2) .eq. 'r') then c rectangular: RRA, PRA, IRA, and CRA matrices skind = -1 elseif (mtype (2:2) .eq. 'U' .or. mtype (2:2) .eq. 'u') then c unsymmetric: RUA, PUA, IUA, and CUA matrices skind = 0 elseif (mtype (2:2) .eq. 'S' .or. mtype (2:2) .eq. 's') then c symmetric: RSA, PSA, ISA, and CSA matrices skind = 1 elseif (mtype (2:2) .eq. 'H' .or. mtype (2:2) .eq. 'h') then c Hermitian: CHA (PHA, IHA, and RHA are valid, but atypical) skind = 2 elseif (mtype (2:2) .eq. 'Z' .or. mtype (2:2) .eq. 'z') then c skew symmetric: RZA, PZA, IZA, and CZA skind = 3 else c error: invalid matrix type info = -5 return endif c ---------------------------------------------------------------- c assembled matrices or elemental matrices (**A, **E) c ---------------------------------------------------------------- if (mtype (3:3) .eq. 'A' .or. mtype (3:3) .eq. 'a') then c assembled - ignore nelnz fem = .false. nelnz = 0 elseif (mtype (3:3) .eq. 'E' .or. mtype (3:3) .eq. 'e') then c finite-element fem = .true. continue else c error: invalid matrix type info = -5 return endif c ---------------------------------------------------------------- c assembled matrices must be square if skind is not R c ---------------------------------------------------------------- if (.not. fem .and. skind .ne. -1 .and. nrow .ne. ncol) then c error: invalid matrix dimensions info = -6 return endif c ---------------------------------------------------------------- c matrix is valid c ---------------------------------------------------------------- info = 0 return c ---------------------------------------------------------------- c error reading file c ---------------------------------------------------------------- 91 info = -91 return end c----------------------------------------------------------------------- c RBpattern: read the column pointers and row indices c----------------------------------------------------------------------- c w and cp are both of size ncol+1 (undefined on input). c c The matrix is contained in Ap, Ai, and Ax on output (undefined on c input). It has nzeros explicit zero entries. cp (1..ncol+1) are c the column pointers for the matrix Z that will contain all the c explicit zero entries. Ax is not read in (see RBrread and c RBcread). c c info is returned as: c 0 ok c -1 invalid column pointers c -2 row index out of range c -3 duplicate entry c -4 entries in upper triangular part of symmetric matrix c -5 invalid matrix type c -6 invalid dimensions c -7 matrix contains unsorted columns c -91 error reading file (header) c -92 error reading file (column pointers) c -93 error reading file (row indices) c -94 error reading file (numerical values: A, or sparse b) c----------------------------------------------------------------------- subroutine RBpattern (ptrfmt, indfmt, nrow, ncol, nnz, skind, $ Ap, Ai, w, cp, info, nw) integer*4 $ nrow, ncol, nnz, skind, info, Ap (ncol+1), Ai (nnz), $ nw, w (nw), cp (ncol+1) character ptrfmt*16, indfmt*16 integer*4 $ j, i, p, ilast c ---------------------------------------------------------------- c read the pointers and check them c ---------------------------------------------------------------- call RBiread (ptrfmt, ncol+1, Ap, info) if (info .lt. 0) then return endif if (Ap (1) .ne. 1 .or. Ap (ncol+1) - 1 .ne. nnz) then c error: invalid matrix (col pointers) info = -1 return endif do 10 j = 2, ncol+1 if (Ap (j) .lt. Ap (j-1)) then c error: invalid matrix (col pointers) info = -1 return endif 10 continue c ---------------------------------------------------------------- c read the row indices and check them c ---------------------------------------------------------------- call RBiread (indfmt, nnz, Ai, info) if (info .lt. 0) then info = -93 return endif do 20 i = 1, nrow w (i) = -1 20 continue do 40 j = 1, ncol ilast = 0 do 30 p = Ap (j), Ap (j+1) - 1 i = Ai (p) if (i .lt. 1 .or. i .gt. nrow) then c error: row index out of range c print *, 'column j, rows!', j, i, nrow info = -2 return endif if (w (i) .eq. j) then c error: duplicate entry in matrix c print *, 'column j, duplicate!', j, i info = -3 return endif w (i) = j if (i .lt. ilast) then c error: matrix contains unsorted columns c print *, 'column j, unsorted!', j, i, ilast info = -7 return endif ilast = i 30 continue 40 continue c ---------------------------------------------------------------- c construct new column pointers for symmetric matrices c ---------------------------------------------------------------- if (skind .gt. 0) then c ------------------------------------------------------------ c compute the column counts for the whole matrix c ------------------------------------------------------------ do 50 j = 1, ncol+1 w (j) = 0 50 continue do 70 j = 1, ncol do 60 p = Ap (j), Ap (j+1)-1 i = Ai (p) if (i .eq. j) then c diagonal entry, only appears as A(j,j) w (j) = w (j) + 1 elseif (i .gt. j) then c entry in lower triangular part, A(i,j) will be c duplicated as A(j,i), so count it in both cols w (i) = w (i) + 1 w (j) = w (j) + 1 else c error: entry in upper triangular part info = -4 return endif 60 continue 70 continue c ------------------------------------------------------------ c compute the new column pointers c ------------------------------------------------------------ cp (1) = 1 do 80 j = 2, ncol+1 cp (j) = cp (j-1) + w (j-1) 80 continue endif c ---------------------------------------------------------------- c matrix is valid c ---------------------------------------------------------------- info = 0 return end c----------------------------------------------------------------------- c RBmangle: convert 1-based matrix into 0-based c----------------------------------------------------------------------- subroutine RBmangle (ncol, Ap, Ai, nnz) integer*4 $ ncol, nnz, p, j, Ap (ncol+1), Ai (*) nnz = Ap (ncol + 1) - 1 do 10 j = 1, ncol+1 Ap (j) = Ap (j) - 1 10 continue do 20 p = 1, nnz Ai (p) = Ai (p) - 1 20 continue return end c----------------------------------------------------------------------- subroutine RBiread (ifmt, n, I, info) integer*4 $ n, I (n), info, p character ifmt*16 info = 0 read (7, ifmt, err = 92, end = 92) (I (p), p = 1, n) return 92 info = -92 return end c----------------------------------------------------------------------- subroutine RBxread (xfmt, n, X, info) integer*4 $ mkind, n, info, p double precision X (n) character xfmt*20 info = 0 read (7, xfmt, err = 94, end = 94) (X (p), p = 1, n) return 94 info = -94 return end c----------------------------------------------------------------------- c RBerr: report an error to MATLAB c----------------------------------------------------------------------- c c info = 0 is OK, info < 0 is a fatal error, info > 0 is a warning subroutine RBerr (info) integer*4 $ info if (info .eq. -7) then call mexErrMsgTxt ('matrix contains unsorted columns') elseif (info .eq. -1) then call mexErrMsgTxt ('invalid matrix (col pointers)') elseif (info .eq. -2) then call mexErrMsgTxt ('row index out of range)') elseif (info .eq. -3) then call mexErrMsgTxt ('duplicate entry in matrix') elseif (info .eq. -4) then call mexErrMsgTxt ('invalid symmetric matrix') elseif (info .eq. -5) then call mexErrMsgTxt ('invalid matrix type') elseif (info .eq. -6) then call mexErrMsgTxt ('invalid matrix dimensions') elseif (info .eq. -911) then call mexErrMsgTxt ('finite-element form not supported') elseif (info .eq. -91) then call mexErrMsgTxt ('error reading file (header)') elseif (info .eq. -92) then call mexErrMsgTxt ('error reading file (column pointers)') elseif (info .eq. -93) then call mexErrMsgTxt ('error reading file (row indices)') elseif (info .eq. -94) then call mexErrMsgTxt ('error reading file (numerical values)') elseif (info .eq. -95) then call mexErrMsgTxt ('error reading file (right-hand-side)') elseif (info .lt. 0) then print *, info call mexErrMsgTxt ('error (unspecified)') elseif (info .gt. 0) then print *, info call mexErrMsgTxt ('warning (unspecified)') endif return end SuiteSparse/RBio/RBread_64.f0000644001170100242450000003031310617640762014432 0ustar davisfacc======================================================================= c=== RBio/RBread_64 ==================================================== c======================================================================= c RBio: a MATLAB toolbox for reading and writing sparse matrices in c Rutherford/Boeing format. c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida c----------------------------------------------------------------------- c RBheader: read Rutherford/Boeing header lines c----------------------------------------------------------------------- c c Rutherford/Boeing file type is a 3-character string: c c (1) R: real, C: complex, P: pattern only, I: integer c mkind: R: 0, P: 1, C: 2, I: 3 c c (2) S: symmetric, U: unsymmetric, H: Hermitian, Z: skew symmetric, c R: rectangular c skind: R: -1, U: 0, S: 1, H: 2, Z: 3 c c (3) A: assembled, E: element form c nelnz = 0 for A, number of elements for E c c pattern matrices are given numerical values of 1 (except PZA). c PZA matrices have +1 in the lower triangular part and -1 in c the upper triangular part. c c The matrix is nrow-by-ncol with nnz entries. c For symmetric matrices, Ai and Ax are of size 2*nnz (the upper c triangular part is constructed). To skip this construction, c pass skind = 0 to RBpattern. c----------------------------------------------------------------------- subroutine RBheader (title, key, mtype, nrow, ncol, nnz, $ ptrfmt, indfmt, valfmt, mkind, cmplex, skind, nelnz, info) integer*8 $ nrow, ncol, nnz, totcrd, ptrcrd, nelnz, $ indcrd, valcrd, mkind, skind, info integer*4 cmplex character title*72, key*8, mtype*3, ptrfmt*16, indfmt*16, $ valfmt*20, rhstyp*3 logical fem c ---------------------------------------------------------------- c read header lines 1-4 c ---------------------------------------------------------------- read (7, 10, err = 91, end = 91) $ title, key, $ totcrd, ptrcrd, indcrd, valcrd, $ mtype, nrow, ncol, nnz, nelnz, $ ptrfmt, indfmt, valfmt 10 format (a72, a8 / 4i14 / a3, 11x, 4i14 / 2a16, a20) if (nrow .lt. 0 .or. ncol .lt. 0 .or. nnz .lt. 0) then c error: invalid matrix dimensions info = -6 return endif c ---------------------------------------------------------------- c skip the Harwell/Boeing header line 5, if present c ---------------------------------------------------------------- read (7, 20, err = 91, end = 91) rhstyp 20 format (a3) if ((rhstyp (1:1) .eq. 'F' .or. rhstyp (1:1) .eq. 'f' .or. $ rhstyp (1:1) .eq. 'M' .or. rhstyp (1:1) .eq. 'm')) then c This is the 5th line Harwell/Boeing format. Ignore it. call mexErrMsgTxt ('Harwell/Boeing RHS ignored') else c Backspace one record, since we just read in one row of c the column pointers. backspace (unit = 7) endif c ---------------------------------------------------------------- c determine if real, pattern, integer, or complex c ---------------------------------------------------------------- if (mtype (1:1) .eq. 'R' .or. mtype (1:1) .eq. 'r') then c real mkind = 0 cmplex = 0 elseif (mtype (1:1) .eq. 'P' .or. mtype (1:1) .eq. 'p') then c pattern mkind = 1 cmplex = 0 elseif (mtype (1:1) .eq. 'C' .or. mtype (1:1) .eq. 'c') then c complex mkind = 2 cmplex = 1 elseif (mtype (1:1) .eq. 'I' .or. mtype (1:1) .eq. 'i') then c integer mkind = 3 cmplex = 0 else c error: invalid matrix type info = -5 return endif c ---------------------------------------------------------------- c determine if the upper part must be constructed c ---------------------------------------------------------------- if (mtype (2:2) .eq. 'R' .or. mtype (2:2) .eq. 'r') then c rectangular: RRA, PRA, IRA, and CRA matrices skind = -1 elseif (mtype (2:2) .eq. 'U' .or. mtype (2:2) .eq. 'u') then c unsymmetric: RUA, PUA, IUA, and CUA matrices skind = 0 elseif (mtype (2:2) .eq. 'S' .or. mtype (2:2) .eq. 's') then c symmetric: RSA, PSA, ISA, and CSA matrices skind = 1 elseif (mtype (2:2) .eq. 'H' .or. mtype (2:2) .eq. 'h') then c Hermitian: CHA (PHA, IHA, and RHA are valid, but atypical) skind = 2 elseif (mtype (2:2) .eq. 'Z' .or. mtype (2:2) .eq. 'z') then c skew symmetric: RZA, PZA, IZA, and CZA skind = 3 else c error: invalid matrix type info = -5 return endif c ---------------------------------------------------------------- c assembled matrices or elemental matrices (**A, **E) c ---------------------------------------------------------------- if (mtype (3:3) .eq. 'A' .or. mtype (3:3) .eq. 'a') then c assembled - ignore nelnz fem = .false. nelnz = 0 elseif (mtype (3:3) .eq. 'E' .or. mtype (3:3) .eq. 'e') then c finite-element fem = .true. continue else c error: invalid matrix type info = -5 return endif c ---------------------------------------------------------------- c assembled matrices must be square if skind is not R c ---------------------------------------------------------------- if (.not. fem .and. skind .ne. -1 .and. nrow .ne. ncol) then c error: invalid matrix dimensions info = -6 return endif c ---------------------------------------------------------------- c matrix is valid c ---------------------------------------------------------------- info = 0 return c ---------------------------------------------------------------- c error reading file c ---------------------------------------------------------------- 91 info = -91 return end c----------------------------------------------------------------------- c RBpattern: read the column pointers and row indices c----------------------------------------------------------------------- c w and cp are both of size ncol+1 (undefined on input). c c The matrix is contained in Ap, Ai, and Ax on output (undefined on c input). It has nzeros explicit zero entries. cp (1..ncol+1) are c the column pointers for the matrix Z that will contain all the c explicit zero entries. Ax is not read in (see RBrread and c RBcread). c c info is returned as: c 0 ok c -1 invalid column pointers c -2 row index out of range c -3 duplicate entry c -4 entries in upper triangular part of symmetric matrix c -5 invalid matrix type c -6 invalid dimensions c -7 matrix contains unsorted columns c -91 error reading file (header) c -92 error reading file (column pointers) c -93 error reading file (row indices) c -94 error reading file (numerical values: A, or sparse b) c----------------------------------------------------------------------- subroutine RBpattern (ptrfmt, indfmt, nrow, ncol, nnz, skind, $ Ap, Ai, w, cp, info, nw) integer*8 $ nrow, ncol, nnz, skind, info, Ap (ncol+1), Ai (nnz), $ nw, w (nw), cp (ncol+1) character ptrfmt*16, indfmt*16 integer*8 $ j, i, p, ilast c ---------------------------------------------------------------- c read the pointers and check them c ---------------------------------------------------------------- call RBiread (ptrfmt, ncol+1, Ap, info) if (info .lt. 0) then return endif if (Ap (1) .ne. 1 .or. Ap (ncol+1) - 1 .ne. nnz) then c error: invalid matrix (col pointers) info = -1 return endif do 10 j = 2, ncol+1 if (Ap (j) .lt. Ap (j-1)) then c error: invalid matrix (col pointers) info = -1 return endif 10 continue c ---------------------------------------------------------------- c read the row indices and check them c ---------------------------------------------------------------- call RBiread (indfmt, nnz, Ai, info) if (info .lt. 0) then info = -93 return endif do 20 i = 1, nrow w (i) = -1 20 continue do 40 j = 1, ncol ilast = 0 do 30 p = Ap (j), Ap (j+1) - 1 i = Ai (p) if (i .lt. 1 .or. i .gt. nrow) then c error: row index out of range c print *, 'column j, rows!', j, i, nrow info = -2 return endif if (w (i) .eq. j) then c error: duplicate entry in matrix c print *, 'column j, duplicate!', j, i info = -3 return endif w (i) = j if (i .lt. ilast) then c error: matrix contains unsorted columns c print *, 'column j, unsorted!', j, i, ilast info = -7 return endif ilast = i 30 continue 40 continue c ---------------------------------------------------------------- c construct new column pointers for symmetric matrices c ---------------------------------------------------------------- if (skind .gt. 0) then c ------------------------------------------------------------ c compute the column counts for the whole matrix c ------------------------------------------------------------ do 50 j = 1, ncol+1 w (j) = 0 50 continue do 70 j = 1, ncol do 60 p = Ap (j), Ap (j+1)-1 i = Ai (p) if (i .eq. j) then c diagonal entry, only appears as A(j,j) w (j) = w (j) + 1 elseif (i .gt. j) then c entry in lower triangular part, A(i,j) will be c duplicated as A(j,i), so count it in both cols w (i) = w (i) + 1 w (j) = w (j) + 1 else c error: entry in upper triangular part info = -4 return endif 60 continue 70 continue c ------------------------------------------------------------ c compute the new column pointers c ------------------------------------------------------------ cp (1) = 1 do 80 j = 2, ncol+1 cp (j) = cp (j-1) + w (j-1) 80 continue endif c ---------------------------------------------------------------- c matrix is valid c ---------------------------------------------------------------- info = 0 return end c----------------------------------------------------------------------- c RBmangle: convert 1-based matrix into 0-based c----------------------------------------------------------------------- subroutine RBmangle (ncol, Ap, Ai, nnz) integer*8 $ ncol, nnz, p, j, Ap (ncol+1), Ai (*) nnz = Ap (ncol + 1) - 1 do 10 j = 1, ncol+1 Ap (j) = Ap (j) - 1 10 continue do 20 p = 1, nnz Ai (p) = Ai (p) - 1 20 continue return end c----------------------------------------------------------------------- subroutine RBiread (ifmt, n, I, info) integer*8 $ n, I (n), info, p character ifmt*16 info = 0 read (7, ifmt, err = 92, end = 92) (I (p), p = 1, n) return 92 info = -92 return end c----------------------------------------------------------------------- subroutine RBxread (xfmt, n, X, info) integer*8 $ mkind, n, info, p double precision X (n) character xfmt*20 info = 0 read (7, xfmt, err = 94, end = 94) (X (p), p = 1, n) return 94 info = -94 return end c----------------------------------------------------------------------- c RBerr: report an error to MATLAB c----------------------------------------------------------------------- c c info = 0 is OK, info < 0 is a fatal error, info > 0 is a warning subroutine RBerr (info) integer*8 $ info if (info .eq. -7) then call mexErrMsgTxt ('matrix contains unsorted columns') elseif (info .eq. -1) then call mexErrMsgTxt ('invalid matrix (col pointers)') elseif (info .eq. -2) then call mexErrMsgTxt ('row index out of range)') elseif (info .eq. -3) then call mexErrMsgTxt ('duplicate entry in matrix') elseif (info .eq. -4) then call mexErrMsgTxt ('invalid symmetric matrix') elseif (info .eq. -5) then call mexErrMsgTxt ('invalid matrix type') elseif (info .eq. -6) then call mexErrMsgTxt ('invalid matrix dimensions') elseif (info .eq. -911) then call mexErrMsgTxt ('finite-element form not supported') elseif (info .eq. -91) then call mexErrMsgTxt ('error reading file (header)') elseif (info .eq. -92) then call mexErrMsgTxt ('error reading file (column pointers)') elseif (info .eq. -93) then call mexErrMsgTxt ('error reading file (row indices)') elseif (info .eq. -94) then call mexErrMsgTxt ('error reading file (numerical values)') elseif (info .eq. -95) then call mexErrMsgTxt ('error reading file (right-hand-side)') elseif (info .lt. 0) then print *, info call mexErrMsgTxt ('error (unspecified)') elseif (info .gt. 0) then print *, info call mexErrMsgTxt ('warning (unspecified)') endif return end SuiteSparse/RBio/RBinstall.m0000644001170100242450000000115310620377733014662 0ustar davisfac%RBINSTALL install the RBio toolbox for use in MATLAB % Compiles the Fortran mexFunctions RBread, RBwrite, RBtype, and RBraw, and % the C mexFunction UFfull_write, and adds the current directory to the MATLAB % path. % % Example: % % RBinstall % % See also RBread, RBwrite, RBtype, RBraw. % % Copyright 2007, Timothy A. Davis help RBio RBmake s = pwd ; addpath (s) ; cd Test testRB1 cd (s) fprintf ('\nRBio is ready to use. Your path has been modified for this\n') ; fprintf ('session, by adding the following path:\n') ; fprintf ('%s\n', s) ; fprintf ('Use the pathtool to modify your path permanently.\n') ; SuiteSparse/RBio/RBrread_32.f0000644001170100242450000001766110617641127014616 0ustar davisfacc======================================================================= c=== RBio/RBrread_32 =================================================== c======================================================================= c RBio: a MATLAB toolbox for reading and writing sparse matrices in c Rutherford/Boeing format. c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida c----------------------------------------------------------------------- c RB*read: read a Rutherford/Boeing matrix c----------------------------------------------------------------------- subroutine RBrread $ (nrow, ncol, nnz, ptrfmt, indfmt, valfmt, $ mkind, skind, Ap, Ai, Ax, nzeros, w, cp, info, nw, nnz1) integer*4 $ nrow, ncol, nnz, mkind, skind, p, j, i, alen, llen, k, $ ilast, nzeros, info, nw, nnz1 integer*4 $ Ap (ncol+1), Ai (nnz1), w (nw), cp (ncol+1) double precision Ax (nnz1), x character ptrfmt*16, indfmt*16, valfmt*20 character*4 s c ---------------------------------------------------------------- c read the column pointers and row indices c ---------------------------------------------------------------- call RBpattern (ptrfmt, indfmt, nrow, ncol, nnz, skind, $ Ap, Ai, w, cp, info, nw) if (info .ne. 0) then c error: pattern is invalid return endif c ---------------------------------------------------------------- c read the values c ---------------------------------------------------------------- if (mkind .eq. 1) then c pattern-only matrix, set all values to 1 do 10 i = 1, nnz Ax (i) = 1 10 continue elseif (mkind .eq. 3) then c Read in nnz integer values, then convert them to real. c use Ai as workspace. If the matrix is symmetric, Ai is c twice as big as nnz, so use Ai (nnz+1...2*nnz) as workspace. c Otherwise, for an iua matrix, use Ai (1..nnz) and then c rewind the file and read Ap and Ai back in again. if (skind .le. 0) then k = 0 else k = nnz endif read (7, valfmt, err = 94, end = 94) (Ai(p), p = k+1, k+nnz) do 5 p = 1, nnz Ax (p) = Ai (p+k) 5 continue if (skind .le. 0) then c now that Ai has been destroyed, rewind the file and read c in Ap and Ai again. Skip the 4-line header first. rewind (unit = 7) read (7, 15) (s (k:k), k = 1,4) 15 format (a1 / a1 / a1 / a1) call RBpattern (ptrfmt, indfmt, nrow, ncol, nnz, skind, $ Ap, Ai, w, cp, info, nw) if (info .ne. 0) then c error: pattern is invalid. This 'cannot' happen, c because the pattern was already read in above. return endif endif else c read nnz values read (7, valfmt, err = 94, end = 94) (Ax (p), p = 1, nnz) endif c ---------------------------------------------------------------- c construct upper triangular part for symmetric matrices c ---------------------------------------------------------------- c If skind is zero, then the upper part is not constructed. This c allows the caller to skip this part, and create the upper part c of a symmetric (S,H,Z) matrix. Just pass skind = 0. if (skind .gt. 0) then c ------------------------------------------------------------ c shift the matrix by adding gaps to the top of each column c ------------------------------------------------------------ do 30 j = ncol, 1, -1 c number of entries in lower tri. part (incl. diagonal) llen = Ap (j+1) - Ap (j) c number of entries in entire column alen = cp (j+1) - cp (j) c move the column from Ai (Ap(j) ... Ap(j+1)-1) c down to Ai (cp(j+1)-llen ... cp(j+1)-1), leaving a gap c at Ai (Ap(j) ... cp(j+1)-llen) do 20 k = 1, llen Ai (cp (j+1) - k) = Ai (Ap (j+1) - k) Ax (cp (j+1) - k) = Ax (Ap (j+1) - k) 20 continue 30 continue c ------------------------------------------------------------ c populate the upper triangular part c ------------------------------------------------------------ c create temporary column pointers to point to the gaps do 40 j = 1, ncol w (j) = cp (j) 40 continue do 60 j = 1, ncol c scan the entries in the lower tri. part, in c Ai (cp(j+1)-llen ... cp(j+1)-1) llen = Ap (j+1) - Ap (j) do 50 k = 1, llen c get the A(i,j) entry in the lower triangular part i = Ai (cp (j+1) - k) x = Ax (cp (j+1) - k) c add A(j,i) as the next entry in column i (excl diag) if (i .ne. j) then p = w (i) w (i) = w (i) + 1 Ai (p) = j if (skind .eq. 1) then c *SA matrix Ax (p) = x elseif (skind .eq. 2) then c *HA matrix Ax (p) = x else c *ZA matrix Ax (p) = -x endif endif 50 continue 60 continue c finalize the column pointers do 70 j = 1, ncol+1 Ap (j) = cp (j) 70 continue endif c ---------------------------------------------------------------- c count the number of explicit zeros c ---------------------------------------------------------------- nzeros = 0 do 90 j = 1, ncol cp (j) = nzeros + 1 do 80 p = Ap (j), Ap (j+1)-1 if (Ax (p) .eq. 0) then nzeros = nzeros + 1 endif 80 continue 90 continue cp (ncol+1) = nzeros + 1 c ---------------------------------------------------------------- c matrix is valid c ---------------------------------------------------------------- info = 0 return c ---------------------------------------------------------------- c error return c ---------------------------------------------------------------- 94 info = -94 return end c----------------------------------------------------------------------- c RB*zeros: extract explicit zero entries c----------------------------------------------------------------------- c c nrow-by-ncol: size of A and Z c cp: column pointers of Z on input c Ap, Ai, Ax: matrix with zeros on input, pruned on output c Zp, Zi, Zx: empty matrix on input, pattern of zeros on output c c----------------------------------------------------------------------- subroutine RBrzeros $ (nrow, ncol, cp, Ap, Ai, Ax, Zp, Zi, Zx) integer*4 $ nrow, ncol, Ap (ncol+1), Ai (*), Zp (ncol+1), Zi (*), $ cp (*), i, j, p, pa, pz, p1 double precision Ax (*), x double precision Zx (*) c ---------------------------------------------------------------- c copy the column pointers if Z is being constructed c ---------------------------------------------------------------- do 10 j = 1, ncol+1 Zp (j) = cp (j) 10 continue c ---------------------------------------------------------------- c split the matrix c ---------------------------------------------------------------- pa = 1 pz = 1 do 30 j = 1, ncol c save the new start of column j of A p1 = Ap (j) Ap (j) = pa pz = Zp (j) c split column j of A do 20 p = p1, Ap (j+1)-1 i = Ai (p) x = Ax (p) if (x .eq. 0) then c copy into Z Zi (pz) = i Zx (pz) = 1 pz = pz + 1 else c copy into A Ai (pa) = i Ax (pa) = x pa = pa + 1 endif 20 continue 30 continue Ap (ncol+1) = pa return end c----------------------------------------------------------------------- c RB*prune: discard explicit zero entries c----------------------------------------------------------------------- c c nrow-by-ncol: size of A c Ap, Ai, Ax: matrix with zeros on input, pruned on output c c----------------------------------------------------------------------- subroutine RBrprune $ (nrow, ncol, Ap, Ai, Ax) integer*4 $ nrow, ncol, Ap (ncol+1), Ai (*), i, j, p, pa, pz, p1 double precision Ax (*), x c ---------------------------------------------------------------- c prune the matrix c ---------------------------------------------------------------- pa = 1 do 20 j = 1, ncol c save the new start of column j of A p1 = Ap (j) Ap (j) = pa c prune column j of A do 10 p = p1, Ap (j+1)-1 i = Ai (p) x = Ax (p) if (x .ne. 0) then c copy into A Ai (pa) = i Ax (pa) = x pa = pa + 1 endif 10 continue 20 continue Ap (ncol+1) = pa return end SuiteSparse/RBio/RBrread_64.f0000644001170100242450000001766110617641006014617 0ustar davisfacc======================================================================= c=== RBio/RBrread_64 =================================================== c======================================================================= c RBio: a MATLAB toolbox for reading and writing sparse matrices in c Rutherford/Boeing format. c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida c----------------------------------------------------------------------- c RB*read: read a Rutherford/Boeing matrix c----------------------------------------------------------------------- subroutine RBrread $ (nrow, ncol, nnz, ptrfmt, indfmt, valfmt, $ mkind, skind, Ap, Ai, Ax, nzeros, w, cp, info, nw, nnz1) integer*8 $ nrow, ncol, nnz, mkind, skind, p, j, i, alen, llen, k, $ ilast, nzeros, info, nw, nnz1 integer*8 $ Ap (ncol+1), Ai (nnz1), w (nw), cp (ncol+1) double precision Ax (nnz1), x character ptrfmt*16, indfmt*16, valfmt*20 character*4 s c ---------------------------------------------------------------- c read the column pointers and row indices c ---------------------------------------------------------------- call RBpattern (ptrfmt, indfmt, nrow, ncol, nnz, skind, $ Ap, Ai, w, cp, info, nw) if (info .ne. 0) then c error: pattern is invalid return endif c ---------------------------------------------------------------- c read the values c ---------------------------------------------------------------- if (mkind .eq. 1) then c pattern-only matrix, set all values to 1 do 10 i = 1, nnz Ax (i) = 1 10 continue elseif (mkind .eq. 3) then c Read in nnz integer values, then convert them to real. c use Ai as workspace. If the matrix is symmetric, Ai is c twice as big as nnz, so use Ai (nnz+1...2*nnz) as workspace. c Otherwise, for an iua matrix, use Ai (1..nnz) and then c rewind the file and read Ap and Ai back in again. if (skind .le. 0) then k = 0 else k = nnz endif read (7, valfmt, err = 94, end = 94) (Ai(p), p = k+1, k+nnz) do 5 p = 1, nnz Ax (p) = Ai (p+k) 5 continue if (skind .le. 0) then c now that Ai has been destroyed, rewind the file and read c in Ap and Ai again. Skip the 4-line header first. rewind (unit = 7) read (7, 15) (s (k:k), k = 1,4) 15 format (a1 / a1 / a1 / a1) call RBpattern (ptrfmt, indfmt, nrow, ncol, nnz, skind, $ Ap, Ai, w, cp, info, nw) if (info .ne. 0) then c error: pattern is invalid. This 'cannot' happen, c because the pattern was already read in above. return endif endif else c read nnz values read (7, valfmt, err = 94, end = 94) (Ax (p), p = 1, nnz) endif c ---------------------------------------------------------------- c construct upper triangular part for symmetric matrices c ---------------------------------------------------------------- c If skind is zero, then the upper part is not constructed. This c allows the caller to skip this part, and create the upper part c of a symmetric (S,H,Z) matrix. Just pass skind = 0. if (skind .gt. 0) then c ------------------------------------------------------------ c shift the matrix by adding gaps to the top of each column c ------------------------------------------------------------ do 30 j = ncol, 1, -1 c number of entries in lower tri. part (incl. diagonal) llen = Ap (j+1) - Ap (j) c number of entries in entire column alen = cp (j+1) - cp (j) c move the column from Ai (Ap(j) ... Ap(j+1)-1) c down to Ai (cp(j+1)-llen ... cp(j+1)-1), leaving a gap c at Ai (Ap(j) ... cp(j+1)-llen) do 20 k = 1, llen Ai (cp (j+1) - k) = Ai (Ap (j+1) - k) Ax (cp (j+1) - k) = Ax (Ap (j+1) - k) 20 continue 30 continue c ------------------------------------------------------------ c populate the upper triangular part c ------------------------------------------------------------ c create temporary column pointers to point to the gaps do 40 j = 1, ncol w (j) = cp (j) 40 continue do 60 j = 1, ncol c scan the entries in the lower tri. part, in c Ai (cp(j+1)-llen ... cp(j+1)-1) llen = Ap (j+1) - Ap (j) do 50 k = 1, llen c get the A(i,j) entry in the lower triangular part i = Ai (cp (j+1) - k) x = Ax (cp (j+1) - k) c add A(j,i) as the next entry in column i (excl diag) if (i .ne. j) then p = w (i) w (i) = w (i) + 1 Ai (p) = j if (skind .eq. 1) then c *SA matrix Ax (p) = x elseif (skind .eq. 2) then c *HA matrix Ax (p) = x else c *ZA matrix Ax (p) = -x endif endif 50 continue 60 continue c finalize the column pointers do 70 j = 1, ncol+1 Ap (j) = cp (j) 70 continue endif c ---------------------------------------------------------------- c count the number of explicit zeros c ---------------------------------------------------------------- nzeros = 0 do 90 j = 1, ncol cp (j) = nzeros + 1 do 80 p = Ap (j), Ap (j+1)-1 if (Ax (p) .eq. 0) then nzeros = nzeros + 1 endif 80 continue 90 continue cp (ncol+1) = nzeros + 1 c ---------------------------------------------------------------- c matrix is valid c ---------------------------------------------------------------- info = 0 return c ---------------------------------------------------------------- c error return c ---------------------------------------------------------------- 94 info = -94 return end c----------------------------------------------------------------------- c RB*zeros: extract explicit zero entries c----------------------------------------------------------------------- c c nrow-by-ncol: size of A and Z c cp: column pointers of Z on input c Ap, Ai, Ax: matrix with zeros on input, pruned on output c Zp, Zi, Zx: empty matrix on input, pattern of zeros on output c c----------------------------------------------------------------------- subroutine RBrzeros $ (nrow, ncol, cp, Ap, Ai, Ax, Zp, Zi, Zx) integer*8 $ nrow, ncol, Ap (ncol+1), Ai (*), Zp (ncol+1), Zi (*), $ cp (*), i, j, p, pa, pz, p1 double precision Ax (*), x double precision Zx (*) c ---------------------------------------------------------------- c copy the column pointers if Z is being constructed c ---------------------------------------------------------------- do 10 j = 1, ncol+1 Zp (j) = cp (j) 10 continue c ---------------------------------------------------------------- c split the matrix c ---------------------------------------------------------------- pa = 1 pz = 1 do 30 j = 1, ncol c save the new start of column j of A p1 = Ap (j) Ap (j) = pa pz = Zp (j) c split column j of A do 20 p = p1, Ap (j+1)-1 i = Ai (p) x = Ax (p) if (x .eq. 0) then c copy into Z Zi (pz) = i Zx (pz) = 1 pz = pz + 1 else c copy into A Ai (pa) = i Ax (pa) = x pa = pa + 1 endif 20 continue 30 continue Ap (ncol+1) = pa return end c----------------------------------------------------------------------- c RB*prune: discard explicit zero entries c----------------------------------------------------------------------- c c nrow-by-ncol: size of A c Ap, Ai, Ax: matrix with zeros on input, pruned on output c c----------------------------------------------------------------------- subroutine RBrprune $ (nrow, ncol, Ap, Ai, Ax) integer*8 $ nrow, ncol, Ap (ncol+1), Ai (*), i, j, p, pa, pz, p1 double precision Ax (*), x c ---------------------------------------------------------------- c prune the matrix c ---------------------------------------------------------------- pa = 1 do 20 j = 1, ncol c save the new start of column j of A p1 = Ap (j) Ap (j) = pa c prune column j of A do 10 p = p1, Ap (j+1)-1 i = Ai (p) x = Ax (p) if (x .ne. 0) then c copy into A Ai (pa) = i Ax (pa) = x pa = pa + 1 endif 10 continue 20 continue Ap (ncol+1) = pa return end SuiteSparse/RBio/README.txt0000644001170100242450000000772210711427431014310 0ustar davisfacRBio: Version 1.1.1, Nov 1, 2007. A MATLAB Toolbox for reading/writing sparse matrices in Rutherford/Boeing format. To install, cd to the RBio directory and type "RBinstall" in the MATLAB command window. RBio is written in Fortran because the Rutherford/Boeing format can require Fortran I/O statements, depending on how the files are stored. Files created by RBio do not require the Fortran I/O library to read them, however. -------------------------------------------------------------------------------- MATLAB help for RBio: -------------------------------------------------------------------------------- RBio - MATLAB toolbox for reading/writing sparse matrices in the Rutherford/ Boeing format, and for reading/writing problems in the UF Sparse Matrix Collection from/to a set of files in a directory. RBread - read a sparse matrix from a Rutherford/Boeing file RBreade - read a symmetric finite-element matrix from a R/B file RBtype - determine the Rutherford/Boeing type of a sparse matrix RBwrite - write a sparse matrix to a Rutherford/Boeing file RBraw - read the raw contents of a Rutherford/Boeing file RBfix - read a possibly corrupted matrix from a R/B file RBinstall - install the RBio toolbox for use in MATLAB Example: load west0479 C = west0479 ; RBwrite ('mywest', C, 'WEST0479 chemical eng. problem', 'west0479') A = RBread ('mywest') ; norm (A-C,1) See also UFget, mread, mwrite. Copyright 2007, Timothy A. Davis -------------------------------------------------------------------------------- Files and directories: -------------------------------------------------------------------------------- README.txt this file Contents.m MATLAB help for the RBio toolbox RBfix.m read a possibly corrupted R/B file RBinstall.m compile and install RBio for use in MATLAB, and run tests RBmake.m compile RBio for use in MATLAB RBraw.m MATLAB help for RBraw RBreade.m read a finite-element sparse matrix RBread.m MATLAB help for RBread RBtype.m MATLAB help for RBtype RBwrite.m MATLAB help for RBwrite RBcread_32.f read a complex sparse matrix, compare with RBrread_*.f RBcread_64.f RBcsplit_32.f split a complex matrix into its real and imaginary parts RBcsplit_64.f RBraw_mex_32.f mexFunction to read the raw contents of a R/B file RBraw_mex_64.f RBread_32.f utility routines for either real or complex matrices RBread_64.f RBread_mex_32.f mexFunction to read a real or complex sparse matrix RBread_mex_64.f RBrread_32.f read a real sparse matrix, compare with RBcread_*.f RBrread_64.f RBtype_mex_32.f mexFunction to determine the Rutherford/Boeing type RBtype_mex_64.f RBwrite_32.f write a real or complex sparse matrix RBwrite_64.f RBwrite_mex_32.f mexFunction to write a real or complex sparse matrix RBwrite_mex_64.f ./Test: directory with test codes and matrices testRB1.m simple test script for RBio testRB2.m simple test script for RBio (requires UFget) bcsstk01.rb HB/bcsstk01 Problem.A from UF Sparse Matrix Collection farm.rb Meszaros/farm Problem.A from UF Sparse Matrix Collection lap_25.pse original Harwell/Boeing version of lap_25 (finite-element) lap_25.rb HB/lap_25 Problem.A from UF Sparse Matrix Collection west0479.rb sparse matrix west0479 from UF Sparse Matrix Collection west0479.rua original Harwell/Boeing version of west0479 Note that the west0479 matrix provided in the Test directory is the correct version. The MATLAB statement "load west0479" gives you a matrix that is slightly incorrect (as of MATLAB Version 7.3, R2006b). ./Doc: directory with additional documentation and license ChangeLog changes since first release dodiff compare 32-bit and 64-bit codes, real and complex gpl.txt GNU license License.txt license SuiteSparse/RBio/RBmake.m0000644001170100242450000000203510620377774014136 0ustar davisfac%RBMAKE compile the RBio toolbox for use in MATLAB % Compiles the Fortran mexFunctions RBread, RBwrite, RBtype, and RBraw. % % Example: % % RBmake % % See also RBread, RBwrite, RBtype, RBraw, RBinstall. % % Copyright 2007, Timothy A. Davis if (~isempty (strfind (computer, '64'))) fprintf ('Compiling 64-bit version of RBio.\n') ; mex -O -output RBread RBread_mex_64.f RBread_64.f RBrread_64.f ... RBcread_64.f RBcsplit_64.f mex -O -output RBtype RBtype_mex_64.f RBwrite_64.f mex -O -output RBwrite RBwrite_mex_64.f RBwrite_64.f mex -O -output RBraw RBraw_mex_64.f RBread_64.f else fprintf ('Compiling 32-bit version of RBio.\n') ; mex -O -output RBread RBread_mex_32.f RBread_32.f RBrread_32.f ... RBcread_32.f RBcsplit_32.f mex -O -output RBtype RBtype_mex_32.f RBwrite_32.f mex -O -output RBwrite RBwrite_mex_32.f RBwrite_32.f mex -O -output RBraw RBraw_mex_32.f RBread_32.f end fprintf ('Note: Fortran compiler is required; this will fail otherwise...\n') ; fprintf ('RBio successfully compiled.\n') ; SuiteSparse/RBio/RBcread_32.f0000644001170100242450000001542610617641056014575 0ustar davisfacc======================================================================= c=== RBio/RBcread_32 =================================================== c======================================================================= c RBio: a MATLAB toolbox for reading and writing sparse matrices in c Rutherford/Boeing format. c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida c----------------------------------------------------------------------- c RB*read: read a Rutherford/Boeing matrix c----------------------------------------------------------------------- subroutine RBcread $ (nrow, ncol, nnz, ptrfmt, indfmt, valfmt, $ mkind, skind, Ap, Ai, Ax, nzeros, w, cp, info, nw, nnz1) integer*4 $ nrow, ncol, nnz, mkind, skind, p, j, i, alen, llen, k, $ ilast, nzeros, info, nw, nnz1 integer*4 $ Ap (ncol+1), Ai (nnz1), w (nw), cp (ncol+1) complex*16 Ax (nnz1), x character ptrfmt*16, indfmt*16, valfmt*20 c ---------------------------------------------------------------- c read the column pointers and row indices c ---------------------------------------------------------------- call RBpattern (ptrfmt, indfmt, nrow, ncol, nnz, skind, $ Ap, Ai, w, cp, info, nw) if (info .ne. 0) then c error: pattern is invalid return endif c ---------------------------------------------------------------- c read the values c ---------------------------------------------------------------- c read nnz values read (7, valfmt, err = 94, end = 94) (Ax (p), p = 1, nnz) c ---------------------------------------------------------------- c construct upper triangular part for symmetric matrices c ---------------------------------------------------------------- c If skind is zero, then the upper part is not constructed. This c allows the caller to skip this part, and create the upper part c of a symmetric (S,H,Z) matrix. Just pass skind = 0. if (skind .gt. 0) then c ------------------------------------------------------------ c shift the matrix by adding gaps to the top of each column c ------------------------------------------------------------ do 30 j = ncol, 1, -1 c number of entries in lower tri. part (incl. diagonal) llen = Ap (j+1) - Ap (j) c number of entries in entire column alen = cp (j+1) - cp (j) c move the column from Ai (Ap(j) ... Ap(j+1)-1) c down to Ai (cp(j+1)-llen ... cp(j+1)-1), leaving a gap c at Ai (Ap(j) ... cp(j+1)-llen) do 20 k = 1, llen Ai (cp (j+1) - k) = Ai (Ap (j+1) - k) Ax (cp (j+1) - k) = Ax (Ap (j+1) - k) 20 continue 30 continue c ------------------------------------------------------------ c populate the upper triangular part c ------------------------------------------------------------ c create temporary column pointers to point to the gaps do 40 j = 1, ncol w (j) = cp (j) 40 continue do 60 j = 1, ncol c scan the entries in the lower tri. part, in c Ai (cp(j+1)-llen ... cp(j+1)-1) llen = Ap (j+1) - Ap (j) do 50 k = 1, llen c get the A(i,j) entry in the lower triangular part i = Ai (cp (j+1) - k) x = Ax (cp (j+1) - k) c add A(j,i) as the next entry in column i (excl diag) if (i .ne. j) then p = w (i) w (i) = w (i) + 1 Ai (p) = j if (skind .eq. 1) then c *SA matrix Ax (p) = x elseif (skind .eq. 2) then c *HA matrix Ax (p) = dconjg (x) else c *ZA matrix Ax (p) = -x endif endif 50 continue 60 continue c finalize the column pointers do 70 j = 1, ncol+1 Ap (j) = cp (j) 70 continue endif c ---------------------------------------------------------------- c count the number of explicit zeros c ---------------------------------------------------------------- nzeros = 0 do 90 j = 1, ncol cp (j) = nzeros + 1 do 80 p = Ap (j), Ap (j+1)-1 if (Ax (p) .eq. 0) then nzeros = nzeros + 1 endif 80 continue 90 continue cp (ncol+1) = nzeros + 1 c ---------------------------------------------------------------- c matrix is valid c ---------------------------------------------------------------- info = 0 return c ---------------------------------------------------------------- c error return c ---------------------------------------------------------------- 94 info = -94 return end c----------------------------------------------------------------------- c RB*zeros: extract explicit zero entries c----------------------------------------------------------------------- c c nrow-by-ncol: size of A and Z c cp: column pointers of Z on input c Ap, Ai, Ax: matrix with zeros on input, pruned on output c Zp, Zi, Zx: empty matrix on input, pattern of zeros on output c c----------------------------------------------------------------------- subroutine RBczeros $ (nrow, ncol, cp, Ap, Ai, Ax, Zp, Zi, Zx) integer*4 $ nrow, ncol, Ap (ncol+1), Ai (*), Zp (ncol+1), Zi (*), $ cp (*), i, j, p, pa, pz, p1 complex*16 Ax (*), x double precision Zx (*) c ---------------------------------------------------------------- c copy the column pointers if Z is being constructed c ---------------------------------------------------------------- do 10 j = 1, ncol+1 Zp (j) = cp (j) 10 continue c ---------------------------------------------------------------- c split the matrix c ---------------------------------------------------------------- pa = 1 pz = 1 do 30 j = 1, ncol c save the new start of column j of A p1 = Ap (j) Ap (j) = pa pz = Zp (j) c split column j of A do 20 p = p1, Ap (j+1)-1 i = Ai (p) x = Ax (p) if (x .eq. 0) then c copy into Z Zi (pz) = i Zx (pz) = 1 pz = pz + 1 else c copy into A Ai (pa) = i Ax (pa) = x pa = pa + 1 endif 20 continue 30 continue Ap (ncol+1) = pa return end c----------------------------------------------------------------------- c RB*prune: discard explicit zero entries c----------------------------------------------------------------------- c c nrow-by-ncol: size of A c Ap, Ai, Ax: matrix with zeros on input, pruned on output c c----------------------------------------------------------------------- subroutine RBcprune $ (nrow, ncol, Ap, Ai, Ax) integer*4 $ nrow, ncol, Ap (ncol+1), Ai (*), i, j, p, pa, pz, p1 complex*16 Ax (*), x c ---------------------------------------------------------------- c prune the matrix c ---------------------------------------------------------------- pa = 1 do 20 j = 1, ncol c save the new start of column j of A p1 = Ap (j) Ap (j) = pa c prune column j of A do 10 p = p1, Ap (j+1)-1 i = Ai (p) x = Ax (p) if (x .ne. 0) then c copy into A Ai (pa) = i Ax (pa) = x pa = pa + 1 endif 10 continue 20 continue Ap (ncol+1) = pa return end SuiteSparse/RBio/RBcread_64.f0000644001170100242450000001542610617640727014606 0ustar davisfacc======================================================================= c=== RBio/RBcread_64 =================================================== c======================================================================= c RBio: a MATLAB toolbox for reading and writing sparse matrices in c Rutherford/Boeing format. c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida c----------------------------------------------------------------------- c RB*read: read a Rutherford/Boeing matrix c----------------------------------------------------------------------- subroutine RBcread $ (nrow, ncol, nnz, ptrfmt, indfmt, valfmt, $ mkind, skind, Ap, Ai, Ax, nzeros, w, cp, info, nw, nnz1) integer*8 $ nrow, ncol, nnz, mkind, skind, p, j, i, alen, llen, k, $ ilast, nzeros, info, nw, nnz1 integer*8 $ Ap (ncol+1), Ai (nnz1), w (nw), cp (ncol+1) complex*16 Ax (nnz1), x character ptrfmt*16, indfmt*16, valfmt*20 c ---------------------------------------------------------------- c read the column pointers and row indices c ---------------------------------------------------------------- call RBpattern (ptrfmt, indfmt, nrow, ncol, nnz, skind, $ Ap, Ai, w, cp, info, nw) if (info .ne. 0) then c error: pattern is invalid return endif c ---------------------------------------------------------------- c read the values c ---------------------------------------------------------------- c read nnz values read (7, valfmt, err = 94, end = 94) (Ax (p), p = 1, nnz) c ---------------------------------------------------------------- c construct upper triangular part for symmetric matrices c ---------------------------------------------------------------- c If skind is zero, then the upper part is not constructed. This c allows the caller to skip this part, and create the upper part c of a symmetric (S,H,Z) matrix. Just pass skind = 0. if (skind .gt. 0) then c ------------------------------------------------------------ c shift the matrix by adding gaps to the top of each column c ------------------------------------------------------------ do 30 j = ncol, 1, -1 c number of entries in lower tri. part (incl. diagonal) llen = Ap (j+1) - Ap (j) c number of entries in entire column alen = cp (j+1) - cp (j) c move the column from Ai (Ap(j) ... Ap(j+1)-1) c down to Ai (cp(j+1)-llen ... cp(j+1)-1), leaving a gap c at Ai (Ap(j) ... cp(j+1)-llen) do 20 k = 1, llen Ai (cp (j+1) - k) = Ai (Ap (j+1) - k) Ax (cp (j+1) - k) = Ax (Ap (j+1) - k) 20 continue 30 continue c ------------------------------------------------------------ c populate the upper triangular part c ------------------------------------------------------------ c create temporary column pointers to point to the gaps do 40 j = 1, ncol w (j) = cp (j) 40 continue do 60 j = 1, ncol c scan the entries in the lower tri. part, in c Ai (cp(j+1)-llen ... cp(j+1)-1) llen = Ap (j+1) - Ap (j) do 50 k = 1, llen c get the A(i,j) entry in the lower triangular part i = Ai (cp (j+1) - k) x = Ax (cp (j+1) - k) c add A(j,i) as the next entry in column i (excl diag) if (i .ne. j) then p = w (i) w (i) = w (i) + 1 Ai (p) = j if (skind .eq. 1) then c *SA matrix Ax (p) = x elseif (skind .eq. 2) then c *HA matrix Ax (p) = dconjg (x) else c *ZA matrix Ax (p) = -x endif endif 50 continue 60 continue c finalize the column pointers do 70 j = 1, ncol+1 Ap (j) = cp (j) 70 continue endif c ---------------------------------------------------------------- c count the number of explicit zeros c ---------------------------------------------------------------- nzeros = 0 do 90 j = 1, ncol cp (j) = nzeros + 1 do 80 p = Ap (j), Ap (j+1)-1 if (Ax (p) .eq. 0) then nzeros = nzeros + 1 endif 80 continue 90 continue cp (ncol+1) = nzeros + 1 c ---------------------------------------------------------------- c matrix is valid c ---------------------------------------------------------------- info = 0 return c ---------------------------------------------------------------- c error return c ---------------------------------------------------------------- 94 info = -94 return end c----------------------------------------------------------------------- c RB*zeros: extract explicit zero entries c----------------------------------------------------------------------- c c nrow-by-ncol: size of A and Z c cp: column pointers of Z on input c Ap, Ai, Ax: matrix with zeros on input, pruned on output c Zp, Zi, Zx: empty matrix on input, pattern of zeros on output c c----------------------------------------------------------------------- subroutine RBczeros $ (nrow, ncol, cp, Ap, Ai, Ax, Zp, Zi, Zx) integer*8 $ nrow, ncol, Ap (ncol+1), Ai (*), Zp (ncol+1), Zi (*), $ cp (*), i, j, p, pa, pz, p1 complex*16 Ax (*), x double precision Zx (*) c ---------------------------------------------------------------- c copy the column pointers if Z is being constructed c ---------------------------------------------------------------- do 10 j = 1, ncol+1 Zp (j) = cp (j) 10 continue c ---------------------------------------------------------------- c split the matrix c ---------------------------------------------------------------- pa = 1 pz = 1 do 30 j = 1, ncol c save the new start of column j of A p1 = Ap (j) Ap (j) = pa pz = Zp (j) c split column j of A do 20 p = p1, Ap (j+1)-1 i = Ai (p) x = Ax (p) if (x .eq. 0) then c copy into Z Zi (pz) = i Zx (pz) = 1 pz = pz + 1 else c copy into A Ai (pa) = i Ax (pa) = x pa = pa + 1 endif 20 continue 30 continue Ap (ncol+1) = pa return end c----------------------------------------------------------------------- c RB*prune: discard explicit zero entries c----------------------------------------------------------------------- c c nrow-by-ncol: size of A c Ap, Ai, Ax: matrix with zeros on input, pruned on output c c----------------------------------------------------------------------- subroutine RBcprune $ (nrow, ncol, Ap, Ai, Ax) integer*8 $ nrow, ncol, Ap (ncol+1), Ai (*), i, j, p, pa, pz, p1 complex*16 Ax (*), x c ---------------------------------------------------------------- c prune the matrix c ---------------------------------------------------------------- pa = 1 do 20 j = 1, ncol c save the new start of column j of A p1 = Ap (j) Ap (j) = pa c prune column j of A do 10 p = p1, Ap (j+1)-1 i = Ai (p) x = Ax (p) if (x .ne. 0) then c copy into A Ai (pa) = i Ax (pa) = x pa = pa + 1 endif 10 continue 20 continue Ap (ncol+1) = pa return end SuiteSparse/RBio/RBread.m0000644001170100242450000000163410711661144014124 0ustar davisfacfunction [A, Z, title, key, mtype] = RBread (filename) %#ok %RBREAD read a sparse matrix from a Rutherford/Boeing file % Usage: % [A Z title key mtype] = RBread (filename) % % A: a sparse matrix (no explicit zero entries) % Z: binary pattern of explicit zero entries in Rutherford/Boeing file. % This always has the same size as A, and is always sparse. % title: the 72-character title string in the file % key: the 8-character matrix name in the file % mtype: the Rutherford/Boeing type (see RBwrite for a description). % This function does not support finite-element matrices (use RBreade % instead). % % Example: % load west0479 % C = west0479 ; % RBwrite ('mywest', C, 'WEST0479 chemical eng. problem', 'west0479') % A = RBread ('mywest') ; % norm (A-C,1) % % See also RBwrite, RBreade, RBtype. % Copyright 2007, Timothy A. Davis error ('RBread mexFunction not found') ; SuiteSparse/RBio/RBtype.m0000644001170100242450000000243210711661154014170 0ustar davisfacfunction [mtype, mkind, skind] = RBtype (A) %#ok %RBTYPE determine the Rutherford/Boeing type of a sparse matrix % Usage: % [mtype mkind skind] = RBtype (A) % % A must be a sparse matrix. RBtype determines the Rutherford/Boeing type of A. % Very little memory is used (just size(A,2) integer workspace), so this can % succeed where a test such as nnz(A-A')==0 will fail. % % mkind: R: (0), A is real, and not binary % P: (1), A is binary (all values or 0 or 1) % C: (2), A is complex % I: (3), A is integer % % skind: R: (-1), A is rectangular % U: (0), A is unsymmetric (not S, H, or Z) % S: (1), A is symmetric (nnz(A-A.') is 0) % H: (2), A is Hermitian (nnz(A-A') is 0) % Z: (3), A is skew symmetric (nnz(A+A.') is 0) % % mtype is a 3-character string, where mtype(1) is the mkind % ('R', 'P', or 'C'). mtype(2) is the skind ('R', 'U', 'S', 'H', or 'Z'), % and mtype(3) is 'A'. % % Example: % load west0479 % A = west0479 ; % RBtype (A) % RBtype (spones (A)) % RBtype (2*spones (A)) % C = A+A' ; % RBtype (C) % % See also RBread, RBwrite. % Copyright 2007, Timothy A. Davis, University of Florida error ('RBtype mexFunction not found') ; SuiteSparse/RBio/RBtype_mex_32.f0000644001170100242450000001022210634267512015336 0ustar davisfacc======================================================================= c=== RBio/RBtype_mex_32 ================================================ c======================================================================= c RBio: a MATLAB toolbox for reading and writing sparse matrices in c Rutherford/Boeing format. c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida c----------------------------------------------------------------------- c RBtype mexFunction: c----------------------------------------------------------------------- c c [mtype mkind skind] = RBtype (A) c c A: a sparse matrix. Determines the Rutherford/Boeing type of the c matrix. Very little memory is used (just size(A,2) integer c workspace), so this can succeed where a test such as nnz(A-A')==0 c will fail. c c mkind: r: (0), A is real, and not binary c p: (1), A is binary c c: (2), A is complex c i: (3), A is integer c c skind: r: (-1), A is rectangular c u: (0), A is unsymmetric (not S, H, Z, below) c s: (1), A is symmetric (nnz(A-A.') is 0) c h: (2), A is Hermitian (nnz(A-A') is 0) c z: (3), A is skew symmetric (nnz(A+A.') is 0) c c mtype is a 3-character string, where mtype(1) is the mkind c ('r', 'p', 'c', or 'i'). mtype(2) is the skind ('r', 'u', 's', 'h', c or 'z'), and mtype(3) is always 'a'. c----------------------------------------------------------------------- subroutine mexfunction (nargout, pargout, nargin, pargin) integer*4 $ pargout (*), pargin (*) integer*4 nargout, nargin c ---------------------------------------------------------------- c MATLAB functions c ---------------------------------------------------------------- integer*4 mxClassIDFromClassName, $ mxIsClass, mxIsSparse, mxIsComplex integer*4 $ mxGetM, mxGetN, mxGetJc, mxGetIr, mxGetPr, mxGetPi, $ mxGetData, mxCreateNumericMatrix, mxCreateDoubleScalar, $ mxCreateString c ---------------------------------------------------------------- c local variables c ---------------------------------------------------------------- integer*4 $ nrow, ncol, nnz, mkind, cp, skind, cpmat, $ Ap, Ai, Ax, Az, kmin, kmax, one integer*4 iclass, cmplex, wcmplex character mtype*3 double precision t c ---------------------------------------------------------------- c check inputs c ---------------------------------------------------------------- if (nargin .ne. 1 .or. nargout .gt. 3) then call mexErrMsgTxt ('[mtype mkind skind] = RBtype (A)') endif c ---------------------------------------------------------------- c get A c ---------------------------------------------------------------- if (mxIsClass (pargin (1), 'double') .ne. 1 .or. $ mxIsSparse (pargin (1)) .ne. 1) then call mexErrMsgTxt ('A must be sparse and double') endif cmplex = mxIsComplex (pargin (1)) Ap = mxGetJc (pargin (1)) Ai = mxGetIr (pargin (1)) Ax = mxGetPr (pargin (1)) Az = mxGetPi (pargin (1)) nrow = mxGetM (pargin (1)) ncol = mxGetN (pargin (1)) c ---------------------------------------------------------------- c allocate workspace c ---------------------------------------------------------------- iclass = mxClassIDFromClassName ('int32') one = 1 wcmplex = 0 cpmat = mxCreateNumericMatrix (ncol+1, one, iclass, wcmplex) cp = mxGetData (cpmat) c ---------------------------------------------------------------- c determine the mtype of A c ---------------------------------------------------------------- call RBkind (nrow, ncol, %val(Ap), %val(Ai), %val(Ax), $ %val(Az), cmplex, mkind, skind, mtype, nnz, %val(cp), $ kmin, kmax) c ---------------------------------------------------------------- c return the result c ---------------------------------------------------------------- pargout (1) = mxCreateString (mtype) if (nargout .ge. 2) then t = mkind pargout (2) = mxCreateDoubleScalar (t) endif if (nargout .ge. 3) then t = skind pargout (3) = mxCreateDoubleScalar (t) endif c ---------------------------------------------------------------- c free workspace c ---------------------------------------------------------------- call mxDestroyArray (%val (cpmat)) return end SuiteSparse/RBio/RBtype_mex_64.f0000644001170100242450000001022210634267540015344 0ustar davisfacc======================================================================= c=== RBio/RBtype_mex_64 ================================================ c======================================================================= c RBio: a MATLAB toolbox for reading and writing sparse matrices in c Rutherford/Boeing format. c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida c----------------------------------------------------------------------- c RBtype mexFunction: c----------------------------------------------------------------------- c c [mtype mkind skind] = RBtype (A) c c A: a sparse matrix. Determines the Rutherford/Boeing type of the c matrix. Very little memory is used (just size(A,2) integer c workspace), so this can succeed where a test such as nnz(A-A')==0 c will fail. c c mkind: r: (0), A is real, and not binary c p: (1), A is binary c c: (2), A is complex c i: (3), A is integer c c skind: r: (-1), A is rectangular c u: (0), A is unsymmetric (not S, H, Z, below) c s: (1), A is symmetric (nnz(A-A.') is 0) c h: (2), A is Hermitian (nnz(A-A') is 0) c z: (3), A is skew symmetric (nnz(A+A.') is 0) c c mtype is a 3-character string, where mtype(1) is the mkind c ('r', 'p', 'c', or 'i'). mtype(2) is the skind ('r', 'u', 's', 'h', c or 'z'), and mtype(3) is always 'a'. c----------------------------------------------------------------------- subroutine mexfunction (nargout, pargout, nargin, pargin) integer*8 $ pargout (*), pargin (*) integer*4 nargout, nargin c ---------------------------------------------------------------- c MATLAB functions c ---------------------------------------------------------------- integer*4 mxClassIDFromClassName, $ mxIsClass, mxIsSparse, mxIsComplex integer*8 $ mxGetM, mxGetN, mxGetJc, mxGetIr, mxGetPr, mxGetPi, $ mxGetData, mxCreateNumericMatrix, mxCreateDoubleScalar, $ mxCreateString c ---------------------------------------------------------------- c local variables c ---------------------------------------------------------------- integer*8 $ nrow, ncol, nnz, mkind, cp, skind, cpmat, $ Ap, Ai, Ax, Az, kmin, kmax, one integer*4 iclass, cmplex, wcmplex character mtype*3 double precision t c ---------------------------------------------------------------- c check inputs c ---------------------------------------------------------------- if (nargin .ne. 1 .or. nargout .gt. 3) then call mexErrMsgTxt ('[mtype mkind skind] = RBtype (A)') endif c ---------------------------------------------------------------- c get A c ---------------------------------------------------------------- if (mxIsClass (pargin (1), 'double') .ne. 1 .or. $ mxIsSparse (pargin (1)) .ne. 1) then call mexErrMsgTxt ('A must be sparse and double') endif cmplex = mxIsComplex (pargin (1)) Ap = mxGetJc (pargin (1)) Ai = mxGetIr (pargin (1)) Ax = mxGetPr (pargin (1)) Az = mxGetPi (pargin (1)) nrow = mxGetM (pargin (1)) ncol = mxGetN (pargin (1)) c ---------------------------------------------------------------- c allocate workspace c ---------------------------------------------------------------- iclass = mxClassIDFromClassName ('int64') one = 1 wcmplex = 0 cpmat = mxCreateNumericMatrix (ncol+1, one, iclass, wcmplex) cp = mxGetData (cpmat) c ---------------------------------------------------------------- c determine the mtype of A c ---------------------------------------------------------------- call RBkind (nrow, ncol, %val(Ap), %val(Ai), %val(Ax), $ %val(Az), cmplex, mkind, skind, mtype, nnz, %val(cp), $ kmin, kmax) c ---------------------------------------------------------------- c return the result c ---------------------------------------------------------------- pargout (1) = mxCreateString (mtype) if (nargout .ge. 2) then t = mkind pargout (2) = mxCreateDoubleScalar (t) endif if (nargout .ge. 3) then t = skind pargout (3) = mxCreateDoubleScalar (t) endif c ---------------------------------------------------------------- c free workspace c ---------------------------------------------------------------- call mxDestroyArray (%val (cpmat)) return end SuiteSparse/RBio/RBcsplit_32.f0000644001170100242450000000145510617641061015006 0ustar davisfacc======================================================================= c=== RBio/RBcsplit_32 ================================================== c======================================================================= c RBio: a MATLAB toolbox for reading and writing sparse matrices in c Rutherford/Boeing format. c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida c----------------------------------------------------------------------- c RBcsplit: split a complex matrix into its real and imaginary parts c----------------------------------------------------------------------- subroutine RBcsplit (Cx, Ax, Az, nnz) integer*4 $ nnz, i complex*16 Cx (*) double precision Ax (*), Az (*) do 10 i = 1, nnz Ax (i) = dreal (Cx (i)) Az (i) = dimag (Cx (i)) 10 continue return end SuiteSparse/RBio/RBcsplit_64.f0000644001170100242450000000145510617640735015022 0ustar davisfacc======================================================================= c=== RBio/RBcsplit_64 ================================================== c======================================================================= c RBio: a MATLAB toolbox for reading and writing sparse matrices in c Rutherford/Boeing format. c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida c----------------------------------------------------------------------- c RBcsplit: split a complex matrix into its real and imaginary parts c----------------------------------------------------------------------- subroutine RBcsplit (Cx, Ax, Az, nnz) integer*8 $ nnz, i complex*16 Cx (*) double precision Ax (*), Az (*) do 10 i = 1, nnz Ax (i) = dreal (Cx (i)) Az (i) = dimag (Cx (i)) 10 continue return end SuiteSparse/RBio/RBwrite.m0000644001170100242450000000265710620377721014355 0ustar davisfacfunction mtype = RBwrite (filename, A, Z, title, key) %#ok %RBWRITE write a sparse matrix to a Rutherford/Boeing file % Usage: % mtype = RBwrite (filename, A, Z, title, key) % % filename: name of the file to create % A: a sparse matrix % Z: binary pattern of explicit zero entries to include in the % Rutherford/Boeing file. This always has the same size as A, and is % always sparse. Not used if empty ([ ]), or if nnz(Z) is 0. % title: title for 1st line of Rutherford/Boeing file, up to 72 characters % key: matrix key, up to 8 characters, for 1st line of the file % % Z is optional. RBwrite (filename, A) uses a default title and key, and does % not include any explicit zeros. RBwrite (filname, A, 'title...', 'key') uses % the given title and key. A must be sparse. Z must be empty, or sparse. % % mtype is a 3-character string with the Rutherford/Boeing type used: % mtype(1): r: real, p: pattern, c: complex, i: integer % mtype(2): r: rectangular, u: unsymmetric, s: symmetric, % h: Hermitian, Z: skew symmetric % mtype(3): a: assembled matrix, e: finite-element (not used by RBwrite) % % Example: % load west0479 % C = west0479 ; % RBwrite ('west0479', C, 'WEST0479 chemical eng. problem', 'west0479') % A = RBread ('west0479') ; % norm (A-C,1) % % See also RBread, RBtype. % Copyright 2007, Timothy A. Davis, University of Florida error ('RBwrite mexFunction not found') ; SuiteSparse/RBio/RBwrite_32.f0000644001170100242450000004326010634270234014641 0ustar davisfacc======================================================================= c=== RBio/RBwrite_32 =================================================== c======================================================================= c RBio: a MATLAB toolbox for reading and writing sparse matrices in c Rutherford/Boeing format. c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida c----------------------------------------------------------------------- c RBkind: determine the type of a MATLAB matrix c----------------------------------------------------------------------- c c input: a zero-based MATLAB sparse matrix c c nrow number of rows of A c ncol number of columns of A c Ap size ncol+1, column pointers c Ai size nnz, row indices (nnz = Ap (ncol+1)) c Ax size nnz, real values c Az size nnz, imaginary values (not accessed if A is real) c cmplex 1 if A is complex, 0 otherwise c c output: c mkind: r: 0 (real), p: 1 (pattern), c: 2 (complex), c i: 3 (integer) c skind: r: -1 (rectangular), u: 0 (unsymmetric), s: 1 symmetric, c h: 2 (Hermitian), z: 3 (skew symmetric) c c workspace: c munch size ncol+1, not defined on input or output c c Note that the MATLAB matrix is zero-based (Ap and Ai). 1 must be c added whenever they are used (see "1+" in the code below). c c See also SuiteSparse/CHOLMOD/MatrixOps/cholmod_symmetry.c, which c also determines if the diagonal is positive. c----------------------------------------------------------------------- subroutine RBkind (nrow, ncol, Ap, Ai, Ax, Az, $ cmplex, mkind, skind, mtype, nnz, munch, kmin, kmax) integer*4 $ nrow, ncol, Ap (ncol+1), Ai (*), mkind, skind, $ munch (ncol+1), p, i, j, pt, nnz, k, kmin, kmax integer*4 cmplex double precision Ax (*), Az (*), x_r, x_i, xtr, xti logical is_p, is_s, is_h, is_z, is_int character mtype*3 c ---------------------------------------------------------------- c determine numeric type (I*A, R*A, P*A, C*A) c ---------------------------------------------------------------- c pattern: if real and all entries are 1. c integer: if real and all entries are integers. c complex: if cmplex is 1. c real: otherwise. nnz = 1+ (Ap (ncol+1) - 1) kmin = 0 kmax = 0 if (cmplex .eq. 1) then c complex matrix (C*A) mtype (1:1) = 'c' mkind = 2 else c select P** format if all entries are equal to 1 c select I** format if all entries are integer and c between -99,999,999 and +999,999,999 is_p = .true. is_int = .true. k = dint (Ax (1)) kmin = k kmax = k do 10 p = 1, nnz if (Ax (p) .ne. 1) then is_p = .false. endif k = dint (Ax (p)) kmin = min (kmin, k) kmax = max (kmax, k) if (k .ne. Ax (p)) then is_int = .false. endif if (k .le. -99999999 .or. k .ge. 999999999) then c use real format for really big integers is_int = .false. endif if (.not. is_int .and. .not. is_p) then goto 20 endif 10 continue 20 continue if (is_p) then c pattern-only matrix (P*A) mtype (1:1) = 'p' mkind = 1 elseif (is_int) then c integer matrix (I*A) mtype (1:1) = 'i' mkind = 3 else c real matrix (R*A) mtype (1:1) = 'r' mkind = 0 endif endif c only assembled matrices are handled mtype (3:3) = 'a' c ---------------------------------------------------------------- c determine symmetry (*RA, *UA, *SA, *HA, *ZA) c ---------------------------------------------------------------- c Note that A must have sorted columns for this method to work. c This is not checked, since all MATLAB matrices "should" have c sorted columns. Use spcheck(A) to check for this, if needed. if (nrow .ne. ncol) then c rectangular matrix (*RA), no need to check values or pattern mtype (2:2) = 'r' skind = -1 return endif c if complex, the matrix is Hermitian until proven otherwise is_h = (cmplex .eq. 1) c the matrix is symmetric until proven otherwise is_s = .true. c a non-pattern matrix is skew symmetric until proven otherwise is_z = (mkind .ne. 1) c if this method returns early, the matrix is unsymmetric mtype (2:2) = 'u' skind = 0 c initialize the munch pointers do 30 j = 1, ncol munch (j) = 1+ (Ap (j)) 30 continue do 50 j = 1, ncol c consider all entries not yet munched in column j do 40 p = munch (j), 1+ (Ap (j+1)-1) i = 1+ (Ai (p)) if (i .lt. j) then c entry A(i,j) is unmatched, matrix is unsymmetric return endif c get the A(j,i) entry, if it exists pt = munch (i) c munch the A(j,i) entry munch (i) = pt + 1 if (pt .ge. 1+ (Ap (i+1))) then c entry A(j,i) doesn't exist, matrix unsymmetric return endif if (1+ (Ai (pt)) .ne. j) then c entry A(j,i) doesn't exist, matrix unsymmetric return endif c A(j,i) exists; check its value with A(i,j) if (cmplex .eq. 1) then c get A(i,j) x_r = Ax (p) x_i = Az (p) c get A(j,i) xtr = Ax (pt) xti = Az (pt) if (x_r .ne. xtr .or. x_i .ne. xti) then c the matrix cannot be *SA is_s = .false. endif if (x_r .ne. -xtr .or. x_i .ne. -xti) then c the matrix cannot be *ZA is_z = .false. endif if (x_r .ne. xtr .or. x_i .ne. -xti) then c the matrix cannot be *HA is_h = .false. endif else c get A(i,j) x_r = Ax (p) c get A(j,i) xtr = Ax (pt) if (x_r .ne. xtr) then c the matrix cannot be *SA is_s = .false. endif if (x_r .ne. -xtr) then c the matrix cannot be *ZA is_z = .false. endif endif if (.not. (is_s .or. is_z .or. is_h)) then c matrix is unsymmetric; terminate the test return endif 40 continue 50 continue c ---------------------------------------------------------------- c return the symmetry c ---------------------------------------------------------------- if (is_h) then c Hermitian matrix (*HA) mtype (2:2) = 'h' skind = 2 elseif (is_s) then c symmetric matrix (*SA) mtype (2:2) = 's' skind = 1 elseif (is_z) then c skew symmetric matrix (*ZA) mtype (2:2) = 'z' skind = 3 endif return end c----------------------------------------------------------------------- c RBformat: determine the format required for an array of values c----------------------------------------------------------------------- c c This function ensures that a sufficiently wide format is used that c can accurately represent the data. It also ensures that when printed, c the numerical values all have at least one blank space between them. c This makes it trivial for a program written in C (say) to read in a c matrix generated by RBwrite. c ww, valfmt, valn, and is_int must be defined on input. They c are modified on output. c----------------------------------------------------------------------- subroutine RBformat (nnz, x, ww, valfmt, valn, is_int, $ kmin, kmax) integer*4 $ nnz, i, ww, k, nf (18), valn, nd (9), kmin, kmax double precision x (nnz), e, a, b logical is_int character*20 f (18), d (9), valfmt character*80 s c ---------------------------------------------------------------- c define all possible formats c ---------------------------------------------------------------- f (1) = '(8E9.1) ' f (2) = '(8E10.2) ' f (3) = '(7E11.3) ' f (4) = '(6E12.4) ' f (5) = '(6E13.5) ' f (6) = '(5E14.6) ' f (7) = '(5E15.7) ' f (8) = '(5E16.8) ' f (9) = '(4E17.9) ' f (10) = '(4E18.10) ' f (11) = '(4E19.11) ' f (12) = '(4E20.12) ' f (13) = '(3E21.13) ' f (14) = '(3E22.14) ' f (15) = '(3E23.15) ' f (16) = '(3E24.16) ' f (17) = '(3E25.17) ' f (18) = '(3E26.18) ' nf (1) = 8 nf (2) = 8 nf (3) = 7 nf (4) = 6 nf (5) = 6 nf (6) = 5 nf (7) = 5 nf (8) = 5 nf (9) = 4 nf (10) = 4 nf (11) = 4 nf (12) = 4 nf (13) = 3 nf (14) = 3 nf (15) = 3 nf (16) = 3 nf (17) = 3 nf (18) = 3 if (is_int) then c ------------------------------------------------------------ c use an integer format c ------------------------------------------------------------ call RBiformat (kmin, kmax, valfmt, valn, ww) else c ------------------------------------------------------------ c determine if the matrix has huge values or NaN's c ------------------------------------------------------------ do 10 i = 1, nnz a = abs (x (i)) if (a .ne. 0) then if (a .ne. a .or. a < 1d-90 .or. a > 1d90) then ww = 18 valfmt = '(2E30.18E3) ' valn = 2 return endif endif 10 continue c ------------------------------------------------------------ c find the required precision for a real or complex matrix c ------------------------------------------------------------ do 20 i = 1, nnz a = x (i) do 30 k = ww,18 c write the value to a string, read back in, and check write (unit = s, fmt = f(k)) a read (unit = s, fmt = f(k)) b if (a .eq. b) then ww = max (ww, k) goto 40 endif 30 continue 40 continue ww = max (ww, k) 20 continue c valn is the number of entries per line valfmt = f (ww) valn = nf (ww) endif return end c----------------------------------------------------------------------- c RBwrite: write portions of the matrix to the file c----------------------------------------------------------------------- c c task 0: just count the total number of entries in the matrix c task 1: do task 0, and also construct w and cp c task 2: write the row indices c task 3: write the numerical values c c Note that the MATLAB arrays A and Z are zero-based. "1+" is added c to each use of Ap, Ai, Zp, and Zi. c----------------------------------------------------------------------- subroutine RBwrite (task, nrow, ncol, skind, cmplex, doZ, Ap, $ Ai, Ax, Az, Zp, Zi, mkind, $ indfmt, indn, valfmt, valn, nnz, w, cp) integer*4 $ task, nrow, ncol, Ap (*), Ai (*), Zp (*), Zi (*), $ cp (*), w (*), nnz, znz, ibuf (80), j, i, nbuf, pa, pz, $ paend, pzend, ia, iz, skind, indn, valn, p, mkind integer*4 cmplex logical doZ double precision xbuf (80), xr, xi, Ax (*), Az (*) character valfmt*20, indfmt*20 c ---------------------------------------------------------------- c determine number of entries in Z c ---------------------------------------------------------------- if (doZ) then znz = 1+ (Zp (ncol+1) - 1) else znz = 0 endif c clear the nonzero counts nnz = 0 do 10 j = 1, ncol w (j) = 0 10 continue c start with an empty buffer nbuf = 0 if (znz .eq. 0) then c ------------------------------------------------------------ c no Z present c ------------------------------------------------------------ do 30 j = 1, ncol do 20 pa = 1+ (Ap (j)), 1+ (Ap (j+1) - 1) i = 1+ (Ai (pa)) xr = Ax (pa) if (cmplex .eq. 1) then xi = Az (pa) endif if (skind .le. 0 .or. i .ge. j) then c consider the (i,j) entry with value (xr,xi) nnz = nnz + 1 if (task .eq. 1) then c only determining nonzero counts w (j) = w (j) + 1 elseif (task .eq. 2) then c printing the row indices call RBiprint (indfmt, ibuf, nbuf, i, indn) elseif (task .eq. 3) then c printing the numerical values call RBxprint (valfmt, xbuf, nbuf, xr, $ valn, mkind) if (cmplex .eq. 1) then call RBxprint (valfmt, xbuf, nbuf, xi, $ valn, mkind) endif endif endif 20 continue 30 continue else c ------------------------------------------------------------ c symmetric, unsymmetric or rectangular matrix, with Z present c ------------------------------------------------------------ do 40 j = 1, ncol c find the set union of A (:,j) and Z (:,j) pa = 1+ (Ap (j)) pz = 1+ (Zp (j)) paend = 1+ (Ap (j+1) - 1) pzend = 1+ (Zp (j+1) - 1) c while entries appear in A or Z 70 continue c get the next entry from A(:,j) if (pa .le. paend) then ia = 1+ (Ai (pa)) else ia = 1+ nrow endif c get the next entry from Z(:,j) if (pz .le. pzend) then iz = 1+ (Zi (pz)) else iz = 1+ nrow endif c exit loop if neither entry is present if (ia .gt. nrow .and. iz .gt. nrow) goto 80 if (ia .lt. iz) then c get A (i,j) i = ia xr = Ax (pa) if (cmplex .eq. 1) then xi = Az (pa) endif pa = pa + 1 else if (iz .lt. ia) then c get Z (i,j) i = iz xr = 0 xi = 0 pz = pz + 1 else c get A (i,j), and delete its matched Z(i,j) i = ia xr = Ax (pa) if (cmplex .eq. 1) then xi = Az (pa) endif pa = pa + 1 pz = pz + 1 endif if (skind .le. 0 .or. i .ge. j) then c consider the (i,j) entry with value (xr,xi) nnz = nnz + 1 if (task .eq. 1) then c only determining nonzero counts w (j) = w (j) + 1 elseif (task .eq. 2) then c printing the row indices call RBiprint (indfmt, ibuf, nbuf, i, indn) elseif (task .eq. 3) then c printing the numerical values call RBxprint (valfmt, xbuf, nbuf, xr, $ valn, mkind) if (cmplex .eq. 1) then call RBxprint (valfmt, xbuf, nbuf, xi, $ valn, mkind) endif endif endif goto 70 c end of while loop 80 continue 40 continue endif c ---------------------------------------------------------------- c determine the new column pointers, or finish printing c ---------------------------------------------------------------- if (task .eq. 1) then cp (1) = 1 do 100 j = 2, ncol+1 cp (j) = cp (j-1) + w (j-1) 100 continue else if (task .eq. 2) then call RBiflush (indfmt, ibuf, nbuf) elseif (task .eq. 3) then call RBxflush (valfmt, xbuf, nbuf, mkind) endif return end c----------------------------------------------------------------------- c RBiprint: print a single integer to the file, flush buffer if needed c----------------------------------------------------------------------- subroutine RBiprint (indfmt, ibuf, nbuf, i, indn) character indfmt*20 integer*4 $ ibuf (80), nbuf, i, indn if (nbuf .ge. indn) then call RBiflush (indfmt, ibuf, nbuf) nbuf = 0 endif nbuf = nbuf + 1 ibuf (nbuf) = i return end c----------------------------------------------------------------------- c RBiflush: flush the integer buffer to the file c----------------------------------------------------------------------- subroutine RBiflush (indfmt, ibuf, nbuf) character indfmt*20 integer*4 $ ibuf (*), nbuf, k write (unit = 7, fmt = indfmt, err = 999) (ibuf (k), k = 1,nbuf) return 999 call mexErrMsgTxt ('error writing ints') return end c----------------------------------------------------------------------- c RBxprint: print a single real to the file, flush the buffer if needed c----------------------------------------------------------------------- subroutine RBxprint (valfmt, xbuf, nbuf, x, valn, mkind) character valfmt*20 integer*4 $ nbuf, valn, mkind double precision xbuf (80), x if (nbuf .ge. valn) then call RBxflush (valfmt, xbuf, nbuf, mkind) nbuf = 0 endif nbuf = nbuf + 1 xbuf (nbuf) = x return end c----------------------------------------------------------------------- c RBxflush: flush the real buffer to the file c----------------------------------------------------------------------- subroutine RBxflush (valfmt, xbuf, nbuf, mkind) character valfmt*20 integer*4 $ nbuf, k, ibuf (80), mkind double precision xbuf (80) if (mkind .eq. 3) then c convert to integer first; valfmt is (10I8), for example do 10 k = 1,nbuf ibuf (k) = dint (xbuf (k)) 10 continue write (unit = 7, fmt = valfmt, err = 999) $ (ibuf (k), k = 1,nbuf) else write (unit = 7, fmt = valfmt, err = 999) $ (xbuf (k), k = 1,nbuf) endif return 999 call mexErrMsgTxt ('error writing numerical values') return end c----------------------------------------------------------------------- c RBiformat: determine format for printing an integer c----------------------------------------------------------------------- subroutine RBiformat (kmin, kmax, indfmt, indn, ww) integer*4 $ n, indn, kmin, kmax, ww character*20 indfmt if (kmin .ge. 0. and. kmax .le. 9) then indfmt = '(40I2) ' ww = 2 indn = 40 elseif (kmin .ge. -9 .and. kmax .le. 99) then indfmt = '(26I3) ' ww = 3 indn = 26 elseif (kmin .ge. -99 .and. kmax .le. 999) then indfmt = '(20I4) ' ww = 4 indn = 20 elseif (kmin .ge. -999 .and. kmax .le. 9999) then indfmt = '(16I5) ' ww = 5 indn = 16 elseif (kmin .ge. -9999 .and. kmax .le. 99999) then indfmt = '(13I6) ' ww = 6 indn = 13 elseif (kmin .ge. -99999 .and. kmax .le. 999999) then indfmt = '(11I7) ' ww = 7 indn = 11 elseif (kmin .ge. -999999 .and. kmax .le. 9999999) then indfmt = '(10I8) ' ww = 8 indn = 10 elseif (kmin .ge. -9999999 .and. kmax .le. 99999999) then indfmt = '(8I9) ' ww = 9 indn = 8 elseif (kmin .ge. -99999999 .and. kmax .le. 999999999) then indfmt = '(8I10) ' ww = 10 indn = 8 else indfmt = '(5I15) ' ww = 15 indn = 5 endif return end c----------------------------------------------------------------------- c RBcards: determine number of cards required c----------------------------------------------------------------------- subroutine RBcards (nitems, nperline, ncards) integer*4 $ nitems, nperline, ncards if (nitems .eq. 0) then ncards = 0 else ncards = ((nitems-1) / nperline) + 1 endif return end SuiteSparse/RBio/RBwrite_64.f0000644001170100242450000004326010634270240014643 0ustar davisfacc======================================================================= c=== RBio/RBwrite_64 =================================================== c======================================================================= c RBio: a MATLAB toolbox for reading and writing sparse matrices in c Rutherford/Boeing format. c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida c----------------------------------------------------------------------- c RBkind: determine the type of a MATLAB matrix c----------------------------------------------------------------------- c c input: a zero-based MATLAB sparse matrix c c nrow number of rows of A c ncol number of columns of A c Ap size ncol+1, column pointers c Ai size nnz, row indices (nnz = Ap (ncol+1)) c Ax size nnz, real values c Az size nnz, imaginary values (not accessed if A is real) c cmplex 1 if A is complex, 0 otherwise c c output: c mkind: r: 0 (real), p: 1 (pattern), c: 2 (complex), c i: 3 (integer) c skind: r: -1 (rectangular), u: 0 (unsymmetric), s: 1 symmetric, c h: 2 (Hermitian), z: 3 (skew symmetric) c c workspace: c munch size ncol+1, not defined on input or output c c Note that the MATLAB matrix is zero-based (Ap and Ai). 1 must be c added whenever they are used (see "1+" in the code below). c c See also SuiteSparse/CHOLMOD/MatrixOps/cholmod_symmetry.c, which c also determines if the diagonal is positive. c----------------------------------------------------------------------- subroutine RBkind (nrow, ncol, Ap, Ai, Ax, Az, $ cmplex, mkind, skind, mtype, nnz, munch, kmin, kmax) integer*8 $ nrow, ncol, Ap (ncol+1), Ai (*), mkind, skind, $ munch (ncol+1), p, i, j, pt, nnz, k, kmin, kmax integer*4 cmplex double precision Ax (*), Az (*), x_r, x_i, xtr, xti logical is_p, is_s, is_h, is_z, is_int character mtype*3 c ---------------------------------------------------------------- c determine numeric type (I*A, R*A, P*A, C*A) c ---------------------------------------------------------------- c pattern: if real and all entries are 1. c integer: if real and all entries are integers. c complex: if cmplex is 1. c real: otherwise. nnz = 1+ (Ap (ncol+1) - 1) kmin = 0 kmax = 0 if (cmplex .eq. 1) then c complex matrix (C*A) mtype (1:1) = 'c' mkind = 2 else c select P** format if all entries are equal to 1 c select I** format if all entries are integer and c between -99,999,999 and +999,999,999 is_p = .true. is_int = .true. k = dint (Ax (1)) kmin = k kmax = k do 10 p = 1, nnz if (Ax (p) .ne. 1) then is_p = .false. endif k = dint (Ax (p)) kmin = min (kmin, k) kmax = max (kmax, k) if (k .ne. Ax (p)) then is_int = .false. endif if (k .le. -99999999 .or. k .ge. 999999999) then c use real format for really big integers is_int = .false. endif if (.not. is_int .and. .not. is_p) then goto 20 endif 10 continue 20 continue if (is_p) then c pattern-only matrix (P*A) mtype (1:1) = 'p' mkind = 1 elseif (is_int) then c integer matrix (I*A) mtype (1:1) = 'i' mkind = 3 else c real matrix (R*A) mtype (1:1) = 'r' mkind = 0 endif endif c only assembled matrices are handled mtype (3:3) = 'a' c ---------------------------------------------------------------- c determine symmetry (*RA, *UA, *SA, *HA, *ZA) c ---------------------------------------------------------------- c Note that A must have sorted columns for this method to work. c This is not checked, since all MATLAB matrices "should" have c sorted columns. Use spcheck(A) to check for this, if needed. if (nrow .ne. ncol) then c rectangular matrix (*RA), no need to check values or pattern mtype (2:2) = 'r' skind = -1 return endif c if complex, the matrix is Hermitian until proven otherwise is_h = (cmplex .eq. 1) c the matrix is symmetric until proven otherwise is_s = .true. c a non-pattern matrix is skew symmetric until proven otherwise is_z = (mkind .ne. 1) c if this method returns early, the matrix is unsymmetric mtype (2:2) = 'u' skind = 0 c initialize the munch pointers do 30 j = 1, ncol munch (j) = 1+ (Ap (j)) 30 continue do 50 j = 1, ncol c consider all entries not yet munched in column j do 40 p = munch (j), 1+ (Ap (j+1)-1) i = 1+ (Ai (p)) if (i .lt. j) then c entry A(i,j) is unmatched, matrix is unsymmetric return endif c get the A(j,i) entry, if it exists pt = munch (i) c munch the A(j,i) entry munch (i) = pt + 1 if (pt .ge. 1+ (Ap (i+1))) then c entry A(j,i) doesn't exist, matrix unsymmetric return endif if (1+ (Ai (pt)) .ne. j) then c entry A(j,i) doesn't exist, matrix unsymmetric return endif c A(j,i) exists; check its value with A(i,j) if (cmplex .eq. 1) then c get A(i,j) x_r = Ax (p) x_i = Az (p) c get A(j,i) xtr = Ax (pt) xti = Az (pt) if (x_r .ne. xtr .or. x_i .ne. xti) then c the matrix cannot be *SA is_s = .false. endif if (x_r .ne. -xtr .or. x_i .ne. -xti) then c the matrix cannot be *ZA is_z = .false. endif if (x_r .ne. xtr .or. x_i .ne. -xti) then c the matrix cannot be *HA is_h = .false. endif else c get A(i,j) x_r = Ax (p) c get A(j,i) xtr = Ax (pt) if (x_r .ne. xtr) then c the matrix cannot be *SA is_s = .false. endif if (x_r .ne. -xtr) then c the matrix cannot be *ZA is_z = .false. endif endif if (.not. (is_s .or. is_z .or. is_h)) then c matrix is unsymmetric; terminate the test return endif 40 continue 50 continue c ---------------------------------------------------------------- c return the symmetry c ---------------------------------------------------------------- if (is_h) then c Hermitian matrix (*HA) mtype (2:2) = 'h' skind = 2 elseif (is_s) then c symmetric matrix (*SA) mtype (2:2) = 's' skind = 1 elseif (is_z) then c skew symmetric matrix (*ZA) mtype (2:2) = 'z' skind = 3 endif return end c----------------------------------------------------------------------- c RBformat: determine the format required for an array of values c----------------------------------------------------------------------- c c This function ensures that a sufficiently wide format is used that c can accurately represent the data. It also ensures that when printed, c the numerical values all have at least one blank space between them. c This makes it trivial for a program written in C (say) to read in a c matrix generated by RBwrite. c ww, valfmt, valn, and is_int must be defined on input. They c are modified on output. c----------------------------------------------------------------------- subroutine RBformat (nnz, x, ww, valfmt, valn, is_int, $ kmin, kmax) integer*8 $ nnz, i, ww, k, nf (18), valn, nd (9), kmin, kmax double precision x (nnz), e, a, b logical is_int character*20 f (18), d (9), valfmt character*80 s c ---------------------------------------------------------------- c define all possible formats c ---------------------------------------------------------------- f (1) = '(8E9.1) ' f (2) = '(8E10.2) ' f (3) = '(7E11.3) ' f (4) = '(6E12.4) ' f (5) = '(6E13.5) ' f (6) = '(5E14.6) ' f (7) = '(5E15.7) ' f (8) = '(5E16.8) ' f (9) = '(4E17.9) ' f (10) = '(4E18.10) ' f (11) = '(4E19.11) ' f (12) = '(4E20.12) ' f (13) = '(3E21.13) ' f (14) = '(3E22.14) ' f (15) = '(3E23.15) ' f (16) = '(3E24.16) ' f (17) = '(3E25.17) ' f (18) = '(3E26.18) ' nf (1) = 8 nf (2) = 8 nf (3) = 7 nf (4) = 6 nf (5) = 6 nf (6) = 5 nf (7) = 5 nf (8) = 5 nf (9) = 4 nf (10) = 4 nf (11) = 4 nf (12) = 4 nf (13) = 3 nf (14) = 3 nf (15) = 3 nf (16) = 3 nf (17) = 3 nf (18) = 3 if (is_int) then c ------------------------------------------------------------ c use an integer format c ------------------------------------------------------------ call RBiformat (kmin, kmax, valfmt, valn, ww) else c ------------------------------------------------------------ c determine if the matrix has huge values or NaN's c ------------------------------------------------------------ do 10 i = 1, nnz a = abs (x (i)) if (a .ne. 0) then if (a .ne. a .or. a < 1d-90 .or. a > 1d90) then ww = 18 valfmt = '(2E30.18E3) ' valn = 2 return endif endif 10 continue c ------------------------------------------------------------ c find the required precision for a real or complex matrix c ------------------------------------------------------------ do 20 i = 1, nnz a = x (i) do 30 k = ww,18 c write the value to a string, read back in, and check write (unit = s, fmt = f(k)) a read (unit = s, fmt = f(k)) b if (a .eq. b) then ww = max (ww, k) goto 40 endif 30 continue 40 continue ww = max (ww, k) 20 continue c valn is the number of entries per line valfmt = f (ww) valn = nf (ww) endif return end c----------------------------------------------------------------------- c RBwrite: write portions of the matrix to the file c----------------------------------------------------------------------- c c task 0: just count the total number of entries in the matrix c task 1: do task 0, and also construct w and cp c task 2: write the row indices c task 3: write the numerical values c c Note that the MATLAB arrays A and Z are zero-based. "1+" is added c to each use of Ap, Ai, Zp, and Zi. c----------------------------------------------------------------------- subroutine RBwrite (task, nrow, ncol, skind, cmplex, doZ, Ap, $ Ai, Ax, Az, Zp, Zi, mkind, $ indfmt, indn, valfmt, valn, nnz, w, cp) integer*8 $ task, nrow, ncol, Ap (*), Ai (*), Zp (*), Zi (*), $ cp (*), w (*), nnz, znz, ibuf (80), j, i, nbuf, pa, pz, $ paend, pzend, ia, iz, skind, indn, valn, p, mkind integer*4 cmplex logical doZ double precision xbuf (80), xr, xi, Ax (*), Az (*) character valfmt*20, indfmt*20 c ---------------------------------------------------------------- c determine number of entries in Z c ---------------------------------------------------------------- if (doZ) then znz = 1+ (Zp (ncol+1) - 1) else znz = 0 endif c clear the nonzero counts nnz = 0 do 10 j = 1, ncol w (j) = 0 10 continue c start with an empty buffer nbuf = 0 if (znz .eq. 0) then c ------------------------------------------------------------ c no Z present c ------------------------------------------------------------ do 30 j = 1, ncol do 20 pa = 1+ (Ap (j)), 1+ (Ap (j+1) - 1) i = 1+ (Ai (pa)) xr = Ax (pa) if (cmplex .eq. 1) then xi = Az (pa) endif if (skind .le. 0 .or. i .ge. j) then c consider the (i,j) entry with value (xr,xi) nnz = nnz + 1 if (task .eq. 1) then c only determining nonzero counts w (j) = w (j) + 1 elseif (task .eq. 2) then c printing the row indices call RBiprint (indfmt, ibuf, nbuf, i, indn) elseif (task .eq. 3) then c printing the numerical values call RBxprint (valfmt, xbuf, nbuf, xr, $ valn, mkind) if (cmplex .eq. 1) then call RBxprint (valfmt, xbuf, nbuf, xi, $ valn, mkind) endif endif endif 20 continue 30 continue else c ------------------------------------------------------------ c symmetric, unsymmetric or rectangular matrix, with Z present c ------------------------------------------------------------ do 40 j = 1, ncol c find the set union of A (:,j) and Z (:,j) pa = 1+ (Ap (j)) pz = 1+ (Zp (j)) paend = 1+ (Ap (j+1) - 1) pzend = 1+ (Zp (j+1) - 1) c while entries appear in A or Z 70 continue c get the next entry from A(:,j) if (pa .le. paend) then ia = 1+ (Ai (pa)) else ia = 1+ nrow endif c get the next entry from Z(:,j) if (pz .le. pzend) then iz = 1+ (Zi (pz)) else iz = 1+ nrow endif c exit loop if neither entry is present if (ia .gt. nrow .and. iz .gt. nrow) goto 80 if (ia .lt. iz) then c get A (i,j) i = ia xr = Ax (pa) if (cmplex .eq. 1) then xi = Az (pa) endif pa = pa + 1 else if (iz .lt. ia) then c get Z (i,j) i = iz xr = 0 xi = 0 pz = pz + 1 else c get A (i,j), and delete its matched Z(i,j) i = ia xr = Ax (pa) if (cmplex .eq. 1) then xi = Az (pa) endif pa = pa + 1 pz = pz + 1 endif if (skind .le. 0 .or. i .ge. j) then c consider the (i,j) entry with value (xr,xi) nnz = nnz + 1 if (task .eq. 1) then c only determining nonzero counts w (j) = w (j) + 1 elseif (task .eq. 2) then c printing the row indices call RBiprint (indfmt, ibuf, nbuf, i, indn) elseif (task .eq. 3) then c printing the numerical values call RBxprint (valfmt, xbuf, nbuf, xr, $ valn, mkind) if (cmplex .eq. 1) then call RBxprint (valfmt, xbuf, nbuf, xi, $ valn, mkind) endif endif endif goto 70 c end of while loop 80 continue 40 continue endif c ---------------------------------------------------------------- c determine the new column pointers, or finish printing c ---------------------------------------------------------------- if (task .eq. 1) then cp (1) = 1 do 100 j = 2, ncol+1 cp (j) = cp (j-1) + w (j-1) 100 continue else if (task .eq. 2) then call RBiflush (indfmt, ibuf, nbuf) elseif (task .eq. 3) then call RBxflush (valfmt, xbuf, nbuf, mkind) endif return end c----------------------------------------------------------------------- c RBiprint: print a single integer to the file, flush buffer if needed c----------------------------------------------------------------------- subroutine RBiprint (indfmt, ibuf, nbuf, i, indn) character indfmt*20 integer*8 $ ibuf (80), nbuf, i, indn if (nbuf .ge. indn) then call RBiflush (indfmt, ibuf, nbuf) nbuf = 0 endif nbuf = nbuf + 1 ibuf (nbuf) = i return end c----------------------------------------------------------------------- c RBiflush: flush the integer buffer to the file c----------------------------------------------------------------------- subroutine RBiflush (indfmt, ibuf, nbuf) character indfmt*20 integer*8 $ ibuf (*), nbuf, k write (unit = 7, fmt = indfmt, err = 999) (ibuf (k), k = 1,nbuf) return 999 call mexErrMsgTxt ('error writing ints') return end c----------------------------------------------------------------------- c RBxprint: print a single real to the file, flush the buffer if needed c----------------------------------------------------------------------- subroutine RBxprint (valfmt, xbuf, nbuf, x, valn, mkind) character valfmt*20 integer*8 $ nbuf, valn, mkind double precision xbuf (80), x if (nbuf .ge. valn) then call RBxflush (valfmt, xbuf, nbuf, mkind) nbuf = 0 endif nbuf = nbuf + 1 xbuf (nbuf) = x return end c----------------------------------------------------------------------- c RBxflush: flush the real buffer to the file c----------------------------------------------------------------------- subroutine RBxflush (valfmt, xbuf, nbuf, mkind) character valfmt*20 integer*8 $ nbuf, k, ibuf (80), mkind double precision xbuf (80) if (mkind .eq. 3) then c convert to integer first; valfmt is (10I8), for example do 10 k = 1,nbuf ibuf (k) = dint (xbuf (k)) 10 continue write (unit = 7, fmt = valfmt, err = 999) $ (ibuf (k), k = 1,nbuf) else write (unit = 7, fmt = valfmt, err = 999) $ (xbuf (k), k = 1,nbuf) endif return 999 call mexErrMsgTxt ('error writing numerical values') return end c----------------------------------------------------------------------- c RBiformat: determine format for printing an integer c----------------------------------------------------------------------- subroutine RBiformat (kmin, kmax, indfmt, indn, ww) integer*8 $ n, indn, kmin, kmax, ww character*20 indfmt if (kmin .ge. 0. and. kmax .le. 9) then indfmt = '(40I2) ' ww = 2 indn = 40 elseif (kmin .ge. -9 .and. kmax .le. 99) then indfmt = '(26I3) ' ww = 3 indn = 26 elseif (kmin .ge. -99 .and. kmax .le. 999) then indfmt = '(20I4) ' ww = 4 indn = 20 elseif (kmin .ge. -999 .and. kmax .le. 9999) then indfmt = '(16I5) ' ww = 5 indn = 16 elseif (kmin .ge. -9999 .and. kmax .le. 99999) then indfmt = '(13I6) ' ww = 6 indn = 13 elseif (kmin .ge. -99999 .and. kmax .le. 999999) then indfmt = '(11I7) ' ww = 7 indn = 11 elseif (kmin .ge. -999999 .and. kmax .le. 9999999) then indfmt = '(10I8) ' ww = 8 indn = 10 elseif (kmin .ge. -9999999 .and. kmax .le. 99999999) then indfmt = '(8I9) ' ww = 9 indn = 8 elseif (kmin .ge. -99999999 .and. kmax .le. 999999999) then indfmt = '(8I10) ' ww = 10 indn = 8 else indfmt = '(5I15) ' ww = 15 indn = 5 endif return end c----------------------------------------------------------------------- c RBcards: determine number of cards required c----------------------------------------------------------------------- subroutine RBcards (nitems, nperline, ncards) integer*8 $ nitems, nperline, ncards if (nitems .eq. 0) then ncards = 0 else ncards = ((nitems-1) / nperline) + 1 endif return end SuiteSparse/RBio/RBfix.m0000644001170100242450000001042710711661061013775 0ustar davisfacfunction [A, Z, title, key, mtype] = RBfix (filename) %RBFIX read a possibly corrupted matrix from a R/B file % (assembled format only). Usage: % % [A Z title key mtype] = RBfix (filename) % % The Rutherford/Boeing format stores a sparse matrix in a file in compressed- % column form, using 3 arrays: Ap, Ai, and Ax. The row indices of entries in % A(:,j) are in Ai(p1:p2) and the corresponding numerical values are Ax(p1:p2), % where p1 = Ap(j) and p2 = Ap(j+1)-1. The row indices ought to be sorted, and % no duplicates should appear, but this function ignores that requirement. % Duplicate entries are summed if they exist, and A is returned with sorted % columns. Symmetric matrices are stored with just their lower triangular % parts in the file. Normally, it is an error if entries are present in the % upper triangular part of a matrix that is declared in the file to be % symmetric. This function simply ignores those entries. % % If CHOLMOD is installed, this function is faster and uses less memory. % % Example: % % load west0479 % RBwrite ('mywest', west0479, [ ], 'My west0479 file', 'west0479') ; % [A Z title key mtype] = RBfix ('mywest') ; % isequal (A, west0479) % title, key, mtype % % See also mread, RBread, RBwrite, RBreade, sparse2. % Optionally uses the CHOLMOD sparse2 mexFunction. % Copyright 2007, Timothy A. Davis %------------------------------------------------------------------------------- % read in the raw contents of the Rutherford/Boeing file %------------------------------------------------------------------------------- [mtype Ap Ai Ax title key nrow] = RBraw (filename) ; mtype = lower (mtype) ; %------------------------------------------------------------------------------- % determine dimension, number of entries, and convert numerical entries %------------------------------------------------------------------------------- % number of columns ncol = length (Ap) - 1 ; % number of entries nz = length (Ai) ; % check column pointers if (any (Ap ~= sort (Ap)) | (Ap (1) ~= 1) | (Ap (ncol+1) - 1 ~= nz)) %#ok error ('invalid column pointers') ; end % check row indices if ((double (max (Ai)) > nrow) | double (min (Ai)) < 1) %#ok error ('invalid row indices') ; end % Ax can be empty, for a p*a matrix if (~isempty (Ax)) if (mtype (1) == 'c') % Ax is real, with real/imaginary parts interleaved if (2 * nz ~= length (Ax)) error ('invalid matrix') ; end Ax = Ax (1:2:end) + (1i * Ax (2:2:end)) ; elseif (mtype (1) == 'i') Ax = double (Ax) ; end % numerical values must be of the right size if (nz ~= length (Ax)) error ('invalid matrix') ; end end %------------------------------------------------------------------------------- % create the triplet form %------------------------------------------------------------------------------- % construct column indices Aj = zeros (nz,1) ; for j = 1:ncol p1 = Ap (j) ; p2 = Ap (j+1) - 1 ; Aj (p1:p2) = j ; end %------------------------------------------------------------------------------- % create the sparse matrix form %------------------------------------------------------------------------------- if (exist ('sparse2') == 3) %#ok % Use sparse2 in CHOLMOD. It's faster, allows integer Ai and Aj, and % returns the Z matrix as the 2nd output argument. if (isempty (Ax)) Ax = 1 ; end % numerical matrix [A Z] = sparse2 (Ai, Aj, Ax, nrow, ncol) ; else % stick with MATLAB, without CHOLMOD. This is slower and takes more memory. Ai = double (Ai) ; Aj = double (Aj) ; if (isempty (Ax)) % pattern-only matrix A = spones (sparse (Ai, Aj, 1, nrow, ncol)) ; Z = sparse (nrow, ncol) ; else % numerical matrix A = sparse (Ai, Aj, Ax, nrow, ncol) ; % determine the pattern of explicit zero entries S = spones (sparse (Ai, Aj, 1, nrow, ncol)) ; Z = S - spones (A) ; end end % check for entries in upper part if (any (mtype (2) == 'shz') & nnz (triu (A,1) > 0)) %#ok fprintf ('entries in upper triangular part of %s matrix ignored\n', mtype); end % add the upper triangular part if (mtype (2) == 's') A = A + tril (A,-1).' ; Z = Z + tril (Z,-1)' ; elseif (mtype (2) == 'h') A = A + tril (A,-1)' ; Z = Z + tril (Z,-1)' ; elseif (mtype (2) == 'z') A = A - tril (A,-1).' ; Z = Z + tril (Z,-1)' ; end SuiteSparse/RBio/RBreade.m0000644001170100242450000000731410711661132014267 0ustar davisfacfunction [A, Z, title, key, mtype] = RBreade (filename) %RBREADE read a symmetric finite-element matrix from a R/B file % Usage: % [A Z title key mtype] = RBreade (filename) % % The file must contain a Rutherford/Boeing matrix of type *se or *he, where * % can be r, p, i, or c. See RBread for a description of the outputs. % % If CHOLMOD is installed, this function is faster and uses less memory. % % Example: % % [A Z title key mtype] = RBreade ('lap_25.pse') ; % % See also RBread, RBraw, sparse2. % Optionally uses the CHOLMOD sparse2 mexFunction. % Copyright 2007, Timothy A. Davis %------------------------------------------------------------------------------- % read in the raw contents of the Rutherford/Boeing file %------------------------------------------------------------------------------- [mtype Ap Ai Ax title key n] = RBraw (filename) ; mtype = lower (mtype) ; if (~(mtype (2) == 's' | mtype (2) == 'h') | (mtype (3) ~= 'e')) %#ok error ('RBreade is only for symmetric unassembled finite-element matrices'); end %------------------------------------------------------------------------------- % determine dimension, number of elements, and convert numerical entries %------------------------------------------------------------------------------- Ap = double (Ap) ; Ai = double (Ai) ; % number of elements ne = length (Ap) - 1 ; % dimension. if (max (Ai) > n) error ('invalid dimension') ; end % determine number of numerical entries nz = 0 ; for e = 1:ne p1 = Ap (e) ; p2 = Ap (e+1) - 1 ; nu = p2 - p1 + 1 ; nz = nz + (nu * (nu+1)/2) ; end % Ax can be empty, for a pse matrix if (~isempty (Ax)) if (mtype (1) == 'c') % Ax is real, with real/imaginary parts interleaved if (2 * nz ~= length (Ax)) error ('invalid matrix (wrong number of complex values)') ; end Ax = Ax (1:2:end) + (1i * Ax (2:2:end)) ; elseif (mtype (1) == 'i') Ax = double (Ax) ; end % numerical values must be of the right size if (nz ~= length (Ax)) error ('invalid matrix (wrong number of values)') ; end end %------------------------------------------------------------------------------- % create triplet form %------------------------------------------------------------------------------- % row and column indices for triplet form of the matrix ii = zeros (nz, 1) ; jj = zeros (nz, 1) ; nx = 0 ; % create triplet row and column indices from finite-element pattern for e = 1:ne p1 = Ap (e) ; p2 = Ap (e+1) - 1 ; for p = p1:p2 j = Ai (p) ; for pp = p:p2 i = Ai (pp) ; nx = nx + 1 ; ii (nx) = max (i,j) ; jj (nx) = min (i,j) ; end end end %------------------------------------------------------------------------------- % create the sparse matrix form %------------------------------------------------------------------------------- if (exist ('sparse2') == 3) %#ok % Use sparse2 in CHOLMOD. It's faster, allows integer Ai and Aj, and % returns the Z matrix as the 2nd output argument. if (isempty (Ax)) Ax = 1 ; end % numerical matrix [A Z] = sparse2 (ii, jj, Ax, n, n) ; else % stick with MATLAB, without CHOLMOD. This is slower and takes more memory. if (isempty (Ax)) % pattern-only matrix A = spones (sparse (ii, jj, 1, n, n)) ; Z = sparse (n, n) ; else % numerical matrix A = sparse (ii, jj, Ax, n, n) ; % determine the pattern of explicit zero entries S = spones (sparse (ii, jj, 1, n, n)) ; Z = S - spones (A) ; end end % add the upper triangular part if (mtype (2) == 's') A = A + tril (A,-1).' ; elseif (mtype (2) == 'h') A = A + tril (A,-1)' ; end Z = Z + tril (Z,-1)' ; % remove duplicates created from triplet form for a pattern-only matrix if (mtype (1) == 'p') A = spones (A) ; end SuiteSparse/RBio/RBraw.m0000644001170100242450000000252010711661117013775 0ustar davisfacfunction [mtype, Ap, Ai, Ax, title, key, nrow] = RBraw (filename) %#ok %RBRAW read the raw contents of a Rutherford/Boeing file % % [mtype Ap Ai Ax title key nrow] = RBraw (filename) % % mtype: Rutherford/Boeing matrix type (psa, rua, rsa, rse, ...) % Ap: column pointers (1-based) % Ai: row indices (1-based) % Ax: numerical values (real, complex, or integer). Empty for p*a matrices. % A complex matrix is read in as a single double array Ax, where the kth % entry has real value Ax(2*k-1) and imaginary value Ax(2*k). % title: a string containing the title from the first line of the R/B file % key: a string containing the 8-character key, from the 1st line of the file % nrow: number of rows in the matrix % % This function works for both assembled and unassembled (finite-element) % matrices. It is also useful for checking the contents of a Rutherford/Boeing % file in detail, in case the file has invalid column pointers, unsorted % columns, duplicate entries, entries in the upper triangular part of the file % for a symmetric matrix, etc. % % Example: % % load west0479 % RBwrite ('mywest', west0479, [ ], 'My west0479 file', 'west0479') ; % [mtype Ap Ai Ax title key nrow] = RBraw ('mywest') ; % % See also RBfix, RBread, RBreade. % Copyright 2007, Timothy A. Davis error ('RBraw mexFunction not found') ; SuiteSparse/CSparse/0000755001170100242450000000000010711431371013305 5ustar davisfacSuiteSparse/CSparse/Doc/0000755001170100242450000000000010711427627014023 5ustar davisfacSuiteSparse/CSparse/Doc/License.txt0000644001170100242450000000160410357542363016150 0ustar davisfacCSparse: a Concise Sparse matrix package. Copyright (c) 2006, Timothy A. Davis. http://www.cise.ufl.edu/research/sparse/CSparse -------------------------------------------------------------------------------- CSparse is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. CSparse is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA SuiteSparse/CSparse/Doc/ChangeLog0000644001170100242450000002072410711427621015574 0ustar davisfacNov 1, 2007, v2.2.1 * very minor change to Include/cs.h: Changed name of 2nd argument of cs_permute, to match the code. This has no affect on the code itself, since the type ("int *") is unchanged. It's just a documentation issue. * minor lint cleanup in mexFunctions Mar 31, 2007, v2.2.0 * few changes to primary Source/ files. Changes mostly affect MATLAB interface. * Source/cs_house.c: correction to comment * Souce/cs_updown.c: whitespace changed to reflect change in CXSparse, no impact at all on CSparse itself. * Doc/, Lib/ and Include/ directories created. * Source/cs.h moved to Include/cs.h, version number changed to 2.2.0. * modification to Makefiles, cs_make.m * correction to help comments in cs_dmperm.m, cs_qr.m, cs_scc2.m, cs_scc.m * if complex matrix passed to CSparse in MATLAB, error message suggests using CXSparse instead * minor performance fix to cs_sparse_mex.c * cs_randperm added to MATLAB/Makefile; already appeared in cs_make.m * minor improvements to MATLAB/ demos. Mar 1, 2007, v2.1.0 * Source/cs_add.c: added test for matrix dimensions * Source/cs_multiply.c: added test for matrix dimensions * correction to MATLAB demo3 (no error in C code version of the demo) * minor corrections to MATLAB m-file help comments. Dec 12, 2006, v2.0.7 * minor MATLAB cleanup Dec 6, 2006, v2.0.6 * Update to UFget. Now relies on the MATLAB urlwrite function instead of my own Java code. Nov 2006, v2.0.5 * Added UFgrep to UFget toolbox. * No changes to C Source code, except for version number and date. * Added two test matrices: ibm32a and ibm32b. ibm32a is the Harwell/ Boeing matrix ibm32, but with the last column removed. ibm32b is the transpose of ibm32a. With optimization enabled (-O), 2 lines in cs_maxtrans.c are not tested; these matrices correct that problem. * Fixed UFget. Earlier version could not download matrices larger than 32MB. * Modified UFget/UFweb, to reflect changes in the UF Sparse Matrix Collection. * Added ccspy.m and cs_scc2.m MATLAB functions * Added examples to help info in each *.m MATLAB file * modified cs_dmspy to speed up the plotting of large matrices with many singletons * minor change to cspy: now draws a box around the matrix. * minor changes to MATLAB demos and tests. Oct 13, 2006, v2.0.4 * minor modification to cs_updown.c. "n" was incorrectly declared "double". It should be "int". This was safe, just a little confusing (n was only used in an argument to cs_malloc, and is thus typecast). Sept 28, 2006, v2.0.3 * minor modifications to MATLAB interface, to allow CSparse to be used in MATLAB 6.5. * added examples to m-files, other minor m-file cleanup. * bug fix to cspy, to handle NaN's properly. Aug 23, 2006: v2.0.2 * change to cs_updown mexFunction, to handle multiple rank updates * symbolic links removed from Tcov/ directory in the distribution. They are now created by Tcov/Makefile as needed. This makes the zip files cleaner. Tcov/*test.c test files renamed. July 19, 2006: * minor fix to cs_must_compile.m and cs_make.m, to allow CSparse to be compiled in MATLAB 6.5 with cs_make. * minor fix to cspy for complex matrices (imaginary part was ignored). * no change to version number or date, since there are no changes that affect the appearance of CSparse in the book ("Direct Methods for Sparse Linear Systems", SIAM, 2006). June 24, 2006: * minor typos in comments corrected. No change in code itself, and no change in version number or date. May 27, 2006, v2.0.1: (this version is printed in the book) * minor bug fix. cs_util.c modified, so that cs_sprealloc (T,0) works properly for a triplet matrix T (setting T->nzmax equal to T->nz). The line in v2.0.0: nzmax = (nzmax <= 0) ? (A->p [A->n]) : nzmax ; changes to the following in v2.0.1: if (nzmax <= 0) nzmax = (CS_CSC (A)) ? (A->p [A->n]) : A->nz ; * minor typographical changes arising from the editting of the book. Apr 12, 2006, v2.0.0: * random permutation option added to cs_maxtrans and cs_dmperm, to help avoid rare cases where the O(|A|n) time complexity is reached in practice (GHS_indef/boyd2 in the UF sparse matrix collection, for example). New cs_randperm function added. Apr 10, 2006: * stylistic changes for the book (except for the bug fix): * "int order" parameter of cs_amd, cs_lusol, cs_cholsol, cs_qrsol, cs_sqr, cs_schol changed. Now 0 means no ordering, 1 is A+A', 2 is S*S', and 3 is A*A'. In v1.2 and earlier, "order" took on a value ranging from -1 to 2. "int n" parameter rearranged for cs_ipvec, cs_pvec, cs_post (int n moved to the end). cs_triplet renamed cs_compress. To ensure that these changes are propagated into user code that calls CSparse, the "order" parameter has been placed as the first parameter in all these routines. Your compiler will complain (gcc will halt) if you upgrade from v1.2 to v2.0 without changing your code. This is much better than a silent error in which you get the wrong ordering by mistake (with a huge penalty in run-time performance and no compiler warnings). New syntax (v2.0 and later): ---------------------------- order = 0: natural ordering order = 1: amd (A+A') order = 2: amd (S'*S), where S=A except dense rows dropped order = 3: amd (A'*A) int cs_cholsol (int order, const cs *A, double *b) ; int cs_lusol (int order, const cs *A, double *b, double tol) ; int cs_qrsol (int order, const cs *A, double *b) ; int *cs_amd (int order, const cs *A) ; css *cs_schol (int order, const cs *A) ; css *cs_sqr (int order, const cs *A, int qr) ; int *cs_post (const int *parent, int n) ; int cs_ipvec (const int *p, const double *b, double *x, int n) ; int cs_pvec (const int *p, const double *b, double *x, int n) ; cs *cs_compress (const cs *T) ; Old syntax (v1.2 and earlier): ------------------------------ order = -1: natural ordering order = 0: amd (A+A') order = 1: amd (S'*S), where S=A except dense rows dropped order = 2: amd (A'*A) int cs_cholsol (const cs *A, double *b, int order) ; int cs_lusol (const cs *A, double *b, int order, double tol) ; int cs_qrsol (const cs *A, double *b, int order) ; int *cs_amd (const cs *A, int order) ; css *cs_schol (const cs *A, int order) ; css *cs_sqr (const cs *A, int order, int qr) ; int *cs_post (int n, const int *parent) ; int cs_ipvec (int n, const int *p, const double *b, double *x) ; int cs_pvec (int n, const int *p, const double *b, double *x) ; cs *cs_triplet (const cs *T) ; * CS_OVERFLOW macro removed (removed from cs_malloc.c; not needed). * S->leftmost added to css (it was tacked onto S->pinv before). * P,Q,R,S components of csd struct changed to p,q,r,s. * Pinv and Q components of css struct changed to pinv and q. * CS_CSC and CS_TRIPLET macros added, to clarify which CSparse functions accept cs matrices in compressed column form, triplet form, or both. * check for negative row/column indices added to cs_entry. * cs_ereach and cs_leaf functions added. * call to cs_sprealloc added to cs_fkeep. * bug fixes in cs_counts and cs_amd (memory leak under rare out-of-memory conditions). Mar 15, 2006: * cs_scc modified so that the row and columns of each component are put in their natural order. cs_dmperm modified so that columns of each block (instead of rows) are placed in their natural order. * cs_splsolve renamed cs_spsolve, generalized to handle both Lx=b and Ux=b, and non-unit diagonal, and placed in its own file (cs_spsolve.c; it was a static function in cs_lu.c). cs_lsolve_mex.c and cs_splsolve_mex.c merged (the latter was removed). cs_spsolve.c file added * cs_dmspy changed, so that block borders line up better with the matrix. Mar 6, 2006: * Makefile modified so that the Tcov tests (which may not be portable) are not compiled and run by the default "make" in the CSparse directory. To compile everything, including the Tcov tests, use "make all". Trivial change to cs.h. Feb 27, 2006: * cs_reach, cs_dfs, cs_splsolve, cs_lu, and cs_scc changed to remove O(n) initialized workspace. * cs_reach and cs_splsolve now user-callable (were static in cs_lu.c). Feb 20, 2006: * various changes to simplify the construction of CXSparse Feb 7, 2006: * changed prototypes, adding "const" where appropriate. SuiteSparse/CSparse/Doc/lesser.txt0000644001170100242450000006350010346315140016053 0ustar davisfac GNU LESSER GENERAL PUBLIC LICENSE Version 2.1, February 1999 Copyright (C) 1991, 1999 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. [This is the first released version of the Lesser GPL. It also counts as the successor of the GNU Library Public License, version 2, hence the version number 2.1.] Preamble The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public Licenses are intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users. 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You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Also add information on how to contact you by electronic and paper mail. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the library, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the library `Frob' (a library for tweaking knobs) written by James Random Hacker. , 1 April 1990 Ty Coon, President of Vice That's all there is to it! SuiteSparse/CSparse/Lib/0000755001170100242450000000000010711435727014024 5ustar davisfacSuiteSparse/CSparse/Lib/Makefile0000644001170100242450000000174210617166425015471 0ustar davisfac# Modify the "-O" optimization option for best performance (-O3 on Linux): CC = cc CFLAGS = -O -I../Include AR = ar cr RANLIB = ranlib all: libcsparse.a CS = cs_add.o cs_amd.o cs_chol.o cs_cholsol.o cs_counts.o cs_cumsum.o \ cs_droptol.o cs_dropzeros.o cs_dupl.o cs_entry.o \ cs_etree.o cs_fkeep.o cs_gaxpy.o cs_happly.o cs_house.o cs_ipvec.o \ cs_lsolve.o cs_ltsolve.o cs_lu.o cs_lusol.o cs_util.o cs_multiply.o \ cs_permute.o cs_pinv.o cs_post.o cs_pvec.o cs_qr.o cs_qrsol.o \ cs_scatter.o cs_schol.o cs_sqr.o cs_symperm.o cs_tdfs.o cs_malloc.o \ cs_transpose.o cs_compress.o cs_usolve.o cs_utsolve.o cs_scc.o \ cs_maxtrans.o cs_dmperm.o cs_updown.o cs_print.o cs_norm.o cs_load.o \ cs_dfs.o cs_reach.o cs_spsolve.o cs_ereach.o cs_leaf.o cs_randperm.o $(CS): ../Include/cs.h Makefile %.o: ../Source/%.c ../Include/cs.h $(CC) $(CFLAGS) -c $< libcsparse.a: $(CS) $(AR) libcsparse.a $(CS) $(RANLIB) libcsparse.a clean: rm -f *.o purge: distclean distclean: clean rm -f *.a SuiteSparse/CSparse/Demo/0000755001170100242450000000000010711435727014202 5ustar davisfacSuiteSparse/CSparse/Demo/Makefile0000644001170100242450000000163510617166127015647 0ustar davisfacCC = cc CFLAGS = -O I = -I../Include CS = ../Lib/libcsparse.a all: lib cs_demo1 cs_demo2 cs_demo3 - ./cs_demo1 < ../Matrix/t1 - ./cs_demo2 < ../Matrix/t1 - ./cs_demo2 < ../Matrix/ash219 - ./cs_demo2 < ../Matrix/bcsstk01 - ./cs_demo2 < ../Matrix/fs_183_1 - ./cs_demo2 < ../Matrix/mbeacxc - ./cs_demo2 < ../Matrix/west0067 - ./cs_demo2 < ../Matrix/lp_afiro - ./cs_demo2 < ../Matrix/bcsstk16 - ./cs_demo3 < ../Matrix/bcsstk01 - ./cs_demo3 < ../Matrix/bcsstk16 lib: ( cd ../Lib ; $(MAKE) ) cs_demo1: lib cs_demo1.c Makefile $(CC) $(CFLAGS) $(I) -o cs_demo1 cs_demo1.c $(CS) -lm cs_demo2: lib cs_demo2.c cs_demo.c cs_demo.h Makefile $(CC) $(CFLAGS) $(I) -o cs_demo2 cs_demo2.c cs_demo.c $(CS) -lm cs_demo3: lib cs_demo3.c cs_demo.c cs_demo.h Makefile $(CC) $(CFLAGS) $(I) -o cs_demo3 cs_demo3.c cs_demo.c $(CS) -lm clean: rm -f *.o purge: distclean distclean: clean rm -f cs_demo1 cs_demo2 cs_demo3 *.a SuiteSparse/CSparse/Demo/cs_demo1.c0000644001170100242450000000201110436111360016016 0ustar davisfac#include "cs.h" int main (void) { cs *T, *A, *Eye, *AT, *C, *D ; int i, m ; T = cs_load (stdin) ; /* load triplet matrix T from stdin */ printf ("T:\n") ; cs_print (T, 0) ; /* print T */ A = cs_compress (T) ; /* A = compressed-column form of T */ printf ("A:\n") ; cs_print (A, 0) ; /* print A */ cs_spfree (T) ; /* clear T */ AT = cs_transpose (A, 1) ; /* AT = A' */ printf ("AT:\n") ; cs_print (AT, 0) ; /* print AT */ m = A ? A->m : 0 ; /* m = # of rows of A */ T = cs_spalloc (m, m, m, 1, 1) ; /* create triplet identity matrix */ for (i = 0 ; i < m ; i++) cs_entry (T, i, i, 1) ; Eye = cs_compress (T) ; /* Eye = speye (m) */ cs_spfree (T) ; C = cs_multiply (A, AT) ; /* C = A*A' */ D = cs_add (C, Eye, 1, cs_norm (C)) ; /* D = C + Eye*norm (C,1) */ printf ("D:\n") ; cs_print (D, 0) ; /* print D */ cs_spfree (A) ; /* clear A AT C D Eye */ cs_spfree (AT) ; cs_spfree (C) ; cs_spfree (D) ; cs_spfree (Eye) ; return (0) ; } SuiteSparse/CSparse/Demo/cs_demo2.c0000644001170100242450000000032010326434515016030 0ustar davisfac#include "cs_demo.h" /* cs_demo2: read a matrix and solve a linear system */ int main (void) { problem *Prob = get_problem (stdin, 1e-14) ; demo2 (Prob) ; free_problem (Prob) ; return (0) ; } SuiteSparse/CSparse/Demo/cs_demo3.c0000644001170100242450000000032410326434521016032 0ustar davisfac#include "cs_demo.h" /* cs_demo3: read a matrix and test Cholesky update/downdate */ int main (void) { problem *Prob = get_problem (stdin, 0) ; demo3 (Prob) ; free_problem (Prob) ; return (0) ; } SuiteSparse/CSparse/Demo/cs_demo.out0000644001170100242450000001240010711432563016334 0ustar davisfac./cs_demo1 < ../Matrix/t1 T: CSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 triplet: 4-by-4, nzmax: 16 nnz: 10 2 2 : 3 1 0 : 3.1 3 3 : 1 0 2 : 3.2 1 1 : 2.9 3 0 : 3.5 3 1 : 0.4 1 3 : 0.9 0 0 : 4.5 2 1 : 1.7 A: CSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 11.1 col 0 : locations 0 to 2 1 : 3.1 3 : 3.5 0 : 4.5 col 1 : locations 3 to 5 1 : 2.9 3 : 0.4 2 : 1.7 col 2 : locations 6 to 7 2 : 3 0 : 3.2 col 3 : locations 8 to 9 3 : 1 1 : 0.9 AT: CSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 7.7 col 0 : locations 0 to 1 0 : 4.5 2 : 3.2 col 1 : locations 2 to 4 0 : 3.1 1 : 2.9 3 : 0.9 col 2 : locations 5 to 6 1 : 1.7 2 : 3 col 3 : locations 7 to 9 0 : 3.5 1 : 0.4 3 : 1 D: CSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 16 nnz: 16, 1-norm: 139.58 col 0 : locations 0 to 3 1 : 13.95 3 : 15.75 0 : 100.28 2 : 9.6 col 1 : locations 4 to 7 1 : 88.62 3 : 12.91 0 : 13.95 2 : 4.93 col 2 : locations 8 to 11 1 : 4.93 3 : 0.68 2 : 81.68 0 : 9.6 col 3 : locations 12 to 15 1 : 12.91 3 : 83.2 0 : 15.75 2 : 0.68 ./cs_demo2 < ../Matrix/t1 --- Matrix: 4-by-4, nnz: 10 (sym: 0: nnz 0), norm: 1.11e+01 blocks: 1 singletons: 0 structural rank: 4 QR natural time: 0.00 resid: 3.06e-17 QR amd(A'*A) time: 0.00 resid: 3.06e-17 LU natural time: 0.00 resid: 1.53e-17 LU amd(A+A') time: 0.00 resid: 1.53e-17 LU amd(S'*S) time: 0.00 resid: 0.00e+00 LU amd(A'*A) time: 0.00 resid: 1.53e-17 ./cs_demo2 < ../Matrix/ash219 --- Matrix: 219-by-85, nnz: 438 (sym: 0: nnz 0), norm: 9.00e+00 blocks: 1 singletons: 0 structural rank: 85 QR natural time: 0.00 resid: 1.61e-02 QR amd(A'*A) time: 0.00 resid: 1.61e-02 ./cs_demo2 < ../Matrix/bcsstk01 --- Matrix: 48-by-48, nnz: 224 (sym: -1: nnz 400), norm: 3.57e+09 blocks: 1 singletons: 0 structural rank: 48 QR natural time: 0.00 resid: 2.62e-19 QR amd(A'*A) time: 0.00 resid: 5.27e-19 LU natural time: 0.00 resid: 2.17e-19 LU amd(A+A') time: 0.00 resid: 1.87e-19 LU amd(S'*S) time: 0.00 resid: 2.38e-19 LU amd(A'*A) time: 0.00 resid: 2.38e-19 Chol natural time: 0.00 resid: 2.64e-19 Chol amd(A+A') time: 0.00 resid: 2.55e-19 ./cs_demo2 < ../Matrix/fs_183_1 --- Matrix: 183-by-183, nnz: 988 (sym: 0: nnz 0), norm: 1.70e+09 zero entries dropped: 71 tiny entries dropped: 10 blocks: 38 singletons: 37 structural rank: 183 QR natural time: 0.01 resid: 6.84e-28 QR amd(A'*A) time: 0.00 resid: 9.38e-28 LU natural time: 0.00 resid: 6.20e-28 LU amd(A+A') time: 0.00 resid: 1.55e-27 LU amd(S'*S) time: 0.01 resid: 6.98e-28 LU amd(A'*A) time: 0.00 resid: 6.98e-28 ./cs_demo2 < ../Matrix/mbeacxc --- Matrix: 492-by-490, nnz: 49920 (sym: 0: nnz 0), norm: 9.29e-01 blocks: 10 singletons: 8 structural rank: 448 QR natural time: 0.14 resid: nan QR amd(A'*A) time: 0.18 resid: nan ./cs_demo2 < ../Matrix/west0067 --- Matrix: 67-by-67, nnz: 294 (sym: 0: nnz 0), norm: 6.14e+00 blocks: 2 singletons: 1 structural rank: 67 QR natural time: 0.00 resid: 7.14e-17 QR amd(A'*A) time: 0.00 resid: 3.10e-17 LU natural time: 0.00 resid: 3.89e-17 LU amd(A+A') time: 0.00 resid: 2.27e-17 LU amd(S'*S) time: 0.00 resid: 1.95e-17 LU amd(A'*A) time: 0.00 resid: 2.60e-17 ./cs_demo2 < ../Matrix/lp_afiro --- Matrix: 27-by-51, nnz: 102 (sym: 0: nnz 0), norm: 3.43e+00 blocks: 1 singletons: 0 structural rank: 27 QR natural time: 0.00 resid: 3.96e-16 QR amd(A'*A) time: 0.00 resid: 2.25e-16 ./cs_demo2 < ../Matrix/bcsstk16 --- Matrix: 4884-by-4884, nnz: 147631 (sym: -1: nnz 290378), norm: 7.01e+09 blocks: 75 singletons: 74 structural rank: 4884 QR amd(A'*A) time: 1.88 resid: 1.39e-22 LU amd(A+A') time: 1.16 resid: 1.10e-22 LU amd(S'*S) time: 1.15 resid: 1.28e-22 LU amd(A'*A) time: 1.20 resid: 1.78e-22 Chol amd(A+A') time: 0.37 resid: 1.19e-22 ./cs_demo3 < ../Matrix/bcsstk01 --- Matrix: 48-by-48, nnz: 224 (sym: -1: nnz 400), norm: 3.57e+09 chol then update/downdate amd(A+A') symbolic chol time 0.00 numeric chol time 0.00 solve chol time 0.00 original: resid: 2.55e-19 update: time: 0.00 update: time: 0.00 (incl solve) resid: 9.66e-19 rechol: time: 0.00 (incl solve) resid: 1.55e-18 downdate: time: 0.00 downdate: time: 0.00 (incl solve) resid: 3.74e-17 ./cs_demo3 < ../Matrix/bcsstk16 --- Matrix: 4884-by-4884, nnz: 147631 (sym: -1: nnz 290378), norm: 7.01e+09 chol then update/downdate amd(A+A') symbolic chol time 0.02 numeric chol time 0.34 solve chol time 0.00 original: resid: 1.19e-22 update: time: 0.00 update: time: 0.01 (incl solve) resid: 1.12e-23 rechol: time: 0.34 (incl solve) resid: 1.17e-23 downdate: time: 0.00 downdate: time: 0.00 (incl solve) resid: 4.09e-22 SuiteSparse/CSparse/Demo/cs_demo.c0000644001170100242450000002315210440110365015745 0ustar davisfac#include "cs_demo.h" #include /* 1 if A is square & upper tri., -1 if square & lower tri., 0 otherwise */ static int is_sym (cs *A) { int is_upper, is_lower, j, p, n = A->n, m = A->m, *Ap = A->p, *Ai = A->i ; if (m != n) return (0) ; is_upper = 1 ; is_lower = 1 ; for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { if (Ai [p] > j) is_upper = 0 ; if (Ai [p] < j) is_lower = 0 ; } } return (is_upper ? 1 : (is_lower ? -1 : 0)) ; } /* true for off-diagonal entries */ static int dropdiag (int i, int j, double aij, void *other) { return (i != j) ;} /* C = A + triu(A,1)' */ static cs *make_sym (cs *A) { cs *AT, *C ; AT = cs_transpose (A, 1) ; /* AT = A' */ cs_fkeep (AT, &dropdiag, NULL) ; /* drop diagonal entries from AT */ C = cs_add (A, AT, 1, 1) ; /* C = A+AT */ cs_spfree (AT) ; return (C) ; } /* create a right-hand side */ static void rhs (double *x, double *b, int m) { int i ; for (i = 0 ; i < m ; i++) b [i] = 1 + ((double) i) / m ; for (i = 0 ; i < m ; i++) x [i] = b [i] ; } /* infinity-norm of x */ static double norm (double *x, int n) { int i ; double normx = 0 ; for (i = 0 ; i < n ; i++) normx = CS_MAX (normx, fabs (x [i])) ; return (normx) ; } /* compute residual, norm(A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf)) */ static void print_resid (int ok, cs *A, double *x, double *b, double *resid) { int i, m, n ; if (!ok) { printf (" (failed)\n") ; return ; } m = A->m ; n = A->n ; for (i = 0 ; i < m ; i++) resid [i] = -b [i] ; /* resid = -b */ cs_gaxpy (A, x, resid) ; /* resid = resid + A*x */ printf ("resid: %8.2e\n", norm (resid,m) / ((n == 0) ? 1 : (cs_norm (A) * norm (x,n) + norm (b,m)))) ; } static double tic (void) { return (clock () / (double) CLOCKS_PER_SEC) ; } static double toc (double t) { double s = tic () ; return (CS_MAX (0, s-t)) ; } static void print_order (int order) { switch (order) { case 0: printf ("natural ") ; break ; case 1: printf ("amd(A+A') ") ; break ; case 2: printf ("amd(S'*S) ") ; break ; case 3: printf ("amd(A'*A) ") ; break ; } } /* read a problem from a file */ problem *get_problem (FILE *f, double tol) { cs *T, *A, *C ; int sym, m, n, mn, nz1, nz2 ; problem *Prob ; Prob = cs_calloc (1, sizeof (problem)) ; if (!Prob) return (NULL) ; T = cs_load (f) ; /* load triplet matrix T from a file */ Prob->A = A = cs_compress (T) ; /* A = compressed-column form of T */ cs_spfree (T) ; /* clear T */ if (!cs_dupl (A)) return (free_problem (Prob)) ; /* sum up duplicates */ Prob->sym = sym = is_sym (A) ; /* determine if A is symmetric */ m = A->m ; n = A->n ; mn = CS_MAX (m,n) ; nz1 = A->p [n] ; cs_dropzeros (A) ; /* drop zero entries */ nz2 = A->p [n] ; if (tol > 0) cs_droptol (A, tol) ; /* drop tiny entries (just to test) */ Prob->C = C = sym ? make_sym (A) : A ; /* C = A + triu(A,1)', or C=A */ if (!C) return (free_problem (Prob)) ; printf ("\n--- Matrix: %d-by-%d, nnz: %d (sym: %d: nnz %d), norm: %8.2e\n", m, n, A->p [n], sym, sym ? C->p [n] : 0, cs_norm (C)) ; if (nz1 != nz2) printf ("zero entries dropped: %d\n", nz1 - nz2) ; if (nz2 != A->p [n]) printf ("tiny entries dropped: %d\n", nz2 - A->p [n]) ; Prob->b = cs_malloc (mn, sizeof (double)) ; Prob->x = cs_malloc (mn, sizeof (double)) ; Prob->resid = cs_malloc (mn, sizeof (double)) ; return ((!Prob->b || !Prob->x || !Prob->resid) ? free_problem (Prob) : Prob) ; } /* free a problem */ problem *free_problem (problem *Prob) { if (!Prob) return (NULL) ; cs_spfree (Prob->A) ; if (Prob->sym) cs_spfree (Prob->C) ; cs_free (Prob->b) ; cs_free (Prob->x) ; cs_free (Prob->resid) ; return (cs_free (Prob)) ; } /* solve a linear system using Cholesky, LU, and QR, with various orderings */ int demo2 (problem *Prob) { cs *A, *C ; double *b, *x, *resid, t, tol ; int k, m, n, ok, order, nb, ns, *r, *s, *rr, sprank ; csd *D ; if (!Prob) return (0) ; A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid; m = A->m ; n = A->n ; tol = Prob->sym ? 0.001 : 1 ; /* partial pivoting tolerance */ D = cs_dmperm (C, 1) ; /* randomized dmperm analysis */ if (!D) return (0) ; nb = D->nb ; r = D->r ; s = D->s ; rr = D->rr ; sprank = rr [3] ; for (ns = 0, k = 0 ; k < nb ; k++) { ns += ((r [k+1] == r [k]+1) && (s [k+1] == s [k]+1)) ; } printf ("blocks: %d singletons: %d structural rank: %d\n", nb, ns, sprank) ; cs_dfree (D) ; for (order = 0 ; order <= 3 ; order += 3) /* natural and amd(A'*A) */ { if (!order && m > 1000) continue ; printf ("QR ") ; print_order (order) ; rhs (x, b, m) ; /* compute right-hand side */ t = tic () ; ok = cs_qrsol (order, C, x) ; /* min norm(Ax-b) with QR */ printf ("time: %8.2f ", toc (t)) ; print_resid (ok, C, x, b, resid) ; /* print residual */ } if (m != n || sprank < n) return (1) ; /* return if rect. or singular*/ for (order = 0 ; order <= 3 ; order++) /* try all orderings */ { if (!order && m > 1000) continue ; printf ("LU ") ; print_order (order) ; rhs (x, b, m) ; /* compute right-hand side */ t = tic () ; ok = cs_lusol (order, C, x, tol) ; /* solve Ax=b with LU */ printf ("time: %8.2f ", toc (t)) ; print_resid (ok, C, x, b, resid) ; /* print residual */ } if (!Prob->sym) return (1) ; for (order = 0 ; order <= 1 ; order++) /* natural and amd(A+A') */ { if (!order && m > 1000) continue ; printf ("Chol ") ; print_order (order) ; rhs (x, b, m) ; /* compute right-hand side */ t = tic () ; ok = cs_cholsol (order, C, x) ; /* solve Ax=b with Cholesky */ printf ("time: %8.2f ", toc (t)) ; print_resid (ok, C, x, b, resid) ; /* print residual */ } return (1) ; } /* free workspace for demo3 */ static int done3 (int ok, css *S, csn *N, double *y, cs *W, cs *E, int *p) { cs_sfree (S) ; cs_nfree (N) ; cs_free (y) ; cs_spfree (W) ; cs_spfree (E) ; cs_free (p) ; return (ok) ; } /* Cholesky update/downdate */ int demo3 (problem *Prob) { cs *A, *C, *W = NULL, *WW, *WT, *E = NULL, *W2 ; int n, k, *Li, *Lp, *Wi, *Wp, p1, p2, *p = NULL, ok ; double *b, *x, *resid, *y = NULL, *Lx, *Wx, s, t, t1 ; css *S = NULL ; csn *N = NULL ; if (!Prob || !Prob->sym || Prob->A->n == 0) return (0) ; A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid; n = A->n ; if (!Prob->sym || n == 0) return (1) ; rhs (x, b, n) ; /* compute right-hand side */ printf ("\nchol then update/downdate ") ; print_order (1) ; y = cs_malloc (n, sizeof (double)) ; t = tic () ; S = cs_schol (1, C) ; /* symbolic Chol, amd(A+A') */ printf ("\nsymbolic chol time %8.2f\n", toc (t)) ; t = tic () ; N = cs_chol (C, S) ; /* numeric Cholesky */ printf ("numeric chol time %8.2f\n", toc (t)) ; if (!S || !N || !y) return (done3 (0, S, N, y, W, E, p)) ; t = tic () ; cs_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_lsolve (N->L, y) ; /* y = L\y */ cs_ltsolve (N->L, y) ; /* y = L'\y */ cs_pvec (S->pinv, y, x, n) ; /* x = P'*y */ printf ("solve chol time %8.2f\n", toc (t)) ; printf ("original: ") ; print_resid (1, C, x, b, resid) ; /* print residual */ k = n/2 ; /* construct W */ W = cs_spalloc (n, 1, n, 1, 0) ; if (!W) return (done3 (0, S, N, y, W, E, p)) ; Lp = N->L->p ; Li = N->L->i ; Lx = N->L->x ; Wp = W->p ; Wi = W->i ; Wx = W->x ; Wp [0] = 0 ; p1 = Lp [k] ; Wp [1] = Lp [k+1] - p1 ; s = Lx [p1] ; srand (1) ; for ( ; p1 < Lp [k+1] ; p1++) { p2 = p1 - Lp [k] ; Wi [p2] = Li [p1] ; Wx [p2] = s * rand () / ((double) RAND_MAX) ; } t = tic () ; ok = cs_updown (N->L, +1, W, S->parent) ; /* update: L*L'+W*W' */ t1 = toc (t) ; printf ("update: time: %8.2f\n", t1) ; if (!ok) return (done3 (0, S, N, y, W, E, p)) ; t = tic () ; cs_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_lsolve (N->L, y) ; /* y = L\y */ cs_ltsolve (N->L, y) ; /* y = L'\y */ cs_pvec (S->pinv, y, x, n) ; /* x = P'*y */ t = toc (t) ; p = cs_pinv (S->pinv, n) ; W2 = cs_permute (W, p, NULL, 1) ; /* E = C + (P'W)*(P'W)' */ WT = cs_transpose (W2,1) ; WW = cs_multiply (W2, WT) ; cs_spfree (WT) ; cs_spfree (W2) ; E = cs_add (C, WW, 1, 1) ; cs_spfree (WW) ; if (!E || !p) return (done3 (0, S, N, y, W, E, p)) ; printf ("update: time: %8.2f (incl solve) ", t1+t) ; print_resid (1, E, x, b, resid) ; /* print residual */ cs_nfree (N) ; /* clear N */ t = tic () ; N = cs_chol (E, S) ; /* numeric Cholesky */ if (!N) return (done3 (0, S, N, y, W, E, p)) ; cs_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_lsolve (N->L, y) ; /* y = L\y */ cs_ltsolve (N->L, y) ; /* y = L'\y */ cs_pvec (S->pinv, y, x, n) ; /* x = P'*y */ t = toc (t) ; printf ("rechol: time: %8.2f (incl solve) ", t) ; print_resid (1, E, x, b, resid) ; /* print residual */ t = tic () ; ok = cs_updown (N->L, -1, W, S->parent) ; /* downdate: L*L'-W*W' */ t1 = toc (t) ; if (!ok) return (done3 (0, S, N, y, W, E, p)) ; printf ("downdate: time: %8.2f\n", t1) ; t = tic () ; cs_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_lsolve (N->L, y) ; /* y = L\y */ cs_ltsolve (N->L, y) ; /* y = L'\y */ cs_pvec (S->pinv, y, x, n) ; /* x = P'*y */ t = toc (t) ; printf ("downdate: time: %8.2f (incl solve) ", t1+t) ; print_resid (1, C, x, b, resid) ; /* print residual */ return (done3 (1, S, N, y, W, E, p)) ; } SuiteSparse/CSparse/Demo/cs_demo.h0000644001170100242450000000044410414325170015754 0ustar davisfac#include "cs.h" typedef struct problem_struct { cs *A ; cs *C ; int sym ; double *x ; double *b ; double *resid ; } problem ; problem *get_problem (FILE *f, double tol) ; int demo2 (problem *Prob) ; int demo3 (problem *Prob) ; problem *free_problem (problem *Prob) ; SuiteSparse/CSparse/Demo/README.txt0000644001170100242450000000045310372176060015675 0ustar davisfacCSparse/Demo: to compile a run the demos, just type "make" in this directory. The printed residuals should all be small, except for the mbeacxc matrix (which is numerically and structurally singular), and ash219 (which is a least-squares problem). See cs_demo.out for the proper output of "make". SuiteSparse/CSparse/Tcov/0000755001170100242450000000000010711175720014223 5ustar davisfacSuiteSparse/CSparse/Tcov/nil0000644001170100242450000000000010325754634014726 0ustar davisfacSuiteSparse/CSparse/Tcov/covs0000755001170100242450000000033110336471716015127 0ustar davisfac#!/bin/csh echo '=================================================================' foreach file (*.?cov) echo $file grep "#####" $file echo '=================================================================' end SuiteSparse/CSparse/Tcov/zero0000644001170100242450000000000610375445021015121 0ustar davisfac0 0 0 SuiteSparse/CSparse/Tcov/cov.awk0000644001170100242450000000026610325730035015517 0ustar davisfac/cannot/ /function/ { f = $8 } /file/ { f = $8 } /lines/ { k = match ($1, "%") ; p = substr ($1, 1, k-1) ; if ((p+0) != 100) { printf "%8s %s\n", p, f } } SuiteSparse/CSparse/Tcov/Makefile0000644001170100242450000000572610617236571015704 0ustar davisfac# To run with valgrind: V = # V = valgrind -q # Linux test coverage CC = gcc CFLAGS = -O -g -fprofile-arcs -ftest-coverage \ -Wall -W -Wshadow -Wmissing-prototypes -Wstrict-prototypes \ -Wredundant-decls -Wnested-externs -Wdisabled-optimization -ansi \ -Wno-unused-parameter -Werror -I../Include -I../Demo run: all run1 runbook run3 runtest ./covall all: cs_demo1 cs_demo2 cs_demo3 cstcov_test CS = cs_add.o cs_amd.o cs_chol.o cs_cholsol.o cs_counts.o cs_cumsum.o \ cs_droptol.o cs_dropzeros.o cs_dupl.o cs_entry.o \ cs_etree.o cs_fkeep.o cs_gaxpy.o cs_happly.o cs_house.o cs_ipvec.o \ cs_lsolve.o cs_ltsolve.o cs_lu.o cs_lusol.o cs_util.o cs_multiply.o \ cs_permute.o cs_pinv.o cs_post.o cs_pvec.o cs_qr.o cs_qrsol.o \ cs_scatter.o cs_schol.o cs_sqr.o cs_symperm.o cs_tdfs.o \ cs_transpose.o cs_compress.o cs_usolve.o cs_scc.o cs_maxtrans.o \ cs_dmperm.o cs_updown.o cs_print.o cs_norm.o cs_load.o cs_dfs.o \ cstcov_malloc_test.o cs_utsolve.o cs_reach.o cs_spsolve.o cs_ereach.o \ cs_leaf.o cs_randperm.o $(CS): ../Include/cs.h cstcov_malloc_test.h .PRECIOUS: cs_%.c cs_dem%.c cs_dem%.c: - ln -s ../Demo/$@ cs_%.c: - ln -s ../Source/$@ cs_demo1: $(CS) cs_demo1.c $(CC) $(CFLAGS) -o cs_demo1 cs_demo1.c $(CS) -lm cs_demo2: $(CS) cs_demo2.c cs_demo.c $(CC) $(CFLAGS) -o cs_demo2 cs_demo2.c cs_demo.c $(CS) -lm cs_demo3: $(CS) cs_demo3.c cs_demo.c $(CC) $(CFLAGS) -o cs_demo3 cs_demo3.c cs_demo.c $(CS) -lm cstcov_test: $(CS) cstcov_test.c cs_demo.c $(CC) $(CFLAGS) -o cstcov_test cstcov_test.c cs_demo.c $(CS) -lm # tiny tests run1: all - $(V) ./cs_demo1 < nil - $(V) ./cs_demo1 < zero - $(V) ./cs_demo2 < nil - $(V) ./cs_demo2 < zero - $(V) ./cs_demo3 < nil # test coverage for book: runbook: all - $(V) ./cs_demo1 < ../Matrix/t1 - $(V) ./cs_demo2 < ../Matrix/bcsstk01 - $(V) ./cs_demo2 < ../Matrix/fs_183_1 - $(V) ./cs_demo2 < ../Matrix/mbeacxc - $(V) ./cs_demo2 < ../Matrix/west0067 - $(V) ./cs_demo2 < ../Matrix/lp_afiro - $(V) ./cs_demo3 < ../Matrix/bcsstk16 # other tests run3: all - $(V) ./cs_demo2 < ../Matrix/t1 - $(V) ./cs_demo2 < ../Matrix/ash219 - $(V) ./cs_demo3 < ../Matrix/bcsstk01 - $(V) ./cs_demo2 < ../Matrix/bcsstk16 - $(V) ./cs_demo2 < ../Matrix/ibm32a - $(V) ./cs_demo2 < ../Matrix/ibm32b # exhaustive memory tests runtest: all - $(V) ./cstcov_test nil > test_nil.out - $(V) ./cstcov_test zero > test_zero.out - $(V) ./cstcov_test ../Matrix/t1 > test_t1.out - $(V) ./cstcov_test ../Matrix/bcsstk01 > test_k1.out - $(V) ./cstcov_test ../Matrix/fs_183_1 > test_fs.out - $(V) ./cstcov_test ../Matrix/west0067 > test_we.out - $(V) ./cstcov_test ../Matrix/ash219 > test_ash.out - $(V) ./cstcov_test ../Matrix/lp_afiro > test_afiro.out readhb: readhb.f f77 -o readhb readhb.f readhb.f: - ln -s readhb.f clean: rm -f *.o *.bbg *.da *.gcov *.gcda *.gcno purge: distclean # remove everything for distribution, including all symbolic links distclean: clean rm -f cs_demo1 cs_demo2 readhb *.out *.a cs_demo3 cstcov_test cov.sort rm -f cs_*.c SuiteSparse/CSparse/Tcov/covall.linux0000755001170100242450000000031110336471635016571 0ustar davisfac#!/bin/csh ./gcovs cs*.c |& awk -f cov.awk | sort -n > cov.out sort -n cov.out > cov.sort ./covs > covs.out echo -n "statments not yet tested: " grep "#####" *gcov | wc -l ./cover *v > cover.out SuiteSparse/CSparse/Tcov/cover0000755001170100242450000000050310325730035015262 0ustar davisfac#!/bin/csh # usage: cover files echo '=================================================================' foreach file ($argv[1-]) echo $file echo '=================================================================' grep "#####" -A5 -B5 $file echo '=================================================================' end SuiteSparse/CSparse/Tcov/gcovs0000755001170100242450000000032510325727753015304 0ustar davisfac# usage: gcovs files echo '=================================================================' foreach file ($argv[1-]) gcov -f $file echo '=================================================================' end SuiteSparse/CSparse/Tcov/cstcov_test.c0000644001170100242450000000144210473073175016736 0ustar davisfac#include "cs_demo.h" /* cs_test: read a matrix and run cs_demo2 and cs_demo3, using malloc tests. */ #include "cstcov_malloc_test.h" int main (int argc, char **argv) { FILE *f ; problem *Prob ; int trials, ok, demo ; if (argc < 2) return (-1) ; printf ("cs_test, file: %s\n", argv [1]) ; for (demo = 2 ; demo <= 3 ; demo++) { printf ("demo: %d\n", demo) ; for (trials = 0 ; trials < 4000 ; trials++) { malloc_count = trials ; f = fopen (argv [1], "r") ; if (!f) return (-1) ; Prob = get_problem (f, (demo == 2) ? 1e-14 : 0) ; fclose (f) ; if (Prob) ok = (demo == 2) ? demo2 (Prob) : demo3 (Prob) ; free_problem (Prob) ; if (malloc_count > 0) break ; } printf ("demo %d # trials: %d\n", demo, trials) ; } return (0) ; } SuiteSparse/CSparse/Tcov/covall0000755001170100242450000000031110325753446015434 0ustar davisfac#!/bin/csh ./gcovs cs*.c |& awk -f cov.awk | sort -n > cov.out sort -n cov.out > cov.sort ./covs > covs.out echo -n "statments not yet tested: " grep "#####" *gcov | wc -l ./cover *v > cover.out SuiteSparse/CSparse/Tcov/covall.sol0000755001170100242450000000020710336471673016235 0ustar davisfac#!/bin/csh tcov -x cm.profile cs*.c >& /dev/null echo -n "statments not yet tested: " ./covs > covs.out grep "#####" *tcov | wc -l SuiteSparse/CSparse/Tcov/README.txt0000644001170100242450000000131010375604036015717 0ustar davisfacCSparse/Tcov: comprehensive test coverage for CSparse. Requires Linux. Type "make" to compile, and then "make run" to run the tests. The test coverage is in cover.out. The test output is printed on stdout, except for cs_test (which prints its output in various *.out files). If the test is successful, the last line printed should be "statements not yet tested: 0", and all printed residuals should be small. Note that you will get warnings about unused parameters for some functions. These warnings can be safely ignored. They are parameters for functions that are passed to cs_fkeep, and all functions used in this manner must have the same calling sequence, even if some of the parameters are not used. SuiteSparse/CSparse/Tcov/cstcov_malloc_test.c0000644001170100242450000000167510473073167020276 0ustar davisfac#include "cstcov_malloc_test.h" int malloc_count = INT_MAX ; /* wrapper for malloc */ void *cs_malloc (int n, size_t size) { if (--malloc_count < 0) return (NULL) ; /* pretend to fail */ return (malloc (CS_MAX (n,1) * size)) ; } /* wrapper for calloc */ void *cs_calloc (int n, size_t size) { if (--malloc_count < 0) return (NULL) ; /* pretend to fail */ return (calloc (CS_MAX (n,1), size)) ; } /* wrapper for free */ void *cs_free (void *p) { if (p) free (p) ; /* free p if it is not already NULL */ return (NULL) ; /* return NULL to simplify the use of cs_free */ } /* wrapper for realloc */ void *cs_realloc (void *p, int n, size_t size, int *ok) { void *pnew ; *ok = 0 ; if (--malloc_count < 0) return (p) ; /* pretend to fail */ pnew = realloc (p, CS_MAX (n,1) * size) ; /* realloc the block */ *ok = (pnew != NULL) ; return ((*ok) ? pnew : p) ; /* return original p if failure */ } SuiteSparse/CSparse/Tcov/cstcov_malloc_test.h0000644001170100242450000000012610425515205020260 0ustar davisfac#include "cs.h" #ifndef EXTERN #define EXTERN extern #endif EXTERN int malloc_count ; SuiteSparse/CSparse/Makefile0000644001170100242450000000067010710676627014766 0ustar davisfac# CSparse Makefile C: ( cd Lib ; $(MAKE) ) ( cd Demo ; $(MAKE) ) all: C cov library: ( cd Lib ; $(MAKE) ) cov: ( cd Tcov ; $(MAKE) ) mex: ( cd MATLAB ; $(MAKE) ) clean: ( cd Lib ; $(MAKE) clean ) ( cd Demo ; $(MAKE) clean ) ( cd Tcov ; $(MAKE) clean ) ( cd MATLAB ; $(MAKE) clean ) purge: ( cd Lib ; $(MAKE) purge ) ( cd Demo ; $(MAKE) purge ) ( cd Tcov ; $(MAKE) purge ) ( cd MATLAB ; $(MAKE) purge ) distclean: purge SuiteSparse/CSparse/MATLAB/0000755001170100242450000000000010712370307014247 5ustar davisfacSuiteSparse/CSparse/MATLAB/Demo/0000755001170100242450000000000010621036611015127 5ustar davisfacSuiteSparse/CSparse/MATLAB/Demo/Contents.m0000644001170100242450000000053210620375215017107 0ustar davisfac% CSparse MATLAB demos. % % cs_demo - run all CSparse demos. % cs_demo1 - MATLAB version of the CSparse/Demo/cs_demo1.c program. % cs_demo2 - MATLAB version of the CSparse/Demo/cs_demo2.c program. % cs_demo3 - MATLAB version of the CSparse/Demo/cs_demo3.c program. % Example: % help cs_demo % Copyright 2006-2007, Timothy A. Davis SuiteSparse/CSparse/MATLAB/Demo/cs_demo1.m0000644001170100242450000000342410621036577017015 0ustar davisfacfunction cs_demo1 (matrixpath) %CS_DEMO1 MATLAB version of the CSparse/Demo/cs_demo1.c program. % Uses both MATLAB functions and CSparse mexFunctions, and compares the two % results. This demo also plots the results, which the C version does not do. % % Example: % cs_demo1 % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (nargin < 1) matrixpath = [] ; end if (isempty (matrixpath)) try % older versions of MATLAB do not have an input argument to mfilename p = mfilename ('fullpath') ; t = strfind (p, filesep) ; matrixpath = [ p(1:t(end)) '../../Matrix' ] ; catch % assume we are in the C*Sparse/MATLAB/CSparse/Demo directory matrixpath = '../../Matrix' ; end end t1 = load ([matrixpath '/t1']) ; T = t1 %#ok A = sparse (T(:,1)+1, T(:,2)+1, T(:,3)) %#ok A2 = cs_sparse (T(:,1)+1, T(:,2)+1, T(:,3)) %#ok fprintf ('A difference: %g\n', norm (A-A2,1)) ; % CSparse/Demo/cs_demo1.c also clears the triplet matrix T at this point: % clear T clf subplot (2,2,1) ; cspy (A) ; title ('A', 'FontSize', 16) ; AT = A' %#ok AT2 = cs_transpose (A) %#ok fprintf ('AT difference: %g\n', norm (AT-AT2,1)) ; subplot (2,2,2) ; cspy (AT) ; title ('A''', 'FontSize', 16) ; n = size (A,2) ; I = speye (n) ; C = A*AT ; C2 = cs_multiply (A, AT) %#ok fprintf ('C difference: %g\n', norm (C-C2,1)) ; subplot (2,2,3) ; cspy (C) ; title ('C=A*A''', 'FontSize', 16) ; cnorm = norm (C,1) ; D = C + I*cnorm %#ok D2 = cs_add (C, I, 1, cnorm) %#ok fprintf ('D difference: %g\n', norm (D-D2,1)) ; subplot (2,2,4) ; cspy (D) ; title ('D=C+I*norm(C,1)', 'FontSize', 16) ; % CSparse/Demo/cs_demo1.c clears all matrices at this point: % clear A AT C D I % clear A2 AT2 C2 D2 SuiteSparse/CSparse/MATLAB/Demo/cs_demo2.m0000644001170100242450000000205210620721047017002 0ustar davisfacfunction cs_demo2 (do_pause, matrixpath) %CS_DEMO2 MATLAB version of the CSparse/Demo/cs_demo2.c program. % Solves a linear system using Cholesky, LU, and QR, with various orderings. % % Example: % cs_demo2 % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (nargin < 2) matrixpath = [] ; end if (isempty (matrixpath)) try % older versions of MATLAB do not have an input argument to mfilename p = mfilename ('fullpath') ; t = strfind (p, filesep) ; matrixpath = [ p(1:t(end)) '../../Matrix' ] ; catch % assume we are in the C*Sparse/MATLAB/CSparse/Demo directory matrixpath = '../../Matrix' ; end end matrices = { 't1', 'HB/fs_183_1', 'HB/west0067', 'LPnetlib/lp_afiro', ... 'HB/ash219', 'HB/mbeacxc', 'HB/bcsstk01', 'HB/bcsstk16' } ; if (nargin < 1) do_pause = 1 ; end for i = 1:length(matrices) name = matrices {i} ; [C sym] = get_problem (matrixpath, name, 1e-14) ; demo2 (C, sym, name) ; if (do_pause) input ('Hit enter to continue: ') ; end end SuiteSparse/CSparse/MATLAB/Demo/cs_demo3.m0000644001170100242450000000164110620721075017007 0ustar davisfacfunction cs_demo3 (do_pause, matrixpath) %CS_DEMO3 MATLAB version of the CSparse/Demo/cs_demo3.c program. % Cholesky update/downdate. % % Example: % cs_demo3 % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (nargin < 2) matrixpath = [] ; end if (isempty (matrixpath)) try % older versions of MATLAB do not have an input argument to mfilename p = mfilename ('fullpath') ; t = strfind (p, filesep) ; matrixpath = [ p(1:t(end)) '../../Matrix' ] ; catch % assume we are in the C*Sparse/MATLAB/CSparse/Demo directory matrixpath = '../../Matrix' ; end end matrices = { 'HB/bcsstk01', 'HB/bcsstk16' } ; if (nargin < 1) do_pause = 1 ; end for i = 1:length(matrices) name = matrices {i} ; [C sym] = get_problem (matrixpath, name, 1e-14) ; demo3 (C, sym, name) ; if (do_pause) input ('Hit enter to continue: ') ; end end SuiteSparse/CSparse/MATLAB/Demo/cs_demo.m0000644001170100242450000000206210620723646016730 0ustar davisfacfunction cs_demo (do_pause, matrixpath) %CS_DEMO run all CSparse demos. % cs_demo(0) will run all demos without pausing. % % Example: % cs_demo % See also: cs_demo1, cs_demo2, cs_demo3 % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse help cs_demo if (nargin < 1) do_pause = 1 ; end if (nargin < 2) matrixpath = [] ; end figure (1) clf fprintf ('\n\n-------------------------------------------------------\n') ; help cs_demo1 ; cs_demo1 (matrixpath) ; fprintf ('\n\n-------------------------------------------------------\n') ; help cs_demo2 cs_demo2 (do_pause, matrixpath) ; fprintf ('\n\n-------------------------------------------------------\n') ; help cs_demo3 cs_demo3 (do_pause, matrixpath) ; fprintf ('\n\n-------------------------------------------------------\n') ; help ex_1 ex_1 fprintf ('\n\n-------------------------------------------------------\n') ; help ex2 ex2 fprintf ('\n\n-------------------------------------------------------\n') ; help ex3 ex3 fprintf ('\nAll CSparse demos finished.\n') ; SuiteSparse/CSparse/MATLAB/Demo/README.txt0000644001170100242450000000010410364236410016623 0ustar davisfacDemo for MATLAB interface for CSparse. See Contents.m for details. SuiteSparse/CSparse/MATLAB/Demo/private/0000755001170100242450000000000010620730542016604 5ustar davisfacSuiteSparse/CSparse/MATLAB/Demo/private/demo2.m0000644001170100242450000000457310620671165020006 0ustar davisfacfunction demo2 (C, sym, name) %DEMO2: solve a linear system using Cholesky, LU, and QR, with various orderings % % Example: % demo2 (C, 1, 'name of system') % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clf subplot (2,2,1) ; cspy (C) ; title (name, 'FontSize', 16, 'Interpreter', 'none') ; [m n] = size (C) ; [p,q,r,s,cc,rr] = cs_dmperm (C) ; subplot (2,2,3) ; cs_dmspy (C) ; subplot (2,2,2) ; ccspy (C) ; drawnow sprnk = rr (4) - 1 ; nb = length (r) - 1 ; ns = sum ((r (2:nb+1) == r (1:nb)+1) & (s (2:nb+1) == s (1:nb)+1)) ; fprintf ('blocks: %d singletons %d structural rank %d\n', nb, ns, sprnk) ; if (sprnk ~= sprank (C)) error ('sprank mismatch!') ; end if (sprnk < min (m,n)) return ; % return if structurally singular end % the following code is not in the C version of this demo: if (m == n) if (sym) try [L,p] = cs_chol (C) ; %#ok subplot (2,2,4) ; cspy (L+triu(L',1)) ; title ('L+L''') ; catch % tol = 0.001 ; [L,U,p,q] = cs_lu (C,0.001) ; %#ok subplot (2,2,4) ; cspy (L+U-speye(n)) ; title ('L+U') ; end else [L,U,p,q] = cs_lu (C) ; %#ok subplot (2,2,4) ; cspy (L+U-speye(n)) ; title ('L+U') ; end else if (m < n) [V,beta,p,R,q] = cs_qr (C') ; %#ok else [V,beta,p,R,q] = cs_qr (C) ; %#ok end subplot (2,2,4) ; cspy (V+R) ; title ('V+R') ; end drawnow % continue with the MATLAB equivalent of the C cs_demo2 program for order = [0 3] if (order == 0 & m > 1000) %#ok continue ; end fprintf ('QR ') ; print_order (order) ; b = rhs (m) ; % compute right-hand-side tic ; x = cs_qrsol (C, b, order) ; fprintf ('time %8.2f ', toc) ; print_resid (C, x, b) ; end if (m ~= n) return ; end for order = 0:3 if (order == 0 & m > 1000) %#ok continue ; end fprintf ('LU ') ; print_order (order) ; b = rhs (m) ; % compute right-hand-side tic ; x = cs_lusol (C, b, order) ; fprintf ('time %8.2f ', toc) ; print_resid (C, x, b) ; end if (sym == 0) return ; end for order = 0:1 if (order == 0 & m > 1000) %#ok continue ; end fprintf ('Chol ') ; print_order (order) ; b = rhs (m) ; % compute right-hand-side tic ; x = cs_cholsol (C, b, order) ; fprintf ('time %8.2f ', toc) ; print_resid (C, x, b) ; end SuiteSparse/CSparse/MATLAB/Demo/private/demo3.m0000644001170100242450000000344310620671175020003 0ustar davisfacfunction demo3 (C, sym, name) %DEMO3: Cholesky update/downdate % % Example: % demo3 (C, 1, 'name of system') % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clf subplot (2,2,1) ; cspy (C) ; title (name, 'FontSize', 16, 'Interpreter', 'none') ; drawnow [m n] = size (C) ; if (m ~= n | ~sym) %#ok return ; end b = rhs (n) ; fprintf ('chol then update/downdate ') ; print_order (0) ; tic ; [L,p] = cs_chol (C) ; t = toc ; fprintf ('\nchol time: %8.2f\n', t) ; subplot (2,2,2) ; cspy (L) ; title ('L') ; drawnow tic ; x = b (p) ; x = cs_lsolve (L,x) ; x = cs_ltsolve (L,x) ; x (p) = x ; t = toc ; fprintf ('solve time: %8.2f\n', t) ; fprintf ('original: ') ; print_resid (C, x, b) ; k = fix (n/2) ; w = L(k,k) * sprand (L (:,k)) ; parent = cs_etree (C (p,p)) ; tic ; L2 = cs_updown (L, w, parent, '+') ; t1 = toc ; fprintf ('update: time: %8.2f\n', t1) ; subplot (2,2,3) ; cspy (L2) ; title ('updated L') ; subplot (2,2,4) ; cspy (L-L2) ; title ('L - updated L') ; drawnow tic ; x = b (p) ; x = cs_lsolve (L2,x) ; x = cs_ltsolve (L2,x) ; x (p) = x ; t = toc ; w2 = sparse (n,1) ; w2 (p) = w ; % w2 = P'*w wt = cs_transpose (w2) ; ww = cs_multiply (w2,wt) ; E = cs_add (C, ww, 1, 1) ; % E = C + w2*w2' ; fprintf ('update: time: %8.2f (incl solve) ', t1+t) ; print_resid (E, x, b) ; tic [L,p2] = cs_chol (E) ; x = b (p2) ; x = cs_lsolve (L,x) ; x = cs_ltsolve (L,x) ; x (p2) = x ; t = toc ; fprintf ('rechol: time: %8.2f (incl solve) ', t) ; print_resid (E, x, b) ; tic ; L3 = cs_updown (L2, w, parent, '-') ; t1 = toc ; fprintf ('downdate: time: %8.2f\n', t1) ; tic ; x = b (p) ; x = cs_lsolve (L3,x) ; x = cs_ltsolve (L3,x) ; x (p) = x ; t = toc ; fprintf ('downdate: time: %8.2f (incl solve) ', t1+t) ; print_resid (C, x, b) ; SuiteSparse/CSparse/MATLAB/Demo/private/ex2.m0000644001170100242450000000370510620725624017472 0ustar davisfacfunction ex2 (n) %EX2: create an n-by-n 2D mesh, four different ways % Example: % ex2 % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (nargin < 1) n = 30 ; end subplot (1,2,1) ; % method 1: create an n-by-n 2D mesh for the 2nd difference operator tic ii = zeros (5*n^2, 1) ; jj = zeros (5*n^2, 1) ; xx = zeros (5*n^2, 1) ; k = 1 ; for j = 0:n-1 for i = 0:n-1 s = j*n+i + 1 ; ii (k:k+4) = [(j-1)*n+i j*n+(i-1) j*n+i j*n+(i+1) (j+1)*n+i ] + 1 ; jj (k:k+4) = [s s s s s] ; xx (k:k+4) = [-1 -1 4 -1 -1] ; k = k + 5 ; end end % remove entries beyond the boundary keep = find (ii >= 1 & ii <= n^2 & jj >= 1 & jj <= n^2) ; ii = ii (keep) ; jj = jj (keep) ; xx = xx (keep) ; A = sparse (ii,jj,xx) ; t1 = toc ; disp (t1) ; % subplot (2,2,1) ; spy (A) title (sprintf ('%d-by-%d 2D mesh\n', n, n)) ; % method 2, using no for loops tic nn = 1:n^2 ; i2 = [nn-n ; nn-1 ; nn ; nn+1 ; nn+n] ; j2 = repmat (nn, 5, 1) ; x2 = repmat ([-1 -1 4 -1 -1]', 1, n^2) ; keep = find (i2 >= 1 & i2 <= n^2 & j2 >= 1 & j2 <= n^2) ; i2 = i2 (keep) ; j2 = j2 (keep) ; x2 = x2 (keep) ; C = sparse (i2,j2,x2) ; t2 = toc ; disp (t2) ; % subplot (2,2,2) ; plot (j2) ; % title ('2D fast j2') ; disp (A-C) ; any (ii-i2) any (jj-jj) % method 3: create an n-by-n-by-n 3D mesh for the 2nd difference operator tic [A, keep, ii, jj, xx] = mesh3d1 (n) ; ii = ii (keep) ; jj = jj (keep) ; xx = xx (keep) ; t3 = toc ; disp (t3) ; tic E = sparse (ii,jj,xx) ; t3b = toc ; disp (t3b) ; subplot (1,2,2) ; spy (E) ; title (sprintf ('%d-by-%d-by-%d 3D mesh\n', n, n, n)) ; % method 4, using no for loops tic nn = 1:n^3 ; i2 = [nn-n^2 ; nn-n ; nn-1 ; nn ; nn+1 ; nn+n ; nn+n^2] ; j2 = repmat (nn, 7, 1) ; x2 = repmat ([-1 -1 -1 6 -1 -1 -1]', 1, n^3) ; keep = find (i2 >= 1 & i2 <= n^3 & j2 >= 1 & j2 <= n^3) ; i2 = i2 (keep) ; j2 = j2 (keep) ; x2 = x2 (keep) ; t4 = toc ; disp (t4) ; tic F = sparse (i2,j2,x2) ; t4b = toc ; disp (t4b) ; disp (E-F) ; SuiteSparse/CSparse/MATLAB/Demo/private/ex3.m0000644001170100242450000000161410620372241017461 0ustar davisfacfunction ex3 %EX3: create 2D and 3D meshes using mesh2d1, mesh2d2, mesh3d1, mesh3d2. % Example: % ex3 % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse t1 = zeros (50,1) ; t2 = zeros (50,1) ; t3 = zeros (50,1) ; t4 = zeros (50,1) ; fprintf ('run times for each method, given n:\n') ; for n = 2:50 tic ; A = mesh2d1 (n) ; t1 (n) = toc ; tic B = mesh2d2 (n) ; t2 (n) = toc ; tic C = mesh3d1 (n) ; t3 (n) = toc ; tic D = mesh3d2 (n) ; t4 (n) = toc ; fprintf ('%3d: %8.3f %8.3f %8.3f %8.3f\n', n, t1(n), t2(n), t3(n), t4(n)) ; subplot (2,2,1) ; spy (A) ; title ('2D mesh, method 1') ; subplot (2,2,2) ; spy (B) ; title ('2D mesh, method 2') ; subplot (2,2,3) ; spy (C) ; title ('3D mesh, method 1') ; subplot (2,2,4) ; spy (D) ; title ('3D mesh, method 2') ; drawnow end SuiteSparse/CSparse/MATLAB/Demo/private/rhs.m0000644001170100242450000000034710620372266017567 0ustar davisfacfunction b = rhs (m) % b = rhs (m), compute a right-hand-side % Example: % b = rhs (30) ; % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse b = ones (m,1) + (0:m-1)'/m ; SuiteSparse/CSparse/MATLAB/Demo/private/print_order.m0000644001170100242450000000072110620372257021316 0ustar davisfacfunction print_order (order) % print_order(order) prints the ordering determined by the order parameter % Example: % print_order (0) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse switch (fix (order)) case 0 fprintf ('natural ') ; case 1 fprintf ('amd(A+A'') ') ; case 2 fprintf ('amd(S''*S) ') ; case 3 fprintf ('amd(A''*A) ') ; otherwise fprintf ('undefined ') ; end SuiteSparse/CSparse/MATLAB/Demo/private/get_problem.m0000644001170100242450000000254710620720547021275 0ustar davisfacfunction [C, sym] = get_problem (prefix, name, tol) % [C, sym] = get_problem(prefix, name,tol) % read a problem from a file, drop entries with abs value < tol % tol defaults to zero if not present % % Example: % [C, sym] = get_problem ('', 'west0067') ; % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse fprintf ('\n------------------- Matrix: %s\n', name) ; if (nargin < 2) tol = 0 ; end s = find (name == '/') ; if (isempty (s)) s = 0 ; end % f = sprintf ('%s..%s..%sMatrix%s%s', ... % prefix, filesep, filesep, filesep, name (s+1:end)) ; % load the triplet version of the matrix T = load ([ prefix '/' name(s+1:end) ]) ; % convert into a sparse matrix and compare with cs_sparse A = sparse (T (:,1)+1, T (:,2)+1, T (:,3)) ; A2 = cs_sparse (T (:,1)+1, T (:,2)+1, T (:,3)) ; err = norm (A-A2,1) ; if (err > 0) fprintf ('A difference: %g\n', err) ; end [m n] = size (A) ; nz2 = nnz (A) ; if (tol > 0) A = cs_droptol (A, tol) ; end % assume A is symmetric if it is upper or lower triangular sym = is_sym (A) ; if (sym) C = A + (A' - diag (diag (A))) ; else C = A ; end fprintf ('--- Matrix: %d-by-%d, nnz: %d (sym: %d nnz %d), norm: %8.2e\n', ... m, n, nnz(A), sym, abs(sym)*nnz(C), norm (C,1)) ; if (nz2 ~= nnz(A)) fprintf ('tiny entries dropped: %d\n', nz2 - nnz(A)) end SuiteSparse/CSparse/MATLAB/Demo/private/is_sym.m0000644001170100242450000000071510620372246020273 0ustar davisfacfunction sym = is_sym (A) % sym = is_sym(A) % 1 if A is square and upper tri., -1 if square and lower tri., 0 otherwise % % Example: % sym = is_sym (A) ; % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; sym = 0 ; if (m == n) is_upper = nnz (tril (A,-1)) == 0 ; is_lower = nnz (triu (A,1)) == 0 ; if (is_upper) sym = 1 ; elseif (is_lower) sym = -1 ; end end SuiteSparse/CSparse/MATLAB/Demo/private/ex_1.m0000644001170100242450000000345010620372224017617 0ustar davisfacfunction ex_1 %EX_1: four methods for creating the same matrix. % (please wait, this can take a while...) % Example: % ex_1 % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = 1000 ; nz = 1e5 ; tic % method 1: A(i,j) = ... rand ('state', 0) ; A = sparse (n,n) ; for k = 1:nz % compute some arbitrary entry and add it into the matrix i = 1 + fix (n * rand (1)) ; j = 1 + fix (n * rand (1)) ; x = rand (1) ; A (i,j) = A (i,j) + x ; % VERY slow, esp. if A(i,j) not already nonzero! end fprintf ('Method 1: ') ; toc A1 = A ; tic % method 2: triplet form, one entry at a time rand ('state', 0) ; ii = zeros (nz, 1) ; % preallocate ii, jj, and xx jj = zeros (nz, 1) ; xx = zeros (nz, 1) ; for k = 1:nz % compute some arbitrary entry and add it into the matrix ii (k) = 1 + fix (n * rand (1)) ; jj (k) = 1 + fix (n * rand (1)) ; xx (k) = rand (1) ; end A = sparse (ii,jj,xx) ; fprintf ('Method 2: ') ; toc A2 = A ; disp (A1-A2) ; tic % method 3: triplet form, one entry at a time, pretend nz is unknown rand ('state', 0) ; len = 16 ; ii = zeros (len, 1) ; jj = zeros (len, 1) ; xx = zeros (len, 1) ; for k = 1:nz % compute some arbitrary entry and add it into the matrix if (k > len) % double the size of ii,jj,xx len = 2*len ; ii (len) = 0 ; jj (len) = 0 ; xx (len) = 0 ; end ii (k) = 1 + fix (n * rand (1)) ; jj (k) = 1 + fix (n * rand (1)) ; xx (k) = rand (1) ; end A = sparse (ii (1:k), jj (1:k), xx (1:k)) ; fprintf ('Method 3: ') ; toc A3 = A ; disp (A1-A3) ; tic % method 4: avoid the for loop rand ('state', 0) ; e = rand (3, nz) ; e (1,:) = 1 + fix (n * e (1,:)) ; e (2,:) = 1 + fix (n * e (2,:)) ; A = sparse (e (1,:), e (2,:), e (3,:)) ; fprintf ('Method 4: ') ; toc A4 = A ; disp (A1-A4) ; SuiteSparse/CSparse/MATLAB/Demo/private/frand.m0000644001170100242450000000133210620372243020053 0ustar davisfacfunction A = frand (n,nel,s) % A = frand (n,nel,s) creates an n-by-n sparse matrix consisting of nel finite % elements, each of which are of size s-by-s with random symmetric nonzero % pattern, plus the identity matrix. % % Example: % A = frand (100, 100, 4) ; cspy (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse ss = s^2 ; nz = nel*ss ; ii = zeros (nz,1) ; jj = zeros (nz,1) ; xx = zeros (nz,1) ; k = 1 ; for e = 1:nel i = 1 + fix (n * rand (s,1)) ; i = repmat (i, 1, s) ; j = i' ; x = rand (s,s) ; ii (k:k+ss-1) = i (:) ; jj (k:k+ss-1) = j (:) ; xx (k:k+ss-1) = x (:) ; k = k + ss ; end A = sparse (ii,jj,xx,n,n) + speye (n) ; SuiteSparse/CSparse/MATLAB/Demo/private/print_resid.m0000644001170100242450000000060310620372261021303 0ustar davisfacfunction print_resid (A, x, b) % print_resid (A, x, b), print the relative residual, % norm (A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf)) % Example: % print_resid (A, x, b) ; % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse fprintf ('resid: %8.2e\n', ... norm (A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf))) ; SuiteSparse/CSparse/MATLAB/Demo/private/mesh2d1.m0000644001170100242450000000130010620372250020215 0ustar davisfacfunction A = mesh2d1 (n) % create an n-by-n 2D mesh for the 2nd difference operator % Example: % A = mesh2d1 (30) ; % a 30-by-30 mesh % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse ii = zeros (5*n^2, 1) ; % preallocate ii, jj, and xx jj = zeros (5*n^2, 1) ; xx = zeros (5*n^2, 1) ; k = 1 ; for j = 0:n-1 for i = 0:n-1 s = j*n+i + 1 ; ii (k:k+4) = [(j-1)*n+i j*n+(i-1) j*n+i j*n+(i+1) (j+1)*n+i ] + 1 ; jj (k:k+4) = [s s s s s] ; xx (k:k+4) = [-1 -1 4 -1 -1] ; k = k + 5 ; end end % remove entries beyond the boundary keep = find (ii >= 1 & ii <= n^2 & jj >= 1 & jj <= n^2) ; A = sparse (ii (keep), jj (keep), xx (keep)) ; SuiteSparse/CSparse/MATLAB/Demo/private/mesh2d2.m0000644001170100242450000000072610620372252020233 0ustar davisfacfunction A = mesh2d2 (n) % create an n-by-n 2D mesh for the 2nd difference operator % Example: % A = mesh2d2 (30) ; % a 30-by-30 mesh % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse nn = 1:n^2 ; ii = [nn-n ; nn-1 ; nn ; nn+1 ; nn+n] ; jj = repmat (nn, 5, 1) ; xx = repmat ([-1 -1 4 -1 -1]', 1, n^2) ; keep = find (ii >= 1 & ii <= n^2 & jj >= 1 & jj <= n^2) ; A = sparse (ii (keep), jj (keep), xx (keep)) ; SuiteSparse/CSparse/MATLAB/Demo/private/mesh3d1.m0000644001170100242450000000151510620725647020242 0ustar davisfacfunction [A, keep, ii, jj, xx] = mesh3d1 (n) % create an n-by-n-by-n 3D mesh for the 2nd difference operator % Example: % A = mesh3d1 (10) ; % a 10-by-10-by-10 mesh % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse ii = zeros (7*n^3, 1) ; jj = zeros (7*n^3, 1) ; xx = zeros (7*n^3, 1) ; t = 1 ; for k = 0:n-1 for j = 0:n-1 for i = 0:n-1 s = k*n^2 + j*n+i + 1 ; ii (t:t+6) = [ (k-1)*n^2 + j*n+i k*n^2 + (j-1)*n+i k*n^2 + j*n+(i-1) k*n^2 + j*n+i k*n^2 + j*n+(i+1) k*n^2 + (j+1)*n+i (k+1)*n^2 + j*n+i ]' + 1 ; jj (t:t+6) = [s s s s s s s] ; xx (t:t+6) = [-1 -1 -1 6 -1 -1 -1] ; t = t + 7 ; end end end keep = find (ii >= 1 & ii <= n^3 & jj >= 1 & jj <= n^3) ; A = sparse (ii (keep), jj (keep), xx (keep)) ; SuiteSparse/CSparse/MATLAB/Demo/private/mesh3d2.m0000644001170100242450000000077110620372255020237 0ustar davisfacfunction A = mesh3d2 (n) % create an n-by-n-by-n 3D mesh for the 2nd difference operator % Example: % A = mesh3d2 (10) ; % a 10-by-10-by-10 mesh % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse nn = 1:n^3 ; ii = [nn-n^2 ; nn-n ; nn-1 ; nn ; nn+1 ; nn+n ; nn+n^2] ; jj = repmat (nn, 7, 1) ; xx = repmat ([-1 -1 -1 6 -1 -1 -1]', 1, n^3) ; keep = find (ii >= 1 & ii <= n^3 & jj >= 1 & jj <= n^3) ; A = sparse (ii (keep), jj (keep), xx (keep)) ; SuiteSparse/CSparse/MATLAB/Test/0000755001170100242450000000000010711653403015166 5ustar davisfacSuiteSparse/CSparse/MATLAB/Test/hmake1.m0000644001170100242450000000127110620373127016514 0ustar davisfacfunction [v,beta,xnorm] = hmake1 (x) %HMAKE1 construct a Householder reflection % Example: % [v,beta,xnorm] = hmake1 (x) % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = length (x) ; if (n == 1) v = 1 ; xnorm = norm (x) ; if (x (1) < 0) beta = 2 ; else beta = 0 ; end return end sigma = x (2:n)'*x(2:n) ; xnorm = sqrt (x (1)^2 + sigma) ; v = x ; if (sigma == 0) v (1) = 1 ; if (x (1) < 0) beta = 2 ; else beta = 0 ; end else if (x (1) <= 0) v (1) = x(1) - xnorm ; else v (1) = -sigma / (x(1) + xnorm) ; end beta = (2*v(1)^2) / (sigma + v(1)^2) ; v = v / v(1) ; end SuiteSparse/CSparse/MATLAB/Test/sqr_example.m0000644001170100242450000000101510620373174017664 0ustar davisfacfunction sqr_example %SQR_EXAMPLE test cs_sqr % Example: % sqr_example % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse Prob = UFget (706) ; A = Prob.A' ; q = colamd (A) ; A = A (:,q) ; A = sprandn (A) ; [m n] = size (A) ; [vnz, rnz, parent, c, leftmost, p] = cs_sqr(A) ; m2 = length (p) ; B = [A ; sparse(m2-m,n)] ; B = B (p,q) ; R1 = gqr3 (B) ; clf subplot (2,2,1) ; spy(A) subplot (2,2,3) ; spy (chol (A'*A + 100*speye(n))) ; subplot (2,2,4) ; spy (R1) ; SuiteSparse/CSparse/MATLAB/Test/cs_sparse2_mex.c0000644001170100242450000000172110415621446020253 0ustar davisfac#include "cs_mex.h" /* A = cs_sparse2 (i,j,x), removing duplicates and numerically zero entries, * and returning A sorted (test cs_entry) */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double *Tx ; cs *A, *C, *T ; int k, m, n, nz, *Ti, *Tj ; if (nargout > 1 || nargin != 3) { mexErrMsgTxt ("Usage: A = cs_sparse2(i,j,x)") ; } nz = mxGetM (pargin [0]) ; Ti = cs_mex_get_int (nz, pargin [0], &m, 1) ; Tj = cs_mex_get_int (nz, pargin [1], &n, 1) ; cs_mex_check (1, nz, 1, 0, 0, 1, pargin [2]) ; Tx = mxGetPr (pargin [2]) ; T = cs_spalloc (n, m, 1, 1, 1) ; for (k = 0 ; k < nz ; k++) { cs_entry (T, Tj [k], Ti [k], Tx [k]) ; } C = cs_compress (T) ; cs_spfree (T) ; cs_dupl (C) ; cs_dropzeros (C) ; A = cs_transpose (C, 1) ; cs_spfree (C) ; pargout [0] = cs_mex_put_sparse (&A) ; cs_free (Ti) ; cs_free (Tj) ; } SuiteSparse/CSparse/MATLAB/Test/cs_rowcnt_mex.c0000644001170100242450000000505110677526747020232 0ustar davisfac/* Compute the row counts of the Cholesky factor L of the matrix A. Uses * the lower triangular part of A. */ #include "cs_mex.h" static void firstdesc (int n, int *parent, int *post, int *first, int *level) { int len, i, k, r, s ; for (i = 0 ; i < n ; i++) first [i] = -1 ; for (k = 0 ; k < n ; k++) { i = post [k] ; /* node i of etree is kth postordered node */ len = 0 ; /* traverse from i towards the root */ for (r = i ; r != -1 && first [r] == -1 ; r = parent [r], len++) first [r] = k ; len += (r == -1) ? (-1) : level [r] ; /* root node or end of path */ for (s = i ; s != r ; s = parent [s]) level [s] = len-- ; } } static int *rowcnt (cs *A, int *parent, int *post) /* return rowcount [0..n-1] */ { int i, j, k, p, q, n, jleaf, *Ap, *Ai, *maxfirst, *ancestor, *prevleaf, *w, *first, *level, *rowcount ; n = A->n ; Ap = A->p ; Ai = A->i ; /* get A */ w = cs_malloc (5*n, sizeof (int)) ; /* get workspace */ ancestor = w ; maxfirst = w+n ; prevleaf = w+2*n ; first = w+3*n ; level = w+4*n ; rowcount = cs_malloc (n, sizeof (int)) ; /* allocate result */ firstdesc (n, parent, post, first, level) ; /* find first and level */ for (i = 0 ; i < n ; i++) { rowcount [i] = 1 ; /* count the diagonal of L */ prevleaf [i] = -1 ; /* no previous leaf of the ith row subtree */ maxfirst [i] = -1 ; /* max first[j] for node j in ith subtree */ ancestor [i] = i ; /* every node is in its own set, by itself */ } for (k = 0 ; k < n ; k++) { j = post [k] ; /* j is the kth node in the postordered etree */ for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; q = cs_leaf (i, j, first, maxfirst, prevleaf, ancestor, &jleaf) ; if (jleaf) rowcount [i] += (level [j] - level [q]) ; } if (parent [j] != -1) ancestor [j] = parent [j] ; } cs_free (w) ; return (rowcount) ; } void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs *A, Amatrix ; double *x ; int i, n, *parent, *post, *rowcount ; if (nargout > 1 || nargin != 3) { mexErrMsgTxt ("Usage: r = rowcnt(A,parent,post)") ; } /* get inputs */ A = cs_mex_get_sparse (&Amatrix, 1, 0, pargin [0]) ; n = A->n ; parent = cs_mex_get_int (n, pargin [1], &i, 0) ; post = cs_mex_get_int (n, pargin [2], &i, 1) ; rowcount = rowcnt (A, parent, post) ; pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ; x = mxGetPr (pargout [0]) ; for (i = 0 ; i < n ; i++) x [i] = rowcount [i] ; cs_free (rowcount) ; } SuiteSparse/CSparse/MATLAB/Test/test_qrsol.m0000644001170100242450000000145610620373304017547 0ustar davisfacfunction test_qrsol %TEST_QRSOL test cs_qrsol % % Example: % test_qrsol % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; k = 0 ; rs1 = zeros (1,0) ; rs2 = zeros (1,0) ; for i = f Prob = UFget (i,index) ; A = Prob.A ; if (~isreal (A)) continue ; end [m n] = size (A) ; %#ok b = rand (m,1) ; x1 = A\b ; x2 = cs_qrsol (A,b) ; x1 (~isfinite (x1)) = 0 ; x2 (~isfinite (x2)) = 0 ; r1 = norm (A*x1-b) ; r2 = norm (A*x2-b) ; k = k + 1 ; rs1 (k) = r1 ; rs2 (k) = r2 ; fprintf ('%30s MATLAB: %6.2e CS: %6.2e\n', Prob.name, r1, r2) ; loglog (rs1, rs2, 'o') ; drawnow clear A b x1 x2 % pack end SuiteSparse/CSparse/MATLAB/Test/check_if_same.m0000644001170100242450000000063110620373016020102 0ustar davisfacfunction check_if_same (p1,p2) %CHECK_IF_SAME check if two inputs are identical or not % % Example: % check_if_same (1:5, 2:6) % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (isempty (p1)) if (~isempty (p2)) p1 %#ok p2 %#ok error ('empty!') ; end elseif (any (p1 ~= p2)) p1 %#ok p2 %#ok error ('!') ; end SuiteSparse/CSparse/MATLAB/Test/qr_left.m0000644001170100242450000000113010620373162016773 0ustar davisfacfunction [V,Beta,R] = qr_left (A) %QR_LEFT left-looking Householder QR factorization. % Example: % [V,Beta,R] = qr_left (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; V = zeros (m,n) ; Beta = zeros (1,n) ; R = zeros (m,n) ; for k = 1:n x = A (:,k) ; for i = 1:k-1 v = V (i:m,i) ; beta = Beta (i) ; x (i:m) = x (i:m) - v * (beta * (v' * x (i:m))) ; end [v,beta,s] = gallery ('house', x (k:m), 2) ; V (k:m,k) = v ; Beta (k) = beta ; R (1:(k-1),k) = x (1:(k-1)) ; R (k,k) = s ; end SuiteSparse/CSparse/MATLAB/Test/test_qr1.m0000644001170100242450000000162410620373300017103 0ustar davisfacfunction test_qr1 %TEST_QR1 test QR factorizations % % Example: % test_qr1 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; for i = f Prob = UFget (i,index) ; A = Prob.A ; if (~isreal (A)) continue ; end [m n] = size (A) ; if (m < n) A = A' ; end t0 = 0 ; k0 = 0 ; while (t0 < 0.1) tic q = colamd (A, [-1 10]) ; % [Q,R] = qr (A (:,q)) ; R = qr (A (:,q)) ; %#ok t = toc ; t0 = t0 + t ; k0 = k0 + 1 ; end t0 = t0 / k0 ; t1 = 0 ; k1 = 0 ; while (t1 < 0.1) tic [V,beta, p, R,q] = cs_qr (A) ; %#ok t = toc ; t1 = t1 + t ; k1 = k1 + 1 ; end t1 = t1 / k1 ; fprintf (... '%25s MATLAB: %10.4f (%8d) CS: %10.4f (%8d) speedup: %8.2f\n', ... Prob.name, t0, k0, t1, k1, t0/t1) ; end SuiteSparse/CSparse/MATLAB/Test/test_sep.m0000644001170100242450000000350610620373310017171 0ustar davisfacfunction test_sep %TEST_SEP test cs_sep, and compare with Gilbert's meshpart vtxsep % (requires MESHPART). % % Example: % test_sep % % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; clf for k = 1:length(f) i = f (k) ; Prob = UFget (i) ; disp (Prob) ; A = spones (Prob.A) ; [m n] = size (A) ; if (m ~= n) A = A'*A ; end A = A|A' ; p = symrcm (A) ; n = size (A,1) ; n2 = fix (n/2) ; a = p (1:n2) ; b = p ((n2+1):n) ; clf subplot (2,3,1) ; spy (A) ; subplot (2,3,2) ; spy (A (p,p)) ; hold on plot ([.5 n2+.5 n2+.5 .5 .5], [.5 .5 n2+.5 n2+.5 .5], 'r', 'LineWidth', 2) ; hold off subplot (2,3,3) ; spy (A (a,b)) ; title ('edge sep') ; subplot (2,3,6) ; cs_dmspy (A (a,b)) ; title ('node sep') ; [s as bs] = vtxsep (A,a,b) ; %#ok [s2 a2 b2] = cs_sep (A,a,b) ; p2 = [a2 b2 s2] ; B = A (p2,p2) ; subplot (2,3,5) ; spy (B) ; hold on px = [s2 a2 b2] ; if (any (sort (px) ~= 1:n)) px %#ok n %#ok error ('!') ; end na = length (a2) ; nb = length (b2) ; ns = length (s2) ; %#ok nab = na + nb ; plot ([.5 na+.5 na+.5 .5 .5], [.5 .5 na+.5 na+.5 .5], 'r', 'LineWidth', 2) ; plot ([na nab nab na na]+0.5, [na na nab nab na]+0.5, 'r', 'LineWidth', 2) ; plot ([.5 nab+.5 nab+.5 .5 .5], [.5 .5 nab+.5 nab+.5 .5], 'g', 'LineWidth', 1) ; hold off nz1 = nnz (A (a2,b2)) ; if (nz1 ~= 0) nz1 %#ok error ('!') ; end nz2 = nnz (A (a2,b2)) ; if (nz2 ~= 0) nz2 %#ok error ('!') ; end if (length (s) ~= length (s2)) fprintf ('lengths differ: %d %d\n', length (s), length (s2)) ; end drawnow % pause end SuiteSparse/CSparse/MATLAB/Test/Makefile0000644001170100242450000000225610620632165016634 0ustar davisfacMEX = mex -O AR = ar cr RANLIB = ranlib all: cs_sparse2.mexglx \ cs_ipvec.mexglx \ cs_pvec.mexglx \ cs_reach.mexglx \ cs_maxtransr.mexglx \ cs_reachr.mexglx \ cs_rowcnt.mexglx \ cs_frand.mexglx mexcsparse: ( cd ../CSparse ; make mexcsparse.a ) I = -I../../Include -I../CSparse cs_ipvec.mexglx: cs_ipvec_mex.c mexcsparse $(MEX) -output cs_ipvec $< $(I) ../CSparse/mexcsparse.a cs_pvec.mexglx: cs_pvec_mex.c mexcsparse $(MEX) -output cs_pvec $< $(I) ../CSparse/mexcsparse.a cs_reach.mexglx: cs_reach_mex.c mexcsparse $(MEX) -output cs_reach $< $(I) ../CSparse/mexcsparse.a cs_sparse2.mexglx: cs_sparse2_mex.c mexcsparse $(MEX) -output cs_sparse2 $< $(I) ../CSparse/mexcsparse.a cs_maxtransr.mexglx: cs_maxtransr_mex.c mexcsparse $(MEX) -output cs_maxtransr $< $(I) ../CSparse/mexcsparse.a cs_reachr.mexglx: cs_reachr_mex.c mexcsparse $(MEX) -output cs_reachr $< $(I) ../CSparse/mexcsparse.a cs_rowcnt.mexglx: cs_rowcnt_mex.c mexcsparse $(MEX) -output cs_rowcnt $< $(I) ../CSparse/mexcsparse.a cs_frand.mexglx: cs_frand_mex.c mexcsparse $(MEX) -output cs_frand $< $(I) ../CSparse/mexcsparse.a clean: rm -f *.o distclean: clean rm -f *.mex* *.dll *.a purge: distclean SuiteSparse/CSparse/MATLAB/Test/givens2.m0000644001170100242450000000061310620373121016714 0ustar davisfacfunction g = givens2(a,b) %GIVENS2 find a Givens rotation. % Example: % g = givens2(a,b) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (b == 0) c = 1 ; s = 0 ; elseif (abs (b) > abs (a)) tau = -a/b ; s = 1 / sqrt (1+tau^2) ; c = s*tau ; else tau = -b/a ; c = 1 / sqrt (1+tau^2) ; s = c*tau ; end g = [c -s ; s c] ; SuiteSparse/CSparse/MATLAB/Test/cs_q1.m0000644001170100242450000000061710620373075016361 0ustar davisfacfunction Q = cs_q1 (V, Beta, p) %CS_Q1 construct Q from Householder vectors % Example: % Q = cs_q1 (V, beta, p) % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (V) ; Q = speye (m) ; if (nargin > 2) Q = Q (:,p) ; end for i = 1:m for k = 1:n Q (i,:) = Q (i,:) - ((Q(i,:) * V(:,k)) * Beta(k)) * V(:,k)' ; end end SuiteSparse/CSparse/MATLAB/Test/cspy_test.m0000644001170100242450000000155510620666207017374 0ustar davisfacfunction cspy_test %CSPY_TEST test cspy and cs_dmspy % Example % cspy_test % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; clf % f = f (523:end) ; % f = f ((find (f == 938)):end) ; for i = f Prob = UFget (i,index) ; disp (Prob) ; A = Prob.A ; try subplot (1,4,1) ; cspy (A) ; drawnow subplot (1,4,2) ; cspy (A,64) ; drawnow subplot (1,4,3) ; cs_dmspy (A) ; drawnow subplot (1,4,4) ; cs_dmspy (A,0) ; drawnow catch fprintf ('failed...\n') ; end [m n] = size (A) ; if (m == n & nnz (diag (A)) == n) %#ok p = cs_dmperm (A) ; if (any (p ~= 1:n)) error ('!') ; end [p q r s cc rr] = cs_dmperm (A) ; %#ok if (any (p ~= q)) error ('not sym!') ; end end drawnow end SuiteSparse/CSparse/MATLAB/Test/cs_maxtransr.m0000644001170100242450000000043710620373065020056 0ustar davisfacfunction p = cs_maxtransr(A) %#ok %CS_MAXTRANSR recursive maximum matching algorithm % Example: % p = cs_maxtransr(A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_maxtransr mexFunction not found') ; SuiteSparse/CSparse/MATLAB/Test/qr2.m0000644001170100242450000000100510620373153016044 0ustar davisfacfunction [V,Beta,R] = qr2 (A) %QR2 QR factorization based on Householder reflections % % Example: % [V,beta,R] = qr2 (A) % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; V = zeros (m,n) ; Beta = zeros (1,n) ; for k = 1:n % [v,beta,s] = gallery ('house', A (k:m,k), 2) ; [v,beta] = house (A (k:m,k)) ; V (k:m,k) = v ; Beta (k) = beta ; A (k:m,k:n) = A (k:m,k:n) - v * (beta * (v' * A (k:m,k:n))) ; end R = triu (A) ; SuiteSparse/CSparse/MATLAB/Test/cholupdown.m0000644001170100242450000000216410620373041017525 0ustar davisfacfunction L = cholupdown (Lold, sigma, w) %CHOLUPDOWN Cholesky update/downdate (Bischof, Pan, and Tang method) % Example: % L = cholupdown (Lold, sigma, w) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse beta = 1 ; n = size (Lold,1) ; L = Lold ; % x = weros (n,1) ; worig = w ; for k = 1:n alpha = w(k) / L(k,k) ; beta_new = sqrt (beta^2 + sigma*alpha^2) ; gamma = alpha / (beta_new * beta) ; if (sigma < 0) % downdate bratio = beta_new / beta ; w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ; L (k,k) = bratio * L (k,k) ; L (k+1:n,k) = bratio * L (k+1:n,k) - gamma*w(k+1:n) ; else % update bratio = beta / beta_new ; % wold = w (k+1:n) ; % w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ; % L (k ,k) = bratio * L (k ,k) + gamma*w(k) ; % L (k+1:n,k) = bratio * L (k+1:n,k) + gamma*wold ; L (k,k) = bratio * L (k,k) + gamma*w(k) ; for i = k+1:n wold = w (i) ; w (i) = w (i) - alpha * L (i,k) ; L (i,k) = bratio * L (i,k) + gamma*wold ; end end w (k) = alpha ; beta = beta_new ; end norm (w-(Lold\worig)) SuiteSparse/CSparse/MATLAB/Test/cs_sparse2.m0000644001170100242450000000064010620373105017405 0ustar davisfacfunction A = cs_sparse2 (i,j,x) %#ok %CS_SPARSE2 same as cs_sparse, to test cs_entry function % A = cs_sparse2 (i,j,x), removing duplicates and numerically zero entries, % and returning A sorted (test cs_entry) % % Example: % A = cs_sparse2 (i,j,x) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_sparse2 mexFunction not found') ; SuiteSparse/CSparse/MATLAB/Test/chol_right.m0000644001170100242450000000063110620373032017462 0ustar davisfacfunction L = chol_right (A) %CHOL_RIGHT right-looking Cholesky factorization. % Example % L = chol_right (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A) ; L = zeros (n) ; for k = 1:n L (k,k) = sqrt (A (k,k)) ; L (k+1:n,k) = A (k+1:n,k) / L (k,k) ; A (k+1:n,k+1:n) = A (k+1:n,k+1:n) - L (k+1:n,k) * L (k+1:n,k)' ; end SuiteSparse/CSparse/MATLAB/Test/signum.m0000644001170100242450000000046010620373167016653 0ustar davisfacfunction s = signum (x) %SIGNUM compute and display the sign of a column vector x % Example % s = signum(x) % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse s = ones (length (x),1) ; s (find (x < 0)) = -1 ; %#ok disp ('s =') ; disp (s) ; SuiteSparse/CSparse/MATLAB/Test/dmperm_test.m0000644001170100242450000000430710620666271017701 0ustar davisfacfunction dmperm_test %DMPERM_TEST test cs_dmperm % % Example: % dmperm_test % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; f = find (index.nrows ~= index.ncols) ; [ignore i] = sort (index.nrows(f) ./ index.ncols(f)) ; f = [209:211 f(i)] ; nmat = length(f) ; tt1 = zeros (1,nmat) ; tt2 = zeros (1,nmat) ; tt3 = zeros (1,nmat) ; tt4 = zeros (1,nmat) ; mm = zeros (1,nmat) ; nn = zeros (1,nmat) ; ss = zeros (1,nmat) ; me = zeros (1,nmat) ; ne = zeros (1,nmat) ; p = cs_dmperm (sparse (1)) ; for k = 1:length(f) i = f(k) ; Prob = UFget (i) %#ok A = Prob.A ; [m n] = size (A) ; if (m > n) % make sure A is short and fat A = A' ; end % C is tall and thin C = A' ; [m n] = size (A) ; k1 = 0 ; t1 = 0 ; while (t1 < 1) tic p = cs_dmperm (A) ; t = toc ; t1 = t1 + t ; k1 = k1 + 1 ; end t1 = t1 / k1 ; s1 = sum (p > 0) ; k2 = 0 ; t2 = 0 ; while (t2 < 1) tic p = cs_dmperm (C) ; t = toc ; t2 = t2 + t ; k2 = k2 + 1 ; end t2 = t2 / k2 ; s2 = sum (p > 0) ; k3 = 0 ; t3 = 0 ; while (t3 < 1) tic p = cs_dmperm_orig (A) ; t = toc ; t3 = t3 + t ; k3 = k3 + 1 ; end t3 = t3 / k3 ; k4 = 0 ; t4 = 0 ; while (t4 < 1) tic p = cs_dmperm_orig (A') ; t = toc ; t4 = t4 + t ; k4 = k4 + 1 ; end t4 = t4 / k4 ; sprnk = sum (p > 0) ; nempty = full (sum (sum (spones (A)) == 0)) ; mempty = full (sum (sum (spones (C)) == 0)) ; fprintf ('[m %d:%d n %d:%d (%d)]:\n', m, mempty, n, nempty, sprnk) ; fprintf (' A: t1 %10.6f (%6d) C: t2 %10.6f (%6d) new\n', ... t1, k1, t2, k2) ; fprintf (' A: t3 %10.6f (%6d) C: t4 %10.6f (%6d) orig\n', ... t3, k3, t4, k4) ; if (s1 ~= sprnk | s2 ~= sprnk) %#ok s1 %#ok s2 %#ok sprnk %#ok error ('!') ; end tt1 (k) = t1 ; tt2 (k) = t2 ; tt3 (k) = t3 ; tt4 (k) = t4 ; mm (k) = m ; nn (k) = n ; ss (k) = sprnk ; me (k) = mempty ; ne (k) = nempty ; clear A C semilogy (ss(1:k) ./ nn(1:k), tt1(1:k) ./ tt3(1:k), 'o', ... [0 1], [1 1], 'r-') ; drawnow end SuiteSparse/CSparse/MATLAB/Test/cs_reachr_mex.c0000644001170100242450000000325410415621443020140 0ustar davisfac#include "cs_mex.h" /* find nonzero pattern of x=L\sparse(b). L must be sparse, real, and lower * triangular. b must be a real sparse vector. */ static void dfsr (int j, const cs *L, int *top, int *xi, int *w) { int p ; w [j] = 1 ; /* mark node j */ for (p = L->p [j] ; p < L->p [j+1] ; p++) /* for each i in L(:,j) */ { if (w [L->i [p]] != 1) /* if i is unmarked */ { dfsr (L->i [p], L, top, xi, w) ; /* start a dfs at i */ } } xi [--(*top)] = j ; /* push j onto the stack */ } /* w [0..n-1] == 0 on input, <= 1 on output. size n */ static int reachr (const cs *L, const cs *B, int *xi, int *w) { int p, n = L->n ; int top = n ; /* stack is empty */ for (p = B->p [0] ; p < B->p [1] ; p++) /* for each i in pattern of b */ { if (w [B->i [p]] != 1) /* if i is unmarked */ { dfsr (B->i [p], L, &top, xi, w) ; /* start a dfs at i */ } } return (top) ; /* return top of stack */ } void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs Lmatrix, Bmatrix, *L, *B ; double *x ; int i, j, top, *xi ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_reachr(L,b)") ; } /* get inputs */ L = cs_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; B = cs_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ; cs_mex_check (0, L->n, 1, 0, 1, 1, pargin [1]) ; xi = cs_calloc (2*L->n, sizeof (int)) ; top = reachr (L, B, xi, xi + L->n) ; pargout [0] = mxCreateDoubleMatrix (L->n - top, 1, mxREAL) ; x = mxGetPr (pargout [0]) ; for (j = 0, i = top ; i < L->n ; i++, j++) x [j] = xi [i] ; cs_free (xi) ; } SuiteSparse/CSparse/MATLAB/Test/chol_left2.m0000644001170100242450000000073510620373026017371 0ustar davisfacfunction L = chol_left2 (A) %CHOL_LEFT2 left-looking Cholesky factorization, more details. % Example % L = chol_left2 (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A,1) ; L = sparse (n,n) ; a = sparse (n,1) ; for k = 1:n a (k:n) = A (k:n,k) ; for j = find (L (k,:)) a (k:n) = a (k:n) - L (k:n,j) * L (k,j) ; end L (k,k) = sqrt (a (k)) ; L (k+1:n,k) = a (k+1:n) / L (k,k) ; end SuiteSparse/CSparse/MATLAB/Test/chol_up.m0000644001170100242450000000056110620373042016774 0ustar davisfacfunction L = chol_up (A) %CHOL_UP up-looking Cholesky factorization. % Example: % L = chol_up (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A) ; L = zeros (n) ; for k = 1:n L (k,1:k-1) = (L (1:k-1,1:k-1) \ A (1:k-1,k))' ; L (k,k) = sqrt (A (k,k) - L (k,1:k-1) * L (k,1:k-1)') ; end SuiteSparse/CSparse/MATLAB/Test/cs_ipvec.m0000644001170100242450000000037010620373063017137 0ustar davisfacfunction x = cs_ipvec (b,p) %#ok %CS_IPVEC x(p)=b % % Example: % x = cs_ipvec (b,p) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_ipvec mexFunction not found') ; SuiteSparse/CSparse/MATLAB/Test/Contents.m0000644001170100242450000001165110620373052017143 0ustar davisfac% CSparse "textbook" MATLAB M-files and mexFunctions, related to CSparse but % not a part of CSparse itself. % % M-files: % % chol_downdate - downdate a Cholesky factorization. % chol_left - left-looking Cholesky factorization. % chol_left2 - left-looking Cholesky factorization, more details. % chol_right - right-looking Cholesky factorization. % chol_super - left-looking "supernodal" Cholesky factorization. % chol_up - up-looking Cholesky factorization. % chol_update - update a Cholesky factorization. % chol_updown - update or downdate a Cholesky factorization. % cond1est - 1-norm condition estimate. % cs_fiedler - the Fiedler vector of a connected graph. % givens2 - find a Givens rotation. % house - find a Householder reflection. % lu_left - left-looking LU factorization. % lu_right - right-looking LU factorization. % lu_rightp - right-looking LU factorization, with partial pivoting. % lu_rightpr - recursive right-looking LU, with partial pivoting. % lu_rightr - recursive right-looking LU. % norm1est - 1-norm estimate. % qr_givens - Givens-rotation QR factorization. % qr_givens_full - Givens-rotation QR factorization, for full matrices. % qr_left - left-looking Householder QR factorization. % qr_right - right-looking Householder QR factorization. % % mexFunctions: % % cs_frand - generate a random finite-element matrix % cs_ipvec - x(p)=b % cs_maxtransr - recursive maximum matching algorithm % cs_pvec - x=b(p) % cs_reach - non-recursive reach (interface to CSparse cs_reach) % cs_reachr - recursive reach (interface to CSparse cs_reachr) % cs_rowcnt - row counts for sparse Cholesky % cs_sparse2 - same as cs_sparse, to test cs_entry function % % Extensive test functions, not for normal usage: % % check_if_same - check if two inputs are identical or not % choldn - Cholesky downdate % cholup - Cholesky update, using Given's rotations % cholupdown - Cholesky update/downdate (Bischof, Pan, and Tang method) % cs_q1 - construct Q from Householder vectors % cs_test_make - compiles the CSparse, Demo, and Test mexFunctions. % dmperm_test - test cs_dmperm % chol_example - simple Cholesky factorization example % etree_sample - construct a sample etree and symbolic factorization % gqr3 - QR factorization, based on Givens rotations % happly - apply Householder reflection to a vector % hmake1 - construct a Householder reflection % mynormest1 - estimate norm(A,1), using LU factorization (L*U = P*A*Q). % myqr - QR factorization using Householder reflections % another_colormap - try another color map % cspy_test - test cspy and cs_dmspy % qr2 - QR factorization based on Householder reflections % sample_colormap - try a colormap for use in cspy % signum - compute and display the sign of a column vector x % sqr_example - test cs_sqr % dmspy_test - test cspy, cs_dmspy, and cs_dmperm % test_qr - test various QR factorization methods % test_randperms - test random permutations % testh - test Householder reflections % test_qr1 - test QR factorizations % test_qrsol - test cs_qrsol % test_sep - test cs_sep, and compare with Gilbert's meshpart vtxsep % testall - test all CSparse functions (run tests 1 to 28 below) % test1 - test cs_transpose % test2 - test cs_sparse % test3 - test cs_lsolve, cs_ltsolve, cs_usolve, cs_chol % test4 - test cs_multiply % test5 - test cs_add % test6 - test cs_reach, cs_reachr, cs_lsolve, cs_usolve % test7 - test cs_lu % test8 - test cs_cholsol, cs_lusol % test9 - test cs_qr % test10 - test cs_qr % test11 - test cs_rowcnt % test12 - test cs_qr and compare with svd % test13 - test cs_counts, cs_etree % test14 - test cs_droptol % test15 - test cs_amd % test16 - test cs_amd % test17 - test cs_qr, cs_qright, cs_q1, cs_qrleft, cs_qrsol % test18 - test iterative refinement after backslash % test19 - test cs_dmperm, cs_maxtransr, cs_dmspy, cs_scc % test20 - test cholupdown % test21 - test cs_updown % test22 - test cond1est % test23 - test cs_dmspy % test24 - test cs_fielder % test25 - test cs_nd % test26 - test cs_dmsol and cs_dmspy % test27 - test cs_qr, cs_utsolve, cs_qrsol % test28 - test cs_randperm, cs_dmperm % Example: % help chol_update % Copyright 2006-2007, Timothy A. Davis SuiteSparse/CSparse/MATLAB/Test/test10.m0000644001170100242450000000354410620373175016476 0ustar davisfacfunction test10 %TEST10 test cs_qr % % Example: % test10 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) ; % f = 185 ; % f = 449 ; clf for trials = 1:100 m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; d = 0.1 * rand (1) ; A = sprandn (m, n, d) ; [m n] = size (A) ; if (m < n) A = A' ; end [m n] = size (A) ; sp = sprank (A) ; % if (sp < n) % continue ; % end Aorig = A ; % A = A (:, colamd (A)) ; tic ; R = qr (A) ; t1 = toc ; % tic ; % [Q,R] = qr (A) ; % t1 = toc ; [c,h,parent] = symbfact (A, 'col') ; %#ok rnz = sum (c) ; %#ok tic ; [V2,Beta2,p,R2] = cs_qr (sparse(A)) ; t2 = toc ; C = A ; m2 = size (V2,1) ; if (m2 > m) C = [A ; sparse(m2-m, n)] ; end C = C (p,:) ; [H1,R1] = myqr (C) ; err1 = norm (R1-R2,1) / norm (R1) ; disp ('err1 = ') ; disp (err1) ; % [svd(A) svd(R1) svd(full(R2))] s1 = svd (full (A)) ; s2 = svd (full (R2)) ; if (n > 0) err2 = norm (s1 - s2) / s1 (1) ; disp ('err2 = ') ; disp (err2) ; else err2 = 0 ; end fprintf ('%10.6f %10.6f cs speedup %8.3f sprank %d vs %d\n', t1, t2, t1/t2, sp, n) ; % H2 = full (H2) % R2 = full (R2) subplot (2,4,1) ; spy (A) ; title ('A colamd') ; subplot (2,4,4) ; spy (Aorig) ; title ('Aorig') ; subplot (2,4,2) ; spy (C) ; title ('A rperm') ; subplot (2,4,5) ; spy (abs(R2)>0) ; title ('spqr R, no zeros') ; subplot (2,4,6) ; spy (R) ; title ('matlab R') ; subplot (2,4,7) ; spy (R2) ; title ('spqr R') ; subplot (2,4,8) ; spy (V2) ; title ('spqr H') ; drawnow if (err2 > 1e-9) error ('!') ; end if (m2 > m) fprintf ('added %d rows, sprank %d n %d\n', m2-m, sp, n) ; end end SuiteSparse/CSparse/MATLAB/Test/test11.m0000644001170100242450000000153410710513051016461 0ustar davisfacfunction test11 %TEST11 test cs_rowcnt % % Example: % test11 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:200) ; for i = f Prob = UFget (i, index) ; disp (Prob) ; A = Prob.A ; [m n] = size (A) ; if (~isreal (A) | m ~= n) %#ok continue end A = spones (A) ; A = A+A' + speye(n) ; [cc h pa po R] = symbfact (A) ; rc1 = full (sum (R)) ; rc2 = cs_rowcnt (A, pa, po) ; if (any (rc1 ~= rc2)) error ('!') ; end try p = amd (A) ; catch p = symamd (A) ; end A = A (p,p) ; [cc h pa po R] = symbfact (A) ; rc1 = full (sum (R)) ; rc2 = cs_rowcnt (A, pa, po) ; if (any (rc1 ~= rc2)) error ('!') ; end end SuiteSparse/CSparse/MATLAB/Test/test12.m0000644001170100242450000000156710620666442016505 0ustar davisfacfunction test12 %TEST12 test cs_qr and compare with svd % % Example: % test12 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse fprintf ('test 12\n') ; rand ('state',0) ; % A = rand (3,4) for trial = 1:100 m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; d = .1 * rand (1) ; A = sprandn (m,n,d) ; fprintf ('m %d n %d nnz %d\n', m, n, nnz(A)) ; if (m < n) continue ; end if (m == 0 | n == 0) %#ok continue ; end % save A A fprintf ('[ ') ; [V,Beta,p,R] = cs_qr (A) ; % [Q,R] = svd (full(A)) ; fprintf (']\n') ; s1 = svd (full (A)) ; s2 = svd (full (R)) ; s2 = s2 (1:length(s1)) ; err = norm (s1-s2) ; if (length (s1) > 1) err = err / s1 (1) ; end fprintf ('err %g\n', err) ; if (err > 1e-12) error ('!') ; end end SuiteSparse/CSparse/MATLAB/Test/test13.m0000644001170100242450000000320110620373203016457 0ustar davisfacfunction test13 %TEST13 test cs_counts, cs_etree % % Example: % test13 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions randn ('state',0) ; rand ('state',0) ; for trial = 1:100 m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; d = .1 * rand (1) ; A = sprandn (n,n,d) ; C = sprandn (m,n,d) ; A = A+A' ; fprintf ('m %4d n %4d nnz(A) %6d nnz(C) %6d\n', m, n, nnz(A), nnz(C)) ; [p1,po1] = etree (A) ; [p2,po2] = cs_etree (A) ; [p3,po3] = cs_etree (A, 'sym') ; % po2 = cs_post (p2) ; check_if_same (p1,p2) ; check_if_same (po1,po2) ; check_if_same (p1,p3) ; check_if_same (po1,po3) ; c1 = symbfact (A) ; c2 = cs_counts (A) ; % A-A' check_if_same (c1,c2) ; c2 = cs_counts (triu (A)) ; check_if_same (c1,c2) ; % pause p0 = etree (A, 'col') ; % p1 = etree2 (A, 'col') ; % CHOLMOD p2 = cs_etree (A, 'col') ; if (~isempty (A)) check_if_same (p0,p2) ; end p0 = etree (C, 'col') ; % p1 = etree2 (C, 'col') ; % CHOLMOD p2 = cs_etree (C, 'col') ; if (~isempty (C)) check_if_same (p0,p2) ; end % find etree of A'A, and postorder it [m n] = size (A) ; %#ok % full (A) [cp0 cpo0] = etree (A, 'col') ; % [cp1 cpo1] = etree2 (A, 'col') ; % CHOLMOD [cp2 cpo2] = cs_etree (A, 'col') ; % cpo2 = cs_post (cp2) ; check_if_same (cp0, cp2) ; check_if_same (cpo0, cpo2) ; c0 = symbfact (A, 'col') ; % c1 = symbfact2 (A, 'col') ; % CHOLMOD c2 = cs_counts (A, 'col') ; check_if_same (c0, c2) ; end SuiteSparse/CSparse/MATLAB/Test/test14.m0000644001170100242450000000134510620373205016471 0ustar davisfacfunction test14 %TEST14 test cs_droptol % % Example: % test14 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) ; for trial = 1:100 m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; d = 0.1*rand (1) ; A = sprandn (m,n,d) ; [i j x] = find (A) ; A = sparse (i,j,2*x-1) ; fprintf ('test14 m %3d n %3d nz %d\n', m, n, nnz (A)) ; % using CSparse tol = 0.5 ; B = cs_droptol (A, tol) ; % using MATLAB A = A .* (abs (A) > tol) ; % [m n] = size (A) ; % s = abs (A) > tol ; % [i j] = find (s) ; % x = A (find (s)) ; % A = sparse (i, j, x, m, n) ; if (norm (A-B,1) > 0) error ('!') ; end end SuiteSparse/CSparse/MATLAB/Test/test15.m0000644001170100242450000000160310620373206016470 0ustar davisfacfunction test15 %TEST15 test cs_amd % % Example: % test15 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) ; randn ('state', 0) ; clf for trials = 1:100 n = fix (200 * rand (1)) ; d = 0.05 * rand (1) ; A = sprandn (n, n, d) ; % add a randomly placed dense column k = fix (n * rand (1)) ; k = max (1, k) ; k = min (n, k) ; A (:,k) = 1 ; try p0 = amd (A) ; catch p0 = symamd (A) ; end p1 = cs_amd (A) ; if (any (sort (p1) ~= 1:n)) error ('not perm!') ; end C = A+A' + speye (n) ; lnz0 = sum (symbfact (C (p0,p0))) ; lnz1 = sum (symbfact (C (p1,p1))) ; subplot (1,3,1) ; spy (C) subplot (1,3,2) ; spy (C (p0,p0)) subplot (1,3,3) ; spy (C (p1,p1)) fprintf ('n %4d nz %6d lnz %6d %6d\n', n, nnz(A), lnz0, lnz1) ; drawnow end SuiteSparse/CSparse/MATLAB/Test/test16.m0000644001170100242450000000342410620373210016467 0ustar davisfacfunction test16 %TEST16 test cs_amd % % Example: % test16 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) ; randn ('state', 0) ; clf index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:200) ; skip = 811 ; % f = 719 for i = f if (any (i == skip)) continue end Prob = UFget (i) ; A = spones (Prob.A) ; Aorig = A ; [m n] = size (A) ; if (m < n) A = A' ; end [m n] = size (A) ; if (m ~= n) A = A'*A ; end fprintf ('n %4d nz %d\n', n, nnz (A)) ; try p0 = amd (A) ; catch p0 = symamd (A) ; end fprintf ('symmetric case:\n') ; p1 = cs_amd (A) ; if (any (sort (p1) ~= 1:n)) error ('not perm!') ; end C = A+A' + speye (n) ; lnz0 = sum (symbfact (C (p0,p0))) ; lnz1 = sum (symbfact (C (p1,p1))) ; subplot (2,3,1) ; spy (C) subplot (2,3,2) ; spy (C (p0,p0)) ; title ('amd') ; subplot (2,3,3) ; spy (C (p1,p1)) ; title ('csamd') ; drawnow if (lnz0 ~= lnz1) fprintf ('----------------- lnz %d %d %9.4f\n', ... lnz0, lnz1, 100*(lnz0-lnz1)/max([1 lnz0])) ; end if (1) p0 = colamd (Aorig) ; [m n] = size (Aorig) ; fprintf ('m %d n %d\n', m, n) ; fprintf ('A''A case, no dense rows (for QR):\n') ; p1 = cs_amd (Aorig, 3) ; if (any (sort (p1) ~= 1:n)) error ('not perm!') ; end subplot (2,3,4) ; spy (Aorig) subplot (2,3,5) ; spy (Aorig (:,p0)) ; title ('colamd') ; subplot (2,3,6) ; spy (Aorig (:,p1)) ; title ('cs amd(A''A)') ; lnz0 = sum (symbfact (Aorig (:,p0), 'col')) ; lnz1 = sum (symbfact (Aorig (:,p1), 'col')) ; fprintf (' A''A: %7d %7d %9.4f\n', ... lnz0, lnz1, 100*(lnz0-lnz1)/max([1 lnz0])) ; drawnow % pause end end SuiteSparse/CSparse/MATLAB/Test/test17.m0000644001170100242450000000407310620373213016474 0ustar davisfacfunction test17 %TEST17 test cs_qr, cs_qright, cs_q1, cs_qrleft, cs_qrsol % % Example: % test17 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions clf rand ('state', 0) ; randn ('state', 0) ; for trials = 1:100 m = 1 + fix (10 * rand (1)) ; n = 1 + fix (10 * rand (1)) ; d = rand (1) ; % n = m ; A = sprandn (m, n, d) ; if (m < n) A = A' ; end [m n] = size (A) ; subplot (3,4,1) ; spy (A) ; [V1, Beta1, p1, R1, q1] = cs_qr (A) ; Q1 = cs_qright (V1, Beta1, p1, speye (size (V1,1))) ; Q1b = cs_q1 (V1, Beta1, p1) ; err = norm (Q1-Q1b,1) ; disp ('err = ') ; disp (err) ; if (err > 1e-12) error ('!') ; end m2 = size (Q1,1) ; A1 = [A ; sparse(m2-m,n)] ; subplot (3,4,5) ; spy (A1 (p1,q1)) ; subplot (3,4,6) ; spy (V1) ; subplot (3,4,7) ; spy (R1) ; subplot (3,4,8) ; spy (Q1) ; [V3, Beta3, R3] = qr2 (A) ; % Q3 = cs_qmake (V3, Beta3) ; Q3 = cs_q1 (V3, Beta3) ; subplot (3,4,9) ; spy (A) ; subplot (3,4,10) ; spy (V3) ; subplot (3,4,11) ; spy (R3) ; subplot (3,4,12) ; spy (Q3) ; err1 = norm (Q1*R1 - A1(:,q1), 1) ; % err2 = norm (Q2*R2 - A (:,q2), 1) ; err3 = norm (Q3*R3 - A, 1) ; fprintf ('m %3d m2 %3d n %3d ::: %3d %6.2e %6.2e\n', ... m, m2, n, m2-m, err1, err3) ; if (err1 > 1e-12) error ('!') ; end % if (err2 > 1e-12) % error ('!') ; % end if (err3 > 1e-12) error ('!') ; end try b = rand (m,1) ; [Q,R] = qr (A (:,q1)) ; x = R\(Q'*b) ; x (q1) = x ; r1 = norm (A*x-b) ; x2 = cs_qrsol (A,b) ; r2 = norm (A*x2(1:n)-b) ; qt = cs_qleft (V1, Beta1, p1, speye(size(V1,1))) ; fprintf ('Q''*A-R: %6.2e\n', norm (qt*A1(:,q1)-R1,1)) ; qtb = cs_qleft (V1, Beta1, p1, b) ; % [V1, Beta1, p1, R1, q1] = cs_qr (A) ; x3 = R1 \ qtb ; r3 = norm (A(:,q1)*x3(1:n)-b) ; fprintf ('least sq: %6.2e %6.2e %6.2e diff %6.2e %6.2e\n', ... r1, r2, r3, r1-r2, r1-r3) ; catch end drawnow % pause end SuiteSparse/CSparse/MATLAB/Test/test18.m0000644001170100242450000000112110620666451016475 0ustar davisfacfunction test18 %TEST18 test iterative refinement after backslash % % Example: % test18 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:100) ; clf % f = f(1) for i = f Prob = UFget (i) ; disp (Prob) ; A = Prob.A ; [m n] = size (A) ; if (~isreal (A) | m ~= n) %#ok continue end b = rand (n,1) ; x = A\b ; r = b - A*x ; x = x + A\r ; fprintf ('\n%6.2e to %6.2e\n', norm (r), norm (b-A*x)) ; end SuiteSparse/CSparse/MATLAB/Test/test19.m0000644001170100242450000000655710620666505016520 0ustar davisfacfunction test19 %TEST19 test cs_dmperm, cs_maxtransr, cs_dmspy, cs_scc % % Example: % test19 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions randn ('state', 0) ; rand ('state', 0) ; clf for trials = 1:1000 m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; % d = 0.1 * rand (1) ; d = rand (1) * 4 * max (m,n) / max (m*n,1) ; A = sprandn (m,n,d) ; S = sprandn (m,m,d) + speye (m) ; subplot (2,3,1) ; cspy (A) ; pp = dmperm (A) ; sprnk = sum (pp > 0) ; pp2 = cs_dmperm (A) ; spr2 = sum (pp2 > 0) ; if (spr2 ~= sprnk) error ('!') end pp2 = cs_maxtransr (A) ; spr2 = sum (pp2 > 0) ; if (spr2 ~= sprnk) error ('!') end [p,q,r,s] = dmperm (A) ; C = A (p,q) ; % r % s nk = length (r) - 1 ; fprintf ('sprnk: %d m %d n %d nb: %d\n', sprnk, m, n, nk) ; subplot (2,3,2) ; hold off spy (C) hold on for k = 1:nk r1 = r(k) ; r2 = r(k+1) ; c1 = s(k) ; c2 = s(k+1) ; plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ; end [p2,q2,rr2,ss2,cp,rp] = cs_dmperm (A) ; if (min (m,n) > 0) if (length (rr2) ~= length (r)) error ('# fine blocks!') ; end end if (rp (4) - 1 ~= sprnk) rp %#ok sprnk %#ok error ('!') ; end if (any (sort (p2) ~= 1:m)) error ('p2!') ; end if (any (sort (q2) ~= 1:n)) error ('q2!') ; end if (cp (5) ~= n+1) error ('cp!') ; end if (rp (5) ~= m+1) error ('rp!') ; end C = A (p2,q2) ; subplot (2,3,3) ; cs_dmspy (A,0) ; % hold off % spy (C) ; % hold on % r1 = rp(1) ; % r2 = rp(2) ; % c1 = cp(1) ; % c2 = cp(2) ; % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ; r1 = rp(1) ; r2 = rp(2) ; c1 = cp(2) ; c2 = cp(3) ; % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ; B = C (r1:r2-1, c1:c2-1) ; if (nnz (diag (B)) ~= size (B,1)) error ('C1 diag!') ; end r1 = rp(2) ; r2 = rp(3) ; c1 = cp(3) ; c2 = cp(4) ; % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'r') ; B = C (r1:r2-1, c1:c2-1) ; if (nnz (diag (B)) ~= size (B,1)) error ('C2 diag!') ; end r1 = rp(3) ; r2 = rp(4) ; c1 = cp(4) ; c2 = cp(5) ; % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ; B = C (r1:r2-1, c1:c2-1) ; if (nnz (diag (B)) ~= size (B,1)) error ('C3 diag!') ; end r1 = rp(4) ; %#ok r2 = rp(5) ; %#ok c1 = cp(4) ; %#ok c2 = cp(5) ; %#ok % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ; if (~isempty (S)) [p1,q1,r0,s0] = dmperm (S) ; [p3,r3] = cs_scc (S) ; if (length (r3) ~= length (r0)) error ('scc size!') ; end if (any (sort (p3) ~= 1:m)) error ('scc perm!') ; end nk = length (r0)-1 ; subplot (2,3,4) ; hold off spy (S (p1,q1)) ; hold on for k = 1:nk r1 = r0(k) ; r2 = r0(k+1) ; c1 = s0(k) ; c2 = s0(k+1) ; plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ; end subplot (2,3,5) ; hold off spy (S (p3,p3)) ; hold on for k = 1:nk r1 = r3(k) ; r2 = r3(k+1) ; c1 = r3(k) ; c2 = r3(k+1) ; plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ; end end subplot (2,3,6) ; cs_dmspy (A) ; drawnow % pause end SuiteSparse/CSparse/MATLAB/Test/test20.m0000644001170100242450000000142010620373223016460 0ustar davisfacfunction test20 %TEST20 test cholupdown % % Example: % test20 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions rand ('state', 0) ; for trials = 1:10 n = fix (100 * rand (1)) ; A = rand (n) ; A1 = A*A' + n*eye (n) ; try L1 = chol (A1)' ; catch continue ; end err1 = norm (L1*L1'-A1) ; w = rand (n,1) ; A2 = A1 + w*w' ; L2 = chol (A2)' ; err2 = norm (L2*L2'-A2) ; % try an update L2b = cholupdown (L1, +1, w) ; err2b = norm (L2b*L2b'-A2) ; % try a downdate L1b = cholupdown (L2, -1, w) ; %#ok err1b = norm (L2b*L2b'-A2) ; fprintf ('%3d: %6.2e %6.2e : %6.2e %6.2e\n', n, err1, err2, err2b, err1b) ; % pause end SuiteSparse/CSparse/MATLAB/Test/test21.m0000644001170100242450000000363610620666527016510 0ustar davisfacfunction test21 %TEST21 test cs_updown % % Example: % test21 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions rand ('state', 0) ; randn ('state', 0) ; clf for trials = 1:10 if (trials <= 1) n = trials ; else n = 1+fix (100 * rand (1)) ; end fprintf ('n: %d\n', n) ; d = 0.1 * rand (1) ; A = sprandn (n,n,d) ; A = A+A' + 100 * speye (n) ; try p = amd (A) ; catch p = symamd (A) ; end A = sparse (A (p,p)) ; try L = chol (A)' ; catch continue ; end parent = etree (A) ; subplot (1,3,1) ; spy (A) ; if (n > 0) subplot (1,3,2) ; treeplot (parent) ; end subplot (1,3,3) ; spy (L) ; drawnow for trials2 = 1:10 k = 1+fix (n * rand (1)) ; if (k <= 0 | k > n) %#ok k = 1 ; end w = sprandn (L (:,k)) ; Anew = A + w*w' ; % Lnew = cs_update (L, w, parent) ; % err1 = norm (Lnew*Lnew' - Anew, 1) ; Lnew = cs_updown (L, w, parent) ; err6 = norm (Lnew*Lnew' - Anew, 1) ; Lnew = cs_updown (L, w, parent, '+') ; err7 = norm (Lnew*Lnew' - Anew, 1) ; [Lnew, wnew] = chol_update (L, w) ; err2 = norm (Lnew*Lnew' - Anew, 1) ; err10 = norm (wnew - (L\w)) ; L3 = chol_updown (L, +1, w) ; err9 = norm (L3*L3' - Anew, 1) ; [L2, wnew] = chol_downdate (Lnew, w) ; err3 = norm (L2*L2' - A, 1) ; err11 = norm (wnew - (Lnew\w)) ; % L2 = cs_downdate (Lnew, w, parent) ; % err4 = norm (L2*L2' - A, 1) ; L2 = cs_updown (Lnew, w, parent, '-') ; err5 = norm (L2*L2' - A, 1) ; L2 = chol_updown (Lnew, -1, w) ; err8 = norm (L2*L2' - A, 1) ; err = max ([err2 err3 err5 err6 err7 err9 err8 err10 err11]) ; fprintf (' k %3d %6.2e\n', k, err) ; if (err > 1e-11) err2 %#ok err3 %#ok err5 %#ok err6 %#ok err7 %#ok err8 %#ok err9 %#ok err10 %#ok err11 %#ok pause end end % pause end SuiteSparse/CSparse/MATLAB/Test/test22.m0000644001170100242450000000211510620666541016474 0ustar davisfacfunction test22 %TEST22 test cond1est % % Example: % test22 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:200) ; clf % f = f(1) nprob = length (f) ; C1 = zeros (nprob,1) ; C2 = zeros (nprob,1) ; C3 = zeros (nprob,1) ; for k = 1:length (f) i = f (k) ; Prob = UFget (i) ; disp (Prob) ; A = Prob.A ; [m n] = size (A) ; if (~isreal (A) | m ~= n) %#ok continue end c1 = condest (A) ; c2 = cond1est (A) ; if (c1 == c2) err = 0 ; else err = (c1-c2)/max(1,c1) ; end c3 = cond (full (A), 1) ; fprintf ('%10.4e %10.4e (%10.4e) : %10.4e\n', c1, c2, c3, err) ; if (err ~= 0) % pause end C1 (k) = c1 ; C2 (k) = c2 ; C3 (k) = c3 ; subplot (1,2,1) ; loglog (C1, C2, 'x', [1 1e20], [1 1e20], 'r') ; subplot (1,2,2) ; loglog (C3, C2, 'x', [1 1e20], [1 1e20], 'r') ; drawnow % pause % if (c3 < c2) % c3 % c2 % c2-c3 % pause % end end SuiteSparse/CSparse/MATLAB/Test/test23.m0000644001170100242450000000101310620373232016461 0ustar davisfacfunction test23 %TEST23 test cs_dmspy % % Example: % test23 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions randn ('state', 0) ; rand ('state', 0) ; clf for trials = 1:1000 % m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; m = n ; % d = 0.1 * rand (1) ; d = rand (1) * 4 * max (m,n) / max (m*n,1) ; A = sprandn (m,n,d) ; % S = sprandn (m,m,d) + speye (m) ; cs_dmspy (A) ; drawnow % pause end SuiteSparse/CSparse/MATLAB/Test/test24.m0000644001170100242450000000153110620373234016471 0ustar davisfacfunction test24 %TEST24 test cs_fielder % % Example: % test24 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:200) ; clf % f = f(1) for k = 1:length (f) i = f (k) ; Prob = UFget (i) ; disp (Prob) ; A = real (Prob.A) ; [m n] = size (A) ; if (m ~= n) continue end tic p1 = symrcm (A) ; t1 = toc ; tic p2 = cs_fiedler (A) ; t2 = toc ; rel = t2 / max (t1,1e-6) ; fprintf ('time: symrcm %8.3f fiedler %8.3f rel %8.2f\n', t1, t2, rel) ; A = A|A' ; subplot (1,3,1) ; spy (A) ; subplot (1,3,2) ; spy (A (p1,p1)) ; subplot (1,3,3) ; spy (A (p2,p2)) ; % evaluate the profile ... drawnow % pause end SuiteSparse/CSparse/MATLAB/Test/test25.m0000644001170100242450000000174110620373241016473 0ustar davisfacfunction test25 %TEST25 test cs_nd % % Example: % test25 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:100) ; clf % f = f(1) for k = 1:length (f) i = f (k) ; Prob = UFget (i) ; disp (Prob) ; A = real (Prob.A) ; [m n] = size (A) ; if (m ~= n) continue end A = A|A' ; tic ; p1 = symrcm (A) ; t1 = toc ; tic ; p2 = cs_nd (sparse (1)) ; toc ; if (p2 ~= 1) error ('!') ; end tic ; p2 = cs_nd (A) ; t2 = toc ; if (any (sort (p2) ~= 1:n)) error ('!') ; end rel = t2 / max (t1,1e-6) ; fprintf ('time: symrcm %8.3f nd %8.3f rel %8.2f\n', t1, t2, rel) ; subplot (1,3,1) ; spy (A) ; subplot (1,3,2) ; spy (A (p1,p1)) ; subplot (1,3,3) ; spy (A (p2,p2)) ; % evaluate the profile ... drawnow % pause end SuiteSparse/CSparse/MATLAB/Test/test26.m0000644001170100242450000000237610620373243016503 0ustar davisfacfunction test26 %TEST26 test cs_dmsol and cs_dmspy % % Example: % test26 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions randn ('state', 0) ; rand ('state', 0) ; clf ntrials = 1000 ; e1 = zeros (ntrials,1) ; e2 = zeros (ntrials,1) ; for trials = 1:ntrials m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; % d = 0.1 * rand (1) ; d = rand (1) * 4 * max (m,n) / max (m*n,1) ; A = sprandn (m,n,d) ; % S = sprandn (m,m,d) + speye (m) ; subplot (1,3,2) ; spy (A) ; subplot (1,3,3) ; cs_dmspy (A) ; b = rand (m,1) ; x1 = A\b ; x2 = cs_dmsol (A,b) ; err1 = norm (A*x1-b) ; err2 = norm (A*x2-b) ; lerr1 = log10 (max (err1, eps)) ; lerr2 = log10 (max (err2, eps)) ; fprintf ('rank: %3d %3d err %6.2e %6.2e : %6.1f\n', ... sprank(A), rank(full(A)), err1, err2, lerr1 - lerr2) ; if (isnan (err1)) lerr1 = 10 ; end if (isnan (err2)) lerr2 = 10 ; end if (lerr2 > lerr1 + 5) % pause end e1 (trials) = lerr1 ; e2 (trials) = lerr2 ; subplot (1,3,1) ; plot (e1, e2, 'o', [-16 10], [-16 10], 'r') ; xlabel ('MATLAB error') ; ylabel ('dmsol error') ; drawnow % pause end SuiteSparse/CSparse/MATLAB/Test/test27.m0000644001170100242450000000116710620373245016503 0ustar davisfacfunction test27 %TEST27 test cs_qr, cs_utsolve, cs_qrsol % % Example: % test27 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions rand ('state', 0) ; Prob = UFget ('HB/ibm32') ; A = Prob.A ; A = A (1:10,:) ; [m n] = size (A) ; [V,Beta,p,R,q] = cs_qr (A') ; b = rand (m,1) ; Rm = R (1:m,1:m) ; bq = b (q) ; rtbq = Rm' \ bq ; rt2 = cs_utsolve (Rm, bq) ; norm (rtbq - rt2) x = [rt2 ; zeros(n-m,1)] ; for k = m:-1:1 x = x - V(:,k) * (Beta (k) * (V (:,k)' * x)) ; end x (p) = x ; norm (A*x-b) x2 = cs_qrsol (A,b) ; norm (A*x2-b) norm (x-x2) SuiteSparse/CSparse/MATLAB/Test/test28.m0000644001170100242450000000420110620666743016504 0ustar davisfacfunction test28 %TEST28 test cs_randperm, cs_dmperm % % Example: % test28 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions rand ('state', 0) ; for n = 1:100 for trials = 1:1000 p = cs_randperm (n, rand) ; if (any (sort (p) ~= 1:n)) n %#ok p %#ok error ('!') end end end index = UFget ; [ignore f] = sort (index.nnz) ; fprintf ('p=dmperm (std, rand, rev) [p,q,r,s]=dmperm (std, rand, rev)\n') ; nmat = min (100, length (f)) ; T1 = zeros (nmat,1) ; T2 = zeros (nmat,1) ; T3 = zeros (nmat,1) ; D1 = zeros (nmat,1) ; D2 = zeros (nmat,1) ; D3 = zeros (nmat,1) ; for k = 1:nmat i = f (k) ; Prob = UFget (i,index) ; A = Prob.A ; [m n] = size (A) ; fprintf ('%35s: ', Prob.name) ; tic p = cs_dmperm (A) ; t1 = toc ; sprank1 = sum (p > 0) ; fprintf (' %8.2f', t1) ; T1 (k) = t1 ; tic p = cs_dmperm (A,1) ; t2 = toc ; sprank2 = sum (p > 0) ; fprintf (' %8.2f', t2) ; T2 (k) = t2 ; tic p = cs_dmperm (A,-1) ; t3 = toc ; sprank3 = sum (p > 0) ; fprintf (' %8.2f', t3) ; T3 (k) = t3 ; if (sprank1 ~= sprank2 | sprank1 ~= sprank3) %#ok error ('!') ; end tic [p1,q1,r1,s1,cc1,rr1] = cs_dmperm (A) ; %#ok d1 = toc ; fprintf (' %8.2f', d1) ; D1 (k) = d1 ; tic [p2,q2,r2,s2,cc2,rr2] = cs_dmperm (A,1) ; %#ok d2 = toc ; fprintf (' %8.2f', d2) ; D2 (k) = d2 ; tic [p3,q3,r3,s3,cc3,rr3] = cs_dmperm (A,-1) ; %#ok d3 = toc ; fprintf (' %8.2f\n', d3) ; D3 (k) = d3 ; if (sprank1 == max (m,n)) nz1 = nnz (diag (A (p1,q1))) ; nz2 = nnz (diag (A (p2,q2))) ; nz3 = nnz (diag (A (p3,q3))) ; if (nz1 ~= sprank1 | nz2 ~= sprank2 | nz3 ~= sprank3) %#ok error ('!') end end subplot (1,2,1) loglog (T1 (1:k), T2 (1:k), 'x', ... T1 (1:k), T3 (1:k), 'go', ... [1e-5 1e3], [1e-5 1e3], 'r-') ; axis equal subplot (1,2,2) loglog (D1 (1:k), D2 (1:k), 'x', ... D1 (1:k), D3 (1:k), 'go', ... [1e-5 1e3], [1e-5 1e3], 'r-') ; axis equal drawnow end SuiteSparse/CSparse/MATLAB/Test/cs_frand_mex.c0000644001170100242450000000266710677527016020010 0ustar davisfac#include "cs_mex.h" /* A = cs_frand (n,nel,s) creates an n-by-n sparse matrix consisting of nel * finite elements, each of which are of size s-by-s with random symmetric * nonzero pattern, plus the identity matrix. * See also MATLAB/Demo/private/frand.m */ static cs *cs_frand (int n, int nel, int s) { int ss = s*s, nz = nel*ss, e, i, j, *P ; cs *A, *T = cs_spalloc (n, n, nz, 1, 1) ; if (!T) return (NULL) ; P = cs_malloc (s, sizeof (int)) ; if (!P) return (cs_spfree (T)) ; for (e = 0 ; e < nel ; e++) { for (i = 0 ; i < s ; i++) P [i] = rand () % n ; for (j = 0 ; j < s ; j++) { for (i = 0 ; i < s ; i++) { cs_entry (T, P [i], P [j], rand () / (double) RAND_MAX) ; } } } for (i = 0 ; i < n ; i++) cs_entry (T, i, i, 1) ; A = cs_compress (T) ; cs_spfree (T) ; return (cs_dupl (A) ? A : cs_spfree (A)) ; } void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { int n, nel, s ; cs *A, *AT ; if (nargout > 1 || nargin != 3) { mexErrMsgTxt ("Usage: C = cs_frand(n,nel,s)") ; } n = mxGetScalar (pargin [0]) ; nel = mxGetScalar (pargin [1]) ; s = mxGetScalar (pargin [2]) ; n = CS_MAX (1,n) ; nel = CS_MAX (1,nel) ; s = CS_MAX (1,s) ; AT = cs_frand (n, nel, s) ; A = cs_transpose (AT, 1) ; cs_spfree (AT) ; cs_dropzeros (A) ; pargout [0] = cs_mex_put_sparse (&A) ; } SuiteSparse/CSparse/MATLAB/Test/cond1est.m0000644001170100242450000000075410620666162017077 0ustar davisfacfunction c = cond1est (A) %COND1EST 1-norm condition estimate. % Example: % c = cond1est(A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; if (m ~= n | ~isreal (A)) %#ok error ('A must be square and real') ; end if isempty(A) c = 0 ; return ; end [L,U,P,Q] = lu (A) ; if (~isempty (find (abs (diag (U)) == 0))) %#ok c = Inf ; else c = norm (A,1) * norm1est (L,U,P,Q) ; end SuiteSparse/CSparse/MATLAB/Test/test1.m0000644001170100242450000000175210620373221016405 0ustar davisfacfunction test1 %TEST1 test cs_transpose % % Example: % test1 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:100) ; for ii = f Prob = UFget (ii) ; disp (Prob) ; A = Prob.A ; if (~isreal (A)) continue end B = A' ; C = cs_transpose (A) ; if (nnz (B-C) ~= 0) error ('!') end [m n] = size (A) ; % if (m == n) x = rand (n,1) ; y = rand (m,1) ; z = y+A*x ; q = cs_gaxpy (A,x,y) ; err = norm (z-q,1) / norm (z,1) ; disp (err) ; if (err > 1e-14) error ('!') end % end [i j x] = find (A) ; p = randperm (length (i)) ; i = i (p) ; j = j (p) ; x = x (p) ; D = sparse (i,j,x) ; E = cs_sparse (i,j,x) ; % [i j x] F = cs_sparse2 (i,j,x) ; if (nnz (D-E) ~= 0) error ('!') end if (nnz (F-E) ~= 0) error ('!') end clear A B C D E F % pause end SuiteSparse/CSparse/MATLAB/Test/test2.m0000644001170100242450000000326710620373251016414 0ustar davisfacfunction test2 %TEST2 test cs_sparse % % Example: % test2 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) % clf for trial = 1:100 m = fix (10 * rand (1)) ; n = fix (10 * rand (1)) ; nz = fix (100 * rand (1)) ; i = 1 + fix (m * rand (nz,1)) ; j = 1 + fix (n * rand (nz,1)) ; x = rand (nz,1) ; A = sparse (i,j,x) ; B = cs_sparse (i,j,x) ; D = cs_sparse2 (i,j,x) ; fprintf ('%3d %3d %6d : %6d %6d : %d\n', ... m, n, nz, nnz (A), nnz(B), nz-nnz(A)) ; err = norm (A-B,1) / norm (A,1) ; if (err > 0) disp ('err = ') ; disp (err) ; end if (err > 1e-14) error ('!') ; end if (nnz (B-D) > 0) error ('!') ; end if (nnz (A) ~= nnz (B)) error ('nz!') ; end if (max (1,nnz (B)) ~= max (1,nzmax (B))) nnz (B) nzmax (B) error ('nzmax!') ; end % pack [m n] = size (A) ; p = randperm (m) ; q = randperm (n) ; C1 = A (p,q) ; C2 = cs_permute (A,p,q) ; err = norm (C1-C2,1) ; if (err > 0) error ('!') ; end % subplot (1,2,1) ; spy (A) % subplot (1,2,2) ; spy (C2) % drawnow x = rand (m,1) ; x1 = x (p) ; x2 = cs_pvec (x, p) ; err = norm (x1-x2,1) ; if (err > 0) error ('!') ; end x1 = zeros (m,1) ; x1 (p) = x ; %#ok x2 = cs_ipvec (x, p) ; %#ok n = min (m,n) ; B = A (1:n, 1:n) ; p = randperm (n) ; B = B+B' ; C1 = triu (B (p,p)) ; C2 = cs_symperm (B,p) ; try pp = amd (C2) ; %#ok catch pp = symamd (C2) ; %#ok end err = norm (C1-C2,1) ; if (err > 0) error ('!') ; end end SuiteSparse/CSparse/MATLAB/Test/test3.m0000644001170100242450000000315610710513042016404 0ustar davisfacfunction test3 %TEST3 test cs_lsolve, cs_ltsolve, cs_usolve, cs_chol % % Example: % test3 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:100) ; clf % f = f(1) for i = f Prob = UFget (i) ; disp (Prob) ; A = Prob.A ; [m n] = size (A) ; if (~isreal (A) | m ~= n) %#ok continue end A = A*A' + 2*n*speye (n) ; try p = amd (A) ; catch p = symamd (A) ; end try L0 = chol (A)' ; catch continue end b = rand (n,1) ; C = A(p,p) ; c = condest (C) ; fprintf ('condest: %g\n', c) ; x1 = L0\b ; x2 = cs_lsolve (L0,b) ; err = norm (x1-x2,1) ; if (err > 1e-12 * c) error ('!') ; end x1 = L0'\b ; x2 = cs_ltsolve (L0,b) ; err = norm (x1-x2,1) ; if (err > 1e-10 * c) error ('!') ; end U = L0' ; x1 = U\b ; x2 = cs_usolve (U,b) ; err = norm (x1-x2,1) ; if (err > 1e-10 * c) error ('!') ; end L2 = cs_chol (A) ; subplot (2,3,1) ; spy (L0) ; subplot (2,3,4) ; spy (L2) ; err = norm (L0-L2,1) ; if (err > 1e-8 * c) error ('!') ; end L1 = chol (C)' ; L2 = cs_chol (C) ; subplot (2,3,2) ; spy (L1) ; subplot (2,3,5) ; spy (L2) ; err = norm (L1-L2,1) ; if (err > 1e-8 * c) error ('!') ; end [L3,p] = cs_chol (A) ; C = A(p,p) ; L4 = chol (C)' ; subplot (2,3,3) ; spy (L4) ; subplot (2,3,6) ; spy (L3) ; err = norm (L4-L3,1) ; if (err > 1e-8 * c) error ('!') ; end drawnow end SuiteSparse/CSparse/MATLAB/Test/test4.m0000644001170100242450000000126710620373256016421 0ustar davisfacfunction test4 %TEST4 test cs_multiply % % Example: % test4 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) ; for trial = 1:100 m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; k = fix (100 * rand (1)) ; d = rand (1) ; A = sprandn (m,n,d) ; B = sprandn (n,k,d) ; C = A*B ; D = cs_multiply (A,B) ; err = nnz (spones (C) - spones (D)) ; if (err > 0) error ('nz!') ; end err = norm (C-D,1) ; fprintf ('m %3d n %3d k %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ... m, n, k, nnz(A), nnz(B), nnz(C), err) ; if (err > 1e-12) error ('!') ; end end SuiteSparse/CSparse/MATLAB/Test/test5.m0000644001170100242450000000236510620373261016416 0ustar davisfacfunction test5 %TEST5 test cs_add % % Example: % test5 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) ; for trial = 1:100 m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; d = rand (1) ; A = sprandn (m,n,d) ; B = sprandn (m,n,d) ; C = A+B ; D = cs_add (A,B) ; err = nnz (spones (C) - spones (D)) ; if (err > 0) error ('nz!') ; end err = norm (C-D,1) ; fprintf ('m %3d n %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ... m, n, nnz(A), nnz(B), nnz(C), err) ; if (err > 1e-12) error ('!') ; end C = pi*A+B ; D = cs_add (A,B,pi) ; err = nnz (spones (C) - spones (D)) ; if (err > 0) error ('nz!') ; end err = norm (C-D,1) ; fprintf ('m %3d n %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ... m, n, nnz(A), nnz(B), nnz(C), err) ; if (err > 1e-12) error ('!') ; end C = pi*A+3*B ; D = cs_add (A,B,pi,3) ; err = nnz (spones (C) - spones (D)) ; if (err > 0) error ('nz!') ; end err = norm (C-D,1) ; fprintf ('m %3d n %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ... m, n, nnz(A), nnz(B), nnz(C), err) ; if (err > 1e-12) error ('!') ; end end SuiteSparse/CSparse/MATLAB/Test/test6.m0000644001170100242450000000265410620373263016422 0ustar davisfacfunction test6 %TEST6 test cs_reach, cs_reachr, cs_lsolve, cs_usolve % % Example: % test6 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) maxerr = 0 ; clf for trial = 1:201 n = fix (100 * rand (1)) ; d = 0.1 * rand (1) ; L = tril (sprandn (n,n,d),-1) + sprand (speye (n)) ; b = sprandn (n,1,d) ; for uplo = 0:1 if (uplo == 1) % solve Ux=b instead ; L = L' ; end x = L\b ; sr = 1 + cs_reachr (L,b) ; sz = 1 + cs_reachr (L,b) ; check_if_same (sr,sz) ; s2 = 1 + cs_reach (L,b) ; if (uplo == 0) x3 = cs_lsolve (L,b) ; else x3 = cs_usolve (L,b) ; end spy ([L b x x3]) drawnow s = sort (sr) ; [i j xx] = find (x) ; %#ok [i3 j3 xx3] = find (x3) ; %#ok if (isempty (i)) if (~isempty (s)) i %#ok s %#ok error ('!') ; end elseif (any (s ~= i)) i %#ok s %#ok error ('!') ; end if (isempty (i3)) if (~isempty (s)) i3 %#ok s %#ok error ('!') ; end elseif (any (s ~= sort (i3))) s %#ok i3 %#ok error ('!') ; end if (any (s2 ~= sr)) s2 %#ok sr %#ok error ('!') ; end err = norm (x-x3,1) ; if (err > 1e-12) x %#ok x3 %#ok uplo %#ok err %#ok error ('!') end maxerr = max (maxerr, err) ; end drawnow end fprintf ('maxerr = %g\n', maxerr) ; SuiteSparse/CSparse/MATLAB/Test/test7.m0000644001170100242450000000356510620373267016431 0ustar davisfacfunction test7 %TEST7 test cs_lu % % Example: % test7 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:100) ; clf for i = f Prob = UFget (i) ; disp (Prob) ; A = Prob.A ; if (~isreal (A)) continue end [m n] = size (A) ; if (m ~= n) continue end [L,U,P] = lu (A) ; udiag = full (diag (U)) ; umin = min (abs (udiag)) ; fprintf ('umin %g\n', umin) ; if (umin > 1e-14) [L2,U2,p] = cs_lu (A) ; subplot (3,4,1) ; spy (A) ; subplot (3,4,2) ; spy (A(p,:)) ; subplot (3,4,3) ; spy (L2) ; subplot (3,4,4) ; spy (U2) ; err1 = norm (L*U-P*A,1) ; err2 = norm (L2*U2-A(p,:),1) ; fprintf ('err %g %g\n', err1, err2) ; end q = colamd (A) ; [L,U,P] = lu (A (:,q)) ; udiag = full (diag (U)) ; umin = min (abs (udiag)) ; fprintf ('umin %g with q\n', umin) ; if (umin > 1e-14) [L2,U2,p,q2] = cs_lu (A) ; subplot (3,4,5) ; spy (A) ; subplot (3,4,6) ; spy (A(p,q2)) ; subplot (3,4,7) ; spy (L2) ; subplot (3,4,8) ; spy (U2) ; err1 = norm (L*U-P*A(:,q),1) ; err2 = norm (L2*U2-A(p,q2),1) ; fprintf ('err %g %g\n', err1, err2) ; end try q = amd (A) ; catch q = symamd (A) ; end tol = 0.01 ; [L,U,P] = lu (A (q,q), tol) ; udiag = full (diag (U)) ; umin = min (abs (udiag)) ; fprintf ('umin %g with amd q\n', umin) ; if (umin > 1e-14) [L2,U2,p,q2] = cs_lu (A,tol) ; subplot (3,4,9) ; spy (A) ; subplot (3,4,10) ; spy (A(p,q2)) ; subplot (3,4,11) ; spy (L2) ; subplot (3,4,12) ; spy (U2) ; err1 = norm (L*U-P*A(q,q),1) ; err2 = norm (L2*U2-A(p,q2),1) ; lbig = full (max (max (abs (L2)))) ; fprintf ('err %g %g lbig %g\n', err1, err2, lbig) ; if (lbig > 1/tol) error ('L!') ; end end drawnow % pause end SuiteSparse/CSparse/MATLAB/Test/test8.m0000644001170100242450000000264610620667025016427 0ustar davisfac%TEST8 test cs_cholsol, cs_lusol % % Example: % test8 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:100) ; % f = f(1) for i = f Prob = UFget (i) ; disp (Prob) ; A = Prob.A ; [m n] = size (A) ; if (~isreal (A) | m ~= n) %#ok continue end spd = 0 ; if (m == n) if (nnz (A-A') == 0) try p = amd (A) ; catch p = symamd (A) ; end [R,p] = chol (A (p,p)) ; spd = (p == 0) ; end end if (spd) C = A ; else C = A*A' + n*speye (n) ; try p = amd (C) ; catch p = symamd (C) ; end try R = chol (C (p,p)) ; catch continue end end b = rand (n,1) ; x1 = C\b ; x2 = cs_cholsol (C,b) ; r1 = norm (C*x1-b,1) / norm (C,1) ; r2 = norm (C*x2-b,1) / norm (C,1) ; err = abs (r1-r2) ; fprintf ('err %g\n', err) ; if (err > 1e-10) error ('!') ; end x2 = cs_lusol (C,b, 1, 0.001) ; r2 = norm (C*x2-b,1) / norm (C,1) ; err = abs (r1-r2) ; fprintf ('err %g (lu with amd(A+A'')\n', err) ; if (err > 1e-10) error ('!') ; end if (m ~= n) continue ; end x1 = A\b ; r1 = norm (A*x1-b,1) / norm (A,1) ; if (r1 < 1e-6) x2 = cs_lusol (A,b) ; r2 = norm (A*x2-b,1) / norm (A,1) ; fprintf ('lu resid %g %g\n', r1, r2) ; end end SuiteSparse/CSparse/MATLAB/Test/test9.m0000644001170100242450000000456110620373272016424 0ustar davisfacfunction test9 %TEST9 test cs_qr % % Example: % test9 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) ; index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:100) ; clf % f = 185 ; % f = 449 ; % f = 186 for i = f Prob = UFget (i) ; disp (Prob) ; A = Prob.A ; [m n] = size (A) ; if (m < n) A = A' ; end [m n] = size (A) ; sp = sprank (A) ; % if (sprank (A) < min (m,n)) % continue % end Aorig = A ; A = A (:, colamd (A)) ; s1 = svd (full (A)) ; tic ; R = qr (A) ; t1 = toc ; %#ok % tic ; % [Q,R] = qr (A) ; % t1 = toc ; [c,h,parent] = symbfact (A, 'col') ; rnz = sum (c) ; %#ok tic ; [V2,Beta2,p,R2] = cs_qr (sparse(A)) ; t2 = toc ; %#ok v2 = full (V2) ; if (any (spones (v2) ~= spones (V2))) error ('got zeros!') ; end C = A ; m2 = size (V2,1) ; if (m2 > m) C = [A ; sparse(m2-m, n)] ; end C = C (p,:) ; % [H1,R1] = myqr (C) ; % err1 = norm (R1-R2,1) / norm (R1) % % [svd(A) svd(R1) svd(full(R2))] % s2 = svd (full (R2)) ; % err2 = norm (s1 - s2) / s1 (1) % fprintf ('%10.6f %10.6f cs speedup %8.3f sprank %d n %d\n', ... % t1, t2, t1/t2, sp, n) ; % err2 % left-looking: [V,Beta3,R3] = qr_left (C) ; %#ok s3 = svd (full (R2)) ; err3 = norm (s1 - s3) / s1 (1) ; disp ('err3 = ') ; disp (err3) ; if (err3 > 1e-12) error ('!') ; end % right-looking: [V,Beta4,R4] = qr_right (C) ; %#ok s4 = svd (full (R2)) ; err4 = norm (s1 - s4) / s1 (1) ; disp ('err4 = ') ; disp (err4) ; if (err4 > 1e-12) error ('!') ; end % H2 = full (H2) % R2 = full (R2) subplot (2,4,1) ; spy (A) ; title ('A colamd') ; subplot (2,4,2) ; spy (C) ; title ('A rperm') ; subplot (2,4,3) ; treeplot (parent) ; subplot (2,4,4) ; spy (Aorig) ; title ('Aorig') ; subplot (2,4,5) ; spy (abs(R2)>0) ; title ('spqr R, no zeros') ; subplot (2,4,6) ; spy (R) ; title ('matlab R') ; subplot (2,4,7) ; spy (R2) ; title ('spqr R') ; subplot (2,4,8) ; spy (V2) ; title ('spqr V') ; drawnow % if (err2 > 1e-9) % error ('!') ; % end if (m2 > m) fprintf ('added %d rows, sprank %d n %d\n', m2-m, sp, n) ; end % pause end SuiteSparse/CSparse/MATLAB/Test/testh.m0000644001170100242450000000315510620373276016505 0ustar davisfacfunction testh %TESTH test Householder reflections % % Example: % testh % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse format long e fprintf ('-------------------------------------------------\n') ; x = [-3 4 5]' ; disp (x) ; [v, beta, s] = house (x) ; disp ('v = ') ; disp (v) ; disp ('beta = ') ; disp (beta) ; disp ('s = ') ; disp (s) ; x = x - v*(beta*(v'*x)) ; disp (x) ; fprintf ('-------------------------------------------------\n') ; x = [3 4 5]' ; disp (x) ; [v, beta, s] = house (x) ; disp ('v = ') ; disp (v) ; disp ('beta = ') ; disp (beta) ; disp ('s = ') ; disp (s) ; x = x - v*(beta*(v'*x)) ; disp (x) ; fprintf ('-------------------------------------------------\n') ; x = [1 eps]' ; disp (x) ; [v, beta, s] = house (x) ; disp ('v = ') ; disp (v) ; disp ('beta = ') ; disp (beta) ; disp ('s = ') ; disp (s) ; x = x - v*(beta*(v'*x)) ; disp (x) ; fprintf ('-------------------------------------------------\n') ; x = pi ; disp (x) ; [v, beta, s] = house (x) ; disp ('v = ') ; disp (v) ; disp ('beta = ') ; disp (beta) ; disp ('s = ') ; disp (s) ; x = x - v*(beta*(v'*x)) ; disp (x) ; fprintf ('-------------------------------------------------\n') ; x = -pi ; disp (x) ; [v, beta, s] = house (x) ; disp ('v = ') ; disp (v) ; disp ('beta = ') ; disp (beta) ; disp ('s = ') ; disp (s) ; x = x - v*(beta*(v'*x)) ; disp (x) ; fprintf ('-------------------------------------------------\n') ; x = [1 0 0]' ; disp (x) ; [v, beta, s] = house (x) ; %#ok x = x - v*(beta*(v'*x)) ; disp (x) ; fprintf ('-------------------------------------------------\n') ; SuiteSparse/CSparse/MATLAB/Test/cs_reach.m0000644001170100242450000000063610620373077017125 0ustar davisfacfunction x = cs_reach(L,b) %#ok %CS_REACH non-recursive reach (interface to CSparse cs_reach) % find nonzero pattern of x=L\sparse(b). L must be sparse, real, and lower % triangular. b must be a real sparse vector. % % Example: % x = cs_reach(L,b) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_reach mexFunction not found') ; SuiteSparse/CSparse/MATLAB/Test/cs_pvec_mex.c0000644001170100242450000000132110415506232017620 0ustar davisfac#include "cs_mex.h" /* x = b(p) */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { int n, k, *p ; double *x, *b, *xx ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_pvec(b,p)") ; } b = mxGetPr (pargin [0]) ; n = mxGetNumberOfElements (pargin [0]) ; if (n != mxGetNumberOfElements (pargin [1])) { mexErrMsgTxt ("b or p wrong size") ; } pargout [0] = mxCreateDoubleMatrix (n, 1, mxREAL) ; xx = mxGetPr (pargin [1]) ; p = cs_malloc (n, sizeof (int)) ; for (k = 0 ; k < n ; k++) p [k] = xx [k] - 1 ; x = mxGetPr (pargout [0]) ; cs_pvec (p, b, x, n) ; cs_free (p) ; } SuiteSparse/CSparse/MATLAB/Test/cs_rowcnt.m0000644001170100242450000000062110620373103017337 0ustar davisfacfunction r = cs_rowcnt(A,parent,post) %#ok %CS_ROWCNT row counts for sparse Cholesky % Compute the row counts of the Cholesky factor L of the matrix A. Uses % the lower triangular part of A. % % Example: % r = cs_rowcnt(A,parent,post) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_rowcnt mexFunction not found') ; SuiteSparse/CSparse/MATLAB/Test/happly.m0000644001170100242450000000047310620373125016644 0ustar davisfacfunction hx = happly (v, beta, x) %HAPPLY apply Householder reflection to a vector % Example: % hx = happly (v,beta,x) ; % computes hx = x - v * (beta * (v' *x)) ; % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse hx = x - v * (beta * (v' *x)) ; SuiteSparse/CSparse/MATLAB/Test/choldn.m0000644001170100242450000000137610620373020016613 0ustar davisfacfunction L = choldn (Lold,w) %CHOLDN Cholesky downdate % given Lold and w, compute L so that L*L' = Lold*Lold' - w*w' % % Example: % L = cholnd (Lold,w) % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (Lold,1) ; L = Lold ; alpha = 1 ; beta = 1 ; wold = w ; wnew = zeros (n,1) ; for i = 1:n a = w (i) / L(i,i) ; alpha = alpha - a^2 ; if (alpha <= 0) error ('not pos def') ; end beta_new = sqrt (alpha) ; b = beta_new / beta ; c = (a / (beta*beta_new)) ; beta = beta_new ; % L (i,i) = b * L (i,i) ; wnew (i) = a ; for k = i:n w (k) = w (k) - a * L (k,i) ; L (k,i) = b * L (k,i) - c * w(k) ; end end % w % wnew disp (wnew - Lold\wold) SuiteSparse/CSparse/MATLAB/Test/cholup.m0000644001170100242450000000075010620373044016637 0ustar davisfacfunction L = cholup (Lold,w) %CHOLUP Cholesky update, using Given's rotations % given Lold and w, compute L so that L*L' = Lold*Lold' + w*w' % Example: % L = cholup (Lold,w) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (Lold,1) ; L = [Lold w] ; for k = 1:n g = givens (L(k,k), L(k,n+1)) ; L (:, [k n+1]) = L (:, [k n+1]) * g' ; disp ('L:') ; disp (L) pause end L = L (:,1:n) ; disp (L) ; SuiteSparse/CSparse/MATLAB/Test/qr_right.m0000644001170100242450000000073610620373164017173 0ustar davisfacfunction [V,Beta,R] = qr_right (A) %QR_RIGHT right-looking Householder QR factorization. % Example: % [V,Beta,R] = qr_right (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; V = zeros (m,n) ; Beta = zeros (1,n) ; for k = 1:n [v,beta] = gallery ('house', A (k:m,k), 2) ; V (k:m,k) = v ; Beta (k) = beta ; A (k:m,k:n) = A (k:m,k:n) - v * (beta * (v' * A (k:m,k:n))) ; end R = A ; SuiteSparse/CSparse/MATLAB/Test/chol_super.m0000644001170100242450000000100110620373034017475 0ustar davisfacfunction L = chol_super (A,s) %CHOL_SUPER left-looking "supernodal" Cholesky factorization. % Example: % L = chol_super (A,s) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A) ; L = zeros (n) ; ss = cumsum ([1 s]) ; for j = 1:length (s) k1 = ss (j) ; k2 = ss (j+1) ; k = k1:(k2-1) ; L (k,k) = chol (A (k,k) - L (k,1:k1-1) * L (k,1:k1-1)')' ; L (k2:n,k) = (A (k2:n,k) - L (k2:n,1:k1-1) * L (k,1:k1-1)') / L (k,k)' ; end SuiteSparse/CSparse/MATLAB/Test/cs_maxtransr_mex.c0000644001170100242450000000544410415621302020710 0ustar davisfac#include "cs_mex.h" /* find an augmenting path starting at column j and extend the match if found */ static int augment (int k, cs *A, int *jmatch, int *cheap, int *w, int j) { int found = 0, p, i = -1, *Ap = A->p, *Ai = A->i ; /* --- Start depth-first-search at node j ------------------------------- */ w [j] = k ; /* mark j as visited for kth path */ for (p = cheap [j] ; p < Ap [j+1] && !found ; p++) { i = Ai [p] ; /* try a cheap assignment (i,j) */ found = (jmatch [i] == -1) ; } cheap [j] = p ; /* start here next time for j */ /* --- Depth-first-search of neighbors of j ----------------------------- */ for (p = Ap [j] ; p < Ap [j+1] && !found ; p++) { i = Ai [p] ; /* consider row i */ if (w [jmatch [i]] == k) continue ; /* skip col jmatch [i] if marked */ found = augment (k, A, jmatch, cheap, w, jmatch [i]) ; } if (found) jmatch [i] = j ; /* augment jmatch if path found */ return (found) ; } /* find a maximum transveral */ static int *maxtrans (cs *A) /* returns jmatch [0..m-1] */ { int i, j, k, n, m, *Ap, *jmatch, *w, *cheap ; if (!A) return (NULL) ; /* check inputs */ n = A->n ; m = A->m ; Ap = A->p ; jmatch = cs_malloc (m, sizeof (int)) ; /* allocate result */ w = cs_malloc (2*n, sizeof (int)) ; /* allocate workspace */ if (!w || !jmatch) return (cs_idone (jmatch, NULL, w, 0)) ; cheap = w + n ; for (j = 0 ; j < n ; j++) cheap [j] = Ap [j] ; /* for cheap assignment */ for (j = 0 ; j < n ; j++) w [j] = -1 ; /* all columns unflagged */ for (i = 0 ; i < m ; i++) jmatch [i] = -1 ; /* no rows matched yet */ for (k = 0 ; k < n ; k++) augment (k, A, jmatch, cheap, w, k) ; return (cs_idone (jmatch, NULL, w, 1)) ; } /* invert a maximum matching */ static int *invmatch (int *jmatch, int m, int n) { int i, j, *imatch ; if (!jmatch) return (NULL) ; imatch = cs_malloc (n, sizeof (int)) ; if (!imatch) return (NULL) ; for (j = 0 ; j < n ; j++) imatch [j] = -1 ; for (i = 0 ; i < m ; i++) if (jmatch [i] >= 0) imatch [jmatch [i]] = i ; return (imatch) ; } void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs *A, Amatrix ; double *x ; int i, m, n, *imatch, *jmatch ; if (nargout > 1 || nargin != 1) { mexErrMsgTxt ("Usage: p = cr_maxtransr(A)") ; } /* get inputs */ A = cs_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ; m = A->m ; n = A->n ; jmatch = maxtrans (A) ; imatch = invmatch (jmatch, m, n) ; /* imatch = inverse of jmatch */ pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ; x = mxGetPr (pargout [0]) ; for (i = 0 ; i < n ; i++) x [i] = imatch [i] + 1 ; cs_free (jmatch) ; cs_free (imatch) ; } SuiteSparse/CSparse/MATLAB/Test/lu_rightp.m0000644001170100242450000000120310620373140017331 0ustar davisfacfunction [L,U,P] = lu_rightp (A) %LU_RIGHTP right-looking LU factorization, with partial pivoting. % % Example: % [L,U,P] = lu_rightp (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A,1) ; P = eye (n) ; for k = 1:n [x,i] = max (abs (A (k:n,k))) ; % partial pivoting i = i+k-1 ; P ([k i],:) = P ([i k], :) ; A ([k i],:) = A ([i k], :) ; % (6.10), (6.11) A (k+1:n,k) = A (k+1:n,k) / A (k,k) ; % (6.12) A (k+1:n,k+1:n) = A (k+1:n,k+1:n) - A (k+1:n,k) * A (k,k+1:n) ; % (6.9) end L = tril (A,-1) + eye (n) ; U = triu (A) ; SuiteSparse/CSparse/MATLAB/Test/lu_rightr.m0000644001170100242450000000102710620373143017342 0ustar davisfacfunction [L,U] = lu_rightr (A) %LU_RIGHTR recursive right-looking LU. % Example: % [L,U] = lu_rightr (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A,1) ; if (n == 1) L = 1 ; U = A ; else u11 = A (1,1) ; % (6.4) u12 = A (1,2:n) ; % (6.5) l21 = A (2:n,1) / u11 ; % (6.6) [L22,U22] = lu_rightr (A (2:n,2:n) - l21*u12) ; % (6.7) L = [ 1 zeros(1,n-1) ; l21 L22 ] ; U = [ u11 u12 ; zeros(n-1,1) U22 ] ; end SuiteSparse/CSparse/MATLAB/Test/dmspy_test.m0000644001170100242450000000125310620373113017534 0ustar davisfacfunction dmspy_test %DMSPY_TEST test cspy, cs_dmspy, and cs_dmperm % Example: % dmspy_test % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; f = find (index.nblocks > 1) ; % f = find (index.nblocks > 1 & index.nrows == index.ncols & ... % index.nnzdiag == index.nrows) ; [ignore i] = sort (index.nnz (f)) ; f = f (i) ; for i = f Prob = UFget (i,index) ; disp (Prob) ; clf subplot (2,2,1) ; cspy (Prob.A) ; subplot (2,2,2) ; cs_dmspy (Prob.A) ; [p,q,r,s,cc,rr] = cs_dmperm (Prob.A) ; %#ok subplot (2,2,3) ; plot (p) ; subplot (2,2,4) ; plot (q) ; drawnow end SuiteSparse/CSparse/MATLAB/Test/gqr3.m0000644001170100242450000000106610620373123016220 0ustar davisfacfunction R = gqr3 (A) %GQR3 QR factorization, based on Givens rotations % % Example: % R = gqr3 (A) % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; % parent = cs_etree (sparse (A), 'col') ; for i = 2:m % i for k = 1:min(i-1,n) % k % Givens rotation to zero out A(i,k) using A(k,k) G = givens2 (A(k,k), A(i,k)) ; A ([k i],k:n) = G * A ([k i],k:n) ; A (i,k) = 0 ; % fprintf ('A(21,25)=%g\n', A(21,25)) ; % if (A(21,25) ~= 0) % pause % end end end R = A ; SuiteSparse/CSparse/MATLAB/Test/lu_rightpr.m0000644001170100242450000000143110620373141017517 0ustar davisfacfunction [L,U,P] = lu_rightpr (A) %LU_RIGHTPR recursive right-looking LU, with partial pivoting. % % Example: % [L,U,P] = lu_rightpr (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A,1) ; if (n == 1) P = 1 ; L = 1 ; U = A ; else [x,i] = max (abs (A (1:n,1))) ; % partial pivoting P1 = eye (n) ; P1 ([1 i],:) = P1 ([i 1], :) ; A = P1*A ; u11 = A (1,1) ; % (6.10) u12 = A (1,2:n) ; % (6.11) l21 = A (2:n,1) / u11 ; % (6.12) [L22,U22,P2] = lu_rightpr (A (2:n,2:n) - l21*u12) ; % (6.9) or (6.13) o = zeros(1,n-1) ; L = [ 1 o ; P2*l21 L22 ] ; % (6.14) U = [ u11 u12 ; o' U22 ] ; P = [ 1 o ; o' P2] * P1 ; end SuiteSparse/CSparse/MATLAB/Test/cs_ipvec_mex.c0000644001170100242450000000132310415506226017776 0ustar davisfac#include "cs_mex.h" /* x(p) = b */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { int n, k, *p ; double *x, *b, *xx ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_ipvec(b,p)") ; } b = mxGetPr (pargin [0]) ; n = mxGetNumberOfElements (pargin [0]) ; if (n != mxGetNumberOfElements (pargin [1])) { mexErrMsgTxt ("b or p wrong size") ; } pargout [0] = mxCreateDoubleMatrix (n, 1, mxREAL) ; xx = mxGetPr (pargin [1]) ; p = cs_malloc (n, sizeof (int)) ; for (k = 0 ; k < n ; k++) p [k] = xx [k] - 1 ; x = mxGetPr (pargout [0]) ; cs_ipvec (p, b, x, n) ; cs_free (p) ; } SuiteSparse/CSparse/MATLAB/Test/myqr.m0000644001170100242450000000202410620373147016335 0ustar davisfacfunction [H,R] = myqr (A) %MYQR QR factorization using Householder reflections % uses function [v,beta,xnorm] = hmake1 (x) % and function hx = happly (v, beta, x) % % Example % [H,R] = myqr (A) % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; H = zeros (m,n) ; R = zeros (m,n) ; for k = 1:n % apply prior H's % fprintf ('\n-----------------init %d\n', k) ; x = A (:,k) ; for i = 1:k-1 v = H(((i+1):m),i) ; v = [1 ; v] ; %#ok beta = H (i,i) ; % n1 = norm (x (i:m)) ; x (i:m) = happly (v, beta, x (i:m)) ; % n2 = norm (x (i:m)) ; % fprintf ('=============== i %d %g %g\n', i, n1, n2) ; % beta % v' % X = x' % pause % i % x end % k % x % make Hk % fprintf ('x(k:m) = ') ; x (k:m) [v,beta,xnorm] = hmake1 (x (k:m)) ; H (k,k) = beta ; H (k+1:m, k) = v (2:end) ; R (1:(k-1),k) = x (1:(k-1)) ; R (k,k) = xnorm ; % full (R) % pause end % s2 = svd (full (R)) ; % [s1 s2 s1-s2] SuiteSparse/CSparse/MATLAB/Test/README.txt0000644001170100242450000000034710366510215016667 0ustar davisfacTest for MATLAB interface for CSparse. Type "testall" to run all the tests. Also includes "textbook" codes for the book "Direct Methods for Sparse Linear Systems", which are not part of CSparse proper, but are used in the tests. SuiteSparse/CSparse/MATLAB/Test/chol_example.m0000644001170100242450000000112010620373024017773 0ustar davisfacfunction chol_example %CHOL_EXAMPLE simple Cholesky factorization example % Example % chol_example % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse D = 10 ; X = 1 ; o = 0 ; A = sparse ([ D o X o o o o X o o o D o o X o o o o X X o D o o o X o o o o o o D o o o o X X o X o o D o o o X X o o o o o D X X o o o o X o o X D o o o X o o o o X o D X X o o o X X o o X D o o X o X X o o X o D ]) ; disp ('A = ') ; disp (A) ; L = chol(A)' ; disp ('L = ') ; disp (L) ; clf subplot (1,2,1) ; spy (A) ; subplot (1,2,2) ; spy (L+L') ; SuiteSparse/CSparse/MATLAB/Test/chol_left.m0000644001170100242450000000062210620373030017275 0ustar davisfacfunction L = chol_left (A) %CHOL_LEFT left-looking Cholesky factorization. % Example % L = chol_left (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A,1) ; L = zeros (n) ; for k = 1:n L (k,k) = sqrt (A (k,k) - L (k,1:k-1) * L (k,1:k-1)') ; L (k+1:n,k) = (A (k+1:n,k) - L (k+1:n,1:k-1) * L (k,1:k-1)') / L (k,k) ; end SuiteSparse/CSparse/MATLAB/Test/chol_update.m0000644001170100242450000000121610620373036017633 0ustar davisfacfunction [L, w] = chol_update (L, w) %CHOL_UPDATE update a Cholesky factorization. % Example: % [L, w] = chol_update (L, w) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse beta = 1 ; n = size (L,1) ; for j = 1:n alpha = w (j) / L (j,j) ; beta2 = sqrt (beta^2 + alpha^2) ; gamma = alpha / (beta2 * beta) ; delta = beta / beta2 ; L (j,j) = delta * L (j,j) + gamma * w (j) ; w (j) = alpha ; beta = beta2 ; if (j == n) return end w1 = w (j+1:n) ; w (j+1:n) = w (j+1:n) - alpha * L (j+1:n,j) ; L (j+1:n,j) = delta * L (j+1:n,j) + gamma * w1 ; end SuiteSparse/CSparse/MATLAB/Test/cs_pvec.m0000644001170100242450000000036410620373067016775 0ustar davisfacfunction x = cs_pvec (b,p) %#ok %CS_PVEC x=b(p) % % Example: % x = cs_pvec (b,p) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_pvec mexFunction not found') ; SuiteSparse/CSparse/MATLAB/Test/chol_updown.m0000644001170100242450000000163210620373037017670 0ustar davisfacfunction [L, w] = chol_updown (L, sigma, w) %CHOL_UPDOWN update or downdate a Cholesky factorization. % Example: % [L, w] = chol_updown (L, sigma, w) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse beta = 1 ; n = size (L,1) ; if (n == 1) L = sqrt (L*L'+sigma*w*w') ; return ; end for k = 1:n alpha = w(k) / L(k,k) ; beta2 = sqrt (beta^2 + sigma*alpha^2) ; gamma = sigma * alpha / (beta2 * beta) ; if (sigma > 0) % update delta = beta / beta2 ; L (k,k) = delta * L (k,k) + gamma * w (k) ; w1 = w (k+1:n) ; w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ; L (k+1:n,k) = delta * L (k+1:n,k) + gamma * w1 ; else % downdate delta = beta2 / beta ; L (k,k) = delta * L (k,k) ; w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ; L (k+1:n,k) = delta * L (k+1:n,k) + gamma * w (k+1:n) ; end w (k) = alpha ; beta = beta2 ; end SuiteSparse/CSparse/MATLAB/Test/cs_test_make.m0000644001170100242450000000164510620666223020016 0ustar davisfacfunction cs_test_make (force) %CS_TEST_MAKE compiles the CSparse, Demo, and Test mexFunctions. % The current directory must be CSparse/MATLAB/Test to use this function. % % Example: % cs_test_make % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (nargin < 1) force = 0 ; end cd ('../CSparse') ; [object_files timestamp] = cs_make ; cd ('../Test') ; mexfunc = { 'cs_ipvec', 'cs_pvec', 'cs_sparse2', ... 'cs_reach', 'cs_maxtransr', 'cs_reachr', 'cs_rowcnt', 'cs_frand' } ; for i = 1:length(mexfunc) [s t tobj] = cs_must_compile ('', mexfunc{i}, '_mex', ... ['.' mexext], 'cs_test_make.m', force) ; if (s | tobj < timestamp) %#ok cmd = ['mex -O -output ' mexfunc{i} ' ' mexfunc{i} '_mex.c -I..' ... filesep '..' filesep 'Include -I..' ... filesep 'CSparse ' object_files] ; fprintf ('%s\n', cmd) ; eval (cmd) ; end end SuiteSparse/CSparse/MATLAB/Test/cs_reachr.m0000644001170100242450000000063710620373100017273 0ustar davisfacfunction x = cs_reachr(L,b) %#ok %CS_REACHR recursive reach (interface to CSparse cs_reachr) % find nonzero pattern of x=L\sparse(b). L must be sparse, real, and lower % triangular. b must be a real sparse vector. % % Example: % x = cs_reachr(L,b) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_reach mexFunction not found') ; SuiteSparse/CSparse/MATLAB/Test/etree_sample.m0000644001170100242450000000227010620373115020010 0ustar davisfacfunction etree_sample % ETREE_SAMPLE construct a sample etree and symbolic factorization % % Example % etree_sample % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clf % desired etree: % 1 2 3 4 5 6 7 8 9 10 11 goal = [6 3 8 6 8 7 9 10 10 11 0] ; o = 0 ; X = 1 ; x = 0 ; A = [ 1 o o o o o o o o o o o 2 o o o o o o o o o o X 3 o o o o o o o o o o o 4 o o o o o o o o o o o 5 o o o o o o X o o X o 6 o o o o o X o o x o x 7 o o o o o X x o X o o 8 o o o x o o x o X x o 9 o o x x X X x X x X x 10 o x x X x X x X X x X 11 ] ; A = A + tril(A,-1)' ; disp ('A = ') ; disp (A) [count,h,parent,post,R] = symbfact (A) ; L = R' ; subplot (2,3,1) ; spy (A) title ('A') ; subplot (2,3,2) ; etreeplot (A) title ('etree') ; % [parent, post] = etree (A) ; subplot (2,3,3) ; spy (L) title ('L, not postordered') ; n = size (A,1) ; for k = 1:n fprintf ('parent (%d) = %d goal: %d ok: %d\n', ... k, parent (k), goal (k), goal (k) == parent(k)) ; end [count,h,parent2,post2,R] = symbfact (A (post,post)) ; L = R' ; subplot (2,3,5) ; spy (A (post,post)) title ('A postordered') ; subplot (2,3,6) ; spy (L) title ('L postordered') ; SuiteSparse/CSparse/MATLAB/Test/another_colormap.m0000644001170100242450000000102010620701546020672 0ustar davisfacfunction another_colormap %ANOTHER_COLORMAP try another color map % % Example: % another_colormap % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse j = jet (128) ; j = j (48:112, :) ; % jj = linspace (0,1,64)' ./ sum (jet,2) ; % j (:,1) = j (:,1) .* jj ; % j (:,2) = j (:,2) .* jj ; % j (:,3) = j (:,3) .* jj ; % white = [1 1 1] ; % gray = [.5 .5 .5] ; %#ok % j = [white ; purple ; j ] ; disp ('j = ') ; disp (j) image (1:size(j,1)) ; colormap (j) ; SuiteSparse/CSparse/MATLAB/Test/test_randperms.m0000644001170100242450000000161110620373306020375 0ustar davisfacfunction test_randperms %TEST_RANDPERMS test random permutations % Example: % test_randperms % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) for trial = 1:100 m = fix (30 * rand (1)) ; n = fix (30 * rand (1)) ; d = rand (1) ; A = sprandn (m,n,d) ; if (m == 0) p = [] ; else p = randperm (m) ; end if (n == 0) q = [] ; else q = randperm (n) ; end C = A(p,q) ; Im = speye (m) ; In = speye (n) ; P = Im (p,:) ; Q = In (:,q) ; q2 = find (Q) ; if (any (q ~= q2')) error ('!') end p2 = find (P') ; if (any (p ~= p2')) error ('!') end E = P*A*Q ; if (norm (C-E,1) ~= 0) error ('!') end P = sparse (1:m, p, 1) ; Q = sparse (q, 1:n, 1) ; E = P*A*Q ; if (norm (C-E,1) ~= 0) error ('2!') end end SuiteSparse/CSparse/MATLAB/Test/sample_colormap.m0000644001170100242450000000157110620373165020530 0ustar davisfacfunction sample_colormap %SAMPLE_COLORMAP try a colormap for use in cspy % % Example: % sample_colormap % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse h = jet (64) ; h = h (64:-1:1,:) ; h = h (20:end,:) ; % h = h (17:128,:) ; % s = sum (jet,2) ; % h (:,1) = h (:,1) ./ s ; % h (:,2) = h (:,2) ./ s ; % h (:,3) = h (:,3) ./ s ; h (1,:) = [1 1 1] ; % white h (2,:) = [1 1 .8] ; % light yellow % h colormap (h) ; clf subplot (5,1,1) ; image (1:size(h,1)) ; h = rgb2hsv (h) ; % h (:,3) = linspace (1,0,64) ; % h= hsv2rgb (h) ; subplot (5,1,2) ; plot (h(:,1)) ; axis ([1 64 0 1]) ; ylabel ('red') ; subplot (5,1,3) ; plot (h(:,2)) ; axis ([1 64 0 1]) ; ylabel ('green') ; subplot (5,1,4) ; plot (h(:,3)) ; axis ([1 64 0 1]) ; ylabel ('blue') ; subplot (5,1,5) ; plot (sum(h,2)) ; axis ([1 64 0 3]) ; ylabel ('sum') ; SuiteSparse/CSparse/MATLAB/Test/house.m0000644001170100242450000000102710620373131016463 0ustar davisfacfunction [v,beta,s] = house (x) %HOUSE find a Householder reflection. % Example: % [v,beta,s] = house (x) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = length (x) ; if (n == 1) sigma = 0 ; else sigma = x (2:n)' * x (2:n) ; end v = x ; if (sigma == 0) s = x (1) ; v (1) = 0 ; beta = 0 ; else s = sqrt (x(1)^2 + sigma) ; if (x (1) <= 0) v (1) = x (1) - s ; else v (1) = -sigma / (x (1) + s) ; end beta = -1 / (s * v(1)) ; end SuiteSparse/CSparse/MATLAB/Test/cs_reach_mex.c0000644001170100242450000000176510415621440017760 0ustar davisfac#include "cs_mex.h" /* find nonzero pattern of x=L\sparse(b). L must be sparse, real, and lower * triangular. b must be a real sparse vector. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs Lmatrix, Bmatrix, *L, *B ; double *x ; int k, i, j, top, *xi, *perm ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_reach(L,b)") ; } /* get inputs */ L = cs_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; B = cs_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ; cs_mex_check (0, L->n, 1, 0, 1, 1, pargin [1]) ; perm = cs_malloc (L->n, sizeof (int)) ; for (k = 0 ; k < L->n ; k++) perm [k] = k ; xi = cs_calloc (3*L->n, sizeof (int)) ; top = cs_reach (L, B, 0, xi, perm) ; pargout [0] = mxCreateDoubleMatrix (L->n - top, 1, mxREAL) ; x = mxGetPr (pargout [0]) ; for (j = 0, i = top ; i < L->n ; i++, j++) x [j] = xi [i] ; cs_free (xi) ; cs_free (perm) ; } SuiteSparse/CSparse/MATLAB/Test/cs_fiedler.m0000644001170100242450000000157210620373057017453 0ustar davisfacfunction [p,v,d] = cs_fiedler (A) %CS_FIEDLER the Fiedler vector of a connected graph. % [p,v,d] = cs_fiedler(A) computes the Fiedler vector v (the eigenvector % corresponding to the 2nd smallest eigenvalue d of the Laplacian of the graph % of A+A'). p is the permutation obtained when v is sorted. A should be a % connected graph. % % Example: % [p,v,d] = cs_fiedler (A) ; % % See also CS_SCC, EIGS, SYMRCM, UNMESH. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A,1) ; if (n < 2) p = 1 ; v = 1 ; d = 0 ; return ; end opt.disp = 0 ; % turn off printing in eigs opt.tol = sqrt (eps) ; S = A | A' | speye (n) ; % compute the Laplacian of A S = diag (sum (S)) - S ; [v,d] = eigs (S, 2, 'SA', opt) ; % find the Fiedler vector v v = v (:,2) ; d = d (2,2) ; [ignore p] = sort (v) ; % sort it to get p SuiteSparse/CSparse/MATLAB/Test/chol_downdate.m0000644001170100242450000000127310620373022020154 0ustar davisfacfunction [L, w] = chol_downdate (L, w) %CHOL_DOWNDATE downdate a Cholesky factorization. % Example % [L, w] = chol_downdate (L, w) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse beta = 1 ; n = size (L,1) ; for j = 1:n alpha = w (j) / L (j,j) ; beta2 = sqrt (beta^2 - alpha^2) ; if (~isreal (beta2)) error ('not positive definite') ; end gamma = alpha / (beta2 * beta) ; delta = beta2 / beta ; L (j,j) = delta * L (j,j) ; w (j) = alpha ; beta = beta2 ; if (j == n) return end w (j+1:n) = w (j+1:n) - alpha * L (j+1:n,j) ; L (j+1:n,j) = delta * L (j+1:n,j) - gamma * w (j+1:n) ; end SuiteSparse/CSparse/MATLAB/Test/qr_givens.m0000644001170100242450000000105610620666403017346 0ustar davisfacfunction R = qr_givens (A) %QR_GIVENS Givens-rotation QR factorization. % Example: % R = qr_givens (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; parent = cs_etree (sparse (A), 'col') ; A = full (A) ; for i = 2:m k = min (find (A (i,:))) ; %#ok if (isempty (k)) continue ; end while (k > 0 & k <= min (i-1,n)) %#ok A ([k i],k:n) = givens2 (A(k,k), A(i,k)) * A ([k i],k:n) ; A (i,k) = 0 ; k = parent (k) ; end end R = sparse (A) ; SuiteSparse/CSparse/MATLAB/Test/cs_frand.m0000644001170100242450000000075010620373060017122 0ustar davisfacfunction A = cs_frand (n,nel,s) %#ok %CS_FRAND generate a random finite-element matrix % A = cs_frand (n,nel,s) creates an n-by-n sparse matrix consisting of nel % finite elements, each of which are of size s-by-s with random symmetric % nonzero pattern, plus the identity matrix. % % Example % A = cs_frand (100, 100, 3) ; % See also cs_demo. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_frand mexFunction not found') ; SuiteSparse/CSparse/MATLAB/Test/lu_right.m0000644001170100242450000000072310620373136017164 0ustar davisfacfunction [L,U] = lu_right (A) %LU_RIGHT right-looking LU factorization. % Example: % [L,U] = lu_right (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A,1) ; L = eye (n) ; U = zeros (n) ; for k = 1:n U (k,k:n) = A (k,k:n) ; % (6.4) and (6.5) L (k+1:n,k) = A (k+1:n,k) / U (k,k) ; % (6.6) A (k+1:n,k+1:n) = A (k+1:n,k+1:n) - L (k+1:n,k) * U (k,k+1:n) ; % (6.7) end SuiteSparse/CSparse/MATLAB/Test/qr_givens_full.m0000644001170100242450000000061710620373155020371 0ustar davisfacfunction R = qr_givens_full (A) %QR_GIVENS_FULL Givens-rotation QR factorization, for full matrices. % Example: % R = qr_givens_full (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; for i = 2:m for k = 1:min(i-1,n) A ([k i],k:n) = givens2 (A(k,k), A(i,k)) * A ([k i],k:n) ; A (i,k) = 0 ; end end R = A ; SuiteSparse/CSparse/MATLAB/Test/lu_left.m0000644001170100242450000000134310620373133016775 0ustar davisfacfunction [L,U,P] = lu_left (A) %LU_LEFT left-looking LU factorization. % Example: % [L,U,P] = lu_left (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A,1) ; P = eye (n) ; L = zeros (n) ; U = zeros (n) ; for k = 1:n x = [ L(:,1:k-1) [ zeros(k-1,n-k+1) ; eye(n-k+1) ]] \ (P * A (:,k)) ; U (1:k-1,k) = x (1:k-1) ; % the column of U [a i] = max (abs (x (k:n))) ; % find the pivot row i i = i + k - 1 ; L ([i k],:) = L ([k i], :) ; % swap rows i and k of L, P, and x P ([i k],:) = P ([k i], :) ; x ([i k]) = x ([k i]) ; U (k,k) = x (k) ; L (k,k) = 1 ; L (k+1:n,k) = x (k+1:n) / x (k) ; % divide the pivot column by U(k,k) end SuiteSparse/CSparse/MATLAB/Test/test_qr.m0000644001170100242450000000240210620667064017032 0ustar davisfacfunction test_qr %TEST_QR test various QR factorization methods % % Example: % test_qr % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows,index.ncols)) ; % f = 276 % f = 706 f = f (1:100) ; for i = f % Prob = UFget (i,index) Prob = UFget (i) ; disp (Prob) ; A = Prob.A ; [m n] = size (A) ; if (m < n) A = A' ; end [m n] = size (A) ; if (sprank (A) < n | ~isreal (A)) %#ok continue ; end [V,beta,p,R1,q] = cs_qr(A) ; A = A (p,q) ; parent = etree (A, 'col') ; %#ok R0 = qr (A) ; R2 = qr_givens (full (A)) ; R3 = qr_givens_full (full (A)) ; subplot (2,2,1) ; cspy (R0) ; title ('matlab') ; subplot (2,2,2) ; cspy (R3) ; title ('qr-full') ; subplot (2,2,3) ; cspy (R2) ; title ('qr-givens') ; subplot (2,2,4) ; cspy (R1) ; title ('cs-qr') ; e0 = norm (A'*A-R0'*R0,1) / norm (A,1) ; e1 = norm (A'*A-R1'*R1,1) / norm (A,1) ; e2 = norm (A'*A-R2'*R2,1) / norm (A,1) ; e3 = norm (A'*A-R3'*R3,1) / norm (A,1) ; fprintf ('error %6.2e %6.2e %6.2e %6.2e\n', e0, e1, e2, e3) ; drawnow if (e1 > e0*1e3 | e2 > e0*1e3) %#ok pause end end SuiteSparse/CSparse/MATLAB/Test/testall.m0000644001170100242450000000275210710513024017013 0ustar davisfacfunction testall %TESTALL test all CSparse functions (run tests 1 to 28 below) % % Example: % testall % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse h = waitbar (0, 'CSparse') ; cs_test_make % compile all CSparse, Demo, Text, and Test mexFunctions ntests = 28 ; testwait (1, ntests, h) ; test1 ; testwait (2, ntests, h) ; test2 ; testwait (3, ntests, h) ; test3 ; testwait (4, ntests, h) ; test4 ; testwait (5, ntests, h) ; test5 ; testwait (6, ntests, h) ; test6 ; testwait (7, ntests, h) ; test7 ; testwait (8, ntests, h) ; test8 ; testwait (9, ntests, h) ; test9 ; testwait (10, ntests, h) ; test10 ; testwait (11, ntests, h) ; test11 ; testwait (12, ntests, h) ; test12 ; testwait (13, ntests, h) ; test13 ; testwait (14, ntests, h) ; test14 ; testwait (15, ntests, h) ; test15 ; testwait (16, ntests, h) ; test16 ; testwait (17, ntests, h) ; test17 ; testwait (18, ntests, h) ; test18 ; testwait (19, ntests, h) ; test19 ; testwait (20, ntests, h) ; test20 ; testwait (21, ntests, h) ; test21 ; testwait (22, ntests, h) ; test22 ; testwait (23, ntests, h) ; test23 ; testwait (24, ntests, h) ; test24 ; testwait (25, ntests, h) ; test25 ; testwait (26, ntests, h) ; test26 ; testwait (27, ntests, h) ; test27 ; testwait (28, ntests, h) ; test28 ; close (h) function testwait (n,ntests,h) fprintf ('\n------------------------ test%d\n', n) ; waitbar (n/(ntests+1), h, sprintf ('CSparse test %d of %d\n', n, ntests)) ; SuiteSparse/CSparse/MATLAB/Test/norm1est.m0000644001170100242450000000126410620666374017131 0ustar davisfacfunction est = norm1est (L,U,P,Q) %NORM1EST 1-norm estimate. % Example: % est = norm1est (L,U,P,Q) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (L,1) ; for k = 1:5 if (k == 1) est = 0 ; x = ones (n,1) / n ; jold = -1 ; else j = min (find (abs (x) == norm (x,inf))) ; %#ok if (j == jold) break end ; x = zeros (n,1) ; x (j) = 1 ; jold = j ; end x = Q * (U \ (L \ (P*x))) ; est_old = est ; est = norm (x,1) ; if (k > 1 & est <= est_old) %#ok break end ; s = ones (n,1) ; s (find (x < 0)) = -1 ; %#ok x = P' * (L' \ (U' \ (Q'*s))) ; end SuiteSparse/CSparse/MATLAB/Test/mynormest1.m0000644001170100242450000000302410620666356017473 0ustar davisfacfunction est = mynormest1 (L, U, P, Q) %MYNORMEST1 estimate norm(A,1), using LU factorization (L*U = P*A*Q). % % Example: % est = mynormest1 (L, U, P, Q) % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (L,1) ; est = 0 ; S = zeros (n,1) ; for k = 1:5 if k == 1 x = ones (n,1) / n ; else j = find (abs (x) == max (abs (x))) ; j = j (1) ; x = zeros (n,1) ; x (j) = 1 ; % fprintf ('eka: k %d j %d est %g\n', k, j, est) ; end % x=A\x, but use the existing P*A*Q=L*U factorization x = Q * (U \ (L \ (P*x))) ; est_old = est ; est = sum (abs (x)) ; unchanged = 1 ; for i = 1:n if (x (i) >= 0) s = 1 ; else s = -1 ; end if (s ~= S (i)) S (i) = s ; unchanged = 0 ; end end if (any (S ~= signum (x))) S' %#ok signum(x)' %#ok error ('Hey!') ; end if k > 1 & (est <= est_old | unchanged) %#ok break ; end x = S ; % x=A'\x, but use the existing P*A*Q=L*U factorization x = P' * (L' \ (U' \ (Q'*x))) ; if k > 1 jnew = find (abs (x) == max (abs (x))) ; if (jnew == j) break ; end end end for k = 1:n x (k) = power (-1, k+1) * (1 + ((k-1)/(n-1))) ; end % x=A\x, but use the existing P*A*Q=L*U factorization x = Q * (U \ (L \ (P*x))) ; est_new = 2 * sum (abs (x)) / (3 * n) ; if (est_new > est) est = est_new ; end function s = signum (x) %SIGNUM compute sign of x s = ones (length (x),1) ; s (find (x < 0)) = -1 ; %#ok SuiteSparse/CSparse/MATLAB/CSparse/0000755001170100242450000000000010711653403015607 5ustar davisfacSuiteSparse/CSparse/MATLAB/CSparse/cs_ltsolve.m0000644001170100242450000000110310620371640020134 0ustar davisfacfunction x = cs_ltsolve (L,b) %#ok %CS_LTSOLVE solve a sparse upper triangular system L'*x=b. % x = cs_ltsolve(L,b) computes x = L'\b, L must be lower triangular with a % zero-free diagonal. b must be a full vector. % % Example: % Prob = UFget ('HB/bcsstk01') ; L = cs_chol (Prob.A) ; n = size (L,1) ; % b = rand (n,1) ; x = cs_ltsolve (L,b) ; norm (L'*x-b) % % See also CS_LSOLVE, CS_USOLVE, CS_UTSOLVE, MLDIVIDE. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_ltsolve mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_cholsol.m0000644001170100242450000000135210620371612020114 0ustar davisfacfunction x = cs_cholsol (A,b,order) %#ok %CS_CHOLSOL solve A*x=b using a sparse Cholesky factorization. % x = cs_cholsol(A,b) computes x = A\b, where A sparse symmetric positive % definite, and b is a full vector. A 3rd input parameter allows the % ordering to be modified: 0: natural, 1:amd(A), 2: amd(S'*S) where S=A except % with no dense rows, 3:amd(A'*A). The default ordering option is 1. % % Example: % Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; b = rand (size (A,1),1) ; % x = cs_cholsol (A,b) ; norm (A*x-b) % % See also CS_CHOL, CS_AMD, CS_LUSOL, CS_QRSOL, MLDIVIDE. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_cholsol mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/Makefile0000644001170100242450000001274710617167305017270 0ustar davisfacMEX = mex -O AR = ar cr RANLIB = ranlib I = -I../../Include all: mexcsparse.a cs_mex.h $(MEX) cs_thumb_mex.c $(I) mexcsparse.a -output cs_thumb $(MEX) cs_print_mex.c $(I) mexcsparse.a -output cs_print $(MEX) cs_updown_mex.c $(I) mexcsparse.a -output cs_updown $(MEX) cs_gaxpy_mex.c $(I) mexcsparse.a -output cs_gaxpy $(MEX) cs_transpose_mex.c $(I) mexcsparse.a -output cs_transpose $(MEX) cs_sparse_mex.c $(I) mexcsparse.a -output cs_sparse $(MEX) cs_multiply_mex.c $(I) mexcsparse.a -output cs_multiply $(MEX) cs_add_mex.c $(I) mexcsparse.a -output cs_add $(MEX) cs_permute_mex.c $(I) mexcsparse.a -output cs_permute $(MEX) cs_symperm_mex.c $(I) mexcsparse.a -output cs_symperm $(MEX) cs_lsolve_mex.c $(I) mexcsparse.a -output cs_lsolve $(MEX) cs_ltsolve_mex.c $(I) mexcsparse.a -output cs_ltsolve $(MEX) cs_usolve_mex.c $(I) mexcsparse.a -output cs_usolve $(MEX) cs_utsolve_mex.c $(I) mexcsparse.a -output cs_utsolve $(MEX) cs_chol_mex.c $(I) mexcsparse.a -output cs_chol $(MEX) cs_etree_mex.c $(I) mexcsparse.a -output cs_etree $(MEX) cs_counts_mex.c $(I) mexcsparse.a -output cs_counts $(MEX) cs_qr_mex.c $(I) mexcsparse.a -output cs_qr $(MEX) cs_amd_mex.c $(I) mexcsparse.a -output cs_amd $(MEX) cs_lu_mex.c $(I) mexcsparse.a -output cs_lu $(MEX) cs_cholsol_mex.c $(I) mexcsparse.a -output cs_cholsol $(MEX) cs_lusol_mex.c $(I) mexcsparse.a -output cs_lusol $(MEX) cs_droptol_mex.c $(I) mexcsparse.a -output cs_droptol $(MEX) cs_qrsol_mex.c $(I) mexcsparse.a -output cs_qrsol $(MEX) cs_dmperm_mex.c $(I) mexcsparse.a -output cs_dmperm $(MEX) cs_scc_mex.c $(I) mexcsparse.a -output cs_scc $(MEX) cs_sqr_mex.c $(I) mexcsparse.a -output cs_sqr $(MEX) cs_randperm_mex.c $(I) mexcsparse.a -output cs_randperm CS = cs_mex.o \ cs_amd.o \ cs_chol.o \ cs_counts.o \ cs_cumsum.o \ cs_fkeep.o \ cs_dfs.o \ cs_dmperm.o \ cs_droptol.o \ cs_dropzeros.o \ cs_dupl.o \ cs_entry.o \ cs_etree.o \ cs_gaxpy.o \ cs_ipvec.o \ cs_lsolve.o \ cs_ltsolve.o \ cs_lu.o \ cs_maxtrans.o \ cs_util.o \ cs_malloc.o \ cs_multiply.o \ cs_add.o \ cs_scatter.o \ cs_permute.o \ cs_pinv.o \ cs_post.o \ cs_tdfs.o \ cs_pvec.o \ cs_qr.o \ cs_happly.o \ cs_house.o \ cs_schol.o \ cs_scc.o \ cs_sqr.o \ cs_symperm.o \ cs_transpose.o \ cs_compress.o \ cs_usolve.o \ cs_utsolve.o \ cs_cholsol.o \ cs_lusol.o \ cs_qrsol.o \ cs_updown.o \ cs_norm.o \ cs_print.o \ cs_load.o \ cs_spsolve.o \ cs_reach.o \ cs_ereach.o \ cs_leaf.o \ cs_randperm.o mexcsparse.a: $(CS) $(AR) mexcsparse.a $(CS) $(RANLIB) mexcsparse.a $(CS): ../../Include/cs.h cs_mex.o: cs_mex.c cs_mex.h $(MEX) -c $(I) $< cs_amd.o: ../../Source/cs_amd.c $(MEX) -c $(I) $< cs_chol.o: ../../Source/cs_chol.c $(MEX) -c $(I) $< cs_ereach.o: ../../Source/cs_ereach.c $(MEX) -c $(I) $< cs_cholsol.o: ../../Source/cs_cholsol.c $(MEX) -c $(I) $< cs_lusol.o: ../../Source/cs_lusol.c $(MEX) -c $(I) $< cs_qrsol.o: ../../Source/cs_qrsol.c $(MEX) -c $(I) $< cs_counts.o: ../../Source/cs_counts.c $(MEX) -c $(I) $< cs_leaf.o: ../../Source/cs_leaf.c $(MEX) -c $(I) $< cs_cumsum.o: ../../Source/cs_cumsum.c $(MEX) -c $(I) $< cs_fkeep.o: ../../Source/cs_fkeep.c $(MEX) -c $(I) $< cs_dfs.o: ../../Source/cs_dfs.c $(MEX) -c $(I) $< cs_droptol.o: ../../Source/cs_droptol.c $(MEX) -c $(I) $< cs_dropzeros.o: ../../Source/cs_dropzeros.c $(MEX) -c $(I) $< cs_dupl.o: ../../Source/cs_dupl.c $(MEX) -c $(I) $< cs_entry.o: ../../Source/cs_entry.c $(MEX) -c $(I) $< cs_etree.o: ../../Source/cs_etree.c $(MEX) -c $(I) $< cs_gaxpy.o: ../../Source/cs_gaxpy.c $(MEX) -c $(I) $< cs_ipvec.o: ../../Source/cs_ipvec.c $(MEX) -c $(I) $< cs_lsolve.o: ../../Source/cs_lsolve.c $(MEX) -c $(I) $< cs_ltsolve.o: ../../Source/cs_ltsolve.c $(MEX) -c $(I) $< cs_lu.o: ../../Source/cs_lu.c $(MEX) -c $(I) $< cs_util.o: ../../Source/cs_util.c $(MEX) -c $(I) $< cs_malloc.o: ../../Source/cs_malloc.c $(MEX) -c $(I) $< cs_multiply.o: ../../Source/cs_multiply.c $(MEX) -c $(I) $< cs_add.o: ../../Source/cs_add.c $(MEX) -c $(I) $< cs_scatter.o: ../../Source/cs_scatter.c $(MEX) -c $(I) $< cs_permute.o: ../../Source/cs_permute.c $(MEX) -c $(I) $< cs_pinv.o: ../../Source/cs_pinv.c $(MEX) -c $(I) $< cs_post.o: ../../Source/cs_post.c $(MEX) -c $(I) $< cs_tdfs.o: ../../Source/cs_tdfs.c $(MEX) -c $(I) $< cs_pvec.o: ../../Source/cs_pvec.c $(MEX) -c $(I) $< cs_qr.o: ../../Source/cs_qr.c $(MEX) -c $(I) $< cs_happly.o: ../../Source/cs_happly.c $(MEX) -c $(I) $< cs_house.o: ../../Source/cs_house.c $(MEX) -c $(I) $< cs_schol.o: ../../Source/cs_schol.c $(MEX) -c $(I) $< cs_spsolve.o: ../../Source/cs_spsolve.c $(MEX) -c $(I) $< cs_reach.o: ../../Source/cs_reach.c $(MEX) -c $(I) $< cs_sqr.o: ../../Source/cs_sqr.c $(MEX) -c $(I) $< cs_symperm.o: ../../Source/cs_symperm.c $(MEX) -c $(I) $< cs_transpose.o: ../../Source/cs_transpose.c $(MEX) -c $(I) $< cs_compress.o: ../../Source/cs_compress.c $(MEX) -c $(I) $< cs_usolve.o: ../../Source/cs_usolve.c $(MEX) -c $(I) $< cs_utsolve.o: ../../Source/cs_utsolve.c $(MEX) -c $(I) $< cs_dmperm.o: ../../Source/cs_dmperm.c $(MEX) -c $(I) $< cs_randperm.o: ../../Source/cs_randperm.c $(MEX) -c $(I) $< cs_maxtrans.o: ../../Source/cs_maxtrans.c $(MEX) -c $(I) $< cs_scc.o: ../../Source/cs_scc.c $(MEX) -c $(I) $< cs_updown.o: ../../Source/cs_updown.c $(MEX) -c $(I) $< cs_print.o: ../../Source/cs_print.c $(MEX) -c $(I) $< cs_norm.o: ../../Source/cs_norm.c $(MEX) -c $(I) $< cs_load.o: ../../Source/cs_load.c $(MEX) -c $(I) $< clean: rm -f *.o distclean: clean rm -f *.mex* *.dll *.a purge: distclean SuiteSparse/CSparse/MATLAB/CSparse/cs_lu.m0000644001170100242450000000240310620371643017073 0ustar davisfacfunction [L,U,p,q] = cs_lu (A,tol) %#ok %CS_LU sparse LU factorization, with fill-reducing ordering. % [L,U,p] = cs_lu(A) factorizes A(p,:) into L*U using no fill-reducing % ordering. % % [L,U,p] = cs_lu(A,tol) factorizes A(p,:) into L*U using no fill-reducing % ordering. Entries on the diagonal are given preference in partial pivoting. % % [L,U,p,q] = cs_lu(A) factorizes A(p,q) into L*U using a fill-reducing % ordering q = cs_amd(A,2). Normal partial pivoting is used. % % [L,U,p,q] = cs_lu(A,tol) factorizes A(p,q) into L*U, using a fill-reducing % ordering q = cs_amd(A,1). Entries on the diagonal are given preference in % partial pivoting. With a pivot tolerance tol, the entries in L have % magnitude 1/tol or less. tol = 1 is normal partial pivoting (with % q = cs_amd(A)). tol = 0 ensures p = q. 0= tol * max(abs(A(:,k))). % % Example: % Prob = UFget ('HB/arc130') ; A = Prob.A ; [L,U,p,q] = cs_lu (A) ; % cspy (A (p,q)) ; cspy (L+U) ; % norm (L*U - A(p,q), 1) % % See also CS_AMD, LU, UMFPACK, AMD, COLAMD. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_lu mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_nd.m0000644001170100242450000000164310620371653017062 0ustar davisfacfunction p = cs_nd (A) %CS_ND generalized nested dissection ordering. % p = cs_nd(A) computes the nested dissection ordering of a matrix. Small % submatrices (order 500 or less) are ordered via cs_amd. A must be sparse % and symmetric (use p = cs_nd(A|A') if it is not symmetric). % % Example: % A = delsq (numgrid ('L', 300)) ; % matrix used in 'bench' % p = cs_nd (A) ; % cspy (A (p,p)) ; % % See also CS_AMD, CS_SEP, CS_ESEP, CS_NSEP, AMD. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A,1) ; if (n == 1) p = 1 ; elseif (n < 500) p = cs_amd (A) ; % use cs_amd on small graphs else [s a b] = cs_nsep (A) ; % find a node separator a = a (cs_nd (A (a,a))) ; % order A(a,a) recursively b = b (cs_nd (A (b,b))) ; % order A(b,b) recursively p = [a b s] ; % concatenate to obtain the final ordering end SuiteSparse/CSparse/MATLAB/CSparse/cs_qr.m0000644001170100242450000000266410620371667017114 0ustar davisfacfunction [V,beta,p,R,q] = cs_qr (A) %#ok %CS_QR sparse QR factorization (Householder-based). % [V,beta,p,R] = cs_qr(A) computes the QR factorization of A(p,:). % [V,beta,p,R,q] = cs_qr(A) computes the QR factorization of A(p,q). % The V, beta, and p terms represent the Householder vectors and coefficients. % The fill-reducing ordering q is found via q = cs_amd(A,3). % The orthogonal factor Q can be obtained via % Q = cs_qright(V,beta,p,speye(size(V,1))), in which case Q*R=A(:,q) is the % resulting factorization (the permutation p is folded into Q). A must be % m-by-n with m >= n. If A is structurally rank deficient, additional empty % rows may have been added to V and R. Note that V is typically much sparser % than Q. % % Example: % % Prob = UFget ('HB/well1033') ; A = Prob.A ; [m n] = size (A) ; % b = rand (m,1) ; % [V,beta,p,R,q] = cs_qr (A) ; % QR factorization of A(p,q) % b1 = cs_qleft (V, beta, p, b) ; % x1 = R (1:n,1:n) \ b1 (1:n) ; % x1 (q) = x1 ; % x2 = A\b ; % norm (x1-x2) % Q = cs_qright(V,beta,p,speye(size(V,1))) ; % Note: p accounted for in Q % norm (Q*R-A(:,q),1) % fprintf ('nnz(R) %d, nnz(V) %d, nnz(Q) %d\n', nnz(R), nnz(V), nnz(Q)) ; % % See also CS_AMD, CS_QRIGHT, CS_QR, CS_DMPERM, QR, COLAMD. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_qr mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_qright.m0000644001170100242450000000154710620371665017765 0ustar davisfacfunction X = cs_qright (V, Beta, p, Y) %CS_QRIGHT apply Householder vectors on the right. % X = cs_qright(V,Beta,p,Y) computes X = Y*P'*H1*H2*...*Hn = Y*Q where Q is % represented by the Householder vectors V, coefficients Beta, and % permutation p. p can be [], which denotes the identity permutation. % To obtain Q itself, use Q = cs_qright(V,Beta,p,speye(size(V,1))). % % Example: % load west0479 ; q = colamd (west0479) ; A = west0479 (:,q) ; % [Q,R] = qr (A) ; norm (Q*R-A, 1) % [V,beta,p,R2] = cs_qr (A) ; % Q2 = cs_qright (V, beta, p, speye(size(V,1))) ; norm (Q2*R2-A, 1) % % See also CS_QR, CS_QLEFT. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (V) ; X = Y ; if (~isempty (p)) X = X (:,p) ; end for k = 1:n X = X - (X * (Beta (k) * V (:,k))) * V (:,k)' ; end SuiteSparse/CSparse/MATLAB/CSparse/cs_amd_mex.c0000644001170100242450000000124410416442526020057 0ustar davisfac#include "cs_mex.h" /* cs_amd: approximate minimum degree ordering */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs Amatrix, *A ; int *P, order ; if (nargout > 1 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: p = cs_amd(A,order)") ; } A = cs_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ; /* get A */ order = (nargin > 1) ? mxGetScalar (pargin [1]) : 1 ; /* get ordering */ order = CS_MAX (order, 1) ; order = CS_MIN (order, 3) ; P = cs_amd (order, A) ; /* min. degree ordering */ pargout [0] = cs_mex_put_int (P, A->n, 1, 1) ; /* return P */ } SuiteSparse/CSparse/MATLAB/CSparse/cs_updown.m0000644001170100242450000000221410620371716017770 0ustar davisfacfunction L = cs_updown (L, c, parent, sigma) %#ok %CS_UPDOWN rank-1 update/downdate of a sparse Cholesky factorization. % L = cs_updown(L,c,parent) computes the rank-1 update L = chol(L*L'+c*c')', % where parent is the elimination tree of L. c must be a sparse column % vector, and find(c) must be a subset of find(L(:,k)) where k = min(find(c)). % L = cs_updown(L,c,parent,'-') is the downdate L = chol(L*L'-c*c'). % L = cs_updown(L,c,parent,'+') is the update L = chol(L*L'+c*c'). % Updating/downdating is much faster than refactorizing the matrix with % cs_chol or chol. L must not have an entries dropped due to numerical % cancellation (use cs_chol(A,0)). % % Example: % Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; n = size (A,1) ; % L = cs_chol (A,0) ; % parent = cs_etree (A) ; % c = sprand (L (:, floor(n/2))) ; % L1 = cs_updown (L, c, parent) ; % L2 = cs_chol (A + c*c', 0) ; % norm (L1-L2, 1) % % See also CS_ETREE, CS_CHOL, ETREE, CHOLUPDATE, CHOL. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_updown mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_counts_mex.c0000644001170100242450000000163210415556454020637 0ustar davisfac#include "cs_mex.h" /* cs_counts: column counts for sparse Cholesky factor L. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs Amatrix, *A ; int n, ata, *parent, *post, *c ; char mode [20] ; if (nargout > 2 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: c = cs_counts(A,mode)") ; } ata = 0 ; /* get mode */ if (nargin > 1 && mxIsChar (pargin [1])) { mxGetString (pargin [1], mode, 8) ; ata = (mode [0] == 'c') ; } A = cs_mex_get_sparse (&Amatrix, !ata, 0, pargin [0]) ; /* get A */ n = A->n ; parent = cs_etree (A, ata) ; /* compute etree */ post = cs_post (parent, n) ; /* postorder the etree*/ c = cs_counts (A, parent, post, ata) ; /* get column counts */ pargout [0] = cs_mex_put_int (c, n, 0, 1) ; /* return counts */ cs_free (parent) ; cs_free (post) ; } SuiteSparse/CSparse/MATLAB/CSparse/cs_permute.m0000644001170100242450000000073610620371657020150 0ustar davisfacfunction C = cs_permute (A,p,q) %#ok %CS_PERMUTE permute a sparse matrix. % C = cs_permute(A,p,q) computes C = A(p,q) % % Example: % Prob = UFget ('HB/arc130') ; A = Prob.A ; [m n] = size (A) ; % p = randperm (m) ; q = randperm (n) ; % C = cs_permute (A,p,q) ; % C = A(p,q) % % See also CS_SYMPERM, SUBSREF. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_permute mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_symperm.m0000644001170100242450000000127010620371706020150 0ustar davisfacfunction C = cs_symperm (A,p) %#ok %CS_SYMPERM symmetric permutation of a symmetric matrix. % C = cs_symperm(A,p) computes C = A(p,p), but accesses only the % upper triangular part of A, and returns C upper triangular (A and C are % symmetric with just their upper triangular parts stored). A must be square. % % Example: % Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; % p = cs_amd (A) ; % C = cs_symperm (A, p) ; % cspy (A (p,p)) ; % cspy (C) ; % C - triu (A (p,p)) % % See also CS_PERMUTE, SUBSREF, TRIU. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_symperm mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_lsolve.m0000644001170100242450000000131510620371636017762 0ustar davisfacfunction x = cs_lsolve (L,b) %#ok %CS_LSOLVE solve a sparse lower triangular system L*x=b. % x = cs_lsolve(L,b) computes x = L\b, L must be lower triangular with a % zero-free diagonal. b must be a column vector. x is full if b is full. % If b is sparse, x is sparse but the nonzero pattern of x is NOT sorted (it % is returned in topological order). % % Example: % Prob = UFget ('HB/bcsstk01') ; L = cs_chol (Prob.A) ; n = size (L,1) ; % b = rand (n,1) ; x = cs_lsolve (L,b) ; norm (L*x-b) % % See also CS_LTSOLVE, CS_USOLVE, CS_UTSOLVE, MLDIVIDE. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_lsolve mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_transpose_mex.c0000644001170100242450000000100210415514670021323 0ustar davisfac#include "cs_mex.h" /* C = cs_transpose (A), computes C=A', where A must be sparse and real */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs Amatrix, *A, *C ; if (nargout > 1 || nargin != 1) { mexErrMsgTxt ("Usage: C = cs_transpose(A)") ; } A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ C = cs_transpose (A, 1) ; /* C = A' */ pargout [0] = cs_mex_put_sparse (&C) ; /* return C */ } SuiteSparse/CSparse/MATLAB/CSparse/cs_utsolve.m0000644001170100242450000000125110620371722020152 0ustar davisfacfunction x = cs_utsolve (U,b) %#ok %CS_UTSOLVE solve a sparse lower triangular system U'*x=b. % x = cs_utsolve(U,b) computes x = U'\b, U must be upper triangular with a % zero-free diagonal. b must be a full vector. % % Example: % Prob = UFget ('HB/arc130') ; A = Prob.A ; n = size (A,1) ; % b = rand (n,1); % [L U p q] = cs_lu (A) ; % x = cs_ltsolve (L, cs_utsolve (U, b(q))) ; % x = L' \ (U' \ b(q)) ; % x (p) = x ; % norm (A'*x-b) % % See also CS_LSOLVE, CS_LTSOLVE, CS_USOLVE, MLDIVIDE. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_utsolve mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_permute_mex.c0000644001170100242450000000162610415514543021001 0ustar davisfac#include "cs_mex.h" /* cs_permute: permute a sparse matrix */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs Amatrix, *A, *C, *D ; int ignore, *P, *Q, *Pinv ; if (nargout > 1 || nargin != 3) { mexErrMsgTxt ("Usage: C = cs_permute(A,p,q)") ; } A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ P = cs_mex_get_int (A->m, pargin [1], &ignore, 1) ; /* get P */ Q = cs_mex_get_int (A->n, pargin [2], &ignore, 1) ; /* get Q */ Pinv = cs_pinv (P, A->m) ; /* P = Pinv' */ C = cs_permute (A, Pinv, Q, 1) ; /* C = A(p,q) */ D = cs_transpose (C, 1) ; /* sort C via double transpose */ cs_spfree (C) ; C = cs_transpose (D, 1) ; cs_spfree (D) ; pargout [0] = cs_mex_put_sparse (&C) ; /* return C */ cs_free (Pinv) ; cs_free (P) ; cs_free (Q) ; } SuiteSparse/CSparse/MATLAB/CSparse/Contents.m0000644001170100242450000000525710620371605017573 0ustar davisfac% CSparse: a Concise Sparse matrix Package. % % Matrices used in CSparse must in general be either sparse and real, % or dense vectors. Ordering methods can accept any sparse matrix. % % cs_add - sparse matrix addition. % cs_amd - approximate minimum degree ordering. % cs_chol - sparse Cholesky factorization. % cs_cholsol - solve A*x=b using a sparse Cholesky factorization. % cs_counts - column counts for sparse Cholesky factor L. % cs_dmperm - maximum matching or Dulmage-Mendelsohn permutation. % cs_dmsol - x=A\b using the coarse Dulmage-Mendelsohn decomposition. % cs_dmspy - plot the Dulmage-Mendelsohn decomposition of a matrix. % cs_droptol - remove small entries from a sparse matrix. % cs_esep - find an edge separator of a symmetric matrix A % cs_etree - elimination tree of A or A'*A. % cs_gaxpy - sparse matrix times vector. % cs_lsolve - solve a sparse lower triangular system L*x=b. % cs_ltsolve - solve a sparse upper triangular system L'*x=b. % cs_lu - sparse LU factorization, with fill-reducing ordering. % cs_lusol - solve Ax=b using LU factorization. % cs_make - compiles CSparse for use in MATLAB. % cs_multiply - sparse matrix multiply. % cs_nd - generalized nested dissection ordering. % cs_nsep - find a node separator of a symmetric matrix A. % cs_permute - permute a sparse matrix. % cs_print - print the contents of a sparse matrix. % cs_qr - sparse QR factorization. % cs_qleft - apply Householder vectors on the left. % cs_qright - apply Householder vectors on the right. % cs_qrsol - solve a sparse least-squares problem. % cs_randperm - random permutation. % cs_sep - convert an edge separator into a node separator. % cs_scc - strongly-connected components of a square sparse matrix. % cs_scc2 - cs_scc, or connected components of a bipartite graph. % cs_sparse - convert a triplet form into a sparse matrix. % cs_sqr - symbolic sparse QR factorization. % cs_symperm - symmetric permutation of a symmetric matrix. % cs_transpose - transpose a real sparse matrix. % cs_updown - rank-1 update/downdate of a sparse Cholesky factorization. % cs_usolve - solve a sparse upper triangular system U*x=b. % cs_utsolve - solve a sparse lower triangular system U'*x=b. % cspy - plot a matrix in color. % ccspy - plot the connected components of a matrix. % Example: % help cs_add % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse % helper function: % cs_must_compile - return 1 if source code f must be compiled, 0 otherwise SuiteSparse/CSparse/MATLAB/CSparse/cs_multiply_mex.c0000644001170100242450000000134510415514210021164 0ustar davisfac#include "cs_mex.h" /* cs_multiply: sparse matrix multiply */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs Amatrix, Bmatrix, *A, *B, *C, *D ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: C = cs_multiply(A,B)") ; } A = cs_transpose (cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]), 1) ; B = cs_transpose (cs_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]), 1) ; D = cs_multiply (B,A) ; /* D = B'*A' */ cs_spfree (A) ; cs_spfree (B) ; cs_dropzeros (D) ; /* drop zeros from D */ C = cs_transpose (D, 1) ; /* C = D', so that C is sorted */ cs_spfree (D) ; pargout [0] = cs_mex_put_sparse (&C) ; /* return C */ } SuiteSparse/CSparse/MATLAB/CSparse/cs_gaxpy_mex.c0000644001170100242450000000120010415514433020432 0ustar davisfac#include "cs_mex.h" /* z = cs_gaxpy (A,x,y) computes z = A*x+y */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs Amatrix, *A ; double *x, *y, *z ; if (nargout > 1 || nargin != 3) { mexErrMsgTxt ("Usage: z = cs_gaxpy(A,x,y)") ; } A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ x = cs_mex_get_double (A->n, pargin [1]) ; /* get x */ y = cs_mex_get_double (A->m, pargin [2]) ; /* get y */ z = cs_mex_put_double (A->m, y, &(pargout [0])) ; /* z = y */ cs_gaxpy (A, x, z) ; /* z = z + A*x */ } SuiteSparse/CSparse/MATLAB/CSparse/cs_print.m0000644001170100242450000000064710620371660017616 0ustar davisfacfunction cs_print (A,brief) %#ok %CS_PRINT print the contents of a sparse matrix. % cs_print(A) prints a sparse matrix. cs_print(A,1) prints just a few entries. % % Example: % Prob = UFget ('vanHeukelum/cage3') ; A = Prob.A % cs_print (A) ; % % See also: DISPLAY. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_print mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_scc_mex.c0000644001170100242450000000211510415514623020061 0ustar davisfac#include "cs_mex.h" /* [p,r] = cs_scc (A) finds the strongly connected components of A */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs Amatrix, *A ; csd *D ; int n, j, *Ap2 ; if (nargout > 2 || nargin != 1) { mexErrMsgTxt ("Usage: [p,r] = cs_scc(A)") ; } A = cs_mex_get_sparse (&Amatrix, 1, 0, pargin [0]) ; /* get A */ /* cs_scc modifies A->p and then restores it (in cs_dfs). Avoid the issue * of a mexFunction modifying its input (even temporarily) by making a copy * of A->p. This issue does not arise in cs_dmperm, because that function * applies cs_scc to a submatrix C, not to A directly. */ n = A->n ; Ap2 = cs_malloc (n+1, sizeof (int)) ; for (j = 0 ; j <= n ; j++) Ap2 [j] = A->p [j] ; A->p = Ap2 ; D = cs_scc (A) ; /* find conn. comp. */ pargout [0] = cs_mex_put_int (D->p, n, 1, 0) ; /* return p */ pargout [1] = cs_mex_put_int (D->r, D->nb+1, 1, 0) ; /* return r */ cs_dfree (D) ; cs_free (Ap2) ; /* free the copy of A->p */ } SuiteSparse/CSparse/MATLAB/CSparse/cs_lu_mex.c0000644001170100242450000000325510677526575017762 0ustar davisfac#include "cs_mex.h" /* cs_lu: sparse LU factorization, with optional fill-reducing ordering */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { css *S ; csn *N ; cs Amatrix, *A, *D ; int n, order, *p ; double tol ; if (nargout > 4 || nargin > 3 || nargin < 1) { mexErrMsgTxt ("Usage: [L,U,p,q] = cs_lu (A,tol)") ; } A = cs_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */ n = A->n ; if (nargin == 2) /* determine tol and ordering */ { tol = mxGetScalar (pargin [1]) ; order = (nargout == 4) ? 1 : 0 ; /* amd (A+A'), or natural */ } else { tol = 1 ; order = (nargout == 4) ? 2 : 0 ; /* amd(S'*S) w/dense rows or I */ } S = cs_sqr (order, A, 0) ; /* symbolic ordering, no QR bound */ N = cs_lu (A, S, tol) ; /* numeric factorization */ if (!N) mexErrMsgTxt ("cs_lu failed (singular, or out of memory)") ; cs_dropzeros (N->L) ; /* drop zeros from L and sort it */ D = cs_transpose (N->L, 1) ; cs_spfree (N->L) ; N->L = cs_transpose (D, 1) ; cs_spfree (D) ; cs_dropzeros (N->U) ; /* drop zeros from U and sort it */ D = cs_transpose (N->U, 1) ; cs_spfree (N->U) ; N->U = cs_transpose (D, 1) ; cs_spfree (D) ; p = cs_pinv (N->pinv, n) ; /* p=pinv' */ pargout [0] = cs_mex_put_sparse (&(N->L)) ; /* return L */ pargout [1] = cs_mex_put_sparse (&(N->U)) ; /* return U */ pargout [2] = cs_mex_put_int (p, n, 1, 1) ; /* return p */ /* return Q */ if (nargout == 4) pargout [3] = cs_mex_put_int (S->q, n, 1, 0) ; cs_nfree (N) ; cs_sfree (S) ; } SuiteSparse/CSparse/MATLAB/CSparse/cs_chol_mex.c0000644001170100242450000000203110416442653020237 0ustar davisfac#include "cs_mex.h" /* cs_chol: sparse Cholesky factorization */ void mexFunction (int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ]) { cs Amatrix, *A ; int order, n, drop, *p ; css *S ; csn *N ; if (nargout > 2 || nargin < 1 || nargin > 2) mexErrMsgTxt ("Usage: [L,p] = cs_chol(A,drop)") ; A = cs_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */ n = A->n ; order = (nargout > 1) ? 1 : 0 ; /* determine ordering */ S = cs_schol (order, A) ; /* symbolic Cholesky */ N = cs_chol (A, S) ; /* numeric Cholesky */ if (!N) mexErrMsgTxt ("cs_chol failed: not positive definite\n") ; drop = (nargin == 1) ? 1 : mxGetScalar (pargin [1]) ; if (drop) cs_dropzeros (N->L) ; /* drop zeros if requested*/ pargout [0] = cs_mex_put_sparse (&(N->L)) ; /* return L */ if (nargout > 1) { p = cs_pinv (S->pinv, n) ; /* p=pinv' */ pargout [1] = cs_mex_put_int (p, n, 1, 1) ; /* return p */ } cs_nfree (N) ; cs_sfree (S) ; } SuiteSparse/CSparse/MATLAB/CSparse/cs_counts.m0000644001170100242450000000135710620371614017773 0ustar davisfacfunction c = cs_counts (A,mode) %#ok %CS_COUNTS column counts for sparse Cholesky factor L. % c = cs_counts(A) returns a vector of the column counts of L, for the % Cholesky factorization L*L' = A. That is, c = sum(spones(chol(A)')), % except the Cholesky factorization is not computed. % c = cs_counts(A), returns counts for cs_chol(A). % c = cs_counts(A,'col'), returns counts for cs_chol(A'*A). % c = cs_counts(A,'sym'), same as cs_counts(A). % % Example: % Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; c = cs_counts (A) % full (sum (spones (chol (A)'))) % % See also SYMBFACT. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_counts mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_dmperm_mex.c0000644001170100242450000000232710567410710020602 0ustar davisfac#include "cs_mex.h" /* cs_dmperm: maximum matching or Dulmage-Mendelsohn permutation. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double seed ; cs *A, Amatrix ; csd *D ; int m, n, *jmatch, iseed ; if (nargin < 1 || nargin > 2 || nargout > 6) { mexErrMsgTxt ("Usage: [p,q,r,s,cc,rr] = cs_dmperm (A,seed)") ; } seed = (nargin > 1) ? mxGetScalar (pargin [1]) : 0 ; /* get seed */ iseed = (seed > 0 && seed < 1) ? (seed * RAND_MAX) : seed ; A = cs_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ; /* get A */ n = A->n ; m = A->m ; if (nargout <= 1) { jmatch = cs_maxtrans (A, iseed) ; /* max. matching */ pargout [0] = cs_mex_put_int (jmatch+m, n, 1, 0) ; /* return imatch */ cs_free (jmatch) ; } else { D = cs_dmperm (A, iseed) ; /* Dulmage-Mendelsohn decomposition */ pargout [0] = cs_mex_put_int (D->p, m, 1, 0) ; pargout [1] = cs_mex_put_int (D->q, n, 1, 0) ; pargout [2] = cs_mex_put_int (D->r, D->nb+1, 1, 0) ; pargout [3] = cs_mex_put_int (D->s, D->nb+1, 1, 0) ; pargout [4] = cs_mex_put_int (D->cc, 5, 1, 0) ; pargout [5] = cs_mex_put_int (D->rr, 5, 1, 0) ; cs_dfree (D) ; } } SuiteSparse/CSparse/MATLAB/CSparse/cs_qleft.m0000644001170100242450000000174310620371664017577 0ustar davisfacfunction X = cs_qleft (V, Beta, p, Y) %CS_QLEFT apply Householder vectors on the left. % X = cs_qleft(V,Beta,p,Y) computes X = Hn*...*H2*H1*P*Y = Q'*Y where Q is % represented by the Householder vectors V, coefficients Beta, and % permutation p. p can be [], which denotes the identity permutation. % % Example: % Prob = UFget ('HB/well1033') ; A = Prob.A ; [m n] = size (A) ; % b = rand (m,1) ; % [V,beta,p,R] = cs_qr (A) ; % QR factorization of A(p,:) % b1 = cs_qleft (V, beta, p, b) ; % x1 = R (1:n,1:n) \ b1 (1:n) ; % x2 = A\b ; % norm (x1-x2) % % See also CS_QR, CS_QRIGHT. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m2 n] = size (V) ; [m ny] = size (Y) ; X = Y ; if (m2 > m) if (issparse (Y)) X = [X ; sparse(m2-m,ny)] ; else X = [X ; zeros(m2-m,ny)] ; end end if (~isempty (p)) X = X (p,:) ; end for k = 1:n X = X - V (:,k) * (Beta (k) * (V (:,k)' * X)) ; end SuiteSparse/CSparse/MATLAB/CSparse/cs_qrsol_mex.c0000644001170100242450000000165010416442477020464 0ustar davisfac#include "cs_mex.h" /* cs_qrsol: solve least squares or underdetermined problem */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs *A, Amatrix ; double *x, *b ; int k, order ; if (nargout > 1 || nargin < 2 || nargin > 3) { mexErrMsgTxt ("Usage: x = cs_qrsol(A,b,order)") ; } A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ b = cs_mex_get_double (A->m, pargin [1]) ; /* get b */ x = cs_calloc (CS_MAX (A->m, A->n), sizeof (double)) ; /* x = b */ for (k = 0 ; k < A->m ; k++) x [k] = b [k] ; order = (nargin < 3) ? 3 : mxGetScalar (pargin [2]) ; order = CS_MAX (order, 0) ; order = CS_MIN (order, 3) ; if (!cs_qrsol (order, A, x)) /* x = A\x */ { mexErrMsgTxt ("QR solve failed") ; } cs_mex_put_double (A->n, x, &(pargout [0])) ; /* return x */ cs_free (x) ; } SuiteSparse/CSparse/MATLAB/CSparse/cs_droptol_mex.c0000644001170100242450000000146110415514420020772 0ustar davisfac#include "cs_mex.h" /* cs_droptol: remove small entries from A */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs Amatrix, *C, *A ; int j, k ; double tol ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: C = cs_droptol(A,tol)") ; } A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ tol = mxGetScalar (pargin [1]) ; /* get tol */ C = cs_spalloc (A->m, A->n, A->nzmax, 1, 0) ; /* C = A */ for (j = 0 ; j <= A->n ; j++) C->p [j] = A->p [j] ; for (k = 0 ; k < A->nzmax ; k++) C->i [k] = A->i [k] ; for (k = 0 ; k < A->nzmax ; k++) C->x [k] = A->x [k] ; cs_droptol (C, tol) ; /* drop from C */ pargout [0] = cs_mex_put_sparse (&C) ; /* return C */ } SuiteSparse/CSparse/MATLAB/CSparse/cs_lsolve_mex.c0000644001170100242450000000363210415514461020622 0ustar davisfac#include "cs_mex.h" /* cs_lsolve: x=L\b. L must be sparse, real, and lower triangular. b must be a * real full or sparse vector. x is full or sparse, depending on b. * * Time taken is O(flop count), which may be less than n if b is sparse, * depending on L and b. * * This function works with MATLAB 7.2, but is not perfectly compatible with * the requirements of a MATLAB mexFunction when b is sparse. X is returned * as an unsorted sparse vector. Also, this mexFunction temporarily modifies * its input, L, by modifying L->p (in the cs_dfs function) and then restoring * it. This could be corrected by creating a copy of L->p * (see cs_dmperm_mex.c), but this would take O(n) time, destroying the * O(flop count) time complexity of this function. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs Lmatrix, Bmatrix, *L, *B, *X ; double *x, *b ; int top, nz, p, *xi ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_lsolve(L,b)") ; } L = cs_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; /* get L */ if (mxIsSparse (pargin [1])) { B = cs_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ;/* get sparse b */ cs_mex_check (0, L->n, 1, 0, 1, 1, pargin [1]) ; xi = cs_malloc (2*L->n, sizeof (int)) ; /* get workspace */ x = cs_malloc (L->n, sizeof (double)) ; top = cs_spsolve (L, B, 0, xi, x, NULL, 1) ; /* x = L\b */ X = cs_spalloc (L->n, 1, L->n-top, 1, 0) ; /* create sparse x*/ X->p [0] = 0 ; nz = 0 ; for (p = top ; p < L->n ; p++) { X->i [nz] = xi [p] ; X->x [nz++] = x [xi [p]] ; } X->p [1] = nz ; pargout [0] = cs_mex_put_sparse (&X) ; cs_free (x) ; cs_free (xi) ; } else { b = cs_mex_get_double (L->n, pargin [1]) ; /* get full b */ x = cs_mex_put_double (L->n, b, &(pargout [0])) ; /* x = b */ cs_lsolve (L, x) ; /* x = L\x */ } } SuiteSparse/CSparse/MATLAB/CSparse/cspy.m0000644001170100242450000000477410620665733016767 0ustar davisfacfunction [s,M,H] = cspy (A,res) %CSPY plot a matrix in color. % cspy(A) plots a matrix, in color, with a default resolution of % 256-by-256. cspy(A,res) changes the resolution to res. Zero entries are % white. Entries with tiny absolute value are light orange. Entries with % large magnitude are black. Entries in the midrange (the median of the % log10 of the nonzero values, +/- one standard deviation) range from light % green to deep blue. With no inputs, the color legend of cspy is plotted. % [s,M,H] = cspy(A) returns the scale factor s, the image M, and colormap H. % % The matrix A can be full or sparse, and either numeric (double, single, % integer) or character type, and either complex or real. % % Example % A = delsq (numgrid ('L', 10)) ; % cspy (A) ; % % See also CS_DMSPY, SPY. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if nargin < 2 res = 256 ; end h = jet (64) ; h = h (64:-1:1,:) ; h = h (30:end,:) ; hmax = size (h,1) ; h (1,:) = [1 1 1] ; % white for zero h (2,:) = [1 .9 .5] ; % light orange for tiny entries h (hmax,:) = [0 0 0] ; % black for very large entries colormap (h) ; if (nargin == 0) image (1:hmax) ; title ('cspy color map') ; return end % convert complex, integers, and strings to real double if (~isreal (A) | ~isa (A, 'double') | ~issparse (A)) %#ok A = sparse (abs (double (A))) ; end [m1 n1] = size (A) ; if (m1 == 0 | n1 == 0) %#ok A (1,1) = 0 ; end [m1 n1] = size (A) ; S = cs_thumb (A,res) ; % get the thumbnail of the matrix [m n] = size (S) ; [i j x] = find (S) ; x = log10 (x) ; if (isempty (x)) S = zeros (size (S)) ; else med = median (x) ; sdev = std (x) ; big = med + sdev ; tiny = med - sdev ; imid = find (x > tiny & x < big) ; itiny = find (x <= tiny) ; ibig = find (x >= big) ; x (imid) = 1 + ceil ((hmax-2) * (x (imid) - tiny) / (big - tiny)) ; x (itiny) = 1 ; %#ok x (ibig) = hmax-1 ; %#ok S = full (1 + sparse (i,j,x,m,n)) ; % title (sprintf ('tiny: %-8.2g median: %-8.2g big: %-8.2g\n', ... % 10^tiny, 10^med, 10^big)) ; end % draw the matrix image (S) ; axis equal ; axis ([-1 n+1 -1 m+1]) ; axis off % draw a box around the whole matrix e = ceil (max (m1,n1) / max (m,n)) ; % scale factor hold on drawbox (1,m1+1,1,n1+1,'k',1,e) ; hold off % return results if (nargout > 0) s = e ; end if (nargout > 1) M = S ; % image end if (nargout > 2) H = h ; % colormap end SuiteSparse/CSparse/MATLAB/CSparse/cs_qrsol.m0000644001170100242450000000160310620371671017615 0ustar davisfacfunction x = cs_qrsol (A,b,order) %#ok %CS_QRSOL solve a sparse least-squares problem. % x = cs_qrsol(A,b) solves the over-determined least squares problem to % find x that minimizes norm(A*x-b), where b is a full vector and % A is m-by-n with m >= n. If m < n, it solves the underdetermined system % Ax=b. A 3rd input argument specifies the ordering method to use % (0: natural, 3: amd(A'*A)). The default ordering is 3. % % Example: % Prob = UFget ('HB/well1033') ; A = Prob.A ; [m n] = size (A) ; % b = rand (m,1) ; % x1 = cs_qrsol (A,b) ; % x2 = A\b ; % norm (x1-x2) % % For this example, cs_qrsol is about 3 times faster than A\b in MATLAB 7.3. % % See also CS_QR, CS_AMD, CS_LUSOL, CS_CHOLSOL, MLDIVIDE. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_qrsol mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_chol.m0000644001170100242450000000141010620371611017370 0ustar davisfacfunction [L,p] = cs_chol (A,drop) %#ok %CS_CHOL sparse Cholesky factorization. % L = cs_chol(A) is the same as L = chol(A)', using triu(A). % [L,p] = cs_chol(A) first orders A with p=cs_amd(A), so that L*L' = A(p,p). % A second optional input argument controls whether or not numerically zero % entries are removed from L. cs_chol(A) and cs_chol(A,1) drop them; % cs_chol(A,0) keeps them. They must be kept for cs_updown to work properly. % % Example: % Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; [L,p] = cs_chol (A) ; % cspy (A (p,p)) ; % cspy (L) ; % % See also CS_AMD, CS_UPDOWN, CHOL, AMD, SYMAMD. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_chol mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_print_mex.c0000644001170100242450000000101710415514560020445 0ustar davisfac#include "cs_mex.h" /* cs_print: print the contents of a sparse matrix. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs Amatrix, *A ; int brief ; if (nargout > 0 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: cs_print(A,brief)") ; } A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ brief = (nargin < 2) ? 0 : mxGetScalar (pargin [1]) ; /* get brief */ cs_print (A, brief) ; /* print A */ } SuiteSparse/CSparse/MATLAB/CSparse/cs_dmsol.m0000644001170100242450000000220610620665615017577 0ustar davisfacfunction x = cs_dmsol (A,b) %CS_DMSOL x=A\b using the coarse Dulmage-Mendelsohn decomposition. % x = cs_dmsol(A,b) computes x=A\b where A may be rectangular and/or % structurally rank deficient, and b is a full vector. % % Example: % Prob = UFget ('HB/arc130') ; A = Prob.A ; b = rand (size (A,1),1) ; % x = cs_dmsol (A,b) ; norm (A*x-b) % % See also CS_QRSOL, CS_LUSOL, CS_DMPERM, SPRANK, RANK. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; [p q r s cc rr] = cs_dmperm (A) ; C = A (p,q) ; b = b (p) ; x = zeros (n,1) ; if (rr(3) <= m & cc(4) <= n) %#ok x (cc(4):n) = cs_qrsol (C (rr(3):m, cc(4):n), b (rr(3):m)) ; b (1:rr(3)-1) = b (1:rr(3)-1) - C (1:rr(3)-1, cc(4):n) * x (cc(4):n) ; end if (rr(2) < rr (3) & cc(3) < cc(4)) %#ok x (cc(3):cc(4)-1) = ... cs_lusol (C (rr(2):rr(3)-1, cc(3):cc(4)-1), b (rr(2):rr(3)-1)) ; b (1:rr(2)-1) = ... b (1:rr(2)-1) - C (1:rr(2)-1, cc(3):cc(4)-1) * x (cc(3):cc(4)-1) ; end if (rr(2) > 1 & cc(3) > 1) %#ok x (1:cc(3)-1) = cs_qrsol (C (1:rr(2)-1, 1:cc(3)-1), b (1:rr(2)-1)) ; end x (q) = x ; SuiteSparse/CSparse/MATLAB/CSparse/cs_dmspy.m0000644001170100242450000000345410620371626017617 0ustar davisfacfunction [p,q,r,s,cc,rr] = cs_dmspy (A,res,seed) %CS_DMSPY plot the Dulmage-Mendelsohn decomposition of a matrix. % [p,q,r,s,cc,rr] = cs_dmspy(A) computes [p,q,r,s,cc,rr] = cs_dmperm(A), % does spy(A(p,q)), and then draws boxes around the coarse and fine % decompositions. A 2nd input argument (cs_dmspy(A,res)) changes the % resolution of the image to res-by-res (default resolution is 256). % If res is zero, spy is used instead of cspy. If the resolution is low, the % picture of the blocks in the figure can overlap. They do not actually % overlap in the matrix. With 3 arguments, cs_dmspy(A,res,seed), % cs_dmperm(A,seed) is used, where seed controls the randomized algorithm % used by cs_dmperm. % % Example: % Prob = UFget ('HB/arc130') ; cs_dmspy (Prob.A) ; % % See also CS_DMPERM, CS_DMSOL, DMPERM, SPRANK, SPY. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (~issparse (A)) A = sparse (A) ; end if (nargin < 2) res = 256 ; end if (nargin < 3) seed = 0 ; end % Dulmage-Mendelsohn permutation [p1,q,r,s,cc,rr] = cs_dmperm (A,seed) ; if (nargout > 0) p = p1 ; end nb = length (r)-1 ; % plot the result S = A (p1,q) ; if (res == 0) spy (S) ; e = 1 ; else e = cspy (S,res) ; end hold on title (sprintf ( ... '%d-by-%d, sprank: %d, fine blocks: %d, coarse blocks: %d-by-%d\n', ... size (A), rr(4)-1, nb, length (find (diff (rr))), ... length (find (diff (cc))))) ; drawboxes (nb, e, r, s) ; [m n] = size (A) ; drawbox (1,m+1,1,n+1,'k',1,e) ; drawbox (rr(1), rr(2), cc(1), cc (2), 'r', 2, e) ; drawbox (rr(1), rr(2), cc(2), cc (3), 'r', 2, e) ; drawbox (rr(2), rr(3), cc(3), cc (4), 'k', 2, e) ; drawbox (rr(3), rr(4), cc(4), cc (5), 'r', 2, e) ; drawbox (rr(4), rr(5), cc(4), cc (5), 'r', 2, e) ; hold off SuiteSparse/CSparse/MATLAB/CSparse/cs_esep.m0000644001170100242450000000113110620371631017401 0ustar davisfacfunction [a,b] = cs_esep (A) %CS_ESEP find an edge separator of a symmetric matrix A % [a,b] = cs_esep(A) finds a edge separator s that splits the graph of A % into two parts a and b of roughly equal size. The edge separator is the % set of entries in A(a,b). % % Example: % Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; % [a,b] = cs_esep (A) ; % cspy (A (a,b)) ; % % See also CS_NSEP, CS_SEP, CS_ND, SYMRCM. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse p = symrcm (A) ; n2 = fix (size(A,1)/2) ; a = p (1:n2) ; b = p (n2+1:end) ; SuiteSparse/CSparse/MATLAB/CSparse/cs_thumb_mex.c0000644001170100242450000000275710507506511020443 0ustar davisfac#include "cs_mex.h" /* cs_thumb: convert a sparse matrix to a dense 2D thumbnail matrix of size * at most k-by-k. k defaults to 256. A helper mexFunction for cspy. */ #define INDEX(i,j,lda) ((i)+(j)*(lda)) #define ISNAN(x) ((x) != (x)) #ifdef DBL_MAX #define BIG_VALUE DBL_MAX #else #define BIG_VALUE 1.7e308 #endif void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs Amatrix, *A ; int m, n, mn, m2, n2, k, s, j, ij, sj, si, p, *Ap, *Ai ; double aij, *S, *Ax ; if (nargout > 1 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: S = cs_thumb(A,k)") ; } A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ m = A->m ; n = A->n ; mn = CS_MAX (m,n) ; k = (nargin == 1) ? 256 : mxGetScalar (pargin [1]) ; /* get k */ /* s = size of each submatrix; A(1:s,1:s) maps to S(1,1) */ s = (mn < k) ? 1 : (int) ceil ((double) mn / (double) k) ; m2 = (int) ceil ((double) m / (double) s) ; n2 = (int) ceil ((double) n / (double) s) ; /* create S */ pargout [0] = mxCreateDoubleMatrix (m2, n2, mxREAL) ; S = mxGetPr (pargout [0]) ; Ap = A->p ; Ai = A->i ; Ax = A->x ; for (j = 0 ; j < n ; j++) { sj = j/s ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { si = Ai [p] / s ; ij = INDEX (si,sj,m2) ; aij = fabs (Ax [p]) ; if (ISNAN (aij)) aij = BIG_VALUE ; aij = CS_MIN (BIG_VALUE, aij) ; S [ij] = CS_MAX (S [ij], aij) ; } } } SuiteSparse/CSparse/MATLAB/CSparse/cs_updown_mex.c0000644001170100242450000000324210474320360020625 0ustar davisfac#include "cs_mex.h" /* cs_updown: sparse Cholesky update/downdate (rank-1 or multiple rank) */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs Lmatrix, *Lin, Cmatrix, *C, *L, Cvector, *Cvec ; int ignore, j, k, n, lnz, *parent, sigma = 1, cp [2] ; char sigma_string [20] ; if (nargout > 1 || nargin < 3 || nargin > 4) { mexErrMsgTxt ("Usage: L = cs_updown(L,C,parent,sigma)") ; } Lin = cs_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; /* get input L */ n = Lin->n ; if (nargin > 3 && mxIsChar (pargin [3])) { mxGetString (pargin [3], sigma_string, 8) ; sigma = (sigma_string [0] == '-') ? (-1) : 1 ; } /* make a copy of L (this can take more work than updating L itself) */ lnz = Lin->p [n] ; L = cs_spalloc (n, n, lnz, 1, 0) ; for (j = 0 ; j <= n ; j++) L->p [j] = Lin->p [j] ; for (k = 0 ; k < lnz ; k++) L->i [k] = Lin->i [k] ; for (k = 0 ; k < lnz ; k++) L->x [k] = Lin->x [k] ; cs_mex_check (0, n, -1, 0, 1, 1, pargin [1]) ; /* get C */ C = cs_mex_get_sparse (&Cmatrix, 0, 1, pargin [1]) ; parent = cs_mex_get_int (n, pargin [2], &ignore, 0) ; /* get parent */ /* do the update one column at a time */ Cvec = &Cvector ; Cvec->m = n ; Cvec->n = 1 ; Cvec->p = cp ; Cvec->nz = -1 ; cp [0] = 0 ; for (k = 0 ; k < C->n ; k++) { /* extract C(:,k) */ cp [1] = C->p [k+1] - C->p [k] ; Cvec->nzmax = cp [1] ; Cvec->i = C->i + C->p [k] ; Cvec->x = C->x + C->p [k] ; cs_updown (L, sigma, Cvec, parent) ; /* update/downdate */ } pargout [0] = cs_mex_put_sparse (&L) ; /* return new L */ } SuiteSparse/CSparse/MATLAB/CSparse/cs_make.m0000644001170100242450000001376410621052132017372 0ustar davisfacfunction [objfiles, timestamp_out] = cs_make (f) %CS_MAKE compiles CSparse for use in MATLAB. % Usage: % cs_make % [objfiles, timestamp] = cs_make (f) % % With no input arguments, or with f=0, only those files needing to be % compiled are compiled (like the Unix/Linux/GNU "make" command, but not % requiring "make"). If f is a nonzero number, all files are compiled. % If f is a string, only that mexFunction is compiled. For example, % cs_make ('cs_add') just compiles the cs_add mexFunction. This option is % useful when developing a single new mexFunction. This function can only be % used if the current directory is CSparse/MATLAB/CSparse. Returns a list of % the object files in CSparse, and the latest modification time of any source % codes. % % To add a new function and its MATLAB mexFunction to CSparse: % % (1) Create a source code file CSparse/Source/cs_mynewfunc.c. % (2) Create a help file, CSparse/MATLAB/CSparse/cs_mynewfunc.m. % This is very useful, but not strictly required. % (3) Add the prototype of cs_mynewfunc to CSparse/Include/cs.h. % (4) Create its MATLAB mexFunction, CSparse/MATLAB/cs_mynewfunc_mex.c. % (5) Edit cs_make.m, and add 'cs_mynewfunc' to the 'cs' and 'csm' lists. % (6) Type 'cs_make' in the CSparse/MATLAB/CSparse directory. % If all goes well, your new function is ready for use in MATLAB. % % (7) Optionally add 'cs_mynewfunc' to CSparse/Source/Makefile % and CSparse/MATLAB/CSparse/Makefile, if you want to use the % Unix/Linux/GNU make command instead of cs_make.m. See where % 'cs_add' and 'cs_add_mex' appear in those files, and add % 'cs_mynewfunc' accordingly. % (8) Optionally add 'cs_mynewfunc' to Tcov/Makefile, and add additional % test code to cs_test.c, and add MATLAB test code to MATLAB/Test/*. % % Example: % cs_make % compile everything % cs_make ('cs_chol') ; % just compile cs_chol mexFunction % % See also MEX. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse fprintf ('Compiling CSparse\n') ; % CSparse source files, in ../../Source, such as ../../Source/cs_add.c. % Note that not all CSparse source files have their own mexFunction. cs = { 'cs_add', 'cs_amd', 'cs_chol', 'cs_cholsol', 'cs_counts', ... 'cs_cumsum', 'cs_dfs', 'cs_dmperm', 'cs_droptol', 'cs_dropzeros', ... 'cs_dupl', 'cs_entry', 'cs_etree', 'cs_fkeep', 'cs_gaxpy', 'cs_happly', ... 'cs_house', 'cs_ipvec', 'cs_load', 'cs_lsolve', 'cs_ltsolve', 'cs_lu', ... 'cs_lusol', 'cs_malloc', 'cs_maxtrans', 'cs_multiply', 'cs_norm', ... 'cs_permute', 'cs_pinv', 'cs_post', 'cs_print', 'cs_pvec', 'cs_qr', ... 'cs_qrsol', 'cs_scatter', 'cs_scc', 'cs_schol', 'cs_sqr', 'cs_symperm', ... 'cs_tdfs', 'cs_transpose', 'cs_compress', 'cs_updown', 'cs_usolve', ... 'cs_utsolve', 'cs_util', 'cs_reach', 'cs_spsolve', 'cs_ereach', ... 'cs_leaf', 'cs_randperm' } ; % add cs_mynewfunc to the above list details = 1 ; kk = 0 ; csm = { } ; if (nargin == 0) force = 0 ; elseif (ischar (f)) fprintf ('cs_make: compiling ../../Source files and %s_mex.c\n', f) ; force = 0 ; csm = {f} ; else force = f ; details = details | (force > 1) ; %#ok if (force & details) %#ok fprintf ('cs_make: re-compiling everything\n') ; end end if (force) fprintf ('Compiling CSparse\n') ; end if (isempty (csm)) % mexFunctions, of the form cs_add_mex.c, etc, in this directory csm = { 'cs_add', 'cs_amd', 'cs_chol', 'cs_cholsol', 'cs_counts', ... 'cs_dmperm', 'cs_droptol', 'cs_etree', 'cs_gaxpy', 'cs_lsolve', ... 'cs_ltsolve', 'cs_lu', 'cs_lusol', 'cs_multiply', 'cs_permute', ... 'cs_print', 'cs_qr', 'cs_qrsol', 'cs_scc', 'cs_symperm', 'cs_thumb', ... 'cs_transpose', 'cs_sparse', 'cs_updown', 'cs_usolve', ... 'cs_utsolve', 'cs_randperm', 'cs_sqr' } ; % add cs_mynewfunc to the above list end try % ispc does not appear in MATLAB 5.3 pc = ispc ; catch % if ispc fails, assume we are on a Windows PC if it's not unix pc = ~isunix ; end if (pc) obj = '.obj' ; else obj = '.o' ; end srcdir = '../../Source/' ; hfile = '../../Include/cs.h' ; % compile each CSparse source file [anysrc timestamp kk] = compile_source ('', 'cs_mex', obj, hfile, force, ... kk, details) ; CS = ['cs_mex' obj] ; if (nargout > 0) objfiles = ['..' filesep 'CSparse' filesep 'cs_mex' obj] ; end for i = 1:length (cs) [s t kk] = compile_source (srcdir, cs {i}, obj, hfile, force, kk, details) ; timestamp = max (timestamp, t) ; anysrc = anysrc | s ; %#ok CS = [CS ' ' cs{i} obj] ; %#ok if (nargout > 0) objfiles = [objfiles ' ..' filesep 'CSparse' filesep cs{i} obj] ; %#ok end end % compile each CSparse mexFunction obj = ['.' mexext] ; for i = 1:length (csm) [s t] = cs_must_compile ('', csm{i}, '_mex', obj, hfile, force) ; timestamp = max (timestamp, t) ; if (anysrc | s) %#ok cmd = sprintf ('mex -O -I../../Include %s_mex.c %s -output %s', ... csm{i}, CS, csm{i}) ; kk = do_cmd (cmd, kk, details) ; end end fprintf ('\n') ; if (nargout > 1) timestamp_out = timestamp ; end if (force) fprintf ('CSparse successfully compiled.\n') ; end %------------------------------------------------------------------------------- function [s,t,kk] = compile_source (srcdir, f, obj, hfile, force, kk, details) % compile a source code file in ../../Source, leaving object file in % this directory. [s t] = cs_must_compile (srcdir, f, '', obj, hfile, force) ; if (s) cmd = sprintf ('mex -O -c -I../../Include %s%s.c', srcdir, f) ; kk = do_cmd (cmd, kk, details) ; end %------------------------------------------------------------------------------- function kk = do_cmd (s, kk, details) %DO_CMD: evaluate a command, and either print it or print a "." if (details) fprintf ('%s\n', s) ; else if (mod (kk, 60) == 0) fprintf ('\n') ; end kk = kk + 1 ; fprintf ('.') ; end eval (s) ; SuiteSparse/CSparse/MATLAB/CSparse/cs_dmperm.m0000644001170100242450000000621410620371623017741 0ustar davisfacfunction [p,q,r,s,cc,rr] = cs_dmperm (A,seed) %#ok %CS_DMPERM maximum matching or Dulmage-Mendelsohn permutation. % p = cs_dmperm(A) finds a maximum matching p such that p(j) = i if column j % is matched to row i, or 0 if column j is unmatched. If A is square and % full structural rank, p is a row permutation and A(p,:) has a zero-free % diagonal. The structural rank of A is sprank(A) = sum(p>0). % % [p,q,r,s,cc,rr] = cs_dmperm(A) finds the Dulmage-Mendelsohn decomposition % of A. p and q are permutation vectors. cc and rr are vectors of length 5. % C = A(p,q) is split into a 4-by-4 set of coarse blocks: % % A11 A12 A13 A14 % 0 0 A23 A24 % 0 0 0 A34 % 0 0 0 A44 % % where A12, A23, and A34 are square with zero-free diagonals. The columns of % A11 are the unmatched columns, and the rows of A44 are the unmatched rows. % Any of these blocks can be empty. In the "coarse" decomposition, the % (i,j)th block is C(rr(i):rr(i+1)-1,cc(j):cc(j+1)-1). In terms of a linear % system, [A11 A12] is the underdetermined part of the system (it is always % rectangular and with more columns and rows, or 0-by-0), A23 is the well- % determined part of the system (it is always square), and [A34 ; A44] is % the over-determined part of the system (it is always rectangular with more % rows than columns, or 0-by-0). % % The structural rank of A is sprank(A) = rr(4)-1, which is an upper bound on % the numerical rank of A. sprank(A) = rank(full(sprand(A))) with probability % 1 in exact arithmetic. % % The A23 submatrix is further subdivided into block upper triangular form % via the "fine" decomposition (the strongly-connected components of A23). % If A is square and structurally non-singular, A23 is the entire matrix. % % C(r(i):r(i+1)-1,s(j):s(j+1)-1) is the (i,j)th block of the fine % decomposition. The (1,1) block is the rectangular block [A11 A12], unless % this block is 0-by-0. The (b,b) block is the rectangular block [A34 ; A44], % unless this block is 0-by-0, where b = length(r)-1. All other blocks of the % form C(r(i):r(i+1)-1,s(i):s(i+1)-1) are diagonal blocks of A23, and are % square with a zero-free diagonal. % % The matching algorithm used in cs_dmperm can take a very long time % in rare cases. This can be avoided by exploiting a randomized algorithm, % with cs_dmperm(A,seed). If seed=0, the non-randomized algorithm is used % (columns are considered in order 1:n). If seed=-1, columns are considered % in reverse order. Otherwise, the columns are considered in a random order, % using seed as the random number generator seed. Try cs_dmpmerm(A,1) or % cs_dmperm(A,rand), for a randomized order, for example. Seed defaults to 0. % % % Example: % Prob = UFget ('HB/west0479') ; A = Prob.A ; cspy (A) ; % p = cs_dmperm (A) ; % cspy (A (p,:)) ; % [p q r s cc rr] = cs_dmperm (A) ; % cspy (A (p,q)) ; % cs_dmspy (A) ; % % See also CS_DMSPY, CS_DMSOL, DMPERM, SPRANK, CS_RANDPERM, RAND % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_dmperm mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/README.txt0000644001170100242450000000007310364236357017316 0ustar davisfacMATLAB interface for CSparse. See Contents.m for details. SuiteSparse/CSparse/MATLAB/CSparse/cs_lusol_mex.c0000644001170100242450000000207410416442472020456 0ustar davisfac#include "cs_mex.h" /* cs_lusol: solve A*x=b using a sparse LU factorization */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs *A, Amatrix ; int order ; double *x, *b, tol ; if (nargout > 1 || nargin < 2 || nargin > 4) { mexErrMsgTxt ("Usage: x = cs_lusol(A,b,order,tol)") ; } A = cs_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */ b = cs_mex_get_double (A->n, pargin [1]) ; /* get b */ x = cs_mex_put_double (A->n, b, &(pargout [0])) ; /* x = b */ order = (nargin < 3) ? 2 : mxGetScalar (pargin [2]) ; order = CS_MAX (order, 0) ; order = CS_MIN (order, 3) ; if (nargin == 2) { tol = 1 ; /* normal partial pivoting */ } else if (nargin == 3) { tol = (order == 1) ? 0.001 : 1 ; /* tol = 0.001 for amd(A+A') */ } else { tol = mxGetScalar (pargin [3]) ; } if (!cs_lusol (order, A, x, tol)) /* x = A\x */ { mexErrMsgTxt ("LU factorization failed (singular or out of memory)") ; } } SuiteSparse/CSparse/MATLAB/CSparse/cs_randperm.m0000644001170100242450000000132010620371673020263 0ustar davisfacfunction p = cs_randperm (n, seed) %#ok %CS_RANDPERM random permutation. % p = cs_randperm (n) returns a repeatable random permutation of 1:n. % p = cs_randperm (n,seed) returns the random permutation using the given % seed for the random number generator (try cs_randperm (n,rand)), where % seed is not 0 or -1. Two special cases are not random permutations at all: % p=cs_randperm (n,0) is 1:n, and p=cs_randperm (n,-1) is n:-1:1. % This function does not change RAND's state. % % Example: % p = cs_randperm (10) % % See also CS_DMPERM, RAND, RANDPERM % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_randperm mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_nsep.m0000644001170100242450000000123110620371655017421 0ustar davisfacfunction [s,a,b] = cs_nsep (A) %CS_NSEP find a node separator of a symmetric matrix A. % [s,a,b] = cs_nsep(A) finds a node separator s that splits the graph of A % into two parts a and b of roughly equal size. If A is unsymmetric, use % cs_nsep(A|A'). The permutation p = [a b s] is a one-level dissection of A. % % Example: % A = delsq (numgrid ('L', 10)) ; % smaller version as used in 'bench' % [s a b] = cs_nsep (A) ; p = [a b s] ; % cspy (A (p,p)) ; % % See also CS_SEP, CS_ESEP, CS_ND. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [a b] = cs_esep (A) ; [s a b] = cs_sep (A, a, b) ; SuiteSparse/CSparse/MATLAB/CSparse/cs_etree_mex.c0000644001170100242450000000160610415514153020417 0ustar davisfac#include "cs_mex.h" /* cs_etree: elimination tree of A or A'*A */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs Amatrix, *A ; int n, ata, *parent, *post ; char mode [20] ; if (nargout > 2 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: [parent,post] = cs_etree(A,mode)") ; } ata = 0 ; /* get mode */ if (nargin > 1 && mxIsChar (pargin [1])) { mxGetString (pargin [1], mode, 8) ; ata = (mode [0] == 'c') ; } A = cs_mex_get_sparse (&Amatrix, !ata, 0, pargin [0]) ; /* get A */ n = A->n ; parent = cs_etree (A, ata) ; /* compute etree */ if (nargout > 1) { post = cs_post (parent, n) ; /* postorder the etree*/ pargout [1] = cs_mex_put_int (post, n, 1, 1) ; /* return post */ } pargout [0] = cs_mex_put_int (parent, n, 1, 1) ; /* return parent */ } SuiteSparse/CSparse/MATLAB/CSparse/cs_scc2.m0000644001170100242450000000354710620666137017324 0ustar davisfacfunction [p, q, r, s] = cs_scc2 (A, bipartite) %CS_SCC2 cs_scc, or connected components of a bipartite graph. % [p,q,r,s] = cs_scc2(A) finds a permutation p so that A(p,q) is permuted into % block upper triangular form (if A is square). In this case, r=s, p=q and % the kth diagonal block is given by A (t,t) where t = r(k):r(k)+1. % The diagonal of A is ignored. Each block is one strongly connected % component of A. % % If A is not square (or for [p,q,r,s] = cs_scc2(A,1)), then the connected % components of the bipartite graph of A are found. A(p,q) is permuted into % block diagonal form, where the diagonal blocks are rectangular. The kth % block is given by A(r(k):r(k+1)-1,s(k):s(k+1)-1). A can be rectangular. % % Example: % Prob = UFget ('HB/arc130') ; A = Prob.A ; [p q r s] = cs_scc2 (A) ; % cspy (A (p,q)) ; % Prob = UFget ('HB/wm1') ; A = Prob.A ; [p q r s] = cs_scc2 (A) ; % cspy (A (p,q)) ; % % See also CS_DMPERM, DMPERM, CS_SCC, CCSPY. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; if (nargin < 2) bipartite = 0 ; end if (m ~= n | bipartite) %#ok % find the connected components of [I A ; A' 0] S = spaugment (A) ; [psym,rsym] = cs_scc (S) ; p = psym (find (psym <= m)) ; %#ok q = psym (find (psym > m)) - m ; %#ok nb = length (rsym) - 1 ; r = zeros (1,nb+1) ; s = zeros (1,nb+1) ; krow = 1 ; kcol = 1 ; for k = 1:nb % find the rows and columns in the kth component r (k) = krow ; s (k) = kcol ; ksym = psym (rsym (k):rsym (k+1)-1) ; krow = krow + length (find (ksym <= m)) ; kcol = kcol + length (find (ksym > m)) ; end r (nb+1) = m+1 ; s (nb+1) = n+1 ; else % find the strongly connected components of A [p,r] = cs_scc (A) ; q = p ; s = r ; end SuiteSparse/CSparse/MATLAB/CSparse/cs_sparse_mex.c0000644001170100242450000000173010571322634020612 0ustar davisfac#include "cs_mex.h" /* cs_sparse: convert triplet form into compress-column form sparse matrix */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs *A, *C, *T, Tmatrix ; if (nargout > 1 || nargin != 3) { mexErrMsgTxt ("Usage: A = cs_sparse(i,j,x)") ; } T = &Tmatrix ; /* get i,j,x and copy to triplet form */ T->nz = mxGetM (pargin [0]) ; T->p = cs_mex_get_int (T->nz, pargin [0], &(T->n), 1) ; T->i = cs_mex_get_int (T->nz, pargin [1], &(T->m), 1) ; cs_mex_check (1, T->nz, 1, 0, 0, 1, pargin [2]) ; T->x = mxGetPr (pargin [2]) ; T->nzmax = T->nz ; C = cs_compress (T) ; /* create sparse matrix C */ cs_dupl (C) ; /* remove duplicates from C */ cs_dropzeros (C) ; /* remove zeros from C */ A = cs_transpose (C, 1) ; /* A=C' */ cs_spfree (C) ; pargout [0] = cs_mex_put_sparse (&A) ; /* return A */ cs_free (T->p) ; cs_free (T->i) ; } SuiteSparse/CSparse/MATLAB/CSparse/cs_usolve.m0000644001170100242450000000145410620371721017772 0ustar davisfacfunction x = cs_usolve (U,b) %#ok %CS_USOLVE solve a sparse upper triangular system U*x=b. % x = cs_usolve(U,b) computes x = U\b, U must be lower triangular with a % zero-free diagonal. b must be a column vector. x is full if b is full. % If b is sparse, x is sparse but nonzero pattern of x is NOT sorted (it is % returned in topological order). % % Example: % Prob = UFget ('HB/arc130') ; A = Prob.A ; n = size (A,1) ; % b = rand (n,1); % [L U p q] = cs_lu (A) ; % x = cs_usolve (U, cs_lsolve (L, b(p))) ; % x = U \ (L \ b(p)) ; % x (q) = x ; % norm (A*x-b) % % See also CS_LSOLVE, CS_LTSOLVE, CS_UTSOLVE, MLDIVIDE. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_usolve mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_droptol.m0000644001170100242450000000104210620371627020136 0ustar davisfacfunction C = cs_droptol (A, tol) %#ok %CS_DROPTOL remove small entries from a sparse matrix. % C = cs_droptol(A,tol) removes entries from A of magnitude less than or % equal to tol. Same as A = A .* (abs (A) >= tol). % % Example: % Prob = UFget ('HB/arc130') ; A = Prob.A ; % cspy (abs (A) >= 1e-10) ; % C = cs_droptol (A, 1e-10) ; % cspy (C) ; % % See also: RELOP, ABS % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_droptol mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_etree.m0000644001170100242450000000130610620371633017557 0ustar davisfacfunction [parent, post] = cs_etree (A, mode) %#ok %CS_ETREE elimination tree of A or A'*A. % parent = cs_etree (A) returns the elimination tree of A. % parent = cs_etree (A,'col') returns the elimination tree of A'*A. % parent = cs_etree (A,'sym') is the same as cs_etree(A). % For the symmetric case (cs_etree(A)), only triu(A) is used. % % [parent,post] = cs_etree(...) also returns a postorder of the tree. % % Example: % Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; % parent = cs_etree (A) ; treeplot (parent) ; % % See also ETREE, TREEPLOT. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_etree mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_add_mex.c0000644001170100242450000000166610415514133020047 0ustar davisfac#include "cs_mex.h" /* cs_add: sparse matrix addition */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double alpha, beta ; cs Amatrix, Bmatrix, *A, *B, *C, *D ; if (nargout > 1 || nargin < 2 || nargin > 4) { mexErrMsgTxt ("Usage: C = cs_add(A,B,alpha,beta)") ; } A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ B = cs_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ; /* get B */ alpha = (nargin < 3) ? 1 : mxGetScalar (pargin [2]) ; /* get alpha */ beta = (nargin < 4) ? 1 : mxGetScalar (pargin [3]) ; /* get beta */ C = cs_add (A,B,alpha,beta) ; /* C = alpha*A + beta *B */ cs_dropzeros (C) ; /* drop zeros */ D = cs_transpose (C, 1) ; /* sort result via double transpose */ cs_spfree (C) ; C = cs_transpose (D, 1) ; cs_spfree (D) ; pargout [0] = cs_mex_put_sparse (&C) ; /* return C */ } SuiteSparse/CSparse/MATLAB/CSparse/cs_ltsolve_mex.c0000644001170100242450000000110510415514466021004 0ustar davisfac#include "cs_mex.h" /* cs_ltsolve: solve an upper triangular system L'*x=b */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs Lmatrix, *L ; double *x, *b ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_ltsolve(L,b)") ; } L = cs_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; /* get L */ b = cs_mex_get_double (L->n, pargin [1]) ; /* get b */ x = cs_mex_put_double (L->n, b, &(pargout [0])) ; /* x = b */ cs_ltsolve (L, x) ; /* x = L'\x */ } SuiteSparse/CSparse/MATLAB/CSparse/cs_must_compile.m0000644001170100242450000000121010620705276021151 0ustar davisfacfunction [s, t, tobj] = cs_must_compile (srcdir, f, suffix, obj, hfile, force) %CS_MUST_COMPILE return 1 if source code f must be compiled, 0 otherwise % Used by cs_make, and MATLAB/Test/cs_test_make.m. % % Example: % none, not meant for end users. % See also: CS_MAKE. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse dobj = dir ([f obj]) ; if (force | isempty (dobj)) %#ok s = 1 ; t = Inf ; tobj = -1 ; return end dsrc = dir ([srcdir f suffix '.c']) ; dh = dir (hfile) ; t = max (datenum (dsrc.date), datenum (dh.date)) ; tobj = datenum (dobj.date) ; s = (tobj < t) ; SuiteSparse/CSparse/MATLAB/CSparse/cs_lusol.m0000644001170100242450000000165210620371644017617 0ustar davisfacfunction x = cs_lusol (A,b,order,tol) %#ok %CS_LUSOL solve Ax=b using LU factorization. % x = cs_lusol(A,b) computes x = A\b, where A is sparse and square, and b is a % full vector. The ordering cs_amd(A,2) is used. % % x = cs_lusol(A,b,1) also computes x = A\b, but uses the cs_amd(A) ordering % with diagonal preference (tol=0.001). % % x = cs_lusol(A,b,order,tol) allows both the ordering and tolerance to be % defined. The ordering defaults to 1, and tol defaults to 1. % ordering: 0: natural, 1: amd(A+A'), 2: amd(S'*S) where S=A except with no % dense rows, 3: amd(A'*A). % % Example: % Prob = UFget ('HB/arc130') ; A = Prob.A ; n = size(A,1) ; % b = rand (n,1) ; x = cs_lusol (A,b) ; norm (A*x-b) % % See also CS_LU, CS_AMD, CS_CHOLSOL, CS_QRSOL, MLDIVIDE. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_lusol mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_gaxpy.m0000644001170100242450000000074410620371634017611 0ustar davisfacfunction z = cs_gaxpy (A,x,y) %#ok %CS_GAXPY sparse matrix times vector. % z = cs_gaxpy(A,x,y) computes z = A*x+y where x and y are full vectors. % % Example: % Prob = UFget ('HB/arc130') ; A = Prob.A ; [m n] = size (A) ; % x = rand (m,1) ; y = rand (n,1) ; % z = cs_gaxpy (A, x, y) ; % % See also PLUS, MTIMES. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_gaxpy mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_symperm_mex.c0000644001170100242450000000145010677526530021020 0ustar davisfac#include "cs_mex.h" /* cs_symperm: symmetric permutation of a symmetric sparse matrix. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs Amatrix, *A, *C, *D ; int ignore, n, *P, *Pinv ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: C = cs_symperm(A,p)") ; } A = cs_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; n = A->n ; P = cs_mex_get_int (n, pargin [1], &ignore, 1) ; /* get P */ Pinv = cs_pinv (P, n) ; /* P=Pinv' */ C = cs_symperm (A, Pinv, 1) ; /* C = A(p,p) */ D = cs_transpose (C, 1) ; /* sort C */ cs_spfree (C) ; C = cs_transpose (D, 1) ; cs_spfree (D) ; pargout [0] = cs_mex_put_sparse (&C) ; /* return C */ cs_free (P) ; cs_free (Pinv) ; } SuiteSparse/CSparse/MATLAB/CSparse/cs_multiply.m0000644001170100242450000000100410620371650020324 0ustar davisfacfunction C = cs_multiply (A,B) %#ok %CS_MULTIPLY sparse matrix multiply. % C = cs_multiply(A,B) computes C = A*B. % % Example: % Prob1 = UFget ('HB/ibm32') ; A = Prob1.A ; % Prob2 = UFget ('Hamrle/Hamrle1') ; B = Prob2.A ; % C = cs_multiply (A,B) ; % D = A*B ; % same as C % % See also CS_GAXPY, CS_ADD, MTIMES. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_mult mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_add.m0000644001170100242450000000111710620371606017203 0ustar davisfacfunction C = cs_add (A,B,alpha,beta) %#ok %CS_ADD sparse matrix addition. % C = cs_add(A,B,alpha,beta) computes C = alpha*A+beta*B, % where alpha and beta default to 1 if not present. % % Example: % Prob1 = UFget ('HB/ibm32') ; A = Prob1.A ; % Prob2 = UFget ('Hamrle/Hamrle1') ; B = Prob2.A ; % C = cs_add (A,B) ; % D = A+B ; % same as C % % See also CS_MULTIPLY, CS_GAXPY, PLUS, MINUS. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_add mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_amd.m0000644001170100242450000000203010620371607017210 0ustar davisfacfunction p = cs_amd (A,order) %#ok %CS_AMD approximate minimum degree ordering. % p = cs_amd(A) finds a minimum degree ordering of A+A' % p = cs_amd(A,order): % order = 1: same as cs_amd(A) % order = 2: minimum degree ordering of S'*S where S = A except that % "dense" rows of A are removed from S (a dense row has % 10*sqrt(n) or more entries where n = size(A,2)). Similar % to p = colamd(A), except that colamd does not form A'*A % explicitly. % order = 3: minimum degree ordering of A'*A. Similar to colamd(A,[n m]) % where [m n] = size(A), except that colamd does not form A'*A % explicitly. % Example: % Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; % p = cs_amd (A) ; % nnz (chol (A)) % nnz (chol (A (p,p))) % % See also AMD, COLAMD, SYMAMD. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_amd mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_mex.c0000644001170100242450000000666510620715616017252 0ustar davisfac#include "cs_mex.h" /* check MATLAB input argument */ void cs_mex_check (int nel, int m, int n, int square, int sparse, int values, const mxArray *A) { int nnel, mm = mxGetM (A), nn = mxGetN (A) ; if (values) { if (mxIsComplex (A)) { mexErrMsgTxt ("matrix must be real; try CXSparse instead") ; } } if (sparse && !mxIsSparse (A)) mexErrMsgTxt ("matrix must be sparse") ; if (!sparse) { if (mxIsSparse (A)) mexErrMsgTxt ("matrix must be full") ; if (values && !mxIsDouble (A)) mexErrMsgTxt ("matrix must be double") ; } if (nel) { /* check number of elements */ nnel = mxGetNumberOfElements (A) ; if (m >= 0 && n >= 0 && m*n != nnel) mexErrMsgTxt ("wrong length") ; } else { /* check row and/or column dimensions */ if (m >= 0 && m != mm) mexErrMsgTxt ("wrong dimension") ; if (n >= 0 && n != nn) mexErrMsgTxt ("wrong dimension") ; } if (square && mm != nn) mexErrMsgTxt ("matrix must be square") ; } /* get a MATLAB sparse matrix and convert to cs */ cs *cs_mex_get_sparse (cs *A, int square, int values, const mxArray *Amatlab) { cs_mex_check (0, -1, -1, square, 1, values, Amatlab) ; A->m = mxGetM (Amatlab) ; A->n = mxGetN (Amatlab) ; A->p = mxGetJc (Amatlab) ; A->i = mxGetIr (Amatlab) ; A->x = values ? mxGetPr (Amatlab) : NULL ; A->nzmax = mxGetNzmax (Amatlab) ; A->nz = -1 ; /* denotes a compressed-col matrix, instead of triplet */ return (A) ; } /* return a sparse matrix to MATLAB */ mxArray *cs_mex_put_sparse (cs **Ahandle) { cs *A ; mxArray *Amatlab ; A = *Ahandle ; Amatlab = mxCreateSparse (0, 0, 0, mxREAL) ; mxSetM (Amatlab, A->m) ; mxSetN (Amatlab, A->n) ; mxSetNzmax (Amatlab, A->nzmax) ; cs_free (mxGetJc (Amatlab)) ; cs_free (mxGetIr (Amatlab)) ; cs_free (mxGetPr (Amatlab)) ; mxSetJc (Amatlab, A->p) ; /* assign A->p pointer to MATLAB A */ mxSetIr (Amatlab, A->i) ; mxSetPr (Amatlab, A->x) ; mexMakeMemoryPersistent (A->p) ; /* ensure MATLAB does not free A->p */ mexMakeMemoryPersistent (A->i) ; mexMakeMemoryPersistent (A->x) ; cs_free (A) ; /* frees A struct only, not A->p, etc */ *Ahandle = NULL ; return (Amatlab) ; } /* get a MATLAB dense column vector */ double *cs_mex_get_double (int n, const mxArray *X) { cs_mex_check (0, n, 1, 0, 0, 1, X) ; return (mxGetPr (X)) ; } /* return a double vector to MATLAB */ double *cs_mex_put_double (int n, const double *b, mxArray **X) { double *x ; int k ; *X = mxCreateDoubleMatrix (n, 1, mxREAL) ; /* create x */ x = mxGetPr (*X) ; for (k = 0 ; k < n ; k++) x [k] = b [k] ; /* copy x = b */ return (x) ; } /* get a MATLAB flint array and convert to int */ int *cs_mex_get_int (int n, const mxArray *Imatlab, int *imax, int lo) { double *p ; int i, k, *C = cs_malloc (n, sizeof (int)) ; cs_mex_check (1, n, 1, 0, 0, 1, Imatlab) ; p = mxGetPr (Imatlab) ; *imax = 0 ; for (k = 0 ; k < n ; k++) { i = p [k] ; C [k] = i - 1 ; if (i < lo) mexErrMsgTxt ("index out of bounds") ; *imax = CS_MAX (*imax, i) ; } return (C) ; } /* return an int array to MATLAB as a flint row vector */ mxArray *cs_mex_put_int (int *p, int n, int offset, int do_free) { mxArray *X = mxCreateDoubleMatrix (1, n, mxREAL) ; double *x = mxGetPr (X) ; int k ; for (k = 0 ; k < n ; k++) x [k] = (p ? p [k] : k) + offset ; if (do_free) cs_free (p) ; return (X) ; } SuiteSparse/CSparse/MATLAB/CSparse/cs_mex.h0000644001170100242450000000100110415513653017231 0ustar davisfac#include "cs.h" #include "mex.h" cs *cs_mex_get_sparse (cs *A, int square, int values, const mxArray *Amatlab) ; mxArray *cs_mex_put_sparse (cs **A) ; void cs_mex_check (int nel, int m, int n, int square, int sparse, int values, const mxArray *A) ; int *cs_mex_get_int (int n, const mxArray *Imatlab, int *imax, int lo) ; mxArray *cs_mex_put_int (int *p, int n, int offset, int do_free) ; double *cs_mex_get_double (int n, const mxArray *X) ; double *cs_mex_put_double (int n, const double *b, mxArray **X) ; SuiteSparse/CSparse/MATLAB/CSparse/cs_scc.m0000644001170100242450000000123410620371677017233 0ustar davisfacfunction [p,r] = cs_scc (A) %#ok %CS_SCC strongly-connected components of a square sparse matrix. % [p,r] = cs_scc(A) finds a permutation p so that A(p,p) is permuted into % block upper triangular form. The diagonal of A is ignored. The kth block % is given by A (s,s) where s = r(k):r(k+1)-1. A must be square. % For bipartite or rectangular graphs, use cs_scc2. % % Example: % Prob = UFget ('HB/arc130') ; A = Prob.A ; [p r] = cs_scc (A) ; % cspy (A (p,p)) ; % % See also CS_DMPERM, DMPERM, CS_SCC2. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_scc mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_sep.m0000644001170100242450000000147410620371701017244 0ustar davisfacfunction [s,as,bs] = cs_sep (A,a,b) %CS_SEP convert an edge separator into a node separator. % [s,as,bs] = cs_sep (A,a,b) converts an edge separator into a node separator. % [a b] is a partition of 1:n, thus the edges in A(a,b) are an edge separator % of A. s is the node separator, consisting of a node cover of the edges of % A(a,b). as and bs are the sets a and b with s removed. % % Example: % type cs_nsep ; % to see a simple example of use in cs_nsep.m % % See also CS_DMPERM, CS_NSEP, CS_ESEP, CS_ND. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [p q r s cc rr] = cs_dmperm (A (a,b)) ; s = [(a (p (1:rr(2)-1))) (b (q (cc(3):(cc(5)-1))))] ; w = ones (1, size (A,1)) ; w (s) = 0 ; as = a (find (w (a))) ; %#ok bs = b (find (w (b))) ; %#ok SuiteSparse/CSparse/MATLAB/CSparse/cs_sqr.m0000644001170100242450000000206710620371704017264 0ustar davisfacfunction [vnz,rnz,parent,c,leftmost,p,q] = cs_sqr (A) %#ok %CS_SQR symbolic sparse QR factorization. % [vnz,rnz,parent,c,leftmost,p] = cs_sqr(A): symbolic QR of A(p,:). % [vnz,rnz,parent,c,leftmost,p,q] = cs_sqr(A) computes the symbolic QR % factorization of A(p,q). The fill-reducing ordering q is found via % q = cs_amd(A,3). % % vnz is the number of entries in the matrix of Householder vectors, V. % rnz is the number of entries in R. parent is elimination tree. % c(i) is the number of entries in R(i,:). leftmost(i) = min(find(A(i,q))). % p is the row permutation used to ensure R has a symbolically zero-free % diagonal (it can be larger than m if A is structurally rank deficient). % q is the fill-reducing ordering, if requested. % % Example: % Prob = UFget ('HB/ibm32') ; A = Prob.A ; % [vnz, rnz, parent, c, leftmost, p, q] = cs_sqr (A) ; % cspy (A (p,q)) ; % % See also CS_AMD, CS_QR. % % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_sqr mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/ccspy.m0000644001170100242450000000333710622674743017127 0ustar davisfacfunction [p, q, r, s] = ccspy (A, bipartite, res) %CCSPY plot the connected components of a matrix. % % Example: % [p, q, r, s] = ccspy (A, bipartite, res) % % If A is square, [p,q,r,s] = ccspy(A) finds a permutation p so that A(p,q) % is permuted into block upper triangular form. In this case, r=s, p=q and % the kth diagonal block is given by A (t,t) where t = r(k):r(k+1)-1. % The diagonal of A is ignored. % % If A is not square (or for [p,q,r,s] = ccspy(A,1)), then the connected % components of the bipartite graph of A are found. A(p,q) is permuted into % block diagonal form, where the diagonal blocks are rectangular. The kth % block is given by A(r(k):r(k+1)-1,s(k):s(k+1)-1). A can be rectangular. % % It then plots the result via cspy, drawing a greenbox around each component. % A 3rd input argument (res) controls the resolution (see cspy for a % description of the res parameter). % % See also CSPY, CS_DMPERM, DMPERM, CS_SCC, CS_SCC2, CS_DMSPY. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (~issparse (A)) A = sparse (A) ; end [m n] = size (A) ; if (nargin < 3) res = 256 ; end if (nargin < 2) bipartite = [ ] ; end if (isempty (bipartite)) bipartite = (m ~= n) ; end % find the strongly connected components [p1 q r s] = cs_scc2 (A, bipartite) ; if (nargout > 0) p = p1 ; end nb = length (r)-1 ; % plot the result S = A (p1,q) ; if (res == 0) spy (S) ; e = 1 ; else e = cspy (S,res) ; end hold on title (sprintf ('%d-by-%d, strongly connected commponents: %d\n', m, n, nb)) ; if (~bipartite) plot ([.5 .5 n+.5 n+.5], [.5 .5 n+.5 n+.5], 'r') ; end drawboxes (nb, e, r, s) ; drawbox (1,m+1,1,n+1,'k',1,e) ; hold off SuiteSparse/CSparse/MATLAB/CSparse/cs_utsolve_mex.c0000644001170100242450000000110410415514715021011 0ustar davisfac#include "cs_mex.h" /* cs_utsolve: solve a lower triangular system U'*x=b */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs Umatrix, *U ; double *x, *b ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_utsolve(U,b)") ; } U = cs_mex_get_sparse (&Umatrix, 1, 1, pargin [0]) ; /* get U */ b = cs_mex_get_double (U->n, pargin [1]) ; /* get b */ x = cs_mex_put_double (U->n, b, &(pargout [0])) ; /* x = b */ cs_utsolve (U, x) ; /* x = U'\x */ } SuiteSparse/CSparse/MATLAB/CSparse/cs_randperm_mex.c0000644001170100242450000000164010417203251021115 0ustar davisfac#include "cs_mex.h" /* cs_randperm: random permutation. p=cs_randperm(n,0) is 1:n, * p=cs_randperm(n,-1) is n:-1:1. p = cs_randperm (n,seed) is a random * permutation using the given seed (where seed is not 0 or -1). * seed defaults to 1. A single seed always gives a repeatable permutation. * Use p = cs_randperm(n,rand) to get a permutation that varies with each use. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double seed ; int iseed, n, *p ; if (nargout > 1 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: p = cs_randperm(n,seed)") ; } seed = (nargin > 1) ? mxGetScalar (pargin [1]) : 1 ; iseed = (seed > 0 && seed < 1) ? (seed * RAND_MAX) : seed ; n = mxGetScalar (pargin [0]) ; n = CS_MAX (n, 0) ; p = cs_randperm (n, iseed) ; pargout [0] = cs_mex_put_int (p, n, 1, 1) ; /* return p */ } SuiteSparse/CSparse/MATLAB/CSparse/cs_sparse.m0000644001170100242450000000105010620371702017741 0ustar davisfacfunction A = cs_sparse (i,j,x) %#ok %CS_SPARSE convert a triplet form into a sparse matrix. % A = cs_sparse(i,j,x) is identical to A = sparse(i,j,x), except that x must % be real, and the length of i, j, and x must be the same. % % Example: % Prob = UFget ('HB/arc130') ; S = Prob.A ; % [i j x] = find (S) ; % A = cs_sparse (i,j,x) ; % S-A % % See also FIND, SPARSE, SPCONVERT. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_sparse mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_usolve_mex.c0000644001170100242450000000363210415514336020634 0ustar davisfac#include "cs_mex.h" /* cs_usolve: x=U\b. U must be sparse, real, and upper triangular. b must be a * real full or sparse vector. x is full or sparse, depending on b. * * Time taken is O(flop count), which may be less than n if b is sparse, * depending on U and b. * * This function works with MATLAB 7.2, but is not perfectly compatible with * the requirements of a MATLAB mexFunction when b is sparse. X is returned * as an unsorted sparse vector. Also, this mexFunction temporarily modifies * its input, U, by modifying U->p (in the cs_dfs function) and then restoring * it. This could be corrected by creating a copy of U->p (see * cs_dmperm_mex.c), but this would take O(n) time, destroying the * O(flop count) time complexity of this function. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs Umatrix, Bmatrix, *U, *B, *X ; double *x, *b ; int top, nz, p, *xi ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_usolve(U,b)") ; } U = cs_mex_get_sparse (&Umatrix, 1, 1, pargin [0]) ; /* get U */ if (mxIsSparse (pargin [1])) { B = cs_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ;/* get sparse b */ cs_mex_check (0, U->n, 1, 0, 1, 1, pargin [1]) ; xi = cs_malloc (2*U->n, sizeof (int)) ; /* get workspace */ x = cs_malloc (U->n, sizeof (double)) ; top = cs_spsolve (U, B, 0, xi, x, NULL, 0) ; /* x = U\b */ X = cs_spalloc (U->n, 1, U->n-top, 1, 0) ; /* create sparse x*/ X->p [0] = 0 ; nz = 0 ; for (p = top ; p < U->n ; p++) { X->i [nz] = xi [p] ; X->x [nz++] = x [xi [p]] ; } X->p [1] = nz ; pargout [0] = cs_mex_put_sparse (&X) ; cs_free (x) ; cs_free (xi) ; } else { b = cs_mex_get_double (U->n, pargin [1]) ; /* get full b */ x = cs_mex_put_double (U->n, b, &(pargout [0])) ; /* x = b */ cs_usolve (U, x) ; /* x = U\x */ } } SuiteSparse/CSparse/MATLAB/CSparse/cs_cholsol_mex.c0000644001170100242450000000145410416442465020766 0ustar davisfac#include "cs_mex.h" /* cs_cholsol: solve A*x=b using a sparse Cholesky factorization */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs *A, Amatrix ; double *x, *b ; int order ; if (nargout > 1 || nargin < 2 || nargin > 3) { mexErrMsgTxt ("Usage: x = cs_cholsol(A,b,order)") ; } A = cs_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */ b = cs_mex_get_double (A->n, pargin [1]) ; /* get b */ x = cs_mex_put_double (A->n, b, &(pargout [0])) ; /* x = b */ order = (nargin < 3) ? 1 : mxGetScalar (pargin [2]) ; order = CS_MAX (order, 0) ; order = CS_MIN (order, 3) ; if (!cs_cholsol (order, A, x)) /* x = A\x */ { mexErrMsgTxt ("A not positive definite") ; } } SuiteSparse/CSparse/MATLAB/CSparse/private/0000755001170100242450000000000010620671144017262 5ustar davisfacSuiteSparse/CSparse/MATLAB/CSparse/private/drawbox.m0000644001170100242450000000127710620671143021114 0ustar davisfacfunction drawbox (r1,r2,c1,c2,color,w,e) %DRAWBOX draw a box around a submatrix in the figure. % Used by cspy, cs_dmspy, and ccspy. % Example: % drawbox (r1,r2,c1,c2,color,w,e) % See also drawboxes, plot % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (r1 == r2 | c1 == c2) %#ok return end if (e == 1) r1 = r1 - .5 ; r2 = r2 - .5 ; c1 = c1 - .5 ; c2 = c2 - .5 ; else r1 = ceil (r1 / e) - .5 ; r2 = ceil ((r2 - 1) / e) + .5 ; c1 = ceil (c1 / e) - .5 ; c2 = ceil ((c2 - 1) / e) + .5 ; end if (c2 > c1 | r2 > r1) %#ok plot ([c1 c2 c2 c1 c1], [r1 r1 r2 r2 r1], color, 'LineWidth', w) ; end SuiteSparse/CSparse/MATLAB/CSparse/private/drawboxes.m0000644001170100242450000000136710620372107021442 0ustar davisfacfunction drawboxes (nb, e, r, s) %DRAWBOXES: helper function for cs_dmpsy and ccspy % Example: % drawboxes (nb, e, r, s) % See also drawbox, plot % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (nb > 1) if (e == 1) r1 = r (1:nb) - .5 ; r2 = r (2:nb+1) - .5 ; c1 = s (1:nb) - .5 ; c2 = s (2:nb+1) - .5 ; else r1 = ceil (r (1:nb) / e) - .5 ; r2 = ceil ((r (2:nb+1) - 1) / e) + .5 ; c1 = ceil (s (1:nb) / e) - .5 ; c2 = ceil ((s (2:nb+1) - 1) / e) + .5 ; end kk = find (diff (c1) > 0 | diff (c2) > 0 | diff (r1) > 0 | diff (r2) > 0) ; kk = [1 kk+1] ; for k = kk plot ([c1(k) c2(k) c2(k) c1(k) c1(k)], ... [r1(k) r1(k) r2(k) r2(k) r1(k)], 'k', 'LineWidth', 1) ; end end SuiteSparse/CSparse/MATLAB/CSparse/cs_transpose.m0000644001170100242450000000070010620371714020466 0ustar davisfacfunction C = cs_transpose (A) %#ok %CS_TRANSPOSE transpose a real sparse matrix. % C = cs_transpose(A), computes C = A' where A must be sparse and real. % % Example: % Prob = UFget ('HB/ibm32') ; A = Prob.A ; % C = cs_transpose (A) ; % C-A' % % See also TRANSPOSE, CTRANSPOSE. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_transpose mexFunction not found') ; SuiteSparse/CSparse/MATLAB/CSparse/cs_sqr_mex.c0000644001170100242450000000254710620706774020137 0ustar davisfac#include "cs_mex.h" /* cs_sqr: symbolic sparse QR factorization */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double s ; css *S ; cs Amatrix, *A ; int m, n, order, *p ; if (nargout > 7 || nargin != 1) { mexErrMsgTxt ("Usage: [vnz,rnz,parent,c,leftmost,p,q] = cs_sqr(A)") ; } A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ m = A->m ; n = A->n ; if (m < n) mexErrMsgTxt ("A must have # rows >= # columns") ; order = (nargout == 7) ? 3 : 0 ; /* determine ordering */ S = cs_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/ if (!S) mexErrMsgTxt ("cs_sqr failed") ; s = S->lnz ; cs_mex_put_double (1, &s, &(pargout [0])) ; /* return nnz(V) */ s = S->unz ; cs_mex_put_double (1, &s, &(pargout [1])) ; /* return nnz(R) */ pargout [2] = cs_mex_put_int (S->parent, n, 1, 0) ; /* return parent */ pargout [3] = cs_mex_put_int (S->cp, n, 0, 0) ; /* return c */ pargout [4] = cs_mex_put_int (S->leftmost, m, 1, 0) ; /* return leftmost*/ p = cs_pinv (S->pinv, S->m2) ; /* p = pinv' */ pargout [5] = cs_mex_put_int (p, S->m2, 1, 1) ; /* return p */ if (nargout > 6) { pargout [6] = cs_mex_put_int (S->q, n, 1, 0) ; /* return q */ } cs_sfree (S) ; } SuiteSparse/CSparse/MATLAB/CSparse/cs_qr_mex.c0000644001170100242450000000305410416442563017742 0ustar davisfac#include "cs_mex.h" /* cs_qr: sparse QR factorization */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { css *S ; csn *N ; cs Amatrix, *A, *D ; int m, n, order, *p ; if (nargout > 5 || nargin != 1) { mexErrMsgTxt ("Usage: [V,beta,p,R,q] = cs_qr(A)") ; } A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ m = A->m ; n = A->n ; if (m < n) mexErrMsgTxt ("A must have # rows >= # columns") ; order = (nargout == 5) ? 3 : 0 ; /* determine ordering */ S = cs_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/ N = cs_qr (A, S) ; /* numeric QR factorization */ if (!N) mexErrMsgTxt ("qr failed") ; cs_dropzeros (N->L) ; /* drop zeros from V and sort */ D = cs_transpose (N->L, 1) ; cs_spfree (N->L) ; N->L = cs_transpose (D, 1) ; cs_spfree (D) ; cs_dropzeros (N->U) ; /* drop zeros from R and sort */ D = cs_transpose (N->U, 1) ; cs_spfree (N->U) ; N->U = cs_transpose (D, 1) ; cs_spfree (D) ; m = N->L->m ; /* m may be larger now */ p = cs_pinv (S->pinv, m) ; /* p = pinv' */ pargout [0] = cs_mex_put_sparse (&(N->L)) ; /* return V */ cs_mex_put_double (n, N->B, &(pargout [1])) ; /* return beta */ pargout [2] = cs_mex_put_int (p, m, 1, 1) ; /* return p */ pargout [3] = cs_mex_put_sparse (&(N->U)) ; /* return R */ pargout [4] = cs_mex_put_int (S->q, n, 1, 0) ; /* return q */ cs_nfree (N) ; cs_sfree (S) ; } SuiteSparse/CSparse/MATLAB/Makefile0000644001170100242450000000032310375340406015707 0ustar davisfacall: ( cd CSparse ; $(MAKE) ) ( cd Test ; $(MAKE) ) clean: ( cd CSparse ; $(MAKE) clean ) ( cd Test ; $(MAKE) clean ) purge: ( cd CSparse ; $(MAKE) purge ) ( cd Test ; $(MAKE) purge ) distclean: purge SuiteSparse/CSparse/MATLAB/UFget/0000755001170100242450000000000010711673300015257 5ustar davisfacSuiteSparse/CSparse/MATLAB/UFget/mat/0000755001170100242450000000000010620672242016043 5ustar davisfacSuiteSparse/CSparse/MATLAB/UFget/mat/UF_Index.mat0000644001170100242450000036260010677525546020236 0ustar davisfacMATLAB 5.0 MAT-file, Platform: GLNX86, Created on: Thu Sep 6 13:49:48 2007 IMxMN@_ n;?IbbXqlЙif HI'p5\}x/4&|ԓg#YXW-;ǗkTa7ωtl4 aV=RBQdpe<T&9&^tPD*.xbn4F!"nĮY]sɍX žnJ!gA`(^[OQ$hb(wikhQBi> Df/Cn$"C2E+?ذB|GxL< %WdLV?Y\x>eϴv{}躧Gnry?\v]"?ޜ)-?Ww#<#<#<#<#<#<#<˱ @DQTK.\0x eגjwKU qqqqqqqqqO 0GرMEwrL!e|d?^/sI3.U?F㧑i]]kGgf˄M󃇇)aazgI;~l%[߇ϥnZ 1 @EQӈIiia5$BpũҤJ3/.ņXkcU_绌|}-e}::::::::::::ܿtڏyOuyyyy 0%˺´a@iY}y W$ఝgpLgm.m^VNM~k3x<x<W#B||ƃ~]Sƴ ';nʞ"U7Íu!sꓮ9x<T_qQK0*?G eU{XXDvoj" ^B^W6 ~OyD,e+y˨쫦vMQfudfe\yɓGmL~0Igqy0H3nxfXU OIY~+w^!Kzq'n(r0ǵ:>:|KD!u):hRGPǻ죃:贡S\2gqy߹ixmˮT;tJٹ+B>[ 0E )]v RȂUFͨ$׷TJTĤW.L-h NgEM^^^U^J|ܳ#`nFʋ~Fs~Gqgˑf+xw]q8pS^Y>; p`c$2慡kGiylc;qp8p|9QBIN:`=ȼ{!w)89W]K0@+D>uEd8m\H?&mW iv[IM\jfdeqVtIVxޛSk^|مF<"wTG^$?."'0Ÿx?Xܞ?tސeb2% q y#b$|QY< c،߄5xӶ}t}ZX5F ^tH|`16ux.[4sQi{{?㯅TiΘ ?fg?>}Y6;i;/dvZZ7؏st]6t5OUBU/i_aՠ朎Re&!|x;F8<*Cj%F?}YJﾽeOY.J98EK/WB726ѓuöו(~&͠coǓxbl1M.Ew-&c>C,ܟ ?$57@A~)g}P#Yg=ҟH#Yg=ҟHG#?#?#?#?#?8`쏃q0`*e=U}m < %&_F)8|blm{Q>7=)]7|~zſ(4~ (l,ퟅ#0?Oip4555k>?pݏk( ΟFώy ^ǟ򧢿pp-)Xqy z zu!|[;\˻{ P+V˭_֊?zG+k݈/z[|!om ͟_~kl"l o8|&?/p k+;1տC;z`EϬ?G맸 (=8ΟKퟒxy=6~̿ 8/U;y}_WX ?7?n6K&ɋ񗖠/~<2#OOh#G~MݙO{{5;7ۯVմ-!5xM}o dx_o_灔R6\Vɳ~ GM˸?yqOn0`ګ64zM8 k\$QVB+.>`aYz/=f~_L[w͉^&KR7_ڎ*(4ZuUj.9?xYɤ;8)ȇ yw׉D`$4-/$9\Lo_ФuhU?ERտm8oٛm8֯_ߜ<t2X4a8qY|{_w|xΠFA'@'ANN;lN;qn\߽=g,I}C= ^jͩsO\yi%>~{x>ѹmgxv潛 u|sopW;fowͻO[wu^_1}ҏgo'?[fyO?SD,KM'_l8͛/|nZ0m\{b|$#Lͯ_U|KSc> -76/^}ca:=vϼ{`-Z1ąI0A+A]36>"x\V#^(~Q_b 1&5h|_LY5iO# D"zM񯜑 sn0L(m/2% Td$-!Fj!#v9ϲ!ZO}oz}Jl} yqdUe}ܤ~ueu:?\]o*:ů{+K`\c?2e8,/͸~[wx_S~] <6yb-SN;ᩦɧn%#}N {2~'y:~%kȟҤ{r\'?oQj%p^+'o-m8Ua'x1S.޿F/7zR_.xݝ=;ljěqԍqYdqxDovi7}azyfV~jj~|p {>, ]}h>/Jwϻ2z>/*z;y?M֟&O+ѓdi?!O~1z w.ۼh h=A'3s+@Wbu#`}p`̻y0=q+Ёu&` X/֋n_yI|.ikn]o0~hS؄g C4IPRH=F=k $w=T*5|Nv7-.^9nS'.qid_t]ۨ}).6hܳU;}QO=˓_&. < y-Y!oRgB~%U _ܾs_ípuQ*ch_ow|=޹,Cƿs<t_~xq=@@N9 rK@.gzFgzFgzFgzFgzFgzA4=ӠgLi3 zA4=c3=c3=c3=c3=c3=c3zf@ =3g̀3zf@ =ĝY3 zfA, 7f CNrsOy<'^~xj &7۪W;Oz;p^\mRoe9H"`a1crdY*89H+#z"yHSJڇ~NkV㤟q?H<)Gc#屑dn03iKVv)ow1ԉcSk~Eu UO^sbom?=7{.HJ'\^!s?PBc8;8 88~6H~6H~$? 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MATLAB 7.0 or later is required. Date: May 31, 2007. Copyright 2005-2007, Tim Davis, University of Florida. Authors: Tim Davis and Erich Mirable. Availability: http://www.cise.ufl.edu/research/sparse/mat/UFget See http://www.cise.ufl.edu/research/sparse/mat/UFget.tar.gz for a single archive file with all the files listed below. UFget/Contents.m help for UFget UFget/README.txt this file UFget/UFget_defaults.m default parameter settings for UFget UFget/UFget_example.m demo for UFget UFget/UFget_lookup.m get the group, name, and id of a matrix UFget/UFget.m primary user interface UFget/UFweb.m opens the URL for a matrix or collection UFget/mat default download directory (can be changed) UFget/mat/UF_Index.mat index to the UF sparse matrix collection To install the package, just add the path containing the UFget directory to your MATLAB path. Type "pathtool" in MATLAB for more details. For a simple example of use, type this command in MATLAB: UFget_example The MATLAB statement Problem = UFget ('HB/arc130') (for example), will download a sparse matrix called HB/arc130 (a laser simulation problem) and load it into MATLAB. You don't need to use your web browser to load the matrix. The statement Problem = UFget (6) will also load same the HB/arc130 matrix. Each matrix in the collection has a unique identifier, in the range 1 to the number of matrices. As new matrices are added, the id's of existing matrices will not change. To view an index of the entire collection, just type UFget in MATLAB. To modify your download directory, edit the UFget_defaults.m file. To open a URL of the entire collection, just type UFweb To open the URL of a group of matrices in the collection: UFweb ('HB') To open the web page for one matrix, use either of these formats: UFweb ('HB/arc130') UFweb (6) For more information on how the index entries were created, see http://www.cise.ufl.edu/research/sparse/SuiteSparse. SuiteSparse/CSparse/MATLAB/UFget/UFget_lookup.m0000644001170100242450000000403210711661566020052 0ustar davisfacfunction [group, name, id] = UFget_lookup (matrix, UF_Index) %UFGET_LOOKUP gets the group, name, and id of a matrix. % % Example: % [group name id] = UFget_lookup (matrix, UF_Index) % % See also UFget. % Copyright 2007, Tim Davis, University of Florida. if (isnumeric (matrix)) % make sure that the matrix parameter is only one integer value % this means that if we get an array, just use the first value id = fix (full (matrix (1))) ; % if the index is less than one or bigger than the length of the array, % then no particular matrix is accessed if (id > length (UF_Index.nrows) | id < 1) %#ok id = 0 ; group = '' ; name = '' ; else % assign the group and name for the given id group = UF_Index.Group {matrix} ; name = UF_Index.Name {matrix} ; end elseif (ischar (matrix)) % the group and matrix name are in the string as in GroupName\MatrixName % find the group index for the file separator % check both types of slashes, and a colon gi = find (matrix == '/') ; if (length (gi) == 0) %#ok gi = find (matrix == '\') ; end if (length (gi) == 0) %#ok gi = find (matrix == ':') ; end % if no name divider is in the string, a whole group is specified if (length (gi) == 0) %#ok id = 0 ; group = matrix ; name = '' ; else % group equals the first part of the string up to the character before % the last file separator group = matrix (1:gi(end)-1) ; % group equals the last section of the string after the last file % separator name = matrix (gi(end)+1:end) ; % validate the given name and group by checking the index for a match refName = strmatch (name, UF_Index.Name) ; refGroup = strmatch (group, UF_Index.Group) ; id = intersect (refName, refGroup) ; if (length (id) >= 1) id = id (1) ; else % the given group/matrix does not exist in the index file id = 0 ; end end else % there is an error in the argument types passed into the function error ('invalid input') ; end SuiteSparse/CSparse/MATLAB/UFget/UFgrep.m0000644001170100242450000000265710620373464016646 0ustar davisfacfunction list = UFgrep (expression, index) %UFGREP search for matrices in the UF Sparse Matrix Collection. % UFgrep returns a list of Problem id's whose Problem.name string matches an % expression. With no output arguments, the list is displayed. Otherwise, it % is returned as a list of integer id's. % % Example: % UFgrep ('HB') ; % all matrices in the HB group % UFgrep ('\= 7.0) addpath ([pwd filesep 'UFget']) ; else fprintf ('UFget not installed (MATLAB 7.0 or later required)\n') ; end cd ('CSparse') ; cs_make (1) ; cd ('../Demo') ; cs_demo (do_pause) %------------------------------------------------------------------------------- function v = getversion % determine the MATLAB version, and return it as a double. v = sscanf (version, '%d.%d.%d') ; v = 10.^(0:-1:-(length(v)-1)) * v ; SuiteSparse/CSparse/Matrix/0000755001170100242450000000000010533354740014557 5ustar davisfacSuiteSparse/CSparse/Matrix/t10000644001170100242450000000012010323544611015012 0ustar davisfac2 2 3.0 1 0 3.1 3 3 1.0 0 2 3.2 1 1 2.9 3 0 3.5 3 1 0.4 1 3 0.9 0 0 4.5 2 1 1.7 SuiteSparse/CSparse/Matrix/west00670000644001170100242450000000753510326012123015775 0ustar davisfac44 55 -1.863354 54 61 -1.863354 29 37 -1.567398 44 56 -1.490683 54 62 -1.490683 9 12 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28 41 0.65 14 18 0.6666667 30 37 0.7222222 31 38 0.7222222 32 39 0.7222222 33 40 0.7222222 34 41 0.7222222 38 58 0.7453416 48 64 0.7453416 2 14 0.7594937 22 39 0.9404389 59 31 0.5 59 32 0.5 59 33 0.5 59 34 0.5 59 35 0.5 29 42 1 44 60 1 54 66 1 55 18 1 56 10 1 56 11 1 56 7 1 56 8 1 56 9 1 57 12 1 57 13 1 57 14 1 57 15 1 57 16 1 58 20 1 58 21 1 58 22 1 58 23 1 58 24 1 59 31 0.5 59 32 0.5 59 33 0.5 59 34 0.5 59 35 0.5 60 1 1 60 2 1 60 3 1 60 4 1 60 5 1 61 37 1 61 38 1 61 39 1 61 40 1 61 41 1 62 49 1 62 50 1 62 51 1 62 52 1 62 53 1 63 25 1 63 26 1 63 27 1 63 28 1 63 29 1 64 55 1 64 56 1 64 57 1 64 58 1 64 59 1 65 43 1 65 44 1 65 45 1 65 46 1 65 47 1 66 61 1 66 62 1 66 63 1 66 64 1 66 65 1 9 17 1 1 13 1.012658 37 57 1.118012 47 63 1.118012 21 38 1.253918 0 12 1.265823 36 56 1.490683 46 62 1.490683 20 37 1.567398 35 55 1.863354 45 61 1.863354 SuiteSparse/CSparse/Matrix/bcsstk010000644001170100242450000001157510326005665016144 0ustar davisfac0 0 2.83226851852e+06 4 0 1.0e+06 5 0 2.08333333333e+06 6 0 -3.33333333333e+03 10 0 1.0e+06 18 0 -2.8e+06 24 0 -2.89351851852e+04 29 0 2.08333333333e+06 1 1 1.63544753086e+06 3 1 -2.0e+06 5 1 5.55555555555e+06 7 1 -6.66666666667e+03 9 1 -2.0e+06 19 1 -3.08641975309e+04 23 1 5.55555555555e+06 25 1 -1.59791666667e+06 2 2 1.72436728395e+06 3 2 -2.08333333333e+06 4 2 -2.77777777778e+06 8 2 -1.68e+06 20 2 -1.54320987654e+04 22 2 -2.77777777778e+06 26 2 -2.89351851852e+04 27 2 -2.08333333333e+06 3 3 1.00333333333e+09 7 3 2.0e+06 9 3 4.0e+08 21 3 -3.33333333333e+06 26 3 2.08333333333e+06 27 3 1.0e+08 4 4 1.06750000000e+09 6 4 -1.0e+06 10 4 2.0e+08 20 4 2.77777777778e+06 22 4 3.33333333333e+08 28 4 -8.33333333333e+05 5 5 1.53533333333e+09 11 5 -2.0e+06 19 5 -5.55555555555e+06 23 5 6.66666666667e+08 24 5 -2.08333333333e+06 29 5 1.0e+08 6 6 2.83226851852e+06 10 6 -1.0e+06 11 6 2.08333333333e+06 12 6 -2.8e+06 30 6 -2.89351851852e+04 35 6 2.08333333333e+06 7 7 1.63544753086e+06 9 7 2.0e+06 11 7 5.55555555555e+06 13 7 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-146456504.1625 4 0 -26666666.44895 6 0 9767101.054332 7 0 21333333.1165 111 0 45108925.89256 112 0 13333333.33771 113 0 13177222.19231 114 0 -107413106.5112 115 0 -13333333.23104 116 0 -65886110.96157 117 0 -9767101.054335 118 0 10666666.5635 119 0 -13177221.94221 1 1 245557954.5208 3 1 -26666666.34228 4 1 -21122150.29068 6 1 31999999.67474 7 1 9767101.054331 111 1 13333333.33771 112 1 25107965.68335 113 1 10541666.55379 114 1 -13333333.17771 115 1 -44745929.54446 116 1 -13177083.26329 117 1 15999999.84525 118 1 -9767101.054335 119 1 15812499.93082 2 2 1 3 3 494473574.2688 4 3 26666666.12895 6 3 15679616.33822 7 3 -26666666.44895 9 3 -99111631.13552 10 3 2.384185791016e-07 12 3 -37577772.88735 13 3 26666666.66229 111 3 -107413106.5112 112 3 -13333333.17771 113 3 65886110.96157 114 3 100730268.7541 115 3 13333333.07105 116 3 0.02774140238762 117 3 -26345045.89131 118 3 -13333333.23105 119 3 16471527.49884 120 3 -88624220.55292 121 3 2.235174179077e-07 122 3 -65886111.10029 123 3 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1941 1816 3.725290298462e-07 1942 1816 -19630743.20649 1943 1816 -694433.4439167 1944 1816 9166666.669676 1945 1816 -17413237.96253 1946 1816 9149300.058182 1817 1817 607013167.9741 1818 1817 2737303.360137 1819 1817 5388804.78494 1820 1817 37600883.93994 1827 1817 2471062.980849 1828 1817 1236089.109403 1829 1817 -7832062.870945 1830 1817 -462970.2969232 1831 1817 -2777733.774298 1832 1817 39890623.87246 1833 1817 -2737270.351624 1834 1817 1541644.664895 1835 1817 -7895194.184061 1911 1817 10279397.69313 1912 1817 -8385422.169798 1913 1817 -16619803.40013 1914 1817 43154829.95728 1915 1817 7802192.5578 1916 1817 -56944833.0873 1923 1817 57871.28717278 1924 1817 -33666688.66265 1925 1817 -39477172.9523 1926 1817 781318.4370322 1927 1817 -2152691.493423 1928 1817 -99821807.80486 1929 1817 11639498.06975 1930 1817 36402939.91804 1931 1817 -55413772.21342 1938 1817 -10337268.9803 1939 1817 -8454866.614265 1940 1817 -16869702.39011 1941 1817 -43935881.45598 1942 1817 -694433.4439167 1943 1817 -57643892.87044 1944 1817 -11639352.31406 1945 1817 9149300.058182 1946 1817 -20870649.36111 1818 1818 387435706.2613 1819 1818 36666666.66065 1820 1818 2662175.186035 1830 1818 -52284795.20658 1831 1818 -36666666.66065 1832 1818 2505785.203048 1833 1818 -203296779.618 1834 1818 -36666973.09101 1835 1818 -2662152.453524 1836 1818 12401143.47877 1837 1818 29333639.75888 1838 1818 -2152799.783064 1914 1818 -4839277.140465 1915 1818 11000114.915 1916 1818 12370128.70975 1926 1818 -14860172.33131 1927 1818 -9166781.581062 1928 1818 -10279526.39882 1929 1818 33963705.33589 1930 1818 9166666.669679 1931 1818 9519894.71657 1941 1818 -18663081.30986 1942 1818 -9166666.669677 1943 1818 -10337268.9803 1944 1818 -73633660.33315 1945 1818 -9166743.277268 1946 1818 -44520628.22528 1947 1818 -7828204.348046 1948 1818 7333409.943332 1949 1818 -9288430.506837 1819 1819 332431392.3218 1820 1819 -6944376.976808 1830 1819 -36666666.66065 1831 1819 -41284001.36615 1832 1819 1263866.887163 1833 1819 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1824 -18569369.18862 1918 1824 9166666.669678 1919 1824 10279397.69313 1920 1824 -59565882.98117 1921 1824 4.91738319397e-07 1922 1824 43739118.52961 1923 1824 -20057887.18154 1924 1824 -9166666.669679 1925 1824 11581481.02689 1932 1824 -1129879.778007 1933 1824 2.369284629822e-06 1934 1824 57871.28717239 1935 1824 54280296.46473 1936 1824 3.09944152832e-06 1937 1824 231485.1485852 1938 1824 -7107625.989141 1939 1824 -6.146728992462e-06 1940 1824 57871.2871768 1950 1824 -18663081.30986 1951 1824 -9166666.669677 1952 1824 -10337268.9803 1953 1824 -59964405.70834 1954 1824 7.525086402893e-07 1955 1824 -43970603.67818 1956 1824 -20163436.42398 1957 1824 9166666.669676 1958 1824 -11639352.31406 1825 1825 531622789.3528 1826 1825 -11110935.09172 1827 1825 -4.798173904419e-06 1828 1825 -55180296.03374 1829 1825 5555467.545859 1839 1825 -36666666.66065 1840 1825 -41284001.36615 1841 1825 1263866.887163 1842 1825 -5.960464477539e-08 1843 1825 22901850.42796 1844 1825 -2777733.774299 1845 1825 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-36666666.66065 1844 1827 2505785.203048 1845 1827 -138432799.5 1846 1827 1.490116119385e-07 1847 1827 -462970.296923 1848 1827 -52308469.44899 1849 1827 36666666.66065 1850 1827 -2702548.129425 1920 1827 -18569369.18862 1921 1827 9166666.669678 1922 1827 10279397.69313 1923 1827 -59565882.98117 1924 1827 4.91738319397e-07 1925 1827 43739118.52961 1926 1827 -20057887.18154 1927 1827 -9166666.669679 1928 1827 11581481.02689 1935 1827 -1129879.778007 1936 1827 2.369284629822e-06 1937 1827 57871.28717239 1938 1827 54280296.46473 1939 1827 3.09944152832e-06 1940 1827 231485.1485852 1941 1827 -7107625.989141 1942 1827 -6.146728992462e-06 1943 1827 57871.2871768 1953 1827 -18663081.30986 1954 1827 -9166666.669677 1955 1827 -10337268.9803 1956 1827 -59964405.70834 1957 1827 7.525086402893e-07 1958 1827 -43970603.67818 1959 1827 -20163436.42398 1960 1827 9166666.669676 1961 1827 -11639352.31406 1828 1828 531622789.3528 1829 1828 -11110935.09172 1830 1828 -4.798173904419e-06 1831 1828 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599591912.5003 1830 1829 231485.1485663 1831 1829 5555467.545859 1832 1829 78550735.85485 1842 1829 2471062.980849 1843 1829 1236089.109403 1844 1829 -7832062.870945 1845 1829 -462970.2969232 1846 1829 -2777733.774298 1847 1829 39890623.87246 1848 1829 -2737270.351624 1849 1829 1541644.664895 1850 1829 -7895194.184061 1920 1829 10279397.69313 1921 1829 -8385422.169798 1922 1829 -16619803.40013 1923 1829 43704396.30741 1924 1829 -694433.4439163 1925 1829 -56581165.5979 1926 1829 11581481.02689 1927 1829 9079855.613715 1928 1829 -20589184.71456 1935 1829 57871.28717278 1936 1829 -33666688.66265 1937 1829 -39477172.9523 1938 1829 231485.148585 1939 1829 -2777733.774298 1940 1829 -118440658.1206 1941 1829 57871.28717716 1942 1829 36444422.43695 1943 1829 -55417829.51533 1953 1829 -10337268.9803 1954 1829 -8454866.614265 1955 1829 -16869702.39011 1956 1829 -43935881.45598 1957 1829 -694433.4439167 1958 1829 -57643892.87044 1959 1829 -11639352.31406 1960 1829 9149300.058182 1961 1829 -20870649.36111 1830 1830 619629140.0329 1831 1830 1.168251037598e-05 1832 1830 925940.5938052 1833 1830 84152766.23505 1834 1830 -4.991888999939e-06 1835 1830 231485.148566 1845 1830 -52284795.20658 1846 1830 -36666666.66065 1847 1830 2505785.203048 1848 1830 -138432799.5 1849 1830 1.490116119385e-07 1850 1830 -462970.296923 1851 1830 -52308469.44899 1852 1830 36666666.66065 1853 1830 -2702548.129425 1923 1830 -18569369.18862 1924 1830 9166666.669678 1925 1830 10279397.69313 1926 1830 -59565882.98117 1927 1830 4.91738319397e-07 1928 1830 43739118.52961 1929 1830 -20057887.18154 1930 1830 -9166666.669679 1931 1830 11581481.02689 1938 1830 -1129879.778007 1939 1830 2.369284629822e-06 1940 1830 57871.28717239 1941 1830 54280296.46473 1942 1830 3.09944152832e-06 1943 1830 231485.1485852 1944 1830 -7107625.989141 1945 1830 -6.146728992462e-06 1946 1830 57871.2871768 1956 1830 -18663081.30986 1957 1830 -9166666.669677 1958 1830 -10337268.9803 1959 1830 -59964405.70834 1960 1830 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1835 -43935881.45598 1963 1835 -694433.4439167 1964 1835 -57643892.87044 1965 1835 -11639352.31406 1966 1835 9149300.058182 1967 1835 -20870649.36111 1836 1836 460873125.4361 1837 1836 -27780651.28176 1838 1836 -1243230.409633 1851 1836 -52284795.20658 1852 1836 -36666666.66065 1853 1836 2505785.203048 1854 1836 -54494915.13083 1855 1836 27775705.0022 1856 1836 -284486.8047392 1857 1836 -253893652.0179 1858 1836 29338279.60807 1859 1836 -277841.1803685 1929 1836 -4839277.140465 1930 1836 11000114.915 1931 1836 12370128.70975 1944 1836 -14860172.33131 1945 1836 -9166781.581062 1946 1836 -10279526.39882 1947 1836 64920055.70775 1948 1836 -6810686.593768 1949 1836 4688786.852337 1962 1836 -18663081.30986 1963 1836 -9166666.669677 1964 1836 -10337268.9803 1965 1836 -28004319.24308 1966 1836 6809529.72167 1967 1836 -24862467.02138 1968 1836 -60799172.28945 1969 1836 7334490.207843 1970 1836 -1215195.31154 1837 1837 860522545.6296 1838 1837 -12063310.05486 1851 1837 -36666666.66065 1852 1837 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1971 1839 -59964405.70834 1972 1839 7.525086402893e-07 1973 1839 -43970603.67818 1974 1839 -20163436.42398 1975 1839 9166666.669676 1976 1839 -11639352.31406 1840 1840 531622789.3528 1841 1840 -11110935.09172 1842 1840 -4.798173904419e-06 1843 1840 -55180296.03374 1844 1840 5555467.545859 1860 1840 -5.960464477539e-08 1861 1840 22901850.42796 1862 1840 -2777733.774299 1863 1840 36666666.66064 1864 1840 -41307675.60857 1865 1840 1513866.887135 1932 1840 -5.811452865601e-07 1933 1840 -19232220.47929 1934 1840 -694433.4439163 1935 1840 -9166666.669679 1936 1840 -17307688.72007 1937 1840 9079855.613715 1950 1840 3.635883331299e-06 1951 1840 32278708.78388 1952 1840 -2777733.774297 1953 1840 -5.349516868591e-06 1954 1840 -41940891.5735 1955 1840 36472200.21471 1971 1840 3.725290298462e-07 1972 1840 -19630743.20649 1973 1840 -694433.4439167 1974 1840 9166666.669676 1975 1840 -17413237.96253 1976 1840 9149300.058182 1841 1841 599591912.5003 1842 1841 231485.1485663 1843 1841 5555467.545859 1844 1841 78550735.85485 1860 1841 -462970.2969232 1861 1841 -2777733.774298 1862 1841 39890623.87246 1863 1841 -2737270.351624 1864 1841 1541644.664895 1865 1841 -7895194.184061 1932 1841 43704396.30741 1933 1841 -694433.4439163 1934 1841 -56581165.5979 1935 1841 11581481.02689 1936 1841 9079855.613715 1937 1841 -20589184.71456 1950 1841 231485.148585 1951 1841 -2777733.774298 1952 1841 -118440658.1206 1953 1841 57871.28717716 1954 1841 36444422.43695 1955 1841 -55417829.51533 1971 1841 -43935881.45598 1972 1841 -694433.4439167 1973 1841 -57643892.87044 1974 1841 -11639352.31406 1975 1841 9149300.058182 1976 1841 -20870649.36111 1842 1842 619629140.0329 1843 1842 1.168251037598e-05 1844 1842 925940.5938052 1845 1842 84152766.23505 1846 1842 -4.991888999939e-06 1847 1842 231485.148566 1860 1842 -52284795.20658 1861 1842 -36666666.66065 1862 1842 2505785.203048 1863 1842 -138432799.5 1864 1842 1.490116119385e-07 1865 1842 -462970.296923 1866 1842 -52308469.44899 1867 1842 36666666.66065 1868 1842 -2702548.129425 1932 1842 -18569369.18862 1933 1842 9166666.669678 1934 1842 10279397.69313 1935 1842 -59565882.98117 1936 1842 4.91738319397e-07 1937 1842 43739118.52961 1938 1842 -20057887.18154 1939 1842 -9166666.669679 1940 1842 11581481.02689 1950 1842 -1129879.778007 1951 1842 2.369284629822e-06 1952 1842 57871.28717239 1953 1842 54280296.46473 1954 1842 3.09944152832e-06 1955 1842 231485.1485852 1956 1842 -7107625.989141 1957 1842 -6.146728992462e-06 1958 1842 57871.2871768 1971 1842 -18663081.30986 1972 1842 -9166666.669677 1973 1842 -10337268.9803 1974 1842 -59964405.70834 1975 1842 7.525086402893e-07 1976 1842 -43970603.67818 1977 1842 -20163436.42398 1978 1842 9166666.669676 1979 1842 -11639352.31406 1843 1843 531622789.3528 1844 1843 -11110935.09172 1845 1843 -4.798173904419e-06 1846 1843 -55180296.03374 1847 1843 5555467.545859 1860 1843 -36666666.66065 1861 1843 -41284001.36615 1862 1843 1263866.887163 1863 1843 -5.960464477539e-08 1864 1843 22901850.42796 1865 1843 -2777733.774299 1866 1843 36666666.66064 1867 1843 -41307675.60857 1868 1843 1513866.887135 1932 1843 9166666.669678 1933 1843 -15819170.72716 1934 1843 -8385422.169798 1935 1843 -5.811452865601e-07 1936 1843 -19232220.47929 1937 1843 -694433.4439163 1938 1843 -9166666.669679 1939 1843 -17307688.72007 1940 1843 9079855.613715 1950 1843 2.913177013397e-06 1951 1843 -35963145.36236 1952 1843 -33694466.44041 1953 1843 3.635883331299e-06 1954 1843 32278708.78388 1955 1843 -2777733.774297 1956 1843 -5.349516868591e-06 1957 1843 -41940891.5735 1958 1843 36472200.21471 1971 1843 -9166666.669677 1972 1843 -15912882.8484 1973 1843 -8454866.614265 1974 1843 3.725290298462e-07 1975 1843 -19630743.20649 1976 1843 -694433.4439167 1977 1843 9166666.669676 1978 1843 -17413237.96253 1979 1843 9149300.058182 1844 1844 599591912.5003 1845 1844 231485.1485663 1846 1844 5555467.545859 1847 1844 78550735.85485 1860 1844 2471062.980849 1861 1844 1236089.109403 1862 1844 -7832062.870945 1863 1844 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-4.798173904419e-06 1849 1846 -55180296.03374 1850 1846 5555467.545859 1863 1846 -36666666.66065 1864 1846 -41284001.36615 1865 1846 1263866.887163 1866 1846 -5.960464477539e-08 1867 1846 22901850.42796 1868 1846 -2777733.774299 1869 1846 36666666.66064 1870 1846 -41307675.60857 1871 1846 1513866.887135 1935 1846 9166666.669678 1936 1846 -15819170.72716 1937 1846 -8385422.169798 1938 1846 -5.811452865601e-07 1939 1846 -19232220.47929 1940 1846 -694433.4439163 1941 1846 -9166666.669679 1942 1846 -17307688.72007 1943 1846 9079855.613715 1953 1846 2.913177013397e-06 1954 1846 -35963145.36236 1955 1846 -33694466.44041 1956 1846 3.635883331299e-06 1957 1846 32278708.78388 1958 1846 -2777733.774297 1959 1846 -5.349516868591e-06 1960 1846 -41940891.5735 1961 1846 36472200.21471 1974 1846 -9166666.669677 1975 1846 -15912882.8484 1976 1846 -8454866.614265 1977 1846 3.725290298462e-07 1978 1846 -19630743.20649 1979 1846 -694433.4439167 1980 1846 9166666.669676 1981 1846 -17413237.96253 1982 1846 9149300.058182 1847 1847 599591912.5003 1848 1847 231485.1485663 1849 1847 5555467.545859 1850 1847 78550735.85485 1863 1847 2471062.980849 1864 1847 1236089.109403 1865 1847 -7832062.870945 1866 1847 -462970.2969232 1867 1847 -2777733.774298 1868 1847 39890623.87246 1869 1847 -2737270.351624 1870 1847 1541644.664895 1871 1847 -7895194.184061 1935 1847 10279397.69313 1936 1847 -8385422.169798 1937 1847 -16619803.40013 1938 1847 43704396.30741 1939 1847 -694433.4439163 1940 1847 -56581165.5979 1941 1847 11581481.02689 1942 1847 9079855.613715 1943 1847 -20589184.71456 1953 1847 57871.28717278 1954 1847 -33666688.66265 1955 1847 -39477172.9523 1956 1847 231485.148585 1957 1847 -2777733.774298 1958 1847 -118440658.1206 1959 1847 57871.28717716 1960 1847 36444422.43695 1961 1847 -55417829.51533 1974 1847 -10337268.9803 1975 1847 -8454866.614265 1976 1847 -16869702.39011 1977 1847 -43935881.45598 1978 1847 -694433.4439167 1979 1847 -57643892.87044 1980 1847 -11639352.31406 1981 1847 9149300.058182 1982 1847 -20870649.36111 1848 1848 619629140.0329 1849 1848 1.168251037598e-05 1850 1848 925940.5938052 1851 1848 84152766.23505 1852 1848 -4.991888999939e-06 1853 1848 231485.148566 1866 1848 -52284795.20658 1867 1848 -36666666.66065 1868 1848 2505785.203048 1869 1848 -138432799.5 1870 1848 1.490116119385e-07 1871 1848 -462970.296923 1872 1848 -52308469.44899 1873 1848 36666666.66065 1874 1848 -2702548.129425 1938 1848 -18569369.18862 1939 1848 9166666.669678 1940 1848 10279397.69313 1941 1848 -59565882.98117 1942 1848 4.91738319397e-07 1943 1848 43739118.52961 1944 1848 -20057887.18154 1945 1848 -9166666.669679 1946 1848 11581481.02689 1956 1848 -1129879.778007 1957 1848 2.369284629822e-06 1958 1848 57871.28717239 1959 1848 54280296.46473 1960 1848 3.09944152832e-06 1961 1848 231485.1485852 1962 1848 -7107625.989141 1963 1848 -6.146728992462e-06 1964 1848 57871.2871768 1977 1848 -18663081.30986 1978 1848 -9166666.669677 1979 1848 -10337268.9803 1980 1848 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1853 57871.28717278 1960 1853 -33666688.66265 1961 1853 -39477172.9523 1962 1853 231485.148585 1963 1853 -2777733.774298 1964 1853 -118440658.1206 1965 1853 57871.28717716 1966 1853 36444422.43695 1967 1853 -55417829.51533 1980 1853 -10337268.9803 1981 1853 -8454866.614265 1982 1853 -16869702.39011 1983 1853 -43935881.45598 1984 1853 -694433.4439167 1985 1853 -57643892.87044 1986 1853 -11639352.31406 1987 1853 9149300.058182 1988 1853 -20870649.36111 1854 1854 525679167.9811 1855 1854 18390868.10895 1856 1854 257230.0209704 1857 1854 -103629435.2263 1858 1854 -78331026.88709 1859 1854 634702.4175476 1872 1854 -52284795.20658 1873 1854 -36666666.66065 1874 1854 2505785.203048 1875 1854 -86773795.75742 1876 1854 24416035.48061 1877 1854 -106696.56214 1878 1854 -50334865.85163 1879 1854 7750891.435108 1880 1854 -153554.2915443 1944 1854 -18569369.18862 1945 1854 9166666.669678 1946 1854 10279397.69313 1947 1854 -27520936.3574 1948 1854 6808951.285619 1949 1854 24530109.1485 1962 1854 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299795956.2502 1863 1862 723381.4630278 1864 1862 2805511.550704 1865 1862 39276420.11598 1950 1862 43704396.30741 1951 1862 -694433.4439163 1952 1862 -56581165.5979 1953 1862 11581481.02689 1954 1862 9079855.613715 1955 1862 -20589184.71456 1971 1862 8796437.017353 1972 1862 -1388866.887151 1973 1862 -59221381.24884 1974 1862 2351018.977684 1975 1862 18229155.66292 1976 1862 -27708914.75766 1863 1863 309814570.0165 1864 1863 6.437301635742e-06 1865 1863 462970.2969034 1866 1863 42076777.68823 1867 1863 7333333.332127 1868 1863 -318285.203467 1950 1863 -18569369.18862 1951 1863 9166666.669678 1952 1863 10279397.69313 1953 1863 -59565882.98117 1954 1863 4.91738319397e-07 1955 1863 43739118.52961 1956 1863 -20057887.18154 1957 1863 -9166666.669679 1958 1863 11581481.02689 1971 1863 -564939.8890041 1972 1863 -1833333.333934 1973 1863 -2032731.023757 1974 1863 27139753.66166 1975 1863 8.344650268555e-07 1976 1863 -8738562.979764 1977 1863 -3553812.994569 1978 1863 1833333.333932 1979 1863 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1865 -19738586.47615 1974 1865 8796437.017353 1975 1865 -1388866.887151 1976 1865 -59221381.24884 1977 1865 2351018.977684 1978 1865 18229155.66292 1979 1865 -27708914.75766 1866 1866 309814570.0165 1867 1866 6.437301635742e-06 1868 1866 462970.2969034 1869 1866 42076777.68823 1870 1866 7333333.332127 1871 1866 -318285.203467 1953 1866 -18569369.18862 1954 1866 9166666.669678 1955 1866 10279397.69313 1956 1866 -59565882.98117 1957 1866 4.91738319397e-07 1958 1866 43739118.52961 1959 1866 -20057887.18154 1960 1866 -9166666.669679 1961 1866 11581481.02689 1974 1866 -564939.8890041 1975 1866 -1833333.333934 1976 1866 -2032731.023757 1977 1866 27139753.66166 1978 1866 8.344650268555e-07 1979 1866 -8738562.979764 1980 1866 -3553812.994569 1981 1866 1833333.333932 1982 1866 -2293147.690507 1867 1867 265811394.6764 1868 1867 -5555467.545855 1869 1867 -7333333.332131 1870 1867 -27589753.44616 1871 1867 2749955.995158 1953 1867 9166666.669678 1954 1867 -15819170.72716 1955 1867 -8385422.169798 1956 1867 -5.811452865601e-07 1957 1867 -19232220.47929 1958 1867 -694433.4439163 1959 1867 -9166666.669679 1960 1867 -17307688.72007 1961 1867 9079855.613715 1974 1867 1833333.333937 1975 1867 -17981572.68118 1976 1867 -16840288.77576 1977 1867 8.940696716309e-07 1978 1867 16138959.82123 1979 1867 -1388866.887151 1980 1867 -1833333.333938 1981 1867 -20970445.78675 1982 1867 18229155.66291 1868 1868 299795956.2502 1869 1868 723381.4630278 1870 1868 2805511.550704 1871 1868 39276420.11598 1953 1868 10279397.69313 1954 1868 -8385422.169798 1955 1868 -16619803.40013 1956 1868 43704396.30741 1957 1868 -694433.4439163 1958 1868 -56581165.5979 1959 1868 11581481.02689 1960 1868 9079855.613715 1961 1868 -20589184.71456 1974 1868 2090602.31093 1975 1868 -16840288.77577 1976 1868 -19738586.47615 1977 1868 8796437.017353 1978 1868 -1388866.887151 1979 1868 -59221381.24884 1980 1868 2351018.977684 1981 1868 18229155.66292 1982 1868 -27708914.75766 1869 1869 309814570.0165 1870 1869 6.437301635742e-06 1871 1869 462970.2969034 1872 1869 42076777.68823 1873 1869 7333333.332127 1874 1869 -318285.203467 1956 1869 -18569369.18862 1957 1869 9166666.669678 1958 1869 10279397.69313 1959 1869 -59565882.98117 1960 1869 4.91738319397e-07 1961 1869 43739118.52961 1962 1869 -20057887.18154 1963 1869 -9166666.669679 1964 1869 11581481.02689 1977 1869 -564939.8890041 1978 1869 -1833333.333934 1979 1869 -2032731.023757 1980 1869 27139753.66166 1981 1869 8.344650268555e-07 1982 1869 -8738562.979764 1983 1869 -3553812.994569 1984 1869 1833333.333932 1985 1869 -2293147.690507 1870 1870 265811394.6764 1871 1870 -5555467.545855 1872 1870 -7333333.332131 1873 1870 -27589753.44616 1874 1870 2749955.995158 1956 1870 9166666.669678 1957 1870 -15819170.72716 1958 1870 -8385422.169798 1959 1870 -5.811452865601e-07 1960 1870 -19232220.47929 1961 1870 -694433.4439163 1962 1870 -9166666.669679 1963 1870 -17307688.72007 1964 1870 9079855.613715 1977 1870 1833333.333937 1978 1870 -17981572.68118 1979 1870 -16840288.77576 1980 1870 8.940696716309e-07 1981 1870 16138959.82123 1982 1870 -1388866.887151 1983 1870 -1833333.333938 1984 1870 -20970445.78675 1985 1870 18229155.66291 1871 1871 299795956.2502 1872 1871 723381.4630278 1873 1871 2805511.550704 1874 1871 39276420.11598 1956 1871 10279397.69313 1957 1871 -8385422.169798 1958 1871 -16619803.40013 1959 1871 43704396.30741 1960 1871 -694433.4439163 1961 1871 -56581165.5979 1962 1871 11581481.02689 1963 1871 9079855.613715 1964 1871 -20589184.71456 1977 1871 2090602.31093 1978 1871 -16840288.77577 1979 1871 -19738586.47615 1980 1871 8796437.017353 1981 1871 -1388866.887151 1982 1871 -59221381.24884 1983 1871 2351018.977684 1984 1871 18229155.66292 1985 1871 -27708914.75766 1872 1872 309814570.0165 1873 1872 6.437301635742e-06 1874 1872 462970.2969034 1875 1872 42076777.68823 1876 1872 7333333.332127 1877 1872 -318285.203467 1959 1872 -18569369.18862 1960 1872 9166666.669678 1961 1872 10279397.69313 1962 1872 -59565882.98117 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723381.4630278 1876 1874 2805511.550704 1877 1874 39276420.11598 1959 1874 10279397.69313 1960 1874 -8385422.169798 1961 1874 -16619803.40013 1962 1874 43704396.30741 1963 1874 -694433.4439163 1964 1874 -56581165.5979 1965 1874 11581481.02689 1966 1874 9079855.613715 1967 1874 -20589184.71456 1980 1874 2090602.31093 1981 1874 -16840288.77577 1982 1874 -19738586.47615 1983 1874 8796437.017353 1984 1874 -1388866.887151 1985 1874 -59221381.24884 1986 1874 2351018.977684 1987 1874 18229155.66292 1988 1874 -27708914.75766 1875 1875 309250160.3896 1876 1875 4535517.963994 1877 1875 2453066.565954 1878 1875 -8612767.502989 1879 1875 -26152871.16708 1880 1875 379949.2240047 1962 1875 -18569369.18862 1963 1875 9166666.669678 1964 1875 10279397.69313 1965 1875 -43745996.76765 1966 1875 6104008.873162 1967 1875 33740166.13061 1968 1875 -19561074.78605 1969 1875 -8033003.905467 1970 1875 11036649.36321 1983 1875 -564939.8890041 1984 1875 -1833333.333934 1985 1875 -2032731.023757 1986 1875 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231485.105844 1927 1925 5388801.904579 1928 1925 80699306.16691 1935 1925 2523146.335561 1936 1925 1277756.032423 1937 1925 -7296493.499545 1938 1925 -254636.8781728 1939 1925 -2777734.286976 1940 1925 42039227.65673 1941 1925 -2685186.996909 1942 1925 1499978.254554 1943 1925 -7359624.812662 2019 1925 10539814.37052 2020 1925 -8593755.37553 2021 1925 -17106970.31658 2022 1925 44746063.01646 2023 1925 -694433.6992574 2024 1925 -58719220.64359 2025 1925 11841897.70428 2026 1925 9288189.074786 2027 1925 -21171048.60074 2031 1925 57871.26589252 2032 1925 -34500021.48517 2033 1925 -41438476.99211 2034 1925 231485.0634617 2035 1925 -2777734.795662 2036 1925 -127043423.7988 2037 1925 57871.26589543 2038 1925 37277756.28083 2039 1925 -57757921.43384 2046 1925 -10597685.63642 2047 1925 -8663199.819997 2048 1925 -17363182.43788 2049 1925 -44977548.07992 2050 1925 -694433.6992576 2051 1925 -59807200.44138 2052 1925 -11899768.97017 2053 1925 9357633.519253 2054 1925 -21458826.37861 1926 1926 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9357633.519253 1943 1943 608211498.9432 1944 1943 231485.105844 1945 1943 5388801.904579 1946 1943 80699306.16691 1956 1943 2523146.335561 1957 1943 1277756.032423 1958 1943 -7296493.499545 1959 1943 -254636.8781728 1960 1943 -2777734.286976 1961 1943 42039227.65673 1962 1943 -2685186.996909 1963 1943 1499978.254554 1964 1943 -7359624.812662 2034 1943 10539814.37052 2035 1943 -8593755.37553 2036 1943 -17106970.31658 2037 1943 44746063.01646 2038 1943 -694433.6992574 2039 1943 -58719220.64359 2040 1943 11841897.70428 2041 1943 9288189.074786 2042 1943 -21171048.60074 2049 1943 57871.26589252 2050 1943 -34500021.48517 2051 1943 -41438476.99211 2052 1943 231485.0634617 2053 1943 -2777734.795662 2054 1943 -127043423.7988 2055 1943 57871.26589543 2056 1943 37277756.28083 2057 1943 -57757921.43384 2067 1943 -10597685.63642 2068 1943 -8663199.819997 2069 1943 -17363182.43788 2070 1943 -44977548.07992 2071 1943 -694433.6992576 2072 1943 -59807200.44138 2073 1943 -11899768.97017 2074 1943 9357633.519253 2075 1943 -21458826.37861 1944 1944 674759689.9124 1945 1944 36667415.0414 1946 1944 3125092.975185 1947 1944 20137287.77529 1948 1944 -36666966.01295 1949 1944 2754655.071165 1959 1944 -52083950.29126 1960 1944 -36666666.66065 1961 1944 2453701.89106 1962 1944 -137627039.3558 1963 1944 -2.235174179077e-07 1964 1944 -671303.5447711 1965 1944 -52107624.53367 1966 1944 36666666.66065 1967 1944 -2754631.441411 2037 1944 -18752053.59425 2038 1944 9166666.66968 2039 1944 10539814.37052 2040 1944 -72726245.22972 2041 1944 -9166776.303506 2042 1944 44231216.90386 2052 1944 -1865379.213624 2053 1944 8.79168510437e-07 2054 1944 57871.26589221 2055 1944 70575234.21716 2056 1944 9166849.392726 2057 1944 781227.3439141 2058 1944 -20203256.3538 2059 1944 -9166739.758899 2060 1944 11899863.74724 2070 1944 -18848133.13973 2071 1944 -9166666.66968 2072 1944 -10597685.63642 2073 1944 -60775629.25067 2074 1944 -1.214444637299e-06 2075 1944 -45012270.30212 2076 1944 -20383999.6175 2077 1944 9166666.669679 2078 1944 -11899768.97017 1945 1945 575752291.8369 1946 1945 -8610912.053949 1947 1945 -36667115.6891 1948 1945 -108195591.755 1949 1945 4777685.365654 1959 1945 -36666666.66065 1960 1945 -41083165.69975 1961 1945 1222200.476822 1962 1945 4.470348358154e-07 1963 1945 23707595.23204 1964 1945 -2777734.286976 1965 1945 36666666.66065 1966 1945 -41106839.94217 1967 1945 1555533.810155 2037 1945 9166666.66968 2038 1945 -16001859.73922 2039 1945 -8593755.37553 2040 1945 -9166739.758897 2041 1945 -29642168.10562 2042 1945 8204934.122165 2052 1945 1.229345798492e-06 2053 1945 -36698646.37071 2054 1945 -34527799.26293 2055 1945 9166849.392726 2056 1945 45823407.30156 2057 1945 -2152765.098743 2058 1945 -9166776.303508 2059 1945 -52286475.83204 2060 1945 37069600.58987 2070 1945 -9166666.669679 2071 1945 -16097939.2847 2072 1945 -8663199.819997 2073 1945 -1.445412635803e-06 2074 1945 -20441974.38895 2075 1945 -694433.6992576 2076 1945 9166666.669678 2077 1945 -17633805.76247 2078 1945 9357633.519253 1946 1946 615008779.2968 1947 1946 2685222.441543 1948 1946 5222139.640517 1949 1946 39437488.39575 1959 1946 2523146.335561 1960 1946 1277756.032423 1961 1946 -7296493.499545 1962 1946 -254636.8781728 1963 1946 -2777734.286976 1964 1946 42039227.65673 1965 1946 -2685186.996909 1966 1946 1499978.254554 1967 1946 -7359624.812662 2037 1946 10539814.37052 2038 1946 -8593755.37553 2039 1946 -17106970.31658 2040 1946 44196492.14387 2041 1946 8010523.495484 2042 1946 -58776166.2905 2052 1946 57871.26589252 2053 1946 -34500021.48517 2054 1946 -41438476.99211 2055 1946 781316.8545274 2056 1946 -2152693.49136 2057 1946 -107886912.3736 2058 1946 11899911.13577 2059 1946 37236269.31883 2060 1946 -57440830.58835 2070 1946 -10597685.63642 2071 1946 -8663199.819997 2072 1946 -17363182.43788 2073 1946 -44977548.07992 2074 1946 -694433.6992576 2075 1946 -59807200.44138 2076 1946 -11899768.97017 2077 1946 9357633.519253 2078 1946 -21458826.37861 1947 1947 434012491.322 1948 1947 -26709105.05296 1949 1947 -725793.543576 1962 1947 -52083950.29126 1963 1947 -36666666.66065 1964 1947 2453701.89106 1965 1947 -56549866.20531 1966 1947 26704759.61057 1967 1947 -385264.5612573 1968 1947 -222386913.2778 1969 1947 29337678.77091 1970 1947 -277833.5794091 2040 1947 -5106206.927443 2041 1947 11000109.63744 2042 1947 12682625.90274 2055 1947 -15511422.68773 2056 1947 -9166776.303506 2057 1947 -10539940.2691 2058 1947 57002220.2306 2059 1947 -6544915.940513 2060 1947 4861555.215121 2073 1947 -18848133.13973 2074 1947 -9166666.66968 2075 1947 -10597685.63642 2076 1947 -29177118.41547 2077 1947 6543892.420132 2078 1947 -25729678.71087 2079 1947 -53961140.25394 2080 1947 7334356.856125 2081 1947 -1354081.113647 1948 1948 781040484.4929 1949 1948 -10574395.88396 1962 1948 -36666666.66065 1963 1948 -41083165.69975 1964 1948 1222200.476822 1965 1948 26702586.88937 1966 1948 87287357.54424 1967 1948 -1789762.243781 1968 1948 44006518.15637 1969 1948 -595920035.2594 1970 1948 5142261.375664 2040 1948 7333406.424962 2041 1948 -5106206.927443 2042 1948 -6763956.526763 2055 1948 -9166739.758897 2056 1948 -47594642.16596 2057 1948 -34569643.89832 2058 1948 -6544915.940513 2059 1948 138242633.1703 2060 1948 1389850.346674 2073 1948 -9166666.669679 2074 1948 -16097939.2847 2075 1948 -8663199.819997 2076 1948 6543380.659941 2077 1948 6841374.023334 2078 1948 5925066.094897 2079 1948 11001535.28419 2080 1948 -141887020.0092 2081 1948 18142632.26191 1949 1949 467013145.2305 1962 1949 2523146.335561 1963 1949 1277756.032423 1964 1949 -7296493.499545 1965 1949 -940793.6136686 1966 1949 -1678594.911864 1967 1949 48688638.16036 1968 1949 -416750.3691136 1969 1949 5031214.44564 1970 1949 -219498646.7591 2040 1949 8455083.935158 2041 1949 -10145934.79014 2042 1949 -13616551.80652 2055 1949 -10539898.30291 2056 1949 -34736312.74845 2057 1949 -44929274.14549 2058 1949 -5398901.65238 2059 1949 -6817695.611917 2060 1949 -15837053.95701 2073 1949 -10597685.63642 2074 1949 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534855157.0519 1952 1951 -11110937.14243 1953 1951 -3.457069396973e-06 1954 1951 -54374606.24745 1955 1951 5722135.237857 1971 1951 4.470348358154e-07 1972 1951 23707595.23204 1973 1951 -2777734.286976 1974 1951 36666666.66065 1975 1951 -41106839.94217 1976 1951 1555533.810155 2043 1951 1.169741153717e-06 2044 1951 -20033981.96478 2045 1951 -694433.6992575 2046 1951 -9166666.66968 2047 1951 -17525889.09577 2048 1951 9288189.074786 2061 1951 1.966953277588e-06 2062 1951 29052683.00161 2063 1951 -2777734.795662 2064 1951 -2.190470695496e-06 2065 1951 -42818438.03636 2066 1951 37305534.05859 2082 1951 -1.445412635803e-06 2083 1951 -20441974.38895 2084 1951 -694433.6992576 2085 1951 9166666.669678 2086 1951 -17633805.76247 2087 1951 9357633.519253 1952 1952 608211498.9432 1953 1952 231485.105844 1954 1952 5388801.904579 1955 1952 80699306.16691 1971 1952 -254636.8781728 1972 1952 -2777734.286976 1973 1952 42039227.65673 1974 1952 -2685186.996909 1975 1952 1499978.254554 1976 1952 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2048 1953 44780785.23866 2049 1953 -20276082.95081 2050 1953 -9166666.66968 2051 1953 11841897.70428 2061 1953 -1865379.213624 2062 1953 8.79168510437e-07 2063 1953 57871.26589221 2064 1953 51054233.83102 2065 1953 1.788139343262e-06 2066 1953 231485.0634618 2067 1953 -7985170.87927 2068 1953 -2.771615982056e-06 2069 1953 57871.2658952 2082 1953 -18848133.13973 2083 1953 -9166666.66968 2084 1953 -10597685.63642 2085 1953 -60775629.25067 2086 1953 -1.214444637299e-06 2087 1953 -45012270.30212 2088 1953 -20383999.6175 2089 1953 9166666.669679 2090 1953 -11899768.97017 1954 1954 534855157.0519 1955 1954 -11110937.14243 1956 1954 -3.457069396973e-06 1957 1954 -54374606.24745 1958 1954 5722135.237857 1971 1954 -36666666.66065 1972 1954 -41083165.69975 1973 1954 1222200.476822 1974 1954 4.470348358154e-07 1975 1954 23707595.23204 1976 1954 -2777734.286976 1977 1954 36666666.66065 1978 1954 -41106839.94217 1979 1954 1555533.810155 2043 1954 9166666.66968 2044 1954 -16001859.73922 2045 1954 -8593755.37553 2046 1954 1.169741153717e-06 2047 1954 -20033981.96478 2048 1954 -694433.6992575 2049 1954 -9166666.66968 2050 1954 -17525889.09577 2051 1954 9288189.074786 2061 1954 1.229345798492e-06 2062 1954 -36698646.37071 2063 1954 -34527799.26293 2064 1954 1.966953277588e-06 2065 1954 29052683.00161 2066 1954 -2777734.795662 2067 1954 -2.190470695496e-06 2068 1954 -42818438.03636 2069 1954 37305534.05859 2082 1954 -9166666.669679 2083 1954 -16097939.2847 2084 1954 -8663199.819997 2085 1954 -1.445412635803e-06 2086 1954 -20441974.38895 2087 1954 -694433.6992576 2088 1954 9166666.669678 2089 1954 -17633805.76247 2090 1954 9357633.519253 1955 1955 608211498.9432 1956 1955 231485.105844 1957 1955 5388801.904579 1958 1955 80699306.16691 1971 1955 2523146.335561 1972 1955 1277756.032423 1973 1955 -7296493.499545 1974 1955 -254636.8781728 1975 1955 -2777734.286976 1976 1955 42039227.65673 1977 1955 -2685186.996909 1978 1955 1499978.254554 1979 1955 -7359624.812662 2043 1955 10539814.37052 2044 1955 -8593755.37553 2045 1955 -17106970.31658 2046 1955 44746063.01646 2047 1955 -694433.6992574 2048 1955 -58719220.64359 2049 1955 11841897.70428 2050 1955 9288189.074786 2051 1955 -21171048.60074 2061 1955 57871.26589252 2062 1955 -34500021.48517 2063 1955 -41438476.99211 2064 1955 231485.0634617 2065 1955 -2777734.795662 2066 1955 -127043423.7988 2067 1955 57871.26589543 2068 1955 37277756.28083 2069 1955 -57757921.43384 2082 1955 -10597685.63642 2083 1955 -8663199.819997 2084 1955 -17363182.43788 2085 1955 -44977548.07992 2086 1955 -694433.6992576 2087 1955 -59807200.44138 2088 1955 -11899768.97017 2089 1955 9357633.519253 2090 1955 -21458826.37861 1956 1956 622861433.7406 1957 1956 1.120567321777e-05 1958 1956 925940.4229136 1959 1956 84958459.17911 1960 1956 -5.066394805908e-06 1961 1956 231485.1058435 1974 1956 -52083950.29126 1975 1956 -36666666.66065 1976 1956 2453701.89106 1977 1956 -137627039.3558 1978 1956 -2.235174179077e-07 1979 1956 -671303.5447711 1980 1956 -52107624.53367 1981 1956 36666666.66065 1982 1956 -2754631.441411 2046 1956 -18752053.59425 2047 1956 9166666.66968 2048 1956 10539814.37052 2049 1956 -60367636.82651 2050 1956 1.877546310425e-06 2051 1956 44780785.23866 2052 1956 -20276082.95081 2053 1956 -9166666.66968 2054 1956 11841897.70428 2064 1956 -1865379.213624 2065 1956 8.79168510437e-07 2066 1956 57871.26589221 2067 1956 51054233.83102 2068 1956 1.788139343262e-06 2069 1956 231485.0634618 2070 1956 -7985170.87927 2071 1956 -2.771615982056e-06 2072 1956 57871.2658952 2085 1956 -18848133.13973 2086 1956 -9166666.66968 2087 1956 -10597685.63642 2088 1956 -60775629.25067 2089 1956 -1.214444637299e-06 2090 1956 -45012270.30212 2091 1956 -20383999.6175 2092 1956 9166666.669679 2093 1956 -11899768.97017 1957 1957 534855157.0519 1958 1957 -11110937.14243 1959 1957 -3.457069396973e-06 1960 1957 -54374606.24745 1961 1957 5722135.237857 1974 1957 -36666666.66065 1975 1957 -41083165.69975 1976 1957 1222200.476822 1977 1957 4.470348358154e-07 1978 1957 23707595.23204 1979 1957 -2777734.286976 1980 1957 36666666.66065 1981 1957 -41106839.94217 1982 1957 1555533.810155 2046 1957 9166666.66968 2047 1957 -16001859.73922 2048 1957 -8593755.37553 2049 1957 1.169741153717e-06 2050 1957 -20033981.96478 2051 1957 -694433.6992575 2052 1957 -9166666.66968 2053 1957 -17525889.09577 2054 1957 9288189.074786 2064 1957 1.229345798492e-06 2065 1957 -36698646.37071 2066 1957 -34527799.26293 2067 1957 1.966953277588e-06 2068 1957 29052683.00161 2069 1957 -2777734.795662 2070 1957 -2.190470695496e-06 2071 1957 -42818438.03636 2072 1957 37305534.05859 2085 1957 -9166666.669679 2086 1957 -16097939.2847 2087 1957 -8663199.819997 2088 1957 -1.445412635803e-06 2089 1957 -20441974.38895 2090 1957 -694433.6992576 2091 1957 9166666.669678 2092 1957 -17633805.76247 2093 1957 9357633.519253 1958 1958 608211498.9432 1959 1958 231485.105844 1960 1958 5388801.904579 1961 1958 80699306.16691 1974 1958 2523146.335561 1975 1958 1277756.032423 1976 1958 -7296493.499545 1977 1958 -254636.8781728 1978 1958 -2777734.286976 1979 1958 42039227.65673 1980 1958 -2685186.996909 1981 1958 1499978.254554 1982 1958 -7359624.812662 2046 1958 10539814.37052 2047 1958 -8593755.37553 2048 1958 -17106970.31658 2049 1958 44746063.01646 2050 1958 -694433.6992574 2051 1958 -58719220.64359 2052 1958 11841897.70428 2053 1958 9288189.074786 2054 1958 -21171048.60074 2064 1958 57871.26589252 2065 1958 -34500021.48517 2066 1958 -41438476.99211 2067 1958 231485.0634617 2068 1958 -2777734.795662 2069 1958 -127043423.7988 2070 1958 57871.26589543 2071 1958 37277756.28083 2072 1958 -57757921.43384 2085 1958 -10597685.63642 2086 1958 -8663199.819997 2087 1958 -17363182.43788 2088 1958 -44977548.07992 2089 1958 -694433.6992576 2090 1958 -59807200.44138 2091 1958 -11899768.97017 2092 1958 9357633.519253 2093 1958 -21458826.37861 1959 1959 622861433.7406 1960 1959 1.120567321777e-05 1961 1959 925940.4229136 1962 1959 84958459.17911 1963 1959 -5.066394805908e-06 1964 1959 231485.1058435 1977 1959 -52083950.29126 1978 1959 -36666666.66065 1979 1959 2453701.89106 1980 1959 -137627039.3558 1981 1959 -2.235174179077e-07 1982 1959 -671303.5447711 1983 1959 -52107624.53367 1984 1959 36666666.66065 1985 1959 -2754631.441411 2049 1959 -18752053.59425 2050 1959 9166666.66968 2051 1959 10539814.37052 2052 1959 -60367636.82651 2053 1959 1.877546310425e-06 2054 1959 44780785.23866 2055 1959 -20276082.95081 2056 1959 -9166666.66968 2057 1959 11841897.70428 2067 1959 -1865379.213624 2068 1959 8.79168510437e-07 2069 1959 57871.26589221 2070 1959 51054233.83102 2071 1959 1.788139343262e-06 2072 1959 231485.0634618 2073 1959 -7985170.87927 2074 1959 -2.771615982056e-06 2075 1959 57871.2658952 2088 1959 -18848133.13973 2089 1959 -9166666.66968 2090 1959 -10597685.63642 2091 1959 -60775629.25067 2092 1959 -1.214444637299e-06 2093 1959 -45012270.30212 2094 1959 -20383999.6175 2095 1959 9166666.669679 2096 1959 -11899768.97017 1960 1960 534855157.0519 1961 1960 -11110937.14243 1962 1960 -3.457069396973e-06 1963 1960 -54374606.24745 1964 1960 5722135.237857 1977 1960 -36666666.66065 1978 1960 -41083165.69975 1979 1960 1222200.476822 1980 1960 4.470348358154e-07 1981 1960 23707595.23204 1982 1960 -2777734.286976 1983 1960 36666666.66065 1984 1960 -41106839.94217 1985 1960 1555533.810155 2049 1960 9166666.66968 2050 1960 -16001859.73922 2051 1960 -8593755.37553 2052 1960 1.169741153717e-06 2053 1960 -20033981.96478 2054 1960 -694433.6992575 2055 1960 -9166666.66968 2056 1960 -17525889.09577 2057 1960 9288189.074786 2067 1960 1.229345798492e-06 2068 1960 -36698646.37071 2069 1960 -34527799.26293 2070 1960 1.966953277588e-06 2071 1960 29052683.00161 2072 1960 -2777734.795662 2073 1960 -2.190470695496e-06 2074 1960 -42818438.03636 2075 1960 37305534.05859 2088 1960 -9166666.669679 2089 1960 -16097939.2847 2090 1960 -8663199.819997 2091 1960 -1.445412635803e-06 2092 1960 -20441974.38895 2093 1960 -694433.6992576 2094 1960 9166666.669678 2095 1960 -17633805.76247 2096 1960 9357633.519253 1961 1961 608211498.9432 1962 1961 231485.105844 1963 1961 5388801.904579 1964 1961 80699306.16691 1977 1961 2523146.335561 1978 1961 1277756.032423 1979 1961 -7296493.499545 1980 1961 -254636.8781728 1981 1961 -2777734.286976 1982 1961 42039227.65673 1983 1961 -2685186.996909 1984 1961 1499978.254554 1985 1961 -7359624.812662 2049 1961 10539814.37052 2050 1961 -8593755.37553 2051 1961 -17106970.31658 2052 1961 44746063.01646 2053 1961 -694433.6992574 2054 1961 -58719220.64359 2055 1961 11841897.70428 2056 1961 9288189.074786 2057 1961 -21171048.60074 2067 1961 57871.26589252 2068 1961 -34500021.48517 2069 1961 -41438476.99211 2070 1961 231485.0634617 2071 1961 -2777734.795662 2072 1961 -127043423.7988 2073 1961 57871.26589543 2074 1961 37277756.28083 2075 1961 -57757921.43384 2088 1961 -10597685.63642 2089 1961 -8663199.819997 2090 1961 -17363182.43788 2091 1961 -44977548.07992 2092 1961 -694433.6992576 2093 1961 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42478440.44814 1975 1971 7333333.332128 1976 1971 -578701.8915792 2061 1971 -60367636.82651 2062 1971 1.877546310425e-06 2063 1971 44780785.23866 2064 1971 -20276082.95081 2065 1971 -9166666.66968 2066 1971 11841897.70428 2082 1971 25526722.3448 2083 1971 -5.960464477539e-08 2084 1971 -8946896.355626 2085 1971 -3992585.439634 2086 1971 1833333.333934 2087 1971 -2345231.034498 1972 1972 267422843.6775 1973 1972 -5555468.571212 1974 1972 -7333333.332131 1975 1972 -27188092.26514 1976 1972 2833289.841157 2061 1972 1.169741153717e-06 2062 1972 -20033981.96478 2063 1972 -694433.6992575 2064 1972 -9166666.66968 2065 1972 -17525889.09577 2066 1972 9288189.074786 2082 1972 6.556510925293e-07 2083 1972 14525946.9301 2084 1972 -1388867.397833 2085 1972 -1833333.333937 2086 1972 -21409219.01818 2087 1972 18645822.58485 1973 1973 304093123.209 1974 1973 462964.7749153 1975 1973 2722178.730064 1976 1973 40347548.70635 2061 1973 44746063.01646 2062 1973 -694433.6992574 2063 1973 -58719220.64359 2064 1973 11841897.70428 2065 1973 9288189.074786 2066 1973 -21171048.60074 2082 1973 9004770.308089 2083 1973 -1388867.397833 2084 1973 -63522764.08798 2085 1973 2403102.300394 2086 1973 18645822.58486 2087 1973 -28878960.71692 1974 1974 311425982.0218 1975 1974 4.053115844727e-06 1976 1974 -578696.4550389 1977 1974 42478440.44814 1978 1974 7333333.332128 1979 1974 -578701.8915792 2061 1974 -18752053.59425 2062 1974 9166666.66968 2063 1974 10539814.37052 2064 1974 -60367636.82651 2065 1974 1.877546310425e-06 2066 1974 44780785.23866 2067 1974 -20276082.95081 2068 1974 -9166666.66968 2069 1974 11841897.70428 2082 1974 -932689.6068121 2083 1974 -1833333.333935 2084 1974 -2084814.367748 2085 1974 25526722.3448 2086 1974 -5.960464477539e-08 2087 1974 -8946896.355626 2088 1974 -3992585.439634 2089 1974 1833333.333934 2090 1974 -2345231.034498 1975 1975 267422843.6775 1976 1975 -5555468.571212 1977 1975 -7333333.332131 1978 1975 -27188092.26514 1979 1975 2833289.841157 2061 1975 9166666.66968 2062 1975 -16001859.73922 2063 1975 -8593755.37553 2064 1975 1.169741153717e-06 2065 1975 -20033981.96478 2066 1975 -694433.6992575 2067 1975 -9166666.66968 2068 1975 -17525889.09577 2069 1975 9288189.074786 2082 1975 1833333.333937 2083 1975 -18349323.18536 2084 1975 -17256955.18702 2085 1975 6.556510925293e-07 2086 1975 14525946.9301 2087 1975 -1388867.397833 2088 1975 -1833333.333937 2089 1975 -21409219.01818 2090 1975 18645822.58485 1976 1976 304093123.209 1977 1976 462964.7749153 1978 1976 2722178.730064 1979 1976 40347548.70635 2061 1976 10539814.37052 2062 1976 -8593755.37553 2063 1976 -17106970.31658 2064 1976 44746063.01646 2065 1976 -694433.6992574 2066 1976 -58719220.64359 2067 1976 11841897.70428 2068 1976 9288189.074786 2069 1976 -21171048.60074 2082 1976 2142685.63364 2083 1976 -17256955.18703 2084 1976 -20719238.49606 2085 1976 9004770.308089 2086 1976 -1388867.397833 2087 1976 -63522764.08798 2088 1976 2403102.300394 2089 1976 18645822.58486 2090 1976 -28878960.71692 1977 1977 311425982.0218 1978 1977 4.053115844727e-06 1979 1977 -578696.4550389 1980 1977 42478440.44814 1981 1977 7333333.332128 1982 1977 -578701.8915792 2064 1977 -18752053.59425 2065 1977 9166666.66968 2066 1977 10539814.37052 2067 1977 -60367636.82651 2068 1977 1.877546310425e-06 2069 1977 44780785.23866 2070 1977 -20276082.95081 2071 1977 -9166666.66968 2072 1977 11841897.70428 2085 1977 -932689.6068121 2086 1977 -1833333.333935 2087 1977 -2084814.367748 2088 1977 25526722.3448 2089 1977 -5.960464477539e-08 2090 1977 -8946896.355626 2091 1977 -3992585.439634 2092 1977 1833333.333934 2093 1977 -2345231.034498 1978 1978 267422843.6775 1979 1978 -5555468.571212 1980 1978 -7333333.332131 1981 1978 -27188092.26514 1982 1978 2833289.841157 2064 1978 9166666.66968 2065 1978 -16001859.73922 2066 1978 -8593755.37553 2067 1978 1.169741153717e-06 2068 1978 -20033981.96478 2069 1978 -694433.6992575 2070 1978 -9166666.66968 2071 1978 -17525889.09577 2072 1978 9288189.074786 2085 1978 1833333.333937 2086 1978 -18349323.18536 2087 1978 -17256955.18702 2088 1978 6.556510925293e-07 2089 1978 14525946.9301 2090 1978 -1388867.397833 2091 1978 -1833333.333937 2092 1978 -21409219.01818 2093 1978 18645822.58485 1979 1979 304093123.209 1980 1979 462964.7749153 1981 1979 2722178.730064 1982 1979 40347548.70635 2064 1979 10539814.37052 2065 1979 -8593755.37553 2066 1979 -17106970.31658 2067 1979 44746063.01646 2068 1979 -694433.6992574 2069 1979 -58719220.64359 2070 1979 11841897.70428 2071 1979 9288189.074786 2072 1979 -21171048.60074 2085 1979 2142685.63364 2086 1979 -17256955.18703 2087 1979 -20719238.49606 2088 1979 9004770.308089 2089 1979 -1388867.397833 2090 1979 -63522764.08798 2091 1979 2403102.300394 2092 1979 18645822.58486 2093 1979 -28878960.71692 1980 1980 311425982.0218 1981 1980 4.053115844727e-06 1982 1980 -578696.4550389 1983 1980 42478440.44814 1984 1980 7333333.332128 1985 1980 -578701.8915792 2067 1980 -18752053.59425 2068 1980 9166666.66968 2069 1980 10539814.37052 2070 1980 -60367636.82651 2071 1980 1.877546310425e-06 2072 1980 44780785.23866 2073 1980 -20276082.95081 2074 1980 -9166666.66968 2075 1980 11841897.70428 2088 1980 -932689.6068121 2089 1980 -1833333.333935 2090 1980 -2084814.367748 2091 1980 25526722.3448 2092 1980 -5.960464477539e-08 2093 1980 -8946896.355626 2094 1980 -3992585.439634 2095 1980 1833333.333934 2096 1980 -2345231.034498 1981 1981 267422843.6775 1982 1981 -5555468.571212 1983 1981 -7333333.332131 1984 1981 -27188092.26514 1985 1981 2833289.841157 2067 1981 9166666.66968 2068 1981 -16001859.73922 2069 1981 -8593755.37553 2070 1981 1.169741153717e-06 2071 1981 -20033981.96478 2072 1981 -694433.6992575 2073 1981 -9166666.66968 2074 1981 -17525889.09577 2075 1981 9288189.074786 2088 1981 1833333.333937 2089 1981 -18349323.18536 2090 1981 -17256955.18702 2091 1981 6.556510925293e-07 2092 1981 14525946.9301 2093 1981 -1388867.397833 2094 1981 -1833333.333937 2095 1981 -21409219.01818 2096 1981 18645822.58485 1982 1982 304093123.209 1983 1982 462964.7749153 1984 1982 2722178.730064 1985 1982 40347548.70635 2067 1982 10539814.37052 2068 1982 -8593755.37553 2069 1982 -17106970.31658 2070 1982 44746063.01646 2071 1982 -694433.6992574 2072 1982 -58719220.64359 2073 1982 11841897.70428 2074 1982 9288189.074786 2075 1982 -21171048.60074 2088 1982 2142685.63364 2089 1982 -17256955.18703 2090 1982 -20719238.49606 2091 1982 9004770.308089 2092 1982 -1388867.397833 2093 1982 -63522764.08798 2094 1982 2403102.300394 2095 1982 18645822.58486 2096 1982 -28878960.71692 1983 1983 311425982.0218 1984 1983 4.053115844727e-06 1985 1983 -578696.4550389 1986 1983 42478440.44814 1987 1983 7333333.332128 1988 1983 -578701.8915792 2070 1983 -18752053.59425 2071 1983 9166666.66968 2072 1983 10539814.37052 2073 1983 -60367636.82651 2074 1983 1.877546310425e-06 2075 1983 44780785.23866 2076 1983 -20276082.95081 2077 1983 -9166666.66968 2078 1983 11841897.70428 2091 1983 -932689.6068121 2092 1983 -1833333.333935 2093 1983 -2084814.367748 2094 1983 25526722.3448 2095 1983 -5.960464477539e-08 2096 1983 -8946896.355626 2097 1983 -3992585.439634 2098 1983 1833333.333934 2099 1983 -2345231.034498 1984 1984 267422843.6775 1985 1984 -5555468.571212 1986 1984 -7333333.332131 1987 1984 -27188092.26514 1988 1984 2833289.841157 2070 1984 9166666.66968 2071 1984 -16001859.73922 2072 1984 -8593755.37553 2073 1984 1.169741153717e-06 2074 1984 -20033981.96478 2075 1984 -694433.6992575 2076 1984 -9166666.66968 2077 1984 -17525889.09577 2078 1984 9288189.074786 2091 1984 1833333.333937 2092 1984 -18349323.18536 2093 1984 -17256955.18702 2094 1984 6.556510925293e-07 2095 1984 14525946.9301 2096 1984 -1388867.397833 2097 1984 -1833333.333937 2098 1984 -21409219.01818 2099 1984 18645822.58485 1985 1985 304093123.209 1986 1985 462964.7749153 1987 1985 2722178.730064 1988 1985 40347548.70635 2070 1985 10539814.37052 2071 1985 -8593755.37553 2072 1985 -17106970.31658 2073 1985 44746063.01646 2074 1985 -694433.6992574 2075 1985 -58719220.64359 2076 1985 11841897.70428 2077 1985 9288189.074786 2078 1985 -21171048.60074 2091 1985 2142685.63364 2092 1985 -17256955.18703 2093 1985 -20719238.49606 2094 1985 9004770.308089 2095 1985 -1388867.397833 2096 1985 -63522764.08798 2097 1985 2403102.300394 2098 1985 18645822.58486 2099 1985 -28878960.71692 1986 1986 310336649.2785 1987 1986 4244617.814256 1988 1986 1415596.36294 1989 1986 -6796753.083789 1990 1986 -25401731.70095 1991 1986 61254.30470198 2073 1986 -18752053.59425 2074 1986 9166666.66968 2075 1986 10539814.37052 2076 1986 -44778234.89159 2077 1986 6015914.059352 2078 1986 35041206.59625 2079 1986 -20008769.25006 2080 1986 -8176439.889681 2081 1986 11299136.49846 2094 1986 -932689.6068121 2095 1986 -1833333.333935 2096 1986 -2084814.367748 2097 1986 25141334.84086 2098 1986 990425.5084367 2099 1986 -8447023.847856 2100 1986 -17627581.50065 2101 1986 -6163233.013846 2102 1986 7435569.639298 1987 1987 292196010.7903 1988 1987 -3573485.612244 1989 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163 -192.4000000026 42 163 -192.3999999997 157 163 -1100 163 163 1292.402525756 42 164 -192.3999999999 71 164 -192.3999999969 164 164 192.4025257558 19 165 -2236.000000018 20 165 -2236.000000018 42 165 -2236 165 165 2236.002525756 23 166 -192.4000000001 42 166 -192.3999999999 166 166 192.4025257559 25 167 -33.30000000023 157 167 -33.3 167 167 33.30252575586 24 168 -192.4000000003 42 168 -192.4000000003 168 168 192.4025257559 28 169 -192.4000000001 42 169 -192.3999999999 169 169 192.4025257559 27 170 -192.4 42 170 -192.4 170 170 192.4025257559 42 171 -192.3999999997 87 171 -192.4 171 171 192.4025257559 42 172 -192.3999999998 87 172 -192.4 172 172 192.4025257558 42 173 -192.4000000002 133 173 -192.3999999999 173 173 192.4025257559 134 174 -192.4000000002 174 174 192.4025257558 29 175 -192.4 42 175 -192.4 175 175 192.4025257559 25 176 -3199.999999985 55 176 -3200 176 176 3200.002525756 106 177 -2236 177 177 2236.002525756 40 178 -2236.000000006 42 178 -2236.000000001 178 178 2236.002525756 108 179 -2236 179 179 2236.002525756 115 180 -2236 180 180 2236.002525756 42 181 -2236.000000002 116 181 -2235.999999999 181 181 2236.002525756 117 182 -2236.000000002 182 182 2236.002525756 SuiteSparse/CSparse/Matrix/lp_afiro0000644001170100242450000000161710336456056016306 0ustar davisfac2 0 1 3 1 1 6 2 1 7 3 1 8 4 1 9 5 1 12 6 1 13 7 1 16 8 1 17 9 1 18 10 1 19 11 1 20 12 1 21 13 1 22 14 1 23 15 1 24 16 1 25 17 1 26 18 1 0 19 -1 1 19 -1.06 2 19 1 23 19 0.301 0 20 1 3 20 -1 0 21 1 21 21 -1 1 22 1 25 22 1 4 23 -1 5 23 -1.06 6 23 1 24 23 0.301 4 24 -1 5 24 -1.06 7 24 1 24 24 0.313 4 25 -1 5 25 -0.96 8 25 1 24 25 0.313 4 26 -1 5 26 -0.86 9 26 1 24 26 0.326 6 27 -1 20 27 2.364 7 28 -1 20 28 2.386 8 29 -1 20 29 2.408 9 30 -1 20 30 2.429 3 31 1.4 4 31 1 4 32 1 22 32 -1 5 33 1 26 33 1 10 34 -1 11 34 -0.43 12 34 1 21 34 0.109 10 35 1 13 35 -1 10 36 1 23 36 -1 10 37 1 20 37 -1 11 38 1 25 38 1 14 39 -0.43 15 39 1 16 39 1 22 39 0.109 14 40 -0.43 15 40 1 17 40 1 22 40 0.108 14 41 -0.39 15 41 1 18 41 1 22 41 0.108 14 42 -0.37 15 42 1 19 42 1 22 42 0.107 16 43 -1 20 43 2.191 17 44 -1 20 44 2.219 18 45 -1 20 45 2.249 19 46 -1 20 46 2.279 13 47 1.4 15 47 -1 15 48 1 24 48 -1 14 49 1 26 49 1 15 50 1 SuiteSparse/CSparse/Include/0000755001170100242450000000000010711427636014701 5ustar davisfacSuiteSparse/CSparse/Include/cs.h0000644001170100242450000001371610711427635015466 0ustar davisfac#ifndef _CS_H #define _CS_H #include #include #include #include #ifdef MATLAB_MEX_FILE #include "mex.h" #endif #define CS_VER 2 /* CSparse Version 2.2.1 */ #define CS_SUBVER 2 #define CS_SUBSUB 1 #define CS_DATE "Nov 1, 2007" /* CSparse release date */ #define CS_COPYRIGHT "Copyright (c) Timothy A. Davis, 2006-2007" /* --- primary CSparse routines and data structures ------------------------- */ typedef struct cs_sparse /* matrix in compressed-column or triplet form */ { int nzmax ; /* maximum number of entries */ int m ; /* number of rows */ int n ; /* number of columns */ int *p ; /* column pointers (size n+1) or col indices (size nzmax) */ int *i ; /* row indices, size nzmax */ double *x ; /* numerical values, size nzmax */ int nz ; /* # of entries in triplet matrix, -1 for compressed-col */ } cs ; cs *cs_add (const cs *A, const cs *B, double alpha, double beta) ; int cs_cholsol (int order, const cs *A, double *b) ; cs *cs_compress (const cs *T) ; int cs_dupl (cs *A) ; int cs_entry (cs *T, int i, int j, double x) ; int cs_gaxpy (const cs *A, const double *x, double *y) ; cs *cs_load (FILE *f) ; int cs_lusol (int order, const cs *A, double *b, double tol) ; cs *cs_multiply (const cs *A, const cs *B) ; double cs_norm (const cs *A) ; int cs_print (const cs *A, int brief) ; int cs_qrsol (int order, const cs *A, double *b) ; cs *cs_transpose (const cs *A, int values) ; /* utilities */ void *cs_calloc (int n, size_t size) ; void *cs_free (void *p) ; void *cs_realloc (void *p, int n, size_t size, int *ok) ; cs *cs_spalloc (int m, int n, int nzmax, int values, int triplet) ; cs *cs_spfree (cs *A) ; int cs_sprealloc (cs *A, int nzmax) ; void *cs_malloc (int n, size_t size) ; /* --- secondary CSparse routines and data structures ----------------------- */ typedef struct cs_symbolic /* symbolic Cholesky, LU, or QR analysis */ { int *pinv ; /* inverse row perm. for QR, fill red. perm for Chol */ int *q ; /* fill-reducing column permutation for LU and QR */ int *parent ; /* elimination tree for Cholesky and QR */ int *cp ; /* column pointers for Cholesky, row counts for QR */ int *leftmost ; /* leftmost[i] = min(find(A(i,:))), for QR */ int m2 ; /* # of rows for QR, after adding fictitious rows */ double lnz ; /* # entries in L for LU or Cholesky; in V for QR */ double unz ; /* # entries in U for LU; in R for QR */ } css ; typedef struct cs_numeric /* numeric Cholesky, LU, or QR factorization */ { cs *L ; /* L for LU and Cholesky, V for QR */ cs *U ; /* U for LU, R for QR, not used for Cholesky */ int *pinv ; /* partial pivoting for LU */ double *B ; /* beta [0..n-1] for QR */ } csn ; typedef struct cs_dmperm_results /* cs_dmperm or cs_scc output */ { int *p ; /* size m, row permutation */ int *q ; /* size n, column permutation */ int *r ; /* size nb+1, block k is rows r[k] to r[k+1]-1 in A(p,q) */ int *s ; /* size nb+1, block k is cols s[k] to s[k+1]-1 in A(p,q) */ int nb ; /* # of blocks in fine dmperm decomposition */ int rr [5] ; /* coarse row decomposition */ int cc [5] ; /* coarse column decomposition */ } csd ; int *cs_amd (int order, const cs *A) ; csn *cs_chol (const cs *A, const css *S) ; csd *cs_dmperm (const cs *A, int seed) ; int cs_droptol (cs *A, double tol) ; int cs_dropzeros (cs *A) ; int cs_happly (const cs *V, int i, double beta, double *x) ; int cs_ipvec (const int *p, const double *b, double *x, int n) ; int cs_lsolve (const cs *L, double *x) ; int cs_ltsolve (const cs *L, double *x) ; csn *cs_lu (const cs *A, const css *S, double tol) ; cs *cs_permute (const cs *A, const int *pinv, const int *q, int values) ; int *cs_pinv (const int *p, int n) ; int cs_pvec (const int *p, const double *b, double *x, int n) ; csn *cs_qr (const cs *A, const css *S) ; css *cs_schol (int order, const cs *A) ; css *cs_sqr (int order, const cs *A, int qr) ; cs *cs_symperm (const cs *A, const int *pinv, int values) ; int cs_updown (cs *L, int sigma, const cs *C, const int *parent) ; int cs_usolve (const cs *U, double *x) ; int cs_utsolve (const cs *U, double *x) ; /* utilities */ css *cs_sfree (css *S) ; csn *cs_nfree (csn *N) ; csd *cs_dfree (csd *D) ; /* --- tertiary CSparse routines -------------------------------------------- */ int *cs_counts (const cs *A, const int *parent, const int *post, int ata) ; double cs_cumsum (int *p, int *c, int n) ; int cs_dfs (int j, cs *G, int top, int *xi, int *pstack, const int *pinv) ; int cs_ereach (const cs *A, int k, const int *parent, int *s, int *w) ; int *cs_etree (const cs *A, int ata) ; int cs_fkeep (cs *A, int (*fkeep) (int, int, double, void *), void *other) ; double cs_house (double *x, double *beta, int n) ; int cs_leaf (int i, int j, const int *first, int *maxfirst, int *prevleaf, int *ancestor, int *jleaf) ; int *cs_maxtrans (const cs *A, int seed) ; int *cs_post (const int *parent, int n) ; int *cs_randperm (int n, int seed) ; int cs_reach (cs *G, const cs *B, int k, int *xi, const int *pinv) ; int cs_scatter (const cs *A, int j, double beta, int *w, double *x, int mark, cs *C, int nz) ; csd *cs_scc (cs *A) ; int cs_spsolve (cs *G, const cs *B, int k, int *xi, double *x, const int *pinv, int lo) ; int cs_tdfs (int j, int k, int *head, const int *next, int *post, int *stack) ; /* utilities */ csd *cs_dalloc (int m, int n) ; csd *cs_ddone (csd *D, cs *C, void *w, int ok) ; cs *cs_done (cs *C, void *w, void *x, int ok) ; int *cs_idone (int *p, cs *C, void *w, int ok) ; csn *cs_ndone (csn *N, cs *C, void *w, void *x, int ok) ; #define CS_MAX(a,b) (((a) > (b)) ? (a) : (b)) #define CS_MIN(a,b) (((a) < (b)) ? (a) : (b)) #define CS_FLIP(i) (-(i)-2) #define CS_UNFLIP(i) (((i) < 0) ? CS_FLIP(i) : (i)) #define CS_MARKED(w,j) (w [j] < 0) #define CS_MARK(w,j) { w [j] = CS_FLIP (w [j]) ; } #define CS_CSC(A) (A && (A->nz == -1)) #define CS_TRIPLET(A) (A && (A->nz >= 0)) #endif SuiteSparse/CSparse/Source/0000755001170100242450000000000010702451113014541 5ustar davisfacSuiteSparse/CSparse/Source/cs_ltsolve.c0000644001170100242450000000072410414335547017101 0ustar davisfac#include "cs.h" /* solve L'x=b where x and b are dense. x=b on input, solution on output. */ int cs_ltsolve (const cs *L, double *x) { int p, j, n, *Lp, *Li ; double *Lx ; if (!CS_CSC (L) || !x) return (0) ; /* check inputs */ n = L->n ; Lp = L->p ; Li = L->i ; Lx = L->x ; for (j = n-1 ; j >= 0 ; j--) { for (p = Lp [j]+1 ; p < Lp [j+1] ; p++) { x [j] -= Lx [p] * x [Li [p]] ; } x [j] /= Lx [Lp [j]] ; } return (1) ; } SuiteSparse/CSparse/Source/cs_cholsol.c0000644001170100242450000000141510416442163017045 0ustar davisfac#include "cs.h" /* x=A\b where A is symmetric positive definite; b overwritten with solution */ int cs_cholsol (int order, const cs *A, double *b) { double *x ; css *S ; csn *N ; int n, ok ; if (!CS_CSC (A) || !b) return (0) ; /* check inputs */ n = A->n ; S = cs_schol (order, A) ; /* ordering and symbolic analysis */ N = cs_chol (A, S) ; /* numeric Cholesky factorization */ x = cs_malloc (n, sizeof (double)) ; /* get workspace */ ok = (S && N && x) ; if (ok) { cs_ipvec (S->pinv, b, x, n) ; /* x = P*b */ cs_lsolve (N->L, x) ; /* x = L\x */ cs_ltsolve (N->L, x) ; /* x = L'\x */ cs_pvec (S->pinv, x, b, n) ; /* b = P'*x */ } cs_free (x) ; cs_sfree (S) ; cs_nfree (N) ; return (ok) ; } SuiteSparse/CSparse/Source/cs_lu.c0000644001170100242450000000657510414563004016032 0ustar davisfac#include "cs.h" /* [L,U,pinv]=lu(A, [q lnz unz]). lnz and unz can be guess */ csn *cs_lu (const cs *A, const css *S, double tol) { cs *L, *U ; csn *N ; double pivot, *Lx, *Ux, *x, a, t ; int *Lp, *Li, *Up, *Ui, *pinv, *xi, *q, n, ipiv, k, top, p, i, col, lnz,unz; if (!CS_CSC (A) || !S) return (NULL) ; /* check inputs */ n = A->n ; q = S->q ; lnz = S->lnz ; unz = S->unz ; x = cs_malloc (n, sizeof (double)) ; /* get double workspace */ xi = cs_malloc (2*n, sizeof (int)) ; /* get int workspace */ N = cs_calloc (1, sizeof (csn)) ; /* allocate result */ if (!x || !xi || !N) return (cs_ndone (N, NULL, xi, x, 0)) ; N->L = L = cs_spalloc (n, n, lnz, 1, 0) ; /* allocate result L */ N->U = U = cs_spalloc (n, n, unz, 1, 0) ; /* allocate result U */ N->pinv = pinv = cs_malloc (n, sizeof (int)) ; /* allocate result pinv */ if (!L || !U || !pinv) return (cs_ndone (N, NULL, xi, x, 0)) ; Lp = L->p ; Up = U->p ; for (i = 0 ; i < n ; i++) x [i] = 0 ; /* clear workspace */ for (i = 0 ; i < n ; i++) pinv [i] = -1 ; /* no rows pivotal yet */ for (k = 0 ; k <= n ; k++) Lp [k] = 0 ; /* no cols of L yet */ lnz = unz = 0 ; for (k = 0 ; k < n ; k++) /* compute L(:,k) and U(:,k) */ { /* --- Triangular solve --------------------------------------------- */ Lp [k] = lnz ; /* L(:,k) starts here */ Up [k] = unz ; /* U(:,k) starts here */ if ((lnz + n > L->nzmax && !cs_sprealloc (L, 2*L->nzmax + n)) || (unz + n > U->nzmax && !cs_sprealloc (U, 2*U->nzmax + n))) { return (cs_ndone (N, NULL, xi, x, 0)) ; } Li = L->i ; Lx = L->x ; Ui = U->i ; Ux = U->x ; col = q ? (q [k]) : k ; top = cs_spsolve (L, A, col, xi, x, pinv, 1) ; /* x = L\A(:,col) */ /* --- Find pivot --------------------------------------------------- */ ipiv = -1 ; a = -1 ; for (p = top ; p < n ; p++) { i = xi [p] ; /* x(i) is nonzero */ if (pinv [i] < 0) /* row i is not yet pivotal */ { if ((t = fabs (x [i])) > a) { a = t ; /* largest pivot candidate so far */ ipiv = i ; } } else /* x(i) is the entry U(pinv[i],k) */ { Ui [unz] = pinv [i] ; Ux [unz++] = x [i] ; } } if (ipiv == -1 || a <= 0) return (cs_ndone (N, NULL, xi, x, 0)) ; if (pinv [col] < 0 && fabs (x [col]) >= a*tol) ipiv = col ; /* --- Divide by pivot ---------------------------------------------- */ pivot = x [ipiv] ; /* the chosen pivot */ Ui [unz] = k ; /* last entry in U(:,k) is U(k,k) */ Ux [unz++] = pivot ; pinv [ipiv] = k ; /* ipiv is the kth pivot row */ Li [lnz] = ipiv ; /* first entry in L(:,k) is L(k,k) = 1 */ Lx [lnz++] = 1 ; for (p = top ; p < n ; p++) /* L(k+1:n,k) = x / pivot */ { i = xi [p] ; if (pinv [i] < 0) /* x(i) is an entry in L(:,k) */ { Li [lnz] = i ; /* save unpermuted row in L */ Lx [lnz++] = x [i] / pivot ; /* scale pivot column */ } x [i] = 0 ; /* x [0..n-1] = 0 for next k */ } } /* --- Finalize L and U ------------------------------------------------- */ Lp [n] = lnz ; Up [n] = unz ; Li = L->i ; /* fix row indices of L for final pinv */ for (p = 0 ; p < lnz ; p++) Li [p] = pinv [Li [p]] ; cs_sprealloc (L, 0) ; /* remove extra space from L and U */ cs_sprealloc (U, 0) ; return (cs_ndone (N, NULL, xi, x, 1)) ; /* success */ } SuiteSparse/CSparse/Source/cs_qr.c0000644001170100242450000000564710571642754016051 0ustar davisfac#include "cs.h" /* sparse QR factorization [V,beta,pinv,R] = qr (A) */ csn *cs_qr (const cs *A, const css *S) { double *Rx, *Vx, *Ax, *x, *Beta ; int i, k, p, m, n, vnz, p1, top, m2, len, col, rnz, *s, *leftmost, *Ap, *Ai, *parent, *Rp, *Ri, *Vp, *Vi, *w, *pinv, *q ; cs *R, *V ; csn *N ; if (!CS_CSC (A) || !S) return (NULL) ; m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; q = S->q ; parent = S->parent ; pinv = S->pinv ; m2 = S->m2 ; vnz = S->lnz ; rnz = S->unz ; leftmost = S->leftmost ; w = cs_malloc (m2+n, sizeof (int)) ; /* get int workspace */ x = cs_malloc (m2, sizeof (double)) ; /* get double workspace */ N = cs_calloc (1, sizeof (csn)) ; /* allocate result */ if (!w || !x || !N) return (cs_ndone (N, NULL, w, x, 0)) ; s = w + m2 ; /* s is size n */ for (k = 0 ; k < m2 ; k++) x [k] = 0 ; /* clear workspace x */ N->L = V = cs_spalloc (m2, n, vnz, 1, 0) ; /* allocate result V */ N->U = R = cs_spalloc (m2, n, rnz, 1, 0) ; /* allocate result R */ N->B = Beta = cs_malloc (n, sizeof (double)) ; /* allocate result Beta */ if (!R || !V || !Beta) return (cs_ndone (N, NULL, w, x, 0)) ; Rp = R->p ; Ri = R->i ; Rx = R->x ; Vp = V->p ; Vi = V->i ; Vx = V->x ; for (i = 0 ; i < m2 ; i++) w [i] = -1 ; /* clear w, to mark nodes */ rnz = 0 ; vnz = 0 ; for (k = 0 ; k < n ; k++) /* compute V and R */ { Rp [k] = rnz ; /* R(:,k) starts here */ Vp [k] = p1 = vnz ; /* V(:,k) starts here */ w [k] = k ; /* add V(k,k) to pattern of V */ Vi [vnz++] = k ; top = n ; col = q ? q [k] : k ; for (p = Ap [col] ; p < Ap [col+1] ; p++) /* find R(:,k) pattern */ { i = leftmost [Ai [p]] ; /* i = min(find(A(i,q))) */ for (len = 0 ; w [i] != k ; i = parent [i]) /* traverse up to k */ { s [len++] = i ; w [i] = k ; } while (len > 0) s [--top] = s [--len] ; /* push path on stack */ i = pinv [Ai [p]] ; /* i = permuted row of A(:,col) */ x [i] = Ax [p] ; /* x (i) = A(:,col) */ if (i > k && w [i] < k) /* pattern of V(:,k) = x (k+1:m) */ { Vi [vnz++] = i ; /* add i to pattern of V(:,k) */ w [i] = k ; } } for (p = top ; p < n ; p++) /* for each i in pattern of R(:,k) */ { i = s [p] ; /* R(i,k) is nonzero */ cs_happly (V, i, Beta [i], x) ; /* apply (V(i),Beta(i)) to x */ Ri [rnz] = i ; /* R(i,k) = x(i) */ Rx [rnz++] = x [i] ; x [i] = 0 ; if (parent [i] == k) vnz = cs_scatter (V, i, 0, w, NULL, k, V, vnz); } for (p = p1 ; p < vnz ; p++) /* gather V(:,k) = x */ { Vx [p] = x [Vi [p]] ; x [Vi [p]] = 0 ; } Ri [rnz] = k ; /* R(k,k) = norm (x) */ Rx [rnz++] = cs_house (Vx+p1, Beta+k, vnz-p1) ; /* [v,beta]=house(x) */ } Rp [n] = rnz ; /* finalize R */ Vp [n] = vnz ; /* finalize V */ return (cs_ndone (N, NULL, w, x, 1)) ; /* success */ } SuiteSparse/CSparse/Source/cs_house.c0000644001170100242450000000125410571117254016530 0ustar davisfac#include "cs.h" /* create a Householder reflection [v,beta,s]=house(x), overwrite x with v, * where (I-beta*v*v')*x = s*e1. See Algo 5.1.1, Golub & Van Loan, 3rd ed. */ double cs_house (double *x, double *beta, int n) { double s, sigma = 0 ; int i ; if (!x || !beta) return (-1) ; /* check inputs */ for (i = 1 ; i < n ; i++) sigma += x [i] * x [i] ; if (sigma == 0) { s = fabs (x [0]) ; /* s = |x(0)| */ (*beta) = (x [0] <= 0) ? 2 : 0 ; x [0] = 1 ; } else { s = sqrt (x [0] * x [0] + sigma) ; /* s = norm (x) */ x [0] = (x [0] <= 0) ? (x [0] - s) : (-sigma / (x [0] + s)) ; (*beta) = -1. / (s * x [0]) ; } return (s) ; } SuiteSparse/CSparse/Source/cs_updown.c0000644001170100242450000000303710571364004016717 0ustar davisfac#include "cs.h" /* sparse Cholesky update/downdate, L*L' + sigma*w*w' (sigma = +1 or -1) */ int cs_updown (cs *L, int sigma, const cs *C, const int *parent) { int n, p, f, j, *Lp, *Li, *Cp, *Ci ; double *Lx, *Cx, alpha, beta = 1, delta, gamma, w1, w2, *w, beta2 = 1 ; if (!CS_CSC (L) || !CS_CSC (C) || !parent) return (0) ; /* check inputs */ Lp = L->p ; Li = L->i ; Lx = L->x ; n = L->n ; Cp = C->p ; Ci = C->i ; Cx = C->x ; if ((p = Cp [0]) >= Cp [1]) return (1) ; /* return if C empty */ w = cs_malloc (n, sizeof (double)) ; /* get workspace */ if (!w) return (0) ; /* out of memory */ f = Ci [p] ; for ( ; p < Cp [1] ; p++) f = CS_MIN (f, Ci [p]) ; /* f = min (find (C)) */ for (j = f ; j != -1 ; j = parent [j]) w [j] = 0 ; /* clear workspace w */ for (p = Cp [0] ; p < Cp [1] ; p++) w [Ci [p]] = Cx [p] ; /* w = C */ for (j = f ; j != -1 ; j = parent [j]) /* walk path f up to root */ { p = Lp [j] ; alpha = w [j] / Lx [p] ; /* alpha = w(j) / L(j,j) */ beta2 = beta*beta + sigma*alpha*alpha ; if (beta2 <= 0) break ; /* not positive definite */ beta2 = sqrt (beta2) ; delta = (sigma > 0) ? (beta / beta2) : (beta2 / beta) ; gamma = sigma * alpha / (beta2 * beta) ; Lx [p] = delta * Lx [p] + ((sigma > 0) ? (gamma * w [j]) : 0) ; beta = beta2 ; for (p++ ; p < Lp [j+1] ; p++) { w1 = w [Li [p]] ; w [Li [p]] = w2 = w1 - alpha * Lx [p] ; Lx [p] = delta * Lx [p] + gamma * ((sigma > 0) ? w1 : w2) ; } } cs_free (w) ; return (beta2 > 0) ; } SuiteSparse/CSparse/Source/cs_cumsum.c0000644001170100242450000000077510414317363016724 0ustar davisfac#include "cs.h" /* p [0..n] = cumulative sum of c [0..n-1], and then copy p [0..n-1] into c */ double cs_cumsum (int *p, int *c, int n) { int i, nz = 0 ; double nz2 = 0 ; if (!p || !c) return (-1) ; /* check inputs */ for (i = 0 ; i < n ; i++) { p [i] = nz ; nz += c [i] ; nz2 += c [i] ; /* also in double to avoid int overflow */ c [i] = p [i] ; /* also copy p[0..n-1] back into c[0..n-1]*/ } p [n] = nz ; return (nz2) ; /* return sum (c [0..n-1]) */ } SuiteSparse/CSparse/Source/cs_malloc.c0000644001170100242450000000154110415504624016651 0ustar davisfac#include "cs.h" #ifdef MATLAB_MEX_FILE #define malloc mxMalloc #define free mxFree #define realloc mxRealloc #define calloc mxCalloc #endif /* wrapper for malloc */ void *cs_malloc (int n, size_t size) { return (malloc (CS_MAX (n,1) * size)) ; } /* wrapper for calloc */ void *cs_calloc (int n, size_t size) { return (calloc (CS_MAX (n,1), size)) ; } /* wrapper for free */ void *cs_free (void *p) { if (p) free (p) ; /* free p if it is not already NULL */ return (NULL) ; /* return NULL to simplify the use of cs_free */ } /* wrapper for realloc */ void *cs_realloc (void *p, int n, size_t size, int *ok) { void *pnew ; pnew = realloc (p, CS_MAX (n,1) * size) ; /* realloc the block */ *ok = (pnew != NULL) ; /* realloc fails if pnew is NULL */ return ((*ok) ? pnew : p) ; /* return original p if failure */ } SuiteSparse/CSparse/Source/cs_permute.c0000644001170100242450000000166010415504764017072 0ustar davisfac#include "cs.h" /* C = A(p,q) where p and q are permutations of 0..m-1 and 0..n-1. */ cs *cs_permute (const cs *A, const int *pinv, const int *q, int values) { int t, j, k, nz = 0, m, n, *Ap, *Ai, *Cp, *Ci ; double *Cx, *Ax ; cs *C ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; C = cs_spalloc (m, n, Ap [n], values && Ax != NULL, 0) ; /* alloc result */ if (!C) return (cs_done (C, NULL, NULL, 0)) ; /* out of memory */ Cp = C->p ; Ci = C->i ; Cx = C->x ; for (k = 0 ; k < n ; k++) { Cp [k] = nz ; /* column k of C is column q[k] of A */ j = q ? (q [k]) : k ; for (t = Ap [j] ; t < Ap [j+1] ; t++) { if (Cx) Cx [nz] = Ax [t] ; /* row i of A is row pinv[i] of C */ Ci [nz++] = pinv ? (pinv [Ai [t]]) : Ai [t] ; } } Cp [n] = nz ; /* finalize the last column of C */ return (cs_done (C, NULL, NULL, 1)) ; } SuiteSparse/CSparse/Source/cs_symperm.c0000644001170100242450000000277410414454316017110 0ustar davisfac#include "cs.h" /* C = A(p,p) where A and C are symmetric the upper part stored; pinv not p */ cs *cs_symperm (const cs *A, const int *pinv, int values) { int i, j, p, q, i2, j2, n, *Ap, *Ai, *Cp, *Ci, *w ; double *Cx, *Ax ; cs *C ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; C = cs_spalloc (n, n, Ap [n], values && (Ax != NULL), 0) ; /* alloc result*/ w = cs_calloc (n, sizeof (int)) ; /* get workspace */ if (!C || !w) return (cs_done (C, w, NULL, 0)) ; /* out of memory */ Cp = C->p ; Ci = C->i ; Cx = C->x ; for (j = 0 ; j < n ; j++) /* count entries in each column of C */ { j2 = pinv ? pinv [j] : j ; /* column j of A is column j2 of C */ for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; if (i > j) continue ; /* skip lower triangular part of A */ i2 = pinv ? pinv [i] : i ; /* row i of A is row i2 of C */ w [CS_MAX (i2, j2)]++ ; /* column count of C */ } } cs_cumsum (Cp, w, n) ; /* compute column pointers of C */ for (j = 0 ; j < n ; j++) { j2 = pinv ? pinv [j] : j ; /* column j of A is column j2 of C */ for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; if (i > j) continue ; /* skip lower triangular part of A*/ i2 = pinv ? pinv [i] : i ; /* row i of A is row i2 of C */ Ci [q = w [CS_MAX (i2, j2)]++] = CS_MIN (i2, j2) ; if (Cx) Cx [q] = Ax [p] ; } } return (cs_done (C, w, NULL, 1)) ; /* success; free workspace, return C */ } SuiteSparse/CSparse/Source/cs_lsolve.c0000644001170100242450000000071710414335545016715 0ustar davisfac#include "cs.h" /* solve Lx=b where x and b are dense. x=b on input, solution on output. */ int cs_lsolve (const cs *L, double *x) { int p, j, n, *Lp, *Li ; double *Lx ; if (!CS_CSC (L) || !x) return (0) ; /* check inputs */ n = L->n ; Lp = L->p ; Li = L->i ; Lx = L->x ; for (j = 0 ; j < n ; j++) { x [j] /= Lx [Lp [j]] ; for (p = Lp [j]+1 ; p < Lp [j+1] ; p++) { x [Li [p]] -= Lx [p] * x [j] ; } } return (1) ; } SuiteSparse/CSparse/Source/cs_happly.c0000644001170100242450000000104410414335542016675 0ustar davisfac#include "cs.h" /* apply the ith Householder vector to x */ int cs_happly (const cs *V, int i, double beta, double *x) { int p, *Vp, *Vi ; double *Vx, tau = 0 ; if (!CS_CSC (V) || !x) return (0) ; /* check inputs */ Vp = V->p ; Vi = V->i ; Vx = V->x ; for (p = Vp [i] ; p < Vp [i+1] ; p++) /* tau = v'*x */ { tau += Vx [p] * x [Vi [p]] ; } tau *= beta ; /* tau = beta*(v'*x) */ for (p = Vp [i] ; p < Vp [i+1] ; p++) /* x = x - v*tau */ { x [Vi [p]] -= Vx [p] * tau ; } return (1) ; } SuiteSparse/CSparse/Source/cs_utsolve.c0000644001170100242450000000072510414335707017111 0ustar davisfac#include "cs.h" /* solve U'x=b where x and b are dense. x=b on input, solution on output. */ int cs_utsolve (const cs *U, double *x) { int p, j, n, *Up, *Ui ; double *Ux ; if (!CS_CSC (U) || !x) return (0) ; /* check inputs */ n = U->n ; Up = U->p ; Ui = U->i ; Ux = U->x ; for (j = 0 ; j < n ; j++) { for (p = Up [j] ; p < Up [j+1]-1 ; p++) { x [j] -= Ux [p] * x [Ui [p]] ; } x [j] /= Ux [Up [j+1]-1] ; } return (1) ; } SuiteSparse/CSparse/Source/cs_ipvec.c0000644001170100242450000000044610415505577016523 0ustar davisfac#include "cs.h" /* x(p) = b, for dense vectors x and b; p=NULL denotes identity */ int cs_ipvec (const int *p, const double *b, double *x, int n) { int k ; if (!x || !b) return (0) ; /* check inputs */ for (k = 0 ; k < n ; k++) x [p ? p [k] : k] = b [k] ; return (1) ; } SuiteSparse/CSparse/Source/cs_print.c0000644001170100242450000000206410376365073016550 0ustar davisfac#include "cs.h" /* print a sparse matrix */ int cs_print (const cs *A, int brief) { int p, j, m, n, nzmax, nz, *Ap, *Ai ; double *Ax ; if (!A) { printf ("(null)\n") ; return (0) ; } m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; nzmax = A->nzmax ; nz = A->nz ; printf ("CSparse Version %d.%d.%d, %s. %s\n", CS_VER, CS_SUBVER, CS_SUBSUB, CS_DATE, CS_COPYRIGHT) ; if (nz < 0) { printf ("%d-by-%d, nzmax: %d nnz: %d, 1-norm: %g\n", m, n, nzmax, Ap [n], cs_norm (A)) ; for (j = 0 ; j < n ; j++) { printf (" col %d : locations %d to %d\n", j, Ap [j], Ap [j+1]-1); for (p = Ap [j] ; p < Ap [j+1] ; p++) { printf (" %d : %g\n", Ai [p], Ax ? Ax [p] : 1) ; if (brief && p > 20) { printf (" ...\n") ; return (1) ; } } } } else { printf ("triplet: %d-by-%d, nzmax: %d nnz: %d\n", m, n, nzmax, nz) ; for (p = 0 ; p < nz ; p++) { printf (" %d %d : %g\n", Ai [p], Ap [p], Ax ? Ax [p] : 1) ; if (brief && p > 20) { printf (" ...\n") ; return (1) ; } } } return (1) ; } SuiteSparse/CSparse/Source/cs_scatter.c0000644001170100242450000000136010414335615017047 0ustar davisfac#include "cs.h" /* x = x + beta * A(:,j), where x is a dense vector and A(:,j) is sparse */ int cs_scatter (const cs *A, int j, double beta, int *w, double *x, int mark, cs *C, int nz) { int i, p, *Ap, *Ai, *Ci ; double *Ax ; if (!CS_CSC (A) || !w || !CS_CSC (C)) return (-1) ; /* check inputs */ Ap = A->p ; Ai = A->i ; Ax = A->x ; Ci = C->i ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; /* A(i,j) is nonzero */ if (w [i] < mark) { w [i] = mark ; /* i is new entry in column j */ Ci [nz++] = i ; /* add i to pattern of C(:,j) */ if (x) x [i] = beta * Ax [p] ; /* x(i) = beta*A(i,j) */ } else if (x) x [i] += beta * Ax [p] ; /* i exists in C(:,j) already */ } return (nz) ; } SuiteSparse/CSparse/Source/cs_counts.c0000644001170100242450000000502310414453543016716 0ustar davisfac#include "cs.h" /* column counts of LL'=A or LL'=A'A, given parent & post ordering */ #define HEAD(k,j) (ata ? head [k] : j) #define NEXT(J) (ata ? next [J] : -1) static void init_ata (cs *AT, const int *post, int *w, int **head, int **next) { int i, k, p, m = AT->n, n = AT->m, *ATp = AT->p, *ATi = AT->i ; *head = w+4*n, *next = w+5*n+1 ; for (k = 0 ; k < n ; k++) w [post [k]] = k ; /* invert post */ for (i = 0 ; i < m ; i++) { for (k = n, p = ATp[i] ; p < ATp[i+1] ; p++) k = CS_MIN (k, w [ATi[p]]); (*next) [i] = (*head) [k] ; /* place row i in linked list k */ (*head) [k] = i ; } } int *cs_counts (const cs *A, const int *parent, const int *post, int ata) { int i, j, k, n, m, J, s, p, q, jleaf, *ATp, *ATi, *maxfirst, *prevleaf, *ancestor, *head = NULL, *next = NULL, *colcount, *w, *first, *delta ; cs *AT ; if (!CS_CSC (A) || !parent || !post) return (NULL) ; /* check inputs */ m = A->m ; n = A->n ; s = 4*n + (ata ? (n+m+1) : 0) ; delta = colcount = cs_malloc (n, sizeof (int)) ; /* allocate result */ w = cs_malloc (s, sizeof (int)) ; /* get workspace */ AT = cs_transpose (A, 0) ; /* AT = A' */ if (!AT || !colcount || !w) return (cs_idone (colcount, AT, w, 0)) ; ancestor = w ; maxfirst = w+n ; prevleaf = w+2*n ; first = w+3*n ; for (k = 0 ; k < s ; k++) w [k] = -1 ; /* clear workspace w [0..s-1] */ for (k = 0 ; k < n ; k++) /* find first [j] */ { j = post [k] ; delta [j] = (first [j] == -1) ? 1 : 0 ; /* delta[j]=1 if j is a leaf */ for ( ; j != -1 && first [j] == -1 ; j = parent [j]) first [j] = k ; } ATp = AT->p ; ATi = AT->i ; if (ata) init_ata (AT, post, w, &head, &next) ; for (i = 0 ; i < n ; i++) ancestor [i] = i ; /* each node in its own set */ for (k = 0 ; k < n ; k++) { j = post [k] ; /* j is the kth node in postordered etree */ if (parent [j] != -1) delta [parent [j]]-- ; /* j is not a root */ for (J = HEAD (k,j) ; J != -1 ; J = NEXT (J)) /* J=j for LL'=A case */ { for (p = ATp [J] ; p < ATp [J+1] ; p++) { i = ATi [p] ; q = cs_leaf (i, j, first, maxfirst, prevleaf, ancestor, &jleaf); if (jleaf >= 1) delta [j]++ ; /* A(i,j) is in skeleton */ if (jleaf == 2) delta [q]-- ; /* account for overlap in q */ } } if (parent [j] != -1) ancestor [j] = parent [j] ; } for (j = 0 ; j < n ; j++) /* sum up delta's of each child */ { if (parent [j] != -1) colcount [parent [j]] += colcount [j] ; } return (cs_idone (colcount, AT, w, 1)) ; /* success: free workspace */ } SuiteSparse/CSparse/Source/cs_reach.c0000644001170100242450000000121210415507221016453 0ustar davisfac#include "cs.h" /* xi [top...n-1] = nodes reachable from graph of G*P' via nodes in B(:,k). * xi [n...2n-1] used as workspace */ int cs_reach (cs *G, const cs *B, int k, int *xi, const int *pinv) { int p, n, top, *Bp, *Bi, *Gp ; if (!CS_CSC (G) || !CS_CSC (B) || !xi) return (-1) ; /* check inputs */ n = G->n ; Bp = B->p ; Bi = B->i ; Gp = G->p ; top = n ; for (p = Bp [k] ; p < Bp [k+1] ; p++) { if (!CS_MARKED (Gp, Bi [p])) /* start a dfs at unmarked node i */ { top = cs_dfs (Bi [p], G, top, xi, xi+n, pinv) ; } } for (p = top ; p < n ; p++) CS_MARK (Gp, xi [p]) ; /* restore G */ return (top) ; } SuiteSparse/CSparse/Source/cs_dropzeros.c0000644001170100242450000000032610414754172017435 0ustar davisfac#include "cs.h" static int cs_nonzero (int i, int j, double aij, void *other) { return (aij != 0) ; } int cs_dropzeros (cs *A) { return (cs_fkeep (A, &cs_nonzero, NULL)) ; /* keep all nonzero entries */ } SuiteSparse/CSparse/Source/cs_qrsol.c0000644001170100242450000000307410416442215016543 0ustar davisfac#include "cs.h" /* x=A\b where A can be rectangular; b overwritten with solution */ int cs_qrsol (int order, const cs *A, double *b) { double *x ; css *S ; csn *N ; cs *AT = NULL ; int k, m, n, ok ; if (!CS_CSC (A) || !b) return (0) ; /* check inputs */ n = A->n ; m = A->m ; if (m >= n) { S = cs_sqr (order, A, 1) ; /* ordering and symbolic analysis */ N = cs_qr (A, S) ; /* numeric QR factorization */ x = cs_calloc (S ? S->m2 : 1, sizeof (double)) ; /* get workspace */ ok = (S && N && x) ; if (ok) { cs_ipvec (S->pinv, b, x, m) ; /* x(0:m-1) = b(p(0:m-1) */ for (k = 0 ; k < n ; k++) /* apply Householder refl. to x */ { cs_happly (N->L, k, N->B [k], x) ; } cs_usolve (N->U, x) ; /* x = R\x */ cs_ipvec (S->q, x, b, n) ; /* b(q(0:n-1)) = x(0:n-1) */ } } else { AT = cs_transpose (A, 1) ; /* Ax=b is underdetermined */ S = cs_sqr (order, AT, 1) ; /* ordering and symbolic analysis */ N = cs_qr (AT, S) ; /* numeric QR factorization of A' */ x = cs_calloc (S ? S->m2 : 1, sizeof (double)) ; /* get workspace */ ok = (AT && S && N && x) ; if (ok) { cs_pvec (S->q, b, x, m) ; /* x(q(0:m-1)) = b(0:m-1) */ cs_utsolve (N->U, x) ; /* x = R'\x */ for (k = m-1 ; k >= 0 ; k--) /* apply Householder refl. to x */ { cs_happly (N->L, k, N->B [k], x) ; } cs_pvec (S->pinv, x, b, n) ; /* b(0:n-1) = x(p(0:n-1)) */ } } cs_free (x) ; cs_sfree (S) ; cs_nfree (N) ; cs_spfree (AT) ; return (ok) ; } SuiteSparse/CSparse/Source/cs_chol.c0000644001170100242450000000462510415615347016342 0ustar davisfac#include "cs.h" /* L = chol (A, [pinv parent cp]), pinv is optional */ csn *cs_chol (const cs *A, const css *S) { double d, lki, *Lx, *x, *Cx ; int top, i, p, k, n, *Li, *Lp, *cp, *pinv, *s, *c, *parent, *Cp, *Ci ; cs *L, *C, *E ; csn *N ; if (!CS_CSC (A) || !S || !S->cp || !S->parent) return (NULL) ; n = A->n ; N = cs_calloc (1, sizeof (csn)) ; /* allocate result */ c = cs_malloc (2*n, sizeof (int)) ; /* get int workspace */ x = cs_malloc (n, sizeof (double)) ; /* get double workspace */ cp = S->cp ; pinv = S->pinv ; parent = S->parent ; C = pinv ? cs_symperm (A, pinv, 1) : ((cs *) A) ; E = pinv ? C : NULL ; /* E is alias for A, or a copy E=A(p,p) */ if (!N || !c || !x || !C) return (cs_ndone (N, E, c, x, 0)) ; s = c + n ; Cp = C->p ; Ci = C->i ; Cx = C->x ; N->L = L = cs_spalloc (n, n, cp [n], 1, 0) ; /* allocate result */ if (!L) return (cs_ndone (N, E, c, x, 0)) ; Lp = L->p ; Li = L->i ; Lx = L->x ; for (k = 0 ; k < n ; k++) Lp [k] = c [k] = cp [k] ; for (k = 0 ; k < n ; k++) /* compute L(:,k) for L*L' = C */ { /* --- Nonzero pattern of L(k,:) ------------------------------------ */ top = cs_ereach (C, k, parent, s, c) ; /* find pattern of L(k,:) */ x [k] = 0 ; /* x (0:k) is now zero */ for (p = Cp [k] ; p < Cp [k+1] ; p++) /* x = full(triu(C(:,k))) */ { if (Ci [p] <= k) x [Ci [p]] = Cx [p] ; } d = x [k] ; /* d = C(k,k) */ x [k] = 0 ; /* clear x for k+1st iteration */ /* --- Triangular solve --------------------------------------------- */ for ( ; top < n ; top++) /* solve L(0:k-1,0:k-1) * x = C(:,k) */ { i = s [top] ; /* s [top..n-1] is pattern of L(k,:) */ lki = x [i] / Lx [Lp [i]] ; /* L(k,i) = x (i) / L(i,i) */ x [i] = 0 ; /* clear x for k+1st iteration */ for (p = Lp [i] + 1 ; p < c [i] ; p++) { x [Li [p]] -= Lx [p] * lki ; } d -= lki * lki ; /* d = d - L(k,i)*L(k,i) */ p = c [i]++ ; Li [p] = k ; /* store L(k,i) in column i */ Lx [p] = lki ; } /* --- Compute L(k,k) ----------------------------------------------- */ if (d <= 0) return (cs_ndone (N, E, c, x, 0)) ; /* not pos def */ p = c [k]++ ; Li [p] = k ; /* store L(k,k) = sqrt (d) in column k */ Lx [p] = sqrt (d) ; } Lp [n] = cp [n] ; /* finalize L */ return (cs_ndone (N, E, c, x, 1)) ; /* success: free E,s,x; return N */ } SuiteSparse/CSparse/Source/cs_dupl.c0000644001170100242450000000200210414335517016341 0ustar davisfac#include "cs.h" /* remove duplicate entries from A */ int cs_dupl (cs *A) { int i, j, p, q, nz = 0, n, m, *Ap, *Ai, *w ; double *Ax ; if (!CS_CSC (A)) return (0) ; /* check inputs */ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; w = cs_malloc (m, sizeof (int)) ; /* get workspace */ if (!w) return (0) ; /* out of memory */ for (i = 0 ; i < m ; i++) w [i] = -1 ; /* row i not yet seen */ for (j = 0 ; j < n ; j++) { q = nz ; /* column j will start at q */ for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; /* A(i,j) is nonzero */ if (w [i] >= q) { Ax [w [i]] += Ax [p] ; /* A(i,j) is a duplicate */ } else { w [i] = nz ; /* record where row i occurs */ Ai [nz] = i ; /* keep A(i,j) */ Ax [nz++] = Ax [p] ; } } Ap [j] = q ; /* record start of column j */ } Ap [n] = nz ; /* finalize A */ cs_free (w) ; /* free workspace */ return (cs_sprealloc (A, 0)) ; /* remove extra space from A */ } SuiteSparse/CSparse/Source/cs_schol.c0000644001170100242450000000212610416444066016516 0ustar davisfac#include "cs.h" /* ordering and symbolic analysis for a Cholesky factorization */ css *cs_schol (int order, const cs *A) { int n, *c, *post, *P ; cs *C ; css *S ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ n = A->n ; S = cs_calloc (1, sizeof (css)) ; /* allocate result S */ if (!S) return (NULL) ; /* out of memory */ P = cs_amd (order, A) ; /* P = amd(A+A'), or natural */ S->pinv = cs_pinv (P, n) ; /* find inverse permutation */ cs_free (P) ; if (order && !S->pinv) return (cs_sfree (S)) ; C = cs_symperm (A, S->pinv, 0) ; /* C = spones(triu(A(P,P))) */ S->parent = cs_etree (C, 0) ; /* find etree of C */ post = cs_post (S->parent, n) ; /* postorder the etree */ c = cs_counts (C, S->parent, post, 0) ; /* find column counts of chol(C) */ cs_free (post) ; cs_spfree (C) ; S->cp = cs_malloc (n+1, sizeof (int)) ; /* allocate result S->cp */ S->unz = S->lnz = cs_cumsum (S->cp, c, n) ; /* find column pointers for L */ cs_free (c) ; return ((S->lnz >= 0) ? S : cs_sfree (S)) ; } SuiteSparse/CSparse/Source/cs_leaf.c0000644001170100242450000000172210414756135016317 0ustar davisfac#include "cs.h" /* consider A(i,j), node j in ith row subtree and return lca(jprev,j) */ int cs_leaf (int i, int j, const int *first, int *maxfirst, int *prevleaf, int *ancestor, int *jleaf) { int q, s, sparent, jprev ; if (!first || !maxfirst || !prevleaf || !ancestor || !jleaf) return (-1) ; *jleaf = 0 ; if (i <= j || first [j] <= maxfirst [i]) return (-1) ; /* j not a leaf */ maxfirst [i] = first [j] ; /* update max first[j] seen so far */ jprev = prevleaf [i] ; /* jprev = previous leaf of ith subtree */ prevleaf [i] = j ; *jleaf = (jprev == -1) ? 1: 2 ; /* j is first or subsequent leaf */ if (*jleaf == 1) return (i) ; /* if 1st leaf, q = root of ith subtree */ for (q = jprev ; q != ancestor [q] ; q = ancestor [q]) ; for (s = jprev ; s != q ; s = sparent) { sparent = ancestor [s] ; /* path compression */ ancestor [s] = q ; } return (q) ; /* q = least common ancester (jprev,j) */ } SuiteSparse/CSparse/Source/cs_dmperm.c0000644001170100242450000001322610417204204016662 0ustar davisfac#include "cs.h" /* breadth-first search for coarse decomposition (C0,C1,R1 or R0,R3,C3) */ static int cs_bfs (const cs *A, int n, int *wi, int *wj, int *queue, const int *imatch, const int *jmatch, int mark) { int *Ap, *Ai, head = 0, tail = 0, j, i, p, j2 ; cs *C ; for (j = 0 ; j < n ; j++) /* place all unmatched nodes in queue */ { if (imatch [j] >= 0) continue ; /* skip j if matched */ wj [j] = 0 ; /* j in set C0 (R0 if transpose) */ queue [tail++] = j ; /* place unmatched col j in queue */ } if (tail == 0) return (1) ; /* quick return if no unmatched nodes */ C = (mark == 1) ? ((cs *) A) : cs_transpose (A, 0) ; if (!C) return (0) ; /* bfs of C=A' to find R3,C3 from R0 */ Ap = C->p ; Ai = C->i ; while (head < tail) /* while queue is not empty */ { j = queue [head++] ; /* get the head of the queue */ for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; if (wi [i] >= 0) continue ; /* skip if i is marked */ wi [i] = mark ; /* i in set R1 (C3 if transpose) */ j2 = jmatch [i] ; /* traverse alternating path to j2 */ if (wj [j2] >= 0) continue ;/* skip j2 if it is marked */ wj [j2] = mark ; /* j2 in set C1 (R3 if transpose) */ queue [tail++] = j2 ; /* add j2 to queue */ } } if (mark != 1) cs_spfree (C) ; /* free A' if it was created */ return (1) ; } /* collect matched rows and columns into p and q */ static void cs_matched (int n, const int *wj, const int *imatch, int *p, int *q, int *cc, int *rr, int set, int mark) { int kc = cc [set], j ; int kr = rr [set-1] ; for (j = 0 ; j < n ; j++) { if (wj [j] != mark) continue ; /* skip if j is not in C set */ p [kr++] = imatch [j] ; q [kc++] = j ; } cc [set+1] = kc ; rr [set] = kr ; } /* collect unmatched rows into the permutation vector p */ static void cs_unmatched (int m, const int *wi, int *p, int *rr, int set) { int i, kr = rr [set] ; for (i = 0 ; i < m ; i++) if (wi [i] == 0) p [kr++] = i ; rr [set+1] = kr ; } /* return 1 if row i is in R2 */ static int cs_rprune (int i, int j, double aij, void *other) { int *rr = (int *) other ; return (i >= rr [1] && i < rr [2]) ; } /* Given A, compute coarse and then fine dmperm */ csd *cs_dmperm (const cs *A, int seed) { int m, n, i, j, k, cnz, nc, *jmatch, *imatch, *wi, *wj, *pinv, *Cp, *Ci, *ps, *rs, nb1, nb2, *p, *q, *cc, *rr, *r, *s, ok ; cs *C ; csd *D, *scc ; /* --- Maximum matching ------------------------------------------------- */ if (!CS_CSC (A)) return (NULL) ; /* check inputs */ m = A->m ; n = A->n ; D = cs_dalloc (m, n) ; /* allocate result */ if (!D) return (NULL) ; p = D->p ; q = D->q ; r = D->r ; s = D->s ; cc = D->cc ; rr = D->rr ; jmatch = cs_maxtrans (A, seed) ; /* max transversal */ imatch = jmatch + m ; /* imatch = inverse of jmatch */ if (!jmatch) return (cs_ddone (D, NULL, jmatch, 0)) ; /* --- Coarse decomposition --------------------------------------------- */ wi = r ; wj = s ; /* use r and s as workspace */ for (j = 0 ; j < n ; j++) wj [j] = -1 ; /* unmark all cols for bfs */ for (i = 0 ; i < m ; i++) wi [i] = -1 ; /* unmark all rows for bfs */ cs_bfs (A, n, wi, wj, q, imatch, jmatch, 1) ; /* find C1, R1 from C0*/ ok = cs_bfs (A, m, wj, wi, p, jmatch, imatch, 3) ; /* find R3, C3 from R0*/ if (!ok) return (cs_ddone (D, NULL, jmatch, 0)) ; cs_unmatched (n, wj, q, cc, 0) ; /* unmatched set C0 */ cs_matched (n, wj, imatch, p, q, cc, rr, 1, 1) ; /* set R1 and C1 */ cs_matched (n, wj, imatch, p, q, cc, rr, 2, -1) ; /* set R2 and C2 */ cs_matched (n, wj, imatch, p, q, cc, rr, 3, 3) ; /* set R3 and C3 */ cs_unmatched (m, wi, p, rr, 3) ; /* unmatched set R0 */ cs_free (jmatch) ; /* --- Fine decomposition ----------------------------------------------- */ pinv = cs_pinv (p, m) ; /* pinv=p' */ if (!pinv) return (cs_ddone (D, NULL, NULL, 0)) ; C = cs_permute (A, pinv, q, 0) ;/* C=A(p,q) (it will hold A(R2,C2)) */ cs_free (pinv) ; if (!C) return (cs_ddone (D, NULL, NULL, 0)) ; Cp = C->p ; nc = cc [3] - cc [2] ; /* delete cols C0, C1, and C3 from C */ if (cc [2] > 0) for (j = cc [2] ; j <= cc [3] ; j++) Cp [j-cc[2]] = Cp [j] ; C->n = nc ; if (rr [2] - rr [1] < m) /* delete rows R0, R1, and R3 from C */ { cs_fkeep (C, cs_rprune, rr) ; cnz = Cp [nc] ; Ci = C->i ; if (rr [1] > 0) for (k = 0 ; k < cnz ; k++) Ci [k] -= rr [1] ; } C->m = nc ; scc = cs_scc (C) ; /* find strongly connected components of C*/ if (!scc) return (cs_ddone (D, C, NULL, 0)) ; /* --- Combine coarse and fine decompositions --------------------------- */ ps = scc->p ; /* C(ps,ps) is the permuted matrix */ rs = scc->r ; /* kth block is rs[k]..rs[k+1]-1 */ nb1 = scc->nb ; /* # of blocks of A(R2,C2) */ for (k = 0 ; k < nc ; k++) wj [k] = q [ps [k] + cc [2]] ; for (k = 0 ; k < nc ; k++) q [k + cc [2]] = wj [k] ; for (k = 0 ; k < nc ; k++) wi [k] = p [ps [k] + rr [1]] ; for (k = 0 ; k < nc ; k++) p [k + rr [1]] = wi [k] ; nb2 = 0 ; /* create the fine block partitions */ r [0] = s [0] = 0 ; if (cc [2] > 0) nb2++ ; /* leading coarse block A (R1, [C0 C1]) */ for (k = 0 ; k < nb1 ; k++) /* coarse block A (R2,C2) */ { r [nb2] = rs [k] + rr [1] ; /* A (R2,C2) splits into nb1 fine blocks */ s [nb2] = rs [k] + cc [2] ; nb2++ ; } if (rr [2] < m) { r [nb2] = rr [2] ; /* trailing coarse block A ([R3 R0], C3) */ s [nb2] = cc [3] ; nb2++ ; } r [nb2] = m ; s [nb2] = n ; D->nb = nb2 ; cs_dfree (scc) ; return (cs_ddone (D, C, NULL, 1)) ; } SuiteSparse/CSparse/Source/cs_load.c0000644001170100242450000000056510414453660016330 0ustar davisfac#include "cs.h" /* load a triplet matrix from a file */ cs *cs_load (FILE *f) { int i, j ; double x ; cs *T ; if (!f) return (NULL) ; /* check inputs */ T = cs_spalloc (0, 0, 1, 1, 1) ; /* allocate result */ while (fscanf (f, "%d %d %lg\n", &i, &j, &x) == 3) { if (!cs_entry (T, i, j, x)) return (cs_spfree (T)) ; } return (T) ; } SuiteSparse/CSparse/Source/README.txt0000644001170100242450000000032210360550613016241 0ustar davisfacCSparse/Source directory: primary ANSI C source code files for CSparse. All of these files are printed verbatim in the book. To compile the libcsparse.a C-callable library, just type "make" in this directory. SuiteSparse/CSparse/Source/cs_norm.c0000644001170100242450000000066410414335566016370 0ustar davisfac#include "cs.h" /* 1-norm of a sparse matrix = max (sum (abs (A))), largest column sum */ double cs_norm (const cs *A) { int p, j, n, *Ap ; double *Ax, norm = 0, s ; if (!CS_CSC (A) || !A->x) return (-1) ; /* check inputs */ n = A->n ; Ap = A->p ; Ax = A->x ; for (j = 0 ; j < n ; j++) { for (s = 0, p = Ap [j] ; p < Ap [j+1] ; p++) s += fabs (Ax [p]) ; norm = CS_MAX (norm, s) ; } return (norm) ; } SuiteSparse/CSparse/Source/cs_randperm.c0000644001170100242450000000143710417245045017217 0ustar davisfac#include "cs.h" /* return a random permutation vector, the identity perm, or p = n-1:-1:0. * seed = -1 means p = n-1:-1:0. seed = 0 means p = identity. otherwise * p = random permutation. */ int *cs_randperm (int n, int seed) { int *p, k, j, t ; if (seed == 0) return (NULL) ; /* return p = NULL (identity) */ p = cs_malloc (n, sizeof (int)) ; /* allocate result */ if (!p) return (NULL) ; /* out of memory */ for (k = 0 ; k < n ; k++) p [k] = n-k-1 ; if (seed == -1) return (p) ; /* return reverse permutation */ srand (seed) ; /* get new random number seed */ for (k = 0 ; k < n ; k++) { j = k + (rand ( ) % (n-k)) ; /* j = rand int in range k to n-1 */ t = p [j] ; /* swap p[k] and p[j] */ p [j] = p [k] ; p [k] = t ; } return (p) ; } SuiteSparse/CSparse/Source/cs_pinv.c0000644001170100242450000000062210414454051016352 0ustar davisfac#include "cs.h" /* pinv = p', or p = pinv' */ int *cs_pinv (int const *p, int n) { int k, *pinv ; if (!p) return (NULL) ; /* p = NULL denotes identity */ pinv = cs_malloc (n, sizeof (int)) ; /* allocate result */ if (!pinv) return (NULL) ; /* out of memory */ for (k = 0 ; k < n ; k++) pinv [p [k]] = k ;/* invert the permutation */ return (pinv) ; /* return result */ } SuiteSparse/CSparse/Source/cs_post.c0000644001170100242450000000171410415505633016372 0ustar davisfac#include "cs.h" /* post order a forest */ int *cs_post (const int *parent, int n) { int j, k = 0, *post, *w, *head, *next, *stack ; if (!parent) return (NULL) ; /* check inputs */ post = cs_malloc (n, sizeof (int)) ; /* allocate result */ w = cs_malloc (3*n, sizeof (int)) ; /* get workspace */ if (!w || !post) return (cs_idone (post, NULL, w, 0)) ; head = w ; next = w + n ; stack = w + 2*n ; for (j = 0 ; j < n ; j++) head [j] = -1 ; /* empty linked lists */ for (j = n-1 ; j >= 0 ; j--) /* traverse nodes in reverse order*/ { if (parent [j] == -1) continue ; /* j is a root */ next [j] = head [parent [j]] ; /* add j to list of its parent */ head [parent [j]] = j ; } for (j = 0 ; j < n ; j++) { if (parent [j] != -1) continue ; /* skip j if it is not a root */ k = cs_tdfs (j, k, head, next, post, stack) ; } return (cs_idone (post, NULL, w, 1)) ; /* success; free w, return post */ } SuiteSparse/CSparse/Source/cs_pvec.c0000644001170100242450000000044510415505525016342 0ustar davisfac#include "cs.h" /* x = b(p), for dense vectors x and b; p=NULL denotes identity */ int cs_pvec (const int *p, const double *b, double *x, int n) { int k ; if (!x || !b) return (0) ; /* check inputs */ for (k = 0 ; k < n ; k++) x [k] = b [p ? p [k] : k] ; return (1) ; } SuiteSparse/CSparse/Source/cs_entry.c0000644001170100242450000000070010414336100016526 0ustar davisfac#include "cs.h" /* add an entry to a triplet matrix; return 1 if ok, 0 otherwise */ int cs_entry (cs *T, int i, int j, double x) { if (!CS_TRIPLET (T) || i < 0 || j < 0) return (0) ; /* check inputs */ if (T->nz >= T->nzmax && !cs_sprealloc (T,2*(T->nzmax))) return (0) ; if (T->x) T->x [T->nz] = x ; T->i [T->nz] = i ; T->p [T->nz++] = j ; T->m = CS_MAX (T->m, i+1) ; T->n = CS_MAX (T->n, j+1) ; return (1) ; } SuiteSparse/CSparse/Source/cs_tdfs.c0000644001170100242450000000142010372172174016341 0ustar davisfac#include "cs.h" /* depth-first search and postorder of a tree rooted at node j */ int cs_tdfs (int j, int k, int *head, const int *next, int *post, int *stack) { int i, p, top = 0 ; if (!head || !next || !post || !stack) return (-1) ; /* check inputs */ stack [0] = j ; /* place j on the stack */ while (top >= 0) /* while (stack is not empty) */ { p = stack [top] ; /* p = top of stack */ i = head [p] ; /* i = youngest child of p */ if (i == -1) { top-- ; /* p has no unordered children left */ post [k++] = p ; /* node p is the kth postordered node */ } else { head [p] = next [i] ; /* remove i from children of p */ stack [++top] = i ; /* start dfs on child node i */ } } return (k) ; } SuiteSparse/CSparse/Source/cs_usolve.c0000644001170100242450000000072610414335705016724 0ustar davisfac#include "cs.h" /* solve Ux=b where x and b are dense. x=b on input, solution on output. */ int cs_usolve (const cs *U, double *x) { int p, j, n, *Up, *Ui ; double *Ux ; if (!CS_CSC (U) || !x) return (0) ; /* check inputs */ n = U->n ; Up = U->p ; Ui = U->i ; Ux = U->x ; for (j = n-1 ; j >= 0 ; j--) { x [j] /= Ux [Up [j+1]-1] ; for (p = Up [j] ; p < Up [j+1]-1 ; p++) { x [Ui [p]] -= Ux [p] * x [j] ; } } return (1) ; } SuiteSparse/CSparse/Source/cs_util.c0000644001170100242450000000733510436047730016371 0ustar davisfac#include "cs.h" /* allocate a sparse matrix (triplet form or compressed-column form) */ cs *cs_spalloc (int m, int n, int nzmax, int values, int triplet) { cs *A = cs_calloc (1, sizeof (cs)) ; /* allocate the cs struct */ if (!A) return (NULL) ; /* out of memory */ A->m = m ; /* define dimensions and nzmax */ A->n = n ; A->nzmax = nzmax = CS_MAX (nzmax, 1) ; A->nz = triplet ? 0 : -1 ; /* allocate triplet or comp.col */ A->p = cs_malloc (triplet ? nzmax : n+1, sizeof (int)) ; A->i = cs_malloc (nzmax, sizeof (int)) ; A->x = values ? cs_malloc (nzmax, sizeof (double)) : NULL ; return ((!A->p || !A->i || (values && !A->x)) ? cs_spfree (A) : A) ; } /* change the max # of entries sparse matrix */ int cs_sprealloc (cs *A, int nzmax) { int ok, oki, okj = 1, okx = 1 ; if (!A) return (0) ; if (nzmax <= 0) nzmax = (CS_CSC (A)) ? (A->p [A->n]) : A->nz ; A->i = cs_realloc (A->i, nzmax, sizeof (int), &oki) ; if (CS_TRIPLET (A)) A->p = cs_realloc (A->p, nzmax, sizeof (int), &okj) ; if (A->x) A->x = cs_realloc (A->x, nzmax, sizeof (double), &okx) ; ok = (oki && okj && okx) ; if (ok) A->nzmax = nzmax ; return (ok) ; } /* free a sparse matrix */ cs *cs_spfree (cs *A) { if (!A) return (NULL) ; /* do nothing if A already NULL */ cs_free (A->p) ; cs_free (A->i) ; cs_free (A->x) ; return (cs_free (A)) ; /* free the cs struct and return NULL */ } /* free a numeric factorization */ csn *cs_nfree (csn *N) { if (!N) return (NULL) ; /* do nothing if N already NULL */ cs_spfree (N->L) ; cs_spfree (N->U) ; cs_free (N->pinv) ; cs_free (N->B) ; return (cs_free (N)) ; /* free the csn struct and return NULL */ } /* free a symbolic factorization */ css *cs_sfree (css *S) { if (!S) return (NULL) ; /* do nothing if S already NULL */ cs_free (S->pinv) ; cs_free (S->q) ; cs_free (S->parent) ; cs_free (S->cp) ; cs_free (S->leftmost) ; return (cs_free (S)) ; /* free the css struct and return NULL */ } /* allocate a cs_dmperm or cs_scc result */ csd *cs_dalloc (int m, int n) { csd *D ; D = cs_calloc (1, sizeof (csd)) ; if (!D) return (NULL) ; D->p = cs_malloc (m, sizeof (int)) ; D->r = cs_malloc (m+6, sizeof (int)) ; D->q = cs_malloc (n, sizeof (int)) ; D->s = cs_malloc (n+6, sizeof (int)) ; return ((!D->p || !D->r || !D->q || !D->s) ? cs_dfree (D) : D) ; } /* free a cs_dmperm or cs_scc result */ csd *cs_dfree (csd *D) { if (!D) return (NULL) ; /* do nothing if D already NULL */ cs_free (D->p) ; cs_free (D->q) ; cs_free (D->r) ; cs_free (D->s) ; return (cs_free (D)) ; } /* free workspace and return a sparse matrix result */ cs *cs_done (cs *C, void *w, void *x, int ok) { cs_free (w) ; /* free workspace */ cs_free (x) ; return (ok ? C : cs_spfree (C)) ; /* return result if OK, else free it */ } /* free workspace and return int array result */ int *cs_idone (int *p, cs *C, void *w, int ok) { cs_spfree (C) ; /* free temporary matrix */ cs_free (w) ; /* free workspace */ return (ok ? p : cs_free (p)) ; /* return result if OK, else free it */ } /* free workspace and return a numeric factorization (Cholesky, LU, or QR) */ csn *cs_ndone (csn *N, cs *C, void *w, void *x, int ok) { cs_spfree (C) ; /* free temporary matrix */ cs_free (w) ; /* free workspace */ cs_free (x) ; return (ok ? N : cs_nfree (N)) ; /* return result if OK, else free it */ } /* free workspace and return a csd result */ csd *cs_ddone (csd *D, cs *C, void *w, int ok) { cs_spfree (C) ; /* free temporary matrix */ cs_free (w) ; /* free workspace */ return (ok ? D : cs_dfree (D)) ; /* return result if OK, else free it */ } SuiteSparse/CSparse/Source/cs_maxtrans.c0000644001170100242450000000746510447326135017256 0ustar davisfac#include "cs.h" /* find an augmenting path starting at column k and extend the match if found */ static void cs_augment (int k, const cs *A, int *jmatch, int *cheap, int *w, int *js, int *is, int *ps) { int found = 0, p, i = -1, *Ap = A->p, *Ai = A->i, head = 0, j ; js [0] = k ; /* start with just node k in jstack */ while (head >= 0) { /* --- Start (or continue) depth-first-search at node j ------------- */ j = js [head] ; /* get j from top of jstack */ if (w [j] != k) /* 1st time j visited for kth path */ { w [j] = k ; /* mark j as visited for kth path */ for (p = cheap [j] ; p < Ap [j+1] && !found ; p++) { i = Ai [p] ; /* try a cheap assignment (i,j) */ found = (jmatch [i] == -1) ; } cheap [j] = p ; /* start here next time j is traversed*/ if (found) { is [head] = i ; /* column j matched with row i */ break ; /* end of augmenting path */ } ps [head] = Ap [j] ; /* no cheap match: start dfs for j */ } /* --- Depth-first-search of neighbors of j ------------------------- */ for (p = ps [head] ; p < Ap [j+1] ; p++) { i = Ai [p] ; /* consider row i */ if (w [jmatch [i]] == k) continue ; /* skip jmatch [i] if marked */ ps [head] = p + 1 ; /* pause dfs of node j */ is [head] = i ; /* i will be matched with j if found */ js [++head] = jmatch [i] ; /* start dfs at column jmatch [i] */ break ; } if (p == Ap [j+1]) head-- ; /* node j is done; pop from stack */ } /* augment the match if path found: */ if (found) for (p = head ; p >= 0 ; p--) jmatch [is [p]] = js [p] ; } /* find a maximum transveral */ int *cs_maxtrans (const cs *A, int seed) /*[jmatch [0..m-1]; imatch [0..n-1]]*/ { int i, j, k, n, m, p, n2 = 0, m2 = 0, *Ap, *jimatch, *w, *cheap, *js, *is, *ps, *Ai, *Cp, *jmatch, *imatch, *q ; cs *C ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ n = A->n ; m = A->m ; Ap = A->p ; Ai = A->i ; w = jimatch = cs_calloc (m+n, sizeof (int)) ; /* allocate result */ if (!jimatch) return (NULL) ; for (k = 0, j = 0 ; j < n ; j++) /* count nonempty rows and columns */ { n2 += (Ap [j] < Ap [j+1]) ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { w [Ai [p]] = 1 ; k += (j == Ai [p]) ; /* count entries already on diagonal */ } } if (k == CS_MIN (m,n)) /* quick return if diagonal zero-free */ { jmatch = jimatch ; imatch = jimatch + m ; for (i = 0 ; i < k ; i++) jmatch [i] = i ; for ( ; i < m ; i++) jmatch [i] = -1 ; for (j = 0 ; j < k ; j++) imatch [j] = j ; for ( ; j < n ; j++) imatch [j] = -1 ; return (cs_idone (jimatch, NULL, NULL, 1)) ; } for (i = 0 ; i < m ; i++) m2 += w [i] ; C = (m2 < n2) ? cs_transpose (A,0) : ((cs *) A) ; /* transpose if needed */ if (!C) return (cs_idone (jimatch, (m2 < n2) ? C : NULL, NULL, 0)) ; n = C->n ; m = C->m ; Cp = C->p ; jmatch = (m2 < n2) ? jimatch + n : jimatch ; imatch = (m2 < n2) ? jimatch : jimatch + m ; w = cs_malloc (5*n, sizeof (int)) ; /* get workspace */ if (!w) return (cs_idone (jimatch, (m2 < n2) ? C : NULL, w, 0)) ; cheap = w + n ; js = w + 2*n ; is = w + 3*n ; ps = w + 4*n ; for (j = 0 ; j < n ; j++) cheap [j] = Cp [j] ; /* for cheap assignment */ for (j = 0 ; j < n ; j++) w [j] = -1 ; /* all columns unflagged */ for (i = 0 ; i < m ; i++) jmatch [i] = -1 ; /* nothing matched yet */ q = cs_randperm (n, seed) ; /* q = random permutation */ for (k = 0 ; k < n ; k++) /* augment, starting at column q[k] */ { cs_augment (q ? q [k]: k, C, jmatch, cheap, w, js, is, ps) ; } cs_free (q) ; for (j = 0 ; j < n ; j++) imatch [j] = -1 ; /* find row match */ for (i = 0 ; i < m ; i++) if (jmatch [i] >= 0) imatch [jmatch [i]] = i ; return (cs_idone (jimatch, (m2 < n2) ? C : NULL, w, 1)) ; } SuiteSparse/CSparse/Source/cs_spsolve.c0000644001170100242450000000225410415246613017100 0ustar davisfac#include "cs.h" /* solve Gx=b(:,k), where G is either upper (lo=0) or lower (lo=1) triangular */ int cs_spsolve (cs *G, const cs *B, int k, int *xi, double *x, const int *pinv, int lo) { int j, J, p, q, px, top, n, *Gp, *Gi, *Bp, *Bi ; double *Gx, *Bx ; if (!CS_CSC (G) || !CS_CSC (B) || !xi || !x) return (-1) ; Gp = G->p ; Gi = G->i ; Gx = G->x ; n = G->n ; Bp = B->p ; Bi = B->i ; Bx = B->x ; top = cs_reach (G, B, k, xi, pinv) ; /* xi[top..n-1]=Reach(B(:,k)) */ for (p = top ; p < n ; p++) x [xi [p]] = 0 ; /* clear x */ for (p = Bp [k] ; p < Bp [k+1] ; p++) x [Bi [p]] = Bx [p] ; /* scatter B */ for (px = top ; px < n ; px++) { j = xi [px] ; /* x(j) is nonzero */ J = pinv ? (pinv [j]) : j ; /* j maps to col J of G */ if (J < 0) continue ; /* column J is empty */ x [j] /= Gx [lo ? (Gp [J]) : (Gp [J+1]-1)] ;/* x(j) /= G(j,j) */ p = lo ? (Gp [J]+1) : (Gp [J]) ; /* lo: L(j,j) 1st entry */ q = lo ? (Gp [J+1]) : (Gp [J+1]-1) ; /* up: U(j,j) last entry */ for ( ; p < q ; p++) { x [Gi [p]] -= Gx [p] * x [j] ; /* x(i) -= G(i,j) * x(j) */ } } return (top) ; /* return top of stack */ } SuiteSparse/CSparse/Source/cs_droptol.c0000644001170100242450000000035410372171107017064 0ustar davisfac#include "cs.h" static int cs_tol (int i, int j, double aij, void *tol) { return (fabs (aij) > *((double *) tol)) ; } int cs_droptol (cs *A, double tol) { return (cs_fkeep (A, &cs_tol, &tol)) ; /* keep all large entries */ } SuiteSparse/CSparse/Source/cs_etree.c0000644001170100242450000000224310414452033016501 0ustar davisfac#include "cs.h" /* compute the etree of A (using triu(A), or A'A without forming A'A */ int *cs_etree (const cs *A, int ata) { int i, k, p, m, n, inext, *Ap, *Ai, *w, *parent, *ancestor, *prev ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; parent = cs_malloc (n, sizeof (int)) ; /* allocate result */ w = cs_malloc (n + (ata ? m : 0), sizeof (int)) ; /* get workspace */ if (!w || !parent) return (cs_idone (parent, NULL, w, 0)) ; ancestor = w ; prev = w + n ; if (ata) for (i = 0 ; i < m ; i++) prev [i] = -1 ; for (k = 0 ; k < n ; k++) { parent [k] = -1 ; /* node k has no parent yet */ ancestor [k] = -1 ; /* nor does k have an ancestor */ for (p = Ap [k] ; p < Ap [k+1] ; p++) { i = ata ? (prev [Ai [p]]) : (Ai [p]) ; for ( ; i != -1 && i < k ; i = inext) /* traverse from i to k */ { inext = ancestor [i] ; /* inext = ancestor of i */ ancestor [i] = k ; /* path compression */ if (inext == -1) parent [i] = k ; /* no anc., parent is k */ } if (ata) prev [Ai [p]] = k ; } } return (cs_idone (parent, NULL, w, 1)) ; } SuiteSparse/CSparse/Source/cs_fkeep.c0000644001170100242450000000142510415722164016476 0ustar davisfac#include "cs.h" /* drop entries for which fkeep(A(i,j)) is false; return nz if OK, else -1 */ int cs_fkeep (cs *A, int (*fkeep) (int, int, double, void *), void *other) { int j, p, nz = 0, n, *Ap, *Ai ; double *Ax ; if (!CS_CSC (A) || !fkeep) return (-1) ; /* check inputs */ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; for (j = 0 ; j < n ; j++) { p = Ap [j] ; /* get current location of col j */ Ap [j] = nz ; /* record new location of col j */ for ( ; p < Ap [j+1] ; p++) { if (fkeep (Ai [p], j, Ax ? Ax [p] : 1, other)) { if (Ax) Ax [nz] = Ax [p] ; /* keep A(i,j) */ Ai [nz++] = Ai [p] ; } } } Ap [n] = nz ; /* finalize A */ cs_sprealloc (A, 0) ; /* remove extra space from A */ return (nz) ; } SuiteSparse/CSparse/Source/cs_lusol.c0000644001170100242450000000142210416442200016526 0ustar davisfac#include "cs.h" /* x=A\b where A is unsymmetric; b overwritten with solution */ int cs_lusol (int order, const cs *A, double *b, double tol) { double *x ; css *S ; csn *N ; int n, ok ; if (!CS_CSC (A) || !b) return (0) ; /* check inputs */ n = A->n ; S = cs_sqr (order, A, 0) ; /* ordering and symbolic analysis */ N = cs_lu (A, S, tol) ; /* numeric LU factorization */ x = cs_malloc (n, sizeof (double)) ; /* get workspace */ ok = (S && N && x) ; if (ok) { cs_ipvec (N->pinv, b, x, n) ; /* x = b(p) */ cs_lsolve (N->L, x) ; /* x = L\x */ cs_usolve (N->U, x) ; /* x = U\x */ cs_ipvec (S->q, x, b, n) ; /* b(q) = x */ } cs_free (x) ; cs_sfree (S) ; cs_nfree (N) ; return (ok) ; } SuiteSparse/CSparse/Source/cs_ereach.c0000644001170100242450000000173610414336415016637 0ustar davisfac#include "cs.h" /* find nonzero pattern of Cholesky L(k,1:k-1) using etree and triu(A(:,k)) */ int cs_ereach (const cs *A, int k, const int *parent, int *s, int *w) { int i, p, n, len, top, *Ap, *Ai ; if (!CS_CSC (A) || !parent || !s || !w) return (-1) ; /* check inputs */ top = n = A->n ; Ap = A->p ; Ai = A->i ; CS_MARK (w, k) ; /* mark node k as visited */ for (p = Ap [k] ; p < Ap [k+1] ; p++) { i = Ai [p] ; /* A(i,k) is nonzero */ if (i > k) continue ; /* only use upper triangular part of A */ for (len = 0 ; !CS_MARKED (w,i) ; i = parent [i]) /* traverse up etree*/ { s [len++] = i ; /* L(k,i) is nonzero */ CS_MARK (w, i) ; /* mark i as visited */ } while (len > 0) s [--top] = s [--len] ; /* push path onto stack */ } for (p = top ; p < n ; p++) CS_MARK (w, s [p]) ; /* unmark all nodes */ CS_MARK (w, k) ; /* unmark node k */ return (top) ; /* s [top..n-1] contains pattern of L(k,:)*/ } SuiteSparse/CSparse/Source/cs_gaxpy.c0000644001170100242450000000061410414335537016536 0ustar davisfac#include "cs.h" /* y = A*x+y */ int cs_gaxpy (const cs *A, const double *x, double *y) { int p, j, n, *Ap, *Ai ; double *Ax ; if (!CS_CSC (A) || !x || !y) return (0) ; /* check inputs */ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { y [Ai [p]] += Ax [p] * x [j] ; } } return (1) ; } SuiteSparse/CSparse/Source/cs_multiply.c0000644001170100242450000000256110567641255017276 0ustar davisfac#include "cs.h" /* C = A*B */ cs *cs_multiply (const cs *A, const cs *B) { int p, j, nz = 0, anz, *Cp, *Ci, *Bp, m, n, bnz, *w, values, *Bi ; double *x, *Bx, *Cx ; cs *C ; if (!CS_CSC (A) || !CS_CSC (B)) return (NULL) ; /* check inputs */ if (A->n != B->m) return (NULL) ; m = A->m ; anz = A->p [A->n] ; n = B->n ; Bp = B->p ; Bi = B->i ; Bx = B->x ; bnz = Bp [n] ; w = cs_calloc (m, sizeof (int)) ; /* get workspace */ values = (A->x != NULL) && (Bx != NULL) ; x = values ? cs_malloc (m, sizeof (double)) : NULL ; /* get workspace */ C = cs_spalloc (m, n, anz + bnz, values, 0) ; /* allocate result */ if (!C || !w || (values && !x)) return (cs_done (C, w, x, 0)) ; Cp = C->p ; for (j = 0 ; j < n ; j++) { if (nz + m > C->nzmax && !cs_sprealloc (C, 2*(C->nzmax)+m)) { return (cs_done (C, w, x, 0)) ; /* out of memory */ } Ci = C->i ; Cx = C->x ; /* C->i and C->x may be reallocated */ Cp [j] = nz ; /* column j of C starts here */ for (p = Bp [j] ; p < Bp [j+1] ; p++) { nz = cs_scatter (A, Bi [p], Bx ? Bx [p] : 1, w, x, j+1, C, nz) ; } if (values) for (p = Cp [j] ; p < nz ; p++) Cx [p] = x [Ci [p]] ; } Cp [n] = nz ; /* finalize the last column of C */ cs_sprealloc (C, 0) ; /* remove extra space from C */ return (cs_done (C, w, x, 1)) ; /* success; free workspace, return C */ } SuiteSparse/CSparse/Source/cs_add.c0000644001170100242450000000242210567641320016134 0ustar davisfac#include "cs.h" /* C = alpha*A + beta*B */ cs *cs_add (const cs *A, const cs *B, double alpha, double beta) { int p, j, nz = 0, anz, *Cp, *Ci, *Bp, m, n, bnz, *w, values ; double *x, *Bx, *Cx ; cs *C ; if (!CS_CSC (A) || !CS_CSC (B)) return (NULL) ; /* check inputs */ if (A->m != B->m || A->n != B->n) return (NULL) ; m = A->m ; anz = A->p [A->n] ; n = B->n ; Bp = B->p ; Bx = B->x ; bnz = Bp [n] ; w = cs_calloc (m, sizeof (int)) ; /* get workspace */ values = (A->x != NULL) && (Bx != NULL) ; x = values ? cs_malloc (m, sizeof (double)) : NULL ; /* get workspace */ C = cs_spalloc (m, n, anz + bnz, values, 0) ; /* allocate result*/ if (!C || !w || (values && !x)) return (cs_done (C, w, x, 0)) ; Cp = C->p ; Ci = C->i ; Cx = C->x ; for (j = 0 ; j < n ; j++) { Cp [j] = nz ; /* column j of C starts here */ nz = cs_scatter (A, j, alpha, w, x, j+1, C, nz) ; /* alpha*A(:,j)*/ nz = cs_scatter (B, j, beta, w, x, j+1, C, nz) ; /* beta*B(:,j) */ if (values) for (p = Cp [j] ; p < nz ; p++) Cx [p] = x [Ci [p]] ; } Cp [n] = nz ; /* finalize the last column of C */ cs_sprealloc (C, 0) ; /* remove extra space from C */ return (cs_done (C, w, x, 1)) ; /* success; free workspace, return C */ } SuiteSparse/CSparse/Source/cs_amd.c0000644001170100242450000003047310447326117016155 0ustar davisfac#include "cs.h" /* clear w */ static int cs_wclear (int mark, int lemax, int *w, int n) { int k ; if (mark < 2 || (mark + lemax < 0)) { for (k = 0 ; k < n ; k++) if (w [k] != 0) w [k] = 1 ; mark = 2 ; } return (mark) ; /* at this point, w [0..n-1] < mark holds */ } /* keep off-diagonal entries; drop diagonal entries */ static int cs_diag (int i, int j, double aij, void *other) { return (i != j) ; } /* p = amd(A+A') if symmetric is true, or amd(A'A) otherwise */ int *cs_amd (int order, const cs *A) /* order 0:natural, 1:Chol, 2:LU, 3:QR */ { cs *C, *A2, *AT ; int *Cp, *Ci, *last, *W, *len, *nv, *next, *P, *head, *elen, *degree, *w, *hhead, *ATp, *ATi, d, dk, dext, lemax = 0, e, elenk, eln, i, j, k, k1, k2, k3, jlast, ln, dense, nzmax, mindeg = 0, nvi, nvj, nvk, mark, wnvi, ok, cnz, nel = 0, p, p1, p2, p3, p4, pj, pk, pk1, pk2, pn, q, n, m, t ; unsigned int h ; /* --- Construct matrix C ----------------------------------------------- */ if (!CS_CSC (A) || order <= 0 || order > 3) return (NULL) ; /* check */ AT = cs_transpose (A, 0) ; /* compute A' */ if (!AT) return (NULL) ; m = A->m ; n = A->n ; dense = CS_MAX (16, 10 * sqrt ((double) n)) ; /* find dense threshold */ dense = CS_MIN (n-2, dense) ; if (order == 1 && n == m) { C = cs_add (A, AT, 0, 0) ; /* C = A+A' */ } else if (order == 2) { ATp = AT->p ; /* drop dense columns from AT */ ATi = AT->i ; for (p2 = 0, j = 0 ; j < m ; j++) { p = ATp [j] ; /* column j of AT starts here */ ATp [j] = p2 ; /* new column j starts here */ if (ATp [j+1] - p > dense) continue ; /* skip dense col j */ for ( ; p < ATp [j+1] ; p++) ATi [p2++] = ATi [p] ; } ATp [m] = p2 ; /* finalize AT */ A2 = cs_transpose (AT, 0) ; /* A2 = AT' */ C = A2 ? cs_multiply (AT, A2) : NULL ; /* C=A'*A with no dense rows */ cs_spfree (A2) ; } else { C = cs_multiply (AT, A) ; /* C=A'*A */ } cs_spfree (AT) ; if (!C) return (NULL) ; cs_fkeep (C, &cs_diag, NULL) ; /* drop diagonal entries */ Cp = C->p ; cnz = Cp [n] ; P = cs_malloc (n+1, sizeof (int)) ; /* allocate result */ W = cs_malloc (8*(n+1), sizeof (int)) ; /* get workspace */ t = cnz + cnz/5 + 2*n ; /* add elbow room to C */ if (!P || !W || !cs_sprealloc (C, t)) return (cs_idone (P, C, W, 0)) ; len = W ; nv = W + (n+1) ; next = W + 2*(n+1) ; head = W + 3*(n+1) ; elen = W + 4*(n+1) ; degree = W + 5*(n+1) ; w = W + 6*(n+1) ; hhead = W + 7*(n+1) ; last = P ; /* use P as workspace for last */ /* --- Initialize quotient graph ---------------------------------------- */ for (k = 0 ; k < n ; k++) len [k] = Cp [k+1] - Cp [k] ; len [n] = 0 ; nzmax = C->nzmax ; Ci = C->i ; for (i = 0 ; i <= n ; i++) { head [i] = -1 ; /* degree list i is empty */ last [i] = -1 ; next [i] = -1 ; hhead [i] = -1 ; /* hash list i is empty */ nv [i] = 1 ; /* node i is just one node */ w [i] = 1 ; /* node i is alive */ elen [i] = 0 ; /* Ek of node i is empty */ degree [i] = len [i] ; /* degree of node i */ } mark = cs_wclear (0, 0, w, n) ; /* clear w */ elen [n] = -2 ; /* n is a dead element */ Cp [n] = -1 ; /* n is a root of assembly tree */ w [n] = 0 ; /* n is a dead element */ /* --- Initialize degree lists ------------------------------------------ */ for (i = 0 ; i < n ; i++) { d = degree [i] ; if (d == 0) /* node i is empty */ { elen [i] = -2 ; /* element i is dead */ nel++ ; Cp [i] = -1 ; /* i is a root of assembly tree */ w [i] = 0 ; } else if (d > dense) /* node i is dense */ { nv [i] = 0 ; /* absorb i into element n */ elen [i] = -1 ; /* node i is dead */ nel++ ; Cp [i] = CS_FLIP (n) ; nv [n]++ ; } else { if (head [d] != -1) last [head [d]] = i ; next [i] = head [d] ; /* put node i in degree list d */ head [d] = i ; } } while (nel < n) /* while (selecting pivots) do */ { /* --- Select node of minimum approximate degree -------------------- */ for (k = -1 ; mindeg < n && (k = head [mindeg]) == -1 ; mindeg++) ; if (next [k] != -1) last [next [k]] = -1 ; head [mindeg] = next [k] ; /* remove k from degree list */ elenk = elen [k] ; /* elenk = |Ek| */ nvk = nv [k] ; /* # of nodes k represents */ nel += nvk ; /* nv[k] nodes of A eliminated */ /* --- Garbage collection ------------------------------------------- */ if (elenk > 0 && cnz + mindeg >= nzmax) { for (j = 0 ; j < n ; j++) { if ((p = Cp [j]) >= 0) /* j is a live node or element */ { Cp [j] = Ci [p] ; /* save first entry of object */ Ci [p] = CS_FLIP (j) ; /* first entry is now CS_FLIP(j) */ } } for (q = 0, p = 0 ; p < cnz ; ) /* scan all of memory */ { if ((j = CS_FLIP (Ci [p++])) >= 0) /* found object j */ { Ci [q] = Cp [j] ; /* restore first entry of object */ Cp [j] = q++ ; /* new pointer to object j */ for (k3 = 0 ; k3 < len [j]-1 ; k3++) Ci [q++] = Ci [p++] ; } } cnz = q ; /* Ci [cnz...nzmax-1] now free */ } /* --- Construct new element ---------------------------------------- */ dk = 0 ; nv [k] = -nvk ; /* flag k as in Lk */ p = Cp [k] ; pk1 = (elenk == 0) ? p : cnz ; /* do in place if elen[k] == 0 */ pk2 = pk1 ; for (k1 = 1 ; k1 <= elenk + 1 ; k1++) { if (k1 > elenk) { e = k ; /* search the nodes in k */ pj = p ; /* list of nodes starts at Ci[pj]*/ ln = len [k] - elenk ; /* length of list of nodes in k */ } else { e = Ci [p++] ; /* search the nodes in e */ pj = Cp [e] ; ln = len [e] ; /* length of list of nodes in e */ } for (k2 = 1 ; k2 <= ln ; k2++) { i = Ci [pj++] ; if ((nvi = nv [i]) <= 0) continue ; /* node i dead, or seen */ dk += nvi ; /* degree[Lk] += size of node i */ nv [i] = -nvi ; /* negate nv[i] to denote i in Lk*/ Ci [pk2++] = i ; /* place i in Lk */ if (next [i] != -1) last [next [i]] = last [i] ; if (last [i] != -1) /* remove i from degree list */ { next [last [i]] = next [i] ; } else { head [degree [i]] = next [i] ; } } if (e != k) { Cp [e] = CS_FLIP (k) ; /* absorb e into k */ w [e] = 0 ; /* e is now a dead element */ } } if (elenk != 0) cnz = pk2 ; /* Ci [cnz...nzmax] is free */ degree [k] = dk ; /* external degree of k - |Lk\i| */ Cp [k] = pk1 ; /* element k is in Ci[pk1..pk2-1] */ len [k] = pk2 - pk1 ; elen [k] = -2 ; /* k is now an element */ /* --- Find set differences ----------------------------------------- */ mark = cs_wclear (mark, lemax, w, n) ; /* clear w if necessary */ for (pk = pk1 ; pk < pk2 ; pk++) /* scan 1: find |Le\Lk| */ { i = Ci [pk] ; if ((eln = elen [i]) <= 0) continue ;/* skip if elen[i] empty */ nvi = -nv [i] ; /* nv [i] was negated */ wnvi = mark - nvi ; for (p = Cp [i] ; p <= Cp [i] + eln - 1 ; p++) /* scan Ei */ { e = Ci [p] ; if (w [e] >= mark) { w [e] -= nvi ; /* decrement |Le\Lk| */ } else if (w [e] != 0) /* ensure e is a live element */ { w [e] = degree [e] + wnvi ; /* 1st time e seen in scan 1 */ } } } /* --- Degree update ------------------------------------------------ */ for (pk = pk1 ; pk < pk2 ; pk++) /* scan2: degree update */ { i = Ci [pk] ; /* consider node i in Lk */ p1 = Cp [i] ; p2 = p1 + elen [i] - 1 ; pn = p1 ; for (h = 0, d = 0, p = p1 ; p <= p2 ; p++) /* scan Ei */ { e = Ci [p] ; if (w [e] != 0) /* e is an unabsorbed element */ { dext = w [e] - mark ; /* dext = |Le\Lk| */ if (dext > 0) { d += dext ; /* sum up the set differences */ Ci [pn++] = e ; /* keep e in Ei */ h += e ; /* compute the hash of node i */ } else { Cp [e] = CS_FLIP (k) ; /* aggressive absorb. e->k */ w [e] = 0 ; /* e is a dead element */ } } } elen [i] = pn - p1 + 1 ; /* elen[i] = |Ei| */ p3 = pn ; p4 = p1 + len [i] ; for (p = p2 + 1 ; p < p4 ; p++) /* prune edges in Ai */ { j = Ci [p] ; if ((nvj = nv [j]) <= 0) continue ; /* node j dead or in Lk */ d += nvj ; /* degree(i) += |j| */ Ci [pn++] = j ; /* place j in node list of i */ h += j ; /* compute hash for node i */ } if (d == 0) /* check for mass elimination */ { Cp [i] = CS_FLIP (k) ; /* absorb i into k */ nvi = -nv [i] ; dk -= nvi ; /* |Lk| -= |i| */ nvk += nvi ; /* |k| += nv[i] */ nel += nvi ; nv [i] = 0 ; elen [i] = -1 ; /* node i is dead */ } else { degree [i] = CS_MIN (degree [i], d) ; /* update degree(i) */ Ci [pn] = Ci [p3] ; /* move first node to end */ Ci [p3] = Ci [p1] ; /* move 1st el. to end of Ei */ Ci [p1] = k ; /* add k as 1st element in of Ei */ len [i] = pn - p1 + 1 ; /* new len of adj. list of node i */ h %= n ; /* finalize hash of i */ next [i] = hhead [h] ; /* place i in hash bucket */ hhead [h] = i ; last [i] = h ; /* save hash of i in last[i] */ } } /* scan2 is done */ degree [k] = dk ; /* finalize |Lk| */ lemax = CS_MAX (lemax, dk) ; mark = cs_wclear (mark+lemax, lemax, w, n) ; /* clear w */ /* --- Supernode detection ------------------------------------------ */ for (pk = pk1 ; pk < pk2 ; pk++) { i = Ci [pk] ; if (nv [i] >= 0) continue ; /* skip if i is dead */ h = last [i] ; /* scan hash bucket of node i */ i = hhead [h] ; hhead [h] = -1 ; /* hash bucket will be empty */ for ( ; i != -1 && next [i] != -1 ; i = next [i], mark++) { ln = len [i] ; eln = elen [i] ; for (p = Cp [i]+1 ; p <= Cp [i] + ln-1 ; p++) w [Ci [p]] = mark; jlast = i ; for (j = next [i] ; j != -1 ; ) /* compare i with all j */ { ok = (len [j] == ln) && (elen [j] == eln) ; for (p = Cp [j] + 1 ; ok && p <= Cp [j] + ln - 1 ; p++) { if (w [Ci [p]] != mark) ok = 0 ; /* compare i and j*/ } if (ok) /* i and j are identical */ { Cp [j] = CS_FLIP (i) ; /* absorb j into i */ nv [i] += nv [j] ; nv [j] = 0 ; elen [j] = -1 ; /* node j is dead */ j = next [j] ; /* delete j from hash bucket */ next [jlast] = j ; } else { jlast = j ; /* j and i are different */ j = next [j] ; } } } } /* --- Finalize new element------------------------------------------ */ for (p = pk1, pk = pk1 ; pk < pk2 ; pk++) /* finalize Lk */ { i = Ci [pk] ; if ((nvi = -nv [i]) <= 0) continue ;/* skip if i is dead */ nv [i] = nvi ; /* restore nv[i] */ d = degree [i] + dk - nvi ; /* compute external degree(i) */ d = CS_MIN (d, n - nel - nvi) ; if (head [d] != -1) last [head [d]] = i ; next [i] = head [d] ; /* put i back in degree list */ last [i] = -1 ; head [d] = i ; mindeg = CS_MIN (mindeg, d) ; /* find new minimum degree */ degree [i] = d ; Ci [p++] = i ; /* place i in Lk */ } nv [k] = nvk ; /* # nodes absorbed into k */ if ((len [k] = p-pk1) == 0) /* length of adj list of element k*/ { Cp [k] = -1 ; /* k is a root of the tree */ w [k] = 0 ; /* k is now a dead element */ } if (elenk != 0) cnz = p ; /* free unused space in Lk */ } /* --- Postordering ----------------------------------------------------- */ for (i = 0 ; i < n ; i++) Cp [i] = CS_FLIP (Cp [i]) ;/* fix assembly tree */ for (j = 0 ; j <= n ; j++) head [j] = -1 ; for (j = n ; j >= 0 ; j--) /* place unordered nodes in lists */ { if (nv [j] > 0) continue ; /* skip if j is an element */ next [j] = head [Cp [j]] ; /* place j in list of its parent */ head [Cp [j]] = j ; } for (e = n ; e >= 0 ; e--) /* place elements in lists */ { if (nv [e] <= 0) continue ; /* skip unless e is an element */ if (Cp [e] != -1) { next [e] = head [Cp [e]] ; /* place e in list of its parent */ head [Cp [e]] = e ; } } for (k = 0, i = 0 ; i <= n ; i++) /* postorder the assembly tree */ { if (Cp [i] == -1) k = cs_tdfs (i, k, head, next, P, w) ; } return (cs_idone (P, C, W, 1)) ; } SuiteSparse/CSparse/Source/cs_dfs.c0000644001170100242450000000253110415506416016157 0ustar davisfac#include "cs.h" /* depth-first-search of the graph of a matrix, starting at node j */ int cs_dfs (int j, cs *G, int top, int *xi, int *pstack, const int *pinv) { int i, p, p2, done, jnew, head = 0, *Gp, *Gi ; if (!CS_CSC (G) || !xi || !pstack) return (-1) ; /* check inputs */ Gp = G->p ; Gi = G->i ; xi [0] = j ; /* initialize the recursion stack */ while (head >= 0) { j = xi [head] ; /* get j from the top of the recursion stack */ jnew = pinv ? (pinv [j]) : j ; if (!CS_MARKED (Gp, j)) { CS_MARK (Gp, j) ; /* mark node j as visited */ pstack [head] = (jnew < 0) ? 0 : CS_UNFLIP (Gp [jnew]) ; } done = 1 ; /* node j done if no unvisited neighbors */ p2 = (jnew < 0) ? 0 : CS_UNFLIP (Gp [jnew+1]) ; for (p = pstack [head] ; p < p2 ; p++) /* examine all neighbors of j */ { i = Gi [p] ; /* consider neighbor node i */ if (CS_MARKED (Gp, i)) continue ; /* skip visited node i */ pstack [head] = p ; /* pause depth-first search of node j */ xi [++head] = i ; /* start dfs at node i */ done = 0 ; /* node j is not done */ break ; /* break, to start dfs (i) */ } if (done) /* depth-first search at node j is done */ { head-- ; /* remove j from the recursion stack */ xi [--top] = j ; /* and place in the output stack */ } } return (top) ; } SuiteSparse/CSparse/Source/cs_scc.c0000644001170100242450000000332410414452565016160 0ustar davisfac#include "cs.h" /* find the strongly connected components of a square matrix */ csd *cs_scc (cs *A) /* matrix A temporarily modified, then restored */ { int n, i, k, b, nb = 0, top, *xi, *pstack, *p, *r, *Ap, *ATp, *rcopy, *Blk ; cs *AT ; csd *D ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ n = A->n ; Ap = A->p ; D = cs_dalloc (n, 0) ; /* allocate result */ AT = cs_transpose (A, 0) ; /* AT = A' */ xi = cs_malloc (2*n+1, sizeof (int)) ; /* get workspace */ if (!D || !AT || !xi) return (cs_ddone (D, AT, xi, 0)) ; Blk = xi ; rcopy = pstack = xi + n ; p = D->p ; r = D->r ; ATp = AT->p ; top = n ; for (i = 0 ; i < n ; i++) /* first dfs(A) to find finish times (xi) */ { if (!CS_MARKED (Ap, i)) top = cs_dfs (i, A, top, xi, pstack, NULL) ; } for (i = 0 ; i < n ; i++) CS_MARK (Ap, i) ; /* restore A; unmark all nodes*/ top = n ; nb = n ; for (k = 0 ; k < n ; k++) /* dfs(A') to find strongly connnected comp */ { i = xi [k] ; /* get i in reverse order of finish times */ if (CS_MARKED (ATp, i)) continue ; /* skip node i if already ordered */ r [nb--] = top ; /* node i is the start of a component in p */ top = cs_dfs (i, AT, top, p, pstack, NULL) ; } r [nb] = 0 ; /* first block starts at zero; shift r up */ for (k = nb ; k <= n ; k++) r [k-nb] = r [k] ; D->nb = nb = n-nb ; /* nb = # of strongly connected components */ for (b = 0 ; b < nb ; b++) /* sort each block in natural order */ { for (k = r [b] ; k < r [b+1] ; k++) Blk [p [k]] = b ; } for (b = 0 ; b <= nb ; b++) rcopy [b] = r [b] ; for (i = 0 ; i < n ; i++) p [rcopy [Blk [i]]++] = i ; return (cs_ddone (D, AT, xi, 1)) ; } SuiteSparse/CSparse/Source/cs_sqr.c0000644001170100242450000000651010416442261016207 0ustar davisfac#include "cs.h" /* compute nnz(V) = S->lnz, S->pinv, S->leftmost, S->m2 from A and S->parent */ static int cs_vcount (const cs *A, css *S) { int i, k, p, pa, n = A->n, m = A->m, *Ap = A->p, *Ai = A->i, *next, *head, *tail, *nque, *pinv, *leftmost, *w, *parent = S->parent ; S->pinv = pinv = cs_malloc (m+n, sizeof (int)) ; /* allocate pinv, */ S->leftmost = leftmost = cs_malloc (m, sizeof (int)) ; /* and leftmost */ w = cs_malloc (m+3*n, sizeof (int)) ; /* get workspace */ if (!pinv || !w || !leftmost) { cs_free (w) ; /* pinv and leftmost freed later */ return (0) ; /* out of memory */ } next = w ; head = w + m ; tail = w + m + n ; nque = w + m + 2*n ; for (k = 0 ; k < n ; k++) head [k] = -1 ; /* queue k is empty */ for (k = 0 ; k < n ; k++) tail [k] = -1 ; for (k = 0 ; k < n ; k++) nque [k] = 0 ; for (i = 0 ; i < m ; i++) leftmost [i] = -1 ; for (k = n-1 ; k >= 0 ; k--) { for (p = Ap [k] ; p < Ap [k+1] ; p++) { leftmost [Ai [p]] = k ; /* leftmost[i] = min(find(A(i,:)))*/ } } for (i = m-1 ; i >= 0 ; i--) /* scan rows in reverse order */ { pinv [i] = -1 ; /* row i is not yet ordered */ k = leftmost [i] ; if (k == -1) continue ; /* row i is empty */ if (nque [k]++ == 0) tail [k] = i ; /* first row in queue k */ next [i] = head [k] ; /* put i at head of queue k */ head [k] = i ; } S->lnz = 0 ; S->m2 = m ; for (k = 0 ; k < n ; k++) /* find row permutation and nnz(V)*/ { i = head [k] ; /* remove row i from queue k */ S->lnz++ ; /* count V(k,k) as nonzero */ if (i < 0) i = S->m2++ ; /* add a fictitious row */ pinv [i] = k ; /* associate row i with V(:,k) */ if (--nque [k] <= 0) continue ; /* skip if V(k+1:m,k) is empty */ S->lnz += nque [k] ; /* nque [k] is nnz (V(k+1:m,k)) */ if ((pa = parent [k]) != -1) /* move all rows to parent of k */ { if (nque [pa] == 0) tail [pa] = tail [k] ; next [tail [k]] = head [pa] ; head [pa] = next [i] ; nque [pa] += nque [k] ; } } for (i = 0 ; i < m ; i++) if (pinv [i] < 0) pinv [i] = k++ ; cs_free (w) ; return (1) ; } /* symbolic ordering and analysis for QR or LU */ css *cs_sqr (int order, const cs *A, int qr) { int n, k, ok = 1, *post ; css *S ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ n = A->n ; S = cs_calloc (1, sizeof (css)) ; /* allocate result S */ if (!S) return (NULL) ; /* out of memory */ S->q = cs_amd (order, A) ; /* fill-reducing ordering */ if (order && !S->q) return (cs_sfree (S)) ; if (qr) /* QR symbolic analysis */ { cs *C = order ? cs_permute (A, NULL, S->q, 0) : ((cs *) A) ; S->parent = cs_etree (C, 1) ; /* etree of C'*C, where C=A(:,q) */ post = cs_post (S->parent, n) ; S->cp = cs_counts (C, S->parent, post, 1) ; /* col counts chol(C'*C) */ cs_free (post) ; ok = C && S->parent && S->cp && cs_vcount (C, S) ; if (ok) for (S->unz = 0, k = 0 ; k < n ; k++) S->unz += S->cp [k] ; ok = ok && S->lnz >= 0 && S->unz >= 0 ; /* int overflow guard */ if (order) cs_spfree (C) ; } else { S->unz = 4*(A->p [n]) + n ; /* for LU factorization only, */ S->lnz = S->unz ; /* guess nnz(L) and nnz(U) */ } return (ok ? S : cs_sfree (S)) ; /* return result S */ } SuiteSparse/CSparse/Source/cs_compress.c0000644001170100242450000000161210436112644017234 0ustar davisfac#include "cs.h" /* C = compressed-column form of a triplet matrix T */ cs *cs_compress (const cs *T) { int m, n, nz, p, k, *Cp, *Ci, *w, *Ti, *Tj ; double *Cx, *Tx ; cs *C ; if (!CS_TRIPLET (T)) return (NULL) ; /* check inputs */ m = T->m ; n = T->n ; Ti = T->i ; Tj = T->p ; Tx = T->x ; nz = T->nz ; C = cs_spalloc (m, n, nz, Tx != NULL, 0) ; /* allocate result */ w = cs_calloc (n, sizeof (int)) ; /* get workspace */ if (!C || !w) return (cs_done (C, w, NULL, 0)) ; /* out of memory */ Cp = C->p ; Ci = C->i ; Cx = C->x ; for (k = 0 ; k < nz ; k++) w [Tj [k]]++ ; /* column counts */ cs_cumsum (Cp, w, n) ; /* column pointers */ for (k = 0 ; k < nz ; k++) { Ci [p = w [Tj [k]]++] = Ti [k] ; /* A(i,j) is the pth entry in C */ if (Cx) Cx [p] = Tx [k] ; } return (cs_done (C, w, NULL, 1)) ; /* success; free w and return C */ } SuiteSparse/CSparse/Source/cs_transpose.c0000644001170100242450000000162310414453156017423 0ustar davisfac#include "cs.h" /* C = A' */ cs *cs_transpose (const cs *A, int values) { int p, q, j, *Cp, *Ci, n, m, *Ap, *Ai, *w ; double *Cx, *Ax ; cs *C ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; C = cs_spalloc (n, m, Ap [n], values && Ax, 0) ; /* allocate result */ w = cs_calloc (m, sizeof (int)) ; /* get workspace */ if (!C || !w) return (cs_done (C, w, NULL, 0)) ; /* out of memory */ Cp = C->p ; Ci = C->i ; Cx = C->x ; for (p = 0 ; p < Ap [n] ; p++) w [Ai [p]]++ ; /* row counts */ cs_cumsum (Cp, w, m) ; /* row pointers */ for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { Ci [q = w [Ai [p]]++] = j ; /* place A(i,j) as entry C(j,i) */ if (Cx) Cx [q] = Ax [p] ; } } return (cs_done (C, w, NULL, 1)) ; /* success; free w and return C */ } SuiteSparse/CSparse/README.txt0000644001170100242450000004374410620606322015016 0ustar davisfacCSparse: a Concise Sparse Matrix package. Version 2.2.0, Copyright (c) 2006-2007, Timothy A. Davis, Mar 31, 2007. Refer to "Direct Methods for Sparse Linear Systems," Timothy A. Davis, SIAM, Philadelphia, 2006. No detailed user guide is included in this package; the user guide is the book itself. The algorithms contained in CSparse have been chosen with five goals in mind: (1) they must embody much of the theory behind sparse matrix algorithms, (2) they must be either asymptotically optimal in their run time and memory usage or be fast in practice, (3) they must be concise so as to be easily understood and short enough to print in the book, (4) they must cover a wide spectrum of matrix operations, and (5) they must be accurate and robust. The focus is on direct methods; iterative methods and solvers for eigenvalue problems are beyond the scope of this package. No detailed user guide is included in this package; the user guide is the book itself. Some indication of how to call the CSparse C routines is given by the M-files in the MATLAB/CSparse directory. Complex matrices are not supported, except for methods that operate only on the nonzero pattern of a matrix. A complex version of CSparse appears as a separate package, CXSparse ("Concise Extended Sparse matrix package"). The performance of the sparse factorization methods in CSparse will not be competitive with UMFPACK or CHOLMOD, but the codes are much more concise and easy to understand (see the above goals). Other methods are competitive. Some of the MATLAB tests require the AMD package. See http://www.cise.ufl.edu/research/sparse for CSparse and the AMD ordering package. See the Doc/License.txt file for the license (GNU LGPL). To compile the C-library (./Source) and C demo programs (./Demo) just type "make" in this directory. This should work on any system with the "make" command. To run the exhaustive tests, type "make" in the Tcov directory (Linux is assumed). To compile the MATLAB mexFunctions type "make mex" in this directory, or just "make" in the MATLAB directory. To remove all files not in the original distribution, type "make distclean". I recommend that you use a different level of optimization than "cc -O", which was chosen so that the Makefile is portable. See Source/Makefile. You can simply type "cs_install" while in the CSparse/MATLAB directory to compile and install CSparse for use in MATLAB. This is especially useful for a typical Microsoft Windows system, which does not include "make". For more details, see CSparse/MATLAB/README.txt. -------------------------------------------------------------------------------- Contents: -------------------------------------------------------------------------------- Demo/ demo C programs that use CSparse Doc/ license and change log Makefile Makefile for the whole package MATLAB/ MATLAB interface, demos, and tests for CSparse Matrix/ sample matrices README.txt this file Source/ primary CSparse source files (C only, no MATLAB) Tcov/ CSparse tests -------------------------------------------------------------------------------- ./Doc: license and change log -------------------------------------------------------------------------------- ChangeLog changes in CSparse since first release lesser.txt the GNU LGPL License.txt license (GNU LGPL) -------------------------------------------------------------------------------- ./Source: Primary source code for CSparse -------------------------------------------------------------------------------- cs_add.c add sparse matrices cs_amd.c approximate minimum degree cs_chol.c sparse Cholesky cs_cholsol.c x=A\b using sparse Cholesky cs_compress.c convert a triplet form to compressed-column form cs_counts.c column counts for Cholesky and QR cs_cumsum.c cumulative sum cs_dfs.c depth-first-search cs_dmperm.c Dulmage-Mendelsohn permutation cs_droptol.c drop small entries from a sparse matrix cs_dropzeros.c drop zeros from a sparse matrix cs_dupl.c remove (and sum) duplicates cs_entry.c add an entry to a triplet matrix cs_ereach.c nonzero pattern of Cholesky L(k,:) from etree and triu(A(:,k)) cs_etree.c find elimination tree cs_fkeep.c drop entries from a sparse matrix cs_gaxpy.c sparse matrix times dense matrix cs.h include file for CSparse cs_happly.c apply Householder reflection cs_house.c compute Householder reflection cs_ipvec.c x(p)=b cs_leaf.c determine if j is a leaf of the skeleton matrix and find lca cs_load.c load a sparse matrix from a file cs_lsolve.c x=L\b cs_ltsolve.c x=L'\b cs_lu.c sparse LU factorization cs_lusol.c x=A\b using sparse LU factorization cs_malloc.c memory manager cs_maxtrans.c maximum transveral (permutation for zero-free diagonal) cs_multiply.c sparse matrix multiply cs_norm.c sparse matrix norm cs_permute.c permute a sparse matrix cs_pinv.c invert a permutation vector cs_post.c postorder an elimination tree cs_print.c print a sparse matrix cs_pvec.c x=b(p) cs_qr.c sparse QR cs_qrsol.c solve a least-squares problem cs_randperm.c random permutation cs_reach.c find nonzero pattern of x=L\b for sparse L and b cs_scatter.c scatter a sparse vector cs_scc.c strongly-connected components cs_schol.c symbolic Cholesky cs_spsolve.c x=G\b where G, x, and b are sparse, and G upper/lower triangular cs_sqr.c symbolic QR (also can be used for LU) cs_symperm.c symmetric permutation of a sparse matrix cs_tdfs.c depth-first-search of a tree cs_transpose.c transpose a sparse matrix cs_updown.c sparse rank-1 Cholesky update/downate cs_usolve.c x=U\b cs_util.c various utilities (allocate/free matrices, workspace, etc) cs_utsolve.c x=U'\b Makefile Makefile for CSparse README.txt README file for CSparse -------------------------------------------------------------------------------- ./Demo: C program demos -------------------------------------------------------------------------------- cs_demo1.c read a matrix from a file and perform basic matrix operations cs_demo2.c read a matrix from a file and solve a linear system cs_demo3.c read a matrix, solve a linear system, update/downdate cs_demo.c support routines for cs_demo*.c cs_demo.h include file for demo programs cs_demo.out output of "make", which runs the demos on some matrices Makefile Makefile for Demo programs readhb.f read a Rutherford-Boeing matrix README.txt Demo README file -------------------------------------------------------------------------------- ./MATLAB: MATLAB interface, demos, and tests -------------------------------------------------------------------------------- cs_install.m MATLAB function for compiling and installing CSparse for MATLAB CSparse/ MATLAB interface for CSparse Demo/ MATLAB demos for CSparse Makefile MATLAB interface Makefile README.txt MATLAB README file Test/ MATLAB test for CSparse, and "textbook" routines UFget/ MATLAB interface to UF Sparse Matrix Collection -------------------------------------------------------------------------------- ./MATLAB/CSparse: MATLAB interface for CSparse -------------------------------------------------------------------------------- Contents.m Contents of MATLAB interface to CSparse cs_add.m add two sparse matrices cs_add_mex.c cs_amd.m approximate minimum degree cs_amd_mex.c cs_chol.m sparse Cholesky cs_chol_mex.c cs_cholsol.m x=A\b using a sparse Cholesky cs_cholsol_mex.c cs_counts.m column counts for Cholesky or QR (like "symbfact" in MATLAB) cs_counts_mex.c cs_dmperm.m Dulmage-Mendelsohn permutation cs_dmperm_mex.c cs_dmsol.m x=A\b using dmperm cs_dmspy.m plot a picture of a dmperm-permuted matrix cs_droptol.m drop small entries cs_droptol_mex.c cs_esep.m find edge separator cs_etree.m compute elimination tree cs_etree_mex.c cs_gaxpy.m sparse matrix times dense vector cs_gaxpy_mex.c cs_lsolve.m x=L\b where L is lower triangular cs_lsolve_mex.c cs_ltsolve.m x=L'\b where L is lower triangular cs_ltsolve_mex.c cs_lu.m sparse LU factorization cs_lu_mex.c cs_lusol.m x=A\b using sparse LU factorization cs_lusol_mex.c cs_make.m compiles CSparse for use in MATLAB cs_mex.c support routines for CSparse mexFunctions cs_mex.h cs_multiply.m sparse matrix multiply cs_multiply_mex.c cs_must_compile.m determine if a source file needs to be compiled with mex cs_nd.m nested dissection cs_nsep.m find node separator cs_permute.m permute a sparse matrix cs_permute_mex.c cs_print.m print a sparse matrix cs_print_mex.c cs_qleft.m apply Householder vectors to the left cs_qright.m apply Householder vectors to the right cs_qr.m sparse QR factorization cs_qr_mex.c cs_qrsol.m solve a sparse least squares problem cs_qrsol_mex.c cs_randperm.m randdom permutation cs_randperm_mex.c cs_scc.m strongly-connected components cs_scc_mex.c cs_sep.m convert an edge separator into a node separator cs_sparse.m convert a triplet form matrix to a compress-column form cs_sparse_mex.c cs_symperm.m symmetric permutation of a sparse matrix cs_symperm_mex.c cs_sqr.m symbolic QR ordering and analysis cs_sqr_mex.c cs_thumb_mex.c compute small "thumbnail" of a sparse matrix (for cspy). cs_transpose.m transpose a sparse matrix cs_transpose_mex.c cs_updown.m sparse Cholesky update/downdate cs_updown_mex.c cs_usolve.m x=U\b where U is upper triangular cs_usolve_mex.c cs_utsolve.m x=U'\b where U is upper triangular cs_utsolve_mex.c cspy.m a color "spy" Makefile Makefile for CSparse MATLAB interface README.txt README file for CSparse MATLAB interface -------------------------------------------------------------------------------- ./MATLAB/Demo: MATLAB demos for CSparse -------------------------------------------------------------------------------- Contents.m Contents of MATLAB demo for CSparse cs_demo.m run all MATLAB demos for CSparse cs_demo1.m MATLAB version of Demo/cs_demo1.c cs_demo2.m MATLAB version of Demo/cs_demo2.c cs_demo3.m MATLAB version of Demo/cs_demo3.c private/ private functions for MATLAB demos README.txt README file for CSparse MATLAB demo -------------------------------------------------------------------------------- ./MATLAB/Demo/private: private functions for MATLAB demos -------------------------------------------------------------------------------- demo2.m demo 2 demo3.m demo 3 ex_1.m example 1 ex2.m example 2 ex3.m example 3 frand.m generate a random finite-element matrix get_problem.m get a matrix is_sym.m determine if a matrix is symmetric mesh2d1.m construct a 2D mesh (method 1) mesh2d2.m construct a 2D mesh (method 2) mesh3d1.m construct a 3D mesh (method 1) mesh3d2.m construct a 3D mesh (method 2) print_order.m print the ordering method used resid.m compute residual rhs.m create right-hand-side -------------------------------------------------------------------------------- ./MATLAB/Test: Extensive test of CSparse, in MATLAB -------------------------------------------------------------------------------- Makefile Makefile for MATLAB Test directory README.txt README file for MATLAB/Test Contents.m Contents of MATLAB/Test, "textbook" files only chol_downdate.m downdate a Cholesky factorization. chol_left.m left-looking Cholesky factorization. chol_left2.m left-looking Cholesky factorization, more details. chol_right.m right-looking Cholesky factorization. chol_super.m left-looking "supernodal" Cholesky factorization. chol_up.m up-looking Cholesky factorization. chol_update.m update a Cholesky factorization. chol_updown.m update or downdate a Cholesky factorization. cond1est.m 1-norm condition estimate. cs_fiedler.m the Fiedler vector of a connected graph. givens2.m find a Givens rotation. house.m find a Householder reflection. lu_left.m left-looking LU factorization. lu_right.m right-looking LU factorization. lu_rightp.m right-looking LU factorization, with partial pivoting. lu_rightpr.m recursive right-looking LU, with partial pivoting. lu_rightr.m recursive right-looking LU. norm1est.m 1-norm estimate. qr_givens.m Givens-rotation QR factorization. qr_givens_full.m Givens-rotation QR factorization, for full matrices. qr_left.m left-looking Householder QR factorization. qr_right.m right-looking Householder QR factorization. cs_fiedler.m Fiedler vector cs_frand.m generate a random finite-element matrix cs_frand_mex.c cs_ipvec.m x(p)=b cs_ipvec_mex.c cs_maxtransr.m recursive maximum matching algorithm cs_maxtransr_mex.c cs_pvec.m x=b(p) cs_pvec_mex.c interface for cs_pvec cs_reach.m non-recursive reach (interface to CSparse cs_reach) cs_reach_mex.c non-recursive x=spones(L\sparse(b)) cs_reachr.m recursive reach (interface to CSparse cs_reachr) cs_reachr_mex.c cs_rowcnt.m row counts for sparse Cholesky cs_rowcnt_mex.c row counts for sparse Cholesky cs_sparse2.m same as cs_sparse, to test cs_entry function cs_sparse2_mex.c like cs_sparse, but for testing cs_entry cs_test_make.m compiles MATLAB tests check_if_same.m check if two inputs are identical or not choldn.m Cholesky downdate cholup.m Cholesky update, using Given's rotations cholupdown.m Cholesky update/downdate (Bischof, Pan, and Tang method) cs_q1.m construct Q from Householder vectors cs_test_make.m compiles the CSparse, Demo, and Test mexFunctions. dmperm_test.m test cs_dmperm chol_example.m simple Cholesky factorization example etree_sample.m construct a sample etree and symbolic factorization gqr3.m QR factorization, based on Givens rotations happly.m apply Householder reflection to a vector hmake1.m construct a Householder reflection mynormest1.m estimate norm(A,1), using LU factorization (L*U = P*A*Q). myqr.m QR factorization using Householder reflections another_colormap.m try another color map cspy_test.m test cspy and cs_dmspy qr2.m QR factorization based on Householder reflections sample_colormap.m try a colormap for use in cspy signum.m compute and display the sign of a column vector x sqr_example.m test cs_sqr dmspy_test.m test cspy, cs_dmspy, and cs_dmperm test_qr.m test various QR factorization methods test_randperms.m test random permutations testh.m test Householder reflections test_qr1.m test QR factorizations test_qrsol.m test cs_qrsol test_sep.m test cs_sep, and compare with Gilbert's meshpart vtxsep testall.m test all CSparse functions (run tests 1 to 28 below) test1.m test cs_transpose test2.m test cs_sparse test3.m test cs_lsolve, cs_ltsolve, cs_usolve, cs_chol test4.m test cs_multiply test5.m test cs_add test6.m test cs_reach, cs_reachr, cs_lsolve, cs_usolve test7.m test cs_lu test8.m test cs_cholsol, cs_lusol test9.m test cs_qr test10.m test cs_qr test11.m test cs_rowcnt test12.m test cs_qr and compare with svd test13.m test cs_counts, cs_etree test14.m test cs_droptol test15.m test cs_amd test16.m test cs_amd test17.m test cs_qr, cs_qright, cs_q1, cs_qrleft, cs_qrsol test18.m test iterative refinement after backslash test19.m test cs_dmperm, cs_maxtransr, cs_dmspy, cs_scc test20.m test cholupdown test21.m test cs_updown test22.m test cond1est test23.m test cs_dmspy test24.m test cs_fielder test25.m test cs_nd test26.m test cs_dmsol and cs_dmspy test27.m test cs_qr, cs_utsolve, cs_qrsol test28.m test cs_randperm, cs_dmperm -------------------------------------------------------------------------------- ./MATLAB/UFget: MATLAB interface for the UF Sparse Matrix Collection -------------------------------------------------------------------------------- Contents.m Contents of UFget mat/ default directory where downloaded matrices will be put README.txt README file for UFget UFget_defaults.m default parameter settings UFget_example.m example of use UFget_install.m installs UFget temporarily (for current session) UFget_java.class read a url and load it in into MATLAB (compiled Java code) UFget_java.java read a url and load it in into MATLAB (Java source code) UFget_lookup.m look up a matrix in the index UFget.m UFget itself (primary user interface) UFweb.m open url for a matrix or collection mat/UF_Index.mat index of matrices in UF Sparse Matrix Collection -------------------------------------------------------------------------------- ./Matrix: Sample matrices, most from Rutherford/Boeing collection -------------------------------------------------------------------------------- ash219 overdetermined pattern of Holland survey. Ashkenazi, 1974. bcsstk01 stiffness matrix for small generalized eigenvalue problem bcsstk16 stiffness matrix, Corp of Engineers dam fs_183_1 unsymmetric facsimile convergence matrix lp_afiro NETLIB afiro linear programming problem mbeacxc US economy, 1972. Dan Szyld, while at NYU t1 small example used in Chapter 2 west0067 Cavett problem with 5 components (chemical eng., Westerberg) -------------------------------------------------------------------------------- ./Tcov: Exhaustive test coverage of CSparse -------------------------------------------------------------------------------- covall same as covall.linux covall.linux find coverage (Linux) covall.sol find coverage (Solaris) cov.awk coverage summary cover print uncovered lines covs print uncovered lines cstcov_malloc_test.c malloc test cstcov_malloc_test.h cstcov_test.c main program for Tcov tests gcovs run gcov (Linux) Makefile Makefile for Tcov tests nil an empty matrix zero a 1-by-1 zero matrix README.txt README file for Tcov directory SuiteSparse/CSparse_to_CXSparse0000755001170100242450000002300310571643144015512 0ustar davisfac#! /usr/bin/perl # Constructs the CXSparse package from CSparse, adding four different sets of # functions (int/UF_long, and double/complex). Backward compatible with # CSparse. No MATLAB interface is provided for CXSparse, however. # # To create CXSparse from CSparse, the ./CXSparse directory should not (yet) # exist. Use the following commands, where CSparse is the CSparse directory: # # ./CSparse_to_CXSparse CSparse CXSparse CXSparse_newfiles.tar.gz # cd CXSparse/Demo # make > cs_demo.out # # Alternatively, use "make cx", using the UFsparse/Makefile, while in the # UFsparse directory. # # Created by David Bateman, Feb. 2006, David dot Bateman atsign motorola # dot com. Modified by Tim Davis, Aug 23, 2006. use strict; use Cwd; use File::Find; use File::Basename; use Text::Wrap; use FileHandle; use IPC::Open3; my $in_dir = @ARGV[0]; my $out_dir = @ARGV[1]; my $tar_file = @ARGV[2]; #------------------------------------------------------------------------------- # copy all files from CSparse to CXSparse #------------------------------------------------------------------------------- system ("cp -pr $in_dir $out_dir") ; #------------------------------------------------------------------------------- # Add the new files from the tar file given by the third argument #------------------------------------------------------------------------------- my $old_pwd = cwd(); chdir($out_dir); system ("tar xpBvzf $old_pwd/$tar_file"); chdir($old_pwd); #------------------------------------------------------------------------------- # Convert Demo/* files #------------------------------------------------------------------------------- # convert demo *.[ch] files into the four different versions (di, dl, ci, cl) my @demo_files = ('demo1.c', 'demo2.c', 'demo3.c', 'demo.c', 'demo.h') ; foreach my $fff ( @demo_files ) { my $infile = sprintf ("%s/Demo/cs_%s", $out_dir, $fff) ; # create di version my $outfile = sprintf ("%s/Demo/cs_di_%s", $out_dir, $fff) ; if (open (OUT, ">$outfile")) { if (open (IN, $infile)) { while () { # change all "cs*" names to "cs_di*", except #include "cs.h" s/\bcs/cs_di/g ; s/cs_di\.h/cs.h/ ; print OUT $_; } close (IN); } close (OUT); } # create dl version my $outfile = sprintf ("%s/Demo/cs_dl_%s", $out_dir, $fff) ; if (open (OUT, ">$outfile")) { if (open (IN, $infile)) { while () { # change all "cs*" names to "cs_dl*", except #include "cs.h" s/\bcs/cs_dl/g ; s/cs_dl\.h/cs.h/ ; # change int to UF_long, except for "int main" s/\bint\b/UF_long/g; s/UF_long main/int main/; # change %d to %ld in printf and scanf s/\%d/\%ld/g; print OUT $_; } close (IN); } close (OUT); } # create ci version my $outfile = sprintf ("%s/Demo/cs_ci_%s", $out_dir, $fff) ; if (open (OUT, ">$outfile")) { if (open (IN, $infile)) { while () { # change all "cs*" names to "cs_ci*", except #include "cs.h" s/\bcs/cs_ci/g ; s/cs_ci\.h/cs.h/ ; # fabs becomes cabs s/fabs/cabs/g; # change double to cs_complex_t s/\bdouble\b/cs_complex_t/g; # (double) typecasts stay double s/\(cs_complex_t\) /(double) /g; # tic, toc, tol, and norm are double, not cs_complex_t s/cs_complex_t norm/double norm/; s/cs_complex_t tic/double tic/; s/cs_complex_t toc \(cs_complex_t/double toc (double/; s/cs_complex_t s = tic/double s = tic/; s/cs_complex_t tol/double tol/; # cumsum, S->lnz, S->unz are double s/cs_complex_t lnz/double lnz/; s/cs_complex_t unz/double unz/; s/cs_complex_t cs_cumsum/double cs_cumsum/; # local variable declarations that stay double s/, / ;\n double / ; print OUT $_; } close (IN); } close (OUT); } # create cl version my $outfile = sprintf ("%s/Demo/cs_cl_%s", $out_dir, $fff) ; if (open (OUT, ">$outfile")) { if (open (IN, $infile)) { while () { # change all "cs*" names to "cs_cl*", except #include "cs.h" s/\bcs/cs_cl/g ; s/cs_cl\.h/cs.h/ ; # change int to UF_long, except for "int main" s/\bint\b/UF_long/g; s/UF_long main/int main/; # change %d to %ld in printf and scanf s/\%d/\%ld/g; # fabs becomes cabs s/fabs/cabs/g; # change double to cs_complex_t s/\bdouble\b/cs_complex_t/g; # (double) typecasts stay double s/\(cs_complex_t\) /(double) /g; # tic, toc, tol, and norm are double, not cs_complex_t s/cs_complex_t norm/double norm/; s/cs_complex_t tic/double tic/; s/cs_complex_t toc \(cs_complex_t/double toc (double/; s/cs_complex_t s = tic/double s = tic/; s/cs_complex_t tol/double tol/; # cumsum, S->lnz, S->unz are double s/cs_complex_t lnz/double lnz/; s/cs_complex_t unz/double unz/; s/cs_complex_t cs_cumsum/double cs_cumsum/; # local variable declarations that stay double s/, / ;\n double / ; print OUT $_; } close (IN); } close (OUT); } } #------------------------------------------------------------------------------- # Convert Source/*.c files (except cs_house.c) #------------------------------------------------------------------------------- # note that cs.h, cs_house.c, cs_updown.c, ... # are not included in this list my @src_files = ('Source/cs_add.c', 'Source/cs_amd.c', 'Source/cs_chol.c', 'Source/cs_cholsol.c', 'Source/cs_counts.c', 'Source/cs_cumsum.c', 'Source/cs_dfs.c', 'Source/cs_dmperm.c', 'Source/cs_droptol.c', 'Source/cs_dropzeros.c', 'Source/cs_dupl.c', 'Source/cs_entry.c', 'Source/cs_etree.c', 'Source/cs_fkeep.c', 'Source/cs_gaxpy.c', 'Source/cs_happly.c', 'Source/cs_ipvec.c', 'Source/cs_load.c', 'Source/cs_lsolve.c', 'Source/cs_ltsolve.c', 'Source/cs_lu.c', 'Source/cs_lusol.c', 'Source/cs_malloc.c', 'Source/cs_maxtrans.c', 'Source/cs_multiply.c', 'Source/cs_norm.c', 'Source/cs_permute.c', 'Source/cs_pinv.c', 'Source/cs_post.c', 'Source/cs_print.c', 'Source/cs_pvec.c', 'Source/cs_qr.c', 'Source/cs_qrsol.c', 'Source/cs_scatter.c', 'Source/cs_scc.c', 'Source/cs_schol.c', 'Source/cs_sqr.c', 'Source/cs_symperm.c', 'Source/cs_tdfs.c', 'Source/cs_transpose.c', 'Source/cs_compress.c', 'Source/cs_usolve.c', 'Source/cs_util.c', 'Source/cs_utsolve.c', 'Source/cs_reach.c', 'Source/cs_spsolve.c', 'Source/cs_leaf.c', 'Source/cs_ereach.c', 'Source/cs_randperm.c' ) ; foreach my $file ( @src_files ) { my $infile = sprintf ("%s/%s", $in_dir, $file) ; my $outfile = sprintf ("%s/%s", $out_dir, $file) ; my $fbase = basename($file,('.c')); if (open(OUT,">$outfile")) { if (open(IN,$infile)) { # my $qrsol_beta_seen = 0; while () { # change the name of the package (for cs_print.c) s/CSparse/CXSparse/g; # fabs becomes CS_ABS s/fabs/CS_ABS/g; # change int to CS_INT s/\bint\b/CS_INT/g; # change %d to "CS_ID" in printf and scanf (except version #'s) s/\%d/"CS_ID"/g; s/"CS_ID"\."CS_ID"\."CS_ID"/%d.%d.%d/; # change double to CS_ENTRY s/\bdouble\b/CS_ENTRY/g; # (double) and (double *) typecasts stay double, # tol and vnz for cs_vcount stays double s/\(CS_ENTRY\) /(double) /g; s/\(CS_ENTRY \*\) /(double \*) /; s/CS_ENTRY tol/double tol/; s/CS_ENTRY \*vnz/double \*vnz/; # local variable declarations that stay double s/, / ;\n double / ; # nargin and nargout stay "int" for MATLAB mexFunctions s/CS_INT nargin/int nargin/; s/CS_INT nargout/int nargout/; #--------------------------------------------------------------- # Special cases. Some undo changes made above. #--------------------------------------------------------------- # cs_mex.c if ($fbase =~ /cs_mex/) { s/matrix must be CS_ENTRY/matrix must be double/; s/A->p =/A->p = (CS_INT *)/; s/A->i =/A->i = (CS_INT *)/; s/, A->p/, (mwIndex *) A->p/; s/, A->i/, (mwIndex *) A->i/; } # fix comments in cs_add_mex.c and cs_permute_mex.c if ($fbase =~ /cs_add_mex/ || $fbase =~ /cs_permute_mex/) { s/via CS_ENTRY transpose/via double transpose/; } # cs_chol if ($fbase =~ /cs_chol/) { s/\(d <= 0\)/(CS_REAL (d) <= 0 || CS_IMAG (d) != 0)\n\t /; s/lki \* lki/lki * CS_CONJ (lki)/; s/ = lki/ = CS_CONJ (lki)/; } # cs_norm if ($fbase =~ /cs_norm/) { s/^CS_ENTRY cs_norm/double cs_norm/; } # cs_cumsum if ($fbase =~ /cs_cumsum/) { s/CS_ENTRY/double/; } # cs_transpose if ($fbase =~ /cs_transpose/) { s/Ax \[p\]/(values > 0) ? CS_CONJ (Ax [p]) : Ax [p]/; } # cs_symperm if ($fbase =~ /cs_symperm/) { s/Ax \[p\]/(i2 <= j2) ? Ax [p] : CS_CONJ (Ax [p])/; } # cs_qr if ($fbase =~ /cs_qr/) { s/n, sizeof \(CS_ENTRY\)/n, sizeof (double)/; } # cs_happly if ($fbase =~ /cs_happly/) { s/^(.*tau.*)(Vx\s*\[p\])/$1CS_CONJ ($2)/; s/CS_ENTRY beta/double beta/; } # cs_ltsolve if ($fbase =~ /cs_ltsolve/) { s/(Lx \[.*?\])(\s+[\*;])/CS_CONJ ($1)$2/; } # cs_utsolve if ($fbase =~ /cs_utsolve/) { s/(Ux \[.*?\])(\s+[\*;])/CS_CONJ ($1)$2/; } # cs_load if ($fbase =~ /cs_load/) { s/CS_ENTRY x ;/double x ;\n#ifdef CS_COMPLEX\n double xi ;\n#endif/ ; s/^(\s*while.*)%lg(.*)&x\) == 3(.*)$/#ifdef CS_COMPLEX\n$1%lg %lg$2&x, &xi) == 4$3\n#else\n$1%lg$2&x) == 3$3\n#endif/; s/(.*cs_entry.*), x(.*)$/#ifdef CS_COMPLEX\n$1, x + xi*I$2\n#else\n$1, x$2\n#endif/ } # cs_print if ($fbase =~ /cs_print/) { s/^(.*)%g(.*)Ax\s*\?\s*Ax\s*\[p\]\s*:\s*1(.*)/#ifdef CS_COMPLEX\n$1(%g, %g)$2\n\t\t Ax ? CS_REAL (Ax [p]) : 1, Ax ? CS_IMAG (Ax [p]) : 0$3\n#else\n$1%g$2Ax ? Ax [p] : 1$3\n#endif/; } print OUT $_; } close (IN); } close (OUT); } } SuiteSparse/Makefile0000644001170100242450000000557510711436073013425 0ustar davisfac#------------------------------------------------------------------------------- # Makefile for all UF sparse matrix packages #------------------------------------------------------------------------------- include UFconfig/UFconfig.mk # Compile the default rules for each package default: ( cd UFconfig/xerbla ; $(MAKE) ) # ( cd metis-4.0 ; $(MAKE) ) ( cd AMD ; $(MAKE) ) ( cd CAMD ; $(MAKE) ) ( cd COLAMD ; $(MAKE) ) ( cd BTF ; $(MAKE) ) ( cd KLU ; $(MAKE) ) ( cd LDL ; $(MAKE) ) ( cd CCOLAMD ; $(MAKE) ) ( cd UMFPACK ; $(MAKE) ) ( cd CHOLMOD ; $(MAKE) ) ( cd CSparse ; $(MAKE) ) ( cd CXSparse ; $(MAKE) ) # ( cd LPDASA ; $(MAKE) ) # ( cd PARAKLETE ; $(MAKE) ) library: default # Compile the MATLAB mexFunctions (except RBio and UFcollection) mex: ( cd AMD ; $(MAKE) mex ) ( cd CAMD ; $(MAKE) mex ) ( cd COLAMD ; $(MAKE) mex ) ( cd BTF ; $(MAKE) mex ) ( cd KLU ; $(MAKE) mex ) ( cd LDL ; $(MAKE) mex ) ( cd CCOLAMD ; $(MAKE) mex ) ( cd CHOLMOD ; $(MAKE) mex ) ( cd UMFPACK ; $(MAKE) mex ) ( cd CXSparse ; $(MAKE) mex ) ( cd CSparse ; $(MAKE) mex ) # Remove all files not in the original distribution purge: ( cd UFconfig/xerbla ; $(MAKE) purge ) # ( cd metis-4.0 ; $(MAKE) realclean ) ( cd AMD ; $(MAKE) purge ) ( cd CAMD ; $(MAKE) purge ) ( cd COLAMD ; $(MAKE) purge ) ( cd BTF ; $(MAKE) purge ) ( cd KLU ; $(MAKE) purge ) ( cd LDL ; $(MAKE) purge ) ( cd CCOLAMD ; $(MAKE) purge ) ( cd UMFPACK ; $(MAKE) purge ) ( cd CHOLMOD ; $(MAKE) purge ) ( cd CSparse ; $(MAKE) purge ) ( cd CXSparse ; $(MAKE) purge ) ( cd RBio ; $(RM) *.mex* ) ( cd UFcollection ; $(RM) *.mex* ) ( cd SSMULT ; $(RM) *.mex* ) # ( cd LPDASA ; $(MAKE) purge ) # ( cd PARAKLETE ; $(MAKE) purge ) # Remove all files not in the original distribution, but keep the libraries clean: ( cd UFconfig/xerbla ; $(MAKE) clean ) # ( cd metis-4.0 ; $(MAKE) clean ) ( cd AMD ; $(MAKE) clean ) ( cd CAMD ; $(MAKE) clean ) ( cd COLAMD ; $(MAKE) clean ) ( cd BTF ; $(MAKE) clean ) ( cd KLU ; $(MAKE) clean ) ( cd LDL ; $(MAKE) clean ) ( cd CCOLAMD ; $(MAKE) clean ) ( cd UMFPACK ; $(MAKE) clean ) ( cd CHOLMOD ; $(MAKE) clean ) ( cd CSparse ; $(MAKE) clean ) ( cd CXSparse ; $(MAKE) clean ) # ( cd LPDASA ; $(MAKE) clean ) # ( cd PARAKLETE ; $(MAKE) clean ) distclean: purge # Create CXSparse from CSparse. Note that the CXSparse directory should # initially not exist. cx: ( cd CSparse ; $(MAKE) purge ) ( cd CXSparse_newfiles ; tar cfv - * | gzip -9 > ../CXSparse_newfiles.tar.gz ) ./CSparse_to_CXSparse CSparse CXSparse CXSparse_newfiles.tar.gz ( cd CXSparse/Demo ; $(MAKE) ) ( cd CXSparse/Demo ; $(MAKE) > cs_demo.out ) ( cd CXSparse ; $(MAKE) purge ) # statement coverage (Linux only); this requires a lot of time. # The umfpack tcov requires a lot of disk space cov: ( cd CXSparse ; $(MAKE) cov ) ( cd CSparse ; $(MAKE) cov ) ( cd KLU ; $(MAKE) cov ) ( cd CHOLMOD ; $(MAKE) cov ) ( cd UMFPACK ; $(MAKE) cov ) SuiteSparse/SuiteSparse_demo.m0000644001170100242450000000507310707710170015405 0ustar davisfacfunction SuiteSparse_demo (matrixpath) %SUITESPARSE_DEMO a demo of all packages in SuiteSparse % % Example: % SuiteSparse_demo % % See also umfpack, cholmod, amd, camd, colamd, ccolamd, btf, klu, % CSparse, CXSparse, ldlsparse % Copyright (c) Timothy A. Davis, Univ. of Florida if (nargin < 1) try % older versions of MATLAB do not have an input argument to mfilename p = mfilename ('fullpath') ; t = strfind (p, filesep) ; matrixpath = [ p(1:t(end)) 'CXSparse/Matrix' ] ; catch % mfilename failed, assume we're in the SuiteSparse directory matrixpath = 'CXSparse/Matrix' ; end end input ('Hit enter to run the CXSparse demo: ') ; try cs_demo (0, matrixpath) catch fprintf ('\nIf you have an older version of MATLAB, you must run the\n') ; fprintf ('SuiteSparse_demo while in the SuiteSparse directory.\n\n') ; fprintf ('CXSparse demo failed\n' ) end input ('Hit enter to run the UMFPACK demo: ') ; try umfpack_demo (1) catch disp (lasterr) ; fprintf ('UMFPACK demo failed\n' ) end input ('Hit enter to run the CHOLMOD demo: ') ; try cholmod_demo catch disp (lasterr) ; fprintf ('CHOLMOD demo failed\n' ) end input ('Hit enter to run the CHOLMOD graph partitioning demo: ') ; try graph_demo catch disp (lasterr) ; fprintf ('graph_demo failed, probably because METIS not installed\n') ; end input ('Hit enter to run the AMD demo: ') ; try amd_demo catch disp (lasterr) ; fprintf ('AMD demo failed\n' ) end input ('Hit enter to run the CAMD demo: ') ; try camd_demo catch disp (lasterr) ; fprintf ('CAMD demo failed\n' ) end input ('Hit enter to run the COLAMD demo: ') ; try colamd_demo catch disp (lasterr) ; fprintf ('COLAMD demo failed\n' ) end input ('Hit enter to run the CCOLAMD demo: ') ; try ccolamd_demo catch disp (lasterr) ; fprintf ('CCOLAMD demo failed\n' ) end input ('Hit enter to run the BTF demo: ') ; try btf_demo catch disp (lasterr) ; fprintf ('BTF demo failed\n' ) end input ('Hit enter to run the KLU demo: ') ; try klu_demo catch disp (lasterr) ; fprintf ('KLU demo failed\n' ) end input ('Hit enter to run the LDL demo: ') ; try ldldemo catch disp (lasterr) ; fprintf ('LDL demo failed\n' ) end input ('Hit enter to run the SSMULT demo: ') ; try ssmult_demo catch disp (lasterr) ; fprintf ('SSMULT demo failed\n' ) end input ('Hit enter to run the MESHND demo: ') ; try meshnd_example catch disp (lasterr) ; fprintf ('MESHND demo failed\n' ) end fprintf ('\n\n---- SuiteSparse demos complete\n') ; SuiteSparse/MESHND/0000755001170100242450000000000010711674716012737 5ustar davisfacSuiteSparse/MESHND/meshnd.m0000644001170100242450000000603110710135075014360 0ustar davisfacfunction [G, p, pinv, Gnew] = meshnd (arg1,n,k) %MESHND creation and nested dissection of a regular 2D or 3D mesh. % [p G pinv Gnew] = meshnd (m,n) constructs a m-by-n 2D mesh G, and then finds % a permuted mesh Gnew where Gnew = pinv(G) and G = p(Gnew). meshnd(m,n,k) % creates an m-by-n-by-k 3D mesh. % % [p G pinv Gnew] = meshnd (G) does not construct G, but uses the mesh G as % given on input instead. % % Example: % [G p pinv Gnew] = meshnd (4,5) ; % % returns % Gnew = % 1 2 17 9 10 % 7 8 18 15 16 % 3 5 19 11 13 % 4 6 20 12 14 % G = % 1 2 3 4 5 % 6 7 8 9 10 % 11 12 13 14 15 % 16 17 18 19 20 % % With no inputs, a few example meshes are generated and plotted. % % See also nested, numgrid. % Copyright 2007, Timothy A. Davis, Univ. of Florida % get the inputs and create the mesh if not provided on input if (nargin == 0) % run a simple example meshnd_example ; elseif (nargin == 1) % the mesh is provided on input G = arg1 ; [m n k] = size (G) ; elseif (nargin == 2) % create the m-by-n-by-k mesh in "natural" (row-major) order. This is how % a typical 2D mesh is ordered. A column-major order would be better, since % in that case G(:) would equal 1:(m*n) ... but let's stick with tradition. m = arg1 ; k = 1 ; G = reshape (1:(m*n*k), n, m, k)' ; elseif (nargin == 3) % create the m-by-n-by-k mesh in column-major order. The first m-by-n-by-1 % slice is in column-major order, followed by all the other slices 2 to k. m = arg1 ; G = reshape (1:(m*n*k), m, n, k) ; else error ('Usage: [G p pinv Gnew] = meshnd(G), meshnd(m,n) or meshnd(m,n,k)') ; end if (nargout > 1) p = nd2 (G)' ; % order the mesh end if (nargout > 2) pinv (p) = 1:(m*n*k) ; % find the inverse permutation end if (nargout > 3) Gnew = pinv (G) ; % find the permuted mesh end %------------------------------------------------------------------------------- function p = nd2 (G) %ND2 p = nd2 (G) permutes a 2D or 3D mesh G. % Compare with nestdiss which uses p as a scalar offset and returns a modified % mesh G that corresponds to Gnew in meshnd. Here, the scalar offset p in % nestdiss is not needed. Instead, p is a permutation, and the modified mesh % Gnew is not returned. [m n k] = size (G) ; if (max ([m n k]) <= 2) % G is small; do not cut it p = G (:) ; elseif k >= max (m,n) % cut G along the middle slice, cutting k in half s = ceil (k/2) ; middle = G (:,:,s) ; p = [(nd2 (G (:,:,1:s-1))) ; (nd2 (G (:,:,s+1:k))) ; middle(:)] ; elseif n >= max (m,k) % cut G along the middle column, cutting n in half s = ceil (n/2) ; middle = G (:,s,:) ; p = [(nd2 (G (:,1:s-1,:))) ; (nd2 (G (:,s+1:n,:))) ; middle(:)] ; else % cut G along the middle row, cutting m in half s = ceil (m/2) ; middle = G (s,:,:) ; p = [(nd2 (G (1:s-1,:,:))) ; (nd2 (G (s+1:m,:,:))) ; middle(:)] ; end SuiteSparse/MESHND/Contents.m0000644001170100242450000000165410711427406014710 0ustar davisfac%MESHND: creation and nested dissection of regular 2D and 3D meshes. % % meshnd - creation and nested dissection of a regular 2D or 3D mesh. % meshnd_quality - test the ordering quality computed by meshnd. % meshsparse - convert a 2D or 3D mesh into a sparse matrix matrix. % meshnd_example - example usage of meshnd and meshsparse. % % The outputs of the meshnd example and meshnd_quality are in meshd.png, % meshnd_quality_out.txt, and meshnd_quality.png. % % Example: % % with no inputs or outputs, meshnd runs a demo: % meshnd % % % create the sparse matrix for a 7-by-5-by-2 mesh: % A = meshsparse (meshnd (7,5,2)) ; % % % create a 7-by-5-by-2 mesh and find the nested dissection ordering: % [G p] = meshnd (7,5,2) ; % A = meshsparse (G) ; % subplot (1,2,1) ; spy (A) ; % subplot (1,2,2) ; spy (A (p,p)) ; % % Copyright 2007, Timothy A. 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Davis, Univ. of Florida help meshnd % 2D mesh, compare with Cleve Moler's demos m = 7 ; n = 7 ; [G p pinv Gnew] = meshnd (m,n) ; fprintf ('Original mesh:\n') ; disp (G) ; fprintf ('Permuted node numbers using meshnd.m (nested dissection):\n') ; disp (Gnew) ; Moler = nested (n+2) ; Moler = Moler (2:n+1,2:n+1) ; fprintf ('Cleve Moler''s nested dissection ordering, using nested.m\n') ; disp (Moler) ; fprintf ('Difference between nested.m and meshnd.m:\n') ; disp (Gnew-Moler) ; % 2D and 3D meshes stencils = [5 9 7 27] ; mm = [7 7 7 7] ; nn = [7 7 7 7] ; kk = [1 1 7 7] ; for s = 1:4 m = mm (s) ; n = nn (s) ; k = kk (s) ; [G p] = meshnd (mm (s), nn (s), kk (s)) ; A = meshsparse (G, stencils (s)) ; C = A (p,p) ; parent = etree (C) ; try L = chol (C, 'lower') ; catch % old version of MATLAB L = chol (C)' ; end subplot (4,5,(s-1)*5 + 1) ; do_spy (A) ; if (k > 1) title (sprintf ('%d-by-%d-by-%d mesh, %d-point stencil', ... m, n, k, stencils (s))) ; else title (sprintf ('%d-by-%d mesh, %d-point stencil', ... m, n, stencils (s))) ; end subplot (4,5,(s-1)*5 + 2) ; do_spy (C) ; title ('nested dissection') ; subplot (4,5,(s-1)*5 + 3) ; treeplot (parent) ; title ('etree') ; xlabel ('') ; subplot (4,5,(s-1)*5 + 4) ; do_spy (L) ; title (sprintf ('Cholesky with nd, nnz %d', nnz (L))) ; try % use the built-in AMD p = amd (A) ; catch try % use AMD from SuiteSparse p = amd2 (A) ; catch % use the older built-in SYMAMD p = symamd (A) ; end end try L = chol (A (p,p), 'lower') ; catch % old version of MATLAB L = chol (A (p,p))' ; end subplot (4,5,(s-1)*5 + 5) ; do_spy (L) ; title (sprintf ('Cholesky with amd, nnz %d', nnz (L))) ; end %------------------------------------------------------------------------------- function do_spy (A) %DO_SPY use cspy(A) to plot a matrix, or spy(A) if cspy not installed. try % This function is in CSparse. It generates better looking plots than spy. cspy (A) ; catch spy (A) ; end SuiteSparse/MESHND/meshnd_quality_out.txt0000644001170100242450000013246710642470476017432 0ustar davisfacprofile on meshnd_quality 2D mesh: 7-by-7, 5-point stencil MESHND: nnz(L) 2.880e+02 flops 1.926e+03 AMD: nnz(L) 2.550e+02 flops 1.483e+03 METIS: nnz(L) 2.680e+02 flops 1.656e+03 2D mesh: 7-by-7, 5-point stencil MESHND: nnz(L) 2.880e+02 flops 1.926e+03 AMD: nnz(L) 2.550e+02 flops 1.483e+03 METIS: nnz(L) 2.680e+02 flops 1.656e+03 2D mesh: 8-by-8, 5-point stencil MESHND: nnz(L) 4.210e+02 flops 3.141e+03 AMD: nnz(L) 3.540e+02 flops 2.192e+03 METIS: nnz(L) 3.800e+02 flops 2.568e+03 2D mesh: 8-by-8, 5-point stencil MESHND: nnz(L) 4.210e+02 flops 3.141e+03 AMD: nnz(L) 3.540e+02 flops 2.192e+03 METIS: nnz(L) 3.800e+02 flops 2.568e+03 2D mesh: 9-by-9, 5-point stencil MESHND: nnz(L) 6.000e+02 flops 5.078e+03 AMD: nnz(L) 5.060e+02 flops 3.722e+03 METIS: nnz(L) 5.230e+02 flops 3.947e+03 2D mesh: 10-by-10, 5-point stencil MESHND: nnz(L) 7.970e+02 flops 7.331e+03 AMD: nnz(L) 6.480e+02 flops 4.936e+03 METIS: nnz(L) 6.840e+02 flops 5.656e+03 2D mesh: 11-by-11, 5-point stencil MESHND: nnz(L) 1.008e+03 flops 9.920e+03 AMD: nnz(L) 8.160e+02 flops 6.636e+03 METIS: nnz(L) 8.610e+02 flops 7.713e+03 2D mesh: 11-by-11, 5-point stencil MESHND: nnz(L) 1.008e+03 flops 9.920e+03 AMD: nnz(L) 8.160e+02 flops 6.636e+03 METIS: nnz(L) 8.610e+02 flops 7.713e+03 2D mesh: 12-by-12, 5-point stencil MESHND: nnz(L) 1.234e+03 flops 1.287e+04 AMD: nnz(L) 1.035e+03 flops 9.143e+03 METIS: nnz(L) 1.076e+03 flops 1.014e+04 2D mesh: 13-by-13, 5-point stencil MESHND: nnz(L) 1.558e+03 flops 1.792e+04 AMD: nnz(L) 1.253e+03 flops 1.166e+04 METIS: nnz(L) 1.301e+03 flops 1.292e+04 2D mesh: 15-by-15, 5-point stencil MESHND: nnz(L) 2.272e+03 flops 2.936e+04 AMD: nnz(L) 1.798e+03 flops 1.886e+04 METIS: nnz(L) 1.916e+03 flops 2.178e+04 2D mesh: 16-by-16, 5-point stencil MESHND: nnz(L) 2.663e+03 flops 3.553e+04 AMD: nnz(L) 2.118e+03 flops 2.307e+04 METIS: nnz(L) 2.351e+03 flops 3.014e+04 2D mesh: 17-by-17, 5-point stencil MESHND: nnz(L) 3.180e+03 flops 4.567e+04 AMD: nnz(L) 2.433e+03 flops 2.755e+04 METIS: nnz(L) 2.678e+03 flops 3.446e+04 2D mesh: 18-by-18, 5-point stencil MESHND: nnz(L) 3.719e+03 flops 5.614e+04 AMD: nnz(L) 2.900e+03 flops 3.612e+04 METIS: nnz(L) 3.068e+03 flops 4.065e+04 2D mesh: 20-by-20, 5-point stencil MESHND: nnz(L) 4.861e+03 flops 7.836e+04 AMD: nnz(L) 3.702e+03 flops 4.831e+04 METIS: nnz(L) 3.931e+03 flops 5.721e+04 2D mesh: 21-by-21, 5-point stencil MESHND: nnz(L) 5.556e+03 flops 9.475e+04 AMD: nnz(L) 4.162e+03 flops 5.684e+04 METIS: nnz(L) 4.525e+03 flops 7.004e+04 2D mesh: 23-by-23, 5-point stencil MESHND: nnz(L) 6.980e+03 flops 1.283e+05 AMD: nnz(L) 5.349e+03 flops 8.331e+04 METIS: nnz(L) 5.677e+03 flops 9.672e+04 2D mesh: 24-by-24, 5-point stencil MESHND: nnz(L) 7.632e+03 flops 1.432e+05 AMD: nnz(L) 5.787e+03 flops 8.703e+04 METIS: nnz(L) 6.285e+03 flops 1.069e+05 2D mesh: 26-by-26, 5-point stencil MESHND: nnz(L) 9.466e+03 flops 1.938e+05 AMD: nnz(L) 7.144e+03 flops 1.174e+05 METIS: nnz(L) 7.424e+03 flops 1.322e+05 2D mesh: 28-by-28, 5-point stencil MESHND: nnz(L) 1.138e+04 flops 2.446e+05 AMD: nnz(L) 8.516e+03 flops 1.479e+05 METIS: nnz(L) 9.940e+03 flops 2.166e+05 2D mesh: 31-by-31, 5-point stencil MESHND: nnz(L) 1.479e+04 flops 3.498e+05 AMD: nnz(L) 1.092e+04 flops 2.059e+05 METIS: nnz(L) 1.283e+04 flops 2.945e+05 2D mesh: 33-by-33, 5-point stencil MESHND: nnz(L) 1.724e+04 flops 4.275e+05 AMD: nnz(L) 1.281e+04 flops 2.623e+05 METIS: nnz(L) 1.402e+04 flops 3.099e+05 2D mesh: 35-by-35, 5-point stencil MESHND: nnz(L) 2.016e+04 flops 5.258e+05 AMD: nnz(L) 1.485e+04 flops 3.194e+05 METIS: nnz(L) 1.684e+04 flops 4.089e+05 2D mesh: 38-by-38, 5-point stencil MESHND: nnz(L) 2.491e+04 flops 6.928e+05 AMD: nnz(L) 1.830e+04 flops 4.217e+05 METIS: nnz(L) 1.888e+04 flops 4.522e+05 2D mesh: 41-by-41, 5-point stencil MESHND: nnz(L) 2.992e+04 flops 8.803e+05 AMD: nnz(L) 2.173e+04 flops 5.265e+05 METIS: nnz(L) 2.416e+04 flops 6.691e+05 2D mesh: 44-by-44, 5-point stencil MESHND: nnz(L) 3.559e+04 flops 1.103e+06 AMD: nnz(L) 2.701e+04 flops 7.580e+05 METIS: nnz(L) 2.805e+04 flops 7.813e+05 2D mesh: 47-by-47, 5-point stencil MESHND: nnz(L) 4.198e+04 flops 1.384e+06 AMD: nnz(L) 3.031e+04 flops 8.216e+05 METIS: nnz(L) 3.359e+04 flops 1.007e+06 2D mesh: 50-by-50, 5-point stencil MESHND: nnz(L) 4.848e+04 flops 1.683e+06 AMD: nnz(L) 3.591e+04 flops 1.042e+06 METIS: nnz(L) 3.832e+04 flops 1.173e+06 2D mesh: 54-by-54, 5-point stencil MESHND: nnz(L) 5.879e+04 flops 2.177e+06 AMD: nnz(L) 4.362e+04 flops 1.368e+06 METIS: nnz(L) 4.469e+04 flops 1.391e+06 2D mesh: 58-by-58, 5-point stencil MESHND: nnz(L) 6.973e+04 flops 2.730e+06 AMD: nnz(L) 5.255e+04 flops 1.801e+06 METIS: nnz(L) 5.679e+04 flops 2.062e+06 2D mesh: 63-by-63, 5-point stencil MESHND: nnz(L) 8.542e+04 flops 3.578e+06 AMD: nnz(L) 6.195e+04 flops 2.170e+06 METIS: nnz(L) 6.725e+04 flops 2.471e+06 2D mesh: 67-by-67, 5-point stencil MESHND: nnz(L) 9.898e+04 flops 4.353e+06 AMD: nnz(L) 7.249e+04 flops 2.712e+06 METIS: nnz(L) 7.963e+04 flops 3.303e+06 2D mesh: 72-by-72, 5-point stencil MESHND: nnz(L) 1.179e+05 flops 5.442e+06 AMD: nnz(L) 9.047e+04 flops 3.802e+06 METIS: nnz(L) 9.518e+04 flops 4.119e+06 2D mesh: 77-by-77, 5-point stencil MESHND: nnz(L) 1.395e+05 flops 6.816e+06 AMD: nnz(L) 1.030e+05 flops 4.537e+06 METIS: nnz(L) 1.038e+05 flops 4.305e+06 2D mesh: 83-by-83, 5-point stencil MESHND: nnz(L) 1.666e+05 flops 8.648e+06 AMD: nnz(L) 1.249e+05 flops 6.030e+06 METIS: nnz(L) 1.275e+05 flops 5.935e+06 2D mesh: 89-by-89, 5-point stencil MESHND: nnz(L) 1.965e+05 flops 1.077e+07 AMD: nnz(L) 1.506e+05 flops 8.109e+06 METIS: nnz(L) 1.479e+05 flops 6.985e+06 2D mesh: 96-by-96, 5-point stencil MESHND: nnz(L) 2.346e+05 flops 1.361e+07 AMD: nnz(L) 1.890e+05 flops 1.119e+07 METIS: nnz(L) 1.780e+05 flops 8.883e+06 2D mesh: 102-by-102, 5-point stencil MESHND: nnz(L) 2.714e+05 flops 1.664e+07 AMD: nnz(L) 2.122e+05 flops 1.239e+07 METIS: nnz(L) 2.082e+05 flops 1.146e+07 2D mesh: 110-by-110, 5-point stencil MESHND: nnz(L) 3.253e+05 flops 2.117e+07 AMD: nnz(L) 2.568e+05 flops 1.617e+07 METIS: nnz(L) 2.463e+05 flops 1.439e+07 2D mesh: 118-by-118, 5-point stencil MESHND: nnz(L) 3.827e+05 flops 2.637e+07 AMD: nnz(L) 3.013e+05 flops 1.973e+07 METIS: nnz(L) 2.714e+05 flops 1.511e+07 2D mesh: 127-by-127, 5-point stencil MESHND: nnz(L) 4.556e+05 flops 3.326e+07 AMD: nnz(L) 3.501e+05 flops 2.484e+07 METIS: nnz(L) 3.516e+05 flops 2.392e+07 2D mesh: 136-by-136, 5-point stencil MESHND: nnz(L) 5.336e+05 flops 4.098e+07 AMD: nnz(L) 4.319e+05 flops 3.296e+07 METIS: nnz(L) 3.998e+05 flops 2.760e+07 2D mesh: 146-by-146, 5-point stencil MESHND: nnz(L) 6.322e+05 flops 5.135e+07 AMD: nnz(L) 5.053e+05 flops 3.980e+07 METIS: nnz(L) 4.773e+05 flops 3.598e+07 2D mesh: 156-by-156, 5-point stencil MESHND: nnz(L) 7.403e+05 flops 6.317e+07 AMD: nnz(L) 6.154e+05 flops 5.580e+07 METIS: nnz(L) 5.572e+05 flops 4.390e+07 2D mesh: 167-by-167, 5-point stencil MESHND: nnz(L) 8.668e+05 flops 7.834e+07 AMD: nnz(L) 6.652e+05 flops 5.757e+07 METIS: nnz(L) 6.114e+05 flops 4.667e+07 2D mesh: 180-by-180, 5-point stencil MESHND: nnz(L) 1.030e+06 flops 9.857e+07 AMD: nnz(L) 8.558e+05 flops 8.577e+07 METIS: nnz(L) 7.593e+05 flops 6.550e+07 2D mesh: 193-by-193, 5-point stencil MESHND: nnz(L) 1.210e+06 flops 1.225e+08 AMD: nnz(L) 9.532e+05 flops 9.653e+07 METIS: nnz(L) 8.647e+05 flops 7.595e+07 2D mesh: 206-by-206, 5-point stencil MESHND: nnz(L) 1.408e+06 flops 1.505e+08 AMD: nnz(L) 1.150e+06 flops 1.205e+08 METIS: nnz(L) 1.040e+06 flops 1.007e+08 2D mesh: 221-by-221, 5-point stencil MESHND: nnz(L) 1.656e+06 flops 1.871e+08 AMD: nnz(L) 1.305e+06 flops 1.469e+08 METIS: nnz(L) 1.194e+06 flops 1.202e+08 2D mesh: 237-by-237, 5-point stencil MESHND: nnz(L) 1.941e+06 flops 2.321e+08 AMD: nnz(L) 1.541e+06 flops 1.839e+08 METIS: nnz(L) 1.429e+06 flops 1.594e+08 2D mesh: 255-by-255, 5-point stencil MESHND: nnz(L) 2.300e+06 flops 2.914e+08 AMD: nnz(L) 1.834e+06 flops 2.329e+08 METIS: nnz(L) 1.652e+06 flops 1.903e+08 2D mesh: 273-by-273, 5-point stencil MESHND: nnz(L) 2.685e+06 flops 3.588e+08 AMD: nnz(L) 2.166e+06 flops 2.976e+08 METIS: nnz(L) 1.954e+06 flops 2.460e+08 2D mesh: 293-by-293, 5-point stencil MESHND: nnz(L) 3.163e+06 flops 4.466e+08 AMD: nnz(L) 2.522e+06 flops 3.557e+08 METIS: nnz(L) 2.301e+06 flops 3.051e+08 2D mesh: 314-by-314, 5-point stencil MESHND: nnz(L) 3.714e+06 flops 5.527e+08 AMD: nnz(L) 3.181e+06 flops 5.084e+08 METIS: nnz(L) 2.639e+06 flops 3.652e+08 2D mesh: 336-by-336, 5-point stencil MESHND: nnz(L) 4.325e+06 flops 6.799e+08 AMD: nnz(L) 3.763e+06 flops 6.432e+08 METIS: nnz(L) 3.172e+06 flops 4.801e+08 2D mesh: 361-by-361, 5-point stencil MESHND: nnz(L) 5.088e+06 flops 8.480e+08 AMD: nnz(L) 4.281e+06 flops 8.179e+08 METIS: nnz(L) 3.709e+06 flops 6.032e+08 2D mesh: 387-by-387, 5-point stencil MESHND: nnz(L) 5.959e+06 flops 1.050e+09 AMD: nnz(L) 5.229e+06 flops 1.056e+09 METIS: nnz(L) 4.294e+06 flops 7.027e+08 2D mesh: 414-by-414, 5-point stencil MESHND: nnz(L) 6.944e+06 flops 1.293e+09 AMD: nnz(L) 6.008e+06 flops 1.184e+09 METIS: nnz(L) 4.992e+06 flops 9.106e+08 2D mesh: 444-by-444, 5-point stencil MESHND: nnz(L) 8.135e+06 flops 1.600e+09 AMD: nnz(L) 7.243e+06 flops 1.637e+09 METIS: nnz(L) 6.077e+06 flops 1.208e+09 2D mesh: 476-by-476, 5-point stencil MESHND: nnz(L) 9.501e+06 flops 1.979e+09 AMD: nnz(L) 8.346e+06 flops 1.859e+09 METIS: nnz(L) 7.009e+06 flops 1.473e+09 2D mesh: 511-by-511, 5-point stencil MESHND: nnz(L) 1.116e+07 flops 2.462e+09 AMD: nnz(L) 9.426e+06 flops 2.345e+09 METIS: nnz(L) 8.167e+06 flops 1.822e+09 2D mesh: 547-by-547, 5-point stencil MESHND: nnz(L) 1.299e+07 flops 3.027e+09 AMD: nnz(L) 1.190e+07 flops 3.313e+09 METIS: nnz(L) 9.654e+06 flops 2.351e+09 2D mesh: 587-by-587, 5-point stencil MESHND: nnz(L) 1.525e+07 flops 3.755e+09 AMD: nnz(L) 1.410e+07 flops 4.259e+09 METIS: nnz(L) 1.120e+07 flops 2.798e+09 2D mesh: 629-by-629, 5-point stencil MESHND: nnz(L) 1.784e+07 flops 4.634e+09 AMD: nnz(L) 1.539e+07 flops 4.645e+09 METIS: nnz(L) 1.337e+07 flops 3.633e+09 2D mesh: 674-by-674, 5-point stencil MESHND: nnz(L) 2.080e+07 flops 5.717e+09 AMD: nnz(L) 1.826e+07 flops 5.280e+09 METIS: nnz(L) 1.517e+07 flops 4.278e+09 2D mesh: 723-by-723, 5-point stencil MESHND: nnz(L) 2.431e+07 flops 7.081e+09 AMD: nnz(L) 2.306e+07 flops 8.546e+09 METIS: nnz(L) 1.825e+07 flops 5.617e+09 2D mesh: 775-by-775, 5-point stencil MESHND: nnz(L) 2.840e+07 flops 8.749e+09 AMD: nnz(L) 2.592e+07 flops 1.053e+10 METIS: nnz(L) 2.100e+07 flops 6.839e+09 2D mesh: 830-by-830, 5-point stencil MESHND: nnz(L) 3.309e+07 flops 1.078e+10 AMD: nnz(L) 2.981e+07 flops 1.064e+10 METIS: nnz(L) 2.402e+07 flops 8.110e+09 2D mesh: 890-by-890, 5-point stencil MESHND: nnz(L) 3.865e+07 flops 1.331e+10 AMD: nnz(L) 3.668e+07 flops 1.607e+10 METIS: nnz(L) 2.793e+07 flops 9.861e+09 2D mesh: 954-by-954, 5-point stencil MESHND: nnz(L) 4.502e+07 flops 1.644e+10 AMD: nnz(L) 4.217e+07 flops 1.812e+10 METIS: nnz(L) 3.252e+07 flops 1.205e+10 2D mesh: 1023-by-1023, 5-point stencil MESHND: nnz(L) 5.262e+07 flops 2.033e+10 AMD: nnz(L) 4.567e+07 flops 1.966e+10 METIS: nnz(L) 3.884e+07 flops 1.660e+10 2D mesh: 7-by-7, 9-point stencil MESHND: nnz(L) 3.540e+02 flops 2.830e+03 AMD: nnz(L) 3.290e+02 flops 2.413e+03 METIS: nnz(L) 3.500e+02 flops 2.758e+03 2D mesh: 7-by-7, 9-point stencil MESHND: nnz(L) 3.540e+02 flops 2.830e+03 AMD: nnz(L) 3.290e+02 flops 2.413e+03 METIS: nnz(L) 3.500e+02 flops 2.758e+03 2D mesh: 8-by-8, 9-point stencil MESHND: nnz(L) 5.200e+02 flops 4.602e+03 AMD: nnz(L) 4.890e+02 flops 4.129e+03 METIS: nnz(L) 5.110e+02 flops 4.595e+03 2D mesh: 8-by-8, 9-point stencil MESHND: nnz(L) 5.200e+02 flops 4.602e+03 AMD: nnz(L) 4.890e+02 flops 4.129e+03 METIS: nnz(L) 5.110e+02 flops 4.595e+03 2D mesh: 9-by-9, 9-point stencil MESHND: nnz(L) 7.450e+02 flops 7.529e+03 AMD: nnz(L) 6.960e+02 flops 6.762e+03 METIS: nnz(L) 7.000e+02 flops 6.798e+03 2D mesh: 10-by-10, 9-point stencil MESHND: nnz(L) 1.000e+03 flops 1.104e+04 AMD: nnz(L) 9.150e+02 flops 9.687e+03 METIS: nnz(L) 9.340e+02 flops 9.900e+03 2D mesh: 11-by-11, 9-point stencil MESHND: nnz(L) 1.248e+03 flops 1.436e+04 AMD: nnz(L) 1.206e+03 flops 1.413e+04 METIS: nnz(L) 1.221e+03 flops 1.396e+04 2D mesh: 11-by-11, 9-point stencil MESHND: nnz(L) 1.248e+03 flops 1.436e+04 AMD: nnz(L) 1.206e+03 flops 1.413e+04 METIS: nnz(L) 1.221e+03 flops 1.396e+04 2D mesh: 12-by-12, 9-point stencil MESHND: nnz(L) 1.513e+03 flops 1.811e+04 AMD: nnz(L) 1.500e+03 flops 1.795e+04 METIS: nnz(L) 1.548e+03 flops 1.931e+04 2D mesh: 13-by-13, 9-point stencil MESHND: nnz(L) 1.904e+03 flops 2.492e+04 AMD: nnz(L) 1.888e+03 flops 2.479e+04 METIS: nnz(L) 1.926e+03 flops 2.557e+04 2D mesh: 15-by-15, 9-point stencil MESHND: nnz(L) 2.778e+03 flops 4.033e+04 AMD: nnz(L) 2.654e+03 flops 3.651e+04 METIS: nnz(L) 2.945e+03 flops 4.859e+04 2D mesh: 16-by-16, 9-point stencil MESHND: nnz(L) 3.258e+03 flops 4.852e+04 AMD: nnz(L) 3.284e+03 flops 5.128e+04 METIS: nnz(L) 3.393e+03 flops 5.508e+04 2D mesh: 17-by-17, 9-point stencil MESHND: nnz(L) 3.877e+03 flops 6.177e+04 AMD: nnz(L) 3.854e+03 flops 6.276e+04 METIS: nnz(L) 3.933e+03 flops 6.594e+04 2D mesh: 18-by-18, 9-point stencil MESHND: nnz(L) 4.534e+03 flops 7.600e+04 AMD: nnz(L) 4.382e+03 flops 7.316e+04 METIS: nnz(L) 4.618e+03 flops 8.215e+04 2D mesh: 20-by-20, 9-point stencil MESHND: nnz(L) 5.944e+03 flops 1.057e+05 AMD: nnz(L) 5.910e+03 flops 1.112e+05 METIS: nnz(L) 6.104e+03 flops 1.189e+05 2D mesh: 21-by-21, 9-point stencil MESHND: nnz(L) 6.775e+03 flops 1.263e+05 AMD: nnz(L) 6.567e+03 flops 1.221e+05 METIS: nnz(L) 6.983e+03 flops 1.413e+05 2D mesh: 23-by-23, 9-point stencil MESHND: nnz(L) 8.452e+03 flops 1.680e+05 AMD: nnz(L) 8.259e+03 flops 1.678e+05 METIS: nnz(L) 9.053e+03 flops 2.052e+05 2D mesh: 24-by-24, 9-point stencil MESHND: nnz(L) 9.215e+03 flops 1.864e+05 AMD: nnz(L) 9.473e+03 flops 2.074e+05 METIS: nnz(L) 1.009e+04 flops 2.353e+05 2D mesh: 26-by-26, 9-point stencil MESHND: nnz(L) 1.137e+04 flops 2.488e+05 AMD: nnz(L) 1.150e+04 flops 2.641e+05 METIS: nnz(L) 1.250e+04 flops 3.157e+05 2D mesh: 28-by-28, 9-point stencil MESHND: nnz(L) 1.367e+04 flops 3.128e+05 AMD: nnz(L) 1.384e+04 flops 3.312e+05 METIS: nnz(L) 1.550e+04 flops 4.276e+05 2D mesh: 31-by-31, 9-point stencil MESHND: nnz(L) 1.767e+04 flops 4.390e+05 AMD: nnz(L) 1.753e+04 flops 4.428e+05 METIS: nnz(L) 1.966e+04 flops 5.658e+05 2D mesh: 33-by-33, 9-point stencil MESHND: nnz(L) 2.056e+04 flops 5.323e+05 AMD: nnz(L) 2.175e+04 flops 6.360e+05 METIS: nnz(L) 2.251e+04 flops 6.479e+05 2D mesh: 35-by-35, 9-point stencil MESHND: nnz(L) 2.398e+04 flops 6.508e+05 AMD: nnz(L) 2.379e+04 flops 6.609e+05 METIS: nnz(L) 2.563e+04 flops 7.559e+05 2D mesh: 38-by-38, 9-point stencil MESHND: nnz(L) 2.954e+04 flops 8.528e+05 AMD: nnz(L) 2.998e+04 flops 9.280e+05 METIS: nnz(L) 3.172e+04 flops 1.009e+06 2D mesh: 41-by-41, 9-point stencil MESHND: nnz(L) 3.548e+04 flops 1.075e+06 AMD: nnz(L) 3.685e+04 flops 1.246e+06 METIS: nnz(L) 3.857e+04 flops 1.298e+06 2D mesh: 44-by-44, 9-point stencil MESHND: nnz(L) 4.218e+04 flops 1.341e+06 AMD: nnz(L) 4.299e+04 flops 1.483e+06 METIS: nnz(L) 4.482e+04 flops 1.514e+06 2D mesh: 47-by-47, 9-point stencil MESHND: nnz(L) 4.948e+04 flops 1.662e+06 AMD: nnz(L) 4.981e+04 flops 1.798e+06 METIS: nnz(L) 5.427e+04 flops 2.006e+06 2D mesh: 50-by-50, 9-point stencil MESHND: nnz(L) 5.695e+04 flops 2.005e+06 AMD: nnz(L) 5.813e+04 flops 2.163e+06 METIS: nnz(L) 6.190e+04 flops 2.326e+06 2D mesh: 54-by-54, 9-point stencil MESHND: nnz(L) 6.879e+04 flops 2.574e+06 AMD: nnz(L) 7.023e+04 flops 2.757e+06 METIS: nnz(L) 7.597e+04 flops 3.063e+06 2D mesh: 58-by-58, 9-point stencil MESHND: nnz(L) 8.146e+04 flops 3.206e+06 AMD: nnz(L) 8.291e+04 flops 3.364e+06 METIS: nnz(L) 8.973e+04 flops 3.797e+06 2D mesh: 63-by-63, 9-point stencil MESHND: nnz(L) 9.945e+04 flops 4.164e+06 AMD: nnz(L) 1.021e+05 flops 4.652e+06 METIS: nnz(L) 1.097e+05 flops 4.874e+06 2D mesh: 67-by-67, 9-point stencil MESHND: nnz(L) 1.150e+05 flops 5.037e+06 AMD: nnz(L) 1.180e+05 flops 5.569e+06 METIS: nnz(L) 1.249e+05 flops 5.648e+06 2D mesh: 72-by-72, 9-point stencil MESHND: nnz(L) 1.369e+05 flops 6.282e+06 AMD: nnz(L) 1.452e+05 flops 7.910e+06 METIS: nnz(L) 1.478e+05 flops 7.046e+06 2D mesh: 77-by-77, 9-point stencil MESHND: nnz(L) 1.614e+05 flops 7.810e+06 AMD: nnz(L) 1.703e+05 flops 9.510e+06 METIS: nnz(L) 1.762e+05 flops 8.938e+06 2D mesh: 83-by-83, 9-point stencil MESHND: nnz(L) 1.925e+05 flops 9.843e+06 AMD: nnz(L) 2.008e+05 flops 1.180e+07 METIS: nnz(L) 2.094e+05 flops 1.112e+07 2D mesh: 89-by-89, 9-point stencil MESHND: nnz(L) 2.268e+05 flops 1.220e+07 AMD: nnz(L) 2.384e+05 flops 1.456e+07 METIS: nnz(L) 2.464e+05 flops 1.444e+07 2D mesh: 96-by-96, 9-point stencil MESHND: nnz(L) 2.699e+05 flops 1.534e+07 AMD: nnz(L) 2.804e+05 flops 1.759e+07 METIS: nnz(L) 2.910e+05 flops 1.693e+07 2D mesh: 102-by-102, 9-point stencil MESHND: nnz(L) 3.111e+05 flops 1.863e+07 AMD: nnz(L) 3.226e+05 flops 2.113e+07 METIS: nnz(L) 3.363e+05 flops 2.036e+07 2D mesh: 110-by-110, 9-point stencil MESHND: nnz(L) 3.717e+05 flops 2.357e+07 AMD: nnz(L) 3.828e+05 flops 2.610e+07 METIS: nnz(L) 4.100e+05 flops 2.657e+07 2D mesh: 118-by-118, 9-point stencil MESHND: nnz(L) 4.367e+05 flops 2.921e+07 AMD: nnz(L) 4.550e+05 flops 3.361e+07 METIS: nnz(L) 4.737e+05 flops 3.190e+07 2D mesh: 127-by-127, 9-point stencil MESHND: nnz(L) 5.186e+05 flops 3.667e+07 AMD: nnz(L) 5.732e+05 flops 5.110e+07 METIS: nnz(L) 5.634e+05 flops 4.015e+07 2D mesh: 136-by-136, 9-point stencil MESHND: nnz(L) 6.067e+05 flops 4.504e+07 AMD: nnz(L) 6.357e+05 flops 5.249e+07 METIS: nnz(L) 6.533e+05 flops 4.822e+07 2D mesh: 146-by-146, 9-point stencil MESHND: nnz(L) 7.171e+05 flops 5.616e+07 AMD: nnz(L) 8.085e+05 flops 8.384e+07 METIS: nnz(L) 7.723e+05 flops 6.055e+07 2D mesh: 156-by-156, 9-point stencil MESHND: nnz(L) 8.381e+05 flops 6.888e+07 AMD: nnz(L) 8.718e+05 flops 8.218e+07 METIS: nnz(L) 9.152e+05 flops 7.528e+07 2D mesh: 167-by-167, 9-point stencil MESHND: nnz(L) 9.800e+05 flops 8.500e+07 AMD: nnz(L) 1.142e+06 flops 1.458e+08 METIS: nnz(L) 1.059e+06 flops 9.115e+07 2D mesh: 180-by-180, 9-point stencil MESHND: nnz(L) 1.163e+06 flops 1.066e+08 AMD: nnz(L) 1.214e+06 flops 1.268e+08 METIS: nnz(L) 1.225e+06 flops 1.111e+08 2D mesh: 193-by-193, 9-point stencil MESHND: nnz(L) 1.363e+06 flops 1.320e+08 AMD: nnz(L) 1.433e+06 flops 1.561e+08 METIS: nnz(L) 1.448e+06 flops 1.383e+08 2D mesh: 206-by-206, 9-point stencil MESHND: nnz(L) 1.582e+06 flops 1.614e+08 AMD: nnz(L) 1.637e+06 flops 1.824e+08 METIS: nnz(L) 1.692e+06 flops 1.693e+08 2D mesh: 221-by-221, 9-point stencil MESHND: nnz(L) 1.857e+06 flops 2.001e+08 AMD: nnz(L) 1.952e+06 flops 2.337e+08 METIS: nnz(L) 2.052e+06 flops 2.293e+08 2D mesh: 237-by-237, 9-point stencil MESHND: nnz(L) 2.173e+06 flops 2.474e+08 AMD: nnz(L) 2.297e+06 flops 2.959e+08 METIS: nnz(L) 2.382e+06 flops 2.825e+08 2D mesh: 255-by-255, 9-point stencil MESHND: nnz(L) 2.569e+06 flops 3.096e+08 AMD: nnz(L) 3.239e+06 flops 6.408e+08 METIS: nnz(L) 2.777e+06 flops 3.271e+08 2D mesh: 273-by-273, 9-point stencil MESHND: nnz(L) 2.996e+06 flops 3.802e+08 AMD: nnz(L) 3.158e+06 flops 4.548e+08 METIS: nnz(L) 3.203e+06 flops 3.979e+08 2D mesh: 293-by-293, 9-point stencil MESHND: nnz(L) 3.523e+06 flops 4.719e+08 AMD: nnz(L) 3.693e+06 flops 5.605e+08 METIS: nnz(L) 3.749e+06 flops 4.883e+08 2D mesh: 314-by-314, 9-point stencil MESHND: nnz(L) 4.130e+06 flops 5.826e+08 AMD: nnz(L) 5.119e+06 flops 1.109e+09 METIS: nnz(L) 4.406e+06 flops 6.167e+08 2D mesh: 336-by-336, 9-point stencil MESHND: nnz(L) 4.806e+06 flops 7.152e+08 AMD: nnz(L) 4.992e+06 flops 8.400e+08 METIS: nnz(L) 5.098e+06 flops 7.461e+08 2D mesh: 361-by-361, 9-point stencil MESHND: nnz(L) 5.647e+06 flops 8.894e+08 AMD: nnz(L) 6.052e+06 flops 1.167e+09 METIS: nnz(L) 5.997e+06 flops 9.406e+08 2D mesh: 387-by-387, 9-point stencil MESHND: nnz(L) 6.603e+06 flops 1.099e+09 AMD: nnz(L) 8.957e+06 flops 2.760e+09 METIS: nnz(L) 7.034e+06 flops 1.201e+09 2D mesh: 414-by-414, 9-point stencil MESHND: nnz(L) 7.677e+06 flops 1.349e+09 AMD: nnz(L) 7.998e+06 flops 1.580e+09 METIS: nnz(L) 8.259e+06 flops 1.479e+09 2D mesh: 444-by-444, 9-point stencil MESHND: nnz(L) 8.979e+06 flops 1.667e+09 AMD: nnz(L) 9.248e+06 flops 1.844e+09 METIS: nnz(L) 9.933e+06 flops 2.032e+09 2D mesh: 476-by-476, 9-point stencil MESHND: nnz(L) 1.047e+07 flops 2.058e+09 AMD: nnz(L) 1.106e+07 flops 2.676e+09 METIS: nnz(L) 1.122e+07 flops 2.153e+09 2D mesh: 511-by-511, 9-point stencil MESHND: nnz(L) 1.228e+07 flops 2.554e+09 AMD: nnz(L) 1.701e+07 flops 6.335e+09 METIS: nnz(L) 1.336e+07 flops 3.011e+09 2D mesh: 547-by-547, 9-point stencil MESHND: nnz(L) 1.428e+07 flops 3.134e+09 AMD: nnz(L) 1.972e+07 flops 7.576e+09 METIS: nnz(L) 1.564e+07 flops 3.740e+09 2D mesh: 587-by-587, 9-point stencil MESHND: nnz(L) 1.674e+07 flops 3.881e+09 AMD: nnz(L) 2.297e+07 flops 9.089e+09 METIS: nnz(L) 1.790e+07 flops 4.116e+09 2D mesh: 629-by-629, 9-point stencil MESHND: nnz(L) 1.956e+07 flops 4.783e+09 AMD: nnz(L) 2.072e+07 flops 6.333e+09 METIS: nnz(L) 2.116e+07 flops 5.333e+09 2D mesh: 674-by-674, 9-point stencil MESHND: nnz(L) 2.278e+07 flops 5.891e+09 AMD: nnz(L) 3.397e+07 flops 1.679e+10 METIS: nnz(L) 2.510e+07 flops 7.157e+09 2D mesh: 723-by-723, 9-point stencil MESHND: nnz(L) 2.661e+07 flops 7.285e+09 AMD: nnz(L) 4.122e+07 flops 2.462e+10 METIS: nnz(L) 3.006e+07 flops 1.027e+10 2D mesh: 775-by-775, 9-point stencil MESHND: nnz(L) 3.104e+07 flops 8.987e+09 AMD: nnz(L) 4.552e+07 flops 2.629e+10 METIS: nnz(L) 3.455e+07 flops 1.175e+10 2D mesh: 830-by-830, 9-point stencil MESHND: nnz(L) 3.610e+07 flops 1.105e+10 AMD: nnz(L) 3.763e+07 flops 1.320e+10 METIS: nnz(L) 4.003e+07 flops 1.444e+10 2D mesh: 890-by-890, 9-point stencil MESHND: nnz(L) 4.211e+07 flops 1.364e+10 AMD: nnz(L) 6.025e+07 flops 3.514e+10 METIS: nnz(L) 4.675e+07 flops 1.695e+10 2D mesh: 954-by-954, 9-point stencil MESHND: nnz(L) 4.900e+07 flops 1.682e+10 AMD: nnz(L) 6.918e+07 flops 4.011e+10 METIS: nnz(L) 5.542e+07 flops 2.311e+10 2D mesh: 1023-by-1023, 9-point stencil MESHND: nnz(L) 5.720e+07 flops 2.078e+10 AMD: nnz(L) 8.545e+07 flops 5.878e+10 METIS: nnz(L) 6.355e+07 flops 2.692e+10 3D mesh: 8-by-8-by-8, 7-point stencil MESHND: nnz(L) 1.680e+04 flops 8.311e+05 AMD: nnz(L) 1.133e+04 flops 4.851e+05 METIS: nnz(L) 1.042e+04 flops 3.922e+05 3D mesh: 8-by-8-by-8, 7-point stencil MESHND: nnz(L) 1.680e+04 flops 8.311e+05 AMD: nnz(L) 1.133e+04 flops 4.851e+05 METIS: nnz(L) 1.042e+04 flops 3.922e+05 3D mesh: 9-by-9-by-9, 7-point stencil MESHND: nnz(L) 2.949e+04 flops 1.792e+06 AMD: nnz(L) 1.894e+04 flops 1.088e+06 METIS: nnz(L) 1.824e+04 flops 9.172e+05 3D mesh: 9-by-9-by-9, 7-point stencil MESHND: nnz(L) 2.949e+04 flops 1.792e+06 AMD: nnz(L) 1.894e+04 flops 1.088e+06 METIS: nnz(L) 1.824e+04 flops 9.172e+05 3D mesh: 10-by-10-by-10, 7-point stencil MESHND: nnz(L) 4.725e+04 flops 3.564e+06 AMD: nnz(L) 3.219e+04 flops 2.333e+06 METIS: nnz(L) 3.309e+04 flops 2.321e+06 3D mesh: 11-by-11-by-11, 7-point stencil MESHND: nnz(L) 7.246e+04 flops 6.518e+06 AMD: nnz(L) 4.807e+04 flops 4.349e+06 METIS: nnz(L) 4.327e+04 flops 3.073e+06 3D mesh: 12-by-12-by-12, 7-point stencil MESHND: nnz(L) 1.058e+05 flops 1.139e+07 AMD: nnz(L) 7.604e+04 flops 8.543e+06 METIS: nnz(L) 6.937e+04 flops 6.329e+06 3D mesh: 12-by-12-by-12, 7-point stencil MESHND: nnz(L) 1.058e+05 flops 1.139e+07 AMD: nnz(L) 7.604e+04 flops 8.543e+06 METIS: nnz(L) 6.937e+04 flops 6.329e+06 3D mesh: 13-by-13-by-13, 7-point stencil MESHND: nnz(L) 1.549e+05 flops 1.942e+07 AMD: nnz(L) 1.045e+05 flops 1.382e+07 METIS: nnz(L) 1.072e+05 flops 1.244e+07 3D mesh: 14-by-14-by-14, 7-point stencil MESHND: nnz(L) 2.147e+05 flops 3.111e+07 AMD: nnz(L) 1.517e+05 flops 2.320e+07 METIS: nnz(L) 1.332e+05 flops 1.707e+07 3D mesh: 16-by-16-by-16, 7-point stencil MESHND: nnz(L) 3.859e+05 flops 7.201e+07 AMD: nnz(L) 2.810e+05 flops 6.000e+07 METIS: nnz(L) 2.347e+05 flops 3.751e+07 3D mesh: 17-by-17-by-17, 7-point stencil MESHND: nnz(L) 5.150e+05 flops 1.082e+08 AMD: nnz(L) 3.773e+05 flops 9.681e+07 METIS: nnz(L) 3.416e+05 flops 6.752e+07 3D mesh: 18-by-18-by-18, 7-point stencil MESHND: nnz(L) 6.624e+05 flops 1.547e+08 AMD: nnz(L) 4.883e+05 flops 1.344e+08 METIS: nnz(L) 4.306e+05 flops 9.356e+07 3D mesh: 19-by-19-by-19, 7-point stencil MESHND: nnz(L) 8.464e+05 flops 2.186e+08 AMD: nnz(L) 6.447e+05 flops 2.091e+08 METIS: nnz(L) 5.905e+05 flops 1.515e+08 3D mesh: 21-by-21-by-21, 7-point stencil MESHND: nnz(L) 1.311e+06 flops 4.129e+08 AMD: nnz(L) 1.040e+06 flops 4.105e+08 METIS: nnz(L) 9.257e+05 flops 2.940e+08 3D mesh: 22-by-22-by-22, 7-point stencil MESHND: nnz(L) 1.603e+06 flops 5.504e+08 AMD: nnz(L) 1.274e+06 flops 5.573e+08 METIS: nnz(L) 1.060e+06 flops 3.527e+08 3D mesh: 24-by-24-by-24, 7-point stencil MESHND: nnz(L) 2.319e+06 flops 9.398e+08 AMD: nnz(L) 1.875e+06 flops 9.692e+08 METIS: nnz(L) 1.563e+06 flops 6.256e+08 3D mesh: 25-by-25-by-25, 7-point stencil MESHND: nnz(L) 2.805e+06 flops 1.237e+09 AMD: nnz(L) 2.407e+06 flops 1.448e+09 METIS: nnz(L) 1.830e+06 flops 7.686e+08 3D mesh: 27-by-27-by-27, 7-point stencil MESHND: nnz(L) 3.940e+06 flops 2.003e+09 AMD: nnz(L) 3.388e+06 flops 2.407e+09 METIS: nnz(L) 2.580e+06 flops 1.289e+09 3D mesh: 29-by-29-by-29, 7-point stencil MESHND: nnz(L) 5.356e+06 flops 3.133e+09 AMD: nnz(L) 4.974e+06 flops 4.313e+09 METIS: nnz(L) 3.524e+06 flops 1.995e+09 3D mesh: 32-by-32-by-32, 7-point stencil MESHND: nnz(L) 8.114e+06 flops 5.700e+09 AMD: nnz(L) 7.747e+06 flops 8.358e+09 METIS: nnz(L) 5.462e+06 flops 3.875e+09 3D mesh: 34-by-34-by-34, 7-point stencil MESHND: nnz(L) 1.064e+07 flops 8.405e+09 AMD: nnz(L) 1.046e+07 flops 1.327e+10 METIS: nnz(L) 7.356e+06 flops 6.089e+09 3D mesh: 36-by-36-by-36, 7-point stencil MESHND: nnz(L) 1.355e+07 flops 1.188e+10 AMD: nnz(L) 1.300e+07 flops 1.701e+10 METIS: nnz(L) 9.141e+06 flops 8.339e+09 3D mesh: 39-by-39-by-39, 7-point stencil MESHND: nnz(L) 1.929e+07 flops 1.978e+10 AMD: nnz(L) 1.989e+07 flops 3.346e+10 METIS: nnz(L) 1.304e+07 flops 1.376e+10 3D mesh: 42-by-42-by-42, 7-point stencil MESHND: nnz(L) 2.635e+07 flops 3.117e+10 AMD: nnz(L) 2.643e+07 flops 4.924e+10 METIS: nnz(L) 1.793e+07 flops 2.216e+10 3D mesh: 45-by-45-by-45, 7-point stencil MESHND: nnz(L) 3.543e+07 flops 4.791e+10 AMD: nnz(L) 3.935e+07 flops 9.450e+10 METIS: nnz(L) 2.439e+07 flops 3.474e+10 3D mesh: 48-by-48-by-48, 7-point stencil MESHND: nnz(L) 4.627e+07 flops 7.053e+10 AMD: nnz(L) 5.230e+07 flops 1.364e+11 METIS: nnz(L) 3.194e+07 flops 5.087e+10 3D mesh: 51-by-51-by-51, 7-point stencil MESHND: nnz(L) 6.040e+07 flops 1.037e+11 AMD: nnz(L) 6.736e+07 flops 1.961e+11 METIS: nnz(L) 4.172e+07 flops 7.570e+10 3D mesh: 55-by-55-by-55, 7-point stencil MESHND: nnz(L) 8.329e+07 flops 1.650e+11 AMD: nnz(L) 1.034e+08 flops 3.906e+11 METIS: nnz(L) 5.757e+07 flops 1.215e+11 3D mesh: 59-by-59-by-59, 7-point stencil MESHND: nnz(L) 1.119e+08 flops 2.539e+11 AMD: nnz(L) 1.341e+08 flops 5.484e+11 METIS: nnz(L) 7.938e+07 flops 1.918e+11 3D mesh: 64-by-64-by-64, 7-point stencil MESHND: nnz(L) 1.566e+08 flops 4.141e+11 AMD: nnz(L) 1.842e+08 flops 8.278e+11 METIS: nnz(L) 1.162e+08 flops 3.359e+11 3D mesh: 68-by-68-by-68, 7-point stencil MESHND: nnz(L) 2.025e+08 flops 6.011e+11 AMD: nnz(L) 2.698e+08 flops 1.634e+12 METIS: nnz(L) 1.470e+08 flops 4.750e+11 3D mesh: 73-by-73-by-73, 7-point stencil MESHND: nnz(L) 2.736e+08 flops 9.344e+11 AMD: nnz(L) 3.668e+08 flops 2.354e+12 METIS: nnz(L) 2.022e+08 flops 7.528e+11 3D mesh: 78-by-78-by-78, 7-point stencil MESHND: nnz(L) 3.618e+08 flops 1.399e+12 AMD: nnz(L) 5.023e+08 flops 3.914e+12 METIS: nnz(L) 2.656e+08 flops 1.121e+12 3D mesh: 84-by-84-by-84, 7-point stencil MESHND: nnz(L) 4.913e+08 flops 2.189e+12 AMD: nnz(L) 6.984e+08 flops 6.325e+12 METIS: nnz(L) 3.599e+08 flops 1.738e+12 3D mesh: 90-by-90-by-90, 7-point stencil MESHND: nnz(L) 6.565e+08 flops 3.348e+12 AMD: nnz(L) 9.696e+08 flops 1.028e+13 METIS: nnz(L) 4.872e+08 flops 2.720e+12 3D mesh: 97-by-97-by-97, 7-point stencil MESHND: nnz(L) 8.967e+08 flops 5.291e+12 AMD: nnz(L) 1.441e+09 flops 1.913e+13 METIS: nnz(L) 7.002e+08 flops 4.607e+12 3D mesh: 103-by-103-by-103, 7-point stencil MESHND: nnz(L) 1.155e+09 flops 7.634e+12 AMD: nnz(L) 1.911e+09 flops 2.882e+13 METIS: nnz(L) 8.864e+08 flops 6.511e+12 3D mesh: 111-by-111-by-111, 7-point stencil MESHND: nnz(L) 1.576e+09 flops 1.203e+13 AMD: nnz(L) 2.729e+09 flops 4.858e+13 METIS: nnz(L) 1.233e+09 flops 1.044e+13 3D mesh: 119-by-119-by-119, 7-point stencil MESHND: nnz(L) 2.101e+09 flops 1.836e+13 AMD: nnz(L) 3.913e+09 flops 8.547e+13 METIS: nnz(L) 1.624e+09 flops 1.564e+13 3D mesh: 128-by-128-by-128, 7-point stencil MESHND: nnz(L) 2.830e+09 flops 2.843e+13 AMD: nnz(L) 5.174e+09 flops 1.317e+14 METIS: nnz(L) 2.214e+09 flops 2.465e+13 3D mesh: 8-by-8-by-8, 27-point stencil MESHND: nnz(L) 2.222e+04 flops 1.217e+06 AMD: nnz(L) 2.493e+04 flops 1.673e+06 METIS: nnz(L) 2.437e+04 flops 1.511e+06 3D mesh: 8-by-8-by-8, 27-point stencil MESHND: nnz(L) 2.222e+04 flops 1.217e+06 AMD: nnz(L) 2.493e+04 flops 1.673e+06 METIS: nnz(L) 2.437e+04 flops 1.511e+06 3D mesh: 9-by-9-by-9, 27-point stencil MESHND: nnz(L) 3.920e+04 flops 2.663e+06 AMD: nnz(L) 4.592e+04 flops 4.291e+06 METIS: nnz(L) 4.200e+04 flops 3.188e+06 3D mesh: 9-by-9-by-9, 27-point stencil MESHND: nnz(L) 3.920e+04 flops 2.663e+06 AMD: nnz(L) 4.592e+04 flops 4.291e+06 METIS: nnz(L) 4.200e+04 flops 3.188e+06 3D mesh: 10-by-10-by-10, 27-point stencil MESHND: nnz(L) 6.278e+04 flops 5.167e+06 AMD: nnz(L) 7.465e+04 flops 8.732e+06 METIS: nnz(L) 6.872e+04 flops 6.315e+06 3D mesh: 11-by-11-by-11, 27-point stencil MESHND: nnz(L) 9.422e+04 flops 9.146e+06 AMD: nnz(L) 1.214e+05 flops 1.789e+07 METIS: nnz(L) 1.056e+05 flops 1.112e+07 3D mesh: 12-by-12-by-12, 27-point stencil MESHND: nnz(L) 1.349e+05 flops 1.537e+07 AMD: nnz(L) 1.755e+05 flops 2.951e+07 METIS: nnz(L) 1.569e+05 flops 1.964e+07 3D mesh: 12-by-12-by-12, 27-point stencil MESHND: nnz(L) 1.349e+05 flops 1.537e+07 AMD: nnz(L) 1.755e+05 flops 2.951e+07 METIS: nnz(L) 1.569e+05 flops 1.964e+07 3D mesh: 13-by-13-by-13, 27-point stencil MESHND: nnz(L) 1.965e+05 flops 2.620e+07 AMD: nnz(L) 2.612e+05 flops 5.341e+07 METIS: nnz(L) 2.149e+05 flops 2.970e+07 3D mesh: 14-by-14-by-14, 27-point stencil MESHND: nnz(L) 2.720e+05 flops 4.148e+07 AMD: nnz(L) 3.461e+05 flops 7.622e+07 METIS: nnz(L) 2.886e+05 flops 4.459e+07 3D mesh: 16-by-16-by-16, 27-point stencil MESHND: nnz(L) 4.793e+05 flops 9.220e+07 AMD: nnz(L) 6.963e+05 flops 2.274e+08 METIS: nnz(L) 5.179e+05 flops 1.017e+08 3D mesh: 17-by-17-by-17, 27-point stencil MESHND: nnz(L) 6.368e+05 flops 1.382e+08 AMD: nnz(L) 9.422e+05 flops 3.422e+08 METIS: nnz(L) 6.736e+05 flops 1.468e+08 3D mesh: 18-by-18-by-18, 27-point stencil MESHND: nnz(L) 8.181e+05 flops 1.965e+08 AMD: nnz(L) 1.214e+06 flops 5.202e+08 METIS: nnz(L) 8.633e+05 flops 2.066e+08 3D mesh: 19-by-19-by-19, 27-point stencil MESHND: nnz(L) 1.040e+06 flops 2.744e+08 AMD: nnz(L) 1.721e+06 flops 8.973e+08 METIS: nnz(L) 1.097e+06 flops 2.900e+08 3D mesh: 21-by-21-by-21, 27-point stencil MESHND: nnz(L) 1.596e+06 flops 5.086e+08 AMD: nnz(L) 2.601e+06 flops 1.580e+09 METIS: nnz(L) 1.710e+06 flops 5.433e+08 3D mesh: 22-by-22-by-22, 27-point stencil MESHND: nnz(L) 1.948e+06 flops 6.750e+08 AMD: nnz(L) 2.931e+06 flops 1.800e+09 METIS: nnz(L) 2.057e+06 flops 7.039e+08 3D mesh: 24-by-24-by-24, 27-point stencil MESHND: nnz(L) 2.775e+06 flops 1.128e+09 AMD: nnz(L) 4.552e+06 flops 3.473e+09 METIS: nnz(L) 3.009e+06 flops 1.205e+09 3D mesh: 25-by-25-by-25, 27-point stencil MESHND: nnz(L) 3.341e+06 flops 1.479e+09 AMD: nnz(L) 5.806e+06 flops 5.075e+09 METIS: nnz(L) 3.561e+06 flops 1.534e+09 3D mesh: 27-by-27-by-27, 27-point stencil MESHND: nnz(L) 4.666e+06 flops 2.373e+09 AMD: nnz(L) 8.688e+06 flops 9.583e+09 METIS: nnz(L) 4.884e+06 flops 2.434e+09 3D mesh: 29-by-29-by-29, 27-point stencil MESHND: nnz(L) 6.307e+06 flops 3.674e+09 AMD: nnz(L) 1.030e+07 flops 1.066e+10 METIS: nnz(L) 6.503e+06 flops 3.713e+09 3D mesh: 32-by-32-by-32, 27-point stencil MESHND: nnz(L) 9.468e+06 flops 6.588e+09 AMD: nnz(L) 1.689e+07 flops 2.414e+10 METIS: nnz(L) 9.909e+06 flops 6.799e+09 3D mesh: 34-by-34-by-34, 27-point stencil MESHND: nnz(L) 1.235e+07 flops 9.670e+09 AMD: nnz(L) 2.352e+07 flops 4.169e+10 METIS: nnz(L) 1.277e+07 flops 9.824e+09 3D mesh: 36-by-36-by-36, 27-point stencil MESHND: nnz(L) 1.568e+07 flops 1.357e+10 AMD: nnz(L) 2.655e+07 flops 4.624e+10 METIS: nnz(L) 1.622e+07 flops 1.391e+10 3D mesh: 39-by-39-by-39, 27-point stencil MESHND: nnz(L) 2.218e+07 flops 2.239e+10 AMD: nnz(L) 4.294e+07 flops 9.642e+10 METIS: nnz(L) 2.277e+07 flops 2.263e+10 3D mesh: 42-by-42-by-42, 27-point stencil MESHND: nnz(L) 3.012e+07 flops 3.502e+10 AMD: nnz(L) 5.621e+07 flops 1.440e+11 METIS: nnz(L) 3.128e+07 flops 3.594e+10 3D mesh: 45-by-45-by-45, 27-point stencil MESHND: nnz(L) 4.029e+07 flops 5.341e+10 AMD: nnz(L) 7.698e+07 flops 2.221e+11 METIS: nnz(L) 4.137e+07 flops 5.373e+10 3D mesh: 48-by-48-by-48, 27-point stencil MESHND: nnz(L) 5.234e+07 flops 7.814e+10 AMD: nnz(L) 9.967e+07 flops 3.390e+11 METIS: nnz(L) 5.464e+07 flops 8.076e+10 3D mesh: 51-by-51-by-51, 27-point stencil MESHND: nnz(L) 6.795e+07 flops 1.143e+11 AMD: nnz(L) 1.553e+08 flops 7.073e+11 METIS: nnz(L) 7.030e+07 flops 1.164e+11 3D mesh: 55-by-55-by-55, 27-point stencil MESHND: nnz(L) 9.324e+07 flops 1.807e+11 AMD: nnz(L) 1.987e+08 flops 9.362e+11 METIS: nnz(L) 9.495e+07 flops 1.813e+11 3D mesh: 59-by-59-by-59, 27-point stencil MESHND: nnz(L) 1.247e+08 flops 2.765e+11 AMD: nnz(L) 3.106e+08 flops 2.025e+12 METIS: nnz(L) 1.263e+08 flops 2.766e+11 3D mesh: 64-by-64-by-64, 27-point stencil MESHND: nnz(L) 1.736e+08 flops 4.483e+11 AMD: nnz(L) 3.518e+08 flops 2.143e+12 METIS: nnz(L) 1.778e+08 flops 4.557e+11 3D mesh: 68-by-68-by-68, 27-point stencil MESHND: nnz(L) 2.237e+08 flops 6.482e+11 AMD: nnz(L) 4.708e+08 flops 3.377e+12 METIS: nnz(L) 2.286e+08 flops 6.596e+11 3D mesh: 73-by-73-by-73, 27-point stencil MESHND: nnz(L) 3.009e+08 flops 1.002e+12 AMD: nnz(L) 6.676e+08 flops 5.964e+12 METIS: nnz(L) 3.050e+08 flops 1.004e+12 3D mesh: 78-by-78-by-78, 27-point stencil MESHND: nnz(L) 3.965e+08 flops 1.495e+12 AMD: nnz(L) 8.348e+08 flops 8.647e+12 METIS: nnz(L) 4.022e+08 flops 1.502e+12 3D mesh: 84-by-84-by-84, 27-point stencil MESHND: nnz(L) 5.363e+08 flops 2.329e+12 AMD: nnz(L) 1.115e+09 flops 1.179e+13 METIS: nnz(L) 5.543e+08 flops 2.445e+12 3D mesh: 90-by-90-by-90, 27-point stencil MESHND: nnz(L) 7.137e+08 flops 3.548e+12 AMD: nnz(L) 1.585e+09 flops 2.062e+13 METIS: nnz(L) 7.255e+08 flops 3.572e+12 3D mesh: 97-by-97-by-97, 27-point stencil MESHND: nnz(L) 9.707e+08 flops 5.583e+12 AMD: nnz(L) 2.101e+09 flops 3.018e+13 METIS: nnz(L) 9.926e+08 flops 5.662e+12 3D mesh: 103-by-103-by-103, 27-point stencil MESHND: nnz(L) 1.246e+09 flops 8.032e+12 AMD: nnz(L) 3.387e+09 flops 7.019e+13 METIS: nnz(L) 1.323e+09 flops 9.197e+12 3D mesh: 111-by-111-by-111, 27-point stencil MESHND: nnz(L) 1.694e+09 flops 1.261e+13 AMD: nnz(L) 4.288e+09 flops 9.780e+13 METIS: nnz(L) 1.789e+09 flops 1.437e+13 SuiteSparse/MESHND/meshnd_quality.m0000644001170100242450000001214110711445703016132 0ustar davisfacfunction meshnd_quality (do_metis) %MESHND_QUALITY test the ordering quality computed by meshnd. % The fill-in and flop count for sparse Cholesky factorization using the meshnd % nested dissection ordering is computed with AMD. If SuiteSparse is installed % with METIS, and if requested, then the metis nested dissection ordering is % also compared. % % Example: % meshnd_quality % compare MESHND and AMD % meshnd_quality (1) % also compare with METIS % % See also meshnd, meshsparse, nested, amd, metis. % Copyright 2007, Timothy A. Davis, Univ. of Florida stencils = [5 9 7 27] ; if (nargin < 1) do_metis = 0 ; end if (do_metis) if (exist ('metis') ~= 3) %#ok % METIS not installed do_metis = 0 ; end end figure (1) clf for sk = 1:4 stencil = stencils (sk) ; is3D = (stencil == 7 | stencil == 27) ; %#ok if (is3D) s = 2.^(3:.1:7) ; % mesh size up to 127-by-127-by-127 else s = 2.^(3:.1:10) - 1 ; % mesh size up to 1023-by-1023 end t = length (s) ; lnz = nan * zeros (3,t) ; fl = nan * zeros (3,t) ; try for t = 1:length (s) n = floor (s (t)) ; % create the mesh and the matrix, and get nested dissection ordering if (is3D) fprintf ('3D mesh: %d-by-%d-by-%d, %d-point stencil\n', ... n, n, n, stencil) ; [G p] = meshnd (n, n, n) ; else fprintf ('2D mesh: %d-by-%d, %d-point stencil\n', n, n,stencil); [G p] = meshnd (n, n) ; end A = meshsparse (G, stencil) ; % ND results c = symbfact (A (p,p)) ; lnz (1,t) = sum (c) ; fl (1,t) = sum (c.^2) ; fprintf (' MESHND: nnz(L) %8.3e flops %8.3e\n', ... lnz (1,t), fl (1,t)) ; clear G % AMD results try p = amd (A) ; catch % assume SuiteSparse is installed p = amd2 (A) ; end c = symbfact (A (p,p)) ; lnz (2,t) = sum (c) ; fl (2,t) = sum (c.^2) ; fprintf (' AMD: nnz(L) %8.3e flops %8.3e\n', ... lnz (2,t), fl (2,t)) ; % METIS results (requires SuiteSparse and METIS) if (do_metis) p = metis (A) ; c = symbfact (A (p,p)) ; lnz (3,t) = sum (c) ; fl (3,t) = sum (c.^2) ; fprintf (... ' METIS: nnz(L) %8.3e flops %8.3e\n', ... lnz (3,t), fl (3,t)) ; end % plot the relative nnz(L) results subplot (2, 4, 2*sk - 1) ; loglog (s (1:t), lnz (2,1:t) ./ lnz (1,1:t), 'b-') ; hold on if (do_metis) loglog (s (1:t), lnz (3,1:t) ./ lnz (1,1:t), 'r-') ; end loglog (s (1:t), ones (1,t), 'k-') ; if (do_metis) ylabel ('nnz(L) for AMD or METIS / nnz(L) for meshnd') ; legend ('AMD', 'METIS') ; else ylabel ('nnz(L) for AMD / nnz(L) for meshnd') ; end xlabel ('mesh size') ; axis ([min(s) max(s) .1 10]) ; set (gca, 'YTick', [.1 .25 .5 .8 1 1.25 2 4 10]) ; if (is3D) set (gca, 'XTick', [1 10 100]) ; title (sprintf ('3D mesh, %d-point stencil', stencil)) ; else set (gca, 'XTick', [1 10 100 1000]) ; title (sprintf ('2D mesh, %d-point stencil', stencil)) ; end % plot the relative flop results subplot (2, 4, 2*sk) ; loglog (s (1:t), fl (2,1:t) ./ fl (1,1:t), 'b-') ; hold on if (do_metis) loglog (s (1:t), fl (3,1:t) ./ fl (1,1:t), 'r-') ; end loglog (s (1:t), ones (1,t), 'k-') ; ylabel ('flops for AMD or METIS / flops for meshnd') ; if (do_metis) ylabel ('flops for AMD or METIS / flops for meshnd') ; legend ('AMD', 'METIS') ; else ylabel ('nnz(L) for AMD / nnz(L) for meshnd') ; end xlabel ('mesh size') ; axis ([min(s) max(s) .1 10]) ; set (gca, 'YTick', [.1 .25 .5 .8 1 1.25 2 4 10]) ; if (is3D) set (gca, 'XTick', [1 10 100]) ; title (sprintf ('3D mesh, %d-point stencil', stencil)) ; else set (gca, 'XTick', [1 10 100 1000]) ; title (sprintf ('2D mesh, %d-point stencil', stencil)) ; end drawnow end catch % out-of-memory is OK, other errors are not disp (lasterr) ; if (isempty (strfind (lasterr, 'Out of memory'))) error (lasterr) ; %#ok else fprintf ('test terminated early, but otherwise OK\n') ; end end end SuiteSparse/MESHND/README.txt0000644001170100242450000000165410711427413014431 0ustar davisfac%MESHND: creation and nested dissection of regular 2D and 3D meshes. % % meshnd - creation and nested dissection of a regular 2D or 3D mesh. % meshnd_quality - test the ordering quality computed by meshnd. % meshsparse - convert a 2D or 3D mesh into a sparse matrix matrix. % meshnd_example - example usage of meshnd and meshsparse. % % The outputs of the meshnd example and meshnd_quality are in meshd.png, % meshnd_quality_out.txt, and meshnd_quality.png. % % Example: % % with no inputs or outputs, meshnd runs a demo: % meshnd % % % create the sparse matrix for a 7-by-5-by-2 mesh: % A = meshsparse (meshnd (7,5,2)) ; % % % create a 7-by-5-by-2 mesh and find the nested dissection ordering: % [G p] = meshnd (7,5,2) ; % A = meshsparse (G) ; % subplot (1,2,1) ; spy (A) ; % subplot (1,2,2) ; spy (A (p,p)) ; % % Copyright 2007, Timothy A. Davis, Univ. of Florida % VERSION 1.1.0, Nov 1, 2007 SuiteSparse/MESHND/meshsparse.m0000644001170100242450000000673110710135122015254 0ustar davisfacfunction A = meshsparse (G, stencil) %MESHSPARSE convert a 2D or 3D mesh into a sparse matrix matrix. % % Example: % A = meshsparse (G) % A = meshsparse (G,5) % 2D 5-point stencil (default for 2D case) % A = meshsparse (G,9) % 2D 9-point stencil % A = meshsparse (G,7) % 3D 7-point stencil (default for 3D case) % A = meshsparse (G,27) % 3D 27-point stencil % A = meshsparse (G,stencil) % user-provided stencil % % To create a sparse matrix for an m-by-n 2D mesh or m-by-n-by-k 3D mesh, use % % A = meshsparse (meshnd (m,n)) ; % A = meshsparse (meshnd (m,n,k)) ; % % G is an m-by-n-by-k matrix, with entries numbered 1 to m*n*k (with k=1 for % the 2D case). The entries in G can appear in any order, but no duplicate % entries can appear. That is sort(G(:))' must equal 1:m*n*k. A is returned as % a sparse matrix with m*n*k rows and columns whose pattern depends on the % stencil. The number of nonzeros in most rows/columns of A is equal to the % number of points in the stencil. For examples on how to specify your own % stencil, see the contents of meshsparse.m. % % See also meshnd. % Copyright 2007, Timothy A. Davis, Univ. of Florida if (nargin < 2) [m n k] = size (G) ; if (k == 1) stencil = 5 ; % 2D default is a 5-point stencil else stencil = 7 ; % 3D default is a 7-point stencil end end if (numel (stencil) == 1) % create the stencil if (stencil == 5) % 5-point stencil (2D) stencil = [ -1 0 % north 1 0 % south 0 1 % east 0 -1 ] ; % west elseif (stencil == 9) % 9-point stencil (2D) stencil = [ -1 0 % north 1 0 % south 0 1 % east 0 -1 % west -1 -1 % north-west -1 1 % north-east 1 -1 % south-west 1 1 ] ; % south-east elseif (stencil == 7) % 7-point stencil (3D) stencil = [ -1 0 0 % north 1 0 0 % south 0 1 0 % east 0 -1 0 % west 0 0 -1 % up 0 0 1] ; % down elseif (stencil == 27) % 27-point stencil (3D) stencil = zeros (26, 3) ; t = 0 ; for i = -1:1 for j = -1:1 for k = -1:1 if (~(i == 0 & j == 0 & k == 0)) %#ok t = t + 1 ; stencil (t,:) = [i j k] ; end end end end end end stencil = fix (stencil) ; [npoints d] = size (stencil) ; if (d == 2) % append zeros onto a 2D stencil to make it "3D" stencil = [stencil zeros(npoints,1)] ; end [npoints d] = size (stencil) ; if (d ~= 3) error ('invalid stencil') ; end [m n k] = size (G) ; i1 = 1:m ; j1 = 1:n ; k1 = 1:k ; Ti = zeros (npoints*m*n*k, 1) ; Tj = zeros (npoints*m*n*k, 1) ; nz = 0 ; for point = 1:npoints % find the overlapping rows of G idelta = stencil (point,1) ; i2 = i1 + idelta ; ki = find (i2 >= 1 & i2 <= m) ; % find the overlapping columns of G jdelta = stencil (point,2) ; j2 = j1 + jdelta ; kj = find (j2 >= 1 & j2 <= n) ; % find the overlapping slices of G kdelta = stencil (point,3) ; k2 = k1 + kdelta ; kk = find (k2 >= 1 & k2 <= k) ; % find the nodes in G the shifted G that touch g2 = G (i2 (ki), j2 (kj), k2 (kk)) ; % shifted mesh g1 = G (i1 (ki), j1 (kj), k1 (kk)) ; % unshifted mesh % place the edges in the triplet list e = numel (g1) ; Ti ((nz+1):(nz+e)) = g1 (:) ; Tj ((nz+1):(nz+e)) = g2 (:) ; nz = nz + e ; end % convert the triplets into a sparse matrix Ti = Ti (1:nz) ; Tj = Tj (1:nz) ; A = npoints * speye (m*n*k) - sparse (Ti, Tj, 1, m*n*k, m*n*k) ; SuiteSparse/MESHND/meshnd.png0000644001170100242450000012343210642456324014724 0ustar davisfacPNG  IHDRy pHYs B(xtIME 3"tEXtCreation Time03-Jul-2007 10:27:32uE$tEXtSoftwareMATLAB, The Mathworks, Inc.R IDATx/ W3`HK Y$!9E i7 NȂ!.I.j$'` I]2`֑eYlY>{kz, gp =  {@$8Ipٓ'dOȞ=  {@$8Ipٓ'dOȞ=  {@$8Ipٓ'dOȞ=  {@$8Ipٓ'dOȞ=  {@$8Ipٓ`Jžc\oi ?U˹R;3w~gE7[oRex3.cg2j'\/\m8wj观j9<ɹaYq ܯgalXNsO \%EsQg]!ذzc@ܢFu]qYȅqn* NxQ nXWӮ1Nw:v-}H'= Yu6-ɞ&1<,{rWݞtN0vnj>5辞$;dQt:c#gHeXz$bX CuϙSA*"y"kk[ ~ui:== )$a Sv{8eϓddch霸 =+mN@[^in).6` `S/"bd-*@B 7'u[st 1v5=xSq*~Uw"Uz`q =$x<[D.qׯUnhTip Hp.HBYj7Φ$%u^}*hߓS} kcNDpnQ<8!54@n/nرsbp '/ '«5pO8-~KT@ d!zA4/WpV3gsD[oBRHdstj꙯dneb5۵N6-*}9|V9M#z?Vt\Hab !~he@4l9:k8]Tyk5V8|VIlTpLN>8Xx,By*!cEA랔՗o-JwH*VW{PEmSsk54zCYlzwwPqѻZ*8lcOU`p˱^?nKin5qAoG}D ,[wTp90L,KȞ<[HZ}_m dce|'g^oJT4d?UnC—S{Uȁab^2[$a`Ggߎ5z9*} j@IȂy}cQTE_#,|_=On_s46R_>|K"q"zWK=-pQg > Z䳯aV=c}f}g"b׫Bql6z{".q'zWK~v <gDD?Et^nd1f.u3r$>^-bmsм+裑dm^C߯m 590L,K+$a`?@.z*?'{Ct5}abDE6)cDIgDjQ`8 USm:2Tn;$al[HKߎ C aVޫTTGd  '0̮1c߷ۿPjEȞ cTWۉCX\u߱uB@ ˕U7TF=iXy9&"^o^Fp %Ҍ TL뒺A{a7wd  '2_u9J961""ޔ\:G'@&`u&EqPu@=^w=cE7t^ [ s^oٍk%*jаuד>B8l.o꓿%M׳?Evi)Djn>GQzсhsi=#K=Ir`XNL|D]2S]#"y0v,o6aX-*@&  0[?@畾o/ˌs4{].]CȰ?8gݱKj&#*nbWQv{NG7_"ߟK>M"M]}~H2?@> }2[$a$ۺwy+Q>hE.5vﺉh^[}p|<:{uD7/G)_TM_!fTS/#&eN*82ua uFCjàDD&"ڲUc\6"e=. 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You must be in the same directory as SuiteSparse_install to use this. % % Packages in SuiteSparse: % % UMFPACK sparse LU factorization (multifrontal) % CHOLMOD sparse Cholesky factorization, and many other operations % AMD sparse symmetric approximate minimum degree ordering % COLAMD sparse column approximate minimum degree ordering % CAMD constrained AMD % CCOLAMD constrained COLAMD % CSparse a Concise Sparse matrix package (32-bit/real only) % CXSparse extended version of CSparse (32-bit/64-bit/real/complex) % UFget interface to UF Sparse Matrix Collection (MATLAB 7.0 or later) % KLU sparse LU factorization (left-looking) % BTF permutation to block triangular form (like dmperm) % LDL sparse LDL' factorization % UFcollection tools for managing the UF Sparse Matrix Collection % RBio read/write Rutherford/Boeing files (requires Fortran compiler) % SSMULT sparse matrix times sparse matrix % MESHND 2D and 3D regular mesh generation and nested dissection % LINFACTOR illustrates the use of LU and CHOL (MATLAB 7.3 or later) % MATLAB_Tools various simple m-files and demos % % CXSparse is installed in place of CSparse; cd to CSparse/MATLAB and type % cs_install if you wish to use the latter. Since Microsoft Windows does not % support ANSI C99, CXSparse does not support complex matrices on Windows. % % Except where noted, all packages work on MATLAB 6.1 or later. They have not % been tested on earlier versions, but they might work there. Please let me % know if you try SuiteSparse on MATLAB 6.0 or earlier, whether it works or not. % % Example: % SuiteSparse_install % help SuiteSparse % for more details % % See also AMD, COLAMD, CAMD, CCOLAMD, CHOLMOD, UMFPACK, CSPARSE, CXSPARSE, % UFget, RBio, UFcollection, KLU, BTF, MESHND, SSMULT, LINFACTOR, % SuiteSparse, PATHTOOL, PATH. % Copyright 1990-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse % In collaboration with Patrick Amestoy, Yanqing Chen, Iain Duff, John Gilbert, % Steve Hadfield, Bill Hager, Stefan Larimore, Esmond Ng, Eka Palamadai, and % Siva Rajamanickam. paths = { } ; SuiteSparse = pwd ; % add MATLAB_Tools to the path (for getversion) cd ([SuiteSparse '/MATLAB_Tools']) ; paths = add_to_path (paths, pwd) ; cd (SuiteSparse) ; % determine the MATLAB version (6.1, 6.5, 7.0, ...) v = getversion ; pc = ispc ; % check if METIS 4.0.1 is present where it's supposed to be have_metis = exist ('metis-4.0', 'dir') ; if (~have_metis) fprintf ('CHOLMOD and KLU optionally use METIS 4.0.1. Download it\n') ; fprintf ('from http://glaros.dtc.umn.edu/gkhome/views/metis\n'); fprintf ('and place the metis-4.0 directory in this directory.\n') ; fprintf ('Now compiling without METIS...\n\n') ; end % print the introduction help SuiteSparse_install fprintf ('MATLAB version %g (%s)\n', v, version) ; % add SuiteSparse to the path fprintf ('\nPlease wait while SuiteSparse is compiled and installed...\n') ; paths = add_to_path (paths, SuiteSparse) ; % compile and install UMFPACK try cd ([SuiteSparse '/UMFPACK/MATLAB']) ; paths = add_to_path (paths, pwd) ; umfpack_make catch try fprintf ('Trying to install with lcc_lib/libmwlapack.lib instead\n') ; umfpack_make ('lcc_lib/libmwlapack.lib') ; catch fprintf ('UMFPACK not installed\n') ; end end % compile and install CHOLMOD try % determine whether or not to compile CHOLMOD cd ([SuiteSparse '/CHOLMOD/MATLAB']) ; paths = add_to_path (paths, pwd) ; if (have_metis) cholmod_make else cholmod_make ('no metis') ; end catch fprintf ('CHOLMOD not installed\n') ; end % compile and install AMD try cd ([SuiteSparse '/AMD/MATLAB']) ; paths = add_to_path (paths, pwd) ; amd_make catch fprintf ('AMD not installed\n') ; end % compile and install COLAMD try cd ([SuiteSparse '/COLAMD/MATLAB']) ; paths = add_to_path (paths, pwd) ; colamd_make catch fprintf ('COLAMD not installed\n') ; end % compile and install CCOLAMD try cd ([SuiteSparse '/CCOLAMD/MATLAB']) ; paths = add_to_path (paths, pwd) ; ccolamd_make catch fprintf ('CCOLAMD not installed\n') ; end % compile and install CAMD try cd ([SuiteSparse '/CAMD/MATLAB']) ; paths = add_to_path (paths, pwd) ; camd_make catch fprintf ('CAMD not installed\n') ; end % compile and install CXSparse and UFget try cd ([SuiteSparse '/CXSparse/MATLAB/CSparse']) ; paths = add_to_path (paths, [SuiteSparse '/CXSparse/MATLAB/CSparse']) ; paths = add_to_path (paths, [SuiteSparse '/CXSparse/MATLAB/Demo']) ; if (v >= 7.0) paths = add_to_path (paths, [SuiteSparse '/CXSparse/MATLAB/UFget']) ; fprintf ('UFget installed successfully\n') ; else fprintf ('UFget skipped; requires MATLAB 7.0 or later\n') ; end if (pc) % Windows does not support ANSI C99 complex, which CXSparse requires fprintf ('Compiling CXSparse without complex support\n') ; cs_make (1, 0) ; else cs_make (1) ; end catch fprintf ('CXSparse not installed\n') ; end % compile and install LDL try cd ([SuiteSparse '/LDL/MATLAB']) ; paths = add_to_path (paths, pwd) ; ldl_make catch fprintf ('LDL not installed\n') ; end % compile and install BTF try cd ([SuiteSparse '/BTF/MATLAB']) ; paths = add_to_path (paths, pwd) ; btf_make catch fprintf ('BTF not installed\n') ; end % compile and install KLU try cd ([SuiteSparse '/KLU/MATLAB']) ; paths = add_to_path (paths, pwd) ; klu_make (have_metis) ; catch fprintf ('KLU not installed\n') ; end % compile and install SSMULT try cd ([SuiteSparse '/SSMULT']) ; paths = add_to_path (paths, pwd) ; ssmult_install (0) ; catch fprintf ('SSMULT not installed\n') ; end % compile and install UFcollection try % do not try to compile with large-file I/O for MATLAB 6.5 or earlier cd ([SuiteSparse '/UFcollection']) ; paths = add_to_path (paths, pwd) ; UFcollection_install (v < 7.0) ; catch fprintf ('UFcollection not installed\n') ; end % install LINFACTOR, MESHND, MATLAB_Tools/* try cd ([SuiteSparse '/MESHND']) ; paths = add_to_path (paths, pwd) ; if (v > 7.2) % LINFACTOR requires MATLAB 7.3 or later cd ([SuiteSparse '/LINFACTOR']) ; paths = add_to_path (paths, pwd) ; fprintf ('LINFACTOR installed\n') ; end cd ([SuiteSparse '/MATLAB_Tools/shellgui']) ; paths = add_to_path (paths, pwd) ; cd ([SuiteSparse '/MATLAB_Tools/waitmex']) ; paths = add_to_path (paths, pwd) ; fprintf ('MESHND, MATLAB_Tools installed\n') ; catch fprintf ('LINFACTOR, MESHND, or MATLAB_Tools not installed\n') ; end % compile and install RBio (not on Windows ... no default Fortran compiler) if (~pc) try cd ([SuiteSparse '/RBio']) ; RBmake paths = add_to_path (paths, pwd) ; catch disp (lasterr) fprintf ('RBio not installed (Fortran compiler required).\n') ; end end % post-install wrapup cd (SuiteSparse) fprintf ('SuiteSparse is now installed.\n') ; if (nargin < 1) % ask if demo should be run y = input ('Hit enter to run the SuiteSparse demo (or "n" to quit): ', 's') ; if (isempty (y)) y = 'y' ; end do_demo = (y (1) ~= 'n') ; end if (do_demo) try SuiteSparse_demo ; catch fprintf ('SuiteSparse demo failed\n') ; end end fprintf ('\nSuiteSparse installation is complete. The following paths\n') ; fprintf ('have been added for this session. Use pathtool to add them\n') ; fprintf ('permanently. If you cannot save the new path because of file\n'); fprintf ('permissions, then add these commands to your startup.m file.\n') ; fprintf ('Type "doc startup" and "doc pathtool" for more information.\n\n') ; for k = 1:length (paths) fprintf ('addpath %s\n', paths {k}) ; end cd (SuiteSparse) fprintf ('\nSuiteSparse for MATLAB %g installation complete\n', getversion) ; %------------------------------------------------------------------------------- function paths = add_to_path (paths, newpath) % add a path addpath (newpath) ; paths = [paths { newpath } ] ; %#ok SuiteSparse/SSMULT/0000755001170100242450000000000010712370230012771 5ustar davisfacSuiteSparse/SSMULT/Contents.m0000644001170100242450000000157010707702576014767 0ustar davisfac% SSMULT: sparse matrix multiplication (sparse times sparse) % % SSMULT computes C=A*B where A and B are sparse. It is typically faster % than C=A*B in MATLAB 7.4 (or earlier), and always uses less memory. % % ssmult - multiplies two sparse matrices. % ssmult_install - compiles, installs, and tests ssmult. % ssmult_unsorted - multiplies two sparse matrices, returning non-standard result. % ssmultsym - computes nnz(C), memory, and flops to compute C=A*B; A and B sparse. % ssmult_test - tests ssmult, ssmultsym (sparse times sparse matrix multiply) % ssmult_demo - simple demo for ssmult. % sstest - exhaustive performance test for SSMULT. % sstest2 - exhaustive performance test for SSMULT. Requires UFget. % % Example: % C = ssmult(A,B) ; % computes C = A*B % % Copyright 2007, Timothy A. Davis, University of Florida SuiteSparse/SSMULT/Results/0000755001170100242450000000000010630012630014426 5ustar davisfacSuiteSparse/SSMULT/Results/CoreDuo_Linux.png0000644001170100242450000007554010625633525017706 0ustar davisfacPNG  IHDR^dL pHYs B(xtIMĖ"tEXtCreation Time25-May-2007 15:17:24Y}O$tEXtSoftwareMATLAB, The Mathworks, Inc.R IDATx풣PusۡQpJ؂?P=] j@$/I^U&yTMP5 j@$/I^U&yTMP5 j@$/I^U&yTMP5 j@$/I^U&yTMP5 j@$/I^U&yTMP5 .4_xtWF<#ӭ9hW5l{7U|O^Yrz8j`.~& P.xI{vm {?mX Жq _m .1sL/ܜ-%?N,~ Fܽ%LlvCJ ØR).'躩ZQMa-Q8[X{SֵOS|[ȜqiUC:wi vr_ ˲>͋o{ɦ+ə_a/s=\/Хղ(f^pWp$&vmy^tyistb/~!,6N''K8ݖcdlZ*v 5ZU5pnz_UtHgghJ|O}4ͲX3Kpwg%~8F@$/I^U8hn0) :|@_g. $$BqPU}TIډt' %:{N5G[=页'@qkGݞ V3҅`5ĺlfD<_&vO赅C*38:`vPeyZ),qWywt܊"䗨M7Et']tK閭_jHϼxOĵί5o82?'&-S-F`ګ\?c66t9[1sۇ_K ̼}ESUMn_\ƩW+E:|"1:5mKo[\w.>H5h.="]w>t?,F}{. 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Davis, University of Florida type ssmult_demo load west0479 A = west0479 ; B = sprand (A) ; C = A*B ; D = ssmult (A,B) ; err = norm (C-D,1) / norm (C,1) ; fprintf ('ssmult west0479 error: %g\n', err) ; SuiteSparse/SSMULT/ssmultsym.c0000644001170100242450000001111010630013635015211 0ustar davisfac/* ========================================================================== */ /* === ssmultsym ============================================================ */ /* ========================================================================== */ /* s = ssmultsym (A,B) computes nnz(A*B), and the flops and memory required to * compute it, where A and B are both sparse. Either A or B, or both, can be * complex. Memory usage includes C itself, and workspace. If C is m-by-n, * ssmultsym requires only 4*m bytes for 32-bit MATLAB, 8*m for 64-bit MATLAB. * * Copyright 2007, Timothy A. Davis, University of Florida. */ #include "ssmult.h" /* -------------------------------------------------------------------------- */ /* ssmultsym mexFunction */ /* -------------------------------------------------------------------------- */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double cnz, flops, mem, e, multadds ; Int *Ap, *Ai, *Bp, *Bi, *Flag ; Int Anrow, Ancol, Bnrow, Bncol, i, j, k, pb, pa, pbend, paend, mark, A_is_complex, B_is_complex, C_is_complex, pbstart, cjnz ; static const char *snames [ ] = { "nz", /* # of nonzeros in C=A*B */ "flops", /* flop count required to compute C=A*B */ "memory" /* memory requirement in bytes */ } ; /* ---------------------------------------------------------------------- */ /* get inputs and workspace */ /* ---------------------------------------------------------------------- */ if (nargin != 2 || nargout > 1) { mexErrMsgTxt ("Usage: s = ssmultsym (A,B)") ; } Ap = mxGetJc (pargin [0]) ; Ai = mxGetIr (pargin [0]) ; Anrow = mxGetM (pargin [0]) ; Ancol = mxGetN (pargin [0]) ; A_is_complex = mxIsComplex (pargin [0]) ; Bp = mxGetJc (pargin [1]) ; Bi = mxGetIr (pargin [1]) ; Bnrow = mxGetM (pargin [1]) ; Bncol = mxGetN (pargin [1]) ; B_is_complex = mxIsComplex (pargin [1]) ; if (Ancol != Bnrow || !mxIsSparse (pargin [0]) || !mxIsSparse (pargin [1])) { mexErrMsgTxt ("wrong dimensions, or A and B not sparse") ; } #ifndef MATLAB_6p1_OR_EARLIER if (!mxIsDouble (pargin [0]) || !mxIsDouble (pargin [1])) { mexErrMsgTxt ("A and B must be of class 'double'") ; } #endif Flag = mxCalloc (Anrow, sizeof (Int)) ; /* workspace */ /* ---------------------------------------------------------------------- */ /* compute # of nonzeros in result, flop count, and memory */ /* ---------------------------------------------------------------------- */ pb = 0 ; cnz = 0 ; multadds = 0 ; for (j = 0 ; j < Bncol ; j++) /* compute C(:,j) */ { mark = j+1 ; pbstart = Bp [j] ; pbend = Bp [j+1] ; cjnz = 0 ; for ( ; pb < pbend ; pb++) { k = Bi [pb] ; /* nonzero entry B(k,j) */ pa = Ap [k] ; paend = Ap [k+1] ; multadds += (paend - pa) ; /* one mult-add per entry in A(:,k) */ if (cjnz == Anrow) { /* C(:,j) is already completely dense; no need to scan A. * Continue scanning B(:,j) to compute flop count. */ continue ; } for ( ; pa < paend ; pa++) { i = Ai [pa] ; /* nonzero entry A(i,k) */ if (Flag [i] != mark) { /* C(i,j) is a new nonzero */ Flag [i] = mark ; /* mark i as appearing in C(:,j) */ cjnz++ ; } } } cnz += cjnz ; } C_is_complex = A_is_complex || B_is_complex ; e = (C_is_complex ? 2 : 1) ; mem = Anrow * sizeof (Int) /* Flag */ #ifndef UNSORTED /* the workspace W is not required if C is returned unsorted */ + e * Anrow * sizeof (double) /* W */ #endif + (Bncol+1) * sizeof (Int) /* Cp */ + cnz * sizeof (Int) /* Ci */ + e * cnz * sizeof (double) ; /* Cx and Cx */ if (A_is_complex) { if (B_is_complex) { /* all of C, A, and B are complex */ flops = 8 * multadds - 2 * cnz ; } else { /* C and A are complex, B is real */ flops = 4 * multadds - 2 * cnz ; } } else { if (B_is_complex) { /* C and B are complex, A is real */ flops = 4 * multadds - 2 * cnz ; } else { /* all of C, A, and B are real */ flops = 2 * multadds - cnz ; } } /* ---------------------------------------------------------------------- */ /* return result */ /* ---------------------------------------------------------------------- */ pargout [0] = mxCreateStructMatrix (1, 1, 3, snames) ; mxSetFieldByNumber (pargout [0], 0, 0, mxCreateScalarDouble (cnz)) ; mxSetFieldByNumber (pargout [0], 0, 1, mxCreateScalarDouble (flops)) ; mxSetFieldByNumber (pargout [0], 0, 2, mxCreateScalarDouble (mem)) ; } SuiteSparse/SSMULT/ssmultsym.m0000644001170100242450000000232010625623527015241 0ustar davisfacfunction s = ssmultsym (A,B) %#ok %SSMULTSYM computes nnz(C), memory, and flops to compute C=A*B; A and B sparse. % s = ssmultsym (A,B) returns a struct s with the following fields: % % s.nz nnz (A*B), assuming no numerical cancelation % s.flops flops required to compute C=A*B % s.memory memory required to compute C=A*B, including C itself. % % Either A or B, or both, can be complex. Only matrices of class "double" are % supported. If i is the size of an integer (4 bytes on 32-bit MATLAB, 8 bytes % on 64-bit MATLAB) and x is the size of an entry (8 bytes if real, 16 if % complex), and [m n]=size(C), then the memory usage of SSMULT is % (i+x)*nnz(C) + i*(n+1) for C itself, and (i+x)*m for temporary workspace. % SSMULTSYM itself does not compute C, and uses only i*m workspace. % % Example: % load west0479 % A = west0479 ; % B = sprand (west0479) ; % C = A*B ; % D = ssmult (A,B) ; % C-D % ssmultsym (A,B) % nnz (C) % whos ('C') % [m n] = size (C) % mem = 12*nnz(C) + 4*(n+1) + (12*m) % assuming real, 32-bit MATLAB % % See also ssmult, mtimes. % Copyright 2007, Timothy A. Davis, University of Florida error ('ssmultsym mexFunction not found') ; SuiteSparse/SSMULT/ssmult_install.m0000644001170100242450000000470110712370230016226 0ustar davisfacfunction ssmult_install (dotests) %SSMULT_INSTALL compiles, installs, and tests ssmult. % Note that the "lcc" compiler provided with MATLAB for Windows can generate % slow code; use another compiler if possible. Your current directory must be % SSMULT for ssmult_install to work properly. If you use Linux/Unix/Mac, I % recommend that you use COPTIMFLAGS='-O3 -DNDEBUG' in your mexopts.sh file. % % Example: % ssmult_install % compile and install % ssmult_install (0) % just compile and install, do not test % % See also ssmult, ssmultsym, ssmult_unsorted, sstest, sstest2, mtimes. % Copyright 2007, Timothy A. Davis, University of Florida %------------------------------------------------------------------------------- % print an introduction %------------------------------------------------------------------------------- help ssmult help ssmult_install %------------------------------------------------------------------------------- % compile ssmult and add it to the path %------------------------------------------------------------------------------- d = '' ; if (~isempty (strfind (computer, '64'))) % 64-bit MATLAB d = ' -largeArrayDims -DIS64' ; end v = getversion ; if (v < 6.5) % mxIsDouble is false for a double sparse matrix in MATLAB 6.1 or earlier d = [d ' -DMATLAB_6p1_OR_EARLIER'] ; end cmd = sprintf ('mex -O%s ssmult.c', d) ; disp (cmd) ; eval (cmd) ; cmd = sprintf ('mex -O%s ssmultsym.c', d) ; disp (cmd) ; eval (cmd) ; cmd = sprintf ('mex -O%s -DUNSORTED ssmult.c -output ssmult_unsorted', d) ; disp (cmd) ; eval (cmd) ; addpath (pwd) ; fprintf ('\nssmult has been compiled, and the following directory has been\n') ; fprintf ('added to your MATLAB path. Use pathtool to add it permanently:\n') ; fprintf ('\n%s\n\n', pwd) ; fprintf ('If you cannot save your path with pathtool, add the following\n') ; fprintf ('to your MATLAB startup.m file (type "doc startup" for help):\n') ; fprintf ('\naddpath (''%s'') ;\n\n', pwd) ; %------------------------------------------------------------------------------- % test ssmult and ssmultsym %------------------------------------------------------------------------------- if (nargin < 1) dotests = 1 ; end if (dotests) ssmult_test ; end %------------------------------------------------------------------------------- function v = getversion % determine the MATLAB version, and return it as a double. v = sscanf (version, '%d.%d.%d') ; v = 10.^(0:-1:-(length(v)-1)) * v ; SuiteSparse/SSMULT/README.txt0000644001170100242450000001044610711427455014507 0ustar davisfacSSMULT version 1.1.0, Nov 1, 2007. Distributed under the GNU GPL license (see below). Copyright (c) 2007, Timothy A. Davis, University of Florida. SSMULT is also available under other licenses; contact the author for details. http://www.cise.ufl.edu/research/sparse SSMULT is a MATLAB toolbox for multiplying two sparse matrices, C = A*B. It always uses less memory than the built-in C=A*B (in MATLAB 7.4 or earlier, at least). It is typically faster, particularly when A or B are complex. It is also much faster when A or B are diagonal or permutations of diagonal matrices. Requires MATLAB 6.1 or later (it may work on earlier versions; it has been tested on MATLAB 6.1, 6.5, 7.0.1, 7.0.4, 7.1, 7.2, 7.3, and 7.4). Works on 32-bit and 64-bit MATLAB. Either A or B, or both, can be complex. It should work in 64-bit Windows, but it has only been tested on Linux for the 64-bit case. Only "double" sparse matrices are supported. To compile, install, and test, type ssmult_install in the MATLAB command window. Then edit your path (with pathtool, or startup.m) to add the SSMULT directory to your MATLAB path. For more extensive tests (which require the UFget package) type sstest2 after installing SSMULT. For best performance, do not use the "lcc" compiler that ships with MATLAB 7.4 (or earlier) for Windows. Use another compiler instead. Type "mex -setup" or "doc mex" for more information. For Linux/Unix/Mac, edit your mexopts.sh file and use the option: COPTIMFLAGS='-O3 -DNDEBUG' Note that there is a workaround for a minor "gcc -O" bug (handling floating- point underflow) in ssmult_template.c. Use -DNO_GCC_BUG if this bug does not affect you, and you might slightly increase your performance. The Results directory contains the result of sstest on various platforms. The first three are all on the same laptop, an Intel Core Duo (2GHz, 2GB memory, 2MB of cache): CoreDuo_Linux.png MATLAB 7.4, Intel Core Duo, Linux, gcc v4.1, -O3 CoreDuo_MS_lcc.png MATLAB 7.4, same laptop as above, lcc compiler. CoreDuo_MS_vc2005.png MATLAB 7.4, same laptop, MS VC++ 2005 compiler. Opteron64_Linux.png MATLAB 7.3, AMD Opteron (64-bit) Pentium4M_Linux.png MATLAB 7.3, Pentium 4M, Linux, gcc version 4.1, -O3 These results show that ssmult is always faster for the matrices in this test, when using gcc -O3 in Linux. Comparing the CoreDuo_*.png results, you can see that lcc generates very slow code; these results are on the same laptop. If you see that ssmult is slower than C=A*B in sstest, then check your compiler and its optimization options. In particular, "lcc" as the default compiler used by the "mex" function in MATLAB on Windows will lead to poor performance. In particular, Microsoft provides Visual C++ 2005 Express Edition for free. Intel's compiler also generates high-quality code. If you do not have a C compiler for Windows (other than "lcc" provided with MATLAB) do the following. Download and install the following from www.microsoft.com: Microsoft Visual C++ 2005 Express Edition Microsoft Platform SDK (Windows Server 2003) Next, install the compiler for use in the MATLAB "mex" command: Right click My Computer and select Properties. Click the Advanced tab. Click the Environment Variables button. Create a new environment variable called MSSdk and set its value to the path to the Microsoft Platform SDK. The default location is C:\Program Files\Microsoft Platform SDK for Windows Server 2003 R2\ In MATLAB, type the command "mex -setup". Select the Microsoft Visual C++ 2005 Express Edition compiler. -------------------------------------------------------------------------------- SSMULT is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. SSMULT is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. SuiteSparse/SSMULT/gpl.txt0000644001170100242450000004313310625564151014332 0ustar davisfac GNU GENERAL PUBLIC LICENSE Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The licenses for most software are designed to take away your freedom to share and change it. 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Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the program `Gnomovision' (which makes passes at compilers) written by James Hacker. , 1 April 1989 Ty Coon, President of Vice This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Library General Public License instead of this License. SuiteSparse/SSMULT/ssmult_test.m0000644001170100242450000000563310707702332015552 0ustar davisfacfunction ssmult_test %SSMULT_TEST tests ssmult, ssmultsym (sparse times sparse matrix multiply) % % Example: % ssmult_test % % See also ssmult, ssmult_unsorted, ssmultsym, sstest, sstest2. % Copyright 2007, Timothy A. Davis, University of Florida fprintf ('Please wait while your new ssmult function is tested ...\n') ; ssmult_demo ; fprintf ('\ntesting large matrices (may fail if you are low on memory):\n') rand ('state', 0) ; n = 10000 ; A = sprand (n, n, 0.01) ; B = sprand (n, n, 0.001) ; test_large (A,B) ; msg = { 'real', 'complex' } ; % all of these calls to ssmult should fail: fprintf ('\ntesting error handling (the errors below are expected):\n') ; A = { 3, 'gunk', sparse(1), sparse(1), sparse(rand(3,2)) } ; B = { 4, 0 , 5, msg, sparse(rand(3,4)) } ; for k = 1:length(A) try % the following statement is supposed to fail C = ssmult (A {k}, B {k}) ; %#ok error ('test failed\n') ; catch disp (lasterr) ; end end fprintf ('error handling tests: ok.\n') ; % err should be zero: rand ('state', 0) for Acomplex = 0:1 for Bcomplex = 0:1 err = 0 ; fprintf ('\ntesting C = A*B where A is %s, B is %s\n', ... msg {Acomplex+1}, msg {Bcomplex+1}) ; for m = [ 0:30 100 ] fprintf ('.') ; for n = [ 0:30 100 ] for k = [ 0:30 100 ] A = sprand (m,k,0.1) ; if (Acomplex) A = A + 1i*sprand (A) ; end B = sprand (k,n,0.1) ; if (Bcomplex) B = B + 1i*sprand (B) ; end C = A*B ; D = ssmult (A,B) ; s = ssmultsym (A,B) ; err = max (err, norm (C-D,1)) ; err = max (err, nnz (C-D)) ; err = max (err, isreal (D) ~= (norm (imag (D), 1) == 0)) ; err = max (err, s.nz > nnz (C)) ; [i j x] = find (D) ; %#ok if (~isempty (x)) err = max (err, any (x == 0)) ; end end end end fprintf (' maximum error: %g\n', err) ; end end sstest ; fprintf ('\nSSMULT tests complete.\n') ; %------------------------------------------------------------------------------- function test_large (A,B) % test large matrices n = size (A,1) ; fprintf ('dimension %d nnz(A): %d nnz(B): %d\n', n, nnz (A), nnz (B)) ; c = ssmultsym (A,B) ; fprintf ('nnz(C): %d flops: %g memory: %g MB\n', ... c.nz, c.flops, c.memory/2^20) ; try % warmup for accurate timings C = A*B ; %#ok D = ssmult (A,B) ; %#ok E = ssmult_unsorted (A,B) ; %#ok tic ; C = A*B ; t1 = toc ; tic ; D = ssmult (A,B) ; t2 = toc ; tic ; E = ssmult_unsorted (A,B) ; t3 = toc ; E = E'' ; % sort E, to be safe ... fprintf ('MATLAB time: %g\n', t1) ; err = norm (C-D,1) ; fprintf ('SSMULT time: %g err: %g\n', t2, err) ; err = norm (C-E,1) ; fprintf ('SSMULT_UNSORTED time: %g err: %g\n', t3, err) ; catch disp (lasterr) fprintf ('tests with large random matrices failed ...\n') ; end clear C D E SuiteSparse/SSMULT/ssmult.c0000644001170100242450000003177410630013635014502 0ustar davisfac/* ========================================================================== */ /* === ssmult =============================================================== */ /* ========================================================================== */ /* C = ssmult (A,B) multiplies two sparse matrices A and B, in MATLAB. Either * A or B, or both, can be complex. C is returned as a proper MATLAB sparse * matrix, with sorted row indices and no explicit zero entries. If A or B are * complex, but the imaginary part of C is computed to be zero, then C is * returned as a real sparse matrix (as in MATLAB). * * These extra checks (sorting, dropping zeros, and dropping the complex part * if it is all zero) take time, particulary the requirement that C have sorted * columns. If you are interested in speed, try compiling with -DUNSORTED. The * resulting matrix C can have columns with unsorted row indices, but many * MATLAB functions work just fine when given a matrix with unsorted columns. * * When compiled to return C sorted, this function is called SSMULT. When * compiled without returning C sorted, this function is called SSMULT_UNSORTED. * * Copyright 2007, Timothy A. Davis, University of Florida */ #include "ssmult.h" #ifndef UNSORTED /* -------------------------------------------------------------------------- */ /* merge Left [0..nleft-1] and Right [0..nright-1] into S [0..nleft+nright-1] */ /* -------------------------------------------------------------------------- */ static void merge ( Int S [ ], /* output of length nleft + nright */ const Int Left [ ], /* left input of length nleft */ const Int nleft, const Int Right [ ], /* right input of length nright */ const Int nright ) { Int p, pleft, pright ; /* merge the two inputs, Left and Right, while both inputs exist */ for (p = 0, pleft = 0, pright = 0 ; pleft < nleft && pright < nright ; p++) { if (Left [pleft] < Right [pright]) { S [p] = Left [pleft++] ; } else { S [p] = Right [pright++] ; } } /* either input is exhausted; copy the remaining list into S */ for ( ; pleft < nleft ; p++) { S [p] = Left [pleft++] ; } for ( ; pright < nright ; p++) { S [p] = Right [pright++] ; } } /* -------------------------------------------------------------------------- */ /* SORT(a,b) sorts [a b] in ascending order, so that a < b holds on output */ /* -------------------------------------------------------------------------- */ #define SORT(a,b) { if (a > b) { t = a ; a = b ; b = t ; } } /* -------------------------------------------------------------------------- */ /* BUBBLE(a,b) sorts [a b] in ascending order, and sets done to 0 if it swaps */ /* -------------------------------------------------------------------------- */ #define BUBBLE(a,b) { if (a > b) { t = a ; a = b ; b = t ; done = 0 ; } } /* -------------------------------------------------------------------------- */ /* mergesort */ /* -------------------------------------------------------------------------- */ /* mergesort (A, W, n) sorts an Int array A of length n in ascending order. W is * a workspace array of size n. function is used for sorting the row indices * in each column of C. Small lists (of length SMALL or less) are sorted with * a bubble sort. A value of 10 for SMALL works well on an Intel Core Duo, an * Intel Pentium 4M, and a 64-bit AMD Opteron. SMALL must be in the range 4 to * 10. */ #ifndef SMALL #define SMALL 10 #endif static void mergesort ( Int A [ ], /* array to sort, of size n */ Int W [ ], /* workspace of size n */ Int n ) { if (n <= SMALL) { /* ------------------------------------------------------------------ */ /* bubble sort for small lists of length SMALL or less */ /* ------------------------------------------------------------------ */ Int t, done ; switch (n) { #if SMALL >= 10 case 10: /* 10-element bubble sort */ done = 1 ; BUBBLE (A [0], A [1]) ; BUBBLE (A [1], A [2]) ; BUBBLE (A [2], A [3]) ; BUBBLE (A [3], A [4]) ; BUBBLE (A [4], A [5]) ; BUBBLE (A [5], A [6]) ; BUBBLE (A [6], A [7]) ; BUBBLE (A [7], A [8]) ; BUBBLE (A [8], A [9]) ; if (done) return ; #endif #if SMALL >= 9 case 9: /* 9-element bubble sort */ done = 1 ; BUBBLE (A [0], A [1]) ; BUBBLE (A [1], A [2]) ; BUBBLE (A [2], A [3]) ; BUBBLE (A [3], A [4]) ; BUBBLE (A [4], A [5]) ; BUBBLE (A [5], A [6]) ; BUBBLE (A [6], A [7]) ; BUBBLE (A [7], A [8]) ; if (done) return ; #endif #if SMALL >= 8 case 8: /* 7-element bubble sort */ done = 1 ; BUBBLE (A [0], A [1]) ; BUBBLE (A [1], A [2]) ; BUBBLE (A [2], A [3]) ; BUBBLE (A [3], A [4]) ; BUBBLE (A [4], A [5]) ; BUBBLE (A [5], A [6]) ; BUBBLE (A [6], A [7]) ; if (done) return ; #endif #if SMALL >= 7 case 7: /* 7-element bubble sort */ done = 1 ; BUBBLE (A [0], A [1]) ; BUBBLE (A [1], A [2]) ; BUBBLE (A [2], A [3]) ; BUBBLE (A [3], A [4]) ; BUBBLE (A [4], A [5]) ; BUBBLE (A [5], A [6]) ; if (done) return ; #endif #if SMALL >= 6 case 6: /* 6-element bubble sort */ done = 1 ; BUBBLE (A [0], A [1]) ; BUBBLE (A [1], A [2]) ; BUBBLE (A [2], A [3]) ; BUBBLE (A [3], A [4]) ; BUBBLE (A [4], A [5]) ; if (done) return ; #endif #if SMALL >= 5 case 5: /* 5-element bubble sort */ done = 1 ; BUBBLE (A [0], A [1]) ; BUBBLE (A [1], A [2]) ; BUBBLE (A [2], A [3]) ; BUBBLE (A [3], A [4]) ; if (done) return ; #endif case 4: /* 4-element bubble sort */ done = 1 ; BUBBLE (A [0], A [1]) ; BUBBLE (A [1], A [2]) ; BUBBLE (A [2], A [3]) ; if (done) return ; case 3: /* 3-element bubble sort */ done = 1 ; BUBBLE (A [0], A [1]) ; BUBBLE (A [1], A [2]) ; if (done) return ; case 2: /* 2-element bubble sort */ SORT (A [0], A [1]) ; case 1: case 0: /* nothing to do */ ; } } else { /* ------------------------------------------------------------------ */ /* recursive mergesort if A has length 5 or more */ /* ------------------------------------------------------------------ */ Int n1, n2, n3, n4, n12, n34, n123 ; n12 = n / 2 ; /* split n into n12 and n34 */ n34 = n - n12 ; n1 = n12 / 2 ; /* split n12 into n1 and n2 */ n2 = n12 - n1 ; n3 = n34 / 2 ; /* split n34 into n3 and n4 */ n4 = n34 - n3 ; n123 = n12 + n3 ; /* start of 4th subset = n1 + n2 + n3 */ mergesort (A, W, n1) ; /* sort A [0 ... n1-1] */ mergesort (A + n1, W, n2) ; /* sort A [n1 ... n12-1] */ mergesort (A + n12, W, n3) ; /* sort A [n12 ... n123-1] */ mergesort (A + n123, W, n4) ; /* sort A [n123 ... n-1] */ /* merge A [0 ... n1-1] and A [n1 ... n12-1] into W [0 ... n12-1] */ merge (W, A, n1, A + n1, n2) ; /* merge A [n12 ... n123-1] and A [n123 ... n-1] into W [n12 ... n-1] */ merge (W + n12, A + n12, n3, A + n123, n4) ; /* merge W [0 ... n12-1] and W [n12 ... n-1] into A [0 ... n-1] */ merge (A, W, n12, W + n12, n34) ; } } #endif /* -------------------------------------------------------------------------- */ /* ssmult mexFunction */ /* -------------------------------------------------------------------------- */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double *Ax, *Az, *Bx, *Bz, *Cx, *Cz, *W, *Wz ; double bkj, bzkj, cij, czij ; Int *Ap, *Ai, *Bp, *Bi, *Cp, *Ci, *Flag ; Int Anrow, Ancol, Bnrow, Bncol, p, i, j, k, cnz, pb, pa, pbend, paend, mark, pc, pcstart, blen, drop, zallzero, pend, needs_sorting, pcmax ; int A_is_complex, B_is_complex, C_is_complex, A_is_diagonal, A_is_permutation ; /* ---------------------------------------------------------------------- */ /* get inputs and workspace */ /* ---------------------------------------------------------------------- */ if (nargin != 2 || nargout > 1) { mexErrMsgTxt ("Usage: C = ssmult (A,B)") ; } Ap = mxGetJc (pargin [0]) ; Ai = mxGetIr (pargin [0]) ; Ax = mxGetPr (pargin [0]) ; Az = mxGetPi (pargin [0]) ; Anrow = mxGetM (pargin [0]) ; Ancol = mxGetN (pargin [0]) ; A_is_complex = mxIsComplex (pargin [0]) ; Bp = mxGetJc (pargin [1]) ; Bi = mxGetIr (pargin [1]) ; Bx = mxGetPr (pargin [1]) ; Bz = mxGetPi (pargin [1]) ; Bnrow = mxGetM (pargin [1]) ; Bncol = mxGetN (pargin [1]) ; B_is_complex = mxIsComplex (pargin [1]) ; if (Ancol != Bnrow || !mxIsSparse (pargin [0]) || !mxIsSparse (pargin [1])) { mexErrMsgTxt ("wrong dimensions, or A and B not sparse") ; } #ifndef MATLAB_6p1_OR_EARLIER if (!mxIsDouble (pargin [0]) || !mxIsDouble (pargin [1])) { mexErrMsgTxt ("A and B must be of class 'double'") ; } #endif Flag = mxCalloc (Anrow, sizeof (Int)) ; /* workspace */ Cp = mxMalloc ((Bncol+1) * sizeof (Int)) ; /* allocate C column pointers */ /* ---------------------------------------------------------------------- */ /* compute # of nonzeros in result */ /* ---------------------------------------------------------------------- */ pb = 0 ; cnz = 0 ; mark = 0 ; for (j = 0 ; j < Bncol ; j++) { /* Compute nnz (C (:,j)) */ mark-- ; /* Flag [0..n-1] != mark is now true */ pb = Bp [j] ; pbend = Bp [j+1] ; pcstart = cnz ; pcmax = cnz + Anrow ; Cp [j] = cnz ; /* cnz += nnz (C (:,j)), stopping early if nnz(C(:,j)) == Anrow */ for ( ; pb < pbend && cnz < pcmax ; pb++) { k = Bi [pb] ; /* nonzero entry B(k,j) */ paend = Ap [k+1] ; for (pa = Ap [k] ; pa < paend ; pa++) { i = Ai [pa] ; /* nonzero entry A(i,k) */ if (Flag [i] != mark) { /* C(i,j) is a new nonzero */ Flag [i] = mark ; /* mark i as appearing in C(:,j) */ cnz++ ; } } } if (cnz < pcstart) { /* integer overflow has occurred */ mexErrMsgTxt ("problem too large") ; } } Cp [Bncol] = cnz ; /* ---------------------------------------------------------------------- */ /* allocate C */ /* ---------------------------------------------------------------------- */ Ci = mxMalloc (MAX (cnz,1) * sizeof (Int)) ; Cx = mxMalloc (MAX (cnz,1) * sizeof (double)) ; C_is_complex = A_is_complex || B_is_complex ; Cz = (C_is_complex) ? mxMalloc (MAX (cnz,1) * sizeof (double)) : NULL ; /* ---------------------------------------------------------------------- */ /* C = A*B */ /* ---------------------------------------------------------------------- */ if (A_is_complex) { if (B_is_complex) { /* all of C, A, and B are complex */ #define ACOMPLEX #define BCOMPLEX #include "ssmult_template.c" } else { /* C and A are complex, B is real */ #define ACOMPLEX #include "ssmult_template.c" } } else { if (B_is_complex) { /* C and B are complex, A is real */ #define BCOMPLEX #include "ssmult_template.c" } else { /* all of C, A, and B are real */ #include "ssmult_template.c" } } /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ mxFree (Flag) ; #ifndef UNSORTED /* ---------------------------------------------------------------------- */ /* convert C to real if Cz is all zero */ /* ---------------------------------------------------------------------- */ if (C_is_complex && zallzero) { C_is_complex = 0 ; mxFree (Cz) ; Cz = NULL ; } /* ---------------------------------------------------------------------- */ /* drop zeros from C and reduce its size, if any zeros appear */ /* ---------------------------------------------------------------------- */ if (drop) { if (C_is_complex) { for (cnz = 0, p = 0, j = 0 ; j < Bncol ; j++) { Cp [j] = cnz ; pend = Cp [j+1] ; for ( ; p < pend ; p++) { if (Cx [p] != 0 || Cz [p] != 0) { Ci [cnz] = Ci [p] ; /* keep this entry */ Cx [cnz] = Cx [p] ; Cz [cnz] = Cz [p] ; cnz++ ; } } } Cz = mxRealloc (Cz, MAX (cnz,1) * sizeof (double)) ; } else { for (cnz = 0, p = 0, j = 0 ; j < Bncol ; j++) { Cp [j] = cnz ; pend = Cp [j+1] ; for ( ; p < pend ; p++) { if (Cx [p] != 0) { Ci [cnz] = Ci [p] ; /* keep this entry */ Cx [cnz] = Cx [p] ; cnz++ ; } } } } Cp [Bncol] = cnz ; Ci = mxRealloc (Ci, MAX (cnz,1) * sizeof (Int)) ; Cx = mxRealloc (Cx, MAX (cnz,1) * sizeof (double)) ; } #endif /* ---------------------------------------------------------------------- */ /* return C */ /* ---------------------------------------------------------------------- */ pargout [0] = mxCreateSparse (0, 0, 0, C_is_complex ? mxCOMPLEX : mxREAL) ; mxFree (mxGetJc (pargout [0])) ; mxFree (mxGetIr (pargout [0])) ; mxFree (mxGetPr (pargout [0])) ; mxFree (mxGetPi (pargout [0])) ; mxSetJc (pargout [0], Cp) ; mxSetIr (pargout [0], Ci) ; mxSetPr (pargout [0], Cx) ; mxSetPi (pargout [0], Cz) ; mxSetNzmax (pargout [0], MAX (cnz,1)) ; mxSetM (pargout [0], Anrow) ; mxSetN (pargout [0], Bncol) ; } SuiteSparse/SSMULT/ssmult.h0000644001170100242450000000112510625574551014507 0ustar davisfac/* ========================================================================== */ /* === ssmult.h ============================================================= */ /* ========================================================================== */ /* Include file for ssmult.c and ssmultsym.c * Copyright 2007, Timothy A. Davis, University of Florida */ #include "mex.h" #include /* define the MATLAB integer */ #ifdef IS64 #define Int mwSignedIndex #else #define Int int #endif /* turn off debugging */ #ifndef NDEBUG #define NDEBUG #endif #define MAX(a,b) (((a) > (b)) ? (a) : (b)) SuiteSparse/SSMULT/ssmult.m0000644001170100242450000000110410625564742014512 0ustar davisfacfunction C = ssmult (A,B) %#ok %SSMULT multiplies two sparse matrices. % C = ssmult (A,B) computes C=A*B where A and B are sparse. This function is % typically faster than C=A*B in MATLAB 7.4, and always uses less memory. % Either A or B, or both, can be complex. Only matrices of class "double" are % supported. % % Example: % load west0479 % A = west0479 ; % B = sprand (west0479) ; % C = A*B ; % D = ssmult (A,B) ; % C-D % % See also ssmultsym, mtimes. % Copyright 2007, Timothy A. Davis, University of Florida error ('ssmult mexFunction not found') ; SuiteSparse/SSMULT/sstest2.m0000644001170100242450000001003510627675010014566 0ustar davisfacfunction sstest2 %SSTEST2 exhaustive performance test for SSMULT. Requires UFget. % UFget is available at http://www.cise.ufl.edu/research/sparse, or in MATLAB % Central. % % Example % sstest2 % % See also ssmult, ssmultsym, ssmult_unsorted, ssmult_install, sstest, UFget, mtimes. % Copyright 2007, Timothy A. Davis, University of Florida. help sstest2 try index = UFget ; catch fprintf ('\nsstest2 requires UFget.\n') ; fprintf ('see http://www.cise.ufl.edu/research/sparse\n') ; return ; end [ignore, f] = sort (index.nnz) ; %#ok nmat = length (f) ; TM = zeros (nmat, 4) ; T1 = zeros (nmat, 4) ; TU = zeros (nmat, 4) ; tlim = 0.01 ; tmin = 1 ; tmax = 0 ; check = 1 ; rand ('state', 0) for k = 1:nmat Prob = UFget (f (k), index) ; A = Prob.A ; clear Prob for kind = 1:4 try if (~isreal (A)) A = spones (A) ; end B = A' ; if (kind == 2) A = sprand (A) + 1i*sprand(A) ; B = sprand (B) ; elseif (kind == 3) A = sprand (A) ; B = sprand (B) + 1i*sprand(B) ; elseif (kind == 4) A = sprand (A) + 1i*sprand(A) ; B = sprand (B) + 1i*sprand(B) ; end C = A*B ; % warmup if (check) D = ssmult (A,B) ; err = norm (C-D,1) ; if (err > 0) fprintf ('err: %g\n', err) ; error ('!') end clear D D = ssmult_unsorted (A,B) ; err = norm (C-D,1) ; if (err > 0) fprintf ('err: %g\n', err) ; error ('!') end clear D else % warmup, for accurate timings C = ssmult_unsorted (A,B) ; %#ok C = ssmult (A,B) ; %#ok clear C end tr = 0 ; tm = 0 ; tic while (tm < tlim) C = A*B ; %#ok clear C tr = tr + 1 ; tm = toc ; end tm = tm / tr ; tr = 0 ; t1 = 0 ; tic while (t1 < tlim) C = ssmult (A,B) ; %#ok clear C tr = tr + 1 ; t1 = toc ; end t1 = t1 / tr ; tr = 0 ; tu = 0 ; tic while (tu < tlim) C = ssmult_unsorted (A,B) ; %#ok clear C tr = tr + 1 ; tu = toc ; end tu = tu / tr ; fprintf ('%4d: %4d ', k, f(k)) ; fprintf (... 'MATLAB %12.6f SSMULT %12.6f unsorted %12.6f speedup %12.3f', .... tm, t1, tu, tm / t1) ; if (tm < t1) fprintf (' ****') ; end fprintf ('\n') ; TM (k,kind) = tm ; T1 (k,kind) = t1 ; TU (k,kind) = tu ; tmin = min (tmin, tm) ; tmax = max (tmax, tm) ; catch disp (lasterr) TM (k,kind) = 1 ; T1 (k,kind) = 1 ; TU (k,kind) = 1 ; end end for kind = 1:4 subplot (2,4,kind) ; r = TM (1:k,kind) ./ T1 (1:k,kind) ; rmin = min (r) ; rmax = max (r) ; loglog (TM (1:k,kind), r, 'o', ... [tmin tmax], [1 1], 'r-', ... [tmin tmax], [1.1 1.1], 'r-', ... [tmin tmax], [1/1.1 1/1.1], 'r-', ... [tmin tmax], [2 2], 'g-', ... [tmin tmax], [1.5 1.5], 'g-', ... [tmin tmax], [1/1.5 1/1.5], 'g-', ... [tmin tmax], [.5 .5], 'g-' ); if (k > 2) axis ([tmin tmax rmin rmax]) ; end xlabel ('MATLAB time') ; ylabel ('MATLAB/SM time') ; if (kind == 1) title ('real*real') ; elseif (kind == 2) title ('complex*real') ; elseif (kind == 3) title ('real*complex') ; elseif (kind == 4) title ('complex*complex') ; end subplot (2,4,kind+4) ; r = T1 (1:k,kind) ./ TU (1:k,kind) ; rmin = min (r) ; rmax = max (r) ; loglog (TM (1:k,kind), r, 'o', ... [tmin tmax], [1 1], 'r-', ... [tmin tmax], [1.1 1.1], 'r-', ... [tmin tmax], [1/1.1 1/1.1], 'r-', ... [tmin tmax], [2 2], 'g-', ... [tmin tmax], [1.5 1.5], 'g-', ... [tmin tmax], [1/1.5 1/1.5], 'g-', ... [tmin tmax], [.5 .5], 'g-' ); if (k > 2) axis ([tmin tmax rmin rmax]) ; end xlabel ('MATLAB time') ; ylabel ('SSMULT/unsorted time') ; if (kind == 1) title ('real*real') ; elseif (kind == 2) title ('complex*real') ; elseif (kind == 3) title ('real*complex') ; elseif (kind == 4) title ('complex*complex') ; end end drawnow clear A B C save sstest2_results.mat TM T1 TU f diary off diary on end SuiteSparse/SSMULT/sstest.m0000644001170100242450000000661610710706771014520 0ustar davisfacfunction sstest %SSTEST exhaustive performance test for SSMULT. % % Example % sstest % % See also ssmult, ssmultsym, ssmult_unsorted, ssmult_install, sstest2, mtimes. % Copyright 2007, Timothy A. Davis, University of Florida. N = [500:50:1000 1100:100:3000 3200:200:5000 ] ; rand ('state',0) ; % warmup for more accurate timings A = sparse (1) ; B = sparse (1) ; C = A*B ; D = ssmult(A,B) ; err = norm (C-D,1) ; if (err > 0) error ('test failure') ; end clear C D titles = { ... 'C=A*B blue, C=B*A red, both real', ... 'A real, B complex', 'A complex, B real', 'both complex' } ; xlabels = { '(A random, B diagonal)', '(A random, B permutation)', ... '(A random, B tridiagonal)' } ; fprintf ('\nIn the next plots, speedup is the time for MATLAB C=A*B divided\n'); fprintf ('by the time for C=ssmult(A,B). The X-axis is n, the dimension\n') ; fprintf ('of the square matrices A and B. A is a sparse random matrix with\n'); fprintf ('1%% nonzero values. B is diagonal in the first row of plots,\n') ; fprintf ('a permutation in the 2nd row, and tridiagonal in the third.\n') ; fprintf ('C=A*B is in blue, C=B*A is in red. A and B are both real in the\n') ; fprintf ('first column of plots, B is complex in the 2nd, A in the 3rd, and\n'); fprintf ('both are complex in the 4th column of plots. You will want to\n') ; fprintf ('maximize the figure; otherwise the text is too hard to read.\n') ; tlim = 0.1 ; figure (1) ; clf ; for fig = 1:3 fprintf ('Testing C=A*B and C=B*A %s\n', xlabels {fig}) ; T = zeros (length(N),4,4) ; for k = 1:length(N) n = N (k) ; try A = sprand (n,n,0.01) ; if (fig == 1) % B diagonal B = spdiags (rand (n,1), 0, n, n) ; elseif (fig == 2) % B permutation B = spdiags (rand (n,1), 0, n, n) ; B = B (:,randperm(n)) ; else % B tridiagonal B = spdiags (rand (n,3), -1:1, n, n) ; end for kind = 1:4 if (kind == 2) % A complex, B real A = A + 1i*sprand (A) ; elseif (kind == 3) % A real, B complex A = real (A) ; B = B + 1i*sprand (B) ; elseif (kind == 4) % both complex A = A + 1i*sprand (A) ; B = B + 1i*sprand (B) ; end t1 = 0 ; trials = 0 ; tic while (t1 < tlim) C = A*B ; trials = trials + 1 ; t1 = toc ; end t1 = t1 / trials ; t2 = 0 ; trials = 0 ; tic while (t2 < tlim) D = ssmult (A,B) ; trials = trials + 1 ; t2 = toc ; end t2 = t2 / trials ; err = norm (C-D,1) ; if (err > 0) error ('test failure') ; end clear C clear D t3 = 0 ; trials = 0 ; tic while (t3 < tlim) C = B*A ; trials = trials + 1 ; t3 = toc ; end t3 = t3 / trials ; t4 = 0 ; trials = 0 ; tic while (t4 < tlim) D = ssmult (B,A) ; trials = trials + 1 ; t4 = toc ; end t4 = t4 / trials ; err = norm (C-D,1) ; if (err > 0) error ('test failure') ; end clear C clear D T (k,kind,1) = t1 ; T (k,kind,2) = t2 ; T (k,kind,3) = t3 ; T (k,kind,4) = t4 ; subplot (3,4,kind + 4*(fig-1)) ; plot (N(1:k), T (1:k,kind,1) ./ T (1:k,kind,2), 'o', ... N(1:k), T (1:k,kind,3) ./ T (1:k,kind,4), 'rx', ... [N(1) n], [1 1], 'k') ; xlabel (['n ' xlabels{fig}]) ; ylabel ('speedup') ; axis tight title (titles {kind}) ; drawnow end catch % probably because we ran out of memory ... disp (lasterr) ; break ; end end end SuiteSparse/SSMULT/ssmult_unsorted.m0000644001170100242450000000272710625565703016447 0ustar davisfacfunction C = ssmult_unsorted (A,B) %#ok %SSMULT_UNSORTED multiplies two sparse matrices, returning non-standard result. % C = ssmult_unsorted (A,B) computes C=A*B where A and B are sparse. It returns % C with unsorted row indices in its columns, and possibly with explicit zero % entries due to numeric cancellation. This does *NOT* conform to the MATLAB % standard (as of MATLAB 7.4 ...) for MATLAB sparse matrices. However, such % matrices are often safe to use in subsequent operations (such as C*X where % X is a full matrix). Computing C'' (a double transpose) gives a sorted % result. This function is typically MUCH faster than C=A*B in MATLAB 7.4, and % uses less memory. Either A or B, or both, can be complex. Only matrices of % class "double" are supported. The primary reason for this function is to % demonstrate how much performance MATLAB loses by insisting on keeping its % sparse matrices sorted. % % *** USE AT YOUR OWN RISK. USE SSMULT TO BE SAFE. *** % % Example: % load west0479 % A = west0479 ; % B = sprand (west0479) ; % tic ; C = A*B ; toc % tic ; D = ssmult_unsorted (A,B) ; toc % C-D % % To see that the result D from ssmult_unsorted has unsorted columns: % % spparms ('spumoni', 1) % colamd (D) ; % spparms ('spumoni', 0) % % See also ssmult, ssmultsym, mtimes. % % *** USE AT YOUR OWN RISK. USE SSMULT TO BE SAFE. *** % Copyright 2007, Timothy A. Davis, University of Florida error ('ssmult_unsorted mexFunction not found') ; SuiteSparse/SSMULT/ssmult_template.c0000644001170100242450000002671310625557022016401 0ustar davisfac/* ========================================================================== */ /* === ssmult_template.c ==================================================== */ /* ========================================================================== */ /* C = A*B, where A and B are sparse. The column pointers for C (the Cp array) * have already been computed. entries are dropped. This code fragment is * #include'd into ssmult.c four times, with all four combinations of ACOMPLEX * (defined or not) and BCOMPLEX (defined or not). * * By default, C is returned with sorted column indices, and with explicit * zero entries dropped. If C is complex with an all-zero imaginary part, then * the imaginary part is freed and C becomes real. Thus, C is a pure MATLAB * sparse matrix. * * If UNSORTED is defined (-DUNSORTED), then the nonzero pattern of C is * returned with unsorted column indices, explicit zeros may be present in C, * and the imaginary of a complex C may be all zero. This is much faster than * returning a pure MATLAB sparse matrix. * * If the compiler bug discussed below does not affect you, then uncomment the * following line, or compile with code with -DNO_GCC_BUG. #define NO_GCC_BUG * The gcc bug occurs when cij underflows to zero: * * cij = aik * bkj ; * if (cij == 0) * { * drop this entry * } * * If cij underflows, cij is zero but the above test is incorrectly FALSE with * gcc -O, using gcc version 4.1.0 on an Intel Pentium. The bug does not appear * on an AMD Opteron with the same compiler. The solution is to store cij to * memory first, and then to read it back in and test it, which is slower. */ /* -------------------------------------------------------------------------- */ /* MULT: multiply (or multiply and accumulate, depending on op) */ /* -------------------------------------------------------------------------- */ /* op can be "=" or "+=" */ #ifdef ACOMPLEX #ifdef BCOMPLEX #define MULT(x,z,op) \ x op Ax [pa] * bkj - Az [pa] * bzkj ; \ z op Az [pa] * bkj + Ax [pa] * bzkj ; #else #define MULT(x,z,op) \ x op Ax [pa] * bkj ; \ z op Az [pa] * bkj ; #endif #else #ifdef BCOMPLEX #define MULT(x,z,op) \ x op Ax [pa] * bkj ; \ z op Ax [pa] * bzkj ; #else #define MULT(x,z,op) \ x op Ax [pa] * bkj ; #endif #endif /* -------------------------------------------------------------------------- */ /* ASSIGN_BKJ: copy B(k,j) into a local scalar */ /* -------------------------------------------------------------------------- */ #ifdef BCOMPLEX #define ASSIGN_BKJ \ bkj = Bx [pb] ; \ bzkj = Bz [pb] ; #else #define ASSIGN_BKJ \ bkj = Bx [pb] ; #endif /* -------------------------------------------------------------------------- */ /* DROP_CHECK: check if an entry must be dropped */ /* -------------------------------------------------------------------------- */ #ifndef UNSORTED #if defined (ACOMPLEX) || defined (BCOMPLEX) #define DROP_CHECK(x,z) \ if (x == 0 && z == 0) drop = 1 ; \ if (z != 0) zallzero = 0 ; #else #define DROP_CHECK(x,z) if (x == 0) drop = 1 ; #endif #else #define DROP_CHECK(x,z) #endif /* -------------------------------------------------------------------------- */ /* sparse matrix multiply template */ /* -------------------------------------------------------------------------- */ { /* ---------------------------------------------------------------------- */ /* initialize drop tests */ /* ---------------------------------------------------------------------- */ #ifndef UNSORTED drop = 0 ; /* true if any entry in C is zero */ zallzero = 1 ; /* true if Cz is all zero */ #endif /* ---------------------------------------------------------------------- */ /* quick check if A is diagonal, or a permutation matrix */ /* ---------------------------------------------------------------------- */ if (Anrow == Ancol && Ap [Ancol] == Ancol) { /* A is square, with n == nnz (A); check the pattern */ A_is_permutation = 1 ; A_is_diagonal = 1 ; for (j = 0 ; j < Ancol ; j++) { if (Ap [j] != j) { /* A has a column with no entries, or more than 1 entry */ A_is_permutation = 0 ; A_is_diagonal = 0 ; break ; } } mark-- ; /* Flag [0..n-1] != mark is now true */ for (j = 0 ; j < Ancol && (A_is_permutation || A_is_diagonal) ; j++) { /* A has one entry in each column, so j == Ap [j] */ i = Ai [j] ; if (i != j) { /* A is not diagonal, but might still be a permutation */ A_is_diagonal = 0 ; } if (Flag [i] == mark) { /* row i appears twice; A is neither permutation nor diagonal */ A_is_permutation = 0 ; A_is_diagonal = 0 ; } /* mark row i, so we know if we see it again */ Flag [i] = mark ; } } else { /* A is not square, or nnz (A) is not equal to n */ A_is_permutation = 0 ; A_is_diagonal = 0 ; } /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ #ifndef UNSORTED W = NULL ; if (!A_is_diagonal) { #if defined (ACOMPLEX) || defined (BCOMPLEX) W = mxMalloc (Anrow * 2 * sizeof (double)) ; Wz = W + Anrow ; #else W = mxMalloc (Anrow * sizeof (double)) ; #endif } #endif /* ---------------------------------------------------------------------- */ /* compute C one column at a time */ /* ---------------------------------------------------------------------- */ if (A_is_diagonal) { /* ------------------------------------------------------------------ */ /* C = A*B where A is diagonal */ /* ------------------------------------------------------------------ */ pb = 0 ; for (j = 0 ; j < Bncol ; j++) { pcstart = pb ; pbend = Bp [j+1] ; /* column B is in Bi,Bx,Bz [pb ... pbend+1] */ for ( ; pb < pbend ; pb++) { k = Bi [pb] ; /* nonzero entry B(k,j) */ ASSIGN_BKJ ; Ci [pb] = k ; pa = k ; MULT (Cx [pb], Cz [pb], =) ; /* C(k,j) = A(k,k)*B(k,j) */ #ifdef NO_GCC_BUG DROP_CHECK (Cx [pb], Cz [pb]) ; /* check if C(k,j) == 0 */ #endif } #ifndef UNSORTED #ifndef NO_GCC_BUG for (pc = pcstart ; pc < pbend ; pc++) { DROP_CHECK (Cx [pc], Cz [pc]) ; /* check if C(k,j) == 0 */ } #endif #endif } } else { /* ------------------------------------------------------------------ */ /* C = A*B, general case, or A permutation */ /* ------------------------------------------------------------------ */ pb = 0 ; cnz = 0 ; for (j = 0 ; j < Bncol ; j++) { /* -------------------------------------------------------------- */ /* compute jth column of C: C(:,j) = A * B(:,j) */ /* -------------------------------------------------------------- */ pbend = Bp [j+1] ; /* column B is in Bi,Bx,Bz [pb ... pbend+1] */ pcstart = cnz ; /* start of column j in C */ blen = pbend - pb ; /* number of entries in B */ needs_sorting = 0 ; /* true if column j needs sorting */ if (blen == 0) { /* ---------------------------------------------------------- */ /* nothing to do, B(:,j) and C(:,j) are empty */ /* ---------------------------------------------------------- */ continue ; } else if (blen == 1) { /* ---------------------------------------------------------- */ /* B(:,j) contains only one nonzero */ /* ---------------------------------------------------------- */ /* since there is only one entry in B, just scale column A(:,k): * C(:,j) = A(:,k) * B(k,j) * C is sorted only if A is sorted on input */ k = Bi [pb] ; /* nonzero entry B(k,j) */ ASSIGN_BKJ ; paend = Ap [k+1] ; for (pa = Ap [k] ; pa < paend ; pa++, cnz++) { Ci [cnz] = Ai [pa] ; /* nonzero entry A(i,k) */ MULT (Cx [cnz], Cz [cnz], =) ; /* C(i,j) = A(i,k)*B(k,j) */ #ifdef NO_GCC_BUG DROP_CHECK (Cx [cnz], Cz [cnz]) ; /* check C(i,j) == 0 */ #endif } pb++ ; #ifndef UNSORTED #ifndef NO_GCC_BUG for (pc = pcstart ; pc < cnz ; pc++) { DROP_CHECK (Cx [pc], Cz [pc]) ; /* check if C(i,j) == 0 */ } #endif #endif } else { /* ---------------------------------------------------------- */ /* B(:,j) has two or more entries */ /* ---------------------------------------------------------- */ if (A_is_permutation) { /* ------------------------------------------------------ */ /* A is a permutation matrix */ /* ------------------------------------------------------ */ needs_sorting = 1 ; for ( ; pb < pbend ; pb++) { k = Bi [pb] ; /* nonzero entry B(k,j) */ ASSIGN_BKJ ; i = Ai [k] ; /* nonzero entry A(i,k) */ Ci [pb] = i ; pa = k ; /* C(i,j) = A(i,k)*B(k,j) */ #ifndef UNSORTED MULT (W [i], Wz [i], =) ; #else MULT (Cx [pb], Cz [pb], =) ; #endif } cnz = pbend ; } else { /* ------------------------------------------------------ */ /* general case */ /* ------------------------------------------------------ */ /* first entry in jth column of B is simpler */ /* C(:,j) = A (:,k) * B (k,j) */ k = Bi [pb] ; /* nonzero entry B(k,j) */ ASSIGN_BKJ ; paend = Ap [k+1] ; for (pa = Ap [k] ; pa < paend ; pa++) { i = Ai [pa] ; /* nonzero entry A(i,k) */ Flag [i] = cnz ; Ci [cnz] = i ; /* new entry C(i,j) */ /* C(i,j) = A(i,k)*B(k,j) */ #ifndef UNSORTED MULT (W [i], Wz [i], =) ; #else MULT (Cx [cnz], Cz [cnz], =) ; #endif cnz++ ; } pb++ ; for ( ; pb < pbend ; pb++) { k = Bi [pb] ; /* nonzero entry B(k,j) */ ASSIGN_BKJ ; /* C(:,j) += A (:,k) * B (k,j) */ paend = Ap [k+1] ; for (pa = Ap [k] ; pa < paend ; pa++) { i = Ai [pa] ; /* nonzero entry A(i,k) */ pc = Flag [i] ; if (pc < pcstart) { pc = cnz++ ; Flag [i] = pc ; Ci [pc] = i ; /* new entry C(i,j) */ /* C(i,j) = A(i,k)*B(k,j) */ #ifndef UNSORTED MULT (W [i], Wz [i], =) ; needs_sorting = 1 ; #else MULT (Cx [pc], Cz [pc], =) ; #endif } else { /* C(i,j) += A(i,k)*B(k,j) */ #ifndef UNSORTED MULT (W [i], Wz [i], +=) ; #else MULT (Cx [pc], Cz [pc], +=) ; #endif } } } } /* ---------------------------------------------------------- */ /* sort the pattern of C(:,j) and gather the values of C(:,j) */ /* ---------------------------------------------------------- */ #ifndef UNSORTED /* Sort the row indices in C(:,j). Use Cx as Int workspace. * This assumes sizeof (Int) < sizeof (double). If blen <= 1, * or if subsequent entries in B(:,j) appended entries onto C, * there is no need to sort C(:,j), assuming A is sorted. */ if (needs_sorting) { mergesort (Ci + pcstart, (Int *) (Cx + pcstart), cnz - pcstart) ; } for (pc = pcstart ; pc < cnz ; pc++) { #if defined (ACOMPLEX) || defined (BCOMPLEX) i = Ci [pc] ; cij = W [i] ; /* get C(i,j) from W */ czij = Wz [i] ; Cx [pc] = cij ; /* copy C(i,j) into C */ Cz [pc] = czij ; #else cij = W [Ci [pc]] ; /* get C(i,j) from W */ Cx [pc] = cij ; /* copy C(i,j) into C */ #endif DROP_CHECK (cij, czij) ; /* check if C(i,j) == 0 */ } #endif } } } /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ #ifndef UNSORTED mxFree (W) ; #endif } #undef ACOMPLEX #undef BCOMPLEX #undef MULT #undef ASSIGN_BKJ #undef DROP_CHECK SuiteSparse/SuiteSparse_test.m0000644001170100242450000001454310712357773015456 0ustar davisfacfunction SuiteSparse_test % SuiteSparse_test exhaustive test of all SuiteSparse packages % % Your current directory must be SuiteSparse for this function to work. % SuiteSparse_install must be run prior to running this test. Warning: % this test takes a *** long **** time. % % Example: % SuiteSparse_test % % See also SuiteSparse_install, SuiteSparse_demo. % Copyright 2007, Tim Davis, University of Florida npackages = 13 ; h = waitbar (0, 'SuiteSparse test:') ; SuiteSparse = pwd ; v = getversion ; if (v < 7) error ('SuiteSparse_test requires MATLAB 7.0 or later') ; end % if at UF, ensure pre-installed UF Sparse Matrix Collection is used uf = { '/cise/homes/davis/Install/UFget', 'd:/UFget', '/share/UFget' } ; for k = 1:length(uf) if (exist (uf {k}, 'dir')) addpath (uf {k}) ; break ; end end try %--------------------------------------------------------------------------- % CSparse (32-bit MATLAB only) %--------------------------------------------------------------------------- if (isempty (strfind (computer, '64'))) % compile and install CSparse (not installed by SuiteSparse_install) waitbar (1/(npackages+1), h, 'SuiteSparse test: CSparse') ; addpath ([SuiteSparse '/CSparse/MATLAB/CSparse']) ; addpath ([SuiteSparse '/CSparse/MATLAB/Demo']) ; cd ([SuiteSparse '/CSparse/MATLAB/CSparse']) ; cs_make ; % test CSparse cd ([SuiteSparse '/CSparse/MATLAB/Test']) ; testall ; % uninstall CSparse by removing it from path rmpath ([SuiteSparse '/CSparse/MATLAB/CSparse']) ; rmpath ([SuiteSparse '/CSparse/MATLAB/Demo']) ; end %--------------------------------------------------------------------------- % CXSparse %--------------------------------------------------------------------------- waitbar (2/(npackages+1), h, 'SuiteSparse test: CXSparse') ; cd ([SuiteSparse '/CXSparse/MATLAB/Test']) ; testall ; %--------------------------------------------------------------------------- % COLAMD %--------------------------------------------------------------------------- waitbar (3/(npackages+1), h, 'SuiteSparse test: COLAMD') ; cd ([SuiteSparse '/COLAMD/MATLAB']) ; colamd_test ; %--------------------------------------------------------------------------- % CCOLAMD %--------------------------------------------------------------------------- waitbar (4/(npackages+1), h, 'SuiteSparse test: CCOLAMD') ; cd ([SuiteSparse '/CCOLAMD/MATLAB']) ; ccolamd_test ; %--------------------------------------------------------------------------- % UMFPACK %--------------------------------------------------------------------------- waitbar (5/(npackages+1), h, 'SuiteSparse test: UMFPACK') ; cd ([SuiteSparse '/UMFPACK/MATLAB']) ; umfpack_test (800) ; %--------------------------------------------------------------------------- % CHOLMOD %--------------------------------------------------------------------------- waitbar (6/(npackages+1), h, 'SuiteSparse test: CHOLMOD') ; cd ([SuiteSparse '/CHOLMOD/MATLAB/Test']) ; cholmod_test ; %--------------------------------------------------------------------------- % BTF %--------------------------------------------------------------------------- waitbar (7/(npackages+1), h, 'SuiteSparse test: BTF') ; cd ([SuiteSparse '/BTF/MATLAB/Test']) ; btf_test ; %--------------------------------------------------------------------------- % KLU %--------------------------------------------------------------------------- waitbar (8/(npackages+1), h, 'SuiteSparse test: KLU') ; cd ([SuiteSparse '/KLU/MATLAB/Test']) ; klu_test ; %--------------------------------------------------------------------------- % LDL %--------------------------------------------------------------------------- waitbar (9/(npackages+1), h, 'SuiteSparse test: LDL') ; cd ([SuiteSparse '/LDL/MATLAB']) ; ldlmain2 ; ldltest ; %--------------------------------------------------------------------------- % LINFACTOR: MATLAB 7.3 (R2006b) or later required %--------------------------------------------------------------------------- if (v > 7.2) waitbar (10/(npackages+1), h, 'SuiteSparse test: LINFACTOR') ; cd ([SuiteSparse '/LINFACTOR']) ; lintests ; end %--------------------------------------------------------------------------- % MESHND %--------------------------------------------------------------------------- waitbar (11/(npackages+1), h, 'SuiteSparse test: MESHND') ; cd ([SuiteSparse '/MESHND']) ; meshnd_quality ; %--------------------------------------------------------------------------- % SSMULT %--------------------------------------------------------------------------- waitbar (12/(npackages+1), h, 'SuiteSparse test: SSMULT') ; cd ([SuiteSparse '/SSMULT']) ; ssmult_test ; %--------------------------------------------------------------------------- % MATLAB_Tools %--------------------------------------------------------------------------- waitbar (13/(npackages+1), h, 'SuiteSparse test: MATLAB Tools') ; cd ([SuiteSparse '/MATLAB_Tools']) ; figure (1) ; clf pagerankdemo (1000) ; figure (2) ; clf seashell ; shellgui ; cd ([SuiteSparse '/MATLAB_Tools/waitmex']) ; waitmex ; url = 'http://www.cise.ufl.edu/research/sparse' ; fprintf ('Click here for more details\n', url) ; hprintf ('or see \n', url) ; %--------------------------------------------------------------------------- % AMD, CAMD, UFcollection, UFget %--------------------------------------------------------------------------- % no exhaustive tests; tested via other packages catch %--------------------------------------------------------------------------- % test failure %--------------------------------------------------------------------------- cd (SuiteSparse) ; disp (lasterr) ; fprintf ('SuiteSparse test: FAILED\n') ; return end %------------------------------------------------------------------------------- % test OK %------------------------------------------------------------------------------- close (h) ; fprintf ('SuiteSparse test: OK\n') ; cd (SuiteSparse) ; SuiteSparse/Contents.m0000644001170100242450000001576710707715566013760 0ustar davisfac% Welcome to SuiteSparse : a Suite of Sparse matrix packages, containing a % collection of sparse matrix packages authored or co-authored by Tim Davis. % Only the primary MATLAB functions are listed below. % % Example: % SuiteSparse_install % compiles and installs all of SuiteSparse, and runs several demos and tests. % %------------------------------------------------------------------------------- % Ordering methods: %------------------------------------------------------------------------------- % % amd2 - approximate minimum degree ordering. % colamd2 - column approximate minimum degree ordering. % symamd2 - symmetrix approximate min degree ordering based on colamd. % camd - constrained amd. % ccolamd - constrained colamd. % csymamd - constrained symamd. % meshnd - nested dissection of regular 2D and 3D meshes % %------------------------------------------------------------------------------- % CHOLMOD: a sparse supernodal Cholesky update/downdate package: %------------------------------------------------------------------------------- % % cholmod2 - computes x=A\b when A is symmetric and positive definite. % chol2 - same as MATLAB chol(sparse(A)), just faster. % lchol - computes an LL' factorization. % ldlchol - computes an LDL' factorization. % ldlupdate - updates an LDL' factorization. % resymbol - recomputes symbolic LL or LDL' factorization. % ldlsolve - solves Ax=b using an LDL' factorization. % ldlsplit - splits LD into L and D. % metis - interface to METIS node-nested-dissection. % nesdis - interface to CHOLMOD's nested-dissection (based on METIS). % septree - prune a separator tree. % bisect - interface to METIS' node bisector. % analyze - order and analyze using CHOLMOD. % etree2 - same as MATLAB "etree", just faster and more reliable. % sparse2 - same as MATLAB "sparse", just faster. % symbfact2 - same as MATLAB "symbfact", just faster and more reliable. % sdmult - same as MATLAB S*F or S'*F (S sparse, F full), just faster. % ldl_normest - compute error in LDL' factorization. % lu_normest - compute error in LU factorization. % mread - read a sparse matrix in Matrix Market format % mwrite - write a sparse matrix in Matrix Market format % spsym - determine the symmetry of a sparse matrix % %------------------------------------------------------------------------------- % CSPARSE / CXSPARSE: a Concise Sparse matrix package: %------------------------------------------------------------------------------- % % Matrices used in CSparse must in general be either sparse and real, or % dense vectors. Ordering methods can accept any sparse matrix. CXSparse % supports complex matrices and 64-bit MATLAB; it is installed by default. % % cs_add - sparse matrix addition. % cs_amd - approximate minimum degree ordering. % cs_chol - sparse Cholesky factorization. % cs_cholsol - solve A*x=b using a sparse Cholesky factorization. % cs_counts - column counts for sparse Cholesky factor L. % cs_dmperm - maximum matching or Dulmage-Mendelsohn permutation. % cs_dmsol - x=A\b using the coarse Dulmage-Mendelsohn decomposition. % cs_dmspy - plot the Dulmage-Mendelsohn decomposition of a matrix. % cs_droptol - remove small entries from a sparse matrix. % cs_esep - find an edge separator of a symmetric matrix A % cs_etree - elimination tree of A or A'*A. % cs_gaxpy - sparse matrix times vector. % cs_lsolve - solve a sparse lower triangular system L*x=b. % cs_ltsolve - solve a sparse upper triangular system L'*x=b. % cs_lu - sparse LU factorization, with fill-reducing ordering. % cs_lusol - solve Ax=b using LU factorization. % cs_make - compiles CSparse for use in MATLAB. % cs_multiply - sparse matrix multiply. % cs_nd - generalized nested dissection ordering. % cs_nsep - find a node separator of a symmetric matrix A. % cs_permute - permute a sparse matrix. % cs_print - print the contents of a sparse matrix. % cs_qr - sparse QR factorization. % cs_qleft - apply Householder vectors on the left. % cs_qright - apply Householder vectors on the right. % cs_qrsol - solve a sparse least-squares problem. % cs_randperm - random permutation. % cs_sep - convert an edge separator into a node separator. % cs_scc - strongly-connected components of a square sparse matrix. % cs_scc2 - cs_scc, or connected components of a bipartite graph. % cs_sparse - convert a triplet form into a sparse matrix. % cs_sqr - symbolic sparse QR factorization. % cs_symperm - symmetric permutation of a symmetric matrix. % cs_transpose - transpose a sparse matrix. % cs_updown - rank-1 update/downdate of a sparse Cholesky factorization. % cs_usolve - solve a sparse upper triangular system U*x=b. % cs_utsolve - solve a sparse lower triangular system U'*x=b. % cspy - plot a sparse matrix in color. % ccspy - plot the connected components of a matrix. % %------------------------------------------------------------------------------- % LDL: Sparse LDL factorization: %------------------------------------------------------------------------------- % % ldlsparse - LDL' factorization of a real, sparse, symmetric matrix. % ldlrow - an m-file description of the algorithm used by LDL. % %------------------------------------------------------------------------------- % UMFPACK: the Unsymmetric MultiFrontal Package: %------------------------------------------------------------------------------- % % umfpack2 - computes x=A\b, x=A/b, or lu (A) for a sparse matrix A % umfpack_details - details on all the options for using umfpack in MATLAB % umfpack_report - prints optional control settings and statistics % umfpack_btf - factorize A using a block triangular form % umfpack_solve - x = A\b or x = b/A % lu_normest - estimates norm (L*U-A,1) without forming L*U-A % (duplicate of CHOLMOD/lu_normest, for completeness) % luflop - given L and U, computes # of flops required % %------------------------------------------------------------------------------- % Other packages: %------------------------------------------------------------------------------- % % UFGET MATLAB interface to the UF Sparse Matrix Collection % MATLAB_Tools various simple m-files % SSMULT sparse matrix times sparse matrix % LINFACTOR solve Ax=b using LU or CHOL % %------------------------------------------------------------------------------- % % For help on compiling SuiteSparse or the demos, testing functions, etc., % please see the help for each individual package. UFcollection and RBio % are two additional toolboxes, for managing the UF Sparse Matrix Collection. % % Copyright 2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse help SuiteSparse SuiteSparse/CXSparse/0000755001170100242450000000000010712165171013440 5ustar davisfacSuiteSparse/CXSparse/Doc/0000755001170100242450000000000010620606360014143 5ustar davisfacSuiteSparse/CXSparse/Doc/License.txt0000644001170100242450000000162210375601211016264 0ustar davisfacCXSparse: a Concise Sparse matrix package - Extended. Copyright (c) 2006, Timothy A. Davis. http://www.cise.ufl.edu/research/sparse/CSparse -------------------------------------------------------------------------------- CXSparse is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. CXSparse is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA SuiteSparse/CXSparse/Doc/ChangeLog0000644001170100242450000002072410711427621015724 0ustar davisfacNov 1, 2007, v2.2.1 * very minor change to Include/cs.h: Changed name of 2nd argument of cs_permute, to match the code. This has no affect on the code itself, since the type ("int *") is unchanged. It's just a documentation issue. * minor lint cleanup in mexFunctions Mar 31, 2007, v2.2.0 * few changes to primary Source/ files. Changes mostly affect MATLAB interface. * Source/cs_house.c: correction to comment * Souce/cs_updown.c: whitespace changed to reflect change in CXSparse, no impact at all on CSparse itself. * Doc/, Lib/ and Include/ directories created. * Source/cs.h moved to Include/cs.h, version number changed to 2.2.0. * modification to Makefiles, cs_make.m * correction to help comments in cs_dmperm.m, cs_qr.m, cs_scc2.m, cs_scc.m * if complex matrix passed to CSparse in MATLAB, error message suggests using CXSparse instead * minor performance fix to cs_sparse_mex.c * cs_randperm added to MATLAB/Makefile; already appeared in cs_make.m * minor improvements to MATLAB/ demos. Mar 1, 2007, v2.1.0 * Source/cs_add.c: added test for matrix dimensions * Source/cs_multiply.c: added test for matrix dimensions * correction to MATLAB demo3 (no error in C code version of the demo) * minor corrections to MATLAB m-file help comments. Dec 12, 2006, v2.0.7 * minor MATLAB cleanup Dec 6, 2006, v2.0.6 * Update to UFget. Now relies on the MATLAB urlwrite function instead of my own Java code. Nov 2006, v2.0.5 * Added UFgrep to UFget toolbox. * No changes to C Source code, except for version number and date. * Added two test matrices: ibm32a and ibm32b. ibm32a is the Harwell/ Boeing matrix ibm32, but with the last column removed. ibm32b is the transpose of ibm32a. With optimization enabled (-O), 2 lines in cs_maxtrans.c are not tested; these matrices correct that problem. * Fixed UFget. Earlier version could not download matrices larger than 32MB. * Modified UFget/UFweb, to reflect changes in the UF Sparse Matrix Collection. * Added ccspy.m and cs_scc2.m MATLAB functions * Added examples to help info in each *.m MATLAB file * modified cs_dmspy to speed up the plotting of large matrices with many singletons * minor change to cspy: now draws a box around the matrix. * minor changes to MATLAB demos and tests. Oct 13, 2006, v2.0.4 * minor modification to cs_updown.c. "n" was incorrectly declared "double". It should be "int". This was safe, just a little confusing (n was only used in an argument to cs_malloc, and is thus typecast). Sept 28, 2006, v2.0.3 * minor modifications to MATLAB interface, to allow CSparse to be used in MATLAB 6.5. * added examples to m-files, other minor m-file cleanup. * bug fix to cspy, to handle NaN's properly. Aug 23, 2006: v2.0.2 * change to cs_updown mexFunction, to handle multiple rank updates * symbolic links removed from Tcov/ directory in the distribution. They are now created by Tcov/Makefile as needed. This makes the zip files cleaner. Tcov/*test.c test files renamed. July 19, 2006: * minor fix to cs_must_compile.m and cs_make.m, to allow CSparse to be compiled in MATLAB 6.5 with cs_make. * minor fix to cspy for complex matrices (imaginary part was ignored). * no change to version number or date, since there are no changes that affect the appearance of CSparse in the book ("Direct Methods for Sparse Linear Systems", SIAM, 2006). June 24, 2006: * minor typos in comments corrected. No change in code itself, and no change in version number or date. May 27, 2006, v2.0.1: (this version is printed in the book) * minor bug fix. cs_util.c modified, so that cs_sprealloc (T,0) works properly for a triplet matrix T (setting T->nzmax equal to T->nz). The line in v2.0.0: nzmax = (nzmax <= 0) ? (A->p [A->n]) : nzmax ; changes to the following in v2.0.1: if (nzmax <= 0) nzmax = (CS_CSC (A)) ? (A->p [A->n]) : A->nz ; * minor typographical changes arising from the editting of the book. Apr 12, 2006, v2.0.0: * random permutation option added to cs_maxtrans and cs_dmperm, to help avoid rare cases where the O(|A|n) time complexity is reached in practice (GHS_indef/boyd2 in the UF sparse matrix collection, for example). New cs_randperm function added. Apr 10, 2006: * stylistic changes for the book (except for the bug fix): * "int order" parameter of cs_amd, cs_lusol, cs_cholsol, cs_qrsol, cs_sqr, cs_schol changed. Now 0 means no ordering, 1 is A+A', 2 is S*S', and 3 is A*A'. In v1.2 and earlier, "order" took on a value ranging from -1 to 2. "int n" parameter rearranged for cs_ipvec, cs_pvec, cs_post (int n moved to the end). cs_triplet renamed cs_compress. To ensure that these changes are propagated into user code that calls CSparse, the "order" parameter has been placed as the first parameter in all these routines. Your compiler will complain (gcc will halt) if you upgrade from v1.2 to v2.0 without changing your code. This is much better than a silent error in which you get the wrong ordering by mistake (with a huge penalty in run-time performance and no compiler warnings). New syntax (v2.0 and later): ---------------------------- order = 0: natural ordering order = 1: amd (A+A') order = 2: amd (S'*S), where S=A except dense rows dropped order = 3: amd (A'*A) int cs_cholsol (int order, const cs *A, double *b) ; int cs_lusol (int order, const cs *A, double *b, double tol) ; int cs_qrsol (int order, const cs *A, double *b) ; int *cs_amd (int order, const cs *A) ; css *cs_schol (int order, const cs *A) ; css *cs_sqr (int order, const cs *A, int qr) ; int *cs_post (const int *parent, int n) ; int cs_ipvec (const int *p, const double *b, double *x, int n) ; int cs_pvec (const int *p, const double *b, double *x, int n) ; cs *cs_compress (const cs *T) ; Old syntax (v1.2 and earlier): ------------------------------ order = -1: natural ordering order = 0: amd (A+A') order = 1: amd (S'*S), where S=A except dense rows dropped order = 2: amd (A'*A) int cs_cholsol (const cs *A, double *b, int order) ; int cs_lusol (const cs *A, double *b, int order, double tol) ; int cs_qrsol (const cs *A, double *b, int order) ; int *cs_amd (const cs *A, int order) ; css *cs_schol (const cs *A, int order) ; css *cs_sqr (const cs *A, int order, int qr) ; int *cs_post (int n, const int *parent) ; int cs_ipvec (int n, const int *p, const double *b, double *x) ; int cs_pvec (int n, const int *p, const double *b, double *x) ; cs *cs_triplet (const cs *T) ; * CS_OVERFLOW macro removed (removed from cs_malloc.c; not needed). * S->leftmost added to css (it was tacked onto S->pinv before). * P,Q,R,S components of csd struct changed to p,q,r,s. * Pinv and Q components of css struct changed to pinv and q. * CS_CSC and CS_TRIPLET macros added, to clarify which CSparse functions accept cs matrices in compressed column form, triplet form, or both. * check for negative row/column indices added to cs_entry. * cs_ereach and cs_leaf functions added. * call to cs_sprealloc added to cs_fkeep. * bug fixes in cs_counts and cs_amd (memory leak under rare out-of-memory conditions). Mar 15, 2006: * cs_scc modified so that the row and columns of each component are put in their natural order. cs_dmperm modified so that columns of each block (instead of rows) are placed in their natural order. * cs_splsolve renamed cs_spsolve, generalized to handle both Lx=b and Ux=b, and non-unit diagonal, and placed in its own file (cs_spsolve.c; it was a static function in cs_lu.c). cs_lsolve_mex.c and cs_splsolve_mex.c merged (the latter was removed). cs_spsolve.c file added * cs_dmspy changed, so that block borders line up better with the matrix. Mar 6, 2006: * Makefile modified so that the Tcov tests (which may not be portable) are not compiled and run by the default "make" in the CSparse directory. To compile everything, including the Tcov tests, use "make all". Trivial change to cs.h. Feb 27, 2006: * cs_reach, cs_dfs, cs_splsolve, cs_lu, and cs_scc changed to remove O(n) initialized workspace. * cs_reach and cs_splsolve now user-callable (were static in cs_lu.c). Feb 20, 2006: * various changes to simplify the construction of CXSparse Feb 7, 2006: * changed prototypes, adding "const" where appropriate. SuiteSparse/CXSparse/Doc/lesser.txt0000644001170100242450000006350010346315140016203 0ustar davisfac GNU LESSER GENERAL PUBLIC LICENSE Version 2.1, February 1999 Copyright (C) 1991, 1999 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. [This is the first released version of the Lesser GPL. It also counts as the successor of the GNU Library Public License, version 2, hence the version number 2.1.] Preamble The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public Licenses are intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users. 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SuiteSparse/CXSparse/Lib/0000755001170100242450000000000010712165433014147 5ustar davisfacSuiteSparse/CXSparse/Lib/Makefile0000644001170100242450000001062010617170455015612 0ustar davisfac# Modify the "-O" optimization option for best performance (-O3 on Linux): CC = cc CFLAGS = -O I = -I../../UFconfig -I../Include AR = ar cr RANLIB = ranlib all: libcxsparse.a CS_SOURCE = cs_add.c cs_amd.c cs_chol.c cs_cholsol.c cs_counts.c cs_cumsum.c \ cs_droptol.c cs_dropzeros.c cs_dupl.c cs_entry.c \ cs_etree.c cs_fkeep.c cs_gaxpy.c cs_happly.c cs_house.c cs_ipvec.c \ cs_lsolve.c cs_ltsolve.c cs_lu.c cs_lusol.c cs_util.c cs_multiply.c \ cs_permute.c cs_pinv.c cs_post.c cs_pvec.c cs_qr.c cs_qrsol.c \ cs_scatter.c cs_schol.c cs_sqr.c cs_symperm.c cs_tdfs.c cs_malloc.c \ cs_transpose.c cs_compress.c cs_usolve.c cs_utsolve.c cs_scc.c \ cs_maxtrans.c cs_dmperm.c cs_updown.c cs_print.c cs_norm.c cs_load.c \ cs_dfs.c cs_reach.c cs_spsolve.c cs_leaf.c cs_ereach.c cs_randperm.c CS_DI_OBJ = cs_add_di.o cs_amd_di.o cs_chol_di.o cs_cholsol_di.o cs_counts_di.o \ cs_cumsum_di.o cs_droptol_di.o cs_dropzeros_di.o cs_dupl_di.o \ cs_entry_di.o cs_etree_di.o cs_fkeep_di.o cs_gaxpy_di.o cs_happly_di.o \ cs_house_di.o cs_ipvec_di.o cs_lsolve_di.o cs_ltsolve_di.o cs_lu_di.o \ cs_lusol_di.o cs_util_di.o cs_multiply_di.o cs_permute_di.o cs_pinv_di.o \ cs_post_di.o cs_pvec_di.o cs_qr_di.o cs_qrsol_di.o cs_scatter_di.o \ cs_schol_di.o cs_sqr_di.o cs_symperm_di.o cs_tdfs_di.o cs_malloc_di.o \ cs_transpose_di.o cs_compress_di.o cs_usolve_di.o cs_utsolve_di.o \ cs_scc_di.o cs_maxtrans_di.o cs_dmperm_di.o cs_updown_di.o cs_print_di.o \ cs_norm_di.o cs_load_di.o cs_dfs_di.o cs_reach_di.o cs_spsolve_di.o \ cs_leaf_di.o cs_ereach_di.o cs_randperm_di.o CS_DL_OBJ = cs_add_dl.o cs_amd_dl.o cs_chol_dl.o cs_cholsol_dl.o cs_counts_dl.o \ cs_cumsum_dl.o cs_droptol_dl.o cs_dropzeros_dl.o cs_dupl_dl.o \ cs_entry_dl.o cs_etree_dl.o cs_fkeep_dl.o cs_gaxpy_dl.o cs_happly_dl.o \ cs_house_dl.o cs_ipvec_dl.o cs_lsolve_dl.o cs_ltsolve_dl.o cs_lu_dl.o \ cs_lusol_dl.o cs_util_dl.o cs_multiply_dl.o cs_permute_dl.o cs_pinv_dl.o \ cs_post_dl.o cs_pvec_dl.o cs_qr_dl.o cs_qrsol_dl.o cs_scatter_dl.o \ cs_schol_dl.o cs_sqr_dl.o cs_symperm_dl.o cs_tdfs_dl.o cs_malloc_dl.o \ cs_transpose_dl.o cs_compress_dl.o cs_usolve_dl.o cs_utsolve_dl.o \ cs_scc_dl.o cs_maxtrans_dl.o cs_dmperm_dl.o cs_updown_dl.o cs_print_dl.o \ cs_norm_dl.o cs_load_dl.o cs_dfs_dl.o cs_reach_dl.o cs_spsolve_dl.o \ cs_leaf_dl.o cs_ereach_dl.o cs_randperm_dl.o CS_CI_OBJ = cs_add_ci.o cs_amd_ci.o cs_chol_ci.o cs_cholsol_ci.o cs_counts_ci.o \ cs_cumsum_ci.o cs_droptol_ci.o cs_dropzeros_ci.o cs_dupl_ci.o \ cs_entry_ci.o cs_etree_ci.o cs_fkeep_ci.o cs_gaxpy_ci.o cs_happly_ci.o \ cs_house_ci.o cs_ipvec_ci.o cs_lsolve_ci.o cs_ltsolve_ci.o cs_lu_ci.o \ cs_lusol_ci.o cs_util_ci.o cs_multiply_ci.o cs_permute_ci.o cs_pinv_ci.o \ cs_post_ci.o cs_pvec_ci.o cs_qr_ci.o cs_qrsol_ci.o cs_scatter_ci.o \ cs_schol_ci.o cs_sqr_ci.o cs_symperm_ci.o cs_tdfs_ci.o cs_malloc_ci.o \ cs_transpose_ci.o cs_compress_ci.o cs_usolve_ci.o cs_utsolve_ci.o \ cs_scc_ci.o cs_maxtrans_ci.o cs_dmperm_ci.o cs_updown_ci.o cs_print_ci.o \ cs_norm_ci.o cs_load_ci.o cs_dfs_ci.o cs_reach_ci.o cs_spsolve_ci.o \ cs_leaf_ci.o cs_ereach_ci.o cs_randperm_ci.o CS_CL_OBJ = cs_add_cl.o cs_amd_cl.o cs_chol_cl.o cs_cholsol_cl.o cs_counts_cl.o \ cs_cumsum_cl.o cs_droptol_cl.o cs_dropzeros_cl.o cs_dupl_cl.o \ cs_entry_cl.o cs_etree_cl.o cs_fkeep_cl.o cs_gaxpy_cl.o cs_happly_cl.o \ cs_house_cl.o cs_ipvec_cl.o cs_lsolve_cl.o cs_ltsolve_cl.o cs_lu_cl.o \ cs_lusol_cl.o cs_util_cl.o cs_multiply_cl.o cs_permute_cl.o cs_pinv_cl.o \ cs_post_cl.o cs_pvec_cl.o cs_qr_cl.o cs_qrsol_cl.o cs_scatter_cl.o \ cs_schol_cl.o cs_sqr_cl.o cs_symperm_cl.o cs_tdfs_cl.o cs_malloc_cl.o \ cs_transpose_cl.o cs_compress_cl.o cs_usolve_cl.o cs_utsolve_cl.o \ cs_scc_cl.o cs_maxtrans_cl.o cs_dmperm_cl.o cs_updown_cl.o cs_print_cl.o \ cs_norm_cl.o cs_load_cl.o cs_dfs_cl.o cs_reach_cl.o cs_spsolve_cl.o \ cs_leaf_cl.o cs_ereach_cl.o cs_randperm_cl.o CS = cs_convert.o $(CS_DI_OBJ) $(CS_DL_OBJ) $(CS_CI_OBJ) $(CS_CL_OBJ) $(CS): ../Include/cs.h Makefile cs_convert.o: ../Source/cs_convert.c $(CC) $(CFLAGS) $(I) -c $< -o $@ %_di.o : ../Source/%.c $(CC) $(CFLAGS) $(I) -c $< -o $@ %_dl.o : ../Source/%.c $(CC) $(CFLAGS) $(I) -DCS_LONG -c $< -o $@ %_ci.o : ../Source/%.c $(CC) $(CFLAGS) $(I) -DCS_COMPLEX -c $< -o $@ %_cl.o : ../Source/%.c $(CC) $(CFLAGS) $(I) -DCS_LONG -DCS_COMPLEX -c $< -o $@ libcxsparse.a: $(CS) $(AR) libcxsparse.a $(CS) $(RANLIB) libcxsparse.a clean: rm -f *.o purge: distclean distclean: clean rm -f *.a SuiteSparse/CXSparse/Demo/0000755001170100242450000000000010712165433014325 5ustar davisfacSuiteSparse/CXSparse/Demo/Makefile0000644001170100242450000001176510620626640015777 0ustar davisfacCC = cc CFLAGS = -O I = -I../Include -I../../UFconfig CS = ../Lib/libcxsparse.a all: $(CS) cs_demo1 cs_demo2 cs_demo3 \ cs_di_demo1 cs_di_demo2 cs_di_demo3 \ cs_dl_demo1 cs_dl_demo2 cs_dl_demo3 \ cs_ci_demo1 cs_ci_demo2 cs_ci_demo3 \ cs_cl_demo1 cs_cl_demo2 cs_cl_demo3 \ tests cs_idemo tests: test_convert test test_di test_dl test_ci test_cl test: cs_demo1 cs_demo2 cs_demo3 - ./cs_demo1 < ../Matrix/t1 - ./cs_demo2 < ../Matrix/t1 - ./cs_demo2 < ../Matrix/fs_183_1 - ./cs_demo2 < ../Matrix/west0067 - ./cs_demo2 < ../Matrix/lp_afiro - ./cs_demo2 < ../Matrix/ash219 - ./cs_demo2 < ../Matrix/mbeacxc - ./cs_demo2 < ../Matrix/bcsstk01 - ./cs_demo3 < ../Matrix/bcsstk01 - ./cs_demo2 < ../Matrix/bcsstk16 - ./cs_demo3 < ../Matrix/bcsstk16 test_di: cs_di_demo1 cs_di_demo2 cs_di_demo3 - ./cs_di_demo1 < ../Matrix/t1 - ./cs_di_demo2 < ../Matrix/t1 - ./cs_di_demo2 < ../Matrix/fs_183_1 - ./cs_di_demo2 < ../Matrix/west0067 - ./cs_di_demo2 < ../Matrix/lp_afiro - ./cs_di_demo2 < ../Matrix/ash219 - ./cs_di_demo2 < ../Matrix/mbeacxc - ./cs_di_demo2 < ../Matrix/bcsstk01 - ./cs_di_demo3 < ../Matrix/bcsstk01 - ./cs_di_demo2 < ../Matrix/bcsstk16 - ./cs_di_demo3 < ../Matrix/bcsstk16 test_dl: cs_dl_demo1 cs_dl_demo2 cs_dl_demo3 - ./cs_dl_demo1 < ../Matrix/t1 - ./cs_dl_demo2 < ../Matrix/t1 - ./cs_dl_demo2 < ../Matrix/fs_183_1 - ./cs_dl_demo2 < ../Matrix/west0067 - ./cs_dl_demo2 < ../Matrix/lp_afiro - ./cs_dl_demo2 < ../Matrix/ash219 - ./cs_dl_demo2 < ../Matrix/mbeacxc - ./cs_dl_demo2 < ../Matrix/bcsstk01 - ./cs_dl_demo3 < ../Matrix/bcsstk01 - ./cs_dl_demo2 < ../Matrix/bcsstk16 - ./cs_dl_demo3 < ../Matrix/bcsstk16 test_ci: cs_ci_demo1 cs_ci_demo2 cs_ci_demo3 - ./cs_ci_demo1 < ../Matrix/t2 - ./cs_ci_demo2 < ../Matrix/t2 - ./cs_ci_demo2 < ../Matrix/t3 - ./cs_ci_demo2 < ../Matrix/t4 - ./cs_ci_demo2 < ../Matrix/c_west0067 - ./cs_ci_demo2 < ../Matrix/c_mbeacxc - ./cs_ci_demo2 < ../Matrix/young1c - ./cs_ci_demo2 < ../Matrix/qc324 - ./cs_ci_demo2 < ../Matrix/neumann - ./cs_ci_demo2 < ../Matrix/c4 - ./cs_ci_demo3 < ../Matrix/c4 - ./cs_ci_demo2 < ../Matrix/mhd1280b - ./cs_ci_demo3 < ../Matrix/mhd1280b test_cl: cs_cl_demo1 cs_cl_demo2 cs_cl_demo3 - ./cs_cl_demo1 < ../Matrix/t2 - ./cs_cl_demo2 < ../Matrix/t2 - ./cs_cl_demo2 < ../Matrix/t3 - ./cs_cl_demo2 < ../Matrix/t4 - ./cs_cl_demo2 < ../Matrix/c_west0067 - ./cs_cl_demo2 < ../Matrix/c_mbeacxc - ./cs_cl_demo2 < ../Matrix/young1c - ./cs_cl_demo2 < ../Matrix/qc324 - ./cs_cl_demo2 < ../Matrix/neumann - ./cs_cl_demo2 < ../Matrix/c4 - ./cs_cl_demo3 < ../Matrix/c4 - ./cs_cl_demo2 < ../Matrix/mhd1280b - ./cs_cl_demo3 < ../Matrix/mhd1280b test_convert: cs_idemo cs_ldemo - ./cs_idemo < ../Matrix/t2 - ./cs_ldemo < ../Matrix/t2 $(CS): ( cd ../Lib ; $(MAKE) ) cs_demo1: $(CS) cs_demo1.c Makefile $(CS) $(CC) $(I) -o cs_demo1 cs_demo1.c $(CS) -lm cs_demo2: $(CS) cs_demo2.c cs_demo.c cs_demo.h Makefile $(CS) $(CC) $(I) -o cs_demo2 cs_demo2.c cs_demo.c $(CS) -lm cs_demo3: $(CS) cs_demo3.c cs_demo.c cs_demo.h Makefile $(CS) $(CC) $(I) -o cs_demo3 cs_demo3.c cs_demo.c $(CS) -lm cs_di_demo1: $(CS) cs_di_demo1.c Makefile $(CS) $(CC) $(I) -o cs_di_demo1 cs_di_demo1.c $(CS) -lm cs_di_demo2: $(CS) cs_di_demo2.c cs_di_demo.c cs_di_demo.h Makefile $(CS) $(CC) $(I) -o cs_di_demo2 cs_di_demo2.c cs_di_demo.c $(CS) -lm cs_di_demo3: $(CS) cs_di_demo3.c cs_di_demo.c cs_di_demo.h Makefile $(CS) $(CC) $(I) -o cs_di_demo3 cs_di_demo3.c cs_di_demo.c $(CS) -lm cs_ci_demo1: $(CS) cs_ci_demo1.c Makefile $(CS) $(CC) $(I) -o cs_ci_demo1 cs_ci_demo1.c $(CS) -lm cs_ci_demo2: $(CS) cs_ci_demo2.c cs_ci_demo.c cs_ci_demo.h Makefile $(CS) $(CC) $(I) -o cs_ci_demo2 cs_ci_demo2.c cs_ci_demo.c $(CS) -lm cs_ci_demo3: $(CS) cs_ci_demo3.c cs_ci_demo.c cs_ci_demo.h Makefile $(CS) $(CC) $(I) -o cs_ci_demo3 cs_ci_demo3.c cs_ci_demo.c $(CS) -lm cs_dl_demo1: $(CS) cs_dl_demo1.c Makefile $(CS) $(CC) $(I) -o cs_dl_demo1 cs_dl_demo1.c $(CS) -lm cs_dl_demo2: $(CS) cs_dl_demo2.c cs_dl_demo.c cs_dl_demo.h Makefile $(CS) $(CC) $(I) -o cs_dl_demo2 cs_dl_demo2.c cs_dl_demo.c $(CS) -lm cs_dl_demo3: $(CS) cs_dl_demo3.c cs_dl_demo.c cs_dl_demo.h Makefile $(CS) $(CC) $(I) -o cs_dl_demo3 cs_dl_demo3.c cs_dl_demo.c $(CS) -lm cs_cl_demo1: $(CS) cs_cl_demo1.c Makefile $(CS) $(CC) $(I) -o cs_cl_demo1 cs_cl_demo1.c $(CS) -lm cs_cl_demo2: $(CS) cs_cl_demo2.c cs_cl_demo.c cs_cl_demo.h Makefile $(CS) $(CC) $(I) -o cs_cl_demo2 cs_cl_demo2.c cs_cl_demo.c $(CS) -lm cs_cl_demo3: $(CS) cs_cl_demo3.c cs_cl_demo.c cs_cl_demo.h Makefile $(CS) $(CC) $(I) -o cs_cl_demo3 cs_cl_demo3.c cs_cl_demo.c $(CS) -lm cs_idemo: $(CS) cs_idemo.c Makefile $(CS) $(CC) $(I) -o cs_idemo cs_idemo.c $(CS) -lm cs_ldemo: $(CS) cs_ldemo.c Makefile $(CS) $(CC) $(I) -DCS_LONG -o cs_ldemo cs_ldemo.c $(CS) -lm clean: rm -f *.o purge: distclean distclean: clean rm -f cs_demo1 cs_demo2 cs_demo3 *.a rm -f cs_di_demo1 cs_di_demo2 cs_di_demo3 rm -f cs_dl_demo1 cs_dl_demo2 cs_dl_demo3 rm -f cs_ci_demo1 cs_ci_demo2 cs_ci_demo3 rm -f cs_cl_demo1 cs_cl_demo2 cs_cl_demo3 rm -f cs_idemo cs_ldemo SuiteSparse/CXSparse/Demo/cs_demo1.c0000644001170100242450000000201110436111360016146 0ustar davisfac#include "cs.h" int main (void) { cs *T, *A, *Eye, *AT, *C, *D ; int i, m ; T = cs_load (stdin) ; /* load triplet matrix T from stdin */ printf ("T:\n") ; cs_print (T, 0) ; /* print T */ A = cs_compress (T) ; /* A = compressed-column form of T */ printf ("A:\n") ; cs_print (A, 0) ; /* print A */ cs_spfree (T) ; /* clear T */ AT = cs_transpose (A, 1) ; /* AT = A' */ printf ("AT:\n") ; cs_print (AT, 0) ; /* print AT */ m = A ? A->m : 0 ; /* m = # of rows of A */ T = cs_spalloc (m, m, m, 1, 1) ; /* create triplet identity matrix */ for (i = 0 ; i < m ; i++) cs_entry (T, i, i, 1) ; Eye = cs_compress (T) ; /* Eye = speye (m) */ cs_spfree (T) ; C = cs_multiply (A, AT) ; /* C = A*A' */ D = cs_add (C, Eye, 1, cs_norm (C)) ; /* D = C + Eye*norm (C,1) */ printf ("D:\n") ; cs_print (D, 0) ; /* print D */ cs_spfree (A) ; /* clear A AT C D Eye */ cs_spfree (AT) ; cs_spfree (C) ; cs_spfree (D) ; cs_spfree (Eye) ; return (0) ; } SuiteSparse/CXSparse/Demo/cs_demo2.c0000644001170100242450000000032010326434515016160 0ustar davisfac#include "cs_demo.h" /* cs_demo2: read a matrix and solve a linear system */ int main (void) { problem *Prob = get_problem (stdin, 1e-14) ; demo2 (Prob) ; free_problem (Prob) ; return (0) ; } SuiteSparse/CXSparse/Demo/cs_demo3.c0000644001170100242450000000032410326434521016162 0ustar davisfac#include "cs_demo.h" /* cs_demo3: read a matrix and test Cholesky update/downdate */ int main (void) { problem *Prob = get_problem (stdin, 0) ; demo3 (Prob) ; free_problem (Prob) ; return (0) ; } SuiteSparse/CXSparse/Demo/cs_demo.out0000644001170100242450000010774710712165431016505 0ustar davisfacmake[1]: Entering directory `/amd/netapp3/vol/research0a/research18/sparse2/SuiteSparse/CXSparse/Demo' ./cs_idemo < ../Matrix/t2 --- cs_idemo, size of CS_INT: 4 T: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 triplet: 4-by-4, nzmax: 16 nnz: 10 2 2 : (3, 3.14159) 1 0 : (3.1, 42) 3 3 : (1, 7) 0 2 : (3.2, 0.1) 1 1 : (2.9, 1.3) 3 0 : (3.5, 0) 3 1 : (0.4, 2.71828) 1 3 : (0.9, 99) 0 0 : (4.5, 6) 2 1 : (1.7, 1) Treal: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 triplet: 4-by-4, nzmax: 16 nnz: 10 2 2 : 3 1 0 : 3.1 3 3 : 1 0 2 : 3.2 1 1 : 2.9 3 0 : 3.5 3 1 : 0.4 1 3 : 0.9 0 0 : 4.5 2 1 : 1.7 Timag: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 triplet: 4-by-4, nzmax: 16 nnz: 10 2 2 : 3.14159 1 0 : 42 3 3 : 7 0 2 : 0.1 1 1 : 1.3 3 0 : 0 3 1 : 2.71828 1 3 : 99 0 0 : 6 2 1 : 1 A: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 106.075 col 0 : locations 0 to 2 1 : (3.1, 42) 3 : (3.5, 0) 0 : (4.5, 6) col 1 : locations 3 to 5 1 : (2.9, 1.3) 3 : (0.4, 2.71828) 2 : (1.7, 1) col 2 : locations 6 to 7 2 : (3, 3.14159) 0 : (3.2, 0.1) col 3 : locations 8 to 9 3 : (1, 7) 1 : (0.9, 99) C1 = real(A): CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 11.1 col 0 : locations 0 to 2 1 : 3.1 3 : 3.5 0 : 4.5 col 1 : locations 3 to 5 1 : 2.9 3 : 0.4 2 : 1.7 col 2 : locations 6 to 7 2 : 3 0 : 3.2 col 3 : locations 8 to 9 3 : 1 1 : 0.9 C2 = imag(A): CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 106 col 0 : locations 0 to 2 1 : 42 3 : 0 0 : 6 col 1 : locations 3 to 5 1 : 1.3 3 : 2.71828 2 : 1 col 2 : locations 6 to 7 2 : 3.14159 0 : 0.1 col 3 : locations 8 to 9 3 : 7 1 : 99 A1: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 11.1 col 0 : locations 0 to 2 1 : (3.1, 0) 3 : (3.5, 0) 0 : (4.5, 0) col 1 : locations 3 to 5 1 : (2.9, 0) 3 : (0.4, 0) 2 : (1.7, 0) col 2 : locations 6 to 7 2 : (3, 0) 0 : (3.2, 0) col 3 : locations 8 to 9 3 : (1, 0) 1 : (0.9, 0) A2: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 106 col 0 : locations 0 to 2 1 : (0, 42) 3 : (0, 0) 0 : (0, 6) col 1 : locations 3 to 5 1 : (0, 1.3) 3 : (0, 2.71828) 2 : (0, 1) col 2 : locations 6 to 7 2 : (0, 3.14159) 0 : (0, 0.1) col 3 : locations 8 to 9 3 : (0, 7) 1 : (0, 99) B = conj(A): CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 106.075 col 0 : locations 0 to 2 1 : (3.1, -42) 3 : (3.5, 0) 0 : (4.5, -6) col 1 : locations 3 to 5 1 : (2.9, -1.3) 3 : (0.4, -2.71828) 2 : (1.7, -1) col 2 : locations 6 to 7 2 : (3, -3.14159) 0 : (3.2, -0.1) col 3 : locations 8 to 9 3 : (1, -7) 1 : (0.9, -99) ./cs_ldemo < ../Matrix/t2 --- cs_ldemo, size of CS_INT: 8 T: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 triplet: 4-by-4, nzmax: 16 nnz: 10 2 2 : (3, 3.14159) 1 0 : (3.1, 42) 3 3 : (1, 7) 0 2 : (3.2, 0.1) 1 1 : (2.9, 1.3) 3 0 : (3.5, 0) 3 1 : (0.4, 2.71828) 1 3 : (0.9, 99) 0 0 : (4.5, 6) 2 1 : (1.7, 1) Treal: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 triplet: 4-by-4, nzmax: 16 nnz: 10 2 2 : 3 1 0 : 3.1 3 3 : 1 0 2 : 3.2 1 1 : 2.9 3 0 : 3.5 3 1 : 0.4 1 3 : 0.9 0 0 : 4.5 2 1 : 1.7 Timag: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 triplet: 4-by-4, nzmax: 16 nnz: 10 2 2 : 3.14159 1 0 : 42 3 3 : 7 0 2 : 0.1 1 1 : 1.3 3 0 : 0 3 1 : 2.71828 1 3 : 99 0 0 : 6 2 1 : 1 A: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 106.075 col 0 : locations 0 to 2 1 : (3.1, 42) 3 : (3.5, 0) 0 : (4.5, 6) col 1 : locations 3 to 5 1 : (2.9, 1.3) 3 : (0.4, 2.71828) 2 : (1.7, 1) col 2 : locations 6 to 7 2 : (3, 3.14159) 0 : (3.2, 0.1) col 3 : locations 8 to 9 3 : (1, 7) 1 : (0.9, 99) C1 = real(A): CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 11.1 col 0 : locations 0 to 2 1 : 3.1 3 : 3.5 0 : 4.5 col 1 : locations 3 to 5 1 : 2.9 3 : 0.4 2 : 1.7 col 2 : locations 6 to 7 2 : 3 0 : 3.2 col 3 : locations 8 to 9 3 : 1 1 : 0.9 C2 = imag(A): CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 106 col 0 : locations 0 to 2 1 : 42 3 : 0 0 : 6 col 1 : locations 3 to 5 1 : 1.3 3 : 2.71828 2 : 1 col 2 : locations 6 to 7 2 : 3.14159 0 : 0.1 col 3 : locations 8 to 9 3 : 7 1 : 99 A1: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 11.1 col 0 : locations 0 to 2 1 : (3.1, 0) 3 : (3.5, 0) 0 : (4.5, 0) col 1 : locations 3 to 5 1 : (2.9, 0) 3 : (0.4, 0) 2 : (1.7, 0) col 2 : locations 6 to 7 2 : (3, 0) 0 : (3.2, 0) col 3 : locations 8 to 9 3 : (1, 0) 1 : (0.9, 0) A2: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 106 col 0 : locations 0 to 2 1 : (0, 42) 3 : (0, 0) 0 : (0, 6) col 1 : locations 3 to 5 1 : (0, 1.3) 3 : (0, 2.71828) 2 : (0, 1) col 2 : locations 6 to 7 2 : (0, 3.14159) 0 : (0, 0.1) col 3 : locations 8 to 9 3 : (0, 7) 1 : (0, 99) B = conj(A): CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 106.075 col 0 : locations 0 to 2 1 : (3.1, -42) 3 : (3.5, 0) 0 : (4.5, -6) col 1 : locations 3 to 5 1 : (2.9, -1.3) 3 : (0.4, -2.71828) 2 : (1.7, -1) col 2 : locations 6 to 7 2 : (3, -3.14159) 0 : (3.2, -0.1) col 3 : locations 8 to 9 3 : (1, -7) 1 : (0.9, -99) ./cs_demo1 < ../Matrix/t1 T: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 triplet: 4-by-4, nzmax: 16 nnz: 10 2 2 : 3 1 0 : 3.1 3 3 : 1 0 2 : 3.2 1 1 : 2.9 3 0 : 3.5 3 1 : 0.4 1 3 : 0.9 0 0 : 4.5 2 1 : 1.7 A: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 11.1 col 0 : locations 0 to 2 1 : 3.1 3 : 3.5 0 : 4.5 col 1 : locations 3 to 5 1 : 2.9 3 : 0.4 2 : 1.7 col 2 : locations 6 to 7 2 : 3 0 : 3.2 col 3 : locations 8 to 9 3 : 1 1 : 0.9 AT: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 7.7 col 0 : locations 0 to 1 0 : 4.5 2 : 3.2 col 1 : locations 2 to 4 0 : 3.1 1 : 2.9 3 : 0.9 col 2 : locations 5 to 6 1 : 1.7 2 : 3 col 3 : locations 7 to 9 0 : 3.5 1 : 0.4 3 : 1 D: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 16 nnz: 16, 1-norm: 139.58 col 0 : locations 0 to 3 1 : 13.95 3 : 15.75 0 : 100.28 2 : 9.6 col 1 : locations 4 to 7 1 : 88.62 3 : 12.91 0 : 13.95 2 : 4.93 col 2 : locations 8 to 11 1 : 4.93 3 : 0.68 2 : 81.68 0 : 9.6 col 3 : locations 12 to 15 1 : 12.91 3 : 83.2 0 : 15.75 2 : 0.68 ./cs_demo2 < ../Matrix/t1 --- Matrix: 4-by-4, nnz: 10 (sym: 0: nnz 0), norm: 1.11e+01 blocks: 1 singletons: 0 structural rank: 4 QR natural time: 0.00 resid: 3.06e-17 QR amd(A'*A) time: 0.00 resid: 2.30e-17 LU natural time: 0.00 resid: 1.53e-17 LU amd(A+A') time: 0.00 resid: 1.53e-17 LU amd(S'*S) time: 0.00 resid: 0.00e+00 LU amd(A'*A) time: 0.00 resid: 1.53e-17 ./cs_demo2 < ../Matrix/fs_183_1 --- Matrix: 183-by-183, nnz: 988 (sym: 0: nnz 0), norm: 1.70e+09 zero entries dropped: 71 tiny entries dropped: 10 blocks: 38 singletons: 37 structural rank: 183 QR natural time: 0.01 resid: 1.42e-27 QR amd(A'*A) time: 0.00 resid: 3.35e-28 LU natural time: 0.01 resid: 6.20e-28 LU amd(A+A') time: 0.00 resid: 1.55e-27 LU amd(S'*S) time: 0.00 resid: 6.98e-28 LU amd(A'*A) time: 0.00 resid: 6.98e-28 ./cs_demo2 < ../Matrix/west0067 --- Matrix: 67-by-67, nnz: 294 (sym: 0: nnz 0), norm: 6.14e+00 blocks: 2 singletons: 1 structural rank: 67 QR natural time: 0.00 resid: 5.19e-17 QR amd(A'*A) time: 0.00 resid: 3.25e-17 LU natural time: 0.00 resid: 3.89e-17 LU amd(A+A') time: 0.00 resid: 2.27e-17 LU amd(S'*S) time: 0.00 resid: 1.95e-17 LU amd(A'*A) time: 0.00 resid: 2.60e-17 ./cs_demo2 < ../Matrix/lp_afiro --- Matrix: 27-by-51, nnz: 102 (sym: 0: nnz 0), norm: 3.43e+00 blocks: 1 singletons: 0 structural rank: 27 QR natural time: 0.00 resid: 3.85e-16 QR amd(A'*A) time: 0.00 resid: 1.50e-16 ./cs_demo2 < ../Matrix/ash219 --- Matrix: 219-by-85, nnz: 438 (sym: 0: nnz 0), norm: 9.00e+00 blocks: 1 singletons: 0 structural rank: 85 QR natural time: 0.00 resid: 1.61e-02 QR amd(A'*A) time: 0.00 resid: 1.61e-02 ./cs_demo2 < ../Matrix/mbeacxc --- Matrix: 492-by-490, nnz: 49920 (sym: 0: nnz 0), norm: 9.29e-01 blocks: 10 singletons: 8 structural rank: 448 QR natural time: 0.13 resid: nan QR amd(A'*A) time: 0.19 resid: nan ./cs_demo2 < ../Matrix/bcsstk01 --- Matrix: 48-by-48, nnz: 224 (sym: -1: nnz 400), norm: 3.57e+09 blocks: 1 singletons: 0 structural rank: 48 QR natural time: 0.00 resid: 3.65e-19 QR amd(A'*A) time: 0.00 resid: 4.02e-19 LU natural time: 0.00 resid: 2.17e-19 LU amd(A+A') time: 0.00 resid: 1.87e-19 LU amd(S'*S) time: 0.00 resid: 2.38e-19 LU amd(A'*A) time: 0.00 resid: 2.38e-19 Chol natural time: 0.00 resid: 2.64e-19 Chol amd(A+A') time: 0.00 resid: 2.55e-19 ./cs_demo3 < ../Matrix/bcsstk01 --- Matrix: 48-by-48, nnz: 224 (sym: -1: nnz 400), norm: 3.57e+09 chol then update/downdate amd(A+A') symbolic chol time 0.00 numeric chol time 0.00 solve chol time 0.00 original: resid: 2.55e-19 update: time: 0.00 update: time: 0.00 (incl solve) resid: 9.66e-19 rechol: time: 0.00 (incl solve) resid: 1.55e-18 downdate: time: 0.00 downdate: time: 0.00 (incl solve) resid: 3.74e-17 ./cs_demo2 < ../Matrix/bcsstk16 --- Matrix: 4884-by-4884, nnz: 147631 (sym: -1: nnz 290378), norm: 7.01e+09 blocks: 75 singletons: 74 structural rank: 4884 QR amd(A'*A) time: 2.13 resid: 2.01e-22 LU amd(A+A') time: 1.19 resid: 1.10e-22 LU amd(S'*S) time: 1.15 resid: 1.28e-22 LU amd(A'*A) time: 1.22 resid: 1.78e-22 Chol amd(A+A') time: 0.37 resid: 1.19e-22 ./cs_demo3 < ../Matrix/bcsstk16 --- Matrix: 4884-by-4884, nnz: 147631 (sym: -1: nnz 290378), norm: 7.01e+09 chol then update/downdate amd(A+A') symbolic chol time 0.02 numeric chol time 0.35 solve chol time 0.00 original: resid: 1.19e-22 update: time: 0.00 update: time: 0.01 (incl solve) resid: 1.12e-23 rechol: time: 0.34 (incl solve) resid: 1.17e-23 downdate: time: 0.00 downdate: time: 0.01 (incl solve) resid: 4.09e-22 ./cs_di_demo1 < ../Matrix/t1 T: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 triplet: 4-by-4, nzmax: 16 nnz: 10 2 2 : 3 1 0 : 3.1 3 3 : 1 0 2 : 3.2 1 1 : 2.9 3 0 : 3.5 3 1 : 0.4 1 3 : 0.9 0 0 : 4.5 2 1 : 1.7 A: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 11.1 col 0 : locations 0 to 2 1 : 3.1 3 : 3.5 0 : 4.5 col 1 : locations 3 to 5 1 : 2.9 3 : 0.4 2 : 1.7 col 2 : locations 6 to 7 2 : 3 0 : 3.2 col 3 : locations 8 to 9 3 : 1 1 : 0.9 AT: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 7.7 col 0 : locations 0 to 1 0 : 4.5 2 : 3.2 col 1 : locations 2 to 4 0 : 3.1 1 : 2.9 3 : 0.9 col 2 : locations 5 to 6 1 : 1.7 2 : 3 col 3 : locations 7 to 9 0 : 3.5 1 : 0.4 3 : 1 D: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 16 nnz: 16, 1-norm: 139.58 col 0 : locations 0 to 3 1 : 13.95 3 : 15.75 0 : 100.28 2 : 9.6 col 1 : locations 4 to 7 1 : 88.62 3 : 12.91 0 : 13.95 2 : 4.93 col 2 : locations 8 to 11 1 : 4.93 3 : 0.68 2 : 81.68 0 : 9.6 col 3 : locations 12 to 15 1 : 12.91 3 : 83.2 0 : 15.75 2 : 0.68 ./cs_di_demo2 < ../Matrix/t1 --- Matrix: 4-by-4, nnz: 10 (sym: 0: nnz 0), norm: 1.11e+01 blocks: 1 singletons: 0 structural rank: 4 QR natural time: 0.00 resid: 3.06e-17 QR amd(A'*A) time: 0.00 resid: 2.30e-17 LU natural time: 0.00 resid: 1.53e-17 LU amd(A+A') time: 0.00 resid: 1.53e-17 LU amd(S'*S) time: 0.00 resid: 0.00e+00 LU amd(A'*A) time: 0.00 resid: 1.53e-17 ./cs_di_demo2 < ../Matrix/fs_183_1 --- Matrix: 183-by-183, nnz: 988 (sym: 0: nnz 0), norm: 1.70e+09 zero entries dropped: 71 tiny entries dropped: 10 blocks: 38 singletons: 37 structural rank: 183 QR natural time: 0.00 resid: 1.42e-27 QR amd(A'*A) time: 0.00 resid: 3.35e-28 LU natural time: 0.01 resid: 6.20e-28 LU amd(A+A') time: 0.00 resid: 1.55e-27 LU amd(S'*S) time: 0.00 resid: 6.98e-28 LU amd(A'*A) time: 0.00 resid: 6.98e-28 ./cs_di_demo2 < ../Matrix/west0067 --- Matrix: 67-by-67, nnz: 294 (sym: 0: nnz 0), norm: 6.14e+00 blocks: 2 singletons: 1 structural rank: 67 QR natural time: 0.00 resid: 5.19e-17 QR amd(A'*A) time: 0.00 resid: 3.25e-17 LU natural time: 0.00 resid: 3.89e-17 LU amd(A+A') time: 0.00 resid: 2.27e-17 LU amd(S'*S) time: 0.00 resid: 1.95e-17 LU amd(A'*A) time: 0.00 resid: 2.60e-17 ./cs_di_demo2 < ../Matrix/lp_afiro --- Matrix: 27-by-51, nnz: 102 (sym: 0: nnz 0), norm: 3.43e+00 blocks: 1 singletons: 0 structural rank: 27 QR natural time: 0.00 resid: 3.85e-16 QR amd(A'*A) time: 0.00 resid: 1.50e-16 ./cs_di_demo2 < ../Matrix/ash219 --- Matrix: 219-by-85, nnz: 438 (sym: 0: nnz 0), norm: 9.00e+00 blocks: 1 singletons: 0 structural rank: 85 QR natural time: 0.00 resid: 1.61e-02 QR amd(A'*A) time: 0.00 resid: 1.61e-02 ./cs_di_demo2 < ../Matrix/mbeacxc --- Matrix: 492-by-490, nnz: 49920 (sym: 0: nnz 0), norm: 9.29e-01 blocks: 10 singletons: 8 structural rank: 448 QR natural time: 0.13 resid: nan QR amd(A'*A) time: 0.19 resid: nan ./cs_di_demo2 < ../Matrix/bcsstk01 --- Matrix: 48-by-48, nnz: 224 (sym: -1: nnz 400), norm: 3.57e+09 blocks: 1 singletons: 0 structural rank: 48 QR natural time: 0.00 resid: 3.65e-19 QR amd(A'*A) time: 0.00 resid: 4.02e-19 LU natural time: 0.00 resid: 2.17e-19 LU amd(A+A') time: 0.00 resid: 1.87e-19 LU amd(S'*S) time: 0.00 resid: 2.38e-19 LU amd(A'*A) time: 0.00 resid: 2.38e-19 Chol natural time: 0.00 resid: 2.64e-19 Chol amd(A+A') time: 0.00 resid: 2.55e-19 ./cs_di_demo3 < ../Matrix/bcsstk01 --- Matrix: 48-by-48, nnz: 224 (sym: -1: nnz 400), norm: 3.57e+09 chol then update/downdate amd(A+A') symbolic chol time 0.00 numeric chol time 0.00 solve chol time 0.00 original: resid: 2.55e-19 update: time: 0.00 update: time: 0.00 (incl solve) resid: 9.66e-19 rechol: time: 0.00 (incl solve) resid: 1.55e-18 downdate: time: 0.00 downdate: time: 0.00 (incl solve) resid: 3.74e-17 ./cs_di_demo2 < ../Matrix/bcsstk16 --- Matrix: 4884-by-4884, nnz: 147631 (sym: -1: nnz 290378), norm: 7.01e+09 blocks: 75 singletons: 74 structural rank: 4884 QR amd(A'*A) time: 2.17 resid: 2.01e-22 LU amd(A+A') time: 1.23 resid: 1.10e-22 LU amd(S'*S) time: 1.18 resid: 1.28e-22 LU amd(A'*A) time: 1.23 resid: 1.78e-22 Chol amd(A+A') time: 0.39 resid: 1.19e-22 ./cs_di_demo3 < ../Matrix/bcsstk16 --- Matrix: 4884-by-4884, nnz: 147631 (sym: -1: nnz 290378), norm: 7.01e+09 chol then update/downdate amd(A+A') symbolic chol time 0.03 numeric chol time 0.33 solve chol time 0.00 original: resid: 1.19e-22 update: time: 0.00 update: time: 0.01 (incl solve) resid: 1.12e-23 rechol: time: 0.34 (incl solve) resid: 1.17e-23 downdate: time: 0.00 downdate: time: 0.01 (incl solve) resid: 4.09e-22 ./cs_dl_demo1 < ../Matrix/t1 T: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 triplet: 4-by-4, nzmax: 16 nnz: 10 2 2 : 3 1 0 : 3.1 3 3 : 1 0 2 : 3.2 1 1 : 2.9 3 0 : 3.5 3 1 : 0.4 1 3 : 0.9 0 0 : 4.5 2 1 : 1.7 A: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 11.1 col 0 : locations 0 to 2 1 : 3.1 3 : 3.5 0 : 4.5 col 1 : locations 3 to 5 1 : 2.9 3 : 0.4 2 : 1.7 col 2 : locations 6 to 7 2 : 3 0 : 3.2 col 3 : locations 8 to 9 3 : 1 1 : 0.9 AT: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 7.7 col 0 : locations 0 to 1 0 : 4.5 2 : 3.2 col 1 : locations 2 to 4 0 : 3.1 1 : 2.9 3 : 0.9 col 2 : locations 5 to 6 1 : 1.7 2 : 3 col 3 : locations 7 to 9 0 : 3.5 1 : 0.4 3 : 1 D: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 16 nnz: 16, 1-norm: 139.58 col 0 : locations 0 to 3 1 : 13.95 3 : 15.75 0 : 100.28 2 : 9.6 col 1 : locations 4 to 7 1 : 88.62 3 : 12.91 0 : 13.95 2 : 4.93 col 2 : locations 8 to 11 1 : 4.93 3 : 0.68 2 : 81.68 0 : 9.6 col 3 : locations 12 to 15 1 : 12.91 3 : 83.2 0 : 15.75 2 : 0.68 ./cs_dl_demo2 < ../Matrix/t1 --- Matrix: 4-by-4, nnz: 10 (sym: 0: nnz 0), norm: 1.11e+01 blocks: 1 singletons: 0 structural rank: 4 QR natural time: 0.00 resid: 3.06e-17 QR amd(A'*A) time: 0.00 resid: 2.30e-17 LU natural time: 0.00 resid: 1.53e-17 LU amd(A+A') time: 0.00 resid: 1.53e-17 LU amd(S'*S) time: 0.00 resid: 0.00e+00 LU amd(A'*A) time: 0.00 resid: 1.53e-17 ./cs_dl_demo2 < ../Matrix/fs_183_1 --- Matrix: 183-by-183, nnz: 988 (sym: 0: nnz 0), norm: 1.70e+09 zero entries dropped: 71 tiny entries dropped: 10 blocks: 38 singletons: 37 structural rank: 183 QR natural time: 0.01 resid: 1.42e-27 QR amd(A'*A) time: 0.00 resid: 3.35e-28 LU natural time: 0.00 resid: 6.20e-28 LU amd(A+A') time: 0.00 resid: 1.55e-27 LU amd(S'*S) time: 0.00 resid: 6.98e-28 LU amd(A'*A) time: 0.01 resid: 6.98e-28 ./cs_dl_demo2 < ../Matrix/west0067 --- Matrix: 67-by-67, nnz: 294 (sym: 0: nnz 0), norm: 6.14e+00 blocks: 2 singletons: 1 structural rank: 67 QR natural time: 0.00 resid: 5.19e-17 QR amd(A'*A) time: 0.00 resid: 3.25e-17 LU natural time: 0.00 resid: 3.89e-17 LU amd(A+A') time: 0.00 resid: 2.27e-17 LU amd(S'*S) time: 0.00 resid: 1.95e-17 LU amd(A'*A) time: 0.00 resid: 2.60e-17 ./cs_dl_demo2 < ../Matrix/lp_afiro --- Matrix: 27-by-51, nnz: 102 (sym: 0: nnz 0), norm: 3.43e+00 blocks: 1 singletons: 0 structural rank: 27 QR natural time: 0.00 resid: 3.85e-16 QR amd(A'*A) time: 0.00 resid: 1.50e-16 ./cs_dl_demo2 < ../Matrix/ash219 --- Matrix: 219-by-85, nnz: 438 (sym: 0: nnz 0), norm: 9.00e+00 blocks: 1 singletons: 0 structural rank: 85 QR natural time: 0.00 resid: 1.61e-02 QR amd(A'*A) time: 0.00 resid: 1.61e-02 ./cs_dl_demo2 < ../Matrix/mbeacxc --- Matrix: 492-by-490, nnz: 49920 (sym: 0: nnz 0), norm: 9.29e-01 blocks: 10 singletons: 8 structural rank: 448 QR natural time: 0.15 resid: nan QR amd(A'*A) time: 0.20 resid: nan ./cs_dl_demo2 < ../Matrix/bcsstk01 --- Matrix: 48-by-48, nnz: 224 (sym: -1: nnz 400), norm: 3.57e+09 blocks: 1 singletons: 0 structural rank: 48 QR natural time: 0.00 resid: 3.65e-19 QR amd(A'*A) time: 0.00 resid: 4.02e-19 LU natural time: 0.00 resid: 2.17e-19 LU amd(A+A') time: 0.00 resid: 1.87e-19 LU amd(S'*S) time: 0.00 resid: 2.38e-19 LU amd(A'*A) time: 0.00 resid: 2.38e-19 Chol natural time: 0.00 resid: 2.64e-19 Chol amd(A+A') time: 0.00 resid: 2.55e-19 ./cs_dl_demo3 < ../Matrix/bcsstk01 --- Matrix: 48-by-48, nnz: 224 (sym: -1: nnz 400), norm: 3.57e+09 chol then update/downdate amd(A+A') symbolic chol time 0.00 numeric chol time 0.00 solve chol time 0.00 original: resid: 2.55e-19 update: time: 0.00 update: time: 0.00 (incl solve) resid: 9.66e-19 rechol: time: 0.00 (incl solve) resid: 1.55e-18 downdate: time: 0.00 downdate: time: 0.00 (incl solve) resid: 3.74e-17 ./cs_dl_demo2 < ../Matrix/bcsstk16 --- Matrix: 4884-by-4884, nnz: 147631 (sym: -1: nnz 290378), norm: 7.01e+09 blocks: 75 singletons: 74 structural rank: 4884 QR amd(A'*A) time: 2.62 resid: 2.01e-22 LU amd(A+A') time: 1.43 resid: 1.10e-22 LU amd(S'*S) time: 1.28 resid: 1.28e-22 LU amd(A'*A) time: 1.35 resid: 1.78e-22 Chol amd(A+A') time: 0.49 resid: 1.19e-22 ./cs_dl_demo3 < ../Matrix/bcsstk16 --- Matrix: 4884-by-4884, nnz: 147631 (sym: -1: nnz 290378), norm: 7.01e+09 chol then update/downdate amd(A+A') symbolic chol time 0.02 numeric chol time 0.46 solve chol time 0.02 original: resid: 1.19e-22 update: time: 0.00 update: time: 0.01 (incl solve) resid: 1.12e-23 rechol: time: 0.52 (incl solve) resid: 1.17e-23 downdate: time: 0.00 downdate: time: 0.01 (incl solve) resid: 4.09e-22 ./cs_ci_demo1 < ../Matrix/t2 T: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 triplet: 4-by-4, nzmax: 16 nnz: 10 2 2 : (3, 3.14159) 1 0 : (3.1, 42) 3 3 : (1, 7) 0 2 : (3.2, 0.1) 1 1 : (2.9, 1.3) 3 0 : (3.5, 0) 3 1 : (0.4, 2.71828) 1 3 : (0.9, 99) 0 0 : (4.5, 6) 2 1 : (1.7, 1) A: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 106.075 col 0 : locations 0 to 2 1 : (3.1, 42) 3 : (3.5, 0) 0 : (4.5, 6) col 1 : locations 3 to 5 1 : (2.9, 1.3) 3 : (0.4, 2.71828) 2 : (1.7, 1) col 2 : locations 6 to 7 2 : (3, 3.14159) 0 : (3.2, 0.1) col 3 : locations 8 to 9 3 : (1, 7) 1 : (0.9, 99) AT: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 144.296 col 0 : locations 0 to 1 0 : (4.5, -6) 2 : (3.2, -0.1) col 1 : locations 2 to 4 0 : (3.1, -42) 1 : (2.9, -1.3) 3 : (0.9, -99) col 2 : locations 5 to 6 1 : (1.7, -1) 2 : (3, -3.14159) col 3 : locations 7 to 9 0 : (3.5, -0) 1 : (0.4, -2.71828) 3 : (1, -7) D: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 16 nnz: 16, 1-norm: 25308.3 col 0 : locations 0 to 3 1 : (265.95, 170.4) 3 : (15.75, -21) 0 : (12720.7, 0) 2 : (9.91416, 9.7531) col 1 : locations 4 to 7 1 : (24239.7, 0) 3 : (709.444, -232.337) 0 : (265.95, -170.4) 2 : (6.23, 0.69) col 2 : locations 8 to 11 1 : (6.23, -0.69) 3 : (3.39828, 4.22108) 2 : (12676.9, 0) 0 : (9.91416, -9.7531) col 3 : locations 12 to 15 1 : (709.444, 232.337) 3 : (12724, 0) 0 : (15.75, 21) 2 : (3.39828, -4.22108) ./cs_ci_demo2 < ../Matrix/t2 --- Matrix: 4-by-4, nnz: 10 (sym: 0: nnz 0), norm: 1.06e+02 blocks: 1 singletons: 0 structural rank: 4 QR natural time: 0.00 resid: 2.06e-17 QR amd(A'*A) time: 0.00 resid: 6.36e-18 LU natural time: 0.00 resid: 4.88e-18 LU amd(A+A') time: 0.00 resid: 2.11e-18 LU amd(S'*S) time: 0.00 resid: 6.36e-18 LU amd(A'*A) time: 0.00 resid: 2.11e-18 ./cs_ci_demo2 < ../Matrix/t3 --- Matrix: 3-by-4, nnz: 12 (sym: 0: nnz 0), norm: 3.06e+00 blocks: 1 singletons: 0 structural rank: 3 QR natural time: 0.00 resid: 1.05e-16 QR amd(A'*A) time: 0.00 resid: 1.05e-16 ./cs_ci_demo2 < ../Matrix/t4 --- Matrix: 2-by-2, nnz: 3 (sym: 1: nnz 4), norm: 2.83e+00 blocks: 1 singletons: 0 structural rank: 2 QR natural time: 0.00 resid: 5.65e-17 QR amd(A'*A) time: 0.00 resid: 5.65e-17 LU natural time: 0.00 resid: 0.00e+00 LU amd(A+A') time: 0.00 resid: 0.00e+00 LU amd(S'*S) time: 0.00 resid: 0.00e+00 LU amd(A'*A) time: 0.00 resid: 0.00e+00 Chol natural time: 0.00 (failed) Chol amd(A+A') time: 0.00 (failed) ./cs_ci_demo2 < ../Matrix/c_west0067 --- Matrix: 67-by-67, nnz: 294 (sym: 0: nnz 0), norm: 6.17e+00 blocks: 2 singletons: 1 structural rank: 67 QR natural time: 0.00 resid: 8.16e-17 QR amd(A'*A) time: 0.00 resid: 5.34e-17 LU natural time: 0.00 resid: 4.54e-17 LU amd(A+A') time: 0.00 resid: 5.90e-17 LU amd(S'*S) time: 0.00 resid: 5.28e-17 LU amd(A'*A) time: 0.00 resid: 4.76e-17 ./cs_ci_demo2 < ../Matrix/c_mbeacxc --- Matrix: 492-by-490, nnz: 49920 (sym: 0: nnz 0), norm: 9.29e-01 blocks: 10 singletons: 8 structural rank: 448 QR natural time: 0.32 resid: nan QR amd(A'*A) time: 0.37 resid: nan ./cs_ci_demo2 < ../Matrix/young1c --- Matrix: 841-by-841, nnz: 4089 (sym: 0: nnz 0), norm: 7.30e+02 blocks: 1 singletons: 0 structural rank: 841 QR natural time: 0.02 resid: 1.51e-16 QR amd(A'*A) time: 0.00 resid: 1.53e-16 LU natural time: 0.01 resid: 1.39e-16 LU amd(A+A') time: 0.01 resid: 2.95e-16 LU amd(S'*S) time: 0.01 resid: 3.37e-16 LU amd(A'*A) time: 0.00 resid: 3.37e-16 ./cs_ci_demo2 < ../Matrix/qc324 --- Matrix: 324-by-324, nnz: 26730 (sym: 0: nnz 0), norm: 1.71e+00 blocks: 1 singletons: 0 structural rank: 324 QR natural time: 0.04 resid: 9.08e-17 QR amd(A'*A) time: 0.05 resid: 8.71e-17 LU natural time: 0.02 resid: 6.01e-17 LU amd(A+A') time: 0.02 resid: 4.05e-17 LU amd(S'*S) time: 0.04 resid: 4.71e-17 LU amd(A'*A) time: 0.03 resid: 4.71e-17 ./cs_ci_demo2 < ../Matrix/neumann --- Matrix: 1600-by-1600, nnz: 7840 (sym: 0: nnz 0), norm: 1.41e+01 blocks: 1 singletons: 0 structural rank: 1600 QR amd(A'*A) time: 0.03 resid: 1.04e-15 LU amd(A+A') time: 0.00 resid: 3.55e-16 LU amd(S'*S) time: 0.02 resid: 4.03e-16 LU amd(A'*A) time: 0.02 resid: 4.03e-16 ./cs_ci_demo2 < ../Matrix/c4 --- Matrix: 4-by-4, nnz: 10 (sym: -1: nnz 16), norm: 7.37e+01 blocks: 1 singletons: 0 structural rank: 4 QR natural time: 0.00 resid: 5.85e-17 QR amd(A'*A) time: 0.00 resid: 5.85e-17 LU natural time: 0.00 resid: 2.29e-17 LU amd(A+A') time: 0.00 resid: 2.29e-17 LU amd(S'*S) time: 0.00 resid: 2.29e-17 LU amd(A'*A) time: 0.00 resid: 2.29e-17 Chol natural time: 0.00 resid: 6.88e-17 Chol amd(A+A') time: 0.00 resid: 6.88e-17 ./cs_ci_demo3 < ../Matrix/c4 --- Matrix: 4-by-4, nnz: 10 (sym: -1: nnz 16), norm: 7.37e+01 chol then update/downdate amd(A+A') symbolic chol time 0.00 numeric chol time 0.00 solve chol time 0.00 original: resid: 6.88e-17 update: time: 0.00 update: time: 0.00 (incl solve) resid: 6.49e-17 rechol: time: 0.00 (incl solve) resid: 6.49e-17 downdate: time: 0.00 downdate: time: 0.00 (incl solve) resid: 5.85e-17 ./cs_ci_demo2 < ../Matrix/mhd1280b --- Matrix: 1280-by-1280, nnz: 11963 (sym: -1: nnz 22646), norm: 8.00e+01 tiny entries dropped: 66 blocks: 20 singletons: 14 structural rank: 1280 QR amd(A'*A) time: 0.01 resid: 6.15e-25 LU amd(A+A') time: 0.01 resid: 2.33e-25 LU amd(S'*S) time: 0.01 resid: 3.96e-25 LU amd(A'*A) time: 0.01 resid: 3.96e-25 Chol amd(A+A') time: 0.00 resid: 1.58e-25 ./cs_ci_demo3 < ../Matrix/mhd1280b --- Matrix: 1280-by-1280, nnz: 12029 (sym: -1: nnz 22778), norm: 8.00e+01 chol then update/downdate amd(A+A') symbolic chol time 0.01 numeric chol time 0.00 solve chol time 0.00 original: resid: 1.51e-25 update: time: 0.00 update: time: 0.00 (incl solve) resid: 1.75e-25 rechol: time: 0.00 (incl solve) resid: 1.71e-25 downdate: time: 0.00 downdate: time: 0.00 (incl solve) resid: 5.85e-25 ./cs_cl_demo1 < ../Matrix/t2 T: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 triplet: 4-by-4, nzmax: 16 nnz: 10 2 2 : (3, 3.14159) 1 0 : (3.1, 42) 3 3 : (1, 7) 0 2 : (3.2, 0.1) 1 1 : (2.9, 1.3) 3 0 : (3.5, 0) 3 1 : (0.4, 2.71828) 1 3 : (0.9, 99) 0 0 : (4.5, 6) 2 1 : (1.7, 1) A: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 106.075 col 0 : locations 0 to 2 1 : (3.1, 42) 3 : (3.5, 0) 0 : (4.5, 6) col 1 : locations 3 to 5 1 : (2.9, 1.3) 3 : (0.4, 2.71828) 2 : (1.7, 1) col 2 : locations 6 to 7 2 : (3, 3.14159) 0 : (3.2, 0.1) col 3 : locations 8 to 9 3 : (1, 7) 1 : (0.9, 99) AT: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 10 nnz: 10, 1-norm: 144.296 col 0 : locations 0 to 1 0 : (4.5, -6) 2 : (3.2, -0.1) col 1 : locations 2 to 4 0 : (3.1, -42) 1 : (2.9, -1.3) 3 : (0.9, -99) col 2 : locations 5 to 6 1 : (1.7, -1) 2 : (3, -3.14159) col 3 : locations 7 to 9 0 : (3.5, -0) 1 : (0.4, -2.71828) 3 : (1, -7) D: CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007 4-by-4, nzmax: 16 nnz: 16, 1-norm: 25308.3 col 0 : locations 0 to 3 1 : (265.95, 170.4) 3 : (15.75, -21) 0 : (12720.7, 0) 2 : (9.91416, 9.7531) col 1 : locations 4 to 7 1 : (24239.7, 0) 3 : (709.444, -232.337) 0 : (265.95, -170.4) 2 : (6.23, 0.69) col 2 : locations 8 to 11 1 : (6.23, -0.69) 3 : (3.39828, 4.22108) 2 : (12676.9, 0) 0 : (9.91416, -9.7531) col 3 : locations 12 to 15 1 : (709.444, 232.337) 3 : (12724, 0) 0 : (15.75, 21) 2 : (3.39828, -4.22108) ./cs_cl_demo2 < ../Matrix/t2 --- Matrix: 4-by-4, nnz: 10 (sym: 0: nnz 0), norm: 1.06e+02 blocks: 1 singletons: 0 structural rank: 4 QR natural time: 0.00 resid: 2.06e-17 QR amd(A'*A) time: 0.00 resid: 6.36e-18 LU natural time: 0.00 resid: 4.88e-18 LU amd(A+A') time: 0.00 resid: 2.11e-18 LU amd(S'*S) time: 0.00 resid: 6.36e-18 LU amd(A'*A) time: 0.00 resid: 2.11e-18 ./cs_cl_demo2 < ../Matrix/t3 --- Matrix: 3-by-4, nnz: 12 (sym: 0: nnz 0), norm: 3.06e+00 blocks: 1 singletons: 0 structural rank: 3 QR natural time: 0.00 resid: 1.05e-16 QR amd(A'*A) time: 0.00 resid: 1.05e-16 ./cs_cl_demo2 < ../Matrix/t4 --- Matrix: 2-by-2, nnz: 3 (sym: 1: nnz 4), norm: 2.83e+00 blocks: 1 singletons: 0 structural rank: 2 QR natural time: 0.00 resid: 5.65e-17 QR amd(A'*A) time: 0.00 resid: 5.65e-17 LU natural time: 0.00 resid: 0.00e+00 LU amd(A+A') time: 0.00 resid: 0.00e+00 LU amd(S'*S) time: 0.00 resid: 0.00e+00 LU amd(A'*A) time: 0.00 resid: 0.00e+00 Chol natural time: 0.00 (failed) Chol amd(A+A') time: 0.00 (failed) ./cs_cl_demo2 < ../Matrix/c_west0067 --- Matrix: 67-by-67, nnz: 294 (sym: 0: nnz 0), norm: 6.17e+00 blocks: 2 singletons: 1 structural rank: 67 QR natural time: 0.00 resid: 8.16e-17 QR amd(A'*A) time: 0.00 resid: 5.34e-17 LU natural time: 0.00 resid: 4.54e-17 LU amd(A+A') time: 0.00 resid: 5.90e-17 LU amd(S'*S) time: 0.00 resid: 5.28e-17 LU amd(A'*A) time: 0.00 resid: 4.76e-17 ./cs_cl_demo2 < ../Matrix/c_mbeacxc --- Matrix: 492-by-490, nnz: 49920 (sym: 0: nnz 0), norm: 9.29e-01 blocks: 10 singletons: 8 structural rank: 448 QR natural time: 0.29 resid: nan QR amd(A'*A) time: 0.35 resid: nan ./cs_cl_demo2 < ../Matrix/young1c --- Matrix: 841-by-841, nnz: 4089 (sym: 0: nnz 0), norm: 7.30e+02 blocks: 1 singletons: 0 structural rank: 841 QR natural time: 0.02 resid: 1.51e-16 QR amd(A'*A) time: 0.01 resid: 1.53e-16 LU natural time: 0.01 resid: 1.39e-16 LU amd(A+A') time: 0.01 resid: 2.95e-16 LU amd(S'*S) time: 0.01 resid: 3.37e-16 LU amd(A'*A) time: 0.00 resid: 3.37e-16 ./cs_cl_demo2 < ../Matrix/qc324 --- Matrix: 324-by-324, nnz: 26730 (sym: 0: nnz 0), norm: 1.71e+00 blocks: 1 singletons: 0 structural rank: 324 QR natural time: 0.04 resid: 9.08e-17 QR amd(A'*A) time: 0.06 resid: 8.71e-17 LU natural time: 0.02 resid: 6.01e-17 LU amd(A+A') time: 0.03 resid: 4.05e-17 LU amd(S'*S) time: 0.03 resid: 4.71e-17 LU amd(A'*A) time: 0.03 resid: 4.71e-17 ./cs_cl_demo2 < ../Matrix/neumann --- Matrix: 1600-by-1600, nnz: 7840 (sym: 0: nnz 0), norm: 1.41e+01 blocks: 1 singletons: 0 structural rank: 1600 QR amd(A'*A) time: 0.03 resid: 1.04e-15 LU amd(A+A') time: 0.01 resid: 3.55e-16 LU amd(S'*S) time: 0.03 resid: 4.03e-16 LU amd(A'*A) time: 0.01 resid: 4.03e-16 ./cs_cl_demo2 < ../Matrix/c4 --- Matrix: 4-by-4, nnz: 10 (sym: -1: nnz 16), norm: 7.37e+01 blocks: 1 singletons: 0 structural rank: 4 QR natural time: 0.00 resid: 5.85e-17 QR amd(A'*A) time: 0.00 resid: 5.85e-17 LU natural time: 0.00 resid: 2.29e-17 LU amd(A+A') time: 0.00 resid: 2.29e-17 LU amd(S'*S) time: 0.00 resid: 2.29e-17 LU amd(A'*A) time: 0.00 resid: 2.29e-17 Chol natural time: 0.00 resid: 6.88e-17 Chol amd(A+A') time: 0.00 resid: 6.88e-17 ./cs_cl_demo3 < ../Matrix/c4 --- Matrix: 4-by-4, nnz: 10 (sym: -1: nnz 16), norm: 7.37e+01 chol then update/downdate amd(A+A') symbolic chol time 0.00 numeric chol time 0.00 solve chol time 0.00 original: resid: 6.88e-17 update: time: 0.00 update: time: 0.00 (incl solve) resid: 6.49e-17 rechol: time: 0.00 (incl solve) resid: 6.49e-17 downdate: time: 0.00 downdate: time: 0.00 (incl solve) resid: 5.85e-17 ./cs_cl_demo2 < ../Matrix/mhd1280b --- Matrix: 1280-by-1280, nnz: 11963 (sym: -1: nnz 22646), norm: 8.00e+01 tiny entries dropped: 66 blocks: 20 singletons: 14 structural rank: 1280 QR amd(A'*A) time: 0.01 resid: 6.15e-25 LU amd(A+A') time: 0.00 resid: 2.33e-25 LU amd(S'*S) time: 0.01 resid: 3.96e-25 LU amd(A'*A) time: 0.00 resid: 3.96e-25 Chol amd(A+A') time: 0.01 resid: 1.58e-25 ./cs_cl_demo3 < ../Matrix/mhd1280b --- Matrix: 1280-by-1280, nnz: 12029 (sym: -1: nnz 22778), norm: 8.00e+01 chol then update/downdate amd(A+A') symbolic chol time 0.01 numeric chol time 0.00 solve chol time 0.00 original: resid: 1.51e-25 update: time: 0.00 update: time: 0.00 (incl solve) resid: 1.75e-25 rechol: time: 0.00 (incl solve) resid: 1.71e-25 downdate: time: 0.00 downdate: time: 0.00 (incl solve) resid: 5.85e-25 make[1]: Leaving directory `/amd/netapp3/vol/research0a/research18/sparse2/SuiteSparse/CXSparse/Demo' SuiteSparse/CXSparse/Demo/cs_demo.c0000644001170100242450000002315210440110365016075 0ustar davisfac#include "cs_demo.h" #include /* 1 if A is square & upper tri., -1 if square & lower tri., 0 otherwise */ static int is_sym (cs *A) { int is_upper, is_lower, j, p, n = A->n, m = A->m, *Ap = A->p, *Ai = A->i ; if (m != n) return (0) ; is_upper = 1 ; is_lower = 1 ; for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { if (Ai [p] > j) is_upper = 0 ; if (Ai [p] < j) is_lower = 0 ; } } return (is_upper ? 1 : (is_lower ? -1 : 0)) ; } /* true for off-diagonal entries */ static int dropdiag (int i, int j, double aij, void *other) { return (i != j) ;} /* C = A + triu(A,1)' */ static cs *make_sym (cs *A) { cs *AT, *C ; AT = cs_transpose (A, 1) ; /* AT = A' */ cs_fkeep (AT, &dropdiag, NULL) ; /* drop diagonal entries from AT */ C = cs_add (A, AT, 1, 1) ; /* C = A+AT */ cs_spfree (AT) ; return (C) ; } /* create a right-hand side */ static void rhs (double *x, double *b, int m) { int i ; for (i = 0 ; i < m ; i++) b [i] = 1 + ((double) i) / m ; for (i = 0 ; i < m ; i++) x [i] = b [i] ; } /* infinity-norm of x */ static double norm (double *x, int n) { int i ; double normx = 0 ; for (i = 0 ; i < n ; i++) normx = CS_MAX (normx, fabs (x [i])) ; return (normx) ; } /* compute residual, norm(A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf)) */ static void print_resid (int ok, cs *A, double *x, double *b, double *resid) { int i, m, n ; if (!ok) { printf (" (failed)\n") ; return ; } m = A->m ; n = A->n ; for (i = 0 ; i < m ; i++) resid [i] = -b [i] ; /* resid = -b */ cs_gaxpy (A, x, resid) ; /* resid = resid + A*x */ printf ("resid: %8.2e\n", norm (resid,m) / ((n == 0) ? 1 : (cs_norm (A) * norm (x,n) + norm (b,m)))) ; } static double tic (void) { return (clock () / (double) CLOCKS_PER_SEC) ; } static double toc (double t) { double s = tic () ; return (CS_MAX (0, s-t)) ; } static void print_order (int order) { switch (order) { case 0: printf ("natural ") ; break ; case 1: printf ("amd(A+A') ") ; break ; case 2: printf ("amd(S'*S) ") ; break ; case 3: printf ("amd(A'*A) ") ; break ; } } /* read a problem from a file */ problem *get_problem (FILE *f, double tol) { cs *T, *A, *C ; int sym, m, n, mn, nz1, nz2 ; problem *Prob ; Prob = cs_calloc (1, sizeof (problem)) ; if (!Prob) return (NULL) ; T = cs_load (f) ; /* load triplet matrix T from a file */ Prob->A = A = cs_compress (T) ; /* A = compressed-column form of T */ cs_spfree (T) ; /* clear T */ if (!cs_dupl (A)) return (free_problem (Prob)) ; /* sum up duplicates */ Prob->sym = sym = is_sym (A) ; /* determine if A is symmetric */ m = A->m ; n = A->n ; mn = CS_MAX (m,n) ; nz1 = A->p [n] ; cs_dropzeros (A) ; /* drop zero entries */ nz2 = A->p [n] ; if (tol > 0) cs_droptol (A, tol) ; /* drop tiny entries (just to test) */ Prob->C = C = sym ? make_sym (A) : A ; /* C = A + triu(A,1)', or C=A */ if (!C) return (free_problem (Prob)) ; printf ("\n--- Matrix: %d-by-%d, nnz: %d (sym: %d: nnz %d), norm: %8.2e\n", m, n, A->p [n], sym, sym ? C->p [n] : 0, cs_norm (C)) ; if (nz1 != nz2) printf ("zero entries dropped: %d\n", nz1 - nz2) ; if (nz2 != A->p [n]) printf ("tiny entries dropped: %d\n", nz2 - A->p [n]) ; Prob->b = cs_malloc (mn, sizeof (double)) ; Prob->x = cs_malloc (mn, sizeof (double)) ; Prob->resid = cs_malloc (mn, sizeof (double)) ; return ((!Prob->b || !Prob->x || !Prob->resid) ? free_problem (Prob) : Prob) ; } /* free a problem */ problem *free_problem (problem *Prob) { if (!Prob) return (NULL) ; cs_spfree (Prob->A) ; if (Prob->sym) cs_spfree (Prob->C) ; cs_free (Prob->b) ; cs_free (Prob->x) ; cs_free (Prob->resid) ; return (cs_free (Prob)) ; } /* solve a linear system using Cholesky, LU, and QR, with various orderings */ int demo2 (problem *Prob) { cs *A, *C ; double *b, *x, *resid, t, tol ; int k, m, n, ok, order, nb, ns, *r, *s, *rr, sprank ; csd *D ; if (!Prob) return (0) ; A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid; m = A->m ; n = A->n ; tol = Prob->sym ? 0.001 : 1 ; /* partial pivoting tolerance */ D = cs_dmperm (C, 1) ; /* randomized dmperm analysis */ if (!D) return (0) ; nb = D->nb ; r = D->r ; s = D->s ; rr = D->rr ; sprank = rr [3] ; for (ns = 0, k = 0 ; k < nb ; k++) { ns += ((r [k+1] == r [k]+1) && (s [k+1] == s [k]+1)) ; } printf ("blocks: %d singletons: %d structural rank: %d\n", nb, ns, sprank) ; cs_dfree (D) ; for (order = 0 ; order <= 3 ; order += 3) /* natural and amd(A'*A) */ { if (!order && m > 1000) continue ; printf ("QR ") ; print_order (order) ; rhs (x, b, m) ; /* compute right-hand side */ t = tic () ; ok = cs_qrsol (order, C, x) ; /* min norm(Ax-b) with QR */ printf ("time: %8.2f ", toc (t)) ; print_resid (ok, C, x, b, resid) ; /* print residual */ } if (m != n || sprank < n) return (1) ; /* return if rect. or singular*/ for (order = 0 ; order <= 3 ; order++) /* try all orderings */ { if (!order && m > 1000) continue ; printf ("LU ") ; print_order (order) ; rhs (x, b, m) ; /* compute right-hand side */ t = tic () ; ok = cs_lusol (order, C, x, tol) ; /* solve Ax=b with LU */ printf ("time: %8.2f ", toc (t)) ; print_resid (ok, C, x, b, resid) ; /* print residual */ } if (!Prob->sym) return (1) ; for (order = 0 ; order <= 1 ; order++) /* natural and amd(A+A') */ { if (!order && m > 1000) continue ; printf ("Chol ") ; print_order (order) ; rhs (x, b, m) ; /* compute right-hand side */ t = tic () ; ok = cs_cholsol (order, C, x) ; /* solve Ax=b with Cholesky */ printf ("time: %8.2f ", toc (t)) ; print_resid (ok, C, x, b, resid) ; /* print residual */ } return (1) ; } /* free workspace for demo3 */ static int done3 (int ok, css *S, csn *N, double *y, cs *W, cs *E, int *p) { cs_sfree (S) ; cs_nfree (N) ; cs_free (y) ; cs_spfree (W) ; cs_spfree (E) ; cs_free (p) ; return (ok) ; } /* Cholesky update/downdate */ int demo3 (problem *Prob) { cs *A, *C, *W = NULL, *WW, *WT, *E = NULL, *W2 ; int n, k, *Li, *Lp, *Wi, *Wp, p1, p2, *p = NULL, ok ; double *b, *x, *resid, *y = NULL, *Lx, *Wx, s, t, t1 ; css *S = NULL ; csn *N = NULL ; if (!Prob || !Prob->sym || Prob->A->n == 0) return (0) ; A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid; n = A->n ; if (!Prob->sym || n == 0) return (1) ; rhs (x, b, n) ; /* compute right-hand side */ printf ("\nchol then update/downdate ") ; print_order (1) ; y = cs_malloc (n, sizeof (double)) ; t = tic () ; S = cs_schol (1, C) ; /* symbolic Chol, amd(A+A') */ printf ("\nsymbolic chol time %8.2f\n", toc (t)) ; t = tic () ; N = cs_chol (C, S) ; /* numeric Cholesky */ printf ("numeric chol time %8.2f\n", toc (t)) ; if (!S || !N || !y) return (done3 (0, S, N, y, W, E, p)) ; t = tic () ; cs_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_lsolve (N->L, y) ; /* y = L\y */ cs_ltsolve (N->L, y) ; /* y = L'\y */ cs_pvec (S->pinv, y, x, n) ; /* x = P'*y */ printf ("solve chol time %8.2f\n", toc (t)) ; printf ("original: ") ; print_resid (1, C, x, b, resid) ; /* print residual */ k = n/2 ; /* construct W */ W = cs_spalloc (n, 1, n, 1, 0) ; if (!W) return (done3 (0, S, N, y, W, E, p)) ; Lp = N->L->p ; Li = N->L->i ; Lx = N->L->x ; Wp = W->p ; Wi = W->i ; Wx = W->x ; Wp [0] = 0 ; p1 = Lp [k] ; Wp [1] = Lp [k+1] - p1 ; s = Lx [p1] ; srand (1) ; for ( ; p1 < Lp [k+1] ; p1++) { p2 = p1 - Lp [k] ; Wi [p2] = Li [p1] ; Wx [p2] = s * rand () / ((double) RAND_MAX) ; } t = tic () ; ok = cs_updown (N->L, +1, W, S->parent) ; /* update: L*L'+W*W' */ t1 = toc (t) ; printf ("update: time: %8.2f\n", t1) ; if (!ok) return (done3 (0, S, N, y, W, E, p)) ; t = tic () ; cs_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_lsolve (N->L, y) ; /* y = L\y */ cs_ltsolve (N->L, y) ; /* y = L'\y */ cs_pvec (S->pinv, y, x, n) ; /* x = P'*y */ t = toc (t) ; p = cs_pinv (S->pinv, n) ; W2 = cs_permute (W, p, NULL, 1) ; /* E = C + (P'W)*(P'W)' */ WT = cs_transpose (W2,1) ; WW = cs_multiply (W2, WT) ; cs_spfree (WT) ; cs_spfree (W2) ; E = cs_add (C, WW, 1, 1) ; cs_spfree (WW) ; if (!E || !p) return (done3 (0, S, N, y, W, E, p)) ; printf ("update: time: %8.2f (incl solve) ", t1+t) ; print_resid (1, E, x, b, resid) ; /* print residual */ cs_nfree (N) ; /* clear N */ t = tic () ; N = cs_chol (E, S) ; /* numeric Cholesky */ if (!N) return (done3 (0, S, N, y, W, E, p)) ; cs_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_lsolve (N->L, y) ; /* y = L\y */ cs_ltsolve (N->L, y) ; /* y = L'\y */ cs_pvec (S->pinv, y, x, n) ; /* x = P'*y */ t = toc (t) ; printf ("rechol: time: %8.2f (incl solve) ", t) ; print_resid (1, E, x, b, resid) ; /* print residual */ t = tic () ; ok = cs_updown (N->L, -1, W, S->parent) ; /* downdate: L*L'-W*W' */ t1 = toc (t) ; if (!ok) return (done3 (0, S, N, y, W, E, p)) ; printf ("downdate: time: %8.2f\n", t1) ; t = tic () ; cs_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_lsolve (N->L, y) ; /* y = L\y */ cs_ltsolve (N->L, y) ; /* y = L'\y */ cs_pvec (S->pinv, y, x, n) ; /* x = P'*y */ t = toc (t) ; printf ("downdate: time: %8.2f (incl solve) ", t1+t) ; print_resid (1, C, x, b, resid) ; /* print residual */ return (done3 (1, S, N, y, W, E, p)) ; } SuiteSparse/CXSparse/Demo/cs_demo.h0000644001170100242450000000044410414325170016104 0ustar davisfac#include "cs.h" typedef struct problem_struct { cs *A ; cs *C ; int sym ; double *x ; double *b ; double *resid ; } problem ; problem *get_problem (FILE *f, double tol) ; int demo2 (problem *Prob) ; int demo3 (problem *Prob) ; problem *free_problem (problem *Prob) ; SuiteSparse/CXSparse/Demo/README.txt0000644001170100242450000000045410375603510016024 0ustar davisfacCXSparse/Demo: to compile a run the demos, just type "make" in this directory. The printed residuals should all be small, except for the mbeacxc matrix (which is numerically and structurally singular), and ash219 (which is a least-squares problem). See cs_demo.out for the proper output of "make". SuiteSparse/CXSparse/Demo/cs_idemo.c0000644001170100242450000000300610623313303016242 0ustar davisfac#include "cs.h" /* test real/complex conversion routines (int version) */ int main (void) { cs_ci *T, *A, *A1, *A2, *B ; cs_di *C1, *C2, *Treal, *Timag ; printf ("\n--- cs_idemo, size of CS_INT: %d\n", (int) sizeof (CS_INT)) ; T = cs_ci_load (stdin) ; /* load a complex triplet matrix, T */ printf ("\nT:\n") ; cs_ci_print (T, 0) ; Treal = cs_i_real (T, 1) ; /* Treal = real part of T */ printf ("\nTreal:\n") ; cs_di_print (Treal, 0) ; Timag = cs_i_real (T, 0) ; /* Treal = imaginary part of T */ printf ("\nTimag:\n") ; cs_di_print (Timag, 0) ; A = cs_ci_compress (T) ; /* A = compressed-column form of T */ printf ("\nA:\n") ; cs_ci_print (A, 0) ; C1 = cs_i_real (A, 1) ; /* C1 = real (A) */ printf ("\nC1 = real(A):\n") ; cs_di_print (C1, 0) ; C2 = cs_i_real (A, 0) ; /* C2 = imag (A) */ printf ("\nC2 = imag(A):\n") ; cs_di_print (C2, 0) ; A1 = cs_i_complex (C1, 1) ; /* A1 = complex version of C1 */ printf ("\nA1:\n") ; cs_ci_print (A1, 0) ; A2 = cs_i_complex (C2, 0) ; /* A2 = complex version of C2 (imag.) */ printf ("\nA2:\n") ; cs_ci_print (A2, 0) ; B = cs_ci_add (A1, A2, 1., -1.) ; /* B = A1 - A2 */ printf ("\nB = conj(A):\n") ; cs_ci_print (B, 0) ; cs_ci_spfree (T) ; cs_ci_spfree (A) ; cs_ci_spfree (A1) ; cs_ci_spfree (A2) ; cs_ci_spfree (B) ; cs_di_spfree (C1) ; cs_di_spfree (C2) ; cs_di_spfree (Treal) ; cs_di_spfree (Timag) ; return (0) ; } SuiteSparse/CXSparse/Demo/cs_ldemo.c0000644001170100242450000000300610623313341016247 0ustar davisfac#include "cs.h" /* test real/complex conversion routines (int version) */ int main (void) { cs_cl *T, *A, *A1, *A2, *B ; cs_dl *C1, *C2, *Treal, *Timag ; printf ("\n--- cs_ldemo, size of CS_INT: %d\n", (int) sizeof (CS_INT)) ; T = cs_cl_load (stdin) ; /* load a complex triplet matrix, T */ printf ("\nT:\n") ; cs_cl_print (T, 0) ; Treal = cs_l_real (T, 1) ; /* Treal = real part of T */ printf ("\nTreal:\n") ; cs_dl_print (Treal, 0) ; Timag = cs_l_real (T, 0) ; /* Treal = imaginary part of T */ printf ("\nTimag:\n") ; cs_dl_print (Timag, 0) ; A = cs_cl_compress (T) ; /* A = compressed-column form of T */ printf ("\nA:\n") ; cs_cl_print (A, 0) ; C1 = cs_l_real (A, 1) ; /* C1 = real (A) */ printf ("\nC1 = real(A):\n") ; cs_dl_print (C1, 0) ; C2 = cs_l_real (A, 0) ; /* C2 = imag (A) */ printf ("\nC2 = imag(A):\n") ; cs_dl_print (C2, 0) ; A1 = cs_l_complex (C1, 1) ; /* A1 = complex version of C1 */ printf ("\nA1:\n") ; cs_cl_print (A1, 0) ; A2 = cs_l_complex (C2, 0) ; /* A2 = complex version of C2 (imag.) */ printf ("\nA2:\n") ; cs_cl_print (A2, 0) ; B = cs_cl_add (A1, A2, 1., -1.) ; /* B = A1 - A2 */ printf ("\nB = conj(A):\n") ; cs_cl_print (B, 0) ; cs_cl_spfree (T) ; cs_cl_spfree (A) ; cs_cl_spfree (A1) ; cs_cl_spfree (A2) ; cs_cl_spfree (B) ; cs_dl_spfree (C1) ; cs_dl_spfree (C2) ; cs_dl_spfree (Treal) ; cs_dl_spfree (Timag) ; return (0) ; } SuiteSparse/CXSparse/Demo/cs_di_demo1.c0000644001170100242450000000211010712165171016630 0ustar davisfac#include "cs.h" int main (void) { cs_di *T, *A, *Eye, *AT, *C, *D ; int i, m ; T = cs_di_load (stdin) ; /* load triplet matrix T from stdin */ printf ("T:\n") ; cs_di_print (T, 0) ; /* print T */ A = cs_di_compress (T) ; /* A = compressed-column form of T */ printf ("A:\n") ; cs_di_print (A, 0) ; /* print A */ cs_di_spfree (T) ; /* clear T */ AT = cs_di_transpose (A, 1) ; /* AT = A' */ printf ("AT:\n") ; cs_di_print (AT, 0) ; /* print AT */ m = A ? A->m : 0 ; /* m = # of rows of A */ T = cs_di_spalloc (m, m, m, 1, 1) ; /* create triplet identity matrix */ for (i = 0 ; i < m ; i++) cs_di_entry (T, i, i, 1) ; Eye = cs_di_compress (T) ; /* Eye = speye (m) */ cs_di_spfree (T) ; C = cs_di_multiply (A, AT) ; /* C = A*A' */ D = cs_di_add (C, Eye, 1, cs_di_norm (C)) ; /* D = C + Eye*norm (C,1) */ printf ("D:\n") ; cs_di_print (D, 0) ; /* print D */ cs_di_spfree (A) ; /* clear A AT C D Eye */ cs_di_spfree (AT) ; cs_di_spfree (C) ; cs_di_spfree (D) ; cs_di_spfree (Eye) ; return (0) ; } SuiteSparse/CXSparse/Demo/cs_dl_demo1.c0000644001170100242450000000211410712165171016637 0ustar davisfac#include "cs.h" int main (void) { cs_dl *T, *A, *Eye, *AT, *C, *D ; UF_long i, m ; T = cs_dl_load (stdin) ; /* load triplet matrix T from stdin */ printf ("T:\n") ; cs_dl_print (T, 0) ; /* print T */ A = cs_dl_compress (T) ; /* A = compressed-column form of T */ printf ("A:\n") ; cs_dl_print (A, 0) ; /* print A */ cs_dl_spfree (T) ; /* clear T */ AT = cs_dl_transpose (A, 1) ; /* AT = A' */ printf ("AT:\n") ; cs_dl_print (AT, 0) ; /* print AT */ m = A ? A->m : 0 ; /* m = # of rows of A */ T = cs_dl_spalloc (m, m, m, 1, 1) ; /* create triplet identity matrix */ for (i = 0 ; i < m ; i++) cs_dl_entry (T, i, i, 1) ; Eye = cs_dl_compress (T) ; /* Eye = speye (m) */ cs_dl_spfree (T) ; C = cs_dl_multiply (A, AT) ; /* C = A*A' */ D = cs_dl_add (C, Eye, 1, cs_dl_norm (C)) ; /* D = C + Eye*norm (C,1) */ printf ("D:\n") ; cs_dl_print (D, 0) ; /* print D */ cs_dl_spfree (A) ; /* clear A AT C D Eye */ cs_dl_spfree (AT) ; cs_dl_spfree (C) ; cs_dl_spfree (D) ; cs_dl_spfree (Eye) ; return (0) ; } SuiteSparse/CXSparse/Demo/cs_ci_demo1.c0000644001170100242450000000211010712165171016627 0ustar davisfac#include "cs.h" int main (void) { cs_ci *T, *A, *Eye, *AT, *C, *D ; int i, m ; T = cs_ci_load (stdin) ; /* load triplet matrix T from stdin */ printf ("T:\n") ; cs_ci_print (T, 0) ; /* print T */ A = cs_ci_compress (T) ; /* A = compressed-column form of T */ printf ("A:\n") ; cs_ci_print (A, 0) ; /* print A */ cs_ci_spfree (T) ; /* clear T */ AT = cs_ci_transpose (A, 1) ; /* AT = A' */ printf ("AT:\n") ; cs_ci_print (AT, 0) ; /* print AT */ m = A ? A->m : 0 ; /* m = # of rows of A */ T = cs_ci_spalloc (m, m, m, 1, 1) ; /* create triplet identity matrix */ for (i = 0 ; i < m ; i++) cs_ci_entry (T, i, i, 1) ; Eye = cs_ci_compress (T) ; /* Eye = speye (m) */ cs_ci_spfree (T) ; C = cs_ci_multiply (A, AT) ; /* C = A*A' */ D = cs_ci_add (C, Eye, 1, cs_ci_norm (C)) ; /* D = C + Eye*norm (C,1) */ printf ("D:\n") ; cs_ci_print (D, 0) ; /* print D */ cs_ci_spfree (A) ; /* clear A AT C D Eye */ cs_ci_spfree (AT) ; cs_ci_spfree (C) ; cs_ci_spfree (D) ; cs_ci_spfree (Eye) ; return (0) ; } SuiteSparse/CXSparse/Demo/cs_cl_demo1.c0000644001170100242450000000211410712165171016636 0ustar davisfac#include "cs.h" int main (void) { cs_cl *T, *A, *Eye, *AT, *C, *D ; UF_long i, m ; T = cs_cl_load (stdin) ; /* load triplet matrix T from stdin */ printf ("T:\n") ; cs_cl_print (T, 0) ; /* print T */ A = cs_cl_compress (T) ; /* A = compressed-column form of T */ printf ("A:\n") ; cs_cl_print (A, 0) ; /* print A */ cs_cl_spfree (T) ; /* clear T */ AT = cs_cl_transpose (A, 1) ; /* AT = A' */ printf ("AT:\n") ; cs_cl_print (AT, 0) ; /* print AT */ m = A ? A->m : 0 ; /* m = # of rows of A */ T = cs_cl_spalloc (m, m, m, 1, 1) ; /* create triplet identity matrix */ for (i = 0 ; i < m ; i++) cs_cl_entry (T, i, i, 1) ; Eye = cs_cl_compress (T) ; /* Eye = speye (m) */ cs_cl_spfree (T) ; C = cs_cl_multiply (A, AT) ; /* C = A*A' */ D = cs_cl_add (C, Eye, 1, cs_cl_norm (C)) ; /* D = C + Eye*norm (C,1) */ printf ("D:\n") ; cs_cl_print (D, 0) ; /* print D */ cs_cl_spfree (A) ; /* clear A AT C D Eye */ cs_cl_spfree (AT) ; cs_cl_spfree (C) ; cs_cl_spfree (D) ; cs_cl_spfree (Eye) ; return (0) ; } SuiteSparse/CXSparse/Demo/cs_di_demo2.c0000644001170100242450000000032610712165171016640 0ustar davisfac#include "cs_di_demo.h" /* cs_di_demo2: read a matrix and solve a linear system */ int main (void) { problem *Prob = get_problem (stdin, 1e-14) ; demo2 (Prob) ; free_problem (Prob) ; return (0) ; } SuiteSparse/CXSparse/Demo/cs_dl_demo2.c0000644001170100242450000000032610712165171016643 0ustar davisfac#include "cs_dl_demo.h" /* cs_dl_demo2: read a matrix and solve a linear system */ int main (void) { problem *Prob = get_problem (stdin, 1e-14) ; demo2 (Prob) ; free_problem (Prob) ; return (0) ; } SuiteSparse/CXSparse/Demo/cs_ci_demo2.c0000644001170100242450000000032610712165171016637 0ustar davisfac#include "cs_ci_demo.h" /* cs_ci_demo2: read a matrix and solve a linear system */ int main (void) { problem *Prob = get_problem (stdin, 1e-14) ; demo2 (Prob) ; free_problem (Prob) ; return (0) ; } SuiteSparse/CXSparse/Demo/cs_cl_demo2.c0000644001170100242450000000032610712165171016642 0ustar davisfac#include "cs_cl_demo.h" /* cs_cl_demo2: read a matrix and solve a linear system */ int main (void) { problem *Prob = get_problem (stdin, 1e-14) ; demo2 (Prob) ; free_problem (Prob) ; return (0) ; } SuiteSparse/CXSparse/Demo/cs_di_demo3.c0000644001170100242450000000033210712165171016636 0ustar davisfac#include "cs_di_demo.h" /* cs_di_demo3: read a matrix and test Cholesky update/downdate */ int main (void) { problem *Prob = get_problem (stdin, 0) ; demo3 (Prob) ; free_problem (Prob) ; return (0) ; } SuiteSparse/CXSparse/Demo/cs_dl_demo3.c0000644001170100242450000000033210712165171016641 0ustar davisfac#include "cs_dl_demo.h" /* cs_dl_demo3: read a matrix and test Cholesky update/downdate */ int main (void) { problem *Prob = get_problem (stdin, 0) ; demo3 (Prob) ; free_problem (Prob) ; return (0) ; } SuiteSparse/CXSparse/Demo/cs_ci_demo3.c0000644001170100242450000000033210712165171016635 0ustar davisfac#include "cs_ci_demo.h" /* cs_ci_demo3: read a matrix and test Cholesky update/downdate */ int main (void) { problem *Prob = get_problem (stdin, 0) ; demo3 (Prob) ; free_problem (Prob) ; return (0) ; } SuiteSparse/CXSparse/Demo/cs_cl_demo3.c0000644001170100242450000000033210712165171016640 0ustar davisfac#include "cs_cl_demo.h" /* cs_cl_demo3: read a matrix and test Cholesky update/downdate */ int main (void) { problem *Prob = get_problem (stdin, 0) ; demo3 (Prob) ; free_problem (Prob) ; return (0) ; } SuiteSparse/CXSparse/Demo/cs_di_demo.c0000644001170100242450000002354010712165171016561 0ustar davisfac#include "cs_di_demo.h" #include /* 1 if A is square & upper tri., -1 if square & lower tri., 0 otherwise */ static int is_sym (cs_di *A) { int is_upper, is_lower, j, p, n = A->n, m = A->m, *Ap = A->p, *Ai = A->i ; if (m != n) return (0) ; is_upper = 1 ; is_lower = 1 ; for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { if (Ai [p] > j) is_upper = 0 ; if (Ai [p] < j) is_lower = 0 ; } } return (is_upper ? 1 : (is_lower ? -1 : 0)) ; } /* true for off-diagonal entries */ static int dropdiag (int i, int j, double aij, void *other) { return (i != j) ;} /* C = A + triu(A,1)' */ static cs_di *make_sym (cs_di *A) { cs_di *AT, *C ; AT = cs_di_transpose (A, 1) ; /* AT = A' */ cs_di_fkeep (AT, &dropdiag, NULL) ; /* drop diagonal entries from AT */ C = cs_di_add (A, AT, 1, 1) ; /* C = A+AT */ cs_di_spfree (AT) ; return (C) ; } /* create a right-hand side */ static void rhs (double *x, double *b, int m) { int i ; for (i = 0 ; i < m ; i++) b [i] = 1 + ((double) i) / m ; for (i = 0 ; i < m ; i++) x [i] = b [i] ; } /* infinity-norm of x */ static double norm (double *x, int n) { int i ; double normx = 0 ; for (i = 0 ; i < n ; i++) normx = CS_MAX (normx, fabs (x [i])) ; return (normx) ; } /* compute residual, norm(A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf)) */ static void print_resid (int ok, cs_di *A, double *x, double *b, double *resid) { int i, m, n ; if (!ok) { printf (" (failed)\n") ; return ; } m = A->m ; n = A->n ; for (i = 0 ; i < m ; i++) resid [i] = -b [i] ; /* resid = -b */ cs_di_gaxpy (A, x, resid) ; /* resid = resid + A*x */ printf ("resid: %8.2e\n", norm (resid,m) / ((n == 0) ? 1 : (cs_di_norm (A) * norm (x,n) + norm (b,m)))) ; } static double tic (void) { return (clock () / (double) CLOCKS_PER_SEC) ; } static double toc (double t) { double s = tic () ; return (CS_MAX (0, s-t)) ; } static void print_order (int order) { switch (order) { case 0: printf ("natural ") ; break ; case 1: printf ("amd(A+A') ") ; break ; case 2: printf ("amd(S'*S) ") ; break ; case 3: printf ("amd(A'*A) ") ; break ; } } /* read a problem from a file */ problem *get_problem (FILE *f, double tol) { cs_di *T, *A, *C ; int sym, m, n, mn, nz1, nz2 ; problem *Prob ; Prob = cs_di_calloc (1, sizeof (problem)) ; if (!Prob) return (NULL) ; T = cs_di_load (f) ; /* load triplet matrix T from a file */ Prob->A = A = cs_di_compress (T) ; /* A = compressed-column form of T */ cs_di_spfree (T) ; /* clear T */ if (!cs_di_dupl (A)) return (free_problem (Prob)) ; /* sum up duplicates */ Prob->sym = sym = is_sym (A) ; /* determine if A is symmetric */ m = A->m ; n = A->n ; mn = CS_MAX (m,n) ; nz1 = A->p [n] ; cs_di_dropzeros (A) ; /* drop zero entries */ nz2 = A->p [n] ; if (tol > 0) cs_di_droptol (A, tol) ; /* drop tiny entries (just to test) */ Prob->C = C = sym ? make_sym (A) : A ; /* C = A + triu(A,1)', or C=A */ if (!C) return (free_problem (Prob)) ; printf ("\n--- Matrix: %d-by-%d, nnz: %d (sym: %d: nnz %d), norm: %8.2e\n", m, n, A->p [n], sym, sym ? C->p [n] : 0, cs_di_norm (C)) ; if (nz1 != nz2) printf ("zero entries dropped: %d\n", nz1 - nz2) ; if (nz2 != A->p [n]) printf ("tiny entries dropped: %d\n", nz2 - A->p [n]) ; Prob->b = cs_di_malloc (mn, sizeof (double)) ; Prob->x = cs_di_malloc (mn, sizeof (double)) ; Prob->resid = cs_di_malloc (mn, sizeof (double)) ; return ((!Prob->b || !Prob->x || !Prob->resid) ? free_problem (Prob) : Prob) ; } /* free a problem */ problem *free_problem (problem *Prob) { if (!Prob) return (NULL) ; cs_di_spfree (Prob->A) ; if (Prob->sym) cs_di_spfree (Prob->C) ; cs_di_free (Prob->b) ; cs_di_free (Prob->x) ; cs_di_free (Prob->resid) ; return (cs_di_free (Prob)) ; } /* solve a linear system using Cholesky, LU, and QR, with various orderings */ int demo2 (problem *Prob) { cs_di *A, *C ; double *b, *x, *resid, t, tol ; int k, m, n, ok, order, nb, ns, *r, *s, *rr, sprank ; cs_did *D ; if (!Prob) return (0) ; A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid; m = A->m ; n = A->n ; tol = Prob->sym ? 0.001 : 1 ; /* partial pivoting tolerance */ D = cs_di_dmperm (C, 1) ; /* randomized dmperm analysis */ if (!D) return (0) ; nb = D->nb ; r = D->r ; s = D->s ; rr = D->rr ; sprank = rr [3] ; for (ns = 0, k = 0 ; k < nb ; k++) { ns += ((r [k+1] == r [k]+1) && (s [k+1] == s [k]+1)) ; } printf ("blocks: %d singletons: %d structural rank: %d\n", nb, ns, sprank) ; cs_di_dfree (D) ; for (order = 0 ; order <= 3 ; order += 3) /* natural and amd(A'*A) */ { if (!order && m > 1000) continue ; printf ("QR ") ; print_order (order) ; rhs (x, b, m) ; /* compute right-hand side */ t = tic () ; ok = cs_di_qrsol (order, C, x) ; /* min norm(Ax-b) with QR */ printf ("time: %8.2f ", toc (t)) ; print_resid (ok, C, x, b, resid) ; /* print residual */ } if (m != n || sprank < n) return (1) ; /* return if rect. or singular*/ for (order = 0 ; order <= 3 ; order++) /* try all orderings */ { if (!order && m > 1000) continue ; printf ("LU ") ; print_order (order) ; rhs (x, b, m) ; /* compute right-hand side */ t = tic () ; ok = cs_di_lusol (order, C, x, tol) ; /* solve Ax=b with LU */ printf ("time: %8.2f ", toc (t)) ; print_resid (ok, C, x, b, resid) ; /* print residual */ } if (!Prob->sym) return (1) ; for (order = 0 ; order <= 1 ; order++) /* natural and amd(A+A') */ { if (!order && m > 1000) continue ; printf ("Chol ") ; print_order (order) ; rhs (x, b, m) ; /* compute right-hand side */ t = tic () ; ok = cs_di_cholsol (order, C, x) ; /* solve Ax=b with Cholesky */ printf ("time: %8.2f ", toc (t)) ; print_resid (ok, C, x, b, resid) ; /* print residual */ } return (1) ; } /* free workspace for demo3 */ static int done3 (int ok, cs_dis *S, cs_din *N, double *y, cs_di *W, cs_di *E, int *p) { cs_di_sfree (S) ; cs_di_nfree (N) ; cs_di_free (y) ; cs_di_spfree (W) ; cs_di_spfree (E) ; cs_di_free (p) ; return (ok) ; } /* Cholesky update/downdate */ int demo3 (problem *Prob) { cs_di *A, *C, *W = NULL, *WW, *WT, *E = NULL, *W2 ; int n, k, *Li, *Lp, *Wi, *Wp, p1, p2, *p = NULL, ok ; double *b, *x, *resid, *y = NULL, *Lx, *Wx, s, t, t1 ; cs_dis *S = NULL ; cs_din *N = NULL ; if (!Prob || !Prob->sym || Prob->A->n == 0) return (0) ; A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid; n = A->n ; if (!Prob->sym || n == 0) return (1) ; rhs (x, b, n) ; /* compute right-hand side */ printf ("\nchol then update/downdate ") ; print_order (1) ; y = cs_di_malloc (n, sizeof (double)) ; t = tic () ; S = cs_di_schol (1, C) ; /* symbolic Chol, amd(A+A') */ printf ("\nsymbolic chol time %8.2f\n", toc (t)) ; t = tic () ; N = cs_di_chol (C, S) ; /* numeric Cholesky */ printf ("numeric chol time %8.2f\n", toc (t)) ; if (!S || !N || !y) return (done3 (0, S, N, y, W, E, p)) ; t = tic () ; cs_di_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_di_lsolve (N->L, y) ; /* y = L\y */ cs_di_ltsolve (N->L, y) ; /* y = L'\y */ cs_di_pvec (S->pinv, y, x, n) ; /* x = P'*y */ printf ("solve chol time %8.2f\n", toc (t)) ; printf ("original: ") ; print_resid (1, C, x, b, resid) ; /* print residual */ k = n/2 ; /* construct W */ W = cs_di_spalloc (n, 1, n, 1, 0) ; if (!W) return (done3 (0, S, N, y, W, E, p)) ; Lp = N->L->p ; Li = N->L->i ; Lx = N->L->x ; Wp = W->p ; Wi = W->i ; Wx = W->x ; Wp [0] = 0 ; p1 = Lp [k] ; Wp [1] = Lp [k+1] - p1 ; s = Lx [p1] ; srand (1) ; for ( ; p1 < Lp [k+1] ; p1++) { p2 = p1 - Lp [k] ; Wi [p2] = Li [p1] ; Wx [p2] = s * rand () / ((double) RAND_MAX) ; } t = tic () ; ok = cs_di_updown (N->L, +1, W, S->parent) ; /* update: L*L'+W*W' */ t1 = toc (t) ; printf ("update: time: %8.2f\n", t1) ; if (!ok) return (done3 (0, S, N, y, W, E, p)) ; t = tic () ; cs_di_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_di_lsolve (N->L, y) ; /* y = L\y */ cs_di_ltsolve (N->L, y) ; /* y = L'\y */ cs_di_pvec (S->pinv, y, x, n) ; /* x = P'*y */ t = toc (t) ; p = cs_di_pinv (S->pinv, n) ; W2 = cs_di_permute (W, p, NULL, 1) ; /* E = C + (P'W)*(P'W)' */ WT = cs_di_transpose (W2,1) ; WW = cs_di_multiply (W2, WT) ; cs_di_spfree (WT) ; cs_di_spfree (W2) ; E = cs_di_add (C, WW, 1, 1) ; cs_di_spfree (WW) ; if (!E || !p) return (done3 (0, S, N, y, W, E, p)) ; printf ("update: time: %8.2f (incl solve) ", t1+t) ; print_resid (1, E, x, b, resid) ; /* print residual */ cs_di_nfree (N) ; /* clear N */ t = tic () ; N = cs_di_chol (E, S) ; /* numeric Cholesky */ if (!N) return (done3 (0, S, N, y, W, E, p)) ; cs_di_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_di_lsolve (N->L, y) ; /* y = L\y */ cs_di_ltsolve (N->L, y) ; /* y = L'\y */ cs_di_pvec (S->pinv, y, x, n) ; /* x = P'*y */ t = toc (t) ; printf ("rechol: time: %8.2f (incl solve) ", t) ; print_resid (1, E, x, b, resid) ; /* print residual */ t = tic () ; ok = cs_di_updown (N->L, -1, W, S->parent) ; /* downdate: L*L'-W*W' */ t1 = toc (t) ; if (!ok) return (done3 (0, S, N, y, W, E, p)) ; printf ("downdate: time: %8.2f\n", t1) ; t = tic () ; cs_di_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_di_lsolve (N->L, y) ; /* y = L\y */ cs_di_ltsolve (N->L, y) ; /* y = L'\y */ cs_di_pvec (S->pinv, y, x, n) ; /* x = P'*y */ t = toc (t) ; printf ("downdate: time: %8.2f (incl solve) ", t1+t) ; print_resid (1, C, x, b, resid) ; /* print residual */ return (done3 (1, S, N, y, W, E, p)) ; } SuiteSparse/CXSparse/Demo/cs_dl_demo.c0000644001170100242450000002367210712165171016572 0ustar davisfac#include "cs_dl_demo.h" #include /* 1 if A is square & upper tri., -1 if square & lower tri., 0 otherwise */ static UF_long is_sym (cs_dl *A) { UF_long is_upper, is_lower, j, p, n = A->n, m = A->m, *Ap = A->p, *Ai = A->i ; if (m != n) return (0) ; is_upper = 1 ; is_lower = 1 ; for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { if (Ai [p] > j) is_upper = 0 ; if (Ai [p] < j) is_lower = 0 ; } } return (is_upper ? 1 : (is_lower ? -1 : 0)) ; } /* true for off-diagonal entries */ static UF_long dropdiag (UF_long i, UF_long j, double aij, void *other) { return (i != j) ;} /* C = A + triu(A,1)' */ static cs_dl *make_sym (cs_dl *A) { cs_dl *AT, *C ; AT = cs_dl_transpose (A, 1) ; /* AT = A' */ cs_dl_fkeep (AT, &dropdiag, NULL) ; /* drop diagonal entries from AT */ C = cs_dl_add (A, AT, 1, 1) ; /* C = A+AT */ cs_dl_spfree (AT) ; return (C) ; } /* create a right-hand side */ static void rhs (double *x, double *b, UF_long m) { UF_long i ; for (i = 0 ; i < m ; i++) b [i] = 1 + ((double) i) / m ; for (i = 0 ; i < m ; i++) x [i] = b [i] ; } /* infinity-norm of x */ static double norm (double *x, UF_long n) { UF_long i ; double normx = 0 ; for (i = 0 ; i < n ; i++) normx = CS_MAX (normx, fabs (x [i])) ; return (normx) ; } /* compute residual, norm(A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf)) */ static void print_resid (UF_long ok, cs_dl *A, double *x, double *b, double *resid) { UF_long i, m, n ; if (!ok) { printf (" (failed)\n") ; return ; } m = A->m ; n = A->n ; for (i = 0 ; i < m ; i++) resid [i] = -b [i] ; /* resid = -b */ cs_dl_gaxpy (A, x, resid) ; /* resid = resid + A*x */ printf ("resid: %8.2e\n", norm (resid,m) / ((n == 0) ? 1 : (cs_dl_norm (A) * norm (x,n) + norm (b,m)))) ; } static double tic (void) { return (clock () / (double) CLOCKS_PER_SEC) ; } static double toc (double t) { double s = tic () ; return (CS_MAX (0, s-t)) ; } static void print_order (UF_long order) { switch (order) { case 0: printf ("natural ") ; break ; case 1: printf ("amd(A+A') ") ; break ; case 2: printf ("amd(S'*S) ") ; break ; case 3: printf ("amd(A'*A) ") ; break ; } } /* read a problem from a file */ problem *get_problem (FILE *f, double tol) { cs_dl *T, *A, *C ; UF_long sym, m, n, mn, nz1, nz2 ; problem *Prob ; Prob = cs_dl_calloc (1, sizeof (problem)) ; if (!Prob) return (NULL) ; T = cs_dl_load (f) ; /* load triplet matrix T from a file */ Prob->A = A = cs_dl_compress (T) ; /* A = compressed-column form of T */ cs_dl_spfree (T) ; /* clear T */ if (!cs_dl_dupl (A)) return (free_problem (Prob)) ; /* sum up duplicates */ Prob->sym = sym = is_sym (A) ; /* determine if A is symmetric */ m = A->m ; n = A->n ; mn = CS_MAX (m,n) ; nz1 = A->p [n] ; cs_dl_dropzeros (A) ; /* drop zero entries */ nz2 = A->p [n] ; if (tol > 0) cs_dl_droptol (A, tol) ; /* drop tiny entries (just to test) */ Prob->C = C = sym ? make_sym (A) : A ; /* C = A + triu(A,1)', or C=A */ if (!C) return (free_problem (Prob)) ; printf ("\n--- Matrix: %ld-by-%ld, nnz: %ld (sym: %ld: nnz %ld), norm: %8.2e\n", m, n, A->p [n], sym, sym ? C->p [n] : 0, cs_dl_norm (C)) ; if (nz1 != nz2) printf ("zero entries dropped: %ld\n", nz1 - nz2) ; if (nz2 != A->p [n]) printf ("tiny entries dropped: %ld\n", nz2 - A->p [n]) ; Prob->b = cs_dl_malloc (mn, sizeof (double)) ; Prob->x = cs_dl_malloc (mn, sizeof (double)) ; Prob->resid = cs_dl_malloc (mn, sizeof (double)) ; return ((!Prob->b || !Prob->x || !Prob->resid) ? free_problem (Prob) : Prob) ; } /* free a problem */ problem *free_problem (problem *Prob) { if (!Prob) return (NULL) ; cs_dl_spfree (Prob->A) ; if (Prob->sym) cs_dl_spfree (Prob->C) ; cs_dl_free (Prob->b) ; cs_dl_free (Prob->x) ; cs_dl_free (Prob->resid) ; return (cs_dl_free (Prob)) ; } /* solve a linear system using Cholesky, LU, and QR, with various orderings */ UF_long demo2 (problem *Prob) { cs_dl *A, *C ; double *b, *x, *resid, t, tol ; UF_long k, m, n, ok, order, nb, ns, *r, *s, *rr, sprank ; cs_dld *D ; if (!Prob) return (0) ; A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid; m = A->m ; n = A->n ; tol = Prob->sym ? 0.001 : 1 ; /* partial pivoting tolerance */ D = cs_dl_dmperm (C, 1) ; /* randomized dmperm analysis */ if (!D) return (0) ; nb = D->nb ; r = D->r ; s = D->s ; rr = D->rr ; sprank = rr [3] ; for (ns = 0, k = 0 ; k < nb ; k++) { ns += ((r [k+1] == r [k]+1) && (s [k+1] == s [k]+1)) ; } printf ("blocks: %ld singletons: %ld structural rank: %ld\n", nb, ns, sprank) ; cs_dl_dfree (D) ; for (order = 0 ; order <= 3 ; order += 3) /* natural and amd(A'*A) */ { if (!order && m > 1000) continue ; printf ("QR ") ; print_order (order) ; rhs (x, b, m) ; /* compute right-hand side */ t = tic () ; ok = cs_dl_qrsol (order, C, x) ; /* min norm(Ax-b) with QR */ printf ("time: %8.2f ", toc (t)) ; print_resid (ok, C, x, b, resid) ; /* print residual */ } if (m != n || sprank < n) return (1) ; /* return if rect. or singular*/ for (order = 0 ; order <= 3 ; order++) /* try all orderings */ { if (!order && m > 1000) continue ; printf ("LU ") ; print_order (order) ; rhs (x, b, m) ; /* compute right-hand side */ t = tic () ; ok = cs_dl_lusol (order, C, x, tol) ; /* solve Ax=b with LU */ printf ("time: %8.2f ", toc (t)) ; print_resid (ok, C, x, b, resid) ; /* print residual */ } if (!Prob->sym) return (1) ; for (order = 0 ; order <= 1 ; order++) /* natural and amd(A+A') */ { if (!order && m > 1000) continue ; printf ("Chol ") ; print_order (order) ; rhs (x, b, m) ; /* compute right-hand side */ t = tic () ; ok = cs_dl_cholsol (order, C, x) ; /* solve Ax=b with Cholesky */ printf ("time: %8.2f ", toc (t)) ; print_resid (ok, C, x, b, resid) ; /* print residual */ } return (1) ; } /* free workspace for demo3 */ static UF_long done3 (UF_long ok, cs_dls *S, cs_dln *N, double *y, cs_dl *W, cs_dl *E, UF_long *p) { cs_dl_sfree (S) ; cs_dl_nfree (N) ; cs_dl_free (y) ; cs_dl_spfree (W) ; cs_dl_spfree (E) ; cs_dl_free (p) ; return (ok) ; } /* Cholesky update/downdate */ UF_long demo3 (problem *Prob) { cs_dl *A, *C, *W = NULL, *WW, *WT, *E = NULL, *W2 ; UF_long n, k, *Li, *Lp, *Wi, *Wp, p1, p2, *p = NULL, ok ; double *b, *x, *resid, *y = NULL, *Lx, *Wx, s, t, t1 ; cs_dls *S = NULL ; cs_dln *N = NULL ; if (!Prob || !Prob->sym || Prob->A->n == 0) return (0) ; A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid; n = A->n ; if (!Prob->sym || n == 0) return (1) ; rhs (x, b, n) ; /* compute right-hand side */ printf ("\nchol then update/downdate ") ; print_order (1) ; y = cs_dl_malloc (n, sizeof (double)) ; t = tic () ; S = cs_dl_schol (1, C) ; /* symbolic Chol, amd(A+A') */ printf ("\nsymbolic chol time %8.2f\n", toc (t)) ; t = tic () ; N = cs_dl_chol (C, S) ; /* numeric Cholesky */ printf ("numeric chol time %8.2f\n", toc (t)) ; if (!S || !N || !y) return (done3 (0, S, N, y, W, E, p)) ; t = tic () ; cs_dl_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_dl_lsolve (N->L, y) ; /* y = L\y */ cs_dl_ltsolve (N->L, y) ; /* y = L'\y */ cs_dl_pvec (S->pinv, y, x, n) ; /* x = P'*y */ printf ("solve chol time %8.2f\n", toc (t)) ; printf ("original: ") ; print_resid (1, C, x, b, resid) ; /* print residual */ k = n/2 ; /* construct W */ W = cs_dl_spalloc (n, 1, n, 1, 0) ; if (!W) return (done3 (0, S, N, y, W, E, p)) ; Lp = N->L->p ; Li = N->L->i ; Lx = N->L->x ; Wp = W->p ; Wi = W->i ; Wx = W->x ; Wp [0] = 0 ; p1 = Lp [k] ; Wp [1] = Lp [k+1] - p1 ; s = Lx [p1] ; srand (1) ; for ( ; p1 < Lp [k+1] ; p1++) { p2 = p1 - Lp [k] ; Wi [p2] = Li [p1] ; Wx [p2] = s * rand () / ((double) RAND_MAX) ; } t = tic () ; ok = cs_dl_updown (N->L, +1, W, S->parent) ; /* update: L*L'+W*W' */ t1 = toc (t) ; printf ("update: time: %8.2f\n", t1) ; if (!ok) return (done3 (0, S, N, y, W, E, p)) ; t = tic () ; cs_dl_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_dl_lsolve (N->L, y) ; /* y = L\y */ cs_dl_ltsolve (N->L, y) ; /* y = L'\y */ cs_dl_pvec (S->pinv, y, x, n) ; /* x = P'*y */ t = toc (t) ; p = cs_dl_pinv (S->pinv, n) ; W2 = cs_dl_permute (W, p, NULL, 1) ; /* E = C + (P'W)*(P'W)' */ WT = cs_dl_transpose (W2,1) ; WW = cs_dl_multiply (W2, WT) ; cs_dl_spfree (WT) ; cs_dl_spfree (W2) ; E = cs_dl_add (C, WW, 1, 1) ; cs_dl_spfree (WW) ; if (!E || !p) return (done3 (0, S, N, y, W, E, p)) ; printf ("update: time: %8.2f (incl solve) ", t1+t) ; print_resid (1, E, x, b, resid) ; /* print residual */ cs_dl_nfree (N) ; /* clear N */ t = tic () ; N = cs_dl_chol (E, S) ; /* numeric Cholesky */ if (!N) return (done3 (0, S, N, y, W, E, p)) ; cs_dl_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_dl_lsolve (N->L, y) ; /* y = L\y */ cs_dl_ltsolve (N->L, y) ; /* y = L'\y */ cs_dl_pvec (S->pinv, y, x, n) ; /* x = P'*y */ t = toc (t) ; printf ("rechol: time: %8.2f (incl solve) ", t) ; print_resid (1, E, x, b, resid) ; /* print residual */ t = tic () ; ok = cs_dl_updown (N->L, -1, W, S->parent) ; /* downdate: L*L'-W*W' */ t1 = toc (t) ; if (!ok) return (done3 (0, S, N, y, W, E, p)) ; printf ("downdate: time: %8.2f\n", t1) ; t = tic () ; cs_dl_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_dl_lsolve (N->L, y) ; /* y = L\y */ cs_dl_ltsolve (N->L, y) ; /* y = L'\y */ cs_dl_pvec (S->pinv, y, x, n) ; /* x = P'*y */ t = toc (t) ; printf ("downdate: time: %8.2f (incl solve) ", t1+t) ; print_resid (1, C, x, b, resid) ; /* print residual */ return (done3 (1, S, N, y, W, E, p)) ; } SuiteSparse/CXSparse/Demo/cs_ci_demo.c0000644001170100242450000002371210712165171016561 0ustar davisfac#include "cs_ci_demo.h" #include /* 1 if A is square & upper tri., -1 if square & lower tri., 0 otherwise */ static int is_sym (cs_ci *A) { int is_upper, is_lower, j, p, n = A->n, m = A->m, *Ap = A->p, *Ai = A->i ; if (m != n) return (0) ; is_upper = 1 ; is_lower = 1 ; for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { if (Ai [p] > j) is_upper = 0 ; if (Ai [p] < j) is_lower = 0 ; } } return (is_upper ? 1 : (is_lower ? -1 : 0)) ; } /* true for off-diagonal entries */ static int dropdiag (int i, int j, cs_complex_t aij, void *other) { return (i != j) ;} /* C = A + triu(A,1)' */ static cs_ci *make_sym (cs_ci *A) { cs_ci *AT, *C ; AT = cs_ci_transpose (A, 1) ; /* AT = A' */ cs_ci_fkeep (AT, &dropdiag, NULL) ; /* drop diagonal entries from AT */ C = cs_ci_add (A, AT, 1, 1) ; /* C = A+AT */ cs_ci_spfree (AT) ; return (C) ; } /* create a right-hand side */ static void rhs (cs_complex_t *x, cs_complex_t *b, int m) { int i ; for (i = 0 ; i < m ; i++) b [i] = 1 + ((double) i) / m ; for (i = 0 ; i < m ; i++) x [i] = b [i] ; } /* infinity-norm of x */ static double norm (cs_complex_t *x, int n) { int i ; double normx = 0 ; for (i = 0 ; i < n ; i++) normx = CS_MAX (normx, cabs (x [i])) ; return (normx) ; } /* compute residual, norm(A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf)) */ static void print_resid (int ok, cs_ci *A, cs_complex_t *x, cs_complex_t *b, cs_complex_t *resid) { int i, m, n ; if (!ok) { printf (" (failed)\n") ; return ; } m = A->m ; n = A->n ; for (i = 0 ; i < m ; i++) resid [i] = -b [i] ; /* resid = -b */ cs_ci_gaxpy (A, x, resid) ; /* resid = resid + A*x */ printf ("resid: %8.2e\n", norm (resid,m) / ((n == 0) ? 1 : (cs_ci_norm (A) * norm (x,n) + norm (b,m)))) ; } static double tic (void) { return (clock () / (double) CLOCKS_PER_SEC) ; } static double toc (double t) { double s = tic () ; return (CS_MAX (0, s-t)) ; } static void print_order (int order) { switch (order) { case 0: printf ("natural ") ; break ; case 1: printf ("amd(A+A') ") ; break ; case 2: printf ("amd(S'*S) ") ; break ; case 3: printf ("amd(A'*A) ") ; break ; } } /* read a problem from a file */ problem *get_problem (FILE *f, double tol) { cs_ci *T, *A, *C ; int sym, m, n, mn, nz1, nz2 ; problem *Prob ; Prob = cs_ci_calloc (1, sizeof (problem)) ; if (!Prob) return (NULL) ; T = cs_ci_load (f) ; /* load triplet matrix T from a file */ Prob->A = A = cs_ci_compress (T) ; /* A = compressed-column form of T */ cs_ci_spfree (T) ; /* clear T */ if (!cs_ci_dupl (A)) return (free_problem (Prob)) ; /* sum up duplicates */ Prob->sym = sym = is_sym (A) ; /* determine if A is symmetric */ m = A->m ; n = A->n ; mn = CS_MAX (m,n) ; nz1 = A->p [n] ; cs_ci_dropzeros (A) ; /* drop zero entries */ nz2 = A->p [n] ; if (tol > 0) cs_ci_droptol (A, tol) ; /* drop tiny entries (just to test) */ Prob->C = C = sym ? make_sym (A) : A ; /* C = A + triu(A,1)', or C=A */ if (!C) return (free_problem (Prob)) ; printf ("\n--- Matrix: %d-by-%d, nnz: %d (sym: %d: nnz %d), norm: %8.2e\n", m, n, A->p [n], sym, sym ? C->p [n] : 0, cs_ci_norm (C)) ; if (nz1 != nz2) printf ("zero entries dropped: %d\n", nz1 - nz2) ; if (nz2 != A->p [n]) printf ("tiny entries dropped: %d\n", nz2 - A->p [n]) ; Prob->b = cs_ci_malloc (mn, sizeof (cs_complex_t)) ; Prob->x = cs_ci_malloc (mn, sizeof (cs_complex_t)) ; Prob->resid = cs_ci_malloc (mn, sizeof (cs_complex_t)) ; return ((!Prob->b || !Prob->x || !Prob->resid) ? free_problem (Prob) : Prob) ; } /* free a problem */ problem *free_problem (problem *Prob) { if (!Prob) return (NULL) ; cs_ci_spfree (Prob->A) ; if (Prob->sym) cs_ci_spfree (Prob->C) ; cs_ci_free (Prob->b) ; cs_ci_free (Prob->x) ; cs_ci_free (Prob->resid) ; return (cs_ci_free (Prob)) ; } /* solve a linear system using Cholesky, LU, and QR, with various orderings */ int demo2 (problem *Prob) { cs_ci *A, *C ; cs_complex_t *b, *x, *resid ; double t, tol ; int k, m, n, ok, order, nb, ns, *r, *s, *rr, sprank ; cs_cid *D ; if (!Prob) return (0) ; A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid; m = A->m ; n = A->n ; tol = Prob->sym ? 0.001 : 1 ; /* partial pivoting tolerance */ D = cs_ci_dmperm (C, 1) ; /* randomized dmperm analysis */ if (!D) return (0) ; nb = D->nb ; r = D->r ; s = D->s ; rr = D->rr ; sprank = rr [3] ; for (ns = 0, k = 0 ; k < nb ; k++) { ns += ((r [k+1] == r [k]+1) && (s [k+1] == s [k]+1)) ; } printf ("blocks: %d singletons: %d structural rank: %d\n", nb, ns, sprank) ; cs_ci_dfree (D) ; for (order = 0 ; order <= 3 ; order += 3) /* natural and amd(A'*A) */ { if (!order && m > 1000) continue ; printf ("QR ") ; print_order (order) ; rhs (x, b, m) ; /* compute right-hand side */ t = tic () ; ok = cs_ci_qrsol (order, C, x) ; /* min norm(Ax-b) with QR */ printf ("time: %8.2f ", toc (t)) ; print_resid (ok, C, x, b, resid) ; /* print residual */ } if (m != n || sprank < n) return (1) ; /* return if rect. or singular*/ for (order = 0 ; order <= 3 ; order++) /* try all orderings */ { if (!order && m > 1000) continue ; printf ("LU ") ; print_order (order) ; rhs (x, b, m) ; /* compute right-hand side */ t = tic () ; ok = cs_ci_lusol (order, C, x, tol) ; /* solve Ax=b with LU */ printf ("time: %8.2f ", toc (t)) ; print_resid (ok, C, x, b, resid) ; /* print residual */ } if (!Prob->sym) return (1) ; for (order = 0 ; order <= 1 ; order++) /* natural and amd(A+A') */ { if (!order && m > 1000) continue ; printf ("Chol ") ; print_order (order) ; rhs (x, b, m) ; /* compute right-hand side */ t = tic () ; ok = cs_ci_cholsol (order, C, x) ; /* solve Ax=b with Cholesky */ printf ("time: %8.2f ", toc (t)) ; print_resid (ok, C, x, b, resid) ; /* print residual */ } return (1) ; } /* free workspace for demo3 */ static int done3 (int ok, cs_cis *S, cs_cin *N, cs_complex_t *y, cs_ci *W, cs_ci *E, int *p) { cs_ci_sfree (S) ; cs_ci_nfree (N) ; cs_ci_free (y) ; cs_ci_spfree (W) ; cs_ci_spfree (E) ; cs_ci_free (p) ; return (ok) ; } /* Cholesky update/downdate */ int demo3 (problem *Prob) { cs_ci *A, *C, *W = NULL, *WW, *WT, *E = NULL, *W2 ; int n, k, *Li, *Lp, *Wi, *Wp, p1, p2, *p = NULL, ok ; cs_complex_t *b, *x, *resid, *y = NULL, *Lx, *Wx, s ; double t, t1 ; cs_cis *S = NULL ; cs_cin *N = NULL ; if (!Prob || !Prob->sym || Prob->A->n == 0) return (0) ; A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid; n = A->n ; if (!Prob->sym || n == 0) return (1) ; rhs (x, b, n) ; /* compute right-hand side */ printf ("\nchol then update/downdate ") ; print_order (1) ; y = cs_ci_malloc (n, sizeof (cs_complex_t)) ; t = tic () ; S = cs_ci_schol (1, C) ; /* symbolic Chol, amd(A+A') */ printf ("\nsymbolic chol time %8.2f\n", toc (t)) ; t = tic () ; N = cs_ci_chol (C, S) ; /* numeric Cholesky */ printf ("numeric chol time %8.2f\n", toc (t)) ; if (!S || !N || !y) return (done3 (0, S, N, y, W, E, p)) ; t = tic () ; cs_ci_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_ci_lsolve (N->L, y) ; /* y = L\y */ cs_ci_ltsolve (N->L, y) ; /* y = L'\y */ cs_ci_pvec (S->pinv, y, x, n) ; /* x = P'*y */ printf ("solve chol time %8.2f\n", toc (t)) ; printf ("original: ") ; print_resid (1, C, x, b, resid) ; /* print residual */ k = n/2 ; /* construct W */ W = cs_ci_spalloc (n, 1, n, 1, 0) ; if (!W) return (done3 (0, S, N, y, W, E, p)) ; Lp = N->L->p ; Li = N->L->i ; Lx = N->L->x ; Wp = W->p ; Wi = W->i ; Wx = W->x ; Wp [0] = 0 ; p1 = Lp [k] ; Wp [1] = Lp [k+1] - p1 ; s = Lx [p1] ; srand (1) ; for ( ; p1 < Lp [k+1] ; p1++) { p2 = p1 - Lp [k] ; Wi [p2] = Li [p1] ; Wx [p2] = s * rand () / ((double) RAND_MAX) ; } t = tic () ; ok = cs_ci_updown (N->L, +1, W, S->parent) ; /* update: L*L'+W*W' */ t1 = toc (t) ; printf ("update: time: %8.2f\n", t1) ; if (!ok) return (done3 (0, S, N, y, W, E, p)) ; t = tic () ; cs_ci_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_ci_lsolve (N->L, y) ; /* y = L\y */ cs_ci_ltsolve (N->L, y) ; /* y = L'\y */ cs_ci_pvec (S->pinv, y, x, n) ; /* x = P'*y */ t = toc (t) ; p = cs_ci_pinv (S->pinv, n) ; W2 = cs_ci_permute (W, p, NULL, 1) ; /* E = C + (P'W)*(P'W)' */ WT = cs_ci_transpose (W2,1) ; WW = cs_ci_multiply (W2, WT) ; cs_ci_spfree (WT) ; cs_ci_spfree (W2) ; E = cs_ci_add (C, WW, 1, 1) ; cs_ci_spfree (WW) ; if (!E || !p) return (done3 (0, S, N, y, W, E, p)) ; printf ("update: time: %8.2f (incl solve) ", t1+t) ; print_resid (1, E, x, b, resid) ; /* print residual */ cs_ci_nfree (N) ; /* clear N */ t = tic () ; N = cs_ci_chol (E, S) ; /* numeric Cholesky */ if (!N) return (done3 (0, S, N, y, W, E, p)) ; cs_ci_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_ci_lsolve (N->L, y) ; /* y = L\y */ cs_ci_ltsolve (N->L, y) ; /* y = L'\y */ cs_ci_pvec (S->pinv, y, x, n) ; /* x = P'*y */ t = toc (t) ; printf ("rechol: time: %8.2f (incl solve) ", t) ; print_resid (1, E, x, b, resid) ; /* print residual */ t = tic () ; ok = cs_ci_updown (N->L, -1, W, S->parent) ; /* downdate: L*L'-W*W' */ t1 = toc (t) ; if (!ok) return (done3 (0, S, N, y, W, E, p)) ; printf ("downdate: time: %8.2f\n", t1) ; t = tic () ; cs_ci_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_ci_lsolve (N->L, y) ; /* y = L\y */ cs_ci_ltsolve (N->L, y) ; /* y = L'\y */ cs_ci_pvec (S->pinv, y, x, n) ; /* x = P'*y */ t = toc (t) ; printf ("downdate: time: %8.2f (incl solve) ", t1+t) ; print_resid (1, C, x, b, resid) ; /* print residual */ return (done3 (1, S, N, y, W, E, p)) ; } SuiteSparse/CXSparse/Demo/cs_cl_demo.c0000644001170100242450000002404410712165171016563 0ustar davisfac#include "cs_cl_demo.h" #include /* 1 if A is square & upper tri., -1 if square & lower tri., 0 otherwise */ static UF_long is_sym (cs_cl *A) { UF_long is_upper, is_lower, j, p, n = A->n, m = A->m, *Ap = A->p, *Ai = A->i ; if (m != n) return (0) ; is_upper = 1 ; is_lower = 1 ; for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { if (Ai [p] > j) is_upper = 0 ; if (Ai [p] < j) is_lower = 0 ; } } return (is_upper ? 1 : (is_lower ? -1 : 0)) ; } /* true for off-diagonal entries */ static UF_long dropdiag (UF_long i, UF_long j, cs_complex_t aij, void *other) { return (i != j) ;} /* C = A + triu(A,1)' */ static cs_cl *make_sym (cs_cl *A) { cs_cl *AT, *C ; AT = cs_cl_transpose (A, 1) ; /* AT = A' */ cs_cl_fkeep (AT, &dropdiag, NULL) ; /* drop diagonal entries from AT */ C = cs_cl_add (A, AT, 1, 1) ; /* C = A+AT */ cs_cl_spfree (AT) ; return (C) ; } /* create a right-hand side */ static void rhs (cs_complex_t *x, cs_complex_t *b, UF_long m) { UF_long i ; for (i = 0 ; i < m ; i++) b [i] = 1 + ((double) i) / m ; for (i = 0 ; i < m ; i++) x [i] = b [i] ; } /* infinity-norm of x */ static double norm (cs_complex_t *x, UF_long n) { UF_long i ; double normx = 0 ; for (i = 0 ; i < n ; i++) normx = CS_MAX (normx, cabs (x [i])) ; return (normx) ; } /* compute residual, norm(A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf)) */ static void print_resid (UF_long ok, cs_cl *A, cs_complex_t *x, cs_complex_t *b, cs_complex_t *resid) { UF_long i, m, n ; if (!ok) { printf (" (failed)\n") ; return ; } m = A->m ; n = A->n ; for (i = 0 ; i < m ; i++) resid [i] = -b [i] ; /* resid = -b */ cs_cl_gaxpy (A, x, resid) ; /* resid = resid + A*x */ printf ("resid: %8.2e\n", norm (resid,m) / ((n == 0) ? 1 : (cs_cl_norm (A) * norm (x,n) + norm (b,m)))) ; } static double tic (void) { return (clock () / (double) CLOCKS_PER_SEC) ; } static double toc (double t) { double s = tic () ; return (CS_MAX (0, s-t)) ; } static void print_order (UF_long order) { switch (order) { case 0: printf ("natural ") ; break ; case 1: printf ("amd(A+A') ") ; break ; case 2: printf ("amd(S'*S) ") ; break ; case 3: printf ("amd(A'*A) ") ; break ; } } /* read a problem from a file */ problem *get_problem (FILE *f, double tol) { cs_cl *T, *A, *C ; UF_long sym, m, n, mn, nz1, nz2 ; problem *Prob ; Prob = cs_cl_calloc (1, sizeof (problem)) ; if (!Prob) return (NULL) ; T = cs_cl_load (f) ; /* load triplet matrix T from a file */ Prob->A = A = cs_cl_compress (T) ; /* A = compressed-column form of T */ cs_cl_spfree (T) ; /* clear T */ if (!cs_cl_dupl (A)) return (free_problem (Prob)) ; /* sum up duplicates */ Prob->sym = sym = is_sym (A) ; /* determine if A is symmetric */ m = A->m ; n = A->n ; mn = CS_MAX (m,n) ; nz1 = A->p [n] ; cs_cl_dropzeros (A) ; /* drop zero entries */ nz2 = A->p [n] ; if (tol > 0) cs_cl_droptol (A, tol) ; /* drop tiny entries (just to test) */ Prob->C = C = sym ? make_sym (A) : A ; /* C = A + triu(A,1)', or C=A */ if (!C) return (free_problem (Prob)) ; printf ("\n--- Matrix: %ld-by-%ld, nnz: %ld (sym: %ld: nnz %ld), norm: %8.2e\n", m, n, A->p [n], sym, sym ? C->p [n] : 0, cs_cl_norm (C)) ; if (nz1 != nz2) printf ("zero entries dropped: %ld\n", nz1 - nz2) ; if (nz2 != A->p [n]) printf ("tiny entries dropped: %ld\n", nz2 - A->p [n]) ; Prob->b = cs_cl_malloc (mn, sizeof (cs_complex_t)) ; Prob->x = cs_cl_malloc (mn, sizeof (cs_complex_t)) ; Prob->resid = cs_cl_malloc (mn, sizeof (cs_complex_t)) ; return ((!Prob->b || !Prob->x || !Prob->resid) ? free_problem (Prob) : Prob) ; } /* free a problem */ problem *free_problem (problem *Prob) { if (!Prob) return (NULL) ; cs_cl_spfree (Prob->A) ; if (Prob->sym) cs_cl_spfree (Prob->C) ; cs_cl_free (Prob->b) ; cs_cl_free (Prob->x) ; cs_cl_free (Prob->resid) ; return (cs_cl_free (Prob)) ; } /* solve a linear system using Cholesky, LU, and QR, with various orderings */ UF_long demo2 (problem *Prob) { cs_cl *A, *C ; cs_complex_t *b, *x, *resid ; double t, tol ; UF_long k, m, n, ok, order, nb, ns, *r, *s, *rr, sprank ; cs_cld *D ; if (!Prob) return (0) ; A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid; m = A->m ; n = A->n ; tol = Prob->sym ? 0.001 : 1 ; /* partial pivoting tolerance */ D = cs_cl_dmperm (C, 1) ; /* randomized dmperm analysis */ if (!D) return (0) ; nb = D->nb ; r = D->r ; s = D->s ; rr = D->rr ; sprank = rr [3] ; for (ns = 0, k = 0 ; k < nb ; k++) { ns += ((r [k+1] == r [k]+1) && (s [k+1] == s [k]+1)) ; } printf ("blocks: %ld singletons: %ld structural rank: %ld\n", nb, ns, sprank) ; cs_cl_dfree (D) ; for (order = 0 ; order <= 3 ; order += 3) /* natural and amd(A'*A) */ { if (!order && m > 1000) continue ; printf ("QR ") ; print_order (order) ; rhs (x, b, m) ; /* compute right-hand side */ t = tic () ; ok = cs_cl_qrsol (order, C, x) ; /* min norm(Ax-b) with QR */ printf ("time: %8.2f ", toc (t)) ; print_resid (ok, C, x, b, resid) ; /* print residual */ } if (m != n || sprank < n) return (1) ; /* return if rect. or singular*/ for (order = 0 ; order <= 3 ; order++) /* try all orderings */ { if (!order && m > 1000) continue ; printf ("LU ") ; print_order (order) ; rhs (x, b, m) ; /* compute right-hand side */ t = tic () ; ok = cs_cl_lusol (order, C, x, tol) ; /* solve Ax=b with LU */ printf ("time: %8.2f ", toc (t)) ; print_resid (ok, C, x, b, resid) ; /* print residual */ } if (!Prob->sym) return (1) ; for (order = 0 ; order <= 1 ; order++) /* natural and amd(A+A') */ { if (!order && m > 1000) continue ; printf ("Chol ") ; print_order (order) ; rhs (x, b, m) ; /* compute right-hand side */ t = tic () ; ok = cs_cl_cholsol (order, C, x) ; /* solve Ax=b with Cholesky */ printf ("time: %8.2f ", toc (t)) ; print_resid (ok, C, x, b, resid) ; /* print residual */ } return (1) ; } /* free workspace for demo3 */ static UF_long done3 (UF_long ok, cs_cls *S, cs_cln *N, cs_complex_t *y, cs_cl *W, cs_cl *E, UF_long *p) { cs_cl_sfree (S) ; cs_cl_nfree (N) ; cs_cl_free (y) ; cs_cl_spfree (W) ; cs_cl_spfree (E) ; cs_cl_free (p) ; return (ok) ; } /* Cholesky update/downdate */ UF_long demo3 (problem *Prob) { cs_cl *A, *C, *W = NULL, *WW, *WT, *E = NULL, *W2 ; UF_long n, k, *Li, *Lp, *Wi, *Wp, p1, p2, *p = NULL, ok ; cs_complex_t *b, *x, *resid, *y = NULL, *Lx, *Wx, s ; double t, t1 ; cs_cls *S = NULL ; cs_cln *N = NULL ; if (!Prob || !Prob->sym || Prob->A->n == 0) return (0) ; A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid; n = A->n ; if (!Prob->sym || n == 0) return (1) ; rhs (x, b, n) ; /* compute right-hand side */ printf ("\nchol then update/downdate ") ; print_order (1) ; y = cs_cl_malloc (n, sizeof (cs_complex_t)) ; t = tic () ; S = cs_cl_schol (1, C) ; /* symbolic Chol, amd(A+A') */ printf ("\nsymbolic chol time %8.2f\n", toc (t)) ; t = tic () ; N = cs_cl_chol (C, S) ; /* numeric Cholesky */ printf ("numeric chol time %8.2f\n", toc (t)) ; if (!S || !N || !y) return (done3 (0, S, N, y, W, E, p)) ; t = tic () ; cs_cl_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_cl_lsolve (N->L, y) ; /* y = L\y */ cs_cl_ltsolve (N->L, y) ; /* y = L'\y */ cs_cl_pvec (S->pinv, y, x, n) ; /* x = P'*y */ printf ("solve chol time %8.2f\n", toc (t)) ; printf ("original: ") ; print_resid (1, C, x, b, resid) ; /* print residual */ k = n/2 ; /* construct W */ W = cs_cl_spalloc (n, 1, n, 1, 0) ; if (!W) return (done3 (0, S, N, y, W, E, p)) ; Lp = N->L->p ; Li = N->L->i ; Lx = N->L->x ; Wp = W->p ; Wi = W->i ; Wx = W->x ; Wp [0] = 0 ; p1 = Lp [k] ; Wp [1] = Lp [k+1] - p1 ; s = Lx [p1] ; srand (1) ; for ( ; p1 < Lp [k+1] ; p1++) { p2 = p1 - Lp [k] ; Wi [p2] = Li [p1] ; Wx [p2] = s * rand () / ((double) RAND_MAX) ; } t = tic () ; ok = cs_cl_updown (N->L, +1, W, S->parent) ; /* update: L*L'+W*W' */ t1 = toc (t) ; printf ("update: time: %8.2f\n", t1) ; if (!ok) return (done3 (0, S, N, y, W, E, p)) ; t = tic () ; cs_cl_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_cl_lsolve (N->L, y) ; /* y = L\y */ cs_cl_ltsolve (N->L, y) ; /* y = L'\y */ cs_cl_pvec (S->pinv, y, x, n) ; /* x = P'*y */ t = toc (t) ; p = cs_cl_pinv (S->pinv, n) ; W2 = cs_cl_permute (W, p, NULL, 1) ; /* E = C + (P'W)*(P'W)' */ WT = cs_cl_transpose (W2,1) ; WW = cs_cl_multiply (W2, WT) ; cs_cl_spfree (WT) ; cs_cl_spfree (W2) ; E = cs_cl_add (C, WW, 1, 1) ; cs_cl_spfree (WW) ; if (!E || !p) return (done3 (0, S, N, y, W, E, p)) ; printf ("update: time: %8.2f (incl solve) ", t1+t) ; print_resid (1, E, x, b, resid) ; /* print residual */ cs_cl_nfree (N) ; /* clear N */ t = tic () ; N = cs_cl_chol (E, S) ; /* numeric Cholesky */ if (!N) return (done3 (0, S, N, y, W, E, p)) ; cs_cl_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_cl_lsolve (N->L, y) ; /* y = L\y */ cs_cl_ltsolve (N->L, y) ; /* y = L'\y */ cs_cl_pvec (S->pinv, y, x, n) ; /* x = P'*y */ t = toc (t) ; printf ("rechol: time: %8.2f (incl solve) ", t) ; print_resid (1, E, x, b, resid) ; /* print residual */ t = tic () ; ok = cs_cl_updown (N->L, -1, W, S->parent) ; /* downdate: L*L'-W*W' */ t1 = toc (t) ; if (!ok) return (done3 (0, S, N, y, W, E, p)) ; printf ("downdate: time: %8.2f\n", t1) ; t = tic () ; cs_cl_ipvec (S->pinv, b, y, n) ; /* y = P*b */ cs_cl_lsolve (N->L, y) ; /* y = L\y */ cs_cl_ltsolve (N->L, y) ; /* y = L'\y */ cs_cl_pvec (S->pinv, y, x, n) ; /* x = P'*y */ t = toc (t) ; printf ("downdate: time: %8.2f (incl solve) ", t1+t) ; print_resid (1, C, x, b, resid) ; /* print residual */ return (done3 (1, S, N, y, W, E, p)) ; } SuiteSparse/CXSparse/Demo/cs_di_demo.h0000644001170100242450000000045210712165171016563 0ustar davisfac#include "cs.h" typedef struct problem_struct { cs_di *A ; cs_di *C ; int sym ; double *x ; double *b ; double *resid ; } problem ; problem *get_problem (FILE *f, double tol) ; int demo2 (problem *Prob) ; int demo3 (problem *Prob) ; problem *free_problem (problem *Prob) ; SuiteSparse/CXSparse/Demo/cs_dl_demo.h0000644001170100242450000000046610712165171016573 0ustar davisfac#include "cs.h" typedef struct problem_struct { cs_dl *A ; cs_dl *C ; UF_long sym ; double *x ; double *b ; double *resid ; } problem ; problem *get_problem (FILE *f, double tol) ; UF_long demo2 (problem *Prob) ; UF_long demo3 (problem *Prob) ; problem *free_problem (problem *Prob) ; SuiteSparse/CXSparse/Demo/cs_ci_demo.h0000644001170100242450000000047410712165171016566 0ustar davisfac#include "cs.h" typedef struct problem_struct { cs_ci *A ; cs_ci *C ; int sym ; cs_complex_t *x ; cs_complex_t *b ; cs_complex_t *resid ; } problem ; problem *get_problem (FILE *f, double tol) ; int demo2 (problem *Prob) ; int demo3 (problem *Prob) ; problem *free_problem (problem *Prob) ; SuiteSparse/CXSparse/Demo/cs_cl_demo.h0000644001170100242450000000051010712165171016560 0ustar davisfac#include "cs.h" typedef struct problem_struct { cs_cl *A ; cs_cl *C ; UF_long sym ; cs_complex_t *x ; cs_complex_t *b ; cs_complex_t *resid ; } problem ; problem *get_problem (FILE *f, double tol) ; UF_long demo2 (problem *Prob) ; UF_long demo3 (problem *Prob) ; problem *free_problem (problem *Prob) ; SuiteSparse/CXSparse/Tcov/0000755001170100242450000000000010617167237014364 5ustar davisfacSuiteSparse/CXSparse/Tcov/nil0000644001170100242450000000000010325754634015056 0ustar davisfacSuiteSparse/CXSparse/Tcov/covs0000755001170100242450000000033110336471716015257 0ustar davisfac#!/bin/csh echo '=================================================================' foreach file (*.?cov) echo $file grep "#####" $file echo '=================================================================' end SuiteSparse/CXSparse/Tcov/zero0000644001170100242450000000000610375445021015251 0ustar davisfac0 0 0 SuiteSparse/CXSparse/Tcov/cov.awk0000644001170100242450000000026610325730035015647 0ustar davisfac/cannot/ /function/ { f = $8 } /file/ { f = $8 } /lines/ { k = match ($1, "%") ; p = substr ($1, 1, k-1) ; if ((p+0) != 100) { printf "%8s %s\n", p, f } } SuiteSparse/CXSparse/Tcov/Makefile0000644001170100242450000002751610617167237016037 0ustar davisfac # To run with valgrind: V = # V = valgrind -q # Linux test coverage CC = gcc CFLAGS = -O -g -fprofile-arcs -ftest-coverage \ -Wall -W -Wshadow -Wmissing-prototypes -Wstrict-prototypes \ -Wredundant-decls -Wnested-externs -Wdisabled-optimization -ansi \ -Wno-unused-parameter -Werror -I../Include -I../Demo -I../../UFconfig run: all run_convert run_di run_dl run_ci run_cl ./covall all: cs_demo1_di cs_demo2_di cs_demo3_di cstcov_test_di \ cs_demo1_dl cs_demo2_dl cs_demo3_dl cstcov_test_dl \ cs_demo1_ci cs_demo2_ci cs_demo3_ci cstcov_test_ci \ cs_demo1_cl cs_demo2_cl cs_demo3_cl cstcov_test_cl \ cs_idemo cs_ldemo CS_DI = cs_add_di.o cs_amd_di.o cs_chol_di.o cs_cholsol_di.o cs_counts_di.o \ cs_cumsum_di.o cs_droptol_di.o cs_dropzeros_di.o cs_dupl_di.o \ cs_entry_di.o cs_etree_di.o cs_fkeep_di.o cs_gaxpy_di.o cs_happly_di.o \ cs_house_di.o cs_ipvec_di.o cs_lsolve_di.o cs_ltsolve_di.o cs_lu_di.o \ cs_lusol_di.o cs_util_di.o cs_multiply_di.o cs_permute_di.o \ cs_pinv_di.o cs_post_di.o cs_pvec_di.o cs_qr_di.o cs_qrsol_di.o \ cs_scatter_di.o cs_schol_di.o cs_sqr_di.o cs_symperm_di.o cs_tdfs_di.o \ cs_transpose_di.o cs_compress_di.o cs_usolve_di.o cs_scc_di.o \ cs_maxtrans_di.o cs_dmperm_di.o cs_updown_di.o cs_print_di.o \ cs_norm_di.o cs_load_di.o cs_dfs_di.o cstcov_malloc_test_di.o \ cs_utsolve_di.o cs_reach_di.o cs_spsolve_di.o \ cs_leaf_di.o cs_ereach_di.o cs_randperm_di.o CS_DL = cs_add_dl.o cs_amd_dl.o cs_chol_dl.o cs_cholsol_dl.o cs_counts_dl.o \ cs_cumsum_dl.o cs_droptol_dl.o cs_dropzeros_dl.o cs_dupl_dl.o \ cs_entry_dl.o cs_etree_dl.o cs_fkeep_dl.o cs_gaxpy_dl.o cs_happly_dl.o \ cs_house_dl.o cs_ipvec_dl.o cs_lsolve_dl.o cs_ltsolve_dl.o cs_lu_dl.o \ cs_lusol_dl.o cs_util_dl.o cs_multiply_dl.o cs_permute_dl.o \ cs_pinv_dl.o cs_post_dl.o cs_pvec_dl.o cs_qr_dl.o cs_qrsol_dl.o \ cs_scatter_dl.o cs_schol_dl.o cs_sqr_dl.o cs_symperm_dl.o cs_tdfs_dl.o \ cs_transpose_dl.o cs_compress_dl.o cs_usolve_dl.o cs_scc_dl.o \ cs_maxtrans_dl.o cs_dmperm_dl.o cs_updown_dl.o cs_print_dl.o \ cs_norm_dl.o cs_load_dl.o cs_dfs_dl.o cstcov_malloc_test_dl.o \ cs_utsolve_dl.o cs_reach_dl.o cs_spsolve_dl.o \ cs_leaf_dl.o cs_ereach_dl.o cs_randperm_dl.o CS_CI = cs_add_ci.o cs_amd_ci.o cs_chol_ci.o cs_cholsol_ci.o cs_counts_ci.o \ cs_cumsum_ci.o cs_droptol_ci.o cs_dropzeros_ci.o cs_dupl_ci.o \ cs_entry_ci.o cs_etree_ci.o cs_fkeep_ci.o cs_gaxpy_ci.o cs_happly_ci.o \ cs_house_ci.o cs_ipvec_ci.o cs_lsolve_ci.o cs_ltsolve_ci.o cs_lu_ci.o \ cs_lusol_ci.o cs_util_ci.o cs_multiply_ci.o cs_permute_ci.o \ cs_pinv_ci.o cs_post_ci.o cs_pvec_ci.o cs_qr_ci.o cs_qrsol_ci.o \ cs_scatter_ci.o cs_schol_ci.o cs_sqr_ci.o cs_symperm_ci.o cs_tdfs_ci.o \ cs_transpose_ci.o cs_compress_ci.o cs_usolve_ci.o cs_scc_ci.o \ cs_maxtrans_ci.o cs_dmperm_ci.o cs_updown_ci.o cs_print_ci.o \ cs_norm_ci.o cs_load_ci.o cs_dfs_ci.o cstcov_malloc_test_ci.o \ cs_utsolve_ci.o cs_reach_ci.o cs_spsolve_ci.o \ cs_leaf_ci.o cs_ereach_ci.o cs_randperm_ci.o CS_CL = cs_add_cl.o cs_amd_cl.o cs_chol_cl.o cs_cholsol_cl.o cs_counts_cl.o \ cs_cumsum_cl.o cs_droptol_cl.o cs_dropzeros_cl.o cs_dupl_cl.o \ cs_entry_cl.o cs_etree_cl.o cs_fkeep_cl.o cs_gaxpy_cl.o cs_happly_cl.o \ cs_house_cl.o cs_ipvec_cl.o cs_lsolve_cl.o cs_ltsolve_cl.o cs_lu_cl.o \ cs_lusol_cl.o cs_util_cl.o cs_multiply_cl.o cs_permute_cl.o \ cs_pinv_cl.o cs_post_cl.o cs_pvec_cl.o cs_qr_cl.o cs_qrsol_cl.o \ cs_scatter_cl.o cs_schol_cl.o cs_sqr_cl.o cs_symperm_cl.o cs_tdfs_cl.o \ cs_transpose_cl.o cs_compress_cl.o cs_usolve_cl.o cs_scc_cl.o \ cs_maxtrans_cl.o cs_dmperm_cl.o cs_updown_cl.o cs_print_cl.o \ cs_norm_cl.o cs_load_cl.o cs_dfs_cl.o cstcov_malloc_test_cl.o \ cs_utsolve_cl.o cs_reach_cl.o cs_spsolve_cl.o \ cs_leaf_cl.o cs_ereach_cl.o cs_randperm_cl.o OBJ = $(CS_DI) $(CS_DL) $(CS_CI) $(CS_CL) cs_convert.o $(OBJ): ../Include/cs.h cstcov_malloc_test.h Makefile .PRECIOUS: %demo.c %demo1.c %demo2.c %demo3.c cs_%.c cs_%_ci.c cs_%_cl.c cs_%_di.c cs_%_dl.c cstcov_%.c %demo.c: - ln -s ../Demo/$*demo.c %demo1.c: - ln -s ../Demo/$*demo1.c %demo2.c: - ln -s ../Demo/$*demo2.c %demo3.c: - ln -s ../Demo/$*demo3.c cstcov_%.c: - ln -s cstcov_malloc_test.c cstcov_$*.c cs_convert.c: - ln -s ../Source/cs_convert.c cs_%_ci.c: - ln -s ../Source/cs_$*.c cs_$*_ci.c cs_%_di.c: - ln -s ../Source/cs_$*.c cs_$*_di.c cs_%_dl.c: - ln -s ../Source/cs_$*.c cs_$*_dl.c cs_%_cl.c: - ln -s ../Source/cs_$*.c cs_$*_cl.c %_di.o: %_di.c $(CC) $(CFLAGS) -c $< %_dl.o: %_dl.c $(CC) $(CFLAGS) -DCS_LONG -c $< %_ci.o: %_ci.c $(CC) $(CFLAGS) -DCS_COMPLEX -c $< %_cl.o: %_cl.c $(CC) $(CFLAGS) -DCS_LONG -DCS_COMPLEX -c $< cs_idemo: $(OBJ) cs_idemo.c $(CC) $(CFLAGS) -o cs_idemo cs_idemo.c $(OBJ) -lm cs_ldemo: $(OBJ) cs_ldemo.c $(CC) $(CFLAGS) -o cs_ldemo cs_ldemo.c $(OBJ) -lm cs_demo1_di: $(CS_DI) cs_di_demo1.c $(CC) $(CFLAGS) -o cs_demo1_di cs_di_demo1.c $(CS_DI) -lm cs_demo2_di: $(CS_DI) cs_di_demo2.c cs_di_demo.c $(CC) $(CFLAGS) -o cs_demo2_di cs_di_demo2.c cs_di_demo.c $(CS_DI) -lm cs_demo3_di: $(CS_DI) cs_di_demo3.c cs_di_demo.c $(CC) $(CFLAGS) -o cs_demo3_di cs_di_demo3.c cs_di_demo.c $(CS_DI) -lm cstcov_test_di: $(CS_DI) cstcov_test.c cs_di_demo.c $(CC) $(CFLAGS) -o cstcov_test_di cstcov_test.c cs_di_demo.c $(CS_DI) -lm cs_demo1_dl: $(CS_DL) cs_dl_demo1.c $(CC) $(CFLAGS) -DCS_LONG -o cs_demo1_dl cs_dl_demo1.c $(CS_DL) -lm cs_demo2_dl: $(CS_DL) cs_dl_demo2.c cs_dl_demo.c $(CC) $(CFLAGS) -DCS_LONG -o cs_demo2_dl cs_dl_demo2.c cs_dl_demo.c $(CS_DL) -lm cs_demo3_dl: $(CS_DL) cs_dl_demo3.c cs_dl_demo.c $(CC) $(CFLAGS) -DCS_LONG -o cs_demo3_dl cs_dl_demo3.c cs_dl_demo.c $(CS_DL) -lm cstcov_test_dl: $(CS_DL) cstcov_test.c cs_dl_demo.c $(CC) $(CFLAGS) -DCS_LONG -o cstcov_test_dl cstcov_test.c cs_dl_demo.c $(CS_DL) -lm cs_demo1_ci: $(CS_CI) cs_ci_demo1.c $(CC) $(CFLAGS) -DCS_COMPLEX -o cs_demo1_ci cs_ci_demo1.c $(CS_CI) -lm cs_demo2_ci: $(CS_CI) cs_ci_demo2.c cs_ci_demo.c $(CC) $(CFLAGS) -DCS_COMPLEX -o cs_demo2_ci cs_ci_demo2.c cs_ci_demo.c $(CS_CI) -lm cs_demo3_ci: $(CS_CI) cs_ci_demo3.c cs_ci_demo.c $(CC) $(CFLAGS) -DCS_COMPLEX -o cs_demo3_ci cs_ci_demo3.c cs_ci_demo.c $(CS_CI) -lm cstcov_test_ci: $(CS_CI) cstcov_test.c cs_ci_demo.c $(CC) $(CFLAGS) -DCS_COMPLEX -o cstcov_test_ci cstcov_test.c cs_ci_demo.c $(CS_CI) -lm cs_demo1_cl: $(CS_CL) cs_cl_demo1.c $(CC) $(CFLAGS) -DCS_LONG -DCS_COMPLEX -o cs_demo1_cl cs_cl_demo1.c $(CS_CL) -lm cs_demo2_cl: $(CS_CL) cs_cl_demo2.c cs_cl_demo.c $(CC) $(CFLAGS) -DCS_LONG -DCS_COMPLEX -o cs_demo2_cl cs_cl_demo2.c cs_cl_demo.c $(CS_CL) -lm cs_demo3_cl: $(CS_CL) cs_cl_demo3.c cs_cl_demo.c $(CC) $(CFLAGS) -DCS_LONG -DCS_COMPLEX -o cs_demo3_cl cs_cl_demo3.c cs_cl_demo.c $(CS_CL) -lm cstcov_test_cl: $(CS_CL) cstcov_test.c cs_cl_demo.c $(CC) $(CFLAGS) -DCS_LONG -DCS_COMPLEX -o cstcov_test_cl cstcov_test.c cs_cl_demo.c $(CS_CL) -lm run_convert: cs_idemo cs_ldemo - $(V) ./cs_idemo < ../Matrix/t2 - $(V) ./cs_ldemo < ../Matrix/t2 run_di: cs_demo1_di cs_demo2_di cs_demo3_di cstcov_test_di - $(V) ./cs_demo1_di < ../Matrix/t1 - $(V) ./cs_demo1_di < nil - $(V) ./cs_demo1_di < zero - $(V) ./cs_demo2_di < nil - $(V) ./cs_demo2_di < zero - $(V) ./cs_demo2_di < ../Matrix/t1 - $(V) ./cs_demo2_di < ../Matrix/bcsstk01 - $(V) ./cs_demo2_di < ../Matrix/fs_183_1 - $(V) ./cs_demo2_di < ../Matrix/west0067 - $(V) ./cs_demo2_di < ../Matrix/lp_afiro - $(V) ./cs_demo2_di < ../Matrix/ash219 - $(V) ./cs_demo2_di < ../Matrix/mbeacxc - $(V) ./cs_demo2_di < ../Matrix/bcsstk16 - $(V) ./cs_demo2_di < ../Matrix/ibm32a - $(V) ./cs_demo2_di < ../Matrix/ibm32b - $(V) ./cs_demo3_di < nil - $(V) ./cs_demo3_di < ../Matrix/bcsstk01 - $(V) ./cs_demo3_di < ../Matrix/bcsstk16 - $(V) ./cstcov_test_di nil > test_di_nil.out - $(V) ./cstcov_test_di zero > test_di_zero.out - $(V) ./cstcov_test_di ../Matrix/t1 > test_di_t1.out - $(V) ./cstcov_test_di ../Matrix/bcsstk01 > test_di_k1.out - $(V) ./cstcov_test_di ../Matrix/fs_183_1 > test_di_fs.out - $(V) ./cstcov_test_di ../Matrix/west0067 > test_di_we.out - $(V) ./cstcov_test_di ../Matrix/ash219 > test_di_ash.out - $(V) ./cstcov_test_di ../Matrix/lp_afiro > test_di_afiro.out run_dl: cs_demo1_dl cs_demo2_dl cs_demo3_dl cstcov_test_dl - $(V) ./cs_demo1_dl < ../Matrix/t1 - $(V) ./cs_demo1_dl < nil - $(V) ./cs_demo1_dl < zero - $(V) ./cs_demo2_dl < nil - $(V) ./cs_demo2_dl < zero - $(V) ./cs_demo2_dl < ../Matrix/t1 - $(V) ./cs_demo2_dl < ../Matrix/bcsstk01 - $(V) ./cs_demo2_dl < ../Matrix/fs_183_1 - $(V) ./cs_demo2_dl < ../Matrix/west0067 - $(V) ./cs_demo2_dl < ../Matrix/lp_afiro - $(V) ./cs_demo2_dl < ../Matrix/ash219 - $(V) ./cs_demo2_dl < ../Matrix/mbeacxc - $(V) ./cs_demo2_dl < ../Matrix/bcsstk16 - $(V) ./cs_demo2_dl < ../Matrix/ibm32a - $(V) ./cs_demo2_dl < ../Matrix/ibm32b - $(V) ./cs_demo3_dl < nil - $(V) ./cs_demo3_dl < ../Matrix/bcsstk01 - $(V) ./cs_demo3_dl < ../Matrix/bcsstk16 - $(V) ./cstcov_test_dl nil > test_dl_nil.out - $(V) ./cstcov_test_dl zero > test_dl_zero.out - $(V) ./cstcov_test_dl ../Matrix/t1 > test_dl_t1.out - $(V) ./cstcov_test_dl ../Matrix/bcsstk01 > test_dl_k1.out - $(V) ./cstcov_test_dl ../Matrix/fs_183_1 > test_dl_fs.out - $(V) ./cstcov_test_dl ../Matrix/west0067 > test_dl_we.out - $(V) ./cstcov_test_dl ../Matrix/ash219 > test_dl_ash.out - $(V) ./cstcov_test_dl ../Matrix/lp_afiro > test_dl_afiro.out run_ci: cs_demo1_ci cs_demo2_ci cs_demo3_ci cstcov_test_ci - $(V) ./cs_demo1_ci < ../Matrix/t2 - $(V) ./cs_demo2_ci < ../Matrix/t2 - $(V) ./cs_demo1_ci < czero - $(V) ./cs_demo2_ci < czero - $(V) ./cs_demo1_ci < ../Matrix/t3 - $(V) ./cs_demo2_ci < ../Matrix/t3 - $(V) ./cs_demo1_ci < ../Matrix/t4 - $(V) ./cs_demo2_ci < ../Matrix/t4 - $(V) ./cs_demo2_ci < ../Matrix/c_west0067 - $(V) ./cs_demo2_ci < ../Matrix/c_mbeacxc - $(V) ./cs_demo2_ci < ../Matrix/c_ibm32a - $(V) ./cs_demo2_ci < ../Matrix/c_ibm32b - $(V) ./cs_demo2_ci < ../Matrix/young1c - $(V) ./cs_demo2_ci < ../Matrix/qc324 - $(V) ./cs_demo2_ci < ../Matrix/neumann - $(V) ./cs_demo2_ci < ../Matrix/c4 - $(V) ./cs_demo3_ci < ../Matrix/c4 - $(V) ./cs_demo2_ci < ../Matrix/mhd1280b - $(V) ./cs_demo3_ci < ../Matrix/mhd1280b - $(V) ./cstcov_test_ci ../Matrix/t2 > test_ci_t2.out - $(V) ./cstcov_test_ci ../Matrix/young1c > test_ci_young1c.out - $(V) ./cstcov_test_ci ../Matrix/qc324 > test_ci_qc324.out - $(V) ./cstcov_test_ci ../Matrix/neumann > test_ci_neumann.out - $(V) ./cstcov_test_ci ../Matrix/mhd1280b > test_ci_mhd1280b.out run_cl: cs_demo1_cl cs_demo2_cl cs_demo3_cl cstcov_test_cl - $(V) ./cs_demo1_cl < ../Matrix/t2 - $(V) ./cs_demo2_cl < ../Matrix/t2 - $(V) ./cs_demo1_cl < czero - $(V) ./cs_demo2_cl < czero - $(V) ./cs_demo1_cl < ../Matrix/t3 - $(V) ./cs_demo2_cl < ../Matrix/t3 - $(V) ./cs_demo1_cl < ../Matrix/t4 - $(V) ./cs_demo2_cl < ../Matrix/t4 - $(V) ./cs_demo2_cl < ../Matrix/c_west0067 - $(V) ./cs_demo2_cl < ../Matrix/c_mbeacxc - $(V) ./cs_demo2_cl < ../Matrix/c_ibm32a - $(V) ./cs_demo2_cl < ../Matrix/c_ibm32b - $(V) ./cs_demo2_cl < ../Matrix/young1c - $(V) ./cs_demo2_cl < ../Matrix/qc324 - $(V) ./cs_demo2_cl < ../Matrix/neumann - $(V) ./cs_demo2_cl < ../Matrix/c4 - $(V) ./cs_demo3_cl < ../Matrix/c4 - $(V) ./cs_demo2_cl < ../Matrix/mhd1280b - $(V) ./cs_demo3_cl < ../Matrix/mhd1280b - $(V) ./cstcov_test_cl ../Matrix/t2 > test_cl_t2.out - $(V) ./cstcov_test_cl ../Matrix/young1c > test_cl_young1c.out - $(V) ./cstcov_test_cl ../Matrix/qc324 > test_cl_qc324.out - $(V) ./cstcov_test_cl ../Matrix/neumann > test_cl_neumann.out - $(V) ./cstcov_test_cl ../Matrix/mhd1280b > test_cl_mhd1280b.out readhb: readhb.f f77 -o readhb readhb.f readhb.f: - ln -s ../Demo/readhb.f clean: rm -f *.o *.bbg *.da *.gcov *.gcda *.gcno purge: distclean distclean: clean rm -f readhb *.out *.a cov.sort rm -f cs_demo1_di cs_demo2_di cs_demo3_di cstcov_test_di rm -f cs_demo1_dl cs_demo2_dl cs_demo3_dl cstcov_test_dl rm -f cs_demo1_ci cs_demo2_ci cs_demo3_ci cstcov_test_ci rm -f cs_demo1_cl cs_demo2_cl cs_demo3_cl cstcov_test_cl rm -f cs_idemo cs_ldemo rm -f cs_*.c rm -f cs*_di.c cs*_dl.c cs*_ci.c cs*_cl.c SuiteSparse/CXSparse/Tcov/covall.linux0000755001170100242450000000031110336471635016721 0ustar davisfac#!/bin/csh ./gcovs cs*.c |& awk -f cov.awk | sort -n > cov.out sort -n cov.out > cov.sort ./covs > covs.out echo -n "statments not yet tested: " grep "#####" *gcov | wc -l ./cover *v > cover.out SuiteSparse/CXSparse/Tcov/cover0000755001170100242450000000050310325730035015412 0ustar davisfac#!/bin/csh # usage: cover files echo '=================================================================' foreach file ($argv[1-]) echo $file echo '=================================================================' grep "#####" -A5 -B5 $file echo '=================================================================' end SuiteSparse/CXSparse/Tcov/gcovs0000755001170100242450000000032510325727753015434 0ustar davisfac# usage: gcovs files echo '=================================================================' foreach file ($argv[1-]) gcov -f $file echo '=================================================================' end SuiteSparse/CXSparse/Tcov/cstcov_test.c0000644001170100242450000000144210473073175017066 0ustar davisfac#include "cs_demo.h" /* cs_test: read a matrix and run cs_demo2 and cs_demo3, using malloc tests. */ #include "cstcov_malloc_test.h" int main (int argc, char **argv) { FILE *f ; problem *Prob ; int trials, ok, demo ; if (argc < 2) return (-1) ; printf ("cs_test, file: %s\n", argv [1]) ; for (demo = 2 ; demo <= 3 ; demo++) { printf ("demo: %d\n", demo) ; for (trials = 0 ; trials < 4000 ; trials++) { malloc_count = trials ; f = fopen (argv [1], "r") ; if (!f) return (-1) ; Prob = get_problem (f, (demo == 2) ? 1e-14 : 0) ; fclose (f) ; if (Prob) ok = (demo == 2) ? demo2 (Prob) : demo3 (Prob) ; free_problem (Prob) ; if (malloc_count > 0) break ; } printf ("demo %d # trials: %d\n", demo, trials) ; } return (0) ; } SuiteSparse/CXSparse/Tcov/covall0000755001170100242450000000031110325753446015564 0ustar davisfac#!/bin/csh ./gcovs cs*.c |& awk -f cov.awk | sort -n > cov.out sort -n cov.out > cov.sort ./covs > covs.out echo -n "statments not yet tested: " grep "#####" *gcov | wc -l ./cover *v > cover.out SuiteSparse/CXSparse/Tcov/covall.sol0000755001170100242450000000020710336471673016365 0ustar davisfac#!/bin/csh tcov -x cm.profile cs*.c >& /dev/null echo -n "statments not yet tested: " ./covs > covs.out grep "#####" *tcov | wc -l SuiteSparse/CXSparse/Tcov/README.txt0000644001170100242450000000131210376376004016053 0ustar davisfacCXSparse/Tcov: comprehensive test coverage for CXSparse. Requires Linux. Type "make" to compile, and then "make run" to run the tests. The test coverage is in cover.out. The test output is printed on stdout, except for cs_test (which prints its output in various *.out files). If the test is successful, the last line printed should be "statements not yet tested: 0", and all printed residuals should be small. Note that you will get warnings about unused parameters for some functions. These warnings can be safely ignored. They are parameters for functions that are passed to cs_fkeep, and all functions used in this manner must have the same calling sequence, even if some of the parameters are not used. SuiteSparse/CXSparse/Tcov/cstcov_malloc_test.c0000644001170100242450000000171110473440334020407 0ustar davisfac#include "cstcov_malloc_test.h" int malloc_count = INT_MAX ; /* wrapper for malloc */ void *cs_malloc (CS_INT n, size_t size) { if (--malloc_count < 0) return (NULL) ; /* pretend to fail */ return (malloc (CS_MAX (n,1) * size)) ; } /* wrapper for calloc */ void *cs_calloc (CS_INT n, size_t size) { if (--malloc_count < 0) return (NULL) ; /* pretend to fail */ return (calloc (CS_MAX (n,1), size)) ; } /* wrapper for free */ void *cs_free (void *p) { if (p) free (p) ; /* free p if it is not already NULL */ return (NULL) ; /* return NULL to simplify the use of cs_free */ } /* wrapper for realloc */ void *cs_realloc (void *p, CS_INT n, size_t size, CS_INT *ok) { void *pnew ; *ok = 0 ; if (--malloc_count < 0) return (p) ; /* pretend to fail */ pnew = realloc (p, CS_MAX (n,1) * size) ; /* realloc the block */ *ok = (pnew != NULL) ; return ((*ok) ? pnew : p) ; /* return original p if failure */ } SuiteSparse/CXSparse/Tcov/cstcov_malloc_test.h0000644001170100242450000000020410473440334020410 0ustar davisfac#include "cs.h" #define malloc_count CS_NAME (_malloc_count) #ifndef EXTERN #define EXTERN extern #endif EXTERN int malloc_count ; SuiteSparse/CXSparse/Tcov/czero0000644001170100242450000000001010376373611015415 0ustar davisfac0 0 0 0 SuiteSparse/CXSparse/Makefile0000644001170100242450000000067010710676627015116 0ustar davisfac# CSparse Makefile C: ( cd Lib ; $(MAKE) ) ( cd Demo ; $(MAKE) ) all: C cov library: ( cd Lib ; $(MAKE) ) cov: ( cd Tcov ; $(MAKE) ) mex: ( cd MATLAB ; $(MAKE) ) clean: ( cd Lib ; $(MAKE) clean ) ( cd Demo ; $(MAKE) clean ) ( cd Tcov ; $(MAKE) clean ) ( cd MATLAB ; $(MAKE) clean ) purge: ( cd Lib ; $(MAKE) purge ) ( cd Demo ; $(MAKE) purge ) ( cd Tcov ; $(MAKE) purge ) ( cd MATLAB ; $(MAKE) purge ) distclean: purge SuiteSparse/CXSparse/MATLAB/0000755001170100242450000000000010712370315014376 5ustar davisfacSuiteSparse/CXSparse/MATLAB/Demo/0000755001170100242450000000000010620375072015265 5ustar davisfacSuiteSparse/CXSparse/MATLAB/Demo/Contents.m0000644001170100242450000000053410620375072017242 0ustar davisfac% CXSparse MATLAB demos. % % cs_demo - run all CXSparse demos. % cs_demo1 - MATLAB version of the CSparse/Demo/cs_demo1.c program. % cs_demo2 - MATLAB version of the CSparse/Demo/cs_demo2.c program. % cs_demo3 - MATLAB version of the CSparse/Demo/cs_demo3.c program. % Example: % help cs_demo % Copyright 2006-2007, Timothy A. Davis SuiteSparse/CXSparse/MATLAB/Demo/cs_demo1.m0000644001170100242450000000342410621036577017145 0ustar davisfacfunction cs_demo1 (matrixpath) %CS_DEMO1 MATLAB version of the CSparse/Demo/cs_demo1.c program. % Uses both MATLAB functions and CSparse mexFunctions, and compares the two % results. This demo also plots the results, which the C version does not do. % % Example: % cs_demo1 % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (nargin < 1) matrixpath = [] ; end if (isempty (matrixpath)) try % older versions of MATLAB do not have an input argument to mfilename p = mfilename ('fullpath') ; t = strfind (p, filesep) ; matrixpath = [ p(1:t(end)) '../../Matrix' ] ; catch % assume we are in the C*Sparse/MATLAB/CSparse/Demo directory matrixpath = '../../Matrix' ; end end t1 = load ([matrixpath '/t1']) ; T = t1 %#ok A = sparse (T(:,1)+1, T(:,2)+1, T(:,3)) %#ok A2 = cs_sparse (T(:,1)+1, T(:,2)+1, T(:,3)) %#ok fprintf ('A difference: %g\n', norm (A-A2,1)) ; % CSparse/Demo/cs_demo1.c also clears the triplet matrix T at this point: % clear T clf subplot (2,2,1) ; cspy (A) ; title ('A', 'FontSize', 16) ; AT = A' %#ok AT2 = cs_transpose (A) %#ok fprintf ('AT difference: %g\n', norm (AT-AT2,1)) ; subplot (2,2,2) ; cspy (AT) ; title ('A''', 'FontSize', 16) ; n = size (A,2) ; I = speye (n) ; C = A*AT ; C2 = cs_multiply (A, AT) %#ok fprintf ('C difference: %g\n', norm (C-C2,1)) ; subplot (2,2,3) ; cspy (C) ; title ('C=A*A''', 'FontSize', 16) ; cnorm = norm (C,1) ; D = C + I*cnorm %#ok D2 = cs_add (C, I, 1, cnorm) %#ok fprintf ('D difference: %g\n', norm (D-D2,1)) ; subplot (2,2,4) ; cspy (D) ; title ('D=C+I*norm(C,1)', 'FontSize', 16) ; % CSparse/Demo/cs_demo1.c clears all matrices at this point: % clear A AT C D I % clear A2 AT2 C2 D2 SuiteSparse/CXSparse/MATLAB/Demo/cs_demo2.m0000644001170100242450000000205210620721047017132 0ustar davisfacfunction cs_demo2 (do_pause, matrixpath) %CS_DEMO2 MATLAB version of the CSparse/Demo/cs_demo2.c program. % Solves a linear system using Cholesky, LU, and QR, with various orderings. % % Example: % cs_demo2 % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (nargin < 2) matrixpath = [] ; end if (isempty (matrixpath)) try % older versions of MATLAB do not have an input argument to mfilename p = mfilename ('fullpath') ; t = strfind (p, filesep) ; matrixpath = [ p(1:t(end)) '../../Matrix' ] ; catch % assume we are in the C*Sparse/MATLAB/CSparse/Demo directory matrixpath = '../../Matrix' ; end end matrices = { 't1', 'HB/fs_183_1', 'HB/west0067', 'LPnetlib/lp_afiro', ... 'HB/ash219', 'HB/mbeacxc', 'HB/bcsstk01', 'HB/bcsstk16' } ; if (nargin < 1) do_pause = 1 ; end for i = 1:length(matrices) name = matrices {i} ; [C sym] = get_problem (matrixpath, name, 1e-14) ; demo2 (C, sym, name) ; if (do_pause) input ('Hit enter to continue: ') ; end end SuiteSparse/CXSparse/MATLAB/Demo/cs_demo3.m0000644001170100242450000000164110620721075017137 0ustar davisfacfunction cs_demo3 (do_pause, matrixpath) %CS_DEMO3 MATLAB version of the CSparse/Demo/cs_demo3.c program. % Cholesky update/downdate. % % Example: % cs_demo3 % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (nargin < 2) matrixpath = [] ; end if (isempty (matrixpath)) try % older versions of MATLAB do not have an input argument to mfilename p = mfilename ('fullpath') ; t = strfind (p, filesep) ; matrixpath = [ p(1:t(end)) '../../Matrix' ] ; catch % assume we are in the C*Sparse/MATLAB/CSparse/Demo directory matrixpath = '../../Matrix' ; end end matrices = { 'HB/bcsstk01', 'HB/bcsstk16' } ; if (nargin < 1) do_pause = 1 ; end for i = 1:length(matrices) name = matrices {i} ; [C sym] = get_problem (matrixpath, name, 1e-14) ; demo3 (C, sym, name) ; if (do_pause) input ('Hit enter to continue: ') ; end end SuiteSparse/CXSparse/MATLAB/Demo/cs_demo.m0000644001170100242450000000206410620723666017064 0ustar davisfacfunction cs_demo (do_pause, matrixpath) %CS_DEMO run all CXSparse demos. % cs_demo(0) will run all demos without pausing. % % Example: % cs_demo % See also: cs_demo1, cs_demo2, cs_demo3 % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse help cs_demo if (nargin < 1) do_pause = 1 ; end if (nargin < 2) matrixpath = [] ; end figure (1) clf fprintf ('\n\n-------------------------------------------------------\n') ; help cs_demo1 ; cs_demo1 (matrixpath) ; fprintf ('\n\n-------------------------------------------------------\n') ; help cs_demo2 cs_demo2 (do_pause, matrixpath) ; fprintf ('\n\n-------------------------------------------------------\n') ; help cs_demo3 cs_demo3 (do_pause, matrixpath) ; fprintf ('\n\n-------------------------------------------------------\n') ; help ex_1 ex_1 fprintf ('\n\n-------------------------------------------------------\n') ; help ex2 ex2 fprintf ('\n\n-------------------------------------------------------\n') ; help ex3 ex3 fprintf ('\nAll CXSparse demos finished.\n') ; SuiteSparse/CXSparse/MATLAB/Demo/README.txt0000644001170100242450000000010510571365661016767 0ustar davisfacDemo for MATLAB interface for CXSparse. See Contents.m for details. SuiteSparse/CXSparse/MATLAB/Demo/private/0000755001170100242450000000000010620730542016734 5ustar davisfacSuiteSparse/CXSparse/MATLAB/Demo/private/demo2.m0000644001170100242450000000457310620671165020136 0ustar davisfacfunction demo2 (C, sym, name) %DEMO2: solve a linear system using Cholesky, LU, and QR, with various orderings % % Example: % demo2 (C, 1, 'name of system') % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clf subplot (2,2,1) ; cspy (C) ; title (name, 'FontSize', 16, 'Interpreter', 'none') ; [m n] = size (C) ; [p,q,r,s,cc,rr] = cs_dmperm (C) ; subplot (2,2,3) ; cs_dmspy (C) ; subplot (2,2,2) ; ccspy (C) ; drawnow sprnk = rr (4) - 1 ; nb = length (r) - 1 ; ns = sum ((r (2:nb+1) == r (1:nb)+1) & (s (2:nb+1) == s (1:nb)+1)) ; fprintf ('blocks: %d singletons %d structural rank %d\n', nb, ns, sprnk) ; if (sprnk ~= sprank (C)) error ('sprank mismatch!') ; end if (sprnk < min (m,n)) return ; % return if structurally singular end % the following code is not in the C version of this demo: if (m == n) if (sym) try [L,p] = cs_chol (C) ; %#ok subplot (2,2,4) ; cspy (L+triu(L',1)) ; title ('L+L''') ; catch % tol = 0.001 ; [L,U,p,q] = cs_lu (C,0.001) ; %#ok subplot (2,2,4) ; cspy (L+U-speye(n)) ; title ('L+U') ; end else [L,U,p,q] = cs_lu (C) ; %#ok subplot (2,2,4) ; cspy (L+U-speye(n)) ; title ('L+U') ; end else if (m < n) [V,beta,p,R,q] = cs_qr (C') ; %#ok else [V,beta,p,R,q] = cs_qr (C) ; %#ok end subplot (2,2,4) ; cspy (V+R) ; title ('V+R') ; end drawnow % continue with the MATLAB equivalent of the C cs_demo2 program for order = [0 3] if (order == 0 & m > 1000) %#ok continue ; end fprintf ('QR ') ; print_order (order) ; b = rhs (m) ; % compute right-hand-side tic ; x = cs_qrsol (C, b, order) ; fprintf ('time %8.2f ', toc) ; print_resid (C, x, b) ; end if (m ~= n) return ; end for order = 0:3 if (order == 0 & m > 1000) %#ok continue ; end fprintf ('LU ') ; print_order (order) ; b = rhs (m) ; % compute right-hand-side tic ; x = cs_lusol (C, b, order) ; fprintf ('time %8.2f ', toc) ; print_resid (C, x, b) ; end if (sym == 0) return ; end for order = 0:1 if (order == 0 & m > 1000) %#ok continue ; end fprintf ('Chol ') ; print_order (order) ; b = rhs (m) ; % compute right-hand-side tic ; x = cs_cholsol (C, b, order) ; fprintf ('time %8.2f ', toc) ; print_resid (C, x, b) ; end SuiteSparse/CXSparse/MATLAB/Demo/private/demo3.m0000644001170100242450000000344310620671175020133 0ustar davisfacfunction demo3 (C, sym, name) %DEMO3: Cholesky update/downdate % % Example: % demo3 (C, 1, 'name of system') % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clf subplot (2,2,1) ; cspy (C) ; title (name, 'FontSize', 16, 'Interpreter', 'none') ; drawnow [m n] = size (C) ; if (m ~= n | ~sym) %#ok return ; end b = rhs (n) ; fprintf ('chol then update/downdate ') ; print_order (0) ; tic ; [L,p] = cs_chol (C) ; t = toc ; fprintf ('\nchol time: %8.2f\n', t) ; subplot (2,2,2) ; cspy (L) ; title ('L') ; drawnow tic ; x = b (p) ; x = cs_lsolve (L,x) ; x = cs_ltsolve (L,x) ; x (p) = x ; t = toc ; fprintf ('solve time: %8.2f\n', t) ; fprintf ('original: ') ; print_resid (C, x, b) ; k = fix (n/2) ; w = L(k,k) * sprand (L (:,k)) ; parent = cs_etree (C (p,p)) ; tic ; L2 = cs_updown (L, w, parent, '+') ; t1 = toc ; fprintf ('update: time: %8.2f\n', t1) ; subplot (2,2,3) ; cspy (L2) ; title ('updated L') ; subplot (2,2,4) ; cspy (L-L2) ; title ('L - updated L') ; drawnow tic ; x = b (p) ; x = cs_lsolve (L2,x) ; x = cs_ltsolve (L2,x) ; x (p) = x ; t = toc ; w2 = sparse (n,1) ; w2 (p) = w ; % w2 = P'*w wt = cs_transpose (w2) ; ww = cs_multiply (w2,wt) ; E = cs_add (C, ww, 1, 1) ; % E = C + w2*w2' ; fprintf ('update: time: %8.2f (incl solve) ', t1+t) ; print_resid (E, x, b) ; tic [L,p2] = cs_chol (E) ; x = b (p2) ; x = cs_lsolve (L,x) ; x = cs_ltsolve (L,x) ; x (p2) = x ; t = toc ; fprintf ('rechol: time: %8.2f (incl solve) ', t) ; print_resid (E, x, b) ; tic ; L3 = cs_updown (L2, w, parent, '-') ; t1 = toc ; fprintf ('downdate: time: %8.2f\n', t1) ; tic ; x = b (p) ; x = cs_lsolve (L3,x) ; x = cs_ltsolve (L3,x) ; x (p) = x ; t = toc ; fprintf ('downdate: time: %8.2f (incl solve) ', t1+t) ; print_resid (C, x, b) ; SuiteSparse/CXSparse/MATLAB/Demo/private/ex2.m0000644001170100242450000000370510620725624017622 0ustar davisfacfunction ex2 (n) %EX2: create an n-by-n 2D mesh, four different ways % Example: % ex2 % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (nargin < 1) n = 30 ; end subplot (1,2,1) ; % method 1: create an n-by-n 2D mesh for the 2nd difference operator tic ii = zeros (5*n^2, 1) ; jj = zeros (5*n^2, 1) ; xx = zeros (5*n^2, 1) ; k = 1 ; for j = 0:n-1 for i = 0:n-1 s = j*n+i + 1 ; ii (k:k+4) = [(j-1)*n+i j*n+(i-1) j*n+i j*n+(i+1) (j+1)*n+i ] + 1 ; jj (k:k+4) = [s s s s s] ; xx (k:k+4) = [-1 -1 4 -1 -1] ; k = k + 5 ; end end % remove entries beyond the boundary keep = find (ii >= 1 & ii <= n^2 & jj >= 1 & jj <= n^2) ; ii = ii (keep) ; jj = jj (keep) ; xx = xx (keep) ; A = sparse (ii,jj,xx) ; t1 = toc ; disp (t1) ; % subplot (2,2,1) ; spy (A) title (sprintf ('%d-by-%d 2D mesh\n', n, n)) ; % method 2, using no for loops tic nn = 1:n^2 ; i2 = [nn-n ; nn-1 ; nn ; nn+1 ; nn+n] ; j2 = repmat (nn, 5, 1) ; x2 = repmat ([-1 -1 4 -1 -1]', 1, n^2) ; keep = find (i2 >= 1 & i2 <= n^2 & j2 >= 1 & j2 <= n^2) ; i2 = i2 (keep) ; j2 = j2 (keep) ; x2 = x2 (keep) ; C = sparse (i2,j2,x2) ; t2 = toc ; disp (t2) ; % subplot (2,2,2) ; plot (j2) ; % title ('2D fast j2') ; disp (A-C) ; any (ii-i2) any (jj-jj) % method 3: create an n-by-n-by-n 3D mesh for the 2nd difference operator tic [A, keep, ii, jj, xx] = mesh3d1 (n) ; ii = ii (keep) ; jj = jj (keep) ; xx = xx (keep) ; t3 = toc ; disp (t3) ; tic E = sparse (ii,jj,xx) ; t3b = toc ; disp (t3b) ; subplot (1,2,2) ; spy (E) ; title (sprintf ('%d-by-%d-by-%d 3D mesh\n', n, n, n)) ; % method 4, using no for loops tic nn = 1:n^3 ; i2 = [nn-n^2 ; nn-n ; nn-1 ; nn ; nn+1 ; nn+n ; nn+n^2] ; j2 = repmat (nn, 7, 1) ; x2 = repmat ([-1 -1 -1 6 -1 -1 -1]', 1, n^3) ; keep = find (i2 >= 1 & i2 <= n^3 & j2 >= 1 & j2 <= n^3) ; i2 = i2 (keep) ; j2 = j2 (keep) ; x2 = x2 (keep) ; t4 = toc ; disp (t4) ; tic F = sparse (i2,j2,x2) ; t4b = toc ; disp (t4b) ; disp (E-F) ; SuiteSparse/CXSparse/MATLAB/Demo/private/ex3.m0000644001170100242450000000161410620372241017611 0ustar davisfacfunction ex3 %EX3: create 2D and 3D meshes using mesh2d1, mesh2d2, mesh3d1, mesh3d2. % Example: % ex3 % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse t1 = zeros (50,1) ; t2 = zeros (50,1) ; t3 = zeros (50,1) ; t4 = zeros (50,1) ; fprintf ('run times for each method, given n:\n') ; for n = 2:50 tic ; A = mesh2d1 (n) ; t1 (n) = toc ; tic B = mesh2d2 (n) ; t2 (n) = toc ; tic C = mesh3d1 (n) ; t3 (n) = toc ; tic D = mesh3d2 (n) ; t4 (n) = toc ; fprintf ('%3d: %8.3f %8.3f %8.3f %8.3f\n', n, t1(n), t2(n), t3(n), t4(n)) ; subplot (2,2,1) ; spy (A) ; title ('2D mesh, method 1') ; subplot (2,2,2) ; spy (B) ; title ('2D mesh, method 2') ; subplot (2,2,3) ; spy (C) ; title ('3D mesh, method 1') ; subplot (2,2,4) ; spy (D) ; title ('3D mesh, method 2') ; drawnow end SuiteSparse/CXSparse/MATLAB/Demo/private/rhs.m0000644001170100242450000000034710620372266017717 0ustar davisfacfunction b = rhs (m) % b = rhs (m), compute a right-hand-side % Example: % b = rhs (30) ; % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse b = ones (m,1) + (0:m-1)'/m ; SuiteSparse/CXSparse/MATLAB/Demo/private/print_order.m0000644001170100242450000000072110620372257021446 0ustar davisfacfunction print_order (order) % print_order(order) prints the ordering determined by the order parameter % Example: % print_order (0) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse switch (fix (order)) case 0 fprintf ('natural ') ; case 1 fprintf ('amd(A+A'') ') ; case 2 fprintf ('amd(S''*S) ') ; case 3 fprintf ('amd(A''*A) ') ; otherwise fprintf ('undefined ') ; end SuiteSparse/CXSparse/MATLAB/Demo/private/get_problem.m0000644001170100242450000000254710620720547021425 0ustar davisfacfunction [C, sym] = get_problem (prefix, name, tol) % [C, sym] = get_problem(prefix, name,tol) % read a problem from a file, drop entries with abs value < tol % tol defaults to zero if not present % % Example: % [C, sym] = get_problem ('', 'west0067') ; % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse fprintf ('\n------------------- Matrix: %s\n', name) ; if (nargin < 2) tol = 0 ; end s = find (name == '/') ; if (isempty (s)) s = 0 ; end % f = sprintf ('%s..%s..%sMatrix%s%s', ... % prefix, filesep, filesep, filesep, name (s+1:end)) ; % load the triplet version of the matrix T = load ([ prefix '/' name(s+1:end) ]) ; % convert into a sparse matrix and compare with cs_sparse A = sparse (T (:,1)+1, T (:,2)+1, T (:,3)) ; A2 = cs_sparse (T (:,1)+1, T (:,2)+1, T (:,3)) ; err = norm (A-A2,1) ; if (err > 0) fprintf ('A difference: %g\n', err) ; end [m n] = size (A) ; nz2 = nnz (A) ; if (tol > 0) A = cs_droptol (A, tol) ; end % assume A is symmetric if it is upper or lower triangular sym = is_sym (A) ; if (sym) C = A + (A' - diag (diag (A))) ; else C = A ; end fprintf ('--- Matrix: %d-by-%d, nnz: %d (sym: %d nnz %d), norm: %8.2e\n', ... m, n, nnz(A), sym, abs(sym)*nnz(C), norm (C,1)) ; if (nz2 ~= nnz(A)) fprintf ('tiny entries dropped: %d\n', nz2 - nnz(A)) end SuiteSparse/CXSparse/MATLAB/Demo/private/is_sym.m0000644001170100242450000000071510620372246020423 0ustar davisfacfunction sym = is_sym (A) % sym = is_sym(A) % 1 if A is square and upper tri., -1 if square and lower tri., 0 otherwise % % Example: % sym = is_sym (A) ; % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; sym = 0 ; if (m == n) is_upper = nnz (tril (A,-1)) == 0 ; is_lower = nnz (triu (A,1)) == 0 ; if (is_upper) sym = 1 ; elseif (is_lower) sym = -1 ; end end SuiteSparse/CXSparse/MATLAB/Demo/private/ex_1.m0000644001170100242450000000345010620372224017747 0ustar davisfacfunction ex_1 %EX_1: four methods for creating the same matrix. % (please wait, this can take a while...) % Example: % ex_1 % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = 1000 ; nz = 1e5 ; tic % method 1: A(i,j) = ... rand ('state', 0) ; A = sparse (n,n) ; for k = 1:nz % compute some arbitrary entry and add it into the matrix i = 1 + fix (n * rand (1)) ; j = 1 + fix (n * rand (1)) ; x = rand (1) ; A (i,j) = A (i,j) + x ; % VERY slow, esp. if A(i,j) not already nonzero! end fprintf ('Method 1: ') ; toc A1 = A ; tic % method 2: triplet form, one entry at a time rand ('state', 0) ; ii = zeros (nz, 1) ; % preallocate ii, jj, and xx jj = zeros (nz, 1) ; xx = zeros (nz, 1) ; for k = 1:nz % compute some arbitrary entry and add it into the matrix ii (k) = 1 + fix (n * rand (1)) ; jj (k) = 1 + fix (n * rand (1)) ; xx (k) = rand (1) ; end A = sparse (ii,jj,xx) ; fprintf ('Method 2: ') ; toc A2 = A ; disp (A1-A2) ; tic % method 3: triplet form, one entry at a time, pretend nz is unknown rand ('state', 0) ; len = 16 ; ii = zeros (len, 1) ; jj = zeros (len, 1) ; xx = zeros (len, 1) ; for k = 1:nz % compute some arbitrary entry and add it into the matrix if (k > len) % double the size of ii,jj,xx len = 2*len ; ii (len) = 0 ; jj (len) = 0 ; xx (len) = 0 ; end ii (k) = 1 + fix (n * rand (1)) ; jj (k) = 1 + fix (n * rand (1)) ; xx (k) = rand (1) ; end A = sparse (ii (1:k), jj (1:k), xx (1:k)) ; fprintf ('Method 3: ') ; toc A3 = A ; disp (A1-A3) ; tic % method 4: avoid the for loop rand ('state', 0) ; e = rand (3, nz) ; e (1,:) = 1 + fix (n * e (1,:)) ; e (2,:) = 1 + fix (n * e (2,:)) ; A = sparse (e (1,:), e (2,:), e (3,:)) ; fprintf ('Method 4: ') ; toc A4 = A ; disp (A1-A4) ; SuiteSparse/CXSparse/MATLAB/Demo/private/frand.m0000644001170100242450000000133210620372243020203 0ustar davisfacfunction A = frand (n,nel,s) % A = frand (n,nel,s) creates an n-by-n sparse matrix consisting of nel finite % elements, each of which are of size s-by-s with random symmetric nonzero % pattern, plus the identity matrix. % % Example: % A = frand (100, 100, 4) ; cspy (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse ss = s^2 ; nz = nel*ss ; ii = zeros (nz,1) ; jj = zeros (nz,1) ; xx = zeros (nz,1) ; k = 1 ; for e = 1:nel i = 1 + fix (n * rand (s,1)) ; i = repmat (i, 1, s) ; j = i' ; x = rand (s,s) ; ii (k:k+ss-1) = i (:) ; jj (k:k+ss-1) = j (:) ; xx (k:k+ss-1) = x (:) ; k = k + ss ; end A = sparse (ii,jj,xx,n,n) + speye (n) ; SuiteSparse/CXSparse/MATLAB/Demo/private/print_resid.m0000644001170100242450000000060310620372261021433 0ustar davisfacfunction print_resid (A, x, b) % print_resid (A, x, b), print the relative residual, % norm (A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf)) % Example: % print_resid (A, x, b) ; % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse fprintf ('resid: %8.2e\n', ... norm (A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf))) ; SuiteSparse/CXSparse/MATLAB/Demo/private/mesh2d1.m0000644001170100242450000000130010620372250020345 0ustar davisfacfunction A = mesh2d1 (n) % create an n-by-n 2D mesh for the 2nd difference operator % Example: % A = mesh2d1 (30) ; % a 30-by-30 mesh % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse ii = zeros (5*n^2, 1) ; % preallocate ii, jj, and xx jj = zeros (5*n^2, 1) ; xx = zeros (5*n^2, 1) ; k = 1 ; for j = 0:n-1 for i = 0:n-1 s = j*n+i + 1 ; ii (k:k+4) = [(j-1)*n+i j*n+(i-1) j*n+i j*n+(i+1) (j+1)*n+i ] + 1 ; jj (k:k+4) = [s s s s s] ; xx (k:k+4) = [-1 -1 4 -1 -1] ; k = k + 5 ; end end % remove entries beyond the boundary keep = find (ii >= 1 & ii <= n^2 & jj >= 1 & jj <= n^2) ; A = sparse (ii (keep), jj (keep), xx (keep)) ; SuiteSparse/CXSparse/MATLAB/Demo/private/mesh2d2.m0000644001170100242450000000072610620372252020363 0ustar davisfacfunction A = mesh2d2 (n) % create an n-by-n 2D mesh for the 2nd difference operator % Example: % A = mesh2d2 (30) ; % a 30-by-30 mesh % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse nn = 1:n^2 ; ii = [nn-n ; nn-1 ; nn ; nn+1 ; nn+n] ; jj = repmat (nn, 5, 1) ; xx = repmat ([-1 -1 4 -1 -1]', 1, n^2) ; keep = find (ii >= 1 & ii <= n^2 & jj >= 1 & jj <= n^2) ; A = sparse (ii (keep), jj (keep), xx (keep)) ; SuiteSparse/CXSparse/MATLAB/Demo/private/mesh3d1.m0000644001170100242450000000151510620725647020372 0ustar davisfacfunction [A, keep, ii, jj, xx] = mesh3d1 (n) % create an n-by-n-by-n 3D mesh for the 2nd difference operator % Example: % A = mesh3d1 (10) ; % a 10-by-10-by-10 mesh % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse ii = zeros (7*n^3, 1) ; jj = zeros (7*n^3, 1) ; xx = zeros (7*n^3, 1) ; t = 1 ; for k = 0:n-1 for j = 0:n-1 for i = 0:n-1 s = k*n^2 + j*n+i + 1 ; ii (t:t+6) = [ (k-1)*n^2 + j*n+i k*n^2 + (j-1)*n+i k*n^2 + j*n+(i-1) k*n^2 + j*n+i k*n^2 + j*n+(i+1) k*n^2 + (j+1)*n+i (k+1)*n^2 + j*n+i ]' + 1 ; jj (t:t+6) = [s s s s s s s] ; xx (t:t+6) = [-1 -1 -1 6 -1 -1 -1] ; t = t + 7 ; end end end keep = find (ii >= 1 & ii <= n^3 & jj >= 1 & jj <= n^3) ; A = sparse (ii (keep), jj (keep), xx (keep)) ; SuiteSparse/CXSparse/MATLAB/Demo/private/mesh3d2.m0000644001170100242450000000077110620372255020367 0ustar davisfacfunction A = mesh3d2 (n) % create an n-by-n-by-n 3D mesh for the 2nd difference operator % Example: % A = mesh3d2 (10) ; % a 10-by-10-by-10 mesh % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse nn = 1:n^3 ; ii = [nn-n^2 ; nn-n ; nn-1 ; nn ; nn+1 ; nn+n ; nn+n^2] ; jj = repmat (nn, 7, 1) ; xx = repmat ([-1 -1 -1 6 -1 -1 -1]', 1, n^3) ; keep = find (ii >= 1 & ii <= n^3 & jj >= 1 & jj <= n^3) ; A = sparse (ii (keep), jj (keep), xx (keep)) ; SuiteSparse/CXSparse/MATLAB/Test/0000755001170100242450000000000010710651265015321 5ustar davisfacSuiteSparse/CXSparse/MATLAB/Test/hmake1.m0000644001170100242450000000127110620373127016644 0ustar davisfacfunction [v,beta,xnorm] = hmake1 (x) %HMAKE1 construct a Householder reflection % Example: % [v,beta,xnorm] = hmake1 (x) % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = length (x) ; if (n == 1) v = 1 ; xnorm = norm (x) ; if (x (1) < 0) beta = 2 ; else beta = 0 ; end return end sigma = x (2:n)'*x(2:n) ; xnorm = sqrt (x (1)^2 + sigma) ; v = x ; if (sigma == 0) v (1) = 1 ; if (x (1) < 0) beta = 2 ; else beta = 0 ; end else if (x (1) <= 0) v (1) = x(1) - xnorm ; else v (1) = -sigma / (x(1) + xnorm) ; end beta = (2*v(1)^2) / (sigma + v(1)^2) ; v = v / v(1) ; end SuiteSparse/CXSparse/MATLAB/Test/sqr_example.m0000644001170100242450000000101510620373174020014 0ustar davisfacfunction sqr_example %SQR_EXAMPLE test cs_sqr % Example: % sqr_example % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse Prob = UFget (706) ; A = Prob.A' ; q = colamd (A) ; A = A (:,q) ; A = sprandn (A) ; [m n] = size (A) ; [vnz, rnz, parent, c, leftmost, p] = cs_sqr(A) ; m2 = length (p) ; B = [A ; sparse(m2-m,n)] ; B = B (p,q) ; R1 = gqr3 (B) ; clf subplot (2,2,1) ; spy(A) subplot (2,2,3) ; spy (chol (A'*A + 100*speye(n))) ; subplot (2,2,4) ; spy (R1) ; SuiteSparse/CXSparse/MATLAB/Test/cs_sparse2_mex.c0000644001170100242450000000276610710251214020403 0ustar davisfac#include "cs_mex.h" /* A = cs_sparse2 (i,j,x), removing duplicates and numerically zero entries, * and returning A sorted (test cs_entry) */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT k, m, n, nz, *Ti, *Tj ; if (nargout > 1 || nargin != 3) { mexErrMsgTxt ("Usage: A = cs_sparse2(i,j,x)") ; } nz = mxGetM (pargin [0]) ; Ti = cs_dl_mex_get_int (nz, pargin [0], &m, 1) ; Tj = cs_dl_mex_get_int (nz, pargin [1], &n, 1) ; cs_mex_check (1, nz, 1, 0, 0, 1, pargin [2]) ; if (mxIsComplex (pargin [2])) { #ifdef NCOMPLEX mexErrMsgTxt ("complex case not supported") ; #else cs_complex_t *Tx ; cs_cl *A, *C, *T ; Tx = cs_cl_mex_get_double (nz, pargin [2]) ; T = cs_cl_spalloc (n, m, 1, 1, 1) ; for (k = 0 ; k < nz ; k++) { cs_cl_entry (T, Tj [k], Ti [k], Tx [k]) ; } C = cs_cl_compress (T) ; cs_cl_spfree (T) ; cs_cl_dupl (C) ; cs_cl_dropzeros (C) ; A = cs_cl_transpose (C, -1) ; cs_cl_spfree (C) ; pargout [0] = cs_cl_mex_put_sparse (&A) ; cs_free (Tx) ; #endif } else { double *Tx ; cs_dl *A, *C, *T ; Tx = mxGetPr (pargin [2]) ; T = cs_dl_spalloc (n, m, 1, 1, 1) ; for (k = 0 ; k < nz ; k++) { cs_dl_entry (T, Tj [k], Ti [k], Tx [k]) ; } C = cs_dl_compress (T) ; cs_dl_spfree (T) ; cs_dl_dupl (C) ; cs_dl_dropzeros (C) ; A = cs_dl_transpose (C, 1) ; cs_dl_spfree (C) ; pargout [0] = cs_dl_mex_put_sparse (&A) ; } cs_free (Ti) ; cs_free (Tj) ; } SuiteSparse/CXSparse/MATLAB/Test/cs_rowcnt_mex.c0000644001170100242450000000521710571353755020354 0ustar davisfac/* Compute the row counts of the Cholesky factor L of the matrix A. Uses * the lower triangular part of A. */ #include "cs_mex.h" static void firstdesc (CS_INT n, CS_INT *parent, CS_INT *post, CS_INT *first, CS_INT *level) { CS_INT len, i, k, r, s ; for (i = 0 ; i < n ; i++) first [i] = -1 ; for (k = 0 ; k < n ; k++) { i = post [k] ; /* node i of etree is kth postordered node */ len = 0 ; /* traverse from i towards the root */ for (r = i ; r != -1 && first [r] == -1 ; r = parent [r], len++) first [r] = k ; len += (r == -1) ? (-1) : level [r] ; /* root node or end of path */ for (s = i ; s != r ; s = parent [s]) level [s] = len-- ; } } /* return rowcount [0..n-1] */ static CS_INT *rowcnt (cs_dl *A, CS_INT *parent, CS_INT *post) { CS_INT i, j, k, len, s, p, jprev, q, n, sparent, jleaf, *Ap, *Ai, *maxfirst, *ancestor, *prevleaf, *w, *first, *level, *rowcount ; n = A->n ; Ap = A->p ; Ai = A->i ; /* get A */ w = cs_dl_malloc (5*n, sizeof (CS_INT)) ; /* get workspace */ ancestor = w ; maxfirst = w+n ; prevleaf = w+2*n ; first = w+3*n ; level = w+4*n ; rowcount = cs_dl_malloc (n, sizeof (CS_INT)) ; /* allocate result */ firstdesc (n, parent, post, first, level) ; /* find first and level */ for (i = 0 ; i < n ; i++) { rowcount [i] = 1 ; /* count the diagonal of L */ prevleaf [i] = -1 ; /* no previous leaf of the ith row subtree */ maxfirst [i] = -1 ; /* max first[j] for node j in ith subtree */ ancestor [i] = i ; /* every node is in its own set, by itself */ } for (k = 0 ; k < n ; k++) { j = post [k] ; /* j is the kth node in the postordered etree */ for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; q = cs_dl_leaf (i, j, first, maxfirst, prevleaf, ancestor, &jleaf) ; if (jleaf) rowcount [i] += (level [j] - level [q]) ; } if (parent [j] != -1) ancestor [j] = parent [j] ; } cs_dl_free (w) ; return (rowcount) ; } void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs_dl *A, Amatrix ; double *x ; CS_INT i, m, n, *parent, *post, *rowcount ; if (nargout > 1 || nargin != 3) { mexErrMsgTxt ("Usage: r = cs_rowcnt(A,parent,post)") ; } /* get inputs */ A = cs_dl_mex_get_sparse (&Amatrix, 1, 0, pargin [0]) ; n = A->n ; parent = cs_dl_mex_get_int (n, pargin [1], &i, 0) ; post = cs_dl_mex_get_int (n, pargin [2], &i, 1) ; rowcount = rowcnt (A, parent, post) ; pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ; x = mxGetPr (pargout [0]) ; for (i = 0 ; i < n ; i++) x [i] = rowcount [i] ; cs_dl_free (rowcount) ; } SuiteSparse/CXSparse/MATLAB/Test/test_qrsol.m0000644001170100242450000000145610620373304017677 0ustar davisfacfunction test_qrsol %TEST_QRSOL test cs_qrsol % % Example: % test_qrsol % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; k = 0 ; rs1 = zeros (1,0) ; rs2 = zeros (1,0) ; for i = f Prob = UFget (i,index) ; A = Prob.A ; if (~isreal (A)) continue ; end [m n] = size (A) ; %#ok b = rand (m,1) ; x1 = A\b ; x2 = cs_qrsol (A,b) ; x1 (~isfinite (x1)) = 0 ; x2 (~isfinite (x2)) = 0 ; r1 = norm (A*x1-b) ; r2 = norm (A*x2-b) ; k = k + 1 ; rs1 (k) = r1 ; rs2 (k) = r2 ; fprintf ('%30s MATLAB: %6.2e CS: %6.2e\n', Prob.name, r1, r2) ; loglog (rs1, rs2, 'o') ; drawnow clear A b x1 x2 % pack end SuiteSparse/CXSparse/MATLAB/Test/check_if_same.m0000644001170100242450000000063110620373016020232 0ustar davisfacfunction check_if_same (p1,p2) %CHECK_IF_SAME check if two inputs are identical or not % % Example: % check_if_same (1:5, 2:6) % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (isempty (p1)) if (~isempty (p2)) p1 %#ok p2 %#ok error ('empty!') ; end elseif (any (p1 ~= p2)) p1 %#ok p2 %#ok error ('!') ; end SuiteSparse/CXSparse/MATLAB/Test/qr_left.m0000644001170100242450000000113010620373162017123 0ustar davisfacfunction [V,Beta,R] = qr_left (A) %QR_LEFT left-looking Householder QR factorization. % Example: % [V,Beta,R] = qr_left (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; V = zeros (m,n) ; Beta = zeros (1,n) ; R = zeros (m,n) ; for k = 1:n x = A (:,k) ; for i = 1:k-1 v = V (i:m,i) ; beta = Beta (i) ; x (i:m) = x (i:m) - v * (beta * (v' * x (i:m))) ; end [v,beta,s] = gallery ('house', x (k:m), 2) ; V (k:m,k) = v ; Beta (k) = beta ; R (1:(k-1),k) = x (1:(k-1)) ; R (k,k) = s ; end SuiteSparse/CXSparse/MATLAB/Test/test_qr1.m0000644001170100242450000000162410620373300017233 0ustar davisfacfunction test_qr1 %TEST_QR1 test QR factorizations % % Example: % test_qr1 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; for i = f Prob = UFget (i,index) ; A = Prob.A ; if (~isreal (A)) continue ; end [m n] = size (A) ; if (m < n) A = A' ; end t0 = 0 ; k0 = 0 ; while (t0 < 0.1) tic q = colamd (A, [-1 10]) ; % [Q,R] = qr (A (:,q)) ; R = qr (A (:,q)) ; %#ok t = toc ; t0 = t0 + t ; k0 = k0 + 1 ; end t0 = t0 / k0 ; t1 = 0 ; k1 = 0 ; while (t1 < 0.1) tic [V,beta, p, R,q] = cs_qr (A) ; %#ok t = toc ; t1 = t1 + t ; k1 = k1 + 1 ; end t1 = t1 / k1 ; fprintf (... '%25s MATLAB: %10.4f (%8d) CS: %10.4f (%8d) speedup: %8.2f\n', ... Prob.name, t0, k0, t1, k1, t0/t1) ; end SuiteSparse/CXSparse/MATLAB/Test/test_sep.m0000644001170100242450000000350610620373310017321 0ustar davisfacfunction test_sep %TEST_SEP test cs_sep, and compare with Gilbert's meshpart vtxsep % (requires MESHPART). % % Example: % test_sep % % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; clf for k = 1:length(f) i = f (k) ; Prob = UFget (i) ; disp (Prob) ; A = spones (Prob.A) ; [m n] = size (A) ; if (m ~= n) A = A'*A ; end A = A|A' ; p = symrcm (A) ; n = size (A,1) ; n2 = fix (n/2) ; a = p (1:n2) ; b = p ((n2+1):n) ; clf subplot (2,3,1) ; spy (A) ; subplot (2,3,2) ; spy (A (p,p)) ; hold on plot ([.5 n2+.5 n2+.5 .5 .5], [.5 .5 n2+.5 n2+.5 .5], 'r', 'LineWidth', 2) ; hold off subplot (2,3,3) ; spy (A (a,b)) ; title ('edge sep') ; subplot (2,3,6) ; cs_dmspy (A (a,b)) ; title ('node sep') ; [s as bs] = vtxsep (A,a,b) ; %#ok [s2 a2 b2] = cs_sep (A,a,b) ; p2 = [a2 b2 s2] ; B = A (p2,p2) ; subplot (2,3,5) ; spy (B) ; hold on px = [s2 a2 b2] ; if (any (sort (px) ~= 1:n)) px %#ok n %#ok error ('!') ; end na = length (a2) ; nb = length (b2) ; ns = length (s2) ; %#ok nab = na + nb ; plot ([.5 na+.5 na+.5 .5 .5], [.5 .5 na+.5 na+.5 .5], 'r', 'LineWidth', 2) ; plot ([na nab nab na na]+0.5, [na na nab nab na]+0.5, 'r', 'LineWidth', 2) ; plot ([.5 nab+.5 nab+.5 .5 .5], [.5 .5 nab+.5 nab+.5 .5], 'g', 'LineWidth', 1) ; hold off nz1 = nnz (A (a2,b2)) ; if (nz1 ~= 0) nz1 %#ok error ('!') ; end nz2 = nnz (A (a2,b2)) ; if (nz2 ~= 0) nz2 %#ok error ('!') ; end if (length (s) ~= length (s2)) fprintf ('lengths differ: %d %d\n', length (s), length (s2)) ; end drawnow % pause end SuiteSparse/CXSparse/MATLAB/Test/Makefile0000644001170100242450000000235610617732311016765 0ustar davisfacinclude ../../../UFconfig/UFconfig.mk MX = $(MEX) -DCS_LONG AR = ar cr RANLIB = ranlib I = -I../../Include -I../../../UFconfig -I../CSparse all: cs_sparse2.mexglx \ cs_ipvec.mexglx \ cs_pvec.mexglx \ cs_reach.mexglx \ cs_maxtransr.mexglx \ cs_reachr.mexglx \ cs_rowcnt.mexglx \ cs_frand.mexglx mexcsparse: ( cd ../CSparse ; make mexcsparse.a ) cs_ipvec.mexglx: cs_ipvec_mex.c mexcsparse $(MX) -output cs_ipvec $< $(I) ../CSparse/mexcsparse.a cs_pvec.mexglx: cs_pvec_mex.c mexcsparse $(MX) -output cs_pvec $< $(I) ../CSparse/mexcsparse.a cs_reach.mexglx: cs_reach_mex.c mexcsparse $(MX) -output cs_reach $< $(I) ../CSparse/mexcsparse.a cs_sparse2.mexglx: cs_sparse2_mex.c mexcsparse $(MX) -output cs_sparse2 $< $(I) ../CSparse/mexcsparse.a cs_maxtransr.mexglx: cs_maxtransr_mex.c mexcsparse $(MX) -output cs_maxtransr $< $(I) ../CSparse/mexcsparse.a cs_reachr.mexglx: cs_reachr_mex.c mexcsparse $(MX) -output cs_reachr $< $(I) ../CSparse/mexcsparse.a cs_rowcnt.mexglx: cs_rowcnt_mex.c mexcsparse $(MX) -output cs_rowcnt $< $(I) ../CSparse/mexcsparse.a cs_frand.mexglx: cs_frand_mex.c mexcsparse $(MX) -output cs_frand $< $(I) ../CSparse/mexcsparse.a clean: rm -f *.o distclean: clean rm -f *.mex* *.a cs_cl_*.c purge: distclean SuiteSparse/CXSparse/MATLAB/Test/givens2.m0000644001170100242450000000061310620373121017044 0ustar davisfacfunction g = givens2(a,b) %GIVENS2 find a Givens rotation. % Example: % g = givens2(a,b) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (b == 0) c = 1 ; s = 0 ; elseif (abs (b) > abs (a)) tau = -a/b ; s = 1 / sqrt (1+tau^2) ; c = s*tau ; else tau = -b/a ; c = 1 / sqrt (1+tau^2) ; s = c*tau ; end g = [c -s ; s c] ; SuiteSparse/CXSparse/MATLAB/Test/cs_q1.m0000644001170100242450000000061710620373075016511 0ustar davisfacfunction Q = cs_q1 (V, Beta, p) %CS_Q1 construct Q from Householder vectors % Example: % Q = cs_q1 (V, beta, p) % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (V) ; Q = speye (m) ; if (nargin > 2) Q = Q (:,p) ; end for i = 1:m for k = 1:n Q (i,:) = Q (i,:) - ((Q(i,:) * V(:,k)) * Beta(k)) * V(:,k)' ; end end SuiteSparse/CXSparse/MATLAB/Test/cspy_test.m0000644001170100242450000000155510620666207017524 0ustar davisfacfunction cspy_test %CSPY_TEST test cspy and cs_dmspy % Example % cspy_test % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; clf % f = f (523:end) ; % f = f ((find (f == 938)):end) ; for i = f Prob = UFget (i,index) ; disp (Prob) ; A = Prob.A ; try subplot (1,4,1) ; cspy (A) ; drawnow subplot (1,4,2) ; cspy (A,64) ; drawnow subplot (1,4,3) ; cs_dmspy (A) ; drawnow subplot (1,4,4) ; cs_dmspy (A,0) ; drawnow catch fprintf ('failed...\n') ; end [m n] = size (A) ; if (m == n & nnz (diag (A)) == n) %#ok p = cs_dmperm (A) ; if (any (p ~= 1:n)) error ('!') ; end [p q r s cc rr] = cs_dmperm (A) ; %#ok if (any (p ~= q)) error ('not sym!') ; end end drawnow end SuiteSparse/CXSparse/MATLAB/Test/cs_maxtransr.m0000644001170100242450000000043710620373065020206 0ustar davisfacfunction p = cs_maxtransr(A) %#ok %CS_MAXTRANSR recursive maximum matching algorithm % Example: % p = cs_maxtransr(A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_maxtransr mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/Test/qr2.m0000644001170100242450000000100510620373153016174 0ustar davisfacfunction [V,Beta,R] = qr2 (A) %QR2 QR factorization based on Householder reflections % % Example: % [V,beta,R] = qr2 (A) % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; V = zeros (m,n) ; Beta = zeros (1,n) ; for k = 1:n % [v,beta,s] = gallery ('house', A (k:m,k), 2) ; [v,beta] = house (A (k:m,k)) ; V (k:m,k) = v ; Beta (k) = beta ; A (k:m,k:n) = A (k:m,k:n) - v * (beta * (v' * A (k:m,k:n))) ; end R = triu (A) ; SuiteSparse/CXSparse/MATLAB/Test/cholupdown.m0000644001170100242450000000236210620701365017661 0ustar davisfacfunction L = cholupdown (Lold, sigma, w) %CHOLUPDOWN Cholesky update/downdate (Bischof, Pan, and Tang method) % This version only works for the real case. See chol_updown2 for % a code that handles both the real and complex cases. % Example: % L = cholupdown (Lold, sigma, w) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse beta = 1 ; n = size (Lold,1) ; L = Lold ; % x = weros (n,1) ; % worig = w ; for k = 1:n alpha = w(k) / L(k,k) ; beta_new = sqrt (beta^2 + sigma*alpha^2) ; gamma = alpha / (beta_new * beta) ; if (sigma < 0) % downdate bratio = beta_new / beta ; w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ; L (k,k) = bratio * L (k,k) ; L (k+1:n,k) = bratio * L (k+1:n,k) - gamma*w(k+1:n) ; else % update bratio = beta / beta_new ; % wold = w (k+1:n) ; % w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ; % L (k ,k) = bratio * L (k ,k) + gamma*w(k) ; % L (k+1:n,k) = bratio * L (k+1:n,k) + gamma*wold ; L (k,k) = bratio * L (k,k) + gamma*w(k) ; for i = k+1:n wold = w (i) ; w (i) = w (i) - alpha * L (i,k) ; L (i,k) = bratio * L (i,k) + gamma*wold ; end end w (k) = alpha ; beta = beta_new ; end % norm (w-(Lold\worig)) SuiteSparse/CXSparse/MATLAB/Test/cs_sparse2.m0000644001170100242450000000064010620373105017535 0ustar davisfacfunction A = cs_sparse2 (i,j,x) %#ok %CS_SPARSE2 same as cs_sparse, to test cs_entry function % A = cs_sparse2 (i,j,x), removing duplicates and numerically zero entries, % and returning A sorted (test cs_entry) % % Example: % A = cs_sparse2 (i,j,x) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_sparse2 mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/Test/chol_right.m0000644001170100242450000000063110620373032017612 0ustar davisfacfunction L = chol_right (A) %CHOL_RIGHT right-looking Cholesky factorization. % Example % L = chol_right (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A) ; L = zeros (n) ; for k = 1:n L (k,k) = sqrt (A (k,k)) ; L (k+1:n,k) = A (k+1:n,k) / L (k,k) ; A (k+1:n,k+1:n) = A (k+1:n,k+1:n) - L (k+1:n,k) * L (k+1:n,k)' ; end SuiteSparse/CXSparse/MATLAB/Test/signum.m0000644001170100242450000000046010620373167017003 0ustar davisfacfunction s = signum (x) %SIGNUM compute and display the sign of a column vector x % Example % s = signum(x) % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse s = ones (length (x),1) ; s (find (x < 0)) = -1 ; %#ok disp ('s =') ; disp (s) ; SuiteSparse/CXSparse/MATLAB/Test/dmperm_test.m0000644001170100242450000000430710620666271020031 0ustar davisfacfunction dmperm_test %DMPERM_TEST test cs_dmperm % % Example: % dmperm_test % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; f = find (index.nrows ~= index.ncols) ; [ignore i] = sort (index.nrows(f) ./ index.ncols(f)) ; f = [209:211 f(i)] ; nmat = length(f) ; tt1 = zeros (1,nmat) ; tt2 = zeros (1,nmat) ; tt3 = zeros (1,nmat) ; tt4 = zeros (1,nmat) ; mm = zeros (1,nmat) ; nn = zeros (1,nmat) ; ss = zeros (1,nmat) ; me = zeros (1,nmat) ; ne = zeros (1,nmat) ; p = cs_dmperm (sparse (1)) ; for k = 1:length(f) i = f(k) ; Prob = UFget (i) %#ok A = Prob.A ; [m n] = size (A) ; if (m > n) % make sure A is short and fat A = A' ; end % C is tall and thin C = A' ; [m n] = size (A) ; k1 = 0 ; t1 = 0 ; while (t1 < 1) tic p = cs_dmperm (A) ; t = toc ; t1 = t1 + t ; k1 = k1 + 1 ; end t1 = t1 / k1 ; s1 = sum (p > 0) ; k2 = 0 ; t2 = 0 ; while (t2 < 1) tic p = cs_dmperm (C) ; t = toc ; t2 = t2 + t ; k2 = k2 + 1 ; end t2 = t2 / k2 ; s2 = sum (p > 0) ; k3 = 0 ; t3 = 0 ; while (t3 < 1) tic p = cs_dmperm_orig (A) ; t = toc ; t3 = t3 + t ; k3 = k3 + 1 ; end t3 = t3 / k3 ; k4 = 0 ; t4 = 0 ; while (t4 < 1) tic p = cs_dmperm_orig (A') ; t = toc ; t4 = t4 + t ; k4 = k4 + 1 ; end t4 = t4 / k4 ; sprnk = sum (p > 0) ; nempty = full (sum (sum (spones (A)) == 0)) ; mempty = full (sum (sum (spones (C)) == 0)) ; fprintf ('[m %d:%d n %d:%d (%d)]:\n', m, mempty, n, nempty, sprnk) ; fprintf (' A: t1 %10.6f (%6d) C: t2 %10.6f (%6d) new\n', ... t1, k1, t2, k2) ; fprintf (' A: t3 %10.6f (%6d) C: t4 %10.6f (%6d) orig\n', ... t3, k3, t4, k4) ; if (s1 ~= sprnk | s2 ~= sprnk) %#ok s1 %#ok s2 %#ok sprnk %#ok error ('!') ; end tt1 (k) = t1 ; tt2 (k) = t2 ; tt3 (k) = t3 ; tt4 (k) = t4 ; mm (k) = m ; nn (k) = n ; ss (k) = sprnk ; me (k) = mempty ; ne (k) = nempty ; clear A C semilogy (ss(1:k) ./ nn(1:k), tt1(1:k) ./ tt3(1:k), 'o', ... [0 1], [1 1], 'r-') ; drawnow end SuiteSparse/CXSparse/MATLAB/Test/cs_reachr_mex.c0000644001170100242450000000332010571353322020263 0ustar davisfac#include "cs_mex.h" /* find nonzero pattern of x=L\sparse(b). L must be sparse and lower * triangular. b must be a sparse vector. */ static void dfsr (CS_INT j, const cs *L, CS_INT *top, CS_INT *xi, CS_INT *w) { CS_INT p ; w [j] = 1 ; /* mark node j */ for (p = L->p [j] ; p < L->p [j+1] ; p++) /* for each i in L(:,j) */ { if (w [L->i [p]] != 1) /* if i is unmarked */ { dfsr (L->i [p], L, top, xi, w) ; /* start a dfs at i */ } } xi [--(*top)] = j ; /* push j onto the stack */ } /* w [0..n-1] == 0 on input, <= 1 on output. size n */ static CS_INT reachr (const cs *L, const cs *B, CS_INT *xi, CS_INT *w) { CS_INT p, n = L->n ; CS_INT top = n ; /* stack is empty */ for (p = B->p [0] ; p < B->p [1] ; p++) /* for each i in pattern of b */ { if (w [B->i [p]] != 1) /* if i is unmarked */ { dfsr (B->i [p], L, &top, xi, w) ; /* start a dfs at i */ } } return (top) ; /* return top of stack */ } void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs_dl Lmatrix, Bmatrix, *L, *B ; double *x ; CS_INT i, j, top, *xi ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_reachr(L,b)") ; } /* get inputs */ L = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ; cs_mex_check (0, L->n, 1, 0, 1, 1, pargin [1]) ; xi = cs_dl_calloc (2*L->n, sizeof (CS_INT)) ; top = reachr (L, B, xi, xi + L->n) ; pargout [0] = mxCreateDoubleMatrix (L->n - top, 1, mxREAL) ; x = mxGetPr (pargout [0]) ; for (j = 0, i = top ; i < L->n ; i++, j++) x [j] = xi [i] ; cs_free (xi) ; } SuiteSparse/CXSparse/MATLAB/Test/chol_left2.m0000644001170100242450000000073510620373026017521 0ustar davisfacfunction L = chol_left2 (A) %CHOL_LEFT2 left-looking Cholesky factorization, more details. % Example % L = chol_left2 (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A,1) ; L = sparse (n,n) ; a = sparse (n,1) ; for k = 1:n a (k:n) = A (k:n,k) ; for j = find (L (k,:)) a (k:n) = a (k:n) - L (k:n,j) * L (k,j) ; end L (k,k) = sqrt (a (k)) ; L (k+1:n,k) = a (k+1:n) / L (k,k) ; end SuiteSparse/CXSparse/MATLAB/Test/chol_up.m0000644001170100242450000000056110620373042017124 0ustar davisfacfunction L = chol_up (A) %CHOL_UP up-looking Cholesky factorization. % Example: % L = chol_up (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A) ; L = zeros (n) ; for k = 1:n L (k,1:k-1) = (L (1:k-1,1:k-1) \ A (1:k-1,k))' ; L (k,k) = sqrt (A (k,k) - L (k,1:k-1) * L (k,1:k-1)') ; end SuiteSparse/CXSparse/MATLAB/Test/cs_ipvec.m0000644001170100242450000000037010620373063017267 0ustar davisfacfunction x = cs_ipvec (b,p) %#ok %CS_IPVEC x(p)=b % % Example: % x = cs_ipvec (b,p) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_ipvec mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/Test/Contents.m0000644001170100242450000001213510620375605017277 0ustar davisfac% CXSparse testing and "textbook" MATLAB M-files and mexFunctions, related to % CXSparse but not a part of CXSparse itself. % % M-files: % % chol_downdate - downdate a Cholesky factorization. % chol_left - left-looking Cholesky factorization. % chol_left2 - left-looking Cholesky factorization, more details. % chol_right - right-looking Cholesky factorization. % chol_super - left-looking "supernodal" Cholesky factorization. % chol_up - up-looking Cholesky factorization. % chol_update - update a Cholesky factorization. % chol_updown - update or downdate a Cholesky factorization. % chol_updown2 - Cholesky update/downdate (real and complex) % cond1est - 1-norm condition estimate. % cs_fiedler - the Fiedler vector of a connected graph. % givens2 - find a Givens rotation. % house - find a Householder reflection. % lu_left - left-looking LU factorization. % lu_right - right-looking LU factorization. % lu_rightp - right-looking LU factorization, with partial pivoting. % lu_rightpr - recursive right-looking LU, with partial pivoting. % lu_rightr - recursive right-looking LU. % norm1est - 1-norm estimate. % qr_givens - Givens-rotation QR factorization. % qr_givens_full - Givens-rotation QR factorization, for full matrices. % qr_left - left-looking Householder QR factorization. % qr_right - right-looking Householder QR factorization. % % mexFunctions: % % cs_frand - generate a random finite-element matrix % cs_ipvec - x(p)=b % cs_maxtransr - recursive maximum matching algorithm % cs_pvec - x=b(p) % cs_reach - non-recursive reach (interface to CSparse cs_reach) % cs_reachr - recursive reach (interface to CSparse cs_reachr) % cs_rowcnt - row counts for sparse Cholesky % cs_sparse2 - same as cs_sparse, to test cs_entry function % % Extensive test functions, not for normal usage: % % check_if_same - check if two inputs are identical or not % choldn - Cholesky downdate % cholup - Cholesky update, using Given's rotations % cholupdown - Cholesky update/downdate (Bischof, Pan, and Tang method) % cs_q1 - construct Q from Householder vectors % cs_test_make - compiles the CSparse, Demo, and Test mexFunctions. % dmperm_test - test cs_dmperm % chol_example - simple Cholesky factorization example % etree_sample - construct a sample etree and symbolic factorization % gqr3 - QR factorization, based on Givens rotations % happly - apply Householder reflection to a vector % hmake1 - construct a Householder reflection % mynormest1 - estimate norm(A,1), using LU factorization (L*U = P*A*Q). % myqr - QR factorization using Householder reflections % another_colormap - try another color map % cspy_test - test cspy and cs_dmspy % qr2 - QR factorization based on Householder reflections % sample_colormap - try a colormap for use in cspy % signum - compute and display the sign of a column vector x % sqr_example - test cs_sqr % dmspy_test - test cspy, cs_dmspy, and cs_dmperm % test_qr - test various QR factorization methods % test_randperms - test random permutations % testh - test Householder reflections % test_qr1 - test QR factorizations % test_qrsol - test cs_qrsol % test_sep - test cs_sep, and compare with Gilbert's meshpart vtxsep % testall - test all CSparse functions (run tests 1 to 28 below) % test1 - test cs_transpose, cs_gaxpy, cs_sparse, cs_sparse2 % test2 - test cs_sparse, cs_permute, cs_pvec, cs_ipvec, cs_symperm % test3 - test cs_lsolve, cs_ltsolve, cs_usolve, cs_chol % test4 - test cs_multiply % test5 - test cs_add % test6 - test cs_reach, cs_reachr, cs_lsolve, cs_usolve % test7 - test cs_lu % test8 - test cs_cholsol, cs_lusol % test9 - test cs_qr % test10 - test cs_qr % test11 - test cs_rowcnt % test12 - test cs_qr and compare with svd % test13 - test cs_counts, cs_etree % test14 - test cs_droptol % test15 - test cs_amd % test16 - test cs_amd % test17 - test cs_qr, cs_qright, cs_q1, cs_qrleft, cs_qrsol % test18 - test iterative refinement after backslash % test19 - test cs_dmperm, cs_maxtransr, cs_dmspy, cs_scc, cspy % test20 - test chol_updown2 % test21 - test cs_updown, chol_updown2 % test22 - test cond1est % test23 - test cs_dmspy % test24 - test cs_fielder % test25 - test cs_nd % test26 - test cs_dmsol and cs_dmspy % test27 - test cs_qr, cs_utsolve, cs_qrsol % test28 - test cs_randperm, cs_dmperm % Example: % help chol_update % Copyright 2006-2007, Timothy A. Davis SuiteSparse/CXSparse/MATLAB/Test/test10.m0000644001170100242450000000371610710254556016630 0ustar davisfacfunction test10 %TEST10 test cs_qr % % Example: % test10 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) ; % f = 185 ; % f = 449 ; clf for trials = 1:100 m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; d = 0.1 * rand (1) ; A = sprandn (m, n, d) ; [m n] = size (A) ; if (m < n) A = A' ; end [m n] = size (A) ; sp = sprank (A) ; % if (sp < n) % continue ; % end for cmplex = 0:double(~ispc) if (cmplex) A = A + 1i * sprand (A) * norm (A,1) / 10 ; end Aorig = A ; % A = A (:, colamd (A)) ; if (cmplex) tic ; R = chol (A'*A + speye (n)) ; t1 = toc ; else tic ; R = qr (A) ; t1 = toc ; end % tic ; % [Q,R] = qr (A) ; % t1 = toc ; [c,h,parent] = symbfact (A, 'col') ; %#ok rnz = sum (c) ; %#ok tic ; [V2,Beta2,p,R2] = cs_qr (sparse(A)) ; t2 = toc ; C = A ; m2 = size (V2,1) ; if (m2 > m) C = [A ; sparse(m2-m, n)] ; end C = C (p,:) ; [H1,R1] = myqr (C) ; err1 = norm (R1-R2,1) / norm (R1) ; disp ('err1 = ') ; disp (err1) ; % [svd(A) svd(R1) svd(full(R2))] s1 = svd (full (A)) ; s2 = svd (full (R2)) ; if (n > 0) err2 = norm (s1 - s2) / s1 (1) ; disp ('err2 = ') ; disp (err2) ; else err2 = 0 ; end fprintf ('%10.6f %10.6f cs speedup %8.3f sprank %d vs %d\n', t1, t2, t1/t2, sp, n) ; % H2 = full (H2) % R2 = full (R2) subplot (2,4,1) ; spy (A) ; title ('A colamd') ; subplot (2,4,4) ; spy (Aorig) ; title ('Aorig') ; subplot (2,4,2) ; spy (C) ; title ('A rperm') ; subplot (2,4,5) ; spy (abs(R2)>0) ; title ('spqr R, no zeros') ; subplot (2,4,6) ; spy (R) ; title ('matlab R') ; subplot (2,4,7) ; spy (R2) ; title ('spqr R') ; subplot (2,4,8) ; spy (V2) ; title ('spqr H') ; drawnow if (err2 > 1e-9) error ('!') ; end if (m2 > m) fprintf ('added %d rows, sprank %d n %d\n', m2-m, sp, n) ; end end end SuiteSparse/CXSparse/MATLAB/Test/test11.m0000644001170100242450000000162510710651265016624 0ustar davisfacfunction test11 %TEST11 test cs_rowcnt % % Example: % test11 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:200) ; for i = f Prob = UFget (i, index) ; disp (Prob) ; A = Prob.A ; [m n] = size (A) ; if (m ~= n) continue end A = spones (A) ; A = A+A' + speye(n) ; if (~ispc) if (rand ( ) > .5) A = A + 1i * sprand (A) ; end end [cc h pa po R] = symbfact (A) ; rc1 = full (sum (R)) ; rc2 = cs_rowcnt (A, pa, po) ; if (any (rc1 ~= rc2)) error ('!') ; end try p = amd (A) ; catch p = symamd (A) ; end A = A (p,p) ; [cc h pa po R] = symbfact (A) ; rc1 = full (sum (R)) ; rc2 = cs_rowcnt (A, pa, po) ; if (any (rc1 ~= rc2)) error ('!') ; end end SuiteSparse/CXSparse/MATLAB/Test/test12.m0000644001170100242450000000154210710254563016623 0ustar davisfacfunction test12 %TEST12 test cs_qr and compare with svd % % Example: % test12 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse fprintf ('test 12\n') ; rand ('state',0) ; % A = rand (3,4) for trial = 1:100 m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; d = .1 * rand (1) ; A = sprandn (m,n,d) ; if (m < n) continue ; end if (m == 0 | n == 0) %#ok continue ; end for cmplex = 0:double(~ispc) if (cmplex) A = A + 1i * sprand (A) ; end fprintf ('m %d n %d nnz %d\n', m, n, nnz(A)) ; [V,Beta,p,R] = cs_qr (A) ; s1 = svd (full (A)) ; s2 = svd (full (R)) ; s2 = s2 (1:length(s1)) ; err = norm (s1-s2) ; if (length (s1) > 1) err = err / s1 (1) ; end fprintf ('err %g\n', err) ; if (err > 1e-12) error ('!') ; end end end SuiteSparse/CXSparse/MATLAB/Test/test13.m0000644001170100242450000000334610710252076016625 0ustar davisfacfunction test13 %TEST13 test cs_counts, cs_etree % % Example: % test13 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions randn ('state',0) ; rand ('state',0) ; for trial = 1:100 m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; d = .1 * rand (1) ; A = sprandn (n,n,d) ; C = sprandn (m,n,d) ; A = A+A' ; fprintf ('m %4d n %4d nnz(A) %6d nnz(C) %6d\n', m, n, nnz(A), nnz(C)) ; if (~ispc) if (rand ( ) > .5) A = A + 1i * sprand (A) ; end end [p1,po1] = etree (A) ; [p2,po2] = cs_etree (A) ; [p3,po3] = cs_etree (A, 'sym') ; % po2 = cs_post (p2) ; check_if_same (p1,p2) ; check_if_same (po1,po2) ; check_if_same (p1,p3) ; check_if_same (po1,po3) ; c1 = symbfact (A) ; c2 = cs_counts (A) ; % A-A' check_if_same (c1,c2) ; c2 = cs_counts (triu (A)) ; check_if_same (c1,c2) ; % pause p0 = etree (A, 'col') ; % p1 = etree2 (A, 'col') ; % CHOLMOD p2 = cs_etree (A, 'col') ; if (~isempty (A)) check_if_same (p0,p2) ; end p0 = etree (C, 'col') ; % p1 = etree2 (C, 'col') ; % CHOLMOD p2 = cs_etree (C, 'col') ; if (~isempty (C)) check_if_same (p0,p2) ; end % find etree of A'A, and postorder it [m n] = size (A) ; %#ok % full (A) [cp0 cpo0] = etree (A, 'col') ; % [cp1 cpo1] = etree2 (A, 'col') ; % CHOLMOD [cp2 cpo2] = cs_etree (A, 'col') ; % cpo2 = cs_post (cp2) ; check_if_same (cp0, cp2) ; check_if_same (cpo0, cpo2) ; c0 = symbfact (A, 'col') ; % c1 = symbfact2 (A, 'col') ; % CHOLMOD c2 = cs_counts (A, 'col') ; check_if_same (c0, c2) ; end SuiteSparse/CXSparse/MATLAB/Test/test14.m0000644001170100242450000000153010710254565016624 0ustar davisfacfunction test14 %TEST14 test cs_droptol % % Example: % test14 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) ; for trial = 1:100 m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; d = 0.1*rand (1) ; A = sprandn (m,n,d) ; [i j x] = find (A) ; A = sparse (i,j,2*x-1) ; fprintf ('test14 m %3d n %3d nz %d\n', m, n, nnz (A)) ; for cmplex = 0:double(~ispc) if (cmplex) A = A + 1i * sparse (i,j,2*rand(size(x))-1) ; end % using CSparse tol = 0.5 ; B = cs_droptol (A, tol) ; % using MATLAB C = A .* (abs (A) > tol) ; % [m n] = size (A) ; % s = abs (A) > tol ; % [i j] = find (s) ; % x = A (find (s)) ; % A = sparse (i, j, x, m, n) ; if (norm (C-B,1) > 0) error ('!') ; end end end SuiteSparse/CXSparse/MATLAB/Test/test15.m0000644001170100242450000000177410710252146016630 0ustar davisfacfunction test15 %TEST15 test cs_amd % % Example: % test15 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) ; randn ('state', 0) ; clf for trials = 1:100 n = fix (200 * rand (1)) ; d = 0.05 * rand (1) ; A = sprandn (n, n, d) ; % add a randomly placed dense column k = fix (n * rand (1)) ; k = max (1, k) ; k = min (n, k) ; if (n > 0) A (:,k) = 1 ; end if (~ispc) if (rand ( ) > .5) A = A + 1i * sprand (A) ; end end try p0 = amd (A) ; catch p0 = symamd (A) ; end p1 = cs_amd (A) ; if (any (sort (p1) ~= 1:n)) error ('not perm!') ; end C = A+A' + speye (n) ; lnz0 = sum (symbfact (C (p0,p0))) ; lnz1 = sum (symbfact (C (p1,p1))) ; subplot (1,3,1) ; spy (C) subplot (1,3,2) ; spy (C (p0,p0)) subplot (1,3,3) ; spy (C (p1,p1)) fprintf ('n %4d nz %6d lnz %6d %6d\n', n, nnz(A), lnz0, lnz1) ; drawnow end SuiteSparse/CXSparse/MATLAB/Test/test16.m0000644001170100242450000000357110710252163016625 0ustar davisfacfunction test16 %TEST16 test cs_amd % % Example: % test16 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) ; randn ('state', 0) ; clf index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:200) ; skip = 811 ; % f = 719 for i = f if (any (i == skip)) continue end Prob = UFget (i) ; A = spones (Prob.A) ; Aorig = A ; [m n] = size (A) ; if (m < n) A = A' ; end [m n] = size (A) ; if (m ~= n) A = A'*A ; end if (~ispc) if (rand ( ) > .5) A = A + 1i * sprand (A) ; end end fprintf ('n %4d nz %d\n', n, nnz (A)) ; try p0 = amd (A) ; catch p0 = symamd (A) ; end fprintf ('symmetric case:\n') ; p1 = cs_amd (A) ; if (any (sort (p1) ~= 1:n)) error ('not perm!') ; end C = A+A' + speye (n) ; lnz0 = sum (symbfact (C (p0,p0))) ; lnz1 = sum (symbfact (C (p1,p1))) ; subplot (2,3,1) ; spy (C) subplot (2,3,2) ; spy (C (p0,p0)) ; title ('amd') ; subplot (2,3,3) ; spy (C (p1,p1)) ; title ('csamd') ; drawnow if (lnz0 ~= lnz1) fprintf ('----------------- lnz %d %d %9.4f\n', ... lnz0, lnz1, 100*(lnz0-lnz1)/max([1 lnz0])) ; end if (1) p0 = colamd (Aorig) ; [m n] = size (Aorig) ; fprintf ('m %d n %d\n', m, n) ; fprintf ('A''A case, no dense rows (for QR):\n') ; p1 = cs_amd (Aorig, 3) ; if (any (sort (p1) ~= 1:n)) error ('not perm!') ; end subplot (2,3,4) ; spy (Aorig) subplot (2,3,5) ; spy (Aorig (:,p0)) ; title ('colamd') ; subplot (2,3,6) ; spy (Aorig (:,p1)) ; title ('cs amd(A''A)') ; lnz0 = sum (symbfact (Aorig (:,p0), 'col')) ; lnz1 = sum (symbfact (Aorig (:,p1), 'col')) ; fprintf (' A''A: %7d %7d %9.4f\n', ... lnz0, lnz1, 100*(lnz0-lnz1)/max([1 lnz0])) ; drawnow % pause end end SuiteSparse/CXSparse/MATLAB/Test/test17.m0000644001170100242450000000430310710252200016610 0ustar davisfacfunction test17 %TEST17 test cs_qr, cs_qright, cs_q1, cs_qrleft, cs_qrsol % % Example: % test17 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions clf rand ('state', 0) ; randn ('state', 0) ; for trials = 1:100 m = 1 + fix (10 * rand (1)) ; n = 1 + fix (10 * rand (1)) ; d = rand (1) ; % n = m ; A = sprandn (m, n, d) ; if (m < n) A = A' ; end [m n] = size (A) ; if (~ispc) if (rand ( ) > .5) A = A + 1i * sprand (A) ; end end subplot (3,4,1) ; spy (A) ; [V1, Beta1, p1, R1, q1] = cs_qr (A) ; Q1 = cs_qright (V1, Beta1, p1, speye (size (V1,1))) ; Q1b = cs_q1 (V1, Beta1, p1) ; err = norm (Q1-Q1b,1) ; disp ('err = ') ; disp (err) ; if (err > 1e-12) error ('!') ; end m2 = size (Q1,1) ; A1 = [A ; sparse(m2-m,n)] ; subplot (3,4,5) ; spy (A1 (p1,q1)) ; subplot (3,4,6) ; spy (V1) ; subplot (3,4,7) ; spy (R1) ; subplot (3,4,8) ; spy (Q1) ; [V3, Beta3, R3] = qr2 (A) ; % Q3 = cs_qmake (V3, Beta3) ; Q3 = cs_q1 (V3, Beta3) ; subplot (3,4,9) ; spy (A) ; subplot (3,4,10) ; spy (V3) ; subplot (3,4,11) ; spy (R3) ; subplot (3,4,12) ; spy (Q3) ; err1 = norm (Q1*R1 - A1(:,q1), 1) ; % err2 = norm (Q2*R2 - A (:,q2), 1) ; err3 = norm (Q3*R3 - A, 1) ; fprintf ('m %3d m2 %3d n %3d ::: %3d %6.2e %6.2e\n', ... m, m2, n, m2-m, err1, err3) ; if (err1 > 1e-12) error ('2!') ; end % if (err2 > 1e-12) % error ('!') ; % end if (err3 > 1e-12) error ('3!') ; end try % this fails if A is complex b = rand (m,1) ; [Q,R] = qr (A (:,q1)) ; x = R\(Q'*b) ; x (q1) = x ; r1 = norm (A*x-b) ; x2 = cs_qrsol (A,b) ; r2 = norm (A*x2(1:n)-b) ; qt = cs_qleft (V1, Beta1, p1, speye(size(V1,1))) ; fprintf ('Q''*A-R: %6.2e\n', norm (qt*A1(:,q1)-R1,1)) ; qtb = cs_qleft (V1, Beta1, p1, b) ; % [V1, Beta1, p1, R1, q1] = cs_qr (A) ; x3 = R1 \ qtb ; r3 = norm (A(:,q1)*x3(1:n)-b) ; fprintf ('least sq: %6.2e %6.2e %6.2e diff %6.2e %6.2e\n', ... r1, r2, r3, r1-r2, r1-r3) ; catch end drawnow % pause end SuiteSparse/CXSparse/MATLAB/Test/test18.m0000644001170100242450000000112110620667511016623 0ustar davisfacfunction test18 %TEST18 test iterative refinement after backslash % % Example: % test18 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:100) ; clf % f = f(1) for i = f Prob = UFget (i) ; disp (Prob) ; A = Prob.A ; [m n] = size (A) ; if (~isreal (A) | m ~= n) %#ok continue end b = rand (n,1) ; x = A\b ; r = b - A*x ; x = x + A\r ; fprintf ('\n%6.2e to %6.2e\n', norm (r), norm (b-A*x)) ; end SuiteSparse/CXSparse/MATLAB/Test/test19.m0000644001170100242450000000704610710252222016625 0ustar davisfacfunction test19 %TEST19 test cs_dmperm, cs_maxtransr, cs_dmspy, cs_scc, cspy % % Example: % test19 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions randn ('state', 0) ; rand ('state', 0) ; clf for trials = 1:100 m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; % d = 0.1 * rand (1) ; d = rand (1) * 4 * max (m,n) / max (m*n,1) ; A = sprandn (m,n,d) ; S = sprandn (m,m,d) + speye (m) ; if (~ispc) if (rand ( ) > .5) A = A + 1i * sprand (A) ; end if (rand ( ) > .5) S = S + 1i * sprand (S) ; end end subplot (2,3,1) ; cspy (A) ; pp = dmperm (A) ; sprnk = sum (pp > 0) ; pp2 = cs_dmperm (A) ; spr2 = sum (pp2 > 0) ; if (spr2 ~= sprnk) error ('!') end pp2 = cs_maxtransr (A) ; spr2 = sum (pp2 > 0) ; if (spr2 ~= sprnk) error ('!') end [p,q,r,s] = dmperm (A) ; C = A (p,q) ; % r % s nk = length (r) - 1 ; fprintf ('sprnk: %d m %d n %d nb: %d\n', sprnk, m, n, nk) ; subplot (2,3,2) ; hold off spy (C) hold on for k = 1:nk r1 = r(k) ; r2 = r(k+1) ; c1 = s(k) ; c2 = s(k+1) ; plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ; end [p2,q2,rr2,ss2,cp,rp] = cs_dmperm (A) ; if (min (m,n) > 0) if (length (rr2) ~= length (r)) error ('# fine blocks!') ; end end if (rp (4) - 1 ~= sprnk) rp %#ok sprnk %#ok error ('!') ; end if (any (sort (p2) ~= 1:m)) error ('p2!') ; end if (any (sort (q2) ~= 1:n)) error ('q2!') ; end if (cp (5) ~= n+1) error ('cp!') ; end if (rp (5) ~= m+1) error ('rp!') ; end C = A (p2,q2) ; subplot (2,3,3) ; cs_dmspy (A,0) ; % hold off % spy (C) ; % hold on % r1 = rp(1) ; % r2 = rp(2) ; % c1 = cp(1) ; % c2 = cp(2) ; % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ; r1 = rp(1) ; r2 = rp(2) ; c1 = cp(2) ; c2 = cp(3) ; % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ; B = C (r1:r2-1, c1:c2-1) ; if (nnz (diag (B)) ~= size (B,1)) error ('C1 diag!') ; end r1 = rp(2) ; r2 = rp(3) ; c1 = cp(3) ; c2 = cp(4) ; % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'r') ; B = C (r1:r2-1, c1:c2-1) ; if (nnz (diag (B)) ~= size (B,1)) error ('C2 diag!') ; end r1 = rp(3) ; r2 = rp(4) ; c1 = cp(4) ; c2 = cp(5) ; % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ; B = C (r1:r2-1, c1:c2-1) ; if (nnz (diag (B)) ~= size (B,1)) error ('C3 diag!') ; end r1 = rp(4) ; %#ok r2 = rp(5) ; %#ok c1 = cp(4) ; %#ok c2 = cp(5) ; %#ok % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ; if (~isempty (S)) [p1,q1,r0,s0] = dmperm (S) ; [p3,r3] = cs_scc (S) ; if (length (r3) ~= length (r0)) error ('scc size!') ; end if (any (sort (p3) ~= 1:m)) error ('scc perm!') ; end nk = length (r0)-1 ; subplot (2,3,4) ; hold off spy (S (p1,q1)) ; hold on for k = 1:nk r1 = r0(k) ; r2 = r0(k+1) ; c1 = s0(k) ; c2 = s0(k+1) ; plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ; end subplot (2,3,5) ; hold off spy (S (p3,p3)) ; hold on for k = 1:nk r1 = r3(k) ; r2 = r3(k+1) ; c1 = r3(k) ; c2 = r3(k+1) ; plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ; end end subplot (2,3,6) ; cs_dmspy (A) ; drawnow % pause end SuiteSparse/CXSparse/MATLAB/Test/test20.m0000644001170100242450000000175610710252311016616 0ustar davisfacfunction test20 %TEST20 test chol_updown2 % % Example: % test20 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions rand ('state', 0) ; maxerr = [0 0 0 0] ; for trials = 1:100 n = fix (100 * rand (1)) ; A = rand (n) ; if (~ispc) if (mod (trials, 2) == 0) A = A + 1i*rand(n) ; end end A1 = A*A' + n*eye (n) ; try L1 = chol (A1)' ; catch continue ; end err1 = norm (L1*L1'-A1) ; w = rand (n,1) ; A2 = A1 + w*w' ; L2 = chol (A2)' ; err2 = norm (L2*L2'-A2) ; % try an update L2b = chol_updown2 (L1, +1, w) ; err2b = norm (L2b*L2b'-A2) ; % try a downdate L1b = chol_updown2 (L2, -1, w) ; %#ok err1b = norm (L1b*L1b'-A1) ; fprintf ('%3d: %6.2e %6.2e : %6.2e %6.2e\n', n, err1, err2, err2b, err1b) ; % pause maxerr = max (maxerr, [err1 err2 err2b err1b]) ; end fprintf ('maxerr: %g\n', maxerr) ; SuiteSparse/CXSparse/MATLAB/Test/test21.m0000644001170100242450000000360410710252335016617 0ustar davisfacfunction test21 %TEST21 test cs_updown, chol_updown2 % % Example: % test21 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions rand ('state', 0) ; randn ('state', 0) ; clf for trials = 1:100 if (trials <= 1) n = trials ; else n = 1+fix (100 * rand (1)) ; end fprintf ('n: %d\n', n) ; d = 0.1 * rand (1) ; A = sprandn (n,n,d) ; if (~ispc) if (rand ( ) > .5) A = A + 1i * sprand (A) ; end end A = A+A' + 100 * speye (n) ; try p = amd (A) ; catch p = symamd (A) ; end A = sparse (A (p,p)) ; try L = chol (A)' ; catch continue ; end parent = etree (A) ; subplot (1,3,1) ; spy (A) ; if (n > 0) subplot (1,3,2) ; treeplot (parent) ; end subplot (1,3,3) ; spy (L) ; drawnow for trials2 = 1:10 k = 1+fix (n * rand (1)) ; if (k <= 0 | k > n) %#ok k = 1 ; end w = sprandn (L (:,k)) ; Anew = A + w*w' ; Lnew = cs_updown (L, w, parent) ; err6 = norm (Lnew*Lnew' - Anew, 1) ; Lnew = cs_updown (L, w, parent, '+') ; err7 = norm (Lnew*Lnew' - Anew, 1) ; [Lnew, wnew] = chol_updown2 (L, 1, w) ; err2 = norm (Lnew*Lnew' - Anew, 1) ; err10 = norm (wnew - (L\w)) ; L3 = chol_updown2 (L, +1, w) ; err9 = norm (L3*L3' - Anew, 1) ; [L2, wnew] = chol_updown2 (Lnew, -1, w) ; err3 = norm (L2*L2' - A, 1) ; err11 = norm (wnew - (Lnew\w)) ; L2 = cs_updown (Lnew, w, parent, '-') ; err5 = norm (L2*L2' - A, 1) ; L2 = chol_updown2 (Lnew, -1, w) ; err8 = norm (L2*L2' - A, 1) ; err = max ([err2 err3 err5 err6 err7 err9 err8 err10 err11]) ; fprintf (' k %3d %6.2e\n', k, err) ; if (err > 1e-11) err2 %#ok err3 %#ok err5 %#ok err6 %#ok err7 %#ok err8 %#ok err9 %#ok err10 %#ok err11 %#ok pause end end % pause end SuiteSparse/CXSparse/MATLAB/Test/test22.m0000644001170100242450000000174610620667553016641 0ustar davisfacfunction test22 %TEST22 test cond1est % % Example: % test22 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:200) ; clf % f = f(1) nprob = length (f) ; C1 = zeros (nprob,1) ; C2 = zeros (nprob,1) ; C3 = zeros (nprob,1) ; for k = 1:length (f) i = f (k) ; Prob = UFget (i) ; disp (Prob) ; A = Prob.A ; [m n] = size (A) ; if (~isreal (A) | m ~= n) %#ok continue end c1 = condest (A) ; c2 = cond1est (A) ; if (c1 == c2) err = 0 ; else err = (c1-c2)/max(1,c1) ; end c3 = cond (full (A), 1) ; fprintf ('%10.4e %10.4e (%10.4e) : %10.4e\n', c1, c2, c3, err) ; C1 (k) = c1 ; C2 (k) = c2 ; C3 (k) = c3 ; subplot (1,2,1) ; loglog (C1, C2, 'x', [1 1e20], [1 1e20], 'r') ; subplot (1,2,2) ; loglog (C3, C2, 'x', [1 1e20], [1 1e20], 'r') ; drawnow end SuiteSparse/CXSparse/MATLAB/Test/test23.m0000644001170100242450000000116010710252361016613 0ustar davisfacfunction test23 %TEST23 test cs_dmspy % % Example: % test23 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions randn ('state', 0) ; rand ('state', 0) ; clf for trials = 1:1000 % m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; m = n ; % d = 0.1 * rand (1) ; d = rand (1) * 4 * max (m,n) / max (m*n,1) ; A = sprandn (m,n,d) ; % S = sprandn (m,m,d) + speye (m) ; if (~ispc) if (rand ( ) > .5) A = A + 1i * sprand (A) ; end end cs_dmspy (A) ; drawnow % pause end SuiteSparse/CXSparse/MATLAB/Test/test24.m0000644001170100242450000000171410710252400016613 0ustar davisfacfunction test24 %TEST24 test cs_fielder % % Example: % test24 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:200) ; clf % f = f(1) for k = 1:length (f) i = f (k) ; Prob = UFget (i) ; disp (Prob) ; A = real (Prob.A) ; [m n] = size (A) ; if (m ~= n) continue end S = A ; if (~ispc) if (mod (k,2) == 0) S = S + 1i * sprand (A) ; end end tic p1 = symrcm (A) ; t1 = toc ; tic p2 = cs_fiedler (S) ; t2 = toc ; rel = t2 / max (t1,1e-6) ; fprintf ('time: symrcm %8.3f fiedler %8.3f rel %8.2f\n', t1, t2, rel) ; A = A|A' ; subplot (1,3,1) ; spy (A) ; subplot (1,3,2) ; spy (A (p1,p1)) ; subplot (1,3,3) ; spy (A (p2,p2)) ; % evaluate the profile ... drawnow % pause end SuiteSparse/CXSparse/MATLAB/Test/test25.m0000644001170100242450000000212310710252417016617 0ustar davisfacfunction test25 %TEST25 test cs_nd % % Example: % test25 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:400) ; clf % f = f(1) for k = 1:length (f) i = f (k) ; Prob = UFget (i) ; disp (Prob) ; A = real (Prob.A) ; [m n] = size (A) ; if (m ~= n) continue end A = A|A' ; S = A ; if (~ispc) if (mod (k,2) == 0) S = S + 1i * sprand (A) ; end end tic ; p1 = symrcm (A) ; t1 = toc ; tic ; p2 = cs_nd (sparse (1)) ; toc ; if (p2 ~= 1) error ('!') ; end tic ; p2 = cs_nd (S) ; t2 = toc ; if (any (sort (p2) ~= 1:n)) error ('!') ; end rel = t2 / max (t1,1e-6) ; fprintf ('time: symrcm %8.3f nd %8.3f rel %8.2f\n', t1, t2, rel) ; subplot (1,3,1) ; spy (A) ; subplot (1,3,2) ; spy (A (p1,p1)) ; subplot (1,3,3) ; spy (A (p2,p2)) ; % evaluate the profile ... drawnow % pause end SuiteSparse/CXSparse/MATLAB/Test/test26.m0000644001170100242450000000335310710252502016621 0ustar davisfacfunction test26 %TEST26 test cs_dmsol and cs_dmspy % % Example: % test26 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions randn ('state', 0) ; rand ('state', 0) ; clf ntrials = 1000 ; e1 = zeros (ntrials,1) ; e2 = zeros (ntrials,1) ; for trials = 1:ntrials m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; % d = 0.1 * rand (1) ; d = rand (1) * 4 * max (m,n) / max (m*n,1) ; A = sprandn (m,n,d) ; % S = sprandn (m,m,d) + speye (m) ; if (~ispc) if (rand ( ) > .5) A = A + 1i * sprand (A) ; end end subplot (1,3,2) ; spy (A) ; subplot (1,3,3) ; cs_dmspy (A) ; b = rand (m,1) ; if (~ispc) if (rand ( ) > .5) b = b + 1i * rand (size (b)) ; end end % MATLAB cannot do A\b when A is sparse and rectangular and either % A or b are complex if (m ~= n & isreal (A) & ~isreal (b)) %#ok x1 = (A\real(b)) + 1i * (A\imag(b)) ; err1 = norm (A*x1-b) ; elseif ((m ~= n) & ~isreal (A)) %#ok err1 = 1 ; else x1 = A\b ; err1 = norm (A*x1-b) ; end x2 = cs_dmsol (A,b) ; err2 = norm (A*x2-b) ; lerr1 = log10 (max (err1, eps)) ; lerr2 = log10 (max (err2, eps)) ; fprintf ('rank: %3d %3d err %6.2e %6.2e : %6.1f\n', ... sprank(A), rank(full(A)), err1, err2, lerr1 - lerr2) ; if (isnan (err1)) lerr1 = 10 ; end if (isnan (err2)) lerr2 = 10 ; end if (lerr2 > lerr1 + 5) % pause end e1 (trials) = lerr1 ; e2 (trials) = lerr2 ; subplot (1,3,1) ; plot (e1, e2, 'o', [-16 10], [-16 10], 'r') ; xlabel ('MATLAB error') ; ylabel ('dmsol error') ; drawnow % pause end SuiteSparse/CXSparse/MATLAB/Test/test27.m0000644001170100242450000000116710620372664016637 0ustar davisfacfunction test27 %TEST27 test cs_qr, cs_utsolve, cs_qrsol % % Example: % test27 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions rand ('state', 0) ; Prob = UFget ('HB/ibm32') ; A = Prob.A ; A = A (1:10,:) ; [m n] = size (A) ; [V,Beta,p,R,q] = cs_qr (A') ; b = rand (m,1) ; Rm = R (1:m,1:m) ; bq = b (q) ; rtbq = Rm' \ bq ; rt2 = cs_utsolve (Rm, bq) ; norm (rtbq - rt2) x = [rt2 ; zeros(n-m,1)] ; for k = m:-1:1 x = x - V(:,k) * (Beta (k) * (V (:,k)' * x)) ; end x (p) = x ; norm (A*x-b) x2 = cs_qrsol (A,b) ; norm (A*x2-b) norm (x-x2) SuiteSparse/CXSparse/MATLAB/Test/test28.m0000644001170100242450000000436310710252523016630 0ustar davisfacfunction test28 %TEST28 test cs_randperm, cs_dmperm % % Example: % test28 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions rand ('state', 0) ; for n = 1:100 for trials = 1:1000 p = cs_randperm (n, rand) ; if (any (sort (p) ~= 1:n)) n %#ok p %#ok error ('!') end end end index = UFget ; [ignore f] = sort (index.nnz) ; fprintf ('p=dmperm (std, rand, rev) [p,q,r,s]=dmperm (std, rand, rev)\n') ; nmat = length (f) ; nmat = min (100, nmat) ; T1 = zeros (nmat,1) ; T2 = zeros (nmat,1) ; T3 = zeros (nmat,1) ; D1 = zeros (nmat,1) ; D2 = zeros (nmat,1) ; D3 = zeros (nmat,1) ; for k = 1:nmat i = f (k) ; Prob = UFget (i,index) ; A = Prob.A ; [m n] = size (A) ; fprintf ('%35s: ', Prob.name) ; if (~ispc) if (rand () > .5) A = A + 1i * sprand (A) ; end end tic p = cs_dmperm (A) ; t1 = toc ; sprank1 = sum (p > 0) ; fprintf (' %8.2f', t1) ; T1 (k) = t1 ; tic p = cs_dmperm (A,1) ; t2 = toc ; sprank2 = sum (p > 0) ; fprintf (' %8.2f', t2) ; T2 (k) = t2 ; tic p = cs_dmperm (A,-1) ; t3 = toc ; sprank3 = sum (p > 0) ; fprintf (' %8.2f', t3) ; T3 (k) = t3 ; if (sprank1 ~= sprank2 | sprank1 ~= sprank3) %#ok error ('!') ; end tic [p1,q1,r1,s1,cc1,rr1] = cs_dmperm (A) ; %#ok d1 = toc ; fprintf (' %8.2f', d1) ; D1 (k) = d1 ; tic [p2,q2,r2,s2,cc2,rr2] = cs_dmperm (A,1) ; %#ok d2 = toc ; fprintf (' %8.2f', d2) ; D2 (k) = d2 ; tic [p3,q3,r3,s3,cc3,rr3] = cs_dmperm (A,-1) ; %#ok d3 = toc ; fprintf (' %8.2f\n', d3) ; D3 (k) = d3 ; if (sprank1 == max (m,n)) nz1 = nnz (diag (A (p1,q1))) ; nz2 = nnz (diag (A (p2,q2))) ; nz3 = nnz (diag (A (p3,q3))) ; if (nz1 ~= sprank1 | nz2 ~= sprank2 | nz3 ~= sprank3) %#ok error ('!') end end subplot (1,2,1) loglog (T1 (1:k), T2 (1:k), 'x', ... T1 (1:k), T3 (1:k), 'go', ... [1e-5 1e3], [1e-5 1e3], 'r-') ; axis equal subplot (1,2,2) loglog (D1 (1:k), D2 (1:k), 'x', ... D1 (1:k), D3 (1:k), 'go', ... [1e-5 1e3], [1e-5 1e3], 'r-') ; axis equal drawnow end SuiteSparse/CXSparse/MATLAB/Test/cs_frand_mex.c0000644001170100242450000000276210571350365020126 0ustar davisfac#include "cs_mex.h" /* A = cs_frand (n,nel,s) creates an n-by-n sparse matrix consisting of nel * finite elements, each of which are of size s-by-s with random symmetric * nonzero pattern, plus the identity matrix. * See also MATLAB/Demo/private/frand.m */ cs_dl *cs_dl_frand (CS_INT n, CS_INT nel, CS_INT s) { CS_INT ss = s*s, nz = nel*ss, e, i, j, *P ; cs *A, *T = cs_dl_spalloc (n, n, nz, 1, 1) ; if (!T) return (NULL) ; P = cs_dl_malloc (s, sizeof (CS_INT)) ; if (!P) return (cs_dl_spfree (T)) ; for (e = 0 ; e < nel ; e++) { for (i = 0 ; i < s ; i++) P [i] = rand () % n ; for (j = 0 ; j < s ; j++) { for (i = 0 ; i < s ; i++) { cs_dl_entry (T, P [i], P [j], rand () / (double) RAND_MAX) ; } } } for (i = 0 ; i < n ; i++) cs_dl_entry (T, i, i, 1) ; A = cs_dl_compress (T) ; cs_dl_spfree (T) ; return (cs_dl_dupl (A) ? A : cs_dl_spfree (A)) ; } void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT n, nel, s ; cs *A, *AT ; if (nargout > 1 || nargin != 3) { mexErrMsgTxt ("Usage: C = cs_frand(n,nel,s)") ; } n = mxGetScalar (pargin [0]) ; nel = mxGetScalar (pargin [1]) ; s = mxGetScalar (pargin [2]) ; n = CS_MAX (1,n) ; nel = CS_MAX (1,nel) ; s = CS_MAX (1,s) ; AT = cs_dl_frand (n, nel, s) ; A = cs_dl_transpose (AT, 1) ; cs_dl_spfree (AT) ; cs_dl_dropzeros (A) ; pargout [0] = cs_dl_mex_put_sparse (&A) ; } SuiteSparse/CXSparse/MATLAB/Test/cond1est.m0000644001170100242450000000075410620666162017227 0ustar davisfacfunction c = cond1est (A) %COND1EST 1-norm condition estimate. % Example: % c = cond1est(A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; if (m ~= n | ~isreal (A)) %#ok error ('A must be square and real') ; end if isempty(A) c = 0 ; return ; end [L,U,P,Q] = lu (A) ; if (~isempty (find (abs (diag (U)) == 0))) %#ok c = Inf ; else c = norm (A,1) * norm1est (L,U,P,Q) ; end SuiteSparse/CXSparse/MATLAB/Test/test1.m0000644001170100242450000000274110710254571016542 0ustar davisfacfunction test1 %TEST1 test cs_transpose, cs_gaxpy, cs_sparse, cs_sparse2 % % Example: % test1 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:100) ; for ii = f Prob = UFget (ii) ; disp (Prob) ; for cmplex = 0:double(~ispc) A = Prob.A ; if (cmplex) A = A + 1i*sprand(A) ; end B = A' ; C = cs_transpose (A) ; if (nnz (B-C) ~= 0) error ('!') end C = cs_transpose (A,0) ; if (nnz (A.'-C) ~= 0) error ('!') end C = cs_transpose (A,1) ; if (nnz (A'-C) ~= 0) error ('!') end [m n] = size (A) ; % if (m == n) x = rand (n,1) ; y = rand (m,1) ; z = y+A*x ; q = cs_gaxpy (A,x,y) ; err = norm (z-q,1) / norm (z,1) ; disp (err) ; if (err > 1e-14) error ('!') end % end if (~ispc) x = x + 1i*rand (n,1) ; y = y + 1i*rand (m,1) ; z = y+A*x ; q = cs_gaxpy (A,x,y) ; err = norm (z-q,1) / norm (z,1) ; disp (err) ; if (err > 1e-14) error ('!') end end [i j x] = find (A) ; p = randperm (length (i)) ; i = i (p) ; j = j (p) ; x = x (p) ; D = sparse (i,j,x) ; E = cs_sparse (i,j,x) ; % [i j x] F = cs_sparse2 (i,j,x) ; if (nnz (D-E) ~= 0) error ('!') end if (nnz (F-E) ~= 0) error ('!') end clear A B C D E F % pause end end SuiteSparse/CXSparse/MATLAB/Test/test2.m0000644001170100242450000000371310710252554016542 0ustar davisfacfunction test2 %TEST2 test cs_sparse, cs_permute, cs_pvec, cs_ipvec, cs_symperm % % Example: % test2 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) % clf for trial = 1:100 m = fix (10 * rand (1)) ; n = fix (10 * rand (1)) ; nz = fix (100 * rand (1)) ; i = 1 + fix (m * rand (nz,1)) ; j = 1 + fix (n * rand (nz,1)) ; x = rand (nz,1) ; if (~ispc) if (mod (trial, 2) == 1) x = x + 1i * (2*rand(nz,1)-1) ; end end A = sparse (i,j,x) ; B = cs_sparse (i,j,x) ; D = cs_sparse2 (i,j,x) ; fprintf ('%3d %3d %6d : %6d %6d : %d\n', ... m, n, nz, nnz (A), nnz(B), nz-nnz(A)) ; err = norm (A-B,1) / max (1, norm (A,1)) ; if (err > 0) disp ('err = ') ; disp (err) ; end if (err > 1e-14) error ('!') ; end if (nnz (B-D) > 0) error ('!') ; end if (nnz (A) ~= nnz (B)) error ('nz!') ; end if (max (1,nnz (B)) ~= max (1,nzmax (B))) nnz (B) nzmax (B) error ('nzmax!') ; end % pack [m n] = size (A) ; p = randperm (m) ; q = randperm (n) ; C1 = A (p,q) ; C2 = cs_permute (A,p,q) ; err = norm (C1-C2,1) ; if (err > 0) error ('!') ; end % subplot (1,2,1) ; spy (A) % subplot (1,2,2) ; spy (C2) % drawnow x = rand (m,1) ; if (~ispc) if (mod (trial, 2) == 1) x = x + 1i * (2*rand(m,1)-1) ; end end x1 = x (p) ; x2 = cs_pvec (x, p) ; err = norm (x1-x2,1) ; if (err > 0) error ('!') ; end x1 = zeros (m,1) ; x1 (p) = x ; %#ok x2 = cs_ipvec (x, p) ; %#ok n = min (m,n) ; B = A (1:n, 1:n) ; p = randperm (n) ; B = B+B' ; C1 = triu (B (p,p)) ; C2 = cs_symperm (B,p) ; try pp = amd (C2) ; %#ok catch pp = symamd (C2) ; %#ok end err = norm (C1-C2,1) ; if (err > 0) error ('!') ; end end SuiteSparse/CXSparse/MATLAB/Test/test3.m0000644001170100242450000000326610710254574016552 0ustar davisfacfunction test3 %TEST3 test cs_lsolve, cs_ltsolve, cs_usolve, cs_chol % % Example: % test3 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:100) ; clf % f = f(1) for i = f Prob = UFget (i) ; disp (Prob) ; for cmplex = 0:double(~ispc) A = Prob.A ; [m n] = size (A) ; if (m ~= n) continue end if (cmplex) A = A + 1i*sprand(A) ; end A = A*A' + 2*n*speye (n) ; try p = amd (A) ; catch p = symamd (A) ; end try L0 = chol (A)' ; catch continue end b = rand (n,1) ; if (~ispc) if (mod (i,2) == 1) b = b + 1i*rand(n,1) ; end end C = A(p,p) ; c = condest (C) ; fprintf ('condest: %g\n', c) ; x1 = L0\b ; x2 = cs_lsolve (L0,b) ; err = norm (x1-x2,1) ; if (err > 1e-12 * c) error ('!') ; end x1 = L0'\b ; x2 = cs_ltsolve (L0,b) ; err = norm (x1-x2,1) ; if (err > 1e-10 * c) error ('!') ; end U = L0' ; x1 = U\b ; x2 = cs_usolve (U,b) ; err = norm (x1-x2,1) ; if (err > 1e-10 * c) error ('!') ; end L2 = cs_chol (A) ; subplot (2,3,1) ; spy (L0) ; subplot (2,3,4) ; spy (L2) ; err = norm (L0-L2,1) ; if (err > 1e-8 * c) error ('!') ; end L1 = chol (C)' ; L2 = cs_chol (C) ; subplot (2,3,2) ; spy (L1) ; subplot (2,3,5) ; spy (L2) ; err = norm (L1-L2,1) ; if (err > 1e-8 * c) error ('!') ; end [L3,p] = cs_chol (A) ; C = A(p,p) ; L4 = chol (C)' ; subplot (2,3,3) ; spy (L4) ; subplot (2,3,6) ; spy (L3) ; err = norm (L4-L3,1) ; if (err > 1e-8 * c) error ('!') ; end drawnow end end SuiteSparse/CXSparse/MATLAB/Test/test4.m0000644001170100242450000000156510710252626016547 0ustar davisfacfunction test4 %TEST4 test cs_multiply % % Example: % test4 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) ; for trial = 1:100 m = fix (10 * rand (1)) ; n = fix (10 * rand (1)) ; k = fix (10 * rand (1)) ; d = rand (1) ; A = sprandn (m,n,d) ; B = sprandn (n,k,d) ; if (~ispc) if (mod (trial, 4) == 0) A = A + 1i * sprandn (A) ; end if (mod (trial, 2) == 0) B = B + 1i * sprandn (B) ; end end C = A*B ; D = cs_multiply (A,B) ; err = nnz (spones (C) - spones (D)) ; if (err > 0) error ('nz!') ; end err = norm (C-D,1) ; fprintf ('m %3d n %3d k %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ... m, n, k, nnz(A), nnz(B), nnz(C), err) ; if (err > 1e-12) error ('!') ; end end SuiteSparse/CXSparse/MATLAB/Test/test5.m0000644001170100242450000000323410710252655016545 0ustar davisfacfunction test5 %TEST5 test cs_add % % Example: % test5 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) ; for trial = 1:200 m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; d = rand (1) ; A = sprandn (m,n,d) ; B = sprandn (m,n,d) ; if (~ispc) if (mod (trial, 4) == 0) A = A + 1i*sprand(A) ; end if (mod (trial, 2) == 0) B = B + 1i*sprand(B) ; end end C = A+B ; D = cs_add (A,B) ; err = nnz (spones (C) - spones (D)) ; if (err > 0) error ('nz!') ; end err = norm (C-D,1) ; fprintf ('m %3d n %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ... m, n, nnz(A), nnz(B), nnz(C), err) ; if (err > 1e-12) error ('!') ; end alpha = pi ; beta = 3 ; if (~ispc) if (rand () > .5) alpha = alpha + rand ( ) * 1i ; end if (rand () > .5) beta = beta + rand ( ) * 1i ; end end C = alpha*A+B ; D = cs_add (A,B,alpha) ; err = nnz (spones (C) - spones (D)) ; if (err > 0) error ('nz!') ; end err = norm (C-D,1) ; fprintf ('m %3d n %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ... m, n, nnz(A), nnz(B), nnz(C), err) ; if (err > 1e-12) error ('!') ; end C = alpha*A + beta*B ; D = cs_add (A,B,alpha,beta) ; err = nnz (spones (C) - spones (D)) ; if (err > 0) error ('nz!') ; end err = norm (C-D,1) ; fprintf ('m %3d n %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ... m, n, nnz(A), nnz(B), nnz(C), err) ; if (err > 1e-12) error ('!') ; end end SuiteSparse/CXSparse/MATLAB/Test/test6.m0000644001170100242450000000342710710252671016550 0ustar davisfacfunction test6 %TEST6 test cs_reach, cs_reachr, cs_lsolve, cs_usolve % % Example: % test6 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) maxerr = 0 ; clf for trial = 1:201 n = fix (100 * rand (1)) ; d = 0.1 * rand (1) ; L = tril (sprandn (n,n,d),-1) + sprand (speye (n)) ; b = sprandn (n,1,d) ; if (~ispc) if (rand ( ) > .5) L = L + 1i*sprand(L) ; end if (rand ( ) > .5) b = b + 1i*sprand(b) ; end end for uplo = 0:1 if (uplo == 1) % solve Ux=b instead ; L = L' ; end x = L\b ; sr = 1 + cs_reachr (L,b) ; sz = 1 + cs_reachr (L,b) ; check_if_same (sr,sz) ; s2 = 1 + cs_reach (L,b) ; try if (uplo == 0) x3 = cs_lsolve (L,b) ; else x3 = cs_usolve (L,b) ; end catch if (isreal (L) & isreal (b)) %#ok lasterr error ('!') ; end % punt: sparse(L)\sparse(b) not handled by cs_lsolve or cs_usolve x3 = L\b ; end spy ([L b x x3]) drawnow s = sort (sr) ; [i j xx] = find (x) ; %#ok [i3 j3 xx3] = find (x3) ; %#ok if (isempty (i)) if (~isempty (s)) i %#ok s %#ok error ('!') ; end elseif (any (s ~= i)) i %#ok s %#ok error ('!') ; end if (isempty (i3)) if (~isempty (s)) i3 %#ok s %#ok error ('!') ; end elseif (any (s ~= sort (i3))) s %#ok i3 %#ok error ('!') ; end if (any (s2 ~= sr)) s2 %#ok sr %#ok error ('!') ; end err = norm (x-x3,1) ; if (err > 1e-12) x %#ok x3 %#ok uplo %#ok err %#ok error ('!') end maxerr = max (maxerr, err) ; end drawnow end fprintf ('maxerr = %g\n', maxerr) ; SuiteSparse/CXSparse/MATLAB/Test/test7.m0000644001170100242450000000505610620667776016571 0ustar davisfacfunction test7 %TEST7 test cs_lu % % Example: % test7 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:100) ; clf maxerr1 = 0 ; maxerr2 = 0 ; for i = f Prob = UFget (i) ; disp (Prob) ; A = Prob.A ; [m n] = size (A) ; if (m ~= n) continue end for cmplex = 0:1 if (cmplex) A = A + norm(A,1) * sprand (A) / 3 ; end [L,U,P] = lu (A) ; udiag = full (diag (U)) ; umin = min (abs (udiag)) ; fprintf ('umin %g\n', umin) ; if (umin > 1e-14) [L2,U2,p] = cs_lu (A) ; subplot (3,4,1) ; spy (A) ; subplot (3,4,2) ; spy (A(p,:)) ; subplot (3,4,3) ; spy (L2) ; subplot (3,4,4) ; spy (U2) ; err1 = norm (L*U-P*A,1) / norm (A,1) ; err2 = norm (L2*U2-A(p,:),1) / norm (A,1) ; fprintf ('err %g %g\n', err1, err2) ; if (err1 > 1e-10 | err2 > 1e-10) %#ok error ('!') ; end maxerr1 = max (maxerr1, err1) ; maxerr2 = max (maxerr2, err2) ; end q = colamd (A) ; [L,U,P] = lu (A (:,q)) ; udiag = full (diag (U)) ; umin = min (abs (udiag)) ; fprintf ('umin %g with q\n', umin) ; if (umin > 1e-14) [L2,U2,p,q2] = cs_lu (A) ; subplot (3,4,5) ; spy (A) ; subplot (3,4,6) ; spy (A(p,q2)) ; subplot (3,4,7) ; spy (L2) ; subplot (3,4,8) ; spy (U2) ; err1 = norm (L*U-P*A(:,q),1) / norm (A,1) ; err2 = norm (L2*U2-A(p,q2),1) / norm (A,1) ; fprintf ('err %g %g\n', err1, err2) ; if (err1 > 1e-10 | err2 > 1e-10) %#ok error ('!') ; end maxerr1 = max (maxerr1, err1) ; maxerr2 = max (maxerr2, err2) ; end try q = amd (A) ; catch q = symamd (A) ; end tol = 0.01 ; [L,U,P] = lu (A (q,q), tol) ; udiag = full (diag (U)) ; umin = min (abs (udiag)) ; fprintf ('umin %g with amd q\n', umin) ; if (umin > 1e-14) [L2,U2,p,q2] = cs_lu (A,tol) ; subplot (3,4,9) ; spy (A) ; subplot (3,4,10) ; spy (A(p,q2)) ; subplot (3,4,11) ; spy (L2) ; subplot (3,4,12) ; spy (U2) ; err1 = norm (L*U-P*A(q,q),1) / norm (A,1) ; err2 = norm (L2*U2-A(p,q2),1) / norm (A,1) ; lbig = full (max (max (abs (L2)))) ; fprintf ('err %g %g lbig %g\n', err1, err2, lbig) ; if (lbig > 1/tol) error ('L!') ; end if (err1 > 1e-10 | err2 > 1e-10) %#ok error ('!') ; end maxerr1 = max (maxerr1, err1) ; maxerr2 = max (maxerr2, err2) ; end drawnow % pause end end fprintf ('maxerr %g %g\n', maxerr1, maxerr2) ; SuiteSparse/CXSparse/MATLAB/Test/test8.m0000644001170100242450000000277110710254600016545 0ustar davisfacfunction test8 %TEST8 test cs_cholsol, cs_lusol % % Example: % test8 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:100) ; % f = f(1) for i = f Prob = UFget (i) ; disp (Prob) ; A = Prob.A ; [m n] = size (A) ; if (m ~= n) continue end for cmplex = 0:double(~ispc) if (cmplex) A = A + 0.1i * (sprand (tril (A,-1) + triu (A,1))) ; end spd = 0 ; if (m == n) if (nnz (A-A') == 0) try p = amd (A) ; catch p = symamd (A) ; end [R,p] = chol (A (p,p)) ; spd = (p == 0) ; end end if (spd) C = A ; else C = A*A' + n*speye (n) ; try p = amd (C) ; catch p = symamd (C) ; end try R = chol (C (p,p)) ; %#ok catch continue end end b = rand (n,1) ; x1 = C\b ; x2 = cs_cholsol (C,b) ; r1 = norm (C*x1-b,1) / norm (C,1) ; r2 = norm (C*x2-b,1) / norm (C,1) ; err = abs (r1-r2) ; fprintf ('err %g\n', err) ; if (err > 1e-10) error ('!') ; end x2 = cs_lusol (C,b, 1, 0.001) ; r2 = norm (C*x2-b,1) / norm (C,1) ; err = abs (r1-r2) ; fprintf ('err %g (lu with amd(A+A'')\n', err) ; if (err > 1e-10) error ('!') ; end if (m ~= n) continue ; end x1 = A\b ; r1 = norm (A*x1-b,1) / norm (A,1) ; if (r1 < 1e-6) x2 = cs_lusol (A,b) ; r2 = norm (A*x2-b,1) / norm (A,1) ; fprintf ('lu resid %g %g\n', r1, r2) ; end end end SuiteSparse/CXSparse/MATLAB/Test/test9.m0000644001170100242450000000504110710254603016542 0ustar davisfacfunction test9 %TEST9 test cs_qr % % Example: % test9 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) ; index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:100) ; clf % f = 185 ; % f = 449 ; % f = 186 for i = f Prob = UFget (i) ; disp (Prob) ; A = Prob.A ; [m n] = size (A) ; if (m < n) A = A' ; end [m n] = size (A) ; sp = sprank (A) ; % if (sprank (A) < min (m,n)) % continue % end for cmplex = 0:double(~ispc) if (cmplex) A = A + 1i * sprand (A) ; end Aorig = A ; A = A (:, colamd (A)) ; s1 = svd (full (A)) ; if (cmplex) try tic ; R = chol (A'*A) ; t1 = toc ; %#ok catch fprintf ('chol (A''*A) failed\n') ; R = [ ] ; end else tic ; R = qr (A) ; t1 = toc ; %#ok end % tic ; % [Q,R] = qr (A) ; % t1 = toc ; [c,h,parent] = symbfact (A, 'col') ; rnz = sum (c) ; %#ok tic ; [V2,Beta2,p,R2] = cs_qr (sparse(A)) ; t2 = toc ; %#ok v2 = full (V2) ; if (any (spones (v2) ~= spones (V2))) error ('got zeros!') ; end C = A ; m2 = size (V2,1) ; if (m2 > m) C = [A ; sparse(m2-m, n)] ; end C = C (p,:) ; % [H1,R1] = myqr (C) ; % err1 = norm (R1-R2,1) / norm (R1) % % [svd(A) svd(R1) svd(full(R2))] % s2 = svd (full (R2)) ; % err2 = norm (s1 - s2) / s1 (1) % fprintf ('%10.6f %10.6f cs speedup %8.3f sprank %d n %d\n', ... % t1, t2, t1/t2, sp, n) ; % err2 % left-looking: [V,Beta3,R3] = qr_left (C) ; %#ok s3 = svd (full (R2)) ; err3 = norm (s1 - s3) / s1 (1) ; disp ('err3 = ') ; disp (err3) ; if (err3 > 1e-12) error ('!') ; end % right-looking: [V,Beta4,R4] = qr_right (C) ; %#ok s4 = svd (full (R2)) ; err4 = norm (s1 - s4) / s1 (1) ; disp ('err4 = ') ; disp (err4) ; if (err4 > 1e-12) error ('!') ; end % H2 = full (H2) % R2 = full (R2) subplot (2,4,1) ; spy (A) ; title ('A colamd') ; subplot (2,4,2) ; spy (C) ; title ('A rperm') ; subplot (2,4,3) ; treeplot (parent) ; subplot (2,4,4) ; spy (Aorig) ; title ('Aorig') ; subplot (2,4,5) ; spy (abs(R2)>0) ; title ('spqr R, no zeros') ; subplot (2,4,6) ; spy (R) ; title ('matlab R') ; subplot (2,4,7) ; spy (R2) ; title ('spqr R') ; subplot (2,4,8) ; spy (V2) ; title ('spqr V') ; drawnow % if (err2 > 1e-9) % error ('!') ; % end if (m2 > m) fprintf ('added %d rows, sprank %d n %d\n', m2-m, sp, n) ; end % pause end end SuiteSparse/CXSparse/MATLAB/Test/testh.m0000644001170100242450000000315510620372711016626 0ustar davisfacfunction testh %TESTH test Householder reflections % % Example: % testh % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse format long e fprintf ('-------------------------------------------------\n') ; x = [-3 4 5]' ; disp (x) ; [v, beta, s] = house (x) ; disp ('v = ') ; disp (v) ; disp ('beta = ') ; disp (beta) ; disp ('s = ') ; disp (s) ; x = x - v*(beta*(v'*x)) ; disp (x) ; fprintf ('-------------------------------------------------\n') ; x = [3 4 5]' ; disp (x) ; [v, beta, s] = house (x) ; disp ('v = ') ; disp (v) ; disp ('beta = ') ; disp (beta) ; disp ('s = ') ; disp (s) ; x = x - v*(beta*(v'*x)) ; disp (x) ; fprintf ('-------------------------------------------------\n') ; x = [1 eps]' ; disp (x) ; [v, beta, s] = house (x) ; disp ('v = ') ; disp (v) ; disp ('beta = ') ; disp (beta) ; disp ('s = ') ; disp (s) ; x = x - v*(beta*(v'*x)) ; disp (x) ; fprintf ('-------------------------------------------------\n') ; x = pi ; disp (x) ; [v, beta, s] = house (x) ; disp ('v = ') ; disp (v) ; disp ('beta = ') ; disp (beta) ; disp ('s = ') ; disp (s) ; x = x - v*(beta*(v'*x)) ; disp (x) ; fprintf ('-------------------------------------------------\n') ; x = -pi ; disp (x) ; [v, beta, s] = house (x) ; disp ('v = ') ; disp (v) ; disp ('beta = ') ; disp (beta) ; disp ('s = ') ; disp (s) ; x = x - v*(beta*(v'*x)) ; disp (x) ; fprintf ('-------------------------------------------------\n') ; x = [1 0 0]' ; disp (x) ; [v, beta, s] = house (x) ; %#ok x = x - v*(beta*(v'*x)) ; disp (x) ; fprintf ('-------------------------------------------------\n') ; SuiteSparse/CXSparse/MATLAB/Test/cs_reach.m0000644001170100242450000000063610620373077017255 0ustar davisfacfunction x = cs_reach(L,b) %#ok %CS_REACH non-recursive reach (interface to CSparse cs_reach) % find nonzero pattern of x=L\sparse(b). L must be sparse, real, and lower % triangular. b must be a real sparse vector. % % Example: % x = cs_reach(L,b) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_reach mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/Test/cs_pvec_mex.c0000644001170100242450000000215210710251202017743 0ustar davisfac#include "cs_mex.h" /* x = b(p) */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT n, k, *p ; double *xx ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_pvec(b,p)") ; } n = mxGetNumberOfElements (pargin [0]) ; if (n != mxGetNumberOfElements (pargin [1])) { mexErrMsgTxt ("b or p wrong size") ; } xx = mxGetPr (pargin [1]) ; p = cs_dl_malloc (n, sizeof (CS_INT)) ; for (k = 0 ; k < n ; k++) p [k] = xx [k] - 1 ; if (mxIsComplex (pargin [0])) { #ifdef NCOMPLEX mexErrMsgTxt ("complex case not supported") ; #else cs_complex_t *x, *b ; b = cs_cl_mex_get_double (n, pargin [0]) ; x = cs_dl_malloc (n, sizeof (cs_complex_t)) ; cs_cl_pvec (p, b, x, n) ; pargout [0] = cs_cl_mex_put_double (n, x) ; cs_free (b) ; /* free copy of complex values */ #endif } else { double *x, *b ; b = cs_dl_mex_get_double (n, pargin [0]) ; pargout [0] = mxCreateDoubleMatrix (n, 1, mxREAL) ; x = mxGetPr (pargout [0]) ; cs_dl_pvec (p, b, x, n) ; } cs_free (p) ; } SuiteSparse/CXSparse/MATLAB/Test/cs_rowcnt.m0000644001170100242450000000062110620373103017467 0ustar davisfacfunction r = cs_rowcnt(A,parent,post) %#ok %CS_ROWCNT row counts for sparse Cholesky % Compute the row counts of the Cholesky factor L of the matrix A. Uses % the lower triangular part of A. % % Example: % r = cs_rowcnt(A,parent,post) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_rowcnt mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/Test/happly.m0000644001170100242450000000047310620373125016774 0ustar davisfacfunction hx = happly (v, beta, x) %HAPPLY apply Householder reflection to a vector % Example: % hx = happly (v,beta,x) ; % computes hx = x - v * (beta * (v' *x)) ; % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse hx = x - v * (beta * (v' *x)) ; SuiteSparse/CXSparse/MATLAB/Test/choldn.m0000644001170100242450000000137610620373020016743 0ustar davisfacfunction L = choldn (Lold,w) %CHOLDN Cholesky downdate % given Lold and w, compute L so that L*L' = Lold*Lold' - w*w' % % Example: % L = cholnd (Lold,w) % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (Lold,1) ; L = Lold ; alpha = 1 ; beta = 1 ; wold = w ; wnew = zeros (n,1) ; for i = 1:n a = w (i) / L(i,i) ; alpha = alpha - a^2 ; if (alpha <= 0) error ('not pos def') ; end beta_new = sqrt (alpha) ; b = beta_new / beta ; c = (a / (beta*beta_new)) ; beta = beta_new ; % L (i,i) = b * L (i,i) ; wnew (i) = a ; for k = i:n w (k) = w (k) - a * L (k,i) ; L (k,i) = b * L (k,i) - c * w(k) ; end end % w % wnew disp (wnew - Lold\wold) SuiteSparse/CXSparse/MATLAB/Test/cholup.m0000644001170100242450000000075010620373044016767 0ustar davisfacfunction L = cholup (Lold,w) %CHOLUP Cholesky update, using Given's rotations % given Lold and w, compute L so that L*L' = Lold*Lold' + w*w' % Example: % L = cholup (Lold,w) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (Lold,1) ; L = [Lold w] ; for k = 1:n g = givens (L(k,k), L(k,n+1)) ; L (:, [k n+1]) = L (:, [k n+1]) * g' ; disp ('L:') ; disp (L) pause end L = L (:,1:n) ; disp (L) ; SuiteSparse/CXSparse/MATLAB/Test/qr_right.m0000644001170100242450000000073610620373164017323 0ustar davisfacfunction [V,Beta,R] = qr_right (A) %QR_RIGHT right-looking Householder QR factorization. % Example: % [V,Beta,R] = qr_right (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; V = zeros (m,n) ; Beta = zeros (1,n) ; for k = 1:n [v,beta] = gallery ('house', A (k:m,k), 2) ; V (k:m,k) = v ; Beta (k) = beta ; A (k:m,k:n) = A (k:m,k:n) - v * (beta * (v' * A (k:m,k:n))) ; end R = A ; SuiteSparse/CXSparse/MATLAB/Test/chol_super.m0000644001170100242450000000100110620373034017625 0ustar davisfacfunction L = chol_super (A,s) %CHOL_SUPER left-looking "supernodal" Cholesky factorization. % Example: % L = chol_super (A,s) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A) ; L = zeros (n) ; ss = cumsum ([1 s]) ; for j = 1:length (s) k1 = ss (j) ; k2 = ss (j+1) ; k = k1:(k2-1) ; L (k,k) = chol (A (k,k) - L (k,1:k1-1) * L (k,1:k1-1)')' ; L (k2:n,k) = (A (k2:n,k) - L (k2:n,1:k1-1) * L (k,1:k1-1)') / L (k,k)' ; end SuiteSparse/CXSparse/MATLAB/Test/cs_maxtransr_mex.c0000644001170100242450000000556710571351706021061 0ustar davisfac#include "cs_mex.h" /* find an augmenting path starting at column j and extend the match if found */ static CS_INT augment (CS_INT k, cs_dl *A, CS_INT *jmatch, CS_INT *cheap, CS_INT *w, CS_INT j) { CS_INT found = 0, p, i = -1, *Ap = A->p, *Ai = A->i ; /* --- Start depth-first-search at node j ------------------------------- */ w [j] = k ; /* mark j as visited for kth path */ for (p = cheap [j] ; p < Ap [j+1] && !found ; p++) { i = Ai [p] ; /* try a cheap assignment (i,j) */ found = (jmatch [i] == -1) ; } cheap [j] = p ; /* start here next time for j */ /* --- Depth-first-search of neighbors of j ----------------------------- */ for (p = Ap [j] ; p < Ap [j+1] && !found ; p++) { i = Ai [p] ; /* consider row i */ if (w [jmatch [i]] == k) continue ; /* skip col jmatch [i] if marked */ found = augment (k, A, jmatch, cheap, w, jmatch [i]) ; } if (found) jmatch [i] = j ; /* augment jmatch if path found */ return (found) ; } /* find a maximum transveral */ static CS_INT *maxtrans (cs_dl *A) /* returns jmatch [0..m-1] */ { CS_INT i, j, k, n, m, *Ap, *jmatch, *w, *cheap ; if (!A) return (NULL) ; /* check inputs */ n = A->n ; m = A->m ; Ap = A->p ; jmatch = cs_dl_malloc (m, sizeof (CS_INT)) ; /* allocate result */ w = cs_dl_malloc (2*n, sizeof (CS_INT)) ; /* allocate workspace */ if (!w || !jmatch) return (cs_dl_idone (jmatch, NULL, w, 0)) ; cheap = w + n ; for (j = 0 ; j < n ; j++) cheap [j] = Ap [j] ; /* for cheap assignment */ for (j = 0 ; j < n ; j++) w [j] = -1 ; /* all columns unflagged */ for (i = 0 ; i < m ; i++) jmatch [i] = -1 ; /* no rows matched yet */ for (k = 0 ; k < n ; k++) augment (k, A, jmatch, cheap, w, k) ; return (cs_dl_idone (jmatch, NULL, w, 1)) ; } /* invert a maximum matching */ static CS_INT *invmatch (CS_INT *jmatch, CS_INT m, CS_INT n) { CS_INT i, j, *imatch ; if (!jmatch) return (NULL) ; imatch = cs_dl_malloc (n, sizeof (CS_INT)) ; if (!imatch) return (NULL) ; for (j = 0 ; j < n ; j++) imatch [j] = -1 ; for (i = 0 ; i < m ; i++) if (jmatch [i] >= 0) imatch [jmatch [i]] = i ; return (imatch) ; } void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs_dl *A, Amatrix ; double *x ; CS_INT i, m, n, *imatch, *jmatch ; if (nargout > 1 || nargin != 1) { mexErrMsgTxt ("Usage: p = cr_maxtransr(A)") ; } /* get inputs */ A = cs_dl_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ; m = A->m ; n = A->n ; jmatch = maxtrans (A) ; imatch = invmatch (jmatch, m, n) ; /* imatch = inverse of jmatch */ pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ; x = mxGetPr (pargout [0]) ; for (i = 0 ; i < n ; i++) x [i] = imatch [i] + 1 ; cs_free (jmatch) ; cs_free (imatch) ; } SuiteSparse/CXSparse/MATLAB/Test/lu_rightp.m0000644001170100242450000000120310620373140017461 0ustar davisfacfunction [L,U,P] = lu_rightp (A) %LU_RIGHTP right-looking LU factorization, with partial pivoting. % % Example: % [L,U,P] = lu_rightp (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A,1) ; P = eye (n) ; for k = 1:n [x,i] = max (abs (A (k:n,k))) ; % partial pivoting i = i+k-1 ; P ([k i],:) = P ([i k], :) ; A ([k i],:) = A ([i k], :) ; % (6.10), (6.11) A (k+1:n,k) = A (k+1:n,k) / A (k,k) ; % (6.12) A (k+1:n,k+1:n) = A (k+1:n,k+1:n) - A (k+1:n,k) * A (k,k+1:n) ; % (6.9) end L = tril (A,-1) + eye (n) ; U = triu (A) ; SuiteSparse/CXSparse/MATLAB/Test/lu_rightr.m0000644001170100242450000000102710620373143017472 0ustar davisfacfunction [L,U] = lu_rightr (A) %LU_RIGHTR recursive right-looking LU. % Example: % [L,U] = lu_rightr (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A,1) ; if (n == 1) L = 1 ; U = A ; else u11 = A (1,1) ; % (6.4) u12 = A (1,2:n) ; % (6.5) l21 = A (2:n,1) / u11 ; % (6.6) [L22,U22] = lu_rightr (A (2:n,2:n) - l21*u12) ; % (6.7) L = [ 1 zeros(1,n-1) ; l21 L22 ] ; U = [ u11 u12 ; zeros(n-1,1) U22 ] ; end SuiteSparse/CXSparse/MATLAB/Test/dmspy_test.m0000644001170100242450000000125310620373113017664 0ustar davisfacfunction dmspy_test %DMSPY_TEST test cspy, cs_dmspy, and cs_dmperm % Example: % dmspy_test % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; f = find (index.nblocks > 1) ; % f = find (index.nblocks > 1 & index.nrows == index.ncols & ... % index.nnzdiag == index.nrows) ; [ignore i] = sort (index.nnz (f)) ; f = f (i) ; for i = f Prob = UFget (i,index) ; disp (Prob) ; clf subplot (2,2,1) ; cspy (Prob.A) ; subplot (2,2,2) ; cs_dmspy (Prob.A) ; [p,q,r,s,cc,rr] = cs_dmperm (Prob.A) ; %#ok subplot (2,2,3) ; plot (p) ; subplot (2,2,4) ; plot (q) ; drawnow end SuiteSparse/CXSparse/MATLAB/Test/gqr3.m0000644001170100242450000000106610620373123016350 0ustar davisfacfunction R = gqr3 (A) %GQR3 QR factorization, based on Givens rotations % % Example: % R = gqr3 (A) % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; % parent = cs_etree (sparse (A), 'col') ; for i = 2:m % i for k = 1:min(i-1,n) % k % Givens rotation to zero out A(i,k) using A(k,k) G = givens2 (A(k,k), A(i,k)) ; A ([k i],k:n) = G * A ([k i],k:n) ; A (i,k) = 0 ; % fprintf ('A(21,25)=%g\n', A(21,25)) ; % if (A(21,25) ~= 0) % pause % end end end R = A ; SuiteSparse/CXSparse/MATLAB/Test/lu_rightpr.m0000644001170100242450000000143110620373141017647 0ustar davisfacfunction [L,U,P] = lu_rightpr (A) %LU_RIGHTPR recursive right-looking LU, with partial pivoting. % % Example: % [L,U,P] = lu_rightpr (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A,1) ; if (n == 1) P = 1 ; L = 1 ; U = A ; else [x,i] = max (abs (A (1:n,1))) ; % partial pivoting P1 = eye (n) ; P1 ([1 i],:) = P1 ([i 1], :) ; A = P1*A ; u11 = A (1,1) ; % (6.10) u12 = A (1,2:n) ; % (6.11) l21 = A (2:n,1) / u11 ; % (6.12) [L22,U22,P2] = lu_rightpr (A (2:n,2:n) - l21*u12) ; % (6.9) or (6.13) o = zeros(1,n-1) ; L = [ 1 o ; P2*l21 L22 ] ; % (6.14) U = [ u11 u12 ; o' U22 ] ; P = [ 1 o ; o' P2] * P1 ; end SuiteSparse/CXSparse/MATLAB/Test/cs_ipvec_mex.c0000644001170100242450000000215510710251173020126 0ustar davisfac#include "cs_mex.h" /* x(p) = b */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT n, k, *p ; double *xx ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_ipvec(b,p)") ; } n = mxGetNumberOfElements (pargin [0]) ; if (n != mxGetNumberOfElements (pargin [1])) { mexErrMsgTxt ("b or p wrong size") ; } xx = mxGetPr (pargin [1]) ; p = cs_dl_malloc (n, sizeof (CS_INT)) ; for (k = 0 ; k < n ; k++) p [k] = xx [k] - 1 ; if (mxIsComplex (pargin [0])) { #ifdef NCOMPLEX mexErrMsgTxt ("complex case not supported") ; #else cs_complex_t *x, *b ; b = cs_cl_mex_get_double (n, pargin [0]) ; x = cs_dl_malloc (n, sizeof (cs_complex_t)) ; cs_cl_ipvec (p, b, x, n) ; pargout [0] = cs_cl_mex_put_double (n, x) ; cs_free (b) ; /* free copy of complex values */ #endif } else { double *x, *b ; b = cs_dl_mex_get_double (n, pargin [0]) ; pargout [0] = mxCreateDoubleMatrix (n, 1, mxREAL) ; x = mxGetPr (pargout [0]) ; cs_dl_ipvec (p, b, x, n) ; } cs_free (p) ; } SuiteSparse/CXSparse/MATLAB/Test/myqr.m0000644001170100242450000000202410620373147016465 0ustar davisfacfunction [H,R] = myqr (A) %MYQR QR factorization using Householder reflections % uses function [v,beta,xnorm] = hmake1 (x) % and function hx = happly (v, beta, x) % % Example % [H,R] = myqr (A) % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; H = zeros (m,n) ; R = zeros (m,n) ; for k = 1:n % apply prior H's % fprintf ('\n-----------------init %d\n', k) ; x = A (:,k) ; for i = 1:k-1 v = H(((i+1):m),i) ; v = [1 ; v] ; %#ok beta = H (i,i) ; % n1 = norm (x (i:m)) ; x (i:m) = happly (v, beta, x (i:m)) ; % n2 = norm (x (i:m)) ; % fprintf ('=============== i %d %g %g\n', i, n1, n2) ; % beta % v' % X = x' % pause % i % x end % k % x % make Hk % fprintf ('x(k:m) = ') ; x (k:m) [v,beta,xnorm] = hmake1 (x (k:m)) ; H (k,k) = beta ; H (k+1:m, k) = v (2:end) ; R (1:(k-1),k) = x (1:(k-1)) ; R (k,k) = xnorm ; % full (R) % pause end % s2 = svd (full (R)) ; % [s1 s2 s1-s2] SuiteSparse/CXSparse/MATLAB/Test/README.txt0000644001170100242450000000035110571641104017012 0ustar davisfacTest for MATLAB interface for CXSparse. Type "testall" to run all the tests. Also includes "textbook" codes for the book "Direct Methods for Sparse Linear Systems", which are not part of CXSparse proper, but are used in the tests. SuiteSparse/CXSparse/MATLAB/Test/chol_example.m0000644001170100242450000000112010620373024020123 0ustar davisfacfunction chol_example %CHOL_EXAMPLE simple Cholesky factorization example % Example % chol_example % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse D = 10 ; X = 1 ; o = 0 ; A = sparse ([ D o X o o o o X o o o D o o X o o o o X X o D o o o X o o o o o o D o o o o X X o X o o D o o o X X o o o o o D X X o o o o X o o X D o o o X o o o o X o D X X o o o X X o o X D o o X o X X o o X o D ]) ; disp ('A = ') ; disp (A) ; L = chol(A)' ; disp ('L = ') ; disp (L) ; clf subplot (1,2,1) ; spy (A) ; subplot (1,2,2) ; spy (L+L') ; SuiteSparse/CXSparse/MATLAB/Test/chol_left.m0000644001170100242450000000062210620373030017425 0ustar davisfacfunction L = chol_left (A) %CHOL_LEFT left-looking Cholesky factorization. % Example % L = chol_left (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A,1) ; L = zeros (n) ; for k = 1:n L (k,k) = sqrt (A (k,k) - L (k,1:k-1) * L (k,1:k-1)') ; L (k+1:n,k) = (A (k+1:n,k) - L (k+1:n,1:k-1) * L (k,1:k-1)') / L (k,k) ; end SuiteSparse/CXSparse/MATLAB/Test/chol_update.m0000644001170100242450000000121610620373036017763 0ustar davisfacfunction [L, w] = chol_update (L, w) %CHOL_UPDATE update a Cholesky factorization. % Example: % [L, w] = chol_update (L, w) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse beta = 1 ; n = size (L,1) ; for j = 1:n alpha = w (j) / L (j,j) ; beta2 = sqrt (beta^2 + alpha^2) ; gamma = alpha / (beta2 * beta) ; delta = beta / beta2 ; L (j,j) = delta * L (j,j) + gamma * w (j) ; w (j) = alpha ; beta = beta2 ; if (j == n) return end w1 = w (j+1:n) ; w (j+1:n) = w (j+1:n) - alpha * L (j+1:n,j) ; L (j+1:n,j) = delta * L (j+1:n,j) + gamma * w1 ; end SuiteSparse/CXSparse/MATLAB/Test/cs_pvec.m0000644001170100242450000000036410620373067017125 0ustar davisfacfunction x = cs_pvec (b,p) %#ok %CS_PVEC x=b(p) % % Example: % x = cs_pvec (b,p) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_pvec mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/Test/chol_updown.m0000644001170100242450000000163210620373037020020 0ustar davisfacfunction [L, w] = chol_updown (L, sigma, w) %CHOL_UPDOWN update or downdate a Cholesky factorization. % Example: % [L, w] = chol_updown (L, sigma, w) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse beta = 1 ; n = size (L,1) ; if (n == 1) L = sqrt (L*L'+sigma*w*w') ; return ; end for k = 1:n alpha = w(k) / L(k,k) ; beta2 = sqrt (beta^2 + sigma*alpha^2) ; gamma = sigma * alpha / (beta2 * beta) ; if (sigma > 0) % update delta = beta / beta2 ; L (k,k) = delta * L (k,k) + gamma * w (k) ; w1 = w (k+1:n) ; w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ; L (k+1:n,k) = delta * L (k+1:n,k) + gamma * w1 ; else % downdate delta = beta2 / beta ; L (k,k) = delta * L (k,k) ; w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ; L (k+1:n,k) = delta * L (k+1:n,k) + gamma * w (k+1:n) ; end w (k) = alpha ; beta = beta2 ; end SuiteSparse/CXSparse/MATLAB/Test/cs_test_make.m0000644001170100242450000000221610710251526020135 0ustar davisfacfunction cs_test_make (force) %CS_TEST_MAKE compiles the CSparse, Demo, and Test mexFunctions. % The current directory must be CSparse/MATLAB/Test to use this function. % % Example: % cs_test_make % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse mexcmd = 'mex -DCS_LONG -I../../../UFconfig' ; if (~isempty (strfind (computer, '64'))) mexcmd = [mexcmd ' -largeArrayDims'] ; end if (nargin < 1) force = 0 ; end cd ('../CSparse') ; [object_files timestamp] = cs_make ; cd ('../Test') ; mexfunc = { 'cs_ipvec', 'cs_pvec', 'cs_sparse2', ... 'cs_reach', 'cs_maxtransr', 'cs_reachr', 'cs_rowcnt', 'cs_frand' } ; if (ispc) % Windows does not support ANSI C99 mexcmd = [mexcmd ' -DNCOMPLEX'] ; end for i = 1:length(mexfunc) [s t tobj] = cs_must_compile ('', mexfunc{i}, '_mex', ... ['.' mexext], 'cs_test_make.m', force) ; if (s | tobj < timestamp) %#ok cmd = [mexcmd ' -O -output ' mexfunc{i} ' ' mexfunc{i} '_mex.c -I..' ... filesep '..' filesep 'Include -I..' ... filesep 'CSparse ' object_files] ; fprintf ('%s\n', cmd) ; eval (cmd) ; end end SuiteSparse/CXSparse/MATLAB/Test/cs_reachr.m0000644001170100242450000000063710620373100017423 0ustar davisfacfunction x = cs_reachr(L,b) %#ok %CS_REACHR recursive reach (interface to CSparse cs_reachr) % find nonzero pattern of x=L\sparse(b). L must be sparse, real, and lower % triangular. b must be a real sparse vector. % % Example: % x = cs_reachr(L,b) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_reach mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/Test/etree_sample.m0000644001170100242450000000227010620373115020140 0ustar davisfacfunction etree_sample % ETREE_SAMPLE construct a sample etree and symbolic factorization % % Example % etree_sample % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clf % desired etree: % 1 2 3 4 5 6 7 8 9 10 11 goal = [6 3 8 6 8 7 9 10 10 11 0] ; o = 0 ; X = 1 ; x = 0 ; A = [ 1 o o o o o o o o o o o 2 o o o o o o o o o o X 3 o o o o o o o o o o o 4 o o o o o o o o o o o 5 o o o o o o X o o X o 6 o o o o o X o o x o x 7 o o o o o X x o X o o 8 o o o x o o x o X x o 9 o o x x X X x X x X x 10 o x x X x X x X X x X 11 ] ; A = A + tril(A,-1)' ; disp ('A = ') ; disp (A) [count,h,parent,post,R] = symbfact (A) ; L = R' ; subplot (2,3,1) ; spy (A) title ('A') ; subplot (2,3,2) ; etreeplot (A) title ('etree') ; % [parent, post] = etree (A) ; subplot (2,3,3) ; spy (L) title ('L, not postordered') ; n = size (A,1) ; for k = 1:n fprintf ('parent (%d) = %d goal: %d ok: %d\n', ... k, parent (k), goal (k), goal (k) == parent(k)) ; end [count,h,parent2,post2,R] = symbfact (A (post,post)) ; L = R' ; subplot (2,3,5) ; spy (A (post,post)) title ('A postordered') ; subplot (2,3,6) ; spy (L) title ('L postordered') ; SuiteSparse/CXSparse/MATLAB/Test/another_colormap.m0000644001170100242450000000102010620701546021022 0ustar davisfacfunction another_colormap %ANOTHER_COLORMAP try another color map % % Example: % another_colormap % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse j = jet (128) ; j = j (48:112, :) ; % jj = linspace (0,1,64)' ./ sum (jet,2) ; % j (:,1) = j (:,1) .* jj ; % j (:,2) = j (:,2) .* jj ; % j (:,3) = j (:,3) .* jj ; % white = [1 1 1] ; % gray = [.5 .5 .5] ; %#ok % j = [white ; purple ; j ] ; disp ('j = ') ; disp (j) image (1:size(j,1)) ; colormap (j) ; SuiteSparse/CXSparse/MATLAB/Test/test_randperms.m0000644001170100242450000000161110620373306020525 0ustar davisfacfunction test_randperms %TEST_RANDPERMS test random permutations % Example: % test_randperms % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) for trial = 1:100 m = fix (30 * rand (1)) ; n = fix (30 * rand (1)) ; d = rand (1) ; A = sprandn (m,n,d) ; if (m == 0) p = [] ; else p = randperm (m) ; end if (n == 0) q = [] ; else q = randperm (n) ; end C = A(p,q) ; Im = speye (m) ; In = speye (n) ; P = Im (p,:) ; Q = In (:,q) ; q2 = find (Q) ; if (any (q ~= q2')) error ('!') end p2 = find (P') ; if (any (p ~= p2')) error ('!') end E = P*A*Q ; if (norm (C-E,1) ~= 0) error ('!') end P = sparse (1:m, p, 1) ; Q = sparse (q, 1:n, 1) ; E = P*A*Q ; if (norm (C-E,1) ~= 0) error ('2!') end end SuiteSparse/CXSparse/MATLAB/Test/sample_colormap.m0000644001170100242450000000157110620373165020660 0ustar davisfacfunction sample_colormap %SAMPLE_COLORMAP try a colormap for use in cspy % % Example: % sample_colormap % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse h = jet (64) ; h = h (64:-1:1,:) ; h = h (20:end,:) ; % h = h (17:128,:) ; % s = sum (jet,2) ; % h (:,1) = h (:,1) ./ s ; % h (:,2) = h (:,2) ./ s ; % h (:,3) = h (:,3) ./ s ; h (1,:) = [1 1 1] ; % white h (2,:) = [1 1 .8] ; % light yellow % h colormap (h) ; clf subplot (5,1,1) ; image (1:size(h,1)) ; h = rgb2hsv (h) ; % h (:,3) = linspace (1,0,64) ; % h= hsv2rgb (h) ; subplot (5,1,2) ; plot (h(:,1)) ; axis ([1 64 0 1]) ; ylabel ('red') ; subplot (5,1,3) ; plot (h(:,2)) ; axis ([1 64 0 1]) ; ylabel ('green') ; subplot (5,1,4) ; plot (h(:,3)) ; axis ([1 64 0 1]) ; ylabel ('blue') ; subplot (5,1,5) ; plot (sum(h,2)) ; axis ([1 64 0 3]) ; ylabel ('sum') ; SuiteSparse/CXSparse/MATLAB/Test/house.m0000644001170100242450000000067410620372614016627 0ustar davisfacfunction [v,beta,s] = house (x) %HOUSE find a Householder reflection. % real or complex case. % Example: % [v,beta,s] = house (x) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse v = x ; s = norm (x) ; if (s == 0) beta = 0 ; v (1) = 1 ; else if (x (1) ~= 0) s = sign (x (1)) * s ; end v (1) = v (1) + s ; beta = 1 / real (conj (s) * v (1)) ; end s = - s ; SuiteSparse/CXSparse/MATLAB/Test/cs_reach_mex.c0000644001170100242450000000200110571352431020074 0ustar davisfac#include "cs_mex.h" /* find nonzero pattern of x=L\sparse(b). L must be sparse and lower * triangular. b must be a sparse vector. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs Lmatrix, Bmatrix, *L, *B ; double *x ; CS_INT k, i, j, top, *xi, *perm ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_reach(L,b)") ; } /* get inputs */ L = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ; cs_mex_check (0, L->n, 1, 0, 1, 1, pargin [1]) ; perm = cs_dl_malloc (L->n, sizeof (CS_INT)) ; for (k = 0 ; k < L->n ; k++) perm [k] = k ; xi = cs_dl_calloc (3*L->n, sizeof (CS_INT)) ; top = cs_dl_reach (L, B, 0, xi, perm) ; pargout [0] = mxCreateDoubleMatrix (L->n - top, 1, mxREAL) ; x = mxGetPr (pargout [0]) ; for (j = 0, i = top ; i < L->n ; i++, j++) x [j] = xi [i] ; cs_free (xi) ; cs_free (perm) ; } SuiteSparse/CXSparse/MATLAB/Test/cs_fiedler.m0000644001170100242450000000164410620372610017575 0ustar davisfacfunction [p,v,d] = cs_fiedler (A) %CS_FIEDLER the Fiedler vector of a connected graph. % [p,v,d] = cs_fiedler(A) computes the Fiedler vector v (the eigenvector % corresponding to the 2nd smallest eigenvalue d of the Laplacian of the graph % of A+A'). p is the permutation obtained when v is sorted. A should be a % connected graph. % % Example: % [p,v,d] = cs_fiedler (A) ; % % See also CS_SCC, EIGS, SYMRCM, UNMESH. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A,1) ; if (n < 2) p = 1 ; v = 1 ; d = 0 ; return ; end opt.disp = 0 ; % turn off printing in eigs opt.tol = sqrt (eps) ; if (~isreal (A)) A = spones (A) ; end S = A | A' | speye (n) ; % compute the Laplacian of A S = diag (sum (S)) - S ; [v,d] = eigs (S, 2, 'SA', opt) ; % find the Fiedler vector v v = v (:,2) ; d = d (2,2) ; [ignore p] = sort (v) ; % sort it to get p SuiteSparse/CXSparse/MATLAB/Test/chol_downdate.m0000644001170100242450000000127310620373022020304 0ustar davisfacfunction [L, w] = chol_downdate (L, w) %CHOL_DOWNDATE downdate a Cholesky factorization. % Example % [L, w] = chol_downdate (L, w) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse beta = 1 ; n = size (L,1) ; for j = 1:n alpha = w (j) / L (j,j) ; beta2 = sqrt (beta^2 - alpha^2) ; if (~isreal (beta2)) error ('not positive definite') ; end gamma = alpha / (beta2 * beta) ; delta = beta2 / beta ; L (j,j) = delta * L (j,j) ; w (j) = alpha ; beta = beta2 ; if (j == n) return end w (j+1:n) = w (j+1:n) - alpha * L (j+1:n,j) ; L (j+1:n,j) = delta * L (j+1:n,j) - gamma * w (j+1:n) ; end SuiteSparse/CXSparse/MATLAB/Test/qr_givens.m0000644001170100242450000000105610620666403017476 0ustar davisfacfunction R = qr_givens (A) %QR_GIVENS Givens-rotation QR factorization. % Example: % R = qr_givens (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; parent = cs_etree (sparse (A), 'col') ; A = full (A) ; for i = 2:m k = min (find (A (i,:))) ; %#ok if (isempty (k)) continue ; end while (k > 0 & k <= min (i-1,n)) %#ok A ([k i],k:n) = givens2 (A(k,k), A(i,k)) * A ([k i],k:n) ; A (i,k) = 0 ; k = parent (k) ; end end R = sparse (A) ; SuiteSparse/CXSparse/MATLAB/Test/cs_frand.m0000644001170100242450000000075010620373060017252 0ustar davisfacfunction A = cs_frand (n,nel,s) %#ok %CS_FRAND generate a random finite-element matrix % A = cs_frand (n,nel,s) creates an n-by-n sparse matrix consisting of nel % finite elements, each of which are of size s-by-s with random symmetric % nonzero pattern, plus the identity matrix. % % Example % A = cs_frand (100, 100, 3) ; % See also cs_demo. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_frand mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/Test/lu_right.m0000644001170100242450000000072310620373136017314 0ustar davisfacfunction [L,U] = lu_right (A) %LU_RIGHT right-looking LU factorization. % Example: % [L,U] = lu_right (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A,1) ; L = eye (n) ; U = zeros (n) ; for k = 1:n U (k,k:n) = A (k,k:n) ; % (6.4) and (6.5) L (k+1:n,k) = A (k+1:n,k) / U (k,k) ; % (6.6) A (k+1:n,k+1:n) = A (k+1:n,k+1:n) - L (k+1:n,k) * U (k,k+1:n) ; % (6.7) end SuiteSparse/CXSparse/MATLAB/Test/qr_givens_full.m0000644001170100242450000000061710620373155020521 0ustar davisfacfunction R = qr_givens_full (A) %QR_GIVENS_FULL Givens-rotation QR factorization, for full matrices. % Example: % R = qr_givens_full (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; for i = 2:m for k = 1:min(i-1,n) A ([k i],k:n) = givens2 (A(k,k), A(i,k)) * A ([k i],k:n) ; A (i,k) = 0 ; end end R = A ; SuiteSparse/CXSparse/MATLAB/Test/lu_left.m0000644001170100242450000000134310620373133017125 0ustar davisfacfunction [L,U,P] = lu_left (A) %LU_LEFT left-looking LU factorization. % Example: % [L,U,P] = lu_left (A) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A,1) ; P = eye (n) ; L = zeros (n) ; U = zeros (n) ; for k = 1:n x = [ L(:,1:k-1) [ zeros(k-1,n-k+1) ; eye(n-k+1) ]] \ (P * A (:,k)) ; U (1:k-1,k) = x (1:k-1) ; % the column of U [a i] = max (abs (x (k:n))) ; % find the pivot row i i = i + k - 1 ; L ([i k],:) = L ([k i], :) ; % swap rows i and k of L, P, and x P ([i k],:) = P ([k i], :) ; x ([i k]) = x ([k i]) ; U (k,k) = x (k) ; L (k,k) = 1 ; L (k+1:n,k) = x (k+1:n) / x (k) ; % divide the pivot column by U(k,k) end SuiteSparse/CXSparse/MATLAB/Test/test_qr.m0000644001170100242450000000240210620667064017162 0ustar davisfacfunction test_qr %TEST_QR test various QR factorization methods % % Example: % test_qr % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows,index.ncols)) ; % f = 276 % f = 706 f = f (1:100) ; for i = f % Prob = UFget (i,index) Prob = UFget (i) ; disp (Prob) ; A = Prob.A ; [m n] = size (A) ; if (m < n) A = A' ; end [m n] = size (A) ; if (sprank (A) < n | ~isreal (A)) %#ok continue ; end [V,beta,p,R1,q] = cs_qr(A) ; A = A (p,q) ; parent = etree (A, 'col') ; %#ok R0 = qr (A) ; R2 = qr_givens (full (A)) ; R3 = qr_givens_full (full (A)) ; subplot (2,2,1) ; cspy (R0) ; title ('matlab') ; subplot (2,2,2) ; cspy (R3) ; title ('qr-full') ; subplot (2,2,3) ; cspy (R2) ; title ('qr-givens') ; subplot (2,2,4) ; cspy (R1) ; title ('cs-qr') ; e0 = norm (A'*A-R0'*R0,1) / norm (A,1) ; e1 = norm (A'*A-R1'*R1,1) / norm (A,1) ; e2 = norm (A'*A-R2'*R2,1) / norm (A,1) ; e3 = norm (A'*A-R3'*R3,1) / norm (A,1) ; fprintf ('error %6.2e %6.2e %6.2e %6.2e\n', e0, e1, e2, e3) ; drawnow if (e1 > e0*1e3 | e2 > e0*1e3) %#ok pause end end SuiteSparse/CXSparse/MATLAB/Test/testall.m0000644001170100242450000000302110710513106017132 0ustar davisfacfunction testall %TESTALL test all CSparse functions (run tests 1 to 28 below) % % Example: % testall % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse h = waitbar (0, 'CXSparse') ; cs_test_make % compile all CSparse, Demo, Text, and Test mexFunctions ntests = 29 ; testwait (1, ntests, h) ; test1 ; testwait (2, ntests, h) ; test2 ; testwait (3, ntests, h) ; test3 ; testwait (4, ntests, h) ; test4 ; testwait (5, ntests, h) ; test5 ; testwait (6, ntests, h) ; test6 ; testwait (7, ntests, h) ; test7 ; testwait (8, ntests, h) ; test8 ; testwait (9, ntests, h) ; test9 ; testwait (10, ntests, h) ; test10 ; testwait (11, ntests, h) ; test11 ; testwait (12, ntests, h) ; test12 ; testwait (13, ntests, h) ; test13 ; testwait (14, ntests, h) ; test14 ; testwait (15, ntests, h) ; test15 ; testwait (16, ntests, h) ; test16 ; testwait (17, ntests, h) ; test17 ; testwait (18, ntests, h) ; test18 ; testwait (19, ntests, h) ; test19 ; testwait (20, ntests, h) ; test20 ; testwait (21, ntests, h) ; test21 ; testwait (22, ntests, h) ; test22 ; testwait (23, ntests, h) ; test23 ; testwait (24, ntests, h) ; test24 ; testwait (25, ntests, h) ; test25 ; testwait (26, ntests, h) ; test26 ; testwait (27, ntests, h) ; test27 ; testwait (28, ntests, h) ; test28 ; testwait (29, ntests, h) ; test_qr ; close (h) function testwait (n,ntests,h) fprintf ('\n------------------------ test%d\n', n) ; waitbar (n/(ntests+1), h, sprintf ('CXSparse test %d of %d\n', n, ntests)) ; SuiteSparse/CXSparse/MATLAB/Test/norm1est.m0000644001170100242450000000131410620667470017253 0ustar davisfacfunction est = norm1est (L,U,P,Q) %NORM1EST 1-norm estimate. % L and U must be real. % Example: % est = norm1est (L,U,P,Q) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (L,1) ; for k = 1:5 if (k == 1) est = 0 ; x = ones (n,1) / n ; jold = -1 ; else j = min (find (abs (x) == norm (x,inf))) ; %#ok if (j == jold) break end ; x = zeros (n,1) ; x (j) = 1 ; jold = j ; end x = Q * (U \ (L \ (P*x))) ; est_old = est ; est = norm (x,1) ; if (k > 1 & est <= est_old) %#ok break end ; s = ones (n,1) ; s (find (x < 0)) = -1 ; %#ok x = P' * (L' \ (U' \ (Q'*s))) ; end SuiteSparse/CXSparse/MATLAB/Test/mynormest1.m0000644001170100242450000000302410620666356017623 0ustar davisfacfunction est = mynormest1 (L, U, P, Q) %MYNORMEST1 estimate norm(A,1), using LU factorization (L*U = P*A*Q). % % Example: % est = mynormest1 (L, U, P, Q) % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (L,1) ; est = 0 ; S = zeros (n,1) ; for k = 1:5 if k == 1 x = ones (n,1) / n ; else j = find (abs (x) == max (abs (x))) ; j = j (1) ; x = zeros (n,1) ; x (j) = 1 ; % fprintf ('eka: k %d j %d est %g\n', k, j, est) ; end % x=A\x, but use the existing P*A*Q=L*U factorization x = Q * (U \ (L \ (P*x))) ; est_old = est ; est = sum (abs (x)) ; unchanged = 1 ; for i = 1:n if (x (i) >= 0) s = 1 ; else s = -1 ; end if (s ~= S (i)) S (i) = s ; unchanged = 0 ; end end if (any (S ~= signum (x))) S' %#ok signum(x)' %#ok error ('Hey!') ; end if k > 1 & (est <= est_old | unchanged) %#ok break ; end x = S ; % x=A'\x, but use the existing P*A*Q=L*U factorization x = P' * (L' \ (U' \ (Q'*x))) ; if k > 1 jnew = find (abs (x) == max (abs (x))) ; if (jnew == j) break ; end end end for k = 1:n x (k) = power (-1, k+1) * (1 + ((k-1)/(n-1))) ; end % x=A\x, but use the existing P*A*Q=L*U factorization x = Q * (U \ (L \ (P*x))) ; est_new = 2 * sum (abs (x)) / (3 * n) ; if (est_new > est) est = est_new ; end function s = signum (x) %SIGNUM compute sign of x s = ones (length (x),1) ; s (find (x < 0)) = -1 ; %#ok SuiteSparse/CXSparse/MATLAB/Test/chol_updown2.m0000644001170100242450000000221410620375657020111 0ustar davisfacfunction [L, w] = chol_updown2 (L, sigma, w) %CHOL_UPDOWN2 Cholesky update/downdate (real and complex) % (real or complex) % Example: % [L, w] = chol_updown2 (L, sigma, w) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis, William W. Hager % http://www.cise.ufl.edu/research/sparse beta = 1 ; n = size (L,1) ; if (n == 1) wnew = L\w ; L = sqrt (L*L'+sigma*w*w') ; w = wnew ; return ; end for k = 1:n alpha = w(k) / L(k,k) ; beta2 = sqrt (beta*beta + sigma*alpha*conj(alpha)) ; gamma = sigma * conj(alpha) / (beta2 * beta) ; if (sigma > 0) % update delta = beta / beta2 ; L (k,k) = delta * L (k,k) + gamma * w (k) ; phase = abs (L (k, k))/L (k, k) ; L (k, k) = phase*L (k, k) ; w1 = w (k+1:n) ; w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ; L (k+1:n,k) = phase * (delta * L (k+1:n,k) + gamma * w1) ; else % downdate delta = beta2 / beta ; L (k,k) = delta * L (k,k) ; phase = abs (L (k, k))/L (k, k) ; L (k, k) = phase*L (k, k) ; w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ; L (k+1:n,k) = phase * (delta * L (k+1:n,k) + gamma * w (k+1:n)) ; end w (k) = alpha ; beta = beta2 ; end SuiteSparse/CXSparse/MATLAB/CSparse/0000755001170100242450000000000010634327246015746 5ustar davisfacSuiteSparse/CXSparse/MATLAB/CSparse/cs_ltsolve.m0000644001170100242450000000110310620371640020264 0ustar davisfacfunction x = cs_ltsolve (L,b) %#ok %CS_LTSOLVE solve a sparse upper triangular system L'*x=b. % x = cs_ltsolve(L,b) computes x = L'\b, L must be lower triangular with a % zero-free diagonal. b must be a full vector. % % Example: % Prob = UFget ('HB/bcsstk01') ; L = cs_chol (Prob.A) ; n = size (L,1) ; % b = rand (n,1) ; x = cs_ltsolve (L,b) ; norm (L'*x-b) % % See also CS_LSOLVE, CS_USOLVE, CS_UTSOLVE, MLDIVIDE. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_ltsolve mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_cholsol.m0000644001170100242450000000135210620371612020244 0ustar davisfacfunction x = cs_cholsol (A,b,order) %#ok %CS_CHOLSOL solve A*x=b using a sparse Cholesky factorization. % x = cs_cholsol(A,b) computes x = A\b, where A sparse symmetric positive % definite, and b is a full vector. A 3rd input parameter allows the % ordering to be modified: 0: natural, 1:amd(A), 2: amd(S'*S) where S=A except % with no dense rows, 3:amd(A'*A). The default ordering option is 1. % % Example: % Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; b = rand (size (A,1),1) ; % x = cs_cholsol (A,b) ; norm (A*x-b) % % See also CS_CHOL, CS_AMD, CS_LUSOL, CS_QRSOL, MLDIVIDE. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_cholsol mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/Makefile0000644001170100242450000000735410617167014017413 0ustar davisfacinclude ../../../UFconfig/UFconfig.mk MX = $(MEX) -DCS_LONG AR = ar cr RANLIB = ranlib I = -I../../Include -I../../../UFconfig all: mexcsparse.a cs_mex.h $(MX) cs_thumb_mex.c $(I) mexcsparse.a -output cs_thumb $(MX) cs_print_mex.c $(I) mexcsparse.a -output cs_print $(MX) cs_updown_mex.c $(I) mexcsparse.a -output cs_updown $(MX) cs_gaxpy_mex.c $(I) mexcsparse.a -output cs_gaxpy $(MX) cs_transpose_mex.c $(I) mexcsparse.a -output cs_transpose $(MX) cs_sparse_mex.c $(I) mexcsparse.a -output cs_sparse $(MX) cs_multiply_mex.c $(I) mexcsparse.a -output cs_multiply $(MX) cs_add_mex.c $(I) mexcsparse.a -output cs_add $(MX) cs_permute_mex.c $(I) mexcsparse.a -output cs_permute $(MX) cs_symperm_mex.c $(I) mexcsparse.a -output cs_symperm $(MX) cs_lsolve_mex.c $(I) mexcsparse.a -output cs_lsolve $(MX) cs_ltsolve_mex.c $(I) mexcsparse.a -output cs_ltsolve $(MX) cs_usolve_mex.c $(I) mexcsparse.a -output cs_usolve $(MX) cs_utsolve_mex.c $(I) mexcsparse.a -output cs_utsolve $(MX) cs_chol_mex.c $(I) mexcsparse.a -output cs_chol $(MX) cs_etree_mex.c $(I) mexcsparse.a -output cs_etree $(MX) cs_counts_mex.c $(I) mexcsparse.a -output cs_counts $(MX) cs_qr_mex.c $(I) mexcsparse.a -output cs_qr $(MX) cs_amd_mex.c $(I) mexcsparse.a -output cs_amd $(MX) cs_lu_mex.c $(I) mexcsparse.a -output cs_lu $(MX) cs_cholsol_mex.c $(I) mexcsparse.a -output cs_cholsol $(MX) cs_lusol_mex.c $(I) mexcsparse.a -output cs_lusol $(MX) cs_droptol_mex.c $(I) mexcsparse.a -output cs_droptol $(MX) cs_qrsol_mex.c $(I) mexcsparse.a -output cs_qrsol $(MX) cs_dmperm_mex.c $(I) mexcsparse.a -output cs_dmperm $(MX) cs_scc_mex.c $(I) mexcsparse.a -output cs_scc $(MX) cs_sqr_mex.c $(I) mexcsparse.a -output cs_sqr $(MX) cs_randperm_mex.c $(I) mexcsparse.a -output cs_randperm CSD = cs_mex.o \ cs_amd.o \ cs_chol.o \ cs_counts.o \ cs_cumsum.o \ cs_fkeep.o \ cs_dfs.o \ cs_dmperm.o \ cs_droptol.o \ cs_dropzeros.o \ cs_dupl.o \ cs_entry.o \ cs_etree.o \ cs_gaxpy.o \ cs_ipvec.o \ cs_lsolve.o \ cs_ltsolve.o \ cs_lu.o \ cs_maxtrans.o \ cs_util.o \ cs_malloc.o \ cs_multiply.o \ cs_add.o \ cs_scatter.o \ cs_permute.o \ cs_pinv.o \ cs_post.o \ cs_tdfs.o \ cs_pvec.o \ cs_qr.o \ cs_happly.o \ cs_house.o \ cs_schol.o \ cs_scc.o \ cs_sqr.o \ cs_symperm.o \ cs_transpose.o \ cs_compress.o \ cs_usolve.o \ cs_utsolve.o \ cs_cholsol.o \ cs_lusol.o \ cs_qrsol.o \ cs_updown.o \ cs_norm.o \ cs_print.o \ cs_load.o \ cs_spsolve.o \ cs_reach.o \ cs_ereach.o \ cs_leaf.o \ cs_randperm.o CSC = \ cs_cl_amd.o \ cs_cl_chol.o \ cs_cl_counts.o \ cs_cl_cumsum.o \ cs_cl_fkeep.o \ cs_cl_dfs.o \ cs_cl_dmperm.o \ cs_cl_droptol.o \ cs_cl_dropzeros.o \ cs_cl_dupl.o \ cs_cl_entry.o \ cs_cl_etree.o \ cs_cl_gaxpy.o \ cs_cl_ipvec.o \ cs_cl_lsolve.o \ cs_cl_ltsolve.o \ cs_cl_lu.o \ cs_cl_maxtrans.o \ cs_cl_util.o \ cs_cl_malloc.o \ cs_cl_multiply.o \ cs_cl_add.o \ cs_cl_scatter.o \ cs_cl_permute.o \ cs_cl_pinv.o \ cs_cl_post.o \ cs_cl_tdfs.o \ cs_cl_pvec.o \ cs_cl_qr.o \ cs_cl_happly.o \ cs_cl_house.o \ cs_cl_schol.o \ cs_cl_scc.o \ cs_cl_sqr.o \ cs_cl_symperm.o \ cs_cl_transpose.o \ cs_cl_compress.o \ cs_cl_usolve.o \ cs_cl_utsolve.o \ cs_cl_cholsol.o \ cs_cl_lusol.o \ cs_cl_qrsol.o \ cs_cl_updown.o \ cs_cl_norm.o \ cs_cl_print.o \ cs_cl_load.o \ cs_cl_spsolve.o \ cs_cl_reach.o \ cs_cl_ereach.o \ cs_cl_leaf.o \ cs_cl_randperm.o CS = $(CSD) $(CSC) mexcsparse.a: $(CS) $(AR) mexcsparse.a $(CS) $(RANLIB) mexcsparse.a $(CS): ../../Include/cs.h cs_mex.o: cs_mex.c cs_mex.h $(MX) -c $(I) $< cs_cl_%.o: ../../Source/cs_%.c cp -f $< cs_cl_$*.c $(MX) -DCS_COMPLEX -c $(I) cs_cl_$*.c cs_%.o: ../../Source/cs_%.c $(MX) -c $(I) $< clean: - rm -f *.o distclean: clean - rm -f *.mex* *.dll *.a cs_cl_*.c purge: distclean SuiteSparse/CXSparse/MATLAB/CSparse/cs_lu.m0000644001170100242450000000240310620371643017223 0ustar davisfacfunction [L,U,p,q] = cs_lu (A,tol) %#ok %CS_LU sparse LU factorization, with fill-reducing ordering. % [L,U,p] = cs_lu(A) factorizes A(p,:) into L*U using no fill-reducing % ordering. % % [L,U,p] = cs_lu(A,tol) factorizes A(p,:) into L*U using no fill-reducing % ordering. Entries on the diagonal are given preference in partial pivoting. % % [L,U,p,q] = cs_lu(A) factorizes A(p,q) into L*U using a fill-reducing % ordering q = cs_amd(A,2). Normal partial pivoting is used. % % [L,U,p,q] = cs_lu(A,tol) factorizes A(p,q) into L*U, using a fill-reducing % ordering q = cs_amd(A,1). Entries on the diagonal are given preference in % partial pivoting. With a pivot tolerance tol, the entries in L have % magnitude 1/tol or less. tol = 1 is normal partial pivoting (with % q = cs_amd(A)). tol = 0 ensures p = q. 0= tol * max(abs(A(:,k))). % % Example: % Prob = UFget ('HB/arc130') ; A = Prob.A ; [L,U,p,q] = cs_lu (A) ; % cspy (A (p,q)) ; cspy (L+U) ; % norm (L*U - A(p,q), 1) % % See also CS_AMD, LU, UMFPACK, AMD, COLAMD. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_lu mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_nd.m0000644001170100242450000000164310620371653017212 0ustar davisfacfunction p = cs_nd (A) %CS_ND generalized nested dissection ordering. % p = cs_nd(A) computes the nested dissection ordering of a matrix. Small % submatrices (order 500 or less) are ordered via cs_amd. A must be sparse % and symmetric (use p = cs_nd(A|A') if it is not symmetric). % % Example: % A = delsq (numgrid ('L', 300)) ; % matrix used in 'bench' % p = cs_nd (A) ; % cspy (A (p,p)) ; % % See also CS_AMD, CS_SEP, CS_ESEP, CS_NSEP, AMD. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A,1) ; if (n == 1) p = 1 ; elseif (n < 500) p = cs_amd (A) ; % use cs_amd on small graphs else [s a b] = cs_nsep (A) ; % find a node separator a = a (cs_nd (A (a,a))) ; % order A(a,a) recursively b = b (cs_nd (A (b,b))) ; % order A(b,b) recursively p = [a b s] ; % concatenate to obtain the final ordering end SuiteSparse/CXSparse/MATLAB/CSparse/cs_qr.m0000644001170100242450000000266410620371667017244 0ustar davisfacfunction [V,beta,p,R,q] = cs_qr (A) %#ok %CS_QR sparse QR factorization (Householder-based). % [V,beta,p,R] = cs_qr(A) computes the QR factorization of A(p,:). % [V,beta,p,R,q] = cs_qr(A) computes the QR factorization of A(p,q). % The V, beta, and p terms represent the Householder vectors and coefficients. % The fill-reducing ordering q is found via q = cs_amd(A,3). % The orthogonal factor Q can be obtained via % Q = cs_qright(V,beta,p,speye(size(V,1))), in which case Q*R=A(:,q) is the % resulting factorization (the permutation p is folded into Q). A must be % m-by-n with m >= n. If A is structurally rank deficient, additional empty % rows may have been added to V and R. Note that V is typically much sparser % than Q. % % Example: % % Prob = UFget ('HB/well1033') ; A = Prob.A ; [m n] = size (A) ; % b = rand (m,1) ; % [V,beta,p,R,q] = cs_qr (A) ; % QR factorization of A(p,q) % b1 = cs_qleft (V, beta, p, b) ; % x1 = R (1:n,1:n) \ b1 (1:n) ; % x1 (q) = x1 ; % x2 = A\b ; % norm (x1-x2) % Q = cs_qright(V,beta,p,speye(size(V,1))) ; % Note: p accounted for in Q % norm (Q*R-A(:,q),1) % fprintf ('nnz(R) %d, nnz(V) %d, nnz(Q) %d\n', nnz(R), nnz(V), nnz(Q)) ; % % See also CS_AMD, CS_QRIGHT, CS_QR, CS_DMPERM, QR, COLAMD. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_qr mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_qright.m0000644001170100242450000000154710620371665020115 0ustar davisfacfunction X = cs_qright (V, Beta, p, Y) %CS_QRIGHT apply Householder vectors on the right. % X = cs_qright(V,Beta,p,Y) computes X = Y*P'*H1*H2*...*Hn = Y*Q where Q is % represented by the Householder vectors V, coefficients Beta, and % permutation p. p can be [], which denotes the identity permutation. % To obtain Q itself, use Q = cs_qright(V,Beta,p,speye(size(V,1))). % % Example: % load west0479 ; q = colamd (west0479) ; A = west0479 (:,q) ; % [Q,R] = qr (A) ; norm (Q*R-A, 1) % [V,beta,p,R2] = cs_qr (A) ; % Q2 = cs_qright (V, beta, p, speye(size(V,1))) ; norm (Q2*R2-A, 1) % % See also CS_QR, CS_QLEFT. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (V) ; X = Y ; if (~isempty (p)) X = X (:,p) ; end for k = 1:n X = X - (X * (Beta (k) * V (:,k))) * V (:,k)' ; end SuiteSparse/CXSparse/MATLAB/CSparse/cs_amd_mex.c0000644001170100242450000000126310573562345020216 0ustar davisfac#include "cs_mex.h" /* cs_amd: approximate minimum degree ordering */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs_dl Amatrix, *A ; CS_INT *P, order ; if (nargout > 1 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: p = cs_amd(A,order)") ; } A = cs_dl_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ; /* get A */ order = (nargin > 1) ? mxGetScalar (pargin [1]) : 1 ; /* get ordering */ order = CS_MAX (order, 1) ; order = CS_MIN (order, 3) ; P = cs_dl_amd (order, A) ; /* min. degree ordering */ pargout [0] = cs_dl_mex_put_int (P, A->n, 1, 1) ; /* return P */ } SuiteSparse/CXSparse/MATLAB/CSparse/cs_updown.m0000644001170100242450000000221410620371716020120 0ustar davisfacfunction L = cs_updown (L, c, parent, sigma) %#ok %CS_UPDOWN rank-1 update/downdate of a sparse Cholesky factorization. % L = cs_updown(L,c,parent) computes the rank-1 update L = chol(L*L'+c*c')', % where parent is the elimination tree of L. c must be a sparse column % vector, and find(c) must be a subset of find(L(:,k)) where k = min(find(c)). % L = cs_updown(L,c,parent,'-') is the downdate L = chol(L*L'-c*c'). % L = cs_updown(L,c,parent,'+') is the update L = chol(L*L'+c*c'). % Updating/downdating is much faster than refactorizing the matrix with % cs_chol or chol. L must not have an entries dropped due to numerical % cancellation (use cs_chol(A,0)). % % Example: % Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; n = size (A,1) ; % L = cs_chol (A,0) ; % parent = cs_etree (A) ; % c = sprand (L (:, floor(n/2))) ; % L1 = cs_updown (L, c, parent) ; % L2 = cs_chol (A + c*c', 0) ; % norm (L1-L2, 1) % % See also CS_ETREE, CS_CHOL, ETREE, CHOLUPDATE, CHOL. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_updown mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_counts_mex.c0000644001170100242450000000165710573562346021000 0ustar davisfac#include "cs_mex.h" /* cs_counts: column counts for sparse Cholesky factor L. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs_dl Amatrix, *A ; CS_INT n, ata, *parent, *post, *c ; char mode [20] ; if (nargout > 2 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: c = cs_counts(A,mode)") ; } ata = 0 ; /* get mode */ if (nargin > 1 && mxIsChar (pargin [1])) { mxGetString (pargin [1], mode, 8) ; ata = (mode [0] == 'c') ; } A = cs_dl_mex_get_sparse (&Amatrix, !ata, 0, pargin [0]) ; /* get A */ n = A->n ; parent = cs_dl_etree (A, ata) ; /* compute etree */ post = cs_dl_post (parent, n) ; /* postorder the etree*/ c = cs_dl_counts (A, parent, post, ata) ; /* get column counts */ pargout [0] = cs_dl_mex_put_int (c, n, 0, 1) ; /* return counts */ cs_free (parent) ; cs_free (post) ; } SuiteSparse/CXSparse/MATLAB/CSparse/cs_permute.m0000644001170100242450000000073610620371657020300 0ustar davisfacfunction C = cs_permute (A,p,q) %#ok %CS_PERMUTE permute a sparse matrix. % C = cs_permute(A,p,q) computes C = A(p,q) % % Example: % Prob = UFget ('HB/arc130') ; A = Prob.A ; [m n] = size (A) ; % p = randperm (m) ; q = randperm (n) ; % C = cs_permute (A,p,q) ; % C = A(p,q) % % See also CS_SYMPERM, SUBSREF. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_permute mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_symperm.m0000644001170100242450000000127010620371706020300 0ustar davisfacfunction C = cs_symperm (A,p) %#ok %CS_SYMPERM symmetric permutation of a symmetric matrix. % C = cs_symperm(A,p) computes C = A(p,p), but accesses only the % upper triangular part of A, and returns C upper triangular (A and C are % symmetric with just their upper triangular parts stored). A must be square. % % Example: % Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; % p = cs_amd (A) ; % C = cs_symperm (A, p) ; % cspy (A (p,p)) ; % cspy (C) ; % C - triu (A (p,p)) % % See also CS_PERMUTE, SUBSREF, TRIU. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_symperm mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_lsolve.m0000644001170100242450000000131510620371636020112 0ustar davisfacfunction x = cs_lsolve (L,b) %#ok %CS_LSOLVE solve a sparse lower triangular system L*x=b. % x = cs_lsolve(L,b) computes x = L\b, L must be lower triangular with a % zero-free diagonal. b must be a column vector. x is full if b is full. % If b is sparse, x is sparse but the nonzero pattern of x is NOT sorted (it % is returned in topological order). % % Example: % Prob = UFget ('HB/bcsstk01') ; L = cs_chol (Prob.A) ; n = size (L,1) ; % b = rand (n,1) ; x = cs_lsolve (L,b) ; norm (L*x-b) % % See also CS_LTSOLVE, CS_USOLVE, CS_UTSOLVE, MLDIVIDE. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_lsolve mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_transpose_mex.c0000644001170100242450000000204110573562353021465 0ustar davisfac#include "cs_mex.h" /* C = cs_transpose (A), computes C=A', where A must be sparse. C = cs_transpose (A,kind) computes C=A.' if kind <= 0, C=A' if kind > 0 */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT values ; if (nargout > 1 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: C = cs_transpose(A,kind)") ; } values = (nargin > 1) ? mxGetScalar (pargin [1]) : 1 ; values = (values <= 0) ? -1 : 1 ; if (mxIsComplex (pargin [0])) { #ifndef NCOMPLEX cs_cl Amatrix, *A, *C ; A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */ C = cs_cl_transpose (A, values) ; /* C = A' */ pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Amatrix, *A, *C ; A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ C = cs_dl_transpose (A, values) ; /* C = A' */ pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */ } } SuiteSparse/CXSparse/MATLAB/CSparse/cs_utsolve.m0000644001170100242450000000125110620371722020302 0ustar davisfacfunction x = cs_utsolve (U,b) %#ok %CS_UTSOLVE solve a sparse lower triangular system U'*x=b. % x = cs_utsolve(U,b) computes x = U'\b, U must be upper triangular with a % zero-free diagonal. b must be a full vector. % % Example: % Prob = UFget ('HB/arc130') ; A = Prob.A ; n = size (A,1) ; % b = rand (n,1); % [L U p q] = cs_lu (A) ; % x = cs_ltsolve (L, cs_utsolve (U, b(q))) ; % x = L' \ (U' \ b(q)) ; % x (p) = x ; % norm (A'*x-b) % % See also CS_LSOLVE, CS_LTSOLVE, CS_USOLVE, MLDIVIDE. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_utsolve mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_permute_mex.c0000644001170100242450000000272410573562351021136 0ustar davisfac#include "cs_mex.h" /* cs_permute: permute a sparse matrix */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT ignore, *P, *Q, *Pinv, m, n ; if (nargout > 1 || nargin != 3) { mexErrMsgTxt ("Usage: C = cs_permute(A,p,q)") ; } m = mxGetM (pargin [0]) ; n = mxGetN (pargin [0]) ; P = cs_dl_mex_get_int (m, pargin [1], &ignore, 1) ; /* get P */ Q = cs_dl_mex_get_int (n, pargin [2], &ignore, 1) ; /* get Q */ Pinv = cs_pinv (P, m) ; /* P = Pinv' */ if (mxIsComplex (pargin [0])) { #ifndef NCOMPLEX cs_cl Amatrix, *A, *C, *D ; A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */ C = cs_cl_permute (A, Pinv, Q, 1) ; /* C = A(p,q) */ cs_cl_free (A->x) ; D = cs_cl_transpose (C, 1) ; /* sort C via double transpose */ cs_cl_spfree (C) ; C = cs_cl_transpose (D, 1) ; cs_cl_spfree (D) ; pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Amatrix, *A, *C, *D ; A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ C = cs_dl_permute (A, Pinv, Q, 1) ; /* C = A(p,q) */ D = cs_dl_transpose (C, 1) ; /* sort C via double transpose */ cs_dl_spfree (C) ; C = cs_dl_transpose (D, 1) ; cs_dl_spfree (D) ; pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */ } cs_free (Pinv) ; cs_free (P) ; cs_free (Q) ; } SuiteSparse/CXSparse/MATLAB/CSparse/Contents.m0000644001170100242450000000537510620374610017723 0ustar davisfac% CXSparse: a Concise Sparse matrix Package. % % Matrices used in CXSparse must in general be either sparse matrices % or dense vectors. Ordering methods can accept any sparse matrix. % CXsparse allows for complex matrices (CSparse does not). % % cs_add - sparse matrix addition. % cs_amd - approximate minimum degree ordering. % cs_chol - sparse Cholesky factorization. % cs_cholsol - solve A*x=b using a sparse Cholesky factorization. % cs_counts - column counts for sparse Cholesky factor L. % cs_dmperm - maximum matching or Dulmage-Mendelsohn permutation. % cs_dmsol - x=A\b using the coarse Dulmage-Mendelsohn decomposition. % cs_dmspy - plot the Dulmage-Mendelsohn decomposition of a matrix. % cs_droptol - remove small entries from a sparse matrix. % cs_esep - find an edge separator of a symmetric matrix A % cs_etree - elimination tree of A or A'*A. % cs_gaxpy - sparse matrix times vector. % cs_lsolve - solve a sparse lower triangular system L*x=b. % cs_ltsolve - solve a sparse upper triangular system L'*x=b. % cs_lu - sparse LU factorization, with fill-reducing ordering. % cs_lusol - solve Ax=b using LU factorization. % cs_make - compiles CXSparse for use in MATLAB. % cs_multiply - sparse matrix multiply. % cs_nd - generalized nested dissection ordering. % cs_nsep - find a node separator of a symmetric matrix A. % cs_permute - permute a sparse matrix. % cs_print - print the contents of a sparse matrix. % cs_qr - sparse QR factorization (Householder-based). % cs_qleft - apply Householder vectors on the left. % cs_qright - apply Householder vectors on the right. % cs_qrsol - solve a sparse least-squares problem. % cs_randperm - random permutation. % cs_sep - convert an edge separator into a node separator. % cs_scc - strongly-connected components of a square sparse matrix. % cs_scc2 - cs_scc, or connected components of a bipartite graph. % cs_sparse - convert a triplet form into a sparse matrix. % cs_sqr - symbolic sparse QR factorization. % cs_symperm - symmetric permutation of a symmetric matrix. % cs_transpose - transpose a sparse matrix. % cs_updown - rank-1 update/downdate of a sparse Cholesky factorization. % cs_usolve - solve a sparse upper triangular system U*x=b. % cs_utsolve - solve a sparse lower triangular system U'*x=b. % cspy - plot a matrix in color. % ccspy - plot the connected components of a matrix. % Example: % help cs_add % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse % helper function: % cs_must_compile - return 1 if source code f must be compiled, 0 otherwise SuiteSparse/CXSparse/MATLAB/CSparse/cs_multiply_mex.c0000644001170100242450000000277010634322566021335 0ustar davisfac#include "cs_mex.h" /* cs_multiply: sparse matrix multiply */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: C = cs_multiply(A,B)") ; } if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { #ifndef NCOMPLEX cs_cl A1matrix, B1matrix, *A, *B, *C, *D, *A1, *B1 ; A1 = cs_cl_mex_get_sparse (&A1matrix, 0, pargin [0]) ; A = cs_cl_transpose (A1, 1) ; cs_cl_free (A1->x) ; /* complex copy no longer needed */ B1 = cs_cl_mex_get_sparse (&B1matrix, 0, pargin [1]) ; B = cs_cl_transpose (B1, 1) ; cs_cl_free (B1->x) ; /* complex copy no longer needed */ D = cs_cl_multiply (B,A) ; /* D = B'*A' */ cs_cl_spfree (A) ; cs_cl_spfree (B) ; cs_cl_dropzeros (D) ; /* drop zeros from D */ C = cs_cl_transpose (D, 1) ; /* C = D', so C is sorted */ cs_cl_spfree (D) ; pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Amatrix, Bmatrix, *A, *B, *C, *D ; A = cs_dl_transpose (cs_dl_mex_get_sparse (&Amatrix, 0,1, pargin[0]),1); B = cs_dl_transpose (cs_dl_mex_get_sparse (&Bmatrix, 0,1, pargin[1]),1); D = cs_dl_multiply (B,A) ; /* D = B'*A' */ cs_dl_spfree (A) ; cs_dl_spfree (B) ; cs_dl_dropzeros (D) ; /* drop zeros from D */ C = cs_dl_transpose (D, 1) ; /* C = D', so C is sorted */ cs_dl_spfree (D) ; pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */ } } SuiteSparse/CXSparse/MATLAB/CSparse/cs_gaxpy_mex.c0000644001170100242450000000230310634322365020573 0ustar davisfac#include "cs_mex.h" /* z = cs_gaxpy (A,x,y) computes z = A*x+y */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { if (nargout > 1 || nargin != 3) { mexErrMsgTxt ("Usage: z = cs_gaxpy(A,x,y)") ; } if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]) || mxIsComplex (pargin [2])) { #ifndef NCOMPLEX cs_cl Amatrix, *A ; cs_complex_t *x, *z ; A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ;/* get A */ x = cs_cl_mex_get_double (A->n, pargin [1]) ; /* get x */ z = cs_cl_mex_get_double (A->m, pargin [2]) ; /* z = y */ cs_cl_gaxpy (A, x, z) ; /* z = z + A*x */ cs_free (x) ; cs_free (A->x) ; pargout [0] = cs_cl_mex_put_double (A->m, z) ; /* return z */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Amatrix, *A ; double *x, *y, *z ; A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ;/* get A */ x = cs_dl_mex_get_double (A->n, pargin [1]) ; /* get x */ y = cs_dl_mex_get_double (A->m, pargin [2]) ; /* get y */ z = cs_dl_mex_put_double (A->m, y, &(pargout [0])) ; /* z = y */ cs_dl_gaxpy (A, x, z) ; /* z = z + A*x */ } } SuiteSparse/CXSparse/MATLAB/CSparse/cs_print.m0000644001170100242450000000064710620371660017746 0ustar davisfacfunction cs_print (A,brief) %#ok %CS_PRINT print the contents of a sparse matrix. % cs_print(A) prints a sparse matrix. cs_print(A,1) prints just a few entries. % % Example: % Prob = UFget ('vanHeukelum/cage3') ; A = Prob.A % cs_print (A) ; % % See also: DISPLAY. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_print mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_scc_mex.c0000644001170100242450000000215310573562352020222 0ustar davisfac#include "cs_mex.h" /* [p,r] = cs_scc (A) finds the strongly connected components of A */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs_dl Amatrix, *A ; cs_dld *D ; CS_INT n, j, *Ap2 ; if (nargout > 2 || nargin != 1) { mexErrMsgTxt ("Usage: [p,r] = cs_scc(A)") ; } A = cs_dl_mex_get_sparse (&Amatrix, 1, 0, pargin [0]) ; /* get A */ /* cs_scc modifies A->p and then restores it (in cs_dfs). Avoid the issue * of a mexFunction modifying its input (even temporarily) by making a copy * of A->p. This issue does not arise in cs_dmperm, because that function * applies cs_scc to a submatrix C, not to A directly. */ n = A->n ; Ap2 = cs_dl_malloc (n+1, sizeof (CS_INT)) ; for (j = 0 ; j <= n ; j++) Ap2 [j] = A->p [j] ; A->p = Ap2 ; D = cs_dl_scc (A) ; /* find conn. comp. */ pargout [0] = cs_dl_mex_put_int (D->p, n, 1, 0) ; /* return p */ pargout [1] = cs_dl_mex_put_int (D->r, D->nb+1, 1, 0) ; /* return r */ cs_dl_dfree (D) ; cs_free (Ap2) ; /* free the copy of A->p */ } SuiteSparse/CXSparse/MATLAB/CSparse/cs_lu_mex.c0000644001170100242450000000562610634322545020076 0ustar davisfac#include "cs_mex.h" /* cs_lu: sparse LU factorization, with optional fill-reducing ordering */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT n, order, *p ; double tol ; if (nargout > 4 || nargin > 3 || nargin < 1) { mexErrMsgTxt ("Usage: [L,U,p,q] = cs_lu (A,tol)") ; } if (nargin == 2) /* determine tol and ordering */ { tol = mxGetScalar (pargin [1]) ; order = (nargout == 4) ? 1 : 0 ; /* amd (A+A'), or natural */ } else { tol = 1 ; order = (nargout == 4) ? 2 : 0 ; /* amd(S'*S) w/dense rows or I */ } if (mxIsComplex (pargin [0])) { #ifndef NCOMPLEX cs_cls *S ; cs_cln *N ; cs_cl Amatrix, *A, *D ; A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ; /* get A */ n = A->n ; S = cs_cl_sqr (order, A, 0) ; /* symbolic ordering, no QR bound */ N = cs_cl_lu (A, S, tol) ; /* numeric factorization */ if (!N) mexErrMsgTxt ("cs_lu failed (singular, or out of memory)") ; cs_cl_free (A->x) ; /* complex copy no longer needed */ cs_cl_dropzeros (N->L) ; /* drop zeros from L and sort it */ D = cs_cl_transpose (N->L, 1) ; cs_cl_spfree (N->L) ; N->L = cs_cl_transpose (D, 1) ; cs_cl_spfree (D) ; cs_cl_dropzeros (N->U) ; /* drop zeros from U and sort it */ D = cs_cl_transpose (N->U, 1) ; cs_cl_spfree (N->U) ; N->U = cs_cl_transpose (D, 1) ; cs_cl_spfree (D) ; p = cs_cl_pinv (N->pinv, n) ; /* p=pinv' */ pargout [0] = cs_cl_mex_put_sparse (&(N->L)) ; /* return L */ pargout [1] = cs_cl_mex_put_sparse (&(N->U)) ; /* return U */ pargout [2] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */ /* return Q */ if (nargout == 4) pargout [3] = cs_dl_mex_put_int (S->q, n, 1, 0) ; cs_cl_nfree (N) ; cs_cl_sfree (S) ; #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dls *S ; cs_dln *N ; cs_dl Amatrix, *A, *D ; A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */ n = A->n ; S = cs_dl_sqr (order, A, 0) ; /* symbolic ordering, no QR bound */ N = cs_dl_lu (A, S, tol) ; /* numeric factorization */ if (!N) mexErrMsgTxt ("cs_lu failed (singular, or out of memory)") ; cs_dl_dropzeros (N->L) ; /* drop zeros from L and sort it */ D = cs_dl_transpose (N->L, 1) ; cs_dl_spfree (N->L) ; N->L = cs_dl_transpose (D, 1) ; cs_dl_spfree (D) ; cs_dl_dropzeros (N->U) ; /* drop zeros from U and sort it */ D = cs_dl_transpose (N->U, 1) ; cs_dl_spfree (N->U) ; N->U = cs_dl_transpose (D, 1) ; cs_dl_spfree (D) ; p = cs_dl_pinv (N->pinv, n) ; /* p=pinv' */ pargout [0] = cs_dl_mex_put_sparse (&(N->L)) ; /* return L */ pargout [1] = cs_dl_mex_put_sparse (&(N->U)) ; /* return U */ pargout [2] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */ /* return Q */ if (nargout == 4) pargout [3] = cs_dl_mex_put_int (S->q, n, 1, 0) ; cs_dl_nfree (N) ; cs_dl_sfree (S) ; } } SuiteSparse/CXSparse/MATLAB/CSparse/cs_chol_mex.c0000644001170100242450000000346710573562345020412 0ustar davisfac#include "cs_mex.h" /* cs_chol: sparse Cholesky factorization */ void mexFunction (int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ]) { CS_INT order, n, drop, *p ; if (nargout > 2 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: [L,p] = cs_chol(A,drop)") ; } drop = (nargin == 1) ? 1 : mxGetScalar (pargin [1]) ; order = (nargout > 1) ? 1 : 0 ; /* determine ordering */ if (mxIsComplex (pargin [0])) { #ifndef NCOMPLEX cs_cl Amatrix, *A ; cs_cls *S ; cs_cln *N ; A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ; /* get A */ n = A->n ; S = cs_cl_schol (order, A) ; /* symbolic Cholesky */ N = cs_cl_chol (A, S) ; /* numeric Cholesky */ if (!N) mexErrMsgTxt ("cs_chol failed: not positive definite\n") ; cs_free (A->x) ; if (drop) cs_cl_dropzeros (N->L) ; /* drop zeros if requested*/ pargout [0] = cs_cl_mex_put_sparse (&(N->L)) ; /* return L */ if (nargout > 1) { p = cs_cl_pinv (S->pinv, n) ; /* p=pinv' */ pargout [1] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */ } cs_cl_nfree (N) ; cs_cl_sfree (S) ; #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Amatrix, *A ; cs_dls *S ; cs_dln *N ; A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */ n = A->n ; S = cs_dl_schol (order, A) ; /* symbolic Cholesky */ N = cs_dl_chol (A, S) ; /* numeric Cholesky */ if (!N) mexErrMsgTxt ("cs_chol failed: not positive definite\n") ; if (drop) cs_dl_dropzeros (N->L) ; /* drop zeros if requested*/ pargout [0] = cs_dl_mex_put_sparse (&(N->L)) ; /* return L */ if (nargout > 1) { p = cs_dl_pinv (S->pinv, n) ; /* p=pinv' */ pargout [1] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */ } cs_dl_nfree (N) ; cs_dl_sfree (S) ; } } SuiteSparse/CXSparse/MATLAB/CSparse/cs_counts.m0000644001170100242450000000135710620371614020123 0ustar davisfacfunction c = cs_counts (A,mode) %#ok %CS_COUNTS column counts for sparse Cholesky factor L. % c = cs_counts(A) returns a vector of the column counts of L, for the % Cholesky factorization L*L' = A. That is, c = sum(spones(chol(A)')), % except the Cholesky factorization is not computed. % c = cs_counts(A), returns counts for cs_chol(A). % c = cs_counts(A,'col'), returns counts for cs_chol(A'*A). % c = cs_counts(A,'sym'), same as cs_counts(A). % % Example: % Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; c = cs_counts (A) % full (sum (spones (chol (A)'))) % % See also SYMBFACT. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_counts mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_dmperm_mex.c0000644001170100242450000000240110573562346020735 0ustar davisfac#include "cs_mex.h" /* cs_dmperm: maximum matching or Dulmage-Mendelsohn permutation. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double seed ; cs_dl *A, Amatrix ; cs_dld *D ; CS_INT m, n, *jmatch, iseed ; if (nargin < 1 || nargin > 2 || nargout > 6) { mexErrMsgTxt ("Usage: [p,q,r,s,cc,rr] = cs_dmperm (A,seed)") ; } seed = (nargin > 1) ? mxGetScalar (pargin [1]) : 0 ; /* get seed */ iseed = (seed > 0 && seed < 1) ? (seed * RAND_MAX) : seed ; A = cs_dl_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ; /* get A */ n = A->n ; m = A->m ; if (nargout <= 1) { jmatch = cs_dl_maxtrans (A, iseed) ; /* max. matching */ pargout [0] = cs_dl_mex_put_int (jmatch+m, n, 1, 0) ; /* return imatch */ cs_free (jmatch) ; } else { D = cs_dl_dmperm (A, iseed) ; /* Dulmage-Mendelsohn decomposition */ pargout [0] = cs_dl_mex_put_int (D->p, m, 1, 0) ; pargout [1] = cs_dl_mex_put_int (D->q, n, 1, 0) ; pargout [2] = cs_dl_mex_put_int (D->r, D->nb+1, 1, 0) ; pargout [3] = cs_dl_mex_put_int (D->s, D->nb+1, 1, 0) ; pargout [4] = cs_dl_mex_put_int (D->cc, 5, 1, 0) ; pargout [5] = cs_dl_mex_put_int (D->rr, 5, 1, 0) ; cs_dl_dfree (D) ; } } SuiteSparse/CXSparse/MATLAB/CSparse/cs_qleft.m0000644001170100242450000000174310620371664017727 0ustar davisfacfunction X = cs_qleft (V, Beta, p, Y) %CS_QLEFT apply Householder vectors on the left. % X = cs_qleft(V,Beta,p,Y) computes X = Hn*...*H2*H1*P*Y = Q'*Y where Q is % represented by the Householder vectors V, coefficients Beta, and % permutation p. p can be [], which denotes the identity permutation. % % Example: % Prob = UFget ('HB/well1033') ; A = Prob.A ; [m n] = size (A) ; % b = rand (m,1) ; % [V,beta,p,R] = cs_qr (A) ; % QR factorization of A(p,:) % b1 = cs_qleft (V, beta, p, b) ; % x1 = R (1:n,1:n) \ b1 (1:n) ; % x2 = A\b ; % norm (x1-x2) % % See also CS_QR, CS_QRIGHT. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m2 n] = size (V) ; [m ny] = size (Y) ; X = Y ; if (m2 > m) if (issparse (Y)) X = [X ; sparse(m2-m,ny)] ; else X = [X ; zeros(m2-m,ny)] ; end end if (~isempty (p)) X = X (p,:) ; end for k = 1:n X = X - V (:,k) * (Beta (k) * (V (:,k)' * X)) ; end SuiteSparse/CXSparse/MATLAB/CSparse/cs_qrsol_mex.c0000644001170100242450000000304110573562351020606 0ustar davisfac#include "cs_mex.h" /* cs_qrsol: solve least squares or underdetermined problem */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT k, order ; if (nargout > 1 || nargin < 2 || nargin > 3) { mexErrMsgTxt ("Usage: x = cs_qrsol(A,b,order)") ; } order = (nargin < 3) ? 3 : mxGetScalar (pargin [2]) ; order = CS_MAX (order, 0) ; order = CS_MIN (order, 3) ; if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { #ifndef NCOMPLEX cs_cl *A, Amatrix ; cs_complex_t *x, *b ; A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */ b = cs_cl_mex_get_double (A->m, pargin [1]) ; /* get b */ x = cs_dl_calloc (CS_MAX (A->m, A->n), sizeof (cs_complex_t)) ; for (k = 0 ; k < A->m ; k++) x [k] = b [k] ; /* x = b */ cs_free (b) ; if (!cs_cl_qrsol (order, A, x)) /* x = A\x */ { mexErrMsgTxt ("QR solve failed") ; } pargout [0] = cs_cl_mex_put_double (A->n, x) ; /* return x */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl *A, Amatrix ; double *x, *b ; A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ b = cs_dl_mex_get_double (A->m, pargin [1]) ; /* get b */ x = cs_dl_calloc (CS_MAX (A->m, A->n), sizeof (double)) ; /* x = b */ for (k = 0 ; k < A->m ; k++) x [k] = b [k] ; if (!cs_dl_qrsol (order, A, x)) /* x = A\x */ { mexErrMsgTxt ("QR solve failed") ; } cs_dl_mex_put_double (A->n, x, &(pargout [0])) ; /* return x */ cs_free (x) ; } } SuiteSparse/CXSparse/MATLAB/CSparse/cs_droptol_mex.c0000644001170100242450000000255410573562346021145 0ustar davisfac#include "cs_mex.h" /* cs_droptol: remove small entries from A */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT j, k ; double tol ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: C = cs_droptol(A,tol)") ; } tol = mxGetScalar (pargin [1]) ; /* get tol */ if (mxIsComplex (pargin [0])) { #ifndef NCOMPLEX cs_cl Amatrix, *C, *A ; A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */ C = cs_cl_spalloc (A->m, A->n, A->nzmax, 1, 0) ; /* C = A */ for (j = 0 ; j <= A->n ; j++) C->p [j] = A->p [j] ; for (k = 0 ; k < A->nzmax ; k++) C->i [k] = A->i [k] ; for (k = 0 ; k < A->nzmax ; k++) C->x [k] = A->x [k] ; cs_cl_droptol (C, tol) ; /* drop from C */ pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Amatrix, *C, *A ; A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ C = cs_dl_spalloc (A->m, A->n, A->nzmax, 1, 0) ; /* C = A */ for (j = 0 ; j <= A->n ; j++) C->p [j] = A->p [j] ; for (k = 0 ; k < A->nzmax ; k++) C->i [k] = A->i [k] ; for (k = 0 ; k < A->nzmax ; k++) C->x [k] = A->x [k] ; cs_dl_droptol (C, tol) ; /* drop from C */ pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */ } } SuiteSparse/CXSparse/MATLAB/CSparse/cs_lsolve_mex.c0000644001170100242450000000574210634322432020754 0ustar davisfac#include "cs_mex.h" /* cs_lsolve: x=L\b. L must be sparse and lower triangular. b must be a * full or sparse vector. x is full or sparse, depending on b. * * Time taken is O(flop count), which may be less than n if b is sparse, * depending on L and b. * * This function works with MATLAB 7.2, but is not perfectly compatible with * the requirements of a MATLAB mexFunction when b is sparse. X is returned * as an unsorted sparse vector. Also, this mexFunction temporarily modifies * its input, L, by modifying L->p (in the cs_dfs function) and then restoring * it. This could be corrected by creating a copy of L->p * (see cs_dmperm_mex.c), but this would take O(n) time, destroying the * O(flop count) time complexity of this function. * * Note that b cannot be sparse complex. This function does not support * sparse complex L and b because the sparse x=L\b only accesses part of the * matrix L. Converting L from a MATLAB complex matrix to a CXSparse complex * matrix requires all of L to be accessed, defeating the purpose of this * function. * * L can be sparse complex, but in that case b must be full real or complex, * not sparse. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT top, nz, p, *xi, n ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_lsolve(L,b)") ; } if (mxIsSparse (pargin [1])) { cs_dl Lmatrix, Bmatrix, *L, *B, *X ; double *x ; if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { mexErrMsgTxt ("sparse complex case not supported") ; } L = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ;/* get L */ n = L->n ; B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ;/* get sparse b*/ cs_mex_check (0, n, 1, 0, 1, 1, pargin [1]) ; xi = cs_dl_malloc (2*n, sizeof (CS_INT)) ; /* get workspace */ x = cs_dl_malloc (n, sizeof (double)) ; top = cs_dl_spsolve (L, B, 0, xi, x, NULL, 1) ; /* x = L\b */ X = cs_dl_spalloc (n, 1, n-top, 1, 0) ; /* create sparse x*/ X->p [0] = 0 ; nz = 0 ; for (p = top ; p < n ; p++) { X->i [nz] = xi [p] ; X->x [nz++] = x [xi [p]] ; } X->p [1] = nz ; pargout [0] = cs_dl_mex_put_sparse (&X) ; cs_free (x) ; cs_free (xi) ; } else if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { #ifndef NCOMPLEX cs_cl Lmatrix, *L ; cs_complex_t *x ; L = cs_cl_mex_get_sparse (&Lmatrix, 1, pargin [0]) ; /* get L */ n = L->n ; x = cs_cl_mex_get_double (n, pargin [1]) ; /* x = b */ cs_cl_lsolve (L, x) ; /* x = L\x */ cs_free (L->x) ; pargout [0] = cs_cl_mex_put_double (n, x) ; /* return x */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Lmatrix, *L ; double *x, *b ; L = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; /* get L */ n = L->n ; b = cs_dl_mex_get_double (n, pargin [1]) ; /* get b */ x = cs_dl_mex_put_double (n, b, &(pargout [0])) ; /* x = b */ cs_dl_lsolve (L, x) ; /* x = L\x */ } } SuiteSparse/CXSparse/MATLAB/CSparse/cspy.m0000644001170100242450000000477410620665733017117 0ustar davisfacfunction [s,M,H] = cspy (A,res) %CSPY plot a matrix in color. % cspy(A) plots a matrix, in color, with a default resolution of % 256-by-256. cspy(A,res) changes the resolution to res. Zero entries are % white. Entries with tiny absolute value are light orange. Entries with % large magnitude are black. Entries in the midrange (the median of the % log10 of the nonzero values, +/- one standard deviation) range from light % green to deep blue. With no inputs, the color legend of cspy is plotted. % [s,M,H] = cspy(A) returns the scale factor s, the image M, and colormap H. % % The matrix A can be full or sparse, and either numeric (double, single, % integer) or character type, and either complex or real. % % Example % A = delsq (numgrid ('L', 10)) ; % cspy (A) ; % % See also CS_DMSPY, SPY. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if nargin < 2 res = 256 ; end h = jet (64) ; h = h (64:-1:1,:) ; h = h (30:end,:) ; hmax = size (h,1) ; h (1,:) = [1 1 1] ; % white for zero h (2,:) = [1 .9 .5] ; % light orange for tiny entries h (hmax,:) = [0 0 0] ; % black for very large entries colormap (h) ; if (nargin == 0) image (1:hmax) ; title ('cspy color map') ; return end % convert complex, integers, and strings to real double if (~isreal (A) | ~isa (A, 'double') | ~issparse (A)) %#ok A = sparse (abs (double (A))) ; end [m1 n1] = size (A) ; if (m1 == 0 | n1 == 0) %#ok A (1,1) = 0 ; end [m1 n1] = size (A) ; S = cs_thumb (A,res) ; % get the thumbnail of the matrix [m n] = size (S) ; [i j x] = find (S) ; x = log10 (x) ; if (isempty (x)) S = zeros (size (S)) ; else med = median (x) ; sdev = std (x) ; big = med + sdev ; tiny = med - sdev ; imid = find (x > tiny & x < big) ; itiny = find (x <= tiny) ; ibig = find (x >= big) ; x (imid) = 1 + ceil ((hmax-2) * (x (imid) - tiny) / (big - tiny)) ; x (itiny) = 1 ; %#ok x (ibig) = hmax-1 ; %#ok S = full (1 + sparse (i,j,x,m,n)) ; % title (sprintf ('tiny: %-8.2g median: %-8.2g big: %-8.2g\n', ... % 10^tiny, 10^med, 10^big)) ; end % draw the matrix image (S) ; axis equal ; axis ([-1 n+1 -1 m+1]) ; axis off % draw a box around the whole matrix e = ceil (max (m1,n1) / max (m,n)) ; % scale factor hold on drawbox (1,m1+1,1,n1+1,'k',1,e) ; hold off % return results if (nargout > 0) s = e ; end if (nargout > 1) M = S ; % image end if (nargout > 2) H = h ; % colormap end SuiteSparse/CXSparse/MATLAB/CSparse/cs_qrsol.m0000644001170100242450000000160310620371671017745 0ustar davisfacfunction x = cs_qrsol (A,b,order) %#ok %CS_QRSOL solve a sparse least-squares problem. % x = cs_qrsol(A,b) solves the over-determined least squares problem to % find x that minimizes norm(A*x-b), where b is a full vector and % A is m-by-n with m >= n. If m < n, it solves the underdetermined system % Ax=b. A 3rd input argument specifies the ordering method to use % (0: natural, 3: amd(A'*A)). The default ordering is 3. % % Example: % Prob = UFget ('HB/well1033') ; A = Prob.A ; [m n] = size (A) ; % b = rand (m,1) ; % x1 = cs_qrsol (A,b) ; % x2 = A\b ; % norm (x1-x2) % % For this example, cs_qrsol is about 3 times faster than A\b in MATLAB 7.3. % % See also CS_QR, CS_AMD, CS_LUSOL, CS_CHOLSOL, MLDIVIDE. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_qrsol mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_chol.m0000644001170100242450000000141010620371611017520 0ustar davisfacfunction [L,p] = cs_chol (A,drop) %#ok %CS_CHOL sparse Cholesky factorization. % L = cs_chol(A) is the same as L = chol(A)', using triu(A). % [L,p] = cs_chol(A) first orders A with p=cs_amd(A), so that L*L' = A(p,p). % A second optional input argument controls whether or not numerically zero % entries are removed from L. cs_chol(A) and cs_chol(A,1) drop them; % cs_chol(A,0) keeps them. They must be kept for cs_updown to work properly. % % Example: % Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; [L,p] = cs_chol (A) ; % cspy (A (p,p)) ; % cspy (L) ; % % See also CS_AMD, CS_UPDOWN, CHOL, AMD, SYMAMD. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_chol mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_print_mex.c0000644001170100242450000000147110573562351020607 0ustar davisfac#include "cs_mex.h" /* cs_print: print the contents of a sparse matrix. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT brief ; if (nargout > 0 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: cs_print(A,brief)") ; } brief = (nargin < 2) ? 0 : mxGetScalar (pargin [1]) ; /* get brief */ if (mxIsComplex (pargin [0])) { #ifndef NCOMPLEX cs_cl Amatrix, *A ; A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */ cs_cl_print (A, brief) ; /* print A */ cs_free (A->x) ; #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Amatrix, *A ; A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ;/* get A */ cs_print (A, brief) ; /* print A */ } } SuiteSparse/CXSparse/MATLAB/CSparse/cs_dmsol.m0000644001170100242450000000220610620665615017727 0ustar davisfacfunction x = cs_dmsol (A,b) %CS_DMSOL x=A\b using the coarse Dulmage-Mendelsohn decomposition. % x = cs_dmsol(A,b) computes x=A\b where A may be rectangular and/or % structurally rank deficient, and b is a full vector. % % Example: % Prob = UFget ('HB/arc130') ; A = Prob.A ; b = rand (size (A,1),1) ; % x = cs_dmsol (A,b) ; norm (A*x-b) % % See also CS_QRSOL, CS_LUSOL, CS_DMPERM, SPRANK, RANK. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; [p q r s cc rr] = cs_dmperm (A) ; C = A (p,q) ; b = b (p) ; x = zeros (n,1) ; if (rr(3) <= m & cc(4) <= n) %#ok x (cc(4):n) = cs_qrsol (C (rr(3):m, cc(4):n), b (rr(3):m)) ; b (1:rr(3)-1) = b (1:rr(3)-1) - C (1:rr(3)-1, cc(4):n) * x (cc(4):n) ; end if (rr(2) < rr (3) & cc(3) < cc(4)) %#ok x (cc(3):cc(4)-1) = ... cs_lusol (C (rr(2):rr(3)-1, cc(3):cc(4)-1), b (rr(2):rr(3)-1)) ; b (1:rr(2)-1) = ... b (1:rr(2)-1) - C (1:rr(2)-1, cc(3):cc(4)-1) * x (cc(3):cc(4)-1) ; end if (rr(2) > 1 & cc(3) > 1) %#ok x (1:cc(3)-1) = cs_qrsol (C (1:rr(2)-1, 1:cc(3)-1), b (1:rr(2)-1)) ; end x (q) = x ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_dmspy.m0000644001170100242450000000345410620371626017747 0ustar davisfacfunction [p,q,r,s,cc,rr] = cs_dmspy (A,res,seed) %CS_DMSPY plot the Dulmage-Mendelsohn decomposition of a matrix. % [p,q,r,s,cc,rr] = cs_dmspy(A) computes [p,q,r,s,cc,rr] = cs_dmperm(A), % does spy(A(p,q)), and then draws boxes around the coarse and fine % decompositions. A 2nd input argument (cs_dmspy(A,res)) changes the % resolution of the image to res-by-res (default resolution is 256). % If res is zero, spy is used instead of cspy. If the resolution is low, the % picture of the blocks in the figure can overlap. They do not actually % overlap in the matrix. With 3 arguments, cs_dmspy(A,res,seed), % cs_dmperm(A,seed) is used, where seed controls the randomized algorithm % used by cs_dmperm. % % Example: % Prob = UFget ('HB/arc130') ; cs_dmspy (Prob.A) ; % % See also CS_DMPERM, CS_DMSOL, DMPERM, SPRANK, SPY. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (~issparse (A)) A = sparse (A) ; end if (nargin < 2) res = 256 ; end if (nargin < 3) seed = 0 ; end % Dulmage-Mendelsohn permutation [p1,q,r,s,cc,rr] = cs_dmperm (A,seed) ; if (nargout > 0) p = p1 ; end nb = length (r)-1 ; % plot the result S = A (p1,q) ; if (res == 0) spy (S) ; e = 1 ; else e = cspy (S,res) ; end hold on title (sprintf ( ... '%d-by-%d, sprank: %d, fine blocks: %d, coarse blocks: %d-by-%d\n', ... size (A), rr(4)-1, nb, length (find (diff (rr))), ... length (find (diff (cc))))) ; drawboxes (nb, e, r, s) ; [m n] = size (A) ; drawbox (1,m+1,1,n+1,'k',1,e) ; drawbox (rr(1), rr(2), cc(1), cc (2), 'r', 2, e) ; drawbox (rr(1), rr(2), cc(2), cc (3), 'r', 2, e) ; drawbox (rr(2), rr(3), cc(3), cc (4), 'k', 2, e) ; drawbox (rr(3), rr(4), cc(4), cc (5), 'r', 2, e) ; drawbox (rr(4), rr(5), cc(4), cc (5), 'r', 2, e) ; hold off SuiteSparse/CXSparse/MATLAB/CSparse/cs_esep.m0000644001170100242450000000120310620372560017533 0ustar davisfacfunction [a,b] = cs_esep (A) %CS_ESEP find an edge separator of a symmetric matrix A % [a,b] = cs_esep(A) finds a edge separator s that splits the graph of A % into two parts a and b of roughly equal size. The edge separator is the % set of entries in A(a,b). % % Example: % Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; % [a,b] = cs_esep (A) ; % cspy (A (a,b)) ; % % See also CS_NSEP, CS_SEP, CS_ND, SYMRCM. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (~isreal (A)) A = spones (A) ; end p = symrcm (A) ; n2 = fix (size(A,1)/2) ; a = p (1:n2) ; b = p (n2+1:end) ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_thumb_mex.c0000644001170100242450000000340610573562353020574 0ustar davisfac#include "cs_mex.h" /* cs_thumb: convert a sparse matrix to a dense 2D thumbnail matrix of size * at most k-by-k. k defaults to 256. A helper mexFunction for cspy. */ #define INDEX(i,j,lda) ((i)+(j)*(lda)) #define ISNAN(x) ((x) != (x)) #ifdef DBL_MAX #define BIG_VALUE DBL_MAX #else #define BIG_VALUE 1.7e308 #endif void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT m, n, mn, m2, n2, k, s, j, ij, sj, si, p, *Ap, *Ai ; double aij, ax, az, *S, *Ax, *Az ; if (nargout > 1 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: S = cs_thumb(A,k)") ; } cs_mex_check (0, -1, -1, 0, 1, 1, pargin [0]) ; m = mxGetM (pargin [0]) ; n = mxGetN (pargin [0]) ; mn = CS_MAX (m,n) ; k = (nargin == 1) ? 256 : mxGetScalar (pargin [1]) ; /* get k */ /* s = size of each submatrix; A(1:s,1:s) maps to S(1,1) */ s = (mn < k) ? 1 : (CS_INT) ceil ((double) mn / (double) k) ; m2 = (CS_INT) ceil ((double) m / (double) s) ; n2 = (CS_INT) ceil ((double) n / (double) s) ; /* create S */ pargout [0] = mxCreateDoubleMatrix (m2, n2, mxREAL) ; S = mxGetPr (pargout [0]) ; Ap = (CS_INT *) mxGetJc (pargin [0]) ; Ai = (CS_INT *) mxGetIr (pargin [0]) ; Ax = mxGetPr (pargin [0]) ; Az = (mxIsComplex (pargin [0])) ? mxGetPi (pargin [0]) : NULL ; for (j = 0 ; j < n ; j++) { sj = j/s ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { si = Ai [p] / s ; ij = INDEX (si,sj,m2) ; ax = Ax [p] ; az = Az ? Az [p] : 0 ; if (az == 0) { aij = fabs (ax) ; } else { aij = sqrt (ax*ax + az*az) ; } if (ISNAN (aij)) aij = BIG_VALUE ; aij = CS_MIN (BIG_VALUE, aij) ; S [ij] = CS_MAX (S [ij], aij) ; } } } SuiteSparse/CXSparse/MATLAB/CSparse/cs_updown_mex.c0000644001170100242450000000612210634327243020762 0ustar davisfac#include "cs_mex.h" /* cs_updown: sparse Cholesky update/downdate (rank-1 or multiple rank) */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT ignore, j, k, n, lnz, *parent, sigma = 1, cp [2], ok ; char sigma_string [20] ; if (nargout > 1 || nargin < 3 || nargin > 4) { mexErrMsgTxt ("Usage: L = cs_updown(L,C,parent,sigma)") ; } if (nargin > 3 && mxIsChar (pargin [3])) { mxGetString (pargin [3], sigma_string, 8) ; sigma = (sigma_string [0] == '-') ? (-1) : 1 ; } n = mxGetN (pargin [0]) ; parent = cs_dl_mex_get_int (n, pargin [2], &ignore, 0) ; /* get parent*/ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { #ifndef NCOMPLEX cs_cl Lmatrix, *Lin, Cmatrix, *C, *L, Cvector, *Cvec ; /* get input L, and copy MATLAB complex to C complex type */ Lin = cs_cl_mex_get_sparse (&Lmatrix, 1, pargin [0]) ; /* make a copy of L (this can take more work than updating L itself) */ lnz = Lin->p [n] ; L = cs_cl_spalloc (n, n, lnz, 0, 0) ; for (j = 0 ; j <= n ; j++) L->p [j] = Lin->p [j] ; for (k = 0 ; k < lnz ; k++) L->i [k] = Lin->i [k] ; /* complex values already copied into Lin->x, use shallow copy for L */ L->x = Lin->x ; cs_mex_check (0, n, -1, 0, 1, 1, pargin [1]) ; /* get C */ C = cs_cl_mex_get_sparse (&Cmatrix, 0, pargin [1]) ; /* do the update one column at a time */ Cvec = &Cvector ; Cvec->m = n ; Cvec->n = 1 ; Cvec->p = cp ; Cvec->nz = -1 ; cp [0] = 0 ; for (k = 0 ; k < C->n ; k++) { /* extract C(:,k) */ cp [1] = C->p [k+1] - C->p [k] ; Cvec->nzmax = cp [1] ; Cvec->i = C->i + C->p [k] ; Cvec->x = C->x + C->p [k] ; /* update/downdate */ ok = cs_cl_updown (L, sigma, Cvec, parent) ; if (!ok) mexErrMsgTxt ("matrix is not positive definite") ; } /* return new L */ pargout [0] = cs_cl_mex_put_sparse (&L) ; cs_free (C->x) ; /* free complex copy of C */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Lmatrix, *Lin, Cmatrix, *C, *L, Cvector, *Cvec ; /* get input L */ Lin = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; /* make a copy of L (this can take more work than updating L itself) */ lnz = Lin->p [n] ; L = cs_dl_spalloc (n, n, lnz, 1, 0) ; for (j = 0 ; j <= n ; j++) L->p [j] = Lin->p [j] ; for (k = 0 ; k < lnz ; k++) L->i [k] = Lin->i [k] ; for (k = 0 ; k < lnz ; k++) L->x [k] = Lin->x [k] ; cs_mex_check (0, n, -1, 0, 1, 1, pargin [1]) ; /* get C */ C = cs_dl_mex_get_sparse (&Cmatrix, 0, 1, pargin [1]) ; /* do the update one column at a time */ Cvec = &Cvector ; Cvec->m = n ; Cvec->n = 1 ; Cvec->p = cp ; Cvec->nz = -1 ; cp [0] = 0 ; for (k = 0 ; k < C->n ; k++) { /* extract C(:,k) */ cp [1] = C->p [k+1] - C->p [k] ; Cvec->nzmax = cp [1] ; Cvec->i = C->i + C->p [k] ; Cvec->x = C->x + C->p [k] ; /* update/downdate */ ok = cs_dl_updown (L, sigma, Cvec, parent) ; if (!ok) mexErrMsgTxt ("matrix is not positive definite") ; } /* return new L */ pargout [0] = cs_dl_mex_put_sparse (&L) ; } } SuiteSparse/CXSparse/MATLAB/CSparse/cs_make.m0000644001170100242450000000613110621037031017511 0ustar davisfacfunction [objfiles, timestamp] = cs_make (f, docomplex) %CS_MAKE compiles CXSparse for use in MATLAB. % Usage: % cs_make % [objfiles, timestamp] = cs_make (f, docomplex) % % With no input arguments, or with f=0, only those files needing to be % compiled are compiled (like the Unix/Linux/GNU "make" command, but not % requiring "make"). If f is a nonzero number, all files are compiled. % If f is a string, only that mexFunction is compiled. For example, % cs_make ('cs_add') just compiles the cs_add mexFunction. This option is % useful when developing a single new mexFunction. This function can only be % used if the current directory is CXSparse/MATLAB/CSparse. Returns a list of % the object files in CXSparse, and the latest modification time of any source % codes. % % NOTE: if your compiler does not support the ANSI C99 complex type (most % notably Microsoft Windows), the CXSparse mexFunctions will not support % complex sparse matrices. The complex case is not attempted if docomplex is % zero. % % To add a new function and its MATLAB mexFunction to CXSparse: % % (1) Create a source code file CXSparse/Source/cs_mynewfunc.c. % (2) Create a help file, CXSparse/MATLAB/CSparse/cs_mynewfunc.m. % This is very useful, but not strictly required. % (3) Add the prototype of cs_mynewfunc to CXSparse/Include/cs.h. % (4) Create its MATLAB mexFunction, CXSparse/MATLAB/cs_mynewfunc_mex.c. % (5) Edit cs_make.m, and add 'cs_mynewfunc' to the 'cs' and 'csm' lists. % (6) Type 'cs_make' in the CXSparse/MATLAB/CSparse directory. % If all goes well, your new function is ready for use in MATLAB. % % (7) Optionally add 'cs_mynewfunc' to CXSparse/Source/Makefile % and CXSparse/MATLAB/CSparse/Makefile, if you want to use the % Unix/Linux/GNU make command instead of cs_make.m. See where % 'cs_add' and 'cs_add_mex' appear in those files, and add % 'cs_mynewfunc' accordingly. % (8) Optionally add 'cs_mynewfunc' to Tcov/Makefile, and add additional % test code to cs_test.c, and add MATLAB test code to MATLAB/Test/*. % % Example: % cs_make % compile everything % cs_make ('cs_chol') ; % just compile cs_chol mexFunction % % See also MEX. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (nargin < 1) f = 0 ; end if (nargin < 2) docomplex = 1 ; end try % ispc does not appear in MATLAB 5.3 pc = ispc ; catch % if ispc fails, assume we are on a Windows PC if it's not unix pc = ~isunix ; end if (pc) docomplex = 0 ; end if (docomplex == 0) % do not attempt to compile with complex matrices [objfiles, timestamp] = cs_make_helper (f, 0) ; else try % try with complex support [objfiles, timestamp] = cs_make_helper (f, 1) ; catch % oops - that failed, try without complex support fprintf ('retrying without complex matrix support\n') ; [objfiles, timestamp] = cs_make_helper (f, 0) ; end end if (f > 0) fprintf ('CXSparse successfully installed.\n') ; end SuiteSparse/CXSparse/MATLAB/CSparse/cs_dmperm.m0000644001170100242450000000621410620371623020071 0ustar davisfacfunction [p,q,r,s,cc,rr] = cs_dmperm (A,seed) %#ok %CS_DMPERM maximum matching or Dulmage-Mendelsohn permutation. % p = cs_dmperm(A) finds a maximum matching p such that p(j) = i if column j % is matched to row i, or 0 if column j is unmatched. If A is square and % full structural rank, p is a row permutation and A(p,:) has a zero-free % diagonal. The structural rank of A is sprank(A) = sum(p>0). % % [p,q,r,s,cc,rr] = cs_dmperm(A) finds the Dulmage-Mendelsohn decomposition % of A. p and q are permutation vectors. cc and rr are vectors of length 5. % C = A(p,q) is split into a 4-by-4 set of coarse blocks: % % A11 A12 A13 A14 % 0 0 A23 A24 % 0 0 0 A34 % 0 0 0 A44 % % where A12, A23, and A34 are square with zero-free diagonals. The columns of % A11 are the unmatched columns, and the rows of A44 are the unmatched rows. % Any of these blocks can be empty. In the "coarse" decomposition, the % (i,j)th block is C(rr(i):rr(i+1)-1,cc(j):cc(j+1)-1). In terms of a linear % system, [A11 A12] is the underdetermined part of the system (it is always % rectangular and with more columns and rows, or 0-by-0), A23 is the well- % determined part of the system (it is always square), and [A34 ; A44] is % the over-determined part of the system (it is always rectangular with more % rows than columns, or 0-by-0). % % The structural rank of A is sprank(A) = rr(4)-1, which is an upper bound on % the numerical rank of A. sprank(A) = rank(full(sprand(A))) with probability % 1 in exact arithmetic. % % The A23 submatrix is further subdivided into block upper triangular form % via the "fine" decomposition (the strongly-connected components of A23). % If A is square and structurally non-singular, A23 is the entire matrix. % % C(r(i):r(i+1)-1,s(j):s(j+1)-1) is the (i,j)th block of the fine % decomposition. The (1,1) block is the rectangular block [A11 A12], unless % this block is 0-by-0. The (b,b) block is the rectangular block [A34 ; A44], % unless this block is 0-by-0, where b = length(r)-1. All other blocks of the % form C(r(i):r(i+1)-1,s(i):s(i+1)-1) are diagonal blocks of A23, and are % square with a zero-free diagonal. % % The matching algorithm used in cs_dmperm can take a very long time % in rare cases. This can be avoided by exploiting a randomized algorithm, % with cs_dmperm(A,seed). If seed=0, the non-randomized algorithm is used % (columns are considered in order 1:n). If seed=-1, columns are considered % in reverse order. Otherwise, the columns are considered in a random order, % using seed as the random number generator seed. Try cs_dmpmerm(A,1) or % cs_dmperm(A,rand), for a randomized order, for example. Seed defaults to 0. % % % Example: % Prob = UFget ('HB/west0479') ; A = Prob.A ; cspy (A) ; % p = cs_dmperm (A) ; % cspy (A (p,:)) ; % [p q r s cc rr] = cs_dmperm (A) ; % cspy (A (p,q)) ; % cs_dmspy (A) ; % % See also CS_DMSPY, CS_DMSOL, DMPERM, SPRANK, CS_RANDPERM, RAND % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_dmperm mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/README.txt0000644001170100242450000000007410571365512017443 0ustar davisfacMATLAB interface for CXSparse. See Contents.m for details. SuiteSparse/CXSparse/MATLAB/CSparse/cs_lusol_mex.c0000644001170100242450000000315710573562350020613 0ustar davisfac#include "cs_mex.h" /* cs_lusol: solve A*x=b using a sparse LU factorization */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double tol ; CS_INT order ; if (nargout > 1 || nargin < 2 || nargin > 4) { mexErrMsgTxt ("Usage: x = cs_lusol(A,b,order,tol)") ; } order = (nargin < 3) ? 2 : mxGetScalar (pargin [2]) ; order = CS_MAX (order, 0) ; order = CS_MIN (order, 3) ; if (nargin == 2) { tol = 1 ; /* normal partial pivoting */ } else if (nargin == 3) { tol = (order == 1) ? 0.001 : 1 ; /* tol = 0.001 for amd(A+A') */ } else { tol = mxGetScalar (pargin [3]) ; } if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { #ifndef NCOMPLEX cs_cl *A, Amatrix ; cs_complex_t *x ; A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ; /* get A */ x = cs_cl_mex_get_double (A->n, pargin [1]) ; /* x = b */ if (!cs_cl_lusol (order, A, x, tol)) /* x = A\x */ { mexErrMsgTxt ("failed (singular or out of memory)") ; } cs_cl_free (A->x) ; /* complex copy no longer needed */ pargout [0] = cs_cl_mex_put_double (A->n, x) ; /* return x */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl *A, Amatrix ; double *x, *b ; A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */ b = cs_dl_mex_get_double (A->n, pargin [1]) ; /* get b */ x = cs_dl_mex_put_double (A->n, b, &(pargout [0])) ; /* x = b */ if (!cs_dl_lusol (order, A, x, tol)) /* x = A\x */ { mexErrMsgTxt ("failed (singular or out of memory)") ; } } } SuiteSparse/CXSparse/MATLAB/CSparse/cs_randperm.m0000644001170100242450000000132010620371673020413 0ustar davisfacfunction p = cs_randperm (n, seed) %#ok %CS_RANDPERM random permutation. % p = cs_randperm (n) returns a repeatable random permutation of 1:n. % p = cs_randperm (n,seed) returns the random permutation using the given % seed for the random number generator (try cs_randperm (n,rand)), where % seed is not 0 or -1. Two special cases are not random permutations at all: % p=cs_randperm (n,0) is 1:n, and p=cs_randperm (n,-1) is n:-1:1. % This function does not change RAND's state. % % Example: % p = cs_randperm (10) % % See also CS_DMPERM, RAND, RANDPERM % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_randperm mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_nsep.m0000644001170100242450000000123110620371655017551 0ustar davisfacfunction [s,a,b] = cs_nsep (A) %CS_NSEP find a node separator of a symmetric matrix A. % [s,a,b] = cs_nsep(A) finds a node separator s that splits the graph of A % into two parts a and b of roughly equal size. If A is unsymmetric, use % cs_nsep(A|A'). The permutation p = [a b s] is a one-level dissection of A. % % Example: % A = delsq (numgrid ('L', 10)) ; % smaller version as used in 'bench' % [s a b] = cs_nsep (A) ; p = [a b s] ; % cspy (A (p,p)) ; % % See also CS_SEP, CS_ESEP, CS_ND. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [a b] = cs_esep (A) ; [s a b] = cs_sep (A, a, b) ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_etree_mex.c0000644001170100242450000000164410573562347020566 0ustar davisfac#include "cs_mex.h" /* cs_etree: elimination tree of A or A'*A */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs_dl Amatrix, *A ; CS_INT n, *parent, *post ; int ata ; char mode [20] ; if (nargout > 2 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: [parent,post] = cs_etree(A,mode)") ; } ata = 0 ; /* get mode */ if (nargin > 1 && mxIsChar (pargin [1])) { mxGetString (pargin [1], mode, 8) ; ata = (mode [0] == 'c') ; } A = cs_dl_mex_get_sparse (&Amatrix, !ata, 0, pargin [0]) ; /* get A */ n = A->n ; parent = cs_dl_etree (A, ata) ; /* compute etree */ if (nargout > 1) { post = cs_dl_post (parent, n) ; /* postorder the etree*/ pargout [1] = cs_dl_mex_put_int (post, n, 1, 1) ; /* return post */ } pargout [0] = cs_dl_mex_put_int (parent, n, 1, 1) ; /* return parent */ } SuiteSparse/CXSparse/MATLAB/CSparse/cs_scc2.m0000644001170100242450000000354710620666137017454 0ustar davisfacfunction [p, q, r, s] = cs_scc2 (A, bipartite) %CS_SCC2 cs_scc, or connected components of a bipartite graph. % [p,q,r,s] = cs_scc2(A) finds a permutation p so that A(p,q) is permuted into % block upper triangular form (if A is square). In this case, r=s, p=q and % the kth diagonal block is given by A (t,t) where t = r(k):r(k)+1. % The diagonal of A is ignored. Each block is one strongly connected % component of A. % % If A is not square (or for [p,q,r,s] = cs_scc2(A,1)), then the connected % components of the bipartite graph of A are found. A(p,q) is permuted into % block diagonal form, where the diagonal blocks are rectangular. The kth % block is given by A(r(k):r(k+1)-1,s(k):s(k+1)-1). A can be rectangular. % % Example: % Prob = UFget ('HB/arc130') ; A = Prob.A ; [p q r s] = cs_scc2 (A) ; % cspy (A (p,q)) ; % Prob = UFget ('HB/wm1') ; A = Prob.A ; [p q r s] = cs_scc2 (A) ; % cspy (A (p,q)) ; % % See also CS_DMPERM, DMPERM, CS_SCC, CCSPY. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; if (nargin < 2) bipartite = 0 ; end if (m ~= n | bipartite) %#ok % find the connected components of [I A ; A' 0] S = spaugment (A) ; [psym,rsym] = cs_scc (S) ; p = psym (find (psym <= m)) ; %#ok q = psym (find (psym > m)) - m ; %#ok nb = length (rsym) - 1 ; r = zeros (1,nb+1) ; s = zeros (1,nb+1) ; krow = 1 ; kcol = 1 ; for k = 1:nb % find the rows and columns in the kth component r (k) = krow ; s (k) = kcol ; ksym = psym (rsym (k):rsym (k+1)-1) ; krow = krow + length (find (ksym <= m)) ; kcol = kcol + length (find (ksym > m)) ; end r (nb+1) = m+1 ; s (nb+1) = n+1 ; else % find the strongly connected components of A [p,r] = cs_scc (A) ; q = p ; s = r ; end SuiteSparse/CXSparse/MATLAB/CSparse/cs_sparse_mex.c0000644001170100242450000000346110573562352020752 0ustar davisfac#include "cs_mex.h" /* cs_sparse: convert triplet form into compress-column form sparse matrix */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { if (nargout > 1 || nargin != 3) { mexErrMsgTxt ("Usage: A = cs_sparse(i,j,x)") ; } if (mxIsComplex (pargin [2])) { #ifndef NCOMPLEX cs_cl *A, *C, *T, Tmatrix ; T = &Tmatrix ; /* get i,j,x and copy to triplet form */ T->nz = mxGetM (pargin [0]) ; T->p = cs_dl_mex_get_int (T->nz, pargin [0], &(T->n), 1) ; T->i = cs_dl_mex_get_int (T->nz, pargin [1], &(T->m), 1) ; cs_mex_check (1, T->nz, 1, 0, 0, 1, pargin [2]) ; T->x = cs_cl_mex_get_double (T->nz, pargin [2]) ; T->nzmax = T->nz ; C = cs_cl_compress (T) ; /* create sparse matrix C */ cs_cl_dupl (C) ; /* remove duplicates from C */ cs_cl_dropzeros (C) ; /* remove zeros from C */ A = cs_cl_transpose (C, -1) ; /* A=C.' */ cs_cl_spfree (C) ; pargout [0] = cs_cl_mex_put_sparse (&A) ; /* return A */ cs_free (T->p) ; cs_free (T->i) ; cs_free (T->x) ; /* free copy of complex values*/ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl *A, *C, *T, Tmatrix ; T = &Tmatrix ; /* get i,j,x and copy to triplet form */ T->nz = mxGetM (pargin [0]) ; T->p = cs_dl_mex_get_int (T->nz, pargin [0], &(T->n), 1) ; T->i = cs_dl_mex_get_int (T->nz, pargin [1], &(T->m), 1) ; cs_mex_check (1, T->nz, 1, 0, 0, 1, pargin [2]) ; T->x = mxGetPr (pargin [2]) ; T->nzmax = T->nz ; C = cs_dl_compress (T) ; /* create sparse matrix C */ cs_dl_dupl (C) ; /* remove duplicates from C */ cs_dl_dropzeros (C) ; /* remove zeros from C */ A = cs_dl_transpose (C, 1) ; /* A=C' */ cs_dl_spfree (C) ; pargout [0] = cs_dl_mex_put_sparse (&A) ; /* return A */ cs_free (T->p) ; cs_free (T->i) ; } } SuiteSparse/CXSparse/MATLAB/CSparse/cs_usolve.m0000644001170100242450000000145410620371721020122 0ustar davisfacfunction x = cs_usolve (U,b) %#ok %CS_USOLVE solve a sparse upper triangular system U*x=b. % x = cs_usolve(U,b) computes x = U\b, U must be lower triangular with a % zero-free diagonal. b must be a column vector. x is full if b is full. % If b is sparse, x is sparse but nonzero pattern of x is NOT sorted (it is % returned in topological order). % % Example: % Prob = UFget ('HB/arc130') ; A = Prob.A ; n = size (A,1) ; % b = rand (n,1); % [L U p q] = cs_lu (A) ; % x = cs_usolve (U, cs_lsolve (L, b(p))) ; % x = U \ (L \ b(p)) ; % x (q) = x ; % norm (A*x-b) % % See also CS_LSOLVE, CS_LTSOLVE, CS_UTSOLVE, MLDIVIDE. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_usolve mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_droptol.m0000644001170100242450000000104210620371627020266 0ustar davisfacfunction C = cs_droptol (A, tol) %#ok %CS_DROPTOL remove small entries from a sparse matrix. % C = cs_droptol(A,tol) removes entries from A of magnitude less than or % equal to tol. Same as A = A .* (abs (A) >= tol). % % Example: % Prob = UFget ('HB/arc130') ; A = Prob.A ; % cspy (abs (A) >= 1e-10) ; % C = cs_droptol (A, 1e-10) ; % cspy (C) ; % % See also: RELOP, ABS % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_droptol mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_etree.m0000644001170100242450000000130610620371633017707 0ustar davisfacfunction [parent, post] = cs_etree (A, mode) %#ok %CS_ETREE elimination tree of A or A'*A. % parent = cs_etree (A) returns the elimination tree of A. % parent = cs_etree (A,'col') returns the elimination tree of A'*A. % parent = cs_etree (A,'sym') is the same as cs_etree(A). % For the symmetric case (cs_etree(A)), only triu(A) is used. % % [parent,post] = cs_etree(...) also returns a postorder of the tree. % % Example: % Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; % parent = cs_etree (A) ; treeplot (parent) ; % % See also ETREE, TREEPLOT. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_etree mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_add_mex.c0000644001170100242450000000403210573562344020201 0ustar davisfac#include "cs_mex.h" /* cs_add: sparse matrix addition */ #ifndef NCOMPLEX static cs_complex_t get_complex (const mxArray *a) { cs_complex_t s = mxGetScalar (a) ; if (mxIsComplex (a)) { double *z = mxGetPi (a) ; s += I * z [0] ; } return (s) ; } #endif void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { if (nargout > 1 || nargin < 2 || nargin > 4) { mexErrMsgTxt ("Usage: C = cs_add(A,B,alpha,beta)") ; } if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]) || (nargin > 2 && mxIsComplex (pargin [2])) || (nargin > 3 && mxIsComplex (pargin [3]))) { #ifndef NCOMPLEX cs_complex_t alpha, beta ; cs_cl Amatrix, Bmatrix, *A, *B, *C, *D ; A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */ B = cs_cl_mex_get_sparse (&Bmatrix, 0, pargin [1]) ; /* get B */ alpha = (nargin < 3) ? 1 : get_complex (pargin [2]) ; /* get alpha */ beta = (nargin < 4) ? 1 : get_complex (pargin [3]) ; /* get beta */ C = cs_cl_add (A,B,alpha,beta) ; /* C = alpha*A + beta *B */ cs_cl_dropzeros (C) ; /* drop zeros */ D = cs_cl_transpose (C, 1) ; /* sort result via double transpose */ cs_cl_spfree (C) ; C = cs_cl_transpose (D, 1) ; cs_cl_spfree (D) ; pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { double alpha, beta ; cs_dl Amatrix, Bmatrix, *A, *B, *C, *D ; A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ; /* get B */ alpha = (nargin < 3) ? 1 : mxGetScalar (pargin [2]) ; /* get alpha */ beta = (nargin < 4) ? 1 : mxGetScalar (pargin [3]) ; /* get beta */ C = cs_dl_add (A,B,alpha,beta) ; /* C = alpha*A + beta *B */ cs_dl_dropzeros (C) ; /* drop zeros */ D = cs_dl_transpose (C, 1) ; /* sort result via double transpose */ cs_dl_spfree (C) ; C = cs_dl_transpose (D, 1) ; cs_dl_spfree (D) ; pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */ } } SuiteSparse/CXSparse/MATLAB/CSparse/cs_ltsolve_mex.c0000644001170100242450000000200610634327040021126 0ustar davisfac#include "cs_mex.h" /* cs_ltsolve: solve an upper triangular system L'*x=b */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_ltsolve(L,b)") ; } if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { #ifndef NCOMPLEX cs_cl Lmatrix, *L ; cs_complex_t *x ; L = cs_cl_mex_get_sparse (&Lmatrix, 1, pargin [0]) ; /* get L */ x = cs_cl_mex_get_double (L->n, pargin [1]) ; /* x = b */ cs_cl_ltsolve (L, x) ; /* x = L'\x */ cs_free (L->x) ; pargout [0] = cs_cl_mex_put_double (L->n, x) ; /* return x */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Lmatrix, *L ; double *x, *b ; L = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; /* get L */ b = cs_dl_mex_get_double (L->n, pargin [1]) ; /* get b */ x = cs_dl_mex_put_double (L->n, b, &(pargout [0])) ; /* x = b */ cs_dl_ltsolve (L, x) ; /* x = L'\x */ } } SuiteSparse/CXSparse/MATLAB/CSparse/cs_must_compile.m0000644001170100242450000000121010620705276021301 0ustar davisfacfunction [s, t, tobj] = cs_must_compile (srcdir, f, suffix, obj, hfile, force) %CS_MUST_COMPILE return 1 if source code f must be compiled, 0 otherwise % Used by cs_make, and MATLAB/Test/cs_test_make.m. % % Example: % none, not meant for end users. % See also: CS_MAKE. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse dobj = dir ([f obj]) ; if (force | isempty (dobj)) %#ok s = 1 ; t = Inf ; tobj = -1 ; return end dsrc = dir ([srcdir f suffix '.c']) ; dh = dir (hfile) ; t = max (datenum (dsrc.date), datenum (dh.date)) ; tobj = datenum (dobj.date) ; s = (tobj < t) ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_lusol.m0000644001170100242450000000165210620371644017747 0ustar davisfacfunction x = cs_lusol (A,b,order,tol) %#ok %CS_LUSOL solve Ax=b using LU factorization. % x = cs_lusol(A,b) computes x = A\b, where A is sparse and square, and b is a % full vector. The ordering cs_amd(A,2) is used. % % x = cs_lusol(A,b,1) also computes x = A\b, but uses the cs_amd(A) ordering % with diagonal preference (tol=0.001). % % x = cs_lusol(A,b,order,tol) allows both the ordering and tolerance to be % defined. The ordering defaults to 1, and tol defaults to 1. % ordering: 0: natural, 1: amd(A+A'), 2: amd(S'*S) where S=A except with no % dense rows, 3: amd(A'*A). % % Example: % Prob = UFget ('HB/arc130') ; A = Prob.A ; n = size(A,1) ; % b = rand (n,1) ; x = cs_lusol (A,b) ; norm (A*x-b) % % See also CS_LU, CS_AMD, CS_CHOLSOL, CS_QRSOL, MLDIVIDE. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_lusol mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_gaxpy.m0000644001170100242450000000074410620371634017741 0ustar davisfacfunction z = cs_gaxpy (A,x,y) %#ok %CS_GAXPY sparse matrix times vector. % z = cs_gaxpy(A,x,y) computes z = A*x+y where x and y are full vectors. % % Example: % Prob = UFget ('HB/arc130') ; A = Prob.A ; [m n] = size (A) ; % x = rand (m,1) ; y = rand (n,1) ; % z = cs_gaxpy (A, x, y) ; % % See also PLUS, MTIMES. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_gaxpy mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_symperm_mex.c0000644001170100242450000000261010634322614021135 0ustar davisfac#include "cs_mex.h" /* cs_symperm: symmetric permutation of a symmetric sparse matrix. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT ignore, n, *P, *Pinv ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: C = cs_symperm(A,p)") ; } if (mxIsComplex (pargin [0])) { #ifndef NCOMPLEX cs_cl Amatrix, *A, *C, *D ; A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ; n = A->n ; P = cs_dl_mex_get_int (n, pargin [1], &ignore, 1) ; /* get P */ Pinv = cs_cl_pinv (P, n) ; /* P=Pinv' */ C = cs_cl_symperm (A, Pinv, 1) ; /* C = A(p,p) */ D = cs_cl_transpose (C, 1) ; /* sort C */ cs_cl_spfree (C) ; C = cs_cl_transpose (D, 1) ; cs_cl_spfree (D) ; pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */ cs_free (P) ; cs_free (Pinv) ; #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Amatrix, *A, *C, *D ; A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; n = A->n ; P = cs_dl_mex_get_int (n, pargin [1], &ignore, 1) ; /* get P */ Pinv = cs_dl_pinv (P, n) ; /* P=Pinv' */ C = cs_dl_symperm (A, Pinv, 1) ; /* C = A(p,p) */ D = cs_dl_transpose (C, 1) ; /* sort C */ cs_dl_spfree (C) ; C = cs_dl_transpose (D, 1) ; cs_dl_spfree (D) ; pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */ cs_free (P) ; cs_free (Pinv) ; } } SuiteSparse/CXSparse/MATLAB/CSparse/cs_multiply.m0000644001170100242450000000100410620371650020454 0ustar davisfacfunction C = cs_multiply (A,B) %#ok %CS_MULTIPLY sparse matrix multiply. % C = cs_multiply(A,B) computes C = A*B. % % Example: % Prob1 = UFget ('HB/ibm32') ; A = Prob1.A ; % Prob2 = UFget ('Hamrle/Hamrle1') ; B = Prob2.A ; % C = cs_multiply (A,B) ; % D = A*B ; % same as C % % See also CS_GAXPY, CS_ADD, MTIMES. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_mult mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_add.m0000644001170100242450000000111710620371606017333 0ustar davisfacfunction C = cs_add (A,B,alpha,beta) %#ok %CS_ADD sparse matrix addition. % C = cs_add(A,B,alpha,beta) computes C = alpha*A+beta*B, % where alpha and beta default to 1 if not present. % % Example: % Prob1 = UFget ('HB/ibm32') ; A = Prob1.A ; % Prob2 = UFget ('Hamrle/Hamrle1') ; B = Prob2.A ; % C = cs_add (A,B) ; % D = A+B ; % same as C % % See also CS_MULTIPLY, CS_GAXPY, PLUS, MINUS. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_add mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_amd.m0000644001170100242450000000203010620371607017340 0ustar davisfacfunction p = cs_amd (A,order) %#ok %CS_AMD approximate minimum degree ordering. % p = cs_amd(A) finds a minimum degree ordering of A+A' % p = cs_amd(A,order): % order = 1: same as cs_amd(A) % order = 2: minimum degree ordering of S'*S where S = A except that % "dense" rows of A are removed from S (a dense row has % 10*sqrt(n) or more entries where n = size(A,2)). Similar % to p = colamd(A), except that colamd does not form A'*A % explicitly. % order = 3: minimum degree ordering of A'*A. Similar to colamd(A,[n m]) % where [m n] = size(A), except that colamd does not form A'*A % explicitly. % Example: % Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; % p = cs_amd (A) ; % nnz (chol (A)) % nnz (chol (A (p,p))) % % See also AMD, COLAMD, SYMAMD. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_amd mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_mex.c0000644001170100242450000001451210634322255017366 0ustar davisfac#include "cs_mex.h" /* check MATLAB input argument */ void cs_mex_check (CS_INT nel, CS_INT m, CS_INT n, int square, int sparse, int values, const mxArray *A) { CS_INT nnel, mm = mxGetM (A), nn = mxGetN (A) ; #ifdef NCOMPLEX if (values) { if (mxIsComplex (A)) mexErrMsgTxt ("complex matrices not supported") ; } #endif if (sparse && !mxIsSparse (A)) mexErrMsgTxt ("matrix must be sparse") ; if (!sparse) { if (mxIsSparse (A)) mexErrMsgTxt ("matrix must be full") ; if (values && !mxIsDouble (A)) mexErrMsgTxt ("matrix must be double") ; } if (nel) { /* check number of elements */ nnel = mxGetNumberOfElements (A) ; if (m >= 0 && n >= 0 && m*n != nnel) mexErrMsgTxt ("wrong length") ; } else { /* check row and/or column dimensions */ if (m >= 0 && m != mm) mexErrMsgTxt ("wrong dimension") ; if (n >= 0 && n != nn) mexErrMsgTxt ("wrong dimension") ; } if (square && mm != nn) mexErrMsgTxt ("matrix must be square") ; } /* get a real (or pattern) MATLAB sparse matrix and convert to cs_dl */ cs_dl *cs_dl_mex_get_sparse (cs_dl *A, int square, int values, const mxArray *Amatlab) { cs_mex_check (0, -1, -1, square, 1, values, Amatlab) ; A->m = mxGetM (Amatlab) ; A->n = mxGetN (Amatlab) ; A->p = (CS_INT *) mxGetJc (Amatlab) ; A->i = (CS_INT *) mxGetIr (Amatlab) ; A->x = values ? mxGetPr (Amatlab) : NULL ; A->nzmax = mxGetNzmax (Amatlab) ; A->nz = -1 ; /* denotes a compressed-col matrix, instead of triplet */ return (A) ; } /* return a real sparse matrix to MATLAB */ mxArray *cs_dl_mex_put_sparse (cs_dl **Ahandle) { cs_dl *A ; mxArray *Amatlab ; A = *Ahandle ; if (!A) mexErrMsgTxt ("failed") ; Amatlab = mxCreateSparse (0, 0, 0, mxREAL) ; mxSetM (Amatlab, A->m) ; mxSetN (Amatlab, A->n) ; mxSetNzmax (Amatlab, A->nzmax) ; cs_free (mxGetJc (Amatlab)) ; cs_free (mxGetIr (Amatlab)) ; cs_free (mxGetPr (Amatlab)) ; mxSetJc (Amatlab, (void *) (A->p)) ; /* assign A->p pointer to MATLAB A */ mxSetIr (Amatlab, (void *) (A->i)) ; mxSetPr (Amatlab, A->x) ; cs_free (A) ; /* frees A struct only, not A->p, etc */ *Ahandle = NULL ; return (Amatlab) ; } /* get a real MATLAB dense column vector */ double *cs_dl_mex_get_double (CS_INT n, const mxArray *X) { cs_mex_check (0, n, 1, 0, 0, 1, X) ; return (mxGetPr (X)) ; } /* return a double vector to MATLAB */ double *cs_dl_mex_put_double (CS_INT n, const double *b, mxArray **X) { double *x ; CS_INT k ; *X = mxCreateDoubleMatrix (n, 1, mxREAL) ; /* create x */ x = mxGetPr (*X) ; for (k = 0 ; k < n ; k++) x [k] = b [k] ; /* copy x = b */ return (x) ; } /* get a MATLAB flint array and convert to CS_INT */ CS_INT *cs_dl_mex_get_int (CS_INT n, const mxArray *Imatlab, CS_INT *imax, int lo) { double *p ; CS_INT i, k, *C = cs_dl_malloc (n, sizeof (CS_INT)) ; cs_mex_check (1, n, 1, 0, 0, 1, Imatlab) ; if (mxIsComplex (Imatlab)) { mexErrMsgTxt ("integer input cannot be complex") ; } p = mxGetPr (Imatlab) ; *imax = 0 ; for (k = 0 ; k < n ; k++) { i = p [k] ; C [k] = i - 1 ; if (i < lo) mexErrMsgTxt ("index out of bounds") ; *imax = CS_MAX (*imax, i) ; } return (C) ; } /* return an CS_INT array to MATLAB as a flint row vector */ mxArray *cs_dl_mex_put_int (CS_INT *p, CS_INT n, CS_INT offset, int do_free) { mxArray *X = mxCreateDoubleMatrix (1, n, mxREAL) ; double *x = mxGetPr (X) ; CS_INT k ; for (k = 0 ; k < n ; k++) x [k] = (p ? p [k] : k) + offset ; if (do_free) cs_free (p) ; return (X) ; } #ifndef NCOMPLEX /* copy a MATLAB real or complex vector into a cs_cl complex vector */ static cs_complex_t *cs_cl_get_vector (CS_INT n, CS_INT size, const mxArray *Xmatlab) { CS_INT p ; double *X, *Z ; cs_complex_t *Y ; X = mxGetPr (Xmatlab) ; Z = (mxIsComplex (Xmatlab)) ? mxGetPi (Xmatlab) : NULL ; Y = cs_dl_malloc (size, sizeof (cs_complex_t)) ; for (p = 0 ; p < n ; p++) { Y [p] = X [p] + I * (Z ? Z [p] : 0) ; } return (Y) ; } /* get a real or complex MATLAB sparse matrix and convert to cs_cl */ cs_cl *cs_cl_mex_get_sparse (cs_cl *A, int square, const mxArray *Amatlab) { cs_mex_check (0, -1, -1, square, 1, 1, Amatlab) ; A->m = mxGetM (Amatlab) ; A->n = mxGetN (Amatlab) ; A->p = (CS_INT *) mxGetJc (Amatlab) ; A->i = (CS_INT *) mxGetIr (Amatlab) ; A->nzmax = mxGetNzmax (Amatlab) ; A->x = cs_cl_get_vector (A->p [A->n], A->nzmax, Amatlab) ; A->nz = -1 ; /* denotes a compressed-col matrix, instead of triplet */ return (A) ; } /* return a complex sparse matrix to MATLAB */ mxArray *cs_cl_mex_put_sparse (cs_cl **Ahandle) { cs_cl *A ; double *x, *z ; mxArray *Amatlab ; CS_INT k ; A = *Ahandle ; if (!A) mexErrMsgTxt ("failed") ; Amatlab = mxCreateSparse (0, 0, 0, mxCOMPLEX) ; mxSetM (Amatlab, A->m) ; mxSetN (Amatlab, A->n) ; mxSetNzmax (Amatlab, A->nzmax) ; cs_cl_free (mxGetJc (Amatlab)) ; cs_cl_free (mxGetIr (Amatlab)) ; cs_cl_free (mxGetPr (Amatlab)) ; cs_cl_free (mxGetPi (Amatlab)) ; mxSetJc (Amatlab, (void *) (A->p)) ; /* assign A->p pointer to MATLAB A */ mxSetIr (Amatlab, (void *) (A->i)) ; x = cs_dl_malloc (A->nzmax, sizeof (double)) ; z = cs_dl_malloc (A->nzmax, sizeof (double)) ; for (k = 0 ; k < A->nzmax ; k++) { x [k] = creal (A->x [k]) ; /* copy and split numerical values */ z [k] = cimag (A->x [k]) ; } cs_cl_free (A->x) ; /* free copy of complex values */ mxSetPr (Amatlab, x) ; mxSetPi (Amatlab, z) ; cs_cl_free (A) ; /* frees A struct only, not A->p, etc */ *Ahandle = NULL ; return (Amatlab) ; } /* get a real or complex MATLAB dense column vector, and copy to cs_complex_t */ cs_complex_t *cs_cl_mex_get_double (CS_INT n, const mxArray *X) { cs_mex_check (0, n, 1, 0, 0, 1, X) ; return (cs_cl_get_vector (n, n, X)) ; } /* copy a complex vector back to MATLAB and free it */ mxArray *cs_cl_mex_put_double (CS_INT n, cs_complex_t *b) { double *x, *z ; mxArray *X ; CS_INT k ; X = mxCreateDoubleMatrix (n, 1, mxCOMPLEX) ; /* create x */ x = mxGetPr (X) ; z = mxGetPi (X) ; for (k = 0 ; k < n ; k++) { x [k] = creal (b [k]) ; /* copy x = b */ z [k] = cimag (b [k]) ; } cs_cl_free (b) ; return (X) ; } #endif SuiteSparse/CXSparse/MATLAB/CSparse/cs_mex.h0000644001170100242450000000153510573562554017406 0ustar davisfac#include "cs.h" #include "mex.h" void cs_mex_check (CS_INT nel, CS_INT m, CS_INT n, int square, int sparse, int values, const mxArray *A) ; CS_INT *cs_dl_mex_get_int (CS_INT n, const mxArray *Imatlab, CS_INT *imax, int lo); mxArray *cs_dl_mex_put_int (CS_INT *p, CS_INT n, CS_INT offset, int do_free) ; double *cs_dl_mex_get_double (CS_INT n, const mxArray *X) ; cs_dl *cs_dl_mex_get_sparse (cs_dl *A, int square, int values, const mxArray *Amatlab) ; double *cs_dl_mex_put_double (CS_INT n, const double *b, mxArray **X) ; mxArray *cs_dl_mex_put_sparse (cs_dl **A) ; #ifndef NCOMPLEX cs_complex_t *cs_cl_mex_get_double (CS_INT n, const mxArray *X) ; cs_cl *cs_cl_mex_get_sparse (cs_cl *A, int square, const mxArray *Amatlab) ; mxArray *cs_cl_mex_put_double (CS_INT n, cs_complex_t *b) ; mxArray *cs_cl_mex_put_sparse (cs_cl **Ahandle) ; #endif SuiteSparse/CXSparse/MATLAB/CSparse/cs_scc.m0000644001170100242450000000123410620371677017363 0ustar davisfacfunction [p,r] = cs_scc (A) %#ok %CS_SCC strongly-connected components of a square sparse matrix. % [p,r] = cs_scc(A) finds a permutation p so that A(p,p) is permuted into % block upper triangular form. The diagonal of A is ignored. The kth block % is given by A (s,s) where s = r(k):r(k+1)-1. A must be square. % For bipartite or rectangular graphs, use cs_scc2. % % Example: % Prob = UFget ('HB/arc130') ; A = Prob.A ; [p r] = cs_scc (A) ; % cspy (A (p,p)) ; % % See also CS_DMPERM, DMPERM, CS_SCC2. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_scc mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_sep.m0000644001170100242450000000147410620371701017374 0ustar davisfacfunction [s,as,bs] = cs_sep (A,a,b) %CS_SEP convert an edge separator into a node separator. % [s,as,bs] = cs_sep (A,a,b) converts an edge separator into a node separator. % [a b] is a partition of 1:n, thus the edges in A(a,b) are an edge separator % of A. s is the node separator, consisting of a node cover of the edges of % A(a,b). as and bs are the sets a and b with s removed. % % Example: % type cs_nsep ; % to see a simple example of use in cs_nsep.m % % See also CS_DMPERM, CS_NSEP, CS_ESEP, CS_ND. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse [p q r s cc rr] = cs_dmperm (A (a,b)) ; s = [(a (p (1:rr(2)-1))) (b (q (cc(3):(cc(5)-1))))] ; w = ones (1, size (A,1)) ; w (s) = 0 ; as = a (find (w (a))) ; %#ok bs = b (find (w (b))) ; %#ok SuiteSparse/CXSparse/MATLAB/CSparse/cs_sqr.m0000644001170100242450000000206710620371704017414 0ustar davisfacfunction [vnz,rnz,parent,c,leftmost,p,q] = cs_sqr (A) %#ok %CS_SQR symbolic sparse QR factorization. % [vnz,rnz,parent,c,leftmost,p] = cs_sqr(A): symbolic QR of A(p,:). % [vnz,rnz,parent,c,leftmost,p,q] = cs_sqr(A) computes the symbolic QR % factorization of A(p,q). The fill-reducing ordering q is found via % q = cs_amd(A,3). % % vnz is the number of entries in the matrix of Householder vectors, V. % rnz is the number of entries in R. parent is elimination tree. % c(i) is the number of entries in R(i,:). leftmost(i) = min(find(A(i,q))). % p is the row permutation used to ensure R has a symbolically zero-free % diagonal (it can be larger than m if A is structurally rank deficient). % q is the fill-reducing ordering, if requested. % % Example: % Prob = UFget ('HB/ibm32') ; A = Prob.A ; % [vnz, rnz, parent, c, leftmost, p, q] = cs_sqr (A) ; % cspy (A (p,q)) ; % % See also CS_AMD, CS_QR. % % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_sqr mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/ccspy.m0000644001170100242450000000333710622674743017257 0ustar davisfacfunction [p, q, r, s] = ccspy (A, bipartite, res) %CCSPY plot the connected components of a matrix. % % Example: % [p, q, r, s] = ccspy (A, bipartite, res) % % If A is square, [p,q,r,s] = ccspy(A) finds a permutation p so that A(p,q) % is permuted into block upper triangular form. In this case, r=s, p=q and % the kth diagonal block is given by A (t,t) where t = r(k):r(k+1)-1. % The diagonal of A is ignored. % % If A is not square (or for [p,q,r,s] = ccspy(A,1)), then the connected % components of the bipartite graph of A are found. A(p,q) is permuted into % block diagonal form, where the diagonal blocks are rectangular. The kth % block is given by A(r(k):r(k+1)-1,s(k):s(k+1)-1). A can be rectangular. % % It then plots the result via cspy, drawing a greenbox around each component. % A 3rd input argument (res) controls the resolution (see cspy for a % description of the res parameter). % % See also CSPY, CS_DMPERM, DMPERM, CS_SCC, CS_SCC2, CS_DMSPY. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (~issparse (A)) A = sparse (A) ; end [m n] = size (A) ; if (nargin < 3) res = 256 ; end if (nargin < 2) bipartite = [ ] ; end if (isempty (bipartite)) bipartite = (m ~= n) ; end % find the strongly connected components [p1 q r s] = cs_scc2 (A, bipartite) ; if (nargout > 0) p = p1 ; end nb = length (r)-1 ; % plot the result S = A (p1,q) ; if (res == 0) spy (S) ; e = 1 ; else e = cspy (S,res) ; end hold on title (sprintf ('%d-by-%d, strongly connected commponents: %d\n', m, n, nb)) ; if (~bipartite) plot ([.5 .5 n+.5 n+.5], [.5 .5 n+.5 n+.5], 'r') ; end drawboxes (nb, e, r, s) ; drawbox (1,m+1,1,n+1,'k',1,e) ; hold off SuiteSparse/CXSparse/MATLAB/CSparse/cs_utsolve_mex.c0000644001170100242450000000200510634322660021141 0ustar davisfac#include "cs_mex.h" /* cs_utsolve: solve a lower triangular system U'*x=b */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_utsolve(U,b)") ; } if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { #ifndef NCOMPLEX cs_cl Umatrix, *U ; cs_complex_t *x ; U = cs_cl_mex_get_sparse (&Umatrix, 1, pargin [0]) ; /* get U */ x = cs_cl_mex_get_double (U->n, pargin [1]) ; /* x = b */ cs_cl_utsolve (U, x) ; /* x = U'\x */ cs_free (U->x) ; pargout [0] = cs_cl_mex_put_double (U->n, x) ; /* return x */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Umatrix, *U ; double *x, *b ; U = cs_dl_mex_get_sparse (&Umatrix, 1, 1, pargin [0]) ; /* get U */ b = cs_dl_mex_get_double (U->n, pargin [1]) ; /* get b */ x = cs_dl_mex_put_double (U->n, b, &(pargout [0])) ; /* x = b */ cs_dl_utsolve (U, x) ; /* x = U'\x */ } } SuiteSparse/CXSparse/MATLAB/CSparse/cs_randperm_mex.c0000644001170100242450000000165110573562351021263 0ustar davisfac#include "cs_mex.h" /* cs_randperm: random permutation. p=cs_randperm(n,0) is 1:n, * p=cs_randperm(n,-1) is n:-1:1. p = cs_randperm (n,seed) is a random * permutation using the given seed (where seed is not 0 or -1). * seed defaults to 1. A single seed always gives a repeatable permutation. * Use p = cs_randperm(n,rand) to get a permutation that varies with each use. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double seed ; CS_INT iseed, n, *p ; if (nargout > 1 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: p = cs_randperm(n,seed)") ; } seed = (nargin > 1) ? mxGetScalar (pargin [1]) : 1 ; iseed = (seed > 0 && seed < 1) ? (seed * RAND_MAX) : seed ; n = mxGetScalar (pargin [0]) ; n = CS_MAX (n, 0) ; p = cs_dl_randperm (n, iseed) ; pargout [0] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */ } SuiteSparse/CXSparse/MATLAB/CSparse/cs_sparse.m0000644001170100242450000000105010620371702020071 0ustar davisfacfunction A = cs_sparse (i,j,x) %#ok %CS_SPARSE convert a triplet form into a sparse matrix. % A = cs_sparse(i,j,x) is identical to A = sparse(i,j,x), except that x must % be real, and the length of i, j, and x must be the same. % % Example: % Prob = UFget ('HB/arc130') ; S = Prob.A ; % [i j x] = find (S) ; % A = cs_sparse (i,j,x) ; % S-A % % See also FIND, SPARSE, SPCONVERT. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_sparse mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_usolve_mex.c0000644001170100242450000000574210634322644020772 0ustar davisfac#include "cs_mex.h" /* cs_usolve: x=U\b. U must be sparse and upper triangular. b must be a * full or sparse vector. x is full or sparse, depending on b. * * Time taken is O(flop count), which may be less than n if b is sparse, * depending on U and b. * * This function works with MATLAB 7.2, but is not perfectly compatible with * the requirements of a MATLAB mexFunction when b is sparse. X is returned * as an unsorted sparse vector. Also, this mexFunction temporarily modifies * its input, U, by modifying U->p (in the cs_dfs function) and then restoring * it. This could be corrected by creating a copy of U->p * (see cs_dmperm_mex.c), but this would take O(n) time, destroying the * O(flop count) time complexity of this function. * * Note that b cannot be sparse complex. This function does not support * sparse complex U and b because the sparse x=U\b only accesses part of the * matrix U. Converting U from a MATLAB complex matrix to a CXSparse complex * matrix requires all of U to be accessed, defeating the purpose of this * function. * * U can be sparse complex, but in that case b must be full real or complex, * not sparse. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT top, nz, p, *xi, n ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_usolve(U,b)") ; } if (mxIsSparse (pargin [1])) { cs_dl Umatrix, Bmatrix, *U, *B, *X ; double *x ; if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { mexErrMsgTxt ("sparse complex case not supported") ; } U = cs_dl_mex_get_sparse (&Umatrix, 1, 1, pargin [0]) ;/* get U */ n = U->n ; B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ;/* get sparse b*/ cs_mex_check (0, n, 1, 0, 1, 1, pargin [1]) ; xi = cs_dl_malloc (2*n, sizeof (CS_INT)) ; /* get workspace */ x = cs_dl_malloc (n, sizeof (double)) ; top = cs_dl_spsolve (U, B, 0, xi, x, NULL, 0) ; /* x = U\b */ X = cs_dl_spalloc (n, 1, n-top, 1, 0) ; /* create sparse x*/ X->p [0] = 0 ; nz = 0 ; for (p = top ; p < n ; p++) { X->i [nz] = xi [p] ; X->x [nz++] = x [xi [p]] ; } X->p [1] = nz ; pargout [0] = cs_dl_mex_put_sparse (&X) ; cs_free (x) ; cs_free (xi) ; } else if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { #ifndef NCOMPLEX cs_cl Umatrix, *U ; cs_complex_t *x ; U = cs_cl_mex_get_sparse (&Umatrix, 1, pargin [0]) ; /* get U */ n = U->n ; x = cs_cl_mex_get_double (n, pargin [1]) ; /* x = b */ cs_cl_usolve (U, x) ; /* x = U\x */ cs_free (U->x) ; pargout [0] = cs_cl_mex_put_double (n, x) ; /* return x */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Umatrix, *U ; double *x, *b ; U = cs_dl_mex_get_sparse (&Umatrix, 1, 1, pargin [0]) ; /* get U */ n = U->n ; b = cs_dl_mex_get_double (n, pargin [1]) ; /* get b */ x = cs_dl_mex_put_double (n, b, &(pargout [0])) ; /* x = b */ cs_dl_usolve (U, x) ; /* x = U\x */ } } SuiteSparse/CXSparse/MATLAB/CSparse/cs_cholsol_mex.c0000644001170100242450000000246510634322337021116 0ustar davisfac#include "cs_mex.h" /* cs_cholsol: solve A*x=b using a sparse Cholesky factorization */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT order ; if (nargout > 1 || nargin < 2 || nargin > 3) { mexErrMsgTxt ("Usage: x = cs_cholsol(A,b,order)") ; } order = (nargin < 3) ? 1 : mxGetScalar (pargin [2]) ; order = CS_MAX (order, 0) ; order = CS_MIN (order, 3) ; if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { #ifndef NCOMPLEX cs_cl *A, Amatrix ; cs_complex_t *x ; A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ; /* get A */ x = cs_cl_mex_get_double (A->n, pargin [1]) ; /* x = b */ if (!cs_cl_cholsol (order, A, x)) /* x = A\x */ { mexErrMsgTxt ("A not positive definite") ; } cs_free (A->x) ; pargout [0] = cs_cl_mex_put_double (A->n, x) ; /* return x */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl *A, Amatrix ; double *x, *b ; A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */ b = cs_dl_mex_get_double (A->n, pargin [1]) ; /* get b */ x = cs_dl_mex_put_double (A->n, b, &(pargout [0])) ; /* x = b */ if (!cs_dl_cholsol (order, A, x)) /* x = A\x */ { mexErrMsgTxt ("A not positive definite") ; } } } SuiteSparse/CXSparse/MATLAB/CSparse/private/0000755001170100242450000000000010621054722017410 5ustar davisfacSuiteSparse/CXSparse/MATLAB/CSparse/private/drawbox.m0000644001170100242450000000127710620671143021244 0ustar davisfacfunction drawbox (r1,r2,c1,c2,color,w,e) %DRAWBOX draw a box around a submatrix in the figure. % Used by cspy, cs_dmspy, and ccspy. % Example: % drawbox (r1,r2,c1,c2,color,w,e) % See also drawboxes, plot % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (r1 == r2 | c1 == c2) %#ok return end if (e == 1) r1 = r1 - .5 ; r2 = r2 - .5 ; c1 = c1 - .5 ; c2 = c2 - .5 ; else r1 = ceil (r1 / e) - .5 ; r2 = ceil ((r2 - 1) / e) + .5 ; c1 = ceil (c1 / e) - .5 ; c2 = ceil ((c2 - 1) / e) + .5 ; end if (c2 > c1 | r2 > r1) %#ok plot ([c1 c2 c2 c1 c1], [r1 r1 r2 r2 r1], color, 'LineWidth', w) ; end SuiteSparse/CXSparse/MATLAB/CSparse/private/drawboxes.m0000644001170100242450000000136710620372107021572 0ustar davisfacfunction drawboxes (nb, e, r, s) %DRAWBOXES: helper function for cs_dmpsy and ccspy % Example: % drawboxes (nb, e, r, s) % See also drawbox, plot % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (nb > 1) if (e == 1) r1 = r (1:nb) - .5 ; r2 = r (2:nb+1) - .5 ; c1 = s (1:nb) - .5 ; c2 = s (2:nb+1) - .5 ; else r1 = ceil (r (1:nb) / e) - .5 ; r2 = ceil ((r (2:nb+1) - 1) / e) + .5 ; c1 = ceil (s (1:nb) / e) - .5 ; c2 = ceil ((s (2:nb+1) - 1) / e) + .5 ; end kk = find (diff (c1) > 0 | diff (c2) > 0 | diff (r1) > 0 | diff (r2) > 0) ; kk = [1 kk+1] ; for k = kk plot ([c1(k) c2(k) c2(k) c1(k) c1(k)], ... [r1(k) r1(k) r2(k) r2(k) r1(k)], 'k', 'LineWidth', 1) ; end end SuiteSparse/CXSparse/MATLAB/CSparse/private/cs_make_helper.m0000644001170100242450000001545610621054716022545 0ustar davisfacfunction [objfiles, timestamp_out] = cs_make_helper (f, docomplex) %CS_MAKE_HELPER compiles CXSparse for use in MATLAB. % Usage: % [objfiles, timestamp] = cs_make (f, docomplex) % % With f=0, only those files needing to be % compiled are compiled (like the Unix/Linux/GNU "make" command, but not % requiring "make"). If f is a nonzero number, all files are compiled. % If f is a string, only that mexFunction is compiled. For example, % cs_make ('cs_add') just compiles the cs_add mexFunction. This option is % useful when developing a single new mexFunction. This function can only be % used if the current directory is CXSparse/MATLAB/CSparse. Returns a list of % the object files in CXSparse, and the latest modification time of any source % codes. % % NOTE: if your compiler does not support the ANSI C99 complex type, the % CXSparse mexFunctions will not support complex sparse matrices. % % To add a new function and its MATLAB mexFunction to CXSparse: % % (1) Create a source code file CXSparse/Source/cs_mynewfunc.c. % (2) Create a help file, CXSparse/MATLAB/CSparse/cs_mynewfunc.m. % This is very useful, but not strictly required. % (3) Add the prototype of cs_mynewfunc to CXSparse/Include/cs.h. % (4) Create its MATLAB mexFunction, CXSparse/MATLAB/cs_mynewfunc_mex.c. % (5) Edit cs_make.m, and add 'cs_mynewfunc' to the 'cs' and 'csm' lists. % (6) Type 'cs_make' in the CXSparse/MATLAB/CSparse directory. % If all goes well, your new function is ready for use in MATLAB. % % (7) Optionally add 'cs_mynewfunc' to CXSparse/Source/Makefile % and CXSparse/MATLAB/CSparse/Makefile, if you want to use the % Unix/Linux/GNU make command instead of cs_make.m. See where % 'cs_add' and 'cs_add_mex' appear in those files, and add % 'cs_mynewfunc' accordingly. % (8) Optionally add 'cs_mynewfunc' to Tcov/Makefile, and add additional % test code to cs_test.c, and add MATLAB test code to MATLAB/Test/*. % % Example: % cs_make_helper (1,1) ; % compile everything % cs_make ('cs_chol', 1) ; % just compile cs_chol mexFunction % % See also MEX. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse mexcmd = 'mex -DCS_LONG -I../../../UFconfig' ; if (~isempty (strfind (computer, '64'))) mexcmd = [mexcmd ' -largeArrayDims'] ; end if (nargin < 2) docomplex = 1 ; end if (~docomplex) mexcmd = [mexcmd ' -DNCOMPLEX'] ; end % CSparse source files, in ../../Source, such as ../../Source/cs_add.c. % Note that not all CSparse source files have their own mexFunction. cs = { 'cs_add', 'cs_amd', 'cs_chol', 'cs_cholsol', 'cs_counts', ... 'cs_cumsum', 'cs_dfs', 'cs_dmperm', 'cs_droptol', 'cs_dropzeros', ... 'cs_dupl', 'cs_entry', 'cs_etree', 'cs_fkeep', 'cs_gaxpy', 'cs_happly', ... 'cs_house', 'cs_ipvec', 'cs_load', 'cs_lsolve', 'cs_ltsolve', 'cs_lu', ... 'cs_lusol', 'cs_malloc', 'cs_maxtrans', 'cs_multiply', 'cs_norm', ... 'cs_permute', 'cs_pinv', 'cs_post', 'cs_print', 'cs_pvec', 'cs_qr', ... 'cs_qrsol', 'cs_scatter', 'cs_scc', 'cs_schol', 'cs_sqr', 'cs_symperm', ... 'cs_tdfs', 'cs_transpose', 'cs_compress', 'cs_updown', 'cs_usolve', ... 'cs_utsolve', 'cs_util', 'cs_reach', 'cs_spsolve', 'cs_ereach', ... 'cs_leaf', 'cs_randperm' } ; % add cs_mynewfunc to the above list details = 1 ; kk = 0 ; csm = { } ; if (nargin == 0) force = 0 ; elseif (ischar (f)) fprintf ('cs_make: compiling ../../Source files and %s_mex.c\n', f) ; force = 0 ; csm = {f} ; else force = f ; details = details | (force > 1) ; %#ok if (force & details) %#ok fprintf ('cs_make: re-compiling everything\n') ; end end if (isempty (csm)) % mexFunctions, of the form cs_add_mex.c, etc, in this directory csm = { 'cs_add', 'cs_amd', 'cs_chol', 'cs_cholsol', 'cs_counts', ... 'cs_dmperm', 'cs_droptol', 'cs_etree', 'cs_gaxpy', 'cs_lsolve', ... 'cs_ltsolve', 'cs_lu', 'cs_lusol', 'cs_multiply', 'cs_permute', ... 'cs_print', 'cs_qr', 'cs_qrsol', 'cs_scc', 'cs_symperm', 'cs_thumb', ... 'cs_transpose', 'cs_sparse', 'cs_updown', 'cs_usolve', ... 'cs_utsolve', 'cs_randperm', 'cs_sqr' } ; % add cs_mynewfunc to the above list end try % ispc does not appear in MATLAB 5.3 pc = ispc ; catch % if ispc fails, assume we are on a Windows PC if it's not unix pc = ~isunix ; end if (pc) obj = '.obj' ; else obj = '.o' ; end srcdir = '../../Source/' ; hfile = '../../Include/cs.h' ; % compile each CSparse source file [anysrc timestamp kk] = compile_source ('', 'cs_mex', obj, hfile, force, ... mexcmd, kk, details) ; CS = ['cs_mex' obj] ; if (nargout > 0) objfiles = ['..' filesep 'CSparse' filesep 'cs_mex' obj] ; end for i = 1:length (cs) [s t kk] = compile_source (srcdir, cs{i}, obj, hfile, force, mexcmd, ... kk, details) ; timestamp = max (timestamp, t) ; anysrc = anysrc | s ; %#ok CS = [CS ' ' cs{i} obj] ; %#ok if (nargout > 0) objfiles = [objfiles ' ..' filesep 'CSparse' filesep cs{i} obj] ; %#ok end % complex version: if (docomplex) csrc = cs {i} ; csrc = [ 'cs_cl_' csrc(4:end) ] ; CS = [CS ' ' csrc obj] ; %#ok if (nargout > 0) objfiles = [objfiles ' ..' filesep 'CSparse' filesep csrc obj] ;%#ok end if (s) copyfile (['../../Source/' cs{i} '.c'], [csrc '.c'], 'f') ; if (details) fprintf ('%s\n', ['cp -f ../../Source/' cs{i} '.c ' csrc '.c']); end cmd = sprintf ('%s -DCS_COMPLEX -O -c -I../../Include %s.c\n', ... mexcmd, csrc) ; kk = do_cmd (cmd, kk, details) ; end end end % compile each CSparse mexFunction obj = ['.' mexext] ; for i = 1:length (csm) [s t] = cs_must_compile ('', csm{i}, '_mex', obj, hfile, force) ; timestamp = max (timestamp, t) ; if (anysrc | s) %#ok cmd = sprintf ('%s -O -I../../Include %s_mex.c %s -output %s\n', ... mexcmd, csm{i}, CS, csm{i}) ; kk = do_cmd (cmd, kk, details) ; end end if (nargout > 1) timestamp_out = timestamp ; end fprintf ('\n') ; %------------------------------------------------------------------------------- function [s,t,kk] = compile_source (srcdir, f, obj, hfile, force, mexcmd, ... kk, details) % compile a source code file in ../../Source, leaving object file in % this directory. [s t] = cs_must_compile (srcdir, f, '', obj, hfile, force) ; if (s) cmd = sprintf ('%s -O -c -I../../Include %s%s.c\n', mexcmd, srcdir, f) ; kk = do_cmd (cmd, kk, details) ; end %------------------------------------------------------------------------------- function kk = do_cmd (s, kk, details) %DO_CMD: evaluate a command, and either print it or print a "." if (details) fprintf ('%s', s) ; else if (mod (kk, 60) == 0) fprintf ('\n') ; end kk = kk + 1 ; fprintf ('.') ; end eval (s) ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_transpose.m0000644001170100242450000000075410620372563020632 0ustar davisfacfunction C = cs_transpose (A) %#ok %CS_TRANSPOSE transpose a sparse matrix. % C = cs_transpose(A), computes C = A' % C = cs_transpose(A,-1) computes C=A.' % C = cs_transpose(A,1) computes C=A' % % Example: % Prob = UFget ('HB/ibm32') ; A = Prob.A ; % C = cs_transpose (A) ; % C-A' % % See also TRANSPOSE, CTRANSPOSE. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_transpose mexFunction not found') ; SuiteSparse/CXSparse/MATLAB/CSparse/cs_sqr_mex.c0000644001170100242450000000260610620711515020250 0ustar davisfac#include "cs_mex.h" /* cs_sqr: symbolic sparse QR factorization */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double s ; cs_dls *S ; cs_dl Amatrix, *A ; CS_INT m, n, order, *p ; if (nargout > 7 || nargin != 1) { mexErrMsgTxt ("Usage: [vnz,rnz,parent,c,leftmost,p,q] = cs_sqr(A)") ; } A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ m = A->m ; n = A->n ; if (m < n) mexErrMsgTxt ("A must have # rows >= # columns") ; order = (nargout == 7) ? 3 : 0 ; /* determine ordering */ S = cs_dl_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/ if (!S) mexErrMsgTxt ("cs_sqr failed") ; s = S->lnz ; cs_dl_mex_put_double (1, &s, &(pargout [0])) ; /* return nnz(V) */ s = S->unz ; cs_dl_mex_put_double (1, &s, &(pargout [1])) ; /* return nnz(R) */ pargout [2] = cs_dl_mex_put_int (S->parent, n, 1, 0) ; /* return parent */ pargout [3] = cs_dl_mex_put_int (S->cp, n, 0, 0) ; /* return c */ pargout [4] = cs_dl_mex_put_int (S->leftmost, m, 1, 0) ;/* return leftmost*/ p = cs_dl_pinv (S->pinv, S->m2) ; /* p = pinv' */ pargout [5] = cs_dl_mex_put_int (p, S->m2, 1, 1) ; /* return p */ if (nargout > 6) { pargout [6] = cs_dl_mex_put_int (S->q, n, 1, 0) ; /* return q */ } cs_dl_sfree (S) ; } SuiteSparse/CXSparse/MATLAB/CSparse/cs_qr_mex.c0000644001170100242450000000543410573562351020100 0ustar davisfac#include "cs_mex.h" /* cs_qr: sparse QR factorization */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT m, n, order, *p ; if (nargout > 5 || nargin != 1) { mexErrMsgTxt ("Usage: [V,beta,p,R,q] = cs_qr(A)") ; } order = (nargout == 5) ? 3 : 0 ; /* determine ordering */ m = mxGetM (pargin [0]) ; n = mxGetN (pargin [0]) ; if (m < n) mexErrMsgTxt ("A must have # rows >= # columns") ; if (mxIsComplex (pargin [0])) { #ifndef NCOMPLEX cs_cls *S ; cs_cln *N ; cs_cl Amatrix, *A, *D ; A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */ S = cs_cl_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/ N = cs_cl_qr (A, S) ; /* numeric QR factorization */ cs_free (A->x) ; if (!N) mexErrMsgTxt ("qr failed") ; cs_cl_dropzeros (N->L) ; /* drop zeros from V and sort */ D = cs_cl_transpose (N->L, 1) ; cs_cl_spfree (N->L) ; N->L = cs_cl_transpose (D, 1) ; cs_cl_spfree (D) ; cs_cl_dropzeros (N->U) ; /* drop zeros from R and sort */ D = cs_cl_transpose (N->U, 1) ; cs_cl_spfree (N->U) ; N->U = cs_cl_transpose (D, 1) ; cs_cl_spfree (D) ; m = N->L->m ; /* m may be larger now */ p = cs_cl_pinv (S->pinv, m) ; /* p = pinv' */ pargout [0] = cs_cl_mex_put_sparse (&(N->L)) ; /* return V */ cs_dl_mex_put_double (n, N->B, &(pargout [1])) ; /* return beta */ pargout [2] = cs_dl_mex_put_int (p, m, 1, 1) ; /* return p */ pargout [3] = cs_cl_mex_put_sparse (&(N->U)) ; /* return R */ pargout [4] = cs_dl_mex_put_int (S->q, n, 1, 0) ; /* return q */ cs_cl_nfree (N) ; cs_cl_sfree (S) ; #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dls *S ; cs_dln *N ; cs_dl Amatrix, *A, *D ; A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ S = cs_dl_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/ N = cs_dl_qr (A, S) ; /* numeric QR factorization */ if (!N) mexErrMsgTxt ("qr failed") ; cs_dl_dropzeros (N->L) ; /* drop zeros from V and sort */ D = cs_dl_transpose (N->L, 1) ; cs_dl_spfree (N->L) ; N->L = cs_dl_transpose (D, 1) ; cs_dl_spfree (D) ; cs_dl_dropzeros (N->U) ; /* drop zeros from R and sort */ D = cs_dl_transpose (N->U, 1) ; cs_dl_spfree (N->U) ; N->U = cs_dl_transpose (D, 1) ; cs_dl_spfree (D) ; m = N->L->m ; /* m may be larger now */ p = cs_dl_pinv (S->pinv, m) ; /* p = pinv' */ pargout [0] = cs_dl_mex_put_sparse (&(N->L)) ; /* return V */ cs_dl_mex_put_double (n, N->B, &(pargout [1])) ; /* return beta */ pargout [2] = cs_dl_mex_put_int (p, m, 1, 1) ; /* return p */ pargout [3] = cs_dl_mex_put_sparse (&(N->U)) ; /* return R */ pargout [4] = cs_dl_mex_put_int (S->q, n, 1, 0) ; /* return q */ cs_dl_nfree (N) ; cs_dl_sfree (S) ; } } SuiteSparse/CXSparse/MATLAB/Makefile0000644001170100242450000000032310375340406016037 0ustar davisfacall: ( cd CSparse ; $(MAKE) ) ( cd Test ; $(MAKE) ) clean: ( cd CSparse ; $(MAKE) clean ) ( cd Test ; $(MAKE) clean ) purge: ( cd CSparse ; $(MAKE) purge ) ( cd Test ; $(MAKE) purge ) distclean: purge SuiteSparse/CXSparse/MATLAB/UFget/0000755001170100242450000000000010711673300015407 5ustar davisfacSuiteSparse/CXSparse/MATLAB/UFget/mat/0000755001170100242450000000000010620672242016173 5ustar davisfacSuiteSparse/CXSparse/MATLAB/UFget/mat/UF_Index.mat0000644001170100242450000036260010677525546020366 0ustar davisfacMATLAB 5.0 MAT-file, Platform: GLNX86, Created on: Thu Sep 6 13:49:48 2007 IMxMN@_ n;?IbbXqlЙif HI'p5\}x/4&|ԓg#YXW-;ǗkTa7ωtl4 aV=RBQdpe<T&9&^tPD*.xbn4F!"nĮY]sɍX žnJ!gA`(^[OQ$hb(wikhQBi> Df/Cn$"C2E+?ذB|GxL< %WdLV?Y\x>eϴv{}躧Gnry?\v]"?ޜ)-?Ww#<#<#<#<#<#<#<˱ @DQTK.\0x eגjwKU qqqqqqqqqO 0GرMEwrL!e|d?^/sI3.U?F㧑i]]kGgf˄M󃇇)aazgI;~l%[߇ϥnZ 1 @EQӈIiia5$BpũҤJ3/.ņXkcU_绌|}-e}::::::::::::ܿtڏyOuyyyy 0%˺´a@iY}y W$ఝgpLgm.m^VNM~k3x<x<W#B||ƃ~]Sƴ ';nʞ"U7Íu!sꓮ9x<T_qQK0*?G eU{XXDvoj" ^B^W6 ~OyD,e+y˨쫦vMQfudfe\yɓGmL~0Igqy0H3nxfXU OIY~+w^!Kzq'n(r0ǵ:>:|KD!u):hRGPǻ죃:贡S\2gqy߹ixmˮT;tJٹ+B>[ 0E )]v RȂUFͨ$׷TJTĤW.L-h NgEM^^^U^J|ܳ#`nFʋ~Fs~Gqgˑf+xw]q8pS^Y>; p`c$2慡kGiylc;qp8p|9QBIN:`=ȼ{!w)89W]K0@+D>uEd8m\H?&mW iv[IM\jfdeqVtIVxޛSk^|مF<"wTG^$?."'0Ÿx?Xܞ?tސeb2% q y#b$|QY< c،߄5xӶ}t}ZX5F ^tH|`16ux.[4sQi{{?㯅TiΘ ?fg?>}Y6;i;/dvZZ7؏st]6t5OUBU/i_aՠ朎Re&!|x;F8<*Cj%F?}YJﾽeOY.J98EK/WB726ѓuöו(~&͠coǓxbl1M.Ew-&c>C,ܟ ?$57@A~)g}P#Yg=ҟH#Yg=ҟHG#?#?#?#?#?8`쏃q0`*e=U}m < %&_F)8|blm{Q>7=)]7|~zſ(4~ (l,ퟅ#0?Oip4555k>?pݏk( ΟFώy ^ǟ򧢿pp-)Xqy z zu!|[;\˻{ P+V˭_֊?zG+k݈/z[|!om ͟_~kl"l o8|&?/p k+;1տC;z`EϬ?G맸 (=8ΟKퟒxy=6~̿ 8/U;y}_WX ?7?n6K&ɋ񗖠/~<2#OOh#G~MݙO{{5;7ۯVմ-!5xM}o dx_o_灔R6\Vɳ~ GM˸?yqOn0`ګ64zM8 k\$QVB+.>`aYz/=f~_L[w͉^&KR7_ڎ*(4ZuUj.9?xYɤ;8)ȇ yw׉D`$4-/$9\Lo_ФuhU?ERտm8oٛm8֯_ߜ<t2X4a8qY|{_w|xΠFA'@'ANN;lN;qn\߽=g,I}C= ^jͩsO\yi%>~{x>ѹmgxv潛 u|sopW;fowͻO[wu^_1}ҏgo'?[fyO?SD,KM'_l8͛/|nZ0m\{b|$#Lͯ_U|KSc> -76/^}ca:=vϼ{`-Z1ąI0A+A]36>"x\V#^(~Q_b 1&5h|_LY5iO# D"zM񯜑 sn0L(m/2% Td$-!Fj!#v9ϲ!ZO}oz}Jl} yqdUe}ܤ~ueu:?\]o*:ů{+K`\c?2e8,/͸~[wx_S~] <6yb-SN;ᩦɧn%#}N {2~'y:~%kȟҤ{r\'?oQj%p^+'o-m8Ua'x1S.޿F/7zR_.xݝ=;ljěqԍqYdqxDovi7}azyfV~jj~|p {>, ]}h>/Jwϻ2z>/*z;y?M֟&O+ѓdi?!O~1z w.ۼh h=A'3s+@Wbu#`}p`̻y0=q+Ёu&` X/֋n_yI|.ikn]o0~hS؄g C4IPRH=F=k $w=T*5|Nv7-.^9nS'.qid_t]ۨ}).6hܳU;}QO=˓_&. < y-Y!oRgB~%U _ܾs_ípuQ*ch_ow|=޹,Cƿs<t_~xq=@@N9 rK@.gzFgzFgzFgzFgzFgzA4=ӠgLi3 zA4=c3=c3=c3=c3=c3=c3zf@ =3g̀3zf@ =ĝY3 zfA, 7f CNrsOy<'^~xj &7۪W;Oz;p^\mRoe9H"`a1crdY*89H+#z"yHSJڇ~NkV㤟q?H<)Gc#屑dn03iKVv)ow1ԉcSk~Eu UO^sbom?=7{.HJ'\^!s?PBc8;8 88~6H~6H~$? 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MATLAB 7.0 or later is required. Date: May 31, 2007. Copyright 2005-2007, Tim Davis, University of Florida. Authors: Tim Davis and Erich Mirable. Availability: http://www.cise.ufl.edu/research/sparse/mat/UFget See http://www.cise.ufl.edu/research/sparse/mat/UFget.tar.gz for a single archive file with all the files listed below. UFget/Contents.m help for UFget UFget/README.txt this file UFget/UFget_defaults.m default parameter settings for UFget UFget/UFget_example.m demo for UFget UFget/UFget_lookup.m get the group, name, and id of a matrix UFget/UFget.m primary user interface UFget/UFweb.m opens the URL for a matrix or collection UFget/mat default download directory (can be changed) UFget/mat/UF_Index.mat index to the UF sparse matrix collection To install the package, just add the path containing the UFget directory to your MATLAB path. Type "pathtool" in MATLAB for more details. For a simple example of use, type this command in MATLAB: UFget_example The MATLAB statement Problem = UFget ('HB/arc130') (for example), will download a sparse matrix called HB/arc130 (a laser simulation problem) and load it into MATLAB. You don't need to use your web browser to load the matrix. The statement Problem = UFget (6) will also load same the HB/arc130 matrix. Each matrix in the collection has a unique identifier, in the range 1 to the number of matrices. As new matrices are added, the id's of existing matrices will not change. To view an index of the entire collection, just type UFget in MATLAB. To modify your download directory, edit the UFget_defaults.m file. To open a URL of the entire collection, just type UFweb To open the URL of a group of matrices in the collection: UFweb ('HB') To open the web page for one matrix, use either of these formats: UFweb ('HB/arc130') UFweb (6) For more information on how the index entries were created, see http://www.cise.ufl.edu/research/sparse/SuiteSparse. SuiteSparse/CXSparse/MATLAB/UFget/UFget_lookup.m0000644001170100242450000000403210711661566020202 0ustar davisfacfunction [group, name, id] = UFget_lookup (matrix, UF_Index) %UFGET_LOOKUP gets the group, name, and id of a matrix. % % Example: % [group name id] = UFget_lookup (matrix, UF_Index) % % See also UFget. % Copyright 2007, Tim Davis, University of Florida. if (isnumeric (matrix)) % make sure that the matrix parameter is only one integer value % this means that if we get an array, just use the first value id = fix (full (matrix (1))) ; % if the index is less than one or bigger than the length of the array, % then no particular matrix is accessed if (id > length (UF_Index.nrows) | id < 1) %#ok id = 0 ; group = '' ; name = '' ; else % assign the group and name for the given id group = UF_Index.Group {matrix} ; name = UF_Index.Name {matrix} ; end elseif (ischar (matrix)) % the group and matrix name are in the string as in GroupName\MatrixName % find the group index for the file separator % check both types of slashes, and a colon gi = find (matrix == '/') ; if (length (gi) == 0) %#ok gi = find (matrix == '\') ; end if (length (gi) == 0) %#ok gi = find (matrix == ':') ; end % if no name divider is in the string, a whole group is specified if (length (gi) == 0) %#ok id = 0 ; group = matrix ; name = '' ; else % group equals the first part of the string up to the character before % the last file separator group = matrix (1:gi(end)-1) ; % group equals the last section of the string after the last file % separator name = matrix (gi(end)+1:end) ; % validate the given name and group by checking the index for a match refName = strmatch (name, UF_Index.Name) ; refGroup = strmatch (group, UF_Index.Group) ; id = intersect (refName, refGroup) ; if (length (id) >= 1) id = id (1) ; else % the given group/matrix does not exist in the index file id = 0 ; end end else % there is an error in the argument types passed into the function error ('invalid input') ; end SuiteSparse/CXSparse/MATLAB/UFget/UFgrep.m0000644001170100242450000000265710620373464016776 0ustar davisfacfunction list = UFgrep (expression, index) %UFGREP search for matrices in the UF Sparse Matrix Collection. % UFgrep returns a list of Problem id's whose Problem.name string matches an % expression. With no output arguments, the list is displayed. Otherwise, it % is returned as a list of integer id's. % % Example: % UFgrep ('HB') ; % all matrices in the HB group % UFgrep ('\= 7.0) addpath ([pwd filesep 'UFget']) ; else fprintf ('UFget not installed (MATLAB 7.0 or later required)\n') ; end cd ('CSparse') ; cs_make (1) ; cd ('../Demo') ; cs_demo (do_pause) %------------------------------------------------------------------------------- function v = getversion % determine the MATLAB version, and return it as a double. v = sscanf (version, '%d.%d.%d') ; v = 10.^(0:-1:-(length(v)-1)) * v ; SuiteSparse/CXSparse/Matrix/0000755001170100242450000000000010567667105014720 5ustar davisfacSuiteSparse/CXSparse/Matrix/t10000644001170100242450000000012010323544611015142 0ustar davisfac2 2 3.0 1 0 3.1 3 3 1.0 0 2 3.2 1 1 2.9 3 0 3.5 3 1 0.4 1 3 0.9 0 0 4.5 2 1 1.7 SuiteSparse/CXSparse/Matrix/west00670000644001170100242450000000753510326012123016125 0ustar davisfac44 55 -1.863354 54 61 -1.863354 29 37 -1.567398 44 56 -1.490683 54 62 -1.490683 9 12 -1.265823 29 38 -1.253918 44 57 -1.118012 54 63 -1.118012 15 31 -1.05 16 32 -1.05 17 33 -1.05 18 34 -1.05 19 35 -1.05 24 31 -1.05 25 32 -1.05 26 33 -1.05 27 34 -1.05 28 35 -1.05 9 13 -1.012658 10 20 -1 11 21 -1 12 22 -1 13 23 -1 14 24 -1 30 49 -0.9722222 31 50 -0.9722222 32 51 -0.9722222 33 52 -0.9722222 34 53 -0.9722222 39 49 -0.9722222 40 50 -0.9722222 41 51 -0.9722222 42 52 -0.9722222 43 53 -0.9722222 35 25 -0.9583187 36 26 -0.9583187 37 27 -0.9583187 38 28 -0.9583187 49 55 -0.9444444 50 56 -0.9444444 51 57 -0.9444444 52 58 -0.9444444 53 59 -0.9444444 29 39 -0.9404389 20 1 -0.9159533 21 2 -0.9159533 22 3 -0.9159533 23 4 -0.9159533 0 7 -0.8341818 1 8 -0.8341818 2 9 -0.8341818 3 10 -0.8341818 45 43 -0.8242248 46 44 -0.8242248 47 45 -0.8242248 48 46 -0.8242248 4 1 -0.8 5 2 -0.8 6 3 -0.8 7 4 -0.8 8 5 -0.8 9 14 -0.7594937 44 58 -0.7453416 54 64 -0.7453416 29 40 -0.6269592 9 15 -0.5063291 44 59 -0.3726708 54 65 -0.3726708 0 17 -0.3361556 29 41 -0.3134796 1 17 -0.2939196 20 42 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0.09789015 19 19 0.09941246 34 36 0.1026879 41 54 0.1061028 31 36 0.1087668 26 36 0.1131608 27 36 0.1150555 26 0 0.1161859 5 6 0.1175679 18 19 0.1192061 15 19 0.1243055 32 36 0.1257342 33 36 0.1278394 16 19 0.1284235 17 19 0.1286524 43 54 0.1315353 42 54 0.1333878 25 0 0.1340093 4 6 0.1344622 24 0 0.1394208 30 43 0.25 31 44 0.25 32 45 0.25 33 46 0.25 34 47 0.25 10 12 0.3333333 11 13 0.3333333 12 14 0.3333333 13 15 0.3333333 14 16 0.3333333 24 1 0.4 25 2 0.4 26 3 0.4 27 4 0.4 28 5 0.4 4 12 0.4 4 7 0.4 5 13 0.4 5 8 0.4 6 14 0.4 6 9 0.4 7 10 0.4 7 15 0.4 8 11 0.4 8 16 0.4 49 61 0.4444444 50 62 0.4444444 51 63 0.4444444 52 64 0.4444444 53 65 0.4444444 15 25 0.45 16 26 0.45 17 27 0.45 18 28 0.45 19 29 0.45 39 55 0.4722222 40 56 0.4722222 41 57 0.4722222 42 58 0.4722222 43 59 0.4722222 39 25 0.5 40 26 0.5 41 27 0.5 42 28 0.5 43 29 0.5 49 43 0.5 50 44 0.5 51 45 0.5 52 46 0.5 53 47 0.5 3 15 0.5063291 15 20 0.6 16 21 0.6 17 22 0.6 18 23 0.6 19 24 0.6 23 40 0.6269592 24 37 0.65 25 38 0.65 26 39 0.65 27 40 0.65 28 41 0.65 14 18 0.6666667 30 37 0.7222222 31 38 0.7222222 32 39 0.7222222 33 40 0.7222222 34 41 0.7222222 38 58 0.7453416 48 64 0.7453416 2 14 0.7594937 22 39 0.9404389 59 31 0.5 59 32 0.5 59 33 0.5 59 34 0.5 59 35 0.5 29 42 1 44 60 1 54 66 1 55 18 1 56 10 1 56 11 1 56 7 1 56 8 1 56 9 1 57 12 1 57 13 1 57 14 1 57 15 1 57 16 1 58 20 1 58 21 1 58 22 1 58 23 1 58 24 1 59 31 0.5 59 32 0.5 59 33 0.5 59 34 0.5 59 35 0.5 60 1 1 60 2 1 60 3 1 60 4 1 60 5 1 61 37 1 61 38 1 61 39 1 61 40 1 61 41 1 62 49 1 62 50 1 62 51 1 62 52 1 62 53 1 63 25 1 63 26 1 63 27 1 63 28 1 63 29 1 64 55 1 64 56 1 64 57 1 64 58 1 64 59 1 65 43 1 65 44 1 65 45 1 65 46 1 65 47 1 66 61 1 66 62 1 66 63 1 66 64 1 66 65 1 9 17 1 1 13 1.012658 37 57 1.118012 47 63 1.118012 21 38 1.253918 0 12 1.265823 36 56 1.490683 46 62 1.490683 20 37 1.567398 35 55 1.863354 45 61 1.863354 SuiteSparse/CXSparse/Matrix/bcsstk010000644001170100242450000001157510326005665016274 0ustar davisfac0 0 2.83226851852e+06 4 0 1.0e+06 5 0 2.08333333333e+06 6 0 -3.33333333333e+03 10 0 1.0e+06 18 0 -2.8e+06 24 0 -2.89351851852e+04 29 0 2.08333333333e+06 1 1 1.63544753086e+06 3 1 -2.0e+06 5 1 5.55555555555e+06 7 1 -6.66666666667e+03 9 1 -2.0e+06 19 1 -3.08641975309e+04 23 1 5.55555555555e+06 25 1 -1.59791666667e+06 2 2 1.72436728395e+06 3 2 -2.08333333333e+06 4 2 -2.77777777778e+06 8 2 -1.68e+06 20 2 -1.54320987654e+04 22 2 -2.77777777778e+06 26 2 -2.89351851852e+04 27 2 -2.08333333333e+06 3 3 1.00333333333e+09 7 3 2.0e+06 9 3 4.0e+08 21 3 -3.33333333333e+06 26 3 2.08333333333e+06 27 3 1.0e+08 4 4 1.06750000000e+09 6 4 -1.0e+06 10 4 2.0e+08 20 4 2.77777777778e+06 22 4 3.33333333333e+08 28 4 -8.33333333333e+05 5 5 1.53533333333e+09 11 5 -2.0e+06 19 5 -5.55555555555e+06 23 5 6.66666666667e+08 24 5 -2.08333333333e+06 29 5 1.0e+08 6 6 2.83226851852e+06 10 6 -1.0e+06 11 6 2.08333333333e+06 12 6 -2.8e+06 30 6 -2.89351851852e+04 35 6 2.08333333333e+06 7 7 1.63544753086e+06 9 7 2.0e+06 11 7 5.55555555555e+06 13 7 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3.47222222222e+06 40 34 4.16666666667e+08 35 35 2.16916666667e+09 37 35 -6.94444444444e+06 41 35 8.33333333333e+08 36 36 3.98587962963e+06 40 36 -1.25e+06 41 36 4.16666666667e+05 42 36 -4.16666666667e+03 46 36 -1.25e+06 37 37 3.41149691358e+06 39 37 2.5e+06 41 37 -6.94444444445e+06 43 37 -8.33333333333e+03 45 37 2.5e+06 38 38 2.43100308642e+06 39 38 -4.16666666667e+05 40 38 3.47222222222e+06 44 38 -2.35500000000e+06 39 39 1.50416666667e+09 43 39 -2.5e+06 45 39 5.0e+08 40 40 1.33516666667e+09 42 40 1.25e+06 46 40 2.5e+08 41 41 2.16916666667e+09 47 41 -2.5e+06 42 42 6.47105806113e+04 46 42 2.39928529451e+06 47 42 1.40838195984e+05 43 43 3.50487988027e+06 44 43 5.17922131816e+05 45 43 -4.79857058902e+06 44 44 4.57738374749e+06 45 44 1.34990274700e+05 45 45 2.47238730198e+09 46 46 9.61679848804e+08 47 46 -1.09779731332e+08 47 47 5.31278103775e+08 SuiteSparse/CXSparse/Matrix/bcsstk160000644001170100242450001632470710326007427016313 0ustar davisfac0 0 285559874.9195 1 0 26666666.66228 3 0 -146456504.1625 4 0 -26666666.44895 6 0 9767101.054332 7 0 21333333.1165 111 0 45108925.89256 112 0 13333333.33771 113 0 13177222.19231 114 0 -107413106.5112 115 0 -13333333.23104 116 0 -65886110.96157 117 0 -9767101.054335 118 0 10666666.5635 119 0 -13177221.94221 1 1 245557954.5208 3 1 -26666666.34228 4 1 -21122150.29068 6 1 31999999.67474 7 1 9767101.054331 111 1 13333333.33771 112 1 25107965.68335 113 1 10541666.55379 114 1 -13333333.17771 115 1 -44745929.54446 116 1 -13177083.26329 117 1 15999999.84525 118 1 -9767101.054335 119 1 15812499.93082 2 2 1 3 3 494473574.2688 4 3 26666666.12895 6 3 15679616.33822 7 3 -26666666.44895 9 3 -99111631.13552 10 3 2.384185791016e-07 12 3 -37577772.88735 13 3 26666666.66229 111 3 -107413106.5112 112 3 -13333333.17771 113 3 65886110.96157 114 3 100730268.7541 115 3 13333333.07105 116 3 0.02774140238762 117 3 -26345045.89131 118 3 -13333333.23105 119 3 16471527.49884 120 3 -88624220.55292 121 3 2.235174179077e-07 122 3 -65886111.10029 123 3 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6 -65886110.96157 126 6 -9767101.054335 127 6 10666666.5635 128 6 -13177221.94221 7 7 245557954.5208 9 7 -26666666.66229 10 7 -29577388.75645 12 7 -26666666.34228 13 7 -21122150.29068 15 7 31999999.67474 16 7 9767101.054331 111 7 10666666.5635 112 7 -9767101.054336 113 7 -10541666.62055 114 7 -13333333.23105 115 7 -73011454.71627 116 7 -52708332.94687 117 7 13333333.33771 118 7 25107965.68335 119 7 10541666.55379 120 7 -13333333.33771 121 7 -24555795.63051 122 7 -13177083.33766 123 7 -13333333.17771 124 7 -44745929.54446 125 7 -13177083.26329 126 7 15999999.84525 127 7 -9767101.054335 128 7 15812499.93082 8 8 1 9 9 456895802.7167 10 9 3.695487976074e-06 12 9 63024490.39561 13 9 -1.102685928345e-06 18 9 -99111631.13552 19 9 2.384185791016e-07 21 9 -37577772.88735 22 9 26666666.66229 114 9 -88624220.55292 115 9 1.043081283569e-07 116 9 65886111.10029 117 9 -28555987.69793 118 9 -13333333.33771 119 9 16471527.78319 120 9 72174281.7049 121 9 1.728534698486e-06 122 9 1.221895217896e-06 123 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124 13 64728540.28304 125 13 0.022192299366 126 13 -13333333.17771 127 13 -73011454.71628 128 13 52708333.03581 129 13 -13333333.33771 130 13 -24555795.63051 131 13 -13177083.33766 132 13 1.9371509552e-07 133 13 -29957235.32024 134 13 -3.8743019104e-07 135 13 13333333.33771 136 13 -24555795.63051 137 13 13177083.33766 14 14 1 15 15 285559874.9195 16 15 26666666.66228 21 15 -37577772.88735 22 15 -26666666.66229 24 15 -146456504.1625 25 15 -26666666.44895 27 15 9767101.054332 28 15 21333333.1165 117 15 -9767101.054335 118 15 15999999.84525 119 15 19765832.91331 123 15 -26345045.8913 124 15 -13333333.17771 125 15 -16471527.35667 126 15 45108925.89256 127 15 13333333.33771 128 15 13177222.19231 132 15 -28555987.69793 133 15 -13333333.33771 134 15 -16471527.78319 135 15 -107413106.5112 136 15 -13333333.23104 137 15 -65886110.96157 138 15 -9767101.054335 139 15 10666666.5635 140 15 -13177221.94221 16 16 245557954.5208 21 16 -26666666.66229 22 16 -29577388.75645 24 16 -26666666.34228 25 16 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1941 1816 3.725290298462e-07 1942 1816 -19630743.20649 1943 1816 -694433.4439167 1944 1816 9166666.669676 1945 1816 -17413237.96253 1946 1816 9149300.058182 1817 1817 607013167.9741 1818 1817 2737303.360137 1819 1817 5388804.78494 1820 1817 37600883.93994 1827 1817 2471062.980849 1828 1817 1236089.109403 1829 1817 -7832062.870945 1830 1817 -462970.2969232 1831 1817 -2777733.774298 1832 1817 39890623.87246 1833 1817 -2737270.351624 1834 1817 1541644.664895 1835 1817 -7895194.184061 1911 1817 10279397.69313 1912 1817 -8385422.169798 1913 1817 -16619803.40013 1914 1817 43154829.95728 1915 1817 7802192.5578 1916 1817 -56944833.0873 1923 1817 57871.28717278 1924 1817 -33666688.66265 1925 1817 -39477172.9523 1926 1817 781318.4370322 1927 1817 -2152691.493423 1928 1817 -99821807.80486 1929 1817 11639498.06975 1930 1817 36402939.91804 1931 1817 -55413772.21342 1938 1817 -10337268.9803 1939 1817 -8454866.614265 1940 1817 -16869702.39011 1941 1817 -43935881.45598 1942 1817 -694433.4439167 1943 1817 -57643892.87044 1944 1817 -11639352.31406 1945 1817 9149300.058182 1946 1817 -20870649.36111 1818 1818 387435706.2613 1819 1818 36666666.66065 1820 1818 2662175.186035 1830 1818 -52284795.20658 1831 1818 -36666666.66065 1832 1818 2505785.203048 1833 1818 -203296779.618 1834 1818 -36666973.09101 1835 1818 -2662152.453524 1836 1818 12401143.47877 1837 1818 29333639.75888 1838 1818 -2152799.783064 1914 1818 -4839277.140465 1915 1818 11000114.915 1916 1818 12370128.70975 1926 1818 -14860172.33131 1927 1818 -9166781.581062 1928 1818 -10279526.39882 1929 1818 33963705.33589 1930 1818 9166666.669679 1931 1818 9519894.71657 1941 1818 -18663081.30986 1942 1818 -9166666.669677 1943 1818 -10337268.9803 1944 1818 -73633660.33315 1945 1818 -9166743.277268 1946 1818 -44520628.22528 1947 1818 -7828204.348046 1948 1818 7333409.943332 1949 1818 -9288430.506837 1819 1819 332431392.3218 1820 1819 -6944376.976808 1830 1819 -36666666.66065 1831 1819 -41284001.36615 1832 1819 1263866.887163 1833 1819 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1824 -18569369.18862 1918 1824 9166666.669678 1919 1824 10279397.69313 1920 1824 -59565882.98117 1921 1824 4.91738319397e-07 1922 1824 43739118.52961 1923 1824 -20057887.18154 1924 1824 -9166666.669679 1925 1824 11581481.02689 1932 1824 -1129879.778007 1933 1824 2.369284629822e-06 1934 1824 57871.28717239 1935 1824 54280296.46473 1936 1824 3.09944152832e-06 1937 1824 231485.1485852 1938 1824 -7107625.989141 1939 1824 -6.146728992462e-06 1940 1824 57871.2871768 1950 1824 -18663081.30986 1951 1824 -9166666.669677 1952 1824 -10337268.9803 1953 1824 -59964405.70834 1954 1824 7.525086402893e-07 1955 1824 -43970603.67818 1956 1824 -20163436.42398 1957 1824 9166666.669676 1958 1824 -11639352.31406 1825 1825 531622789.3528 1826 1825 -11110935.09172 1827 1825 -4.798173904419e-06 1828 1825 -55180296.03374 1829 1825 5555467.545859 1839 1825 -36666666.66065 1840 1825 -41284001.36615 1841 1825 1263866.887163 1842 1825 -5.960464477539e-08 1843 1825 22901850.42796 1844 1825 -2777733.774299 1845 1825 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-36666666.66065 1844 1827 2505785.203048 1845 1827 -138432799.5 1846 1827 1.490116119385e-07 1847 1827 -462970.296923 1848 1827 -52308469.44899 1849 1827 36666666.66065 1850 1827 -2702548.129425 1920 1827 -18569369.18862 1921 1827 9166666.669678 1922 1827 10279397.69313 1923 1827 -59565882.98117 1924 1827 4.91738319397e-07 1925 1827 43739118.52961 1926 1827 -20057887.18154 1927 1827 -9166666.669679 1928 1827 11581481.02689 1935 1827 -1129879.778007 1936 1827 2.369284629822e-06 1937 1827 57871.28717239 1938 1827 54280296.46473 1939 1827 3.09944152832e-06 1940 1827 231485.1485852 1941 1827 -7107625.989141 1942 1827 -6.146728992462e-06 1943 1827 57871.2871768 1953 1827 -18663081.30986 1954 1827 -9166666.669677 1955 1827 -10337268.9803 1956 1827 -59964405.70834 1957 1827 7.525086402893e-07 1958 1827 -43970603.67818 1959 1827 -20163436.42398 1960 1827 9166666.669676 1961 1827 -11639352.31406 1828 1828 531622789.3528 1829 1828 -11110935.09172 1830 1828 -4.798173904419e-06 1831 1828 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599591912.5003 1830 1829 231485.1485663 1831 1829 5555467.545859 1832 1829 78550735.85485 1842 1829 2471062.980849 1843 1829 1236089.109403 1844 1829 -7832062.870945 1845 1829 -462970.2969232 1846 1829 -2777733.774298 1847 1829 39890623.87246 1848 1829 -2737270.351624 1849 1829 1541644.664895 1850 1829 -7895194.184061 1920 1829 10279397.69313 1921 1829 -8385422.169798 1922 1829 -16619803.40013 1923 1829 43704396.30741 1924 1829 -694433.4439163 1925 1829 -56581165.5979 1926 1829 11581481.02689 1927 1829 9079855.613715 1928 1829 -20589184.71456 1935 1829 57871.28717278 1936 1829 -33666688.66265 1937 1829 -39477172.9523 1938 1829 231485.148585 1939 1829 -2777733.774298 1940 1829 -118440658.1206 1941 1829 57871.28717716 1942 1829 36444422.43695 1943 1829 -55417829.51533 1953 1829 -10337268.9803 1954 1829 -8454866.614265 1955 1829 -16869702.39011 1956 1829 -43935881.45598 1957 1829 -694433.4439167 1958 1829 -57643892.87044 1959 1829 -11639352.31406 1960 1829 9149300.058182 1961 1829 -20870649.36111 1830 1830 619629140.0329 1831 1830 1.168251037598e-05 1832 1830 925940.5938052 1833 1830 84152766.23505 1834 1830 -4.991888999939e-06 1835 1830 231485.148566 1845 1830 -52284795.20658 1846 1830 -36666666.66065 1847 1830 2505785.203048 1848 1830 -138432799.5 1849 1830 1.490116119385e-07 1850 1830 -462970.296923 1851 1830 -52308469.44899 1852 1830 36666666.66065 1853 1830 -2702548.129425 1923 1830 -18569369.18862 1924 1830 9166666.669678 1925 1830 10279397.69313 1926 1830 -59565882.98117 1927 1830 4.91738319397e-07 1928 1830 43739118.52961 1929 1830 -20057887.18154 1930 1830 -9166666.669679 1931 1830 11581481.02689 1938 1830 -1129879.778007 1939 1830 2.369284629822e-06 1940 1830 57871.28717239 1941 1830 54280296.46473 1942 1830 3.09944152832e-06 1943 1830 231485.1485852 1944 1830 -7107625.989141 1945 1830 -6.146728992462e-06 1946 1830 57871.2871768 1956 1830 -18663081.30986 1957 1830 -9166666.669677 1958 1830 -10337268.9803 1959 1830 -59964405.70834 1960 1830 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1835 -43935881.45598 1963 1835 -694433.4439167 1964 1835 -57643892.87044 1965 1835 -11639352.31406 1966 1835 9149300.058182 1967 1835 -20870649.36111 1836 1836 460873125.4361 1837 1836 -27780651.28176 1838 1836 -1243230.409633 1851 1836 -52284795.20658 1852 1836 -36666666.66065 1853 1836 2505785.203048 1854 1836 -54494915.13083 1855 1836 27775705.0022 1856 1836 -284486.8047392 1857 1836 -253893652.0179 1858 1836 29338279.60807 1859 1836 -277841.1803685 1929 1836 -4839277.140465 1930 1836 11000114.915 1931 1836 12370128.70975 1944 1836 -14860172.33131 1945 1836 -9166781.581062 1946 1836 -10279526.39882 1947 1836 64920055.70775 1948 1836 -6810686.593768 1949 1836 4688786.852337 1962 1836 -18663081.30986 1963 1836 -9166666.669677 1964 1836 -10337268.9803 1965 1836 -28004319.24308 1966 1836 6809529.72167 1967 1836 -24862467.02138 1968 1836 -60799172.28945 1969 1836 7334490.207843 1970 1836 -1215195.31154 1837 1837 860522545.6296 1838 1837 -12063310.05486 1851 1837 -36666666.66065 1852 1837 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1971 1839 -59964405.70834 1972 1839 7.525086402893e-07 1973 1839 -43970603.67818 1974 1839 -20163436.42398 1975 1839 9166666.669676 1976 1839 -11639352.31406 1840 1840 531622789.3528 1841 1840 -11110935.09172 1842 1840 -4.798173904419e-06 1843 1840 -55180296.03374 1844 1840 5555467.545859 1860 1840 -5.960464477539e-08 1861 1840 22901850.42796 1862 1840 -2777733.774299 1863 1840 36666666.66064 1864 1840 -41307675.60857 1865 1840 1513866.887135 1932 1840 -5.811452865601e-07 1933 1840 -19232220.47929 1934 1840 -694433.4439163 1935 1840 -9166666.669679 1936 1840 -17307688.72007 1937 1840 9079855.613715 1950 1840 3.635883331299e-06 1951 1840 32278708.78388 1952 1840 -2777733.774297 1953 1840 -5.349516868591e-06 1954 1840 -41940891.5735 1955 1840 36472200.21471 1971 1840 3.725290298462e-07 1972 1840 -19630743.20649 1973 1840 -694433.4439167 1974 1840 9166666.669676 1975 1840 -17413237.96253 1976 1840 9149300.058182 1841 1841 599591912.5003 1842 1841 231485.1485663 1843 1841 5555467.545859 1844 1841 78550735.85485 1860 1841 -462970.2969232 1861 1841 -2777733.774298 1862 1841 39890623.87246 1863 1841 -2737270.351624 1864 1841 1541644.664895 1865 1841 -7895194.184061 1932 1841 43704396.30741 1933 1841 -694433.4439163 1934 1841 -56581165.5979 1935 1841 11581481.02689 1936 1841 9079855.613715 1937 1841 -20589184.71456 1950 1841 231485.148585 1951 1841 -2777733.774298 1952 1841 -118440658.1206 1953 1841 57871.28717716 1954 1841 36444422.43695 1955 1841 -55417829.51533 1971 1841 -43935881.45598 1972 1841 -694433.4439167 1973 1841 -57643892.87044 1974 1841 -11639352.31406 1975 1841 9149300.058182 1976 1841 -20870649.36111 1842 1842 619629140.0329 1843 1842 1.168251037598e-05 1844 1842 925940.5938052 1845 1842 84152766.23505 1846 1842 -4.991888999939e-06 1847 1842 231485.148566 1860 1842 -52284795.20658 1861 1842 -36666666.66065 1862 1842 2505785.203048 1863 1842 -138432799.5 1864 1842 1.490116119385e-07 1865 1842 -462970.296923 1866 1842 -52308469.44899 1867 1842 36666666.66065 1868 1842 -2702548.129425 1932 1842 -18569369.18862 1933 1842 9166666.669678 1934 1842 10279397.69313 1935 1842 -59565882.98117 1936 1842 4.91738319397e-07 1937 1842 43739118.52961 1938 1842 -20057887.18154 1939 1842 -9166666.669679 1940 1842 11581481.02689 1950 1842 -1129879.778007 1951 1842 2.369284629822e-06 1952 1842 57871.28717239 1953 1842 54280296.46473 1954 1842 3.09944152832e-06 1955 1842 231485.1485852 1956 1842 -7107625.989141 1957 1842 -6.146728992462e-06 1958 1842 57871.2871768 1971 1842 -18663081.30986 1972 1842 -9166666.669677 1973 1842 -10337268.9803 1974 1842 -59964405.70834 1975 1842 7.525086402893e-07 1976 1842 -43970603.67818 1977 1842 -20163436.42398 1978 1842 9166666.669676 1979 1842 -11639352.31406 1843 1843 531622789.3528 1844 1843 -11110935.09172 1845 1843 -4.798173904419e-06 1846 1843 -55180296.03374 1847 1843 5555467.545859 1860 1843 -36666666.66065 1861 1843 -41284001.36615 1862 1843 1263866.887163 1863 1843 -5.960464477539e-08 1864 1843 22901850.42796 1865 1843 -2777733.774299 1866 1843 36666666.66064 1867 1843 -41307675.60857 1868 1843 1513866.887135 1932 1843 9166666.669678 1933 1843 -15819170.72716 1934 1843 -8385422.169798 1935 1843 -5.811452865601e-07 1936 1843 -19232220.47929 1937 1843 -694433.4439163 1938 1843 -9166666.669679 1939 1843 -17307688.72007 1940 1843 9079855.613715 1950 1843 2.913177013397e-06 1951 1843 -35963145.36236 1952 1843 -33694466.44041 1953 1843 3.635883331299e-06 1954 1843 32278708.78388 1955 1843 -2777733.774297 1956 1843 -5.349516868591e-06 1957 1843 -41940891.5735 1958 1843 36472200.21471 1971 1843 -9166666.669677 1972 1843 -15912882.8484 1973 1843 -8454866.614265 1974 1843 3.725290298462e-07 1975 1843 -19630743.20649 1976 1843 -694433.4439167 1977 1843 9166666.669676 1978 1843 -17413237.96253 1979 1843 9149300.058182 1844 1844 599591912.5003 1845 1844 231485.1485663 1846 1844 5555467.545859 1847 1844 78550735.85485 1860 1844 2471062.980849 1861 1844 1236089.109403 1862 1844 -7832062.870945 1863 1844 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-4.798173904419e-06 1849 1846 -55180296.03374 1850 1846 5555467.545859 1863 1846 -36666666.66065 1864 1846 -41284001.36615 1865 1846 1263866.887163 1866 1846 -5.960464477539e-08 1867 1846 22901850.42796 1868 1846 -2777733.774299 1869 1846 36666666.66064 1870 1846 -41307675.60857 1871 1846 1513866.887135 1935 1846 9166666.669678 1936 1846 -15819170.72716 1937 1846 -8385422.169798 1938 1846 -5.811452865601e-07 1939 1846 -19232220.47929 1940 1846 -694433.4439163 1941 1846 -9166666.669679 1942 1846 -17307688.72007 1943 1846 9079855.613715 1953 1846 2.913177013397e-06 1954 1846 -35963145.36236 1955 1846 -33694466.44041 1956 1846 3.635883331299e-06 1957 1846 32278708.78388 1958 1846 -2777733.774297 1959 1846 -5.349516868591e-06 1960 1846 -41940891.5735 1961 1846 36472200.21471 1974 1846 -9166666.669677 1975 1846 -15912882.8484 1976 1846 -8454866.614265 1977 1846 3.725290298462e-07 1978 1846 -19630743.20649 1979 1846 -694433.4439167 1980 1846 9166666.669676 1981 1846 -17413237.96253 1982 1846 9149300.058182 1847 1847 599591912.5003 1848 1847 231485.1485663 1849 1847 5555467.545859 1850 1847 78550735.85485 1863 1847 2471062.980849 1864 1847 1236089.109403 1865 1847 -7832062.870945 1866 1847 -462970.2969232 1867 1847 -2777733.774298 1868 1847 39890623.87246 1869 1847 -2737270.351624 1870 1847 1541644.664895 1871 1847 -7895194.184061 1935 1847 10279397.69313 1936 1847 -8385422.169798 1937 1847 -16619803.40013 1938 1847 43704396.30741 1939 1847 -694433.4439163 1940 1847 -56581165.5979 1941 1847 11581481.02689 1942 1847 9079855.613715 1943 1847 -20589184.71456 1953 1847 57871.28717278 1954 1847 -33666688.66265 1955 1847 -39477172.9523 1956 1847 231485.148585 1957 1847 -2777733.774298 1958 1847 -118440658.1206 1959 1847 57871.28717716 1960 1847 36444422.43695 1961 1847 -55417829.51533 1974 1847 -10337268.9803 1975 1847 -8454866.614265 1976 1847 -16869702.39011 1977 1847 -43935881.45598 1978 1847 -694433.4439167 1979 1847 -57643892.87044 1980 1847 -11639352.31406 1981 1847 9149300.058182 1982 1847 -20870649.36111 1848 1848 619629140.0329 1849 1848 1.168251037598e-05 1850 1848 925940.5938052 1851 1848 84152766.23505 1852 1848 -4.991888999939e-06 1853 1848 231485.148566 1866 1848 -52284795.20658 1867 1848 -36666666.66065 1868 1848 2505785.203048 1869 1848 -138432799.5 1870 1848 1.490116119385e-07 1871 1848 -462970.296923 1872 1848 -52308469.44899 1873 1848 36666666.66065 1874 1848 -2702548.129425 1938 1848 -18569369.18862 1939 1848 9166666.669678 1940 1848 10279397.69313 1941 1848 -59565882.98117 1942 1848 4.91738319397e-07 1943 1848 43739118.52961 1944 1848 -20057887.18154 1945 1848 -9166666.669679 1946 1848 11581481.02689 1956 1848 -1129879.778007 1957 1848 2.369284629822e-06 1958 1848 57871.28717239 1959 1848 54280296.46473 1960 1848 3.09944152832e-06 1961 1848 231485.1485852 1962 1848 -7107625.989141 1963 1848 -6.146728992462e-06 1964 1848 57871.2871768 1977 1848 -18663081.30986 1978 1848 -9166666.669677 1979 1848 -10337268.9803 1980 1848 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1853 57871.28717278 1960 1853 -33666688.66265 1961 1853 -39477172.9523 1962 1853 231485.148585 1963 1853 -2777733.774298 1964 1853 -118440658.1206 1965 1853 57871.28717716 1966 1853 36444422.43695 1967 1853 -55417829.51533 1980 1853 -10337268.9803 1981 1853 -8454866.614265 1982 1853 -16869702.39011 1983 1853 -43935881.45598 1984 1853 -694433.4439167 1985 1853 -57643892.87044 1986 1853 -11639352.31406 1987 1853 9149300.058182 1988 1853 -20870649.36111 1854 1854 525679167.9811 1855 1854 18390868.10895 1856 1854 257230.0209704 1857 1854 -103629435.2263 1858 1854 -78331026.88709 1859 1854 634702.4175476 1872 1854 -52284795.20658 1873 1854 -36666666.66065 1874 1854 2505785.203048 1875 1854 -86773795.75742 1876 1854 24416035.48061 1877 1854 -106696.56214 1878 1854 -50334865.85163 1879 1854 7750891.435108 1880 1854 -153554.2915443 1944 1854 -18569369.18862 1945 1854 9166666.669678 1946 1854 10279397.69313 1947 1854 -27520936.3574 1948 1854 6808951.285619 1949 1854 24530109.1485 1962 1854 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299795956.2502 1863 1862 723381.4630278 1864 1862 2805511.550704 1865 1862 39276420.11598 1950 1862 43704396.30741 1951 1862 -694433.4439163 1952 1862 -56581165.5979 1953 1862 11581481.02689 1954 1862 9079855.613715 1955 1862 -20589184.71456 1971 1862 8796437.017353 1972 1862 -1388866.887151 1973 1862 -59221381.24884 1974 1862 2351018.977684 1975 1862 18229155.66292 1976 1862 -27708914.75766 1863 1863 309814570.0165 1864 1863 6.437301635742e-06 1865 1863 462970.2969034 1866 1863 42076777.68823 1867 1863 7333333.332127 1868 1863 -318285.203467 1950 1863 -18569369.18862 1951 1863 9166666.669678 1952 1863 10279397.69313 1953 1863 -59565882.98117 1954 1863 4.91738319397e-07 1955 1863 43739118.52961 1956 1863 -20057887.18154 1957 1863 -9166666.669679 1958 1863 11581481.02689 1971 1863 -564939.8890041 1972 1863 -1833333.333934 1973 1863 -2032731.023757 1974 1863 27139753.66166 1975 1863 8.344650268555e-07 1976 1863 -8738562.979764 1977 1863 -3553812.994569 1978 1863 1833333.333932 1979 1863 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1865 -19738586.47615 1974 1865 8796437.017353 1975 1865 -1388866.887151 1976 1865 -59221381.24884 1977 1865 2351018.977684 1978 1865 18229155.66292 1979 1865 -27708914.75766 1866 1866 309814570.0165 1867 1866 6.437301635742e-06 1868 1866 462970.2969034 1869 1866 42076777.68823 1870 1866 7333333.332127 1871 1866 -318285.203467 1953 1866 -18569369.18862 1954 1866 9166666.669678 1955 1866 10279397.69313 1956 1866 -59565882.98117 1957 1866 4.91738319397e-07 1958 1866 43739118.52961 1959 1866 -20057887.18154 1960 1866 -9166666.669679 1961 1866 11581481.02689 1974 1866 -564939.8890041 1975 1866 -1833333.333934 1976 1866 -2032731.023757 1977 1866 27139753.66166 1978 1866 8.344650268555e-07 1979 1866 -8738562.979764 1980 1866 -3553812.994569 1981 1866 1833333.333932 1982 1866 -2293147.690507 1867 1867 265811394.6764 1868 1867 -5555467.545855 1869 1867 -7333333.332131 1870 1867 -27589753.44616 1871 1867 2749955.995158 1953 1867 9166666.669678 1954 1867 -15819170.72716 1955 1867 -8385422.169798 1956 1867 -5.811452865601e-07 1957 1867 -19232220.47929 1958 1867 -694433.4439163 1959 1867 -9166666.669679 1960 1867 -17307688.72007 1961 1867 9079855.613715 1974 1867 1833333.333937 1975 1867 -17981572.68118 1976 1867 -16840288.77576 1977 1867 8.940696716309e-07 1978 1867 16138959.82123 1979 1867 -1388866.887151 1980 1867 -1833333.333938 1981 1867 -20970445.78675 1982 1867 18229155.66291 1868 1868 299795956.2502 1869 1868 723381.4630278 1870 1868 2805511.550704 1871 1868 39276420.11598 1953 1868 10279397.69313 1954 1868 -8385422.169798 1955 1868 -16619803.40013 1956 1868 43704396.30741 1957 1868 -694433.4439163 1958 1868 -56581165.5979 1959 1868 11581481.02689 1960 1868 9079855.613715 1961 1868 -20589184.71456 1974 1868 2090602.31093 1975 1868 -16840288.77577 1976 1868 -19738586.47615 1977 1868 8796437.017353 1978 1868 -1388866.887151 1979 1868 -59221381.24884 1980 1868 2351018.977684 1981 1868 18229155.66292 1982 1868 -27708914.75766 1869 1869 309814570.0165 1870 1869 6.437301635742e-06 1871 1869 462970.2969034 1872 1869 42076777.68823 1873 1869 7333333.332127 1874 1869 -318285.203467 1956 1869 -18569369.18862 1957 1869 9166666.669678 1958 1869 10279397.69313 1959 1869 -59565882.98117 1960 1869 4.91738319397e-07 1961 1869 43739118.52961 1962 1869 -20057887.18154 1963 1869 -9166666.669679 1964 1869 11581481.02689 1977 1869 -564939.8890041 1978 1869 -1833333.333934 1979 1869 -2032731.023757 1980 1869 27139753.66166 1981 1869 8.344650268555e-07 1982 1869 -8738562.979764 1983 1869 -3553812.994569 1984 1869 1833333.333932 1985 1869 -2293147.690507 1870 1870 265811394.6764 1871 1870 -5555467.545855 1872 1870 -7333333.332131 1873 1870 -27589753.44616 1874 1870 2749955.995158 1956 1870 9166666.669678 1957 1870 -15819170.72716 1958 1870 -8385422.169798 1959 1870 -5.811452865601e-07 1960 1870 -19232220.47929 1961 1870 -694433.4439163 1962 1870 -9166666.669679 1963 1870 -17307688.72007 1964 1870 9079855.613715 1977 1870 1833333.333937 1978 1870 -17981572.68118 1979 1870 -16840288.77576 1980 1870 8.940696716309e-07 1981 1870 16138959.82123 1982 1870 -1388866.887151 1983 1870 -1833333.333938 1984 1870 -20970445.78675 1985 1870 18229155.66291 1871 1871 299795956.2502 1872 1871 723381.4630278 1873 1871 2805511.550704 1874 1871 39276420.11598 1956 1871 10279397.69313 1957 1871 -8385422.169798 1958 1871 -16619803.40013 1959 1871 43704396.30741 1960 1871 -694433.4439163 1961 1871 -56581165.5979 1962 1871 11581481.02689 1963 1871 9079855.613715 1964 1871 -20589184.71456 1977 1871 2090602.31093 1978 1871 -16840288.77577 1979 1871 -19738586.47615 1980 1871 8796437.017353 1981 1871 -1388866.887151 1982 1871 -59221381.24884 1983 1871 2351018.977684 1984 1871 18229155.66292 1985 1871 -27708914.75766 1872 1872 309814570.0165 1873 1872 6.437301635742e-06 1874 1872 462970.2969034 1875 1872 42076777.68823 1876 1872 7333333.332127 1877 1872 -318285.203467 1959 1872 -18569369.18862 1960 1872 9166666.669678 1961 1872 10279397.69313 1962 1872 -59565882.98117 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723381.4630278 1876 1874 2805511.550704 1877 1874 39276420.11598 1959 1874 10279397.69313 1960 1874 -8385422.169798 1961 1874 -16619803.40013 1962 1874 43704396.30741 1963 1874 -694433.4439163 1964 1874 -56581165.5979 1965 1874 11581481.02689 1966 1874 9079855.613715 1967 1874 -20589184.71456 1980 1874 2090602.31093 1981 1874 -16840288.77577 1982 1874 -19738586.47615 1983 1874 8796437.017353 1984 1874 -1388866.887151 1985 1874 -59221381.24884 1986 1874 2351018.977684 1987 1874 18229155.66292 1988 1874 -27708914.75766 1875 1875 309250160.3896 1876 1875 4535517.963994 1877 1875 2453066.565954 1878 1875 -8612767.502989 1879 1875 -26152871.16708 1880 1875 379949.2240047 1962 1875 -18569369.18862 1963 1875 9166666.669678 1964 1875 10279397.69313 1965 1875 -43745996.76765 1966 1875 6104008.873162 1967 1875 33740166.13061 1968 1875 -19561074.78605 1969 1875 -8033003.905467 1970 1875 11036649.36321 1983 1875 -564939.8890041 1984 1875 -1833333.333934 1985 1875 -2032731.023757 1986 1875 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231485.105844 1927 1925 5388801.904579 1928 1925 80699306.16691 1935 1925 2523146.335561 1936 1925 1277756.032423 1937 1925 -7296493.499545 1938 1925 -254636.8781728 1939 1925 -2777734.286976 1940 1925 42039227.65673 1941 1925 -2685186.996909 1942 1925 1499978.254554 1943 1925 -7359624.812662 2019 1925 10539814.37052 2020 1925 -8593755.37553 2021 1925 -17106970.31658 2022 1925 44746063.01646 2023 1925 -694433.6992574 2024 1925 -58719220.64359 2025 1925 11841897.70428 2026 1925 9288189.074786 2027 1925 -21171048.60074 2031 1925 57871.26589252 2032 1925 -34500021.48517 2033 1925 -41438476.99211 2034 1925 231485.0634617 2035 1925 -2777734.795662 2036 1925 -127043423.7988 2037 1925 57871.26589543 2038 1925 37277756.28083 2039 1925 -57757921.43384 2046 1925 -10597685.63642 2047 1925 -8663199.819997 2048 1925 -17363182.43788 2049 1925 -44977548.07992 2050 1925 -694433.6992576 2051 1925 -59807200.44138 2052 1925 -11899768.97017 2053 1925 9357633.519253 2054 1925 -21458826.37861 1926 1926 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9357633.519253 1943 1943 608211498.9432 1944 1943 231485.105844 1945 1943 5388801.904579 1946 1943 80699306.16691 1956 1943 2523146.335561 1957 1943 1277756.032423 1958 1943 -7296493.499545 1959 1943 -254636.8781728 1960 1943 -2777734.286976 1961 1943 42039227.65673 1962 1943 -2685186.996909 1963 1943 1499978.254554 1964 1943 -7359624.812662 2034 1943 10539814.37052 2035 1943 -8593755.37553 2036 1943 -17106970.31658 2037 1943 44746063.01646 2038 1943 -694433.6992574 2039 1943 -58719220.64359 2040 1943 11841897.70428 2041 1943 9288189.074786 2042 1943 -21171048.60074 2049 1943 57871.26589252 2050 1943 -34500021.48517 2051 1943 -41438476.99211 2052 1943 231485.0634617 2053 1943 -2777734.795662 2054 1943 -127043423.7988 2055 1943 57871.26589543 2056 1943 37277756.28083 2057 1943 -57757921.43384 2067 1943 -10597685.63642 2068 1943 -8663199.819997 2069 1943 -17363182.43788 2070 1943 -44977548.07992 2071 1943 -694433.6992576 2072 1943 -59807200.44138 2073 1943 -11899768.97017 2074 1943 9357633.519253 2075 1943 -21458826.37861 1944 1944 674759689.9124 1945 1944 36667415.0414 1946 1944 3125092.975185 1947 1944 20137287.77529 1948 1944 -36666966.01295 1949 1944 2754655.071165 1959 1944 -52083950.29126 1960 1944 -36666666.66065 1961 1944 2453701.89106 1962 1944 -137627039.3558 1963 1944 -2.235174179077e-07 1964 1944 -671303.5447711 1965 1944 -52107624.53367 1966 1944 36666666.66065 1967 1944 -2754631.441411 2037 1944 -18752053.59425 2038 1944 9166666.66968 2039 1944 10539814.37052 2040 1944 -72726245.22972 2041 1944 -9166776.303506 2042 1944 44231216.90386 2052 1944 -1865379.213624 2053 1944 8.79168510437e-07 2054 1944 57871.26589221 2055 1944 70575234.21716 2056 1944 9166849.392726 2057 1944 781227.3439141 2058 1944 -20203256.3538 2059 1944 -9166739.758899 2060 1944 11899863.74724 2070 1944 -18848133.13973 2071 1944 -9166666.66968 2072 1944 -10597685.63642 2073 1944 -60775629.25067 2074 1944 -1.214444637299e-06 2075 1944 -45012270.30212 2076 1944 -20383999.6175 2077 1944 9166666.669679 2078 1944 -11899768.97017 1945 1945 575752291.8369 1946 1945 -8610912.053949 1947 1945 -36667115.6891 1948 1945 -108195591.755 1949 1945 4777685.365654 1959 1945 -36666666.66065 1960 1945 -41083165.69975 1961 1945 1222200.476822 1962 1945 4.470348358154e-07 1963 1945 23707595.23204 1964 1945 -2777734.286976 1965 1945 36666666.66065 1966 1945 -41106839.94217 1967 1945 1555533.810155 2037 1945 9166666.66968 2038 1945 -16001859.73922 2039 1945 -8593755.37553 2040 1945 -9166739.758897 2041 1945 -29642168.10562 2042 1945 8204934.122165 2052 1945 1.229345798492e-06 2053 1945 -36698646.37071 2054 1945 -34527799.26293 2055 1945 9166849.392726 2056 1945 45823407.30156 2057 1945 -2152765.098743 2058 1945 -9166776.303508 2059 1945 -52286475.83204 2060 1945 37069600.58987 2070 1945 -9166666.669679 2071 1945 -16097939.2847 2072 1945 -8663199.819997 2073 1945 -1.445412635803e-06 2074 1945 -20441974.38895 2075 1945 -694433.6992576 2076 1945 9166666.669678 2077 1945 -17633805.76247 2078 1945 9357633.519253 1946 1946 615008779.2968 1947 1946 2685222.441543 1948 1946 5222139.640517 1949 1946 39437488.39575 1959 1946 2523146.335561 1960 1946 1277756.032423 1961 1946 -7296493.499545 1962 1946 -254636.8781728 1963 1946 -2777734.286976 1964 1946 42039227.65673 1965 1946 -2685186.996909 1966 1946 1499978.254554 1967 1946 -7359624.812662 2037 1946 10539814.37052 2038 1946 -8593755.37553 2039 1946 -17106970.31658 2040 1946 44196492.14387 2041 1946 8010523.495484 2042 1946 -58776166.2905 2052 1946 57871.26589252 2053 1946 -34500021.48517 2054 1946 -41438476.99211 2055 1946 781316.8545274 2056 1946 -2152693.49136 2057 1946 -107886912.3736 2058 1946 11899911.13577 2059 1946 37236269.31883 2060 1946 -57440830.58835 2070 1946 -10597685.63642 2071 1946 -8663199.819997 2072 1946 -17363182.43788 2073 1946 -44977548.07992 2074 1946 -694433.6992576 2075 1946 -59807200.44138 2076 1946 -11899768.97017 2077 1946 9357633.519253 2078 1946 -21458826.37861 1947 1947 434012491.322 1948 1947 -26709105.05296 1949 1947 -725793.543576 1962 1947 -52083950.29126 1963 1947 -36666666.66065 1964 1947 2453701.89106 1965 1947 -56549866.20531 1966 1947 26704759.61057 1967 1947 -385264.5612573 1968 1947 -222386913.2778 1969 1947 29337678.77091 1970 1947 -277833.5794091 2040 1947 -5106206.927443 2041 1947 11000109.63744 2042 1947 12682625.90274 2055 1947 -15511422.68773 2056 1947 -9166776.303506 2057 1947 -10539940.2691 2058 1947 57002220.2306 2059 1947 -6544915.940513 2060 1947 4861555.215121 2073 1947 -18848133.13973 2074 1947 -9166666.66968 2075 1947 -10597685.63642 2076 1947 -29177118.41547 2077 1947 6543892.420132 2078 1947 -25729678.71087 2079 1947 -53961140.25394 2080 1947 7334356.856125 2081 1947 -1354081.113647 1948 1948 781040484.4929 1949 1948 -10574395.88396 1962 1948 -36666666.66065 1963 1948 -41083165.69975 1964 1948 1222200.476822 1965 1948 26702586.88937 1966 1948 87287357.54424 1967 1948 -1789762.243781 1968 1948 44006518.15637 1969 1948 -595920035.2594 1970 1948 5142261.375664 2040 1948 7333406.424962 2041 1948 -5106206.927443 2042 1948 -6763956.526763 2055 1948 -9166739.758897 2056 1948 -47594642.16596 2057 1948 -34569643.89832 2058 1948 -6544915.940513 2059 1948 138242633.1703 2060 1948 1389850.346674 2073 1948 -9166666.669679 2074 1948 -16097939.2847 2075 1948 -8663199.819997 2076 1948 6543380.659941 2077 1948 6841374.023334 2078 1948 5925066.094897 2079 1948 11001535.28419 2080 1948 -141887020.0092 2081 1948 18142632.26191 1949 1949 467013145.2305 1962 1949 2523146.335561 1963 1949 1277756.032423 1964 1949 -7296493.499545 1965 1949 -940793.6136686 1966 1949 -1678594.911864 1967 1949 48688638.16036 1968 1949 -416750.3691136 1969 1949 5031214.44564 1970 1949 -219498646.7591 2040 1949 8455083.935158 2041 1949 -10145934.79014 2042 1949 -13616551.80652 2055 1949 -10539898.30291 2056 1949 -34736312.74845 2057 1949 -44929274.14549 2058 1949 -5398901.65238 2059 1949 -6817695.611917 2060 1949 -15837053.95701 2073 1949 -10597685.63642 2074 1949 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534855157.0519 1952 1951 -11110937.14243 1953 1951 -3.457069396973e-06 1954 1951 -54374606.24745 1955 1951 5722135.237857 1971 1951 4.470348358154e-07 1972 1951 23707595.23204 1973 1951 -2777734.286976 1974 1951 36666666.66065 1975 1951 -41106839.94217 1976 1951 1555533.810155 2043 1951 1.169741153717e-06 2044 1951 -20033981.96478 2045 1951 -694433.6992575 2046 1951 -9166666.66968 2047 1951 -17525889.09577 2048 1951 9288189.074786 2061 1951 1.966953277588e-06 2062 1951 29052683.00161 2063 1951 -2777734.795662 2064 1951 -2.190470695496e-06 2065 1951 -42818438.03636 2066 1951 37305534.05859 2082 1951 -1.445412635803e-06 2083 1951 -20441974.38895 2084 1951 -694433.6992576 2085 1951 9166666.669678 2086 1951 -17633805.76247 2087 1951 9357633.519253 1952 1952 608211498.9432 1953 1952 231485.105844 1954 1952 5388801.904579 1955 1952 80699306.16691 1971 1952 -254636.8781728 1972 1952 -2777734.286976 1973 1952 42039227.65673 1974 1952 -2685186.996909 1975 1952 1499978.254554 1976 1952 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2048 1953 44780785.23866 2049 1953 -20276082.95081 2050 1953 -9166666.66968 2051 1953 11841897.70428 2061 1953 -1865379.213624 2062 1953 8.79168510437e-07 2063 1953 57871.26589221 2064 1953 51054233.83102 2065 1953 1.788139343262e-06 2066 1953 231485.0634618 2067 1953 -7985170.87927 2068 1953 -2.771615982056e-06 2069 1953 57871.2658952 2082 1953 -18848133.13973 2083 1953 -9166666.66968 2084 1953 -10597685.63642 2085 1953 -60775629.25067 2086 1953 -1.214444637299e-06 2087 1953 -45012270.30212 2088 1953 -20383999.6175 2089 1953 9166666.669679 2090 1953 -11899768.97017 1954 1954 534855157.0519 1955 1954 -11110937.14243 1956 1954 -3.457069396973e-06 1957 1954 -54374606.24745 1958 1954 5722135.237857 1971 1954 -36666666.66065 1972 1954 -41083165.69975 1973 1954 1222200.476822 1974 1954 4.470348358154e-07 1975 1954 23707595.23204 1976 1954 -2777734.286976 1977 1954 36666666.66065 1978 1954 -41106839.94217 1979 1954 1555533.810155 2043 1954 9166666.66968 2044 1954 -16001859.73922 2045 1954 -8593755.37553 2046 1954 1.169741153717e-06 2047 1954 -20033981.96478 2048 1954 -694433.6992575 2049 1954 -9166666.66968 2050 1954 -17525889.09577 2051 1954 9288189.074786 2061 1954 1.229345798492e-06 2062 1954 -36698646.37071 2063 1954 -34527799.26293 2064 1954 1.966953277588e-06 2065 1954 29052683.00161 2066 1954 -2777734.795662 2067 1954 -2.190470695496e-06 2068 1954 -42818438.03636 2069 1954 37305534.05859 2082 1954 -9166666.669679 2083 1954 -16097939.2847 2084 1954 -8663199.819997 2085 1954 -1.445412635803e-06 2086 1954 -20441974.38895 2087 1954 -694433.6992576 2088 1954 9166666.669678 2089 1954 -17633805.76247 2090 1954 9357633.519253 1955 1955 608211498.9432 1956 1955 231485.105844 1957 1955 5388801.904579 1958 1955 80699306.16691 1971 1955 2523146.335561 1972 1955 1277756.032423 1973 1955 -7296493.499545 1974 1955 -254636.8781728 1975 1955 -2777734.286976 1976 1955 42039227.65673 1977 1955 -2685186.996909 1978 1955 1499978.254554 1979 1955 -7359624.812662 2043 1955 10539814.37052 2044 1955 -8593755.37553 2045 1955 -17106970.31658 2046 1955 44746063.01646 2047 1955 -694433.6992574 2048 1955 -58719220.64359 2049 1955 11841897.70428 2050 1955 9288189.074786 2051 1955 -21171048.60074 2061 1955 57871.26589252 2062 1955 -34500021.48517 2063 1955 -41438476.99211 2064 1955 231485.0634617 2065 1955 -2777734.795662 2066 1955 -127043423.7988 2067 1955 57871.26589543 2068 1955 37277756.28083 2069 1955 -57757921.43384 2082 1955 -10597685.63642 2083 1955 -8663199.819997 2084 1955 -17363182.43788 2085 1955 -44977548.07992 2086 1955 -694433.6992576 2087 1955 -59807200.44138 2088 1955 -11899768.97017 2089 1955 9357633.519253 2090 1955 -21458826.37861 1956 1956 622861433.7406 1957 1956 1.120567321777e-05 1958 1956 925940.4229136 1959 1956 84958459.17911 1960 1956 -5.066394805908e-06 1961 1956 231485.1058435 1974 1956 -52083950.29126 1975 1956 -36666666.66065 1976 1956 2453701.89106 1977 1956 -137627039.3558 1978 1956 -2.235174179077e-07 1979 1956 -671303.5447711 1980 1956 -52107624.53367 1981 1956 36666666.66065 1982 1956 -2754631.441411 2046 1956 -18752053.59425 2047 1956 9166666.66968 2048 1956 10539814.37052 2049 1956 -60367636.82651 2050 1956 1.877546310425e-06 2051 1956 44780785.23866 2052 1956 -20276082.95081 2053 1956 -9166666.66968 2054 1956 11841897.70428 2064 1956 -1865379.213624 2065 1956 8.79168510437e-07 2066 1956 57871.26589221 2067 1956 51054233.83102 2068 1956 1.788139343262e-06 2069 1956 231485.0634618 2070 1956 -7985170.87927 2071 1956 -2.771615982056e-06 2072 1956 57871.2658952 2085 1956 -18848133.13973 2086 1956 -9166666.66968 2087 1956 -10597685.63642 2088 1956 -60775629.25067 2089 1956 -1.214444637299e-06 2090 1956 -45012270.30212 2091 1956 -20383999.6175 2092 1956 9166666.669679 2093 1956 -11899768.97017 1957 1957 534855157.0519 1958 1957 -11110937.14243 1959 1957 -3.457069396973e-06 1960 1957 -54374606.24745 1961 1957 5722135.237857 1974 1957 -36666666.66065 1975 1957 -41083165.69975 1976 1957 1222200.476822 1977 1957 4.470348358154e-07 1978 1957 23707595.23204 1979 1957 -2777734.286976 1980 1957 36666666.66065 1981 1957 -41106839.94217 1982 1957 1555533.810155 2046 1957 9166666.66968 2047 1957 -16001859.73922 2048 1957 -8593755.37553 2049 1957 1.169741153717e-06 2050 1957 -20033981.96478 2051 1957 -694433.6992575 2052 1957 -9166666.66968 2053 1957 -17525889.09577 2054 1957 9288189.074786 2064 1957 1.229345798492e-06 2065 1957 -36698646.37071 2066 1957 -34527799.26293 2067 1957 1.966953277588e-06 2068 1957 29052683.00161 2069 1957 -2777734.795662 2070 1957 -2.190470695496e-06 2071 1957 -42818438.03636 2072 1957 37305534.05859 2085 1957 -9166666.669679 2086 1957 -16097939.2847 2087 1957 -8663199.819997 2088 1957 -1.445412635803e-06 2089 1957 -20441974.38895 2090 1957 -694433.6992576 2091 1957 9166666.669678 2092 1957 -17633805.76247 2093 1957 9357633.519253 1958 1958 608211498.9432 1959 1958 231485.105844 1960 1958 5388801.904579 1961 1958 80699306.16691 1974 1958 2523146.335561 1975 1958 1277756.032423 1976 1958 -7296493.499545 1977 1958 -254636.8781728 1978 1958 -2777734.286976 1979 1958 42039227.65673 1980 1958 -2685186.996909 1981 1958 1499978.254554 1982 1958 -7359624.812662 2046 1958 10539814.37052 2047 1958 -8593755.37553 2048 1958 -17106970.31658 2049 1958 44746063.01646 2050 1958 -694433.6992574 2051 1958 -58719220.64359 2052 1958 11841897.70428 2053 1958 9288189.074786 2054 1958 -21171048.60074 2064 1958 57871.26589252 2065 1958 -34500021.48517 2066 1958 -41438476.99211 2067 1958 231485.0634617 2068 1958 -2777734.795662 2069 1958 -127043423.7988 2070 1958 57871.26589543 2071 1958 37277756.28083 2072 1958 -57757921.43384 2085 1958 -10597685.63642 2086 1958 -8663199.819997 2087 1958 -17363182.43788 2088 1958 -44977548.07992 2089 1958 -694433.6992576 2090 1958 -59807200.44138 2091 1958 -11899768.97017 2092 1958 9357633.519253 2093 1958 -21458826.37861 1959 1959 622861433.7406 1960 1959 1.120567321777e-05 1961 1959 925940.4229136 1962 1959 84958459.17911 1963 1959 -5.066394805908e-06 1964 1959 231485.1058435 1977 1959 -52083950.29126 1978 1959 -36666666.66065 1979 1959 2453701.89106 1980 1959 -137627039.3558 1981 1959 -2.235174179077e-07 1982 1959 -671303.5447711 1983 1959 -52107624.53367 1984 1959 36666666.66065 1985 1959 -2754631.441411 2049 1959 -18752053.59425 2050 1959 9166666.66968 2051 1959 10539814.37052 2052 1959 -60367636.82651 2053 1959 1.877546310425e-06 2054 1959 44780785.23866 2055 1959 -20276082.95081 2056 1959 -9166666.66968 2057 1959 11841897.70428 2067 1959 -1865379.213624 2068 1959 8.79168510437e-07 2069 1959 57871.26589221 2070 1959 51054233.83102 2071 1959 1.788139343262e-06 2072 1959 231485.0634618 2073 1959 -7985170.87927 2074 1959 -2.771615982056e-06 2075 1959 57871.2658952 2088 1959 -18848133.13973 2089 1959 -9166666.66968 2090 1959 -10597685.63642 2091 1959 -60775629.25067 2092 1959 -1.214444637299e-06 2093 1959 -45012270.30212 2094 1959 -20383999.6175 2095 1959 9166666.669679 2096 1959 -11899768.97017 1960 1960 534855157.0519 1961 1960 -11110937.14243 1962 1960 -3.457069396973e-06 1963 1960 -54374606.24745 1964 1960 5722135.237857 1977 1960 -36666666.66065 1978 1960 -41083165.69975 1979 1960 1222200.476822 1980 1960 4.470348358154e-07 1981 1960 23707595.23204 1982 1960 -2777734.286976 1983 1960 36666666.66065 1984 1960 -41106839.94217 1985 1960 1555533.810155 2049 1960 9166666.66968 2050 1960 -16001859.73922 2051 1960 -8593755.37553 2052 1960 1.169741153717e-06 2053 1960 -20033981.96478 2054 1960 -694433.6992575 2055 1960 -9166666.66968 2056 1960 -17525889.09577 2057 1960 9288189.074786 2067 1960 1.229345798492e-06 2068 1960 -36698646.37071 2069 1960 -34527799.26293 2070 1960 1.966953277588e-06 2071 1960 29052683.00161 2072 1960 -2777734.795662 2073 1960 -2.190470695496e-06 2074 1960 -42818438.03636 2075 1960 37305534.05859 2088 1960 -9166666.669679 2089 1960 -16097939.2847 2090 1960 -8663199.819997 2091 1960 -1.445412635803e-06 2092 1960 -20441974.38895 2093 1960 -694433.6992576 2094 1960 9166666.669678 2095 1960 -17633805.76247 2096 1960 9357633.519253 1961 1961 608211498.9432 1962 1961 231485.105844 1963 1961 5388801.904579 1964 1961 80699306.16691 1977 1961 2523146.335561 1978 1961 1277756.032423 1979 1961 -7296493.499545 1980 1961 -254636.8781728 1981 1961 -2777734.286976 1982 1961 42039227.65673 1983 1961 -2685186.996909 1984 1961 1499978.254554 1985 1961 -7359624.812662 2049 1961 10539814.37052 2050 1961 -8593755.37553 2051 1961 -17106970.31658 2052 1961 44746063.01646 2053 1961 -694433.6992574 2054 1961 -58719220.64359 2055 1961 11841897.70428 2056 1961 9288189.074786 2057 1961 -21171048.60074 2067 1961 57871.26589252 2068 1961 -34500021.48517 2069 1961 -41438476.99211 2070 1961 231485.0634617 2071 1961 -2777734.795662 2072 1961 -127043423.7988 2073 1961 57871.26589543 2074 1961 37277756.28083 2075 1961 -57757921.43384 2088 1961 -10597685.63642 2089 1961 -8663199.819997 2090 1961 -17363182.43788 2091 1961 -44977548.07992 2092 1961 -694433.6992576 2093 1961 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42478440.44814 1975 1971 7333333.332128 1976 1971 -578701.8915792 2061 1971 -60367636.82651 2062 1971 1.877546310425e-06 2063 1971 44780785.23866 2064 1971 -20276082.95081 2065 1971 -9166666.66968 2066 1971 11841897.70428 2082 1971 25526722.3448 2083 1971 -5.960464477539e-08 2084 1971 -8946896.355626 2085 1971 -3992585.439634 2086 1971 1833333.333934 2087 1971 -2345231.034498 1972 1972 267422843.6775 1973 1972 -5555468.571212 1974 1972 -7333333.332131 1975 1972 -27188092.26514 1976 1972 2833289.841157 2061 1972 1.169741153717e-06 2062 1972 -20033981.96478 2063 1972 -694433.6992575 2064 1972 -9166666.66968 2065 1972 -17525889.09577 2066 1972 9288189.074786 2082 1972 6.556510925293e-07 2083 1972 14525946.9301 2084 1972 -1388867.397833 2085 1972 -1833333.333937 2086 1972 -21409219.01818 2087 1972 18645822.58485 1973 1973 304093123.209 1974 1973 462964.7749153 1975 1973 2722178.730064 1976 1973 40347548.70635 2061 1973 44746063.01646 2062 1973 -694433.6992574 2063 1973 -58719220.64359 2064 1973 11841897.70428 2065 1973 9288189.074786 2066 1973 -21171048.60074 2082 1973 9004770.308089 2083 1973 -1388867.397833 2084 1973 -63522764.08798 2085 1973 2403102.300394 2086 1973 18645822.58486 2087 1973 -28878960.71692 1974 1974 311425982.0218 1975 1974 4.053115844727e-06 1976 1974 -578696.4550389 1977 1974 42478440.44814 1978 1974 7333333.332128 1979 1974 -578701.8915792 2061 1974 -18752053.59425 2062 1974 9166666.66968 2063 1974 10539814.37052 2064 1974 -60367636.82651 2065 1974 1.877546310425e-06 2066 1974 44780785.23866 2067 1974 -20276082.95081 2068 1974 -9166666.66968 2069 1974 11841897.70428 2082 1974 -932689.6068121 2083 1974 -1833333.333935 2084 1974 -2084814.367748 2085 1974 25526722.3448 2086 1974 -5.960464477539e-08 2087 1974 -8946896.355626 2088 1974 -3992585.439634 2089 1974 1833333.333934 2090 1974 -2345231.034498 1975 1975 267422843.6775 1976 1975 -5555468.571212 1977 1975 -7333333.332131 1978 1975 -27188092.26514 1979 1975 2833289.841157 2061 1975 9166666.66968 2062 1975 -16001859.73922 2063 1975 -8593755.37553 2064 1975 1.169741153717e-06 2065 1975 -20033981.96478 2066 1975 -694433.6992575 2067 1975 -9166666.66968 2068 1975 -17525889.09577 2069 1975 9288189.074786 2082 1975 1833333.333937 2083 1975 -18349323.18536 2084 1975 -17256955.18702 2085 1975 6.556510925293e-07 2086 1975 14525946.9301 2087 1975 -1388867.397833 2088 1975 -1833333.333937 2089 1975 -21409219.01818 2090 1975 18645822.58485 1976 1976 304093123.209 1977 1976 462964.7749153 1978 1976 2722178.730064 1979 1976 40347548.70635 2061 1976 10539814.37052 2062 1976 -8593755.37553 2063 1976 -17106970.31658 2064 1976 44746063.01646 2065 1976 -694433.6992574 2066 1976 -58719220.64359 2067 1976 11841897.70428 2068 1976 9288189.074786 2069 1976 -21171048.60074 2082 1976 2142685.63364 2083 1976 -17256955.18703 2084 1976 -20719238.49606 2085 1976 9004770.308089 2086 1976 -1388867.397833 2087 1976 -63522764.08798 2088 1976 2403102.300394 2089 1976 18645822.58486 2090 1976 -28878960.71692 1977 1977 311425982.0218 1978 1977 4.053115844727e-06 1979 1977 -578696.4550389 1980 1977 42478440.44814 1981 1977 7333333.332128 1982 1977 -578701.8915792 2064 1977 -18752053.59425 2065 1977 9166666.66968 2066 1977 10539814.37052 2067 1977 -60367636.82651 2068 1977 1.877546310425e-06 2069 1977 44780785.23866 2070 1977 -20276082.95081 2071 1977 -9166666.66968 2072 1977 11841897.70428 2085 1977 -932689.6068121 2086 1977 -1833333.333935 2087 1977 -2084814.367748 2088 1977 25526722.3448 2089 1977 -5.960464477539e-08 2090 1977 -8946896.355626 2091 1977 -3992585.439634 2092 1977 1833333.333934 2093 1977 -2345231.034498 1978 1978 267422843.6775 1979 1978 -5555468.571212 1980 1978 -7333333.332131 1981 1978 -27188092.26514 1982 1978 2833289.841157 2064 1978 9166666.66968 2065 1978 -16001859.73922 2066 1978 -8593755.37553 2067 1978 1.169741153717e-06 2068 1978 -20033981.96478 2069 1978 -694433.6992575 2070 1978 -9166666.66968 2071 1978 -17525889.09577 2072 1978 9288189.074786 2085 1978 1833333.333937 2086 1978 -18349323.18536 2087 1978 -17256955.18702 2088 1978 6.556510925293e-07 2089 1978 14525946.9301 2090 1978 -1388867.397833 2091 1978 -1833333.333937 2092 1978 -21409219.01818 2093 1978 18645822.58485 1979 1979 304093123.209 1980 1979 462964.7749153 1981 1979 2722178.730064 1982 1979 40347548.70635 2064 1979 10539814.37052 2065 1979 -8593755.37553 2066 1979 -17106970.31658 2067 1979 44746063.01646 2068 1979 -694433.6992574 2069 1979 -58719220.64359 2070 1979 11841897.70428 2071 1979 9288189.074786 2072 1979 -21171048.60074 2085 1979 2142685.63364 2086 1979 -17256955.18703 2087 1979 -20719238.49606 2088 1979 9004770.308089 2089 1979 -1388867.397833 2090 1979 -63522764.08798 2091 1979 2403102.300394 2092 1979 18645822.58486 2093 1979 -28878960.71692 1980 1980 311425982.0218 1981 1980 4.053115844727e-06 1982 1980 -578696.4550389 1983 1980 42478440.44814 1984 1980 7333333.332128 1985 1980 -578701.8915792 2067 1980 -18752053.59425 2068 1980 9166666.66968 2069 1980 10539814.37052 2070 1980 -60367636.82651 2071 1980 1.877546310425e-06 2072 1980 44780785.23866 2073 1980 -20276082.95081 2074 1980 -9166666.66968 2075 1980 11841897.70428 2088 1980 -932689.6068121 2089 1980 -1833333.333935 2090 1980 -2084814.367748 2091 1980 25526722.3448 2092 1980 -5.960464477539e-08 2093 1980 -8946896.355626 2094 1980 -3992585.439634 2095 1980 1833333.333934 2096 1980 -2345231.034498 1981 1981 267422843.6775 1982 1981 -5555468.571212 1983 1981 -7333333.332131 1984 1981 -27188092.26514 1985 1981 2833289.841157 2067 1981 9166666.66968 2068 1981 -16001859.73922 2069 1981 -8593755.37553 2070 1981 1.169741153717e-06 2071 1981 -20033981.96478 2072 1981 -694433.6992575 2073 1981 -9166666.66968 2074 1981 -17525889.09577 2075 1981 9288189.074786 2088 1981 1833333.333937 2089 1981 -18349323.18536 2090 1981 -17256955.18702 2091 1981 6.556510925293e-07 2092 1981 14525946.9301 2093 1981 -1388867.397833 2094 1981 -1833333.333937 2095 1981 -21409219.01818 2096 1981 18645822.58485 1982 1982 304093123.209 1983 1982 462964.7749153 1984 1982 2722178.730064 1985 1982 40347548.70635 2067 1982 10539814.37052 2068 1982 -8593755.37553 2069 1982 -17106970.31658 2070 1982 44746063.01646 2071 1982 -694433.6992574 2072 1982 -58719220.64359 2073 1982 11841897.70428 2074 1982 9288189.074786 2075 1982 -21171048.60074 2088 1982 2142685.63364 2089 1982 -17256955.18703 2090 1982 -20719238.49606 2091 1982 9004770.308089 2092 1982 -1388867.397833 2093 1982 -63522764.08798 2094 1982 2403102.300394 2095 1982 18645822.58486 2096 1982 -28878960.71692 1983 1983 311425982.0218 1984 1983 4.053115844727e-06 1985 1983 -578696.4550389 1986 1983 42478440.44814 1987 1983 7333333.332128 1988 1983 -578701.8915792 2070 1983 -18752053.59425 2071 1983 9166666.66968 2072 1983 10539814.37052 2073 1983 -60367636.82651 2074 1983 1.877546310425e-06 2075 1983 44780785.23866 2076 1983 -20276082.95081 2077 1983 -9166666.66968 2078 1983 11841897.70428 2091 1983 -932689.6068121 2092 1983 -1833333.333935 2093 1983 -2084814.367748 2094 1983 25526722.3448 2095 1983 -5.960464477539e-08 2096 1983 -8946896.355626 2097 1983 -3992585.439634 2098 1983 1833333.333934 2099 1983 -2345231.034498 1984 1984 267422843.6775 1985 1984 -5555468.571212 1986 1984 -7333333.332131 1987 1984 -27188092.26514 1988 1984 2833289.841157 2070 1984 9166666.66968 2071 1984 -16001859.73922 2072 1984 -8593755.37553 2073 1984 1.169741153717e-06 2074 1984 -20033981.96478 2075 1984 -694433.6992575 2076 1984 -9166666.66968 2077 1984 -17525889.09577 2078 1984 9288189.074786 2091 1984 1833333.333937 2092 1984 -18349323.18536 2093 1984 -17256955.18702 2094 1984 6.556510925293e-07 2095 1984 14525946.9301 2096 1984 -1388867.397833 2097 1984 -1833333.333937 2098 1984 -21409219.01818 2099 1984 18645822.58485 1985 1985 304093123.209 1986 1985 462964.7749153 1987 1985 2722178.730064 1988 1985 40347548.70635 2070 1985 10539814.37052 2071 1985 -8593755.37553 2072 1985 -17106970.31658 2073 1985 44746063.01646 2074 1985 -694433.6992574 2075 1985 -58719220.64359 2076 1985 11841897.70428 2077 1985 9288189.074786 2078 1985 -21171048.60074 2091 1985 2142685.63364 2092 1985 -17256955.18703 2093 1985 -20719238.49606 2094 1985 9004770.308089 2095 1985 -1388867.397833 2096 1985 -63522764.08798 2097 1985 2403102.300394 2098 1985 18645822.58486 2099 1985 -28878960.71692 1986 1986 310336649.2785 1987 1986 4244617.814256 1988 1986 1415596.36294 1989 1986 -6796753.083789 1990 1986 -25401731.70095 1991 1986 61254.30470198 2073 1986 -18752053.59425 2074 1986 9166666.66968 2075 1986 10539814.37052 2076 1986 -44778234.89159 2077 1986 6015914.059352 2078 1986 35041206.59625 2079 1986 -20008769.25006 2080 1986 -8176439.889681 2081 1986 11299136.49846 2094 1986 -932689.6068121 2095 1986 -1833333.333935 2096 1986 -2084814.367748 2097 1986 25141334.84086 2098 1986 990425.5084367 2099 1986 -8447023.847856 2100 1986 -17627581.50065 2101 1986 -6163233.013846 2102 1986 7435569.639298 1987 1987 292196010.7903 1988 1987 -3573485.612244 1989 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1092 1132 -1 -1 1131 1132 -1 -1 1132 1132 4 4 1133 1132 -1 -1 1172 1132 -1 -1 1093 1133 -1 -1 1132 1133 -1 -1 1133 1133 4 4 1134 1133 -1 -1 1173 1133 -1 -1 1094 1134 -1 -1 1133 1134 -1 -1 1134 1134 4 4 1135 1134 -1 -1 1174 1134 -1 -1 1095 1135 -1 -1 1134 1135 -1 -1 1135 1135 4 4 1136 1135 -1 -1 1175 1135 -1 -1 1096 1136 -1 -1 1135 1136 -1 -1 1136 1136 4 4 1137 1136 -1 -1 1176 1136 -1 -1 1097 1137 -1 -1 1136 1137 -1 -1 1137 1137 4 4 1138 1137 -1 -1 1177 1137 -1 -1 1098 1138 -1 -1 1137 1138 -1 -1 1138 1138 4 4 1139 1138 -1 -1 1178 1138 -1 -1 1099 1139 -1 -1 1138 1139 -1 -1 1139 1139 4 4 1140 1139 -1 -1 1179 1139 -1 -1 1100 1140 -1 -1 1139 1140 -1 -1 1140 1140 4 4 1141 1140 -1 -1 1180 1140 -1 -1 1101 1141 -1 -1 1140 1141 -1 -1 1141 1141 4 4 1142 1141 -1 -1 1181 1141 -1 -1 1102 1142 -1 -1 1141 1142 -1 -1 1142 1142 4 4 1143 1142 -1 -1 1182 1142 -1 -1 1103 1143 -1 -1 1142 1143 -1 -1 1143 1143 4 4 1144 1143 -1 -1 1183 1143 -1 -1 1104 1144 -1 -1 1143 1144 -1 -1 1144 1144 4 4 1145 1144 -1 -1 1184 1144 -1 -1 1105 1145 -1 -1 1144 1145 -1 -1 1145 1145 4 4 1146 1145 -1 -1 1185 1145 -1 -1 1106 1146 -1 -1 1145 1146 -1 -1 1146 1146 4 4 1147 1146 -1 -1 1186 1146 -1 -1 1107 1147 -1 -1 1146 1147 -1 -1 1147 1147 4 4 1148 1147 -1 -1 1187 1147 -1 -1 1108 1148 -1 -1 1147 1148 -1 -1 1148 1148 4 4 1149 1148 -1 -1 1188 1148 -1 -1 1109 1149 -1 -1 1148 1149 -1 -1 1149 1149 4 4 1150 1149 -1 -1 1189 1149 -1 -1 1110 1150 -1 -1 1149 1150 -1 -1 1150 1150 4 4 1151 1150 -1 -1 1190 1150 -1 -1 1111 1151 -1 -1 1150 1151 -1 -1 1151 1151 4 4 1152 1151 -1 -1 1191 1151 -1 -1 1112 1152 -1 -1 1151 1152 -1 -1 1152 1152 4 4 1153 1152 -1 -1 1192 1152 -1 -1 1113 1153 -1 -1 1152 1153 -1 -1 1153 1153 4 4 1154 1153 -1 -1 1193 1153 -1 -1 1114 1154 -1 -1 1153 1154 -1 -1 1154 1154 4 4 1155 1154 -1 -1 1194 1154 -1 -1 1115 1155 -1 -1 1154 1155 -1 -1 1155 1155 4 4 1156 1155 -1 -1 1195 1155 -1 -1 1116 1156 -1 -1 1155 1156 -1 -1 1156 1156 4 4 1157 1156 -1 -1 1196 1156 -1 -1 1117 1157 -1 -1 1156 1157 -1 -1 1157 1157 4 4 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_CXS_H #define _CXS_H #include #include #include #include #ifdef MATLAB_MEX_FILE #include "mex.h" #endif #ifdef __cplusplus #ifndef NCOMPLEX #include typedef std::complex cs_complex_t ; #endif extern "C" { #else #ifndef NCOMPLEX #include #define cs_complex_t double _Complex #endif #endif #define CS_VER 2 /* CXSparse Version 2.2.1 */ #define CS_SUBVER 2 #define CS_SUBSUB 1 #define CS_DATE "Nov 1, 2007" /* CXSparse release date */ #define CS_COPYRIGHT "Copyright (c) Timothy A. Davis, 2006-2007" #define CXSPARSE /* define UF_long */ #include "UFconfig.h" /* -------------------------------------------------------------------------- */ /* double/int version of CXSparse */ /* -------------------------------------------------------------------------- */ /* --- primary CSparse routines and data structures ------------------------- */ typedef struct cs_di_sparse /* matrix in compressed-column or triplet form */ { int nzmax ; /* maximum number of entries */ int m ; /* number of rows */ int n ; /* number of columns */ int *p ; /* column pointers (size n+1) or col indices (size nzmax) */ int *i ; /* row indices, size nzmax */ double *x ; /* numerical values, size nzmax */ int nz ; /* # of entries in triplet matrix, -1 for compressed-col */ } cs_di ; cs_di *cs_di_add (const cs_di *A, const cs_di *B, double alpha, double beta) ; int cs_di_cholsol (int order, const cs_di *A, double *b) ; int cs_di_dupl (cs_di *A) ; int cs_di_entry (cs_di *T, int i, int j, double x) ; int cs_di_lusol (int order, const cs_di *A, double *b, double tol) ; int cs_di_gaxpy (const cs_di *A, const double *x, double *y) ; cs_di *cs_di_multiply (const cs_di *A, const cs_di *B) ; int cs_di_qrsol (int order, const cs_di *A, double *b) ; cs_di *cs_di_transpose (const cs_di *A, int values) ; cs_di *cs_di_compress (const cs_di *T) ; double cs_di_norm (const cs_di *A) ; int cs_di_print (const cs_di *A, int brief) ; cs_di *cs_di_load (FILE *f) ; /* utilities */ void *cs_di_calloc (int n, size_t size) ; void *cs_di_free (void *p) ; void *cs_di_realloc (void *p, int n, size_t size, int *ok) ; cs_di *cs_di_spalloc (int m, int n, int nzmax, int values, int t) ; cs_di *cs_di_spfree (cs_di *A) ; int cs_di_sprealloc (cs_di *A, int nzmax) ; void *cs_di_malloc (int n, size_t size) ; /* --- secondary CSparse routines and data structures ----------------------- */ typedef struct cs_di_symbolic /* symbolic Cholesky, LU, or QR analysis */ { int *pinv ; /* inverse row perm. for QR, fill red. perm for Chol */ int *q ; /* fill-reducing column permutation for LU and QR */ int *parent ; /* elimination tree for Cholesky and QR */ int *cp ; /* column pointers for Cholesky, row counts for QR */ int *leftmost ; /* leftmost[i] = min(find(A(i,:))), for QR */ int m2 ; /* # of rows for QR, after adding fictitious rows */ double lnz ; /* # entries in L for LU or Cholesky; in V for QR */ double unz ; /* # entries in U for LU; in R for QR */ } cs_dis ; typedef struct cs_di_numeric /* numeric Cholesky, LU, or QR factorization */ { cs_di *L ; /* L for LU and Cholesky, V for QR */ cs_di *U ; /* U for LU, r for QR, not used for Cholesky */ int *pinv ; /* partial pivoting for LU */ double *B ; /* beta [0..n-1] for QR */ } cs_din ; typedef struct cs_di_dmperm_results /* cs_di_dmperm or cs_di_scc output */ { int *p ; /* size m, row permutation */ int *q ; /* size n, column permutation */ int *r ; /* size nb+1, block k is rows r[k] to r[k+1]-1 in A(p,q) */ int *s ; /* size nb+1, block k is cols s[k] to s[k+1]-1 in A(p,q) */ int nb ; /* # of blocks in fine dmperm decomposition */ int rr [5] ; /* coarse row decomposition */ int cc [5] ; /* coarse column decomposition */ } cs_did ; int *cs_di_amd (int order, const cs_di *A) ; cs_din *cs_di_chol (const cs_di *A, const cs_dis *S) ; cs_did *cs_di_dmperm (const cs_di *A, int seed) ; int cs_di_droptol (cs_di *A, double tol) ; int cs_di_dropzeros (cs_di *A) ; int cs_di_happly (const cs_di *V, int i, double beta, double *x) ; int cs_di_ipvec (const int *p, const double *b, double *x, int n) ; int cs_di_lsolve (const cs_di *L, double *x) ; int cs_di_ltsolve (const cs_di *L, double *x) ; cs_din *cs_di_lu (const cs_di *A, const cs_dis *S, double tol) ; cs_di *cs_di_permute (const cs_di *A, const int *pinv, const int *q, int values) ; int *cs_di_pinv (const int *p, int n) ; int cs_di_pvec (const int *p, const double *b, double *x, int n) ; cs_din *cs_di_qr (const cs_di *A, const cs_dis *S) ; cs_dis *cs_di_schol (int order, const cs_di *A) ; cs_dis *cs_di_sqr (int order, const cs_di *A, int qr) ; cs_di *cs_di_symperm (const cs_di *A, const int *pinv, int values) ; int cs_di_usolve (const cs_di *U, double *x) ; int cs_di_utsolve (const cs_di *U, double *x) ; int cs_di_updown (cs_di *L, int sigma, const cs_di *C, const int *parent) ; /* utilities */ cs_dis *cs_di_sfree (cs_dis *S) ; cs_din *cs_di_nfree (cs_din *N) ; cs_did *cs_di_dfree (cs_did *D) ; /* --- tertiary CSparse routines -------------------------------------------- */ int *cs_di_counts (const cs_di *A, const int *parent, const int *post, int ata) ; double cs_di_cumsum (int *p, int *c, int n) ; int cs_di_dfs (int j, cs_di *G, int top, int *xi, int *pstack, const int *pinv) ; int *cs_di_etree (const cs_di *A, int ata) ; int cs_di_fkeep (cs_di *A, int (*fkeep) (int, int, double, void *), void *other) ; double cs_di_house (double *x, double *beta, int n) ; int *cs_di_maxtrans (const cs_di *A, int seed) ; int *cs_di_post (const int *parent, int n) ; cs_did *cs_di_scc (cs_di *A) ; int cs_di_scatter (const cs_di *A, int j, double beta, int *w, double *x, int mark, cs_di *C, int nz) ; int cs_di_tdfs (int j, int k, int *head, const int *next, int *post, int *stack) ; int cs_di_leaf (int i, int j, const int *first, int *maxfirst, int *prevleaf, int *ancestor, int *jleaf) ; int cs_di_reach (cs_di *G, const cs_di *B, int k, int *xi, const int *pinv) ; int cs_di_spsolve (cs_di *L, const cs_di *B, int k, int *xi, double *x, const int *pinv, int lo) ; int cs_di_ereach (const cs_di *A, int k, const int *parent, int *s, int *w) ; int *cs_di_randperm (int n, int seed) ; /* utilities */ cs_did *cs_di_dalloc (int m, int n) ; cs_di *cs_di_done (cs_di *C, void *w, void *x, int ok) ; int *cs_di_idone (int *p, cs_di *C, void *w, int ok) ; cs_din *cs_di_ndone (cs_din *N, cs_di *C, void *w, void *x, int ok) ; cs_did *cs_di_ddone (cs_did *D, cs_di *C, void *w, int ok) ; /* -------------------------------------------------------------------------- */ /* double/UF_long version of CXSparse */ /* -------------------------------------------------------------------------- */ /* --- primary CSparse routines and data structures ------------------------- */ typedef struct cs_dl_sparse /* matrix in compressed-column or triplet form */ { UF_long nzmax ; /* maximum number of entries */ UF_long m ; /* number of rows */ UF_long n ; /* number of columns */ UF_long *p ; /* column pointers (size n+1) or col indlces (size nzmax) */ UF_long *i ; /* row indices, size nzmax */ double *x ; /* numerical values, size nzmax */ UF_long nz ; /* # of entries in triplet matrix, -1 for compressed-col */ } cs_dl ; cs_dl *cs_dl_add (const cs_dl *A, const cs_dl *B, double alpha, double beta) ; UF_long cs_dl_cholsol (UF_long order, const cs_dl *A, double *b) ; UF_long cs_dl_dupl (cs_dl *A) ; UF_long cs_dl_entry (cs_dl *T, UF_long i, UF_long j, double x) ; UF_long cs_dl_lusol (UF_long order, const cs_dl *A, double *b, double tol) ; UF_long cs_dl_gaxpy (const cs_dl *A, const double *x, double *y) ; cs_dl *cs_dl_multiply (const cs_dl *A, const cs_dl *B) ; UF_long cs_dl_qrsol (UF_long order, const cs_dl *A, double *b) ; cs_dl *cs_dl_transpose (const cs_dl *A, UF_long values) ; cs_dl *cs_dl_compress (const cs_dl *T) ; double cs_dl_norm (const cs_dl *A) ; UF_long cs_dl_print (const cs_dl *A, UF_long brief) ; cs_dl *cs_dl_load (FILE *f) ; /* utilities */ void *cs_dl_calloc (UF_long n, size_t size) ; void *cs_dl_free (void *p) ; void *cs_dl_realloc (void *p, UF_long n, size_t size, UF_long *ok) ; cs_dl *cs_dl_spalloc (UF_long m, UF_long n, UF_long nzmax, UF_long values, UF_long t) ; cs_dl *cs_dl_spfree (cs_dl *A) ; UF_long cs_dl_sprealloc (cs_dl *A, UF_long nzmax) ; void *cs_dl_malloc (UF_long n, size_t size) ; /* --- secondary CSparse routines and data structures ----------------------- */ typedef struct cs_dl_symbolic /* symbolic Cholesky, LU, or QR analysis */ { UF_long *pinv ; /* inverse row perm. for QR, fill red. perm for Chol */ UF_long *q ; /* fill-reducing column permutation for LU and QR */ UF_long *parent ; /* elimination tree for Cholesky and QR */ UF_long *cp ; /* column pointers for Cholesky, row counts for QR */ UF_long *leftmost ; /* leftmost[i] = min(find(A(i,:))), for QR */ UF_long m2 ; /* # of rows for QR, after adding fictitious rows */ double lnz ; /* # entries in L for LU or Cholesky; in V for QR */ double unz ; /* # entries in U for LU; in R for QR */ } cs_dls ; typedef struct cs_dl_numeric /* numeric Cholesky, LU, or QR factorization */ { cs_dl *L ; /* L for LU and Cholesky, V for QR */ cs_dl *U ; /* U for LU, r for QR, not used for Cholesky */ UF_long *pinv ; /* partial pivoting for LU */ double *B ; /* beta [0..n-1] for QR */ } cs_dln ; typedef struct cs_dl_dmperm_results /* cs_dl_dmperm or cs_dl_scc output */ { UF_long *p ; /* size m, row permutation */ UF_long *q ; /* size n, column permutation */ UF_long *r ; /* size nb+1, block k is rows r[k] to r[k+1]-1 in A(p,q) */ UF_long *s ; /* size nb+1, block k is cols s[k] to s[k+1]-1 in A(p,q) */ UF_long nb ; /* # of blocks in fine dmperm decomposition */ UF_long rr [5] ; /* coarse row decomposition */ UF_long cc [5] ; /* coarse column decomposition */ } cs_dld ; UF_long *cs_dl_amd (UF_long order, const cs_dl *A) ; cs_dln *cs_dl_chol (const cs_dl *A, const cs_dls *S) ; cs_dld *cs_dl_dmperm (const cs_dl *A, UF_long seed) ; UF_long cs_dl_droptol (cs_dl *A, double tol) ; UF_long cs_dl_dropzeros (cs_dl *A) ; UF_long cs_dl_happly (const cs_dl *V, UF_long i, double beta, double *x) ; UF_long cs_dl_ipvec (const UF_long *p, const double *b, double *x, UF_long n) ; UF_long cs_dl_lsolve (const cs_dl *L, double *x) ; UF_long cs_dl_ltsolve (const cs_dl *L, double *x) ; cs_dln *cs_dl_lu (const cs_dl *A, const cs_dls *S, double tol) ; cs_dl *cs_dl_permute (const cs_dl *A, const UF_long *pinv, const UF_long *q, UF_long values) ; UF_long *cs_dl_pinv (const UF_long *p, UF_long n) ; UF_long cs_dl_pvec (const UF_long *p, const double *b, double *x, UF_long n) ; cs_dln *cs_dl_qr (const cs_dl *A, const cs_dls *S) ; cs_dls *cs_dl_schol (UF_long order, const cs_dl *A) ; cs_dls *cs_dl_sqr (UF_long order, const cs_dl *A, UF_long qr) ; cs_dl *cs_dl_symperm (const cs_dl *A, const UF_long *pinv, UF_long values) ; UF_long cs_dl_usolve (const cs_dl *U, double *x) ; UF_long cs_dl_utsolve (const cs_dl *U, double *x) ; UF_long cs_dl_updown (cs_dl *L, UF_long sigma, const cs_dl *C, const UF_long *parent) ; /* utilities */ cs_dls *cs_dl_sfree (cs_dls *S) ; cs_dln *cs_dl_nfree (cs_dln *N) ; cs_dld *cs_dl_dfree (cs_dld *D) ; /* --- tertiary CSparse routines -------------------------------------------- */ UF_long *cs_dl_counts (const cs_dl *A, const UF_long *parent, const UF_long *post, UF_long ata) ; double cs_dl_cumsum (UF_long *p, UF_long *c, UF_long n) ; UF_long cs_dl_dfs (UF_long j, cs_dl *G, UF_long top, UF_long *xi, UF_long *pstack, const UF_long *pinv) ; UF_long *cs_dl_etree (const cs_dl *A, UF_long ata) ; UF_long cs_dl_fkeep (cs_dl *A, UF_long (*fkeep) (UF_long, UF_long, double, void *), void *other) ; double cs_dl_house (double *x, double *beta, UF_long n) ; UF_long *cs_dl_maxtrans (const cs_dl *A, UF_long seed) ; UF_long *cs_dl_post (const UF_long *parent, UF_long n) ; cs_dld *cs_dl_scc (cs_dl *A) ; UF_long cs_dl_scatter (const cs_dl *A, UF_long j, double beta, UF_long *w, double *x, UF_long mark,cs_dl *C, UF_long nz) ; UF_long cs_dl_tdfs (UF_long j, UF_long k, UF_long *head, const UF_long *next, UF_long *post, UF_long *stack) ; UF_long cs_dl_leaf (UF_long i, UF_long j, const UF_long *first, UF_long *maxfirst, UF_long *prevleaf, UF_long *ancestor, UF_long *jleaf) ; UF_long cs_dl_reach (cs_dl *G, const cs_dl *B, UF_long k, UF_long *xi, const UF_long *pinv) ; UF_long cs_dl_spsolve (cs_dl *L, const cs_dl *B, UF_long k, UF_long *xi, double *x, const UF_long *pinv, UF_long lo) ; UF_long cs_dl_ereach (const cs_dl *A, UF_long k, const UF_long *parent, UF_long *s, UF_long *w) ; UF_long *cs_dl_randperm (UF_long n, UF_long seed) ; /* utilities */ cs_dld *cs_dl_dalloc (UF_long m, UF_long n) ; cs_dl *cs_dl_done (cs_dl *C, void *w, void *x, UF_long ok) ; UF_long *cs_dl_idone (UF_long *p, cs_dl *C, void *w, UF_long ok) ; cs_dln *cs_dl_ndone (cs_dln *N, cs_dl *C, void *w, void *x, UF_long ok) ; cs_dld *cs_dl_ddone (cs_dld *D, cs_dl *C, void *w, UF_long ok) ; /* -------------------------------------------------------------------------- */ /* complex/int version of CXSparse */ /* -------------------------------------------------------------------------- */ #ifndef NCOMPLEX /* --- primary CSparse routines and data structures ------------------------- */ typedef struct cs_ci_sparse /* matrix in compressed-column or triplet form */ { int nzmax ; /* maximum number of entries */ int m ; /* number of rows */ int n ; /* number of columns */ int *p ; /* column pointers (size n+1) or col indices (size nzmax) */ int *i ; /* row indices, size nzmax */ cs_complex_t *x ; /* numerical values, size nzmax */ int nz ; /* # of entries in triplet matrix, -1 for compressed-col */ } cs_ci ; cs_ci *cs_ci_add (const cs_ci *A, const cs_ci *B, cs_complex_t alpha, cs_complex_t beta) ; int cs_ci_cholsol (int order, const cs_ci *A, cs_complex_t *b) ; int cs_ci_dupl (cs_ci *A) ; int cs_ci_entry (cs_ci *T, int i, int j, cs_complex_t x) ; int cs_ci_lusol (int order, const cs_ci *A, cs_complex_t *b, double tol) ; int cs_ci_gaxpy (const cs_ci *A, const cs_complex_t *x, cs_complex_t *y) ; cs_ci *cs_ci_multiply (const cs_ci *A, const cs_ci *B) ; int cs_ci_qrsol (int order, const cs_ci *A, cs_complex_t *b) ; cs_ci *cs_ci_transpose (const cs_ci *A, int values) ; cs_ci *cs_ci_compress (const cs_ci *T) ; double cs_ci_norm (const cs_ci *A) ; int cs_ci_print (const cs_ci *A, int brief) ; cs_ci *cs_ci_load (FILE *f) ; /* utilities */ void *cs_ci_calloc (int n, size_t size) ; void *cs_ci_free (void *p) ; void *cs_ci_realloc (void *p, int n, size_t size, int *ok) ; cs_ci *cs_ci_spalloc (int m, int n, int nzmax, int values, int t) ; cs_ci *cs_ci_spfree (cs_ci *A) ; int cs_ci_sprealloc (cs_ci *A, int nzmax) ; void *cs_ci_malloc (int n, size_t size) ; /* --- secondary CSparse routines and data structures ----------------------- */ typedef struct cs_ci_symbolic /* symbolic Cholesky, LU, or QR analysis */ { int *pinv ; /* inverse row perm. for QR, fill red. perm for Chol */ int *q ; /* fill-reducing column permutation for LU and QR */ int *parent ; /* elimination tree for Cholesky and QR */ int *cp ; /* column pointers for Cholesky, row counts for QR */ int *leftmost ; /* leftmost[i] = min(find(A(i,:))), for QR */ int m2 ; /* # of rows for QR, after adding fictitious rows */ double lnz ; /* # entries in L for LU or Cholesky; in V for QR */ double unz ; /* # entries in U for LU; in R for QR */ } cs_cis ; typedef struct cs_ci_numeric /* numeric Cholesky, LU, or QR factorization */ { cs_ci *L ; /* L for LU and Cholesky, V for QR */ cs_ci *U ; /* U for LU, r for QR, not used for Cholesky */ int *pinv ; /* partial pivoting for LU */ double *B ; /* beta [0..n-1] for QR */ } cs_cin ; typedef struct cs_ci_dmperm_results /* cs_ci_dmperm or cs_ci_scc output */ { int *p ; /* size m, row permutation */ int *q ; /* size n, column permutation */ int *r ; /* size nb+1, block k is rows r[k] to r[k+1]-1 in A(p,q) */ int *s ; /* size nb+1, block k is cols s[k] to s[k+1]-1 in A(p,q) */ int nb ; /* # of blocks in fine dmperm decomposition */ int rr [5] ; /* coarse row decomposition */ int cc [5] ; /* coarse column decomposition */ } cs_cid ; int *cs_ci_amd (int order, const cs_ci *A) ; cs_cin *cs_ci_chol (const cs_ci *A, const cs_cis *S) ; cs_cid *cs_ci_dmperm (const cs_ci *A, int seed) ; int cs_ci_droptol (cs_ci *A, double tol) ; int cs_ci_dropzeros (cs_ci *A) ; int cs_ci_happly (const cs_ci *V, int i, double beta, cs_complex_t *x) ; int cs_ci_ipvec (const int *p, const cs_complex_t *b, cs_complex_t *x, int n) ; int cs_ci_lsolve (const cs_ci *L, cs_complex_t *x) ; int cs_ci_ltsolve (const cs_ci *L, cs_complex_t *x) ; cs_cin *cs_ci_lu (const cs_ci *A, const cs_cis *S, double tol) ; cs_ci *cs_ci_permute (const cs_ci *A, const int *pinv, const int *q, int values) ; int *cs_ci_pinv (const int *p, int n) ; int cs_ci_pvec (const int *p, const cs_complex_t *b, cs_complex_t *x, int n) ; cs_cin *cs_ci_qr (const cs_ci *A, const cs_cis *S) ; cs_cis *cs_ci_schol (int order, const cs_ci *A) ; cs_cis *cs_ci_sqr (int order, const cs_ci *A, int qr) ; cs_ci *cs_ci_symperm (const cs_ci *A, const int *pinv, int values) ; int cs_ci_usolve (const cs_ci *U, cs_complex_t *x) ; int cs_ci_utsolve (const cs_ci *U, cs_complex_t *x) ; int cs_ci_updown (cs_ci *L, int sigma, const cs_ci *C, const int *parent) ; /* utilities */ cs_cis *cs_ci_sfree (cs_cis *S) ; cs_cin *cs_ci_nfree (cs_cin *N) ; cs_cid *cs_ci_dfree (cs_cid *D) ; /* --- tertiary CSparse routines -------------------------------------------- */ int *cs_ci_counts (const cs_ci *A, const int *parent, const int *post, int ata) ; double cs_ci_cumsum (int *p, int *c, int n) ; int cs_ci_dfs (int j, cs_ci *G, int top, int *xi, int *pstack, const int *pinv) ; int *cs_ci_etree (const cs_ci *A, int ata) ; int cs_ci_fkeep (cs_ci *A, int (*fkeep) (int, int, cs_complex_t, void *), void *other) ; cs_complex_t cs_ci_house (cs_complex_t *x, double *beta, int n) ; int *cs_ci_maxtrans (const cs_ci *A, int seed) ; int *cs_ci_post (const int *parent, int n) ; cs_cid *cs_ci_scc (cs_ci *A) ; int cs_ci_scatter (const cs_ci *A, int j, cs_complex_t beta, int *w, cs_complex_t *x, int mark,cs_ci *C, int nz) ; int cs_ci_tdfs (int j, int k, int *head, const int *next, int *post, int *stack) ; int cs_ci_leaf (int i, int j, const int *first, int *maxfirst, int *prevleaf, int *ancestor, int *jleaf) ; int cs_ci_reach (cs_ci *G, const cs_ci *B, int k, int *xi, const int *pinv) ; int cs_ci_spsolve (cs_ci *L, const cs_ci *B, int k, int *xi, cs_complex_t *x, const int *pinv, int lo) ; int cs_ci_ereach (const cs_ci *A, int k, const int *parent, int *s, int *w) ; int *cs_ci_randperm (int n, int seed) ; /* utilities */ cs_cid *cs_ci_dalloc (int m, int n) ; cs_ci *cs_ci_done (cs_ci *C, void *w, void *x, int ok) ; int *cs_ci_idone (int *p, cs_ci *C, void *w, int ok) ; cs_cin *cs_ci_ndone (cs_cin *N, cs_ci *C, void *w, void *x, int ok) ; cs_cid *cs_ci_ddone (cs_cid *D, cs_ci *C, void *w, int ok) ; /* -------------------------------------------------------------------------- */ /* complex/UF_long version of CXSparse */ /* -------------------------------------------------------------------------- */ /* --- primary CSparse routines and data structures ------------------------- */ typedef struct cs_cl_sparse /* matrix in compressed-column or triplet form */ { UF_long nzmax ; /* maximum number of entries */ UF_long m ; /* number of rows */ UF_long n ; /* number of columns */ UF_long *p ; /* column pointers (size n+1) or col indlces (size nzmax) */ UF_long *i ; /* row indices, size nzmax */ cs_complex_t *x ; /* numerical values, size nzmax */ UF_long nz ; /* # of entries in triplet matrix, -1 for compressed-col */ } cs_cl ; cs_cl *cs_cl_add (const cs_cl *A, const cs_cl *B, cs_complex_t alpha, cs_complex_t beta) ; UF_long cs_cl_cholsol (UF_long order, const cs_cl *A, cs_complex_t *b) ; UF_long cs_cl_dupl (cs_cl *A) ; UF_long cs_cl_entry (cs_cl *T, UF_long i, UF_long j, cs_complex_t x) ; UF_long cs_cl_lusol (UF_long order, const cs_cl *A, cs_complex_t *b, double tol) ; UF_long cs_cl_gaxpy (const cs_cl *A, const cs_complex_t *x, cs_complex_t *y) ; cs_cl *cs_cl_multiply (const cs_cl *A, const cs_cl *B) ; UF_long cs_cl_qrsol (UF_long order, const cs_cl *A, cs_complex_t *b) ; cs_cl *cs_cl_transpose (const cs_cl *A, UF_long values) ; cs_cl *cs_cl_compress (const cs_cl *T) ; double cs_cl_norm (const cs_cl *A) ; UF_long cs_cl_print (const cs_cl *A, UF_long brief) ; cs_cl *cs_cl_load (FILE *f) ; /* utilities */ void *cs_cl_calloc (UF_long n, size_t size) ; void *cs_cl_free (void *p) ; void *cs_cl_realloc (void *p, UF_long n, size_t size, UF_long *ok) ; cs_cl *cs_cl_spalloc (UF_long m, UF_long n, UF_long nzmax, UF_long values, UF_long t) ; cs_cl *cs_cl_spfree (cs_cl *A) ; UF_long cs_cl_sprealloc (cs_cl *A, UF_long nzmax) ; void *cs_cl_malloc (UF_long n, size_t size) ; /* --- secondary CSparse routines and data structures ----------------------- */ typedef struct cs_cl_symbolic /* symbolic Cholesky, LU, or QR analysis */ { UF_long *pinv ; /* inverse row perm. for QR, fill red. perm for Chol */ UF_long *q ; /* fill-reducing column permutation for LU and QR */ UF_long *parent ; /* elimination tree for Cholesky and QR */ UF_long *cp ; /* column pointers for Cholesky, row counts for QR */ UF_long *leftmost ; /* leftmost[i] = min(find(A(i,:))), for QR */ UF_long m2 ; /* # of rows for QR, after adding fictitious rows */ double lnz ; /* # entries in L for LU or Cholesky; in V for QR */ double unz ; /* # entries in U for LU; in R for QR */ } cs_cls ; typedef struct cs_cl_numeric /* numeric Cholesky, LU, or QR factorization */ { cs_cl *L ; /* L for LU and Cholesky, V for QR */ cs_cl *U ; /* U for LU, r for QR, not used for Cholesky */ UF_long *pinv ; /* partial pivoting for LU */ double *B ; /* beta [0..n-1] for QR */ } cs_cln ; typedef struct cs_cl_dmperm_results /* cs_cl_dmperm or cs_cl_scc output */ { UF_long *p ; /* size m, row permutation */ UF_long *q ; /* size n, column permutation */ UF_long *r ; /* size nb+1, block k is rows r[k] to r[k+1]-1 in A(p,q) */ UF_long *s ; /* size nb+1, block k is cols s[k] to s[k+1]-1 in A(p,q) */ UF_long nb ; /* # of blocks in fine dmperm decomposition */ UF_long rr [5] ; /* coarse row decomposition */ UF_long cc [5] ; /* coarse column decomposition */ } cs_cld ; UF_long *cs_cl_amd (UF_long order, const cs_cl *A) ; cs_cln *cs_cl_chol (const cs_cl *A, const cs_cls *S) ; cs_cld *cs_cl_dmperm (const cs_cl *A, UF_long seed) ; UF_long cs_cl_droptol (cs_cl *A, double tol) ; UF_long cs_cl_dropzeros (cs_cl *A) ; UF_long cs_cl_happly (const cs_cl *V, UF_long i, double beta, cs_complex_t *x) ; UF_long cs_cl_ipvec (const UF_long *p, const cs_complex_t *b, cs_complex_t *x, UF_long n) ; UF_long cs_cl_lsolve (const cs_cl *L, cs_complex_t *x) ; UF_long cs_cl_ltsolve (const cs_cl *L, cs_complex_t *x) ; cs_cln *cs_cl_lu (const cs_cl *A, const cs_cls *S, double tol) ; cs_cl *cs_cl_permute (const cs_cl *A, const UF_long *pinv, const UF_long *q, UF_long values) ; UF_long *cs_cl_pinv (const UF_long *p, UF_long n) ; UF_long cs_cl_pvec (const UF_long *p, const cs_complex_t *b, cs_complex_t *x, UF_long n) ; cs_cln *cs_cl_qr (const cs_cl *A, const cs_cls *S) ; cs_cls *cs_cl_schol (UF_long order, const cs_cl *A) ; cs_cls *cs_cl_sqr (UF_long order, const cs_cl *A, UF_long qr) ; cs_cl *cs_cl_symperm (const cs_cl *A, const UF_long *pinv, UF_long values) ; UF_long cs_cl_usolve (const cs_cl *U, cs_complex_t *x) ; UF_long cs_cl_utsolve (const cs_cl *U, cs_complex_t *x) ; UF_long cs_cl_updown (cs_cl *L, UF_long sigma, const cs_cl *C, const UF_long *parent) ; /* utilities */ cs_cls *cs_cl_sfree (cs_cls *S) ; cs_cln *cs_cl_nfree (cs_cln *N) ; cs_cld *cs_cl_dfree (cs_cld *D) ; /* --- tertiary CSparse routines -------------------------------------------- */ UF_long *cs_cl_counts (const cs_cl *A, const UF_long *parent, const UF_long *post, UF_long ata) ; double cs_cl_cumsum (UF_long *p, UF_long *c, UF_long n) ; UF_long cs_cl_dfs (UF_long j, cs_cl *G, UF_long top, UF_long *xi, UF_long *pstack, const UF_long *pinv) ; UF_long *cs_cl_etree (const cs_cl *A, UF_long ata) ; UF_long cs_cl_fkeep (cs_cl *A, UF_long (*fkeep) (UF_long, UF_long, cs_complex_t, void *), void *other) ; cs_complex_t cs_cl_house (cs_complex_t *x, double *beta, UF_long n) ; UF_long *cs_cl_maxtrans (const cs_cl *A, UF_long seed) ; UF_long *cs_cl_post (const UF_long *parent, UF_long n) ; cs_cld *cs_cl_scc (cs_cl *A) ; UF_long cs_cl_scatter (const cs_cl *A, UF_long j, cs_complex_t beta, UF_long *w, cs_complex_t *x, UF_long mark,cs_cl *C, UF_long nz) ; UF_long cs_cl_tdfs (UF_long j, UF_long k, UF_long *head, const UF_long *next, UF_long *post, UF_long *stack) ; UF_long cs_cl_leaf (UF_long i, UF_long j, const UF_long *first, UF_long *maxfirst, UF_long *prevleaf, UF_long *ancestor, UF_long *jleaf) ; UF_long cs_cl_reach (cs_cl *G, const cs_cl *B, UF_long k, UF_long *xi, const UF_long *pinv) ; UF_long cs_cl_spsolve (cs_cl *L, const cs_cl *B, UF_long k, UF_long *xi, cs_complex_t *x, const UF_long *pinv, UF_long lo) ; UF_long cs_cl_ereach (const cs_cl *A, UF_long k, const UF_long *parent, UF_long *s, UF_long *w) ; UF_long *cs_cl_randperm (UF_long n, UF_long seed) ; /* utilities */ cs_cld *cs_cl_dalloc (UF_long m, UF_long n) ; cs_cl *cs_cl_done (cs_cl *C, void *w, void *x, UF_long ok) ; UF_long *cs_cl_idone (UF_long *p, cs_cl *C, void *w, UF_long ok) ; cs_cln *cs_cl_ndone (cs_cln *N, cs_cl *C, void *w, void *x, UF_long ok) ; cs_cld *cs_cl_ddone (cs_cld *D, cs_cl *C, void *w, UF_long ok) ; #endif /* -------------------------------------------------------------------------- */ /* Macros for constructing each version of CSparse */ /* -------------------------------------------------------------------------- */ #ifdef CS_LONG #define CS_INT UF_long #define CS_INT_MAX UF_long_max #define CS_ID UF_long_id #ifdef CS_COMPLEX #define CS_ENTRY cs_complex_t #define CS_NAME(nm) cs_cl ## nm #define cs cs_cl #else #define CS_ENTRY double #define CS_NAME(nm) cs_dl ## nm #define cs cs_dl #endif #else #define CS_INT int #define CS_INT_MAX INT_MAX #define CS_ID "%d" #ifdef CS_COMPLEX #define CS_ENTRY cs_complex_t #define CS_NAME(nm) cs_ci ## nm #define cs cs_ci #else #define CS_ENTRY double #define CS_NAME(nm) cs_di ## nm #define cs cs_di #endif #endif #ifdef CS_COMPLEX #define CS_REAL(x) creal(x) #define CS_IMAG(x) cimag(x) #define CS_CONJ(x) conj(x) #define CS_ABS(x) cabs(x) #else #define CS_REAL(x) (x) #define CS_IMAG(x) (0.) #define CS_CONJ(x) (x) #define CS_ABS(x) fabs(x) #endif #define CS_MAX(a,b) (((a) > (b)) ? (a) : (b)) #define CS_MIN(a,b) (((a) < (b)) ? (a) : (b)) #define CS_FLIP(i) (-(i)-2) #define CS_UNFLIP(i) (((i) < 0) ? CS_FLIP(i) : (i)) #define CS_MARKED(w,j) (w [j] < 0) #define CS_MARK(w,j) { w [j] = CS_FLIP (w [j]) ; } #define CS_CSC(A) (A && (A->nz == -1)) #define CS_TRIPLET(A) (A && (A->nz >= 0)) /* --- primary CSparse routines and data structures ------------------------- */ #define cs_add CS_NAME (_add) #define cs_cholsol CS_NAME (_cholsol) #define cs_dupl CS_NAME (_dupl) #define cs_entry CS_NAME (_entry) #define cs_lusol CS_NAME (_lusol) #define cs_gaxpy CS_NAME (_gaxpy) #define cs_multiply CS_NAME (_multiply) #define cs_qrsol CS_NAME (_qrsol) #define cs_transpose CS_NAME (_transpose) #define cs_compress CS_NAME (_compress) #define cs_norm CS_NAME (_norm) #define cs_print CS_NAME (_print) #define cs_load CS_NAME (_load) /* utilities */ #define cs_calloc CS_NAME (_calloc) #define cs_free CS_NAME (_free) #define cs_realloc CS_NAME (_realloc) #define cs_spalloc CS_NAME (_spalloc) #define cs_spfree CS_NAME (_spfree) #define cs_sprealloc CS_NAME (_sprealloc) #define cs_malloc CS_NAME (_malloc) /* --- secondary CSparse routines and data structures ----------------------- */ #define css CS_NAME (s) #define csn CS_NAME (n) #define csd CS_NAME (d) #define cs_amd CS_NAME (_amd) #define cs_chol CS_NAME (_chol) #define cs_dmperm CS_NAME (_dmperm) #define cs_droptol CS_NAME (_droptol) #define cs_dropzeros CS_NAME (_dropzeros) #define cs_happly CS_NAME (_happly) #define cs_ipvec CS_NAME (_ipvec) #define cs_lsolve CS_NAME (_lsolve) #define cs_ltsolve CS_NAME (_ltsolve) #define cs_lu CS_NAME (_lu) #define cs_permute CS_NAME (_permute) #define cs_pinv CS_NAME (_pinv) #define cs_pvec CS_NAME (_pvec) #define cs_qr CS_NAME (_qr) #define cs_schol CS_NAME (_schol) #define cs_sqr CS_NAME (_sqr) #define cs_symperm CS_NAME (_symperm) #define cs_usolve CS_NAME (_usolve) #define cs_utsolve CS_NAME (_utsolve) #define cs_updown CS_NAME (_updown) /* utilities */ #define cs_sfree CS_NAME (_sfree) #define cs_nfree CS_NAME (_nfree) #define cs_dfree CS_NAME (_dfree) /* --- tertiary CSparse routines -------------------------------------------- */ #define cs_counts CS_NAME (_counts) #define cs_cumsum CS_NAME (_cumsum) #define cs_dfs CS_NAME (_dfs) #define cs_etree CS_NAME (_etree) #define cs_fkeep CS_NAME (_fkeep) #define cs_house CS_NAME (_house) #define cs_invmatch CS_NAME (_invmatch) #define cs_maxtrans CS_NAME (_maxtrans) #define cs_post CS_NAME (_post) #define cs_scc CS_NAME (_scc) #define cs_scatter CS_NAME (_scatter) #define cs_tdfs CS_NAME (_tdfs) #define cs_reach CS_NAME (_reach) #define cs_spsolve CS_NAME (_spsolve) #define cs_ereach CS_NAME (_ereach) #define cs_randperm CS_NAME (_randperm) #define cs_leaf CS_NAME (_leaf) /* utilities */ #define cs_dalloc CS_NAME (_dalloc) #define cs_done CS_NAME (_done) #define cs_idone CS_NAME (_idone) #define cs_ndone CS_NAME (_ndone) #define cs_ddone CS_NAME (_ddone) /* -------------------------------------------------------------------------- */ /* Conversion routines */ /* -------------------------------------------------------------------------- */ #ifndef NCOMPLEX cs_di *cs_i_real (cs_ci *A, int real) ; cs_ci *cs_i_complex (cs_di *A, int real) ; cs_dl *cs_l_real (cs_cl *A, UF_long real) ; cs_cl *cs_l_complex (cs_dl *A, UF_long real) ; #endif #ifdef __cplusplus } #endif #endif SuiteSparse/CXSparse/Source/0000755001170100242450000000000010711425510014673 5ustar davisfacSuiteSparse/CXSparse/Source/cs_ltsolve.c0000644001170100242450000000076210712165171017226 0ustar davisfac#include "cs.h" /* solve L'x=b where x and b are dense. x=b on input, solution on output. */ CS_INT cs_ltsolve (const cs *L, CS_ENTRY *x) { CS_INT p, j, n, *Lp, *Li ; CS_ENTRY *Lx ; if (!CS_CSC (L) || !x) return (0) ; /* check inputs */ n = L->n ; Lp = L->p ; Li = L->i ; Lx = L->x ; for (j = n-1 ; j >= 0 ; j--) { for (p = Lp [j]+1 ; p < Lp [j+1] ; p++) { x [j] -= CS_CONJ (Lx [p]) * x [Li [p]] ; } x [j] /= CS_CONJ (Lx [Lp [j]]) ; } return (1) ; } SuiteSparse/CXSparse/Source/cs_cholsol.c0000644001170100242450000000143410712165171017176 0ustar davisfac#include "cs.h" /* x=A\b where A is symmetric positive definite; b overwritten with solution */ CS_INT cs_cholsol (CS_INT order, const cs *A, CS_ENTRY *b) { CS_ENTRY *x ; css *S ; csn *N ; CS_INT n, ok ; if (!CS_CSC (A) || !b) return (0) ; /* check inputs */ n = A->n ; S = cs_schol (order, A) ; /* ordering and symbolic analysis */ N = cs_chol (A, S) ; /* numeric Cholesky factorization */ x = cs_malloc (n, sizeof (CS_ENTRY)) ; /* get workspace */ ok = (S && N && x) ; if (ok) { cs_ipvec (S->pinv, b, x, n) ; /* x = P*b */ cs_lsolve (N->L, x) ; /* x = L\x */ cs_ltsolve (N->L, x) ; /* x = L'\x */ cs_pvec (S->pinv, x, b, n) ; /* b = P'*x */ } cs_free (x) ; cs_sfree (S) ; cs_nfree (N) ; return (ok) ; } SuiteSparse/CXSparse/Source/cs_lu.c0000644001170100242450000000663610712165171016164 0ustar davisfac#include "cs.h" /* [L,U,pinv]=lu(A, [q lnz unz]). lnz and unz can be guess */ csn *cs_lu (const cs *A, const css *S, double tol) { cs *L, *U ; csn *N ; CS_ENTRY pivot, *Lx, *Ux, *x ; double a, t ; CS_INT *Lp, *Li, *Up, *Ui, *pinv, *xi, *q, n, ipiv, k, top, p, i, col, lnz,unz; if (!CS_CSC (A) || !S) return (NULL) ; /* check inputs */ n = A->n ; q = S->q ; lnz = S->lnz ; unz = S->unz ; x = cs_malloc (n, sizeof (CS_ENTRY)) ; /* get CS_ENTRY workspace */ xi = cs_malloc (2*n, sizeof (CS_INT)) ; /* get CS_INT workspace */ N = cs_calloc (1, sizeof (csn)) ; /* allocate result */ if (!x || !xi || !N) return (cs_ndone (N, NULL, xi, x, 0)) ; N->L = L = cs_spalloc (n, n, lnz, 1, 0) ; /* allocate result L */ N->U = U = cs_spalloc (n, n, unz, 1, 0) ; /* allocate result U */ N->pinv = pinv = cs_malloc (n, sizeof (CS_INT)) ; /* allocate result pinv */ if (!L || !U || !pinv) return (cs_ndone (N, NULL, xi, x, 0)) ; Lp = L->p ; Up = U->p ; for (i = 0 ; i < n ; i++) x [i] = 0 ; /* clear workspace */ for (i = 0 ; i < n ; i++) pinv [i] = -1 ; /* no rows pivotal yet */ for (k = 0 ; k <= n ; k++) Lp [k] = 0 ; /* no cols of L yet */ lnz = unz = 0 ; for (k = 0 ; k < n ; k++) /* compute L(:,k) and U(:,k) */ { /* --- Triangular solve --------------------------------------------- */ Lp [k] = lnz ; /* L(:,k) starts here */ Up [k] = unz ; /* U(:,k) starts here */ if ((lnz + n > L->nzmax && !cs_sprealloc (L, 2*L->nzmax + n)) || (unz + n > U->nzmax && !cs_sprealloc (U, 2*U->nzmax + n))) { return (cs_ndone (N, NULL, xi, x, 0)) ; } Li = L->i ; Lx = L->x ; Ui = U->i ; Ux = U->x ; col = q ? (q [k]) : k ; top = cs_spsolve (L, A, col, xi, x, pinv, 1) ; /* x = L\A(:,col) */ /* --- Find pivot --------------------------------------------------- */ ipiv = -1 ; a = -1 ; for (p = top ; p < n ; p++) { i = xi [p] ; /* x(i) is nonzero */ if (pinv [i] < 0) /* row i is not yet pivotal */ { if ((t = CS_ABS (x [i])) > a) { a = t ; /* largest pivot candidate so far */ ipiv = i ; } } else /* x(i) is the entry U(pinv[i],k) */ { Ui [unz] = pinv [i] ; Ux [unz++] = x [i] ; } } if (ipiv == -1 || a <= 0) return (cs_ndone (N, NULL, xi, x, 0)) ; if (pinv [col] < 0 && CS_ABS (x [col]) >= a*tol) ipiv = col ; /* --- Divide by pivot ---------------------------------------------- */ pivot = x [ipiv] ; /* the chosen pivot */ Ui [unz] = k ; /* last entry in U(:,k) is U(k,k) */ Ux [unz++] = pivot ; pinv [ipiv] = k ; /* ipiv is the kth pivot row */ Li [lnz] = ipiv ; /* first entry in L(:,k) is L(k,k) = 1 */ Lx [lnz++] = 1 ; for (p = top ; p < n ; p++) /* L(k+1:n,k) = x / pivot */ { i = xi [p] ; if (pinv [i] < 0) /* x(i) is an entry in L(:,k) */ { Li [lnz] = i ; /* save unpermuted row in L */ Lx [lnz++] = x [i] / pivot ; /* scale pivot column */ } x [i] = 0 ; /* x [0..n-1] = 0 for next k */ } } /* --- Finalize L and U ------------------------------------------------- */ Lp [n] = lnz ; Up [n] = unz ; Li = L->i ; /* fix row indices of L for final pinv */ for (p = 0 ; p < lnz ; p++) Li [p] = pinv [Li [p]] ; cs_sprealloc (L, 0) ; /* remove extra space from L and U */ cs_sprealloc (U, 0) ; return (cs_ndone (N, NULL, xi, x, 1)) ; /* success */ } SuiteSparse/CXSparse/Source/cs_qr.c0000644001170100242450000000570110712165171016156 0ustar davisfac#include "cs.h" /* sparse QR factorization [V,beta,pinv,R] = qr (A) */ csn *cs_qr (const cs *A, const css *S) { CS_ENTRY *Rx, *Vx, *Ax, *x ; double *Beta ; CS_INT i, k, p, m, n, vnz, p1, top, m2, len, col, rnz, *s, *leftmost, *Ap, *Ai, *parent, *Rp, *Ri, *Vp, *Vi, *w, *pinv, *q ; cs *R, *V ; csn *N ; if (!CS_CSC (A) || !S) return (NULL) ; m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; q = S->q ; parent = S->parent ; pinv = S->pinv ; m2 = S->m2 ; vnz = S->lnz ; rnz = S->unz ; leftmost = S->leftmost ; w = cs_malloc (m2+n, sizeof (CS_INT)) ; /* get CS_INT workspace */ x = cs_malloc (m2, sizeof (CS_ENTRY)) ; /* get CS_ENTRY workspace */ N = cs_calloc (1, sizeof (csn)) ; /* allocate result */ if (!w || !x || !N) return (cs_ndone (N, NULL, w, x, 0)) ; s = w + m2 ; /* s is size n */ for (k = 0 ; k < m2 ; k++) x [k] = 0 ; /* clear workspace x */ N->L = V = cs_spalloc (m2, n, vnz, 1, 0) ; /* allocate result V */ N->U = R = cs_spalloc (m2, n, rnz, 1, 0) ; /* allocate result R */ N->B = Beta = cs_malloc (n, sizeof (double)) ; /* allocate result Beta */ if (!R || !V || !Beta) return (cs_ndone (N, NULL, w, x, 0)) ; Rp = R->p ; Ri = R->i ; Rx = R->x ; Vp = V->p ; Vi = V->i ; Vx = V->x ; for (i = 0 ; i < m2 ; i++) w [i] = -1 ; /* clear w, to mark nodes */ rnz = 0 ; vnz = 0 ; for (k = 0 ; k < n ; k++) /* compute V and R */ { Rp [k] = rnz ; /* R(:,k) starts here */ Vp [k] = p1 = vnz ; /* V(:,k) starts here */ w [k] = k ; /* add V(k,k) to pattern of V */ Vi [vnz++] = k ; top = n ; col = q ? q [k] : k ; for (p = Ap [col] ; p < Ap [col+1] ; p++) /* find R(:,k) pattern */ { i = leftmost [Ai [p]] ; /* i = min(find(A(i,q))) */ for (len = 0 ; w [i] != k ; i = parent [i]) /* traverse up to k */ { s [len++] = i ; w [i] = k ; } while (len > 0) s [--top] = s [--len] ; /* push path on stack */ i = pinv [Ai [p]] ; /* i = permuted row of A(:,col) */ x [i] = Ax [p] ; /* x (i) = A(:,col) */ if (i > k && w [i] < k) /* pattern of V(:,k) = x (k+1:m) */ { Vi [vnz++] = i ; /* add i to pattern of V(:,k) */ w [i] = k ; } } for (p = top ; p < n ; p++) /* for each i in pattern of R(:,k) */ { i = s [p] ; /* R(i,k) is nonzero */ cs_happly (V, i, Beta [i], x) ; /* apply (V(i),Beta(i)) to x */ Ri [rnz] = i ; /* R(i,k) = x(i) */ Rx [rnz++] = x [i] ; x [i] = 0 ; if (parent [i] == k) vnz = cs_scatter (V, i, 0, w, NULL, k, V, vnz); } for (p = p1 ; p < vnz ; p++) /* gather V(:,k) = x */ { Vx [p] = x [Vi [p]] ; x [Vi [p]] = 0 ; } Ri [rnz] = k ; /* R(k,k) = norm (x) */ Rx [rnz++] = cs_house (Vx+p1, Beta+k, vnz-p1) ; /* [v,beta]=house(x) */ } Rp [n] = rnz ; /* finalize R */ Vp [n] = vnz ; /* finalize V */ return (cs_ndone (N, NULL, w, x, 1)) ; /* success */ } SuiteSparse/CXSparse/Source/cs_house.c0000644001170100242450000000143610630067063016660 0ustar davisfac#include "cs.h" /* create a Householder reflection [v,beta,s]=house(x), overwrite x with v, * where (I-beta*v*v')*x = s*e1 and e1 = [1 0 ... 0]'. * Note that this CXSparse version is different than CSparse. See Higham, * Accuracy & Stability of Num Algorithms, 2nd ed, 2002, page 357. */ CS_ENTRY cs_house (CS_ENTRY *x, double *beta, CS_INT n) { CS_ENTRY s = 0 ; CS_INT i ; if (!x || !beta) return (-1) ; /* check inputs */ /* s = norm(x) */ for (i = 0 ; i < n ; i++) s += x [i] * CS_CONJ (x [i]) ; s = sqrt (s) ; if (s == 0) { (*beta) = 0 ; x [0] = 1 ; } else { /* s = sign(x[0]) * norm (x) ; */ if (x [0] != 0) { s *= x [0] / CS_ABS (x [0]) ; } x [0] += s ; (*beta) = 1. / CS_REAL (CS_CONJ (s) * x [0]) ; } return (-s) ; } SuiteSparse/CXSparse/Source/cs_updown.c0000644001170100242450000000354610571364723017064 0ustar davisfac#include "cs.h" /* sparse Cholesky update/downdate, L*L' + sigma*w*w' (sigma = +1 or -1) */ CS_INT cs_updown (cs *L, CS_INT sigma, const cs *C, const CS_INT *parent) { CS_INT n, p, f, j, *Lp, *Li, *Cp, *Ci ; CS_ENTRY *Lx, *Cx, alpha, gamma, w1, w2, *w ; double beta = 1, beta2 = 1, delta ; #ifdef CS_COMPLEX cs_complex_t phase ; #endif if (!CS_CSC (L) || !CS_CSC (C) || !parent) return (0) ; /* check inputs */ Lp = L->p ; Li = L->i ; Lx = L->x ; n = L->n ; Cp = C->p ; Ci = C->i ; Cx = C->x ; if ((p = Cp [0]) >= Cp [1]) return (1) ; /* return if C empty */ w = cs_malloc (n, sizeof (CS_ENTRY)) ; /* get workspace */ if (!w) return (0) ; /* out of memory */ f = Ci [p] ; for ( ; p < Cp [1] ; p++) f = CS_MIN (f, Ci [p]) ; /* f = min (find (C)) */ for (j = f ; j != -1 ; j = parent [j]) w [j] = 0 ; /* clear workspace w */ for (p = Cp [0] ; p < Cp [1] ; p++) w [Ci [p]] = Cx [p] ; /* w = C */ for (j = f ; j != -1 ; j = parent [j]) /* walk path f up to root */ { p = Lp [j] ; alpha = w [j] / Lx [p] ; /* alpha = w(j) / L(j,j) */ beta2 = beta*beta + sigma*alpha*CS_CONJ(alpha) ; if (beta2 <= 0) break ; /* not positive definite */ beta2 = sqrt (beta2) ; delta = (sigma > 0) ? (beta / beta2) : (beta2 / beta) ; gamma = sigma * CS_CONJ(alpha) / (beta2 * beta) ; Lx [p] = delta * Lx [p] + ((sigma > 0) ? (gamma * w [j]) : 0) ; beta = beta2 ; #ifdef CS_COMPLEX phase = CS_ABS (Lx [p]) / Lx [p] ; /* phase = abs(L(j,j))/L(j,j)*/ Lx [p] *= phase ; /* L(j,j) = L(j,j) * phase */ #endif for (p++ ; p < Lp [j+1] ; p++) { w1 = w [Li [p]] ; w [Li [p]] = w2 = w1 - alpha * Lx [p] ; Lx [p] = delta * Lx [p] + gamma * ((sigma > 0) ? w1 : w2) ; #ifdef CS_COMPLEX Lx [p] *= phase ; /* L(i,j) = L(i,j) * phase */ #endif } } cs_free (w) ; return (beta2 > 0) ; } SuiteSparse/CXSparse/Source/cs_cumsum.c0000644001170100242450000000101410712165171017036 0ustar davisfac#include "cs.h" /* p [0..n] = cumulative sum of c [0..n-1], and then copy p [0..n-1] into c */ double cs_cumsum (CS_INT *p, CS_INT *c, CS_INT n) { CS_INT i, nz = 0 ; double nz2 = 0 ; if (!p || !c) return (-1) ; /* check inputs */ for (i = 0 ; i < n ; i++) { p [i] = nz ; nz += c [i] ; nz2 += c [i] ; /* also in double to avoid CS_INT overflow */ c [i] = p [i] ; /* also copy p[0..n-1] back into c[0..n-1]*/ } p [n] = nz ; return (nz2) ; /* return sum (c [0..n-1]) */ } SuiteSparse/CXSparse/Source/cs_malloc.c0000644001170100242450000000155510712165171017006 0ustar davisfac#include "cs.h" #ifdef MATLAB_MEX_FILE #define malloc mxMalloc #define free mxFree #define realloc mxRealloc #define calloc mxCalloc #endif /* wrapper for malloc */ void *cs_malloc (CS_INT n, size_t size) { return (malloc (CS_MAX (n,1) * size)) ; } /* wrapper for calloc */ void *cs_calloc (CS_INT n, size_t size) { return (calloc (CS_MAX (n,1), size)) ; } /* wrapper for free */ void *cs_free (void *p) { if (p) free (p) ; /* free p if it is not already NULL */ return (NULL) ; /* return NULL to simplify the use of cs_free */ } /* wrapper for realloc */ void *cs_realloc (void *p, CS_INT n, size_t size, CS_INT *ok) { void *pnew ; pnew = realloc (p, CS_MAX (n,1) * size) ; /* realloc the block */ *ok = (pnew != NULL) ; /* realloc fails if pnew is NULL */ return ((*ok) ? pnew : p) ; /* return original p if failure */ } SuiteSparse/CXSparse/Source/cs_permute.c0000644001170100242450000000167610712165171017224 0ustar davisfac#include "cs.h" /* C = A(p,q) where p and q are permutations of 0..m-1 and 0..n-1. */ cs *cs_permute (const cs *A, const CS_INT *pinv, const CS_INT *q, CS_INT values) { CS_INT t, j, k, nz = 0, m, n, *Ap, *Ai, *Cp, *Ci ; CS_ENTRY *Cx, *Ax ; cs *C ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; C = cs_spalloc (m, n, Ap [n], values && Ax != NULL, 0) ; /* alloc result */ if (!C) return (cs_done (C, NULL, NULL, 0)) ; /* out of memory */ Cp = C->p ; Ci = C->i ; Cx = C->x ; for (k = 0 ; k < n ; k++) { Cp [k] = nz ; /* column k of C is column q[k] of A */ j = q ? (q [k]) : k ; for (t = Ap [j] ; t < Ap [j+1] ; t++) { if (Cx) Cx [nz] = Ax [t] ; /* row i of A is row pinv[i] of C */ Ci [nz++] = pinv ? (pinv [Ai [t]]) : Ai [t] ; } } Cp [n] = nz ; /* finalize the last column of C */ return (cs_done (C, NULL, NULL, 1)) ; } SuiteSparse/CXSparse/Source/cs_symperm.c0000644001170100242450000000305210712165171017225 0ustar davisfac#include "cs.h" /* C = A(p,p) where A and C are symmetric the upper part stored; pinv not p */ cs *cs_symperm (const cs *A, const CS_INT *pinv, CS_INT values) { CS_INT i, j, p, q, i2, j2, n, *Ap, *Ai, *Cp, *Ci, *w ; CS_ENTRY *Cx, *Ax ; cs *C ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; C = cs_spalloc (n, n, Ap [n], values && (Ax != NULL), 0) ; /* alloc result*/ w = cs_calloc (n, sizeof (CS_INT)) ; /* get workspace */ if (!C || !w) return (cs_done (C, w, NULL, 0)) ; /* out of memory */ Cp = C->p ; Ci = C->i ; Cx = C->x ; for (j = 0 ; j < n ; j++) /* count entries in each column of C */ { j2 = pinv ? pinv [j] : j ; /* column j of A is column j2 of C */ for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; if (i > j) continue ; /* skip lower triangular part of A */ i2 = pinv ? pinv [i] : i ; /* row i of A is row i2 of C */ w [CS_MAX (i2, j2)]++ ; /* column count of C */ } } cs_cumsum (Cp, w, n) ; /* compute column pointers of C */ for (j = 0 ; j < n ; j++) { j2 = pinv ? pinv [j] : j ; /* column j of A is column j2 of C */ for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; if (i > j) continue ; /* skip lower triangular part of A*/ i2 = pinv ? pinv [i] : i ; /* row i of A is row i2 of C */ Ci [q = w [CS_MAX (i2, j2)]++] = CS_MIN (i2, j2) ; if (Cx) Cx [q] = (i2 <= j2) ? Ax [p] : CS_CONJ (Ax [p]) ; } } return (cs_done (C, w, NULL, 1)) ; /* success; free workspace, return C */ } SuiteSparse/CXSparse/Source/cs_lsolve.c0000644001170100242450000000073110712165171017036 0ustar davisfac#include "cs.h" /* solve Lx=b where x and b are dense. x=b on input, solution on output. */ CS_INT cs_lsolve (const cs *L, CS_ENTRY *x) { CS_INT p, j, n, *Lp, *Li ; CS_ENTRY *Lx ; if (!CS_CSC (L) || !x) return (0) ; /* check inputs */ n = L->n ; Lp = L->p ; Li = L->i ; Lx = L->x ; for (j = 0 ; j < n ; j++) { x [j] /= Lx [Lp [j]] ; for (p = Lp [j]+1 ; p < Lp [j+1] ; p++) { x [Li [p]] -= Lx [p] * x [j] ; } } return (1) ; } SuiteSparse/CXSparse/Source/cs_happly.c0000644001170100242450000000107310712165171017027 0ustar davisfac#include "cs.h" /* apply the ith Householder vector to x */ CS_INT cs_happly (const cs *V, CS_INT i, double beta, CS_ENTRY *x) { CS_INT p, *Vp, *Vi ; CS_ENTRY *Vx, tau = 0 ; if (!CS_CSC (V) || !x) return (0) ; /* check inputs */ Vp = V->p ; Vi = V->i ; Vx = V->x ; for (p = Vp [i] ; p < Vp [i+1] ; p++) /* tau = v'*x */ { tau += CS_CONJ (Vx [p]) * x [Vi [p]] ; } tau *= beta ; /* tau = beta*(v'*x) */ for (p = Vp [i] ; p < Vp [i+1] ; p++) /* x = x - v*tau */ { x [Vi [p]] -= Vx [p] * tau ; } return (1) ; } SuiteSparse/CXSparse/Source/cs_utsolve.c0000644001170100242450000000076310712165171017240 0ustar davisfac#include "cs.h" /* solve U'x=b where x and b are dense. x=b on input, solution on output. */ CS_INT cs_utsolve (const cs *U, CS_ENTRY *x) { CS_INT p, j, n, *Up, *Ui ; CS_ENTRY *Ux ; if (!CS_CSC (U) || !x) return (0) ; /* check inputs */ n = U->n ; Up = U->p ; Ui = U->i ; Ux = U->x ; for (j = 0 ; j < n ; j++) { for (p = Up [j] ; p < Up [j+1]-1 ; p++) { x [j] -= CS_CONJ (Ux [p]) * x [Ui [p]] ; } x [j] /= CS_CONJ (Ux [Up [j+1]-1]) ; } return (1) ; } SuiteSparse/CXSparse/Source/cs_ipvec.c0000644001170100242450000000046610712165171016645 0ustar davisfac#include "cs.h" /* x(p) = b, for dense vectors x and b; p=NULL denotes identity */ CS_INT cs_ipvec (const CS_INT *p, const CS_ENTRY *b, CS_ENTRY *x, CS_INT n) { CS_INT k ; if (!x || !b) return (0) ; /* check inputs */ for (k = 0 ; k < n ; k++) x [p ? p [k] : k] = b [k] ; return (1) ; } SuiteSparse/CXSparse/Source/cs_print.c0000644001170100242450000000266310712165171016674 0ustar davisfac#include "cs.h" /* print a sparse matrix */ CS_INT cs_print (const cs *A, CS_INT brief) { CS_INT p, j, m, n, nzmax, nz, *Ap, *Ai ; CS_ENTRY *Ax ; if (!A) { printf ("(null)\n") ; return (0) ; } m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; nzmax = A->nzmax ; nz = A->nz ; printf ("CXSparse Version %d.%d.%d, %s. %s\n", CS_VER, CS_SUBVER, CS_SUBSUB, CS_DATE, CS_COPYRIGHT) ; if (nz < 0) { printf (""CS_ID"-by-"CS_ID", nzmax: "CS_ID" nnz: "CS_ID", 1-norm: %g\n", m, n, nzmax, Ap [n], cs_norm (A)) ; for (j = 0 ; j < n ; j++) { printf (" col "CS_ID" : locations "CS_ID" to "CS_ID"\n", j, Ap [j], Ap [j+1]-1); for (p = Ap [j] ; p < Ap [j+1] ; p++) { #ifdef CS_COMPLEX printf (" "CS_ID" : (%g, %g)\n", Ai [p], Ax ? CS_REAL (Ax [p]) : 1, Ax ? CS_IMAG (Ax [p]) : 0) ; #else printf (" "CS_ID" : %g\n", Ai [p], Ax ? Ax [p] : 1) ; #endif if (brief && p > 20) { printf (" ...\n") ; return (1) ; } } } } else { printf ("triplet: "CS_ID"-by-"CS_ID", nzmax: "CS_ID" nnz: "CS_ID"\n", m, n, nzmax, nz) ; for (p = 0 ; p < nz ; p++) { #ifdef CS_COMPLEX printf (" "CS_ID" "CS_ID" : (%g, %g)\n", Ai [p], Ap [p], Ax ? CS_REAL (Ax [p]) : 1, Ax ? CS_IMAG (Ax [p]) : 0) ; #else printf (" "CS_ID" "CS_ID" : %g\n", Ai [p], Ap [p], Ax ? Ax [p] : 1) ; #endif if (brief && p > 20) { printf (" ...\n") ; return (1) ; } } } return (1) ; } SuiteSparse/CXSparse/Source/cs_scatter.c0000644001170100242450000000141010712165171017172 0ustar davisfac#include "cs.h" /* x = x + beta * A(:,j), where x is a dense vector and A(:,j) is sparse */ CS_INT cs_scatter (const cs *A, CS_INT j, CS_ENTRY beta, CS_INT *w, CS_ENTRY *x, CS_INT mark, cs *C, CS_INT nz) { CS_INT i, p, *Ap, *Ai, *Ci ; CS_ENTRY *Ax ; if (!CS_CSC (A) || !w || !CS_CSC (C)) return (-1) ; /* check inputs */ Ap = A->p ; Ai = A->i ; Ax = A->x ; Ci = C->i ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; /* A(i,j) is nonzero */ if (w [i] < mark) { w [i] = mark ; /* i is new entry in column j */ Ci [nz++] = i ; /* add i to pattern of C(:,j) */ if (x) x [i] = beta * Ax [p] ; /* x(i) = beta*A(i,j) */ } else if (x) x [i] += beta * Ax [p] ; /* i exists in C(:,j) already */ } return (nz) ; } SuiteSparse/CXSparse/Source/cs_counts.c0000644001170100242450000000506710712165171017054 0ustar davisfac#include "cs.h" /* column counts of LL'=A or LL'=A'A, given parent & post ordering */ #define HEAD(k,j) (ata ? head [k] : j) #define NEXT(J) (ata ? next [J] : -1) static void init_ata (cs *AT, const CS_INT *post, CS_INT *w, CS_INT **head, CS_INT **next) { CS_INT i, k, p, m = AT->n, n = AT->m, *ATp = AT->p, *ATi = AT->i ; *head = w+4*n, *next = w+5*n+1 ; for (k = 0 ; k < n ; k++) w [post [k]] = k ; /* invert post */ for (i = 0 ; i < m ; i++) { for (k = n, p = ATp[i] ; p < ATp[i+1] ; p++) k = CS_MIN (k, w [ATi[p]]); (*next) [i] = (*head) [k] ; /* place row i in linked list k */ (*head) [k] = i ; } } CS_INT *cs_counts (const cs *A, const CS_INT *parent, const CS_INT *post, CS_INT ata) { CS_INT i, j, k, n, m, J, s, p, q, jleaf, *ATp, *ATi, *maxfirst, *prevleaf, *ancestor, *head = NULL, *next = NULL, *colcount, *w, *first, *delta ; cs *AT ; if (!CS_CSC (A) || !parent || !post) return (NULL) ; /* check inputs */ m = A->m ; n = A->n ; s = 4*n + (ata ? (n+m+1) : 0) ; delta = colcount = cs_malloc (n, sizeof (CS_INT)) ; /* allocate result */ w = cs_malloc (s, sizeof (CS_INT)) ; /* get workspace */ AT = cs_transpose (A, 0) ; /* AT = A' */ if (!AT || !colcount || !w) return (cs_idone (colcount, AT, w, 0)) ; ancestor = w ; maxfirst = w+n ; prevleaf = w+2*n ; first = w+3*n ; for (k = 0 ; k < s ; k++) w [k] = -1 ; /* clear workspace w [0..s-1] */ for (k = 0 ; k < n ; k++) /* find first [j] */ { j = post [k] ; delta [j] = (first [j] == -1) ? 1 : 0 ; /* delta[j]=1 if j is a leaf */ for ( ; j != -1 && first [j] == -1 ; j = parent [j]) first [j] = k ; } ATp = AT->p ; ATi = AT->i ; if (ata) init_ata (AT, post, w, &head, &next) ; for (i = 0 ; i < n ; i++) ancestor [i] = i ; /* each node in its own set */ for (k = 0 ; k < n ; k++) { j = post [k] ; /* j is the kth node in postordered etree */ if (parent [j] != -1) delta [parent [j]]-- ; /* j is not a root */ for (J = HEAD (k,j) ; J != -1 ; J = NEXT (J)) /* J=j for LL'=A case */ { for (p = ATp [J] ; p < ATp [J+1] ; p++) { i = ATi [p] ; q = cs_leaf (i, j, first, maxfirst, prevleaf, ancestor, &jleaf); if (jleaf >= 1) delta [j]++ ; /* A(i,j) is in skeleton */ if (jleaf == 2) delta [q]-- ; /* account for overlap in q */ } } if (parent [j] != -1) ancestor [j] = parent [j] ; } for (j = 0 ; j < n ; j++) /* sum up delta's of each child */ { if (parent [j] != -1) colcount [parent [j]] += colcount [j] ; } return (cs_idone (colcount, AT, w, 1)) ; /* success: free workspace */ } SuiteSparse/CXSparse/Source/cs_reach.c0000644001170100242450000000123110712165171016610 0ustar davisfac#include "cs.h" /* xi [top...n-1] = nodes reachable from graph of G*P' via nodes in B(:,k). * xi [n...2n-1] used as workspace */ CS_INT cs_reach (cs *G, const cs *B, CS_INT k, CS_INT *xi, const CS_INT *pinv) { CS_INT p, n, top, *Bp, *Bi, *Gp ; if (!CS_CSC (G) || !CS_CSC (B) || !xi) return (-1) ; /* check inputs */ n = G->n ; Bp = B->p ; Bi = B->i ; Gp = G->p ; top = n ; for (p = Bp [k] ; p < Bp [k+1] ; p++) { if (!CS_MARKED (Gp, Bi [p])) /* start a dfs at unmarked node i */ { top = cs_dfs (Bi [p], G, top, xi, xi+n, pinv) ; } } for (p = top ; p < n ; p++) CS_MARK (Gp, xi [p]) ; /* restore G */ return (top) ; } SuiteSparse/CXSparse/Source/cs_dropzeros.c0000644001170100242450000000034410712165171017561 0ustar davisfac#include "cs.h" static CS_INT cs_nonzero (CS_INT i, CS_INT j, CS_ENTRY aij, void *other) { return (aij != 0) ; } CS_INT cs_dropzeros (cs *A) { return (cs_fkeep (A, &cs_nonzero, NULL)) ; /* keep all nonzero entries */ } SuiteSparse/CXSparse/Source/cs_qrsol.c0000644001170100242450000000311510712165171016671 0ustar davisfac#include "cs.h" /* x=A\b where A can be rectangular; b overwritten with solution */ CS_INT cs_qrsol (CS_INT order, const cs *A, CS_ENTRY *b) { CS_ENTRY *x ; css *S ; csn *N ; cs *AT = NULL ; CS_INT k, m, n, ok ; if (!CS_CSC (A) || !b) return (0) ; /* check inputs */ n = A->n ; m = A->m ; if (m >= n) { S = cs_sqr (order, A, 1) ; /* ordering and symbolic analysis */ N = cs_qr (A, S) ; /* numeric QR factorization */ x = cs_calloc (S ? S->m2 : 1, sizeof (CS_ENTRY)) ; /* get workspace */ ok = (S && N && x) ; if (ok) { cs_ipvec (S->pinv, b, x, m) ; /* x(0:m-1) = b(p(0:m-1) */ for (k = 0 ; k < n ; k++) /* apply Householder refl. to x */ { cs_happly (N->L, k, N->B [k], x) ; } cs_usolve (N->U, x) ; /* x = R\x */ cs_ipvec (S->q, x, b, n) ; /* b(q(0:n-1)) = x(0:n-1) */ } } else { AT = cs_transpose (A, 1) ; /* Ax=b is underdetermined */ S = cs_sqr (order, AT, 1) ; /* ordering and symbolic analysis */ N = cs_qr (AT, S) ; /* numeric QR factorization of A' */ x = cs_calloc (S ? S->m2 : 1, sizeof (CS_ENTRY)) ; /* get workspace */ ok = (AT && S && N && x) ; if (ok) { cs_pvec (S->q, b, x, m) ; /* x(q(0:m-1)) = b(0:m-1) */ cs_utsolve (N->U, x) ; /* x = R'\x */ for (k = m-1 ; k >= 0 ; k--) /* apply Householder refl. to x */ { cs_happly (N->L, k, N->B [k], x) ; } cs_pvec (S->pinv, x, b, n) ; /* b(0:n-1) = x(p(0:n-1)) */ } } cs_free (x) ; cs_sfree (S) ; cs_nfree (N) ; cs_spfree (AT) ; return (ok) ; } SuiteSparse/CXSparse/Source/cs_chol.c0000644001170100242450000000473310712165171016465 0ustar davisfac#include "cs.h" /* L = chol (A, [pinv parent cp]), pinv is optional */ csn *cs_chol (const cs *A, const css *S) { CS_ENTRY d, lki, *Lx, *x, *Cx ; CS_INT top, i, p, k, n, *Li, *Lp, *cp, *pinv, *s, *c, *parent, *Cp, *Ci ; cs *L, *C, *E ; csn *N ; if (!CS_CSC (A) || !S || !S->cp || !S->parent) return (NULL) ; n = A->n ; N = cs_calloc (1, sizeof (csn)) ; /* allocate result */ c = cs_malloc (2*n, sizeof (CS_INT)) ; /* get CS_INT workspace */ x = cs_malloc (n, sizeof (CS_ENTRY)) ; /* get CS_ENTRY workspace */ cp = S->cp ; pinv = S->pinv ; parent = S->parent ; C = pinv ? cs_symperm (A, pinv, 1) : ((cs *) A) ; E = pinv ? C : NULL ; /* E is alias for A, or a copy E=A(p,p) */ if (!N || !c || !x || !C) return (cs_ndone (N, E, c, x, 0)) ; s = c + n ; Cp = C->p ; Ci = C->i ; Cx = C->x ; N->L = L = cs_spalloc (n, n, cp [n], 1, 0) ; /* allocate result */ if (!L) return (cs_ndone (N, E, c, x, 0)) ; Lp = L->p ; Li = L->i ; Lx = L->x ; for (k = 0 ; k < n ; k++) Lp [k] = c [k] = cp [k] ; for (k = 0 ; k < n ; k++) /* compute L(:,k) for L*L' = C */ { /* --- Nonzero pattern of L(k,:) ------------------------------------ */ top = cs_ereach (C, k, parent, s, c) ; /* find pattern of L(k,:) */ x [k] = 0 ; /* x (0:k) is now zero */ for (p = Cp [k] ; p < Cp [k+1] ; p++) /* x = full(triu(C(:,k))) */ { if (Ci [p] <= k) x [Ci [p]] = Cx [p] ; } d = x [k] ; /* d = C(k,k) */ x [k] = 0 ; /* clear x for k+1st iteration */ /* --- Triangular solve --------------------------------------------- */ for ( ; top < n ; top++) /* solve L(0:k-1,0:k-1) * x = C(:,k) */ { i = s [top] ; /* s [top..n-1] is pattern of L(k,:) */ lki = x [i] / Lx [Lp [i]] ; /* L(k,i) = x (i) / L(i,i) */ x [i] = 0 ; /* clear x for k+1st iteration */ for (p = Lp [i] + 1 ; p < c [i] ; p++) { x [Li [p]] -= Lx [p] * lki ; } d -= lki * CS_CONJ (lki) ; /* d = d - L(k,i)*L(k,i) */ p = c [i]++ ; Li [p] = k ; /* store L(k,i) in column i */ Lx [p] = CS_CONJ (lki) ; } /* --- Compute L(k,k) ----------------------------------------------- */ if (CS_REAL (d) <= 0 || CS_IMAG (d) != 0) return (cs_ndone (N, E, c, x, 0)) ; /* not pos def */ p = c [k]++ ; Li [p] = k ; /* store L(k,k) = sqrt (d) in column k */ Lx [p] = sqrt (d) ; } Lp [n] = cp [n] ; /* finalize L */ return (cs_ndone (N, E, c, x, 1)) ; /* success: free E,s,x; return N */ } SuiteSparse/CXSparse/Source/cs_dupl.c0000644001170100242450000000201510712165171016473 0ustar davisfac#include "cs.h" /* remove duplicate entries from A */ CS_INT cs_dupl (cs *A) { CS_INT i, j, p, q, nz = 0, n, m, *Ap, *Ai, *w ; CS_ENTRY *Ax ; if (!CS_CSC (A)) return (0) ; /* check inputs */ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; w = cs_malloc (m, sizeof (CS_INT)) ; /* get workspace */ if (!w) return (0) ; /* out of memory */ for (i = 0 ; i < m ; i++) w [i] = -1 ; /* row i not yet seen */ for (j = 0 ; j < n ; j++) { q = nz ; /* column j will start at q */ for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; /* A(i,j) is nonzero */ if (w [i] >= q) { Ax [w [i]] += Ax [p] ; /* A(i,j) is a duplicate */ } else { w [i] = nz ; /* record where row i occurs */ Ai [nz] = i ; /* keep A(i,j) */ Ax [nz++] = Ax [p] ; } } Ap [j] = q ; /* record start of column j */ } Ap [n] = nz ; /* finalize A */ cs_free (w) ; /* free workspace */ return (cs_sprealloc (A, 0)) ; /* remove extra space from A */ } SuiteSparse/CXSparse/Source/cs_schol.c0000644001170100242450000000213710712165171016644 0ustar davisfac#include "cs.h" /* ordering and symbolic analysis for a Cholesky factorization */ css *cs_schol (CS_INT order, const cs *A) { CS_INT n, *c, *post, *P ; cs *C ; css *S ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ n = A->n ; S = cs_calloc (1, sizeof (css)) ; /* allocate result S */ if (!S) return (NULL) ; /* out of memory */ P = cs_amd (order, A) ; /* P = amd(A+A'), or natural */ S->pinv = cs_pinv (P, n) ; /* find inverse permutation */ cs_free (P) ; if (order && !S->pinv) return (cs_sfree (S)) ; C = cs_symperm (A, S->pinv, 0) ; /* C = spones(triu(A(P,P))) */ S->parent = cs_etree (C, 0) ; /* find etree of C */ post = cs_post (S->parent, n) ; /* postorder the etree */ c = cs_counts (C, S->parent, post, 0) ; /* find column counts of chol(C) */ cs_free (post) ; cs_spfree (C) ; S->cp = cs_malloc (n+1, sizeof (CS_INT)) ; /* allocate result S->cp */ S->unz = S->lnz = cs_cumsum (S->cp, c, n) ; /* find column pointers for L */ cs_free (c) ; return ((S->lnz >= 0) ? S : cs_sfree (S)) ; } SuiteSparse/CXSparse/Source/cs_leaf.c0000644001170100242450000000175510712165171016450 0ustar davisfac#include "cs.h" /* consider A(i,j), node j in ith row subtree and return lca(jprev,j) */ CS_INT cs_leaf (CS_INT i, CS_INT j, const CS_INT *first, CS_INT *maxfirst, CS_INT *prevleaf, CS_INT *ancestor, CS_INT *jleaf) { CS_INT q, s, sparent, jprev ; if (!first || !maxfirst || !prevleaf || !ancestor || !jleaf) return (-1) ; *jleaf = 0 ; if (i <= j || first [j] <= maxfirst [i]) return (-1) ; /* j not a leaf */ maxfirst [i] = first [j] ; /* update max first[j] seen so far */ jprev = prevleaf [i] ; /* jprev = previous leaf of ith subtree */ prevleaf [i] = j ; *jleaf = (jprev == -1) ? 1: 2 ; /* j is first or subsequent leaf */ if (*jleaf == 1) return (i) ; /* if 1st leaf, q = root of ith subtree */ for (q = jprev ; q != ancestor [q] ; q = ancestor [q]) ; for (s = jprev ; s != q ; s = sparent) { sparent = ancestor [s] ; /* path compression */ ancestor [s] = q ; } return (q) ; /* q = least common ancester (jprev,j) */ } SuiteSparse/CXSparse/Source/cs_dmperm.c0000644001170100242450000001337310712165171017024 0ustar davisfac#include "cs.h" /* breadth-first search for coarse decomposition (C0,C1,R1 or R0,R3,C3) */ static CS_INT cs_bfs (const cs *A, CS_INT n, CS_INT *wi, CS_INT *wj, CS_INT *queue, const CS_INT *imatch, const CS_INT *jmatch, CS_INT mark) { CS_INT *Ap, *Ai, head = 0, tail = 0, j, i, p, j2 ; cs *C ; for (j = 0 ; j < n ; j++) /* place all unmatched nodes in queue */ { if (imatch [j] >= 0) continue ; /* skip j if matched */ wj [j] = 0 ; /* j in set C0 (R0 if transpose) */ queue [tail++] = j ; /* place unmatched col j in queue */ } if (tail == 0) return (1) ; /* quick return if no unmatched nodes */ C = (mark == 1) ? ((cs *) A) : cs_transpose (A, 0) ; if (!C) return (0) ; /* bfs of C=A' to find R3,C3 from R0 */ Ap = C->p ; Ai = C->i ; while (head < tail) /* while queue is not empty */ { j = queue [head++] ; /* get the head of the queue */ for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; if (wi [i] >= 0) continue ; /* skip if i is marked */ wi [i] = mark ; /* i in set R1 (C3 if transpose) */ j2 = jmatch [i] ; /* traverse alternating path to j2 */ if (wj [j2] >= 0) continue ;/* skip j2 if it is marked */ wj [j2] = mark ; /* j2 in set C1 (R3 if transpose) */ queue [tail++] = j2 ; /* add j2 to queue */ } } if (mark != 1) cs_spfree (C) ; /* free A' if it was created */ return (1) ; } /* collect matched rows and columns into p and q */ static void cs_matched (CS_INT n, const CS_INT *wj, const CS_INT *imatch, CS_INT *p, CS_INT *q, CS_INT *cc, CS_INT *rr, CS_INT set, CS_INT mark) { CS_INT kc = cc [set], j ; CS_INT kr = rr [set-1] ; for (j = 0 ; j < n ; j++) { if (wj [j] != mark) continue ; /* skip if j is not in C set */ p [kr++] = imatch [j] ; q [kc++] = j ; } cc [set+1] = kc ; rr [set] = kr ; } /* collect unmatched rows into the permutation vector p */ static void cs_unmatched (CS_INT m, const CS_INT *wi, CS_INT *p, CS_INT *rr, CS_INT set) { CS_INT i, kr = rr [set] ; for (i = 0 ; i < m ; i++) if (wi [i] == 0) p [kr++] = i ; rr [set+1] = kr ; } /* return 1 if row i is in R2 */ static CS_INT cs_rprune (CS_INT i, CS_INT j, CS_ENTRY aij, void *other) { CS_INT *rr = (CS_INT *) other ; return (i >= rr [1] && i < rr [2]) ; } /* Given A, compute coarse and then fine dmperm */ csd *cs_dmperm (const cs *A, CS_INT seed) { CS_INT m, n, i, j, k, cnz, nc, *jmatch, *imatch, *wi, *wj, *pinv, *Cp, *Ci, *ps, *rs, nb1, nb2, *p, *q, *cc, *rr, *r, *s, ok ; cs *C ; csd *D, *scc ; /* --- Maximum matching ------------------------------------------------- */ if (!CS_CSC (A)) return (NULL) ; /* check inputs */ m = A->m ; n = A->n ; D = cs_dalloc (m, n) ; /* allocate result */ if (!D) return (NULL) ; p = D->p ; q = D->q ; r = D->r ; s = D->s ; cc = D->cc ; rr = D->rr ; jmatch = cs_maxtrans (A, seed) ; /* max transversal */ imatch = jmatch + m ; /* imatch = inverse of jmatch */ if (!jmatch) return (cs_ddone (D, NULL, jmatch, 0)) ; /* --- Coarse decomposition --------------------------------------------- */ wi = r ; wj = s ; /* use r and s as workspace */ for (j = 0 ; j < n ; j++) wj [j] = -1 ; /* unmark all cols for bfs */ for (i = 0 ; i < m ; i++) wi [i] = -1 ; /* unmark all rows for bfs */ cs_bfs (A, n, wi, wj, q, imatch, jmatch, 1) ; /* find C1, R1 from C0*/ ok = cs_bfs (A, m, wj, wi, p, jmatch, imatch, 3) ; /* find R3, C3 from R0*/ if (!ok) return (cs_ddone (D, NULL, jmatch, 0)) ; cs_unmatched (n, wj, q, cc, 0) ; /* unmatched set C0 */ cs_matched (n, wj, imatch, p, q, cc, rr, 1, 1) ; /* set R1 and C1 */ cs_matched (n, wj, imatch, p, q, cc, rr, 2, -1) ; /* set R2 and C2 */ cs_matched (n, wj, imatch, p, q, cc, rr, 3, 3) ; /* set R3 and C3 */ cs_unmatched (m, wi, p, rr, 3) ; /* unmatched set R0 */ cs_free (jmatch) ; /* --- Fine decomposition ----------------------------------------------- */ pinv = cs_pinv (p, m) ; /* pinv=p' */ if (!pinv) return (cs_ddone (D, NULL, NULL, 0)) ; C = cs_permute (A, pinv, q, 0) ;/* C=A(p,q) (it will hold A(R2,C2)) */ cs_free (pinv) ; if (!C) return (cs_ddone (D, NULL, NULL, 0)) ; Cp = C->p ; nc = cc [3] - cc [2] ; /* delete cols C0, C1, and C3 from C */ if (cc [2] > 0) for (j = cc [2] ; j <= cc [3] ; j++) Cp [j-cc[2]] = Cp [j] ; C->n = nc ; if (rr [2] - rr [1] < m) /* delete rows R0, R1, and R3 from C */ { cs_fkeep (C, cs_rprune, rr) ; cnz = Cp [nc] ; Ci = C->i ; if (rr [1] > 0) for (k = 0 ; k < cnz ; k++) Ci [k] -= rr [1] ; } C->m = nc ; scc = cs_scc (C) ; /* find strongly connected components of C*/ if (!scc) return (cs_ddone (D, C, NULL, 0)) ; /* --- Combine coarse and fine decompositions --------------------------- */ ps = scc->p ; /* C(ps,ps) is the permuted matrix */ rs = scc->r ; /* kth block is rs[k]..rs[k+1]-1 */ nb1 = scc->nb ; /* # of blocks of A(R2,C2) */ for (k = 0 ; k < nc ; k++) wj [k] = q [ps [k] + cc [2]] ; for (k = 0 ; k < nc ; k++) q [k + cc [2]] = wj [k] ; for (k = 0 ; k < nc ; k++) wi [k] = p [ps [k] + rr [1]] ; for (k = 0 ; k < nc ; k++) p [k + rr [1]] = wi [k] ; nb2 = 0 ; /* create the fine block partitions */ r [0] = s [0] = 0 ; if (cc [2] > 0) nb2++ ; /* leading coarse block A (R1, [C0 C1]) */ for (k = 0 ; k < nb1 ; k++) /* coarse block A (R2,C2) */ { r [nb2] = rs [k] + rr [1] ; /* A (R2,C2) splits into nb1 fine blocks */ s [nb2] = rs [k] + cc [2] ; nb2++ ; } if (rr [2] < m) { r [nb2] = rr [2] ; /* trailing coarse block A ([R3 R0], C3) */ s [nb2] = cc [3] ; nb2++ ; } r [nb2] = m ; s [nb2] = n ; D->nb = nb2 ; cs_dfree (scc) ; return (cs_ddone (D, C, NULL, 1)) ; } SuiteSparse/CXSparse/Source/cs_load.c0000644001170100242450000000116010712165171016446 0ustar davisfac#include "cs.h" /* load a triplet matrix from a file */ cs *cs_load (FILE *f) { CS_INT i, j ; double x ; #ifdef CS_COMPLEX double xi ; #endif cs *T ; if (!f) return (NULL) ; /* check inputs */ T = cs_spalloc (0, 0, 1, 1, 1) ; /* allocate result */ #ifdef CS_COMPLEX while (fscanf (f, ""CS_ID" "CS_ID" %lg %lg\n", &i, &j, &x, &xi) == 4) #else while (fscanf (f, ""CS_ID" "CS_ID" %lg\n", &i, &j, &x) == 3) #endif { #ifdef CS_COMPLEX if (!cs_entry (T, i, j, x + xi*I)) return (cs_spfree (T)) ; #else if (!cs_entry (T, i, j, x)) return (cs_spfree (T)) ; #endif } return (T) ; } SuiteSparse/CXSparse/Source/README.txt0000644001170100242450000000023710375603427016406 0ustar davisfacCXSparse/Source directory: primary ANSI C source code files for CXSparse. To compile the libcxsparse.a C-callable library, just type "make" in this directory. SuiteSparse/CXSparse/Source/cs_norm.c0000644001170100242450000000070610712165171016507 0ustar davisfac#include "cs.h" /* 1-norm of a sparse matrix = max (sum (abs (A))), largest column sum */ double cs_norm (const cs *A) { CS_INT p, j, n, *Ap ; CS_ENTRY *Ax ; double norm = 0, s ; if (!CS_CSC (A) || !A->x) return (-1) ; /* check inputs */ n = A->n ; Ap = A->p ; Ax = A->x ; for (j = 0 ; j < n ; j++) { for (s = 0, p = Ap [j] ; p < Ap [j+1] ; p++) s += CS_ABS (Ax [p]) ; norm = CS_MAX (norm, s) ; } return (norm) ; } SuiteSparse/CXSparse/Source/cs_randperm.c0000644001170100242450000000146110712165171017343 0ustar davisfac#include "cs.h" /* return a random permutation vector, the identity perm, or p = n-1:-1:0. * seed = -1 means p = n-1:-1:0. seed = 0 means p = identity. otherwise * p = random permutation. */ CS_INT *cs_randperm (CS_INT n, CS_INT seed) { CS_INT *p, k, j, t ; if (seed == 0) return (NULL) ; /* return p = NULL (identity) */ p = cs_malloc (n, sizeof (CS_INT)) ; /* allocate result */ if (!p) return (NULL) ; /* out of memory */ for (k = 0 ; k < n ; k++) p [k] = n-k-1 ; if (seed == -1) return (p) ; /* return reverse permutation */ srand (seed) ; /* get new random number seed */ for (k = 0 ; k < n ; k++) { j = k + (rand ( ) % (n-k)) ; /* j = rand CS_INT in range k to n-1 */ t = p [j] ; /* swap p[k] and p[j] */ p [j] = p [k] ; p [k] = t ; } return (p) ; } SuiteSparse/CXSparse/Source/cs_pinv.c0000644001170100242450000000064110712165171016506 0ustar davisfac#include "cs.h" /* pinv = p', or p = pinv' */ CS_INT *cs_pinv (CS_INT const *p, CS_INT n) { CS_INT k, *pinv ; if (!p) return (NULL) ; /* p = NULL denotes identity */ pinv = cs_malloc (n, sizeof (CS_INT)) ; /* allocate result */ if (!pinv) return (NULL) ; /* out of memory */ for (k = 0 ; k < n ; k++) pinv [p [k]] = k ;/* invert the permutation */ return (pinv) ; /* return result */ } SuiteSparse/CXSparse/Source/cs_post.c0000644001170100242450000000173610712165171016525 0ustar davisfac#include "cs.h" /* post order a forest */ CS_INT *cs_post (const CS_INT *parent, CS_INT n) { CS_INT j, k = 0, *post, *w, *head, *next, *stack ; if (!parent) return (NULL) ; /* check inputs */ post = cs_malloc (n, sizeof (CS_INT)) ; /* allocate result */ w = cs_malloc (3*n, sizeof (CS_INT)) ; /* get workspace */ if (!w || !post) return (cs_idone (post, NULL, w, 0)) ; head = w ; next = w + n ; stack = w + 2*n ; for (j = 0 ; j < n ; j++) head [j] = -1 ; /* empty linked lists */ for (j = n-1 ; j >= 0 ; j--) /* traverse nodes in reverse order*/ { if (parent [j] == -1) continue ; /* j is a root */ next [j] = head [parent [j]] ; /* add j to list of its parent */ head [parent [j]] = j ; } for (j = 0 ; j < n ; j++) { if (parent [j] != -1) continue ; /* skip j if it is not a root */ k = cs_tdfs (j, k, head, next, post, stack) ; } return (cs_idone (post, NULL, w, 1)) ; /* success; free w, return post */ } SuiteSparse/CXSparse/Source/cs_pvec.c0000644001170100242450000000046510712165171016473 0ustar davisfac#include "cs.h" /* x = b(p), for dense vectors x and b; p=NULL denotes identity */ CS_INT cs_pvec (const CS_INT *p, const CS_ENTRY *b, CS_ENTRY *x, CS_INT n) { CS_INT k ; if (!x || !b) return (0) ; /* check inputs */ for (k = 0 ; k < n ; k++) x [k] = b [p ? p [k] : k] ; return (1) ; } SuiteSparse/CXSparse/Source/cs_entry.c0000644001170100242450000000071310712165171016673 0ustar davisfac#include "cs.h" /* add an entry to a triplet matrix; return 1 if ok, 0 otherwise */ CS_INT cs_entry (cs *T, CS_INT i, CS_INT j, CS_ENTRY x) { if (!CS_TRIPLET (T) || i < 0 || j < 0) return (0) ; /* check inputs */ if (T->nz >= T->nzmax && !cs_sprealloc (T,2*(T->nzmax))) return (0) ; if (T->x) T->x [T->nz] = x ; T->i [T->nz] = i ; T->p [T->nz++] = j ; T->m = CS_MAX (T->m, i+1) ; T->n = CS_MAX (T->n, j+1) ; return (1) ; } SuiteSparse/CXSparse/Source/cs_tdfs.c0000644001170100242450000000145010712165171016471 0ustar davisfac#include "cs.h" /* depth-first search and postorder of a tree rooted at node j */ CS_INT cs_tdfs (CS_INT j, CS_INT k, CS_INT *head, const CS_INT *next, CS_INT *post, CS_INT *stack) { CS_INT i, p, top = 0 ; if (!head || !next || !post || !stack) return (-1) ; /* check inputs */ stack [0] = j ; /* place j on the stack */ while (top >= 0) /* while (stack is not empty) */ { p = stack [top] ; /* p = top of stack */ i = head [p] ; /* i = youngest child of p */ if (i == -1) { top-- ; /* p has no unordered children left */ post [k++] = p ; /* node p is the kth postordered node */ } else { head [p] = next [i] ; /* remove i from children of p */ stack [++top] = i ; /* start dfs on child node i */ } } return (k) ; } SuiteSparse/CXSparse/Source/cs_usolve.c0000644001170100242450000000074010712165171017047 0ustar davisfac#include "cs.h" /* solve Ux=b where x and b are dense. x=b on input, solution on output. */ CS_INT cs_usolve (const cs *U, CS_ENTRY *x) { CS_INT p, j, n, *Up, *Ui ; CS_ENTRY *Ux ; if (!CS_CSC (U) || !x) return (0) ; /* check inputs */ n = U->n ; Up = U->p ; Ui = U->i ; Ux = U->x ; for (j = n-1 ; j >= 0 ; j--) { x [j] /= Ux [Up [j+1]-1] ; for (p = Up [j] ; p < Up [j+1]-1 ; p++) { x [Ui [p]] -= Ux [p] * x [j] ; } } return (1) ; } SuiteSparse/CXSparse/Source/cs_util.c0000644001170100242450000000745410712165171016520 0ustar davisfac#include "cs.h" /* allocate a sparse matrix (triplet form or compressed-column form) */ cs *cs_spalloc (CS_INT m, CS_INT n, CS_INT nzmax, CS_INT values, CS_INT triplet) { cs *A = cs_calloc (1, sizeof (cs)) ; /* allocate the cs struct */ if (!A) return (NULL) ; /* out of memory */ A->m = m ; /* define dimensions and nzmax */ A->n = n ; A->nzmax = nzmax = CS_MAX (nzmax, 1) ; A->nz = triplet ? 0 : -1 ; /* allocate triplet or comp.col */ A->p = cs_malloc (triplet ? nzmax : n+1, sizeof (CS_INT)) ; A->i = cs_malloc (nzmax, sizeof (CS_INT)) ; A->x = values ? cs_malloc (nzmax, sizeof (CS_ENTRY)) : NULL ; return ((!A->p || !A->i || (values && !A->x)) ? cs_spfree (A) : A) ; } /* change the max # of entries sparse matrix */ CS_INT cs_sprealloc (cs *A, CS_INT nzmax) { CS_INT ok, oki, okj = 1, okx = 1 ; if (!A) return (0) ; if (nzmax <= 0) nzmax = (CS_CSC (A)) ? (A->p [A->n]) : A->nz ; A->i = cs_realloc (A->i, nzmax, sizeof (CS_INT), &oki) ; if (CS_TRIPLET (A)) A->p = cs_realloc (A->p, nzmax, sizeof (CS_INT), &okj) ; if (A->x) A->x = cs_realloc (A->x, nzmax, sizeof (CS_ENTRY), &okx) ; ok = (oki && okj && okx) ; if (ok) A->nzmax = nzmax ; return (ok) ; } /* free a sparse matrix */ cs *cs_spfree (cs *A) { if (!A) return (NULL) ; /* do nothing if A already NULL */ cs_free (A->p) ; cs_free (A->i) ; cs_free (A->x) ; return (cs_free (A)) ; /* free the cs struct and return NULL */ } /* free a numeric factorization */ csn *cs_nfree (csn *N) { if (!N) return (NULL) ; /* do nothing if N already NULL */ cs_spfree (N->L) ; cs_spfree (N->U) ; cs_free (N->pinv) ; cs_free (N->B) ; return (cs_free (N)) ; /* free the csn struct and return NULL */ } /* free a symbolic factorization */ css *cs_sfree (css *S) { if (!S) return (NULL) ; /* do nothing if S already NULL */ cs_free (S->pinv) ; cs_free (S->q) ; cs_free (S->parent) ; cs_free (S->cp) ; cs_free (S->leftmost) ; return (cs_free (S)) ; /* free the css struct and return NULL */ } /* allocate a cs_dmperm or cs_scc result */ csd *cs_dalloc (CS_INT m, CS_INT n) { csd *D ; D = cs_calloc (1, sizeof (csd)) ; if (!D) return (NULL) ; D->p = cs_malloc (m, sizeof (CS_INT)) ; D->r = cs_malloc (m+6, sizeof (CS_INT)) ; D->q = cs_malloc (n, sizeof (CS_INT)) ; D->s = cs_malloc (n+6, sizeof (CS_INT)) ; return ((!D->p || !D->r || !D->q || !D->s) ? cs_dfree (D) : D) ; } /* free a cs_dmperm or cs_scc result */ csd *cs_dfree (csd *D) { if (!D) return (NULL) ; /* do nothing if D already NULL */ cs_free (D->p) ; cs_free (D->q) ; cs_free (D->r) ; cs_free (D->s) ; return (cs_free (D)) ; } /* free workspace and return a sparse matrix result */ cs *cs_done (cs *C, void *w, void *x, CS_INT ok) { cs_free (w) ; /* free workspace */ cs_free (x) ; return (ok ? C : cs_spfree (C)) ; /* return result if OK, else free it */ } /* free workspace and return CS_INT array result */ CS_INT *cs_idone (CS_INT *p, cs *C, void *w, CS_INT ok) { cs_spfree (C) ; /* free temporary matrix */ cs_free (w) ; /* free workspace */ return (ok ? p : cs_free (p)) ; /* return result if OK, else free it */ } /* free workspace and return a numeric factorization (Cholesky, LU, or QR) */ csn *cs_ndone (csn *N, cs *C, void *w, void *x, CS_INT ok) { cs_spfree (C) ; /* free temporary matrix */ cs_free (w) ; /* free workspace */ cs_free (x) ; return (ok ? N : cs_nfree (N)) ; /* return result if OK, else free it */ } /* free workspace and return a csd result */ csd *cs_ddone (csd *D, cs *C, void *w, CS_INT ok) { cs_spfree (C) ; /* free temporary matrix */ cs_free (w) ; /* free workspace */ return (ok ? D : cs_dfree (D)) ; /* return result if OK, else free it */ } SuiteSparse/CXSparse/Source/cs_maxtrans.c0000644001170100242450000000753410712165171017377 0ustar davisfac#include "cs.h" /* find an augmenting path starting at column k and extend the match if found */ static void cs_augment (CS_INT k, const cs *A, CS_INT *jmatch, CS_INT *cheap, CS_INT *w, CS_INT *js, CS_INT *is, CS_INT *ps) { CS_INT found = 0, p, i = -1, *Ap = A->p, *Ai = A->i, head = 0, j ; js [0] = k ; /* start with just node k in jstack */ while (head >= 0) { /* --- Start (or continue) depth-first-search at node j ------------- */ j = js [head] ; /* get j from top of jstack */ if (w [j] != k) /* 1st time j visited for kth path */ { w [j] = k ; /* mark j as visited for kth path */ for (p = cheap [j] ; p < Ap [j+1] && !found ; p++) { i = Ai [p] ; /* try a cheap assignment (i,j) */ found = (jmatch [i] == -1) ; } cheap [j] = p ; /* start here next time j is traversed*/ if (found) { is [head] = i ; /* column j matched with row i */ break ; /* end of augmenting path */ } ps [head] = Ap [j] ; /* no cheap match: start dfs for j */ } /* --- Depth-first-search of neighbors of j ------------------------- */ for (p = ps [head] ; p < Ap [j+1] ; p++) { i = Ai [p] ; /* consider row i */ if (w [jmatch [i]] == k) continue ; /* skip jmatch [i] if marked */ ps [head] = p + 1 ; /* pause dfs of node j */ is [head] = i ; /* i will be matched with j if found */ js [++head] = jmatch [i] ; /* start dfs at column jmatch [i] */ break ; } if (p == Ap [j+1]) head-- ; /* node j is done; pop from stack */ } /* augment the match if path found: */ if (found) for (p = head ; p >= 0 ; p--) jmatch [is [p]] = js [p] ; } /* find a maximum transveral */ CS_INT *cs_maxtrans (const cs *A, CS_INT seed) /*[jmatch [0..m-1]; imatch [0..n-1]]*/ { CS_INT i, j, k, n, m, p, n2 = 0, m2 = 0, *Ap, *jimatch, *w, *cheap, *js, *is, *ps, *Ai, *Cp, *jmatch, *imatch, *q ; cs *C ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ n = A->n ; m = A->m ; Ap = A->p ; Ai = A->i ; w = jimatch = cs_calloc (m+n, sizeof (CS_INT)) ; /* allocate result */ if (!jimatch) return (NULL) ; for (k = 0, j = 0 ; j < n ; j++) /* count nonempty rows and columns */ { n2 += (Ap [j] < Ap [j+1]) ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { w [Ai [p]] = 1 ; k += (j == Ai [p]) ; /* count entries already on diagonal */ } } if (k == CS_MIN (m,n)) /* quick return if diagonal zero-free */ { jmatch = jimatch ; imatch = jimatch + m ; for (i = 0 ; i < k ; i++) jmatch [i] = i ; for ( ; i < m ; i++) jmatch [i] = -1 ; for (j = 0 ; j < k ; j++) imatch [j] = j ; for ( ; j < n ; j++) imatch [j] = -1 ; return (cs_idone (jimatch, NULL, NULL, 1)) ; } for (i = 0 ; i < m ; i++) m2 += w [i] ; C = (m2 < n2) ? cs_transpose (A,0) : ((cs *) A) ; /* transpose if needed */ if (!C) return (cs_idone (jimatch, (m2 < n2) ? C : NULL, NULL, 0)) ; n = C->n ; m = C->m ; Cp = C->p ; jmatch = (m2 < n2) ? jimatch + n : jimatch ; imatch = (m2 < n2) ? jimatch : jimatch + m ; w = cs_malloc (5*n, sizeof (CS_INT)) ; /* get workspace */ if (!w) return (cs_idone (jimatch, (m2 < n2) ? C : NULL, w, 0)) ; cheap = w + n ; js = w + 2*n ; is = w + 3*n ; ps = w + 4*n ; for (j = 0 ; j < n ; j++) cheap [j] = Cp [j] ; /* for cheap assignment */ for (j = 0 ; j < n ; j++) w [j] = -1 ; /* all columns unflagged */ for (i = 0 ; i < m ; i++) jmatch [i] = -1 ; /* nothing matched yet */ q = cs_randperm (n, seed) ; /* q = random permutation */ for (k = 0 ; k < n ; k++) /* augment, starting at column q[k] */ { cs_augment (q ? q [k]: k, C, jmatch, cheap, w, js, is, ps) ; } cs_free (q) ; for (j = 0 ; j < n ; j++) imatch [j] = -1 ; /* find row match */ for (i = 0 ; i < m ; i++) if (jmatch [i] >= 0) imatch [jmatch [i]] = i ; return (cs_idone (jimatch, (m2 < n2) ? C : NULL, w, 1)) ; } SuiteSparse/CXSparse/Source/cs_spsolve.c0000644001170100242450000000230210712165171017221 0ustar davisfac#include "cs.h" /* solve Gx=b(:,k), where G is either upper (lo=0) or lower (lo=1) triangular */ CS_INT cs_spsolve (cs *G, const cs *B, CS_INT k, CS_INT *xi, CS_ENTRY *x, const CS_INT *pinv, CS_INT lo) { CS_INT j, J, p, q, px, top, n, *Gp, *Gi, *Bp, *Bi ; CS_ENTRY *Gx, *Bx ; if (!CS_CSC (G) || !CS_CSC (B) || !xi || !x) return (-1) ; Gp = G->p ; Gi = G->i ; Gx = G->x ; n = G->n ; Bp = B->p ; Bi = B->i ; Bx = B->x ; top = cs_reach (G, B, k, xi, pinv) ; /* xi[top..n-1]=Reach(B(:,k)) */ for (p = top ; p < n ; p++) x [xi [p]] = 0 ; /* clear x */ for (p = Bp [k] ; p < Bp [k+1] ; p++) x [Bi [p]] = Bx [p] ; /* scatter B */ for (px = top ; px < n ; px++) { j = xi [px] ; /* x(j) is nonzero */ J = pinv ? (pinv [j]) : j ; /* j maps to col J of G */ if (J < 0) continue ; /* column J is empty */ x [j] /= Gx [lo ? (Gp [J]) : (Gp [J+1]-1)] ;/* x(j) /= G(j,j) */ p = lo ? (Gp [J]+1) : (Gp [J]) ; /* lo: L(j,j) 1st entry */ q = lo ? (Gp [J+1]) : (Gp [J+1]-1) ; /* up: U(j,j) last entry */ for ( ; p < q ; p++) { x [Gi [p]] -= Gx [p] * x [j] ; /* x(i) -= G(i,j) * x(j) */ } } return (top) ; /* return top of stack */ } SuiteSparse/CXSparse/Source/cs_droptol.c0000644001170100242450000000037410712165171017220 0ustar davisfac#include "cs.h" static CS_INT cs_tol (CS_INT i, CS_INT j, CS_ENTRY aij, void *tol) { return (CS_ABS (aij) > *((double *) tol)) ; } CS_INT cs_droptol (cs *A, double tol) { return (cs_fkeep (A, &cs_tol, &tol)) ; /* keep all large entries */ } SuiteSparse/CXSparse/Source/cs_etree.c0000644001170100242450000000226210712165171016637 0ustar davisfac#include "cs.h" /* compute the etree of A (using triu(A), or A'A without forming A'A */ CS_INT *cs_etree (const cs *A, CS_INT ata) { CS_INT i, k, p, m, n, inext, *Ap, *Ai, *w, *parent, *ancestor, *prev ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; parent = cs_malloc (n, sizeof (CS_INT)) ; /* allocate result */ w = cs_malloc (n + (ata ? m : 0), sizeof (CS_INT)) ; /* get workspace */ if (!w || !parent) return (cs_idone (parent, NULL, w, 0)) ; ancestor = w ; prev = w + n ; if (ata) for (i = 0 ; i < m ; i++) prev [i] = -1 ; for (k = 0 ; k < n ; k++) { parent [k] = -1 ; /* node k has no parent yet */ ancestor [k] = -1 ; /* nor does k have an ancestor */ for (p = Ap [k] ; p < Ap [k+1] ; p++) { i = ata ? (prev [Ai [p]]) : (Ai [p]) ; for ( ; i != -1 && i < k ; i = inext) /* traverse from i to k */ { inext = ancestor [i] ; /* inext = ancestor of i */ ancestor [i] = k ; /* path compression */ if (inext == -1) parent [i] = k ; /* no anc., parent is k */ } if (ata) prev [Ai [p]] = k ; } } return (cs_idone (parent, NULL, w, 1)) ; } SuiteSparse/CXSparse/Source/cs_fkeep.c0000644001170100242450000000145010712165171016623 0ustar davisfac#include "cs.h" /* drop entries for which fkeep(A(i,j)) is false; return nz if OK, else -1 */ CS_INT cs_fkeep (cs *A, CS_INT (*fkeep) (CS_INT, CS_INT, CS_ENTRY, void *), void *other) { CS_INT j, p, nz = 0, n, *Ap, *Ai ; CS_ENTRY *Ax ; if (!CS_CSC (A) || !fkeep) return (-1) ; /* check inputs */ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; for (j = 0 ; j < n ; j++) { p = Ap [j] ; /* get current location of col j */ Ap [j] = nz ; /* record new location of col j */ for ( ; p < Ap [j+1] ; p++) { if (fkeep (Ai [p], j, Ax ? Ax [p] : 1, other)) { if (Ax) Ax [nz] = Ax [p] ; /* keep A(i,j) */ Ai [nz++] = Ai [p] ; } } } Ap [n] = nz ; /* finalize A */ cs_sprealloc (A, 0) ; /* remove extra space from A */ return (nz) ; } SuiteSparse/CXSparse/Source/cs_lusol.c0000644001170100242450000000144110712165171016667 0ustar davisfac#include "cs.h" /* x=A\b where A is unsymmetric; b overwritten with solution */ CS_INT cs_lusol (CS_INT order, const cs *A, CS_ENTRY *b, double tol) { CS_ENTRY *x ; css *S ; csn *N ; CS_INT n, ok ; if (!CS_CSC (A) || !b) return (0) ; /* check inputs */ n = A->n ; S = cs_sqr (order, A, 0) ; /* ordering and symbolic analysis */ N = cs_lu (A, S, tol) ; /* numeric LU factorization */ x = cs_malloc (n, sizeof (CS_ENTRY)) ; /* get workspace */ ok = (S && N && x) ; if (ok) { cs_ipvec (N->pinv, b, x, n) ; /* x = b(p) */ cs_lsolve (N->L, x) ; /* x = L\x */ cs_usolve (N->U, x) ; /* x = U\x */ cs_ipvec (S->q, x, b, n) ; /* b(q) = x */ } cs_free (x) ; cs_sfree (S) ; cs_nfree (N) ; return (ok) ; } SuiteSparse/CXSparse/Source/cs_ereach.c0000644001170100242450000000176010712165171016764 0ustar davisfac#include "cs.h" /* find nonzero pattern of Cholesky L(k,1:k-1) using etree and triu(A(:,k)) */ CS_INT cs_ereach (const cs *A, CS_INT k, const CS_INT *parent, CS_INT *s, CS_INT *w) { CS_INT i, p, n, len, top, *Ap, *Ai ; if (!CS_CSC (A) || !parent || !s || !w) return (-1) ; /* check inputs */ top = n = A->n ; Ap = A->p ; Ai = A->i ; CS_MARK (w, k) ; /* mark node k as visited */ for (p = Ap [k] ; p < Ap [k+1] ; p++) { i = Ai [p] ; /* A(i,k) is nonzero */ if (i > k) continue ; /* only use upper triangular part of A */ for (len = 0 ; !CS_MARKED (w,i) ; i = parent [i]) /* traverse up etree*/ { s [len++] = i ; /* L(k,i) is nonzero */ CS_MARK (w, i) ; /* mark i as visited */ } while (len > 0) s [--top] = s [--len] ; /* push path onto stack */ } for (p = top ; p < n ; p++) CS_MARK (w, s [p]) ; /* unmark all nodes */ CS_MARK (w, k) ; /* unmark node k */ return (top) ; /* s [top..n-1] contains pattern of L(k,:)*/ } SuiteSparse/CXSparse/Source/cs_gaxpy.c0000644001170100242450000000063010712165171016660 0ustar davisfac#include "cs.h" /* y = A*x+y */ CS_INT cs_gaxpy (const cs *A, const CS_ENTRY *x, CS_ENTRY *y) { CS_INT p, j, n, *Ap, *Ai ; CS_ENTRY *Ax ; if (!CS_CSC (A) || !x || !y) return (0) ; /* check inputs */ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { y [Ai [p]] += Ax [p] * x [j] ; } } return (1) ; } SuiteSparse/CXSparse/Source/cs_multiply.c0000644001170100242450000000257310712165171017417 0ustar davisfac#include "cs.h" /* C = A*B */ cs *cs_multiply (const cs *A, const cs *B) { CS_INT p, j, nz = 0, anz, *Cp, *Ci, *Bp, m, n, bnz, *w, values, *Bi ; CS_ENTRY *x, *Bx, *Cx ; cs *C ; if (!CS_CSC (A) || !CS_CSC (B)) return (NULL) ; /* check inputs */ if (A->n != B->m) return (NULL) ; m = A->m ; anz = A->p [A->n] ; n = B->n ; Bp = B->p ; Bi = B->i ; Bx = B->x ; bnz = Bp [n] ; w = cs_calloc (m, sizeof (CS_INT)) ; /* get workspace */ values = (A->x != NULL) && (Bx != NULL) ; x = values ? cs_malloc (m, sizeof (CS_ENTRY)) : NULL ; /* get workspace */ C = cs_spalloc (m, n, anz + bnz, values, 0) ; /* allocate result */ if (!C || !w || (values && !x)) return (cs_done (C, w, x, 0)) ; Cp = C->p ; for (j = 0 ; j < n ; j++) { if (nz + m > C->nzmax && !cs_sprealloc (C, 2*(C->nzmax)+m)) { return (cs_done (C, w, x, 0)) ; /* out of memory */ } Ci = C->i ; Cx = C->x ; /* C->i and C->x may be reallocated */ Cp [j] = nz ; /* column j of C starts here */ for (p = Bp [j] ; p < Bp [j+1] ; p++) { nz = cs_scatter (A, Bi [p], Bx ? Bx [p] : 1, w, x, j+1, C, nz) ; } if (values) for (p = Cp [j] ; p < nz ; p++) Cx [p] = x [Ci [p]] ; } Cp [n] = nz ; /* finalize the last column of C */ cs_sprealloc (C, 0) ; /* remove extra space from C */ return (cs_done (C, w, x, 1)) ; /* success; free workspace, return C */ } SuiteSparse/CXSparse/Source/cs_add.c0000644001170100242450000000244010712165171016261 0ustar davisfac#include "cs.h" /* C = alpha*A + beta*B */ cs *cs_add (const cs *A, const cs *B, CS_ENTRY alpha, CS_ENTRY beta) { CS_INT p, j, nz = 0, anz, *Cp, *Ci, *Bp, m, n, bnz, *w, values ; CS_ENTRY *x, *Bx, *Cx ; cs *C ; if (!CS_CSC (A) || !CS_CSC (B)) return (NULL) ; /* check inputs */ if (A->m != B->m || A->n != B->n) return (NULL) ; m = A->m ; anz = A->p [A->n] ; n = B->n ; Bp = B->p ; Bx = B->x ; bnz = Bp [n] ; w = cs_calloc (m, sizeof (CS_INT)) ; /* get workspace */ values = (A->x != NULL) && (Bx != NULL) ; x = values ? cs_malloc (m, sizeof (CS_ENTRY)) : NULL ; /* get workspace */ C = cs_spalloc (m, n, anz + bnz, values, 0) ; /* allocate result*/ if (!C || !w || (values && !x)) return (cs_done (C, w, x, 0)) ; Cp = C->p ; Ci = C->i ; Cx = C->x ; for (j = 0 ; j < n ; j++) { Cp [j] = nz ; /* column j of C starts here */ nz = cs_scatter (A, j, alpha, w, x, j+1, C, nz) ; /* alpha*A(:,j)*/ nz = cs_scatter (B, j, beta, w, x, j+1, C, nz) ; /* beta*B(:,j) */ if (values) for (p = Cp [j] ; p < nz ; p++) Cx [p] = x [Ci [p]] ; } Cp [n] = nz ; /* finalize the last column of C */ cs_sprealloc (C, 0) ; /* remove extra space from C */ return (cs_done (C, w, x, 1)) ; /* success; free workspace, return C */ } SuiteSparse/CXSparse/Source/cs_amd.c0000644001170100242450000003055210712165171016277 0ustar davisfac#include "cs.h" /* clear w */ static CS_INT cs_wclear (CS_INT mark, CS_INT lemax, CS_INT *w, CS_INT n) { CS_INT k ; if (mark < 2 || (mark + lemax < 0)) { for (k = 0 ; k < n ; k++) if (w [k] != 0) w [k] = 1 ; mark = 2 ; } return (mark) ; /* at this point, w [0..n-1] < mark holds */ } /* keep off-diagonal entries; drop diagonal entries */ static CS_INT cs_diag (CS_INT i, CS_INT j, CS_ENTRY aij, void *other) { return (i != j) ; } /* p = amd(A+A') if symmetric is true, or amd(A'A) otherwise */ CS_INT *cs_amd (CS_INT order, const cs *A) /* order 0:natural, 1:Chol, 2:LU, 3:QR */ { cs *C, *A2, *AT ; CS_INT *Cp, *Ci, *last, *W, *len, *nv, *next, *P, *head, *elen, *degree, *w, *hhead, *ATp, *ATi, d, dk, dext, lemax = 0, e, elenk, eln, i, j, k, k1, k2, k3, jlast, ln, dense, nzmax, mindeg = 0, nvi, nvj, nvk, mark, wnvi, ok, cnz, nel = 0, p, p1, p2, p3, p4, pj, pk, pk1, pk2, pn, q, n, m, t ; unsigned CS_INT h ; /* --- Construct matrix C ----------------------------------------------- */ if (!CS_CSC (A) || order <= 0 || order > 3) return (NULL) ; /* check */ AT = cs_transpose (A, 0) ; /* compute A' */ if (!AT) return (NULL) ; m = A->m ; n = A->n ; dense = CS_MAX (16, 10 * sqrt ((double) n)) ; /* find dense threshold */ dense = CS_MIN (n-2, dense) ; if (order == 1 && n == m) { C = cs_add (A, AT, 0, 0) ; /* C = A+A' */ } else if (order == 2) { ATp = AT->p ; /* drop dense columns from AT */ ATi = AT->i ; for (p2 = 0, j = 0 ; j < m ; j++) { p = ATp [j] ; /* column j of AT starts here */ ATp [j] = p2 ; /* new column j starts here */ if (ATp [j+1] - p > dense) continue ; /* skip dense col j */ for ( ; p < ATp [j+1] ; p++) ATi [p2++] = ATi [p] ; } ATp [m] = p2 ; /* finalize AT */ A2 = cs_transpose (AT, 0) ; /* A2 = AT' */ C = A2 ? cs_multiply (AT, A2) : NULL ; /* C=A'*A with no dense rows */ cs_spfree (A2) ; } else { C = cs_multiply (AT, A) ; /* C=A'*A */ } cs_spfree (AT) ; if (!C) return (NULL) ; cs_fkeep (C, &cs_diag, NULL) ; /* drop diagonal entries */ Cp = C->p ; cnz = Cp [n] ; P = cs_malloc (n+1, sizeof (CS_INT)) ; /* allocate result */ W = cs_malloc (8*(n+1), sizeof (CS_INT)) ; /* get workspace */ t = cnz + cnz/5 + 2*n ; /* add elbow room to C */ if (!P || !W || !cs_sprealloc (C, t)) return (cs_idone (P, C, W, 0)) ; len = W ; nv = W + (n+1) ; next = W + 2*(n+1) ; head = W + 3*(n+1) ; elen = W + 4*(n+1) ; degree = W + 5*(n+1) ; w = W + 6*(n+1) ; hhead = W + 7*(n+1) ; last = P ; /* use P as workspace for last */ /* --- Initialize quotient graph ---------------------------------------- */ for (k = 0 ; k < n ; k++) len [k] = Cp [k+1] - Cp [k] ; len [n] = 0 ; nzmax = C->nzmax ; Ci = C->i ; for (i = 0 ; i <= n ; i++) { head [i] = -1 ; /* degree list i is empty */ last [i] = -1 ; next [i] = -1 ; hhead [i] = -1 ; /* hash list i is empty */ nv [i] = 1 ; /* node i is just one node */ w [i] = 1 ; /* node i is alive */ elen [i] = 0 ; /* Ek of node i is empty */ degree [i] = len [i] ; /* degree of node i */ } mark = cs_wclear (0, 0, w, n) ; /* clear w */ elen [n] = -2 ; /* n is a dead element */ Cp [n] = -1 ; /* n is a root of assembly tree */ w [n] = 0 ; /* n is a dead element */ /* --- Initialize degree lists ------------------------------------------ */ for (i = 0 ; i < n ; i++) { d = degree [i] ; if (d == 0) /* node i is empty */ { elen [i] = -2 ; /* element i is dead */ nel++ ; Cp [i] = -1 ; /* i is a root of assembly tree */ w [i] = 0 ; } else if (d > dense) /* node i is dense */ { nv [i] = 0 ; /* absorb i into element n */ elen [i] = -1 ; /* node i is dead */ nel++ ; Cp [i] = CS_FLIP (n) ; nv [n]++ ; } else { if (head [d] != -1) last [head [d]] = i ; next [i] = head [d] ; /* put node i in degree list d */ head [d] = i ; } } while (nel < n) /* while (selecting pivots) do */ { /* --- Select node of minimum approximate degree -------------------- */ for (k = -1 ; mindeg < n && (k = head [mindeg]) == -1 ; mindeg++) ; if (next [k] != -1) last [next [k]] = -1 ; head [mindeg] = next [k] ; /* remove k from degree list */ elenk = elen [k] ; /* elenk = |Ek| */ nvk = nv [k] ; /* # of nodes k represents */ nel += nvk ; /* nv[k] nodes of A eliminated */ /* --- Garbage collection ------------------------------------------- */ if (elenk > 0 && cnz + mindeg >= nzmax) { for (j = 0 ; j < n ; j++) { if ((p = Cp [j]) >= 0) /* j is a live node or element */ { Cp [j] = Ci [p] ; /* save first entry of object */ Ci [p] = CS_FLIP (j) ; /* first entry is now CS_FLIP(j) */ } } for (q = 0, p = 0 ; p < cnz ; ) /* scan all of memory */ { if ((j = CS_FLIP (Ci [p++])) >= 0) /* found object j */ { Ci [q] = Cp [j] ; /* restore first entry of object */ Cp [j] = q++ ; /* new pointer to object j */ for (k3 = 0 ; k3 < len [j]-1 ; k3++) Ci [q++] = Ci [p++] ; } } cnz = q ; /* Ci [cnz...nzmax-1] now free */ } /* --- Construct new element ---------------------------------------- */ dk = 0 ; nv [k] = -nvk ; /* flag k as in Lk */ p = Cp [k] ; pk1 = (elenk == 0) ? p : cnz ; /* do in place if elen[k] == 0 */ pk2 = pk1 ; for (k1 = 1 ; k1 <= elenk + 1 ; k1++) { if (k1 > elenk) { e = k ; /* search the nodes in k */ pj = p ; /* list of nodes starts at Ci[pj]*/ ln = len [k] - elenk ; /* length of list of nodes in k */ } else { e = Ci [p++] ; /* search the nodes in e */ pj = Cp [e] ; ln = len [e] ; /* length of list of nodes in e */ } for (k2 = 1 ; k2 <= ln ; k2++) { i = Ci [pj++] ; if ((nvi = nv [i]) <= 0) continue ; /* node i dead, or seen */ dk += nvi ; /* degree[Lk] += size of node i */ nv [i] = -nvi ; /* negate nv[i] to denote i in Lk*/ Ci [pk2++] = i ; /* place i in Lk */ if (next [i] != -1) last [next [i]] = last [i] ; if (last [i] != -1) /* remove i from degree list */ { next [last [i]] = next [i] ; } else { head [degree [i]] = next [i] ; } } if (e != k) { Cp [e] = CS_FLIP (k) ; /* absorb e into k */ w [e] = 0 ; /* e is now a dead element */ } } if (elenk != 0) cnz = pk2 ; /* Ci [cnz...nzmax] is free */ degree [k] = dk ; /* external degree of k - |Lk\i| */ Cp [k] = pk1 ; /* element k is in Ci[pk1..pk2-1] */ len [k] = pk2 - pk1 ; elen [k] = -2 ; /* k is now an element */ /* --- Find set differences ----------------------------------------- */ mark = cs_wclear (mark, lemax, w, n) ; /* clear w if necessary */ for (pk = pk1 ; pk < pk2 ; pk++) /* scan 1: find |Le\Lk| */ { i = Ci [pk] ; if ((eln = elen [i]) <= 0) continue ;/* skip if elen[i] empty */ nvi = -nv [i] ; /* nv [i] was negated */ wnvi = mark - nvi ; for (p = Cp [i] ; p <= Cp [i] + eln - 1 ; p++) /* scan Ei */ { e = Ci [p] ; if (w [e] >= mark) { w [e] -= nvi ; /* decrement |Le\Lk| */ } else if (w [e] != 0) /* ensure e is a live element */ { w [e] = degree [e] + wnvi ; /* 1st time e seen in scan 1 */ } } } /* --- Degree update ------------------------------------------------ */ for (pk = pk1 ; pk < pk2 ; pk++) /* scan2: degree update */ { i = Ci [pk] ; /* consider node i in Lk */ p1 = Cp [i] ; p2 = p1 + elen [i] - 1 ; pn = p1 ; for (h = 0, d = 0, p = p1 ; p <= p2 ; p++) /* scan Ei */ { e = Ci [p] ; if (w [e] != 0) /* e is an unabsorbed element */ { dext = w [e] - mark ; /* dext = |Le\Lk| */ if (dext > 0) { d += dext ; /* sum up the set differences */ Ci [pn++] = e ; /* keep e in Ei */ h += e ; /* compute the hash of node i */ } else { Cp [e] = CS_FLIP (k) ; /* aggressive absorb. e->k */ w [e] = 0 ; /* e is a dead element */ } } } elen [i] = pn - p1 + 1 ; /* elen[i] = |Ei| */ p3 = pn ; p4 = p1 + len [i] ; for (p = p2 + 1 ; p < p4 ; p++) /* prune edges in Ai */ { j = Ci [p] ; if ((nvj = nv [j]) <= 0) continue ; /* node j dead or in Lk */ d += nvj ; /* degree(i) += |j| */ Ci [pn++] = j ; /* place j in node list of i */ h += j ; /* compute hash for node i */ } if (d == 0) /* check for mass elimination */ { Cp [i] = CS_FLIP (k) ; /* absorb i into k */ nvi = -nv [i] ; dk -= nvi ; /* |Lk| -= |i| */ nvk += nvi ; /* |k| += nv[i] */ nel += nvi ; nv [i] = 0 ; elen [i] = -1 ; /* node i is dead */ } else { degree [i] = CS_MIN (degree [i], d) ; /* update degree(i) */ Ci [pn] = Ci [p3] ; /* move first node to end */ Ci [p3] = Ci [p1] ; /* move 1st el. to end of Ei */ Ci [p1] = k ; /* add k as 1st element in of Ei */ len [i] = pn - p1 + 1 ; /* new len of adj. list of node i */ h %= n ; /* finalize hash of i */ next [i] = hhead [h] ; /* place i in hash bucket */ hhead [h] = i ; last [i] = h ; /* save hash of i in last[i] */ } } /* scan2 is done */ degree [k] = dk ; /* finalize |Lk| */ lemax = CS_MAX (lemax, dk) ; mark = cs_wclear (mark+lemax, lemax, w, n) ; /* clear w */ /* --- Supernode detection ------------------------------------------ */ for (pk = pk1 ; pk < pk2 ; pk++) { i = Ci [pk] ; if (nv [i] >= 0) continue ; /* skip if i is dead */ h = last [i] ; /* scan hash bucket of node i */ i = hhead [h] ; hhead [h] = -1 ; /* hash bucket will be empty */ for ( ; i != -1 && next [i] != -1 ; i = next [i], mark++) { ln = len [i] ; eln = elen [i] ; for (p = Cp [i]+1 ; p <= Cp [i] + ln-1 ; p++) w [Ci [p]] = mark; jlast = i ; for (j = next [i] ; j != -1 ; ) /* compare i with all j */ { ok = (len [j] == ln) && (elen [j] == eln) ; for (p = Cp [j] + 1 ; ok && p <= Cp [j] + ln - 1 ; p++) { if (w [Ci [p]] != mark) ok = 0 ; /* compare i and j*/ } if (ok) /* i and j are identical */ { Cp [j] = CS_FLIP (i) ; /* absorb j into i */ nv [i] += nv [j] ; nv [j] = 0 ; elen [j] = -1 ; /* node j is dead */ j = next [j] ; /* delete j from hash bucket */ next [jlast] = j ; } else { jlast = j ; /* j and i are different */ j = next [j] ; } } } } /* --- Finalize new element------------------------------------------ */ for (p = pk1, pk = pk1 ; pk < pk2 ; pk++) /* finalize Lk */ { i = Ci [pk] ; if ((nvi = -nv [i]) <= 0) continue ;/* skip if i is dead */ nv [i] = nvi ; /* restore nv[i] */ d = degree [i] + dk - nvi ; /* compute external degree(i) */ d = CS_MIN (d, n - nel - nvi) ; if (head [d] != -1) last [head [d]] = i ; next [i] = head [d] ; /* put i back in degree list */ last [i] = -1 ; head [d] = i ; mindeg = CS_MIN (mindeg, d) ; /* find new minimum degree */ degree [i] = d ; Ci [p++] = i ; /* place i in Lk */ } nv [k] = nvk ; /* # nodes absorbed into k */ if ((len [k] = p-pk1) == 0) /* length of adj list of element k*/ { Cp [k] = -1 ; /* k is a root of the tree */ w [k] = 0 ; /* k is now a dead element */ } if (elenk != 0) cnz = p ; /* free unused space in Lk */ } /* --- Postordering ----------------------------------------------------- */ for (i = 0 ; i < n ; i++) Cp [i] = CS_FLIP (Cp [i]) ;/* fix assembly tree */ for (j = 0 ; j <= n ; j++) head [j] = -1 ; for (j = n ; j >= 0 ; j--) /* place unordered nodes in lists */ { if (nv [j] > 0) continue ; /* skip if j is an element */ next [j] = head [Cp [j]] ; /* place j in list of its parent */ head [Cp [j]] = j ; } for (e = n ; e >= 0 ; e--) /* place elements in lists */ { if (nv [e] <= 0) continue ; /* skip unless e is an element */ if (Cp [e] != -1) { next [e] = head [Cp [e]] ; /* place e in list of its parent */ head [Cp [e]] = e ; } } for (k = 0, i = 0 ; i <= n ; i++) /* postorder the assembly tree */ { if (Cp [i] == -1) k = cs_tdfs (i, k, head, next, P, w) ; } return (cs_idone (P, C, W, 1)) ; } SuiteSparse/CXSparse/Source/cs_dfs.c0000644001170100242450000000255610712165171016315 0ustar davisfac#include "cs.h" /* depth-first-search of the graph of a matrix, starting at node j */ CS_INT cs_dfs (CS_INT j, cs *G, CS_INT top, CS_INT *xi, CS_INT *pstack, const CS_INT *pinv) { CS_INT i, p, p2, done, jnew, head = 0, *Gp, *Gi ; if (!CS_CSC (G) || !xi || !pstack) return (-1) ; /* check inputs */ Gp = G->p ; Gi = G->i ; xi [0] = j ; /* initialize the recursion stack */ while (head >= 0) { j = xi [head] ; /* get j from the top of the recursion stack */ jnew = pinv ? (pinv [j]) : j ; if (!CS_MARKED (Gp, j)) { CS_MARK (Gp, j) ; /* mark node j as visited */ pstack [head] = (jnew < 0) ? 0 : CS_UNFLIP (Gp [jnew]) ; } done = 1 ; /* node j done if no unvisited neighbors */ p2 = (jnew < 0) ? 0 : CS_UNFLIP (Gp [jnew+1]) ; for (p = pstack [head] ; p < p2 ; p++) /* examine all neighbors of j */ { i = Gi [p] ; /* consider neighbor node i */ if (CS_MARKED (Gp, i)) continue ; /* skip visited node i */ pstack [head] = p ; /* pause depth-first search of node j */ xi [++head] = i ; /* start dfs at node i */ done = 0 ; /* node j is not done */ break ; /* break, to start dfs (i) */ } if (done) /* depth-first search at node j is done */ { head-- ; /* remove j from the recursion stack */ xi [--top] = j ; /* and place in the output stack */ } } return (top) ; } SuiteSparse/CXSparse/Source/cs_scc.c0000644001170100242450000000333210712165171016302 0ustar davisfac#include "cs.h" /* find the strongly connected components of a square matrix */ csd *cs_scc (cs *A) /* matrix A temporarily modified, then restored */ { CS_INT n, i, k, b, nb = 0, top, *xi, *pstack, *p, *r, *Ap, *ATp, *rcopy, *Blk ; cs *AT ; csd *D ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ n = A->n ; Ap = A->p ; D = cs_dalloc (n, 0) ; /* allocate result */ AT = cs_transpose (A, 0) ; /* AT = A' */ xi = cs_malloc (2*n+1, sizeof (CS_INT)) ; /* get workspace */ if (!D || !AT || !xi) return (cs_ddone (D, AT, xi, 0)) ; Blk = xi ; rcopy = pstack = xi + n ; p = D->p ; r = D->r ; ATp = AT->p ; top = n ; for (i = 0 ; i < n ; i++) /* first dfs(A) to find finish times (xi) */ { if (!CS_MARKED (Ap, i)) top = cs_dfs (i, A, top, xi, pstack, NULL) ; } for (i = 0 ; i < n ; i++) CS_MARK (Ap, i) ; /* restore A; unmark all nodes*/ top = n ; nb = n ; for (k = 0 ; k < n ; k++) /* dfs(A') to find strongly connnected comp */ { i = xi [k] ; /* get i in reverse order of finish times */ if (CS_MARKED (ATp, i)) continue ; /* skip node i if already ordered */ r [nb--] = top ; /* node i is the start of a component in p */ top = cs_dfs (i, AT, top, p, pstack, NULL) ; } r [nb] = 0 ; /* first block starts at zero; shift r up */ for (k = nb ; k <= n ; k++) r [k-nb] = r [k] ; D->nb = nb = n-nb ; /* nb = # of strongly connected components */ for (b = 0 ; b < nb ; b++) /* sort each block in natural order */ { for (k = r [b] ; k < r [b+1] ; k++) Blk [p [k]] = b ; } for (b = 0 ; b <= nb ; b++) rcopy [b] = r [b] ; for (i = 0 ; i < n ; i++) p [rcopy [Blk [i]]++] = i ; return (cs_ddone (D, AT, xi, 1)) ; } SuiteSparse/CXSparse/Source/cs_sqr.c0000644001170100242450000000654310712165171016346 0ustar davisfac#include "cs.h" /* compute nnz(V) = S->lnz, S->pinv, S->leftmost, S->m2 from A and S->parent */ static CS_INT cs_vcount (const cs *A, css *S) { CS_INT i, k, p, pa, n = A->n, m = A->m, *Ap = A->p, *Ai = A->i, *next, *head, *tail, *nque, *pinv, *leftmost, *w, *parent = S->parent ; S->pinv = pinv = cs_malloc (m+n, sizeof (CS_INT)) ; /* allocate pinv, */ S->leftmost = leftmost = cs_malloc (m, sizeof (CS_INT)) ; /* and leftmost */ w = cs_malloc (m+3*n, sizeof (CS_INT)) ; /* get workspace */ if (!pinv || !w || !leftmost) { cs_free (w) ; /* pinv and leftmost freed later */ return (0) ; /* out of memory */ } next = w ; head = w + m ; tail = w + m + n ; nque = w + m + 2*n ; for (k = 0 ; k < n ; k++) head [k] = -1 ; /* queue k is empty */ for (k = 0 ; k < n ; k++) tail [k] = -1 ; for (k = 0 ; k < n ; k++) nque [k] = 0 ; for (i = 0 ; i < m ; i++) leftmost [i] = -1 ; for (k = n-1 ; k >= 0 ; k--) { for (p = Ap [k] ; p < Ap [k+1] ; p++) { leftmost [Ai [p]] = k ; /* leftmost[i] = min(find(A(i,:)))*/ } } for (i = m-1 ; i >= 0 ; i--) /* scan rows in reverse order */ { pinv [i] = -1 ; /* row i is not yet ordered */ k = leftmost [i] ; if (k == -1) continue ; /* row i is empty */ if (nque [k]++ == 0) tail [k] = i ; /* first row in queue k */ next [i] = head [k] ; /* put i at head of queue k */ head [k] = i ; } S->lnz = 0 ; S->m2 = m ; for (k = 0 ; k < n ; k++) /* find row permutation and nnz(V)*/ { i = head [k] ; /* remove row i from queue k */ S->lnz++ ; /* count V(k,k) as nonzero */ if (i < 0) i = S->m2++ ; /* add a fictitious row */ pinv [i] = k ; /* associate row i with V(:,k) */ if (--nque [k] <= 0) continue ; /* skip if V(k+1:m,k) is empty */ S->lnz += nque [k] ; /* nque [k] is nnz (V(k+1:m,k)) */ if ((pa = parent [k]) != -1) /* move all rows to parent of k */ { if (nque [pa] == 0) tail [pa] = tail [k] ; next [tail [k]] = head [pa] ; head [pa] = next [i] ; nque [pa] += nque [k] ; } } for (i = 0 ; i < m ; i++) if (pinv [i] < 0) pinv [i] = k++ ; cs_free (w) ; return (1) ; } /* symbolic ordering and analysis for QR or LU */ css *cs_sqr (CS_INT order, const cs *A, CS_INT qr) { CS_INT n, k, ok = 1, *post ; css *S ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ n = A->n ; S = cs_calloc (1, sizeof (css)) ; /* allocate result S */ if (!S) return (NULL) ; /* out of memory */ S->q = cs_amd (order, A) ; /* fill-reducing ordering */ if (order && !S->q) return (cs_sfree (S)) ; if (qr) /* QR symbolic analysis */ { cs *C = order ? cs_permute (A, NULL, S->q, 0) : ((cs *) A) ; S->parent = cs_etree (C, 1) ; /* etree of C'*C, where C=A(:,q) */ post = cs_post (S->parent, n) ; S->cp = cs_counts (C, S->parent, post, 1) ; /* col counts chol(C'*C) */ cs_free (post) ; ok = C && S->parent && S->cp && cs_vcount (C, S) ; if (ok) for (S->unz = 0, k = 0 ; k < n ; k++) S->unz += S->cp [k] ; ok = ok && S->lnz >= 0 && S->unz >= 0 ; /* CS_INT overflow guard */ if (order) cs_spfree (C) ; } else { S->unz = 4*(A->p [n]) + n ; /* for LU factorization only, */ S->lnz = S->unz ; /* guess nnz(L) and nnz(U) */ } return (ok ? S : cs_sfree (S)) ; /* return result S */ } SuiteSparse/CXSparse/Source/cs_compress.c0000644001170100242450000000162210712165171017365 0ustar davisfac#include "cs.h" /* C = compressed-column form of a triplet matrix T */ cs *cs_compress (const cs *T) { CS_INT m, n, nz, p, k, *Cp, *Ci, *w, *Ti, *Tj ; CS_ENTRY *Cx, *Tx ; cs *C ; if (!CS_TRIPLET (T)) return (NULL) ; /* check inputs */ m = T->m ; n = T->n ; Ti = T->i ; Tj = T->p ; Tx = T->x ; nz = T->nz ; C = cs_spalloc (m, n, nz, Tx != NULL, 0) ; /* allocate result */ w = cs_calloc (n, sizeof (CS_INT)) ; /* get workspace */ if (!C || !w) return (cs_done (C, w, NULL, 0)) ; /* out of memory */ Cp = C->p ; Ci = C->i ; Cx = C->x ; for (k = 0 ; k < nz ; k++) w [Tj [k]]++ ; /* column counts */ cs_cumsum (Cp, w, n) ; /* column pointers */ for (k = 0 ; k < nz ; k++) { Ci [p = w [Tj [k]]++] = Ti [k] ; /* A(i,j) is the pth entry in C */ if (Cx) Cx [p] = Tx [k] ; } return (cs_done (C, w, NULL, 1)) ; /* success; free w and return C */ } SuiteSparse/CXSparse/Source/cs_transpose.c0000644001170100242450000000170010712165171017545 0ustar davisfac#include "cs.h" /* C = A' */ cs *cs_transpose (const cs *A, CS_INT values) { CS_INT p, q, j, *Cp, *Ci, n, m, *Ap, *Ai, *w ; CS_ENTRY *Cx, *Ax ; cs *C ; if (!CS_CSC (A)) return (NULL) ; /* check inputs */ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; C = cs_spalloc (n, m, Ap [n], values && Ax, 0) ; /* allocate result */ w = cs_calloc (m, sizeof (CS_INT)) ; /* get workspace */ if (!C || !w) return (cs_done (C, w, NULL, 0)) ; /* out of memory */ Cp = C->p ; Ci = C->i ; Cx = C->x ; for (p = 0 ; p < Ap [n] ; p++) w [Ai [p]]++ ; /* row counts */ cs_cumsum (Cp, w, m) ; /* row pointers */ for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { Ci [q = w [Ai [p]]++] = j ; /* place A(i,j) as entry C(j,i) */ if (Cx) Cx [q] = (values > 0) ? CS_CONJ (Ax [p]) : Ax [p] ; } } return (cs_done (C, w, NULL, 1)) ; /* success; free w and return C */ } SuiteSparse/CXSparse/Source/cs_convert.c0000644001170100242450000000662010566670105017222 0ustar davisfac#include "cs.h" /* convert from complex to real (int version) */ /* C = real(A) if real is true, imag(A) otherwise */ cs_di *cs_i_real (cs_ci *A, int real) { cs_di *C ; int n, triplet, nn, p, nz, *Ap, *Ai, *Cp, *Ci ; cs_complex_t *Ax ; double *Cx ; if (!A || !A->x) return (NULL) ; /* return if A NULL or pattern-only */ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; triplet = (A->nz >= 0) ; /* true if A is a triplet matrix */ nz = triplet ? A->nz : Ap [n] ; C = cs_di_spalloc (A->m, n, A->nzmax, 1, triplet) ; if (!C) return (NULL) ; Cp = C->p ; Ci = C->i ; Cx = C->x ; nn = triplet ? nz : (n+1) ; for (p = 0 ; p < nz ; p++) Ci [p] = Ai [p] ; for (p = 0 ; p < nn ; p++) Cp [p] = Ap [p] ; for (p = 0 ; p < nz ; p++) Cx [p] = real ? creal (Ax [p]) : cimag (Ax [p]) ; if (triplet) C->nz = nz ; return (C) ; } /* convert from real to complex (int version) */ /* C = A if real is true, or C = i*A otherwise */ cs_ci *cs_i_complex (cs_di *A, int real) { cs_ci *C ; int n, triplet, nn, p, nz, *Ap, *Ai, *Cp, *Ci ; double *Ax ; cs_complex_t *Cx ; if (!A || !A->x) return (NULL) ; /* return if A NULL or pattern-only */ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; triplet = (A->nz >= 0) ; /* true if A is a triplet matrix */ nz = triplet ? A->nz : Ap [n] ; C = cs_ci_spalloc (A->m, n, A->nzmax, 1, triplet) ; if (!C) return (NULL) ; Cp = C->p ; Ci = C->i ; Cx = C->x ; nn = triplet ? nz : (n+1) ; for (p = 0 ; p < nz ; p++) Ci [p] = Ai [p] ; for (p = 0 ; p < nn ; p++) Cp [p] = Ap [p] ; for (p = 0 ; p < nz ; p++) Cx [p] = real ? Ax [p] : (I * Ax [p]) ; if (triplet) C->nz = nz ; return (C) ; } /* convert from complex to real (UF_long version) */ /* C = real(A) if real is true, imag(A) otherwise */ cs_dl *cs_l_real (cs_cl *A, UF_long real) { cs_dl *C ; UF_long n, triplet, nn, p, nz, *Ap, *Ai, *Cp, *Ci ; cs_complex_t *Ax ; double *Cx ; if (!A || !A->x) return (NULL) ; /* return if A NULL or pattern-only */ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; triplet = (A->nz >= 0) ; /* true if A is a triplet matrix */ nz = triplet ? A->nz : Ap [n] ; C = cs_dl_spalloc (A->m, n, A->nzmax, 1, triplet) ; if (!C) return (NULL) ; Cp = C->p ; Ci = C->i ; Cx = C->x ; nn = triplet ? nz : (n+1) ; for (p = 0 ; p < nz ; p++) Ci [p] = Ai [p] ; for (p = 0 ; p < nn ; p++) Cp [p] = Ap [p] ; for (p = 0 ; p < nz ; p++) Cx [p] = real ? creal (Ax [p]) : cimag (Ax [p]) ; if (triplet) C->nz = nz ; return (C) ; } /* convert from real to complex (UF_long version) */ /* C = A if real is true, or C = i*A otherwise */ cs_cl *cs_l_complex (cs_dl *A, UF_long real) { cs_cl *C ; UF_long n, triplet, nn, p, nz, *Ap, *Ai, *Cp, *Ci ; double *Ax ; cs_complex_t *Cx ; if (!A || !A->x) return (NULL) ; /* return if A NULL or pattern-only */ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; triplet = (A->nz >= 0) ; /* true if A is a triplet matrix */ nz = triplet ? A->nz : Ap [n] ; C = cs_cl_spalloc (A->m, n, A->nzmax, 1, triplet) ; if (!C) return (NULL) ; Cp = C->p ; Ci = C->i ; Cx = C->x ; nn = triplet ? nz : (n+1) ; for (p = 0 ; p < nz ; p++) Ci [p] = Ai [p] ; for (p = 0 ; p < nn ; p++) Cp [p] = Ap [p] ; for (p = 0 ; p < nz ; p++) Cx [p] = real ? Ax [p] : (I * Ax [p]) ; if (triplet) C->nz = nz ; return (C) ; } SuiteSparse/CXSparse/README.txt0000644001170100242450000005751210711425615015151 0ustar davisfacCXSparse: a Concise Sparse Matrix package - Extended. Version 2.2.0, Copyright (c) 2006-2007, Timothy A. Davis. Derived from CSparse. Conversion originally by David Bateman, Motorola, and then modified by Tim Davis. ANSI C99 is required, with support for the _Complex data type. (if you use a C++ compiler, the C++ complex type is used instead). CXSparse is a version of CSparse that operates on both real and complex matrices, using either int or UF_long integers. A UF_long is normally just a long on most platforms, but becomes __int64 on WIN64. It now includes a MATLAB interface, enabling the use of CXSparse functions on both 32-bit and 64-bit platforms. To install for use in MATLAB, simply type "cs_install" in the MATLAB Command Window, while in the CXSparse/MATLAB directory. (NOTE: Windows users cannot use the "lcc" command; run "mex -setup" first, and select a different compiler). If you use the Unix "make" command in that directory instead and are using a 64-bit platform, then you must edit the CXSparse/MATLAB/Makefile first. Refer to the instructions in that file. Refer to "Direct Methods for Sparse Linear Systems," Timothy A. Davis, SIAM, Philadelphia, 2006. No detailed user guide is included in this package; the user guide is the book itself. To compile the C-library (./Source), C demo programs (./Demo) just type "make" in this directory. To run the exhaustive statement coverage tests, type "make" in the Tcov directory; the Tcov tests assume you are using Linux. To remove all files not in the original distribution, type "make distclean". I recommend that you use a different level of optimization than "cc -O", which was chosen so that the Makefile is portable. See Source/Makefile. If your C compiler does not support the ANSI C99 complex type, the #include statement will fail. If this happens, compile the code with the -DNCOMPLEX flag (the MATLAB cs_install will do this for you). This package is backward compatible with CSparse. That is, user code that uses CSparse may switch to using CXSparse without any changes to the user code. Each CXSparse function has a generic version with the same name as the CSparse function, and four type-specific versions. For example: cs_add same as cs_add_di by default, but can be changed to use UF_long integers if user code is compiled with -DCS_LONG, and/or can be changed to operate on complex matrices with -DCS_COMPLEX. cs_di_add double/int version of cs_add cs_dl_add double/UF_long version of cs_add cs_ci_add complex/int version of cs_add cs_cl_add complex/UF_long version of cs_add The sparse matrix data structures are treated in the same way: cs, css, csn, and csd become cs_di, cs_dis, cs_din, and cs_did for the double/int case, cs_cl, cs_cls, cs_cln, and cs_cld for the complex/UF_long case, and so on. See cs_demo.c for a type-generic user program, and cs_cl_demo.c for a type-specific version of the same program (complex/UF_long). Several macros are available in CXSparse (but not in CSparse) to allow user code to be written in a type-generic manner: CS_INT int by default, UF_long if -DCS_LONG compiler flag is used CS_ENTRY double by default, double complex if -DCS_COMPLEX flag is used. CS_ID "%d" or "%ld", for printf and scanf of the CS_INT type. CS_INT_MAX INT_MAX or LONG_MAX, the largest possible value of CS_INT. CS_REAL(x) x or creal(x) CS_IMAG(x) 0 or cimag(x) CS_CONJ(x) x or conj(x) CS_ABS(x) fabs(x) or cabs(x) Even the name of the include file (cs.h) is the same. To use CXSparse instead of CSparse, simply compile with -ICXSparse/Source instead of -ICSparse/Source, and link against libcxsparse.a instead of the CSparse libcsparse.a library. To determine at compile time if CXSparse or CSparse is being used: #ifdef CXSPARSE CXSparse is in use. The generic functions equivalent to CSparse may be used (cs_add, etc). These generic functions can use different types, depending on the -DCS_LONG and -DCS_COMPLEX compile flags, with the default being double/int. The type-specific functions and data types (cs_di_add, cs_di, CS_INT, etc.) can be used. #else CSparse is in use. Only the generic functions "cs_add", etc., are available, and they are of type double/int. #endif See cs.h for the prototypes of each function, and the book "Direct Methods for Sparse Linear Systems" for full documentation of CSparse and CXSparse. Other changes from CSparse: cs_transpose performs the complex conjugate transpose if values>0 (C=A'), the pattern-only transpose if values=0 (C=spones(A') in MATLAB), and the array transpose if values<0 (C=A.' in MATLAB notation). A set of four conversion routines are included in CXSparse, to convert real matrices to/from complex matrices. The Householder reflection constructed by cs_house.c also differs slightly, to accomodate both the real and complex cases properly. CXSparse is generated automatically from CSparse. Refer to http://www.cise.ufl.edu/research/sparse/CSparse for details. -------------------------------------------------------------------------------- Contents: -------------------------------------------------------------------------------- Demo/ demo C programs that use CXSparse Doc/ license and change log Makefile Makefile for the whole package MATLAB/ MATLAB interface, demos, and tests for CXSparse Matrix/ sample matrices (with extra complex matrices for CXSparse) README.txt this file Source/ primary CXSparse source files Tcov/ CXSparse tests -------------------------------------------------------------------------------- ./Doc: license and change log -------------------------------------------------------------------------------- ChangeLog changes in CSparse since first release lesser.txt the GNU LGPL License.txt license (GNU LGPL) -------------------------------------------------------------------------------- ./Source: Primary source code for CXSparse -------------------------------------------------------------------------------- cs_add.c add sparse matrices cs_amd.c approximate minimum degree cs_chol.c sparse Cholesky cs_cholsol.c x=A\b using sparse Cholesky cs_compress.c convert a compress form to compressed-column form cs_counts.c column counts for Cholesky and QR cs_convert.c convert real to complex and complex to real (not in CSparse) cs_cumsum.c cumulative sum cs_dfs.c depth-first-search cs_dmperm.c Dulmage-Mendelsohn permutation cs_droptol.c drop small entries from a sparse matrix cs_dropzeros.c drop zeros from a sparse matrix cs_dupl.c remove (and sum) duplicates cs_entry.c add an entry to a triplet matrix cs_ereach.c nonzero pattern of Cholesky L(k,:) from etree and triu(A(:,k)) cs_etree.c find elimination tree cs_fkeep.c drop entries from a sparse matrix cs_gaxpy.c sparse matrix times dense matrix cs.h include file for CXSparse cs_happly.c apply Householder reflection cs_house.c Householder reflection (*** NOTE: different algo. from CSparse) cs_ipvec.c x(p)=b cs_leaf.c determine if j is a leaf of the skeleton matrix and find lca cs_load.c load a sparse matrix from a file cs_lsolve.c x=L\b cs_ltsolve.c x=L'\b cs_lu.c sparse LU factorization cs_lusol.c x=A\b using sparse LU factorization cs_malloc.c memory manager cs_maxtrans.c maximum transveral (permutation for zero-free diagonal) cs_multiply.c sparse matrix multiply cs_norm.c sparse matrix norm cs_permute.c permute a sparse matrix cs_pinv.c invert a permutation vector cs_post.c postorder an elimination tree cs_print.c print a sparse matrix cs_pvec.c x=b(p) cs_qr.c sparse QR cs_qrsol.c solve a least-squares problem cs_randperm.c random permutation cs_reach.c find nonzero pattern of x=L\b for sparse L and b cs_scatter.c scatter a sparse vector cs_scc.c strongly-connected components cs_schol.c symbolic Cholesky cs_spsolve.c x=Z\b where Z, x, and b are sparse, and Z upper/lower triangular cs_sqr.c symbolic QR (also can be used for LU) cs_symperm.c symmetric permutation of a sparse matrix cs_tdfs.c depth-first-search of a tree cs_transpose.c transpose a sparse matrix cs_updown.c sparse rank-1 Cholesky update/downate cs_usolve.c x=U\b cs_util.c various utilities (allocate/free matrices, workspace, etc) cs_utsolve.c x=U'\b Makefile Makefile for CXSparse README.txt README file for CXSparse -------------------------------------------------------------------------------- ./Demo: C program demos -------------------------------------------------------------------------------- cs_ci_demo1.c complex/int version of cs_demo1.c cs_ci_demo2.c complex/int version of cs_demo2.c cs_ci_demo3.c complex/int version of cs_demo3.c cs_ci_demo.c complex/int version of cs_demo.c cs_ci_demo.h complex/int version of cs_demo.h cs_cl_demo1.c complex/UF_long version of cs_demo1.c cs_cl_demo2.c complex/UF_long version of cs_demo2.c cs_cl_demo3.c complex/UF_long version of cs_demo3.c cs_cl_demo.c complex/UF_long version of cs_demo.c cs_cl_demo.h complex/UF_long version of cs_demo.h cs_demo1.c read a matrix from a file and perform basic matrix operations cs_demo2.c read a matrix from a file and solve a linear system cs_demo3.c read a matrix, solve a linear system, update/downdate cs_demo.c support routines for cs_demo*.c cs_demo.h include file for demo programs cs_demo.out output of "make", which runs the demos on some matrices cs_di_demo1.c double/int version of cs_demo1.c cs_di_demo2.c double/int version of cs_demo2.c cs_di_demo3.c double/int version of cs_demo3.c cs_di_demo.c double/int version of cs_demo.c cs_di_demo.h double/int version of cs_demo.h cs_dl_demo1.c double/UF_long version of cs_demo1.c cs_dl_demo2.c double/UF_long version of cs_demo2.c cs_dl_demo3.c double/UF_long version of cs_demo3.c cs_dl_demo.c double/UF_long version of cs_demo.c cs_dl_demo.h double/UF_long version of cs_demo.h cs_idemo.c convert real matrices to/from complex (int version) cs_ldemo.c convert real matrices to/from complex (UF_long version) Makefile Makefile for Demo programs readhb.f read a Rutherford-Boeing matrix (real matrices only) README.txt Demo README file -------------------------------------------------------------------------------- ./MATLAB: MATLAB interface, demos, and tests -------------------------------------------------------------------------------- cs_install.m MATLAB function for compiling and installing CSparse for MATLAB CSparse/ MATLAB interface for CSparse Demo/ MATLAB demos for CSparse Makefile MATLAB interface Makefile README.txt MATLAB README file Test/ MATLAB test for CSparse, and "textbook" routines UFget/ MATLAB interface to UF Sparse Matrix Collection -------------------------------------------------------------------------------- ./MATLAB/CSparse: MATLAB interface for CSparse -------------------------------------------------------------------------------- Contents.m Contents of MATLAB interface to CSparse cs_add.m add two sparse matrices cs_add_mex.c cs_amd.m approximate minimum degree cs_amd_mex.c cs_chol.m sparse Cholesky cs_chol_mex.c cs_cholsol.m x=A\b using a sparse Cholesky cs_cholsol_mex.c cs_counts.m column counts for Cholesky or QR (like "symbfact" in MATLAB) cs_counts_mex.c cs_dmperm.m Dulmage-Mendelsohn permutation cs_dmperm_mex.c cs_dmsol.m x=A\b using dmperm cs_dmspy.m plot a picture of a dmperm-permuted matrix cs_droptol.m drop small entries cs_droptol_mex.c cs_esep.m find edge separator cs_etree.m compute elimination tree cs_etree_mex.c cs_gaxpy.m sparse matrix times dense vector cs_gaxpy_mex.c cs_lsolve.m x=L\b where L is lower triangular cs_lsolve_mex.c cs_ltsolve.m x=L'\b where L is lower triangular cs_ltsolve_mex.c cs_lu.m sparse LU factorization cs_lu_mex.c cs_lusol.m x=A\b using sparse LU factorization cs_lusol_mex.c cs_make.m compiles CSparse for use in MATLAB cs_mex.c support routines for CSparse mexFunctions cs_mex.h cs_multiply.m sparse matrix multiply cs_multiply_mex.c cs_must_compile.m determine if a source file needs to be compiled with mex cs_nd.m nested dissection cs_nsep.m find node separator cs_permute.m permute a sparse matrix cs_permute_mex.c cs_print.m print a sparse matrix cs_print_mex.c cs_qleft.m apply Householder vectors to the left cs_qright.m apply Householder vectors to the right cs_qr.m sparse QR factorization cs_qr_mex.c cs_qrsol.m solve a sparse least squares problem cs_qrsol_mex.c cs_randperm.m randdom permutation cs_randperm_mex.c cs_scc.m strongly-connected components cs_scc_mex.c cs_sep.m convert an edge separator into a node separator cs_sparse.m convert a triplet form matrix to a compress-column form cs_sparse_mex.c cs_symperm.m symmetric permutation of a sparse matrix cs_symperm_mex.c cs_sqr.m symbolic QR ordering and analysis cs_sqr_mex.c cs_thumb_mex.c compute small "thumbnail" of a sparse matrix (for cspy). cs_transpose.m transpose a sparse matrix cs_transpose_mex.c cs_updown.m sparse Cholesky update/downdate cs_updown_mex.c cs_usolve.m x=U\b where U is upper triangular cs_usolve_mex.c cs_utsolve.m x=U'\b where U is upper triangular cs_utsolve_mex.c cspy.m a color "spy" Makefile Makefile for CSparse MATLAB interface README.txt README file for CSparse MATLAB interface -------------------------------------------------------------------------------- ./MATLAB/Demo: MATLAB demos for CSparse -------------------------------------------------------------------------------- Contents.m Contents of MATLAB demo for CSparse cs_demo.m run all MATLAB demos for CSparse cs_demo1.m MATLAB version of Demo/cs_demo1.c cs_demo2.m MATLAB version of Demo/cs_demo2.c cs_demo3.m MATLAB version of Demo/cs_demo3.c private/ private functions for MATLAB demos README.txt README file for CSparse MATLAB demo -------------------------------------------------------------------------------- ./MATLAB/Demo/private: private functions for MATLAB demos -------------------------------------------------------------------------------- demo2.m demo 2 demo3.m demo 3 ex_1.m example 1 ex2.m example 2 ex3.m example 3 frand.m generate a random finite-element matrix get_problem.m get a matrix is_sym.m determine if a matrix is symmetric mesh2d1.m construct a 2D mesh (method 1) mesh2d2.m construct a 2D mesh (method 2) mesh3d1.m construct a 3D mesh (method 1) mesh3d2.m construct a 3D mesh (method 2) print_order.m print the ordering method used resid.m compute residual rhs.m create right-hand-side -------------------------------------------------------------------------------- ./MATLAB/Test: Extensive test of CSparse, in MATLAB -------------------------------------------------------------------------------- Makefile Makefile for MATLAB Test directory README.txt README file for MATLAB/Test Contents.m Contents of MATLAB/Test, "textbook" files only chol_downdate.m downdate a Cholesky factorization. chol_left.m left-looking Cholesky factorization. chol_left2.m left-looking Cholesky factorization, more details. chol_right.m right-looking Cholesky factorization. chol_super.m left-looking "supernodal" Cholesky factorization. chol_up.m up-looking Cholesky factorization. chol_update.m update a Cholesky factorization. chol_updown.m update or downdate a Cholesky factorization. cond1est.m 1-norm condition estimate. cs_fiedler.m the Fiedler vector of a connected graph. givens2.m find a Givens rotation. house.m find a Householder reflection. lu_left.m left-looking LU factorization. lu_right.m right-looking LU factorization. lu_rightp.m right-looking LU factorization, with partial pivoting. lu_rightpr.m recursive right-looking LU, with partial pivoting. lu_rightr.m recursive right-looking LU. norm1est.m 1-norm estimate. qr_givens.m Givens-rotation QR factorization. qr_givens_full.m Givens-rotation QR factorization, for full matrices. qr_left.m left-looking Householder QR factorization. qr_right.m right-looking Householder QR factorization. cs_fiedler.m Fiedler vector cs_frand.m generate a random finite-element matrix cs_frand_mex.c cs_ipvec.m x(p)=b cs_ipvec_mex.c cs_maxtransr.m recursive maximum matching algorithm cs_maxtransr_mex.c cs_pvec.m x=b(p) cs_pvec_mex.c interface for cs_pvec cs_reach.m non-recursive reach (interface to CSparse cs_reach) cs_reach_mex.c non-recursive x=spones(L\sparse(b)) cs_reachr.m recursive reach (interface to CSparse cs_reachr) cs_reachr_mex.c cs_rowcnt.m row counts for sparse Cholesky cs_rowcnt_mex.c row counts for sparse Cholesky cs_sparse2.m same as cs_sparse, to test cs_entry function cs_sparse2_mex.c like cs_sparse, but for testing cs_entry cs_test_make.m compiles MATLAB tests check_if_same.m check if two inputs are identical or not choldn.m Cholesky downdate cholup.m Cholesky update, using Given's rotations cholupdown.m Cholesky update/downdate (Bischof, Pan, and Tang method) cs_q1.m construct Q from Householder vectors cs_test_make.m compiles the CSparse, Demo, and Test mexFunctions. dmperm_test.m test cs_dmperm chol_example.m simple Cholesky factorization example etree_sample.m construct a sample etree and symbolic factorization gqr3.m QR factorization, based on Givens rotations happly.m apply Householder reflection to a vector hmake1.m construct a Householder reflection mynormest1.m estimate norm(A,1), using LU factorization (L*U = P*A*Q). myqr.m QR factorization using Householder reflections another_colormap.m try another color map cspy_test.m test cspy and cs_dmspy qr2.m QR factorization based on Householder reflections sample_colormap.m try a colormap for use in cspy signum.m compute and display the sign of a column vector x sqr_example.m test cs_sqr dmspy_test.m test cspy, cs_dmspy, and cs_dmperm test_qr.m test various QR factorization methods test_randperms.m test random permutations testh.m test Householder reflections test_qr1.m test QR factorizations test_qrsol.m test cs_qrsol test_sep.m test cs_sep, and compare with Gilbert's meshpart vtxsep testall.m test all CSparse functions (run tests 1 to 28 below) test1.m test cs_transpose test2.m test cs_sparse test3.m test cs_lsolve, cs_ltsolve, cs_usolve, cs_chol test4.m test cs_multiply test5.m test cs_add test6.m test cs_reach, cs_reachr, cs_lsolve, cs_usolve test7.m test cs_lu test8.m test cs_cholsol, cs_lusol test9.m test cs_qr test10.m test cs_qr test11.m test cs_rowcnt test12.m test cs_qr and compare with svd test13.m test cs_counts, cs_etree test14.m test cs_droptol test15.m test cs_amd test16.m test cs_amd test17.m test cs_qr, cs_qright, cs_q1, cs_qrleft, cs_qrsol test18.m test iterative refinement after backslash test19.m test cs_dmperm, cs_maxtransr, cs_dmspy, cs_scc test20.m test cholupdown test21.m test cs_updown test22.m test cond1est test23.m test cs_dmspy test24.m test cs_fielder test25.m test cs_nd test26.m test cs_dmsol and cs_dmspy test27.m test cs_qr, cs_utsolve, cs_qrsol test28.m test cs_randperm, cs_dmperm -------------------------------------------------------------------------------- ./MATLAB/UFget: MATLAB interface for the UF Sparse Matrix Collection -------------------------------------------------------------------------------- Contents.m Contents of UFget mat/ default directory where downloaded matrices will be put README.txt README file for UFget UFget_defaults.m default parameter settings UFget_example.m example of use UFget_install.m installs UFget temporarily (for current session) UFget_java.class read a url and load it in into MATLAB (compiled Java code) UFget_java.java read a url and load it in into MATLAB (Java source code) UFget_lookup.m look up a matrix in the index UFget.m UFget itself (primary user interface) UFweb.m open url for a matrix or collection mat/UF_Index.mat index of matrices in UF Sparse Matrix Collection -------------------------------------------------------------------------------- ./Matrix: Sample matrices, most from Rutherford/Boeing collection -------------------------------------------------------------------------------- ash219 overdetermined pattern of Holland survey. Ashkenazi, 1974. bcsstk01 stiffness matrix for small generalized eigenvalue problem bcsstk16 stiffness matrix, Corp of Engineers dam fs_183_1 unsymmetric facsimile convergence matrix lp_afiro NETLIB afiro linear programming problem mbeacxc US economy, 1972. Dan Szyld, while at NYU t1 small example used in Chapter 2 west0067 Cavett problem with 5 components (chemical eng., Westerberg) c_mbeacxc complex version of mbeacxc c_west0067 complex version of west0067 mhd1280b Alfven spectra in magnetohydrodynamics (complex) neumann complex matrix qc324 model of H+ in an electromagnetic field (complex) t2 small complex matrix t3 small complex matrix t4 small complex matrix c4 small complex matrix young1c aeronautical problem (complex matrix) -------------------------------------------------------------------------------- ./Tcov: Exhaustive test coverage of CXSparse -------------------------------------------------------------------------------- covall same as covall.linux covall.linux find coverage (Linux) covall.sol find coverage (Solaris) cov.awk coverage summary cover print uncovered lines covs print uncovered lines cstcov_malloc_test.c malloc test cstcov_malloc_test.h cstcov_test.c main program for Tcov tests gcovs run gcov (Linux) Makefile Makefile for Tcov tests nil an empty matrix zero a 1-by-1 zero matrix czero a 1-by-1 complex zero matrix README.txt README file for Tcov directory -------------------------------------------------------------------------------- Change Log: -------------------------------------------------------------------------------- Refer to CSparse for changes in CSparse, which are immediately propagated into CXSparse (those Change Log entries are not repeated here). Nov 1, 2007. version 2.2.1 CXSparse/MATLAB/Test ported to Windows May 31, 2007. version 2.2.0 * back-port to MATLAB 7.2 and earlier (which does not have mwIndex). * more graceful failure in cs_make when attempting complex matrix support (Windows, in particular) * correction to CXSparse/Demo/Makefile * added sizeof(CS_INT) printout to cs_idemo.c, cs_ldemo.c Mar 14, 2007. Version 2.1.0. * MATLAB interface added for CXSparse. * cs_complex_t type added (a #define for "double _Complex", which is the complex type used in CXSparse 2.0.x). When compiling with a C++ compiler, the std::compex type is used for the complex case. * bug fix in complex sparse Cholesky (cs_chol.c). * bug fix in complex sparse Cholesky update/downdate (cs_updown.c). * bug fix in cs_symperm for the complex case. * "beta" changed from complex to real, in sparse QR (cs_house.c, cs_happly.c, cs_qr.c), (a performance/memory improvement, not a bug fix). Similar change to "nz2" in cs_cumsum.c. May 5, 2006. Version 2.0.1 released. * long changed to UF_long, dependency in ../UFconfig/UFconfig.h added. "UF_long" is a #define'd term in UFconfig.h. It is normally defined as "long", but can be redefined as something else if desired. On Windows-64, it becomes __int64. Mar 6, 2006 "double complex" changed to "double _Complex", to avoid conflicts when CXSparse is compiled with a C++ compiler. Other minor changes to cs.h. SuiteSparse/UMFPACK/0000755001170100242450000000000010711725117013037 5ustar davisfacSuiteSparse/UMFPACK/Doc/0000755001170100242450000000000010711436607013547 5ustar davisfacSuiteSparse/UMFPACK/Doc/Makefile0000644001170100242450000000417210367442014015207 0ustar davisfac#------------------------------------------------------------------------------- # UMFPACK Makefile for compiling on Unix systems (for GNU or original make) #------------------------------------------------------------------------------- # UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis. # All Rights Reserved. See ../Doc/License for License. default: dist include ../../UFconfig/UFconfig.mk #------------------------------------------------------------------------------- # Remove all but the files in the original distribution #------------------------------------------------------------------------------- # Note that UserGuide.tex is created from UserGuide.stex, the files in # the ../Include directory, and the ../Demo/umfpack_simple.c file. purge: clean - $(RM) *.aux *.bbl *.blg *.log *.toc - $(RM) UserGuide.tex clean: - $(RM) $(CLEAN) #------------------------------------------------------------------------------- # Create the User Guide and Quick Start Guide #------------------------------------------------------------------------------- UMFPACK = umfpack_col_to_triplet umfpack_defaults umfpack_free_numeric \ umfpack_free_symbolic umfpack_get_numeric umfpack_get_lunz \ umfpack_get_determinant \ umfpack_get_symbolic umfpack_numeric umfpack_qsymbolic \ umfpack_report_control umfpack_report_info umfpack_report_matrix \ umfpack_report_numeric umfpack_report_perm umfpack_report_status \ umfpack_report_symbolic umfpack_report_triplet \ umfpack_report_vector umfpack_solve umfpack_symbolic \ umfpack_transpose umfpack_triplet_to_col umfpack_scale UMFPACKW = umfpack_wsolve USER = $(UMFPACKW) $(UMFPACK) SRC = $(addprefix ../Include/, $(addsuffix .h,$(USER))) ../Demo/umfpack_simple.c UserGuide.pdf: UserGuide.stex UserGuide.sed1 UserGuide.sed2 $(SRC) UserGuide.bib sed -f UserGuide.sed1 < UserGuide.stex | sed -f UserGuide.sed2 \ | expand -8 > UserGuide.tex pdflatex UserGuide bibtex UserGuide pdflatex UserGuide pdflatex UserGuide QuickStart.pdf: QuickStart.tex pdflatex QuickStart pdflatex QuickStart dist: QuickStart.pdf UserGuide.pdf - $(RM) *.aux *.bbl *.blg *.log *.toc - $(RM) UserGuide.tex SuiteSparse/UMFPACK/Doc/UserGuide.bib0000644001170100242450000002046310425403737016126 0ustar davisfac@string{TOMS = "ACM Trans. Math. Softw."} @string{SIMAX = "SIAM J. Matrix Anal. Applic."} @string{SINUM = "SIAM J. Numer. Anal."} @string{SIAMJSC = "SIAM J. Sci. Comput."} @string{SIAMJSSC = "SIAM J. Sci. Statist. Comput."} @string{IJNME = "Internat. J. Numer. Methods Eng."} @string{SIAMJADM = "SIAM J. Alg. Disc. Meth."} @article{AmestoyDavisDuff96, author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.}, title={An approximate minimum degree ordering algorithm}, journal=SIMAX, year={1996} ,volume={17} ,number={4} ,pages={886-905}} @article{AmestoyDavisDuff03, author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.}, title={Algorithm 837: {AMD}, an approximate minimum degree ordering algorithm}, journal=TOMS, year={2004} ,volume={30} ,number={3} ,pages={381-388}} @techreport{AmestoyDavisDuff03_user, author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.}, title={{AMD} Version 1.0 User Guide}, institution={CISE Dept., Univ. of Florida}, year={2003} ,number={TR-03-011} ,address={Gainesville, FL} ,note={www.cise.ufl.edu/tech-reports.} } @article{Davis03, author={Davis, T. A.}, title={A column pre-ordering strategy for the unsymmetric-pattern multifrontal method}, journal=TOMS, year={2004} ,volume={30} ,number={2} ,pages={165-195}} @article{Davis03_algo, author={Davis, T. A.}, title={Algorithm 832: {UMFPACK}, an unsymmetric-pattern multifrontal method}, journal=TOMS, year={2004} ,volume={30} ,number={2} ,pages={196-199}} @techreport{Davis03_umf, author={Davis, T. A.}, title={{UMFPACK} User Guide}, institution={Univ. of Florida, CISE Dept.}, year={2005} ,number={TR-04-003 (revised)} ,address={Gainesville, FL} ,note={(www.cise.ufl.edu/tech-reports)} } @techreport{Davis03_umfquick, author={Davis, T. A.}, title={{UMFPACK} Quick Start Guide}, institution={Univ. of Florida, CISE Dept.}, year={2005} ,number={TR-04-005 (revised)} ,address={Gainesville, FL} ,note={(www.cise.ufl.edu/tech-reports)} } @article{DavisDuff97, author={Davis, T. A. and Duff, I. S.}, title={An unsymmetric-pattern multifrontal method for sparse {LU} factorization}, journal=SIMAX, year={1997} ,volume={18} ,number={1} ,pages={140-158}} @article{DavisDuff99, author={Davis, T. A. and Duff, I. S.}, title={A combined unifrontal/multifrontal method for unsymmetric sparse matrices}, journal=TOMS, volume={25}, number={1}, pages={1-19}, year={1999}} @article{SuperLU99, author={Demmel, J. W. and Eisenstat, S. C. and Gilbert, J. R. and Li, X. S. and Liu, J. W. H.}, title={A supernodal approach to sparse partial pivoting}, journal=SIMAX, year={1999} ,volume={20} ,number={3} ,pages={720-755} ,note={www.netlib.org} } @article{ACM679a, author={Dongarra, J. J. and Du Croz, J. and Duff, I. S. and Hammarling, S.}, title={A set of level-3 basic linear algebra subprograms}, journal=TOMS, year={1990} ,volume={16} ,number={1} ,pages={1--17}} @article{netlib, author={Dongarra, J. J. and Grosse, E.}, title={Distribution of mathematical software via electronic mail}, journal={Comm. ACM}, year={1987} ,volume={30} ,pages={403-407} ,note={www.netlib.org} } @article{Duff78b, author={Duff, I. S. and Reid, J. K.}, year={1978}, title={Algorithm 529: Permutations to Block Triangular Form}, journal=TOMS, volume={4}, annote={f}, number={2}, pages={189-192}, keywords={102 ordering block triangular form}} @article{Duff81b, author={Duff, I. S.}, year={1981}, title={Algorithm 575: Permutations for a Zero-Free Diagonal}, journal=TOMS, annote={f}, volume={7}, pages={387-390}, keywords={ordering, zero-free diagonal}} @techreport{GotoVandeGeijn02, author = {Goto, K. and van de Geijn, R.}, title = {On Reducing {TLB} Misses in Matrix Multiplication, {FLAME} Working Note 9}, institution={The University of Texas at Austin, Department of Computer Sciences}, number={TR-2002-55}, month={Nov.}, year={2002}} @article{GeorgeNg85, author={George, A. and Ng, E. G.}, year={1985}, title={An Implementation of {G}aussian Elimination with Partial Pivoting for Sparse Systems}, journal=SIAMJSSC, volume={6}, number={2}, pages={390-409}} @article{GeorgeNg87, author={George, A. and Ng, E. G.}, year={1987}, title={Symbolic Factorization for Sparse {G}aussian Elimination with Partial Pivoting}, journal={SIAM J. Sci. Statist. Comput.}, volume={8}, number={6}, pages={877-898}} @article{GilbertMolerSchreiber, author={Gilbert, J. R. and Moler, C. and Schreiber, R.}, title={Sparse matrices in {MATLAB}: design and implementation}, journal=SIMAX, year={1992} ,volume={13} ,number={1} ,pages={333-356}} @article{GilbertPeierls88, author={Gilbert, J. R. and Peierls, T.}, year={1988}, title={Sparse Partial Pivoting in Time Proportional to Arithmetic Operations}, journal={SIAM J. Sci. Statist. Comput.}, volume={9}, pages={862-874}} @article{Gustavson78, author={Gustavson, F. G.}, year={1978}, title={Two Fast Algorithms for Sparse Matrices: Multiplication and Permuted Transposition}, journal=TOMS, volume={4}, number={3}, pages={250-269}} @techreport{Larimore98, author={Larimore, S. I.}, title={An approximate minimum degree column ordering algorithm}, institution={Univ. of Florida, CISE Dept.}, year={1998} ,number={TR-98-016} ,address={Gainesville, FL} ,note={www.cise.ufl.edu/tech-reports}} @article{DavisGilbertLarimoreNg00, author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.}, title={A column approximate minimum degree ordering algorithm}, journal=TOMS, year={2004} ,volume={30} ,number={3} ,pages={353-376}} @article{DavisGilbertLarimoreNg00_algo, author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.}, title={Algorithm 836: {COLAMD}, a column approximate minimum degree ordering algorithm}, journal=TOMS, year={2004} ,volume={30} ,number={3} ,pages={377-380}} @INCOLLECTION{GilbertNg93, author = {J. R. Gilbert and E. G. Ng}, editor = {A. George and J. R. Gilbert and J. W.H. Liu}, year = 1993, title = {Predicting Structure in Nonsymmetric Sparse Matrix Factorizations}, booktitle = {Graph Theory and Sparse Matrix Computation}, series = {Volume 56 of the {IMA} Volumes in Mathematics and its Applications}, pages = {107-139}, publisher = {Springer-Verlag} } @techreport{ATLAS, author={Whaley, R. C and Petitet, A. and Dongarra, J. J.}, title={Automated Emperical Optimization of Software and the {ATLAS} Project}, institution={Computer Science Department, The University of Tennessee}, year={2000} ,number={LAPACK Working Note 147} ,month={September} ,note={www.netlib.org/atlas} } @article{DaydeDuff99, author = "M. J. Dayd\'{e} and I. S. Duff", title = "The {RISC} {BLAS}: A Blocked Implementation of Level 3 {BLAS} for {RISC} Processors", journal = TOMS, volume = "25", number = "3", month = {Sept.}, year ="1999" } @article{ardd:89, author = {M. Arioli and J. W. Demmel and I. S. Duff}, year = "1989", title = {Solving sparse linear systems with sparse backward error}, journal = SIMAX, volume = {10}, pages = {165-190} } @article{DavisHager99, author={Davis, T. A. and Hager, W. W.}, title={Modifying a sparse {C}holesky factorization}, journal=SIMAX, year={1999} ,volume={20} ,number={3} ,pages={606-627} } @article{dusc:96, author = {I. S. Duff and J. A. Scott}, title = {The design of a new frontal code for solving sparse unsymmetric systems}, journal = TOMS, year = "1996", volume = "22", number = "1", pages = "30-45" } @article{Duff78a, author={Duff, I. S. and Reid, J. K.}, year={1978}, title={An Implementation of {T}arjan's Algorithm for the Block Triangularization of a Matrix}, journal=TOMS, volume={4}, number={2}, pages={137-147} } @book{GeorgeLiu, author={George, A. and Liu, J. W. H.}, year={1981}, title={Computer Solution of Large Sparse Positive Definite Systems}, publisher={Englewood Cliffs, New Jersey: Prentice-Hall} } @article{GilbertNgPeyton94, author={Gilbert, J. R. and Ng, E. G. and Peyton, B. W.}, title={An efficient algorithm to compute row and column counts for sparse {C}holesky factorization}, journal=SIMAX, year={1994} ,volume={15} ,number={4} ,pages={1075-1091} } @techreport{DuffGrimesLewis87b, author={Duff, I. S. and Grimes, R. G. and Lewis, J. G.}, year={1987}, title={Users' Guide for the Harwell-Boeing Sparse Matrix Test Collection}, institution={AERE Harwell Laboratory, United Kingdom Atomic Energy Authority}} SuiteSparse/UMFPACK/Doc/UserGuide.pdf0000644001170100242450000141763610711436316016155 0ustar davisfac%PDF-1.4 3 0 obj << /Length 2966 /Filter /FlateDecode >> stream xڍYKs8WDUY4 9=Nhc;.[(XH IEHJ@~:_;t7{'GhvIFdz52jGY %L]njZ%}vZd5}4gOX=3KnqWUxX[fFb[9:"ନ P[Ss8 " 3<%^Ι!$+j R] cZgE^46Ƚʾ#?* X]E̊lY'GeG-QuT'c4+:08l{X}[]F>Ly-9UɛMJQ4j CAY{<~U? *)e,p9b \UZκS`U6<?`+ }J g`s<ΓcaC<0T$}AslG#w.SP]?\ ,F =lU-D:q4<b%2{hJ0׶Hm3:Z1twQmLhئpF{S炕Dv0LCT9N\ \Mz@0^!0Q|;19M3Y휦jcjspVgGa:T8`.T&>y,K3!T RYHZ//3{!yLٙAa3OF"?p&aą4v9>&څHWJ7zf6*=b;J]@uk L`J.TaElx< H9ʈG&uJ_4f[N 6P܉LVLjl,&-$k'>3ȉ[Ѭ1 Df_$kLzX{V(= x5_C`1>)DGjKwUJݠ"9/i=EP#0d|347nv\0N fQ% 91%W>LqG ()Ҽ:uk->}XͷnЅ:nvCҷo@ThK5ndJ*0<." r P~;Lq[Wsޠ/n>"b累qgvw]A=xnn8،.ЙAF?eeVbG7PB,r X@99o|a _cF-[! 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umfpack_free_numeric.h/r ../Include/umfpack_free_numeric.h /INCLUDE umfpack_free_symbolic.h/r ../Include/umfpack_free_symbolic.h /INCLUDE umfpack_get_lunz.h/r ../Include/umfpack_get_lunz.h /INCLUDE umfpack_get_numeric.h/r ../Include/umfpack_get_numeric.h /INCLUDE umfpack_get_symbolic.h/r ../Include/umfpack_get_symbolic.h /INCLUDE umfpack_get_scale.h/r ../Include/umfpack_get_scale.h /INCLUDE umfpack_numeric.h/r ../Include/umfpack_numeric.h /INCLUDE umfpack_qsymbolic.h/r ../Include/umfpack_qsymbolic.h /INCLUDE umfpack_report_control.h/r ../Include/umfpack_report_control.h /INCLUDE umfpack_report_info.h/r ../Include/umfpack_report_info.h /INCLUDE umfpack_report_matrix.h/r ../Include/umfpack_report_matrix.h /INCLUDE umfpack_report_numeric.h/r ../Include/umfpack_report_numeric.h /INCLUDE umfpack_report_perm.h/r ../Include/umfpack_report_perm.h /INCLUDE umfpack_report_status.h/r ../Include/umfpack_report_status.h /INCLUDE umfpack_report_symbolic.h/r ../Include/umfpack_report_symbolic.h /INCLUDE umfpack_report_triplet.h/r ../Include/umfpack_report_triplet.h /INCLUDE umfpack_report_vector.h/r ../Include/umfpack_report_vector.h /INCLUDE umfpack_simple.c/r ../Demo/umfpack_simple.c /INCLUDE umfpack_solve.h/r ../Include/umfpack_solve.h /INCLUDE umfpack_scale.h/r ../Include/umfpack_scale.h /INCLUDE umfpack_symbolic.h/r ../Include/umfpack_symbolic.h /INCLUDE umfpack_timer.h/r ../Include/umfpack_timer.h /INCLUDE umfpack_tictoc.h/r ../Include/umfpack_tictoc.h /INCLUDE umfpack_transpose.h/r ../Include/umfpack_transpose.h /INCLUDE umfpack_triplet_to_col.h/r ../Include/umfpack_triplet_to_col.h /INCLUDE umfpack_wsolve.h/r ../Include/umfpack_wsolve.h /INCLUDE umfpack_load_numeric.h/r ../Include/umfpack_load_numeric.h /INCLUDE umfpack_load_symbolic.h/r ../Include/umfpack_load_symbolic.h /INCLUDE umfpack_save_numeric.h/r ../Include/umfpack_save_numeric.h /INCLUDE umfpack_save_symbolic.h/r ../Include/umfpack_save_symbolic.h /INCLUDE umfpack_get_determinant.h/r ../Include/umfpack_get_determinant.h SuiteSparse/UMFPACK/Doc/UserGuide.sed20000644001170100242450000000004710006260703016210 0ustar davisfac/[/][*]/d /[*][/]/d /INCLUDE umfpack/d SuiteSparse/UMFPACK/Doc/UserGuide.stex0000644001170100242450000033454110711430613016351 0ustar davisfac%------------------------------------------------------------------------------- % The UserGuide.stex file. Processed into UserGuide.tex via sed. %------------------------------------------------------------------------------- \documentclass[11pt]{article} \newcommand{\m}[1]{{\bf{#1}}} % for matrices and vectors \newcommand{\tr}{^{\sf T}} % transpose \newcommand{\he}{^{\sf H}} % complex conjugate transpose \newcommand{\implies}{\rightarrow} \topmargin 0in \textheight 9in \oddsidemargin 0pt \evensidemargin 0pt \textwidth 6.5in \begin{document} \author{Timothy A. Davis \\ Dept. of Computer and Information Science and Engineering \\ Univ. of Florida, Gainesville, FL} \title{UMFPACK Version 5.2.0 User Guide} \date{Nov 1, 2007} \maketitle %------------------------------------------------------------------------------- \begin{abstract} UMFPACK is a set of routines for solving unsymmetric sparse linear systems, $\m{Ax}=\m{b}$, using the Unsymmetric MultiFrontal method and direct sparse LU factorization. It is written in ANSI/ISO C, with a MATLAB interface. UMFPACK relies on the Level-3 Basic Linear Algebra Subprograms (dense matrix multiply) for its performance. This code works on Windows and many versions of Unix (Sun Solaris, Red Hat Linux, IBM AIX, SGI IRIX, and Compaq Alpha). \end{abstract} %------------------------------------------------------------------------------- Technical Report TR-04-003 (revised) UMFPACK Version 5.2.0, Copyright\copyright 1995-2006 by Timothy A. Davis. All Rights Reserved. UMFPACK is available under alternate licences; contact T. Davis for details. {\bf UMFPACK License:} Your use or distribution of UMFPACK or any modified version of UMFPACK implies that you agree to this License. This library is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Permission is hereby granted to use or copy this program under the terms of the GNU GPL, provided that the Copyright, this License, and the Availability of the original version is retained on all copies. User documentation of any code that uses this code or any modified version of this code must cite the Copyright, this License, the Availability note, and "Used by permission." Permission to modify the code and to distribute modified code is granted, provided the Copyright, this License, and the Availability note are retained, and a notice that the code was modified is included. {\bf Availability:} http://www.cise.ufl.edu/research/sparse/umfpack {\bf Acknowledgments:} This work was supported by the National Science Foundation, under grants DMS-9504974, DMS-9803599, and CCR-0203270. The upgrade to Version 4.1 and the inclusion of the symmetric and 2-by-2 pivoting strategies were done while the author was on sabbatical at Stanford University and Lawrence Berkeley National Laboratory. %------------------------------------------------------------------------------- \newpage %------------------------------------------------------------------------------- \tableofcontents %------------------------------------------------------------------------------- \newpage \section{Overview} %------------------------------------------------------------------------------- UMFPACK\footnote{Pronounced with two syllables: umph-pack} is a set of routines for solving systems of linear equations, $\m{Ax}=\m{b}$, when $\m{A}$ is sparse and unsymmetric. It is based on the Unsymmetric-pattern MultiFrontal method \cite{DavisDuff97,DavisDuff99}. UMFPACK factorizes $\m{PAQ}$, $\m{PRAQ}$, or $\m{PR}^{-1}\m{AQ}$ into the product $\m{LU}$, where $\m{L}$ and $\m{U}$ are lower and upper triangular, respectively, $\m{P}$ and $\m{Q}$ are permutation matrices, and $\m{R}$ is a diagonal matrix of row scaling factors (or $\m{R}=\m{I}$ if row-scaling is not used). Both $\m{P}$ and $\m{Q}$ are chosen to reduce fill-in (new nonzeros in $\m{L}$ and $\m{U}$ that are not present in $\m{A}$). The permutation $\m{P}$ has the dual role of reducing fill-in and maintaining numerical accuracy (via relaxed partial pivoting and row interchanges). The sparse matrix $\m{A}$ can be square or rectangular, singular or non-singular, and real or complex (or any combination). Only square matrices $\m{A}$ can be used to solve $\m{Ax}=\m{b}$ or related systems. Rectangular matrices can only be factorized. UMFPACK first finds a column pre-ordering that reduces fill-in, without regard to numerical values. It scales and analyzes the matrix, and then automatically selects one of three strategies for pre-ordering the rows and columns: {\em unsymmetric}, {\em 2-by-2}, and {\em symmetric}. These strategies are described below. First, all pivots with zero Markowitz cost are eliminated and placed in the LU factors. The remaining submatrix $\m{S}$ is then analyzed. The following rules are applied, and the first one that matches defines the strategy. \begin{itemize} \item Rule 1: $\m{A}$ rectangular $\implies$ unsymmetric. \item Rule 2: If the zero-Markowitz elimination results in a rectangular $\m{S}$, or an $\m{S}$ whose diagonal has not been preserved, the unsymmetric strategy is used. \item The symmetry $\sigma_1$ of $\m{S}$ is computed. It is defined as the number of {\em matched} off-diagonal entries, divided by the total number of off-diagonal entries. An entry $s_{ij}$ is matched if $s_{ji}$ is also an entry. They need not be numerically equal. An {\em entry} is a value in $\m{A}$ which is present in the input data structure. All nonzeros are entries, but some entries may be numerically zero. Rule 3: $\sigma_1 < 0.1 \implies$ unsymmetric. The matrix is very unsymmetric. \item Let $d$ be the number of nonzero entries on the diagonal of $\m{S}$. Let $\m{S}$ be $\nu$-by-$\nu$. Rule 4: $(\sigma_1 \ge 0.7) \:\wedge\: (d = \nu) \implies$ symmetric. The matrix has a nearly symmetric nonzero pattern, and a zero-free diagonal. \end{itemize} If the strategy has not yet been determined, the 2-by-2 strategy is attempted. A row permutation $\m{P}_2$ is found which attempts to reduce the number of small diagonal entries of $\m{P}_2 \m{S}$. An entry $s_{ij}$ is determined to be small if $|s_{ij}| < 0.01 \max |s_{*j}|$, or large otherwise. If $s_{ii}$ is numerically small, the method attempts to swap two rows $i$ and $j$, such that both $s_{ij}$ and $s_{ji}$ are large. Once these rows are swapped, they remain in place. Let $\sigma_2$ be the symmetry of $\m{P}_2 \m{S}$, and let $d_2$ be the number of nonzero entries (either small or large) on the diagonal of $\m{P}_2 \m{S}$. \begin{itemize} \item Rule 5: ($\sigma_2 > 1.1 \sigma_1) \:\wedge\: (d_2 > 0.9 \nu) \implies$ 2-by-2. The 2-by-2 permutation has made the matrix significantly more symmetric. \item Rule 6: $\sigma_2 < 0.7 \sigma_1 \implies$ unsymmetric. The 2-by-2 strategy has significantly deteriorated the symmetry, \item Rule 7: $\sigma_2 < 0.25 \implies$ unsymmetric. The matrix is still very unsymmetric. \item Rule 8: $\sigma_2 \ge 0.51 \implies$ 2-by-2. The matrix is roughly symmetric. \item Rule 9: $\sigma_2 \ge 0.999 \sigma_1 \implies$ 2-by-2. The 2-by-2 permutation has preserved symmetry, or made it only slightly worse. \item Rule 10: if no rule has yet triggered, use the unsymmetric strategy. \end{itemize} Each strategy is described below: \begin{itemize} \item {\em unsymmetric}: The column pre-ordering of $\m{S}$ is computed by a modified version of COLAMD \cite{DavisGilbertLarimoreNg00_algo,DavisGilbertLarimoreNg00,Larimore98}. The method finds a symmetric permutation $\m{Q}$ of the matrix $\m{S}\tr\m{S}$ (without forming $\m{S}\tr\m{S}$ explicitly). This is a good choice for $\m{Q}$, since the Cholesky factors of $\m{(SQ)\tr(SQ)}$ are an upper bound (in terms of nonzero pattern) of the factor $\m{U}$ for the unsymmetric LU factorization ($\m{PSQ}=\m{LU}$) regardless of the choice of $\m{P}$ \cite{GeorgeNg85,GeorgeNg87,GilbertNg93}. This modified version of COLAMD also computes the column elimination tree and post-orders the tree. It finds the upper bound on the number of nonzeros in L and U. It also has a different threshold for determining dense rows and columns. During factorization, the column pre-ordering can be modified. Columns within a single super-column can be reshuffled, to reduce fill-in. Threshold partial pivoting is used with no preference given to the diagonal entry. Within a given pivot column $j$, an entry $a_{ij}$ can be chosen if $|a_{ij}| \ge 0.1 \max |a_{*j}|$. Among those numerically acceptable entries, the sparsest row $i$ is chosen as the pivot row. \item {\em 2-by-2}: The symmetric strategy (see below) is applied to the matrix $\m{P}_2 \m{S}$, rather than $\m{S}$. \item {\em symmetric}: The column ordering is computed from AMD \cite{AmestoyDavisDuff96,AmestoyDavisDuff03}, applied to the pattern of $\m{S}+\m{S}\tr$ followed by a post-ordering of the supernodal elimination tree of $\m{S}+\m{S}\tr$. No modification of the column pre-ordering is made during numerical factorization. Threshold partial pivoting is used, with a strong preference given to the diagonal entry. The diagonal entry is chosen if $a_{jj} \ge 0.001 \max |a_{*j}|$. Otherwise, a sparse row is selected, using the same method used by the unsymmetric strategy. \end{itemize} The symmetric and 2-by-2 strategies, and their automatic selection, are new to Version 4.1. Version 4.0 only used the unsymmetric strategy. Once the strategy is selected, the factorization of the matrix $\m{A}$ is broken down into the factorization of a sequence of dense rectangular frontal matrices. The frontal matrices are related to each other by a supernodal column elimination tree, in which each node in the tree represents one frontal matrix. This analysis phase also determines upper bounds on the memory usage, the floating-point operation count, and the number of nonzeros in the LU factors. UMFPACK factorizes each {\em chain} of frontal matrices in a single working array, similar to how the unifrontal method \cite{dusc:96} factorizes the whole matrix. A chain of frontal matrices is a sequence of fronts where the parent of front $i$ is $i$+1 in the supernodal column elimination tree. For the nonsingular matrices factorized with the unsymmetric strategy, there are exactly the same number of chains as there are leaves in the supernodal column elimination tree. UMFPACK is an outer-product based, right-looking method. At the $k$-th step of Gaussian elimination, it represents the updated submatrix $\m{A}_k$ as an implicit summation of a set of dense sub-matrices (referred to as {\em elements}, borrowing a phrase from finite-element methods) that arise when the frontal matrices are factorized and their pivot rows and columns eliminated. Each frontal matrix represents the elimination of one or more columns; each column of $\m{A}$ will be eliminated in a specific frontal matrix, and which frontal matrix will be used for which column is determined by the pre-analysis phase. The pre-analysis phase also determines the worst-case size of each frontal matrix so that they can hold any candidate pivot column and any candidate pivot row. From the perspective of the analysis phase, any candidate pivot column in the frontal matrix is identical (in terms of nonzero pattern), and so is any row. However, the numeric factorization phase has more information than the analysis phase. It uses this information to reorder the columns within each frontal matrix to reduce fill-in. Similarly, since the number of nonzeros in each row and column are maintained (more precisely, COLMMD-style approximate degrees \cite{GilbertMolerSchreiber}), a pivot row can be selected based on sparsity-preserving criteria (low degree) as well as numerical considerations (relaxed threshold partial pivoting). When the symmetric or 2-by-2 strategies are used, the column preordering is not refined during numeric factorization. Row pivoting for sparsity and numerical accuracy is performed if the diagonal entry is too small. More details of the method, including experimental results, are described in \cite{Davis03,Davis03_algo}, available at http://www.cise.ufl.edu/tech-reports. %------------------------------------------------------------------------------- \section{Availability} %------------------------------------------------------------------------------- In addition to appearing as a Collected Algorithm of the ACM, UMFPACK is available at http://www.cise.ufl.edu/research/sparse. It is included as a built-in routine in MATLAB. Version 4.0 (in MATLAB 6.5) does not have the symmetric or 2-by-2 strategies and it takes less advantage of the level-3 BLAS \cite{DaydeDuff99,ACM679a,ATLAS,GotoVandeGeijn02}. Versions 5.x through v4.1 tend to be much faster than Version 4.0, particularly on unsymmetric matrices with mostly symmetric nonzero pattern (such as finite element and circuit simulation matrices). Version 3.0 and following make use of a modified version of COLAMD V2.0 by Timothy A.~Davis, Stefan Larimore, John Gilbert, and Esmond Ng. The original COLAMD V2.1 is available in as a built-in routine in MATLAB V6.0 (or later), and at http://www.cise.ufl.edu/research/sparse. These codes are also available in Netlib \cite{netlib} at http://www.netlib.org. UMFPACK Versions 2.2.1 and earlier, co-authored with Iain Duff, are available at http://www.cise.ufl.edu/research/sparse and as MA38 (functionally equivalent to Version 2.2.1) in the Harwell Subroutine Library. {\bf NOTE: you must use the correct version of AMD with UMFPACK; using an old version of AMD with a newer version of UMFPACK can fail.} %------------------------------------------------------------------------------- \section{Primary changes from prior versions} %------------------------------------------------------------------------------- A detailed list of changes is in the {\tt ChangeLog} file. %------------------------------------------------------------------------------- \subsection{Version 5.2.0} %------------------------------------------------------------------------------- Change of license from GNU Lesser GPL to the GNU GPL. %------------------------------------------------------------------------------- \subsection{Version 5.1.0} %------------------------------------------------------------------------------- Port of MATLAB interface to 64-bit MATLAB. %------------------------------------------------------------------------------- \subsection{Version 5.0.3} %------------------------------------------------------------------------------- Renamed the MATLAB function to {\tt umfpack2}, so as not to confict with itself (the MATLAB built-in version of UMFPACK). %------------------------------------------------------------------------------- \subsection{Version 5.0} %------------------------------------------------------------------------------- Changed {\tt long} to {\tt UF\_long}, controlled by the {\tt UFconfig.h} file. A {\tt UF\_long} is normally just {\tt long}, except on the Windows 64 (WIN64) platform. In that case, it becomes {\tt \_\_int64}. %------------------------------------------------------------------------------- \subsection{Version 4.6} %------------------------------------------------------------------------------- Added additional options to {\tt umf\_solve.c}. %------------------------------------------------------------------------------- \subsection{Version 4.5} %------------------------------------------------------------------------------- Added function pointers for malloc, calloc, realloc, free, printf, hypot, and complex divisiion, so that these functions can be redefined at run-time. Added a version number so you can determine the version of UMFPACK at run time or compile time. UMFPACK requires AMD v2.0 or later. %------------------------------------------------------------------------------- \subsection{Version 4.4} %------------------------------------------------------------------------------- Bug fix in strategy selection in {\tt umfpack\_*\_qsymbolic}. Added packed complex case for all complex input/output arguments. Added {\tt umfpack\_get\_determinant}. Added minimal support for Microsoft Visual Studio (the {\tt umf\_multicompile.c} file). %------------------------------------------------------------------------------- \subsection{Version 4.3.1} %------------------------------------------------------------------------------- Minor bug fix in the forward/backsolve. This bug had the effect of turning off iterative refinement when solving $\m{A}\tr\m{x}=\m{b}$ after factorizing $\m{A}$. UMFPACK mexFunction now factorizes $\m{A}\tr$ in its forward-slash operation. %------------------------------------------------------------------------------- \subsection{Version 4.3} %------------------------------------------------------------------------------- No changes are visible to the C or MATLAB user, except the presence of one new control parameter in the {\tt Control} array, and three new statistics in the {\tt Info} array. The primary change is the addition of an (optional) drop tolerance. %------------------------------------------------------------------------------- \subsection{Version 4.1} %------------------------------------------------------------------------------- The following is a summary of the main changes that are visible to the C or MATLAB user: \begin{enumerate} \item New ordering strategies added. No changes are required in user code (either C or MATLAB) to use the new default strategy, which is an automatic selection of the unsymmetric, symmetric, or 2-by-2 strategies. \item Row scaling added. This is only visible to the MATLAB caller when using the form {\tt [L,U,P,Q,R] = umfpack (A)}, to retrieve the LU factors. Likewise, it is only visible to the C caller when the LU factors are retrieved, or when solving systems with just $\m{L}$ or $\m{U}$. New C-callable and MATLAB-callable routines are included to get and to apply the scale factors computed by UMFPACK. Row scaling is enabled by default, but can be disabled. Row scaling usually leads to a better factorization, particularly when the symmetric strategy is used. \item Error code {\tt UMFPACK\_ERROR\_problem\_to\_large} removed. Version 4.0 would generate this error when the upper bound memory usage exceeded 2GB (for the {\tt int} version), even when the actual memory usage was less than this. The new version properly handles this case, and can successfully factorize the matrix if sufficient memory is available. \item New control parameters and statistics provided. \item The AMD symmetric approximate minimum degree ordering routine added \cite{AmestoyDavisDuff96,AmestoyDavisDuff03}. It is used by UMFPACK, and can also be called independently from C or MATLAB. \item The {\tt umfpack} mexFunction now returns permutation matrices, not permutation vectors, when using the form {\tt [L,U,P,Q] = umfpack (A)} or the new form {\tt [L,U,P,Q,R] = umfpack (A)}. \item New arguments added to the user-callable routines {\tt umfpack\_*\_symbolic}, {\tt umfpack\_*\_qsymbolic}, {\tt umfpack\_*\_get\_numeric}, and {\tt umfpack\_*\_get\_symbolic}. The symbolic analysis now makes use of the numerical values of the matrix $\m{A}$, to guide the 2-by-2 strategy. The subsequent matrix passed to the numeric factorization step does not have to have the same numerical values. All of the new arguments are optional. If you do not wish to include them, simply pass {\tt NULL} pointers instead. The 2-by-2 strategy will assume all entries are numerically large, for example. \item New routines added to save and load the {\tt Numeric} and {\tt Symbolic} objects to and from a binary file. \item A Fortran interface added. It provides access to a subset of UMFPACK's features. \item You can compute an incomplete LU factorization, by dropping small entries from $\m{L}$ and $\m{U}$. By default, no nonzero entry is dropped, no matter how small in absolute value. This feature is new to Version 4.3. \end{enumerate} %------------------------------------------------------------------------------- \section{Using UMFPACK in MATLAB} %------------------------------------------------------------------------------- The easiest way to use UMFPACK is within MATLAB. Version 4.3 is a built-in routine in MATLAB 7.0.4, and is used in {\tt x = A}$\backslash${\tt b} when {\tt A} is sparse, square, unsymmetric (or symmetric but not positive definite), and with nonzero entries that are not confined in a narrow band. It is also used for the {\tt [L,U,P,Q] = lu (A)} usage of {\tt lu}. Type {\tt help lu} in MATLAB 6.5 or later for more details. To use the UMFPACK mexFunction, you must download and compile it, since the mexFunction itself is not part of MATLAB. The following discussion assumes that you have MATLAB Version 6.0 or later (which includes the BLAS, and the {\tt colamd} ordering routine). To compile both the UMFPACK and AMD mexFunctions, just type {\tt make} in the Unix system shell, while in the {\tt UMFPACK} directory. You can also type {\tt umfpack\_make} in MATLAB, if you are in the {\tt UMFPACK/MATLAB} directory, or if that directory is in your MATLAB path. This works on any system with MATLAB, including Windows. See Section~\ref{Install} for more details on how to install UMFPACK. Once installed, the UMFPACK mexFunction can analyze, factor, and solve linear systems. Table~\ref{matlab} summarizes some of the more common uses of the UMFPACK mexFunction within MATLAB. An optional input argument can be used to modify the control parameters for UMFPACK, and an optional output argument provides statistics on the factorization. Refer to the AMD User Guide for more details about the AMD mexFunction. \begin{table} \caption{Using UMFPACK's MATLAB interface} \label{matlab} \vspace{0.1in} {\footnotesize \begin{tabular}{l|l|l} \hline Function & Using UMFPACK & MATLAB 6.0 equivalent \\ \hline & & \\ \begin{minipage}[t]{1.5in} Solve $\m{Ax}=\m{b}$. \end{minipage} & \begin{minipage}[t]{2.2in} \begin{verbatim} x = umfpack (A,'\',b) ; \end{verbatim} \end{minipage} & \begin{minipage}[t]{2.2in} \begin{verbatim} x = A \ b ; \end{verbatim} \end{minipage} \\ & & \\ \hline & & \\ \begin{minipage}[t]{1.5in} Solve $\m{Ax}=\m{b}$ using a different row and column pre-ordering (symmetric ordering). \end{minipage} & \begin{minipage}[t]{2.2in} \begin{verbatim} S = spones (A) ; Q = symamd (S+S') ; Control = umfpack ; Control (6) = 3 ; x = umfpack (A,Q,'\',b,Control) ; \end{verbatim} \end{minipage} & \begin{minipage}[t]{2.2in} \begin{verbatim} spparms ('autommd',0) ; S = spones (A) ; Q = symamd (S+S') ; x = A (Q,Q) \ b (Q) ; x (Q) = x ; spparms ('autommd',1) ; \end{verbatim} \end{minipage} \\ & & \\ \hline & & \\ \begin{minipage}[t]{1.5in} Solve $\m{A}\tr\m{x}\tr = \m{b}\tr$. \end{minipage} & \begin{minipage}[t]{2.2in} \begin{verbatim} x = umfpack (b,'/',A) ; \end{verbatim} Note: $\m{A}$ is factorized. \end{minipage} & \begin{minipage}[t]{2.2in} \begin{verbatim} x = b / A ; \end{verbatim} Note: $\m{A}\tr$ is factorized. \end{minipage} \\ & & \\ \hline & & \\ \begin{minipage}[t]{1.5in} Scale and factorize $\m{A}$, then solve $\m{Ax}=\m{b}$. \end{minipage} & \begin{minipage}[t]{2.2in} \begin{verbatim} [L,U,P,Q,R] = umfpack (A) ; c = P * (R \ b) ; x = Q * (U \ (L \ c)) ; \end{verbatim} \end{minipage} & \begin{minipage}[t]{2.2in} \begin{verbatim} [m n] = size (A) ; r = full (sum (abs (A), 2)) ; r (find (r == 0)) = 1 ; R = spdiags (r, 0, m, m) ; I = speye (n) ; Q = I (:, colamd (A)) ; [L,U,P] = lu ((R\A)*Q) ; c = P * (R \ b) ; x = Q * (U \ (L \ c)) ; \end{verbatim} \end{minipage} \\ & & \\ \hline \end{tabular} } \end{table} Note: in MATLAB 6.5 or later, use {\tt spparms ('autoamd',0)} in addition to {\tt spparms ('autommd',0)}, in Table~\ref{matlab}, to turn off MATLAB's default reordering. UMFPACK requires {\tt b} to be a dense vector (real or complex) of the appropriate dimension. This is more restrictive than what you can do with MATLAB's backslash or forward slash. See {\tt umfpack\_solve} for an M-file that removes this restriction. This restriction does not apply to the built-in backslash operator in MATLAB 6.5 or later, which uses UMFPACK to factorize the matrix. You can do this yourself in MATLAB: {\footnotesize \begin{verbatim} [L,U,P,Q,R] = umfpack (A) ; x = Q * (U \ (L \ (P * (R \ b)))) ; \end{verbatim} } or, with no row scaling: {\footnotesize \begin{verbatim} [L,U,P,Q] = umfpack (A) ; x = Q * (U \ (L \ (P * b))) ; \end{verbatim} } The above examples do not make use of the iterative refinement that is built into {\tt x = }{\tt umfpack (A,'}$\backslash${\tt ',b)} however. MATLAB's {\tt [L,U,P] = lu(A)} returns a lower triangular {\tt L}, an upper triangular {\tt U}, and a permutation matrix {\tt P} such that {\tt P*A} is equal to {\tt L*U}. UMFPACK behaves differently. By default, it scales the rows of {\tt A} and reorders the columns of {\tt A} prior to factorization, so that {\tt L*U} is equal to {\tt P*(R}$\backslash${\tt A)*Q}, where {\tt R} is a diagonal sparse matrix of scale factors for the rows of {\tt A}. The scale factors {\tt R} are applied to {\tt A} via the MATLAB expression {\tt R}$\backslash${\tt A} to avoid multiplying by the reciprocal, which can be numerically inaccurate. There are more options; you can provide your own column pre-ordering (in which case UMFPACK does not call COLAMD or AMD), you can modify other control settings (similar to the {\tt spparms} in MATLAB), and you can get various statistics on the analysis, factorization, and solution of the linear system. Type {\tt umfpack\_details} and {\tt umfpack\_report} in MATLAB for more information. Two demo M-files are provided. Just type {\tt umfpack\_simple} and {\tt umfpack\_demo} to run them. The output of these two programs should be about the same as the files {\tt umfpack\_simple.m.out} and {\tt umfpack\_demo.m.out} that are provided. Factorizing {\tt A'} (or {\tt A.'}) and using the transposed factors can sometimes be faster than factorizing {\tt A}. It can also be preferable to factorize {\tt A'} if {\tt A} is rectangular. UMFPACK pre-orders the columns to maintain sparsity; the row ordering is not determined until the matrix is factorized. Thus, if {\tt A} is {\tt m} by {\tt n} with structural rank {\tt m} and {\tt m} $<$ {\tt n}, then {\tt umfpack} might not find a factor {\tt U} with a structurally zero-free diagonal. Unless the matrix ill-conditioned or poorly scaled, factorizing {\tt A'} in this case will guarantee that both factors will have zero-free diagonals. Note that there is no guarantee as to the size of the diagonal entries of {\tt U}; UMFPACK does not do a rank-revealing factorization. Here's how you can factorize {\tt A'} and get the factors of {\tt A} instead: \begin{verbatim} [l,u,p,q] = umfpack (A') ; L = u' ; U = l' ; P = q ; Q = p ; clear l u p q \end{verbatim} This is an alternative to {\tt [L,U,P,Q]=umfpack(A)}. A simple M-file ({\tt umfpack\_btf}) is provided that first permutes the matrix to upper block triangular form, using MATLAB's {\tt dmperm} routine, and then solves each block. The LU factors are not returned. Its usage is simple: {\tt x = umfpack\_btf(A,b)}. Type {\tt help umfpack\_btf} for more options. An estimate of the 1-norm of {\tt L*U-P*A*Q} can be computed in MATLAB as {\tt lu\_normest(P*A*Q,L,U)}, using the {\tt lu\_normest.m} M-file by Hager and Davis \cite{DavisHager99} that is included with the UMFPACK distribution. With row scaling enabled, use {\tt lu\_normest(P*(R}$\backslash${\tt A)*Q,L,U)} instead. One issue you may encounter is how UMFPACK allocates its memory when being used in a mexFunction. One part of its working space is of variable size. The symbolic analysis phase determines an upper bound on the size of this memory, but not all of this memory will typically be used in the numerical factorization. UMFPACK tries to allocate a decent amount of working space. This is 70\% of the upper bound, by default, for the unsymmetric strategy. For the symmetric strategy, the fraction of the upper bound is computed automatically (assuming a best-case scenario with no numerical pivoting required during numeric factorization). If this initial allocation fails, it reduces its request and uses less memory. If the space is not large enough during factorization, it is increased via {\tt mxRealloc}. However, {\tt mxMalloc} and {\tt mxRealloc} abort the {\tt umfpack} mexFunction if they fail, so this strategy does not work in MATLAB. To compute the determinant with UMFPACK: \begin{verbatim} d = umfpack (A, 'det') ; [d e] = umfpack (A, 'det') ; \end{verbatim} The first case is identical to MATLAB's {\tt det}. The second case returns the determinant in the form $d \times 10^e$, which avoids overflow if $e$ is large. %------------------------------------------------------------------------------- \section{Using UMFPACK in a C program} \label{C} %------------------------------------------------------------------------------- The C-callable UMFPACK library consists of 32 user-callable routines and one include file. All but three of the routines come in four versions, with different sizes of integers and for real or complex floating-point numbers: \begin{enumerate} \item {\tt umfpack\_di\_*}: real double precision, {\tt int} integers. \item {\tt umfpack\_dl\_*}: real double precision, {\tt UF\_long} integers. \item {\tt umfpack\_zi\_*}: complex double precision, {\tt int} integers. \item {\tt umfpack\_zl\_*}: complex double precision, {\tt UF\_long} integers. \end{enumerate} where {\tt *} denotes the specific name of one of the routines. Routine names beginning with {\tt umf\_} are internal to the package, and should not be called by the user. The include file {\tt umfpack.h} must be included in any C program that uses UMFPACK. The other three routines are the same for all four versions. In addition, the C-callable AMD library distributed with UMFPACK includes 4 user-callable routines (in two versions with {\tt int} and {\tt UF\_long} integers) and one include file. Refer to the AMD documentation for more details. Use only one version for any one problem; do not attempt to use one version to analyze the matrix and another version to factorize the matrix, for example. The notation {\tt umfpack\_di\_*} refers to all user-callable routines for the real double precision and {\tt int} integer case. The notation {\tt umfpack\_*\_numeric}, for example, refers all four versions (real/complex, int/UF\_long) of a single operation (in this case numeric factorization). %------------------------------------------------------------------------------- \subsection{The size of an integer} %------------------------------------------------------------------------------- The {\tt umfpack\_di\_*} and {\tt umfpack\_zi\_*} routines use {\tt int} integer arguments; those starting with {\tt umfpack\_dl\_} or {\tt umfpack\_zl\_} use {\tt UF\_long} integer arguments. If you compile UMFPACK in the standard ILP32 mode (32-bit {\tt int}'s, {\tt long}'s, and pointers) then the versions are essentially identical. You will be able to solve problems using up to 2GB of memory. If you compile UMFPACK in the standard LP64 mode, the size of an {\tt int} remains 32-bits, but the size of a {\tt long} and a pointer both get promoted to 64-bits. In the LP64 mode, the {\tt umfpack\_dl\_*} and {\tt umfpack\_zl\_*} routines can solve huge problems (not limited to 2GB), limited of course by the amount of available memory. The only drawback to the 64-bit mode is that not all BLAS libraries support 64-bit integers. This limits the performance you will obtain. Those that do support 64-bit integers are specific to particular architectures, and are not portable. UMFPACK and AMD should be compiled in the same mode. If you compile UMFPACK and AMD in the LP64 mode, be sure to add {\tt -DLP64} to the compilation command. See the examples in the {\tt UFconfig/UFconfig.mk} file. %------------------------------------------------------------------------------- \subsection{Real and complex floating-point} %------------------------------------------------------------------------------- The {\tt umfpack\_di\_*} and {\tt umfpack\_dl\_*} routines take (real) double precision arguments, and return double precision arguments. In the {\tt umfpack\_zi\_*} and {\tt umfpack\_zl\_*} routines, these same arguments hold the real part of the matrices; and second double precision arrays hold the imaginary part of the input and output matrices. Internally, complex numbers are stored in arrays with their real and imaginary parts interleaved, as required by the BLAS (``packed'' complex form). New to Version 4.4 is the option of providing input/output arguments in packed complex form. %------------------------------------------------------------------------------- \subsection{Primary routines, and a simple example} %------------------------------------------------------------------------------- Five primary UMFPACK routines are required to factorize $\m{A}$ or solve $\m{Ax}=\m{b}$. They are fully described in Section~\ref{Primary}: \begin{itemize} \item {\tt umfpack\_*\_symbolic}: Pre-orders the columns of $\m{A}$ to reduce fill-in. Returns an opaque {\tt Symbolic} object as a {\tt void *} pointer. The object contains the symbolic analysis and is needed for the numeric factorization. This routine requires only $O(|\m{A}|)$ space, where $|\m{A}|$ is the number of nonzero entries in the matrix. It computes upper bounds on the nonzeros in $\m{L}$ and $\m{U}$, the floating-point operations required, and the memory usage of {\tt umfpack\_*\_numeric}. The {\tt Symbolic} object is small; it contains just the column pre-ordering, the supernodal column elimination tree, and information about each frontal matrix. It is no larger than about $13n$ integers if $\m{A}$ is $n$-by-$n$. \item {\tt umfpack\_*\_numeric}: Numerically scales and then factorizes a sparse matrix into $\m{PAQ}$, $\m{PRAQ}$, or $\m{PR}^{-1}\m{AQ}$ into the product $\m{LU}$, where $\m{P}$ and $\m{Q}$ are permutation matrices, $\m{R}$ is a diagonal matrix of scale factors, $\m{L}$ is lower triangular with unit diagonal, and $\m{U}$ is upper triangular. Requires the symbolic ordering and analysis computed by {\tt umfpack\_*\_symbolic} or {\tt umfpack\_*\_qsymbolic}. Returns an opaque {\tt Numeric} object as a {\tt void *} pointer. The object contains the numerical factorization and is used by {\tt umfpack\_*\_solve}. You can factorize a new matrix with a different values (but identical pattern) as the matrix analyzed by {\tt umfpack\_*\_symbolic} or {\tt umfpack\_*\_qsymbolic} by re-using the {\tt Symbolic} object (this feature is available when using UMFPACK in a C or Fortran program, but not in MATLAB). The matrix $\m{U}$ will have zeros on the diagonal if $\m{A}$ is singular; this produces a warning, but the factorization is still valid. \item {\tt umfpack\_*\_solve}: Solves a sparse linear system ($\m{Ax}=\m{b}$, $\m{A}\tr\m{x}=\m{b}$, or systems involving just $\m{L}$ or $\m{U}$), using the numeric factorization computed by {\tt umfpack\_*\_numeric}. Iterative refinement with sparse backward error \cite{ardd:89} is used by default. The matrix $\m{A}$ must be square. If it is singular, then a divide-by-zero will occur, and your solution with contain IEEE Inf's or NaN's in the appropriate places. \item {\tt umfpack\_*\_free\_symbolic}: Frees the {\tt Symbolic} object created by {\tt umfpack\_*\_symbolic} or {\tt umfpack\_*\_qsymbolic}. \item {\tt umfpack\_*\_free\_numeric}: Frees the {\tt Numeric} object created by {\tt umfpack\_*\_numeric}. \end{itemize} Be careful not to free a {\tt Symbolic} object with {\tt umfpack\_*\_free\_numeric}. Nor should you attempt to free a {\tt Numeric} object with {\tt umfpack\_*\_free\_symbolic}. Failure to free these objects will lead to memory leaks. The matrix $\m{A}$ is represented in compressed column form, which is identical to the sparse matrix representation used by MATLAB. It consists of three or four arrays, where the matrix is {\tt m}-by-{\tt n}, with {\tt nz} entries. For the {\tt int} version of UMFPACK: {\footnotesize \begin{verbatim} int Ap [n+1] ; int Ai [nz] ; double Ax [nz] ; \end{verbatim} } For the {\tt UF\_long} version of UMFPACK: {\footnotesize \begin{verbatim} UF_long Ap [n+1] ; UF_long Ai [nz] ; double Ax [nz] ; \end{verbatim} } The complex versions add another array for the imaginary part: {\footnotesize \begin{verbatim} double Az [nz] ; \end{verbatim} } Alternatively, if {\tt Az} is {\tt NULL}, the real part of the $k$th entry is located in {\tt Ax[2*k]} and the imaginary part is located in {\tt Ax[2*k+1]}, and the {\tt Ax} array is of size {\tt 2*nz}. All nonzeros are entries, but an entry may be numerically zero. The row indices of entries in column {\tt j} are stored in {\tt Ai[Ap[j]} \ldots {\tt Ap[j+1]-1]}. The corresponding numerical values are stored in {\tt Ax[Ap[j]} \ldots {\tt Ap[j+1]-1]}. The imaginary part, for the complex versions, is stored in {\tt Az[Ap[j]} \ldots {\tt Ap[j+1]-1]} (see above for the packed complex case). No duplicate row indices may be present, and the row indices in any given column must be sorted in ascending order. The first entry {\tt Ap[0]} must be zero. The total number of entries in the matrix is thus {\tt nz = Ap[n]}. Except for the fact that extra zero entries can be included, there is thus a unique compressed column representation of any given matrix $\m{A}$. For a more flexible method for providing an input matrix to UMFPACK, see Section~\ref{triplet}. Here is a simple main program, {\tt umfpack\_simple.c}, that illustrates the basic usage of UMFPACK. See Section~\ref{Synopsis} for a short description of each calling sequence, including a list of options for the first argument of {\tt umfpack\_di\_solve}. {\footnotesize \begin{verbatim} INCLUDE umfpack_simple.c via sed \end{verbatim} } The {\tt Ap}, {\tt Ai}, and {\tt Ax} arrays represent the matrix \[ \m{A} = \left[ \begin{array}{rrrrr} 2 & 3 & 0 & 0 & 0 \\ 3 & 0 & 4 & 0 & 6 \\ 0 & -1 & -3 & 2 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 4 & 2 & 0 & 1 \\ \end{array} \right]. \] and the solution to $\m{Ax}=\m{b}$ is $\m{x} = [1 \, 2 \, 3 \, 4 \, 5]\tr$. The program uses default control settings and does not return any statistics about the ordering, factorization, or solution ({\tt Control} and {\tt Info} are both {\tt (double *) NULL}). It also ignores the status value returned by most user-callable UMFPACK routines. %------------------------------------------------------------------------------- \subsection{A note about zero-sized arrays} %------------------------------------------------------------------------------- UMFPACK uses many user-provided arrays of size {\tt m} or {\tt n} (the order of the matrix), and of size {\tt nz} (the number of nonzeros in a matrix). UMFPACK does not handle zero-dimensioned arrays; it returns an error code if {\tt m} or {\tt n} are zero. However, {\tt nz} can be zero, since all singular matrices are handled correctly. If you attempt to {\tt malloc} an array of size {\tt nz} = 0, however, {\tt malloc} will return a null pointer which UMFPACK will report as a missing argument. If you {\tt malloc} an array of size {\tt nz} to pass to UMFPACK, make sure that you handle the {\tt nz} = 0 case correctly (use a size equal to the maximum of {\tt nz} and 1, or use a size of {\tt nz+1}). %------------------------------------------------------------------------------- \subsection{Alternative routines} %------------------------------------------------------------------------------- Three alternative routines are provided that modify UMFPACK's default behavior. They are fully described in Section~\ref{Alternative}: \begin{itemize} \item {\tt umfpack\_*\_defaults}: Sets the default control parameters in the {\tt Control} array. These can then be modified as desired before passing the array to the other UMFPACK routines. Control parameters are summarized in Section~\ref{control_param}. Three particular parameters deserve special notice. UMFPACK uses relaxed partial pivoting, where a candidate pivot entry is numerically acceptable if its magnitude is greater than or equal to a tolerance parameter times the magnitude of the largest entry in the same column. The parameter {\tt Control [UMFPACK\_PIVOT\_TOLERANCE]} has a default value of 0.1, and is used for the unsymmetric strategy. For complex matrices, a cheap approximation of the absolute value is used for the threshold pivoting test ($|a| \approx |a_{\mbox{real}}|+|a_{\mbox{imag}}|$). For the symmetric strategy, a second tolerance is used for diagonal entries: \newline {\tt Control [UMFPACK\_SYM\_PIVOT\_TOLERANCE]}, with a default value of 0.001. The first parameter (with a default of 0.1) is used for any off-diagonal candidate pivot entries. These two parameters may be too small for some matrices, particularly for ill-conditioned or poorly scaled ones. With the default pivot tolerances and default iterative refinement, {\tt x = umfpack (A,'}$\backslash${\tt ',b)} is just as accurate as (or more accurate) than {\tt x = A}$\backslash${\tt b} in MATLAB 6.1 for nearly all matrices. If {\tt Control [UMFPACK\_PIVOT\_TOLERANCE]} is zero, than any nonzero entry is acceptable as a pivot (this is changed from Version 4.0, which treated a value of 0.0 the same as 1.0). If the symmetric strategy is used, and {\tt Control [UMFPACK\_SYM\_PIVOT\_TOLERANCE]} is zero, then any nonzero entry on the diagonal is accepted as a pivot. Off-diagonal pivoting will still occur if the diagonal entry is exactly zero. The {\tt Control [UMFPACK\_SYM\_PIVOT\_TOLERANCE]} parameter is new to Version 4.1. It is similar in function to the pivot tolerance for left-looking methods (the MATLAB {\tt THRESH} option in {\tt [L,U,P] = lu (A, THRESH)}, and the pivot tolerance parameter in SuperLU). The parameter {\tt Control [UMFPACK\_STRATEGY]} can be used to bypass UMFPACK's automatic strategy selection. The automatic strategy nearly always selects the best method. When it does not, the different methods nearly always give about the same quality of results. There may be cases where the automatic strategy fails to pick a good strategy. Also, you can save some computing time if you know the right strategy for your set of matrix problems. \item {\tt umfpack\_*\_qsymbolic}: An alternative to {\tt umfpack\_*\_symbolic}. Allows the user to specify his or her own column pre-ordering, rather than using the default COLAMD or AMD pre-orderings. For example, a graph partitioning-based order of $\m{A}\tr\m{A}$ would be suitable for UMFPACK's unsymmetric strategy. A partitioning of $\m{A}+\m{A}\tr$ would be suitable for UMFPACK's symmetric or 2-by-2 strategies. \item {\tt umfpack\_*\_wsolve}: An alternative to {\tt umfpack\_*\_solve} which does not dynamically allocate any memory. Requires the user to pass two additional work arrays. \end{itemize} %------------------------------------------------------------------------------- \subsection{Matrix manipulation routines} \label{triplet} %------------------------------------------------------------------------------- The compressed column data structure is compact, and simplifies the UMFPACK routines that operate on the sparse matrix $\m{A}$. However, it can be inconvenient for the user to generate. Section~\ref{Manipulate} presents the details of routines for manipulating sparse matrices in {\em triplet} form, compressed column form, and compressed row form (the transpose of the compressed column form). The triplet form of a matrix consists of three or four arrays. For the {\tt int} version of UMFPACK: {\footnotesize \begin{verbatim} int Ti [nz] ; int Tj [nz] ; double Tx [nz] ; \end{verbatim} } For the {\tt UF\_long} version: {\footnotesize \begin{verbatim} UF_long Ti [nz] ; UF_long Tj [nz] ; double Tx [nz] ; \end{verbatim} } The complex versions use another array to hold the imaginary part: {\footnotesize \begin{verbatim} double Tz [nz] ; \end{verbatim} } The {\tt k}-th triplet is $(i,j,a_{ij})$, where $i =$ {\tt Ti[k]}, $j =$ {\tt Tj[k]}, and $a_{ij} =$ {\tt Tx[k]}. For the complex versions, {\tt Tx[k]} is the real part of $a_{ij}$ and {\tt Tz[k]} is the imaginary part. The triplets can be in any order in the {\tt Ti}, {\tt Tj}, and {\tt Tx} arrays (and {\tt Tz} for the complex versions), and duplicate entries may exist. If {\tt Tz} is NULL, then the array {\tt Tx} becomes of size {\tt 2*nz}, and the real and imaginary parts of the {\tt k}-th triplet are located in {\tt Tx[2*k]} and {\tt Tx[2*k+1]}, respectively. Any duplicate entries are summed when the triplet form is converted to compressed column form. This is a convenient way to create a matrix arising in finite-element methods, for example. Four routines are provided for manipulating sparse matrices: \begin{itemize} \item {\tt umfpack\_*\_triplet\_to\_col}: Converts a triplet form of a matrix to compressed column form (ready for input to \newline {\tt umfpack\_*\_symbolic}, {\tt umfpack\_*\_qsymbolic}, and {\tt umfpack\_*\_numeric}). Identical to {\tt A = spconvert(i,j,x)} in MATLAB, except that zero entries are not removed, so that the pattern of entries in the compressed column form of $\m{A}$ are fully under user control. This is important if you want to factorize a new matrix with the {\tt Symbolic} object from a prior matrix with the same pattern as the new one. \item {\tt umfpack\_*\_col\_to\_triplet}: The opposite of {\tt umfpack\_*\_triplet\_to\_col}. Identical to {\tt [i,j,x] = find(A)} in MATLAB, except that numerically zero entries may be included. \item {\tt umfpack\_*\_transpose}: Transposes and optionally permutes a column form matrix \cite{Gustavson78}. Identical to {\tt R = A(P,Q)'} (linear algebraic transpose, using the complex conjugate) or {\tt R = A(P,Q).'} (the array transpose) in MATLAB, except for the presence of numerically zero entries. Factorizing $\m{A}\tr$ and then solving $\m{Ax}=\m{b}$ with the transposed factors can sometimes be much faster or much slower than factorizing $\m{A}$. It is highly dependent on your particular matrix. \item {\tt umfpack\_*\_scale}: Applies the row scale factors to a user-provided vector. This is not required to solve the sparse linear system $\m{Ax}=\m{b}$ or $\m{A}\tr\m{x}=\m{b}$, since {\tt umfpack\_*\_solve} applies the scale factors for those systems. \end{itemize} It is quite easy to add matrices in triplet form, subtract them, transpose them, permute them, construct a submatrix, and multiply a triplet-form matrix times a vector. UMFPACK does not provide code for these basic operations, however. Refer to the discussion of {\tt umfpack\_*\_triplet\_to\_col} in Section~\ref{Manipulate} for more details on how to compute these operations in your own code. The only primary matrix operation not provided by UMFPACK is the multiplication of two sparse matrices \cite{Gustavson78}. The CHOLMOD provides many of these matrix operations, which can then be used in conjunction with UMFPACK. See my web page for details. %------------------------------------------------------------------------------- \subsection{Getting the contents of opaque objects} %------------------------------------------------------------------------------- There are cases where you may wish to do more with the LU factorization of a matrix than solve a linear system. The opaque {\tt Symbolic} and {\tt Numeric} objects are just that - opaque. You cannot do anything with them except to pass them back to subsequent calls to UMFPACK. Three routines are provided for copying their contents into user-provided arrays using simpler data structures. Four routines are provided for saving and loading the {\tt Numeric} and {\tt Symbolic} objects to/from binary files. An additional routine is provided that computes the determinant. They are fully described in Section~\ref{Get}: \begin{itemize} \item {\tt umfpack\_*\_get\_lunz}: Returns the number of nonzeros in $\m{L}$ and $\m{U}$. \item {\tt umfpack\_*\_get\_numeric}: Copies $\m{L}$, $\m{U}$, $\m{P}$, $\m{Q}$, and $\m{R}$ from the {\tt Numeric} object into arrays provided by the user. The matrix $\m{L}$ is returned in compressed row form (with the column indices in each row sorted in ascending order). The matrix $\m{U}$ is returned in compressed column form (with sorted columns). There are no explicit zero entries in $\m{L}$ and $\m{U}$, but such entries may exist in the {\tt Numeric} object. The permutations $\m{P}$ and $\m{Q}$ are represented as permutation vectors, where {\tt P[k] = i} means that row {\tt i} of the original matrix is the the {\tt k}-th row of $\m{PAQ}$, and where {\tt Q[k] = j} means that column {\tt j} of the original matrix is the {\tt k}-th column of $\m{PAQ}$. This is identical to how MATLAB uses permutation vectors (type {\tt help colamd} in MATLAB 6.1 or later). \item {\tt umfpack\_*\_get\_symbolic}: Copies the contents of the {\tt Symbolic} object (the initial row and column preordering, supernodal column elimination tree, and information about each frontal matrix) into arrays provided by the user. \item {\tt umfpack\_*\_get\_determinant}: Computes the determinant from the diagonal of $\m{U}$ and the permutations $\m{P}$ and $\m{Q}$. This is mostly of theoretical interest. It is not a good test to determine if your matrix is singular or not. \item {\tt umfpack\_*\_save\_numeric}: Saves a copy of the {\tt Numeric} object to a file, in binary format. \item {\tt umfpack\_*\_load\_numeric}: Creates a {\tt Numeric} object by loading it from a file created by {\tt umfpack\_*\_save\_numeric}. \item {\tt umfpack\_*\_save\_symbolic}: Saves a copy of the {\tt Symbolic} object to a file, in binary format. \item {\tt umfpack\_*\_load\_symbolic}: Creates a {\tt Symbolic} object by loading it from a file created by {\tt umfpack\_*\_save\_symbolic}. \end{itemize} UMFPACK itself does not make use of these routines; they are provided solely for returning the contents of the opaque {\tt Symbolic} and {\tt Numeric} objects to the user, and saving/loading them to/from a binary file. None of them do any computation, except for {\tt umfpack\_*\_get\_determinant}. %------------------------------------------------------------------------------- \subsection{Reporting routines} \label{Reporting} %------------------------------------------------------------------------------- None of the UMFPACK routines discussed so far prints anything, even when an error occurs. UMFPACK provides you with nine routines for printing the input and output arguments (including the {\tt Control} settings and {\tt Info} statistics) of UMFPACK routines discussed above. They are fully described in Section~\ref{Report}: \begin{itemize} \item {\tt umfpack\_*\_report\_status}: Prints the status (return value) of other {\tt umfpack\_*} routines. \item {\tt umfpack\_*\_report\_info}: Prints the statistics returned in the {\tt Info} array by {\tt umfpack\_*\_*symbolic}, {\tt umfpack\_*\_numeric}, and {\tt umfpack\_*\_*solve}. \item {\tt umfpack\_*\_report\_control}: Prints the {\tt Control} settings. \item {\tt umfpack\_*\_report\_matrix}: Verifies and prints a compressed column-form or compressed row-form sparse matrix. \item {\tt umfpack\_*\_report\_triplet}: Verifies and prints a matrix in triplet form. \item {\tt umfpack\_*\_report\_symbolic}: Verifies and prints a {\tt Symbolic} object. \item {\tt umfpack\_*\_report\_numeric}: Verifies and prints a {\tt Numeric} object. \item {\tt umfpack\_*\_report\_perm}: Verifies and prints a permutation vector. \item {\tt umfpack\_*\_report\_vector}: Verifies and prints a real or complex vector. \end{itemize} The {\tt umfpack\_*\_report\_*} routines behave slightly differently when compiled into the C-callable UMFPACK library than when used in the MATLAB mexFunction. MATLAB stores its sparse matrices using the same compressed column data structure discussed above, where row and column indices of an $m$-by-$n$ matrix are in the range 0 to $m-1$ or $n-1$, respectively\footnote{Complex matrices in MATLAB use the split array form, with one {\tt double} array for the real part and another array for the imaginary part. UMFPACK supports that format, as well as the packed complex format (new to Version 4.4).} It prints them as if they are in the range 1 to $m$ or $n$. The UMFPACK mexFunction behaves the same way. You can control how much the {\tt umfpack\_*\_report\_*} routines print by modifying the {\tt Control [UMFPACK\_PRL]} parameter. Its default value is 1. Here is a summary of how the routines use this print level parameter: \begin{itemize} \item {\tt umfpack\_*\_report\_status}: No output if the print level is 0 or less, even when an error occurs. If 1, then error messages are printed, and nothing is printed if the status is {\tt UMFPACK\_OK}. A warning message is printed if the matrix is singular. If 2 or more, then the status is always printed. If 4 or more, then the UMFPACK Copyright is printed. If 6 or more, then the UMFPACK License is printed. See also the first page of this User Guide for the Copyright and License. \item {\tt umfpack\_*\_report\_control}: No output if the print level is 1 or less. If 2 or more, all of {\tt Control} is printed. \item {\tt umfpack\_*\_report\_info}: No output if the print level is 1 or less. If 2 or more, all of {\tt Info} is printed. \item all other {\tt umfpack\_*\_report\_*} routines: If the print level is 2 or less, then these routines return silently without checking their inputs. If 3 or more, the inputs are fully verified and a short status summary is printed. If 4, then the first few entries of the input arguments are printed. If 5, then all of the input arguments are printed. \end{itemize} This print level parameter has an additional effect on the MATLAB mexFunction. If zero, then no warnings of singular or nearly singular matrices are printed (similar to the MATLAB commands {\tt warning off MATLAB:singularMatrix} and {\tt warning off MATLAB:nearlySingularMatrix}). %------------------------------------------------------------------------------- \subsection{Utility routines} %------------------------------------------------------------------------------- UMFPACK v4.0 included a routine that returns the time used by the process, {\tt umfpack\_timer}. The routine uses either {\tt getrusage} (which is preferred), or the ANSI C {\tt clock} routine if that is not available. It is fully described in Section~\ref{Utility}. It is still available in UMFPACK v4.1 and following, but not used internally. Two new timing routines are provided in UMFPACK Version 4.1 and following, {\tt umfpack\_tic} and {\tt umfpack\_toc}. They use POSIX-compliant {\tt sysconf} and {\tt times} routines to find both the CPU time and wallclock time. These three routines are the only user-callable routine that is identical in all four {\tt int}/{\tt UF\_long}, real/complex versions (there is no {\tt umfpack\_di\_timer} routine, for example). %------------------------------------------------------------------------------- \subsection{Control parameters} \label{control_param} %------------------------------------------------------------------------------- UMFPACK uses an optional {\tt double} array (currently of size 20) to modify its control parameters. If you pass {\tt (double *) NULL} instead of a {\tt Control} array, then defaults are used. These defaults provide nearly optimal performance (both speed, memory usage, and numerical accuracy) for a wide range of matrices from real applications. This array will almost certainly grow in size in future releases, so be sure to dimension your {\tt Control} array to be of size {\tt UMFPACK\_CONTROL}. That constant is currently defined to be 20, but may increase in future versions, since all 20 entries are in use. The contents of this array may be modified by the user (see {\tt umfpack\_*\_defaults}). Each user-callable routine includes a complete description of how each control setting modifies its behavior. Table~\ref{control} summarizes the entire contents of the {\tt Control} array. Note that ANSI C uses 0-based indexing, while MATLAB uses 1-based indexing. Thus, {\tt Control(1)} in MATLAB is the same as {\tt Control[0]} or {\tt Control[UMFPACK\_PRL]} in ANSI C. \begin{table} \caption{UMFPACK Control parameters} \label{control} {\footnotesize \begin{tabular}{llll} \hline MATLAB & ANSI C & default & description \\ \hline {\tt Control(1)} & {\tt Control[UMFPACK\_PRL]} & 1 & printing level \\ {\tt Control(2)} & {\tt Control[UMFPACK\_DENSE\_ROW]} & 0.2 & dense row parameter \\ {\tt Control(3)} & {\tt Control[UMFPACK\_DENSE\_COL]} & 0.2 & dense column parameter \\ {\tt Control(4)} & {\tt Control[UMFPACK\_PIVOT\_TOLERANCE]} & 0.1 & partial pivoting tolerance \\ {\tt Control(5)} & {\tt Control[UMFPACK\_BLOCK\_SIZE]} & 32 & BLAS block size \\ {\tt Control(6)} & {\tt Control[UMFPACK\_STRATEGY]} & 0 (auto) & select strategy \\ {\tt Control(7)} & {\tt Control[UMFPACK\_ALLOC\_INIT]} & 0.7 & initial memory allocation \\ {\tt Control(8)} & {\tt Control[UMFPACK\_IRSTEP]} & 2 & max iter. refinement steps \\ {\tt Control(13)} & {\tt Control[UMFPACK\_2BY2\_TOLERANCE]} & 0.01 & defines ``large'' entries \\ {\tt Control(14)} & {\tt Control[UMFPACK\_FIXQ]} & 0 (auto) & fix or modify Q \\ {\tt Control(15)} & {\tt Control[UMFPACK\_AMD\_DENSE]} & 10 & AMD dense row/column parameter \\ {\tt Control(16)} & {\tt Control[UMFPACK\_SYM\_PIVOT\_TOLERANCE]} & 0.001 & for diagonal entries \\ {\tt Control(17)} & {\tt Control[UMFPACK\_SCALE]} & 1 (sum) & row scaling (none, sum, or max) \\ {\tt Control(18)} & {\tt Control[UMFPACK\_FRONT\_ALLOC\_INIT]} & 0.5 & frontal matrix allocation ratio \\ {\tt Control(19)} & {\tt Control[UMFPACK\_DROPTOL]} & 0 & drop tolerance \\ {\tt Control(20)} & {\tt Control[UMFPACK\_AGGRESSIVE]} & 1 (yes) & aggressive absorption \\ & & & in AMD and COLAMD \\ % \hline \multicolumn{4}{l}{Can only be changed at compile time:} \\ {\tt Control(9)} & {\tt Control[UMFPACK\_COMPILED\_WITH\_BLAS]} & - & true if BLAS is used \\ {\tt Control(10)} & {\tt Control[UMFPACK\_COMPILED\_FOR\_MATLAB]} & - & true for mexFunction \\ {\tt Control(11)} & {\tt Control[UMFPACK\_COMPILED\_WITH\_GETRUSAGE]} & - & 1 if {\tt getrusage} used \\ {\tt Control(12)} & {\tt Control[UMFPACK\_COMPILED\_IN\_DEBUG\_MODE]} & - & true if debug mode enabled \\ \hline \end{tabular} } \end{table} Let $\alpha_r = ${\tt Control [UMFPACK\_DENSE\_ROW]}, $\alpha_c = ${\tt Control [UMFPACK\_DENSE\_COL]}, and $\alpha = ${\tt Control [UMFPACK\_AMD\_DENSE]}. Suppose the submatrix $\m{S}$, obtained after eliminating pivots with zero Markowitz cost, is $m$-by-$n$. Then a row is considered ``dense'' if it has more than $\max (16, 16 \alpha_r \sqrt{n})$ entries. A column is considered ``dense'' if it has more than $\max (16, 16 \alpha_c \sqrt{m})$ entries. These rows and columns are treated different in COLAMD and during numerical factorization. In COLAMD, dense columns are placed last in their natural order, and dense rows are ignored. During numerical factorization, dense rows are stored differently. In AMD, a row/column of the square matrix $\m{S}+\m{S}\tr$ is considered ``dense'' if it has more than $\max (16, \alpha \sqrt{n})$ entries. These rows/columns are placed last in AMD's output ordering. For more details on the control parameters, refer to the documentation of {\tt umfpack\_*\_qsymbolic}, {\tt umfpack\_*\_numeric}, {\tt umfpack\_*\_solve}, and the {\tt umfpack\_*\_report\_*} routines, in Sections~\ref{Primary}~through~\ref{Report}, below. %------------------------------------------------------------------------------- \subsection{Error codes} \label{error_codes} %------------------------------------------------------------------------------- Many of the routines return a {\tt status} value. This is also returned as the first entry in the {\tt Info} array, for those routines with that argument. The following list summarizes all of the error codes in UMFPACK. Each error code is given a specific name in the {\tt umfpack.h} include file, so you can use those constants instead of hard-coded values in your program. Future versions may report additional error codes. A value of zero means everything was successful, and the matrix is non-singular. A value greater than zero means the routine was successful, but a warning occurred. A negative value means the routine was not successful. In this case, no {\tt Symbolic} or {\tt Numeric} object was created. \begin{itemize} \item {\tt UMFPACK\_OK}, (0): UMFPACK was successful. \item {\tt UMFPACK\_WARNING\_singular\_matrix}, (1): Matrix is singular. There are exact zeros on the diagonal of $\m{U}$. \item {\tt UMFPACK\_WARNING\_determinant\_underflow}, (2): The determinant is nonzero, but smaller in magnitude than the smallest positive floating-point number. \item {\tt UMFPACK\_WARNING\_determinant\_overflow}, (3): The determinant is larger in magnitude than the largest positive floating-point number (IEEE Inf). \item {\tt UMFPACK\_ERROR\_out\_of\_memory}, (-1): Not enough memory. The ANSI C {\tt malloc} or {\tt realloc} routine failed. \item {\tt UMFPACK\_ERROR\_invalid\_Numeric\_object}, (-3): Routines that take a {\tt Numeric} object as input (or load it from a file) check this object and return this error code if it is invalid. This can be caused by a memory leak or overrun in your program, which can overwrite part of the Numeric object. It can also be caused by passing a Symbolic object by mistake, or some other pointer. If you try to factorize a matrix using one version of UMFPACK and then use the factors in another version, this error code will trigger as well. You cannot factor your matrix using version 4.0 and then solve with version 4.1, for example.\footnote{ Exception: v4.3, v4.3.1, and v4.4 use identical data structures for the {\tt Numeric} and {\tt Symbolic} objects}. You cannot use different precisions of the same version (real and complex, for example). It is possible for the {\tt Numeric} object to be corrupted by your program in subtle ways that are not detectable by this quick check. In this case, you may see an {\tt UMFPACK\_ERROR\_different\_pattern} error code, or even an {\tt UMFPACK\_ERROR\_internal\_error}. \item {\tt UMFPACK\_ERROR\_invalid\_Symbolic\_object}, (-4): Routines that take a {\tt Symbolic} object as input (or load it from a file) check this object and return this error code if it is invalid. The causes of this error are analogous to the {\tt UMFPACK\_ERROR\_invalid\_Numeric\_object} error described above. \item {\tt UMFPACK\_ERROR\_argument\_missing}, (-5): Some arguments of some are optional (you can pass a {\tt NULL} pointer instead of an array). This error code occurs if you pass a {\tt NULL} pointer when that argument is required to be present. \item {\tt UMFPACK\_ERROR\_n\_nonpositive} (-6): The number of rows or columns of the matrix must be greater than zero. \item {\tt UMFPACK\_ERROR\_invalid\_matrix} (-8): The matrix is invalid. For the column-oriented input, this error code will occur if the contents of {\tt Ap} and/or {\tt Ai} are invalid. {\tt Ap} is an integer array of size {\tt n\_col+1}. On input, it holds the ``pointers'' for the column form of the sparse matrix $\m{A}$. Column {\tt j} of the matrix A is held in {\tt Ai [(Ap [j])} \ldots {\tt (Ap [j+1]-1)]}. The first entry, {\tt Ap [0]}, must be zero, and {\tt Ap [j]} $\le$ {\tt Ap [j+1]} must hold for all {\tt j} in the range 0 to {\tt n\_col-1}. The value {\tt nz = Ap [n\_col]} is thus the total number of entries in the pattern of the matrix A. {\tt nz} must be greater than or equal to zero. The nonzero pattern (row indices) for column {\tt j} is stored in {\tt Ai [(Ap [j])} \ldots {\tt (Ap [j+1]-1)]}. The row indices in a given column {\tt j} must be in ascending order, and no duplicate row indices may be present. Row indices must be in the range 0 to {\tt n\_row-1} (the matrix is 0-based). Some routines take a triplet-form input, with arguments {\tt nz}, {\tt Ti}, and {\tt Tj}. This error code is returned if {\tt nz} is less than zero, if any row index in {\tt Ti} is outside the range 0 to {\tt n\_col-1}, or if any column index in {\tt Tj} is outside the range 0 to {\tt n\_row-1}. \item {\tt UMFPACK\_ERROR\_different\_pattern}, (-11): The most common cause of this error is that the pattern of the matrix has changed between the symbolic and numeric factorization. It can also occur if the {\tt Numeric} or {\tt Symbolic} object has been subtly corrupted by your program. \item {\tt UMFPACK\_ERROR\_invalid\_system}, (-13): The {\tt sys} argument provided to one of the solve routines is invalid. \item {\tt UMFPACK\_ERROR\_invalid\_permutation}, (-15): The permutation vector provided as input is invalid. \item {\tt UMFPACK\_ERROR\_file\_IO}, (-17): This error code is returned by the routines that save and load the {\tt Numeric} or {\tt Symbolic} objects to/from a file, if a file I/O error has occurred. The file may not exist or may not be readable, you may be trying to create a file that you don't have permission to create, or you may be out of disk space. The file you are trying to read might be the wrong one, and an earlier end-of-file condition would then result in this error. \item {\tt UMFPACK\_ERROR\_internal\_error}, (-911): An internal error has occurred, of unknown cause. This is either a bug in UMFPACK, or the result of a memory overrun from your program. Try modifying the file {\tt AMD/Include/amd\_internal.h} and adding the statement {\tt \#undef NDEBUG}, to enable the debugging mode. Recompile UMFPACK and rerun your program. A failed assertion might occur which can give you a better indication as to what is going wrong. Be aware that UMFPACK will be extraordinarily slow when running in debug mode. If all else fails, contact the developer (davis@cise.ufl.edu) with as many details as possible. \end{itemize} %------------------------------------------------------------------------------- \subsection{Larger examples} %------------------------------------------------------------------------------- Full examples of all user-callable UMFPACK routines are available in four stand-alone C main programs, {\tt umfpack\_*\_demo.c}. Another example is the UMFPACK mexFunction, {\tt umfpackmex.c}. The mexFunction accesses only the user-callable C interface to UMFPACK. The only features that it does not use are the support for the triplet form (MATLAB's sparse arrays are already in the compressed column form) and the ability to reuse the {\tt Symbolic} object to numerically factorize a matrix whose pattern is the same as a prior matrix analyzed by {\tt umfpack\_*\_symbolic} or {\tt umfpack\_*\_qsymbolic}. The latter is an important feature, but the mexFunction does not return its opaque {\tt Symbolic} and {\tt Numeric} objects to MATLAB. Instead, it gets the contents of these objects after extracting them via the {\tt umfpack\_*\_get\_*} routines, and returns them as MATLAB sparse matrices. The {\tt umf4.c} program for reading matrices in Harwell/Boeing format \cite{DuffGrimesLewis87b} is provided. It requires three Fortran 77 programs ({\tt readhb.f}, {\tt readhb\_nozeros.f}, and {\tt readhb\_size.f}) for reading in the sample Harwell/Boeing files in the {\tt UMFPACK/Demo/HB} directory. More matrices are available at http://www.cise.ufl.edu/research/sparse/matrices. Type {\tt make hb} in the {\tt UMFPACK/Demo/HB} directory to compile and run this demo. This program was used for the experimental results in \cite{Davis03}. %------------------------------------------------------------------------------- \section{Synopsis of C-callable routines} \label{Synopsis} %------------------------------------------------------------------------------- Each subsection, below, summarizes the input variables, output variables, return values, and calling sequences of the routines in one category. Variables with the same name as those already listed in a prior category have the same size and type. The real, {\tt UF\_long} integer {\tt umfpack\_dl\_*} routines are identical to the real, {\tt int} routines, except that {\tt \_di\_} is replaced with {\tt \_dl\_} in the name, and all {\tt int} arguments become {\tt UF\_long}. Similarly, the complex, {\tt UF\_long} integer {\tt umfpack\_zl\_*} routines are identical to the complex, {\tt int} routines, except that {\tt \_zi\_} is replaced with {\tt \_zl\_} in the name, and all {\tt int} arguments become {\tt UF\_long}. Only the real and complex {\tt int} versions are listed in the synopsis below. The matrix $\m{A}$ is {\tt m}-by-{\tt n} with {\tt nz} entries. The {\tt sys} argument of {\tt umfpack\_*\_solve} is an integer in the range 0 to 14 which defines which linear system is to be solved. \footnote{Integer values for {\tt sys} are used instead of strings (as in LINPACK and LAPACK) to avoid C-to-Fortran portability issues.} Valid values are listed in Table~\ref{sys}. The notation $\m{A}\he$ refers to the matrix transpose, which is the complex conjugate transpose for complex matrices ({\tt A'} in MATLAB). The array transpose is $\m{A}\tr$, which is {\tt A.'} in MATLAB. \begin{table} \begin{center} \caption{UMFPACK {\tt sys} parameter} \label{sys} {\footnotesize \begin{tabular}{ll|l} \hline Value & & system \\ \hline & & \\ {\tt UMFPACK\_A} & (0) & $\m{Ax}=\m{b}$ \\ {\tt UMFPACK\_At} & (1) & $\m{A}\he\m{x}=\m{b}$ \\ {\tt UMFPACK\_Aat} & (2) & $\m{A}\tr\m{x}=\m{b}$ \\ & & \\ \hline & & \\ {\tt UMFPACK\_Pt\_L} & (3) & $\m{P}\tr\m{Lx}=\m{b}$ \\ {\tt UMFPACK\_L} & (4) & $\m{Lx}=\m{b}$ \\ {\tt UMFPACK\_Lt\_P} & (5) & $\m{L}\he\m{Px}=\m{b}$ \\ {\tt UMFPACK\_Lat\_P} & (6) & $\m{L}\tr\m{Px}=\m{b}$ \\ {\tt UMFPACK\_Lt} & (7) & $\m{L}\he\m{x}=\m{b}$ \\ {\tt UMFPACK\_Lat} & (8) & $\m{L}\tr\m{x}=\m{b}$ \\ & & \\ \hline & & \\ {\tt UMFPACK\_U\_Qt} & (9) & $\m{UQ}\tr\m{x}=\m{b}$ \\ {\tt UMFPACK\_U} & (10) & $\m{Ux}=\m{b}$ \\ {\tt UMFPACK\_Q\_Ut} & (11) & $\m{QU}\he\m{x}=\m{b}$ \\ {\tt UMFPACK\_Q\_Uat} & (12) & $\m{QU}\tr\m{x}=\m{b}$ \\ {\tt UMFPACK\_Ut} & (13) & $\m{U}\he\m{x}=\m{b}$ \\ {\tt UMFPACK\_Uat} & (14) & $\m{U}\tr\m{x}=\m{b}$ \\ & & \\ \hline \end{tabular} } \end{center} \end{table} %------------------------------------------------------------------------------- \subsection{Primary routines: real/{\tt int}} %------------------------------------------------------------------------------- {\footnotesize \begin{verbatim} #include "umfpack.h" int status, sys, n, m, nz, Ap [n+1], Ai [nz] ; double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], Ax [nz], X [n], B [n] ; void *Symbolic, *Numeric ; status = umfpack_di_symbolic (m, n, Ap, Ai, Ax, &Symbolic, Control, Info) ; status = umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric, Control, Info) ; status = umfpack_di_solve (sys, Ap, Ai, Ax, X, B, Numeric, Control, Info) ; umfpack_di_free_symbolic (&Symbolic) ; umfpack_di_free_numeric (&Numeric) ; \end{verbatim} } %------------------------------------------------------------------------------- \subsection{Alternative routines: real/{\tt int}} %------------------------------------------------------------------------------- {\footnotesize \begin{verbatim} int Qinit [n], Wi [n] ; double W [5*n] ; umfpack_di_defaults (Control) ; status = umfpack_di_qsymbolic (m, n, Ap, Ai, Ax, Qinit, &Symbolic, Control, Info) ; status = umfpack_di_wsolve (sys, Ap, Ai, Ax, X, B, Numeric, Control, Info, Wi, W) ; \end{verbatim} } %------------------------------------------------------------------------------- \subsection{Matrix manipulation routines: real/{\tt int}} %------------------------------------------------------------------------------- {\footnotesize \begin{verbatim} int Ti [nz], Tj [nz], P [m], Q [n], Rp [m+1], Ri [nz], Map [nz] ; double Tx [nz], Rx [nz], Y [m], Z [m] ; status = umfpack_di_col_to_triplet (n, Ap, Tj) ; status = umfpack_di_triplet_to_col (m, n, nz, Ti, Tj, Tx, Ap, Ai, Ax, Map) ; status = umfpack_di_transpose (m, n, Ap, Ai, Ax, P, Q, Rp, Ri, Rx) ; status = umfpack_di_scale (Y, Z, Numeric) ; \end{verbatim} } %------------------------------------------------------------------------------- \subsection{Getting the contents of opaque objects: real/{\tt int}} %------------------------------------------------------------------------------- The {\tt filename} string should be large enough to hold the name of a file. {\footnotesize \begin{verbatim} int lnz, unz, Lp [m+1], Lj [lnz], Up [n+1], Ui [unz], do_recip ; double Lx [lnz], Ux [unz], D [min (m,n)], Rs [m], Mx [1], Ex [1] ; int nfr, nchains, P1 [m], Q1 [n], Front_npivcol [n+1], Front_parent [n+1], Front_1strow [n+1], Front_leftmostdesc [n+1], Chain_start [n+1], Chain_maxrows [n+1], Chain_maxcols [n+1] ; char filename [100] ; status = umfpack_di_get_lunz (&lnz, &unz, &m, &n, &nz_udiag, Numeric) ; status = umfpack_di_get_numeric (Lp, Lj, Lx, Up, Ui, Ux, P, Q, D, &do_recip, Rs, Numeric) ; status = umfpack_di_get_symbolic (&m, &n, &n1, &nz, &nfr, &nchains, P1, Q1, Front_npivcol, Front_parent, Front_1strow, Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ; status = umfpack_di_load_numeric (&Numeric, filename) ; status = umfpack_di_save_numeric (Numeric, filename) ; status = umfpack_di_load_symbolic (&Symbolic, filename) ; status = umfpack_di_save_symbolic (Symbolic, filename) ; status = umfapck_di_get_determinant (Mx, Ex, Numeric, Info) ; \end{verbatim} } %------------------------------------------------------------------------------- \subsection{Reporting routines: real/{\tt int}} %------------------------------------------------------------------------------- {\footnotesize \begin{verbatim} umfpack_di_report_status (Control, status) ; umfpack_di_report_control (Control) ; umfpack_di_report_info (Control, Info) ; status = umfpack_di_report_matrix (m, n, Ap, Ai, Ax, 1, Control) ; status = umfpack_di_report_matrix (m, n, Rp, Ri, Rx, 0, Control) ; status = umfpack_di_report_numeric (Numeric, Control) ; status = umfpack_di_report_perm (m, P, Control) ; status = umfpack_di_report_perm (n, Q, Control) ; status = umfpack_di_report_symbolic (Symbolic, Control) ; status = umfpack_di_report_triplet (m, n, nz, Ti, Tj, Tx, Control) ; status = umfpack_di_report_vector (n, X, Control) ; \end{verbatim} } %------------------------------------------------------------------------------- \subsection{Primary routines: complex/{\tt int}} %------------------------------------------------------------------------------- {\footnotesize \begin{verbatim} double Az [nz], Xx [n], Xz [n], Bx [n], Bz [n] ; status = umfpack_zi_symbolic (m, n, Ap, Ai, Ax, Az, &Symbolic, Control, Info) ; status = umfpack_zi_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric, Control, Info) ; status = umfpack_zi_solve (sys, Ap, Ai, Ax, Az, Xx, Xz, Bx, Bz, Numeric, Control, Info) ; umfpack_zi_free_symbolic (&Symbolic) ; umfpack_zi_free_numeric (&Numeric) ; \end{verbatim} } The arrays {\tt Ax}, {\tt Bx}, and {\tt Xx} double in size if any imaginary argument ({\tt Az}, {\tt Xz}, or {\tt Bz}) is {\tt NULL}. %------------------------------------------------------------------------------- \subsection{Alternative routines: complex/{\tt int}} %------------------------------------------------------------------------------- {\footnotesize \begin{verbatim} double Wz [10*n] ; umfpack_zi_defaults (Control) ; status = umfpack_zi_qsymbolic (m, n, Ap, Ai, Ax, Az, Qinit, &Symbolic, Control, Info) ; status = umfpack_zi_wsolve (sys, Ap, Ai, Ax, Az, Xx, Xz, Bx, Bz, Numeric, Control, Info, Wi, Wz) ; \end{verbatim} } %------------------------------------------------------------------------------- \subsection{Matrix manipulation routines: complex/{\tt int}} %------------------------------------------------------------------------------- {\footnotesize \begin{verbatim} double Tz [nz], Rz [nz], Yx [m], Yz [m], Zx [m], Zz [m] ; status = umfpack_zi_col_to_triplet (n, Ap, Tj) ; status = umfpack_zi_triplet_to_col (m, n, nz, Ti, Tj, Tx, Tz, Ap, Ai, Ax, Az, Map) ; status = umfpack_zi_transpose (m, n, Ap, Ai, Ax, Az, P, Q, Rp, Ri, Rx, Rz, 1) ; status = umfpack_zi_transpose (m, n, Ap, Ai, Ax, Az, P, Q, Rp, Ri, Rx, Rz, 0) ; status = umfpack_zi_scale (Yx, Yz, Zx, Zz, Numeric) ; \end{verbatim} } The arrays {\tt Tx}, {\tt Rx}, {\tt Yx}, and {\tt Zx} double in size if any imaginary argument ({\tt Tz}, {\tt Rz}, {\tt Yz}, or {\tt Zz}) is {\tt NULL}. %------------------------------------------------------------------------------- \subsection{Getting the contents of opaque objects: complex/{\tt int}} %------------------------------------------------------------------------------- {\footnotesize \begin{verbatim} double Lz [lnz], Uz [unz], Dx [min (m,n)], Dz [min (m,n)], Mz [1] ; status = umfpack_zi_get_lunz (&lnz, &unz, &m, &n, &nz_udiag, Numeric) ; status = umfpack_zi_get_numeric (Lp, Lj, Lx, Lz, Up, Ui, Ux, Uz, P, Q, Dx, Dz, &do_recip, Rs, Numeric) ; status = umfpack_zi_get_symbolic (&m, &n, &n1, &nz, &nfr, &nchains, P1, Q1, Front_npivcol, Front_parent, Front_1strow, Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ; status = umfpack_zi_load_numeric (&Numeric, filename) ; status = umfpack_zi_save_numeric (Numeric, filename) ; status = umfpack_zi_load_symbolic (&Symbolic, filename) ; status = umfpack_zi_save_symbolic (Symbolic, filename) ; status = umfapck_zi_get_determinant (Mx, Mz, Ex, Numeric, Info) ; \end{verbatim} } The arrays {\tt Lx}, {\tt Ux}, {\tt Dx}, and {\tt Mx} double in size if any imaginary argument ({\tt Lz}, {\tt Uz}, {\tt Dz}, or {\tt Mz}) is {\tt NULL}. %------------------------------------------------------------------------------- \subsection{Reporting routines: complex/{\tt int}} %------------------------------------------------------------------------------- {\footnotesize \begin{verbatim} umfpack_zi_report_status (Control, status) ; umfpack_zi_report_control (Control) ; umfpack_zi_report_info (Control, Info) ; status = umfpack_zi_report_matrix (m, n, Ap, Ai, Ax, Az, 1, Control) ; status = umfpack_zi_report_matrix (m, n, Rp, Ri, Rx, Rz, 0, Control) ; status = umfpack_zi_report_numeric (Numeric, Control) ; status = umfpack_zi_report_perm (m, P, Control) ; status = umfpack_zi_report_perm (n, Q, Control) ; status = umfpack_zi_report_symbolic (Symbolic, Control) ; status = umfpack_zi_report_triplet (m, n, nz, Ti, Tj, Tx, Tz, Control) ; status = umfpack_zi_report_vector (n, Xx, Xz, Control) ; \end{verbatim} } The arrays {\tt Ax}, {\tt Rx}, {\tt Tx}, and {\tt Xx} double in size if any imaginary argument ({\tt Az}, {\tt Rz}, {\tt Tz}, or {\tt Xz}) is {\tt NULL}. %------------------------------------------------------------------------------- \subsection{Utility routines} %------------------------------------------------------------------------------- These routines are the same in all four versions of UMFPACK. {\footnotesize \begin{verbatim} double t, s [2] ; t = umfpack_timer ( ) ; umfpack_tic (s) ; umfpack_toc (s) ; \end{verbatim} } %------------------------------------------------------------------------------- \subsection{AMD ordering routines} %------------------------------------------------------------------------------- UMFPACK makes use of the AMD ordering package for its symmetric ordering strategy. You may also use these four user-callable routines in your own C programs. You need to include the {\tt amd.h} file only if you make direct calls to the AMD routines themselves. The {\tt int} versions are summarized below; {\tt UF\_long} versions are also available. Refer to the AMD User Guide for more information, or to the file {\tt amd.h} which documents these routines. {\footnotesize \begin{verbatim} #include "amd.h" double amd_control [AMD_CONTROL], amd_info [AMD_INFO] ; amd_defaults (amd_control) ; status = amd_order (n, Ap, Ai, P, amd_control, amd_info) ; amd_control (amd_control) ; amd_info (amd_info) ; \end{verbatim} } %------------------------------------------------------------------------------- \section{Using UMFPACK in a Fortran program} %------------------------------------------------------------------------------- UMFPACK includes a basic Fortran 77 interface to some of the C-callable UMFPACK routines. Since interfacing C and Fortran programs is not portable, this interface might not work with all C and Fortran compilers. Refer to Section~\ref{Install} for more details. The following Fortran routines are provided. The list includes the C-callable routines that the Fortran interface routine calls. Refer to the corresponding C routines in Section~\ref{C} for more details on what the Fortran routine does. \begin{itemize} \item {\tt umf4def}: sets the default control parameters ({\tt umfpack\_di\_defaults}). \item {\tt umf4sym}: pre-ordering and symbolic factorization ({\tt umfpack\_di\_symbolic}). \item {\tt umf4num}: numeric factorization ({\tt umfpack\_di\_numeric}). \item {\tt umf4solr}: solve a linear system with iterative refinement ({\tt umfpack\_di\_solve}). \item {\tt umf4sol}: solve a linear system without iterative refinement ({\tt umfpack\_di\_solve}). Sets {\tt Control [UMFPACK\_IRSTEP]} to zero, and does not require the matrix $\m{A}$. \item {\tt umf4scal}: scales a vector using UMFPACK's scale factors ({\tt umfpack\_di\_scale}). \item {\tt umf4fnum}: free the {\tt Numeric} object ({\tt umfpack\_di\_free\_numeric}). \item {\tt umf4fsym}: free the {\tt Symbolic} object ({\tt umfpack\_di\_free\_symbolic}). \item {\tt umf4pcon}: prints the control parameters ({\tt umfpack\_di\_report\_control}). \item {\tt umf4pinf}: print statistics ({\tt umfpack\_di\_report\_info}). \item {\tt umf4snum}: save the {\tt Numeric} object to a file ({\tt umfpack\_di\_save\_numeric}). \item {\tt umf4ssym}: save the {\tt Symbolic} object to a file ({\tt umfpack\_di\_save\_symbolic}). \item {\tt umf4lnum}: load the {\tt Numeric} object from a file ({\tt umfpack\_di\_load\_numeric}). \item {\tt umf4lsym}: load the {\tt Symbolic} object from a file ({\tt umfpack\_di\_load\_symbolic}). \end{itemize} The matrix $\m{A}$ is passed to UMFPACK in compressed column form, with 0-based indices. In Fortran, for an {\tt m}-by-{\tt n} matrix $\m{A}$ with {\tt nz} entries, the row indices of the first column (column 1) are in {\tt Ai (Ap(1)+1} \ldots {\tt Ap(2))}, with values in {\tt Ax (Ap(1)+1} \ldots {\tt Ap(2))}. The last column (column {\tt n}) is in {\tt Ai (Ap(n)+1} \ldots {\tt Ap(n+1))} and {\tt Ax (Ap(n)+1} \ldots {\tt Ap(n+1))}. The number of entries in the matrix is thus {\tt nz = Ap (n+1)}. The row indices in {\tt Ai} are in the range 0 to {\tt m}-1. They must be sorted, with no duplicate entries allowed. None of the UMFPACK routines modify the input matrix $\m{A}$. The following definitions apply for the Fortran routines: {\footnotesize \begin{verbatim} integer m, n, Ap (n+1), Ai (nz), symbolic, numeric, filenum, status double precision Ax (nz), control (20), info (90), x (n), b (n) \end{verbatim} } UMFPACK's status is returned in either a {\tt status} argument, or in {\tt info (1)}. It is zero if UMFPACK was successful, 1 if the matrix is singular (this is a warning, not an error), and negative if an error occurred. Section~\ref{error_codes} summarizes the possible values of {\tt status} and {\tt info (1)}. See Table~\ref{sys} for a list of the values of the {\tt sys} argument. See Table~\ref{control} for a list of the control parameters (the Fortran usage is the same as the MATLAB usage for this array). For the {\tt Numeric} and {\tt Symbolic} handles, it is probably safe to assume that a Fortran {\tt integer} is sufficient to store a C pointer. If that does not work, try defining {\tt numeric} and {\tt symbolic} in your Fortran program as integer arrays of size 2. You will need to define them as {\tt integer*8} if you compile UMFPACK in the 64-bit mode. To avoid passing strings between C and Fortran in the load/save routines, a file number is passed instead, and the C interface constructs a file name (if {\tt filenum} is 42, the {\tt Numeric} file name is {\tt n42.umf}, and the {\tt Symbolic} file name is {\tt s42.umf}). The following is a summary of the calling sequence of each Fortran interface routine. An example of their use is in the {\tt Demo/umf4hb.f} file. That routine also includes an example of how to convert a 1-based sparse matrix into 0-based form. For more details on the arguments of each routine, refer to the arguments of the same name in the corresponding C-callable routine, in Sections~\ref{Primary}~through~\ref{Utility}. The only exception is the {\tt control} argument of {\tt umf4sol}, which sets {\tt control (8)} to zero to disable iterative refinement. Note that the solve routines do not overwrite {\tt b} with the solution, but return their solution in a different array, {\tt x}. {\footnotesize \begin{verbatim} call umf4def (control) call umf4sym (m, n, Ap, Ai, Ax, symbolic, control, info) call umf4num (Ap, Ai, Ax, symbolic, numeric, control, info) call umf4solr (sys, Ap, Ai, Ax, x, b, numeric, control, info) call umf4sol (sys, x, b, numeric, control, info) call umf4scal (x, b, numeric, status) call umf4fnum (numeric) call umf4fsym (symbolic) call umf4pcon (control) call umf4pinf (control) call umf4snum (numeric, filenum, status) call umf4ssym (symbolic, filenum, status) call umf4lnum (numeric, filenum, status) call umf4lsym (symbolic, filenum, status) \end{verbatim} } Access to the complex routines in UMFPACK is provided by the interface routines in {\tt umf4\_f77zwrapper.c}. The following is a synopsis of each routine. All the arguments are the same as the real versions, except {\tt Az}, {\tt xz}, and {\tt bz} are the imaginary parts of the matrix, solution, and right-hand side, respectively. The {\tt Ax}, {\tt x}, and {\tt b} are the real parts. {\footnotesize \begin{verbatim} call umf4zdef (control) call umf4zsym (m, n, Ap, Ai, Ax, Az, symbolic, control, info) call umf4znum (Ap, Ai, Ax, Az, symbolic, numeric, control, info) call umf4zsolr (sys, Ap, Ai, Ax, Az, x, xz, b, bz, numeric, control, info) call umf4zsol (sys, x, xz, b, bz, numeric, control, info) call umf4zscal (x, xz, b, bz, numeric, status) call umf4zfnum (numeric) call umf4zfsym (symbolic) call umf4zpcon (control) call umf4zpinf (control) call umf4zsnum (numeric, filenum, status) call umf4zssym (symbolic, filenum, status) call umf4zlnum (numeric, filenum, status) call umf4zlsym (symbolic, filenum, status) \end{verbatim} } The Fortran interface does not support the packed complex case. %------------------------------------------------------------------------------- \section{Installation} \label{Install} %------------------------------------------------------------------------------- %------------------------------------------------------------------------------- \subsection{Installing the C library} %------------------------------------------------------------------------------- The following discussion assumes you have the {\tt make} program, either in Unix, or in Windows with Cygwin\footnote{www.cygwin.com}. You can skip this section and go to next one if all you want to use is the UMFPACK and AMD mexFunctions in MATLAB. You will need to install both UMFPACK and AMD to use UMFPACK. The {\tt UMFPACK} and {\tt AMD} subdirectories must be placed side-by-side within the same directory. AMD is a stand-alone package that is required by UMFPACK. UMFPACK can be compiled without the BLAS \cite{DaydeDuff99,ACM679a,ATLAS,GotoVandeGeijn02}, but your performance will be much less than what it should be. System-dependent configurations are in the {\tt UFconfig/UFconfig.mk} file. The default settings will work on most systems, except that UMFPACK will be compiled so that it does not use the BLAS. Sample configurations are provided for Linux, Sun Solaris, SGI IRIX, IBM AIX, and the DEC/Compaq Alpha. To compile and install both packages, go to the {\tt UMFPACK} directory and type {\tt make}. This will compile the libraries ({\tt AMD/Lib/libamd.a} and {\tt UMFPACK/Lib/libumfpack.a}). A demo of the AMD ordering routine will be compiled and tested in the {\tt AMD/Demo} directory, and five demo programs will then be compiled and tested in the {\tt UMFPACK/Demo} directory. The outputs of these demo programs will then be compared with output files in the distribution. Expect to see a few differences, such as residual norms, compile-time control settings, and perhaps memory usage differences. To use {\tt make} to compile the MATLAB mexFunctions for MATLAB and AMD, you can either type {\tt make mex} in the UMFPACK directory. You may first need to edit the {\tt UFconfig/UFconfig.mk} file to modify the definition of the {\tt MEX}, if you have a version of MATLAB older than Version 7.2. Remove the {\tt -largeArrayDims} definition. If you use the MATLAB command {\tt umfpack\_make} in the MATLAB directory, then this case is handled for you automatically. If you have the GNU version of {\tt make}, the {\tt Lib/GNUmakefile} and {\tt MATLAB/GNUmakefile} files are used. These are much more concise than what the ``old'' version of {\tt make} can handle. If you do not have GNU {\tt make}, the {\tt Lib/Makefile} and {\tt MATLAB/Makefile} files are used instead. Each UMFPACK source file is compiled into four versions ({\tt double} / complex, and {\tt int} / {\tt UF\_long}). A proper old-style {\tt Makefile} is cumbersome in this case, so these two {\tt Makefile}'s have been constructed by brute force. They ignore dependencies, and simply compile everything. I highly recommend using GNU {\tt make} if you wish to modify UMFPACK. If you compile UMFPACK and AMD and then later change the {\tt UFconfig/UFconfig.mk} file then you should type {\tt make purge} and then {\tt make} to recompile. Here are the various parameters that you can control in your {\tt UFconfig/UFconfig.mk} file: \begin{itemize} \item {\tt CC = } your C compiler, such as {\tt cc}. \item {\tt RANLIB = } your system's {\tt ranlib} program, if needed. \item {\tt CFLAGS = } optimization flags, such as {\tt -O}. \item {\tt UMFPACK\_CONFIG = } configuration settings for the BLAS, memory allocation routines, and timing routines. \item {\tt LIB = } your libraries, such as {\tt -lm} or {\tt -lblas}. \item {\tt RM =} the command to delete a file. \item {\tt MV =} the command to rename a file. \item {\tt MEX =} the command to compile a MATLAB mexFunction. If you are using MATLAB 5, you need to add {\tt -DNBLAS} and {\tt -DNUTIL} to this command. \item {\tt F77 =} the command to compile a Fortran program (optional). \item {\tt F77FLAGS =} the Fortran compiler flags (optional). \item {\tt F77LIB =} the Fortran libraries (optional). \end{itemize} The {\tt UMFPACK\_CONFIG} string can include combinations of the following; most deal with how the BLAS are called: \begin{itemize} \item {\tt -DNBLAS} if you do not have any BLAS at all. \item {\tt -DNSUNPERF} if you are on Solaris but do not have the Sun Performance Library (for the BLAS). \item {\tt -DLONGBLAS} if your BLAS takes non-{\tt int} integer arguments. \item {\tt -DBLAS\_INT = } the integer used by the BLAS. \item {\tt -DBLAS\_NO\_UNDERSCORE} for controlling how C calls the Fortran BLAS. This is set automatically for Windows, Sun Solaris, SGI Irix, Red Hat Linux, Compaq Alpha, and AIX (the IBM RS 6000). \item {\tt -DGETRUSAGE} if you have the {\tt getrusage} function. \item {\tt -DNPOSIX} if you do not have the POSIX-compliant {\tt sysconf} and {\tt times} routines used by {\tt umfpack\_tic} and {\tt umfpack\_toc}. \item {\tt -DNRECIPROCAL} controls a trade-off between speed and accuracy. If defined (or if the pivot value itself is less than $10^{-12}$), then the pivot column is divided by the pivot value during numeric factorization. Otherwise, it is multiplied by the reciprocal of the pivot, which is faster but can be less accurate. The default is to multiply by the reciprocal unless the pivot value is small. This option also modifies how the rows of the matrix $\m{A}$ are scaled. If {\tt -DNRECIPROCAL} is defined (or if any scale factor is less than $10^{-12}$), entries in the rows of $\m{A}$ are divided by the scale factors. Otherwise, they are multiplied by the reciprocal. When compiling the complex routines with the GNU {\tt gcc} compiler, the pivot column is always divided by the pivot entry, because of a numerical accuracy issue encountered with {\tt gcc} version 3.2 with a few complex matrices on a Pentium 4M (running Linux). You can still use {\tt -DNRECIPROCAL} to control how the scale factors for the rows of $\m{A}$ are applied. \item {\tt -DNO\_DIVIDE\_BY\_ZERO} controls how UMFPACK treats zeros on the diagonal of $\m{U}$, for a singular matrix $\m{A}$. If defined, then no division by zero is performed (a zero entry on the diagonal of $\m{U}$ is treated as if it were equal to one). By default, UMFPACK will divide by zero. \item {\tt -DNO\_TIMER} controls whether or not timing routines are to be called. If defined, no timers are used. Timers are included by default. \end{itemize} If a Fortran BLAS package is used you may see compiler warnings. The BLAS routines {\tt dgemm}, {\tt dgemv}, {\tt dger}, {\tt dtrsm}, {\tt dtrsv}, {\tt dscal} and their corresponding complex versions are used. Header files are not provided for the Fortran BLAS. You may safely ignore all of these warnings. I highly recommend the recent BLAS by Goto and van de Geijn \cite{GotoVandeGeijn02}. Using this BLAS increased the performance of UMFPACK by up to 50\% on a Dell Latitude C840 laptop (2GHz Pentium 4M, 512K L2 cache, 1GB main memory). The peak performance of {\tt umfpack\_di\_numeric} with Goto and van de Geijn's BLAS is 1.6 Gflops on this computer. In MATLAB, the peak performance of UMFPACK on a dense matrix (stored in sparse format) is 900 Mflops, as compared to 1 Gflop for {\tt x = A}$\backslash${\tt b} when {\tt A} is stored as a regular full matrix. When you compile your program that uses the C-callable UMFPACK library, you need to link your program with both libraries ({\tt UMFPACK/Lib/libumfpack.a} and {\tt AMD/Lib/libamd.a}) and you need to tell your compiler to look in the directories {\tt UMFPACK/Include} and {\tt AMD/Include} for include files. See {\tt UMFPACK/Demo/Makefile} for an example. You do not need to directly include any AMD include files in your program, unless you directly call AMD routines. You only need the \begin{verbatim} #include "umfpack.h" \end{verbatim} statement, as described in Section~\ref{Synopsis}. If you would like to compile both 32-bit and 64-bit versions of the libraries, you will need to do it in two steps. Modify your {\tt UFconfig/UFconfig.mk} file, and select the 32-bit option. Type {\tt make} in the {\tt UMFPACK} directory, which creates the {\tt UMFPACK/Lib/libumfpack.a} and {\tt AMD/Lib/libamd.a} libraries. Rename those two files. Edit your {\tt UFconfig/UFconfig.mk} file and select the 64-bit option. Type {\tt make purge}, and then {\tt make}, and you will create the 64-bit libraries. You can use the same {\tt umfpack.h} include file for both 32-bit and 64-bit versions. Simply link your program with the appropriate 32-bit or 64-bit compiled version of the UMFPACK and AMD libraries. Type {\tt make hb} in the {\tt UMFPACK/Demo/HB} directory to compile and run a C program that reads in and factorizes Harwell/Boeing matrices. Note that this uses a stand-alone Fortran program to read in the Fortran-formatted Harwell/Boeing matrices and write them to a file which can be read by a C program. The {\tt umf\_multicompile.c} file has been added to assist in the compilation of UMFPACK in Microsoft Visual Studio, for Windows. %------------------------------------------------------------------------------- \subsection{Installing the MATLAB interface} %------------------------------------------------------------------------------- If all you want to do is use the UMFPACK mexFunction in MATLAB, you can skip the use of the {\tt make} command described above. Simply type {\tt umfpack\_make} in MATLAB while in the {\tt UMFPACK/MATLAB} directory. You can also type {\tt amd\_make} in the {\tt AMD/MATLAB} directory to compile the stand-alone AMD mexFunction (this is not required to compile the UMFPACK mexFunction). This works on any computer with MATLAB, including Windows. If you are using Windows and the {\tt lcc} compiler bundled with MATLAB 6.1, then you may need to copy the {\tt UMFPACK}$\backslash${\tt MATLAB}$\backslash${\tt lcc\_lib}$\backslash${\tt libmwlapack.lib} file into the {\tt }$\backslash${\tt extern}$\backslash${\tt lib}$\backslash${\tt win32}$\backslash${\tt lcc}$\backslash$ directory. Next, type {\tt mex -setup} at the MATLAB prompt, and ask MATLAB to select the {\tt lcc} compiler. MATLAB 6.1 has built-in BLAS, but in that version of MATLAB the BLAS cannot be accessed by a mexFunction compiled by {\tt lcc} without first copying this file to the location listed above. If you have MATLAB 6.5 or later, you can probably skip this step. %------------------------------------------------------------------------------- \subsection{Installing the Fortran interface} %------------------------------------------------------------------------------- Once the 32-bit C-callable UMFPACK library is compiled, you can also compile the Fortran interface, by typing {\tt make fortran}. This will create the {\tt umf4hb} program, test it, and compare the output with the file {\tt umf4hb.out} in the distribution. If you compiled UMFPACK in 64-bit mode, you need to use {\tt make fortran64} instead, which compiles the {\tt umf4hb64} program and compares its output with the file {\tt umf4hb64.out}. Refer to the comments in the {\tt Demo/umf4\_f77wrapper.c} file for more details. This interface is {\bf highly} non-portable, since it depends on how C and Fortran are interfaced. Because of this issue, the interface is included in the {\tt Demo} directory, and not as a primary part of the UMFPACK library. The interface routines are not included in the compiled {\tt UMFPACK/Lib/libumfpack.a} library, but left as stand-alone compiled files ({\tt umf4\_f77wrapper.o} and {\tt umf4\_f77wrapper64.o} in the {\tt Demo} directory). You may need to modify the interface routines in the file {\tt umf4\_f77wrapper.c} if you are using compilers for which this interface has not been tested. %------------------------------------------------------------------------------- \subsection{Known Issues} %------------------------------------------------------------------------------- The Microsoft C or C++ compilers on a Pentium badly break the IEEE 754 standard, and do not treat NaN's properly. According to IEEE 754, the expression {\tt (x != x)} is supposed to be true if and only if {\tt x} is NaN. For non-compliant compilers in Windows that expression is always false, and another test must be used: {\tt (x < x)} is true if and only if {\tt x} is NaN. For compliant compilers, {\tt (x < x)} is always false, for any value of {\tt x} (including NaN). To cover both cases, UMFPACK when running under Microsoft Windows defines the following macro, which is true if and only if {\tt x} is NaN, regardless of whether your compiler is compliant or not: \begin{verbatim} #define SCALAR_IS_NAN(x) (((x) != (x)) || ((x) < (x))) \end{verbatim} If your compiler breaks this test, then UMFPACK will fail catastrophically if it encounters a NaN. You will not just see NaN's in your output; UMFPACK will probably crash with a segmentation fault. In that case, you might try to see if the common (but non-ANSI C) routine {\tt isnan} is available, and modify the macro {\tt SCALAR\_IS\_NAN} in {\tt umf\_version.h} accordingly. The simpler (and IEEE 754-compliant) test {\tt (x != x)} is always true with Linux on a PC, and on every Unix compiler I have tested. Some compilers will complain about the Fortran BLAS being defined implicitly. C prototypes for the BLAS are not used, except the C-BLAS. Some compilers will complain about unrecognized {\tt \#pragma}'s. You may safely ignore all of these warnings. %------------------------------------------------------------------------------- \section{Future work} \label{Future} %------------------------------------------------------------------------------- Here are a few features that are not in the current version of UMFPACK, in no particular order. They may appear in a future release of UMFPACK. If you are interested, let me know and I could consider including them: \begin{enumerate} \item Remove the restriction that the column-oriented form be given with sorted columns. This has already been done in AMD Version 2.0. \item Future versions may have different default {\tt Control} parameters. Future versions may return more statistics in the {\tt Info} array, and they may use more entries in the {\tt Control} array. These two arrays will probably become larger, since there are very few unused entries. If they change in size, the constants {\tt UMFPACK\_CONTROL} and {\tt UMFPACK\_INFO} defined in {\tt umfpack.h} will be changed to reflect their new size. Your C program should use these constants when declaring the size of these two arrays. Do not define them as {\tt Control [20]} and {\tt Info [90]}. \item Forward/back solvers for the conventional row or column-form data structure for $\m{L}$ and $\m{U}$ (the output of {\tt umfpack\_*\_di\_get\_numeric}). This would enable a separate solver that could be used to write a MATLAB mexFunction {\tt x = lu\_refine (A, b, L, U, P, Q, R)} that gives MATLAB access to the iterative refinement algorithm with sparse backward error analysis. It would also be easier to handle sparse right-hand sides in this data structure, and end up with good asymptotic run-time in this case (particularly for $\m{Lx}=\m{b}$; see \cite{GilbertPeierls88}). See also CSparse and CXSparse for software for handling sparse right-hand sides. \item Complex absolute value computations could be based on FDLIBM (see \newline http://www.netlib.org/fdlibm), using the {\tt hypot(x,y)} routine. \item When using iterative refinement, the residual $\m{Ax}-\m{b}$ could be returned by {\tt umfpack\_solve}. \item The solve routines could handle multiple right-hand sides, and sparse right-hand sides. See {\tt umfpack\_solve} for the MATLAB version of this feature. See also CSparse and CXSparse for software for handling sparse right-hand sides. \item An option to redirect the error and diagnostic output. \item Permutation to block-triangular-form \cite{Duff78a} for the C-callable interface. There are two routines in the ACM Collected Algorithms (529 and 575) \cite{Duff81b,Duff78b} that could be translated from Fortran to C and included in UMFPACK. This would result in better performance for matrices from circuit simulation and chemical process engineering. See {\tt umfpack\_btf.m} for the MATLAB version of this feature. KLU includes this feature. See also {\tt cs\_dmperm} in CSparse and CXSparse. \item The ability to use user-provided work arrays, so that {\tt malloc}, {\tt free}, and {\tt realloc} realloc are not called. The {\tt umfpack\_*\_wsolve} routine is one example. \item A method that takes time proportional to the number of nonzeros in $\m{A}$ to compute the symbolic factorization \cite{GilbertNgPeyton94}. This would improve the performance of the symmetric and 2-by-2 strategies, and the unsymmetric strategy when dense rows are present. The current method takes time proportional to the number of nonzeros in the upper bound of $\m{U}$. The method used in UMFPACK exploits super-columns, however, so this bound is rarely reached. See {\tt cs\_counts} in CSparse and CXSparse, and {\tt cholmod\_analyze} in CHOLMOD. \item Other basic sparse matrix operations, such as sparse matrix multiplication, could be included. \item A more complete Fortran interface. \item A C++ interface. \item A parallel version using MPI. This would require a large amount of effort. \end{enumerate} %------------------------------------------------------------------------------- \newpage \section{The primary UMFPACK routines} \label{Primary} %------------------------------------------------------------------------------- The include files are the same for all four versions of UMFPACK. The generic integer type is {\tt Int}, which is an {\tt int} or {\tt UF\_long}, depending on which version of UMFPACK you are using. \subsection{umfpack\_*\_symbolic} {\footnotesize \begin{verbatim} INCLUDE umfpack_symbolic.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_numeric} {\footnotesize \begin{verbatim} INCLUDE umfpack_numeric.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_solve} {\footnotesize \begin{verbatim} INCLUDE umfpack_solve.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_free\_symbolic} {\footnotesize \begin{verbatim} INCLUDE umfpack_free_symbolic.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_free\_numeric} {\footnotesize \begin{verbatim} INCLUDE umfpack_free_numeric.h via sed \end{verbatim} } %------------------------------------------------------------------------------- \newpage \section{Alternative routines} \label{Alternative} %------------------------------------------------------------------------------- \subsection{umfpack\_*\_defaults} {\footnotesize \begin{verbatim} INCLUDE umfpack_defaults.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_qsymbolic} {\footnotesize \begin{verbatim} INCLUDE umfpack_qsymbolic.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_wsolve} {\footnotesize \begin{verbatim} INCLUDE umfpack_wsolve.h via sed \end{verbatim} } %------------------------------------------------------------------------------- \newpage \section{Matrix manipulation routines} \label{Manipulate} %------------------------------------------------------------------------------- \subsection{umfpack\_*\_col\_to\_triplet} {\footnotesize \begin{verbatim} INCLUDE umfpack_col_to_triplet.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_triplet\_to\_col} {\footnotesize \begin{verbatim} INCLUDE umfpack_triplet_to_col.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_transpose} {\footnotesize \begin{verbatim} INCLUDE umfpack_transpose.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_scale} {\footnotesize \begin{verbatim} INCLUDE umfpack_scale.h via sed \end{verbatim} } %------------------------------------------------------------------------------- \newpage \section{Getting the contents of opaque objects} \label{Get} %------------------------------------------------------------------------------- \subsection{umfpack\_*\_get\_lunz} {\footnotesize \begin{verbatim} INCLUDE umfpack_get_lunz.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_get\_numeric} {\footnotesize \begin{verbatim} INCLUDE umfpack_get_numeric.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_get\_symbolic} {\footnotesize \begin{verbatim} INCLUDE umfpack_get_symbolic.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_save\_numeric} {\footnotesize \begin{verbatim} INCLUDE umfpack_save_numeric.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_load\_numeric} {\footnotesize \begin{verbatim} INCLUDE umfpack_load_numeric.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_save\_symbolic} {\footnotesize \begin{verbatim} INCLUDE umfpack_save_symbolic.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_load\_symbolic} {\footnotesize \begin{verbatim} INCLUDE umfpack_load_symbolic.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_get\_determinant} {\footnotesize \begin{verbatim} INCLUDE umfpack_get_determinant.h via sed \end{verbatim} } %------------------------------------------------------------------------------- \newpage \section{Reporting routines} \label{Report} %------------------------------------------------------------------------------- \subsection{umfpack\_*\_report\_status} {\footnotesize \begin{verbatim} INCLUDE umfpack_report_status.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_report\_control} {\footnotesize \begin{verbatim} INCLUDE umfpack_report_control.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_report\_info} {\footnotesize \begin{verbatim} INCLUDE umfpack_report_info.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_report\_matrix} {\footnotesize \begin{verbatim} INCLUDE umfpack_report_matrix.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_report\_numeric} {\footnotesize \begin{verbatim} INCLUDE umfpack_report_numeric.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_report\_perm} {\footnotesize \begin{verbatim} INCLUDE umfpack_report_perm.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_report\_symbolic} {\footnotesize \begin{verbatim} INCLUDE umfpack_report_symbolic.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_report\_triplet} {\footnotesize \begin{verbatim} INCLUDE umfpack_report_triplet.h via sed \end{verbatim} } \newpage \subsection{umfpack\_*\_report\_vector} {\footnotesize \begin{verbatim} INCLUDE umfpack_report_vector.h via sed \end{verbatim} } %------------------------------------------------------------------------------- \newpage \section{Utility routines} \label{Utility} %------------------------------------------------------------------------------- \subsection{umfpack\_timer} {\footnotesize \begin{verbatim} INCLUDE umfpack_timer.h via sed \end{verbatim} } \newpage \subsection{umfpack\_tic and umfpack\_toc} {\footnotesize \begin{verbatim} INCLUDE umfpack_tictoc.h via sed \end{verbatim} } %------------------------------------------------------------------------------- \newpage % References %------------------------------------------------------------------------------- \bibliographystyle{plain} \bibliography{UserGuide} \end{document} SuiteSparse/UMFPACK/Doc/License0000644001170100242450000000326410677537576015103 0ustar davisfacUMFPACK Version 5.1.1, Copyright 1995-2007 by Timothy A. Davis. All Rights Reserved. UMFPACK is available under alternate licenses, contact T. Davis for details. UMFPACK License: Your use or distribution of UMFPACK or any modified version of UMFPACK implies that you agree to this License. This library is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. 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If the Program specifies a version number of this License which applies to it and "any later version", you have the option of following the terms and conditions either of that version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of this License, you may choose any version ever published by the Free Software Foundation. 10. If you wish to incorporate parts of the Program into other free programs whose distribution conditions are different, write to the author to ask for permission. For software which is copyrighted by the Free Software Foundation, write to the Free Software Foundation; we sometimes make exceptions for this. Our decision will be guided by the two goals of preserving the free status of all derivatives of our free software and of promoting the sharing and reuse of software generally. NO WARRANTY 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. END OF TERMS AND CONDITIONS How to Apply These Terms to Your New Programs If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms. To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively convey the exclusion of warranty; and each file should have at least the "copyright" line and a pointer to where the full notice is found. Copyright (C) This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Also add information on how to contact you by electronic and paper mail. If the program is interactive, make it output a short notice like this when it starts in an interactive mode: Gnomovision version 69, Copyright (C) year name of author Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the program `Gnomovision' (which makes passes at compilers) written by James Hacker. , 1 April 1989 Ty Coon, President of Vice This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Library General Public License instead of this License. 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Davis \\ Dept. of Computer and Information Science and Engineering \\ Univ. of Florida, Gainesville, FL} \title{UMFPACK Version 5.2 Quick Start Guide} \date{Nov 1, 2007} \maketitle %------------------------------------------------------------------------------- \begin{abstract} UMFPACK is a set of routines for solving unsymmetric sparse linear systems, $\m{Ax}=\m{b}$, using the Unsymmetric-pattern MultiFrontal method and direct sparse LU factorization. It is written in ANSI/ISO C, with a MATLAB interface. UMFPACK relies on the Level-3 Basic Linear Algebra Subprograms (dense matrix multiply) for its performance. This code works on Windows and many versions of Unix (Sun Solaris, Red Hat Linux, IBM AIX, SGI IRIX, and Compaq Alpha). This is a ``quick start'' guide for Unix users of the C interface. \end{abstract} %------------------------------------------------------------------------------- UMFPACK Version 5.2, Copyright\copyright 1995-2006 by Timothy A. Davis. All Rights Reserved. Refer to the UMFPACK User Guide for the License. See \newline http://www.cise.ufl.edu/research/sparse/umfpack for the code and full documentation. %------------------------------------------------------------------------------- \section{Overview} %------------------------------------------------------------------------------- UMFPACK is a set of routines for solving systems of linear equations, $\m{Ax}=\m{b}$, when $\m{A}$ is sparse and unsymmetric. The sparse matrix $\m{A}$ can be square or rectangular, singular or non-singular, and real or complex (or any combination). Only square matrices $\m{A}$ can be used to solve $\m{Ax}=\m{b}$ or related systems. Rectangular matrices can only be factorized. UMFPACK is a built-in routine in MATLAB used by the forward and backslash operator, and the {\tt lu} routine. The following is a short introduction to Unix users of the C interface of UMFPACK. %------------------------------------------------------------------------------- The C-callable UMFPACK library consists of 32 user-callable routines and one include file. Twenty-eight of the routines come in four versions, with different sizes of integers and for real or complex floating-point numbers. This Quick Start Guide assumes you are working with real matrices (not complex) and with {\tt int}'s as integers (not {\tt long}'s). Refer to the User Guide for information about the complex and long integer versions. The include file {\tt umfpack.h} must be included in any C program that uses UMFPACK. For more details, see: {\em A column pre-ordering strategy for the unsymmetric-pattern multifrontal method}, Davis, T. A., ACM Trans. Math. Software, vol 30. no 2, 2004, pp. 165-195, and {\em Algorithm 832: {UMFPACK}, an unsymmetric-pattern multifrontal method}, same issue, pp. 196-199. %------------------------------------------------------------------------------- \section{Primary routines, and a simple example} %------------------------------------------------------------------------------- Five primary UMFPACK routines are required to factorize $\m{A}$ or solve $\m{Ax}=\m{b}$. An overview of the primary features of the routines is given in Section~\ref{Primary}. Additional routines are available for passing a different column ordering to UMFPACK, changing default parameters, manipulating sparse matrices, getting the LU factors, save and loading the LU factors from a file, computing the determinant, and reporting results. See the User Guide for more information. \begin{itemize} \item {\tt umfpack\_di\_symbolic}: Pre-orders the columns of $\m{A}$ to reduce fill-in and performs a symbolic analysis. Returns an opaque {\tt Symbolic} object as a {\tt void *} pointer. The object contains the symbolic analysis and is needed for the numerical factorization. \item {\tt umfpack\_di\_numeric}: Numerically scales and then factorizes a sparse matrix $\m{PAQ}$, $\m{PRAQ}$, or $\m{PR}^{-1}\m{AQ}$ into the product $\m{LU}$, where $\m{P}$ and $\m{Q}$ are permutation matrices, $\m{R}$ is a diagonal matrix of scale factors, $\m{L}$ is lower triangular with unit diagonal, and $\m{U}$ is upper triangular. Requires the symbolic ordering and analysis computed by {\tt umfpack\_di\_symbolic}. Returns an opaque {\tt Numeric} object as a {\tt void *} pointer. The object contains the numerical factorization and is used by {\tt umfpack\_di\_solve}. \item {\tt umfpack\_di\_solve}: Solves a sparse linear system ($\m{Ax}=\m{b}$, $\m{A}\tr\m{x}=\m{b}$, or systems involving just $\m{L}$ or $\m{U}$), using the numeric factorization computed by {\tt umfpack\_di\_numeric}. \item {\tt umfpack\_di\_free\_symbolic}: Frees the {\tt Symbolic} object created by {\tt umfpack\_di\_symbolic}. \item {\tt umfpack\_di\_free\_numeric}: Frees the {\tt Numeric} object created by {\tt umfpack\_di\_numeric}. \end{itemize} The matrix $\m{A}$ is represented in compressed column form, which is identical to the sparse matrix representation used by MATLAB. It consists of three arrays, where the matrix is {\tt m}-by-{\tt n}, with {\tt nz} entries: {\footnotesize \begin{verbatim} int Ap [n+1] ; int Ai [nz] ; double Ax [nz] ; \end{verbatim} } All nonzeros are entries, but an entry may be numerically zero. The row indices of entries in column {\tt j} are stored in {\tt Ai[Ap[j]} ... {\tt Ap[j+1]-1]}. The corresponding numerical values are stored in {\tt Ax[Ap[j]} ... {\tt Ap[j+1]-1]}. No duplicate row indices may be present, and the row indices in any given column must be sorted in ascending order. The first entry {\tt Ap[0]} must be zero. The total number of entries in the matrix is thus {\tt nz = Ap[n]}. Except for the fact that extra zero entries can be included, there is thus a unique compressed column representation of any given matrix $\m{A}$. Here is a simple main program, {\tt umfpack\_simple.c}, that illustrates the basic usage of UMFPACK. {\footnotesize \begin{verbatim} #include #include "umfpack.h" int n = 5 ; int Ap [ ] = {0, 2, 5, 9, 10, 12} ; int Ai [ ] = { 0, 1, 0, 2, 4, 1, 2, 3, 4, 2, 1, 4} ; double Ax [ ] = {2., 3., 3., -1., 4., 4., -3., 1., 2., 2., 6., 1.} ; double b [ ] = {8., 45., -3., 3., 19.} ; double x [5] ; int main (void) { double *null = (double *) NULL ; int i ; void *Symbolic, *Numeric ; (void) umfpack_di_symbolic (n, n, Ap, Ai, Ax, &Symbolic, null, null) ; (void) umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric, null, null) ; umfpack_di_free_symbolic (&Symbolic) ; (void) umfpack_di_solve (UMFPACK_A, Ap, Ai, Ax, x, b, Numeric, null, null) ; umfpack_di_free_numeric (&Numeric) ; for (i = 0 ; i < n ; i++) printf ("x [%d] = %g\n", i, x [i]) ; return (0) ; } \end{verbatim} } The {\tt Ap}, {\tt Ai}, and {\tt Ax} arrays represent the matrix \[ \m{A} = \left[ \begin{array}{rrrrr} 2 & 3 & 0 & 0 & 0 \\ 3 & 0 & 4 & 0 & 6 \\ 0 & -1 & -3 & 2 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 4 & 2 & 0 & 1 \\ \end{array} \right]. \] and the solution is $\m{x} = [1 \, 2 \, 3 \, 4 \, 5]\tr$. The program uses default control settings and does not return any statistics about the ordering, factorization, or solution ({\tt Control} and {\tt Info} are both {\tt (double *) NULL}). For routines to manipulate a simpler ``triplet-form'' data structure for your sparse matrix $\m{A}$, refer to the UMFPACK User Guide. %------------------------------------------------------------------------------- \section{Synopsis of primary C-callable routines} \label{Synopsis} %------------------------------------------------------------------------------- The matrix $\m{A}$ is {\tt m}-by-{\tt n} with {\tt nz} entries. The optional {\tt umfpack\_di\_defaults} routine loads the default control parameters into the {\tt Control} array. The settings can then be modified before passing the array to the other routines. Refer to Section~\ref{Primary} for more details. {\footnotesize \begin{verbatim} #include "umfpack.h" int status, sys, n, m, nz, Ap [n+1], Ai [nz] ; double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], Ax [nz], X [n], B [n] ; void *Symbolic, *Numeric ; status = umfpack_di_symbolic (m, n, Ap, Ai, Ax, &Symbolic, Control, Info) ; status = umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric, Control, Info) ; status = umfpack_di_solve (sys, Ap, Ai, Ax, X, B, Numeric, Control, Info) ; umfpack_di_free_symbolic (&Symbolic) ; umfpack_di_free_numeric (&Numeric) ; umfpack_di_defaults (Control) ; \end{verbatim} } %------------------------------------------------------------------------------- \section{Installation} \label{Install} %------------------------------------------------------------------------------- You will need to install both UMFPACK v5.2 and AMD v2.2 to use UMFPACK. Note that UMFPACK v5.2 cannot use AMD v1.2 or earlier. The {\tt UMFPACK} and {\tt AMD} subdirectories must be placed side-by-side within the same parent directory. AMD is a stand-alone package that is required by UMFPACK. UMFPACK can be compiled without the BLAS but your performance will be much less than what it should be. System-dependent configurations are in the {\tt UFconfig/UFconfig.mk} file. The default settings will work on most systems, except for the BLAS definition. Sample configurations are provided for Linux, Sun Solaris, SGI IRIX, IBM AIX, and the DEC/Compaq Alpha. To compile and install both packages, go to the UMFPACK directory and type {\tt make}. This will compile the libraries ({\tt AMD/Lib/libamd.a} and {\tt UMFPACK/Lib/libumfpack.a}). A demo of the AMD ordering routine will be compiled and tested in the {\tt AMD/Demo} directory, and five demo programs will then be compiled and tested in the {\tt UMFPACK/Demo} directory. The outputs of these demo programs will then be compared with output files in the distribution. Expect to see a few differences, such as residual norms, compile-time control settings, and perhaps memory usage differences. To use {\tt make} to compile the MATLAB mexFunctions for MATLAB and AMD, you can either type {\tt make mex} in the UMFPACK directory. You may first need to edit the {\tt UFconfig/UFconfig.mk} file to modify the definition of the {\tt MEX}, if you have a version of MATLAB older than Version 7.2. Remove the {\tt -largeArrayDims} definition. If you use the MATLAB command {\tt umfpack\_make} in the MATLAB directory, then this case is handled for you automatically. If you compile UMFPACK and AMD and then later change the {\tt UFconfig/UFconfig.mk} file then you should type {\tt make purge} and then {\tt make} to recompile. Here are the various parameters that you can control in your {\tt UFconfig/UFconfig.mk} file: \begin{itemize} \item {\tt CC = } your C compiler, such as {\tt cc}. \item {\tt RANLIB = } your system's {\tt ranlib} program, if needed. \item {\tt CFLAGS = } optimization flags, such as {\tt -O}. \item {\tt UMFPACK\_CONFIG = } configuration settings, for the BLAS, memory allocation routines, and timing routines. \item {\tt LIB = } your libraries, such as {\tt -lm} or {\tt -lblas}. \item {\tt RM =} the command to delete a file. \item {\tt MV =} the command to rename a file. \item {\tt MEX =} the command to compile a MATLAB mexFunction. \item {\tt F77 =} the command to compile a Fortran program (optional). \item {\tt F77FLAGS =} the Fortran compiler flags (optional). \item {\tt F77LIB =} the Fortran libraries (optional). \end{itemize} The {\tt UMFPACK\_CONFIG} string can include combinations of the following; most deal with how the BLAS are called: \begin{itemize} \item {\tt -DNBLAS} if you do not have any BLAS at all. \item {\tt -DNSUNPERF} if you are on Solaris but do not have the Sun Performance Library. \item {\tt -DLONGBLAS} if your BLAS takes non-{\tt int} integer arguments. \item {\tt -DBLAS\_INT = } the integer used by the BLAS. \item {\tt -DBLAS\_NO\_UNDERSCORE} for controlling how C calls the Fortran BLAS. This is set automatically for Windows, Sun Solaris, SGI Irix, Red Hat Linux, Compaq Alpha, and AIX (the IBM RS 6000). \item {\tt -DGETRUSAGE} if you have the {\tt getrusage} function. \item {\tt -DNPOSIX} if you do not have the POSIX-compliant {\tt sysconf} and {\tt times} routines. \item {\tt -DNRECIPROCAL} controls a trade-off between speed and accuracy. This is off by default (speed preferred over accuracy) except when compiling for MATLAB. \end{itemize} When you compile your program that uses the C-callable UMFPACK library, you need to add the both {\tt UMFPACK/Lib/libumfpack.a} and {\tt AMD/Lib/libamd.a} libraries, and you need to tell your compiler to look in the directories {\tt UMFPACK/Include} and {\tt AMD/Include} for include files. See {\tt UMFPACK/Demo/Makefile} for an example. You do not need to directly include any AMD include files in your program, unless you directly call AMD routines. You only need the \begin{verbatim} #include "umfpack.h" \end{verbatim} statement, as described in Section~\ref{Synopsis}. %------------------------------------------------------------------------------- \newpage \section{The primary UMFPACK routines} \label{Primary} %------------------------------------------------------------------------------- \subsection{umfpack\_di\_symbolic} {\footnotesize \begin{verbatim} int umfpack_di_symbolic ( int n_row, int n_col, const int Ap [ ], const int Ai [ ], const double Ax [ ], void **Symbolic, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO] ) ; Purpose: Given nonzero pattern of a sparse matrix A in column-oriented form, umfpack_di_symbolic performs a column pre-ordering to reduce fill-in (using COLAMD or AMD) and a symbolic factorization. This is required before the matrix can be numerically factorized with umfpack_di_numeric. For the following discussion, let S be the submatrix of A obtained after eliminating all pivots of zero Markowitz cost. S has dimension (n_row-n1-nempty_row) -by- (n_col-n1-nempty_col), where n1 = Info [UMFPACK_COL_SINGLETONS] + Info [UMFPACK_ROW_SINGLETONS], nempty_row = Info [UMFPACK_NEMPTY_ROW] and nempty_col = Info [UMFPACK_NEMPTY_COL]. Returns: The status code is returned. See Info [UMFPACK_STATUS], below. Arguments: int n_row ; Input argument, not modified. int n_col ; Input argument, not modified. A is an n_row-by-n_col matrix. Restriction: n_row > 0 and n_col > 0. int Ap [n_col+1] ; Input argument, not modified. Ap is an integer array of size n_col+1. On input, it holds the "pointers" for the column form of the sparse matrix A. Column j of the matrix A is held in Ai [(Ap [j]) ... (Ap [j+1]-1)]. The first entry, Ap [0], must be zero, and Ap [j] <= Ap [j+1] must hold for all j in the range 0 to n_col-1. The value nz = Ap [n_col] is thus the total number of entries in the pattern of the matrix A. nz must be greater than or equal to zero. int Ai [nz] ; Input argument, not modified, of size nz = Ap [n_col]. The nonzero pattern (row indices) for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)]. The row indices in a given column j must be in ascending order, and no duplicate row indices may be present. Row indices must be in the range 0 to n_row-1 (the matrix is 0-based). double Ax [nz] ; Optional input argument, not modified. The numerical values of the sparse matrix A. The nonzero pattern (row indices) for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and the corresponding numerical values are stored in Ax [(Ap [j]) ... (Ap [j+1]-1)]. Used only by the 2-by-2 strategy to determine whether entries are "large" or "small". You do not have to pass the same numerical values to umfpack_di_numeric. If Ax is not present (a (double *) NULL pointer), then any entry in A is assumed to be "large". void **Symbolic ; Output argument. **Symbolic is the address of a (void *) pointer variable in the user's calling routine (see Syntax, above). On input, the contents of this variable are not defined. On output, this variable holds a (void *) pointer to the Symbolic object (if successful), or (void *) NULL if a failure occurred. double Control [UMFPACK_CONTROL] ; Input argument, not modified. If a (double *) NULL pointer is passed, then the default control settings are used. Only the primary parameters are listed below: Control [UMFPACK_STRATEGY]: This is the most important control parameter. It determines what kind of ordering and pivoting strategy that UMFPACK should use. It is new to Version 4.1 There are 4 options: UMFPACK_STRATEGY_AUTO: This is the default. The input matrix is analyzed to determine how symmetric the nonzero pattern is, and how many entries there are on the diagonal. It then selects one of the following strategies. Refer to the User Guide for a description of how the strategy is automatically selected. UMFPACK_STRATEGY_UNSYMMETRIC: Use the unsymmetric strategy. COLAMD is used to order the columns of A, followed by a postorder of the column elimination tree. No attempt is made to perform diagonal pivoting. The column ordering is refined during factorization. This strategy was the only one provided with UMFPACK V4.0. In the numerical factorization, the Control [UMFPACK_SYM_PIVOT_TOLERANCE] parameter is ignored. A pivot is selected if its magnitude is >= Control [UMFPACK_PIVOT_TOLERANCE] (default 0.1) times the largest entry in its column. UMFPACK_STRATEGY_SYMMETRIC: Use the symmetric strategy (new to Version 4.1). In this method, the approximate minimum degree ordering (AMD) is applied to A+A', followed by a postorder of the elimination tree of A+A'. UMFPACK attempts to perform diagonal pivoting during numerical factorization. No refinement of the column preordering is performed during factorization. In the numerical factorization, a nonzero entry on the diagonal is selected as the pivot if its magnitude is >= Control [UMFPACK_SYM_PIVOT_TOLERANCE] (default 0.001) times the largest entry in its column. If this is not acceptable, then an off-diagonal pivot is selected with magnitude >= Control [UMFPACK_PIVOT_TOLERANCE] (default 0.1) times the largest entry in its column. UMFPACK_STRATEGY_2BY2: a row permutation P2 is found that places large entries on the diagonal. The matrix P2*A is then factorized using the symmetric strategy, described above. Refer to the User Guide for more information. Control [UMFPACK_2BY2_TOLERANCE]: a diagonal entry S (k,k) is considered "small" if it is < tol * max (abs (S (:,k))), where S a submatrix of the scaled input matrix, with pivots of zero Markowitz cost removed. Control [UMFPACK_SCALE]: This parameter is new to V4.1. See umfpack_numeric.h for a description. Only affects the 2-by-2 strategy. Default: UMFPACK_SCALE_SUM. double Info [UMFPACK_INFO] ; Output argument, not defined on input. Contains statistics about the symbolic analysis. If a (double *) NULL pointer is passed, then no statistics are returned in Info (this is not an error condition). The entire Info array is cleared (all entries set to -1) and then the following statistics are computed (only the primary statistics are listed): Info [UMFPACK_STATUS]: status code. This is also the return value, whether or not Info is present. UMFPACK_OK Each column of the input matrix contained row indices in increasing order, with no duplicates. Only in this case does umfpack_di_symbolic compute a valid symbolic factorization. For the other cases below, no Symbolic object is created (*Symbolic is (void *) NULL). UMFPACK_ERROR_n_nonpositive n is less than or equal to zero. UMFPACK_ERROR_invalid_matrix Number of entries in the matrix is negative, Ap [0] is nonzero, a column has a negative number of entries, a row index is out of bounds, or the columns of input matrix were jumbled (unsorted columns or duplicate entries). UMFPACK_ERROR_out_of_memory Insufficient memory to perform the symbolic analysis. If the analysis requires more than 2GB of memory and you are using the 32-bit ("int") version of UMFPACK, then you are guaranteed to run out of memory. Try using the 64-bit version of UMFPACK. UMFPACK_ERROR_argument_missing One or more required arguments is missing. UMFPACK_ERROR_internal_error Something very serious went wrong. This is a bug. Please contact the author (davis@cise.ufl.edu). Info [UMFPACK_SIZE_OF_UNIT]: the number of bytes in a Unit, for memory usage statistics below. Info [UMFPACK_SYMBOLIC_PEAK_MEMORY]: the amount of memory (in Units) required for umfpack_di_symbolic to complete. This count includes the size of the Symbolic object itself, which is also reported in Info [UMFPACK_SYMBOLIC_SIZE]. Info [UMFPACK_NUMERIC_SIZE_ESTIMATE]: an estimate of the final size (in Units) of the entire Numeric object (both fixed-size and variable- sized parts), which holds the LU factorization (including the L, U, P and Q matrices). Info [UMFPACK_PEAK_MEMORY_ESTIMATE]: an estimate of the total amount of memory (in Units) required by umfpack_di_symbolic and umfpack_di_numeric to perform both the symbolic and numeric factorization. This is the larger of the amount of memory needed in umfpack_di_numeric itself, and the amount of memory needed in umfpack_di_symbolic (Info [UMFPACK_SYMBOLIC_PEAK_MEMORY]). The count includes the size of both the Symbolic and Numeric objects themselves. It can be a very loose upper bound, particularly when the symmetric or 2-by-2 strategies are used. Info [UMFPACK_FLOPS_ESTIMATE]: an estimate of the total floating-point operations required to factorize the matrix. This is a "true" theoretical estimate of the number of flops that would be performed by a flop-parsimonious sparse LU algorithm. It assumes that no extra flops are performed except for what is strictly required to compute the LU factorization. It ignores, for example, the flops performed by umfpack_di_numeric to add contribution blocks of frontal matrices together. If L and U are the upper bound on the pattern of the factors, then this flop count estimate can be represented in MATLAB (for real matrices, not complex) as: Lnz = full (sum (spones (L))) - 1 ; % nz in each col of L Unz = full (sum (spones (U')))' - 1 ; % nz in each row of U flops = 2*Lnz*Unz + sum (Lnz) ; The actual "true flop" count found by umfpack_di_numeric will be less than this estimate. Info [UMFPACK_LNZ_ESTIMATE]: an estimate of the number of nonzeros in L, including the diagonal. Since L is unit-diagonal, the diagonal of L is not stored. This estimate is a strict upper bound on the actual nonzeros in L to be computed by umfpack_di_numeric. Info [UMFPACK_UNZ_ESTIMATE]: an estimate of the number of nonzeros in U, including the diagonal. This estimate is a strict upper bound on the actual nonzeros in U to be computed by umfpack_di_numeric. Info [UMFPACK_SYMBOLIC_TIME]: The CPU time taken, in seconds. Info [UMFPACK_STRATEGY_USED]: The ordering strategy used: UMFPACK_STRATEGY_SYMMETRIC, UMFPACK_STRATEGY_UNSYMMETRIC, or UMFPACK_STRATEGY_2BY2. \end{verbatim} } %------------------------------------------------------------------------------- \newpage \subsection{umfpack\_di\_numeric} {\footnotesize \begin{verbatim} int umfpack_di_numeric ( const int Ap [ ], const int Ai [ ], const double Ax [ ], void *Symbolic, void **Numeric, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO] ) ; Purpose: Given a sparse matrix A in column-oriented form, and a symbolic analysis computed by umfpack_di_symbolic, the umfpack_di_numeric routine performs the numerical factorization, PAQ=LU, PRAQ=LU, or P(R\A)Q=LU, where P and Q are permutation matrices (represented as permutation vectors), R is the row scaling, L is unit-lower triangular, and U is upper triangular. This is required before the system Ax=b (or other related linear systems) can be solved. umfpack_di_numeric can be called multiple times for each call to umfpack_di_symbolic, to factorize a sequence of matrices with identical nonzero pattern. Simply compute the Symbolic object once, with umfpack_di_symbolic, and reuse it for subsequent matrices. umfpack_di_numeric safely detects if the pattern changes, and sets an appropriate error code. Returns: The status code is returned. See Info [UMFPACK_STATUS], below. Arguments: int Ap [n_col+1] ; Input argument, not modified. This must be identical to the Ap array passed to umfpack_di_symbolic. The value of n_col is what was passed to umfpack_di_symbolic (this is held in the Symbolic object). int Ai [nz] ; Input argument, not modified, of size nz = Ap [n_col]. This must be identical to the Ai array passed to umfpack_di_symbolic. double Ax [nz] ; Input argument, not modified, of size nz = Ap [n_col]. The numerical values of the sparse matrix A. The nonzero pattern (row indices) for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and the corresponding numerical values are stored in Ax [(Ap [j]) ... (Ap [j+1]-1)]. void *Symbolic ; Input argument, not modified. The Symbolic object, which holds the symbolic factorization computed by umfpack_di_symbolic. The Symbolic object is not modified by umfpack_di_numeric. void **Numeric ; Output argument. **Numeric is the address of a (void *) pointer variable in the user's calling routine (see Syntax, above). On input, the contents of this variable are not defined. On output, this variable holds a (void *) pointer to the Numeric object (if successful), or (void *) NULL if a failure occurred. double Control [UMFPACK_CONTROL] ; Input argument, not modified. If a (double *) NULL pointer is passed, then the default control settings are used. Only the primary parameters are listed below: Control [UMFPACK_PIVOT_TOLERANCE]: relative pivot tolerance for threshold partial pivoting with row interchanges. In any given column, an entry is numerically acceptable if its absolute value is greater than or equal to Control [UMFPACK_PIVOT_TOLERANCE] times the largest absolute value in the column. A value of 1.0 gives true partial pivoting. If less than or equal to zero, then any nonzero entry is numerically acceptable as a pivot (this is changed from Version 4.0). Default: 0.1. Smaller values tend to lead to sparser LU factors, but the solution to the linear system can become inaccurate. Larger values can lead to a more accurate solution (but not always), and usually an increase in the total work. Control [UMFPACK_SYM_PIVOT_TOLERANCE]: This parameter is new to V4.1. If diagonal pivoting is attempted (the symmetric or symmetric-2by2 strategies are used) then this parameter is used to control when the diagonal entry is selected in a given pivot column. The absolute value of the entry must be >= Control [UMFPACK_SYM_PIVOT_TOLERANCE] times the largest absolute value in the column. A value of zero will ensure that no off-diagonal pivoting is performed, except that zero diagonal entries are not selected if there are any off-diagonal nonzero entries. If an off-diagonal pivot is selected, an attempt is made to restore symmetry later on. Suppose A (i,j) is selected, where i != j. If column i has not yet been selected as a pivot column, then the entry A (j,i) is redefined as a "diagonal" entry, except that the tighter tolerance (Control [UMFPACK_PIVOT_TOLERANCE]) is applied. This strategy has an effect similar to 2-by-2 pivoting for symmetric indefinite matrices. If a 2-by-2 block pivot with nonzero structure i j i: 0 x j: x 0 is selected in a symmetric indefinite factorization method, the 2-by-2 block is inverted and a rank-2 update is applied. In UMFPACK, this 2-by-2 block would be reordered as j i i: x 0 j: 0 x In both cases, the symmetry of the Schur complement is preserved. Control [UMFPACK_SCALE]: This parameter is new to V4.1. Version 4.0 did not scale the matrix. Note that the user's input matrix is never modified, only an internal copy is scaled. There are three valid settings for this parameter. If any other value is provided, the default is used. UMFPACK_SCALE_NONE: no scaling is performed. UMFPACK_SCALE_SUM: each row of the input matrix A is divided by the sum of the absolute values of the entries in that row. The scaled matrix has an infinity norm of 1. UMFPACK_SCALE_MAX: each row of the input matrix A is divided by the maximum the absolute values of the entries in that row. In the scaled matrix the largest entry in each row has a magnitude exactly equal to 1. Scaling is very important for the "symmetric" strategy when diagonal pivoting is attempted. It also improves the performance of the "unsymmetric" strategy. Default: UMFPACK_SCALE_SUM. double Info [UMFPACK_INFO] ; Output argument. Contains statistics about the numeric factorization. If a (double *) NULL pointer is passed, then no statistics are returned in Info (this is not an error condition). The following statistics are computed in umfpack_di_numeric (only the primary statistics are listed): Info [UMFPACK_STATUS]: status code. This is also the return value, whether or not Info is present. UMFPACK_OK Numeric factorization was successful. umfpack_di_numeric computed a valid numeric factorization. UMFPACK_WARNING_singular_matrix Numeric factorization was successful, but the matrix is singular. umfpack_di_numeric computed a valid numeric factorization, but you will get a divide by zero in umfpack_di_solve. For the other cases below, no Numeric object is created (*Numeric is (void *) NULL). UMFPACK_ERROR_out_of_memory Insufficient memory to complete the numeric factorization. UMFPACK_ERROR_argument_missing One or more required arguments are missing. UMFPACK_ERROR_invalid_Symbolic_object Symbolic object provided as input is invalid. UMFPACK_ERROR_different_pattern The pattern (Ap and/or Ai) has changed since the call to umfpack_di_symbolic which produced the Symbolic object. Info [UMFPACK_NUMERIC_SIZE]: the actual final size (in Units) of the entire Numeric object, including the final size of the variable part of the object. Info [UMFPACK_NUMERIC_SIZE_ESTIMATE], an estimate, was computed by umfpack_di_symbolic. The estimate is normally an upper bound on the actual final size, but this is not guaranteed. Info [UMFPACK_PEAK_MEMORY]: the actual peak memory usage (in Units) of both umfpack_di_symbolic and umfpack_di_numeric. An estimate, Info [UMFPACK_PEAK_MEMORY_ESTIMATE], was computed by umfpack_di_symbolic. The estimate is normally an upper bound on the actual peak usage, but this is not guaranteed. With testing on hundreds of matrix arising in real applications, I have never observed a matrix where this estimate or the Numeric size estimate was less than the actual result, but this is theoretically possible. Please send me one if you find such a matrix. Info [UMFPACK_FLOPS]: the actual count of the (useful) floating-point operations performed. An estimate, Info [UMFPACK_FLOPS_ESTIMATE], was computed by umfpack_di_symbolic. The estimate is guaranteed to be an upper bound on this flop count. The flop count excludes "useless" flops on zero values, flops performed during the pivot search (for tentative updates and assembly of candidate columns), and flops performed to add frontal matrices together. Info [UMFPACK_LNZ]: the actual nonzero entries in final factor L, including the diagonal. This excludes any zero entries in L, although some of these are stored in the Numeric object. The Info [UMFPACK_LU_ENTRIES] statistic does account for all explicitly stored zeros, however. Info [UMFPACK_LNZ_ESTIMATE], an estimate, was computed by umfpack_di_symbolic. The estimate is guaranteed to be an upper bound on Info [UMFPACK_LNZ]. Info [UMFPACK_UNZ]: the actual nonzero entries in final factor U, including the diagonal. This excludes any zero entries in U, although some of these are stored in the Numeric object. The Info [UMFPACK_LU_ENTRIES] statistic does account for all explicitly stored zeros, however. Info [UMFPACK_UNZ_ESTIMATE], an estimate, was computed by umfpack_di_symbolic. The estimate is guaranteed to be an upper bound on Info [UMFPACK_UNZ]. Info [UMFPACK_NUMERIC_TIME]: The CPU time taken, in seconds. \end{verbatim} } %------------------------------------------------------------------------------- \newpage \subsection{umfpack\_di\_solve} {\footnotesize \begin{verbatim} int umfpack_di_solve ( int sys, const int Ap [ ], const int Ai [ ], const double Ax [ ], double X [ ], const double B [ ], void *Numeric, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO] ) ; Purpose: Given LU factors computed by umfpack_di_numeric (PAQ=LU, PRAQ=LU, or P(R\A)Q=LU) and the right-hand-side, B, solve a linear system for the solution X. Iterative refinement is optionally performed. Only square systems are handled. Singular matrices result in a divide-by-zero for all systems except those involving just the matrix L. Iterative refinement is not performed for singular matrices. In the discussion below, n is equal to n_row and n_col, because only square systems are handled. Returns: The status code is returned. See Info [UMFPACK_STATUS], below. Arguments: int sys ; Input argument, not modified. Defines which system to solve. (') is the linear algebraic transpose. sys value system solved UMFPACK_A Ax=b UMFPACK_At A'x=b UMFPACK_Pt_L P'Lx=b UMFPACK_L Lx=b UMFPACK_Lt_P L'Px=b UMFPACK_Lt L'x=b UMFPACK_U_Qt UQ'x=b UMFPACK_U Ux=b UMFPACK_Q_Ut QU'x=b UMFPACK_Ut U'x=b Iterative refinement can be optionally performed when sys is any of the following: UMFPACK_A Ax=b UMFPACK_At A'x=b For the other values of the sys argument, iterative refinement is not performed (Control [UMFPACK_IRSTEP], Ap, Ai, and Ax are ignored). int Ap [n+1] ; Input argument, not modified. int Ai [nz] ; Input argument, not modified. double Ax [nz] ; Input argument, not modified. If iterative refinement is requested (Control [UMFPACK_IRSTEP] >= 1, Ax=b or A'x=b is being solved, and A is nonsingular), then these arrays must be identical to the same ones passed to umfpack_di_numeric. The umfpack_di_solve routine does not check the contents of these arguments, so the results are undefined if Ap, Ai, Ax, are modified between the calls the umfpack_di_numeric and umfpack_di_solve. These three arrays do not need to be present (NULL pointers can be passed) if Control [UMFPACK_IRSTEP] is zero, or if a system other than Ax=b or A'x=b is being solved, or if A is singular, since in each of these cases A is not accessed. double X [n] ; Output argument. The solution to the linear system, where n = n_row = n_col is the dimension of the matrices A, L, and U. double B [n] ; Input argument, not modified. The right-hand side vector, b, stored as a conventional array of size n (or two arrays of size n for complex versions). This routine does not solve for multiple right-hand-sides, nor does it allow b to be stored in a sparse-column form. void *Numeric ; Input argument, not modified. Numeric must point to a valid Numeric object, computed by umfpack_di_numeric. double Control [UMFPACK_CONTROL] ; Input argument, not modified. If a (double *) NULL pointer is passed, then the default control settings are used. Control [UMFPACK_IRSTEP]: The maximum number of iterative refinement steps to attempt. A value less than zero is treated as zero. If less than 1, or if Ax=b or A'x=b is not being solved, or if A is singular, then the Ap, Ai, and Ax arguments are not accessed. Default: 2. double Info [UMFPACK_INFO] ; Output argument. Contains statistics about the solution factorization. If a (double *) NULL pointer is passed, then no statistics are returned in Info (this is not an error condition). The following statistics are computed in umfpack_di_solve (only the primary statistics are listed): Info [UMFPACK_STATUS]: status code. This is also the return value, whether or not Info is present. UMFPACK_OK The linear system was successfully solved. UMFPACK_WARNING_singular_matrix A divide-by-zero occurred. Your solution will contain Inf's and/or NaN's. Some parts of the solution may be valid. For example, solving Ax=b with A = [2 0] b = [ 1 ] returns x = [ 0.5 ] [0 0] [ 0 ] [ Inf ] UMFPACK_ERROR_out_of_memory Insufficient memory to solve the linear system. UMFPACK_ERROR_argument_missing One or more required arguments are missing. The B and X arguments are always required. Info and Control are not required. Ap, Ai and Ax are required if Ax=b or A'x=b is to be solved, the (default) iterative refinement is requested, and the matrix A is nonsingular. UMFPACK_ERROR_invalid_system The sys argument is not valid, or the matrix A is not square. UMFPACK_ERROR_invalid_Numeric_object The Numeric object is not valid. Info [UMFPACK_SOLVE_FLOPS]: the number of floating point operations performed to solve the linear system. This includes the work taken for all iterative refinement steps, including the backtrack (if any). Info [UMFPACK_SOLVE_TIME]: The time taken, in seconds. \end{verbatim} } %------------------------------------------------------------------------------- \newpage \subsection{umfpack\_di\_free\_symbolic} {\footnotesize \begin{verbatim} void umfpack_di_free_symbolic ( void **Symbolic ) ; Purpose: Deallocates the Symbolic object and sets the Symbolic handle to NULL. Arguments: void **Symbolic ; Input argument, deallocated and Symbolic is set to (void *) NULL on output. \end{verbatim} } %------------------------------------------------------------------------------- \subsection{umfpack\_di\_free\_numeric} {\footnotesize \begin{verbatim} void umfpack_di_free_numeric ( void **Numeric ) ; Purpose: Deallocates the Numeric object and sets the Numeric handle to NULL. Arguments: void **Numeric ; Input argument, deallocated and Numeric is set to (void *) NULL on output. \end{verbatim} } %------------------------------------------------------------------------------- \subsection{umfpack\_di\_defaults} {\footnotesize \begin{verbatim} void umfpack_di_defaults ( double Control [UMFPACK_CONTROL] ) ; Purpose: Sets the default control parameter settings. Arguments: double Control [UMFPACK_CONTROL] ; Output argument. Control is set to the default control parameter settings. \end{verbatim} } \end{document} SuiteSparse/UMFPACK/Doc/ChangeLog0000644001170100242450000004366410711430364015330 0ustar davisfacNov 1, 2007, version 5.2.0 * change of license to GNU GPL from GNU LGPL. This is the primary change to this version. * minor lint cleanup * port to MATLAB 7.5 (added -lmwblas to mex command) * added info output to the umfpack_btf command. May 31, 2007, version 5.1.0 * port to 64-bit MATLAB * Makefiles updated to reflect directory changes to AMD (UMFPACK v5.1.0 requires AMD v2.2.0) * Source/Makefile and GNUMakefile moved to Lib/ Dec 12, 2006: version 5.0.3 * minor MATLAB cleanup. Renamed umfpack mexFunction to umfpack2, to avoid filename clash with the built-in version of umfpack. Dec 2, 2006, version 5.0.2 * minor change to umfpack_report_info: does not print timings less than 0.001 seconds. * bug fix for complex case when using a non-gcc compiler (simplified the scaling of the pivot column). Does not affect the use of UMFPACK in MATLAB. Aug 31, 2006, version 5.0.1 * Minor correction to comments in umfpack_get_numeric.h. May 5, 2006, version 5.0 * Tcov subdirectory added. This has existed since the first C version of UMFPACK, but is only now included in the released version. It provides a near 100% test coverage for UMFPACK. The code isn't pretty, but it works. * now uses CHOLMOD's method for interfacing to the BLAS, including the BLAS_INT definition. This way, the UF_long version of UMFPACK can call the int BLAS. * revised to use AMD v2.0 Apr 7, 2006 * Minor correction to UMFPACK/Source/Makefile, for those who do not have GNU make. No change to version number, because no code was modified. Oct 10, 2005, version 4.6 * umf_solve.c modified for the complex case. A, X, and b can be split complex or unsplit. Prior version required the form of A, X, and B to be identical (all split or all unsplit). (Thanks to David Bateman). * added Cygwin to architecture detection. * added UMFPACK_SUBSUB_VERSION Aug. 30, 2005: v4.5 released * License changed to GNU LGPL. * The Make/ directory removed; configurations are now in ../UFconfig. * requires AMD v1.2 or later * added UMFPACK_MAIN_VERSION and UMFPACK_SUB_VERSION, defined as 4 and 5, respectively, for version 4.5. These macros will be updated for all future versions. See Include/umfpack.h for details. * function pointers used for malloc, free, calloc, realloc, printf, hypot, and complex divide. Defined in AMD/Source/amd_global.c, AMD/Source/amd_internal.h, UMFPACK/Source/umfpack_global.c, and UMFPACK/Include/umfpack_global.h. Compile-time dependence on The MathWorks "util.h", ut* routines and ut* macros removed. Jan. 28, 2005: v4.4 released * bug fix: when Qinit is provided to umfpack_*_qsymbolic, only the symmetric and unsymmetric strategies are now permitted. The auto and 2-by-2 strategies are not allowed. In v4.3 and earlier, providing Qinit and requesting the symmetric strategy did not always work (you got the unsymmetric strategy instead). This does not affect umfpack_*_symbolic, which computes its own ordering and can use all 4 strategies (auto, symmetric, unsymmetric, and 2-by-2). * umfpack_get_determinant added. (Thanks to David Bateman). * packed complex case added for all routines (previously only used in umfpack_report_vector). This allows arrays of ANSI C/C++ complex type to be passed directly to UMFPACK. * added umf_multicomple.c to assist in the compilation of UMFPACK in Microsoft Visual Studio, which does not have the required flexibility of the Unix "make" command. * local variable declarations reordered to encourage double-word alignment of double's and Entry's, for better performance. * note that with the exception of the behavior when a user-provided ordering is passed to umfpack_*_qsymbolic, versions 4.1 through 4.4 have comparable performance (ordering quality, memory usage, and run time). v4.1 is much better than v4.0 in performance. Jan. 11, 2005: v4.3.1 released * bug fix in umf_solve. This bug is only the 4th one found in the C versions of UMFPACK to date (Version 3.0 to 4.3.1, from March 2001 to Jan. 2005, excluding workarounds for quirky compilers). No bugs have been reported in the last Fortran version of UMFPACK (MA38, or UMFPACK V2.2.1) since its release in Jan. 1998. In Version 4.3, a bug in umf_solve caused iterative refinement to be disabled when solving A'x=b or A.'x=b after factorizing A. Modified the umfpack mexFunction to factorize A and then solve A'x=b when performing the operation x=b/A (as "umfpack(b,'/',A). Note that this has no effect on the use of UMFPACK in MATLAB itself, since MATLAB does not use the umfpack mexFunction for x=b/A. When computing x=b/A, MATLAB factorizes A' and computes x=(A'\b')' instead. The following source code files changed: UMFPACK/MATLAB/umfpackmex.c (see above) UMFPACK/Source/umf_solve.c (see source code: 2 lines changed) UMFPACK/Include/umfpack.h (version and date changed) UMFPACK/MATLAB/umfpack_test.m (new file) Jan. 16, 2004: v4.3 released. * user interface of v4.3 is upwardly-compatible with v4.2 and v4.1. No bugs found in v4.1 (except for one workaround for an old compiler). These changes add features only. * Note that v4.0 has a bug in umf_scale_column.c. The bug was patched in that version on Jan. 12, 2004. The bug does not appear in v4.1 and later. The bug is thus present in MATLAB 6.5, but it occurs very rarely, fortunately. It can occur when dividing a nonzero entry in the pivot column by the pivot value results in an underflow. * added to umfpackmex.c, for DBL_EPSILON. Some non-standard compilers (Microsoft Visual C++) require this. * #pragma added to umf_analyze.c, as a workaround around a bug in an old Intel compiler. * mexFunction interface to MATLAB modified. Call to mexCallMATLAB removed, which can be slow. In V4.1 it was used only to get MATLAB's spparms ('spumoni') value. * The AMD mexFunction was also modified in the same way (v1.1), with the call to mexCallMATLAB removed. Note that UMFPACK v4.1 through v4.3 can use either AMD v1.0 or AMD v1.1. * -DNO_DIVIDE_BY_ZERO option added. If this non-default option is enabled at compile time, and if the pivot value is zero, then no division occurs (zeros on the diagonal of U are treated as if they were equal to one). By default, the division by zero does occur. * -DNO_TIMER option added. If this non-default option is enabled at compile time, then no timers (times ( ), clock ( ), getrusage ( )) are used. V4.2: A special release for COMSOL, Inc., only (FEMLAB) * drop tolerance added. A few new parameters in the Control array are used, and a few new Info entries. May 6, 2003: V4.1 released. * No bugs were found in the prior version, Version 4.0. New features added only. Major changes throughout the code. User interface nearly unchanged, however. * Version 4.1 is upward-compatible with Version 4.0. The calling sequence of some user-callable routines in Version 4.0 have changed in this version. The routines umfpack_*_symbolic, umfpack_*_qsymbolic, umfpack_*_get_symbolic, and umfpack_*_get_numeric have new arguments added to them. The new arguments are optional. If you want to use a calling sequence similar to v4.0, simply pass NULL pointers in place of the new arguments. There are two new timing routines, umfpack_tic and umfpack_toc. A new user-callable routine, umfpack_*_scale, has been added. * "auto", "unsymmetric", "symmetric", and "2-by-2" strategies added. The symmetric strategy uses AMD on A+A' as the column preordering, followed by a postorder of the assembly tree of A+A'. Column ordering refinement is turned off, and diagonal entries are prefered as pivots. V4.0 only had the unsymmetric strategy. The 2-by-2 strategy does row permutations and attempts to find a zero-free diagonal while at the same time maintaining structural symmetry, and then uses the symmetric strategy on the permuted matrix. * row-scaling added. The default is to divide each row by the sum of the absolute values of each row. Other options are no scaling, and to divide each row by the max abs value in each row. * Matrices with upper bound memory usage greater than the maximum integer (2GB for 32-bit int's) can now be factorized (assuming the actual memory usage is still less than the maximum integer). With this change, the UMFPACK_ERROR_problem_too_large error code is no longer returned. * The current frontal matrix (Work->Fx) is no longer allocated as a static size, via malloc. It can grow and shrink, and is allocated from Numeric->Memory. * The AMD (Version 1.0) package is now required. It is available separately. To compile UMFPACK, it must appear as ../AMD if you are in the main UMFPACK directory. * The UMFPACK mexFunction now uses the internal utMalloc, utRealloc, and utFree routines, by default (except on Windows). * Three control parameters for modifying relaxed amalgamation removed. These values are now fixed at compile-time. * Many new statistics added to Info, and new control parameters added. * The umfpack mexFunction now returns permutation matrices for P and Q, not permutation vectors. It also returns the scale factors as a diagonal matrix. The factorization is now L*U = P*(R\A)*Q. * Option added for controlling the initial allocation of the workspace for the current frontal matrix. * pivot tolerance of zero treated differently. symmetric pivot tolerance added. * Makefile and GNUmakefile changed. umf_* routines with no double or complex values are now compiled just twice (int and long versions) rather than 4 times. * New routines added to save and load the Numeric and Symbolic objects to/from binary files. * Simple Fortran interface added. Apr 11, 2002: * Version 4.0 released. * bug fix: the Microsoft compiler doesn't handle NaN's properly. utIsNaN, and other ut* routines, added for MathWorks version to handle this properly. Apr 1, 2002: * bug fix: if a column was all NaN's, then UMFPACK would fail to find a pivot row. umf_row_search.c and umf_internal.h modified to fix this problem. Mar 9, 2002: V4.0beta released * Map argument added to umfpack_*_triplet_to_col. New files (umf_triplet.[ch]) added. * minor changes made so that UMFPACK can be compiled with g++ * additional error checking added to umfpack_*_numeric, for detecting more changes in pattern (Ap, Ai) since last call to umfpack_*_symbolic Feb 21, 2002: * User Guide explains the Makefile vs. GNUmakefile * umf_config.h modified, so that the complex SCSL C-BLAS uses (void *) arguments instead of (scsl_zomplex *). gcc generates some spurious warnings (cc doesn't complain). Affects the SGI IRIX only. * ported to Compaq Alpha Feb 20, 2002: V4.0 (alpha) released. * V4.0 not yet ported to the Compaq Alpha (V3.2 was ported). Feb 6 to Feb 19, 2002: * Relaxed restrictions on sizes of arrays for umfpack_*_transpose and umfpack_*_triplet_to_col. Size of "max(n,nz)" now just size nz. * workspace for umfpack_*_wsolve increased in size. * two user arrays for umfpack_*_get_symbolic increased in size, by 1 (Chain_maxrows, Chain_maxcols). * lu_normest.m added. Jan 18 to Feb 5, 2002: * The matrix A can be complex, singular, and/or rectangular. The solve step that uses the LU factors can only handle matrices that are complex or real, singuluar or non-singular, and *** square ***, however. * Estimate of the condition number computed: (min (abs (diag (U))) / (max (abs (diag (U))))) * Forward/backsolves can solve with A.' as well as A'. * char * arguments removed from user-callable routines to make it easier for Fortran to call UMFPACK. No Fortran interface is (yet) provided, however. The solve codes for umfpack_*_*solve changed to #define'd integers: UMFPACK_A Ax=b UMFPACK_At A'x=b UMFPACK_Aat A.'x=b UMFPACK_Pt_L P'Lx=b UMFPACK_L Lx=b UMFPACK_Lt_P L'Px=b UMFPACK_Lat_P L.'Px=b UMFPACK_Lt L'x=b UMFPACK_U_Qt UQ'x=b UMFPACK_U Ux=b UMFPACK_Q_Ut QU'x=b UMFPACK_Q_Uat QU.'x=b UMFPACK_Ut U'x=b UMFPACK_Uat U.'x=b All arguments are now either int, long scalars (pass by value), or int, long, double arrays (pass by reference), or void * pointers (pass by value or reference). A void * pointer is of size 32 or 64 bits on most machines. There is no need for the caller (C or Fortran) to dereference the void * pointers, so these can be treated as integer*4 or integer*8 in Fortran. A Fortran interface would have to have all arguments passed by reference. * All user-callable routine names changed. The four sets are now: umfpack_di_* real (double precision), int's as integers umfpack_dl_* real (double precision), longs's as integers umfpack_zi_* real (double precision), int's as integers umfpack_zl_* real (double precision), longs's as integers * Ptree (row preordering) and info on pivotal rows for each front added to Symbolic object (extracted by umfpack_*_get_symbolic). Ptree added as output argument to "umfpack (A, 'symbolic')" mexFunction. * umfpack_*_transpose can do A' or A.' * umfpack_wsolve.c file removed (now generated from umfpack_solve.c). * Can now extract just the diagonal of U with umfpack_*_get_numeric, without having to extract the entire matrix U. * UMFPACK_ERROR_singular_matrix (-2) removed. * UMFPACK_WARNING_singular_matrix (1) added. * Control [UMFPACK_PIVOT_OPTION] removed. No longer any symmetric pivot option (conflicts with the handling of singular and rectangular matrices). * Iterative refinement can do Ax=b, A'x=b, or A.'x=b. * Most floating-point operations done in macros, to support the complex versions. * Info [UMFPACK_N] is now Info [UMFPACK_NROW] * Info [UMFPACK_NCOL], Info [UMFPACK_UDIAG_NZ], Info [UMFPACK_UDIAG_NZ] added. * umfpack_* routines with "n" as input now use two arguments, n_row and n_col. * umfpack mexFunction now explicitly transposes A for b/A. It computes it using the array transpose as (A.'\b.').' January 1, 2002: UMFPACK Version 3.2 released. Submitted to ACM Trans. on Mathematical Software. * The umfpack mexFunction now returns the Info array when the matrix is singular. Returned an empty array prior to this change. * Renamed variable that conflicted with system library routines (system and j1). * Added a #ifdef MATHWORKS definition, so the built-in UMFPACK routine (in a future release of MATLAB) can use the internal ut* memory allocation routines, ut* assertion routine, and utPrintf. * MAX and MIN are not defined if they are already defined. * A bug fix in umf_kernel_init (a variable was not properly initialized). * Removed unused variables. October 8, 2001: UMFPACK Version 3.1 released. August-October, 2001: * added umfpack_btf M-file. * modified the BLAS update in the frontal matrix. If there are only a few pivots in remaining in the current front, then the BLAS3 update is delayed to include pivots in the next front. * Removed the special-case handling of dense columns from the numerical factorization (kept it in the colamd preordering). This improves the performance of UMFPACK on dense matrices by a factor of 5 or so, and simplifies the code. * Added a symmetric-preference pivoting option. The option slightly (but uniformly) improves the ordering when factorizing matrices with symmetric nonzero pattern. That class of matrix is better handled by the symmetric-pattern multifrontal method (MA41 in the Harwell Subroutine Library), however. * Fixed the detection of integer overflow. The 32-bit version cannot make use of more than 2GB of main memory (use the 64-bit version in that case, instead). The 32-bit version did not correctly detect when it was trying to factorize too large of a matrix. May 4, 2001: * SGI port extended. It can now call the SCSL Scientific Library, with 64-bit BLAS. Make.sgi and umf_config.h modified. April 30, 2001: UMFPACK Version 3.0 released. Changes since 3.0Beta release: * long integer version added (umfpack_l_* user-callable routines). * Peak memory usage in the numerical factorization reduced by a total of 12n integers (8n temporary workspace used during numerical factorization, and 4n for the permanent LU factors which was allocated at the beginning of factorization). * Ported to the IBM RS 6000 and Compaq Alpha, with help from Anshul Gupta and Friedrich Grund, respectively. * 64-bit version added. Uses dgemm_64, dgemv_64, and dger_64 in the Sun Performance Library. 64-bit versions with the BLAS might not work on any other platform, because they take int's as their integer input arguments instead of long's. Unfortunately, the proposed ANSI definition of the C-BLAS also uses int's as input integer arguments. It ought to use long's, or include a version that uses long's, just like the Sun Performance Library BLAS. * Additional statistics returned in Info: Info [UMFPACK_SIZE_OF_INT] sizeof (int) Info [UMFPACK_SIZE_OF_LONG] sizeof (long) Info [UMFPACK_SIZE_OF_POINTER] sizeof (void *) Info [UMFPACK_SIZE_OF_ENTRY] (was Info [UMFPACK_WORD]) Info [UMFPACK_MAX_FRONT_SIZE_ESTIMATE] est. front matrix size Info [UMFPACK_MAX_FRONT_SIZE] actual max frontal matrix size. Contents of Info rearranged. * UMFPACK_ERROR_bad_configurution error code replaced with UMFPACK_ERROR_problem_too_large error code. The "bad configuration" error occured when sizeof (int) < sizeof (size_t). Now, the int version of UMFPACK can use 32-bit int's and 64-bit pointers, and the long version can use 64-bit long's and 64-bit pointers. Both versions check to see if the array sizes allocated are larger than what can be accessed by an integer index variable (int or long, depending on the version), and returns UMFPACK_ERROR_problem_too_large if they become too large. March 15, 2001: UMFPACK Version 3.0Beta released. SuiteSparse/UMFPACK/Lib/0000755001170100242450000000000010711435725013550 5ustar davisfacSuiteSparse/UMFPACK/Lib/Makefile0000644001170100242450000007656210617157777015245 0ustar davisfac#------------------------------------------------------------------------------- # UMFPACK Makefile for compiling on Unix systems (for original make only) #------------------------------------------------------------------------------- # This is a very ugly Makefile, and is only provided for those who do not # have GNU make. Note that it is not used if you have GNU make. It ignores # dependency checking and just compiles everything. default: everything include ../../UFconfig/UFconfig.mk C = $(CC) $(CFLAGS) $(UMFPACK_CONFIG) -I../Include -I../../AMD/Include \ -I../Source everything: $(C) -c ../Source/umfpack_global.c -o umfpack_gn_global.o $(C) -DDINT -c ../Source/umf_analyze.c -o umf_i_analyze.o $(C) -DDINT -c ../Source/umf_apply_order.c -o umf_i_apply_order.o $(C) -DDINT -c ../Source/umf_colamd.c -o umf_i_colamd.o $(C) -DDINT -c ../Source/umf_free.c -o umf_i_free.o $(C) -DDINT -c ../Source/umf_fsize.c -o umf_i_fsize.o $(C) -DDINT -c ../Source/umf_is_permutation.c -o umf_i_is_permutation.o $(C) -DDINT -c ../Source/umf_malloc.c -o umf_i_malloc.o $(C) -DDINT -c ../Source/umf_realloc.c -o umf_i_realloc.o $(C) -DDINT -c ../Source/umf_report_perm.c -o umf_i_report_perm.o $(C) -DDINT -c ../Source/umf_singletons.c -o umf_i_singletons.o $(C) -DDLONG -c ../Source/umf_analyze.c -o umf_l_analyze.o $(C) -DDLONG -c ../Source/umf_apply_order.c -o umf_l_apply_order.o $(C) -DDLONG -c ../Source/umf_colamd.c -o umf_l_colamd.o $(C) -DDLONG -c ../Source/umf_free.c -o umf_l_free.o $(C) -DDLONG -c ../Source/umf_fsize.c -o umf_l_fsize.o $(C) -DDLONG -c ../Source/umf_is_permutation.c -o umf_l_is_permutation.o $(C) -DDLONG -c ../Source/umf_malloc.c -o umf_l_malloc.o $(C) -DDLONG -c ../Source/umf_realloc.c -o umf_l_realloc.o $(C) -DDLONG -c ../Source/umf_report_perm.c -o umf_l_report_perm.o $(C) -DDLONG -c ../Source/umf_singletons.c -o umf_l_singletons.o $(C) -c ../Source/umfpack_timer.c -o umfpack_gn_timer.o $(C) -c ../Source/umfpack_tictoc.c -o umfpack_gn_tictoc.o $(C) -DDINT -DCONJUGATE_SOLVE -c ../Source/umf_ltsolve.c -o umf_di_lhsolve.o $(C) -DDINT -DCONJUGATE_SOLVE -c ../Source/umf_utsolve.c -o umf_di_uhsolve.o $(C) -DDINT -DDO_MAP -c ../Source/umf_triplet.c -o umf_di_triplet_map_nox.o $(C) -DDINT -DDO_VALUES -c ../Source/umf_triplet.c -o umf_di_triplet_nomap_x.o $(C) -DDINT -c ../Source/umf_triplet.c -o umf_di_triplet_nomap_nox.o $(C) -DDINT -DDO_MAP -DDO_VALUES -c ../Source/umf_triplet.c -o umf_di_triplet_map_x.o $(C) -DDINT -DFIXQ -c ../Source/umf_assemble.c -o umf_di_assemble_fixq.o $(C) -DDINT -DDROP -c ../Source/umf_store_lu.c -o umf_di_store_lu_drop.o $(C) -DDINT -c ../Source/umf_assemble.c -o umf_di_assemble.o $(C) -DDINT -c ../Source/umf_blas3_update.c -o umf_di_blas3_update.o $(C) -DDINT -c ../Source/umf_build_tuples.c -o umf_di_build_tuples.o $(C) -DDINT -c ../Source/umf_create_element.c -o umf_di_create_element.o $(C) -DDINT -c ../Source/umf_dump.c -o umf_di_dump.o $(C) -DDINT -c ../Source/umf_extend_front.c -o umf_di_extend_front.o $(C) -DDINT -c ../Source/umf_garbage_collection.c -o umf_di_garbage_collection.o $(C) -DDINT -c ../Source/umf_get_memory.c -o umf_di_get_memory.o $(C) -DDINT -c ../Source/umf_init_front.c -o umf_di_init_front.o $(C) -DDINT -c ../Source/umf_kernel.c -o umf_di_kernel.o $(C) -DDINT -c ../Source/umf_kernel_init.c -o umf_di_kernel_init.o $(C) -DDINT -c ../Source/umf_kernel_wrapup.c -o umf_di_kernel_wrapup.o $(C) -DDINT -c ../Source/umf_local_search.c -o umf_di_local_search.o $(C) -DDINT -c ../Source/umf_lsolve.c -o umf_di_lsolve.o $(C) -DDINT -c ../Source/umf_ltsolve.c -o umf_di_ltsolve.o $(C) -DDINT -c ../Source/umf_mem_alloc_element.c -o umf_di_mem_alloc_element.o $(C) -DDINT -c ../Source/umf_mem_alloc_head_block.c -o umf_di_mem_alloc_head_block.o $(C) -DDINT -c ../Source/umf_mem_alloc_tail_block.c -o umf_di_mem_alloc_tail_block.o $(C) -DDINT -c ../Source/umf_mem_free_tail_block.c -o umf_di_mem_free_tail_block.o $(C) -DDINT -c ../Source/umf_mem_init_memoryspace.c -o umf_di_mem_init_memoryspace.o $(C) -DDINT -c ../Source/umf_report_vector.c -o umf_di_report_vector.o $(C) -DDINT -c ../Source/umf_row_search.c -o umf_di_row_search.o $(C) -DDINT -c ../Source/umf_scale_column.c -o umf_di_scale_column.o $(C) -DDINT -c ../Source/umf_set_stats.c -o umf_di_set_stats.o $(C) -DDINT -c ../Source/umf_solve.c -o umf_di_solve.o $(C) -DDINT -c ../Source/umf_symbolic_usage.c -o umf_di_symbolic_usage.o $(C) -DDINT -c ../Source/umf_transpose.c -o umf_di_transpose.o $(C) -DDINT -c ../Source/umf_tuple_lengths.c -o umf_di_tuple_lengths.o $(C) -DDINT -c ../Source/umf_usolve.c -o umf_di_usolve.o $(C) -DDINT -c ../Source/umf_utsolve.c -o umf_di_utsolve.o $(C) -DDINT -c ../Source/umf_valid_numeric.c -o umf_di_valid_numeric.o $(C) -DDINT -c ../Source/umf_valid_symbolic.c -o umf_di_valid_symbolic.o $(C) -DDINT -c ../Source/umf_grow_front.c -o umf_di_grow_front.o $(C) -DDINT -c ../Source/umf_start_front.c -o umf_di_start_front.o $(C) -DDINT -c ../Source/umf_2by2.c -o umf_di_2by2.o $(C) -DDINT -c ../Source/umf_store_lu.c -o umf_di_store_lu.o $(C) -DDINT -c ../Source/umf_scale.c -o umf_di_scale.o $(C) -DDINT -DWSOLVE -c ../Source/umfpack_solve.c -o umfpack_di_wsolve.o $(C) -DDINT -c ../Source/umfpack_col_to_triplet.c -o umfpack_di_col_to_triplet.o $(C) -DDINT -c ../Source/umfpack_defaults.c -o umfpack_di_defaults.o $(C) -DDINT -c ../Source/umfpack_free_numeric.c -o umfpack_di_free_numeric.o $(C) -DDINT -c ../Source/umfpack_free_symbolic.c -o umfpack_di_free_symbolic.o $(C) -DDINT -c ../Source/umfpack_get_numeric.c -o umfpack_di_get_numeric.o $(C) -DDINT -c ../Source/umfpack_get_lunz.c -o umfpack_di_get_lunz.o $(C) -DDINT -c ../Source/umfpack_get_symbolic.c -o umfpack_di_get_symbolic.o $(C) -DDINT -c ../Source/umfpack_get_determinant.c -o umfpack_di_get_determinant.o $(C) -DDINT -c ../Source/umfpack_numeric.c -o umfpack_di_numeric.o $(C) -DDINT -c ../Source/umfpack_qsymbolic.c -o umfpack_di_qsymbolic.o $(C) -DDINT -c ../Source/umfpack_report_control.c -o umfpack_di_report_control.o $(C) -DDINT -c ../Source/umfpack_report_info.c -o umfpack_di_report_info.o $(C) -DDINT -c ../Source/umfpack_report_matrix.c -o umfpack_di_report_matrix.o $(C) -DDINT -c ../Source/umfpack_report_numeric.c -o umfpack_di_report_numeric.o $(C) -DDINT -c ../Source/umfpack_report_perm.c -o umfpack_di_report_perm.o $(C) -DDINT -c ../Source/umfpack_report_status.c -o umfpack_di_report_status.o $(C) -DDINT -c ../Source/umfpack_report_symbolic.c -o umfpack_di_report_symbolic.o $(C) -DDINT -c ../Source/umfpack_report_triplet.c -o umfpack_di_report_triplet.o $(C) -DDINT -c ../Source/umfpack_report_vector.c -o umfpack_di_report_vector.o $(C) -DDINT -c ../Source/umfpack_solve.c -o umfpack_di_solve.o $(C) -DDINT -c ../Source/umfpack_symbolic.c -o umfpack_di_symbolic.o $(C) -DDINT -c ../Source/umfpack_transpose.c -o umfpack_di_transpose.o $(C) -DDINT -c ../Source/umfpack_triplet_to_col.c -o umfpack_di_triplet_to_col.o $(C) -DDINT -c ../Source/umfpack_scale.c -o umfpack_di_scale.o $(C) -DDINT -c ../Source/umfpack_load_numeric.c -o umfpack_di_load_numeric.o $(C) -DDINT -c ../Source/umfpack_save_numeric.c -o umfpack_di_save_numeric.o $(C) -DDINT -c ../Source/umfpack_load_symbolic.c -o umfpack_di_load_symbolic.o $(C) -DDINT -c ../Source/umfpack_save_symbolic.c -o umfpack_di_save_symbolic.o $(C) -DDLONG -DCONJUGATE_SOLVE -c ../Source/umf_ltsolve.c -o umf_dl_lhsolve.o $(C) -DDLONG -DCONJUGATE_SOLVE -c ../Source/umf_utsolve.c -o umf_dl_uhsolve.o $(C) -DDLONG -DDO_MAP -c ../Source/umf_triplet.c -o umf_dl_triplet_map_nox.o $(C) -DDLONG -DDO_VALUES -c ../Source/umf_triplet.c -o umf_dl_triplet_nomap_x.o $(C) -DDLONG -c ../Source/umf_triplet.c -o umf_dl_triplet_nomap_nox.o $(C) -DDLONG -DDO_MAP -DDO_VALUES -c ../Source/umf_triplet.c -o umf_dl_triplet_map_x.o $(C) -DDLONG -DFIXQ -c ../Source/umf_assemble.c -o umf_dl_assemble_fixq.o $(C) -DDLONG -DDROP -c ../Source/umf_store_lu.c -o umf_dl_store_lu_drop.o $(C) -DDLONG -c ../Source/umf_assemble.c -o umf_dl_assemble.o $(C) -DDLONG -c ../Source/umf_blas3_update.c -o umf_dl_blas3_update.o $(C) -DDLONG -c ../Source/umf_build_tuples.c -o umf_dl_build_tuples.o $(C) -DDLONG -c ../Source/umf_create_element.c -o umf_dl_create_element.o $(C) -DDLONG -c ../Source/umf_dump.c -o umf_dl_dump.o $(C) -DDLONG -c ../Source/umf_extend_front.c -o umf_dl_extend_front.o $(C) -DDLONG -c ../Source/umf_garbage_collection.c -o umf_dl_garbage_collection.o $(C) -DDLONG -c ../Source/umf_get_memory.c -o umf_dl_get_memory.o $(C) -DDLONG -c ../Source/umf_init_front.c -o umf_dl_init_front.o $(C) -DDLONG -c ../Source/umf_kernel.c -o umf_dl_kernel.o $(C) -DDLONG -c ../Source/umf_kernel_init.c -o umf_dl_kernel_init.o $(C) -DDLONG -c ../Source/umf_kernel_wrapup.c -o umf_dl_kernel_wrapup.o $(C) -DDLONG -c ../Source/umf_local_search.c -o umf_dl_local_search.o $(C) -DDLONG -c ../Source/umf_lsolve.c -o umf_dl_lsolve.o $(C) -DDLONG -c ../Source/umf_ltsolve.c -o umf_dl_ltsolve.o $(C) -DDLONG -c ../Source/umf_mem_alloc_element.c -o umf_dl_mem_alloc_element.o $(C) -DDLONG -c ../Source/umf_mem_alloc_head_block.c -o umf_dl_mem_alloc_head_block.o $(C) -DDLONG -c ../Source/umf_mem_alloc_tail_block.c -o umf_dl_mem_alloc_tail_block.o $(C) -DDLONG -c ../Source/umf_mem_free_tail_block.c -o umf_dl_mem_free_tail_block.o $(C) -DDLONG -c ../Source/umf_mem_init_memoryspace.c -o umf_dl_mem_init_memoryspace.o $(C) -DDLONG -c ../Source/umf_report_vector.c -o umf_dl_report_vector.o $(C) -DDLONG -c ../Source/umf_row_search.c -o umf_dl_row_search.o $(C) -DDLONG -c ../Source/umf_scale_column.c -o umf_dl_scale_column.o $(C) -DDLONG -c ../Source/umf_set_stats.c -o umf_dl_set_stats.o $(C) -DDLONG -c ../Source/umf_solve.c -o umf_dl_solve.o $(C) -DDLONG -c ../Source/umf_symbolic_usage.c -o umf_dl_symbolic_usage.o $(C) -DDLONG -c ../Source/umf_transpose.c -o umf_dl_transpose.o $(C) -DDLONG -c ../Source/umf_tuple_lengths.c -o umf_dl_tuple_lengths.o $(C) -DDLONG -c ../Source/umf_usolve.c -o umf_dl_usolve.o $(C) -DDLONG -c ../Source/umf_utsolve.c -o umf_dl_utsolve.o $(C) -DDLONG -c ../Source/umf_valid_numeric.c -o umf_dl_valid_numeric.o $(C) -DDLONG -c ../Source/umf_valid_symbolic.c -o umf_dl_valid_symbolic.o $(C) -DDLONG -c ../Source/umf_grow_front.c -o umf_dl_grow_front.o $(C) -DDLONG -c ../Source/umf_start_front.c -o umf_dl_start_front.o $(C) -DDLONG -c ../Source/umf_2by2.c -o umf_dl_2by2.o $(C) -DDLONG -c ../Source/umf_store_lu.c -o umf_dl_store_lu.o $(C) -DDLONG -c ../Source/umf_scale.c -o umf_dl_scale.o $(C) -DDLONG -DWSOLVE -c ../Source/umfpack_solve.c -o umfpack_dl_wsolve.o $(C) -DDLONG -c ../Source/umfpack_col_to_triplet.c -o umfpack_dl_col_to_triplet.o $(C) -DDLONG -c ../Source/umfpack_defaults.c -o umfpack_dl_defaults.o $(C) -DDLONG -c ../Source/umfpack_free_numeric.c -o umfpack_dl_free_numeric.o $(C) -DDLONG -c ../Source/umfpack_free_symbolic.c -o umfpack_dl_free_symbolic.o $(C) -DDLONG -c ../Source/umfpack_get_numeric.c -o umfpack_dl_get_numeric.o $(C) -DDLONG -c ../Source/umfpack_get_lunz.c -o umfpack_dl_get_lunz.o $(C) -DDLONG -c ../Source/umfpack_get_symbolic.c -o umfpack_dl_get_symbolic.o $(C) -DDLONG -c ../Source/umfpack_get_determinant.c -o umfpack_dl_get_determinant.o $(C) -DDLONG -c ../Source/umfpack_numeric.c -o umfpack_dl_numeric.o $(C) -DDLONG -c ../Source/umfpack_qsymbolic.c -o umfpack_dl_qsymbolic.o $(C) -DDLONG -c ../Source/umfpack_report_control.c -o umfpack_dl_report_control.o $(C) -DDLONG -c ../Source/umfpack_report_info.c -o umfpack_dl_report_info.o $(C) -DDLONG -c ../Source/umfpack_report_matrix.c -o umfpack_dl_report_matrix.o $(C) -DDLONG -c ../Source/umfpack_report_numeric.c -o umfpack_dl_report_numeric.o $(C) -DDLONG -c ../Source/umfpack_report_perm.c -o umfpack_dl_report_perm.o $(C) -DDLONG -c ../Source/umfpack_report_status.c -o umfpack_dl_report_status.o $(C) -DDLONG -c ../Source/umfpack_report_symbolic.c -o umfpack_dl_report_symbolic.o $(C) -DDLONG -c ../Source/umfpack_report_triplet.c -o umfpack_dl_report_triplet.o $(C) -DDLONG -c ../Source/umfpack_report_vector.c -o umfpack_dl_report_vector.o $(C) -DDLONG -c ../Source/umfpack_solve.c -o umfpack_dl_solve.o $(C) -DDLONG -c ../Source/umfpack_symbolic.c -o umfpack_dl_symbolic.o $(C) -DDLONG -c ../Source/umfpack_transpose.c -o umfpack_dl_transpose.o $(C) -DDLONG -c ../Source/umfpack_triplet_to_col.c -o umfpack_dl_triplet_to_col.o $(C) -DDLONG -c ../Source/umfpack_scale.c -o umfpack_dl_scale.o $(C) -DDLONG -c ../Source/umfpack_load_numeric.c -o umfpack_dl_load_numeric.o $(C) -DDLONG -c ../Source/umfpack_save_numeric.c -o umfpack_dl_save_numeric.o $(C) -DDLONG -c ../Source/umfpack_load_symbolic.c -o umfpack_dl_load_symbolic.o $(C) -DDLONG -c ../Source/umfpack_save_symbolic.c -o umfpack_dl_save_symbolic.o $(C) -DZINT -DCONJUGATE_SOLVE -c ../Source/umf_ltsolve.c -o umf_zi_lhsolve.o $(C) -DZINT -DCONJUGATE_SOLVE -c ../Source/umf_utsolve.c -o umf_zi_uhsolve.o $(C) -DZINT -DDO_MAP -c ../Source/umf_triplet.c -o umf_zi_triplet_map_nox.o $(C) -DZINT -DDO_VALUES -c ../Source/umf_triplet.c -o umf_zi_triplet_nomap_x.o $(C) -DZINT -c ../Source/umf_triplet.c -o umf_zi_triplet_nomap_nox.o $(C) -DZINT -DDO_MAP -DDO_VALUES -c ../Source/umf_triplet.c -o umf_zi_triplet_map_x.o $(C) -DZINT -DFIXQ -c ../Source/umf_assemble.c -o umf_zi_assemble_fixq.o $(C) -DZINT -DDROP -c ../Source/umf_store_lu.c -o umf_zi_store_lu_drop.o $(C) -DZINT -c ../Source/umf_assemble.c -o umf_zi_assemble.o $(C) -DZINT -c ../Source/umf_blas3_update.c -o umf_zi_blas3_update.o $(C) -DZINT -c ../Source/umf_build_tuples.c -o umf_zi_build_tuples.o $(C) -DZINT -c ../Source/umf_create_element.c -o umf_zi_create_element.o $(C) -DZINT -c ../Source/umf_dump.c -o umf_zi_dump.o $(C) -DZINT -c ../Source/umf_extend_front.c -o umf_zi_extend_front.o $(C) -DZINT -c ../Source/umf_garbage_collection.c -o umf_zi_garbage_collection.o $(C) -DZINT -c ../Source/umf_get_memory.c -o umf_zi_get_memory.o $(C) -DZINT -c ../Source/umf_init_front.c -o umf_zi_init_front.o $(C) -DZINT -c ../Source/umf_kernel.c -o umf_zi_kernel.o $(C) -DZINT -c ../Source/umf_kernel_init.c -o umf_zi_kernel_init.o $(C) -DZINT -c ../Source/umf_kernel_wrapup.c -o umf_zi_kernel_wrapup.o $(C) -DZINT -c ../Source/umf_local_search.c -o umf_zi_local_search.o $(C) -DZINT -c ../Source/umf_lsolve.c -o umf_zi_lsolve.o $(C) -DZINT -c ../Source/umf_ltsolve.c -o umf_zi_ltsolve.o $(C) -DZINT -c ../Source/umf_mem_alloc_element.c -o umf_zi_mem_alloc_element.o $(C) -DZINT -c ../Source/umf_mem_alloc_head_block.c -o umf_zi_mem_alloc_head_block.o $(C) -DZINT -c ../Source/umf_mem_alloc_tail_block.c -o umf_zi_mem_alloc_tail_block.o $(C) -DZINT -c ../Source/umf_mem_free_tail_block.c -o umf_zi_mem_free_tail_block.o $(C) -DZINT -c ../Source/umf_mem_init_memoryspace.c -o umf_zi_mem_init_memoryspace.o $(C) -DZINT -c ../Source/umf_report_vector.c -o umf_zi_report_vector.o $(C) -DZINT -c ../Source/umf_row_search.c -o umf_zi_row_search.o $(C) -DZINT -c ../Source/umf_scale_column.c -o umf_zi_scale_column.o $(C) -DZINT -c ../Source/umf_set_stats.c -o umf_zi_set_stats.o $(C) -DZINT -c ../Source/umf_solve.c -o umf_zi_solve.o $(C) -DZINT -c ../Source/umf_symbolic_usage.c -o umf_zi_symbolic_usage.o $(C) -DZINT -c ../Source/umf_transpose.c -o umf_zi_transpose.o $(C) -DZINT -c ../Source/umf_tuple_lengths.c -o umf_zi_tuple_lengths.o $(C) -DZINT -c ../Source/umf_usolve.c -o umf_zi_usolve.o $(C) -DZINT -c ../Source/umf_utsolve.c -o umf_zi_utsolve.o $(C) -DZINT -c ../Source/umf_valid_numeric.c -o umf_zi_valid_numeric.o $(C) -DZINT -c ../Source/umf_valid_symbolic.c -o umf_zi_valid_symbolic.o $(C) -DZINT -c ../Source/umf_grow_front.c -o umf_zi_grow_front.o $(C) -DZINT -c ../Source/umf_start_front.c -o umf_zi_start_front.o $(C) -DZINT -c ../Source/umf_2by2.c -o umf_zi_2by2.o $(C) -DZINT -c ../Source/umf_store_lu.c -o umf_zi_store_lu.o $(C) -DZINT -c ../Source/umf_scale.c -o umf_zi_scale.o $(C) -DZINT -DWSOLVE -c ../Source/umfpack_solve.c -o umfpack_zi_wsolve.o $(C) -DZINT -c ../Source/umfpack_col_to_triplet.c -o umfpack_zi_col_to_triplet.o $(C) -DZINT -c ../Source/umfpack_defaults.c -o umfpack_zi_defaults.o $(C) -DZINT -c ../Source/umfpack_free_numeric.c -o umfpack_zi_free_numeric.o $(C) -DZINT -c ../Source/umfpack_free_symbolic.c -o umfpack_zi_free_symbolic.o $(C) -DZINT -c ../Source/umfpack_get_numeric.c -o umfpack_zi_get_numeric.o $(C) -DZINT -c ../Source/umfpack_get_lunz.c -o umfpack_zi_get_lunz.o $(C) -DZINT -c ../Source/umfpack_get_symbolic.c -o umfpack_zi_get_symbolic.o $(C) -DZINT -c ../Source/umfpack_get_determinant.c -o umfpack_zi_get_determinant.o $(C) -DZINT -c ../Source/umfpack_numeric.c -o umfpack_zi_numeric.o $(C) -DZINT -c ../Source/umfpack_qsymbolic.c -o umfpack_zi_qsymbolic.o $(C) -DZINT -c ../Source/umfpack_report_control.c -o umfpack_zi_report_control.o $(C) -DZINT -c ../Source/umfpack_report_info.c -o umfpack_zi_report_info.o $(C) -DZINT -c ../Source/umfpack_report_matrix.c -o umfpack_zi_report_matrix.o $(C) -DZINT -c ../Source/umfpack_report_numeric.c -o umfpack_zi_report_numeric.o $(C) -DZINT -c ../Source/umfpack_report_perm.c -o umfpack_zi_report_perm.o $(C) -DZINT -c ../Source/umfpack_report_status.c -o umfpack_zi_report_status.o $(C) -DZINT -c ../Source/umfpack_report_symbolic.c -o umfpack_zi_report_symbolic.o $(C) -DZINT -c ../Source/umfpack_report_triplet.c -o umfpack_zi_report_triplet.o $(C) -DZINT -c ../Source/umfpack_report_vector.c -o umfpack_zi_report_vector.o $(C) -DZINT -c ../Source/umfpack_solve.c -o umfpack_zi_solve.o $(C) -DZINT -c ../Source/umfpack_symbolic.c -o umfpack_zi_symbolic.o $(C) -DZINT -c ../Source/umfpack_transpose.c -o umfpack_zi_transpose.o $(C) -DZINT -c ../Source/umfpack_triplet_to_col.c -o umfpack_zi_triplet_to_col.o $(C) -DZINT -c ../Source/umfpack_scale.c -o umfpack_zi_scale.o $(C) -DZINT -c ../Source/umfpack_load_numeric.c -o umfpack_zi_load_numeric.o $(C) -DZINT -c ../Source/umfpack_save_numeric.c -o umfpack_zi_save_numeric.o $(C) -DZINT -c ../Source/umfpack_load_symbolic.c -o umfpack_zi_load_symbolic.o $(C) -DZINT -c ../Source/umfpack_save_symbolic.c -o umfpack_zi_save_symbolic.o $(C) -DZLONG -DCONJUGATE_SOLVE -c ../Source/umf_ltsolve.c -o umf_zl_lhsolve.o $(C) -DZLONG -DCONJUGATE_SOLVE -c ../Source/umf_utsolve.c -o umf_zl_uhsolve.o $(C) -DZLONG -DDO_MAP -c ../Source/umf_triplet.c -o umf_zl_triplet_map_nox.o $(C) -DZLONG -DDO_VALUES -c ../Source/umf_triplet.c -o umf_zl_triplet_nomap_x.o $(C) -DZLONG -c ../Source/umf_triplet.c -o umf_zl_triplet_nomap_nox.o $(C) -DZLONG -DDO_MAP -DDO_VALUES -c ../Source/umf_triplet.c -o umf_zl_triplet_map_x.o $(C) -DZLONG -DFIXQ -c ../Source/umf_assemble.c -o umf_zl_assemble_fixq.o $(C) -DZLONG -DDROP -c ../Source/umf_store_lu.c -o umf_zl_store_lu_drop.o $(C) -DZLONG -c ../Source/umf_assemble.c -o umf_zl_assemble.o $(C) -DZLONG -c ../Source/umf_blas3_update.c -o umf_zl_blas3_update.o $(C) -DZLONG -c ../Source/umf_build_tuples.c -o umf_zl_build_tuples.o $(C) -DZLONG -c ../Source/umf_create_element.c -o umf_zl_create_element.o $(C) -DZLONG -c ../Source/umf_dump.c -o umf_zl_dump.o $(C) -DZLONG -c ../Source/umf_extend_front.c -o umf_zl_extend_front.o $(C) -DZLONG -c ../Source/umf_garbage_collection.c -o umf_zl_garbage_collection.o $(C) -DZLONG -c ../Source/umf_get_memory.c -o umf_zl_get_memory.o $(C) -DZLONG -c ../Source/umf_init_front.c -o umf_zl_init_front.o $(C) -DZLONG -c ../Source/umf_kernel.c -o umf_zl_kernel.o $(C) -DZLONG -c ../Source/umf_kernel_init.c -o umf_zl_kernel_init.o $(C) -DZLONG -c ../Source/umf_kernel_wrapup.c -o umf_zl_kernel_wrapup.o $(C) -DZLONG -c ../Source/umf_local_search.c -o umf_zl_local_search.o $(C) -DZLONG -c ../Source/umf_lsolve.c -o umf_zl_lsolve.o $(C) -DZLONG -c ../Source/umf_ltsolve.c -o umf_zl_ltsolve.o $(C) -DZLONG -c ../Source/umf_mem_alloc_element.c -o umf_zl_mem_alloc_element.o $(C) -DZLONG -c ../Source/umf_mem_alloc_head_block.c -o umf_zl_mem_alloc_head_block.o $(C) -DZLONG -c ../Source/umf_mem_alloc_tail_block.c -o umf_zl_mem_alloc_tail_block.o $(C) -DZLONG -c ../Source/umf_mem_free_tail_block.c -o umf_zl_mem_free_tail_block.o $(C) -DZLONG -c ../Source/umf_mem_init_memoryspace.c -o umf_zl_mem_init_memoryspace.o $(C) -DZLONG -c ../Source/umf_report_vector.c -o umf_zl_report_vector.o $(C) -DZLONG -c ../Source/umf_row_search.c -o umf_zl_row_search.o $(C) -DZLONG -c ../Source/umf_scale_column.c -o umf_zl_scale_column.o $(C) -DZLONG -c ../Source/umf_set_stats.c -o umf_zl_set_stats.o $(C) -DZLONG -c ../Source/umf_solve.c -o umf_zl_solve.o $(C) -DZLONG -c ../Source/umf_symbolic_usage.c -o umf_zl_symbolic_usage.o $(C) -DZLONG -c ../Source/umf_transpose.c -o umf_zl_transpose.o $(C) -DZLONG -c ../Source/umf_tuple_lengths.c -o umf_zl_tuple_lengths.o $(C) -DZLONG -c ../Source/umf_usolve.c -o umf_zl_usolve.o $(C) -DZLONG -c ../Source/umf_utsolve.c -o umf_zl_utsolve.o $(C) -DZLONG -c ../Source/umf_valid_numeric.c -o umf_zl_valid_numeric.o $(C) -DZLONG -c ../Source/umf_valid_symbolic.c -o umf_zl_valid_symbolic.o $(C) -DZLONG -c ../Source/umf_grow_front.c -o umf_zl_grow_front.o $(C) -DZLONG -c ../Source/umf_start_front.c -o umf_zl_start_front.o $(C) -DZLONG -c ../Source/umf_2by2.c -o umf_zl_2by2.o $(C) -DZLONG -c ../Source/umf_store_lu.c -o umf_zl_store_lu.o $(C) -DZLONG -c ../Source/umf_scale.c -o umf_zl_scale.o $(C) -DZLONG -DWSOLVE -c ../Source/umfpack_solve.c -o umfpack_zl_wsolve.o $(C) -DZLONG -c ../Source/umfpack_col_to_triplet.c -o umfpack_zl_col_to_triplet.o $(C) -DZLONG -c ../Source/umfpack_defaults.c -o umfpack_zl_defaults.o $(C) -DZLONG -c ../Source/umfpack_free_numeric.c -o umfpack_zl_free_numeric.o $(C) -DZLONG -c ../Source/umfpack_free_symbolic.c -o umfpack_zl_free_symbolic.o $(C) -DZLONG -c ../Source/umfpack_get_numeric.c -o umfpack_zl_get_numeric.o $(C) -DZLONG -c ../Source/umfpack_get_lunz.c -o umfpack_zl_get_lunz.o $(C) -DZLONG -c ../Source/umfpack_get_symbolic.c -o umfpack_zl_get_symbolic.o $(C) -DZLONG -c ../Source/umfpack_get_determinant.c -o umfpack_zl_get_determinant.o $(C) -DZLONG -c ../Source/umfpack_numeric.c -o umfpack_zl_numeric.o $(C) -DZLONG -c ../Source/umfpack_qsymbolic.c -o umfpack_zl_qsymbolic.o $(C) -DZLONG -c ../Source/umfpack_report_control.c -o umfpack_zl_report_control.o $(C) -DZLONG -c ../Source/umfpack_report_info.c -o umfpack_zl_report_info.o $(C) -DZLONG -c ../Source/umfpack_report_matrix.c -o umfpack_zl_report_matrix.o $(C) -DZLONG -c ../Source/umfpack_report_numeric.c -o umfpack_zl_report_numeric.o $(C) -DZLONG -c ../Source/umfpack_report_perm.c -o umfpack_zl_report_perm.o $(C) -DZLONG -c ../Source/umfpack_report_status.c -o umfpack_zl_report_status.o $(C) -DZLONG -c ../Source/umfpack_report_symbolic.c -o umfpack_zl_report_symbolic.o $(C) -DZLONG -c ../Source/umfpack_report_triplet.c -o umfpack_zl_report_triplet.o $(C) -DZLONG -c ../Source/umfpack_report_vector.c -o umfpack_zl_report_vector.o $(C) -DZLONG -c ../Source/umfpack_solve.c -o umfpack_zl_solve.o $(C) -DZLONG -c ../Source/umfpack_symbolic.c -o umfpack_zl_symbolic.o $(C) -DZLONG -c ../Source/umfpack_transpose.c -o umfpack_zl_transpose.o $(C) -DZLONG -c ../Source/umfpack_triplet_to_col.c -o umfpack_zl_triplet_to_col.o $(C) -DZLONG -c ../Source/umfpack_scale.c -o umfpack_zl_scale.o $(C) -DZLONG -c ../Source/umfpack_load_numeric.c -o umfpack_zl_load_numeric.o $(C) -DZLONG -c ../Source/umfpack_save_numeric.c -o umfpack_zl_save_numeric.o $(C) -DZLONG -c ../Source/umfpack_load_symbolic.c -o umfpack_zl_load_symbolic.o $(C) -DZLONG -c ../Source/umfpack_save_symbolic.c -o umfpack_zl_save_symbolic.o $(AR) ../Lib/libumfpack.a \ umfpack_gn_global.o \ umf_i_analyze.o umf_i_apply_order.o umf_i_colamd.o umf_i_free.o \ umf_i_fsize.o umf_i_is_permutation.o umf_i_malloc.o umf_i_realloc.o \ umf_i_report_perm.o umf_i_singletons.o \ umf_l_analyze.o umf_l_apply_order.o umf_l_colamd.o umf_l_free.o \ umf_l_fsize.o umf_l_is_permutation.o umf_l_malloc.o umf_l_realloc.o \ umf_l_report_perm.o umf_l_singletons.o \ umfpack_gn_timer.o umfpack_gn_tictoc.o \ umf_di_lhsolve.o \ umf_di_uhsolve.o umf_di_triplet_map_nox.o umf_di_triplet_nomap_x.o \ umf_di_triplet_nomap_nox.o umf_di_triplet_map_x.o \ umf_di_assemble_fixq.o umf_di_store_lu_drop.o umf_di_assemble.o \ umf_di_blas3_update.o umf_di_build_tuples.o \ umf_di_create_element.o umf_di_dump.o umf_di_extend_front.o \ umf_di_garbage_collection.o umf_di_get_memory.o \ umf_di_init_front.o umf_di_kernel.o umf_di_kernel_init.o \ umf_di_kernel_wrapup.o umf_di_local_search.o umf_di_lsolve.o \ umf_di_ltsolve.o umf_di_mem_alloc_element.o \ umf_di_mem_alloc_head_block.o umf_di_mem_alloc_tail_block.o \ umf_di_mem_free_tail_block.o umf_di_mem_init_memoryspace.o \ umf_di_report_vector.o umf_di_row_search.o umf_di_scale_column.o \ umf_di_set_stats.o umf_di_solve.o umf_di_symbolic_usage.o \ umf_di_transpose.o umf_di_tuple_lengths.o umf_di_usolve.o \ umf_di_utsolve.o umf_di_valid_numeric.o umf_di_valid_symbolic.o \ umf_di_grow_front.o umf_di_start_front.o umf_di_2by2.o \ umf_di_store_lu.o umf_di_scale.o umfpack_di_wsolve.o \ umfpack_di_col_to_triplet.o umfpack_di_defaults.o \ umfpack_di_free_numeric.o umfpack_di_free_symbolic.o \ umfpack_di_get_numeric.o umfpack_di_get_lunz.o \ umfpack_di_get_symbolic.o umfpack_di_get_determinant.o \ umfpack_di_numeric.o \ umfpack_di_qsymbolic.o umfpack_di_report_control.o \ umfpack_di_report_info.o umfpack_di_report_matrix.o \ umfpack_di_report_numeric.o umfpack_di_report_perm.o \ umfpack_di_report_status.o umfpack_di_report_symbolic.o \ umfpack_di_report_triplet.o umfpack_di_report_vector.o \ umfpack_di_solve.o umfpack_di_symbolic.o umfpack_di_transpose.o \ umfpack_di_triplet_to_col.o umfpack_di_scale.o \ umfpack_di_load_numeric.o umfpack_di_save_numeric.o \ umfpack_di_load_symbolic.o umfpack_di_save_symbolic.o \ umf_dl_lhsolve.o \ umf_dl_uhsolve.o umf_dl_triplet_map_nox.o umf_dl_triplet_nomap_x.o \ umf_dl_triplet_nomap_nox.o umf_dl_triplet_map_x.o \ umf_dl_assemble_fixq.o umf_dl_store_lu_drop.o umf_dl_assemble.o \ umf_dl_blas3_update.o umf_dl_build_tuples.o \ umf_dl_create_element.o umf_dl_dump.o umf_dl_extend_front.o \ umf_dl_garbage_collection.o umf_dl_get_memory.o \ umf_dl_init_front.o umf_dl_kernel.o umf_dl_kernel_init.o \ umf_dl_kernel_wrapup.o umf_dl_local_search.o umf_dl_lsolve.o \ umf_dl_ltsolve.o umf_dl_mem_alloc_element.o \ umf_dl_mem_alloc_head_block.o umf_dl_mem_alloc_tail_block.o \ umf_dl_mem_free_tail_block.o umf_dl_mem_init_memoryspace.o \ umf_dl_report_vector.o umf_dl_row_search.o umf_dl_scale_column.o \ umf_dl_set_stats.o umf_dl_solve.o umf_dl_symbolic_usage.o \ umf_dl_transpose.o umf_dl_tuple_lengths.o umf_dl_usolve.o \ umf_dl_utsolve.o umf_dl_valid_numeric.o umf_dl_valid_symbolic.o \ umf_dl_grow_front.o umf_dl_start_front.o umf_dl_2by2.o \ umf_dl_store_lu.o umf_dl_scale.o umfpack_dl_wsolve.o \ umfpack_dl_col_to_triplet.o umfpack_dl_defaults.o \ umfpack_dl_free_numeric.o umfpack_dl_free_symbolic.o \ umfpack_dl_get_numeric.o umfpack_dl_get_lunz.o \ umfpack_dl_get_symbolic.o umfpack_dl_get_determinant.o \ umfpack_dl_numeric.o \ umfpack_dl_qsymbolic.o umfpack_dl_report_control.o \ umfpack_dl_report_info.o umfpack_dl_report_matrix.o \ umfpack_dl_report_numeric.o umfpack_dl_report_perm.o \ umfpack_dl_report_status.o umfpack_dl_report_symbolic.o \ umfpack_dl_report_triplet.o umfpack_dl_report_vector.o \ umfpack_dl_solve.o umfpack_dl_symbolic.o umfpack_dl_transpose.o \ umfpack_dl_triplet_to_col.o umfpack_dl_scale.o \ umfpack_dl_load_numeric.o umfpack_dl_save_numeric.o \ umfpack_dl_load_symbolic.o umfpack_dl_save_symbolic.o \ umf_zi_lhsolve.o \ umf_zi_uhsolve.o umf_zi_triplet_map_nox.o umf_zi_triplet_nomap_x.o \ umf_zi_triplet_nomap_nox.o umf_zi_triplet_map_x.o \ umf_zi_assemble_fixq.o umf_zi_store_lu_drop.o umf_zi_assemble.o \ umf_zi_blas3_update.o umf_zi_build_tuples.o \ umf_zi_create_element.o umf_zi_dump.o umf_zi_extend_front.o \ umf_zi_garbage_collection.o umf_zi_get_memory.o \ umf_zi_init_front.o umf_zi_kernel.o umf_zi_kernel_init.o \ umf_zi_kernel_wrapup.o umf_zi_local_search.o umf_zi_lsolve.o \ umf_zi_ltsolve.o umf_zi_mem_alloc_element.o \ umf_zi_mem_alloc_head_block.o umf_zi_mem_alloc_tail_block.o \ umf_zi_mem_free_tail_block.o umf_zi_mem_init_memoryspace.o \ umf_zi_report_vector.o umf_zi_row_search.o umf_zi_scale_column.o \ umf_zi_set_stats.o umf_zi_solve.o umf_zi_symbolic_usage.o \ umf_zi_transpose.o umf_zi_tuple_lengths.o umf_zi_usolve.o \ umf_zi_utsolve.o umf_zi_valid_numeric.o umf_zi_valid_symbolic.o \ umf_zi_grow_front.o umf_zi_start_front.o umf_zi_2by2.o \ umf_zi_store_lu.o umf_zi_scale.o umfpack_zi_wsolve.o \ umfpack_zi_col_to_triplet.o umfpack_zi_defaults.o \ umfpack_zi_free_numeric.o umfpack_zi_free_symbolic.o \ umfpack_zi_get_numeric.o umfpack_zi_get_lunz.o \ umfpack_zi_get_symbolic.o umfpack_zi_get_determinant.o \ umfpack_zi_numeric.o \ umfpack_zi_qsymbolic.o umfpack_zi_report_control.o \ umfpack_zi_report_info.o umfpack_zi_report_matrix.o \ umfpack_zi_report_numeric.o umfpack_zi_report_perm.o \ umfpack_zi_report_status.o umfpack_zi_report_symbolic.o \ umfpack_zi_report_triplet.o umfpack_zi_report_vector.o \ umfpack_zi_solve.o umfpack_zi_symbolic.o umfpack_zi_transpose.o \ umfpack_zi_triplet_to_col.o umfpack_zi_scale.o \ umfpack_zi_load_numeric.o umfpack_zi_save_numeric.o \ umfpack_zi_load_symbolic.o umfpack_zi_save_symbolic.o \ umf_zl_lhsolve.o \ umf_zl_uhsolve.o umf_zl_triplet_map_nox.o umf_zl_triplet_nomap_x.o \ umf_zl_triplet_nomap_nox.o umf_zl_triplet_map_x.o \ umf_zl_assemble_fixq.o umf_zl_store_lu_drop.o umf_zl_assemble.o \ umf_zl_blas3_update.o umf_zl_build_tuples.o \ umf_zl_create_element.o umf_zl_dump.o umf_zl_extend_front.o \ umf_zl_garbage_collection.o umf_zl_get_memory.o \ umf_zl_init_front.o umf_zl_kernel.o umf_zl_kernel_init.o \ umf_zl_kernel_wrapup.o umf_zl_local_search.o umf_zl_lsolve.o \ umf_zl_ltsolve.o umf_zl_mem_alloc_element.o \ umf_zl_mem_alloc_head_block.o umf_zl_mem_alloc_tail_block.o \ umf_zl_mem_free_tail_block.o umf_zl_mem_init_memoryspace.o \ umf_zl_report_vector.o umf_zl_row_search.o umf_zl_scale_column.o \ umf_zl_set_stats.o umf_zl_solve.o umf_zl_symbolic_usage.o \ umf_zl_transpose.o umf_zl_tuple_lengths.o umf_zl_usolve.o \ umf_zl_utsolve.o umf_zl_valid_numeric.o umf_zl_valid_symbolic.o \ umf_zl_grow_front.o umf_zl_start_front.o umf_zl_2by2.o \ umf_zl_store_lu.o umf_zl_scale.o umfpack_zl_wsolve.o \ umfpack_zl_col_to_triplet.o umfpack_zl_defaults.o \ umfpack_zl_free_numeric.o umfpack_zl_free_symbolic.o \ umfpack_zl_get_numeric.o umfpack_zl_get_lunz.o \ umfpack_zl_get_symbolic.o umfpack_zl_get_determinant.o \ umfpack_zl_numeric.o \ umfpack_zl_qsymbolic.o umfpack_zl_report_control.o \ umfpack_zl_report_info.o umfpack_zl_report_matrix.o \ umfpack_zl_report_numeric.o umfpack_zl_report_perm.o \ umfpack_zl_report_status.o umfpack_zl_report_symbolic.o \ umfpack_zl_report_triplet.o umfpack_zl_report_vector.o \ umfpack_zl_solve.o umfpack_zl_symbolic.o umfpack_zl_transpose.o \ umfpack_zl_triplet_to_col.o umfpack_zl_scale.o \ umfpack_zl_load_numeric.o umfpack_zl_save_numeric.o \ umfpack_zl_load_symbolic.o umfpack_zl_save_symbolic.o - $(RANLIB) ../Lib/libumfpack.a #------------------------------------------------------------------------------- # Remove all but the files in the original distribution #------------------------------------------------------------------------------- purge: clean - $(RM) ../Lib/libumfpack.a clean: - $(RM) $(CLEAN) SuiteSparse/UMFPACK/Lib/GNUmakefile0000644001170100242450000002306410617345232015625 0ustar davisfac#------------------------------------------------------------------------------- # UMFPACK Makefile for compiling on Unix systems (for GNU Make) #------------------------------------------------------------------------------- default: ../Lib/libumfpack.a include ../../UFconfig/UFconfig.mk C = $(CC) $(CFLAGS) $(UMFPACK_CONFIG) \ -I../Include -I../Source -I../../AMD/Include -I../../UFconfig #------------------------------------------------------------------------------- # source files #------------------------------------------------------------------------------- # non-user-callable umf_*.[ch] files: UMFCH = umf_assemble umf_blas3_update umf_build_tuples umf_create_element \ umf_dump umf_extend_front umf_garbage_collection umf_get_memory \ umf_init_front umf_kernel umf_kernel_init umf_kernel_wrapup \ umf_local_search umf_lsolve umf_ltsolve umf_mem_alloc_element \ umf_mem_alloc_head_block umf_mem_alloc_tail_block \ umf_mem_free_tail_block umf_mem_init_memoryspace \ umf_report_vector umf_row_search umf_scale_column \ umf_set_stats umf_solve umf_symbolic_usage umf_transpose \ umf_tuple_lengths umf_usolve umf_utsolve umf_valid_numeric \ umf_valid_symbolic umf_grow_front umf_start_front umf_2by2 \ umf_store_lu umf_scale # non-user-callable umf_*.[ch] files, int/UF_long versions only (no real/complex): UMFINT = umf_analyze umf_apply_order umf_colamd umf_free umf_fsize \ umf_is_permutation umf_malloc umf_realloc umf_report_perm \ umf_singletons # non-user-callable, created from umf_ltsolve.c, umf_utsolve.c, # umf_triplet.c, and umf_assemble.c , with int/UF_long and real/complex versions: UMF_CREATED = umf_lhsolve umf_uhsolve umf_triplet_map_nox \ umf_triplet_nomap_x umf_triplet_nomap_nox umf_triplet_map_x \ umf_assemble_fixq umf_store_lu_drop # non-user-callable, int/UF_long and real/complex versions: UMF = $(UMF_CREATED) $(UMFCH) # user-callable umfpack_*.[ch] files (int/UF_long and real/complex): UMFPACK = umfpack_col_to_triplet umfpack_defaults umfpack_free_numeric \ umfpack_free_symbolic umfpack_get_numeric umfpack_get_lunz \ umfpack_get_symbolic umfpack_get_determinant umfpack_numeric \ umfpack_qsymbolic umfpack_report_control umfpack_report_info \ umfpack_report_matrix umfpack_report_numeric umfpack_report_perm \ umfpack_report_status umfpack_report_symbolic umfpack_report_triplet \ umfpack_report_vector umfpack_solve umfpack_symbolic \ umfpack_transpose umfpack_triplet_to_col umfpack_scale \ umfpack_load_numeric umfpack_save_numeric \ umfpack_load_symbolic umfpack_save_symbolic # user-callable, created from umfpack_solve.c (umfpack_wsolve.h exists, though): # with int/UF_long and real/complex versions: UMFPACKW = umfpack_wsolve USER = $(UMFPACKW) $(UMFPACK) # user-callable, only one version for int/UF_long, real/complex, *.[ch] files: GENERIC = umfpack_timer umfpack_tictoc umfpack_global #------------------------------------------------------------------------------- # include files: #------------------------------------------------------------------------------- INC = ../Include/umfpack.h ../../UFconfig/UFconfig.h \ ../Source/umf_config.h ../Source/umf_version.h \ ../Source/umf_internal.h ../Source/umf_triplet.h \ $(addprefix ../Source/, $(addsuffix .h,$(UMFCH))) \ $(addprefix ../Source/, $(addsuffix .h,$(UMFINT))) \ $(addprefix ../Include/, $(addsuffix .h,$(USER))) \ $(addprefix ../Include/, $(addsuffix .h,$(GENERIC))) \ ../../AMD/Include/amd_internal.h ../../AMD/Include/amd.h #------------------------------------------------------------------------------- # object files for each version #------------------------------------------------------------------------------- DI = $(addsuffix .o, $(subst umf_,umf_di_,$(UMF)) $(subst umfpack_,umfpack_di_,$(USER))) DL = $(addsuffix .o, $(subst umf_,umf_dl_,$(UMF)) $(subst umfpack_,umfpack_dl_,$(USER))) ZI = $(addsuffix .o, $(subst umf_,umf_zi_,$(UMF)) $(subst umfpack_,umfpack_zi_,$(USER))) ZL = $(addsuffix .o, $(subst umf_,umf_zl_,$(UMF)) $(subst umfpack_,umfpack_zl_,$(USER))) II = $(addsuffix .o, $(subst umf_,umf_i_,$(UMFINT))) LL = $(addsuffix .o, $(subst umf_,umf_l_,$(UMFINT))) GN = $(addsuffix .o, $(subst umfpack_,umfpack_gn_,$(GENERIC))) #------------------------------------------------------------------------------- # compile each int and UF_long routine (with no real/complex version) #------------------------------------------------------------------------------- umf_i_%.o: ../Source/umf_%.c $(INC) $(C) -DDINT -c $< -o $@ umf_l_%.o: ../Source/umf_%.c $(INC) $(C) -DDLONG -c $< -o $@ #------------------------------------------------------------------------------- # compile each routine in the DI version #------------------------------------------------------------------------------- umf_di_%.o: ../Source/umf_%.c $(INC) $(C) -DDINT -c $< -o $@ umf_di_%hsolve.o: ../Source/umf_%tsolve.c $(INC) $(C) -DDINT -DCONJUGATE_SOLVE -c $< -o $@ umf_di_triplet_map_x.o: ../Source/umf_triplet.c $(INC) $(C) -DDINT -DDO_MAP -DDO_VALUES -c $< -o $@ umf_di_triplet_map_nox.o: ../Source/umf_triplet.c $(INC) $(C) -DDINT -DDO_MAP -c $< -o $@ umf_di_triplet_nomap_x.o: ../Source/umf_triplet.c $(INC) $(C) -DDINT -DDO_VALUES -c $< -o $@ umf_di_triplet_nomap_nox.o: ../Source/umf_triplet.c $(INC) $(C) -DDINT -c $< -o $@ umf_di_assemble_fixq.o: ../Source/umf_assemble.c $(INC) $(C) -DDINT -DFIXQ -c $< -o $@ umf_di_store_lu_drop.o: ../Source/umf_store_lu.c $(INC) $(C) -DDINT -DDROP -c $< -o $@ umfpack_di_wsolve.o: ../Source/umfpack_solve.c $(INC) $(C) -DDINT -DWSOLVE -c $< -o $@ umfpack_di_%.o: ../Source/umfpack_%.c $(INC) $(C) -DDINT -c $< -o $@ #------------------------------------------------------------------------------- # compile each routine in the DL version #------------------------------------------------------------------------------- umf_dl_%.o: ../Source/umf_%.c $(INC) $(C) -DDLONG -c $< -o $@ umf_dl_%hsolve.o: ../Source/umf_%tsolve.c $(INC) $(C) -DDLONG -DCONJUGATE_SOLVE -c $< -o $@ umf_dl_triplet_map_x.o: ../Source/umf_triplet.c $(INC) $(C) -DDLONG -DDO_MAP -DDO_VALUES -c $< -o $@ umf_dl_triplet_map_nox.o: ../Source/umf_triplet.c $(INC) $(C) -DDLONG -DDO_MAP -c $< -o $@ umf_dl_triplet_nomap_x.o: ../Source/umf_triplet.c $(INC) $(C) -DDLONG -DDO_VALUES -c $< -o $@ umf_dl_triplet_nomap_nox.o: ../Source/umf_triplet.c $(INC) $(C) -DDLONG -c $< -o $@ umf_dl_assemble_fixq.o: ../Source/umf_assemble.c $(INC) $(C) -DDLONG -DFIXQ -c $< -o $@ umf_dl_store_lu_drop.o: ../Source/umf_store_lu.c $(INC) $(C) -DDLONG -DDROP -c $< -o $@ umfpack_dl_wsolve.o: ../Source/umfpack_solve.c $(INC) $(C) -DDLONG -DWSOLVE -c $< -o $@ umfpack_dl_%.o: ../Source/umfpack_%.c $(INC) $(C) -DDLONG -c $< -o $@ #------------------------------------------------------------------------------- # compile each routine in the ZI version #------------------------------------------------------------------------------- umf_zi_%.o: ../Source/umf_%.c $(INC) $(C) -DZINT -c $< -o $@ umf_zi_%hsolve.o: ../Source/umf_%tsolve.c $(INC) $(C) -DZINT -DCONJUGATE_SOLVE -c $< -o $@ umf_zi_triplet_map_x.o: ../Source/umf_triplet.c $(INC) $(C) -DZINT -DDO_MAP -DDO_VALUES -c $< -o $@ umf_zi_triplet_map_nox.o: ../Source/umf_triplet.c $(INC) $(C) -DZINT -DDO_MAP -c $< -o $@ umf_zi_triplet_nomap_x.o: ../Source/umf_triplet.c $(INC) $(C) -DZINT -DDO_VALUES -c $< -o $@ umf_zi_triplet_nomap_nox.o: ../Source/umf_triplet.c $(INC) $(C) -DZINT -c $< -o $@ umf_zi_assemble_fixq.o: ../Source/umf_assemble.c $(INC) $(C) -DZINT -DFIXQ -c $< -o $@ umf_zi_store_lu_drop.o: ../Source/umf_store_lu.c $(INC) $(C) -DZINT -DDROP -c $< -o $@ umfpack_zi_wsolve.o: ../Source/umfpack_solve.c $(INC) $(C) -DZINT -DWSOLVE -c $< -o $@ umfpack_zi_%.o: ../Source/umfpack_%.c $(INC) $(C) -DZINT -c $< -o $@ #------------------------------------------------------------------------------- # compile each routine in the ZL version #------------------------------------------------------------------------------- umf_zl_%.o: ../Source/umf_%.c $(INC) $(C) -DZLONG -c $< -o $@ umf_zl_%hsolve.o: ../Source/umf_%tsolve.c $(INC) $(C) -DZLONG -DCONJUGATE_SOLVE -c $< -o $@ umf_zl_triplet_map_x.o: ../Source/umf_triplet.c $(INC) $(C) -DZLONG -DDO_MAP -DDO_VALUES -c $< -o $@ umf_zl_triplet_map_nox.o: ../Source/umf_triplet.c $(INC) $(C) -DZLONG -DDO_MAP -c $< -o $@ umf_zl_triplet_nomap_x.o: ../Source/umf_triplet.c $(INC) $(C) -DZLONG -DDO_VALUES -c $< -o $@ umf_zl_triplet_nomap_nox.o: ../Source/umf_triplet.c $(INC) $(C) -DZLONG -c $< -o $@ umf_zl_assemble_fixq.o: ../Source/umf_assemble.c $(INC) $(C) -DZLONG -DFIXQ -c $< -o $@ umf_zl_store_lu_drop.o: ../Source/umf_store_lu.c $(INC) $(C) -DZLONG -DDROP -c $< -o $@ umfpack_zl_wsolve.o: ../Source/umfpack_solve.c $(INC) $(C) -DZLONG -DWSOLVE -c $< -o $@ umfpack_zl_%.o: ../Source/umfpack_%.c $(INC) $(C) -DZLONG -c $< -o $@ #------------------------------------------------------------------------------- # Create the generic routines (GN) using a generic rule #------------------------------------------------------------------------------- umfpack_gn_%.o: ../Source/umfpack_%.c $(INC) $(C) -c $< -o $@ #------------------------------------------------------------------------------- # Create the ../Lib/libumfpack.a library #------------------------------------------------------------------------------- ../Lib/libumfpack.a: $(II) $(LL) $(GN) $(DI) $(DL) $(ZI) $(ZL) $(AR) ../Lib/libumfpack.a $^ - $(RANLIB) ../Lib/libumfpack.a #------------------------------------------------------------------------------- # Remove all but the files in the original distribution #------------------------------------------------------------------------------- purge: clean - $(RM) ../Lib/libumfpack.a clean: - $(RM) $(CLEAN) SuiteSparse/UMFPACK/Lib/libumfpack.def0000644001170100242450000000447510170555533016356 0ustar davisfacLIBRARY libumfpack.dll EXPORTS umfpack_di_col_to_triplet umfpack_di_defaults umfpack_di_free_numeric umfpack_di_free_symbolic umfpack_di_get_numeric umfpack_di_get_lunz umfpack_di_get_symbolic umfpack_di_get_determinant umfpack_di_numeric umfpack_di_qsymbolic umfpack_di_report_control umfpack_di_report_info umfpack_di_report_matrix umfpack_di_report_numeric umfpack_di_report_perm umfpack_di_report_status umfpack_di_report_symbolic umfpack_di_report_triplet umfpack_di_report_vector umfpack_di_solve umfpack_di_wsolve umfpack_di_symbolic umfpack_di_transpose umfpack_di_triplet_to_col umfpack_di_scale umfpack_dl_col_to_triplet umfpack_dl_defaults umfpack_dl_free_numeric umfpack_dl_free_symbolic umfpack_dl_get_numeric umfpack_dl_get_lunz umfpack_dl_get_symbolic umfpack_dl_get_determinant umfpack_dl_numeric umfpack_dl_qsymbolic umfpack_dl_report_control umfpack_dl_report_info umfpack_dl_report_matrix umfpack_dl_report_numeric umfpack_dl_report_perm umfpack_dl_report_status umfpack_dl_report_symbolic umfpack_dl_report_triplet umfpack_dl_report_vector umfpack_dl_solve umfpack_dl_wsolve umfpack_dl_symbolic umfpack_dl_transpose umfpack_dl_triplet_to_col umfpack_dl_scale umfpack_zi_col_to_triplet umfpack_zi_defaults umfpack_zi_free_numeric umfpack_zi_free_symbolic umfpack_zi_get_numeric umfpack_zi_get_lunz umfpack_zi_get_symbolic umfpack_zi_get_determinant umfpack_zi_numeric umfpack_zi_qsymbolic umfpack_zi_report_control umfpack_zi_report_info umfpack_zi_report_matrix umfpack_zi_report_numeric umfpack_zi_report_perm umfpack_zi_report_status umfpack_zi_report_symbolic umfpack_zi_report_triplet umfpack_zi_report_vector umfpack_zi_solve umfpack_zi_wsolve umfpack_zi_symbolic umfpack_zi_transpose umfpack_zi_triplet_to_col umfpack_zi_scale umfpack_zl_col_to_triplet umfpack_zl_defaults umfpack_zl_free_numeric umfpack_zl_free_symbolic umfpack_zl_get_numeric umfpack_zl_get_lunz umfpack_zl_get_symbolic umfpack_zl_get_determinant umfpack_zl_numeric umfpack_zl_qsymbolic umfpack_zl_report_control umfpack_zl_report_info umfpack_zl_report_matrix umfpack_zl_report_numeric umfpack_zl_report_perm umfpack_zl_report_status umfpack_zl_report_symbolic umfpack_zl_report_triplet umfpack_zl_report_vector umfpack_zl_solve umfpack_zl_wsolve umfpack_zl_symbolic umfpack_zl_transpose umfpack_zl_triplet_to_col umfpack_zl_scale umfpack_timer umfpack_tic umfpack_toc SuiteSparse/UMFPACK/Demo/0000755001170100242450000000000010711435725013726 5ustar davisfacSuiteSparse/UMFPACK/Demo/HB/0000755001170100242450000000000010006260706014207 5ustar davisfacSuiteSparse/UMFPACK/Demo/HB/can_24.psa0000644001170100242450000000171410006260706015765 0ustar davisfac1SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981. CAN 24 8 2 6 0 0 PSA 24 24 92 0 (16I5) (16I5) 1 10 16 22 28 34 39 45 52 55 60 65 69 71 73 74 77 78 81 83 86 89 91 92 93 1 6 7 13 14 18 19 20 22 2 9 10 14 15 18 3 7 12 21 22 23 4 8 11 16 19 20 5 8 10 15 16 17 6 7 13 14 18 7 12 13 20 22 24 8 10 15 16 17 18 19 9 10 15 10 14 15 18 19 11 19 20 21 22 12 13 22 24 13 24 14 18 15 16 17 19 17 18 19 20 19 20 20 21 22 21 22 23 22 23 23 24 SuiteSparse/UMFPACK/Demo/HB/arc130.rua0000644001170100242450000012003210006260706015707 0ustar davisfac1UNSYMMETRIC MATRIX FROM LASER PROBLEM. A.R.CURTIS, OCT 1974 ARC130 502 9 65 428 0 RUA 130 130 1282 0 (16I5) (20I4) (1P3D24.15) 1 41 102 163 224 285 325 344 363 380 397 413 423 433 443 452 461 471 595 597 721 722 723 724 725 726 732 737 744 750 755 761 766 773 779 785 791 796 801 806 812 818 824 830 836 841 847 852 858 863 868 874 879 884 889 896 903 908 914 919 925 931 936 943 948 953 959 964 971 976 981 986 991 997 1002 1008 1013 1018 1023 1028 1033 1038 1043 1048 1053 1058 1063 1068 1073 1078 1083 1088 1093 1098 1103 1108 1113 1118 1123 1128 1133 1138 1143 1148 1153 1158 1163 1168 1173 1178 1183 1188 1193 1198 1203 1208 1213 1218 1223 1228 1233 1238 1243 1248 1253 1258 1263 1268 1273 1278 1283 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 20 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 106 111 116 121 126 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 20 26 27 31 32 36 37 41 42 46 47 51 52 56 57 61 62 66 67 71 72 76 77 81 82 86 87 91 92 96 97 101 102 106 107 111 112 116 117 121 122 126 127 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 20 27 28 32 33 37 38 42 43 47 48 52 53 57 58 62 63 67 68 72 73 77 78 82 83 87 88 92 93 97 98 102 103 107 108 112 113 117 118 122 123 127 128 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 20 28 29 33 34 38 39 43 44 48 49 53 54 58 59 63 64 68 69 73 74 78 79 83 84 88 89 93 94 98 99 103 104 108 109 113 114 118 119 123 124 128 129 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 20 29 30 34 35 39 40 44 45 49 50 54 55 59 60 64 65 69 70 74 75 79 80 84 85 89 90 94 95 99 100 104 105 109 110 114 115 119 120 124 125 129 130 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 20 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 20 1 2 3 4 5 6 7 8 9 12 13 14 15 17 18 19 20 1 2 3 4 5 6 7 8 10 11 12 14 15 17 18 19 20 1 2 3 4 5 6 7 8 11 12 14 15 17 18 19 20 7 9 11 12 13 14 15 18 19 20 7 9 11 12 13 14 15 18 19 20 8 10 11 12 14 15 17 18 19 20 1 2 3 4 5 6 15 18 20 1 2 3 4 5 6 16 18 20 1 2 3 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CHU QC324 19512 21 1671 17820 0 CUA 324 324 26730 0 (16I5) (16I5) (3D22.16) (3D22.16) 1 83 165 247 329 411 493 575 657 739 821 903 985 1067 1149 1231 1313 1395 1477 1559 1641 1723 1805 1887 1969 2051 2133 2215 2297 2379 2461 2543 2625 2707 2789 2871 2953 3035 3117 3199 3281 3363 3445 3527 3609 3691 3773 3855 3937 4019 4101 4183 4265 4347 4429 4511 4593 4675 4757 4839 4921 5003 5085 5167 5249 5331 5413 5495 5577 5659 5741 5823 5905 5987 6069 6151 6233 6315 6397 6479 6561 6643 6726 6809 6892 6975 7058 7141 7224 7307 7390 7473 7556 7639 7722 7805 7888 7971 8054 8137 8220 8303 8386 8469 8552 8635 8718 8801 8884 8967 9050 9133 9216 9299 9382 9465 9548 9631 9714 9797 9880 9963100461012910212102951037810461 10544106271071010793108761095911042111251120811291113741145711540116231170611789 11872119551203812121122041228712370124531253612619127021278512868129511303413117 13200132831336613449135321361513698137811386413947140301411314196142791436214445 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====================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* A demo of UMFPACK: umfpack_zi_* version. First, factor and solve a 5-by-5 system, Ax=b, using default parameters. Then solve A'x=b using the factors of A. Modify one entry (A (1,4) = 0, where the row and column indices range from 0 to 4. The pattern of A has not changed (it has explicitly zero entry), so a reanalysis with umfpack_zi_symbolic does not need to be done. Refactorize (with umfpack_zi_numeric), and solve Ax=b. Note that the pivot ordering has changed. Next, change all of the entries in A, but not the pattern. Finally, compute C = A', and do the symbolic and numeric factorization of C. Factorizing A' can sometimes be better than factorizing A itself (less work and memory usage). Solve C'x=b twice; the solution is the same as the solution to Ax=b. A note about zero-sized arrays: UMFPACK uses many user-provided arrays of size n (order of the matrix), and of size nz (the number of nonzeros in a matrix). n cannot be zero; UMFPACK does not handle zero-dimensioned arrays. However, nz can be zero. If you attempt to malloc an array of size nz = 0, however, malloc will return a null pointer which UMFPACK will report as a "missing argument." Thus, nz1 in this code is set to MAX (nz,1), and similarly for lnz and unz. Lnz can never be zero, however, since L is always unit diagonal. */ /* -------------------------------------------------------------------------- */ /* definitions */ /* -------------------------------------------------------------------------- */ #include #include #include "umfpack.h" /* use a cheap approximate absolute value for complex numbers: */ #define ABS(x,z) ((x) >= 0 ? (x) : -(x)) + ((z) >= 0 ? (z) : -(z)) #define MAX(a,b) (((a) > (b)) ? (a) : (b)) #ifndef TRUE #define TRUE (1) #endif #ifndef FALSE #define FALSE (0) #endif /* -------------------------------------------------------------------------- */ /* triplet form of the matrix. The triplets can be in any order. */ /* -------------------------------------------------------------------------- */ static int n = 5, nz = 12 ; static int Arow [ ] = { 0, 4, 1, 1, 2, 2, 0, 1, 2, 3, 4, 4} ; static int Acol [ ] = { 0, 4, 0, 2, 1, 2, 1, 4, 3, 2, 1, 2} ; static double Aval [ ] = {2., 1., 3., 4., -1., -3., 3., 6., 2., 1., 4., 2.} ; static double Avalz[ ] = {1., .4, .1, .2, -1., -.2, 0., 6., 3., 0., .3, .3} ; static double b [ ] = {8., 45., -3., 3., 19.}, x [5], r [5] ; static double bz[ ] = {1., -5., -2., 0., 2.2}, xz[5], rz[5] ; /* Avalz, bz: imaginary part of A and b */ /* -------------------------------------------------------------------------- */ /* error: print a message and exit */ /* -------------------------------------------------------------------------- */ static void error ( char *message ) { printf ("\n\n====== error: %s =====\n\n", message) ; exit (1) ; } /* -------------------------------------------------------------------------- */ /* resid: compute the residual, r = Ax-b or r = A'x=b and return maxnorm (r) */ /* A' is the complex conjugate transpose, not the array transpose */ /* -------------------------------------------------------------------------- */ static double resid ( int transpose, int Ap [ ], int Ai [ ], double Ax [ ] , double Az [ ] ) { int i, j, p ; double norm ; for (i = 0 ; i < n ; i++) { r [i] = -b [i] ; rz[i] = -bz[i] ; } if (transpose) { for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; /* complex: r(j) += conj (Aij) * x (i) */ r [j] += Ax [p] * x [i] ; r [j] += Az [p] * xz[i] ; rz[j] -= Az [p] * x [i] ; rz[j] += Ax [p] * xz[i] ; } } } else { for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; r [i] += Ax [p] * x [j] ; r [i] -= Az [p] * xz[j] ; rz[i] += Az [p] * x [j] ; rz[i] += Ax [p] * xz[j] ; } } } norm = 0. ; for (i = 0 ; i < n ; i++) { norm = MAX (ABS (r [i], rz [i]), norm) ; } return (norm) ; } /* -------------------------------------------------------------------------- */ /* main program */ /* -------------------------------------------------------------------------- */ int main (int argc, char **argv) { double Info [UMFPACK_INFO], Control [UMFPACK_CONTROL], *Ax, *Cx, *Lx, *Ux, *W, t [2], *Dx, rnorm, *Rb, *y, *Rs ; double *Az, *Lz, *Uz, *Dz, *Cz, *Rbz, *yz ; int *Ap, *Ai, *Cp, *Ci, row, col, p, lnz, unz, nr, nc, *Lp, *Li, *Ui, *Up, *P, *Q, *Lj, i, j, k, anz, nfr, nchains, *Qinit, fnpiv, lnz1, unz1, nz1, status, *Front_npivcol, *Front_parent, *Chain_start, *Wi, *Pinit, n1, *Chain_maxrows, *Chain_maxcols, *Front_1strow, *Front_leftmostdesc, nzud, do_recip ; void *Symbolic, *Numeric ; /* ---------------------------------------------------------------------- */ /* initializations */ /* ---------------------------------------------------------------------- */ umfpack_tic (t) ; printf ("\nUMFPACK V%d.%d (%s) demo: _zi_ version\n", UMFPACK_MAIN_VERSION, UMFPACK_SUB_VERSION, UMFPACK_DATE) ; /* get the default control parameters */ umfpack_zi_defaults (Control) ; /* change the default print level for this demo */ /* (otherwise, nothing will print) */ Control [UMFPACK_PRL] = 6 ; /* print the license agreement */ umfpack_zi_report_status (Control, UMFPACK_OK) ; Control [UMFPACK_PRL] = 5 ; /* print the control parameters */ umfpack_zi_report_control (Control) ; /* ---------------------------------------------------------------------- */ /* print A and b, and convert A to column-form */ /* ---------------------------------------------------------------------- */ /* print the right-hand-side */ printf ("\nb: ") ; (void) umfpack_zi_report_vector (n, b, bz, Control) ; /* print the triplet form of the matrix */ printf ("\nA: ") ; (void) umfpack_zi_report_triplet (n, n, nz, Arow, Acol, Aval, Avalz, Control) ; /* convert to column form */ nz1 = MAX (nz,1) ; /* ensure arrays are not of size zero. */ Ap = (int *) malloc ((n+1) * sizeof (int)) ; Ai = (int *) malloc (nz1 * sizeof (int)) ; Ax = (double *) malloc (nz1 * sizeof (double)) ; Az = (double *) malloc (nz1 * sizeof (double)) ; if (!Ap || !Ai || !Ax || !Az) { error ("out of memory") ; } status = umfpack_zi_triplet_to_col (n, n, nz, Arow, Acol, Aval, Avalz, Ap, Ai, Ax, Az, (int *) NULL) ; if (status < 0) { umfpack_zi_report_status (Control, status) ; error ("umfpack_zi_triplet_to_col failed") ; } /* print the column-form of A */ printf ("\nA: ") ; (void) umfpack_zi_report_matrix (n, n, Ap, Ai, Ax, Az, 1, Control) ; /* ---------------------------------------------------------------------- */ /* symbolic factorization */ /* ---------------------------------------------------------------------- */ status = umfpack_zi_symbolic (n, n, Ap, Ai, Ax, Az, &Symbolic, Control, Info) ; if (status < 0) { umfpack_zi_report_info (Control, Info) ; umfpack_zi_report_status (Control, status) ; error ("umfpack_zi_symbolic failed") ; } /* print the symbolic factorization */ printf ("\nSymbolic factorization of A: ") ; (void) umfpack_zi_report_symbolic (Symbolic, Control) ; /* ---------------------------------------------------------------------- */ /* numeric factorization */ /* ---------------------------------------------------------------------- */ status = umfpack_zi_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric, Control, Info) ; if (status < 0) { umfpack_zi_report_info (Control, Info) ; umfpack_zi_report_status (Control, status) ; error ("umfpack_zi_numeric failed") ; } /* print the numeric factorization */ printf ("\nNumeric factorization of A: ") ; (void) umfpack_zi_report_numeric (Numeric, Control) ; /* ---------------------------------------------------------------------- */ /* solve Ax=b */ /* ---------------------------------------------------------------------- */ status = umfpack_zi_solve (UMFPACK_A, Ap, Ai, Ax, Az, x, xz, b, bz, Numeric, Control, Info) ; umfpack_zi_report_info (Control, Info) ; umfpack_zi_report_status (Control, status) ; if (status < 0) { error ("umfpack_zi_solve failed") ; } printf ("\nx (solution of Ax=b): ") ; (void) umfpack_zi_report_vector (n, x, xz, Control) ; rnorm = resid (FALSE, Ap, Ai, Ax, Az) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* compute the determinant */ /* ---------------------------------------------------------------------- */ status = umfpack_zi_get_determinant (x, xz, r, Numeric, Info) ; umfpack_zi_report_status (Control, status) ; if (status < 0) { error ("umfpack_zi_get_determinant failed") ; } printf ("determinant: (%g", x [0]) ; printf ("+ (%g)i", xz [0]) ; /* complex */ printf (") * 10^(%g)\n", r [0]) ; /* ---------------------------------------------------------------------- */ /* solve Ax=b, broken down into steps */ /* ---------------------------------------------------------------------- */ /* Rb = R*b */ Rb = (double *) malloc (n * sizeof (double)) ; Rbz = (double *) malloc (n * sizeof (double)) ; y = (double *) malloc (n * sizeof (double)) ; yz = (double *) malloc (n * sizeof (double)) ; if (!Rb || !y) error ("out of memory") ; if (!Rbz || !yz) error ("out of memory") ; status = umfpack_zi_scale (Rb, Rbz, b, bz, Numeric) ; if (status < 0) error ("umfpack_zi_scale failed") ; /* solve Ly = P*(Rb) */ status = umfpack_zi_solve (UMFPACK_Pt_L, Ap, Ai, Ax, Az, y, yz, Rb, Rbz, Numeric, Control, Info) ; if (status < 0) error ("umfpack_zi_solve failed") ; /* solve UQ'x=y */ status = umfpack_zi_solve (UMFPACK_U_Qt, Ap, Ai, Ax, Az, x, xz, y, yz, Numeric, Control, Info) ; if (status < 0) error ("umfpack_zi_solve failed") ; printf ("\nx (solution of Ax=b, solve is split into 3 steps): ") ; (void) umfpack_zi_report_vector (n, x, xz, Control) ; rnorm = resid (FALSE, Ap, Ai, Ax, Az) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; free (Rb) ; free (Rbz) ; free (y) ; free (yz) ; /* ---------------------------------------------------------------------- */ /* solve A'x=b */ /* ---------------------------------------------------------------------- */ /* note that this is the complex conjugate transpose, A' */ status = umfpack_zi_solve (UMFPACK_At, Ap, Ai, Ax, Az, x, xz, b, bz, Numeric, Control, Info) ; umfpack_zi_report_info (Control, Info) ; if (status < 0) { error ("umfpack_zi_solve failed") ; } printf ("\nx (solution of A'x=b): ") ; (void) umfpack_zi_report_vector (n, x, xz, Control) ; rnorm = resid (TRUE, Ap, Ai, Ax, Az) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* modify one numerical value in the column-form of A */ /* ---------------------------------------------------------------------- */ /* change A (1,4), look for row index 1 in column 4. */ row = 1 ; col = 4 ; for (p = Ap [col] ; p < Ap [col+1] ; p++) { if (row == Ai [p]) { printf ("\nchanging A (%d,%d) to zero\n", row, col) ; Ax [p] = 0.0 ; Az [p] = 0.0 ; break ; } } printf ("\nmodified A: ") ; (void) umfpack_zi_report_matrix (n, n, Ap, Ai, Ax, Az, 1, Control) ; /* ---------------------------------------------------------------------- */ /* redo the numeric factorization */ /* ---------------------------------------------------------------------- */ /* The pattern (Ap and Ai) hasn't changed, so the symbolic factorization */ /* doesn't have to be redone, no matter how much we change Ax. */ /* We don't need the Numeric object any more, so free it. */ umfpack_zi_free_numeric (&Numeric) ; /* Note that a memory leak would have occurred if the old Numeric */ /* had not been free'd with umfpack_zi_free_numeric above. */ status = umfpack_zi_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric, Control, Info) ; if (status < 0) { umfpack_zi_report_info (Control, Info) ; umfpack_zi_report_status (Control, status) ; error ("umfpack_zi_numeric failed") ; } printf ("\nNumeric factorization of modified A: ") ; (void) umfpack_zi_report_numeric (Numeric, Control) ; /* ---------------------------------------------------------------------- */ /* solve Ax=b, with the modified A */ /* ---------------------------------------------------------------------- */ status = umfpack_zi_solve (UMFPACK_A, Ap, Ai, Ax, Az, x, xz, b, bz, Numeric, Control, Info) ; umfpack_zi_report_info (Control, Info) ; if (status < 0) { umfpack_zi_report_status (Control, status) ; error ("umfpack_zi_solve failed") ; } printf ("\nx (with modified A): ") ; (void) umfpack_zi_report_vector (n, x, xz, Control) ; rnorm = resid (FALSE, Ap, Ai, Ax, Az) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* modify all of the numerical values of A, but not the pattern */ /* ---------------------------------------------------------------------- */ for (col = 0 ; col < n ; col++) { for (p = Ap [col] ; p < Ap [col+1] ; p++) { row = Ai [p] ; printf ("changing ") ; /* complex: */ printf ("real part of ") ; printf ("A (%d,%d) from %g", row, col, Ax [p]) ; Ax [p] = Ax [p] + col*10 - row ; printf (" to %g\n", Ax [p]) ; } } printf ("\ncompletely modified A (same pattern): ") ; (void) umfpack_zi_report_matrix (n, n, Ap, Ai, Ax, Az, 1, Control) ; /* ---------------------------------------------------------------------- */ /* save the Symbolic object to file, free it, and load it back in */ /* ---------------------------------------------------------------------- */ /* use the default filename, "symbolic.umf" */ printf ("\nSaving symbolic object:\n") ; status = umfpack_zi_save_symbolic (Symbolic, (char *) NULL) ; if (status < 0) { umfpack_zi_report_status (Control, status) ; error ("umfpack_zi_save_symbolic failed") ; } printf ("\nFreeing symbolic object:\n") ; umfpack_zi_free_symbolic (&Symbolic) ; printf ("\nLoading symbolic object:\n") ; status = umfpack_zi_load_symbolic (&Symbolic, (char *) NULL) ; if (status < 0) { umfpack_zi_report_status (Control, status) ; error ("umfpack_zi_load_symbolic failed") ; } printf ("\nDone loading symbolic object\n") ; /* ---------------------------------------------------------------------- */ /* redo the numeric factorization */ /* ---------------------------------------------------------------------- */ umfpack_zi_free_numeric (&Numeric) ; status = umfpack_zi_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric, Control, Info) ; if (status < 0) { umfpack_zi_report_info (Control, Info) ; umfpack_zi_report_status (Control, status) ; error ("umfpack_zi_numeric failed") ; } printf ("\nNumeric factorization of completely modified A: ") ; (void) umfpack_zi_report_numeric (Numeric, Control) ; /* ---------------------------------------------------------------------- */ /* solve Ax=b, with the modified A */ /* ---------------------------------------------------------------------- */ status = umfpack_zi_solve (UMFPACK_A, Ap, Ai, Ax, Az, x, xz, b, bz, Numeric, Control, Info) ; umfpack_zi_report_info (Control, Info) ; if (status < 0) { umfpack_zi_report_status (Control, status) ; error ("umfpack_zi_solve failed") ; } printf ("\nx (with completely modified A): ") ; (void) umfpack_zi_report_vector (n, x, xz, Control) ; rnorm = resid (FALSE, Ap, Ai, Ax, Az) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* free the symbolic and numeric factorization */ /* ---------------------------------------------------------------------- */ umfpack_zi_free_symbolic (&Symbolic) ; umfpack_zi_free_numeric (&Numeric) ; /* ---------------------------------------------------------------------- */ /* C = transpose of A */ /* ---------------------------------------------------------------------- */ Cp = (int *) malloc ((n+1) * sizeof (int)) ; Ci = (int *) malloc (nz1 * sizeof (int)) ; Cx = (double *) malloc (nz1 * sizeof (double)) ; Cz = (double *) malloc (nz1 * sizeof (double)) ; if (!Cp || !Ci || !Cx || !Cz) { error ("out of memory") ; } status = umfpack_zi_transpose (n, n, Ap, Ai, Ax, Az, (int *) NULL, (int *) NULL, Cp, Ci, Cx, Cz, TRUE) ; if (status < 0) { umfpack_zi_report_status (Control, status) ; error ("umfpack_zi_transpose failed: ") ; } printf ("\nC (transpose of A): ") ; (void) umfpack_zi_report_matrix (n, n, Cp, Ci, Cx, Cz, 1, Control) ; /* ---------------------------------------------------------------------- */ /* symbolic factorization of C */ /* ---------------------------------------------------------------------- */ status = umfpack_zi_symbolic (n, n, Cp, Ci, Cx, Cz, &Symbolic, Control, Info) ; if (status < 0) { umfpack_zi_report_info (Control, Info) ; umfpack_zi_report_status (Control, status) ; error ("umfpack_zi_symbolic failed") ; } printf ("\nSymbolic factorization of C: ") ; (void) umfpack_zi_report_symbolic (Symbolic, Control) ; /* ---------------------------------------------------------------------- */ /* copy the contents of Symbolic into user arrays print them */ /* ---------------------------------------------------------------------- */ printf ("\nGet the contents of the Symbolic object for C:\n") ; printf ("(compare with umfpack_zi_report_symbolic output, above)\n") ; Pinit = (int *) malloc ((n+1) * sizeof (int)) ; Qinit = (int *) malloc ((n+1) * sizeof (int)) ; Front_npivcol = (int *) malloc ((n+1) * sizeof (int)) ; Front_1strow = (int *) malloc ((n+1) * sizeof (int)) ; Front_leftmostdesc = (int *) malloc ((n+1) * sizeof (int)) ; Front_parent = (int *) malloc ((n+1) * sizeof (int)) ; Chain_start = (int *) malloc ((n+1) * sizeof (int)) ; Chain_maxrows = (int *) malloc ((n+1) * sizeof (int)) ; Chain_maxcols = (int *) malloc ((n+1) * sizeof (int)) ; if (!Pinit || !Qinit || !Front_npivcol || !Front_parent || !Chain_start || !Chain_maxrows || !Chain_maxcols || !Front_1strow || !Front_leftmostdesc) { error ("out of memory") ; } status = umfpack_zi_get_symbolic (&nr, &nc, &n1, &anz, &nfr, &nchains, Pinit, Qinit, Front_npivcol, Front_parent, Front_1strow, Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ; if (status < 0) { error ("symbolic factorization invalid") ; } printf ("From the Symbolic object, C is of dimension %d-by-%d\n", nr, nc); printf (" with nz = %d, number of fronts = %d,\n", nz, nfr) ; printf (" number of frontal matrix chains = %d\n", nchains) ; printf ("\nPivot columns in each front, and parent of each front:\n") ; k = 0 ; for (i = 0 ; i < nfr ; i++) { fnpiv = Front_npivcol [i] ; printf (" Front %d: parent front: %d number of pivot cols: %d\n", i, Front_parent [i], fnpiv) ; for (j = 0 ; j < fnpiv ; j++) { col = Qinit [k] ; printf ( " %d-th pivot column is column %d in original matrix\n", k, col) ; k++ ; } } printf ("\nNote that the column ordering, above, will be refined\n") ; printf ("in the numeric factorization below. The assignment of pivot\n") ; printf ("columns to frontal matrices will always remain unchanged.\n") ; printf ("\nTotal number of pivot columns in frontal matrices: %d\n", k) ; printf ("\nFrontal matrix chains:\n") ; for (j = 0 ; j < nchains ; j++) { printf (" Frontal matrices %d to %d are factorized in a single\n", Chain_start [j], Chain_start [j+1] - 1) ; printf (" working array of size %d-by-%d\n", Chain_maxrows [j], Chain_maxcols [j]) ; } /* ---------------------------------------------------------------------- */ /* numeric factorization of C */ /* ---------------------------------------------------------------------- */ status = umfpack_zi_numeric (Cp, Ci, Cx, Cz, Symbolic, &Numeric, Control, Info) ; if (status < 0) { error ("umfpack_zi_numeric failed") ; } printf ("\nNumeric factorization of C: ") ; (void) umfpack_zi_report_numeric (Numeric, Control) ; /* ---------------------------------------------------------------------- */ /* extract the LU factors of C and print them */ /* ---------------------------------------------------------------------- */ if (umfpack_zi_get_lunz (&lnz, &unz, &nr, &nc, &nzud, Numeric) < 0) { error ("umfpack_zi_get_lunz failed") ; } /* ensure arrays are not of zero size */ lnz1 = MAX (lnz,1) ; unz1 = MAX (unz,1) ; Lp = (int *) malloc ((n+1) * sizeof (int)) ; Lj = (int *) malloc (lnz1 * sizeof (int)) ; Lx = (double *) malloc (lnz1 * sizeof (double)) ; Lz = (double *) malloc (lnz1 * sizeof (double)) ; Up = (int *) malloc ((n+1) * sizeof (int)) ; Ui = (int *) malloc (unz1 * sizeof (int)) ; Ux = (double *) malloc (unz1 * sizeof (double)) ; Uz = (double *) malloc (unz1 * sizeof (double)) ; P = (int *) malloc (n * sizeof (int)) ; Q = (int *) malloc (n * sizeof (int)) ; Dx = (double *) NULL ; /* D vector not requested */ Dz = (double *) NULL ; Rs = (double *) malloc (n * sizeof (double)) ; if (!Lp || !Lj || !Lx || !Lz || !Up || !Ui || !Ux || !Uz || !P || !Q || !Rs) { error ("out of memory") ; } status = umfpack_zi_get_numeric (Lp, Lj, Lx, Lz, Up, Ui, Ux, Uz, P, Q, Dx, Dz, &do_recip, Rs, Numeric) ; if (status < 0) { error ("umfpack_zi_get_numeric failed") ; } printf ("\nL (lower triangular factor of C): ") ; (void) umfpack_zi_report_matrix (n, n, Lp, Lj, Lx, Lz, 0, Control) ; printf ("\nU (upper triangular factor of C): ") ; (void) umfpack_zi_report_matrix (n, n, Up, Ui, Ux, Uz, 1, Control) ; printf ("\nP: ") ; (void) umfpack_zi_report_perm (n, P, Control) ; printf ("\nQ: ") ; (void) umfpack_zi_report_perm (n, Q, Control) ; printf ("\nScale factors: row i of A is to be ") ; if (do_recip) { printf ("multiplied by the ith scale factor\n") ; } else { printf ("divided by the ith scale factor\n") ; } for (i = 0 ; i < n ; i++) printf ("%d: %g\n", i, Rs [i]) ; /* ---------------------------------------------------------------------- */ /* convert L to triplet form and print it */ /* ---------------------------------------------------------------------- */ /* Note that L is in row-form, so it is the row indices that are created */ /* by umfpack_zi_col_to_triplet. */ printf ("\nConverting L to triplet form, and printing it:\n") ; Li = (int *) malloc (lnz1 * sizeof (int)) ; if (!Li) { error ("out of memory") ; } if (umfpack_zi_col_to_triplet (n, Lp, Li) < 0) { error ("umfpack_zi_col_to_triplet failed") ; } printf ("\nL, in triplet form: ") ; (void) umfpack_zi_report_triplet (n, n, lnz, Li, Lj, Lx, Lz, Control) ; /* ---------------------------------------------------------------------- */ /* save the Numeric object to file, free it, and load it back in */ /* ---------------------------------------------------------------------- */ /* use the default filename, "numeric.umf" */ printf ("\nSaving numeric object:\n") ; status = umfpack_zi_save_numeric (Numeric, (char *) NULL) ; if (status < 0) { umfpack_zi_report_status (Control, status) ; error ("umfpack_zi_save_numeric failed") ; } printf ("\nFreeing numeric object:\n") ; umfpack_zi_free_numeric (&Numeric) ; printf ("\nLoading numeric object:\n") ; status = umfpack_zi_load_numeric (&Numeric, (char *) NULL) ; if (status < 0) { umfpack_zi_report_status (Control, status) ; error ("umfpack_zi_load_numeric failed") ; } printf ("\nDone loading numeric object\n") ; /* ---------------------------------------------------------------------- */ /* solve C'x=b */ /* ---------------------------------------------------------------------- */ status = umfpack_zi_solve (UMFPACK_At, Cp, Ci, Cx, Cz, x, xz, b, bz, Numeric, Control, Info) ; umfpack_zi_report_info (Control, Info) ; if (status < 0) { umfpack_zi_report_status (Control, status) ; error ("umfpack_zi_solve failed") ; } printf ("\nx (solution of C'x=b): ") ; (void) umfpack_zi_report_vector (n, x, xz, Control) ; rnorm = resid (TRUE, Cp, Ci, Cx, Cz) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* solve C'x=b again, using umfpack_zi_wsolve instead */ /* ---------------------------------------------------------------------- */ printf ("\nSolving C'x=b again, using umfpack_zi_wsolve instead:\n") ; Wi = (int *) malloc (n * sizeof (int)) ; W = (double *) malloc (10*n * sizeof (double)) ; if (!Wi || !W) { error ("out of memory") ; } status = umfpack_zi_wsolve (UMFPACK_At, Cp, Ci, Cx, Cz, x, xz, b, bz, Numeric, Control, Info, Wi, W) ; umfpack_zi_report_info (Control, Info) ; if (status < 0) { umfpack_zi_report_status (Control, status) ; error ("umfpack_zi_wsolve failed") ; } printf ("\nx (solution of C'x=b): ") ; (void) umfpack_zi_report_vector (n, x, xz, Control) ; rnorm = resid (TRUE, Cp, Ci, Cx, Cz) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* free everything */ /* ---------------------------------------------------------------------- */ /* This is not strictly required since the process is exiting and the */ /* system will reclaim the memory anyway. It's useful, though, just as */ /* a list of what is currently malloc'ed by this program. Plus, it's */ /* always a good habit to explicitly free whatever you malloc. */ free (Ap) ; free (Ai) ; free (Ax) ; free (Az) ; free (Cp) ; free (Ci) ; free (Cx) ; free (Cz) ; free (Pinit) ; free (Qinit) ; free (Front_npivcol) ; free (Front_1strow) ; free (Front_leftmostdesc) ; free (Front_parent) ; free (Chain_start) ; free (Chain_maxrows) ; free (Chain_maxcols) ; free (Lp) ; free (Lj) ; free (Lx) ; free (Lz) ; free (Up) ; free (Ui) ; free (Ux) ; free (Uz) ; free (P) ; free (Q) ; free (Li) ; free (Wi) ; free (W) ; umfpack_zi_free_symbolic (&Symbolic) ; umfpack_zi_free_numeric (&Numeric) ; /* ---------------------------------------------------------------------- */ /* print the total time spent in this demo */ /* ---------------------------------------------------------------------- */ umfpack_toc (t) ; printf ("\numfpack_zi_demo complete.\nTotal time: %5.2f seconds" " (CPU time), %5.2f seconds (wallclock time)\n", t [1], t [0]) ; return (0) ; } SuiteSparse/UMFPACK/Demo/umf4zhb.out0000644001170100242450000001614510711433367016045 0ustar davisfac Matrix key: QC324 UMFPACK V5.2.0 (Nov 1, 2007), Control: Matrix entry defined as: double complex Int (generic integer) defined as: int 0: print level: 2 1: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 2: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 3: pivot tolerance: 0.1 4: block size for dense matrix kernels: 32 5: strategy: 0 (auto) 6: initial allocation ratio: 0.7 7: max iterative refinement steps: 2 12: 2-by-2 pivot tolerance: 0.01 13: Q fixed during numerical factorization: 0 (auto) 14: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 15: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 16: scaling: 1 (divide each row by sum of abs. values in each row) 17: frontal matrix allocation ratio: 0.5 18: drop tolerance: 0 19: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4 9: compiled for ANSI C 10: CPU timer is POSIX times ( ) routine. 11: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 16 (in bytes) symbolic analysis: status: 0. time: 0.00E+00 (sec) estimates (upper bound) for numeric LU: size of LU: 1.17 (MB) memory needed: 2.40 (MB) flop count: 0.26E+08 nnz (L): 24027. nnz (U): 39609. numeric factorization: status: 0. time: 0.10E-01 actual numeric LU statistics: size of LU: 0.72 (MB) memory needed: 1.14 (MB) flop count: 0.14E+08 nnz (L): 23247. nnz (U): 23247. UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double complex Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 324 number of columns in matrix A: 324 entries in matrix A: 26730 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 16 bytes strategy used: symmetric ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 0 submatrix S after removing zero-cost pivots: number of "dense" rows: 324 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 324 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 26406 nz on diagonal of matrix S: 324 fraction of nz on diagonal: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 1.55342e+07 est. nz in L+U (incl. diagonal): 47730 est. largest front (# entries): 14641 est. max nz in any column of L: 121 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 63473 symbolic memory usage (MBytes): 0.5 Symbolic size (Units): 1425 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.01 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 2.55982e-01 maximum sum (abs (rows of A)): 1.82217e+00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 98341 97691 99% peak size (Units) 307744 142557 46% final size (Units) 150384 92058 61% Numeric final size (Units) 153188 94700 62% Numeric final size (MBytes) 1.2 0.7 62% peak memory usage (Units) 314864 149677 48% peak memory usage (MBytes) 2.4 1.1 48% numeric factorization flops 2.56313e+07 1.43519e+07 56% nz in L (incl diagonal) 24027 23247 97% nz in U (incl diagonal) 39609 23247 59% nz in L+U (incl diagonal) 63312 46170 73% largest front (# entries) 19723 6724 34% largest # rows in front 121 82 68% largest # columns in front 163 82 50% initial allocation ratio used: 1.2 # of forced updates due to frontal growth: 0 number of off-diagonal pivots: 0 nz in L (incl diagonal), if none dropped 23247 nz in U (incl diagonal), if none dropped 23247 number of small entries dropped 0 nonzeros on diagonal of U: 324 min abs. value on diagonal of U: 5.47e-03 max abs. value on diagonal of U: 8.25e-01 estimate of reciprocal of condition number: 6.63e-03 indices in compressed pattern: 485 numerical values stored in Numeric object: 46170 numeric factorization defragmentations: 0 numeric factorization reallocations: 0 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.01 numeric factorization wallclock time (sec): 0.01 numeric factorization mflops (CPU time): 1435.19 numeric factorization mflops (wallclock): 1435.19 symbolic + numeric wall clock time (sec): 0.02 symbolic + numeric mflops (wall clock): 717.60 solve flops: 3.70332e+05 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 1.47223e+07 norm (A*x-b): 0. SuiteSparse/UMFPACK/Demo/Makefile0000644001170100242450000001460310617160607015371 0ustar davisfac#------------------------------------------------------------------------------- # compile the UMFPACK demos (for GNU make and original make) #------------------------------------------------------------------------------- # UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis. # All Rights Reserved. See ../Doc/License for License. default: libs run include ../../UFconfig/UFconfig.mk C = $(CC) $(CFLAGS) $(UMFPACK_CONFIG) -I../Include -I../../AMD/Include \ -I../../UFconfig INC = ../Include/umfpack.h ../../AMD/Include/amd.h ../../UFconfig/UFconfig.h LIBS = $(BLAS) $(XERBLA) $(LIB) ../Lib/libumfpack.a: ( cd ../Lib ; $(MAKE) ) ../../AMD/Lib/libamd.a: ( cd ../../AMD ; $(MAKE) library ) UMFPACK = ../Lib/libumfpack.a ../../AMD/Lib/libamd.a libs: ( cd ../Lib ; $(MAKE) ) ( cd ../../AMD ; $(MAKE) library ) #------------------------------------------------------------------------------- # Create the demo programs, run them, and compare the output #------------------------------------------------------------------------------- dist: umfpack_di_demo.c umfpack_dl_demo.c umfpack_zi_demo.c umfpack_zl_demo.c umfpack_simple: umfpack_simple.c $(INC) $(UMFPACK) $(C) -o umfpack_simple umfpack_simple.c $(UMFPACK) $(LIBS) # the GNU rules are simpler: # umfpack_%_demo.c: umfpack_xx_demo.c umfpack_%_demo.sed # - sed -f umfpack_$*_demo.sed < umfpack_xx_demo.c > umfpack_$*_demo.c # # umfpack_%_demo: umfpack_%_demo.c $(INC) $(UMFPACK) # $(C) -o umfpack_$*_demo umfpack_$*_demo.c $(UMFPACK) $(LIBS) # ./umfpack_$*_demo > my_umfpack_$*_demo.out # but do this via brute-force, so we can use just a single Makefile: # double-precision, int verion: umfpack_di_demo.c: umfpack_xx_demo.c umfpack_di_demo.sed - sed -f umfpack_di_demo.sed < umfpack_xx_demo.c > umfpack_di_demo.c umfpack_di_demo: umfpack_di_demo.c $(INC) $(UMFPACK) $(C) -o umfpack_di_demo umfpack_di_demo.c $(UMFPACK) $(LIBS) # double-precision, UF_long verion: umfpack_dl_demo.c: umfpack_xx_demo.c umfpack_dl_demo.sed - sed -f umfpack_dl_demo.sed < umfpack_xx_demo.c > umfpack_dl_demo.c umfpack_dl_demo: umfpack_dl_demo.c $(INC) $(UMFPACK) $(C) -o umfpack_dl_demo umfpack_dl_demo.c $(UMFPACK) $(LIBS) # complex, int verion: umfpack_zi_demo.c: umfpack_xx_demo.c umfpack_zi_demo.sed - sed -f umfpack_zi_demo.sed < umfpack_xx_demo.c > umfpack_zi_demo.c umfpack_zi_demo: umfpack_zi_demo.c $(INC) $(UMFPACK) $(C) -o umfpack_zi_demo umfpack_zi_demo.c $(UMFPACK) $(LIBS) # complex, UF_long verion: umfpack_zl_demo.c: umfpack_xx_demo.c umfpack_zl_demo.sed - sed -f umfpack_zl_demo.sed < umfpack_xx_demo.c > umfpack_zl_demo.c umfpack_zl_demo: umfpack_zl_demo.c $(INC) $(UMFPACK) $(C) -o umfpack_zl_demo umfpack_zl_demo.c $(UMFPACK) $(LIBS) run: umfpack_di_demo umfpack_zi_demo umfpack_dl_demo umfpack_zl_demo umfpack_simple ./umfpack_simple ./umfpack_di_demo > my_umfpack_di_demo.out - diff umfpack_di_demo.out my_umfpack_di_demo.out ./umfpack_dl_demo > my_umfpack_dl_demo.out - diff umfpack_dl_demo.out my_umfpack_dl_demo.out ./umfpack_zi_demo > my_umfpack_zi_demo.out - diff umfpack_zi_demo.out my_umfpack_zi_demo.out ./umfpack_zl_demo > my_umfpack_zl_demo.out - diff umfpack_zl_demo.out my_umfpack_zl_demo.out #------------------------------------------------------------------------------- # create a demo program that reads in Harwell/Boeing matrices, and run it #------------------------------------------------------------------------------- # the output of "make hb" is in the file umf4.out hb: $(UMFPACK) umf4 readhb readhb_nozeros readhb_size - ./readhb_nozeros < HB/can_24.psa > tmp/A - ./readhb_size < HB/can_24.psa > tmp/Asize - ./umf4 - ./readhb_nozeros < HB/west0067.rua > tmp/A - ./readhb_size < HB/west0067.rua > tmp/Asize - ./umf4 - ./readhb_nozeros < HB/fs_183_6.rua > tmp/A - ./readhb_size < HB/fs_183_6.rua > tmp/Asize - ./umf4 - ./readhb < HB/fs_183_6.rua > tmp/A - ./readhb_size < HB/fs_183_6.rua > tmp/Asize - ./umf4 - ./readhb < HB/arc130.rua > tmp/A - ./readhb_size < HB/arc130.rua > tmp/Asize - ./umf4 - ./readhb_nozeros < HB/arc130.rua > tmp/A - ./readhb_size < HB/arc130.rua > tmp/Asize - ./umf4 - ./readhb_nozeros < HB/arc130.rua > tmp/A - ./readhb_size < HB/arc130.rua > tmp/Asize - ./umf4 a 1e-6 umf4: umf4.c $(UMFPACK) $(C) -o umf4 umf4.c $(UMFPACK) $(LIBS) readhb: readhb.f $(F77) $(F77FLAGS) -o readhb readhb.f $(F77LIB) readhb_size: readhb_size.f $(F77) $(F77FLAGS) -o readhb_size readhb_size.f $(F77LIB) readhb_nozeros: readhb_nozeros.f $(F77) $(F77FLAGS) -o readhb_nozeros readhb_nozeros.f $(F77LIB) #------------------------------------------------------------------------------- # compile the FORTRAN interface and demo #------------------------------------------------------------------------------- fortran: $(UMFPACK) umf4hb.f umf4_f77wrapper.o umf4zhb.f umf4_f77zwrapper.o $(UMFPACK) $(F77) $(F77FLAGS) -o umf4hb umf4hb.f umf4_f77wrapper.o \ $(UMFPACK) $(LIBS) - ./umf4hb < HB/west0067.rua > my_umf4hb.out - diff my_umf4hb.out umf4hb.out $(F77) $(F77FLAGS) -o umf4zhb umf4zhb.f umf4_f77zwrapper.o \ $(UMFPACK) $(LIBS) - ./umf4zhb < HB/qc324.cua > my_umf4zhb.out - diff my_umf4zhb.out umf4zhb.out fortran64: $(UMFPACK) umf4hb64.f umf4_f77wrapper64.o umf4_f77zwrapper64.o $(UMFPACK) $(F77) $(F77FLAGS) -o umf4hb64 umf4hb64.f umf4_f77wrapper64.o \ $(UMFPACK) $(LIBS) - ./umf4hb64 < HB/west0067.rua > my_umf4hb64.out - diff my_umf4hb64.out umf4hb64.out umf4_f77wrapper.o: umf4_f77wrapper.c $(INC) $(C) -c umf4_f77wrapper.c -o umf4_f77wrapper.o umf4_f77zwrapper.o: umf4_f77zwrapper.c $(INC) $(C) -c umf4_f77zwrapper.c -o umf4_f77zwrapper.o umf4_f77wrapper64.o: umf4_f77wrapper.c $(INC) $(C) -DDLONG -c umf4_f77wrapper.c -o umf4_f77wrapper64.o umf4_f77zwrapper64.o: umf4_f77zwrapper.c $(INC) $(C) -DDLONG -c umf4_f77zwrapper.c -o umf4_f77zwrapper64.o #------------------------------------------------------------------------------- # Remove all but the files in the original distribution #------------------------------------------------------------------------------- purge: clean - $(RM) umfpack_simple a.out - $(RM) umfpack_di_demo my_umfpack_di_demo.out - $(RM) umfpack_dl_demo my_umfpack_dl_demo.out - $(RM) umfpack_zi_demo my_umfpack_zi_demo.out - $(RM) umfpack_zl_demo my_umfpack_zl_demo.out - $(RM) umf4hb umf4zhb *.umf my_umf4hb.out - $(RM) umf4hb64 my_umf4hb64.out my_umf4zhb.out - $(RM) umf4 readhb readhb_nozeros readhb_size tmp/* clean: - $(RM) $(CLEAN) SuiteSparse/UMFPACK/Demo/umfpack_simple.c0000644001170100242450000000225610617161021017064 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ #include #include "umfpack.h" int n = 5 ; int Ap [ ] = {0, 2, 5, 9, 10, 12} ; int Ai [ ] = { 0, 1, 0, 2, 4, 1, 2, 3, 4, 2, 1, 4} ; double Ax [ ] = {2., 3., 3., -1., 4., 4., -3., 1., 2., 2., 6., 1.} ; double b [ ] = {8., 45., -3., 3., 19.} ; double x [5] ; int main (void) { double *null = (double *) NULL ; int i ; void *Symbolic, *Numeric ; (void) umfpack_di_symbolic (n, n, Ap, Ai, Ax, &Symbolic, null, null) ; (void) umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric, null, null) ; umfpack_di_free_symbolic (&Symbolic) ; (void) umfpack_di_solve (UMFPACK_A, Ap, Ai, Ax, x, b, Numeric, null, null) ; umfpack_di_free_numeric (&Numeric) ; for (i = 0 ; i < n ; i++) printf ("x [%d] = %g\n", i, x [i]) ; return (0) ; } SuiteSparse/UMFPACK/Demo/readhb_size.f0000644001170100242450000000330710172176356016362 0ustar davisfacc======================================================================= c== readhb_size ======================================================== c======================================================================= c----------------------------------------------------------------------- c UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis. CISE c Dept, Univ. of Florida. All Rights Reserved. See ../Doc/License for c License. web: http://www.cise.ufl.edu/research/sparse/umfpack c----------------------------------------------------------------------- c readhb_size: c read a sparse matrix in the Harwell/Boeing format and output the c size of the matrix (# rows, # columns, and # of entries) c c usage (for example): c c readhb_size < HB/arc130.rua > tmp/Asize integer nz, totcrd, ptrcrd, $ indcrd, valcrd, rhscrd, ncol, nrow, nrhs character title*72, key*30, type*3, ptrfmt*16, $ indfmt*16, valfmt*20, rhsfmt*20 character rhstyp*3 integer nzrhs, nel c----------------------------------------------------------------------- c read header information from Harwell/Boeing matrix read (5, 10, err = 998) $ title, key, $ totcrd, ptrcrd, indcrd, valcrd, rhscrd, $ type, nrow, ncol, nz, nel, $ ptrfmt, indfmt, valfmt, rhsfmt if (rhscrd .gt. 0) then c new Harwell/Boeing format: read (5, 20, err = 998) rhstyp,nrhs,nzrhs endif 10 format (a72, a8 / 5i14 / a3, 11x, 4i14 / 2a16, 2a20) 20 format (a3, 11x, 2i14) write (6, *) nrow, ncol, nz stop 998 write (0, *) 'Read error' stop end SuiteSparse/UMFPACK/Demo/dospd0000755001170100242450000000270510252110540014752 0ustar davisfac#!/bin/csh # usage: dospd file.rsa.gz # # file.rsa.gz is a compressed Harwell/Boeing file containing # a symmetric positive definite matrix # echo '=================================================================' echo 'Matrix:: ' $1:t:r:r echo '3' > tmp/control.umf4 ; # 1: print level echo '0.2' >> tmp/control.umf4 ; # 2: dense row control echo '0.2' >> tmp/control.umf4 ; # 3: dense col control echo '0' >> tmp/control.umf4 ; # 4: pivot tol (offdiag) NON-DEFAULT echo '32' >> tmp/control.umf4 ; # 5: block size echo '3' >> tmp/control.umf4 ; # 6: symmetric strategy, NON-DEFAULT echo '0.7' >> tmp/control.umf4 ; # 7: initial alloc echo '2' >> tmp/control.umf4 ; # 8: max iter. refinement echo '1' >> tmp/control.umf4 ; # 9: echo '0' >> tmp/control.umf4 ; # 10: echo '0' >> tmp/control.umf4 ; # 11: echo '0' >> tmp/control.umf4 ; # 12: echo '0.01' >> tmp/control.umf4 ; # 13: 2-by-2 tolerance echo '0' >> tmp/control.umf4 ; # 14: Q fixed (auto) echo '10' >> tmp/control.umf4 ; # 15: AMD dense row control echo '0' >> tmp/control.umf4 ; # 16: diag pivot tolerance, NON-DEFAULT echo '0' >> tmp/control.umf4 ; # 17: scaling, NON-DEFAULT echo '0.5' >> tmp/control.umf4 ; # 18: frontal matrix alloc. echo '0' >> tmp/control.umf4 ; # 19: drop tolerance echo '1' >> tmp/control.umf4 ; # 20: AMD/COLAMD aggressive absorption zcat $1 | readhb_nozeros > tmp/A zcat $1 | readhb_size > tmp/Asize umf4 s echo '=================================================================' SuiteSparse/UMFPACK/Demo/umf4_f77zwrapper.c0000644001170100242450000004111310617161012017211 0ustar davisfac/* ========================================================================== */ /* === umf4_f77zwrapper ===================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* FORTRAN interface for the C-callable UMFPACK library (complex / int version * only and complex / UF_long versions only). This is HIGHLY non-portable. You * will need to modify this depending on how your FORTRAN and C compilers * behave. * * See umf4z_f77wrapper.c for more information. * * The complex values are provided in two separate arrays. Ax contains the * real part and Az contains the imaginary part. The solution vector is in * x (the real part) and xz (the imaginary part. b is the real part of the * right-hand-side and bz is the imaginary part. Does not support the * packed complex type. */ #include "umfpack.h" #include #include #ifdef NULL #undef NULL #endif #define NULL 0 #define LEN 200 /* -------------------------------------------------------------------------- */ /* integer type: int or UF_long */ /* -------------------------------------------------------------------------- */ #if defined (ZLONG) #define Int UF_long #define UMFPACK_defaults umfpack_zl_defaults #define UMFPACK_free_numeric umfpack_zl_free_numeric #define UMFPACK_free_symbolic umfpack_zl_free_symbolic #define UMFPACK_numeric umfpack_zl_numeric #define UMFPACK_report_control umfpack_zl_report_control #define UMFPACK_report_info umfpack_zl_report_info #define UMFPACK_save_numeric umfpack_zl_save_numeric #define UMFPACK_save_symbolic umfpack_zl_save_symbolic #define UMFPACK_load_numeric umfpack_zl_load_numeric #define UMFPACK_load_symbolic umfpack_zl_load_symbolic #define UMFPACK_scale umfpack_zl_scale #define UMFPACK_solve umfpack_zl_solve #define UMFPACK_symbolic umfpack_zl_symbolic #else #define Int int #define UMFPACK_defaults umfpack_zi_defaults #define UMFPACK_free_numeric umfpack_zi_free_numeric #define UMFPACK_free_symbolic umfpack_zi_free_symbolic #define UMFPACK_numeric umfpack_zi_numeric #define UMFPACK_report_control umfpack_zi_report_control #define UMFPACK_report_info umfpack_zi_report_info #define UMFPACK_save_numeric umfpack_zi_save_numeric #define UMFPACK_save_symbolic umfpack_zi_save_symbolic #define UMFPACK_load_numeric umfpack_zi_load_numeric #define UMFPACK_load_symbolic umfpack_zi_load_symbolic #define UMFPACK_scale umfpack_zi_scale #define UMFPACK_solve umfpack_zi_solve #define UMFPACK_symbolic umfpack_zi_symbolic #endif /* -------------------------------------------------------------------------- */ /* construct a file name from a file number (not user-callable) */ /* -------------------------------------------------------------------------- */ static void make_filename (Int filenum, char *prefix, char *filename) { char *psrc, *pdst ; #ifdef ZLONG sprintf (filename, "%s%ld.umf", prefix, filenum) ; #else sprintf (filename, "%s%d.umf", prefix, filenum) ; #endif /* remove any spaces in the filename */ pdst = filename ; for (psrc = filename ; *psrc ; psrc++) { if (!isspace (*psrc)) *pdst++ = *psrc ; } *pdst = '\0' ; } /* ========================================================================== */ /* === with underscore ====================================================== */ /* ========================================================================== */ /* Solaris, Linux, and SGI IRIX. Probably Compaq Alpha as well. */ /* -------------------------------------------------------------------------- */ /* umf4zdef: set default control parameters */ /* -------------------------------------------------------------------------- */ /* call umf4zdef (control) */ void umf4zdef_ (double Control [UMFPACK_CONTROL]) { UMFPACK_defaults (Control) ; } /* -------------------------------------------------------------------------- */ /* umf4zpcon: print control parameters */ /* -------------------------------------------------------------------------- */ /* call umf4zpcon (control) */ void umf4zpcon_ (double Control [UMFPACK_CONTROL]) { fflush (stdout) ; UMFPACK_report_control (Control) ; fflush (stdout) ; } /* -------------------------------------------------------------------------- */ /* umf4zsym: pre-ordering and symbolic factorization */ /* -------------------------------------------------------------------------- */ /* call umf4zsym (m, n, Ap, Ai, Ax, Az, symbolic, control, info) */ void umf4zsym_ (Int *m, Int *n, Int Ap [ ], Int Ai [ ], double Ax [ ], double Az [ ], void **Symbolic, double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO]) { (void) UMFPACK_symbolic (*m, *n, Ap, Ai, Ax, Az, Symbolic, Control, Info) ; } /* -------------------------------------------------------------------------- */ /* umf4znum: numeric factorization */ /* -------------------------------------------------------------------------- */ /* call umf4znum (Ap, Ai, Ax, Az, symbolic, numeric, control, info) */ void umf4znum_ (Int Ap [ ], Int Ai [ ], double Ax [ ], double Az [ ], void **Symbolic, void **Numeric, double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO]) { (void) UMFPACK_numeric (Ap, Ai, Ax, Az, *Symbolic, Numeric, Control, Info); } /* -------------------------------------------------------------------------- */ /* umf4zsolr: solve a linear system with iterative refinement */ /* -------------------------------------------------------------------------- */ /* call umf4zsolr (sys, Ap, Ai, Ax, Az, x, xz, b, bz, numeric, control, info) */ void umf4zsolr_ (Int *sys, Int Ap [ ], Int Ai [ ], double Ax [ ], double Az [ ], double x [ ], double xz [ ], double b [ ], double bz [ ], void **Numeric, double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO]) { (void) UMFPACK_solve (*sys, Ap, Ai, Ax, Az, x, xz, b, bz, *Numeric, Control, Info) ; } /* -------------------------------------------------------------------------- */ /* umf4zsol: solve a linear system without iterative refinement */ /* -------------------------------------------------------------------------- */ /* call umf4zsol (sys, x, xz, b, bz, numeric, control, info) */ void umf4zsol_ (Int *sys, double x [ ], double xz [ ], double b [ ], double bz [ ], void **Numeric, double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO]) { Control [UMFPACK_IRSTEP] = 0 ; (void) UMFPACK_solve (*sys, (Int *) NULL, (Int *) NULL, (double *) NULL, (double *) NULL, x, xz, b, bz, *Numeric, Control, Info) ; } /* -------------------------------------------------------------------------- */ /* umf4zscal: scale a vector using UMFPACK's scale factors */ /* -------------------------------------------------------------------------- */ /* call umf4zscal (x, xz, b, bz, numeric, status) */ void umf4zscal_ (double x [ ], double xz [ ], double b [ ], double bz [ ], void **Numeric, Int *status) { *status = UMFPACK_scale (x, xz, b, bz, *Numeric) ; } /* -------------------------------------------------------------------------- */ /* umf4zpinf: print info */ /* -------------------------------------------------------------------------- */ /* call umf4zpinf (control) */ void umf4zpinf_ (double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO]) { fflush (stdout) ; UMFPACK_report_info (Control, Info) ; fflush (stdout) ; } /* -------------------------------------------------------------------------- */ /* umf4zfnum: free the Numeric object */ /* -------------------------------------------------------------------------- */ /* call umf4zfnum (numeric) */ void umf4zfnum_ (void **Numeric) { UMFPACK_free_numeric (Numeric) ; } /* -------------------------------------------------------------------------- */ /* umf4zfsym: free the Symbolic object */ /* -------------------------------------------------------------------------- */ /* call umf4zfsym (symbolic) */ void umf4zfsym_ (void **Symbolic) { UMFPACK_free_symbolic (Symbolic) ; } /* -------------------------------------------------------------------------- */ /* umf4zsnum: save the Numeric object to a file */ /* -------------------------------------------------------------------------- */ /* call umf4zsnum (numeric, filenum, status) */ void umf4zsnum_ (void **Numeric, Int *filenum, Int *status) { char filename [LEN] ; make_filename (*filenum, "n", filename) ; *status = UMFPACK_save_numeric (*Numeric, filename) ; } /* -------------------------------------------------------------------------- */ /* umf4zssym: save the Symbolic object to a file */ /* -------------------------------------------------------------------------- */ /* call umf4zssym (symbolic, filenum, status) */ void umf4zssym_ (void **Symbolic, Int *filenum, Int *status) { char filename [LEN] ; make_filename (*filenum, "s", filename) ; *status = UMFPACK_save_symbolic (*Symbolic, filename) ; } /* -------------------------------------------------------------------------- */ /* umf4zlnum: load the Numeric object from a file */ /* -------------------------------------------------------------------------- */ /* call umf4zlnum (numeric, filenum, status) */ void umf4zlnum_ (void **Numeric, Int *filenum, Int *status) { char filename [LEN] ; make_filename (*filenum, "n", filename) ; *status = UMFPACK_load_numeric (Numeric, filename) ; } /* -------------------------------------------------------------------------- */ /* umf4zlsym: load the Symbolic object from a file */ /* -------------------------------------------------------------------------- */ /* call umf4zlsym (symbolic, filenum, status) */ void umf4zlsym_ (void **Symbolic, Int *filenum, Int *status) { char filename [LEN] ; make_filename (*filenum, "s", filename) ; *status = UMFPACK_load_symbolic (Symbolic, filename) ; } /* ========================================================================== */ /* === with no underscore =================================================== */ /* ========================================================================== */ /* IBM AIX. Probably Microsoft Windows and HP Unix as well. */ /* -------------------------------------------------------------------------- */ /* umf4zdef: set default control parameters */ /* -------------------------------------------------------------------------- */ /* call umf4zdef (control) */ void umf4zdef (double Control [UMFPACK_CONTROL]) { UMFPACK_defaults (Control) ; } /* -------------------------------------------------------------------------- */ /* umf4zpcon: print control parameters */ /* -------------------------------------------------------------------------- */ /* call umf4zpcon (control) */ void umf4zpcon (double Control [UMFPACK_CONTROL]) { fflush (stdout) ; UMFPACK_report_control (Control) ; fflush (stdout) ; } /* -------------------------------------------------------------------------- */ /* umf4zsym: pre-ordering and symbolic factorization */ /* -------------------------------------------------------------------------- */ /* call umf4zsym (m, n, Ap, Ai, Ax, Az, symbolic, control, info) */ void umf4zsym (Int *m, Int *n, Int Ap [ ], Int Ai [ ], double Ax [ ], double Az [ ], void **Symbolic, double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO]) { (void) UMFPACK_symbolic (*m, *n, Ap, Ai, Ax, Az, Symbolic, Control, Info) ; } /* -------------------------------------------------------------------------- */ /* umf4znum: numeric factorization */ /* -------------------------------------------------------------------------- */ /* call umf4znum (Ap, Ai, Ax, Az, symbolic, numeric, control, info) */ void umf4znum (Int Ap [ ], Int Ai [ ], double Ax [ ], double Az [ ], void **Symbolic, void **Numeric, double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO]) { (void) UMFPACK_numeric (Ap, Ai, Ax, Az, *Symbolic, Numeric, Control, Info); } /* -------------------------------------------------------------------------- */ /* umf4zsolr: solve a linear system with iterative refinement */ /* -------------------------------------------------------------------------- */ /* call umf4zsolr (sys, Ap, Ai, Ax, Az, x, xz, b, bz, numeric, control, info) */ void umf4zsolr (Int *sys, Int Ap [ ], Int Ai [ ], double Ax [ ], double Az [ ], double x [ ], double xz [ ], double b [ ], double bz [ ], void **Numeric, double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO]) { (void) UMFPACK_solve (*sys, Ap, Ai, Ax, Az, x, xz, b, bz, *Numeric, Control, Info) ; } /* -------------------------------------------------------------------------- */ /* umf4zsol: solve a linear system without iterative refinement */ /* -------------------------------------------------------------------------- */ /* call umf4zsol (sys, x, xz, b, bz, numeric, control, info) */ void umf4zsol (Int *sys, double x [ ], double xz [ ], double b [ ], double bz [ ], void **Numeric, double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO]) { Control [UMFPACK_IRSTEP] = 0 ; (void) UMFPACK_solve (*sys, (Int *) NULL, (Int *) NULL, (double *) NULL, (double *) NULL, x, xz, b, bz, *Numeric, Control, Info) ; } /* -------------------------------------------------------------------------- */ /* umf4zscal: scale a vector using UMFPACK's scale factors */ /* -------------------------------------------------------------------------- */ /* call umf4zscal (x, xz, b, bz, numeric, status) */ void umf4zscal (double x [ ], double xz [ ], double b [ ], double bz [ ], void **Numeric, Int *status) { *status = UMFPACK_scale (x, xz, b, bz, *Numeric) ; } /* -------------------------------------------------------------------------- */ /* umf4zpinf: print info */ /* -------------------------------------------------------------------------- */ /* call umf4zpinf (control) */ void umf4zpinf (double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO]) { fflush (stdout) ; UMFPACK_report_info (Control, Info) ; fflush (stdout) ; } /* -------------------------------------------------------------------------- */ /* umf4zfnum: free the Numeric object */ /* -------------------------------------------------------------------------- */ /* call umf4zfnum (numeric) */ void umf4zfnum (void **Numeric) { UMFPACK_free_numeric (Numeric) ; } /* -------------------------------------------------------------------------- */ /* umf4zfsym: free the Symbolic object */ /* -------------------------------------------------------------------------- */ /* call umf4zfsym (symbolic) */ void umf4zfsym (void **Symbolic) { UMFPACK_free_symbolic (Symbolic) ; } /* -------------------------------------------------------------------------- */ /* umf4zsnum: save the Numeric object to a file */ /* -------------------------------------------------------------------------- */ /* call umf4zsnum (numeric, filenum, status) */ void umf4zsnum (void **Numeric, Int *filenum, Int *status) { char filename [LEN] ; make_filename (*filenum, "n", filename) ; *status = UMFPACK_save_numeric (*Numeric, filename) ; } /* -------------------------------------------------------------------------- */ /* umf4zssym: save the Symbolic object to a file */ /* -------------------------------------------------------------------------- */ /* call umf4zssym (symbolic, filenum, status) */ void umf4zssym (void **Symbolic, Int *filenum, Int *status) { char filename [LEN] ; make_filename (*filenum, "s", filename) ; *status = UMFPACK_save_symbolic (*Symbolic, filename) ; } /* -------------------------------------------------------------------------- */ /* umf4zlnum: load the Numeric object from a file */ /* -------------------------------------------------------------------------- */ /* call umf4zlnum (numeric, filenum, status) */ void umf4zlnum (void **Numeric, Int *filenum, Int *status) { char filename [LEN] ; make_filename (*filenum, "n", filename) ; *status = UMFPACK_load_numeric (Numeric, filename) ; } /* -------------------------------------------------------------------------- */ /* umf4zlsym: load the Symbolic object from a file */ /* -------------------------------------------------------------------------- */ /* call umf4zlsym (symbolic, filenum, status) */ void umf4zlsym (void **Symbolic, Int *filenum, Int *status) { char filename [LEN] ; make_filename (*filenum, "s", filename) ; *status = UMFPACK_load_symbolic (Symbolic, filename) ; } SuiteSparse/UMFPACK/Demo/umfpack_dl_demo.c0000644001170100242450000006465410617501641017216 0ustar davisfac/* ========================================================================== */ /* === umfpack_dl_demo ====================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* A demo of UMFPACK: umfpack_dl_* version. First, factor and solve a 5-by-5 system, Ax=b, using default parameters. Then solve A'x=b using the factors of A. Modify one entry (A (1,4) = 0, where the row and column indices range from 0 to 4. The pattern of A has not changed (it has explicitly zero entry), so a reanalysis with umfpack_dl_symbolic does not need to be done. Refactorize (with umfpack_dl_numeric), and solve Ax=b. Note that the pivot ordering has changed. Next, change all of the entries in A, but not the pattern. Finally, compute C = A', and do the symbolic and numeric factorization of C. Factorizing A' can sometimes be better than factorizing A itself (less work and memory usage). Solve C'x=b twice; the solution is the same as the solution to Ax=b. A note about zero-sized arrays: UMFPACK uses many user-provided arrays of size n (order of the matrix), and of size nz (the number of nonzeros in a matrix). n cannot be zero; UMFPACK does not handle zero-dimensioned arrays. However, nz can be zero. If you attempt to malloc an array of size nz = 0, however, malloc will return a null pointer which UMFPACK will report as a "missing argument." Thus, nz1 in this code is set to MAX (nz,1), and similarly for lnz and unz. Lnz can never be zero, however, since L is always unit diagonal. */ /* -------------------------------------------------------------------------- */ /* definitions */ /* -------------------------------------------------------------------------- */ #include #include #include "umfpack.h" #define ABS(x) ((x) >= 0 ? (x) : -(x)) #define MAX(a,b) (((a) > (b)) ? (a) : (b)) #ifndef TRUE #define TRUE (1) #endif #ifndef FALSE #define FALSE (0) #endif /* -------------------------------------------------------------------------- */ /* triplet form of the matrix. The triplets can be in any order. */ /* -------------------------------------------------------------------------- */ static UF_long n = 5, nz = 12 ; static UF_long Arow [ ] = { 0, 4, 1, 1, 2, 2, 0, 1, 2, 3, 4, 4} ; static UF_long Acol [ ] = { 0, 4, 0, 2, 1, 2, 1, 4, 3, 2, 1, 2} ; static double Aval [ ] = {2., 1., 3., 4., -1., -3., 3., 6., 2., 1., 4., 2.} ; static double b [ ] = {8., 45., -3., 3., 19.}, x [5], r [5] ; /* -------------------------------------------------------------------------- */ /* error: print a message and exit */ /* -------------------------------------------------------------------------- */ static void error ( char *message ) { printf ("\n\n====== error: %s =====\n\n", message) ; exit (1) ; } /* -------------------------------------------------------------------------- */ /* resid: compute the residual, r = Ax-b or r = A'x=b and return maxnorm (r) */ /* -------------------------------------------------------------------------- */ static double resid ( UF_long transpose, UF_long Ap [ ], UF_long Ai [ ], double Ax [ ] ) { UF_long i, j, p ; double norm ; for (i = 0 ; i < n ; i++) { r [i] = -b [i] ; } if (transpose) { for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; r [j] += Ax [p] * x [i] ; } } } else { for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; r [i] += Ax [p] * x [j] ; } } } norm = 0. ; for (i = 0 ; i < n ; i++) { norm = MAX (ABS (r [i]), norm) ; } return (norm) ; } /* -------------------------------------------------------------------------- */ /* main program */ /* -------------------------------------------------------------------------- */ int main (int argc, char **argv) { double Info [UMFPACK_INFO], Control [UMFPACK_CONTROL], *Ax, *Cx, *Lx, *Ux, *W, t [2], *Dx, rnorm, *Rb, *y, *Rs ; UF_long *Ap, *Ai, *Cp, *Ci, row, col, p, lnz, unz, nr, nc, *Lp, *Li, *Ui, *Up, *P, *Q, *Lj, i, j, k, anz, nfr, nchains, *Qinit, fnpiv, lnz1, unz1, nz1, status, *Front_npivcol, *Front_parent, *Chain_start, *Wi, *Pinit, n1, *Chain_maxrows, *Chain_maxcols, *Front_1strow, *Front_leftmostdesc, nzud, do_recip ; void *Symbolic, *Numeric ; /* ---------------------------------------------------------------------- */ /* initializations */ /* ---------------------------------------------------------------------- */ umfpack_tic (t) ; printf ("\nUMFPACK V%d.%d (%s) demo: _dl_ version\n", UMFPACK_MAIN_VERSION, UMFPACK_SUB_VERSION, UMFPACK_DATE) ; /* get the default control parameters */ umfpack_dl_defaults (Control) ; /* change the default print level for this demo */ /* (otherwise, nothing will print) */ Control [UMFPACK_PRL] = 6 ; /* print the license agreement */ umfpack_dl_report_status (Control, UMFPACK_OK) ; Control [UMFPACK_PRL] = 5 ; /* print the control parameters */ umfpack_dl_report_control (Control) ; /* ---------------------------------------------------------------------- */ /* print A and b, and convert A to column-form */ /* ---------------------------------------------------------------------- */ /* print the right-hand-side */ printf ("\nb: ") ; (void) umfpack_dl_report_vector (n, b, Control) ; /* print the triplet form of the matrix */ printf ("\nA: ") ; (void) umfpack_dl_report_triplet (n, n, nz, Arow, Acol, Aval, Control) ; /* convert to column form */ nz1 = MAX (nz,1) ; /* ensure arrays are not of size zero. */ Ap = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Ai = (UF_long *) malloc (nz1 * sizeof (UF_long)) ; Ax = (double *) malloc (nz1 * sizeof (double)) ; if (!Ap || !Ai || !Ax) { error ("out of memory") ; } status = umfpack_dl_triplet_to_col (n, n, nz, Arow, Acol, Aval, Ap, Ai, Ax, (UF_long *) NULL) ; if (status < 0) { umfpack_dl_report_status (Control, status) ; error ("umfpack_dl_triplet_to_col failed") ; } /* print the column-form of A */ printf ("\nA: ") ; (void) umfpack_dl_report_matrix (n, n, Ap, Ai, Ax, 1, Control) ; /* ---------------------------------------------------------------------- */ /* symbolic factorization */ /* ---------------------------------------------------------------------- */ status = umfpack_dl_symbolic (n, n, Ap, Ai, Ax, &Symbolic, Control, Info) ; if (status < 0) { umfpack_dl_report_info (Control, Info) ; umfpack_dl_report_status (Control, status) ; error ("umfpack_dl_symbolic failed") ; } /* print the symbolic factorization */ printf ("\nSymbolic factorization of A: ") ; (void) umfpack_dl_report_symbolic (Symbolic, Control) ; /* ---------------------------------------------------------------------- */ /* numeric factorization */ /* ---------------------------------------------------------------------- */ status = umfpack_dl_numeric (Ap, Ai, Ax, Symbolic, &Numeric, Control, Info) ; if (status < 0) { umfpack_dl_report_info (Control, Info) ; umfpack_dl_report_status (Control, status) ; error ("umfpack_dl_numeric failed") ; } /* print the numeric factorization */ printf ("\nNumeric factorization of A: ") ; (void) umfpack_dl_report_numeric (Numeric, Control) ; /* ---------------------------------------------------------------------- */ /* solve Ax=b */ /* ---------------------------------------------------------------------- */ status = umfpack_dl_solve (UMFPACK_A, Ap, Ai, Ax, x, b, Numeric, Control, Info) ; umfpack_dl_report_info (Control, Info) ; umfpack_dl_report_status (Control, status) ; if (status < 0) { error ("umfpack_dl_solve failed") ; } printf ("\nx (solution of Ax=b): ") ; (void) umfpack_dl_report_vector (n, x, Control) ; rnorm = resid (FALSE, Ap, Ai, Ax) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* compute the determinant */ /* ---------------------------------------------------------------------- */ status = umfpack_dl_get_determinant (x, r, Numeric, Info) ; umfpack_dl_report_status (Control, status) ; if (status < 0) { error ("umfpack_dl_get_determinant failed") ; } printf ("determinant: (%g", x [0]) ; printf (") * 10^(%g)\n", r [0]) ; /* ---------------------------------------------------------------------- */ /* solve Ax=b, broken down into steps */ /* ---------------------------------------------------------------------- */ /* Rb = R*b */ Rb = (double *) malloc (n * sizeof (double)) ; y = (double *) malloc (n * sizeof (double)) ; if (!Rb || !y) error ("out of memory") ; status = umfpack_dl_scale (Rb, b, Numeric) ; if (status < 0) error ("umfpack_dl_scale failed") ; /* solve Ly = P*(Rb) */ status = umfpack_dl_solve (UMFPACK_Pt_L, Ap, Ai, Ax, y, Rb, Numeric, Control, Info) ; if (status < 0) error ("umfpack_dl_solve failed") ; /* solve UQ'x=y */ status = umfpack_dl_solve (UMFPACK_U_Qt, Ap, Ai, Ax, x, y, Numeric, Control, Info) ; if (status < 0) error ("umfpack_dl_solve failed") ; printf ("\nx (solution of Ax=b, solve is split into 3 steps): ") ; (void) umfpack_dl_report_vector (n, x, Control) ; rnorm = resid (FALSE, Ap, Ai, Ax) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; free (Rb) ; free (y) ; /* ---------------------------------------------------------------------- */ /* solve A'x=b */ /* ---------------------------------------------------------------------- */ status = umfpack_dl_solve (UMFPACK_At, Ap, Ai, Ax, x, b, Numeric, Control, Info) ; umfpack_dl_report_info (Control, Info) ; if (status < 0) { error ("umfpack_dl_solve failed") ; } printf ("\nx (solution of A'x=b): ") ; (void) umfpack_dl_report_vector (n, x, Control) ; rnorm = resid (TRUE, Ap, Ai, Ax) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* modify one numerical value in the column-form of A */ /* ---------------------------------------------------------------------- */ /* change A (1,4), look for row index 1 in column 4. */ row = 1 ; col = 4 ; for (p = Ap [col] ; p < Ap [col+1] ; p++) { if (row == Ai [p]) { printf ("\nchanging A (%ld,%ld) to zero\n", row, col) ; Ax [p] = 0.0 ; break ; } } printf ("\nmodified A: ") ; (void) umfpack_dl_report_matrix (n, n, Ap, Ai, Ax, 1, Control) ; /* ---------------------------------------------------------------------- */ /* redo the numeric factorization */ /* ---------------------------------------------------------------------- */ /* The pattern (Ap and Ai) hasn't changed, so the symbolic factorization */ /* doesn't have to be redone, no matter how much we change Ax. */ /* We don't need the Numeric object any more, so free it. */ umfpack_dl_free_numeric (&Numeric) ; /* Note that a memory leak would have occurred if the old Numeric */ /* had not been free'd with umfpack_dl_free_numeric above. */ status = umfpack_dl_numeric (Ap, Ai, Ax, Symbolic, &Numeric, Control, Info) ; if (status < 0) { umfpack_dl_report_info (Control, Info) ; umfpack_dl_report_status (Control, status) ; error ("umfpack_dl_numeric failed") ; } printf ("\nNumeric factorization of modified A: ") ; (void) umfpack_dl_report_numeric (Numeric, Control) ; /* ---------------------------------------------------------------------- */ /* solve Ax=b, with the modified A */ /* ---------------------------------------------------------------------- */ status = umfpack_dl_solve (UMFPACK_A, Ap, Ai, Ax, x, b, Numeric, Control, Info) ; umfpack_dl_report_info (Control, Info) ; if (status < 0) { umfpack_dl_report_status (Control, status) ; error ("umfpack_dl_solve failed") ; } printf ("\nx (with modified A): ") ; (void) umfpack_dl_report_vector (n, x, Control) ; rnorm = resid (FALSE, Ap, Ai, Ax) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* modify all of the numerical values of A, but not the pattern */ /* ---------------------------------------------------------------------- */ for (col = 0 ; col < n ; col++) { for (p = Ap [col] ; p < Ap [col+1] ; p++) { row = Ai [p] ; printf ("changing ") ; printf ("A (%ld,%ld) from %g", row, col, Ax [p]) ; Ax [p] = Ax [p] + col*10 - row ; printf (" to %g\n", Ax [p]) ; } } printf ("\ncompletely modified A (same pattern): ") ; (void) umfpack_dl_report_matrix (n, n, Ap, Ai, Ax, 1, Control) ; /* ---------------------------------------------------------------------- */ /* save the Symbolic object to file, free it, and load it back in */ /* ---------------------------------------------------------------------- */ /* use the default filename, "symbolic.umf" */ printf ("\nSaving symbolic object:\n") ; status = umfpack_dl_save_symbolic (Symbolic, (char *) NULL) ; if (status < 0) { umfpack_dl_report_status (Control, status) ; error ("umfpack_dl_save_symbolic failed") ; } printf ("\nFreeing symbolic object:\n") ; umfpack_dl_free_symbolic (&Symbolic) ; printf ("\nLoading symbolic object:\n") ; status = umfpack_dl_load_symbolic (&Symbolic, (char *) NULL) ; if (status < 0) { umfpack_dl_report_status (Control, status) ; error ("umfpack_dl_load_symbolic failed") ; } printf ("\nDone loading symbolic object\n") ; /* ---------------------------------------------------------------------- */ /* redo the numeric factorization */ /* ---------------------------------------------------------------------- */ umfpack_dl_free_numeric (&Numeric) ; status = umfpack_dl_numeric (Ap, Ai, Ax, Symbolic, &Numeric, Control, Info) ; if (status < 0) { umfpack_dl_report_info (Control, Info) ; umfpack_dl_report_status (Control, status) ; error ("umfpack_dl_numeric failed") ; } printf ("\nNumeric factorization of completely modified A: ") ; (void) umfpack_dl_report_numeric (Numeric, Control) ; /* ---------------------------------------------------------------------- */ /* solve Ax=b, with the modified A */ /* ---------------------------------------------------------------------- */ status = umfpack_dl_solve (UMFPACK_A, Ap, Ai, Ax, x, b, Numeric, Control, Info) ; umfpack_dl_report_info (Control, Info) ; if (status < 0) { umfpack_dl_report_status (Control, status) ; error ("umfpack_dl_solve failed") ; } printf ("\nx (with completely modified A): ") ; (void) umfpack_dl_report_vector (n, x, Control) ; rnorm = resid (FALSE, Ap, Ai, Ax) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* free the symbolic and numeric factorization */ /* ---------------------------------------------------------------------- */ umfpack_dl_free_symbolic (&Symbolic) ; umfpack_dl_free_numeric (&Numeric) ; /* ---------------------------------------------------------------------- */ /* C = transpose of A */ /* ---------------------------------------------------------------------- */ Cp = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Ci = (UF_long *) malloc (nz1 * sizeof (UF_long)) ; Cx = (double *) malloc (nz1 * sizeof (double)) ; if (!Cp || !Ci || !Cx) { error ("out of memory") ; } status = umfpack_dl_transpose (n, n, Ap, Ai, Ax, (UF_long *) NULL, (UF_long *) NULL, Cp, Ci, Cx) ; if (status < 0) { umfpack_dl_report_status (Control, status) ; error ("umfpack_dl_transpose failed: ") ; } printf ("\nC (transpose of A): ") ; (void) umfpack_dl_report_matrix (n, n, Cp, Ci, Cx, 1, Control) ; /* ---------------------------------------------------------------------- */ /* symbolic factorization of C */ /* ---------------------------------------------------------------------- */ status = umfpack_dl_symbolic (n, n, Cp, Ci, Cx, &Symbolic, Control, Info) ; if (status < 0) { umfpack_dl_report_info (Control, Info) ; umfpack_dl_report_status (Control, status) ; error ("umfpack_dl_symbolic failed") ; } printf ("\nSymbolic factorization of C: ") ; (void) umfpack_dl_report_symbolic (Symbolic, Control) ; /* ---------------------------------------------------------------------- */ /* copy the contents of Symbolic into user arrays print them */ /* ---------------------------------------------------------------------- */ printf ("\nGet the contents of the Symbolic object for C:\n") ; printf ("(compare with umfpack_dl_report_symbolic output, above)\n") ; Pinit = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Qinit = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Front_npivcol = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Front_1strow = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Front_leftmostdesc = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Front_parent = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Chain_start = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Chain_maxrows = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Chain_maxcols = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; if (!Pinit || !Qinit || !Front_npivcol || !Front_parent || !Chain_start || !Chain_maxrows || !Chain_maxcols || !Front_1strow || !Front_leftmostdesc) { error ("out of memory") ; } status = umfpack_dl_get_symbolic (&nr, &nc, &n1, &anz, &nfr, &nchains, Pinit, Qinit, Front_npivcol, Front_parent, Front_1strow, Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ; if (status < 0) { error ("symbolic factorization invalid") ; } printf ("From the Symbolic object, C is of dimension %ld-by-%ld\n", nr, nc); printf (" with nz = %ld, number of fronts = %ld,\n", nz, nfr) ; printf (" number of frontal matrix chains = %ld\n", nchains) ; printf ("\nPivot columns in each front, and parent of each front:\n") ; k = 0 ; for (i = 0 ; i < nfr ; i++) { fnpiv = Front_npivcol [i] ; printf (" Front %ld: parent front: %ld number of pivot cols: %ld\n", i, Front_parent [i], fnpiv) ; for (j = 0 ; j < fnpiv ; j++) { col = Qinit [k] ; printf ( " %ld-th pivot column is column %ld in original matrix\n", k, col) ; k++ ; } } printf ("\nNote that the column ordering, above, will be refined\n") ; printf ("in the numeric factorization below. The assignment of pivot\n") ; printf ("columns to frontal matrices will always remain unchanged.\n") ; printf ("\nTotal number of pivot columns in frontal matrices: %ld\n", k) ; printf ("\nFrontal matrix chains:\n") ; for (j = 0 ; j < nchains ; j++) { printf (" Frontal matrices %ld to %ld are factorized in a single\n", Chain_start [j], Chain_start [j+1] - 1) ; printf (" working array of size %ld-by-%ld\n", Chain_maxrows [j], Chain_maxcols [j]) ; } /* ---------------------------------------------------------------------- */ /* numeric factorization of C */ /* ---------------------------------------------------------------------- */ status = umfpack_dl_numeric (Cp, Ci, Cx, Symbolic, &Numeric, Control, Info) ; if (status < 0) { error ("umfpack_dl_numeric failed") ; } printf ("\nNumeric factorization of C: ") ; (void) umfpack_dl_report_numeric (Numeric, Control) ; /* ---------------------------------------------------------------------- */ /* extract the LU factors of C and print them */ /* ---------------------------------------------------------------------- */ if (umfpack_dl_get_lunz (&lnz, &unz, &nr, &nc, &nzud, Numeric) < 0) { error ("umfpack_dl_get_lunz failed") ; } /* ensure arrays are not of zero size */ lnz1 = MAX (lnz,1) ; unz1 = MAX (unz,1) ; Lp = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Lj = (UF_long *) malloc (lnz1 * sizeof (UF_long)) ; Lx = (double *) malloc (lnz1 * sizeof (double)) ; Up = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Ui = (UF_long *) malloc (unz1 * sizeof (UF_long)) ; Ux = (double *) malloc (unz1 * sizeof (double)) ; P = (UF_long *) malloc (n * sizeof (UF_long)) ; Q = (UF_long *) malloc (n * sizeof (UF_long)) ; Dx = (double *) NULL ; /* D vector not requested */ Rs = (double *) malloc (n * sizeof (double)) ; if (!Lp || !Lj || !Lx || !Up || !Ui || !Ux || !P || !Q || !Rs) { error ("out of memory") ; } status = umfpack_dl_get_numeric (Lp, Lj, Lx, Up, Ui, Ux, P, Q, Dx, &do_recip, Rs, Numeric) ; if (status < 0) { error ("umfpack_dl_get_numeric failed") ; } printf ("\nL (lower triangular factor of C): ") ; (void) umfpack_dl_report_matrix (n, n, Lp, Lj, Lx, 0, Control) ; printf ("\nU (upper triangular factor of C): ") ; (void) umfpack_dl_report_matrix (n, n, Up, Ui, Ux, 1, Control) ; printf ("\nP: ") ; (void) umfpack_dl_report_perm (n, P, Control) ; printf ("\nQ: ") ; (void) umfpack_dl_report_perm (n, Q, Control) ; printf ("\nScale factors: row i of A is to be ") ; if (do_recip) { printf ("multiplied by the ith scale factor\n") ; } else { printf ("divided by the ith scale factor\n") ; } for (i = 0 ; i < n ; i++) printf ("%ld: %g\n", i, Rs [i]) ; /* ---------------------------------------------------------------------- */ /* convert L to triplet form and print it */ /* ---------------------------------------------------------------------- */ /* Note that L is in row-form, so it is the row indices that are created */ /* by umfpack_dl_col_to_triplet. */ printf ("\nConverting L to triplet form, and printing it:\n") ; Li = (UF_long *) malloc (lnz1 * sizeof (UF_long)) ; if (!Li) { error ("out of memory") ; } if (umfpack_dl_col_to_triplet (n, Lp, Li) < 0) { error ("umfpack_dl_col_to_triplet failed") ; } printf ("\nL, in triplet form: ") ; (void) umfpack_dl_report_triplet (n, n, lnz, Li, Lj, Lx, Control) ; /* ---------------------------------------------------------------------- */ /* save the Numeric object to file, free it, and load it back in */ /* ---------------------------------------------------------------------- */ /* use the default filename, "numeric.umf" */ printf ("\nSaving numeric object:\n") ; status = umfpack_dl_save_numeric (Numeric, (char *) NULL) ; if (status < 0) { umfpack_dl_report_status (Control, status) ; error ("umfpack_dl_save_numeric failed") ; } printf ("\nFreeing numeric object:\n") ; umfpack_dl_free_numeric (&Numeric) ; printf ("\nLoading numeric object:\n") ; status = umfpack_dl_load_numeric (&Numeric, (char *) NULL) ; if (status < 0) { umfpack_dl_report_status (Control, status) ; error ("umfpack_dl_load_numeric failed") ; } printf ("\nDone loading numeric object\n") ; /* ---------------------------------------------------------------------- */ /* solve C'x=b */ /* ---------------------------------------------------------------------- */ status = umfpack_dl_solve (UMFPACK_At, Cp, Ci, Cx, x, b, Numeric, Control, Info) ; umfpack_dl_report_info (Control, Info) ; if (status < 0) { umfpack_dl_report_status (Control, status) ; error ("umfpack_dl_solve failed") ; } printf ("\nx (solution of C'x=b): ") ; (void) umfpack_dl_report_vector (n, x, Control) ; rnorm = resid (TRUE, Cp, Ci, Cx) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* solve C'x=b again, using umfpack_dl_wsolve instead */ /* ---------------------------------------------------------------------- */ printf ("\nSolving C'x=b again, using umfpack_dl_wsolve instead:\n") ; Wi = (UF_long *) malloc (n * sizeof (UF_long)) ; W = (double *) malloc (5*n * sizeof (double)) ; if (!Wi || !W) { error ("out of memory") ; } status = umfpack_dl_wsolve (UMFPACK_At, Cp, Ci, Cx, x, b, Numeric, Control, Info, Wi, W) ; umfpack_dl_report_info (Control, Info) ; if (status < 0) { umfpack_dl_report_status (Control, status) ; error ("umfpack_dl_wsolve failed") ; } printf ("\nx (solution of C'x=b): ") ; (void) umfpack_dl_report_vector (n, x, Control) ; rnorm = resid (TRUE, Cp, Ci, Cx) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* free everything */ /* ---------------------------------------------------------------------- */ /* This is not strictly required since the process is exiting and the */ /* system will reclaim the memory anyway. It's useful, though, just as */ /* a list of what is currently malloc'ed by this program. Plus, it's */ /* always a good habit to explicitly free whatever you malloc. */ free (Ap) ; free (Ai) ; free (Ax) ; free (Cp) ; free (Ci) ; free (Cx) ; free (Pinit) ; free (Qinit) ; free (Front_npivcol) ; free (Front_1strow) ; free (Front_leftmostdesc) ; free (Front_parent) ; free (Chain_start) ; free (Chain_maxrows) ; free (Chain_maxcols) ; free (Lp) ; free (Lj) ; free (Lx) ; free (Up) ; free (Ui) ; free (Ux) ; free (P) ; free (Q) ; free (Li) ; free (Wi) ; free (W) ; umfpack_dl_free_symbolic (&Symbolic) ; umfpack_dl_free_numeric (&Numeric) ; /* ---------------------------------------------------------------------- */ /* print the total time spent in this demo */ /* ---------------------------------------------------------------------- */ umfpack_toc (t) ; printf ("\numfpack_dl_demo complete.\nTotal time: %5.2f seconds" " (CPU time), %5.2f seconds (wallclock time)\n", t [1], t [0]) ; return (0) ; } SuiteSparse/UMFPACK/Demo/dodefault0000755001170100242450000000267310252126302015617 0ustar davisfac#!/bin/csh # usage: dodefault file.rsa.gz # # file.rsa.gz is a compressed Harwell/Boeing file containing # a symmetric positive definite matrix # echo '=================================================================' echo 'Matrix:: ' $1:t:r:r echo '3' > tmp/control.umf4 ; # 1: print level echo '0.2' >> tmp/control.umf4 ; # 2: dense row control echo '0.2' >> tmp/control.umf4 ; # 3: dense col control echo '0.1' >> tmp/control.umf4 ; # 4: pivot tol (offdiag) DEFAULT echo '32' >> tmp/control.umf4 ; # 5: block size echo '0' >> tmp/control.umf4 ; # 6: auto strategy, DEFAULT echo '0.7' >> tmp/control.umf4 ; # 7: initial alloc echo '2' >> tmp/control.umf4 ; # 8: max iter. refinement echo '1' >> tmp/control.umf4 ; # 9: echo '0' >> tmp/control.umf4 ; # 10: echo '0' >> tmp/control.umf4 ; # 11: echo '0' >> tmp/control.umf4 ; # 12: echo '0.01' >> tmp/control.umf4 ; # 13: 2-by-2 tolerance echo '0' >> tmp/control.umf4 ; # 14: Q fixed (auto) echo '10' >> tmp/control.umf4 ; # 15: AMD dense row control echo '0.001' >> tmp/control.umf4 ; # 16: diag pivot tolerance DEFAULT echo '0' >> tmp/control.umf4 ; # 17: scaling, NON-DEFAULT echo '0.5' >> tmp/control.umf4 ; # 18: frontal matrix alloc. echo '0' >> tmp/control.umf4 ; # 19: drop tolerance echo '1' >> tmp/control.umf4 ; # 20: AMD/COLAMD aggressive absorption zcat $1 | readhb_nozeros > tmp/A zcat $1 | readhb_size > tmp/Asize umf4 echo '=================================================================' SuiteSparse/UMFPACK/Demo/umf4hb64.out0000644001170100242450000001436410711433440016016 0ustar davisfac Matrix key: WEST0067 UMFPACK V5.2.0 (Nov 1, 2007), Control: Matrix entry defined as: double Int (generic integer) defined as: UF_long 0: print level: 2 1: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 2: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 3: pivot tolerance: 0.1 4: block size for dense matrix kernels: 32 5: strategy: 0 (auto) 6: initial allocation ratio: 0.7 7: max iterative refinement steps: 2 12: 2-by-2 pivot tolerance: 0.01 13: Q fixed during numerical factorization: 0 (auto) 14: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 15: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 16: scaling: 1 (divide each row by sum of abs. values in each row) 17: frontal matrix allocation ratio: 0.5 18: drop tolerance: 0 19: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4 9: compiled for ANSI C 10: CPU timer is POSIX times ( ) routine. 11: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 UF_long: 8 Int: 8 pointer: 8 double: 8 Entry: 8 (in bytes) symbolic analysis: status: 0. time: 0.00E+00 (sec) estimates (upper bound) for numeric LU: size of LU: 0.02 (MB) memory needed: 0.08 (MB) flop count: 0.14E+05 nnz (L): 542. nnz (U): 902. numeric factorization: status: 0. time: 0.00E+00 actual numeric LU statistics: size of LU: 0.01 (MB) memory needed: 0.06 (MB) flop count: 0.25E+04 nnz (L): 323. nnz (U): 339. UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: UF_long BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 67 number of columns in matrix A: 67 entries in matrix A: 294 memory usage reported in: 16-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 1 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S not square or diagonal not preserved symbolic factorization defragmentations: 1 symbolic memory usage (Units): 1595 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 241 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 6.59006e+00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 1517 1448 95% peak size (Units) 3917 2423 62% final size (Units) 981 435 44% Numeric final size (Units) 1381 802 58% Numeric final size (MBytes) 0.0 0.0 58% peak memory usage (Units) 5133 3639 71% peak memory usage (MBytes) 0.1 0.1 71% numeric factorization flops 1.41920e+04 2.50100e+03 18% nz in L (incl diagonal) 542 323 60% nz in U (incl diagonal) 902 339 38% nz in L+U (incl diagonal) 1377 595 43% largest front (# entries) 483 80 17% largest # rows in front 21 10 48% largest # columns in front 23 11 48% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 323 nz in U (incl diagonal), if none dropped 339 number of small entries dropped 0 nonzeros on diagonal of U: 67 min abs. value on diagonal of U: 2.74e-02 max abs. value on diagonal of U: 2.28e+00 estimate of reciprocal of condition number: 1.20e-02 indices in compressed pattern: 249 numerical values stored in Numeric object: 605 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 1.19000e+03 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 3.69100e+03 norm (A*x-b): 3.10862447E-15 norm (A*x-b): 2.13162821E-14 norm (A*x-b): 2.13162821E-14 SuiteSparse/UMFPACK/Demo/umfpack_di_demo.c0000644001170100242450000006430410617501641017203 0ustar davisfac/* ========================================================================== */ /* === umfpack_di_demo ====================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* A demo of UMFPACK: umfpack_di_* version. First, factor and solve a 5-by-5 system, Ax=b, using default parameters. Then solve A'x=b using the factors of A. Modify one entry (A (1,4) = 0, where the row and column indices range from 0 to 4. The pattern of A has not changed (it has explicitly zero entry), so a reanalysis with umfpack_di_symbolic does not need to be done. Refactorize (with umfpack_di_numeric), and solve Ax=b. Note that the pivot ordering has changed. Next, change all of the entries in A, but not the pattern. Finally, compute C = A', and do the symbolic and numeric factorization of C. Factorizing A' can sometimes be better than factorizing A itself (less work and memory usage). Solve C'x=b twice; the solution is the same as the solution to Ax=b. A note about zero-sized arrays: UMFPACK uses many user-provided arrays of size n (order of the matrix), and of size nz (the number of nonzeros in a matrix). n cannot be zero; UMFPACK does not handle zero-dimensioned arrays. However, nz can be zero. If you attempt to malloc an array of size nz = 0, however, malloc will return a null pointer which UMFPACK will report as a "missing argument." Thus, nz1 in this code is set to MAX (nz,1), and similarly for lnz and unz. Lnz can never be zero, however, since L is always unit diagonal. */ /* -------------------------------------------------------------------------- */ /* definitions */ /* -------------------------------------------------------------------------- */ #include #include #include "umfpack.h" #define ABS(x) ((x) >= 0 ? (x) : -(x)) #define MAX(a,b) (((a) > (b)) ? (a) : (b)) #ifndef TRUE #define TRUE (1) #endif #ifndef FALSE #define FALSE (0) #endif /* -------------------------------------------------------------------------- */ /* triplet form of the matrix. The triplets can be in any order. */ /* -------------------------------------------------------------------------- */ static int n = 5, nz = 12 ; static int Arow [ ] = { 0, 4, 1, 1, 2, 2, 0, 1, 2, 3, 4, 4} ; static int Acol [ ] = { 0, 4, 0, 2, 1, 2, 1, 4, 3, 2, 1, 2} ; static double Aval [ ] = {2., 1., 3., 4., -1., -3., 3., 6., 2., 1., 4., 2.} ; static double b [ ] = {8., 45., -3., 3., 19.}, x [5], r [5] ; /* -------------------------------------------------------------------------- */ /* error: print a message and exit */ /* -------------------------------------------------------------------------- */ static void error ( char *message ) { printf ("\n\n====== error: %s =====\n\n", message) ; exit (1) ; } /* -------------------------------------------------------------------------- */ /* resid: compute the residual, r = Ax-b or r = A'x=b and return maxnorm (r) */ /* -------------------------------------------------------------------------- */ static double resid ( int transpose, int Ap [ ], int Ai [ ], double Ax [ ] ) { int i, j, p ; double norm ; for (i = 0 ; i < n ; i++) { r [i] = -b [i] ; } if (transpose) { for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; r [j] += Ax [p] * x [i] ; } } } else { for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; r [i] += Ax [p] * x [j] ; } } } norm = 0. ; for (i = 0 ; i < n ; i++) { norm = MAX (ABS (r [i]), norm) ; } return (norm) ; } /* -------------------------------------------------------------------------- */ /* main program */ /* -------------------------------------------------------------------------- */ int main (int argc, char **argv) { double Info [UMFPACK_INFO], Control [UMFPACK_CONTROL], *Ax, *Cx, *Lx, *Ux, *W, t [2], *Dx, rnorm, *Rb, *y, *Rs ; int *Ap, *Ai, *Cp, *Ci, row, col, p, lnz, unz, nr, nc, *Lp, *Li, *Ui, *Up, *P, *Q, *Lj, i, j, k, anz, nfr, nchains, *Qinit, fnpiv, lnz1, unz1, nz1, status, *Front_npivcol, *Front_parent, *Chain_start, *Wi, *Pinit, n1, *Chain_maxrows, *Chain_maxcols, *Front_1strow, *Front_leftmostdesc, nzud, do_recip ; void *Symbolic, *Numeric ; /* ---------------------------------------------------------------------- */ /* initializations */ /* ---------------------------------------------------------------------- */ umfpack_tic (t) ; printf ("\nUMFPACK V%d.%d (%s) demo: _di_ version\n", UMFPACK_MAIN_VERSION, UMFPACK_SUB_VERSION, UMFPACK_DATE) ; /* get the default control parameters */ umfpack_di_defaults (Control) ; /* change the default print level for this demo */ /* (otherwise, nothing will print) */ Control [UMFPACK_PRL] = 6 ; /* print the license agreement */ umfpack_di_report_status (Control, UMFPACK_OK) ; Control [UMFPACK_PRL] = 5 ; /* print the control parameters */ umfpack_di_report_control (Control) ; /* ---------------------------------------------------------------------- */ /* print A and b, and convert A to column-form */ /* ---------------------------------------------------------------------- */ /* print the right-hand-side */ printf ("\nb: ") ; (void) umfpack_di_report_vector (n, b, Control) ; /* print the triplet form of the matrix */ printf ("\nA: ") ; (void) umfpack_di_report_triplet (n, n, nz, Arow, Acol, Aval, Control) ; /* convert to column form */ nz1 = MAX (nz,1) ; /* ensure arrays are not of size zero. */ Ap = (int *) malloc ((n+1) * sizeof (int)) ; Ai = (int *) malloc (nz1 * sizeof (int)) ; Ax = (double *) malloc (nz1 * sizeof (double)) ; if (!Ap || !Ai || !Ax) { error ("out of memory") ; } status = umfpack_di_triplet_to_col (n, n, nz, Arow, Acol, Aval, Ap, Ai, Ax, (int *) NULL) ; if (status < 0) { umfpack_di_report_status (Control, status) ; error ("umfpack_di_triplet_to_col failed") ; } /* print the column-form of A */ printf ("\nA: ") ; (void) umfpack_di_report_matrix (n, n, Ap, Ai, Ax, 1, Control) ; /* ---------------------------------------------------------------------- */ /* symbolic factorization */ /* ---------------------------------------------------------------------- */ status = umfpack_di_symbolic (n, n, Ap, Ai, Ax, &Symbolic, Control, Info) ; if (status < 0) { umfpack_di_report_info (Control, Info) ; umfpack_di_report_status (Control, status) ; error ("umfpack_di_symbolic failed") ; } /* print the symbolic factorization */ printf ("\nSymbolic factorization of A: ") ; (void) umfpack_di_report_symbolic (Symbolic, Control) ; /* ---------------------------------------------------------------------- */ /* numeric factorization */ /* ---------------------------------------------------------------------- */ status = umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric, Control, Info) ; if (status < 0) { umfpack_di_report_info (Control, Info) ; umfpack_di_report_status (Control, status) ; error ("umfpack_di_numeric failed") ; } /* print the numeric factorization */ printf ("\nNumeric factorization of A: ") ; (void) umfpack_di_report_numeric (Numeric, Control) ; /* ---------------------------------------------------------------------- */ /* solve Ax=b */ /* ---------------------------------------------------------------------- */ status = umfpack_di_solve (UMFPACK_A, Ap, Ai, Ax, x, b, Numeric, Control, Info) ; umfpack_di_report_info (Control, Info) ; umfpack_di_report_status (Control, status) ; if (status < 0) { error ("umfpack_di_solve failed") ; } printf ("\nx (solution of Ax=b): ") ; (void) umfpack_di_report_vector (n, x, Control) ; rnorm = resid (FALSE, Ap, Ai, Ax) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* compute the determinant */ /* ---------------------------------------------------------------------- */ status = umfpack_di_get_determinant (x, r, Numeric, Info) ; umfpack_di_report_status (Control, status) ; if (status < 0) { error ("umfpack_di_get_determinant failed") ; } printf ("determinant: (%g", x [0]) ; printf (") * 10^(%g)\n", r [0]) ; /* ---------------------------------------------------------------------- */ /* solve Ax=b, broken down into steps */ /* ---------------------------------------------------------------------- */ /* Rb = R*b */ Rb = (double *) malloc (n * sizeof (double)) ; y = (double *) malloc (n * sizeof (double)) ; if (!Rb || !y) error ("out of memory") ; status = umfpack_di_scale (Rb, b, Numeric) ; if (status < 0) error ("umfpack_di_scale failed") ; /* solve Ly = P*(Rb) */ status = umfpack_di_solve (UMFPACK_Pt_L, Ap, Ai, Ax, y, Rb, Numeric, Control, Info) ; if (status < 0) error ("umfpack_di_solve failed") ; /* solve UQ'x=y */ status = umfpack_di_solve (UMFPACK_U_Qt, Ap, Ai, Ax, x, y, Numeric, Control, Info) ; if (status < 0) error ("umfpack_di_solve failed") ; printf ("\nx (solution of Ax=b, solve is split into 3 steps): ") ; (void) umfpack_di_report_vector (n, x, Control) ; rnorm = resid (FALSE, Ap, Ai, Ax) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; free (Rb) ; free (y) ; /* ---------------------------------------------------------------------- */ /* solve A'x=b */ /* ---------------------------------------------------------------------- */ status = umfpack_di_solve (UMFPACK_At, Ap, Ai, Ax, x, b, Numeric, Control, Info) ; umfpack_di_report_info (Control, Info) ; if (status < 0) { error ("umfpack_di_solve failed") ; } printf ("\nx (solution of A'x=b): ") ; (void) umfpack_di_report_vector (n, x, Control) ; rnorm = resid (TRUE, Ap, Ai, Ax) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* modify one numerical value in the column-form of A */ /* ---------------------------------------------------------------------- */ /* change A (1,4), look for row index 1 in column 4. */ row = 1 ; col = 4 ; for (p = Ap [col] ; p < Ap [col+1] ; p++) { if (row == Ai [p]) { printf ("\nchanging A (%d,%d) to zero\n", row, col) ; Ax [p] = 0.0 ; break ; } } printf ("\nmodified A: ") ; (void) umfpack_di_report_matrix (n, n, Ap, Ai, Ax, 1, Control) ; /* ---------------------------------------------------------------------- */ /* redo the numeric factorization */ /* ---------------------------------------------------------------------- */ /* The pattern (Ap and Ai) hasn't changed, so the symbolic factorization */ /* doesn't have to be redone, no matter how much we change Ax. */ /* We don't need the Numeric object any more, so free it. */ umfpack_di_free_numeric (&Numeric) ; /* Note that a memory leak would have occurred if the old Numeric */ /* had not been free'd with umfpack_di_free_numeric above. */ status = umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric, Control, Info) ; if (status < 0) { umfpack_di_report_info (Control, Info) ; umfpack_di_report_status (Control, status) ; error ("umfpack_di_numeric failed") ; } printf ("\nNumeric factorization of modified A: ") ; (void) umfpack_di_report_numeric (Numeric, Control) ; /* ---------------------------------------------------------------------- */ /* solve Ax=b, with the modified A */ /* ---------------------------------------------------------------------- */ status = umfpack_di_solve (UMFPACK_A, Ap, Ai, Ax, x, b, Numeric, Control, Info) ; umfpack_di_report_info (Control, Info) ; if (status < 0) { umfpack_di_report_status (Control, status) ; error ("umfpack_di_solve failed") ; } printf ("\nx (with modified A): ") ; (void) umfpack_di_report_vector (n, x, Control) ; rnorm = resid (FALSE, Ap, Ai, Ax) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* modify all of the numerical values of A, but not the pattern */ /* ---------------------------------------------------------------------- */ for (col = 0 ; col < n ; col++) { for (p = Ap [col] ; p < Ap [col+1] ; p++) { row = Ai [p] ; printf ("changing ") ; printf ("A (%d,%d) from %g", row, col, Ax [p]) ; Ax [p] = Ax [p] + col*10 - row ; printf (" to %g\n", Ax [p]) ; } } printf ("\ncompletely modified A (same pattern): ") ; (void) umfpack_di_report_matrix (n, n, Ap, Ai, Ax, 1, Control) ; /* ---------------------------------------------------------------------- */ /* save the Symbolic object to file, free it, and load it back in */ /* ---------------------------------------------------------------------- */ /* use the default filename, "symbolic.umf" */ printf ("\nSaving symbolic object:\n") ; status = umfpack_di_save_symbolic (Symbolic, (char *) NULL) ; if (status < 0) { umfpack_di_report_status (Control, status) ; error ("umfpack_di_save_symbolic failed") ; } printf ("\nFreeing symbolic object:\n") ; umfpack_di_free_symbolic (&Symbolic) ; printf ("\nLoading symbolic object:\n") ; status = umfpack_di_load_symbolic (&Symbolic, (char *) NULL) ; if (status < 0) { umfpack_di_report_status (Control, status) ; error ("umfpack_di_load_symbolic failed") ; } printf ("\nDone loading symbolic object\n") ; /* ---------------------------------------------------------------------- */ /* redo the numeric factorization */ /* ---------------------------------------------------------------------- */ umfpack_di_free_numeric (&Numeric) ; status = umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric, Control, Info) ; if (status < 0) { umfpack_di_report_info (Control, Info) ; umfpack_di_report_status (Control, status) ; error ("umfpack_di_numeric failed") ; } printf ("\nNumeric factorization of completely modified A: ") ; (void) umfpack_di_report_numeric (Numeric, Control) ; /* ---------------------------------------------------------------------- */ /* solve Ax=b, with the modified A */ /* ---------------------------------------------------------------------- */ status = umfpack_di_solve (UMFPACK_A, Ap, Ai, Ax, x, b, Numeric, Control, Info) ; umfpack_di_report_info (Control, Info) ; if (status < 0) { umfpack_di_report_status (Control, status) ; error ("umfpack_di_solve failed") ; } printf ("\nx (with completely modified A): ") ; (void) umfpack_di_report_vector (n, x, Control) ; rnorm = resid (FALSE, Ap, Ai, Ax) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* free the symbolic and numeric factorization */ /* ---------------------------------------------------------------------- */ umfpack_di_free_symbolic (&Symbolic) ; umfpack_di_free_numeric (&Numeric) ; /* ---------------------------------------------------------------------- */ /* C = transpose of A */ /* ---------------------------------------------------------------------- */ Cp = (int *) malloc ((n+1) * sizeof (int)) ; Ci = (int *) malloc (nz1 * sizeof (int)) ; Cx = (double *) malloc (nz1 * sizeof (double)) ; if (!Cp || !Ci || !Cx) { error ("out of memory") ; } status = umfpack_di_transpose (n, n, Ap, Ai, Ax, (int *) NULL, (int *) NULL, Cp, Ci, Cx) ; if (status < 0) { umfpack_di_report_status (Control, status) ; error ("umfpack_di_transpose failed: ") ; } printf ("\nC (transpose of A): ") ; (void) umfpack_di_report_matrix (n, n, Cp, Ci, Cx, 1, Control) ; /* ---------------------------------------------------------------------- */ /* symbolic factorization of C */ /* ---------------------------------------------------------------------- */ status = umfpack_di_symbolic (n, n, Cp, Ci, Cx, &Symbolic, Control, Info) ; if (status < 0) { umfpack_di_report_info (Control, Info) ; umfpack_di_report_status (Control, status) ; error ("umfpack_di_symbolic failed") ; } printf ("\nSymbolic factorization of C: ") ; (void) umfpack_di_report_symbolic (Symbolic, Control) ; /* ---------------------------------------------------------------------- */ /* copy the contents of Symbolic into user arrays print them */ /* ---------------------------------------------------------------------- */ printf ("\nGet the contents of the Symbolic object for C:\n") ; printf ("(compare with umfpack_di_report_symbolic output, above)\n") ; Pinit = (int *) malloc ((n+1) * sizeof (int)) ; Qinit = (int *) malloc ((n+1) * sizeof (int)) ; Front_npivcol = (int *) malloc ((n+1) * sizeof (int)) ; Front_1strow = (int *) malloc ((n+1) * sizeof (int)) ; Front_leftmostdesc = (int *) malloc ((n+1) * sizeof (int)) ; Front_parent = (int *) malloc ((n+1) * sizeof (int)) ; Chain_start = (int *) malloc ((n+1) * sizeof (int)) ; Chain_maxrows = (int *) malloc ((n+1) * sizeof (int)) ; Chain_maxcols = (int *) malloc ((n+1) * sizeof (int)) ; if (!Pinit || !Qinit || !Front_npivcol || !Front_parent || !Chain_start || !Chain_maxrows || !Chain_maxcols || !Front_1strow || !Front_leftmostdesc) { error ("out of memory") ; } status = umfpack_di_get_symbolic (&nr, &nc, &n1, &anz, &nfr, &nchains, Pinit, Qinit, Front_npivcol, Front_parent, Front_1strow, Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ; if (status < 0) { error ("symbolic factorization invalid") ; } printf ("From the Symbolic object, C is of dimension %d-by-%d\n", nr, nc); printf (" with nz = %d, number of fronts = %d,\n", nz, nfr) ; printf (" number of frontal matrix chains = %d\n", nchains) ; printf ("\nPivot columns in each front, and parent of each front:\n") ; k = 0 ; for (i = 0 ; i < nfr ; i++) { fnpiv = Front_npivcol [i] ; printf (" Front %d: parent front: %d number of pivot cols: %d\n", i, Front_parent [i], fnpiv) ; for (j = 0 ; j < fnpiv ; j++) { col = Qinit [k] ; printf ( " %d-th pivot column is column %d in original matrix\n", k, col) ; k++ ; } } printf ("\nNote that the column ordering, above, will be refined\n") ; printf ("in the numeric factorization below. The assignment of pivot\n") ; printf ("columns to frontal matrices will always remain unchanged.\n") ; printf ("\nTotal number of pivot columns in frontal matrices: %d\n", k) ; printf ("\nFrontal matrix chains:\n") ; for (j = 0 ; j < nchains ; j++) { printf (" Frontal matrices %d to %d are factorized in a single\n", Chain_start [j], Chain_start [j+1] - 1) ; printf (" working array of size %d-by-%d\n", Chain_maxrows [j], Chain_maxcols [j]) ; } /* ---------------------------------------------------------------------- */ /* numeric factorization of C */ /* ---------------------------------------------------------------------- */ status = umfpack_di_numeric (Cp, Ci, Cx, Symbolic, &Numeric, Control, Info) ; if (status < 0) { error ("umfpack_di_numeric failed") ; } printf ("\nNumeric factorization of C: ") ; (void) umfpack_di_report_numeric (Numeric, Control) ; /* ---------------------------------------------------------------------- */ /* extract the LU factors of C and print them */ /* ---------------------------------------------------------------------- */ if (umfpack_di_get_lunz (&lnz, &unz, &nr, &nc, &nzud, Numeric) < 0) { error ("umfpack_di_get_lunz failed") ; } /* ensure arrays are not of zero size */ lnz1 = MAX (lnz,1) ; unz1 = MAX (unz,1) ; Lp = (int *) malloc ((n+1) * sizeof (int)) ; Lj = (int *) malloc (lnz1 * sizeof (int)) ; Lx = (double *) malloc (lnz1 * sizeof (double)) ; Up = (int *) malloc ((n+1) * sizeof (int)) ; Ui = (int *) malloc (unz1 * sizeof (int)) ; Ux = (double *) malloc (unz1 * sizeof (double)) ; P = (int *) malloc (n * sizeof (int)) ; Q = (int *) malloc (n * sizeof (int)) ; Dx = (double *) NULL ; /* D vector not requested */ Rs = (double *) malloc (n * sizeof (double)) ; if (!Lp || !Lj || !Lx || !Up || !Ui || !Ux || !P || !Q || !Rs) { error ("out of memory") ; } status = umfpack_di_get_numeric (Lp, Lj, Lx, Up, Ui, Ux, P, Q, Dx, &do_recip, Rs, Numeric) ; if (status < 0) { error ("umfpack_di_get_numeric failed") ; } printf ("\nL (lower triangular factor of C): ") ; (void) umfpack_di_report_matrix (n, n, Lp, Lj, Lx, 0, Control) ; printf ("\nU (upper triangular factor of C): ") ; (void) umfpack_di_report_matrix (n, n, Up, Ui, Ux, 1, Control) ; printf ("\nP: ") ; (void) umfpack_di_report_perm (n, P, Control) ; printf ("\nQ: ") ; (void) umfpack_di_report_perm (n, Q, Control) ; printf ("\nScale factors: row i of A is to be ") ; if (do_recip) { printf ("multiplied by the ith scale factor\n") ; } else { printf ("divided by the ith scale factor\n") ; } for (i = 0 ; i < n ; i++) printf ("%d: %g\n", i, Rs [i]) ; /* ---------------------------------------------------------------------- */ /* convert L to triplet form and print it */ /* ---------------------------------------------------------------------- */ /* Note that L is in row-form, so it is the row indices that are created */ /* by umfpack_di_col_to_triplet. */ printf ("\nConverting L to triplet form, and printing it:\n") ; Li = (int *) malloc (lnz1 * sizeof (int)) ; if (!Li) { error ("out of memory") ; } if (umfpack_di_col_to_triplet (n, Lp, Li) < 0) { error ("umfpack_di_col_to_triplet failed") ; } printf ("\nL, in triplet form: ") ; (void) umfpack_di_report_triplet (n, n, lnz, Li, Lj, Lx, Control) ; /* ---------------------------------------------------------------------- */ /* save the Numeric object to file, free it, and load it back in */ /* ---------------------------------------------------------------------- */ /* use the default filename, "numeric.umf" */ printf ("\nSaving numeric object:\n") ; status = umfpack_di_save_numeric (Numeric, (char *) NULL) ; if (status < 0) { umfpack_di_report_status (Control, status) ; error ("umfpack_di_save_numeric failed") ; } printf ("\nFreeing numeric object:\n") ; umfpack_di_free_numeric (&Numeric) ; printf ("\nLoading numeric object:\n") ; status = umfpack_di_load_numeric (&Numeric, (char *) NULL) ; if (status < 0) { umfpack_di_report_status (Control, status) ; error ("umfpack_di_load_numeric failed") ; } printf ("\nDone loading numeric object\n") ; /* ---------------------------------------------------------------------- */ /* solve C'x=b */ /* ---------------------------------------------------------------------- */ status = umfpack_di_solve (UMFPACK_At, Cp, Ci, Cx, x, b, Numeric, Control, Info) ; umfpack_di_report_info (Control, Info) ; if (status < 0) { umfpack_di_report_status (Control, status) ; error ("umfpack_di_solve failed") ; } printf ("\nx (solution of C'x=b): ") ; (void) umfpack_di_report_vector (n, x, Control) ; rnorm = resid (TRUE, Cp, Ci, Cx) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* solve C'x=b again, using umfpack_di_wsolve instead */ /* ---------------------------------------------------------------------- */ printf ("\nSolving C'x=b again, using umfpack_di_wsolve instead:\n") ; Wi = (int *) malloc (n * sizeof (int)) ; W = (double *) malloc (5*n * sizeof (double)) ; if (!Wi || !W) { error ("out of memory") ; } status = umfpack_di_wsolve (UMFPACK_At, Cp, Ci, Cx, x, b, Numeric, Control, Info, Wi, W) ; umfpack_di_report_info (Control, Info) ; if (status < 0) { umfpack_di_report_status (Control, status) ; error ("umfpack_di_wsolve failed") ; } printf ("\nx (solution of C'x=b): ") ; (void) umfpack_di_report_vector (n, x, Control) ; rnorm = resid (TRUE, Cp, Ci, Cx) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* free everything */ /* ---------------------------------------------------------------------- */ /* This is not strictly required since the process is exiting and the */ /* system will reclaim the memory anyway. It's useful, though, just as */ /* a list of what is currently malloc'ed by this program. Plus, it's */ /* always a good habit to explicitly free whatever you malloc. */ free (Ap) ; free (Ai) ; free (Ax) ; free (Cp) ; free (Ci) ; free (Cx) ; free (Pinit) ; free (Qinit) ; free (Front_npivcol) ; free (Front_1strow) ; free (Front_leftmostdesc) ; free (Front_parent) ; free (Chain_start) ; free (Chain_maxrows) ; free (Chain_maxcols) ; free (Lp) ; free (Lj) ; free (Lx) ; free (Up) ; free (Ui) ; free (Ux) ; free (P) ; free (Q) ; free (Li) ; free (Wi) ; free (W) ; umfpack_di_free_symbolic (&Symbolic) ; umfpack_di_free_numeric (&Numeric) ; /* ---------------------------------------------------------------------- */ /* print the total time spent in this demo */ /* ---------------------------------------------------------------------- */ umfpack_toc (t) ; printf ("\numfpack_di_demo complete.\nTotal time: %5.2f seconds" " (CPU time), %5.2f seconds (wallclock time)\n", t [1], t [0]) ; return (0) ; } SuiteSparse/UMFPACK/Demo/readhb_nozeros.f0000644001170100242450000000757210172176352017113 0ustar davisfacc======================================================================= c== readhb_nozeros ===================================================== c======================================================================= c----------------------------------------------------------------------- c UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis. CISE c Dept, Univ. of Florida. All Rights Reserved. See ../Doc/License for c License. web: http://www.cise.ufl.edu/research/sparse/umfpack c----------------------------------------------------------------------- c readhb_nozeros: c read a sparse matrix in the Harwell/Boeing format and c output a matrix in triplet format. c Identical to readhb, except that this version removes explicit c zero entries from the matrix. c c usage (for example): c c in a Unix shell: c readhb_nozeros < HB/arc130.rua > tmp/A c c Then, in MATLAB, you can do the following: c >> load tmp/A c >> A = spconvert (A) ; c >> spy (A) integer nzmax, nmax parameter (nzmax = 10000000, nmax = 250000) integer Ptr (nmax), Index (nzmax), n, nz, totcrd, ptrcrd, $ indcrd, valcrd, rhscrd, ncol, nrow, nrhs, row, col, p character title*72, key*30, type*3, ptrfmt*16, $ indfmt*16, valfmt*20, rhsfmt*20 logical sym double precision Value (nzmax), skew character rhstyp*3 integer nzrhs, nel integer ne, nnz c----------------------------------------------------------------------- c read header information from Harwell/Boeing matrix read (5, 10, err = 998) $ title, key, $ totcrd, ptrcrd, indcrd, valcrd, rhscrd, $ type, nrow, ncol, nz, nel, $ ptrfmt, indfmt, valfmt, rhsfmt if (rhscrd .gt. 0) then c new Harwell/Boeing format: read (5, 20, err = 998) rhstyp,nrhs,nzrhs endif 10 format (a72, a8 / 5i14 / a3, 11x, 4i14 / 2a16, 2a20) 20 format (a3, 11x, 2i14) skew = 0.0 if (type (2:2) .eq. 'Z' .or. type (2:2) .eq. 'z') skew = -1.0 if (type (2:2) .eq. 'S' .or. type (2:2) .eq. 's') skew = 1.0 sym = skew .ne. 0.0 write (0, 31) key 31 format ('Matrix key: ', a8) n = max (nrow, ncol) if (n .ge. nmax .or. nz .gt. nzmax) then write (0, *) 'Matrix too big!' write (0, *) '(recompile readhb_nozeros.f with larger', $ ' nzmax, nmax)' stop endif read (5, ptrfmt, err = 998) (Ptr (p), p = 1, ncol+1) read (5, indfmt, err = 998) (Index (p), p = 1, nz) do 55 col = ncol+2, n+1 Ptr (col) = Ptr (ncol+1) 55 continue c read the values if (valcrd .gt. 0) then read (5, valfmt, err = 998) (Value (p), p = 1, nz) else do 50 p = 1, nz Value (p) = 1 50 continue endif c create the triplet form of the input matrix ne = 0 nnz = 0 do 100 col = 1, n do 90 p = Ptr (col), Ptr (col+1) - 1 row = Index (p) c remove zeros, to compare fairly with LU in MATLAB c (MATLAB always removes explicit zeros) ne = ne + 1 if (Value (p) .ne. 0) then nnz = nnz + 1 write (6, 200) row, col, Value (p) endif if (sym .and. row .ne. col) then ne = ne + 1 if (Value (p) .ne. 0) then nnz = nnz + 1 write (6, 200) col, row, skew * Value (p) endif endif 90 continue 100 continue 200 format (2i7, e30.18e3) c write (0,*) 'Number of entries: ',ne,' True nonzeros: ', nnz stop 998 write (0,*) 'Read error: Harwell/Boeing matrix' stop end SuiteSparse/UMFPACK/Demo/umf4_f77wrapper.c0000644001170100242450000004566410617161007017042 0ustar davisfac/* ========================================================================== */ /* === umf4_f77wrapper ====================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* FORTRAN interface for the C-callable UMFPACK library (double / int version * only and double / UF_long versions only). This is HIGHLY non-portable. You * will need to modify this depending on how your FORTRAN and C compilers * behave. This has been tested in Linux, Sun Solaris, SGI IRIX, and IBM AIX, * with various compilers. It has not been exhaustively tested on all possible * combinations of C and FORTRAN compilers. The UF_long version works on * Solaris, SGI IRIX, and IBM AIX when the UMFPACK library is compiled in * 64-bit mode. * * Only a subset of UMFPACK's capabilities are provided. Refer to the UMFPACK * User Guide for details. * * For some C and FORTRAN compilers, the FORTRAN compiler appends a single * underscore ("_") after each routine name. C doesn't do this, so the * translation is made here. Other FORTRAN compilers treat underscores * differently. For example, a FORTRAN call to a_b gets translated to a call * to a_b__ by g77, and to a_b_ by most other FORTRAN compilers. Thus, the * FORTRAN names here do not use underscores. The xlf compiler in IBM AIX * doesn't add an underscore. * * The matrix A is passed to UMFPACK in compressed column form, with 0-based * indices. In FORTRAN, for an m-by-n matrix A with nz entries, the row * indices of the first column (column 1) are in Ai (Ap (1) + 1 ... Ap (2)), * with values in Ax (Ap (1) + 1 ... Ap (2)). The last column (column n) is * in Ai (Ap (n) + 1 ... Ap (n+1)) and Ax (Ap (n) + 1 ... Ap (n+1)). The row * indices in Ai are in the range 0 to m-1. They must be sorted, with no * duplicate entries allowed. Refer to umfpack_di_triplet_to_col for a more * flexible format for the input matrix. The following defintions apply * for each of the routines in this file: * * integer m, n, Ap (n+1), Ai (nz), symbolic, numeric, filenum, status * double precision Ax (nz), control (20), info (90), x (n), b (n) * * UMFPACK's status is returned in either a status argument, or in info (1). * It is zero if everything is OK, 1 if the matrix is singular (this is a * warning, not an error), and negative if an error occurred. See umfpack.h * for more details on the contents of the control and info arrays, and the * value of the sys argument. * * For the Numeric and Symbolic handles, it's probably safe to assume that a * FORTRAN integer is sufficient to store a C pointer. If that doesn't work, * try defining numeric and symbolic as integer arrays of size 2, or as * integer*8, in the FORTRAN routine that calls these wrapper routines. * The latter is required on Solaris, SGI IRIX, and IBM AIX when UMFPACK is * compiled in 64-bit mode. * * If you want to use 64-bit integers, try compiling this file with the -DDLONG * compiler option (via "make fortran64"). First modify your UFconfig.mk * file to compile UMFPACK in LP64 mode (see the User Guide for details). * Your FORTRAN code should use integer*8. See umf4hb64.f for an example. * * Tested with the following compilers: * * Solaris with cc and f77 from Sun WorkShop 6 update 1 * (32-bit and 64-bit modes) * * SGI Irix with MIPSpro cc and f77 compilers version 7.4 * (32-bit and 64-bit modes) * * Linux with GNU gcc and Intel's icc, and GNU g77 and Intel's * ifc FORTRAN compiler. See the comments above about g77 and * underscores. Only supports 32-bit mode. * * IBM AIX xlc and xlf compilers. * (32-bit and 64-bit modes) * * This interface files when using the ABSOFT Fortran compiler on both * Linux and Windows. There is no known fix. */ #include "umfpack.h" #include #include #ifdef NULL #undef NULL #endif #define NULL 0 #define LEN 200 /* -------------------------------------------------------------------------- */ /* integer type: int or UF_long */ /* -------------------------------------------------------------------------- */ #if defined (DLONG) #define Int UF_long #define UMFPACK_defaults umfpack_dl_defaults #define UMFPACK_free_numeric umfpack_dl_free_numeric #define UMFPACK_free_symbolic umfpack_dl_free_symbolic #define UMFPACK_numeric umfpack_dl_numeric #define UMFPACK_report_control umfpack_dl_report_control #define UMFPACK_report_info umfpack_dl_report_info #define UMFPACK_save_numeric umfpack_dl_save_numeric #define UMFPACK_save_symbolic umfpack_dl_save_symbolic #define UMFPACK_load_numeric umfpack_dl_load_numeric #define UMFPACK_load_symbolic umfpack_dl_load_symbolic #define UMFPACK_scale umfpack_dl_scale #define UMFPACK_solve umfpack_dl_solve #define UMFPACK_symbolic umfpack_dl_symbolic #else #define Int int #define UMFPACK_defaults umfpack_di_defaults #define UMFPACK_free_numeric umfpack_di_free_numeric #define UMFPACK_free_symbolic umfpack_di_free_symbolic #define UMFPACK_numeric umfpack_di_numeric #define UMFPACK_report_control umfpack_di_report_control #define UMFPACK_report_info umfpack_di_report_info #define UMFPACK_save_numeric umfpack_di_save_numeric #define UMFPACK_save_symbolic umfpack_di_save_symbolic #define UMFPACK_load_numeric umfpack_di_load_numeric #define UMFPACK_load_symbolic umfpack_di_load_symbolic #define UMFPACK_scale umfpack_di_scale #define UMFPACK_solve umfpack_di_solve #define UMFPACK_symbolic umfpack_di_symbolic #endif /* -------------------------------------------------------------------------- */ /* construct a file name from a file number (not user-callable) */ /* -------------------------------------------------------------------------- */ static void make_filename (Int filenum, char *prefix, char *filename) { char *psrc, *pdst ; #ifdef DLONG sprintf (filename, "%s%ld.umf", prefix, filenum) ; #else sprintf (filename, "%s%d.umf", prefix, filenum) ; #endif /* remove any spaces in the filename */ pdst = filename ; for (psrc = filename ; *psrc ; psrc++) { if (!isspace (*psrc)) *pdst++ = *psrc ; } *pdst = '\0' ; } /* ========================================================================== */ /* === with underscore ====================================================== */ /* ========================================================================== */ /* Solaris, Linux, and SGI IRIX. Probably Compaq Alpha as well. */ /* -------------------------------------------------------------------------- */ /* umf4def: set default control parameters */ /* -------------------------------------------------------------------------- */ /* call umf4def (control) */ void umf4def_ (double Control [UMFPACK_CONTROL]) { UMFPACK_defaults (Control) ; } /* -------------------------------------------------------------------------- */ /* umf4pcon: print control parameters */ /* -------------------------------------------------------------------------- */ /* call umf4pcon (control) */ void umf4pcon_ (double Control [UMFPACK_CONTROL]) { fflush (stdout) ; UMFPACK_report_control (Control) ; fflush (stdout) ; } /* -------------------------------------------------------------------------- */ /* umf4sym: pre-ordering and symbolic factorization */ /* -------------------------------------------------------------------------- */ /* call umf4sym (m, n, Ap, Ai, Ax, symbolic, control, info) */ void umf4sym_ (Int *m, Int *n, Int Ap [ ], Int Ai [ ], double Ax [ ], void **Symbolic, double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO]) { (void) UMFPACK_symbolic (*m, *n, Ap, Ai, Ax, Symbolic, Control, Info) ; } /* -------------------------------------------------------------------------- */ /* umf4num: numeric factorization */ /* -------------------------------------------------------------------------- */ /* call umf4num (Ap, Ai, Ax, symbolic, numeric, control, info) */ void umf4num_ (Int Ap [ ], Int Ai [ ], double Ax [ ], void **Symbolic, void **Numeric, double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO]) { (void) UMFPACK_numeric (Ap, Ai, Ax, *Symbolic, Numeric, Control, Info); } /* -------------------------------------------------------------------------- */ /* umf4solr: solve a linear system with iterative refinement */ /* -------------------------------------------------------------------------- */ /* call umf4solr (sys, Ap, Ai, Ax, x, b, numeric, control, info) */ void umf4solr_ (Int *sys, Int Ap [ ], Int Ai [ ], double Ax [ ], double x [ ], double b [ ], void **Numeric, double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO]) { (void) UMFPACK_solve (*sys, Ap, Ai, Ax, x, b, *Numeric, Control, Info) ; } /* -------------------------------------------------------------------------- */ /* umf4sol: solve a linear system without iterative refinement */ /* -------------------------------------------------------------------------- */ /* call umf4sol (sys, x, b, numeric, control, info) */ void umf4sol_ (Int *sys, double x [ ], double b [ ], void **Numeric, double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO]) { Control [UMFPACK_IRSTEP] = 0 ; (void) UMFPACK_solve (*sys, (Int *) NULL, (Int *) NULL, (double *) NULL, x, b, *Numeric, Control, Info) ; } /* -------------------------------------------------------------------------- */ /* umf4scal: scale a vector using UMFPACK's scale factors */ /* -------------------------------------------------------------------------- */ /* call umf4scal (x, b, numeric, status) */ void umf4scal_ (double x [ ], double b [ ], void **Numeric, Int *status) { *status = UMFPACK_scale (x, b, *Numeric) ; } /* -------------------------------------------------------------------------- */ /* umf4pinf: print info */ /* -------------------------------------------------------------------------- */ /* call umf4pinf (control) */ void umf4pinf_ (double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO]) { fflush (stdout) ; UMFPACK_report_info (Control, Info) ; fflush (stdout) ; } /* -------------------------------------------------------------------------- */ /* umf4fnum: free the Numeric object */ /* -------------------------------------------------------------------------- */ /* call umf4fnum (numeric) */ void umf4fnum_ (void **Numeric) { UMFPACK_free_numeric (Numeric) ; } /* -------------------------------------------------------------------------- */ /* umf4fsym: free the Symbolic object */ /* -------------------------------------------------------------------------- */ /* call umf4fsym (symbolic) */ void umf4fsym_ (void **Symbolic) { UMFPACK_free_symbolic (Symbolic) ; } /* -------------------------------------------------------------------------- */ /* umf4snum: save the Numeric object to a file */ /* -------------------------------------------------------------------------- */ /* call umf4snum (numeric, filenum, status) */ void umf4snum_ (void **Numeric, Int *filenum, Int *status) { char filename [LEN] ; make_filename (*filenum, "n", filename) ; *status = UMFPACK_save_numeric (*Numeric, filename) ; } /* -------------------------------------------------------------------------- */ /* umf4ssym: save the Symbolic object to a file */ /* -------------------------------------------------------------------------- */ /* call umf4ssym (symbolic, filenum, status) */ void umf4ssym_ (void **Symbolic, Int *filenum, Int *status) { char filename [LEN] ; make_filename (*filenum, "s", filename) ; *status = UMFPACK_save_symbolic (*Symbolic, filename) ; } /* -------------------------------------------------------------------------- */ /* umf4lnum: load the Numeric object from a file */ /* -------------------------------------------------------------------------- */ /* call umf4lnum (numeric, filenum, status) */ void umf4lnum_ (void **Numeric, Int *filenum, Int *status) { char filename [LEN] ; make_filename (*filenum, "n", filename) ; *status = UMFPACK_load_numeric (Numeric, filename) ; } /* -------------------------------------------------------------------------- */ /* umf4lsym: load the Symbolic object from a file */ /* -------------------------------------------------------------------------- */ /* call umf4lsym (symbolic, filenum, status) */ void umf4lsym_ (void **Symbolic, Int *filenum, Int *status) { char filename [LEN] ; make_filename (*filenum, "s", filename) ; *status = UMFPACK_load_symbolic (Symbolic, filename) ; } /* ========================================================================== */ /* === with no underscore =================================================== */ /* ========================================================================== */ /* IBM AIX. Probably Microsoft Windows and HP Unix as well. */ /* -------------------------------------------------------------------------- */ /* umf4def: set default control parameters */ /* -------------------------------------------------------------------------- */ /* call umf4def (control) */ void umf4def (double Control [UMFPACK_CONTROL]) { UMFPACK_defaults (Control) ; } /* -------------------------------------------------------------------------- */ /* umf4pcon: print control parameters */ /* -------------------------------------------------------------------------- */ /* call umf4pcon (control) */ void umf4pcon (double Control [UMFPACK_CONTROL]) { fflush (stdout) ; UMFPACK_report_control (Control) ; fflush (stdout) ; } /* -------------------------------------------------------------------------- */ /* umf4sym: pre-ordering and symbolic factorization */ /* -------------------------------------------------------------------------- */ /* call umf4sym (m, n, Ap, Ai, Ax, symbolic, control, info) */ void umf4sym (Int *m, Int *n, Int Ap [ ], Int Ai [ ], double Ax [ ], void **Symbolic, double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO]) { (void) UMFPACK_symbolic (*m, *n, Ap, Ai, Ax, Symbolic, Control, Info) ; } /* -------------------------------------------------------------------------- */ /* umf4num: numeric factorization */ /* -------------------------------------------------------------------------- */ /* call umf4num (Ap, Ai, Ax, symbolic, numeric, control, info) */ void umf4num (Int Ap [ ], Int Ai [ ], double Ax [ ], void **Symbolic, void **Numeric, double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO]) { (void) UMFPACK_numeric (Ap, Ai, Ax, *Symbolic, Numeric, Control, Info); } /* -------------------------------------------------------------------------- */ /* umf4solr: solve a linear system with iterative refinement */ /* -------------------------------------------------------------------------- */ /* call umf4solr (sys, Ap, Ai, Ax, x, b, numeric, control, info) */ void umf4solr (Int *sys, Int Ap [ ], Int Ai [ ], double Ax [ ], double x [ ], double b [ ], void **Numeric, double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO]) { (void) UMFPACK_solve (*sys, Ap, Ai, Ax, x, b, *Numeric, Control, Info) ; } /* -------------------------------------------------------------------------- */ /* umf4sol: solve a linear system without iterative refinement */ /* -------------------------------------------------------------------------- */ /* call umf4sol (sys, x, b, numeric, control, info) */ void umf4sol (Int *sys, double x [ ], double b [ ], void **Numeric, double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO]) { Control [UMFPACK_IRSTEP] = 0 ; (void) UMFPACK_solve (*sys, (Int *) NULL, (Int *) NULL, (double *) NULL, x, b, *Numeric, Control, Info) ; } /* -------------------------------------------------------------------------- */ /* umf4scal: scale a vector using UMFPACK's scale factors */ /* -------------------------------------------------------------------------- */ /* call umf4scal (x, b, numeric, status) */ void umf4scal (double x [ ], double b [ ], void **Numeric, Int *status) { *status = UMFPACK_scale (x, b, *Numeric) ; } /* -------------------------------------------------------------------------- */ /* umf4pinf: print info */ /* -------------------------------------------------------------------------- */ /* call umf4pinf (control) */ void umf4pinf (double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO]) { fflush (stdout) ; UMFPACK_report_info (Control, Info) ; fflush (stdout) ; } /* -------------------------------------------------------------------------- */ /* umf4fnum: free the Numeric object */ /* -------------------------------------------------------------------------- */ /* call umf4fnum (numeric) */ void umf4fnum (void **Numeric) { UMFPACK_free_numeric (Numeric) ; } /* -------------------------------------------------------------------------- */ /* umf4fsym: free the Symbolic object */ /* -------------------------------------------------------------------------- */ /* call umf4fsym (symbolic) */ void umf4fsym (void **Symbolic) { UMFPACK_free_symbolic (Symbolic) ; } /* -------------------------------------------------------------------------- */ /* umf4snum: save the Numeric object to a file */ /* -------------------------------------------------------------------------- */ /* call umf4snum (numeric, filenum, status) */ void umf4snum (void **Numeric, Int *filenum, Int *status) { char filename [LEN] ; make_filename (*filenum, "n", filename) ; *status = UMFPACK_save_numeric (*Numeric, filename) ; } /* -------------------------------------------------------------------------- */ /* umf4ssym: save the Symbolic object to a file */ /* -------------------------------------------------------------------------- */ /* call umf4ssym (symbolic, filenum, status) */ void umf4ssym (void **Symbolic, Int *filenum, Int *status) { char filename [LEN] ; make_filename (*filenum, "s", filename) ; *status = UMFPACK_save_symbolic (*Symbolic, filename) ; } /* -------------------------------------------------------------------------- */ /* umf4lnum: load the Numeric object from a file */ /* -------------------------------------------------------------------------- */ /* call umf4lnum (numeric, filenum, status) */ void umf4lnum (void **Numeric, Int *filenum, Int *status) { char filename [LEN] ; make_filename (*filenum, "n", filename) ; *status = UMFPACK_load_numeric (Numeric, filename) ; } /* -------------------------------------------------------------------------- */ /* umf4lsym: load the Symbolic object from a file */ /* -------------------------------------------------------------------------- */ /* call umf4lsym (symbolic, filenum, status) */ void umf4lsym (void **Symbolic, Int *filenum, Int *status) { char filename [LEN] ; make_filename (*filenum, "s", filename) ; *status = UMFPACK_load_symbolic (Symbolic, filename) ; } SuiteSparse/UMFPACK/Demo/umfpack_dl_demo.out0000644001170100242450000015255610711433150017574 0ustar davisfac UMFPACK V5.2 (Nov 1, 2007) demo: _dl_ version UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. UMFPACK License: UMFPACK is available under alternate licenses, contact T. Davis for details. Your use or distribution of UMFPACK or any modified version of UMFPACK implies that you agree to this License. This library is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Permission is hereby granted to use or copy this program under the terms of the GNU GPL, provided that the Copyright, this License, and the Availability of the original version is retained on all copies. User documentation of any code that uses this code or any modified version of this code must cite the Copyright, this License, the Availability note, and "Used by permission." Permission to modify the code and to distribute modified code is granted, provided the Copyright, this License, and the Availability note are retained, and a notice that the code was modified is included. Availability: http://www.cise.ufl.edu/research/sparse/umfpack UMFPACK V5.2.0 (Nov 1, 2007): OK UMFPACK V5.2.0 (Nov 1, 2007), Control: Matrix entry defined as: double Int (generic integer) defined as: UF_long 0: print level: 5 1: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 2: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 3: pivot tolerance: 0.1 4: block size for dense matrix kernels: 32 5: strategy: 0 (auto) 6: initial allocation ratio: 0.7 7: max iterative refinement steps: 2 12: 2-by-2 pivot tolerance: 0.01 13: Q fixed during numerical factorization: 0 (auto) 14: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 15: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 16: scaling: 1 (divide each row by sum of abs. values in each row) 17: frontal matrix allocation ratio: 0.5 18: drop tolerance: 0 19: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4 9: compiled for ANSI C 10: CPU timer is POSIX times ( ) routine. 11: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 UF_long: 8 Int: 8 pointer: 8 double: 8 Entry: 8 (in bytes) b: dense vector, n = 5. 0 : (8) 1 : (45) 2 : (-3) 3 : (3) 4 : (19) dense vector OK A: triplet-form matrix, n_row = 5, n_col = 5 nz = 12. 0 : 0 0 (2) 1 : 4 4 (1) 2 : 1 0 (3) 3 : 1 2 (4) 4 : 2 1 (-1) 5 : 2 2 (-3) 6 : 0 1 (3) 7 : 1 4 (6) 8 : 2 3 (2) 9 : 3 2 (1) 10 : 4 1 (4) 11 : 4 2 (2) triplet-form matrix OK A: column-form matrix, n_row 5 n_col 5, nz = 12. column 0: start: 0 end: 1 entries: 2 row 0 : (2) row 1 : (3) column 1: start: 2 end: 4 entries: 3 row 0 : (3) row 2 : (-1) row 4 : (4) column 2: start: 5 end: 8 entries: 4 row 1 : (4) row 2 : (-3) row 3 : (1) row 4 : (2) column 3: start: 9 end: 9 entries: 1 row 2 : (2) column 4: start: 10 end: 11 entries: 2 row 1 : (6) row 4 : (1) column-form matrix OK Symbolic factorization of A: Symbolic object: matrix to be factorized: n_row: 5 n_col: 5 number of entries: 12 block size used for dense matrix kernels: 32 strategy used: unsymmetric ordering used: colamd on A performn column etree postorder: yes prefer diagonal pivoting (attempt P=Q): no variable-size part of Numeric object: minimum initial size (Units): 69 (MBytes): 0.0 estimated peak size (Units): 681 (MBytes): 0.0 estimated final size (Units): 10 (MBytes): 0.0 symbolic factorization memory usage (Units): 138 (MBytes): 0.0 frontal matrices / supercolumns: number of frontal chains: 1 number of frontal matrices: 1 largest frontal matrix row dimension: 3 largest frontal matrix column dimension: 3 Frontal chain: 0. Frontal matrices 0 to 0 Largest frontal matrix in Frontal chain: 3-by-3 Front: 0 pivot cols: 3 (pivot columns 0 to 2) pivot row candidates: 2 to 4 leftmost descendant: 0 1st new candidate row : 2 parent: (none) Initial column permutation, Q1: permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK Initial row permutation, P1: permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 1 4 : 4 permutation vector OK Symbolic object: OK Numeric factorization of A: Numeric object: n_row: 5 n_col: 5 relative pivot tolerance used: 0.1 relative symmetric pivot tolerance used: 0.001 matrix scaled: yes (divided each row by sum abs value in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 1.30000e+01 initial allocation parameter used: 0.7 frontal matrix allocation parameter used: 0.5 final total size of Numeric object (Units): 67 final total size of Numeric object (MBytes): 0.0 peak size of variable-size part (Units): 675 peak size of variable-size part (MBytes): 0.0 largest actual frontal matrix size: 4 memory defragmentations: 1 memory reallocations: 1 costly memory reallocations: 0 entries in compressed pattern (L and U): 2 number of nonzeros in L (excl diag): 4 number of entries stored in L (excl diag): 2 number of nonzeros in U (excl diag): 4 number of entries stored in U (excl diag): 2 factorization floating-point operations: 6 number of nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.42857e-01 max abs. value on diagonal of U: 2.19231e+00 reciprocal condition number estimate: 6.52e-02 Scale factors applied via multiplication Scale factors, Rs: dense vector, n = 5. 0 : (0.2) 1 : (0.0769231) 2 : (0.166667) 3 : (1) 4 : (0.142857) dense vector OK P: row permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 4 4 : 1 permutation vector OK Q: column permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK L in Numeric object, in column-oriented compressed-pattern form: Diagonal entries are all equal to 1.0 (not stored) column 0: length 0. column 1: length 2. row 4 : (0.307692) row 3 : (0.285714) column 2: add 1 entries. length 1. Start of Lchain. row 4 : (0.576923) column 3: length 1. row 4 : (3.23077) column 4: length 0. Start of Lchain. U in Numeric object, in row-oriented compressed-pattern form: Diagonal is stored separately. row 4: length 0. End of Uchain. row 3: length 1. End of Uchain. col 4 : (0.571429) row 2: length 1. col 4 : (0.6) row 1: length 0. End of Uchain. row 1: length 0. row 0: length 2. col 1 : (-0.5) col 4 : (-0.166667) diagonal of U: dense vector, n = 5. 0 : (0.333333) 1 : (1) 2 : (0.4) 3 : (0.142857) 4 : (-2.19231) dense vector OK Numeric object: OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: UF_long BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 16-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 138 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 41 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 1.30000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 69 64 93% peak size (Units) 681 675 99% final size (Units) 10 11 110% Numeric final size (Units) 69 68 99% Numeric final size (MBytes) 0.0 0.0 99% peak memory usage (Units) 832 826 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 1.30000e+01 6.00000e+00 46% nz in L (incl diagonal) 10 9 90% nz in U (incl diagonal) 10 9 90% nz in L+U (incl diagonal) 15 13 87% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 9 nz in U (incl diagonal), if none dropped 9 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.43e-01 max abs. value on diagonal of U: 2.19e+00 estimate of reciprocal of condition number: 6.52e-02 indices in compressed pattern: 2 numerical values stored in Numeric object: 9 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 1.19000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 1.18e-16 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 1.25000e+02 UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. UMFPACK V5.2.0 (Nov 1, 2007): OK x (solution of Ax=b): dense vector, n = 5. 0 : (1) 1 : (2) 2 : (3) 3 : (4) 4 : (5) dense vector OK maxnorm of residual: 1.06581e-14 UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. UMFPACK V5.2.0 (Nov 1, 2007): OK determinant: (1.14) * 10^(2) x (solution of Ax=b, solve is split into 3 steps): dense vector, n = 5. 0 : (1) 1 : (2) 2 : (3) 3 : (4) 4 : (5) dense vector OK maxnorm of residual: 1.06581e-14 UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: UF_long BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 16-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 138 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 41 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 1.30000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 69 64 93% peak size (Units) 681 675 99% final size (Units) 10 11 110% Numeric final size (Units) 69 68 99% Numeric final size (MBytes) 0.0 0.0 99% peak memory usage (Units) 832 826 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 1.30000e+01 6.00000e+00 46% nz in L (incl diagonal) 10 9 90% nz in U (incl diagonal) 10 9 90% nz in L+U (incl diagonal) 15 13 87% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 9 nz in U (incl diagonal), if none dropped 9 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.43e-01 max abs. value on diagonal of U: 2.19e+00 estimate of reciprocal of condition number: 6.52e-02 indices in compressed pattern: 2 numerical values stored in Numeric object: 9 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 1.11000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 7.64e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 1.17000e+02 x (solution of A'x=b): dense vector, n = 5. 0 : (1.81579) 1 : (1.45614) 2 : (1.5) 3 : (-24.8509) 4 : (10.2632) dense vector OK maxnorm of residual: 7.10543e-15 changing A (1,4) to zero modified A: column-form matrix, n_row 5 n_col 5, nz = 12. column 0: start: 0 end: 1 entries: 2 row 0 : (2) row 1 : (3) column 1: start: 2 end: 4 entries: 3 row 0 : (3) row 2 : (-1) row 4 : (4) column 2: start: 5 end: 8 entries: 4 row 1 : (4) row 2 : (-3) row 3 : (1) row 4 : (2) column 3: start: 9 end: 9 entries: 1 row 2 : (2) column 4: start: 10 end: 11 entries: 2 row 1 : (0) row 4 : (1) column-form matrix OK Numeric factorization of modified A: Numeric object: n_row: 5 n_col: 5 relative pivot tolerance used: 0.1 relative symmetric pivot tolerance used: 0.001 matrix scaled: yes (divided each row by sum abs value in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 7.00000e+00 initial allocation parameter used: 0.7 frontal matrix allocation parameter used: 0.5 final total size of Numeric object (Units): 66 final total size of Numeric object (MBytes): 0.0 peak size of variable-size part (Units): 675 peak size of variable-size part (MBytes): 0.0 largest actual frontal matrix size: 4 memory defragmentations: 1 memory reallocations: 1 costly memory reallocations: 0 entries in compressed pattern (L and U): 2 number of nonzeros in L (excl diag): 4 number of entries stored in L (excl diag): 2 number of nonzeros in U (excl diag): 3 number of entries stored in U (excl diag): 1 factorization floating-point operations: 4 number of nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.50000e-01 max abs. value on diagonal of U: 1.00000e+00 reciprocal condition number estimate: 1.50e-01 Scale factors applied via multiplication Scale factors, Rs: dense vector, n = 5. 0 : (0.2) 1 : (0.142857) 2 : (0.166667) 3 : (1) 4 : (0.142857) dense vector OK P: row permutation vector, n = 5. 0 : 2 1 : 3 2 : 1 3 : 4 4 : 0 permutation vector OK Q: column permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 1 4 : 4 permutation vector OK L in Numeric object, in column-oriented compressed-pattern form: Diagonal entries are all equal to 1.0 (not stored) column 0: length 0. column 1: length 2. row 2 : (0.571429) row 3 : (0.285714) column 2: add 1 entries. length 1. Start of Lchain. row 4 : (0.933333) column 3: length 1. row 4 : (1.05) column 4: length 0. Start of Lchain. U in Numeric object, in row-oriented compressed-pattern form: Diagonal is stored separately. row 4: length 0. End of Uchain. row 3: length 1. End of Uchain. col 4 : (0.142857) row 2: length 0. End of Uchain. row 1: length 0. End of Uchain. row 1: length 0. row 0: length 2. col 1 : (-0.5) col 3 : (-0.166667) diagonal of U: dense vector, n = 5. 0 : (0.333333) 1 : (1) 2 : (0.428571) 3 : (0.571429) 4 : (-0.15) dense vector OK Numeric object: OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: UF_long BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 16-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 138 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 41 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 7.00000e+00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 69 64 93% peak size (Units) 681 675 99% final size (Units) 10 10 100% Numeric final size (Units) 69 67 97% Numeric final size (MBytes) 0.0 0.0 97% peak memory usage (Units) 832 826 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 1.30000e+01 4.00000e+00 31% nz in L (incl diagonal) 10 9 90% nz in U (incl diagonal) 10 8 80% nz in L+U (incl diagonal) 15 12 80% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 9 nz in U (incl diagonal), if none dropped 8 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.50e-01 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 1.50e-01 indices in compressed pattern: 2 numerical values stored in Numeric object: 8 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 1.17000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 7.89e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 1.21000e+02 x (with modified A): dense vector, n = 5. 0 : (11) 1 : (-4.66667) 2 : (3) 3 : (0.666667) 4 : (31.6667) dense vector OK maxnorm of residual: 7.10543e-15 changing A (0,0) from 2 to 2 changing A (1,0) from 3 to 2 changing A (0,1) from 3 to 13 changing A (2,1) from -1 to 7 changing A (4,1) from 4 to 10 changing A (1,2) from 4 to 23 changing A (2,2) from -3 to 15 changing A (3,2) from 1 to 18 changing A (4,2) from 2 to 18 changing A (2,3) from 2 to 30 changing A (1,4) from 0 to 39 changing A (4,4) from 1 to 37 completely modified A (same pattern): column-form matrix, n_row 5 n_col 5, nz = 12. column 0: start: 0 end: 1 entries: 2 row 0 : (2) row 1 : (2) column 1: start: 2 end: 4 entries: 3 row 0 : (13) row 2 : (7) row 4 : (10) column 2: start: 5 end: 8 entries: 4 row 1 : (23) row 2 : (15) row 3 : (18) row 4 : (18) column 3: start: 9 end: 9 entries: 1 row 2 : (30) column 4: start: 10 end: 11 entries: 2 row 1 : (39) row 4 : (37) column-form matrix OK Saving symbolic object: Freeing symbolic object: Loading symbolic object: Done loading symbolic object Numeric factorization of completely modified A: Numeric object: n_row: 5 n_col: 5 relative pivot tolerance used: 0.1 relative symmetric pivot tolerance used: 0.001 matrix scaled: yes (divided each row by sum abs value in each row) minimum sum (abs (rows of A)): 1.50000e+01 maximum sum (abs (rows of A)): 6.50000e+01 initial allocation parameter used: 0.7 frontal matrix allocation parameter used: 0.5 final total size of Numeric object (Units): 67 final total size of Numeric object (MBytes): 0.0 peak size of variable-size part (Units): 675 peak size of variable-size part (MBytes): 0.0 largest actual frontal matrix size: 4 memory defragmentations: 1 memory reallocations: 1 costly memory reallocations: 0 entries in compressed pattern (L and U): 2 number of nonzeros in L (excl diag): 4 number of entries stored in L (excl diag): 2 number of nonzeros in U (excl diag): 4 number of entries stored in U (excl diag): 2 factorization floating-point operations: 6 number of nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.33333e-01 max abs. value on diagonal of U: 1.00000e+00 reciprocal condition number estimate: 1.33e-01 Scale factors applied via multiplication Scale factors, Rs: dense vector, n = 5. 0 : (0.0666667) 1 : (0.015625) 2 : (0.0192308) 3 : (0.0555556) 4 : (0.0153846) dense vector OK P: row permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 4 4 : 1 permutation vector OK Q: column permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK L in Numeric object, in column-oriented compressed-pattern form: Diagonal entries are all equal to 1.0 (not stored) column 0: length 0. column 1: length 2. row 4 : (0.359375) row 3 : (0.276923) column 2: add 1 entries. length 1. Start of Lchain. row 4 : (0.234375) column 3: length 1. row 4 : (1.07052) column 4: length 0. Start of Lchain. U in Numeric object, in row-oriented compressed-pattern form: Diagonal is stored separately. row 4: length 0. End of Uchain. row 3: length 1. End of Uchain. col 4 : (0.153846) row 2: length 1. col 4 : (0.866667) row 1: length 0. End of Uchain. row 1: length 0. row 0: length 2. col 1 : (0.288462) col 4 : (0.134615) diagonal of U: dense vector, n = 5. 0 : (0.576923) 1 : (1) 2 : (0.133333) 3 : (0.569231) 4 : (-0.367821) dense vector OK Numeric object: OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: UF_long BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 16-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 138 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 41 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.50000e+01 maximum sum (abs (rows of A)): 6.50000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 69 64 93% peak size (Units) 681 675 99% final size (Units) 10 11 110% Numeric final size (Units) 69 68 99% Numeric final size (MBytes) 0.0 0.0 99% peak memory usage (Units) 832 826 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 1.30000e+01 6.00000e+00 46% nz in L (incl diagonal) 10 9 90% nz in U (incl diagonal) 10 9 90% nz in L+U (incl diagonal) 15 13 87% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 9 nz in U (incl diagonal), if none dropped 9 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.33e-01 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 1.33e-01 indices in compressed pattern: 2 numerical values stored in Numeric object: 9 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 1.19000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 1.04e-16 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 1.25000e+02 x (with completely modified A): dense vector, n = 5. 0 : (8.50124) 1 : (-0.692499) 2 : (0.166667) 3 : (-0.0217502) 4 : (0.619594) dense vector OK maxnorm of residual: 3.55271e-15 C (transpose of A): column-form matrix, n_row 5 n_col 5, nz = 12. column 0: start: 0 end: 1 entries: 2 row 0 : (2) row 1 : (13) column 1: start: 2 end: 4 entries: 3 row 0 : (2) row 2 : (23) row 4 : (39) column 2: start: 5 end: 7 entries: 3 row 1 : (7) row 2 : (15) row 3 : (30) column 3: start: 8 end: 8 entries: 1 row 2 : (18) column 4: start: 9 end: 11 entries: 3 row 1 : (10) row 2 : (18) row 4 : (37) column-form matrix OK Symbolic factorization of C: Symbolic object: matrix to be factorized: n_row: 5 n_col: 5 number of entries: 12 block size used for dense matrix kernels: 32 strategy used: unsymmetric ordering used: colamd on A performn column etree postorder: yes prefer diagonal pivoting (attempt P=Q): no variable-size part of Numeric object: minimum initial size (Units): 71 (MBytes): 0.0 estimated peak size (Units): 683 (MBytes): 0.0 estimated final size (Units): 12 (MBytes): 0.0 symbolic factorization memory usage (Units): 138 (MBytes): 0.0 frontal matrices / supercolumns: number of frontal chains: 1 number of frontal matrices: 1 largest frontal matrix row dimension: 3 largest frontal matrix column dimension: 3 Frontal chain: 0. Frontal matrices 0 to 0 Largest frontal matrix in Frontal chain: 3-by-3 Front: 0 pivot cols: 3 (pivot columns 0 to 2) pivot row candidates: 2 to 4 leftmost descendant: 0 1st new candidate row : 2 parent: (none) Initial column permutation, Q1: permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK Initial row permutation, P1: permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 1 4 : 4 permutation vector OK Symbolic object: OK Get the contents of the Symbolic object for C: (compare with umfpack_dl_report_symbolic output, above) From the Symbolic object, C is of dimension 5-by-5 with nz = 12, number of fronts = 1, number of frontal matrix chains = 1 Pivot columns in each front, and parent of each front: Front 0: parent front: -1 number of pivot cols: 3 0-th pivot column is column 3 in original matrix 1-th pivot column is column 2 in original matrix 2-th pivot column is column 0 in original matrix Note that the column ordering, above, will be refined in the numeric factorization below. The assignment of pivot columns to frontal matrices will always remain unchanged. Total number of pivot columns in frontal matrices: 3 Frontal matrix chains: Frontal matrices 0 to 0 are factorized in a single working array of size 3-by-3 Numeric factorization of C: Numeric object: n_row: 5 n_col: 5 relative pivot tolerance used: 0.1 relative symmetric pivot tolerance used: 0.001 matrix scaled: yes (divided each row by sum abs value in each row) minimum sum (abs (rows of A)): 4.00000e+00 maximum sum (abs (rows of A)): 7.60000e+01 initial allocation parameter used: 0.7 frontal matrix allocation parameter used: 0.5 final total size of Numeric object (Units): 69 final total size of Numeric object (MBytes): 0.0 peak size of variable-size part (Units): 677 peak size of variable-size part (MBytes): 0.0 largest actual frontal matrix size: 4 memory defragmentations: 1 memory reallocations: 1 costly memory reallocations: 0 entries in compressed pattern (L and U): 2 number of nonzeros in L (excl diag): 3 number of entries stored in L (excl diag): 2 number of nonzeros in U (excl diag): 5 number of entries stored in U (excl diag): 2 factorization floating-point operations: 6 number of nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 2.43243e-01 max abs. value on diagonal of U: 1.00000e+00 reciprocal condition number estimate: 2.43e-01 Scale factors applied via multiplication Scale factors, Rs: dense vector, n = 5. 0 : (0.25) 1 : (0.0333333) 2 : (0.0135135) 3 : (0.0333333) 4 : (0.0131579) dense vector OK P: row permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 4 4 : 1 permutation vector OK Q: column permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK L in Numeric object, in column-oriented compressed-pattern form: Diagonal entries are all equal to 1.0 (not stored) column 0: length 0. column 1: length 1. row 4 : (0.233333) column 2: add 1 entries. length 1. Start of Lchain. row 4 : (0.866667) column 3: length 1. row 4 : (0.684685) column 4: length 0. Start of Lchain. U in Numeric object, in row-oriented compressed-pattern form: Diagonal is stored separately. row 4: length 0. End of Uchain. row 3: length 1. End of Uchain. col 4 : (0.513158) row 2: length 1. col 4 : (0.5) row 1: length 0. End of Uchain. row 1: length 0. row 0: length 3. col 1 : (0.202703) col 3 : (0.243243) col 4 : (0.310811) diagonal of U: dense vector, n = 5. 0 : (0.243243) 1 : (1) 2 : (0.5) 3 : (0.486842) 4 : (-0.784685) dense vector OK Numeric object: OK L (lower triangular factor of C): row-form matrix, n_row 5 n_col 5, nz = 8. row 0: start: 0 end: 0 entries: 1 column 0 : (1) row 1: start: 1 end: 1 entries: 1 column 1 : (1) row 2: start: 2 end: 2 entries: 1 column 2 : (1) row 3: start: 3 end: 3 entries: 1 column 3 : (1) row 4: start: 4 end: 7 entries: 4 column 1 : (0.233333) column 2 : (0.866667) column 3 : (0.684685) column 4 : (1) row-form matrix OK U (upper triangular factor of C): column-form matrix, n_row 5 n_col 5, nz = 10. column 0: start: 0 end: 0 entries: 1 row 0 : (0.243243) column 1: start: 1 end: 2 entries: 2 row 0 : (0.202703) row 1 : (1) column 2: start: 3 end: 3 entries: 1 row 2 : (0.5) column 3: start: 4 end: 5 entries: 2 row 0 : (0.243243) row 3 : (0.486842) column 4: start: 6 end: 9 entries: 4 row 0 : (0.310811) row 2 : (0.5) row 3 : (0.513158) row 4 : (-0.784685) column-form matrix OK P: permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 4 4 : 1 permutation vector OK Q: permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK Scale factors: row i of A is to be multiplied by the ith scale factor 0: 0.25 1: 0.0333333 2: 0.0135135 3: 0.0333333 4: 0.0131579 Converting L to triplet form, and printing it: L, in triplet form: triplet-form matrix, n_row = 5, n_col = 5 nz = 8. 0 : 0 0 (1) 1 : 1 1 (1) 2 : 2 2 (1) 3 : 3 3 (1) 4 : 4 1 (0.233333) 5 : 4 2 (0.866667) 6 : 4 3 (0.684685) 7 : 4 4 (1) triplet-form matrix OK Saving numeric object: Freeing numeric object: Loading numeric object: Done loading numeric object UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: UF_long BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 16-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 138 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 41 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 4.00000e+00 maximum sum (abs (rows of A)): 7.60000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 71 66 93% peak size (Units) 683 677 99% final size (Units) 12 13 108% Numeric final size (Units) 71 70 99% Numeric final size (MBytes) 0.0 0.0 99% peak memory usage (Units) 834 828 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 1.30000e+01 6.00000e+00 46% nz in L (incl diagonal) 9 8 89% nz in U (incl diagonal) 11 10 91% nz in L+U (incl diagonal) 15 13 87% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 8 nz in U (incl diagonal), if none dropped 10 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 2.43e-01 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 2.43e-01 indices in compressed pattern: 2 numerical values stored in Numeric object: 9 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 1.11000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 8.07e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 1.17000e+02 x (solution of C'x=b): dense vector, n = 5. 0 : (8.50124) 1 : (-0.692499) 2 : (0.166667) 3 : (-0.0217502) 4 : (0.619594) dense vector OK maxnorm of residual: 3.55271e-15 Solving C'x=b again, using umfpack_dl_wsolve instead: UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: UF_long BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 16-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 138 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 41 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 4.00000e+00 maximum sum (abs (rows of A)): 7.60000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 71 66 93% peak size (Units) 683 677 99% final size (Units) 12 13 108% Numeric final size (Units) 71 70 99% Numeric final size (MBytes) 0.0 0.0 99% peak memory usage (Units) 834 828 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 1.30000e+01 6.00000e+00 46% nz in L (incl diagonal) 9 8 89% nz in U (incl diagonal) 11 10 91% nz in L+U (incl diagonal) 15 13 87% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 8 nz in U (incl diagonal), if none dropped 10 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 2.43e-01 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 2.43e-01 indices in compressed pattern: 2 numerical values stored in Numeric object: 9 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 1.11000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 8.07e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 1.17000e+02 x (solution of C'x=b): dense vector, n = 5. 0 : (8.50124) 1 : (-0.692499) 2 : (0.166667) 3 : (-0.0217502) 4 : (0.619594) dense vector OK maxnorm of residual: 3.55271e-15 umfpack_dl_demo complete. Total time: 0.00 seconds (CPU time), 0.00 seconds (wallclock time) SuiteSparse/UMFPACK/Demo/umfpack_dl_demo.sed0000644001170100242450000000122010425652546017533 0ustar davisfac/::/d 1,$s/_xx_/_dl_/g 1,$s/Int/UF_long/g 1,$s/WSIZE/5/ /define ABS/ { s/ABS/ABS(x) ((x) >= 0 ? (x) : -(x))/ } /, rz \[i\]/ { s/, rz \[i\]// } /, Avalz/ { s/, Avalz// } /, rz/ { s/, rz// } /, bz/ { s/, bz// } /, xz/ { s/, xz// } /, Lz/ { s/, Lz// } /, Uz/ { s/, Uz// } /, Dz/ { s/, Dz// } /, Az/ { s/, Az// } /, Cz, TRUE/ { s/, Cz, TRUE// } /, Cz/ { s/, Cz// } /, Rbz/ { s/, Rbz// } /, yz/ { s/, yz// } / || !Lz/ { s/ || !Lz// } / || !Uz/ { s/ || !Uz// } / || !Dz/ { s/ || !Dz// } / || !Az/ { s/ || !Az// } / || !Cz/ { s/ || !Cz// } /rz/d /Rbz/d /yz/d /Avalz/d /Az/d /Cz/d /bz/d /xz/d /Lz/d /Uz/d /Dz/d /complex/d SuiteSparse/UMFPACK/Demo/umf4zhb.f0000644001170100242450000002254010172176370015456 0ustar davisfacc======================================================================= c== umf4zhb ============================================================ c======================================================================= c----------------------------------------------------------------------- c UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis. CISE c Dept, Univ. of Florida. All Rights Reserved. See ../Doc/License for c License. web: http://www.cise.ufl.edu/research/sparse/umfpack c----------------------------------------------------------------------- c umf4zhb: c read a sparse matrix in the Harwell/Boeing format, factorizes c it, and solves Ax=b. Also saves and loads the factors to/from a c file. Saving to a file is not required, it's just here to c demonstrate how to use this feature of UMFPACK. This program c only works on square CUA-type matrices. c c This is HIGHLY non-portable. It may not work with your C and c FORTRAN compilers. See umf4z_f77wrapper.c for more details. c c usage (for example): c c in a Unix shell: c umf4zhb < HB/arc130.cua integer $ nzmax, nmax parameter (nzmax = 5000000, nmax = 160000) integer $ Ap (nmax), Ai (nzmax), n, nz, totcrd, ptrcrd, i, j, p, $ indcrd, valcrd, rhscrd, ncol, nrow, nrhs, nzrhs, nel, $ numeric, symbolic, status, sys, filenum character title*72, key*30, type*3, ptrfmt*16, $ indfmt*16, valfmt*20, rhsfmt*20 double precision Ax (nzmax), x (nmax), b (nmax), $ control (20), info (90) complex*16 AA (nzmax), XX (nmax), BB (nmax), r (nmax), aij, xj double precision Az (nmax), xz (nmax), bz (nmax), xi, xr character rhstyp*3 c ---------------------------------------------------------------- c read the Harwell/Boeing matrix c ---------------------------------------------------------------- read (5, 10, err = 998) $ title, key, $ totcrd, ptrcrd, indcrd, valcrd, rhscrd, $ type, nrow, ncol, nz, nel, $ ptrfmt, indfmt, valfmt, rhsfmt if (rhscrd .gt. 0) then c new Harwell/Boeing format: read (5, 20, err = 998) rhstyp, nrhs, nzrhs endif 10 format (a72, a8 / 5i14 / a3, 11x, 4i14 / 2a16, 2a20) 20 format (a3, 11x, 2i14) print *, 'Matrix key: ', key n = nrow if (type .ne. 'CUA' .or. nrow .ne. ncol) then print *, 'Error: can only handle square CUA matrices' stop endif if (n .ge. nmax .or. nz .gt. nzmax) then print *, ' Matrix too big!' stop endif c read the matrix (1-based) read (5, ptrfmt, err = 998) (Ap (p), p = 1, ncol+1) read (5, indfmt, err = 998) (Ai (p), p = 1, nz) read (5, valfmt, err = 998) (AA (p), p = 1, nz) do 15 p = 1, nz Ax (p) = dble (AA (p)) Az (p) = imag (AA (p)) 15 continue c ---------------------------------------------------------------- c create the right-hand-side, assume c x (i) = (1 + i/n), (n + i/100) c ---------------------------------------------------------------- do 30 i = 1,n BB (i) = 0 30 continue c b = A*x do 50 j = 1,n xr = j xi = n xi = xi + xr/100 xr = 1 + xr / n xj = dcmplx (xr, xi) do 40 p = Ap (j), Ap (j+1)-1 i = Ai (p) aij = AA (p) BB (i) = BB (i) + aij * xj 40 continue 50 continue do 32 i = 1,n b (i) = dble (BB (i)) bz (i) = imag (BB (i)) 32 continue c ---------------------------------------------------------------- c convert from 1-based to 0-based c ---------------------------------------------------------------- do 60 j = 1, n+1 Ap (j) = Ap (j) - 1 60 continue do 70 p = 1, nz Ai (p) = Ai (p) - 1 70 continue c ---------------------------------------------------------------- c factor the matrix and save to a file c ---------------------------------------------------------------- c set default parameters call umf4zdef (control) c print control parameters. set control (1) to 1 to print c error messages only control (1) = 2 call umf4zpcon (control) c pre-order and symbolic analysis call umf4zsym (n, n, Ap, Ai, Ax, Az, symbolic, control, info) c print statistics computed so far c call umf4zpinf (control, info) could also be done. print 80, info (1), info (16), $ (info (21) * info (4)) / 2**20, $ (info (22) * info (4)) / 2**20, $ info (23), info (24), info (25) 80 format ('symbolic analysis:',/, $ ' status: ', f5.0, /, $ ' time: ', e10.2, ' (sec)'/, $ ' estimates (upper bound) for numeric LU:', /, $ ' size of LU: ', f10.2, ' (MB)', /, $ ' memory needed: ', f10.2, ' (MB)', /, $ ' flop count: ', e10.2, / $ ' nnz (L): ', f10.0, / $ ' nnz (U): ', f10.0) c check umf4zsym error condition if (info (1) .lt. 0) then print *, 'Error occurred in umf4zsym: ', info (1) stop endif c numeric factorization call umf4znum (Ap, Ai, Ax, Az, symbolic, numeric, control, info) c print statistics for the numeric factorization c call umf4zpinf (control, info) could also be done. print 90, info (1), info (66), $ (info (41) * info (4)) / 2**20, $ (info (42) * info (4)) / 2**20, $ info (43), info (44), info (45) 90 format ('numeric factorization:',/, $ ' status: ', f5.0, /, $ ' time: ', e10.2, /, $ ' actual numeric LU statistics:', /, $ ' size of LU: ', f10.2, ' (MB)', /, $ ' memory needed: ', f10.2, ' (MB)', /, $ ' flop count: ', e10.2, / $ ' nnz (L): ', f10.0, / $ ' nnz (U): ', f10.0) c check umf4znum error condition if (info (1) .lt. 0) then print *, 'Error occurred in umf4znum: ', info (1) stop endif c save the symbolic analysis to the file s42.umf c note that this is not needed until another matrix is c factorized, below. filenum = 42 call umf4zssym (symbolic, filenum, status) if (status .lt. 0) then print *, 'Error occurred in umf4zssym: ', status stop endif c save the LU factors to the file n0.umf call umf4zsnum (numeric, filenum, status) if (status .lt. 0) then print *, 'Error occurred in umf4zsnum: ', status stop endif c free the symbolic analysis call umf4zfsym (symbolic) c free the numeric factorization call umf4zfnum (numeric) c No LU factors (symbolic or numeric) are in memory at this point. c ---------------------------------------------------------------- c load the LU factors back in, and solve the system c ---------------------------------------------------------------- c At this point the program could terminate and load the LU C factors (numeric) from the n0.umf file, and solve the c system (see below). Note that the symbolic object is not c required. c load the numeric factorization back in (filename: n0.umf) call umf4zlnum (numeric, filenum, status) if (status .lt. 0) then print *, 'Error occurred in umf4zlnum: ', status stop endif c solve Ax=b, without iterative refinement sys = 0 call umf4zsol (sys, x, xz, b, bz, numeric, control, info) if (info (1) .lt. 0) then print *, 'Error occurred in umf4zsol: ', info (1) stop endif do 33 i = 1,n XX (i) = dcmplx (x (i), xz (i)) 33 continue c free the numeric factorization call umf4zfnum (numeric) c No LU factors (symbolic or numeric) are in memory at this point. c print final statistics call umf4zpinf (control, info) c print the residual. x (i) should be 1 + i/n call resid (n, nz, Ap, Ai, AA, XX, BB, r) stop 998 print *, 'Read error: Harwell/Boeing matrix' stop end c======================================================================= c== resid ============================================================== c======================================================================= c Compute the residual, r = Ax-b, its max-norm, and print the max-norm C Note that A is zero-based. subroutine resid (n, nz, Ap, Ai, A, x, b, r) integer $ n, nz, Ap (n+1), Ai (n), j, i, p complex*16 A (nz), x (n), b (n), r (n), aij double precision rmax do 10 i = 1, n r (i) = -b (i) 10 continue do 30 j = 1,n do 20 p = Ap (j) + 1, Ap (j+1) i = Ai (p) + 1 aij = A (p) r (i) = r (i) + aij * x (j) 20 continue 30 continue rmax = 0 do 40 i = 1, n rmax = max (rmax, abs (r (i))) 40 continue print *, 'norm (A*x-b): ', rmax return end SuiteSparse/UMFPACK/Demo/umfpack_zl_demo.out0000644001170100242450000015633210711433210017613 0ustar davisfac UMFPACK V5.2 (Nov 1, 2007) demo: _zl_ version UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. UMFPACK License: UMFPACK is available under alternate licenses, contact T. Davis for details. Your use or distribution of UMFPACK or any modified version of UMFPACK implies that you agree to this License. This library is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Permission is hereby granted to use or copy this program under the terms of the GNU GPL, provided that the Copyright, this License, and the Availability of the original version is retained on all copies. User documentation of any code that uses this code or any modified version of this code must cite the Copyright, this License, the Availability note, and "Used by permission." Permission to modify the code and to distribute modified code is granted, provided the Copyright, this License, and the Availability note are retained, and a notice that the code was modified is included. Availability: http://www.cise.ufl.edu/research/sparse/umfpack UMFPACK V5.2.0 (Nov 1, 2007): OK UMFPACK V5.2.0 (Nov 1, 2007), Control: Matrix entry defined as: double complex Int (generic integer) defined as: UF_long 0: print level: 5 1: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 2: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 3: pivot tolerance: 0.1 4: block size for dense matrix kernels: 32 5: strategy: 0 (auto) 6: initial allocation ratio: 0.7 7: max iterative refinement steps: 2 12: 2-by-2 pivot tolerance: 0.01 13: Q fixed during numerical factorization: 0 (auto) 14: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 15: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 16: scaling: 1 (divide each row by sum of abs. values in each row) 17: frontal matrix allocation ratio: 0.5 18: drop tolerance: 0 19: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4 9: compiled for ANSI C 10: CPU timer is POSIX times ( ) routine. 11: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 UF_long: 8 Int: 8 pointer: 8 double: 8 Entry: 16 (in bytes) b: dense vector, n = 5. 0 : (8 + 1i) 1 : (45 - 5i) 2 : (-3 - 2i) 3 : (3 + 0i) 4 : (19 + 2.2i) dense vector OK A: triplet-form matrix, n_row = 5, n_col = 5 nz = 12. 0 : 0 0 (2 + 1i) 1 : 4 4 (1 + 0.4i) 2 : 1 0 (3 + 0.1i) 3 : 1 2 (4 + 0.2i) 4 : 2 1 (-1 - 1i) 5 : 2 2 (-3 - 0.2i) 6 : 0 1 (3 + 0i) 7 : 1 4 (6 + 6i) 8 : 2 3 (2 + 3i) 9 : 3 2 (1 + 0i) 10 : 4 1 (4 + 0.3i) 11 : 4 2 (2 + 0.3i) triplet-form matrix OK A: column-form matrix, n_row 5 n_col 5, nz = 12. column 0: start: 0 end: 1 entries: 2 row 0 : (2 + 1i) row 1 : (3 + 0.1i) column 1: start: 2 end: 4 entries: 3 row 0 : (3 + 0i) row 2 : (-1 - 1i) row 4 : (4 + 0.3i) column 2: start: 5 end: 8 entries: 4 row 1 : (4 + 0.2i) row 2 : (-3 - 0.2i) row 3 : (1 + 0i) row 4 : (2 + 0.3i) column 3: start: 9 end: 9 entries: 1 row 2 : (2 + 3i) column 4: start: 10 end: 11 entries: 2 row 1 : (6 + 6i) row 4 : (1 + 0.4i) column-form matrix OK Symbolic factorization of A: Symbolic object: matrix to be factorized: n_row: 5 n_col: 5 number of entries: 12 block size used for dense matrix kernels: 32 strategy used: unsymmetric ordering used: colamd on A performn column etree postorder: yes prefer diagonal pivoting (attempt P=Q): no variable-size part of Numeric object: minimum initial size (Units): 74 (MBytes): 0.0 estimated peak size (Units): 1301 (MBytes): 0.0 estimated final size (Units): 15 (MBytes): 0.0 symbolic factorization memory usage (Units): 138 (MBytes): 0.0 frontal matrices / supercolumns: number of frontal chains: 1 number of frontal matrices: 1 largest frontal matrix row dimension: 3 largest frontal matrix column dimension: 3 Frontal chain: 0. Frontal matrices 0 to 0 Largest frontal matrix in Frontal chain: 3-by-3 Front: 0 pivot cols: 3 (pivot columns 0 to 2) pivot row candidates: 2 to 4 leftmost descendant: 0 1st new candidate row : 2 parent: (none) Initial column permutation, Q1: permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK Initial row permutation, P1: permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 1 4 : 4 permutation vector OK Symbolic object: OK Numeric factorization of A: Numeric object: n_row: 5 n_col: 5 relative pivot tolerance used: 0.1 relative symmetric pivot tolerance used: 0.001 matrix scaled: yes (divided each row by sum abs value in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 1.93000e+01 initial allocation parameter used: 0.7 frontal matrix allocation parameter used: 0.5 final total size of Numeric object (Units): 74 final total size of Numeric object (MBytes): 0.0 peak size of variable-size part (Units): 1292 peak size of variable-size part (MBytes): 0.0 largest actual frontal matrix size: 4 memory defragmentations: 1 memory reallocations: 1 costly memory reallocations: 0 entries in compressed pattern (L and U): 2 number of nonzeros in L (excl diag): 4 number of entries stored in L (excl diag): 2 number of nonzeros in U (excl diag): 4 number of entries stored in U (excl diag): 2 factorization floating-point operations: 34 number of nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.34629e-01 max abs. value on diagonal of U: 1.77313e+00 reciprocal condition number estimate: 7.59e-02 Scale factors applied via multiplication Scale factors, Rs: dense vector, n = 5. 0 : (0.166667) 1 : (0.0518135) 2 : (0.0980392) 3 : (1) 4 : (0.125) dense vector OK P: row permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 4 4 : 1 permutation vector OK Q: column permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK L in Numeric object, in column-oriented compressed-pattern form: Diagonal entries are all equal to 1.0 (not stored) column 0: length 0. column 1: length 2. row 4 : (0.207254 + 0.0103627i) row 3 : (0.25 + 0.0375i) column 2: add 1 entries. length 1. Start of Lchain. row 4 : (0.379275 - 0.174093i) column 3: length 1. row 4 : (3.00161 + 1.2864i) column 4: length 0. Start of Lchain. U in Numeric object, in row-oriented compressed-pattern form: Diagonal is stored separately. row 4: length 0. End of Uchain. row 3: length 1. End of Uchain. col 4 : (0.5 + 0.0375i) row 2: length 1. col 4 : (0.5 + 0i) row 1: length 0. End of Uchain. row 1: length 0. row 0: length 2. col 1 : (-0.294118 - 0.0196078i) col 4 : (-0.0980392 - 0.0980392i) diagonal of U: dense vector, n = 5. 0 : (0.196078 + 0.294118i) 1 : (1 + 0i) 2 : (0.333333 + 0.166667i) 3 : (0.125 + 0.05i) 4 : (-1.6422 - 0.668715i) dense vector OK Numeric object: OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double complex Int (generic integer) defined as: UF_long BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 16-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 16 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 138 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 41 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 1.93000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 74 69 93% peak size (Units) 1301 1292 99% final size (Units) 15 13 87% Numeric final size (Units) 79 75 95% Numeric final size (MBytes) 0.0 0.0 95% peak memory usage (Units) 1463 1454 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 6.70000e+01 3.40000e+01 51% nz in L (incl diagonal) 10 9 90% nz in U (incl diagonal) 10 9 90% nz in L+U (incl diagonal) 15 13 87% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 9 nz in U (incl diagonal), if none dropped 9 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.35e-01 max abs. value on diagonal of U: 1.77e+00 estimate of reciprocal of condition number: 7.59e-02 indices in compressed pattern: 2 numerical values stored in Numeric object: 9 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 1.02800e+03 iterative refinement steps taken: 1 iterative refinement steps attempted: 1 sparse backward error omega1: 5.28e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 1.06200e+03 UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. UMFPACK V5.2.0 (Nov 1, 2007): OK x (solution of Ax=b): dense vector, n = 5. 0 : (0.121188 - 0.561001i) 1 : (2.39887 + 0.666938i) 2 : (3 + 0i) 3 : (1.57395 - 1.52801i) 4 : (2.3876 - 3.04245i) dense vector OK maxnorm of residual: 1.77636e-15 UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. UMFPACK V5.2.0 (Nov 1, 2007): OK determinant: (-1.7814+ (2.3784)i) * 10^(2) x (solution of Ax=b, solve is split into 3 steps): dense vector, n = 5. 0 : (0.121188 - 0.561001i) 1 : (2.39887 + 0.666938i) 2 : (3 + 0i) 3 : (1.57395 - 1.52801i) 4 : (2.3876 - 3.04245i) dense vector OK maxnorm of residual: 1.77636e-14 UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double complex Int (generic integer) defined as: UF_long BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 16-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 16 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 138 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 41 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 1.93000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 74 69 93% peak size (Units) 1301 1292 99% final size (Units) 15 13 87% Numeric final size (Units) 79 75 95% Numeric final size (MBytes) 0.0 0.0 95% peak memory usage (Units) 1463 1454 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 6.70000e+01 3.40000e+01 51% nz in L (incl diagonal) 10 9 90% nz in U (incl diagonal) 10 9 90% nz in L+U (incl diagonal) 15 13 87% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 9 nz in U (incl diagonal), if none dropped 9 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.35e-01 max abs. value on diagonal of U: 1.77e+00 estimate of reciprocal of condition number: 7.59e-02 indices in compressed pattern: 2 numerical values stored in Numeric object: 9 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 4.80000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 7.82e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 5.14000e+02 x (solution of A'x=b): dense vector, n = 5. 0 : (3.39246 + 0.13257i) 1 : (0.31463 + 1.38626i) 2 : (0.461538 + 0.692308i) 3 : (-20.9089 - 1.55801i) 4 : (9.04015 - 0.613724i) dense vector OK maxnorm of residual: 4.52416e-15 changing A (1,4) to zero modified A: column-form matrix, n_row 5 n_col 5, nz = 12. column 0: start: 0 end: 1 entries: 2 row 0 : (2 + 1i) row 1 : (3 + 0.1i) column 1: start: 2 end: 4 entries: 3 row 0 : (3 + 0i) row 2 : (-1 - 1i) row 4 : (4 + 0.3i) column 2: start: 5 end: 8 entries: 4 row 1 : (4 + 0.2i) row 2 : (-3 - 0.2i) row 3 : (1 + 0i) row 4 : (2 + 0.3i) column 3: start: 9 end: 9 entries: 1 row 2 : (2 + 3i) column 4: start: 10 end: 11 entries: 2 row 1 : (0 + 0i) row 4 : (1 + 0.4i) column-form matrix OK Numeric factorization of modified A: Numeric object: n_row: 5 n_col: 5 relative pivot tolerance used: 0.1 relative symmetric pivot tolerance used: 0.001 matrix scaled: yes (divided each row by sum abs value in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 1.02000e+01 initial allocation parameter used: 0.7 frontal matrix allocation parameter used: 0.5 final total size of Numeric object (Units): 73 final total size of Numeric object (MBytes): 0.0 peak size of variable-size part (Units): 1292 peak size of variable-size part (MBytes): 0.0 largest actual frontal matrix size: 4 memory defragmentations: 1 memory reallocations: 1 costly memory reallocations: 0 entries in compressed pattern (L and U): 2 number of nonzeros in L (excl diag): 3 number of entries stored in L (excl diag): 1 number of nonzeros in U (excl diag): 4 number of entries stored in U (excl diag): 2 factorization floating-point operations: 17 number of nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.34629e-01 max abs. value on diagonal of U: 1.00000e+00 reciprocal condition number estimate: 1.35e-01 Scale factors applied via multiplication Scale factors, Rs: dense vector, n = 5. 0 : (0.166667) 1 : (0.136986) 2 : (0.0980392) 3 : (1) 4 : (0.125) dense vector OK P: row permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 4 4 : 1 permutation vector OK Q: column permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK L in Numeric object, in column-oriented compressed-pattern form: Diagonal entries are all equal to 1.0 (not stored) column 0: length 0. column 1: length 2. row 4 : (0.547945 + 0.0273973i) row 3 : (0.25 + 0.0375i) column 2: add 1 entries. length 1. Start of Lchain. row 4 : (1.00274 - 0.460274i) column 3: length 0. Start of Lchain. column 4: length 0. Start of Lchain. U in Numeric object, in row-oriented compressed-pattern form: Diagonal is stored separately. row 4: length 0. End of Uchain. row 3: length 1. End of Uchain. col 4 : (0.5 + 0.0375i) row 2: length 1. col 4 : (0.5 + 0i) row 1: length 0. End of Uchain. row 1: length 0. row 0: length 2. col 1 : (-0.294118 - 0.0196078i) col 4 : (-0.0980392 - 0.0980392i) diagonal of U: dense vector, n = 5. 0 : (0.196078 + 0.294118i) 1 : (1 + 0i) 2 : (0.333333 + 0.166667i) 3 : (0.125 + 0.05i) 4 : (-0.50137 + 0.230137i) dense vector OK Numeric object: OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double complex Int (generic integer) defined as: UF_long BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 16-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 16 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 138 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 41 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 1.02000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 74 69 93% peak size (Units) 1301 1292 99% final size (Units) 15 12 80% Numeric final size (Units) 79 74 94% Numeric final size (MBytes) 0.0 0.0 94% peak memory usage (Units) 1463 1454 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 6.70000e+01 1.70000e+01 25% nz in L (incl diagonal) 10 8 80% nz in U (incl diagonal) 10 9 90% nz in L+U (incl diagonal) 15 12 80% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 8 nz in U (incl diagonal), if none dropped 9 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.35e-01 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 1.35e-01 indices in compressed pattern: 2 numerical values stored in Numeric object: 8 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 5.15000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 6.01e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 5.32000e+02 x (with modified A): dense vector, n = 5. 0 : (10.9256 - 2.23085i) 1 : (-5.36071 - 1.82131i) 2 : (3 + 0i) 3 : (-1.60191 - 1.88814i) 4 : (32.7361 - 2.90097i) dense vector OK maxnorm of residual: 4.66294e-15 changing real part of A (0,0) from 2 to 2 changing real part of A (1,0) from 3 to 2 changing real part of A (0,1) from 3 to 13 changing real part of A (2,1) from -1 to 7 changing real part of A (4,1) from 4 to 10 changing real part of A (1,2) from 4 to 23 changing real part of A (2,2) from -3 to 15 changing real part of A (3,2) from 1 to 18 changing real part of A (4,2) from 2 to 18 changing real part of A (2,3) from 2 to 30 changing real part of A (1,4) from 0 to 39 changing real part of A (4,4) from 1 to 37 completely modified A (same pattern): column-form matrix, n_row 5 n_col 5, nz = 12. column 0: start: 0 end: 1 entries: 2 row 0 : (2 + 1i) row 1 : (2 + 0.1i) column 1: start: 2 end: 4 entries: 3 row 0 : (13 + 0i) row 2 : (7 - 1i) row 4 : (10 + 0.3i) column 2: start: 5 end: 8 entries: 4 row 1 : (23 + 0.2i) row 2 : (15 - 0.2i) row 3 : (18 + 0i) row 4 : (18 + 0.3i) column 3: start: 9 end: 9 entries: 1 row 2 : (30 + 3i) column 4: start: 10 end: 11 entries: 2 row 1 : (39 + 0i) row 4 : (37 + 0.4i) column-form matrix OK Saving symbolic object: Freeing symbolic object: Loading symbolic object: Done loading symbolic object Numeric factorization of completely modified A: Numeric object: n_row: 5 n_col: 5 relative pivot tolerance used: 0.1 relative symmetric pivot tolerance used: 0.001 matrix scaled: yes (divided each row by sum abs value in each row) minimum sum (abs (rows of A)): 1.60000e+01 maximum sum (abs (rows of A)): 6.60000e+01 initial allocation parameter used: 0.7 frontal matrix allocation parameter used: 0.5 final total size of Numeric object (Units): 74 final total size of Numeric object (MBytes): 0.0 peak size of variable-size part (Units): 1292 peak size of variable-size part (MBytes): 0.0 largest actual frontal matrix size: 4 memory defragmentations: 1 memory reallocations: 1 costly memory reallocations: 0 entries in compressed pattern (L and U): 2 number of nonzeros in L (excl diag): 4 number of entries stored in L (excl diag): 2 number of nonzeros in U (excl diag): 4 number of entries stored in U (excl diag): 2 factorization floating-point operations: 34 number of nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.39754e-01 max abs. value on diagonal of U: 1.00000e+00 reciprocal condition number estimate: 1.40e-01 Scale factors applied via multiplication Scale factors, Rs: dense vector, n = 5. 0 : (0.0625) 1 : (0.0155521) 2 : (0.0177936) 3 : (0.0555556) 4 : (0.0151515) dense vector OK P: row permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 4 4 : 1 permutation vector OK Q: column permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK L in Numeric object, in column-oriented compressed-pattern form: Diagonal entries are all equal to 1.0 (not stored) column 0: length 0. column 1: length 2. row 4 : (0.357698 + 0.00311042i) row 3 : (0.272727 + 0.00454545i) column 2: add 1 entries. length 1. Start of Lchain. row 4 : (0.204044 - 0.0895801i) column 3: length 1. row 4 : (1.0818 - 0.0116951i) column 4: length 0. Start of Lchain. U in Numeric object, in row-oriented compressed-pattern form: Diagonal is stored separately. row 4: length 0. End of Uchain. row 3: length 1. End of Uchain. col 4 : (0.151515 + 0.00454545i) row 2: length 1. col 4 : (0.8125 + 0i) row 1: length 0. End of Uchain. row 1: length 0. row 0: length 2. col 1 : (0.266904 - 0.00355872i) col 4 : (0.124555 - 0.0177936i) diagonal of U: dense vector, n = 5. 0 : (0.533808 + 0.0533808i) 1 : (1 + 0i) 2 : (0.125 + 0.0625i) 3 : (0.560606 + 0.00606061i) 4 : (-0.329747 + 0.0696386i) dense vector OK Numeric object: OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double complex Int (generic integer) defined as: UF_long BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 16-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 16 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 138 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 41 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.60000e+01 maximum sum (abs (rows of A)): 6.60000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 74 69 93% peak size (Units) 1301 1292 99% final size (Units) 15 13 87% Numeric final size (Units) 79 75 95% Numeric final size (MBytes) 0.0 0.0 95% peak memory usage (Units) 1463 1454 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 6.70000e+01 3.40000e+01 51% nz in L (incl diagonal) 10 9 90% nz in U (incl diagonal) 10 9 90% nz in L+U (incl diagonal) 15 13 87% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 9 nz in U (incl diagonal), if none dropped 9 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.40e-01 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 1.40e-01 indices in compressed pattern: 2 numerical values stored in Numeric object: 9 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 5.23000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 8.05e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 5.57000e+02 x (with completely modified A): dense vector, n = 5. 0 : (7.56307 - 3.68974i) 1 : (-0.831991 + 0.0627998i) 2 : (0.166667 + 0i) 3 : (-0.00206892 - 0.107735i) 4 : (0.658245 + 0.0407649i) dense vector OK maxnorm of residual: 9.10383e-15 C (transpose of A): column-form matrix, n_row 5 n_col 5, nz = 12. column 0: start: 0 end: 1 entries: 2 row 0 : (2 - 1i) row 1 : (13 + 0i) column 1: start: 2 end: 4 entries: 3 row 0 : (2 - 0.1i) row 2 : (23 - 0.2i) row 4 : (39 + 0i) column 2: start: 5 end: 7 entries: 3 row 1 : (7 + 1i) row 2 : (15 + 0.2i) row 3 : (30 - 3i) column 3: start: 8 end: 8 entries: 1 row 2 : (18 + 0i) column 4: start: 9 end: 11 entries: 3 row 1 : (10 - 0.3i) row 2 : (18 - 0.3i) row 4 : (37 - 0.4i) column-form matrix OK Symbolic factorization of C: Symbolic object: matrix to be factorized: n_row: 5 n_col: 5 number of entries: 12 block size used for dense matrix kernels: 32 strategy used: unsymmetric ordering used: colamd on A performn column etree postorder: yes prefer diagonal pivoting (attempt P=Q): no variable-size part of Numeric object: minimum initial size (Units): 75 (MBytes): 0.0 estimated peak size (Units): 1302 (MBytes): 0.0 estimated final size (Units): 16 (MBytes): 0.0 symbolic factorization memory usage (Units): 138 (MBytes): 0.0 frontal matrices / supercolumns: number of frontal chains: 1 number of frontal matrices: 1 largest frontal matrix row dimension: 3 largest frontal matrix column dimension: 3 Frontal chain: 0. Frontal matrices 0 to 0 Largest frontal matrix in Frontal chain: 3-by-3 Front: 0 pivot cols: 3 (pivot columns 0 to 2) pivot row candidates: 2 to 4 leftmost descendant: 0 1st new candidate row : 2 parent: (none) Initial column permutation, Q1: permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK Initial row permutation, P1: permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 1 4 : 4 permutation vector OK Symbolic object: OK Get the contents of the Symbolic object for C: (compare with umfpack_zl_report_symbolic output, above) From the Symbolic object, C is of dimension 5-by-5 with nz = 12, number of fronts = 1, number of frontal matrix chains = 1 Pivot columns in each front, and parent of each front: Front 0: parent front: -1 number of pivot cols: 3 0-th pivot column is column 3 in original matrix 1-th pivot column is column 2 in original matrix 2-th pivot column is column 0 in original matrix Note that the column ordering, above, will be refined in the numeric factorization below. The assignment of pivot columns to frontal matrices will always remain unchanged. Total number of pivot columns in frontal matrices: 3 Frontal matrix chains: Frontal matrices 0 to 0 are factorized in a single working array of size 3-by-3 Numeric factorization of C: Numeric object: n_row: 5 n_col: 5 relative pivot tolerance used: 0.1 relative symmetric pivot tolerance used: 0.001 matrix scaled: yes (divided each row by sum abs value in each row) minimum sum (abs (rows of A)): 5.10000e+00 maximum sum (abs (rows of A)): 7.64000e+01 initial allocation parameter used: 0.7 frontal matrix allocation parameter used: 0.5 final total size of Numeric object (Units): 75 final total size of Numeric object (MBytes): 0.0 peak size of variable-size part (Units): 1293 peak size of variable-size part (MBytes): 0.0 largest actual frontal matrix size: 4 memory defragmentations: 1 memory reallocations: 1 costly memory reallocations: 0 entries in compressed pattern (L and U): 2 number of nonzeros in L (excl diag): 3 number of entries stored in L (excl diag): 2 number of nonzeros in U (excl diag): 5 number of entries stored in U (excl diag): 2 factorization floating-point operations: 34 number of nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 2.40964e-01 max abs. value on diagonal of U: 9.13625e-01 reciprocal condition number estimate: 2.64e-01 Scale factors applied via multiplication Scale factors, Rs: dense vector, n = 5. 0 : (0.196078) 1 : (0.0319489) 2 : (0.0133869) 3 : (0.030303) 4 : (0.013089) dense vector OK P: row permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 4 4 : 1 permutation vector OK Q: column permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK L in Numeric object, in column-oriented compressed-pattern form: Diagonal entries are all equal to 1.0 (not stored) column 0: length 0. column 1: length 1. row 4 : (0.240091 + 0.0591529i) column 2: add 1 entries. length 1. Start of Lchain. row 4 : (0.847284 + 0.423642i) column 3: length 1. row 4 : (0.659838 - 0.0126577i) column 4: length 0. Start of Lchain. U in Numeric object, in row-oriented compressed-pattern form: Diagonal is stored separately. row 4: length 0. End of Uchain. row 3: length 1. End of Uchain. col 4 : (0.510471 + 0i) row 2: length 1. col 4 : (0.392157 - 0.0196078i) row 1: length 0. End of Uchain. row 1: length 0. row 0: length 3. col 1 : (0.200803 + 0.00267738i) col 3 : (0.240964 - 0.00401606i) col 4 : (0.307898 - 0.00267738i) diagonal of U: dense vector, n = 5. 0 : (0.240964 + 0i) 1 : (0.909091 - 0.0909091i) 2 : (0.392157 - 0.196078i) 3 : (0.484293 - 0.0052356i) 4 : (-0.677403 - 0.143059i) dense vector OK Numeric object: OK L (lower triangular factor of C): row-form matrix, n_row 5 n_col 5, nz = 8. row 0: start: 0 end: 0 entries: 1 column 0 : (1 + 0i) row 1: start: 1 end: 1 entries: 1 column 1 : (1 + 0i) row 2: start: 2 end: 2 entries: 1 column 2 : (1 + 0i) row 3: start: 3 end: 3 entries: 1 column 3 : (1 + 0i) row 4: start: 4 end: 7 entries: 4 column 1 : (0.240091 + 0.0591529i) column 2 : (0.847284 + 0.423642i) column 3 : (0.659838 - 0.0126577i) column 4 : (1 + 0i) row-form matrix OK U (upper triangular factor of C): column-form matrix, n_row 5 n_col 5, nz = 10. column 0: start: 0 end: 0 entries: 1 row 0 : (0.240964 + 0i) column 1: start: 1 end: 2 entries: 2 row 0 : (0.200803 + 0.00267738i) row 1 : (0.909091 - 0.0909091i) column 2: start: 3 end: 3 entries: 1 row 2 : (0.392157 - 0.196078i) column 3: start: 4 end: 5 entries: 2 row 0 : (0.240964 - 0.00401606i) row 3 : (0.484293 - 0.0052356i) column 4: start: 6 end: 9 entries: 4 row 0 : (0.307898 - 0.00267738i) row 2 : (0.392157 - 0.0196078i) row 3 : (0.510471 + 0i) row 4 : (-0.677403 - 0.143059i) column-form matrix OK P: permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 4 4 : 1 permutation vector OK Q: permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK Scale factors: row i of A is to be multiplied by the ith scale factor 0: 0.196078 1: 0.0319489 2: 0.0133869 3: 0.030303 4: 0.013089 Converting L to triplet form, and printing it: L, in triplet form: triplet-form matrix, n_row = 5, n_col = 5 nz = 8. 0 : 0 0 (1 + 0i) 1 : 1 1 (1 + 0i) 2 : 2 2 (1 + 0i) 3 : 3 3 (1 + 0i) 4 : 4 1 (0.240091 + 0.0591529i) 5 : 4 2 (0.847284 + 0.423642i) 6 : 4 3 (0.659838 - 0.0126577i) 7 : 4 4 (1 + 0i) triplet-form matrix OK Saving numeric object: Freeing numeric object: Loading numeric object: Done loading numeric object UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double complex Int (generic integer) defined as: UF_long BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 16-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 16 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 138 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 41 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 5.10000e+00 maximum sum (abs (rows of A)): 7.64000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 75 70 93% peak size (Units) 1302 1293 99% final size (Units) 16 14 88% Numeric final size (Units) 80 76 95% Numeric final size (MBytes) 0.0 0.0 95% peak memory usage (Units) 1464 1455 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 6.70000e+01 3.40000e+01 51% nz in L (incl diagonal) 9 8 89% nz in U (incl diagonal) 11 10 91% nz in L+U (incl diagonal) 15 13 87% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 8 nz in U (incl diagonal), if none dropped 10 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 2.41e-01 max abs. value on diagonal of U: 9.14e-01 estimate of reciprocal of condition number: 2.64e-01 indices in compressed pattern: 2 numerical values stored in Numeric object: 9 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 4.80000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 9.42e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 5.14000e+02 x (solution of C'x=b): dense vector, n = 5. 0 : (7.56307 - 3.68974i) 1 : (-0.831991 + 0.0627998i) 2 : (0.166667 + 0i) 3 : (-0.00206892 - 0.107735i) 4 : (0.658245 + 0.0407649i) dense vector OK maxnorm of residual: 4.88498e-15 Solving C'x=b again, using umfpack_zl_wsolve instead: UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double complex Int (generic integer) defined as: UF_long BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 16-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 16 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 138 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 41 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 5.10000e+00 maximum sum (abs (rows of A)): 7.64000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 75 70 93% peak size (Units) 1302 1293 99% final size (Units) 16 14 88% Numeric final size (Units) 80 76 95% Numeric final size (MBytes) 0.0 0.0 95% peak memory usage (Units) 1464 1455 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 6.70000e+01 3.40000e+01 51% nz in L (incl diagonal) 9 8 89% nz in U (incl diagonal) 11 10 91% nz in L+U (incl diagonal) 15 13 87% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 8 nz in U (incl diagonal), if none dropped 10 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 2.41e-01 max abs. value on diagonal of U: 9.14e-01 estimate of reciprocal of condition number: 2.64e-01 indices in compressed pattern: 2 numerical values stored in Numeric object: 9 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 4.80000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 9.42e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 5.14000e+02 x (solution of C'x=b): dense vector, n = 5. 0 : (7.56307 - 3.68974i) 1 : (-0.831991 + 0.0627998i) 2 : (0.166667 + 0i) 3 : (-0.00206892 - 0.107735i) 4 : (0.658245 + 0.0407649i) dense vector OK maxnorm of residual: 4.88498e-15 umfpack_zl_demo complete. Total time: 0.00 seconds (CPU time), 0.01 seconds (wallclock time) SuiteSparse/UMFPACK/Demo/umfpack_zl_demo.sed0000644001170100242450000000021610425655501017557 0ustar davisfac/::/d 1,$s/_xx_/_zl_/g 1,$s/Int/UF_long/g 1,$s/WSIZE/10/ /define ABS/ { s/ABS/ABS(x,z) ((x) >= 0 ? (x) : -(x)) + ((z) >= 0 ? (z) : -(z))/ } SuiteSparse/UMFPACK/Demo/simple_compile0000755001170100242450000000707410425665454016673 0ustar davisfac#!/bin/csh # This one-line command compiles all of UMFPACK and the double/int demo. # It forms a useful prototype for Microsoft Visual Studio, which does not # have the flexibility of Unix/Linux "make". The latter can be configured # to compile one file multiple times (as required by UMFPACK). Here, # that requirement is solved with a single file, umf_multicompile.c. # # No BLAS is used here. You should modify this to add your BLAS. # Otherwise your performance will be low. cc -DDINT -DNBLAS -I../../UFconfig \ -I../Include -I../Source -I../../AMD/Include -I../../AMD/Source \ umfpack_di_demo.c \ ../Source/umf_multicompile.c \ ../Source/umfpack_global.c \ ../Source/umf_ltsolve.c \ ../Source/umf_utsolve.c \ ../Source/umf_triplet.c \ ../Source/umf_assemble.c \ ../Source/umf_store_lu.c \ ../Source/umfpack_solve.c \ ../../AMD/Source/amd_1.c \ ../../AMD/Source/amd_2.c \ ../../AMD/Source/amd_aat.c \ ../../AMD/Source/amd_control.c \ ../../AMD/Source/amd_defaults.c \ ../../AMD/Source/amd_global.c \ ../../AMD/Source/amd_dump.c \ ../../AMD/Source/amd_info.c \ ../../AMD/Source/amd_order.c \ ../../AMD/Source/amd_post_tree.c \ ../../AMD/Source/amd_postorder.c \ ../../AMD/Source/amd_preprocess.c \ ../../AMD/Source/amd_valid.c \ ../Source/umf_2by2.c \ ../Source/umf_analyze.c \ ../Source/umf_apply_order.c \ ../Source/umf_blas3_update.c \ ../Source/umf_build_tuples.c \ ../Source/umf_colamd.c \ ../Source/umf_create_element.c \ ../Source/umf_dump.c \ ../Source/umf_extend_front.c \ ../Source/umf_free.c \ ../Source/umf_fsize.c \ ../Source/umf_garbage_collection.c \ ../Source/umf_get_memory.c \ ../Source/umf_grow_front.c \ ../Source/umf_init_front.c \ ../Source/umf_is_permutation.c \ ../Source/umf_kernel.c \ ../Source/umf_kernel_init.c \ ../Source/umf_kernel_wrapup.c \ ../Source/umf_local_search.c \ ../Source/umf_lsolve.c \ ../Source/umf_malloc.c \ ../Source/umf_mem_alloc_element.c \ ../Source/umf_mem_alloc_head_block.c \ ../Source/umf_mem_alloc_tail_block.c \ ../Source/umf_mem_free_tail_block.c \ ../Source/umf_mem_init_memoryspace.c \ ../Source/umf_realloc.c \ ../Source/umf_report_perm.c \ ../Source/umf_report_vector.c \ ../Source/umf_row_search.c \ ../Source/umf_scale.c \ ../Source/umf_scale_column.c \ ../Source/umf_set_stats.c \ ../Source/umf_singletons.c \ ../Source/umf_solve.c \ ../Source/umf_start_front.c \ ../Source/umf_symbolic_usage.c \ ../Source/umf_transpose.c \ ../Source/umf_tuple_lengths.c \ ../Source/umf_usolve.c \ ../Source/umf_valid_numeric.c \ ../Source/umf_valid_symbolic.c \ ../Source/umfpack_col_to_triplet.c \ ../Source/umfpack_defaults.c \ ../Source/umfpack_free_numeric.c \ ../Source/umfpack_free_symbolic.c \ ../Source/umfpack_get_determinant.c \ ../Source/umfpack_get_lunz.c \ ../Source/umfpack_get_numeric.c \ ../Source/umfpack_get_symbolic.c \ ../Source/umfpack_load_numeric.c \ ../Source/umfpack_load_symbolic.c \ ../Source/umfpack_numeric.c \ ../Source/umfpack_qsymbolic.c \ ../Source/umfpack_report_control.c \ ../Source/umfpack_report_info.c \ ../Source/umfpack_report_matrix.c \ ../Source/umfpack_report_numeric.c \ ../Source/umfpack_report_perm.c \ ../Source/umfpack_report_status.c \ ../Source/umfpack_report_symbolic.c \ ../Source/umfpack_report_triplet.c \ ../Source/umfpack_report_vector.c \ ../Source/umfpack_save_numeric.c \ ../Source/umfpack_save_symbolic.c \ ../Source/umfpack_scale.c \ ../Source/umfpack_symbolic.c \ ../Source/umfpack_tictoc.c \ ../Source/umfpack_timer.c \ ../Source/umfpack_transpose.c \ ../Source/umfpack_triplet_to_col.c \ -lm # now run the demo ./a.out SuiteSparse/UMFPACK/Demo/umf4.c0000644001170100242450000004162310617161004014742 0ustar davisfac/* ========================================================================== */ /* === umf4 ================================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Demo program for UMFPACK. Reads in a triplet-form matrix in the * directory tmp/A, whose size and # of nonzeros are in the file tmp/Asize. * Then calls UMFPACK to analyze, factor, and solve the system. * * Syntax: * * umf4 default "auto" strategy, 1-norm row scaling * umf4 a default "auto" strategy, 1-norm row scaling * umf4 u unsymmetric strategy, 1-norm row scaling * umf4 s symmetric strategy, 1-norm row scaling * umf4 2 2-by-2 strategy, maxnorm row scaling * umf4 A default "auto" strategy, maxnorm row scaling * umf4 U unsymmetric strategy, maxnorm row scaling * umf4 S symmetric strategy, maxnorm row scaling * umf4 T 2-by-2 strategy , maxnorm row scaling * * To test a matrix in the Harwell/Boeing format, do the following: * * readhb < HB/arc130.rua > tmp/A * readhb_size < HB/arc130.rua > tmp/Asize * umf4 * * The above options do not drop any nonzero entry in L or U. To compute an * incomplete factorization, you can add a second argument to give the drop * tolerance. Entries less than or equal to the drop tolerance are then * removed from L and U during factorization, unless dropping those entries * does not save any memory space. For example: * * umf4 a 1e-6 default "auto" strategy, 1-norm row scaling, * drop tolerance of 1e-6. * * Note that adding a drop tolerance can lead to an apparent (but not real) * increase in peak memory usage. This is illustrated in the arc130.rua * matrix. With a drop tolerance, garbage collection happens to be avoided * for this matrix. During garbage collection, both internal and external * fragmentation in the memory space is removed. Peak memory usage includes * all internal memory fragmentation, even though this can be removed via * garbage collection. * * Control parameters can also be set in the optional tmp/control.umf4 file. * The right-hand-side can be provided in the optional tmp/b file. The solution * is written to tmp/x, and the output statistics are written to tmp/info.umf4. * * After the matrix is factorized, solved, and the LU factors deallocated, * this program then test the AMD ordering routine. This call to AMD is NOT * part of the UMFPACK analysis, factorize, or solve steps. It is just a * separate test of the AMD ordering routine. If the matrix is unsymmetric, * AMD orders the pattern of A+A'. */ #include #include #include #include "umfpack.h" #include "amd.h" #define SMAX 256 #define ABS(x) ((x) >= 0 ? (x) : -(x)) #define MAX(a,b) (((a) > (b)) ? (a) : (b)) #define XTRUE(i,n) (1.0 + ((double) i) / ((double) n)) #ifndef FALSE #define FALSE 0 #endif #ifndef TRUE #define TRUE 1 #endif /* -------------------------------------------------------------------------- */ /* err: compute the relative error, ||x-xtrue||/||xtrue|| */ /* -------------------------------------------------------------------------- */ static double err ( int n, double x [ ] ) { int i ; double enorm, e, abse, absxtrue, xnorm ; enorm = 0 ; xnorm = 0 ; for (i = 0 ; i < n ; i++) { if (isnan (x [i])) { enorm = x [i] ; break ; } e = x [i] - XTRUE (i,n) ; abse = ABS (e) ; enorm = MAX (enorm, abse) ; } for (i = 0 ; i < n ; i++) { /* XTRUE is positive, but do this in case XTRUE is redefined */ absxtrue = ABS (XTRUE (i,n)) ; xnorm = MAX (xnorm, absxtrue) ; } if (xnorm == 0) { xnorm = 1 ; } return (enorm / xnorm) ; } /* -------------------------------------------------------------------------- */ /* resid: compute the relative residual, ||Ax-b||/||b|| or ||A'x-b||/||b|| */ /* -------------------------------------------------------------------------- */ static double resid ( int n, int Ap [ ], int Ai [ ], double Ax [ ], double x [ ], double r [ ], double b [ ], int transpose ) { int i, j, p ; double rnorm, absr, absb, bnorm ; for (i = 0 ; i < n ; i++) { r [i] = 0 ; } if (transpose) { for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; r [j] += Ax [p] * x [i] ; } } } else { for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; r [i] += Ax [p] * x [j] ; } } } for (i = 0 ; i < n ; i++) { r [i] -= b [i] ; } rnorm = 0. ; bnorm = 0. ; for (i = 0 ; i < n ; i++) { if (isnan (r [i])) { rnorm = r [i] ; break ; } absr = ABS (r [i]) ; rnorm = MAX (rnorm, absr) ; } for (i = 0 ; i < n ; i++) { if (isnan (b [i])) { bnorm = b [i] ; break ; } absb = ABS (b [i]) ; bnorm = MAX (bnorm, absb) ; } if (bnorm == 0) { bnorm = 1 ; } return (rnorm / bnorm) ; } /* -------------------------------------------------------------------------- */ /* Atimesx: compute y = A*x or A'*x, where x (i) = 1 + i/n */ /* -------------------------------------------------------------------------- */ static void Atimesx ( int n, int Ap [ ], int Ai [ ], double Ax [ ], double y [ ], int transpose ) { int i, j, p ; for (i = 0 ; i < n ; i++) { y [i] = 0 ; } if (transpose) { for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; y [j] += Ax [p] * XTRUE (i,n) ; } } } else { for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; y [i] += Ax [p] * XTRUE (j,n) ; } } } } /* -------------------------------------------------------------------------- */ /* main program */ /* -------------------------------------------------------------------------- */ int main (int argc, char **argv) { int i, j, k, n, nz, *Ap, *Ai, *Ti, *Tj, status, *Pamd, nrow, ncol, rhs ; double *Ax, *b, *x, Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], aij, *Tx, *r, amd_Control [AMD_CONTROL], amd_Info [AMD_INFO], tamd [2], stats [2], droptol ; void *Symbolic, *Numeric ; FILE *f, *f2 ; char s [SMAX] ; /* ---------------------------------------------------------------------- */ /* set controls */ /* ---------------------------------------------------------------------- */ printf ("\n===========================================================\n" "=== UMFPACK v%d.%d.%d ========================================\n" "===========================================================\n", UMFPACK_MAIN_VERSION, UMFPACK_SUB_VERSION, UMFPACK_SUBSUB_VERSION) ; umfpack_di_defaults (Control) ; Control [UMFPACK_PRL] = 3 ; Control [UMFPACK_BLOCK_SIZE] = 32 ; f = fopen ("tmp/control.umf4", "r") ; if (f != (FILE *) NULL) { printf ("Reading control file tmp/control.umf4\n") ; for (i = 0 ; i < UMFPACK_CONTROL ; i++) { fscanf (f, "%lg\n", & Control [i]) ; } fclose (f) ; } if (argc > 1) { char *s = argv [1] ; /* get the strategy */ if (s [0] == 'u') { Control [UMFPACK_STRATEGY] = UMFPACK_STRATEGY_UNSYMMETRIC ; } else if (s [0] == 'a') { Control [UMFPACK_STRATEGY] = UMFPACK_STRATEGY_AUTO ; } else if (s [0] == 's') { Control [UMFPACK_STRATEGY] = UMFPACK_STRATEGY_SYMMETRIC ; } else if (s [0] == '2') { Control [UMFPACK_STRATEGY] = UMFPACK_STRATEGY_2BY2 ; } else if (s [0] == 'U') { Control [UMFPACK_STRATEGY] = UMFPACK_STRATEGY_UNSYMMETRIC ; Control [UMFPACK_SCALE] = UMFPACK_SCALE_MAX ; } else if (s [0] == 'A') { Control [UMFPACK_STRATEGY] = UMFPACK_STRATEGY_AUTO ; Control [UMFPACK_SCALE] = UMFPACK_SCALE_MAX ; } else if (s [0] == 'S') { Control [UMFPACK_STRATEGY] = UMFPACK_STRATEGY_SYMMETRIC ; Control [UMFPACK_SCALE] = UMFPACK_SCALE_MAX ; } else if (s [0] == 'T') { Control [UMFPACK_STRATEGY] = UMFPACK_STRATEGY_2BY2 ; Control [UMFPACK_SCALE] = UMFPACK_SCALE_MAX ; } else { printf ("unrecognized strategy: %s\n", argv [1]) ; } if (s [1] == 'n') { /* no aggressive absorption */ Control [UMFPACK_AGGRESSIVE] = FALSE ; } } if (argc > 2) { /* get the drop tolerance */ sscanf (argv [2], "%lg", &droptol) ; printf ("droptol %g\n", droptol) ; Control [UMFPACK_DROPTOL] = droptol ; } umfpack_di_report_control (Control) ; /* ---------------------------------------------------------------------- */ /* open the matrix file (tmp/A) */ /* ---------------------------------------------------------------------- */ printf ("File: tmp/A\n") ; f = fopen ("tmp/A", "r") ; if (!f) { printf ("Unable to open file\n") ; exit (1) ; } /* ---------------------------------------------------------------------- */ /* get n and nz */ /* ---------------------------------------------------------------------- */ printf ("File: tmp/Asize\n") ; f2 = fopen ("tmp/Asize", "r") ; if (f2) { fscanf (f2, "%d %d %d\n", &nrow, &ncol, &nz) ; fclose (f2) ; } else { nrow = 1 ; ncol = 1 ; } nz = 0 ; while (fgets (s, SMAX, f) != (char *) NULL) { sscanf (s, "%d %d %lg", &i, &j, &aij) ; #ifdef ZERO_BASED /* matrix is zero based */ i++ ; j++ ; #endif nrow = MAX (nrow, i) ; ncol = MAX (ncol, j) ; nz++ ; } fclose (f) ; n = MAX (nrow, ncol) ; printf ("n %d nrow %d ncol %d nz %d\n", n, nrow, ncol, nz) ; /* ---------------------------------------------------------------------- */ /* allocate space for the input triplet form */ /* ---------------------------------------------------------------------- */ Ti = (int *) malloc (nz * sizeof (int)) ; Tj = (int *) malloc (nz * sizeof (int)) ; Tx = (double *) malloc (nz * sizeof (double)) ; if (!Ti || !Tj || !Tx) { printf ("out of memory for input matrix\n") ; exit (1) ; } /* ---------------------------------------------------------------------- */ /* read in the triplet form */ /* ---------------------------------------------------------------------- */ f2 = fopen ("tmp/A", "r") ; if (!f2) { printf ("Unable to open file\n") ; exit (1) ; } k = 0 ; while (fgets (s, SMAX, f2) != (char *) NULL) { sscanf (s, "%d %d %lg", &i, &j, &aij) ; #ifndef ZERO_BASED i-- ; /* convert to 0-based */ j-- ; #endif if (k >= nz) { printf ("Error! Matrix size is wrong\n") ; exit (1) ; } Ti [k] = i ; Tj [k] = j ; Tx [k] = aij ; k++ ; } fclose (f2) ; (void) umfpack_di_report_triplet (nrow, ncol, nz, Ti, Tj, Tx, Control) ; /* ---------------------------------------------------------------------- */ /* convert to column form */ /* ---------------------------------------------------------------------- */ /* convert to column form */ Ap = (int *) malloc ((n+1) * sizeof (int)) ; Ai = (int *) malloc (nz * sizeof (int)) ; Ax = (double *) malloc (nz * sizeof (double)) ; b = (double *) malloc (n * sizeof (double)) ; r = (double *) malloc (n * sizeof (double)) ; x = (double *) malloc (n * sizeof (double)) ; if (!Ap || !Ai || !Ax || !b || !r) { printf ("out of memory") ; exit (1) ; } umfpack_tic (stats) ; status = umfpack_di_triplet_to_col (nrow, ncol, nz, Ti, Tj, Tx, Ap, Ai, Ax, (int *) NULL) ; umfpack_toc (stats) ; printf ("triplet-to-col time: wall %g cpu %g\n", stats [0], stats [1]) ; if (status != UMFPACK_OK) { umfpack_di_report_status (Control, status) ; printf ("umfpack_di_triplet_to_col failed") ; exit (1) ; } /* print the column-form of A */ (void) umfpack_di_report_matrix (nrow, ncol, Ap, Ai, Ax, 1, Control) ; /* b = A * xtrue */ rhs = FALSE ; if (nrow == ncol) { f = fopen ("tmp/b", "r") ; if (f != (FILE *) NULL) { printf ("Reading tmp/b\n") ; rhs = TRUE ; for (i = 0 ; i < n ; i++) { fscanf (f, "%lg\n", &b [i]) ; } fclose (f) ; } else { Atimesx (n, Ap, Ai, Ax, b, FALSE) ; } } /* ---------------------------------------------------------------------- */ /* free the triplet form */ /* ---------------------------------------------------------------------- */ free (Ti) ; free (Tj) ; free (Tx) ; /* ---------------------------------------------------------------------- */ /* symbolic factorization */ /* ---------------------------------------------------------------------- */ status = umfpack_di_symbolic (nrow, ncol, Ap, Ai, Ax, &Symbolic, Control, Info) ; umfpack_di_report_info (Control, Info) ; if (status != UMFPACK_OK) { umfpack_di_report_status (Control, status) ; printf ("umfpack_di_symbolic failed") ; exit (1) ; } /* print the symbolic factorization */ (void) umfpack_di_report_symbolic (Symbolic, Control) ; /* ---------------------------------------------------------------------- */ /* numeric factorization */ /* ---------------------------------------------------------------------- */ status = umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric, Control, Info); if (status < UMFPACK_OK) { umfpack_di_report_info (Control, Info) ; umfpack_di_report_status (Control, status) ; fprintf (stderr, "umfpack_di_numeric failed: %d\n", status) ; printf ("umfpack_di_numeric failed\n") ; exit (1) ; } /* print the numeric factorization */ (void) umfpack_di_report_numeric (Numeric, Control) ; /* ---------------------------------------------------------------------- */ /* solve Ax=b */ /* ---------------------------------------------------------------------- */ if (nrow == ncol && status == UMFPACK_OK) { status = umfpack_di_solve (UMFPACK_A, Ap, Ai, Ax, x, b, Numeric, Control, Info) ; umfpack_di_report_info (Control, Info) ; umfpack_di_report_status (Control, status) ; if (status < UMFPACK_OK) { printf ("umfpack_di_solve failed\n") ; exit (1) ; } (void) umfpack_di_report_vector (n, x, Control) ; printf ("relative maxnorm of residual, ||Ax-b||/||b||: %g\n", resid (n, Ap, Ai, Ax, x, r, b, FALSE)) ; if (!rhs) { printf ("relative maxnorm of error, ||x-xtrue||/||xtrue||: %g\n\n", err (n, x)) ; } f = fopen ("tmp/x", "w") ; if (f != (FILE *) NULL) { printf ("Writing tmp/x\n") ; for (i = 0 ; i < n ; i++) { fprintf (f, "%30.20e\n", x [i]) ; } fclose (f) ; } else { printf ("Unable to write output x!\n") ; exit (1) ; } f = fopen ("tmp/info.umf4", "w") ; if (f != (FILE *) NULL) { printf ("Writing tmp/info.umf4\n") ; for (i = 0 ; i < UMFPACK_INFO ; i++) { fprintf (f, "%30.20e\n", Info [i]) ; } fclose (f) ; } else { printf ("Unable to write output info!\n") ; exit (1) ; } } else { /* don't solve, just report the results */ umfpack_di_report_info (Control, Info) ; umfpack_di_report_status (Control, status) ; } /* ---------------------------------------------------------------------- */ /* free the Symbolic and Numeric factorization */ /* ---------------------------------------------------------------------- */ umfpack_di_free_symbolic (&Symbolic) ; umfpack_di_free_numeric (&Numeric) ; printf ("umf4 done, strategy: %g\n", Control [UMFPACK_STRATEGY]) ; /* ---------------------------------------------------------------------- */ /* test just AMD ordering (not part of UMFPACK, but a separate test) */ /* ---------------------------------------------------------------------- */ /* first make the matrix square */ if (ncol < n) { for (j = ncol+1 ; j <= n ; j++) { Ap [j] = Ap [ncol] ; } } printf ( "\n\n===========================================================\n" "=== AMD ===================================================\n" "===========================================================\n") ; printf ("\n\n------- Now trying the AMD ordering. This not part of\n" "the UMFPACK analysis or factorization, above, but a separate\n" "test of just the AMD ordering routine.\n") ; Pamd = (int *) malloc (n * sizeof (int)) ; if (!Pamd) { printf ("out of memory\n") ; exit (1) ; } amd_defaults (amd_Control) ; amd_control (amd_Control) ; umfpack_tic (tamd) ; status = amd_order (n, Ap, Ai, Pamd, amd_Control, amd_Info) ; umfpack_toc (tamd) ; printf ("AMD ordering time: cpu %10.2f wall %10.2f\n", tamd [1], tamd [0]) ; if (status != AMD_OK) { printf ("amd failed: %d\n", status) ; exit (1) ; } amd_info (amd_Info) ; free (Pamd) ; printf ("AMD test done\n") ; return (0) ; } SuiteSparse/UMFPACK/Demo/umf4hb.out0000644001170100242450000001430710711433323015641 0ustar davisfac Matrix key: WEST0067 UMFPACK V5.2.0 (Nov 1, 2007), Control: Matrix entry defined as: double Int (generic integer) defined as: int 0: print level: 2 1: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 2: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 3: pivot tolerance: 0.1 4: block size for dense matrix kernels: 32 5: strategy: 0 (auto) 6: initial allocation ratio: 0.7 7: max iterative refinement steps: 2 12: 2-by-2 pivot tolerance: 0.01 13: Q fixed during numerical factorization: 0 (auto) 14: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 15: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 16: scaling: 1 (divide each row by sum of abs. values in each row) 17: frontal matrix allocation ratio: 0.5 18: drop tolerance: 0 19: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4 9: compiled for ANSI C 10: CPU timer is POSIX times ( ) routine. 11: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes) symbolic analysis: status: 0. time: 0.00E+00 (sec) estimates (upper bound) for numeric LU: size of LU: 0.02 (MB) memory needed: 0.06 (MB) flop count: 0.14E+05 nnz (L): 542. nnz (U): 902. numeric factorization: status: 0. time: 0.00E+00 actual numeric LU statistics: size of LU: 0.01 (MB) memory needed: 0.04 (MB) flop count: 0.25E+04 nnz (L): 323. nnz (U): 339. UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 67 number of columns in matrix A: 67 entries in matrix A: 294 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 1 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S not square or diagonal not preserved symbolic factorization defragmentations: 1 symbolic memory usage (Units): 1639 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 252 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 6.59006e+00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 1711 1577 92% peak size (Units) 6115 3581 59% final size (Units) 1628 682 42% Numeric final size (Units) 2108 1129 54% Numeric final size (MBytes) 0.0 0.0 54% peak memory usage (Units) 7476 4942 66% peak memory usage (MBytes) 0.1 0.0 66% numeric factorization flops 1.41920e+04 2.50100e+03 18% nz in L (incl diagonal) 542 323 60% nz in U (incl diagonal) 902 339 38% nz in L+U (incl diagonal) 1377 595 43% largest front (# entries) 483 80 17% largest # rows in front 21 10 48% largest # columns in front 23 11 48% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 323 nz in U (incl diagonal), if none dropped 339 number of small entries dropped 0 nonzeros on diagonal of U: 67 min abs. value on diagonal of U: 2.74e-02 max abs. value on diagonal of U: 2.28e+00 estimate of reciprocal of condition number: 1.20e-02 indices in compressed pattern: 263 numerical values stored in Numeric object: 599 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 1.19000e+03 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 3.69100e+03 norm (A*x-b): 0. norm (A*x-b): 0. norm (A*x-b): 0. SuiteSparse/UMFPACK/Demo/umf4hb64.f0000644001170100242450000002771110172176362015444 0ustar davisfacc======================================================================= c== umf4hb ============================================================= c======================================================================= c----------------------------------------------------------------------- c UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis. CISE c Dept, Univ. of Florida. All Rights Reserved. See ../Doc/License for c License. web: http://www.cise.ufl.edu/research/sparse/umfpack c----------------------------------------------------------------------- c umf4hb64: c read a sparse matrix in the Harwell/Boeing format, factorizes c it, and solves Ax=b. Also saves and loads the factors to/from a c file. Saving to a file is not required, it's just here to c demonstrate how to use this feature of UMFPACK. This program c only works on square RUA-type matrices. c c This is HIGHLY non-portable. It may not work with your C and c FORTRAN compilers. See umf4_f77wrapper.c for more details. c c usage (for example): c c in a Unix shell: c umf4hb64 < HB/arc130.rua integer*8 $ nzmax, nmax parameter (nzmax = 5000000, nmax = 160000) integer*8 $ Ap (nmax), Ai (nzmax), n, nz, totcrd, ptrcrd, i, j, p, $ indcrd, valcrd, rhscrd, ncol, nrow, nrhs, nzrhs, nel, $ numeric, symbolic, status, sys, filenum character title*72, key*30, type*3, ptrfmt*16, $ indfmt*16, valfmt*20, rhsfmt*20 double precision Ax (nzmax), x (nmax), b (nmax), aij, xj, $ r (nmax), control (20), info (90) character rhstyp*3 c ---------------------------------------------------------------- c read the Harwell/Boeing matrix c ---------------------------------------------------------------- read (5, 10, err = 998) $ title, key, $ totcrd, ptrcrd, indcrd, valcrd, rhscrd, $ type, nrow, ncol, nz, nel, $ ptrfmt, indfmt, valfmt, rhsfmt if (rhscrd .gt. 0) then c new Harwell/Boeing format: read (5, 20, err = 998) rhstyp, nrhs, nzrhs endif 10 format (a72, a8 / 5i14 / a3, 11x, 4i14 / 2a16, 2a20) 20 format (a3, 11x, 2i14) print *, 'Matrix key: ', key n = nrow if (type .ne. 'RUA' .or. nrow .ne. ncol) then print *, 'Error: can only handle square RUA matrices' stop endif if (n .ge. nmax .or. nz .gt. nzmax) then print *, ' Matrix too big!' stop endif c read the matrix (1-based) read (5, ptrfmt, err = 998) (Ap (p), p = 1, ncol+1) read (5, indfmt, err = 998) (Ai (p), p = 1, nz) read (5, valfmt, err = 998) (Ax (p), p = 1, nz) c ---------------------------------------------------------------- c create the right-hand-side, assume x (i) = 1 + i/n c ---------------------------------------------------------------- do 30 i = 1,n b (i) = 0 30 continue c b = A*x do 50 j = 1,n xj = j xj = 1 + xj / n do 40 p = Ap (j), Ap (j+1)-1 i = Ai (p) aij = Ax (p) b (i) = b (i) + aij * xj 40 continue 50 continue c ---------------------------------------------------------------- c convert from 1-based to 0-based c ---------------------------------------------------------------- do 60 j = 1, n+1 Ap (j) = Ap (j) - 1 60 continue do 70 p = 1, nz Ai (p) = Ai (p) - 1 70 continue c ---------------------------------------------------------------- c factor the matrix and save to a file c ---------------------------------------------------------------- c set default parameters call umf4def (control) c print control parameters. set control (1) to 1 to print c error messages only control (1) = 2 call umf4pcon (control) c pre-order and symbolic analysis call umf4sym (n, n, Ap, Ai, Ax, symbolic, control, info) c print statistics computed so far c call umf4pinf (control, info) could also be done. print 80, info (1), info (16), $ (info (21) * info (4)) / 2**20, $ (info (22) * info (4)) / 2**20, $ info (23), info (24), info (25) 80 format ('symbolic analysis:',/, $ ' status: ', f5.0, /, $ ' time: ', e10.2, ' (sec)'/, $ ' estimates (upper bound) for numeric LU:', /, $ ' size of LU: ', f10.2, ' (MB)', /, $ ' memory needed: ', f10.2, ' (MB)', /, $ ' flop count: ', e10.2, / $ ' nnz (L): ', f10.0, / $ ' nnz (U): ', f10.0) c check umf4sym error condition if (info (1) .lt. 0) then print *, 'Error occurred in umf4sym: ', info (1) stop endif c numeric factorization call umf4num (Ap, Ai, Ax, symbolic, numeric, control, info) c print statistics for the numeric factorization c call umf4pinf (control, info) could also be done. print 90, info (1), info (66), $ (info (41) * info (4)) / 2**20, $ (info (42) * info (4)) / 2**20, $ info (43), info (44), info (45) 90 format ('numeric factorization:',/, $ ' status: ', f5.0, /, $ ' time: ', e10.2, /, $ ' actual numeric LU statistics:', /, $ ' size of LU: ', f10.2, ' (MB)', /, $ ' memory needed: ', f10.2, ' (MB)', /, $ ' flop count: ', e10.2, / $ ' nnz (L): ', f10.0, / $ ' nnz (U): ', f10.0) c check umf4num error condition if (info (1) .lt. 0) then print *, 'Error occurred in umf4num: ', info (1) stop endif c save the symbolic analysis to the file s0.umf c note that this is not needed until another matrix is c factorized, below. filenum = 0 call umf4ssym (symbolic, filenum, status) if (status .lt. 0) then print *, 'Error occurred in umf4ssym: ', status stop endif c save the LU factors to the file n0.umf call umf4snum (numeric, filenum, status) if (status .lt. 0) then print *, 'Error occurred in umf4snum: ', status stop endif c free the symbolic analysis call umf4fsym (symbolic) c free the numeric factorization call umf4fnum (numeric) c No LU factors (symbolic or numeric) are in memory at this point. c ---------------------------------------------------------------- c load the LU factors back in, and solve the system c ---------------------------------------------------------------- c At this point the program could terminate and load the LU C factors (numeric) from the n0.umf file, and solve the c system (see below). Note that the symbolic object is not c required. c load the numeric factorization back in (filename: n0.umf) call umf4lnum (numeric, filenum, status) if (status .lt. 0) then print *, 'Error occurred in umf4lnum: ', status stop endif c solve Ax=b, without iterative refinement sys = 0 call umf4sol (sys, x, b, numeric, control, info) if (info (1) .lt. 0) then print *, 'Error occurred in umf4sol: ', info (1) stop endif c free the numeric factorization call umf4fnum (numeric) c No LU factors (symbolic or numeric) are in memory at this point. c print final statistics call umf4pinf (control, info) c print the residual. x (i) should be 1 + i/n call resid (n, nz, Ap, Ai, Ax, x, b, r) c ---------------------------------------------------------------- c load the symbolic analysis back in, and factorize a new matrix c ---------------------------------------------------------------- c Again, the program could terminate here, recreate the matrix, c and refactorize. Note that umf4sym is not called. c load the symbolic factorization back in (filename: s0.umf) call umf4lsym (symbolic, filenum, status) if (status .lt. 0) then print *, 'Error occurred in umf4lsym: ', status stop endif c arbitrarily change the values of the matrix but not the pattern do 100 p = 1, nz Ax (p) = Ax (p) + 3.14159 / 100.0 100 continue c numeric factorization of the modified matrix call umf4num (Ap, Ai, Ax, symbolic, numeric, control, info) if (info (1) .lt. 0) then print *, 'Error occurred in umf4num: ', info (1) stop endif c free the symbolic analysis call umf4fsym (symbolic) c create a new right-hand-side, assume x (i) = 7 - i/n do 110 i = 1,n b (i) = 0 110 continue c b = A*x, with the modified matrix A (note that A is now 0-based) do 130 j = 1,n xj = j xj = 7 - xj / n do 120 p = Ap (j) + 1, Ap (j+1) i = Ai (p) + 1 aij = Ax (p) b (i) = b (i) + aij * xj 120 continue 130 continue c ---------------------------------------------------------------- c solve Ax=b, with iterative refinement c ---------------------------------------------------------------- sys = 0 call umf4solr (sys, Ap, Ai, Ax, x, b, numeric, control, info) if (info (1) .lt. 0) then print *, 'Error occurred in umf4solr: ', info (1) stop endif c print the residual. x (i) should be 7 - i/n call resid (n, nz, Ap, Ai, Ax, x, b, r) c ---------------------------------------------------------------- c solve Ax=b, without iterative refinement, broken into steps c ---------------------------------------------------------------- c the factorization is PAQ=LU, PRAQ=LU, or P(R\A)Q=LU. c x = R*b (or x=R\b, or x=b, as appropriate) call umf4scal (x, b, numeric, status) if (status .lt. 0) then print *, 'Error occurred in umf4scal: ', status stop endif c solve P'Lr=x for r (using r as workspace) sys = 3 call umf4sol (sys, r, x, numeric, control, info) if (info (1) .lt. 0) then print *, 'Error occurred in umf4sol: ', info (1) stop endif c solve UQ'x=r for x sys = 9 call umf4sol (sys, x, r, numeric, control, info) if (info (1) .lt. 0) then print *, 'Error occurred in umf4sol: ', info (1) stop endif c free the numeric factorization call umf4fnum (numeric) c print the residual. x (i) should be 7 - i/n call resid (n, nz, Ap, Ai, Ax, x, b, r) stop 998 print *, 'Read error: Harwell/Boeing matrix' stop end c======================================================================= c== resid ============================================================== c======================================================================= c Compute the residual, r = Ax-b, its max-norm, and print the max-norm C Note that A is zero-based. subroutine resid (n, nz, Ap, Ai, Ax, x, b, r) integer*8 $ n, nz, Ap (n+1), Ai (n), j, i, p double precision Ax (nz), x (n), b (n), r (n), rmax, aij do 10 i = 1, n r (i) = -b (i) 10 continue do 30 j = 1,n do 20 p = Ap (j) + 1, Ap (j+1) i = Ai (p) + 1 aij = Ax (p) r (i) = r (i) + aij * x (j) 20 continue 30 continue rmax = 0 do 40 i = 1, n rmax = max (rmax, r (i)) 40 continue print *, 'norm (A*x-b): ', rmax return end SuiteSparse/UMFPACK/Demo/umfpack_di_demo.out0000644001170100242450000015252210711433150017562 0ustar davisfac UMFPACK V5.2 (Nov 1, 2007) demo: _di_ version UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. UMFPACK License: UMFPACK is available under alternate licenses, contact T. Davis for details. Your use or distribution of UMFPACK or any modified version of UMFPACK implies that you agree to this License. This library is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Permission is hereby granted to use or copy this program under the terms of the GNU GPL, provided that the Copyright, this License, and the Availability of the original version is retained on all copies. User documentation of any code that uses this code or any modified version of this code must cite the Copyright, this License, the Availability note, and "Used by permission." Permission to modify the code and to distribute modified code is granted, provided the Copyright, this License, and the Availability note are retained, and a notice that the code was modified is included. Availability: http://www.cise.ufl.edu/research/sparse/umfpack UMFPACK V5.2.0 (Nov 1, 2007): OK UMFPACK V5.2.0 (Nov 1, 2007), Control: Matrix entry defined as: double Int (generic integer) defined as: int 0: print level: 5 1: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 2: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 3: pivot tolerance: 0.1 4: block size for dense matrix kernels: 32 5: strategy: 0 (auto) 6: initial allocation ratio: 0.7 7: max iterative refinement steps: 2 12: 2-by-2 pivot tolerance: 0.01 13: Q fixed during numerical factorization: 0 (auto) 14: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 15: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 16: scaling: 1 (divide each row by sum of abs. values in each row) 17: frontal matrix allocation ratio: 0.5 18: drop tolerance: 0 19: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4 9: compiled for ANSI C 10: CPU timer is POSIX times ( ) routine. 11: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes) b: dense vector, n = 5. 0 : (8) 1 : (45) 2 : (-3) 3 : (3) 4 : (19) dense vector OK A: triplet-form matrix, n_row = 5, n_col = 5 nz = 12. 0 : 0 0 (2) 1 : 4 4 (1) 2 : 1 0 (3) 3 : 1 2 (4) 4 : 2 1 (-1) 5 : 2 2 (-3) 6 : 0 1 (3) 7 : 1 4 (6) 8 : 2 3 (2) 9 : 3 2 (1) 10 : 4 1 (4) 11 : 4 2 (2) triplet-form matrix OK A: column-form matrix, n_row 5 n_col 5, nz = 12. column 0: start: 0 end: 1 entries: 2 row 0 : (2) row 1 : (3) column 1: start: 2 end: 4 entries: 3 row 0 : (3) row 2 : (-1) row 4 : (4) column 2: start: 5 end: 8 entries: 4 row 1 : (4) row 2 : (-3) row 3 : (1) row 4 : (2) column 3: start: 9 end: 9 entries: 1 row 2 : (2) column 4: start: 10 end: 11 entries: 2 row 1 : (6) row 4 : (1) column-form matrix OK Symbolic factorization of A: Symbolic object: matrix to be factorized: n_row: 5 n_col: 5 number of entries: 12 block size used for dense matrix kernels: 32 strategy used: unsymmetric ordering used: colamd on A performn column etree postorder: yes prefer diagonal pivoting (attempt P=Q): no variable-size part of Numeric object: minimum initial size (Units): 80 (MBytes): 0.0 estimated peak size (Units): 1301 (MBytes): 0.0 estimated final size (Units): 15 (MBytes): 0.0 symbolic factorization memory usage (Units): 151 (MBytes): 0.0 frontal matrices / supercolumns: number of frontal chains: 1 number of frontal matrices: 1 largest frontal matrix row dimension: 3 largest frontal matrix column dimension: 3 Frontal chain: 0. Frontal matrices 0 to 0 Largest frontal matrix in Frontal chain: 3-by-3 Front: 0 pivot cols: 3 (pivot columns 0 to 2) pivot row candidates: 2 to 4 leftmost descendant: 0 1st new candidate row : 2 parent: (none) Initial column permutation, Q1: permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK Initial row permutation, P1: permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 1 4 : 4 permutation vector OK Symbolic object: OK Numeric factorization of A: Numeric object: n_row: 5 n_col: 5 relative pivot tolerance used: 0.1 relative symmetric pivot tolerance used: 0.001 matrix scaled: yes (divided each row by sum abs value in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 1.30000e+01 initial allocation parameter used: 0.7 frontal matrix allocation parameter used: 0.5 final total size of Numeric object (Units): 87 final total size of Numeric object (MBytes): 0.0 peak size of variable-size part (Units): 1292 peak size of variable-size part (MBytes): 0.0 largest actual frontal matrix size: 4 memory defragmentations: 1 memory reallocations: 1 costly memory reallocations: 0 entries in compressed pattern (L and U): 2 number of nonzeros in L (excl diag): 4 number of entries stored in L (excl diag): 2 number of nonzeros in U (excl diag): 4 number of entries stored in U (excl diag): 2 factorization floating-point operations: 6 number of nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.42857e-01 max abs. value on diagonal of U: 2.19231e+00 reciprocal condition number estimate: 6.52e-02 Scale factors applied via multiplication Scale factors, Rs: dense vector, n = 5. 0 : (0.2) 1 : (0.0769231) 2 : (0.166667) 3 : (1) 4 : (0.142857) dense vector OK P: row permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 4 4 : 1 permutation vector OK Q: column permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK L in Numeric object, in column-oriented compressed-pattern form: Diagonal entries are all equal to 1.0 (not stored) column 0: length 0. column 1: length 2. row 4 : (0.307692) row 3 : (0.285714) column 2: add 1 entries. length 1. Start of Lchain. row 4 : (0.576923) column 3: length 1. row 4 : (3.23077) column 4: length 0. Start of Lchain. U in Numeric object, in row-oriented compressed-pattern form: Diagonal is stored separately. row 4: length 0. End of Uchain. row 3: length 1. End of Uchain. col 4 : (0.571429) row 2: length 1. col 4 : (0.6) row 1: length 0. End of Uchain. row 1: length 0. row 0: length 2. col 1 : (-0.5) col 4 : (-0.166667) diagonal of U: dense vector, n = 5. 0 : (0.333333) 1 : (1) 2 : (0.4) 3 : (0.142857) 4 : (-2.19231) dense vector OK Numeric object: OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 151 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 52 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 1.30000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 80 70 88% peak size (Units) 1301 1292 99% final size (Units) 15 13 87% Numeric final size (Units) 92 88 96% Numeric final size (MBytes) 0.0 0.0 96% peak memory usage (Units) 1487 1478 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 1.30000e+01 6.00000e+00 46% nz in L (incl diagonal) 10 9 90% nz in U (incl diagonal) 10 9 90% nz in L+U (incl diagonal) 15 13 87% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 9 nz in U (incl diagonal), if none dropped 9 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.43e-01 max abs. value on diagonal of U: 2.19e+00 estimate of reciprocal of condition number: 6.52e-02 indices in compressed pattern: 2 numerical values stored in Numeric object: 9 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 1.19000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 1.18e-16 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 1.25000e+02 UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. UMFPACK V5.2.0 (Nov 1, 2007): OK x (solution of Ax=b): dense vector, n = 5. 0 : (1) 1 : (2) 2 : (3) 3 : (4) 4 : (5) dense vector OK maxnorm of residual: 1.06581e-14 UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. UMFPACK V5.2.0 (Nov 1, 2007): OK determinant: (1.14) * 10^(2) x (solution of Ax=b, solve is split into 3 steps): dense vector, n = 5. 0 : (1) 1 : (2) 2 : (3) 3 : (4) 4 : (5) dense vector OK maxnorm of residual: 1.06581e-14 UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 151 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 52 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 1.30000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 80 70 88% peak size (Units) 1301 1292 99% final size (Units) 15 13 87% Numeric final size (Units) 92 88 96% Numeric final size (MBytes) 0.0 0.0 96% peak memory usage (Units) 1487 1478 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 1.30000e+01 6.00000e+00 46% nz in L (incl diagonal) 10 9 90% nz in U (incl diagonal) 10 9 90% nz in L+U (incl diagonal) 15 13 87% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 9 nz in U (incl diagonal), if none dropped 9 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.43e-01 max abs. value on diagonal of U: 2.19e+00 estimate of reciprocal of condition number: 6.52e-02 indices in compressed pattern: 2 numerical values stored in Numeric object: 9 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 1.11000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 7.64e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 1.17000e+02 x (solution of A'x=b): dense vector, n = 5. 0 : (1.81579) 1 : (1.45614) 2 : (1.5) 3 : (-24.8509) 4 : (10.2632) dense vector OK maxnorm of residual: 7.10543e-15 changing A (1,4) to zero modified A: column-form matrix, n_row 5 n_col 5, nz = 12. column 0: start: 0 end: 1 entries: 2 row 0 : (2) row 1 : (3) column 1: start: 2 end: 4 entries: 3 row 0 : (3) row 2 : (-1) row 4 : (4) column 2: start: 5 end: 8 entries: 4 row 1 : (4) row 2 : (-3) row 3 : (1) row 4 : (2) column 3: start: 9 end: 9 entries: 1 row 2 : (2) column 4: start: 10 end: 11 entries: 2 row 1 : (0) row 4 : (1) column-form matrix OK Numeric factorization of modified A: Numeric object: n_row: 5 n_col: 5 relative pivot tolerance used: 0.1 relative symmetric pivot tolerance used: 0.001 matrix scaled: yes (divided each row by sum abs value in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 7.00000e+00 initial allocation parameter used: 0.7 frontal matrix allocation parameter used: 0.5 final total size of Numeric object (Units): 86 final total size of Numeric object (MBytes): 0.0 peak size of variable-size part (Units): 1292 peak size of variable-size part (MBytes): 0.0 largest actual frontal matrix size: 4 memory defragmentations: 1 memory reallocations: 1 costly memory reallocations: 0 entries in compressed pattern (L and U): 2 number of nonzeros in L (excl diag): 4 number of entries stored in L (excl diag): 2 number of nonzeros in U (excl diag): 3 number of entries stored in U (excl diag): 1 factorization floating-point operations: 4 number of nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.50000e-01 max abs. value on diagonal of U: 1.00000e+00 reciprocal condition number estimate: 1.50e-01 Scale factors applied via multiplication Scale factors, Rs: dense vector, n = 5. 0 : (0.2) 1 : (0.142857) 2 : (0.166667) 3 : (1) 4 : (0.142857) dense vector OK P: row permutation vector, n = 5. 0 : 2 1 : 3 2 : 1 3 : 4 4 : 0 permutation vector OK Q: column permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 1 4 : 4 permutation vector OK L in Numeric object, in column-oriented compressed-pattern form: Diagonal entries are all equal to 1.0 (not stored) column 0: length 0. column 1: length 2. row 2 : (0.571429) row 3 : (0.285714) column 2: add 1 entries. length 1. Start of Lchain. row 4 : (0.933333) column 3: length 1. row 4 : (1.05) column 4: length 0. Start of Lchain. U in Numeric object, in row-oriented compressed-pattern form: Diagonal is stored separately. row 4: length 0. End of Uchain. row 3: length 1. End of Uchain. col 4 : (0.142857) row 2: length 0. End of Uchain. row 1: length 0. End of Uchain. row 1: length 0. row 0: length 2. col 1 : (-0.5) col 3 : (-0.166667) diagonal of U: dense vector, n = 5. 0 : (0.333333) 1 : (1) 2 : (0.428571) 3 : (0.571429) 4 : (-0.15) dense vector OK Numeric object: OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 151 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 52 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 7.00000e+00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 80 70 88% peak size (Units) 1301 1292 99% final size (Units) 15 12 80% Numeric final size (Units) 92 87 95% Numeric final size (MBytes) 0.0 0.0 95% peak memory usage (Units) 1487 1478 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 1.30000e+01 4.00000e+00 31% nz in L (incl diagonal) 10 9 90% nz in U (incl diagonal) 10 8 80% nz in L+U (incl diagonal) 15 12 80% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 9 nz in U (incl diagonal), if none dropped 8 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.50e-01 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 1.50e-01 indices in compressed pattern: 2 numerical values stored in Numeric object: 8 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 1.17000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 7.89e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 1.21000e+02 x (with modified A): dense vector, n = 5. 0 : (11) 1 : (-4.66667) 2 : (3) 3 : (0.666667) 4 : (31.6667) dense vector OK maxnorm of residual: 7.10543e-15 changing A (0,0) from 2 to 2 changing A (1,0) from 3 to 2 changing A (0,1) from 3 to 13 changing A (2,1) from -1 to 7 changing A (4,1) from 4 to 10 changing A (1,2) from 4 to 23 changing A (2,2) from -3 to 15 changing A (3,2) from 1 to 18 changing A (4,2) from 2 to 18 changing A (2,3) from 2 to 30 changing A (1,4) from 0 to 39 changing A (4,4) from 1 to 37 completely modified A (same pattern): column-form matrix, n_row 5 n_col 5, nz = 12. column 0: start: 0 end: 1 entries: 2 row 0 : (2) row 1 : (2) column 1: start: 2 end: 4 entries: 3 row 0 : (13) row 2 : (7) row 4 : (10) column 2: start: 5 end: 8 entries: 4 row 1 : (23) row 2 : (15) row 3 : (18) row 4 : (18) column 3: start: 9 end: 9 entries: 1 row 2 : (30) column 4: start: 10 end: 11 entries: 2 row 1 : (39) row 4 : (37) column-form matrix OK Saving symbolic object: Freeing symbolic object: Loading symbolic object: Done loading symbolic object Numeric factorization of completely modified A: Numeric object: n_row: 5 n_col: 5 relative pivot tolerance used: 0.1 relative symmetric pivot tolerance used: 0.001 matrix scaled: yes (divided each row by sum abs value in each row) minimum sum (abs (rows of A)): 1.50000e+01 maximum sum (abs (rows of A)): 6.50000e+01 initial allocation parameter used: 0.7 frontal matrix allocation parameter used: 0.5 final total size of Numeric object (Units): 87 final total size of Numeric object (MBytes): 0.0 peak size of variable-size part (Units): 1292 peak size of variable-size part (MBytes): 0.0 largest actual frontal matrix size: 4 memory defragmentations: 1 memory reallocations: 1 costly memory reallocations: 0 entries in compressed pattern (L and U): 2 number of nonzeros in L (excl diag): 4 number of entries stored in L (excl diag): 2 number of nonzeros in U (excl diag): 4 number of entries stored in U (excl diag): 2 factorization floating-point operations: 6 number of nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.33333e-01 max abs. value on diagonal of U: 1.00000e+00 reciprocal condition number estimate: 1.33e-01 Scale factors applied via multiplication Scale factors, Rs: dense vector, n = 5. 0 : (0.0666667) 1 : (0.015625) 2 : (0.0192308) 3 : (0.0555556) 4 : (0.0153846) dense vector OK P: row permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 4 4 : 1 permutation vector OK Q: column permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK L in Numeric object, in column-oriented compressed-pattern form: Diagonal entries are all equal to 1.0 (not stored) column 0: length 0. column 1: length 2. row 4 : (0.359375) row 3 : (0.276923) column 2: add 1 entries. length 1. Start of Lchain. row 4 : (0.234375) column 3: length 1. row 4 : (1.07052) column 4: length 0. Start of Lchain. U in Numeric object, in row-oriented compressed-pattern form: Diagonal is stored separately. row 4: length 0. End of Uchain. row 3: length 1. End of Uchain. col 4 : (0.153846) row 2: length 1. col 4 : (0.866667) row 1: length 0. End of Uchain. row 1: length 0. row 0: length 2. col 1 : (0.288462) col 4 : (0.134615) diagonal of U: dense vector, n = 5. 0 : (0.576923) 1 : (1) 2 : (0.133333) 3 : (0.569231) 4 : (-0.367821) dense vector OK Numeric object: OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 151 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 52 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.50000e+01 maximum sum (abs (rows of A)): 6.50000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 80 70 88% peak size (Units) 1301 1292 99% final size (Units) 15 13 87% Numeric final size (Units) 92 88 96% Numeric final size (MBytes) 0.0 0.0 96% peak memory usage (Units) 1487 1478 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 1.30000e+01 6.00000e+00 46% nz in L (incl diagonal) 10 9 90% nz in U (incl diagonal) 10 9 90% nz in L+U (incl diagonal) 15 13 87% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 9 nz in U (incl diagonal), if none dropped 9 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.33e-01 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 1.33e-01 indices in compressed pattern: 2 numerical values stored in Numeric object: 9 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 1.19000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 1.04e-16 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 1.25000e+02 x (with completely modified A): dense vector, n = 5. 0 : (8.50124) 1 : (-0.692499) 2 : (0.166667) 3 : (-0.0217502) 4 : (0.619594) dense vector OK maxnorm of residual: 3.55271e-15 C (transpose of A): column-form matrix, n_row 5 n_col 5, nz = 12. column 0: start: 0 end: 1 entries: 2 row 0 : (2) row 1 : (13) column 1: start: 2 end: 4 entries: 3 row 0 : (2) row 2 : (23) row 4 : (39) column 2: start: 5 end: 7 entries: 3 row 1 : (7) row 2 : (15) row 3 : (30) column 3: start: 8 end: 8 entries: 1 row 2 : (18) column 4: start: 9 end: 11 entries: 3 row 1 : (10) row 2 : (18) row 4 : (37) column-form matrix OK Symbolic factorization of C: Symbolic object: matrix to be factorized: n_row: 5 n_col: 5 number of entries: 12 block size used for dense matrix kernels: 32 strategy used: unsymmetric ordering used: colamd on A performn column etree postorder: yes prefer diagonal pivoting (attempt P=Q): no variable-size part of Numeric object: minimum initial size (Units): 81 (MBytes): 0.0 estimated peak size (Units): 1302 (MBytes): 0.0 estimated final size (Units): 16 (MBytes): 0.0 symbolic factorization memory usage (Units): 151 (MBytes): 0.0 frontal matrices / supercolumns: number of frontal chains: 1 number of frontal matrices: 1 largest frontal matrix row dimension: 3 largest frontal matrix column dimension: 3 Frontal chain: 0. Frontal matrices 0 to 0 Largest frontal matrix in Frontal chain: 3-by-3 Front: 0 pivot cols: 3 (pivot columns 0 to 2) pivot row candidates: 2 to 4 leftmost descendant: 0 1st new candidate row : 2 parent: (none) Initial column permutation, Q1: permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK Initial row permutation, P1: permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 1 4 : 4 permutation vector OK Symbolic object: OK Get the contents of the Symbolic object for C: (compare with umfpack_di_report_symbolic output, above) From the Symbolic object, C is of dimension 5-by-5 with nz = 12, number of fronts = 1, number of frontal matrix chains = 1 Pivot columns in each front, and parent of each front: Front 0: parent front: -1 number of pivot cols: 3 0-th pivot column is column 3 in original matrix 1-th pivot column is column 2 in original matrix 2-th pivot column is column 0 in original matrix Note that the column ordering, above, will be refined in the numeric factorization below. The assignment of pivot columns to frontal matrices will always remain unchanged. Total number of pivot columns in frontal matrices: 3 Frontal matrix chains: Frontal matrices 0 to 0 are factorized in a single working array of size 3-by-3 Numeric factorization of C: Numeric object: n_row: 5 n_col: 5 relative pivot tolerance used: 0.1 relative symmetric pivot tolerance used: 0.001 matrix scaled: yes (divided each row by sum abs value in each row) minimum sum (abs (rows of A)): 4.00000e+00 maximum sum (abs (rows of A)): 7.60000e+01 initial allocation parameter used: 0.7 frontal matrix allocation parameter used: 0.5 final total size of Numeric object (Units): 88 final total size of Numeric object (MBytes): 0.0 peak size of variable-size part (Units): 1293 peak size of variable-size part (MBytes): 0.0 largest actual frontal matrix size: 4 memory defragmentations: 1 memory reallocations: 1 costly memory reallocations: 0 entries in compressed pattern (L and U): 2 number of nonzeros in L (excl diag): 3 number of entries stored in L (excl diag): 2 number of nonzeros in U (excl diag): 5 number of entries stored in U (excl diag): 2 factorization floating-point operations: 6 number of nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 2.43243e-01 max abs. value on diagonal of U: 1.00000e+00 reciprocal condition number estimate: 2.43e-01 Scale factors applied via multiplication Scale factors, Rs: dense vector, n = 5. 0 : (0.25) 1 : (0.0333333) 2 : (0.0135135) 3 : (0.0333333) 4 : (0.0131579) dense vector OK P: row permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 4 4 : 1 permutation vector OK Q: column permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK L in Numeric object, in column-oriented compressed-pattern form: Diagonal entries are all equal to 1.0 (not stored) column 0: length 0. column 1: length 1. row 4 : (0.233333) column 2: add 1 entries. length 1. Start of Lchain. row 4 : (0.866667) column 3: length 1. row 4 : (0.684685) column 4: length 0. Start of Lchain. U in Numeric object, in row-oriented compressed-pattern form: Diagonal is stored separately. row 4: length 0. End of Uchain. row 3: length 1. End of Uchain. col 4 : (0.513158) row 2: length 1. col 4 : (0.5) row 1: length 0. End of Uchain. row 1: length 0. row 0: length 3. col 1 : (0.202703) col 3 : (0.243243) col 4 : (0.310811) diagonal of U: dense vector, n = 5. 0 : (0.243243) 1 : (1) 2 : (0.5) 3 : (0.486842) 4 : (-0.784685) dense vector OK Numeric object: OK L (lower triangular factor of C): row-form matrix, n_row 5 n_col 5, nz = 8. row 0: start: 0 end: 0 entries: 1 column 0 : (1) row 1: start: 1 end: 1 entries: 1 column 1 : (1) row 2: start: 2 end: 2 entries: 1 column 2 : (1) row 3: start: 3 end: 3 entries: 1 column 3 : (1) row 4: start: 4 end: 7 entries: 4 column 1 : (0.233333) column 2 : (0.866667) column 3 : (0.684685) column 4 : (1) row-form matrix OK U (upper triangular factor of C): column-form matrix, n_row 5 n_col 5, nz = 10. column 0: start: 0 end: 0 entries: 1 row 0 : (0.243243) column 1: start: 1 end: 2 entries: 2 row 0 : (0.202703) row 1 : (1) column 2: start: 3 end: 3 entries: 1 row 2 : (0.5) column 3: start: 4 end: 5 entries: 2 row 0 : (0.243243) row 3 : (0.486842) column 4: start: 6 end: 9 entries: 4 row 0 : (0.310811) row 2 : (0.5) row 3 : (0.513158) row 4 : (-0.784685) column-form matrix OK P: permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 4 4 : 1 permutation vector OK Q: permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK Scale factors: row i of A is to be multiplied by the ith scale factor 0: 0.25 1: 0.0333333 2: 0.0135135 3: 0.0333333 4: 0.0131579 Converting L to triplet form, and printing it: L, in triplet form: triplet-form matrix, n_row = 5, n_col = 5 nz = 8. 0 : 0 0 (1) 1 : 1 1 (1) 2 : 2 2 (1) 3 : 3 3 (1) 4 : 4 1 (0.233333) 5 : 4 2 (0.866667) 6 : 4 3 (0.684685) 7 : 4 4 (1) triplet-form matrix OK Saving numeric object: Freeing numeric object: Loading numeric object: Done loading numeric object UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 151 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 52 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 4.00000e+00 maximum sum (abs (rows of A)): 7.60000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 81 71 88% peak size (Units) 1302 1293 99% final size (Units) 16 14 88% Numeric final size (Units) 93 89 96% Numeric final size (MBytes) 0.0 0.0 96% peak memory usage (Units) 1488 1479 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 1.30000e+01 6.00000e+00 46% nz in L (incl diagonal) 9 8 89% nz in U (incl diagonal) 11 10 91% nz in L+U (incl diagonal) 15 13 87% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 8 nz in U (incl diagonal), if none dropped 10 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 2.43e-01 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 2.43e-01 indices in compressed pattern: 2 numerical values stored in Numeric object: 9 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 1.11000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 8.07e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 1.17000e+02 x (solution of C'x=b): dense vector, n = 5. 0 : (8.50124) 1 : (-0.692499) 2 : (0.166667) 3 : (-0.0217502) 4 : (0.619594) dense vector OK maxnorm of residual: 3.55271e-15 Solving C'x=b again, using umfpack_di_wsolve instead: UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 151 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 52 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 4.00000e+00 maximum sum (abs (rows of A)): 7.60000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 81 71 88% peak size (Units) 1302 1293 99% final size (Units) 16 14 88% Numeric final size (Units) 93 89 96% Numeric final size (MBytes) 0.0 0.0 96% peak memory usage (Units) 1488 1479 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 1.30000e+01 6.00000e+00 46% nz in L (incl diagonal) 9 8 89% nz in U (incl diagonal) 11 10 91% nz in L+U (incl diagonal) 15 13 87% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 8 nz in U (incl diagonal), if none dropped 10 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 2.43e-01 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 2.43e-01 indices in compressed pattern: 2 numerical values stored in Numeric object: 9 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 1.11000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 8.07e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 1.17000e+02 x (solution of C'x=b): dense vector, n = 5. 0 : (8.50124) 1 : (-0.692499) 2 : (0.166667) 3 : (-0.0217502) 4 : (0.619594) dense vector OK maxnorm of residual: 3.55271e-15 umfpack_di_demo complete. Total time: 0.00 seconds (CPU time), 0.00 seconds (wallclock time) SuiteSparse/UMFPACK/Demo/umfpack_di_demo.sed0000644001170100242450000000123210006260704017515 0ustar davisfac/::/d 1,$s/_xx_/_di_/g 1,$s/Int/int/g 1,$s/WSIZE/5/ 1,$s/%ld/%d/g /define ABS/ { s/ABS/ABS(x) ((x) >= 0 ? (x) : -(x))/ } /, rz \[i\]/ { s/, rz \[i\]// } /, Avalz/ { s/, Avalz// } /, rz/ { s/, rz// } /, bz/ { s/, bz// } /, xz/ { s/, xz// } /, Lz/ { s/, Lz// } /, Uz/ { s/, Uz// } /, Dz/ { s/, Dz// } /, Az/ { s/, Az// } /, Cz, TRUE/ { s/, Cz, TRUE// } /, Cz/ { s/, Cz// } /, Rbz/ { s/, Rbz// } /, yz/ { s/, yz// } / || !Lz/ { s/ || !Lz// } / || !Uz/ { s/ || !Uz// } / || !Dz/ { s/ || !Dz// } / || !Az/ { s/ || !Az// } / || !Cz/ { s/ || !Cz// } /rz/d /Rbz/d /yz/d /Avalz/d /Az/d /Cz/d /bz/d /xz/d /Lz/d /Uz/d /Dz/d /complex/d SuiteSparse/UMFPACK/Demo/umfpack_zl_demo.c0000644001170100242450000006777310617501641017251 0ustar davisfac/* ========================================================================== */ /* === umfpack_zl_demo ====================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* A demo of UMFPACK: umfpack_zl_* version. First, factor and solve a 5-by-5 system, Ax=b, using default parameters. Then solve A'x=b using the factors of A. Modify one entry (A (1,4) = 0, where the row and column indices range from 0 to 4. The pattern of A has not changed (it has explicitly zero entry), so a reanalysis with umfpack_zl_symbolic does not need to be done. Refactorize (with umfpack_zl_numeric), and solve Ax=b. Note that the pivot ordering has changed. Next, change all of the entries in A, but not the pattern. Finally, compute C = A', and do the symbolic and numeric factorization of C. Factorizing A' can sometimes be better than factorizing A itself (less work and memory usage). Solve C'x=b twice; the solution is the same as the solution to Ax=b. A note about zero-sized arrays: UMFPACK uses many user-provided arrays of size n (order of the matrix), and of size nz (the number of nonzeros in a matrix). n cannot be zero; UMFPACK does not handle zero-dimensioned arrays. However, nz can be zero. If you attempt to malloc an array of size nz = 0, however, malloc will return a null pointer which UMFPACK will report as a "missing argument." Thus, nz1 in this code is set to MAX (nz,1), and similarly for lnz and unz. Lnz can never be zero, however, since L is always unit diagonal. */ /* -------------------------------------------------------------------------- */ /* definitions */ /* -------------------------------------------------------------------------- */ #include #include #include "umfpack.h" /* use a cheap approximate absolute value for complex numbers: */ #define ABS(x,z) ((x) >= 0 ? (x) : -(x)) + ((z) >= 0 ? (z) : -(z)) #define MAX(a,b) (((a) > (b)) ? (a) : (b)) #ifndef TRUE #define TRUE (1) #endif #ifndef FALSE #define FALSE (0) #endif /* -------------------------------------------------------------------------- */ /* triplet form of the matrix. The triplets can be in any order. */ /* -------------------------------------------------------------------------- */ static UF_long n = 5, nz = 12 ; static UF_long Arow [ ] = { 0, 4, 1, 1, 2, 2, 0, 1, 2, 3, 4, 4} ; static UF_long Acol [ ] = { 0, 4, 0, 2, 1, 2, 1, 4, 3, 2, 1, 2} ; static double Aval [ ] = {2., 1., 3., 4., -1., -3., 3., 6., 2., 1., 4., 2.} ; static double Avalz[ ] = {1., .4, .1, .2, -1., -.2, 0., 6., 3., 0., .3, .3} ; static double b [ ] = {8., 45., -3., 3., 19.}, x [5], r [5] ; static double bz[ ] = {1., -5., -2., 0., 2.2}, xz[5], rz[5] ; /* Avalz, bz: imaginary part of A and b */ /* -------------------------------------------------------------------------- */ /* error: print a message and exit */ /* -------------------------------------------------------------------------- */ static void error ( char *message ) { printf ("\n\n====== error: %s =====\n\n", message) ; exit (1) ; } /* -------------------------------------------------------------------------- */ /* resid: compute the residual, r = Ax-b or r = A'x=b and return maxnorm (r) */ /* A' is the complex conjugate transpose, not the array transpose */ /* -------------------------------------------------------------------------- */ static double resid ( UF_long transpose, UF_long Ap [ ], UF_long Ai [ ], double Ax [ ] , double Az [ ] ) { UF_long i, j, p ; double norm ; for (i = 0 ; i < n ; i++) { r [i] = -b [i] ; rz[i] = -bz[i] ; } if (transpose) { for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; /* complex: r(j) += conj (Aij) * x (i) */ r [j] += Ax [p] * x [i] ; r [j] += Az [p] * xz[i] ; rz[j] -= Az [p] * x [i] ; rz[j] += Ax [p] * xz[i] ; } } } else { for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; r [i] += Ax [p] * x [j] ; r [i] -= Az [p] * xz[j] ; rz[i] += Az [p] * x [j] ; rz[i] += Ax [p] * xz[j] ; } } } norm = 0. ; for (i = 0 ; i < n ; i++) { norm = MAX (ABS (r [i], rz [i]), norm) ; } return (norm) ; } /* -------------------------------------------------------------------------- */ /* main program */ /* -------------------------------------------------------------------------- */ int main (int argc, char **argv) { double Info [UMFPACK_INFO], Control [UMFPACK_CONTROL], *Ax, *Cx, *Lx, *Ux, *W, t [2], *Dx, rnorm, *Rb, *y, *Rs ; double *Az, *Lz, *Uz, *Dz, *Cz, *Rbz, *yz ; UF_long *Ap, *Ai, *Cp, *Ci, row, col, p, lnz, unz, nr, nc, *Lp, *Li, *Ui, *Up, *P, *Q, *Lj, i, j, k, anz, nfr, nchains, *Qinit, fnpiv, lnz1, unz1, nz1, status, *Front_npivcol, *Front_parent, *Chain_start, *Wi, *Pinit, n1, *Chain_maxrows, *Chain_maxcols, *Front_1strow, *Front_leftmostdesc, nzud, do_recip ; void *Symbolic, *Numeric ; /* ---------------------------------------------------------------------- */ /* initializations */ /* ---------------------------------------------------------------------- */ umfpack_tic (t) ; printf ("\nUMFPACK V%d.%d (%s) demo: _zl_ version\n", UMFPACK_MAIN_VERSION, UMFPACK_SUB_VERSION, UMFPACK_DATE) ; /* get the default control parameters */ umfpack_zl_defaults (Control) ; /* change the default print level for this demo */ /* (otherwise, nothing will print) */ Control [UMFPACK_PRL] = 6 ; /* print the license agreement */ umfpack_zl_report_status (Control, UMFPACK_OK) ; Control [UMFPACK_PRL] = 5 ; /* print the control parameters */ umfpack_zl_report_control (Control) ; /* ---------------------------------------------------------------------- */ /* print A and b, and convert A to column-form */ /* ---------------------------------------------------------------------- */ /* print the right-hand-side */ printf ("\nb: ") ; (void) umfpack_zl_report_vector (n, b, bz, Control) ; /* print the triplet form of the matrix */ printf ("\nA: ") ; (void) umfpack_zl_report_triplet (n, n, nz, Arow, Acol, Aval, Avalz, Control) ; /* convert to column form */ nz1 = MAX (nz,1) ; /* ensure arrays are not of size zero. */ Ap = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Ai = (UF_long *) malloc (nz1 * sizeof (UF_long)) ; Ax = (double *) malloc (nz1 * sizeof (double)) ; Az = (double *) malloc (nz1 * sizeof (double)) ; if (!Ap || !Ai || !Ax || !Az) { error ("out of memory") ; } status = umfpack_zl_triplet_to_col (n, n, nz, Arow, Acol, Aval, Avalz, Ap, Ai, Ax, Az, (UF_long *) NULL) ; if (status < 0) { umfpack_zl_report_status (Control, status) ; error ("umfpack_zl_triplet_to_col failed") ; } /* print the column-form of A */ printf ("\nA: ") ; (void) umfpack_zl_report_matrix (n, n, Ap, Ai, Ax, Az, 1, Control) ; /* ---------------------------------------------------------------------- */ /* symbolic factorization */ /* ---------------------------------------------------------------------- */ status = umfpack_zl_symbolic (n, n, Ap, Ai, Ax, Az, &Symbolic, Control, Info) ; if (status < 0) { umfpack_zl_report_info (Control, Info) ; umfpack_zl_report_status (Control, status) ; error ("umfpack_zl_symbolic failed") ; } /* print the symbolic factorization */ printf ("\nSymbolic factorization of A: ") ; (void) umfpack_zl_report_symbolic (Symbolic, Control) ; /* ---------------------------------------------------------------------- */ /* numeric factorization */ /* ---------------------------------------------------------------------- */ status = umfpack_zl_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric, Control, Info) ; if (status < 0) { umfpack_zl_report_info (Control, Info) ; umfpack_zl_report_status (Control, status) ; error ("umfpack_zl_numeric failed") ; } /* print the numeric factorization */ printf ("\nNumeric factorization of A: ") ; (void) umfpack_zl_report_numeric (Numeric, Control) ; /* ---------------------------------------------------------------------- */ /* solve Ax=b */ /* ---------------------------------------------------------------------- */ status = umfpack_zl_solve (UMFPACK_A, Ap, Ai, Ax, Az, x, xz, b, bz, Numeric, Control, Info) ; umfpack_zl_report_info (Control, Info) ; umfpack_zl_report_status (Control, status) ; if (status < 0) { error ("umfpack_zl_solve failed") ; } printf ("\nx (solution of Ax=b): ") ; (void) umfpack_zl_report_vector (n, x, xz, Control) ; rnorm = resid (FALSE, Ap, Ai, Ax, Az) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* compute the determinant */ /* ---------------------------------------------------------------------- */ status = umfpack_zl_get_determinant (x, xz, r, Numeric, Info) ; umfpack_zl_report_status (Control, status) ; if (status < 0) { error ("umfpack_zl_get_determinant failed") ; } printf ("determinant: (%g", x [0]) ; printf ("+ (%g)i", xz [0]) ; /* complex */ printf (") * 10^(%g)\n", r [0]) ; /* ---------------------------------------------------------------------- */ /* solve Ax=b, broken down into steps */ /* ---------------------------------------------------------------------- */ /* Rb = R*b */ Rb = (double *) malloc (n * sizeof (double)) ; Rbz = (double *) malloc (n * sizeof (double)) ; y = (double *) malloc (n * sizeof (double)) ; yz = (double *) malloc (n * sizeof (double)) ; if (!Rb || !y) error ("out of memory") ; if (!Rbz || !yz) error ("out of memory") ; status = umfpack_zl_scale (Rb, Rbz, b, bz, Numeric) ; if (status < 0) error ("umfpack_zl_scale failed") ; /* solve Ly = P*(Rb) */ status = umfpack_zl_solve (UMFPACK_Pt_L, Ap, Ai, Ax, Az, y, yz, Rb, Rbz, Numeric, Control, Info) ; if (status < 0) error ("umfpack_zl_solve failed") ; /* solve UQ'x=y */ status = umfpack_zl_solve (UMFPACK_U_Qt, Ap, Ai, Ax, Az, x, xz, y, yz, Numeric, Control, Info) ; if (status < 0) error ("umfpack_zl_solve failed") ; printf ("\nx (solution of Ax=b, solve is split into 3 steps): ") ; (void) umfpack_zl_report_vector (n, x, xz, Control) ; rnorm = resid (FALSE, Ap, Ai, Ax, Az) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; free (Rb) ; free (Rbz) ; free (y) ; free (yz) ; /* ---------------------------------------------------------------------- */ /* solve A'x=b */ /* ---------------------------------------------------------------------- */ /* note that this is the complex conjugate transpose, A' */ status = umfpack_zl_solve (UMFPACK_At, Ap, Ai, Ax, Az, x, xz, b, bz, Numeric, Control, Info) ; umfpack_zl_report_info (Control, Info) ; if (status < 0) { error ("umfpack_zl_solve failed") ; } printf ("\nx (solution of A'x=b): ") ; (void) umfpack_zl_report_vector (n, x, xz, Control) ; rnorm = resid (TRUE, Ap, Ai, Ax, Az) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* modify one numerical value in the column-form of A */ /* ---------------------------------------------------------------------- */ /* change A (1,4), look for row index 1 in column 4. */ row = 1 ; col = 4 ; for (p = Ap [col] ; p < Ap [col+1] ; p++) { if (row == Ai [p]) { printf ("\nchanging A (%ld,%ld) to zero\n", row, col) ; Ax [p] = 0.0 ; Az [p] = 0.0 ; break ; } } printf ("\nmodified A: ") ; (void) umfpack_zl_report_matrix (n, n, Ap, Ai, Ax, Az, 1, Control) ; /* ---------------------------------------------------------------------- */ /* redo the numeric factorization */ /* ---------------------------------------------------------------------- */ /* The pattern (Ap and Ai) hasn't changed, so the symbolic factorization */ /* doesn't have to be redone, no matter how much we change Ax. */ /* We don't need the Numeric object any more, so free it. */ umfpack_zl_free_numeric (&Numeric) ; /* Note that a memory leak would have occurred if the old Numeric */ /* had not been free'd with umfpack_zl_free_numeric above. */ status = umfpack_zl_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric, Control, Info) ; if (status < 0) { umfpack_zl_report_info (Control, Info) ; umfpack_zl_report_status (Control, status) ; error ("umfpack_zl_numeric failed") ; } printf ("\nNumeric factorization of modified A: ") ; (void) umfpack_zl_report_numeric (Numeric, Control) ; /* ---------------------------------------------------------------------- */ /* solve Ax=b, with the modified A */ /* ---------------------------------------------------------------------- */ status = umfpack_zl_solve (UMFPACK_A, Ap, Ai, Ax, Az, x, xz, b, bz, Numeric, Control, Info) ; umfpack_zl_report_info (Control, Info) ; if (status < 0) { umfpack_zl_report_status (Control, status) ; error ("umfpack_zl_solve failed") ; } printf ("\nx (with modified A): ") ; (void) umfpack_zl_report_vector (n, x, xz, Control) ; rnorm = resid (FALSE, Ap, Ai, Ax, Az) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* modify all of the numerical values of A, but not the pattern */ /* ---------------------------------------------------------------------- */ for (col = 0 ; col < n ; col++) { for (p = Ap [col] ; p < Ap [col+1] ; p++) { row = Ai [p] ; printf ("changing ") ; /* complex: */ printf ("real part of ") ; printf ("A (%ld,%ld) from %g", row, col, Ax [p]) ; Ax [p] = Ax [p] + col*10 - row ; printf (" to %g\n", Ax [p]) ; } } printf ("\ncompletely modified A (same pattern): ") ; (void) umfpack_zl_report_matrix (n, n, Ap, Ai, Ax, Az, 1, Control) ; /* ---------------------------------------------------------------------- */ /* save the Symbolic object to file, free it, and load it back in */ /* ---------------------------------------------------------------------- */ /* use the default filename, "symbolic.umf" */ printf ("\nSaving symbolic object:\n") ; status = umfpack_zl_save_symbolic (Symbolic, (char *) NULL) ; if (status < 0) { umfpack_zl_report_status (Control, status) ; error ("umfpack_zl_save_symbolic failed") ; } printf ("\nFreeing symbolic object:\n") ; umfpack_zl_free_symbolic (&Symbolic) ; printf ("\nLoading symbolic object:\n") ; status = umfpack_zl_load_symbolic (&Symbolic, (char *) NULL) ; if (status < 0) { umfpack_zl_report_status (Control, status) ; error ("umfpack_zl_load_symbolic failed") ; } printf ("\nDone loading symbolic object\n") ; /* ---------------------------------------------------------------------- */ /* redo the numeric factorization */ /* ---------------------------------------------------------------------- */ umfpack_zl_free_numeric (&Numeric) ; status = umfpack_zl_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric, Control, Info) ; if (status < 0) { umfpack_zl_report_info (Control, Info) ; umfpack_zl_report_status (Control, status) ; error ("umfpack_zl_numeric failed") ; } printf ("\nNumeric factorization of completely modified A: ") ; (void) umfpack_zl_report_numeric (Numeric, Control) ; /* ---------------------------------------------------------------------- */ /* solve Ax=b, with the modified A */ /* ---------------------------------------------------------------------- */ status = umfpack_zl_solve (UMFPACK_A, Ap, Ai, Ax, Az, x, xz, b, bz, Numeric, Control, Info) ; umfpack_zl_report_info (Control, Info) ; if (status < 0) { umfpack_zl_report_status (Control, status) ; error ("umfpack_zl_solve failed") ; } printf ("\nx (with completely modified A): ") ; (void) umfpack_zl_report_vector (n, x, xz, Control) ; rnorm = resid (FALSE, Ap, Ai, Ax, Az) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* free the symbolic and numeric factorization */ /* ---------------------------------------------------------------------- */ umfpack_zl_free_symbolic (&Symbolic) ; umfpack_zl_free_numeric (&Numeric) ; /* ---------------------------------------------------------------------- */ /* C = transpose of A */ /* ---------------------------------------------------------------------- */ Cp = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Ci = (UF_long *) malloc (nz1 * sizeof (UF_long)) ; Cx = (double *) malloc (nz1 * sizeof (double)) ; Cz = (double *) malloc (nz1 * sizeof (double)) ; if (!Cp || !Ci || !Cx || !Cz) { error ("out of memory") ; } status = umfpack_zl_transpose (n, n, Ap, Ai, Ax, Az, (UF_long *) NULL, (UF_long *) NULL, Cp, Ci, Cx, Cz, TRUE) ; if (status < 0) { umfpack_zl_report_status (Control, status) ; error ("umfpack_zl_transpose failed: ") ; } printf ("\nC (transpose of A): ") ; (void) umfpack_zl_report_matrix (n, n, Cp, Ci, Cx, Cz, 1, Control) ; /* ---------------------------------------------------------------------- */ /* symbolic factorization of C */ /* ---------------------------------------------------------------------- */ status = umfpack_zl_symbolic (n, n, Cp, Ci, Cx, Cz, &Symbolic, Control, Info) ; if (status < 0) { umfpack_zl_report_info (Control, Info) ; umfpack_zl_report_status (Control, status) ; error ("umfpack_zl_symbolic failed") ; } printf ("\nSymbolic factorization of C: ") ; (void) umfpack_zl_report_symbolic (Symbolic, Control) ; /* ---------------------------------------------------------------------- */ /* copy the contents of Symbolic into user arrays print them */ /* ---------------------------------------------------------------------- */ printf ("\nGet the contents of the Symbolic object for C:\n") ; printf ("(compare with umfpack_zl_report_symbolic output, above)\n") ; Pinit = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Qinit = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Front_npivcol = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Front_1strow = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Front_leftmostdesc = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Front_parent = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Chain_start = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Chain_maxrows = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Chain_maxcols = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; if (!Pinit || !Qinit || !Front_npivcol || !Front_parent || !Chain_start || !Chain_maxrows || !Chain_maxcols || !Front_1strow || !Front_leftmostdesc) { error ("out of memory") ; } status = umfpack_zl_get_symbolic (&nr, &nc, &n1, &anz, &nfr, &nchains, Pinit, Qinit, Front_npivcol, Front_parent, Front_1strow, Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ; if (status < 0) { error ("symbolic factorization invalid") ; } printf ("From the Symbolic object, C is of dimension %ld-by-%ld\n", nr, nc); printf (" with nz = %ld, number of fronts = %ld,\n", nz, nfr) ; printf (" number of frontal matrix chains = %ld\n", nchains) ; printf ("\nPivot columns in each front, and parent of each front:\n") ; k = 0 ; for (i = 0 ; i < nfr ; i++) { fnpiv = Front_npivcol [i] ; printf (" Front %ld: parent front: %ld number of pivot cols: %ld\n", i, Front_parent [i], fnpiv) ; for (j = 0 ; j < fnpiv ; j++) { col = Qinit [k] ; printf ( " %ld-th pivot column is column %ld in original matrix\n", k, col) ; k++ ; } } printf ("\nNote that the column ordering, above, will be refined\n") ; printf ("in the numeric factorization below. The assignment of pivot\n") ; printf ("columns to frontal matrices will always remain unchanged.\n") ; printf ("\nTotal number of pivot columns in frontal matrices: %ld\n", k) ; printf ("\nFrontal matrix chains:\n") ; for (j = 0 ; j < nchains ; j++) { printf (" Frontal matrices %ld to %ld are factorized in a single\n", Chain_start [j], Chain_start [j+1] - 1) ; printf (" working array of size %ld-by-%ld\n", Chain_maxrows [j], Chain_maxcols [j]) ; } /* ---------------------------------------------------------------------- */ /* numeric factorization of C */ /* ---------------------------------------------------------------------- */ status = umfpack_zl_numeric (Cp, Ci, Cx, Cz, Symbolic, &Numeric, Control, Info) ; if (status < 0) { error ("umfpack_zl_numeric failed") ; } printf ("\nNumeric factorization of C: ") ; (void) umfpack_zl_report_numeric (Numeric, Control) ; /* ---------------------------------------------------------------------- */ /* extract the LU factors of C and print them */ /* ---------------------------------------------------------------------- */ if (umfpack_zl_get_lunz (&lnz, &unz, &nr, &nc, &nzud, Numeric) < 0) { error ("umfpack_zl_get_lunz failed") ; } /* ensure arrays are not of zero size */ lnz1 = MAX (lnz,1) ; unz1 = MAX (unz,1) ; Lp = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Lj = (UF_long *) malloc (lnz1 * sizeof (UF_long)) ; Lx = (double *) malloc (lnz1 * sizeof (double)) ; Lz = (double *) malloc (lnz1 * sizeof (double)) ; Up = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ; Ui = (UF_long *) malloc (unz1 * sizeof (UF_long)) ; Ux = (double *) malloc (unz1 * sizeof (double)) ; Uz = (double *) malloc (unz1 * sizeof (double)) ; P = (UF_long *) malloc (n * sizeof (UF_long)) ; Q = (UF_long *) malloc (n * sizeof (UF_long)) ; Dx = (double *) NULL ; /* D vector not requested */ Dz = (double *) NULL ; Rs = (double *) malloc (n * sizeof (double)) ; if (!Lp || !Lj || !Lx || !Lz || !Up || !Ui || !Ux || !Uz || !P || !Q || !Rs) { error ("out of memory") ; } status = umfpack_zl_get_numeric (Lp, Lj, Lx, Lz, Up, Ui, Ux, Uz, P, Q, Dx, Dz, &do_recip, Rs, Numeric) ; if (status < 0) { error ("umfpack_zl_get_numeric failed") ; } printf ("\nL (lower triangular factor of C): ") ; (void) umfpack_zl_report_matrix (n, n, Lp, Lj, Lx, Lz, 0, Control) ; printf ("\nU (upper triangular factor of C): ") ; (void) umfpack_zl_report_matrix (n, n, Up, Ui, Ux, Uz, 1, Control) ; printf ("\nP: ") ; (void) umfpack_zl_report_perm (n, P, Control) ; printf ("\nQ: ") ; (void) umfpack_zl_report_perm (n, Q, Control) ; printf ("\nScale factors: row i of A is to be ") ; if (do_recip) { printf ("multiplied by the ith scale factor\n") ; } else { printf ("divided by the ith scale factor\n") ; } for (i = 0 ; i < n ; i++) printf ("%ld: %g\n", i, Rs [i]) ; /* ---------------------------------------------------------------------- */ /* convert L to triplet form and print it */ /* ---------------------------------------------------------------------- */ /* Note that L is in row-form, so it is the row indices that are created */ /* by umfpack_zl_col_to_triplet. */ printf ("\nConverting L to triplet form, and printing it:\n") ; Li = (UF_long *) malloc (lnz1 * sizeof (UF_long)) ; if (!Li) { error ("out of memory") ; } if (umfpack_zl_col_to_triplet (n, Lp, Li) < 0) { error ("umfpack_zl_col_to_triplet failed") ; } printf ("\nL, in triplet form: ") ; (void) umfpack_zl_report_triplet (n, n, lnz, Li, Lj, Lx, Lz, Control) ; /* ---------------------------------------------------------------------- */ /* save the Numeric object to file, free it, and load it back in */ /* ---------------------------------------------------------------------- */ /* use the default filename, "numeric.umf" */ printf ("\nSaving numeric object:\n") ; status = umfpack_zl_save_numeric (Numeric, (char *) NULL) ; if (status < 0) { umfpack_zl_report_status (Control, status) ; error ("umfpack_zl_save_numeric failed") ; } printf ("\nFreeing numeric object:\n") ; umfpack_zl_free_numeric (&Numeric) ; printf ("\nLoading numeric object:\n") ; status = umfpack_zl_load_numeric (&Numeric, (char *) NULL) ; if (status < 0) { umfpack_zl_report_status (Control, status) ; error ("umfpack_zl_load_numeric failed") ; } printf ("\nDone loading numeric object\n") ; /* ---------------------------------------------------------------------- */ /* solve C'x=b */ /* ---------------------------------------------------------------------- */ status = umfpack_zl_solve (UMFPACK_At, Cp, Ci, Cx, Cz, x, xz, b, bz, Numeric, Control, Info) ; umfpack_zl_report_info (Control, Info) ; if (status < 0) { umfpack_zl_report_status (Control, status) ; error ("umfpack_zl_solve failed") ; } printf ("\nx (solution of C'x=b): ") ; (void) umfpack_zl_report_vector (n, x, xz, Control) ; rnorm = resid (TRUE, Cp, Ci, Cx, Cz) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* solve C'x=b again, using umfpack_zl_wsolve instead */ /* ---------------------------------------------------------------------- */ printf ("\nSolving C'x=b again, using umfpack_zl_wsolve instead:\n") ; Wi = (UF_long *) malloc (n * sizeof (UF_long)) ; W = (double *) malloc (10*n * sizeof (double)) ; if (!Wi || !W) { error ("out of memory") ; } status = umfpack_zl_wsolve (UMFPACK_At, Cp, Ci, Cx, Cz, x, xz, b, bz, Numeric, Control, Info, Wi, W) ; umfpack_zl_report_info (Control, Info) ; if (status < 0) { umfpack_zl_report_status (Control, status) ; error ("umfpack_zl_wsolve failed") ; } printf ("\nx (solution of C'x=b): ") ; (void) umfpack_zl_report_vector (n, x, xz, Control) ; rnorm = resid (TRUE, Cp, Ci, Cx, Cz) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* free everything */ /* ---------------------------------------------------------------------- */ /* This is not strictly required since the process is exiting and the */ /* system will reclaim the memory anyway. It's useful, though, just as */ /* a list of what is currently malloc'ed by this program. Plus, it's */ /* always a good habit to explicitly free whatever you malloc. */ free (Ap) ; free (Ai) ; free (Ax) ; free (Az) ; free (Cp) ; free (Ci) ; free (Cx) ; free (Cz) ; free (Pinit) ; free (Qinit) ; free (Front_npivcol) ; free (Front_1strow) ; free (Front_leftmostdesc) ; free (Front_parent) ; free (Chain_start) ; free (Chain_maxrows) ; free (Chain_maxcols) ; free (Lp) ; free (Lj) ; free (Lx) ; free (Lz) ; free (Up) ; free (Ui) ; free (Ux) ; free (Uz) ; free (P) ; free (Q) ; free (Li) ; free (Wi) ; free (W) ; umfpack_zl_free_symbolic (&Symbolic) ; umfpack_zl_free_numeric (&Numeric) ; /* ---------------------------------------------------------------------- */ /* print the total time spent in this demo */ /* ---------------------------------------------------------------------- */ umfpack_toc (t) ; printf ("\numfpack_zl_demo complete.\nTotal time: %5.2f seconds" " (CPU time), %5.2f seconds (wallclock time)\n", t [1], t [0]) ; return (0) ; } SuiteSparse/UMFPACK/Demo/umf4.out0000644001170100242450000026164210711433273015341 0ustar davisfaccc -O3 -I../Include -I../../AMD/Include -I../../UFconfig -o umf4 umf4.c ../Lib/libumfpack.a ../../AMD/Lib/libamd.a -lblas -lgfortran -lgfortranbegin -lm f77 -O -o readhb readhb.f f77 -O -o readhb_nozeros readhb_nozeros.f f77 -O -o readhb_size readhb_size.f ./readhb_nozeros < HB/can_24.psa > tmp/A ./readhb_size < HB/can_24.psa > tmp/Asize ./umf4 =========================================================== === UMFPACK v5.2.0 ======================================== =========================================================== UMFPACK V5.2.0 (Nov 1, 2007), Control: Matrix entry defined as: double Int (generic integer) defined as: int 0: print level: 3 1: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 2: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 3: pivot tolerance: 0.1 4: block size for dense matrix kernels: 32 5: strategy: 0 (auto) 6: initial allocation ratio: 0.7 7: max iterative refinement steps: 2 12: 2-by-2 pivot tolerance: 0.01 13: Q fixed during numerical factorization: 0 (auto) 14: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 15: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 16: scaling: 1 (divide each row by sum of abs. values in each row) 17: frontal matrix allocation ratio: 0.5 18: drop tolerance: 0 19: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4 9: compiled for ANSI C 10: CPU timer is POSIX times ( ) routine. 11: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes) File: tmp/A File: tmp/Asize n 24 nrow 24 ncol 24 nz 160 triplet-form matrix, n_row = 24, n_col = 24 nz = 160. OK triplet-to-col time: wall 0 cpu 0 column-form matrix, n_row 24 n_col 24, nz = 160. OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 24 number of columns in matrix A: 24 entries in matrix A: 160 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: symmetric ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 0 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 24 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 136 nz on diagonal of matrix S: 24 fraction of nz on diagonal: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 1.00300e+03 est. nz in L+U (incl. diagonal): 218 est. largest front (# entries): 64 est. max nz in any column of L: 8 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 725 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 131 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 763 - - peak size (Units) 3244 - - final size (Units) 393 - - Numeric final size (Units) 598 - - Numeric final size (MBytes) 0.0 - - peak memory usage (Units) 3840 - - peak memory usage (MBytes) 0.0 - - numeric factorization flops 2.37900e+03 - - nz in L (incl diagonal) 149 - - nz in U (incl diagonal) 208 - - nz in L+U (incl diagonal) 333 - - largest front (# entries) 182 - - largest # rows in front 13 - - largest # columns in front 14 - - Symbolic object: OK Numeric object: OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 24 number of columns in matrix A: 24 entries in matrix A: 160 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: symmetric ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 0 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 24 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 136 nz on diagonal of matrix S: 24 fraction of nz on diagonal: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 1.00300e+03 est. nz in L+U (incl. diagonal): 218 est. largest front (# entries): 64 est. max nz in any column of L: 8 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 725 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 131 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 4.00000e+00 maximum sum (abs (rows of A)): 9.00000e+00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 763 711 93% peak size (Units) 3244 2709 84% final size (Units) 393 133 34% Numeric final size (Units) 598 326 55% Numeric final size (MBytes) 0.0 0.0 55% peak memory usage (Units) 3840 3305 86% peak memory usage (MBytes) 0.0 0.0 86% numeric factorization flops 2.37900e+03 1.57000e+02 7% nz in L (incl diagonal) 149 53 36% nz in U (incl diagonal) 208 73 35% nz in L+U (incl diagonal) 333 102 31% largest front (# entries) 182 78 43% largest # rows in front 13 7 54% largest # columns in front 14 13 93% initial allocation ratio used: 1.2 # of forced updates due to frontal growth: 0 number of off-diagonal pivots: 10 nz in L (incl diagonal), if none dropped 53 nz in U (incl diagonal), if none dropped 73 number of small entries dropped 0 nonzeros on diagonal of U: 24 min abs. value on diagonal of U: 1.11e-01 max abs. value on diagonal of U: 2.50e-01 estimate of reciprocal of condition number: 4.44e-01 indices in compressed pattern: 76 numerical values stored in Numeric object: 102 numeric factorization defragmentations: 0 numeric factorization reallocations: 0 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 1.06000e+03 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 7.86e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 1.21700e+03 UMFPACK V5.2.0 (Nov 1, 2007): OK dense vector, n = 24. OK relative maxnorm of residual, ||Ax-b||/||b||: 2.58379e-16 relative maxnorm of error, ||x-xtrue||/||xtrue||: 1.92754e-15 Writing tmp/x Writing tmp/info.umf4 umf4 done, strategy: 0 =========================================================== === AMD =================================================== =========================================================== ------- Now trying the AMD ordering. This not part of the UMFPACK analysis or factorization, above, but a separate test of just the AMD ordering routine. AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD ordering time: cpu 0.00 wall 0.00 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 24 nz, number of nonzeros in A: 160 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 136 # dense rows/columns of A+A': 0 memory used, in bytes: 1516 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 97 nonzeros in L (including diagonal): 121 # divide operations for LDL' or LU: 97 # multiply-subtract operations for LDL': 275 # multiply-subtract operations for LU: 453 max nz. in any column of L (incl. diagonal): 8 chol flop count for real A, sqrt counted as 1 flop: 671 LDL' flop count for real A: 647 LDL' flop count for complex A: 3073 LU flop count for real A (with no pivoting): 1003 LU flop count for complex A (with no pivoting): 4497 AMD test done ./readhb_nozeros < HB/west0067.rua > tmp/A ./readhb_size < HB/west0067.rua > tmp/Asize ./umf4 =========================================================== === UMFPACK v5.2.0 ======================================== =========================================================== UMFPACK V5.2.0 (Nov 1, 2007), Control: Matrix entry defined as: double Int (generic integer) defined as: int 0: print level: 3 1: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 2: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 3: pivot tolerance: 0.1 4: block size for dense matrix kernels: 32 5: strategy: 0 (auto) 6: initial allocation ratio: 0.7 7: max iterative refinement steps: 2 12: 2-by-2 pivot tolerance: 0.01 13: Q fixed during numerical factorization: 0 (auto) 14: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 15: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 16: scaling: 1 (divide each row by sum of abs. values in each row) 17: frontal matrix allocation ratio: 0.5 18: drop tolerance: 0 19: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4 9: compiled for ANSI C 10: CPU timer is POSIX times ( ) routine. 11: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes) File: tmp/A File: tmp/Asize n 67 nrow 67 ncol 67 nz 294 triplet-form matrix, n_row = 67, n_col = 67 nz = 294. OK triplet-to-col time: wall 0 cpu 0 column-form matrix, n_row 67 n_col 67, nz = 294. OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 67 number of columns in matrix A: 67 entries in matrix A: 294 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 1 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S not square or diagonal not preserved symbolic factorization defragmentations: 1 symbolic memory usage (Units): 1639 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 252 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 1711 - - peak size (Units) 6115 - - final size (Units) 1628 - - Numeric final size (Units) 2108 - - Numeric final size (MBytes) 0.0 - - peak memory usage (Units) 7476 - - peak memory usage (MBytes) 0.1 - - numeric factorization flops 1.41920e+04 - - nz in L (incl diagonal) 542 - - nz in U (incl diagonal) 902 - - nz in L+U (incl diagonal) 1377 - - largest front (# entries) 483 - - largest # rows in front 21 - - largest # columns in front 23 - - Symbolic object: OK Numeric object: OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 67 number of columns in matrix A: 67 entries in matrix A: 294 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 1 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S not square or diagonal not preserved symbolic factorization defragmentations: 1 symbolic memory usage (Units): 1639 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 252 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.01 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 6.59006e+00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 1711 1577 92% peak size (Units) 6115 3581 59% final size (Units) 1628 682 42% Numeric final size (Units) 2108 1129 54% Numeric final size (MBytes) 0.0 0.0 54% peak memory usage (Units) 7476 4942 66% peak memory usage (MBytes) 0.1 0.0 66% numeric factorization flops 1.41920e+04 2.50100e+03 18% nz in L (incl diagonal) 542 323 60% nz in U (incl diagonal) 902 339 38% nz in L+U (incl diagonal) 1377 595 43% largest front (# entries) 483 80 17% largest # rows in front 21 10 48% largest # columns in front 23 11 48% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 323 nz in U (incl diagonal), if none dropped 339 number of small entries dropped 0 nonzeros on diagonal of U: 67 min abs. value on diagonal of U: 2.74e-02 max abs. value on diagonal of U: 2.28e+00 estimate of reciprocal of condition number: 1.20e-02 indices in compressed pattern: 263 numerical values stored in Numeric object: 599 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 6.16500e+03 iterative refinement steps taken: 1 iterative refinement steps attempted: 1 sparse backward error omega1: 1.32e-16 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 8.66600e+03 UMFPACK V5.2.0 (Nov 1, 2007): OK dense vector, n = 67. OK relative maxnorm of residual, ||Ax-b||/||b||: 9.15507e-17 relative maxnorm of error, ||x-xtrue||/||xtrue||: 2.349e-15 Writing tmp/x Writing tmp/info.umf4 umf4 done, strategy: 0 =========================================================== === AMD =================================================== =========================================================== ------- Now trying the AMD ordering. This not part of the UMFPACK analysis or factorization, above, but a separate test of just the AMD ordering routine. AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD ordering time: cpu 0.00 wall 0.00 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 67 nz, number of nonzeros in A: 294 symmetry of A: 0.0342 number of nonzeros on diagonal: 2 nonzeros in pattern of A+A' (excl. diagonal): 574 # dense rows/columns of A+A': 0 memory used, in bytes: 5164 # of memory compactions: 1 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 930 nonzeros in L (including diagonal): 997 # divide operations for LDL' or LU: 930 # multiply-subtract operations for LDL': 9170 # multiply-subtract operations for LU: 17410 max nz. in any column of L (incl. diagonal): 33 chol flop count for real A, sqrt counted as 1 flop: 19337 LDL' flop count for real A: 19270 LDL' flop count for complex A: 81730 LU flop count for real A (with no pivoting): 35750 LU flop count for complex A (with no pivoting): 147650 AMD test done ./readhb_nozeros < HB/fs_183_6.rua > tmp/A ./readhb_size < HB/fs_183_6.rua > tmp/Asize ./umf4 =========================================================== === UMFPACK v5.2.0 ======================================== =========================================================== UMFPACK V5.2.0 (Nov 1, 2007), Control: Matrix entry defined as: double Int (generic integer) defined as: int 0: print level: 3 1: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 2: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 3: pivot tolerance: 0.1 4: block size for dense matrix kernels: 32 5: strategy: 0 (auto) 6: initial allocation ratio: 0.7 7: max iterative refinement steps: 2 12: 2-by-2 pivot tolerance: 0.01 13: Q fixed during numerical factorization: 0 (auto) 14: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 15: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 16: scaling: 1 (divide each row by sum of abs. values in each row) 17: frontal matrix allocation ratio: 0.5 18: drop tolerance: 0 19: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4 9: compiled for ANSI C 10: CPU timer is POSIX times ( ) routine. 11: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes) File: tmp/A File: tmp/Asize n 183 nrow 183 ncol 183 nz 1000 triplet-form matrix, n_row = 183, n_col = 183 nz = 1000. OK triplet-to-col time: wall 0 cpu 0 column-form matrix, n_row 183 n_col 183, nz = 1000. OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 183 number of columns in matrix A: 183 entries in matrix A: 1000 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: symmetric 2-by-2 ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 36 submatrix S after removing zero-cost pivots: number of "dense" rows: 4 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 147 symmetry of nonzero pattern: 0.490515 nz in S+S' (excl. diagonal): 1114 nz on diagonal of matrix S: 147 fraction of nz on diagonal: 1.000000 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 7 # unmatched: 7 symmetry of P2*S: 0.490515 nz in P2*S+(P2*S)' (excl. diag.): 1114 nz on diagonal of P2*S: 147 fraction of nz on diag of P2*S: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 1.02930e+04 est. nz in L+U (incl. diagonal): 1625 est. largest front (# entries): 196 est. max nz in any column of L: 14 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 4846 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 763 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 4458 - - peak size (Units) 26277 - - final size (Units) 15717 - - Numeric final size (Units) 16951 - - Numeric final size (MBytes) 0.1 - - peak memory usage (Units) 29687 - - peak memory usage (MBytes) 0.2 - - numeric factorization flops 2.67903e+05 - - nz in L (incl diagonal) 2122 - - nz in U (incl diagonal) 9931 - - nz in L+U (incl diagonal) 11870 - - largest front (# entries) 2337 - - largest # rows in front 21 - - largest # columns in front 136 - - Symbolic object: OK Numeric object: OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 183 number of columns in matrix A: 183 entries in matrix A: 1000 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: symmetric 2-by-2 ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 36 submatrix S after removing zero-cost pivots: number of "dense" rows: 4 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 147 symmetry of nonzero pattern: 0.490515 nz in S+S' (excl. diagonal): 1114 nz on diagonal of matrix S: 147 fraction of nz on diagonal: 1.000000 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 7 # unmatched: 7 symmetry of P2*S: 0.490515 nz in P2*S+(P2*S)' (excl. diag.): 1114 nz on diagonal of P2*S: 147 fraction of nz on diag of P2*S: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 1.02930e+04 est. nz in L+U (incl. diagonal): 1625 est. largest front (# entries): 196 est. max nz in any column of L: 14 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 4846 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 763 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.84689e-01 maximum sum (abs (rows of A)): 8.73139e+08 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 4458 4090 92% peak size (Units) 26277 8488 32% final size (Units) 15717 1658 11% Numeric final size (Units) 16951 2801 17% Numeric final size (MBytes) 0.1 0.0 17% peak memory usage (Units) 29687 11898 40% peak memory usage (MBytes) 0.2 0.1 40% numeric factorization flops 2.67903e+05 7.82700e+03 3% nz in L (incl diagonal) 2122 838 39% nz in U (incl diagonal) 9931 804 8% nz in L+U (incl diagonal) 11870 1459 12% largest front (# entries) 2337 420 18% largest # rows in front 21 14 67% largest # columns in front 136 36 26% initial allocation ratio used: 0.265 # of forced updates due to frontal growth: 0 number of off-diagonal pivots: 3 nz in L (incl diagonal), if none dropped 838 nz in U (incl diagonal), if none dropped 804 number of small entries dropped 0 nonzeros on diagonal of U: 183 min abs. value on diagonal of U: 2.30e-09 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 2.30e-09 indices in compressed pattern: 550 numerical values stored in Numeric object: 1396 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 2.73290e+04 iterative refinement steps taken: 1 iterative refinement steps attempted: 2 sparse backward error omega1: 2.78e-16 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 3.51560e+04 UMFPACK V5.2.0 (Nov 1, 2007): OK dense vector, n = 183. OK relative maxnorm of residual, ||Ax-b||/||b||: 1.55669e-16 relative maxnorm of error, ||x-xtrue||/||xtrue||: 9.12839e-07 Writing tmp/x Writing tmp/info.umf4 umf4 done, strategy: 0 =========================================================== === AMD =================================================== =========================================================== ------- Now trying the AMD ordering. This not part of the UMFPACK analysis or factorization, above, but a separate test of just the AMD ordering routine. AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD ordering time: cpu 0.00 wall 0.00 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 183 nz, number of nonzeros in A: 1000 symmetry of A: 0.4431 number of nonzeros on diagonal: 183 nonzeros in pattern of A+A' (excl. diagonal): 1272 # dense rows/columns of A+A': 0 memory used, in bytes: 12692 # of memory compactions: 1 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 882 nonzeros in L (including diagonal): 1065 # divide operations for LDL' or LU: 882 # multiply-subtract operations for LDL': 3378 # multiply-subtract operations for LU: 5874 max nz. in any column of L (incl. diagonal): 15 chol flop count for real A, sqrt counted as 1 flop: 7821 LDL' flop count for real A: 7638 LDL' flop count for complex A: 34962 LU flop count for real A (with no pivoting): 12630 LU flop count for complex A (with no pivoting): 54930 AMD test done ./readhb < HB/fs_183_6.rua > tmp/A ./readhb_size < HB/fs_183_6.rua > tmp/Asize ./umf4 =========================================================== === UMFPACK v5.2.0 ======================================== =========================================================== UMFPACK V5.2.0 (Nov 1, 2007), Control: Matrix entry defined as: double Int (generic integer) defined as: int 0: print level: 3 1: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 2: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 3: pivot tolerance: 0.1 4: block size for dense matrix kernels: 32 5: strategy: 0 (auto) 6: initial allocation ratio: 0.7 7: max iterative refinement steps: 2 12: 2-by-2 pivot tolerance: 0.01 13: Q fixed during numerical factorization: 0 (auto) 14: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 15: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 16: scaling: 1 (divide each row by sum of abs. values in each row) 17: frontal matrix allocation ratio: 0.5 18: drop tolerance: 0 19: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4 9: compiled for ANSI C 10: CPU timer is POSIX times ( ) routine. 11: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes) File: tmp/A File: tmp/Asize n 183 nrow 183 ncol 183 nz 1069 triplet-form matrix, n_row = 183, n_col = 183 nz = 1069. OK triplet-to-col time: wall 0 cpu 0 column-form matrix, n_row 183 n_col 183, nz = 1069. OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 183 number of columns in matrix A: 183 entries in matrix A: 1069 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: symmetric 2-by-2 ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 29 submatrix S after removing zero-cost pivots: number of "dense" rows: 4 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 154 symmetry of nonzero pattern: 0.446860 nz in S+S' (excl. diagonal): 1286 nz on diagonal of matrix S: 154 fraction of nz on diagonal: 1.000000 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 7 # unmatched: 7 symmetry of P2*S: 0.446860 nz in P2*S+(P2*S)' (excl. diag.): 1286 nz on diagonal of P2*S: 154 fraction of nz on diag of P2*S: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 1.78450e+04 est. nz in L+U (incl. diagonal): 2080 est. largest front (# entries): 400 est. max nz in any column of L: 20 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 4966 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 773 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 4742 - - peak size (Units) 26357 - - final size (Units) 17822 - - Numeric final size (Units) 19056 - - Numeric final size (MBytes) 0.1 - - peak memory usage (Units) 29809 - - peak memory usage (MBytes) 0.2 - - numeric factorization flops 3.51312e+05 - - nz in L (incl diagonal) 2633 - - nz in U (incl diagonal) 10968 - - nz in L+U (incl diagonal) 13418 - - largest front (# entries) 3220 - - largest # rows in front 25 - - largest # columns in front 140 - - Symbolic object: OK Numeric object: OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 183 number of columns in matrix A: 183 entries in matrix A: 1069 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: symmetric 2-by-2 ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 29 submatrix S after removing zero-cost pivots: number of "dense" rows: 4 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 154 symmetry of nonzero pattern: 0.446860 nz in S+S' (excl. diagonal): 1286 nz on diagonal of matrix S: 154 fraction of nz on diagonal: 1.000000 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 7 # unmatched: 7 symmetry of P2*S: 0.446860 nz in P2*S+(P2*S)' (excl. diag.): 1286 nz on diagonal of P2*S: 154 fraction of nz on diag of P2*S: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 1.78450e+04 est. nz in L+U (incl. diagonal): 2080 est. largest front (# entries): 400 est. max nz in any column of L: 20 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 4966 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 773 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.84689e-01 maximum sum (abs (rows of A)): 8.73139e+08 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 4742 4372 92% peak size (Units) 26357 11189 42% final size (Units) 17822 2107 12% Numeric final size (Units) 19056 3250 17% Numeric final size (MBytes) 0.1 0.0 17% peak memory usage (Units) 29809 14641 49% peak memory usage (MBytes) 0.2 0.1 49% numeric factorization flops 3.51312e+05 1.19670e+04 3% nz in L (incl diagonal) 2633 1136 43% nz in U (incl diagonal) 10968 870 8% nz in L+U (incl diagonal) 13418 1823 14% largest front (# entries) 3220 728 23% largest # rows in front 25 20 80% largest # columns in front 140 58 41% initial allocation ratio used: 0.282 # of forced updates due to frontal growth: 1 number of off-diagonal pivots: 3 nz in L (incl diagonal), if none dropped 1136 nz in U (incl diagonal), if none dropped 870 number of small entries dropped 0 nonzeros on diagonal of U: 183 min abs. value on diagonal of U: 2.30e-09 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 2.30e-09 indices in compressed pattern: 741 numerical values stored in Numeric object: 1781 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 1 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 3.04790e+04 iterative refinement steps taken: 1 iterative refinement steps attempted: 2 sparse backward error omega1: 3.97e-16 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 4.24460e+04 UMFPACK V5.2.0 (Nov 1, 2007): OK dense vector, n = 183. OK relative maxnorm of residual, ||Ax-b||/||b||: 1.55669e-16 relative maxnorm of error, ||x-xtrue||/||xtrue||: 1.0186e-06 Writing tmp/x Writing tmp/info.umf4 umf4 done, strategy: 0 =========================================================== === AMD =================================================== =========================================================== ------- Now trying the AMD ordering. This not part of the UMFPACK analysis or factorization, above, but a separate test of just the AMD ordering routine. AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD ordering time: cpu 0.00 wall 0.00 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 183 nz, number of nonzeros in A: 1069 symmetry of A: 0.4176 number of nonzeros on diagonal: 183 nonzeros in pattern of A+A' (excl. diagonal): 1402 # dense rows/columns of A+A': 0 memory used, in bytes: 13316 # of memory compactions: 1 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 1072 nonzeros in L (including diagonal): 1255 # divide operations for LDL' or LU: 1072 # multiply-subtract operations for LDL': 5320 # multiply-subtract operations for LU: 9568 max nz. in any column of L (incl. diagonal): 21 chol flop count for real A, sqrt counted as 1 flop: 11895 LDL' flop count for real A: 11712 LDL' flop count for complex A: 52208 LU flop count for real A (with no pivoting): 20208 LU flop count for complex A (with no pivoting): 86192 AMD test done ./readhb < HB/arc130.rua > tmp/A ./readhb_size < HB/arc130.rua > tmp/Asize ./umf4 =========================================================== === UMFPACK v5.2.0 ======================================== =========================================================== UMFPACK V5.2.0 (Nov 1, 2007), Control: Matrix entry defined as: double Int (generic integer) defined as: int 0: print level: 3 1: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 2: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 3: pivot tolerance: 0.1 4: block size for dense matrix kernels: 32 5: strategy: 0 (auto) 6: initial allocation ratio: 0.7 7: max iterative refinement steps: 2 12: 2-by-2 pivot tolerance: 0.01 13: Q fixed during numerical factorization: 0 (auto) 14: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 15: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 16: scaling: 1 (divide each row by sum of abs. values in each row) 17: frontal matrix allocation ratio: 0.5 18: drop tolerance: 0 19: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4 9: compiled for ANSI C 10: CPU timer is POSIX times ( ) routine. 11: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes) File: tmp/A File: tmp/Asize n 130 nrow 130 ncol 130 nz 1282 triplet-form matrix, n_row = 130, n_col = 130 nz = 1282. OK triplet-to-col time: wall 0 cpu 0 column-form matrix, n_row 130 n_col 130, nz = 1282. OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 130 number of columns in matrix A: 130 entries in matrix A: 1282 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: symmetric ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 6 submatrix S after removing zero-cost pivots: number of "dense" rows: 7 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 124 symmetry of nonzero pattern: 0.841193 nz in S+S' (excl. diagonal): 1204 nz on diagonal of matrix S: 124 fraction of nz on diagonal: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 8.27000e+03 est. nz in L+U (incl. diagonal): 1336 est. largest front (# entries): 324 est. max nz in any column of L: 18 number of "dense" rows/columns in S+S': 2 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 4766 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 644 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 4729 - - peak size (Units) 25036 - - final size (Units) 12837 - - Numeric final size (Units) 13731 - - Numeric final size (MBytes) 0.1 - - peak memory usage (Units) 27695 - - peak memory usage (MBytes) 0.2 - - numeric factorization flops 9.41610e+04 - - nz in L (incl diagonal) 1009 - - nz in U (incl diagonal) 7849 - - nz in L+U (incl diagonal) 8728 - - largest front (# entries) 2337 - - largest # rows in front 19 - - largest # columns in front 123 - - Symbolic object: OK Numeric object: OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 130 number of columns in matrix A: 130 entries in matrix A: 1282 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: symmetric ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 6 submatrix S after removing zero-cost pivots: number of "dense" rows: 7 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 124 symmetry of nonzero pattern: 0.841193 nz in S+S' (excl. diagonal): 1204 nz on diagonal of matrix S: 124 fraction of nz on diagonal: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 8.27000e+03 est. nz in L+U (incl. diagonal): 1336 est. largest front (# entries): 324 est. max nz in any column of L: 18 number of "dense" rows/columns in S+S': 2 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 4766 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 644 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 7.94859e-01 maximum sum (abs (rows of A)): 1.08460e+06 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 4729 4451 94% peak size (Units) 25036 6477 26% final size (Units) 12837 1054 8% Numeric final size (Units) 13731 1883 14% Numeric final size (MBytes) 0.1 0.0 14% peak memory usage (Units) 27695 9136 33% peak memory usage (MBytes) 0.2 0.1 33% numeric factorization flops 9.41610e+04 4.20900e+03 4% nz in L (incl diagonal) 1009 417 41% nz in U (incl diagonal) 7849 787 10% nz in L+U (incl diagonal) 8728 1074 12% largest front (# entries) 2337 270 12% largest # rows in front 19 18 95% largest # columns in front 123 15 12% initial allocation ratio used: 0.36 # of forced updates due to frontal growth: 0 number of off-diagonal pivots: 0 nz in L (incl diagonal), if none dropped 417 nz in U (incl diagonal), if none dropped 796 number of small entries dropped 9 nonzeros on diagonal of U: 130 min abs. value on diagonal of U: 9.22e-07 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 9.22e-07 indices in compressed pattern: 79 numerical values stored in Numeric object: 977 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 1.80440e+04 iterative refinement steps taken: 1 iterative refinement steps attempted: 1 sparse backward error omega1: 1.06e-16 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 2.22530e+04 UMFPACK V5.2.0 (Nov 1, 2007): OK dense vector, n = 130. OK relative maxnorm of residual, ||Ax-b||/||b||: 4.12105e-16 relative maxnorm of error, ||x-xtrue||/||xtrue||: 2.15116e-10 Writing tmp/x Writing tmp/info.umf4 umf4 done, strategy: 0 =========================================================== === AMD =================================================== =========================================================== ------- Now trying the AMD ordering. This not part of the UMFPACK analysis or factorization, above, but a separate test of just the AMD ordering routine. AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD ordering time: cpu 0.00 wall 0.00 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 130 nz, number of nonzeros in A: 1282 symmetry of A: 0.7587 number of nonzeros on diagonal: 130 nonzeros in pattern of A+A' (excl. diagonal): 1430 # dense rows/columns of A+A': 2 memory used, in bytes: 11544 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 756 nonzeros in L (including diagonal): 886 # divide operations for LDL' or LU: 756 # multiply-subtract operations for LDL': 2959 # multiply-subtract operations for LU: 5162 max nz. in any column of L (incl. diagonal): 18 chol flop count for real A, sqrt counted as 1 flop: 6804 LDL' flop count for real A: 6674 LDL' flop count for complex A: 30476 LU flop count for real A (with no pivoting): 11080 LU flop count for complex A (with no pivoting): 48100 AMD test done ./readhb_nozeros < HB/arc130.rua > tmp/A ./readhb_size < HB/arc130.rua > tmp/Asize ./umf4 =========================================================== === UMFPACK v5.2.0 ======================================== =========================================================== UMFPACK V5.2.0 (Nov 1, 2007), Control: Matrix entry defined as: double Int (generic integer) defined as: int 0: print level: 3 1: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 2: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 3: pivot tolerance: 0.1 4: block size for dense matrix kernels: 32 5: strategy: 0 (auto) 6: initial allocation ratio: 0.7 7: max iterative refinement steps: 2 12: 2-by-2 pivot tolerance: 0.01 13: Q fixed during numerical factorization: 0 (auto) 14: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 15: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 16: scaling: 1 (divide each row by sum of abs. values in each row) 17: frontal matrix allocation ratio: 0.5 18: drop tolerance: 0 19: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4 9: compiled for ANSI C 10: CPU timer is POSIX times ( ) routine. 11: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes) File: tmp/A File: tmp/Asize n 130 nrow 130 ncol 130 nz 1037 triplet-form matrix, n_row = 130, n_col = 130 nz = 1037. OK triplet-to-col time: wall 0 cpu 0 column-form matrix, n_row 130 n_col 130, nz = 1037. OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 130 number of columns in matrix A: 130 entries in matrix A: 1037 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: symmetric ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 54 submatrix S after removing zero-cost pivots: number of "dense" rows: 5 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 76 symmetry of nonzero pattern: 0.733224 nz in S+S' (excl. diagonal): 774 nz on diagonal of matrix S: 76 fraction of nz on diagonal: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 5.81700e+03 est. nz in L+U (incl. diagonal): 858 est. largest front (# entries): 289 est. max nz in any column of L: 17 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 4118 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 534 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 3326 - - peak size (Units) 9801 - - final size (Units) 4259 - - Numeric final size (Units) 5153 - - Numeric final size (MBytes) 0.0 - - peak memory usage (Units) 12149 - - peak memory usage (MBytes) 0.1 - - numeric factorization flops 2.47640e+04 - - nz in L (incl diagonal) 606 - - nz in U (incl diagonal) 2537 - - nz in L+U (incl diagonal) 3013 - - largest front (# entries) 459 - - largest # rows in front 17 - - largest # columns in front 48 - - Symbolic object: OK Numeric object: OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 130 number of columns in matrix A: 130 entries in matrix A: 1037 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: symmetric ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 54 submatrix S after removing zero-cost pivots: number of "dense" rows: 5 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 76 symmetry of nonzero pattern: 0.733224 nz in S+S' (excl. diagonal): 774 nz on diagonal of matrix S: 76 fraction of nz on diagonal: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 5.81700e+03 est. nz in L+U (incl. diagonal): 858 est. largest front (# entries): 289 est. max nz in any column of L: 17 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 4118 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 534 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.01 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 7.94859e-01 maximum sum (abs (rows of A)): 1.08460e+06 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 3326 3062 92% peak size (Units) 9801 6376 65% final size (Units) 4259 1141 27% Numeric final size (Units) 5153 1970 38% Numeric final size (MBytes) 0.0 0.0 38% peak memory usage (Units) 12149 8724 72% peak memory usage (MBytes) 0.1 0.1 72% numeric factorization flops 2.47640e+04 4.10700e+03 17% nz in L (incl diagonal) 606 409 67% nz in U (incl diagonal) 2537 792 31% nz in L+U (incl diagonal) 3013 1071 36% largest front (# entries) 459 240 52% largest # rows in front 17 16 94% largest # columns in front 48 15 31% initial allocation ratio used: 0.755 # of forced updates due to frontal growth: 0 number of off-diagonal pivots: 0 nz in L (incl diagonal), if none dropped 409 nz in U (incl diagonal), if none dropped 792 number of small entries dropped 0 nonzeros on diagonal of U: 130 min abs. value on diagonal of U: 9.22e-07 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 9.22e-07 indices in compressed pattern: 70 numerical values stored in Numeric object: 782 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 1.58270e+04 iterative refinement steps taken: 1 iterative refinement steps attempted: 1 sparse backward error omega1: 1.06e-16 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 1.99340e+04 UMFPACK V5.2.0 (Nov 1, 2007): OK dense vector, n = 130. OK relative maxnorm of residual, ||Ax-b||/||b||: 2.74736e-16 relative maxnorm of error, ||x-xtrue||/||xtrue||: 1.92322e-10 Writing tmp/x Writing tmp/info.umf4 umf4 done, strategy: 0 =========================================================== === AMD =================================================== =========================================================== ------- Now trying the AMD ordering. This not part of the UMFPACK analysis or factorization, above, but a separate test of just the AMD ordering routine. AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD ordering time: cpu 0.00 wall 0.00 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 130 nz, number of nonzeros in A: 1037 symmetry of A: 0.4939 number of nonzeros on diagonal: 130 nonzeros in pattern of A+A' (excl. diagonal): 1366 # dense rows/columns of A+A': 2 memory used, in bytes: 11236 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 725 nonzeros in L (including diagonal): 855 # divide operations for LDL' or LU: 725 # multiply-subtract operations for LDL': 2742 # multiply-subtract operations for LU: 4759 max nz. in any column of L (incl. diagonal): 18 chol flop count for real A, sqrt counted as 1 flop: 6339 LDL' flop count for real A: 6209 LDL' flop count for complex A: 28461 LU flop count for real A (with no pivoting): 10243 LU flop count for complex A (with no pivoting): 44597 AMD test done ./readhb_nozeros < HB/arc130.rua > tmp/A ./readhb_size < HB/arc130.rua > tmp/Asize ./umf4 a 1e-6 =========================================================== === UMFPACK v5.2.0 ======================================== =========================================================== droptol 1e-06 UMFPACK V5.2.0 (Nov 1, 2007), Control: Matrix entry defined as: double Int (generic integer) defined as: int 0: print level: 3 1: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 2: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 3: pivot tolerance: 0.1 4: block size for dense matrix kernels: 32 5: strategy: 0 (auto) 6: initial allocation ratio: 0.7 7: max iterative refinement steps: 2 12: 2-by-2 pivot tolerance: 0.01 13: Q fixed during numerical factorization: 0 (auto) 14: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 15: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 16: scaling: 1 (divide each row by sum of abs. values in each row) 17: frontal matrix allocation ratio: 0.5 18: drop tolerance: 1e-06 19: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4 9: compiled for ANSI C 10: CPU timer is POSIX times ( ) routine. 11: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes) File: tmp/A File: tmp/Asize n 130 nrow 130 ncol 130 nz 1037 triplet-form matrix, n_row = 130, n_col = 130 nz = 1037. OK triplet-to-col time: wall 0 cpu 0 column-form matrix, n_row 130 n_col 130, nz = 1037. OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 130 number of columns in matrix A: 130 entries in matrix A: 1037 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: symmetric ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 54 submatrix S after removing zero-cost pivots: number of "dense" rows: 5 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 76 symmetry of nonzero pattern: 0.733224 nz in S+S' (excl. diagonal): 774 nz on diagonal of matrix S: 76 fraction of nz on diagonal: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 5.81700e+03 est. nz in L+U (incl. diagonal): 858 est. largest front (# entries): 289 est. max nz in any column of L: 17 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 4118 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 534 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 3326 - - peak size (Units) 9801 - - final size (Units) 4259 - - Numeric final size (Units) 5153 - - Numeric final size (MBytes) 0.0 - - peak memory usage (Units) 12149 - - peak memory usage (MBytes) 0.1 - - numeric factorization flops 2.47640e+04 - - nz in L (incl diagonal) 606 - - nz in U (incl diagonal) 2537 - - nz in L+U (incl diagonal) 3013 - - largest front (# entries) 459 - - largest # rows in front 17 - - largest # columns in front 48 - - Symbolic object: OK Numeric object: OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 130 number of columns in matrix A: 130 entries in matrix A: 1037 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: symmetric ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 54 submatrix S after removing zero-cost pivots: number of "dense" rows: 5 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 76 symmetry of nonzero pattern: 0.733224 nz in S+S' (excl. diagonal): 774 nz on diagonal of matrix S: 76 fraction of nz on diagonal: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 5.81700e+03 est. nz in L+U (incl. diagonal): 858 est. largest front (# entries): 289 est. max nz in any column of L: 17 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 4118 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 534 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 7.94859e-01 maximum sum (abs (rows of A)): 1.08460e+06 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 3326 2762 83% peak size (Units) 9801 5323 54% final size (Units) 4259 457 11% Numeric final size (Units) 5153 1286 25% Numeric final size (MBytes) 0.0 0.0 25% peak memory usage (Units) 12149 7671 63% peak memory usage (MBytes) 0.1 0.1 63% numeric factorization flops 2.47640e+04 4.10700e+03 17% nz in L (incl diagonal) 606 318 52% nz in U (incl diagonal) 2537 285 11% nz in L+U (incl diagonal) 3013 473 16% largest front (# entries) 459 240 52% largest # rows in front 17 16 94% largest # columns in front 48 15 31% initial allocation ratio used: 0.755 # of forced updates due to frontal growth: 0 number of off-diagonal pivots: 0 nz in L (incl diagonal), if none dropped 409 nz in U (incl diagonal), if none dropped 792 number of small entries dropped 598 nonzeros on diagonal of U: 130 min abs. value on diagonal of U: 9.22e-07 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 9.22e-07 indices in compressed pattern: 82 numerical values stored in Numeric object: 386 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 2.06060e+04 iterative refinement steps taken: 2 iterative refinement steps attempted: 2 sparse backward error omega1: 1.47e-16 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 2.47130e+04 UMFPACK V5.2.0 (Nov 1, 2007): OK dense vector, n = 130. OK relative maxnorm of residual, ||Ax-b||/||b||: 2.74736e-16 relative maxnorm of error, ||x-xtrue||/||xtrue||: 1.92269e-10 Writing tmp/x Writing tmp/info.umf4 umf4 done, strategy: 0 =========================================================== === AMD =================================================== =========================================================== ------- Now trying the AMD ordering. This not part of the UMFPACK analysis or factorization, above, but a separate test of just the AMD ordering routine. AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 4 AMD ordering time: cpu 0.00 wall 0.00 AMD version 2.2.0, May 31, 2007, results: status: OK n, dimension of A: 130 nz, number of nonzeros in A: 1037 symmetry of A: 0.4939 number of nonzeros on diagonal: 130 nonzeros in pattern of A+A' (excl. diagonal): 1366 # dense rows/columns of A+A': 2 memory used, in bytes: 11236 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 725 nonzeros in L (including diagonal): 855 # divide operations for LDL' or LU: 725 # multiply-subtract operations for LDL': 2742 # multiply-subtract operations for LU: 4759 max nz. in any column of L (incl. diagonal): 18 chol flop count for real A, sqrt counted as 1 flop: 6339 LDL' flop count for real A: 6209 LDL' flop count for complex A: 28461 LU flop count for real A (with no pivoting): 10243 LU flop count for complex A (with no pivoting): 44597 AMD test done SuiteSparse/UMFPACK/Demo/umf4hb.f0000644001170100242450000002767710474367401015306 0ustar davisfacc======================================================================= c== umf4hb ============================================================= c======================================================================= c----------------------------------------------------------------------- c UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis. CISE c Dept, Univ. of Florida. All Rights Reserved. See ../Doc/License for c License. web: http://www.cise.ufl.edu/research/sparse/umfpack c----------------------------------------------------------------------- c umf4hb: c read a sparse matrix in the Harwell/Boeing format, factorizes c it, and solves Ax=b. Also saves and loads the factors to/from a c file. Saving to a file is not required, it's just here to c demonstrate how to use this feature of UMFPACK. This program c only works on square RUA-type matrices. c c This is HIGHLY non-portable. It may not work with your C and c FORTRAN compilers. See umf4_f77wrapper.c for more details. c c usage (for example): c c in a Unix shell: c umf4hb < HB/arc130.rua integer $ nzmax, nmax parameter (nzmax = 5000000, nmax = 160000) integer $ Ap (nmax), Ai (nzmax), n, nz, totcrd, ptrcrd, i, j, p, $ indcrd, valcrd, rhscrd, ncol, nrow, nrhs, nzrhs, nel, $ numeric, symbolic, status, sys, filenum character title*72, key*30, type*3, ptrfmt*16, $ indfmt*16, valfmt*20, rhsfmt*20 double precision Ax (nzmax), x (nmax), b (nmax), aij, xj, $ r (nmax), control (20), info (90) character rhstyp*3 c ---------------------------------------------------------------- c read the Harwell/Boeing matrix c ---------------------------------------------------------------- read (5, 10, err = 998) $ title, key, $ totcrd, ptrcrd, indcrd, valcrd, rhscrd, $ type, nrow, ncol, nz, nel, $ ptrfmt, indfmt, valfmt, rhsfmt if (rhscrd .gt. 0) then c new Harwell/Boeing format: read (5, 20, err = 998) rhstyp, nrhs, nzrhs endif 10 format (a72, a8 / 5i14 / a3, 11x, 4i14 / 2a16, 2a20) 20 format (a3, 11x, 2i14) print *, 'Matrix key: ', key n = nrow if (type .ne. 'RUA' .or. nrow .ne. ncol) then print *, 'Error: can only handle square RUA matrices' stop endif if (n .ge. nmax .or. nz .gt. nzmax) then print *, ' Matrix too big!' stop endif c read the matrix (1-based) read (5, ptrfmt, err = 998) (Ap (p), p = 1, ncol+1) read (5, indfmt, err = 998) (Ai (p), p = 1, nz) read (5, valfmt, err = 998) (Ax (p), p = 1, nz) c ---------------------------------------------------------------- c create the right-hand-side, assume x (i) = 1 + i/n c ---------------------------------------------------------------- do 30 i = 1,n b (i) = 0 30 continue c b = A*x do 50 j = 1,n xj = j xj = 1 + xj / n do 40 p = Ap (j), Ap (j+1)-1 i = Ai (p) aij = Ax (p) b (i) = b (i) + aij * xj 40 continue 50 continue c ---------------------------------------------------------------- c convert from 1-based to 0-based c ---------------------------------------------------------------- do 60 j = 1, n+1 Ap (j) = Ap (j) - 1 60 continue do 70 p = 1, nz Ai (p) = Ai (p) - 1 70 continue c ---------------------------------------------------------------- c factor the matrix and save to a file c ---------------------------------------------------------------- c set default parameters call umf4def (control) c print control parameters. set control (1) to 1 to print c error messages only control (1) = 2 call umf4pcon (control) c pre-order and symbolic analysis call umf4sym (n, n, Ap, Ai, Ax, symbolic, control, info) c print statistics computed so far c call umf4pinf (control, info) could also be done. print 80, info (1), info (16), $ (info (21) * info (4)) / 2**20, $ (info (22) * info (4)) / 2**20, $ info (23), info (24), info (25) 80 format ('symbolic analysis:',/, $ ' status: ', f5.0, /, $ ' time: ', e10.2, ' (sec)'/, $ ' estimates (upper bound) for numeric LU:', /, $ ' size of LU: ', f10.2, ' (MB)', /, $ ' memory needed: ', f10.2, ' (MB)', /, $ ' flop count: ', e10.2, / $ ' nnz (L): ', f10.0, / $ ' nnz (U): ', f10.0) c check umf4sym error condition if (info (1) .lt. 0) then print *, 'Error occurred in umf4sym: ', info (1) stop endif c numeric factorization call umf4num (Ap, Ai, Ax, symbolic, numeric, control, info) c print statistics for the numeric factorization c call umf4pinf (control, info) could also be done. print 90, info (1), info (66), $ (info (41) * info (4)) / 2**20, $ (info (42) * info (4)) / 2**20, $ info (43), info (44), info (45) 90 format ('numeric factorization:',/, $ ' status: ', f5.0, /, $ ' time: ', e10.2, /, $ ' actual numeric LU statistics:', /, $ ' size of LU: ', f10.2, ' (MB)', /, $ ' memory needed: ', f10.2, ' (MB)', /, $ ' flop count: ', e10.2, / $ ' nnz (L): ', f10.0, / $ ' nnz (U): ', f10.0) c check umf4num error condition if (info (1) .lt. 0) then print *, 'Error occurred in umf4num: ', info (1) stop endif c save the symbolic analysis to the file s0.umf c note that this is not needed until another matrix is c factorized, below. filenum = 0 call umf4ssym (symbolic, filenum, status) if (status .lt. 0) then print *, 'Error occurred in umf4ssym: ', status stop endif c save the LU factors to the file n0.umf call umf4snum (numeric, filenum, status) if (status .lt. 0) then print *, 'Error occurred in umf4snum: ', status stop endif c free the symbolic analysis call umf4fsym (symbolic) c free the numeric factorization call umf4fnum (numeric) c No LU factors (symbolic or numeric) are in memory at this point. c ---------------------------------------------------------------- c load the LU factors back in, and solve the system c ---------------------------------------------------------------- c At this point the program could terminate and load the LU C factors (numeric) from the n0.umf file, and solve the c system (see below). Note that the symbolic object is not c required. c load the numeric factorization back in (filename: n0.umf) call umf4lnum (numeric, filenum, status) if (status .lt. 0) then print *, 'Error occurred in umf4lnum: ', status stop endif c solve Ax=b, without iterative refinement sys = 0 call umf4sol (sys, x, b, numeric, control, info) if (info (1) .lt. 0) then print *, 'Error occurred in umf4sol: ', info (1) stop endif c free the numeric factorization call umf4fnum (numeric) c No LU factors (symbolic or numeric) are in memory at this point. c print final statistics call umf4pinf (control, info) c print the residual. x (i) should be 1 + i/n call resid (n, nz, Ap, Ai, Ax, x, b, r) c ---------------------------------------------------------------- c load the symbolic analysis back in, and factorize a new matrix c ---------------------------------------------------------------- c Again, the program could terminate here, recreate the matrix, c and refactorize. Note that umf4sym is not called. c load the symbolic factorization back in (filename: s0.umf) call umf4lsym (symbolic, filenum, status) if (status .lt. 0) then print *, 'Error occurred in umf4lsym: ', status stop endif c arbitrarily change the values of the matrix but not the pattern do 100 p = 1, nz Ax (p) = Ax (p) + 3.14159 / 100.0 100 continue c numeric factorization of the modified matrix call umf4num (Ap, Ai, Ax, symbolic, numeric, control, info) if (info (1) .lt. 0) then print *, 'Error occurred in umf4num: ', info (1) stop endif c free the symbolic analysis call umf4fsym (symbolic) c create a new right-hand-side, assume x (i) = 7 - i/n do 110 i = 1,n b (i) = 0 110 continue c b = A*x, with the modified matrix A (note that A is now 0-based) do 130 j = 1,n xj = j xj = 7 - xj / n do 120 p = Ap (j) + 1, Ap (j+1) i = Ai (p) + 1 aij = Ax (p) b (i) = b (i) + aij * xj 120 continue 130 continue c ---------------------------------------------------------------- c solve Ax=b, with iterative refinement c ---------------------------------------------------------------- sys = 0 call umf4solr (sys, Ap, Ai, Ax, x, b, numeric, control, info) if (info (1) .lt. 0) then print *, 'Error occurred in umf4solr: ', info (1) stop endif c print the residual. x (i) should be 7 - i/n call resid (n, nz, Ap, Ai, Ax, x, b, r) c ---------------------------------------------------------------- c solve Ax=b, without iterative refinement, broken into steps c ---------------------------------------------------------------- c the factorization is PAQ=LU, PRAQ=LU, or P(R\A)Q=LU. c x = R*b (or x=R\b, or x=b, as appropriate) call umf4scal (x, b, numeric, status) if (status .lt. 0) then print *, 'Error occurred in umf4scal: ', status stop endif c solve P'Lr=x for r (using r as workspace) sys = 3 call umf4sol (sys, r, x, numeric, control, info) if (info (1) .lt. 0) then print *, 'Error occurred in umf4sol: ', info (1) stop endif c solve UQ'x=r for x sys = 9 call umf4sol (sys, x, r, numeric, control, info) if (info (1) .lt. 0) then print *, 'Error occurred in umf4sol: ', info (1) stop endif c free the numeric factorization call umf4fnum (numeric) c print the residual. x (i) should be 7 - i/n call resid (n, nz, Ap, Ai, Ax, x, b, r) stop 998 print *, 'Read error: Harwell/Boeing matrix' stop end c======================================================================= c== resid ============================================================== c======================================================================= c Compute the residual, r = Ax-b, its max-norm, and print the max-norm C Note that A is zero-based. subroutine resid (n, nz, Ap, Ai, Ax, x, b, r) integer $ n, nz, Ap (n+1), Ai (n), j, i, p double precision Ax (nz), x (n), b (n), r (n), rmax, aij do 10 i = 1, n r (i) = -b (i) 10 continue do 30 j = 1,n do 20 p = Ap (j) + 1, Ap (j+1) i = Ai (p) + 1 aij = Ax (p) r (i) = r (i) + aij * x (j) 20 continue 30 continue rmax = 0 do 40 i = 1, n rmax = max (rmax, r (i)) 40 continue print *, 'norm (A*x-b): ', rmax return end SuiteSparse/UMFPACK/Demo/umfpack_zi_demo.out0000644001170100242450000015627410711433150017620 0ustar davisfac UMFPACK V5.2 (Nov 1, 2007) demo: _zi_ version UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. UMFPACK License: UMFPACK is available under alternate licenses, contact T. Davis for details. Your use or distribution of UMFPACK or any modified version of UMFPACK implies that you agree to this License. This library is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Permission is hereby granted to use or copy this program under the terms of the GNU GPL, provided that the Copyright, this License, and the Availability of the original version is retained on all copies. User documentation of any code that uses this code or any modified version of this code must cite the Copyright, this License, the Availability note, and "Used by permission." Permission to modify the code and to distribute modified code is granted, provided the Copyright, this License, and the Availability note are retained, and a notice that the code was modified is included. Availability: http://www.cise.ufl.edu/research/sparse/umfpack UMFPACK V5.2.0 (Nov 1, 2007): OK UMFPACK V5.2.0 (Nov 1, 2007), Control: Matrix entry defined as: double complex Int (generic integer) defined as: int 0: print level: 5 1: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 2: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 3: pivot tolerance: 0.1 4: block size for dense matrix kernels: 32 5: strategy: 0 (auto) 6: initial allocation ratio: 0.7 7: max iterative refinement steps: 2 12: 2-by-2 pivot tolerance: 0.01 13: Q fixed during numerical factorization: 0 (auto) 14: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 15: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 16: scaling: 1 (divide each row by sum of abs. values in each row) 17: frontal matrix allocation ratio: 0.5 18: drop tolerance: 0 19: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4 9: compiled for ANSI C 10: CPU timer is POSIX times ( ) routine. 11: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 16 (in bytes) b: dense vector, n = 5. 0 : (8 + 1i) 1 : (45 - 5i) 2 : (-3 - 2i) 3 : (3 + 0i) 4 : (19 + 2.2i) dense vector OK A: triplet-form matrix, n_row = 5, n_col = 5 nz = 12. 0 : 0 0 (2 + 1i) 1 : 4 4 (1 + 0.4i) 2 : 1 0 (3 + 0.1i) 3 : 1 2 (4 + 0.2i) 4 : 2 1 (-1 - 1i) 5 : 2 2 (-3 - 0.2i) 6 : 0 1 (3 + 0i) 7 : 1 4 (6 + 6i) 8 : 2 3 (2 + 3i) 9 : 3 2 (1 + 0i) 10 : 4 1 (4 + 0.3i) 11 : 4 2 (2 + 0.3i) triplet-form matrix OK A: column-form matrix, n_row 5 n_col 5, nz = 12. column 0: start: 0 end: 1 entries: 2 row 0 : (2 + 1i) row 1 : (3 + 0.1i) column 1: start: 2 end: 4 entries: 3 row 0 : (3 + 0i) row 2 : (-1 - 1i) row 4 : (4 + 0.3i) column 2: start: 5 end: 8 entries: 4 row 1 : (4 + 0.2i) row 2 : (-3 - 0.2i) row 3 : (1 + 0i) row 4 : (2 + 0.3i) column 3: start: 9 end: 9 entries: 1 row 2 : (2 + 3i) column 4: start: 10 end: 11 entries: 2 row 1 : (6 + 6i) row 4 : (1 + 0.4i) column-form matrix OK Symbolic factorization of A: Symbolic object: matrix to be factorized: n_row: 5 n_col: 5 number of entries: 12 block size used for dense matrix kernels: 32 strategy used: unsymmetric ordering used: colamd on A performn column etree postorder: yes prefer diagonal pivoting (attempt P=Q): no variable-size part of Numeric object: minimum initial size (Units): 90 (MBytes): 0.0 estimated peak size (Units): 2542 (MBytes): 0.0 estimated final size (Units): 25 (MBytes): 0.0 symbolic factorization memory usage (Units): 151 (MBytes): 0.0 frontal matrices / supercolumns: number of frontal chains: 1 number of frontal matrices: 1 largest frontal matrix row dimension: 3 largest frontal matrix column dimension: 3 Frontal chain: 0. Frontal matrices 0 to 0 Largest frontal matrix in Frontal chain: 3-by-3 Front: 0 pivot cols: 3 (pivot columns 0 to 2) pivot row candidates: 2 to 4 leftmost descendant: 0 1st new candidate row : 2 parent: (none) Initial column permutation, Q1: permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK Initial row permutation, P1: permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 1 4 : 4 permutation vector OK Symbolic object: OK Numeric factorization of A: Numeric object: n_row: 5 n_col: 5 relative pivot tolerance used: 0.1 relative symmetric pivot tolerance used: 0.001 matrix scaled: yes (divided each row by sum abs value in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 1.93000e+01 initial allocation parameter used: 0.7 frontal matrix allocation parameter used: 0.5 final total size of Numeric object (Units): 106 final total size of Numeric object (MBytes): 0.0 peak size of variable-size part (Units): 2527 peak size of variable-size part (MBytes): 0.0 largest actual frontal matrix size: 4 memory defragmentations: 1 memory reallocations: 1 costly memory reallocations: 0 entries in compressed pattern (L and U): 2 number of nonzeros in L (excl diag): 4 number of entries stored in L (excl diag): 2 number of nonzeros in U (excl diag): 4 number of entries stored in U (excl diag): 2 factorization floating-point operations: 34 number of nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.34629e-01 max abs. value on diagonal of U: 1.77313e+00 reciprocal condition number estimate: 7.59e-02 Scale factors applied via multiplication Scale factors, Rs: dense vector, n = 5. 0 : (0.166667) 1 : (0.0518135) 2 : (0.0980392) 3 : (1) 4 : (0.125) dense vector OK P: row permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 4 4 : 1 permutation vector OK Q: column permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK L in Numeric object, in column-oriented compressed-pattern form: Diagonal entries are all equal to 1.0 (not stored) column 0: length 0. column 1: length 2. row 4 : (0.207254 + 0.0103627i) row 3 : (0.25 + 0.0375i) column 2: add 1 entries. length 1. Start of Lchain. row 4 : (0.379275 - 0.174093i) column 3: length 1. row 4 : (3.00161 + 1.2864i) column 4: length 0. Start of Lchain. U in Numeric object, in row-oriented compressed-pattern form: Diagonal is stored separately. row 4: length 0. End of Uchain. row 3: length 1. End of Uchain. col 4 : (0.5 + 0.0375i) row 2: length 1. col 4 : (0.5 + 0i) row 1: length 0. End of Uchain. row 1: length 0. row 0: length 2. col 1 : (-0.294118 - 0.0196078i) col 4 : (-0.0980392 - 0.0980392i) diagonal of U: dense vector, n = 5. 0 : (0.196078 + 0.294118i) 1 : (1 + 0i) 2 : (0.333333 + 0.166667i) 3 : (0.125 + 0.05i) 4 : (-1.6422 - 0.668715i) dense vector OK Numeric object: OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double complex Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 16 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 151 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 52 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 1.93000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 90 80 89% peak size (Units) 2542 2527 99% final size (Units) 25 21 84% Numeric final size (Units) 113 107 95% Numeric final size (MBytes) 0.0 0.0 95% peak memory usage (Units) 2751 2736 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 6.70000e+01 3.40000e+01 51% nz in L (incl diagonal) 10 9 90% nz in U (incl diagonal) 10 9 90% nz in L+U (incl diagonal) 15 13 87% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 9 nz in U (incl diagonal), if none dropped 9 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.35e-01 max abs. value on diagonal of U: 1.77e+00 estimate of reciprocal of condition number: 7.59e-02 indices in compressed pattern: 2 numerical values stored in Numeric object: 9 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 1.02800e+03 iterative refinement steps taken: 1 iterative refinement steps attempted: 1 sparse backward error omega1: 5.28e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 1.06200e+03 UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. UMFPACK V5.2.0 (Nov 1, 2007): OK x (solution of Ax=b): dense vector, n = 5. 0 : (0.121188 - 0.561001i) 1 : (2.39887 + 0.666938i) 2 : (3 + 0i) 3 : (1.57395 - 1.52801i) 4 : (2.3876 - 3.04245i) dense vector OK maxnorm of residual: 1.77636e-15 UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. UMFPACK V5.2.0 (Nov 1, 2007): OK determinant: (-1.7814+ (2.3784)i) * 10^(2) x (solution of Ax=b, solve is split into 3 steps): dense vector, n = 5. 0 : (0.121188 - 0.561001i) 1 : (2.39887 + 0.666938i) 2 : (3 + 0i) 3 : (1.57395 - 1.52801i) 4 : (2.3876 - 3.04245i) dense vector OK maxnorm of residual: 1.77636e-14 UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double complex Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 16 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 151 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 52 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 1.93000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 90 80 89% peak size (Units) 2542 2527 99% final size (Units) 25 21 84% Numeric final size (Units) 113 107 95% Numeric final size (MBytes) 0.0 0.0 95% peak memory usage (Units) 2751 2736 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 6.70000e+01 3.40000e+01 51% nz in L (incl diagonal) 10 9 90% nz in U (incl diagonal) 10 9 90% nz in L+U (incl diagonal) 15 13 87% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 9 nz in U (incl diagonal), if none dropped 9 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.35e-01 max abs. value on diagonal of U: 1.77e+00 estimate of reciprocal of condition number: 7.59e-02 indices in compressed pattern: 2 numerical values stored in Numeric object: 9 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 4.80000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 7.82e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 5.14000e+02 x (solution of A'x=b): dense vector, n = 5. 0 : (3.39246 + 0.13257i) 1 : (0.31463 + 1.38626i) 2 : (0.461538 + 0.692308i) 3 : (-20.9089 - 1.55801i) 4 : (9.04015 - 0.613724i) dense vector OK maxnorm of residual: 4.52416e-15 changing A (1,4) to zero modified A: column-form matrix, n_row 5 n_col 5, nz = 12. column 0: start: 0 end: 1 entries: 2 row 0 : (2 + 1i) row 1 : (3 + 0.1i) column 1: start: 2 end: 4 entries: 3 row 0 : (3 + 0i) row 2 : (-1 - 1i) row 4 : (4 + 0.3i) column 2: start: 5 end: 8 entries: 4 row 1 : (4 + 0.2i) row 2 : (-3 - 0.2i) row 3 : (1 + 0i) row 4 : (2 + 0.3i) column 3: start: 9 end: 9 entries: 1 row 2 : (2 + 3i) column 4: start: 10 end: 11 entries: 2 row 1 : (0 + 0i) row 4 : (1 + 0.4i) column-form matrix OK Numeric factorization of modified A: Numeric object: n_row: 5 n_col: 5 relative pivot tolerance used: 0.1 relative symmetric pivot tolerance used: 0.001 matrix scaled: yes (divided each row by sum abs value in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 1.02000e+01 initial allocation parameter used: 0.7 frontal matrix allocation parameter used: 0.5 final total size of Numeric object (Units): 104 final total size of Numeric object (MBytes): 0.0 peak size of variable-size part (Units): 2527 peak size of variable-size part (MBytes): 0.0 largest actual frontal matrix size: 4 memory defragmentations: 1 memory reallocations: 1 costly memory reallocations: 0 entries in compressed pattern (L and U): 2 number of nonzeros in L (excl diag): 3 number of entries stored in L (excl diag): 1 number of nonzeros in U (excl diag): 4 number of entries stored in U (excl diag): 2 factorization floating-point operations: 17 number of nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.34629e-01 max abs. value on diagonal of U: 1.00000e+00 reciprocal condition number estimate: 1.35e-01 Scale factors applied via multiplication Scale factors, Rs: dense vector, n = 5. 0 : (0.166667) 1 : (0.136986) 2 : (0.0980392) 3 : (1) 4 : (0.125) dense vector OK P: row permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 4 4 : 1 permutation vector OK Q: column permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK L in Numeric object, in column-oriented compressed-pattern form: Diagonal entries are all equal to 1.0 (not stored) column 0: length 0. column 1: length 2. row 4 : (0.547945 + 0.0273973i) row 3 : (0.25 + 0.0375i) column 2: add 1 entries. length 1. Start of Lchain. row 4 : (1.00274 - 0.460274i) column 3: length 0. Start of Lchain. column 4: length 0. Start of Lchain. U in Numeric object, in row-oriented compressed-pattern form: Diagonal is stored separately. row 4: length 0. End of Uchain. row 3: length 1. End of Uchain. col 4 : (0.5 + 0.0375i) row 2: length 1. col 4 : (0.5 + 0i) row 1: length 0. End of Uchain. row 1: length 0. row 0: length 2. col 1 : (-0.294118 - 0.0196078i) col 4 : (-0.0980392 - 0.0980392i) diagonal of U: dense vector, n = 5. 0 : (0.196078 + 0.294118i) 1 : (1 + 0i) 2 : (0.333333 + 0.166667i) 3 : (0.125 + 0.05i) 4 : (-0.50137 + 0.230137i) dense vector OK Numeric object: OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double complex Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 16 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 151 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 52 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 1.02000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 90 80 89% peak size (Units) 2542 2527 99% final size (Units) 25 19 76% Numeric final size (Units) 113 105 93% Numeric final size (MBytes) 0.0 0.0 93% peak memory usage (Units) 2751 2736 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 6.70000e+01 1.70000e+01 25% nz in L (incl diagonal) 10 8 80% nz in U (incl diagonal) 10 9 90% nz in L+U (incl diagonal) 15 12 80% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 8 nz in U (incl diagonal), if none dropped 9 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.35e-01 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 1.35e-01 indices in compressed pattern: 2 numerical values stored in Numeric object: 8 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 5.15000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 6.01e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 5.32000e+02 x (with modified A): dense vector, n = 5. 0 : (10.9256 - 2.23085i) 1 : (-5.36071 - 1.82131i) 2 : (3 + 0i) 3 : (-1.60191 - 1.88814i) 4 : (32.7361 - 2.90097i) dense vector OK maxnorm of residual: 4.66294e-15 changing real part of A (0,0) from 2 to 2 changing real part of A (1,0) from 3 to 2 changing real part of A (0,1) from 3 to 13 changing real part of A (2,1) from -1 to 7 changing real part of A (4,1) from 4 to 10 changing real part of A (1,2) from 4 to 23 changing real part of A (2,2) from -3 to 15 changing real part of A (3,2) from 1 to 18 changing real part of A (4,2) from 2 to 18 changing real part of A (2,3) from 2 to 30 changing real part of A (1,4) from 0 to 39 changing real part of A (4,4) from 1 to 37 completely modified A (same pattern): column-form matrix, n_row 5 n_col 5, nz = 12. column 0: start: 0 end: 1 entries: 2 row 0 : (2 + 1i) row 1 : (2 + 0.1i) column 1: start: 2 end: 4 entries: 3 row 0 : (13 + 0i) row 2 : (7 - 1i) row 4 : (10 + 0.3i) column 2: start: 5 end: 8 entries: 4 row 1 : (23 + 0.2i) row 2 : (15 - 0.2i) row 3 : (18 + 0i) row 4 : (18 + 0.3i) column 3: start: 9 end: 9 entries: 1 row 2 : (30 + 3i) column 4: start: 10 end: 11 entries: 2 row 1 : (39 + 0i) row 4 : (37 + 0.4i) column-form matrix OK Saving symbolic object: Freeing symbolic object: Loading symbolic object: Done loading symbolic object Numeric factorization of completely modified A: Numeric object: n_row: 5 n_col: 5 relative pivot tolerance used: 0.1 relative symmetric pivot tolerance used: 0.001 matrix scaled: yes (divided each row by sum abs value in each row) minimum sum (abs (rows of A)): 1.60000e+01 maximum sum (abs (rows of A)): 6.60000e+01 initial allocation parameter used: 0.7 frontal matrix allocation parameter used: 0.5 final total size of Numeric object (Units): 106 final total size of Numeric object (MBytes): 0.0 peak size of variable-size part (Units): 2527 peak size of variable-size part (MBytes): 0.0 largest actual frontal matrix size: 4 memory defragmentations: 1 memory reallocations: 1 costly memory reallocations: 0 entries in compressed pattern (L and U): 2 number of nonzeros in L (excl diag): 4 number of entries stored in L (excl diag): 2 number of nonzeros in U (excl diag): 4 number of entries stored in U (excl diag): 2 factorization floating-point operations: 34 number of nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.39754e-01 max abs. value on diagonal of U: 1.00000e+00 reciprocal condition number estimate: 1.40e-01 Scale factors applied via multiplication Scale factors, Rs: dense vector, n = 5. 0 : (0.0625) 1 : (0.0155521) 2 : (0.0177936) 3 : (0.0555556) 4 : (0.0151515) dense vector OK P: row permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 4 4 : 1 permutation vector OK Q: column permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK L in Numeric object, in column-oriented compressed-pattern form: Diagonal entries are all equal to 1.0 (not stored) column 0: length 0. column 1: length 2. row 4 : (0.357698 + 0.00311042i) row 3 : (0.272727 + 0.00454545i) column 2: add 1 entries. length 1. Start of Lchain. row 4 : (0.204044 - 0.0895801i) column 3: length 1. row 4 : (1.0818 - 0.0116951i) column 4: length 0. Start of Lchain. U in Numeric object, in row-oriented compressed-pattern form: Diagonal is stored separately. row 4: length 0. End of Uchain. row 3: length 1. End of Uchain. col 4 : (0.151515 + 0.00454545i) row 2: length 1. col 4 : (0.8125 + 0i) row 1: length 0. End of Uchain. row 1: length 0. row 0: length 2. col 1 : (0.266904 - 0.00355872i) col 4 : (0.124555 - 0.0177936i) diagonal of U: dense vector, n = 5. 0 : (0.533808 + 0.0533808i) 1 : (1 + 0i) 2 : (0.125 + 0.0625i) 3 : (0.560606 + 0.00606061i) 4 : (-0.329747 + 0.0696386i) dense vector OK Numeric object: OK UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double complex Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 16 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 151 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 52 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.60000e+01 maximum sum (abs (rows of A)): 6.60000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 90 80 89% peak size (Units) 2542 2527 99% final size (Units) 25 21 84% Numeric final size (Units) 113 107 95% Numeric final size (MBytes) 0.0 0.0 95% peak memory usage (Units) 2751 2736 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 6.70000e+01 3.40000e+01 51% nz in L (incl diagonal) 10 9 90% nz in U (incl diagonal) 10 9 90% nz in L+U (incl diagonal) 15 13 87% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 9 nz in U (incl diagonal), if none dropped 9 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 1.40e-01 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 1.40e-01 indices in compressed pattern: 2 numerical values stored in Numeric object: 9 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 5.23000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 8.05e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 5.57000e+02 x (with completely modified A): dense vector, n = 5. 0 : (7.56307 - 3.68974i) 1 : (-0.831991 + 0.0627998i) 2 : (0.166667 + 0i) 3 : (-0.00206892 - 0.107735i) 4 : (0.658245 + 0.0407649i) dense vector OK maxnorm of residual: 9.10383e-15 C (transpose of A): column-form matrix, n_row 5 n_col 5, nz = 12. column 0: start: 0 end: 1 entries: 2 row 0 : (2 - 1i) row 1 : (13 + 0i) column 1: start: 2 end: 4 entries: 3 row 0 : (2 - 0.1i) row 2 : (23 - 0.2i) row 4 : (39 + 0i) column 2: start: 5 end: 7 entries: 3 row 1 : (7 + 1i) row 2 : (15 + 0.2i) row 3 : (30 - 3i) column 3: start: 8 end: 8 entries: 1 row 2 : (18 + 0i) column 4: start: 9 end: 11 entries: 3 row 1 : (10 - 0.3i) row 2 : (18 - 0.3i) row 4 : (37 - 0.4i) column-form matrix OK Symbolic factorization of C: Symbolic object: matrix to be factorized: n_row: 5 n_col: 5 number of entries: 12 block size used for dense matrix kernels: 32 strategy used: unsymmetric ordering used: colamd on A performn column etree postorder: yes prefer diagonal pivoting (attempt P=Q): no variable-size part of Numeric object: minimum initial size (Units): 91 (MBytes): 0.0 estimated peak size (Units): 2543 (MBytes): 0.0 estimated final size (Units): 26 (MBytes): 0.0 symbolic factorization memory usage (Units): 151 (MBytes): 0.0 frontal matrices / supercolumns: number of frontal chains: 1 number of frontal matrices: 1 largest frontal matrix row dimension: 3 largest frontal matrix column dimension: 3 Frontal chain: 0. Frontal matrices 0 to 0 Largest frontal matrix in Frontal chain: 3-by-3 Front: 0 pivot cols: 3 (pivot columns 0 to 2) pivot row candidates: 2 to 4 leftmost descendant: 0 1st new candidate row : 2 parent: (none) Initial column permutation, Q1: permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK Initial row permutation, P1: permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 1 4 : 4 permutation vector OK Symbolic object: OK Get the contents of the Symbolic object for C: (compare with umfpack_zi_report_symbolic output, above) From the Symbolic object, C is of dimension 5-by-5 with nz = 12, number of fronts = 1, number of frontal matrix chains = 1 Pivot columns in each front, and parent of each front: Front 0: parent front: -1 number of pivot cols: 3 0-th pivot column is column 3 in original matrix 1-th pivot column is column 2 in original matrix 2-th pivot column is column 0 in original matrix Note that the column ordering, above, will be refined in the numeric factorization below. The assignment of pivot columns to frontal matrices will always remain unchanged. Total number of pivot columns in frontal matrices: 3 Frontal matrix chains: Frontal matrices 0 to 0 are factorized in a single working array of size 3-by-3 Numeric factorization of C: Numeric object: n_row: 5 n_col: 5 relative pivot tolerance used: 0.1 relative symmetric pivot tolerance used: 0.001 matrix scaled: yes (divided each row by sum abs value in each row) minimum sum (abs (rows of A)): 5.10000e+00 maximum sum (abs (rows of A)): 7.64000e+01 initial allocation parameter used: 0.7 frontal matrix allocation parameter used: 0.5 final total size of Numeric object (Units): 107 final total size of Numeric object (MBytes): 0.0 peak size of variable-size part (Units): 2528 peak size of variable-size part (MBytes): 0.0 largest actual frontal matrix size: 4 memory defragmentations: 1 memory reallocations: 1 costly memory reallocations: 0 entries in compressed pattern (L and U): 2 number of nonzeros in L (excl diag): 3 number of entries stored in L (excl diag): 2 number of nonzeros in U (excl diag): 5 number of entries stored in U (excl diag): 2 factorization floating-point operations: 34 number of nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 2.40964e-01 max abs. value on diagonal of U: 9.13625e-01 reciprocal condition number estimate: 2.64e-01 Scale factors applied via multiplication Scale factors, Rs: dense vector, n = 5. 0 : (0.196078) 1 : (0.0319489) 2 : (0.0133869) 3 : (0.030303) 4 : (0.013089) dense vector OK P: row permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 4 4 : 1 permutation vector OK Q: column permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK L in Numeric object, in column-oriented compressed-pattern form: Diagonal entries are all equal to 1.0 (not stored) column 0: length 0. column 1: length 1. row 4 : (0.240091 + 0.0591529i) column 2: add 1 entries. length 1. Start of Lchain. row 4 : (0.847284 + 0.423642i) column 3: length 1. row 4 : (0.659838 - 0.0126577i) column 4: length 0. Start of Lchain. U in Numeric object, in row-oriented compressed-pattern form: Diagonal is stored separately. row 4: length 0. End of Uchain. row 3: length 1. End of Uchain. col 4 : (0.510471 + 0i) row 2: length 1. col 4 : (0.392157 - 0.0196078i) row 1: length 0. End of Uchain. row 1: length 0. row 0: length 3. col 1 : (0.200803 + 0.00267738i) col 3 : (0.240964 - 0.00401606i) col 4 : (0.307898 - 0.00267738i) diagonal of U: dense vector, n = 5. 0 : (0.240964 + 0i) 1 : (0.909091 - 0.0909091i) 2 : (0.392157 - 0.196078i) 3 : (0.484293 - 0.0052356i) 4 : (-0.677403 - 0.143059i) dense vector OK Numeric object: OK L (lower triangular factor of C): row-form matrix, n_row 5 n_col 5, nz = 8. row 0: start: 0 end: 0 entries: 1 column 0 : (1 + 0i) row 1: start: 1 end: 1 entries: 1 column 1 : (1 + 0i) row 2: start: 2 end: 2 entries: 1 column 2 : (1 + 0i) row 3: start: 3 end: 3 entries: 1 column 3 : (1 + 0i) row 4: start: 4 end: 7 entries: 4 column 1 : (0.240091 + 0.0591529i) column 2 : (0.847284 + 0.423642i) column 3 : (0.659838 - 0.0126577i) column 4 : (1 + 0i) row-form matrix OK U (upper triangular factor of C): column-form matrix, n_row 5 n_col 5, nz = 10. column 0: start: 0 end: 0 entries: 1 row 0 : (0.240964 + 0i) column 1: start: 1 end: 2 entries: 2 row 0 : (0.200803 + 0.00267738i) row 1 : (0.909091 - 0.0909091i) column 2: start: 3 end: 3 entries: 1 row 2 : (0.392157 - 0.196078i) column 3: start: 4 end: 5 entries: 2 row 0 : (0.240964 - 0.00401606i) row 3 : (0.484293 - 0.0052356i) column 4: start: 6 end: 9 entries: 4 row 0 : (0.307898 - 0.00267738i) row 2 : (0.392157 - 0.0196078i) row 3 : (0.510471 + 0i) row 4 : (-0.677403 - 0.143059i) column-form matrix OK P: permutation vector, n = 5. 0 : 2 1 : 3 2 : 0 3 : 4 4 : 1 permutation vector OK Q: permutation vector, n = 5. 0 : 3 1 : 2 2 : 0 3 : 4 4 : 1 permutation vector OK Scale factors: row i of A is to be multiplied by the ith scale factor 0: 0.196078 1: 0.0319489 2: 0.0133869 3: 0.030303 4: 0.013089 Converting L to triplet form, and printing it: L, in triplet form: triplet-form matrix, n_row = 5, n_col = 5 nz = 8. 0 : 0 0 (1 + 0i) 1 : 1 1 (1 + 0i) 2 : 2 2 (1 + 0i) 3 : 3 3 (1 + 0i) 4 : 4 1 (0.240091 + 0.0591529i) 5 : 4 2 (0.847284 + 0.423642i) 6 : 4 3 (0.659838 - 0.0126577i) 7 : 4 4 (1 + 0i) triplet-form matrix OK Saving numeric object: Freeing numeric object: Loading numeric object: Done loading numeric object UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double complex Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 16 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 151 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 52 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 5.10000e+00 maximum sum (abs (rows of A)): 7.64000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 91 81 89% peak size (Units) 2543 2528 99% final size (Units) 26 22 85% Numeric final size (Units) 114 108 95% Numeric final size (MBytes) 0.0 0.0 95% peak memory usage (Units) 2752 2737 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 6.70000e+01 3.40000e+01 51% nz in L (incl diagonal) 9 8 89% nz in U (incl diagonal) 11 10 91% nz in L+U (incl diagonal) 15 13 87% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 8 nz in U (incl diagonal), if none dropped 10 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 2.41e-01 max abs. value on diagonal of U: 9.14e-01 estimate of reciprocal of condition number: 2.64e-01 indices in compressed pattern: 2 numerical values stored in Numeric object: 9 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 4.80000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 9.42e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 5.14000e+02 x (solution of C'x=b): dense vector, n = 5. 0 : (7.56307 - 3.68974i) 1 : (-0.831991 + 0.0627998i) 2 : (0.166667 + 0i) 3 : (-0.00206892 - 0.107735i) 4 : (0.658245 + 0.0407649i) dense vector OK maxnorm of residual: 4.88498e-15 Solving C'x=b again, using umfpack_zi_wsolve instead: UMFPACK V5.2.0 (Nov 1, 2007), Info: matrix entry defined as: double complex Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 5 number of columns in matrix A: 5 entries in matrix A: 12 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 16 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 2 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 3 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 4 nz on diagonal of matrix S: 2 fraction of nz on diagonal: 0.666667 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 1 # unmatched: 0 symmetry of P2*S: 0.000000 nz in P2*S+(P2*S)' (excl. diag.): 6 nz on diagonal of P2*S: 3 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 151 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 52 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 5.10000e+00 maximum sum (abs (rows of A)): 7.64000e+01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 91 81 89% peak size (Units) 2543 2528 99% final size (Units) 26 22 85% Numeric final size (Units) 114 108 95% Numeric final size (MBytes) 0.0 0.0 95% peak memory usage (Units) 2752 2737 99% peak memory usage (MBytes) 0.0 0.0 99% numeric factorization flops 6.70000e+01 3.40000e+01 51% nz in L (incl diagonal) 9 8 89% nz in U (incl diagonal) 11 10 91% nz in L+U (incl diagonal) 15 13 87% largest front (# entries) 9 4 44% largest # rows in front 3 2 67% largest # columns in front 3 2 67% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 8 nz in U (incl diagonal), if none dropped 10 number of small entries dropped 0 nonzeros on diagonal of U: 5 min abs. value on diagonal of U: 2.41e-01 max abs. value on diagonal of U: 9.14e-01 estimate of reciprocal of condition number: 2.64e-01 indices in compressed pattern: 2 numerical values stored in Numeric object: 9 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 solve flops: 4.80000e+02 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 9.42e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 5.14000e+02 x (solution of C'x=b): dense vector, n = 5. 0 : (7.56307 - 3.68974i) 1 : (-0.831991 + 0.0627998i) 2 : (0.166667 + 0i) 3 : (-0.00206892 - 0.107735i) 4 : (0.658245 + 0.0407649i) dense vector OK maxnorm of residual: 4.88498e-15 umfpack_zi_demo complete. Total time: 0.00 seconds (CPU time), 0.00 seconds (wallclock time) SuiteSparse/UMFPACK/Demo/umfpack_zi_demo.sed0000644001170100242450000000023010006260704017540 0ustar davisfac/::/d 1,$s/_xx_/_zi_/g 1,$s/Int/int/g 1,$s/WSIZE/10/ 1,$s/%ld/%d/g /define ABS/ { s/ABS/ABS(x,z) ((x) >= 0 ? (x) : -(x)) + ((z) >= 0 ? (z) : -(z))/ } SuiteSparse/UMFPACK/Demo/readhb.f0000644001170100242450000000706710252104243015320 0ustar davisfacc======================================================================= c== readhb ============================================================= c======================================================================= c----------------------------------------------------------------------- c UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis. CISE c Dept, Univ. of Florida. All Rights Reserved. See ../Doc/License for c License. web: http://www.cise.ufl.edu/research/sparse/umfpack c----------------------------------------------------------------------- c readhb: c read a sparse matrix in the Harwell/Boeing format and c output a matrix in triplet format. c c usage (for example): c c in a Unix shell: c readhb < HB/arc130.rua > tmp/A c c Then, in MATLAB, you can do the following: c >> load tmp/A c >> A = spconvert (A) ; c >> spy (A) integer nzmax, nmax parameter (nzmax = 20000000, nmax = 250000) integer Ptr (nmax), Index (nzmax), n, nz, totcrd, ptrcrd, $ indcrd, valcrd, rhscrd, ncol, nrow, nrhs, row, col, p character title*72, key*30, type*3, ptrfmt*16, $ indfmt*16, valfmt*20, rhsfmt*20 logical sym double precision Value (nzmax), skew character rhstyp*3 integer nzrhs, nel integer ne, nnz c----------------------------------------------------------------------- c read header information from Harwell/Boeing matrix read (5, 10, err = 998) $ title, key, $ totcrd, ptrcrd, indcrd, valcrd, rhscrd, $ type, nrow, ncol, nz, nel, $ ptrfmt, indfmt, valfmt, rhsfmt if (rhscrd .gt. 0) then c new Harwell/Boeing format: read (5, 20, err = 998) rhstyp,nrhs,nzrhs endif 10 format (a72, a8 / 5i14 / a3, 11x, 4i14 / 2a16, 2a20) 20 format (a3, 11x, 2i14) skew = 0.0 if (type (2:2) .eq. 'Z' .or. type (2:2) .eq. 'z') skew = -1.0 if (type (2:2) .eq. 'S' .or. type (2:2) .eq. 's') skew = 1.0 sym = skew .ne. 0.0 write (0, 31) key 31 format ('Matrix key: ', a8) n = max (nrow, ncol) if (n .ge. nmax .or. nz .gt. nzmax) then write (0, *) 'Matrix too big!' write (0, *) '(recompile readhb.f with larger nzmax, nmax)' stop endif read (5, ptrfmt, err = 998) (Ptr (p), p = 1, ncol+1) read (5, indfmt, err = 998) (Index (p), p = 1, nz) do 55 col = ncol+2, n+1 Ptr (col) = Ptr (ncol+1) 55 continue c read the values if (valcrd .gt. 0) then read (5, valfmt, err = 998) (Value (p), p = 1, nz) else do 50 p = 1, nz Value (p) = 1 50 continue endif c create the triplet form of the input matrix ne = 0 nnz = 0 do 100 col = 1, n do 90 p = Ptr (col), Ptr (col+1) - 1 row = Index (p) ne = ne + 1 nnz = nnz + 1 write (6, 200) row, col, Value (p) if (sym .and. row .ne. col) then ne = ne + 1 if (Value (p) .ne. 0) then nnz = nnz + 1 write (6, 200) col, row, skew * Value (p) endif endif 90 continue 100 continue 200 format (2i7, e30.18e3) c write (0,*) 'Number of entries: ',ne,' True nonzeros: ', nnz stop 998 write (0,*) 'Read error: Harwell/Boeing matrix' stop end SuiteSparse/UMFPACK/Demo/umfpack_xx_demo.c0000644001170100242450000007160010617501640017242 0ustar davisfac/* ========================================================================== */ /* === umfpack_xx_demo ====================================================== */ /* ========================================================================== */ :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :: Do not attempt to compile this file! It is processed via sed scripts into :: four different C demo programs: :: :: umfpack_di_demo.c: double precision, int integers :: umfpack_dl_demo.c: double precision, UF_long integers :: umfpack_zi_demo.c: complex double precision, int integers :: umfpack_zl_demo.c: complex double precision, UF_long integers :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* A demo of UMFPACK: umfpack_xx_* version. First, factor and solve a 5-by-5 system, Ax=b, using default parameters. Then solve A'x=b using the factors of A. Modify one entry (A (1,4) = 0, where the row and column indices range from 0 to 4. The pattern of A has not changed (it has explicitly zero entry), so a reanalysis with umfpack_xx_symbolic does not need to be done. Refactorize (with umfpack_xx_numeric), and solve Ax=b. Note that the pivot ordering has changed. Next, change all of the entries in A, but not the pattern. Finally, compute C = A', and do the symbolic and numeric factorization of C. Factorizing A' can sometimes be better than factorizing A itself (less work and memory usage). Solve C'x=b twice; the solution is the same as the solution to Ax=b. A note about zero-sized arrays: UMFPACK uses many user-provided arrays of size n (order of the matrix), and of size nz (the number of nonzeros in a matrix). n cannot be zero; UMFPACK does not handle zero-dimensioned arrays. However, nz can be zero. If you attempt to malloc an array of size nz = 0, however, malloc will return a null pointer which UMFPACK will report as a "missing argument." Thus, nz1 in this code is set to MAX (nz,1), and similarly for lnz and unz. Lnz can never be zero, however, since L is always unit diagonal. */ /* -------------------------------------------------------------------------- */ /* definitions */ /* -------------------------------------------------------------------------- */ #include #include #include "umfpack.h" /* use a cheap approximate absolute value for complex numbers: */ :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :: ABS is |xreal|+|ximag| for the complex case, and |x| for the real case. :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: #define ABS #define MAX(a,b) (((a) > (b)) ? (a) : (b)) #ifndef TRUE #define TRUE (1) #endif #ifndef FALSE #define FALSE (0) #endif /* -------------------------------------------------------------------------- */ /* triplet form of the matrix. The triplets can be in any order. */ /* -------------------------------------------------------------------------- */ :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :: Int is either int or UF_long: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: static Int n = 5, nz = 12 ; static Int Arow [ ] = { 0, 4, 1, 1, 2, 2, 0, 1, 2, 3, 4, 4} ; static Int Acol [ ] = { 0, 4, 0, 2, 1, 2, 1, 4, 3, 2, 1, 2} ; static double Aval [ ] = {2., 1., 3., 4., -1., -3., 3., 6., 2., 1., 4., 2.} ; static double Avalz[ ] = {1., .4, .1, .2, -1., -.2, 0., 6., 3., 0., .3, .3} ; static double b [ ] = {8., 45., -3., 3., 19.}, x [5], r [5] ; static double bz[ ] = {1., -5., -2., 0., 2.2}, xz[5], rz[5] ; /* Avalz, bz: imaginary part of A and b */ /* -------------------------------------------------------------------------- */ /* error: print a message and exit */ /* -------------------------------------------------------------------------- */ static void error ( char *message ) { printf ("\n\n====== error: %s =====\n\n", message) ; exit (1) ; } /* -------------------------------------------------------------------------- */ /* resid: compute the residual, r = Ax-b or r = A'x=b and return maxnorm (r) */ /* A' is the complex conjugate transpose, not the array transpose */ /* -------------------------------------------------------------------------- */ static double resid ( Int transpose, Int Ap [ ], Int Ai [ ], double Ax [ ] , double Az [ ] ) { Int i, j, p ; double norm ; for (i = 0 ; i < n ; i++) { r [i] = -b [i] ; rz[i] = -bz[i] ; } if (transpose) { for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; /* complex: r(j) += conj (Aij) * x (i) */ r [j] += Ax [p] * x [i] ; r [j] += Az [p] * xz[i] ; rz[j] -= Az [p] * x [i] ; rz[j] += Ax [p] * xz[i] ; } } } else { for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; r [i] += Ax [p] * x [j] ; r [i] -= Az [p] * xz[j] ; rz[i] += Az [p] * x [j] ; rz[i] += Ax [p] * xz[j] ; } } } norm = 0. ; for (i = 0 ; i < n ; i++) { norm = MAX (ABS (r [i], rz [i]), norm) ; } return (norm) ; } /* -------------------------------------------------------------------------- */ /* main program */ /* -------------------------------------------------------------------------- */ int main (int argc, char **argv) { double Info [UMFPACK_INFO], Control [UMFPACK_CONTROL], *Ax, *Cx, *Lx, *Ux, *W, t [2], *Dx, rnorm, *Rb, *y, *Rs ; double *Az, *Lz, *Uz, *Dz, *Cz, *Rbz, *yz ; Int *Ap, *Ai, *Cp, *Ci, row, col, p, lnz, unz, nr, nc, *Lp, *Li, *Ui, *Up, *P, *Q, *Lj, i, j, k, anz, nfr, nchains, *Qinit, fnpiv, lnz1, unz1, nz1, status, *Front_npivcol, *Front_parent, *Chain_start, *Wi, *Pinit, n1, *Chain_maxrows, *Chain_maxcols, *Front_1strow, *Front_leftmostdesc, nzud, do_recip ; void *Symbolic, *Numeric ; /* ---------------------------------------------------------------------- */ /* initializations */ /* ---------------------------------------------------------------------- */ umfpack_tic (t) ; printf ("\nUMFPACK V%d.%d (%s) demo: _xx_ version\n", UMFPACK_MAIN_VERSION, UMFPACK_SUB_VERSION, UMFPACK_DATE) ; /* get the default control parameters */ umfpack_xx_defaults (Control) ; /* change the default print level for this demo */ /* (otherwise, nothing will print) */ Control [UMFPACK_PRL] = 6 ; /* print the license agreement */ umfpack_xx_report_status (Control, UMFPACK_OK) ; Control [UMFPACK_PRL] = 5 ; /* print the control parameters */ umfpack_xx_report_control (Control) ; /* ---------------------------------------------------------------------- */ /* print A and b, and convert A to column-form */ /* ---------------------------------------------------------------------- */ /* print the right-hand-side */ printf ("\nb: ") ; (void) umfpack_xx_report_vector (n, b, bz, Control) ; /* print the triplet form of the matrix */ printf ("\nA: ") ; (void) umfpack_xx_report_triplet (n, n, nz, Arow, Acol, Aval, Avalz, Control) ; /* convert to column form */ nz1 = MAX (nz,1) ; /* ensure arrays are not of size zero. */ Ap = (Int *) malloc ((n+1) * sizeof (Int)) ; Ai = (Int *) malloc (nz1 * sizeof (Int)) ; Ax = (double *) malloc (nz1 * sizeof (double)) ; Az = (double *) malloc (nz1 * sizeof (double)) ; if (!Ap || !Ai || !Ax || !Az) { error ("out of memory") ; } status = umfpack_xx_triplet_to_col (n, n, nz, Arow, Acol, Aval, Avalz, Ap, Ai, Ax, Az, (Int *) NULL) ; if (status < 0) { umfpack_xx_report_status (Control, status) ; error ("umfpack_xx_triplet_to_col failed") ; } /* print the column-form of A */ printf ("\nA: ") ; (void) umfpack_xx_report_matrix (n, n, Ap, Ai, Ax, Az, 1, Control) ; /* ---------------------------------------------------------------------- */ /* symbolic factorization */ /* ---------------------------------------------------------------------- */ status = umfpack_xx_symbolic (n, n, Ap, Ai, Ax, Az, &Symbolic, Control, Info) ; if (status < 0) { umfpack_xx_report_info (Control, Info) ; umfpack_xx_report_status (Control, status) ; error ("umfpack_xx_symbolic failed") ; } /* print the symbolic factorization */ printf ("\nSymbolic factorization of A: ") ; (void) umfpack_xx_report_symbolic (Symbolic, Control) ; /* ---------------------------------------------------------------------- */ /* numeric factorization */ /* ---------------------------------------------------------------------- */ status = umfpack_xx_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric, Control, Info) ; if (status < 0) { umfpack_xx_report_info (Control, Info) ; umfpack_xx_report_status (Control, status) ; error ("umfpack_xx_numeric failed") ; } /* print the numeric factorization */ printf ("\nNumeric factorization of A: ") ; (void) umfpack_xx_report_numeric (Numeric, Control) ; /* ---------------------------------------------------------------------- */ /* solve Ax=b */ /* ---------------------------------------------------------------------- */ status = umfpack_xx_solve (UMFPACK_A, Ap, Ai, Ax, Az, x, xz, b, bz, Numeric, Control, Info) ; umfpack_xx_report_info (Control, Info) ; umfpack_xx_report_status (Control, status) ; if (status < 0) { error ("umfpack_xx_solve failed") ; } printf ("\nx (solution of Ax=b): ") ; (void) umfpack_xx_report_vector (n, x, xz, Control) ; rnorm = resid (FALSE, Ap, Ai, Ax, Az) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* compute the determinant */ /* ---------------------------------------------------------------------- */ status = umfpack_xx_get_determinant (x, xz, r, Numeric, Info) ; umfpack_xx_report_status (Control, status) ; if (status < 0) { error ("umfpack_xx_get_determinant failed") ; } printf ("determinant: (%g", x [0]) ; printf ("+ (%g)i", xz [0]) ; /* complex */ printf (") * 10^(%g)\n", r [0]) ; /* ---------------------------------------------------------------------- */ /* solve Ax=b, broken down into steps */ /* ---------------------------------------------------------------------- */ /* Rb = R*b */ Rb = (double *) malloc (n * sizeof (double)) ; Rbz = (double *) malloc (n * sizeof (double)) ; y = (double *) malloc (n * sizeof (double)) ; yz = (double *) malloc (n * sizeof (double)) ; if (!Rb || !y) error ("out of memory") ; if (!Rbz || !yz) error ("out of memory") ; status = umfpack_xx_scale (Rb, Rbz, b, bz, Numeric) ; if (status < 0) error ("umfpack_xx_scale failed") ; /* solve Ly = P*(Rb) */ status = umfpack_xx_solve (UMFPACK_Pt_L, Ap, Ai, Ax, Az, y, yz, Rb, Rbz, Numeric, Control, Info) ; if (status < 0) error ("umfpack_xx_solve failed") ; /* solve UQ'x=y */ status = umfpack_xx_solve (UMFPACK_U_Qt, Ap, Ai, Ax, Az, x, xz, y, yz, Numeric, Control, Info) ; if (status < 0) error ("umfpack_xx_solve failed") ; printf ("\nx (solution of Ax=b, solve is split into 3 steps): ") ; (void) umfpack_xx_report_vector (n, x, xz, Control) ; rnorm = resid (FALSE, Ap, Ai, Ax, Az) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; free (Rb) ; free (Rbz) ; free (y) ; free (yz) ; /* ---------------------------------------------------------------------- */ /* solve A'x=b */ /* ---------------------------------------------------------------------- */ /* note that this is the complex conjugate transpose, A' */ status = umfpack_xx_solve (UMFPACK_At, Ap, Ai, Ax, Az, x, xz, b, bz, Numeric, Control, Info) ; umfpack_xx_report_info (Control, Info) ; if (status < 0) { error ("umfpack_xx_solve failed") ; } printf ("\nx (solution of A'x=b): ") ; (void) umfpack_xx_report_vector (n, x, xz, Control) ; rnorm = resid (TRUE, Ap, Ai, Ax, Az) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* modify one numerical value in the column-form of A */ /* ---------------------------------------------------------------------- */ /* change A (1,4), look for row index 1 in column 4. */ row = 1 ; col = 4 ; for (p = Ap [col] ; p < Ap [col+1] ; p++) { if (row == Ai [p]) { printf ("\nchanging A (%ld,%ld) to zero\n", row, col) ; Ax [p] = 0.0 ; Az [p] = 0.0 ; break ; } } printf ("\nmodified A: ") ; (void) umfpack_xx_report_matrix (n, n, Ap, Ai, Ax, Az, 1, Control) ; /* ---------------------------------------------------------------------- */ /* redo the numeric factorization */ /* ---------------------------------------------------------------------- */ /* The pattern (Ap and Ai) hasn't changed, so the symbolic factorization */ /* doesn't have to be redone, no matter how much we change Ax. */ /* We don't need the Numeric object any more, so free it. */ umfpack_xx_free_numeric (&Numeric) ; /* Note that a memory leak would have occurred if the old Numeric */ /* had not been free'd with umfpack_xx_free_numeric above. */ status = umfpack_xx_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric, Control, Info) ; if (status < 0) { umfpack_xx_report_info (Control, Info) ; umfpack_xx_report_status (Control, status) ; error ("umfpack_xx_numeric failed") ; } printf ("\nNumeric factorization of modified A: ") ; (void) umfpack_xx_report_numeric (Numeric, Control) ; /* ---------------------------------------------------------------------- */ /* solve Ax=b, with the modified A */ /* ---------------------------------------------------------------------- */ status = umfpack_xx_solve (UMFPACK_A, Ap, Ai, Ax, Az, x, xz, b, bz, Numeric, Control, Info) ; umfpack_xx_report_info (Control, Info) ; if (status < 0) { umfpack_xx_report_status (Control, status) ; error ("umfpack_xx_solve failed") ; } printf ("\nx (with modified A): ") ; (void) umfpack_xx_report_vector (n, x, xz, Control) ; rnorm = resid (FALSE, Ap, Ai, Ax, Az) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* modify all of the numerical values of A, but not the pattern */ /* ---------------------------------------------------------------------- */ for (col = 0 ; col < n ; col++) { for (p = Ap [col] ; p < Ap [col+1] ; p++) { row = Ai [p] ; printf ("changing ") ; /* complex: */ printf ("real part of ") ; printf ("A (%ld,%ld) from %g", row, col, Ax [p]) ; Ax [p] = Ax [p] + col*10 - row ; printf (" to %g\n", Ax [p]) ; } } printf ("\ncompletely modified A (same pattern): ") ; (void) umfpack_xx_report_matrix (n, n, Ap, Ai, Ax, Az, 1, Control) ; /* ---------------------------------------------------------------------- */ /* save the Symbolic object to file, free it, and load it back in */ /* ---------------------------------------------------------------------- */ /* use the default filename, "symbolic.umf" */ printf ("\nSaving symbolic object:\n") ; status = umfpack_xx_save_symbolic (Symbolic, (char *) NULL) ; if (status < 0) { umfpack_xx_report_status (Control, status) ; error ("umfpack_xx_save_symbolic failed") ; } printf ("\nFreeing symbolic object:\n") ; umfpack_xx_free_symbolic (&Symbolic) ; printf ("\nLoading symbolic object:\n") ; status = umfpack_xx_load_symbolic (&Symbolic, (char *) NULL) ; if (status < 0) { umfpack_xx_report_status (Control, status) ; error ("umfpack_xx_load_symbolic failed") ; } printf ("\nDone loading symbolic object\n") ; /* ---------------------------------------------------------------------- */ /* redo the numeric factorization */ /* ---------------------------------------------------------------------- */ umfpack_xx_free_numeric (&Numeric) ; status = umfpack_xx_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric, Control, Info) ; if (status < 0) { umfpack_xx_report_info (Control, Info) ; umfpack_xx_report_status (Control, status) ; error ("umfpack_xx_numeric failed") ; } printf ("\nNumeric factorization of completely modified A: ") ; (void) umfpack_xx_report_numeric (Numeric, Control) ; /* ---------------------------------------------------------------------- */ /* solve Ax=b, with the modified A */ /* ---------------------------------------------------------------------- */ status = umfpack_xx_solve (UMFPACK_A, Ap, Ai, Ax, Az, x, xz, b, bz, Numeric, Control, Info) ; umfpack_xx_report_info (Control, Info) ; if (status < 0) { umfpack_xx_report_status (Control, status) ; error ("umfpack_xx_solve failed") ; } printf ("\nx (with completely modified A): ") ; (void) umfpack_xx_report_vector (n, x, xz, Control) ; rnorm = resid (FALSE, Ap, Ai, Ax, Az) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* free the symbolic and numeric factorization */ /* ---------------------------------------------------------------------- */ umfpack_xx_free_symbolic (&Symbolic) ; umfpack_xx_free_numeric (&Numeric) ; /* ---------------------------------------------------------------------- */ /* C = transpose of A */ /* ---------------------------------------------------------------------- */ Cp = (Int *) malloc ((n+1) * sizeof (Int)) ; Ci = (Int *) malloc (nz1 * sizeof (Int)) ; Cx = (double *) malloc (nz1 * sizeof (double)) ; Cz = (double *) malloc (nz1 * sizeof (double)) ; if (!Cp || !Ci || !Cx || !Cz) { error ("out of memory") ; } status = umfpack_xx_transpose (n, n, Ap, Ai, Ax, Az, (Int *) NULL, (Int *) NULL, Cp, Ci, Cx, Cz, TRUE) ; if (status < 0) { umfpack_xx_report_status (Control, status) ; error ("umfpack_xx_transpose failed: ") ; } printf ("\nC (transpose of A): ") ; (void) umfpack_xx_report_matrix (n, n, Cp, Ci, Cx, Cz, 1, Control) ; /* ---------------------------------------------------------------------- */ /* symbolic factorization of C */ /* ---------------------------------------------------------------------- */ status = umfpack_xx_symbolic (n, n, Cp, Ci, Cx, Cz, &Symbolic, Control, Info) ; if (status < 0) { umfpack_xx_report_info (Control, Info) ; umfpack_xx_report_status (Control, status) ; error ("umfpack_xx_symbolic failed") ; } printf ("\nSymbolic factorization of C: ") ; (void) umfpack_xx_report_symbolic (Symbolic, Control) ; /* ---------------------------------------------------------------------- */ /* copy the contents of Symbolic into user arrays print them */ /* ---------------------------------------------------------------------- */ printf ("\nGet the contents of the Symbolic object for C:\n") ; printf ("(compare with umfpack_xx_report_symbolic output, above)\n") ; Pinit = (Int *) malloc ((n+1) * sizeof (Int)) ; Qinit = (Int *) malloc ((n+1) * sizeof (Int)) ; Front_npivcol = (Int *) malloc ((n+1) * sizeof (Int)) ; Front_1strow = (Int *) malloc ((n+1) * sizeof (Int)) ; Front_leftmostdesc = (Int *) malloc ((n+1) * sizeof (Int)) ; Front_parent = (Int *) malloc ((n+1) * sizeof (Int)) ; Chain_start = (Int *) malloc ((n+1) * sizeof (Int)) ; Chain_maxrows = (Int *) malloc ((n+1) * sizeof (Int)) ; Chain_maxcols = (Int *) malloc ((n+1) * sizeof (Int)) ; if (!Pinit || !Qinit || !Front_npivcol || !Front_parent || !Chain_start || !Chain_maxrows || !Chain_maxcols || !Front_1strow || !Front_leftmostdesc) { error ("out of memory") ; } status = umfpack_xx_get_symbolic (&nr, &nc, &n1, &anz, &nfr, &nchains, Pinit, Qinit, Front_npivcol, Front_parent, Front_1strow, Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ; if (status < 0) { error ("symbolic factorization invalid") ; } printf ("From the Symbolic object, C is of dimension %ld-by-%ld\n", nr, nc); printf (" with nz = %ld, number of fronts = %ld,\n", nz, nfr) ; printf (" number of frontal matrix chains = %ld\n", nchains) ; printf ("\nPivot columns in each front, and parent of each front:\n") ; k = 0 ; for (i = 0 ; i < nfr ; i++) { fnpiv = Front_npivcol [i] ; printf (" Front %ld: parent front: %ld number of pivot cols: %ld\n", i, Front_parent [i], fnpiv) ; for (j = 0 ; j < fnpiv ; j++) { col = Qinit [k] ; printf ( " %ld-th pivot column is column %ld in original matrix\n", k, col) ; k++ ; } } printf ("\nNote that the column ordering, above, will be refined\n") ; printf ("in the numeric factorization below. The assignment of pivot\n") ; printf ("columns to frontal matrices will always remain unchanged.\n") ; printf ("\nTotal number of pivot columns in frontal matrices: %ld\n", k) ; printf ("\nFrontal matrix chains:\n") ; for (j = 0 ; j < nchains ; j++) { printf (" Frontal matrices %ld to %ld are factorized in a single\n", Chain_start [j], Chain_start [j+1] - 1) ; printf (" working array of size %ld-by-%ld\n", Chain_maxrows [j], Chain_maxcols [j]) ; } /* ---------------------------------------------------------------------- */ /* numeric factorization of C */ /* ---------------------------------------------------------------------- */ status = umfpack_xx_numeric (Cp, Ci, Cx, Cz, Symbolic, &Numeric, Control, Info) ; if (status < 0) { error ("umfpack_xx_numeric failed") ; } printf ("\nNumeric factorization of C: ") ; (void) umfpack_xx_report_numeric (Numeric, Control) ; /* ---------------------------------------------------------------------- */ /* extract the LU factors of C and print them */ /* ---------------------------------------------------------------------- */ if (umfpack_xx_get_lunz (&lnz, &unz, &nr, &nc, &nzud, Numeric) < 0) { error ("umfpack_xx_get_lunz failed") ; } /* ensure arrays are not of zero size */ lnz1 = MAX (lnz,1) ; unz1 = MAX (unz,1) ; Lp = (Int *) malloc ((n+1) * sizeof (Int)) ; Lj = (Int *) malloc (lnz1 * sizeof (Int)) ; Lx = (double *) malloc (lnz1 * sizeof (double)) ; Lz = (double *) malloc (lnz1 * sizeof (double)) ; Up = (Int *) malloc ((n+1) * sizeof (Int)) ; Ui = (Int *) malloc (unz1 * sizeof (Int)) ; Ux = (double *) malloc (unz1 * sizeof (double)) ; Uz = (double *) malloc (unz1 * sizeof (double)) ; P = (Int *) malloc (n * sizeof (Int)) ; Q = (Int *) malloc (n * sizeof (Int)) ; Dx = (double *) NULL ; /* D vector not requested */ Dz = (double *) NULL ; Rs = (double *) malloc (n * sizeof (double)) ; if (!Lp || !Lj || !Lx || !Lz || !Up || !Ui || !Ux || !Uz || !P || !Q || !Rs) { error ("out of memory") ; } status = umfpack_xx_get_numeric (Lp, Lj, Lx, Lz, Up, Ui, Ux, Uz, P, Q, Dx, Dz, &do_recip, Rs, Numeric) ; if (status < 0) { error ("umfpack_xx_get_numeric failed") ; } printf ("\nL (lower triangular factor of C): ") ; (void) umfpack_xx_report_matrix (n, n, Lp, Lj, Lx, Lz, 0, Control) ; printf ("\nU (upper triangular factor of C): ") ; (void) umfpack_xx_report_matrix (n, n, Up, Ui, Ux, Uz, 1, Control) ; printf ("\nP: ") ; (void) umfpack_xx_report_perm (n, P, Control) ; printf ("\nQ: ") ; (void) umfpack_xx_report_perm (n, Q, Control) ; printf ("\nScale factors: row i of A is to be ") ; if (do_recip) { printf ("multiplied by the ith scale factor\n") ; } else { printf ("divided by the ith scale factor\n") ; } for (i = 0 ; i < n ; i++) printf ("%ld: %g\n", i, Rs [i]) ; /* ---------------------------------------------------------------------- */ /* convert L to triplet form and print it */ /* ---------------------------------------------------------------------- */ /* Note that L is in row-form, so it is the row indices that are created */ /* by umfpack_xx_col_to_triplet. */ printf ("\nConverting L to triplet form, and printing it:\n") ; Li = (Int *) malloc (lnz1 * sizeof (Int)) ; if (!Li) { error ("out of memory") ; } if (umfpack_xx_col_to_triplet (n, Lp, Li) < 0) { error ("umfpack_xx_col_to_triplet failed") ; } printf ("\nL, in triplet form: ") ; (void) umfpack_xx_report_triplet (n, n, lnz, Li, Lj, Lx, Lz, Control) ; /* ---------------------------------------------------------------------- */ /* save the Numeric object to file, free it, and load it back in */ /* ---------------------------------------------------------------------- */ /* use the default filename, "numeric.umf" */ printf ("\nSaving numeric object:\n") ; status = umfpack_xx_save_numeric (Numeric, (char *) NULL) ; if (status < 0) { umfpack_xx_report_status (Control, status) ; error ("umfpack_xx_save_numeric failed") ; } printf ("\nFreeing numeric object:\n") ; umfpack_xx_free_numeric (&Numeric) ; printf ("\nLoading numeric object:\n") ; status = umfpack_xx_load_numeric (&Numeric, (char *) NULL) ; if (status < 0) { umfpack_xx_report_status (Control, status) ; error ("umfpack_xx_load_numeric failed") ; } printf ("\nDone loading numeric object\n") ; /* ---------------------------------------------------------------------- */ /* solve C'x=b */ /* ---------------------------------------------------------------------- */ status = umfpack_xx_solve (UMFPACK_At, Cp, Ci, Cx, Cz, x, xz, b, bz, Numeric, Control, Info) ; umfpack_xx_report_info (Control, Info) ; if (status < 0) { umfpack_xx_report_status (Control, status) ; error ("umfpack_xx_solve failed") ; } printf ("\nx (solution of C'x=b): ") ; (void) umfpack_xx_report_vector (n, x, xz, Control) ; rnorm = resid (TRUE, Cp, Ci, Cx, Cz) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* solve C'x=b again, using umfpack_xx_wsolve instead */ /* ---------------------------------------------------------------------- */ printf ("\nSolving C'x=b again, using umfpack_xx_wsolve instead:\n") ; Wi = (Int *) malloc (n * sizeof (Int)) ; :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :: WSIZE is 5 for the real case, 10 for complex. :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: W = (double *) malloc (WSIZE*n * sizeof (double)) ; if (!Wi || !W) { error ("out of memory") ; } status = umfpack_xx_wsolve (UMFPACK_At, Cp, Ci, Cx, Cz, x, xz, b, bz, Numeric, Control, Info, Wi, W) ; umfpack_xx_report_info (Control, Info) ; if (status < 0) { umfpack_xx_report_status (Control, status) ; error ("umfpack_xx_wsolve failed") ; } printf ("\nx (solution of C'x=b): ") ; (void) umfpack_xx_report_vector (n, x, xz, Control) ; rnorm = resid (TRUE, Cp, Ci, Cx, Cz) ; printf ("maxnorm of residual: %g\n\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* free everything */ /* ---------------------------------------------------------------------- */ /* This is not strictly required since the process is exiting and the */ /* system will reclaim the memory anyway. It's useful, though, just as */ /* a list of what is currently malloc'ed by this program. Plus, it's */ /* always a good habit to explicitly free whatever you malloc. */ free (Ap) ; free (Ai) ; free (Ax) ; free (Az) ; free (Cp) ; free (Ci) ; free (Cx) ; free (Cz) ; free (Pinit) ; free (Qinit) ; free (Front_npivcol) ; free (Front_1strow) ; free (Front_leftmostdesc) ; free (Front_parent) ; free (Chain_start) ; free (Chain_maxrows) ; free (Chain_maxcols) ; free (Lp) ; free (Lj) ; free (Lx) ; free (Lz) ; free (Up) ; free (Ui) ; free (Ux) ; free (Uz) ; free (P) ; free (Q) ; free (Li) ; free (Wi) ; free (W) ; umfpack_xx_free_symbolic (&Symbolic) ; umfpack_xx_free_numeric (&Numeric) ; /* ---------------------------------------------------------------------- */ /* print the total time spent in this demo */ /* ---------------------------------------------------------------------- */ umfpack_toc (t) ; printf ("\numfpack_xx_demo complete.\nTotal time: %5.2f seconds" " (CPU time), %5.2f seconds (wallclock time)\n", t [1], t [0]) ; return (0) ; } SuiteSparse/UMFPACK/Tcov/0000755001170100242450000000000010711722400013742 5ustar davisfacSuiteSparse/UMFPACK/Tcov/DO0000755001170100242450000000506110617407350014205 0ustar davisfac#!/bin/csh echo '################################################################################' echo 'Tcov test:' $1 $2 $3 echo '################################################################################' #------------------------------------------------------------------------------- # get a clean directory # /bin/mv Out/$1_$2 `mktemp -d Trash/XXXXXX` # delete the directory /bin/rm -rf Out/$1_$2 mkdir Out/$1_$2 # put in UMFPACK (excluding Tcov and MATLAB directories) and AMD mkdir Out/$1_$2/UMFPACK mkdir Out/$1_$2/UMFPACK/Doc /bin/cp -prL ../Source Out/$1_$2/UMFPACK /bin/cp -prL ../Lib Out/$1_$2/UMFPACK /bin/cp -prL ../Include Out/$1_$2/UMFPACK /bin/cp -prL ../Demo Out/$1_$2/UMFPACK /bin/cp -prL Top_Makefile Out/$1_$2/UMFPACK/Makefile /bin/cp -prL Out/$1_$2/UMFPACK/Lib/GNUmakefile Out/$1_$2/UMFPACK/Source/Makefile /bin/cp -prL Demo_Makefile Out/$1_$2/UMFPACK/Demo/Makefile /bin/cp -prL ../Doc/License Out/$1_$2/UMFPACK/Doc # put in AMD /bin/cp -prL ../../AMD Out/$1_$2 /bin/cp -prL Top_Makefile Out/$1_$2/AMD/Makefile /bin/cp -prL Out/$1_$2/AMD/Lib/GNUmakefile Out/$1_$2/AMD/Source/Makefile /bin/cp -prL AMD_Demo_Makefile Out/$1_$2/AMD/Demo/Makefile /bin/cp debug.* Out/$1_$2 # put in the makefile /bin/cp GNUmakefile.$2 Out/$1_$2/GNUmakefile # put in the UFconfig.mk and UFconfig.h files mkdir Out/$1_$2/UFconfig /bin/cp -f Make.$1 Out/$1_$2/UFconfig/UFconfig.mk /bin/cp -f ../../UFconfig/UFconfig.h Out/$1_$2/UFconfig # put in the main program /bin/cp ut.c Out/$1_$2 # put in the test matrices /bin/cp -f badnum*.umf Out/$1_$2 /bin/cp -f badsym*.umf Out/$1_$2 /bin/cp -pr TestMat Out/$1_$2 # put in the gcov files /bin/cp -f ucov.* Out/$1_$2/UMFPACK/Source /bin/cp -f acov.* Out/$1_$2/AMD/Source # compile and run ( cd Out/$1_$2 ; time make $3 > $1_$2.out ) # delete the directory #### /bin/rm -rf Out/$1_$2 # ( cd $1_$2 ; tail -5 ut.out > ut.tail ; 'rm' -rf ut.out ) # for Solaris # ( cd Out/$1_$2 ; tcov -x ut.profile/UMFPACK/Source/umfp*.c ) # ( cd Out/$1_$2 ; tcov -x ut.profile/UMFPACK/Source/umf_[0-c]*.c ) # ( cd Out/$1_$2 ; tcov -x ut.profile/UMFPACK/Source/umf_[e-z]*.c ) # ( cd Out/$1_$2 ; tcov -x ut.profile/AMD/Source/amd_[0-c]*.c ) # ( cd Out/$1_$2 ; tcov -x ut.profile/AMD/Source/amd_de*.c ) # ( cd Out/$1_$2 ; tcov -x ut.profile/AMD/Source/amd_[e-z]*.c ) # grep -n "#####" Out/$1_$2/*cov > $1_$2.cov # cov Out/$1_$2/UMFPACK/Source/umfp*cov # cov Out/$1_$2/UMFPACK/Source/umf_[0-c]*cov # cov Out/$1_$2/UMFPACK/Source/umf_[e-z]*cov # cov Out/$1_$2/AMD/Source/amd_[0-c]*cov # cov Out/$1_$2/AMD/Source/amd_de*cov # cov Out/$1_$2/AMD/Source/amd_[e-z]*cov SuiteSparse/UMFPACK/Tcov/DO20000755001170100242450000000010710006265115014254 0ustar davisfac# # DO 1g zi run DO 1g zl run DO 2g zl run DO 3g zl run DO 4g zl run SuiteSparse/UMFPACK/Tcov/Out/0000755001170100242450000000000010711176033014516 5ustar davisfacSuiteSparse/UMFPACK/Tcov/cov0000755001170100242450000000060110006265115014456 0ustar davisfac#!/bin/csh foreach file ($argv[1-]) echo "================================================================================" echo $file # cat -n $file | grep -B 5 -A 5 '#####' cat -n $file | grep '#####' end echo "================================================================================" # echo "Total lines not covered:" # cat $argv[1-] | grep "#####" | wc SuiteSparse/UMFPACK/Tcov/DOsol20000755001170100242450000000340510534134476015011 0ustar davisfac#!/bin/csh #------------------------------------------------------------------------------- echo '################################################################################' echo 'Tcov test:' $1 $2 echo '################################################################################' # get a clean directory # /bin/mv Tests/$1_$2 `mktemp -d Trash2/XXXXXX` # mkdir SolOut/$1_$2 # put in UMFPACK (excluding Tcov and MATLAB directories) and AMD mkdir SolOut/$1_$2/UMFPACK mkdir SolOut/$1_$2/UMFPACK/Doc /bin/cp -prL ../Source SolOut/$1_$2/UMFPACK /bin/cp -prL ../Lib SolOut/$1_$2/UMFPACK /bin/cp -prL ../Include SolOut/$1_$2/UMFPACK /bin/cp -prL ../Demo SolOut/$1_$2/UMFPACK /bin/cp -prL ../Makefile SolOut/$1_$2/UMFPACK/Makefile /bin/cp -prL ../Doc/License SolOut/$1_$2/UMFPACK/Doc /bin/cp -prL ../../AMD SolOut/$1_$2 /bin/cp debug.* SolOut/$1_$2 # put in the makefile /bin/cp GNUmakefile.$2 SolOut/$1_$2/GNUmakefile # put in the UFconfig.mk and UFconfig.h files mkdir SolOut/$1_$2/UFconfig /bin/cp -f Make.$1 SolOut/$1_$2/UFconfig/UFconfig.mk /bin/cp -f ../../UFconfig/UFconfig.h SolOut/$1_$2/UFconfig # put in the main program /bin/cp ut.c SolOut/$1_$2 # put in the test matrices /bin/cp -f badnum*.umf SolOut/$1_$2 /bin/cp -f badsym*.umf SolOut/$1_$2 /bin/cp -pr TestMat SolOut/$1_$2 # compile and run ( cd SolOut/$1_$2 ; time make $3 > $1_$2.out ) # for Solaris ( cd SolOut/$1_$2 ; tail -5 ut.out > $1_$2.tail ) ( cd SolOut/$1_$2 ; tcov -x ut.profile */Source/*.c ) ( cd SolOut/$1_$2 ; grep -n "#####" *cov > $1_$2.cov ) # /bin/rm -rf SolOut/$1_$2 # cov $1_$2/UMFPACK/Source/umfp*cov # cov $1_$2/UMFPACK/Source/umf_[0-c]*cov # cov $1_$2/UMFPACK/Source/umf_[e-z]*cov # cov $1_$2/AMD/Source/amd_[0-c]*cov # cov $1_$2/AMD/Source/amd_de*cov # cov $1_$2/AMD/Source/amd_[e-z]*cov SuiteSparse/UMFPACK/Tcov/ut.c0000644001170100242450000074267510617162536014600 0ustar davisfac/* ========================================================================== */ /* === umfpack tcov ========================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* (Nearly) exhaustive statement-coverage testing for UMFPACK. */ /* #define DEBUGGING */ #include #include #include #include #include #include #include "umfpack.h" #include "amd.h" #include "umf_internal.h" #include "umf_is_permutation.h" /* #include "umf_free.h" #include "umf_malloc.h" */ #include "umf_report_perm.h" #include "umf_realloc.h" #include "umf_free.h" #include "umf_malloc.h" /* #if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG) #include "umf_malloc.h" #endif */ #define TOL 1e-3 #define INULL ((Int *) NULL) #define DNULL ((double *) NULL) #ifdef COMPLEX #define CARG(real,imag) real,imag #define C1ARG(a) ,a #else #define CARG(real,imag) real #define C1ARG(a) #endif int check_tol ; static double divide (double x, double y) { return (x/y) ; } /* ========================================================================== */ /* inv_umfpack_dense: inverse of UMFPACK_DENSE_COUNT */ /* ========================================================================== */ /* the inverse of UMFPACK_DENSE_COUNT: given a col count, find alpha */ static double inv_umfpack_dense (Int d, Int n) { if (d <= 16) { return (0.0) ; } else { return (((double) d) / (16 * sqrt ((double) n))) ; } } /* ========================================================================== */ static void dump_mat (char *name, Int m, Int n, Int Ap [ ], Int Ai [ ], double Ax [ ] #ifdef COMPLEX , double Az [ ] #endif ) { Entry aa ; Int j, p ; printf ("\n%s = sparse ("ID", "ID") ;\n", name, m, n) ; for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { #ifdef COMPLEX ASSIGN (aa, Ax, Az, p, SPLIT (Az)) ; printf ("%s ("ID","ID") = %30.20g + (1i * %30.20g);\n", name, 1+Ai [p], j+1, REAL_COMPONENT(aa), IMAG_COMPONENT(aa)) ; #else printf ("%s ("ID","ID") = %30.20g ;\n", name, 1+Ai [p], j+1, Ax [p]) ; #endif } } } /* ========================================================================== */ static void dump_vec (char *name, Int n, double X [ ], double Xz[ ]) { Int j ; printf ("\n%s = [\n", name) ; for (j = 0 ; j < n ; j++) { printf ("%30.20g", X [j]) ; if (Xz) printf (" + (1i*%30.20g)", Xz[j]) ; printf ("\n") ; } printf ("] ; \n") ; } /* ========================================================================== */ static void dump_perm (char *name, Int n, Int P [ ]) { Int j ; printf ("\n%s = [\n", name) ; for (j = 0 ; j < n ; j++) { printf (""ID"\n", 1+P [j]) ; } printf ("] ; \n") ; printf ("%s = %s' ;\n", name, name) ; } /* ========================================================================== */ /* error: display message and exit */ /* ========================================================================== */ static void error (char *s, double x) { printf ("TEST FAILURE: %s %g ", s, x) ; #if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG) printf (" umf_malloc_count "ID"\n", UMF_malloc_count) ; #endif printf ("\n") ; exit (1) ; } /* ========================================================================== */ /* resid: compute the (possibly permuted) residual. return maxnorm of resid */ /* ========================================================================== */ static double resid ( Int n, Int Ap [ ], Int Ai [ ], double Ax [ ], double Az [ ], double x [ ], double xz [ ], double b [ ], double bz [ ], double r [ ], double rz [ ], Int transpose, Int P [ ], Int Q [ ], double Wx [ ] /* size 2*n double workspace */ ) { Int i, j, k, p ; double norm, ra, *wx, *wz ; Entry bb, xx, aa ; wx = Wx ; wz = wx + n ; /* transpose: UMFPACK_A r = P'AQ'x - b Pr = AQ'x - Pb we compute and return Pr, not r. transpose: UMFPACK_At r = QA'Px - b Q'r = A'Px - Q'b we compute and return Q'r, not r. transpose: UMFPACK_Aat r = QA.'Px - b Q'r = A.'Px - Q'b we compute and return Q'r, not r. */ if (transpose == UMFPACK_A) { if (!P) /* r = -b */ { for (i = 0 ; i < n ; i++) { ASSIGN (bb, b, bz, i, SPLIT(bz)) ; r [i] = -REAL_COMPONENT (bb) ; rz[i] = -IMAG_COMPONENT (bb) ; } } else /* r = -Pb */ { for (k = 0 ; k < n ; k++) { ASSIGN (bb, b, bz, P [k], SPLIT(bz)) ; r [k] = -REAL_COMPONENT (bb) ; rz[k] = -IMAG_COMPONENT (bb) ; } } if (!Q) /* w = x */ { for (j = 0 ; j < n ; j++) { ASSIGN (xx, x, xz, j, SPLIT(xz)) ; wx[j] = REAL_COMPONENT (xx) ; wz[j] = IMAG_COMPONENT (xx) ; } } else /* w = Q'x */ { for (k = 0 ; k < n ; k++) { ASSIGN (xx, x, xz, Q [k], SPLIT(xz)) ; wx[k] = REAL_COMPONENT (xx) ; wz[k] = IMAG_COMPONENT (xx) ; } } /* r = r + Aw */ for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; ASSIGN (aa, Ax, Az, p, SPLIT(Az)) ; r [i] += REAL_COMPONENT(aa) * wx[j] ; r [i] -= IMAG_COMPONENT(aa) * wz[j] ; rz[i] += IMAG_COMPONENT(aa) * wx[j] ; rz[i] += REAL_COMPONENT(aa) * wz[j] ; } } /* note that we just computed Pr, not r */ } else if (transpose == UMFPACK_At) { if (!Q) /* r = -b */ { for (i = 0 ; i < n ; i++) { ASSIGN (bb, b, bz, i, SPLIT(bz)) ; r [i] = -REAL_COMPONENT (bb) ; rz[i] = -IMAG_COMPONENT (bb) ; } } else /* r = -Q'b */ { for (k = 0 ; k < n ; k++) { ASSIGN (bb, b, bz, Q [k], SPLIT(bz)) ; r [k] = -REAL_COMPONENT (bb) ; rz[k] = -IMAG_COMPONENT (bb) ; } } if (!P) /* w = x */ { for (j = 0 ; j < n ; j++) { ASSIGN (xx, x, xz, j, SPLIT(xz)) ; wx[j] = REAL_COMPONENT (xx) ; wz[j] = IMAG_COMPONENT (xx) ; } } else /* w = Px */ { for (k = 0 ; k < n ; k++) { ASSIGN (xx, x, xz, P [k], SPLIT(xz)) ; wx[k] = REAL_COMPONENT (xx) ; wz[k] = IMAG_COMPONENT (xx) ; } } /* r = r + A'w */ for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; ASSIGN (aa, Ax, Az, p, SPLIT(Az)) ; /* complex conjugate */ r [j] += REAL_COMPONENT(aa) * wx[i] ; r [j] += IMAG_COMPONENT(aa) * wz[i] ; rz[j] -= IMAG_COMPONENT(aa) * wx[i] ; rz[j] += REAL_COMPONENT(aa) * wz[i] ; } } /* note that we just computed Q'r, not r */ } else if (transpose == UMFPACK_Aat) { if (!Q) /* r = -b */ { for (i = 0 ; i < n ; i++) { ASSIGN (bb, b, bz, i, SPLIT(bz)) ; r [i] = -REAL_COMPONENT (bb) ; rz[i] = -IMAG_COMPONENT (bb) ; } } else /* r = -Q'b */ { for (k = 0 ; k < n ; k++) { ASSIGN (bb, b, bz, Q [k], SPLIT(bz)) ; r [k] = -REAL_COMPONENT (bb) ; rz[k] = -IMAG_COMPONENT (bb) ; } } if (!P) /* w = x */ { for (j = 0 ; j < n ; j++) { ASSIGN (xx, x, xz, j, SPLIT(xz)) ; wx[j] = REAL_COMPONENT (xx) ; wz[j] = IMAG_COMPONENT (xx) ; } } else /* w = Px */ { for (k = 0 ; k < n ; k++) { ASSIGN (xx, x, xz, P [k], SPLIT(xz)) ; wx[k] = REAL_COMPONENT (xx) ; wz[k] = IMAG_COMPONENT (xx) ; } } /* r = r + A.'w */ for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; ASSIGN (aa, Ax, Az, p, SPLIT(Az)) ; /* not complex conjugate */ r [j] += REAL_COMPONENT(aa) * wx[i] ; r [j] -= IMAG_COMPONENT(aa) * wz[i] ; rz[j] += IMAG_COMPONENT(aa) * wx[i] ; rz[j] += REAL_COMPONENT(aa) * wz[i] ; } } /* note that we just computed Q'r, not r */ } norm = 0. ; for (i = 0 ; i < n ; i++) { Entry rr ; /* --- */ /* ASSIGN (rr, r [i], rz [i]) ; */ ASSIGN (rr, r, rz, i, TRUE) ; /* --- */ ABS (ra, rr) ; norm = MAX (norm, ra) ; } return (norm) ; } /* ========================================================================== */ /* irand: return a random Integer in the range 0 to n-1 */ /* ========================================================================== */ static Int irand (Int n) { return (rand ( ) % n) ; } /* ========================================================================== */ /* xrand: return a random double, > 0 and <= 1 */ /* ========================================================================== */ /* rand ( ) returns an Integer in the range 0 to RAND_MAX */ static double xrand ( ) { return ((1.0 + (double) rand ( )) / (1.0 + (double) RAND_MAX)) ; } /* ========================================================================== */ /* randperm: generate a random permutation of 0..n-1 */ /* ========================================================================== */ static void randperm (Int n, Int P [ ]) { Int i, t, k ; for (i = 0 ; i < n ; i++) { P [i] = i ; } for (i = n-1 ; i > 0 ; i--) { k = irand (i) ; /* swap positions i and k */ t = P [k] ; P [k] = P [i] ; P [i] = t ; } } /* ========================================================================== */ /* do_solvers: test Ax=b, etc */ /* ========================================================================== */ static double do_solvers ( Int n_row, Int n_col, Int Ap [ ], Int Ai [ ], double Ax [ ], double Az [ ], double b [ ], double bz [ ], double Control [ ], double Info [ ], void *Numeric, Int Lp [ ], Int Li [ ], double Lx [ ], double Lz [ ], Int Up [ ], Int Ui [ ], double Ux [ ], double Uz [ ], Int P [ ], Int Q [ ], double x [ ], double xz [ ], double r [ ], double rz [ ], Int W [ ], double Wx [ ], Int split /* TRUE if complex variables split, FALSE if merged */ ) { double maxrnorm = 0.0, rnorm, xnorm, xa, xaz, *Rb, *Rbz, *y, *yz, *Rs, *Cx, *Cz ; double Con [UMFPACK_CONTROL] ; Int *noP = INULL, *noQ = INULL, irstep, orig, i, prl, status, n, s1, s2, do_recip, *Cp, *Ci, nz, scale ; Entry bb, xx, xtrue ; NumericType *Num ; #ifdef COMPLEX if (split) { if (!Az || !bz || !xz || !Lz || !Uz || !xz) error ("bad split\n", 0.) ; } else { if ( Az || bz || xz || Lz || Uz || xz) error ("bad merge\n", 0.) ; } /* rz is never passed to umfpack, and is always split in ut.c */ if (!rz) error ("bad rz\n", 0.) ; #endif /* ---------------------------------------------------------------------- */ /* get parameters */ /* ---------------------------------------------------------------------- */ n = MAX (n_row, n_col) ; if (n == 0) error ("n zero", 0.) ; /* n = MAX (n,1) ; */ /* n_inner = MIN (n_row, n_col) ; */ if (Control) { orig = Control [UMFPACK_IRSTEP] ; prl = Control [UMFPACK_PRL] ; } else { prl = UMFPACK_DEFAULT_PRL ; } if (n_row == n_col) { nz = Ap [n_col] ; nz = MAX (nz, Lp [n_col]) ; nz = MAX (nz, Up [n_col]) ; Cp = (Int *) malloc ((n_col+1) * sizeof (Int)) ; Ci = (Int *) malloc ((nz+1) * sizeof (Int)) ; Cx = (double *) calloc (2*(nz+1) , sizeof (double)) ; if (split) { Cz = Cx + nz ; } else { Cz = DNULL ; } if (!Cp || !Ci || !Cx) error ("out of memory (0)", 0.) ; } else { Cp = INULL ; Ci = INULL ; Cx = DNULL ; } Num = (NumericType *) Numeric ; scale = (Num->Rs != DNULL) ; /* ---------------------------------------------------------------------- */ /* error handling */ /* ---------------------------------------------------------------------- */ if (n_row != n_col) { status = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az) , CARG(x,xz), CARG(b,bz), Numeric, DNULL, DNULL) ; if (status != UMFPACK_ERROR_invalid_system) error ("rectangular Ax=b should have failed\n", 0.) ; } else { status = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az) , CARG(DNULL,xz), CARG(b,bz), Numeric, DNULL, DNULL) ; if (status != UMFPACK_ERROR_argument_missing) error ("missing x should have failed\n", 0.) ; status = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(DNULL,Az) , CARG(DNULL,xz), CARG(b,bz), Numeric, DNULL, DNULL) ; if (status != UMFPACK_ERROR_argument_missing) error ("missing Ax should have failed\n", 0.) ; } /* ---------------------------------------------------------------------- */ /* Ax=b */ /* ---------------------------------------------------------------------- */ for (irstep = -1 ; irstep <= 3 ; irstep++) { if (Control) { for (i = 0 ; i < UMFPACK_CONTROL ; i++) Con [i] = Control [i] ; } else { UMFPACK_defaults (Con) ; } Con [UMFPACK_PRL] = prl ; Con [UMFPACK_IRSTEP] = MAX (0, irstep) ; if (prl >= 2) printf ("1: do solve: Ax=b: "ID"\n", irstep) ; if (irstep == -1) { status = UMFPACK_solve (UMFPACK_A, INULL, INULL, CARG(DNULL,DNULL) , CARG(x,xz), CARG(b,bz), Numeric, Con, Info) ; } else { status = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az) , CARG(x,xz), CARG(b,bz), Numeric, Con, Info) ; } UMFPACK_report_status (Con, status) ; UMFPACK_report_info (Con, Info) ; if (n_row != n_col) { if (status != UMFPACK_ERROR_invalid_system) { dump_mat ("A", n_row, n_col, Ap, Ai, CARG(Ax,Az)) ; error ("rectangular Ax=b should have failed\n", 0.) ; } /* return immediately if the matrix is rectangular */ return (0.) ; } if (status == UMFPACK_WARNING_singular_matrix) { if (prl >= 2) printf ("Ax=b singular\n") ; } else if (status != UMFPACK_OK) { dump_mat ("A", n, n, Ap, Ai, CARG(Ax,Az)) ; error ("Ax=b failed\n", 0.) ; } else { rnorm = resid (n, Ap, Ai, Ax, Az, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ; if (prl >= 2) printf ("1: rnorm Ax=b is %g\n", rnorm) ; maxrnorm = MAX (rnorm, maxrnorm) ; /* compare x with xtrue */ xnorm = 0. ; for (i = 0 ; i < n ; i++) { REAL_COMPONENT(xtrue) = 1.0 + ((double) i) / ((double) n) ; #ifdef COMPLEX IMAG_COMPONENT(xtrue) = 1.3 - ((double) i) / ((double) n) ; #endif /* --- */ /* ASSIGN (xx, x [i] - xtrue, xz[i]-xtruez) ; */ ASSIGN (xx, x, xz, i, SPLIT(xz)) ; DECREMENT (xx, xtrue) ; /* --- */ ABS (xa, xx) ; xnorm = MAX (xnorm, xa) ; } #if 0 { FILE *f ; char s [200] ; sprintf (s, "b_XXXXXX") ; mkstemp (s) ; f = fopen (s, "w") ; for (i = 0 ; i < n ; i++) fprintf (f, "%40.25e %40.25e\n", b [i], bz [i]) ; fclose (f) ; s [0] = 'x' ; f = fopen (s, "w") ; for (i = 0 ; i < n ; i++) fprintf (f, "%40.25e %40.25e\n", x [i], xz [i]) ; fclose (f) ; } #endif if (check_tol && (status == UMFPACK_OK && (rnorm > TOL || xnorm > TOL))) { Con [UMFPACK_PRL] = 5 ; UMFPACK_report_control (Con) ; printf ("Ax=b inaccurate %g %g\n", rnorm, xnorm) ; dump_mat ("A", n, n, Ap, Ai, CARG(Ax,Az)) ; printf ("\nb: ") ; UMFPACK_report_vector (n, CARG(b,bz), Con) ; printf ("\nx: ") ; UMFPACK_report_vector (n, CARG(x,xz), Con) ; error ("Ax=b inaccurate", MAX (rnorm, xnorm)) ; } maxrnorm = MAX (xnorm, maxrnorm) ; } #ifdef DEBUGGING printf ("\n") ; #endif if (prl >= 2) printf ("Ax=b irstep "ID" attempted %g\n", irstep, Info [UMFPACK_IR_ATTEMPTED]) ; if (irstep > Info [UMFPACK_IR_ATTEMPTED]) { break ; } } if (n != n_row && n != n_col && n <= 0) error ("huh?", 0.) ; /* ---------------------------------------------------------------------- */ /* A'x=b */ /* ---------------------------------------------------------------------- */ for (irstep = 0 ; irstep <= 3 ; irstep++) { if (Control) { for (i = 0 ; i < UMFPACK_CONTROL ; i++) Con [i] = Control [i] ; } else { UMFPACK_defaults (Con) ; } Con [UMFPACK_PRL] = prl ; Con [UMFPACK_IRSTEP] = irstep ; if (prl >= 2) printf ("do solve: A'x=b: "ID"\n", irstep) ; status = UMFPACK_solve (UMFPACK_At, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info) ; UMFPACK_report_status (Con, status) ; /* UMFPACK_report_info (Con, Info) ; */ if (status == UMFPACK_WARNING_singular_matrix) { if (prl >= 2) printf ("A'x=b singular\n") ; } else if (status != UMFPACK_OK) { dump_mat ("A", n, n, Ap, Ai, CARG(Ax,Az)) ; error ("A'x=b failed\n", 0.) ; } else { rnorm = resid (n, Ap, Ai, Ax, Az, x, xz, b, bz, r, rz, UMFPACK_At, noP, noQ, Wx) ; if (prl >= 2) printf ("2: rnorm A'x=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { Con [UMFPACK_PRL] = 99 ; printf ("A'x=b inaccurate %g\n", rnorm) ; dump_mat ("A", n, n, Ap, Ai, CARG(Ax,Az)) ; /* printf ("\nA: ") ; UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ; printf ("\nb: ") ; UMFPACK_report_vector (n, CARG(b,bz), Con) ; printf ("\nx: ") ; UMFPACK_report_vector (n, CARG(x,xz), Con) ; error ("A'x=b inaccurate", MAX (rnorm, xnorm)) ; */ } maxrnorm = MAX (rnorm, maxrnorm) ; /* also check using UMFPACK_transpose */ status = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), noP, noQ, Cp, Ci, CARG(Cx,Cz) C1ARG(1)) ; if (status != UMFPACK_OK) { error ("transposed A'x=b failed\n", 0.) ; } rnorm = resid (n, Cp, Ci, Cx, Cz, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ; if (prl >= 2) printf ("2b: rnorm A'x=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { Con [UMFPACK_PRL] = 99 ; printf ("transpose A'x=b inaccurate %g\n", rnorm) ; /* printf ("\nA: ") ; UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ; printf ("\nb: ") ; UMFPACK_report_vector (n, CARG(b,bz), Con) ; printf ("\nx: ") ; UMFPACK_report_vector (n, CARG(x,xz), Con) ; error ("A'x=b inaccurate", MAX (rnorm, xnorm)) ; */ } maxrnorm = MAX (rnorm, maxrnorm) ; } if (prl >= 2) printf ("A'x=b irstep "ID" attempted %g\n", irstep, Info [UMFPACK_IR_ATTEMPTED]) ; if (irstep > Info [UMFPACK_IR_ATTEMPTED]) { break ; } } /* ---------------------------------------------------------------------- */ /* A.'x=b */ /* ---------------------------------------------------------------------- */ for (irstep = 0 ; irstep <= 3 ; irstep++) { if (Control) { for (i = 0 ; i < UMFPACK_CONTROL ; i++) Con [i] = Control [i] ; } else { UMFPACK_defaults (Con) ; } Con [UMFPACK_PRL] = prl ; Con [UMFPACK_IRSTEP] = irstep ; if (prl >= 2) printf ("do solve: A.'x=b: "ID"\n", irstep) ; status = UMFPACK_solve (UMFPACK_Aat, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info) ; UMFPACK_report_status (Con, status) ; /* UMFPACK_report_info (Con, Info) ; */ if (status == UMFPACK_WARNING_singular_matrix) { if (prl >= 2) printf ("A.'x=b singular\n") ; } else if (status != UMFPACK_OK) { dump_mat ("A", n, n, Ap, Ai, CARG(Ax,Az)) ; error ("A.'x=b failed\n", 0.) ; } else { rnorm = resid (n, Ap, Ai, Ax, Az, x, xz, b, bz, r, rz, UMFPACK_Aat, noP, noQ, Wx) ; if (prl >= 2) printf ("3: rnorm A.'x=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { Con [UMFPACK_PRL] = 99 ; printf ("A.'x=b inaccurate %g\n", rnorm) ; /* dump_mat ("A", n, n, Ap, Ai, CARG(Ax,Az)) ; printf ("\nA: ") ; UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ; printf ("\nb: ") ; UMFPACK_report_vector (n, CARG(b,bz), Con) ; printf ("\nx: ") ; UMFPACK_report_vector (n, CARG(x,xz), Con) ; error ("A.'x=b inaccurate %g\n", MAX (rnorm, xnorm)) ; */ } maxrnorm = MAX (rnorm, maxrnorm) ; /* also check using UMFPACK_transpose */ status = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), noP, noQ, Cp, Ci, CARG(Cx,Cz) C1ARG(0)) ; if (status != UMFPACK_OK) { error ("transposed A.'x=b failed\n", 0.) ; } rnorm = resid (n, Cp, Ci, Cx, Cz, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ; if (prl >= 2) printf ("2b: rnorm A'x=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { Con [UMFPACK_PRL] = 99 ; printf ("transpose A'x=b inaccurate %g\n", rnorm) ; /* printf ("\nA: ") ; UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ; printf ("\nb: ") ; UMFPACK_report_vector (n, CARG(b,bz), Con) ; printf ("\nx: ") ; UMFPACK_report_vector (n, CARG(x,xz), Con) ; error ("A'x=b inaccurate", MAX (rnorm, xnorm)) ; */ } maxrnorm = MAX (rnorm, maxrnorm) ; } if (prl >= 2) printf ("A.'x=b irstep "ID" attempted %g\n", irstep, Info [UMFPACK_IR_ATTEMPTED]) ; if (irstep > Info [UMFPACK_IR_ATTEMPTED]) { break ; } } if (Control) { for (i = 0 ; i < UMFPACK_CONTROL ; i++) Con [i] = Control [i] ; } else { UMFPACK_defaults (Con) ; } /* ---------------------------------------------------------------------- */ /* wsolve Ax=b */ /* ---------------------------------------------------------------------- */ /* printf ("do wsolve: Ax=b:\n") ; */ if (Control) Control [UMFPACK_IRSTEP] = 1 ; if (prl >= 2) printf ("2: do solve: Ax=b: "ID" (wsolve) \n", irstep) ; status = UMFPACK_wsolve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info, W, Wx) ; /* UMFPACK_report_info (Control, Info) ; */ if (status == UMFPACK_WARNING_singular_matrix) { if (prl >= 2) printf ("Ax=b wsolve singular\n") ; } else if (status != UMFPACK_OK) { dump_mat ("A", n, n, Ap, Ai, CARG(Ax,Az)) ; error ("Ax=b wsolve failure\n", 0.) ; } else { rnorm = resid (n, Ap, Ai, Ax, Az, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ; if (prl >= 2) printf ("4: rnorm Ax=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { dump_mat ("A", n, n, Ap, Ai, CARG(Ax,Az)) ; error ("wsolve inaccurate %g\n", rnorm) ; } maxrnorm = MAX (rnorm, maxrnorm) ; } if (Control) Control [UMFPACK_IRSTEP] = orig ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* prl = 999 ; */ Rs = (double *) malloc (n * sizeof (double)) ; /* [ */ Rb = (double *) calloc (2*n , sizeof (double)) ; /* [ */ y = (double *) calloc (2*n , sizeof (double)) ; /* [ */ /* ---------------------------------------------------------------------- */ /* Ax=b with individual calls */ /* ---------------------------------------------------------------------- */ if (split) { yz = y + n ; Rbz = Rb + n ; } else { yz = DNULL ; Rbz = DNULL ; } /* status = UMFPACK_get_scale (Rs, Numeric) ; */ status = UMFPACK_get_numeric ( INULL, INULL, CARG(DNULL,DNULL), INULL, INULL, CARG(DNULL,DNULL), INULL, INULL, CARG (DNULL,DNULL), &do_recip, Rs, Numeric) ; if (status != UMFPACK_OK) error ("get Rs failed", (double) status) ; /* printf ("Rs:\n") ; for (i = 0 ; i < n ; i++) { printf (" Rs [%d] = %g\n", i, Rs [i]) ; } */ if (prl >= 2) printf ("3: do solve: Ax=b in different steps:\n") ; /* Rb = R*b */ /* dump_vec ("b", n, b, bz) ; */ status = UMFPACK_scale (CARG (Rb, Rbz), CARG (b,bz), Numeric) ; if (status != UMFPACK_OK) error ("Rb failed", (double) status) ; /* dump_vec ("R*b", n, Rb, Rbz) ; */ /* UMFPACK_defaults (Con) ; Con [UMFPACK_PRL] = 999 ; printf ("Rb:\n") ; UMFPACK_report_vector (n, CARG(Rb,Rbz), Con) ; printf ("b:\n") ; UMFPACK_report_vector (n, CARG(b,bz), Con) ; error ("finish early\n", rnorm) ; */ /* solve Ly = P*(Rb) */ s1 = UMFPACK_solve (UMFPACK_Pt_L, Ap, Ai, CARG(Ax,Az), CARG(y,yz), CARG(Rb,Rbz), Numeric, Control, Info) ; if (! (s1 == UMFPACK_OK || s1 == UMFPACK_WARNING_singular_matrix)) { error ("P'Ly=Rb failed", (double) status) ; } /* solve UQ'x=y */ s2 = UMFPACK_solve (UMFPACK_U_Qt, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(y,yz), Numeric, Control, Info) ; if (! (s2 == UMFPACK_OK || s2 == UMFPACK_WARNING_singular_matrix)) { error ("UQ'x=y failed", (double) status) ; } if (s1 == UMFPACK_OK && s2 == UMFPACK_OK) { rnorm = resid (n, Ap, Ai, Ax, Az, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ; if (prl >= 2) printf ("5: rnorm Ax=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { /* error ("Ax=b (different steps) inaccurate ", rnorm) ; */ printf ("Ax=b (different steps) inaccurate %g !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!", rnorm) ; } maxrnorm = MAX (rnorm, maxrnorm) ; } if (prl >= 2) printf ("4: do solve: Ax=b, different steps, own scale:\n") ; /* Rb = R*b */ if (do_recip) { for (i = 0 ; i < n ; i++) { ASSIGN (bb, b, bz, i, SPLIT(bz)) ; SCALE (bb, Rs [i]) ; if (split) { Rb [i] = REAL_COMPONENT(bb) ; Rbz [i] = IMAG_COMPONENT(bb) ; } else { Rb [2*i] = REAL_COMPONENT(bb) ; Rb [2*i+1] = IMAG_COMPONENT(bb) ; } /* Rb [i] = REAL_COMPONENT(bb) * Rs [i] ; Rbz [i] = IMAG_COMPONENT(bb) * Rs [i] ; */ } } else { for (i = 0 ; i < n ; i++) { ASSIGN (bb, b, bz, i, SPLIT(bz)) ; SCALE_DIV (bb, Rs [i]) ; if (split) { Rb [i] = REAL_COMPONENT(bb) ; Rbz [i] = IMAG_COMPONENT(bb) ; } else { Rb [2*i] = REAL_COMPONENT(bb) ; Rb [2*i+1] = IMAG_COMPONENT(bb) ; } /* Rb [i] = REAL_COMPONENT(bb) / Rs [i] ; Rbz [i] = IMAG_COMPONENT(bb) / Rs [i] ; */ } } /* solve Ly = P*(Rb) */ s1 = UMFPACK_solve (UMFPACK_Pt_L, Ap, Ai, CARG(Ax,Az), CARG(y,yz), CARG(Rb,Rbz), Numeric, Control, Info) ; if (! (s1 == UMFPACK_OK || s1 == UMFPACK_WARNING_singular_matrix)) { error ("P'Ly=Rb failed", (double) status) ; } /* solve UQ'x=y */ s2 = UMFPACK_solve (UMFPACK_U_Qt, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(y,yz), Numeric, Control, Info) ; if (! (s2 == UMFPACK_OK || s2 == UMFPACK_WARNING_singular_matrix)) { error ("UQ'x=y failed", (double) status) ; } if (s1 == UMFPACK_OK && s2 == UMFPACK_OK) { rnorm = resid (n, Ap, Ai, Ax, Az, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ; if (prl >= 2) printf ("6: rnorm Ax=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { error ("Ax=b (different steps, own scale) inaccurate ", rnorm) ; } maxrnorm = MAX (rnorm, maxrnorm) ; } /* ---------------------------------------------------------------------- */ /* (PAQ)'x=b with individual calls, no scaling */ /* ---------------------------------------------------------------------- */ if (!scale) { int k ; s1 = UMFPACK_solve (UMFPACK_Ut, Ap, Ai, CARG(Ax,Az), CARG(y,yz), CARG(b,bz), Numeric, Control, Info) ; if (! (s1 == UMFPACK_OK || s1 == UMFPACK_WARNING_singular_matrix)) { error ("U'y=b failed", (double) status) ; } s2 = UMFPACK_solve (UMFPACK_Lt, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(y,yz), Numeric, Control, Info) ; if (! (s2 == UMFPACK_OK || s2 == UMFPACK_WARNING_singular_matrix)) { error ("L'x=y failed", (double) status) ; } /* check using UMFPACK_transpose */ if (s1 == UMFPACK_OK && s2 == UMFPACK_OK) { status = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), P, Q, Cp, Ci, CARG(Cx,Cz) C1ARG(1)) ; if (status != UMFPACK_OK) { error ("transposed (PAQ)'x=b failed\n", 0.) ; } rnorm = resid (n, Cp, Ci, Cx, Cz, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ; if (prl >= 2) printf ("99b: rnorm (PAQ)'x=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { dump_mat ("A", n, n, Ap, Ai, CARG(Ax,Az)) ; dump_mat ("C", n, n, Cp, Ci, CARG(Cx,Cz)) ; dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ; dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ; printf ("P = [ ") ; for (k = 0 ; k < n ; k++) printf ("%d ", P [k]) ; printf ("]\n") ; printf ("Q = [ ") ; for (k = 0 ; k < n ; k++) printf ("%d ", Q [k]) ; printf ("]\n") ; error ("transposed (PAQ)'x=b inaccurate\n",rnorm) ; } maxrnorm = MAX (rnorm, maxrnorm) ; } } /* ---------------------------------------------------------------------- */ /* (PAQ).'x=b with individual calls, no scaling */ /* ---------------------------------------------------------------------- */ if (!scale) { int k ; s1 = UMFPACK_solve (UMFPACK_Uat, Ap, Ai, CARG(Ax,Az), CARG(y,yz), CARG(b,bz), Numeric, Control, Info) ; if (! (s1 == UMFPACK_OK || s1 == UMFPACK_WARNING_singular_matrix)) { error ("U'y=b failed", (double) status) ; } s2 = UMFPACK_solve (UMFPACK_Lat, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(y,yz), Numeric, Control, Info) ; if (! (s2 == UMFPACK_OK || s2 == UMFPACK_WARNING_singular_matrix)) { error ("L'x=y failed", (double) status) ; } /* check using UMFPACK_transpose */ if (s1 == UMFPACK_OK && s2 == UMFPACK_OK) { status = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), P, Q, Cp, Ci, CARG(Cx,Cz) C1ARG(0)) ; if (status != UMFPACK_OK) { error ("transposed (PAQ).'x=b failed\n", 0.) ; } rnorm = resid (n, Cp, Ci, Cx, Cz, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ; /* printf ("98b: rnorm (PAQ)'x=b is %g\n", rnorm) ; */ if (check_tol && rnorm > TOL) { dump_mat ("A", n, n, Ap, Ai, CARG(Ax,Az)) ; dump_mat ("C", n, n, Cp, Ci, CARG(Cx,Cz)) ; dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ; dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ; printf ("P = [ ") ; for (k = 0 ; k < n ; k++) printf ("%d ", P [k]) ; printf ("]\n") ; printf ("Q = [ ") ; for (k = 0 ; k < n ; k++) printf ("%d ", Q [k]) ; printf ("]\n") ; error ("transposed (PAQ).'x=b inaccurate\n",rnorm) ; } maxrnorm = MAX (rnorm, maxrnorm) ; } } /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ free (y) ; /* ] */ free (Rb) ; /* ] */ free (Rs) ; /* ] */ /* ---------------------------------------------------------------------- */ /* Lx=b */ /* ---------------------------------------------------------------------- */ if (prl >= 2) printf ("do solve: Lx=b:\n") ; status = UMFPACK_solve (UMFPACK_L, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ; /* UMFPACK_report_info (Control, Info) ; */ if (status == UMFPACK_WARNING_singular_matrix) { error ("Lx=b solve singular!", 0.) ; } else if (status != UMFPACK_OK) { dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ; error ("Lx=b failed\n", 0.) ; } else { rnorm = resid (n, Lp, Li, Lx, Lz, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ; if (prl >= 2) printf ("7: rnorm Lx=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ; error ("Lx=b inaccurate %g", rnorm) ; } maxrnorm = MAX (rnorm, maxrnorm) ; } /* ---------------------------------------------------------------------- */ /* L'x=b */ /* ---------------------------------------------------------------------- */ if (prl >= 2) printf ("do solve: L'x=b:\n") ; status = UMFPACK_solve (UMFPACK_Lt, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ; /* UMFPACK_report_info (Control, Info) ; */ if (status == UMFPACK_WARNING_singular_matrix) { dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ; error ("L'x=b solve singular!", 0.) ; } else if (status != UMFPACK_OK) { dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ; error ("L'x=b failed\n", 0.) ; } else { rnorm = resid (n, Lp, Li, Lx, Lz, x, xz, b, bz, r, rz, UMFPACK_At, noP, noQ, Wx) ; if (prl >= 2) printf ("7: rnorm L'x=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ; error ("L'x=b inaccurate %g\n",rnorm) ; } maxrnorm = MAX (rnorm, maxrnorm) ; /* also check using UMFPACK_transpose */ status = UMFPACK_transpose (n, n, Lp, Li, CARG(Lx,Lz), noP, noQ, Cp, Ci, CARG(Cx,Cz) C1ARG(1)) ; if (status != UMFPACK_OK) { error ("transposed L'x=b failed\n", 0.) ; } rnorm = resid (n, Cp, Ci, Cx, Cz, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ; if (prl >= 2) printf ("7b: rnorm L'x=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ; error ("transposed L'x=b inaccurate %g\n",rnorm) ; } maxrnorm = MAX (rnorm, maxrnorm) ; } /* ---------------------------------------------------------------------- */ /* L.'x=b */ /* ---------------------------------------------------------------------- */ if (prl >= 2) printf ("do solve: L.'x=b:\n") ; status = UMFPACK_solve (UMFPACK_Lat, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ; /* UMFPACK_report_info (Control, Info) ; */ if (status == UMFPACK_WARNING_singular_matrix) { dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ; error ("L.'x=b solve singular!", 0.) ; } else if (status != UMFPACK_OK) { dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ; error ("L.'x=b failed\n", 0.) ; } else { rnorm = resid (n, Lp, Li, Lx, Lz, x, xz, b, bz, r, rz, UMFPACK_Aat, noP, noQ, Wx) ; if (prl >= 2) printf ("8: rnorm L.'x=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ; error ("L.'x=b inaccurate %g\n",rnorm) ; } maxrnorm = MAX (rnorm, maxrnorm) ; /* also check using UMFPACK_transpose */ status = UMFPACK_transpose (n, n, Lp, Li, CARG(Lx,Lz), noP, noQ, Cp, Ci, CARG(Cx,Cz) C1ARG(0)) ; if (status != UMFPACK_OK) { error ("transposed L'x=b failed\n", 0.) ; } rnorm = resid (n, Cp, Ci, Cx, Cz, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ; if (prl >= 2) printf ("8b: rnorm L'x=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ; error ("8b transposed L'x=b inaccurate %g\n",rnorm) ; } maxrnorm = MAX (rnorm, maxrnorm) ; } /* ---------------------------------------------------------------------- */ /* Ux=b */ /* ---------------------------------------------------------------------- */ if (prl >= 2) printf ("do solve: Ux=b:\n") ; status = UMFPACK_solve (UMFPACK_U, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ; /* UMFPACK_report_info (Control, Info) ; */ if (status == UMFPACK_WARNING_singular_matrix) { if (prl >= 2) printf ("Ux=b solve singular\n") ; } else if (status != UMFPACK_OK) { dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ; error ("Ux=b failed\n", 0.) ; } else { rnorm = resid (n, Up, Ui, Ux, Uz, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ; if (prl >= 2) printf ("9: rnorm Ux=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ; error ("Ux=b inaccurate %g\n",rnorm) ; } maxrnorm = MAX (rnorm, maxrnorm) ; } /* ---------------------------------------------------------------------- */ /* U'x=b */ /* ---------------------------------------------------------------------- */ if (prl >= 2) printf ("do solve: U'x=b:\n") ; status = UMFPACK_solve (UMFPACK_Ut, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ; /* UMFPACK_report_info (Control, Info) ; */ if (status == UMFPACK_WARNING_singular_matrix) { if (prl >= 2) printf ("U'x=b solve singular\n") ; } else if (status != UMFPACK_OK) { dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ; error ("U'x=b failed\n", 0.) ; } else { rnorm = resid (n, Up, Ui, Ux, Uz, x, xz, b, bz, r, rz, UMFPACK_At, noP, noQ, Wx) ; if (prl >= 2) printf ("10: rnorm U'x=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ; error ("U'x=b inaccurate %g\n",rnorm) ; } maxrnorm = MAX (rnorm, maxrnorm) ; /* also check using UMFPACK_transpose */ status = UMFPACK_transpose (n, n, Up, Ui, CARG(Ux,Uz), noP, noQ, Cp, Ci, CARG(Cx,Cz) C1ARG(1)) ; if (status != UMFPACK_OK) { error ("transposed U'x=b failed\n", 0.) ; } rnorm = resid (n, Cp, Ci, Cx, Cz, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ; if (prl >= 2) printf ("10b: rnorm U'x=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ; error ("10b transposed U'x=b inaccurate %g\n",rnorm) ; } maxrnorm = MAX (rnorm, maxrnorm) ; } /* ---------------------------------------------------------------------- */ /* U.'x=b */ /* ---------------------------------------------------------------------- */ if (prl >= 2) printf ("do solve: U.'x=b:\n") ; status = UMFPACK_solve (UMFPACK_Uat, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ; /* UMFPACK_report_info (Control, Info) ; */ if (status == UMFPACK_WARNING_singular_matrix) { if (prl >= 2) printf ("U.'x=b solve singular\n") ; } else if (status != UMFPACK_OK) { dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ; error ("U.'x=b failed\n", 0.) ; } else { rnorm = resid (n, Up, Ui, Ux, Uz, x, xz, b, bz, r, rz, UMFPACK_Aat, noP, noQ, Wx) ; if (prl >= 2) printf ("11: rnorm U.'x=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ; error ("U.'x=b inaccurate %g\n",rnorm) ; } maxrnorm = MAX (rnorm, maxrnorm) ; /* also check using UMFPACK_transpose */ status = UMFPACK_transpose (n, n, Up, Ui, CARG(Ux,Uz), noP, noQ, Cp, Ci, CARG(Cx,Cz) C1ARG(0)) ; if (status != UMFPACK_OK) { error ("11b transposed U.'x=b failed\n", 0.) ; } rnorm = resid (n, Cp, Ci, Cx, Cz, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ; if (prl >= 2) printf ("11b: rnorm U'x=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ; error ("11b transposed U'x=b inaccurate %g\n",rnorm) ; } maxrnorm = MAX (rnorm, maxrnorm) ; } /* ---------------------------------------------------------------------- */ /* P'Lx=b */ /* ---------------------------------------------------------------------- */ if (prl >= 2) printf ("do solve: P'Lx=b:\n") ; status = UMFPACK_solve (UMFPACK_Pt_L, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ; /* UMFPACK_report_info (Control, Info) ; */ if (status == UMFPACK_WARNING_singular_matrix) { dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ; error ("P'Lx=b solve singular!", 0.) ; } else if (status != UMFPACK_OK) { dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ; error ("P'Lx=b failed\n", 0.) ; } else { rnorm = resid (n, Lp, Li, Lx, Lz, x, xz, b, bz, r, rz, UMFPACK_A, P, noQ, Wx) ; if (prl >= 2) printf ("12: rnorm P'Lx=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ; error ("P'Lx=b inaccurate: %g\n",rnorm) ; } maxrnorm = MAX (rnorm, maxrnorm) ; } /* ---------------------------------------------------------------------- */ /* L'Px=b */ /* ---------------------------------------------------------------------- */ if (prl >= 2) printf ("do solve: L'Px=b:\n") ; status = UMFPACK_solve (UMFPACK_Lt_P, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ; /* UMFPACK_report_info (Control, Info) ; */ if (status == UMFPACK_WARNING_singular_matrix) { error ("L'Px=b solve singular!", 0.) ; } else if (status != UMFPACK_OK) { dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ; error ("L'Px=b failed\n", 0.) ; } else { rnorm = resid (n, Lp, Li, Lx, Lz, x, xz, b, bz, r, rz, UMFPACK_At, P, noQ, Wx) ; if (prl >= 2) printf ("13: rnorm L'Px=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ; error ("L'Px=b inaccurate %g\n",rnorm) ; } maxrnorm = MAX (rnorm, maxrnorm) ; } /* ---------------------------------------------------------------------- */ /* L.'Px=b */ /* ---------------------------------------------------------------------- */ if (prl >= 2) printf ("do solve: L.'Px=b:\n") ; status = UMFPACK_solve (UMFPACK_Lat_P, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ; /* UMFPACK_report_info (Control, Info) ; */ if (status == UMFPACK_WARNING_singular_matrix) { error ("L.'Px=b solve singular!", 0.) ; } else if (status != UMFPACK_OK) { dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ; error ("L.'Px=b failed\n", 0.) ; } else { rnorm = resid (n, Lp, Li, Lx, Lz, x, xz, b, bz, r, rz, UMFPACK_Aat, P, noQ, Wx) ; if (prl >= 2) printf ("14: rnorm L.'Px=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ; error ("L.'Px=b inaccurate %g\n",rnorm) ; } maxrnorm = MAX (rnorm, maxrnorm) ; } /* ---------------------------------------------------------------------- */ /* UQ'x=b */ /* ---------------------------------------------------------------------- */ if (prl >= 2) printf ("do solve: UQ'x=b:\n") ; status = UMFPACK_solve (UMFPACK_U_Qt, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ; /* UMFPACK_report_info (Control, Info) ; */ if (status == UMFPACK_WARNING_singular_matrix) { if (prl >= 2) printf ("UQ'x=b solve singular\n") ; } else if (status != UMFPACK_OK) { dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ; error ("UQ'x=b failed\n", 0.) ; } else { rnorm = resid (n, Up, Ui, Ux, Uz, x, xz, b, bz, r, rz, UMFPACK_A, noP, Q, Wx) ; if (prl >= 2) printf ("15: rnorm UQ'x=b is %g\n", rnorm) ; if (check_tol && status == UMFPACK_OK && rnorm > TOL) { dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ; error ("UQ'x=b inaccurate %g\n",rnorm) ; } maxrnorm = MAX (rnorm, maxrnorm) ; } /* ---------------------------------------------------------------------- */ /* QU'x=b */ /* ---------------------------------------------------------------------- */ if (prl >= 2) printf ("do solve: QU'x=b:\n") ; status = UMFPACK_solve (UMFPACK_Q_Ut, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ; /* UMFPACK_report_info (Control, Info) ; */ if (status == UMFPACK_WARNING_singular_matrix) { if (prl >= 2) printf ("QU'x=b solve singular\n") ; } else if (status != UMFPACK_OK) { dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ; error ("QU'x=b failed\n", 0.) ; } else { rnorm = resid (n, Up, Ui, Ux, Uz, x, xz, b, bz, r, rz, UMFPACK_At, noP, Q, Wx) ; if (prl >= 2) printf ("16: rnorm QU'x=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ; error ("QU'x=b inaccurate %g\n",rnorm) ; } maxrnorm = MAX (rnorm, maxrnorm) ; } /* ---------------------------------------------------------------------- */ /* QU.'x=b */ /* ---------------------------------------------------------------------- */ if (prl >= 2) printf ("do solve: QU.'x=b:\n") ; status = UMFPACK_solve (UMFPACK_Q_Uat, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ; /* UMFPACK_report_info (Control, Info) ; */ if (status == UMFPACK_WARNING_singular_matrix) { if (prl >= 2) printf ("QU.'x=b solve singular\n") ; } else if (status != UMFPACK_OK) { dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ; error ("QU.'x=b failed\n", 0.) ; } else { rnorm = resid (n, Up, Ui, Ux, Uz, x, xz, b, bz, r, rz, UMFPACK_Aat, noP, Q, Wx) ; if (prl >= 2) printf ("17: rnorm QU.'x=b is %g\n", rnorm) ; if (check_tol && rnorm > TOL) { dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ; error ("QU.'x=b inaccurate %g\n",rnorm) ; } maxrnorm = MAX (rnorm, maxrnorm) ; } /* ---------------------------------------------------------------------- */ /* done */ /* ---------------------------------------------------------------------- */ if (n_row == n_col) { free (Cp) ; free (Ci) ; free (Cx) ; } return (maxrnorm) ; } /* ========================================================================== */ /* do_symnum: factor A once, and then test the solves - return if error */ /* ========================================================================== */ static double do_symnum ( Int n_row, Int n_col, Int Ap [ ], Int Ai [ ], double Ax [ ], double Az [ ], double b [ ], double bz [ ], double Control [ ], Int Qinit [ ], double x [ ], double xz [ ], double r [ ], double rz [ ], double Wx [ ], Int P [ ], Int Q [ ], Int Qtree [ ], Int Ptree [ ], Int W [ ], Int Lp [ ], Int Up [ ], Int save_and_load, Int split, /* TRUE if complex variables split, FALSE if merged */ Int det_check, double det_x, double det_z ) { void *Symbolic, *Numeric ; double *Lx, *Ux, *Lz, *Uz, rnorm, *Rs ; Int *noP = INULL, *noQ = INULL, *Li, *Ui, n, n_inner, n1, do_recip ; Int lnz, unz, nz, nn, nfr, nchains, nsparse_col, status ; Int *Front_npivots, *Front_parent, *Chain_start, *Chain_maxrows ; Int *Chain_maxcols, *Lrowi, *Lrowp, is_singular ; double Info [UMFPACK_INFO], *Lrowx, *Lrowz, *Dx, *Dz ; Int nnrow, nncol, nzud, *Front_1strow, *Front_leftmostdesc, prl, i ; double mind, maxd, rcond ; Entry d ; double da, deterr ; NumericType *Num ; SymbolicType *Sym ; double Mx [2], Mz, Exp ; #ifdef COMPLEX if (split) { if (!Az || !bz || !xz) error ("bad split\n", 0.) ; } else { if ( Az || bz || xz) error ("bad merge\n", 0.) ; } if (!rz) error ("bad rz\n", 0.) ; #endif /* ---------------------------------------------------------------------- */ /* do the symbolic factorization */ /* ---------------------------------------------------------------------- */ prl = Control ? Control [UMFPACK_PRL] : UMFPACK_DEFAULT_PRL ; n = MAX (n_row, n_col) ; n = MAX (n,1) ; n_inner = MIN (n_row, n_col) ; if (prl > 2) { printf ("\nA::\n") ; status = UMFPACK_report_matrix (n_row, n_col, Ap, Ai, CARG(Ax,Az), 1, Control) ; printf ("\nb::\n") ; if (n_row == n_col) UMFPACK_report_vector (n, CARG(b,bz), Control) ; } if (Qinit) { /* dump_perm ("Qinit", n_col, Qinit) ; */ status = UMFPACK_qsymbolic (n_row, n_col, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Control, Info) ; /* ( */ } else { status = UMFPACK_symbolic (n_row, n_col, Ap, Ai, CARG(Ax,Az), &Symbolic, Control, Info) ; } UMFPACK_report_status (Control, status) ; UMFPACK_report_info (Control, Info) ; if (!Symbolic) { UMFPACK_report_info (Control, Info) ; error ("symbolic invalid\n", 0.) ; } /* ---------------------------------------------------------------------- */ /* test save and load */ /* ---------------------------------------------------------------------- */ status = UMFPACK_save_symbolic (Symbolic, "s.umf") ; if (status != UMFPACK_OK) { error ("save symbolic failed\n", 0.) ; } UMFPACK_free_symbolic (&Symbolic) ; status = UMFPACK_load_symbolic (&Symbolic, "s.umf") ; if (status != UMFPACK_OK) { error ("load symbolic failed\n", 0.) ; } if (n < 15) { int umf_fail_save [3], memcnt ; status = UMFPACK_save_symbolic (Symbolic, (char *) NULL) ; if (status != UMFPACK_OK) { error ("save symbolic failed\n", 0.) ; } UMFPACK_free_symbolic (&Symbolic) ; status = UMFPACK_load_symbolic (&Symbolic, (char *) NULL) ; if (status != UMFPACK_OK) { error ("load symbolic failed\n", 0.) ; } /* test memory handling */ umf_fail_save [0] = umf_fail ; umf_fail_save [1] = umf_fail_lo ; umf_fail_save [2] = umf_fail_hi ; umf_fail = -1 ; umf_fail_lo = 0 ; umf_fail_hi = 0 ; UMFPACK_free_symbolic (&Symbolic) ; status = UMFPACK_load_symbolic (&Symbolic, (char *) NULL) ; if (status != UMFPACK_OK) { error ("load symbolic failed\n", 0.) ; } Sym = (SymbolicType *) Symbolic ; memcnt = 12 ; if (Sym->esize > 0) { memcnt++ ; } if (Sym->prefer_diagonal > 0) { memcnt++ ; } for (i = 1 ; i <= memcnt ; i++) { umf_fail = i ; UMFPACK_free_symbolic (&Symbolic) ; status = UMFPACK_load_symbolic (&Symbolic, (char *) NULL) ; if (status != UMFPACK_ERROR_out_of_memory) { error ("load symbolic should have failed\n", 0.) ; } } umf_fail = memcnt + 1 ; UMFPACK_free_symbolic (&Symbolic) ; status = UMFPACK_load_symbolic (&Symbolic, (char *) NULL) ; if (status != UMFPACK_OK) { error ("load symbolic failed (edge)\n", 0.) ; } umf_fail = umf_fail_save [0] ; umf_fail_lo = umf_fail_save [1] ; umf_fail_hi = umf_fail_save [2] ; UMFPACK_free_symbolic (&Symbolic) ; status = UMFPACK_load_symbolic (&Symbolic, "s.umf") ; if (status != UMFPACK_OK) { error ("load symbolic failed\n", 0.) ; } } /* ---------------------------------------------------------------------- */ /* get the symbolic factorization */ /* ---------------------------------------------------------------------- */ if (prl > 2) printf ("\nSymbolic: ") ; status = UMFPACK_report_symbolic (Symbolic, Control) ; if (status != UMFPACK_OK) { UMFPACK_free_symbolic (&Symbolic) ; error ("bad symbolic report\n", 0.) ; } Front_npivots = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ Front_parent = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ Front_1strow = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ Front_leftmostdesc = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ Chain_start = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ Chain_maxrows = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ Chain_maxcols = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ if (!Front_npivots || !Front_parent || !Chain_start || !Chain_maxrows || !Front_leftmostdesc || !Front_1strow || !Chain_maxcols || !Qtree || !Ptree) error ("out of memory (1)",0.) ; status = UMFPACK_get_symbolic (&nnrow, &nncol, &n1, &nz, &nfr, &nchains, Ptree, Qtree, Front_npivots, Front_parent, Front_1strow, Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ; if (status != UMFPACK_OK) { UMFPACK_report_info (Control, Info) ; error ("get symbolic failed\n", 0.) ; } free (Chain_maxcols) ; /* ] */ free (Chain_maxrows) ; /* ] */ free (Chain_start) ; /* ] */ free (Front_leftmostdesc) ; /* ] */ free (Front_1strow) ; /* ] */ free (Front_parent) ; /* ] */ free (Front_npivots) ; /* ] */ if (!UMF_is_permutation (Qtree, W, n_col, n_col)) { error ("Qtree invalid\n", 0.) ; } if (!UMF_is_permutation (Ptree, W, n_row, n_row)) { error ("Ptree invalid\n", 0.) ; } /* ---------------------------------------------------------------------- */ /* do the numerical factorization */ /* ---------------------------------------------------------------------- */ status = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ; /* [ */ if (status != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; is_singular = (status == UMFPACK_WARNING_singular_matrix) ; UMFPACK_report_status (Control, status) ; UMFPACK_report_info (Control, Info) ; UMFPACK_free_symbolic (&Symbolic) ; /* ) */ if (!Numeric) { /* printf ("numeric bad: %g\n", Control [UMFPACK_ALLOC_INIT]) ; */ fflush (stdout) ; return (9e10) ; } if (prl > 2) printf ("Numeric: ") ; status = UMFPACK_report_numeric (Numeric, Control) ; if (status != UMFPACK_OK) { UMFPACK_free_numeric (&Numeric) ; error ("bad numeric report\n", 0.) ; } /* ---------------------------------------------------------------------- */ /* get the determinant */ /* ---------------------------------------------------------------------- */ Mx [0] = 0. ; Mx [1] = 0. ; Mz = 0. ; Exp = 0. ; for (i = 0 ; i <= 3 ; i++) { if (i == 0) { status = UMFPACK_get_determinant (CARG (Mx, &Mz), &Exp, Numeric, Info) ; } else if (i == 1) { status = UMFPACK_get_determinant (CARG (Mx, &Mz), &Exp, Numeric, DNULL) ; } else if (i == 2) { status = UMFPACK_get_determinant (CARG (Mx, &Mz), DNULL, Numeric, Info) ; } else if (i == 3) { status = UMFPACK_get_determinant (CARG (Mx, DNULL), DNULL, Numeric, Info) ; } if (n_row == n_col) { if (status != UMFPACK_OK) { error ("bad det\n", 0.) ; } if (det_check && SCALAR_ABS (det_x < 1e100)) { if (i == 0 || i == 1) { deterr = SCALAR_ABS (det_x - (Mx [0] * pow (10.0, Exp))) ; } else if (i == 2 || i == 3) { deterr = SCALAR_ABS (det_x - Mx [0]) ; } if (deterr > 1e-7) { printf ("det: real err %g i: %d\n", deterr, i) ; error ("det: bad real part", det_x) ; } #ifdef COMPLEX if (i == 0 || i == 1) { deterr = SCALAR_ABS (det_z - (Mz * pow (10.0, Exp))) ; } else if (i == 2) { deterr = SCALAR_ABS (det_z - Mz) ; } else if (i == 3) { deterr = SCALAR_ABS (det_z - Mx [1]) ; } if (deterr > 1e-7) { printf ("det: imag err %g\n", deterr) ; error ("det: bad imag part", det_z) ; } #endif } } else { if (status != UMFPACK_ERROR_invalid_system) { error ("bad det (rectangluar)\n", 0.) ; } } } /* ---------------------------------------------------------------------- */ /* test save and load */ /* ---------------------------------------------------------------------- */ status = UMFPACK_save_numeric (Numeric, "n.umf") ; if (status != UMFPACK_OK) { error ("save numeric failed\n", 0.) ; } UMFPACK_free_numeric (&Numeric) ; status = UMFPACK_load_numeric (&Numeric, "n.umf") ; if (status != UMFPACK_OK) { error ("load numeric failed\n", 0.) ; } if (n < 15) { int umf_fail_save [3], memcnt ; status = UMFPACK_save_numeric (Numeric, (char *) NULL) ; if (status != UMFPACK_OK) { error ("save numeric failed\n", 0.) ; } UMFPACK_free_numeric (&Numeric) ; status = UMFPACK_load_numeric (&Numeric, (char *) NULL) ; if (status != UMFPACK_OK) { error ("load numeric failed\n", 0.) ; } /* test memory handling */ umf_fail_save [0] = umf_fail ; umf_fail_save [1] = umf_fail_lo ; umf_fail_save [2] = umf_fail_hi ; umf_fail = -1 ; umf_fail_lo = 0 ; umf_fail_hi = 0 ; UMFPACK_free_numeric (&Numeric) ; status = UMFPACK_load_numeric (&Numeric, (char *) NULL) ; if (status != UMFPACK_OK) { error ("load numeric failed\n", 0.) ; } Num = (NumericType *) Numeric ; memcnt = 11 ; if (Num->scale != UMFPACK_SCALE_NONE) { memcnt++ ; } if (Num->ulen > 0) { memcnt++ ; } for (i = 1 ; i <= memcnt ; i++) { umf_fail = i ; UMFPACK_free_numeric (&Numeric) ; status = UMFPACK_load_numeric (&Numeric, (char *) NULL) ; if (status != UMFPACK_ERROR_out_of_memory) { error ("load numeric should have failed\n", 0.) ; } } umf_fail = memcnt + 1 ; UMFPACK_free_numeric (&Numeric) ; status = UMFPACK_load_numeric (&Numeric, (char *) NULL) ; if (status != UMFPACK_OK) { printf ("memcnt %d\n", memcnt) ; error ("load numeric failed (edge)\n", 0.) ; } umf_fail = umf_fail_save [0] ; umf_fail_lo = umf_fail_save [1] ; umf_fail_hi = umf_fail_save [2] ; UMFPACK_free_numeric (&Numeric) ; status = UMFPACK_load_numeric (&Numeric, "n.umf") ; if (status != UMFPACK_OK) { error ("load numeric failed\n", 0.) ; } } /* ---------------------------------------------------------------------- */ /* get the LU factorization */ /* ---------------------------------------------------------------------- */ status = UMFPACK_get_lunz (&lnz, &unz, &nnrow, &nncol, &nzud, Numeric) ; if (status != UMFPACK_OK) { UMFPACK_report_info (Control, Info) ; error ("get lunz failure\n", 0.) ; UMFPACK_free_numeric (&Numeric) ; } /* guard against malloc of zero-sized arrays */ lnz = MAX (lnz,1) ; unz = MAX (unz,1) ; Rs = (double *) malloc ((n+1) * sizeof (double)) ; /* [ */ Li = (Int *) malloc (lnz * sizeof (Int)) ; /* [ */ Lx = (double *) calloc (2*lnz , sizeof (double)) ; /* [ */ Ui = (Int *) malloc (unz * sizeof (Int)) ; /* [ */ Ux = (double *) calloc (2*unz , sizeof (double)) ; /* [ */ Dx = (double *) calloc (2*n , sizeof (double)) ; /* [ */ Lrowp = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ Lrowi = (Int *) malloc (lnz * sizeof (Int)) ; /* [ */ Lrowx = (double *) calloc (2*lnz , sizeof (double)) ; /* [ */ if (!Li || !Lx || !Ui || !Ux || !Lrowp || !Lrowi || !Lrowx) error ("out of memory (2)\n",0.) ; if (split) { Dz = Dx + n ; Lrowz = Lrowx + lnz ; Lz = Lx + lnz ; Uz = Ux + unz ; } else { Dz = DNULL ; Lrowz = DNULL ; Lz = DNULL ; Uz = DNULL ; } status = UMFPACK_get_numeric (Lrowp, Lrowi, CARG(Lrowx,Lrowz), Up, Ui, CARG(Ux,Uz), P, Q, CARG(Dx,Dz), &do_recip, Rs, Numeric) ; if (status != UMFPACK_OK) { UMFPACK_report_info (Control, Info) ; error ("get LU failed\n", 0.) ; } if (!UMF_is_permutation (P, W, n_row, n_row)) { error ("P invalid\n", 0.) ; } if (!UMF_is_permutation (Q, W, n_col, n_col)) { error ("Q invalid\n", 0.) ; } if (prl > 2) printf ("\nP: ") ; status = UMFPACK_report_perm (n_row, P, Control) ; if (status != UMFPACK_OK) { error ("bad P 1\n", 0.) ; } if (prl > 2) printf ("\nQ: ") ; status = UMFPACK_report_perm (n_col, Q, Control) ; if (status != UMFPACK_OK) { error ("bad Q 1\n", 0.) ; } if (prl > 2) printf ("\nL row: ") ; status = UMFPACK_report_matrix (n_row, n_inner, Lrowp, Lrowi, CARG(Lrowx,Lrowz), 0, Control) ; if (status != UMFPACK_OK) { error ("bad Lrow\n", 0.) ; } if (prl > 2) printf ("\nD, diag of U: ") ; status = UMFPACK_report_vector (n_inner, CARG(Dx,Dz), Control) ; if (status != UMFPACK_OK) { error ("bad D\n", 0.) ; } /* --- */ /* ASSIGN (d, Dx [0], Dz [0]) ; */ ASSIGN (d, Dx, Dz, 0, SPLIT(Dz)) ; /* --- */ ABS (da, d) ; mind = da ; maxd = da ; for (i = 1 ; i < n_inner ; i++) { /* --- */ /* ASSIGN (d, Dx [i], Dz [i]) ; */ ASSIGN (d, Dx, Dz, i, SPLIT(Dz)) ; /* --- */ ABS (da, d) ; mind = MIN (mind, da) ; maxd = MAX (maxd, da) ; } if (maxd == 0.) { rcond = 0. ; } else { rcond = mind / maxd ; } if (prl > 2) printf ("mind: %g maxd: %g rcond: %g %g\n", mind, maxd, rcond, Info [UMFPACK_RCOND]) ; if (rcond == 0.0 && Info [UMFPACK_RCOND] != 0.0) { printf ("rcond error %30.20e %30.20e\n", rcond, Info [UMFPACK_RCOND]) ; error ("rcond", 0.) ; } if (SCALAR_ABS (rcond - Info [UMFPACK_RCOND]) / rcond > 1e-10) { printf ("rcond error %30.20e %30.20e\n", rcond, Info [UMFPACK_RCOND]) ; error ("rcond", 0.) ; } /* get L = Lrow' */ status = UMFPACK_transpose (n_inner, n_row, Lrowp, Lrowi, CARG(Lrowx,Lrowz), noP, noQ, Lp, Li, CARG(Lx,Lz) C1ARG(0)) ; if (status != UMFPACK_OK) { error ("L=Lrow' failed\n", 0.) ; } if (prl > 2) printf ("\nL col: ") ; status = UMFPACK_report_matrix (n_row, n_inner, Lp, Li, CARG(Lx,Lz), 1, Control) ; if (status != UMFPACK_OK) { error ("bad Lrow\n", 0.) ; } if (prl > 2) printf ("\nU col: ") ; status = UMFPACK_report_matrix (n_inner, n_col, Up, Ui, CARG(Ux,Uz), 1, Control) ; if (status != UMFPACK_OK) { error ("bad Ucol\n", 0.) ; } free (Lrowx) ; /* ] */ free (Lrowi) ; /* ] */ free (Lrowp) ; /* ] */ rnorm = do_solvers (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, Info, Numeric, Lp, Li, Lx,Lz, Up, Ui, Ux,Uz, P, Q, x,xz, r,rz, W, Wx, split) ; UMFPACK_report_info (Control, Info) ; /* ---------------------------------------------------------------------- */ /* free everything */ /* ---------------------------------------------------------------------- */ free (Dx) ; /* ] */ free (Ux) ; /* ] */ free (Ui) ; /* ] */ free (Lx) ; /* ] */ free (Li) ; /* ] */ free (Rs) ; /* ] */ UMFPACK_free_numeric (&Numeric) ; /* ] */ return (rnorm) ; } /* ========================================================================== */ /* do_once: factor A once, and then test the solves - return if error */ /* ========================================================================== */ /* exit if an error occurs. otherwise, return the largest residual norm seen. */ static double do_once ( Int n_row, Int n_col, Int Ap [ ], Int Ai [ ], double Ax [ ], double Az [ ], double b [ ], double bz [ ], double Control [ ], Int Qinit [ ], Int MemControl [6], Int save_and_load, Int split, /* TRUE if complex variables split, FALSE if merged */ Int det_check, double det_x, double det_z ) { double *x, rnorm, *r, *Wx, *xz, *rz ; Int *P, *Q, *Lp, *Up, *W, *Qtree, *Ptree, n ; #ifdef COMPLEX if (split) { if (!Az || !bz) error ("bad split\n", 0.) ; } else { if ( Az || bz) error ("bad merge\n", 0.) ; } #endif /* ---------------------------------------------------------------------- */ /* malloc and realloc failure control */ /* ---------------------------------------------------------------------- */ umf_fail = MemControl [0] ; umf_fail_hi = MemControl [1] ; umf_fail_lo = MemControl [2] ; umf_realloc_fail = MemControl [3] ; umf_realloc_hi = MemControl [4] ; umf_realloc_lo = MemControl [5] ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ n = MAX (n_row, n_col) ; n = MAX (n,1) ; r = (double *) calloc (2*n , sizeof (double)) ; /* [ */ x = (double *) calloc (2*n , sizeof (double)) ; /* [ */ rz = r + n ; if (split) { /* real/complex are in r/rz and x/xz */ xz = x + n ; } else { /* r and z are treated as array of size n Entry's */ xz = DNULL ; } Wx = (double *) malloc (10*n * sizeof (double)) ; /* [ */ P = (Int *) malloc (n * sizeof (Int)) ; /* [ */ Q = (Int *) malloc (n * sizeof (Int)) ; /* [ */ Qtree = (Int *) malloc (n * sizeof (Int)) ; /* [ */ Ptree = (Int *) malloc (n * sizeof (Int)) ; /* [ */ W = (Int *) malloc (n * sizeof (Int)) ; /* [ */ Lp = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ Up = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ if (!x || !Wx || !r || !P || !Q || !Qtree || !Ptree || !W || !Lp || !Up) error ("out of memory (3)",0.) ; /* ---------------------------------------------------------------------- */ /* report controls */ /* ---------------------------------------------------------------------- */ if (Control) { if (Control [UMFPACK_PRL] >= 2) { UMFPACK_report_control (Control) ; } } /* ---------------------------------------------------------------------- */ /* do the symbolic & numeric factorization, and solvers */ /* ---------------------------------------------------------------------- */ rnorm = do_symnum (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, Qinit, x,xz, r,rz, Wx, P, Q, Qtree, Ptree, W, Lp, Up, save_and_load, split, det_check, det_x, det_z) ; /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ free (Up) ; /* ] */ free (Lp) ; /* ] */ free (W) ; /* ] */ free (Ptree) ; /* ] */ free (Qtree) ; /* ] */ free (Q) ; /* ] */ free (P) ; /* ] */ free (Wx) ; /* ] */ free (x) ; /* ] */ free (r) ; /* ] */ #if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG) if (UMF_malloc_count != 0) error ("umfpack memory leak!!",0.) ; #endif return (rnorm) ; } /* ========================================================================== */ /* do_many: factor A once, and then test the solves - return if error */ /* ========================================================================== */ /* runs do_once with complex variables split, and again with them merged */ static double do_many ( Int n_row, Int n_col, Int Ap [ ], Int Ai [ ], double Ax [ ], double Az [ ], double b [ ], double bz [ ], double Control [ ], Int Qinit [ ], Int MemControl [6], Int save_and_load, Int det_check, double det_x, double det_z ) { double rnorm, r ; Entry *A, *B, a ; Int p, i, nz ; rnorm = 0 ; #ifdef COMPLEX if (!Az || !bz) error ("do_many missing imag parts!\n", 0.) ; nz = Ap [n_col] ; A = (Entry *) malloc ((nz+1) * sizeof (Entry)) ; B = (Entry *) malloc ((n_col+1) * sizeof (Entry)) ; if (!A || !B) error ("out of memory (4)",0.) ; for (p = 0 ; p < nz ; p++) { ASSIGN (A [p], Ax, Az, p, TRUE) ; } for (i = 0 ; i < n_col ; i++) { ASSIGN (B [i], b, bz, i, TRUE) ; } /* with complex variables merged */ r = do_once (n_row, n_col, Ap, Ai, (double *)A,DNULL, (double *)B,DNULL, Control, Qinit, MemControl, save_and_load, FALSE, det_check, det_x, det_z) ; free (A) ; free (B) ; rnorm = MAX (r, rnorm) ; #endif /* with complex variables split */ r = do_once (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemControl, save_and_load, TRUE, det_check, det_x, det_z) ; rnorm = MAX (r, rnorm) ; return (rnorm) ; } /* ========================================================================== */ /* bgen: b = A*xtrue, where xtrue (i) = 1 + i/n */ /* ========================================================================== */ static void bgen ( Int n, Int Ap [ ], Int Ai [ ], double Ax [ ], double Az [ ], double b [ ], double bz [ ] ) { Int i, col, p ; double xtrue, xtruez ; for (i = 0 ; i < n ; i++) { b [i] = 0.0 ; bz[i] = 0.0 ; } for (col = 0 ; col < n ; col++) { xtrue = 1.0 + ((double) col) / ((double) n) ; #ifdef COMPLEX xtruez= 1.3 - ((double) col) / ((double) n) ; #else xtruez= 0. ; #endif for (p = Ap [col] ; p < Ap [col+1] ; p++) { i = Ai [p] ; b [i] += Ax [p] * xtrue ; b [i] -= Az [p] * xtruez ; bz[i] += Az [p] * xtrue ; bz[i] += Ax [p] * xtruez ; } } } /* ========================================================================== */ /* do_matrix: process one matrix with lots of options - exit if errors */ /* ========================================================================== */ /* return the largest residual norm seen, or exit if error occured */ static double do_matrix ( Int n, Int Ap [ ], Int Ai [ ], double Ax [ ], double Az [ ], double Controls [UMFPACK_CONTROL][1000], Int Ncontrols [UMFPACK_CONTROL], Int MemControl [6], Int do_dense ) { double Control [UMFPACK_CONTROL], *b, *bz, maxrnorm, rnorm, tol, init ; Int *colhist, *rowhist, *rowdeg, *noQinit, *Qinit, *cknob, *rknob, c, r, cs, rs, row, col, i, coldeg, p, d, nb, ck, rk, *Head, *Next, col1, col2, d1, d2, k, status, n_amd, i_tol, i_nb, i_init, n_tol, n_nb, n_init, n_scale, i_scale, scale, i_pivot, n_pivot, pivopt ; /* ---------------------------------------------------------------------- */ /* initializations */ /* ---------------------------------------------------------------------- */ maxrnorm = 0.0 ; /* get the default control parameters */ UMFPACK_defaults (Control) ; UMFPACK_report_control (Control) ; #ifdef DEBUGGING Control [UMFPACK_PRL] = 5 ; #endif status = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Control) ; if (status != UMFPACK_OK) { error ("bad A do_matrix\n", 0.) ; } /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ rowdeg = (Int *) malloc ((n+1) * sizeof (Int)) ; /* ( */ rowhist = (Int *) malloc ((n+1) * sizeof (Int)) ; /* ( */ colhist = (Int *) malloc ((n+1) * sizeof (Int)) ; /* ( */ cknob = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ rknob = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ /* ---------------------------------------------------------------------- */ /* count the dense rows and columns */ /* ---------------------------------------------------------------------- */ for (i = 0 ; i < n ; i++) { colhist [i] = 0 ; rowhist [i] = 0 ; rowdeg [i] = 0 ; } for (col = 0 ; col < n ; col++) { coldeg = Ap [col+1] - Ap [col] ; colhist [coldeg]++ ; for (p = Ap [col] ; p < Ap [col+1] ; p++) { rowdeg [Ai [p]]++ ; } } for (row = 0 ; row < n ; row++) { rowhist [rowdeg [row]]++ ; } rs = 0 ; if (do_dense) { if (n < 16) { rknob [rs++] = 0 ; /* all dense rows */ } for (d = 16 ; d < n ; d++) { if (rowhist [d] > 0) { rknob [rs++] = d ; } } } rknob [rs++] = n ; /* no dense rows */ cs = 0 ; if (do_dense) { if (n < 16) { cknob [cs++] = 0 ; /* all dense columns */ } for (d = 16 ; d < n ; d++) { if (colhist [d] > 0) { cknob [cs++] = d ; } } } cknob [cs++] = n ; /* no dense cols */ free (colhist) ; /* ) */ free (rowhist) ; /* ) */ /* ---------------------------------------------------------------------- */ /* compute b assuming xtrue (i) = 1 + i/n */ /* ---------------------------------------------------------------------- */ b = (double *) malloc (n * sizeof (double)) ; /* [ */ bz= (double *) calloc (n , sizeof (double)) ; /* [ */ if (!b) error ("out of memory (5)",0.) ; if (!bz) error ("out of memory (6)",0.) ; bgen (n, Ap, Ai, Ax, Az, b, bz) ; /* ---------------------------------------------------------------------- */ /* compute Qinit = sort by colcounts */ /* ---------------------------------------------------------------------- */ noQinit = INULL ; Qinit = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ if (!Qinit) error ("out of memory (7)",0.) ; Head = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ Next = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ for (d = 0 ; d <= n ; d++) { Head [d] = EMPTY ; } for (col = n-1 ; col >= 0 ; col--) { d = Ap [col+1] - Ap [col] ; Next [col] = Head [d] ; Head [d] = col ; } k = 0 ; for (d = 0 ; d <= n ; d++) { for (col = Head [d] ; col != EMPTY ; col = Next [col]) { Qinit [k++] = col ; } } free (Next) ; /* ] */ free (Head) ; /* ] */ if (k != n) error ("Qinit error\n",0.) ; /* use rowdeg for workspace */ if (!UMF_is_permutation (Qinit, rowdeg, n, n)) error ("Qinit, colsort, not a permutation vector",0.) ; for (k = 1 ; k < n ; k++) { col1 = Qinit [k-1] ; col2 = Qinit [k] ; d1 = Ap [col1+1] - Ap [col1] ; d2 = Ap [col2+1] - Ap [col2] ; if (d1 > d2) error ("Qinit error = not sorted\n",0.) ; } free (rowdeg) ; /* ) */ /* ---------------------------------------------------------------------- */ /* exhaustive test */ /* ---------------------------------------------------------------------- */ n_tol = Ncontrols [UMFPACK_PIVOT_TOLERANCE] ; n_nb = Ncontrols [UMFPACK_BLOCK_SIZE] ; n_init = Ncontrols [UMFPACK_ALLOC_INIT] ; n_scale = Ncontrols [UMFPACK_SCALE] ; n_amd = Ncontrols [UMFPACK_AMD_DENSE] ; printf (" cs "ID" rs "ID" : "ID" ", cs, rs, 2 + (cs * rs * n_tol * n_nb * n_init )) ; fflush (stdout) ; /* with defaults - null Control array, Qinit */ printf ("with qinit:\n") ; rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, DNULL, Qinit, MemControl, FALSE, FALSE, 0., 0.) ; maxrnorm = MAX (rnorm, maxrnorm) ; /* with defaults - null Control array */ printf ("with null control array:\n") ; rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, DNULL, noQinit, MemControl, FALSE, FALSE, 0., 0.) ; maxrnorm = MAX (rnorm, maxrnorm) ; /* with defaults */ printf ("with defaults:\n") ; rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, noQinit, MemControl, FALSE, FALSE, 0., 0.) ; maxrnorm = MAX (rnorm, maxrnorm) ; printf ("with defaults and qinit:\n") ; rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemControl, FALSE, FALSE, 0., 0.) ; maxrnorm = MAX (rnorm, maxrnorm) ; printf ("starting lengthy tests\n") ; for (c = 0 ; c <= cs ; c++) { if (c == cs) { rs = n_amd ; } for (r = 0 ; r < rs ; r++) { if (c == cs) { Control [UMFPACK_DENSE_COL] = UMFPACK_DEFAULT_DENSE_COL ; Control [UMFPACK_DENSE_ROW] = UMFPACK_DEFAULT_DENSE_ROW ; Control [UMFPACK_AMD_DENSE] = Controls [UMFPACK_AMD_DENSE][r] ; } else { ck = cknob [c] ; rk = rknob [r] ; /* ignore columns with degree > ck and rows with degree > rk */ Control [UMFPACK_DENSE_COL] = inv_umfpack_dense (ck, n) ; Control [UMFPACK_DENSE_ROW] = inv_umfpack_dense (rk, n) ; Control [UMFPACK_AMD_DENSE] = UMFPACK_DEFAULT_AMD_DENSE ; } for (i_tol = 0 ; i_tol < n_tol ; i_tol++) { tol = Controls [UMFPACK_PIVOT_TOLERANCE][i_tol] ; Control [UMFPACK_PIVOT_TOLERANCE] = tol ; for (i_nb = 0 ; i_nb < n_nb ; i_nb++) { nb = (Int) Controls [UMFPACK_BLOCK_SIZE][i_nb] ; Control [UMFPACK_BLOCK_SIZE] = (double) nb ; for (i_init = 0 ; i_init < n_init ; i_init++) { init = Controls [UMFPACK_ALLOC_INIT][i_init] ; Control [UMFPACK_ALLOC_INIT] = init ; for (i_scale = 0 ; i_scale < n_scale ; i_scale++) { Int strategy, fixQ ; scale = Controls [UMFPACK_SCALE][i_scale] ; Control [UMFPACK_SCALE] = scale ; for (strategy = UMFPACK_STRATEGY_AUTO ; strategy <= UMFPACK_STRATEGY_SYMMETRIC ; strategy ++) { Control [UMFPACK_STRATEGY] = strategy ; { rnorm = do_once (n, n, Ap, Ai, Ax,Az, b,bz, Control, noQinit, MemControl, FALSE, TRUE, FALSE, 0., 0.) ; maxrnorm = MAX (rnorm, maxrnorm) ; rnorm = do_once (n, n, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemControl, FALSE, TRUE, FALSE, 0., 0.) ; maxrnorm = MAX (rnorm, maxrnorm) ; } } } } } } } } free (Qinit) ; /* ] */ free (bz) ; /* ] */ free (b) ; /* ] */ free (rknob) ; /* ] */ free (cknob) ; /* ] */ return (maxrnorm) ; } /* ========================================================================== */ /* matgen_dense: generate a dense matrix */ /* ========================================================================== */ /* allocates Ap, Ai, Ax, and Az */ static void matgen_dense ( Int n, Int **Ap, Int **Ai, double **Ax, double **Az ) { Int nz, *Bp, *Bi, *Ti, *Tj, k, i, j, *P, status ; double *Bx, *Tx, *Bz, *Tz ; nz = n*n + n ; /* allocate Bp, Bi, and Bx - but do not free them */ Bp = (Int *) malloc ((n+1) * sizeof (Int)) ; Bi = (Int *) malloc ((nz+1) * sizeof (Int)) ; Bx = (double *) malloc ((nz+1) * sizeof (double)) ; Bz = (double *) calloc ((nz+1) , sizeof (double)) ; Ti = (Int *) malloc ((nz+1) * sizeof (Int)) ; /* [ */ Tj = (Int *) malloc ((nz+1) * sizeof (Int)) ; /* [ */ Tx = (double *) malloc ((nz+1) * sizeof (double)) ; /* [ */ Tz = (double *) calloc ((nz+1) , sizeof (double)) ; /* [ */ P = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ if (!Bp || !Bi || !Bx || !Ti || !Tj || !Tx || !P) error ("out of memory (8)",0.) ; if (!Bz || !Tz) error ("outof memory",0.) ; k = 0 ; for (i = 0 ; i < n ; i++) { for (j = 0 ; j < n ; j++) { Ti [k] = i ; Tj [k] = j ; Tx [k] = 2.0 * (xrand ( ) - 1.0) ; #ifdef COMPLEX Tz [k] = 2.0 * (xrand ( ) - 1.0) ; #else Tz [k] = 0. ; #endif k++ ; } } /* beef up each column and row */ randperm (n, P) ; for (i = 0 ; i < n ; i++) { Ti [k] = i ; Tj [k] = P [i] ; Tx [k] = xrand ( ) ; #ifdef COMPLEX Tz [k] = xrand ( ) ; #else Tz [k] = 0. ; #endif k++ ; } if (k != nz) error ("matgen_dense error",0.) ; /* convert to column form */ status = UMFPACK_triplet_to_col (n, n, k, Ti, Tj, CARG(Tx,Tz), Bp, Bi, CARG(Bx,Bz), (Int *) NULL) ; if (status != UMFPACK_OK) error ("matgen_dense triplet_to_col failed 2",0.) ; /* return the allocated column-form */ *Ap = Bp ; *Ai = Bi ; *Ax = Bx ; *Az = Bz ; free (P) ; /* ] */ free (Tz) ; /* ] */ free (Tx) ; /* ] */ free (Tj) ; /* ] */ free (Ti) ; /* ] */ } /* ========================================================================== */ /* matgen_funky: generate a kind of arrowhead matrix */ /* ========================================================================== */ /* allocates Ap, Ai, Ax, and Az A = speye (n) ; A (n, 2:3) = rand (1,2) ; A (3, 3:n) = rand (1, n-2) ; A (3:n, 1) = rand (n-2, 1) ; */ static void matgen_funky ( Int n, Int **Ap, Int **Ai, double **Ax, double **Az ) { Int nz, *Bp, *Bi, *Ti, *Tj, k, i, j, *P, status ; double *Bx, *Tx, *Bz, *Tz ; nz = 4*n + 5 ; /* allocate Bp, Bi, and Bx - but do not free them */ Bp = (Int *) malloc ((n+1) * sizeof (Int)) ; Bi = (Int *) malloc (nz * sizeof (Int)) ; Bx = (double *) malloc (nz * sizeof (double)) ; Bz = (double *) calloc (nz , sizeof (double)) ; Ti = (Int *) malloc (nz * sizeof (Int)) ; /* [ */ Tj = (Int *) malloc (nz * sizeof (Int)) ; /* [ */ Tx = (double *) malloc (nz * sizeof (double)) ; /* [ */ Tz = (double *) calloc (nz , sizeof (double)) ; /* [ */ P = (Int *) malloc (n * sizeof (Int)) ; /* [ */ if (!Bp || !Bi || !Bx || !Ti || !Tj || !Tx || !P) error ("out of memory (9)",0.) ; if (!Bz || !Tz) error ("outof memory",0.) ; k = 0 ; /* A = speye (n) ; */ for (i = 0 ; i < n ; i++) { Ti [k] = i ; Tj [k] = i ; Tx [k] = 1.0 ; #ifdef COMPLEX Tz [k] = 1.0 ; #endif k++ ; } /* A (n, 2:3) = rand (1,2) ; */ for (j = 1 ; j <= 2 ; j++) { Ti [k] = n-1 ; Tj [k] = j ; Tx [k] = 1.0 ; #ifdef COMPLEX Tz [k] = 1.0 ; #endif k++ ; } /* A (3, 3:n) = rand (1, n-2) ; */ for (j = 2 ; j < n ; j++) { Ti [k] = 2 ; Tj [k] = j ; Tx [k] = 1.0 ; #ifdef COMPLEX Tz [k] = 1.0 ; #endif k++ ; } /* A (3:n, 1) = rand (n-2, 1) ; */ for (i = 2 ; i < n ; i++) { Ti [k] = i ; Tj [k] = 0 ; Tx [k] = 1.0 ; #ifdef COMPLEX Tz [k] = 1.0 ; #endif k++ ; } /* convert to column form */ status = UMFPACK_triplet_to_col (n, n, k, Ti, Tj, CARG(Tx,Tz), Bp, Bi, CARG(Bx,Bz), (Int *) NULL) ; if (status != UMFPACK_OK) error ("matgen_dense triplet_to_col failed 1",0.) ; /* return the allocated column-form */ *Ap = Bp ; *Ai = Bi ; *Ax = Bx ; *Az = Bz ; free (P) ; /* ] */ free (Tz) ; /* ] */ free (Tx) ; /* ] */ free (Tj) ; /* ] */ free (Ti) ; /* ] */ } /* ========================================================================== */ /* matgen_band: generate a banded matrix */ /* ========================================================================== */ /* allocates Ap, Ai, and Ax */ static void matgen_band ( Int n, Int lo, /* lo = 0: upper triangular only */ Int up, /* up = 0: lower triangular only */ Int ndrow, /* plus ndrow dense rows, each of degree rdeg */ Int rdeg, Int ndcol, /* plus ndcol dense cols, each of degree cdeg */ Int cdeg, Int **Ap, Int **Ai, double **Ax, double **Az ) { Int nz, *Bp, *Bi, *Ti, *Tj, k, i, j, jlo, jup, j1, i1, k1, status ; double *Bx, *Bz, *Tx, *Tz ; /* an upper bound */ nz = n * (lo + 1 + up) + n + ndrow*rdeg + ndcol*cdeg ; /* allocate Bp, Bi, and Bx - but do not free them */ Bp = (Int *) malloc ((n+1) * sizeof (Int)) ; Bi = (Int *) malloc (nz * sizeof (Int)) ; Bx = (double *) malloc (nz * sizeof (double)) ; Bz = (double *) calloc (nz , sizeof (double)) ; Ti = (Int *) malloc (nz * sizeof (Int)) ; /* [ */ Tj = (Int *) malloc (nz * sizeof (Int)) ; /* [ */ Tx = (double *) malloc (nz * sizeof (double)) ; /* [ */ Tz = (double *) calloc (nz , sizeof (double)) ; /* [ */ if (!Bp || !Bi || !Bx || !Ti || !Tj || !Tx) error ("out of memory (10)",0.) ; if (!Bz || !Tz) error ("out ofmemory", 0.) ; k = 0 ; for (i = 0 ; i < n ; i++) { jlo = MAX (0, i - lo) ; jup = MIN (n-1, i + up) ; for (j = jlo ; j <= jup ; j++) { Ti [k] = i ; Tj [k] = j ; Tx [k] = 2.0 * (xrand ( ) - 1.0) ; #ifdef COMPLEX Tz [k] = 2.0 * (xrand ( ) - 1.0) ; #else Tz [k] = 0. ; #endif k++ ; } } /* beef up the diagonal */ for (i = 0 ; i < n ; i++) { Ti [k] = i ; Tj [k] = i ; Tx [k] = xrand ( ) ; #ifdef COMPLEX Tz [k] = xrand ( ) ; #else Tz [k] = 0. ; #endif k++ ; } /* add ndrow rows of degree rdeg */ for (i1 = 0 ; i1 < ndrow ; i1++) { i = irand (n) ; for (k1 = 0 ; k1 < rdeg ; k1++) { Ti [k] = i ; Tj [k] = irand (n) ; Tx [k] = 0.1 * xrand ( ) ; #ifdef COMPLEX Tz [k] = 0.1 * xrand ( ) ; #else Tz [k] = 0. ; #endif k++ ; } } /* add ndcol rows of degree cdeg */ for (j1 = 0 ; j1 < ndcol ; j1++) { j = irand (n) ; for (k1 = 0 ; k1 < cdeg ; k1++) { Ti [k] = irand (n) ; Tj [k] = j ; Tx [k] = 0.1 * xrand ( ) ; #ifdef COMPLEX Tz [k] = 0.1 * xrand ( ) ; #else Tz [k] = 0. ; #endif k++ ; } } if (k > nz) error ("matgen_band error\n",0.) ; /* convert to column form */ status = UMFPACK_triplet_to_col (n, n, k, Ti, Tj, CARG(Tx,Tz), Bp, Bi, CARG(Bx,Bz), (Int *) NULL) ; if (status != UMFPACK_OK) error ("matgen_band triplet_to_col failed\n",0.) ; /* return the allocated column-form */ *Ap = Bp ; *Ai = Bi ; *Ax = Bx ; *Az = Bz ; free (Tz) ; /* ] */ free (Tx) ; /* ] */ free (Tj) ; /* ] */ free (Ti) ; /* ] */ } /* ========================================================================== */ /* test_col */ /* ========================================================================== */ static void test_col ( Int n, Int Bp [ ], Int Bi [ ], double Bx [ ], double Bz [ ], Int prl ) { Int *Ci, *Cj, *Ep, *Ei, k, s, t, i, j, nz, p, status, *Map, *noMap ; double *Cx, *Cz, *Ex, *Ez, z, Control [UMFPACK_CONTROL] ; noMap = (Int *) NULL ; printf ("\n\n===== test col -> triplet and triplet -> col\n") ; UMFPACK_defaults (Control) ; Control [UMFPACK_PRL] = prl ; UMFPACK_report_control (Control) ; nz = Bp [n] ; Ci = (Int *) malloc ((2*nz+1) * sizeof (Int)) ; /* [ */ Cj = (Int *) malloc ((2*nz+1) * sizeof (Int)) ; /* [ */ Cx = (double *) calloc (2*(2*nz+1) , sizeof (double)) ; /* [ */ Cz = Cx + (2*nz+1) ; Ep = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ Ei = (Int *) malloc ((2*nz+1) * sizeof (Int)) ; /* [ */ Ex = (double *) calloc (2*(2*nz+1) , sizeof (double)) ; /* [ */ Ez = Ex + (2*nz+1) ; Map = (Int *) malloc ((2*nz+1) * sizeof (Int)) ; /* [ */ if (!Ci || !Cj || !Cx || !Ep || !Ei || !Ex) error ("out of memory (11)",0.) ; /* ---------------------------------------------------------------------- */ /* test with split complex values */ /* ---------------------------------------------------------------------- */ /* convert B (col) to C (triplet) */ status = UMFPACK_col_to_triplet (n, Bp, Cj) ; if (status != UMFPACK_OK) error ("col->triplet",0.) ; for (k = 0 ; k < nz ; k++) { Ci [k] = Bi [k] ; Cx [k] = Bx [k] ; Cz [k] = Bz [k] ; } /* convert C (triplet) to E (col) */ status = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(Cx,Cz), Ep, Ei, CARG(Ex,Ez), Map) ; if (status != UMFPACK_OK) error ("t->col failed (1)",0.) ; /* compare E and B, they should be identical */ if (nz != Ep [n]) error ("E nz (1)",0.) ; for (j = 0 ; j < n ; j++) { if (Bp [j] != Ep [j]) error ("Ep j",0.) ; if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ; for (p = Bp [j] ; p < Bp [j+1] ; p++) { if (Bi [p] != Ei [p]) error ("Ei",0.) ; if (SCALAR_ABS (Bx [p] - Ex [p]) > 1e-15) error ("Ex",0.) ; if (SCALAR_ABS (Bz [p] - Ez [p]) > 1e-15) error ("Ez (1)",0.) ; } } /* convert C (triplet) to E (col), no map */ status = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(Cx,Cz), Ep, Ei, CARG(Ex,Ez), noMap) ; if (status != UMFPACK_OK) error ("t->col failed (1)",0.) ; /* compare E and B, they should be identical */ if (nz != Ep [n]) error ("E nz (2)",0.) ; for (j = 0 ; j < n ; j++) { if (Bp [j] != Ep [j]) error ("Ep j",0.) ; if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ; for (p = Bp [j] ; p < Bp [j+1] ; p++) { if (Bi [p] != Ei [p]) error ("Ei",0.) ; if (SCALAR_ABS (Bx [p] - Ex [p]) > 1e-15) error ("Ex",0.) ; if (SCALAR_ABS (Bz [p] - Ez [p]) > 1e-15) error ("Ez",0.) ; } } /* jumble C a little bit */ for (k = 0 ; k < MIN (nz,4) ; k++) { s = irand (nz) ; /* swap positions s and k */ t = Ci [k] ; Ci [k] = Ci [s] ; Ci [s] = t ; t = Cj [k] ; Cj [k] = Cj [s] ; Cj [s] = t ; z = Cx [k] ; Cx [k] = Cx [s] ; Cx [s] = z ; z = Cz [k] ; Cz [k] = Cz [s] ; Cz [s] = z ; } /* convert C (triplet) to E (col) */ status = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(Cx,Cz), Ep, Ei, CARG(Ex,Ez), Map) ; if (status != UMFPACK_OK) error ("t->col failed (1)",0.) ; /* compare E and B, they should be identical */ if (nz != Ep [n]) error ("E nz (3)",0.) ; for (j = 0 ; j < n ; j++) { if (Bp [j] != Ep [j]) error ("Ep j",0.) ; if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ; for (p = Bp [j] ; p < Bp [j+1] ; p++) { if (Bi [p] != Ei [p]) error ("Ei",0.) ; if (SCALAR_ABS (Bx [p] - Ex [p]) > 1e-15) error ("Ex",0.) ; if (SCALAR_ABS (Bz [p] - Ez [p]) > 1e-15) error ("Ez",0.) ; } } /* convert C (triplet) to E (col), no map */ status = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(Cx,Cz), Ep, Ei, CARG(Ex,Ez), noMap) ; if (status != UMFPACK_OK) error ("t->col failed (1)",0.) ; /* compare E and B, they should be identical */ if (nz != Ep [n]) error ("E nz (4)",0.) ; for (j = 0 ; j < n ; j++) { if (Bp [j] != Ep [j]) error ("Ep j",0.) ; if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ; for (p = Bp [j] ; p < Bp [j+1] ; p++) { if (Bi [p] != Ei [p]) error ("Ei",0.) ; if (SCALAR_ABS (Bx [p] - Ex [p]) > 1e-15) error ("Ex",0.) ; if (SCALAR_ABS (Bz [p] - Ez [p]) > 1e-15) error ("Ez",0.) ; } } /* jumble C a lot */ for (k = 0 ; k < nz ; k++) { s = irand (nz) ; /* swap positions s and k */ t = Ci [k] ; Ci [k] = Ci [s] ; Ci [s] = t ; t = Cj [k] ; Cj [k] = Cj [s] ; Cj [s] = t ; z = Cx [k] ; Cx [k] = Cx [s] ; Cx [s] = z ; z = Cz [k] ; Cz [k] = Cz [s] ; Cz [s] = z ; } /* add duplicates to C, but preserve pattern and values */ for (k = nz ; k < 2*nz ; k++) { /* add a duplicate */ s = irand (k) ; Ci [k] = Ci [s] ; Cj [k] = Cj [s] ; z = Cx [s] ; Cx [s] = z/2 ; Cx [k] = z/2 ; z = Cz [s] ; Cz [s] = z/2 ; Cz [k] = z/2 ; } if (prl > 2) printf ("\ntest c->t,t->c: ") ; status = UMFPACK_report_triplet (n, n, 2*nz, Ci, Cj, CARG(Cx,Cz), Control) ; if (status != UMFPACK_OK) error ("report col->triplet",0.) ; /* convert C (triplet) to E (col), no Map */ status = UMFPACK_triplet_to_col (n, n, 2*nz, Ci, Cj, CARG(Cx,Cz), Ep, Ei, CARG(Ex,Ez), noMap) ; if (status != UMFPACK_OK) error ("t->col failed",0.) ; /* compare E and B, they should be identical */ if (nz != Ep [n]) error ("E nz (5)",0.) ; for (j = 0 ; j < n ; j++) { if (Bp [j] != Ep [j]) error ("Ep j",0.) ; if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ; for (p = Bp [j] ; p < Bp [j+1] ; p++) { if (Bi [p] != Ei [p]) error ("Ei",0.) ; if (SCALAR_ABS (Bx [p] - Ex [p]) > 1e-15) error ("Ex",0.) ; if (SCALAR_ABS (Bz [p] - Ez [p]) > 1e-15) { printf ("%30.18e %30.18e %g\n", Bz[p], Ez[p], Bz[p]-Ez[p]) ; error ("Ez (5)",0.) ; } } } /* convert C (triplet) to E (col) */ status = UMFPACK_triplet_to_col (n, n, 2*nz, Ci, Cj, CARG(Cx,Cz), Ep, Ei, CARG(Ex,Ez), Map) ; if (status != UMFPACK_OK) error ("t->col failed",0.) ; /* compare E and B, they should be identical */ if (nz != Ep [n]) error ("E nz (6)",0.) ; for (j = 0 ; j < n ; j++) { if (Bp [j] != Ep [j]) error ("Ep j",0.) ; if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ; for (p = Bp [j] ; p < Bp [j+1] ; p++) { if (Bi [p] != Ei [p]) error ("Ei",0.) ; if (SCALAR_ABS (Bx [p] - Ex [p]) > 1e-15) error ("Ex",0.) ; if (SCALAR_ABS (Bz [p] - Ez [p]) > 1e-15) error ("Ez",0.) ; } } /* convert C (triplet) to E (col), using Map */ for (p = 0 ; p < Ep [n] ; p++) { Ex [p] = 0. ; Ez [p] = 0. ; } for (k = 0 ; k < 2*nz ; k++) { p = Map [k] ; i = Ci [k] ; j = Cj [k] ; if (i != Ei [p]) error ("Map", 0.) ; if (!(Ep [j] <= p && p < Ep [j+1])) error ("Map Ep", 0.) ; Ex [p] += Cx [k] ; Ez [p] += Cz [k] ; } /* compare E and B, they should be identical */ for (j = 0 ; j < n ; j++) { for (p = Bp [j] ; p < Bp [j+1] ; p++) { z = SCALAR_ABS (Bx [p] - Ex [p]) ; if (z > 1e-15) error ("Ex",z) ; z = SCALAR_ABS (Bz [p] - Ez [p]) ; if (z > 1e-15) error ("Ez (7)",z) ; } } #ifdef COMPLEX /* ---------------------------------------------------------------------- */ /* repeat, but with merged complex values */ /* ---------------------------------------------------------------------- */ /* convert B (col) to C (triplet) */ status = UMFPACK_col_to_triplet (n, Bp, Cj) ; if (status != UMFPACK_OK) error ("col->triplet",0.) ; for (k = 0 ; k < nz ; k++) { Ci [k] = Bi [k] ; Cx [2*k ] = Bx [k] ; Cx [2*k+1] = Bz [k] ; } /* convert C (triplet) to E (col) */ status = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(Cx,DNULL), Ep, Ei, CARG(Ex,DNULL), Map) ; if (status != UMFPACK_OK) error ("t->col failed (1)",0.) ; /* compare E and B, they should be identical */ if (nz != Ep [n]) error ("E nz (7)",0.) ; for (j = 0 ; j < n ; j++) { if (Bp [j] != Ep [j]) error ("Ep j",0.) ; if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ; for (p = Bp [j] ; p < Bp [j+1] ; p++) { if (Bi [p] != Ei [p]) error ("Ei",0.) ; if (SCALAR_ABS (Bx [p] - Ex [2*p ]) > 1e-15) error ("Ex (merge)",0.) ; if (SCALAR_ABS (Bz [p] - Ex [2*p+1]) > 1e-15) error ("Ez (merge)",0.) ; } } /* convert C (triplet) to E (col) no Map */ status = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(Cx,DNULL), Ep, Ei, CARG(Ex,DNULL), noMap) ; if (status != UMFPACK_OK) error ("t->col failed (1)",0.) ; /* compare E and B, they should be identical */ if (nz != Ep [n]) error ("E nz (8)",0.) ; for (j = 0 ; j < n ; j++) { if (Bp [j] != Ep [j]) error ("Ep j",0.) ; if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ; for (p = Bp [j] ; p < Bp [j+1] ; p++) { if (Bi [p] != Ei [p]) error ("Ei",0.) ; if (SCALAR_ABS (Bx [p] - Ex [2*p ]) > 1e-15) error ("Ex (merge)",0.) ; if (SCALAR_ABS (Bz [p] - Ex [2*p+1]) > 1e-15) error ("Ez (merge)",0.) ; } } /* jumble C a little bit */ for (k = 0 ; k < MIN (nz,4) ; k++) { s = irand (nz) ; /* swap positions s and k */ t = Ci [k] ; Ci [k] = Ci [s] ; Ci [s] = t ; t = Cj [k] ; Cj [k] = Cj [s] ; Cj [s] = t ; z = Cx [2*k ] ; Cx [2*k ] = Cx [2*s ] ; Cx [2*s ] = z ; z = Cx [2*k+1] ; Cx [2*k+1] = Cx [2*s+1] ; Cx [2*s+1] = z ; } /* convert C (triplet) to E (col) */ status = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(Cx,DNULL), Ep, Ei, CARG(Ex,DNULL), Map) ; if (status != UMFPACK_OK) error ("t->col failed (1)",0.) ; /* compare E and B, they should be identical */ if (nz != Ep [n]) error ("E nz (9)",0.) ; for (j = 0 ; j < n ; j++) { if (Bp [j] != Ep [j]) error ("Ep j",0.) ; if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ; for (p = Bp [j] ; p < Bp [j+1] ; p++) { if (Bi [p] != Ei [p]) error ("Ei",0.) ; if (SCALAR_ABS (Bx [p] - Ex [2*p ]) > 1e-15) error ("Ex (merge)",0.) ; if (SCALAR_ABS (Bz [p] - Ex [2*p+1]) > 1e-15) error ("Ez (merge)",0.) ; } } /* convert C (triplet) to E (col) no Map */ status = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(Cx,DNULL), Ep, Ei, CARG(Ex,DNULL), noMap) ; if (status != UMFPACK_OK) error ("t->col failed (1)",0.) ; /* compare E and B, they should be identical */ if (nz != Ep [n]) error ("E nz (10)",0.) ; for (j = 0 ; j < n ; j++) { if (Bp [j] != Ep [j]) error ("Ep j",0.) ; if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ; for (p = Bp [j] ; p < Bp [j+1] ; p++) { if (Bi [p] != Ei [p]) error ("Ei",0.) ; if (SCALAR_ABS (Bx [p] - Ex [2*p ]) > 1e-15) error ("Ex (merge)",0.) ; if (SCALAR_ABS (Bz [p] - Ex [2*p+1]) > 1e-15) error ("Ez (merge)",0.) ; } } /* jumble C */ for (k = 0 ; k < nz ; k++) { s = irand (nz) ; /* swap positions s and k */ t = Ci [k] ; Ci [k] = Ci [s] ; Ci [s] = t ; t = Cj [k] ; Cj [k] = Cj [s] ; Cj [s] = t ; z = Cx [2*k ] ; Cx [2*k ] = Cx [2*s ] ; Cx [2*s ] = z ; z = Cx [2*k+1] ; Cx [2*k+1] = Cx [2*s+1] ; Cx [2*s+1] = z ; } /* add duplicates to C, but preserve pattern and values */ for (k = nz ; k < 2*nz ; k++) { /* add a duplicate */ s = irand (k) ; Ci [k] = Ci [s] ; Cj [k] = Cj [s] ; z = Cx [2*s] ; Cx [2*s] = z/2 ; Cx [2*k] = z/2 ; z = Cx [2*s+1] ; Cx [2*s+1] = z/2 ; Cx [2*k+1] = z/2 ; } if (prl > 2) printf ("\ntest c->t,t->c: ") ; status = UMFPACK_report_triplet (n, n, 2*nz, Ci, Cj, CARG(Cx,DNULL), Control) ; if (status != UMFPACK_OK) error ("report col->triplet",0.) ; /* convert C (triplet) to E (col) */ status = UMFPACK_triplet_to_col (n, n, 2*nz, Ci, Cj, CARG(Cx,DNULL), Ep, Ei, CARG(Ex,DNULL), noMap) ; if (status != UMFPACK_OK) error ("t->col failed",0.) ; /* compare E and B, they should be identical */ if (nz != Ep [n]) error ("E nz (11)",0.) ; for (j = 0 ; j < n ; j++) { if (Bp [j] != Ep [j]) error ("Ep j",0.) ; if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ; for (p = Bp [j] ; p < Bp [j+1] ; p++) { if (Bi [p] != Ei [p]) error ("Ei",0.) ; if (SCALAR_ABS (Bx [p] - Ex [2*p ]) > 1e-15) error ("Ex (merge)",0.) ; if (SCALAR_ABS (Bz [p] - Ex [2*p+1]) > 1e-15) error ("Ez (merge)",0.) ; } } /* convert C (triplet) to E (col) */ status = UMFPACK_triplet_to_col (n, n, 2*nz, Ci, Cj, CARG(Cx,DNULL), Ep, Ei, CARG(Ex,DNULL), Map) ; if (status != UMFPACK_OK) error ("t->col failed",0.) ; /* compare E and B, they should be identical */ if (nz != Ep [n]) error ("E nz (12)",0.) ; for (j = 0 ; j < n ; j++) { if (Bp [j] != Ep [j]) error ("Ep j",0.) ; if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ; for (p = Bp [j] ; p < Bp [j+1] ; p++) { if (Bi [p] != Ei [p]) error ("Ei",0.) ; if (SCALAR_ABS (Bx [p] - Ex [2*p ]) > 1e-15) error ("Ex (merge)",0.) ; if (SCALAR_ABS (Bz [p] - Ex [2*p+1]) > 1e-15) error ("Ez (merge)",0.) ; } } /* convert C (triplet) to E (col), using Map */ for (p = 0 ; p < Ep [n] ; p++) { Ex [2*p ] = 0. ; Ex [2*p+1] = 0. ; } for (k = 0 ; k < 2*nz ; k++) { p = Map [k] ; i = Ci [k] ; j = Cj [k] ; if (i != Ei [p]) error ("Map", 0.) ; if (!(Ep [j] <= p && p < Ep [j+1])) error ("Map Ep", 0.) ; Ex [2*p ] += Cx [2*k ] ; Ex [2*p+1] += Cx [2*k+1] ; } /* compare E and B, they should be identical */ for (j = 0 ; j < n ; j++) { for (p = Bp [j] ; p < Bp [j+1] ; p++) { z = SCALAR_ABS (Bx [p] - Ex [2*p ]) ; if (z > 1e-15) error ("Ex merged",z) ; z = SCALAR_ABS (Bz [p] - Ex [2*p+1]) ; if (z > 1e-15) error ("Ez merged 7",z) ; } } #endif printf ("\n =============== test OK\n\n") ; free (Map) ; /* ] */ free (Ex) ; /* ] */ free (Ei) ; /* ] */ free (Ep) ; /* ] */ free (Cx) ; /* ] */ free (Cj) ; /* ] */ free (Ci) ; /* ] */ } /* ========================================================================== */ /* matgen_compaction: generate a matrix to test umf_symbolic compaction */ /* ========================================================================== */ static void matgen_compaction ( Int n, Int **Ap, Int **Ai, double **Ax, double **Az ) { Int nz, *Bp, *Bi, *Ti, *Tj, k, i, j, prl, status ; double *Bx, *Tx, *Bz, *Tz, Control [UMFPACK_INFO] ; prl = Control ? Control [UMFPACK_PRL] : UMFPACK_DEFAULT_PRL ; UMFPACK_defaults (Control) ; UMFPACK_report_control (Control) ; nz = 5*n ; /* allocate Bp, Bi, and Bx - but do not free them */ Bp = (Int *) malloc ((n+1) * sizeof (Int)) ; Bi = (Int *) malloc (nz * sizeof (Int)) ; Bx = (double *) malloc (nz * sizeof (double)) ; Bz = (double *) calloc (nz , sizeof (double)) ; Ti = (Int *) malloc (nz * sizeof (Int)) ; /* [ */ Tj = (Int *) malloc (nz * sizeof (Int)) ; /* [ */ Tx = (double *) malloc (nz * sizeof (double)) ; /* [ */ Tz = (double *) calloc (nz , sizeof (double)) ; /* [ */ if (!Bp || !Bi || !Bx || !Ti || !Tj || !Tx) error ("out of memory (12)",0.) ; if (!Bz || !Tz) error ("out of mery",0.) ; k = 0 ; for (i = 0 ; i < n ; i++) { if (i > 0) { Ti [k] = i ; Tj [k] = i-1 ; Tx [k] = xrand ( ) ; #ifdef COMPLEX Tz [k] = xrand ( ) ; #else Tz [k] = 0. ; #endif k++ ; } Ti [k] = i ; Tj [k] = i ; Tx [k] = xrand ( ) ; k++ ; if (i < n-1) { Ti [k] = i ; Tj [k] = i+1 ; Tx [k] = xrand ( ) ; #ifdef COMPLEX Tz [k] = xrand ( ) ; #else Tz [k] = 0. ; #endif k++ ; } } for (j = 0 ; j < n ; j += 2) { Ti [k] = 0 ; Tj [k] = j ; Tx [k] = xrand ( ) ; #ifdef COMPLEX Tz [k] = xrand ( ) ; #else Tz [k] = 0. ; #endif k++ ; } for (j = 1 ; j < n ; j += 2) { Ti [k] = 1 ; Tj [k] = j ; Tx [k] = xrand ( ) ; #ifdef COMPLEX Tz [k] = xrand ( ) ; #else Tz [k] = 0. ; #endif k++ ; } if (prl > 2) printf ("\nmatgen_compact: ") ; status = UMFPACK_report_triplet (n, n, k, Ti, Tj, CARG(Tx,Tz), Control) ; if (status != UMFPACK_OK) error ("bad triplet report",0.) ; /* convert to column form */ status = UMFPACK_triplet_to_col (n, n, k, Ti, Tj, CARG(Tx,Tz), Bp, Bi, CARG(Bx,Bz), (Int *) NULL) ; if (status != UMFPACK_OK) error ("matgen_compact triplet_to_col failed",0.) ; if (prl > 2) printf ("\nmatgen_compact: ") ; status = UMFPACK_report_matrix (n, n, Bp, Bi, CARG(Bx,Bz), 1, Control) ; if (status != UMFPACK_OK) error ("bad A matget sparse",0.) ; /* return the allocated column-form */ *Ap = Bp ; *Ai = Bi ; *Ax = Bx ; *Az = Bz ; free (Tz) ; /* ] */ free (Tx) ; /* ] */ free (Tj) ; /* ] */ free (Ti) ; /* ] */ } /* ========================================================================== */ /* matgen_sparse: generate a matrix with random pattern */ /* ========================================================================== */ /* allocates Ap, Ai, Ax, and Az */ static void matgen_sparse ( Int n, Int s, /* s random entries, and one more in each row and column */ Int ndrow, /* plus ndrow dense rows, each of degree rdeg */ Int rdeg, Int ndcol, /* plus ndcol dense cols, each of degree cdeg */ Int cdeg, Int **Ap, Int **Ai, double **Ax, double **Az, Int prl, Int has_nans ) { Int nz, *Bp, *Bi, *Ti, *Tj, k, i, j, j1, i1, k1, *P, status, *Map, p, *Cp, *Ci, *noMap ; double *Bx, *Tx, *Bz, *Tz, Control [UMFPACK_CONTROL], xnan, xinf, x, *Txx, *Cx ; noMap = (Int *) NULL ; if (has_nans) { xnan = divide (0., 0.) ; xinf = divide (1., 0.) ; } UMFPACK_defaults (Control) ; Control [UMFPACK_PRL] = prl ; UMFPACK_report_control (Control) ; nz = s + n + rdeg*ndrow + cdeg*ndcol ; if (nz == 0) nz++ ; /* allocate Bp, Bi, and Bx - but do not free them */ Bp = (Int *) malloc ((n+1) * sizeof (Int)) ; Bi = (Int *) malloc ((nz+1) * sizeof (Int)) ; Bx = (double *) malloc ((nz+1) * sizeof (double)) ; Bz = (double *) calloc ((nz+1) , sizeof (double)) ; Ti = (Int *) malloc (nz * sizeof (Int)) ; /* [ */ Tj = (Int *) malloc (nz * sizeof (Int)) ; /* [ */ Tx = (double *) malloc (nz * sizeof (double)) ; /* [ */ Tz = (double *) calloc (nz , sizeof (double)) ; /* [ */ P = (Int *) malloc (n * sizeof (Int)) ; /* [ */ Map = (Int *) malloc (nz * sizeof (Int)) ; /* [ */ Txx = (double *) calloc (2*(nz+1) , sizeof (double)) ; /* [ */ Cp = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ Ci = (Int *) malloc ((nz+1) * sizeof (Int)) ; /* [ */ Cx = (double *) calloc (2*(nz+1) , sizeof (double)) ; /* [ */ if (!Bp || !Bi || !Bx || !Ti || !Tj || !Tx || !P) error ("out of memory (13)",0.) ; if (!Bz || !Tz) error ("out of m",0.) ; if (!Txx || !Cx || !Cp || !Ci) error ("out of mem xx",0.) ; for (k = 0 ; k < s ; k++) { Ti [k] = irand (n) ; Tj [k] = irand (n) ; if (has_nans) { x = xrand ( ) ; Tx [k] = (x > 0.8) ? ((x > 0.9) ? xnan : xinf) : (2*x-1) ; #ifdef COMPLEX x = xrand ( ) ; Tz [k] = (x > 0.8) ? ((x > 0.9) ? xnan : xinf) : (2*x-1) ; #else Tz [k] = 0. ; #endif } else { Tx [k] = 2.0 * (xrand ( ) - 1.0) ; #ifdef COMPLEX Tz [k] = 2.0 * (xrand ( ) - 1.0) ; #else Tz [k] = 0. ; #endif } } /* beef up each column and row */ randperm (n, P) ; for (i = 0 ; i < n ; i++) { Ti [k] = i ; Tj [k] = P [i] ; Tx [k] = xrand ( ) ; #ifdef COMPLEX Tz [k] = xrand ( ) ; #else Tz [k] = 0. ; #endif k++ ; } /* add ndrow rows of degree rdeg */ for (i1 = 0 ; i1 < ndrow ; i1++) { i = irand (n) ; for (k1 = 0 ; k1 < rdeg ; k1++) { Ti [k] = i ; Tj [k] = irand (n) ; Tx [k] = 0.1 * xrand ( ) ; #ifdef COMPLEX Tz [k] = 0.1 * xrand ( ) ; #else Tz [k] = 0. ; #endif k++ ; } } /* add ndcol rows of degree cdeg */ for (j1 = 0 ; j1 < ndcol ; j1++) { j = irand (n) ; for (k1 = 0 ; k1 < cdeg ; k1++) { Ti [k] = irand (n) ; Tj [k] = j ; Tx [k] = 0.1 * xrand ( ) ; #ifdef COMPLEX Tz [k] = 0.1 * xrand ( ) ; #else Tz [k] = 0. ; #endif k++ ; } } if (k != nz) error ("matgen_sparse error",0.) ; if (prl > 2) printf ("\nmatgen_sparse: ") ; status = UMFPACK_report_triplet (n, n, k, Ti, Tj, CARG(Tx,Tz), Control) ; if (status != UMFPACK_OK) error ("bad triplet report",0.) ; /* convert to column form */ status = UMFPACK_triplet_to_col (n, n, k, Ti, Tj, CARG(Tx,Tz), Bp, Bi, CARG(Bx,Bz), Map) ; if (status != UMFPACK_OK) error ("matgen_sparse triplet_to_col failed",0.) ; /* convert to column form, no values and no map */ status = UMFPACK_triplet_to_col (n, n, k, Ti, Tj, CARG(DNULL,DNULL), Cp, Ci, CARG(DNULL,DNULL), noMap) ; if (status != UMFPACK_OK) error ("matgen_sparse triplet_to_col failed",0.) ; /* compare C and B, they should be identical */ for (j = 0 ; j < n ; j++) { if (Bp [j] != Cp [j]) error ("Cp j",0.) ; if (Bp [j+1] != Cp [j+1]) error ("Cp j",0.) ; for (p = Bp [j] ; p < Bp [j+1] ; p++) { if (Bi [p] != Ci [p]) error ("Ci",0.) ; } } /* convert to column form, no values and with map */ status = UMFPACK_triplet_to_col (n, n, k, Ti, Tj, CARG(DNULL,DNULL), Cp, Ci, CARG(DNULL,DNULL), Map) ; if (status != UMFPACK_OK) error ("matgen_sparse triplet_to_col failed",0.) ; /* compare C and B, they should be identical */ for (j = 0 ; j < n ; j++) { if (Bp [j] != Cp [j]) error ("Cp j",0.) ; if (Bp [j+1] != Cp [j+1]) error ("Cp j",0.) ; for (p = Bp [j] ; p < Bp [j+1] ; p++) { if (Bi [p] != Ci [p]) error ("Ci",0.) ; } } #ifdef COMPLEX /* test with merged case too */ for (p = 0 ; p < k ; p++) { Txx [2*p ] = Tx [p] ; Txx [2*p+1] = Tz [p] ; } /* convert to column form, no map */ status = UMFPACK_triplet_to_col (n, n, k, Ti, Tj, CARG(Txx,DNULL), Cp, Ci, CARG(Cx,DNULL), noMap) ; if (status != UMFPACK_OK) error ("matgen_sparse triplet_to_col failed",0.) ; /* compare C and B, they should be identical */ for (j = 0 ; j < n ; j++) { if (Bp [j] != Cp [j]) error ("Cp j",0.) ; if (Bp [j+1] != Cp [j+1]) error ("Cp j",0.) ; for (p = Bp [j] ; p < Bp [j+1] ; p++) { if (Bi [p] != Ci [p]) error ("Ci",0.) ; if (SCALAR_ABS (Bx [p] - Cx [2*p ]) > 1e-15) error ("Cx",0.) ; if (SCALAR_ABS (Bz [p] - Cx [2*p+1]) > 1e-15) error ("Cz (1)",0.) ; } } /* convert to column form */ status = UMFPACK_triplet_to_col (n, n, k, Ti, Tj, CARG(Txx,DNULL), Cp, Ci, CARG(Cx,DNULL), Map) ; if (status != UMFPACK_OK) error ("matgen_sparse triplet_to_col failed",0.) ; /* compare C and B, they should be identical */ for (j = 0 ; j < n ; j++) { if (Bp [j] != Cp [j]) error ("Cp j",0.) ; if (Bp [j+1] != Cp [j+1]) error ("Cp j",0.) ; for (p = Bp [j] ; p < Bp [j+1] ; p++) { if (Bi [p] != Ci [p]) error ("Ci",0.) ; if (SCALAR_ABS (Bx [p] - Cx [2*p ]) > 1e-15) error ("Cx",0.) ; if (SCALAR_ABS (Bz [p] - Cx [2*p+1]) > 1e-15) error ("Cz (1)",0.) ; } } #endif if (prl > 2) printf ("\nmatgen_sparse: ") ; status = UMFPACK_report_matrix (n, n, Bp, Bi, CARG(Bx,Bz), 1, Control) ; if (status != UMFPACK_OK) error ("bad A matgen sparse",0.) ; /* check the Map */ for (k = 0 ; k < nz ; k++) { p = Map [k] ; i = Ti [k] ; j = Tj [k] ; if (i != Bi [p]) error ("Map Bi", 0.) ; if (!(Bp [j] <= p && p < Bp [j+1])) error ("Map Bp", 0.) ; } /* test triplet->col and col->triplet */ test_col (n, Bp, Bi, Bx,Bz, prl) ; /* return the allocated column-form */ *Ap = Bp ; *Ai = Bi ; *Ax = Bx ; *Az = Bz ; free (Cx) ; /* ] */ free (Ci) ; /* ] */ free (Cp) ; /* ] */ free (Txx) ; /* ] */ free (Map) ; /* ] */ free (P) ; /* ] */ free (Tz) ; /* ] */ free (Tx) ; /* ] */ free (Tj) ; /* ] */ free (Ti) ; /* ] */ } /* ========================================================================== */ /* matgen_transpose: B = A(P,Q)', where P and Q are random */ /* ========================================================================== */ static void matgen_transpose ( Int n, Int Ap [ ], Int Ai [ ], double Ax [ ], double Az [ ], Int **Bp, Int **Bi, double **Bx, double **Bz ) { Int nz, *P, *Q, *Cp, *Ci, status ; double *Cx, *Cz ; #ifdef DEBUGGING double Control [UMFPACK_CONTROL] ; #endif nz = Ap [n] ; P = (Int *) malloc (n * sizeof (Int)) ; /* [ */ Q = (Int *) malloc (n * sizeof (Int)) ; /* [ */ Cp = (Int *) malloc ((n+1) * sizeof (Int)) ; Ci = (Int *) malloc ((nz+1) * sizeof (Int)) ; Cx = (double *) malloc ((nz+1) * sizeof (double)) ; Cz = (double *) calloc ((nz+1) , sizeof (double)) ; if (!P || !Q || !Bp || !Bi || !Bx) error ("out of memory (14)",0.) ; if (!Cz) error ("out mem", 0.) ; randperm (n, P) ; randperm (n, Q) ; #ifdef DEBUGGING UMFPACK_defaults (Control) ; Control [UMFPACK_PRL] = 5 ; printf ("\nA: ") ; status = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Control) ; if (status != UMFPACK_OK) error ("bad A",0.) ; printf ("Random P: ") ; UMFPACK_report_perm (n, P, Control) ; if (status != UMFPACK_OK) error ("bad random P",0.) ; printf ("Random Q: ") ; status = UMFPACK_report_perm (n, Q, Control) ; if (status != UMFPACK_OK) error ("bad random Q",0.) ; #endif /* do complex conjugate transpose */ status = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), P, Q, Cp, Ci, CARG(Cx,Cz) C1ARG(1)) ; if (status != UMFPACK_OK) error ("transpose failed",0.) ; #ifdef DEBUGGING printf ("\nC: ") ; status = UMFPACK_report_matrix (n, n, Cp, Ci, CARG(Cx,Cz), 1, Control) ; if (status != UMFPACK_OK) error ("bad C",0.) ; #endif /* do not free Cp, Ci, and Cx */ *Bp = Cp ; *Bi = Ci ; *Bx = Cx ; *Bz = Cz ; free (P) ; /* ] */ free (Q) ; /* ] */ } /* ========================================================================== */ /* matgen_file: read a (1-based) matrix and a Qinit from a file */ /* ========================================================================== */ /* File syntax: * 1st line: nrows ncols nnz isreal * next nnz lines: i j x ... or ... i j xreal ximag * next ncols lines: Qk * one line determinant (real and imag. part if A is complex) * last line determinant of real part of A only */ static void matgen_file ( char *filename, Int *n_row, Int *n_col, Int **Ap, Int **Ai, double **Ax, double **Az, Int **Qinit, Int prl, double *det_x, double *det_z ) { FILE *f ; Int i, j, k, *Ti, *Tj, nr, nc, nz, *Bp, *Bi, *Q, status, isreal, nz1, n ; double x, *Tx, *Bx, *Tz, *Bz, ximag, Control [UMFPACK_CONTROL], d_x, d_z, d_real ; printf ("\nFile: %s\n", filename) ; f = fopen (filename, "r") ; if (!f) error ("bad file", 0.) ; fscanf (f, ""ID" "ID" "ID" "ID"\n", &nr, &nc, &nz, &isreal) ; n = MAX (nr, nc) ; n = MAX (n,1) ; nz1 = MAX (nz,1) ; Ti = (Int *) malloc (nz1 * sizeof (Int)) ; /* [ */ Tj = (Int *) malloc (nz1 * sizeof (Int)) ; /* [ */ Tx = (double *) malloc (nz1 * sizeof (double)) ; /* [ */ Tz = (double *) calloc (nz1 , sizeof (double)) ; /* [ */ /* allocate Bp, Bi, Bx, and Q - but do not free them */ Bp = (Int *) malloc ((n+1) * sizeof (Int)) ; Bi = (Int *) malloc (nz1 * sizeof (Int)) ; Bx = (double *) malloc (nz1 * sizeof (double)) ; Q = (Int *) malloc (n * sizeof (Int)) ; Bz = (double *) calloc (nz1 , sizeof (double)) ; for (k = 0 ; k < nz ; k++) { if (isreal) { fscanf (f, ""ID" "ID" %lg\n", &i, &j, &x) ; ximag = 0. ; } else { fscanf (f, ""ID" "ID" %lg %lg\n", &i, &j, &x, &ximag) ; } Ti [k] = i-1 ; /* convert to 0-based */ Tj [k] = j-1 ; Tx [k] = x ; #ifdef COMPLEX Tz [k] = ximag ; #else /* the file may have a complex part, but set it to zero */ Tz [k] = 0. ; #endif } for (k = 0 ; k < nc ; k++) { fscanf (f, ""ID"\n", &i) ; Q [k] = i-1 ; /* convert to 0-based */ } if (isreal) { fscanf (f, "%lg\n", &d_x) ; d_z = 0 ; } else { fscanf (f, "%lg %lg\n", &d_x, &d_z) ; } fscanf (f, "%lg\n", &d_real) ; printf ("%s det: %g + (%g)i, real(A): %g\n", filename, d_x, d_z, d_real) ; #ifdef COMPLEX *det_x = d_x ; *det_z = d_z ; #else /* imaginary part of matrix is ignored */ *det_x = d_real ; *det_z = 0 ; #endif UMFPACK_defaults (Control) ; Control [UMFPACK_PRL] = prl ; if (prl > 2) printf ("\nmatgen_file: ") ; status = UMFPACK_report_triplet (nr, nc, nz, Ti, Tj, CARG(Tx,Tz), Control) ; if (status != UMFPACK_OK) error ("bad triplet report",0.) ; /* convert to column form */ status = UMFPACK_triplet_to_col (nr, nc, nz, Ti, Tj, CARG(Tx,Tz), Bp, Bi, CARG(Bx,Bz), (Int *) NULL) ; if (status != UMFPACK_OK) error ("matgen_file triplet_to_col failed",0.) ; if (prl > 2) printf ("\nmatgen_file: ") ; status = UMFPACK_report_matrix (nr, nc, Bp, Bi, CARG(Bx,Bz), 1, Control) ; if (status != UMFPACK_OK) error ("bad A matgen_file",0.) ; /* return the allocated column-form */ *n_row = nr ; *n_col = nc ; *Ap = Bp ; *Ai = Bi ; *Ax = Bx ; *Az = Bz ; *Qinit = Q ; free (Tz) ; /* ] */ free (Tx) ; /* ] */ free (Tj) ; /* ] */ free (Ti) ; /* ] */ fclose (f) ; } /* ========================================================================== */ /* matgen_arrow: create an arrowhead matrix */ /* ========================================================================== */ static Int matgen_arrow ( Int n, Int **Ap, Int **Ai, Int **Q ) { Int nz, *Bp, *Bi, i, j, p, *Qp ; nz = n + 2*(n-1) ; printf ("matgen_arrow: n = "ID" nz = "ID"\n", n, nz) ; Bp = (Int *) malloc ((n+1) * sizeof (Int)) ; Bi = (Int *) malloc (nz * sizeof (Int)) ; Qp = (Int *) malloc (n * sizeof (Int)) ; if (!Bp || !Bi || !Qp) { free (Bp) ; free (Bi) ; free (Qp) ; printf ("arrow failed\n") ; return (FALSE) ; } /* row and column 0, and diagonal, are dense */ /* column 0 */ p = 0 ; Bp [0] = p ; for (i = 0 ; i < n ; i++) { Bi [p] = i ; Qp [p] = i ; p++ ; } /* columns 1 to n-1 */ for (j = 1 ; j < n ; j++) { Bp [j] = p ; Bi [p] = 0 ; /* row 0 */ p++ ; Bi [p] = j ; /* row j (diagonal) */ } Bp [n] = p ; *Ap = Bp ; *Ai = Bi ; *Q = Qp ; printf ("matgen_arrow: n = "ID" nz = "ID" done.\n", n, nz) ; return (TRUE) ; } /* ========================================================================== */ /* do_and_free: do a matrix, its random transpose, and then free it */ /* ========================================================================== */ static double do_and_free ( Int n, Int Ap [ ], Int Ai [ ], double Ax [ ], double Az [ ], double Controls [UMFPACK_CONTROL][1000], Int Ncontrols [UMFPACK_CONTROL], Int MemControl [6], Int do_dense ) { Int *Bp, *Bi ; double *Bx, *Bz, rnorm1, rnorm2 ; /* A */ rnorm1 = do_matrix (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemControl, do_dense) ; /* B = A (P,Q), P and Q random */ matgen_transpose (n, Ap, Ai, Ax, Az, &Bp, &Bi, &Bx, &Bz) ; free (Ap) ; free (Ai) ; free (Ax) ; free (Az) ; rnorm2 = do_matrix (n, Bp, Bi, Bx, Bz, Controls, Ncontrols, MemControl, do_dense) ; free (Bp) ; free (Bi) ; free (Bx) ; free (Bz) ; return (MAX (rnorm1, rnorm2)) ; } /* ========================================================================== */ /* AMD */ /* ========================================================================== */ static int do_amd ( Int n, Int Ap [], Int Ai [], Int P [] ) { #if 0 #ifndef NDEBUG FILE *f ; f = fopen ("apx.m", "w") ; Int j, p, nz ; if (Ap && Ai && P) { nz = Ap [n] ; fprintf (f, "ApX = [ ") ; for (j = 0 ; j <= n ; j++) fprintf (f, ID" ", Ap [j]) ; fprintf (f, "] ; \n nzx = "ID" ;\n Ax = [\n", nz) ; for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { fprintf (f, ID" "ID" 1\n", 1+j, 1+Ai [p]) ; } } fprintf (f, ID" "ID" 0] ;\n", n, n) ; fclose (f) ; } #endif #endif #if (defined (DINT) || defined (ZINT)) return (amd_order (n, Ap, Ai, P, DNULL, DNULL)) ; #else return (amd_l_order (n, Ap, Ai, P, DNULL, DNULL)) ; #endif } static int do_amd_transpose ( Int n, Int Ap [], Int Ai [], Int Rp [], Int Ri [] ) { Int *W, *Flag ; #if (defined (DINT) || defined (ZINT)) if (amd_valid (n, n, Ap, Ai) < AMD_OK || !Ri || !Rp) { return (AMD_INVALID) ; } #else if (amd_l_valid (n, n, Ap, Ai) < AMD_OK || !Ri || !Rp) { return (AMD_INVALID) ; } #endif W = amd_malloc (MAX (n,1) * sizeof (Int)) ; Flag = amd_malloc (MAX (n,1) * sizeof (Int)) ; if (!W || !Flag) { amd_free (W) ; amd_free (Flag) ; return (AMD_OUT_OF_MEMORY) ; } #if (defined (DINT) || defined (ZINT)) amd_preprocess (n, Ap, Ai, Rp, Ri, W, Flag) ; #else amd_l_preprocess (n, Ap, Ai, Rp, Ri, W, Flag) ; #endif amd_free (W) ; amd_free (Flag) ; return (AMD_OK) ; } /* ========================================================================== */ /* do_file: read a matrix from a matrix and call do_many */ /* ========================================================================== */ static double do_file ( char *filename, Int prl, Int MemControl [6] ) { Int n_row, n_col, *Ap, *Ai, *Qinit, n, *P, s, *W, scale, row, col, p, strategy, fixQ ; double *Ax, *Az, Control [UMFPACK_CONTROL], *b, rnorm, *bz, maxrnorm, bad, det_x, det_z ; UMFPACK_defaults (Control) ; Control [UMFPACK_PRL] = prl ; maxrnorm = 0 ; /* get the matrix A and preordering Qinit */ matgen_file (filename, &n_row, &n_col, &Ap, &Ai, &Ax, &Az, &Qinit, prl, &det_x, &det_z) ; /* [[[[[ */ check_tol = SCALAR_ABS (det_x < 1e100) ; /* test amd, on A and A transpose */ if (n_row == n_col) { Int k, *Rp, *Ri ; P = (Int *) malloc (n_row * sizeof (Int)) ; /* [ */ W = (Int *) malloc (n_row * sizeof (Int)) ; /* [ */ Rp = (Int *) malloc ((n_row+1) * sizeof (Int)) ; /* [ */ Ri = (Int *) malloc ((Ap [n_row]) * sizeof (Int)) ; /* [ */ s = do_amd (n_row, Ap, Ai, P) ; if (s != AMD_OK) error ("amd2", (double) s) ; s = UMF_report_perm (n_row, P, W, 3, 0) ; if (s != UMFPACK_OK) error ("amd3", (double) s) ; s = do_amd_transpose (n_row, Ap, Ai, Rp, Ri) ; if (s != AMD_OK) error ("amd4", (double) s) ; s = do_amd (n_row, Rp, Ri, P) ; if (s != AMD_OK) error ("amd5", (double) s) ; s = UMF_report_perm (n_row, P, W, 3, 0) ; if (s != UMFPACK_OK) error ("amd6", (double) s) ; free (Ri) ; /* ] */ free (Rp) ; /* ] */ free (W) ; /* ] */ free (P) ; /* ] */ } /* do the matrix */ n = MAX (n_row, n_col) ; n = MAX (n,1) ; b = (double *) calloc (n, sizeof (double)) ; /* [ */ bz= (double *) calloc (n, sizeof (double)) ; /* [ */ if (n_row == n_col) { bgen (n, Ap, Ai, Ax,Az, b,bz) ; } if (prl == 5 && MAX (n_row, n_col) > 600) { /* do nothing */ ; } else if (prl >= 3 || MAX (n_row, n_col) > 15) { /* quick test */ printf ("Control strategy auto Q prl "ID"\n", prl) ; printf ("quick test..\n") ; rnorm = do_many (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemControl, TRUE, TRUE, det_x, det_z) ; printf ("quick test.. done\n") ; printf ("Control strategy auto Q prl "ID" :: rnorm %g\n", prl, rnorm) ; if (check_tol) { if (rnorm >= TOL) error ("bad do_file", rnorm) ; maxrnorm = rnorm ; } /* quick test - no aggressive absorption */ printf ("Control strategy auto Q prl "ID" no aggressive\n", prl) ; Control [UMFPACK_AGGRESSIVE] = 0 ; rnorm = do_many (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemControl, TRUE, TRUE, det_x, det_z) ; printf ("Control strategy auto Q prl "ID" no aggressive:: rnorm %g\n", prl, rnorm) ; if (check_tol) { if (rnorm >= TOL) error ("bad do_file", rnorm) ; maxrnorm = rnorm ; } /* quick test - symmetric strategy, no aggressive absorption */ printf ("Control strategy auto Q prl "ID" no aggressive, symmetric\n", prl) ; Control [UMFPACK_STRATEGY] = UMFPACK_STRATEGY_SYMMETRIC ; UMFPACK_report_control (Control) ; rnorm = do_many (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemControl, TRUE, TRUE, det_x, det_z) ; printf ("Control strategy auto Q prl "ID" no aggressive, symmetric:: rnorm %g\n", prl, rnorm) ; if (check_tol) { if (rnorm >= TOL) error ("bad do_file", rnorm) ; maxrnorm = rnorm ; } } else { /* full test */ for (strategy = -1 ; strategy <= UMFPACK_STRATEGY_SYMMETRIC ; strategy ++) { Control [UMFPACK_STRATEGY] = strategy ; if (strategy == UMFPACK_STRATEGY_SYMMETRIC) { if (n < 5) UMFPACK_report_control (Control) ; for (fixQ = -1 ; fixQ <= 1 ; fixQ++) { Control [UMFPACK_FIXQ] = fixQ ; for (scale = -1 ; scale <= UMFPACK_SCALE_MAX ; scale++) { Control [UMFPACK_SCALE] = scale ; printf ("Control strategy "ID" "ID" noQ prl "ID" scale "ID"\n", strategy, fixQ, prl, scale) ; rnorm = do_many (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, INULL, MemControl, TRUE, TRUE, det_x, det_z) ; printf ("Control strategy "ID" "ID" noQ prl "ID" scale "ID" :: rnorm %g\n", strategy, fixQ, prl, scale, rnorm) ; if (check_tol) { maxrnorm = MAX (maxrnorm, rnorm) ; if (rnorm >= TOL) error ("bad do_file", rnorm) ; } } printf ("Control strategy "ID" "ID" Q\n", strategy, fixQ) ; rnorm = do_many (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemControl, TRUE, TRUE, det_x, det_z) ; printf ("Control strategy "ID" "ID" Q :: rnorm %g\n", strategy, fixQ, rnorm) ; if (check_tol) { maxrnorm = MAX (maxrnorm, rnorm) ; if (rnorm >= TOL) error ("bad do_file", rnorm) ; } } Control [UMFPACK_FIXQ] = UMFPACK_DEFAULT_FIXQ ; } else { printf ("Control strategy "ID" Q prl "ID"\n", strategy, prl) ; rnorm = do_many (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemControl, TRUE, TRUE, det_x, det_z) ; printf ("Control strategy "ID" Q prl "ID" :: rnorm %g\n", strategy, prl, rnorm) ; if (check_tol) { maxrnorm = MAX (maxrnorm, rnorm) ; if (rnorm >= TOL) error ("bad do_file", rnorm) ; } printf ("Control strategy "ID" noQ\n", strategy) ; rnorm = do_many (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, INULL, MemControl, TRUE, TRUE, det_x, det_z) ; printf ("Control strategy "ID" noQ :: rnorm %g\n", strategy, rnorm) ; if (check_tol) { maxrnorm = MAX (maxrnorm, rnorm) ; if (rnorm >= TOL) error ("bad do_file", rnorm) ; } #ifdef UMFPACK_DROPTOL Control [UMFPACK_DROPTOL] = 1e-25 ; printf ("Control strategy "ID" noQ droptol 1e-25\n", strategy) ; rnorm = do_many (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, INULL, MemControl, TRUE, TRUE, det_x, det_z) ; printf ("Control strategy "ID" noQ droptol 1e-25 :: rnorm %g\n", strategy, rnorm) ; if (check_tol) { maxrnorm = MAX (maxrnorm, rnorm) ; if (rnorm >= TOL) error ("bad do_file", rnorm) ; } Control [UMFPACK_DROPTOL] = 0 ; #endif } } } UMFPACK_defaults (Control) ; Control [UMFPACK_PRL] = 3 ; /* scale row 0 */ for (col = 0 ; col < n_col ; col++) { for (p = Ap [col] ; p < Ap [col+1] ; p++) { row = Ai [p] ; if (row == 0) { Ax [p] *= 1e-20 ; Az [p] *= 1e-20 ; } } } b [0] *= 1e-20 ; bz [0] *= 1e-20 ; printf ("Control defaults noQ tiny row 0\n") ; rnorm = do_many (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, INULL, MemControl, TRUE, TRUE, 1e-20*det_x, 1e-20*det_z) ; printf ("Control defaults noQ tiny row 0:: rnorm %g\n", rnorm) ; if (check_tol) { maxrnorm = MAX (maxrnorm, rnorm) ; if (rnorm >= TOL) error ("bad do_file", rnorm) ; } free (bz) ; /* ] */ free (b) ; /* ] */ free (Ap) ; /* ] */ free (Ai) ; /* ] */ free (Ax) ; /* ] */ free (Az) ; /* ] */ free (Qinit) ; /* ] */ check_tol = TRUE ; return (maxrnorm) ; } /* ========================================================================== */ /* main */ /* ========================================================================== */ #if 0 /* compile with -lefence and -DEFENCE */ #ifndef EXTERN #define EXTERN extern #endif EXTERN int EF_PROTECT_FREE ; EXTERN int EF_PROTECT_BELOW ; #endif int main (int argc, char **argv) { double *Lx, *Ux, *x, *Cx, *Bx, *Ax, *b, *Ax2, *Lz, *Uz, *xz, *Cz, *Bz, *Az, *bz,*Az2, rnorm, maxrnorm, *Con, Info [UMFPACK_INFO], *Wx, *Rs, xnan, xinf, ttt, Controls [UMFPACK_CONTROL][1000], Control [UMFPACK_CONTROL], alphas [ ] = {-1.0, 0.0, 0.1, 0.5, 10.}, *info, maxrnorm_shl0, rnorm_omega2, maxrnorm_arc130, det_x, det_z, Mx, Mz, Exp ; Int Ncontrols [UMFPACK_CONTROL], c, i, n, prl, *Qinit, *Qinit2, n1, *Ap, *Ai, *Aj, nz, *Ap2, *Ai2, p, j, d, s, s2, *Pinit, k, n2, *Map, *Lp, *Li, *P, *Q, *Up, *Ui, lnz, unz, nn, *Cp, *Ci, *Cj, *Bi, *Bp, *Bj, *Pa, *Front_npivots, *Front_parent, *Chain_start, *Chain_maxrows, *ip, *Chain_maxcols, nfr, nchains, nsparse_col, *Qtree, *Ptree, nnz, MemOK [6], MemBad [6], nnrow, nncol, nzud, n_row, n_col, n_row2, n_col2, scale, *Front_1strow, *Front_leftmostdesc, strategy, t, aggressive, *Pamd, mem1, mem2, do_recip ; void *Symbolic, *Numeric ; SymbolicType *Sym ; NumericType *Num ; DIR *dir ; struct dirent *direntp ; char filename [200] ; FILE *f ; /* turn off debugging */ { f = fopen ("debug.umf", "w") ; fprintf (f, "-45\n") ; fclose (f) ; } { f = fopen ("debug.amd", "w") ; fprintf (f, "-45\n") ; fclose (f) ; } #if 0 /* compile with -lefence */ EF_PROTECT_FREE = 0 ; /* 1 to test modifications to free'd memory */ EF_PROTECT_BELOW = 0 ; /* 1 to test modifications above an obj. */ #endif c = UMFPACK_PIVOT_TOLERANCE ; Controls [c][0] = UMFPACK_DEFAULT_PIVOT_TOLERANCE ; Ncontrols [c] = 1 ; c = UMFPACK_SCALE ; Controls [c][0] = UMFPACK_SCALE_SUM ; /* also the default */ Ncontrols [c] = 1 ; c = UMFPACK_BLOCK_SIZE ; Controls [c][0] = 32 ; Ncontrols [c] = 1 ; c = UMFPACK_ALLOC_INIT ; Controls [c][0] = 1.0 ; Ncontrols [c] = 1 ; c = UMFPACK_AMD_DENSE ; Controls [c][0] = UMFPACK_DEFAULT_AMD_DENSE ; Ncontrols [c] = 1 ; /* ---------------------------------------------------------------------- */ /* test malloc, realloc, and free */ /* ---------------------------------------------------------------------- */ P = (Int *) UMF_malloc (Int_MAX, 2) ; if (P) error ("should have failed\n", 0.) ; printf ("reallocing...\n") ; P = (Int *) UMF_realloc (P, 1, 4) ; if (!P) error ("should have succeeded\n", 0.) ; #if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG) if (UMF_malloc_count != 1) error ("should be 1", 0.) ; #endif printf ("ok here...\n") ; P = UMF_free (P) ; if (P) error ("should have free'd it\n", 0.) ; #if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG) if (UMF_malloc_count != 0) error ("should be 0", 0.) ; #endif xnan = divide (0., 0.) ; xinf = divide (1., 0.) ; /* ---------------------------------------------------------------------- */ /* malloc and realloc control */ /* ---------------------------------------------------------------------- */ MemOK [0] = -1 ; MemOK [1] = 0 ; MemOK [2] = 0 ; MemOK [3] = -1 ; MemOK [4] = 0 ; MemOK [5] = 0 ; /* malloc always succeeds */ umf_fail = -1 ; umf_fail_lo = 0 ; umf_fail_hi = 0 ; /* realloc always succeeds */ umf_realloc_fail = -1 ; umf_realloc_lo = 0 ; umf_realloc_hi = 0 ; UMFPACK_defaults (Control) ; maxrnorm_shl0 = 0.0 ; /* for shl0 only */ maxrnorm = 0.0 ; /* for all other matrices */ check_tol = TRUE ; /* ---------------------------------------------------------------------- */ printf ("load/save error handling tests:\n") ; /* load a bad symbolic object */ s = UMFPACK_load_symbolic (&Symbolic, "badsym.umf") ; if (s == UMFPACK_OK) { error ("load symbolic failed\n", 0.) ; } s = UMFPACK_load_symbolic (&Symbolic, "badsym2.umf") ; if (s == UMFPACK_OK) { error ("load symbolic failed (2)\n", 0.) ; } /* load a bad numeric object */ s = UMFPACK_load_numeric (&Numeric, "badnum.umf") ; if (s == UMFPACK_OK) { error ("load numeric failed\n", 0.) ; } s = UMFPACK_load_numeric (&Numeric, "badnum2.umf") ; if (s == UMFPACK_OK) { error ("load numeric failed (2)\n", 0.) ; } /* ---------------------------------------------------------------------- */ /* reset rand ( ) */ /* ---------------------------------------------------------------------- */ srand (1) ; /* ---------------------------------------------------------------------- */ /* test a tiny matrix */ /* ---------------------------------------------------------------------- */ n = 2 ; printf ("\n tiny\n") ; check_tol = TRUE ; matgen_dense (n, &Ap, &Ai, &Ax, &Az) ; rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 0) ; printf ("rnorm tiny %g\n", rnorm) ; if (rnorm > 1e-12) { error ("bad rnorm for tiny matrix", rnorm) ; } /* ---------------------------------------------------------------------- */ /* test a tiny matrix with a NaN in it */ /* ---------------------------------------------------------------------- */ c = UMFPACK_SCALE ; Controls [c][0] = UMFPACK_SCALE_SUM ; /* also the default */ Controls [c][1] = UMFPACK_SCALE_NONE ; Ncontrols [c] = 2 ; n = 2 ; printf ("\n tiny\n") ; check_tol = TRUE ; matgen_dense (n, &Ap, &Ai, &Ax, &Az) ; Ax [0] = xnan ; Az [0] = 0 ; rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 0) ; printf ("rnorm tiny %g with NaN\n", rnorm) ; n = 2 ; printf ("\n tiny\n") ; check_tol = TRUE ; matgen_dense (n, &Ap, &Ai, &Ax, &Az) ; Ax [1] = 1e-20 ; Az [1] = 0 ; Ax [2] = 2e-20 ; Az [2] = 0 ; Ax [3] = 3e-20 ; Az [3] = 0 ; rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 0) ; printf ("rnorm tiny %g with NaN and small row\n", rnorm) ; n = 2 ; printf ("\n tiny\n") ; check_tol = TRUE ; matgen_dense (n, &Ap, &Ai, &Ax, &Az) ; Ax [0] = 0 ; rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 0) ; printf ("rnorm tiny %g with small row\n", rnorm) ; c = UMFPACK_SCALE ; Controls [c][0] = UMFPACK_SCALE_SUM ; /* also the default */ Ncontrols [c] = 1 ; /* ---------------------------------------------------------------------- */ /* test omega2 */ /* ---------------------------------------------------------------------- */ srand (1) ; n = 500 ; printf ("\n omega 2 test\n") ; matgen_sparse (n, 2*n, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az, 0, 0) ; f = fopen ("A500", "w") ; fprintf (f, ID" "ID" 0 0\n", n, n) ; for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { fprintf (f, ID" "ID" %40.25e %40.25e\n", Ai [p], j, Ax [p], Az [p]) ; } } fclose (f) ; rnorm_omega2 = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 0) ; printf ("rnorm %g omega-2 test\n", rnorm_omega2) ; /* ---------------------------------------------------------------------- */ /* reset rand ( ) */ /* ---------------------------------------------------------------------- */ srand (1) ; /* this is not solved very accurately (about 1e-7) */ maxrnorm_shl0 = do_file ("TestMat/shl0", 4, MemOK) ; printf ("rnorm shl0 %10.4e\n", maxrnorm_shl0) ; /* this is not solved very accurately (about 1e-5, because of U'x=b) */ maxrnorm_arc130 = do_file ("TestMat/arc130", 4, MemOK) ; printf ("rnorm arc130 %10.4e\n", maxrnorm_arc130) ; /* ---------------------------------------------------------------------- */ /* test random sparse matrices */ /* ---------------------------------------------------------------------- */ n = 30 ; printf ("sparse %7d 4*n nz's", n) ; matgen_sparse (n, 4*n, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az, 1, 0) ; /* [[[[ */ rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 1) ; /* ]]]] */ maxrnorm = MAX (rnorm, maxrnorm) ; printf ("rnorm %10.4e %10.4e\n", rnorm, maxrnorm) ; /* ---------------------------------------------------------------------- */ /* reset rand ( ) */ /* ---------------------------------------------------------------------- */ srand (1) ; rnorm = do_file ("TestMat/matrix5", 5, MemOK) ; maxrnorm = MAX (rnorm, maxrnorm) ; printf ("rnorm matrix 5 %10.4e %10.4e\n", rnorm, maxrnorm) ; /* malloc always succeeds */ umf_fail = -1 ; umf_fail_lo = 0 ; umf_fail_hi = 0 ; /* realloc always fails */ umf_realloc_fail = 0 ; umf_realloc_lo = -9999999 ; umf_realloc_hi = 0 ; /* ---------------------------------------------------------------------- */ /* do all test matrices from TestMat directory */ /* ---------------------------------------------------------------------- */ /* quick tests */ prl = 1 ; matgen_file ("TestMat/matrix1", &n_row, &n_col, &Ap, &Ai, &Ax, &Az, &Qinit, prl, &det_x, &det_z) ; /* [[[[[ */ Control [UMFPACK_ALLOC_INIT] = -211 ; /* with no Qinit, out of memory in extend front */ s = UMFPACK_symbolic (n_row, n_col, Ap, Ai, CARG(Ax,Az), &Symbolic, Control, Info) ; /* [ */ if (s != UMFPACK_OK) error ("TestMat matrix1 sym", (double) s) ; s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ; /* [ */ if (s != UMFPACK_ERROR_out_of_memory) error ("TestMat matrix1 num", (double) s) ; UMFPACK_free_numeric (&Numeric) ; /* ] */ UMFPACK_free_symbolic (&Symbolic) ; /* ] */ free (Ax) ; /* ] */ free (Ap) ; /* ] */ free (Ai) ; /* ] */ free (Az) ; /* ] */ free (Qinit) ; /* ] */ matgen_file ("TestMat/matrix10", &n_row, &n_col, &Ap, &Ai, &Ax, &Az, &Qinit, prl, &det_x, &det_z) ; /* [[[[[ */ Control [UMFPACK_ALLOC_INIT] = -1321 ; /* with Qinit, out of memory in create front (2) */ s = UMFPACK_qsymbolic (n_row, n_col, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Control, Info) ; /* [ */ if (s != UMFPACK_OK) error ("TestMat matrix10 qsym1", (double) s) ; s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ; /* [ */ if (s != UMFPACK_ERROR_out_of_memory) error ("TestMat matrix10 qnum1", (double) s) ; UMFPACK_free_numeric (&Numeric) ; /* ] */ UMFPACK_free_symbolic (&Symbolic) ; /* ] */ Control [UMFPACK_ALLOC_INIT] = -1326 ; /* with Qinit, out of memory in init front */ s = UMFPACK_qsymbolic (n_row, n_col, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Control, Info) ; /* [ */ if (s != UMFPACK_OK) error ("TestMat matrix10 qsym", (double) s) ; s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ; /* [ */ if (s != UMFPACK_ERROR_out_of_memory) error ("TestMat matrix10 qnum", (double) s) ; UMFPACK_free_numeric (&Numeric) ; /* ] */ UMFPACK_free_symbolic (&Symbolic) ; /* ] */ free (Ax) ; /* ] */ free (Ap) ; /* ] */ free (Ai) ; /* ] */ free (Az) ; /* ] */ free (Qinit) ; /* ] */ printf ("\ndone with TestMat memory sizes.\n\n") ; UMFPACK_defaults (Control) ; /* ---------------------------------------------------------------------- */ /* reset rand ( ) */ /* ---------------------------------------------------------------------- */ srand (1) ; /* ---------------------------------------------------------------------- */ /* test amd */ /* ---------------------------------------------------------------------- */ n = 50 ; P = (Int *) malloc (n * sizeof (Int)) ; /* [ */ for (k = 0 ; k < 10 ; k++) { matgen_sparse (n, 4*n, 3, 2*n, 0, 0, &Ap, &Ai, &Ax, &Az, 0, 0) ; /* [[[[ */ for (aggressive = 0 ; aggressive <= 2 ; aggressive++) { for (i = 0 ; i < 3 ; i++) { #if (defined (DINT) || defined (ZINT)) amd_defaults (Control) ; Control [AMD_AGGRESSIVE] = aggressive ; Control [AMD_DENSE] = alphas [i] ; Con = (aggressive == 2) ? DNULL : Control ; info = (aggressive == 2) ? DNULL : Info ; amd_control (Con) ; s = amd_order (n, Ap, Ai, P, Con, info) ; if (s != AMD_OK) error ("amd", (double) s) ; amd_info (info) ; #else amd_l_defaults (Control) ; Control [AMD_AGGRESSIVE] = aggressive ; Control [AMD_DENSE] = alphas [i] ; Con = (aggressive == 2) ? DNULL : Control ; info = (aggressive == 2) ? DNULL : Info ; amd_l_control (Con) ; s = amd_l_order (n, Ap, Ai, P, Con, info) ; if (s != AMD_OK) error ("amd", (double) s) ; amd_l_info (info) ; #endif UMFPACK_defaults (Control) ; Control [UMFPACK_PRL] = 3 ; UMFPACK_report_perm (n, P, Control) ; } } free (Ap) ; /* ] */ free (Ai) ; /* ] */ free (Ax) ; /* ] */ free (Az) ; /* ] */ } free (P) ; /* ] */ if (AMD_valid (-1, -1, INULL, INULL) >= AMD_OK) error ("amd error", 0.) ; Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ; AMD_info (Info) ; Info [AMD_STATUS] = AMD_INVALID ; AMD_info (Info) ; Info [AMD_STATUS] = -911 ; AMD_info (Info) ; /* ---------------------------------------------------------------------- */ /* malloc and realloc control */ /* ---------------------------------------------------------------------- */ MemOK [0] = -1 ; MemOK [1] = 0 ; MemOK [2] = 0 ; MemOK [3] = -1 ; MemOK [4] = 0 ; MemOK [5] = 0 ; umf_fail = -1 ; umf_fail_lo = 0 ; umf_fail_hi = 0 ; umf_realloc_fail = -1 ; umf_realloc_lo = 0 ; umf_realloc_hi = 0 ; for (i = 0 ; i < UMFPACK_CONTROL ; i++) { Ncontrols [i] = 0 ; } UMFPACK_defaults (Control) ; /* ---------------------------------------------------------------------- */ /* do three funky sizes to test int overflow cases */ /* ---------------------------------------------------------------------- */ { /* Int funky_sizes [ ] = { 14402, 16400, 600000 } ; */ Int funky_sizes [ ] = { 144, 164, 600 } ; UMFPACK_defaults (Control) ; Control [UMFPACK_PRL] = 1 ; Control [UMFPACK_STRATEGY] = 3 ; Control [UMFPACK_FRONT_ALLOC_INIT] = 1 ; for (k = 0 ; k < 3 ; k++) { n = funky_sizes [k] ; printf ("funky matrix, n = "ID"\n", n) ; matgen_funky (n, &Ap, &Ai, &Ax, &Az) ; /* [[[[ */ b = (double *) malloc (n * sizeof (double)) ; /* [ */ bz= (double *) calloc (n , sizeof (double)) ; /* [ */ Qinit = (Int *) malloc (n * sizeof (Int)) ; /* [ */ if (!b) error ("out of memory (15)",0.) ; if (!bz) error ("out of memory (16)",0.) ; if (!Qinit) error ("out of memory (17)",0.) ; bgen (n, Ap, Ai, Ax, Az, b, bz) ; for (i = 0 ; i < n ; i++) Qinit [i] = i ; fflush (stdout) ; Control [UMFPACK_FIXQ] = 1 ; rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemOK, FALSE, FALSE, 0., 0.) ; printf ("funky matrix rnorm (fixQ): %g\n", rnorm) ; fflush (stdout) ; maxrnorm = MAX (rnorm, maxrnorm) ; Control [UMFPACK_FIXQ] = 0 ; rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemOK, FALSE, FALSE, 0., 0.) ; printf ("funky matrix rnorm (no fixQ): %g\n", rnorm) ; fflush (stdout) ; maxrnorm = MAX (rnorm, maxrnorm) ; free (Qinit) ; /* ] */ free (bz) ; /* ] */ free (b) ; /* ] */ free (Ap) ; /* ] */ free (Ai) ; /* ] */ free (Ax) ; /* ] */ free (Az) ; /* ] */ } } /* maxrnorm = 0 ; */ /* ---------------------------------------------------------------------- */ /* reset rand ( ) */ /* ---------------------------------------------------------------------- */ srand (1) ; /* ---------------------------------------------------------------------- */ /* tight controls */ /* ---------------------------------------------------------------------- */ c = UMFPACK_PIVOT_TOLERANCE ; Controls [c][0] = UMFPACK_DEFAULT_PIVOT_TOLERANCE ; Ncontrols [c] = 1 ; c = UMFPACK_SCALE ; Controls [c][1] = UMFPACK_DEFAULT_SCALE ; Ncontrols [c] = 1 ; c = UMFPACK_BLOCK_SIZE ; Controls [c][0] = UMFPACK_DEFAULT_BLOCK_SIZE ; Ncontrols [c] = 1 ; c = UMFPACK_ALLOC_INIT ; Controls [c][0] = UMFPACK_DEFAULT_ALLOC_INIT ; Ncontrols [c] = 1 ; c = UMFPACK_AMD_DENSE ; Controls [c][0] = UMFPACK_DEFAULT_AMD_DENSE ; Ncontrols [c] = 1 ; /* ---------------------------------------------------------------------- */ /* license */ /* ---------------------------------------------------------------------- */ Control [UMFPACK_PRL] = 6 ; UMFPACK_report_status (Control, UMFPACK_OK) ; /* ---------------------------------------------------------------------- */ /* do all test matrices from TestMat directory */ /* ---------------------------------------------------------------------- */ printf ("\nStarting TestMat:\n") ; for (prl = 5 ; prl >= 0 ; prl--) { printf ("=====================TestMat PRL "ID"\n", prl) ; dir = opendir ("TestMat") ; if (!dir) { printf ("opendir TestMat failed\n") ; exit (1) ; } while (TRUE) { errno = 0 ; if ((direntp = readdir (dir)) != NULL) { /* skip this */ if (direntp->d_name [0] == '.') continue ; sprintf (filename, "TestMat/%s", direntp->d_name) ; rnorm = do_file (filename, prl, MemOK) ; if (strcmp (filename, "TestMat/shl0") == 0) { printf ("shl0 rnorm: %g\n", rnorm) ; maxrnorm_shl0 = MAX (maxrnorm_shl0, rnorm) ; } else if (strcmp (filename, "TestMat/arc130") == 0) { printf ("arc130 rnorm: %g\n", rnorm) ; maxrnorm_arc130 = MAX (maxrnorm_arc130, rnorm) ; } else { printf ("other testmat rnorm: %g\n", rnorm) ; maxrnorm = MAX (maxrnorm, rnorm) ; } } else { if (errno != 0) { printf ("read error\n") ; exit (1) ; } closedir (dir) ; break ; } } printf ("\n\n@@@@@@ Largest TestMat do_file rnorm: %g shl0: %g @@@@@@ arc130: %g\n\n", maxrnorm, maxrnorm_shl0, maxrnorm_arc130) ; } printf ("\ndone with TestMat.\n\n") ; /* ---------------------------------------------------------------------- */ /* reset rand ( ) */ /* ---------------------------------------------------------------------- */ srand (1) ; /* ---------------------------------------------------------------------- */ /* test change of pattern */ /* ---------------------------------------------------------------------- */ Control [UMFPACK_PRL] = 5 ; Control [UMFPACK_ALLOC_INIT] = 0. ; matgen_file ("TestMat/matrix1", &n_row, &n_col, &Ap, &Ai, &Ax, &Az, &Qinit, 5, &det_x, &det_z) ; /* [[[[[ */ s = UMFPACK_qsymbolic (n_row, n_col, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Control, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; if (!Symbolic || Info [UMFPACK_STATUS] != UMFPACK_OK) error ("p1",0.) ; printf ("\nGood symbolic, pattern test: ") ; s = UMFPACK_report_symbolic (Symbolic, Control) ; UMFPACK_report_status (Control, s) ; if (s != UMFPACK_OK) error ("p1c",0.) ; UMFPACK_report_control (Control) ; s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; printf ("p1b status: "ID" Numeric handle bad "ID"\n", s, !Numeric) ; s2 = UMFPACK_report_numeric (Numeric, Control) ; if (!Numeric || s != UMFPACK_OK) error ("p1b",0.) ; printf ("Good numeric, pattern test: ") ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; UMFPACK_report_status (Control, s) ; if (s2 != UMFPACK_OK) error ("p1d",0.) ; UMFPACK_free_numeric (&Numeric) ; /* corrupted Ap (negative degree) */ c = Ap [1] ; Ap [1] = -1 ; printf ("Bad Ap [1] = -1: \n") ; s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; if (Numeric || s != UMFPACK_ERROR_different_pattern) error ("zzz1",0.) ; Ap [1] = c ; /* corrupted Ai (out of bounds) */ c = Ai [1] ; Ai [1] = -1 ; printf ("Bad Ai [1] = -1: \n") ; s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; if (Numeric || s != UMFPACK_ERROR_different_pattern) error ("zzz2",0.) ; Ai [1] = c ; /* corrupted Ai (out of bounds) */ c = Ai [1] ; Ai [1] = n_row ; printf ("Bad Ai [1] = "ID": \n", n_row) ; s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; if (Numeric || s != UMFPACK_ERROR_different_pattern) error ("zzz3",0.) ; Ai [1] = c ; free (Ap) ; /* ] */ free (Ai) ; /* ] */ free (Ax) ; /* ] */ free (Az) ; /* ] */ free (Qinit) ; /* ] */ /* one more entry */ printf ("one more entry\n") ; matgen_file ("TestMat/matrix2", &n_row2, &n_col2, &Ap2, &Ai2, &Ax2, &Az2, &Qinit2, 5, &det_x, &det_z) ; /* [[[[[ */ s = UMFPACK_numeric (Ap2, Ai2, CARG(Ax2,Az2), Symbolic, &Numeric, Control, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; if (Numeric || s != UMFPACK_ERROR_different_pattern) error ("p2",0.) ; free (Ap2) ; /* ] */ free (Ai2) ; /* ] */ free (Ax2) ; /* ] */ free (Az2) ; /* ] */ free (Qinit2) ; /* ] */ printf ("one more entry done\n") ; /* one less entry */ matgen_file ("TestMat/matrix3", &n_row2, &n_col2, &Ap2, &Ai2, &Ax2, &Az2, &Qinit2, 5, &det_x, &det_z) ; /* [[[[[ */ s = UMFPACK_numeric (Ap2, Ai2, CARG(Ax2,Az2), Symbolic, &Numeric, Control, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; if (Numeric || s != UMFPACK_ERROR_different_pattern) error ("p3",0.) ; free (Ap2) ; /* ] */ free (Ai2) ; /* ] */ free (Ax2) ; /* ] */ free (Az2) ; /* ] */ free (Qinit2) ; /* ] */ /* many more entries */ matgen_file ("TestMat/matrix4", &n_row2, &n_col2, &Ap2, &Ai2, &Ax2, &Az2, &Qinit2, 5, &det_x, &det_z) ; /* [[[[[ */ s = UMFPACK_numeric (Ap2, Ai2, CARG(Ax2,Ax2), Symbolic, &Numeric, Control, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; if (Numeric || s != UMFPACK_ERROR_different_pattern) error ("p4",0.) ; free (Ap2) ; /* ] */ free (Ai2) ; /* ] */ free (Ax2) ; /* ] */ free (Az2) ; /* ] */ free (Qinit2) ; /* ] */ /* some more entries */ matgen_file ("TestMat/matrix5", &n_row2, &n_col2, &Ap2, &Ai2, &Ax2, &Az2, &Qinit2, 5, &det_x, &det_z) ; /* [[[[[ */ s = UMFPACK_numeric (Ap2, Ai2, CARG(Ax2,Az2), Symbolic, &Numeric, Control, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; if (Numeric || s != UMFPACK_ERROR_different_pattern) error ("p5",0.) ; free (Ap2) ; /* ] */ free (Ai2) ; /* ] */ free (Ax2) ; /* ] */ free (Az2) ; /* ] */ free (Qinit2) ; /* ] */ /* same entries - but different pattern */ matgen_file ("TestMat/matrix6", &n_row2, &n_col2, &Ap2, &Ai2, &Ax2, &Az2, &Qinit2, 5, &det_x, &det_z) ; /* [[[[[ */ s = UMFPACK_numeric (Ap2, Ai2, CARG(Ax2,Az2), Symbolic, &Numeric, Control, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; if (Numeric || s != UMFPACK_ERROR_different_pattern) error ("p6",0.) ; free (Ap2) ; /* ] */ free (Ai2) ; /* ] */ free (Ax2) ; /* ] */ free (Az2) ; /* ] */ free (Qinit2) ; /* ] */ /* same entries - but different pattern */ matgen_file ("TestMat/matrix7", &n_row2, &n_col2, &Ap2, &Ai2, &Ax2, &Az2, &Qinit2, 5, &det_x, &det_z) ; /* [[[[[ */ s = UMFPACK_numeric (Ap2, Ai2, CARG(Ax2,Az2), Symbolic, &Numeric, Control, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; if (Numeric || s != UMFPACK_ERROR_different_pattern) error ("p7",0.) ; free (Ap2) ; /* ] */ free (Ai2) ; /* ] */ free (Ax2) ; /* ] */ free (Az2) ; /* ] */ free (Qinit2) ; /* ] */ /* same entries - but different pattern */ matgen_file ("TestMat/matrix8", &n_row2, &n_col2, &Ap2, &Ai2, &Ax2, &Az2, &Qinit2, 5, &det_x, &det_z) ; /* [[[[[ */ s = UMFPACK_numeric (Ap2, Ai2, CARG(Ax2,Az2), Symbolic, &Numeric, Control, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; if (Numeric || s != UMFPACK_ERROR_different_pattern) error ("p8",0.) ; free (Ap2) ; /* ] */ free (Ai2) ; /* ] */ free (Ax2) ; /* ] */ free (Az2) ; /* ] */ free (Qinit2) ; /* ] */ UMFPACK_free_symbolic (&Symbolic) ; /* start over, use a bigger matrix */ matgen_file ("TestMat/matrix10", &n_row, &n_col, &Ap, &Ai, &Ax, &Az, &Qinit, 5, &det_x, &det_z) ; /* [[[[[ */ s = UMFPACK_qsymbolic (n_row, n_col, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Control, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; if (prl > 2) printf ("\nGood matrix10 symbolic, pattern test: ") ; s = UMFPACK_report_symbolic (Symbolic, Control) ; if (!Symbolic || Info [UMFPACK_STATUS] != UMFPACK_OK) error ("p10",0.) ; if (s != UMFPACK_OK) error ("p10",0.) ; s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; if (!Numeric || s != UMFPACK_OK) error ("p10b",0.) ; printf ("Good matrix10matrix10 numeric, pattern test:") ; s = UMFPACK_report_numeric (Numeric, Control) ; if (s != UMFPACK_OK) error ("p10b",0.) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; UMFPACK_free_numeric (&Numeric) ; /* kludge Symbolic to force a huge dmax */ printf ("\nKludge symbolic to force dmax int overflow:\n") ; Control [UMFPACK_PRL] = 3 ; Sym = (SymbolicType *) Symbolic ; Sym->amd_dmax = 16400 ; s = UMFPACK_report_symbolic (Symbolic, Control) ; if (!Symbolic || Info [UMFPACK_STATUS] != UMFPACK_OK) error ("p10e",0.) ; s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ; if (!Numeric || s != UMFPACK_OK) error ("p10c",0.) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; UMFPACK_free_numeric (&Numeric) ; free (Ap) ; /* ] */ free (Ai) ; /* ] */ free (Ax) ; /* ] */ free (Az) ; /* ] */ free (Qinit) ; /* ] */ UMFPACK_free_symbolic (&Symbolic) ; /* ---------------------------------------------------------------------- */ /* reset controls */ /* ---------------------------------------------------------------------- */ UMFPACK_defaults (Control) ; /* ---------------------------------------------------------------------- */ /* reset rand ( ) */ /* ---------------------------------------------------------------------- */ srand (1) ; /* ---------------------------------------------------------------------- */ /* test realloc */ /* ---------------------------------------------------------------------- */ /* malloc always succeeds */ MemBad [0] = -1 ; MemBad [1] = 0 ; MemBad [2] = 0 ; /* realloc always fails */ MemBad [3] = 0 ; MemBad [4] = 0 ; MemBad [5] = -99999 ; c = UMFPACK_ALLOC_INIT ; Ncontrols [c] = 1 ; Controls [c][0] = 0.001 ; #ifdef DINT printf ("\n all realloc fails sparse + dense rows %7d 4*n nz's\n", n) ; matgen_sparse (n, 4*n, 3, 2*n, 0, 0, &Ap, &Ai, &Ax, &Az, 0, 0) ; rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemBad, 0) ; printf ("rnorm %g should be 9e10\n", rnorm) ; if (rnorm != 9e10) error ("MemBad 1 failure", rnorm) ; printf ("\n all realloc fails sparse %7d 30*n nz's\n", n) ; matgen_sparse (n, 30*n, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az, 0, 0) ; rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemBad, 0) ; printf ("rnorm %g should be 9e10\n", rnorm) ; if (rnorm != 9e10) error ("MemBad 2 failure", rnorm) ; #endif /* ---------------------------------------------------------------------- */ /* reset rand ( ) */ /* ---------------------------------------------------------------------- */ srand (1) ; /* ---------------------------------------------------------------------- */ /* umf_symbolic compaction test */ /* ---------------------------------------------------------------------- */ n = 100 ; Control [UMFPACK_PRL] = 4 ; Qinit = (Int *) malloc (n * sizeof (Int)) ; /* [ */ b = (double *) malloc (n * sizeof (double)) ; /* [ */ bz= (double *) calloc (n , sizeof (double)) ; /* [ */ for (i = 0 ; i < n ; i++) Qinit [i] = i ; matgen_compaction (n, &Ap, &Ai, &Ax, &Az) ; /* [[[[ */ bgen (n, Ap, Ai, Ax, Az, b, bz) ; printf ("\nA compaction: ") ; s = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Control) ; if (s != UMFPACK_OK) error ("219", 0.) ; rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemOK, FALSE, FALSE, 0., 0.) ; printf ("rnorm %g A compaction\n", rnorm) ; Control [UMFPACK_PRL] = 1 ; printf ("do_and_free for compacted matrix:\n") ; rnorm = do_and_free (n, Ap, Ai, Ax,Az, Controls, Ncontrols, MemOK, 0) ; /* ]]]] */ printf ("rnorm for compacted matrix %g\n", rnorm) ; free (b) ; /* ] */ free (bz) ; /* ] */ free (Qinit) ; /* ] */ /* ---------------------------------------------------------------------- */ /* umf_symbolic compaction test, again (read a file) */ /* ---------------------------------------------------------------------- */ matgen_file ("TestMat/shl0", &n_row, &n_col, &Ap, &Ai, &Ax, &Az, &Qinit, 5, &det_x, &det_z) ; /* [[[[[ */ n = n_row ; b = (double *) malloc (n * sizeof (double)) ; /* [ */ bz= (double *) calloc (n , sizeof (double)) ; /* [ */ bgen (n, Ap, Ai, Ax, Az, b, bz) ; Control [UMFPACK_PRL] = 5 ; Control [UMFPACK_DENSE_ROW] = 0.1 ; Control [UMFPACK_DENSE_COL] = 2.0 ; printf ("\nshl0 b: ") ; UMFPACK_report_vector (n, CARG(b,bz), Control) ; printf ("\nshl0 A: ") ; UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Control) ; rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemOK, FALSE, FALSE, 0., 0.) ; printf ("rnorm %g for shl0", rnorm) ; maxrnorm_shl0 = MAX (maxrnorm_shl0, rnorm) ; free (bz) ; /* ] */ free (b) ; /* ] */ free (Ap) ; /* ] */ free (Ai) ; /* ] */ free (Az) ; /* ] */ free (Ax) ; /* ] */ free (Qinit) ; /* ] */ /* ---------------------------------------------------------------------- */ /* normal Controls */ /* ---------------------------------------------------------------------- */ c = UMFPACK_PIVOT_TOLERANCE ; Controls [c][0] = UMFPACK_DEFAULT_PIVOT_TOLERANCE ; Controls [c][1] = 0.5 ; Controls [c][2] = 1.0 ; Ncontrols [c] = 3 ; c = UMFPACK_SCALE ; Controls [c][0] = UMFPACK_SCALE_SUM ; /* also the default */ Controls [c][1] = UMFPACK_SCALE_NONE ; Controls [c][2] = UMFPACK_SCALE_MAX ; Ncontrols [c] = 3 ; c = UMFPACK_BLOCK_SIZE ; Controls [c][0] = 1 ; Controls [c][1] = 8 ; Controls [c][2] = 16 ; /* not the default */ Ncontrols [c] = 3 ; c = UMFPACK_ALLOC_INIT ; Controls [c][0] = 0.0 ; Controls [c][1] = 0.5 ; Controls [c][2] = 1.0 ; /* not the default */ Controls [c][3] = -10000 ; Ncontrols [c] = 4 ; c = UMFPACK_AMD_DENSE ; Controls [c][0] = -1 ; Controls [c][1] = 0.5 ; Controls [c][2] = UMFPACK_DEFAULT_AMD_DENSE ; Ncontrols [c] = 3 ; UMFPACK_defaults (Control) ; /* ---------------------------------------------------------------------- */ /* reset rand ( ) */ /* ---------------------------------------------------------------------- */ srand (1) ; /* ---------------------------------------------------------------------- */ /* test realloc */ /* ---------------------------------------------------------------------- */ /* malloc always succeeds */ MemBad [0] = -1 ; MemBad [1] = 0 ; MemBad [2] = 0 ; /* realloc always fails */ MemBad [3] = 0 ; MemBad [4] = 0 ; MemBad [5] = -99999 ; n = 10 ; printf ("\n all realloc fails sparse %7d 4*n nz's\n", n) ; matgen_sparse (n, 4*n, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az, 1, 0) ; rnorm = do_and_free (n, Ap, Ai, Ax,Az, Controls, Ncontrols, MemBad, 1) ; printf ("rnorm %g for all-realloc-fails\n", rnorm) ; /* ---------------------------------------------------------------------- */ /* reset rand ( ) */ /* ---------------------------------------------------------------------- */ srand (1) ; /* ---------------------------------------------------------------------- */ /* reset malloc and realloc failure */ /* ---------------------------------------------------------------------- */ umf_fail = -1 ; umf_fail_lo = 0 ; umf_fail_hi = 0 ; umf_realloc_fail = -1 ; umf_realloc_lo = 0 ; umf_realloc_hi = 0 ; /* ---------------------------------------------------------------------- */ /* test errors */ /* ---------------------------------------------------------------------- */ n = 32 ; Pamd = (Int *) malloc (2*n * sizeof (Int)) ; /* [ */ Qinit = (Int *) malloc (2*n * sizeof (Int)) ; /* [ */ Pinit = (Int *) malloc (2*n * sizeof (Int)) ; /* [ */ Qinit2 = (Int *) malloc (2*n * sizeof (Int)) ; /* [ */ b = (double *) malloc (2*n * sizeof (double)) ; /* [ */ bz= (double *) calloc (2*n , sizeof (double)) ; /* [ */ x = (double *) malloc (2*n * sizeof (double)) ; /* [ */ xz= (double *) calloc (2*n , sizeof (double)) ; /* [ */ Ap2 = (Int *) malloc ((2*n+1) * sizeof (Int)) ; /* [ */ if (!Qinit || !b || !Ap2 || !Qinit2 || !Pinit) error ("out of memory (18)",0.) ; if (!xz || !bz) error ("memr again",0.) ; UMFPACK_defaults (DNULL) ; UMFPACK_defaults (Control) ; randperm (n, Pinit) ; for (prl = 5 ; prl >= -1 ; prl--) { for (strategy = UMFPACK_STRATEGY_AUTO ; strategy <= UMFPACK_STRATEGY_SYMMETRIC ; strategy++) { Int *Rp, *Ri ; printf ("\n[[[[ PRL = "ID" strategy = "ID"\n", prl, strategy) ; for (k = 0 ; k < n ; k++) Pamd [k] = EMPTY ; Control [UMFPACK_PRL] = prl ; Control [UMFPACK_STRATEGY] = strategy ; UMFPACK_report_control (Control) ; i = UMFPACK_DENSE_DEGREE_THRESHOLD (0.2, n) ; printf ("(default) dense row/col degree threshold: "ID"\n", i) ; /* ------------------------------------------------------------------ */ matgen_sparse (n, 4*n, 10, 2*n, 10, 2*n, &Ap, &Ai, &Ax, &Az, prl, 0) ; /* [[[[ */ bgen (n, Ap, Ai, Ax,Az, b,bz) ; nz = Ap [n] ; Aj = (Int *) malloc ((nz+n+1) * sizeof (Int)) ; /* [ */ Ai2 = (Int *) malloc ((nz+n) * sizeof (Int)) ; /* [ */ Ax2 = (double *) malloc ((nz+n) * sizeof (double)) ; /* [ */ Az2 = (double *) calloc ((nz+n) , sizeof (double)) ; /* [ */ if (!Aj || !Ai2 || !Ax2 || !Az2) error ("out of memory (19)",0.) ; Rp = Aj ; Ri = Ai2 ; /* ------------------------------------------------------------------ */ Con = (prl == -1) ? (DNULL) : Control ; UMFPACK_report_control (Con) ; /* ------------------------------------------------------------------ */ randperm (n, Qinit) ; if (prl > 2) printf ("Qinit OK: ") ; s = UMFPACK_report_perm (n, Qinit, Con) ; if (s != UMFPACK_OK) error ("Qinit OK", 0.) ; randperm (2*n, Qinit2) ; if (prl > 2) printf ("Qinit2 OK: ") ; s = UMFPACK_report_perm (2*n, Qinit2, Con) ; if (s != UMFPACK_OK) error ("Qinit2 OK", 0.) ; /* ------------------------------------------------------------------ */ if (prl > 2) printf ("\nb OK: ") ; s = UMFPACK_report_vector (n, CARG(b,bz), Con) ; if (s != UMFPACK_OK) error ("0",0.) ; /* ------------------------------------------------------------------ */ if (prl > 2) printf ("\nn=-1: ") ; s = UMFPACK_report_vector (-1, CARG(b,bz), Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_n_nonpositive)) error ("2",0.) ; /* ------------------------------------------------------------------ */ if (prl > 2) printf ("\nb null: ") ; s = UMFPACK_report_vector (n, CARG(DNULL,DNULL), Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_argument_missing)) error ("2",0.) ; /* ------------------------------------------------------------------ */ if (prl > 2) printf ("\nA OK: ") ; s = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ; if (s != UMFPACK_OK) error ("2a",0.) ; /* ------------------------------------------------------------------ */ if (prl > 2) printf ("\nA pattern OK: ") ; s = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(DNULL,DNULL), 1, Con) ; if (s != UMFPACK_OK) error ("2c",0.) ; /* ------------------------------------------------------------------ */ if (prl > 2) printf ("\nA OK row: ") ; s = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 0, Con) ; if (s != UMFPACK_OK) error ("2b",0.) ; /* ------------------------------------------------------------------ */ if (prl > 2) printf ("\nn=zero: ") ; s = UMFPACK_report_matrix (0, 0, Ap, Ai, CARG(Ax,Az), 1, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_n_nonpositive)) error ("2",0.) ; s = UMFPACK_symbolic (0, 0, Ap, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Symbolic || s != UMFPACK_ERROR_n_nonpositive) error ("2b",0.) ; s = UMFPACK_qsymbolic (0, 0, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_info (Con, Info) ; if (Symbolic || s != UMFPACK_ERROR_n_nonpositive) error ("2c",0.) ; /* ------------------------------------------------------------------ */ s = do_amd (-1, Ap, Ai, Pamd) ; if (s != AMD_INVALID) error ("amd 1", (double) s) ; s = do_amd (n, INULL, Ai, Pamd) ; if (s != AMD_INVALID) error ("amd 2", (double) s) ; s = do_amd (n, Ap, INULL, Pamd) ; if (s != AMD_INVALID) error ("amd 3", (double) s) ; s = do_amd (n, Ap, Ai, INULL) ; if (s != AMD_INVALID) error ("amd 4", (double) s) ; s = do_amd (0, Ap, Ai, Pamd) ; if (s != AMD_OK) error ("amd 5", (double) s) ; s = do_amd_transpose (-1, Ap, Ai, Rp, Ri) ; if (s != AMD_INVALID) error ("amd 1t", (double) s) ; s = do_amd_transpose (n, INULL, Ai, Rp, Ri) ; if (s != AMD_INVALID) error ("amd 2t", (double) s) ; s = do_amd_transpose (n, Ap, INULL, Rp, Ri) ; if (s != AMD_INVALID) error ("amd 3t", (double) s) ; s = do_amd_transpose (n, Ap, Ai, INULL, Ri) ; if (s != AMD_INVALID) error ("amd 7t", (double) s) ; s = do_amd_transpose (n, Ap, Ai, Rp, INULL) ; if (s != AMD_INVALID) error ("amd 8t", (double) s) ; s = do_amd_transpose (0, Ap, Ai, Rp, Ri) ; if (s != AMD_OK) error ("amd 5t", (double) s) ; #if 0 { f = fopen ("debug.amd", "w") ; fprintf (f, "999\n") ; fclose (f) ; } #endif /* ------------------------------------------------------------------ */ if (prl > 2) printf ("\nAp null: ") ; s = UMFPACK_report_matrix (n, n, INULL, Ai, CARG(Ax,Az), 1, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_argument_missing)) error ("3",0.) ; s = UMFPACK_symbolic (n, n, INULL, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Symbolic || s != UMFPACK_ERROR_argument_missing) error ("3b",0.) ; s = UMFPACK_qsymbolic (n, n, INULL, Ai, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Symbolic || s != UMFPACK_ERROR_argument_missing) error ("3c",0.) ; s = UMFPACK_transpose (n, n, INULL, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG(Ax2,Az2) C1ARG(0)) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_argument_missing) error ("52",0.); s = do_amd (n, Ap, Ai, Pamd) ; if (s != AMD_OK) error ("amd 6b", (double) s) ; /* ------------------------------------------------------------------ */ if (prl > 2) printf ("\nAi null: ") ; s = UMFPACK_report_matrix (n, n, Ap, INULL, CARG(Ax,Az), 1, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_argument_missing)) error ("4",0.) ; s = UMFPACK_symbolic (n, n, Ap, INULL, CARG(Ax,Az), &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Symbolic || s != UMFPACK_ERROR_argument_missing) error ("4b",0.) ; s = UMFPACK_qsymbolic (n, n, Ap, INULL, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Symbolic || s != UMFPACK_ERROR_argument_missing) error ("4c",0.) ; /* ------------------------------------------------------------------ */ Ap [0] = 1 ; /* Ap broken [ */ if (prl > 2) printf ("\nAp [0] != 0: ") ; s = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_matrix)) error ("5",0.) ; s = UMFPACK_symbolic (n, n, Ap, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("5b",0.) ; s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("5c",0.) ; if (prl > 2) printf ("\nCalling umfpack_transpose:\n") ; s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG(Ax2,Az2) C1ARG(0)) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_invalid_matrix) error ("53",0.); s = do_amd (n, Ap, Ai, Pamd) ; if (s != AMD_INVALID) error ("amd 6", (double) s) ; Ap [0] = 0 ; /* Ap fixed ] */ /* ------------------------------------------------------------------ */ Ap [n] = -1 ; /* Ap broken [ */ if (prl > 2) printf ("\nnz < 0: ") ; s = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_matrix)) error ("6",0.) ; s = UMFPACK_symbolic (n, n, Ap, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("6b",0.) ; s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("6c",0.) ; s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG(Ax2,Az2) C1ARG(0)) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_invalid_matrix) error ("51h",0.); s = UMFPACK_col_to_triplet (n, Ap, Aj) ; if (s != UMFPACK_ERROR_invalid_matrix) error ("52j",0.); s = do_amd (n, Ap, Ai, Pamd) ; if (s != AMD_INVALID) error ("amd 6b", (double) s) ; Ap [n] = nz ; /* Ap fixed ] */ /* ------------------------------------------------------------------ */ #if 0 Ap [n] = Int_MAX ; s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ; if (s != UMFPACK_ERROR_problem_too_large) error ("177a",0.); Ap [n] = nz ; #endif /* ------------------------------------------------------------------ */ printf ("Ap [2] negative:\n") ; UMFPACK_report_control (Con) ; c = Ap [2] ; /* Ap broken [ */ Ap [2] = -1 ; if (prl > 2) printf ("\nAp[2]<0: ") ; s = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_matrix)) error ("8",0.) ; s = UMFPACK_symbolic (n, n, Ap, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("8b",0.) ; s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("8c",0.) ; s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG(Ax2,Az2) C1ARG(0)) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_invalid_matrix) error ("55",0.); s = do_amd (n, Ap, Ai, Pamd) ; if (s != AMD_INVALID) error ("amd 7", (double) s) ; Ap [2] = c ; /* Ap fixed ] */ /* ------------------------------------------------------------------ */ c = Ap [2] ; /* Ap broken [ */ Ap [2] = nz+1 ; if (prl > 2) printf ("\nAp [2] > nz: ") ; s = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_matrix)) error ("9",0.) ; s = UMFPACK_symbolic (n, n, Ap, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; s = Info [UMFPACK_STATUS] ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("9b",0.) ; s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("9c",0.) ; s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG(Ax2,Az2) C1ARG(0)) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_invalid_matrix) error ("51i",0.); s = do_amd (n, Ap, Ai, Pamd) ; if (s != AMD_INVALID) error ("amd 8", (double) s) ; Ap [2] = c ; /* Ap fixed ] */ /* ------------------------------------------------------------------ */ c = Ap [4] ; /* Ap broken [ */ Ap [4] = Ap [3]-1 ; if (prl > 2) printf ("\nAp [4] < Ap [3]-1: ") ; s = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_matrix)) error ("10",0.) ; s = UMFPACK_symbolic (n, n, Ap, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("8b",0.) ; s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("8c",0.) ; s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG(Ax2,Az2) C1ARG(0)) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_invalid_matrix) error ("51j",0.); s = do_amd (n, Ap, Ai, Pamd) ; if (s != AMD_INVALID) error ("amd 9", (double) s) ; Ap [4] = c ; /* Ap fixed ] */ /* ------------------------------------------------------------------ */ c = Ai [4] ; /* Ai broken [ */ Ai [4] = -1 ; if (prl > 2) printf ("\nAi [4] = -1: ") ; s = UMFPACK_report_matrix (n , n, Ap, Ai, CARG(Ax,Az), 1, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_matrix)) error ("12",0.) ; s = UMFPACK_symbolic (n, n, Ap, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("12b",0.) ; s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("12c",0.) ; s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG(Ax2,Az2) C1ARG(0)) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_invalid_matrix) error ("51k",0.); s = do_amd (n, Ap, Ai, Pamd) ; if (s != AMD_INVALID) error ("amd 10", (double) s) ; Ai [4] = c ; /* Ai fixed ] */ /* ------------------------------------------------------------------ */ if (Ap [4] - Ap [3] < 3) error ("col 3 too short",0.) ; c = Ai [Ap [3] + 1] ; /* Ai broken [ */ Ai [Ap [3] + 1] = 0 ; if (prl > 2) printf ("\ncol 3 jumbled: ") ; s = UMFPACK_report_matrix (n , n, Ap, Ai, CARG(Ax,Az), 1, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_matrix)) error ("13",0.) ; s = UMFPACK_symbolic (n, n, Ap, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("13b",0.) ; s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("13c",0.) ; s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG(Ax2,Az2) C1ARG(0)) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_invalid_matrix) error ("51k",0.); s = do_amd (n, Ap, Ai, Pamd) ; printf ("amd jumbled: %d\n", s) ; if (s != AMD_OK_BUT_JUMBLED) error ("amd 11", (double) s) ; Ai [Ap [3] + 1] = c ; /* Ai fixed ] */ /* ------------------------------------------------------------------ */ #if 0 { f = fopen ("debug.amd", "w") ; fprintf (f, "999\n") ; fclose (f) ; } #endif for (i = 0 ; i < n ; i++) Ap2 [i] = Ap [i] ; for (i = n ; i <= 2*n ; i++) Ap2 [i] = nz ; s = do_amd (2*n, Ap2, Ai, Pamd) ; if (s != AMD_OK) error ("amd 12a", (double) s) ; if (prl > 2) printf ("\nhalf empty: ") ; s = UMFPACK_report_matrix (2*n, 2*n, Ap2, Ai, CARG(Ax,Az), 1, Con) ; if (s != UMFPACK_OK) error ("14",0.) ; s = UMFPACK_symbolic (2*n, 2*n, Ap2, Ai, CARG(DNULL,DNULL), &Symbolic, Con, Info) ; if (!Symbolic || s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (!Symbolic || s != UMFPACK_OK) error ("14b",0.) ; UMFPACK_free_symbolic (&Symbolic) ; s = UMFPACK_symbolic (2*n, 2*n, Ap2, Ai, CARG(DNULL,DNULL), &Symbolic, Con, DNULL) ; if (s != UMFPACK_OK) error ("13d2", 0.) ; if (!Symbolic) error ("13d",0.) ; UMFPACK_free_symbolic (&Symbolic) ; s = UMFPACK_qsymbolic (2*n, 2*n, Ap2, Ai, CARG(DNULL,DNULL), Qinit2, &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (!Symbolic || s != UMFPACK_OK) error ("14c",0.) ; UMFPACK_free_symbolic (&Symbolic) ; s = do_amd (2*n, Ap2, Ai, Pamd) ; if (s != AMD_OK) error ("amd 12", (double) s) ; /* ------------------------------------------------------------------ */ for (i = 0 ; i <= n ; i++) Ap2 [i] = 0 ; if (prl > 2) printf ("\nall empty: ") ; s = UMFPACK_report_matrix (n, n, Ap2, Ai, CARG(Ax,Az), 1, Con) ; if (s != UMFPACK_OK) error ("141",0.) ; s = UMFPACK_col_to_triplet (n, Ap, Aj) ; if (s != UMFPACK_OK) error ("151",0.) ; s = UMFPACK_symbolic (n, n, Ap2, Ai, CARG(DNULL,DNULL), &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (!Symbolic || s != UMFPACK_OK) error ("142",0.) ; UMFPACK_free_symbolic (&Symbolic) ; s = UMFPACK_symbolic (n, n, Ap2, Ai, CARG(DNULL,DNULL), &Symbolic, Con, DNULL) ; if (s != UMFPACK_OK) error ("142b", 0.) ; if (!Symbolic) error ("143",0.) ; UMFPACK_free_symbolic (&Symbolic) ; s = UMFPACK_qsymbolic (n, n, Ap2, Ai, CARG(DNULL,DNULL), Qinit, &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (!Symbolic || s != UMFPACK_OK) error ("144",0.) ; UMFPACK_free_symbolic (&Symbolic) ; s = do_amd (n, Ap, Ai, Pamd) ; if (s != AMD_OK) error ("amd 13", (double) s) ; /* ------------------------------------------------------------------ */ for (i = 0 ; i <= n ; i++) Ap2 [i] = Ap [i] ; for (p = 0 ; p < nz ; p++) { Ai2 [p] = Ai [p] ; Ax2 [p] = Ax [p] ; } for (i = n ; i < 2*n ; i++) { Ap2 [i] = p ; /* add a dense row 0 */ Ai2 [p] = 0 ; Ax2 [p] = 1.0 ; p++ ; } Ap2 [2*n] = p ; if (prl > 2) printf ("\nhalf empty rows: ") ; s = UMFPACK_report_matrix (2*n, 2*n, Ap2, Ai2, CARG(Ax2,Az2), 1, Con) ; if (s != UMFPACK_OK) error ("30",0.) ; s = UMFPACK_symbolic (2*n, 2*n, Ap2, Ai2, CARG(Ax2,Az2), &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (!Symbolic || s != UMFPACK_OK) error ("30b",0.) ; UMFPACK_free_symbolic (&Symbolic) ; s = UMFPACK_qsymbolic (2*n, 2*n, Ap2, Ai2, CARG(Ax2,Az2), Qinit2, &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (!Symbolic || s != UMFPACK_OK) error ("30c",0.) ; UMFPACK_free_symbolic (&Symbolic) ; s = do_amd (2*n, Ap2, Ai2, Pamd) ; if (s != AMD_OK) error ("amd 14", (double) s) ; /* ------------------------------------------------------------------ */ for (i = 0 ; i <= 2*n ; i++) Ap2 [i] = 0 ; if (prl > 2) printf ("\nall empty: ") ; s = UMFPACK_report_matrix (2*n, 2*n, Ap2, Ai, CARG(Ax,Az), 1, Con) ; if (s != UMFPACK_OK) error ("15",0.) ; s = do_amd (2*n, Ap2, Ai2, Pamd) ; if (s != AMD_OK) error ("amd 14b", (double) s) ; /* ------------------------------------------------------------------ */ if (prl > 2) printf ("\nold null form was same as col_form: ") ; s = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ; if (s != UMFPACK_OK) error ("16",0.) ; /* ================================================================== */ /* test Numeric [ */ /* ================================================================== */ s = UMFPACK_symbolic (n, n, Ap, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ; /* [ */ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (!Symbolic || s != UMFPACK_OK) error ("16a",0.) ; /* ------------------------------------------------------------------ */ for (scale = UMFPACK_SCALE_NONE ; scale <= UMFPACK_SCALE_MAX ; scale++) { if (Con) Con [UMFPACK_SCALE] = scale ; s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, Info) ; /* [ */ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; Info [UMFPACK_FLOPS_ESTIMATE] = -1 ; UMFPACK_report_info (Con, Info) ; if (!Numeric || s != UMFPACK_OK) error ("31",0.) ; if (prl > 2) printf ("good Numeric: ") ; s = UMFPACK_report_numeric ( Numeric, Con) ; if (s != UMFPACK_OK) error ("90",0.) ; /* ------------------------------------------------------------------ */ s = UMFPACK_get_lunz (INULL, &unz, &nnrow, &nncol, &nzud, Numeric) ; if (s != UMFPACK_ERROR_argument_missing) error ("57",0.) ; /* ------------------------------------------------------------------ */ s = UMFPACK_get_lunz (&lnz, &unz, &nnrow, &nncol, &nzud, Numeric) ; printf ("lnz "ID" unz "ID" nn "ID"\n", lnz, unz, nn) ; if (s != UMFPACK_OK) error ("58",0.) ; /* ------------------------------------------------------------------ */ Lp = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ Li = (Int *) malloc ((lnz+1) * sizeof (Int)) ; /* [ */ Lx = (double *) malloc ((lnz+1) * sizeof (double)) ; /* [ */ Lz = (double *) calloc (lnz , sizeof (double)) ; /* [ */ Up = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ Ui = (Int *) malloc ((unz+1) * sizeof (Int)) ; /* [ */ Ux = (double *) malloc ((unz+1) * sizeof (double)) ; /* [ */ Uz = (double *) calloc ((unz+1) , sizeof (double)) ; /* [ */ P = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ Q = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ Pa = (Int *) malloc (n * sizeof (Int)) ; /* [ */ Wx = (double *) malloc ((10*n) * sizeof (double)) ; /* [ */ Rs = (double *) malloc ((n+1) * sizeof (double)) ; /* [ */ if (!Lp || !Li || !Lx || !Up || !Ui || !Ux || !P || !Q) error ("out of memory (20)",0.) ; if (!Pa || !Wx || !Rs) error ("out of memory (20)",0.) ; if (!Uz || !Lz) error ("out of memory (21)",0.) ; if (prl > 2) printf ("good Numeric again: ") ; s = UMFPACK_report_numeric ( Numeric, Con) ; if (s != UMFPACK_OK) error ("77",0.) ; s = UMFPACK_get_numeric (Lp, Li, CARG(Lx,Lz), Up, Ui, CARG(Ux,Uz), P, Q, CARG(DNULL,DNULL), &do_recip, Rs, Numeric) ; if (s != UMFPACK_OK) error ("59", 0.) ; s = UMFPACK_get_numeric (Lp, Li, CARG(Lx,Lz), Up, Ui, CARG(Ux,Uz), P, Q, CARG(DNULL,DNULL), &do_recip, DNULL, Numeric) ; if (s != UMFPACK_OK) error ("59b", 0.) ; s = UMFPACK_get_numeric (Lp, Li, CARG(Lx,Lz), Up, Ui, CARG(Ux,Uz), P, Q, CARG(DNULL,DNULL), INULL, DNULL, Numeric) ; if (s != UMFPACK_OK) error ("59r", 0.) ; if (prl > 2) printf ("good Numeric yet again: ") ; s = UMFPACK_report_numeric ( Numeric, Con) ; if (s != UMFPACK_OK) error ("75",0.) ; dump_perm ("goodP1", n, Pamd) ; if (prl > 2) printf ("\nL test: ") ; s = UMFPACK_report_matrix (n, n, Lp, Li, CARG(Lx,Lz), 0, Con) ; if (s != UMFPACK_OK) error ("60",0.) ; if (prl > 2) printf ("\nU test: ") ; s = UMFPACK_report_matrix (n, n, Up, Ui, CARG(Ux,Uz), 1, Con) ; if (s != UMFPACK_OK) error ("61",0.) ; dump_perm ("goodP", n, Pamd) ; if (prl > 2) printf ("P test: ") ; s = UMFPACK_report_perm (n, P, Con) ; if (s != UMFPACK_OK) error ("62",0.) ; if (prl > 2) printf ("Q test: ") ; s = UMFPACK_report_perm (n, Q, Con) ; if (s != UMFPACK_OK) error ("63",0.) ; s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; if (s != UMFPACK_OK) error ("64",0.) ; s = UMFPACK_scale (CARG(DNULL,xz), CARG(b,bz), Numeric) ; if (s != UMFPACK_ERROR_argument_missing) error ("64z",0.) ; s = UMFPACK_scale (CARG(x,xz), CARG(DNULL,bz), Numeric) ; if (s != UMFPACK_ERROR_argument_missing) error ("64y",0.) ; s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(DNULL,xz), CARG(b,bz), Numeric, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; if (s != UMFPACK_ERROR_argument_missing) error ("64e",0.) ; s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(DNULL,bz), Numeric, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; if (s != UMFPACK_ERROR_argument_missing) error ("64f",0.) ; s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(DNULL,Az), CARG(x,xz), CARG(DNULL,bz), Numeric, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; if (s != UMFPACK_ERROR_argument_missing) error ("64g",0.) ; s = UMFPACK_wsolve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info, Pa, Wx) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; if (s != UMFPACK_OK) error ("64a",0.) ; s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, DNULL) ; if (s != UMFPACK_OK) error ("64b",0.) ; s = UMFPACK_wsolve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, DNULL, Pa, Wx) ; if (s != UMFPACK_OK) error ("64c",0.) ; s = UMFPACK_solve (UMFPACK_A, INULL, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_control (Con) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (s != UMFPACK_ERROR_argument_missing) error ("65a",0.) ; s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(DNULL,xz), CARG(b,bz), Numeric, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; if (s != UMFPACK_ERROR_argument_missing) error ("65a",0.) ; s = UMFPACK_wsolve (UMFPACK_A, INULL, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info, Pa, Wx) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; if (s != UMFPACK_ERROR_argument_missing) error ("65b",0.) ; s = UMFPACK_solve (UMFPACK_At, INULL, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; if (s != UMFPACK_ERROR_argument_missing) error ("65c",0.) ; s = UMFPACK_wsolve (UMFPACK_At, INULL, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info, Pa, Wx) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; if (s != UMFPACK_ERROR_argument_missing) error ("66",0.) ; s = UMFPACK_wsolve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info, INULL, Wx) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; if (s != UMFPACK_ERROR_argument_missing) error ("67",0.) ; s = UMFPACK_wsolve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info, Pa, DNULL) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; if (s != UMFPACK_ERROR_argument_missing) error ("68",0.) ; if (prl > 2) printf ("erroroneous sys arg for umfpack_solve:\n") ; s = UMFPACK_solve (-1, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (s != UMFPACK_ERROR_invalid_system) error ("65d",0.) ; /* check internal error message */ UMFPACK_report_status (Con, UMFPACK_ERROR_internal_error) ; /* check unrecognized error code */ UMFPACK_report_status (Con, 123123999) ; s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), (void *) NULL, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("70",0.) ; s = UMFPACK_wsolve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), (void *) NULL, Con, Info, Pa, Wx) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("71",0.) ; s = UMFPACK_get_determinant (CARG (&Mx, &Mz), &Exp, (void *) NULL, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("71det",0.) ; s = UMFPACK_get_determinant (CARG (DNULL, &Mz), &Exp, Numeric, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh??", (double) __LINE__) ; if (s != UMFPACK_ERROR_argument_missing) error ("72det",0.) ; /* corrupt Numeric */ Num = (NumericType *) Numeric ; Num->valid = 4909284 ; s = UMFPACK_get_numeric (Lp, Li, CARG(Lx,Lz), Up, Ui, CARG(Ux,Uz), P, Q, CARG(DNULL,DNULL), &do_recip, Rs, Numeric) ; if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("91",0.) ; s = UMFPACK_save_numeric (Numeric, "nbad.umf") ; if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("70num",0.) ; s = UMFPACK_get_lunz (&lnz, &unz, &nnrow, &nncol, &nzud, Numeric) ; printf ("s "ID"\n", s) ; if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("70b",0.) ; s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), (void *) NULL, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("70",0.) ; s = UMFPACK_wsolve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), (void *) NULL, Con, Info, Pa, Wx) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("71",0.) ; if (prl > 2) printf ("bad Numeric: ") ; s = UMFPACK_report_numeric ( Numeric, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("82",0.) ; /* fix numeric */ Num->valid = NUMERIC_VALID ; if (prl > 2) printf ("fixed Numeric: ") ; s = UMFPACK_report_numeric (Numeric, Con) ; if (s != UMFPACK_OK) error ("82",0.) ; /* valid Numeric, but no permissions */ s = UMFPACK_save_numeric (Numeric, "/root/nbad.umf") ; if (s != UMFPACK_ERROR_file_IO) error ("72num",0.) ; /* corrupt Numeric again */ Num->n_row = -1 ; s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), (void *) NULL, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("72",0.) ; s = UMFPACK_wsolve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), (void *) NULL, Con, Info, Pa, Wx) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("73",0.) ; s = UMFPACK_scale (CARG(x,xz), CARG(b,bz), (void *) NULL) ; if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("72f",0.) ; /* fix numeric */ if (prl > 2) printf ("bad Numeric again: ") ; s = UMFPACK_report_numeric (Numeric, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("81",0.) ; Num->n_row = n ; if (prl > 2) printf ("fixed Numeric again: ") ; s = UMFPACK_report_numeric (Numeric, Con) ; if (s != UMFPACK_OK) error ("80",0.) ; /* corrupt Numeric again (bad P), then fix it */ c = Num->Rperm [0] ; Num->Rperm [0] = -1 ; if (prl > 2) printf ("bad Numeric (P): ") ; s = UMFPACK_report_numeric (Numeric, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("200",0.) ; Num->Rperm [0] = c ; if (prl > 2) printf ("fixed Numeric again: ") ; s = UMFPACK_report_numeric (Numeric, Con) ; if (s != UMFPACK_OK) error ("200b",0.) ; /* corrupt Numeric again (bad Q), then fix it */ c = Num->Cperm [0] ; Num->Cperm [0] = -1 ; if (prl > 2) printf ("bad Numeric (Q): ") ; s = UMFPACK_report_numeric (Numeric, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("201",0.) ; Num->Cperm [0] = c ; if (prl > 2) printf ("fixed Numeric again: ") ; s = UMFPACK_report_numeric (Numeric, Con) ; if (s != UMFPACK_OK) error ("201b",0.) ; /* corrupt Numeric again (bad Lpos), then fix it */ for (k = 0 ; k < n ; k++) { if (Num->Lpos [k] != EMPTY) break ; } c = Num->Lpos [k] ; Num->Lpos [k] = c + 1 ; if (prl > 2) printf ("bad Numeric (Lpos [k]): ") ; s = UMFPACK_report_numeric (Numeric, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("204",0.) ; Num->Lpos [k] = c ; if (prl > 2) printf ("fixed Numeric again: ") ; s = UMFPACK_report_numeric (Numeric, Con) ; if (s != UMFPACK_OK) error ("204b",0.) ; /* corrupt Numeric again (bad Upos), then fix it */ for (k = 0 ; k < n ; k++) { if (Num->Upos [k] != EMPTY) break ; } c = Num->Upos [k] ; Num->Upos [k] = 9999999 ; if (prl > 2) printf ("bad Numeric (Upos [0]): ") ; s = UMFPACK_report_numeric (Numeric, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("204c",0.) ; Num->Upos [k] = c ; if (prl > 2) printf ("fixed Numeric again: ") ; s = UMFPACK_report_numeric (Numeric, Con) ; if (s != UMFPACK_OK) error ("204d",0.) ; /* corrupt Numeric again (bad Lilen), then fix it */ c = Num->Lilen [0] ; Num->Lilen [0] = -1 ; if (prl > 2) printf ("bad Numeric (Lilen [0]): ") ; s = UMFPACK_report_numeric (Numeric, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("205",0.) ; Num->Lilen [0] = c ; if (prl > 2) printf ("fixed Numeric again: ") ; s = UMFPACK_report_numeric (Numeric, Con) ; if (s != UMFPACK_OK) error ("205b",0.) ; /* corrupt Numeric again (bad Lip), then fix it */ c = Num->Lip [0] ; Num->Lip [0] = -9999999 ; printf ("Bad numeric (Lip [0])\n") ; fflush (stdout) ; if (prl > 2) printf ("bad Numeric (Lip [0]): ") ; s = UMFPACK_report_numeric (Numeric, Con) ; fflush (stdout) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("206",0.) ; Num->Lip [0] = c ; printf ("Fixed numeric (Lip [0])\n") ; fflush (stdout) ; if (prl > 2) printf ("fixed Numeric again: ") ; s = UMFPACK_report_numeric (Numeric, Con) ; if (s != UMFPACK_OK) error ("206b",0.) ; fflush (stdout) ; /* corrupt Numeric again (bad LPattern), then fix it */ c = Num->Memory [1].header.size ; Num->Memory [1].header.size = -1 ; if (prl > 2) printf ("bad Numeric (Pattern): ") ; s = UMFPACK_report_numeric (Numeric, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("208",0.) ; Num->Memory [1].header.size = c ; if (prl > 2) printf ("fixed Numeric again: ") ; s = UMFPACK_report_numeric (Numeric, Con) ; if (s != UMFPACK_OK) error ("208b",0.) ; /* corrupt Numeric again (bad UPattern), then fix it */ printf ("test 208d:\n") ; for (k = n-1 ; k >= 0 ; k--) { if (Num->Uilen [k] > 0) break ; } ip = (Int *) (Num->Memory + SCALAR_ABS (Num->Uip [k])) ; c = *ip ; printf ("Corrupting Num->Uip [k="ID"] = "ID"\n", k, c) ; *ip = -1 ; if (prl > 2) printf ("bad Numeric (UPattern): ") ; s = UMFPACK_report_numeric (Numeric, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("208c",0.) ; *ip = c ; if (prl > 2) printf ("fixed Numeric again: ") ; s = UMFPACK_report_numeric (Numeric, Con) ; if (s != UMFPACK_OK) error ("208d",0.) ; /* corrupt Numeric again (bad Uilen), then fix it */ c = Num->Uilen [k] ; printf ("Corrupting Num->Uilen [k="ID"] = "ID"\n", k, c) ; Num->Uilen [k] = -1 ; if (prl > 2) printf ("bad Numeric (Uilen [k]): ") ; s = UMFPACK_report_numeric (Numeric, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("205c",0.) ; Num->Uilen [k] = c ; s = UMFPACK_report_numeric (Numeric, Con) ; if (prl > 2) printf ("fixed Numeric again: ") ; if (s != UMFPACK_OK) error ("205d",0.) ; /* corrupt Numeric again (bad Uilen), then fix it */ c = Num->Uilen [k-1] ; Num->Uilen [k-1] = 99999 ; if (prl > 2) printf ("bad Numeric (Uilen [k-1]): ") ; s = UMFPACK_report_numeric (Numeric, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("210",0.) ; Num->Uilen [k-1] = c ; if (prl > 2) printf ("fixed Numeric again: ") ; s = UMFPACK_report_numeric (Numeric, Con) ; if (s != UMFPACK_OK) error ("210b",0.) ; /* corrupt Numeric again (bad Uip), then fix it */ c = Num->Uip [k] ; Num->Uip [k] = -999999 ; printf ("Bad numeric Uip [k]\n") ; fflush (stdout) ; if (prl > 2) printf ("bad Numeric (Uip [k]): ") ; s = UMFPACK_report_numeric (Numeric, Con) ; fflush (stdout) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("206c",0.) ; Num->Uip [k] = c ; printf ("Fixed numeric Uip [k]\n") ; fflush (stdout) ; s = UMFPACK_report_numeric (Numeric, Con) ; if (prl > 2) printf ("fixed Numeric again: ") ; fflush (stdout) ; if (s != UMFPACK_OK) error ("206d",0.) ; free (Rs) ; /* ] */ free (Wx) ; /* ] */ free (Pa) ; /* ] */ free (Q) ; /* ] */ free (P) ; /* ] */ free (Uz) ; /* ] */ free (Ux) ; /* ] */ free (Ui) ; /* ] */ free (Up) ; /* ] */ free (Lz) ; /* ] */ free (Lx) ; /* ] */ free (Li) ; /* ] */ free (Lp) ; /* ] */ UMFPACK_free_numeric (&Numeric) ; /* ] */ if (prl > 2) printf ("Numeric file not found:\n") ; s = UMFPACK_load_numeric (&Numeric, "file_not_found") ; if (s != UMFPACK_ERROR_file_IO) error ("71num",0.) ; } /* ------------------------------------------------------------------ */ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, DNULL) ; if (!Numeric || s != UMFPACK_OK) error ("31b",0.) ; UMFPACK_free_numeric (&Numeric) ; /* ------------------------------------------------------------------ */ /* change the pattern */ if (Con) { Con [UMFPACK_SCALE] = UMFPACK_SCALE_NONE ; } printf ("change of pattern between symbolic and numeric:\n") ; c = Ap [2] ; Ap [2] = -1 ; s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, DNULL) ; if (s != UMFPACK_ERROR_different_pattern) error ("97a", (double) s) ; Ap [2] = c ; c = Ai [2] ; Ai [2] = -1 ; s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, DNULL) ; if (s != UMFPACK_ERROR_different_pattern) error ("97b", (double) s) ; Ai [2] = c ; c = Ai [2] ; Ai [2] = 9990099 ; s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, DNULL) ; if (s != UMFPACK_ERROR_different_pattern) error ("97c", (double) s) ; Ai [2] = c ; c = Ap [n] ; Ai [Ap [n]++] = n-1 ; s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, DNULL) ; if (s != UMFPACK_ERROR_different_pattern) error ("97d", (double) s) ; Ap [n] = c ; printf ("done testing change of pattern between symbolic and numeric.\n") ; if (Con) { Con [UMFPACK_SCALE] = UMFPACK_DEFAULT_SCALE ; } /* ------------------------------------------------------------------ */ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, DNULL) ; if (!Numeric || s != UMFPACK_OK) error ("31c",0.) ; UMFPACK_free_numeric (&Numeric) ; /* ------------------------------------------------------------------ */ printf ("free nothing:\n") ; UMFPACK_free_numeric ((void **) NULL) ; UMFPACK_free_symbolic ((void **) NULL) ; printf ("free nothing OK\n") ; /* ------------------------------------------------------------------ */ /* test for singular matrix (IN_IN case) */ for (j = 0 ; j < n ; j++) { for (p = 0 ; p < nz ; p++) Ax2 [p] = Ax [p] ; for (p = 0 ; p < nz ; p++) Az2 [p] = Az [p] ; printf ("lastcol = "ID"\n", j) ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { Ax2 [p] = 0.0 ; Az2 [p] = 0.0 ; } s = UMFPACK_numeric (Ap, Ai, CARG(Ax2,Az2), Symbolic, &Numeric, Con, Info) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; if (!Numeric || s != UMFPACK_WARNING_singular_matrix) error ("120",0.) ; UMFPACK_free_numeric (&Numeric) ; } /* ------------------------------------------------------------------ */ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), (void *) NULL, &Numeric, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Numeric || s != UMFPACK_ERROR_invalid_Symbolic_object) error ("32",0.) ; /* ------------------------------------------------------------------ */ s = UMFPACK_numeric (INULL, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Numeric || s != UMFPACK_ERROR_argument_missing) error ("32b",0.) ; /* ------------------------------------------------------------------ */ for (p = 0 ; p < nz ; p++) Ax2 [p] = 0.0 ; for (p = 0 ; p < nz ; p++) Az2 [p] = 0.0 ; s = UMFPACK_numeric (Ap, Ai, CARG(Ax2,Az2), Symbolic, &Numeric, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (!Numeric || s != UMFPACK_WARNING_singular_matrix) error ("33",0.) ; UMFPACK_free_numeric (&Numeric) ; /* ------------------------------------------------------------------ */ for (p = 0 ; p < nz ; p++) Ax2 [p] = Ax [p] ; for (p = 0 ; p < nz ; p++) Az2 [p] = Ax [p] ; i = UMFPACK_DENSE_DEGREE_THRESHOLD (0.2, n) ; for (j = 0 ; j < n ; j++) { d = Ap [j+1] - Ap [j] ; if (d > i) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { Ax2 [p] = 0.0 ; Az2 [p] = 0.0 ; } } } s = UMFPACK_numeric (Ap, Ai, CARG(Ax2,Az2), Symbolic, &Numeric, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (!Numeric || s != UMFPACK_WARNING_singular_matrix) error ("33",0.) ; UMFPACK_free_numeric (&Numeric) ; /* ------------------------------------------------------------------ */ /* corrupt the Symbolic object */ Sym = (SymbolicType *) Symbolic ; printf ("32c:\n") ; fflush (stdout) ; Sym->valid = 4040404 ; if (prl > 2) printf ("\nSymbolic busted: ") ; s = UMFPACK_report_symbolic ((void *) Sym, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Symbolic_object)) error ("79",0.) ; Front_leftmostdesc = (Int *) malloc (n * sizeof (Int)) ; /* [ */ Front_1strow = (Int *) malloc (n * sizeof (Int)) ; /* [ */ Front_npivots = (Int *) malloc (n * sizeof (Int)) ; /* [ */ Front_parent = (Int *) malloc (n * sizeof (Int)) ; /* [ */ Chain_start = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ Chain_maxrows = (Int *) malloc (n * sizeof (Int)) ; /* [ */ Chain_maxcols = (Int *) malloc (n * sizeof (Int)) ; /* [ */ Qtree = (Int *) malloc (n * sizeof (Int)) ; /* [ */ Ptree = (Int *) malloc (n * sizeof (Int)) ; /* [ */ if (!Front_npivots || !Front_parent || !Chain_start || !Chain_maxrows || !Chain_maxcols || !Qtree) error ("out of memory (22)",0.) ; s = UMFPACK_get_symbolic (&nnrow, &nncol, &n1, &nnz, &nfr, &nchains, Ptree, Qtree, Front_npivots, Front_parent, Front_1strow, Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ; if (s != UMFPACK_ERROR_invalid_Symbolic_object) error ("93", 0.) ; free (Ptree) ; /* ] */ free (Qtree) ; /* ] */ free (Chain_maxcols) ; /* ] */ free (Chain_maxrows) ; /* ] */ free (Chain_start) ; /* ] */ free (Front_parent) ; /* ] */ free (Front_npivots) ; /* ] */ free (Front_1strow) ; /* ] */ free (Front_leftmostdesc) ; /* ] */ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; printf ("32c s: "ID"\n", s) ; if (Numeric || s != UMFPACK_ERROR_invalid_Symbolic_object) error ("32c",0.) ; Sym->valid = SYMBOLIC_VALID ; if (prl > 2) printf ("\nSymbolic fixed: ") ; s = UMFPACK_report_symbolic (Symbolic, Con) ; if (s != UMFPACK_OK) error ("78",0.) ; /* valid Symbolic, but no permissions */ s = UMFPACK_save_symbolic (Symbolic, "/root/sbad.umf") ; if (s != UMFPACK_ERROR_file_IO) error ("72sym",0.) ; /* corrupt Symbolic again (bad Qinit) and then fix it */ c = Sym->Cperm_init [0] ; Sym->Cperm_init [0] = -1 ; if (prl > 2) printf ("\nSymbolic busted (bad Qinit): ") ; s = UMFPACK_report_symbolic (Symbolic, Con) ; Sym->Cperm_init [0] = c ; /* ------------------------------------------------------------------ */ /* corrupt the Symbolic object again */ printf ("32d:\n") ; fflush (stdout) ; Sym->Cperm_init = (Int *) UMF_free ((void *) Sym->Cperm_init) ; s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Numeric || s != UMFPACK_ERROR_invalid_Symbolic_object) error ("32d",0.) ; s = UMFPACK_save_symbolic (Symbolic, "sbad.umf") ; if (s != UMFPACK_ERROR_invalid_Symbolic_object) error ("70sym",0.) ; /* ------------------------------------------------------------------ */ UMFPACK_free_symbolic (&Symbolic) ; /* ] */ printf ("Symbolic file not found:\n") ; s = UMFPACK_load_symbolic (&Symbolic, "file_not_found") ; if (s != UMFPACK_ERROR_file_IO) error ("71sym",0.) ; #if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG) if (UMF_malloc_count != 0) error ("umfpack memory leak!!",0.) ; #endif /* printf (" made it here "ID"\n", umf_fail) ; */ fflush (stdout) ; /* == done ] ======================================================== */ /* ------------------------------------------------------------------ */ s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(DNULL,DNULL), Qinit, &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; /* printf (" made it here 3 "ID"\n", umf_fail) ; */ fflush (stdout) ; s = Info [UMFPACK_STATUS] ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (!Symbolic || s != UMFPACK_OK) error ("16b",0.) ; /* printf (" made it here too "ID"\n", umf_fail) ; */ UMFPACK_free_symbolic (&Symbolic) ; /* ------------------------------------------------------------------ */ if (prl > 2) printf ("Qinit missing: ") ; s = UMFPACK_report_perm (n, INULL, Con) ; if (s != UMFPACK_OK) error ("17",0.) ; s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(DNULL,DNULL), INULL, &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (!Symbolic || s != UMFPACK_OK) error ("17b",0.) ; UMFPACK_free_symbolic (&Symbolic) ; /* ------------------------------------------------------------------ */ if (prl > 2) printf ("Qinit n=0: ") ; s = UMFPACK_report_perm (0, Qinit, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_n_nonpositive)) error ("18",0.) ; /* ------------------------------------------------------------------ */ c = Qinit [5] ; Qinit [5]++ ; if (prl > 2) printf ("Qinit bad: ") ; s = UMFPACK_report_perm (n, Qinit, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_permutation)) error ("19",0.) ; s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(DNULL,DNULL), Qinit, &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Symbolic || s != UMFPACK_ERROR_invalid_permutation) error ("19b",0.) ; Qinit [5] = c ; /* ------------------------------------------------------------------ */ c = Qinit [5] ; Qinit [5] = -1 ; if (prl > 2) printf ("Qinit bad (out of range): ") ; s = UMFPACK_report_perm (n, Qinit, Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_permutation)) error ("19c",0.) ; s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(DNULL,DNULL), Qinit, &Symbolic, Con, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (Symbolic || s != UMFPACK_ERROR_invalid_permutation) error ("19d",0.) ; Qinit [5] = c ; /* ------------------------------------------------------------------ */ s = UMFPACK_col_to_triplet (n, Ap, INULL) ; if (s != UMFPACK_ERROR_argument_missing) error ("20a",0.) ; /* ------------------------------------------------------------------ */ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG (Ax2,Az2) C1ARG(0)) ; if (s != UMFPACK_OK) error ("50",0.); /* ------------------------------------------------------------------ */ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(DNULL,DNULL), Pinit, Qinit, Ap2, Ai2, CARG (DNULL,DNULL) C1ARG(0)) ; if (s != UMFPACK_OK) error ("50e",0.); /* ------------------------------------------------------------------ */ if (prl > 2) printf ("UMFPACK transpose test R = A(P,:)'\n") ; s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, INULL, Ap2, Ai2, CARG (Ax2,Az2) C1ARG(1)) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (s != UMFPACK_OK) error ("50",0.); if (prl > 2) printf ("\nPinit: ") ; s = UMFPACK_report_perm (n, Pinit, Con) ; if (prl > 2) printf ("\nR: ") ; s = UMFPACK_report_matrix (n , n, Ap2, Ai2, CARG (Ax2,Az2), 1, Con) ; if (s != UMFPACK_OK) error ("50e",0.); s = UMFPACK_col_to_triplet (n, Ap2, Aj) ; if (s != UMFPACK_OK) error ("50i",0.); if (prl > 2) printf ("\nR, triplet form: ") ; s = UMFPACK_report_triplet (n, n, nz, Ai2, Aj, CARG(Ax2,Az2), Con) ; if (s != UMFPACK_OK) error ("50y",0.); /* ------------------------------------------------------------------ */ if (prl > 2) printf ("UMFPACK transpose test R = pattern of A(P,:).'\n") ; s = UMFPACK_transpose (n, n, Ap, Ai, CARG(DNULL,DNULL), Pinit, INULL, Ap2, Ai2, CARG (DNULL,DNULL) C1ARG(0)) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (s != UMFPACK_OK) error ("50f",0.); if (prl > 2) printf ("\npattern of R: ") ; s = UMFPACK_report_matrix (n , n, Ap2, Ai2, CARG (DNULL,DNULL), 1, Con) ; if (s != UMFPACK_OK) error ("50g",0.); s = UMFPACK_col_to_triplet (n, Ap2, Aj) ; if (s != UMFPACK_OK) error ("50k",0.); if (prl > 2) printf ("\npattern of R, triplet form: ") ; s = UMFPACK_report_triplet (n, n, nz, Ai2, Aj, CARG (DNULL,DNULL), Con) ; if (s != UMFPACK_OK) error ("50z",0.); /* ------------------------------------------------------------------ */ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), INULL, INULL, Ap2, Ai2, CARG (Ax2,Az2) C1ARG(0)) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_OK) error ("51a",0.); /* ------------------------------------------------------------------ */ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, INULL, Ap2, Ai2, CARG (Ax2,Az2) C1ARG(0)) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_OK) error ("51b",0.); /* ------------------------------------------------------------------ */ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), INULL, Qinit, Ap2, Ai2, CARG (Ax2,Az2) C1ARG(0)) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_OK) error ("51c",0.); /* ------------------------------------------------------------------ */ s = UMFPACK_transpose (0, 0, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG (Ax2,Az2) C1ARG(0)) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_n_nonpositive) error ("54",0.); /* ------------------------------------------------------------------ */ c = Pinit [5] ; Pinit [5] = n-1 ; s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG (Ax2,Az2) C1ARG(0)) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_invalid_permutation) error ("51e",0.); Pinit [5] = c ; /* ------------------------------------------------------------------ */ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG (Ax2,Az2) C1ARG(0)) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_OK) error ("51d",0.); /* ------------------------------------------------------------------ */ c = Pinit [5] ; Pinit [5] = -1 ; s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG (Ax2,Az2) C1ARG(0)) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_invalid_permutation) error ("56",0.); Pinit [5] = c ; /* ------------------------------------------------------------------ */ s = UMFPACK_col_to_triplet (n, INULL, Aj) ; if (s != UMFPACK_ERROR_argument_missing) error ("20b",0.) ; /* ------------------------------------------------------------------ */ s = UMFPACK_col_to_triplet (0, Ap, Aj) ; if (s != UMFPACK_ERROR_n_nonpositive) error ("20c",0.) ; /* ------------------------------------------------------------------ */ Ap [0] = 99 ; s = UMFPACK_col_to_triplet (n, Ap, Aj) ; if (s != UMFPACK_ERROR_invalid_matrix) error ("20d",0.) ; s = do_amd_transpose (n, Ap, Aj, Ap2, Ai2) ; if (s != AMD_INVALID) error ("20d_amd",0.) ; Ap [0] = 0 ; /* ------------------------------------------------------------------ */ Ap [n] = 0 ; s = UMFPACK_col_to_triplet (n, Ap, Aj) ; if (s != UMFPACK_ERROR_invalid_matrix) error ("20e",0.) ; Ap [n] = nz ; /* ------------------------------------------------------------------ */ c = Ap [3] ; Ap [3] = nz+1 ; s = UMFPACK_col_to_triplet (n, Ap, Aj) ; if (s != UMFPACK_ERROR_invalid_matrix) error ("20f",0.) ; s = do_amd_transpose (n, Ap, Aj, Ap2, Ai2) ; if (s != AMD_INVALID) error ("20f_amd",0.) ; Ap [3] = c ; /* ------------------------------------------------------------------ */ c = Aj [0] ; Aj [0] = -1 ; s = do_amd_transpose (n, Ap, Aj, Ap2, Ai2) ; if (s != AMD_INVALID) error ("20z_amd",0.) ; Aj [0] = c ; /* ------------------------------------------------------------------ */ c = Ap [4] ; Ap [4] = Ap [3]-1 ; s = UMFPACK_col_to_triplet (n, Ap, Aj) ; if (s != UMFPACK_ERROR_invalid_matrix) error ("20i",0.) ; Ap [4] = c ; /* ------------------------------------------------------------------ */ s = UMFPACK_col_to_triplet (n, Ap, Aj) ; if (s != UMFPACK_OK) error ("20",0.) ; /* ------------------------------------------------------------------ */ if (prl > 2) printf ("\nTriples OK: ") ; s = UMFPACK_report_triplet (n, n, nz, Ai, Aj, CARG(Ax,Az), Con) ; if (s != UMFPACK_OK) error ("21",0.) ; /* ------------------------------------------------------------------ */ if (prl > 2) printf ("\nTriples pattern OK: ") ; s = UMFPACK_report_triplet (n, n, nz, Ai, Aj, CARG(DNULL,DNULL), Con) ; if (s != UMFPACK_OK) error ("21b",0.) ; /* ------------------------------------------------------------------ */ if (prl > 2) printf ("\nTriples, Ai null: ") ; s = UMFPACK_report_triplet (n, n, nz, INULL, Aj, CARG(Ax,Az), Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_argument_missing)) error ("22",0.) ; /* ------------------------------------------------------------------ */ if (prl > 2) printf ("\nTriples, nz=0: ") ; s = UMFPACK_report_triplet (n, n, 0, Ai, Aj, CARG(Ax,Az), Con) ; if (s != UMFPACK_OK) error ("23a",0.) ; if (prl > 2) printf ("\nTriples, nz=-1: ") ; s = UMFPACK_report_triplet (n, n, -1, Ai, Aj, CARG(Ax,Az), Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_matrix)) error ("23",0.) ; /* ------------------------------------------------------------------ */ if (prl > 2) printf ("\nTriples, n=0: ") ; s = UMFPACK_report_triplet (0, 0, nz, Ai, Aj, CARG(Ax,Az), Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_n_nonpositive)) error ("24",0.) ; /* ------------------------------------------------------------------ */ Map = (Int *) malloc (nz * sizeof (Int)) ; /* [ */ c = Aj [1] ; Aj [1] = -1 ; if (prl > 2) printf ("\nTriples, Aj bad: ") ; s = UMFPACK_report_triplet (n, n, nz, Ai, Aj, CARG(Ax,Az), Con) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_matrix)) error ("41",0.) ; s = UMFPACK_triplet_to_col (n, n, nz, Ai, Aj, CARG(Ax,Az), Ap2, Ai2, CARG (Ax2,Az2), (Int *) NULL) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_invalid_matrix) error ("41",0.) ; s = UMFPACK_triplet_to_col (n, n, nz, Ai, Aj, CARG(Ax,Az), Ap2, Ai2, CARG (Ax2,Az2), (Int *) NULL) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_invalid_matrix) error ("42",0.); s = UMFPACK_triplet_to_col (n, n, nz, Ai, Aj, CARG(DNULL,DNULL), Ap2, Ai2, CARG (DNULL,DNULL), Map) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_invalid_matrix) error ("42cc",0.); s = UMFPACK_triplet_to_col (n, n, nz, Ai, Aj, CARG(DNULL,DNULL), Ap2, Ai2, CARG (Ax2,Az2), (Int *) NULL) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_invalid_matrix) error ("42b",0.); Aj [1] = c ; /* ------------------------------------------------------------------ */ s = UMFPACK_triplet_to_col (n, n, nz, Ai, Aj, CARG(Ax,Az), Ap2, Ai2, CARG (Ax2,Az2), (Int *) NULL) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_OK) error ("42c",0.); s = UMFPACK_triplet_to_col (n, n, nz, Ai, Aj, CARG(Ax,Az), Ap2, Ai2, CARG (Ax2,Az2), Map) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_OK) error ("42c.2",0.); /* check the Map */ for (k = 0 ; k < nz ; k++) { p = Map [k] ; i = Ai [k] ; j = Aj [k] ; if (i != Ai2 [p]) error ("Map Ai2.2", 0.) ; if (!(Ap2 [j] <= p && p < Ap2 [j+1])) error ("Map Ap2.2", 0.) ; } /* ------------------------------------------------------------------ */ s = UMFPACK_triplet_to_col (n, n, nz, Ai, Aj, CARG(DNULL,DNULL), Ap2, Ai2, CARG (Ax2,Az2), (Int *) NULL) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_OK) error ("42d",0.); s = UMFPACK_triplet_to_col (n, n, nz, Ai, Aj, CARG(DNULL,DNULL), Ap2, Ai2, CARG (Ax2,Az2), Map) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_OK) error ("42d.1",0.); /* check the Map */ for (k = 0 ; k < nz ; k++) { p = Map [k] ; i = Ai [k] ; j = Aj [k] ; if (i != Ai2 [p]) error ("Map Ai2.1", 0.) ; if (!(Ap2 [j] <= p && p < Ap2 [j+1])) error ("Map Ap2.1", 0.) ; } c = Aj [1] ; Aj [1] = -1 ; s = UMFPACK_triplet_to_col (n, n, nz, Ai, Aj, CARG(Ax,Az), Ap2, Ai2, CARG (Ax2,Az2), Map) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_invalid_matrix) error ("42c.3",0.); Aj [1] = c ; free (Map) ; /* ] */ /* ------------------------------------------------------------------ */ s = UMFPACK_triplet_to_col (0, 0, nz, Ai, Aj, CARG(Ax,Az), Ap2, Ai2, CARG (Ax2,Az2), (Int *) NULL) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_n_nonpositive) error ("44",0.); /* ------------------------------------------------------------------ */ s = UMFPACK_triplet_to_col (n, n, 0, Ai, Aj, CARG(Ax,Az), Ap2, Ai2, CARG (Ax2,Az2), (Int *) NULL) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_OK) error ("45a",0.); if (prl > 2) printf ("\nall empty A2: ") ; s = UMFPACK_report_matrix (n , n, Ap2, Ai2, CARG (Ax2,Az2), 1, Con) ; if (s != UMFPACK_OK) error ("45c",0.) ; /* ------------------------------------------------------------------ */ s = UMFPACK_triplet_to_col (n, n, -1, Ai, Aj, CARG(Ax,Az), Ap2, Ai2, CARG (Ax2,Az2), (Int *) NULL) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_invalid_matrix) error ("45",0.); /* ------------------------------------------------------------------ */ s = UMFPACK_triplet_to_col (n, n, nz, INULL, Aj, CARG(Ax,Az), Ap2, Ai2, CARG (Ax2,Az2), (Int *) NULL) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_argument_missing) error ("46",0.); /* ------------------------------------------------------------------ */ free (Az2) ; /* ] */ free (Ax2) ; /* ] */ free (Ai2) ; /* ] */ free (Aj) ; /* ] */ free (Az) ; /* ] */ free (Ax) ; /* ] */ free (Ai) ; /* ] */ free (Ap) ; /* ] */ #if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG) if (UMF_malloc_count != 0) error ("umfpack memory leak!!",0.) ; #endif printf ("\n]]]]\n\n\n") ; } } free (Ap2) ; /* ] */ free (xz) ; /* ] */ free (x) ; /* ] */ free (bz) ; /* ] */ free (b) ; /* ] */ free (Qinit2) ; /* ] */ free (Pinit) ; /* ] */ free (Qinit) ; /* ] */ free (Pamd) ; /* ] */ /* ---------------------------------------------------------------------- */ /* reset rand ( ) */ /* ---------------------------------------------------------------------- */ srand (1) ; /* ---------------------------------------------------------------------- */ /* test memory allocation */ /* ---------------------------------------------------------------------- */ n = 200 ; printf ("memory test\n") ; #if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG) if (UMF_malloc_count != 0) error ("umfpack mem test starts memory leak!!\n",0.) ; #endif matgen_sparse (n, 8*n, 0, 0, 4, 2*n, &Ap, &Ai, &Ax, &Az, 1, 0) ; /* [[[[ */ Qinit = (Int *) malloc (n * sizeof (Int)) ; /* [ */ b = (double *) malloc (n * sizeof (double)) ; /* [ */ bz= (double *) calloc (n , sizeof (double)) ; /* [ */ x = (double *) malloc (n * sizeof (double)) ; /* [ */ xz= (double *) calloc (n , sizeof (double)) ; /* [ */ bgen (n, Ap, Ai, Ax,Az, b,bz) ; nz = Ap [n] ; randperm (n, Qinit) ; UMFPACK_defaults (Control) ; for (prl = 5 ; prl >= -1 ; prl--) { printf ("prl "ID" memtest\n", prl) ; fflush (stdout) ; umf_realloc_fail = -1 ; umf_realloc_hi = 0 ; umf_realloc_lo = 0 ; umf_fail_hi = 0 ; umf_fail_lo = 0 ; Control [UMFPACK_PRL] = (Int) prl ; umf_fail = 1 ; if (prl > 2) printf ("Memfail Qinit: ") ; s = UMFPACK_report_perm (n, Qinit, Control) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_out_of_memory)) error ("101",0.) ; Cp = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ Cj = (Int *) malloc (nz * sizeof (Int)) ; /* [ */ Ci = (Int *) malloc (nz * sizeof (Int)) ; /* [ */ Cx = (double *) malloc (nz * sizeof (double)) ; /* [ */ Cz = (double *) calloc (nz , sizeof (double)) ; /* [ */ Bp = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ Bj = (Int *) malloc (nz * sizeof (Int)) ; /* [ */ Bi = (Int *) malloc (nz * sizeof (Int)) ; /* [ */ Bx = (double *) malloc (nz * sizeof (double)) ; /* [ */ Bz = (double *) calloc (nz , sizeof (double)) ; /* [ */ Map = (Int *) malloc (nz * sizeof (Int)) ; /* [ */ if (!Cp || !Ci || !Cx || !Cj) error ("out of memory (23)",0.) ; if (!Bp || !Bi || !Bx || !Bj) error ("out of memory (24)",0.) ; if (!Bz || !Cz) error ("out of memory (25)",0.) ; umf_fail = 1 ; s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), INULL, INULL, Cp, Ci, CARG(Cx,Cz) C1ARG(0)) ; if (s != UMFPACK_ERROR_out_of_memory) error ("113", 0.) ; for (k = 0 ; k < nz ; k++) { Ci [k] = irand (n) ; Cj [k] = irand (n) ; Cx [k] = 2.0 * (xrand ( ) - 1.0) ; #ifdef COMPLEX Cx [k] = 2.0 * (xrand ( ) - 1.0) ; #else Cx [k] = 0. ; #endif } for (i = 1 ; i <= 4 ; i++) { umf_fail = i ; s = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(DNULL,DNULL), Bp, Bi, CARG(DNULL,DNULL), (Int *) NULL) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_out_of_memory) error ("114", (double) i) ; } for (i = 1 ; i <= 5 ; i++) { umf_fail = i ; s = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(Cx,Cz), Bp, Bi, CARG(Bx,Bz), (Int *) NULL) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_out_of_memory) error ("115", (double) i) ; } for (i = 1 ; i <= 5 ; i++) { umf_fail = i ; s = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(DNULL,DNULL), Bp, Bi, CARG(DNULL,DNULL), Map) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_out_of_memory) error ("114", (double) i) ; } for (i = 1 ; i <= 6 ; i++) { umf_fail = i ; s = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(Cx,Cz), Bp, Bi, CARG(Bx,Bz), Map) ; UMFPACK_report_status (Con, s) ; if (s != UMFPACK_ERROR_out_of_memory) error ("115", (double) i) ; } free (Map) ; /* ] */ free (Bz) ; /* ] */ free (Bx) ; /* ] */ free (Bi) ; /* ] */ free (Bj) ; /* ] */ free (Bp) ; /* ] */ free (Cz) ; /* ] */ free (Cx) ; /* ] */ free (Ci) ; /* ] */ free (Cj) ; /* ] */ free (Cp) ; /* ] */ for (i = 1 ; i <= 24 ; i++) { umf_fail = i ; printf ("umf_fail starts at "ID"\n", umf_fail) ; fflush (stdout) ; #if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG) if (UMF_malloc_count != 0) error ("umfpack mem test starts memory leak!!\n",0.) ; #endif s = UMFPACK_symbolic (n, n, Ap, Ai, CARG(Ax,Az), &Symbolic, Control, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; if (Symbolic || Info [UMFPACK_STATUS] != UMFPACK_ERROR_out_of_memory) error ("104", (double) i) ; } umf_fail = 25 ; s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Control, Info) ; /* [ */ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; if (!Symbolic || s != UMFPACK_OK) error ("105", 0.) ; umf_fail = 1 ; if (prl > 2) printf ("\nMemfail Symbolic: ") ; s = UMFPACK_report_symbolic (Symbolic, Control) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_out_of_memory)) error ("102",0.) ; /* alloc reallocs succeed */ umf_realloc_fail = -1 ; umf_realloc_hi = 0 ; umf_realloc_lo = 0 ; /* Initial Numeric->Memory allocation fails when umf_fail is 28, and never succeeds. * All mallocs succeed if umf_fail is 16 + 11 + 1 */ umf_fail_lo = -9999999 ; for (i = 1 ; i <= 29 ; i++) { umf_fail = i ; printf ("\nDoing numeric, umf_fail = "ID"\n", umf_fail) ; s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; if (i < 29) { if (Numeric || s != UMFPACK_ERROR_out_of_memory) error ("106", (double) i) ; } else { if (!Numeric || s != UMFPACK_OK) error ("106z", (double) umf_fail) ; UMFPACK_free_numeric (&Numeric) ; } } /* everything succeeds, use a small alloc_init */ printf ("106y:\n") ; Control [UMFPACK_ALLOC_INIT] = -30000 ; UMFPACK_report_control (Control) ; umf_fail = 29 ; s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; if (!Numeric || s != UMFPACK_OK) error ("106y", (double) umf_fail) ; UMFPACK_free_numeric (&Numeric) ; /* all malloc's succeed - no realloc during factorization */ umf_fail = -1 ; umf_fail_lo = 0 ; umf_fail_hi = 0 ; umf_realloc_fail = 1 ; umf_realloc_hi = 0 ; umf_realloc_lo = -9999999 ; /* restore Control */ UMFPACK_defaults (Control) ; Control [UMFPACK_PRL] = (Int) prl ; /* alloc init the smallest size */ Control [UMFPACK_ALLOC_INIT] = 0.0 ; s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; if (Numeric) { UMFPACK_free_numeric (&Numeric) ; printf ("107 succeeded\n") ; } /* initial allocation fails once, retry succeeds */ umf_realloc_fail = 1 ; umf_realloc_hi = 0 ; umf_realloc_lo = -2 ; s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ; /* ( */ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; if (!Numeric || s != UMFPACK_OK) error ("110", (double) umf_fail) ; /* all reallocs succeed */ umf_realloc_fail = -1 ; umf_realloc_hi = 0 ; umf_realloc_lo = 0 ; UMFPACK_free_symbolic (&Symbolic) ; /* ] */ umf_fail = 1 ; if (prl > 2) printf ("Memfail Numeric: ") ; s = UMFPACK_report_numeric (Numeric, Control) ; if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_out_of_memory)) error ("108",0.) ; for (i = 1 ; i <= 2 ; i++) { umf_fail = i ; printf ("\nTest 109, "ID"\n", umf_fail) ; s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; if (s != UMFPACK_ERROR_out_of_memory) error ("109", (double) i) ; } for (i = 1 ; i <= 2 ; i++) { umf_fail = i ; s = UMFPACK_solve (UMFPACK_L, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ; if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ; UMFPACK_report_status (Control, s) ; UMFPACK_report_info (Control, Info) ; if (s != UMFPACK_ERROR_out_of_memory) error ("109b", (double) i) ; } s = UMFPACK_get_lunz (&lnz, &unz, &nnrow, &nncol, &nzud, Numeric) ; if (s != UMFPACK_OK) error ("111", 0.) ; Rs = (double *) malloc ((n+1) * sizeof (double)) ; /* [ */ Lp = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ Li = (Int *) malloc ((lnz+1) * sizeof (Int)) ; /* [ */ Lx = (double *) malloc ((lnz+1) * sizeof (double)) ; /* [ */ Lz = (double *) calloc ((lnz+1) , sizeof (double)) ; /* [ */ Up = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ Ui = (Int *) malloc ((unz+1) * sizeof (Int)) ; /* [ */ Ux = (double *) malloc ((unz+1) * sizeof (double)) ; /* [ */ Uz = (double *) calloc ((unz+1) , sizeof (double)) ; /* [ */ P = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ Q = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */ if (!Lp || !Li || !Lx || !Up || !Ui || !Ux || !P || !Q) error ("out of memory (26)",0.) ; if (!Lz || !Uz) error ("out of memory (27)",0.) ; for (i = 1 ; i <= 2 ; i++) { umf_fail = i ; s = UMFPACK_get_numeric (Lp, Li, CARG(Lx,Lz), Up, Ui, CARG(Ux,Uz), P, Q, CARG(DNULL,DNULL), &do_recip, Rs, Numeric) ; if (s != UMFPACK_ERROR_out_of_memory) error ("112", (double) i) ; } umf_fail = 1 ; s = UMFPACK_get_determinant (CARG (&Mx, &Mz), &Exp, Numeric, Info) ; if (s != Info [UMFPACK_STATUS]) { printf ("s %d %g\n", s, Info [UMFPACK_STATUS]) ; error ("huh", (double) __LINE__) ; } if (s != UMFPACK_ERROR_out_of_memory) error ("73det",0.) ; UMFPACK_free_numeric (&Numeric) ; /* ) */ free (Q) ; /* ] */ free (P) ; /* ] */ free (Uz) ; /* ] */ free (Ux) ; /* ] */ free (Ui) ; /* ] */ free (Up) ; /* ] */ free (Lz) ; /* ] */ free (Lx) ; /* ] */ free (Li) ; /* ] */ free (Lp) ; /* ] */ free (Rs) ; /* ] */ #if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG) if (UMF_malloc_count != 0) error ("umfpack memory test leak!!\n",0.) ; #endif } free (xz) ; /* ] */ free (x) ; /* ] */ free (bz) ; /* ] */ free (b) ; /* ] */ free (Qinit) ; /* ] */ free (Ap) ; /* ] */ free (Ai) ; /* ] */ free (Ax) ; /* ] */ free (Az) ; /* ] */ /* ---------------------------------------------------------------------- */ /* NaN/Inf */ /* ---------------------------------------------------------------------- */ umf_fail = -1 ; umf_fail_lo = 0 ; umf_fail_hi = 0 ; umf_realloc_fail = -1 ; umf_realloc_lo = 0 ; umf_realloc_hi = 0 ; printf ("matrices with NaN/Infs:\n") ; n = 100 ; for (k = 0 ; k <= 100 ; k++) { printf ("NaN/Inf %7d 4*n nz's, k= "ID"\n", n, k) ; matgen_sparse (n, 4*n, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az, 1, 1) ; /* [[[[ */ if (k == 100) { /* make a matrix of all NaN's */ for (i = 0 ; i < Ap [n] ; i++) { Ax [i] = xnan ; #ifdef COMPLEX Az [i] = xnan ; #endif } } b = (double *) malloc (n * sizeof (double)) ; /* [ */ bz = (double *) malloc (n * sizeof (double)) ; /* [ */ bgen (n, Ap, Ai, Ax, Az, b, bz) ; x = (double *) malloc (n * sizeof (double)) ; /* [ */ xz = (double *) malloc (n * sizeof (double)) ; /* [ */ for (prl = 2 ; prl >= -1 ; prl--) { printf ("NaN / Inf matrix: \n") ; UMFPACK_defaults (Control) ; Control [UMFPACK_PRL] = prl ; for (scale = UMFPACK_SCALE_NONE ; scale <= UMFPACK_SCALE_MAX ; scale++) { Control [UMFPACK_SCALE] = scale ; Con = (prl == -1) ? (DNULL) : Control ; UMFPACK_report_control (Con) ; s = UMFPACK_symbolic (n, n, Ap, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ; /* [ */ UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (!(s == UMFPACK_OK || s == UMFPACK_WARNING_singular_matrix)) error ("887", 0.) ; s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, Info) ; /* [ */ UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (!(s == UMFPACK_OK || s == UMFPACK_WARNING_singular_matrix)) error ("888", 0.) ; s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az) , CARG(x,xz), CARG(b,bz), Numeric, Con, Info) ; UMFPACK_report_status (Con, s) ; UMFPACK_report_info (Con, Info) ; if (!(s == UMFPACK_OK || s == UMFPACK_WARNING_singular_matrix)) error ("889", 0.) ; UMFPACK_free_numeric (&Numeric) ; /* ] */ UMFPACK_free_symbolic (&Symbolic) ; /* ] */ } } free (xz) ; /* ] */ free (x) ; /* ] */ free (bz) ; /* ] */ free (b) ; /* ] */ free (Az) ; /* ] */ free (Ax) ; /* ] */ free (Ai) ; /* ] */ free (Ap) ; /* ] */ } #if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG) if (UMF_malloc_count != 0) error ("umfpack memory leak!!\n",0.) ; #endif /* ---------------------------------------------------------------------- */ /* reset rand ( ) */ /* ---------------------------------------------------------------------- */ srand (1) ; /* ---------------------------------------------------------------------- */ /* test report routines */ /* ---------------------------------------------------------------------- */ n = 32 ; printf ("\n so far: rnorm %10.4e %10.4e\n", rnorm, maxrnorm) ; Qinit = (Int *) malloc (n * sizeof (Int)) ; /* [ */ b = (double *) malloc (n * sizeof (double)) ; /* [ */ bz= (double *) calloc (n , sizeof (double)) ; /* [ */ if (!Qinit || !b || !bz) error ("out of memory (28)",0.) ; UMFPACK_defaults (Control) ; for (prl = 5 ; prl >= 0 ; prl--) { printf ("\n[[[[ PRL = "ID"\n", prl) ; Control [UMFPACK_PRL] = prl ; i = UMFPACK_DENSE_DEGREE_THRESHOLD (0.2, n) ; printf ("(default) dense row/col degree threshold: "ID"\n", i) ; matgen_sparse (n, 12*n, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az, prl, 0) ; /* [[[[ */ bgen (n, Ap, Ai, Ax,Az, b,bz) ; /* also test NaN/Inf handling in solvers */ b [16] = xnan ; b [15] = xinf ; /* test col->triplet and triplet->col */ test_col (n, Ap, Ai, Ax,Az, prl) ; rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, INULL, MemOK, FALSE, FALSE, 0., 0.) ; printf ("\nrnorm %10.4e %10.4e\n", rnorm, maxrnorm) ; randperm (n, Qinit) ; rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemOK, FALSE, FALSE, 0., 0.) ; printf ("\nrnorm %10.4e %10.4e\n", rnorm, maxrnorm) ; free (Ap) ; /* ] */ free (Ai) ; /* ] */ free (Ax) ; /* ] */ free (Az) ; /* ] */ printf ("\n]]]]\n\n\n") ; } /* ---------------------------------------------------------------------- */ /* reset rand ( ) */ /* ---------------------------------------------------------------------- */ srand (1) ; /* test report with more than 10 dense columns */ UMFPACK_defaults (Control) ; printf ("\nrnorm %10.4e %10.4e\n", rnorm, maxrnorm) ; Control [UMFPACK_PRL] = 4 ; printf ("\nreport dense matrix with n = "ID"\n", n) ; matgen_dense (n, &Ap, &Ai, &Ax, &Az) ; /* [[[[ */ bgen (n, Ap, Ai, Ax,Az, b,bz) ; rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemOK, FALSE, FALSE, 0., 0.) ; maxrnorm = MAX (rnorm, maxrnorm) ; printf ("\nrnorm %10.4e %10.4e\n", rnorm, maxrnorm) ; free (Ap) ; /* ] */ free (Ai) ; /* ] */ free (Ax) ; /* ] */ free (Az) ; /* ] */ free (bz) ; /* ] */ free (b) ; /* ] */ free (Qinit) ; /* ] */ Control [UMFPACK_PRL] = 5 ; /* ---------------------------------------------------------------------- */ /* reset rand ( ) */ /* ---------------------------------------------------------------------- */ srand (1) ; /* ---------------------------------------------------------------------- */ /* test random sparse matrices */ /* ---------------------------------------------------------------------- */ n = 30 ; printf ("sparse %7d 4*n nz's", n) ; matgen_sparse (n, 4*n, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az, 1, 0) ; /* [[[[ */ rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 1) ; /* ]]]] */ maxrnorm = MAX (rnorm, maxrnorm) ; printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ; n = 200 ; printf ("sparse %7d 4*n nz's", n) ; matgen_sparse (n, 4*n, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az, 1, 0) ; /* [[[[ */ /* rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 1) ; */ UMFPACK_defaults (Control) ; Control [UMFPACK_DENSE_COL] = 0.883883 ; Control [UMFPACK_DENSE_ROW] = 0.883883 ; Control [UMFPACK_AMD_DENSE] = 10 ; Control [UMFPACK_PIVOT_TOLERANCE] = 0.5 ; Control [UMFPACK_BLOCK_SIZE] = 1 ; Control [UMFPACK_ALLOC_INIT] = 0 ; Control [UMFPACK_SCALE] = 0 ; Control [UMFPACK_STRATEGY] = 3 ; Control [UMFPACK_FIXQ] = 1 ; b = (double *) malloc (n * sizeof (double)) ; /* [ */ bz= (double *) calloc (n , sizeof (double)) ; /* [ */ if (!b || !bz) error ("out of memory (29)",0.) ; bgen (n, Ap, Ai, Ax, Az, b, bz) ; rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, INULL, MemOK, FALSE, FALSE, 0., 0.) ; UMFPACK_defaults (Control) ; Control [UMFPACK_FRONT_ALLOC_INIT] = -10 ; Control [UMFPACK_PRL] = 2 ; printf ("negative front alloc init\n") ; rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, INULL, MemOK, FALSE, FALSE, 0., 0.) ; Control [UMFPACK_FRONT_ALLOC_INIT] = -10 ; Control [UMFPACK_STRATEGY] = UMFPACK_STRATEGY_SYMMETRIC ; Control [UMFPACK_AMD_DENSE] = -1 ; printf ("symmetric strategy, no dense rows/cols\n") ; rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, INULL, MemOK, FALSE, FALSE, 0., 0.) ; free (bz) ; /* ] */ free (b) ; /* ] */ free (Ap) ; /* ] */ free (Ai) ; /* ] */ free (Ax) ; /* ] */ free (Az) ; /* ] */ maxrnorm = MAX (rnorm, maxrnorm) ; printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ; /* ---------------------------------------------------------------------- */ /* reset rand ( ) */ /* ---------------------------------------------------------------------- */ srand (1) ; #if 0 n = 200 ; printf ("sparse %7d few nz's", n) ; matgen_sparse (n, 20, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az, 1, 0) ; rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 1) ; maxrnorm = MAX (rnorm, maxrnorm) ; printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ; /* ---------------------------------------------------------------------- */ /* test random sparse matrices + 4 dense rows */ /* ---------------------------------------------------------------------- */ n = 100 ; printf ("sparse+dense rows %7d ", n) ; matgen_sparse (n, 4*n, 4, 2*n, 0, 0, &Ap, &Ai, &Ax, &Az, 1, 0) ; rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 1) ; maxrnorm = MAX (rnorm, maxrnorm) ; printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ; /* ---------------------------------------------------------------------- */ /* reset rand ( ) */ /* ---------------------------------------------------------------------- */ srand (1) ; /* ---------------------------------------------------------------------- */ /* test random sparse matrices + 4 dense rows & cols */ /* ---------------------------------------------------------------------- */ n = 100 ; /* reduce the number of controls - otherwise this takes too much time */ c = UMFPACK_BLOCK_SIZE ; Controls [c][0] = UMFPACK_DEFAULT_BLOCK_SIZE ; Ncontrols [c] = 1 ; c = UMFPACK_ALLOC_INIT ; Controls [c][0] = 1.0 ; Ncontrols [c] = 1 ; printf ("sparse+dense rows and cols %7d ", n) ; matgen_sparse (n, 4*n, 4, 2*n, 4, 2*n, &Ap, &Ai, &Ax, &Az, 1, 0) ; rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 1) ; maxrnorm = MAX (rnorm, maxrnorm) ; printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ; c = UMFPACK_BLOCK_SIZE ; Controls [c][0] = 1 ; Controls [c][1] = 8 ; Controls [c][2] = UMFPACK_DEFAULT_BLOCK_SIZE ; Ncontrols [c] = 3 ; c = UMFPACK_ALLOC_INIT ; Controls [c][0] = 0.0 ; Controls [c][1] = 0.5 ; Controls [c][2] = 1.0 ; /* not the default */ Ncontrols [c] = 3 ; n = 100 ; printf ("very sparse+dense cols %7d ", n) ; matgen_sparse (n, 2, 0, 0, 4, 2*n, &Ap, &Ai, &Ax, &Az, 1, 0) ; rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 1) ; maxrnorm = MAX (rnorm, maxrnorm) ; printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ; /* ---------------------------------------------------------------------- */ /* test all diagonal matrices */ /* ---------------------------------------------------------------------- */ for (n = 1 ; n < 16 ; n++) { printf ("diagonal %7d ", n) ; matgen_band (n, 0, 0, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az) ; rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 1) ; maxrnorm = MAX (rnorm, maxrnorm) ; printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ; } for (n = 100 ; n <= 500 ; n += 100) { printf ("diagonal %7d ", n) ; matgen_band (n, 0, 0, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az) ; rnorm = do_and_free (n, Ap, Ai, Ax,Az, Controls, Ncontrols, MemOK, 1) ; maxrnorm = MAX (rnorm, maxrnorm) ; printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ; } /* ---------------------------------------------------------------------- */ /* test all tri-diagonal matrices */ /* ---------------------------------------------------------------------- */ for (n = 1 ; n < 16 ; n++) { printf ("tri-diagonal %7d ", n) ; matgen_band (n, 1, 1, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az) ; rnorm = do_and_free (n, Ap, Ai, Ax,Az, Controls, Ncontrols, MemOK, 1) ; maxrnorm = MAX (rnorm, maxrnorm) ; printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ; } for (n = 100 ; n <= 500 ; n += 100) { printf ("tri-diagonal %7d ", n) ; matgen_band (n, 1, 1, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az) ; rnorm = do_and_free (n, Ap, Ai, Ax,Az, Controls, Ncontrols, MemOK, 1) ; maxrnorm = MAX (rnorm, maxrnorm) ; printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ; } /* ---------------------------------------------------------------------- */ /* test all tri-diagonal matrices + one "dense" row */ /* ---------------------------------------------------------------------- */ n = 100 ; printf ("tri-diagonal+dense row %7d ", n) ; matgen_band (n, 1, 1, 1, n, 0, 0, &Ap, &Ai, &Ax, &Az) ; rnorm = do_and_free (n, Ap, Ai, Ax,Az, Controls, Ncontrols, MemOK, 1) ; maxrnorm = MAX (rnorm, maxrnorm) ; printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ; /* ---------------------------------------------------------------------- */ /* test all tri-diagonal matrices + one "dense" row and col */ /* ---------------------------------------------------------------------- */ n = 100 ; printf ("tri-diagonal+dense row and col %7d ", n) ; matgen_band (n, 1, 1, 1, n, 1, n, &Ap, &Ai, &Ax, &Az) ; rnorm = do_and_free (n, Ap, Ai, Ax,Az, Controls, Ncontrols, MemOK, 1) ; maxrnorm = MAX (rnorm, maxrnorm) ; printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ; /* ---------------------------------------------------------------------- */ /* test all small dense matrices */ /* ---------------------------------------------------------------------- */ for (n = 1 ; n < 16 ; n++) { printf ("dense %7d ", n) ; matgen_dense (n, &Ap, &Ai, &Ax, &Az) ; rnorm = do_and_free (n, Ap, Ai, Ax,Az, Controls, Ncontrols, MemOK, 1) ; maxrnorm = MAX (rnorm, maxrnorm) ; printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ; } for (n = 20 ; n <= 80 ; n += 20 ) { printf ("dense %7d ", n) ; matgen_dense (n, &Ap, &Ai, &Ax, &Az) ; rnorm = do_and_free (n, Ap, Ai, Ax,Az, Controls, Ncontrols, MemOK, 1) ; maxrnorm = MAX (rnorm, maxrnorm) ; printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ; } n = 130 ; printf ("dense %7d ", n) ; matgen_dense (n, &Ap, &Ai, &Ax, &Az) ; rnorm = do_and_free (n, Ap, Ai, Ax,Az, Controls, Ncontrols, MemOK, 1) ; maxrnorm = MAX (rnorm, maxrnorm) ; printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ; #endif /* ---------------------------------------------------------------------- */ /* done with accurate matrices */ /* ---------------------------------------------------------------------- */ ttt = umfpack_timer ( ) ; fprintf (stderr, "ALL TESTS PASSED: rnorm %8.2e (%8.2e shl0, %8.2e arc130 %8.2e omega2) cputime %g\n", maxrnorm, maxrnorm_shl0, maxrnorm_arc130, rnorm_omega2, ttt) ; printf ( "ALL TESTS PASSED: rnorm %8.2e (%8.2e shl0, %8.2e arc130 %8.2e omega2) cputime %g\n", maxrnorm, maxrnorm_shl0, maxrnorm_arc130, rnorm_omega2, ttt) ; #if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG) if (UMF_malloc_count != 0) error ("umfpack memory leak!!\n",0.) ; #endif return (0) ; } SuiteSparse/UMFPACK/Tcov/Makefile0000644001170100242450000000031510534022164015404 0ustar davisfac include ../../UFconfig/UFconfig.mk linux: distclean ./DO.linux sol: distclean ./DO.solaris distclean: - ( cd .. ; make purge ) - ( cd ../../AMD ; make purge ) - $(RM) -rf Out/* purge: distclean SuiteSparse/UMFPACK/Tcov/DO6780000755001170100242450000000014710006265125014444 0ustar davisfac# # DO 6 di DO 6 dl DO 6 zi DO 6 zl DO 7 di DO 7 dl DO 7 zi DO 7 zl DO 8 di DO 8 dl DO 8 zi DO 8 zl SuiteSparse/UMFPACK/Tcov/DOsol0000755001170100242450000000023010172736061014714 0ustar davisfac#!/bin/csh #------------------------------------------------------------------------------- mkdir SolOut/$1_$2 DOsol2 $1 $2 $3 >& SolOut/$1_$2.stderr SuiteSparse/UMFPACK/Tcov/Make.10000644001170100242450000000106310425273454014715 0ustar davisfac#=============================================================================== # ILP32 mode, no BLAS, test for integer overflow. #=============================================================================== CC = gcc CFLAGS = -O0 -ftest-coverage -fprofile-arcs -O0 UMFPACK_CONFIG = -DNBLAS -DTEST_FOR_INTEGER_OVERFLOW -DTESTING LIB = -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.20000644001170100242450000000106510711722241014707 0ustar davisfac#=============================================================================== # ILP32 mode, BLAS, do not test for integer overflow. #=============================================================================== CC = gcc CFLAGS = -O0 -ftest-coverage -fprofile-arcs -O0 UMFPACK_CONFIG = -DTESTING LIB = -lblas -lgfortran -lgfortranbegin -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.30000644001170100242450000000117110425373631014715 0ustar davisfac#=============================================================================== # ILP32 mode, C interface /ATLAS BLAS, do not test for integer overflow. #=============================================================================== CC = gcc CFLAGS = -O0 -ftest-coverage -fprofile-arcs -O0 UMFPACK_CONFIG = -DCBLAS -DTESTING -I/cise/research/sparse/Install/ATLAS/Linux_P4SSE2/include LIB = -lcblas -latlas -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.40000644001170100242450000000123710425373652014724 0ustar davisfac#=============================================================================== # ILP32 mode, Fortran interface to ATLAS BLAS, do not test for integer overflow. #=============================================================================== CC = gcc CFLAGS = -O0 -ftest-coverage -fprofile-arcs -O0 UMFPACK_CONFIG = -DTESTING CONFIG = -DTESTING -I/cise/research/sparse/Install/ATLAS/Linux_P4SSE2/include LIB = -lf77blas -latlas -lfrtbegin -lg2c -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.50000644001170100242450000000112010425373670014714 0ustar davisfac#=============================================================================== # ILP32 mode, no BLAS, test for integer overflow, no reciprocal #=============================================================================== CC = gcc CFLAGS = -O0 -ftest-coverage -fprofile-arcs -O0 UMFPACK_CONFIG = -DNBLAS -DTEST_FOR_INTEGER_OVERFLOW -DTESTING -DNRECIPROCAL LIB = -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.60000644001170100242450000000111310711722350014706 0ustar davisfac#=============================================================================== # ILP32 mode, BLAS, do not test for integer overflow. No timers #=============================================================================== CC = gcc CFLAGS = -O0 -ftest-coverage -fprofile-arcs -O0 UMFPACK_CONFIG = -DTESTING -DNO_TIMER LIB = -lblas -lgfortran -lgfortranbegin -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.70000644001170100242450000000113310425373701014715 0ustar davisfac#=============================================================================== # ILP32 mode, no BLAS, test for integer overflow. No divide by zero #=============================================================================== CC = gcc CFLAGS = -O0 -ftest-coverage -fprofile-arcs -O0 UMFPACK_CONFIG = -DNBLAS -DTEST_FOR_INTEGER_OVERFLOW -DTESTING -DNO_DIVIDE_BY_ZERO LIB = -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.80000644001170100242450000000113410711722306014714 0ustar davisfac#=============================================================================== # ILP32 mode, BLAS, do not test for integer overflow. No divide by zero. #=============================================================================== CC = gcc CFLAGS = -O0 -ftest-coverage -fprofile-arcs -O0 UMFPACK_CONFIG = -DTESTING -DNO_DIVIDE_BY_ZERO LIB = -lblas -lgfortran -lgfortranbegin -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/cover.out_May50000644001170100242450000010062410426670101016512 0ustar davisfac================================================================================ umf_2by2.c ================================================================================ ================================================================================ umf_analyze.c ================================================================================ 24 219 #####: 216: return (FALSE) ; /* internal error! */ ================================================================================ umf_apply_order.c ================================================================================ ================================================================================ umf_assemble.c ================================================================================ ================================================================================ umf_assemble_fixq.c ================================================================================ ================================================================================ umf_blas3_update.c ================================================================================ ================================================================================ umf_build_tuples.c ================================================================================ 24 80 #####: 77: return (FALSE) ; /* out of memory for row tuples */ 24 98 #####: 95: return (FALSE) ; /* out of memory for col tuples */ ================================================================================ umf_colamd.c ================================================================================ 24 2706 #####: 2703: KILL_ROW (r) ; ================================================================================ umf_create_element.c ================================================================================ 24 250 #####: 247: return (FALSE) ; /* out of memory */ 24 261 #####: 258: return (FALSE) ; /* out of memory */ 24 437 #####: 434: return (UMF_get_memory (Numeric, Work, 0, r2, c2,do_Fcpos)); 24 540 #####: 537: return (UMF_get_memory (Numeric, Work, 0, r2, c2,do_Fcpos)); ================================================================================ umf_extend_front.c ================================================================================ ================================================================================ umf_free.c ================================================================================ ================================================================================ umf_fsize.c ================================================================================ 24 55 #####: 52: frsize = Int_MAX ; ================================================================================ umf_garbage_collection.c ================================================================================ ================================================================================ umf_get_memory.c ================================================================================ 24 111 #####: 108: newsize = (Int) bsize ; /* we cannot increase the size beyond bsize */ ================================================================================ umf_grow_front.c ================================================================================ 24 90 #####: 87: return (FALSE) ; 24 118 #####: 115: double a = 0.9 * sqrt ((Int_MAX / sizeof (Entry)) / s) ; 24 119 #####: 116: fnr2 = MAX (fnr_min, a * fnr2) ; 24 120 #####: 117: fnc2 = MAX (fnc_min, a * fnc2) ; 24 122 #####: 119: newsize = fnr2 * fnc2 ; 24 124 #####: 121: if (fnr2 % 2 == 0) fnr2++ ; 24 125 #####: 122: fnc2 = newsize / fnr2 ; 24 183 #####: 180: return (FALSE) ; /* out of memory */ ================================================================================ umf_init_front.c ================================================================================ 24 77 #####: 74: return (FALSE) ; ================================================================================ umf_is_permutation.c ================================================================================ ================================================================================ umf_kernel.c ================================================================================ ================================================================================ umf_kernel_init.c ================================================================================ 24 514 #####: 511: return (FALSE) ; /* pattern changed */ 24 542 #####: 539: return (FALSE) ; /* pattern changed */ 24 606 #####: 603: return (FALSE) ; /* pattern has changed */ 24 642 #####: 639: return (FALSE) ; /* pattern has changed */ 24 710 #####: 707: return (FALSE) ; /* pattern changed */ 24 723 #####: 720: return (FALSE) ; /* pattern changed */ 24 735 #####: 732: return (FALSE) ; /* pattern changed */ 24 827 #####: 824: return (FALSE) ; /* pattern changed */ 24 863 #####: 860: return (FALSE) ; /* pattern changed */ 24 905 #####: 902: return (FALSE) ; /* pattern changed */ 24 919 #####: 916: return (FALSE) ; /* pattern changed */ 24 1031 #####: 1028: return (FALSE) ; /* pattern changed */ ================================================================================ umf_kernel_wrapup.c ================================================================================ ================================================================================ umf_lhsolve.c ================================================================================ ================================================================================ umf_local_search.c ================================================================================ 24 654 #####: 651: return (UMFPACK_ERROR_different_pattern) ; 24 743 #####: 740: return (UMFPACK_ERROR_different_pattern) ; ================================================================================ umf_lsolve.c ================================================================================ ================================================================================ umf_ltsolve.c ================================================================================ ================================================================================ umf_malloc.c ================================================================================ ================================================================================ umf_mem_alloc_element.c ================================================================================ 24 46 #####: 43: return (0) ; /* problem is too large */ ================================================================================ umf_mem_alloc_head_block.c ================================================================================ ================================================================================ umf_mem_alloc_tail_block.c ================================================================================ ================================================================================ umf_mem_free_tail_block.c ================================================================================ ================================================================================ umf_mem_init_memoryspace.c ================================================================================ ================================================================================ umf_realloc.c ================================================================================ 24 55 #####: 52: return ((void *) NULL) ; ================================================================================ umf_report_perm.c ================================================================================ ================================================================================ umf_report_vector.c ================================================================================ ================================================================================ umf_row_search.c ================================================================================ 24 616 #####: 613: return (UMFPACK_ERROR_different_pattern) ; 24 662 #####: 659: return (UMFPACK_ERROR_different_pattern) ; 24 749 #####: 746: return (UMFPACK_ERROR_different_pattern) ; ================================================================================ umf_scale.c ================================================================================ ================================================================================ umf_scale_column.c ================================================================================ ================================================================================ umf_set_stats.c ================================================================================ ================================================================================ umf_singletons.c ================================================================================ ================================================================================ umf_solve.c ================================================================================ 24 1313 #####: 1310: omega [1] = tau ; 24 1314 #####: 1311: omega [2] = tau ; 24 1315 #####: 1312: break ; ================================================================================ umf_start_front.c ================================================================================ 24 153 #####: 150: maxfrsize = Int_MAX / sizeof (Entry) ; 24 172 #####: 169: fsize = Int_MAX / sizeof (Entry) ; 24 190 #####: 187: fsize2 = Int_MAX / sizeof (Entry) ; ================================================================================ umf_store_lu.c ================================================================================ 24 346 #####: 343: return (FALSE) ; /* out of memory */ 24 352 #####: 349: return (FALSE) ; /* out of memory */ 24 771 #####: 768: return (FALSE) ; /* out of memory */ 24 778 #####: 775: return (FALSE) ; /* out of memory */ ================================================================================ umf_store_lu_drop.c ================================================================================ 24 326 #####: 323: Int r2, c2 ; 24 329 #####: 326: if (Work->do_grow) 24 333 #####: 330: r2 = fnrows ; 24 334 #####: 331: c2 = fncols ; 24 339 #####: 336: r2 = MAX (fnrows, Work->fnrows_new + 1) ; 24 340 #####: 337: c2 = MAX (fncols, Work->fncols_new + 1) ; 24 343 #####: 340: if (!UMF_get_memory (Numeric, Work, size, r2, c2, TRUE)) 24 346 #####: 343: return (FALSE) ; /* out of memory */ 24 348 #####: 345: p = UMF_mem_alloc_head_block (Numeric, size) ; 24 349 #####: 346: if (!p) 24 352 #####: 349: return (FALSE) ; /* out of memory */ 24 355 #####: 352: fnc_curr = Work->fnc_curr ; 24 356 #####: 353: fnr_curr = Work->fnr_curr ; 24 357 #####: 354: Flublock = Work->Flublock ; 24 358 #####: 355: Flblock = Work->Flblock ; 24 359 #####: 356: Fublock = Work->Fublock ; 24 360 #####: 357: Fl1 = Flublock + kk * nb ; 24 361 #####: 358: Fl2 = Flblock + kk * fnr_curr ; 24 494 #####: 491: pos = llen++ ; 24 495 #####: 492: Lpattern [pos] = row2 ; 24 496 #####: 493: Lpos [row2] = pos ; 24 497 #####: 494: *Li++ = row2 ; 24 750 #####: 747: Int r2, c2 ; 24 753 #####: 750: if (Work->do_grow) 24 757 #####: 754: r2 = fnrows ; 24 758 #####: 755: c2 = fncols ; 24 763 #####: 760: r2 = MAX (fnrows, Work->fnrows_new + 1) ; 24 764 #####: 761: c2 = MAX (fncols, Work->fncols_new + 1) ; 24 767 #####: 764: if (!UMF_get_memory (Numeric, Work, size, r2, c2, TRUE)) 24 771 #####: 768: return (FALSE) ; /* out of memory */ 24 773 #####: 770: p = UMF_mem_alloc_head_block (Numeric, size) ; 24 774 #####: 771: if (!p) 24 778 #####: 775: return (FALSE) ; /* out of memory */ 24 781 #####: 778: fnc_curr = Work->fnc_curr ; 24 782 #####: 779: fnr_curr = Work->fnr_curr ; 24 783 #####: 780: Flublock = Work->Flublock ; 24 784 #####: 781: Flblock = Work->Flblock ; 24 785 #####: 782: Fublock = Work->Fublock ; 24 786 #####: 783: Fu1 = Flublock + kk ; 24 787 #####: 784: Fu2 = Fublock + kk * fnc_curr ; ================================================================================ umf_symbolic_usage.c ================================================================================ ================================================================================ umf_transpose.c ================================================================================ ================================================================================ umf_triplet_map_nox.c ================================================================================ ================================================================================ umf_triplet_map_x.c ================================================================================ ================================================================================ umf_triplet_nomap_nox.c ================================================================================ ================================================================================ umf_triplet_nomap_x.c ================================================================================ ================================================================================ umf_tuple_lengths.c ================================================================================ ================================================================================ umf_uhsolve.c ================================================================================ ================================================================================ umf_usolve.c ================================================================================ ================================================================================ umf_utsolve.c ================================================================================ ================================================================================ umf_valid_numeric.c ================================================================================ ================================================================================ umf_valid_symbolic.c ================================================================================ ================================================================================ umfpack_col_to_triplet.c ================================================================================ ================================================================================ umfpack_defaults.c ================================================================================ ================================================================================ umfpack_free_numeric.c ================================================================================ ================================================================================ umfpack_free_symbolic.c ================================================================================ ================================================================================ umfpack_get_determinant.c ================================================================================ 24 217 #####: 214: Info [UMFPACK_STATUS] = UMFPACK_WARNING_singular_matrix ; 24 218 #####: 215: break ; ================================================================================ umfpack_get_lunz.c ================================================================================ ================================================================================ umfpack_get_numeric.c ================================================================================ ================================================================================ umfpack_get_symbolic.c ================================================================================ ================================================================================ umfpack_load_numeric.c ================================================================================ 24 99 #####: 96: (void) UMF_free ((void *) Numeric) ; 24 100 #####: 97: fclose (f) ; 24 101 #####: 98: return (UMFPACK_ERROR_file_IO) ; 24 158 #####: 155: UMFPACK_free_numeric ((void **) &Numeric) ; 24 159 #####: 156: return (UMFPACK_ERROR_invalid_Numeric_object) ; ================================================================================ umfpack_load_symbolic.c ================================================================================ 24 99 #####: 96: (void) UMF_free ((void *) Symbolic) ; 24 100 #####: 97: fclose (f) ; 24 101 #####: 98: return (UMFPACK_ERROR_file_IO) ; 24 162 #####: 159: UMFPACK_free_symbolic ((void **) &Symbolic) ; 24 163 #####: 160: return (UMFPACK_ERROR_invalid_Symbolic_object) ; ================================================================================ umfpack_numeric.c ================================================================================ 24 186 #####: 183: Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; 24 187 #####: 184: return (UMFPACK_ERROR_out_of_memory) ; ================================================================================ umfpack_qsymbolic.c ================================================================================ 24 516 #####: 513: Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; 24 517 #####: 514: return (UMFPACK_ERROR_out_of_memory) ; 24 891 #####: 888: Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; 24 892 #####: 889: error (&Symbolic, SW) ; 24 893 #####: 890: return (UMFPACK_ERROR_out_of_memory) ; 24 912 #####: 909: Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; 24 913 #####: 910: error (&Symbolic, SW) ; 24 914 #####: 911: return (UMFPACK_ERROR_out_of_memory) ; 24 981 #####: 978: strategy = UMFPACK_STRATEGY_2BY2 ; 24 1461 #####: 1458: Info [UMFPACK_STATUS] = UMFPACK_ERROR_internal_error ; 24 1462 #####: 1459: error (&Symbolic, SW) ; 24 1463 #####: 1460: return (UMFPACK_ERROR_internal_error) ; 24 1815 #####: 1812: Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; 24 1816 #####: 1813: error (&Symbolic, SW) ; 24 1817 #####: 1814: return (UMFPACK_ERROR_out_of_memory) ; ================================================================================ umfpack_report_control.c ================================================================================ ================================================================================ umfpack_report_info.c ================================================================================ ================================================================================ umfpack_report_matrix.c ================================================================================ ================================================================================ umfpack_report_numeric.c ================================================================================ 24 324 #####: 321: return (FALSE) ; 24 330 #####: 327: PRINTF (("\t...\n")) ; 24 331 #####: 328: prl-- ; 24 532 #####: 529: return (FALSE) ; 24 639 #####: 636: PRINTF ((" ...\n")) ; 24 640 #####: 637: prl-- ; 24 651 #####: 648: return (FALSE) ; 24 657 #####: 654: PRINTF (("\t...\n")) ; 24 658 #####: 655: prl-- ; ================================================================================ umfpack_report_perm.c ================================================================================ ================================================================================ umfpack_report_status.c ================================================================================ ================================================================================ umfpack_report_symbolic.c ================================================================================ ================================================================================ umfpack_report_triplet.c ================================================================================ ================================================================================ umfpack_report_vector.c ================================================================================ ================================================================================ umfpack_save_numeric.c ================================================================================ ================================================================================ umfpack_save_symbolic.c ================================================================================ ================================================================================ umfpack_scale.c ================================================================================ ================================================================================ umfpack_solve.c ================================================================================ ================================================================================ umfpack_symbolic.c ================================================================================ ================================================================================ umfpack_tictoc.c ================================================================================ ================================================================================ umfpack_timer.c ================================================================================ ================================================================================ umfpack_transpose.c ================================================================================ ================================================================================ umfpack_triplet_to_col.c ================================================================================ ================================================================================ umfpack_wsolve.c ================================================================================ 24 144 #####: 141: Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_system ; 24 145 #####: 142: return (UMFPACK_ERROR_invalid_system) ; 24 158 #####: 155: Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ; 24 159 #####: 156: return (UMFPACK_ERROR_argument_missing) ; 24 165 #####: 162: irstep = 0 ; ================================================================================ amd_1.c ================================================================================ ================================================================================ amd_2.c ================================================================================ ================================================================================ amd_aat.c ================================================================================ ================================================================================ amd_control.c ================================================================================ ================================================================================ amd_defaults.c ================================================================================ ================================================================================ amd_info.c ================================================================================ ================================================================================ amd_order.c ================================================================================ 24 82 #####: 79: if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ; 24 83 #####: 80: return (AMD_OUT_OF_MEMORY) ; /* problem too large */ 24 103 #####: 100: amd_free (Len) ; 24 104 #####: 101: amd_free (Pinv) ; 24 105 #####: 102: if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ; 24 106 #####: 103: return (AMD_OUT_OF_MEMORY) ; 24 120 #####: 117: amd_free (Rp) ; 24 121 #####: 118: amd_free (Ri) ; 24 122 #####: 119: amd_free (Len) ; 24 123 #####: 120: amd_free (Pinv) ; 24 124 #####: 121: if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ; 24 125 #####: 122: return (AMD_OUT_OF_MEMORY) ; 24 173 #####: 170: amd_free (Rp) ; 24 174 #####: 171: amd_free (Ri) ; 24 175 #####: 172: amd_free (Len) ; 24 176 #####: 173: amd_free (Pinv) ; 24 177 #####: 174: if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ; 24 178 #####: 175: return (AMD_OUT_OF_MEMORY) ; ================================================================================ amd_postorder.c ================================================================================ ================================================================================ amd_post_tree.c ================================================================================ ================================================================================ amd_preprocess.c ================================================================================ ================================================================================ amd_valid.c ================================================================================ ================================================================================ Last line of each output file: ================================================================================ Out/1_di/ut.out ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 59.09 ================================================================= Out/1_dl/ut.out ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 51.26 ================================================================= Out/1g_di/ut.out ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 39.95 ================================================================= Out/1g_dl/ut.out ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 34.86 ================================================================= Out/1g_zi/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 5.84e-05 arc130 3.66e-10 omega2) cputime 75.33 ================================================================= Out/1g_zl/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 5.84e-05 arc130 3.66e-10 omega2) cputime 75.14 ================================================================= Out/1_zi/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 98.83 ================================================================= Out/1_zl/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 97.77 ================================================================= Out/2_di/ut.out ALL TESTS PASSED: rnorm 1.49e-10 (1.19e-07 shl0, 6.76e-05 arc130 2.84e-08 omega2) cputime 52.76 ================================================================= Out/2_dl/ut.out ALL TESTS PASSED: rnorm 1.49e-10 (1.19e-07 shl0, 6.76e-05 arc130 2.84e-08 omega2) cputime 44.59 ================================================================= Out/2g_di/ut.out ALL TESTS PASSED: rnorm 1.06e-10 (1.19e-07 shl0, 5.65e-05 arc130 1.16e-08 omega2) cputime 33.96 ================================================================= Out/2g_dl/ut.out ALL TESTS PASSED: rnorm 1.06e-10 (1.19e-07 shl0, 5.65e-05 arc130 1.16e-08 omega2) cputime 30.15 ================================================================= Out/2g_zi/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 5.69e-05 arc130 1.34e-09 omega2) cputime 58.91 ================================================================= Out/2g_zl/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 5.69e-05 arc130 1.34e-09 omega2) cputime 58.82 ================================================================= Out/2_zi/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 6.77e-05 arc130 1.65e-09 omega2) cputime 79.13 ================================================================= Out/2_zl/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 6.77e-05 arc130 1.65e-09 omega2) cputime 79.21 ================================================================= Out/5_di/ut.out ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 8.09e-05 arc130 1.44e-08 omega2) cputime 59.41 ================================================================= Out/5_dl/ut.out ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 8.09e-05 arc130 1.44e-08 omega2) cputime 49.39 ================================================================= Out/5_zi/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 8.10e-05 arc130 1.13e-09 omega2) cputime 98.82 ================================================================= Out/5_zl/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 8.10e-05 arc130 1.13e-09 omega2) cputime 98.19 ================================================================= Out/6_di/ut.out ALL TESTS PASSED: rnorm 1.49e-10 (1.19e-07 shl0, 6.76e-05 arc130 2.84e-08 omega2) cputime 0 ================================================================= Out/6_dl/ut.out ALL TESTS PASSED: rnorm 1.49e-10 (1.19e-07 shl0, 6.76e-05 arc130 2.84e-08 omega2) cputime 0 ================================================================= Out/6_zi/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 6.77e-05 arc130 1.65e-09 omega2) cputime 0 ================================================================= Out/6_zl/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 6.77e-05 arc130 1.65e-09 omega2) cputime 0 ================================================================= Out/7_di/ut.out ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 61.16 ================================================================= Out/7_dl/ut.out ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 49.42 ================================================================= Out/7_zi/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 96.29 ================================================================= Out/7_zl/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 95.47 ================================================================= Out/8_di/ut.out ALL TESTS PASSED: rnorm 1.49e-10 (1.19e-07 shl0, 6.76e-05 arc130 2.84e-08 omega2) cputime 51.65 ================================================================= Out/8_dl/ut.out ALL TESTS PASSED: rnorm 1.49e-10 (1.19e-07 shl0, 6.76e-05 arc130 2.84e-08 omega2) cputime 44.36 ================================================================= Out/8_zi/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 6.77e-05 arc130 1.65e-09 omega2) cputime 78.02 ================================================================= Out/8_zl/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 6.77e-05 arc130 1.65e-09 omega2) cputime 78.32 ================================================================= SuiteSparse/UMFPACK/Tcov/DO.linux.Jan240000644001170100242450000006325010175232354016220 0ustar davisfac################################################################################ Tcov test: 1 di ################################################################################ /bin/mv: cannot stat `Out/1_di': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 52.85 62.928u 18.396s 1:40.67 80.7% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 1 dl ################################################################################ /bin/mv: cannot stat `Out/1_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.44 55.002u 17.076s 1:47.74 66.8% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 1 zi ################################################################################ /bin/mv: cannot stat `Out/1_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.08 94.574u 19.999s 2:12.31 86.5% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 1 zl ################################################################################ /bin/mv: cannot stat `Out/1_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 85.85 94.178u 20.267s 2:20.97 81.1% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 2 di ################################################################################ /bin/mv: cannot stat `Out/2_di': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 2.67e-08 omega2) cputime 43.74 54.336u 17.934s 1:27.28 82.7% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 2 dl ################################################################################ /bin/mv: cannot stat `Out/2_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 42.64 54.068u 17.068s 1:26.00 82.6% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 2 zi ################################################################################ /bin/mv: cannot stat `Out/2_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.81e-09 omega2) cputime 66.69 75.192u 19.914s 1:51.89 84.9% 0+0k 0+0io 1pf+0w ################################################################################ Tcov test: 2 zl ################################################################################ /bin/mv: cannot stat `Out/2_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 85.1 93.816u 19.893s 2:09.71 87.6% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 3 di ################################################################################ /bin/mv: cannot stat `Out/3_di': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 6.76e-05 arc130 1.70e-08 omega2) cputime 49.18 61.050u 19.339s 1:41.90 78.8% 0+0k 0+0io 1pf+0w ################################################################################ Tcov test: 3 dl ################################################################################ /bin/mv: cannot stat `Out/3_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 42.82 55.075u 18.830s 1:34.96 77.8% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 3 zi ################################################################################ /bin/mv: cannot stat `Out/3_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.97e-09 omega2) cputime 84.1 93.431u 21.713s 2:25.67 79.0% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 3 zl ################################################################################ /bin/mv: cannot stat `Out/3_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 84.87 94.509u 21.778s 2:24.09 80.6% 0+0k 0+0io 3pf+0w ################################################################################ Tcov test: 4 di ################################################################################ /bin/mv: cannot stat `Out/4_di': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 6.76e-05 arc130 1.70e-08 omega2) cputime 49.36 60.263u 19.414s 1:41.11 78.7% 0+0k 0+0io 52pf+0w ################################################################################ Tcov test: 4 dl ################################################################################ /bin/mv: cannot stat `Out/4_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.08 54.299u 18.897s 1:34.41 77.5% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 4 zi ################################################################################ /bin/mv: cannot stat `Out/4_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.97e-09 omega2) cputime 84.28 92.899u 21.968s 2:18.25 83.0% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 4 zl ################################################################################ /bin/mv: cannot stat `Out/4_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 84.85 93.851u 21.883s 2:25.45 79.5% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 5 di ################################################################################ /bin/mv: cannot stat `Out/5_di': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 8.09e-05 arc130 1.44e-08 omega2) cputime 51.97 62.156u 17.755s 1:42.14 78.2% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 5 dl ################################################################################ /bin/mv: cannot stat `Out/5_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 8.09e-05 arc130 1.44e-08 omega2) cputime 43.55 54.453u 17.032s 1:32.39 77.3% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 5 zi ################################################################################ /bin/mv: cannot stat `Out/5_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 8.10e-05 arc130 1.13e-09 omega2) cputime 85.39 93.782u 19.825s 2:15.94 83.5% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 5 zl ################################################################################ /bin/mv: cannot stat `Out/5_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 8.10e-05 arc130 1.13e-09 omega2) cputime 85.99 94.275u 19.921s 2:17.38 83.1% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 6 di ################################################################################ /bin/mv: cannot stat `Out/6_di': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 2.67e-08 omega2) cputime 0 53.854u 17.179s 1:34.05 75.5% 0+0k 0+0io 14pf+0w ################################################################################ Tcov test: 6 dl ################################################################################ /bin/mv: cannot stat `Out/6_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 0 53.387u 16.482s 1:31.79 76.1% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 6 zi ################################################################################ /bin/mv: cannot stat `Out/6_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.81e-09 omega2) cputime 0 74.485u 19.371s 1:58.33 79.3% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 6 zl ################################################################################ /bin/mv: cannot stat `Out/6_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 0 93.386u 19.579s 2:23.34 78.7% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 7 di ################################################################################ /bin/mv: cannot stat `Out/7_di': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 52.13 62.467u 17.903s 1:42.73 78.2% 0+0k 0+0io 2pf+0w ################################################################################ Tcov test: 7 dl ################################################################################ /bin/mv: cannot stat `Out/7_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.24 54.250u 17.355s 1:35.45 75.0% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 7 zi ################################################################################ /bin/mv: cannot stat `Out/7_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 85.36 93.683u 20.174s 2:19.06 81.8% 0+0k 0+0io 3pf+0w ################################################################################ Tcov test: 7 zl ################################################################################ /bin/mv: cannot stat `Out/7_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 85.8 93.905u 20.169s 2:18.58 82.3% 0+0k 0+0io 3pf+0w ################################################################################ Tcov test: 8 di ################################################################################ /bin/mv: cannot stat `Out/8_di': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 2.67e-08 omega2) cputime 44.16 54.565u 17.959s 1:46.61 68.0% 0+0k 0+0io 69pf+0w ################################################################################ Tcov test: 8 dl ################################################################################ /bin/mv: cannot stat `Out/8_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 42.92 54.176u 17.162s 1:40.86 70.7% 0+0k 0+0io 50pf+0w ################################################################################ Tcov test: 8 zi ################################################################################ /bin/mv: cannot stat `Out/8_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.81e-09 omega2) cputime 66.15 74.497u 20.146s 1:59.21 79.3% 0+0k 0+0io 3pf+0w ################################################################################ Tcov test: 8 zl ################################################################################ /bin/mv: cannot stat `Out/8_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 85.29 93.557u 20.215s 2:22.60 79.7% 0+0k 0+0io 51pf+0w ################################################################################ Tcov test: 1g di ################################################################################ /bin/mv: cannot stat `Out/1g_di': No such file or directory make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 36.37 73.776u 18.042s 1:56.90 78.5% 0+0k 0+0io 61pf+0w ################################################################################ Tcov test: 1g dl ################################################################################ /bin/mv: cannot stat `Out/1g_dl': No such file or directory make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 30.98 69.221u 16.983s 1:46.11 81.2% 0+0k 0+0io 3pf+0w ################################################################################ Tcov test: 1g zi ################################################################################ /bin/mv: cannot stat `Out/1g_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.27 104.147u 19.969s 2:30.77 82.3% 0+0k 0+0io 3pf+0w ################################################################################ Tcov test: 1g zl ################################################################################ /bin/mv: cannot stat `Out/1g_zl': No such file or directory make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.11 103.657u 19.929s 2:25.30 85.0% 0+0k 0+0io 32pf+0w ################################################################################ Tcov test: 2g di ################################################################################ /bin/mv: cannot stat `Out/2g_di': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.06e-10 (1.37e-07 shl0, 5.65e-05 arc130 1.98e-08 omega2) cputime 29.92 68.398u 17.843s 1:45.71 81.5% 0+0k 0+0io 15pf+0w ################################################################################ Tcov test: 2g dl ################################################################################ /bin/mv: cannot stat `Out/2g_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 30.88 70.119u 16.902s 1:46.55 81.6% 0+0k 0+0io 5pf+0w ################################################################################ Tcov test: 2g zi ################################################################################ /bin/mv: cannot stat `Out/2g_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 7.77e-05 arc130 2.29e-09 omega2) cputime 49.79 86.583u 19.904s 2:07.59 83.4% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 2g zl ################################################################################ /bin/mv: cannot stat `Out/2g_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 67.68 104.484u 19.575s 2:25.99 84.9% 0+0k 0+0io 9pf+0w ################################################################################ Tcov test: 3g di ################################################################################ /bin/mv: cannot stat `Out/3g_di': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 8.27e-09 omega2) cputime 35.6 74.788u 20.351s 2:20.99 67.4% 0+0k 0+0io 6pf+0w ################################################################################ Tcov test: 3g dl ################################################################################ /bin/mv: cannot stat `Out/3g_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 31.32 70.806u 19.300s 2:01.74 74.0% 0+0k 0+0io 9pf+0w ################################################################################ Tcov test: 3g zi ################################################################################ /bin/mv: cannot stat `Out/3g_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 7.77e-05 arc130 2.57e-09 omega2) cputime 68.26 105.768u 22.114s 2:31.22 84.5% 0+0k 0+0io 6pf+0w ################################################################################ Tcov test: 3g zl ################################################################################ /bin/mv: cannot stat `Out/3g_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.65 106.120u 21.851s 2:31.80 84.3% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 4g di ################################################################################ /bin/mv: cannot stat `Out/4g_di': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 8.27e-09 omega2) cputime 36.36 74.674u 20.200s 1:58.26 80.2% 0+0k 0+0io 1pf+0w ################################################################################ Tcov test: 4g dl ################################################################################ /bin/mv: cannot stat `Out/4g_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 31.27 70.664u 19.197s 1:53.65 79.0% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 4g zi ################################################################################ /bin/mv: cannot stat `Out/4g_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 7.77e-05 arc130 2.57e-09 omega2) cputime 68.53 105.067u 22.053s 2:32.00 83.6% 0+0k 0+0io 3pf+0w ################################################################################ Tcov test: 4g zl ################################################################################ /bin/mv: cannot stat `Out/4g_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 69.12 105.423u 22.370s 2:33.38 83.3% 0+0k 0+0io 0pf+0w SuiteSparse/UMFPACK/Tcov/SolOut/0000755001170100242450000000000010206700651015172 5ustar davisfacSuiteSparse/UMFPACK/Tcov/DO.linux0000755001170100242450000000167610711722340015345 0ustar davisfac# # # ILP32, no BLAS, test for int overflow ./DO 1 di ./DO 1 dl ./DO 1 zi ./DO 1 zl # ILP32, BLAS, do not test for int overflow ./DO 2 di ./DO 2 dl ./DO 2 zi ./DO 2 zl # ILP32, no BLAS, test for int overflow, no reciprocal ./DO 5 di ./DO 5 dl ./DO 5 zi ./DO 5 zl # ILP32, BLAS, do not test for int overflow. No timers ./DO 6 di ./DO 6 dl ./DO 6 zi ./DO 6 zl # ILP32, no BLAS, test for int overflow, no divide-by-zero ./DO 7 di ./DO 7 dl ./DO 7 zi ./DO 7 zl # ILP32, BLAS, do not test for int overflow. No divide-by-zero ./DO 8 di ./DO 8 dl ./DO 8 zi ./DO 8 zl # ILP32, no BLAS, test for int overflow. Optimizations turned on ./DO 1g di run ./DO 1g dl run ./DO 1g zi run ./DO 1g zl run # ILP32, BLAS, do not test for int overflow. Optimizations turned on ./DO 2g di run ./DO 2g dl run ./DO 2g zi run ./DO 2g zl run # coverage summary, include lines not tested by the above 24 coverage tests ./covall | awk -f cover.awk > cover.out cat cover.out SuiteSparse/UMFPACK/Tcov/debug.amd0000644001170100242450000000000310006265124015506 0ustar davisfac-5 SuiteSparse/UMFPACK/Tcov/debug.umf0000644001170100242450000000000310006265124015534 0ustar davisfac-5 SuiteSparse/UMFPACK/Tcov/badnum2.umf0000644001170100242450000000001010171173060015774 0ustar davisfacbadnum2 SuiteSparse/UMFPACK/Tcov/badsym.umf0000644001170100242450000000054410006265123015736 0ustar davisfacT@.@b@?R@.@p@mmppm`mpmPmllm0m JB?SuiteSparse/UMFPACK/Tcov/cover.awk0000644001170100242450000000003710425400630015564 0ustar davisfac/^[a-Z]/ /^=====/ /^ 24/ SuiteSparse/UMFPACK/Tcov/cover.out0000644001170100242450000010167110711173732015627 0ustar davisfac================================================================================ umf_2by2.c ================================================================================ ================================================================================ umf_analyze.c ================================================================================ 24 222 #####: 217: return (FALSE) ; /* internal error! */ ================================================================================ umf_apply_order.c ================================================================================ ================================================================================ umf_assemble.c ================================================================================ ================================================================================ umf_assemble_fixq.c ================================================================================ ================================================================================ umf_blas3_update.c ================================================================================ ================================================================================ umf_build_tuples.c ================================================================================ 24 83 #####: 78: return (FALSE) ; /* out of memory for row tuples */ 24 101 #####: 96: return (FALSE) ; /* out of memory for col tuples */ ================================================================================ umf_colamd.c ================================================================================ 24 2708 #####: 2703: KILL_ROW (r) ; ================================================================================ umf_create_element.c ================================================================================ 24 253 #####: 248: return (FALSE) ; /* out of memory */ 24 264 #####: 259: return (FALSE) ; /* out of memory */ 24 440 #####: 435: return (UMF_get_memory (Numeric, Work, 0, r2, c2,do_Fcpos)); 24 543 #####: 538: return (UMF_get_memory (Numeric, Work, 0, r2, c2,do_Fcpos)); ================================================================================ umf_extend_front.c ================================================================================ ================================================================================ umf_free.c ================================================================================ ================================================================================ umf_fsize.c ================================================================================ 24 58 #####: 53: frsize = Int_MAX ; ================================================================================ umf_garbage_collection.c ================================================================================ ================================================================================ umf_get_memory.c ================================================================================ 24 114 #####: 109: newsize = (Int) bsize ; /* we cannot increase the size beyond bsize */ ================================================================================ umf_grow_front.c ================================================================================ 24 93 #####: 88: return (FALSE) ; 24 121 #####: 116: double a = 0.9 * sqrt ((Int_MAX / sizeof (Entry)) / s) ; 24 122 #####: 117: fnr2 = MAX (fnr_min, a * fnr2) ; 24 123 #####: 118: fnc2 = MAX (fnc_min, a * fnc2) ; 24 125 #####: 120: newsize = fnr2 * fnc2 ; 24 127 #####: 122: if (fnr2 % 2 == 0) fnr2++ ; 24 128 #####: 123: fnc2 = newsize / fnr2 ; 24 186 #####: 181: return (FALSE) ; /* out of memory */ ================================================================================ umf_init_front.c ================================================================================ 24 80 #####: 75: return (FALSE) ; ================================================================================ umf_is_permutation.c ================================================================================ ================================================================================ umf_kernel.c ================================================================================ ================================================================================ umf_kernel_init.c ================================================================================ 24 517 #####: 512: return (FALSE) ; /* pattern changed */ 24 545 #####: 540: return (FALSE) ; /* pattern changed */ 24 609 #####: 604: return (FALSE) ; /* pattern has changed */ 24 645 #####: 640: return (FALSE) ; /* pattern has changed */ 24 713 #####: 708: return (FALSE) ; /* pattern changed */ 24 726 #####: 721: return (FALSE) ; /* pattern changed */ 24 738 #####: 733: return (FALSE) ; /* pattern changed */ 24 830 #####: 825: return (FALSE) ; /* pattern changed */ 24 866 #####: 861: return (FALSE) ; /* pattern changed */ 24 908 #####: 903: return (FALSE) ; /* pattern changed */ 24 922 #####: 917: return (FALSE) ; /* pattern changed */ 24 1034 #####: 1029: return (FALSE) ; /* pattern changed */ ================================================================================ umf_kernel_wrapup.c ================================================================================ ================================================================================ umf_lhsolve.c ================================================================================ ================================================================================ umf_local_search.c ================================================================================ 24 657 #####: 652: return (UMFPACK_ERROR_different_pattern) ; 24 746 #####: 741: return (UMFPACK_ERROR_different_pattern) ; ================================================================================ umf_lsolve.c ================================================================================ ================================================================================ umf_ltsolve.c ================================================================================ ================================================================================ umf_malloc.c ================================================================================ ================================================================================ umf_mem_alloc_element.c ================================================================================ 24 49 #####: 44: return (0) ; /* problem is too large */ ================================================================================ umf_mem_alloc_head_block.c ================================================================================ ================================================================================ umf_mem_alloc_tail_block.c ================================================================================ ================================================================================ umf_mem_free_tail_block.c ================================================================================ ================================================================================ umf_mem_init_memoryspace.c ================================================================================ ================================================================================ umf_realloc.c ================================================================================ 24 58 #####: 53: return ((void *) NULL) ; ================================================================================ umf_report_perm.c ================================================================================ ================================================================================ umf_report_vector.c ================================================================================ ================================================================================ umf_row_search.c ================================================================================ 24 618 #####: 613: return (UMFPACK_ERROR_different_pattern) ; 24 664 #####: 659: return (UMFPACK_ERROR_different_pattern) ; 24 751 #####: 746: return (UMFPACK_ERROR_different_pattern) ; ================================================================================ umf_scale.c ================================================================================ ================================================================================ umf_scale_column.c ================================================================================ ================================================================================ umf_set_stats.c ================================================================================ ================================================================================ umf_singletons.c ================================================================================ ================================================================================ umf_solve.c ================================================================================ 24 1316 #####: 1311: omega [1] = tau ; 24 1317 #####: 1312: omega [2] = tau ; 24 1318 #####: 1313: break ; ================================================================================ umf_start_front.c ================================================================================ 24 156 #####: 151: maxfrsize = Int_MAX / sizeof (Entry) ; 24 175 #####: 170: fsize = Int_MAX / sizeof (Entry) ; 24 193 #####: 188: fsize2 = Int_MAX / sizeof (Entry) ; ================================================================================ umf_store_lu.c ================================================================================ 24 349 #####: 344: return (FALSE) ; /* out of memory */ 24 355 #####: 350: return (FALSE) ; /* out of memory */ 24 774 #####: 769: return (FALSE) ; /* out of memory */ 24 781 #####: 776: return (FALSE) ; /* out of memory */ ================================================================================ umf_store_lu_drop.c ================================================================================ 24 332 #####: 327: if (Work->do_grow) 24 336 #####: 331: r2 = fnrows ; 24 337 #####: 332: c2 = fncols ; 24 342 #####: 337: r2 = MAX (fnrows, Work->fnrows_new + 1) ; 24 343 #####: 338: c2 = MAX (fncols, Work->fncols_new + 1) ; 24 346 #####: 341: if (!UMF_get_memory (Numeric, Work, size, r2, c2, TRUE)) 24 349 #####: 344: return (FALSE) ; /* out of memory */ 24 351 #####: 346: p = UMF_mem_alloc_head_block (Numeric, size) ; 24 352 #####: 347: if (!p) 24 355 #####: 350: return (FALSE) ; /* out of memory */ 24 358 #####: 353: fnc_curr = Work->fnc_curr ; 24 359 #####: 354: fnr_curr = Work->fnr_curr ; 24 360 #####: 355: Flublock = Work->Flublock ; 24 361 #####: 356: Flblock = Work->Flblock ; 24 362 #####: 357: Fublock = Work->Fublock ; 24 363 #####: 358: Fl1 = Flublock + kk * nb ; 24 364 #####: 359: Fl2 = Flblock + kk * fnr_curr ; 24 497 #####: 492: pos = llen++ ; 24 498 #####: 493: Lpattern [pos] = row2 ; 24 499 #####: 494: Lpos [row2] = pos ; 24 500 #####: 495: *Li++ = row2 ; 24 756 #####: 751: if (Work->do_grow) 24 760 #####: 755: r2 = fnrows ; 24 761 #####: 756: c2 = fncols ; 24 766 #####: 761: r2 = MAX (fnrows, Work->fnrows_new + 1) ; 24 767 #####: 762: c2 = MAX (fncols, Work->fncols_new + 1) ; 24 770 #####: 765: if (!UMF_get_memory (Numeric, Work, size, r2, c2, TRUE)) 24 774 #####: 769: return (FALSE) ; /* out of memory */ 24 776 #####: 771: p = UMF_mem_alloc_head_block (Numeric, size) ; 24 777 #####: 772: if (!p) 24 781 #####: 776: return (FALSE) ; /* out of memory */ 24 784 #####: 779: fnc_curr = Work->fnc_curr ; 24 785 #####: 780: fnr_curr = Work->fnr_curr ; 24 786 #####: 781: Flublock = Work->Flublock ; 24 787 #####: 782: Flblock = Work->Flblock ; 24 788 #####: 783: Fublock = Work->Fublock ; 24 789 #####: 784: Fu1 = Flublock + kk ; 24 790 #####: 785: Fu2 = Fublock + kk * fnc_curr ; ================================================================================ umf_symbolic_usage.c ================================================================================ ================================================================================ umf_transpose.c ================================================================================ ================================================================================ umf_triplet_map_nox.c ================================================================================ ================================================================================ umf_triplet_map_x.c ================================================================================ ================================================================================ umf_triplet_nomap_nox.c ================================================================================ ================================================================================ umf_triplet_nomap_x.c ================================================================================ ================================================================================ umf_tuple_lengths.c ================================================================================ ================================================================================ umf_uhsolve.c ================================================================================ ================================================================================ umf_usolve.c ================================================================================ ================================================================================ umf_utsolve.c ================================================================================ ================================================================================ umf_valid_numeric.c ================================================================================ ================================================================================ umf_valid_symbolic.c ================================================================================ ================================================================================ umfpack_col_to_triplet.c ================================================================================ ================================================================================ umfpack_defaults.c ================================================================================ ================================================================================ umfpack_free_numeric.c ================================================================================ ================================================================================ umfpack_free_symbolic.c ================================================================================ ================================================================================ umfpack_get_determinant.c ================================================================================ 24 219 #####: 214: Info [UMFPACK_STATUS] = UMFPACK_WARNING_singular_matrix ; 24 220 #####: 215: break ; ================================================================================ umfpack_get_lunz.c ================================================================================ ================================================================================ umfpack_get_numeric.c ================================================================================ ================================================================================ umfpack_get_symbolic.c ================================================================================ ================================================================================ umfpack_load_numeric.c ================================================================================ 24 101 #####: 96: (void) UMF_free ((void *) Numeric) ; 24 102 #####: 97: fclose (f) ; 24 103 #####: 98: return (UMFPACK_ERROR_file_IO) ; 24 160 #####: 155: UMFPACK_free_numeric ((void **) &Numeric) ; 24 161 #####: 156: return (UMFPACK_ERROR_invalid_Numeric_object) ; ================================================================================ umfpack_load_symbolic.c ================================================================================ 24 101 #####: 96: (void) UMF_free ((void *) Symbolic) ; 24 102 #####: 97: fclose (f) ; 24 103 #####: 98: return (UMFPACK_ERROR_file_IO) ; 24 164 #####: 159: UMFPACK_free_symbolic ((void **) &Symbolic) ; 24 165 #####: 160: return (UMFPACK_ERROR_invalid_Symbolic_object) ; ================================================================================ umfpack_numeric.c ================================================================================ 24 188 #####: 183: Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; 24 189 #####: 184: return (UMFPACK_ERROR_out_of_memory) ; ================================================================================ umfpack_qsymbolic.c ================================================================================ 24 518 #####: 513: Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; 24 519 #####: 514: return (UMFPACK_ERROR_out_of_memory) ; 24 893 #####: 888: Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; 24 894 #####: 889: error (&Symbolic, SW) ; 24 895 #####: 890: return (UMFPACK_ERROR_out_of_memory) ; 24 914 #####: 909: Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; 24 915 #####: 910: error (&Symbolic, SW) ; 24 916 #####: 911: return (UMFPACK_ERROR_out_of_memory) ; 24 983 #####: 978: strategy = UMFPACK_STRATEGY_2BY2 ; 24 1463 #####: 1458: Info [UMFPACK_STATUS] = UMFPACK_ERROR_internal_error ; 24 1464 #####: 1459: error (&Symbolic, SW) ; 24 1465 #####: 1460: return (UMFPACK_ERROR_internal_error) ; 24 1817 #####: 1812: Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; 24 1818 #####: 1813: error (&Symbolic, SW) ; 24 1819 #####: 1814: return (UMFPACK_ERROR_out_of_memory) ; ================================================================================ umfpack_report_control.c ================================================================================ ================================================================================ umfpack_report_info.c ================================================================================ 24 506 #####: 501: PRINT_INFO ( 24 529 #####: 524: twtot = twsym + twnum ; 24 530 #####: 525: PRINT_INFO (" symbolic + numeric wall clock time (sec): %.2f\n", 24 532 #####: 527: if (ftot > 0 && twtot > TMIN) 24 534 #####: 529: PRINT_INFO ( 24 570 #####: 565: PRINT_INFO ( 24 601 #####: 596: if (twtot >= TMIN && ftot >= 0) 24 603 #####: 598: twtot += tsolve ; 24 604 #####: 599: PRINT_INFO ( 24 607 #####: 602: if (ftot > 0 && twtot > TMIN) 24 609 #####: 604: PRINT_INFO ( ================================================================================ umfpack_report_matrix.c ================================================================================ ================================================================================ umfpack_report_numeric.c ================================================================================ 24 326 #####: 321: return (FALSE) ; 24 332 #####: 327: PRINTF (("\t...\n")) ; 24 333 #####: 328: prl-- ; 24 534 #####: 529: return (FALSE) ; 24 641 #####: 636: PRINTF ((" ...\n")) ; 24 642 #####: 637: prl-- ; 24 653 #####: 648: return (FALSE) ; 24 659 #####: 654: PRINTF (("\t...\n")) ; 24 660 #####: 655: prl-- ; ================================================================================ umfpack_report_perm.c ================================================================================ ================================================================================ umfpack_report_status.c ================================================================================ ================================================================================ umfpack_report_symbolic.c ================================================================================ ================================================================================ umfpack_report_triplet.c ================================================================================ ================================================================================ umfpack_report_vector.c ================================================================================ ================================================================================ umfpack_save_numeric.c ================================================================================ ================================================================================ umfpack_save_symbolic.c ================================================================================ ================================================================================ umfpack_scale.c ================================================================================ ================================================================================ umfpack_solve.c ================================================================================ ================================================================================ umfpack_symbolic.c ================================================================================ ================================================================================ umfpack_tictoc.c ================================================================================ ================================================================================ umfpack_timer.c ================================================================================ ================================================================================ umfpack_transpose.c ================================================================================ ================================================================================ umfpack_triplet_to_col.c ================================================================================ ================================================================================ umfpack_wsolve.c ================================================================================ 24 146 #####: 141: Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_system ; 24 147 #####: 142: return (UMFPACK_ERROR_invalid_system) ; 24 160 #####: 155: Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ; 24 161 #####: 156: return (UMFPACK_ERROR_argument_missing) ; 24 167 #####: 162: irstep = 0 ; ================================================================================ amd_1.c ================================================================================ ================================================================================ amd_2.c ================================================================================ ================================================================================ amd_aat.c ================================================================================ ================================================================================ amd_control.c ================================================================================ ================================================================================ amd_defaults.c ================================================================================ ================================================================================ amd_info.c ================================================================================ ================================================================================ amd_order.c ================================================================================ 24 84 #####: 79: if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ; 24 85 #####: 80: return (AMD_OUT_OF_MEMORY) ; /* problem too large */ 24 105 #####: 100: amd_free (Len) ; 24 106 #####: 101: amd_free (Pinv) ; 24 107 #####: 102: if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ; 24 108 #####: 103: return (AMD_OUT_OF_MEMORY) ; 24 122 #####: 117: amd_free (Rp) ; 24 123 #####: 118: amd_free (Ri) ; 24 124 #####: 119: amd_free (Len) ; 24 125 #####: 120: amd_free (Pinv) ; 24 126 #####: 121: if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ; 24 127 #####: 122: return (AMD_OUT_OF_MEMORY) ; 24 175 #####: 170: amd_free (Rp) ; 24 176 #####: 171: amd_free (Ri) ; 24 177 #####: 172: amd_free (Len) ; 24 178 #####: 173: amd_free (Pinv) ; 24 179 #####: 174: if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ; 24 180 #####: 175: return (AMD_OUT_OF_MEMORY) ; ================================================================================ amd_postorder.c ================================================================================ ================================================================================ amd_post_tree.c ================================================================================ ================================================================================ amd_preprocess.c ================================================================================ ================================================================================ amd_valid.c ================================================================================ ================================================================================ Last line of each output file: ================================================================================ Out/1_di/ut.out ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.54e-08 omega2) cputime 68.89 ================================================================= Out/1_dl/ut.out ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.54e-08 omega2) cputime 60.89 ================================================================= Out/1g_di/ut.out ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 53.72 ================================================================= Out/1g_dl/ut.out ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 46.99 ================================================================= Out/1g_zi/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 5.84e-05 arc130 3.66e-10 omega2) cputime 89.22 ================================================================= Out/1g_zl/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 5.84e-05 arc130 3.66e-10 omega2) cputime 87.79 ================================================================= Out/1_zi/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 110.06 ================================================================= Out/1_zl/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 109.89 ================================================================= Out/2_di/ut.out ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 1.73e-08 omega2) cputime 60.81 ================================================================= Out/2_dl/ut.out ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 1.73e-08 omega2) cputime 55.15 ================================================================= Out/2g_di/ut.out ALL TESTS PASSED: rnorm 1.06e-10 (1.37e-07 shl0, 5.65e-05 arc130 8.07e-09 omega2) cputime 46.87 ================================================================= Out/2g_dl/ut.out ALL TESTS PASSED: rnorm 1.06e-10 (1.37e-07 shl0, 5.65e-05 arc130 8.07e-09 omega2) cputime 42.94 ================================================================= Out/2g_zi/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 5.69e-05 arc130 1.14e-09 omega2) cputime 67.54 ================================================================= Out/2g_zl/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 5.69e-05 arc130 1.14e-09 omega2) cputime 68.33 ================================================================= Out/2_zi/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.77e-09 omega2) cputime 90.34 ================================================================= Out/2_zl/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.77e-09 omega2) cputime 90.37 ================================================================= Out/5_di/ut.out ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 8.09e-05 arc130 1.44e-08 omega2) cputime 68.49 ================================================================= Out/5_dl/ut.out ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 8.09e-05 arc130 1.44e-08 omega2) cputime 60.57 ================================================================= Out/5_zi/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 8.10e-05 arc130 1.13e-09 omega2) cputime 109.19 ================================================================= Out/5_zl/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 8.10e-05 arc130 1.13e-09 omega2) cputime 110.08 ================================================================= Out/6_di/ut.out ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 1.73e-08 omega2) cputime 0 ================================================================= Out/6_dl/ut.out ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 1.73e-08 omega2) cputime 0 ================================================================= Out/6_zi/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.77e-09 omega2) cputime 0 ================================================================= Out/6_zl/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.77e-09 omega2) cputime 0 ================================================================= Out/7_di/ut.out ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.54e-08 omega2) cputime 69.52 ================================================================= Out/7_dl/ut.out ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.54e-08 omega2) cputime 59.27 ================================================================= Out/7_zi/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 109.28 ================================================================= Out/7_zl/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 110.39 ================================================================= Out/8_di/ut.out ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 1.73e-08 omega2) cputime 61.45 ================================================================= Out/8_dl/ut.out ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 1.73e-08 omega2) cputime 55.82 ================================================================= Out/8_zi/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.77e-09 omega2) cputime 90.46 ================================================================= Out/8_zl/ut.out ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.77e-09 omega2) cputime 89.24 ================================================================= SuiteSparse/UMFPACK/Tcov/covall0000755001170100242450000000613110426667763015200 0ustar davisfac#!/bin/csh # only print those lines that are "#####" in all tests. foreach file ( \ umf_2by2.c umf_analyze.c umf_apply_order.c umf_assemble.c \ umf_assemble_fixq.c umf_blas3_update.c umf_build_tuples.c \ umf_colamd.c umf_create_element.c umf_extend_front.c \ umf_free.c umf_fsize.c umf_garbage_collection.c umf_get_memory.c \ umf_grow_front.c umf_init_front.c umf_is_permutation.c umf_kernel.c \ umf_kernel_init.c umf_kernel_wrapup.c umf_lhsolve.c umf_local_search.c \ umf_lsolve.c umf_ltsolve.c umf_malloc.c umf_mem_alloc_element.c \ umf_mem_alloc_head_block.c umf_mem_alloc_tail_block.c \ umf_mem_free_tail_block.c umf_mem_init_memoryspace.c \ umf_realloc.c umf_report_perm.c umf_report_vector.c umf_row_search.c \ umf_scale.c umf_scale_column.c umf_set_stats.c umf_singletons.c \ umf_solve.c umf_start_front.c umf_store_lu.c umf_store_lu_drop.c \ umf_symbolic_usage.c \ umf_transpose.c umf_triplet_map_nox.c umf_triplet_map_x.c \ umf_triplet_nomap_nox.c umf_triplet_nomap_x.c umf_tuple_lengths.c \ umf_uhsolve.c umf_usolve.c umf_utsolve.c umf_valid_numeric.c \ umf_valid_symbolic.c umfpack_col_to_triplet.c umfpack_defaults.c \ umfpack_free_numeric.c umfpack_free_symbolic.c umfpack_get_determinant.c \ umfpack_get_lunz.c umfpack_get_numeric.c umfpack_get_symbolic.c \ umfpack_load_numeric.c umfpack_load_symbolic.c umfpack_numeric.c \ umfpack_qsymbolic.c umfpack_report_control.c umfpack_report_info.c \ umfpack_report_matrix.c umfpack_report_numeric.c umfpack_report_perm.c \ umfpack_report_status.c umfpack_report_symbolic.c umfpack_report_triplet.c \ umfpack_report_vector.c umfpack_save_numeric.c umfpack_save_symbolic.c \ umfpack_scale.c umfpack_solve.c umfpack_symbolic.c \ umfpack_tictoc.c umfpack_timer.c umfpack_transpose.c \ umfpack_triplet_to_col.c umfpack_wsolve.c \ ) echo '================================================================================' echo $file echo '================================================================================' cat /dev/null > Out/tcov_tmp foreach fdirs (Out/?_??) cat -n $fdirs/UMFPACK/Source/$file.gcov | grep '#####' >> Out/tcov_tmp end sort -n Out/tcov_tmp | uniq -c end foreach file ( \ amd_1.c amd_2.c amd_aat.c amd_control.c amd_defaults.c \ amd_info.c amd_order.c amd_postorder.c amd_post_tree.c \ amd_preprocess.c amd_valid.c \ ) echo '================================================================================' echo $file echo '================================================================================' cat /dev/null > Out/tcov_tmp foreach fdirs (Out/?_??) cat -n $fdirs/AMD/Source/$file.gcov | grep '#####' >> Out/tcov_tmp end sort -n Out/tcov_tmp | uniq -c end echo '================================================================================' echo 'Last line of each output file: ' echo '================================================================================' foreach file (Out/*_*/ut.out) echo $file tail -1 $file echo '=================================================================' end SuiteSparse/UMFPACK/Tcov/DO.linux.out20000644001170100242450000005657110174010732016234 0ustar davisfac################################################################################ Tcov test: 1 di ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 58.08 65.957u 21.743s 4:14.39 34.4% 0+0k 0+0io 56pf+0w ################################################################################ Tcov test: 1 dl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 47.61 57.147u 19.907s 2:36.09 49.3% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 1 zi ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 87.9 96.431u 21.184s 5:53.60 33.2% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 1 zl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 87.89 95.638u 21.373s 4:55.24 39.6% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 2 di ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 2.67e-08 omega2) cputime 44.76 55.884u 18.499s 2:30.76 49.3% 0+0k 0+0io 1pf+0w ################################################################################ Tcov test: 2 dl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.58 55.066u 17.643s 2:27.94 49.1% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 2 zi ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.81e-09 omega2) cputime 68.18 76.674u 21.814s 3:18.86 49.5% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 2 zl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 87.68 95.713u 21.981s 4:56.13 39.7% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 3 di ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 6.76e-05 arc130 1.70e-08 omega2) cputime 52.99 63.135u 22.242s 4:26.20 32.0% 0+0k 0+0io 1pf+0w ################################################################################ Tcov test: 3 dl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 45.62 57.047u 21.076s 5:13.79 24.8% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 3 zi ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.97e-09 omega2) cputime 85.67 95.359u 23.257s 4:00.29 49.3% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 3 zl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 87.52 96.462u 23.746s 5:27.63 36.6% 0+0k 0+0io 3pf+0w ################################################################################ Tcov test: 4 di ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 6.76e-05 arc130 1.70e-08 omega2) cputime 50.86 62.001u 21.885s 3:16.46 42.6% 0+0k 0+0io 55pf+0w ################################################################################ Tcov test: 4 dl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.79 55.750u 20.866s 2:41.32 47.4% 0+0k 0+0io 2pf+0w ################################################################################ Tcov test: 4 zi ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.97e-09 omega2) cputime 85.85 95.295u 24.087s 4:09.94 47.7% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 4 zl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.78 95.469u 22.687s 3:56.27 50.0% 0+0k 0+0io 57pf+0w ################################################################################ Tcov test: 5 di ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 8.09e-05 arc130 1.44e-08 omega2) cputime 54.79 64.073u 19.475s 3:18.85 42.0% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 5 dl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 8.09e-05 arc130 1.44e-08 omega2) cputime 44.3 54.864u 18.963s 3:20.43 36.8% 0+0k 0+0io 2pf+0w ################################################################################ Tcov test: 5 zi ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 8.10e-05 arc130 1.13e-09 omega2) cputime 86.29 94.274u 21.352s 5:45.72 33.4% 0+0k 0+0io 55pf+0w ################################################################################ Tcov test: 5 zl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 8.10e-05 arc130 1.13e-09 omega2) cputime 86.48 94.614u 20.459s 4:14.05 45.2% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 6 di ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 2.67e-08 omega2) cputime 0 54.133u 18.431s 2:38.62 45.7% 0+0k 0+0io 1pf+0w ################################################################################ Tcov test: 6 dl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 0 53.685u 17.717s 2:18.76 51.4% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 6 zi ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.81e-09 omega2) cputime 0 74.530u 20.591s 3:07.82 50.6% 0+0k 0+0io 3pf+0w ################################################################################ Tcov test: 6 zl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 0 93.008u 21.095s 3:47.37 50.1% 0+0k 0+0io 3pf+0w ################################################################################ Tcov test: 7 di ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 52 62.595u 18.109s 2:39.53 50.5% 0+0k 0+0io 2pf+0w ################################################################################ Tcov test: 7 dl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.48 54.331u 19.149s 2:32.31 48.2% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 7 zi ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.22 94.291u 22.044s 4:07.57 46.9% 0+0k 0+0io 35pf+0w ################################################################################ Tcov test: 7 zl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 85.77 94.190u 21.226s 4:00.99 47.8% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 8 di ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 2.67e-08 omega2) cputime 45.21 55.138u 19.192s 2:53.18 42.9% 0+0k 0+0io 1pf+0w ################################################################################ Tcov test: 8 dl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.36 54.424u 18.817s 2:51.32 42.7% 0+0k 0+0io 57pf+0w ################################################################################ Tcov test: 8 zi ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.81e-09 omega2) cputime 66.59 74.890u 21.514s 4:01.29 39.9% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 8 zl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 85.8 93.133u 21.256s 4:41.13 40.6% 0+0k 0+0io 57pf+0w ################################################################################ Tcov test: 1g di ################################################################################ make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 36.45 74.444u 18.155s 4:12.64 36.6% 0+0k 0+0io 4pf+0w ################################################################################ Tcov test: 1g dl ################################################################################ make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 31.88 70.117u 18.138s 4:06.43 35.8% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 1g zi ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.88 104.228u 21.576s 4:20.17 48.3% 0+0k 0+0io 3pf+0w ################################################################################ Tcov test: 1g zl ################################################################################ make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.77 103.874u 21.334s 4:04.77 51.1% 0+0k 0+0io 2pf+0w ################################################################################ Tcov test: 2g di ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.06e-10 (1.37e-07 shl0, 5.65e-05 arc130 1.98e-08 omega2) cputime 30.14 68.834u 18.537s 2:59.16 48.7% 0+0k 0+0io 11pf+0w ################################################################################ Tcov test: 2g dl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 32.02 70.467u 18.482s 2:49.67 52.4% 0+0k 0+0io 10pf+0w ################################################################################ Tcov test: 2g zi ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 7.77e-05 arc130 2.29e-09 omega2) cputime 49.84 86.839u 20.261s 3:27.29 51.6% 0+0k 0+0io 3pf+0w ################################################################################ Tcov test: 2g zl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 67.93 104.755u 20.972s 4:03.31 51.6% 0+0k 0+0io 64pf+0w ################################################################################ Tcov test: 3g di ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 8.27e-09 omega2) cputime 36.48 75.152u 23.653s 3:10.42 51.8% 0+0k 0+0io 1pf+0w ################################################################################ Tcov test: 3g dl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 31.52 71.320u 21.093s 3:01.30 50.9% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 3g zi ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 7.77e-05 arc130 2.57e-09 omega2) cputime 67.75 105.546u 22.796s 4:07.55 51.8% 0+0k 0+0io 40pf+0w ################################################################################ Tcov test: 3g zl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.72 106.281u 23.809s 4:12.22 51.5% 0+0k 0+0io 7pf+0w ################################################################################ Tcov test: 4g di ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 8.27e-09 omega2) cputime 35.69 74.646u 22.580s 3:44.05 43.3% 0+0k 0+0io 46pf+0w ################################################################################ Tcov test: 4g dl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 31.21 70.200u 19.713s 3:47.80 39.4% 0+0k 0+0io 9pf+0w ################################################################################ Tcov test: 4g zi ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 7.77e-05 arc130 2.57e-09 omega2) cputime 68.15 105.008u 22.823s 5:40.93 37.4% 0+0k 0+0io 3pf+0w ################################################################################ Tcov test: 4g zl ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.44 105.124u 22.060s 5:40.31 37.3% 0+0k 0+0io 0pf+0w SuiteSparse/UMFPACK/Tcov/ucov.di0000755001170100242450000001072610171013722015245 0ustar davisfac#!/bin/csh # ucov.di: construct gcov files for umfpack, di version gcov -o umf_i_analyze umf_analyze.c gcov -o umf_i_apply_order umf_apply_order.c gcov -o umf_i_colamd umf_colamd.c gcov -o umf_i_free umf_free.c gcov -o umf_i_fsize umf_fsize.c gcov -o umf_i_is_permutation umf_is_permutation.c gcov -o umf_i_malloc umf_malloc.c gcov -o umf_i_realloc umf_realloc.c gcov -o umf_i_report_perm umf_report_perm.c gcov -o umf_i_singletons umf_singletons.c gcov -o umf_di_2by2 umf_2by2.c gcov -o umf_di_blas3_update umf_blas3_update.c gcov -o umf_di_build_tuples umf_build_tuples.c gcov -o umf_di_create_element umf_create_element.c gcov -o umf_di_extend_front umf_extend_front.c gcov -o umf_di_garbage_collection umf_garbage_collection.c gcov -o umf_di_get_memory umf_get_memory.c gcov -o umf_di_grow_front umf_grow_front.c gcov -o umf_di_init_front umf_init_front.c gcov -o umf_di_kernel umf_kernel.c gcov -o umf_di_kernel_init umf_kernel_init.c gcov -o umf_di_kernel_wrapup umf_kernel_wrapup.c gcov -o umf_di_local_search umf_local_search.c gcov -o umf_di_lsolve umf_lsolve.c gcov -o umf_di_mem_alloc_element umf_mem_alloc_element.c gcov -o umf_di_mem_alloc_head_block umf_mem_alloc_head_block.c gcov -o umf_di_mem_alloc_tail_block umf_mem_alloc_tail_block.c gcov -o umf_di_mem_free_tail_block umf_mem_free_tail_block.c gcov -o umf_di_mem_init_memoryspace umf_mem_init_memoryspace.c gcov -o umf_di_report_vector umf_report_vector.c gcov -o umf_di_row_search umf_row_search.c gcov -o umf_di_scale umf_scale.c gcov -o umf_di_scale_column umf_scale_column.c gcov -o umf_di_set_stats umf_set_stats.c gcov -o umf_di_solve umf_solve.c gcov -o umf_di_start_front umf_start_front.c gcov -o umf_di_symbolic_usage umf_symbolic_usage.c gcov -o umf_di_transpose umf_transpose.c gcov -o umf_di_tuple_lengths umf_tuple_lengths.c gcov -o umf_di_usolve umf_usolve.c gcov -o umf_di_valid_numeric umf_valid_numeric.c gcov -o umf_di_valid_symbolic umf_valid_symbolic.c gcov -o umfpack_di_col_to_triplet umfpack_col_to_triplet.c gcov -o umfpack_di_defaults umfpack_defaults.c gcov -o umfpack_di_free_numeric umfpack_free_numeric.c gcov -o umfpack_di_free_symbolic umfpack_free_symbolic.c gcov -o umfpack_di_get_lunz umfpack_get_lunz.c gcov -o umfpack_di_get_numeric umfpack_get_numeric.c gcov -o umfpack_di_get_determinant umfpack_get_determinant.c gcov -o umfpack_di_get_symbolic umfpack_get_symbolic.c gcov -o umfpack_di_load_numeric umfpack_load_numeric.c gcov -o umfpack_di_load_symbolic umfpack_load_symbolic.c gcov -o umfpack_di_numeric umfpack_numeric.c gcov -o umfpack_di_qsymbolic umfpack_qsymbolic.c gcov -o umfpack_di_report_control umfpack_report_control.c gcov -o umfpack_di_report_info umfpack_report_info.c gcov -o umfpack_di_report_matrix umfpack_report_matrix.c gcov -o umfpack_di_report_numeric umfpack_report_numeric.c gcov -o umfpack_di_report_perm umfpack_report_perm.c gcov -o umfpack_di_report_status umfpack_report_status.c gcov -o umfpack_di_report_symbolic umfpack_report_symbolic.c gcov -o umfpack_di_report_triplet umfpack_report_triplet.c gcov -o umfpack_di_report_vector umfpack_report_vector.c gcov -o umfpack_di_save_numeric umfpack_save_numeric.c gcov -o umfpack_di_save_symbolic umfpack_save_symbolic.c gcov -o umfpack_di_scale umfpack_scale.c gcov -o umfpack_di_symbolic umfpack_symbolic.c gcov -o umfpack_di_transpose umfpack_transpose.c gcov -o umfpack_di_triplet_to_col umfpack_triplet_to_col.c gcov -o umfpack_gn_tictoc umfpack_tictoc.c gcov -o umfpack_gn_timer umfpack_timer.c # multiple versions gcov -o umf_di_uhsolve umf_utsolve.c ; mv -f umf_utsolve.c.gcov umf_uhsolve.c.gcov gcov -o umf_di_utsolve umf_utsolve.c gcov -o umf_di_lhsolve umf_ltsolve.c ; mv -f umf_ltsolve.c.gcov umf_lhsolve.c.gcov gcov -o umf_di_ltsolve umf_ltsolve.c gcov -o umfpack_di_wsolve umfpack_solve.c ; mv -f umfpack_solve.c.gcov umfpack_wsolve.c.gcov gcov -o umfpack_di_solve umfpack_solve.c gcov -o umf_di_store_lu_drop umf_store_lu.c ; mv -f umf_store_lu.c.gcov umf_store_lu_drop.c.gcov gcov -o umf_di_store_lu umf_store_lu.c gcov -o umf_di_assemble_fixq umf_assemble.c ; mv -f umf_assemble.c.gcov umf_assemble_fixq.c.gcov gcov -o umf_di_assemble umf_assemble.c gcov -o umf_di_triplet_map_x umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_map_x.c.gcov gcov -o umf_di_triplet_nomap_x umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_nomap_x.c.gcov gcov -o umf_di_triplet_map_nox umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_map_nox.c.gcov gcov -o umf_di_triplet_nomap_nox umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_nomap_nox.c.gcov SuiteSparse/UMFPACK/Tcov/ucov.dl0000755001170100242450000001072610171013727015255 0ustar davisfac#!/bin/csh # ucov.dl: construct gcov files for umfpack, dl version gcov -o umf_l_analyze umf_analyze.c gcov -o umf_l_apply_order umf_apply_order.c gcov -o umf_l_colamd umf_colamd.c gcov -o umf_l_free umf_free.c gcov -o umf_l_fsize umf_fsize.c gcov -o umf_l_is_permutation umf_is_permutation.c gcov -o umf_l_malloc umf_malloc.c gcov -o umf_l_realloc umf_realloc.c gcov -o umf_l_report_perm umf_report_perm.c gcov -o umf_l_singletons umf_singletons.c gcov -o umf_dl_2by2 umf_2by2.c gcov -o umf_dl_blas3_update umf_blas3_update.c gcov -o umf_dl_build_tuples umf_build_tuples.c gcov -o umf_dl_create_element umf_create_element.c gcov -o umf_dl_extend_front umf_extend_front.c gcov -o umf_dl_garbage_collection umf_garbage_collection.c gcov -o umf_dl_get_memory umf_get_memory.c gcov -o umf_dl_grow_front umf_grow_front.c gcov -o umf_dl_init_front umf_init_front.c gcov -o umf_dl_kernel umf_kernel.c gcov -o umf_dl_kernel_init umf_kernel_init.c gcov -o umf_dl_kernel_wrapup umf_kernel_wrapup.c gcov -o umf_dl_local_search umf_local_search.c gcov -o umf_dl_lsolve umf_lsolve.c gcov -o umf_dl_mem_alloc_element umf_mem_alloc_element.c gcov -o umf_dl_mem_alloc_head_block umf_mem_alloc_head_block.c gcov -o umf_dl_mem_alloc_tail_block umf_mem_alloc_tail_block.c gcov -o umf_dl_mem_free_tail_block umf_mem_free_tail_block.c gcov -o umf_dl_mem_init_memoryspace umf_mem_init_memoryspace.c gcov -o umf_dl_report_vector umf_report_vector.c gcov -o umf_dl_row_search umf_row_search.c gcov -o umf_dl_scale umf_scale.c gcov -o umf_dl_scale_column umf_scale_column.c gcov -o umf_dl_set_stats umf_set_stats.c gcov -o umf_dl_solve umf_solve.c gcov -o umf_dl_start_front umf_start_front.c gcov -o umf_dl_symbolic_usage umf_symbolic_usage.c gcov -o umf_dl_transpose umf_transpose.c gcov -o umf_dl_tuple_lengths umf_tuple_lengths.c gcov -o umf_dl_usolve umf_usolve.c gcov -o umf_dl_valid_numeric umf_valid_numeric.c gcov -o umf_dl_valid_symbolic umf_valid_symbolic.c gcov -o umfpack_dl_col_to_triplet umfpack_col_to_triplet.c gcov -o umfpack_dl_defaults umfpack_defaults.c gcov -o umfpack_dl_free_numeric umfpack_free_numeric.c gcov -o umfpack_dl_free_symbolic umfpack_free_symbolic.c gcov -o umfpack_dl_get_lunz umfpack_get_lunz.c gcov -o umfpack_dl_get_numeric umfpack_get_numeric.c gcov -o umfpack_dl_get_determinant umfpack_get_determinant.c gcov -o umfpack_dl_get_symbolic umfpack_get_symbolic.c gcov -o umfpack_dl_load_numeric umfpack_load_numeric.c gcov -o umfpack_dl_load_symbolic umfpack_load_symbolic.c gcov -o umfpack_dl_numeric umfpack_numeric.c gcov -o umfpack_dl_qsymbolic umfpack_qsymbolic.c gcov -o umfpack_dl_report_control umfpack_report_control.c gcov -o umfpack_dl_report_info umfpack_report_info.c gcov -o umfpack_dl_report_matrix umfpack_report_matrix.c gcov -o umfpack_dl_report_numeric umfpack_report_numeric.c gcov -o umfpack_dl_report_perm umfpack_report_perm.c gcov -o umfpack_dl_report_status umfpack_report_status.c gcov -o umfpack_dl_report_symbolic umfpack_report_symbolic.c gcov -o umfpack_dl_report_triplet umfpack_report_triplet.c gcov -o umfpack_dl_report_vector umfpack_report_vector.c gcov -o umfpack_dl_save_numeric umfpack_save_numeric.c gcov -o umfpack_dl_save_symbolic umfpack_save_symbolic.c gcov -o umfpack_dl_scale umfpack_scale.c gcov -o umfpack_dl_symbolic umfpack_symbolic.c gcov -o umfpack_dl_transpose umfpack_transpose.c gcov -o umfpack_dl_triplet_to_col umfpack_triplet_to_col.c gcov -o umfpack_gn_tictoc umfpack_tictoc.c gcov -o umfpack_gn_timer umfpack_timer.c # multiple versions gcov -o umf_dl_uhsolve umf_utsolve.c ; mv -f umf_utsolve.c.gcov umf_uhsolve.c.gcov gcov -o umf_dl_utsolve umf_utsolve.c gcov -o umf_dl_lhsolve umf_ltsolve.c ; mv -f umf_ltsolve.c.gcov umf_lhsolve.c.gcov gcov -o umf_dl_ltsolve umf_ltsolve.c gcov -o umfpack_dl_wsolve umfpack_solve.c ; mv -f umfpack_solve.c.gcov umfpack_wsolve.c.gcov gcov -o umfpack_dl_solve umfpack_solve.c gcov -o umf_dl_store_lu_drop umf_store_lu.c ; mv -f umf_store_lu.c.gcov umf_store_lu_drop.c.gcov gcov -o umf_dl_store_lu umf_store_lu.c gcov -o umf_dl_assemble_fixq umf_assemble.c ; mv -f umf_assemble.c.gcov umf_assemble_fixq.c.gcov gcov -o umf_dl_assemble umf_assemble.c gcov -o umf_dl_triplet_map_x umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_map_x.c.gcov gcov -o umf_dl_triplet_nomap_x umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_nomap_x.c.gcov gcov -o umf_dl_triplet_map_nox umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_map_nox.c.gcov gcov -o umf_dl_triplet_nomap_nox umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_nomap_nox.c.gcov SuiteSparse/UMFPACK/Tcov/ucov.zi0000755001170100242450000001072610171013735015277 0ustar davisfac#!/bin/csh # ucov.zi: construct gcov files for umfpack, zi version gcov -o umf_i_analyze umf_analyze.c gcov -o umf_i_apply_order umf_apply_order.c gcov -o umf_i_colamd umf_colamd.c gcov -o umf_i_free umf_free.c gcov -o umf_i_fsize umf_fsize.c gcov -o umf_i_is_permutation umf_is_permutation.c gcov -o umf_i_malloc umf_malloc.c gcov -o umf_i_realloc umf_realloc.c gcov -o umf_i_report_perm umf_report_perm.c gcov -o umf_i_singletons umf_singletons.c gcov -o umf_zi_2by2 umf_2by2.c gcov -o umf_zi_blas3_update umf_blas3_update.c gcov -o umf_zi_build_tuples umf_build_tuples.c gcov -o umf_zi_create_element umf_create_element.c gcov -o umf_zi_extend_front umf_extend_front.c gcov -o umf_zi_garbage_collection umf_garbage_collection.c gcov -o umf_zi_get_memory umf_get_memory.c gcov -o umf_zi_grow_front umf_grow_front.c gcov -o umf_zi_init_front umf_init_front.c gcov -o umf_zi_kernel umf_kernel.c gcov -o umf_zi_kernel_init umf_kernel_init.c gcov -o umf_zi_kernel_wrapup umf_kernel_wrapup.c gcov -o umf_zi_local_search umf_local_search.c gcov -o umf_zi_lsolve umf_lsolve.c gcov -o umf_zi_mem_alloc_element umf_mem_alloc_element.c gcov -o umf_zi_mem_alloc_head_block umf_mem_alloc_head_block.c gcov -o umf_zi_mem_alloc_tail_block umf_mem_alloc_tail_block.c gcov -o umf_zi_mem_free_tail_block umf_mem_free_tail_block.c gcov -o umf_zi_mem_init_memoryspace umf_mem_init_memoryspace.c gcov -o umf_zi_report_vector umf_report_vector.c gcov -o umf_zi_row_search umf_row_search.c gcov -o umf_zi_scale umf_scale.c gcov -o umf_zi_scale_column umf_scale_column.c gcov -o umf_zi_set_stats umf_set_stats.c gcov -o umf_zi_solve umf_solve.c gcov -o umf_zi_start_front umf_start_front.c gcov -o umf_zi_symbolic_usage umf_symbolic_usage.c gcov -o umf_zi_transpose umf_transpose.c gcov -o umf_zi_tuple_lengths umf_tuple_lengths.c gcov -o umf_zi_usolve umf_usolve.c gcov -o umf_zi_valid_numeric umf_valid_numeric.c gcov -o umf_zi_valid_symbolic umf_valid_symbolic.c gcov -o umfpack_zi_col_to_triplet umfpack_col_to_triplet.c gcov -o umfpack_zi_defaults umfpack_defaults.c gcov -o umfpack_zi_free_numeric umfpack_free_numeric.c gcov -o umfpack_zi_free_symbolic umfpack_free_symbolic.c gcov -o umfpack_zi_get_lunz umfpack_get_lunz.c gcov -o umfpack_zi_get_numeric umfpack_get_numeric.c gcov -o umfpack_zi_get_determinant umfpack_get_determinant.c gcov -o umfpack_zi_get_symbolic umfpack_get_symbolic.c gcov -o umfpack_zi_load_numeric umfpack_load_numeric.c gcov -o umfpack_zi_load_symbolic umfpack_load_symbolic.c gcov -o umfpack_zi_numeric umfpack_numeric.c gcov -o umfpack_zi_qsymbolic umfpack_qsymbolic.c gcov -o umfpack_zi_report_control umfpack_report_control.c gcov -o umfpack_zi_report_info umfpack_report_info.c gcov -o umfpack_zi_report_matrix umfpack_report_matrix.c gcov -o umfpack_zi_report_numeric umfpack_report_numeric.c gcov -o umfpack_zi_report_perm umfpack_report_perm.c gcov -o umfpack_zi_report_status umfpack_report_status.c gcov -o umfpack_zi_report_symbolic umfpack_report_symbolic.c gcov -o umfpack_zi_report_triplet umfpack_report_triplet.c gcov -o umfpack_zi_report_vector umfpack_report_vector.c gcov -o umfpack_zi_save_numeric umfpack_save_numeric.c gcov -o umfpack_zi_save_symbolic umfpack_save_symbolic.c gcov -o umfpack_zi_scale umfpack_scale.c gcov -o umfpack_zi_symbolic umfpack_symbolic.c gcov -o umfpack_zi_transpose umfpack_transpose.c gcov -o umfpack_zi_triplet_to_col umfpack_triplet_to_col.c gcov -o umfpack_gn_tictoc umfpack_tictoc.c gcov -o umfpack_gn_timer umfpack_timer.c # multiple versions gcov -o umf_zi_uhsolve umf_utsolve.c ; mv -f umf_utsolve.c.gcov umf_uhsolve.c.gcov gcov -o umf_zi_utsolve umf_utsolve.c gcov -o umf_zi_lhsolve umf_ltsolve.c ; mv -f umf_ltsolve.c.gcov umf_lhsolve.c.gcov gcov -o umf_zi_ltsolve umf_ltsolve.c gcov -o umfpack_zi_wsolve umfpack_solve.c ; mv -f umfpack_solve.c.gcov umfpack_wsolve.c.gcov gcov -o umfpack_zi_solve umfpack_solve.c gcov -o umf_zi_store_lu_drop umf_store_lu.c ; mv -f umf_store_lu.c.gcov umf_store_lu_drop.c.gcov gcov -o umf_zi_store_lu umf_store_lu.c gcov -o umf_zi_assemble_fixq umf_assemble.c ; mv -f umf_assemble.c.gcov umf_assemble_fixq.c.gcov gcov -o umf_zi_assemble umf_assemble.c gcov -o umf_zi_triplet_map_x umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_map_x.c.gcov gcov -o umf_zi_triplet_nomap_x umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_nomap_x.c.gcov gcov -o umf_zi_triplet_map_nox umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_map_nox.c.gcov gcov -o umf_zi_triplet_nomap_nox umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_nomap_nox.c.gcov SuiteSparse/UMFPACK/Tcov/ucov.zl0000755001170100242450000001072610171013741015277 0ustar davisfac#!/bin/csh # ucov.zl: construct gcov files for umfpack, zl version gcov -o umf_l_analyze umf_analyze.c gcov -o umf_l_apply_order umf_apply_order.c gcov -o umf_l_colamd umf_colamd.c gcov -o umf_l_free umf_free.c gcov -o umf_l_fsize umf_fsize.c gcov -o umf_l_is_permutation umf_is_permutation.c gcov -o umf_l_malloc umf_malloc.c gcov -o umf_l_realloc umf_realloc.c gcov -o umf_l_report_perm umf_report_perm.c gcov -o umf_l_singletons umf_singletons.c gcov -o umf_zl_2by2 umf_2by2.c gcov -o umf_zl_blas3_update umf_blas3_update.c gcov -o umf_zl_build_tuples umf_build_tuples.c gcov -o umf_zl_create_element umf_create_element.c gcov -o umf_zl_extend_front umf_extend_front.c gcov -o umf_zl_garbage_collection umf_garbage_collection.c gcov -o umf_zl_get_memory umf_get_memory.c gcov -o umf_zl_grow_front umf_grow_front.c gcov -o umf_zl_init_front umf_init_front.c gcov -o umf_zl_kernel umf_kernel.c gcov -o umf_zl_kernel_init umf_kernel_init.c gcov -o umf_zl_kernel_wrapup umf_kernel_wrapup.c gcov -o umf_zl_local_search umf_local_search.c gcov -o umf_zl_lsolve umf_lsolve.c gcov -o umf_zl_mem_alloc_element umf_mem_alloc_element.c gcov -o umf_zl_mem_alloc_head_block umf_mem_alloc_head_block.c gcov -o umf_zl_mem_alloc_tail_block umf_mem_alloc_tail_block.c gcov -o umf_zl_mem_free_tail_block umf_mem_free_tail_block.c gcov -o umf_zl_mem_init_memoryspace umf_mem_init_memoryspace.c gcov -o umf_zl_report_vector umf_report_vector.c gcov -o umf_zl_row_search umf_row_search.c gcov -o umf_zl_scale umf_scale.c gcov -o umf_zl_scale_column umf_scale_column.c gcov -o umf_zl_set_stats umf_set_stats.c gcov -o umf_zl_solve umf_solve.c gcov -o umf_zl_start_front umf_start_front.c gcov -o umf_zl_symbolic_usage umf_symbolic_usage.c gcov -o umf_zl_transpose umf_transpose.c gcov -o umf_zl_tuple_lengths umf_tuple_lengths.c gcov -o umf_zl_usolve umf_usolve.c gcov -o umf_zl_valid_numeric umf_valid_numeric.c gcov -o umf_zl_valid_symbolic umf_valid_symbolic.c gcov -o umfpack_zl_col_to_triplet umfpack_col_to_triplet.c gcov -o umfpack_zl_defaults umfpack_defaults.c gcov -o umfpack_zl_free_numeric umfpack_free_numeric.c gcov -o umfpack_zl_free_symbolic umfpack_free_symbolic.c gcov -o umfpack_zl_get_lunz umfpack_get_lunz.c gcov -o umfpack_zl_get_numeric umfpack_get_numeric.c gcov -o umfpack_zl_get_determinant umfpack_get_determinant.c gcov -o umfpack_zl_get_symbolic umfpack_get_symbolic.c gcov -o umfpack_zl_load_numeric umfpack_load_numeric.c gcov -o umfpack_zl_load_symbolic umfpack_load_symbolic.c gcov -o umfpack_zl_numeric umfpack_numeric.c gcov -o umfpack_zl_qsymbolic umfpack_qsymbolic.c gcov -o umfpack_zl_report_control umfpack_report_control.c gcov -o umfpack_zl_report_info umfpack_report_info.c gcov -o umfpack_zl_report_matrix umfpack_report_matrix.c gcov -o umfpack_zl_report_numeric umfpack_report_numeric.c gcov -o umfpack_zl_report_perm umfpack_report_perm.c gcov -o umfpack_zl_report_status umfpack_report_status.c gcov -o umfpack_zl_report_symbolic umfpack_report_symbolic.c gcov -o umfpack_zl_report_triplet umfpack_report_triplet.c gcov -o umfpack_zl_report_vector umfpack_report_vector.c gcov -o umfpack_zl_save_numeric umfpack_save_numeric.c gcov -o umfpack_zl_save_symbolic umfpack_save_symbolic.c gcov -o umfpack_zl_scale umfpack_scale.c gcov -o umfpack_zl_symbolic umfpack_symbolic.c gcov -o umfpack_zl_transpose umfpack_transpose.c gcov -o umfpack_zl_triplet_to_col umfpack_triplet_to_col.c gcov -o umfpack_gn_tictoc umfpack_tictoc.c gcov -o umfpack_gn_timer umfpack_timer.c # multiple versions gcov -o umf_zl_uhsolve umf_utsolve.c ; mv -f umf_utsolve.c.gcov umf_uhsolve.c.gcov gcov -o umf_zl_utsolve umf_utsolve.c gcov -o umf_zl_lhsolve umf_ltsolve.c ; mv -f umf_ltsolve.c.gcov umf_lhsolve.c.gcov gcov -o umf_zl_ltsolve umf_ltsolve.c gcov -o umfpack_zl_wsolve umfpack_solve.c ; mv -f umfpack_solve.c.gcov umfpack_wsolve.c.gcov gcov -o umfpack_zl_solve umfpack_solve.c gcov -o umf_zl_store_lu_drop umf_store_lu.c ; mv -f umf_store_lu.c.gcov umf_store_lu_drop.c.gcov gcov -o umf_zl_store_lu umf_store_lu.c gcov -o umf_zl_assemble_fixq umf_assemble.c ; mv -f umf_assemble.c.gcov umf_assemble_fixq.c.gcov gcov -o umf_zl_assemble umf_assemble.c gcov -o umf_zl_triplet_map_x umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_map_x.c.gcov gcov -o umf_zl_triplet_nomap_x umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_nomap_x.c.gcov gcov -o umf_zl_triplet_map_nox umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_map_nox.c.gcov gcov -o umf_zl_triplet_nomap_nox umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_nomap_nox.c.gcov SuiteSparse/UMFPACK/Tcov/DO.solaris0000755001170100242450000000133610322350057015653 0ustar davisfac# # # # ./DOsol s1 di run ./DOsol s1 dl run ./DOsol s1 zi run ./DOsol s1 zl run ./DOsol s2 di run ./DOsol s2 dl run ./DOsol s2 zi run ./DOsol s2 zl run ./DOsol s3 di run ./DOsol s3 dl run ./DOsol s3 zi run ./DOsol s3 zl run ./DOsol s4 di run ./DOsol s4 dl run ./DOsol s4 zi run ./DOsol s4 zl run ./DOsol s5 di run ./DOsol s5 dl run ./DOsol s5 zi run ./DOsol s5 zl run ./DOsol n1 di run ./DOsol n1 dl run ./DOsol n1 zi run ./DOsol n1 zl run ./DOsol n2 di run ./DOsol n2 dl run ./DOsol n2 zi run ./DOsol n2 zl run ./DOsol n3 di run ./DOsol n3 dl run ./DOsol n3 zi run ./DOsol n3 zl run ./DOsol n4 di run ./DOsol n4 dl run ./DOsol n4 zi run ./DOsol n4 zl run SuiteSparse/UMFPACK/Tcov/DO.solaris.out.Jan240000644001170100242450000000000010175217033017320 0ustar davisfacSuiteSparse/UMFPACK/Tcov/GNUmakefile.di0000644001170100242450000000106610425661751016427 0ustar davisfacall: go include UFconfig/UFconfig.mk go: run - ( cd UMFPACK/Source ; ./ucov.di ) - ( cd AMD/Source ; ./acov.di ) run: prog - ./ut > ut.out - tail ut.out #- $(RM) ut.out prog: ( cd UMFPACK ; make library ) ( cd AMD ; make library ) $(CC) -DDINT $(CFLAGS) $(UMFPACK_CONFIG) -IUMFPACK/Source -IUMFPACK/Include -IAMD/Source -IAMD/Include -IUFconfig -o ut ut.c UMFPACK/Lib/libumfpack.a AMD/Lib/libamd.a $(LIB) utcov: - ( cd UMFPACK/Source ; ./ucov.di ) - ( cd AMD/Source ; ./acov.di ) purge: ( cd UMFPACK ; make purge ) ( cd AMD ; make purge ) SuiteSparse/UMFPACK/Tcov/GNUmakefile.dl0000644001170100242450000000106610425661754016435 0ustar davisfacall: go include UFconfig/UFconfig.mk go: run - ( cd UMFPACK/Source ; ./ucov.dl ) - ( cd AMD/Source ; ./acov.dl ) run: prog - ./ut > ut.out - tail ut.out #- $(RM) ut.out prog: ( cd UMFPACK ; make library ) ( cd AMD ; make library ) $(CC) -DDLONG $(CFLAGS) $(UMFPACK_CONFIG) -IUMFPACK/Source -IUMFPACK/Include -IAMD/Source -IAMD/Include -IUFconfig -o ut ut.c UMFPACK/Lib/libumfpack.a AMD/Lib/libamd.a $(LIB) utcov: - ( cd UMFPACK/Source ; ./ucov.dl ) - ( cd AMD/Source ; ./acov.dl ) purge: ( cd UMFPACK ; make purge ) ( cd AMD ; make purge ) SuiteSparse/UMFPACK/Tcov/GNUmakefile.zi0000644001170100242450000000106510425661756016461 0ustar davisfacall: go include UFconfig/UFconfig.mk go: run - ( cd UMFPACK/Source ; ./ucov.zi ) - ( cd AMD/Source ; ./acov.zi ) run: prog - ./ut > ut.out - tail ut.out #- $(RM) ut.out prog: ( cd UMFPACK ; make library ) ( cd AMD ; make library ) $(CC) -DZINT $(CFLAGS) $(UMFPACK_CONFIG) -IUMFPACK/Source -IUMFPACK/Include -IAMD/Source -IAMD/Include -IUFconfig -o ut ut.c UMFPACK/Lib/libumfpack.a AMD/Lib/libamd.a $(LIB) utcov: - ( cd UMFPACK/Source ; ./ucov.zi ) - ( cd AMD/Source ; ./acov.zi ) purge: ( cd UMFPACK ; make purge ) ( cd AMD ; make purge ) SuiteSparse/UMFPACK/Tcov/GNUmakefile.zl0000644001170100242450000000106610425661760016460 0ustar davisfacall: go include UFconfig/UFconfig.mk go: run - ( cd UMFPACK/Source ; ./ucov.zl ) - ( cd AMD/Source ; ./acov.zl ) run: prog - ./ut > ut.out - tail ut.out #- $(RM) ut.out prog: ( cd UMFPACK ; make library ) ( cd AMD ; make library ) $(CC) -DZLONG $(CFLAGS) $(UMFPACK_CONFIG) -IUMFPACK/Source -IUMFPACK/Include -IAMD/Source -IAMD/Include -IUFconfig -o ut ut.c UMFPACK/Lib/libumfpack.a AMD/Lib/libamd.a $(LIB) utcov: - ( cd UMFPACK/Source ; ./ucov.zl ) - ( cd AMD/Source ; ./acov.zl ) purge: ( cd UMFPACK ; make purge ) ( cd AMD ; make purge ) SuiteSparse/UMFPACK/Tcov/badnum.umf0000644001170100242450000000120410006265116015721 0ustar davisfac@?MbP?ffffff??@S@*Y7"??*Y7"?qXt(sHsshssstsr(tF *Y7"???k(?‘L#  ??к??(?#u)?*Y7"?F>S????^?k?SuiteSparse/UMFPACK/Tcov/acov.di0000755001170100242450000000065710167575302015237 0ustar davisfac#!/bin/csh # acov.di: construct gcov files for AMD, di version gcov -o amd_i_1 amd_1.c gcov -o amd_i_2 amd_2.c gcov -o amd_i_aat amd_aat.c gcov -o amd_i_control amd_control.c gcov -o amd_i_defaults amd_defaults.c gcov -o amd_i_info amd_info.c gcov -o amd_i_order amd_order.c gcov -o amd_i_post_tree amd_post_tree.c gcov -o amd_i_postorder amd_postorder.c gcov -o amd_i_preprocess amd_preprocess.c gcov -o amd_i_valid amd_valid.c SuiteSparse/UMFPACK/Tcov/acov.dl0000755001170100242450000000065710167575360015246 0ustar davisfac#!/bin/csh # acov.dl: construct gcov files for AMD, dl version gcov -o amd_l_1 amd_1.c gcov -o amd_l_2 amd_2.c gcov -o amd_l_aat amd_aat.c gcov -o amd_l_control amd_control.c gcov -o amd_l_defaults amd_defaults.c gcov -o amd_l_info amd_info.c gcov -o amd_l_order amd_order.c gcov -o amd_l_post_tree amd_post_tree.c gcov -o amd_l_postorder amd_postorder.c gcov -o amd_l_preprocess amd_preprocess.c gcov -o amd_l_valid amd_valid.c SuiteSparse/UMFPACK/Tcov/acov.zi0000755001170100242450000000065710167575460015272 0ustar davisfac#!/bin/csh # acov.zi: construct gcov files for AMD, zi version gcov -o amd_i_1 amd_1.c gcov -o amd_i_2 amd_2.c gcov -o amd_i_aat amd_aat.c gcov -o amd_i_control amd_control.c gcov -o amd_i_defaults amd_defaults.c gcov -o amd_i_info amd_info.c gcov -o amd_i_order amd_order.c gcov -o amd_i_post_tree amd_post_tree.c gcov -o amd_i_postorder amd_postorder.c gcov -o amd_i_preprocess amd_preprocess.c gcov -o amd_i_valid amd_valid.c SuiteSparse/UMFPACK/Tcov/acov.zl0000755001170100242450000000065710167575474015302 0ustar davisfac#!/bin/csh # acov.zl: construct gcov files for AMD, zl version gcov -o amd_l_1 amd_1.c gcov -o amd_l_2 amd_2.c gcov -o amd_l_aat amd_aat.c gcov -o amd_l_control amd_control.c gcov -o amd_l_defaults amd_defaults.c gcov -o amd_l_info amd_info.c gcov -o amd_l_order amd_order.c gcov -o amd_l_post_tree amd_post_tree.c gcov -o amd_l_postorder amd_postorder.c gcov -o amd_l_preprocess amd_preprocess.c gcov -o amd_l_valid amd_valid.c SuiteSparse/UMFPACK/Tcov/README.txt0000644001170100242450000000515210711722365015455 0ustar davisfacThis is the UMFPACK Tcov directory. It runs a large number of tests on UMFPACK and checks the statement coverage (using gcc and gcov on Linux, or tcov on Solaris). You must first do "make purge" in AMD and UMFPACK. You must also make sure the "Out" symbolic link is a valid link. It should point to a large scratch space, for temporary files. Finally, type DO.linux or DO.solaris. Alternatively, just type "make" in this directory, for Linux, or "make sol" for Solaris. The last line of each */ut.out file should read ALL TESTS PASSED largest maxrnorm 1e-07 These lines are summarized at the end of the "DO.linux" test. If you see "TEST FAILURE" then something went wrong. "ERROR" messages in the output files tmp/*.out are OK. Those are supposed to be there; the test exercises the error-reporting features of UMFPACK. DO.all does all tests DO 1 di runs one test (Make.1 and GNUmakefile.di, in this case) Out/* subdirectories for each test, contents can be destroyed when done. Make.1 gcc, no optimize Linux no BLAS, test int overflow Make.2 gcc, no optimize Linux BLAS Make.3 gcc, no optimize Linux ATLAS C-Blas Make.4 gcc, no optimize Linux ATLAS Fortran BLAS Make.5 gcc, no optimize Linux no BLAS, test int overflow no reciprocal Make.1i icc, optimize, Linux no BLAS, test int overflow Make.2i icc, optimize, Linux BLAS Make.3i icc, optimize, Linux ATLAS C-Blas Make.4i icc, optimize, Linux ATLAS Fortran BLAS Make.1n icc, no optimize, Linux no BLAS, test int overflow Make.2n icc, no optimize, Linux BLAS Make.3n icc, no optimize, Linux ATLAS C-Blas Make.4n icc, no optimize, Linux ATLAS Fortran BLAS Make.1g gcc, optimize, Linux no BLAS, test int overflow Make.2g gcc, optimize, Linux BLAS Make.3g gcc, optimize, Linux ATLAS C-Blas Make.4g gcc, optimize, Linux ATLAS Fortran BLAS Make.s1 tcov, Solaris 32 bit, no BLAS Make.s2 tcov, Solaris 32 bit, Sunperf BLAS Make.s3 tcov, Solaris 64 bit, no BLAS Make.s4 tcov, Solaris 64 bit, Sunperf BLAS Make.s5 tcov, Solaris 32 bit, no BLAS, test int overflow, no recip. Make.n1 optimize, Solaris 32 bit, no BLAS Make.n2 optimize, Solaris 32 bit, Sunperf BLAS Make.n3 optimize, Solaris 64 bit, no BLAS Make.n4 optimize, Solaris 64 bit, Sunperf BLAS Makefile.di Makefile for *di (double, int) Makefile.dl Makefile for *dl (double, UF_long) Makefile.zi Makefile for *zi (complex, int) Makefile.zl Makefile for *zl (complex, UF_long) TestMat test matrices for ut.c ../../UMFPACK UMFPACK original distribution ../../AMD AMD original distribution ../../UFconfig configuration directory for all of UFsparse covall for summarizing tcov output ut.c the test program SuiteSparse/UMFPACK/Tcov/Make.1g0000644001170100242450000000102610425373574015067 0ustar davisfac#=============================================================================== # ILP32 mode, no BLAS, test for integer overflow. #=============================================================================== CC = gcc CFLAGS = -O3 -fPIC UMFPACK_CONFIG = -DNBLAS -DTEST_FOR_INTEGER_OVERFLOW -DTESTING LIB = -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.1i0000644001170100242450000000115510425373577015077 0ustar davisfac#=============================================================================== # ILP32 mode, no BLAS, test for integer overflow. #=============================================================================== # Using Intel's icc compiler: CC = icc CFLAGS = -ansi -O3 -ip -tpp7 -xW -vec_report0 UMFPACK_CONFIG = -DNBLAS -DTEST_FOR_INTEGER_OVERFLOW -DTESTING # LIB = -lm -lunwind -lcprts LIB = -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.1n0000644001170100242450000000111610425373603015067 0ustar davisfac#=============================================================================== # ILP32 mode, no BLAS, test for integer overflow. #=============================================================================== # Using Intel's icc compiler: CC = icc CFLAGS = -ansi UMFPACK_CONFIG = -DNBLAS -DTEST_FOR_INTEGER_OVERFLOW -DTESTING # LIB = -lm -lunwind -lcprts LIB = -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.2g0000644001170100242450000000103010711722250015046 0ustar davisfac#=============================================================================== # ILP32 mode, BLAS, do not test for integer overflow. #=============================================================================== CC = gcc CFLAGS = -O3 -fPIC UMFPACK_CONFIG = -DTESTING LIB = -lblas -lgfortran -lgfortranbegin -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.2i0000644001170100242450000000112210711722323015053 0ustar davisfac#=============================================================================== # ILP32 mode, BLAS, do not test for integer overflow. #=============================================================================== # Using Intel's icc compiler: CC = icc CFLAGS = -ansi -O3 -ip -tpp7 -xW -vec_report0 UMFPACK_CONFIG = -DTESTING LIB = -lblas -lgfortran -lgfortranbegin -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.2n0000644001170100242450000000106310711722274015071 0ustar davisfac#=============================================================================== # ILP32 mode, BLAS, do not test for integer overflow. #=============================================================================== # Using Intel's icc compiler: CC = icc CFLAGS = -ansi UMFPACK_CONFIG = -DTESTING LIB = -lblas -lgfortran -lgfortranbegin -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.3g0000644001170100242450000000113410425373634015066 0ustar davisfac#=============================================================================== # ILP32 mode, C interface /ATLAS BLAS, do not test for integer overflow. #=============================================================================== CC = gcc CFLAGS = -O3 -fPIC UMFPACK_CONFIG = -DCBLAS -DTESTING -I/cise/research/sparse/Install/ATLAS/Linux_P4SSE2/include LIB = -lcblas -latlas -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.3i0000644001170100242450000000122710425373642015072 0ustar davisfac#=============================================================================== # ILP32 mode, C interface /ATLAS BLAS, do not test for integer overflow. #=============================================================================== # Using Intel's icc compiler: CC = icc CFLAGS = -ansi -O3 -ip -tpp7 -xW -vec_report0 UMFPACK_CONFIG = -DCBLAS -DTESTING -I/cise/research/sparse/Install/ATLAS/Linux_P4SSE2/include LIB = -lcblas -latlas -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.3n0000644001170100242450000000116710425373646015106 0ustar davisfac#=============================================================================== # ILP32 mode, C interface /ATLAS BLAS, do not test for integer overflow. #=============================================================================== # Using Intel's icc compiler: CC = icc CFLAGS = -ansi UMFPACK_CONFIG = -DCBLAS -DTESTING -I/cise/research/sparse/Install/ATLAS/Linux_P4SSE2/include LIB = -lcblas -latlas -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.4g0000644001170100242450000000116010425373656015072 0ustar davisfac#=============================================================================== # ILP32 mode, Fortran interface to ATLAS BLAS, do not test for integer overflow. #=============================================================================== CC = gcc CFLAGS = -O3 -fPIC UMFPACK_CONFIG = -DTESTING -I/cise/research/sparse/Install/ATLAS/Linux_P4SSE2/include LIB = -lf77blas -latlas -lfrtbegin -lg2c -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.4i0000644001170100242450000000115610425373661015075 0ustar davisfac#=============================================================================== # ILP32 mode, Fortran interface to ATLAS BLAS, do not test for integer overflow. #=============================================================================== # Using Intel's icc compiler: CC = icc CFLAGS = -ansi -O3 -ip -tpp7 -xW -vec_report0 UMFPACK_CONFIG = -DTESTING LIB = -lf77blas -latlas -lfrtbegin -lg2c -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.4n0000644001170100242450000000111710425373665015103 0ustar davisfac#=============================================================================== # ILP32 mode, Fortran interface to ATLAS BLAS, do not test for integer overflow. #=============================================================================== # Using Intel's icc compiler: CC = icc CFLAGS = -ansi UMFPACK_CONFIG = -DTESTING LIB = -lf77blas -latlas -lfrtbegin -lg2c -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.n10000644001170100242450000000106610425373711015073 0ustar davisfac#=============================================================================== # Solaris ILP32 mode, no BLAS, test for integer overflow. #=============================================================================== CC = cc CFLAGS = -xO5 -xlibmil -Xc -xdepend -dalign UMFPACK_CONFIG = -DNBLAS -DTEST_FOR_INTEGER_OVERFLOW -DTESTING LIB = -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.n20000644001170100242450000000105410425373715015075 0ustar davisfac#=============================================================================== # Solaris ILP32 mode, Sunperf BLAS, no test for integer overflow. #=============================================================================== CC = cc CFLAGS = -xO5 -xlibmil -Xc -xdepend -dalign UMFPACK_CONFIG = -DTESTING LIB = -xlic_lib=sunperf -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.n30000644001170100242450000000106110425373721015071 0ustar davisfac#=============================================================================== # Solaris LP64 mode, no BLAS, do not test for integer overflow. #=============================================================================== CC = cc CFLAGS = -xO5 -xlibmil -Xc -xdepend -dalign UMFPACK_CONFIG = -DNBLAS -DLP64 -xarch=v9 -DTESTING LIB = -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.n40000644001170100242450000000111010425373726015072 0ustar davisfac#=============================================================================== # Solaris LP64 mode, Sun Performance BLAS, do not test for integer overflow. #=============================================================================== CC = cc CFLAGS = -xO5 -xlibmil -Xc -xdepend -dalign UMFPACK_CONFIG = -DLP64 -xarch=v9 -DTESTING LIB = -xlic_lib=sunperf -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.s10000644001170100242450000000106110425373731015075 0ustar davisfac#=============================================================================== # Solaris ILP32 mode, no BLAS, test for integer overflow. #=============================================================================== CC = cc CFLAGS = -Xc -g -xprofile=tcov -dalign UMFPACK_CONFIG = -DNBLAS -DTEST_FOR_INTEGER_OVERFLOW -DTESTING LIB = -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.s20000644001170100242450000000104710425373736015107 0ustar davisfac#=============================================================================== # Solaris ILP32 mode, Sunperf BLAS, no test for integer overflow. #=============================================================================== CC = cc CFLAGS = -Xc -g -xprofile=tcov -dalign UMFPACK_CONFIG = -DTESTING LIB = -xlic_lib=sunperf -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.s30000644001170100242450000000105410425373742015103 0ustar davisfac#=============================================================================== # Solaris LP64 mode, no BLAS, do not test for integer overflow. #=============================================================================== CC = cc CFLAGS = -Xc -g -xprofile=tcov -dalign UMFPACK_CONFIG = -DNBLAS -DLP64 -xarch=v9 -DTESTING LIB = -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.s40000644001170100242450000000110310425373747015104 0ustar davisfac#=============================================================================== # Solaris LP64 mode, Sun Performance BLAS, do not test for integer overflow. #=============================================================================== CC = cc CFLAGS = -Xc -g -xprofile=tcov -dalign UMFPACK_CONFIG = -DLP64 -xarch=v9 -DTESTING LIB = -xlic_lib=sunperf -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/Make.s50000644001170100242450000000107710425373753015114 0ustar davisfac#=============================================================================== # Solaris ILP32 mode, no BLAS, test for integer overflow. #=============================================================================== CC = cc CFLAGS = -Xc -g -xprofile=tcov -dalign UMFPACK_CONFIG = -DNBLAS -DTEST_FOR_INTEGER_OVERFLOW -DTESTING -DNRECIPROCAL LIB = -lm RANLIB = ranlib MV = mv -f RM = rm -f MEX = mex -inline -g AR = ar cr #=============================================================================== CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out SuiteSparse/UMFPACK/Tcov/ss.awk0000644001170100242450000000002710171304315015073 0ustar davisfac/TestMat/ /final det/ SuiteSparse/UMFPACK/Tcov/Make_file0000644001170100242450000000105310534021373015544 0ustar davisfacall: go include UFconfig/UFconfig.mk go: prog - ut > ut.out - tail ut.out #- $(RM) ut.out - ( cd UMFPACK/Source ; gcovs umf*.c ) - ( cd AMD/Source ; gcovs amd*.c ) prog: ( cd UMFPACK ; make library ) ( cd AMD ; make library ) $(CC) -DDINT $(CFLAGS) $(UMFPACK_CONFIG) -IUMFPACK/Source -IUMFPACK/Include -IAMD/Source -IAMD/Include -o ut ut.c UMFPACK/Lib/libumfpack.a AMD/Lib/libamd.a $(LIB) utcov: - ( cd UMFPACK/Source ; gcovs umf*.c ) - ( cd AMD/Source ; gcovs amd*.c ) purge: ( cd UMFPACK ; make purge ) ( cd AMD ; make purge ) SuiteSparse/UMFPACK/Tcov/AMD_Demo_Makefile0000644001170100242450000000552710617407331017050 0ustar davisfac#----------------------------------------------------------------------------- # compile the AMD demo (for both GNU make or original make) #----------------------------------------------------------------------------- default: amd_simple amd_demo amd_demo2 amd_l_demo include ../../UFconfig/UFconfig.mk C = $(CC) $(CFLAGS) -I../Include -I../../UFconfig INC = ../Include/amd.h ../../UFconfig/UFconfig.h library: ( cd ../Source ; $(MAKE) ) f77lib: ( cd ../Lib ; $(MAKE) fortran ) #------------------------------------------------------------------------------ # Create the demo program, run it, and compare the output #------------------------------------------------------------------------------ dist: amd_demo: amd_demo.c library $(INC) $(C) -o amd_demo amd_demo.c ../Lib/libamd.a $(LIB) ./amd_demo > my_amd_demo.out - diff amd_demo.out my_amd_demo.out amd_l_demo: amd_l_demo.c library $(INC) $(C) -o amd_l_demo amd_l_demo.c ../Lib/libamd.a $(LIB) ./amd_l_demo > my_amd_l_demo.out - diff amd_l_demo.out my_amd_l_demo.out amd_demo2: amd_demo2.c library $(INC) $(C) -o amd_demo2 amd_demo2.c ../Lib/libamd.a $(LIB) ./amd_demo2 > my_amd_demo2.out - diff amd_demo2.out my_amd_demo2.out amd_simple: amd_simple.c library $(INC) $(C) -o amd_simple amd_simple.c ../Lib/libamd.a $(LIB) ./amd_simple > my_amd_simple.out - diff amd_simple.out my_amd_simple.out #------------------------------------------------------------------------------ # compile the Fortran demo #------------------------------------------------------------------------------ fortran: amd_f77demo amd_f77simple cross: amd_f77cross amd_f77demo: amd_f77demo.f f77lib $(F77) $(F77FLAGS) -o amd_f77demo amd_f77demo.f ../Lib/libamdf77.a \ $(F77LIB) ./amd_f77demo > my_amd_f77demo.out - diff amd_f77demo.out my_amd_f77demo.out amd_f77simple: amd_f77simple.f f77lib $(F77) $(F77FLAGS) -o amd_f77simple amd_f77simple.f \ ../Lib/libamdf77.a $(F77LIB) ./amd_f77simple > my_amd_f77simple.out - diff amd_f77simple.out my_amd_f77simple.out amd_f77wrapper.o: amd_f77wrapper.c $(C) -DDINT -c amd_f77wrapper.c amd_f77cross: amd_f77cross.f amd_f77wrapper.o ../Lib/libamd.a $(F77) $(F77FLAGS) -o amd_f77cross amd_f77cross.f amd_f77wrapper.o \ ../Lib/libamd.a $(F77LIB) ./amd_f77cross > my_amd_f77cross.out - diff amd_f77cross.out my_amd_f77cross.out #------------------------------------------------------------------------------ # Remove all but the files in the original distribution #------------------------------------------------------------------------------ clean: - $(RM) $(CLEAN) purge: distclean distclean: clean - $(RM) amd_demo my_amd_demo.out - $(RM) amd_l_demo my_amd_l_demo.out - $(RM) amd_demo2 my_amd_demo2.out - $(RM) amd_simple my_amd_simple.out - $(RM) amd_f77demo my_amd_f77demo.out - $(RM) amd_f77simple my_amd_f77simple.out - $(RM) amd_f77cross my_amd_f77cross.out SuiteSparse/UMFPACK/Tcov/Top_Makefile0000644001170100242450000000050710617345143016240 0ustar davisfac#------------------------------------------------------------------------------- # UMFPACK and AMD top-level makefile (for Tcov tests) #------------------------------------------------------------------------------- default: library include ../UFconfig/UFconfig.mk library: ( cd Source ; $(MAKE) ) ( cd Demo ; $(MAKE) ) SuiteSparse/UMFPACK/Tcov/TestMat/0000755001170100242450000000000010617501241015326 5ustar davisfacSuiteSparse/UMFPACK/Tcov/TestMat/shl00000644001170100242450000020301310171311674016122 0ustar davisfac663 663 1687 1 1 1 1 2 2 1 3 3 1 538 4 1 539 5 1 540 6 1 541 7 1 542 8 1 543 9 1 544 10 1 545 11 1 546 12 1 547 13 1 548 14 1 549 15 1 550 16 1 551 17 1 552 18 1 553 19 1 554 20 1 555 21 1 556 22 1 557 23 1 558 24 1 559 25 1 560 26 1 561 27 1 562 28 1 563 29 1 564 30 1 565 31 1 566 32 1 567 33 1 568 34 1 569 35 1 570 36 1 571 37 1 572 38 1 573 39 1 574 40 1 575 41 1 576 42 1 577 43 1 578 44 1 579 45 1 580 46 1 581 47 1 582 48 1 583 49 1 584 50 -1 585 51 -1 586 52 1 587 53 -1 588 54 1 589 55 1 590 56 1 591 57 1 592 58 1 593 59 1 594 60 1 595 61 1 596 62 1 597 63 1 598 64 1 599 65 1 600 66 1 601 67 1 602 68 1 603 69 1 604 70 1 605 71 1 606 72 1 607 73 1 608 74 1 609 75 1 610 76 1 611 77 -1 612 78 -1 613 79 1 614 80 -1 615 81 1 616 82 1 617 83 1 618 84 1 619 85 1 620 86 1 621 87 1 622 88 1 623 89 1 624 90 1 625 91 1 626 92 1 627 93 1 628 94 1 629 95 1 630 96 1 631 97 1 632 98 1 633 99 1 634 100 1 635 101 1 636 102 1 637 103 -1 638 104 -1 639 105 1 640 106 -1 641 107 1 642 108 1 643 109 1 644 110 1 645 111 1 646 112 1 647 113 1 648 114 1 649 115 1 650 116 1 651 117 1 652 118 1 653 119 1 654 120 1 655 121 1 656 122 1 657 123 1 658 124 1 659 125 1 660 126 1 661 127 1 662 128 1 663 129 1 4 130 -1 9 130 1 538 130 1 9 131 1 1 132 3966 9 132 -1 15 132 1 539 132 1 1 133 3914 9 133 -1 12 133 1 1 134 4055 9 134 -1 11 134 1 540 134 1 1 135 3818 9 135 -1 13 135 1 541 135 1 1 136 3619 9 136 -1 26 136 1 1 137 31 10 137 -1 22 137 1 22 138 1 10 139 -1 71 139 1 1 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SuiteSparse/UMFPACK/Tcov/TestMat/cage30000644001170100242450000000135210171264274016243 0ustar davisfac5 5 19 1 1 1 6.66666666666666962726e-01 2 1 1.00036889486115998515e-01 3 1 1.22185332736106003204e-01 4 1 5.00184447430579992577e-02 5 1 6.10926663680530987466e-02 1 2 3.66555998208319022691e-01 2 2 5.33407112305565034305e-01 4 2 1.00036889486115998515e-01 1 3 3.00110668458347995546e-01 3 3 5.77703998805546015127e-01 5 3 1.22185332736106003204e-01 1 4 3.66555998208319022691e-01 2 4 2.00073778972231997031e-01 4 4 2.83314888590274982505e-01 5 4 1.50055334229173997773e-01 1 5 3.00110668458347995546e-01 3 5 2.44370665472212006408e-01 4 5 1.83277999104159011745e-01 5 5 2.72240666965279987100e-01 1 2 3 4 5 4.15610579898172301239e-03 4.15610579898172301239e-03 SuiteSparse/UMFPACK/Tcov/TestMat/d_dyn0000644001170100242450000002111610171264274016356 0ustar davisfac87 87 230 1 2 1 -1.00000000000000000000e+00 3 1 6.32455500000000036750e-04 6 2 -1.00009299999999989872e+00 9 2 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SuiteSparse/UMFPACK/Tcov/DO.linux.out0000644001170100242450000006414210173742511016151 0ustar davisfac################################################################################ Tcov test: 1 di ################################################################################ make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 53.07 63.358u 18.812s 2:43.04 50.3% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 1 dl ################################################################################ /bin/mv: cannot stat `Out/1_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.34 54.784u 17.836s 2:23.80 50.4% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 1 zi ################################################################################ /bin/mv: cannot stat `Out/1_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.4 95.249u 20.442s 3:50.15 50.2% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 1 zl ################################################################################ /bin/mv: cannot stat `Out/1_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.94 94.957u 21.488s 3:50.65 50.4% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 2 di ################################################################################ /bin/mv: cannot stat `Out/2_di': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 2.67e-08 omega2) cputime 44.55 54.828u 19.260s 2:24.94 51.1% 0+0k 0+0io 2pf+0w ################################################################################ Tcov test: 2 dl ################################################################################ /bin/mv: cannot stat `Out/2_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.36 54.572u 18.252s 2:25.22 50.1% 0+0k 0+0io 2pf+0w ################################################################################ Tcov test: 2 zi ################################################################################ /bin/mv: cannot stat `Out/2_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.81e-09 omega2) cputime 67.31 75.985u 20.963s 3:11.22 50.6% 0+0k 0+0io 1pf+0w ################################################################################ Tcov test: 2 zl ################################################################################ /bin/mv: cannot stat `Out/2_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.25 94.456u 21.096s 3:49.94 50.2% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 3 di ################################################################################ /bin/mv: cannot stat `Out/3_di': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 6.76e-05 arc130 1.70e-08 omega2) cputime 50.18 62.426u 21.521s 2:42.80 51.5% 0+0k 0+0io 1pf+0w ################################################################################ Tcov test: 3 dl ################################################################################ /bin/mv: cannot stat `Out/3_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.28 56.212u 20.576s 2:29.84 51.2% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 3 zi ################################################################################ /bin/mv: cannot stat `Out/3_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.97e-09 omega2) cputime 85.12 95.214u 23.764s 3:53.59 50.9% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 3 zl ################################################################################ /bin/mv: cannot stat `Out/3_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.2 96.296u 23.560s 3:59.43 50.0% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 4 di ################################################################################ /bin/mv: cannot stat `Out/4_di': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 6.76e-05 arc130 1.70e-08 omega2) cputime 49.83 61.486u 21.044s 2:42.11 50.9% 0+0k 0+0io 1pf+0w ################################################################################ Tcov test: 4 dl ################################################################################ /bin/mv: cannot stat `Out/4_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.4 55.564u 20.220s 2:29.76 50.6% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 4 zi ################################################################################ /bin/mv: cannot stat `Out/4_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.97e-09 omega2) cputime 84.96 94.538u 23.473s 3:53.76 50.4% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 4 zl ################################################################################ /bin/mv: cannot stat `Out/4_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.08 95.423u 23.338s 3:57.96 49.9% 0+0k 0+0io 2pf+0w ################################################################################ Tcov test: 5 di ################################################################################ /bin/mv: cannot stat `Out/5_di': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 8.09e-05 arc130 1.44e-08 omega2) cputime 53 63.501u 17.943s 2:41.69 50.3% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 5 dl ################################################################################ /bin/mv: cannot stat `Out/5_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 8.09e-05 arc130 1.44e-08 omega2) cputime 43.84 55.084u 17.315s 2:30.54 48.0% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 5 zi ################################################################################ /bin/mv: cannot stat `Out/5_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 8.10e-05 arc130 1.13e-09 omega2) cputime 86.48 94.907u 21.155s 3:49.30 50.6% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 5 zl ################################################################################ /bin/mv: cannot stat `Out/5_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 8.10e-05 arc130 1.13e-09 omega2) cputime 86.93 94.868u 21.236s 3:52.25 49.9% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 6 di ################################################################################ /bin/mv: cannot stat `Out/6_di': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 2.67e-08 omega2) cputime 0 54.642u 17.587s 2:27.30 49.0% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 6 dl ################################################################################ /bin/mv: cannot stat `Out/6_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 0 54.264u 17.736s 2:20.31 51.3% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 6 zi ################################################################################ /bin/mv: cannot stat `Out/6_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.81e-09 omega2) cputime 0 75.619u 21.189s 3:13.07 50.1% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 6 zl ################################################################################ /bin/mv: cannot stat `Out/6_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 0 94.182u 21.320s 3:49.63 50.2% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 7 di ################################################################################ /bin/mv: cannot stat `Out/7_di': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 52.86 63.384u 19.469s 2:43.77 50.5% 0+0k 0+0io 55pf+0w ################################################################################ Tcov test: 7 dl ################################################################################ /bin/mv: cannot stat `Out/7_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.86 54.944u 19.117s 2:26.11 50.6% 0+0k 0+0io 58pf+0w ################################################################################ Tcov test: 7 zi ################################################################################ /bin/mv: cannot stat `Out/7_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.22 94.791u 21.833s 3:52.75 50.1% 0+0k 0+0io 60pf+0w ################################################################################ Tcov test: 7 zl ################################################################################ /bin/mv: cannot stat `Out/7_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.55 94.694u 22.253s 3:53.30 50.1% 0+0k 0+0io 60pf+0w ################################################################################ Tcov test: 8 di ################################################################################ /bin/mv: cannot stat `Out/8_di': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 2.67e-08 omega2) cputime 44.71 54.990u 20.140s 2:29.47 50.2% 0+0k 0+0io 60pf+0w ################################################################################ Tcov test: 8 dl ################################################################################ /bin/mv: cannot stat `Out/8_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.58 54.709u 19.432s 2:26.94 50.4% 0+0k 0+0io 60pf+0w ################################################################################ Tcov test: 8 zi ################################################################################ /bin/mv: cannot stat `Out/8_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.81e-09 omega2) cputime 67.5 75.658u 21.959s 3:14.44 50.1% 0+0k 0+0io 60pf+0w ################################################################################ Tcov test: 8 zl ################################################################################ /bin/mv: cannot stat `Out/8_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.02 94.103u 22.569s 3:53.56 49.9% 0+0k 0+0io 57pf+0w ################################################################################ Tcov test: 1g di ################################################################################ /bin/mv: cannot stat `Out/1g_di': No such file or directory make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 36.56 74.372u 19.090s 2:57.83 52.5% 0+0k 0+0io 61pf+0w ################################################################################ Tcov test: 1g dl ################################################################################ /bin/mv: cannot stat `Out/1g_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 31.58 70.071u 18.354s 2:48.39 52.5% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 1g zi ################################################################################ /bin/mv: cannot stat `Out/1g_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.92 104.920u 21.081s 4:06.48 51.1% 0+0k 0+0io 41pf+0w ################################################################################ Tcov test: 1g zl ################################################################################ /bin/mv: cannot stat `Out/1g_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.64 104.824u 21.455s 4:06.01 51.3% 0+0k 0+0io 63pf+0w ################################################################################ Tcov test: 2g di ################################################################################ /bin/mv: cannot stat `Out/2g_di': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.06e-10 (1.37e-07 shl0, 5.65e-05 arc130 1.98e-08 omega2) cputime 30.1 68.093u 19.363s 2:46.78 52.4% 0+0k 0+0io 56pf+0w ################################################################################ Tcov test: 2g dl ################################################################################ /bin/mv: cannot stat `Out/2g_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 31.43 70.067u 18.610s 2:47.30 53.0% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 2g zi ################################################################################ /bin/mv: cannot stat `Out/2g_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 7.77e-05 arc130 2.29e-09 omega2) cputime 50.74 86.726u 20.994s 3:28.71 51.6% 0+0k 0+0io 51pf+0w ################################################################################ Tcov test: 2g zl ################################################################################ /bin/mv: cannot stat `Out/2g_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.44 104.450u 21.097s 4:04.16 51.4% 0+0k 0+0io 37pf+0w ################################################################################ Tcov test: 3g di ################################################################################ /bin/mv: cannot stat `Out/3g_di': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 8.27e-09 omega2) cputime 35.71 75.583u 21.676s 3:00.23 53.9% 0+0k 0+0io 56pf+0w ################################################################################ Tcov test: 3g dl ################################################################################ /bin/mv: cannot stat `Out/3g_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 31.56 72.222u 21.825s 2:53.57 54.1% 0+0k 0+0io 47pf+0w ################################################################################ Tcov test: 3g zi ################################################################################ /bin/mv: cannot stat `Out/3g_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 7.77e-05 arc130 2.57e-09 omega2) cputime 68.43 106.248u 24.758s 4:07.88 52.8% 0+0k 0+0io 37pf+0w ################################################################################ Tcov test: 3g zl ################################################################################ /bin/mv: cannot stat `Out/3g_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.55 106.854u 24.459s 4:10.50 52.4% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 4g di ################################################################################ /bin/mv: cannot stat `Out/4g_di': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 8.27e-09 omega2) cputime 36.01 74.958u 21.536s 3:02.32 52.9% 0+0k 0+0io 32pf+0w ################################################################################ Tcov test: 4g dl ################################################################################ /bin/mv: cannot stat `Out/4g_dl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 31.32 70.889u 21.137s 2:49.23 54.3% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 4g zi ################################################################################ /bin/mv: cannot stat `Out/4g_zi': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 7.77e-05 arc130 2.57e-09 omega2) cputime 68.48 105.539u 24.499s 4:08.27 52.3% 0+0k 0+0io 0pf+0w ################################################################################ Tcov test: 4g zl ################################################################################ /bin/mv: cannot stat `Out/4g_zl': No such file or directory make[2]: [umfpack_di_demo] Error 1 (ignored) make[2]: [umfpack_zi_demo] Error 1 (ignored) make[2]: [umfpack_dl_demo] Error 1 (ignored) make[2]: [umfpack_zl_demo] Error 1 (ignored) ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.66 106.270u 23.930s 4:06.74 52.7% 0+0k 0+0io 0pf+0w SuiteSparse/UMFPACK/Tcov/Demo_Makefile0000644001170100242450000001461110617340124016355 0ustar davisfac#------------------------------------------------------------------------------- # compile the UMFPACK demos (for GNU make and original make) #------------------------------------------------------------------------------- # UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis. # All Rights Reserved. See ../Doc/License for License. default: libs run include ../../UFconfig/UFconfig.mk C = $(CC) $(CFLAGS) $(UMFPACK_CONFIG) -I../Include -I../../AMD/Include \ -I../../UFconfig INC = ../Include/umfpack.h ../../AMD/Include/amd.h ../../UFconfig/UFconfig.h LIBS = $(BLAS) $(XERBLA) $(LIB) ../Lib/libumfpack.a: ( cd ../Source ; $(MAKE) ) ../../AMD/Lib/libamd.a: ( cd ../../AMD ; $(MAKE) library ) UMFPACK = ../Lib/libumfpack.a ../../AMD/Lib/libamd.a libs: ( cd ../Source ; $(MAKE) ) ( cd ../../AMD ; $(MAKE) library ) #------------------------------------------------------------------------------- # Create the demo programs, run them, and compare the output #------------------------------------------------------------------------------- dist: umfpack_di_demo.c umfpack_dl_demo.c umfpack_zi_demo.c umfpack_zl_demo.c umfpack_simple: umfpack_simple.c $(INC) $(UMFPACK) $(C) -o umfpack_simple umfpack_simple.c $(UMFPACK) $(LIBS) # the GNU rules are simpler: # umfpack_%_demo.c: umfpack_xx_demo.c umfpack_%_demo.sed # - sed -f umfpack_$*_demo.sed < umfpack_xx_demo.c > umfpack_$*_demo.c # # umfpack_%_demo: umfpack_%_demo.c $(INC) $(UMFPACK) # $(C) -o umfpack_$*_demo umfpack_$*_demo.c $(UMFPACK) $(LIBS) # ./umfpack_$*_demo > my_umfpack_$*_demo.out # but do this via brute-force, so we can use just a single Makefile: # double-precision, int verion: umfpack_di_demo.c: umfpack_xx_demo.c umfpack_di_demo.sed - sed -f umfpack_di_demo.sed < umfpack_xx_demo.c > umfpack_di_demo.c umfpack_di_demo: umfpack_di_demo.c $(INC) $(UMFPACK) $(C) -o umfpack_di_demo umfpack_di_demo.c $(UMFPACK) $(LIBS) # double-precision, UF_long verion: umfpack_dl_demo.c: umfpack_xx_demo.c umfpack_dl_demo.sed - sed -f umfpack_dl_demo.sed < umfpack_xx_demo.c > umfpack_dl_demo.c umfpack_dl_demo: umfpack_dl_demo.c $(INC) $(UMFPACK) $(C) -o umfpack_dl_demo umfpack_dl_demo.c $(UMFPACK) $(LIBS) # complex, int verion: umfpack_zi_demo.c: umfpack_xx_demo.c umfpack_zi_demo.sed - sed -f umfpack_zi_demo.sed < umfpack_xx_demo.c > umfpack_zi_demo.c umfpack_zi_demo: umfpack_zi_demo.c $(INC) $(UMFPACK) $(C) -o umfpack_zi_demo umfpack_zi_demo.c $(UMFPACK) $(LIBS) # complex, UF_long verion: umfpack_zl_demo.c: umfpack_xx_demo.c umfpack_zl_demo.sed - sed -f umfpack_zl_demo.sed < umfpack_xx_demo.c > umfpack_zl_demo.c umfpack_zl_demo: umfpack_zl_demo.c $(INC) $(UMFPACK) $(C) -o umfpack_zl_demo umfpack_zl_demo.c $(UMFPACK) $(LIBS) run: umfpack_di_demo umfpack_zi_demo umfpack_dl_demo umfpack_zl_demo umfpack_simple ./umfpack_simple ./umfpack_di_demo > my_umfpack_di_demo.out - diff umfpack_di_demo.out my_umfpack_di_demo.out ./umfpack_dl_demo > my_umfpack_dl_demo.out - diff umfpack_dl_demo.out my_umfpack_dl_demo.out ./umfpack_zi_demo > my_umfpack_zi_demo.out - diff umfpack_zi_demo.out my_umfpack_zi_demo.out ./umfpack_zl_demo > my_umfpack_zl_demo.out - diff umfpack_zl_demo.out my_umfpack_zl_demo.out #------------------------------------------------------------------------------- # create a demo program that reads in Harwell/Boeing matrices, and run it #------------------------------------------------------------------------------- # the output of "make hb" is in the file umf4.out hb: $(UMFPACK) umf4 readhb readhb_nozeros readhb_size - ./readhb_nozeros < HB/can_24.psa > tmp/A - ./readhb_size < HB/can_24.psa > tmp/Asize - ./umf4 - ./readhb_nozeros < HB/west0067.rua > tmp/A - ./readhb_size < HB/west0067.rua > tmp/Asize - ./umf4 - ./readhb_nozeros < HB/fs_183_6.rua > tmp/A - ./readhb_size < HB/fs_183_6.rua > tmp/Asize - ./umf4 - ./readhb < HB/fs_183_6.rua > tmp/A - ./readhb_size < HB/fs_183_6.rua > tmp/Asize - ./umf4 - ./readhb < HB/arc130.rua > tmp/A - ./readhb_size < HB/arc130.rua > tmp/Asize - ./umf4 - ./readhb_nozeros < HB/arc130.rua > tmp/A - ./readhb_size < HB/arc130.rua > tmp/Asize - ./umf4 - ./readhb_nozeros < HB/arc130.rua > tmp/A - ./readhb_size < HB/arc130.rua > tmp/Asize - ./umf4 a 1e-6 umf4: umf4.c $(UMFPACK) $(C) -o umf4 umf4.c $(UMFPACK) $(LIBS) readhb: readhb.f $(F77) $(F77FLAGS) -o readhb readhb.f $(F77LIB) readhb_size: readhb_size.f $(F77) $(F77FLAGS) -o readhb_size readhb_size.f $(F77LIB) readhb_nozeros: readhb_nozeros.f $(F77) $(F77FLAGS) -o readhb_nozeros readhb_nozeros.f $(F77LIB) #------------------------------------------------------------------------------- # compile the FORTRAN interface and demo #------------------------------------------------------------------------------- fortran: $(UMFPACK) umf4hb.f umf4_f77wrapper.o umf4zhb.f umf4_f77zwrapper.o $(UMFPACK) $(F77) $(F77FLAGS) -o umf4hb umf4hb.f umf4_f77wrapper.o \ $(UMFPACK) $(LIBS) - ./umf4hb < HB/west0067.rua > my_umf4hb.out - diff my_umf4hb.out umf4hb.out $(F77) $(F77FLAGS) -o umf4zhb umf4zhb.f umf4_f77zwrapper.o \ $(UMFPACK) $(LIBS) - ./umf4zhb < HB/qc324.cua > my_umf4zhb.out - diff my_umf4zhb.out umf4zhb.out fortran64: $(UMFPACK) umf4hb64.f umf4_f77wrapper64.o umf4_f77zwrapper64.o $(UMFPACK) $(F77) $(F77FLAGS) -o umf4hb64 umf4hb64.f umf4_f77wrapper64.o \ $(UMFPACK) $(LIBS) - ./umf4hb64 < HB/west0067.rua > my_umf4hb64.out - diff my_umf4hb64.out umf4hb64.out umf4_f77wrapper.o: umf4_f77wrapper.c $(INC) $(C) -c umf4_f77wrapper.c -o umf4_f77wrapper.o umf4_f77zwrapper.o: umf4_f77zwrapper.c $(INC) $(C) -c umf4_f77zwrapper.c -o umf4_f77zwrapper.o umf4_f77wrapper64.o: umf4_f77wrapper.c $(INC) $(C) -DDLONG -c umf4_f77wrapper.c -o umf4_f77wrapper64.o umf4_f77zwrapper64.o: umf4_f77zwrapper.c $(INC) $(C) -DDLONG -c umf4_f77zwrapper.c -o umf4_f77zwrapper64.o #------------------------------------------------------------------------------- # Remove all but the files in the original distribution #------------------------------------------------------------------------------- purge: clean - $(RM) umfpack_simple a.out - $(RM) umfpack_di_demo my_umfpack_di_demo.out - $(RM) umfpack_dl_demo my_umfpack_dl_demo.out - $(RM) umfpack_zi_demo my_umfpack_zi_demo.out - $(RM) umfpack_zl_demo my_umfpack_zl_demo.out - $(RM) umf4hb umf4zhb *.umf my_umf4hb.out - $(RM) umf4hb64 my_umf4hb64.out my_umf4zhb.out - $(RM) umf4 readhb readhb_nozeros readhb_size tmp/* clean: - $(RM) $(CLEAN) SuiteSparse/UMFPACK/Tcov/DO.linux20000755001170100242450000000205610322347757015435 0ustar davisfac# # ./DO 1 di ./DO 1 dl ./DO 1 zi ./DO 1 zl ./DO 2 di ./DO 2 dl ./DO 2 zi ./DO 2 zl ./DO 3 di ./DO 3 dl ./DO 3 zi ./DO 3 zl ./DO 4 di ./DO 4 dl ./DO 4 zi ./DO 4 zl ./DO 5 di ./DO 5 dl ./DO 5 zi ./DO 5 zl ./DO 6 di ./DO 6 dl ./DO 6 zi ./DO 6 zl ./DO 7 di ./DO 7 dl ./DO 7 zi ./DO 7 zl ./DO 8 di ./DO 8 dl ./DO 8 zi ./DO 8 zl ./DO 1g di run ./DO 1g dl run ./DO 1g zi run ./DO 1g zl run ./DO 2g di run ./DO 2g dl run ./DO 2g zi run ./DO 2g zl run ./DO 3g di run ./DO 3g dl run ./DO 3g zi run ./DO 3g zl run ./DO 4g di run ./DO 4g dl run ./DO 4g zi run ./DO 4g zl run ./DO 1i di run ./DO 1i dl run ./DO 1i zi run ./DO 1i zl run ./DO 2i di run ./DO 2i dl run ./DO 2i zi run ./DO 2i zl run ./DO 3i di run ./DO 3i dl run ./DO 3i zi run ./DO 3i zl run ./DO 4i di run ./DO 4i dl run ./DO 4i zi run ./DO 4i zl run ./DO 1n di run ./DO 1n dl run ./DO 1n zi run ./DO 1n zl run ./DO 2n di run ./DO 2n dl run ./DO 2n zi run ./DO 2n zl run ./DO 3n di run ./DO 3n dl run ./DO 3n zi run ./DO 3n zl run ./DO 4n di run ./DO 4n dl run ./DO 4n zi run ./DO 4n zl run SuiteSparse/UMFPACK/Tcov/badsym2.umf0000644001170100242450000000001010171173060016005 0ustar davisfacbadsym2 SuiteSparse/UMFPACK/Makefile0000644001170100242450000000371610711725113014502 0ustar davisfac#------------------------------------------------------------------------------- # UMFPACK makefile (for GNU make or original make) #------------------------------------------------------------------------------- # UMFPACK requires the AMD package to be in ../AMD default: library include ../UFconfig/UFconfig.mk # compile all C code (except hb, fortran, and fortran64), including AMD and the # MATLAB mexFunctions all: ( cd ../AMD ; $(MAKE) library ) ( cd ../AMD ; $(MAKE) mex ) ( cd Lib ; $(MAKE) ) ( cd Demo ; $(MAKE) ) ( cd MATLAB ; $(MAKE) ) - cat Doc/License # compile just the C-callable libraries and demo programs (not mexFunctions) library: ( cd ../AMD ; $(MAKE) library ) ( cd Lib ; $(MAKE) ) ( cd Demo ; $(MAKE) ) - cat Doc/License # compile the FORTRAN interface and demo program fortran: ( cd Demo ; $(MAKE) fortran ) # compile the 64-bit FORTRAN interface and demo program fortran64: ( cd Demo ; $(MAKE) fortran64 ) # compile the Harwell/Boeing demo program hb: ( cd Demo ; $(MAKE) hb ) # remove object files, but keep the compiled programs and library archives clean: ( cd ../AMD ; $(MAKE) clean ) ( cd Lib ; $(MAKE) clean ) ( cd Demo ; $(MAKE) clean ) ( cd MATLAB ; $(MAKE) clean ) ( cd Doc ; $(MAKE) clean ) # clean, and then remove compiled programs and library archives purge: ( cd ../AMD ; $(MAKE) purge ) ( cd Lib ; $(MAKE) purge ) ( cd Demo ; $(MAKE) purge ) ( cd MATLAB ; $(MAKE) purge ) ( cd Doc ; $(MAKE) purge ) # create PDF documents for the original distribution doc: ( cd ../AMD ; $(MAKE) doc ) ( cd Doc ; $(MAKE) ) # get ready for distribution dist: purge ( cd ../AMD ; $(MAKE) dist ) ( cd Demo ; $(MAKE) dist ) ( cd Doc ; $(MAKE) ) distclean: purge ccode: library # compile the MATLAB mexFunction mex: ( cd ../AMD/MATLAB ; $(MAKE) ) ( cd MATLAB ; $(MAKE) ) # statement coverage (requires Linux; takes a lot of time and disk space) cov: purge ( cd Tcov ; ./DO.linux ; ./covall ) SuiteSparse/UMFPACK/MATLAB/0000755001170100242450000000000010712370342013774 5ustar davisfacSuiteSparse/UMFPACK/MATLAB/Makefile0000644001170100242450000005336110617155413015450 0ustar davisfac#------------------------------------------------------------------------------- # UMFPACK Makefile for the UMFPACK MATLAB mexFunction (old "make" only) #------------------------------------------------------------------------------- # This is a very ugly Makefile, and is only provided for those who do not # have GNU make. Note that it is not used if you have GNU make. It ignores # dependency checking and just compiles everything. default: umfpack luflop include ../../UFconfig/UFconfig.mk MX = $(MEX) -I../Include -I../Source -I../../AMD/Include -I../../UFconfig umfpack: $(MX) -c ../Source/umfpack_global.c $(MV) -f umfpack_global.o umfpack_m_global.o $(MX) -DDLONG -c ../Source/umf_analyze.c $(MV) -f umf_analyze.o umf_m_analyze.o $(MX) -DDLONG -c ../Source/umf_apply_order.c $(MV) -f umf_apply_order.o umf_m_apply_order.o $(MX) -DDLONG -c ../Source/umf_colamd.c $(MV) -f umf_colamd.o umf_m_colamd.o $(MX) -DDLONG -c ../Source/umf_free.c $(MV) -f umf_free.o umf_m_free.o $(MX) -DDLONG -c ../Source/umf_fsize.c $(MV) -f umf_fsize.o umf_m_fsize.o $(MX) -DDLONG -c ../Source/umf_is_permutation.c $(MV) -f umf_is_permutation.o umf_m_is_permutation.o $(MX) -DDLONG -c ../Source/umf_malloc.c $(MV) -f umf_malloc.o umf_m_malloc.o $(MX) -DDLONG -c ../Source/umf_realloc.c $(MV) -f umf_realloc.o umf_m_realloc.o $(MX) -DDLONG -c ../Source/umf_report_perm.c $(MV) -f umf_report_perm.o umf_m_report_perm.o $(MX) -DDLONG -c ../Source/umf_singletons.c $(MV) -f umf_singletons.o umf_m_singletons.o $(MX) -DDLONG -DCONJUGATE_SOLVE -c ../Source/umf_ltsolve.c $(MV) -f umf_ltsolve.o umf_md_lhsolve.o $(MX) -DDLONG -DCONJUGATE_SOLVE -c ../Source/umf_utsolve.c $(MV) -f umf_utsolve.o umf_md_uhsolve.o $(MX) -DDLONG -DDO_MAP -c ../Source/umf_triplet.c $(MV) -f umf_triplet.o umf_md_triplet_map_nox.o $(MX) -DDLONG -DDO_VALUES -c ../Source/umf_triplet.c $(MV) -f umf_triplet.o umf_md_triplet_nomap_x.o $(MX) -DDLONG -c ../Source/umf_triplet.c $(MV) -f umf_triplet.o umf_md_triplet_nomap_nox.o $(MX) -DDLONG -DDO_MAP -DDO_VALUES -c ../Source/umf_triplet.c $(MV) -f umf_triplet.o umf_md_triplet_map_x.o $(MX) -DDLONG -DFIXQ -c ../Source/umf_assemble.c $(MV) -f umf_assemble.o umf_md_assemble_fixq.o $(MX) -DDLONG -DDROP -c ../Source/umf_store_lu.c $(MV) -f umf_store_lu.o umf_md_store_lu_drop.o $(MX) -DDLONG -c ../Source/umf_assemble.c $(MV) -f umf_assemble.o umf_md_assemble.o $(MX) -DDLONG -c ../Source/umf_blas3_update.c $(MV) -f umf_blas3_update.o umf_md_blas3_update.o $(MX) -DDLONG -c ../Source/umf_build_tuples.c $(MV) -f umf_build_tuples.o umf_md_build_tuples.o $(MX) -DDLONG -c ../Source/umf_create_element.c $(MV) -f umf_create_element.o umf_md_create_element.o $(MX) -DDLONG -c ../Source/umf_dump.c $(MV) -f umf_dump.o umf_md_dump.o $(MX) -DDLONG -c ../Source/umf_extend_front.c $(MV) -f umf_extend_front.o umf_md_extend_front.o $(MX) -DDLONG -c ../Source/umf_garbage_collection.c $(MV) -f umf_garbage_collection.o umf_md_garbage_collection.o $(MX) -DDLONG -c ../Source/umf_get_memory.c $(MV) -f umf_get_memory.o umf_md_get_memory.o $(MX) -DDLONG -c ../Source/umf_init_front.c $(MV) -f umf_init_front.o umf_md_init_front.o $(MX) -DDLONG -c ../Source/umf_kernel.c $(MV) -f umf_kernel.o umf_md_kernel.o $(MX) -DDLONG -c ../Source/umf_kernel_init.c $(MV) -f umf_kernel_init.o umf_md_kernel_init.o $(MX) -DDLONG -c ../Source/umf_kernel_wrapup.c $(MV) -f umf_kernel_wrapup.o umf_md_kernel_wrapup.o $(MX) -DDLONG -c ../Source/umf_local_search.c $(MV) -f umf_local_search.o umf_md_local_search.o $(MX) -DDLONG -c ../Source/umf_lsolve.c $(MV) -f umf_lsolve.o umf_md_lsolve.o $(MX) -DDLONG -c ../Source/umf_ltsolve.c $(MV) -f umf_ltsolve.o umf_md_ltsolve.o $(MX) -DDLONG -c ../Source/umf_mem_alloc_element.c $(MV) -f umf_mem_alloc_element.o umf_md_mem_alloc_element.o $(MX) -DDLONG -c ../Source/umf_mem_alloc_head_block.c $(MV) -f umf_mem_alloc_head_block.o umf_md_mem_alloc_head_block.o $(MX) -DDLONG -c ../Source/umf_mem_alloc_tail_block.c $(MV) -f umf_mem_alloc_tail_block.o umf_md_mem_alloc_tail_block.o $(MX) -DDLONG -c ../Source/umf_mem_free_tail_block.c $(MV) -f umf_mem_free_tail_block.o umf_md_mem_free_tail_block.o $(MX) -DDLONG -c ../Source/umf_mem_init_memoryspace.c $(MV) -f umf_mem_init_memoryspace.o umf_md_mem_init_memoryspace.o $(MX) -DDLONG -c ../Source/umf_report_vector.c $(MV) -f umf_report_vector.o umf_md_report_vector.o $(MX) -DDLONG -c ../Source/umf_row_search.c $(MV) -f umf_row_search.o umf_md_row_search.o $(MX) -DDLONG -c ../Source/umf_scale_column.c $(MV) -f umf_scale_column.o umf_md_scale_column.o $(MX) -DDLONG -c ../Source/umf_set_stats.c $(MV) -f umf_set_stats.o umf_md_set_stats.o $(MX) -DDLONG -c ../Source/umf_solve.c $(MV) -f umf_solve.o umf_md_solve.o $(MX) -DDLONG -c ../Source/umf_symbolic_usage.c $(MV) -f umf_symbolic_usage.o umf_md_symbolic_usage.o $(MX) -DDLONG -c ../Source/umf_transpose.c $(MV) -f umf_transpose.o umf_md_transpose.o $(MX) -DDLONG -c ../Source/umf_tuple_lengths.c $(MV) -f umf_tuple_lengths.o umf_md_tuple_lengths.o $(MX) -DDLONG -c ../Source/umf_usolve.c $(MV) -f umf_usolve.o umf_md_usolve.o $(MX) -DDLONG -c ../Source/umf_utsolve.c $(MV) -f umf_utsolve.o umf_md_utsolve.o $(MX) -DDLONG -c ../Source/umf_valid_numeric.c $(MV) -f umf_valid_numeric.o umf_md_valid_numeric.o $(MX) -DDLONG -c ../Source/umf_valid_symbolic.c $(MV) -f umf_valid_symbolic.o umf_md_valid_symbolic.o $(MX) -DDLONG -c ../Source/umf_grow_front.c $(MV) -f umf_grow_front.o umf_md_grow_front.o $(MX) -DDLONG -c ../Source/umf_start_front.c $(MV) -f umf_start_front.o umf_md_start_front.o $(MX) -DDLONG -c ../Source/umf_2by2.c $(MV) -f umf_2by2.o umf_md_2by2.o $(MX) -DDLONG -c ../Source/umf_store_lu.c $(MV) -f umf_store_lu.o umf_md_store_lu.o $(MX) -DDLONG -c ../Source/umf_scale.c $(MV) -f umf_scale.o umf_md_scale.o $(MX) -DDLONG -DWSOLVE -c ../Source/umfpack_solve.c $(MV) -f umfpack_solve.o umfpack_md_wsolve.o $(MX) -DDLONG -c ../Source/umfpack_col_to_triplet.c $(MV) -f umfpack_col_to_triplet.o umfpack_md_col_to_triplet.o $(MX) -DDLONG -c ../Source/umfpack_defaults.c $(MV) -f umfpack_defaults.o umfpack_md_defaults.o $(MX) -DDLONG -c ../Source/umfpack_free_numeric.c $(MV) -f umfpack_free_numeric.o umfpack_md_free_numeric.o $(MX) -DDLONG -c ../Source/umfpack_free_symbolic.c $(MV) -f umfpack_free_symbolic.o umfpack_md_free_symbolic.o $(MX) -DDLONG -c ../Source/umfpack_get_numeric.c $(MV) -f umfpack_get_numeric.o umfpack_md_get_numeric.o $(MX) -DDLONG -c ../Source/umfpack_get_lunz.c $(MV) -f umfpack_get_lunz.o umfpack_md_get_lunz.o $(MX) -DDLONG -c ../Source/umfpack_get_symbolic.c $(MV) -f umfpack_get_symbolic.o umfpack_md_get_symbolic.o $(MX) -DDLONG -c ../Source/umfpack_get_determinant.c $(MV) -f umfpack_get_determinant.o umfpack_md_get_determinant.o $(MX) -DDLONG -c ../Source/umfpack_numeric.c $(MV) -f umfpack_numeric.o umfpack_md_numeric.o $(MX) -DDLONG -c ../Source/umfpack_qsymbolic.c $(MV) -f umfpack_qsymbolic.o umfpack_md_qsymbolic.o $(MX) -DDLONG -c ../Source/umfpack_report_control.c $(MV) -f umfpack_report_control.o umfpack_md_report_control.o $(MX) -DDLONG -c ../Source/umfpack_report_info.c $(MV) -f umfpack_report_info.o umfpack_md_report_info.o $(MX) -DDLONG -c ../Source/umfpack_report_matrix.c $(MV) -f umfpack_report_matrix.o umfpack_md_report_matrix.o $(MX) -DDLONG -c ../Source/umfpack_report_numeric.c $(MV) -f umfpack_report_numeric.o umfpack_md_report_numeric.o $(MX) -DDLONG -c ../Source/umfpack_report_perm.c $(MV) -f umfpack_report_perm.o umfpack_md_report_perm.o $(MX) -DDLONG -c ../Source/umfpack_report_status.c $(MV) -f umfpack_report_status.o umfpack_md_report_status.o $(MX) -DDLONG -c ../Source/umfpack_report_symbolic.c $(MV) -f umfpack_report_symbolic.o umfpack_md_report_symbolic.o $(MX) -DDLONG -c ../Source/umfpack_report_triplet.c $(MV) -f umfpack_report_triplet.o umfpack_md_report_triplet.o $(MX) -DDLONG -c ../Source/umfpack_report_vector.c $(MV) -f umfpack_report_vector.o umfpack_md_report_vector.o $(MX) -DDLONG -c ../Source/umfpack_solve.c $(MV) -f umfpack_solve.o umfpack_md_solve.o $(MX) -DDLONG -c ../Source/umfpack_symbolic.c $(MV) -f umfpack_symbolic.o umfpack_md_symbolic.o $(MX) -DDLONG -c ../Source/umfpack_transpose.c $(MV) -f umfpack_transpose.o umfpack_md_transpose.o $(MX) -DDLONG -c ../Source/umfpack_triplet_to_col.c $(MV) -f umfpack_triplet_to_col.o umfpack_md_triplet_to_col.o $(MX) -DDLONG -c ../Source/umfpack_scale.c $(MV) -f umfpack_scale.o umfpack_md_scale.o $(MX) -DDLONG -c ../Source/umfpack_load_numeric.c $(MV) -f umfpack_load_numeric.o umfpack_md_load_numeric.o $(MX) -DDLONG -c ../Source/umfpack_save_numeric.c $(MV) -f umfpack_save_numeric.o umfpack_md_save_numeric.o $(MX) -DDLONG -c ../Source/umfpack_load_symbolic.c $(MV) -f umfpack_load_symbolic.o umfpack_md_load_symbolic.o $(MX) -DDLONG -c ../Source/umfpack_save_symbolic.c $(MV) -f umfpack_save_symbolic.o umfpack_md_save_symbolic.o $(MX) -DZLONG -DCONJUGATE_SOLVE -c ../Source/umf_ltsolve.c $(MV) -f umf_ltsolve.o umf_mz_lhsolve.o $(MX) -DZLONG -DCONJUGATE_SOLVE -c ../Source/umf_utsolve.c $(MV) -f umf_utsolve.o umf_mz_uhsolve.o $(MX) -DZLONG -DDO_MAP -c ../Source/umf_triplet.c $(MV) -f umf_triplet.o umf_mz_triplet_map_nox.o $(MX) -DZLONG -DDO_VALUES -c ../Source/umf_triplet.c $(MV) -f umf_triplet.o umf_mz_triplet_nomap_x.o $(MX) -DZLONG -c ../Source/umf_triplet.c $(MV) -f umf_triplet.o umf_mz_triplet_nomap_nox.o $(MX) -DZLONG -DDO_MAP -DDO_VALUES -c ../Source/umf_triplet.c $(MV) -f umf_triplet.o umf_mz_triplet_map_x.o $(MX) -DZLONG -DFIXQ -c ../Source/umf_assemble.c $(MV) -f umf_assemble.o umf_mz_assemble_fixq.o $(MX) -DZLONG -DDROP -c ../Source/umf_store_lu.c $(MV) -f umf_store_lu.o umf_mz_store_lu_drop.o $(MX) -DZLONG -c ../Source/umf_assemble.c $(MV) -f umf_assemble.o umf_mz_assemble.o $(MX) -DZLONG -c ../Source/umf_blas3_update.c $(MV) -f umf_blas3_update.o umf_mz_blas3_update.o $(MX) -DZLONG -c ../Source/umf_build_tuples.c $(MV) -f umf_build_tuples.o umf_mz_build_tuples.o $(MX) -DZLONG -c ../Source/umf_create_element.c $(MV) -f umf_create_element.o umf_mz_create_element.o $(MX) -DZLONG -c ../Source/umf_dump.c $(MV) -f umf_dump.o umf_mz_dump.o $(MX) -DZLONG -c ../Source/umf_extend_front.c $(MV) -f umf_extend_front.o umf_mz_extend_front.o $(MX) -DZLONG -c ../Source/umf_garbage_collection.c $(MV) -f umf_garbage_collection.o umf_mz_garbage_collection.o $(MX) -DZLONG -c ../Source/umf_get_memory.c $(MV) -f umf_get_memory.o umf_mz_get_memory.o $(MX) -DZLONG -c ../Source/umf_init_front.c $(MV) -f umf_init_front.o umf_mz_init_front.o $(MX) -DZLONG -c ../Source/umf_kernel.c $(MV) -f umf_kernel.o umf_mz_kernel.o $(MX) -DZLONG -c ../Source/umf_kernel_init.c $(MV) -f umf_kernel_init.o umf_mz_kernel_init.o $(MX) -DZLONG -c ../Source/umf_kernel_wrapup.c $(MV) -f umf_kernel_wrapup.o umf_mz_kernel_wrapup.o $(MX) -DZLONG -c ../Source/umf_local_search.c $(MV) -f umf_local_search.o umf_mz_local_search.o $(MX) -DZLONG -c ../Source/umf_lsolve.c $(MV) -f umf_lsolve.o umf_mz_lsolve.o $(MX) -DZLONG -c ../Source/umf_ltsolve.c $(MV) -f umf_ltsolve.o umf_mz_ltsolve.o $(MX) -DZLONG -c ../Source/umf_mem_alloc_element.c $(MV) -f umf_mem_alloc_element.o umf_mz_mem_alloc_element.o $(MX) -DZLONG -c ../Source/umf_mem_alloc_head_block.c $(MV) -f umf_mem_alloc_head_block.o umf_mz_mem_alloc_head_block.o $(MX) -DZLONG -c ../Source/umf_mem_alloc_tail_block.c $(MV) -f umf_mem_alloc_tail_block.o umf_mz_mem_alloc_tail_block.o $(MX) -DZLONG -c ../Source/umf_mem_free_tail_block.c $(MV) -f umf_mem_free_tail_block.o umf_mz_mem_free_tail_block.o $(MX) -DZLONG -c ../Source/umf_mem_init_memoryspace.c $(MV) -f umf_mem_init_memoryspace.o umf_mz_mem_init_memoryspace.o $(MX) -DZLONG -c ../Source/umf_report_vector.c $(MV) -f umf_report_vector.o umf_mz_report_vector.o $(MX) -DZLONG -c ../Source/umf_row_search.c $(MV) -f umf_row_search.o umf_mz_row_search.o $(MX) -DZLONG -c ../Source/umf_scale_column.c $(MV) -f umf_scale_column.o umf_mz_scale_column.o $(MX) -DZLONG -c ../Source/umf_set_stats.c $(MV) -f umf_set_stats.o umf_mz_set_stats.o $(MX) -DZLONG -c ../Source/umf_solve.c $(MV) -f umf_solve.o umf_mz_solve.o $(MX) -DZLONG -c ../Source/umf_symbolic_usage.c $(MV) -f umf_symbolic_usage.o umf_mz_symbolic_usage.o $(MX) -DZLONG -c ../Source/umf_transpose.c $(MV) -f umf_transpose.o umf_mz_transpose.o $(MX) -DZLONG -c ../Source/umf_tuple_lengths.c $(MV) -f umf_tuple_lengths.o umf_mz_tuple_lengths.o $(MX) -DZLONG -c ../Source/umf_usolve.c $(MV) -f umf_usolve.o umf_mz_usolve.o $(MX) -DZLONG -c ../Source/umf_utsolve.c $(MV) -f umf_utsolve.o umf_mz_utsolve.o $(MX) -DZLONG -c ../Source/umf_valid_numeric.c $(MV) -f umf_valid_numeric.o umf_mz_valid_numeric.o $(MX) -DZLONG -c ../Source/umf_valid_symbolic.c $(MV) -f umf_valid_symbolic.o umf_mz_valid_symbolic.o $(MX) -DZLONG -c ../Source/umf_grow_front.c $(MV) -f umf_grow_front.o umf_mz_grow_front.o $(MX) -DZLONG -c ../Source/umf_start_front.c $(MV) -f umf_start_front.o umf_mz_start_front.o $(MX) -DZLONG -c ../Source/umf_2by2.c $(MV) -f umf_2by2.o umf_mz_2by2.o $(MX) -DZLONG -c ../Source/umf_store_lu.c $(MV) -f umf_store_lu.o umf_mz_store_lu.o $(MX) -DZLONG -c ../Source/umf_scale.c $(MV) -f umf_scale.o umf_mz_scale.o $(MX) -DZLONG -DWSOLVE -c ../Source/umfpack_solve.c $(MV) -f umfpack_solve.o umfpack_mz_wsolve.o $(MX) -DZLONG -c ../Source/umfpack_col_to_triplet.c $(MV) -f umfpack_col_to_triplet.o umfpack_mz_col_to_triplet.o $(MX) -DZLONG -c ../Source/umfpack_defaults.c $(MV) -f umfpack_defaults.o umfpack_mz_defaults.o $(MX) -DZLONG -c ../Source/umfpack_free_numeric.c $(MV) -f umfpack_free_numeric.o umfpack_mz_free_numeric.o $(MX) -DZLONG -c ../Source/umfpack_free_symbolic.c $(MV) -f umfpack_free_symbolic.o umfpack_mz_free_symbolic.o $(MX) -DZLONG -c ../Source/umfpack_get_numeric.c $(MV) -f umfpack_get_numeric.o umfpack_mz_get_numeric.o $(MX) -DZLONG -c ../Source/umfpack_get_lunz.c $(MV) -f umfpack_get_lunz.o umfpack_mz_get_lunz.o $(MX) -DZLONG -c ../Source/umfpack_get_symbolic.c $(MV) -f umfpack_get_symbolic.o umfpack_mz_get_symbolic.o $(MX) -DZLONG -c ../Source/umfpack_get_determinant.c $(MV) -f umfpack_get_determinant.o umfpack_mz_get_determinant.o $(MX) -DZLONG -c ../Source/umfpack_numeric.c $(MV) -f umfpack_numeric.o umfpack_mz_numeric.o $(MX) -DZLONG -c ../Source/umfpack_qsymbolic.c $(MV) -f umfpack_qsymbolic.o umfpack_mz_qsymbolic.o $(MX) -DZLONG -c ../Source/umfpack_report_control.c $(MV) -f umfpack_report_control.o umfpack_mz_report_control.o $(MX) -DZLONG -c ../Source/umfpack_report_info.c $(MV) -f umfpack_report_info.o umfpack_mz_report_info.o $(MX) -DZLONG -c ../Source/umfpack_report_matrix.c $(MV) -f umfpack_report_matrix.o umfpack_mz_report_matrix.o $(MX) -DZLONG -c ../Source/umfpack_report_numeric.c $(MV) -f umfpack_report_numeric.o umfpack_mz_report_numeric.o $(MX) -DZLONG -c ../Source/umfpack_report_perm.c $(MV) -f umfpack_report_perm.o umfpack_mz_report_perm.o $(MX) -DZLONG -c ../Source/umfpack_report_status.c $(MV) -f umfpack_report_status.o umfpack_mz_report_status.o $(MX) -DZLONG -c ../Source/umfpack_report_symbolic.c $(MV) -f umfpack_report_symbolic.o umfpack_mz_report_symbolic.o $(MX) -DZLONG -c ../Source/umfpack_report_triplet.c $(MV) -f umfpack_report_triplet.o umfpack_mz_report_triplet.o $(MX) -DZLONG -c ../Source/umfpack_report_vector.c $(MV) -f umfpack_report_vector.o umfpack_mz_report_vector.o $(MX) -DZLONG -c ../Source/umfpack_solve.c $(MV) -f umfpack_solve.o umfpack_mz_solve.o $(MX) -DZLONG -c ../Source/umfpack_symbolic.c $(MV) -f umfpack_symbolic.o umfpack_mz_symbolic.o $(MX) -DZLONG -c ../Source/umfpack_transpose.c $(MV) -f umfpack_transpose.o umfpack_mz_transpose.o $(MX) -DZLONG -c ../Source/umfpack_triplet_to_col.c $(MV) -f umfpack_triplet_to_col.o umfpack_mz_triplet_to_col.o $(MX) -DZLONG -c ../Source/umfpack_scale.c $(MV) -f umfpack_scale.o umfpack_mz_scale.o $(MX) -DZLONG -c ../Source/umfpack_load_numeric.c $(MV) -f umfpack_load_numeric.o umfpack_mz_load_numeric.o $(MX) -DZLONG -c ../Source/umfpack_save_numeric.c $(MV) -f umfpack_save_numeric.o umfpack_mz_save_numeric.o $(MX) -DZLONG -c ../Source/umfpack_load_symbolic.c $(MV) -f umfpack_load_symbolic.o umfpack_mz_load_symbolic.o $(MX) -DZLONG -c ../Source/umfpack_save_symbolic.c $(MV) -f umfpack_save_symbolic.o umfpack_mz_save_symbolic.o $(MX) -c ../Source/umfpack_timer.c $(MV) -f umfpack_timer.o umfpack_m_timer.o $(MX) -c ../Source/umfpack_tictoc.c $(MV) -f umfpack_tictoc.o umfpack_m_tictoc.o $(MX) -DDLONG -c ../../AMD/Source/amd_global.c $(MV) -f amd_global.o amd_m_global.o $(MX) -DDLONG -c ../../AMD/Source/amd_aat.c $(MV) -f amd_aat.o amd_m_aat.o $(MX) -DDLONG -c ../../AMD/Source/amd_1.c $(MV) -f amd_1.o amd_m_1.o $(MX) -DDLONG -c ../../AMD/Source/amd_2.c $(MV) -f amd_2.o amd_m_2.o $(MX) -DDLONG -c ../../AMD/Source/amd_dump.c $(MV) -f amd_dump.o amd_m_dump.o $(MX) -DDLONG -c ../../AMD/Source/amd_postorder.c $(MV) -f amd_postorder.o amd_m_postorder.o $(MX) -DDLONG -c ../../AMD/Source/amd_post_tree.c $(MV) -f amd_post_tree.o amd_m_post_tree.o $(MX) -DDLONG -c ../../AMD/Source/amd_defaults.c $(MV) -f amd_defaults.o amd_m_defaults.o $(MX) -DDLONG -c ../../AMD/Source/amd_order.c $(MV) -f amd_order.o amd_m_order.o $(MX) -DDLONG -c ../../AMD/Source/amd_control.c $(MV) -f amd_control.o amd_m_control.o $(MX) -DDLONG -c ../../AMD/Source/amd_info.c $(MV) -f amd_info.o amd_m_info.o $(MX) -DDLONG -c ../../AMD/Source/amd_valid.c $(MV) -f amd_valid.o amd_m_valid.o $(MX) -output umfpack2 umfpackmex.c \ umf_m_analyze.o umf_m_apply_order.o umf_m_colamd.o umf_m_free.o \ umf_m_fsize.o umf_m_is_permutation.o umf_m_malloc.o \ umf_m_realloc.o umf_m_report_perm.o umf_m_singletons.o \ umf_md_lhsolve.o umf_md_uhsolve.o umf_md_triplet_map_nox.o \ umf_md_triplet_nomap_x.o umf_md_triplet_nomap_nox.o \ umf_md_triplet_map_x.o umf_md_assemble_fixq.o \ umf_md_store_lu_drop.o umf_md_assemble.o umf_md_blas3_update.o \ umf_md_build_tuples.o umf_md_create_element.o umf_md_dump.o \ umf_md_extend_front.o umf_md_garbage_collection.o \ umf_md_get_memory.o umf_md_init_front.o umf_md_kernel.o \ umf_md_kernel_init.o umf_md_kernel_wrapup.o umf_md_local_search.o \ umf_md_lsolve.o umf_md_ltsolve.o umf_md_mem_alloc_element.o \ umf_md_mem_alloc_head_block.o umf_md_mem_alloc_tail_block.o \ umf_md_mem_free_tail_block.o umf_md_mem_init_memoryspace.o \ umf_md_report_vector.o umf_md_row_search.o umf_md_scale_column.o \ umf_md_set_stats.o umf_md_solve.o umf_md_symbolic_usage.o \ umf_md_transpose.o umf_md_tuple_lengths.o umf_md_usolve.o \ umf_md_utsolve.o umf_md_valid_numeric.o umf_md_valid_symbolic.o \ umf_md_grow_front.o umf_md_start_front.o umf_md_2by2.o \ umf_md_store_lu.o umf_md_scale.o umfpack_md_wsolve.o \ umfpack_md_col_to_triplet.o umfpack_md_defaults.o \ umfpack_md_free_numeric.o umfpack_md_free_symbolic.o \ umfpack_md_get_numeric.o umfpack_md_get_lunz.o \ umfpack_md_get_symbolic.o umfpack_md_get_determinant.o \ umfpack_md_numeric.o \ umfpack_md_qsymbolic.o umfpack_md_report_control.o \ umfpack_md_report_info.o umfpack_md_report_matrix.o \ umfpack_md_report_numeric.o umfpack_md_report_perm.o \ umfpack_md_report_status.o umfpack_md_report_symbolic.o \ umfpack_md_report_triplet.o umfpack_md_report_vector.o \ umfpack_md_solve.o umfpack_md_symbolic.o umfpack_md_transpose.o \ umfpack_md_triplet_to_col.o umfpack_md_scale.o \ umfpack_md_load_numeric.o umfpack_md_save_numeric.o \ umfpack_md_load_symbolic.o umfpack_md_save_symbolic.o \ umf_mz_lhsolve.o umf_mz_uhsolve.o umf_mz_triplet_map_nox.o \ umf_mz_triplet_nomap_x.o umf_mz_triplet_nomap_nox.o \ umf_mz_triplet_map_x.o umf_mz_assemble_fixq.o \ umf_mz_store_lu_drop.o umf_mz_assemble.o umf_mz_blas3_update.o \ umf_mz_build_tuples.o umf_mz_create_element.o umf_mz_dump.o \ umf_mz_extend_front.o umf_mz_garbage_collection.o \ umf_mz_get_memory.o umf_mz_init_front.o umf_mz_kernel.o \ umf_mz_kernel_init.o umf_mz_kernel_wrapup.o umf_mz_local_search.o \ umf_mz_lsolve.o umf_mz_ltsolve.o umf_mz_mem_alloc_element.o \ umf_mz_mem_alloc_head_block.o umf_mz_mem_alloc_tail_block.o \ umf_mz_mem_free_tail_block.o umf_mz_mem_init_memoryspace.o \ umf_mz_report_vector.o umf_mz_row_search.o umf_mz_scale_column.o \ umf_mz_set_stats.o umf_mz_solve.o umf_mz_symbolic_usage.o \ umf_mz_transpose.o umf_mz_tuple_lengths.o umf_mz_usolve.o \ umf_mz_utsolve.o umf_mz_valid_numeric.o umf_mz_valid_symbolic.o \ umf_mz_grow_front.o umf_mz_start_front.o umf_mz_2by2.o \ umf_mz_store_lu.o umf_mz_scale.o umfpack_mz_wsolve.o \ umfpack_mz_col_to_triplet.o umfpack_mz_defaults.o \ umfpack_mz_free_numeric.o umfpack_mz_free_symbolic.o \ umfpack_mz_get_numeric.o umfpack_mz_get_lunz.o \ umfpack_mz_get_symbolic.o umfpack_mz_get_determinant.o \ umfpack_mz_numeric.o \ umfpack_mz_qsymbolic.o umfpack_mz_report_control.o \ umfpack_mz_report_info.o umfpack_mz_report_matrix.o \ umfpack_mz_report_numeric.o umfpack_mz_report_perm.o \ umfpack_mz_report_status.o umfpack_mz_report_symbolic.o \ umfpack_mz_report_triplet.o umfpack_mz_report_vector.o \ umfpack_mz_solve.o umfpack_mz_symbolic.o umfpack_mz_transpose.o \ umfpack_mz_triplet_to_col.o umfpack_mz_scale.o \ umfpack_mz_load_numeric.o umfpack_mz_save_numeric.o \ umfpack_mz_load_symbolic.o umfpack_mz_save_symbolic.o \ umfpack_m_timer.o umfpack_m_tictoc.o umfpack_m_global.o \ amd_m_global.o \ amd_m_aat.o amd_m_1.o amd_m_2.o amd_m_dump.o \ amd_m_postorder.o amd_m_post_tree.o amd_m_defaults.o amd_m_order.o \ amd_m_control.o amd_m_info.o amd_m_valid.o luflop: luflopmex.c $(MX) -output luflop luflopmex.c #------------------------------------------------------------------------------- # Remove all but the files in the original distribution #------------------------------------------------------------------------------- purge: clean - $(RM) *.mex* clean: - $(RM) $(CLEAN) SuiteSparse/UMFPACK/MATLAB/umfpack_make.m0000644001170100242450000002647410712370340016610 0ustar davisfacfunction umfpack_make (lapack) %UMFPACK_MAKE to compile umfpack2 for use in MATLAB % % Compiles the umfpack2 mexFunction and then runs a simple demo. % % Example: % umfpack_make % use default LAPACK and BLAS % umfpack_make ('lcc_lib/libmwlapack.lib') % for Windows % umfpack_make ('-lmwlapack -lmwblas') % for Linux, Unix, Mac % % the string gives the locations of the LAPACK and BLAS libraries. % % See also: umfpack, umfpack2, umfpack_details, umfpack_report, umfpack_demo, % and umfpack_simple. % Copyright 1995-2007 by Timothy A. Davis. details = 0 ; d = '' ; if (~isempty (strfind (computer, '64'))) d = ' -largeArrayDims' ; end v = getversion ; try % ispc does not appear in MATLAB 5.3 pc = ispc ; catch % if ispc fails, assume we are on a Windows PC if it's not unix pc = ~isunix ; end fprintf ('Compiling UMFPACK for MATLAB Version %g\n', v) ; if (pc) obj = 'obj' ; else obj = 'o' ; end kk = 0 ; %------------------------------------------------------------------------------- % BLAS option %------------------------------------------------------------------------------- % This is exceedingly ugly. The MATLAB mex command needs to be told where to % fine the LAPACK and BLAS libraries, which is a real portability nightmare. if (nargin < 1) if (pc) if (v < 6.5) % MATLAB 6.1 and earlier: use the version supplied here lapack = 'lcc_lib/libmwlapack.lib' ; fprintf ('Using %s. If this fails with dgemm and others\n',lapack); fprintf ('undefined, then edit umfpack_make.m and modify the') ; fprintf (' statement:\nlapack = ''%s'' ;\n', lapack) ; elseif (v < 7.5) lapack = 'libmwlapack.lib' ; else % MATLAB R2007b (7.5) made the problem worse lapack = 'libmwlapack.lib libmwblas.lib' ; end else % For other systems, mex should find lapack on its own, but this has % been broken in MATLAB R2007a; the following is now required. if (v < 7.5) lapack = '-lmwlapack' ; else % MATLAB R2007b (7.5) made the problem worse lapack = '-lmwlapack -lmwblas' ; end end end %------------------------------------------------------------------------------- % -DNPOSIX option (for sysconf and times timer routines) %------------------------------------------------------------------------------- posix = '' ; % if (~pc) % msg = [ ... % '--------------------------------------------------------------\n', ... % '\nUMFPACK can use the POSIX routines sysconf () and times ()\n', ... % 'to provide CPU time and wallclock time statistics. If you do not\n', ... % 'have a POSIX-compliant operating system, then UMFPACK won''t\n', ... % 'compile. If you don''t know which option to pick, try the\n', ... % 'default. If you get an error saying that sysconf and/or times\n', ... % 'are not defined, then recompile with the non-POSIX option.\n', ... % '\nPlease select one of the following options:\n', ... % ' 1: use POSIX sysconf and times routines (default)\n', ... % ' 2: do not use POSIX routines\n'] ; % fprintf (msg) ; % posix = str2num (input (': ', 's')) ; % if (isempty (posix)) % posix = 1 ; % end % if (posix == 2) % fprintf ('\nNot using POSIX sysconf and times routines.\n') ; % posix = ' -DNPOSIX' ; % else % fprintf ('\nUsing POSIX sysconf and times routines.\n') ; % posix = '' ; % end % end %------------------------------------------------------------------------------- % mex command %------------------------------------------------------------------------------- umfdir = '../Source/' ; amddir = '../../AMD/Source/' ; incdir = ' -I../Include -I../Source -I../../AMD/Include -I../../UFconfig' ; mx = sprintf ('mex -O%s%s%s ', posix, incdir, d) ; % fprintf ('compile options:\n%s\n', mx) ; %------------------------------------------------------------------------------- % source files %------------------------------------------------------------------------------- % non-user-callable umf_*.[ch] files: umfch = { 'assemble', 'blas3_update', ... 'build_tuples', 'create_element', ... 'dump', 'extend_front', 'garbage_collection', ... 'get_memory', 'init_front', 'kernel', ... 'kernel_init', 'kernel_wrapup', ... 'local_search', 'lsolve', 'ltsolve', ... 'mem_alloc_element', 'mem_alloc_head_block', ... 'mem_alloc_tail_block', 'mem_free_tail_block', ... 'mem_init_memoryspace', ... 'report_vector', 'row_search', 'scale_column', ... 'set_stats', 'solve', 'symbolic_usage', 'transpose', ... 'tuple_lengths', 'usolve', 'utsolve', 'valid_numeric', ... 'valid_symbolic', 'grow_front', 'start_front', '2by2', ... 'store_lu', 'scale' } ; % non-user-callable umf_*.[ch] files, int versions only (no real/complex): umfint = { 'analyze', 'apply_order', 'colamd', 'free', 'fsize', ... 'is_permutation', 'malloc', 'realloc', 'report_perm', ... 'singletons' } ; % non-user-callable and user-callable amd_*.[ch] files (int versions only): amdsrc = { 'aat', '1', '2', 'dump', 'postorder', 'post_tree', 'defaults', ... 'order', 'control', 'info', 'valid', 'preprocess', 'global' } ; % user-callable umfpack_*.[ch] files (real/complex): user = { 'col_to_triplet', 'defaults', 'free_numeric', ... 'free_symbolic', 'get_numeric', 'get_lunz', ... 'get_symbolic', 'get_determinant', 'numeric', 'qsymbolic', ... 'report_control', 'report_info', 'report_matrix', ... 'report_numeric', 'report_perm', 'report_status', ... 'report_symbolic', 'report_triplet', ... 'report_vector', 'solve', 'symbolic', ... 'transpose', 'triplet_to_col', 'scale' ... 'load_numeric', 'save_numeric', 'load_symbolic', 'save_symbolic' } ; % user-callable umfpack_*.[ch], only one version generic = { 'timer', 'tictoc', 'global' } ; M = cell (0) ; %------------------------------------------------------------------------------- % Create the umfpack2 and amd2 mexFunctions for MATLAB (int versions only) %------------------------------------------------------------------------------- for k = 1:length(umfint) [M, kk] = make (M, '%s -DDLONG -c %sumf_%s.c', 'umf_%s.%s', ... 'umf_%s_%s.%s', mx, umfint {k}, umfint {k}, 'm', obj, umfdir, ... kk, details) ; end rules = { [mx ' -DDLONG'] , [mx ' -DZLONG'] } ; kinds = { 'md', 'mz' } ; for what = 1:2 rule = rules {what} ; kind = kinds {what} ; [M, kk] = make (M, '%s -DCONJUGATE_SOLVE -c %sumf_%s.c', 'umf_%s.%s', ... 'umf_%s_%s.%s', rule, 'ltsolve', 'lhsolve', kind, obj, umfdir, ... kk, details) ; [M, kk] = make (M, '%s -DCONJUGATE_SOLVE -c %sumf_%s.c', 'umf_%s.%s', ... 'umf_%s_%s.%s', rule, 'utsolve', 'uhsolve', kind, obj, umfdir, ... kk, details) ; [M, kk] = make (M, '%s -DDO_MAP -c %sumf_%s.c', 'umf_%s.%s', ... 'umf_%s_%s_map_nox.%s', rule, 'triplet', 'triplet', kind, obj, ... umfdir, kk, details) ; [M, kk] = make (M, '%s -DDO_VALUES -c %sumf_%s.c', 'umf_%s.%s', ... 'umf_%s_%s_nomap_x.%s', rule, 'triplet', 'triplet', kind, obj, ... umfdir, kk, details) ; [M, kk] = make (M, '%s -c %sumf_%s.c', 'umf_%s.%s', ... 'umf_%s_%s_nomap_nox.%s', rule, 'triplet', 'triplet', kind, obj, ... umfdir, kk, details) ; [M, kk] = make (M, '%s -DDO_MAP -DDO_VALUES -c %sumf_%s.c', 'umf_%s.%s', ... 'umf_%s_%s_map_x.%s', rule, 'triplet', 'triplet', kind, obj, ... umfdir, kk, details) ; [M, kk] = make (M, '%s -DFIXQ -c %sumf_%s.c', 'umf_%s.%s', ... 'umf_%s_%s_fixq.%s', rule, 'assemble', 'assemble', kind, obj, ... umfdir, kk, details) ; [M, kk] = make (M, '%s -DDROP -c %sumf_%s.c', 'umf_%s.%s', ... 'umf_%s_%s_drop.%s', rule, 'store_lu', 'store_lu', kind, obj, ... umfdir, kk, details) ; for k = 1:length(umfch) [M, kk] = make (M, '%s -c %sumf_%s.c', 'umf_%s.%s', 'umf_%s_%s.%s', ... rule, umfch {k}, umfch {k}, kind, obj, umfdir, kk, details) ; end [M, kk] = make (M, '%s -DWSOLVE -c %sumfpack_%s.c', 'umfpack_%s.%s', ... 'umfpack_%s_w%s.%s', rule, 'solve', 'solve', kind, obj, umfdir, ... kk, details) ; for k = 1:length(user) [M, kk] = make (M, '%s -c %sumfpack_%s.c', 'umfpack_%s.%s', ... 'umfpack_%s_%s.%s', rule, user {k}, user {k}, kind, obj, ... umfdir, kk, details) ; end end for k = 1:length(generic) [M, kk] = make (M, '%s -c %sumfpack_%s.c', 'umfpack_%s.%s', ... 'umfpack_%s_%s.%s', mx, generic {k}, generic {k}, 'm', obj, ... umfdir, kk, details) ; end %---------------------------------------- % AMD routines (int only) %---------------------------------------- for k = 1:length(amdsrc) [M, kk] = make (M, '%s -DDLONG -c %samd_%s.c', 'amd_%s.%s', ... 'amd_%s_%s.%s', mx, amdsrc {k}, amdsrc {k}, 'm', obj, amddir, ... kk, details) ; end %---------------------------------------- % compile the umfpack2 mexFunction %---------------------------------------- C = sprintf ('%s -output umfpack2 umfpackmex.c', mx) ; for i = 1:length (M) C = [C ' ' (M {i})] ; %#ok end C = [C ' ' lapack] ; kk = cmd (C, kk, details) ; %---------------------------------------- % delete the object files %---------------------------------------- for i = 1:length (M) rmfile (M {i}) ; end %---------------------------------------- % compile the luflop mexFunction %---------------------------------------- cmd (sprintf ('%s -output luflop luflopmex.c', mx), kk, details) ; fprintf ('\nUMFPACK successfully compiled\n') ; %=============================================================================== % end of umfpack_make %=============================================================================== %------------------------------------------------------------------------------- function rmfile (file) % rmfile: delete a file, but only if it exists if (length (dir (file)) > 0) %#ok delete (file) ; end %------------------------------------------------------------------------------- function cpfile (src, dst) % cpfile: copy the src file to the filename dst, overwriting dst if it exists rmfile (dst) if (length (dir (src)) == 0) %#ok fprintf ('File does not exist: %s\n', src) ; error ('File does not exist') ; end copyfile (src, dst) ; %------------------------------------------------------------------------------- function mvfile (src, dst) % mvfile: move the src file to the filename dst, overwriting dst if it exists cpfile (src, dst) ; rmfile (src) ; %------------------------------------------------------------------------------- function kk = cmd (s, kk, details) %CMD: evaluate a command, and either print it or print a "." if (details) fprintf ('%s\n', s) ; else if (mod (kk, 60) == 0) fprintf ('\n') ; end kk = kk + 1 ; fprintf ('.') ; end eval (s) ; %------------------------------------------------------------------------------- function [M, kk] = make (M, s, src, dst, rule, file1, file2, kind, obj, ... srcdir, kk, details) % make: execute a "make" command for a source file kk = cmd (sprintf (s, rule, srcdir, file1), kk, details) ; src = sprintf (src, file1, obj) ; dst = sprintf (dst, kind, file2, obj) ; mvfile (src, dst) ; M {end + 1} = dst ; %------------------------------------------------------------------------------- function v = getversion % determine the MATLAB version, and return it as a double. v = sscanf (version, '%d.%d.%d') ; v = 10.^(0:-1:-(length(v)-1)) * v ; SuiteSparse/UMFPACK/MATLAB/umfpack_details.m0000644001170100242450000002050010677545567017331 0ustar davisfacfunction umfpack_details %UMFPACK_DETAILS details on all the options for using umfpack2 in MATLAB % % Factor or solve a sparse linear system, returning either the solution x to % Ax=b or A'x'=b', the factorization LU=PAQ, or LU=P(R\A)Q. A must be sparse. % For the solve, A must be square and b must be a dense n-by-1 vector. For LU % factorization, A can be rectangular. In both cases, A and/or b can be real % or complex. % % UMFPACK analyzes the matrix and selects one of three strategies to factorize % the matrix. It first finds a set of k initial pivot entries of zero Markowitz % cost. This forms the first k rows and columns of L and U. The remaining % submatrix S is then analyzed, based on the symmetry of the nonzero pattern of % the submatrix and the values on the diagaonal. The strategies include: % % (1) unsymmetric: use a COLAMD pre-ordering, a column elimination tree % post-ordering, refine the column ordering during factorization, % and make no effort at selecting pivots on the diagonal. % (2) 2-by-2: like the symmetric strategy (see below), except that local % row permutations are first made to attempt to place large entries % on the diagonal. % (3) symmetric: use an AMD pre-ordering on the matrix S+S', an % elimination tree post-ordering, do not refine the column ordering % during factorization, and attempt to select pivots on the diagonal. % % Each of the following uses of umfpack2 (except for "Control = umfpack2") is % stand-alone. That is, no call to umfpack2 is required for any subsequent % call. In each usage, the Info output argument is optional. % % Example: % % [x, Info] = umfpack2 (A, '\', b) ; % [x, Info] = umfpack2 (A, '\', b, Control) ; % [x, Info] = umfpack2 (A, Qinit, '\', b, Control) ; % [x, Info] = umfpack2 (A, Qinit, '\', b) ; % % Solves Ax=b (similar to x = A\b in MATLAB). % % [x, Info] = umfpack2 (b, '/', A) ; % [x, Info] = umfpack2 (b, '/', A, Control) ; % [x, Info] = umfpack2 (b, '/', A, Qinit) ; % [x, Info] = umfpack2 (b, '/', A, Qinit, Control) ; % % Solves A'x'=b' (similar to x = b/A in MATLAB). % % [L, U, P, Q, R, Info] = umfpack2 (A) ; % [L, U, P, Q, R, Info] = umfpack2 (A, Control) ; % [L, U, P, Q, R, Info] = umfpack2 (A, Qinit) ; % [L, U, P, Q, R, Info] = umfpack2 (A, Qinit, Control) ; % % Returns the LU factorization of A. P and Q are returned as permutation % matrices. R is a diagonal sparse matrix of scale factors for the rows % of A, L is lower triangular, and U is upper triangular. The % factorization is L*U = P*(R\A)*Q. You can turn off scaling by setting % Control (17) to zero (in which case R = speye (m)), or by using the % following syntaxes (in which case Control (17) is ignored): % % [L, U, P, Q] = umfpack2 (A) ; % [L, U, P, Q] = umfpack2 (A, Control) ; % [L, U, P, Q] = umfpack2 (A, Qinit) ; % [L, U, P, Q] = umfpack2 (A, Qinit, Control) ; % % Same as above, except that no row scaling is performed. The Info array % is not returned, either. % % [P1, Q1, Fr, Ch, Info] = umfpack2 (A, 'symbolic') ; % [P1, Q1, Fr, Ch, Info] = umfpack2 (A, 'symbolic', Control) ; % [P1, Q1, Fr, Ch, Info] = umfpack2 (A, Qinit, 'symbolic') ; % [P1, Q1, Fr, Ch, Info] = umfpack2 (A, Qinit, 'symbolic', Control); % % Performs only the fill-reducing column pre-ordering (including the % elimination tree post-ordering) and symbolic factorization. Q1 is the % initial column permutation (either from colamd, amd, or the input % ordering Qinit), possibly followed by a column elimination tree post- % ordering or a symmetric elimination tree post-ordering, depending on % the strategy used. % % For the unsymmetric strategy, P1 is the row ordering induced by Q1 % (row-merge order). For the 2-by-2 strategy, P1 is the row ordering that % places large entries on the diagonal of P1*A*Q1. For the symmetric % strategy, P1 = Q1. % % Fr is a (nfr+1)-by-4 array containing information about each frontal % matrix, where nfr <= n is the number of frontal matrices. Fr (:,1) is % the number of pivot columns in each front, and Fr (:,2) is the parent % of each front in the supercolumn elimination tree. Fr (k,2) is zero if % k is a root. The first Fr (1,1) columns of P1*A*Q1 are the pivot % columns for the first front, the next Fr (2,1) columns of P1*A*Q1 % are the pivot columns for the second front, and so on. % % For the unsymmetric strategy, Fr (:,3) is the row index of the first % row in P1*A*Q1 whose leftmost nonzero entry is in a pivot column for % the kth front. Fr (:,4) is the leftmost descendent of the kth front. % Rows in the range Fr (Fr (k,4),3) to Fr (k+1,3)-1 form the entire set % of candidate pivot rows for the kth front (some of these will typically % have been selected as pivot rows of fronts Fr (k,3) to k-1, before the % factorization reaches the kth front. If front k is a leaf node, then % Fr (k,4) is k. % % Ch is a (nchains+1)-by-3 array containing information about each "chain" % (unifrontal sequence) of frontal matrices, and where nchains <= nfr % is the number of chains. The ith chain consists of frontal matrices. % Chain (i,1) to Chain (i+1,1)-1, and the largest front in chain i is % Chain (i,2)-by-Chain (i,3). % % This use of umfpack2 is not required to factor or solve a linear system % in MATLAB. It analyzes the matrix A and provides information only. % The MATLAB statement "treeplot (Fr (:,2)')" plots the column elimination % tree. % % Control = umfpack2 ; % % Returns a 20-by-1 vector of default parameter settings for umfpack2. % % umfpack_report (Control, Info) ; % % Prints the current Control settings, and Info % % det = umfpack2 (A, 'det') ; % [det dexp] = umfpack2 (A, 'det') ; % % Computes the determinant of A. The 2nd form returns the determinant % in the form det*10^dexp, where det is in the range +/- 1 to 10, % which helps to avoid overflow/underflow when dexp is out of range of % normal floating-point numbers. % % If present, Qinit is a user-supplied 1-by-n permutation vector. It is an % initial fill-reducing column pre-ordering for A; if not present, then colamd % or amd are used instead. If present, Control is a user-supplied 20-by-1 % array. Control and Info are optional; if Control is not present, defaults % are used. If a Control entry is NaN, then the default is used for that entry. % % % Copyright 1995-2007 by Timothy A. Davis, University of Florida. % All Rights Reserved. % UMFPACK is available under alternate licenses, contact T. Davis for details. % % UMFPACK License: % % Your use or distribution of UMFPACK or any modified version of % UMFPACK implies that you agree to this License. % % This library is free software; you can redistribute it and/or % modify it under the terms of the GNU General Public % License as published by the Free Software Foundation; either % version 2 of the License, or (at your option) any later version. % % This library is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU % General Public License for more details. % % You should have received a copy of the GNU General Public % License along with this library; if not, write to the Free Software % Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 % USA % % Permission is hereby granted to use or copy this program under the % terms of the GNU GPL, provided that the Copyright, this License, % and the Availability of the original version is retained on all copies. % User documentation of any code that uses this code or any modified % version of this code must cite the Copyright, this License, the % Availability note, and "Used by permission." Permission to modify % the code and to distribute modified code is granted, provided the % Copyright, this License, and the Availability note are retained, % and a notice that the code was modified is included. % % Availability: http://www.cise.ufl.edu/research/sparse/umfpack % % See also umfpack, umfpack2, umfpack_make, umfpack_report, % umfpack_demo, and umfpack_simple. more on help umfpack_details more off SuiteSparse/UMFPACK/MATLAB/umfpack_simple.m0000644001170100242450000000235310677545610017170 0ustar davisfac%UMFPACK_SIMPLE a simple demo % % Example: % umfpack_simple % % Copyright 1995-2007 by Timothy A. Davis. % % UMFPACK License: % % Your use or distribution of UMFPACK or any modified version of % UMFPACK implies that you agree to this License. UMFPACK is % is free software; you can redistribute it and/or % modify it under the terms of the GNU General Public % License as published by the Free Software Foundation; either % version 2 of the License, or (at your option) any later version. % Availability: http://www.cise.ufl.edu/research/sparse/umfpack % % See also: umfpack, umfpack2, umfpack_details help umfpack_simple format short A = [ 2 3 0 0 0 3 0 4 0 6 0 -1 -3 2 0 0 0 1 0 0 0 4 2 0 1 ] ; fprintf ('A = \n') ; disp (A) ; A = sparse (A) ; b = [8 45 -3 3 19]' ; fprintf ('b = \n') ; disp (b) ; fprintf ('Solution to Ax=b via UMFPACK:\n') ; fprintf ('x1 = umfpack2 (A, ''\\'', b)\n') ; x1 = umfpack2 (A, '\', b) ; fprintf ('x1 = \n') ; disp (x1) ; fprintf ('Solution to Ax=b via MATLAB:\n') ; fprintf ('x2 = A\\b\n') ; x2 = A\b ; fprintf ('x2 = \n') ; disp (x2) ; fprintf ('norm (x1-x2) should be small: %g\n', norm (x1-x2)) ; fprintf ('Type ''umfpack_demo'' for a full demo of UMFPACK\n') ; SuiteSparse/UMFPACK/MATLAB/west.mat0000644001170100242450000000353510537767601015504 0ustar davisfacMATLAB 5.0 MAT-file, Platform: GLNX86, Created on: Sun Nov 19 20:03:34 2006 IMxyPGRYN# XE!<YDTŋw, +CNs6J?S F4{I3ɞ55J%LMgjS9euY\['P!A+bb1~0~9V16f? SDxؑ2~Dt$xb葼V޲14p5hhkfƸnS=^s}sc]GwԓødžcN@W+źbLb걘cf-PsX0I0n-EE |[`\Y~ 5 D qGk軶pı5cm1ok9<õ%'ΓYL8SNb¹rz k`oǝ Z5vcqbϱsĞ vE\\ bg?"H`0> 9|X d9: `?p(TNg*"P47[] x HK^]w>:~Mg.yyXcYDg{ v-z:"/|(c߯^E|la_F[2"ճ[$[rŲSwWд>PJql5hsǢ椖l[Ej=_s%7۟w!fsu;}%Ogk d^KL^yA!/ҷiSӍϝ% g)$ ?o:mvS㟨mɆ%]ߝ**:.yIUрGRZ̜u' ݗ0/Kw?¼a}ߢgq *x9jP{|qJlo }G9߿ӻr3<8C1tث8UǤ:Zu~^G7<}}fu3$ú7qԩ(:71QGI4).(3Ҙ_pVSuiteSparse/UMFPACK/MATLAB/lcc_lib/0000755001170100242450000000000010006260712015356 5ustar davisfacSuiteSparse/UMFPACK/MATLAB/lcc_lib/lapacksyms.def0000644001170100242450000001145310006260712020211 0ustar davisfacLIBRARY liblapack.dll EXPORTS dasum daxpy dbdsdc dbdsqr dcopy ddisna ddot dgbbrd dgbcon dgbequ dgbmv dgbrfs dgbsv dgbsvx dgbtf2 dgbtrf dgbtrs dgebak dgebal dgebd2 dgebrd dgecon dgeequ dgees dgeesx dgeev dgeevx dgegs dgegv dgehd2 dgehrd dgelq2 dgelqf dgels dgelsd dgelss dgelsx dgelsy dgemm dgemv dgeql2 dgeqlf dgeqp3 dgeqpf dgeqr2 dgeqrf dger dgerfs dgerq2 dgerqf dgesc2 dgesdd dgesv dgesvd dgesvx dgetc2 dgetf2 dgetrf dgetri 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ztzrzf.text .idata$7.idata$5.idata$4.idata$6 _ztzrzf__imp__ztzrzf$hlapacksyms692.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zung2l.text .idata$7.idata$5.idata$4.idata$6 _zung2l__imp__zung2l$hlapacksyms693.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zung2r.text .idata$7.idata$5.idata$4.idata$6 _zung2r__imp__zung2r$hlapacksyms694.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zungbr.text .idata$7.idata$5.idata$4.idata$6 _zungbr__imp__zungbr$hlapacksyms695.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zunghr.text .idata$7.idata$5.idata$4.idata$6 _zunghr__imp__zunghr$hlapacksyms696.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zungl2.text .idata$7.idata$5.idata$4.idata$6 _zungl2__imp__zungl2$hlapacksyms697.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zunglq.text .idata$7.idata$5.idata$4.idata$6 _zunglq__imp__zunglq$hlapacksyms698.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zungql.text .idata$7.idata$5.idata$4.idata$6 _zungql__imp__zungql$hlapacksyms699.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zungqr.text .idata$7.idata$5.idata$4.idata$6 _zungqr__imp__zungqr$hlapacksyms700.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zungr2.text .idata$7.idata$5.idata$4.idata$6 _zungr2__imp__zungr2$hlapacksyms701.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zungrq.text .idata$7.idata$5.idata$4.idata$6 _zungrq__imp__zungrq$hlapacksyms702.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zungtr.text .idata$7.idata$5.idata$4.idata$6 _zungtr__imp__zungtr$hlapacksyms703.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zunm2l.text .idata$7.idata$5.idata$4.idata$6 _zunm2l__imp__zunm2l$hlapacksyms704.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zunm2r.text .idata$7.idata$5.idata$4.idata$6 _zunm2r__imp__zunm2r$hlapacksyms705.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zunmbr.text .idata$7.idata$5.idata$4.idata$6 _zunmbr__imp__zunmbr$hlapacksyms706.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zunmhr.text .idata$7.idata$5.idata$4.idata$6 _zunmhr__imp__zunmhr$hlapacksyms707.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zunml2.text .idata$7.idata$5.idata$4.idata$6 _zunml2__imp__zunml2$hlapacksyms708.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zunmlq.text .idata$7.idata$5.idata$4.idata$6 _zunmlq__imp__zunmlq$hlapacksyms709.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zunmql.text .idata$7.idata$5.idata$4.idata$6 _zunmql__imp__zunmql$hlapacksyms710.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zunmqr.text .idata$7.idata$5.idata$4.idata$6 _zunmqr__imp__zunmqr$hlapacksyms711.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zunmr2.text .idata$7.idata$5.idata$4.idata$6 _zunmr2__imp__zunmr2$hlapacksyms712.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zunmr3.text .idata$7.idata$5.idata$4.idata$6 _zunmr3__imp__zunmr3$hlapacksyms713.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zunmrq.text .idata$7.idata$5.idata$4.idata$6 _zunmrq__imp__zunmrq$hlapacksyms714.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zunmrz.text .idata$7.idata$5.idata$4.idata$6 _zunmrz__imp__zunmrz$hlapacksyms715.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zunmtr.text .idata$7.idata$5.idata$4.idata$6 _zunmtr__imp__zunmtr$hlapacksyms716.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zupgtr.text .idata$7.idata$5.idata$4.idata$6 _zupgtr__imp__zupgtr$hlapacksyms717.obj/ 1013176938 0 0 0 560 ` Ljc<& .text  `.idata$7.idata$5.idata$4.idata$6 % zupmtr.text .idata$7.idata$5.idata$4.idata$6 _zupmtr__imp__zupmtr$hlapacksyms718.obj/ 1013176938 0 0 0 536 ` Ljc< .text `.data@.bss.idata$7 .idata$4.idata$5libmwlapack.dll.text.data.bss.idata$7.idata$4.idata$5$tlapacksymsSuiteSparse/UMFPACK/MATLAB/umfpack_test.m0000644001170100242450000001047210711445727016654 0ustar davisfacfunction umfpack_test (nmat) %UMFPACK_TEST for testing umfpack2 (requires UFget) % % Example: % umfpack_test % umfpack_test (100) % runs the first 100 matrices % See also umfpack2 % Copyright 1995-2007 by Timothy A. Davis. index = UFget ; f = find (index.nrows == index.ncols) ; [ignore, i] = sort (index.nrows (f)) ; f = f (i) ; if (nargin < 1) nmat = length (f) ; else nmat = min (nmat, length (f)) ; end nmat = max (nmat, 1) ; f = f (1:nmat) ; Control = umfpack2 ; Control (1) = 0 ; figure (1) clf h = waitbar (0, 'UMFPACK test') ; for k = 1:nmat i = f (k) ; waitbar (k/nmat, h, 'UMFPACK test') ; try fprintf ('\nmatrix: %s %s %d\n', ... index.Group{i}, index.Name{i}, index.nrows(i)) ; Prob = UFget (i) ; A = Prob.A ; n = size (A,1) ; b = rand (1,n) ; c = b' ; %----------------------------------------------------------------------- % symbolic factorization %----------------------------------------------------------------------- [P1, Q1, Fr, Ch, Info] = umfpack2 (A, 'symbolic') ; subplot (2,2,1) spy (A) title ('A') subplot (2,2,2) treeplot (Fr (1:end-1,2)') ; title ('supercolumn etree') %----------------------------------------------------------------------- % P(R\A)Q = LU %----------------------------------------------------------------------- [L,U,P,Q,R,Info] = umfpack2 (A) ; err = lu_normest (P*(R\A)*Q, L, U) ; fprintf ('norm est PR\\AQ-LU: %g relative: %g\n', ... err, err / norm (A,1)) ; subplot (2,2,3) spy (P*A*Q) title ('PAQ') ; cs = Info (57) ; rs = Info (58) ; subplot (2,2,4) hold off try spy (L+U) catch end hold on if (cs > 0) plot ([0 cs n n 0] + .5, [0 cs cs 0 0]+.5, 'c') ; end if (rs > 0) plot ([0 rs rs 0 0] + cs +.5, [cs cs+rs n n cs]+.5, 'r') ; end title ('LU factors') drawnow %----------------------------------------------------------------------- % PAQ = LU %----------------------------------------------------------------------- [L,U,P,Q] = umfpack2 (A) ; err = lu_normest (P*A*Q, L, U) ; fprintf ('norm est PAQ-LU: %g relative: %g\n', ... err, err / norm (A,1)) ; %----------------------------------------------------------------------- % solve %----------------------------------------------------------------------- x1 = b/A ; y1 = A\c ; m1 = norm (b-x1*A) ; m2 = norm (A*y1-c) ; % factor the transpose Control (8) = 2 ; [x, info] = umfpack2 (A', '\', c, Control) ; lunz0 = info (44) + info (45) - info (67) ; r = norm (A'*x-c) ; fprintf (':: %8.2e matlab: %8.2e %8.2e\n', r, m1, m2) ; % factor the original matrix and solve xA=b for ir = 0:4 Control (8) = ir ; [x, info] = umfpack2 (b, '/', A, Control) ; r = norm (b-x*A) ; if (ir == 0) lunz1 = info (44) + info (45) - info (67) ; end fprintf ('%d: %8.2e %d %d\n', ir, r, info (81), info (82)) ; end % factor the original matrix and solve Ax=b for ir = 0:4 Control (8) = ir ; [x, info] = umfpack2 (A, '\', c, Control) ; r = norm (A*x-c) ; fprintf ('%d: %8.2e %d %d\n', ir, r, info (81), info (82)) ; end fprintf (... 'lunz trans %12d no trans: %12d trans/notrans: %10.4f\n', ... lunz0, lunz1, lunz0 / lunz1) ; %----------------------------------------------------------------------- % get the determinant %----------------------------------------------------------------------- det1 = det (A) ; det2 = umfpack2 (A, 'det') ; [det3 dexp3] = umfpack2 (A, 'det') ; err = abs (det1-det2) ; err3 = abs (det1 - (det3 * 10^dexp3)) ; denom = det1 ; if (denom == 0) denom = 1 ; end err = err / denom ; err3 = err3 / denom ; fprintf ('det: %20.12e + (%20.12e)i MATLAB\n', ... real(det1), imag(det1)) ; fprintf ('det: %20.12e + (%20.12e)i umfpack2\n', ... real(det2), imag(det2)) ; fprintf ('det: (%20.12e + (%20.12e)i) * 10^(%g) umfpack2\n', ... real(det3), imag(det3), dexp3) ; fprintf ('diff %g %g\n', err, err3) ; catch % out-of-memory is OK, other errors are not disp (lasterr) ; if (isempty (strfind (lasterr, 'Out of memory'))) error (lasterr) ; %#ok else fprintf ('test terminated early, but otherwise OK\n') ; end end end close (h) ; % close the waitbar SuiteSparse/UMFPACK/MATLAB/Contents.m0000644001170100242450000000274210620401416015747 0ustar davisfac%Contents of the UMFPACK sparse matrix toolbox: % % umfpack2 - computes x=A\b, x=A/b, or lu (A) for a sparse matrix A % umfpack_make - to compile umfpack2 for use in MATLAB % umfpack_install - to compile and install umfpack2 and amd2 for use in MATLAB % umfpack_details - details on all the options for using umfpack2 in MATLAB % umfpack_report - prints optional control settings and statistics % umfpack_demo - a lenghty demo % umfpack_simple - a simple demo % umfpack_btf - factorize A using a block triangular form % umfpack_solve - x = A\b or x = b/A % lu_normest - estimates norm (L*U-A, 1) without forming L*U-A % luflop - given L and U, computes # of flops required to compute them % umfpack_test - for testing umfpack2 (requires UFget) % % Example: % x = umfpack2 (A, '\', b) ; % same as x = A\b, if A square and unsymmetric % % See also these built-in functions: % umfpack the built-in version of UMFPACK % amd symmetric minimum degree ordering % colamd unsymmetric column approx minimum degree ordering % symamd symmetric approx minimum degree ordering, based on colamd % % NOTE: UMFPACK is a built-in function in MATLAB, used in x=A\b. This is the % source code for the built-in umfpack, but the MATLAB function has been renamed % here to umfpack2, to avoid a filename clash with itself. % % Copyright 1995-2007 by Timothy A. Davis. % All Rights Reserved. Type umfpack_details for License. help Contents SuiteSparse/UMFPACK/MATLAB/umfpack_install.m0000644001170100242450000000161510620713536017335 0ustar davisfacfunction umfpack_install %UMFPACK_INSTALL to compile and install umfpack2 and amd2 for use in MATLAB % Your current directory must be UMFPACK/MATLAB for this function to work. % % Example: % umfpack_install % % See also umfpack2, amd2. % Copyright 1995-2007 by Timothy A. Davis. % compile and install UMFPACK umfpack_path = pwd ; addpath (umfpack_path) ; try umfpack_make catch fprintf ('Trying to install with lcc_lib/libmwlapack.lib instead\n') ; umfpack_make ('lcc_lib/libmwlapack.lib') ; end % compile and install AMD cd ../../AMD/MATLAB amd_path = pwd ; addpath (amd_path) ; amd_make ; cd (umfpack_path) fprintf ('Now trying the umfpack_simple demo.\n'); umfpack_simple fprintf ('Added the following directories to the path. You may wish to add\n'); fprintf ('these permanently with the MATLAB pathtool command:\n') ; fprintf ('%s\n', umfpack_path) ; fprintf ('%s\n', amd_path) ; SuiteSparse/UMFPACK/MATLAB/umfpack2.m0000644001170100242450000000431110620401533015654 0ustar davisfacfunction [out1, out2, out3, out4, out5] = umfpack2(in1, in2, in3, in4, in5) %#ok %UMFPACK2 computes x=A\b, x=A/b, or lu (A) for a sparse matrix A % It is also a built-in function in MATLAB, used in x=A\b. % % Example: % % UMFPACK: | MATLAB approximate equivalent: % --------------------------------------------------------------------- % x = umfpack2 (A, '\', b) ; | x = A \ b % | % x = umfpack2 (b, '/', A) ; | x = b / A % | % [L,U,P,Q] = umfpack2 (A) ; | [m,n] = size (A) ; % | I = speye (n) ; % | Q = I (:, colamd (A)) ; % | [L,U,P] = lu (A*Q) ; % | % [L,U,P,Q,R] = umfpack2 (A) ; | [m,n] = size (A) ; % | I = speye (n) ; % | Q = I (:, colamd (A)) ; % | r = full (sum (abs (A), 2)) ; % | r (find (r == 0)) = 1 ; % | R = spdiags (r, 0, m, m) ; % | [L,U,P] = lu ((R\A)*Q) ; % | % [P,Q,F,C] = umfpack2 (A, 'symbolic')| [m,n] = size (A) ; % | I = speye (n) ; % | Q = I (:, colamd (A)) ; % | [count,h,parent,post] = ... % | symbfact (A*Q, 'col') ; % % A must be sparse. It can be complex, singular, and/or rectangular. A must be % square for '/' or '\'. b must be a full real or complex vector. For % [L,U,P,Q,R] = umfpack2 (A), the factorization is L*U = P*(R\A)*Q. If A has a % mostly symmetric nonzero pattern, then replace "colamd" with "amd" in the % MATLAB-equivalent column in the table above. Type umfpack_details for more % information. % % See also: lu_normest, colamd, amd, umfpack. % To use UMFPACK for an arbitrary b, see umfpack_solve. % Copyright 1995-2007 by Timothy A. Davis. help umfpack2 error ('umfpack2 mexFunction not found') ; SuiteSparse/UMFPACK/MATLAB/lu_normest.m0000644001170100242450000000700610620401717016343 0ustar davisfacfunction rho = lu_normest (A, L, U) %LU_NORMEST estimates norm (L*U-A, 1) without forming L*U-A % % Example: % % rho = lu_normest (A, L, U) % % which estimates the computation of the 1-norm: % % rho = norm (A-L*U, 1) % % Authors: William W. Hager, Math Dept., Univ. of Florida % Timothy A. Davis, CISE Dept., Univ. of Florida % Gainesville, FL, 32611, USA. % based on normest1, contributed on November, 1997 % % This code can be quite easily adapted to estimate the 1-norm of any % matrix E, where E itself is dense or not explicitly represented, but the % computation of E (and E') times a vector is easy. In this case, our matrix % of interest is: % % E = A-L*U % % That is, L*U is the LU factorization of A, where A, L and U % are sparse. This code works for dense matrices A and L too, % but it would not be needed in that case, since E is easy to compute % explicitly. For sparse A, L, and U, computing E explicitly would be quite % expensive, and thus normest (A-L*U) would be prohibitive. % % For a detailed description, see Davis, T. A. and Hager, W. W., % Modifying a sparse Cholesky factorization, SIAM J. Matrix Analysis and % Applications, 1999, vol. 20, no. 3, 606-627. % % See also normest % The three places that the matrix-vector multiply E*x is used are highlighted. % Note that E is never formed explicity. % Copyright 1995-2007 by William W. Hager and Timothy A. Davis [m n] = size (A) ; if (m ~= n) % pad A, L, and U with zeros so that they are all square if (m < n) U = [ U ; (sparse (n-m,n)) ] ; L = [ L , (sparse (m,n-m)) ; (sparse (n-m,n)) ] ; A = [ A ; (sparse (n-m,n)) ] ; else U = [ U , (sparse (n,m-n)) ; (sparse (m-n,m)) ] ; L = [ L , (sparse (m,m-n)) ] ; A = [ A , (sparse (m,m-n)) ] ; end end [m n] = size (A) ; %#ok notvisited = ones (m, 1) ; % nonvisited(j) is zero if j is visited, 1 otherwise rho = 0 ; % the global rho for trial = 1:3 % { x = notvisited ./ sum (notvisited) ; rho1 = 0 ; % the current rho for this trial %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% COMPUTE Ex1 = E*x EFFICIENTLY: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Ex1 = (A*x) - L*(U*x) ; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% rho2 = norm (Ex1, 1) ; while rho2 > rho1 % { rho1 = rho2 ; y = 2*(Ex1 >= 0) - 1 ; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% COMPUTE z = E'*y EFFICIENTLY: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% z = (A'*y) - U'*(L'*y) ; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% [zj, j] = max (abs (z .* notvisited)) ; j = j (1) ; if (abs (z (j)) > z'*x) % { x = zeros (m, 1) ; x (j) = 1 ; notvisited (j) = 0 ; else % } { break ; end % } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% COMPUTE Ex1 = E*x EFFICIENTLY: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Ex1 = (A*x) - L*(U*x) ; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% rho2 = norm (Ex1, 1) ; end % } rho = max (rho, rho1) ; end % } SuiteSparse/UMFPACK/MATLAB/umfpackmex.c0000644001170100242450000011510310617241511016300 0ustar davisfac/* ========================================================================== */ /* === UMFPACK mexFunction ================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* MATLAB interface for umfpack. Factor or solve a sparse linear system, returning either the solution x to Ax=b or A'x'=b', or the factorization LU=P(R\A)Q or LU=PAQ. A must be sparse, with nonzero dimensions, but it may be complex, singular, and/or rectangular. b must be a dense n-by-1 vector (real or complex). L is unit lower triangular, U is upper triangular, and R is diagonal. P and Q are permutation matrices (permutations of an identity matrix). The matrix A is scaled, by default. Each row i is divided by r (i), where r (i) is the sum of the absolute values of the entries in that row. The scaled matrix has an infinity norm of 1. The scale factors r (i) are returned in a diagonal sparse matrix. If the factorization is: [L, U, P, Q, R] = umfpack (A) ; then the factorization is L*U = P * (R \ A) * Q This is safer than returning a matrix R such that L*U = P*R*A*Q, because it avoids the division by small entries. If r(i) is subnormal, multiplying by 1/r(i) would result in an IEEE Infinity, but dividing by r(i) is safe. The factorization [L, U, P, Q] = umfpack (A) ; returns LU factors such that L*U = P*A*Q, with no scaling. See umfpack.m, umfpack_details.m, and umfpack.h for details. Note that this mexFunction accesses only the user-callable UMFPACK routines. Thus, is also provides another example of how user C code can access UMFPACK. If NO_TRANSPOSE_FORWARD_SLASH is not defined at compile time, then the forward slash (/) operator acts almost like x = b/A in MATLAB 6.1. It is solved by factorizing the array transpose, and then x = (A.'\b.').' is solved. This is the default behavior (for historical reasons), since factorizing A can behave perform much differently than factorizing its transpose. If NO_TRANSPOSE_FORWARD_SLASH is defined at compile time, then the forward slash operator does not act like x=b/A in MATLAB 6.1. It is solved by factorizing A, and then solving via the transposed L and U matrices. The solution is still x = (A.'\b.').', except that A is factorized instead of A.'. Modified for v4.3.1, Jan 10, 2005: default has been changed to NO_TRANSPOSE_FORWARD_SLASH, to test iterative refinement for b/A. v4.4: added method for computing the determinant. v5.1: port to 64-bit MATLAB */ #define NO_TRANSPOSE_FORWARD_SLASH /* default has changed for v4.3.1 */ #include "UFconfig.h" #include "umfpack.h" #include "mex.h" #include "matrix.h" #include #include #include #define MIN(a,b) (((a) < (b)) ? (a) : (b)) #define MAX(a,b) (((a) > (b)) ? (a) : (b)) #define STRING_MATCH(s1,s2) (strcmp ((s1), (s2)) == 0) #ifndef TRUE #define TRUE (1) #endif #ifndef FALSE #define FALSE (0) #endif /* ========================================================================== */ /* === error ================================================================ */ /* ========================================================================== */ /* Return an error message */ static void error ( char *s, UF_long A_is_complex, int nargout, mxArray *pargout [ ], double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO], UF_long status, UF_long do_info ) { UF_long i ; double *Out_Info ; if (A_is_complex) { umfpack_zl_report_status (Control, status) ; umfpack_zl_report_info (Control, Info) ; } else { umfpack_dl_report_status (Control, status) ; umfpack_dl_report_info (Control, Info) ; } if (do_info > 0) { /* return Info */ pargout [do_info] = mxCreateDoubleMatrix (1, UMFPACK_INFO, mxREAL) ; Out_Info = mxGetPr (pargout [do_info]) ; for (i = 0 ; i < UMFPACK_INFO ; i++) { Out_Info [i] = Info [i] ; } } mexErrMsgTxt (s) ; } /* ========================================================================== */ /* === UMFPACK ============================================================== */ /* ========================================================================== */ void mexFunction ( int nargout, /* number of outputs */ mxArray *pargout [ ], /* output arguments */ int nargin, /* number of inputs */ const mxArray *pargin [ ] /* input arguments */ ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ double Info [UMFPACK_INFO], Control [UMFPACK_CONTROL], dx, dz, dexp ; double *Lx, *Lz, *Ux, *Uz, *Ax, *Az, *Bx, *Bz, *Xx, *Xz, *User_Control, *p, *q, *Out_Info, *p1, *p2, *p3, *p4, *Ltx, *Ltz, *Rs, *Px, *Qx ; void *Symbolic, *Numeric ; UF_long *Lp, *Li, *Up, *Ui, *Ap, *Ai, *P, *Q, do_solve, lnz, unz, nn, i, transpose, size, do_info, do_numeric, *Front_npivcol, op, k, *Rp, *Ri, *Front_parent, *Chain_start, *Chain_maxrows, *Chain_maxcols, nz, status, nfronts, nchains, *Ltp, *Ltj, *Qinit, print_level, status2, no_scale, *Front_1strow, *Front_leftmostdesc, n_row, n_col, n_inner, sys, ignore1, ignore2, ignore3, A_is_complex, B_is_complex, X_is_complex, *Pp, *Pi, *Qp, *Qi, do_recip, do_det ; mxArray *Amatrix, *Bmatrix, *User_Control_matrix, *User_Qinit ; char *operator, *operation ; mxComplexity Atype, Xtype ; char warning [200] ; #ifndef NO_TRANSPOSE_FORWARD_SLASH UF_long *Cp, *Ci ; double *Cx, *Cz ; #endif /* ---------------------------------------------------------------------- */ /* define the memory manager and printf functions for UMFPACK and AMD */ /* ---------------------------------------------------------------------- */ /* with these settings, the UMFPACK mexFunction can use ../Lib/libumfpack.a * and ../Lib/libamd.a, instead compiling UMFPACK and AMD specifically for * the MATLAB mexFunction. */ amd_malloc = mxMalloc ; amd_free = mxFree ; amd_calloc = mxCalloc ; amd_realloc = mxRealloc ; amd_printf = mexPrintf ; /* The default values for these function pointers are fine. umfpack_hypot = umf_hypot ; umfpack_divcomplex = umf_divcomplex ; */ /* ---------------------------------------------------------------------- */ /* get inputs A, b, and the operation to perform */ /* ---------------------------------------------------------------------- */ User_Control_matrix = (mxArray *) NULL ; User_Qinit = (mxArray *) NULL ; do_info = 0 ; do_solve = FALSE ; do_numeric = TRUE ; transpose = FALSE ; no_scale = FALSE ; do_det = FALSE ; /* find the operator */ op = 0 ; for (i = 0 ; i < nargin ; i++) { if (mxIsChar (pargin [i])) { op = i ; break ; } } if (op > 0) { operator = mxArrayToString (pargin [op]) ; if (STRING_MATCH (operator, "\\")) { /* -------------------------------------------------------------- */ /* matrix left divide, x = A\b */ /* -------------------------------------------------------------- */ /* [x, Info] = umfpack (A, '\', b) ; [x, Info] = umfpack (A, '\', b, Control) ; [x, Info] = umfpack (A, Qinit, '\', b, Control) ; [x, Info] = umfpack (A, Qinit, '\', b) ; */ operation = "x = A\\b" ; do_solve = TRUE ; Amatrix = (mxArray *) pargin [0] ; Bmatrix = (mxArray *) pargin [op+1] ; if (nargout == 2) { do_info = 1 ; } if (op == 2) { User_Qinit = (mxArray *) pargin [1] ; } if ((op == 1 && nargin == 4) || (op == 2 && nargin == 5)) { User_Control_matrix = (mxArray *) pargin [nargin-1] ; } if (nargin < 3 || nargin > 5 || nargout > 2) { mexErrMsgTxt ("wrong number of arguments") ; } } else if (STRING_MATCH (operator, "/")) { /* -------------------------------------------------------------- */ /* matrix right divide, x = b/A */ /* -------------------------------------------------------------- */ /* [x, Info] = umfpack (b, '/', A) ; [x, Info] = umfpack (b, '/', A, Control) ; [x, Info] = umfpack (b, '/', A, Qinit) ; [x, Info] = umfpack (b, '/', A, Qinit, Control) ; */ operation = "x = b/A" ; do_solve = TRUE ; transpose = TRUE ; Amatrix = (mxArray *) pargin [2] ; Bmatrix = (mxArray *) pargin [0] ; if (nargout == 2) { do_info = 1 ; } if (nargin == 5) { User_Qinit = (mxArray *) pargin [3] ; User_Control_matrix = (mxArray *) pargin [4] ; } else if (nargin == 4) { /* Control is k-by-1 where k > 1, Qinit is 1-by-n */ if (mxGetM (pargin [3]) == 1) { User_Qinit = (mxArray *) pargin [3] ; } else { User_Control_matrix = (mxArray *) pargin [3] ; } } else if (nargin < 3 || nargin > 5 || nargout > 2) { mexErrMsgTxt ("wrong number of arguments") ; } } else if (STRING_MATCH (operator, "symbolic")) { /* -------------------------------------------------------------- */ /* symbolic factorization only */ /* -------------------------------------------------------------- */ /* [P Q Fr Ch Info] = umfpack (A, 'symbolic') ; [P Q Fr Ch Info] = umfpack (A, 'symbolic', Control) ; [P Q Fr Ch Info] = umfpack (A, Qinit, 'symbolic') ; [P Q Fr Ch Info] = umfpack (A, Qinit, 'symbolic', Control) ; */ operation = "symbolic factorization" ; do_numeric = FALSE ; Amatrix = (mxArray *) pargin [0] ; if (nargout == 5) { do_info = 4 ; } if (op == 2) { User_Qinit = (mxArray *) pargin [1] ; } if ((op == 1 && nargin == 3) || (op == 2 && nargin == 4)) { User_Control_matrix = (mxArray *) pargin [nargin-1] ; } if (nargin < 2 || nargin > 4 || nargout > 5 || nargout < 4) { mexErrMsgTxt ("wrong number of arguments") ; } } else if (STRING_MATCH (operator, "det")) { /* -------------------------------------------------------------- */ /* compute the determinant */ /* -------------------------------------------------------------- */ /* * [det] = umfpack (A, 'det') ; * [dmantissa dexp] = umfpack (A, 'det') ; */ operation = "determinant" ; do_det = TRUE ; Amatrix = (mxArray *) pargin [0] ; if (nargin > 2 || nargout > 2) { mexErrMsgTxt ("wrong number of arguments") ; } } else { mexErrMsgTxt ("operator must be '/', '\\', or 'symbolic'") ; } mxFree (operator) ; } else if (nargin > 0) { /* ------------------------------------------------------------------ */ /* LU factorization */ /* ------------------------------------------------------------------ */ /* with scaling: [L, U, P, Q, R, Info] = umfpack (A) ; [L, U, P, Q, R, Info] = umfpack (A, Qinit) ; scaling determined by Control settings: [L, U, P, Q, R, Info] = umfpack (A, Control) ; [L, U, P, Q, R, Info] = umfpack (A, Qinit, Control) ; with no scaling: [L, U, P, Q] = umfpack (A) ; [L, U, P, Q] = umfpack (A, Control) ; [L, U, P, Q] = umfpack (A, Qinit) ; [L, U, P, Q] = umfpack (A, Qinit, Control) ; */ operation = "numeric factorization" ; Amatrix = (mxArray *) pargin [0] ; no_scale = nargout <= 4 ; if (nargout == 6) { do_info = 5 ; } if (nargin == 3) { User_Qinit = (mxArray *) pargin [1] ; User_Control_matrix = (mxArray *) pargin [2] ; } else if (nargin == 2) { /* Control is k-by-1 where k > 1, Qinit is 1-by-n */ if (mxGetM (pargin [1]) == 1) { User_Qinit = (mxArray *) pargin [1] ; } else { User_Control_matrix = (mxArray *) pargin [1] ; } } else if (nargin > 3 || nargout > 6 || nargout < 4) { mexErrMsgTxt ("wrong number of arguments") ; } } else { /* ------------------------------------------------------------------ */ /* return default control settings */ /* ------------------------------------------------------------------ */ /* Control = umfpack ; umfpack ; */ if (nargout > 1) { mexErrMsgTxt ("wrong number of arguments") ; } pargout [0] = mxCreateDoubleMatrix (UMFPACK_CONTROL, 1, mxREAL) ; User_Control = mxGetPr (pargout [0]) ; umfpack_dl_defaults (User_Control) ; return ; } /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ if (mxGetNumberOfDimensions (Amatrix) != 2) { mexErrMsgTxt ("input matrix A must be 2-dimensional") ; } n_row = mxGetM (Amatrix) ; n_col = mxGetN (Amatrix) ; nn = MAX (n_row, n_col) ; n_inner = MIN (n_row, n_col) ; if (do_solve && n_row != n_col) { mexErrMsgTxt ("input matrix A must square for '\\' or '/'") ; } if (!mxIsSparse (Amatrix)) { mexErrMsgTxt ("input matrix A must be sparse") ; } if (n_row == 0 || n_col == 0) { mexErrMsgTxt ("input matrix A cannot have zero rows or zero columns") ; } /* The real/complex status of A determines which version to use, */ /* (umfpack_dl_* or umfpack_zl_*). */ A_is_complex = mxIsComplex (Amatrix) ; Atype = A_is_complex ? mxCOMPLEX : mxREAL ; Ap = (UF_long *) mxGetJc (Amatrix) ; Ai = (UF_long *) mxGetIr (Amatrix) ; Ax = mxGetPr (Amatrix) ; Az = mxGetPi (Amatrix) ; if (do_solve) { if (n_row != n_col) { mexErrMsgTxt ("A must be square for \\ or /") ; } if (transpose) { if (mxGetM (Bmatrix) != 1 || mxGetN (Bmatrix) != nn) { mexErrMsgTxt ("b has the wrong dimensions") ; } } else { if (mxGetM (Bmatrix) != nn || mxGetN (Bmatrix) != 1) { mexErrMsgTxt ("b has the wrong dimensions") ; } } if (mxGetNumberOfDimensions (Bmatrix) != 2) { mexErrMsgTxt ("input matrix b must be 2-dimensional") ; } if (mxIsSparse (Bmatrix)) { mexErrMsgTxt ("input matrix b cannot be sparse") ; } if (mxGetClassID (Bmatrix) != mxDOUBLE_CLASS) { mexErrMsgTxt ("input matrix b must double precision matrix") ; } B_is_complex = mxIsComplex (Bmatrix) ; Bx = mxGetPr (Bmatrix) ; Bz = mxGetPi (Bmatrix) ; X_is_complex = A_is_complex || B_is_complex ; Xtype = X_is_complex ? mxCOMPLEX : mxREAL ; } /* ---------------------------------------------------------------------- */ /* set the Control parameters */ /* ---------------------------------------------------------------------- */ if (A_is_complex) { umfpack_zl_defaults (Control) ; } else { umfpack_dl_defaults (Control) ; } if (User_Control_matrix) { if (mxGetClassID (User_Control_matrix) != mxDOUBLE_CLASS || mxIsSparse (User_Control_matrix)) { mexErrMsgTxt ("Control must be a dense real matrix") ; } size = UMFPACK_CONTROL ; size = MIN (size, mxGetNumberOfElements (User_Control_matrix)) ; User_Control = mxGetPr (User_Control_matrix) ; for (i = 0 ; i < size ; i++) { Control [i] = User_Control [i] ; } } if (no_scale) { /* turn off scaling for [L, U, P, Q] = umfpack (A) ; * ignoring the input value of Control (24) for the usage * [L, U, P, Q] = umfpack (A, Control) ; */ Control [UMFPACK_SCALE] = UMFPACK_SCALE_NONE ; } if (mxIsNaN (Control [UMFPACK_PRL])) { print_level = UMFPACK_DEFAULT_PRL ; } else { print_level = (UF_long) Control [UMFPACK_PRL] ; } Control [UMFPACK_PRL] = print_level ; /* ---------------------------------------------------------------------- */ /* get Qinit, if present */ /* ---------------------------------------------------------------------- */ if (User_Qinit) { if (mxGetM (User_Qinit) != 1 || mxGetN (User_Qinit) != n_col) { mexErrMsgTxt ("Qinit must be 1-by-n_col") ; } if (mxGetNumberOfDimensions (User_Qinit) != 2) { mexErrMsgTxt ("input Qinit must be 2-dimensional") ; } if (mxIsComplex (User_Qinit)) { mexErrMsgTxt ("input Qinit must not be complex") ; } if (mxGetClassID (User_Qinit) != mxDOUBLE_CLASS) { mexErrMsgTxt ("input Qinit must be a double matrix") ; } if (mxIsSparse (User_Qinit)) { mexErrMsgTxt ("input Qinit must be dense") ; } Qinit = (UF_long *) mxMalloc (n_col * sizeof (UF_long)) ; p = mxGetPr (User_Qinit) ; for (k = 0 ; k < n_col ; k++) { /* convert from 1-based to 0-based indexing */ Qinit [k] = ((UF_long) (p [k])) - 1 ; } } else { /* umfpack_*_qsymbolic will call colamd to get Qinit. This is the */ /* same as calling umfpack_*_symbolic with Qinit set to NULL*/ Qinit = (UF_long *) NULL ; } /* ---------------------------------------------------------------------- */ /* report the inputs A and Qinit */ /* ---------------------------------------------------------------------- */ if (print_level >= 2) { /* print the operation */ mexPrintf ("\numfpack: %s\n", operation) ; } if (A_is_complex) { umfpack_zl_report_control (Control) ; if (print_level >= 3) mexPrintf ("\nA: ") ; (void) umfpack_zl_report_matrix (n_row, n_col, Ap, Ai, Ax, Az, 1, Control) ; if (Qinit) { if (print_level >= 3) mexPrintf ("\nQinit: ") ; (void) umfpack_zl_report_perm (n_col, Qinit, Control) ; } } else { umfpack_dl_report_control (Control) ; if (print_level >= 3) mexPrintf ("\nA: ") ; (void) umfpack_dl_report_matrix (n_row, n_col, Ap, Ai, Ax, 1, Control) ; if (Qinit) { if (print_level >= 3) mexPrintf ("\nQinit: ") ; (void) umfpack_dl_report_perm (n_col, Qinit, Control) ; } } #ifndef NO_TRANSPOSE_FORWARD_SLASH /* ---------------------------------------------------------------------- */ /* create the array transpose for x = b/A */ /* ---------------------------------------------------------------------- */ if (transpose) { /* note that in this case A will be square (nn = n_row = n_col) */ /* x = (A.'\b.').' will be computed */ /* make sure Ci and Cx exist, avoid malloc of zero-sized arrays. */ nz = MAX (Ap [nn], 1) ; Cp = (UF_long *) mxMalloc ((nn+1) * sizeof (UF_long)) ; Ci = (UF_long *) mxMalloc (nz * sizeof (UF_long)) ; Cx = (double *) mxMalloc (nz * sizeof (double)) ; if (A_is_complex) { Cz = (double *) mxMalloc (nz * sizeof (double)) ; status = umfpack_zl_transpose (nn, nn, Ap, Ai, Ax, Az, (UF_long *) NULL, (UF_long *) NULL, Cp, Ci, Cx, Cz, FALSE) ; } else { status = umfpack_dl_transpose (nn, nn, Ap, Ai, Ax, (UF_long *) NULL, (UF_long *) NULL, Cp, Ci, Cx) ; } if (status != UMFPACK_OK) { error ("transpose of A failed", A_is_complex, nargout, pargout, Control, Info, status, do_info); return ; } /* modify pointers so that C will be factorized and solved, not A */ Ap = Cp ; Ai = Ci ; Ax = Cx ; if (A_is_complex) { Az = Cz ; } } #endif /* ---------------------------------------------------------------------- */ /* perform the symbolic factorization */ /* ---------------------------------------------------------------------- */ if (A_is_complex) { status = umfpack_zl_qsymbolic (n_row, n_col, Ap, Ai, Ax, Az, Qinit, &Symbolic, Control, Info) ; } else { status = umfpack_dl_qsymbolic (n_row, n_col, Ap, Ai, Ax, Qinit, &Symbolic, Control, Info) ; } if (Qinit) { mxFree (Qinit) ; } if (status < 0) { error ("symbolic factorization failed", A_is_complex, nargout, pargout, Control, Info, status, do_info) ; return ; } /* ---------------------------------------------------------------------- */ /* report the Symbolic object */ /* ---------------------------------------------------------------------- */ if (A_is_complex) { (void) umfpack_zl_report_symbolic (Symbolic, Control) ; } else { (void) umfpack_dl_report_symbolic (Symbolic, Control) ; } /* ---------------------------------------------------------------------- */ /* perform numeric factorization, or just return symbolic factorization */ /* ---------------------------------------------------------------------- */ if (do_numeric) { /* ------------------------------------------------------------------ */ /* perform the numeric factorization */ /* ------------------------------------------------------------------ */ if (A_is_complex) { status = umfpack_zl_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric, Control, Info) ; } else { status = umfpack_dl_numeric (Ap, Ai, Ax, Symbolic, &Numeric, Control, Info) ; } /* ------------------------------------------------------------------ */ /* free the symbolic factorization */ /* ------------------------------------------------------------------ */ if (A_is_complex) { umfpack_zl_free_symbolic (&Symbolic) ; } else { umfpack_dl_free_symbolic (&Symbolic) ; } /* ------------------------------------------------------------------ */ /* report the Numeric object */ /* ------------------------------------------------------------------ */ if (status < 0) { error ("numeric factorization failed", A_is_complex, nargout, pargout, Control, Info, status, do_info); return ; } if (A_is_complex) { (void) umfpack_zl_report_numeric (Numeric, Control) ; } else { (void) umfpack_dl_report_numeric (Numeric, Control) ; } /* ------------------------------------------------------------------ */ /* return the solution, determinant, or the factorization */ /* ------------------------------------------------------------------ */ if (do_solve) { /* -------------------------------------------------------------- */ /* solve Ax=b or A'x'=b', and return just the solution x */ /* -------------------------------------------------------------- */ #ifndef NO_TRANSPOSE_FORWARD_SLASH if (transpose) { /* A.'x.'=b.' gives the same x=b/A as solving A'x'=b' */ /* since C=A.' was factorized, solve with sys = UMFPACK_A */ /* since x and b are vectors, x.' and b.' are implicit */ pargout [0] = mxCreateDoubleMatrix (1, nn, Xtype) ; } else { pargout [0] = mxCreateDoubleMatrix (nn, 1, Xtype) ; } sys = UMFPACK_A ; #else if (transpose) { /* If A is real, A'x=b is the same as A.'x=b. */ /* x and b are vectors, so x and b are the same as x' and b'. */ /* If A is complex, then A.'x.'=b.' gives the same solution x */ /* as the complex conjugate transpose. If we used the A'x=b */ /* option in umfpack_*_solve, we would have to form b' on */ /* input and x' on output (negating the imaginary part). */ /* We can save this work by just using the A.'x=b option in */ /* umfpack_*_solve. Then, forming x.' and b.' is implicit, */ /* since x and b are just vectors anyway. */ /* In both cases, the system to solve is A.'x=b */ pargout [0] = mxCreateDoubleMatrix (1, nn, Xtype) ; sys = UMFPACK_Aat ; } else { pargout [0] = mxCreateDoubleMatrix (nn, 1, Xtype) ; sys = UMFPACK_A ; } #endif /* -------------------------------------------------------------- */ /* print the right-hand-side, B */ /* -------------------------------------------------------------- */ if (print_level >= 3) mexPrintf ("\nright-hand side, b: ") ; if (B_is_complex) { (void) umfpack_zl_report_vector (nn, Bx, Bz, Control) ; } else { (void) umfpack_dl_report_vector (nn, Bx, Control) ; } /* -------------------------------------------------------------- */ /* solve the system */ /* -------------------------------------------------------------- */ Xx = mxGetPr (pargout [0]) ; Xz = mxGetPi (pargout [0]) ; status2 = UMFPACK_OK ; if (A_is_complex) { if (!B_is_complex) { /* umfpack_zl_solve expects a complex B */ Bz = (double *) mxCalloc (nn, sizeof (double)) ; } status = umfpack_zl_solve (sys, Ap, Ai, Ax, Az, Xx, Xz, Bx, Bz, Numeric, Control, Info) ; if (!B_is_complex) { mxFree (Bz) ; } } else { if (B_is_complex) { /* Ax=b when b is complex and A is sparse can be split */ /* into two systems, A*xr=br and A*xi=bi, where r denotes */ /* the real part and i the imaginary part of x and b. */ status2 = umfpack_dl_solve (sys, Ap, Ai, Ax, Xz, Bz, Numeric, Control, Info) ; } status = umfpack_dl_solve (sys, Ap, Ai, Ax, Xx, Bx, Numeric, Control, Info) ; } #ifndef NO_TRANSPOSE_FORWARD_SLASH /* -------------------------------------------------------------- */ /* free the transposed matrix C */ /* -------------------------------------------------------------- */ if (transpose) { mxFree (Cp) ; mxFree (Ci) ; mxFree (Cx) ; if (A_is_complex) { mxFree (Cz) ; } } #endif /* -------------------------------------------------------------- */ /* free the Numeric object */ /* -------------------------------------------------------------- */ if (A_is_complex) { umfpack_zl_free_numeric (&Numeric) ; } else { umfpack_dl_free_numeric (&Numeric) ; } /* -------------------------------------------------------------- */ /* check error status */ /* -------------------------------------------------------------- */ if (status < 0 || status2 < 0) { mxDestroyArray (pargout [0]) ; error ("solve failed", A_is_complex, nargout, pargout, Control, Info, status, do_info) ; return ; } /* -------------------------------------------------------------- */ /* print the solution, X */ /* -------------------------------------------------------------- */ if (print_level >= 3) mexPrintf ("\nsolution, x: ") ; if (X_is_complex) { (void) umfpack_zl_report_vector (nn, Xx, Xz, Control) ; } else { (void) umfpack_dl_report_vector (nn, Xx, Control) ; } /* -------------------------------------------------------------- */ /* warn about singular or near-singular matrices */ /* -------------------------------------------------------------- */ /* no warning is given if Control (1) is zero */ if (Control [UMFPACK_PRL] >= 1) { if (status == UMFPACK_WARNING_singular_matrix) { sprintf (warning, "matrix is singular\n" "Try increasing Control (%d) and Control (%d).\n" "(Suppress this warning with Control (%d) = 0.)\n", 1+UMFPACK_PIVOT_TOLERANCE, 1+UMFPACK_SYM_PIVOT_TOLERANCE, 1+UMFPACK_PRL) ; mexWarnMsgTxt (warning) ; } else if (Info [UMFPACK_RCOND] < DBL_EPSILON) { sprintf (warning, "matrix is nearly singular, rcond = %g\n" "Try increasing Control (%d) and Control (%d).\n" "(Suppress this warning with Control (%d) = 0.)\n", Info [UMFPACK_RCOND], 1+UMFPACK_PIVOT_TOLERANCE, 1+UMFPACK_SYM_PIVOT_TOLERANCE, 1+UMFPACK_PRL) ; mexWarnMsgTxt (warning) ; } } } else if (do_det) { /* -------------------------------------------------------------- */ /* get the determinant */ /* -------------------------------------------------------------- */ if (nargout == 2) { /* [det dexp] = umfpack (A, 'det') ; * return determinant in the form det * 10^dexp */ p = &dexp ; } else { /* [det] = umfpack (A, 'det') ; * return determinant as a single scalar (overflow or * underflow is much more likely) */ p = (double *) NULL ; } if (A_is_complex) { status = umfpack_zl_get_determinant (&dx, &dz, p, Numeric, Info) ; umfpack_zl_free_numeric (&Numeric) ; } else { status = umfpack_dl_get_determinant (&dx, p, Numeric, Info) ; umfpack_dl_free_numeric (&Numeric) ; dz = 0 ; } if (status < 0) { error ("extracting LU factors failed", A_is_complex, nargout, pargout, Control, Info, status, do_info) ; } if (A_is_complex) { pargout [0] = mxCreateDoubleMatrix (1, 1, mxCOMPLEX) ; p = mxGetPr (pargout [0]) ; *p = dx ; p = mxGetPi (pargout [0]) ; *p = dz ; } else { pargout [0] = mxCreateDoubleMatrix (1, 1, mxREAL) ; p = mxGetPr (pargout [0]) ; *p = dx ; } if (nargout == 2) { pargout [1] = mxCreateDoubleMatrix (1, 1, mxREAL) ; p = mxGetPr (pargout [1]) ; *p = dexp ; } } else { /* -------------------------------------------------------------- */ /* get L, U, P, Q, and r */ /* -------------------------------------------------------------- */ if (A_is_complex) { status = umfpack_zl_get_lunz (&lnz, &unz, &ignore1, &ignore2, &ignore3, Numeric) ; } else { status = umfpack_dl_get_lunz (&lnz, &unz, &ignore1, &ignore2, &ignore3, Numeric) ; } if (status < 0) { if (A_is_complex) { umfpack_zl_free_numeric (&Numeric) ; } else { umfpack_dl_free_numeric (&Numeric) ; } error ("extracting LU factors failed", A_is_complex, nargout, pargout, Control, Info, status, do_info) ; return ; } /* avoid malloc of zero-sized arrays */ lnz = MAX (lnz, 1) ; unz = MAX (unz, 1) ; /* get temporary space, for the *** ROW *** form of L */ Ltp = (UF_long *) mxMalloc ((n_row+1) * sizeof (UF_long)) ; Ltj = (UF_long *) mxMalloc (lnz * sizeof (UF_long)) ; Ltx = (double *) mxMalloc (lnz * sizeof (double)) ; if (A_is_complex) { Ltz = (double *) mxMalloc (lnz * sizeof (double)) ; } else { Ltz = (double *) NULL ; } /* create permanent copy of the output matrix U */ pargout [1] = mxCreateSparse (n_inner, n_col, unz, Atype) ; Up = (UF_long *) mxGetJc (pargout [1]) ; Ui = (UF_long *) mxGetIr (pargout [1]) ; Ux = mxGetPr (pargout [1]) ; Uz = mxGetPi (pargout [1]) ; /* temporary space for the integer permutation vectors */ P = (UF_long *) mxMalloc (n_row * sizeof (UF_long)) ; Q = (UF_long *) mxMalloc (n_col * sizeof (UF_long)) ; /* get scale factors, if requested */ status2 = UMFPACK_OK ; if (!no_scale) { /* create a diagonal sparse matrix for the scale factors */ pargout [4] = mxCreateSparse (n_row, n_row, n_row, mxREAL) ; Rp = (UF_long *) mxGetJc (pargout [4]) ; Ri = (UF_long *) mxGetIr (pargout [4]) ; for (i = 0 ; i < n_row ; i++) { Rp [i] = i ; Ri [i] = i ; } Rp [n_row] = n_row ; Rs = mxGetPr (pargout [4]) ; } else { Rs = (double *) NULL ; } /* get Lt, U, P, Q, and Rs from the numeric object */ if (A_is_complex) { status = umfpack_zl_get_numeric (Ltp, Ltj, Ltx, Ltz, Up, Ui, Ux, Uz, P, Q, (double *) NULL, (double *) NULL, &do_recip, Rs, Numeric) ; umfpack_zl_free_numeric (&Numeric) ; } else { status = umfpack_dl_get_numeric (Ltp, Ltj, Ltx, Up, Ui, Ux, P, Q, (double *) NULL, &do_recip, Rs, Numeric) ; umfpack_dl_free_numeric (&Numeric) ; } /* for the mexFunction, -DNRECIPROCAL must be set, * so do_recip must be FALSE */ if (status < 0 || status2 < 0 || do_recip) { mxFree (Ltp) ; mxFree (Ltj) ; mxFree (Ltx) ; if (Ltz) mxFree (Ltz) ; mxFree (P) ; mxFree (Q) ; mxDestroyArray (pargout [1]) ; error ("extracting LU factors failed", A_is_complex, nargout, pargout, Control, Info, status, do_info) ; return ; } /* create sparse permutation matrix for P */ pargout [2] = mxCreateSparse (n_row, n_row, n_row, mxREAL) ; Pp = (UF_long *) mxGetJc (pargout [2]) ; Pi = (UF_long *) mxGetIr (pargout [2]) ; Px = mxGetPr (pargout [2]) ; for (k = 0 ; k < n_row ; k++) { Pp [k] = k ; Px [k] = 1 ; Pi [P [k]] = k ; } Pp [n_row] = n_row ; /* create sparse permutation matrix for Q */ pargout [3] = mxCreateSparse (n_col, n_col, n_col, mxREAL) ; Qp = (UF_long *) mxGetJc (pargout [3]) ; Qi = (UF_long *) mxGetIr (pargout [3]) ; Qx = mxGetPr (pargout [3]) ; for (k = 0 ; k < n_col ; k++) { Qp [k] = k ; Qx [k] = 1 ; Qi [k] = Q [k] ; } Qp [n_col] = n_col ; /* permanent copy of L */ pargout [0] = mxCreateSparse (n_row, n_inner, lnz, Atype) ; Lp = (UF_long *) mxGetJc (pargout [0]) ; Li = (UF_long *) mxGetIr (pargout [0]) ; Lx = mxGetPr (pargout [0]) ; Lz = mxGetPi (pargout [0]) ; /* convert L from row form to column form */ if (A_is_complex) { /* non-conjugate array transpose */ status = umfpack_zl_transpose (n_inner, n_row, Ltp, Ltj, Ltx, Ltz, (UF_long *) NULL, (UF_long *) NULL, Lp, Li, Lx, Lz, FALSE) ; } else { status = umfpack_dl_transpose (n_inner, n_row, Ltp, Ltj, Ltx, (UF_long *) NULL, (UF_long *) NULL, Lp, Li, Lx) ; } mxFree (Ltp) ; mxFree (Ltj) ; mxFree (Ltx) ; if (Ltz) mxFree (Ltz) ; if (status < 0) { mxFree (P) ; mxFree (Q) ; mxDestroyArray (pargout [0]) ; mxDestroyArray (pargout [1]) ; mxDestroyArray (pargout [2]) ; mxDestroyArray (pargout [3]) ; error ("constructing L failed", A_is_complex, nargout, pargout, Control, Info, status, do_info) ; return ; } /* -------------------------------------------------------------- */ /* print L, U, P, and Q */ /* -------------------------------------------------------------- */ if (A_is_complex) { if (print_level >= 3) mexPrintf ("\nL: ") ; (void) umfpack_zl_report_matrix (n_row, n_inner, Lp, Li, Lx, Lz, 1, Control) ; if (print_level >= 3) mexPrintf ("\nU: ") ; (void) umfpack_zl_report_matrix (n_inner, n_col, Up, Ui, Ux, Uz, 1, Control) ; if (print_level >= 3) mexPrintf ("\nP: ") ; (void) umfpack_zl_report_perm (n_row, P, Control) ; if (print_level >= 3) mexPrintf ("\nQ: ") ; (void) umfpack_zl_report_perm (n_col, Q, Control) ; } else { if (print_level >= 3) mexPrintf ("\nL: ") ; (void) umfpack_dl_report_matrix (n_row, n_inner, Lp, Li, Lx, 1, Control) ; if (print_level >= 3) mexPrintf ("\nU: ") ; (void) umfpack_dl_report_matrix (n_inner, n_col, Up, Ui, Ux, 1, Control) ; if (print_level >= 3) mexPrintf ("\nP: ") ; (void) umfpack_dl_report_perm (n_row, P, Control) ; if (print_level >= 3) mexPrintf ("\nQ: ") ; (void) umfpack_dl_report_perm (n_col, Q, Control) ; } mxFree (P) ; mxFree (Q) ; } } else { /* ------------------------------------------------------------------ */ /* return the symbolic factorization */ /* ------------------------------------------------------------------ */ Q = (UF_long *) mxMalloc (n_col * sizeof (UF_long)) ; P = (UF_long *) mxMalloc (n_row * sizeof (UF_long)) ; Front_npivcol = (UF_long *) mxMalloc ((nn+1) * sizeof (UF_long)) ; Front_parent = (UF_long *) mxMalloc ((nn+1) * sizeof (UF_long)) ; Front_1strow = (UF_long *) mxMalloc ((nn+1) * sizeof (UF_long)) ; Front_leftmostdesc = (UF_long *) mxMalloc ((nn+1) * sizeof (UF_long)) ; Chain_start = (UF_long *) mxMalloc ((nn+1) * sizeof (UF_long)) ; Chain_maxrows = (UF_long *) mxMalloc ((nn+1) * sizeof (UF_long)) ; Chain_maxcols = (UF_long *) mxMalloc ((nn+1) * sizeof (UF_long)) ; if (A_is_complex) { status = umfpack_zl_get_symbolic (&ignore1, &ignore2, &ignore3, &nz, &nfronts, &nchains, P, Q, Front_npivcol, Front_parent, Front_1strow, Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ; umfpack_zl_free_symbolic (&Symbolic) ; } else { status = umfpack_dl_get_symbolic (&ignore1, &ignore2, &ignore3, &nz, &nfronts, &nchains, P, Q, Front_npivcol, Front_parent, Front_1strow, Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ; umfpack_dl_free_symbolic (&Symbolic) ; } if (status < 0) { mxFree (P) ; mxFree (Q) ; mxFree (Front_npivcol) ; mxFree (Front_parent) ; mxFree (Front_1strow) ; mxFree (Front_leftmostdesc) ; mxFree (Chain_start) ; mxFree (Chain_maxrows) ; mxFree (Chain_maxcols) ; error ("extracting symbolic factors failed", A_is_complex, nargout, pargout, Control, Info, status, do_info) ; return ; } /* create sparse permutation matrix for P */ pargout [0] = mxCreateSparse (n_row, n_row, n_row, mxREAL) ; Pp = (UF_long *) mxGetJc (pargout [0]) ; Pi = (UF_long *) mxGetIr (pargout [0]) ; Px = mxGetPr (pargout [0]) ; for (k = 0 ; k < n_row ; k++) { Pp [k] = k ; Px [k] = 1 ; Pi [P [k]] = k ; } Pp [n_row] = n_row ; /* create sparse permutation matrix for Q */ pargout [1] = mxCreateSparse (n_col, n_col, n_col, mxREAL) ; Qp = (UF_long *) mxGetJc (pargout [1]) ; Qi = (UF_long *) mxGetIr (pargout [1]) ; Qx = mxGetPr (pargout [1]) ; for (k = 0 ; k < n_col ; k++) { Qp [k] = k ; Qx [k] = 1 ; Qi [k] = Q [k] ; } Qp [n_col] = n_col ; /* create Fr */ pargout [2] = mxCreateDoubleMatrix (nfronts+1, 4, mxREAL) ; p1 = mxGetPr (pargout [2]) ; p2 = p1 + nfronts + 1 ; p3 = p2 + nfronts + 1 ; p4 = p3 + nfronts + 1 ; for (i = 0 ; i <= nfronts ; i++) { /* convert parent, 1strow, and leftmostdesc to 1-based */ p1 [i] = (double) (Front_npivcol [i]) ; p2 [i] = (double) (Front_parent [i] + 1) ; p3 [i] = (double) (Front_1strow [i] + 1) ; p4 [i] = (double) (Front_leftmostdesc [i] + 1) ; } /* create Ch */ pargout [3] = mxCreateDoubleMatrix (nchains+1, 3, mxREAL) ; p1 = mxGetPr (pargout [3]) ; p2 = p1 + nchains + 1 ; p3 = p2 + nchains + 1 ; for (i = 0 ; i < nchains ; i++) { p1 [i] = (double) (Chain_start [i] + 1) ; /* convert to 1-based */ p2 [i] = (double) (Chain_maxrows [i]) ; p3 [i] = (double) (Chain_maxcols [i]) ; } p1 [nchains] = Chain_start [nchains] + 1 ; p2 [nchains] = 0 ; p3 [nchains] = 0 ; mxFree (P) ; mxFree (Q) ; mxFree (Front_npivcol) ; mxFree (Front_parent) ; mxFree (Front_1strow) ; mxFree (Front_leftmostdesc) ; mxFree (Chain_start) ; mxFree (Chain_maxrows) ; mxFree (Chain_maxcols) ; } /* ---------------------------------------------------------------------- */ /* report Info */ /* ---------------------------------------------------------------------- */ if (A_is_complex) { umfpack_zl_report_info (Control, Info) ; } else { umfpack_dl_report_info (Control, Info) ; } if (do_info > 0) { /* return Info */ pargout [do_info] = mxCreateDoubleMatrix (1, UMFPACK_INFO, mxREAL) ; Out_Info = mxGetPr (pargout [do_info]) ; for (i = 0 ; i < UMFPACK_INFO ; i++) { Out_Info [i] = Info [i] ; } } } SuiteSparse/UMFPACK/MATLAB/luflop.m0000644001170100242450000000145510620402005015446 0ustar davisfacfunction f = luflop (L, U) %#ok %LUFLOP given L and U, computes # of flops required to compute them % % Example: % f = luflop (L, U) % % Given an LU factorization, compute how many flops took to compute it. This % is the same as (assuming U has a zero-free diagonal): % % Lnz = full (sum (spones (L))) - 1 ; % Unz = full (sum (spones (U')))' - 1 ; % f = 2*Lnz*Unz + sum (Lnz) ; % % except that no extra workspace is allocated for spones (L) and spones (U). % L and U must be sparse. % % Note: the above expression has a subtle undercount when exact numerical % cancelation occurs. Try [L,U,P] = lu (sparse (ones (10))) and then % luflop (L,U). % % See also LU % Copyright 1995-2007 by Timothy A. Davis. help luflop error ('luflop mexFunction not found! Use umfpack_make to compile luflop.') ; SuiteSparse/UMFPACK/MATLAB/umfpack_btf.m0000644001170100242450000001105310711673060016435 0ustar davisfacfunction [x, info] = umfpack_btf (A, b, Control) %UMFPACK_BTF factorize A using a block triangular form % % Example: % x = umfpack_btf (A, b, Control) % % solve Ax=b by first permuting the matrix A to block triangular form via dmperm % and then using UMFPACK to factorize each diagonal block. Adjacent 1-by-1 % blocks are merged into a single upper triangular block, and solved via % MATLAB's \ operator. The Control parameter is optional (Type umfpack_details % and umfpack_report for details on its use). A must be square. % % See also umfpack, umfpack2, umfpack_details, dmperm % Copyright 1995-2007 by Timothy A. Davis. if (nargin < 2) help umfpack_btf error ('Usage: x = umfpack_btf (A, b, Control)') ; end [m n] = size (A) ; if (m ~= n) help umfpack_btf error ('umfpack_btf: A must be square') ; end m1 = size (b,1) ; if (m1 ~= n) help umfpack_btf error ('umfpack_btf: b has the wrong dimensions') ; end if (nargin < 3) Control = umfpack2 ; end %------------------------------------------------------------------------------- % find the block triangular form %------------------------------------------------------------------------------- % dmperm built-in may segfault in MATLAB 7.4 or earlier; fixed in MATLAB 7.5 % since dmperm now uses CSparse [p,q,r] = dmperm (A) ; nblocks = length (r) - 1 ; info = [0 0 0] ; % [nnz(L), nnz(U), nnz(F)], optional 2nd output %------------------------------------------------------------------------------- % solve the system %------------------------------------------------------------------------------- if (nblocks == 1 | sprank (A) < n) %#ok %--------------------------------------------------------------------------- % matrix is irreducible or structurally singular %--------------------------------------------------------------------------- [x info2] = umfpack2 (A, '\', b, Control) ; info = [info2(78) info2(79) 0] ; else %--------------------------------------------------------------------------- % A (p,q) is in block triangular form %--------------------------------------------------------------------------- b = b (p,:) ; A = A (p,q) ; x = zeros (size (b)) ; %--------------------------------------------------------------------------- % merge adjacent singletons into a single upper triangular block %--------------------------------------------------------------------------- [r, nblocks, is_triangular] = merge_singletons (r) ; %--------------------------------------------------------------------------- % solve the system: x (q) = A\b %--------------------------------------------------------------------------- for k = nblocks:-1:1 % get the kth block k1 = r (k) ; k2 = r (k+1) - 1 ; % solve the system [x2 info2] = solver (A (k1:k2, k1:k2), b (k1:k2,:), ... is_triangular (k), Control) ; x (k1:k2,:) = x2 ; % off-diagonal block back substitution F2 = A (1:k1-1, k1:k2) ; b (1:k1-1,:) = b (1:k1-1,:) - F2 * x (k1:k2,:) ; info (1:2) = info (1:2) + info2 (1:2) ; info (3) = info (3) + nnz (F2) ; end x (q,:) = x ; end %------------------------------------------------------------------------------- % merge_singletons %------------------------------------------------------------------------------- function [r, nblocks, is_triangular] = merge_singletons (r) % % Given r from [p,q,r] = dmperm (A), where A is square, return a modified r that % reflects the merger of adjacent singletons into a single upper triangular % block. is_triangular (k) is 1 if the kth block is upper triangular. nblocks % is the number of new blocks. nblocks = length (r) - 1 ; bsize = r (2:nblocks+1) - r (1:nblocks) ; t = [0 (bsize == 1)] ; z = (t (1:nblocks) == 0 & t (2:nblocks+1) == 1) | t (2:nblocks+1) == 0 ; y = [(find (z)) nblocks+1] ; r = r (y) ; nblocks = length (y) - 1 ; is_triangular = y (2:nblocks+1) - y (1:nblocks) > 1 ; %------------------------------------------------------------------------------- % solve Ax=b, but check for small and/or triangular systems %------------------------------------------------------------------------------- function [x, info] = solver (A, b, is_triangular, Control) if (is_triangular) % back substitution only x = A \ b ; info = [nnz(A) 0 0] ; elseif (size (A,1) < 4) % a very small matrix, solve it as a dense linear system x = full (A) \ b ; n = size (A,1) ; info = [(n^2+n)/2 (n^2+n)/2 0] ; else % solve it as a sparse linear system [x info] = umfpack_solve (A, '\', b, Control) ; end SuiteSparse/UMFPACK/MATLAB/umfpack_simple.m.out0000644001170100242450000000203310711435546017764 0ustar davisfacumfpack_simple UMFPACK_SIMPLE a simple demo Example: umfpack_simple Copyright 1995-2007 by Timothy A. Davis. UMFPACK License: Your use or distribution of UMFPACK or any modified version of UMFPACK implies that you agree to this License. UMFPACK is is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. A = 2 3 0 0 0 3 0 4 0 6 0 -1 -3 2 0 0 0 1 0 0 0 4 2 0 1 b = 8 45 -3 3 19 Solution to Ax=b via UMFPACK: x1 = umfpack2 (A, '\', b) x1 = 1.0000 2.0000 3.0000 4.0000 5.0000 Solution to Ax=b via MATLAB: x2 = A\b x2 = 1.0000 2.0000 3.0000 4.0000 5.0000 norm (x1-x2) should be small: 1.28037e-15 Type 'umfpack_demo' for a full demo of UMFPACK diary off SuiteSparse/UMFPACK/MATLAB/GNUmakefile0000644001170100242450000002003710617241612016051 0ustar davisfac#------------------------------------------------------------------------------- # UMFPACK GNUmakefile for the UMFPACK MATLAB mexFunction (GNU "make" only) #------------------------------------------------------------------------------- default: umfpack2 luflop include ../../UFconfig/UFconfig.mk I = -I../Include -I../Source -I../../AMD/Include -I../../UFconfig MX = $(MEX) $(I) #------------------------------------------------------------------------------- # source files #------------------------------------------------------------------------------- # non-user-callable umf_*.[ch] files: UMFCH = umf_assemble umf_blas3_update \ umf_build_tuples umf_create_element \ umf_dump umf_extend_front umf_garbage_collection \ umf_get_memory umf_init_front umf_kernel \ umf_kernel_init umf_kernel_wrapup \ umf_local_search umf_lsolve umf_ltsolve \ umf_mem_alloc_element umf_mem_alloc_head_block \ umf_mem_alloc_tail_block umf_mem_free_tail_block \ umf_mem_init_memoryspace \ umf_report_vector umf_row_search umf_scale_column \ umf_set_stats umf_solve umf_symbolic_usage umf_transpose \ umf_tuple_lengths umf_usolve umf_utsolve umf_valid_numeric \ umf_valid_symbolic umf_grow_front umf_start_front umf_2by2 \ umf_store_lu umf_scale # non-user-callable umf_*.[ch] files, int/UF_long versions only (no real/complex): UMFINT = umf_analyze umf_apply_order umf_colamd umf_free umf_fsize \ umf_is_permutation umf_malloc umf_realloc umf_report_perm \ umf_singletons # non-user-callable and user-callable amd_*.[ch] files (int/UF_long versions only): AMD = amd_aat amd_1 amd_2 amd_dump amd_postorder amd_post_tree amd_defaults \ amd_order amd_control amd_info amd_valid amd_preprocess amd_global # non-user-callable, created from umf_ltsolve.c, umf_utsolve.c, # umf_triplet.c, and umf_assemble.c , with int/UF_long and real/complex versions: UMF_CREATED = umf_lhsolve umf_uhsolve umf_triplet_map_nox \ umf_triplet_nomap_x umf_triplet_nomap_nox umf_triplet_map_x \ umf_assemble_fixq umf_store_lu_drop # non-user-callable, int/UF_long and real/complex versions: UMF = $(UMF_CREATED) $(UMFCH) # user-callable umfpack_*.[ch] files (int/UF_long and real/complex): UMFPACK = umfpack_col_to_triplet umfpack_defaults umfpack_free_numeric \ umfpack_free_symbolic umfpack_get_numeric umfpack_get_lunz \ umfpack_get_symbolic umfpack_get_determinant umfpack_numeric \ umfpack_qsymbolic umfpack_report_control umfpack_report_info \ umfpack_report_matrix umfpack_report_numeric umfpack_report_perm \ umfpack_report_status umfpack_report_symbolic umfpack_report_triplet \ umfpack_report_vector umfpack_solve umfpack_symbolic \ umfpack_transpose umfpack_triplet_to_col umfpack_scale \ umfpack_load_numeric umfpack_save_numeric \ umfpack_load_symbolic umfpack_save_symbolic # user-callable, created from umfpack_solve.c (umfpack_wsolve.h exists, though): # with int/UF_long and real/complex versions: UMFPACKW = umfpack_wsolve USER = $(UMFPACKW) $(UMFPACK) # user-callable, only one version for int/UF_long, real/complex, *.[ch] files: GENERIC = umfpack_timer umfpack_tictoc umfpack_global #------------------------------------------------------------------------------- # include files: #------------------------------------------------------------------------------- AMDH = ../../AMD/Include/amd_internal.h ../../AMD/Include/amd.h \ ../../UFconfig/UFconfig.h INC1 = umf_config.h umf_version.h umf_internal.h umf_triplet.h INC = ../Include/umfpack.h \ $(addprefix ../Source/, $(INC1)) \ $(addprefix ../Source/, $(addsuffix .h,$(UMFCH))) \ $(addprefix ../Source/, $(addsuffix .h,$(UMFINT))) \ $(addprefix ../Include/, $(addsuffix .h,$(USER))) \ $(addprefix ../Include/, $(addsuffix .h,$(GENERIC))) \ $(AMDH) #------------------------------------------------------------------------------- # Create the umfpack and amd mexFunctions for MATLAB (int versions only) #------------------------------------------------------------------------------- MEXI = $(addsuffix .o, $(subst umf_,umf_m_,$(UMFINT))) MEXDI = $(addsuffix .o, $(subst umf_,umf_md_,$(UMF)) $(subst umfpack_,umfpack_md_,$(USER))) MEXZI = $(addsuffix .o, $(subst umf_,umf_mz_,$(UMF)) $(subst umfpack_,umfpack_mz_,$(USER)) ) MEXAMD = $(addsuffix .o, $(subst amd_,amd_m_,$(AMD))) MEXGN = $(addsuffix .o, $(subst umfpack_,umfpack_m_,$(GENERIC))) MEXUMFPACK = $(MEXI) $(MEXDI) $(MEXZI) $(MEXGN) # Note that mex has no "-o" option, thus the need for $(MV) commands. # If it did, then the rules would be much simpler: # $(MX) -DDLONG -c $< -o $@ #---------------------------------------- # integer-only routines (no real/complex): #---------------------------------------- amd_m_%.o: ../../AMD/Source/amd_%.c $(AMDH) $(MX) -DDLONG -c $< - $(MV) amd_$*.o $@ umf_m_%.o: ../Source/umf_%.c $(INC) $(MX) -DDLONG -c $< - $(MV) umf_$*.o $@ #---------------------------------------- # Double precision, int version, for MATLAB #---------------------------------------- umf_md_%.o: ../Source/umf_%.c $(INC) $(MX) -DDLONG -c $< - $(MV) umf_$*.o $@ umf_md_%hsolve.o: ../Source/umf_%tsolve.c $(INC) $(MX) -DDLONG -DCONJUGATE_SOLVE -c $< - $(MV) umf_$*tsolve.o $@ umf_md_triplet_map_x.o: ../Source/umf_triplet.c $(INC) $(MX) -DDLONG -DDO_MAP -DDO_VALUES -c $< - $(MV) umf_triplet.o $@ umf_md_triplet_map_nox.o: ../Source/umf_triplet.c $(INC) $(MX) -DDLONG -DDO_MAP -c $< - $(MV) umf_triplet.o $@ umf_md_triplet_nomap_x.o: ../Source/umf_triplet.c $(INC) $(MX) -DDLONG -DDO_VALUES -c $< - $(MV) umf_triplet.o $@ umf_md_triplet_nomap_nox.o: ../Source/umf_triplet.c $(INC) $(MX) -DDLONG -c $< - $(MV) umf_triplet.o $@ umf_md_assemble_fixq.o: ../Source/umf_assemble.c $(INC) $(MX) -DDLONG -DFIXQ -c $< - $(MV) umf_assemble.o $@ umf_md_store_lu_drop.o: ../Source/umf_store_lu.c $(INC) $(MX) -DDLONG -DDROP -c $< - $(MV) umf_store_lu.o $@ umfpack_md_wsolve.o: ../Source/umfpack_solve.c $(INC) $(MX) -DDLONG -DWSOLVE -c $< - $(MV) umfpack_solve.o $@ umfpack_md_%.o: ../Source/umfpack_%.c $(INC) $(MX) -DDLONG -c $< - $(MV) umfpack_$*.o $@ #---------------------------------------- # Complex double precision, int version, for MATLAB #---------------------------------------- umf_mz_%.o: ../Source/umf_%.c $(INC) $(MX) -DZLONG -c $< - $(MV) umf_$*.o $@ umf_mz_%hsolve.o: ../Source/umf_%tsolve.c $(INC) $(MX) -DZLONG -DCONJUGATE_SOLVE -c $< - $(MV) umf_$*tsolve.o $@ umf_mz_triplet_map_x.o: ../Source/umf_triplet.c $(INC) $(MX) -DZLONG -DDO_MAP -DDO_VALUES -c $< - $(MV) umf_triplet.o $@ umf_mz_triplet_map_nox.o: ../Source/umf_triplet.c $(INC) $(MX) -DZLONG -DDO_MAP -c $< - $(MV) umf_triplet.o $@ umf_mz_triplet_nomap_x.o: ../Source/umf_triplet.c $(INC) $(MX) -DZLONG -DDO_VALUES -c $< - $(MV) umf_triplet.o $@ umf_mz_triplet_nomap_nox.o: ../Source/umf_triplet.c $(INC) $(MX) -DZLONG -c $< - $(MV) umf_triplet.o $@ umf_mz_assemble_fixq.o: ../Source/umf_assemble.c $(INC) $(MX) -DZLONG -DFIXQ -c $< - $(MV) umf_assemble.o $@ umf_mz_store_lu_drop.o: ../Source/umf_store_lu.c $(INC) $(MX) -DZLONG -DDROP -c $< - $(MV) umf_store_lu.o $@ umfpack_mz_wsolve.o: ../Source/umfpack_solve.c $(INC) $(MX) -DZLONG -DWSOLVE -c $< - $(MV) umfpack_solve.o $@ umfpack_mz_%.o: ../Source/umfpack_%.c $(INC) $(MX) -DZLONG -c $< - $(MV) umfpack_$*.o $@ #---------------------------------------- # Generic routines for MATLAB #---------------------------------------- umfpack_m_timer.o: ../Source/umfpack_timer.c $(INC) $(MX) -c $< - $(MV) umfpack_timer.o $@ umfpack_m_tictoc.o: ../Source/umfpack_tictoc.c $(INC) $(MX) -c $< - $(MV) umfpack_tictoc.o $@ umfpack_m_global.o: ../Source/umfpack_global.c $(INC) $(MX) -c $< - $(MV) umfpack_global.o $@ #---------------------------------------- # umfpack mexFunction #---------------------------------------- umfpack2: umfpackmex.c $(MEXUMFPACK) $(MEXAMD) $(MX) -output umfpack2 umfpackmex.c $(MEXUMFPACK) $(MEXAMD) luflop: luflopmex.c $(MX) -output luflop luflopmex.c #------------------------------------------------------------------------------- # Remove all but the files in the original distribution #------------------------------------------------------------------------------- purge: clean - $(RM) *.mex* clean: - $(RM) $(CLEAN) SuiteSparse/UMFPACK/MATLAB/west0067_triplet0000644001170100242450000000731010301472773016767 0ustar davisfac 5 1 -0.278842 6 1 -0.268019 7 1 -0.232372 8 1 -0.157508 9 1 -0.0632598 25 1 0.139421 26 1 0.134009 27 1 0.116186 28 1 0.0787541 29 1 0.0316299 5 2 -0.8 21 2 -0.915953 25 2 0.4 61 2 1 6 3 -0.8 22 3 -0.915953 26 3 0.4 61 3 1 7 4 -0.8 23 4 -0.915953 27 4 0.4 61 4 1 8 5 -0.8 24 5 -0.915953 28 5 0.4 61 5 1 9 6 -0.8 29 6 0.4 61 6 1 5 7 0.134462 6 7 0.117568 7 7 0.0885926 8 7 0.0475944 9 7 0.0117829 1 8 -0.834182 5 8 0.4 57 8 1 2 9 -0.834182 6 9 0.4 57 9 1 3 10 -0.834182 7 10 0.4 57 10 1 4 11 -0.834182 8 11 0.4 57 11 1 9 12 0.4 57 12 1 1 13 1.26582 5 13 0.4 10 13 -1.26582 11 13 0.333333 58 13 1 2 14 1.01266 6 14 0.4 10 14 -1.01266 12 14 0.333333 58 14 1 3 15 0.759494 7 15 0.4 10 15 -0.759494 13 15 0.333333 58 15 1 4 16 0.506329 8 16 0.4 10 16 -0.506329 14 16 0.333333 58 16 1 9 17 0.4 10 17 -0.253165 15 17 0.333333 58 17 1 1 18 -0.336156 2 18 -0.29392 3 18 -0.221481 4 18 -0.118986 10 18 1 15 19 0.666667 56 19 1 11 20 -0.207176 12 20 -0.214039 13 20 -0.214421 14 20 -0.198677 15 20 -0.165687 16 20 0.124305 17 20 0.128423 18 20 0.128652 19 20 0.119206 20 20 0.0994125 11 21 -1 16 21 0.6 59 21 1 12 22 -1 17 22 0.6 59 22 1 13 23 -1 18 23 0.6 59 23 1 14 24 -1 19 24 0.6 59 24 1 15 25 -1 20 25 0.6 59 25 1 16 26 0.45 36 26 -0.958319 40 26 0.5 64 26 1 17 27 0.45 37 27 -0.958319 41 27 0.5 64 27 1 18 28 0.45 38 28 -0.958319 42 28 0.5 64 28 1 19 29 0.45 39 29 -0.958319 43 29 0.5 64 29 1 20 30 0.45 44 30 0.5 64 30 1 16 31 -0.207099 17 31 -0.2233 18 31 -0.228626 19 31 -0.202453 20 31 -0.138523 25 31 -0.207099 26 31 -0.2233 27 31 -0.228626 28 31 -0.202453 29 31 -0.138523 16 32 -1.05 25 32 -1.05 60 32 1 17 33 -1.05 26 33 -1.05 60 33 1 18 34 -1.05 27 34 -1.05 60 34 1 19 35 -1.05 28 35 -1.05 60 35 1 20 36 -1.05 29 36 -1.05 60 36 1 25 37 0.0814745 26 37 0.0978901 27 37 0.113161 28 37 0.115056 29 37 0.0924191 31 37 0.0905272 32 37 0.108767 33 37 0.125734 34 37 0.127839 35 37 0.102688 21 38 1.5674 25 38 0.65 30 38 -1.5674 31 38 0.722222 62 38 1 22 39 1.25392 26 39 0.65 30 39 -1.25392 32 39 0.722222 62 39 1 23 40 0.940439 27 40 0.65 30 40 -0.940439 33 40 0.722222 62 40 1 24 41 0.626959 28 41 0.65 30 41 -0.626959 34 41 0.722222 62 41 1 29 42 0.65 30 42 -0.31348 35 42 0.722222 62 42 1 21 43 -0.278842 22 43 -0.268019 23 43 -0.232372 24 43 -0.157508 30 43 1 31 44 0.25 46 44 -0.824225 50 44 0.5 66 44 1 32 45 0.25 47 45 -0.824225 51 45 0.5 66 45 1 33 46 0.25 48 46 -0.824225 52 46 0.5 66 46 1 34 47 0.25 49 47 -0.824225 53 47 0.5 66 47 1 35 48 0.25 54 48 0.5 66 48 1 31 49 -0.158163 32 49 -0.194771 33 49 -0.230392 34 49 -0.236285 35 49 -0.18039 40 49 -0.158163 41 49 -0.194771 42 49 -0.230392 43 49 -0.236285 44 49 -0.18039 31 50 -0.972222 40 50 -0.972222 63 50 1 32 51 -0.972222 41 51 -0.972222 63 51 1 33 52 -0.972222 42 52 -0.972222 63 52 1 34 53 -0.972222 43 53 -0.972222 63 53 1 35 54 -0.972222 44 54 -0.972222 63 54 1 40 55 0.0532286 41 55 0.0757454 42 55 0.106103 43 55 0.133388 44 55 0.131535 50 55 -0.106457 51 55 -0.151491 52 55 -0.212206 53 55 -0.266776 54 55 -0.263071 36 56 1.86335 40 56 0.472222 45 56 -1.86335 50 56 -0.944444 65 56 1 37 57 1.49068 41 57 0.472222 45 57 -1.49068 51 57 -0.944444 65 57 1 38 58 1.11801 42 58 0.472222 45 58 -1.11801 52 58 -0.944444 65 58 1 39 59 0.745342 43 59 0.472222 45 59 -0.745342 53 59 -0.944444 65 59 1 44 60 0.472222 45 60 -0.372671 54 60 -0.944444 65 60 1 36 61 -0.206995 37 61 -0.235647 38 61 -0.247567 39 61 -0.207487 45 61 1 46 62 1.86335 50 62 0.444444 55 62 -1.86335 67 62 1 47 63 1.49068 51 63 0.444444 55 63 -1.49068 67 63 1 48 64 1.11801 52 64 0.444444 55 64 -1.11801 67 64 1 49 65 0.745342 53 65 0.444444 55 65 -0.745342 67 65 1 54 66 0.444444 55 66 -0.372671 67 66 1 46 67 -0.144335 47 67 -0.191856 48 67 -0.24215 49 67 -0.254119 55 67 1 SuiteSparse/UMFPACK/MATLAB/luflopmex.c0000644001170100242450000000704610617161224016163 0ustar davisfac/* ========================================================================== */ /* === luflop mexFunction ================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* f = luflop (L, U) ; Given L and U, compute: Lnz = full (sum (spones (L))) - 1 ; Unz = full (sum (spones (U')))' - 1 ; f = 2*Lnz*Unz + sum (Lnz) ; without allocating O (lunz) space. v5.1: port to 64-bit MATLAB */ #include "mex.h" #include "UFconfig.h" #ifndef TRUE #define TRUE (1) #endif #ifndef FALSE #define FALSE (0) #endif void mexFunction ( int nlhs, /* number of left-hand sides */ mxArray *plhs [ ], /* left-hand side matrices */ int nrhs, /* number of right--hand sides */ const mxArray *prhs [ ] /* right-hand side matrices */ ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ double flop_count ; double *pflop ; UF_long *Lp, *Li, *Up, *Ui, *Unz, n, k, row, col, p, Lnz_k, Unz_k ; mxArray *Lmatrix, *Umatrix ; /* ---------------------------------------------------------------------- */ /* get inputs L, U */ /* ---------------------------------------------------------------------- */ if (nrhs != 2) { mexErrMsgTxt ("Usage: f = luflop (L, U)") ; } Lmatrix = (mxArray *) prhs [0] ; Umatrix = (mxArray *) prhs [1] ; n = mxGetM (Lmatrix) ; if (n != mxGetN (Lmatrix) || n != mxGetM (Umatrix) || n != mxGetN (Umatrix)) { mexErrMsgTxt ("Usage: f = luflop (L, U) ; L and U must be square") ; } if (!mxIsSparse (Lmatrix) || !mxIsSparse (Umatrix)) { mexErrMsgTxt ("Usage: f = luflop (L, U) ; L and U must be sparse") ; } Lp = (UF_long *) mxGetJc (Lmatrix) ; Li = (UF_long *) mxGetIr (Lmatrix) ; Up = (UF_long *) mxGetJc (Umatrix) ; Ui = (UF_long *) mxGetIr (Umatrix) ; Unz = (UF_long *) mxMalloc (n * sizeof (UF_long)) ; /* ---------------------------------------------------------------------- */ /* count the nonzeros in each row of U */ /* ---------------------------------------------------------------------- */ for (row = 0 ; row < n ; row++) { Unz [row] = 0 ; } for (col = 0 ; col < n ; col++) { for (p = Up [col] ; p < Up [col+1] ; p++) { row = Ui [p] ; Unz [row]++ ; } } /* ---------------------------------------------------------------------- */ /* count the flops */ /* ---------------------------------------------------------------------- */ flop_count = 0.0 ; for (k = 0 ; k < n ; k++) { /* off-diagonal nonzeros in column k of L: */ Lnz_k = Lp [k+1] - Lp [k] - 1 ; Unz_k = Unz [k] - 1 ; flop_count += (2 * Lnz_k * Unz_k) + Lnz_k ; } /* ---------------------------------------------------------------------- */ /* return the result */ /* ---------------------------------------------------------------------- */ plhs [0] = mxCreateDoubleMatrix (1, 1, mxREAL) ; pflop = mxGetPr (plhs [0]) ; pflop [0] = flop_count ; } SuiteSparse/UMFPACK/MATLAB/umfpack_demo.m.out0000644001170100242450000000507410711435546017427 0ustar davisfacumfpack_demo Enter the printing level for UMFPACK's output statistics: 0: none, 1: errors only, 2: statistics, 4: print some outputs 5: print all output [default is 1]: -------------------------------------------------------------- Factor and solve a small system, Ax=b, using default parameters Solving Ax=b via UMFPACK: Solving Ax=b via MATLAB: Difference between UMFPACK and MATLAB solution: 0 -------------------------------------------------------------- Factorizing [L, U, P, Q, R] = umfpack2 (A) P * (R\A) * Q - L*U should be zero: norm (P*(R\A)*Q - L*U, 1) = 2.77556e-16 (exact) 1.21864e-16 (estimated) Solution to Ax=b via UMFPACK factorization: x = Q * (U \ (L \ (P * (R \ b)))) UMFPACK flop count: 2453 Factorizing [L, U, P] = lu (A (:, q)) If you are using a version of MATLAB prior to V6.0, then the following statement (q = colamd (A)) may fail. Either download colamd from http://www.cise.ufl.edu/research/sparse, upgrade to MATLAB V6.0 or later, or replace the statement with q = colmmd (A) ; Solution to Ax=b via MATLAB factorization: x = U \ (L \ (P * b)) ; x (q) = x ; Difference between UMFPACK and MATLAB solution: 5.55112e-15 MATLAB LU flop count: 3160 -------------------------------------------------------------- Solve A'x=b: Solving A'x=b via UMFPACK: Solving A'x=b via MATLAB: Difference between UMFPACK and MATLAB solution: 1.77636e-15 -------------------------------------------------------------- Compute C = A', and compute the LU factorization of C. Factorizing A' can sometimes be better than factorizing A itself (less work and memory usage). Solve C'x=b; the solution is the same as the solution to Ax=b for the original A. P * (R\C) * Q - L*U should be zero: norm (P*(R\C)*Q - L*U, 1) = 1.17961e-16 (exact) 5.60533e-17 (estimated) Solution to Ax=b via UMFPACK, using the factors of C: x = R \ (P' * (L' \ (U' \ (Q' * b)))) ; Solution to Ax=b via MATLAB: Difference between UMFPACK and MATLAB solution: 3.55271e-15 -------------------------------------------------------------- Solve AX=B, where B is n-by-10, and sparse Difference between UMFPACK and MATLAB solution: 6.3926e-14 -------------------------------------------------------------- Solve AX=B, where B is n-by-10, and sparse, using umfpack_btf Difference between UMFPACK and MATLAB solution: 4.41347e-14 -------------------------------------------------------------- Solve A'X=B, where B is n-by-10, and sparse Difference between UMFPACK and MATLAB solution: 8.90054e-14 -------------------------------------------------------------- det(A): -4.07453e-05 UMFPACK determinant: -4.07453e-05 diary off SuiteSparse/UMFPACK/MATLAB/umfpack_demo.m0000644001170100242450000001541410711652036016613 0ustar davisfacfunction umfpack_demo (c) %UMFPACK_DEMO a lenghty demo % % A demo of UMFPACK for MATLAB. % % Example: % umfpack_demo % % See also umfpack, umfpack2, umfpack_make, umfpack_details, umfpack_report, % and umfpack_simple. % Copyright 1995-2007 by Timothy A. Davis. %------------------------------------------------------------------------------- % get default control parameters %------------------------------------------------------------------------------- control = umfpack2 ; if (nargin < 1) fprintf ('\nEnter the printing level for UMFPACK''s output statistics:\n') ; fprintf ('0: none, 1: errors only, 2: statistics, 4: print some outputs\n'); c = input ('5: print all output [default is 1]: ', 's') ; c = str2double (c) ; end if (isempty (c)) c = 1 ; end control (1) = c ; %------------------------------------------------------------------------------- % solve a simple system %------------------------------------------------------------------------------- fprintf ('\n--------------------------------------------------------------\n') ; fprintf ('Factor and solve a small system, Ax=b, using default parameters\n') ; if (control (1) > 1) fprintf ('(except for verbose printing enabled)\n') ; end load west0067_triplet A = spconvert (west0067_triplet) ; n = size (A, 1) ; b = rand (n, 1) ; fprintf ('Solving Ax=b via UMFPACK:\n') ; xu = umfpack2 (A, '\', b, control) ; fprintf ('Solving Ax=b via MATLAB:\n') ; xm = A\b ; fprintf ('Difference between UMFPACK and MATLAB solution: %g\n', ... norm (xu - xm, Inf)) ; %------------------------------------------------------------------------------- % spy the results %------------------------------------------------------------------------------- figure (1) clf subplot (2,3,1) spy (A) title ('The matrix A') ; subplot (2,3,2) [P1, Q1, Fr, Ch, Info] = umfpack2 (A, 'symbolic') ; %#ok treeplot (Fr (1:end-1,2)') ; title ('Supernodal column elimination tree') ; subplot (2,3,3) spy (P1 * A * Q1) title ('A, with initial row and column order') ; subplot (2,3,4) fprintf ('\n--------------------------------------------------------------\n') ; fprintf ('\nFactorizing [L, U, P, Q, R] = umfpack2 (A)\n') ; [L, U, P, Q, R] = umfpack2 (A) ; spy (P*A*Q) title ('A, with final row/column order') ; fprintf ('\nP * (R\\A) * Q - L*U should be zero:\n') ; fprintf ('norm (P*(R\\A)*Q - L*U, 1) = %g (exact) %g (estimated)\n', ... norm (P * (R\A) * Q - L*U, 1), lu_normest (P * (R\A) * Q, L, U)) ; fprintf ('\nSolution to Ax=b via UMFPACK factorization:\n') ; fprintf ('x = Q * (U \\ (L \\ (P * (R \\ b))))\n') ; xu = Q * (U \ (L \ (P * (R \ b)))) ; fprintf ('\nUMFPACK flop count: %d\n', luflop (L, U)) ; subplot (2,3,5) spy (spones (L) + spones (U)) title ('UMFPACK LU factors') ; subplot (2,3,6) fprintf ('\nFactorizing [L, U, P] = lu (A (:, q))\n') ; fprintf ('If you are using a version of MATLAB prior to V6.0, then the\n') ; fprintf ('following statement (q = colamd (A)) may fail. Either download\n'); fprintf ('colamd from http://www.cise.ufl.edu/research/sparse, upgrade to\n') ; fprintf ('MATLAB V6.0 or later, or replace the statement with\n') ; fprintf ('q = colmmd (A) ;\n') ; try q = colamd (A) ; catch fprintf ('\n *** colamd not found, using colmmd instead *** \n') ; q = colmmd (A) ; end [L, U, P] = lu (A (:,q)) ; spy (spones (L) + spones (U)) title ('MATLAB LU factors') ; fprintf ('\nSolution to Ax=b via MATLAB factorization:\n') ; fprintf ('x = U \\ (L \\ (P * b)) ; x (q) = x ;\n') ; xm = U \ (L \ (P * b)) ; xm (q) = xm ; fprintf ('Difference between UMFPACK and MATLAB solution: %g\n', ... norm (xu - xm, Inf)) ; fprintf ('\nMATLAB LU flop count: %d\n', luflop (L, U)) ; %------------------------------------------------------------------------------- % solve A'x=b %------------------------------------------------------------------------------- fprintf ('\n--------------------------------------------------------------\n') ; fprintf ('Solve A''x=b:\n') ; fprintf ('Solving A''x=b via UMFPACK:\n') ; xu = umfpack2 (b', '/', A, control) ; xu = xu' ; fprintf ('Solving A''x=b via MATLAB:\n') ; xm = (b'/A)' ; fprintf ('Difference between UMFPACK and MATLAB solution: %g\n', ... norm (xu - xm, Inf)) ; %------------------------------------------------------------------------------- % factor A' and then solve Ax=b using the factors of A' %------------------------------------------------------------------------------- fprintf ('\n--------------------------------------------------------------\n') ; fprintf ('Compute C = A'', and compute the LU factorization of C.\n') ; fprintf ('Factorizing A'' can sometimes be better than factorizing A itself\n'); fprintf ('(less work and memory usage). Solve C''x=b; the solution is the\n') ; fprintf ('same as the solution to Ax=b for the original A.\n'); C = A' ; % factorize C (P,Q) = L*U [L, U, P, Q, R, info] = umfpack2 (C, control) ; %#ok fprintf ('\nP * (R\\C) * Q - L*U should be zero:\n') ; fprintf ('norm (P*(R\\C)*Q - L*U, 1) = %g (exact) %g (estimated)\n', ... norm (P * (R\C) * Q - L*U, 1), lu_normest (P * (R\C) * Q, L, U)) ; fprintf ('\nSolution to Ax=b via UMFPACK, using the factors of C:\n') ; fprintf ('x = R \\ (P'' * (L'' \\ (U'' \\ (Q'' * b)))) ;\n') ; xu = R \ (P' * (L' \ (U' \ (Q' * b)))) ; fprintf ('Solution to Ax=b via MATLAB:\n') ; xm = A\b ; fprintf ('Difference between UMFPACK and MATLAB solution: %g\n', ... norm (xu - xm, Inf)) ; %------------------------------------------------------------------------------- % solve Ax=B %------------------------------------------------------------------------------- fprintf ('\n--------------------------------------------------------------\n') ; fprintf ('\nSolve AX=B, where B is n-by-10, and sparse\n') ; B = sprandn (n, 10, 0.05) ; XU = umfpack_solve (A, '\', B, control) ; XM = A\B ; fprintf ('Difference between UMFPACK and MATLAB solution: %g\n', ... norm (XU - XM, Inf)) ; fprintf ('\n--------------------------------------------------------------\n') ; fprintf ('\nSolve AX=B, where B is n-by-10, and sparse, using umfpack_btf\n') ; XU = umfpack_btf (A, B, control) ; fprintf ('Difference between UMFPACK and MATLAB solution: %g\n', ... norm (XU - XM, Inf)) ; fprintf ('\n--------------------------------------------------------------\n') ; fprintf ('\nSolve A''X=B, where B is n-by-10, and sparse\n') ; XU = umfpack_solve (B', '/', A, control) ; XM = B'/A ; fprintf ('Difference between UMFPACK and MATLAB solution: %g\n', ... norm (XU - XM, Inf)) ; %------------------------------------------------------------------------------- % compute the determinant %------------------------------------------------------------------------------- fprintf ('\n--------------------------------------------------------------\n') ; fprintf ('det(A): %g UMFPACK determinant: %g\n', det (A), umfpack2 (A, 'det')); SuiteSparse/UMFPACK/MATLAB/umfpack_report.m0000644001170100242450000003721710620664622017212 0ustar davisfacfunction umfpack_report (Control, Info) %UMFPACK_REPORT prints optional control settings and statistics % % Example: % umfpack_report (Control, Info) ; % % Prints the current Control settings for umfpack2, and the statistical % information returned by umfpack2 in the Info array. If Control is % an empty matrix, then the default control settings are printed. % % Control is 20-by-1, and Info is 90-by-1. Not all entries are used. % % Alternative usages: % % umfpack_report ([ ], Info) ; print the default control parameters % and the Info array. % umfpack_report (Control) ; print the control parameters only. % umfpack_report ; print the default control parameters % and an empty Info array. % % See also umfpack, umfpack2, umfpack_make, umfpack_details, % umfpack_demo, and umfpack_simple. % Copyright 1995-2007 by Timothy A. Davis. %------------------------------------------------------------------------------- % get inputs, use defaults if input arguments not present %------------------------------------------------------------------------------- % The contents of Control and Info are defined in umfpack.h if (nargin < 1) Control = [] ; end if (nargin < 2) Info = [] ; end if (isempty (Control)) Control = umfpack2 ; end if (isempty (Info)) Info = [ 0 (-ones (1, 89)) ] ; end %------------------------------------------------------------------------------- % control settings %------------------------------------------------------------------------------- fprintf ('\nUMFPACK: Control settings:\n\n') ; fprintf (' Control (1): print level: %d\n', Control (1)) ; fprintf (' Control (2): dense row parameter: %g\n', Control (2)) ; fprintf (' "dense" rows have > max (16, (%g)*16*sqrt(n_col)) entries\n', Control (2)) ; fprintf (' Control (3): dense column parameter: %g\n', Control (3)) ; fprintf (' "dense" columns have > max (16, (%g)*16*sqrt(n_row)) entries\n', Control (3)) ; fprintf (' Control (4): pivot tolerance: %g\n', Control (4)) ; fprintf (' Control (5): max block size for dense matrix kernels: %d\n', Control (5)) ; prstrat (' Control (6): strategy: %g ', Control (6)) ; fprintf (' Control (7): initial allocation ratio: %g\n', Control (7)) ; fprintf (' Control (8): max iterative refinement steps: %d\n', Control (8)) ; fprintf (' Control (13): 2-by-2 pivot tolerance: %g\n', Control (13)) ; fprintf (' Control (14): Q fixed during numeric factorization: %g ', Control (14)) ; if (Control (14) > 0) fprintf ('(yes)\n') ; elseif (Control (14) < 0) fprintf ('(no)\n') ; else fprintf ('(auto)\n') ; end fprintf (' Control (15): AMD dense row/column parameter: %g\n', Control (15)) ; fprintf (' "dense" rows/columns in A+A'' have > max (16, (%g)*sqrt(n)) entries.\n', Control (15)) ; fprintf (' Only used if the AMD ordering is used.\n') ; fprintf (' Control (16): diagonal pivot tolerance: %g\n', Control (16)) ; fprintf (' Only used if diagonal pivoting is attempted.\n') ; fprintf (' Control (17): scaling option: %g ', Control (17)) ; if (Control (17) == 0) fprintf ('(none)\n') ; elseif (Control (17) == 2) fprintf ('(scale the matrix by\n') ; fprintf (' dividing each row by max. abs. value in each row)\n') ; else fprintf ('(scale the matrix by\n') ; fprintf (' dividing each row by sum of abs. values in each row)\n') ; end fprintf (' Control (18): frontal matrix allocation ratio: %g\n', Control (18)) ; fprintf (' Control (19): drop tolerance: %g\n', Control (19)) ; fprintf (' Control (20): AMD and COLAMD aggressive absorption: %g ', Control (20)) ; yes_no (Control (20)) ; % compile-time options: fprintf ('\n The following options can only be changed at compile-time:\n') ; if (Control (9) == 1) fprintf (' Control (9): compiled to use the BLAS\n') ; else fprintf (' Control (9): compiled without the BLAS\n') ; fprintf (' (you will not get the best possible performance)\n') ; end if (Control (10) == 1) fprintf (' Control (10): compiled for MATLAB\n') ; elseif (Control (10) == 2) fprintf (' Control (10): compiled for MATLAB\n') ; else fprintf (' Control (10): not compiled for MATLAB\n') ; fprintf (' Printing will be in terms of 0-based matrix indexing,\n') ; fprintf (' not 1-based as is expected in MATLAB. Diary output may\n') ; fprintf (' not be properly recorded.\n') ; end if (Control (11) == 2) fprintf (' Control (11): uses POSIX times ( ) to get CPU time and wallclock time.\n') ; elseif (Control (11) == 1) fprintf (' Control (11): uses getrusage to get CPU time.\n') ; else fprintf (' Control (11): uses ANSI C clock to get CPU time.\n') ; fprintf (' The CPU time may wrap around, type "help cputime".\n') ; end if (Control (12) == 1) fprintf (' Control (12): compiled with debugging enabled\n') ; fprintf (' ###########################################\n') ; fprintf (' ### This will be exceedingly slow! ########\n') ; fprintf (' ###########################################\n') ; else fprintf (' Control (12): compiled for normal operation (no debugging)\n') ; end %------------------------------------------------------------------------------- % Info: %------------------------------------------------------------------------------- if (nargin == 1) return end status = Info (1) ; fprintf ('\nUMFPACK status: Info (1): %d, ', status) ; if (status == 0) fprintf ('OK\n') ; elseif (status == 1) fprintf ('WARNING matrix is singular\n') ; elseif (status == -1) fprintf ('ERROR out of memory\n') ; elseif (status == -3) fprintf ('ERROR numeric LU factorization is invalid\n') ; elseif (status == -4) fprintf ('ERROR symbolic LU factorization is invalid\n') ; elseif (status == -5) fprintf ('ERROR required argument is missing\n') ; elseif (status == -6) fprintf ('ERROR n <= 0\n') ; elseif (status <= -7 & status >= -12 | status == -14) %#ok fprintf ('ERROR matrix A is corrupted\n') ; elseif (status == -13) fprintf ('ERROR invalid system\n') ; elseif (status == -15) fprintf ('ERROR invalid permutation\n') ; elseif (status == -911) fprintf ('ERROR internal error!\n') ; fprintf ('Please report this error to Tim Davis (davis@cise.ufl.edu)\n') ; else fprintf ('ERROR unrecognized error. Info array corrupted\n') ; end fprintf (' (a -1 means the entry has not been computed):\n') ; fprintf ('\n Basic statistics:\n') ; fprintf (' Info (2): %d, # of rows of A\n', Info (2)) ; fprintf (' Info (17): %d, # of columns of A\n', Info (17)) ; fprintf (' Info (3): %d, nnz (A)\n', Info (3)) ; fprintf (' Info (4): %d, Unit size, in bytes, for memory usage reported below\n', Info (4)) ; fprintf (' Info (5): %d, size of int (in bytes)\n', Info (5)) ; fprintf (' Info (6): %d, size of UF_long (in bytes)\n', Info (6)) ; fprintf (' Info (7): %d, size of pointer (in bytes)\n', Info (7)) ; fprintf (' Info (8): %d, size of numerical entry (in bytes)\n', Info (8)) ; fprintf ('\n Pivots with zero Markowitz cost removed to obtain submatrix S:\n') ; fprintf (' Info (57): %d, # of pivots with one entry in pivot column\n', Info (57)) ; fprintf (' Info (58): %d, # of pivots with one entry in pivot row\n', Info (58)) ; fprintf (' Info (59): %d, # of rows/columns in submatrix S (if square)\n', Info (59)) ; fprintf (' Info (60): ') ; if (Info (60) > 0) fprintf ('submatrix S square and diagonal preserved\n') ; elseif (Info (60) == 0) fprintf ('submatrix S not square or diagonal not preserved\n') ; else fprintf ('\n') ; end fprintf (' Info (9): %d, # of "dense" rows in S\n', Info (9)) ; fprintf (' Info (10): %d, # of empty rows in S\n', Info (10)) ; fprintf (' Info (11): %d, # of "dense" columns in S\n', Info (11)) ; fprintf (' Info (12): %d, # of empty columns in S\n', Info (12)) ; fprintf (' Info (34): %g, symmetry of pattern of S\n', Info (34)) ; fprintf (' Info (35): %d, # of off-diagonal nonzeros in S+S''\n', Info (35)) ; fprintf (' Info (36): %d, nnz (diag (S))\n', Info (36)) ; fprintf ('\n 2-by-2 pivoting to place large entries on diagonal:\n') ; fprintf (' Info (52): %d, # of small diagonal entries of S\n', Info (52)) ; fprintf (' Info (53): %d, # of unmatched small diagonal entries\n', Info (53)) ; fprintf (' Info (54): %g, symmetry of P2*S\n', Info (54)) ; fprintf (' Info (55): %d, # of off-diagonal entries in (P2*S)+(P2*S)''\n', Info (55)) ; fprintf (' Info (56): %d, nnz (diag (P2*S))\n', Info (56)) ; fprintf ('\n AMD results, for strict diagonal pivoting:\n') ; fprintf (' Info (37): %d, est. nz in L and U\n', Info (37)) ; fprintf (' Info (38): %g, est. flop count\n', Info (38)) ; fprintf (' Info (39): %g, # of "dense" rows in S+S''\n', Info (39)) ; fprintf (' Info (40): %g, est. max. nz in any column of L\n', Info (40)) ; fprintf ('\n Final strategy selection, based on the analysis above:\n') ; prstrat (' Info (19): %d, strategy used ', Info (19)) ; fprintf (' Info (20): %d, ordering used ', Info (20)) ; if (Info (20) == 0) fprintf ('(COLAMD on A)\n') ; elseif (Info (20) == 1) fprintf ('(AMD on A+A'')\n') ; elseif (Info (20) == 2) fprintf ('(provided by user)\n') ; else fprintf ('(undefined ordering option)\n') ; end fprintf (' Info (32): %d, Q fixed during numeric factorization: ', Info (32)) ; yes_no (Info (32)) ; fprintf (' Info (33): %d, prefer diagonal pivoting: ', Info (33)) ; yes_no (Info (33)) ; fprintf ('\n symbolic analysis time and memory usage:\n') ; fprintf (' Info (13): %d, defragmentations during symbolic analysis\n', Info (13)) ; fprintf (' Info (14): %d, memory used during symbolic analysis (Units)\n', Info (14)) ; fprintf (' Info (15): %d, final size of symbolic factors (Units)\n', Info (15)) ; fprintf (' Info (16): %.2f, symbolic analysis CPU time (seconds)\n', Info (16)) ; fprintf (' Info (18): %.2f, symbolic analysis wall clock time (seconds)\n', Info (18)) ; fprintf ('\n Estimates computed in the symbolic analysis:\n') ; fprintf (' Info (21): %d, est. size of LU factors (Units)\n', Info (21)) ; fprintf (' Info (22): %d, est. total peak memory usage (Units)\n', Info (22)) ; fprintf (' Info (23): %d, est. factorization flop count\n', Info (23)) ; fprintf (' Info (24): %d, est. nnz (L)\n', Info (24)) ; fprintf (' Info (25): %d, est. nnz (U)\n', Info (25)) ; fprintf (' Info (26): %d, est. initial size, variable-part of LU (Units)\n', Info (26)) ; fprintf (' Info (27): %d, est. peak size, of variable-part of LU (Units)\n', Info (27)) ; fprintf (' Info (28): %d, est. final size, of variable-part of LU (Units)\n', Info (28)) ; fprintf (' Info (29): %d, est. max frontal matrix size (# of entries)\n', Info (29)) ; fprintf (' Info (30): %d, est. max # of rows in frontal matrix\n', Info (30)) ; fprintf (' Info (31): %d, est. max # of columns in frontal matrix\n', Info (31)) ; fprintf ('\n Computed in the numeric factorization (estimates shown above):\n') ; fprintf (' Info (41): %d, size of LU factors (Units)\n', Info (41)) ; fprintf (' Info (42): %d, total peak memory usage (Units)\n', Info (42)) ; fprintf (' Info (43): %d, factorization flop count\n', Info (43)) ; fprintf (' Info (44): %d, nnz (L)\n', Info (44)) ; fprintf (' Info (45): %d, nnz (U)\n', Info (45)) ; fprintf (' Info (46): %d, initial size of variable-part of LU (Units)\n', Info (46)) ; fprintf (' Info (47): %d, peak size of variable-part of LU (Units)\n', Info (47)) ; fprintf (' Info (48): %d, final size of variable-part of LU (Units)\n', Info (48)) ; fprintf (' Info (49): %d, max frontal matrix size (# of numerical entries)\n', Info (49)) ; fprintf (' Info (50): %d, max # of rows in frontal matrix\n', Info (50)) ; fprintf (' Info (51): %d, max # of columns in frontal matrix\n', Info (51)) ; fprintf ('\n Computed in the numeric factorization (no estimates computed a priori):\n') ; fprintf (' Info (61): %d, defragmentations during numeric factorization\n', Info (61)) ; fprintf (' Info (62): %d, reallocations during numeric factorization\n', Info (62)) ; fprintf (' Info (63): %d, costly reallocations during numeric factorization\n', Info (63)) ; fprintf (' Info (64): %d, integer indices in compressed pattern of L and U\n', Info (64)) ; fprintf (' Info (65): %d, numerical values stored in L and U\n', Info (65)) ; fprintf (' Info (66): %.2f, numeric factorization CPU time (seconds)\n', Info (66)) ; fprintf (' Info (76): %.2f, numeric factorization wall clock time (seconds)\n', Info (76)) ; if (Info (66) > 0.05 & Info (43) > 0) %#ok fprintf (' mflops in numeric factorization phase: %.2f\n', 1e-6 * Info (43) / Info (66)) ; end fprintf (' Info (67): %d, nnz (diag (U))\n', Info (67)) ; fprintf (' Info (68): %g, reciprocal condition number estimate\n', Info (68)) ; fprintf (' Info (69): %g, matrix was ', Info (69)) ; if (Info (69) == 0) fprintf ('not scaled\n') ; elseif (Info (69) == 2) fprintf ('scaled (row max)\n') ; else fprintf ('scaled (row sum)\n') ; end fprintf (' Info (70): %g, min. scale factor of rows of A\n', Info (70)) ; fprintf (' Info (71): %g, max. scale factor of rows of A\n', Info (71)) ; fprintf (' Info (72): %g, min. abs. on diagonal of U\n', Info (72)) ; fprintf (' Info (73): %g, max. abs. on diagonal of U\n', Info (73)) ; fprintf (' Info (74): %g, initial allocation parameter used\n', Info (74)) ; fprintf (' Info (75): %g, # of forced updates due to frontal growth\n', Info (75)) ; fprintf (' Info (77): %d, # of off-diaogonal pivots\n', Info (77)) ; fprintf (' Info (78): %d, nnz (L), if no small entries dropped\n', Info (78)) ; fprintf (' Info (79): %d, nnz (U), if no small entries dropped\n', Info (79)) ; fprintf (' Info (80): %d, # of small entries dropped\n', Info (80)) ; fprintf ('\n Computed in the solve step:\n') ; fprintf (' Info (81): %d, iterative refinement steps taken\n', Info (81)) ; fprintf (' Info (82): %d, iterative refinement steps attempted\n', Info (82)) ; fprintf (' Info (83): %g, omega(1), sparse-backward error estimate\n', Info (83)) ; fprintf (' Info (84): %g, omega(2), sparse-backward error estimate\n', Info (84)) ; fprintf (' Info (85): %d, solve flop count\n', Info (85)) ; fprintf (' Info (86): %.2f, solve CPU time (seconds)\n', Info (86)) ; fprintf (' Info (87): %.2f, solve wall clock time (seconds)\n', Info (87)) ; fprintf ('\n Info (88:90): unused\n\n') ; %------------------------------------------------------------------------------- function prstrat (fmt, strategy) % prstrat print the ordering strategy fprintf (fmt, strategy) ; if (strategy == 1) fprintf ('(unsymmetric)\n') ; fprintf (' Q = COLAMD (A), Q refined during numerical\n') ; fprintf (' factorization, and no attempt at diagonal pivoting.\n') ; elseif (strategy == 2) fprintf ('(symmetric, with 2-by-2 pivoting)\n') ; fprintf (' P2 = row permutation to place large values on the diagonal\n') ; fprintf (' Q = AMD (P2*A+(P2*A)''), Q not refined during numeric factorization,\n') ; fprintf (' and diagonal pivoting attempted.\n') ; elseif (strategy == 3) fprintf ('(symmetric)\n') ; fprintf (' Q = AMD (A+A''), Q not refined during numeric factorization,\n') ; fprintf (' and diagonal pivoting (P=Q'') attempted.\n') ; else % strategy = 0 ; fprintf ('(auto)\n') ; end %------------------------------------------------------------------------------- function yes_no (s) % yes_no print yes or no if (s == 0) fprintf ('(no)\n') ; else fprintf ('(yes)\n') ; end SuiteSparse/UMFPACK/MATLAB/umfpack_solve.m0000644001170100242450000000505110711660504017012 0ustar davisfacfunction [x, info] = umfpack_solve (arg1, op, arg2, Control) %UMFPACK_SOLVE x = A\b or x = b/A % % Example: % x = umfpack_solve (A, '\', b, Control) % x = umfpack_solve (b, '/', A, Control) % % Computes x = A\b, or b/A, where A is square. Uses UMFPACK if A is sparse. % The Control argument is optional. % % See also umfpack, umfpack2, umfpack_make, umfpack_details, umfpack_report, % and umfpack_simple. % Copyright 1995-2007 by Timothy A. Davis. %------------------------------------------------------------------------------- % check inputs and get default control parameters %------------------------------------------------------------------------------- if (op == '\') A = arg1 ; b = arg2 ; elseif (op == '/') A = arg2 ; b = arg1 ; else help umfack_solve error ('umfpack_solve: unrecognized operator') ; end [m n] = size (A) ; if (m ~= n) help umfpack_solve error ('umfpack_solve: A must be square') ; end [m1 n1] = size (b) ; if ((op == '\' & n ~= m1) | (op == '/' & n1 ~= m)) %#ok help umfpack_solve error ('umfpack_solve: b has the wrong dimensions') ; end if (nargin < 4) Control = umfpack2 ; end info = [0 0 0] ; % [nnz(L), nnz(U), 0], optional 2nd output %------------------------------------------------------------------------------- % solve the system %------------------------------------------------------------------------------- if (op == '\') if (~issparse (A)) % A is not sparse, so just use MATLAB x = A\b ; elseif (n1 == 1 & ~issparse (b)) %#ok % the UMFPACK '\' requires b to be a dense column vector [x info] = umfpack2 (A, '\', b, Control) ; info = [info(78) info(79) 0] ; else % factorize with UMFPACK and do the forward/back solves in MATLAB [L, U, P, Q, R, info] = umfpack2 (A, Control) ; x = Q * (U \ (L \ (P * (R \ b)))) ; info = [info(78) info(79) 0] ; end else if (~issparse (A)) % A is not sparse, so just use MATLAB x = b/A ; elseif (m1 == 1 & ~issparse (b)) %#ok % the UMFPACK '\' requires b to be a dense column vector [x info] = umfpack2 (b, '/', A, Control) ; info = [info(78) info(79) 0] ; else % factorize with UMFPACK and do the forward/back solves in MATLAB % this mimics the behavior of x = b/A, except for the row scaling [L, U, P, Q, R, info] = umfpack2 (A.', Control) ; x = (Q * (U \ (L \ (P * (R \ (b.')))))).' ; info = [info(78) info(79) 0] ; % an alternative method: % [L, U, P, Q, r] = umfpack2 (A, Control) ; % x = (R \ (P' * (L.' \ (U.' \ (Q' * b.'))))).' ; end end SuiteSparse/UMFPACK/Include/0000755001170100242450000000000010711431031014407 5ustar davisfacSuiteSparse/UMFPACK/Include/umfpack_report_numeric.h0000644001170100242450000000703410617161103021334 0ustar davisfac/* ========================================================================== */ /* === umfpack_report_numeric =============================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_report_numeric ( void *Numeric, const double Control [UMFPACK_CONTROL] ) ; UF_long umfpack_dl_report_numeric ( void *Numeric, const double Control [UMFPACK_CONTROL] ) ; int umfpack_zi_report_numeric ( void *Numeric, const double Control [UMFPACK_CONTROL] ) ; UF_long umfpack_zl_report_numeric ( void *Numeric, const double Control [UMFPACK_CONTROL] ) ; /* double int Syntax: #include "umfpack.h" void *Numeric ; double Control [UMFPACK_CONTROL] ; int status ; status = umfpack_di_report_numeric (Numeric, Control) ; double UF_long Syntax: #include "umfpack.h" void *Numeric ; double Control [UMFPACK_CONTROL] ; UF_long status ; status = umfpack_dl_report_numeric (Numeric, Control) ; complex int Syntax: #include "umfpack.h" void *Numeric ; double Control [UMFPACK_CONTROL] ; int status ; status = umfpack_zi_report_numeric (Numeric, Control) ; complex UF_long Syntax: #include "umfpack.h" void *Numeric ; double Control [UMFPACK_CONTROL] ; UF_long status ; status = umfpack_zl_report_numeric (Numeric, Control) ; Purpose: Verifies and prints a Numeric object (the LU factorization, both its pattern numerical values, and permutation vectors P and Q). This routine checks the object more carefully than the computational routines. Normally, this check is not required, since umfpack_*_numeric either returns (void *) NULL, or a valid Numeric object. However, if you suspect that your own code has corrupted the Numeric object (by overruning memory bounds, for example), then this routine might be able to detect a corrupted Numeric object. Since this is a complex object, not all such user-generated errors are guaranteed to be caught by this routine. Returns: UMFPACK_OK if Control [UMFPACK_PRL] <= 2 (the input is not checked). Otherwise: UMFPACK_OK if the Numeric object is valid. UMFPACK_ERROR_invalid_Numeric_object if the Numeric object is invalid. UMFPACK_ERROR_out_of_memory if out of memory. Arguments: void *Numeric ; Input argument, not modified. The Numeric object, which holds the numeric factorization computed by umfpack_*_numeric. double Control [UMFPACK_CONTROL] ; Input argument, not modified. If a (double *) NULL pointer is passed, then the default control settings are used. Otherwise, the settings are determined from the Control array. See umfpack_*_defaults on how to fill the Control array with the default settings. If Control contains NaN's, the defaults are used. The following Control parameters are used: Control [UMFPACK_PRL]: printing level. 2 or less: no output. returns silently without checking anything. 3: fully check input, and print a short summary of its status 4: as 3, but print first few entries of the input 5: as 3, but print all of the input Default: 1 */ SuiteSparse/UMFPACK/Include/umfpack_timer.h0000644001170100242450000000326710617161136017431 0ustar davisfac/* ========================================================================== */ /* === umfpack_timer ======================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ double umfpack_timer ( void ) ; /* Syntax (for all versions: di, dl, zi, and zl): #include "umfpack.h" double t ; t = umfpack_timer ( ) ; Purpose: Returns the CPU time used by the process. Includes both "user" and "system" time (the latter is time spent by the system on behalf of the process, and is thus charged to the process). It does not return the wall clock time. See umfpack_tic and umfpack_toc (the file umfpack_tictoc.h) for the timer used internally by UMFPACK. This routine uses the Unix getrusage routine, if available. It is less subject to overflow than the ANSI C clock routine. If getrusage is not available, the portable ANSI C clock routine is used instead. Unfortunately, clock ( ) overflows if the CPU time exceeds 2147 seconds (about 36 minutes) when sizeof (clock_t) is 4 bytes. If you have getrusage, be sure to compile UMFPACK with the -DGETRUSAGE flag set; see umf_config.h and the User Guide for details. Even the getrusage routine can overlow. Arguments: None. */ SuiteSparse/UMFPACK/Include/umfpack_transpose.h0000644001170100242450000001740210617161140020316 0ustar davisfac/* ========================================================================== */ /* === umfpack_transpose ==================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_transpose ( int n_row, int n_col, const int Ap [ ], const int Ai [ ], const double Ax [ ], const int P [ ], const int Q [ ], int Rp [ ], int Ri [ ], double Rx [ ] ) ; UF_long umfpack_dl_transpose ( UF_long n_row, UF_long n_col, const UF_long Ap [ ], const UF_long Ai [ ], const double Ax [ ], const UF_long P [ ], const UF_long Q [ ], UF_long Rp [ ], UF_long Ri [ ], double Rx [ ] ) ; int umfpack_zi_transpose ( int n_row, int n_col, const int Ap [ ], const int Ai [ ], const double Ax [ ], const double Az [ ], const int P [ ], const int Q [ ], int Rp [ ], int Ri [ ], double Rx [ ], double Rz [ ], int do_conjugate ) ; UF_long umfpack_zl_transpose ( UF_long n_row, UF_long n_col, const UF_long Ap [ ], const UF_long Ai [ ], const double Ax [ ], const double Az [ ], const UF_long P [ ], const UF_long Q [ ], UF_long Rp [ ], UF_long Ri [ ], double Rx [ ], double Rz [ ], UF_long do_conjugate ) ; /* double int Syntax: #include "umfpack.h" int n_row, n_col, status, *Ap, *Ai, *P, *Q, *Rp, *Ri ; double *Ax, *Rx ; status = umfpack_di_transpose (n_row, n_col, Ap, Ai, Ax, P, Q, Rp, Ri, Rx) ; double UF_long Syntax: #include "umfpack.h" UF_long n_row, n_col, status, *Ap, *Ai, *P, *Q, *Rp, *Ri ; double *Ax, *Rx ; status = umfpack_dl_transpose (n_row, n_col, Ap, Ai, Ax, P, Q, Rp, Ri, Rx) ; complex int Syntax: #include "umfpack.h" int n_row, n_col, status, *Ap, *Ai, *P, *Q, *Rp, *Ri, do_conjugate ; double *Ax, *Az, *Rx, *Rz ; status = umfpack_zi_transpose (n_row, n_col, Ap, Ai, Ax, Az, P, Q, Rp, Ri, Rx, Rz, do_conjugate) ; complex UF_long Syntax: #include "umfpack.h" UF_long n_row, n_col, status, *Ap, *Ai, *P, *Q, *Rp, *Ri, do_conjugate ; double *Ax, *Az, *Rx, *Rz ; status = umfpack_zl_transpose (n_row, n_col, Ap, Ai, Ax, Az, P, Q, Rp, Ri, Rx, Rz, do_conjugate) ; packed complex Syntax: Same as above, except Az are Rz are NULL. Purpose: Transposes and optionally permutes a sparse matrix in row or column-form, R = (PAQ)'. In MATLAB notation, R = (A (P,Q))' or R = (A (P,Q)).' doing either the linear algebraic transpose or the array transpose. Alternatively, this routine can be viewed as converting A (P,Q) from column-form to row-form, or visa versa (for the array transpose). Empty rows and columns may exist. The matrix A may be singular and/or rectangular. umfpack_*_transpose is useful if you want to factorize A' or A.' instead of A. Factorizing A' or A.' instead of A can be much better, particularly if AA' is much sparser than A'A. You can still solve Ax=b if you factorize A' or A.', by solving with the sys argument UMFPACK_At or UMFPACK_Aat, respectively, in umfpack_*_*solve. Returns: UMFPACK_OK if successful. UMFPACK_ERROR_out_of_memory if umfpack_*_transpose fails to allocate a size-max (n_row,n_col) workspace. UMFPACK_ERROR_argument_missing if Ai, Ap, Ri, and/or Rp are missing. UMFPACK_ERROR_n_nonpositive if n_row <= 0 or n_col <= 0 UMFPACK_ERROR_invalid_permutation if P and/or Q are invalid. UMFPACK_ERROR_invalid_matrix if Ap [n_col] < 0, if Ap [0] != 0, if Ap [j] > Ap [j+1] for any j in the range 0 to n_col-1, if any row index i is < 0 or >= n_row, or if the row indices in any column are not in ascending order. Arguments: Int n_row ; Input argument, not modified. Int n_col ; Input argument, not modified. A is an n_row-by-n_col matrix. Restriction: n_row > 0 and n_col > 0. Int Ap [n_col+1] ; Input argument, not modified. The column pointers of the column-oriented form of the matrix A. See umfpack_*_symbolic for a description. The number of entries in the matrix is nz = Ap [n_col]. Ap [0] must be zero, Ap [n_col] must be => 0, and Ap [j] <= Ap [j+1] and Ap [j] <= Ap [n_col] must be true for all j in the range 0 to n_col-1. Empty columns are OK (that is, Ap [j] may equal Ap [j+1] for any j in the range 0 to n_col-1). Int Ai [nz] ; Input argument, not modified, of size nz = Ap [n_col]. The nonzero pattern (row indices) for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)]. The row indices in a given column j must be in ascending order, and no duplicate row indices may be present. Row indices must be in the range 0 to n_row-1 (the matrix is 0-based). double Ax [nz] ; Input argument, not modified, of size nz = Ap [n_col]. Size 2*nz if Az or Rz are NULL. double Az [nz] ; Input argument, not modified, for complex versions. If present, these are the numerical values of the sparse matrix A. The nonzero pattern (row indices) for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and the corresponding real numerical values are stored in Ax [(Ap [j]) ... (Ap [j+1]-1)]. The imaginary values are stored in Az [(Ap [j]) ... (Ap [j+1]-1)]. The values are transposed only if Ax and Rx are present. This is not an error conditions; you are able to transpose and permute just the pattern of a matrix. If Az or Rz are NULL, then both real and imaginary parts are contained in Ax[0..2*nz-1], with Ax[2*k] and Ax[2*k+1] being the real and imaginary part of the kth entry. Int P [n_row] ; Input argument, not modified. The permutation vector P is defined as P [k] = i, where the original row i of A is the kth row of PAQ. If you want to use the identity permutation for P, simply pass (Int *) NULL for P. This is not an error condition. P is a complete permutation of all the rows of A; this routine does not support the creation of a transposed submatrix of A (R = A (1:3,:)' where A has more than 3 rows, for example, cannot be done; a future version might support this operation). Int Q [n_col] ; Input argument, not modified. The permutation vector Q is defined as Q [k] = j, where the original column j of A is the kth column of PAQ. If you want to use the identity permutation for Q, simply pass (Int *) NULL for Q. This is not an error condition. Q is a complete permutation of all the columns of A; this routine does not support the creation of a transposed submatrix of A. Int Rp [n_row+1] ; Output argument. The column pointers of the matrix R = (A (P,Q))' or (A (P,Q)).', in the same form as the column pointers Ap for the matrix A. Int Ri [nz] ; Output argument. The row indices of the matrix R = (A (P,Q))' or (A (P,Q)).' , in the same form as the row indices Ai for the matrix A. double Rx [nz] ; Output argument. Size 2*nz if Az or Rz are NULL. double Rz [nz] ; Output argument, imaginary part for complex versions. If present, these are the numerical values of the sparse matrix R, in the same form as the values Ax and Az of the matrix A. If Az or Rz are NULL, then both real and imaginary parts are contained in Rx[0..2*nz-1], with Rx[2*k] and Rx[2*k+1] being the real and imaginary part of the kth entry. Int do_conjugate ; Input argument for complex versions only. If true, and if Ax and Rx are present, then the linear algebraic transpose is computed (complex conjugate). If false, the array transpose is computed instead. */ SuiteSparse/UMFPACK/Include/umfpack_report_status.h0000644001170100242450000000500310617161106021212 0ustar davisfac/* ========================================================================== */ /* === umfpack_report_status ================================================ */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ void umfpack_di_report_status ( const double Control [UMFPACK_CONTROL], int status ) ; void umfpack_dl_report_status ( const double Control [UMFPACK_CONTROL], UF_long status ) ; void umfpack_zi_report_status ( const double Control [UMFPACK_CONTROL], int status ) ; void umfpack_zl_report_status ( const double Control [UMFPACK_CONTROL], UF_long status ) ; /* double int Syntax: #include "umfpack.h" double Control [UMFPACK_CONTROL] ; int status ; umfpack_di_report_status (Control, status) ; double UF_long Syntax: #include "umfpack.h" double Control [UMFPACK_CONTROL] ; UF_long status ; umfpack_dl_report_status (Control, status) ; complex int Syntax: #include "umfpack.h" double Control [UMFPACK_CONTROL] ; int status ; umfpack_zi_report_status (Control, status) ; complex UF_long Syntax: #include "umfpack.h" double Control [UMFPACK_CONTROL] ; UF_long status ; umfpack_zl_report_status (Control, status) ; Purpose: Prints the status (return value) of other umfpack_* routines. Arguments: double Control [UMFPACK_CONTROL] ; Input argument, not modified. If a (double *) NULL pointer is passed, then the default control settings are used. Otherwise, the settings are determined from the Control array. See umfpack_*_defaults on how to fill the Control array with the default settings. If Control contains NaN's, the defaults are used. The following Control parameters are used: Control [UMFPACK_PRL]: printing level. 0 or less: no output, even when an error occurs 1: error messages only 2 or more: print status, whether or not an error occurred 4 or more: also print the UMFPACK Copyright 6 or more: also print the UMFPACK License Default: 1 Int status ; Input argument, not modified. The return value from another umfpack_* routine. */ SuiteSparse/UMFPACK/Include/umfpack_symbolic.h0000644001170100242450000005341310617161131020123 0ustar davisfac/* ========================================================================== */ /* === umfpack_symbolic ===================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_symbolic ( int n_row, int n_col, const int Ap [ ], const int Ai [ ], const double Ax [ ], void **Symbolic, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO] ) ; UF_long umfpack_dl_symbolic ( UF_long n_row, UF_long n_col, const UF_long Ap [ ], const UF_long Ai [ ], const double Ax [ ], void **Symbolic, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO] ) ; int umfpack_zi_symbolic ( int n_row, int n_col, const int Ap [ ], const int Ai [ ], const double Ax [ ], const double Az [ ], void **Symbolic, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO] ) ; UF_long umfpack_zl_symbolic ( UF_long n_row, UF_long n_col, const UF_long Ap [ ], const UF_long Ai [ ], const double Ax [ ], const double Az [ ], void **Symbolic, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO] ) ; /* double int Syntax: #include "umfpack.h" void *Symbolic ; int n_row, n_col, *Ap, *Ai, status ; double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax ; status = umfpack_di_symbolic (n_row, n_col, Ap, Ai, Ax, &Symbolic, Control, Info) ; double UF_long Syntax: #include "umfpack.h" void *Symbolic ; UF_long n_row, n_col, *Ap, *Ai, status ; double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax ; status = umfpack_dl_symbolic (n_row, n_col, Ap, Ai, Ax, &Symbolic, Control, Info) ; complex int Syntax: #include "umfpack.h" void *Symbolic ; int n_row, n_col, *Ap, *Ai, status ; double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax, *Az ; status = umfpack_zi_symbolic (n_row, n_col, Ap, Ai, Ax, Az, &Symbolic, Control, Info) ; complex UF_long Syntax: #include "umfpack.h" void *Symbolic ; UF_long n_row, n_col, *Ap, *Ai, status ; double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax, *Az ; status = umfpack_zl_symbolic (n_row, n_col, Ap, Ai, Ax, Az, &Symbolic, Control, Info) ; packed complex Syntax: Same as above, except Az is NULL. Purpose: Given nonzero pattern of a sparse matrix A in column-oriented form, umfpack_*_symbolic performs a column pre-ordering to reduce fill-in (using COLAMD or AMD) and a symbolic factorization. This is required before the matrix can be numerically factorized with umfpack_*_numeric. If you wish to bypass the COLAMD or AMD pre-ordering and provide your own ordering, use umfpack_*_qsymbolic instead. Since umfpack_*_symbolic and umfpack_*_qsymbolic are very similar, options for both routines are discussed below. For the following discussion, let S be the submatrix of A obtained after eliminating all pivots of zero Markowitz cost. S has dimension (n_row-n1-nempty_row) -by- (n_col-n1-nempty_col), where n1 = Info [UMFPACK_COL_SINGLETONS] + Info [UMFPACK_ROW_SINGLETONS], nempty_row = Info [UMFPACK_NEMPTY_ROW] and nempty_col = Info [UMFPACK_NEMPTY_COL]. Returns: The status code is returned. See Info [UMFPACK_STATUS], below. Arguments: Int n_row ; Input argument, not modified. Int n_col ; Input argument, not modified. A is an n_row-by-n_col matrix. Restriction: n_row > 0 and n_col > 0. Int Ap [n_col+1] ; Input argument, not modified. Ap is an integer array of size n_col+1. On input, it holds the "pointers" for the column form of the sparse matrix A. Column j of the matrix A is held in Ai [(Ap [j]) ... (Ap [j+1]-1)]. The first entry, Ap [0], must be zero, and Ap [j] <= Ap [j+1] must hold for all j in the range 0 to n_col-1. The value nz = Ap [n_col] is thus the total number of entries in the pattern of the matrix A. nz must be greater than or equal to zero. Int Ai [nz] ; Input argument, not modified, of size nz = Ap [n_col]. The nonzero pattern (row indices) for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)]. The row indices in a given column j must be in ascending order, and no duplicate row indices may be present. Row indices must be in the range 0 to n_row-1 (the matrix is 0-based). See umfpack_*_triplet_to_col for how to sort the columns of a matrix and sum up the duplicate entries. See umfpack_*_report_matrix for how to print the matrix A. double Ax [nz] ; Optional input argument, not modified. Size 2*nz for packed complex case. The numerical values of the sparse matrix A. The nonzero pattern (row indices) for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and the corresponding numerical values are stored in Ax [(Ap [j]) ... (Ap [j+1]-1)]. Used only by the 2-by-2 strategy to determine whether entries are "large" or "small". You do not have to pass the same numerical values to umfpack_*_numeric. If Ax is not present (a (double *) NULL pointer), then any entry in A is assumed to be "large". double Az [nz] ; Optional input argument, not modified, for complex versions. For the complex versions, this holds the imaginary part of A. The imaginary part of column j is held in Az [(Ap [j]) ... (Ap [j+1]-1)]. If Az is NULL, then both real and imaginary parts are contained in Ax[0..2*nz-1], with Ax[2*k] and Ax[2*k+1] being the real and imaginary part of the kth entry. Used by the 2-by-2 strategy only. See the description of Ax, above. void **Symbolic ; Output argument. **Symbolic is the address of a (void *) pointer variable in the user's calling routine (see Syntax, above). On input, the contents of this variable are not defined. On output, this variable holds a (void *) pointer to the Symbolic object (if successful), or (void *) NULL if a failure occurred. double Control [UMFPACK_CONTROL] ; Input argument, not modified. If a (double *) NULL pointer is passed, then the default control settings are used (the defaults are suitable for all matrices, ranging from those with highly unsymmetric nonzero pattern, to symmetric matrices). Otherwise, the settings are determined from the Control array. See umfpack_*_defaults on how to fill the Control array with the default settings. If Control contains NaN's, the defaults are used. The following Control parameters are used: Control [UMFPACK_STRATEGY]: This is the most important control parameter. It determines what kind of ordering and pivoting strategy that UMFPACK should use. There are 4 options: UMFPACK_STRATEGY_AUTO: This is the default. The input matrix is analyzed to determine how symmetric the nonzero pattern is, and how many entries there are on the diagonal. It then selects one of the following strategies. Refer to the User Guide for a description of how the strategy is automatically selected. UMFPACK_STRATEGY_UNSYMMETRIC: Use the unsymmetric strategy. COLAMD is used to order the columns of A, followed by a postorder of the column elimination tree. No attempt is made to perform diagonal pivoting. The column ordering is refined during factorization. In the numerical factorization, the Control [UMFPACK_SYM_PIVOT_TOLERANCE] parameter is ignored. A pivot is selected if its magnitude is >= Control [UMFPACK_PIVOT_TOLERANCE] (default 0.1) times the largest entry in its column. UMFPACK_STRATEGY_SYMMETRIC: Use the symmetric strategy In this method, the approximate minimum degree ordering (AMD) is applied to A+A', followed by a postorder of the elimination tree of A+A'. UMFPACK attempts to perform diagonal pivoting during numerical factorization. No refinement of the column pre-ordering is performed during factorization. In the numerical factorization, a nonzero entry on the diagonal is selected as the pivot if its magnitude is >= Control [UMFPACK_SYM_PIVOT_TOLERANCE] (default 0.001) times the largest entry in its column. If this is not acceptable, then an off-diagonal pivot is selected with magnitude >= Control [UMFPACK_PIVOT_TOLERANCE] (default 0.1) times the largest entry in its column. UMFPACK_STRATEGY_2BY2: a row permutation P2 is found that places large entries on the diagonal. The matrix P2*A is then factorized using the symmetric strategy, described above. Refer to the User Guide for more information. Control [UMFPACK_DENSE_COL]: If COLAMD is used, columns with more than max (16, Control [UMFPACK_DENSE_COL] * 16 * sqrt (n_row)) entries are placed placed last in the column pre-ordering. Default: 0.2. Control [UMFPACK_DENSE_ROW]: Rows with more than max (16, Control [UMFPACK_DENSE_ROW] * 16 * sqrt (n_col)) entries are treated differently in the COLAMD pre-ordering, and in the internal data structures during the subsequent numeric factorization. Default: 0.2. Control [UMFPACK_AMD_DENSE]: rows/columns in A+A' with more than max (16, Control [UMFPACK_AMD_DENSE] * sqrt (n)) entries (where n = n_row = n_col) are ignored in the AMD pre-ordering. Default: 10. Control [UMFPACK_BLOCK_SIZE]: the block size to use for Level-3 BLAS in the subsequent numerical factorization (umfpack_*_numeric). A value less than 1 is treated as 1. Default: 32. Modifying this parameter affects when updates are applied to the working frontal matrix, and can indirectly affect fill-in and operation count. Assuming the block size is large enough (8 or so), this parameter has a modest effect on performance. Control [UMFPACK_2BY2_TOLERANCE]: a diagonal entry S (k,k) is considered "small" if it is < tol * max (abs (S (:,k))), where S a submatrix of the scaled input matrix, with pivots of zero Markowitz cost removed. Control [UMFPACK_SCALE]: See umfpack_numeric.h for a description. Only affects the 2-by-2 strategy. Default: UMFPACK_SCALE_SUM. Control [UMFPACK_FIXQ]: If > 0, then the pre-ordering Q is not modified during numeric factorization. If < 0, then Q may be modified. If zero, then this is controlled automatically (the unsymmetric strategy modifies Q, the others do not). Default: 0. Control [UMFPACK_AGGRESSIVE]: If nonzero, aggressive absorption is used in COLAMD and AMD. Default: 1. double Info [UMFPACK_INFO] ; Output argument, not defined on input. Contains statistics about the symbolic analysis. If a (double *) NULL pointer is passed, then no statistics are returned in Info (this is not an error condition). The entire Info array is cleared (all entries set to -1) and then the following statistics are computed: Info [UMFPACK_STATUS]: status code. This is also the return value, whether or not Info is present. UMFPACK_OK Each column of the input matrix contained row indices in increasing order, with no duplicates. Only in this case does umfpack_*_symbolic compute a valid symbolic factorization. For the other cases below, no Symbolic object is created (*Symbolic is (void *) NULL). UMFPACK_ERROR_n_nonpositive n is less than or equal to zero. UMFPACK_ERROR_invalid_matrix Number of entries in the matrix is negative, Ap [0] is nonzero, a column has a negative number of entries, a row index is out of bounds, or the columns of input matrix were jumbled (unsorted columns or duplicate entries). UMFPACK_ERROR_out_of_memory Insufficient memory to perform the symbolic analysis. If the analysis requires more than 2GB of memory and you are using the 32-bit ("int") version of UMFPACK, then you are guaranteed to run out of memory. Try using the 64-bit version of UMFPACK. UMFPACK_ERROR_argument_missing One or more required arguments is missing. UMFPACK_ERROR_internal_error Something very serious went wrong. This is a bug. Please contact the author (davis@cise.ufl.edu). Info [UMFPACK_NROW]: the value of the input argument n_row. Info [UMFPACK_NCOL]: the value of the input argument n_col. Info [UMFPACK_NZ]: the number of entries in the input matrix (Ap [n_col]). Info [UMFPACK_SIZE_OF_UNIT]: the number of bytes in a Unit, for memory usage statistics below. Info [UMFPACK_SIZE_OF_INT]: the number of bytes in an int. Info [UMFPACK_SIZE_OF_LONG]: the number of bytes in a UF_long. Info [UMFPACK_SIZE_OF_POINTER]: the number of bytes in a void * pointer. Info [UMFPACK_SIZE_OF_ENTRY]: the number of bytes in a numerical entry. Info [UMFPACK_NDENSE_ROW]: number of "dense" rows in A. These rows are ignored when the column pre-ordering is computed in COLAMD. They are also treated differently during numeric factorization. If > 0, then the matrix had to be re-analyzed by UMF_analyze, which does not ignore these rows. Info [UMFPACK_NEMPTY_ROW]: number of "empty" rows in A, as determined These are rows that either have no entries, or whose entries are all in pivot columns of zero-Markowitz-cost pivots. Info [UMFPACK_NDENSE_COL]: number of "dense" columns in A. COLAMD orders these columns are ordered last in the factorization, but before "empty" columns. Info [UMFPACK_NEMPTY_COL]: number of "empty" columns in A. These are columns that either have no entries, or whose entries are all in pivot rows of zero-Markowitz-cost pivots. These columns are ordered last in the factorization, to the right of "dense" columns. Info [UMFPACK_SYMBOLIC_DEFRAG]: number of garbage collections performed during ordering and symbolic pre-analysis. Info [UMFPACK_SYMBOLIC_PEAK_MEMORY]: the amount of memory (in Units) required for umfpack_*_symbolic to complete. This count includes the size of the Symbolic object itself, which is also reported in Info [UMFPACK_SYMBOLIC_SIZE]. Info [UMFPACK_SYMBOLIC_SIZE]: the final size of the Symbolic object (in Units). This is fairly small, roughly 2*n to 13*n integers, depending on the matrix. Info [UMFPACK_VARIABLE_INIT_ESTIMATE]: the Numeric object contains two parts. The first is fixed in size (O (n_row+n_col)). The second part holds the sparse LU factors and the contribution blocks from factorized frontal matrices. This part changes in size during factorization. Info [UMFPACK_VARIABLE_INIT_ESTIMATE] is the exact size (in Units) required for this second variable-sized part in order for the numerical factorization to start. Info [UMFPACK_VARIABLE_PEAK_ESTIMATE]: the estimated peak size (in Units) of the variable-sized part of the Numeric object. This is usually an upper bound, but that is not guaranteed. Info [UMFPACK_VARIABLE_FINAL_ESTIMATE]: the estimated final size (in Units) of the variable-sized part of the Numeric object. This is usually an upper bound, but that is not guaranteed. It holds just the sparse LU factors. Info [UMFPACK_NUMERIC_SIZE_ESTIMATE]: an estimate of the final size (in Units) of the entire Numeric object (both fixed-size and variable- sized parts), which holds the LU factorization (including the L, U, P and Q matrices). Info [UMFPACK_PEAK_MEMORY_ESTIMATE]: an estimate of the total amount of memory (in Units) required by umfpack_*_symbolic and umfpack_*_numeric to perform both the symbolic and numeric factorization. This is the larger of the amount of memory needed in umfpack_*_numeric itself, and the amount of memory needed in umfpack_*_symbolic (Info [UMFPACK_SYMBOLIC_PEAK_MEMORY]). The count includes the size of both the Symbolic and Numeric objects themselves. It can be a very loose upper bound, particularly when the symmetric or 2-by-2 strategies are used. Info [UMFPACK_FLOPS_ESTIMATE]: an estimate of the total floating-point operations required to factorize the matrix. This is a "true" theoretical estimate of the number of flops that would be performed by a flop-parsimonious sparse LU algorithm. It assumes that no extra flops are performed except for what is strictly required to compute the LU factorization. It ignores, for example, the flops performed by umfpack_di_numeric to add contribution blocks of frontal matrices together. If L and U are the upper bound on the pattern of the factors, then this flop count estimate can be represented in MATLAB (for real matrices, not complex) as: Lnz = full (sum (spones (L))) - 1 ; % nz in each col of L Unz = full (sum (spones (U')))' - 1 ; % nz in each row of U flops = 2*Lnz*Unz + sum (Lnz) ; The actual "true flop" count found by umfpack_*_numeric will be less than this estimate. For the real version, only (+ - * /) are counted. For the complex version, the following counts are used: operation flops c = 1/b 6 c = a*b 6 c -= a*b 8 Info [UMFPACK_LNZ_ESTIMATE]: an estimate of the number of nonzeros in L, including the diagonal. Since L is unit-diagonal, the diagonal of L is not stored. This estimate is a strict upper bound on the actual nonzeros in L to be computed by umfpack_*_numeric. Info [UMFPACK_UNZ_ESTIMATE]: an estimate of the number of nonzeros in U, including the diagonal. This estimate is a strict upper bound on the actual nonzeros in U to be computed by umfpack_*_numeric. Info [UMFPACK_MAX_FRONT_SIZE_ESTIMATE]: estimate of the size of the largest frontal matrix (# of entries), for arbitrary partial pivoting during numerical factorization. Info [UMFPACK_SYMBOLIC_TIME]: The CPU time taken, in seconds. Info [UMFPACK_SYMBOLIC_WALLTIME]: The wallclock time taken, in seconds. Info [UMFPACK_STRATEGY_USED]: The ordering strategy used: UMFPACK_STRATEGY_SYMMETRIC, UMFPACK_STRATEGY_UNSYMMETRIC, or UMFPACK_STRATEGY_2BY2. Info [UMFPACK_ORDERING_USED]: The ordering method used: UMFPACK_ORDERING_COLAMD or UMFPACK_ORDERING_AMD. It can be UMFPACK_ORDERING_GIVEN for umfpack_*_qsymbolic. Info [UMFPACK_QFIXED]: 1 if the column pre-ordering will be refined during numerical factorization, 0 if not. Info [UMFPACK_DIAG_PREFERED]: 1 if diagonal pivoting will be attempted, 0 if not. Info [UMFPACK_COL_SINGLETONS]: the matrix A is analyzed by first eliminating all pivots with zero Markowitz cost. This count is the number of these pivots with exactly one nonzero in their pivot column. Info [UMFPACK_ROW_SINGLETONS]: the number of zero-Markowitz-cost pivots with exactly one nonzero in their pivot row. Info [UMFPACK_PATTERN_SYMMETRY]: the symmetry of the pattern of S. Info [UMFPACK_NZ_A_PLUS_AT]: the number of off-diagonal entries in S+S'. Info [UMFPACK_NZDIAG]: the number of entries on the diagonal of S. Info [UMFPACK_N2]: if S is square, and nempty_row = nempty_col, this is equal to n_row - n1 - nempty_row. Info [UMFPACK_S_SYMMETRIC]: 1 if S is square and its diagonal has been preserved, 0 otherwise. Info [UMFPACK_MAX_FRONT_NROWS_ESTIMATE]: estimate of the max number of rows in any frontal matrix, for arbitrary partial pivoting. Info [UMFPACK_MAX_FRONT_NCOLS_ESTIMATE]: estimate of the max number of columns in any frontal matrix, for arbitrary partial pivoting. ------------------------------------------------------------------------ The next four statistics are computed only if AMD is used: ------------------------------------------------------------------------ Info [UMFPACK_SYMMETRIC_LUNZ]: The number of nonzeros in L and U, assuming no pivoting during numerical factorization, and assuming a zero-free diagonal of U. Excludes the entries on the diagonal of L. If the matrix has a purely symmetric nonzero pattern, this is often a lower bound on the nonzeros in the actual L and U computed in the numerical factorization, for matrices that fit the criteria for the "symmetric" strategy. Info [UMFPACK_SYMMETRIC_FLOPS]: The floating-point operation count in the numerical factorization phase, assuming no pivoting. If the pattern of the matrix is symmetric, this is normally a lower bound on the floating-point operation count in the actual numerical factorization, for matrices that fit the criteria for the symmetric or 2-by-2 strategies Info [UMFPACK_SYMMETRIC_NDENSE]: The number of "dense" rows/columns of S+S' that were ignored during the AMD ordering. These are placed last in the output order. If > 0, then the Info [UMFPACK_SYMMETRIC_*] statistics, above are rough upper bounds. Info [UMFPACK_SYMMETRIC_DMAX]: The maximum number of nonzeros in any column of L, if no pivoting is performed during numerical factorization. Excludes the part of the LU factorization for pivots with zero Markowitz cost. ------------------------------------------------------------------------ The following statistics are computed only if the 2-by-2 strategy is used or attempted: ------------------------------------------------------------------------ Info [UMFPACK_2BY2_NWEAK]: the number of small diagonal entries in S. Info [UMFPACK_2BY2_UNMATCHED]: the number of small diagonal entries in P2*S. Info [UMFPACK_2BY2_PATTERN_SYMMETRY]: the symmetry of P2*S. Info [UMFPACK_2BY2_NZ_PA_PLUS_AT]: the number of off-diagonal entries in (P2*S)+(P2*S)'. Info [UMFPACK_2BY2_NZDIAG]: the number of nonzero entries on the diagonal of P2*S. At the start of umfpack_*_symbolic, all of Info is set of -1, and then after that only the above listed Info [...] entries are accessed. Future versions might modify different parts of Info. */ SuiteSparse/UMFPACK/Include/umfpack_col_to_triplet.h0000644001170100242450000000720010617161031021314 0ustar davisfac/* ========================================================================== */ /* === umfpack_col_to_triplet =============================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_col_to_triplet ( int n_col, const int Ap [ ], int Tj [ ] ) ; UF_long umfpack_dl_col_to_triplet ( UF_long n_col, const UF_long Ap [ ], UF_long Tj [ ] ) ; int umfpack_zi_col_to_triplet ( int n_col, const int Ap [ ], int Tj [ ] ) ; UF_long umfpack_zl_col_to_triplet ( UF_long n_col, const UF_long Ap [ ], UF_long Tj [ ] ) ; /* double int Syntax: #include "umfpack.h" int n_col, *Tj, *Ap, status ; status = umfpack_di_col_to_triplet (n_col, Ap, Tj) ; double UF_long Syntax: #include "umfpack.h" UF_long n_col, *Tj, *Ap, status ; status = umfpack_dl_col_to_triplet (n_col, Ap, Tj) ; complex int Syntax: #include "umfpack.h" int n_col, *Tj, *Ap, status ; status = umfpack_zi_col_to_triplet (n_col, Ap, Tj) ; complex UF_long Syntax: #include "umfpack.h" UF_long n_col, *Tj, *Ap, status ; status = umfpack_zl_col_to_triplet (n_col, Ap, Tj) ; Purpose: Converts a column-oriented matrix to a triplet form. Only the column pointers, Ap, are required, and only the column indices of the triplet form are constructed. This routine is the opposite of umfpack_*_triplet_to_col. The matrix may be singular and/or rectangular. Analogous to [i, Tj, x] = find (A) in MATLAB, except that zero entries present in the column-form of A are present in the output, and i and x are not created (those are just Ai and Ax+Az*1i, respectively, for a column-form matrix A). Returns: UMFPACK_OK if successful UMFPACK_ERROR_argument_missing if Ap or Tj is missing UMFPACK_ERROR_n_nonpositive if n_col <= 0 UMFPACK_ERROR_invalid_matrix if Ap [n_col] < 0, Ap [0] != 0, or Ap [j] > Ap [j+1] for any j in the range 0 to n-1. Unsorted columns and duplicate entries do not cause an error (these would only be evident by examining Ai). Empty rows and columns are OK. Arguments: Int n_col ; Input argument, not modified. A is an n_row-by-n_col matrix. Restriction: n_col > 0. (n_row is not required) Int Ap [n_col+1] ; Input argument, not modified. The column pointers of the column-oriented form of the matrix. See umfpack_*_*symbolic for a description. The number of entries in the matrix is nz = Ap [n_col]. Restrictions on Ap are the same as those for umfpack_*_transpose. Ap [0] must be zero, nz must be >= 0, and Ap [j] <= Ap [j+1] and Ap [j] <= Ap [n_col] must be true for all j in the range 0 to n_col-1. Empty columns are OK (that is, Ap [j] may equal Ap [j+1] for any j in the range 0 to n_col-1). Int Tj [nz] ; Output argument. Tj is an integer array of size nz on input, where nz = Ap [n_col]. Suppose the column-form of the matrix is held in Ap, Ai, Ax, and Az (see umfpack_*_*symbolic for a description). Then on output, the triplet form of the same matrix is held in Ai (row indices), Tj (column indices), and Ax (numerical values). Note, however, that this routine does not require Ai and Ax (or Az for the complex version) in order to do the conversion. */ SuiteSparse/UMFPACK/Include/umfpack_get_numeric.h0000644001170100242450000002147310617161047020612 0ustar davisfac/* ========================================================================== */ /* === umfpack_get_numeric ================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_get_numeric ( int Lp [ ], int Lj [ ], double Lx [ ], int Up [ ], int Ui [ ], double Ux [ ], int P [ ], int Q [ ], double Dx [ ], int *do_recip, double Rs [ ], void *Numeric ) ; UF_long umfpack_dl_get_numeric ( UF_long Lp [ ], UF_long Lj [ ], double Lx [ ], UF_long Up [ ], UF_long Ui [ ], double Ux [ ], UF_long P [ ], UF_long Q [ ], double Dx [ ], UF_long *do_recip, double Rs [ ], void *Numeric ) ; int umfpack_zi_get_numeric ( int Lp [ ], int Lj [ ], double Lx [ ], double Lz [ ], int Up [ ], int Ui [ ], double Ux [ ], double Uz [ ], int P [ ], int Q [ ], double Dx [ ], double Dz [ ], int *do_recip, double Rs [ ], void *Numeric ) ; UF_long umfpack_zl_get_numeric ( UF_long Lp [ ], UF_long Lj [ ], double Lx [ ], double Lz [ ], UF_long Up [ ], UF_long Ui [ ], double Ux [ ], double Uz [ ], UF_long P [ ], UF_long Q [ ], double Dx [ ], double Dz [ ], UF_long *do_recip, double Rs [ ], void *Numeric ) ; /* double int Syntax: #include "umfpack.h" void *Numeric ; int *Lp, *Lj, *Up, *Ui, *P, *Q, status, do_recip ; double *Lx, *Ux, *Dx, *Rs ; status = umfpack_di_get_numeric (Lp, Lj, Lx, Up, Ui, Ux, P, Q, Dx, &do_recip, Rs, Numeric) ; double UF_long Syntax: #include "umfpack.h" void *Numeric ; UF_long *Lp, *Lj, *Up, *Ui, *P, *Q, status, do_recip ; double *Lx, *Ux, *Dx, *Rs ; status = umfpack_dl_get_numeric (Lp, Lj, Lx, Up, Ui, Ux, P, Q, Dx, &do_recip, Rs, Numeric) ; complex int Syntax: #include "umfpack.h" void *Numeric ; int *Lp, *Lj, *Up, *Ui, *P, *Q, status, do_recip ; double *Lx, *Lz, *Ux, *Uz, *Dx, *Dz, *Rs ; status = umfpack_zi_get_numeric (Lp, Lj, Lx, Lz, Up, Ui, Ux, Uz, P, Q, Dx, Dz, &do_recip, Rs, Numeric) ; complex UF_long Syntax: #include "umfpack.h" void *Numeric ; UF_long *Lp, *Lj, *Up, *Ui, *P, *Q, status, do_recip ; double *Lx, *Lz, *Ux, *Uz, *Dx, *Dz, *Rs ; status = umfpack_zl_get_numeric (Lp, Lj, Lx, Lz, Up, Ui, Ux, Uz, P, Q, Dx, Dz, &do_recip, Rs, Numeric) ; packed complex int/UF_long Syntax: Same as above, except Lz, Uz, and Dz are all NULL. Purpose: This routine copies the LU factors and permutation vectors from the Numeric object into user-accessible arrays. This routine is not needed to solve a linear system. Note that the output arrays Lp, Lj, Lx, Up, Ui, Ux, P, Q, Dx, and Rs are not allocated by umfpack_*_get_numeric; they must exist on input. All output arguments are optional. If any of them are NULL on input, then that part of the LU factorization is not copied. You can use this routine to extract just the parts of the LU factorization that you want. For example, to retrieve just the column permutation Q, use: #define noD (double *) NULL #define noI (int *) NULL status = umfpack_di_get_numeric (noI, noI, noD, noI, noI, noD, noI, Q, noD, noI, noD, Numeric) ; Returns: Returns UMFPACK_OK if successful. Returns UMFPACK_ERROR_out_of_memory if insufficient memory is available for the 2*max(n_row,n_col) integer workspace that umfpack_*_get_numeric allocates to construct L and/or U. Returns UMFPACK_ERROR_invalid_Numeric_object if the Numeric object provided as input is invalid. Arguments: Int Lp [n_row+1] ; Output argument. Int Lj [lnz] ; Output argument. double Lx [lnz] ; Output argument. Size 2*lnz for packed complex case. double Lz [lnz] ; Output argument for complex versions. The n_row-by-min(n_row,n_col) matrix L is returned in compressed-row form. The column indices of row i and corresponding numerical values are in: Lj [Lp [i] ... Lp [i+1]-1] Lx [Lp [i] ... Lp [i+1]-1] real part Lz [Lp [i] ... Lp [i+1]-1] imaginary part (complex versions) respectively. Each row is stored in sorted order, from low column indices to higher. The last entry in each row is the diagonal, which is numerically equal to one. The sizes of Lp, Lj, Lx, and Lz are returned by umfpack_*_get_lunz. If Lp, Lj, or Lx are not present, then the matrix L is not returned. This is not an error condition. The L matrix can be printed if n_row, Lp, Lj, Lx (and Lz for the split complex case) are passed to umfpack_*_report_matrix (using the "row" form). If Lx is present and Lz is NULL, then both real and imaginary parts are returned in Lx[0..2*lnz-1], with Lx[2*k] and Lx[2*k+1] being the real and imaginary part of the kth entry. Int Up [n_col+1] ; Output argument. Int Ui [unz] ; Output argument. double Ux [unz] ; Output argument. Size 2*unz for packed complex case. double Uz [unz] ; Output argument for complex versions. The min(n_row,n_col)-by-n_col matrix U is returned in compressed-column form. The row indices of column j and corresponding numerical values are in Ui [Up [j] ... Up [j+1]-1] Ux [Up [j] ... Up [j+1]-1] real part Uz [Up [j] ... Up [j+1]-1] imaginary part (complex versions) respectively. Each column is stored in sorted order, from low row indices to higher. The last entry in each column is the diagonal (assuming that it is nonzero). The sizes of Up, Ui, Ux, and Uz are returned by umfpack_*_get_lunz. If Up, Ui, or Ux are not present, then the matrix U is not returned. This is not an error condition. The U matrix can be printed if n_col, Up, Ui, Ux (and Uz for the split complex case) are passed to umfpack_*_report_matrix (using the "column" form). If Ux is present and Uz is NULL, then both real and imaginary parts are returned in Ux[0..2*unz-1], with Ux[2*k] and Ux[2*k+1] being the real and imaginary part of the kth entry. Int P [n_row] ; Output argument. The permutation vector P is defined as P [k] = i, where the original row i of A is the kth pivot row in PAQ. If you do not want the P vector to be returned, simply pass (Int *) NULL for P. This is not an error condition. You can print P and Q with umfpack_*_report_perm. Int Q [n_col] ; Output argument. The permutation vector Q is defined as Q [k] = j, where the original column j of A is the kth pivot column in PAQ. If you not want the Q vector to be returned, simply pass (Int *) NULL for Q. This is not an error condition. Note that Q is not necessarily identical to Qtree, the column pre-ordering held in the Symbolic object. Refer to the description of Qtree and Front_npivcol in umfpack_*_get_symbolic for details. double Dx [min(n_row,n_col)] ; Output argument. Size 2*n for the packed complex case. double Dz [min(n_row,n_col)] ; Output argument for complex versions. The diagonal of U is also returned in Dx and Dz. You can extract the diagonal of U without getting all of U by passing a non-NULL Dx (and Dz for the complex version) and passing Up, Ui, and Ux as NULL. Dx is the real part of the diagonal, and Dz is the imaginary part. If Dx is present and Dz is NULL, then both real and imaginary parts are returned in Dx[0..2*min(n_row,n_col)-1], with Dx[2*k] and Dx[2*k+1] being the real and imaginary part of the kth entry. Int *do_recip ; Output argument. This argument defines how the scale factors Rs are to be interpretted. If do_recip is TRUE (one), then the scale factors Rs [i] are to be used by multiplying row i by Rs [i]. Otherwise, the entries in row i are to be divided by Rs [i]. If UMFPACK has been compiled with gcc, or for MATLAB as either a built-in routine or as a mexFunction, then the NRECIPROCAL flag is set, and do_recip will always be FALSE (zero). double Rs [n_row] ; Output argument. The row scale factors are returned in Rs [0..n_row-1]. Row i of A is scaled by dividing or multiplying its values by Rs [i]. If default scaling is in use, Rs [i] is the sum of the absolute values of row i (or its reciprocal). If max row scaling is in use, then Rs [i] is the maximum absolute value in row i (or its reciprocal). Otherwise, Rs [i] = 1. If row i is all zero, Rs [i] = 1 as well. For the complex version, an approximate absolute value is used (|x_real|+|x_imag|). void *Numeric ; Input argument, not modified. Numeric must point to a valid Numeric object, computed by umfpack_*_numeric. */ SuiteSparse/UMFPACK/Include/umfpack_global.h0000644001170100242450000000200510617161053017534 0ustar davisfac/* ========================================================================== */ /* === umfpack_global ======================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* prototypes for global variables, and basic operators for complex values */ #ifndef EXTERN #define EXTERN extern #endif EXTERN double (*umfpack_hypot) (double, double) ; EXTERN int (*umfpack_divcomplex) (double, double, double, double, double *, double *) ; double umf_hypot (double x, double y) ; int umf_divcomplex (double, double, double, double, double *, double *) ; SuiteSparse/UMFPACK/Include/umfpack.h0000644001170100242450000004601710711430425016224 0ustar davisfac/* ========================================================================== */ /* === umfpack.h ============================================================ */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* This is the umfpack.h include file, and should be included in all user code that uses UMFPACK. Do not include any of the umf_* header files in user code. All routines in UMFPACK starting with "umfpack_" are user-callable. All other routines are prefixed "umf_XY_", (where X is d or z, and Y is i or l) and are not user-callable. */ #ifndef UMFPACK_H #define UMFPACK_H /* -------------------------------------------------------------------------- */ /* Make it easy for C++ programs to include UMFPACK */ /* -------------------------------------------------------------------------- */ #ifdef __cplusplus extern "C" { #endif /* define UF_long */ #include "UFconfig.h" /* -------------------------------------------------------------------------- */ /* size of Info and Control arrays */ /* -------------------------------------------------------------------------- */ /* These might be larger in future versions, since there are only 3 unused * entries in Info, and no unused entries in Control. */ #define UMFPACK_INFO 90 #define UMFPACK_CONTROL 20 /* -------------------------------------------------------------------------- */ /* User-callable routines */ /* -------------------------------------------------------------------------- */ /* Primary routines: */ #include "umfpack_symbolic.h" #include "umfpack_numeric.h" #include "umfpack_solve.h" #include "umfpack_free_symbolic.h" #include "umfpack_free_numeric.h" /* Alternative routines: */ #include "umfpack_defaults.h" #include "umfpack_qsymbolic.h" #include "umfpack_wsolve.h" /* Matrix manipulation routines: */ #include "umfpack_triplet_to_col.h" #include "umfpack_col_to_triplet.h" #include "umfpack_transpose.h" #include "umfpack_scale.h" /* Getting the contents of the Symbolic and Numeric opaque objects: */ #include "umfpack_get_lunz.h" #include "umfpack_get_numeric.h" #include "umfpack_get_symbolic.h" #include "umfpack_save_numeric.h" #include "umfpack_load_numeric.h" #include "umfpack_save_symbolic.h" #include "umfpack_load_symbolic.h" #include "umfpack_get_determinant.h" /* Reporting routines (the above 14 routines print nothing): */ #include "umfpack_report_status.h" #include "umfpack_report_info.h" #include "umfpack_report_control.h" #include "umfpack_report_matrix.h" #include "umfpack_report_triplet.h" #include "umfpack_report_vector.h" #include "umfpack_report_symbolic.h" #include "umfpack_report_numeric.h" #include "umfpack_report_perm.h" /* Utility routines: */ #include "umfpack_timer.h" #include "umfpack_tictoc.h" /* AMD */ #include "amd.h" /* global function pointers */ #include "umfpack_global.h" /* -------------------------------------------------------------------------- */ /* Version, copyright, and license */ /* -------------------------------------------------------------------------- */ #define UMFPACK_VERSION "UMFPACK V5.2.0 (Nov 1, 2007)" #define UMFPACK_COPYRIGHT \ "UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved.\n" #define UMFPACK_LICENSE_PART1 \ "\nUMFPACK License:\n" \ "\n" \ " UMFPACK is available under alternate licenses,\n" \ " contact T. Davis for details.\n" \ "\n" \ " Your use or distribution of UMFPACK or any modified version of\n" \ " UMFPACK implies that you agree to this License.\n" \ "\n" \ " This library is free software; you can redistribute it and/or\n" \ " modify it under the terms of the GNU General Public\n" \ " License as published by the Free Software Foundation; either\n" \ " version 2 of the License, or (at your option) any later version.\n" \ "\n" \ " This library is distributed in the hope that it will be useful,\n" \ " but WITHOUT ANY WARRANTY; without even the implied warranty of\n" \ " MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU\n" \ " General Public License for more details.\n" \ "\n" \ " You should have received a copy of the GNU General Public\n" \ " License along with this library; if not, write to the Free Software\n" \ " Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301\n" \ " USA\n" \ #define UMFPACK_LICENSE_PART2 \ "\n" \ " Permission is hereby granted to use or copy this program under the\n" \ " terms of the GNU GPL, provided that the Copyright, this License,\n" \ " and the Availability of the original version is retained on all copies.\n" \ " User documentation of any code that uses this code or any modified\n" \ " version of this code must cite the Copyright, this License, the\n" \ " Availability note, and \"Used by permission.\" Permission to modify\n" \ " the code and to distribute modified code is granted, provided the\n" \ " Copyright, this License, and the Availability note are retained,\n" \ " and a notice that the code was modified is included.\n" #define UMFPACK_LICENSE_PART3 \ "\n" \ "Availability: http://www.cise.ufl.edu/research/sparse/umfpack\n" \ "\n" /* UMFPACK Version 4.5 and later will include the following definitions. * As an example, to test if the version you are using is 4.5 or later: * * #ifdef UMFPACK_VER * if (UMFPACK_VER >= UMFPACK_VER_CODE (4,5)) ... * #endif * * This also works during compile-time: * * #if defined(UMFPACK_VER) && (UMFPACK >= UMFPACK_VER_CODE (4,5)) * printf ("This is version 4.5 or later\n") ; * #else * printf ("This is an early version\n") ; * #endif * * Versions 4.4 and earlier of UMFPACK do not include a #define'd version * number, although they do include the UMFPACK_VERSION string, defined * above. */ #define UMFPACK_DATE "Nov 1, 2007" #define UMFPACK_VER_CODE(main,sub) ((main) * 1000 + (sub)) #define UMFPACK_MAIN_VERSION 5 #define UMFPACK_SUB_VERSION 2 #define UMFPACK_SUBSUB_VERSION 0 #define UMFPACK_VER UMFPACK_VER_CODE(UMFPACK_MAIN_VERSION,UMFPACK_SUB_VERSION) /* -------------------------------------------------------------------------- */ /* contents of Info */ /* -------------------------------------------------------------------------- */ /* Note that umfpack_report.m must coincide with these definitions. S is * the submatrix of A after removing row/col singletons and empty rows/cols. */ /* returned by all routines that use Info: */ #define UMFPACK_STATUS 0 /* UMFPACK_OK, or other result */ #define UMFPACK_NROW 1 /* n_row input value */ #define UMFPACK_NCOL 16 /* n_col input value */ #define UMFPACK_NZ 2 /* # of entries in A */ /* computed in UMFPACK_*symbolic and UMFPACK_numeric: */ #define UMFPACK_SIZE_OF_UNIT 3 /* sizeof (Unit) */ /* computed in UMFPACK_*symbolic: */ #define UMFPACK_SIZE_OF_INT 4 /* sizeof (int) */ #define UMFPACK_SIZE_OF_LONG 5 /* sizeof (UF_long) */ #define UMFPACK_SIZE_OF_POINTER 6 /* sizeof (void *) */ #define UMFPACK_SIZE_OF_ENTRY 7 /* sizeof (Entry), real or complex */ #define UMFPACK_NDENSE_ROW 8 /* number of dense rows */ #define UMFPACK_NEMPTY_ROW 9 /* number of empty rows */ #define UMFPACK_NDENSE_COL 10 /* number of dense rows */ #define UMFPACK_NEMPTY_COL 11 /* number of empty rows */ #define UMFPACK_SYMBOLIC_DEFRAG 12 /* # of memory compactions */ #define UMFPACK_SYMBOLIC_PEAK_MEMORY 13 /* memory used by symbolic analysis */ #define UMFPACK_SYMBOLIC_SIZE 14 /* size of Symbolic object, in Units */ #define UMFPACK_SYMBOLIC_TIME 15 /* time (sec.) for symbolic analysis */ #define UMFPACK_SYMBOLIC_WALLTIME 17 /* wall clock time for sym. analysis */ #define UMFPACK_STRATEGY_USED 18 /* strategy used: sym, unsym, 2by2 */ #define UMFPACK_ORDERING_USED 19 /* ordering used: colamd, amd, given */ #define UMFPACK_QFIXED 31 /* whether Q is fixed or refined */ #define UMFPACK_DIAG_PREFERRED 32 /* whether diagonal pivoting attempted*/ #define UMFPACK_PATTERN_SYMMETRY 33 /* symmetry of pattern of S */ #define UMFPACK_NZ_A_PLUS_AT 34 /* nnz (S+S'), excl. diagonal */ #define UMFPACK_NZDIAG 35 /* nnz (diag (S)) */ /* AMD statistics, computed in UMFPACK_*symbolic: */ #define UMFPACK_SYMMETRIC_LUNZ 36 /* nz in L+U, if AMD ordering used */ #define UMFPACK_SYMMETRIC_FLOPS 37 /* flops for LU, if AMD ordering used */ #define UMFPACK_SYMMETRIC_NDENSE 38 /* # of "dense" rows/cols in S+S' */ #define UMFPACK_SYMMETRIC_DMAX 39 /* max nz in cols of L, for AMD */ /* statistics for 2-by-2 strategy */ #define UMFPACK_2BY2_NWEAK 51 /* number of weak diagonal entries*/ #define UMFPACK_2BY2_UNMATCHED 52 /* # of weak diagonals not matched*/ #define UMFPACK_2BY2_PATTERN_SYMMETRY 53 /* symmetry of pattern of P*S */ #define UMFPACK_2BY2_NZ_PA_PLUS_PAT 54 /* nz in PS+(PS)' */ #define UMFPACK_2BY2_NZDIAG 55 /* nz on diagonal of PS+(PS)' */ /* statistcs for singleton pruning */ #define UMFPACK_COL_SINGLETONS 56 /* # of column singletons */ #define UMFPACK_ROW_SINGLETONS 57 /* # of row singletons */ #define UMFPACK_N2 58 /* size of S */ #define UMFPACK_S_SYMMETRIC 59 /* 1 if S square and symmetricly perm.*/ /* estimates computed in UMFPACK_*symbolic: */ #define UMFPACK_NUMERIC_SIZE_ESTIMATE 20 /* final size of Numeric->Memory */ #define UMFPACK_PEAK_MEMORY_ESTIMATE 21 /* for symbolic & numeric */ #define UMFPACK_FLOPS_ESTIMATE 22 /* flop count */ #define UMFPACK_LNZ_ESTIMATE 23 /* nz in L, incl. diagonal */ #define UMFPACK_UNZ_ESTIMATE 24 /* nz in U, incl. diagonal */ #define UMFPACK_VARIABLE_INIT_ESTIMATE 25 /* initial size of Numeric->Memory*/ #define UMFPACK_VARIABLE_PEAK_ESTIMATE 26 /* peak size of Numeric->Memory */ #define UMFPACK_VARIABLE_FINAL_ESTIMATE 27 /* final size of Numeric->Memory */ #define UMFPACK_MAX_FRONT_SIZE_ESTIMATE 28 /* max frontal matrix size */ #define UMFPACK_MAX_FRONT_NROWS_ESTIMATE 29 /* max # rows in any front */ #define UMFPACK_MAX_FRONT_NCOLS_ESTIMATE 30 /* max # columns in any front */ /* exact values, (estimates shown above) computed in UMFPACK_numeric: */ #define UMFPACK_NUMERIC_SIZE 40 /* final size of Numeric->Memory */ #define UMFPACK_PEAK_MEMORY 41 /* for symbolic & numeric */ #define UMFPACK_FLOPS 42 /* flop count */ #define UMFPACK_LNZ 43 /* nz in L, incl. diagonal */ #define UMFPACK_UNZ 44 /* nz in U, incl. diagonal */ #define UMFPACK_VARIABLE_INIT 45 /* initial size of Numeric->Memory*/ #define UMFPACK_VARIABLE_PEAK 46 /* peak size of Numeric->Memory */ #define UMFPACK_VARIABLE_FINAL 47 /* final size of Numeric->Memory */ #define UMFPACK_MAX_FRONT_SIZE 48 /* max frontal matrix size */ #define UMFPACK_MAX_FRONT_NROWS 49 /* max # rows in any front */ #define UMFPACK_MAX_FRONT_NCOLS 50 /* max # columns in any front */ /* computed in UMFPACK_numeric: */ #define UMFPACK_NUMERIC_DEFRAG 60 /* # of garbage collections */ #define UMFPACK_NUMERIC_REALLOC 61 /* # of memory reallocations */ #define UMFPACK_NUMERIC_COSTLY_REALLOC 62 /* # of costlly memory realloc's */ #define UMFPACK_COMPRESSED_PATTERN 63 /* # of integers in LU pattern */ #define UMFPACK_LU_ENTRIES 64 /* # of reals in LU factors */ #define UMFPACK_NUMERIC_TIME 65 /* numeric factorization time */ #define UMFPACK_UDIAG_NZ 66 /* nz on diagonal of U */ #define UMFPACK_RCOND 67 /* est. reciprocal condition # */ #define UMFPACK_WAS_SCALED 68 /* none, max row, or sum row */ #define UMFPACK_RSMIN 69 /* min (max row) or min (sum row) */ #define UMFPACK_RSMAX 70 /* max (max row) or max (sum row) */ #define UMFPACK_UMIN 71 /* min abs diagonal entry of U */ #define UMFPACK_UMAX 72 /* max abs diagonal entry of U */ #define UMFPACK_ALLOC_INIT_USED 73 /* alloc_init parameter used */ #define UMFPACK_FORCED_UPDATES 74 /* # of forced updates */ #define UMFPACK_NUMERIC_WALLTIME 75 /* numeric wall clock time */ #define UMFPACK_NOFF_DIAG 76 /* number of off-diagonal pivots */ #define UMFPACK_ALL_LNZ 77 /* nz in L, if no dropped entries */ #define UMFPACK_ALL_UNZ 78 /* nz in U, if no dropped entries */ #define UMFPACK_NZDROPPED 79 /* # of dropped small entries */ /* computed in UMFPACK_solve: */ #define UMFPACK_IR_TAKEN 80 /* # of iterative refinement steps taken */ #define UMFPACK_IR_ATTEMPTED 81 /* # of iter. refinement steps attempted */ #define UMFPACK_OMEGA1 82 /* omega1, sparse backward error estimate */ #define UMFPACK_OMEGA2 83 /* omega2, sparse backward error estimate */ #define UMFPACK_SOLVE_FLOPS 84 /* flop count for solve */ #define UMFPACK_SOLVE_TIME 85 /* solve time (seconds) */ #define UMFPACK_SOLVE_WALLTIME 86 /* solve time (wall clock, seconds) */ /* Info [87, 88, 89] unused */ /* Unused parts of Info may be used in future versions of UMFPACK. */ /* -------------------------------------------------------------------------- */ /* Info [UMFPACK_ORDERING_USED] is one of the following: */ #define UMFPACK_ORDERING_COLAMD 0 /* COLAMD(A) */ #define UMFPACK_ORDERING_AMD 1 /* AMD(A+A') */ #define UMFPACK_ORDERING_GIVEN 2 /* Q is provided on input */ /* -------------------------------------------------------------------------- */ /* contents of Control */ /* -------------------------------------------------------------------------- */ /* used in all UMFPACK_report_* routines: */ #define UMFPACK_PRL 0 /* print level */ /* used in UMFPACK_*symbolic only: */ #define UMFPACK_DENSE_ROW 1 /* dense row parameter */ #define UMFPACK_DENSE_COL 2 /* dense col parameter */ #define UMFPACK_BLOCK_SIZE 4 /* BLAS-3 block size */ #define UMFPACK_STRATEGY 5 /* auto, symmetric, unsym., or 2by2 */ #define UMFPACK_2BY2_TOLERANCE 12 /* 2-by-2 pivot tolerance */ #define UMFPACK_FIXQ 13 /* -1: no fixQ, 0: default, 1: fixQ */ #define UMFPACK_AMD_DENSE 14 /* for AMD ordering */ #define UMFPACK_AGGRESSIVE 19 /* whether or not to use aggressive * absorption in AMD and COLAMD */ /* used in UMFPACK_numeric only: */ #define UMFPACK_PIVOT_TOLERANCE 3 /* threshold partial pivoting setting */ #define UMFPACK_ALLOC_INIT 6 /* initial allocation ratio */ #define UMFPACK_SYM_PIVOT_TOLERANCE 15 /* threshold, only for diag. entries */ #define UMFPACK_SCALE 16 /* what row scaling to do */ #define UMFPACK_FRONT_ALLOC_INIT 17 /* frontal matrix allocation ratio */ #define UMFPACK_DROPTOL 18 /* drop tolerance for entries in L,U */ /* used in UMFPACK_*solve only: */ #define UMFPACK_IRSTEP 7 /* max # of iterative refinements */ /* compile-time settings - Control [8..11] cannot be changed at run time: */ #define UMFPACK_COMPILED_WITH_BLAS 8 /* uses the BLAS */ #define UMFPACK_COMPILED_FOR_MATLAB 9 /* 1 if MATLAB mexFunction, etc. */ #define UMFPACK_COMPILED_WITH_GETRUSAGE 10 /* uses getrusage timer, or not */ #define UMFPACK_COMPILED_IN_DEBUG_MODE 11 /* debugging enabled (very slow!) */ /* -------------------------------------------------------------------------- */ /* Control [UMFPACK_STRATEGY] is one of the following: */ #define UMFPACK_STRATEGY_AUTO 0 /* use sym. or unsym. strategy */ #define UMFPACK_STRATEGY_UNSYMMETRIC 1 /* COLAMD(A), coletree postorder, not prefer diag*/ #define UMFPACK_STRATEGY_2BY2 2 /* AMD(PA+PA'), no coletree postorder, prefer diag(PA) where P is pseudo max transversal */ #define UMFPACK_STRATEGY_SYMMETRIC 3 /* AMD(A+A'), no coletree postorder, prefer diagonal */ /* Control [UMFPACK_SCALE] is one of the following: */ #define UMFPACK_SCALE_NONE 0 /* no scaling */ #define UMFPACK_SCALE_SUM 1 /* default: divide each row by sum (abs (row))*/ #define UMFPACK_SCALE_MAX 2 /* divide each row by max (abs (row)) */ /* -------------------------------------------------------------------------- */ /* default values of Control: */ /* -------------------------------------------------------------------------- */ #define UMFPACK_DEFAULT_PRL 1 #define UMFPACK_DEFAULT_DENSE_ROW 0.2 #define UMFPACK_DEFAULT_DENSE_COL 0.2 #define UMFPACK_DEFAULT_PIVOT_TOLERANCE 0.1 #define UMFPACK_DEFAULT_2BY2_TOLERANCE 0.01 #define UMFPACK_DEFAULT_SYM_PIVOT_TOLERANCE 0.001 #define UMFPACK_DEFAULT_BLOCK_SIZE 32 #define UMFPACK_DEFAULT_ALLOC_INIT 0.7 #define UMFPACK_DEFAULT_FRONT_ALLOC_INIT 0.5 #define UMFPACK_DEFAULT_IRSTEP 2 #define UMFPACK_DEFAULT_SCALE UMFPACK_SCALE_SUM #define UMFPACK_DEFAULT_STRATEGY UMFPACK_STRATEGY_AUTO #define UMFPACK_DEFAULT_AMD_DENSE AMD_DEFAULT_DENSE #define UMFPACK_DEFAULT_FIXQ 0 #define UMFPACK_DEFAULT_AGGRESSIVE 1 #define UMFPACK_DEFAULT_DROPTOL 0 /* default values of Control may change in future versions of UMFPACK. */ /* -------------------------------------------------------------------------- */ /* status codes */ /* -------------------------------------------------------------------------- */ #define UMFPACK_OK (0) /* status > 0 means a warning, but the method was successful anyway. */ /* A Symbolic or Numeric object was still created. */ #define UMFPACK_WARNING_singular_matrix (1) /* The following warnings were added in umfpack_*_get_determinant */ #define UMFPACK_WARNING_determinant_underflow (2) #define UMFPACK_WARNING_determinant_overflow (3) /* status < 0 means an error, and the method was not successful. */ /* No Symbolic of Numeric object was created. */ #define UMFPACK_ERROR_out_of_memory (-1) #define UMFPACK_ERROR_invalid_Numeric_object (-3) #define UMFPACK_ERROR_invalid_Symbolic_object (-4) #define UMFPACK_ERROR_argument_missing (-5) #define UMFPACK_ERROR_n_nonpositive (-6) #define UMFPACK_ERROR_invalid_matrix (-8) #define UMFPACK_ERROR_different_pattern (-11) #define UMFPACK_ERROR_invalid_system (-13) #define UMFPACK_ERROR_invalid_permutation (-15) #define UMFPACK_ERROR_internal_error (-911) /* yes, call me if you get this! */ #define UMFPACK_ERROR_file_IO (-17) /* -------------------------------------------------------------------------- */ /* solve codes */ /* -------------------------------------------------------------------------- */ /* Solve the system ( )x=b, where ( ) is defined below. "t" refers to the */ /* linear algebraic transpose (complex conjugate if A is complex), or the (') */ /* operator in MATLAB. "at" refers to the array transpose, or the (.') */ /* operator in MATLAB. */ #define UMFPACK_A (0) /* Ax=b */ #define UMFPACK_At (1) /* A'x=b */ #define UMFPACK_Aat (2) /* A.'x=b */ #define UMFPACK_Pt_L (3) /* P'Lx=b */ #define UMFPACK_L (4) /* Lx=b */ #define UMFPACK_Lt_P (5) /* L'Px=b */ #define UMFPACK_Lat_P (6) /* L.'Px=b */ #define UMFPACK_Lt (7) /* L'x=b */ #define UMFPACK_Lat (8) /* L.'x=b */ #define UMFPACK_U_Qt (9) /* UQ'x=b */ #define UMFPACK_U (10) /* Ux=b */ #define UMFPACK_Q_Ut (11) /* QU'x=b */ #define UMFPACK_Q_Uat (12) /* QU.'x=b */ #define UMFPACK_Ut (13) /* U'x=b */ #define UMFPACK_Uat (14) /* U.'x=b */ /* -------------------------------------------------------------------------- */ /* Integer constants are used for status and solve codes instead of enum */ /* to make it easier for a Fortran code to call UMFPACK. */ #ifdef __cplusplus } #endif #endif /* UMFPACK_H */ SuiteSparse/UMFPACK/Include/umfpack_get_symbolic.h0000644001170100242450000003154210617161051020762 0ustar davisfac/* ========================================================================== */ /* === umfpack_get_symbolic ================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_get_symbolic ( int *n_row, int *n_col, int *n1, int *nz, int *nfr, int *nchains, int P [ ], int Q [ ], int Front_npivcol [ ], int Front_parent [ ], int Front_1strow [ ], int Front_leftmostdesc [ ], int Chain_start [ ], int Chain_maxrows [ ], int Chain_maxcols [ ], void *Symbolic ) ; UF_long umfpack_dl_get_symbolic ( UF_long *n_row, UF_long *n_col, UF_long *n1, UF_long *nz, UF_long *nfr, UF_long *nchains, UF_long P [ ], UF_long Q [ ], UF_long Front_npivcol [ ], UF_long Front_parent [ ], UF_long Front_1strow [ ], UF_long Front_leftmostdesc [ ], UF_long Chain_start [ ], UF_long Chain_maxrows [ ], UF_long Chain_maxcols [ ], void *Symbolic ) ; int umfpack_zi_get_symbolic ( int *n_row, int *n_col, int *n1, int *nz, int *nfr, int *nchains, int P [ ], int Q [ ], int Front_npivcol [ ], int Front_parent [ ], int Front_1strow [ ], int Front_leftmostdesc [ ], int Chain_start [ ], int Chain_maxrows [ ], int Chain_maxcols [ ], void *Symbolic ) ; UF_long umfpack_zl_get_symbolic ( UF_long *n_row, UF_long *n_col, UF_long *n1, UF_long *nz, UF_long *nfr, UF_long *nchains, UF_long P [ ], UF_long Q [ ], UF_long Front_npivcol [ ], UF_long Front_parent [ ], UF_long Front_1strow [ ], UF_long Front_leftmostdesc [ ], UF_long Chain_start [ ], UF_long Chain_maxrows [ ], UF_long Chain_maxcols [ ], void *Symbolic ) ; /* double int Syntax: #include "umfpack.h" int status, n_row, n_col, nz, nfr, nchains, *P, *Q, *Front_npivcol, *Front_parent, *Front_1strow, *Front_leftmostdesc, *Chain_start, *Chain_maxrows, *Chain_maxcols ; void *Symbolic ; status = umfpack_di_get_symbolic (&n_row, &n_col, &nz, &nfr, &nchains, P, Q, Front_npivcol, Front_parent, Front_1strow, Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ; double UF_long Syntax: #include "umfpack.h" UF_long status, n_row, n_col, nz, nfr, nchains, *P, *Q, *Front_npivcol, *Front_parent, *Front_1strow, *Front_leftmostdesc, *Chain_start, *Chain_maxrows, *Chain_maxcols ; void *Symbolic ; status = umfpack_dl_get_symbolic (&n_row, &n_col, &nz, &nfr, &nchains, P, Q, Front_npivcol, Front_parent, Front_1strow, Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ; complex int Syntax: #include "umfpack.h" int status, n_row, n_col, nz, nfr, nchains, *P, *Q, *Front_npivcol, *Front_parent, *Front_1strow, *Front_leftmostdesc, *Chain_start, *Chain_maxrows, *Chain_maxcols ; void *Symbolic ; status = umfpack_zi_get_symbolic (&n_row, &n_col, &nz, &nfr, &nchains, P, Q, Front_npivcol, Front_parent, Front_1strow, Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ; complex UF_long Syntax: #include "umfpack.h" UF_long status, n_row, n_col, nz, nfr, nchains, *P, *Q, *Front_npivcol, *Front_parent, *Front_1strow, *Front_leftmostdesc, *Chain_start, *Chain_maxrows, *Chain_maxcols ; void *Symbolic ; status = umfpack_zl_get_symbolic (&n_row, &n_col, &nz, &nfr, &nchains, P, Q, Front_npivcol, Front_parent, Front_1strow, Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ; Purpose: Copies the contents of the Symbolic object into simple integer arrays accessible to the user. This routine is not needed to factorize and/or solve a sparse linear system using UMFPACK. Note that the output arrays P, Q, Front_npivcol, Front_parent, Front_1strow, Front_leftmostdesc, Chain_start, Chain_maxrows, and Chain_maxcols are not allocated by umfpack_*_get_symbolic; they must exist on input. All output arguments are optional. If any of them are NULL on input, then that part of the symbolic analysis is not copied. You can use this routine to extract just the parts of the symbolic analysis that you want. For example, to retrieve just the column permutation Q, use: #define noI (int *) NULL status = umfpack_di_get_symbolic (noI, noI, noI, noI, noI, noI, noI, Q, noI, noI, noI, noI, noI, noI, noI, Symbolic) ; The only required argument the last one, the pointer to the Symbolic object. The Symbolic object is small. Its size for an n-by-n square matrix varies from 4*n to 13*n, depending on the matrix. The object holds the initial column permutation, the supernodal column elimination tree, and information about each frontal matrix. You can print it with umfpack_*_report_symbolic. Returns: Returns UMFPACK_OK if successful, UMFPACK_ERROR_invalid_Symbolic_object if Symbolic is an invalid object. Arguments: Int *n_row ; Output argument. Int *n_col ; Output argument. The dimensions of the matrix A analyzed by the call to umfpack_*_symbolic that generated the Symbolic object. Int *n1 ; Output argument. The number of pivots with zero Markowitz cost (they have just one entry in the pivot row, or the pivot column, or both). These appear first in the output permutations P and Q. Int *nz ; Output argument. The number of nonzeros in A. Int *nfr ; Output argument. The number of frontal matrices that will be used by umfpack_*_numeric to factorize the matrix A. It is in the range 0 to n_col. Int *nchains ; Output argument. The frontal matrices are related to one another by the supernodal column elimination tree. Each node in this tree is one frontal matrix. The tree is partitioned into a set of disjoint paths, and a frontal matrix chain is one path in this tree. Each chain is factorized using a unifrontal technique, with a single working array that holds each frontal matrix in the chain, one at a time. nchains is in the range 0 to nfr. Int P [n_row] ; Output argument. The initial row permutation. If P [k] = i, then this means that row i is the kth row in the pre-ordered matrix. In general, this P is not the same as the final row permutation computed by umfpack_*_numeric. For the unsymmetric strategy, P defines the row-merge order. Let j be the column index of the leftmost nonzero entry in row i of A*Q. Then P defines a sort of the rows according to this value. A row can appear earlier in this ordering if it is aggressively absorbed before it can become a pivot row. If P [k] = i, row i typically will not be the kth pivot row. For the symmetric strategy, P = Q. For the 2-by-2 strategy, P is the row permutation that places large entries on the diagonal of P*A*Q. If no pivoting occurs during numerical factorization, P [k] = i also defines the final permutation of umfpack_*_numeric, for either the symmetric or 2-by-2 strategies. Int Q [n_col] ; Output argument. The initial column permutation. If Q [k] = j, then this means that column j is the kth pivot column in the pre-ordered matrix. Q is not necessarily the same as the final column permutation Q, computed by umfpack_*_numeric. The numeric factorization may reorder the pivot columns within each frontal matrix to reduce fill-in. If the matrix is structurally singular, and if the symmetric or 2-by-2 strategies or used (or if Control [UMFPACK_FIXQ] > 0), then this Q will be the same as the final column permutation computed in umfpack_*_numeric. Int Front_npivcol [n_col+1] ; Output argument. This array should be of size at least n_col+1, in order to guarantee that it will be large enough to hold the output. Only the first nfr+1 entries are used, however. The kth frontal matrix holds Front_npivcol [k] pivot columns. Thus, the first frontal matrix, front 0, is used to factorize the first Front_npivcol [0] columns; these correspond to the original columns Q [0] through Q [Front_npivcol [0]-1]. The next frontal matrix is used to factorize the next Front_npivcol [1] columns, which are thus the original columns Q [Front_npivcol [0]] through Q [Front_npivcol [0] + Front_npivcol [1] - 1], and so on. Columns with no entries at all are put in a placeholder "front", Front_npivcol [nfr]. The sum of Front_npivcol [0..nfr] is equal to n_col. Any modifications that umfpack_*_numeric makes to the initial column permutation are constrained to within each frontal matrix. Thus, for the first frontal matrix, Q [0] through Q [Front_npivcol [0]-1] is some permutation of the columns Q [0] through Q [Front_npivcol [0]-1]. For second frontal matrix, Q [Front_npivcol [0]] through Q [Front_npivcol [0] + Front_npivcol[1]-1] is some permutation of the same portion of Q, and so on. All pivot columns are numerically factorized within the frontal matrix originally determined by the symbolic factorization; there is no delayed pivoting across frontal matrices. Int Front_parent [n_col+1] ; Output argument. This array should be of size at least n_col+1, in order to guarantee that it will be large enough to hold the output. Only the first nfr+1 entries are used, however. Front_parent [0..nfr] holds the supernodal column elimination tree (including the placeholder front nfr, which may be empty). Each node in the tree corresponds to a single frontal matrix. The parent of node f is Front_parent [f]. Int Front_1strow [n_col+1] ; Output argument. This array should be of size at least n_col+1, in order to guarantee that it will be large enough to hold the output. Only the first nfr+1 entries are used, however. Front_1strow [k] is the row index of the first row in A (P,Q) whose leftmost entry is in a pivot column for the kth front. This is necessary only to properly factorize singular matrices. Rows in the range Front_1strow [k] to Front_1strow [k+1]-1 first become pivot row candidates at the kth front. Any rows not eliminated in the kth front may be selected as pivot rows in the parent of k (Front_parent [k]) and so on up the tree. Int Front_leftmostdesc [n_col+1] ; Output argument. This array should be of size at least n_col+1, in order to guarantee that it will be large enough to hold the output. Only the first nfr+1 entries are used, however. Front_leftmostdesc [k] is the leftmost descendant of front k, or k if the front has no children in the tree. Since the rows and columns (P and Q) have been post-ordered via a depth-first-search of the tree, rows in the range Front_1strow [Front_leftmostdesc [k]] to Front_1strow [k+1]-1 form the entire set of candidate pivot rows for the kth front (some of these will typically have already been selected by fronts in the range Front_leftmostdesc [k] to front k-1, before the factorization reaches front k). Chain_start [n_col+1] ; Output argument. This array should be of size at least n_col+1, in order to guarantee that it will be large enough to hold the output. Only the first nchains+1 entries are used, however. The kth frontal matrix chain consists of frontal matrices Chain_start[k] through Chain_start [k+1]-1. Thus, Chain_start [0] is always 0, and Chain_start [nchains] is the total number of frontal matrices, nfr. For two adjacent fronts f and f+1 within a single chain, f+1 is always the parent of f (that is, Front_parent [f] = f+1). Int Chain_maxrows [n_col+1] ; Output argument. Int Chain_maxcols [n_col+1] ; Output argument. These arrays should be of size at least n_col+1, in order to guarantee that they will be large enough to hold the output. Only the first nchains entries are used, however. The kth frontal matrix chain requires a single working array of dimension Chain_maxrows [k] by Chain_maxcols [k], for the unifrontal technique that factorizes the frontal matrix chain. Since the symbolic factorization only provides an upper bound on the size of each frontal matrix, not all of the working array is necessarily used during the numerical factorization. Note that the upper bound on the number of rows and columns of each frontal matrix is computed by umfpack_*_symbolic, but all that is required by umfpack_*_numeric is the maximum of these two sets of values for each frontal matrix chain. Thus, the size of each individual frontal matrix is not preserved in the Symbolic object. void *Symbolic ; Input argument, not modified. The Symbolic object, which holds the symbolic factorization computed by umfpack_*_symbolic. The Symbolic object is not modified by umfpack_*_get_symbolic. */ SuiteSparse/UMFPACK/Include/umfpack_load_numeric.h0000644001170100242450000000503110617161061020736 0ustar davisfac/* ========================================================================== */ /* === umfpack_load_numeric ================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_load_numeric ( void **Numeric, char *filename ) ; UF_long umfpack_dl_load_numeric ( void **Numeric, char *filename ) ; int umfpack_zi_load_numeric ( void **Numeric, char *filename ) ; UF_long umfpack_zl_load_numeric ( void **Numeric, char *filename ) ; /* double int Syntax: #include "umfpack.h" int status ; char *filename ; void *Numeric ; status = umfpack_di_load_numeric (&Numeric, filename) ; double UF_long Syntax: #include "umfpack.h" UF_long status ; char *filename ; void *Numeric ; status = umfpack_dl_load_numeric (&Numeric, filename) ; complex int Syntax: #include "umfpack.h" int status ; char *filename ; void *Numeric ; status = umfpack_zi_load_numeric (&Numeric, filename) ; complex UF_long Syntax: #include "umfpack.h" UF_long status ; char *filename ; void *Numeric ; status = umfpack_zl_load_numeric (&Numeric, filename) ; Purpose: Loads a Numeric object from a file created by umfpack_*_save_numeric. The Numeric handle passed to this routine is overwritten with the new object. If that object exists prior to calling this routine, a memory leak will occur. The contents of Numeric are ignored on input. Returns: UMFPACK_OK if successful. UMFPACK_ERROR_out_of_memory if not enough memory is available. UMFPACK_ERROR_file_IO if an I/O error occurred. Arguments: void **Numeric ; Output argument. **Numeric is the address of a (void *) pointer variable in the user's calling routine (see Syntax, above). On input, the contents of this variable are not defined. On output, this variable holds a (void *) pointer to the Numeric object (if successful), or (void *) NULL if a failure occurred. char *filename ; Input argument, not modified. A string that contains the filename from which to read the Numeric object. */ SuiteSparse/UMFPACK/Include/umfpack_report_triplet.h0000644001170100242450000001143510617161113021356 0ustar davisfac/* ========================================================================== */ /* === umfpack_report_triplet =============================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_report_triplet ( int n_row, int n_col, int nz, const int Ti [ ], const int Tj [ ], const double Tx [ ], const double Control [UMFPACK_CONTROL] ) ; UF_long umfpack_dl_report_triplet ( UF_long n_row, UF_long n_col, UF_long nz, const UF_long Ti [ ], const UF_long Tj [ ], const double Tx [ ], const double Control [UMFPACK_CONTROL] ) ; int umfpack_zi_report_triplet ( int n_row, int n_col, int nz, const int Ti [ ], const int Tj [ ], const double Tx [ ], const double Tz [ ], const double Control [UMFPACK_CONTROL] ) ; UF_long umfpack_zl_report_triplet ( UF_long n_row, UF_long n_col, UF_long nz, const UF_long Ti [ ], const UF_long Tj [ ], const double Tx [ ], const double Tz [ ], const double Control [UMFPACK_CONTROL] ) ; /* double int Syntax: #include "umfpack.h" int n_row, n_col, nz, *Ti, *Tj, status ; double *Tx, Control [UMFPACK_CONTROL] ; status = umfpack_di_report_triplet (n_row, n_col, nz, Ti, Tj, Tx, Control) ; double UF_long Syntax: #include "umfpack.h" UF_long n_row, n_col, nz, *Ti, *Tj, status ; double *Tx, Control [UMFPACK_CONTROL] ; status = umfpack_dl_report_triplet (n_row, n_col, nz, Ti, Tj, Tx, Control) ; complex int Syntax: #include "umfpack.h" int n_row, n_col, nz, *Ti, *Tj, status ; double *Tx, *Tz, Control [UMFPACK_CONTROL] ; status = umfpack_zi_report_triplet (n_row, n_col, nz, Ti, Tj, Tx, Tz, Control) ; complex UF_long Syntax: #include "umfpack.h" UF_long n_row, n_col, nz, *Ti, *Tj, status ; double *Tx, *Tz, Control [UMFPACK_CONTROL] ; status = umfpack_zl_report_triplet (n_row, n_col, nz, Ti, Tj, Tx, Tz, Control) ; packed complex Syntax: Same as above, except Tz is NULL. Purpose: Verifies and prints a matrix in triplet form. Returns: UMFPACK_OK if Control [UMFPACK_PRL] <= 2 (the input is not checked). Otherwise: UMFPACK_OK if the Triplet matrix is OK. UMFPACK_ERROR_argument_missing if Ti and/or Tj are missing. UMFPACK_ERROR_n_nonpositive if n_row <= 0 or n_col <= 0. UMFPACK_ERROR_invalid_matrix if nz < 0, or if any row or column index in Ti and/or Tj is not in the range 0 to n_row-1 or 0 to n_col-1, respectively. Arguments: Int n_row ; Input argument, not modified. Int n_col ; Input argument, not modified. A is an n_row-by-n_col matrix. Int nz ; Input argument, not modified. The number of entries in the triplet form of the matrix. Int Ti [nz] ; Input argument, not modified. Int Tj [nz] ; Input argument, not modified. double Tx [nz] ; Input argument, not modified. Size 2*nz for packed complex case. double Tz [nz] ; Input argument, not modified, for complex versions. Ti, Tj, Tx (and Tz for complex versions) hold the "triplet" form of a sparse matrix. The kth nonzero entry is in row i = Ti [k], column j = Tj [k], the real numerical value of a_ij is Tx [k], and the imaginary part of a_ij is Tz [k] (for complex versions). The row and column indices i and j must be in the range 0 to n_row-1 or 0 to n_col-1, respectively. Duplicate entries may be present. The "triplets" may be in any order. Tx and Tz are optional; if Tx is not present ((double *) NULL), then the numerical values are not printed. If Tx is present and Tz is NULL, then both real and imaginary parts are contained in Tx[0..2*nz-1], with Tx[2*k] and Tx[2*k+1] being the real and imaginary part of the kth entry. double Control [UMFPACK_CONTROL] ; Input argument, not modified. If a (double *) NULL pointer is passed, then the default control settings are used. Otherwise, the settings are determined from the Control array. See umfpack_*_defaults on how to fill the Control array with the default settings. If Control contains NaN's, the defaults are used. The following Control parameters are used: Control [UMFPACK_PRL]: printing level. 2 or less: no output. returns silently without checking anything. 3: fully check input, and print a short summary of its status 4: as 3, but print first few entries of the input 5: as 3, but print all of the input Default: 1 */ SuiteSparse/UMFPACK/Include/umfpack_save_numeric.h0000644001170100242450000000430310617161120020752 0ustar davisfac/* ========================================================================== */ /* === umfpack_save_numeric ================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_save_numeric ( void *Numeric, char *filename ) ; UF_long umfpack_dl_save_numeric ( void *Numeric, char *filename ) ; int umfpack_zi_save_numeric ( void *Numeric, char *filename ) ; UF_long umfpack_zl_save_numeric ( void *Numeric, char *filename ) ; /* double int Syntax: #include "umfpack.h" int status ; char *filename ; void *Numeric ; status = umfpack_di_save_numeric (Numeric, filename) ; double UF_long Syntax: #include "umfpack.h" UF_long status ; char *filename ; void *Numeric ; status = umfpack_dl_save_numeric (Numeric, filename) ; complex int Syntax: #include "umfpack.h" int status ; char *filename ; void *Numeric ; status = umfpack_zi_save_numeric (Numeric, filename) ; complex UF_long Syntax: #include "umfpack.h" UF_long status ; char *filename ; void *Numeric ; status = umfpack_zl_save_numeric (Numeric, filename) ; Purpose: Saves a Numeric object to a file, which can later be read by umfpack_*_load_numeric. The Numeric object is not modified. Returns: UMFPACK_OK if successful. UMFPACK_ERROR_invalid_Numeric_object if Numeric is not valid. UMFPACK_ERROR_file_IO if an I/O error occurred. Arguments: void *Numeric ; Input argument, not modified. Numeric must point to a valid Numeric object, computed by umfpack_*_numeric or loaded by umfpack_*_load_numeric. char *filename ; Input argument, not modified. A string that contains the filename to which the Numeric object is written. */ SuiteSparse/UMFPACK/Include/umfpack_numeric.h0000644001170100242450000005525710617161065017762 0ustar davisfac/* ========================================================================== */ /* === umfpack_numeric ====================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_numeric ( const int Ap [ ], const int Ai [ ], const double Ax [ ], void *Symbolic, void **Numeric, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO] ) ; UF_long umfpack_dl_numeric ( const UF_long Ap [ ], const UF_long Ai [ ], const double Ax [ ], void *Symbolic, void **Numeric, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO] ) ; int umfpack_zi_numeric ( const int Ap [ ], const int Ai [ ], const double Ax [ ], const double Az [ ], void *Symbolic, void **Numeric, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO] ) ; UF_long umfpack_zl_numeric ( const UF_long Ap [ ], const UF_long Ai [ ], const double Ax [ ], const double Az [ ], void *Symbolic, void **Numeric, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO] ) ; /* double int Syntax: #include "umfpack.h" void *Symbolic, *Numeric ; int *Ap, *Ai, status ; double *Ax, Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ; status = umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric, Control, Info); double UF_long Syntax: #include "umfpack.h" void *Symbolic, *Numeric ; UF_long *Ap, *Ai, status ; double *Ax, Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ; status = umfpack_dl_numeric (Ap, Ai, Ax, Symbolic, &Numeric, Control, Info); complex int Syntax: #include "umfpack.h" void *Symbolic, *Numeric ; int *Ap, *Ai, status ; double *Ax, *Az, Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ; status = umfpack_zi_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric, Control, Info) ; complex UF_long Syntax: #include "umfpack.h" void *Symbolic, *Numeric ; UF_long *Ap, *Ai, status ; double *Ax, *Az, Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ; status = umfpack_zl_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric, Control, Info) ; packed complex Syntax: Same as above, except that Az is NULL. Purpose: Given a sparse matrix A in column-oriented form, and a symbolic analysis computed by umfpack_*_*symbolic, the umfpack_*_numeric routine performs the numerical factorization, PAQ=LU, PRAQ=LU, or P(R\A)Q=LU, where P and Q are permutation matrices (represented as permutation vectors), R is the row scaling, L is unit-lower triangular, and U is upper triangular. This is required before the system Ax=b (or other related linear systems) can be solved. umfpack_*_numeric can be called multiple times for each call to umfpack_*_*symbolic, to factorize a sequence of matrices with identical nonzero pattern. Simply compute the Symbolic object once, with umfpack_*_*symbolic, and reuse it for subsequent matrices. This routine safely detects if the pattern changes, and sets an appropriate error code. Returns: The status code is returned. See Info [UMFPACK_STATUS], below. Arguments: Int Ap [n_col+1] ; Input argument, not modified. This must be identical to the Ap array passed to umfpack_*_*symbolic. The value of n_col is what was passed to umfpack_*_*symbolic (this is held in the Symbolic object). Int Ai [nz] ; Input argument, not modified, of size nz = Ap [n_col]. This must be identical to the Ai array passed to umfpack_*_*symbolic. double Ax [nz] ; Input argument, not modified, of size nz = Ap [n_col]. Size 2*nz for packed complex case. The numerical values of the sparse matrix A. The nonzero pattern (row indices) for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and the corresponding numerical values are stored in Ax [(Ap [j]) ... (Ap [j+1]-1)]. double Az [nz] ; Input argument, not modified, for complex versions. For the complex versions, this holds the imaginary part of A. The imaginary part of column j is held in Az [(Ap [j]) ... (Ap [j+1]-1)]. If Az is NULL, then both real and imaginary parts are contained in Ax[0..2*nz-1], with Ax[2*k] and Ax[2*k+1] being the real and imaginary part of the kth entry. void *Symbolic ; Input argument, not modified. The Symbolic object, which holds the symbolic factorization computed by umfpack_*_*symbolic. The Symbolic object is not modified by umfpack_*_numeric. void **Numeric ; Output argument. **Numeric is the address of a (void *) pointer variable in the user's calling routine (see Syntax, above). On input, the contents of this variable are not defined. On output, this variable holds a (void *) pointer to the Numeric object (if successful), or (void *) NULL if a failure occurred. double Control [UMFPACK_CONTROL] ; Input argument, not modified. If a (double *) NULL pointer is passed, then the default control settings are used. Otherwise, the settings are determined from the Control array. See umfpack_*_defaults on how to fill the Control array with the default settings. If Control contains NaN's, the defaults are used. The following Control parameters are used: Control [UMFPACK_PIVOT_TOLERANCE]: relative pivot tolerance for threshold partial pivoting with row interchanges. In any given column, an entry is numerically acceptable if its absolute value is greater than or equal to Control [UMFPACK_PIVOT_TOLERANCE] times the largest absolute value in the column. A value of 1.0 gives true partial pivoting. If less than or equal to zero, then any nonzero entry is numerically acceptable as a pivot. Default: 0.1. Smaller values tend to lead to sparser LU factors, but the solution to the linear system can become inaccurate. Larger values can lead to a more accurate solution (but not always), and usually an increase in the total work. For complex matrices, a cheap approximate of the absolute value is used for the threshold partial pivoting test (|a_real| + |a_imag| instead of the more expensive-to-compute exact absolute value sqrt (a_real^2 + a_imag^2)). Control [UMFPACK_SYM_PIVOT_TOLERANCE]: If diagonal pivoting is attempted (the symmetric or symmetric-2by2 strategies are used) then this parameter is used to control when the diagonal entry is selected in a given pivot column. The absolute value of the entry must be >= Control [UMFPACK_SYM_PIVOT_TOLERANCE] times the largest absolute value in the column. A value of zero will ensure that no off-diagonal pivoting is performed, except that zero diagonal entries are not selected if there are any off-diagonal nonzero entries. If an off-diagonal pivot is selected, an attempt is made to restore symmetry later on. Suppose A (i,j) is selected, where i != j. If column i has not yet been selected as a pivot column, then the entry A (j,i) is redefined as a "diagonal" entry, except that the tighter tolerance (Control [UMFPACK_PIVOT_TOLERANCE]) is applied. This strategy has an effect similar to 2-by-2 pivoting for symmetric indefinite matrices. If a 2-by-2 block pivot with nonzero structure i j i: 0 x j: x 0 is selected in a symmetric indefinite factorization method, the 2-by-2 block is inverted and a rank-2 update is applied. In UMFPACK, this 2-by-2 block would be reordered as j i i: x 0 j: 0 x In both cases, the symmetry of the Schur complement is preserved. Control [UMFPACK_SCALE]: Note that the user's input matrix is never modified, only an internal copy is scaled. There are three valid settings for this parameter. If any other value is provided, the default is used. UMFPACK_SCALE_NONE: no scaling is performed. UMFPACK_SCALE_SUM: each row of the input matrix A is divided by the sum of the absolute values of the entries in that row. The scaled matrix has an infinity norm of 1. UMFPACK_SCALE_MAX: each row of the input matrix A is divided by the maximum the absolute values of the entries in that row. In the scaled matrix the largest entry in each row has a magnitude exactly equal to 1. Note that for complex matrices, a cheap approximate absolute value is used, |a_real| + |a_imag|, instead of the exact absolute value sqrt ((a_real)^2 + (a_imag)^2). Scaling is very important for the "symmetric" strategy when diagonal pivoting is attempted. It also improves the performance of the "unsymmetric" strategy. Default: UMFPACK_SCALE_SUM. Control [UMFPACK_ALLOC_INIT]: When umfpack_*_numeric starts, it allocates memory for the Numeric object. Part of this is of fixed size (approximately n double's + 12*n integers). The remainder is of variable size, which grows to hold the LU factors and the frontal matrices created during factorization. A estimate of the upper bound is computed by umfpack_*_*symbolic, and returned by umfpack_*_*symbolic in Info [UMFPACK_VARIABLE_PEAK_ESTIMATE] (in Units). If Control [UMFPACK_ALLOC_INIT] is >= 0, umfpack_*_numeric initially allocates space for the variable-sized part equal to this estimate times Control [UMFPACK_ALLOC_INIT]. Typically, for matrices for which the "unsymmetric" strategy applies, umfpack_*_numeric needs only about half the estimated memory space, so a setting of 0.5 or 0.6 often provides enough memory for umfpack_*_numeric to factorize the matrix with no subsequent increases in the size of this block. If the matrix is ordered via AMD, then this non-negative parameter is ignored. The initial allocation ratio computed automatically, as 1.2 * (nz + Info [UMFPACK_SYMMETRIC_LUNZ]) / (Info [UMFPACK_LNZ_ESTIMATE] + Info [UMFPACK_UNZ_ESTIMATE] - min (n_row, n_col)). If Control [UMFPACK_ALLOC_INIT] is negative, then umfpack_*_numeric allocates a space with initial size (in Units) equal to (-Control [UMFPACK_ALLOC_INIT]). Regardless of the value of this parameter, a space equal to or greater than the the bare minimum amount of memory needed to start the factorization is always initially allocated. The bare initial memory required is returned by umfpack_*_*symbolic in Info [UMFPACK_VARIABLE_INIT_ESTIMATE] (an exact value, not an estimate). If the variable-size part of the Numeric object is found to be too small sometime after numerical factorization has started, the memory is increased in size by a factor of 1.2. If this fails, the request is reduced by a factor of 0.95 until it succeeds, or until it determines that no increase in size is possible. Garbage collection then occurs. The strategy of attempting to "malloc" a working space, and re-trying with a smaller space, may not work when UMFPACK is used as a mexFunction MATLAB, since mxMalloc aborts the mexFunction if it fails. This issue does not affect the use of UMFPACK as a part of the built-in x=A\b in MATLAB 6.5 and later. If you are using the umfpack mexFunction, decrease the magnitude of Control [UMFPACK_ALLOC_INIT] if you run out of memory in MATLAB. Default initial allocation size: 0.7. Thus, with the default control settings and the "unsymmetric" strategy, the upper-bound is reached after two reallocations (0.7 * 1.2 * 1.2 = 1.008). Changing this parameter has little effect on fill-in or operation count. It has a small impact on run-time (the extra time required to do the garbage collection and memory reallocation). Control [UMFPACK_FRONT_ALLOC_INIT]: When UMFPACK starts the factorization of each "chain" of frontal matrices, it allocates a working array to hold the frontal matrices as they are factorized. The symbolic factorization computes the size of the largest possible frontal matrix that could occur during the factorization of each chain. If Control [UMFPACK_FRONT_ALLOC_INIT] is >= 0, the following strategy is used. If the AMD ordering was used, this non-negative parameter is ignored. A front of size (d+2)*(d+2) is allocated, where d = Info [UMFPACK_SYMMETRIC_DMAX]. Otherwise, a front of size Control [UMFPACK_FRONT_ALLOC_INIT] times the largest front possible for this chain is allocated. If Control [UMFPACK_FRONT_ALLOC_INIT] is negative, then a front of size (-Control [UMFPACK_FRONT_ALLOC_INIT]) is allocated (where the size is in terms of the number of numerical entries). This is done regardless of the ordering method or ordering strategy used. Default: 0.5. Control [UMFPACK_DROPTOL]: Entries in L and U with absolute value less than or equal to the drop tolerance are removed from the data structures (unless leaving them there reduces memory usage by reducing the space required for the nonzero pattern of L and U). Default: 0.0. double Info [UMFPACK_INFO] ; Output argument. Contains statistics about the numeric factorization. If a (double *) NULL pointer is passed, then no statistics are returned in Info (this is not an error condition). The following statistics are computed in umfpack_*_numeric: Info [UMFPACK_STATUS]: status code. This is also the return value, whether or not Info is present. UMFPACK_OK Numeric factorization was successful. umfpack_*_numeric computed a valid numeric factorization. UMFPACK_WARNING_singular_matrix Numeric factorization was successful, but the matrix is singular. umfpack_*_numeric computed a valid numeric factorization, but you will get a divide by zero in umfpack_*_*solve. For the other cases below, no Numeric object is created (*Numeric is (void *) NULL). UMFPACK_ERROR_out_of_memory Insufficient memory to complete the numeric factorization. UMFPACK_ERROR_argument_missing One or more required arguments are missing. UMFPACK_ERROR_invalid_Symbolic_object Symbolic object provided as input is invalid. UMFPACK_ERROR_different_pattern The pattern (Ap and/or Ai) has changed since the call to umfpack_*_*symbolic which produced the Symbolic object. Info [UMFPACK_NROW]: the value of n_row stored in the Symbolic object. Info [UMFPACK_NCOL]: the value of n_col stored in the Symbolic object. Info [UMFPACK_NZ]: the number of entries in the input matrix. This value is obtained from the Symbolic object. Info [UMFPACK_SIZE_OF_UNIT]: the number of bytes in a Unit, for memory usage statistics below. Info [UMFPACK_VARIABLE_INIT]: the initial size (in Units) of the variable-sized part of the Numeric object. If this differs from Info [UMFPACK_VARIABLE_INIT_ESTIMATE], then the pattern (Ap and/or Ai) has changed since the last call to umfpack_*_*symbolic, which is an error condition. Info [UMFPACK_VARIABLE_PEAK]: the peak size (in Units) of the variable-sized part of the Numeric object. This size is the amount of space actually used inside the block of memory, not the space allocated via UMF_malloc. You can reduce UMFPACK's memory requirements by setting Control [UMFPACK_ALLOC_INIT] to the ratio Info [UMFPACK_VARIABLE_PEAK] / Info[UMFPACK_VARIABLE_PEAK_ESTIMATE]. This will ensure that no memory reallocations occur (you may want to add 0.001 to make sure that integer roundoff does not lead to a memory size that is 1 Unit too small; otherwise, garbage collection and reallocation will occur). Info [UMFPACK_VARIABLE_FINAL]: the final size (in Units) of the variable-sized part of the Numeric object. It holds just the sparse LU factors. Info [UMFPACK_NUMERIC_SIZE]: the actual final size (in Units) of the entire Numeric object, including the final size of the variable part of the object. Info [UMFPACK_NUMERIC_SIZE_ESTIMATE], an estimate, was computed by umfpack_*_*symbolic. The estimate is normally an upper bound on the actual final size, but this is not guaranteed. Info [UMFPACK_PEAK_MEMORY]: the actual peak memory usage (in Units) of both umfpack_*_*symbolic and umfpack_*_numeric. An estimate, Info [UMFPACK_PEAK_MEMORY_ESTIMATE], was computed by umfpack_*_*symbolic. The estimate is normally an upper bound on the actual peak usage, but this is not guaranteed. With testing on hundreds of matrix arising in real applications, I have never observed a matrix where this estimate or the Numeric size estimate was less than the actual result, but this is theoretically possible. Please send me one if you find such a matrix. Info [UMFPACK_FLOPS]: the actual count of the (useful) floating-point operations performed. An estimate, Info [UMFPACK_FLOPS_ESTIMATE], was computed by umfpack_*_*symbolic. The estimate is guaranteed to be an upper bound on this flop count. The flop count excludes "useless" flops on zero values, flops performed during the pivot search (for tentative updates and assembly of candidate columns), and flops performed to add frontal matrices together. For the real version, only (+ - * /) are counted. For the complex version, the following counts are used: operation flops c = 1/b 6 c = a*b 6 c -= a*b 8 Info [UMFPACK_LNZ]: the actual nonzero entries in final factor L, including the diagonal. This excludes any zero entries in L, although some of these are stored in the Numeric object. The Info [UMFPACK_LU_ENTRIES] statistic does account for all explicitly stored zeros, however. Info [UMFPACK_LNZ_ESTIMATE], an estimate, was computed by umfpack_*_*symbolic. The estimate is guaranteed to be an upper bound on Info [UMFPACK_LNZ]. Info [UMFPACK_UNZ]: the actual nonzero entries in final factor U, including the diagonal. This excludes any zero entries in U, although some of these are stored in the Numeric object. The Info [UMFPACK_LU_ENTRIES] statistic does account for all explicitly stored zeros, however. Info [UMFPACK_UNZ_ESTIMATE], an estimate, was computed by umfpack_*_*symbolic. The estimate is guaranteed to be an upper bound on Info [UMFPACK_UNZ]. Info [UMFPACK_NUMERIC_DEFRAG]: The number of garbage collections performed during umfpack_*_numeric, to compact the contents of the variable-sized workspace used by umfpack_*_numeric. No estimate was computed by umfpack_*_*symbolic. In the current version of UMFPACK, garbage collection is performed and then the memory is reallocated, so this statistic is the same as Info [UMFPACK_NUMERIC_REALLOC], below. It may differ in future releases. Info [UMFPACK_NUMERIC_REALLOC]: The number of times that the Numeric object was increased in size from its initial size. A rough upper bound on the peak size of the Numeric object was computed by umfpack_*_*symbolic, so reallocations should be rare. However, if umfpack_*_numeric is unable to allocate that much storage, it reduces its request until either the allocation succeeds, or until it gets too small to do anything with. If the memory that it finally got was small, but usable, then the reallocation count could be high. No estimate of this count was computed by umfpack_*_*symbolic. Info [UMFPACK_NUMERIC_COSTLY_REALLOC]: The number of times that the system realloc library routine (or mxRealloc for the mexFunction) had to move the workspace. Realloc can sometimes increase the size of a block of memory without moving it, which is much faster. This statistic will always be <= Info [UMFPACK_NUMERIC_REALLOC]. If your memory space is fragmented, then the number of "costly" realloc's will be equal to Info [UMFPACK_NUMERIC_REALLOC]. Info [UMFPACK_COMPRESSED_PATTERN]: The number of integers used to represent the pattern of L and U. Info [UMFPACK_LU_ENTRIES]: The total number of numerical values that are stored for the LU factors. Some of the values may be explicitly zero in order to save space (allowing for a smaller compressed pattern). Info [UMFPACK_NUMERIC_TIME]: The CPU time taken, in seconds. Info [UMFPACK_RCOND]: A rough estimate of the condition number, equal to min (abs (diag (U))) / max (abs (diag (U))), or zero if the diagonal of U is all zero. Info [UMFPACK_UDIAG_NZ]: The number of numerically nonzero values on the diagonal of U. Info [UMFPACK_UMIN]: the smallest absolute value on the diagonal of U. Info [UMFPACK_UMAX]: the smallest absolute value on the diagonal of U. Info [UMFPACK_MAX_FRONT_SIZE]: the size of the largest frontal matrix (number of entries). Info [UMFPACK_NUMERIC_WALLTIME]: The wallclock time taken, in seconds. Info [UMFPACK_MAX_FRONT_NROWS]: the max number of rows in any frontal matrix. Info [UMFPACK_MAX_FRONT_NCOLS]: the max number of columns in any frontal matrix. Info [UMFPACK_WAS_SCALED]: the scaling used, either UMFPACK_SCALE_NONE, UMFPACK_SCALE_SUM, or UMFPACK_SCALE_MAX. Info [UMFPACK_RSMIN]: if scaling is performed, the smallest scale factor for any row (either the smallest sum of absolute entries, or the smallest maximum of absolute entries). Info [UMFPACK_RSMAX]: if scaling is performed, the largest scale factor for any row (either the largest sum of absolute entries, or the largest maximum of absolute entries). Info [UMFPACK_ALLOC_INIT_USED]: the initial allocation parameter used. Info [UMFPACK_FORCED_UPDATES]: the number of BLAS-3 updates to the frontal matrices that were required because the frontal matrix grew larger than its current working array. Info [UMFPACK_NOFF_DIAG]: number of off-diagonal pivots selected, if the symmetric or 2-by-2 strategies are used. Info [UMFPACK_NZDROPPED]: the number of entries smaller in absolute value than Control [UMFPACK_DROPTOL] that were dropped from L and U. Note that entries on the diagonal of U are never dropped. Info [UMFPACK_ALL_LNZ]: the number of entries in L, including the diagonal, if no small entries are dropped. Info [UMFPACK_ALL_UNZ]: the number of entries in U, including the diagonal, if no small entries are dropped. Only the above listed Info [...] entries are accessed. The remaining entries of Info are not accessed or modified by umfpack_*_numeric. Future versions might modify different parts of Info. */ SuiteSparse/UMFPACK/Include/umfpack_get_lunz.h0000644001170100242450000000762510617161043020137 0ustar davisfac/* ========================================================================== */ /* === umfpack_get_lunz ===================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_get_lunz ( int *lnz, int *unz, int *n_row, int *n_col, int *nz_udiag, void *Numeric ) ; UF_long umfpack_dl_get_lunz ( UF_long *lnz, UF_long *unz, UF_long *n_row, UF_long *n_col, UF_long *nz_udiag, void *Numeric ) ; int umfpack_zi_get_lunz ( int *lnz, int *unz, int *n_row, int *n_col, int *nz_udiag, void *Numeric ) ; UF_long umfpack_zl_get_lunz ( UF_long *lnz, UF_long *unz, UF_long *n_row, UF_long *n_col, UF_long *nz_udiag, void *Numeric ) ; /* double int Syntax: #include "umfpack.h" void *Numeric ; int status, lnz, unz, n_row, n_col, nz_udiag ; status = umfpack_di_get_lunz (&lnz, &unz, &n_row, &n_col, &nz_udiag, Numeric) ; double UF_long Syntax: #include "umfpack.h" void *Numeric ; UF_long status, lnz, unz, n_row, n_col, nz_udiag ; status = umfpack_dl_get_lunz (&lnz, &unz, &n_row, &n_col, &nz_udiag, Numeric) ; complex int Syntax: #include "umfpack.h" void *Numeric ; int status, lnz, unz, n_row, n_col, nz_udiag ; status = umfpack_zi_get_lunz (&lnz, &unz, &n_row, &n_col, &nz_udiag, Numeric) ; complex UF_long Syntax: #include "umfpack.h" void *Numeric ; UF_long status, lnz, unz, n_row, n_col, nz_udiag ; status = umfpack_zl_get_lunz (&lnz, &unz, &n_row, &n_col, &nz_udiag, Numeric) ; Purpose: Determines the size and number of nonzeros in the LU factors held by the Numeric object. These are also the sizes of the output arrays required by umfpack_*_get_numeric. The matrix L is n_row -by- min(n_row,n_col), with lnz nonzeros, including the entries on the unit diagonal of L. The matrix U is min(n_row,n_col) -by- n_col, with unz nonzeros, including nonzeros on the diagonal of U. Returns: UMFPACK_OK if successful. UMFPACK_ERROR_invalid_Numeric_object if Numeric is not a valid object. UMFPACK_ERROR_argument_missing if any other argument is (Int *) NULL. Arguments: Int *lnz ; Output argument. The number of nonzeros in L, including the diagonal (which is all one's). This value is the required size of the Lj and Lx arrays as computed by umfpack_*_get_numeric. The value of lnz is identical to Info [UMFPACK_LNZ], if that value was returned by umfpack_*_numeric. Int *unz ; Output argument. The number of nonzeros in U, including the diagonal. This value is the required size of the Ui and Ux arrays as computed by umfpack_*_get_numeric. The value of unz is identical to Info [UMFPACK_UNZ], if that value was returned by umfpack_*_numeric. Int *n_row ; Output argument. Int *n_col ; Output argument. The order of the L and U matrices. L is n_row -by- min(n_row,n_col) and U is min(n_row,n_col) -by- n_col. Int *nz_udiag ; Output argument. The number of numerically nonzero values on the diagonal of U. The matrix is singular if nz_diag < min(n_row,n_col). A divide-by-zero will occur if nz_diag < n_row == n_col when solving a sparse system involving the matrix U in umfpack_*_*solve. The value of nz_udiag is identical to Info [UMFPACK_UDIAG_NZ] if that value was returned by umfpack_*_numeric. void *Numeric ; Input argument, not modified. Numeric must point to a valid Numeric object, computed by umfpack_*_numeric. */ SuiteSparse/UMFPACK/Include/umfpack_report_control.h0000644001170100242450000000422510617161075021361 0ustar davisfac/* ========================================================================== */ /* === umfpack_report_control =============================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ void umfpack_di_report_control ( const double Control [UMFPACK_CONTROL] ) ; void umfpack_dl_report_control ( const double Control [UMFPACK_CONTROL] ) ; void umfpack_zi_report_control ( const double Control [UMFPACK_CONTROL] ) ; void umfpack_zl_report_control ( const double Control [UMFPACK_CONTROL] ) ; /* double int Syntax: #include "umfpack.h" double Control [UMFPACK_CONTROL] ; umfpack_di_report_control (Control) ; double UF_long Syntax: #include "umfpack.h" double Control [UMFPACK_CONTROL] ; umfpack_dl_report_control (Control) ; complex int Syntax: #include "umfpack.h" double Control [UMFPACK_CONTROL] ; umfpack_zi_report_control (Control) ; double UF_long Syntax: #include "umfpack.h" double Control [UMFPACK_CONTROL] ; umfpack_zl_report_control (Control) ; Purpose: Prints the current control settings. Note that with the default print level, nothing is printed. Does nothing if Control is (double *) NULL. Arguments: double Control [UMFPACK_CONTROL] ; Input argument, not modified. If a (double *) NULL pointer is passed, then the default control settings are used. Otherwise, the settings are determined from the Control array. See umfpack_*_defaults on how to fill the Control array with the default settings. If Control contains NaN's, the defaults are used. The following Control parameters are used: Control [UMFPACK_PRL]: printing level. 1 or less: no output 2 or more: print all of Control Default: 1 */ SuiteSparse/UMFPACK/Include/umfpack_save_symbolic.h0000644001170100242450000000434210617161122021136 0ustar davisfac/* ========================================================================== */ /* === umfpack_save_symbolic================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_save_symbolic ( void *Symbolic, char *filename ) ; UF_long umfpack_dl_save_symbolic ( void *Symbolic, char *filename ) ; int umfpack_zi_save_symbolic ( void *Symbolic, char *filename ) ; UF_long umfpack_zl_save_symbolic ( void *Symbolic, char *filename ) ; /* double int Syntax: #include "umfpack.h" int status ; char *filename ; void *Symbolic ; status = umfpack_di_save_symbolic (Symbolic, filename) ; double UF_long Syntax: #include "umfpack.h" UF_long status ; char *filename ; void *Symbolic ; status = umfpack_dl_save_symbolic (Symbolic, filename) ; complex int Syntax: #include "umfpack.h" int status ; char *filename ; void *Symbolic ; status = umfpack_zi_save_symbolic (Symbolic, filename) ; complex UF_long Syntax: #include "umfpack.h" UF_long status ; char *filename ; void *Symbolic ; status = umfpack_zl_save_symbolic (Symbolic, filename) ; Purpose: Saves a Symbolic object to a file, which can later be read by umfpack_*_load_symbolic. The Symbolic object is not modified. Returns: UMFPACK_OK if successful. UMFPACK_ERROR_invalid_Symbolic_object if Symbolic is not valid. UMFPACK_ERROR_file_IO if an I/O error occurred. Arguments: void *Symbolic ; Input argument, not modified. Symbolic must point to a valid Symbolic object, computed by umfpack_*_symbolic or loaded by umfpack_*_load_symbolic. char *filename ; Input argument, not modified. A string that contains the filename to which the Symbolic object is written. */ SuiteSparse/UMFPACK/Include/umfpack_get_determinant.h0000644001170100242450000001417610617161041021456 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_get_determinant ============================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* UMFPACK_get_determinant contributed by David Bateman, Motorola, Paris. */ /* -------------------------------------------------------------------------- */ int umfpack_di_get_determinant ( double *Mx, double *Ex, void *NumericHandle, double User_Info [UMFPACK_INFO] ) ; UF_long umfpack_dl_get_determinant ( double *Mx, double *Ex, void *NumericHandle, double User_Info [UMFPACK_INFO] ) ; int umfpack_zi_get_determinant ( double *Mx, double *Mz, double *Ex, void *NumericHandle, double User_Info [UMFPACK_INFO] ) ; UF_long umfpack_zl_get_determinant ( double *Mx, double *Mz, double *Ex, void *NumericHandle, double User_Info [UMFPACK_INFO] ) ; /* double int Syntax: #include "umfpack.h" void *Numeric ; int status ; double Mx, Ex, Info [UMFPACK_INFO] ; status = umfpack_di_get_determinant (&Mx, &Ex, Numeric, Info) ; double UF_long Syntax: #include "umfpack.h" void *Numeric ; UF_long status ; double Mx, Ex, Info [UMFPACK_INFO] ; status = umfpack_dl_get_determinant (&Mx, &Ex, Numeric, Info) ; complex int Syntax: #include "umfpack.h" void *Numeric ; int status ; double Mx, Mz, Ex, Info [UMFPACK_INFO] ; status = umfpack_zi_get_determinant (&Mx, &Mz, &Ex, Numeric, Info) ; complex int Syntax: #include "umfpack.h" void *Numeric ; UF_long status ; double *Mx, *Mz, *Ex, Info [UMFPACK_INFO] ; status = umfpack_zl_get_determinant (&Mx, &Mz, &Ex, Numeric, Info) ; packed complex int Syntax: Same as above, except Mz is NULL. Author: Contributed by David Bateman, Motorola, Paris Purpose: Using the LU factors and the permutation vectors contained in the Numeric object, calculate the determinant of the matrix A. The value of the determinant can be returned in two forms, depending on whether Ex is NULL or not. If Ex is NULL then the value of the determinant is returned on Mx and Mz for the real and imaginary parts. However, to avoid over- or underflows, the determinant can be split into a mantissa and exponent, and the parts returned separately, in which case Ex is not NULL. The actual determinant is then given by double det ; det = Mx * pow (10.0, Ex) ; for the double case, or double det [2] ; det [0] = Mx * pow (10.0, Ex) ; // real part det [1] = Mz * pow (10.0, Ex) ; // imaginary part for the complex case. Information on if the determinant will or has over or under-flowed is given by Info [UMFPACK_STATUS]. In the "packed complex" syntax, Mx [0] holds the real part and Mx [1] holds the imaginary part. Mz is not used (it is NULL). Returns: Returns UMFPACK_OK if sucessful. Returns UMFPACK_ERROR_out_of_memory if insufficient memory is available for the n_row integer workspace that umfpack_*_get_determinant allocates to construct pivots from the permutation vectors. Returns UMFPACK_ERROR_invalid_Numeric_object if the Numeric object provided as input is invalid. Returns UMFPACK_WARNING_singular_matrix if the determinant is zero. Returns UMFPACK_WARNING_determinant_underflow or UMFPACK_WARNING_determinant_overflow if the determinant has underflowed overflowed (for the case when Ex is NULL), or will overflow if Ex is not NULL and det is computed (see above) in the user program. Arguments: double *Mx ; Output argument (array of size 1, or size 2 if Mz is NULL) double *Mz ; Output argument (optional) double *Ex ; Output argument (optional) The determinant returned in mantissa/exponent form, as discussed above. If Mz is NULL, then both the original and imaginary parts will be returned in Mx. If Ex is NULL then the determinant is returned directly in Mx and Mz (or Mx [0] and Mx [1] if Mz is NULL), rather than in mantissa/exponent form. void *Numeric ; Input argument, not modified. Numeric must point to a valid Numeric object, computed by umfpack_*_numeric. double Info [UMFPACK_INFO] ; Output argument. Contains information about the calculation of the determinant. If a (double *) NULL pointer is passed, then no statistics are returned in Info (this is not an error condition). The following statistics are computed in umfpack_*_determinant: Info [UMFPACK_STATUS]: status code. This is also the return value, whether or not Info is present. UMFPACK_OK The determinant was successfully found. UMFPACK_ERROR_out_of_memory Insufficient memory to solve the linear system. UMFPACK_ERROR_argument_missing Mx is missing (NULL). UMFPACK_ERROR_invalid_Numeric_object The Numeric object is not valid. UMFPACK_ERROR_invalid_system The matrix is rectangular. Only square systems can be handled. UMFPACK_WARNING_singluar_matrix The determinant is zero or NaN. The matrix is singular. UMFPACK_WARNING_determinant_underflow When passing from mantissa/exponent form to the determinant an underflow has or will occur. If the mantissa/exponent from of obtaining the determinant is used, the underflow will occur in the user program. If the single argument method of obtaining the determinant is used, the underflow has already occurred. UMFPACK_WARNING_determinant_overflow When passing from mantissa/exponent form to the determinant an overflow has or will occur. If the mantissa/exponent from of obtaining the determinant is used, the overflow will occur in the user program. If the single argument method of obtaining the determinant is used, the overflow has already occurred. */ SuiteSparse/UMFPACK/Include/umfpack_tictoc.h0000644001170100242450000000426110617161134017567 0ustar davisfac/* ========================================================================== */ /* === umfpack_tictoc ======================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ void umfpack_tic (double stats [2]) ; void umfpack_toc (double stats [2]) ; /* Syntax (for all versions: di, dl, zi, and zl): #include "umfpack.h" double stats [2] ; umfpack_tic (stats) ; ... umfpack_toc (stats) ; Purpose: umfpack_tic returns the CPU time and wall clock time used by the process. The CPU time includes both "user" and "system" time (the latter is time spent by the system on behalf of the process, and is thus charged to the process). umfpack_toc returns the CPU time and wall clock time since the last call to umfpack_tic with the same stats array. Typical usage: umfpack_tic (stats) ; ... do some work ... umfpack_toc (stats) ; then stats [1] contains the time in seconds used by the code between umfpack_tic and umfpack_toc, and stats [0] contains the wall clock time elapsed between the umfpack_tic and umfpack_toc. These two routines act just like tic and toc in MATLAB, except that the both process time and wall clock time are returned. This routine normally uses the sysconf and times routines in the POSIX standard. If -DNPOSIX is defined at compile time, then the ANSI C clock routine is used instead, and only the CPU time is returned (stats [0] is set to zero). umfpack_tic and umfpack_toc are the routines used internally in UMFPACK to time the symbolic analysis, numerical factorization, and the forward/ backward solve. Arguments: double stats [2]: stats [0]: wall clock time, in seconds stats [1]: CPU time, in seconds */ SuiteSparse/UMFPACK/Include/umfpack_defaults.h0000644001170100242450000000354410617161033020112 0ustar davisfac/* ========================================================================== */ /* === umfpack_defaults ===================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ void umfpack_di_defaults ( double Control [UMFPACK_CONTROL] ) ; void umfpack_dl_defaults ( double Control [UMFPACK_CONTROL] ) ; void umfpack_zi_defaults ( double Control [UMFPACK_CONTROL] ) ; void umfpack_zl_defaults ( double Control [UMFPACK_CONTROL] ) ; /* double int Syntax: #include "umfpack.h" double Control [UMFPACK_CONTROL] ; umfpack_di_defaults (Control) ; double UF_long Syntax: #include "umfpack.h" double Control [UMFPACK_CONTROL] ; umfpack_dl_defaults (Control) ; complex int Syntax: #include "umfpack.h" double Control [UMFPACK_CONTROL] ; umfpack_zi_defaults (Control) ; complex UF_long Syntax: #include "umfpack.h" double Control [UMFPACK_CONTROL] ; umfpack_zl_defaults (Control) ; Purpose: Sets the default control parameter settings. Arguments: double Control [UMFPACK_CONTROL] ; Output argument. Control is set to the default control parameter settings. You can then modify individual settings by changing specific entries in the Control array. If Control is a (double *) NULL pointer, then umfpack_*_defaults returns silently (no error is generated, since passing a NULL pointer for Control to any UMFPACK routine is valid). */ SuiteSparse/UMFPACK/Include/umfpack_report_vector.h0000644001170100242450000001063310617161116021177 0ustar davisfac/* ========================================================================== */ /* === umfpack_report_vector ================================================ */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_report_vector ( int n, const double X [ ], const double Control [UMFPACK_CONTROL] ) ; UF_long umfpack_dl_report_vector ( UF_long n, const double X [ ], const double Control [UMFPACK_CONTROL] ) ; int umfpack_zi_report_vector ( int n, const double Xx [ ], const double Xz [ ], const double Control [UMFPACK_CONTROL] ) ; UF_long umfpack_zl_report_vector ( UF_long n, const double Xx [ ], const double Xz [ ], const double Control [UMFPACK_CONTROL] ) ; /* double int Syntax: #include "umfpack.h" int n, status ; double *X, Control [UMFPACK_CONTROL] ; status = umfpack_di_report_vector (n, X, Control) ; double UF_long Syntax: #include "umfpack.h" UF_long n, status ; double *X, Control [UMFPACK_CONTROL] ; status = umfpack_dl_report_vector (n, X, Control) ; complex int Syntax: #include "umfpack.h" int n, status ; double *Xx, *Xz, Control [UMFPACK_CONTROL] ; status = umfpack_zi_report_vector (n, Xx, Xz, Control) ; complex UF_long Syntax: #include "umfpack.h" UF_long n, status ; double *Xx, *Xz, Control [UMFPACK_CONTROL] ; status = umfpack_zl_report_vector (n, Xx, Xz, Control) ; Purpose: Verifies and prints a dense vector. Returns: UMFPACK_OK if Control [UMFPACK_PRL] <= 2 (the input is not checked). Otherwise: UMFPACK_OK if the vector is valid. UMFPACK_ERROR_argument_missing if X or Xx is missing. UMFPACK_ERROR_n_nonpositive if n <= 0. Arguments: Int n ; Input argument, not modified. X is a real or complex vector of size n. Restriction: n > 0. double X [n] ; Input argument, not modified. For real versions. A real vector of size n. X must not be (double *) NULL. double Xx [n or 2*n] ; Input argument, not modified. For complex versions. double Xz [n or 0] ; Input argument, not modified. For complex versions. A complex vector of size n, in one of two storage formats. Xx must not be (double *) NULL. If Xz is not (double *) NULL, then Xx [i] is the real part of X (i) and Xz [i] is the imaginary part of X (i). Both vectors are of length n. This is the "split" form of the complex vector X. If Xz is (double *) NULL, then Xx holds both real and imaginary parts, where Xx [2*i] is the real part of X (i) and Xx [2*i+1] is the imaginary part of X (i). Xx is of length 2*n doubles. If you have an ANSI C99 compiler with the intrinsic double _Complex type, then Xx can be of type double _Complex in the calling routine and typecast to (double *) when passed to umfpack_*_report_vector (this is untested, however). This is the "merged" form of the complex vector X. Note that all complex routines in UMFPACK V4.4 and later use this same strategy for their complex arguments. The split format is useful for MATLAB, which holds its real and imaginary parts in seperate arrays. The packed format is compatible with the intrinsic double _Complex type in ANSI C99, and is also compatible with SuperLU's method of storing complex matrices. In Version 4.3, this routine was the only one that allowed for packed complex arguments. double Control [UMFPACK_CONTROL] ; Input argument, not modified. If a (double *) NULL pointer is passed, then the default control settings are used. Otherwise, the settings are determined from the Control array. See umfpack_*_defaults on how to fill the Control array with the default settings. If Control contains NaN's, the defaults are used. The following Control parameters are used: Control [UMFPACK_PRL]: printing level. 2 or less: no output. returns silently without checking anything. 3: fully check input, and print a short summary of its status 4: as 3, but print first few entries of the input 5: as 3, but print all of the input Default: 1 */ SuiteSparse/UMFPACK/Include/umfpack_free_numeric.h0000644001170100242450000000323210617161035020742 0ustar davisfac/* ========================================================================== */ /* === umfpack_free_numeric ================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ void umfpack_di_free_numeric ( void **Numeric ) ; void umfpack_dl_free_numeric ( void **Numeric ) ; void umfpack_zi_free_numeric ( void **Numeric ) ; void umfpack_zl_free_numeric ( void **Numeric ) ; /* double int Syntax: #include "umfpack.h" void *Numeric ; umfpack_di_free_numeric (&Numeric) ; double UF_long Syntax: #include "umfpack.h" void *Numeric ; umfpack_dl_free_numeric (&Numeric) ; complex int Syntax: #include "umfpack.h" void *Numeric ; umfpack_zi_free_numeric (&Numeric) ; complex UF_long Syntax: #include "umfpack.h" void *Numeric ; umfpack_zl_free_numeric (&Numeric) ; Purpose: Deallocates the Numeric object and sets the Numeric handle to NULL. This routine is the only valid way of destroying the Numeric object. Arguments: void **Numeric ; Input argument, set to (void *) NULL on output. Numeric points to a valid Numeric object, computed by umfpack_*_numeric. No action is taken if Numeric is a (void *) NULL pointer. */ SuiteSparse/UMFPACK/Include/umfpack_qsymbolic.h0000644001170100242450000001204510617161073020305 0ustar davisfac/* ========================================================================== */ /* === umfpack_qsymbolic ==================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_qsymbolic ( int n_row, int n_col, const int Ap [ ], const int Ai [ ], const double Ax [ ], const int Qinit [ ], void **Symbolic, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO] ) ; UF_long umfpack_dl_qsymbolic ( UF_long n_row, UF_long n_col, const UF_long Ap [ ], const UF_long Ai [ ], const double Ax [ ], const UF_long Qinit [ ], void **Symbolic, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO] ) ; int umfpack_zi_qsymbolic ( int n_row, int n_col, const int Ap [ ], const int Ai [ ], const double Ax [ ], const double Az [ ], const int Qinit [ ], void **Symbolic, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO] ) ; UF_long umfpack_zl_qsymbolic ( UF_long n_row, UF_long n_col, const UF_long Ap [ ], const UF_long Ai [ ], const double Ax [ ], const double Az [ ], const UF_long Qinit [ ], void **Symbolic, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO] ) ; /* double int Syntax: #include "umfpack.h" void *Symbolic ; int n_row, n_col, *Ap, *Ai, *Qinit, status ; double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax ; status = umfpack_di_qsymbolic (n_row, n_col, Ap, Ai, Ax, Qinit, &Symbolic, Control, Info) ; double UF_long Syntax: #include "umfpack.h" void *Symbolic ; UF_long n_row, n_col, *Ap, *Ai, *Qinit, status ; double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax ; status = umfpack_dl_qsymbolic (n_row, n_col, Ap, Ai, Ax, Qinit, &Symbolic, Control, Info) ; complex int Syntax: #include "umfpack.h" void *Symbolic ; int n_row, n_col, *Ap, *Ai, *Qinit, status ; double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax, *Az ; status = umfpack_zi_qsymbolic (n_row, n_col, Ap, Ai, Ax, Az, Qinit, &Symbolic, Control, Info) ; complex UF_long Syntax: #include "umfpack.h" void *Symbolic ; UF_long n_row, n_col, *Ap, *Ai, *Qinit, status ; double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax, *Az ; status = umfpack_zl_qsymbolic (n_row, n_col, Ap, Ai, Ax, Az, Qinit, &Symbolic, Control, Info) ; packed complex Syntax: Same as above, except Az is NULL. Purpose: Given the nonzero pattern of a sparse matrix A in column-oriented form, and a sparsity preserving column pre-ordering Qinit, umfpack_*_qsymbolic performs the symbolic factorization of A*Qinit (or A (:,Qinit) in MATLAB notation). This is identical to umfpack_*_symbolic, except that neither COLAMD nor AMD are called and the user input column order Qinit is used instead. Note that in general, the Qinit passed to umfpack_*_qsymbolic can differ from the final Q found in umfpack_*_numeric. The unsymmetric strategy will perform a column etree postordering done in umfpack_*_qsymbolic and sparsity-preserving modifications are made within each frontal matrix during umfpack_*_numeric. The symmetric and 2-by-2 strategies will preserve Qinit, unless the matrix is structurally singular. See umfpack_*_symbolic for more information. *** WARNING *** A poor choice of Qinit can easily cause umfpack_*_numeric to use a huge amount of memory and do a lot of work. The "default" symbolic analysis method is umfpack_*_symbolic, not this routine. If you use this routine, the performance of UMFPACK is your responsibility; UMFPACK will not try to second-guess a poor choice of Qinit. Returns: The value of Info [UMFPACK_STATUS]; see umfpack_*_symbolic. Also returns UMFPACK_ERROR_invalid_permuation if Qinit is not a valid permutation vector. Arguments: All arguments are the same as umfpack_*_symbolic, except for the following: Int Qinit [n_col] ; Input argument, not modified. The user's fill-reducing initial column pre-ordering. This must be a permutation of 0..n_col-1. If Qinit [k] = j, then column j is the kth column of the matrix A (:,Qinit) to be factorized. If Qinit is an (Int *) NULL pointer, then COLAMD or AMD are called instead. double Control [UMFPACK_CONTROL] ; Input argument, not modified. If Qinit is not NULL, then only two strategies are recognized: the unsymmetric strategy and the symmetric strategy. If Control [UMFPACK_STRATEGY] is UMFPACK_STRATEGY_SYMMETRIC, then the symmetric strategy is used. Otherwise the unsymmetric strategy is used. */ SuiteSparse/UMFPACK/Include/umfpack_load_symbolic.h0000644001170100242450000000506410617161063021125 0ustar davisfac/* ========================================================================== */ /* === umfpack_load_symbolic ================================================ */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_load_symbolic ( void **Symbolic, char *filename ) ; UF_long umfpack_dl_load_symbolic ( void **Symbolic, char *filename ) ; int umfpack_zi_load_symbolic ( void **Symbolic, char *filename ) ; UF_long umfpack_zl_load_symbolic ( void **Symbolic, char *filename ) ; /* double int Syntax: #include "umfpack.h" int status ; char *filename ; void *Symbolic ; status = umfpack_di_load_symbolic (&Symbolic, filename) ; double UF_long Syntax: #include "umfpack.h" UF_long status ; char *filename ; void *Symbolic ; status = umfpack_dl_load_symbolic (&Symbolic, filename) ; complex int Syntax: #include "umfpack.h" int status ; char *filename ; void *Symbolic ; status = umfpack_zi_load_symbolic (&Symbolic, filename) ; complex UF_long Syntax: #include "umfpack.h" UF_long status ; char *filename ; void *Symbolic ; status = umfpack_zl_load_symbolic (&Symbolic, filename) ; Purpose: Loads a Symbolic object from a file created by umfpack_*_save_symbolic. The Symbolic handle passed to this routine is overwritten with the new object. If that object exists prior to calling this routine, a memory leak will occur. The contents of Symbolic are ignored on input. Returns: UMFPACK_OK if successful. UMFPACK_ERROR_out_of_memory if not enough memory is available. UMFPACK_ERROR_file_IO if an I/O error occurred. Arguments: void **Symbolic ; Output argument. **Symbolic is the address of a (void *) pointer variable in the user's calling routine (see Syntax, above). On input, the contents of this variable are not defined. On output, this variable holds a (void *) pointer to the Symbolic object (if successful), or (void *) NULL if a failure occurred. char *filename ; Input argument, not modified. A string that contains the filename from which to read the Symbolic object. */ SuiteSparse/UMFPACK/Include/umfpack_report_symbolic.h0000644001170100242450000000673710617161110021522 0ustar davisfac/* ========================================================================== */ /* === umfpack_report_symbolic ============================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_report_symbolic ( void *Symbolic, const double Control [UMFPACK_CONTROL] ) ; UF_long umfpack_dl_report_symbolic ( void *Symbolic, const double Control [UMFPACK_CONTROL] ) ; int umfpack_zi_report_symbolic ( void *Symbolic, const double Control [UMFPACK_CONTROL] ) ; UF_long umfpack_zl_report_symbolic ( void *Symbolic, const double Control [UMFPACK_CONTROL] ) ; /* double int Syntax: #include "umfpack.h" void *Symbolic ; double Control [UMFPACK_CONTROL] ; int status ; status = umfpack_di_report_symbolic (Symbolic, Control) ; double UF_long Syntax: #include "umfpack.h" void *Symbolic ; double Control [UMFPACK_CONTROL] ; UF_long status ; status = umfpack_dl_report_symbolic (Symbolic, Control) ; complex int Syntax: #include "umfpack.h" void *Symbolic ; double Control [UMFPACK_CONTROL] ; int status ; status = umfpack_zi_report_symbolic (Symbolic, Control) ; complex UF_long Syntax: #include "umfpack.h" void *Symbolic ; double Control [UMFPACK_CONTROL] ; UF_long status ; status = umfpack_zl_report_symbolic (Symbolic, Control) ; Purpose: Verifies and prints a Symbolic object. This routine checks the object more carefully than the computational routines. Normally, this check is not required, since umfpack_*_*symbolic either returns (void *) NULL, or a valid Symbolic object. However, if you suspect that your own code has corrupted the Symbolic object (by overruning memory bounds, for example), then this routine might be able to detect a corrupted Symbolic object. Since this is a complex object, not all such user-generated errors are guaranteed to be caught by this routine. Returns: UMFPACK_OK if Control [UMFPACK_PRL] is <= 2 (no inputs are checked). Otherwise: UMFPACK_OK if the Symbolic object is valid. UMFPACK_ERROR_invalid_Symbolic_object if the Symbolic object is invalid. UMFPACK_ERROR_out_of_memory if out of memory. Arguments: void *Symbolic ; Input argument, not modified. The Symbolic object, which holds the symbolic factorization computed by umfpack_*_*symbolic. double Control [UMFPACK_CONTROL] ; Input argument, not modified. If a (double *) NULL pointer is passed, then the default control settings are used. Otherwise, the settings are determined from the Control array. See umfpack_*_defaults on how to fill the Control array with the default settings. If Control contains NaN's, the defaults are used. The following Control parameters are used: Control [UMFPACK_PRL]: printing level. 2 or less: no output. returns silently without checking anything. 3: fully check input, and print a short summary of its status 4: as 3, but print first few entries of the input 5: as 3, but print all of the input Default: 1 */ SuiteSparse/UMFPACK/Include/umfpack_report_info.h0000644001170100242450000000511710617161077020637 0ustar davisfac/* ========================================================================== */ /* === umfpack_report_info ================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ void umfpack_di_report_info ( const double Control [UMFPACK_CONTROL], const double Info [UMFPACK_INFO] ) ; void umfpack_dl_report_info ( const double Control [UMFPACK_CONTROL], const double Info [UMFPACK_INFO] ) ; void umfpack_zi_report_info ( const double Control [UMFPACK_CONTROL], const double Info [UMFPACK_INFO] ) ; void umfpack_zl_report_info ( const double Control [UMFPACK_CONTROL], const double Info [UMFPACK_INFO] ) ; /* double int Syntax: #include "umfpack.h" double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ; umfpack_di_report_info (Control, Info) ; double UF_long Syntax: #include "umfpack.h" double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ; umfpack_dl_report_info (Control, Info) ; complex int Syntax: #include "umfpack.h" double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ; umfpack_zi_report_info (Control, Info) ; complex UF_long Syntax: #include "umfpack.h" double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ; umfpack_zl_report_info (Control, Info) ; Purpose: Reports statistics from the umfpack_*_*symbolic, umfpack_*_numeric, and umfpack_*_*solve routines. Arguments: double Control [UMFPACK_CONTROL] ; Input argument, not modified. If a (double *) NULL pointer is passed, then the default control settings are used. Otherwise, the settings are determined from the Control array. See umfpack_*_defaults on how to fill the Control array with the default settings. If Control contains NaN's, the defaults are used. The following Control parameters are used: Control [UMFPACK_PRL]: printing level. 0 or less: no output, even when an error occurs 1: error messages only 2 or more: error messages, and print all of Info Default: 1 double Info [UMFPACK_INFO] ; Input argument, not modified. Info is an output argument of several UMFPACK routines. The contents of Info are printed on standard output. */ SuiteSparse/UMFPACK/Include/umfpack_scale.h0000644001170100242450000000613110617161125017367 0ustar davisfac/* ========================================================================== */ /* === umfpack_scale ======================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_scale ( double X [ ], const double B [ ], void *Numeric ) ; UF_long umfpack_dl_scale ( double X [ ], const double B [ ], void *Numeric ) ; int umfpack_zi_scale ( double Xx [ ], double Xz [ ], const double Bx [ ], const double Bz [ ], void *Numeric ) ; UF_long umfpack_zl_scale ( double Xx [ ], double Xz [ ], const double Bx [ ], const double Bz [ ], void *Numeric ) ; /* double int Syntax: #include "umfpack.h" void *Numeric ; double *B, *X ; status = umfpack_di_scale (X, B, Numeric) ; double UF_long Syntax: #include "umfpack.h" void *Numeric ; double *B, *X ; status = umfpack_dl_scale (X, B, Numeric) ; complex int Syntax: #include "umfpack.h" void *Numeric ; double *Bx, *Bz, *Xx, *Xz ; status = umfpack_zi_scale (Xx, Xz, Bx, Bz, Numeric) ; complex UF_long Syntax: #include "umfpack.h" void *Numeric ; double *Bx, *Bz, *Xx, *Xz ; status = umfpack_zl_scale (Xx, Xz, Bx, Bz, Numeric) ; packed complex Syntax: Same as above, except both Xz and Bz are NULL. Purpose: Given LU factors computed by umfpack_*_numeric (PAQ=LU, PRAQ=LU, or P(R\A)Q=LU), and a vector B, this routine computes X = B, X = R*B, or X = R\B, as appropriate. X and B must be vectors equal in length to the number of rows of A. Returns: The status code is returned. UMFPACK_OK is returned if successful. UMFPACK_ERROR_invalid_Numeric_object is returned in the Numeric object is invalid. UMFPACK_ERROR_argument_missing is returned if any of the input vectors are missing (X and B for the real version, and Xx and Bx for the complex version). Arguments: double X [n_row] ; Output argument. or: double Xx [n_row] ; Output argument, real part. Size 2*n_row for packed complex case. double Xz [n_row] ; Output argument, imaginary part. The output vector X. If either Xz or Bz are NULL, the vector X is in packed complex form, with the kth entry in Xx [2*k] and Xx [2*k+1], and likewise for B. double B [n_row] ; Input argument, not modified. or: double Bx [n_row] ; Input argument, not modified, real part. Size 2*n_row for packed complex case. double Bz [n_row] ; Input argument, not modified, imaginary part. The input vector B. See above if either Xz or Bz are NULL. void *Numeric ; Input argument, not modified. Numeric must point to a valid Numeric object, computed by umfpack_*_numeric. */ SuiteSparse/UMFPACK/Include/umfpack_triplet_to_col.h0000644001170100242450000002431210617161142021322 0ustar davisfac/* ========================================================================== */ /* === umfpack_triplet_to_col =============================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_triplet_to_col ( int n_row, int n_col, int nz, const int Ti [ ], const int Tj [ ], const double Tx [ ], int Ap [ ], int Ai [ ], double Ax [ ], int Map [ ] ) ; UF_long umfpack_dl_triplet_to_col ( UF_long n_row, UF_long n_col, UF_long nz, const UF_long Ti [ ], const UF_long Tj [ ], const double Tx [ ], UF_long Ap [ ], UF_long Ai [ ], double Ax [ ], UF_long Map [ ] ) ; int umfpack_zi_triplet_to_col ( int n_row, int n_col, int nz, const int Ti [ ], const int Tj [ ], const double Tx [ ], const double Tz [ ], int Ap [ ], int Ai [ ], double Ax [ ], double Az [ ], int Map [ ] ) ; UF_long umfpack_zl_triplet_to_col ( UF_long n_row, UF_long n_col, UF_long nz, const UF_long Ti [ ], const UF_long Tj [ ], const double Tx [ ], const double Tz [ ], UF_long Ap [ ], UF_long Ai [ ], double Ax [ ], double Az [ ], UF_long Map [ ] ) ; /* double int Syntax: #include "umfpack.h" int n_row, n_col, nz, *Ti, *Tj, *Ap, *Ai, status, *Map ; double *Tx, *Ax ; status = umfpack_di_triplet_to_col (n_row, n_col, nz, Ti, Tj, Tx, Ap, Ai, Ax, Map) ; double UF_long Syntax: #include "umfpack.h" UF_long n_row, n_col, nz, *Ti, *Tj, *Ap, *Ai, status, *Map ; double *Tx, *Ax ; status = umfpack_dl_triplet_to_col (n_row, n_col, nz, Ti, Tj, Tx, Ap, Ai, Ax, Map) ; complex int Syntax: #include "umfpack.h" int n_row, n_col, nz, *Ti, *Tj, *Ap, *Ai, status, *Map ; double *Tx, *Tz, *Ax, *Az ; status = umfpack_zi_triplet_to_col (n_row, n_col, nz, Ti, Tj, Tx, Tz, Ap, Ai, Ax, Az, Map) ; UF_long Syntax: #include "umfpack.h" UF_long n_row, n_col, nz, *Ti, *Tj, *Ap, *Ai, status, *Map ; double *Tx, *Tz, *Ax, *Az ; status = umfpack_zl_triplet_to_col (n_row, n_col, nz, Ti, Tj, Tx, Tz, Ap, Ai, Ax, Az, Map) ; packed complex Syntax: Same as above, except Tz and Az are NULL. Purpose: Converts a sparse matrix from "triplet" form to compressed-column form. Analogous to A = spconvert (Ti, Tj, Tx + Tz*1i) in MATLAB, except that zero entries present in the triplet form are present in A. The triplet form of a matrix is a very simple data structure for basic sparse matrix operations. For example, suppose you wish to factorize a matrix A coming from a finite element method, in which A is a sum of dense submatrices, A = E1 + E2 + E3 + ... . The entries in each element matrix Ei can be concatenated together in the three triplet arrays, and any overlap between the elements will be correctly summed by umfpack_*_triplet_to_col. Transposing a matrix in triplet form is simple; just interchange the use of Ti and Tj. You can construct the complex conjugate transpose by negating Tz, for the complex versions. Permuting a matrix in triplet form is also simple. If you want the matrix PAQ, or A (P,Q) in MATLAB notation, where P [k] = i means that row i of A is the kth row of PAQ and Q [k] = j means that column j of A is the kth column of PAQ, then do the following. First, create inverse permutations Pinv and Qinv such that Pinv [i] = k if P [k] = i and Qinv [j] = k if Q [k] = j. Next, for the mth triplet (Ti [m], Tj [m], Tx [m], Tz [m]), replace Ti [m] with Pinv [Ti [m]] and replace Tj [m] with Qinv [Tj [m]]. If you have a column-form matrix with duplicate entries or unsorted columns, you can sort it and sum up the duplicates by first converting it to triplet form with umfpack_*_col_to_triplet, and then converting it back with umfpack_*_triplet_to_col. Constructing a submatrix is also easy. Just scan the triplets and remove those entries outside the desired subset of 0...n_row-1 and 0...n_col-1, and renumber the indices according to their position in the subset. You can do all these operations on a column-form matrix by first converting it to triplet form with umfpack_*_col_to_triplet, doing the operation on the triplet form, and then converting it back with umfpack_*_triplet_to_col. The only operation not supported easily in the triplet form is the multiplication of two sparse matrices (UMFPACK does not provide this operation). You can print the input triplet form with umfpack_*_report_triplet, and the output matrix with umfpack_*_report_matrix. The matrix may be singular (nz can be zero, and empty rows and/or columns may exist). It may also be rectangular and/or complex. Returns: UMFPACK_OK if successful. UMFPACK_ERROR_argument_missing if Ap, Ai, Ti, and/or Tj are missing. UMFPACK_ERROR_n_nonpositive if n_row <= 0 or n_col <= 0. UMFPACK_ERROR_invalid_matrix if nz < 0, or if for any k, Ti [k] and/or Tj [k] are not in the range 0 to n_row-1 or 0 to n_col-1, respectively. UMFPACK_ERROR_out_of_memory if unable to allocate sufficient workspace. Arguments: Int n_row ; Input argument, not modified. Int n_col ; Input argument, not modified. A is an n_row-by-n_col matrix. Restriction: n_row > 0 and n_col > 0. All row and column indices in the triplet form must be in the range 0 to n_row-1 and 0 to n_col-1, respectively. Int nz ; Input argument, not modified. The number of entries in the triplet form of the matrix. Restriction: nz >= 0. Int Ti [nz] ; Input argument, not modified. Int Tj [nz] ; Input argument, not modified. double Tx [nz] ; Input argument, not modified. Size 2*nz if Tz or Az are NULL. double Tz [nz] ; Input argument, not modified, for complex versions. Ti, Tj, Tx, and Tz hold the "triplet" form of a sparse matrix. The kth nonzero entry is in row i = Ti [k], column j = Tj [k], and the real part of a_ij is Tx [k]. The imaginary part of a_ij is Tz [k], for complex versions. The row and column indices i and j must be in the range 0 to n_row-1 and 0 to n_col-1, respectively. Duplicate entries may be present; they are summed in the output matrix. This is not an error condition. The "triplets" may be in any order. Tx, Tz, Ax, and Az are optional. Ax is computed only if both Ax and Tx are present (not (double *) NULL). This is not error condition; the routine can create just the pattern of the output matrix from the pattern of the triplets. If Az or Tz are NULL, then both real and imaginary parts are contained in Tx[0..2*nz-1], with Tx[2*k] and Tx[2*k+1] being the real and imaginary part of the kth entry. Int Ap [n_col+1] ; Output argument. Ap is an integer array of size n_col+1 on input. On output, Ap holds the "pointers" for the column form of the sparse matrix A. Column j of the matrix A is held in Ai [(Ap [j]) ... (Ap [j+1]-1)]. The first entry, Ap [0], is zero, and Ap [j] <= Ap [j+1] holds for all j in the range 0 to n_col-1. The value nz2 = Ap [n_col] is thus the total number of entries in the pattern of the matrix A. Equivalently, the number of duplicate triplets is nz - Ap [n_col]. Int Ai [nz] ; Output argument. Ai is an integer array of size nz on input. Note that only the first Ap [n_col] entries are used. The nonzero pattern (row indices) for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)]. The row indices in a given column j are in ascending order, and no duplicate row indices are present. Row indices are in the range 0 to n_col-1 (the matrix is 0-based). double Ax [nz] ; Output argument. Size 2*nz if Tz or Az are NULL. double Az [nz] ; Output argument for complex versions. Ax and Az (for the complex versions) are double arrays of size nz on input. Note that only the first Ap [n_col] entries are used in both arrays. Ax is optional; if Tx and/or Ax are not present (a (double *) NULL pointer), then Ax is not computed. If present, Ax holds the numerical values of the the real part of the sparse matrix A and Az holds the imaginary parts. The nonzero pattern (row indices) for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and the corresponding numerical values are stored in Ax [(Ap [j]) ... (Ap [j+1]-1)]. The imaginary parts are stored in Az [(Ap [j]) ... (Ap [j+1]-1)], for the complex versions. If Az or Tz are NULL, then both real and imaginary parts are returned in Ax[0..2*nz2-1], with Ax[2*k] and Ax[2*k+1] being the real and imaginary part of the kth entry. int Map [nz] ; Optional output argument. If Map is present (a non-NULL pointer to an Int array of size nz), then on output it holds the position of the triplets in the column-form matrix. That is, suppose p = Map [k], and the k-th triplet is i=Ti[k], j=Tj[k], and aij=Tx[k]. Then i=Ai[p], and aij will have been summed into Ax[p] (or simply aij=Ax[p] if there were no duplicate entries also in row i and column j). Also, Ap[j] <= p < Ap[j+1]. The Map array is not computed if it is (Int *) NULL. The Map array is useful for converting a subsequent triplet form matrix with the same pattern as the first one, without calling this routine. If Ti and Tj do not change, then Ap, and Ai can be reused from the prior call to umfpack_*_triplet_to_col. You only need to recompute Ax (and Az for the split complex version). This code excerpt properly sums up all duplicate values (for the real version): for (p = 0 ; p < Ap [n_col] ; p++) Ax [p] = 0 ; for (k = 0 ; k < nz ; k++) Ax [Map [k]] += Tx [k] ; This feature is useful (along with the reuse of the Symbolic object) if you need to factorize a sequence of triplet matrices with identical nonzero pattern (the order of the triplets in the Ti,Tj,Tx arrays must also remain unchanged). It is faster than calling this routine for each matrix, and requires no workspace. */ SuiteSparse/UMFPACK/Include/umfpack_report_matrix.h0000644001170100242450000001552510617161100021177 0ustar davisfac/* ========================================================================== */ /* === umfpack_report_matrix ================================================ */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_report_matrix ( int n_row, int n_col, const int Ap [ ], const int Ai [ ], const double Ax [ ], int col_form, const double Control [UMFPACK_CONTROL] ) ; UF_long umfpack_dl_report_matrix ( UF_long n_row, UF_long n_col, const UF_long Ap [ ], const UF_long Ai [ ], const double Ax [ ], UF_long col_form, const double Control [UMFPACK_CONTROL] ) ; int umfpack_zi_report_matrix ( int n_row, int n_col, const int Ap [ ], const int Ai [ ], const double Ax [ ], const double Az [ ], int col_form, const double Control [UMFPACK_CONTROL] ) ; UF_long umfpack_zl_report_matrix ( UF_long n_row, UF_long n_col, const UF_long Ap [ ], const UF_long Ai [ ], const double Ax [ ], const double Az [ ], UF_long col_form, const double Control [UMFPACK_CONTROL] ) ; /* double int Syntax: #include "umfpack.h" int n_row, n_col, *Ap, *Ai, status ; double *Ax, Control [UMFPACK_CONTROL] ; status = umfpack_di_report_matrix (n_row, n_col, Ap, Ai, Ax, 1, Control) ; or: status = umfpack_di_report_matrix (n_row, n_col, Ap, Ai, Ax, 0, Control) ; double UF_long Syntax: #include "umfpack.h" UF_long n_row, n_col, *Ap, *Ai, status ; double *Ax, Control [UMFPACK_CONTROL] ; status = umfpack_dl_report_matrix (n_row, n_col, Ap, Ai, Ax, 1, Control) ; or: status = umfpack_dl_report_matrix (n_row, n_col, Ap, Ai, Ax, 0, Control) ; complex int Syntax: #include "umfpack.h" int n_row, n_col, *Ap, *Ai, status ; double *Ax, *Az, Control [UMFPACK_CONTROL] ; status = umfpack_zi_report_matrix (n_row, n_col, Ap, Ai, Ax, Az, 1, Control) ; or: status = umfpack_zi_report_matrix (n_row, n_col, Ap, Ai, Ax, Az, 0, Control) ; complex UF_long Syntax: #include "umfpack.h" UF_long n_row, n_col, *Ap, *Ai, status ; double *Ax, Control [UMFPACK_CONTROL] ; status = umfpack_zl_report_matrix (n_row, n_col, Ap, Ai, Ax, Az, 1, Control) ; or: status = umfpack_zl_report_matrix (n_row, n_col, Ap, Ai, Ax, Az, 0, Control) ; packed complex Syntax: Same as above, except Az is NULL. Purpose: Verifies and prints a row or column-oriented sparse matrix. Returns: UMFPACK_OK if Control [UMFPACK_PRL] <= 2 (the input is not checked). Otherwise (where n is n_col for the column form and n_row for row and let ni be n_row for the column form and n_col for row): UMFPACK_OK if the matrix is valid. UMFPACK_ERROR_n_nonpositive if n_row <= 0 or n_col <= 0. UMFPACK_ERROR_argument_missing if Ap and/or Ai are missing. UMFPACK_ERROR_invalid_matrix if Ap [n] < 0, if Ap [0] is not zero, if Ap [j+1] < Ap [j] for any j in the range 0 to n-1, if any row index in Ai is not in the range 0 to ni-1, or if the row indices in any column are not in ascending order, or contain duplicates. UMFPACK_ERROR_out_of_memory if out of memory. Arguments: Int n_row ; Input argument, not modified. Int n_col ; Input argument, not modified. A is an n_row-by-n_row matrix. Restriction: n_row > 0 and n_col > 0. Int Ap [n+1] ; Input argument, not modified. n is n_row for a row-form matrix, and n_col for a column-form matrix. Ap is an integer array of size n+1. If col_form is true (nonzero), then on input, it holds the "pointers" for the column form of the sparse matrix A. The row indices of column j of the matrix A are held in Ai [(Ap [j]) ... (Ap [j+1]-1)]. Otherwise, Ap holds the row pointers, and the column indices of row j of the matrix are held in Ai [(Ap [j]) ... (Ap [j+1]-1)]. The first entry, Ap [0], must be zero, and Ap [j] <= Ap [j+1] must hold for all j in the range 0 to n-1. The value nz = Ap [n] is thus the total number of entries in the pattern of the matrix A. Int Ai [nz] ; Input argument, not modified, of size nz = Ap [n]. If col_form is true (nonzero), then the nonzero pattern (row indices) for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)]. Row indices must be in the range 0 to n_row-1 (the matrix is 0-based). Otherwise, the nonzero pattern (column indices) for row j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)]. Column indices must be in the range 0 to n_col-1 (the matrix is 0-based). double Ax [nz] ; Input argument, not modified, of size nz = Ap [n]. Size 2*nz for packed complex case. The numerical values of the sparse matrix A. If col_form is true (nonzero), then the nonzero pattern (row indices) for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and the corresponding (real) numerical values are stored in Ax [(Ap [j]) ... (Ap [j+1]-1)]. The imaginary parts are stored in Az [(Ap [j]) ... (Ap [j+1]-1)], for the complex versions (see below if Az is NULL). Otherwise, the nonzero pattern (column indices) for row j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and the corresponding (real) numerical values are stored in Ax [(Ap [j]) ... (Ap [j+1]-1)]. The imaginary parts are stored in Az [(Ap [j]) ... (Ap [j+1]-1)], for the complex versions (see below if Az is NULL). No numerical values are printed if Ax is NULL. double Az [nz] ; Input argument, not modified, for complex versions. The imaginary values of the sparse matrix A. See the description of Ax, above. If Az is NULL, then both real and imaginary parts are contained in Ax[0..2*nz-1], with Ax[2*k] and Ax[2*k+1] being the real and imaginary part of the kth entry. Int col_form ; Input argument, not modified. The matrix is in row-oriented form if form is col_form is false (0). Otherwise, the matrix is in column-oriented form. double Control [UMFPACK_CONTROL] ; Input argument, not modified. If a (double *) NULL pointer is passed, then the default control settings are used. Otherwise, the settings are determined from the Control array. See umfpack_*_defaults on how to fill the Control array with the default settings. If Control contains NaN's, the defaults are used. The following Control parameters are used: Control [UMFPACK_PRL]: printing level. 2 or less: no output. returns silently without checking anything. 3: fully check input, and print a short summary of its status 4: as 3, but print first few entries of the input 5: as 3, but print all of the input Default: 1 */ SuiteSparse/UMFPACK/Include/umfpack_report_perm.h0000644001170100242450000000670010617161105020636 0ustar davisfac/* ========================================================================== */ /* === umfpack_report_perm ================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_report_perm ( int np, const int Perm [ ], const double Control [UMFPACK_CONTROL] ) ; UF_long umfpack_dl_report_perm ( UF_long np, const UF_long Perm [ ], const double Control [UMFPACK_CONTROL] ) ; int umfpack_zi_report_perm ( int np, const int Perm [ ], const double Control [UMFPACK_CONTROL] ) ; UF_long umfpack_zl_report_perm ( UF_long np, const UF_long Perm [ ], const double Control [UMFPACK_CONTROL] ) ; /* double int Syntax: #include "umfpack.h" int np, *Perm, status ; double Control [UMFPACK_CONTROL] ; status = umfpack_di_report_perm (np, Perm, Control) ; double UF_long Syntax: #include "umfpack.h" UF_long np, *Perm, status ; double Control [UMFPACK_CONTROL] ; status = umfpack_dl_report_perm (np, Perm, Control) ; complex int Syntax: #include "umfpack.h" int np, *Perm, status ; double Control [UMFPACK_CONTROL] ; status = umfpack_zi_report_perm (np, Perm, Control) ; complex UF_long Syntax: #include "umfpack.h" UF_long np, *Perm, status ; double Control [UMFPACK_CONTROL] ; status = umfpack_zl_report_perm (np, Perm, Control) ; Purpose: Verifies and prints a permutation vector. Returns: UMFPACK_OK if Control [UMFPACK_PRL] <= 2 (the input is not checked). Otherwise: UMFPACK_OK if the permutation vector is valid (this includes that case when Perm is (Int *) NULL, which is not an error condition). UMFPACK_ERROR_n_nonpositive if np <= 0. UMFPACK_ERROR_out_of_memory if out of memory. UMFPACK_ERROR_invalid_permutation if Perm is not a valid permutation vector. Arguments: Int np ; Input argument, not modified. Perm is an integer vector of size np. Restriction: np > 0. Int Perm [np] ; Input argument, not modified. A permutation vector of size np. If Perm is not present (an (Int *) NULL pointer), then it is assumed to be the identity permutation. This is consistent with its use as an input argument to umfpack_*_qsymbolic, and is not an error condition. If Perm is present, the entries in Perm must range between 0 and np-1, and no duplicates may exist. double Control [UMFPACK_CONTROL] ; Input argument, not modified. If a (double *) NULL pointer is passed, then the default control settings are used. Otherwise, the settings are determined from the Control array. See umfpack_*_defaults on how to fill the Control array with the default settings. If Control contains NaN's, the defaults are used. The following Control parameters are used: Control [UMFPACK_PRL]: printing level. 2 or less: no output. returns silently without checking anything. 3: fully check input, and print a short summary of its status 4: as 3, but print first few entries of the input 5: as 3, but print all of the input Default: 1 */ SuiteSparse/UMFPACK/Include/umfpack_free_symbolic.h0000644001170100242450000000325410617161037021127 0ustar davisfac/* ========================================================================== */ /* === umfpack_free_symbolic ================================================ */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ void umfpack_di_free_symbolic ( void **Symbolic ) ; void umfpack_dl_free_symbolic ( void **Symbolic ) ; void umfpack_zi_free_symbolic ( void **Symbolic ) ; void umfpack_zl_free_symbolic ( void **Symbolic ) ; /* double int Syntax: #include "umfpack.h" void *Symbolic ; umfpack_di_free_symbolic (&Symbolic) ; double UF_long Syntax: #include "umfpack.h" void *Symbolic ; umfpack_dl_free_symbolic (&Symbolic) ; complex int Syntax: #include "umfpack.h" void *Symbolic ; umfpack_zi_free_symbolic (&Symbolic) ; complex UF_long Syntax: #include "umfpack.h" void *Symbolic ; umfpack_zl_free_symbolic (&Symbolic) ; Purpose: Deallocates the Symbolic object and sets the Symbolic handle to NULL. This routine is the only valid way of destroying the Symbolic object. Arguments: void **Symbolic ; Input argument, set to (void *) NULL on output. Points to a valid Symbolic object computed by umfpack_*_symbolic. No action is taken if Symbolic is a (void *) NULL pointer. */ SuiteSparse/UMFPACK/Include/umfpack_wsolve.h0000644001170100242450000001264610617161243017630 0ustar davisfac/* ========================================================================== */ /* === umfpack_wsolve ======================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_wsolve ( int sys, const int Ap [ ], const int Ai [ ], const double Ax [ ], double X [ ], const double B [ ], void *Numeric, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO], int Wi [ ], double W [ ] ) ; UF_long umfpack_dl_wsolve ( UF_long sys, const UF_long Ap [ ], const UF_long Ai [ ], const double Ax [ ], double X [ ], const double B [ ], void *Numeric, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO], UF_long Wi [ ], double W [ ] ) ; int umfpack_zi_wsolve ( int sys, const int Ap [ ], const int Ai [ ], const double Ax [ ], const double Az [ ], double Xx [ ], double Xz [ ], const double Bx [ ], const double Bz [ ], void *Numeric, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO], int Wi [ ], double W [ ] ) ; UF_long umfpack_zl_wsolve ( UF_long sys, const UF_long Ap [ ], const UF_long Ai [ ], const double Ax [ ], const double Az [ ], double Xx [ ], double Xz [ ], const double Bx [ ], const double Bz [ ], void *Numeric, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO], UF_long Wi [ ], double W [ ] ) ; /* double int Syntax: #include "umfpack.h" void *Numeric ; int status, *Ap, *Ai, *Wi, sys ; double *B, *X, *Ax, *W, Info [UMFPACK_INFO], Control [UMFPACK_CONTROL] ; status = umfpack_di_wsolve (sys, Ap, Ai, Ax, X, B, Numeric, Control, Info, Wi, W) ; double UF_long Syntax: #include "umfpack.h" void *Numeric ; UF_long status, *Ap, *Ai, *Wi, sys ; double *B, *X, *Ax, *W, Info [UMFPACK_INFO], Control [UMFPACK_CONTROL] ; status = umfpack_dl_wsolve (sys, Ap, Ai, Ax, X, B, Numeric, Control, Info, Wi, W) ; complex int Syntax: #include "umfpack.h" void *Numeric ; int status, *Ap, *Ai, *Wi, sys ; double *Bx, *Bz, *Xx, *Xz, *Ax, *Az, *W, Info [UMFPACK_INFO], Control [UMFPACK_CONTROL] ; status = umfpack_zi_wsolve (sys, Ap, Ai, Ax, Az, Xx, Xz, Bx, Bz, Numeric, Control, Info, Wi, W) ; complex UF_long Syntax: #include "umfpack.h" void *Numeric ; UF_long status, *Ap, *Ai, *Wi, sys ; double *Bx, *Bz, *Xx, *Xz, *Ax, *Az, *W, Info [UMFPACK_INFO], Control [UMFPACK_CONTROL] ; status = umfpack_zl_wsolve (sys, Ap, Ai, Ax, Az, Xx, Xz, Bx, Bz, Numeric, Control, Info, Wi, W) ; packed complex Syntax: Same as above, except Az, Xz, and Bz are NULL. Purpose: Given LU factors computed by umfpack_*_numeric (PAQ=LU) and the right-hand-side, B, solve a linear system for the solution X. Iterative refinement is optionally performed. This routine is identical to umfpack_*_solve, except that it does not dynamically allocate any workspace. When you have many linear systems to solve, this routine is faster than umfpack_*_solve, since the workspace (Wi, W) needs to be allocated only once, prior to calling umfpack_*_wsolve. Returns: The status code is returned. See Info [UMFPACK_STATUS], below. Arguments: Int sys ; Input argument, not modified. Int Ap [n+1] ; Input argument, not modified. Int Ai [nz] ; Input argument, not modified. double Ax [nz] ; Input argument, not modified. Size 2*nz in packed complex case. double X [n] ; Output argument. double B [n] ; Input argument, not modified. void *Numeric ; Input argument, not modified. double Control [UMFPACK_CONTROL] ; Input argument, not modified. double Info [UMFPACK_INFO] ; Output argument. for complex versions: double Az [nz] ; Input argument, not modified, imaginary part double Xx [n] ; Output argument, real part. Size 2*n in packed complex case. double Xz [n] ; Output argument, imaginary part double Bx [n] ; Input argument, not modified, real part. Size 2*n in packed complex case. double Bz [n] ; Input argument, not modified, imaginary part The above arguments are identical to umfpack_*_solve, except that the error code UMFPACK_ERROR_out_of_memory will not be returned in Info [UMFPACK_STATUS], since umfpack_*_wsolve does not allocate any memory. Int Wi [n] ; Workspace. double W [c*n] ; Workspace, where c is defined below. The Wi and W arguments are workspace used by umfpack_*_wsolve. They need not be initialized on input, and their contents are undefined on output. The size of W depends on whether or not iterative refinement is used, and which version (real or complex) is called. Iterative refinement is performed if Ax=b, A'x=b, or A.'x=b is being solved, Control [UMFPACK_IRSTEP] > 0, and A is nonsingular. The size of W is given below: no iter. with iter. refinement refinement umfpack_di_wsolve n 5*n umfpack_dl_wsolve n 5*n umfpack_zi_wsolve 4*n 10*n umfpack_zl_wsolve 4*n 10*n */ SuiteSparse/UMFPACK/Include/umfpack_solve.h0000644001170100242450000002470510617161126017440 0ustar davisfac/* ========================================================================== */ /* === umfpack_solve ======================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ int umfpack_di_solve ( int sys, const int Ap [ ], const int Ai [ ], const double Ax [ ], double X [ ], const double B [ ], void *Numeric, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO] ) ; UF_long umfpack_dl_solve ( UF_long sys, const UF_long Ap [ ], const UF_long Ai [ ], const double Ax [ ], double X [ ], const double B [ ], void *Numeric, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO] ) ; int umfpack_zi_solve ( int sys, const int Ap [ ], const int Ai [ ], const double Ax [ ], const double Az [ ], double Xx [ ], double Xz [ ], const double Bx [ ], const double Bz [ ], void *Numeric, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO] ) ; UF_long umfpack_zl_solve ( UF_long sys, const UF_long Ap [ ], const UF_long Ai [ ], const double Ax [ ], const double Az [ ], double Xx [ ], double Xz [ ], const double Bx [ ], const double Bz [ ], void *Numeric, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO] ) ; /* double int Syntax: #include "umfpack.h" void *Numeric ; int status, *Ap, *Ai, sys ; double *B, *X, *Ax, Info [UMFPACK_INFO], Control [UMFPACK_CONTROL] ; status = umfpack_di_solve (sys, Ap, Ai, Ax, X, B, Numeric, Control, Info) ; double UF_long Syntax: #include "umfpack.h" void *Numeric ; UF_long status, *Ap, *Ai, sys ; double *B, *X, *Ax, Info [UMFPACK_INFO], Control [UMFPACK_CONTROL] ; status = umfpack_dl_solve (sys, Ap, Ai, Ax, X, B, Numeric, Control, Info) ; complex int Syntax: #include "umfpack.h" void *Numeric ; int status, *Ap, *Ai, sys ; double *Bx, *Bz, *Xx, *Xz, *Ax, *Az, Info [UMFPACK_INFO], Control [UMFPACK_CONTROL] ; status = umfpack_zi_solve (sys, Ap, Ai, Ax, Az, Xx, Xz, Bx, Bz, Numeric, Control, Info) ; complex UF_long Syntax: #include "umfpack.h" void *Numeric ; UF_long status, *Ap, *Ai, sys ; double *Bx, *Bz, *Xx, *Xz, *Ax, *Az, Info [UMFPACK_INFO], Control [UMFPACK_CONTROL] ; status = umfpack_zl_solve (sys, Ap, Ai, Ax, Az, Xx, Xz, Bx, Bz, Numeric, Control, Info) ; packed complex Syntax: Same as above, Xz, Bz, and Az are NULL. Purpose: Given LU factors computed by umfpack_*_numeric (PAQ=LU, PRAQ=LU, or P(R\A)Q=LU) and the right-hand-side, B, solve a linear system for the solution X. Iterative refinement is optionally performed. Only square systems are handled. Singular matrices result in a divide-by-zero for all systems except those involving just the matrix L. Iterative refinement is not performed for singular matrices. In the discussion below, n is equal to n_row and n_col, because only square systems are handled. Returns: The status code is returned. See Info [UMFPACK_STATUS], below. Arguments: Int sys ; Input argument, not modified. Defines which system to solve. (') is the linear algebraic transpose (complex conjugate if A is complex), and (.') is the array transpose. sys value system solved UMFPACK_A Ax=b UMFPACK_At A'x=b UMFPACK_Aat A.'x=b UMFPACK_Pt_L P'Lx=b UMFPACK_L Lx=b UMFPACK_Lt_P L'Px=b UMFPACK_Lat_P L.'Px=b UMFPACK_Lt L'x=b UMFPACK_U_Qt UQ'x=b UMFPACK_U Ux=b UMFPACK_Q_Ut QU'x=b UMFPACK_Q_Uat QU.'x=b UMFPACK_Ut U'x=b UMFPACK_Uat U.'x=b Iterative refinement can be optionally performed when sys is any of the following: UMFPACK_A Ax=b UMFPACK_At A'x=b UMFPACK_Aat A.'x=b For the other values of the sys argument, iterative refinement is not performed (Control [UMFPACK_IRSTEP], Ap, Ai, Ax, and Az are ignored). Int Ap [n+1] ; Input argument, not modified. Int Ai [nz] ; Input argument, not modified. double Ax [nz] ; Input argument, not modified. Size 2*nz for packed complex case. double Az [nz] ; Input argument, not modified, for complex versions. If iterative refinement is requested (Control [UMFPACK_IRSTEP] >= 1, Ax=b, A'x=b, or A.'x=b is being solved, and A is nonsingular), then these arrays must be identical to the same ones passed to umfpack_*_numeric. The umfpack_*_solve routine does not check the contents of these arguments, so the results are undefined if Ap, Ai, Ax, and/or Az are modified between the calls the umfpack_*_numeric and umfpack_*_solve. These three arrays do not need to be present (NULL pointers can be passed) if Control [UMFPACK_IRSTEP] is zero, or if a system other than Ax=b, A'x=b, or A.'x=b is being solved, or if A is singular, since in each of these cases A is not accessed. If Az, Xz, or Bz are NULL, then both real and imaginary parts are contained in Ax[0..2*nz-1], with Ax[2*k] and Ax[2*k+1] being the real and imaginary part of the kth entry. double X [n] ; Output argument. or: double Xx [n] ; Output argument, real part Size 2*n for packed complex case. double Xz [n] ; Output argument, imaginary part. The solution to the linear system, where n = n_row = n_col is the dimension of the matrices A, L, and U. If Az, Xz, or Bz are NULL, then both real and imaginary parts are returned in Xx[0..2*n-1], with Xx[2*k] and Xx[2*k+1] being the real and imaginary part of the kth entry. double B [n] ; Input argument, not modified. or: double Bx [n] ; Input argument, not modified, real part. Size 2*n for packed complex case. double Bz [n] ; Input argument, not modified, imaginary part. The right-hand side vector, b, stored as a conventional array of size n (or two arrays of size n for complex versions). This routine does not solve for multiple right-hand-sides, nor does it allow b to be stored in a sparse-column form. If Az, Xz, or Bz are NULL, then both real and imaginary parts are contained in Bx[0..2*n-1], with Bx[2*k] and Bx[2*k+1] being the real and imaginary part of the kth entry. void *Numeric ; Input argument, not modified. Numeric must point to a valid Numeric object, computed by umfpack_*_numeric. double Control [UMFPACK_CONTROL] ; Input argument, not modified. If a (double *) NULL pointer is passed, then the default control settings are used. Otherwise, the settings are determined from the Control array. See umfpack_*_defaults on how to fill the Control array with the default settings. If Control contains NaN's, the defaults are used. The following Control parameters are used: Control [UMFPACK_IRSTEP]: The maximum number of iterative refinement steps to attempt. A value less than zero is treated as zero. If less than 1, or if Ax=b, A'x=b, or A.'x=b is not being solved, or if A is singular, then the Ap, Ai, Ax, and Az arguments are not accessed. Default: 2. double Info [UMFPACK_INFO] ; Output argument. Contains statistics about the solution factorization. If a (double *) NULL pointer is passed, then no statistics are returned in Info (this is not an error condition). The following statistics are computed in umfpack_*_solve: Info [UMFPACK_STATUS]: status code. This is also the return value, whether or not Info is present. UMFPACK_OK The linear system was successfully solved. UMFPACK_WARNING_singular_matrix A divide-by-zero occurred. Your solution will contain Inf's and/or NaN's. Some parts of the solution may be valid. For example, solving Ax=b with A = [2 0] b = [ 1 ] returns x = [ 0.5 ] [0 0] [ 0 ] [ Inf ] UMFPACK_ERROR_out_of_memory Insufficient memory to solve the linear system. UMFPACK_ERROR_argument_missing One or more required arguments are missing. The B, X, (or Bx and Xx for the complex versions) arguments are always required. Info and Control are not required. Ap, Ai, Ax are required if Ax=b, A'x=b, A.'x=b is to be solved, the (default) iterative refinement is requested, and the matrix A is nonsingular. UMFPACK_ERROR_invalid_system The sys argument is not valid, or the matrix A is not square. UMFPACK_ERROR_invalid_Numeric_object The Numeric object is not valid. Info [UMFPACK_NROW], Info [UMFPACK_NCOL]: The dimensions of the matrix A (L is n_row-by-n_inner and U is n_inner-by-n_col, with n_inner = min(n_row,n_col)). Info [UMFPACK_NZ]: the number of entries in the input matrix, Ap [n], if iterative refinement is requested (Ax=b, A'x=b, or A.'x=b is being solved, Control [UMFPACK_IRSTEP] >= 1, and A is nonsingular). Info [UMFPACK_IR_TAKEN]: The number of iterative refinement steps effectively taken. The number of steps attempted may be one more than this; the refinement algorithm backtracks if the last refinement step worsens the solution. Info [UMFPACK_IR_ATTEMPTED]: The number of iterative refinement steps attempted. The number of times a linear system was solved is one more than this (once for the initial Ax=b, and once for each Ay=r solved for each iterative refinement step attempted). Info [UMFPACK_OMEGA1]: sparse backward error estimate, omega1, if iterative refinement was performed, or -1 if iterative refinement not performed. Info [UMFPACK_OMEGA2]: sparse backward error estimate, omega2, if iterative refinement was performed, or -1 if iterative refinement not performed. Info [UMFPACK_SOLVE_FLOPS]: the number of floating point operations performed to solve the linear system. This includes the work taken for all iterative refinement steps, including the backtrack (if any). Info [UMFPACK_SOLVE_TIME]: The time taken, in seconds. Info [UMFPACK_SOLVE_WALLTIME]: The wallclock time taken, in seconds. Only the above listed Info [...] entries are accessed. The remaining entries of Info are not accessed or modified by umfpack_*_solve. Future versions might modify different parts of Info. */ SuiteSparse/UMFPACK/Source/0000755001170100242450000000000010711431063014271 5ustar davisfacSuiteSparse/UMFPACK/Source/umf_free.c0000644001170100242450000000265110677540711016245 0ustar davisfac/* ========================================================================== */ /* === UMF_free ============================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Free a block previously allocated by UMF_malloc and return NULL. Usage is p = UMF_free (p), to ensure that we don't free it twice. Also maintains the UMFPACK malloc count. */ #include "umf_internal.h" #include "umf_free.h" #if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG) #include "umf_malloc.h" #endif GLOBAL void *UMF_free ( void *p ) { DEBUG0 (("UMF_free: "ID"\n", (Int) p)) ; if (p) { /* see AMD/Source/amd_global.c for the memory allocator selection */ amd_free (p) ; #if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG) /* One more object has been free'd. Keep track of the count. */ /* (purely for sanity checks). */ UMF_malloc_count-- ; DEBUG0 ((" new malloc count: "ID"\n", UMF_malloc_count)) ; #endif } return ((void *) NULL) ; } SuiteSparse/UMFPACK/Source/umf_free.h0000644001170100242450000000067610617161555016256 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL void *UMF_free ( void *p ) ; SuiteSparse/UMFPACK/Source/umf_grow_front.c0000644001170100242450000002363010677541577017525 0ustar davisfac/* ========================================================================== */ /* === UMF_grow_front ======================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Current frontal matrix is too small. Make it bigger. */ #include "umf_internal.h" #include "umf_grow_front.h" #include "umf_mem_free_tail_block.h" #include "umf_mem_alloc_tail_block.h" #include "umf_get_memory.h" GLOBAL Int UMF_grow_front ( NumericType *Numeric, Int fnr2, /* desired size is fnr2-by-fnc2 */ Int fnc2, WorkType *Work, Int do_what /* -1: UMF_start_front * 0: UMF_init_front, do not recompute Fcpos * 1: UMF_extend_front * 2: UMF_init_front, recompute Fcpos */ ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ double s ; Entry *Fcold, *Fcnew ; Int j, i, col, *Fcpos, *Fcols, fnrows_max, fncols_max, fnr_curr, nb, fnrows_new, fncols_new, fnr_min, fnc_min, minsize, newsize, fnrows, fncols, *E, eloc ; /* ---------------------------------------------------------------------- */ /* get parameters */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG if (do_what != -1) UMF_debug++ ; DEBUG0 (("\n\n====================GROW FRONT: do_what: "ID"\n", do_what)) ; if (do_what != -1) UMF_debug-- ; ASSERT (Work->do_grow) ; ASSERT (Work->fnpiv == 0) ; #endif Fcols = Work->Fcols ; Fcpos = Work->Fcpos ; E = Work->E ; /* ---------------------------------------------------------------------- */ /* The current front is too small, find the new size */ /* ---------------------------------------------------------------------- */ /* maximum size of frontal matrix for this chain */ nb = Work->nb ; fnrows_max = Work->fnrows_max + nb ; fncols_max = Work->fncols_max + nb ; ASSERT (fnrows_max >= 0 && (fnrows_max % 2) == 1) ; DEBUG0 (("Max size: "ID"-by-"ID" (incl. "ID" pivot block\n", fnrows_max, fncols_max, nb)) ; /* current dimensions of frontal matrix: fnr-by-fnc */ DEBUG0 (("Current : "ID"-by-"ID" (excl "ID" pivot blocks)\n", Work->fnr_curr, Work->fnc_curr, nb)) ; ASSERT (Work->fnr_curr >= 0) ; ASSERT ((Work->fnr_curr % 2 == 1) || Work->fnr_curr == 0) ; /* required dimensions of frontal matrix: fnr_min-by-fnc_min */ fnrows_new = Work->fnrows_new + 1 ; fncols_new = Work->fncols_new + 1 ; ASSERT (fnrows_new >= 0) ; if (fnrows_new % 2 == 0) fnrows_new++ ; fnrows_new += nb ; fncols_new += nb ; fnr_min = MIN (fnrows_new, fnrows_max) ; fnc_min = MIN (fncols_new, fncols_max) ; minsize = fnr_min * fnc_min ; if (INT_OVERFLOW ((double) fnr_min * (double) fnc_min * sizeof (Entry))) { /* :: the minimum front size is bigger than the integer maximum :: */ return (FALSE) ; } ASSERT (fnr_min >= 0) ; ASSERT (fnr_min % 2 == 1) ; DEBUG0 (("Min : "ID"-by-"ID"\n", fnr_min, fnc_min)) ; /* grow the front to fnr2-by-fnc2, but no bigger than the maximum, * and no smaller than the minumum. */ DEBUG0 (("Desired : ("ID"+"ID")-by-("ID"+"ID")\n", fnr2, nb, fnc2, nb)) ; fnr2 += nb ; fnc2 += nb ; ASSERT (fnr2 >= 0) ; if (fnr2 % 2 == 0) fnr2++ ; fnr2 = MAX (fnr2, fnr_min) ; fnc2 = MAX (fnc2, fnc_min) ; fnr2 = MIN (fnr2, fnrows_max) ; fnc2 = MIN (fnc2, fncols_max) ; DEBUG0 (("Try : "ID"-by-"ID"\n", fnr2, fnc2)) ; ASSERT (fnr2 >= 0) ; ASSERT (fnr2 % 2 == 1) ; s = ((double) fnr2) * ((double) fnc2) ; if (INT_OVERFLOW (s * sizeof (Entry))) { /* :: frontal matrix size int overflow :: */ /* the desired front size is bigger than the integer maximum */ /* compute a such that a*a*s < Int_MAX / sizeof (Entry) */ double a = 0.9 * sqrt ((Int_MAX / sizeof (Entry)) / s) ; fnr2 = MAX (fnr_min, a * fnr2) ; fnc2 = MAX (fnc_min, a * fnc2) ; /* the new frontal size is a*r*a*c = a*a*s */ newsize = fnr2 * fnc2 ; ASSERT (fnr2 >= 0) ; if (fnr2 % 2 == 0) fnr2++ ; fnc2 = newsize / fnr2 ; } fnr2 = MAX (fnr2, fnr_min) ; fnc2 = MAX (fnc2, fnc_min) ; newsize = fnr2 * fnc2 ; ASSERT (fnr2 >= 0) ; ASSERT (fnr2 % 2 == 1) ; ASSERT (fnr2 >= fnr_min) ; ASSERT (fnc2 >= fnc_min) ; ASSERT (newsize >= minsize) ; /* ---------------------------------------------------------------------- */ /* free the current front if it is empty of any numerical values */ /* ---------------------------------------------------------------------- */ if (E [0] && do_what != 1) { /* free the current front, if it exists and has nothing in it */ DEBUG0 (("Freeing empty front\n")) ; UMF_mem_free_tail_block (Numeric, E [0]) ; E [0] = 0 ; Work->Flublock = (Entry *) NULL ; Work->Flblock = (Entry *) NULL ; Work->Fublock = (Entry *) NULL ; Work->Fcblock = (Entry *) NULL ; } /* ---------------------------------------------------------------------- */ /* allocate the new front, doing garbage collection if necessary */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG UMF_allocfail = FALSE ; if (UMF_gprob > 0) /* a double relop, but ignore NaN case */ { double rrr = ((double) (rand ( ))) / (((double) RAND_MAX) + 1) ; DEBUG1 (("Check random %e %e\n", rrr, UMF_gprob)) ; UMF_allocfail = rrr < UMF_gprob ; if (UMF_allocfail) DEBUGm2 (("Random garbage collection (grow)\n")) ; } #endif DEBUG0 (("Attempt size: "ID"-by-"ID"\n", fnr2, fnc2)) ; eloc = UMF_mem_alloc_tail_block (Numeric, UNITS (Entry, newsize)) ; if (!eloc) { /* Do garbage collection, realloc, and try again. Compact the current * contribution block in the front to fnrows-by-fncols. Note that * there are no pivot rows/columns in current front. Do not recompute * Fcpos in UMF_garbage_collection. */ DEBUGm3 (("get_memory from umf_grow_front\n")) ; if (!UMF_get_memory (Numeric, Work, 1 + UNITS (Entry, newsize), Work->fnrows, Work->fncols, FALSE)) { /* :: out of memory in umf_grow_front :: */ return (FALSE) ; /* out of memory */ } DEBUG0 (("Attempt size: "ID"-by-"ID" again\n", fnr2, fnc2)) ; eloc = UMF_mem_alloc_tail_block (Numeric, UNITS (Entry, newsize)) ; } /* try again with something smaller */ while ((fnr2 != fnr_min || fnc2 != fnc_min) && !eloc) { fnr2 = MIN (fnr2 - 2, fnr2 * UMF_REALLOC_REDUCTION) ; fnc2 = MIN (fnc2 - 2, fnc2 * UMF_REALLOC_REDUCTION) ; ASSERT (fnr_min >= 0) ; ASSERT (fnr_min % 2 == 1) ; fnr2 = MAX (fnr_min, fnr2) ; fnc2 = MAX (fnc_min, fnc2) ; ASSERT (fnr2 >= 0) ; if (fnr2 % 2 == 0) fnr2++ ; newsize = fnr2 * fnc2 ; DEBUGm3 (("Attempt smaller size: "ID"-by-"ID" minsize "ID"-by-"ID"\n", fnr2, fnc2, fnr_min, fnc_min)) ; eloc = UMF_mem_alloc_tail_block (Numeric, UNITS (Entry, newsize)) ; } /* try again with the smallest possible size */ if (!eloc) { fnr2 = fnr_min ; fnc2 = fnc_min ; newsize = minsize ; DEBUG0 (("Attempt minsize: "ID"-by-"ID"\n", fnr2, fnc2)) ; eloc = UMF_mem_alloc_tail_block (Numeric, UNITS (Entry, newsize)) ; } if (!eloc) { /* out of memory */ return (FALSE) ; } ASSERT (fnr2 >= 0) ; ASSERT (fnr2 % 2 == 1) ; ASSERT (fnr2 >= fnr_min && fnc2 >= fnc_min) ; /* ---------------------------------------------------------------------- */ /* copy the old frontal matrix into the new one */ /* ---------------------------------------------------------------------- */ /* old contribution block (if any) */ fnr_curr = Work->fnr_curr ; /* garbage collection can change fn*_curr */ ASSERT (fnr_curr >= 0) ; ASSERT ((fnr_curr % 2 == 1) || fnr_curr == 0) ; fnrows = Work->fnrows ; fncols = Work->fncols ; Fcold = Work->Fcblock ; /* remove nb from the sizes */ fnr2 -= nb ; fnc2 -= nb ; /* new frontal matrix */ Work->Flublock = (Entry *) (Numeric->Memory + eloc) ; Work->Flblock = Work->Flublock + nb * nb ; Work->Fublock = Work->Flblock + nb * fnr2 ; Work->Fcblock = Work->Fublock + nb * fnc2 ; Fcnew = Work->Fcblock ; if (E [0]) { /* copy the old contribution block into the new one */ for (j = 0 ; j < fncols ; j++) { col = Fcols [j] ; DEBUG1 (("copy col "ID" \n",col)) ; ASSERT (col >= 0 && col < Work->n_col) ; for (i = 0 ; i < fnrows ; i++) { Fcnew [i] = Fcold [i] ; } Fcnew += fnr2 ; Fcold += fnr_curr ; DEBUG1 (("new offset col "ID" "ID"\n",col, j * fnr2)) ; Fcpos [col] = j * fnr2 ; } } else if (do_what == 2) { /* just find the new column offsets */ for (j = 0 ; j < fncols ; j++) { col = Fcols [j] ; DEBUG1 (("new offset col "ID" "ID"\n",col, j * fnr2)) ; Fcpos [col] = j * fnr2 ; } } /* free the old frontal matrix */ UMF_mem_free_tail_block (Numeric, E [0]) ; /* ---------------------------------------------------------------------- */ /* new frontal matrix size */ /* ---------------------------------------------------------------------- */ E [0] = eloc ; Work->fnr_curr = fnr2 ; /* C block is fnr2-by-fnc2 */ Work->fnc_curr = fnc2 ; Work->fcurr_size = newsize ; /* including LU, L, U, and C blocks */ Work->do_grow = FALSE ; /* the front has just been grown */ ASSERT (Work->fnr_curr >= 0) ; ASSERT (Work->fnr_curr % 2 == 1) ; DEBUG0 (("Newly grown front: "ID"+"ID" by "ID"+"ID"\n", Work->fnr_curr, nb, Work->fnc_curr, nb)) ; return (TRUE) ; } SuiteSparse/UMFPACK/Source/umf_grow_front.h0000644001170100242450000000102010617161610017473 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_grow_front ( NumericType *Numeric, Int fnr2, Int fnc2, WorkType *Work, Int do_what ) ; SuiteSparse/UMFPACK/Source/umf_symbolic_usage.c0000644001170100242450000000276710677542436020347 0ustar davisfac/* ========================================================================== */ /* === UMF_symbolic_usage =================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Returns the final size of the Symbolic object, in Units */ #include "umf_internal.h" #include "umf_symbolic_usage.h" GLOBAL double UMF_symbolic_usage ( Int n_row, Int n_col, Int nchains, Int nfr, Int esize, /* zero if no dense rows. Otherwise, equal to the * number of non-singleton, non-empty columns */ Int prefer_diagonal ) { double units ; units = DUNITS (SymbolicType, 1) /* Symbolic structure */ + 2 * DUNITS (Int, n_col+1) /* Cperm_init, Cdeg */ + 2 * DUNITS (Int, n_row+1) /* Rperm_init, Rdeg */ + 3 * DUNITS (Int, nchains+1) /* Chain_ */ + 4 * DUNITS (Int, nfr+1) ; /* Front_ */ /* if dense rows are present */ units += DUNITS (Int, esize) ; /* Esize */ /* for diagonal pivoting */ if (prefer_diagonal) { units += DUNITS (Int, n_col+1) ; /* Diagonal_map */ } return (units) ; } SuiteSparse/UMFPACK/Source/umf_symbolic_usage.h0000644001170100242450000000104010617162441020317 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL double UMF_symbolic_usage ( Int n_row, Int n_col, Int nchains, Int nfr, Int esize, Int prefer_diagonal ) ; SuiteSparse/UMFPACK/Source/umf_solve.c0000644001170100242450000010174610677542413016462 0ustar davisfac/* ========================================================================== */ /* === UMF_solve ============================================================ */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Not user-callable. Solves a linear system using the numerical factorization computed by UMFPACK_numeric. No workspace is dynamically allocated. Counts flops, but excludes floating-point comparisons (thus real abs (...) are zero flops, but complex abs (...) takes 6 flops). Returns UMFPACK_OK if successful, UMFPACK_ERROR_argument_missing if required arguments are missing, UMFPACK_ERROR_invalid_system if the sys string is not valid or if the matrix A is not square. Uses the sparse backward error method of Arioli, Demmel, and Duff (Solving sparse linear systems with sparse backward error, SIAM J. Matrix Analysis and Applic., vol 10, pp. 165-190). Added on option that allows the complex A and X to be split differently than B, Oct 10, 2005. Contributed by David Bateman. */ #include "umf_internal.h" #include "umf_solve.h" #include "umf_lsolve.h" #include "umf_usolve.h" #include "umf_ltsolve.h" #include "umf_utsolve.h" #include "umf_report_vector.h" PRIVATE Int do_step ( double omega [3], Int step, const double B2 [ ], Entry X [ ], const Entry W [ ], const double Y [ ], const double Z2 [ ], Entry S [ ], Int n, double Info [UMFPACK_INFO] ) ; /* ========================================================================== */ /* === UMF_solve ============================================================ */ /* ========================================================================== */ GLOBAL Int UMF_solve ( Int sys, const Int Ap [ ], const Int Ai [ ], const double Ax [ ], double Xx [ ], const double Bx [ ], #ifdef COMPLEX const double Az [ ], double Xz [ ], const double Bz [ ], #endif NumericType *Numeric, Int irstep, double Info [UMFPACK_INFO], Int Pattern [ ], /* size n */ double SolveWork [ ] /* if irstep>0 real: size 5*n. complex:10*n */ /* otherwise real: size n. complex: 4*n */ ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Entry axx, wi, xj, zi, xi, aij, bi ; double omega [3], d, z2i, yi, flops ; Entry *W, *Z, *S, *X ; double *Z2, *Y, *B2, *Rs ; Int *Rperm, *Cperm, i, n, p, step, j, nz, status, p2, do_scale ; #ifdef COMPLEX Int AXsplit ; Int Bsplit ; #endif #ifndef NRECIPROCAL Int do_recip = Numeric->do_recip ; #endif /* ---------------------------------------------------------------------- */ /* initializations */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG UMF_dump_lu (Numeric) ; ASSERT (Numeric && Xx && Bx && Pattern && SolveWork && Info) ; #endif nz = 0 ; omega [0] = 0. ; omega [1] = 0. ; omega [2] = 0. ; Rperm = Numeric->Rperm ; Cperm = Numeric->Cperm ; Rs = Numeric->Rs ; /* row scale factors */ do_scale = (Rs != (double *) NULL) ; flops = 0 ; Info [UMFPACK_SOLVE_FLOPS] = 0 ; Info [UMFPACK_IR_TAKEN] = 0 ; Info [UMFPACK_IR_ATTEMPTED] = 0 ; /* UMFPACK_solve does not call this routine if A is rectangular */ ASSERT (Numeric->n_row == Numeric->n_col) ; n = Numeric->n_row ; if (Numeric->nnzpiv < n || SCALAR_IS_ZERO (Numeric->rcond) || SCALAR_IS_NAN (Numeric->rcond)) { /* Note that systems involving just L return UMFPACK_OK, even if */ /* A is singular (L is always has a unit diagonal). */ DEBUGm4 (("Note, matrix is singular in umf_solve\n")) ; status = UMFPACK_WARNING_singular_matrix ; irstep = 0 ; } else { status = UMFPACK_OK ; } irstep = MAX (0, irstep) ; /* make sure irstep is >= 0 */ W = (Entry *) SolveWork ; /* Entry W [0..n-1] */ Z = (Entry *) NULL ; /* unused if no iterative refinement */ S = (Entry *) NULL ; Y = (double *) NULL ; Z2 = (double *) NULL ; B2 = (double *) NULL ; #ifdef COMPLEX if (irstep > 0) { if (!Ap || !Ai || !Ax) { return (UMFPACK_ERROR_argument_missing) ; } /* A, B, and X in split format if Az, Bz, and Xz present */ AXsplit = SPLIT (Az) || SPLIT(Xz); Z = (Entry *) (SolveWork + 4*n) ; /* Entry Z [0..n-1] */ S = (Entry *) (SolveWork + 6*n) ; /* Entry S [0..n-1] */ Y = (double *) (SolveWork + 8*n) ; /* double Y [0..n-1] */ B2 = (double *) (SolveWork + 9*n) ; /* double B2 [0..n-1] */ Z2 = (double *) Z ; /* double Z2 [0..n-1], equiv. to Z */ } else { /* A is ignored, only look at X for split/packed cases */ AXsplit = SPLIT(Xz); } Bsplit = SPLIT (Bz); if (AXsplit) { X = (Entry *) (SolveWork + 2*n) ; /* Entry X [0..n-1] */ } else { X = (Entry *) Xx ; /* Entry X [0..n-1] */ } #else X = (Entry *) Xx ; /* Entry X [0..n-1] */ if (irstep > 0) { if (!Ap || !Ai || !Ax) { return (UMFPACK_ERROR_argument_missing) ; } Z = (Entry *) (SolveWork + n) ; /* Entry Z [0..n-1] */ S = (Entry *) (SolveWork + 2*n) ; /* Entry S [0..n-1] */ Y = (double *) (SolveWork + 3*n) ; /* double Y [0..n-1] */ B2 = (double *) (SolveWork + 4*n) ; /* double B2 [0..n-1] */ Z2 = (double *) Z ; /* double Z2 [0..n-1], equiv. to Z */ } #endif /* ---------------------------------------------------------------------- */ /* determine which system to solve */ /* ---------------------------------------------------------------------- */ if (sys == UMFPACK_A) { /* ------------------------------------------------------------------ */ /* solve A x = b with optional iterative refinement */ /* ------------------------------------------------------------------ */ if (irstep > 0) { /* -------------------------------------------------------------- */ /* using iterative refinement: compute Y and B2 */ /* -------------------------------------------------------------- */ nz = Ap [n] ; Info [UMFPACK_NZ] = nz ; /* A is stored by column */ /* Y (i) = ||R A_i||, 1-norm of row i of R A */ for (i = 0 ; i < n ; i++) { Y [i] = 0. ; } flops += (ABS_FLOPS + 1) * nz ; p2 = Ap [n] ; for (p = 0 ; p < p2 ; p++) { /* Y [Ai [p]] += ABS (Ax [p]) ; */ ASSIGN (aij, Ax, Az, p, AXsplit) ; ABS (d, aij) ; Y [Ai [p]] += d ; } /* B2 = abs (B) */ flops += ABS_FLOPS * n ; for (i = 0 ; i < n ; i++) { /* B2 [i] = ABS (B [i]) ; */ ASSIGN (bi, Bx, Bz, i, Bsplit) ; ABS (B2 [i], bi) ; } /* scale Y and B2. */ if (do_scale) { /* Y = R Y */ /* B2 = R B2 */ #ifndef NRECIPROCAL if (do_recip) { /* multiply by the scale factors */ for (i = 0 ; i < n ; i++) { Y [i] *= Rs [i] ; B2 [i] *= Rs [i] ; } } else #endif { /* divide by the scale factors */ for (i = 0 ; i < n ; i++) { Y [i] /= Rs [i] ; B2 [i] /= Rs [i] ; } } flops += 2 * n ; } } for (step = 0 ; step <= irstep ; step++) { /* -------------------------------------------------------------- */ /* Solve A x = b (step 0): */ /* x = Q (U \ (L \ (P R b))) */ /* and then perform iterative refinement (step > 0): */ /* x = x + Q (U \ (L \ (P R (b - A x)))) */ /* -------------------------------------------------------------- */ if (step == 0) { if (do_scale) { /* W = P R b, using X as workspace, since Z is not * allocated if irstep = 0. */ #ifndef NRECIPROCAL if (do_recip) { /* multiply by the scale factors */ for (i = 0 ; i < n ; i++) { ASSIGN (X [i], Bx, Bz, i, Bsplit) ; SCALE (X [i], Rs [i]) ; } } else #endif { /* divide by the scale factors */ for (i = 0 ; i < n ; i++) { ASSIGN (X [i], Bx, Bz, i, Bsplit) ; SCALE_DIV (X [i], Rs [i]) ; } } flops += SCALE_FLOPS * n ; for (i = 0 ; i < n ; i++) { W [i] = X [Rperm [i]] ; } } else { /* W = P b, since the row scaling R = I */ for (i = 0 ; i < n ; i++) { /* W [i] = B [Rperm [i]] ; */ ASSIGN (W [i], Bx, Bz, Rperm [i], Bsplit) ; } } } else { for (i = 0 ; i < n ; i++) { /* Z [i] = B [i] ; */ ASSIGN (Z [i], Bx, Bz, i, Bsplit) ; } flops += MULTSUB_FLOPS * nz ; for (i = 0 ; i < n ; i++) { xi = X [i] ; p2 = Ap [i+1] ; for (p = Ap [i] ; p < p2 ; p++) { /* Z [Ai [p]] -= Ax [p] * xi ; */ ASSIGN (aij, Ax, Az, p, AXsplit) ; MULT_SUB (Z [Ai [p]], aij, xi) ; } } /* scale, Z = R Z */ if (do_scale) { #ifndef NRECIPROCAL if (do_recip) { /* multiply by the scale factors */ for (i = 0 ; i < n ; i++) { SCALE (Z [i], Rs [i]) ; } } else #endif { /* divide by the scale factors */ for (i = 0 ; i < n ; i++) { SCALE_DIV (Z [i], Rs [i]) ; } } flops += SCALE_FLOPS * n ; } for (i = 0 ; i < n ; i++) { W [i] = Z [Rperm [i]] ; } } flops += UMF_lsolve (Numeric, W, Pattern) ; flops += UMF_usolve (Numeric, W, Pattern) ; if (step == 0) { for (i = 0 ; i < n ; i++) { X [Cperm [i]] = W [i] ; } } else { flops += ASSEMBLE_FLOPS * n ; for (i = 0 ; i < n ; i++) { /* X [Cperm [i]] += W [i] ; */ ASSEMBLE (X [Cperm [i]], W [i]) ; } } /* -------------------------------------------------------------- */ /* sparse backward error estimate */ /* -------------------------------------------------------------- */ if (irstep > 0) { /* ---------------------------------------------------------- */ /* A is stored by column */ /* W (i) = R (b - A x)_i, residual */ /* Z2 (i) = R (|A||x|)_i */ /* ---------------------------------------------------------- */ for (i = 0 ; i < n ; i++) { /* W [i] = B [i] ; */ ASSIGN (W [i], Bx, Bz, i, Bsplit) ; Z2 [i] = 0. ; } flops += (MULT_FLOPS + DECREMENT_FLOPS + ABS_FLOPS + 1) * nz ; for (j = 0 ; j < n ; j++) { xj = X [j] ; p2 = Ap [j+1] ; for (p = Ap [j] ; p < p2 ; p++) { i = Ai [p] ; /* axx = Ax [p] * xj ; */ ASSIGN (aij, Ax, Az, p, AXsplit) ; MULT (axx, aij, xj) ; /* W [i] -= axx ; */ DECREMENT (W [i], axx) ; /* Z2 [i] += ABS (axx) ; */ ABS (d, axx) ; Z2 [i] += d ; } } /* scale W and Z2 */ if (do_scale) { /* Z2 = R Z2 */ /* W = R W */ #ifndef NRECIPROCAL if (do_recip) { /* multiply by the scale factors */ for (i = 0 ; i < n ; i++) { SCALE (W [i], Rs [i]) ; Z2 [i] *= Rs [i] ; } } else #endif { /* divide by the scale factors */ for (i = 0 ; i < n ; i++) { SCALE_DIV (W [i], Rs [i]) ; Z2 [i] /= Rs [i] ; } } flops += (SCALE_FLOPS + 1) * n ; } flops += (2*ABS_FLOPS + 5) * n ; if (do_step (omega, step, B2, X, W, Y, Z2, S, n, Info)) { /* iterative refinement is done */ break ; } } } } else if (sys == UMFPACK_At) { /* ------------------------------------------------------------------ */ /* solve A' x = b with optional iterative refinement */ /* ------------------------------------------------------------------ */ /* A' is the complex conjugate transpose */ if (irstep > 0) { /* -------------------------------------------------------------- */ /* using iterative refinement: compute Y */ /* -------------------------------------------------------------- */ nz = Ap [n] ; Info [UMFPACK_NZ] = nz ; /* A' is stored by row */ /* Y (i) = ||(A' R)_i||, 1-norm of row i of A' R */ if (do_scale) { flops += (ABS_FLOPS + 2) * nz ; #ifndef NRECIPROCAL if (do_recip) { /* multiply by the scale factors */ for (i = 0 ; i < n ; i++) { yi = 0. ; p2 = Ap [i+1] ; for (p = Ap [i] ; p < p2 ; p++) { /* yi += ABS (Ax [p]) * Rs [Ai [p]] ; */ /* note that abs (aij) is the same as * abs (conj (aij)) */ ASSIGN (aij, Ax, Az, p, AXsplit) ; ABS (d, aij) ; yi += (d * Rs [Ai [p]]) ; } Y [i] = yi ; } } else #endif { /* divide by the scale factors */ for (i = 0 ; i < n ; i++) { yi = 0. ; p2 = Ap [i+1] ; for (p = Ap [i] ; p < p2 ; p++) { /* yi += ABS (Ax [p]) / Rs [Ai [p]] ; */ /* note that abs (aij) is the same as * abs (conj (aij)) */ ASSIGN (aij, Ax, Az, p, AXsplit) ; ABS (d, aij) ; yi += (d / Rs [Ai [p]]) ; } Y [i] = yi ; } } } else { /* no scaling */ flops += (ABS_FLOPS + 1) * nz ; for (i = 0 ; i < n ; i++) { yi = 0. ; p2 = Ap [i+1] ; for (p = Ap [i] ; p < p2 ; p++) { /* yi += ABS (Ax [p]) ; */ /* note that abs (aij) is the same as * abs (conj (aij)) */ ASSIGN (aij, Ax, Az, p, AXsplit) ; ABS (d, aij) ; yi += d ; } Y [i] = yi ; } } /* B2 = abs (B) */ for (i = 0 ; i < n ; i++) { /* B2 [i] = ABS (B [i]) ; */ ASSIGN (bi, Bx, Bz, i, Bsplit) ; ABS (B2 [i], bi) ; } } for (step = 0 ; step <= irstep ; step++) { /* -------------------------------------------------------------- */ /* Solve A' x = b (step 0): */ /* x = R P' (L' \ (U' \ (Q' b))) */ /* and then perform iterative refinement (step > 0): */ /* x = x + R P' (L' \ (U' \ (Q' (b - A' x)))) */ /* -------------------------------------------------------------- */ if (step == 0) { /* W = Q' b */ for (i = 0 ; i < n ; i++) { /* W [i] = B [Cperm [i]] ; */ ASSIGN (W [i], Bx, Bz, Cperm [i], Bsplit) ; } } else { /* Z = b - A' x */ for (i = 0 ; i < n ; i++) { /* Z [i] = B [i] ; */ ASSIGN (Z [i], Bx, Bz, i, Bsplit) ; } flops += MULTSUB_FLOPS * nz ; for (i = 0 ; i < n ; i++) { zi = Z [i] ; p2 = Ap [i+1] ; for (p = Ap [i] ; p < p2 ; p++) { /* zi -= conjugate (Ax [p]) * X [Ai [p]] ; */ ASSIGN (aij, Ax, Az, p, Bsplit) ; MULT_SUB_CONJ (zi, X [Ai [p]], aij) ; } Z [i] = zi ; } /* W = Q' Z */ for (i = 0 ; i < n ; i++) { W [i] = Z [Cperm [i]] ; } } flops += UMF_uhsolve (Numeric, W, Pattern) ; flops += UMF_lhsolve (Numeric, W, Pattern) ; if (step == 0) { /* X = R P' W */ /* do not use Z, since it isn't allocated if irstep = 0 */ /* X = P' W */ for (i = 0 ; i < n ; i++) { X [Rperm [i]] = W [i] ; } if (do_scale) { /* X = R X */ #ifndef NRECIPROCAL if (do_recip) { /* multiply by the scale factors */ for (i = 0 ; i < n ; i++) { SCALE (X [i], Rs [i]) ; } } else #endif { /* divide by the scale factors */ for (i = 0 ; i < n ; i++) { SCALE_DIV (X [i], Rs [i]) ; } } flops += SCALE_FLOPS * n ; } } else { /* Z = P' W */ for (i = 0 ; i < n ; i++) { Z [Rperm [i]] = W [i] ; } if (do_scale) { /* Z = R Z */ #ifndef NRECIPROCAL if (do_recip) { /* multiply by the scale factors */ for (i = 0 ; i < n ; i++) { SCALE (Z [i], Rs [i]) ; } } else #endif { /* divide by the scale factors */ for (i = 0 ; i < n ; i++) { SCALE_DIV (Z [i], Rs [i]) ; } } flops += SCALE_FLOPS * n ; } flops += ASSEMBLE_FLOPS * n ; /* X += Z */ for (i = 0 ; i < n ; i++) { /* X [i] += Z [i] ; was +=W[i] in v4.3, which is wrong */ ASSEMBLE (X [i], Z [i]) ; /* bug fix, v4.3.1 */ } } /* -------------------------------------------------------------- */ /* sparse backward error estimate */ /* -------------------------------------------------------------- */ if (irstep > 0) { /* ---------------------------------------------------------- */ /* A' is stored by row */ /* W (i) = (b - A' x)_i, residual */ /* Z2 (i) = (|A'||x|)_i */ /* ---------------------------------------------------------- */ flops += (MULT_FLOPS + DECREMENT_FLOPS + ABS_FLOPS + 1) * nz ; for (i = 0 ; i < n ; i++) { /* wi = B [i] ; */ ASSIGN (wi, Bx, Bz, i, Bsplit) ; z2i = 0. ; p2 = Ap [i+1] ; for (p = Ap [i] ; p < p2 ; p++) { /* axx = conjugate (Ax [p]) * X [Ai [p]] ; */ ASSIGN (aij, Ax, Az, p, AXsplit) ; MULT_CONJ (axx, X [Ai [p]], aij) ; /* wi -= axx ; */ DECREMENT (wi, axx) ; /* z2i += ABS (axx) ; */ ABS (d, axx) ; z2i += d ; } W [i] = wi ; Z2 [i] = z2i ; } flops += (2*ABS_FLOPS + 5) * n ; if (do_step (omega, step, B2, X, W, Y, Z2, S, n, Info)) { /* iterative refinement is done */ break ; } } } } else if (sys == UMFPACK_Aat) { /* ------------------------------------------------------------------ */ /* solve A.' x = b with optional iterative refinement */ /* ------------------------------------------------------------------ */ /* A' is the array transpose */ if (irstep > 0) { /* -------------------------------------------------------------- */ /* using iterative refinement: compute Y */ /* -------------------------------------------------------------- */ nz = Ap [n] ; Info [UMFPACK_NZ] = nz ; /* A.' is stored by row */ /* Y (i) = ||(A.' R)_i||, 1-norm of row i of A.' R */ if (do_scale) { flops += (ABS_FLOPS + 2) * nz ; #ifndef NRECIPROCAL if (do_recip) { /* multiply by the scale factors */ for (i = 0 ; i < n ; i++) { yi = 0. ; p2 = Ap [i+1] ; for (p = Ap [i] ; p < p2 ; p++) { /* yi += ABS (Ax [p]) * Rs [Ai [p]] ; */ /* note that A.' is the array transpose, * so no conjugate */ ASSIGN (aij, Ax, Az, p, AXsplit) ; ABS (d, aij) ; yi += (d * Rs [Ai [p]]) ; } Y [i] = yi ; } } else #endif { /* divide by the scale factors */ for (i = 0 ; i < n ; i++) { yi = 0. ; p2 = Ap [i+1] ; for (p = Ap [i] ; p < p2 ; p++) { /* yi += ABS (Ax [p]) / Rs [Ai [p]] ; */ /* note that A.' is the array transpose, * so no conjugate */ ASSIGN (aij, Ax, Az, p, AXsplit) ; ABS (d, aij) ; yi += (d / Rs [Ai [p]]) ; } Y [i] = yi ; } } } else { /* no scaling */ flops += (ABS_FLOPS + 1) * nz ; for (i = 0 ; i < n ; i++) { yi = 0. ; p2 = Ap [i+1] ; for (p = Ap [i] ; p < p2 ; p++) { /* yi += ABS (Ax [p]) */ /* note that A.' is the array transpose, * so no conjugate */ ASSIGN (aij, Ax, Az, p, AXsplit) ; ABS (d, aij) ; yi += d ; } Y [i] = yi ; } } /* B2 = abs (B) */ for (i = 0 ; i < n ; i++) { /* B2 [i] = ABS (B [i]) ; */ ASSIGN (bi, Bx, Bz, i, Bsplit) ; ABS (B2 [i], bi) ; } } for (step = 0 ; step <= irstep ; step++) { /* -------------------------------------------------------------- */ /* Solve A.' x = b (step 0): */ /* x = R P' (L.' \ (U.' \ (Q' b))) */ /* and then perform iterative refinement (step > 0): */ /* x = x + R P' (L.' \ (U.' \ (Q' (b - A.' x)))) */ /* -------------------------------------------------------------- */ if (step == 0) { /* W = Q' b */ for (i = 0 ; i < n ; i++) { /* W [i] = B [Cperm [i]] ; */ ASSIGN (W [i], Bx, Bz, Cperm [i], Bsplit) ; } } else { /* Z = b - A.' x */ for (i = 0 ; i < n ; i++) { /* Z [i] = B [i] ; */ ASSIGN (Z [i], Bx, Bz, i, Bsplit) ; } flops += MULTSUB_FLOPS * nz ; for (i = 0 ; i < n ; i++) { zi = Z [i] ; p2 = Ap [i+1] ; for (p = Ap [i] ; p < p2 ; p++) { /* zi -= Ax [p] * X [Ai [p]] ; */ ASSIGN (aij, Ax, Az, p, AXsplit) ; MULT_SUB (zi, aij, X [Ai [p]]) ; } Z [i] = zi ; } /* W = Q' Z */ for (i = 0 ; i < n ; i++) { W [i] = Z [Cperm [i]] ; } } flops += UMF_utsolve (Numeric, W, Pattern) ; flops += UMF_ltsolve (Numeric, W, Pattern) ; if (step == 0) { /* X = R P' W */ /* do not use Z, since it isn't allocated if irstep = 0 */ /* X = P' W */ for (i = 0 ; i < n ; i++) { X [Rperm [i]] = W [i] ; } if (do_scale) { /* X = R X */ #ifndef NRECIPROCAL if (do_recip) { /* multiply by the scale factors */ for (i = 0 ; i < n ; i++) { SCALE (X [i], Rs [i]) ; } } else #endif { /* divide by the scale factors */ for (i = 0 ; i < n ; i++) { SCALE_DIV (X [i], Rs [i]) ; } } flops += SCALE_FLOPS * n ; } } else { /* Z = P' W */ for (i = 0 ; i < n ; i++) { Z [Rperm [i]] = W [i] ; } if (do_scale) { /* Z = R Z */ #ifndef NRECIPROCAL if (do_recip) { /* multiply by the scale factors */ for (i = 0 ; i < n ; i++) { SCALE (Z [i], Rs [i]) ; } } else #endif { /* divide by the scale factors */ for (i = 0 ; i < n ; i++) { SCALE_DIV (Z [i], Rs [i]) ; } } flops += SCALE_FLOPS * n ; } flops += ASSEMBLE_FLOPS * n ; /* X += Z */ for (i = 0 ; i < n ; i++) { /* X [i] += Z [i] ; was +=W[i] in v4.3, which is wrong */ ASSEMBLE (X [i], Z [i]) ; /* bug fix, v4.3.1 */ } } /* -------------------------------------------------------------- */ /* sparse backward error estimate */ /* -------------------------------------------------------------- */ if (irstep > 0) { /* ---------------------------------------------------------- */ /* A.' is stored by row */ /* W (i) = (b - A.' x)_i, residual */ /* Z (i) = (|A.'||x|)_i */ /* ---------------------------------------------------------- */ flops += (MULT_FLOPS + DECREMENT_FLOPS + ABS_FLOPS + 1) * nz ; for (i = 0 ; i < n ; i++) { /* wi = B [i] ; */ ASSIGN (wi, Bx, Bz, i, Bsplit) ; z2i = 0. ; p2 = Ap [i+1] ; for (p = Ap [i] ; p < p2 ; p++) { /* axx = Ax [p] * X [Ai [p]] ; */ ASSIGN (aij, Ax, Az, p, AXsplit) ; MULT (axx, aij, X [Ai [p]]) ; /* wi -= axx ; */ DECREMENT (wi, axx) ; /* z2i += ABS (axx) ; */ ABS (d, axx) ; z2i += d ; } W [i] = wi ; Z2 [i] = z2i ; } flops += (2*ABS_FLOPS + 5) * n ; if (do_step (omega, step, B2, X, W, Y, Z2, S, n, Info)) { /* iterative refinement is done */ break ; } } } } else if (sys == UMFPACK_Pt_L) { /* ------------------------------------------------------------------ */ /* Solve P'Lx=b: x = L \ Pb */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < n ; i++) { /* X [i] = B [Rperm [i]] ; */ ASSIGN (X [i], Bx, Bz, Rperm [i], Bsplit) ; } flops = UMF_lsolve (Numeric, X, Pattern) ; status = UMFPACK_OK ; } else if (sys == UMFPACK_L) { /* ------------------------------------------------------------------ */ /* Solve Lx=b: x = L \ b */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < n ; i++) { /* X [i] = B [i] ; */ ASSIGN (X [i], Bx, Bz, i, Bsplit) ; } flops = UMF_lsolve (Numeric, X, Pattern) ; status = UMFPACK_OK ; } else if (sys == UMFPACK_Lt_P) { /* ------------------------------------------------------------------ */ /* Solve L'Px=b: x = P' (L' \ b) */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < n ; i++) { /* W [i] = B [i] ; */ ASSIGN (W [i], Bx, Bz, i, Bsplit) ; } flops = UMF_lhsolve (Numeric, W, Pattern) ; for (i = 0 ; i < n ; i++) { X [Rperm [i]] = W [i] ; } status = UMFPACK_OK ; } else if (sys == UMFPACK_Lat_P) { /* ------------------------------------------------------------------ */ /* Solve L.'Px=b: x = P' (L.' \ b) */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < n ; i++) { /* W [i] = B [i] ; */ ASSIGN (W [i], Bx, Bz, i, Bsplit) ; } flops = UMF_ltsolve (Numeric, W, Pattern) ; for (i = 0 ; i < n ; i++) { X [Rperm [i]] = W [i] ; } status = UMFPACK_OK ; } else if (sys == UMFPACK_Lt) { /* ------------------------------------------------------------------ */ /* Solve L'x=b: x = L' \ b */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < n ; i++) { /* X [i] = B [i] ; */ ASSIGN (X [i], Bx, Bz, i, Bsplit) ; } flops = UMF_lhsolve (Numeric, X, Pattern) ; status = UMFPACK_OK ; } else if (sys == UMFPACK_Lat) { /* ------------------------------------------------------------------ */ /* Solve L.'x=b: x = L.' \ b */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < n ; i++) { /* X [i] = B [i] ; */ ASSIGN (X [i], Bx, Bz, i, Bsplit) ; } flops = UMF_ltsolve (Numeric, X, Pattern) ; status = UMFPACK_OK ; } else if (sys == UMFPACK_U_Qt) { /* ------------------------------------------------------------------ */ /* Solve UQ'x=b: x = Q (U \ b) */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < n ; i++) { /* W [i] = B [i] ; */ ASSIGN (W [i], Bx, Bz, i, Bsplit) ; } flops = UMF_usolve (Numeric, W, Pattern) ; for (i = 0 ; i < n ; i++) { X [Cperm [i]] = W [i] ; } } else if (sys == UMFPACK_U) { /* ------------------------------------------------------------------ */ /* Solve Ux=b: x = U \ b */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < n ; i++) { /* X [i] = B [i] ; */ ASSIGN (X [i], Bx, Bz, i, Bsplit) ; } flops = UMF_usolve (Numeric, X, Pattern) ; } else if (sys == UMFPACK_Q_Ut) { /* ------------------------------------------------------------------ */ /* Solve QU'x=b: x = U' \ Q'b */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < n ; i++) { /* X [i] = B [Cperm [i]] ; */ ASSIGN (X [i], Bx, Bz, Cperm [i], Bsplit) ; } flops = UMF_uhsolve (Numeric, X, Pattern) ; } else if (sys == UMFPACK_Q_Uat) { /* ------------------------------------------------------------------ */ /* Solve QU.'x=b: x = U.' \ Q'b */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < n ; i++) { /* X [i] = B [Cperm [i]] ; */ ASSIGN (X [i], Bx, Bz, Cperm [i], Bsplit) ; } flops = UMF_utsolve (Numeric, X, Pattern) ; } else if (sys == UMFPACK_Ut) { /* ------------------------------------------------------------------ */ /* Solve U'x=b: x = U' \ b */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < n ; i++) { /* X [i] = B [i] ; */ ASSIGN (X [i], Bx, Bz, i, Bsplit) ; } flops = UMF_uhsolve (Numeric, X, Pattern) ; } else if (sys == UMFPACK_Uat) { /* ------------------------------------------------------------------ */ /* Solve U'x=b: x = U' \ b */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < n ; i++) { /* X [i] = B [i] ; */ ASSIGN (X [i], Bx, Bz, i, Bsplit) ; } flops = UMF_utsolve (Numeric, X, Pattern) ; } else { return (UMFPACK_ERROR_invalid_system) ; } #ifdef COMPLEX /* copy the solution back, from Entry X [ ] to double Xx [ ] and Xz [ ] */ if (AXsplit) { for (i = 0 ; i < n ; i++) { Xx [i] = REAL_COMPONENT (X [i]) ; Xz [i] = IMAG_COMPONENT (X [i]) ; } } #endif /* return UMFPACK_OK, or UMFPACK_WARNING_singular_matrix */ /* Note that systems involving just L will return UMFPACK_OK */ Info [UMFPACK_SOLVE_FLOPS] = flops ; return (status) ; } /* ========================================================================== */ /* === do_step ============================================================== */ /* ========================================================================== */ /* Perform one step of iterative refinement, for A x = b or A' x = b */ PRIVATE Int do_step /* return TRUE if iterative refinement done */ ( double omega [3], Int step, /* which step of iterative refinement to do */ const double B2 [ ], /* abs (B) */ Entry X [ ], const Entry W [ ], const double Y [ ], const double Z2 [ ], Entry S [ ], Int n, double Info [UMFPACK_INFO] ) { double last_omega [3], tau, nctau, d1, wd1, d2, wd2, xi, yix, wi, xnorm ; Int i ; /* DBL_EPSILON is a standard ANSI C term defined in */ /* It is the smallest positive x such that 1.0+x != 1.0 */ nctau = 1000 * n * DBL_EPSILON ; DEBUG0 (("do_step start: nctau = %30.20e\n", nctau)) ; ASSERT (UMF_report_vector (n, (double *) X, (double *) NULL, UMF_debug, FALSE, FALSE) == UMFPACK_OK) ; /* for approximate flop count, assume d1 > tau is always true */ /* flops += (2*ABS_FLOPS + 5) * n ; (done in UMF_solve, above) */ /* ---------------------------------------------------------------------- */ /* save the last iteration in case we need to reinstate it */ /* ---------------------------------------------------------------------- */ last_omega [0] = omega [0] ; last_omega [1] = omega [1] ; last_omega [2] = omega [2] ; /* ---------------------------------------------------------------------- */ /* compute sparse backward errors: omega [1] and omega [2] */ /* ---------------------------------------------------------------------- */ /* xnorm = ||x|| maxnorm */ xnorm = 0.0 ; for (i = 0 ; i < n ; i++) { /* xi = ABS (X [i]) ; */ ABS (xi, X [i]) ; if (SCALAR_IS_NAN (xi)) { xnorm = xi ; break ; } /* no NaN's to consider here: */ xnorm = MAX (xnorm, xi) ; } omega [1] = 0. ; omega [2] = 0. ; for (i = 0 ; i < n ; i++) { yix = Y [i] * xnorm ; tau = (yix + B2 [i]) * nctau ; d1 = Z2 [i] + B2 [i] ; /* wi = ABS (W [i]) ; */ ABS (wi, W [i]) ; if (SCALAR_IS_NAN (d1)) { omega [1] = d1 ; omega [2] = d1 ; break ; } if (SCALAR_IS_NAN (tau)) { omega [1] = tau ; omega [2] = tau ; break ; } if (d1 > tau) /* a double relop, but no NaN's here */ { wd1 = wi / d1 ; omega [1] = MAX (omega [1], wd1) ; } else if (tau > 0.0) /* a double relop, but no NaN's here */ { d2 = Z2 [i] + yix ; wd2 = wi / d2 ; omega [2] = MAX (omega [2], wd2) ; } } omega [0] = omega [1] + omega [2] ; Info [UMFPACK_OMEGA1] = omega [1] ; Info [UMFPACK_OMEGA2] = omega [2] ; /* ---------------------------------------------------------------------- */ /* stop the iterations if the backward error is small, or NaN */ /* ---------------------------------------------------------------------- */ Info [UMFPACK_IR_TAKEN] = step ; Info [UMFPACK_IR_ATTEMPTED] = step ; if (SCALAR_IS_NAN (omega [0])) { DEBUG0 (("omega[0] is NaN - done.\n")) ; ASSERT (UMF_report_vector (n, (double *) X, (double *) NULL, UMF_debug, FALSE, FALSE) == UMFPACK_OK) ; return (TRUE) ; } if (omega [0] < DBL_EPSILON) /* double relop, but no NaN case here */ { DEBUG0 (("omega[0] too small - done.\n")) ; ASSERT (UMF_report_vector (n, (double *) X, (double *) NULL, UMF_debug, FALSE, FALSE) == UMFPACK_OK) ; return (TRUE) ; } /* ---------------------------------------------------------------------- */ /* stop if insufficient decrease in omega */ /* ---------------------------------------------------------------------- */ /* double relop, but no NaN case here: */ if (step > 0 && omega [0] > last_omega [0] / 2) { DEBUG0 (("stop refinement\n")) ; if (omega [0] > last_omega [0]) { /* last iteration better than this one, reinstate it */ DEBUG0 (("last iteration better\n")) ; for (i = 0 ; i < n ; i++) { X [i] = S [i] ; } Info [UMFPACK_OMEGA1] = last_omega [1] ; Info [UMFPACK_OMEGA2] = last_omega [2] ; } Info [UMFPACK_IR_TAKEN] = step - 1 ; ASSERT (UMF_report_vector (n, (double *) X, (double *) NULL, UMF_debug, FALSE, FALSE) == UMFPACK_OK) ; return (TRUE) ; } /* ---------------------------------------------------------------------- */ /* save current solution in case we need to reinstate */ /* ---------------------------------------------------------------------- */ for (i = 0 ; i < n ; i++) { S [i] = X [i] ; } /* ---------------------------------------------------------------------- */ /* iterative refinement continues */ /* ---------------------------------------------------------------------- */ ASSERT (UMF_report_vector (n, (double *) X, (double *) NULL, UMF_debug, FALSE, FALSE) == UMFPACK_OK) ; return (FALSE) ; } SuiteSparse/UMFPACK/Source/umf_solve.h0000644001170100242450000000140210617162417016447 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_solve ( Int sys, const Int Ap [ ], const Int Ai [ ], const double Ax [ ], double Xx [ ], const double Bx [ ], #ifdef COMPLEX const double Az [ ], double Xz [ ], const double Bz [ ], #endif NumericType *Numeric, Int irstep, double Info [UMFPACK_INFO], Int Pattern [ ], double SolveWork [ ] ) ; SuiteSparse/UMFPACK/Source/umfpack_report_numeric.c0000644001170100242450000004161710617162121021212 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_report_numeric =============================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Prints the Numeric object. See umfpack_report_numeric.h for details. Dynamic memory usage: Allocates a size n*sizeof(Int) workspace via a single call to UMF_malloc and then frees all of it via UMF_free on return. The workspace is not allocated if an early error return occurs before the workspace is needed. */ #include "umf_internal.h" #include "umf_valid_numeric.h" #include "umf_report_perm.h" #include "umf_report_vector.h" #include "umf_malloc.h" #include "umf_free.h" PRIVATE Int report_L ( NumericType *Numeric, Int Pattern [ ], Int prl ) ; PRIVATE Int report_U ( NumericType *Numeric, Int Pattern [ ], Int prl ) ; /* ========================================================================== */ /* === UMFPACK_report_numeric =============================================== */ /* ========================================================================== */ GLOBAL Int UMFPACK_report_numeric ( void *NumericHandle, const double Control [UMFPACK_CONTROL] ) { Int prl, *W, nn, n_row, n_col, n_inner, num_fixed_size, numeric_size, npiv ; NumericType *Numeric ; prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ; if (prl <= 2) { return (UMFPACK_OK) ; } PRINTF (("Numeric object: ")) ; Numeric = (NumericType *) NumericHandle ; if (!UMF_valid_numeric (Numeric)) { PRINTF (("ERROR: LU factors invalid\n\n")) ; return (UMFPACK_ERROR_invalid_Numeric_object) ; } n_row = Numeric->n_row ; n_col = Numeric->n_col ; nn = MAX (n_row, n_col) ; n_inner = MIN (n_row, n_col) ; npiv = Numeric->npiv ; DEBUG1 (("n_row "ID" n_col "ID" nn "ID" n_inner "ID" npiv "ID"\n", n_row, n_col, nn, n_inner, npiv)) ; /* size of Numeric object, except Numeric->Memory and Numeric->Upattern */ /* see also UMF_set_stats */ num_fixed_size = UNITS (NumericType, 1) /* Numeric structure */ + UNITS (Entry, n_inner+1) /* D */ + UNITS (Int, n_row+1) /* Rperm */ + UNITS (Int, n_col+1) /* Cperm */ + 6 * UNITS (Int, npiv+1) /* Lpos, Uilen, Uip, Upos, Lilen, Lip */ + ((Numeric->scale != UMFPACK_SCALE_NONE) ? UNITS (Entry, n_row) : 0) ; /* Rs */ DEBUG1 (("num fixed size: "ID"\n", num_fixed_size)) ; DEBUG1 (("Numeric->size "ID"\n", Numeric->size)) ; DEBUG1 (("ulen units "ID"\n", UNITS (Int, Numeric->ulen))) ; /* size of Numeric->Memory is Numeric->size */ /* size of Numeric->Upattern is Numeric->ulen */ numeric_size = num_fixed_size + Numeric->size + UNITS (Int, Numeric->ulen) ; DEBUG1 (("numeric total size "ID"\n", numeric_size)) ; if (prl >= 4) { PRINTF (("\n n_row: "ID" n_col: "ID"\n", n_row, n_col)) ; PRINTF ((" relative pivot tolerance used: %g\n", Numeric->relpt)) ; PRINTF ((" relative symmetric pivot tolerance used: %g\n", Numeric->relpt2)) ; PRINTF ((" matrix scaled: ")) ; if (Numeric->scale == UMFPACK_SCALE_NONE) { PRINTF (("no")) ; } else if (Numeric->scale == UMFPACK_SCALE_SUM) { PRINTF (("yes (divided each row by sum abs value in each row)\n")) ; PRINTF ((" minimum sum (abs (rows of A)): %.5e\n", Numeric->rsmin)) ; PRINTF ((" maximum sum (abs (rows of A)): %.5e", Numeric->rsmax)) ; } else if (Numeric->scale == UMFPACK_SCALE_MAX) { PRINTF (("yes (divided each row by max abs value in each row)\n")) ; PRINTF ((" minimum max (abs (rows of A)): %.5e\n", Numeric->rsmin)) ; PRINTF ((" maximum max (abs (rows of A)): %.5e", Numeric->rsmax)) ; } PRINTF (("\n")) ; PRINTF ((" initial allocation parameter used: %g\n", Numeric->alloc_init)) ; PRINTF ((" frontal matrix allocation parameter used: %g\n", Numeric->front_alloc_init)) ; PRINTF ((" final total size of Numeric object (Units): "ID"\n", numeric_size)) ; PRINTF ((" final total size of Numeric object (MBytes): %.1f\n", MBYTES (numeric_size))) ; PRINTF ((" peak size of variable-size part (Units): "ID"\n", Numeric->max_usage)) ; PRINTF ((" peak size of variable-size part (MBytes): %.1f\n", MBYTES (Numeric->max_usage))) ; PRINTF ((" largest actual frontal matrix size: "ID"\n", Numeric->maxfrsize)) ; PRINTF ((" memory defragmentations: "ID"\n", Numeric->ngarbage)) ; PRINTF ((" memory reallocations: "ID"\n", Numeric->nrealloc)) ; PRINTF ((" costly memory reallocations: "ID"\n", Numeric->ncostly)) ; PRINTF ((" entries in compressed pattern (L and U): "ID"\n", Numeric->isize)) ; PRINTF ((" number of nonzeros in L (excl diag): "ID"\n", Numeric->lnz)) ; PRINTF ((" number of entries stored in L (excl diag): "ID"\n", Numeric->nLentries)) ; PRINTF ((" number of nonzeros in U (excl diag): "ID"\n", Numeric->unz)) ; PRINTF ((" number of entries stored in U (excl diag): "ID"\n", Numeric->nUentries)) ; PRINTF ((" factorization floating-point operations: %g\n", Numeric->flops)) ; PRINTF ((" number of nonzeros on diagonal of U: "ID"\n", Numeric->nnzpiv)) ; PRINTF ((" min abs. value on diagonal of U: %.5e\n", Numeric->min_udiag)) ; PRINTF ((" max abs. value on diagonal of U: %.5e\n", Numeric->max_udiag)) ; PRINTF ((" reciprocal condition number estimate: %.2e\n", Numeric->rcond)) ; } W = (Int *) UMF_malloc (nn, sizeof (Int)) ; if (!W) { PRINTF ((" ERROR: out of memory to check Numeric object\n\n")) ; return (UMFPACK_ERROR_out_of_memory) ; } if (Numeric->Rs) { #ifndef NRECIPROCAL if (Numeric->do_recip) { PRINTF4 (("\nScale factors applied via multiplication\n")) ; } else #endif { PRINTF4 (("\nScale factors applied via division\n")) ; } PRINTF4 (("Scale factors, Rs: ")) ; (void) UMF_report_vector (n_row, Numeric->Rs, (double *) NULL, prl, FALSE, TRUE) ; } else { PRINTF4 (("Scale factors, Rs: (not present)\n")) ; } PRINTF4 (("\nP: row ")) ; if (UMF_report_perm (n_row, Numeric->Rperm, W, prl, 0) != UMFPACK_OK) { (void) UMF_free ((void *) W) ; return (UMFPACK_ERROR_invalid_Numeric_object) ; } PRINTF4 (("\nQ: column ")) ; if (UMF_report_perm (n_col, Numeric->Cperm, W, prl, 0) != UMFPACK_OK) { (void) UMF_free ((void *) W) ; return (UMFPACK_ERROR_invalid_Numeric_object) ; } if (!report_L (Numeric, W, prl)) { (void) UMF_free ((void *) W) ; PRINTF ((" ERROR: L factor invalid\n\n")) ; return (UMFPACK_ERROR_invalid_Numeric_object) ; } if (!report_U (Numeric, W, prl)) { (void) UMF_free ((void *) W) ; PRINTF ((" ERROR: U factor invalid\n\n")) ; return (UMFPACK_ERROR_invalid_Numeric_object) ; } /* The diagonal of U is in "merged" (Entry) form, not "split" form. */ PRINTF4 (("\ndiagonal of U: ")) ; (void) UMF_report_vector (n_inner, (double *) Numeric->D, (double *) NULL, prl, FALSE, FALSE) ; (void) UMF_free ((void *) W) ; PRINTF4 ((" Numeric object: ")) ; PRINTF (("OK\n\n")) ; return (UMFPACK_OK) ; } /* ========================================================================== */ /* === report_L ============================================================= */ /* ========================================================================== */ PRIVATE Int report_L ( NumericType *Numeric, Int Pattern [ ], Int prl ) { Int k, deg, *ip, j, row, n_row, *Lpos, *Lilen, valid, k1, *Lip, newLchain, llen, prl1, pos, lp, p, npiv, n1, *Li ; Entry *xp, *Lval ; /* ---------------------------------------------------------------------- */ ASSERT (prl >= 3) ; n_row = Numeric->n_row ; npiv = Numeric->npiv ; n1 = Numeric->n1 ; Lpos = Numeric->Lpos ; Lilen = Numeric->Lilen ; Lip = Numeric->Lip ; prl1 = prl ; deg = 0 ; PRINTF4 (( "\nL in Numeric object, in column-oriented compressed-pattern form:\n" " Diagonal entries are all equal to 1.0 (not stored)\n")) ; ASSERT (Pattern != (Int *) NULL) ; /* ---------------------------------------------------------------------- */ /* print L */ /* ---------------------------------------------------------------------- */ k1 = 12 ; /* ---------------------------------------------------------------------- */ /* print the singleton columns of L */ /* ---------------------------------------------------------------------- */ for (k = 0 ; k < n1 ; k++) { if (k1 > 0) { prl = prl1 ; } lp = Lip [k] ; deg = Lilen [k] ; Li = (Int *) (Numeric->Memory + lp) ; lp += UNITS (Int, deg) ; Lval = (Entry *) (Numeric->Memory + lp) ; if (k1-- > 0) { prl = prl1 ; } else if (prl == 4) { PRINTF ((" ...\n")) ; prl-- ; } PRINTF4 (("\n column "ID":", INDEX (k))) ; PRINTF4 ((" length "ID".\n", deg)) ; for (j = 0 ; j < deg ; j++) { row = Li [j] ; PRINTF4 (("\trow "ID" : ", INDEX (row))) ; if (prl >= 4) PRINT_ENTRY (Lval [j]) ; if (row <= k || row >= n_row) { return (FALSE) ; } PRINTF4 (("\n")) ; /* truncate printout, but continue to check L */ if (prl == 4 && j == 9 && deg > 10) { PRINTF (("\t...\n")) ; prl-- ; } } } /* ---------------------------------------------------------------------- */ /* print the regular columns of L */ /* ---------------------------------------------------------------------- */ for (k = n1 ; k < npiv ; k++) { /* if prl is 4, print the first 10 entries of the first 10 columns */ if (k1 > 0) { prl = prl1 ; } lp = Lip [k] ; newLchain = (lp < 0) ; if (newLchain) { lp = -lp ; deg = 0 ; } if (k1-- > 0) { prl = prl1 ; } else if (prl == 4) { PRINTF ((" ...\n")) ; prl-- ; } PRINTF4 (("\n column "ID":", INDEX (k))) ; /* ------------------------------------------------------------------ */ /* make column of L in Pattern [0..deg-1] */ /* ------------------------------------------------------------------ */ /* remove pivot row */ pos = Lpos [k] ; if (pos != EMPTY) { PRINTF4 ((" remove row "ID" at position "ID".", INDEX (Pattern [pos]), INDEX (pos))) ; valid = (!newLchain) && (deg > 0) && (pos < deg) && (pos >= 0) && (Pattern [pos] == k) ; if (!valid) { return (FALSE) ; } Pattern [pos] = Pattern [--deg] ; } /* concatenate the pattern */ llen = Lilen [k] ; if (llen < 0) { return (FALSE) ; } p = lp + UNITS (Int, llen) ; xp = (Entry *) (Numeric->Memory + p) ; if ((llen > 0 || deg > 0) && (p + (Int) UNITS (Entry, deg) > Numeric->size)) { return (FALSE) ; } if (llen > 0) { PRINTF4 ((" add "ID" entries.", llen)) ; ip = (Int *) (Numeric->Memory + lp) ; for (j = 0 ; j < llen ; j++) { Pattern [deg++] = *ip++ ; } } /* ------------------------------------------------------------------ */ /* print column k of L */ /* ------------------------------------------------------------------ */ PRINTF4 ((" length "ID".", deg)) ; if (newLchain) { PRINTF4 ((" Start of Lchain.")) ; } PRINTF4 (("\n")) ; for (j = 0 ; j < deg ; j++) { row = Pattern [j] ; PRINTF4 (("\trow "ID" : ", INDEX (row))) ; if (prl >= 4) PRINT_ENTRY (*xp) ; if (row <= k || row >= n_row) { return (FALSE) ; } PRINTF4 (("\n")) ; xp++ ; /* truncate printout, but continue to check L */ if (prl == 4 && j == 9 && deg > 10) { PRINTF (("\t...\n")) ; prl-- ; } } } PRINTF4 (("\n")) ; return (TRUE) ; } /* ========================================================================== */ /* === report_U ============================================================= */ /* ========================================================================== */ PRIVATE Int report_U ( NumericType *Numeric, Int Pattern [ ], Int prl ) { /* ---------------------------------------------------------------------- */ Int k, deg, j, *ip, col, *Upos, *Uilen, k1, prl1, pos, *Uip, n_col, ulen, p, newUchain, up, npiv, n1, *Ui ; Entry *xp, *Uval ; /* ---------------------------------------------------------------------- */ ASSERT (prl >= 3) ; n_col = Numeric->n_col ; npiv = Numeric->npiv ; n1 = Numeric->n1 ; Upos = Numeric->Upos ; Uilen = Numeric->Uilen ; Uip = Numeric->Uip ; prl1 = prl ; PRINTF4 (( "\nU in Numeric object, in row-oriented compressed-pattern form:\n" " Diagonal is stored separately.\n")) ; ASSERT (Pattern != (Int *) NULL) ; k1 = 12 ; /* ---------------------------------------------------------------------- */ /* print the sparse part of U */ /* ---------------------------------------------------------------------- */ deg = Numeric->ulen ; if (deg > 0) { /* make last pivot row of U (singular matrices only) */ for (j = 0 ; j < deg ; j++) { Pattern [j] = Numeric->Upattern [j] ; } } PRINTF4 (("\n row "ID": length "ID". End of Uchain.\n", INDEX (npiv-1), deg)) ; for (k = npiv-1 ; k >= n1 ; k--) { /* ------------------------------------------------------------------ */ /* print row k of U */ /* ------------------------------------------------------------------ */ /* if prl is 3, print the first 10 entries of the first 10 columns */ if (k1 > 0) { prl = prl1 ; } up = Uip [k] ; ulen = Uilen [k] ; if (ulen < 0) { return (FALSE) ; } newUchain = (up < 0) ; if (newUchain) { up = -up ; p = up + UNITS (Int, ulen) ; } else { p = up ; } xp = (Entry *) (Numeric->Memory + p) ; if (deg > 0 && (p + (Int) UNITS (Entry, deg) > Numeric->size)) { return (FALSE) ; } for (j = 0 ; j < deg ; j++) { col = Pattern [j] ; PRINTF4 (("\tcol "ID" :", INDEX (col))) ; if (prl >= 4) PRINT_ENTRY (*xp) ; if (col <= k || col >= n_col) { return (FALSE) ; } PRINTF4 (("\n")) ; xp++ ; /* truncate printout, but continue to check U */ if (prl == 4 && j == 9 && deg > 10) { PRINTF (("\t...\n")) ; prl-- ; } } /* ------------------------------------------------------------------ */ /* make row k-1 of U in Pattern [0..deg-1] */ /* ------------------------------------------------------------------ */ if (k1-- > 0) { prl = prl1 ; } else if (prl == 4) { PRINTF ((" ...\n")) ; prl-- ; } if (k > 0) { PRINTF4 (("\n row "ID": ", INDEX (k-1))) ; } if (newUchain) { /* next row is a new Uchain */ if (k > 0) { deg = ulen ; PRINTF4 (("length "ID". End of Uchain.\n", deg)) ; if (up + (Int) UNITS (Int, ulen) > Numeric->size) { return (FALSE) ; } ip = (Int *) (Numeric->Memory + up) ; for (j = 0 ; j < deg ; j++) { Pattern [j] = *ip++ ; } } } else { if (ulen > 0) { PRINTF4 (("remove "ID" entries. ", ulen)) ; } deg -= ulen ; if (deg < 0) { return (FALSE) ; } pos = Upos [k] ; if (pos != EMPTY) { /* add the pivot column */ PRINTF4 (("add column "ID" at position "ID". ", INDEX (k), INDEX (pos))) ; if (pos < 0 || pos > deg) { return (FALSE) ; } Pattern [deg++] = Pattern [pos] ; Pattern [pos] = k ; } PRINTF4 (("length "ID".\n", deg)) ; } } /* ---------------------------------------------------------------------- */ /* print the singleton rows of U */ /* ---------------------------------------------------------------------- */ for (k = n1 - 1 ; k >= 0 ; k--) { if (k1 > 0) { prl = prl1 ; } up = Uip [k] ; deg = Uilen [k] ; Ui = (Int *) (Numeric->Memory + up) ; up += UNITS (Int, deg) ; Uval = (Entry *) (Numeric->Memory + up) ; if (k1-- > 0) { prl = prl1 ; } else if (prl == 4) { PRINTF ((" ...\n")) ; prl-- ; } PRINTF4 (("\n row "ID":", INDEX (k))) ; PRINTF4 ((" length "ID".\n", deg)) ; for (j = 0 ; j < deg ; j++) { col = Ui [j] ; PRINTF4 (("\tcol "ID" : ", INDEX (col))) ; if (prl >= 4) PRINT_ENTRY (Uval [j]) ; if (col <= k || col >= n_col) { return (FALSE) ; } PRINTF4 (("\n")) ; /* truncate printout, but continue to check U */ if (prl == 4 && j == 9 && deg > 10) { PRINTF (("\t...\n")) ; prl-- ; } } } prl = prl1 ; PRINTF4 (("\n")) ; return (TRUE) ; } SuiteSparse/UMFPACK/Source/umf_valid_numeric.c0000644001170100242450000000313010677542501020135 0ustar davisfac/* ========================================================================== */ /* === UMF_valid_numeric ==================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Returns TRUE if the Numeric object is valid, FALSE otherwise. */ /* Does not check everything. UMFPACK_report_numeric checks more. */ #include "umf_internal.h" #include "umf_valid_numeric.h" GLOBAL Int UMF_valid_numeric ( NumericType *Numeric ) { /* This routine does not check the contents of the individual arrays, so */ /* it can miss some errors. All it checks for is the presence of the */ /* arrays, and the Numeric "valid" entry. */ if (!Numeric) { return (FALSE) ; } if (Numeric->valid != NUMERIC_VALID) { /* Numeric does not point to a NumericType object */ return (FALSE) ; } if (Numeric->n_row <= 0 || Numeric->n_col <= 0 || !Numeric->D || !Numeric->Rperm || !Numeric->Cperm || !Numeric->Lpos || !Numeric->Upos || !Numeric->Lilen || !Numeric->Uilen || !Numeric->Lip || !Numeric->Uip || !Numeric->Memory || (Numeric->ulen > 0 && !Numeric->Upattern)) { return (FALSE) ; } return (TRUE) ; } SuiteSparse/UMFPACK/Source/umf_valid_numeric.h0000644001170100242450000000072210617162515020143 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_valid_numeric ( NumericType *Numeric ) ; SuiteSparse/UMFPACK/Source/umfpack_timer.c0000644001170100242450000000546710677542720017315 0ustar davisfac/* ========================================================================== */ /* === umfpack_timer ======================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Returns the time in seconds used by the process. BE CAREFUL: if you compare the run time of UMFPACK with other sparse matrix packages, be sure to use the same timer. See umfpack_timer.h for details. See umfpack_tictoc.h, which is the timer used internally by UMFPACK. */ #include "umfpack_timer.h" #ifdef NO_TIMER /* -------------------------------------------------------------------------- */ /* no timer used if -DNO_TIMER is defined at compile time */ /* -------------------------------------------------------------------------- */ double umfpack_timer ( void ) { return (0) ; } #else #ifdef GETRUSAGE /* -------------------------------------------------------------------------- */ /* use getrusage for accurate process times (and no overflow) */ /* -------------------------------------------------------------------------- */ /* This works under Solaris, SGI Irix, Linux, IBM RS 6000 (AIX), and Compaq Alpha. It might work on other Unix systems, too. Includes both the "user time" and the "system time". The system time is the time spent by the operating system on behalf of the process, and thus should be charged to the process. */ #include #include double umfpack_timer ( void ) { struct rusage ru ; double user_time, sys_time ; (void) getrusage (RUSAGE_SELF, &ru) ; user_time = ru.ru_utime.tv_sec /* user time (seconds) */ + 1e-6 * ru.ru_utime.tv_usec ; /* user time (microseconds) */ sys_time = ru.ru_stime.tv_sec /* system time (seconds) */ + 1e-6 * ru.ru_stime.tv_usec ; /* system time (microseconds) */ return (user_time + sys_time) ; } #else /* -------------------------------------------------------------------------- */ /* Generic ANSI C: use the ANSI clock function */ /* -------------------------------------------------------------------------- */ /* This is portable, but may overflow. On Sun Solaris, when compiling in */ /* 32-bit mode, the overflow occurs in only 2147 seconds (about 36 minutes). */ #include double umfpack_timer ( void ) { return (((double) (clock ( ))) / ((double) (CLOCKS_PER_SEC))) ; } #endif #endif SuiteSparse/UMFPACK/Source/umfpack_transpose.c0000644001170100242450000000705410617162204020172 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_transpose ==================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User callable. Computes a permuted transpose, R = (A (P,Q))' in MATLAB notation. See umfpack_transpose.h for details. A and R can be rectangular. The matrix A may be singular. The complex version can do transpose (') or array transpose (.'). Dynamic memory usage: A single call to UMF_malloc is made, for a workspace of size max (n_row,n_col,1) * sizeof(Int). This is then free'd on return, via UMF_free. */ #include "umf_internal.h" #include "umf_transpose.h" #include "umf_malloc.h" #include "umf_free.h" #ifndef NDEBUG PRIVATE Int init_count ; #endif /* ========================================================================== */ GLOBAL Int UMFPACK_transpose ( Int n_row, Int n_col, const Int Ap [ ], /* size n_col+1 */ const Int Ai [ ], /* size nz = Ap [n_col] */ const double Ax [ ], /* size nz, if present */ #ifdef COMPLEX const double Az [ ], /* size nz, if present */ #endif const Int P [ ], /* P [k] = i means original row i is kth row in A(P,Q)*/ /* P is identity if not present */ /* size n_row, if present */ const Int Q [ ], /* Q [k] = j means original col j is kth col in A(P,Q)*/ /* Q is identity if not present */ /* size n_col, if present */ Int Rp [ ], /* size n_row+1 */ Int Ri [ ], /* size nz */ double Rx [ ] /* size nz, if present */ #ifdef COMPLEX , double Rz [ ] /* size nz, if present */ , Int do_conjugate /* if true, then to conjugate transpose */ /* otherwise, do array transpose */ #endif ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Int status, *W, nn ; #ifndef NDEBUG init_count = UMF_malloc_count ; UMF_dump_start ( ) ; #endif /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ nn = MAX (n_row, n_col) ; nn = MAX (nn, 1) ; W = (Int *) UMF_malloc (nn, sizeof (Int)) ; if (!W) { DEBUGm4 (("out of memory: transpose work\n")) ; ASSERT (UMF_malloc_count == init_count) ; return (UMFPACK_ERROR_out_of_memory) ; } ASSERT (UMF_malloc_count == init_count + 1) ; /* ---------------------------------------------------------------------- */ /* C = (A (P,Q))' or (A (P,Q)).' */ /* ---------------------------------------------------------------------- */ status = UMF_transpose (n_row, n_col, Ap, Ai, Ax, P, Q, n_col, Rp, Ri, Rx, W, TRUE #ifdef COMPLEX , Az, Rz, do_conjugate #endif ) ; /* ---------------------------------------------------------------------- */ /* free the workspace */ /* ---------------------------------------------------------------------- */ (void) UMF_free ((void *) W) ; ASSERT (UMF_malloc_count == init_count) ; return (status) ; } SuiteSparse/UMFPACK/Source/umf_set_stats.c0000644001170100242450000001324110677542401017330 0ustar davisfac/* ========================================================================== */ /* === UMF_set_stats ======================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Sets statistics in Info array. Calculates everything in double precision, rather than Int or size_t, so that usage estimates can be computed even if the problem is so large that it would cause integer overflow. This routine has many double relop's, but the NaN case is ignored. */ #include "umf_internal.h" #include "umf_set_stats.h" #include "umf_symbolic_usage.h" GLOBAL void UMF_set_stats ( double Info [ ], SymbolicType *Symbolic, double max_usage, /* peak size of Numeric->Memory, in Units */ double num_mem_size, /* final size of Numeric->Memory, in Units */ double flops, /* "true flops" */ double lnz, /* nz in L */ double unz, /* nz in U */ double maxfrsize, /* largest front size */ double ulen, /* size of Numeric->Upattern */ double npiv, /* number of pivots found */ double maxnrows, /* largest #rows in front */ double maxncols, /* largest #cols in front */ Int scale, /* true if scaling the rows of A */ Int prefer_diagonal, /* true if diagonal pivoting (only square A) */ Int what /* ESTIMATE or ACTUAL */ ) { double sym_size, work_usage, nn, n_row, n_col, n_inner, num_On_size1, num_On_size2, num_usage, sym_maxncols, sym_maxnrows, elen, n1 ; n_col = Symbolic->n_col ; n_row = Symbolic->n_row ; n1 = Symbolic->n1 ; nn = MAX (n_row, n_col) ; n_inner = MIN (n_row, n_col) ; sym_maxncols = MIN (Symbolic->maxncols + Symbolic->nb, n_col) ; sym_maxnrows = MIN (Symbolic->maxnrows + Symbolic->nb, n_row) ; elen = (n_col - n1) + (n_row - n1) + MIN (n_col - n1, n_row - n1) + 1 ; /* final Symbolic object size */ sym_size = UMF_symbolic_usage (Symbolic->n_row, Symbolic->n_col, Symbolic->nchains, Symbolic->nfr, Symbolic->esize, prefer_diagonal) ; /* size of O(n) part of Numeric object during factorization, */ /* except Numeric->Memory and Numeric->Upattern */ num_On_size1 = DUNITS (NumericType, 1) /* Numeric structure */ + DUNITS (Entry, n_inner+1) /* D */ + 4 * DUNITS (Int, n_row+1) /* Rperm, Lpos, Uilen, Uip */ + 4 * DUNITS (Int, n_col+1) /* Cperm, Upos, Lilen, Lip */ + (scale ? DUNITS (Entry, n_row) : 0) ; /* Rs, row scale factors */ /* size of O(n) part of Numeric object after factorization, */ /* except Numeric->Memory and Numeric->Upattern */ num_On_size2 = DUNITS (NumericType, 1) /* Numeric structure */ + DUNITS (Entry, n_inner+1) /* D */ + DUNITS (Int, n_row+1) /* Rperm */ + DUNITS (Int, n_col+1) /* Cperm */ + 6 * DUNITS (Int, npiv+1) /* Lpos, Uilen, Uip, Upos, Lilen, Lip */ + (scale ? DUNITS (Entry, n_row) : 0) ; /* Rs, row scale factors */ DEBUG1 (("num O(n) size2: %g\n", num_On_size2)) ; /* peak size of Numeric->Memory, including LU factors, current frontal * matrix, elements, and tuple lists. */ Info [UMFPACK_VARIABLE_PEAK + what] = max_usage ; /* final size of Numeric->Memory (LU factors only) */ Info [UMFPACK_VARIABLE_FINAL + what] = num_mem_size ; /* final size of Numeric object, including Numeric->Memory and ->Upattern */ Info [UMFPACK_NUMERIC_SIZE + what] = num_On_size2 + num_mem_size /* final Numeric->Memory size */ + DUNITS (Int, ulen+1) ;/* Numeric->Upattern (from Work->Upattern) */ DEBUG1 (("num mem size: %g\n", num_mem_size)) ; DEBUG1 (("ulen units %g\n", DUNITS (Int, ulen))) ; DEBUG1 (("numeric size %g\n", Info [UMFPACK_NUMERIC_SIZE + what])) ; /* largest front size (working array size, or actual size used) */ Info [UMFPACK_MAX_FRONT_SIZE + what] = maxfrsize ; Info [UMFPACK_MAX_FRONT_NROWS + what] = maxnrows ; Info [UMFPACK_MAX_FRONT_NCOLS + what] = maxncols ; DEBUGm4 (("maxnrows %g maxncols %g\n", maxnrows, maxncols)) ; DEBUGm4 (("maxfrsize %g\n", maxfrsize)) ; /* UMF_kernel usage, from work_alloc routine in umf_kernel.c */ work_usage = /* Work-> arrays, except for current frontal matrix which is allocated * inside Numeric->Memory. */ 2 * DUNITS (Entry, sym_maxnrows + 1) /* Wx, Wy */ + 2 * DUNITS (Int, n_row+1) /* Frpos, Lpattern */ + 2 * DUNITS (Int, n_col+1) /* Fcpos, Upattern */ + DUNITS (Int, nn + 1) /* Wp */ + DUNITS (Int, MAX (n_col, sym_maxnrows) + 1) /* Wrp */ + 2 * DUNITS (Int, sym_maxnrows + 1) /* Frows, Wm */ + 3 * DUNITS (Int, sym_maxncols + 1) /* Fcols, Wio, Woi */ + DUNITS (Int, MAX (sym_maxnrows, sym_maxncols) + 1) /* Woo */ + DUNITS (Int, elen) /* E */ + DUNITS (Int, Symbolic->nfr + 1) /* Front_new1strow */ + ((n_row == n_col) ? (2 * DUNITS (Int, nn)) : 0) ; /* Diag map,imap */ /* Peak memory for just UMFPACK_numeric. */ num_usage = sym_size /* size of Symbolic object */ + num_On_size1 /* O(n) part of Numeric object (excl. Upattern) */ + work_usage /* Work-> arrays (including Upattern) */ + max_usage ; /* peak size of Numeric->Memory */ /* peak memory usage for both UMFPACK_*symbolic and UMFPACK_numeric. */ Info [UMFPACK_PEAK_MEMORY + what] = MAX (Symbolic->peak_sym_usage, num_usage) ; Info [UMFPACK_FLOPS + what] = flops ; Info [UMFPACK_LNZ + what] = lnz ; Info [UMFPACK_UNZ + what] = unz ; } SuiteSparse/UMFPACK/Source/umf_set_stats.h0000644001170100242450000000133710617162311017330 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL void UMF_set_stats ( double Info [ ], SymbolicType *Symbolic, double max_usage, double num_mem_size, double flops, double lnz, double unz, double maxfrsize, double ulen, double npiv, double maxnrows, double maxncols, Int scale, Int prefer_diagonal, Int what ) ; SuiteSparse/UMFPACK/Source/umfpack_report_status.c0000644001170100242450000000737310617162131021075 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_report_status ================================================ */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Prints the return value from other UMFPACK_* routines. See umfpack_report_status.h for details. */ #include "umf_internal.h" GLOBAL void UMFPACK_report_status ( const double Control [UMFPACK_CONTROL], Int status ) { Int prl ; /* ---------------------------------------------------------------------- */ /* get control settings and status to determine what to print */ /* ---------------------------------------------------------------------- */ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ; if (prl < 1) { /* no output generated if prl is less than 1 */ return ; } if (status == UMFPACK_OK && prl <= 1) { /* no output generated if prl is 1 or less and no error occurred. */ /* note that the default printing level is 1. */ return ; } /* ---------------------------------------------------------------------- */ /* print umfpack license, copyright, version, and status condition */ /* ---------------------------------------------------------------------- */ PRINTF (("\n")) ; PRINTF4 (("%s\n", UMFPACK_COPYRIGHT)) ; PRINTF6 (("%s", UMFPACK_LICENSE_PART1)) ; PRINTF6 (("%s", UMFPACK_LICENSE_PART2)) ; PRINTF6 (("%s", UMFPACK_LICENSE_PART3)) ; PRINTF (("UMFPACK V%d.%d.%d (%s): ", UMFPACK_MAIN_VERSION, UMFPACK_SUB_VERSION, UMFPACK_SUBSUB_VERSION, UMFPACK_DATE)) ; switch (status) { case UMFPACK_OK: PRINTF (("OK\n")) ; break ; case UMFPACK_WARNING_singular_matrix: PRINTF (("WARNING: matrix is singular\n")) ; break ; case UMFPACK_ERROR_out_of_memory: PRINTF (("ERROR: out of memory\n")) ; break ; case UMFPACK_ERROR_invalid_Numeric_object: PRINTF (("ERROR: Numeric object is invalid\n")) ; break ; case UMFPACK_ERROR_invalid_Symbolic_object: PRINTF (("ERROR: Symbolic object is invalid\n")) ; break ; case UMFPACK_ERROR_argument_missing: PRINTF (("ERROR: required argument(s) missing\n")) ; break ; case UMFPACK_ERROR_n_nonpositive: PRINTF (("ERROR: dimension (n_row or n_col) must be > 0\n")) ; break ; case UMFPACK_ERROR_invalid_matrix: PRINTF (("ERROR: input matrix is invalid\n")) ; break ; case UMFPACK_ERROR_invalid_system: PRINTF (("ERROR: system argument invalid\n")) ; break ; case UMFPACK_ERROR_invalid_permutation: PRINTF (("ERROR: invalid permutation\n")) ; break ; case UMFPACK_ERROR_different_pattern: PRINTF (("ERROR: pattern of matrix (Ap and/or Ai) has changed\n")) ; break ; case UMFPACK_ERROR_internal_error: PRINTF (("INTERNAL ERROR!\n" "Input arguments might be corrupted or aliased, or an internal\n" "error has occurred. Check your input arguments with the\n" "umfpack_*_report_* routines before calling the umfpack_*\n" "computational routines. Recompile UMFPACK with debugging\n" "enabled, and look for failed assertions. If all else fails\n" "please report this error to Tim Davis (davis@cise.ufl.edu).\n" )) ; break ; default: PRINTF (("ERROR: Unrecognized error code: "ID"\n", status)) ; } PRINTF (("\n")) ; } SuiteSparse/UMFPACK/Source/umf_report_perm.c0000644001170100242450000000402410677541023017653 0ustar davisfac/* ========================================================================== */ /* === UMF_report_perm ====================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ #include "umf_internal.h" #include "umf_report_perm.h" #define PRINTF4U(params) { if (user || prl >= 4) PRINTF (params) ; } GLOBAL Int UMF_report_perm ( Int n, const Int P [ ], Int W [ ], /* workspace of size n */ Int prl, Int user ) { Int i, k, valid, prl1 ; ASSERT (prl >= 3) ; PRINTF4U (("permutation vector, n = "ID". ", n)) ; if (n <= 0) { PRINTF (("ERROR: length of permutation is <= 0\n\n")) ; return (UMFPACK_ERROR_n_nonpositive) ; } if (!P) { /* if P is (Int *) NULL, this is the identity permutation */ PRINTF (("(not present)\n\n")) ; return (UMFPACK_OK) ; } if (!W) { PRINTF (("ERROR: out of memory\n\n")) ; return (UMFPACK_ERROR_out_of_memory) ; } PRINTF4 (("\n")) ; for (i = 0 ; i < n ; i++) { W [i] = TRUE ; } prl1 = prl ; for (k = 0 ; k < n ; k++) { i = P [k] ; PRINTF4 ((" "ID" : "ID" ", INDEX (k), INDEX (i))) ; valid = (i >= 0 && i < n) ; if (valid) { valid = W [i] ; W [i] = FALSE ; } if (!valid) { /* out of range or duplicate entry */ PRINTF (("ERROR: invalid\n\n")) ; return (UMFPACK_ERROR_invalid_permutation) ; } PRINTF4 (("\n")) ; if (prl == 4 && k == 9 && n > 10) { PRINTF ((" ...\n")) ; prl-- ; } } prl = prl1 ; PRINTF4 ((" permutation vector ")) ; PRINTF4U (("OK\n\n")) ; return (UMFPACK_OK) ; } SuiteSparse/UMFPACK/Source/umf_report_perm.h0000644001170100242450000000100010617162226017645 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_report_perm ( Int n, const Int P [ ], Int W [ ], Int prl, Int user ) ; SuiteSparse/UMFPACK/Source/umf_kernel.c0000644001170100242450000002275210677541633016614 0ustar davisfac/* ========================================================================== */ /* === UMF_kernel =========================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Primary factorization routine. Called by UMFPACK_numeric. Returns: UMFPACK_OK if successful, UMFPACK_ERROR_out_of_memory if out of memory, or UMFPACK_ERROR_different_pattern if pattern of matrix (Ap and/or Ai) has changed since the call to UMFPACK_*symbolic. */ #include "umf_internal.h" #include "umf_kernel.h" #include "umf_kernel_init.h" #include "umf_init_front.h" #include "umf_start_front.h" #include "umf_assemble.h" #include "umf_scale_column.h" #include "umf_local_search.h" #include "umf_create_element.h" #include "umf_extend_front.h" #include "umf_blas3_update.h" #include "umf_store_lu.h" #include "umf_kernel_wrapup.h" /* perform an action, and return if out of memory */ #define DO(action) { if (! (action)) { return (UMFPACK_ERROR_out_of_memory) ; }} GLOBAL Int UMF_kernel ( const Int Ap [ ], const Int Ai [ ], const double Ax [ ], #ifdef COMPLEX const double Az [ ], #endif NumericType *Numeric, WorkType *Work, SymbolicType *Symbolic ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Int j, f1, f2, chain, nchains, *Chain_start, status, fixQ, evaporate, *Front_npivcol, jmax, nb, drop ; /* ---------------------------------------------------------------------- */ /* initialize memory space and load the matrix. Optionally scale. */ /* ---------------------------------------------------------------------- */ if (!UMF_kernel_init (Ap, Ai, Ax, #ifdef COMPLEX Az, #endif Numeric, Work, Symbolic)) { /* UMF_kernel_init is guaranteed to succeed, since UMFPACK_numeric */ /* either allocates enough space or if not, UMF_kernel does not get */ /* called. So running out of memory here is a fatal error, and means */ /* that the user changed Ap and/or Ai since the call to */ /* UMFPACK_*symbolic. */ DEBUGm4 (("kernel init failed\n")) ; return (UMFPACK_ERROR_different_pattern) ; } /* ---------------------------------------------------------------------- */ /* get the symbolic factorization */ /* ---------------------------------------------------------------------- */ nchains = Symbolic->nchains ; Chain_start = Symbolic->Chain_start ; Front_npivcol = Symbolic->Front_npivcol ; nb = Symbolic->nb ; fixQ = Symbolic->fixQ ; drop = Numeric->droptol > 0.0 ; #ifndef NDEBUG for (chain = 0 ; chain < nchains ; chain++) { Int i ; f1 = Chain_start [chain] ; f2 = Chain_start [chain+1] - 1 ; DEBUG1 (("\nCHain: "ID" start "ID" end "ID"\n", chain, f1, f2)) ; for (i = f1 ; i <= f2 ; i++) { DEBUG1 (("Front "ID", npivcol "ID"\n", i, Front_npivcol [i])) ; } } #endif /* ---------------------------------------------------------------------- */ /* factorize each chain of frontal matrices */ /* ---------------------------------------------------------------------- */ for (chain = 0 ; chain < nchains ; chain++) { f1 = Chain_start [chain] ; f2 = Chain_start [chain+1] - 1 ; /* ------------------------------------------------------------------ */ /* get the initial frontal matrix size for this chain */ /* ------------------------------------------------------------------ */ DO (UMF_start_front (chain, Numeric, Work, Symbolic)) ; /* ------------------------------------------------------------------ */ /* factorize each front in the chain */ /* ------------------------------------------------------------------ */ for (Work->frontid = f1 ; Work->frontid <= f2 ; Work->frontid++) { /* -------------------------------------------------------------- */ /* Initialize the pivot column candidate set */ /* -------------------------------------------------------------- */ Work->ncand = Front_npivcol [Work->frontid] ; Work->lo = Work->nextcand ; Work->hi = Work->nextcand + Work->ncand - 1 ; jmax = MIN (MAX_CANDIDATES, Work->ncand) ; DEBUGm1 ((">>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Starting front " ID", npivcol: "ID"\n", Work->frontid, Work->ncand)) ; if (fixQ) { /* do not modify the column order */ jmax = 1 ; } DEBUGm1 (("Initial candidates: ")) ; for (j = 0 ; j < jmax ; j++) { DEBUGm1 ((" "ID, Work->nextcand)) ; ASSERT (Work->nextcand <= Work->hi) ; Work->Candidates [j] = Work->nextcand++ ; } Work->nCandidates = jmax ; DEBUGm1 (("\n")) ; /* -------------------------------------------------------------- */ /* Assemble and factorize the current frontal matrix */ /* -------------------------------------------------------------- */ while (Work->ncand > 0) { /* ---------------------------------------------------------- */ /* get the pivot row and column */ /* ---------------------------------------------------------- */ status = UMF_local_search (Numeric, Work, Symbolic) ; if (status == UMFPACK_ERROR_different_pattern) { /* :: pattern change detected in umf_local_search :: */ /* input matrix has changed since umfpack_*symbolic */ DEBUGm4 (("local search failed\n")) ; return (UMFPACK_ERROR_different_pattern) ; } if (status == UMFPACK_WARNING_singular_matrix) { /* no pivot found, discard and try again */ continue ; } /* ---------------------------------------------------------- */ /* update if front not extended or too many zeros in L,U */ /* ---------------------------------------------------------- */ if (Work->do_update) { UMF_blas3_update (Work) ; if (drop) { DO (UMF_store_lu_drop (Numeric, Work)) ; } else { DO (UMF_store_lu (Numeric, Work)) ; } } /* ---------------------------------------------------------- */ /* extend the frontal matrix, or start a new one */ /* ---------------------------------------------------------- */ if (Work->do_extend) { /* extend the current front */ DO (UMF_extend_front (Numeric, Work)) ; } else { /* finish the current front (if any) and start a new one */ DO (UMF_create_element (Numeric, Work, Symbolic)) ; DO (UMF_init_front (Numeric, Work)) ; } /* ---------------------------------------------------------- */ /* Numerical & symbolic assembly into current frontal matrix */ /* ---------------------------------------------------------- */ if (fixQ) { UMF_assemble_fixq (Numeric, Work) ; } else { UMF_assemble (Numeric, Work) ; } /* ---------------------------------------------------------- */ /* scale the pivot column */ /* ---------------------------------------------------------- */ UMF_scale_column (Numeric, Work) ; /* ---------------------------------------------------------- */ /* Numerical update if enough pivots accumulated */ /* ---------------------------------------------------------- */ evaporate = Work->fnrows == 0 || Work->fncols == 0 ; if (Work->fnpiv >= nb || evaporate) { UMF_blas3_update (Work) ; if (drop) { DO (UMF_store_lu_drop (Numeric, Work)) ; } else { DO (UMF_store_lu (Numeric, Work)) ; } } Work->pivrow_in_front = FALSE ; Work->pivcol_in_front = FALSE ; /* ---------------------------------------------------------- */ /* If front is empty, evaporate it */ /* ---------------------------------------------------------- */ if (evaporate) { /* This does not create an element, just evaporates it. * It ensures that a front is not 0-by-c or r-by-0. No * memory is allocated, so it is guaranteed to succeed. */ (void) UMF_create_element (Numeric, Work, Symbolic) ; Work->fnrows = 0 ; Work->fncols = 0 ; } } } /* ------------------------------------------------------------------ * Wrapup the current frontal matrix. This is the last in a chain * in the column elimination tree. The next frontal matrix * cannot overlap with the current one, which will be its sibling * in the column etree. * ------------------------------------------------------------------ */ UMF_blas3_update (Work) ; if (drop) { DO (UMF_store_lu_drop (Numeric, Work)) ; } else { DO (UMF_store_lu (Numeric, Work)) ; } Work->fnrows_new = Work->fnrows ; Work->fncols_new = Work->fncols ; DO (UMF_create_element (Numeric, Work, Symbolic)) ; /* ------------------------------------------------------------------ */ /* current front is now empty */ /* ------------------------------------------------------------------ */ Work->fnrows = 0 ; Work->fncols = 0 ; } /* ---------------------------------------------------------------------- */ /* end the last Lchain and Uchain and finalize the LU factors */ /* ---------------------------------------------------------------------- */ UMF_kernel_wrapup (Numeric, Symbolic, Work) ; /* note that the matrix may be singular (this is OK) */ return (UMFPACK_OK) ; } SuiteSparse/UMFPACK/Source/umf_kernel.h0000644001170100242450000000115710617161654016610 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_kernel ( const Int Ap [ ], const Int Ai [ ], const double Ax [ ], #ifdef COMPLEX const double Az [ ], #endif NumericType *Numeric, WorkType *Work, SymbolicType *Symbolic ) ; SuiteSparse/UMFPACK/Source/umf_triplet.c0000644001170100242450000002306010677541202017000 0ustar davisfac/* ========================================================================== */ /* === UMF_triplet ========================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Not user callable. Converts triplet input to column-oriented form. Duplicate entries may exist (they are summed in the output). The columns of the column-oriented form are in sorted order. The input is not modified. Returns 1 if OK, 0 if an error occurred. Compiled into four different routines for each version (di, dl, zi, zl), for a total of 16 different routines. */ #include "umf_internal.h" #include "umf_triplet.h" #ifdef DO_MAP #ifdef DO_VALUES GLOBAL Int UMF_triplet_map_x #else GLOBAL Int UMF_triplet_map_nox #endif #else #ifdef DO_VALUES GLOBAL Int UMF_triplet_nomap_x #else GLOBAL Int UMF_triplet_nomap_nox #endif #endif ( Int n_row, Int n_col, Int nz, const Int Ti [ ], /* size nz */ const Int Tj [ ], /* size nz */ Int Ap [ ], /* size n_col + 1 */ Int Ai [ ], /* size nz */ Int Rp [ ], /* size n_row + 1 */ Int Rj [ ], /* size nz */ Int W [ ], /* size max (n_row, n_col) */ Int RowCount [ ] /* size n_row */ #ifdef DO_VALUES , const double Tx [ ] /* size nz */ , double Ax [ ] /* size nz */ , double Rx [ ] /* size nz */ #ifdef COMPLEX , const double Tz [ ] /* size nz */ , double Az [ ] /* size nz */ , double Rz [ ] /* size nz */ #endif #endif #ifdef DO_MAP , Int Map [ ] /* size nz */ , Int Map2 [ ] /* size nz */ #endif ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Int i, j, k, p, cp, p1, p2, pdest, pj ; #ifdef DO_MAP Int duplicates ; #endif #ifdef DO_VALUES #ifdef COMPLEX Int split = SPLIT (Tz) && SPLIT (Az) && SPLIT (Rz) ; #endif #endif /* ---------------------------------------------------------------------- */ /* count the entries in each row (also counting duplicates) */ /* ---------------------------------------------------------------------- */ /* use W as workspace for row counts (including duplicates) */ for (i = 0 ; i < n_row ; i++) { W [i] = 0 ; } for (k = 0 ; k < nz ; k++) { i = Ti [k] ; j = Tj [k] ; if (i < 0 || i >= n_row || j < 0 || j >= n_col) { return (UMFPACK_ERROR_invalid_matrix) ; } W [i]++ ; #ifndef NDEBUG DEBUG1 ((ID " triplet: "ID" "ID" ", k, i, j)) ; #ifdef DO_VALUES { Entry tt ; ASSIGN (tt, Tx, Tz, k, split) ; EDEBUG2 (tt) ; DEBUG1 (("\n")) ; } #endif #endif } /* ---------------------------------------------------------------------- */ /* compute the row pointers */ /* ---------------------------------------------------------------------- */ Rp [0] = 0 ; for (i = 0 ; i < n_row ; i++) { Rp [i+1] = Rp [i] + W [i] ; W [i] = Rp [i] ; } /* W is now equal to the row pointers */ /* ---------------------------------------------------------------------- */ /* construct the row form */ /* ---------------------------------------------------------------------- */ for (k = 0 ; k < nz ; k++) { p = W [Ti [k]]++ ; #ifdef DO_MAP Map [k] = p ; #endif Rj [p] = Tj [k] ; #ifdef DO_VALUES #ifdef COMPLEX if (split) { Rx [p] = Tx [k] ; Rz [p] = Tz [k] ; } else { Rx [2*p ] = Tx [2*k ] ; Rx [2*p+1] = Tx [2*k+1] ; } #else Rx [p] = Tx [k] ; #endif #endif } /* Rp stays the same, but W [i] is advanced to the start of row i+1 */ #ifndef NDEBUG for (i = 0 ; i < n_row ; i++) { ASSERT (W [i] == Rp [i+1]) ; } #ifdef DO_MAP for (k = 0 ; k < nz ; k++) { /* make sure that kth triplet is mapped correctly */ p = Map [k] ; DEBUG1 (("First row map: Map ["ID"] = "ID"\n", k, p)) ; i = Ti [k] ; j = Tj [k] ; ASSERT (j == Rj [p]) ; ASSERT (Rp [i] <= p && p < Rp [i+1]) ; } #endif #endif /* ---------------------------------------------------------------------- */ /* sum up duplicates */ /* ---------------------------------------------------------------------- */ /* use W [j] to hold position in Ri/Rx/Rz of a_ij, for row i [ */ for (j = 0 ; j < n_col ; j++) { W [j] = EMPTY ; } #ifdef DO_MAP duplicates = FALSE ; #endif for (i = 0 ; i < n_row ; i++) { p1 = Rp [i] ; p2 = Rp [i+1] ; pdest = p1 ; /* At this point, W [j] < p1 holds true for all columns j, */ /* because Ri/Rx/Rz is stored in row oriented order. */ #ifndef NDEBUG if (UMF_debug >= -2) { for (j = 0 ; j < n_col ; j++) { ASSERT (W [j] < p1) ; } } #endif for (p = p1 ; p < p2 ; p++) { j = Rj [p] ; ASSERT (j >= 0 && j < n_col) ; pj = W [j] ; if (pj >= p1) { /* this column index, j, is already in row i, at position pj */ ASSERT (pj < p) ; ASSERT (Rj [pj] == j) ; #ifdef DO_MAP Map2 [p] = pj ; duplicates = TRUE ; #endif #ifdef DO_VALUES /* sum the entry */ #ifdef COMPLEX if (split) { Rx [pj] += Rx [p] ; Rz [pj] += Rz [p] ; } else { Rx[2*pj ] += Rx[2*p ] ; Rx[2*pj+1] += Rx[2*p+1] ; } #else Rx [pj] += Rx [p] ; #endif #endif } else { /* keep the entry */ /* also keep track in W[j] of position of a_ij for case above */ W [j] = pdest ; #ifdef DO_MAP Map2 [p] = pdest ; #endif /* no need to move the entry if pdest is equal to p */ if (pdest != p) { Rj [pdest] = j ; #ifdef DO_VALUES #ifdef COMPLEX if (split) { Rx [pdest] = Rx [p] ; Rz [pdest] = Rz [p] ; } else { Rx [2*pdest ] = Rx [2*p ] ; Rx [2*pdest+1] = Rx [2*p+1] ; } #else Rx [pdest] = Rx [p] ; #endif #endif } pdest++ ; } } RowCount [i] = pdest - p1 ; } /* done using W for position of a_ij ] */ /* ---------------------------------------------------------------------- */ /* merge Map and Map2 into a single Map */ /* ---------------------------------------------------------------------- */ #ifdef DO_MAP if (duplicates) { for (k = 0 ; k < nz ; k++) { Map [k] = Map2 [Map [k]] ; } } #ifndef NDEBUG else { /* no duplicates, so no need to recompute Map */ for (k = 0 ; k < nz ; k++) { ASSERT (Map2 [k] == k) ; } } for (k = 0 ; k < nz ; k++) { /* make sure that kth triplet is mapped correctly */ p = Map [k] ; DEBUG1 (("Second row map: Map ["ID"] = "ID"\n", k, p)) ; i = Ti [k] ; j = Tj [k] ; ASSERT (j == Rj [p]) ; ASSERT (Rp [i] <= p && p < Rp [i+1]) ; } #endif #endif /* now the kth triplet maps to p = Map [k], and thus to Rj/Rx [p] */ /* ---------------------------------------------------------------------- */ /* count the entries in each column */ /* ---------------------------------------------------------------------- */ /* [ use W as work space for column counts of A */ for (j = 0 ; j < n_col ; j++) { W [j] = 0 ; } for (i = 0 ; i < n_row ; i++) { for (p = Rp [i] ; p < Rp [i] + RowCount [i] ; p++) { j = Rj [p] ; ASSERT (j >= 0 && j < n_col) ; W [j]++ ; } } /* ---------------------------------------------------------------------- */ /* create the column pointers */ /* ---------------------------------------------------------------------- */ Ap [0] = 0 ; for (j = 0 ; j < n_col ; j++) { Ap [j+1] = Ap [j] + W [j] ; } /* done using W as workspace for column counts of A ] */ for (j = 0 ; j < n_col ; j++) { W [j] = Ap [j] ; } /* ---------------------------------------------------------------------- */ /* construct the column form */ /* ---------------------------------------------------------------------- */ for (i = 0 ; i < n_row ; i++) { for (p = Rp [i] ; p < Rp [i] + RowCount [i] ; p++) { cp = W [Rj [p]]++ ; #ifdef DO_MAP Map2 [p] = cp ; #endif Ai [cp] = i ; #ifdef DO_VALUES #ifdef COMPLEX if (split) { Ax [cp] = Rx [p] ; Az [cp] = Rz [p] ; } else { Ax [2*cp ] = Rx [2*p ] ; Ax [2*cp+1] = Rx [2*p+1] ; } #else Ax [cp] = Rx [p] ; #endif #endif } } /* ---------------------------------------------------------------------- */ /* merge Map and Map2 into a single Map */ /* ---------------------------------------------------------------------- */ #ifdef DO_MAP for (k = 0 ; k < nz ; k++) { Map [k] = Map2 [Map [k]] ; } #endif /* now the kth triplet maps to p = Map [k], and thus to Ai/Ax [p] */ #ifndef NDEBUG for (j = 0 ; j < n_col ; j++) { ASSERT (W [j] == Ap [j+1]) ; } UMF_dump_col_matrix ( #ifdef DO_VALUES Ax, #ifdef COMPLEX Az, #endif #else (double *) NULL, #ifdef COMPLEX (double *) NULL, #endif #endif Ai, Ap, n_row, n_col, nz) ; #ifdef DO_MAP for (k = 0 ; k < nz ; k++) { /* make sure that kth triplet is mapped correctly */ p = Map [k] ; DEBUG1 (("Col map: Map ["ID"] = "ID"\t", k, p)) ; i = Ti [k] ; j = Tj [k] ; ASSERT (i == Ai [p]) ; DEBUG1 ((" i "ID" j "ID" Ap[j] "ID" p "ID" Ap[j+1] "ID"\n", i, j, Ap [j], p, Ap [j+1])) ; ASSERT (Ap [j] <= p && p < Ap [j+1]) ; } #endif #endif return (UMFPACK_OK) ; } SuiteSparse/UMFPACK/Source/umf_triplet.h0000644001170100242450000000322310617162461017004 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_triplet_map_x ( Int n_row, Int n_col, Int nz, const Int Ti [ ], const Int Tj [ ], Int Ap [ ], Int Ai [ ], Int Rp [ ], Int Rj [ ], Int W [ ], Int RowCount [ ] , const double Tx [ ] , double Ax [ ] , double Rx [ ] #ifdef COMPLEX , const double Tz [ ] , double Az [ ] , double Rz [ ] #endif , Int Map [ ] , Int Map2 [ ] ) ; GLOBAL Int UMF_triplet_map_nox ( Int n_row, Int n_col, Int nz, const Int Ti [ ], const Int Tj [ ], Int Ap [ ], Int Ai [ ], Int Rp [ ], Int Rj [ ], Int W [ ], Int RowCount [ ] , Int Map [ ] , Int Map2 [ ] ) ; GLOBAL Int UMF_triplet_nomap_x ( Int n_row, Int n_col, Int nz, const Int Ti [ ], const Int Tj [ ], Int Ap [ ], Int Ai [ ], Int Rp [ ], Int Rj [ ], Int W [ ], Int RowCount [ ] , const double Tx [ ] , double Ax [ ] , double Rx [ ] #ifdef COMPLEX , const double Tz [ ] , double Az [ ] , double Rz [ ] #endif ) ; GLOBAL Int UMF_triplet_nomap_nox ( Int n_row, Int n_col, Int nz, const Int Ti [ ], const Int Tj [ ], Int Ap [ ], Int Ai [ ], Int Rp [ ], Int Rj [ ], Int W [ ], Int RowCount [ ] ) ; SuiteSparse/UMFPACK/Source/umf_ltsolve.c0000644001170100242450000001442510677541701017016 0ustar davisfac/* ========================================================================== */ /* === UMF_ltsolve ========================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Solves L'x = b or L.'x=b, where L is the lower triangular factor of a */ /* matrix. B is overwritten with the solution X. */ /* Returns the floating point operation count */ #include "umf_internal.h" #include "umf_ltsolve.h" GLOBAL double #ifdef CONJUGATE_SOLVE UMF_lhsolve /* solve L'x=b (complex conjugate transpose) */ #else UMF_ltsolve /* solve L.'x=b (array transpose) */ #endif ( NumericType *Numeric, Entry X [ ], /* b on input, solution x on output */ Int Pattern [ ] /* a work array of size n */ ) { Entry xk ; Entry *xp, *Lval ; Int k, deg, *ip, j, row, *Lpos, *Lilen, kstart, kend, *Lip, llen, lp, pos, npiv, n1, *Li ; /* ---------------------------------------------------------------------- */ if (Numeric->n_row != Numeric->n_col) return (0.) ; npiv = Numeric->npiv ; Lpos = Numeric->Lpos ; Lilen = Numeric->Lilen ; Lip = Numeric->Lip ; kstart = npiv ; n1 = Numeric->n1 ; #ifndef NDEBUG DEBUG4 (("Ltsolve start:\n")) ; for (j = 0 ; j < Numeric->n_row ; j++) { DEBUG4 (("Ltsolve start "ID": ", j)) ; EDEBUG4 (X [j]) ; DEBUG4 (("\n")) ; } #endif /* ---------------------------------------------------------------------- */ /* non-singletons */ /* ---------------------------------------------------------------------- */ for (kend = npiv-1 ; kend >= n1 ; kend = kstart-1) { /* ------------------------------------------------------------------ */ /* find the start of this Lchain */ /* ------------------------------------------------------------------ */ /* for (kstart = kend ; kstart >= 0 && Lip [kstart] > 0 ; kstart--) ; */ kstart = kend ; while (kstart >= 0 && Lip [kstart] > 0) { kstart-- ; } /* the Lchain goes from kstart to kend */ /* ------------------------------------------------------------------ */ /* scan the whole chain to find the pattern of the last column of L */ /* ------------------------------------------------------------------ */ deg = 0 ; DEBUG4 (("start of chain for column of L\n")) ; for (k = kstart ; k <= kend ; k++) { ASSERT (k >= 0 && k < npiv) ; /* -------------------------------------------------------------- */ /* make column k of L in Pattern [0..deg-1] */ /* -------------------------------------------------------------- */ /* remove pivot row */ pos = Lpos [k] ; if (pos != EMPTY) { DEBUG4 ((" k "ID" removing row "ID" at position "ID"\n", k, Pattern [pos], pos)) ; ASSERT (k != kstart) ; ASSERT (deg > 0) ; ASSERT (pos >= 0 && pos < deg) ; ASSERT (Pattern [pos] == k) ; Pattern [pos] = Pattern [--deg] ; } /* concatenate the pattern */ lp = Lip [k] ; if (k == kstart) { lp = -lp ; } ASSERT (lp > 0) ; ip = (Int *) (Numeric->Memory + lp) ; llen = Lilen [k] ; for (j = 0 ; j < llen ; j++) { row = *ip++ ; DEBUG4 ((" row "ID" k "ID"\n", row, k)) ; ASSERT (row > k) ; Pattern [deg++] = row ; } } /* Pattern [0..deg-1] is now the pattern of column kend */ /* ------------------------------------------------------------------ */ /* solve using this chain, in reverse order */ /* ------------------------------------------------------------------ */ DEBUG4 (("Unwinding Lchain\n")) ; for (k = kend ; k >= kstart ; k--) { /* -------------------------------------------------------------- */ /* use column k of L */ /* -------------------------------------------------------------- */ ASSERT (k >= 0 && k < npiv) ; lp = Lip [k] ; if (k == kstart) { lp = -lp ; } ASSERT (lp > 0) ; llen = Lilen [k] ; xp = (Entry *) (Numeric->Memory + lp + UNITS (Int, llen)) ; xk = X [k] ; for (j = 0 ; j < deg ; j++) { DEBUG4 ((" row "ID" k "ID" value", Pattern [j], k)) ; EDEBUG4 (*xp) ; DEBUG4 (("\n")) ; #ifdef CONJUGATE_SOLVE /* xk -= X [Pattern [j]] * conjugate (*xp) ; */ MULT_SUB_CONJ (xk, X [Pattern [j]], *xp) ; #else /* xk -= X [Pattern [j]] * (*xp) ; */ MULT_SUB (xk, X [Pattern [j]], *xp) ; #endif xp++ ; } X [k] = xk ; /* -------------------------------------------------------------- */ /* construct column k-1 of L */ /* -------------------------------------------------------------- */ /* un-concatenate the pattern */ deg -= llen ; /* add pivot row */ pos = Lpos [k] ; if (pos != EMPTY) { DEBUG4 ((" k "ID" adding row "ID" at position "ID"\n", k, k, pos)) ; ASSERT (k != kstart) ; ASSERT (pos >= 0 && pos <= deg) ; Pattern [deg++] = Pattern [pos] ; Pattern [pos] = k ; } } } /* ---------------------------------------------------------------------- */ /* singletons */ /* ---------------------------------------------------------------------- */ for (k = n1 - 1 ; k >= 0 ; k--) { DEBUG4 (("Singleton k "ID"\n", k)) ; deg = Lilen [k] ; if (deg > 0) { xk = X [k] ; lp = Lip [k] ; Li = (Int *) (Numeric->Memory + lp) ; lp += UNITS (Int, deg) ; Lval = (Entry *) (Numeric->Memory + lp) ; for (j = 0 ; j < deg ; j++) { DEBUG4 ((" row "ID" k "ID" value", Li [j], k)) ; EDEBUG4 (Lval [j]) ; DEBUG4 (("\n")) ; #ifdef CONJUGATE_SOLVE /* xk -= X [Li [j]] * conjugate (Lval [j]) ; */ MULT_SUB_CONJ (xk, X [Li [j]], Lval [j]) ; #else /* xk -= X [Li [j]] * Lval [j] ; */ MULT_SUB (xk, X [Li [j]], Lval [j]) ; #endif } X [k] = xk ; } } #ifndef NDEBUG for (j = 0 ; j < Numeric->n_row ; j++) { DEBUG4 (("Ltsolve done "ID": ", j)) ; EDEBUG4 (X [j]) ; DEBUG4 (("\n")) ; } DEBUG4 (("Ltsolve done.\n")) ; #endif return (MULTSUB_FLOPS * ((double) Numeric->lnz)) ; } SuiteSparse/UMFPACK/Source/umf_ltsolve.h0000644001170100242450000000112510617161724017011 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL double UMF_ltsolve ( NumericType *Numeric, Entry X [ ], Int Pattern [ ] ) ; GLOBAL double UMF_lhsolve ( NumericType *Numeric, Entry X [ ], Int Pattern [ ] ) ; SuiteSparse/UMFPACK/Source/umf_create_element.c0000644001170100242450000004151010677541371020300 0ustar davisfac/* ========================================================================== */ /* === UMF_create_element =================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Factorization of a frontal matrix is complete. Create a new element for later assembly into a subsequent frontal matrix. Returns TRUE if successful, FALSE if out of memory. */ #include "umf_internal.h" #include "umf_create_element.h" #include "umf_mem_alloc_element.h" #include "umf_mem_alloc_tail_block.h" #include "umf_mem_free_tail_block.h" #include "umf_get_memory.h" /* ========================================================================== */ /* === copy_column ========================================================== */ /* ========================================================================== */ PRIVATE void copy_column (Int len, Entry *X, Entry *Y) { Int i ; #pragma ivdep for (i = 0 ; i < len ; i++) { Y [i] = X [i] ; } } /* ========================================================================== */ /* === UMF_create_element =================================================== */ /* ========================================================================== */ GLOBAL Int UMF_create_element ( NumericType *Numeric, WorkType *Work, SymbolicType *Symbolic ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Int j, col, row, *Fcols, *Frows, fnrows, fncols, *Cols, len, needunits, t1, t2, size, e, i, *E, *Fcpos, *Frpos, *Rows, eloc, fnr_curr, f, got_memory, *Row_tuples, *Row_degree, *Row_tlen, *Col_tuples, max_mark, *Col_degree, *Col_tlen, nn, n_row, n_col, r2, c2, do_Fcpos ; Entry *C, *Fcol ; Element *ep ; Unit *p, *Memory ; Tuple *tp, *tp1, *tp2, tuple, *tpend ; #ifndef NDEBUG DEBUG2 (("FRONTAL WRAPUP\n")) ; UMF_dump_current_front (Numeric, Work, TRUE) ; #endif /* ---------------------------------------------------------------------- */ /* get parameters */ /* ---------------------------------------------------------------------- */ ASSERT (Work->fnpiv == 0) ; ASSERT (Work->fnzeros == 0) ; Row_degree = Numeric->Rperm ; Row_tuples = Numeric->Uip ; Row_tlen = Numeric->Uilen ; Col_degree = Numeric->Cperm ; Col_tuples = Numeric->Lip ; Col_tlen = Numeric->Lilen ; n_row = Work->n_row ; n_col = Work->n_col ; nn = MAX (n_row, n_col) ; Fcols = Work->Fcols ; Frows = Work->Frows ; Fcpos = Work->Fcpos ; Frpos = Work->Frpos ; Memory = Numeric->Memory ; fncols = Work->fncols ; fnrows = Work->fnrows ; tp = (Tuple *) NULL ; tp1 = (Tuple *) NULL ; tp2 = (Tuple *) NULL ; /* ---------------------------------------------------------------------- */ /* add the current frontal matrix to the degrees of each column */ /* ---------------------------------------------------------------------- */ if (!Symbolic->fixQ) { /* but only if the column ordering is not fixed */ #pragma ivdep for (j = 0 ; j < fncols ; j++) { /* add the current frontal matrix to the degree */ ASSERT (Fcols [j] >= 0 && Fcols [j] < n_col) ; Col_degree [Fcols [j]] += fnrows ; } } /* ---------------------------------------------------------------------- */ /* add the current frontal matrix to the degrees of each row */ /* ---------------------------------------------------------------------- */ #pragma ivdep for (i = 0 ; i < fnrows ; i++) { /* add the current frontal matrix to the degree */ ASSERT (Frows [i] >= 0 && Frows [i] < n_row) ; Row_degree [Frows [i]] += fncols ; } /* ---------------------------------------------------------------------- */ /* Reset the external degree counters */ /* ---------------------------------------------------------------------- */ E = Work->E ; max_mark = MAX_MARK (nn) ; if (!Work->pivcol_in_front) { /* clear the external column degrees. no more Usons of current front */ Work->cdeg0 += (nn + 1) ; if (Work->cdeg0 >= max_mark) { /* guard against integer overflow. This is very rare */ DEBUG1 (("Integer overflow, cdeg\n")) ; Work->cdeg0 = 1 ; #pragma ivdep for (e = 1 ; e <= Work->nel ; e++) { if (E [e]) { ep = (Element *) (Memory + E [e]) ; ep->cdeg = 0 ; } } } } if (!Work->pivrow_in_front) { /* clear the external row degrees. no more Lsons of current front */ Work->rdeg0 += (nn + 1) ; if (Work->rdeg0 >= max_mark) { /* guard against integer overflow. This is very rare */ DEBUG1 (("Integer overflow, rdeg\n")) ; Work->rdeg0 = 1 ; #pragma ivdep for (e = 1 ; e <= Work->nel ; e++) { if (E [e]) { ep = (Element *) (Memory + E [e]) ; ep->rdeg = 0 ; } } } } /* ---------------------------------------------------------------------- */ /* clear row/col offsets */ /* ---------------------------------------------------------------------- */ if (!Work->pivrow_in_front) { #pragma ivdep for (j = 0 ; j < fncols ; j++) { Fcpos [Fcols [j]] = EMPTY ; } } if (!Work->pivcol_in_front) { #pragma ivdep for (i = 0 ; i < fnrows ; i++) { Frpos [Frows [i]] = EMPTY ; } } if (fncols <= 0 || fnrows <= 0) { /* no element to create */ DEBUG2 (("Element evaporation\n")) ; Work->prior_element = EMPTY ; return (TRUE) ; } /* ---------------------------------------------------------------------- */ /* create element for later assembly */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG UMF_allocfail = FALSE ; if (UMF_gprob > 0) { double rrr = ((double) (rand ( ))) / (((double) RAND_MAX) + 1) ; DEBUG4 (("Check random %e %e\n", rrr, UMF_gprob)) ; UMF_allocfail = rrr < UMF_gprob ; if (UMF_allocfail) DEBUGm2 (("Random garbage collection (create)\n")); } #endif needunits = 0 ; got_memory = FALSE ; eloc = UMF_mem_alloc_element (Numeric, fnrows, fncols, &Rows, &Cols, &C, &needunits, &ep) ; /* if UMF_get_memory needs to be called */ if (Work->do_grow) { /* full compaction of current frontal matrix, since UMF_grow_front will * be called next anyway. */ r2 = fnrows ; c2 = fncols ; do_Fcpos = FALSE ; } else { /* partial compaction. */ r2 = MAX (fnrows, Work->fnrows_new + 1) ; c2 = MAX (fncols, Work->fncols_new + 1) ; /* recompute Fcpos if pivot row is in the front */ do_Fcpos = Work->pivrow_in_front ; } if (!eloc) { /* Do garbage collection, realloc, and try again. */ /* Compact the current front if it needs to grow anyway. */ /* Note that there are no pivot rows or columns in the current front */ DEBUGm3 (("get_memory from umf_create_element, 1\n")) ; if (!UMF_get_memory (Numeric, Work, needunits, r2, c2, do_Fcpos)) { /* :: out of memory in umf_create_element (1) :: */ DEBUGm4 (("out of memory: create element (1)\n")) ; return (FALSE) ; /* out of memory */ } got_memory = TRUE ; Memory = Numeric->Memory ; eloc = UMF_mem_alloc_element (Numeric, fnrows, fncols, &Rows, &Cols, &C, &needunits, &ep) ; ASSERT (eloc >= 0) ; if (!eloc) { /* :: out of memory in umf_create_element (2) :: */ DEBUGm4 (("out of memory: create element (2)\n")) ; return (FALSE) ; /* out of memory */ } } e = ++(Work->nel) ; /* get the name of this new frontal matrix */ Work->prior_element = e ; DEBUG8 (("wrapup e "ID" nel "ID"\n", e, Work->nel)) ; ASSERT (e > 0 && e < Work->elen) ; ASSERT (E [e] == 0) ; E [e] = eloc ; if (Work->pivcol_in_front) { /* the new element is a Uson of the next frontal matrix */ ep->cdeg = Work->cdeg0 ; } if (Work->pivrow_in_front) { /* the new element is an Lson of the next frontal matrix */ ep->rdeg = Work->rdeg0 ; } /* ---------------------------------------------------------------------- */ /* copy frontal matrix into the new element */ /* ---------------------------------------------------------------------- */ #pragma ivdep for (i = 0 ; i < fnrows ; i++) { Rows [i] = Frows [i] ; } #pragma ivdep for (i = 0 ; i < fncols ; i++) { Cols [i] = Fcols [i] ; } Fcol = Work->Fcblock ; DEBUG0 (("copy front "ID" by "ID"\n", fnrows, fncols)) ; fnr_curr = Work->fnr_curr ; ASSERT (fnr_curr >= 0 && fnr_curr % 2 == 1) ; for (j = 0 ; j < fncols ; j++) { copy_column (fnrows, Fcol, C) ; Fcol += fnr_curr ; C += fnrows ; } DEBUG8 (("element copied\n")) ; /* ---------------------------------------------------------------------- */ /* add tuples for the new element */ /* ---------------------------------------------------------------------- */ tuple.e = e ; if (got_memory) { /* ------------------------------------------------------------------ */ /* UMF_get_memory ensures enough space exists for each new tuple */ /* ------------------------------------------------------------------ */ /* place (e,f) in the element list of each column */ for (tuple.f = 0 ; tuple.f < fncols ; tuple.f++) { col = Fcols [tuple.f] ; ASSERT (col >= 0 && col < n_col) ; ASSERT (NON_PIVOTAL_COL (col)) ; ASSERT (Col_tuples [col]) ; tp = ((Tuple *) (Memory + Col_tuples [col])) + Col_tlen [col]++ ; *tp = tuple ; } /* ------------------------------------------------------------------ */ /* place (e,f) in the element list of each row */ for (tuple.f = 0 ; tuple.f < fnrows ; tuple.f++) { row = Frows [tuple.f] ; ASSERT (row >= 0 && row < n_row) ; ASSERT (NON_PIVOTAL_ROW (row)) ; ASSERT (Row_tuples [row]) ; tp = ((Tuple *) (Memory + Row_tuples [row])) + Row_tlen [row]++ ; *tp = tuple ; } } else { /* ------------------------------------------------------------------ */ /* place (e,f) in the element list of each column */ /* ------------------------------------------------------------------ */ /* might not have enough space for each tuple */ for (tuple.f = 0 ; tuple.f < fncols ; tuple.f++) { col = Fcols [tuple.f] ; ASSERT (col >= 0 && col < n_col) ; ASSERT (NON_PIVOTAL_COL (col)) ; t1 = Col_tuples [col] ; DEBUG1 (("Placing on col:"ID" , tuples at "ID"\n", col, Col_tuples [col])) ; size = 0 ; len = 0 ; if (t1) { p = Memory + t1 ; tp = (Tuple *) p ; size = GET_BLOCK_SIZE (p) ; len = Col_tlen [col] ; tp2 = tp + len ; } needunits = UNITS (Tuple, len + 1) ; DEBUG1 (("len: "ID" size: "ID" needunits: "ID"\n", len, size, needunits)); if (needunits > size && t1) { /* prune the tuples */ tp1 = tp ; tp2 = tp ; tpend = tp + len ; for ( ; tp < tpend ; tp++) { e = tp->e ; ASSERT (e > 0 && e <= Work->nel) ; if (!E [e]) continue ; /* element already deallocated */ f = tp->f ; p = Memory + E [e] ; ep = (Element *) p ; p += UNITS (Element, 1) ; Cols = (Int *) p ; ; if (Cols [f] == EMPTY) continue ; /* already assembled */ ASSERT (col == Cols [f]) ; *tp2++ = *tp ; /* leave the tuple in the list */ } len = tp2 - tp1 ; Col_tlen [col] = len ; needunits = UNITS (Tuple, len + 1) ; } if (needunits > size) { /* no room exists - reallocate elsewhere */ DEBUG1 (("REALLOCATE Col: "ID", size "ID" to "ID"\n", col, size, 2*needunits)) ; #ifndef NDEBUG UMF_allocfail = FALSE ; if (UMF_gprob > 0) /* a double relop, but ignore NaN case */ { double rrr = ((double) (rand ( ))) / (((double) RAND_MAX) + 1) ; DEBUG1 (("Check random %e %e\n", rrr, UMF_gprob)) ; UMF_allocfail = rrr < UMF_gprob ; if (UMF_allocfail) DEBUGm2 (("Random gar. (col tuple)\n")) ; } #endif needunits = MIN (2*needunits, (Int) UNITS (Tuple, nn)) ; t2 = UMF_mem_alloc_tail_block (Numeric, needunits) ; if (!t2) { /* :: get memory in umf_create_element (1) :: */ /* get memory, reconstruct all tuple lists, and return */ /* Compact the current front if it needs to grow anyway. */ /* Note: no pivot rows or columns in the current front */ DEBUGm4 (("get_memory from umf_create_element, 1\n")) ; return (UMF_get_memory (Numeric, Work, 0, r2, c2,do_Fcpos)); } Col_tuples [col] = t2 ; tp2 = (Tuple *) (Memory + t2) ; if (t1) { for (i = 0 ; i < len ; i++) { *tp2++ = *tp1++ ; } UMF_mem_free_tail_block (Numeric, t1) ; } } /* place the new (e,f) tuple in the element list of the column */ Col_tlen [col]++ ; *tp2 = tuple ; } /* ------------------------------------------------------------------ */ /* place (e,f) in the element list of each row */ /* ------------------------------------------------------------------ */ for (tuple.f = 0 ; tuple.f < fnrows ; tuple.f++) { row = Frows [tuple.f] ; ASSERT (row >= 0 && row < n_row) ; ASSERT (NON_PIVOTAL_ROW (row)) ; t1 = Row_tuples [row] ; DEBUG1 (("Placing on row:"ID" , tuples at "ID"\n", row, Row_tuples [row])) ; size = 0 ; len = 0 ; if (t1) { p = Memory + t1 ; tp = (Tuple *) p ; size = GET_BLOCK_SIZE (p) ; len = Row_tlen [row] ; tp2 = tp + len ; } needunits = UNITS (Tuple, len + 1) ; DEBUG1 (("len: "ID" size: "ID" needunits: "ID"\n", len, size, needunits)) ; if (needunits > size && t1) { /* prune the tuples */ tp1 = tp ; tp2 = tp ; tpend = tp + len ; for ( ; tp < tpend ; tp++) { e = tp->e ; ASSERT (e > 0 && e <= Work->nel) ; if (!E [e]) { continue ; /* element already deallocated */ } f = tp->f ; p = Memory + E [e] ; ep = (Element *) p ; p += UNITS (Element, 1) ; Cols = (Int *) p ; Rows = Cols + (ep->ncols) ; if (Rows [f] == EMPTY) continue ; /* already assembled */ ASSERT (row == Rows [f]) ; *tp2++ = *tp ; /* leave the tuple in the list */ } len = tp2 - tp1 ; Row_tlen [row] = len ; needunits = UNITS (Tuple, len + 1) ; } if (needunits > size) { /* no room exists - reallocate elsewhere */ DEBUG1 (("REALLOCATE Row: "ID", size "ID" to "ID"\n", row, size, 2*needunits)) ; #ifndef NDEBUG UMF_allocfail = FALSE ; if (UMF_gprob > 0) /* a double relop, but ignore NaN case */ { double rrr = ((double) (rand ( ))) / (((double) RAND_MAX) + 1) ; DEBUG1 (("Check random %e %e\n", rrr, UMF_gprob)) ; UMF_allocfail = rrr < UMF_gprob ; if (UMF_allocfail) DEBUGm2 (("Random gar. (row tuple)\n")) ; } #endif needunits = MIN (2*needunits, (Int) UNITS (Tuple, nn)) ; t2 = UMF_mem_alloc_tail_block (Numeric, needunits) ; if (!t2) { /* :: get memory in umf_create_element (2) :: */ /* get memory, reconstruct all tuple lists, and return */ /* Compact the current front if it needs to grow anyway. */ /* Note: no pivot rows or columns in the current front */ DEBUGm4 (("get_memory from umf_create_element, 2\n")) ; return (UMF_get_memory (Numeric, Work, 0, r2, c2,do_Fcpos)); } Row_tuples [row] = t2 ; tp2 = (Tuple *) (Memory + t2) ; if (t1) { for (i = 0 ; i < len ; i++) { *tp2++ = *tp1++ ; } UMF_mem_free_tail_block (Numeric, t1) ; } } /* place the new (e,f) tuple in the element list of the row */ Row_tlen [row]++ ; *tp2 = tuple ; } } /* ---------------------------------------------------------------------- */ #ifndef NDEBUG DEBUG1 (("Done extending\nFINAL: element row pattern: len="ID"\n", fncols)); for (j = 0 ; j < fncols ; j++) DEBUG1 ((""ID"\n", Fcols [j])) ; DEBUG1 (("FINAL: element col pattern: len="ID"\n", fnrows)) ; for (j = 0 ; j < fnrows ; j++) DEBUG1 ((""ID"\n", Frows [j])) ; for (j = 0 ; j < fncols ; j++) { col = Fcols [j] ; ASSERT (col >= 0 && col < n_col) ; UMF_dump_rowcol (1, Numeric, Work, col, !Symbolic->fixQ) ; } for (j = 0 ; j < fnrows ; j++) { row = Frows [j] ; ASSERT (row >= 0 && row < n_row) ; UMF_dump_rowcol (0, Numeric, Work, row, TRUE) ; } if (n_row < 1000 && n_col < 1000) { UMF_dump_memory (Numeric) ; } DEBUG1 (("New element, after filling with stuff: "ID"\n", e)) ; UMF_dump_element (Numeric, Work, e, TRUE) ; if (nn < 1000) { DEBUG4 (("Matrix dump, after New element: "ID"\n", e)) ; UMF_dump_matrix (Numeric, Work, TRUE) ; } DEBUG3 (("FRONTAL WRAPUP DONE\n")) ; #endif return (TRUE) ; } SuiteSparse/UMFPACK/Source/umf_create_element.h0000644001170100242450000000100310617161531020264 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_create_element ( NumericType *Numeric, WorkType *Work, SymbolicType *Symbolic ) ; SuiteSparse/UMFPACK/Source/umf_garbage_collection.c0000644001170100242450000005143510677541430021132 0ustar davisfac/* ========================================================================== */ /* === UMF_garbage_collection =============================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Compress the elements at the tail of Numeric->Memory, and delete the tuples. Elements are renumbered. The new numbering space is compressed, and in the order of element creation (original elements of A first, followed by the new elements in the order that they were formed). Only called by UMF_get_memory. There are 5 ways in which garbage collection can be performed: Allocate a new working array for the current frontal matrix. In this case, there are never any pivot rows/columns in the current frontal matrix (fnpiv = 0), and the old working array for the current frontal matrix can always be fully compacted, to fnrows-by-fncols. UMF_kernel : UMF_extend : UMF_grow_front : UMF_get_memory UMF_kernel : UMF_init_front : UMF_grow_front : UMF_get_memory UMF_kernel : UMF_start_front : UMF_grow_front : UMF_get_memory Allocate a new element. In this case, UMF_grow_front may or may not be subsequently called, depending on Work->do_grow. There are never any pivot rows/columns in the current frontal matrix (fnpiv=0), but one may be added if UMF_init_front is to be called just after UMF_create_element. If do_grow is true, then the current front can be fully compacted, to fnrows-by-fncols. Otherwise, it can only be partially compacted, to MAX (fnrows, fnrows_new + 1) -by- MAX (fncols, fncols_new + 1). UMF_kernel : UMF_create_element : UMF_get_memory Allocate rows of L and columns of U. In this case, the current frontal matrix is only partially compacted, to (fnrows_new + 1)-by- (fncols_new + 1). There are pivots in the frontal matrix (fnpiv > 0). UMF_kernel : UMF_store_lu : UMF_get_memory */ #include "umf_internal.h" #include "umf_garbage_collection.h" GLOBAL void UMF_garbage_collection ( NumericType *Numeric, WorkType *Work, Int drnew, /* compact current front to drnew-by-dcnew */ Int dcnew, Int do_Fcpos ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Int size, e, n_row, n_col, nrows, ncols, nrowsleft, ncolsleft, prevsize, csize, size2, i2, j2, i, j, cdeg, rdeg, *E, row, col, *Rows, *Cols, *Rows2, *Cols2, nel, e2, *Row_tuples, *Col_tuples, *Row_degree, *Col_degree ; Entry *C, *C1, *C3, *C2 ; Unit *psrc, *pdest, *p, *pnext ; Element *epsrc, *epdest ; #ifndef NDEBUG Int nmark ; #endif /* ---------------------------------------------------------------------- */ /* get parameters */ /* ---------------------------------------------------------------------- */ Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro */ Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro */ Row_tuples = Numeric->Uip ; Col_tuples = Numeric->Lip ; E = Work->E ; n_row = Work->n_row ; n_col = Work->n_col ; /* note that the tuple lengths (Col_tlen and Row_tlen) are updated, but */ /* the tuple lists themselves are stale and are about to be destroyed */ /* and recreated. Do not attempt to scan them until they are recreated. */ #ifndef NDEBUG DEBUGm1 (("::::GARBAGE COLLECTION::::\n")) ; UMF_dump_memory (Numeric) ; #endif Numeric->ngarbage++ ; /* ---------------------------------------------------------------------- */ /* delete the tuple lists by marking the blocks as free */ /* ---------------------------------------------------------------------- */ /* do not modify Row_tlen and Col_tlen */ /* those are needed for UMF_build_tuples */ for (row = 0 ; row < n_row ; row++) { if (NON_PIVOTAL_ROW (row) && Row_tuples [row]) { DEBUG2 (("row "ID" tuples "ID"\n", row, Row_tuples [row])) ; p = Numeric->Memory + Row_tuples [row] - 1 ; DEBUG2 (("Freeing tuple list row "ID", p-S "ID", size "ID"\n", row, (Int) (p-Numeric->Memory), p->header.size)) ; ASSERT (p->header.size > 0) ; ASSERT (p >= Numeric->Memory + Numeric->itail) ; ASSERT (p < Numeric->Memory + Numeric->size) ; p->header.size = -p->header.size ; Row_tuples [row] = 0 ; } } for (col = 0 ; col < n_col ; col++) { if (NON_PIVOTAL_COL (col) && Col_tuples [col]) { DEBUG2 (("col "ID" tuples "ID"\n", col, Col_tuples [col])) ; p = Numeric->Memory + Col_tuples [col] - 1 ; DEBUG2 (("Freeing tuple list col "ID", p-S "ID", size "ID"\n", col, (Int) (p-Numeric->Memory), p->header.size)) ; ASSERT (p->header.size > 0) ; ASSERT (p >= Numeric->Memory + Numeric->itail) ; ASSERT (p < Numeric->Memory + Numeric->size) ; p->header.size = -p->header.size ; Col_tuples [col] = 0 ; } } /* ---------------------------------------------------------------------- */ /* mark the elements, and compress the name space */ /* ---------------------------------------------------------------------- */ nel = Work->nel ; ASSERT (nel < Work->elen) ; #ifndef NDEBUG nmark = 0 ; UMF_dump_current_front (Numeric, Work, FALSE) ; DEBUGm1 (("E [0] "ID" \n", E [0])) ; ASSERT (IMPLIES (E [0], Work->Flublock == (Entry *) (Numeric->Memory + E [0]))) ; ASSERT (IMPLIES (Work->Flublock, Work->Flublock == (Entry *) (Numeric->Memory + E [0]))) ; ASSERT ((E [0] != 0) == (Work->Flublock != (Entry *) NULL)) ; #endif e2 = 0 ; for (e = 0 ; e <= nel ; e++) /* for all elements in order of creation */ { if (E [e]) { psrc = Numeric->Memory + E [e] ; psrc-- ; /* get the header of this block */ if (e > 0) { e2++ ; /* do not renumber element zero */ } ASSERT (psrc->header.size > 0) ; psrc->header.size = e2 ; /* store the new name in the header */ #ifndef NDEBUG nmark++ ; #endif DEBUG7 ((ID":: Mark e "ID" at psrc-S "ID", new e "ID"\n", nmark, e, (Int) (psrc-Numeric->Memory), e2)) ; E [e] = 0 ; if (e == Work->prior_element) { Work->prior_element = e2 ; } } } /* all 1..e2 are now in use (element zero may or may not be in use) */ Work->nel = e2 ; nel = Work->nel ; #ifndef NDEBUG for (e = 0 ; e < Work->elen ; e++) { ASSERT (!E [e]) ; } #endif /* ---------------------------------------------------------------------- */ /* compress the elements */ /* ---------------------------------------------------------------------- */ /* point to tail marker block of size 1 + header */ psrc = Numeric->Memory + Numeric->size - 2 ; pdest = psrc ; prevsize = psrc->header.prevsize ; DEBUG7 (("Starting the compression:\n")) ; while (prevsize > 0) { /* ------------------------------------------------------------------ */ /* move up to the next element above the current header, and */ /* get the element name and size */ /* (if it is an element, the name will be positive) */ /* ------------------------------------------------------------------ */ size = prevsize ; psrc -= (size + 1) ; e = psrc->header.size ; prevsize = psrc->header.prevsize ; /* top block at tail has prevsize of 0 */ /* a free block will have a negative size, so skip it */ /* otherwise, if size >= 0, it holds the element name, not the size */ DEBUG8 (("psrc-S: "ID" prevsize: "ID" size: "ID, (Int) (psrc-Numeric->Memory), prevsize, size)) ; if (e == 0) { /* -------------------------------------------------------------- */ /* this is the current frontal matrix */ /* -------------------------------------------------------------- */ Entry *F1, *F2, *Fsrc, *Fdst ; Int c, r, k, dr, dc, gap, gap1, gap2, nb ; /* shift the frontal matrix down */ F1 = (Entry *) (psrc + 1) ; /* get the size of the current front. r and c could be zero */ k = Work->fnpiv ; dr = Work->fnr_curr ; dc = Work->fnc_curr ; r = Work->fnrows ; c = Work->fncols ; nb = Work->nb ; ASSERT ((dr >= 0 && (dr % 2) == 1) || dr == 0) ; ASSERT (drnew >= 0) ; if (drnew % 2 == 0) { /* make sure leading frontal matrix dimension is always odd */ drnew++ ; } drnew = MIN (dr, drnew) ; ASSERT ((drnew >= 0 && (drnew % 2) == 1) || drnew == 0) ; pnext = pdest ; #ifndef NDEBUG DEBUGm2 (("move front: dr "ID" dc "ID" r "ID" drnew "ID" c "ID " dcnew " ID" k "ID"\n", dr, dc, r, drnew, c, dcnew, k)) ; DEBUG7 (("\n")) ; DEBUG7 ((ID":: Move current frontal matrix from: psrc-S: "ID" \n", nmark, (Int) (psrc-Numeric->Memory))) ; nmark-- ; ASSERT (E [e] == 0) ; ASSERT (Work->Flublock == F1) ; ASSERT (Work->Flblock == Work->Flublock + nb*nb) ; ASSERT (Work->Fublock == Work->Flblock + dr*nb) ; ASSERT (Work->Fcblock == Work->Fublock + nb*dc) ; DEBUG7 (("C block: ")) ; UMF_dump_dense (Work->Fcblock, dr, r, c) ; DEBUG7 (("L block: ")) ; UMF_dump_dense (Work->Flblock, dr, r, k); DEBUG7 (("U' block: ")) ; UMF_dump_dense (Work->Fublock, dc, c, k) ; DEBUG7 (("LU block: ")) ; UMF_dump_dense (Work->Flublock, nb, k, k) ; ASSERT (r <= drnew && c <= dcnew && drnew <= dr && dcnew <= dc) ; #endif /* compact frontal matrix to drnew-by-dcnew before moving it */ /* do not compact the LU block (nb-by-nb) */ /* compact the columns of L (from dr-by-nb to drnew-by-nb) */ Fsrc = Work->Flblock ; Fdst = Work->Flblock ; ASSERT (Fdst == F1 + nb*nb) ; gap1 = dr - r ; gap2 = drnew - r ; ASSERT (gap1 >= 0) ; for (j = 0 ; j < k ; j++) { for (i = 0 ; i < r ; i++) { *Fdst++ = *Fsrc++ ; } Fsrc += gap1 ; Fdst += gap2 ; } ASSERT (Fdst == F1 + nb*nb + drnew*k) ; Fdst += drnew * (nb - k) ; /* compact the rows of U (U' from dc-by-nb to dcnew-by-nb) */ Fsrc = Work->Fublock ; ASSERT (Fdst == F1 + nb*nb + drnew*nb) ; gap1 = dc - c ; gap2 = dcnew - c ; for (i = 0 ; i < k ; i++) { for (j = 0 ; j < c ; j++) { *Fdst++ = *Fsrc++ ; } Fsrc += gap1 ; Fdst += gap2 ; } ASSERT (Fdst == F1 + nb*nb + drnew*nb + dcnew*k) ; Fdst += dcnew * (nb - k) ; /* compact the columns of C (from dr-by-dc to drnew-by-dcnew) */ Fsrc = Work->Fcblock ; ASSERT (Fdst == F1 + nb*nb + drnew*nb + nb*dcnew) ; gap1 = dr - r ; gap2 = drnew - r ; for (j = 0 ; j < c ; j++) { for (i = 0 ; i < r ; i++) { *Fdst++ = *Fsrc++ ; } Fsrc += gap1 ; Fdst += gap2 ; } ASSERT (Fdst == F1 + nb*nb + drnew*nb + nb*dcnew + drnew*c) ; /* recompute Fcpos, if necessary */ if (do_Fcpos) { Int *Fcols, *Fcpos ; Fcols = Work->Fcols ; Fcpos = Work->Fcpos ; for (j = 0 ; j < c ; j++) { col = Fcols [j] ; ASSERT (col >= 0 && col < Work->n_col) ; ASSERT (Fcpos [col] == j * dr) ; Fcpos [col] = j * drnew ; } #ifndef NDEBUG { Int cnt = 0 ; for (j = 0 ; j < Work->n_col ; j++) { if (Fcpos [j] != EMPTY) cnt++ ; } DEBUGm2 (("Recompute Fcpos cnt "ID" c "ID"\n", cnt, c)) ; ASSERT (cnt == c) ; } #endif } #ifndef NDEBUG DEBUGm2 (("Compacted front, drnew "ID" dcnew "ID"\n", drnew, dcnew)) ; DEBUG7 (("C block: ")) ; UMF_dump_dense (F1 + nb*nb + drnew*nb + nb*dcnew, drnew, r, c) ; DEBUG7 (("L block: ")) ; UMF_dump_dense (F1 + nb*nb, drnew, r, k) ; DEBUG7 (("U block: ")) ; UMF_dump_dense (F1 + nb*nb + drnew*nb, nb, k, c) ; DEBUG7 (("LU block: ")) ; UMF_dump_dense (F1, nb, k, k) ; #endif /* Compacted dimensions of the new frontal matrix. */ Work->fnr_curr = drnew ; Work->fnc_curr = dcnew ; Work->fcurr_size = (drnew + nb) * (dcnew + nb) ; size = UNITS (Entry, Work->fcurr_size) ; /* make sure the object doesn't evaporate. The front can have * zero size (Work->fcurr_size = 0), but the size of the memory * block containing it cannot have zero size. */ size = MAX (1, size) ; /* get the destination of frontal matrix */ pnext->header.prevsize = size ; pdest -= (size + 1) ; F2 = (Entry *) (pdest + 1) ; ASSERT ((unsigned Int) psrc + 1 + size <= (unsigned Int) pnext) ; ASSERT (psrc <= pdest) ; ASSERT (F1 <= F2) ; /* move the C block first */ Fsrc = F1 + nb*nb + drnew*nb + nb*dcnew + drnew*c ; Fdst = F2 + nb*nb + drnew*nb + nb*dcnew + drnew*c ; gap = drnew - r ; for (j = c-1 ; j >= 0 ; j--) { Fsrc -= gap ; Fdst -= gap ; /* move column j of C */ for (i = r-1 ; i >= 0 ; i--) { *--Fdst = *--Fsrc ; } } ASSERT (Fsrc == F1 + nb*nb + drnew*nb + nb*dcnew) ; ASSERT (Fdst == F2 + nb*nb + drnew*nb + nb*dcnew) ; /* move the U block */ Fsrc -= dcnew * (nb - k) ; Fdst -= dcnew * (nb - k) ; ASSERT (Fsrc == F1 + nb*nb + drnew*nb + dcnew*k) ; ASSERT (Fdst == F2 + nb*nb + drnew*nb + dcnew*k) ; gap = dcnew - c ; for (i = k-1 ; i >= 0 ; i--) { Fsrc -= gap ; Fdst -= gap ; for (j = c-1 ; j >= 0 ; j--) { *--Fdst = *--Fsrc ; } } ASSERT (Fsrc == F1 + nb*nb + drnew*nb) ; ASSERT (Fdst == F2 + nb*nb + drnew*nb) ; /* move the L block */ Fsrc -= drnew * (nb - k) ; Fdst -= drnew * (nb - k) ; ASSERT (Fsrc == F1 + nb*nb + drnew*k) ; ASSERT (Fdst == F2 + nb*nb + drnew*k) ; gap = drnew - r ; for (j = k-1 ; j >= 0 ; j--) { Fsrc -= gap ; Fdst -= gap ; for (i = r-1 ; i >= 0 ; i--) { *--Fdst = *--Fsrc ; } } ASSERT (Fsrc == F1 + nb*nb) ; ASSERT (Fdst == F2 + nb*nb) ; /* move the LU block */ Fsrc -= nb * (nb - k) ; Fdst -= nb * (nb - k) ; ASSERT (Fsrc == F1 + nb*k) ; ASSERT (Fdst == F2 + nb*k) ; gap = nb - k ; for (j = k-1 ; j >= 0 ; j--) { Fsrc -= gap ; Fdst -= gap ; for (i = k-1 ; i >= 0 ; i--) { *--Fdst = *--Fsrc ; } } ASSERT (Fsrc == F1) ; ASSERT (Fdst == F2) ; E [0] = (pdest + 1) - Numeric->Memory ; Work->Flublock = (Entry *) (Numeric->Memory + E [0]) ; ASSERT (Work->Flublock == F2) ; Work->Flblock = Work->Flublock + nb * nb ; Work->Fublock = Work->Flblock + drnew * nb ; Work->Fcblock = Work->Fublock + nb * dcnew ; pdest->header.prevsize = 0 ; pdest->header.size = size ; #ifndef NDEBUG DEBUG7 (("After moving compressed current frontal matrix:\n")) ; DEBUG7 (("C block: ")) ; UMF_dump_dense (Work->Fcblock, drnew, r, c) ; DEBUG7 (("L block: ")) ; UMF_dump_dense (Work->Flblock, drnew, r, k); DEBUG7 (("U' block: ")) ; UMF_dump_dense (Work->Fublock, dcnew, c, k) ; DEBUG7 (("LU block: ")) ; UMF_dump_dense (Work->Flublock, nb, k, k) ; #endif } else if (e > 0) { /* -------------------------------------------------------------- */ /* this is an element, compress and move from psrc down to pdest */ /* -------------------------------------------------------------- */ #ifndef NDEBUG DEBUG7 (("\n")) ; DEBUG7 ((ID":: Move element "ID": from: "ID" \n", nmark, e, (Int) (psrc-Numeric->Memory))) ; nmark-- ; ASSERT (e <= nel) ; ASSERT (E [e] == 0) ; #endif /* -------------------------------------------------------------- */ /* get the element scalars, and pointers to C, Rows, and Cols: */ /* -------------------------------------------------------------- */ p = psrc + 1 ; GET_ELEMENT (epsrc, p, Cols, Rows, ncols, nrows, C) ; nrowsleft = epsrc->nrowsleft ; ncolsleft = epsrc->ncolsleft ; cdeg = epsrc->cdeg ; rdeg = epsrc->rdeg ; #ifndef NDEBUG DEBUG7 ((" nrows "ID" nrowsleft "ID"\n", nrows, nrowsleft)) ; DEBUG7 ((" ncols "ID" ncolsleft "ID"\n", ncols, ncolsleft)) ; DEBUG8 ((" Rows:")) ; for (i = 0 ; i < nrows ; i++) DEBUG8 ((" "ID, Rows [i])) ; DEBUG8 (("\n Cols:")) ; for (j = 0 ; j < ncols ; j++) DEBUG8 ((" "ID, Cols [j])) ; DEBUG8 (("\n")) ; #endif /* -------------------------------------------------------------- */ /* determine the layout of the new element */ /* -------------------------------------------------------------- */ csize = nrowsleft * ncolsleft ; size2 = UNITS (Element, 1) + UNITS (Int, nrowsleft + ncolsleft) + UNITS (Entry, csize) ; DEBUG7 (("Old size "ID" New size "ID"\n", size, size2)) ; pnext = pdest ; pnext->header.prevsize = size2 ; pdest -= (size2 + 1) ; ASSERT (size2 <= size) ; ASSERT ((unsigned Int) psrc + 1 + size <= (unsigned Int) pnext) ; ASSERT (psrc <= pdest) ; p = pdest + 1 ; epdest = (Element *) p ; p += UNITS (Element, 1) ; Cols2 = (Int *) p ; Rows2 = Cols2 + ncolsleft ; p += UNITS (Int, nrowsleft + ncolsleft) ; C2 = (Entry *) p ; ASSERT (epdest >= epsrc) ; ASSERT (Rows2 >= Rows) ; ASSERT (Cols2 >= Cols) ; ASSERT (C2 >= C) ; ASSERT (p + UNITS (Entry, csize) == pnext) ; /* -------------------------------------------------------------- */ /* move the contribution block */ /* -------------------------------------------------------------- */ /* overlap = psrc + size + 1 > pdest ; */ if (nrowsleft < nrows || ncolsleft < ncols) { /* ---------------------------------------------------------- */ /* compress contribution block in place prior to moving it */ /* ---------------------------------------------------------- */ DEBUG7 (("Compress C in place prior to move:\n")); #ifndef NDEBUG UMF_dump_dense (C, nrows, nrows, ncols) ; #endif C1 = C ; C3 = C ; for (j = 0 ; j < ncols ; j++) { if (Cols [j] >= 0) { for (i = 0 ; i < nrows ; i++) { if (Rows [i] >= 0) { *C3++ = C1 [i] ; } } } C1 += nrows ; } ASSERT (C3-C == csize) ; DEBUG8 (("Newly compressed contrib. block (all in use):\n")) ; #ifndef NDEBUG UMF_dump_dense (C, nrowsleft, nrowsleft, ncolsleft) ; #endif } /* shift the contribution block down */ C += csize ; C2 += csize ; for (i = 0 ; i < csize ; i++) { *--C2 = *--C ; } /* -------------------------------------------------------------- */ /* move the row indices */ /* -------------------------------------------------------------- */ i2 = nrowsleft ; for (i = nrows - 1 ; i >= 0 ; i--) { ASSERT (Rows2+i2 >= Rows+i) ; if (Rows [i] >= 0) { Rows2 [--i2] = Rows [i] ; } } ASSERT (i2 == 0) ; j2 = ncolsleft ; for (j = ncols - 1 ; j >= 0 ; j--) { ASSERT (Cols2+j2 >= Cols+j) ; if (Cols [j] >= 0) { Cols2 [--j2] = Cols [j] ; } } ASSERT (j2 == 0) ; /* -------------------------------------------------------------- */ /* construct the new header */ /* -------------------------------------------------------------- */ /* E [0...e] is now valid */ E [e] = (pdest + 1) - Numeric->Memory ; epdest = (Element *) (pdest + 1) ; epdest->next = EMPTY ; /* destroys the son list */ epdest->ncols = ncolsleft ; epdest->nrows = nrowsleft ; epdest->ncolsleft = ncolsleft ; epdest->nrowsleft = nrowsleft ; epdest->rdeg = rdeg ; epdest->cdeg = cdeg ; ASSERT (size2 <= size) ; pdest->header.prevsize = 0 ; pdest->header.size = size2 ; DEBUG7 (("After moving it:\n")) ; #ifndef NDEBUG UMF_dump_element (Numeric, Work, e, FALSE) ; #endif } #ifndef NDEBUG else { DEBUG8 ((" free\n")) ; } #endif DEBUG7 (("psrc "ID" tail "ID"\n", (Int) (psrc-Numeric->Memory), Numeric->itail)) ; } ASSERT (psrc == Numeric->Memory + Numeric->itail) ; ASSERT (nmark == 0) ; /* ---------------------------------------------------------------------- */ /* final tail pointer */ /* ---------------------------------------------------------------------- */ ASSERT (pdest >= Numeric->Memory + Numeric->itail) ; Numeric->itail = pdest - Numeric->Memory ; pdest->header.prevsize = 0 ; Numeric->ibig = EMPTY ; Numeric->tail_usage = Numeric->size - Numeric->itail ; /* ---------------------------------------------------------------------- */ /* clear the unused E [nel+1 .. Work->elen - 1] */ /* ---------------------------------------------------------------------- */ for (e = nel+1 ; e < Work->elen ; e++) { E [e] = 0 ; } #ifndef NDEBUG UMF_dump_packed_memory (Numeric, Work) ; #endif DEBUG8 (("::::GARBAGE COLLECTION DONE::::\n")) ; } SuiteSparse/UMFPACK/Source/umf_garbage_collection.h0000644001170100242450000000103410617161572021124 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL void UMF_garbage_collection ( NumericType *Numeric, WorkType *Work, Int drnew, Int dcnew, Int do_Fcpos ) ; SuiteSparse/UMFPACK/Source/umf_fsize.c0000644001170100242450000000432610677540657016456 0ustar davisfac/* ========================================================================== */ /* === UMF_fsize ============================================================ */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Determine the largest frontal matrix size for each subtree. Called by * UMF_colamd and UMF_analyze. Only required to sort the children of each * node prior to AMD_postorder. */ #include "umf_internal.h" #include "umf_fsize.h" GLOBAL void UMF_fsize ( Int nn, Int Fsize [ ], Int Fnrows [ ], Int Fncols [ ], Int Parent [ ], Int Npiv [ ] ) { Int j, parent, frsize, r, c ; for (j = 0 ; j < nn ; j++) { Fsize [j] = EMPTY ; } /* ---------------------------------------------------------------------- */ /* find max front size for tree rooted at node j, for each front j */ /* ---------------------------------------------------------------------- */ DEBUG1 (("\n\n========================================FRONTS:\n")) ; for (j = 0 ; j < nn ; j++) { if (Npiv [j] > 0) { /* this is a frontal matrix */ parent = Parent [j] ; r = Fnrows [j] ; c = Fncols [j] ; frsize = r * c ; /* avoid integer overflow */ if (INT_OVERFLOW (((double) r) * ((double) c))) { /* :: frsize int overflow :: */ frsize = Int_MAX ; } DEBUG1 ((""ID" : npiv "ID" size "ID" parent "ID" ", j, Npiv [j], frsize, parent)) ; Fsize [j] = MAX (Fsize [j], frsize) ; DEBUG1 (("Fsize [j = "ID"] = "ID"\n", j, Fsize [j])) ; if (parent != EMPTY) { /* find the maximum frontsize of self and children */ ASSERT (Npiv [parent] > 0) ; ASSERT (parent > j) ; Fsize [parent] = MAX (Fsize [parent], Fsize [j]) ; DEBUG1 (("Fsize [parent = "ID"] = "ID"\n", parent, Fsize [parent])); } } } } SuiteSparse/UMFPACK/Source/umf_fsize.h0000644001170100242450000000104110617161564016440 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL void UMF_fsize ( Int nn, Int MaxFsize [ ], Int Fnrows [ ], Int Fncols [ ], Int Parent [ ], Int Npiv [ ] ) ; SuiteSparse/UMFPACK/Source/umfpack_symbolic.c0000644001170100242450000000230510617162172017773 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_symbolic ===================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Performs a symbolic factorization. See umfpack_symbolic.h for details. */ #include "umf_internal.h" GLOBAL Int UMFPACK_symbolic ( Int n_row, Int n_col, const Int Ap [ ], const Int Ai [ ], const double Ax [ ], #ifdef COMPLEX const double Az [ ], #endif void **SymbolicHandle, const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO] ) { Int *Qinit = (Int *) NULL ; return (UMFPACK_qsymbolic (n_row, n_col, Ap, Ai, Ax, #ifdef COMPLEX Az, #endif Qinit, SymbolicHandle, Control, Info)) ; } SuiteSparse/UMFPACK/Source/umf_mem_free_tail_block.c0000644001170100242450000001103610677542155021267 0ustar davisfac/* ========================================================================== */ /* === UMF_mem_free_tail_block ============================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* The UMF_mem_* routines manage the Numeric->Memory memory space. */ /* free a block from the tail of Numeric->memory */ #include "umf_internal.h" #include "umf_mem_free_tail_block.h" GLOBAL void UMF_mem_free_tail_block ( NumericType *Numeric, Int i ) { Unit *pprev, *pnext, *p, *pbig ; Int sprev ; ASSERT (Numeric != (NumericType *) NULL) ; ASSERT (Numeric->Memory != (Unit *) NULL) ; if (i == EMPTY || i == 0) return ; /* already deallocated */ /* ---------------------------------------------------------------------- */ /* get the block */ /* ---------------------------------------------------------------------- */ p = Numeric->Memory + i ; p-- ; /* get the corresponding header */ DEBUG2 (("free block: p: "ID, (Int) (p-Numeric->Memory))) ; ASSERT (p >= Numeric->Memory + Numeric->itail) ; ASSERT (p < Numeric->Memory + Numeric->size) ; ASSERT (p->header.size > 0) ; /* block not already free */ ASSERT (p->header.prevsize >= 0) ; Numeric->tail_usage -= p->header.size + 1 ; /* ---------------------------------------------------------------------- */ /* merge with next free block, if any */ /* ---------------------------------------------------------------------- */ pnext = p + 1 + p->header.size ; DEBUG2 (("size: "ID" next: "ID" ", p->header.size, (Int) (pnext-Numeric->Memory))) ; ASSERT (pnext < Numeric->Memory + Numeric->size) ; ASSERT (pnext->header.prevsize == p->header.size) ; ASSERT (pnext->header.size != 0) ; if (pnext->header.size < 0) { /* next block is also free - merge with current block */ p->header.size += (-(pnext->header.size)) + 1 ; DEBUG2 ((" NEXT FREE ")) ; } /* ---------------------------------------------------------------------- */ /* merge with previous free block, if any */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG if (p == Numeric->Memory + Numeric->itail) { DEBUG2 ((" at top of tail ")) ; ASSERT (p->header.prevsize == 0) ; } #endif if (p > Numeric->Memory + Numeric->itail) { ASSERT (p->header.prevsize > 0) ; pprev = p - 1 - p->header.prevsize ; DEBUG2 ((" prev: "ID" ", (Int) (pprev-Numeric->Memory))) ; ASSERT (pprev >= Numeric->Memory + Numeric->itail) ; sprev = pprev->header.size ; if (sprev < 0) { /* previous block is also free - merge it with current block */ ASSERT (p->header.prevsize == -sprev) ; pprev->header.size = p->header.size + (-sprev) + 1 ; p = pprev ; DEBUG2 ((" PREV FREE ")) ; /* note that p may now point to Numeric->itail */ } #ifndef NDEBUG else { ASSERT (p->header.prevsize == sprev) ; } #endif } /* ---------------------------------------------------------------------- */ /* free the block, p */ /* ---------------------------------------------------------------------- */ pnext = p + 1 + p->header.size ; ASSERT (pnext < Numeric->Memory + Numeric->size) ; if (p == Numeric->Memory + Numeric->itail) { /* top block in list is freed */ Numeric->itail = pnext - Numeric->Memory ; pnext->header.prevsize = 0 ; DEBUG2 ((" NEW TAIL : "ID" ", Numeric->itail)) ; ASSERT (pnext->header.size > 0) ; if (Numeric->ibig != EMPTY && Numeric->ibig <= Numeric->itail) { /* the big free block is now above the tail */ Numeric->ibig = EMPTY ; } } else { /* keep track of the biggest free block seen */ if (Numeric->ibig == EMPTY) { Numeric->ibig = p - Numeric->Memory ; } else { pbig = Numeric->Memory + Numeric->ibig ; if (-(pbig->header.size) < p->header.size) { Numeric->ibig = p - Numeric->Memory ; } } /* flag the block as free, somewhere in the middle of the tail */ pnext->header.prevsize = p->header.size ; p->header.size = -(p->header.size) ; } DEBUG2 (("new p: "ID" freesize: "ID"\n", (Int) (p-Numeric->Memory), -(p->header.size))) ; } SuiteSparse/UMFPACK/Source/umf_mem_free_tail_block.h0000644001170100242450000000074410617161771021273 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL void UMF_mem_free_tail_block ( NumericType *Numeric, Int i ) ; SuiteSparse/UMFPACK/Source/umf_usolve.c0000644001170100242450000001421410677542466016650 0ustar davisfac/* ========================================================================== */ /* === UMF_usolve =========================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* solves Ux = b, where U is the upper triangular factor of a matrix. */ /* B is overwritten with the solution X. */ /* Returns the floating point operation count */ #include "umf_internal.h" #include "umf_usolve.h" GLOBAL double UMF_usolve ( NumericType *Numeric, Entry X [ ], /* b on input, solution x on output */ Int Pattern [ ] /* a work array of size n */ ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Entry xk ; Entry *xp, *D, *Uval ; Int k, deg, j, *ip, col, *Upos, *Uilen, pos, *Uip, n, ulen, up, newUchain, npiv, n1, *Ui ; /* ---------------------------------------------------------------------- */ /* get parameters */ /* ---------------------------------------------------------------------- */ if (Numeric->n_row != Numeric->n_col) return (0.) ; n = Numeric->n_row ; npiv = Numeric->npiv ; Upos = Numeric->Upos ; Uilen = Numeric->Uilen ; Uip = Numeric->Uip ; D = Numeric->D ; n1 = Numeric->n1 ; #ifndef NDEBUG DEBUG4 (("Usolve start: npiv = "ID" n = "ID"\n", npiv, n)) ; for (j = 0 ; j < n ; j++) { DEBUG4 (("Usolve start "ID": ", j)) ; EDEBUG4 (X [j]) ; DEBUG4 (("\n")) ; } #endif /* ---------------------------------------------------------------------- */ /* singular case */ /* ---------------------------------------------------------------------- */ #ifndef NO_DIVIDE_BY_ZERO /* handle the singular part of D, up to just before the last pivot */ for (k = n-1 ; k >= npiv ; k--) { /* This is an *** intentional *** divide-by-zero, to get Inf or Nan, * as appropriate. It is not a bug. */ ASSERT (IS_ZERO (D [k])) ; xk = X [k] ; /* X [k] = xk / D [k] ; */ DIV (X [k], xk, D [k]) ; } #else /* Do not divide by zero */ #endif deg = Numeric->ulen ; if (deg > 0) { /* :: make last pivot row of U (singular matrices only) :: */ for (j = 0 ; j < deg ; j++) { DEBUG1 (("Last row of U: j="ID"\n", j)) ; DEBUG1 (("Last row of U: Upattern[j]="ID"\n", Numeric->Upattern [j]) ); Pattern [j] = Numeric->Upattern [j] ; } } /* ---------------------------------------------------------------------- */ /* nonsingletons */ /* ---------------------------------------------------------------------- */ for (k = npiv-1 ; k >= n1 ; k--) { /* ------------------------------------------------------------------ */ /* use row k of U */ /* ------------------------------------------------------------------ */ up = Uip [k] ; ulen = Uilen [k] ; newUchain = (up < 0) ; if (newUchain) { up = -up ; xp = (Entry *) (Numeric->Memory + up + UNITS (Int, ulen)) ; } else { xp = (Entry *) (Numeric->Memory + up) ; } xk = X [k] ; for (j = 0 ; j < deg ; j++) { DEBUG4 ((" k "ID" col "ID" value", k, Pattern [j])) ; EDEBUG4 (*xp) ; DEBUG4 (("\n")) ; /* xk -= X [Pattern [j]] * (*xp) ; */ MULT_SUB (xk, X [Pattern [j]], *xp) ; xp++ ; } #ifndef NO_DIVIDE_BY_ZERO /* Go ahead and divide by zero if D [k] is zero */ /* X [k] = xk / D [k] ; */ DIV (X [k], xk, D [k]) ; #else /* Do not divide by zero */ if (IS_NONZERO (D [k])) { /* X [k] = xk / D [k] ; */ DIV (X [k], xk, D [k]) ; } #endif /* ------------------------------------------------------------------ */ /* make row k-1 of U in Pattern [0..deg-1] */ /* ------------------------------------------------------------------ */ if (k == n1) break ; if (newUchain) { /* next row is a new Uchain */ deg = ulen ; ASSERT (IMPLIES (k == 0, deg == 0)) ; DEBUG4 (("end of chain for row of U "ID" deg "ID"\n", k-1, deg)) ; ip = (Int *) (Numeric->Memory + up) ; for (j = 0 ; j < deg ; j++) { col = *ip++ ; DEBUG4 ((" k "ID" col "ID"\n", k-1, col)) ; ASSERT (k <= col) ; Pattern [j] = col ; } } else { deg -= ulen ; DEBUG4 (("middle of chain for row of U "ID" deg "ID"\n", k, deg)) ; ASSERT (deg >= 0) ; pos = Upos [k] ; if (pos != EMPTY) { /* add the pivot column */ DEBUG4 (("k "ID" add pivot entry at pos "ID"\n", k, pos)) ; ASSERT (pos >= 0 && pos <= deg) ; Pattern [deg++] = Pattern [pos] ; Pattern [pos] = k ; } } } /* ---------------------------------------------------------------------- */ /* singletons */ /* ---------------------------------------------------------------------- */ for (k = n1 - 1 ; k >= 0 ; k--) { deg = Uilen [k] ; xk = X [k] ; DEBUG4 (("Singleton k "ID"\n", k)) ; if (deg > 0) { up = Uip [k] ; Ui = (Int *) (Numeric->Memory + up) ; up += UNITS (Int, deg) ; Uval = (Entry *) (Numeric->Memory + up) ; for (j = 0 ; j < deg ; j++) { DEBUG4 ((" k "ID" col "ID" value", k, Ui [j])) ; EDEBUG4 (Uval [j]) ; DEBUG4 (("\n")) ; /* xk -= X [Ui [j]] * Uval [j] ; */ ASSERT (Ui [j] >= 0 && Ui [j] < n) ; MULT_SUB (xk, X [Ui [j]], Uval [j]) ; } } #ifndef NO_DIVIDE_BY_ZERO /* Go ahead and divide by zero if D [k] is zero */ /* X [k] = xk / D [k] ; */ DIV (X [k], xk, D [k]) ; #else /* Do not divide by zero */ if (IS_NONZERO (D [k])) { /* X [k] = xk / D [k] ; */ DIV (X [k], xk, D [k]) ; } #endif } #ifndef NDEBUG for (j = 0 ; j < n ; j++) { DEBUG4 (("Usolve done "ID": ", j)) ; EDEBUG4 (X [j]) ; DEBUG4 (("\n")) ; } DEBUG4 (("Usolve done.\n")) ; #endif return (DIV_FLOPS * ((double) n) + MULTSUB_FLOPS * ((double) Numeric->unz)); } SuiteSparse/UMFPACK/Source/umf_usolve.h0000644001170100242450000000076410617162475016652 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL double UMF_usolve ( NumericType *Numeric, Entry X [ ], Int Pattern [ ] ) ; SuiteSparse/UMFPACK/Source/umf_multicompile.c0000644001170100242450000000421710617162026020020 0ustar davisfac/* ========================================================================== */ /* === UMF_multicompile ===================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* This file is not needed if you have the Unix/Linux "make" command for * compiling UMFPACK. Microsoft Visual Studio cannot be configured to compile * one file multiple times, with different -D flags. In this case, you can * use this file instead. To use this file, see the Demo/simple_compile file. * * This file includes the following source files: * * umf_ltsolve.c * umf_utsolve.c * umf_triplet.c * umf_assemble.c * umf_store_lu.c * umfpack_solve.c * * This file simply compiles the above files with different pre-#define'd flags, * by defining the flags and then #include'ing the source files themselves. * This is a rather unconventional approach, since by convention #include is * supposed to be used with *.h files not *.c. However, it is one way of * working around the limitations of Microsoft Visual Studio. * * You still need to compile all files separately as well, with none of the * pre-#define'd terms listed below. */ /* compile the complex conjugate forward/backsolves */ #define CONJUGATE_SOLVE #include "umf_ltsolve.c" #include "umf_utsolve.c" /* compile umf_triplet with DO_MAP, DO_VALUES and DO_MAP, and just DO_VALUES */ #define DO_MAP #include "umf_triplet.c" #define DO_VALUES #include "umf_triplet.c" #undef DO_MAP #include "umf_triplet.c" /* compile the FIXQ version of umf_assemble */ #define FIXQ #include "umf_assemble.c" /* compile the DROP version of umf_store_lu */ #define DROP #include "umf_store_lu.c" /* compile umfpack_wsolve */ #define WSOLVE #include "umfpack_solve.c" SuiteSparse/UMFPACK/Source/umf_store_lu.c0000644001170100242450000006331410677541301017157 0ustar davisfac/* ========================================================================== */ /* === UMF_store_lu ========================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Store the LU factors. Called by the kernel. Returns TRUE if successful, FALSE if out of memory. */ #include "umf_internal.h" #include "umf_store_lu.h" #include "umf_mem_alloc_head_block.h" #include "umf_get_memory.h" /* ========================================================================== */ #ifdef DROP GLOBAL Int UMF_store_lu_drop #else GLOBAL Int UMF_store_lu #endif ( NumericType *Numeric, WorkType *Work ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Entry pivot_value ; #ifdef DROP double droptol ; #endif Entry *D, *Lval, *Uval, *Fl1, *Fl2, *Fu1, *Fu2, *Flublock, *Flblock, *Fublock ; Int i, k, fnr_curr, fnrows, fncols, row, col, pivrow, pivcol, *Frows, *Fcols, *Lpattern, *Upattern, *Lpos, *Upos, llen, ulen, fnc_curr, fnpiv, uilen, lnz, unz, nb, *Lilen, *Uilen, *Lip, *Uip, *Li, *Ui, pivcol_position, newLchain, newUchain, pivrow_position, p, size, lip, uip, lnzi, lnzx, unzx, lnz2i, lnz2x, unz2i, unz2x, zero_pivot, *Pivrow, *Pivcol, kk, Lnz [MAXNB] ; #ifndef NDEBUG Int *Col_degree, *Row_degree ; #endif #ifdef DROP Int all_lnz, all_unz ; droptol = Numeric->droptol ; #endif /* ---------------------------------------------------------------------- */ /* get parameters */ /* ---------------------------------------------------------------------- */ fnrows = Work->fnrows ; fncols = Work->fncols ; fnpiv = Work->fnpiv ; Lpos = Numeric->Lpos ; Upos = Numeric->Upos ; Lilen = Numeric->Lilen ; Uilen = Numeric->Uilen ; Lip = Numeric->Lip ; Uip = Numeric->Uip ; D = Numeric->D ; Flublock = Work->Flublock ; Flblock = Work->Flblock ; Fublock = Work->Fublock ; fnr_curr = Work->fnr_curr ; fnc_curr = Work->fnc_curr ; Frows = Work->Frows ; Fcols = Work->Fcols ; #ifndef NDEBUG Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro */ Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro */ #endif Lpattern = Work->Lpattern ; llen = Work->llen ; Upattern = Work->Upattern ; ulen = Work->ulen ; nb = Work->nb ; #ifndef NDEBUG DEBUG1 (("\nSTORE LU: fnrows "ID " fncols "ID"\n", fnrows, fncols)) ; DEBUG2 (("\nFrontal matrix, including all space:\n" "fnr_curr "ID" fnc_curr "ID" nb "ID"\n" "fnrows "ID" fncols "ID" fnpiv "ID"\n", fnr_curr, fnc_curr, nb, fnrows, fncols, fnpiv)) ; DEBUG2 (("\nJust the active part:\n")) ; DEBUG7 (("C block: ")) ; UMF_dump_dense (Work->Fcblock, fnr_curr, fnrows, fncols) ; DEBUG7 (("L block: ")) ; UMF_dump_dense (Work->Flblock, fnr_curr, fnrows, fnpiv); DEBUG7 (("U' block: ")) ; UMF_dump_dense (Work->Fublock, fnc_curr, fncols, fnpiv) ; DEBUG7 (("LU block: ")) ; UMF_dump_dense (Work->Flublock, nb, fnpiv, fnpiv) ; DEBUG7 (("Current frontal matrix: (prior to store LU)\n")) ; UMF_dump_current_front (Numeric, Work, TRUE) ; #endif Pivrow = Work->Pivrow ; Pivcol = Work->Pivcol ; /* ---------------------------------------------------------------------- */ /* store the columns of L */ /* ---------------------------------------------------------------------- */ for (kk = 0 ; kk < fnpiv ; kk++) { /* ------------------------------------------------------------------ */ /* one more pivot row and column is being stored into L and U */ /* ------------------------------------------------------------------ */ k = Work->npiv + kk ; /* ------------------------------------------------------------------ */ /* find the kth pivot row and pivot column */ /* ------------------------------------------------------------------ */ pivrow = Pivrow [kk] ; pivcol = Pivcol [kk] ; #ifndef NDEBUG ASSERT (pivrow >= 0 && pivrow < Work->n_row) ; ASSERT (pivcol >= 0 && pivcol < Work->n_col) ; DEBUGm4 (( "\n -------------------------------------------------------------" "Store LU: step " ID"\n", k)) ; ASSERT (k < MIN (Work->n_row, Work->n_col)) ; DEBUG2 (("Store column of L, k = "ID", llen "ID"\n", k, llen)) ; for (i = 0 ; i < llen ; i++) { row = Lpattern [i] ; ASSERT (row >= 0 && row < Work->n_row) ; DEBUG2 ((" Lpattern["ID"] "ID" Lpos "ID, i, row, Lpos [row])) ; if (row == pivrow) DEBUG2 ((" <- pivot row")) ; DEBUG2 (("\n")) ; ASSERT (i == Lpos [row]) ; } #endif /* ------------------------------------------------------------------ */ /* remove pivot row from L */ /* ------------------------------------------------------------------ */ /* remove pivot row index from current column of L */ /* if a new Lchain starts, then all entries are removed later */ DEBUG2 (("Removing pivrow from Lpattern, k = "ID"\n", k)) ; ASSERT (!NON_PIVOTAL_ROW (pivrow)) ; pivrow_position = Lpos [pivrow] ; if (pivrow_position != EMPTY) { /* place the last entry in the column in the */ /* position of the pivot row index */ ASSERT (pivrow == Lpattern [pivrow_position]) ; row = Lpattern [--llen] ; /* ASSERT (NON_PIVOTAL_ROW (row)) ; */ Lpattern [pivrow_position] = row ; Lpos [row] = pivrow_position ; Lpos [pivrow] = EMPTY ; } /* ------------------------------------------------------------------ */ /* store the pivot value, for the diagonal matrix D */ /* ------------------------------------------------------------------ */ /* kk-th column of LU block */ Fl1 = Flublock + kk * nb ; /* kk-th column of L in the L block */ Fl2 = Flblock + kk * fnr_curr ; /* kk-th pivot in frontal matrix located in Flublock [kk, kk] */ pivot_value = Fl1 [kk] ; D [k] = pivot_value ; zero_pivot = IS_ZERO (pivot_value) ; DEBUG4 (("Pivot D["ID"]=", k)) ; EDEBUG4 (pivot_value) ; DEBUG4 (("\n")) ; /* ------------------------------------------------------------------ */ /* count nonzeros in kth column of L */ /* ------------------------------------------------------------------ */ lnz = 0 ; lnz2i = 0 ; lnz2x = llen ; #ifdef DROP all_lnz = 0 ; for (i = kk + 1 ; i < fnpiv ; i++) { Entry x ; double s ; x = Fl1 [i] ; if (IS_ZERO (x)) continue ; all_lnz++ ; APPROX_ABS (s, x) ; if (s <= droptol) continue ; lnz++ ; if (Lpos [Pivrow [i]] == EMPTY) lnz2i++ ; } for (i = 0 ; i < fnrows ; i++) { Entry x ; double s ; x = Fl2 [i] ; if (IS_ZERO (x)) continue ; all_lnz++ ; APPROX_ABS (s, x) ; if (s <= droptol) continue ; lnz++ ; if (Lpos [Frows [i]] == EMPTY) lnz2i++ ; } #else for (i = kk + 1 ; i < fnpiv ; i++) { if (IS_ZERO (Fl1 [i])) continue ; lnz++ ; if (Lpos [Pivrow [i]] == EMPTY) lnz2i++ ; } for (i = 0 ; i < fnrows ; i++) { if (IS_ZERO (Fl2 [i])) continue ; lnz++ ; if (Lpos [Frows [i]] == EMPTY) lnz2i++ ; } #endif lnz2x += lnz2i ; /* determine if we start a new Lchain or continue the old one */ if (llen == 0 || zero_pivot) { /* llen == 0 means there is no prior Lchain */ /* D [k] == 0 means the pivot column is empty */ newLchain = TRUE ; } else { newLchain = /* storage for starting a new Lchain */ UNITS (Entry, lnz) + UNITS (Int, lnz) <= /* storage for continuing a prior Lchain */ UNITS (Entry, lnz2x) + UNITS (Int, lnz2i) ; } if (newLchain) { /* start a new chain for column k of L */ DEBUG2 (("Start new Lchain, k = "ID"\n", k)) ; pivrow_position = EMPTY ; /* clear the prior Lpattern */ for (i = 0 ; i < llen ; i++) { row = Lpattern [i] ; Lpos [row] = EMPTY ; } llen = 0 ; lnzi = lnz ; lnzx = lnz ; } else { /* continue the prior Lchain */ DEBUG2 (("Continue Lchain, k = "ID"\n", k)) ; lnzi = lnz2i ; lnzx = lnz2x ; } /* ------------------------------------------------------------------ */ /* allocate space for the column of L */ /* ------------------------------------------------------------------ */ size = UNITS (Int, lnzi) + UNITS (Entry, lnzx) ; #ifndef NDEBUG UMF_allocfail = FALSE ; if (UMF_gprob > 0) { double rrr = ((double) (rand ( ))) / (((double) RAND_MAX) + 1) ; DEBUG4 (("Check random %e %e\n", rrr, UMF_gprob)) ; UMF_allocfail = rrr < UMF_gprob ; if (UMF_allocfail) DEBUGm2 (("Random garbage coll. (store LU)\n")); } #endif p = UMF_mem_alloc_head_block (Numeric, size) ; if (!p) { Int r2, c2 ; /* Do garbage collection, realloc, and try again. */ /* Note that there are pivot rows/columns in current front. */ if (Work->do_grow) { /* full compaction of current frontal matrix, since * UMF_grow_front will be called next anyway. */ r2 = fnrows ; c2 = fncols ; } else { /* partial compaction. */ r2 = MAX (fnrows, Work->fnrows_new + 1) ; c2 = MAX (fncols, Work->fncols_new + 1) ; } DEBUGm3 (("get_memory from umf_store_lu:\n")) ; if (!UMF_get_memory (Numeric, Work, size, r2, c2, TRUE)) { DEBUGm4 (("out of memory: store LU (1)\n")) ; return (FALSE) ; /* out of memory */ } p = UMF_mem_alloc_head_block (Numeric, size) ; if (!p) { DEBUGm4 (("out of memory: store LU (2)\n")) ; return (FALSE) ; /* out of memory */ } /* garbage collection may have moved the current front */ fnc_curr = Work->fnc_curr ; fnr_curr = Work->fnr_curr ; Flublock = Work->Flublock ; Flblock = Work->Flblock ; Fublock = Work->Fublock ; Fl1 = Flublock + kk * nb ; Fl2 = Flblock + kk * fnr_curr ; } /* ------------------------------------------------------------------ */ /* store the column of L */ /* ------------------------------------------------------------------ */ lip = p ; Li = (Int *) (Numeric->Memory + p) ; p += UNITS (Int, lnzi) ; Lval = (Entry *) (Numeric->Memory + p) ; p += UNITS (Entry, lnzx) ; for (i = 0 ; i < lnzx ; i++) { CLEAR (Lval [i]) ; } /* store the numerical entries */ if (newLchain) { /* flag the first column in the Lchain by negating Lip [k] */ lip = -lip ; ASSERT (llen == 0) ; #ifdef DROP for (i = kk + 1 ; i < fnpiv ; i++) { Entry x ; double s ; Int row2, pos ; x = Fl1 [i] ; APPROX_ABS (s, x) ; if (s <= droptol) continue ; row2 = Pivrow [i] ; pos = llen++ ; Lpattern [pos] = row2 ; Lpos [row2] = pos ; Li [pos] = row2 ; Lval [pos] = x ; } for (i = 0 ; i < fnrows ; i++) { Entry x ; double s ; Int row2, pos ; x = Fl2 [i] ; APPROX_ABS (s, x) ; if (s <= droptol) continue ; row2 = Frows [i] ; pos = llen++ ; Lpattern [pos] = row2 ; Lpos [row2] = pos ; Li [pos] = row2 ; Lval [pos] = x ; } #else for (i = kk + 1 ; i < fnpiv ; i++) { Entry x ; Int row2, pos ; x = Fl1 [i] ; if (IS_ZERO (x)) continue ; row2 = Pivrow [i] ; pos = llen++ ; Lpattern [pos] = row2 ; Lpos [row2] = pos ; Li [pos] = row2 ; Lval [pos] = x ; } for (i = 0 ; i < fnrows ; i++) { Entry x ; Int row2, pos ; x = Fl2 [i] ; if (IS_ZERO (x)) continue ; row2 = Frows [i] ; pos = llen++ ; Lpattern [pos] = row2 ; Lpos [row2] = pos ; Li [pos] = row2 ; Lval [pos] = x ; } #endif } else { ASSERT (llen > 0) ; #ifdef DROP for (i = kk + 1 ; i < fnpiv ; i++) { Entry x ; double s ; Int row2, pos ; x = Fl1 [i] ; APPROX_ABS (s, x) ; if (s <= droptol) continue ; row2 = Pivrow [i] ; pos = Lpos [row2] ; if (pos == EMPTY) { pos = llen++ ; Lpattern [pos] = row2 ; Lpos [row2] = pos ; *Li++ = row2 ; } Lval [pos] = x ; } for (i = 0 ; i < fnrows ; i++) { Entry x ; double s ; Int row2, pos ; x = Fl2 [i] ; APPROX_ABS (s, x) ; if (s <= droptol) continue ; row2 = Frows [i] ; pos = Lpos [row2] ; if (pos == EMPTY) { pos = llen++ ; Lpattern [pos] = row2 ; Lpos [row2] = pos ; *Li++ = row2 ; } Lval [pos] = x ; } #else for (i = kk + 1 ; i < fnpiv ; i++) { Entry x ; Int row2, pos ; x = Fl1 [i] ; if (IS_ZERO (x)) continue ; row2 = Pivrow [i] ; pos = Lpos [row2] ; if (pos == EMPTY) { pos = llen++ ; Lpattern [pos] = row2 ; Lpos [row2] = pos ; *Li++ = row2 ; } Lval [pos] = x ; } for (i = 0 ; i < fnrows ; i++) { Entry x ; Int row2, pos ; x = Fl2 [i] ; if (IS_ZERO (x)) continue ; row2 = Frows [i] ; pos = Lpos [row2] ; if (pos == EMPTY) { pos = llen++ ; Lpattern [pos] = row2 ; Lpos [row2] = pos ; *Li++ = row2 ; } Lval [pos] = x ; } #endif } DEBUG4 (("llen "ID" lnzx "ID"\n", llen, lnzx)) ; ASSERT (llen == lnzx) ; ASSERT (lnz <= llen) ; DEBUG4 (("lnz "ID" \n", lnz)) ; #ifdef DROP DEBUG4 (("all_lnz "ID" \n", all_lnz)) ; ASSERT (lnz <= all_lnz) ; Numeric->lnz += lnz ; Numeric->all_lnz += all_lnz ; Lnz [kk] = all_lnz ; #else Numeric->lnz += lnz ; Numeric->all_lnz += lnz ; Lnz [kk] = lnz ; #endif Numeric->nLentries += lnzx ; Work->llen = llen ; Numeric->isize += lnzi ; /* ------------------------------------------------------------------ */ /* the pivot column is fully assembled and scaled, and is now the */ /* k-th column of L */ /* ------------------------------------------------------------------ */ Lpos [pivrow] = pivrow_position ; /* not aliased */ Lip [pivcol] = lip ; /* aliased with Col_tuples */ Lilen [pivcol] = lnzi ; /* aliased with Col_tlen */ } /* ---------------------------------------------------------------------- */ /* store the rows of U */ /* ---------------------------------------------------------------------- */ for (kk = 0 ; kk < fnpiv ; kk++) { /* ------------------------------------------------------------------ */ /* one more pivot row and column is being stored into L and U */ /* ------------------------------------------------------------------ */ k = Work->npiv + kk ; /* ------------------------------------------------------------------ */ /* find the kth pivot row and pivot column */ /* ------------------------------------------------------------------ */ pivrow = Pivrow [kk] ; pivcol = Pivcol [kk] ; #ifndef NDEBUG ASSERT (pivrow >= 0 && pivrow < Work->n_row) ; ASSERT (pivcol >= 0 && pivcol < Work->n_col) ; DEBUG2 (("Store row of U, k = "ID", ulen "ID"\n", k, ulen)) ; for (i = 0 ; i < ulen ; i++) { col = Upattern [i] ; DEBUG2 ((" Upattern["ID"] "ID, i, col)) ; if (col == pivcol) DEBUG2 ((" <- pivot col")) ; DEBUG2 (("\n")) ; ASSERT (col >= 0 && col < Work->n_col) ; ASSERT (i == Upos [col]) ; } #endif /* ------------------------------------------------------------------ */ /* get the pivot value, for the diagonal matrix D */ /* ------------------------------------------------------------------ */ zero_pivot = IS_ZERO (D [k]) ; /* ------------------------------------------------------------------ */ /* count the nonzeros in the row of U */ /* ------------------------------------------------------------------ */ /* kk-th row of U in the LU block */ Fu1 = Flublock + kk ; /* kk-th row of U in the U block */ Fu2 = Fublock + kk * fnc_curr ; unz = 0 ; unz2i = 0 ; unz2x = ulen ; DEBUG2 (("unz2x is "ID", lnzx "ID"\n", unz2x, lnzx)) ; /* if row k does not end a Uchain, pivcol not included in ulen */ ASSERT (!NON_PIVOTAL_COL (pivcol)) ; pivcol_position = Upos [pivcol] ; if (pivcol_position != EMPTY) { unz2x-- ; DEBUG2 (("(exclude pivcol) unz2x is now "ID"\n", unz2x)) ; } ASSERT (unz2x >= 0) ; #ifdef DROP all_unz = 0 ; for (i = kk + 1 ; i < fnpiv ; i++) { Entry x ; double s ; x = Fu1 [i*nb] ; if (IS_ZERO (x)) continue ; all_unz++ ; APPROX_ABS (s, x) ; if (s <= droptol) continue ; unz++ ; if (Upos [Pivcol [i]] == EMPTY) unz2i++ ; } for (i = 0 ; i < fncols ; i++) { Entry x ; double s ; x = Fu2 [i] ; if (IS_ZERO (x)) continue ; all_unz++ ; APPROX_ABS (s, x) ; if (s <= droptol) continue ; unz++ ; if (Upos [Fcols [i]] == EMPTY) unz2i++ ; } #else for (i = kk + 1 ; i < fnpiv ; i++) { if (IS_ZERO (Fu1 [i*nb])) continue ; unz++ ; if (Upos [Pivcol [i]] == EMPTY) unz2i++ ; } for (i = 0 ; i < fncols ; i++) { if (IS_ZERO (Fu2 [i])) continue ; unz++ ; if (Upos [Fcols [i]] == EMPTY) unz2i++ ; } #endif unz2x += unz2i ; ASSERT (IMPLIES (k == 0, ulen == 0)) ; /* determine if we start a new Uchain or continue the old one */ if (ulen == 0 || zero_pivot) { /* ulen == 0 means there is no prior Uchain */ /* D [k] == 0 means the matrix is singular (pivot row might */ /* not be empty, however, but start a new Uchain to prune zero */ /* entries for the deg > 0 test in UMF_u*solve) */ newUchain = TRUE ; } else { newUchain = /* approximate storage for starting a new Uchain */ UNITS (Entry, unz) + UNITS (Int, unz) <= /* approximate storage for continuing a prior Uchain */ UNITS (Entry, unz2x) + UNITS (Int, unz2i) ; /* this would be exact, except for the Int to Unit rounding, */ /* because the Upattern is stored only at the end of the Uchain */ } /* ------------------------------------------------------------------ */ /* allocate space for the row of U */ /* ------------------------------------------------------------------ */ size = 0 ; if (newUchain) { /* store the pattern of the last row in the prior Uchain */ size += UNITS (Int, ulen) ; unzx = unz ; } else { unzx = unz2x ; } size += UNITS (Entry, unzx) ; #ifndef NDEBUG UMF_allocfail = FALSE ; if (UMF_gprob > 0) { double rrr = ((double) (rand ( ))) / (((double) RAND_MAX) + 1) ; DEBUG4 (("Check random %e %e\n", rrr, UMF_gprob)) ; UMF_allocfail = rrr < UMF_gprob ; if (UMF_allocfail) DEBUGm2 (("Random garbage coll. (store LU)\n")); } #endif p = UMF_mem_alloc_head_block (Numeric, size) ; if (!p) { Int r2, c2 ; /* Do garbage collection, realloc, and try again. */ /* Note that there are pivot rows/columns in current front. */ if (Work->do_grow) { /* full compaction of current frontal matrix, since * UMF_grow_front will be called next anyway. */ r2 = fnrows ; c2 = fncols ; } else { /* partial compaction. */ r2 = MAX (fnrows, Work->fnrows_new + 1) ; c2 = MAX (fncols, Work->fncols_new + 1) ; } DEBUGm3 (("get_memory from umf_store_lu:\n")) ; if (!UMF_get_memory (Numeric, Work, size, r2, c2, TRUE)) { /* :: get memory, column of L :: */ DEBUGm4 (("out of memory: store LU (1)\n")) ; return (FALSE) ; /* out of memory */ } p = UMF_mem_alloc_head_block (Numeric, size) ; if (!p) { /* :: out of memory, column of U :: */ DEBUGm4 (("out of memory: store LU (2)\n")) ; return (FALSE) ; /* out of memory */ } /* garbage collection may have moved the current front */ fnc_curr = Work->fnc_curr ; fnr_curr = Work->fnr_curr ; Flublock = Work->Flublock ; Flblock = Work->Flblock ; Fublock = Work->Fublock ; Fu1 = Flublock + kk ; Fu2 = Fublock + kk * fnc_curr ; } /* ------------------------------------------------------------------ */ /* store the row of U */ /* ------------------------------------------------------------------ */ uip = p ; if (newUchain) { /* starting a new Uchain - flag this by negating Uip [k] */ uip = -uip ; DEBUG2 (("Start new Uchain, k = "ID"\n", k)) ; pivcol_position = EMPTY ; /* end the prior Uchain */ /* save the current Upattern, and then */ /* clear it and start a new Upattern */ DEBUG2 (("Ending prior chain, k-1 = "ID"\n", k-1)) ; uilen = ulen ; Ui = (Int *) (Numeric->Memory + p) ; Numeric->isize += ulen ; p += UNITS (Int, ulen) ; for (i = 0 ; i < ulen ; i++) { col = Upattern [i] ; ASSERT (col >= 0 && col < Work->n_col) ; Upos [col] = EMPTY ; Ui [i] = col ; } ulen = 0 ; } else { /* continue the prior Uchain */ DEBUG2 (("Continue Uchain, k = "ID"\n", k)) ; ASSERT (k > 0) ; /* remove pivot col index from current row of U */ /* if a new Uchain starts, then all entries are removed later */ DEBUG2 (("Removing pivcol from Upattern, k = "ID"\n", k)) ; if (pivcol_position != EMPTY) { /* place the last entry in the row in the */ /* position of the pivot col index */ ASSERT (pivcol == Upattern [pivcol_position]) ; col = Upattern [--ulen] ; ASSERT (col >= 0 && col < Work->n_col) ; Upattern [pivcol_position] = col ; Upos [col] = pivcol_position ; Upos [pivcol] = EMPTY ; } /* this row continues the Uchain. Keep track of how much */ /* to trim from the k-th length to get the length of the */ /* (k-1)st row of U */ uilen = unz2i ; } Uval = (Entry *) (Numeric->Memory + p) ; /* p += UNITS (Entry, unzx), no need to increment p */ for (i = 0 ; i < unzx ; i++) { CLEAR (Uval [i]) ; } if (newUchain) { ASSERT (ulen == 0) ; #ifdef DROP for (i = kk + 1 ; i < fnpiv ; i++) { Entry x ; double s ; Int col2, pos ; x = Fu1 [i*nb] ; APPROX_ABS (s, x) ; if (s <= droptol) continue ; col2 = Pivcol [i] ; pos = ulen++ ; Upattern [pos] = col2 ; Upos [col2] = pos ; Uval [pos] = x ; } for (i = 0 ; i < fncols ; i++) { Entry x ; double s ; Int col2, pos ; x = Fu2 [i] ; APPROX_ABS (s, x) ; if (s <= droptol) continue ; col2 = Fcols [i] ; pos = ulen++ ; Upattern [pos] = col2 ; Upos [col2] = pos ; Uval [pos] = x ; } #else for (i = kk + 1 ; i < fnpiv ; i++) { Entry x ; Int col2, pos ; x = Fu1 [i*nb] ; if (IS_ZERO (x)) continue ; col2 = Pivcol [i] ; pos = ulen++ ; Upattern [pos] = col2 ; Upos [col2] = pos ; Uval [pos] = x ; } for (i = 0 ; i < fncols ; i++) { Entry x ; Int col2, pos ; x = Fu2 [i] ; if (IS_ZERO (x)) continue ; col2 = Fcols [i] ; pos = ulen++ ; Upattern [pos] = col2 ; Upos [col2] = pos ; Uval [pos] = x ; } #endif } else { ASSERT (ulen > 0) ; /* store the numerical entries and find new nonzeros */ #ifdef DROP for (i = kk + 1 ; i < fnpiv ; i++) { Entry x ; double s ; Int col2, pos ; x = Fu1 [i*nb] ; APPROX_ABS (s, x) ; if (s <= droptol) continue ; col2 = Pivcol [i] ; pos = Upos [col2] ; if (pos == EMPTY) { pos = ulen++ ; Upattern [pos] = col2 ; Upos [col2] = pos ; } Uval [pos] = x ; } for (i = 0 ; i < fncols ; i++) { Entry x ; double s ; Int col2, pos ; x = Fu2 [i] ; APPROX_ABS (s, x) ; if (s <= droptol) continue ; col2 = Fcols [i] ; pos = Upos [col2] ; if (pos == EMPTY) { pos = ulen++ ; Upattern [pos] = col2 ; Upos [col2] = pos ; } Uval [pos] = x ; } #else for (i = kk + 1 ; i < fnpiv ; i++) { Entry x ; Int col2, pos ; x = Fu1 [i*nb] ; if (IS_ZERO (x)) continue ; col2 = Pivcol [i] ; pos = Upos [col2] ; if (pos == EMPTY) { pos = ulen++ ; Upattern [pos] = col2 ; Upos [col2] = pos ; } Uval [pos] = x ; } for (i = 0 ; i < fncols ; i++) { Entry x ; Int col2, pos ; x = Fu2 [i] ; if (IS_ZERO (x)) continue ; col2 = Fcols [i] ; pos = Upos [col2] ; if (pos == EMPTY) { pos = ulen++ ; Upattern [pos] = col2 ; Upos [col2] = pos ; } Uval [pos] = x ; } #endif } ASSERT (ulen == unzx) ; ASSERT (unz <= ulen) ; DEBUG4 (("unz "ID" \n", unz)) ; #ifdef DROP DEBUG4 (("all_unz "ID" \n", all_unz)) ; ASSERT (unz <= all_unz) ; Numeric->unz += unz ; Numeric->all_unz += all_unz ; /* count the "true" flops, based on LU pattern only */ Numeric->flops += DIV_FLOPS * Lnz [kk] /* scale pivot column */ + MULTSUB_FLOPS * (Lnz [kk] * all_unz) ; /* outer product */ #else Numeric->unz += unz ; Numeric->all_unz += unz ; /* count the "true" flops, based on LU pattern only */ Numeric->flops += DIV_FLOPS * Lnz [kk] /* scale pivot column */ + MULTSUB_FLOPS * (Lnz [kk] * unz) ; /* outer product */ #endif Numeric->nUentries += unzx ; Work->ulen = ulen ; DEBUG1 (("Work->ulen = "ID" at end of pivot step, k: "ID"\n", ulen, k)); /* ------------------------------------------------------------------ */ /* the pivot row is the k-th row of U */ /* ------------------------------------------------------------------ */ Upos [pivcol] = pivcol_position ; /* not aliased */ Uip [pivrow] = uip ; /* aliased with Row_tuples */ Uilen [pivrow] = uilen ; /* aliased with Row_tlen */ } /* ---------------------------------------------------------------------- */ /* no more pivots in frontal working array */ /* ---------------------------------------------------------------------- */ Work->npiv += fnpiv ; Work->fnpiv = 0 ; Work->fnzeros = 0 ; return (TRUE) ; } SuiteSparse/UMFPACK/Source/umf_store_lu.h0000644001170100242450000000106210617162433017153 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_store_lu ( NumericType *Numeric, WorkType *Work ) ; GLOBAL Int UMF_store_lu_drop ( NumericType *Numeric, WorkType *Work ) ; SuiteSparse/UMFPACK/Source/umf_kernel_init.c0000644001170100242450000007161010677541650017633 0ustar davisfac/* ========================================================================== */ /* === UMF_kernel_init ====================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Initialize the kernel: scale the matrix, load the initial elements, and build the tuple lists. Returns TRUE if successful, FALSE if out of memory or if the pattern has changed since UMFPACK_*symbolic. UMFPACK_numeric allocates at least enough space for UMF_kernel_init to succeed; otherwise it does not call UMF_kernel_init. So an out-of-memory condition means that the pattern must have gotten larger. */ #include "umf_internal.h" #include "umf_kernel_init.h" #include "umf_tuple_lengths.h" #include "umf_build_tuples.h" #include "umf_mem_init_memoryspace.h" #include "umf_mem_alloc_element.h" #include "umf_mem_alloc_head_block.h" #include "umf_mem_alloc_tail_block.h" #include "umf_mem_free_tail_block.h" #include "umf_scale.h" /* ========================================================================== */ /* === packsp =============================================================== */ /* ========================================================================== */ /* remove zero or small entries from a column of L or a row of U */ PRIVATE Int packsp /* returns new value of pnew */ ( Int pnew, /* index into Memory of next free space */ Int *p_p, /* ptr to index of old pattern in Memory on input, new pattern on output */ Int *p_len, /* ptr to length of old pattern on input, new pattern on output */ Int drop, /* TRUE if small nonzero entries are to be dropped */ double droptol, /* the drop tolerance */ Unit *Memory /* contains the sparse vector on input and output */ ) { Entry x ; double s ; Entry *Bx, *Bx2 ; Int p, i, len, len_new, *Bi, *Bi2 ; /* get the pointers to the sparse vector, and its length */ p = *p_p ; len = *p_len ; Bi = (Int *) (Memory + p) ; p += UNITS (Int, len) ; Bx = (Entry *) (Memory + p) ; p += UNITS (Entry, len) ; DEBUGm4 ((" p "ID" len "ID" pnew "ID"\n", p, len, pnew)) ; /* the vector resides in Bi [0..len-1] and Bx [0..len-1] */ /* first, compact the vector in place */ len_new = 0 ; for (p = 0 ; p < len ; p++) { i = Bi [p] ; x = Bx [p] ; DEBUGm4 ((" old vector: i "ID" value: ", i)) ; EDEBUGk (-4, x) ; DEBUGm4 (("\n")) ; ASSERT (i >= 0) ; /* skip if zero or below drop tolerance */ if (IS_ZERO (x)) continue ; if (drop) { APPROX_ABS (s, x) ; if (s <= droptol) continue ; } /* store the value back into the vector */ if (len_new != p) { Bi [len_new] = i ; Bx [len_new] = x ; } len_new++ ; } ASSERT (len_new <= len) ; /* the vector is now in Bi [0..len_new-1] and Bx [0..len_new-1] */ #ifndef NDEBUG for (p = 0 ; p < len_new ; p++) { DEBUGm4 ((" new vector: i "ID" value: ", Bi [p])) ; EDEBUGk (-4, Bx [p]) ; DEBUGm4 (("\n")) ; ASSERT (Bi [p] >= 0) ; } #endif /* allocate new space for the compacted vector */ *p_p = pnew ; *p_len = len_new ; Bi2 = (Int *) (Memory + pnew) ; pnew += UNITS (Int, len_new) ; Bx2 = (Entry *) (Memory + pnew) ; pnew += UNITS (Entry, len_new) ; DEBUGm4 ((" pnew "ID" len_new "ID"\n", pnew, len_new)) ; /* shift the vector upwards, into its new space */ for (p = 0 ; p < len_new ; p++) { Bi2 [p] = Bi [p] ; } for (p = 0 ; p < len_new ; p++) { Bx2 [p] = Bx [p] ; } #ifndef NDEBUG for (p = 0 ; p < len_new ; p++) { DEBUGm4 ((" packed vec: i "ID" value: ", Bi2 [p])) ; EDEBUGk (-4, Bx2 [p]) ; DEBUGm4 (("\n")) ; ASSERT (Bi2 [p] >= 0) ; } #endif /* return the pointer to the space just after the new vector */ return (pnew) ; } /* ========================================================================== */ /* === UMF_kernel_init ====================================================== */ /* ========================================================================== */ GLOBAL Int UMF_kernel_init ( const Int Ap [ ], /* user's input matrix (not modified) */ const Int Ai [ ], const double Ax [ ], #ifdef COMPLEX const double Az [ ], #endif NumericType *Numeric, WorkType *Work, SymbolicType *Symbolic ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Entry x, pivot_value ; double unused = 0, rsmin, rsmax, rs, droptol ; Entry *D, *C, *Lval, **Rpx ; double *Rs ; Int row, k, oldcol, size, e, p1, p2, p, nz, *Rows, *Cols, *E, i, *Upos, *Lpos, n_row, n_col, *Wp, *Cperm_init, *Frpos, *Fcpos, *Row_degree, nn, *Row_tlen, *Col_degree, *Col_tlen, oldrow, newrow, ilast, *Wrp, *Rperm_init, col, n_inner, prefer_diagonal, *Diagonal_map, nempty, *Diagonal_imap, fixQ, rdeg, cdeg, nempty_col, *Esize, esize, pnew, *Lip, *Uip, *Lilen, *Uilen, llen, pa, *Cdeg, *Rdeg, n1, clen, do_scale, lnz, unz, lip, uip, k1, *Rperm, *Cperm, pivcol, *Li, lilen, drop, **Rpi, nempty_row, dense_row_threshold, empty_elements, rpi, rpx ; Element *ep ; Unit *Memory ; #ifdef COMPLEX Int split = SPLIT (Az) ; #endif #ifndef NRECIPROCAL Int do_recip = FALSE ; #endif /* ---------------------------------------------------------------------- */ /* get parameters */ /* ---------------------------------------------------------------------- */ DEBUG0 (("KERNEL INIT\n")) ; n_row = Symbolic->n_row ; n_col = Symbolic->n_col ; nn = MAX (n_row, n_col) ; n_inner = MIN (n_row, n_col) ; nempty_col = Symbolic->nempty_col ; nempty_row = Symbolic->nempty_row ; nempty = MIN (nempty_row, nempty_col) ; ASSERT (n_row > 0 && n_col > 0) ; Cperm_init = Symbolic->Cperm_init ; Rperm_init = Symbolic->Rperm_init ; Cdeg = Symbolic->Cdeg ; Rdeg = Symbolic->Rdeg ; n1 = Symbolic->n1 ; dense_row_threshold = Symbolic->dense_row_threshold ; DEBUG0 (("Singletons: "ID"\n", n1)) ; Work->nforced = 0 ; Work->ndiscard = 0 ; Work->noff_diagonal = 0 ; nz = Ap [n_col] ; if (nz < 0 || Ap [0] != 0 || nz != Symbolic->nz) { DEBUGm4 (("nz or Ap [0] bad\n")) ; return (FALSE) ; /* pattern changed */ } prefer_diagonal = Symbolic->prefer_diagonal ; Diagonal_map = Work->Diagonal_map ; Diagonal_imap = Work->Diagonal_imap ; /* ---------------------------------------------------------------------- */ /* initialize the Numeric->Memory space for LU, elements, and tuples */ /* ---------------------------------------------------------------------- */ UMF_mem_init_memoryspace (Numeric) ; DEBUG1 (("Kernel init head usage, before allocs: "ID"\n", Numeric->ihead)) ; /* ---------------------------------------------------------------------- */ /* initialize the Work and Numeric objects */ /* ---------------------------------------------------------------------- */ /* current front is empty */ Work->fnpiv = 0 ; Work->fncols = 0 ; Work->fnrows = 0 ; Work->fncols_max = 0 ; Work->fnrows_max = 0 ; Work->fnzeros = 0 ; Work->fcurr_size = 0 ; Work->fnr_curr = 0 ; Work->fnc_curr = 0 ; Work->nz = nz ; Work->prior_element = EMPTY ; Work->ulen = 0 ; Work->llen = 0 ; Work->npiv = n1 ; Work->frontid = 0 ; Work->nextcand = n1 ; Memory = Numeric->Memory ; Rperm = Numeric->Rperm ; Cperm = Numeric->Cperm ; Row_degree = Numeric->Rperm ; Col_degree = Numeric->Cperm ; /* Row_tuples = Numeric->Uip ; not needed */ Row_tlen = Numeric->Uilen ; /* Col_tuples = Numeric->Lip ; not needed */ Col_tlen = Numeric->Lilen ; Lip = Numeric->Lip ; Uip = Numeric->Uip ; Lilen = Numeric->Lilen ; Uilen = Numeric->Uilen ; Frpos = Work->Frpos ; Fcpos = Work->Fcpos ; Wp = Work->Wp ; Wrp = Work->Wrp ; D = Numeric->D ; Upos = Numeric->Upos ; Lpos = Numeric->Lpos ; for (k = 0 ; k < n_inner ; k++) { CLEAR (D [k]) ; } Rs = Numeric->Rs ; for (row = 0 ; row <= n_row ; row++) { Lpos [row] = EMPTY ; /* Row_tuples [row] = 0 ; set in UMF_build_tuples */ /* Row_degree [row] = 0 ; initialized below */ Row_tlen [row] = 0 ; /* Frpos [row] = EMPTY ; do this later */ } for (col = 0 ; col <= n_col ; col++) { Upos [col] = EMPTY ; /* Col_tuples [col] = 0 ; set in UMF_build_tuples */ /* Col_degree [col] = 0 ; initialized below */ Col_tlen [col] = 0 ; Fcpos [col] = EMPTY ; Wrp [col] = 0 ; } Work->Wrpflag = 1 ; /* When cleared, Wp [0..nn] is < 0 */ for (i = 0 ; i <= nn ; i++) { Wp [i] = EMPTY ; } /* In col search, Wp [row] is set to a position, which is >= 0. */ /* When cleared, Wrp [0..n_col] is < Wrpflag */ /* In row search, Wrp [col] is set to Wrpflag. */ /* no need to initialize Wm, Wio, Woi, and Woo */ /* clear the external degree counters */ Work->cdeg0 = 1 ; Work->rdeg0 = 1 ; fixQ = Symbolic->fixQ ; E = Work->E ; Numeric->n_row = n_row ; Numeric->n_col = n_col ; Numeric->npiv = 0 ; Numeric->nnzpiv = 0 ; Numeric->min_udiag = 0.0 ; Numeric->max_udiag = 0.0 ; Numeric->rcond = 0.0 ; Numeric->isize = 0 ; Numeric->nLentries = 0 ; Numeric->nUentries = 0 ; Numeric->lnz = 0 ; Numeric->unz = 0 ; Numeric->all_lnz = 0 ; Numeric->all_unz = 0 ; Numeric->maxfrsize = 0 ; Numeric->maxnrows = 0 ; Numeric->maxncols = 0 ; Numeric->flops = 0. ; Numeric->n1 = n1 ; droptol = Numeric->droptol ; drop = (droptol > 0) ; /* ---------------------------------------------------------------------- */ /* compute the scale factors, if requested, and check the input matrix */ /* ---------------------------------------------------------------------- */ /* UMFPACK_SCALE_SUM: Rs [i] = sum of the absolute values in row i. * UMFPACK_SCALE_MAX: Rs [i] = max of the absolute values in row i. * * If A is complex, an approximate abs is used (|xreal| + |ximag|). * * If min (Rs [0..n_row]) >= RECIPROCAL_TOLERANCE, then the scale * factors are inverted, and the rows of A are multiplied by the scale * factors. Otherwise, the rows are divided by the scale factors. If * NRECIPROCAL is defined, then the rows are always divided by the scale * factors. * * For MATLAB (either built-in routine or mexFunction), or for gcc, * the rows are always divided by the scale factors. */ do_scale = (Numeric->scale != UMFPACK_SCALE_NONE) ; if (do_scale) { int do_max = Numeric->scale == UMFPACK_SCALE_MAX ; for (row = 0 ; row < n_row ; row++) { Rs [row] = 0.0 ; } for (col = 0 ; col < n_col ; col++) { ilast = EMPTY ; p1 = Ap [col] ; p2 = Ap [col+1] ; if (p1 > p2) { /* invalid matrix */ DEBUGm4 (("invalid matrix (Ap)\n")) ; return (FALSE) ; } for (p = p1 ; p < p2 ; p++) { Entry aij ; double value ; row = Ai [p] ; if (row <= ilast || row >= n_row) { /* invalid matrix, columns must be sorted, no duplicates */ DEBUGm4 (("invalid matrix (Ai)\n")) ; return (FALSE) ; } ASSIGN (aij, Ax, Az, p, split) ; APPROX_ABS (value, aij) ; rs = Rs [row] ; if (!SCALAR_IS_NAN (rs)) { if (SCALAR_IS_NAN (value)) { /* if any entry in the row is NaN, then the scale factor * is NaN too (for now) and then set to 1.0 below */ Rs [row] = value ; } else if (do_max) { Rs [row] = MAX (rs, value) ; } else { Rs [row] += value ; } } DEBUG4 (("i "ID" j "ID" value %g, Rs[i]: %g\n", row, col, value, Rs[row])) ; ilast = row ; } } DEBUG2 (("Rs[0] = %30.20e\n", Rs [0])) ; for (row = 0 ; row < n_row ; row++) { rs = Rs [row] ; if (SCALAR_IS_ZERO (rs) || SCALAR_IS_NAN (rs)) { /* don't scale a completely zero row, or one with NaN's */ Rs [row] = 1.0 ; } } rsmin = Rs [0] ; rsmax = Rs [0] ; for (row = 0 ; row < n_row ; row++) { DEBUG2 (("sum %30.20e ", Rs [row])) ; rsmin = MIN (rsmin, Rs [row]) ; rsmax = MAX (rsmax, Rs [row]) ; DEBUG2 (("Rs["ID"] = %30.20e\n", row, Rs [row])) ; } #ifndef NRECIPROCAL /* multiply by the reciprocal if Rs is not too small */ do_recip = (rsmin >= RECIPROCAL_TOLERANCE) ; if (do_recip) { /* invert the scale factors */ for (row = 0 ; row < n_row ; row++) { Rs [row] = 1.0 / Rs [row] ; } } #endif } else { /* no scaling, rsmin and rsmax not computed */ rsmin = -1 ; rsmax = -1 ; #ifndef NRECIPROCAL do_recip = FALSE ; #endif /* check the input matrix */ if (AMD_valid (n_row, n_col, Ap, Ai) != AMD_OK) { /* matrix is invalid */ return (FALSE) ; } } Numeric->rsmin = rsmin ; Numeric->rsmax = rsmax ; #ifndef NRECIPROCAL Numeric->do_recip = do_recip ; #else Numeric->do_recip = FALSE ; #endif /* ---------------------------------------------------------------------- */ /* construct the inverse row Rperm_init permutation (use Frpos as temp) */ /* ---------------------------------------------------------------------- */ DEBUG3 (("\n\n===================LOAD_MATRIX:\n")) ; for (newrow = 0 ; newrow < n_row ; newrow++) { oldrow = Rperm_init [newrow] ; ASSERT (oldrow >= 0 && oldrow < n_row) ; Frpos [oldrow] = newrow ; } /* ---------------------------------------------------------------------- */ /* construct the diagonal imap if doing symmetric pivoting */ /* ---------------------------------------------------------------------- */ if (prefer_diagonal) { ASSERT (n_row == n_col) ; ASSERT (nempty_col == Symbolic->nempty_row) ; ASSERT (nempty_col == nempty) ; for (i = 0 ; i < nn ; i++) { Diagonal_map [i] = EMPTY ; Diagonal_imap [i] = EMPTY ; } for (k = n1 ; k < nn - nempty ; k++) { newrow = Symbolic->Diagonal_map [k] ; Diagonal_map [k] = newrow ; Diagonal_imap [newrow] = k ; } } /* ---------------------------------------------------------------------- */ /* allocate O (n_row) workspace at the tail end of Memory */ /* ---------------------------------------------------------------------- */ rpi = UMF_mem_alloc_tail_block (Numeric, UNITS (Int *, n_row+1)) ; rpx = UMF_mem_alloc_tail_block (Numeric, UNITS (Entry *, n_row+1)) ; if (!rpi || !rpx) { /* :: pattern change (out of memory for Rpx, Rpx) :: */ /* out of memory, which can only mean that the pattern has changed */ return (FALSE) ; /* pattern changed */ } Rpi = (Int **) (Memory + rpx) ; Rpx = (Entry **) (Memory + rpi) ; /* ---------------------------------------------------------------------- */ /* allocate the LU factors for the columns of the singletons */ /* ---------------------------------------------------------------------- */ DEBUG1 (("Allocating singletons:\n")) ; for (k = 0 ; k < n1 ; k++) { lnz = Cdeg [k] - 1 ; unz = Rdeg [k] - 1 ; DEBUG1 (("Singleton k "ID" pivrow "ID" pivcol "ID" cdeg "ID" rdeg " ID"\n", k, Rperm_init [k], Cperm_init [k], Cdeg [k], Rdeg [k])) ; ASSERT (unz >= 0 && lnz >= 0 && (lnz == 0 || unz == 0)) ; DEBUG1 ((" lnz "ID" unz "ID"\n", lnz, unz)) ; size = UNITS (Int, lnz) + UNITS (Entry, lnz) + UNITS (Int, unz) + UNITS (Entry, unz) ; p = UMF_mem_alloc_head_block (Numeric, size) ; DEBUG1 (("Kernel init head usage: "ID"\n", Numeric->ihead)) ; if (!p) { /* :: pattern change (out of memory for singletons) :: */ DEBUG0 (("Pattern has gotten larger - kernel init failed\n")) ; return (FALSE) ; /* pattern changed */ } Numeric->all_lnz += lnz ; Numeric->all_unz += unz ; /* allocate the column of L */ lip = p ; p += UNITS (Int, lnz) ; p += UNITS (Entry, lnz) ; /* allocate the row of U */ uip = p ; Rpi [k] = (Int *) (Memory + p) ; p += UNITS (Int, unz) ; Rpx [k] = (Entry *) (Memory + p) ; /* p += UNITS (Entry, unz) ; (not needed) */ /* a single column of L (no Lchains) */ Lip [k] = lip ; Lilen [k] = lnz ; /* a single row of L (no Uchains) */ Uip [k] = uip ; Uilen [k] = unz ; Wp [k] = unz ; /* save row and column inverse permutation */ k1 = ONES_COMPLEMENT (k) ; Rperm [k] = k1 ; /* aliased with Row_degree */ Cperm [k] = k1 ; /* aliased with Col_degree */ } /* ---------------------------------------------------------------------- */ /* current frontal matrix is empty */ /* ---------------------------------------------------------------------- */ e = 0 ; E [e] = 0 ; Work->Flublock = (Entry *) NULL ; Work->Flblock = (Entry *) NULL ; Work->Fublock = (Entry *) NULL ; Work->Fcblock = (Entry *) NULL ; /* ---------------------------------------------------------------------- */ /* allocate the column elements */ /* ---------------------------------------------------------------------- */ Esize = Symbolic->Esize ; empty_elements = FALSE ; for (k = n1 ; k < n_col - nempty_col ; k++) { e = k - n1 + 1 ; ASSERT (e < Work->elen) ; esize = Esize ? Esize [k-n1] : Cdeg [k] ; if (esize > 0) { /* allocate an element for this column */ E [e] = UMF_mem_alloc_element (Numeric, esize, 1, &Rows, &Cols, &C, &size, &ep) ; if (E [e] <= 0) { /* :: pattern change (out of memory for column elements) :: */ return (FALSE) ; /* pattern has changed */ } Cols [0] = k ; DEBUG0 (("Got column element e "ID" esize "ID"\n", e, esize)) ; } else { /* all rows in this column are dense, or empty */ E [e] = 0 ; empty_elements = TRUE ; DEBUG0 (("column element e is empty "ID"\n", e)) ; } } DEBUG0 (("e "ID" n_col "ID" nempty_col "ID" n1 "ID"\n", e, n_col, nempty_col, n1)) ; ASSERT (e == n_col - nempty_col - n1) ; /* ---------------------------------------------------------------------- */ /* allocate the row elements for dense rows of A (if any) */ /* ---------------------------------------------------------------------- */ if (Esize) { for (k = n1 ; k < n_row - nempty_row ; k++) { rdeg = Rdeg [k] ; if (rdeg > dense_row_threshold) { /* allocate an element for this dense row */ e++ ; ASSERT (e < Work->elen) ; E [e] = UMF_mem_alloc_element (Numeric, 1, rdeg, &Rows, &Cols, &C, &size, &ep) ; if (E [e] <= 0) { /* :: pattern change (out of memory for row elements) :: */ return (FALSE) ; /* pattern has changed */ } Rows [0] = k ; Rpi [k] = Cols ; Rpx [k] = C ; Wp [k] = rdeg ; DEBUG0 (("Got row element e "ID" rdeg "ID"\n", e, rdeg)) ; } } } /* elements are currently in the range 0 to e */ Work->nel = e ; /* ---------------------------------------------------------------------- */ /* create the first n1 columns of L and U */ /* ---------------------------------------------------------------------- */ for (k = 0 ; k < n1 ; k++) { pivcol = Cperm_init [k] ; p2 = Ap [pivcol+1] ; /* get the kth column of L */ p = Lip [k] ; Li = (Int *) (Memory + p) ; lilen = Lilen [k] ; p += UNITS (Int, lilen) ; Lval = (Entry *) (Memory + p) ; llen = 0 ; for (pa = Ap [pivcol] ; pa < p2 ; pa++) { oldrow = Ai [pa] ; newrow = Frpos [oldrow] ; ASSIGN (x, Ax, Az, pa, split) ; /* scale the value using the scale factors, Rs */ if (do_scale) { #ifndef NRECIPROCAL if (do_recip) { SCALE (x, Rs [oldrow]) ; } else #endif { SCALE_DIV (x, Rs [oldrow]) ; } } if (newrow == k) { /* this is the pivot entry itself */ ASSERT (oldrow == Rperm_init [k]) ; D [k] = x ; } else if (newrow < k) { /* this entry goes in a row of U */ DEBUG1 (("Singleton row of U: k "ID" newrow "ID"\n", k, newrow)) ; if (--(Wp [newrow]) < 0) { /* :: pattern change (singleton row too lengthy) :: */ DEBUGm4 (("bad U singleton row (too lengthy)\n")) ; return (FALSE) ; /* pattern changed */ } *(Rpi [newrow]++) = k ; *(Rpx [newrow]++) = x ; } else { /* this entry goes in a column of L */ DEBUG1 (("Singleton col of L: k "ID" newrow "ID"\n", k, newrow)) ; if (llen >= lilen) { DEBUGm4 (("bad L singleton col (too lengthy)\n")) ; return (FALSE) ; /* pattern changed */ } Li [llen] = newrow ; Lval [llen] = x ; llen++ ; } } if (llen != lilen) { /* :: pattern change (singleton column too lengthy) :: */ DEBUGm4 (("bad L singleton col (too short)\n")) ; return (FALSE) ; /* pattern changed */ } /* scale the column of L */ if (llen > 0) { pivot_value = D [k] ; UMF_scale (llen, pivot_value, Lval) ; } } /* ---------------------------------------------------------------------- */ /* allocate the elements and copy the columns of A */ /* ---------------------------------------------------------------------- */ /* also apply the row and column pre-ordering. */ for (k = n1 ; k < n_col ; k++) { /* The newcol is k, which is what the name of the column is in the * UMFPACK kernel. The user's name for the column is oldcol. */ oldcol = Cperm_init [k] ; ASSERT (oldcol >= 0 && oldcol < n_col) ; p2 = Ap [oldcol+1] ; cdeg = Cdeg [k] ; ASSERT (cdeg >= 0) ; ASSERT (IMPLIES ( (Symbolic->ordering != UMFPACK_ORDERING_GIVEN) && n1 > 0, cdeg > 1 || cdeg == 0)) ; /* if fixQ: set Col_degree to 0 for the NON_PIVOTAL_COL macro */ Col_degree [k] = fixQ ? 0 : cdeg ; /* get the element for this column (if any) */ e = k - n1 + 1 ; if (k < n_col - nempty_col) { esize = Esize ? Esize [k-n1] : cdeg ; if (E [e]) { Int ncols, nrows ; Unit *pp ; pp = Memory + E [e] ; GET_ELEMENT (ep, pp, Cols, Rows, ncols, nrows, C) ; ASSERT (ncols == 1) ; ASSERT (nrows == esize) ; ASSERT (Cols [0] == k) ; } } else { ASSERT (cdeg == 0) ; esize = 0 ; } clen = 0 ; for (pa = Ap [oldcol] ; pa < p2 ; pa++) { oldrow = Ai [pa] ; newrow = Frpos [oldrow] ; ASSIGN (x, Ax, Az, pa, split) ; /* scale the value using the scale factors, Rs */ if (do_scale) { #ifndef NRECIPROCAL if (do_recip) { /* multiply by the reciprocal */ SCALE (x, Rs [oldrow]) ; } else #endif { /* divide instead */ SCALE_DIV (x, Rs [oldrow]) ; } } rdeg = Rdeg [newrow] ; if (newrow < n1 || rdeg > dense_row_threshold) { /* this entry goes in a row of U or into a dense row */ DEBUG1 (("Singleton/dense row of U: k "ID" newrow "ID"\n", k, newrow)) ; if (--(Wp [newrow]) < 0) { DEBUGm4 (("bad row of U or A (too lengthy)\n")) ; return (FALSE) ; /* pattern changed */ } *(Rpi [newrow]++) = k ; *(Rpx [newrow]++) = x ; } else { /* this entry goes in an initial element */ DEBUG1 (("In element k "ID" e "ID" newrow "ID"\n", k, e, newrow)) ; if (clen >= esize) { DEBUGm4 (("bad A column (too lengthy)\n")) ; return (FALSE) ; /* pattern changed */ } ASSERT (E [e]) ; ASSERT (k < n_col - nempty_col) ; Rows [clen] = newrow ; C [clen] = x ; clen++ ; #ifndef NDEBUG if (Diagonal_map && (newrow == Diagonal_map [k])) { DEBUG0 (("Diagonal: old: row "ID" col "ID" : " "new: row "ID" col "ID" : ", oldrow, oldcol, newrow, k)) ; EDEBUGk (0, x) ; } #endif } } if (clen != esize) { /* :: pattern change (singleton column too short) :: */ DEBUGm4 (("bad A column (too short)\n")) ; return (FALSE) ; /* pattern changed */ } } /* ---------------------------------------------------------------------- */ /* free the Rpi and Rpx workspace at the tail end of memory */ /* ---------------------------------------------------------------------- */ UMF_mem_free_tail_block (Numeric, rpi) ; UMF_mem_free_tail_block (Numeric, rpx) ; /* ---------------------------------------------------------------------- */ /* prune zeros and small entries from the singleton rows and columns */ /* ---------------------------------------------------------------------- */ if (n1 > 0) { pnew = Lip [0] ; ASSERT (pnew == 1) ; for (k = 0 ; k < n1 ; k++) { DEBUGm4 (("\nPrune singleton L col "ID"\n", k)) ; pnew = packsp (pnew, &Lip [k], &Lilen [k], drop, droptol, Memory) ; Numeric->lnz += Lilen [k] ; DEBUGm4 (("\nPrune singleton U row "ID"\n", k)) ; pnew = packsp (pnew, &Uip [k], &Uilen [k], drop, droptol, Memory) ; Numeric->unz += Uilen [k] ; } /* free the unused space at the head of memory */ Numeric->ihead = pnew ; } /* ---------------------------------------------------------------------- */ /* initialize row degrees */ /* ---------------------------------------------------------------------- */ for (k = 0 ; k < n1 ; k++) { if (Wp [k] != 0) { /* :: pattern change (singleton row too short) :: */ DEBUGm4 (("bad U singleton row (too short)\n")) ; return (FALSE) ; /* pattern changed */ } } for (k = n1 ; k < n_row ; k++) { DEBUG1 (("Initial row degree k "ID" oldrow "ID" Rdeg "ID"\n", k, Rperm_init [k], Rdeg [k])) ; rdeg = Rdeg [k] ; Row_degree [k] = rdeg ; if (rdeg > dense_row_threshold && Wp [k] != 0) { /* :: pattern change (dense row too short) :: */ DEBUGm4 (("bad dense row (too short)\n")) ; return (FALSE) ; /* pattern changed */ } } #ifndef NDEBUG if (prefer_diagonal) { Entry aij ; Int *InvCperm, newcol ; UMF_dump_diagonal_map (Diagonal_map, Diagonal_imap, n1, nn, nempty) ; InvCperm = (Int *) malloc (n_col * sizeof (Int)) ; ASSERT (InvCperm != (Int *) NULL) ; for (newcol = 0 ; newcol < n_col ; newcol++) { oldcol = Cperm_init [newcol] ; InvCperm [oldcol] = newcol ; } DEBUGm3 (("Diagonal of P2*A:\n")) ; for (oldcol = 0 ; oldcol < n_col ; oldcol++) { newcol = InvCperm [oldcol] ; for (p = Ap [oldcol] ; p < Ap [oldcol+1] ; p++) { oldrow = Ai [p] ; newrow = Frpos [oldrow] ; ASSIGN (aij, Ax, Az, p, split) ; if (newrow == Diagonal_map [newcol]) { DEBUG0 (("old row "ID" col "ID" new row "ID" col "ID, oldrow, oldcol, newrow, newcol)) ; EDEBUGk (0, aij) ; DEBUG0 ((" scaled ")) ; if (do_scale) { #ifndef NRECIPROCAL if (do_recip) { SCALE (aij, Rs [oldrow]) ; } else #endif { SCALE_DIV (aij, Rs [oldrow]) ; } } EDEBUGk (0, aij) ; DEBUG0 (("\n")) ; } } } free (InvCperm) ; } #endif Col_degree [n_col] = 0 ; /* ---------------------------------------------------------------------- */ /* pack the element name space */ /* ---------------------------------------------------------------------- */ if (empty_elements) { Int e2 = 0 ; DEBUG0 (("\n\n============= Packing element space\n")) ; for (e = 1 ; e <= Work->nel ; e++) { if (E [e]) { e2++ ; E [e2] = E [e] ; } } Work->nel = e2 ; } #ifndef NDEBUG DEBUG0 (("Number of initial elements: "ID"\n", Work->nel)) ; for (e = 0 ; e <= Work->nel ; e++) UMF_dump_element (Numeric, Work,e,TRUE) ; #endif for (e = Work->nel + 1 ; e < Work->elen ; e++) { E [e] = 0 ; } /* Frpos no longer needed */ for (row = 0 ; row <= n_row ; row++) { Frpos [row] = EMPTY ; } /* clear Wp */ for (i = 0 ; i <= nn ; i++) { Wp [i] = EMPTY ; } DEBUG1 (("Kernel init head usage: "ID"\n", Numeric->ihead)) ; /* ---------------------------------------------------------------------- */ /* build the tuple lists */ /* ---------------------------------------------------------------------- */ /* if the memory usage changes, then the pattern has changed */ (void) UMF_tuple_lengths (Numeric, Work, &unused) ; if (!UMF_build_tuples (Numeric, Work)) { /* :: pattern change (out of memory in umf_build_tuples) :: */ /* We ran out of memory, which can only mean that */ /* the pattern (Ap and or Ai) has changed (gotten larger). */ DEBUG0 (("Pattern has gotten larger - build tuples failed\n")) ; return (FALSE) ; /* pattern changed */ } Numeric->init_usage = Numeric->max_usage ; /* ---------------------------------------------------------------------- */ /* construct the row merge sets */ /* ---------------------------------------------------------------------- */ for (i = 0 ; i <= Symbolic->nfr ; i++) { Work->Front_new1strow [i] = Symbolic->Front_1strow [i] ; } #ifndef NDEBUG UMF_dump_rowmerge (Numeric, Symbolic, Work) ; DEBUG6 (("Column form of original matrix:\n")) ; UMF_dump_col_matrix (Ax, #ifdef COMPLEX Az, #endif Ai, Ap, n_row, n_col, nz) ; UMF_dump_memory (Numeric) ; UMF_dump_matrix (Numeric, Work, FALSE) ; DEBUG0 (("kernel init done...\n")) ; #endif return (TRUE) ; } SuiteSparse/UMFPACK/Source/umf_kernel_init.h0000644001170100242450000000116410617161663017631 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_kernel_init ( const Int Ap [ ], const Int Ai [ ], const double Ax [ ], #ifdef COMPLEX const double Az [ ], #endif NumericType *Numeric, WorkType *Work, SymbolicType *Symbolic ) ; SuiteSparse/UMFPACK/Source/umf_init_front.c0000644001170100242450000002003610677541615017500 0ustar davisfac/* ========================================================================== */ /* === UMF_init_front ======================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ #include "umf_internal.h" #include "umf_init_front.h" #include "umf_grow_front.h" /* ========================================================================== */ /* === zero_init_front ====================================================== */ /* ========================================================================== */ /* Set the initial frontal matrix to zero. */ PRIVATE void zero_init_front (Int m, Int n, Entry *Fcblock, Int d) { Int i, j ; Entry *F, *Fj = Fcblock ; for (j = 0 ; j < m ; j++) { F = Fj ; Fj += d ; for (i = 0 ; i < n ; i++) { /* CLEAR (Fcblock [i + j*d]) ; */ CLEAR (*F) ; F++ ; } } } /* ========================================================================== */ /* === UMF_init_front ======================================================= */ /* ========================================================================== */ GLOBAL Int UMF_init_front ( NumericType *Numeric, WorkType *Work ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Int i, j, fnr_curr, row, col, *Frows, *Fcols, *Fcpos, *Frpos, fncols, fnrows, *Wrow, fnr2, fnc2, rrdeg, ccdeg, *Wm, fnrows_extended ; Entry *Fcblock, *Fl, *Wy, *Wx ; /* ---------------------------------------------------------------------- */ /* get current frontal matrix and check for frontal growth */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG DEBUG0 (("INIT FRONT\n")) ; DEBUG1 (("CURR before init:\n")) ; UMF_dump_current_front (Numeric, Work, FALSE) ; #endif if (Work->do_grow) { fnr2 = UMF_FRONTAL_GROWTH * Work->fnrows_new + 2 ; fnc2 = UMF_FRONTAL_GROWTH * Work->fncols_new + 2 ; if (!UMF_grow_front (Numeric, fnr2, fnc2, Work, Work->pivrow_in_front ? 2 : 0)) { /* :: out of memory in umf_init_front :: */ DEBUGm4 (("out of memory: init front\n")) ; return (FALSE) ; } } #ifndef NDEBUG DEBUG1 (("CURR after grow:\n")) ; UMF_dump_current_front (Numeric, Work, FALSE) ; DEBUG1 (("fnrows new "ID" fncols new "ID"\n", Work->fnrows_new, Work->fncols_new)) ; #endif ASSERT (Work->fnpiv == 0) ; fnr_curr = Work->fnr_curr ; ASSERT (Work->fnrows_new + 1 <= fnr_curr) ; ASSERT (Work->fncols_new + 1 <= Work->fnc_curr) ; ASSERT (fnr_curr >= 0) ; ASSERT (fnr_curr % 2 == 1) ; /* ---------------------------------------------------------------------- */ /* get parameters */ /* ---------------------------------------------------------------------- */ /* current front is defined by pivot row and column */ Frows = Work->Frows ; Fcols = Work->Fcols ; Frpos = Work->Frpos ; Fcpos = Work->Fcpos ; Work->fnzeros = 0 ; ccdeg = Work->ccdeg ; rrdeg = Work->rrdeg ; fnrows = Work->fnrows ; fncols = Work->fncols ; /* if both pivrow and pivcol are in front, then we extend the old one */ /* in UMF_extend_front, rather than starting a new one here. */ ASSERT (! (Work->pivrow_in_front && Work->pivcol_in_front)) ; /* ---------------------------------------------------------------------- */ /* place pivot column pattern in frontal matrix */ /* ---------------------------------------------------------------------- */ Fl = Work->Flblock ; if (Work->pivcol_in_front) { /* Append the pivot column extension. * Note that all we need to do is increment the size, since the * candidate pivot column pattern is already in place in * Frows [0 ... fnrows-1] (the old pattern), and * Frows [fnrows ... fnrows + Work->ccdeg - 1] (the new * pattern). Frpos is also properly defined. */ /* make a list of the new rows to scan */ Work->fscan_row = fnrows ; /* only scan the new rows */ Work->NewRows = Work->Wrp ; Wy = Work->Wy ; for (i = 0 ; i < fnrows ; i++) { Fl [i] = Wy [i] ; } fnrows_extended = fnrows + ccdeg ; for (i = fnrows ; i < fnrows_extended ; i++) { Fl [i] = Wy [i] ; /* flip the row index, since Wrp must be < 0 */ row = Frows [i] ; Work->NewRows [i] = FLIP (row) ; } fnrows = fnrows_extended ; } else { /* this is a completely new column */ Work->fscan_row = 0 ; /* scan all the rows */ Work->NewRows = Frows ; Wm = Work->Wm ; Wx = Work->Wx ; for (i = 0 ; i < ccdeg ; i++) { Fl [i] = Wx [i] ; row = Wm [i] ; Frows [i] = row ; Frpos [row] = i ; } fnrows = ccdeg ; } Work->fnrows = fnrows ; #ifndef NDEBUG DEBUG3 (("New Pivot col "ID" now in front, length "ID"\n", Work->pivcol, fnrows)) ; for (i = 0 ; i < fnrows ; i++) { DEBUG4 ((" "ID": row "ID"\n", i, Frows [i])) ; ASSERT (Frpos [Frows [i]] == i) ; } #endif /* ---------------------------------------------------------------------- */ /* place pivot row pattern in frontal matrix */ /* ---------------------------------------------------------------------- */ Wrow = Work->Wrow ; if (Work->pivrow_in_front) { /* append the pivot row extension */ Work->fscan_col = fncols ; /* only scan the new columns */ Work->NewCols = Work->Wp ; #ifndef NDEBUG for (j = 0 ; j < fncols ; j++) { col = Fcols [j] ; ASSERT (col >= 0 && col < Work->n_col) ; ASSERT (Fcpos [col] == j * fnr_curr) ; } #endif /* Wrow == Fcol for the IN_IN case, and for the OUT_IN case when * the pivrow [IN][IN] happens to be the same as pivrow [OUT][IN]. * See UMF_local_search for more details. */ ASSERT (IMPLIES (Work->pivcol_in_front, Wrow == Fcols)) ; if (Wrow == Fcols) { for (j = fncols ; j < rrdeg ; j++) { col = Wrow [j] ; /* Fcols [j] = col ; not needed */ /* flip the col index, since Wp must be < 0 */ Work->NewCols [j] = FLIP (col) ; Fcpos [col] = j * fnr_curr ; } } else { for (j = fncols ; j < rrdeg ; j++) { col = Wrow [j] ; Fcols [j] = col ; /* flip the col index, since Wp must be < 0 */ Work->NewCols [j] = FLIP (col) ; Fcpos [col] = j * fnr_curr ; } } } else { /* this is a completely new row */ Work->fscan_col = 0 ; /* scan all the columns */ Work->NewCols = Fcols ; for (j = 0 ; j < rrdeg ; j++) { col = Wrow [j] ; Fcols [j] = col ; Fcpos [col] = j * fnr_curr ; } } DEBUGm1 (("rrdeg "ID" fncols "ID"\n", rrdeg, fncols)) ; fncols = rrdeg ; Work->fncols = fncols ; /* ---------------------------------------------------------------------- */ /* clear the frontal matrix */ /* ---------------------------------------------------------------------- */ ASSERT (fnrows == Work->fnrows_new + 1) ; ASSERT (fncols == Work->fncols_new + 1) ; Fcblock = Work->Fcblock ; ASSERT (Fcblock != (Entry *) NULL) ; zero_init_front (fncols, fnrows, Fcblock, fnr_curr) ; #ifndef NDEBUG DEBUG3 (("New Pivot row "ID" now in front, length "ID" fnr_curr "ID"\n", Work->pivrow, fncols, fnr_curr)) ; for (j = 0 ; j < fncols ; j++) { DEBUG4 (("col "ID" position "ID"\n", j, Fcols [j])) ; ASSERT (Fcpos [Fcols [j]] == j * fnr_curr) ; } #endif /* ---------------------------------------------------------------------- */ /* current workspace usage: */ /* ---------------------------------------------------------------------- */ /* Fcblock [0..fnr_curr-1, 0..fnc_curr-1]: space for the new frontal * matrix. Fcblock (i,j) is located at Fcblock [i+j*fnr_curr] */ return (TRUE) ; } SuiteSparse/UMFPACK/Source/umf_init_front.h0000644001170100242450000000074310617161634017501 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_init_front ( NumericType *Numeric, WorkType *Work ) ; SuiteSparse/UMFPACK/Source/umf_transpose.c0000644001170100242450000002145510677542446017354 0ustar davisfac/* ========================================================================== */ /* === UMF_transpose ======================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Not user-callable. Computes a permuted transpose, R = (A (P,Q(1:nq)))' in MATLAB notation, where R is in column-form. A is n_row-by-n_col, the row-form matrix R is n_row-by-nq, where nq <= n_col. A may be singular. The complex version can do transpose (') or array transpose (.'). Uses Gustavson's method (Two Fast Algorithms for Sparse Matrices: Multiplication and Permuted Transposition, ACM Trans. on Math. Softw., vol 4, no 3, pp. 250-269). */ #include "umf_internal.h" #include "umf_transpose.h" #include "umf_is_permutation.h" GLOBAL Int UMF_transpose ( Int n_row, /* A is n_row-by-n_col */ Int n_col, const Int Ap [ ], /* size n_col+1 */ const Int Ai [ ], /* size nz = Ap [n_col] */ const double Ax [ ], /* size nz if present */ const Int P [ ], /* P [k] = i means original row i is kth row in A(P,Q)*/ /* P is identity if not present */ /* size n_row, if present */ const Int Q [ ], /* Q [k] = j means original col j is kth col in A(P,Q)*/ /* Q is identity if not present */ /* size nq, if present */ Int nq, /* size of Q, ignored if Q is (Int *) NULL */ /* output matrix: Rp, Ri, Rx, and Rz: */ Int Rp [ ], /* size n_row+1 */ Int Ri [ ], /* size nz */ double Rx [ ], /* size nz, if present */ Int W [ ], /* size max (n_row,n_col) workspace */ Int check /* if true, then check inputs */ #ifdef COMPLEX , const double Az [ ] /* size nz */ , double Rz [ ] /* size nz */ , Int do_conjugate /* if true, then do conjugate transpose */ /* otherwise, do array transpose */ #endif ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Int i, j, k, p, bp, newj, do_values ; #ifdef COMPLEX Int split ; #endif /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG Int nz ; ASSERT (n_col >= 0) ; nz = (Ap != (Int *) NULL) ? Ap [n_col] : 0 ; DEBUG2 (("UMF_transpose: "ID"-by-"ID" nz "ID"\n", n_row, n_col, nz)) ; #endif if (check) { /* UMFPACK_symbolic skips this check */ /* UMFPACK_transpose always does this check */ if (!Ai || !Ap || !Ri || !Rp || !W) { return (UMFPACK_ERROR_argument_missing) ; } if (n_row <= 0 || n_col <= 0) /* n_row,n_col must be > 0 */ { return (UMFPACK_ERROR_n_nonpositive) ; } if (!UMF_is_permutation (P, W, n_row, n_row) || !UMF_is_permutation (Q, W, nq, nq)) { return (UMFPACK_ERROR_invalid_permutation) ; } if (AMD_valid (n_row, n_col, Ap, Ai) != AMD_OK) { return (UMFPACK_ERROR_invalid_matrix) ; } } #ifndef NDEBUG DEBUG2 (("UMF_transpose, input matrix:\n")) ; UMF_dump_col_matrix (Ax, #ifdef COMPLEX Az, #endif Ai, Ap, n_row, n_col, nz) ; #endif /* ---------------------------------------------------------------------- */ /* count the entries in each row of A */ /* ---------------------------------------------------------------------- */ /* use W as workspace for RowCount */ for (i = 0 ; i < n_row ; i++) { W [i] = 0 ; Rp [i] = 0 ; } if (Q != (Int *) NULL) { for (newj = 0 ; newj < nq ; newj++) { j = Q [newj] ; ASSERT (j >= 0 && j < n_col) ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; ASSERT (i >= 0 && i < n_row) ; W [i]++ ; } } } else { for (j = 0 ; j < n_col ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; ASSERT (i >= 0 && i < n_row) ; W [i]++ ; } } } /* ---------------------------------------------------------------------- */ /* compute the row pointers for R = A (P,Q) */ /* ---------------------------------------------------------------------- */ if (P != (Int *) NULL) { Rp [0] = 0 ; for (k = 0 ; k < n_row ; k++) { i = P [k] ; ASSERT (i >= 0 && i < n_row) ; Rp [k+1] = Rp [k] + W [i] ; } for (k = 0 ; k < n_row ; k++) { i = P [k] ; ASSERT (i >= 0 && i < n_row) ; W [i] = Rp [k] ; } } else { Rp [0] = 0 ; for (i = 0 ; i < n_row ; i++) { Rp [i+1] = Rp [i] + W [i] ; } for (i = 0 ; i < n_row ; i++) { W [i] = Rp [i] ; } } ASSERT (Rp [n_row] <= Ap [n_col]) ; /* at this point, W holds the permuted row pointers */ /* ---------------------------------------------------------------------- */ /* construct the row form of B */ /* ---------------------------------------------------------------------- */ do_values = Ax && Rx ; #ifdef COMPLEX split = SPLIT (Az) && SPLIT (Rz) ; if (do_conjugate && do_values) { if (Q != (Int *) NULL) { if (split) { /* R = A (P,Q)' */ for (newj = 0 ; newj < nq ; newj++) { j = Q [newj] ; ASSERT (j >= 0 && j < n_col) ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { bp = W [Ai [p]]++ ; Ri [bp] = newj ; Rx [bp] = Ax [p] ; Rz [bp] = -Az [p] ; } } } else { /* R = A (P,Q)' (merged complex values) */ for (newj = 0 ; newj < nq ; newj++) { j = Q [newj] ; ASSERT (j >= 0 && j < n_col) ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { bp = W [Ai [p]]++ ; Ri [bp] = newj ; Rx [2*bp] = Ax [2*p] ; Rx [2*bp+1] = -Ax [2*p+1] ; } } } } else { if (split) { /* R = A (P,:)' */ for (j = 0 ; j < n_col ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { bp = W [Ai [p]]++ ; Ri [bp] = j ; Rx [bp] = Ax [p] ; Rz [bp] = -Az [p] ; } } } else { /* R = A (P,:)' (merged complex values) */ for (j = 0 ; j < n_col ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { bp = W [Ai [p]]++ ; Ri [bp] = j ; Rx [2*bp] = Ax [2*p] ; Rx [2*bp+1] = -Ax [2*p+1] ; } } } } } else #endif { if (Q != (Int *) NULL) { if (do_values) { #ifdef COMPLEX if (split) #endif { /* R = A (P,Q).' */ for (newj = 0 ; newj < nq ; newj++) { j = Q [newj] ; ASSERT (j >= 0 && j < n_col) ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { bp = W [Ai [p]]++ ; Ri [bp] = newj ; Rx [bp] = Ax [p] ; #ifdef COMPLEX Rz [bp] = Az [p] ; #endif } } } #ifdef COMPLEX else { /* R = A (P,Q).' (merged complex values) */ for (newj = 0 ; newj < nq ; newj++) { j = Q [newj] ; ASSERT (j >= 0 && j < n_col) ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { bp = W [Ai [p]]++ ; Ri [bp] = newj ; Rx [2*bp] = Ax [2*p] ; Rx [2*bp+1] = Ax [2*p+1] ; } } } #endif } else { /* R = pattern of A (P,Q).' */ for (newj = 0 ; newj < nq ; newj++) { j = Q [newj] ; ASSERT (j >= 0 && j < n_col) ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { Ri [W [Ai [p]]++] = newj ; } } } } else { if (do_values) { #ifdef COMPLEX if (split) #endif { /* R = A (P,:).' */ for (j = 0 ; j < n_col ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { bp = W [Ai [p]]++ ; Ri [bp] = j ; Rx [bp] = Ax [p] ; #ifdef COMPLEX Rz [bp] = Az [p] ; #endif } } } #ifdef COMPLEX else { /* R = A (P,:).' (merged complex values) */ for (j = 0 ; j < n_col ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { bp = W [Ai [p]]++ ; Ri [bp] = j ; Rx [2*bp] = Ax [2*p] ; Rx [2*bp+1] = Ax [2*p+1] ; } } } #endif } else { /* R = pattern of A (P,:).' */ for (j = 0 ; j < n_col ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { Ri [W [Ai [p]]++] = j ; } } } } } #ifndef NDEBUG for (k = 0 ; k < n_row ; k++) { if (P != (Int *) NULL) { i = P [k] ; } else { i = k ; } DEBUG3 ((ID": W[i] "ID" Rp[k+1] "ID"\n", i, W [i], Rp [k+1])) ; ASSERT (W [i] == Rp [k+1]) ; } DEBUG2 (("UMF_transpose, output matrix:\n")) ; UMF_dump_col_matrix (Rx, #ifdef COMPLEX Rz, #endif Ri, Rp, n_col, n_row, Rp [n_row]) ; ASSERT (AMD_valid (n_col, n_row, Rp, Ri) == AMD_OK) ; #endif return (UMFPACK_OK) ; } SuiteSparse/UMFPACK/Source/umf_transpose.h0000644001170100242450000000137110617162452017341 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_transpose ( Int n_row, Int n_col, const Int Ap [ ], const Int Ai [ ], const double Ax [ ], const Int P [ ], const Int Q [ ], Int nq, Int Rp [ ], Int Ri [ ], double Rx [ ], Int W [ ], Int check #ifdef COMPLEX , const double Az [ ] , double Rz [ ] , Int do_conjugate #endif ) ; SuiteSparse/UMFPACK/Source/umfpack_col_to_triplet.c0000644001170100242450000000372010677542010021175 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_col_to_triplet =============================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User callable. Converts a column-oriented input matrix to triplet form by constructing the column indices Tj from the column pointers Ap. The matrix may be singular. See umfpack_col_to_triplet.h for details. */ #include "umf_internal.h" GLOBAL Int UMFPACK_col_to_triplet ( Int n_col, const Int Ap [ ], Int Tj [ ] ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Int nz, j, p, p1, p2, length ; /* ---------------------------------------------------------------------- */ /* construct the column indices */ /* ---------------------------------------------------------------------- */ if (!Ap || !Tj) { return (UMFPACK_ERROR_argument_missing) ; } if (n_col <= 0) { return (UMFPACK_ERROR_n_nonpositive) ; } if (Ap [0] != 0) { return (UMFPACK_ERROR_invalid_matrix) ; } nz = Ap [n_col] ; if (nz < 0) { return (UMFPACK_ERROR_invalid_matrix) ; } for (j = 0 ; j < n_col ; j++) { p1 = Ap [j] ; p2 = Ap [j+1] ; length = p2 - p1 ; if (length < 0 || p2 > nz) { return (UMFPACK_ERROR_invalid_matrix) ; } for (p = p1 ; p < p2 ; p++) { Tj [p] = j ; } } return (UMFPACK_OK) ; } SuiteSparse/UMFPACK/Source/umfpack_get_numeric.c0000644001170100242450000006532010617162056020462 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_get_numeric ================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Gets the LU factors and the permutation vectors held in the Numeric object. L is returned in sparse row form with sorted rows, U is returned in sparse column form with sorted columns, and P and Q are returned as permutation vectors. See umfpack_get_numeric.h for a more detailed description. Returns TRUE if successful, FALSE if the Numeric object is invalid or if out of memory. Dynamic memory usage: calls UMF_malloc twice, for a total space of 2*n integers, and then frees all of it via UMF_free when done. */ #include "umf_internal.h" #include "umf_valid_numeric.h" #include "umf_malloc.h" #include "umf_free.h" #ifndef NDEBUG PRIVATE Int init_count ; #endif PRIVATE void get_L ( Int Lp [ ], Int Lj [ ], double Lx [ ], #ifdef COMPLEX double Lz [ ], #endif NumericType *Numeric, Int Pattern [ ], Int Wi [ ] ) ; PRIVATE void get_U ( Int Up [ ], Int Ui [ ], double Ux [ ], #ifdef COMPLEX double Uz [ ], #endif NumericType *Numeric, Int Pattern [ ], Int Wi [ ] ) ; /* ========================================================================== */ /* === UMFPACK_get_numeric ================================================== */ /* ========================================================================== */ GLOBAL Int UMFPACK_get_numeric ( Int Lp [ ], Int Lj [ ], double Lx [ ], #ifdef COMPLEX double Lz [ ], #endif Int Up [ ], Int Ui [ ], double Ux [ ], #ifdef COMPLEX double Uz [ ], #endif Int P [ ], Int Q [ ], double Dx [ ], #ifdef COMPLEX double Dz [ ], #endif Int *p_do_recip, double Rs [ ], void *NumericHandle ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ NumericType *Numeric ; Int getL, getU, *Rperm, *Cperm, k, nn, n_row, n_col, *Wi, *Pattern, n_inner ; double *Rs1 ; Entry *D ; #ifndef NDEBUG init_count = UMF_malloc_count ; #endif Wi = (Int *) NULL ; Pattern = (Int *) NULL ; /* ---------------------------------------------------------------------- */ /* check input parameters */ /* ---------------------------------------------------------------------- */ Numeric = (NumericType *) NumericHandle ; if (!UMF_valid_numeric (Numeric)) { return (UMFPACK_ERROR_invalid_Numeric_object) ; } n_row = Numeric->n_row ; n_col = Numeric->n_col ; nn = MAX (n_row, n_col) ; n_inner = MIN (n_row, n_col) ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ getL = Lp && Lj && Lx ; getU = Up && Ui && Ux ; if (getL || getU) { Wi = (Int *) UMF_malloc (nn, sizeof (Int)) ; Pattern = (Int *) UMF_malloc (nn, sizeof (Int)) ; if (!Wi || !Pattern) { (void) UMF_free ((void *) Wi) ; (void) UMF_free ((void *) Pattern) ; ASSERT (UMF_malloc_count == init_count) ; DEBUGm4 (("out of memory: get numeric\n")) ; return (UMFPACK_ERROR_out_of_memory) ; } ASSERT (UMF_malloc_count == init_count + 2) ; } /* ---------------------------------------------------------------------- */ /* get contents of Numeric */ /* ---------------------------------------------------------------------- */ if (P != (Int *) NULL) { Rperm = Numeric->Rperm ; for (k = 0 ; k < n_row ; k++) { P [k] = Rperm [k] ; } } if (Q != (Int *) NULL) { Cperm = Numeric->Cperm ; for (k = 0 ; k < n_col ; k++) { Q [k] = Cperm [k] ; } } if (getL) { get_L (Lp, Lj, Lx, #ifdef COMPLEX Lz, #endif Numeric, Pattern, Wi) ; } if (getU) { get_U (Up, Ui, Ux, #ifdef COMPLEX Uz, #endif Numeric, Pattern, Wi) ; } if (Dx != (double *) NULL) { D = Numeric->D ; #ifdef COMPLEX if (SPLIT (Dz)) { for (k = 0 ; k < n_inner ; k++) { Dx [k] = REAL_COMPONENT (D [k]) ; Dz [k] = IMAG_COMPONENT (D [k]) ; } } else { for (k = 0 ; k < n_inner ; k++) { Dx [2*k ] = REAL_COMPONENT (D [k]) ; Dx [2*k+1] = IMAG_COMPONENT (D [k]) ; } } #else { D = Numeric->D ; for (k = 0 ; k < n_inner ; k++) { Dx [k] = D [k] ; } } #endif } /* return the flag stating whether the scale factors are to be multiplied, * or divided. If do_recip is TRUE, multiply. Otherwise, divided. * If NRECIPROCAL is defined at compile time, the scale factors are always * to be used by dividing. */ if (p_do_recip != (Int *) NULL) { #ifndef NRECIPROCAL *p_do_recip = Numeric->do_recip ; #else *p_do_recip = FALSE ; #endif } if (Rs != (double *) NULL) { Rs1 = Numeric->Rs ; if (Rs1 == (double *) NULL) { /* R is the identity matrix. */ for (k = 0 ; k < n_row ; k++) { Rs [k] = 1.0 ; } } else { for (k = 0 ; k < n_row ; k++) { Rs [k] = Rs1 [k] ; } } } /* ---------------------------------------------------------------------- */ /* free the workspace */ /* ---------------------------------------------------------------------- */ (void) UMF_free ((void *) Wi) ; (void) UMF_free ((void *) Pattern) ; ASSERT (UMF_malloc_count == init_count) ; return (UMFPACK_OK) ; } /* ========================================================================== */ /* === get_L ================================================================ */ /* ========================================================================== */ /* The matrix L is stored in the following arrays in the Numeric object: Int Lpos [0..npiv] Int Lip [0..npiv], index into Numeric->Memory Int Lilen [0..npiv] Unit *(Numeric->Memory), pointer to memory space holding row indices and numerical values where npiv is the number of pivot entries found. If A is n_row-by-n_col, then npiv <= MIN (n_row,n_col). Let L_k denote the pattern of entries in column k of L (excluding the diagonal). An Lchain is a sequence of columns of L whose nonzero patterns are related. The start of an Lchain is denoted by a negative value of Lip [k]. To obtain L_k: (1) If column k starts an Lchain, then L_k is stored in its entirety. |Lip [k]| is an index into Numeric->Memory for the integer row indices in L_k. The number of entries in the column is |L_k| = Lilen [k]. This defines the pattern of the "leading" column of this chain. Lpos [k] is not used for the first column in the chain. Column zero is always a leading column. (2) If column k does not start an Lchain, then L_k is represented as a superset of L_k-1. Define Lnew_k such that (L_k-1 - {k} union Lnew_k) = L_k, where Lnew_k and (L_k-1)-{k} are disjoint. Lnew_k are the entries in L_k that are not in L_k-1. Lpos [k] holds the position of pivot row index k in the prior pattern L_k-1 (if it is present), so that the set subtraction (L_k-1)-{k} can be computed quickly, when computing the pattern of L_k from L_k-1. The number of new entries in L_k is stored in Lilen [k] = |Lnew_k|. Note that this means we must have the pattern L_k-1 to compute L_k. In both cases (1) and (2), we obtain the pattern L_k. The numerical values are stored in Numeric->Memory, starting at the index |Lip [k]| + Lilen [k]. It is stored in the same order as the entries in L_k, after L_k is obtained from cases (1) or (2), above. The advantage of using this "packed" data structure is that it can dramatically reduce the amount of storage needed for the pattern of L. The disadvantage is that it can be difficult for the user to access, and it does not match the sparse matrix data structure used in MATLAB. Thus, this routine is provided to create a conventional sparse matrix data structure for L, in sparse-row form. A row-form of L appears to MATLAB to be a column-oriented from of the transpose of L. If you would like a column-form of L, then use UMFPACK_transpose (an example of this is in umfpackmex.c). */ /* ========================================================================== */ PRIVATE void get_L ( Int Lp [ ], /* of size n_row+1 */ Int Lj [ ], /* of size lnz, where lnz = Lp [n_row] */ double Lx [ ], /* of size lnz */ #ifdef COMPLEX double Lz [ ], /* of size lnz */ #endif NumericType *Numeric, Int Pattern [ ], /* workspace of size n_row */ Int Wi [ ] /* workspace of size n_row */ ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Entry value ; Entry *xp, *Lval ; Int deg, *ip, j, row, n_row, n_col, n_inner, *Lpos, *Lilen, *Lip, p, llen, lnz2, lp, newLchain, k, pos, npiv, *Li, n1 ; #ifdef COMPLEX Int split = SPLIT (Lz) ; #endif /* ---------------------------------------------------------------------- */ /* get parameters */ /* ---------------------------------------------------------------------- */ DEBUG4 (("get_L start:\n")) ; n_row = Numeric->n_row ; n_col = Numeric->n_col ; n_inner = MIN (n_row, n_col) ; npiv = Numeric->npiv ; n1 = Numeric->n1 ; Lpos = Numeric->Lpos ; Lilen = Numeric->Lilen ; Lip = Numeric->Lip ; deg = 0 ; /* ---------------------------------------------------------------------- */ /* count the nonzeros in each row of L */ /* ---------------------------------------------------------------------- */ #pragma ivdep for (row = 0 ; row < n_inner ; row++) { /* include the diagonal entry in the row counts */ Wi [row] = 1 ; } #pragma ivdep for (row = n_inner ; row < n_row ; row++) { Wi [row] = 0 ; } /* singletons */ for (k = 0 ; k < n1 ; k++) { DEBUG4 (("Singleton k "ID"\n", k)) ; deg = Lilen [k] ; if (deg > 0) { lp = Lip [k] ; Li = (Int *) (Numeric->Memory + lp) ; lp += UNITS (Int, deg) ; Lval = (Entry *) (Numeric->Memory + lp) ; for (j = 0 ; j < deg ; j++) { row = Li [j] ; value = Lval [j] ; DEBUG4 ((" row "ID" k "ID" value", row, k)) ; EDEBUG4 (value) ; DEBUG4 (("\n")) ; if (IS_NONZERO (value)) { Wi [row]++ ; } } } } /* non-singletons */ for (k = n1 ; k < npiv ; k++) { /* ------------------------------------------------------------------ */ /* make column of L in Pattern [0..deg-1] */ /* ------------------------------------------------------------------ */ lp = Lip [k] ; newLchain = (lp < 0) ; if (newLchain) { lp = -lp ; deg = 0 ; DEBUG4 (("start of chain for column of L\n")) ; } /* remove pivot row */ pos = Lpos [k] ; if (pos != EMPTY) { DEBUG4 ((" k "ID" removing row "ID" at position "ID"\n", k, Pattern [pos], pos)) ; ASSERT (!newLchain) ; ASSERT (deg > 0) ; ASSERT (pos >= 0 && pos < deg) ; ASSERT (Pattern [pos] == k) ; Pattern [pos] = Pattern [--deg] ; } /* concatenate the pattern */ ip = (Int *) (Numeric->Memory + lp) ; llen = Lilen [k] ; for (j = 0 ; j < llen ; j++) { row = *ip++ ; DEBUG4 ((" row "ID" k "ID"\n", row, k)) ; ASSERT (row > k && row < n_row) ; Pattern [deg++] = row ; } xp = (Entry *) (Numeric->Memory + lp + UNITS (Int, llen)) ; for (j = 0 ; j < deg ; j++) { DEBUG4 ((" row "ID" k "ID" value", Pattern [j], k)) ; row = Pattern [j] ; value = *xp++ ; EDEBUG4 (value) ; DEBUG4 (("\n")) ; if (IS_NONZERO (value)) { Wi [row]++ ; } } } /* ---------------------------------------------------------------------- */ /* construct the final row form of L */ /* ---------------------------------------------------------------------- */ /* create the row pointers */ lnz2 = 0 ; for (row = 0 ; row < n_row ; row++) { Lp [row] = lnz2 ; lnz2 += Wi [row] ; Wi [row] = Lp [row] ; } Lp [n_row] = lnz2 ; ASSERT (Numeric->lnz + n_inner == lnz2) ; /* add entries from the rows of L (singletons) */ for (k = 0 ; k < n1 ; k++) { DEBUG4 (("Singleton k "ID"\n", k)) ; deg = Lilen [k] ; if (deg > 0) { lp = Lip [k] ; Li = (Int *) (Numeric->Memory + lp) ; lp += UNITS (Int, deg) ; Lval = (Entry *) (Numeric->Memory + lp) ; for (j = 0 ; j < deg ; j++) { row = Li [j] ; value = Lval [j] ; DEBUG4 ((" row "ID" k "ID" value", row, k)) ; EDEBUG4 (value) ; DEBUG4 (("\n")) ; if (IS_NONZERO (value)) { p = Wi [row]++ ; Lj [p] = k ; #ifdef COMPLEX if (split) { Lx [p] = REAL_COMPONENT (value) ; Lz [p] = IMAG_COMPONENT (value) ; } else { Lx [2*p ] = REAL_COMPONENT (value) ; Lx [2*p+1] = IMAG_COMPONENT (value) ; } #else Lx [p] = value ; #endif } } } } /* add entries from the rows of L (non-singletons) */ for (k = n1 ; k < npiv ; k++) { /* ------------------------------------------------------------------ */ /* make column of L in Pattern [0..deg-1] */ /* ------------------------------------------------------------------ */ lp = Lip [k] ; newLchain = (lp < 0) ; if (newLchain) { lp = -lp ; deg = 0 ; DEBUG4 (("start of chain for column of L\n")) ; } /* remove pivot row */ pos = Lpos [k] ; if (pos != EMPTY) { DEBUG4 ((" k "ID" removing row "ID" at position "ID"\n", k, Pattern [pos], pos)) ; ASSERT (!newLchain) ; ASSERT (deg > 0) ; ASSERT (pos >= 0 && pos < deg) ; ASSERT (Pattern [pos] == k) ; Pattern [pos] = Pattern [--deg] ; } /* concatenate the pattern */ ip = (Int *) (Numeric->Memory + lp) ; llen = Lilen [k] ; for (j = 0 ; j < llen ; j++) { row = *ip++ ; DEBUG4 ((" row "ID" k "ID"\n", row, k)) ; ASSERT (row > k) ; Pattern [deg++] = row ; } xp = (Entry *) (Numeric->Memory + lp + UNITS (Int, llen)) ; for (j = 0 ; j < deg ; j++) { DEBUG4 ((" row "ID" k "ID" value", Pattern [j], k)) ; row = Pattern [j] ; value = *xp++ ; EDEBUG4 (value) ; DEBUG4 (("\n")) ; if (IS_NONZERO (value)) { p = Wi [row]++ ; Lj [p] = k ; #ifdef COMPLEX if (split) { Lx [p] = REAL_COMPONENT (value) ; Lz [p] = IMAG_COMPONENT (value) ; } else { Lx [2*p ] = REAL_COMPONENT (value) ; Lx [2*p+1] = IMAG_COMPONENT (value) ; } #else Lx [p] = value ; #endif } } } /* add all of the diagonal entries (L is unit diagonal) */ for (row = 0 ; row < n_inner ; row++) { p = Wi [row]++ ; Lj [p] = row ; #ifdef COMPLEX if (split) { Lx [p] = 1. ; Lz [p] = 0. ; } else { Lx [2*p ] = 1. ; Lx [2*p+1] = 0. ; } #else Lx [p] = 1. ; #endif ASSERT (Wi [row] == Lp [row+1]) ; } #ifndef NDEBUG DEBUG6 (("L matrix (stored by rows):")) ; UMF_dump_col_matrix (Lx, #ifdef COMPLEX Lz, #endif Lj, Lp, n_inner, n_row, Numeric->lnz+n_inner) ; #endif DEBUG4 (("get_L done:\n")) ; } /* ========================================================================== */ /* === get_U ================================================================ */ /* ========================================================================== */ /* The matrix U is stored in the following arrays in the Numeric object: Int Upos [0..npiv] Int Uip [0..npiv], index into Numeric->Memory Int Uilen [0..npiv] Unit *(Numeric->Memory), pointer to memory space holding column indices and numerical values where npiv is the number of pivot entries found. If A is n_row-by-n_col, then npiv <= MIN (n_row,n_col). Let U_k denote the pattern of entries in row k of U (excluding the diagonal). A Uchain is a sequence of columns of U whose nonzero patterns are related. The start of a Uchain is denoted by a negative value of Uip [k]. To obtain U_k-1: (1) If row k is the start of a Uchain then Uip [k] is negative and |Uip [k]| is an index into Numeric->Memory for the integer column indices in U_k-1. The number of entries in the row is |U_k-1| = Uilen [k]. This defines the pattern of the "trailing" row of this chain that ends at row k-1. (2) If row k is not the start of a Uchain, then U_k-1 is a subset of U_k. The indices in U_k are arranged so that last Uilen [k] entries of U_k are those indices not in U_k-1. Next, the pivot column index k is added if it appears in row U_k-1 (it never appears in U_k). Upos [k] holds the position of pivot column index k in the pattern U_k-1 (if it is present), so that the set union (U_k-1)+{k} can be computed quickly, when computing the pattern of U_k-1 from U_k. Note that this means we must have the pattern U_k to compute L_k-1. In both cases (1) and (2), we obtain the pattern U_k. The numerical values are stored in Numeric->Memory. If k is the start of a Uchain, then the offset is |Uip [k]| plus the size of the space needed to store the pattern U_k-1. Otherwise, Uip [k] is the offset itself of the numerical values, since in this case no pattern is stored. The numerical values are stored in the same order as the entries in U_k, after U_k is obtained from cases (1) or (2), above. The advantage of using this "packed" data structure is that it can dramatically reduce the amount of storage needed for the pattern of U. The disadvantage is that it can be difficult for the user to access, and it does not match the sparse matrix data structure used in MATLAB. Thus, this routine is provided to create a conventional sparse matrix data structure for U, in sparse-column form. */ /* ========================================================================== */ PRIVATE void get_U ( Int Up [ ], /* of size n_col+1 */ Int Ui [ ], /* of size unz, where unz = Up [n_col] */ double Ux [ ], /* of size unz */ #ifdef COMPLEX double Uz [ ], /* of size unz */ #endif NumericType *Numeric, Int Pattern [ ], /* workspace of size n_col */ Int Wi [ ] /* workspace of size n_col */ ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Entry value ; Entry *xp, *D, *Uval ; Int deg, j, *ip, col, *Upos, *Uilen, *Uip, n_col, ulen, *Usi, unz2, p, k, up, newUchain, pos, npiv, n1 ; #ifdef COMPLEX Int split = SPLIT (Uz) ; #endif #ifndef NDEBUG Int nnzpiv = 0 ; #endif /* ---------------------------------------------------------------------- */ /* get parameters */ /* ---------------------------------------------------------------------- */ DEBUG4 (("get_U start:\n")) ; n_col = Numeric->n_col ; n1 = Numeric->n1 ; npiv = Numeric->npiv ; Upos = Numeric->Upos ; Uilen = Numeric->Uilen ; Uip = Numeric->Uip ; D = Numeric->D ; /* ---------------------------------------------------------------------- */ /* count the nonzeros in each column of U */ /* ---------------------------------------------------------------------- */ for (col = 0 ; col < npiv ; col++) { /* include the diagonal entry in the column counts */ DEBUG4 (("D ["ID"] = ", col)) ; EDEBUG4 (D [col]) ; Wi [col] = IS_NONZERO (D [col]) ; DEBUG4 ((" is nonzero: "ID"\n", Wi [col])) ; #ifndef NDEBUG nnzpiv += IS_NONZERO (D [col]) ; #endif } DEBUG4 (("nnzpiv "ID" "ID"\n", nnzpiv, Numeric->nnzpiv)) ; ASSERT (nnzpiv == Numeric->nnzpiv) ; for (col = npiv ; col < n_col ; col++) { /* diagonal entries are zero for structurally singular part */ Wi [col] = 0 ; } deg = Numeric->ulen ; if (deg > 0) { /* make last pivot row of U (singular matrices only) */ DEBUG0 (("Last pivot row of U: ulen "ID"\n", deg)) ; for (j = 0 ; j < deg ; j++) { Pattern [j] = Numeric->Upattern [j] ; DEBUG0 ((" column "ID"\n", Pattern [j])) ; } } /* non-singletons */ for (k = npiv-1 ; k >= n1 ; k--) { /* ------------------------------------------------------------------ */ /* use row k of U */ /* ------------------------------------------------------------------ */ up = Uip [k] ; ulen = Uilen [k] ; newUchain = (up < 0) ; if (newUchain) { up = -up ; xp = (Entry *) (Numeric->Memory + up + UNITS (Int, ulen)) ; } else { xp = (Entry *) (Numeric->Memory + up) ; } for (j = 0 ; j < deg ; j++) { DEBUG4 ((" k "ID" col "ID" value\n", k, Pattern [j])) ; col = Pattern [j] ; ASSERT (col >= 0 && col < n_col) ; value = *xp++ ; EDEBUG4 (value) ; DEBUG4 (("\n")) ; if (IS_NONZERO (value)) { Wi [col]++ ; } } /* ------------------------------------------------------------------ */ /* make row k-1 of U in Pattern [0..deg-1] */ /* ------------------------------------------------------------------ */ if (k == n1) break ; if (newUchain) { /* next row is a new Uchain */ deg = ulen ; DEBUG4 (("end of chain for row of U "ID" deg "ID"\n", k-1, deg)) ; ip = (Int *) (Numeric->Memory + up) ; for (j = 0 ; j < deg ; j++) { col = *ip++ ; DEBUG4 ((" k "ID" col "ID"\n", k-1, col)) ; ASSERT (k <= col) ; Pattern [j] = col ; } } else { deg -= ulen ; DEBUG4 (("middle of chain for row of U "ID" deg "ID"\n", k-1, deg)); ASSERT (deg >= 0) ; pos = Upos [k] ; if (pos != EMPTY) { /* add the pivot column */ DEBUG4 (("k "ID" add pivot entry at position "ID"\n", k, pos)) ; ASSERT (pos >= 0 && pos <= deg) ; Pattern [deg++] = Pattern [pos] ; Pattern [pos] = k ; } } } /* singletons */ for (k = n1 - 1 ; k >= 0 ; k--) { deg = Uilen [k] ; DEBUG4 (("Singleton k "ID"\n", k)) ; if (deg > 0) { up = Uip [k] ; Usi = (Int *) (Numeric->Memory + up) ; up += UNITS (Int, deg) ; Uval = (Entry *) (Numeric->Memory + up) ; for (j = 0 ; j < deg ; j++) { col = Usi [j] ; value = Uval [j] ; DEBUG4 ((" k "ID" col "ID" value", k, col)) ; EDEBUG4 (value) ; DEBUG4 (("\n")) ; if (IS_NONZERO (value)) { Wi [col]++ ; } } } } /* ---------------------------------------------------------------------- */ /* construct the final column form of U */ /* ---------------------------------------------------------------------- */ /* create the column pointers */ unz2 = 0 ; for (col = 0 ; col < n_col ; col++) { Up [col] = unz2 ; unz2 += Wi [col] ; } Up [n_col] = unz2 ; DEBUG1 (("Numeric->unz "ID" npiv "ID" nnzpiv "ID" unz2 "ID"\n", Numeric->unz, npiv, Numeric->nnzpiv, unz2)) ; ASSERT (Numeric->unz + Numeric->nnzpiv == unz2) ; for (col = 0 ; col < n_col ; col++) { Wi [col] = Up [col+1] ; } /* add all of the diagonal entries */ for (col = 0 ; col < npiv ; col++) { if (IS_NONZERO (D [col])) { p = --(Wi [col]) ; Ui [p] = col ; #ifdef COMPLEX if (split) { Ux [p] = REAL_COMPONENT (D [col]) ; Uz [p] = IMAG_COMPONENT (D [col]) ; } else { Ux [2*p ] = REAL_COMPONENT (D [col]) ; Ux [2*p+1] = IMAG_COMPONENT (D [col]) ; } #else Ux [p] = D [col] ; #endif } } /* add all the entries from the rows of U */ deg = Numeric->ulen ; if (deg > 0) { /* make last pivot row of U (singular matrices only) */ for (j = 0 ; j < deg ; j++) { Pattern [j] = Numeric->Upattern [j] ; } } /* non-singletons */ for (k = npiv-1 ; k >= n1 ; k--) { /* ------------------------------------------------------------------ */ /* use row k of U */ /* ------------------------------------------------------------------ */ up = Uip [k] ; ulen = Uilen [k] ; newUchain = (up < 0) ; if (newUchain) { up = -up ; xp = (Entry *) (Numeric->Memory + up + UNITS (Int, ulen)) ; } else { xp = (Entry *) (Numeric->Memory + up) ; } xp += deg ; for (j = deg-1 ; j >= 0 ; j--) { DEBUG4 ((" k "ID" col "ID" value", k, Pattern [j])) ; col = Pattern [j] ; ASSERT (col >= 0 && col < n_col) ; value = *(--xp) ; EDEBUG4 (value) ; DEBUG4 (("\n")) ; if (IS_NONZERO (value)) { p = --(Wi [col]) ; Ui [p] = k ; #ifdef COMPLEX if (split) { Ux [p] = REAL_COMPONENT (value) ; Uz [p] = IMAG_COMPONENT (value) ; } else { Ux [2*p ] = REAL_COMPONENT (value) ; Ux [2*p+1] = IMAG_COMPONENT (value) ; } #else Ux [p] = value ; #endif } } /* ------------------------------------------------------------------ */ /* make row k-1 of U in Pattern [0..deg-1] */ /* ------------------------------------------------------------------ */ if (newUchain) { /* next row is a new Uchain */ deg = ulen ; DEBUG4 (("end of chain for row of U "ID" deg "ID"\n", k-1, deg)) ; ip = (Int *) (Numeric->Memory + up) ; for (j = 0 ; j < deg ; j++) { col = *ip++ ; DEBUG4 ((" k "ID" col "ID"\n", k-1, col)) ; ASSERT (k <= col) ; Pattern [j] = col ; } } else { deg -= ulen ; DEBUG4 (("middle of chain for row of U "ID" deg "ID"\n", k-1, deg)); ASSERT (deg >= 0) ; pos = Upos [k] ; if (pos != EMPTY) { /* add the pivot column */ DEBUG4 (("k "ID" add pivot entry at position "ID"\n", k, pos)) ; ASSERT (pos >= 0 && pos <= deg) ; Pattern [deg++] = Pattern [pos] ; Pattern [pos] = k ; } } } /* singletons */ for (k = n1 - 1 ; k >= 0 ; k--) { deg = Uilen [k] ; DEBUG4 (("Singleton k "ID"\n", k)) ; if (deg > 0) { up = Uip [k] ; Usi = (Int *) (Numeric->Memory + up) ; up += UNITS (Int, deg) ; Uval = (Entry *) (Numeric->Memory + up) ; for (j = 0 ; j < deg ; j++) { col = Usi [j] ; value = Uval [j] ; DEBUG4 ((" k "ID" col "ID" value", k, col)) ; EDEBUG4 (value) ; DEBUG4 (("\n")) ; if (IS_NONZERO (value)) { p = --(Wi [col]) ; Ui [p] = k ; #ifdef COMPLEX if (split) { Ux [p] = REAL_COMPONENT (value) ; Uz [p] = IMAG_COMPONENT (value) ; } else { Ux [2*p ] = REAL_COMPONENT (value) ; Ux [2*p+1] = IMAG_COMPONENT (value) ; } #else Ux [p] = value ; #endif } } } } #ifndef NDEBUG DEBUG6 (("U matrix:")) ; UMF_dump_col_matrix (Ux, #ifdef COMPLEX Uz, #endif Ui, Up, Numeric->n_row, n_col, Numeric->unz + Numeric->nnzpiv) ; #endif } SuiteSparse/UMFPACK/Source/umfpack_global.c0000644001170100242450000000742510617162064017422 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_global ======================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Global variables. UMFPACK uses these function pointers for several user-redefinable functions. The amd_* functions are defined in AMD/Source/amd_global.c. Function pointer default for mexFunction (see MATLAB/umfpackmex.c) ---------------- ------- --------------- amd_malloc malloc mxMalloc amd_free free mxFree amd_realloc realloc mxRealloc amd_calloc calloc mxCalloc amd_printf printf mexPrintf umfpack_hypot umf_hypot umf_hypot umfpack_divcomplex umf_divcomplex umf_divcomplex This routine is compiled just once for all four versions of UMFPACK (int/UF_long, double/complex). */ #include "umf_internal.h" double (*umfpack_hypot) (double, double) = umf_hypot ; int (*umfpack_divcomplex) (double, double, double, double, double *, double *) = umf_divcomplex ; /* ========================================================================== */ /* === umf_hypot ============================================================ */ /* ========================================================================== */ /* There is an equivalent routine called hypot in , which conforms * to ANSI C99. However, UMFPACK does not assume that ANSI C99 is available. * You can use the ANSI C99 hypot routine with: * * #include * umfpack_hypot = hypot ; * * prior to calling any UMFPACK routine. * * s = hypot (x,y) computes s = sqrt (x*x + y*y) but does so more accurately. * * The NaN case for the double relops x >= y and x+y == x is safely ignored. */ double umf_hypot (double x, double y) { double s, r ; x = SCALAR_ABS (x) ; y = SCALAR_ABS (y) ; if (x >= y) { if (x + y == x) { s = x ; } else { r = y / x ; s = x * sqrt (1.0 + r*r) ; } } else { if (y + x == y) { s = y ; } else { r = x / y ; s = y * sqrt (1.0 + r*r) ; } } return (s) ; } /* ========================================================================== */ /* === umf_divcomplex ======================================================= */ /* ========================================================================== */ /* c = a/b where c, a, and b are complex. The real and imaginary parts are * passed as separate arguments to this routine. The NaN case is ignored * for the double relop br >= bi. Returns TRUE (1) if the denominator is * zero, FALSE (0) otherwise. * * This uses ACM Algo 116, by R. L. Smith, 1962, which tries to avoid * underflow and overflow. * * c can be the same variable as a or b. */ int umf_divcomplex ( double ar, double ai, /* real and imaginary parts of a */ double br, double bi, /* real and imaginary parts of b */ double *cr, double *ci /* real and imaginary parts of c */ ) { double tr, ti, r, den ; if (SCALAR_ABS (br) >= SCALAR_ABS (bi)) { r = bi / br ; den = br + r * bi ; tr = (ar + ai * r) / den ; ti = (ai - ar * r) / den ; } else { r = br / bi ; den = r * br + bi ; tr = (ar * r + ai) / den ; ti = (ai * r - ar) / den ; } *cr = tr ; *ci = ti ; return (SCALAR_IS_ZERO (den)) ; } SuiteSparse/UMFPACK/Source/umf_get_memory.c0000644001170100242450000001615210677541454017501 0ustar davisfac/* ========================================================================== */ /* === UMF_get_memory ======================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Reallocate the workspace (Numeric->Memory) and shift elements downwards. needunits: increase in size so that the free space is at least this many Units (to which the tuple lengths is added). Return TRUE if successful, FALSE if out of memory. */ #include "umf_internal.h" #include "umf_get_memory.h" #include "umf_garbage_collection.h" #include "umf_tuple_lengths.h" #include "umf_build_tuples.h" #include "umf_mem_free_tail_block.h" #include "umf_realloc.h" GLOBAL Int UMF_get_memory ( NumericType *Numeric, WorkType *Work, Int needunits, Int r2, /* compact current front to r2-by-c2 */ Int c2, Int do_Fcpos ) { double nsize, bsize, tsize ; Int i, minsize, newsize, newmem, costly, row, col, *Row_tlen, *Col_tlen, n_row, n_col, *Row_degree, *Col_degree ; Unit *mnew, *p ; /* ---------------------------------------------------------------------- */ /* get and check parameters */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG DEBUG1 (("::::GET MEMORY::::\n")) ; UMF_dump_memory (Numeric) ; #endif n_row = Work->n_row ; n_col = Work->n_col ; Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro */ Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro */ Row_tlen = Numeric->Uilen ; Col_tlen = Numeric->Lilen ; /* ---------------------------------------------------------------------- */ /* initialize the tuple list lengths */ /* ---------------------------------------------------------------------- */ for (row = 0 ; row < n_row ; row++) { if (NON_PIVOTAL_ROW (row)) { Row_tlen [row] = 0 ; } } for (col = 0 ; col < n_col ; col++) { if (NON_PIVOTAL_COL (col)) { Col_tlen [col] = 0 ; } } /* ---------------------------------------------------------------------- */ /* determine how much memory is needed for the tuples */ /* ---------------------------------------------------------------------- */ nsize = (double) needunits + 2 ; needunits += UMF_tuple_lengths (Numeric, Work, &tsize) ; nsize += tsize ; needunits += 2 ; /* add 2, so that newmem >= 2 is true if realloc'd */ /* note: Col_tlen and Row_tlen are updated, but the tuple lists */ /* themselves are not. Do not attempt to scan the tuple lists. */ /* They are now stale, and are about to be destroyed and recreated. */ /* ---------------------------------------------------------------------- */ /* determine the desired new size of memory */ /* ---------------------------------------------------------------------- */ DEBUG0 (("UMF_get_memory: needunits: "ID"\n", needunits)) ; minsize = Numeric->size + needunits ; nsize += (double) Numeric->size ; bsize = ((double) Int_MAX) / sizeof (Unit) - 1 ; newsize = (Int) (UMF_REALLOC_INCREASE * ((double) minsize)) ; nsize *= UMF_REALLOC_INCREASE ; nsize += 1 ; if (newsize < 0 || nsize > bsize) { /* :: realloc Numeric->Memory int overflow :: */ DEBUGm3 (("Realloc hit integer limit\n")) ; newsize = (Int) bsize ; /* we cannot increase the size beyond bsize */ } else { ASSERT (newsize <= nsize) ; newsize = MAX (newsize, minsize) ; } newsize = MAX (newsize, Numeric->size) ; DEBUG0 (( "REALLOC MEMORY: needunits "ID" old size: "ID" new size: "ID" Units \n", needunits, Numeric->size, newsize)) ; /* Forget where the biggest free block is (we no longer need it) */ /* since garbage collection will occur shortly. */ Numeric->ibig = EMPTY ; DEBUG0 (("Before realloc E [0] "ID"\n", Work->E [0])) ; /* ---------------------------------------------------------------------- */ /* reallocate the memory, if possible, and make it bigger */ /* ---------------------------------------------------------------------- */ mnew = (Unit *) NULL ; while (!mnew) { mnew = (Unit *) UMF_realloc (Numeric->Memory, newsize, sizeof (Unit)) ; if (!mnew) { if (newsize == minsize) /* last realloc attempt failed */ { /* We failed to get the minimum. Just stick with the */ /* current allocation and hope that garbage collection */ /* can recover enough space. */ mnew = Numeric->Memory ; /* no new memory available */ newsize = Numeric->size ; } else { /* otherwise, reduce the request and keep trying */ newsize = (Int) (UMF_REALLOC_REDUCTION * ((double) newsize)) ; newsize = MAX (minsize, newsize) ; } } } ASSERT (mnew != (Unit *) NULL) ; /* see if realloc had to copy, rather than just extend memory */ costly = (mnew != Numeric->Memory) ; /* ---------------------------------------------------------------------- */ /* extend the tail portion of memory downwards */ /* ---------------------------------------------------------------------- */ Numeric->Memory = mnew ; if (Work->E [0]) { Int nb, dr, dc ; nb = Work->nb ; dr = Work->fnr_curr ; dc = Work->fnc_curr ; Work->Flublock = (Entry *) (Numeric->Memory + Work->E [0]) ; Work->Flblock = Work->Flublock + nb * nb ; Work->Fublock = Work->Flblock + dr * nb ; Work->Fcblock = Work->Fublock + nb * dc ; DEBUG0 (("after realloc E [0] "ID"\n", Work->E [0])) ; } ASSERT (IMPLIES (!(Work->E [0]), Work->Flublock == (Entry *) NULL)) ; newmem = newsize - Numeric->size ; ASSERT (newmem == 0 || newmem >= 2) ; if (newmem >= 2) { /* reallocation succeeded */ /* point to the old tail marker block of size 1 + header */ p = Numeric->Memory + Numeric->size - 2 ; /* create a new block out of the newly extended memory */ p->header.size = newmem - 1 ; i = Numeric->size - 1 ; p += newmem ; /* create a new tail marker block */ p->header.prevsize = newmem - 1 ; p->header.size = 1 ; Numeric->size = newsize ; /* free the new block */ UMF_mem_free_tail_block (Numeric, i) ; Numeric->nrealloc++ ; if (costly) { Numeric->ncostly++ ; } } DEBUG1 (("Done with realloc memory\n")) ; /* ---------------------------------------------------------------------- */ /* garbage collection on the tail of Numeric->memory (destroys tuples) */ /* ---------------------------------------------------------------------- */ UMF_garbage_collection (Numeric, Work, r2, c2, do_Fcpos) ; /* ---------------------------------------------------------------------- */ /* rebuild the tuples */ /* ---------------------------------------------------------------------- */ return (UMF_build_tuples (Numeric, Work)) ; } SuiteSparse/UMFPACK/Source/umf_get_memory.h0000644001170100242450000000104010617161601017456 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_get_memory ( NumericType *Numeric, WorkType *Work, Int needunits, Int r2, Int c2, Int do_Fcpos ) ; SuiteSparse/UMFPACK/Source/umf_2by2.c0000644001170100242450000005620410677541510016103 0ustar davisfac/* ========================================================================== */ /* === UMF_2by2 ============================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Not user-callable. Computes a row permutation P so that A (P,:) has a * mostly zero-free diagonal, with large entries on the diagonal. It does this * by swapping pairs of rows. Once a row is swapped it is not swapped again. * This is a "cheap" assignment, not a complete max. transversal or * bi-partite matching. It is only a partial matching. For most matrices * for which this algorithm is used, however, the matching is complete (in * UMFPACK this algorithm is used for matrices with roughly symmetric pattern, * and these matrices typically have a mostly-zero-free diagonal to begin with. * This algorithm is not meant to be used on arbitrary unsymmetric matrices * (for those matrices, UMFPACK uses its unsymmetric strategy and does not * use this algorithm). * * Even if incomplete, the matching is usually good enough for UMFPACK's * symmetric strategy, which can easily pivot off the diagonal during numerical * factorization if it finds a weak diagonal entry. * * The algorithms works as follows. First, row scaling factors are computed, * and weak diagonal entries are found. A weak entry is a value A(k,k) whose * absolute value is < tol * max (abs (A (:,k))). For each weak diagonal k in * increasing order of degree in A+A', the algorithm finds an index j such * that A (k,j) and A (j,k) are "large" (greater than or equal to tol times * the largest magnitude in their columns). Row j must also not have already * been swapped. Rows j and k are then swapped. If we come to a diagonal k * that has already been swapped, then it is not modified. This case occurs * for "oxo" pivots: * * k j * k o x * j x o * * which are swapped once to obtain * * k j * j x o * k o x * * These two rows are then not modified any further (A (j,j) was weak, but * after one swap the permuted the jth diagonal entry is strong. * * This algorithm only works on square matrices (real, complex, or pattern- * only). The numerical values are optional. If not present, each entry is * treated as numerically acceptable (tol is ignored), and the algorithm * operates by just using the pattern, not the values. Each column of the * input matrix A must be sorted, with no duplicate entries. The matrix A * can be optionally scaled prior to the numerical test. The matrix A (:,P) * has the same diagonal entries as A (:,P), except in different order. So * the output permutation P can also be used to swap the columns of A. */ #include "umf_internal.h" #include "umf_2by2.h" #ifndef NDEBUG #include "umf_is_permutation.h" #endif /* x is "weak" if it is less than ctol. If x or ctol are NaN, then define * x as not "weak". This is a rather arbitrary choice, made to simplify the * computation. On all but a PC with Microsoft C/C++, this test becomes * ((x) - ctol < 0). */ #define WEAK(x,ctol) (SCALAR_IS_LTZERO ((x)-(ctol))) /* For flag value in Next [col] */ #define IS_WEAK -2 /* ========================================================================== */ /* === two_by_two =========================================================== */ /* ========================================================================== */ PRIVATE Int two_by_two /* returns # unmatched weak diagonals */ ( /* input, not modified */ Int n2, /* C is n2-by-n2 */ Int Cp [ ], /* size n2+1, column pointers for C */ Int Ci [ ], /* size snz = Cp [n2], row indices for C */ Int Degree [ ], /* Degree [i] = degree of row i of C+C' */ /* input, not defined on output */ Int Next [ ], /* Next [k] == IS_WEAK if k is a weak diagonal */ Int Ri [ ], /* Ri [i] is the length of row i in C */ /* output, not defined on input */ Int P [ ], /* workspace, not defined on input or output */ Int Rp [ ], Int Head [ ] ) { Int deg, newcol, row, col, p, p2, unmatched, k, j, j2, j_best, best, jdiff, jdiff_best, jdeg, jdeg_best, cp, cp1, cp2, rp, rp1, rp2, maxdeg, mindeg ; /* ---------------------------------------------------------------------- */ /* place weak diagonals in the degree lists */ /* ---------------------------------------------------------------------- */ for (deg = 0 ; deg < n2 ; deg++) { Head [deg] = EMPTY ; } maxdeg = 0 ; mindeg = Int_MAX ; for (newcol = n2-1 ; newcol >= 0 ; newcol--) { if (Next [newcol] == IS_WEAK) { /* add this column to the list of weak nodes */ DEBUGm1 ((" newcol "ID" has a weak diagonal deg "ID"\n", newcol, deg)) ; deg = Degree [newcol] ; ASSERT (deg >= 0 && deg < n2) ; Next [newcol] = Head [deg] ; Head [deg] = newcol ; maxdeg = MAX (maxdeg, deg) ; mindeg = MIN (mindeg, deg) ; } } /* ---------------------------------------------------------------------- */ /* construct R = C' (C = strong entries in pruned submatrix) */ /* ---------------------------------------------------------------------- */ /* Ri [0..n2-1] is the length of each row of R */ /* use P as temporary pointer into the row form of R [ */ Rp [0] = 0 ; for (row = 0 ; row < n2 ; row++) { Rp [row+1] = Rp [row] + Ri [row] ; P [row] = Rp [row] ; } /* Ri no longer needed for row counts */ /* all entries in C are strong */ for (col = 0 ; col < n2 ; col++) { p2 = Cp [col+1] ; for (p = Cp [col] ; p < p2 ; p++) { /* place the column index in row = Ci [p] */ Ri [P [Ci [p]]++] = col ; } } /* contents of P no longer needed ] */ #ifndef NDEBUG DEBUG0 (("==================R: row form of strong entries in A:\n")) ; UMF_dump_col_matrix ((double *) NULL, #ifdef COMPLEX (double *) NULL, #endif Ri, Rp, n2, n2, Rp [n2]) ; #endif ASSERT (AMD_valid (n2, n2, Rp, Ri) == AMD_OK) ; /* ---------------------------------------------------------------------- */ /* for each weak diagonal, find a pair of strong off-diagonal entries */ /* ---------------------------------------------------------------------- */ for (row = 0 ; row < n2 ; row++) { P [row] = EMPTY ; } unmatched = 0 ; best = EMPTY ; jdiff = EMPTY ; jdeg = EMPTY ; for (deg = mindeg ; deg <= maxdeg ; deg++) { /* find the next weak diagonal of lowest degree */ DEBUGm2 (("---------------------------------- Deg: "ID"\n", deg)) ; for (k = Head [deg] ; k != EMPTY ; k = Next [k]) { DEBUGm2 (("k: "ID"\n", k)) ; if (P [k] == EMPTY) { /* C (k,k) is a weak diagonal entry. Find an index j != k such * that C (j,k) and C (k,j) are both strong, and also such * that Degree [j] is minimized. In case of a tie, pick * the smallest index j. C and R contain the pattern of * strong entries only. * * Note that row k of R and column k of C are both sorted. */ DEBUGm4 (("===== Weak diagonal k = "ID"\n", k)) ; DEBUG1 (("Column k of C:\n")) ; for (p = Cp [k] ; p < Cp [k+1] ; p++) { DEBUG1 ((" "ID": deg "ID"\n", Ci [p], Degree [Ci [p]])); } DEBUG1 (("Row k of R (strong entries only):\n")) ; for (p = Rp [k] ; p < Rp [k+1] ; p++) { DEBUG1 ((" "ID": deg "ID"\n", Ri [p], Degree [Ri [p]])); } /* no (C (k,j), C (j,k)) pair exists yet */ j_best = EMPTY ; jdiff_best = Int_MAX ; jdeg_best = Int_MAX ; /* pointers into column k (including values) */ cp1 = Cp [k] ; cp2 = Cp [k+1] ; cp = cp1 ; /* pointers into row k (strong entries only, no values) */ rp1 = Rp [k] ; rp2 = Rp [k+1] ; rp = rp1 ; /* while entries searched in column k and row k */ while (TRUE) { if (cp >= cp2) { /* no more entries in this column */ break ; } /* get C (j,k), which is strong */ j = Ci [cp] ; if (rp >= rp2) { /* no more entries in this column */ break ; } /* get R (k,j2), which is strong */ j2 = Ri [rp] ; if (j < j2) { /* C (j,k) is strong, but R (k,j) is not strong */ cp++ ; continue ; } if (j2 < j) { /* C (k,j2) is strong, but R (j2,k) is not strong */ rp++ ; continue ; } /* j == j2: C (j,k) is strong and R (k,j) is strong */ best = FALSE ; if (P [j] == EMPTY) { /* j has not yet been matched */ jdeg = Degree [j] ; jdiff = SCALAR_ABS (k-j) ; DEBUG1 (("Try candidate j "ID" deg "ID" diff "ID "\n", j, jdeg, jdiff)) ; if (j_best == EMPTY) { /* this is the first candidate seen */ DEBUG1 ((" first\n")) ; best = TRUE ; } else { if (jdeg < jdeg_best) { /* the degree of j is best seen so far. */ DEBUG1 ((" least degree\n")) ; best = TRUE ; } else if (jdeg == jdeg_best) { /* degree of j and j_best are the same */ /* tie break by nearest node number */ if (jdiff < jdiff_best) { DEBUG1 ((" tie degree, closer\n")) ; best = TRUE ; } else if (jdiff == jdiff_best) { /* |j-k| = |j_best-k|. For any given k * and j_best there is only one other j * than can be just as close as j_best. * Tie break by picking the smaller of * j and j_best */ DEBUG1 ((" tie degree, as close\n")); best = j < j_best ; } } else { /* j has higher degree than best so far */ best = FALSE ; } } } if (best) { /* j is best match for k */ /* found a strong pair, A (j,k) and A (k,j) */ DEBUG1 ((" --- Found pair k: "ID" j: " ID " jdeg: "ID" jdiff: "ID"\n", k, j, jdeg, jdiff)) ; ASSERT (jdiff != EMPTY) ; ASSERT (jdeg != EMPTY) ; j_best = j ; jdeg_best = jdeg ; jdiff_best = jdiff ; } /* get the next entries in column k and row k */ cp++ ; rp++ ; } /* save the pair (j,k), if we found one */ if (j_best != EMPTY) { j = j_best ; DEBUGm4 ((" --- best pair j: "ID" for k: "ID"\n", j, k)) ; P [k] = j ; P [j] = k ; } else { /* no match was found for k */ unmatched++ ; } } } } /* ---------------------------------------------------------------------- */ /* finalize the row permutation, P */ /* ---------------------------------------------------------------------- */ for (k = 0 ; k < n2 ; k++) { if (P [k] == EMPTY) { P [k] = k ; } } ASSERT (UMF_is_permutation (P, Rp, n2, n2)) ; return (unmatched) ; } /* ========================================================================== */ /* === UMF_2by2 ============================================================= */ /* ========================================================================== */ GLOBAL void UMF_2by2 ( /* input, not modified: */ Int n, /* A is n-by-n */ const Int Ap [ ], /* size n+1 */ const Int Ai [ ], /* size nz = Ap [n] */ const double Ax [ ], /* size nz if present */ #ifdef COMPLEX const double Az [ ], /* size nz if present */ #endif double tol, /* tolerance for determining whether or not an * entry is numerically acceptable. If tol <= 0 * then all numerical values ignored. */ Int scale, /* scaling to perform (none, sum, or max) */ Int Cperm1 [ ], /* singleton permutations */ #ifndef NDEBUG Int Rperm1 [ ], /* not needed, since Rperm1 = Cperm1 for submatrix S */ #endif Int InvRperm1 [ ], /* inverse of Rperm1 */ Int n1, /* number of singletons */ Int nempty, /* number of empty rows/cols */ /* input, contents undefined on output: */ Int Degree [ ], /* Degree [j] is the number of off-diagonal * entries in row/column j of S+S', where * where S = A (Cperm1 [n1..], Rperm1 [n1..]). * Note that S is not used, nor formed. */ /* output: */ Int P [ ], /* P [k] = i means original row i is kth row in S(P,:) * where S = A (Cperm1 [n1..], Rperm1 [n1..]) */ Int *p_nweak, Int *p_unmatched, /* workspace (not defined on input or output): */ Int Ri [ ], /* of size >= max (nz, n) */ Int Rp [ ], /* of size n+1 */ double Rs [ ], /* of size n if present. Rs = sum (abs (A),2) or * max (abs (A),2), the sum or max of each row. Unused * if scale is equal to UMFPACK_SCALE_NONE. */ Int Head [ ], /* of size n. Head pointers for bucket sort */ Int Next [ ], /* of size n. Next pointers for bucket sort */ Int Ci [ ], /* size nz */ Int Cp [ ] /* size n+1 */ ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Entry aij ; double cmax, value, rs, ctol, dvalue ; Int k, p, row, col, do_values, do_sum, do_max, do_scale, nweak, weak, p1, p2, dfound, unmatched, n2, oldrow, newrow, oldcol, newcol, pp ; #ifdef COMPLEX Int split = SPLIT (Az) ; #endif #ifndef NRECIPROCAL Int do_recip = FALSE ; #endif #ifndef NDEBUG /* UMF_debug += 99 ; */ DEBUGm3 (("\n ==================================UMF_2by2: tol %g\n", tol)) ; ASSERT (AMD_valid (n, n, Ap, Ai) == AMD_OK) ; for (k = n1 ; k < n - nempty ; k++) { ASSERT (Cperm1 [k] == Rperm1 [k]) ; } #endif /* ---------------------------------------------------------------------- */ /* determine scaling options */ /* ---------------------------------------------------------------------- */ /* use the values, but only if they are present */ /* ignore the values if tol <= 0 */ do_values = (tol > 0) && (Ax != (double *) NULL) ; if (do_values && (Rs != (double *) NULL)) { do_sum = (scale == UMFPACK_SCALE_SUM) ; do_max = (scale == UMFPACK_SCALE_MAX) ; } else { /* no scaling */ do_sum = FALSE ; do_max = FALSE ; } do_scale = do_max || do_sum ; DEBUGm3 (("do_values "ID" do_sum "ID" do_max "ID" do_scale "ID"\n", do_values, do_sum, do_max, do_scale)) ; /* ---------------------------------------------------------------------- */ /* compute the row scaling, if requested */ /* ---------------------------------------------------------------------- */ /* see also umf_kernel_init */ if (do_scale) { #ifndef NRECIPROCAL double rsmin ; #endif for (row = 0 ; row < n ; row++) { Rs [row] = 0.0 ; } for (col = 0 ; col < n ; col++) { p2 = Ap [col+1] ; for (p = Ap [col] ; p < p2 ; p++) { row = Ai [p] ; ASSIGN (aij, Ax, Az, p, split) ; APPROX_ABS (value, aij) ; rs = Rs [row] ; if (!SCALAR_IS_NAN (rs)) { if (SCALAR_IS_NAN (value)) { /* if any entry in a row is NaN, then the scale factor * for the row is NaN. It will be set to 1 later. */ Rs [row] = value ; } else if (do_max) { Rs [row] = MAX (rs, value) ; } else { Rs [row] += value ; } } } } #ifndef NRECIPROCAL rsmin = Rs [0] ; if (SCALAR_IS_ZERO (rsmin) || SCALAR_IS_NAN (rsmin)) { rsmin = 1.0 ; } #endif for (row = 0 ; row < n ; row++) { /* do not scale an empty row, or a row with a NaN */ rs = Rs [row] ; if (SCALAR_IS_ZERO (rs) || SCALAR_IS_NAN (rs)) { Rs [row] = 1.0 ; } #ifndef NRECIPROCAL rsmin = MIN (rsmin, Rs [row]) ; #endif } #ifndef NRECIPROCAL /* multiply by the reciprocal if Rs is not too small */ do_recip = (rsmin >= RECIPROCAL_TOLERANCE) ; if (do_recip) { /* invert the scale factors */ for (row = 0 ; row < n ; row++) { Rs [row] = 1.0 / Rs [row] ; } } #endif } /* ---------------------------------------------------------------------- */ /* compute the max in each column and find diagonal */ /* ---------------------------------------------------------------------- */ nweak = 0 ; #ifndef NDEBUG for (k = 0 ; k < n ; k++) { ASSERT (Rperm1 [k] >= 0 && Rperm1 [k] < n) ; ASSERT (InvRperm1 [Rperm1 [k]] == k) ; } #endif n2 = n - n1 - nempty ; /* use Ri to count the number of strong entries in each row */ for (row = 0 ; row < n2 ; row++) { Ri [row] = 0 ; } pp = 0 ; ctol = 0 ; dvalue = 1 ; /* construct C = pruned submatrix, strong values only, column form */ for (k = n1 ; k < n - nempty ; k++) { oldcol = Cperm1 [k] ; newcol = k - n1 ; Next [newcol] = EMPTY ; DEBUGm1 (("Column "ID" newcol "ID" oldcol "ID"\n", k, newcol, oldcol)) ; Cp [newcol] = pp ; dfound = FALSE ; p1 = Ap [oldcol] ; p2 = Ap [oldcol+1] ; if (do_values) { cmax = 0 ; dvalue = 0 ; if (!do_scale) { /* no scaling */ for (p = p1 ; p < p2 ; p++) { oldrow = Ai [p] ; ASSERT (oldrow >= 0 && oldrow < n) ; newrow = InvRperm1 [oldrow] - n1 ; ASSERT (newrow >= -n1 && newrow < n2) ; if (newrow < 0) continue ; ASSIGN (aij, Ax, Az, p, split) ; APPROX_ABS (value, aij) ; /* if either cmax or value is NaN, define cmax as NaN */ if (!SCALAR_IS_NAN (cmax)) { if (SCALAR_IS_NAN (value)) { cmax = value ; } else { cmax = MAX (cmax, value) ; } } if (oldrow == oldcol) { /* we found the diagonal entry in this column */ dvalue = value ; dfound = TRUE ; ASSERT (newrow == newcol) ; } } } #ifndef NRECIPROCAL else if (do_recip) { /* multiply by the reciprocal */ for (p = p1 ; p < p2 ; p++) { oldrow = Ai [p] ; ASSERT (oldrow >= 0 && oldrow < n) ; newrow = InvRperm1 [oldrow] - n1 ; ASSERT (newrow >= -n1 && newrow < n2) ; if (newrow < 0) continue ; ASSIGN (aij, Ax, Az, p, split) ; APPROX_ABS (value, aij) ; value *= Rs [oldrow] ; /* if either cmax or value is NaN, define cmax as NaN */ if (!SCALAR_IS_NAN (cmax)) { if (SCALAR_IS_NAN (value)) { cmax = value ; } else { cmax = MAX (cmax, value) ; } } if (oldrow == oldcol) { /* we found the diagonal entry in this column */ dvalue = value ; dfound = TRUE ; ASSERT (newrow == newcol) ; } } } #endif else { /* divide instead */ for (p = p1 ; p < p2 ; p++) { oldrow = Ai [p] ; ASSERT (oldrow >= 0 && oldrow < n) ; newrow = InvRperm1 [oldrow] - n1 ; ASSERT (newrow >= -n1 && newrow < n2) ; if (newrow < 0) continue ; ASSIGN (aij, Ax, Az, p, split) ; APPROX_ABS (value, aij) ; value /= Rs [oldrow] ; /* if either cmax or value is NaN, define cmax as NaN */ if (!SCALAR_IS_NAN (cmax)) { if (SCALAR_IS_NAN (value)) { cmax = value ; } else { cmax = MAX (cmax, value) ; } } if (oldrow == oldcol) { /* we found the diagonal entry in this column */ dvalue = value ; dfound = TRUE ; ASSERT (newrow == newcol) ; } } } ctol = tol * cmax ; DEBUGm1 ((" cmax col "ID" %g ctol %g\n", oldcol, cmax, ctol)) ; } else { for (p = p1 ; p < p2 ; p++) { oldrow = Ai [p] ; ASSERT (oldrow >= 0 && oldrow < n) ; newrow = InvRperm1 [oldrow] - n1 ; ASSERT (newrow >= -n1 && newrow < n2) ; if (newrow < 0) continue ; Ci [pp++] = newrow ; if (oldrow == oldcol) { /* we found the diagonal entry in this column */ ASSERT (newrow == newcol) ; dfound = TRUE ; } /* count the entries in each column */ Ri [newrow]++ ; } } /* ------------------------------------------------------------------ */ /* flag the weak diagonals */ /* ------------------------------------------------------------------ */ if (!dfound) { /* no diagonal entry present */ weak = TRUE ; } else { /* diagonal entry is present, check its value */ weak = (do_values) ? WEAK (dvalue, ctol) : FALSE ; } if (weak) { /* flag this column as weak */ DEBUG0 (("Weak!\n")) ; Next [newcol] = IS_WEAK ; nweak++ ; } /* ------------------------------------------------------------------ */ /* count entries in each row that are not numerically weak */ /* ------------------------------------------------------------------ */ if (do_values) { if (!do_scale) { /* no scaling */ for (p = p1 ; p < p2 ; p++) { oldrow = Ai [p] ; newrow = InvRperm1 [oldrow] - n1 ; if (newrow < 0) continue ; ASSIGN (aij, Ax, Az, p, split) ; APPROX_ABS (value, aij) ; weak = WEAK (value, ctol) ; if (!weak) { DEBUG0 ((" strong: row "ID": %g\n", oldrow, value)) ; Ci [pp++] = newrow ; Ri [newrow]++ ; } } } #ifndef NRECIPROCAL else if (do_recip) { /* multiply by the reciprocal */ for (p = p1 ; p < p2 ; p++) { oldrow = Ai [p] ; newrow = InvRperm1 [oldrow] - n1 ; if (newrow < 0) continue ; ASSIGN (aij, Ax, Az, p, split) ; APPROX_ABS (value, aij) ; value *= Rs [oldrow] ; weak = WEAK (value, ctol) ; if (!weak) { DEBUG0 ((" strong: row "ID": %g\n", oldrow, value)) ; Ci [pp++] = newrow ; Ri [newrow]++ ; } } } #endif else { /* divide instead */ for (p = p1 ; p < p2 ; p++) { oldrow = Ai [p] ; newrow = InvRperm1 [oldrow] - n1 ; if (newrow < 0) continue ; ASSIGN (aij, Ax, Az, p, split) ; APPROX_ABS (value, aij) ; value /= Rs [oldrow] ; weak = WEAK (value, ctol) ; if (!weak) { DEBUG0 ((" strong: row "ID": %g\n", oldrow, value)) ; Ci [pp++] = newrow ; Ri [newrow]++ ; } } } } } Cp [n2] = pp ; ASSERT (AMD_valid (n2, n2, Cp, Ci) == AMD_OK) ; if (nweak == 0) { /* nothing to do, quick return */ DEBUGm2 (("\n =============================UMF_2by2: quick return\n")) ; for (k = 0 ; k < n ; k++) { P [k] = k ; } *p_nweak = 0 ; *p_unmatched = 0 ; return ; } #ifndef NDEBUG for (k = 0 ; k < n2 ; k++) { P [k] = EMPTY ; } for (k = 0 ; k < n2 ; k++) { ASSERT (Degree [k] >= 0 && Degree [k] < n2) ; } #endif /* ---------------------------------------------------------------------- */ /* find the 2-by-2 permutation */ /* ---------------------------------------------------------------------- */ /* The matrix S is now mapped to the index range 0 to n2-1. We have * S = A (Rperm [n1 .. n-nempty-1], Cperm [n1 .. n-nempty-1]), and then * C = pattern of strong entries in S. A weak diagonal k in S is marked * with Next [k] = IS_WEAK. */ unmatched = two_by_two (n2, Cp, Ci, Degree, Next, Ri, P, Rp, Head) ; /* ---------------------------------------------------------------------- */ *p_nweak = nweak ; *p_unmatched = unmatched ; #ifndef NDEBUG DEBUGm4 (("UMF_2by2: weak "ID" unmatched "ID"\n", nweak, unmatched)) ; for (row = 0 ; row < n ; row++) { DEBUGm2 (("P ["ID"] = "ID"\n", row, P [row])) ; } DEBUGm2 (("\n =============================UMF_2by2: done\n\n")) ; #endif } SuiteSparse/UMFPACK/Source/umf_2by2.h0000644001170100242450000000157710617161320016102 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL void UMF_2by2 ( Int n, const Int Ap [ ], const Int Ai [ ], const double Ax [ ], #ifdef COMPLEX const double Az [ ], #endif double tol, Int scale, Int Cperm1 [ ], #ifndef NDEBUG Int Rperm1 [ ], #endif Int InvRperm [ ], Int n1, Int nempty, Int Degree [ ], Int P [ ], Int *p_nweak, Int *p_nmatched, Int Ri [ ], Int Rp [ ], double Rs [ ], Int Head [ ], Int Next [ ], Int Si [ ], Int Sp [ ] ) ; SuiteSparse/UMFPACK/Source/umfpack_get_symbolic.c0000644001170100242450000001002310617162061020623 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_get_symbolic ================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Gets the symbolic information held in the Symbolic object. See umfpack_get_symbolic.h for a more detailed description. */ #include "umf_internal.h" #include "umf_valid_symbolic.h" GLOBAL Int UMFPACK_get_symbolic ( Int *p_n_row, Int *p_n_col, Int *p_n1, /* number of singletons */ Int *p_nz, Int *p_nfr, Int *p_nchains, Int P [ ], Int Q [ ], Int Front_npivcol [ ], Int Front_parent [ ], Int Front_1strow [ ], Int Front_leftmostdesc [ ], Int Chain_start [ ], Int Chain_maxrows [ ], Int Chain_maxcols [ ], void *SymbolicHandle ) { SymbolicType *Symbolic ; Int k, n_row, n_col, n1, nfr, nchains, *p ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ Symbolic = (SymbolicType *) SymbolicHandle ; if (!UMF_valid_symbolic (Symbolic)) { return (UMFPACK_ERROR_invalid_Symbolic_object) ; } /* ---------------------------------------------------------------------- */ /* get contents of Symbolic */ /* ---------------------------------------------------------------------- */ n_row = Symbolic->n_row ; n_col = Symbolic->n_col ; n1 = Symbolic->n1 ; nfr = Symbolic->nfr ; nchains = Symbolic->nchains ; if (p_n_row) { *p_n_row = n_row ; } if (p_n_col) { *p_n_col = n_col ; } if (p_n1) { *p_n1 = n1 ; } if (p_nz) { *p_nz = Symbolic->nz ; } if (p_nfr) { *p_nfr = nfr ; } if (p_nchains) { *p_nchains = nchains ; } if (P != (Int *) NULL) { Int *Rperm_init, *Diagonal_map ; Rperm_init = Symbolic->Rperm_init ; Diagonal_map = Symbolic->Diagonal_map ; if (Diagonal_map != (Int *) NULL) { ASSERT (n_row == n_col) ; /* next pivot rows are found in the diagonal map */ for (k = 0 ; k < n_row ; k++) { P [k] = Rperm_init [Diagonal_map [k]] ; } } else { /* there is no diagonal map. */ for (k = 0 ; k < n_row ; k++) { P [k] = Rperm_init [k] ; } } } if (Q != (Int *) NULL) { p = Symbolic->Cperm_init ; for (k = 0 ; k < n_col ; k++) { Q [k] = p [k] ; } } if (Front_npivcol != (Int *) NULL) { p = Symbolic->Front_npivcol ; for (k = 0 ; k <= nfr ; k++) { Front_npivcol [k] = p [k] ; } } if (Front_parent != (Int *) NULL) { p = Symbolic->Front_parent ; for (k = 0 ; k <= nfr ; k++) { Front_parent [k] = p [k] ; } } if (Front_1strow != (Int *) NULL) { p = Symbolic->Front_1strow ; for (k = 0 ; k <= nfr ; k++) { Front_1strow [k] = p [k] ; } } if (Front_leftmostdesc != (Int *) NULL) { p = Symbolic->Front_leftmostdesc ; for (k = 0 ; k <= nfr ; k++) { Front_leftmostdesc [k] = p [k] ; } } if (Chain_start != (Int *) NULL) { p = Symbolic->Chain_start ; for (k = 0 ; k <= nchains ; k++) { Chain_start [k] = p [k] ; } } if (Chain_maxrows != (Int *) NULL) { p = Symbolic->Chain_maxrows ; for (k = 0 ; k < nchains ; k++) { Chain_maxrows [k] = p [k] ; } Chain_maxrows [nchains] = 0 ; } if (Chain_maxcols != (Int *) NULL) { p = Symbolic->Chain_maxcols ; for (k = 0 ; k < nchains ; k++) { Chain_maxcols [k] = p [k] ; } Chain_maxcols [nchains] = 0 ; } return (UMFPACK_OK) ; } SuiteSparse/UMFPACK/Source/umf_report_vector.c0000644001170100242450000000533110677542325020222 0ustar davisfac/* ========================================================================== */ /* === UMF_report_vector ==================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ #include "umf_internal.h" #include "umf_report_vector.h" /* ========================================================================== */ /* === print_value ========================================================== */ /* ========================================================================== */ PRIVATE void print_value ( Int i, const double Xx [ ], const double Xz [ ], /* used for complex case only */ Int scalar /* if true, then print real part only */ ) { Entry xi ; /* if Xz is null, then X is in "merged" format (compatible with Entry, */ /* and ANSI C99 double _Complex type). */ PRINTF ((" "ID" :", INDEX (i))) ; if (scalar) { PRINT_SCALAR (Xx [i]) ; } else { ASSIGN (xi, Xx, Xz, i, SPLIT (Xz)) ; PRINT_ENTRY (xi) ; } PRINTF (("\n")) ; } /* ========================================================================== */ /* === UMF_report_vector ==================================================== */ /* ========================================================================== */ GLOBAL Int UMF_report_vector ( Int n, const double Xx [ ], const double Xz [ ], Int prl, Int user, Int scalar ) { Int n2, i ; if (user || prl >= 4) { PRINTF (("dense vector, n = "ID". ", n)) ; } if (user) { if (!Xx) { PRINTF (("ERROR: vector not present\n\n")) ; return (UMFPACK_ERROR_argument_missing) ; } if (n < 0) { PRINTF (("ERROR: length of vector is < 0\n\n")) ; return (UMFPACK_ERROR_n_nonpositive) ; } } if (user || prl >= 4) { PRINTF4 (("\n")) ; } if (prl == 4) { /* print level of 4 */ n2 = MIN (10, n) ; for (i = 0 ; i < n2 ; i++) { print_value (i, Xx, Xz, scalar) ; } if (n2 < n) { PRINTF ((" ...\n")) ; print_value (n-1, Xx, Xz, scalar) ; } } else if (prl > 4) { /* print level 4 or more */ for (i = 0 ; i < n ; i++) { print_value (i, Xx, Xz, scalar) ; } } PRINTF4 ((" dense vector ")) ; if (user || prl >= 4) { PRINTF (("OK\n\n")) ; } return (UMFPACK_OK) ; } SuiteSparse/UMFPACK/Source/umf_report_vector.h0000644001170100242450000000104010617162235020210 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_report_vector ( Int n, const double Xx [ ], const double Xz [ ], Int prl, Int user, Int scalar ) ; SuiteSparse/UMFPACK/Source/umf_utsolve.c0000644001170100242450000002213610677541167017033 0ustar davisfac/* ========================================================================== */ /* === UMF_utsolve ========================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* solves U'x = b or U.'x=b, where U is the upper triangular factor of a */ /* matrix. B is overwritten with the solution X. */ /* Returns the floating point operation count */ #include "umf_internal.h" #include "umf_utsolve.h" GLOBAL double #ifdef CONJUGATE_SOLVE UMF_uhsolve /* solve U'x=b (complex conjugate transpose) */ #else UMF_utsolve /* solve U.'x=b (array transpose) */ #endif ( NumericType *Numeric, Entry X [ ], /* b on input, solution x on output */ Int Pattern [ ] /* a work array of size n */ ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Entry xk ; Entry *xp, *D, *Uval ; Int k, deg, j, *ip, col, *Upos, *Uilen, kstart, kend, up, *Uip, n, uhead, ulen, pos, npiv, n1, *Ui ; /* ---------------------------------------------------------------------- */ /* get parameters */ /* ---------------------------------------------------------------------- */ if (Numeric->n_row != Numeric->n_col) return (0.) ; n = Numeric->n_row ; npiv = Numeric->npiv ; Upos = Numeric->Upos ; Uilen = Numeric->Uilen ; Uip = Numeric->Uip ; D = Numeric->D ; kend = 0 ; n1 = Numeric->n1 ; #ifndef NDEBUG DEBUG4 (("Utsolve start: npiv "ID" n "ID"\n", npiv, n)) ; for (j = 0 ; j < n ; j++) { DEBUG4 (("Utsolve start "ID": ", j)) ; EDEBUG4 (X [j]) ; DEBUG4 (("\n")) ; } #endif /* ---------------------------------------------------------------------- */ /* singletons */ /* ---------------------------------------------------------------------- */ for (k = 0 ; k < n1 ; k++) { DEBUG4 (("Singleton k "ID"\n", k)) ; #ifndef NO_DIVIDE_BY_ZERO /* Go ahead and divide by zero if D [k] is zero. */ #ifdef CONJUGATE_SOLVE /* xk = X [k] / conjugate (D [k]) ; */ DIV_CONJ (xk, X [k], D [k]) ; #else /* xk = X [k] / D [k] ; */ DIV (xk, X [k], D [k]) ; #endif #else /* Do not divide by zero */ if (IS_NONZERO (D [k])) { #ifdef CONJUGATE_SOLVE /* xk = X [k] / conjugate (D [k]) ; */ DIV_CONJ (xk, X [k], D [k]) ; #else /* xk = X [k] / D [k] ; */ DIV (xk, X [k], D [k]) ; #endif } #endif X [k] = xk ; deg = Uilen [k] ; if (deg > 0 && IS_NONZERO (xk)) { up = Uip [k] ; Ui = (Int *) (Numeric->Memory + up) ; up += UNITS (Int, deg) ; Uval = (Entry *) (Numeric->Memory + up) ; for (j = 0 ; j < deg ; j++) { DEBUG4 ((" k "ID" col "ID" value", k, Ui [j])) ; EDEBUG4 (Uval [j]) ; DEBUG4 (("\n")) ; #ifdef CONJUGATE_SOLVE /* X [Ui [j]] -= xk * conjugate (Uval [j]) ; */ MULT_SUB_CONJ (X [Ui [j]], xk, Uval [j]) ; #else /* X [Ui [j]] -= xk * Uval [j] ; */ MULT_SUB (X [Ui [j]], xk, Uval [j]) ; #endif } } } /* ---------------------------------------------------------------------- */ /* nonsingletons */ /* ---------------------------------------------------------------------- */ for (kstart = n1 ; kstart < npiv ; kstart = kend + 1) { /* ------------------------------------------------------------------ */ /* find the end of this Uchain */ /* ------------------------------------------------------------------ */ DEBUG4 (("kstart "ID" kend "ID"\n", kstart, kend)) ; /* for (kend = kstart ; kend < npiv && Uip [kend+1] > 0 ; kend++) ; */ kend = kstart ; while (kend < npiv && Uip [kend+1] > 0) { kend++ ; } /* ------------------------------------------------------------------ */ /* scan the whole Uchain to find the pattern of the first row of U */ /* ------------------------------------------------------------------ */ k = kend+1 ; DEBUG4 (("\nKend "ID" K "ID"\n", kend, k)) ; /* ------------------------------------------------------------------ */ /* start with last row in Uchain of U in Pattern [0..deg-1] */ /* ------------------------------------------------------------------ */ if (k == npiv) { deg = Numeric->ulen ; if (deg > 0) { /* :: make last pivot row of U (singular matrices only) :: */ for (j = 0 ; j < deg ; j++) { Pattern [j] = Numeric->Upattern [j] ; } } } else { ASSERT (k >= 0 && k < npiv) ; up = -Uip [k] ; ASSERT (up > 0) ; deg = Uilen [k] ; DEBUG4 (("end of chain for row of U "ID" deg "ID"\n", k-1, deg)) ; ip = (Int *) (Numeric->Memory + up) ; for (j = 0 ; j < deg ; j++) { col = *ip++ ; DEBUG4 ((" k "ID" col "ID"\n", k-1, col)) ; ASSERT (k <= col) ; Pattern [j] = col ; } } /* empty the stack at the bottom of Pattern */ uhead = n ; for (k = kend ; k > kstart ; k--) { /* Pattern [0..deg-1] is the pattern of row k of U */ /* -------------------------------------------------------------- */ /* make row k-1 of U in Pattern [0..deg-1] */ /* -------------------------------------------------------------- */ ASSERT (k >= 0 && k < npiv) ; ulen = Uilen [k] ; /* delete, and push on the stack */ for (j = 0 ; j < ulen ; j++) { ASSERT (uhead >= deg) ; Pattern [--uhead] = Pattern [--deg] ; } DEBUG4 (("middle of chain for row of U "ID" deg "ID"\n", k, deg)) ; ASSERT (deg >= 0) ; pos = Upos [k] ; if (pos != EMPTY) { /* add the pivot column */ DEBUG4 (("k "ID" add pivot entry at position "ID"\n", k, pos)) ; ASSERT (pos >= 0 && pos <= deg) ; Pattern [deg++] = Pattern [pos] ; Pattern [pos] = k ; } } /* Pattern [0..deg-1] is now the pattern of the first row in Uchain */ /* ------------------------------------------------------------------ */ /* solve using this Uchain, in reverse order */ /* ------------------------------------------------------------------ */ DEBUG4 (("Unwinding Uchain\n")) ; for (k = kstart ; k <= kend ; k++) { /* -------------------------------------------------------------- */ /* construct row k */ /* -------------------------------------------------------------- */ ASSERT (k >= 0 && k < npiv) ; pos = Upos [k] ; if (pos != EMPTY) { /* remove the pivot column */ DEBUG4 (("k "ID" add pivot entry at position "ID"\n", k, pos)) ; ASSERT (k > kstart) ; ASSERT (pos >= 0 && pos < deg) ; ASSERT (Pattern [pos] == k) ; Pattern [pos] = Pattern [--deg] ; } up = Uip [k] ; ulen = Uilen [k] ; if (k > kstart) { /* concatenate the deleted pattern; pop from the stack */ for (j = 0 ; j < ulen ; j++) { ASSERT (deg <= uhead && uhead < n) ; Pattern [deg++] = Pattern [uhead++] ; } DEBUG4 (("middle of chain, row of U "ID" deg "ID"\n", k, deg)) ; ASSERT (deg >= 0) ; } /* -------------------------------------------------------------- */ /* use row k of U */ /* -------------------------------------------------------------- */ #ifndef NO_DIVIDE_BY_ZERO /* Go ahead and divide by zero if D [k] is zero. */ #ifdef CONJUGATE_SOLVE /* xk = X [k] / conjugate (D [k]) ; */ DIV_CONJ (xk, X [k], D [k]) ; #else /* xk = X [k] / D [k] ; */ DIV (xk, X [k], D [k]) ; #endif #else /* Do not divide by zero */ if (IS_NONZERO (D [k])) { #ifdef CONJUGATE_SOLVE /* xk = X [k] / conjugate (D [k]) ; */ DIV_CONJ (xk, X [k], D [k]) ; #else /* xk = X [k] / D [k] ; */ DIV (xk, X [k], D [k]) ; #endif } #endif X [k] = xk ; if (IS_NONZERO (xk)) { if (k == kstart) { up = -up ; xp = (Entry *) (Numeric->Memory + up + UNITS (Int, ulen)) ; } else { xp = (Entry *) (Numeric->Memory + up) ; } for (j = 0 ; j < deg ; j++) { DEBUG4 ((" k "ID" col "ID" value", k, Pattern [j])) ; EDEBUG4 (*xp) ; DEBUG4 (("\n")) ; #ifdef CONJUGATE_SOLVE /* X [Pattern [j]] -= xk * conjugate (*xp) ; */ MULT_SUB_CONJ (X [Pattern [j]], xk, *xp) ; #else /* X [Pattern [j]] -= xk * (*xp) ; */ MULT_SUB (X [Pattern [j]], xk, *xp) ; #endif xp++ ; } } } ASSERT (uhead == n) ; } #ifndef NO_DIVIDE_BY_ZERO for (k = npiv ; k < n ; k++) { /* This is an *** intentional *** divide-by-zero, to get Inf or Nan, * as appropriate. It is not a bug. */ ASSERT (IS_ZERO (D [k])) ; /* For conjugate solve, D [k] == conjugate (D [k]), in this case */ /* xk = X [k] / D [k] ; */ DIV (xk, X [k], D [k]) ; X [k] = xk ; } #endif #ifndef NDEBUG for (j = 0 ; j < n ; j++) { DEBUG4 (("Utsolve done "ID": ", j)) ; EDEBUG4 (X [j]) ; DEBUG4 (("\n")) ; } DEBUG4 (("Utsolve done.\n")) ; #endif return (DIV_FLOPS * ((double) n) + MULTSUB_FLOPS * ((double) Numeric->unz)); } SuiteSparse/UMFPACK/Source/umfpack_load_numeric.c0000644001170100242450000001175510677543207020634 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_load_numeric ================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Loads a Numeric object from a file created by umfpack_*_save_numeric. */ #include "umf_internal.h" #include "umf_valid_numeric.h" #include "umf_malloc.h" #include "umf_free.h" #define READ(object,type,n) \ { \ object = (type *) UMF_malloc (n, sizeof (type)) ; \ if (object == (type *) NULL) \ { \ UMFPACK_free_numeric ((void **) &Numeric) ; \ fclose (f) ; \ return (UMFPACK_ERROR_out_of_memory) ; \ } \ if (fread (object, sizeof (type), n, f) != (size_t) n) \ { \ UMFPACK_free_numeric ((void **) &Numeric) ; \ fclose (f) ; \ return (UMFPACK_ERROR_file_IO) ; \ } \ if (ferror (f)) \ { \ UMFPACK_free_numeric ((void **) &Numeric) ; \ fclose (f) ; \ return (UMFPACK_ERROR_file_IO) ; \ } \ } /* ========================================================================== */ /* === UMFPACK_load_numeric ================================================= */ /* ========================================================================== */ GLOBAL Int UMFPACK_load_numeric ( void **NumericHandle, char *user_filename ) { NumericType *Numeric ; char *filename ; FILE *f ; *NumericHandle = (void *) NULL ; /* ---------------------------------------------------------------------- */ /* get the filename, or use the default name if filename is NULL */ /* ---------------------------------------------------------------------- */ if (user_filename == (char *) NULL) { filename = "numeric.umf" ; } else { filename = user_filename ; } f = fopen (filename, "rb") ; if (!f) { return (UMFPACK_ERROR_file_IO) ; } /* ---------------------------------------------------------------------- */ /* read the Numeric header from the file, in binary */ /* ---------------------------------------------------------------------- */ Numeric = (NumericType *) UMF_malloc (1, sizeof (NumericType)) ; if (Numeric == (NumericType *) NULL) { fclose (f) ; return (UMFPACK_ERROR_out_of_memory) ; } if (fread (Numeric, sizeof (NumericType), 1, f) != 1) { (void) UMF_free ((void *) Numeric) ; fclose (f) ; return (UMFPACK_ERROR_file_IO) ; } if (ferror (f)) { (void) UMF_free ((void *) Numeric) ; fclose (f) ; return (UMFPACK_ERROR_file_IO) ; } if (Numeric->valid != NUMERIC_VALID || Numeric->n_row <= 0 || Numeric->n_col <= 0 || Numeric->npiv < 0 || Numeric->ulen < 0 || Numeric->size <= 0) { /* Numeric does not point to a NumericType object */ (void) UMF_free ((void *) Numeric) ; fclose (f) ; return (UMFPACK_ERROR_invalid_Numeric_object) ; } Numeric->D = (Entry *) NULL ; Numeric->Rperm = (Int *) NULL ; Numeric->Cperm = (Int *) NULL ; Numeric->Lpos = (Int *) NULL ; Numeric->Lilen = (Int *) NULL ; Numeric->Lip = (Int *) NULL ; Numeric->Upos = (Int *) NULL ; Numeric->Uilen = (Int *) NULL ; Numeric->Uip = (Int *) NULL ; Numeric->Rs = (double *) NULL ; Numeric->Memory = (Unit *) NULL ; Numeric->Upattern = (Int *) NULL ; /* umfpack_free_numeric can now be safely called if an error occurs */ /* ---------------------------------------------------------------------- */ /* read the rest of the Numeric object */ /* ---------------------------------------------------------------------- */ READ (Numeric->D, Entry, MIN (Numeric->n_row, Numeric->n_col)+1) ; READ (Numeric->Rperm, Int, Numeric->n_row+1) ; READ (Numeric->Cperm, Int, Numeric->n_col+1) ; READ (Numeric->Lpos, Int, Numeric->npiv+1) ; READ (Numeric->Lilen, Int, Numeric->npiv+1) ; READ (Numeric->Lip, Int, Numeric->npiv+1) ; READ (Numeric->Upos, Int, Numeric->npiv+1) ; READ (Numeric->Uilen, Int, Numeric->npiv+1) ; READ (Numeric->Uip, Int, Numeric->npiv+1) ; if (Numeric->scale != UMFPACK_SCALE_NONE) { READ (Numeric->Rs, double, Numeric->n_row) ; } if (Numeric->ulen > 0) { READ (Numeric->Upattern, Int, Numeric->ulen+1) ; } READ (Numeric->Memory, Unit, Numeric->size) ; /* close the file */ fclose (f) ; /* make sure the Numeric object is valid */ if (!UMF_valid_numeric (Numeric)) { UMFPACK_free_numeric ((void **) &Numeric) ; return (UMFPACK_ERROR_invalid_Numeric_object) ; } *NumericHandle = (void *) Numeric ; return (UMFPACK_OK) ; } SuiteSparse/UMFPACK/Source/umfpack_report_triplet.c0000644001170100242450000000457110617162137021240 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_report_triplet =============================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Prints a matrix in triplet form. See umfpack_report_triplet.h for details. */ #include "umf_internal.h" GLOBAL Int UMFPACK_report_triplet ( Int n_row, Int n_col, Int nz, const Int Ti [ ], const Int Tj [ ], const double Tx [ ], #ifdef COMPLEX const double Tz [ ], #endif const double Control [UMFPACK_CONTROL] ) { Entry t ; Int prl, prl1, k, i, j, do_values ; #ifdef COMPLEX Int split = SPLIT (Tz) ; #endif prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ; if (prl <= 2) { return (UMFPACK_OK) ; } PRINTF (("triplet-form matrix, n_row = "ID", n_col = "ID" nz = "ID". ", n_row, n_col, nz)) ; if (!Ti || !Tj) { PRINTF (("ERROR: indices not present\n\n")) ; return (UMFPACK_ERROR_argument_missing) ; } if (n_row <= 0 || n_col <= 0) { PRINTF (("ERROR: n_row or n_col is <= 0\n\n")) ; return (UMFPACK_ERROR_n_nonpositive) ; } if (nz < 0) { PRINTF (("ERROR: nz is < 0\n\n")) ; return (UMFPACK_ERROR_invalid_matrix) ; } PRINTF4 (("\n")) ; do_values = Tx != (double *) NULL ; prl1 = prl ; for (k = 0 ; k < nz ; k++) { i = Ti [k] ; j = Tj [k] ; PRINTF4 ((" "ID" : "ID" "ID" ", INDEX (k), INDEX (i), INDEX (j))) ; if (do_values && prl >= 4) { ASSIGN (t, Tx, Tz, k, split) ; PRINT_ENTRY (t) ; } PRINTF4 (("\n")) ; if (i < 0 || i >= n_row || j < 0 || j >= n_col) { /* invalid triplet */ PRINTF (("ERROR: invalid triplet\n\n")) ; return (UMFPACK_ERROR_invalid_matrix) ; } if (prl == 4 && k == 9 && nz > 10) { PRINTF ((" ...\n")) ; prl-- ; } } prl = prl1 ; PRINTF4 ((" triplet-form matrix ")) ; PRINTF (("OK\n\n")) ; return (UMFPACK_OK) ; } SuiteSparse/UMFPACK/Source/umf_utsolve.h0000644001170100242450000000112610617162505017021 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL double UMF_utsolve ( NumericType *Numeric, Entry X [ ], Int Pattern [ ] ) ; GLOBAL double UMF_uhsolve ( NumericType *Numeric, Entry X [ ], Int Pattern [ ] ) ; SuiteSparse/UMFPACK/Source/umf_mem_alloc_element.c0000644001170100242450000000507010677541716020771 0ustar davisfac/* ========================================================================== */ /* === UMF_mem_alloc_element ================================================ */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* The UMF_mem_* routines manage the Numeric->Memory memory space. */ /* Allocate a nrows-by-ncols element, and initialize it. */ /* Returns the index into Numeric->Memory if successful, or 0 on failure. */ #include "umf_internal.h" #include "umf_mem_alloc_element.h" #include "umf_mem_alloc_tail_block.h" GLOBAL Int UMF_mem_alloc_element ( NumericType *Numeric, Int nrows, Int ncols, Int **Rows, Int **Cols, Entry **C, Int *size, Element **epout ) { Element *ep ; Unit *p ; Int i ; ASSERT (Numeric != (NumericType *) NULL) ; ASSERT (Numeric->Memory != (Unit *) NULL) ; *size = GET_ELEMENT_SIZE (nrows, ncols) ; if (INT_OVERFLOW (DGET_ELEMENT_SIZE (nrows, ncols) + 1)) { /* :: allocate element, int overflow :: */ return (0) ; /* problem is too large */ } i = UMF_mem_alloc_tail_block (Numeric, *size) ; (*size)++ ; if (!i) { DEBUG0 (("alloc element failed - out of memory\n")) ; return (0) ; /* out of memory */ } p = Numeric->Memory + i ; ep = (Element *) p ; DEBUG2 (("alloc_element done ("ID" x "ID"): p: "ID" i "ID"\n", nrows, ncols, (Int) (p-Numeric->Memory), i)) ; /* Element data structure, in order: */ p += UNITS (Element, 1) ; /* (1) Element header */ *Cols = (Int *) p ; /* (2) col [0..ncols-1] indices */ *Rows = *Cols + ncols ; /* (3) row [0..nrows-1] indices */ p += UNITS (Int, ncols + nrows) ; *C = (Entry *) p ; /* (4) C [0..nrows-1, 0..ncols-1] */ ep->nrows = nrows ; /* initialize the header information */ ep->ncols = ncols ; ep->nrowsleft = nrows ; ep->ncolsleft = ncols ; ep->cdeg = 0 ; ep->rdeg = 0 ; ep->next = EMPTY ; DEBUG2 (("new block size: "ID" ", GET_BLOCK_SIZE (Numeric->Memory + i))) ; DEBUG2 (("Element size needed "ID"\n", GET_ELEMENT_SIZE (nrows, ncols))) ; *epout = ep ; /* return the offset into Numeric->Memory */ return (i) ; } SuiteSparse/UMFPACK/Source/umf_mem_alloc_element.h0000644001170100242450000000110710617161743020763 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_mem_alloc_element ( NumericType *Numeric, Int nrows, Int ncols, Int **Rows, Int **Cols, Entry **C, Int *size, Element **epout ) ; SuiteSparse/UMFPACK/Source/cholmod_blas.h0000644001170100242450000003223710677545073017121 0ustar davisfac/* ========================================================================== */ /* === Include/cholmod_blas.h =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_blas.h. * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis * CHOLMOD/Include/cholmod_blas.h is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* This does not need to be included in the user's program. */ #ifndef CHOLMOD_BLAS_H #define CHOLMOD_BLAS_H /* ========================================================================== */ /* === Architecture ========================================================= */ /* ========================================================================== */ #if defined (__sun) || defined (MSOL2) || defined (ARCH_SOL2) #define CHOLMOD_SOL2 #define CHOLMOD_ARCHITECTURE "Sun Solaris" #elif defined (__sgi) || defined (MSGI) || defined (ARCH_SGI) #define CHOLMOD_SGI #define CHOLMOD_ARCHITECTURE "SGI Irix" #elif defined (__linux) || defined (MGLNX86) || defined (ARCH_GLNX86) #define CHOLMOD_LINUX #define CHOLMOD_ARCHITECTURE "Linux" #elif defined (_AIX) || defined (MIBM_RS) || defined (ARCH_IBM_RS) #define CHOLMOD_AIX #define CHOLMOD_ARCHITECTURE "IBM AIX" #define BLAS_NO_UNDERSCORE #elif defined (__alpha) || defined (MALPHA) || defined (ARCH_ALPHA) #define CHOLMOD_ALPHA #define CHOLMOD_ARCHITECTURE "Compaq Alpha" #elif defined (_WIN32) || defined (WIN32) || defined (_WIN64) || defined (WIN64) #if defined (__MINGW32__) || defined (__MINGW32__) #define CHOLMOD_MINGW #elif defined (__CYGWIN32__) || defined (__CYGWIN32__) #define CHOLMOD_CYGWIN #else #define CHOLMOD_WINDOWS #define BLAS_NO_UNDERSCORE #endif #define CHOLMOD_ARCHITECTURE "Microsoft Windows" #elif defined (__hppa) || defined (__hpux) || defined (MHPUX) || defined (ARCH_HPUX) #define CHOLMOD_HP #define CHOLMOD_ARCHITECTURE "HP Unix" #define BLAS_NO_UNDERSCORE #elif defined (__hp700) || defined (MHP700) || defined (ARCH_HP700) #define CHOLMOD_HP #define CHOLMOD_ARCHITECTURE "HP 700 Unix" #define BLAS_NO_UNDERSCORE #else /* If the architecture is unknown, and you call the BLAS, you may need to */ /* define BLAS_BY_VALUE, BLAS_NO_UNDERSCORE, and/or BLAS_CHAR_ARG yourself. */ #define CHOLMOD_ARCHITECTURE "unknown" #endif /* ========================================================================== */ /* === BLAS and LAPACK names ================================================ */ /* ========================================================================== */ /* Prototypes for the various versions of the BLAS. */ /* Determine if the 64-bit Sun Performance BLAS is to be used */ #if defined(CHOLMOD_SOL2) && !defined(NSUNPERF) && defined(LONG) && defined(LONGBLAS) #define SUN64 #endif #ifdef SUN64 #define BLAS_DTRSV dtrsv_64_ #define BLAS_DGEMV dgemv_64_ #define BLAS_DTRSM dtrsm_64_ #define BLAS_DGEMM dgemm_64_ #define BLAS_DSYRK dsyrk_64_ #define BLAS_DGER dger_64_ #define BLAS_DSCAL dscal_64_ #define LAPACK_DPOTRF dpotrf_64_ #define BLAS_ZTRSV ztrsv_64_ #define BLAS_ZGEMV zgemv_64_ #define BLAS_ZTRSM ztrsm_64_ #define BLAS_ZGEMM zgemm_64_ #define BLAS_ZHERK zherk_64_ #define BLAS_ZGER zgeru_64_ #define BLAS_ZSCAL zscal_64_ #define LAPACK_ZPOTRF zpotrf_64_ #elif defined (BLAS_NO_UNDERSCORE) #define BLAS_DTRSV dtrsv #define BLAS_DGEMV dgemv #define BLAS_DTRSM dtrsm #define BLAS_DGEMM dgemm #define BLAS_DSYRK dsyrk #define BLAS_DGER dger #define BLAS_DSCAL dscal #define LAPACK_DPOTRF dpotrf #define BLAS_ZTRSV ztrsv #define BLAS_ZGEMV zgemv #define BLAS_ZTRSM ztrsm #define BLAS_ZGEMM zgemm #define BLAS_ZHERK zherk #define BLAS_ZGER zgeru #define BLAS_ZSCAL zscal #define LAPACK_ZPOTRF zpotrf #else #define BLAS_DTRSV dtrsv_ #define BLAS_DGEMV dgemv_ #define BLAS_DTRSM dtrsm_ #define BLAS_DGEMM dgemm_ #define BLAS_DSYRK dsyrk_ #define BLAS_DGER dger_ #define BLAS_DSCAL dscal_ #define LAPACK_DPOTRF dpotrf_ #define BLAS_ZTRSV ztrsv_ #define BLAS_ZGEMV zgemv_ #define BLAS_ZTRSM ztrsm_ #define BLAS_ZGEMM zgemm_ #define BLAS_ZHERK zherk_ #define BLAS_ZGER zgeru_ #define BLAS_ZSCAL zscal_ #define LAPACK_ZPOTRF zpotrf_ #endif /* ========================================================================== */ /* === BLAS and LAPACK integer arguments ==================================== */ /* ========================================================================== */ /* CHOLMOD can be compiled with -D'LONGBLAS=long' for the Sun Performance * Library, or -D'LONGBLAS=long long' for SGI's SCSL BLAS. This defines the * integer used in the BLAS for the cholmod_l_* routines. * * The "int" version of CHOLMOD always uses the "int" version of the BLAS. */ #if defined (LONGBLAS) && defined (LONG) #define BLAS_INT LONGBLAS #else #define BLAS_INT int #endif /* If the BLAS integer is smaller than the basic CHOLMOD integer, then we need * to check for integer overflow when converting from one to the other. If * any integer overflows, the externally-defined blas_ok variable is set to * FALSE. blas_ok should be set to TRUE before calling any BLAS_* macro. */ #define CHECK_BLAS_INT (sizeof (BLAS_INT) < sizeof (Int)) #define EQ(K,k) (((BLAS_INT) K) == ((Int) k)) /* ========================================================================== */ /* === BLAS and LAPACK prototypes and macros ================================ */ /* ========================================================================== */ void BLAS_DGEMV (char *trans, BLAS_INT *m, BLAS_INT *n, double *alpha, double *A, BLAS_INT *lda, double *X, BLAS_INT *incx, double *beta, double *Y, BLAS_INT *incy) ; #define BLAS_dgemv(trans,m,n,alpha,A,lda,X,incx,beta,Y,incy) \ { \ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \ && EQ (INCY,incy) ; \ } \ if (blas_ok) \ { \ BLAS_DGEMV (trans, &M, &N, alpha, A, &LDA, X, &INCX, beta, Y, &INCY) ; \ } \ } void BLAS_ZGEMV (char *trans, BLAS_INT *m, BLAS_INT *n, double *alpha, double *A, BLAS_INT *lda, double *X, BLAS_INT *incx, double *beta, double *Y, BLAS_INT *incy) ; #define BLAS_zgemv(trans,m,n,alpha,A,lda,X,incx,beta,Y,incy) \ { \ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \ && EQ (INCY,incy) ; \ } \ if (blas_ok) \ { \ BLAS_ZGEMV (trans, &M, &N, alpha, A, &LDA, X, &INCX, beta, Y, &INCY) ; \ } \ } void BLAS_DTRSV (char *uplo, char *trans, char *diag, BLAS_INT *n, double *A, BLAS_INT *lda, double *X, BLAS_INT *incx) ; #define BLAS_dtrsv(uplo,trans,diag,n,A,lda,X,incx) \ { \ BLAS_INT N = n, LDA = lda, INCX = incx ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) ; \ } \ if (blas_ok) \ { \ BLAS_DTRSV (uplo, trans, diag, &N, A, &LDA, X, &INCX) ; \ } \ } void BLAS_ZTRSV (char *uplo, char *trans, char *diag, BLAS_INT *n, double *A, BLAS_INT *lda, double *X, BLAS_INT *incx) ; #define BLAS_ztrsv(uplo,trans,diag,n,A,lda,X,incx) \ { \ BLAS_INT N = n, LDA = lda, INCX = incx ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) ; \ } \ if (blas_ok) \ { \ BLAS_ZTRSV (uplo, trans, diag, &N, A, &LDA, X, &INCX) ; \ } \ } void BLAS_DTRSM (char *side, char *uplo, char *transa, char *diag, BLAS_INT *m, BLAS_INT *n, double *alpha, double *A, BLAS_INT *lda, double *B, BLAS_INT *ldb) ; #define BLAS_dtrsm(side,uplo,transa,diag,m,n,alpha,A,lda,B,ldb) \ { \ BLAS_INT M = m, N = n, LDA = lda, LDB = ldb ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (LDB,ldb) ; \ } \ if (blas_ok) \ { \ BLAS_DTRSM (side, uplo, transa, diag, &M, &N, alpha, A, &LDA, B, &LDB);\ } \ } void BLAS_ZTRSM (char *side, char *uplo, char *transa, char *diag, BLAS_INT *m, BLAS_INT *n, double *alpha, double *A, BLAS_INT *lda, double *B, BLAS_INT *ldb) ; #define BLAS_ztrsm(side,uplo,transa,diag,m,n,alpha,A,lda,B,ldb) \ { \ BLAS_INT M = m, N = n, LDA = lda, LDB = ldb ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (LDB,ldb) ; \ } \ if (blas_ok) \ { \ BLAS_ZTRSM (side, uplo, transa, diag, &M, &N, alpha, A, &LDA, B, &LDB);\ } \ } void BLAS_DGEMM (char *transa, char *transb, BLAS_INT *m, BLAS_INT *n, BLAS_INT *k, double *alpha, double *A, BLAS_INT *lda, double *B, BLAS_INT *ldb, double *beta, double *C, BLAS_INT *ldc) ; #define BLAS_dgemm(transa,transb,m,n,k,alpha,A,lda,B,ldb,beta,C,ldc) \ { \ BLAS_INT M = m, N = n, K = k, LDA = lda, LDB = ldb, LDC = ldc ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (K,k) && EQ (LDA,lda) \ && EQ (LDB,ldb) && EQ (LDC,ldc) ; \ } \ if (blas_ok) \ { \ BLAS_DGEMM (transa, transb, &M, &N, &K, alpha, A, &LDA, B, &LDB, beta, \ C, &LDC) ; \ } \ } void BLAS_ZGEMM (char *transa, char *transb, BLAS_INT *m, BLAS_INT *n, BLAS_INT *k, double *alpha, double *A, BLAS_INT *lda, double *B, BLAS_INT *ldb, double *beta, double *C, BLAS_INT *ldc) ; #define BLAS_zgemm(transa,transb,m,n,k,alpha,A,lda,B,ldb,beta,C,ldc) \ { \ BLAS_INT M = m, N = n, K = k, LDA = lda, LDB = ldb, LDC = ldc ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (K,k) && EQ (LDA,lda) \ && EQ (LDB,ldb) && EQ (LDC,ldc) ; \ } \ if (blas_ok) \ { \ BLAS_ZGEMM (transa, transb, &M, &N, &K, alpha, A, &LDA, B, &LDB, beta, \ C, &LDC) ; \ } \ } void BLAS_DSYRK (char *uplo, char *trans, BLAS_INT *n, BLAS_INT *k, double *alpha, double *A, BLAS_INT *lda, double *beta, double *C, BLAS_INT *ldc) ; #define BLAS_dsyrk(uplo,trans,n,k,alpha,A,lda,beta,C,ldc) \ { \ BLAS_INT N = n, K = k, LDA = lda, LDC = ldc ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (N,n) && EQ (K,k) && EQ (LDA,lda) && EQ (LDC,ldc) ; \ } \ if (blas_ok) \ { \ BLAS_DSYRK (uplo, trans, &N, &K, alpha, A, &LDA, beta, C, &LDC) ; \ } \ } \ void BLAS_ZHERK (char *uplo, char *trans, BLAS_INT *n, BLAS_INT *k, double *alpha, double *A, BLAS_INT *lda, double *beta, double *C, BLAS_INT *ldc) ; #define BLAS_zherk(uplo,trans,n,k,alpha,A,lda,beta,C,ldc) \ { \ BLAS_INT N = n, K = k, LDA = lda, LDC = ldc ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (N,n) && EQ (K,k) && EQ (LDA,lda) && EQ (LDC,ldc) ; \ } \ if (blas_ok) \ { \ BLAS_ZHERK (uplo, trans, &N, &K, alpha, A, &LDA, beta, C, &LDC) ; \ } \ } \ void LAPACK_DPOTRF (char *uplo, BLAS_INT *n, double *A, BLAS_INT *lda, BLAS_INT *info) ; #define LAPACK_dpotrf(uplo,n,A,lda,info) \ { \ BLAS_INT N = n, LDA = lda, INFO = 1 ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (N,n) && EQ (LDA,lda) ; \ } \ if (blas_ok) \ { \ LAPACK_DPOTRF (uplo, &N, A, &LDA, &INFO) ; \ } \ info = INFO ; \ } void LAPACK_ZPOTRF (char *uplo, BLAS_INT *n, double *A, BLAS_INT *lda, BLAS_INT *info) ; #define LAPACK_zpotrf(uplo,n,A,lda,info) \ { \ BLAS_INT N = n, LDA = lda, INFO = 1 ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (N,n) && EQ (LDA,lda) ; \ } \ if (blas_ok) \ { \ LAPACK_ZPOTRF (uplo, &N, A, &LDA, &INFO) ; \ } \ info = INFO ; \ } /* ========================================================================== */ void BLAS_DSCAL (BLAS_INT *n, double *alpha, double *Y, BLAS_INT *incy) ; #define BLAS_dscal(n,alpha,Y,incy) \ { \ BLAS_INT N = n, INCY = incy ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (N,n) && EQ (INCY,incy) ; \ } \ if (blas_ok) \ { \ BLAS_DSCAL (&N, alpha, Y, &INCY) ; \ } \ } void BLAS_ZSCAL (BLAS_INT *n, double *alpha, double *Y, BLAS_INT *incy) ; #define BLAS_zscal(n,alpha,Y,incy) \ { \ BLAS_INT N = n, INCY = incy ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (N,n) && EQ (INCY,incy) ; \ } \ if (blas_ok) \ { \ BLAS_ZSCAL (&N, alpha, Y, &INCY) ; \ } \ } void BLAS_DGER (BLAS_INT *m, BLAS_INT *n, double *alpha, double *X, BLAS_INT *incx, double *Y, BLAS_INT *incy, double *A, BLAS_INT *lda) ; #define BLAS_dger(m,n,alpha,X,incx,Y,incy,A,lda) \ { \ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \ && EQ (INCY,incy) ; \ } \ if (blas_ok) \ { \ BLAS_DGER (&M, &N, alpha, X, &INCX, Y, &INCY, A, &LDA) ; \ } \ } void BLAS_ZGER (BLAS_INT *m, BLAS_INT *n, double *alpha, double *X, BLAS_INT *incx, double *Y, BLAS_INT *incy, double *A, BLAS_INT *lda) ; #define BLAS_zgeru(m,n,alpha,X,incx,Y,incy,A,lda) \ { \ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \ && EQ (INCY,incy) ; \ } \ if (blas_ok) \ { \ BLAS_ZGER (&M, &N, alpha, X, &INCX, Y, &INCY, A, &LDA) ; \ } \ } #endif SuiteSparse/UMFPACK/Source/umfpack_save_numeric.c0000644001170100242450000000551010677543227020645 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_save_numeric ================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Saves a Numeric object to a file. It can later be read back in via a call to umfpack_*_load_numeric. */ #include "umf_internal.h" #include "umf_valid_numeric.h" #define WRITE(object,type,n) \ { \ ASSERT (object != (type *) NULL) ; \ if (fwrite (object, sizeof (type), n, f) != (size_t) n) \ { \ fclose (f) ; \ return (UMFPACK_ERROR_file_IO) ; \ } \ } /* ========================================================================== */ /* === UMFPACK_save_numeric ================================================= */ /* ========================================================================== */ GLOBAL Int UMFPACK_save_numeric ( void *NumericHandle, char *user_filename ) { NumericType *Numeric ; char *filename ; FILE *f ; /* get the Numeric object */ Numeric = (NumericType *) NumericHandle ; /* make sure the Numeric object is valid */ if (!UMF_valid_numeric (Numeric)) { return (UMFPACK_ERROR_invalid_Numeric_object) ; } /* get the filename, or use the default name if filename is NULL */ if (user_filename == (char *) NULL) { filename = "numeric.umf" ; } else { filename = user_filename ; } f = fopen (filename, "wb") ; if (!f) { return (UMFPACK_ERROR_file_IO) ; } /* write the Numeric object to the file, in binary */ WRITE (Numeric, NumericType, 1) ; WRITE (Numeric->D, Entry, MIN (Numeric->n_row, Numeric->n_col)+1) ; WRITE (Numeric->Rperm, Int, Numeric->n_row+1) ; WRITE (Numeric->Cperm, Int, Numeric->n_col+1) ; WRITE (Numeric->Lpos, Int, Numeric->npiv+1) ; WRITE (Numeric->Lilen, Int, Numeric->npiv+1) ; WRITE (Numeric->Lip, Int, Numeric->npiv+1) ; WRITE (Numeric->Upos, Int, Numeric->npiv+1) ; WRITE (Numeric->Uilen, Int, Numeric->npiv+1) ; WRITE (Numeric->Uip, Int, Numeric->npiv+1) ; if (Numeric->scale != UMFPACK_SCALE_NONE) { WRITE (Numeric->Rs, double, Numeric->n_row) ; } if (Numeric->ulen > 0) { WRITE (Numeric->Upattern, Int, Numeric->ulen+1) ; } WRITE (Numeric->Memory, Unit, Numeric->size) ; /* close the file */ fclose (f) ; return (UMFPACK_OK) ; } SuiteSparse/UMFPACK/Source/umfpack_numeric.c0000644001170100242450000006751610617162075017635 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_numeric ====================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Factorizes A into its LU factors, given a symbolic pre-analysis computed by UMFPACK_symbolic. See umfpack_numeric.h for a description. Dynamic memory allocation: substantial. See comments (1) through (7), below. If an error occurs, all allocated space is free'd by UMF_free. If successful, the Numeric object contains 11 to 13 objects allocated by UMF_malloc that hold the LU factors of the input matrix. */ #include "umf_internal.h" #include "umf_valid_symbolic.h" #include "umf_set_stats.h" #include "umf_kernel.h" #include "umf_malloc.h" #include "umf_free.h" #include "umf_realloc.h" #ifndef NDEBUG PRIVATE Int init_count ; #endif PRIVATE Int work_alloc ( WorkType *Work, SymbolicType *Symbolic ) ; PRIVATE void free_work ( WorkType *Work ) ; PRIVATE Int numeric_alloc ( NumericType **NumericHandle, SymbolicType *Symbolic, double alloc_init, Int scale ) ; PRIVATE void error ( NumericType **Numeric, WorkType *Work ) ; /* ========================================================================== */ /* === UMFPACK_numeric ====================================================== */ /* ========================================================================== */ GLOBAL Int UMFPACK_numeric ( const Int Ap [ ], const Int Ai [ ], const double Ax [ ], #ifdef COMPLEX const double Az [ ], #endif void *SymbolicHandle, void **NumericHandle, const double Control [UMFPACK_CONTROL], double User_Info [UMFPACK_INFO] ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ double Info2 [UMFPACK_INFO], alloc_init, relpt, relpt2, droptol, front_alloc_init, stats [2] ; double *Info ; WorkType WorkSpace, *Work ; NumericType *Numeric ; SymbolicType *Symbolic ; Int n_row, n_col, n_inner, newsize, i, status, *inew, npiv, ulen, scale ; Unit *mnew ; /* ---------------------------------------------------------------------- */ /* get the amount of time used by the process so far */ /* ---------------------------------------------------------------------- */ umfpack_tic (stats) ; /* ---------------------------------------------------------------------- */ /* initialize and check inputs */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG UMF_dump_start ( ) ; init_count = UMF_malloc_count ; DEBUGm4 (("\nUMFPACK numeric: U transpose version\n")) ; #endif /* If front_alloc_init negative then allocate that size of front in * UMF_start_front. If alloc_init negative, then allocate that initial * size of Numeric->Memory. */ relpt = GET_CONTROL (UMFPACK_PIVOT_TOLERANCE, UMFPACK_DEFAULT_PIVOT_TOLERANCE) ; relpt2 = GET_CONTROL (UMFPACK_SYM_PIVOT_TOLERANCE, UMFPACK_DEFAULT_SYM_PIVOT_TOLERANCE) ; alloc_init = GET_CONTROL (UMFPACK_ALLOC_INIT, UMFPACK_DEFAULT_ALLOC_INIT) ; front_alloc_init = GET_CONTROL (UMFPACK_FRONT_ALLOC_INIT, UMFPACK_DEFAULT_FRONT_ALLOC_INIT) ; scale = GET_CONTROL (UMFPACK_SCALE, UMFPACK_DEFAULT_SCALE) ; droptol = GET_CONTROL (UMFPACK_DROPTOL, UMFPACK_DEFAULT_DROPTOL) ; relpt = MAX (0.0, MIN (relpt, 1.0)) ; relpt2 = MAX (0.0, MIN (relpt2, 1.0)) ; droptol = MAX (0.0, droptol) ; front_alloc_init = MIN (1.0, front_alloc_init) ; if (scale != UMFPACK_SCALE_NONE && scale != UMFPACK_SCALE_MAX) { scale = UMFPACK_DEFAULT_SCALE ; } if (User_Info != (double *) NULL) { /* return Info in user's array */ Info = User_Info ; /* clear the parts of Info that are set by UMFPACK_numeric */ for (i = UMFPACK_NUMERIC_SIZE ; i <= UMFPACK_MAX_FRONT_NCOLS ; i++) { Info [i] = EMPTY ; } for (i = UMFPACK_NUMERIC_DEFRAG ; i < UMFPACK_IR_TAKEN ; i++) { Info [i] = EMPTY ; } } else { /* no Info array passed - use local one instead */ Info = Info2 ; for (i = 0 ; i < UMFPACK_INFO ; i++) { Info [i] = EMPTY ; } } Symbolic = (SymbolicType *) SymbolicHandle ; Numeric = (NumericType *) NULL ; if (!UMF_valid_symbolic (Symbolic)) { Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_Symbolic_object ; return (UMFPACK_ERROR_invalid_Symbolic_object) ; } /* compute alloc_init automatically for AMD ordering */ if (Symbolic->ordering == UMFPACK_ORDERING_AMD && alloc_init >= 0) { alloc_init = (Symbolic->nz + Symbolic->amd_lunz) / Symbolic->lunz_bound; alloc_init = MIN (1.0, alloc_init) ; alloc_init *= UMF_REALLOC_INCREASE ; } n_row = Symbolic->n_row ; n_col = Symbolic->n_col ; n_inner = MIN (n_row, n_col) ; /* check for integer overflow in Numeric->Memory minimum size */ if (INT_OVERFLOW (Symbolic->dnum_mem_init_usage * sizeof (Unit))) { /* :: int overflow, initial Numeric->Memory size :: */ /* There's no hope to allocate a Numeric object big enough simply to * hold the initial matrix, so return an out-of-memory condition */ DEBUGm4 (("out of memory: numeric int overflow\n")) ; Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; return (UMFPACK_ERROR_out_of_memory) ; } Info [UMFPACK_STATUS] = UMFPACK_OK ; Info [UMFPACK_NROW] = n_row ; Info [UMFPACK_NCOL] = n_col ; Info [UMFPACK_SIZE_OF_UNIT] = (double) (sizeof (Unit)) ; if (!Ap || !Ai || !Ax || !NumericHandle) { Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ; return (UMFPACK_ERROR_argument_missing) ; } Info [UMFPACK_NZ] = Ap [n_col] ; *NumericHandle = (void *) NULL ; /* ---------------------------------------------------------------------- */ /* allocate the Work object */ /* ---------------------------------------------------------------------- */ /* (1) calls UMF_malloc 15 or 17 times, to obtain temporary workspace of * size c+1 Entry's and 2*(n_row+1) + 3*(n_col+1) + (n_col+n_inner+1) + * (nn+1) + * 3*(c+1) + 2*(r+1) + max(r,c) + (nfr+1) integers plus 2*nn * more integers if diagonal pivoting is to be done. r is the maximum * number of rows in any frontal matrix, c is the maximum number of columns * in any frontal matrix, n_inner is min (n_row,n_col), nn is * max (n_row,n_col), and nfr is the number of frontal matrices. For a * square matrix, this is c+1 Entry's and about 8n + 3c + 2r + max(r,c) + * nfr integers, plus 2n more for diagonal pivoting. */ Work = &WorkSpace ; Work->n_row = n_row ; Work->n_col = n_col ; Work->nfr = Symbolic->nfr ; Work->nb = Symbolic->nb ; Work->n1 = Symbolic->n1 ; if (!work_alloc (Work, Symbolic)) { DEBUGm4 (("out of memory: numeric work\n")) ; Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; error (&Numeric, Work) ; return (UMFPACK_ERROR_out_of_memory) ; } ASSERT (UMF_malloc_count == init_count + 16 + 2*Symbolic->prefer_diagonal) ; /* ---------------------------------------------------------------------- */ /* allocate Numeric object */ /* ---------------------------------------------------------------------- */ /* (2) calls UMF_malloc 10 or 11 times, for a total space of * sizeof (NumericType) bytes, 4*(n_row+1) + 4*(n_row+1) integers, and * (n_inner+1) Entry's, plus n_row Entry's if row scaling is to be done. * sizeof (NumericType) is a small constant. Next, it calls UMF_malloc * once, for the variable-sized part of the Numeric object * (Numeric->Memory). The size of this object is the larger of * (Control [UMFPACK_ALLOC_INIT]) * (the approximate upper bound computed * by UMFPACK_symbolic), and the minimum required to start the numerical * factorization. * This request is reduced if it fails. */ if (!numeric_alloc (&Numeric, Symbolic, alloc_init, scale)) { DEBUGm4 (("out of memory: initial numeric\n")) ; Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; error (&Numeric, Work) ; return (UMFPACK_ERROR_out_of_memory) ; } DEBUG0 (("malloc: init_count "ID" UMF_malloc_count "ID"\n", init_count, UMF_malloc_count)) ; ASSERT (UMF_malloc_count == init_count + (16 + 2*Symbolic->prefer_diagonal) + (11 + (scale != UMFPACK_SCALE_NONE))) ; /* set control parameters */ Numeric->relpt = relpt ; Numeric->relpt2 = relpt2 ; Numeric->droptol = droptol ; Numeric->alloc_init = alloc_init ; Numeric->front_alloc_init = front_alloc_init ; Numeric->scale = scale ; DEBUG0 (("umf relpt %g %g init %g %g inc %g red %g\n", relpt, relpt2, alloc_init, front_alloc_init, UMF_REALLOC_INCREASE, UMF_REALLOC_REDUCTION)) ; /* ---------------------------------------------------------------------- */ /* scale and factorize */ /* ---------------------------------------------------------------------- */ /* (3) During numerical factorization (inside UMF_kernel), the variable-size * block of memory is increased in size via a call to UMF_realloc if it is * found to be too small. During factorization, this block holds the * pattern and values of L and U at the top end, and the elements * (contibution blocks) and the current frontal matrix (Work->F*) at the * bottom end. The peak size of the variable-sized object is estimated in * UMFPACK_*symbolic (Info [UMFPACK_VARIABLE_PEAK_ESTIMATE]), although this * upper bound can be very loose. The size of the Symbolic object * (which is currently allocated) is in Info [UMFPACK_SYMBOLIC_SIZE], and * is between 2*n and 13*n integers. */ DEBUG0 (("Calling umf_kernel\n")) ; status = UMF_kernel (Ap, Ai, Ax, #ifdef COMPLEX Az, #endif Numeric, Work, Symbolic) ; Info [UMFPACK_STATUS] = status ; if (status < UMFPACK_OK) { /* out of memory, or pattern has changed */ error (&Numeric, Work) ; return (status) ; } Info [UMFPACK_FORCED_UPDATES] = Work->nforced ; Info [UMFPACK_VARIABLE_INIT] = Numeric->init_usage ; if (Symbolic->prefer_diagonal) { Info [UMFPACK_NOFF_DIAG] = Work->noff_diagonal ; } DEBUG0 (("malloc: init_count "ID" UMF_malloc_count "ID"\n", init_count, UMF_malloc_count)) ; npiv = Numeric->npiv ; /* = n_inner for nonsingular matrices */ ulen = Numeric->ulen ; /* = 0 for square nonsingular matrices */ /* ---------------------------------------------------------------------- */ /* free Work object */ /* ---------------------------------------------------------------------- */ /* (4) After numerical factorization all of the objects allocated in step * (1) are freed via UMF_free, except that one object of size n_col+1 is * kept if there are off-diagonal nonzeros in the last pivot row (can only * occur for singular or rectangular matrices). This is Work->Upattern, * which is transfered to Numeric->Upattern if ulen > 0. */ DEBUG0 (("malloc: init_count "ID" UMF_malloc_count "ID"\n", init_count, UMF_malloc_count)) ; free_work (Work) ; DEBUG0 (("malloc: init_count "ID" UMF_malloc_count "ID"\n", init_count, UMF_malloc_count)) ; DEBUG0 (("Numeric->ulen: "ID" scale: "ID"\n", ulen, scale)) ; ASSERT (UMF_malloc_count == init_count + (ulen > 0) + (11 + (scale != UMFPACK_SCALE_NONE))) ; /* ---------------------------------------------------------------------- */ /* reduce Lpos, Lilen, Lip, Upos, Uilen and Uip to size npiv+1 */ /* ---------------------------------------------------------------------- */ /* (5) Six components of the Numeric object are reduced in size if the * matrix is singular or rectangular. The original size is 3*(n_row+1) + * 3*(n_col+1) integers. The new size is 6*(npiv+1) integers. For * square non-singular matrices, these two sizes are the same. */ if (npiv < n_row) { /* reduce Lpos, Uilen, and Uip from size n_row+1 to size npiv */ inew = (Int *) UMF_realloc (Numeric->Lpos, npiv+1, sizeof (Int)) ; if (inew) { Numeric->Lpos = inew ; } inew = (Int *) UMF_realloc (Numeric->Uilen, npiv+1, sizeof (Int)) ; if (inew) { Numeric->Uilen = inew ; } inew = (Int *) UMF_realloc (Numeric->Uip, npiv+1, sizeof (Int)) ; if (inew) { Numeric->Uip = inew ; } } if (npiv < n_col) { /* reduce Upos, Lilen, and Lip from size n_col+1 to size npiv */ inew = (Int *) UMF_realloc (Numeric->Upos, npiv+1, sizeof (Int)) ; if (inew) { Numeric->Upos = inew ; } inew = (Int *) UMF_realloc (Numeric->Lilen, npiv+1, sizeof (Int)) ; if (inew) { Numeric->Lilen = inew ; } inew = (Int *) UMF_realloc (Numeric->Lip, npiv+1, sizeof (Int)) ; if (inew) { Numeric->Lip = inew ; } } /* ---------------------------------------------------------------------- */ /* reduce Numeric->Upattern from size n_col+1 to size ulen+1 */ /* ---------------------------------------------------------------------- */ /* (6) The size of Numeric->Upattern (formerly Work->Upattern) is reduced * from size n_col+1 to size ulen + 1. If ulen is zero, the object does * not exist. */ DEBUG4 (("ulen: "ID" Upattern "ID"\n", ulen, (Int) Numeric->Upattern)) ; ASSERT (IMPLIES (ulen == 0, Numeric->Upattern == (Int *) NULL)) ; if (ulen > 0 && ulen < n_col) { inew = (Int *) UMF_realloc (Numeric->Upattern, ulen+1, sizeof (Int)) ; if (inew) { Numeric->Upattern = inew ; } } /* ---------------------------------------------------------------------- */ /* reduce Numeric->Memory to hold just the LU factors at the head */ /* ---------------------------------------------------------------------- */ /* (7) The variable-sized block (Numeric->Memory) is reduced to hold just L * and U, via a call to UMF_realloc, since the frontal matrices are no * longer needed. */ newsize = Numeric->ihead ; if (newsize < Numeric->size) { mnew = (Unit *) UMF_realloc (Numeric->Memory, newsize, sizeof (Unit)) ; if (mnew) { /* realloc succeeded (how can it fail since the size is reduced?) */ Numeric->Memory = mnew ; Numeric->size = newsize ; } } Numeric->ihead = Numeric->size ; Numeric->itail = Numeric->ihead ; Numeric->tail_usage = 0 ; Numeric->ibig = EMPTY ; /* UMF_mem_alloc_tail_block can no longer be called (no tail marker) */ /* ---------------------------------------------------------------------- */ /* report the results and return the Numeric object */ /* ---------------------------------------------------------------------- */ UMF_set_stats ( Info, Symbolic, (double) Numeric->max_usage, /* actual peak Numeric->Memory */ (double) Numeric->size, /* actual final Numeric->Memory */ Numeric->flops, /* actual "true flops" */ (double) Numeric->lnz + n_inner, /* actual nz in L */ (double) Numeric->unz + Numeric->nnzpiv, /* actual nz in U */ (double) Numeric->maxfrsize, /* actual largest front size */ (double) ulen, /* actual Numeric->Upattern size */ (double) npiv, /* actual # pivots found */ (double) Numeric->maxnrows, /* actual largest #rows in front */ (double) Numeric->maxncols, /* actual largest #cols in front */ scale != UMFPACK_SCALE_NONE, Symbolic->prefer_diagonal, ACTUAL) ; Info [UMFPACK_ALLOC_INIT_USED] = Numeric->alloc_init ; Info [UMFPACK_NUMERIC_DEFRAG] = Numeric->ngarbage ; Info [UMFPACK_NUMERIC_REALLOC] = Numeric->nrealloc ; Info [UMFPACK_NUMERIC_COSTLY_REALLOC] = Numeric->ncostly ; Info [UMFPACK_COMPRESSED_PATTERN] = Numeric->isize ; Info [UMFPACK_LU_ENTRIES] = Numeric->nLentries + Numeric->nUentries + Numeric->npiv ; Info [UMFPACK_UDIAG_NZ] = Numeric->nnzpiv ; Info [UMFPACK_RSMIN] = Numeric->rsmin ; Info [UMFPACK_RSMAX] = Numeric->rsmax ; Info [UMFPACK_WAS_SCALED] = Numeric->scale ; /* nz in L and U with no dropping of small entries */ Info [UMFPACK_ALL_LNZ] = Numeric->all_lnz + n_inner ; Info [UMFPACK_ALL_UNZ] = Numeric->all_unz + Numeric->nnzpiv ; Info [UMFPACK_NZDROPPED] = (Numeric->all_lnz - Numeric->lnz) + (Numeric->all_unz - Numeric->unz) ; /* estimate of the reciprocal of the condition number. */ if (SCALAR_IS_ZERO (Numeric->min_udiag) || SCALAR_IS_ZERO (Numeric->max_udiag) || SCALAR_IS_NAN (Numeric->min_udiag) || SCALAR_IS_NAN (Numeric->max_udiag)) { /* rcond is zero if there is any zero or NaN on the diagonal */ Numeric->rcond = 0.0 ; } else { /* estimate of the recipricol of the condition number. */ /* This is NaN if diagonal is zero-free, but has one or more NaN's. */ Numeric->rcond = Numeric->min_udiag / Numeric->max_udiag ; } Info [UMFPACK_UMIN] = Numeric->min_udiag ; Info [UMFPACK_UMAX] = Numeric->max_udiag ; Info [UMFPACK_RCOND] = Numeric->rcond ; if (Numeric->nnzpiv < n_inner || SCALAR_IS_ZERO (Numeric->rcond) || SCALAR_IS_NAN (Numeric->rcond)) { /* there are zeros and/or NaN's on the diagonal of U */ DEBUG0 (("Warning, matrix is singular in umfpack_numeric\n")) ; DEBUG0 (("nnzpiv "ID" n_inner "ID" rcond %g\n", Numeric->nnzpiv, n_inner, Numeric->rcond)) ; status = UMFPACK_WARNING_singular_matrix ; Info [UMFPACK_STATUS] = status ; } Numeric->valid = NUMERIC_VALID ; *NumericHandle = (void *) Numeric ; /* Numeric has 11 to 13 objects */ ASSERT (UMF_malloc_count == init_count + 11 + + (ulen > 0) /* Numeric->Upattern */ + (scale != UMFPACK_SCALE_NONE)) ; /* Numeric->Rs */ /* ---------------------------------------------------------------------- */ /* get the time used by UMFPACK_numeric */ /* ---------------------------------------------------------------------- */ umfpack_toc (stats) ; Info [UMFPACK_NUMERIC_WALLTIME] = stats [0] ; Info [UMFPACK_NUMERIC_TIME] = stats [1] ; /* return UMFPACK_OK or UMFPACK_WARNING_singular_matrix */ return (status) ; } /* ========================================================================== */ /* === numeric_alloc ======================================================== */ /* ========================================================================== */ /* Allocate the Numeric object */ PRIVATE Int numeric_alloc ( NumericType **NumericHandle, SymbolicType *Symbolic, double alloc_init, Int scale ) { double nsize, bsize ; Int n_row, n_col, n_inner, min_usage, trying ; NumericType *Numeric ; DEBUG0 (("numeric alloc:\n")) ; n_row = Symbolic->n_row ; n_col = Symbolic->n_col ; n_inner = MIN (n_row, n_col) ; *NumericHandle = (NumericType *) NULL ; /* 1 allocation: accounted for in UMF_set_stats (num_On_size1), * free'd in umfpack_free_numeric */ Numeric = (NumericType *) UMF_malloc (1, sizeof (NumericType)) ; if (!Numeric) { return (FALSE) ; /* out of memory */ } Numeric->valid = 0 ; *NumericHandle = Numeric ; /* 9 allocations: accounted for in UMF_set_stats (num_On_size1), * free'd in umfpack_free_numeric */ Numeric->D = (Entry *) UMF_malloc (n_inner+1, sizeof (Entry)) ; Numeric->Rperm = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ; Numeric->Cperm = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ; Numeric->Lpos = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ; Numeric->Lilen = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ; Numeric->Lip = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ; Numeric->Upos = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ; Numeric->Uilen = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ; Numeric->Uip = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ; /* 1 allocation if scaling: in UMF_set_stats (num_On_size1), * free'd in umfpack_free_numeric */ if (scale != UMFPACK_SCALE_NONE) { DEBUG0 (("Allocating scale factors\n")) ; Numeric->Rs = (double *) UMF_malloc (n_row, sizeof (double)) ; } else { DEBUG0 (("No scale factors allocated (R = I)\n")) ; Numeric->Rs = (double *) NULL ; } Numeric->Memory = (Unit *) NULL ; /* Upattern has already been allocated as part of the Work object. If * the matrix is singular or rectangular, and there are off-diagonal * nonzeros in the last pivot row, then Work->Upattern is not free'd. * Instead it is transfered to Numeric->Upattern. If it exists, * Numeric->Upattern is free'd in umfpack_free_numeric. */ Numeric->Upattern = (Int *) NULL ; /* used for singular matrices only */ if (!Numeric->D || !Numeric->Rperm || !Numeric->Cperm || !Numeric->Upos || !Numeric->Lpos || !Numeric->Lilen || !Numeric->Uilen || !Numeric->Lip || !Numeric->Uip || (scale != UMFPACK_SCALE_NONE && !Numeric->Rs)) { return (FALSE) ; /* out of memory */ } /* ---------------------------------------------------------------------- */ /* allocate initial Numeric->Memory for LU factors and elements */ /* ---------------------------------------------------------------------- */ if (alloc_init < 0) { /* -alloc_init is the exact size to initially allocate */ nsize = -alloc_init ; } else { /* alloc_init is a ratio of the upper bound memory usage */ nsize = (alloc_init * Symbolic->num_mem_usage_est) + 1 ; } min_usage = Symbolic->num_mem_init_usage ; /* Numeric->Memory must be large enough for UMF_kernel_init */ nsize = MAX (min_usage, nsize) ; /* Numeric->Memory cannot be larger in size than Int_MAX / sizeof(Unit) */ /* For ILP32 mode: 2GB (nsize cannot be bigger than 256 Mwords) */ bsize = ((double) Int_MAX) / sizeof (Unit) - 1 ; DEBUG0 (("bsize %g\n", bsize)) ; nsize = MIN (nsize, bsize) ; Numeric->size = (Int) nsize ; DEBUG0 (("Num init %g usage_est %g numsize "ID" minusage "ID"\n", alloc_init, Symbolic->num_mem_usage_est, Numeric->size, min_usage)) ; /* allocates 1 object: */ /* keep trying until successful, or memory request is too small */ trying = TRUE ; while (trying) { Numeric->Memory = (Unit *) UMF_malloc (Numeric->size, sizeof (Unit)) ; if (Numeric->Memory) { DEBUG0 (("Successful Numeric->size: "ID"\n", Numeric->size)) ; return (TRUE) ; } /* too much, reduce the request (but not below the minimum) */ /* and try again */ trying = Numeric->size > min_usage ; Numeric->size = (Int) (UMF_REALLOC_REDUCTION * ((double) Numeric->size)) ; Numeric->size = MAX (min_usage, Numeric->size) ; } return (FALSE) ; /* we failed to allocate Numeric->Memory */ } /* ========================================================================== */ /* === work_alloc =========================================================== */ /* ========================================================================== */ /* Allocate the Work object. Return TRUE if successful. */ PRIVATE Int work_alloc ( WorkType *Work, SymbolicType *Symbolic ) { Int n_row, n_col, nn, maxnrows, maxncols, nfr, ok, maxnrc, n1 ; n_row = Work->n_row ; n_col = Work->n_col ; nn = MAX (n_row, n_col) ; nfr = Work->nfr ; n1 = Symbolic->n1 ; ASSERT (n1 <= n_row && n1 <= n_col) ; maxnrows = Symbolic->maxnrows + Symbolic->nb ; maxnrows = MIN (n_row, maxnrows) ; maxncols = Symbolic->maxncols + Symbolic->nb ; maxncols = MIN (n_col, maxncols) ; maxnrc = MAX (maxnrows, maxncols) ; DEBUG0 (("work alloc: maxnrows+nb "ID" maxncols+nb "ID"\n", maxnrows, maxncols)) ; /* 15 allocations, freed in free_work: */ /* accounted for in UMF_set_stats (work_usage) */ Work->Wx = (Entry *) UMF_malloc (maxnrows + 1, sizeof (Entry)) ; Work->Wy = (Entry *) UMF_malloc (maxnrows + 1, sizeof (Entry)) ; Work->Frpos = (Int *) UMF_malloc (n_row + 1, sizeof (Int)) ; Work->Lpattern = (Int *) UMF_malloc (n_row + 1, sizeof (Int)) ; Work->Fcpos = (Int *) UMF_malloc (n_col + 1, sizeof (Int)) ; Work->Wp = (Int *) UMF_malloc (nn + 1, sizeof (Int)) ; Work->Wrp = (Int *) UMF_malloc (MAX (n_col,maxnrows) + 1, sizeof (Int)) ; Work->Frows = (Int *) UMF_malloc (maxnrows + 1, sizeof (Int)) ; Work->Wm = (Int *) UMF_malloc (maxnrows + 1, sizeof (Int)) ; Work->Fcols = (Int *) UMF_malloc (maxncols + 1, sizeof (Int)) ; Work->Wio = (Int *) UMF_malloc (maxncols + 1, sizeof (Int)) ; Work->Woi = (Int *) UMF_malloc (maxncols + 1, sizeof (Int)) ; Work->Woo = (Int *) UMF_malloc (maxnrc + 1, sizeof (Int)); Work->elen = (n_col - n1) + (n_row - n1) + MIN (n_col-n1, n_row-n1) + 1 ; Work->E = (Int *) UMF_malloc (Work->elen, sizeof (Int)) ; Work->Front_new1strow = (Int *) UMF_malloc (nfr + 1, sizeof (Int)) ; ok = (Work->Frpos && Work->Fcpos && Work->Lpattern && Work->Wp && Work->Wrp && Work->Frows && Work->Fcols && Work->Wio && Work->Woi && Work->Woo && Work->Wm && Work->E && Work->Front_new1strow && Work->Wx && Work->Wy) ; /* 2 allocations: accounted for in UMF_set_stats (work_usage) */ if (Symbolic->prefer_diagonal) { Work->Diagonal_map = (Int *) UMF_malloc (nn, sizeof (Int)) ; Work->Diagonal_imap = (Int *) UMF_malloc (nn, sizeof (Int)) ; ok = ok && Work->Diagonal_map && Work->Diagonal_imap ; } else { /* no diagonal map needed for rectangular matrices */ Work->Diagonal_map = (Int *) NULL ; Work->Diagonal_imap = (Int *) NULL ; } /* 1 allocation, may become part of Numeric (if singular or rectangular): */ Work->Upattern = (Int *) UMF_malloc (n_col + 1, sizeof (Int)) ; ok = ok && Work->Upattern ; /* current frontal matrix does not yet exist */ Work->Flublock = (Entry *) NULL ; Work->Flblock = (Entry *) NULL ; Work->Fublock = (Entry *) NULL ; Work->Fcblock = (Entry *) NULL ; DEBUG0 (("work alloc done.\n")) ; return (ok) ; } /* ========================================================================== */ /* === free_work ============================================================ */ /* ========================================================================== */ PRIVATE void free_work ( WorkType *Work ) { DEBUG0 (("work free:\n")) ; if (Work) { /* these 16 objects do exist */ Work->Wx = (Entry *) UMF_free ((void *) Work->Wx) ; Work->Wy = (Entry *) UMF_free ((void *) Work->Wy) ; Work->Frpos = (Int *) UMF_free ((void *) Work->Frpos) ; Work->Fcpos = (Int *) UMF_free ((void *) Work->Fcpos) ; Work->Lpattern = (Int *) UMF_free ((void *) Work->Lpattern) ; Work->Upattern = (Int *) UMF_free ((void *) Work->Upattern) ; Work->Wp = (Int *) UMF_free ((void *) Work->Wp) ; Work->Wrp = (Int *) UMF_free ((void *) Work->Wrp) ; Work->Frows = (Int *) UMF_free ((void *) Work->Frows) ; Work->Fcols = (Int *) UMF_free ((void *) Work->Fcols) ; Work->Wio = (Int *) UMF_free ((void *) Work->Wio) ; Work->Woi = (Int *) UMF_free ((void *) Work->Woi) ; Work->Woo = (Int *) UMF_free ((void *) Work->Woo) ; Work->Wm = (Int *) UMF_free ((void *) Work->Wm) ; Work->E = (Int *) UMF_free ((void *) Work->E) ; Work->Front_new1strow = (Int *) UMF_free ((void *) Work->Front_new1strow) ; /* these objects might not exist */ Work->Diagonal_map = (Int *) UMF_free ((void *) Work->Diagonal_map) ; Work->Diagonal_imap = (Int *) UMF_free ((void *) Work->Diagonal_imap) ; } DEBUG0 (("work free done.\n")) ; } /* ========================================================================== */ /* === error ================================================================ */ /* ========================================================================== */ /* Error return from UMFPACK_numeric. Free all allocated memory. */ PRIVATE void error ( NumericType **Numeric, WorkType *Work ) { free_work (Work) ; UMFPACK_free_numeric ((void **) Numeric) ; ASSERT (UMF_malloc_count == init_count) ; } SuiteSparse/UMFPACK/Source/umfpack_get_lunz.c0000644001170100242450000000317010617162053020000 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_get_lunz ===================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Determines the number of nonzeros in L and U, and the size of L and U. */ #include "umf_internal.h" #include "umf_valid_numeric.h" GLOBAL Int UMFPACK_get_lunz ( Int *lnz, Int *unz, Int *n_row, Int *n_col, Int *nz_udiag, void *NumericHandle ) { NumericType *Numeric ; Numeric = (NumericType *) NumericHandle ; if (!UMF_valid_numeric (Numeric)) { return (UMFPACK_ERROR_invalid_Numeric_object) ; } if (!lnz || !unz || !n_row || !n_col || !nz_udiag) { return (UMFPACK_ERROR_argument_missing) ; } *n_row = Numeric->n_row ; *n_col = Numeric->n_col ; /* number of nz's in L below diagonal, plus the unit diagonal of L */ *lnz = Numeric->lnz + MIN (Numeric->n_row, Numeric->n_col) ; /* number of nz's in U above diagonal, plus nz's on diagaonal of U */ *unz = Numeric->unz + Numeric->nnzpiv ; /* number of nz's on the diagonal */ *nz_udiag = Numeric->nnzpiv ; return (UMFPACK_OK) ; } SuiteSparse/UMFPACK/Source/umfpack_report_control.c0000644001170100242450000003125210617162106021225 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_report_control =============================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Prints the control settings. See umfpack_report_control.h for details. */ #include "umf_internal.h" GLOBAL void UMFPACK_report_control ( const double Control [UMFPACK_CONTROL] ) { double drow, dcol, relpt, relpt2, alloc_init, front_alloc_init, amd_alpha, tol, force_fixQ, droptol, aggr ; Int prl, nb, irstep, strategy, scale, s ; prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ; if (prl < 2) { /* default is to print nothing */ return ; } PRINTF (("UMFPACK V%d.%d.%d (%s), Control:\n", UMFPACK_MAIN_VERSION, UMFPACK_SUB_VERSION, UMFPACK_SUBSUB_VERSION, UMFPACK_DATE)) ; /* ---------------------------------------------------------------------- */ /* run-time options */ /* ---------------------------------------------------------------------- */ /* This is a "run-time" option because all four umfpack_* versions */ /* compiled into the UMFPACK library. */ #ifdef DINT PRINTF ((" Matrix entry defined as: double\n")) ; PRINTF ((" Int (generic integer) defined as: int\n")) ; #endif #ifdef DLONG PRINTF ((" Matrix entry defined as: double\n")) ; PRINTF ((" Int (generic integer) defined as: UF_long\n")) ; #endif #ifdef ZINT PRINTF ((" Matrix entry defined as: double complex\n")) ; PRINTF ((" Int (generic integer) defined as: int\n")) ; #endif #ifdef ZLONG PRINTF ((" Matrix entry defined as: double complex\n")) ; PRINTF ((" Int (generic integer) defined as: UF_long\n")) ; #endif /* ---------------------------------------------------------------------- */ /* printing level */ /* ---------------------------------------------------------------------- */ PRINTF (("\n "ID": print level: "ID"\n", (Int) INDEX (UMFPACK_PRL), prl)) ; /* ---------------------------------------------------------------------- */ /* dense row/col parameters */ /* ---------------------------------------------------------------------- */ drow = GET_CONTROL (UMFPACK_DENSE_ROW, UMFPACK_DEFAULT_DENSE_ROW) ; dcol = GET_CONTROL (UMFPACK_DENSE_COL, UMFPACK_DEFAULT_DENSE_COL) ; PRINTF ((" "ID": dense row parameter: %g\n", (Int) INDEX (UMFPACK_DENSE_ROW), drow)) ; PRINTF ((" \"dense\" rows have > max (16, (%g)*16*sqrt(n_col)" " entries)\n", drow)) ; PRINTF ((" "ID": dense column parameter: %g\n", (Int) INDEX (UMFPACK_DENSE_COL), dcol)) ; PRINTF ((" \"dense\" columns have > max (16, (%g)*16*sqrt(n_row)" " entries)\n", dcol)) ; /* ---------------------------------------------------------------------- */ /* pivot tolerance */ /* ---------------------------------------------------------------------- */ relpt = GET_CONTROL (UMFPACK_PIVOT_TOLERANCE, UMFPACK_DEFAULT_PIVOT_TOLERANCE) ; relpt = MAX (0.0, MIN (relpt, 1.0)) ; PRINTF ((" "ID": pivot tolerance: %g\n", (Int) INDEX (UMFPACK_PIVOT_TOLERANCE), relpt)) ; /* ---------------------------------------------------------------------- */ /* block size */ /* ---------------------------------------------------------------------- */ nb = GET_CONTROL (UMFPACK_BLOCK_SIZE, UMFPACK_DEFAULT_BLOCK_SIZE) ; nb = MAX (1, nb) ; PRINTF ((" "ID": block size for dense matrix kernels: "ID"\n", (Int) INDEX (UMFPACK_BLOCK_SIZE), nb)) ; /* ---------------------------------------------------------------------- */ /* strategy */ /* ---------------------------------------------------------------------- */ strategy = GET_CONTROL (UMFPACK_STRATEGY, UMFPACK_DEFAULT_STRATEGY) ; if (strategy < UMFPACK_STRATEGY_AUTO || strategy > UMFPACK_STRATEGY_SYMMETRIC) { strategy = UMFPACK_STRATEGY_AUTO ; } PRINTF ((" "ID": strategy: "ID, (Int) INDEX (UMFPACK_STRATEGY), strategy)) ; if (strategy == UMFPACK_STRATEGY_SYMMETRIC) { PRINTF ((" (symmetric)\n" " Q = AMD (A+A'), Q not refined during numerical\n" " factorization, and diagonal pivoting (P=Q') attempted.\n")) ; } else if (strategy == UMFPACK_STRATEGY_UNSYMMETRIC) { PRINTF ((" (unsymmetric)\n" " Q = COLAMD (A), Q refined during numerical\n" " factorization, and no attempt at diagonal pivoting.\n")) ; } else if (strategy == UMFPACK_STRATEGY_2BY2) { PRINTF ((" (symmetric, with 2-by-2 block pivoting)\n" " P2 = row permutation that tries to place large entries on\n" " the diagonal. Q = AMD (P2*A+(P2*A)'), Q not refined during\n" " numerical factorization, attempt to select pivots from the\n" " diagonal of P2*A.\n")) ; } else /* auto strategy */ { strategy = UMFPACK_STRATEGY_AUTO ; PRINTF ((" (auto)\n")) ; } /* ---------------------------------------------------------------------- */ /* initial allocation parameter */ /* ---------------------------------------------------------------------- */ alloc_init = GET_CONTROL (UMFPACK_ALLOC_INIT, UMFPACK_DEFAULT_ALLOC_INIT) ; if (alloc_init >= 0) { PRINTF ((" "ID": initial allocation ratio: %g\n", (Int) INDEX (UMFPACK_ALLOC_INIT), alloc_init)) ; } else { s = -alloc_init ; s = MAX (1, s) ; PRINTF ((" "ID": initial allocation (in Units): "ID"\n", (Int) INDEX (UMFPACK_ALLOC_INIT), s)) ; } /* ---------------------------------------------------------------------- */ /* maximum iterative refinement steps */ /* ---------------------------------------------------------------------- */ irstep = GET_CONTROL (UMFPACK_IRSTEP, UMFPACK_DEFAULT_IRSTEP) ; irstep = MAX (0, irstep) ; PRINTF ((" "ID": max iterative refinement steps: "ID"\n", (Int) INDEX (UMFPACK_IRSTEP), irstep)) ; /* ---------------------------------------------------------------------- */ /* 2-by-2 pivot tolerance */ /* ---------------------------------------------------------------------- */ tol = GET_CONTROL (UMFPACK_2BY2_TOLERANCE, UMFPACK_DEFAULT_2BY2_TOLERANCE) ; tol = MAX (0.0, MIN (tol, 1.0)) ; PRINTF ((" "ID": 2-by-2 pivot tolerance: %g\n", (Int) INDEX (UMFPACK_2BY2_TOLERANCE), tol)) ; /* ---------------------------------------------------------------------- */ /* force fixQ */ /* ---------------------------------------------------------------------- */ force_fixQ = GET_CONTROL (UMFPACK_FIXQ, UMFPACK_DEFAULT_FIXQ) ; PRINTF ((" "ID": Q fixed during numerical factorization: %g ", (Int) INDEX (UMFPACK_FIXQ), force_fixQ)) ; if (force_fixQ > 0) { PRINTF (("(yes)\n")) ; } else if (force_fixQ < 0) { PRINTF (("(no)\n")) ; } else { PRINTF (("(auto)\n")) ; } /* ---------------------------------------------------------------------- */ /* AMD parameters */ /* ---------------------------------------------------------------------- */ amd_alpha = GET_CONTROL (UMFPACK_AMD_DENSE, UMFPACK_DEFAULT_AMD_DENSE) ; PRINTF ((" "ID": AMD dense row/col parameter: %g\n", (Int) INDEX (UMFPACK_AMD_DENSE), amd_alpha)) ; if (amd_alpha < 0) { PRINTF ((" no \"dense\" rows/columns\n")) ; } else { PRINTF ((" \"dense\" rows/columns have > max (16, (%g)*sqrt(n))" " entries\n", amd_alpha)) ; } PRINTF ((" Only used if the AMD ordering is used.\n")) ; /* ---------------------------------------------------------------------- */ /* pivot tolerance for symmetric pivoting */ /* ---------------------------------------------------------------------- */ relpt2 = GET_CONTROL (UMFPACK_SYM_PIVOT_TOLERANCE, UMFPACK_DEFAULT_SYM_PIVOT_TOLERANCE) ; relpt2 = MAX (0.0, MIN (relpt2, 1.0)) ; PRINTF ((" "ID": diagonal pivot tolerance: %g\n" " Only used if diagonal pivoting is attempted.\n", (Int) INDEX (UMFPACK_SYM_PIVOT_TOLERANCE), relpt2)) ; /* ---------------------------------------------------------------------- */ /* scaling */ /* ---------------------------------------------------------------------- */ scale = GET_CONTROL (UMFPACK_SCALE, UMFPACK_DEFAULT_SCALE) ; if (scale != UMFPACK_SCALE_NONE && scale != UMFPACK_SCALE_MAX) { scale = UMFPACK_DEFAULT_SCALE ; } PRINTF ((" "ID": scaling: "ID, (Int) INDEX (UMFPACK_SCALE), scale)) ; if (scale == UMFPACK_SCALE_NONE) { PRINTF ((" (no)")) ; } else if (scale == UMFPACK_SCALE_SUM) { PRINTF ((" (divide each row by sum of abs. values in each row)")) ; } else if (scale == UMFPACK_SCALE_MAX) { PRINTF ((" (divide each row by max. abs. value in each row)")) ; } PRINTF (("\n")) ; /* ---------------------------------------------------------------------- */ /* frontal matrix allocation parameter */ /* ---------------------------------------------------------------------- */ front_alloc_init = GET_CONTROL (UMFPACK_FRONT_ALLOC_INIT, UMFPACK_DEFAULT_FRONT_ALLOC_INIT) ; front_alloc_init = MIN (1.0, front_alloc_init) ; if (front_alloc_init >= 0) { PRINTF ((" "ID": frontal matrix allocation ratio: %g\n", (Int) INDEX (UMFPACK_FRONT_ALLOC_INIT), front_alloc_init)) ; } else { s = -front_alloc_init ; s = MAX (1, s) ; PRINTF ((" "ID": initial frontal matrix size (# of Entry's): "ID"\n", (Int) INDEX (UMFPACK_FRONT_ALLOC_INIT), s)) ; } /* ---------------------------------------------------------------------- */ /* drop tolerance */ /* ---------------------------------------------------------------------- */ droptol = GET_CONTROL (UMFPACK_DROPTOL, UMFPACK_DEFAULT_DROPTOL) ; PRINTF ((" "ID": drop tolerance: %g\n", (Int) INDEX (UMFPACK_DROPTOL), droptol)) ; /* ---------------------------------------------------------------------- */ /* aggressive absorption */ /* ---------------------------------------------------------------------- */ aggr = GET_CONTROL (UMFPACK_AGGRESSIVE, UMFPACK_DEFAULT_AGGRESSIVE) ; PRINTF ((" "ID": AMD and COLAMD aggressive absorption: %g", (Int) INDEX (UMFPACK_AGGRESSIVE), aggr)) ; if (aggr != 0.0) { PRINTF ((" (yes)\n")) ; } else { PRINTF ((" (no)\n")) ; } /* ---------------------------------------------------------------------- */ /* compile-time options */ /* ---------------------------------------------------------------------- */ PRINTF (( "\n The following options can only be changed at compile-time:\n")) ; PRINTF ((" "ID": BLAS library used: ", (Int) INDEX (UMFPACK_COMPILED_WITH_BLAS))) ; #ifdef NBLAS PRINTF (("none. UMFPACK will be slow.\n")) ; #else PRINTF (("Fortran BLAS. size of BLAS integer: "ID"\n", (Int) (sizeof (BLAS_INT)))) ; #endif #ifdef MATLAB_MEX_FILE PRINTF ((" "ID": compiled for MATLAB\n", (Int) INDEX (UMFPACK_COMPILED_FOR_MATLAB))) ; #else #ifdef MATHWORKS PRINTF ((" "ID": compiled for MATLAB\n", (Int) INDEX (UMFPACK_COMPILED_FOR_MATLAB))) ; #else PRINTF ((" "ID": compiled for ANSI C\n", (Int) INDEX (UMFPACK_COMPILED_FOR_MATLAB))) ; #endif #endif #ifdef NO_TIMER PRINTF ((" "ID": no CPU timer \n", (Int) INDEX (UMFPACK_COMPILED_WITH_GETRUSAGE))) ; #else #ifndef NPOSIX PRINTF ((" "ID": CPU timer is POSIX times ( ) routine.\n", (Int) INDEX (UMFPACK_COMPILED_WITH_GETRUSAGE))) ; #else #ifdef GETRUSAGE PRINTF ((" "ID": CPU timer is getrusage.\n", (Int) INDEX (UMFPACK_COMPILED_WITH_GETRUSAGE))) ; #else PRINTF ((" "ID": CPU timer is ANSI C clock (may wrap around).\n", (Int) INDEX (UMFPACK_COMPILED_WITH_GETRUSAGE))) ; #endif #endif #endif #ifndef NDEBUG PRINTF (( "**** Debugging enabled (UMFPACK will be exceedingly slow!) *****************\n" " "ID": compiled with debugging enabled. ", (Int) INDEX (UMFPACK_COMPILED_IN_DEBUG_MODE))) ; #else PRINTF ((" "ID": compiled for normal operation (debugging disabled)\n", (Int) INDEX (UMFPACK_COMPILED_IN_DEBUG_MODE))) ; #endif PRINTF ((" computer/operating system: %s\n", UMFPACK_ARCHITECTURE)) ; PRINTF ((" size of int: %g UF_long: %g Int: %g pointer: %g" " double: %g Entry: %g (in bytes)\n\n", (double) sizeof (int), (double) sizeof (UF_long), (double) sizeof (Int), (double) sizeof (void *), (double) sizeof (double), (double) sizeof (Entry))) ; } SuiteSparse/UMFPACK/Source/umfpack_save_symbolic.c0000644001170100242450000000616510677543752021036 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_save_symbolic ================================================ */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Saves a Symbolic object to a file. It can later be read back in via a call to umfpack_*_load_symbolic. */ #include "umf_internal.h" #include "umf_valid_symbolic.h" #define WRITE(object,type,n) \ { \ ASSERT (object != (type *) NULL) ; \ if (fwrite (object, sizeof (type), n, f) != (size_t) n) \ { \ fclose (f) ; \ return (UMFPACK_ERROR_file_IO) ; \ } \ } /* ========================================================================== */ /* === UMFPACK_save_symbolic ================================================ */ /* ========================================================================== */ GLOBAL Int UMFPACK_save_symbolic ( void *SymbolicHandle, char *user_filename ) { SymbolicType *Symbolic ; char *filename ; FILE *f ; /* get the Symbolic object */ Symbolic = (SymbolicType *) SymbolicHandle ; /* make sure the Symbolic object is valid */ if (!UMF_valid_symbolic (Symbolic)) { return (UMFPACK_ERROR_invalid_Symbolic_object) ; } /* get the filename, or use the default name if filename is NULL */ if (user_filename == (char *) NULL) { filename = "symbolic.umf" ; } else { filename = user_filename ; } f = fopen (filename, "wb") ; if (!f) { return (UMFPACK_ERROR_file_IO) ; } /* write the Symbolic object to the file, in binary */ WRITE (Symbolic, SymbolicType, 1) ; WRITE (Symbolic->Cperm_init, Int, Symbolic->n_col+1) ; WRITE (Symbolic->Rperm_init, Int, Symbolic->n_row+1) ; WRITE (Symbolic->Front_npivcol, Int, Symbolic->nfr+1) ; WRITE (Symbolic->Front_parent, Int, Symbolic->nfr+1) ; WRITE (Symbolic->Front_1strow, Int, Symbolic->nfr+1) ; WRITE (Symbolic->Front_leftmostdesc, Int, Symbolic->nfr+1) ; WRITE (Symbolic->Chain_start, Int, Symbolic->nchains+1) ; WRITE (Symbolic->Chain_maxrows, Int, Symbolic->nchains+1) ; WRITE (Symbolic->Chain_maxcols, Int, Symbolic->nchains+1) ; WRITE (Symbolic->Cdeg, Int, Symbolic->n_col+1) ; WRITE (Symbolic->Rdeg, Int, Symbolic->n_row+1) ; if (Symbolic->esize > 0) { /* only when dense rows are present */ WRITE (Symbolic->Esize, Int, Symbolic->esize) ; } if (Symbolic->prefer_diagonal) { /* only when diagonal pivoting is prefered */ WRITE (Symbolic->Diagonal_map, Int, Symbolic->n_col+1) ; } /* close the file */ fclose (f) ; return (UMFPACK_OK) ; } SuiteSparse/UMFPACK/Source/umf_apply_order.c0000644001170100242450000000266010677540545017651 0ustar davisfac/* ========================================================================== */ /* === UMF_apply_order ====================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Apply post-ordering of supernodal elimination tree. */ #include "umf_internal.h" #include "umf_apply_order.h" GLOBAL void UMF_apply_order ( Int Front [ ], /* of size nn on input, size nfr on output */ const Int Order [ ], /* Order [i] = k, i in the range 0..nn-1, * and k in the range 0..nfr-1, means that node * i is the kth node in the postordered tree. */ Int Temp [ ], /* workspace of size nfr */ Int nn, /* nodes are numbered in the range 0..nn-1 */ Int nfr /* the number of nodes actually in use */ ) { Int i, k ; for (i = 0 ; i < nn ; i++) { k = Order [i] ; ASSERT (k >= EMPTY && k < nfr) ; if (k != EMPTY) { Temp [k] = Front [i] ; } } for (k = 0 ; k < nfr ; k++) { Front [k] = Temp [k] ; } } SuiteSparse/UMFPACK/Source/umf_apply_order.h0000644001170100242450000000102110617161401017624 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL void UMF_apply_order ( Int Front [ ], const Int Order [ ], Int Temp [ ], Int n_col, Int nfr ) ; SuiteSparse/UMFPACK/Source/umfpack_get_determinant.c0000644001170100242450000001776510623346332021342 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_get_determinant ============================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* UMFPACK_get_determinant contributed by David Bateman, Motorola, Paris. */ /* -------------------------------------------------------------------------- */ /* User-callable. From the LU factors, scale factor, and permutation vectors held in the Numeric object, calculates the determinant of the matrix A. See umfpack_get_determinant.h for a more detailed description. Dynamic memory usage: calls UMF_malloc once, for a total space of n integers, and then frees all of it via UMF_free when done. Contributed by David Bateman, Motorola, Nov. 2004. Modified for V4.4, Jan. 2005. */ #include "umf_internal.h" #include "umf_valid_numeric.h" #include "umf_malloc.h" #include "umf_free.h" /* ========================================================================== */ /* === rescale_determinant ================================================== */ /* ========================================================================== */ /* If the mantissa is too big or too small, rescale it and change exponent */ PRIVATE Int rescale_determinant ( Entry *d_mantissa, double *d_exponent ) { double d_abs ; ABS (d_abs, *d_mantissa) ; if (SCALAR_IS_ZERO (d_abs)) { /* the determinant is zero */ *d_exponent = 0 ; return (FALSE) ; } if (SCALAR_IS_NAN (d_abs)) { /* the determinant is NaN */ return (FALSE) ; } while (d_abs < 1.) { SCALE (*d_mantissa, 10.0) ; *d_exponent = *d_exponent - 1.0 ; ABS (d_abs, *d_mantissa) ; } while (d_abs >= 10.) { SCALE (*d_mantissa, 0.1) ; *d_exponent = *d_exponent + 1.0 ; ABS (d_abs, *d_mantissa) ; } return (TRUE) ; } /* ========================================================================== */ /* === UMFPACK_get_determinant ============================================== */ /* ========================================================================== */ GLOBAL Int UMFPACK_get_determinant ( double *Mx, #ifdef COMPLEX double *Mz, #endif double *Ex, void *NumericHandle, double User_Info [UMFPACK_INFO] ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Entry d_mantissa, d_tmp ; double d_exponent, Info2 [UMFPACK_INFO], one [2] = {1.0, 0.0}, d_sign ; Entry *D ; double *Info, *Rs ; NumericType *Numeric ; Int i, n, itmp, npiv, *Wi, *Rperm, *Cperm, do_scale ; #ifndef NRECIPROCAL Int do_recip ; #endif /* ---------------------------------------------------------------------- */ /* check input parameters */ /* ---------------------------------------------------------------------- */ if (User_Info != (double *) NULL) { /* return Info in user's array */ Info = User_Info ; } else { /* no Info array passed - use local one instead */ Info = Info2 ; for (i = 0 ; i < UMFPACK_INFO ; i++) { Info [i] = EMPTY ; } } Info [UMFPACK_STATUS] = UMFPACK_OK ; Numeric = (NumericType *) NumericHandle ; if (!UMF_valid_numeric (Numeric)) { Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_Numeric_object ; return (UMFPACK_ERROR_invalid_Numeric_object) ; } if (Numeric->n_row != Numeric->n_col) { /* only square systems can be handled */ Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_system ; return (UMFPACK_ERROR_invalid_system) ; } if (Mx == (double *) NULL) { Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ; return (UMFPACK_ERROR_argument_missing) ; } n = Numeric->n_row ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ Wi = (Int *) UMF_malloc (n, sizeof (Int)) ; if (!Wi) { DEBUGm4 (("out of memory: get determinant\n")) ; Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; return (UMFPACK_ERROR_out_of_memory) ; } /* ---------------------------------------------------------------------- */ /* compute the determinant */ /* ---------------------------------------------------------------------- */ Rs = Numeric->Rs ; /* row scale factors */ do_scale = (Rs != (double *) NULL) ; #ifndef NRECIPROCAL do_recip = Numeric->do_recip ; #endif d_mantissa = ((Entry *) one) [0] ; d_exponent = 0.0 ; D = Numeric->D ; /* compute product of diagonal entries of U */ for (i = 0 ; i < n ; i++) { MULT (d_tmp, d_mantissa, D [i]) ; d_mantissa = d_tmp ; if (!rescale_determinant (&d_mantissa, &d_exponent)) { /* the determinant is zero or NaN */ Info [UMFPACK_STATUS] = UMFPACK_WARNING_singular_matrix ; /* no need to compute the determinant of R */ do_scale = FALSE ; break ; } } /* compute product of diagonal entries of R (or its inverse) */ if (do_scale) { for (i = 0 ; i < n ; i++) { #ifndef NRECIPROCAL if (do_recip) { /* compute determinant of R inverse */ SCALE_DIV (d_mantissa, Rs [i]) ; } else #endif { /* compute determinant of R */ SCALE (d_mantissa, Rs [i]) ; } if (!rescale_determinant (&d_mantissa, &d_exponent)) { /* the determinant is zero or NaN. This is very unlikey to * occur here, since the scale factors for a tiny or zero row * are set to 1. */ Info [UMFPACK_STATUS] = UMFPACK_WARNING_singular_matrix ; break ; } } } /* ---------------------------------------------------------------------- */ /* determine if P and Q are odd or even permutations */ /* ---------------------------------------------------------------------- */ npiv = 0 ; Rperm = Numeric->Rperm ; for (i = 0 ; i < n ; i++) { Wi [i] = Rperm [i] ; } for (i = 0 ; i < n ; i++) { while (Wi [i] != i) { itmp = Wi [Wi [i]] ; Wi [Wi [i]] = Wi [i] ; Wi [i] = itmp ; npiv++ ; } } Cperm = Numeric->Cperm ; for (i = 0 ; i < n ; i++) { Wi [i] = Cperm [i] ; } for (i = 0 ; i < n ; i++) { while (Wi [i] != i) { itmp = Wi [Wi [i]] ; Wi [Wi [i]] = Wi [i] ; Wi [i] = itmp ; npiv++ ; } } /* if npiv is odd, the sign is -1. if it is even, the sign is +1 */ d_sign = (npiv % 2) ? -1. : 1. ; /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ (void) UMF_free ((void *) Wi) ; /* ---------------------------------------------------------------------- */ /* compute the magnitude and exponent of the determinant */ /* ---------------------------------------------------------------------- */ if (Ex == (double *) NULL) { /* Ex is not provided, so return the entire determinant in d_mantissa */ SCALE (d_mantissa, pow (10.0, d_exponent)) ; } else { Ex [0] = d_exponent ; } Mx [0] = d_sign * REAL_COMPONENT (d_mantissa) ; #ifdef COMPLEX if (SPLIT (Mz)) { Mz [0] = d_sign * IMAG_COMPONENT (d_mantissa) ; } else { Mx [1] = d_sign * IMAG_COMPONENT (d_mantissa) ; } #endif /* determine if the determinant has (or will) overflow or underflow */ if (d_exponent + 1.0 > log10 (DBL_MAX)) { Info [UMFPACK_STATUS] = UMFPACK_WARNING_determinant_overflow ; } else if (d_exponent - 1.0 < log10 (DBL_MIN)) { Info [UMFPACK_STATUS] = UMFPACK_WARNING_determinant_underflow ; } return (UMFPACK_OK) ; } SuiteSparse/UMFPACK/Source/umf_internal.h0000644001170100242450000006330410617161637017147 0ustar davisfac/* ========================================================================== */ /* === umf_internal.h ======================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* This file is for internal use in UMFPACK itself, and should not be included in user code. Use umfpack.h instead. User-accessible file names and routine names all start with the letters "umfpack_". Non-user-accessible file names and routine names all start with "umf_". */ #ifndef _UMF_INTERNAL #define _UMF_INTERNAL /* -------------------------------------------------------------------------- */ /* ANSI standard include files */ /* -------------------------------------------------------------------------- */ /* from float.h: DBL_EPSILON */ #include /* from string.h: strcmp */ #include /* when debugging, assert.h and the assert macro are used (see umf_dump.h) */ /* -------------------------------------------------------------------------- */ /* Architecture */ /* -------------------------------------------------------------------------- */ #if defined (__sun) || defined (MSOL2) || defined (ARCH_SOL2) #define UMF_SOL2 #define UMFPACK_ARCHITECTURE "Sun Solaris" #elif defined (__sgi) || defined (MSGI) || defined (ARCH_SGI) #define UMF_SGI #define UMFPACK_ARCHITECTURE "SGI Irix" #elif defined (__linux) || defined (MGLNX86) || defined (ARCH_GLNX86) #define UMF_LINUX #define UMFPACK_ARCHITECTURE "Linux" #elif defined (_AIX) || defined (MIBM_RS) || defined (ARCH_IBM_RS) #define UMF_AIX #define UMFPACK_ARCHITECTURE "IBM AIX" #elif defined (__alpha) || defined (MALPHA) || defined (ARCH_ALPHA) #define UMF_ALPHA #define UMFPACK_ARCHITECTURE "Compaq Alpha" #elif defined (_WIN32) || defined (WIN32) #if defined (__MINGW32__) #define UMF_MINGW #elif defined (__CYGWIN32__) #define UMF_CYGWIN #else #define UMF_WINDOWS #endif #define UMFPACK_ARCHITECTURE "Microsoft Windows" #elif defined (__hppa) || defined (__hpux) || defined (MHPUX) || defined (ARCH_HPUX) #define UMF_HP #define UMFPACK_ARCHITECTURE "HP Unix" #elif defined (__hp700) || defined (MHP700) || defined (ARCH_HP700) #define UMF_HP #define UMFPACK_ARCHITECTURE "HP 700 Unix" #else /* If the architecture is unknown, and you call the BLAS, you may need to */ /* define BLAS_BY_VALUE, BLAS_NO_UNDERSCORE, and/or BLAS_CHAR_ARG yourself. */ #define UMFPACK_ARCHITECTURE "unknown" #endif /* -------------------------------------------------------------------------- */ /* basic definitions (see also amd_internal.h) */ /* -------------------------------------------------------------------------- */ #define ONES_COMPLEMENT(r) (-(r)-1) /* -------------------------------------------------------------------------- */ /* AMD include file */ /* -------------------------------------------------------------------------- */ /* stdio.h, stdlib.h, limits.h, and math.h, NDEBUG definition, assert.h */ #include "amd_internal.h" /* -------------------------------------------------------------------------- */ /* MATLAB include files */ /* -------------------------------------------------------------------------- */ /* only used when compiling the UMFPACK mexFunction */ #ifdef MATLAB_MEX_FILE #include "matrix.h" #include "mex.h" #endif /* -------------------------------------------------------------------------- */ /* Real/complex and int/UF_long definitions, double relops */ /* -------------------------------------------------------------------------- */ #include "umf_version.h" /* -------------------------------------------------------------------------- */ /* Compile-time configurations */ /* -------------------------------------------------------------------------- */ #include "umf_config.h" /* -------------------------------------------------------------------------- */ /* umfpack include file */ /* -------------------------------------------------------------------------- */ #include "umfpack.h" /* -------------------------------------------------------------------------- */ /* for contents of Info. This must correlate with umfpack.h */ /* -------------------------------------------------------------------------- */ #define ESTIMATE (UMFPACK_NUMERIC_SIZE_ESTIMATE - UMFPACK_NUMERIC_SIZE) #define ACTUAL 0 /* -------------------------------------------------------------------------- */ /* get a parameter from the Control array */ /* -------------------------------------------------------------------------- */ #define GET_CONTROL(i,default) \ ((Control != (double *) NULL) ? \ (SCALAR_IS_NAN (Control [i]) ? default : Control [i]) \ : default) /* -------------------------------------------------------------------------- */ /* for clearing the external degree counters */ /* -------------------------------------------------------------------------- */ #define MAX_MARK(n) Int_MAX - (2*(n)+1) /* -------------------------------------------------------------------------- */ /* convert number of Units to MBytes */ /* -------------------------------------------------------------------------- */ #define MBYTES(units) (((units) * sizeof (Unit)) / 1048576.0) /* -------------------------------------------------------------------------- */ /* dense row/column macro */ /* -------------------------------------------------------------------------- */ /* In order for a row or column to be treated as "dense", it must have more */ /* entries than the value returned by this macro. n is the dimension of the */ /* matrix, and alpha is the dense row/column control parameter. */ /* Note: this is not defined if alpha is NaN or Inf: */ #define UMFPACK_DENSE_DEGREE_THRESHOLD(alpha,n) \ ((Int) MAX (16.0, (alpha) * 16.0 * sqrt ((double) (n)))) /* -------------------------------------------------------------------------- */ /* PRINTF */ /* -------------------------------------------------------------------------- */ #define PRINTFk(k,params) { if (prl >= (k)) { PRINTF (params) ; } } #define PRINTF1(params) PRINTFk (1, params) #define PRINTF2(params) PRINTFk (2, params) #define PRINTF3(params) PRINTFk (3, params) #define PRINTF4(params) PRINTFk (4, params) #define PRINTF5(params) PRINTFk (5, params) #define PRINTF6(params) PRINTFk (6, params) /* -------------------------------------------------------------------------- */ /* Fixed control parameters */ /* -------------------------------------------------------------------------- */ /* maximum number of columns to consider at one time, in a single front */ #define MAX_CANDIDATES 128 /* reduce Numeric->Memory request by this ratio, if allocation fails */ #define UMF_REALLOC_REDUCTION (0.95) /* increase Numeric->Memory request by this ratio, if we need more */ #define UMF_REALLOC_INCREASE (1.2) /* increase the dimensions of the current frontal matrix by this factor * when it needs to grow. */ #define UMF_FRONTAL_GROWTH (1.2) /* largest BLAS block size permitted */ #define MAXNB 64 /* if abs (y) < RECIPROCAL_TOLERANCE, then compute x/y. Otherwise x*(1/y). * Ignored if NRECIPROCAL is defined */ #define RECIPROCAL_TOLERANCE 1e-12 /* -------------------------------------------------------------------------- */ /* Memory allocator */ /* -------------------------------------------------------------------------- */ /* See AMD/Source/amd_global.c and AMD/Source/amd.h for the * definition of the memory allocator used by UMFPACK. Versions 4.4 and * earlier had their memory allocator definitions here. Other global * function pointers for UMFPACK are located in umf_global.c. * * The MATLAB mexFunction uses MATLAB's memory manager and mexPrintf, while the * C-callable AMD library uses the ANSI C malloc, free, realloc, and printf * routines. */ /* -------------------------------------------------------------------------- */ /* Memory space definitions */ /* -------------------------------------------------------------------------- */ /* for memory alignment - assume double has worst case alignment */ typedef double Align ; /* get number of bytes required to hold n items of a type: */ /* note that this will not overflow, because sizeof (type) is always */ /* greater than or equal to sizeof (Int) >= 2 */ #define BYTES(type,n) (sizeof (type) * (n)) /* ceiling of (b/u). Assumes b >= 0 and u > 0 */ #define CEILING(b,u) (((b) + (u) - 1) / (u)) /* get number of Units required to hold n items of a type: */ #define UNITS(type,n) (CEILING (BYTES (type, n), sizeof (Unit))) /* same as DUNITS, but use double instead of int to avoid overflow */ #define DUNITS(type,n) (ceil (BYTES (type, (double) n) / sizeof (Unit))) union Unit_union { /* memory is allocated in multiples of Unit */ struct { Int size, /* size, in Units, of the block, excl. header block */ /* size >= 0: block is in use */ /* size < 0: block is free, of |size| Units */ prevsize ; /* size, in Units, of preceding block in S->Memory */ /* during garbage_collection, prevsize is set to -e-1 */ /* for element e, or positive (and thus a free block) */ /* otherwise */ } header ; /* block header */ Align xxxxxx ; /* force alignment of blocks (xxxxxx is never used) */ } ; typedef union Unit_union Unit ; /* get the size of an allocated block */ #define GET_BLOCK_SIZE(p) (((p)-1)->header.size) /* -------------------------------------------------------------------------- */ /* Numeric */ /* -------------------------------------------------------------------------- */ /* NUMERIC_VALID and SYMBOLIC_VALID: The different values of SYBOLIC_VALID and NUMERIC_VALID are chosen as a first defense against corrupted *Symbolic or *Numeric pointers passed to an UMFPACK routine. They also ensure that the objects are used only by the same version that created them (umfpack_di_*, umfpack_dl_*, umfpack_zi_*, or umfpack_zl_*). The values have also been changed since prior releases of the code to ensure that all routines that operate on the objects are of the same release. The values themselves are purely arbitrary. The are less than the ANSI C required minimums of INT_MAX and LONG_MAX, respectively. */ #ifdef DINT #define NUMERIC_VALID 15977 #define SYMBOLIC_VALID 41937 #endif #ifdef DLONG #define NUMERIC_VALID 399789720 #define SYMBOLIC_VALID 399192713 #endif #ifdef ZINT #define NUMERIC_VALID 17957 #define SYMBOLIC_VALID 40927 #endif #ifdef ZLONG #define NUMERIC_VALID 129987754 #define SYMBOLIC_VALID 110291734 #endif typedef struct /* NumericType */ { double flops, /* "true" flop count */ relpt, /* relative pivot tolerance used */ relpt2, /* relative pivot tolerance used for sym. */ droptol, alloc_init, /* initial allocation of Numeric->memory */ front_alloc_init, /* frontal matrix allocation parameter */ rsmin, /* smallest row sum */ rsmax, /* largest row sum */ min_udiag, /* smallest abs value on diagonal of D */ max_udiag, /* smallest abs value on diagonal of D */ rcond ; /* min (D) / max (D) */ Int scale ; Int valid ; /* set to NUMERIC_VALID, for validity check */ /* Memory space for A and LU factors */ Unit *Memory ; /* working memory for A and LU factors */ Int ihead, /* pointer to tail of LU factors, in Numeric->Memory */ itail, /* pointer to top of elements & tuples, */ /* in Numeric->Memory */ ibig, /* pointer to largest free block seen in tail */ size ; /* size of Memory, in Units */ Int *Rperm, /* pointer to row perm array, size: n+1 */ /* after UMF_kernel: Rperm [new] = old */ /* during UMF_kernel: Rperm [old] = new */ *Cperm, /* pointer to col perm array, size: n+1 */ /* after UMF_kernel: Cperm [new] = old */ /* during UMF_kernel: Cperm [old] = new */ *Upos, /* see UMFPACK_get_numeric for a description */ *Lpos, *Lip, *Lilen, *Uip, *Uilen, *Upattern ; /* pattern of last row of U (if singular) */ Int ulen, /* length of Upattern */ npiv, /* number of structural pivots found (sprank approx) */ nnzpiv ; /* number of numerical (nonzero) pivots found */ Entry *D ; /* D [i] is the diagonal entry of U */ Int do_recip ; double *Rs ; /* scale factors for the rows of A and b */ /* do_recip FALSE: Divide row i by Rs [i] */ /* do_recip TRUE: Multiply row i by Rs [i] */ Int n_row, n_col, /* A is n_row-by-n_row */ n1 ; /* number of singletons */ /* for information only: */ Int tail_usage, /* amount of memory allocated in tail */ /* head_usage is Numeric->ihead */ init_usage, /* memory usage just after UMF_kernel_init */ max_usage, /* peak memory usage (excludes internal and external */ /* fragmentation in the tail) */ ngarbage, /* number of garbage collections performed */ nrealloc, /* number of reallocations performed */ ncostly, /* number of costly reallocations performed */ isize, /* size of integer pattern of L and U */ nLentries, /* number of entries in L, excluding diagonal */ nUentries, /* number of entries in U, including diagonal */ /* Some entries may be numerically zero. */ lnz, /* number of nonzero entries in L, excl. diagonal */ all_lnz, /* lnz plus entries dropped from L */ unz, /* number of nonzero entries in U, excl. diagonal */ all_unz, /* unz plus entries dropped form U */ maxfrsize ; /* largest actual front size */ Int maxnrows, maxncols ; /* not the same as Symbolic->maxnrows/cols* */ } NumericType ; /* -------------------------------------------------------------------------- */ /* Element tuples for connecting elements together in a matrix */ /* -------------------------------------------------------------------------- */ typedef struct /* Tuple */ { /* The (e,f) tuples for the element lists */ Int e, /* element */ f ; /* contribution to the row/col appears at this offset */ } Tuple ; #define TUPLES(t) MAX (4, (t) + 1) /* Col_degree is aliased with Cperm, and Row_degree with Rperm */ #define NON_PIVOTAL_COL(col) (Col_degree [col] >= 0) #define NON_PIVOTAL_ROW(row) (Row_degree [row] >= 0) /* -------------------------------------------------------------------------- */ /* An element */ /* -------------------------------------------------------------------------- */ typedef struct /* Element */ { Int cdeg, /* external column degree + cdeg0 offset */ rdeg, /* external row degree + rdeg0 offset */ nrowsleft, /* number of rows remaining */ ncolsleft, /* number of columns remaining */ nrows, /* number of rows */ ncols, /* number of columns */ next ; /* for list link of sons, used during assembly only */ /* followed in memory by: Int col [0..ncols-1], column indices of this element row [0..nrows-1] ; row indices of this element Entry (suitably aligned, see macro below) C [0...nrows-1, 0...ncols-1] ; size of C is nrows*ncols Entry's */ } Element ; /* macros for computing pointers to row/col indices, and contribution block: */ #define GET_ELEMENT_SIZE(nr,nc) \ (UNITS (Element, 1) + UNITS (Int, (nc) + (nr)) + UNITS (Entry, (nc) * (nr))) #define DGET_ELEMENT_SIZE(nr,nc) \ (DUNITS (Element, 1) + DUNITS (Int, (nc) + (nr)) + DUNITS (Entry, (nc) * (nr))) #define GET_ELEMENT_COLS(ep,p,Cols) { \ ASSERT (p != (Unit *) NULL) ; \ ASSERT (p >= Numeric->Memory + Numeric->itail) ; \ ASSERT (p <= Numeric->Memory + Numeric->size) ; \ ep = (Element *) p ; \ p += UNITS (Element, 1) ; \ Cols = (Int *) p ; \ } #define GET_ELEMENT_PATTERN(ep,p,Cols,Rows,ncm) { \ GET_ELEMENT_COLS (ep, p, Cols) ; \ ncm = ep->ncols ; \ Rows = Cols + ncm ; \ } #define GET_ELEMENT(ep,p,Cols,Rows,ncm,nrm,C) { \ GET_ELEMENT_PATTERN (ep, p, Cols, Rows, ncm) ; \ nrm = ep->nrows ; \ p += UNITS (Int, ncm + nrm) ; \ C = (Entry *) p ; \ } /* -------------------------------------------------------------------------- */ /* Work data structure */ /* -------------------------------------------------------------------------- */ /* This data structure holds items needed only during factorization. All of this is freed when UMFPACK_numeric completes. Note that some of it is stored in the tail end of Numeric->S (namely, the Tuples and the Elements). */ typedef struct /* WorkType */ { /* ---------------------------------------------------------------------- */ /* information about each row and col of A */ /* ---------------------------------------------------------------------- */ /* Row_tuples: pointer to tuple list (alias with Numeric->Uip) Row_tlen: number of tuples (alias with Numeric->Uilen) Col_tuples: pointer to tuple list (alias with Numeric->Lip) Col_tlen: number of tuples (alias with Numeric->Lilen) Row_degree: degree of the row or column (alias Numeric->Rperm) Col_degree: degree of the row or column (alias Numeric->Cperm) The Row_degree and Col_degree are MATLAB-style colmmd approximations, are equal to the sum of the sizes of the elements (contribution blocks) in each row and column. They are maintained when elements are created and assembled. They are used only during the pivot row and column search. They are not needed to represent the pattern of the remaining matrix. */ /* ---------------------------------------------------------------------- */ /* information about each element */ /* ---------------------------------------------------------------------- */ Int *E ; /* E [0 .. Work->elen-1] element "pointers" */ /* (offsets in Numeric->Memory) */ /* ---------------------------------------------------------------------- */ /* generic workspace */ /* ---------------------------------------------------------------------- */ Entry *Wx, *Wy ; /* each of size maxnrows+1 */ Int /* Sizes: nn = MAX (n_row, n_col) */ *Wp, /* nn+1 */ *Wrp, /* n_col+1 */ *Wm, /* maxnrows+1 */ *Wio, /* maxncols+1 */ *Woi, /* maxncols+1 */ *Woo, /* MAX (maxnrows,maxncols)+1 */ *Wrow, /* pointer to Fcols, Wio, or Woi */ *NewRows, /* list of rows to scan */ *NewCols ; /* list of cols to scan */ /* ---------------------------------------------------------------------- */ Int *Lpattern, /* pattern of column of L, for one Lchain */ *Upattern, /* pattern of row of U, for one Uchain */ ulen, llen ; /* length of Upattern and Lpattern */ Int *Diagonal_map, /* used for symmetric pivoting, of size nn+1 */ *Diagonal_imap ;/* used for symmetric pivoting, of size nn+1 */ /* ---------------------------------------------------------------------- */ Int n_row, n_col, /* matrix is n_row-by-n_col */ nz, /* nonzeros in the elements for this matrix */ n1, /* number of row and col singletons */ elen, /* max possible number of elements */ npiv, /* number of pivot rows and columns so far */ ndiscard, /* number of discarded pivot columns */ Wrpflag, nel, /* elements in use are in the range 1..nel */ noff_diagonal, prior_element, rdeg0, cdeg0, rrdeg, ccdeg, Candidates [MAX_CANDIDATES], /* current candidate pivot columns */ nCandidates, /* number of candidates in Candidate set */ ksuper, firstsuper, jsuper, ncand, /* number of candidates (some not in Candidates[ ]) */ nextcand, /* next candidate to place in Candidate search set */ lo, hi, pivrow, /* current pivot row */ pivcol, /* current pivot column */ do_extend, /* true if the next pivot extends the current front */ do_update, /* true if update should be applied */ nforced, /* number of forced updates because of frontal growth */ any_skip, do_scan2row, do_scan2col, do_grow, pivot_case, frontid, /* id of current frontal matrix */ nfr ; /* number of frontal matrices */ /* ---------------------------------------------------------------------- */ /* For row-merge tree */ /* ---------------------------------------------------------------------- */ Int *Front_new1strow ; /* ---------------------------------------------------------------------- */ /* current frontal matrix, F */ /* ---------------------------------------------------------------------- */ Int Pivrow [MAXNB], Pivcol [MAXNB] ; Entry *Flublock, /* LU block, nb-by-nb */ *Flblock, /* L block, fnr_curr-by-nb */ *Fublock, /* U block, nb-by-fnc_curr, or U' fnc_curr-by-nb */ *Fcblock ; /* C block, fnr_curr-by-fnc_curr */ Int *Frows, /* Frows [0.. ]: row indices of F */ *Fcols, /* Fcols [0.. ]: column indices of F */ *Frpos, /* position of row indices in F, or -1 if not present */ /* if Frows[i] == row, then Frpos[row] == i */ *Fcpos, /* position of col indices in F, or -1 if not present */ /* if Fcols[j] == col, then */ /* Fcpos[col] == j*Work->fnr_curr */ fnrows, /* number of rows in contribution block in F */ fncols, /* number of columns in contribution block in F */ fnr_curr, /* maximum # of rows in F (leading dimension) */ fnc_curr, /* maximum # of columns in F */ fcurr_size, /* current size of F */ fnrows_max, /* max possible column-dimension (max # of rows) of F */ fncols_max, /* max possible row-dimension (max # of columns) of F */ nb, fnpiv, /* number of pivots in F */ fnzeros, /* number of explicit zero entries in LU block */ fscan_row, /* where to start scanning rows of F in UMF_assemble */ fscan_col, /* where to start scanning cols of F in UMF_assemble */ fnrows_new, /* number of new row indices in F after pivot added */ fncols_new, /* number of new col indices in F after pivot added */ pivrow_in_front, /* true if current pivot row in Frows */ pivcol_in_front ; /* true if current pivot column in Fcols */ /* ---------------------------------------------------------------------- * Current frontal matrix * ---------------------------------------------------------------------- * The current frontal matrix is held as a single block of memory allocated * from the "tail" end of Numeric->Memory. It is subdivided into four * parts: an LU block, an L block, a U block, and a C block. * * Let k = fnpiv, r = fnrows, and c = fncols for the following discussion. * Let dr = fnr_curr and dc = fnc_curr. Note that r <= dr and c <= dc. * * The LU block is of dimension nb-by-nb. The first k-by-k part holds the * "diagonal" part of the LU factors for these k pivot rows and columns. * The k pivot row and column indices in this part are Pivrow [0..k-1] and * Pivcol [0..k-1], respectively. * * The L block is of dimension dr-by-nb. It holds the k pivot columns, * except for the leading k-by-k part in the LU block. Only the leading * r-by-k part is in use. * * The U block is of dimension dc-by-nb. It holds the k pivot rows, * except for the leading k-by-k part in the LU block. It is stored in * row-oriented form. Only the leading c-by-k part is in use. * * The C block is of dimension dr-by-dc. It holds the current contribution * block. Only the leading r-by-c part is in use. The column indices in * the C block are Fcols [0..c-1], and the row indices are Frows [0..r-1]. * * dr is always odd, to avoid bad cache behavior. */ } WorkType ; /* -------------------------------------------------------------------------- */ /* Symbolic */ /* -------------------------------------------------------------------------- */ /* This is is constructed by UMFPACK_symbolic, and is needed by UMFPACK_numeric to factor the matrix. */ typedef struct /* SymbolicType */ { double num_mem_usage_est, /* estimated max Numeric->Memory size */ num_mem_size_est, /* estimated final Numeric->Memory size */ peak_sym_usage, /* peak Symbolic and SymbolicWork usage */ sym, /* symmetry of pattern */ dnum_mem_init_usage, /* min Numeric->Memory for UMF_kernel_init */ amd_lunz, /* nz in LU for AMD, with symmetric pivoting */ lunz_bound ; /* max nx in LU, for arbitrary row pivoting */ Int valid, /* set to SYMBOLIC_VALID, for validity check */ max_nchains, nchains, *Chain_start, *Chain_maxrows, *Chain_maxcols, maxnrows, /* largest number of rows in any front */ maxncols, /* largest number of columns in any front */ *Front_npivcol, /* Front_npivcol [j] = size of jth supercolumn*/ *Front_1strow, /* first row index in front j */ *Front_leftmostdesc, /* leftmost desc of front j */ *Front_parent, /* super-column elimination tree */ *Cperm_init, /* initial column ordering */ *Rperm_init, /* initial row ordering */ *Cdeg, *Rdeg, *Esize, dense_row_threshold, n1, /* number of singletons */ nempty, /* MIN (nempty_row, nempty_col) */ *Diagonal_map, /* initial "diagonal" (after 2by2) */ esize, /* size of Esize array */ nfr, n_row, n_col, /* matrix A is n_row-by-n_col */ nz, /* nz of original matrix */ nb, /* block size for BLAS 3 */ num_mem_init_usage, /* min Numeric->Memory for UMF_kernel_init */ nempty_row, nempty_col, strategy, ordering, fixQ, prefer_diagonal, nzaat, nzdiag, amd_dmax ; } SymbolicType ; /* -------------------------------------------------------------------------- */ /* for debugging only: */ /* -------------------------------------------------------------------------- */ #include "umf_dump.h" /* -------------------------------------------------------------------------- */ /* for statement coverage testing only: */ /* -------------------------------------------------------------------------- */ #ifdef TESTING /* for testing integer overflow: */ #ifdef TEST_FOR_INTEGER_OVERFLOW #undef MAX_MARK #define MAX_MARK(n) (3*(n)) #endif /* for testing out-of-memory conditions: */ #define UMF_TCOV_TEST #ifndef EXTERN #define EXTERN extern #endif GLOBAL EXTERN int umf_fail, umf_fail_lo, umf_fail_hi ; GLOBAL EXTERN int umf_realloc_fail, umf_realloc_lo, umf_realloc_hi ; /* for testing malloc count: */ #define UMF_MALLOC_COUNT #endif #endif SuiteSparse/UMFPACK/Source/umf_mem_alloc_head_block.c0000644001170100242450000000342610677541726021417 0ustar davisfac/* ========================================================================== */ /* === UMF_mem_alloc_head_block ============================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* The UMF_mem_* routines manage the Numeric->Memory memory space. */ /* allocate nunits from head of Numeric->Memory. No header allocated. */ /* Returns the index into Numeric->Memory if successful, or 0 on failure. */ #include "umf_internal.h" #include "umf_mem_alloc_head_block.h" GLOBAL Int UMF_mem_alloc_head_block ( NumericType *Numeric, Int nunits ) { Int p, usage ; DEBUG2 (("GET BLOCK: from head, size "ID" ", nunits)) ; ASSERT (Numeric != (NumericType *) NULL) ; ASSERT (Numeric->Memory != (Unit *) NULL) ; #ifndef NDEBUG if (UMF_allocfail) { /* pretend to fail, to test garbage_collection */ DEBUGm2 (("UMF_mem_alloc_head_block: pretend to fail\n")) ; UMF_allocfail = FALSE ; /* don't fail the next time */ return (0) ; } #endif if (nunits > (Numeric->itail - Numeric->ihead)) { DEBUG2 ((" failed\n")) ; return (0) ; } /* return p as an offset from Numeric->Memory */ p = Numeric->ihead ; Numeric->ihead += nunits ; DEBUG2 (("p: "ID"\n", p)) ; usage = Numeric->ihead + Numeric->tail_usage ; Numeric->max_usage = MAX (Numeric->max_usage, usage) ; return (p) ; } SuiteSparse/UMFPACK/Source/umf_analyze.c0000644001170100242450000005056310677541517017001 0ustar davisfac/* ========================================================================== */ /* === UMF_analyze ========================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Symbolic LL' factorization of A'*A, to get upper bounds on the size of L and U for LU = PAQ, and to determine the frontal matrices and (supernodal) column elimination tree. No fill-reducing column pre-ordering is used. Returns TRUE if successful, FALSE if out of memory. UMF_analyze can only run out of memory if anzmax (which is Ap [n_row]) is too small. Uses workspace of size O(nonzeros in A). On input, the matrix A is stored in row-form at the tail end of Ai. It is destroyed on output. The rows of A must be sorted by increasing first column index. The matrix is assumed to be valid. Empty rows and columns have already been removed. */ #include "umf_internal.h" #include "umf_analyze.h" #include "umf_apply_order.h" #include "umf_fsize.h" /* ========================================================================== */ GLOBAL Int UMF_analyze ( Int n_row, /* A is n_row-by-n_col */ Int n_col, Int Ai [ ], /* Ai [Ap [0]..Ap[n_row]-1]: column indices */ /* destroyed on output. Note that this is NOT the */ /* user's Ai that was passed to UMFPACK_*symbolic */ /* size of Ai, Ap [n_row] = anzmax >= anz + n_col */ /* Ap [0] must be => n_col. The space to the */ /* front of Ai is used as workspace. */ Int Ap [ ], /* of size MAX (n_row, n_col) + 1 */ /* Ap [0..n_row]: row pointers */ /* Row i is in Ai [Ap [i] ... Ap [i+1]-1] */ /* rows must have smallest col index first, or be */ /* in sorted form. Used as workspace of size n_col */ /* and destroyed. */ /* Note that this is NOT the */ /* user's Ap that was passed to UMFPACK_*symbolic */ Int Up [ ], /* workspace of size n_col, and output column perm. * for column etree postorder. */ Int fixQ, /* temporary workspaces: */ Int W [ ], /* W [0..n_col-1] */ Int Link [ ], /* Link [0..n_col-1] */ /* output: information about each frontal matrix: */ Int Front_ncols [ ], /* size n_col */ Int Front_nrows [ ], /* of size n_col */ Int Front_npivcol [ ], /* of size n_col */ Int Front_parent [ ], /* of size n_col */ Int *nfr_out, Int *p_ncompactions /* number of compactions in UMF_analyze */ ) { /* ====================================================================== */ /* ==== local variables ================================================= */ /* ====================================================================== */ Int j, j3, col, k, row, parent, j2, pdest, p, p2, thickness, npivots, nfr, i, *Winv, kk, npiv, jnext, krow, knext, pfirst, jlast, ncompactions, *Front_stack, *Front_order, *Front_child, *Front_sibling, Wflag, npivcol, fallrows, fallcols, fpiv, frows, fcols, *Front_size ; nfr = 0 ; DEBUG0 (("UMF_analyze: anzmax "ID" anrow "ID" ancol "ID"\n", Ap [n_row], n_row, n_col)) ; /* ====================================================================== */ /* ==== initializations ================================================= */ /* ====================================================================== */ #pragma ivdep for (j = 0 ; j < n_col ; j++) { Link [j] = EMPTY ; W [j] = EMPTY ; Up [j] = EMPTY ; /* Frontal matrix data structure: */ Front_npivcol [j] = 0 ; /* number of pivot columns */ Front_nrows [j] = 0 ; /* number of rows, incl. pivot rows */ Front_ncols [j] = 0 ; /* number of cols, incl. pivot cols */ Front_parent [j] = EMPTY ; /* parent front */ /* Note that only non-pivotal columns are stored in a front (a "row" */ /* of U) during elimination. */ } /* the rows must be sorted by increasing min col */ krow = 0 ; pfirst = Ap [0] ; jlast = EMPTY ; jnext = EMPTY ; Wflag = 0 ; /* this test requires the size of Ai to be >= n_col + nz */ ASSERT (pfirst >= n_col) ; /* Ai must be large enough */ /* pdest points to the first free space in Ai */ pdest = 0 ; ncompactions = 0 ; /* ====================================================================== */ /* === compute symbolic LL' factorization (unsorted) ==================== */ /* ====================================================================== */ for (j = 0 ; j < n_col ; j = jnext) { DEBUG1 (("\n\n============Front "ID" starting. nfr = "ID"\n", j, nfr)) ; /* ================================================================== */ /* === garbage collection =========================================== */ /* ================================================================== */ if (pdest + (n_col-j) > pfirst) { /* we might run out ... compact the rows of U */ #ifndef NDEBUG DEBUG0 (("UMF_analyze COMPACTION, j="ID" pfirst="ID"\n", j, pfirst)) ; for (row = 0 ; row < j ; row++) { if (Up [row] != EMPTY) { /* this is a live row of U */ DEBUG1 (("Live row: "ID" cols: ", row)) ; p = Up [row] ; ASSERT (Front_ncols [row] > Front_npivcol [row]) ; p2 = p + (Front_ncols [row] - Front_npivcol [row]) ; for ( ; p < p2 ; p++) { DEBUG1 ((ID, Ai [p])) ; ASSERT (p < pfirst) ; ASSERT (Ai [p] > row && Ai [p] < n_col) ; } DEBUG1 (("\n")) ; } } DEBUG1 (("\nStarting to compact:\n")) ; #endif pdest = 0 ; ncompactions++ ; for (row = 0 ; row < j ; row++) { if (Up [row] != EMPTY) { /* this is a live row of U */ DEBUG1 (("Live row: "ID" cols: ", row)) ; ASSERT (row < n_col) ; p = Up [row] ; ASSERT (Front_ncols [row] > Front_npivcol [row]) ; p2 = p + (Front_ncols [row] - Front_npivcol [row]) ; Up [row] = pdest ; for ( ; p < p2 ; p++) { DEBUG1 ((ID, Ai [p])) ; ASSERT (p < pfirst) ; ASSERT (Ai [p] > row && Ai [p] < n_col) ; Ai [pdest++] = Ai [p] ; ASSERT (pdest <= pfirst) ; } DEBUG1 (("\n")) ; } } #ifndef NDEBUG DEBUG1 (("\nAFTER COMPACTION, j="ID" pfirst="ID"\n", j, pfirst)) ; for (row = 0 ; row < j ; row++) { if (Up [row] != EMPTY) { /* this is a live row of U */ DEBUG1 (("Live row: "ID" cols: ", row)) ; p = Up [row] ; ASSERT (Front_ncols [row] > Front_npivcol [row]) ; p2 = p + (Front_ncols [row] - Front_npivcol [row]) ; for ( ; p < p2 ; p++) { DEBUG1 ((ID, Ai [p])) ; ASSERT (p < pfirst) ; ASSERT (Ai [p] > row && Ai [p] < n_col) ; } DEBUG1 (("\n")) ; } } #endif } if (pdest + (n_col-j) > pfirst) { /* :: out of memory in umf_analyze :: */ /* it can't happen, if pfirst >= n_col */ return (FALSE) ; /* internal error! */ } /* ------------------------------------------------------------------ */ /* is the last front a child of this one? */ /* ------------------------------------------------------------------ */ if (jlast != EMPTY && Link [j] == jlast) { /* yes - create row j by appending to jlast */ DEBUG1 (("GOT:last front is child of this one: j "ID" jlast "ID"\n", j, jlast)) ; ASSERT (jlast >= 0 && jlast < j) ; Up [j] = Up [jlast] ; Up [jlast] = EMPTY ; /* find the parent, delete column j, and update W */ parent = n_col ; for (p = Up [j] ; p < pdest ; ) { j3 = Ai [p] ; DEBUG1 (("Initial row of U: col "ID" ", j3)) ; ASSERT (j3 >= 0 && j3 < n_col) ; DEBUG1 (("W: "ID" \n", W [j3])) ; ASSERT (W [j3] == Wflag) ; if (j == j3) { DEBUG1 (("Found column j at p = "ID"\n", p)) ; Ai [p] = Ai [--pdest] ; } else { if (j3 < parent) { parent = j3 ; } p++ ; } } /* delete jlast from the link list of j */ Link [j] = Link [jlast] ; ASSERT (Front_nrows [jlast] > Front_npivcol [jlast]) ; thickness = (Front_nrows [jlast] - Front_npivcol [jlast]) ; DEBUG1 (("initial thickness: "ID"\n", thickness)) ; } else { Up [j] = pdest ; parent = n_col ; /* thickness: number of (nonpivotal) rows in frontal matrix j */ thickness = 0 ; Wflag = j ; } /* ================================================================== */ /* === compute row j of A*A' ======================================== */ /* ================================================================== */ /* ------------------------------------------------------------------ */ /* flag the diagonal entry in row U, but do not add to pattern */ /* ------------------------------------------------------------------ */ ASSERT (pdest <= pfirst) ; W [j] = Wflag ; DEBUG1 (("\nComputing row "ID" of A'*A\n", j)) ; DEBUG2 ((" col: "ID" (diagonal)\n", j)) ; /* ------------------------------------------------------------------ */ /* find the rows the contribute to this column j */ /* ------------------------------------------------------------------ */ jnext = n_col ; for (knext = krow ; knext < n_row ; knext++) { ASSERT (Ap [knext] < Ap [knext+1]) ; ASSERT (Ap [knext] >= pfirst && Ap [knext] <= Ap [n_row]) ; jnext = Ai [Ap [knext]] ; ASSERT (jnext >= j) ; if (jnext != j) { break ; } } /* rows krow ... knext-1 all have first column index of j */ /* (or are empty) */ /* row knext has first column index of jnext */ /* if knext = n_row, then jnext is n_col */ if (knext == n_row) { jnext = n_col ; } ASSERT (jnext > j) ; ASSERT (jnext <= n_col) ; /* ------------------------------------------------------------------ */ /* for each nonzero A (k,j) in column j of A do: */ /* ------------------------------------------------------------------ */ for (k = krow ; k < knext ; k++) { p = Ap [k] ; p2 = Ap [k+1] ; ASSERT (p < p2) ; /* merge row k of A into W */ DEBUG2 ((" ---- A row "ID" ", k)) ; ASSERT (k >= 0 && k < n_row) ; ASSERT (Ai [p] == j) ; DEBUG2 ((" p "ID" p2 "ID"\n cols:", p, p2)) ; ASSERT (p >= pfirst && p < Ap [n_row]) ; ASSERT (p2 > pfirst && p2 <= Ap [n_row]) ; for ( ; p < p2 ; p++) { /* add to pattern if seen for the first time */ col = Ai [p] ; ASSERT (col >= j && col < n_col) ; DEBUG3 ((" "ID, col)) ; if (W [col] != Wflag) { Ai [pdest++] = col ; ASSERT (pdest <= pfirst) ; /* flag this column has having been seen for row j */ W [col] = Wflag ; if (col < parent) { parent = col ; } } } DEBUG2 (("\n")) ; thickness++ ; } #ifndef NDEBUG DEBUG3 (("\nRow "ID" of A'A:\n", j)) ; for (p = Up [j] ; p < pdest ; p++) { DEBUG3 ((" "ID, Ai [p])) ; } DEBUG3 (("\n")) ; #endif /* ------------------------------------------------------------------ */ /* delete rows up to but not including knext */ /* ------------------------------------------------------------------ */ krow = knext ; pfirst = Ap [knext] ; /* we can now use Ai [0..pfirst-1] as workspace for rows of U */ /* ================================================================== */ /* === compute jth row of U ========================================= */ /* ================================================================== */ /* for each nonzero U (k,j) in column j of U (1:j-1,:) do */ for (k = Link [j] ; k != EMPTY ; k = Link [k]) { /* merge row k of U into W */ DEBUG2 ((" ---- U row "ID, k)) ; ASSERT (k >= 0 && k < n_col) ; ASSERT (Up [k] != EMPTY) ; p = Up [k] ; ASSERT (Front_ncols [k] > Front_npivcol [k]) ; p2 = p + (Front_ncols [k] - Front_npivcol [k]) ; DEBUG2 ((" p "ID" p2 "ID"\n cols:", p, p2)) ; ASSERT (p <= pfirst) ; ASSERT (p2 <= pfirst) ; for ( ; p < p2 ; p++) { /* add to pattern if seen for the first time */ col = Ai [p] ; ASSERT (col >= j && col < n_col) ; DEBUG3 ((" "ID, col)) ; if (W [col] != Wflag) { Ai [pdest++] = col ; ASSERT (pdest <= pfirst) ; /* flag this col has having been seen for row j */ W [col] = Wflag ; if (col < parent) { parent = col ; } } } DEBUG2 (("\n")) ; /* mark the row k as deleted */ Up [k] = EMPTY ; ASSERT (Front_nrows [k] > Front_npivcol [k]) ; thickness += (Front_nrows [k] - Front_npivcol [k]) ; ASSERT (Front_parent [k] == j) ; } #ifndef NDEBUG DEBUG3 (("\nRow "ID" of U prior to supercolumn detection:\n", j)); for (p = Up [j] ; p < pdest ; p++) { DEBUG3 ((" "ID, Ai [p])) ; } DEBUG3 (("\n")) ; DEBUG1 (("thickness, prior to supercol detect: "ID"\n", thickness)) ; #endif /* ================================================================== */ /* === quicky mass elimination ====================================== */ /* ================================================================== */ /* this code detects some supernodes, but it might miss */ /* some because the elimination tree (created on the fly) */ /* is not yet post-ordered, and because the pattern of A'*A */ /* is also computed on the fly. */ /* j2 is incremented because the pivot columns are not stored */ for (j2 = j+1 ; j2 < jnext ; j2++) { ASSERT (j2 >= 0 && j2 < n_col) ; if (W [j2] != Wflag || Link [j2] != EMPTY) { break ; } } /* the loop above terminated with j2 at the first non-supernode */ DEBUG1 (("jnext = "ID"\n", jnext)) ; ASSERT (j2 <= jnext) ; jnext = j2 ; j2-- ; DEBUG1 (("j2 = "ID"\n", j2)) ; ASSERT (j2 < n_col) ; npivots = j2-j+1 ; DEBUG1 (("Number of pivot columns: "ID"\n", npivots)) ; /* rows j:j2 have the same nonzero pattern, except for columns j:j2-1 */ if (j2 > j) { /* supernode detected, prune the pattern of new row j */ ASSERT (parent == j+1) ; ASSERT (j2 < n_col) ; DEBUG1 (("Supernode detected, j "ID" to j2 "ID"\n", j, j2)) ; parent = n_col ; p2 = pdest ; pdest = Up [j] ; for (p = Up [j] ; p < p2 ; p++) { col = Ai [p] ; ASSERT (col >= 0 && col < n_col) ; ASSERT (W [col] == Wflag) ; if (col > j2) { /* keep this col in the pattern of the new row j */ Ai [pdest++] = col ; if (col < parent) { parent = col ; } } } } DEBUG1 (("Parent ["ID"] = "ID"\n", j, parent)) ; ASSERT (parent > j2) ; if (parent == n_col) { /* this front has no parent - it is the root of a subtree */ parent = EMPTY ; } #ifndef NDEBUG DEBUG3 (("\nFinal row "ID" of U after supercolumn detection:\n", j)) ; for (p = Up [j] ; p < pdest ; p++) { ASSERT (Ai [p] >= 0 && Ai [p] < n_col) ; DEBUG3 ((" "ID" ("ID")", Ai [p], W [Ai [p]])) ; ASSERT (W [Ai [p]] == Wflag) ; } DEBUG3 (("\n")) ; #endif /* ================================================================== */ /* === frontal matrix =============================================== */ /* ================================================================== */ /* front has Front_npivcol [j] pivot columns */ /* entire front is Front_nrows [j] -by- Front_ncols [j] */ /* j is first column in the front */ npivcol = npivots ; fallrows = thickness ; fallcols = npivots + pdest - Up [j] ; /* number of pivots in the front (rows and columns) */ fpiv = MIN (npivcol, fallrows) ; /* size of contribution block */ frows = fallrows - fpiv ; fcols = fallcols - fpiv ; if (frows == 0 || fcols == 0) { /* front has no contribution block and thus needs no parent */ DEBUG1 (("Frontal matrix evaporation\n")) ; Up [j] = EMPTY ; parent = EMPTY ; } Front_npivcol [j] = npivots ; Front_nrows [j] = fallrows ; Front_ncols [j] = fallcols ; Front_parent [j] = parent ; ASSERT (npivots > 0) ; /* Front_parent [j] is the first column of the parent frontal matrix */ DEBUG1 (("\n\n==== Front "ID", nfr "ID" pivot columns "ID":"ID " all front: "ID"-by-"ID" Parent: "ID"\n", j, nfr, j,j+npivots-1, Front_nrows [j], Front_ncols [j], Front_parent [j])) ; nfr++ ; /* ================================================================== */ /* === prepare this row for its parent ============================== */ /* ================================================================== */ if (parent != EMPTY) { Link [j] = Link [parent] ; Link [parent] = j ; } ASSERT (jnext > j) ; jlast = j ; } /* ====================================================================== */ /* === postorder the fronts ============================================= */ /* ====================================================================== */ *nfr_out = nfr ; Front_order = W ; /* use W for Front_order [ */ if (fixQ) { /* do not postorder the fronts if Q is fixed */ DEBUG1 (("\nNo postorder (Q is fixed)\n")) ; k = 0 ; /* Pragma added May 14, 2003. The Intel compiler icl 6.0 (an old * version) incorrectly vectorizes this loop. */ #pragma novector for (j = 0 ; j < n_col ; j++) { if (Front_npivcol [j] > 0) { Front_order [j] = k++ ; DEBUG1 (("Front order of j: "ID" is:"ID"\n", j, Front_order [j])) ; } else { Front_order [j] = EMPTY ; } } } else { /* use Ap for Front_child and use Link for Front_sibling [ */ Front_child = Ap ; Front_sibling = Link ; /* use Ai for Front_stack, size of Ai is >= 2*n_col */ Front_stack = Ai ; Front_size = Front_stack + n_col ; UMF_fsize (n_col, Front_size, Front_nrows, Front_ncols, Front_parent, Front_npivcol) ; AMD_postorder (n_col, Front_parent, Front_npivcol, Front_size, Front_order, Front_child, Front_sibling, Front_stack) ; /* done with Front_child, Front_sibling, Front_size, and Front_stack ]*/ /* ------------------------------------------------------------------ */ /* construct the column permutation (return in Up) */ /* ------------------------------------------------------------------ */ /* Front_order [i] = k means that front i is kth front in the new order. * i is in the range 0 to n_col-1, and k is in the range 0 to nfr-1 */ /* Use Ai as workspace for Winv [ */ Winv = Ai ; for (k = 0 ; k < nfr ; k++) { Winv [k] = EMPTY ; } /* compute the inverse of Front_order, so that Winv [k] = i */ /* if Front_order [i] = k */ DEBUG1 (("\n\nComputing output column permutation:\n")) ; for (i = 0 ; i < n_col ; i++) { k = Front_order [i] ; if (k != EMPTY) { DEBUG1 (("Front "ID" new order: "ID"\n", i, k)) ; ASSERT (k >= 0 && k < nfr) ; ASSERT (Winv [k] == EMPTY) ; Winv [k] = i ; } } /* Use Up as output permutation */ kk = 0 ; for (k = 0 ; k < nfr ; k++) { i = Winv [k] ; DEBUG1 (("Old Front "ID" New Front "ID" npivots "ID" nrows "ID " ncols "ID"\n", i, k, Front_npivcol [i], Front_nrows [i], Front_ncols [i])) ; ASSERT (i >= 0 && i < n_col) ; ASSERT (Front_npivcol [i] > 0) ; for (npiv = 0 ; npiv < Front_npivcol [i] ; npiv++) { Up [kk] = i + npiv ; DEBUG1 ((" Cperm ["ID"] = "ID"\n", kk, Up [kk])) ; kk++ ; } } ASSERT (kk == n_col) ; /* Winv no longer needed ] */ } /* ---------------------------------------------------------------------- */ /* apply the postorder traversal to renumber the frontal matrices */ /* (or pack them in same order, if fixQ) */ /* ---------------------------------------------------------------------- */ /* use Ai as workspace */ UMF_apply_order (Front_npivcol, Front_order, Ai, n_col, nfr) ; UMF_apply_order (Front_nrows, Front_order, Ai, n_col, nfr) ; UMF_apply_order (Front_ncols, Front_order, Ai, n_col, nfr) ; UMF_apply_order (Front_parent, Front_order, Ai, n_col, nfr) ; /* fix the parent to refer to the new numbering */ for (i = 0 ; i < nfr ; i++) { parent = Front_parent [i] ; if (parent != EMPTY) { ASSERT (parent >= 0 && parent < n_col) ; ASSERT (Front_order [parent] >= 0 && Front_order [parent] < nfr) ; Front_parent [i] = Front_order [parent] ; } } /* Front_order longer needed ] */ #ifndef NDEBUG DEBUG1 (("\nFinal frontal matrices:\n")) ; for (i = 0 ; i < nfr ; i++) { DEBUG1 (("Final front "ID": npiv "ID" nrows "ID" ncols "ID" parent " ID"\n", i, Front_npivcol [i], Front_nrows [i], Front_ncols [i], Front_parent [i])) ; } #endif *p_ncompactions = ncompactions ; return (TRUE) ; } SuiteSparse/UMFPACK/Source/umf_mem_alloc_head_block.h0000644001170100242450000000075110617161751021410 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_mem_alloc_head_block ( NumericType *Numeric, Int nunits ) ; SuiteSparse/UMFPACK/Source/umf_analyze.h0000644001170100242450000000130110617161366016762 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_analyze ( Int n_row, Int n_col, Int Ai [ ], Int Ap [ ], Int Up [ ], Int fixQ, Int Front_ncols [ ], Int W [ ], Int Link [ ], Int Front_nrows [ ], Int Front_npivcol [ ], Int Front_parent [ ], Int *nfr_out, Int *p_ncompactions ) ; SuiteSparse/UMFPACK/Source/umf_build_tuples.c0000644001170100242450000001251710677541344020024 0ustar davisfac/* ========================================================================== */ /* === UMF_build_tuples ===================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Construct the tuple lists from a set of packed elements (no holes in elements, no internal or external fragmentation, and a packed (0..Work->nel) element name space). Assume no tuple lists are currently allocated, but that the tuple lengths have been initialized by UMF_tuple_lengths. Returns TRUE if successful, FALSE if not enough memory. */ #include "umf_internal.h" #include "umf_build_tuples.h" #include "umf_mem_alloc_tail_block.h" GLOBAL Int UMF_build_tuples ( NumericType *Numeric, WorkType *Work ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Int e, nrows, ncols, nel, *Rows, *Cols, row, col, n_row, n_col, *E, *Row_tuples, *Row_degree, *Row_tlen, *Col_tuples, *Col_degree, *Col_tlen, n1 ; Element *ep ; Unit *p ; Tuple tuple, *tp ; /* ---------------------------------------------------------------------- */ /* get parameters */ /* ---------------------------------------------------------------------- */ E = Work->E ; Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro */ Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro */ Row_tuples = Numeric->Uip ; Row_tlen = Numeric->Uilen ; Col_tuples = Numeric->Lip ; Col_tlen = Numeric->Lilen ; n_row = Work->n_row ; n_col = Work->n_col ; nel = Work->nel ; n1 = Work->n1 ; DEBUG3 (("BUILD_TUPLES: n_row "ID" n_col "ID" nel "ID"\n", n_row, n_col, nel)) ; /* ---------------------------------------------------------------------- */ /* allocate space for the tuple lists */ /* ---------------------------------------------------------------------- */ /* Garbage collection and memory reallocation have already attempted to */ /* ensure that there is enough memory for all the tuple lists. If */ /* memory allocation fails here, then there is nothing more to be done. */ for (row = n1 ; row < n_row ; row++) { if (NON_PIVOTAL_ROW (row)) { Row_tuples [row] = UMF_mem_alloc_tail_block (Numeric, UNITS (Tuple, TUPLES (Row_tlen [row]))) ; if (!Row_tuples [row]) { /* :: out of memory for row tuples :: */ DEBUGm4 (("out of memory: build row tuples\n")) ; return (FALSE) ; /* out of memory for row tuples */ } Row_tlen [row] = 0 ; } } /* push on stack in reverse order, so column tuples are in the order */ /* that they will be deleted. */ for (col = n_col-1 ; col >= n1 ; col--) { if (NON_PIVOTAL_COL (col)) { Col_tuples [col] = UMF_mem_alloc_tail_block (Numeric, UNITS (Tuple, TUPLES (Col_tlen [col]))) ; if (!Col_tuples [col]) { /* :: out of memory for col tuples :: */ DEBUGm4 (("out of memory: build col tuples\n")) ; return (FALSE) ; /* out of memory for col tuples */ } Col_tlen [col] = 0 ; } } #ifndef NDEBUG UMF_dump_memory (Numeric) ; #endif /* ---------------------------------------------------------------------- */ /* create the tuple lists (exclude element 0) */ /* ---------------------------------------------------------------------- */ /* for all elements, in order of creation */ for (e = 1 ; e <= nel ; e++) { DEBUG9 (("Adding tuples for element: "ID" at "ID"\n", e, E [e])) ; ASSERT (E [e]) ; /* no external fragmentation */ p = Numeric->Memory + E [e] ; GET_ELEMENT_PATTERN (ep, p, Cols, Rows, ncols) ; nrows = ep->nrows ; ASSERT (e != 0) ; ASSERT (e == 0 || nrows == ep->nrowsleft) ; ASSERT (e == 0 || ncols == ep->ncolsleft) ; tuple.e = e ; for (tuple.f = 0 ; tuple.f < ncols ; tuple.f++) { col = Cols [tuple.f] ; ASSERT (col >= n1 && col < n_col) ; ASSERT (NON_PIVOTAL_COL (col)) ; ASSERT (Col_tuples [col]) ; tp = ((Tuple *) (Numeric->Memory + Col_tuples [col])) + Col_tlen [col]++ ; *tp = tuple ; #ifndef NDEBUG UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ; #endif } for (tuple.f = 0 ; tuple.f < nrows ; tuple.f++) { row = Rows [tuple.f] ; ASSERT (row >= n1 && row < n_row) ; ASSERT (NON_PIVOTAL_COL (col)) ; ASSERT (Row_tuples [row]) ; tp = ((Tuple *) (Numeric->Memory + Row_tuples [row])) + Row_tlen [row]++ ; *tp = tuple ; #ifndef NDEBUG UMF_dump_rowcol (0, Numeric, Work, row, FALSE) ; #endif } } /* ---------------------------------------------------------------------- */ /* the tuple lists are now valid, and can be scanned */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG UMF_dump_memory (Numeric) ; UMF_dump_matrix (Numeric, Work, FALSE) ; #endif DEBUG3 (("BUILD_TUPLES: done\n")) ; return (TRUE) ; } SuiteSparse/UMFPACK/Source/umf_build_tuples.h0000644001170100242450000000074510617161431020016 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_build_tuples ( NumericType *Numeric, WorkType *Work ) ; SuiteSparse/UMFPACK/Source/umfpack_tictoc.c0000644001170100242450000000605210617162176017446 0ustar davisfac/* ========================================================================== */ /* === umfpack_tictoc ======================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Returns the time in seconds used by the process, and the current wall clock time. BE CAREFUL: if you compare the run time of UMFPACK with other sparse matrix packages, be sure to use the same timer. See umfpack_tictoc.h for details. These routines conform to the POSIX standard. See umf_config.h for more details. */ #include "umf_internal.h" #ifdef NO_TIMER /* -------------------------------------------------------------------------- */ /* no timer used if -DNO_TIMER is defined at compile time */ /* -------------------------------------------------------------------------- */ void umfpack_tic (double stats [2]) { stats [0] = 0 ; stats [1] = 0 ; } void umfpack_toc (double stats [2]) { stats [0] = 0 ; stats [1] = 0 ; } #else /* -------------------------------------------------------------------------- */ /* timer routines, using either times() or clock() */ /* -------------------------------------------------------------------------- */ #define TINY_TIME 1e-4 #ifndef NPOSIX #include #include void umfpack_tic (double stats [2]) { /* Return the current time */ /* stats [0]: current wallclock time, in seconds */ /* stats [1]: user + system time for the process, in seconds */ double ticks ; struct tms t ; ticks = (double) sysconf (_SC_CLK_TCK) ; stats [0] = (double) times (&t) / ticks ; stats [1] = (double) (t.tms_utime + t.tms_stime) / ticks ; /* if time is tiny, just return zero */ if (stats [0] < TINY_TIME) stats [0] = 0 ; if (stats [1] < TINY_TIME) stats [1] = 0 ; } #else /* Generic ANSI C: use the ANSI clock function. No wallclock time. */ #include void umfpack_tic (double stats [2]) { stats [0] = 0 ; stats [1] = ((double) (clock ( ))) / ((double) (CLOCKS_PER_SEC)) ; if (stats [1] < TINY_TIME) stats [1] = 0 ; } #endif /* -------------------------------------------------------------------------- */ void umfpack_toc (double stats [2]) { /* Return the current time since the last call to umfpack_tic. */ /* On input, stats holds the values returned by umfpack_tic. */ /* On ouput, stats holds the time since the last umfpack_tic. */ double done [2] ; umfpack_tic (done) ; stats [0] = done [0] - stats [0] ; stats [1] = done [1] - stats [1] ; if (stats [0] < 0) stats [0] = 0 ; if (stats [1] < 0) stats [1] = 0 ; } #endif SuiteSparse/UMFPACK/Source/umf_extend_front.c0000644001170100242450000002670210677541411020024 0ustar davisfac/* ========================================================================== */ /* === UMF_extend_front ===================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Called by kernel. */ #include "umf_internal.h" #include "umf_extend_front.h" #include "umf_grow_front.h" /* ========================================================================== */ /* === zero_front =========================================================== */ /* ========================================================================== */ PRIVATE void zero_front ( Entry *Flblock, Entry *Fublock, Entry *Fcblock, Int fnrows, Int fncols, Int fnr_curr, Int fnc_curr, Int fnpiv, Int fnrows_extended, Int fncols_extended) { Int j, i ; Entry *F, *Fj, *Fi ; Fj = Fcblock + fnrows ; for (j = 0 ; j < fncols ; j++) { /* zero the new rows in the contribution block: */ F = Fj ; Fj += fnr_curr ; #pragma ivdep for (i = fnrows ; i < fnrows_extended ; i++) { /* CLEAR (Fcblock [i + j*fnr_curr]) ; */ CLEAR_AND_INCREMENT (F) ; } } Fj -= fnrows ; for (j = fncols ; j < fncols_extended ; j++) { /* zero the new columns in the contribution block: */ F = Fj ; Fj += fnr_curr ; #pragma ivdep for (i = 0 ; i < fnrows_extended ; i++) { /* CLEAR (Fcblock [i + j*fnr_curr]) ; */ CLEAR_AND_INCREMENT (F) ; } } Fj = Flblock + fnrows ; for (j = 0 ; j < fnpiv ; j++) { /* zero the new rows in L block: */ F = Fj ; Fj += fnr_curr ; #pragma ivdep for (i = fnrows ; i < fnrows_extended ; i++) { /* CLEAR (Flblock [i + j*fnr_curr]) ; */ CLEAR_AND_INCREMENT (F) ; } } Fi = Fublock + fncols ; for (i = 0 ; i < fnpiv ; i++) { /* zero the new columns in U block: */ F = Fi ; Fi += fnc_curr ; #pragma ivdep for (j = fncols ; j < fncols_extended ; j++) { /* CLEAR (Fublock [i*fnc_curr + j]) ; */ CLEAR_AND_INCREMENT (F) ; } } } /* ========================================================================== */ /* === UMF_extend_front ===================================================== */ /* ========================================================================== */ GLOBAL Int UMF_extend_front ( NumericType *Numeric, WorkType *Work ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Int j, i, *Frows, row, col, *Wrow, fnr2, fnc2, *Frpos, *Fcpos, *Fcols, fnrows_extended, rrdeg, ccdeg, fncols_extended, fnr_curr, fnc_curr, fnrows, fncols, pos, fnpiv, *Wm ; Entry *Wx, *Wy, *Fu, *Fl ; /* ---------------------------------------------------------------------- */ /* get current frontal matrix and check for frontal growth */ /* ---------------------------------------------------------------------- */ fnpiv = Work->fnpiv ; #ifndef NDEBUG DEBUG2 (("EXTEND FRONT\n")) ; DEBUG2 (("Work->fnpiv "ID"\n", fnpiv)) ; ASSERT (Work->Flblock == Work->Flublock + Work->nb*Work->nb) ; ASSERT (Work->Fublock == Work->Flblock + Work->fnr_curr*Work->nb) ; ASSERT (Work->Fcblock == Work->Fublock + Work->nb*Work->fnc_curr) ; DEBUG7 (("C block: ")) ; UMF_dump_dense (Work->Fcblock, Work->fnr_curr, Work->fnrows, Work->fncols) ; DEBUG7 (("L block: ")) ; UMF_dump_dense (Work->Flblock, Work->fnr_curr, Work->fnrows, fnpiv); DEBUG7 (("U' block: ")) ; UMF_dump_dense (Work->Fublock, Work->fnc_curr, Work->fncols, fnpiv) ; DEBUG7 (("LU block: ")) ; UMF_dump_dense (Work->Flublock, Work->nb, fnpiv, fnpiv) ; #endif if (Work->do_grow) { fnr2 = UMF_FRONTAL_GROWTH * Work->fnrows_new + 2 ; fnc2 = UMF_FRONTAL_GROWTH * Work->fncols_new + 2 ; if (!UMF_grow_front (Numeric, fnr2, fnc2, Work, 1)) { DEBUGm4 (("out of memory: extend front\n")) ; return (FALSE) ; } } fnr_curr = Work->fnr_curr ; fnc_curr = Work->fnc_curr ; ASSERT (Work->fnrows_new + 1 <= fnr_curr) ; ASSERT (Work->fncols_new + 1 <= fnc_curr) ; ASSERT (fnr_curr >= 0 && fnr_curr % 2 == 1) ; /* ---------------------------------------------------------------------- */ /* get parameters */ /* ---------------------------------------------------------------------- */ Frows = Work->Frows ; Frpos = Work->Frpos ; Fcols = Work->Fcols ; Fcpos = Work->Fcpos ; fnrows = Work->fnrows ; fncols = Work->fncols ; rrdeg = Work->rrdeg ; ccdeg = Work->ccdeg ; /* scan starts at the first new column in Fcols */ /* also scan the pivot column if it was not in the front */ Work->fscan_col = fncols ; Work->NewCols = Fcols ; /* scan1 starts at the first new row in Frows */ /* also scan the pivot row if it was not in the front */ Work->fscan_row = fnrows ; Work->NewRows = Frows ; /* ---------------------------------------------------------------------- */ /* extend row pattern of the front with the new pivot column */ /* ---------------------------------------------------------------------- */ fnrows_extended = fnrows ; fncols_extended = fncols ; #ifndef NDEBUG DEBUG2 (("Pivot col, before extension: "ID"\n", fnrows)) ; for (i = 0 ; i < fnrows ; i++) { DEBUG2 ((" "ID": row "ID"\n", i, Frows [i])) ; ASSERT (Frpos [Frows [i]] == i) ; } DEBUG2 (("Extending pivot column: pivcol_in_front: "ID"\n", Work->pivcol_in_front)) ; #endif Fl = Work->Flblock + fnpiv * fnr_curr ; if (Work->pivcol_in_front) { /* extended pattern and position already in Frows, Frpos. Values above * the diagonal are already in LU block. Values on and below the * diagonal are in Wy [0 .. fnrows_extended-1]. Copy into the L * block. */ fnrows_extended += ccdeg ; Wy = Work->Wy ; for (i = 0 ; i < fnrows_extended ; i++) { Fl [i] = Wy [i] ; #ifndef NDEBUG row = Frows [i] ; DEBUG2 ((" "ID": row "ID" ", i, row)) ; EDEBUG2 (Fl [i]) ; if (row == Work->pivrow) DEBUG2 ((" <- pivrow")) ; DEBUG2 (("\n")) ; if (i == fnrows - 1) DEBUG2 ((" :::::::\n")) ; ASSERT (row >= 0 && row < Work->n_row) ; ASSERT (Frpos [row] == i) ; #endif } } else { /* extended pattern,values is in (Wm,Wx), not yet in the front */ Entry *F ; Fu = Work->Flublock + fnpiv * Work->nb ; Wm = Work->Wm ; Wx = Work->Wx ; F = Fu ; for (i = 0 ; i < fnpiv ; i++) { CLEAR_AND_INCREMENT (F) ; } F = Fl ; for (i = 0 ; i < fnrows ; i++) { CLEAR_AND_INCREMENT (F) ; } for (i = 0 ; i < ccdeg ; i++) { row = Wm [i] ; #ifndef NDEBUG DEBUG2 ((" "ID": row "ID" (ext) ", fnrows_extended, row)) ; EDEBUG2 (Wx [i]) ; if (row == Work->pivrow) DEBUG2 ((" <- pivrow")) ; DEBUG2 (("\n")) ; ASSERT (row >= 0 && row < Work->n_row) ; #endif pos = Frpos [row] ; if (pos < 0) { pos = fnrows_extended++ ; Frows [pos] = row ; Frpos [row] = pos ; } Fl [pos] = Wx [i] ; } } ASSERT (fnrows_extended <= fnr_curr) ; /* ---------------------------------------------------------------------- */ /* extend the column pattern of the front with the new pivot row */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG DEBUG6 (("Pivot row, before extension: "ID"\n", fncols)) ; for (j = 0 ; j < fncols ; j++) { DEBUG7 ((" "ID": col "ID"\n", j, Fcols [j])) ; ASSERT (Fcpos [Fcols [j]] == j * fnr_curr) ; } DEBUG6 (("Extending pivot row:\n")) ; #endif if (Work->pivrow_in_front) { if (Work->pivcol_in_front) { ASSERT (Fcols == Work->Wrow) ; for (j = fncols ; j < rrdeg ; j++) { #ifndef NDEBUG col = Fcols [j] ; DEBUG2 ((" "ID": col "ID" (ext)\n", j, col)) ; ASSERT (col != Work->pivcol) ; ASSERT (col >= 0 && col < Work->n_col) ; ASSERT (Fcpos [col] < 0) ; #endif Fcpos [Fcols [j]] = j * fnr_curr ; } } else { /* OUT-IN option: pivcol not in front, but pivrow is in front */ Wrow = Work->Wrow ; ASSERT (IMPLIES (Work->pivcol_in_front, Wrow == Fcols)) ; if (Wrow == Fcols) { /* Wrow and Fcols are equivalenced */ for (j = fncols ; j < rrdeg ; j++) { col = Wrow [j] ; DEBUG2 ((" "ID": col "ID" (ext)\n", j, col)) ; ASSERT (Fcpos [col] < 0) ; /* Fcols [j] = col ; not needed */ Fcpos [col] = j * fnr_curr ; } } else { for (j = fncols ; j < rrdeg ; j++) { col = Wrow [j] ; DEBUG2 ((" "ID": col "ID" (ext)\n", j, col)) ; ASSERT (Fcpos [col] < 0) ; Fcols [j] = col ; Fcpos [col] = j * fnr_curr ; } } } fncols_extended = rrdeg ; } else { ASSERT (Fcols != Work->Wrow) ; Wrow = Work->Wrow ; for (j = 0 ; j < rrdeg ; j++) { col = Wrow [j] ; ASSERT (col >= 0 && col < Work->n_col) ; if (Fcpos [col] < 0) { DEBUG2 ((" col:: "ID" (ext)\n", col)) ; Fcols [fncols_extended] = col ; Fcpos [col] = fncols_extended * fnr_curr ; fncols_extended++ ; } } } /* ---------------------------------------------------------------------- */ /* pivot row and column have been extended */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG ASSERT (fncols_extended <= fnc_curr) ; ASSERT (fnrows_extended <= fnr_curr) ; DEBUG6 (("Pivot col, after ext: "ID" "ID"\n", fnrows,fnrows_extended)) ; for (i = 0 ; i < fnrows_extended ; i++) { row = Frows [i] ; DEBUG7 ((" "ID": row "ID" pos "ID" old: %d", i, row, Frpos [row], i < fnrows)) ; if (row == Work->pivrow ) DEBUG7 ((" <-- pivrow")) ; DEBUG7 (("\n")) ; ASSERT (Frpos [Frows [i]] == i) ; } DEBUG6 (("Pivot row position: "ID"\n", Frpos [Work->pivrow])) ; ASSERT (Frpos [Work->pivrow] >= 0) ; ASSERT (Frpos [Work->pivrow] < fnrows_extended) ; DEBUG6 (("Pivot row, after ext: "ID" "ID"\n", fncols,fncols_extended)) ; for (j = 0 ; j < fncols_extended ; j++) { col = Fcols [j] ; DEBUG7 ((" "ID": col "ID" pos "ID" old: %d", j, col, Fcpos [col], j < fncols)) ; if (col == Work->pivcol ) DEBUG7 ((" <-- pivcol")) ; DEBUG7 (("\n")) ; ASSERT (Fcpos [Fcols [j]] == j * fnr_curr) ; } DEBUG6 (("Pivot col position: "ID"\n", Fcpos [Work->pivcol])) ; ASSERT (Fcpos [Work->pivcol] >= 0) ; ASSERT (Fcpos [Work->pivcol] < fncols_extended * fnr_curr) ; #endif /* ---------------------------------------------------------------------- */ /* Zero the newly extended frontal matrix */ /* ---------------------------------------------------------------------- */ zero_front (Work->Flblock, Work->Fublock, Work->Fcblock, fnrows, fncols, fnr_curr, fnc_curr, fnpiv, fnrows_extended, fncols_extended) ; /* ---------------------------------------------------------------------- */ /* finalize extended row and column pattern of the frontal matrix */ /* ---------------------------------------------------------------------- */ Work->fnrows = fnrows_extended ; Work->fncols = fncols_extended ; ASSERT (fnrows_extended == Work->fnrows_new + 1) ; ASSERT (fncols_extended == Work->fncols_new + 1) ; return (TRUE) ; } SuiteSparse/UMFPACK/Source/umf_extend_front.h0000644001170100242450000000074510617161547020032 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_extend_front ( NumericType *Numeric, WorkType *Work ) ; SuiteSparse/UMFPACK/Source/umf_singletons.c0000644001170100242450000006250610677541050017513 0ustar davisfac/* ========================================================================== */ /* === UMF_singletons ======================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Find and order the row and column singletons of a matrix A. If there are * row and column singletons, the output is a row and column permutation such * that the matrix is in the following form: * * x x x x x x x x x * . x x x x x x x x * . . x x x x x x x * . . . x . . . . . * . . . x x . . . . * . . . x x s s s s * . . . x x s s s s * . . . x x s s s s * . . . x x s s s s * * The above example has 3 column singletons (the first three columns and * their corresponding pivot rows) and 2 row singletons. The singletons are * ordered first, because they have zero Markowitz cost. The LU factorization * for these first five rows and columns is free - there is no work to do * (except to scale the pivot columns for the 2 row singletons), and no * fill-in occurs. The remaining submatrix (4-by-4 in the above example) * has no rows or columns with degree one. It may have empty rows or columns. * * This algorithm does not perform a full permutation to block triangular * form. If there are one or more singletons, then the matrix can be * permuted to block triangular form, but UMFPACK does not perform the full * BTF permutation (see also "dmperm" in MATLAB, CSparse cs_dmperm, * and SuiteSparse/BTF). */ #include "umf_internal.h" #include "umf_singletons.h" #ifndef NDEBUG /* ========================================================================== */ /* === debug routines ======================================================= */ /* ========================================================================== */ /* Dump the singleton queue */ PRIVATE void dump_singletons ( Int head, /* head of the queue */ Int tail, /* tail of the queue */ Int Next [ ], /* Next [i] is the next object after i */ char *name, /* "row" or "col" */ Int Deg [ ], /* Deg [i] is the degree of object i */ Int n /* objects are in the range 0 to n-1 */ ) { Int i, next, cnt ; DEBUG6 (("%s Singleton list: head "ID" tail "ID"\n", name, head, tail)) ; i = head ; ASSERT (head >= EMPTY && head < n) ; ASSERT (tail >= EMPTY && tail < n) ; cnt = 0 ; while (i != EMPTY) { DEBUG7 ((" "ID": "ID" deg: "ID"\n", cnt, i, Deg [i])) ; ASSERT (i >= 0 && i < n) ; next = Next [i] ; if (i == tail) ASSERT (next == EMPTY) ; i = next ; cnt++ ; ASSERT (cnt <= n) ; } } PRIVATE void dump_mat ( char *xname, char *yname, Int nx, Int ny, const Int Xp [ ], const Int Xi [ ], Int Xdeg [ ], Int Ydeg [ ] ) { Int x, y, p, p1, p2, xdeg, do_xdeg, ydeg ; DEBUG6 (("\n ==== Dump %s mat:\n", xname)) ; for (x = 0 ; x < nx ; x++) { p1 = Xp [x] ; p2 = Xp [x+1] ; xdeg = Xdeg [x] ; DEBUG6 (("Dump %s "ID" p1 "ID" p2 "ID" deg "ID"\n", xname, x, p1, p2, xdeg)) ; do_xdeg = (xdeg >= 0) ; for (p = p1 ; p < p2 ; p++) { y = Xi [p] ; DEBUG7 ((" %s "ID" deg: ", yname, y)) ; ASSERT (y >= 0 && y < ny) ; ydeg = Ydeg [y] ; DEBUG7 ((ID"\n", ydeg)) ; if (do_xdeg && ydeg >= 0) { xdeg-- ; } } ASSERT (IMPLIES (do_xdeg, xdeg == 0)) ; } } #endif /* ========================================================================== */ /* === create_row_form ====================================================== */ /* ========================================================================== */ /* Create the row-form R of the column-form input matrix A. This could be done * by UMF_transpose, except that Rdeg has already been computed. */ PRIVATE void create_row_form ( /* input, not modified: */ Int n_row, /* A is n_row-by-n_col, nz = Ap [n_col] */ Int n_col, const Int Ap [ ], /* Ap [0..n_col]: column pointers for A */ const Int Ai [ ], /* Ai [0..nz-1]: row indices for A */ Int Rdeg [ ], /* Rdeg [0..n_row-1]: row degrees */ /* output, not defined on input: */ Int Rp [ ], /* Rp [0..n_row]: row pointers for R */ Int Ri [ ], /* Ri [0..nz-1]: column indices for R */ /* workspace, not defined on input or output */ Int W [ ] /* size n_row */ ) { Int row, col, p, p2 ; /* create the row pointers */ Rp [0] = 0 ; W [0] = 0 ; for (row = 0 ; row < n_row ; row++) { Rp [row+1] = Rp [row] + Rdeg [row] ; W [row] = Rp [row] ; } /* create the indices for the row-form */ for (col = 0 ; col < n_col ; col++) { p2 = Ap [col+1] ; for (p = Ap [col] ; p < p2 ; p++) { Ri [W [Ai [p]]++] = col ; } } } /* ========================================================================== */ /* === order_singletons ===================================================== */ /* ========================================================================== */ PRIVATE int order_singletons /* return new number of singletons */ ( Int k, /* the number of singletons so far */ Int head, Int tail, Int Next [ ], Int Xdeg [ ], Int Xperm [ ], const Int Xp [ ], const Int Xi [ ], Int Ydeg [ ], Int Yperm [ ], const Int Yp [ ], const Int Yi [ ] #ifndef NDEBUG , char *xname, char *yname, Int nx, Int ny #endif ) { Int xpivot, x, y, ypivot, p, p2, deg ; #ifndef NDEBUG Int i, k1 = k ; dump_singletons (head, tail, Next, xname, Xdeg, nx) ; dump_mat (xname, yname, nx, ny, Xp, Xi, Xdeg, Ydeg) ; dump_mat (yname, xname, ny, nx, Yp, Yi, Ydeg, Xdeg) ; #endif while (head != EMPTY) { /* remove the singleton at the head of the queue */ xpivot = head ; DEBUG1 (("------ Order %s singleton: "ID"\n", xname, xpivot)) ; head = Next [xpivot] ; if (head == EMPTY) tail = EMPTY ; #ifndef NDEBUG if (k % 100 == 0) dump_singletons (head, tail, Next, xname, Xdeg, nx) ; #endif ASSERT (Xdeg [xpivot] >= 0) ; if (Xdeg [xpivot] != 1) { /* This row/column x is empty. The matrix is singular. * x will be ordered last in Xperm. */ DEBUG1 (("empty %s, after singletons removed\n", xname)) ; continue ; } /* find the ypivot to match with this xpivot */ #ifndef NDEBUG /* there can only be one ypivot, since the degree of x is 1 */ deg = 0 ; p2 = Xp [xpivot+1] ; for (p = Xp [xpivot] ; p < p2 ; p++) { y = Xi [p] ; DEBUG1 (("%s: "ID"\n", yname, y)) ; if (Ydeg [y] >= 0) { /* this is a live index in this xpivot vector */ deg++ ; } } ASSERT (deg == 1) ; #endif ypivot = EMPTY ; p2 = Xp [xpivot+1] ; for (p = Xp [xpivot] ; p < p2 ; p++) { y = Xi [p] ; DEBUG1 (("%s: "ID"\n", yname, y)) ; if (Ydeg [y] >= 0) { /* this is a live index in this xpivot vector */ ypivot = y ; break ; } } DEBUG1 (("Pivot %s: "ID"\n", yname, ypivot)) ; ASSERT (ypivot != EMPTY) ; DEBUG1 (("deg "ID"\n", Ydeg [ypivot])) ; ASSERT (Ydeg [ypivot] >= 0) ; /* decrement the degrees after removing this singleton */ DEBUG1 (("p1 "ID"\n", Yp [ypivot])) ; DEBUG1 (("p2 "ID"\n", Yp [ypivot+1])) ; p2 = Yp [ypivot+1] ; for (p = Yp [ypivot] ; p < p2 ; p++) { x = Yi [p] ; DEBUG1 ((" %s: "ID" deg: "ID"\n", xname, x, Xdeg [x])) ; if (Xdeg [x] < 0) continue ; ASSERT (Xdeg [x] > 0) ; if (x == xpivot) continue ; deg = --(Xdeg [x]) ; ASSERT (Xdeg [x] >= 0) ; if (deg == 1) { /* this is a new singleton, put at the end of the queue */ Next [x] = EMPTY ; if (head == EMPTY) { head = x ; } else { ASSERT (tail != EMPTY) ; Next [tail] = x ; } tail = x ; DEBUG1 ((" New %s singleton: "ID"\n", xname, x)) ; #ifndef NDEBUG if (k % 100 == 0) { dump_singletons (head, tail, Next, xname, Xdeg, nx) ; } #endif } } /* flag the xpivot and ypivot by FLIP'ing the degrees */ Xdeg [xpivot] = FLIP (1) ; Ydeg [ypivot] = FLIP (Ydeg [ypivot]) ; /* keep track of the pivot row and column */ Xperm [k] = xpivot ; Yperm [k] = ypivot ; k++ ; #ifndef NDEBUG if (k % 1000 == 0) { dump_mat (xname, yname, nx, ny, Xp, Xi, Xdeg, Ydeg) ; dump_mat (yname, xname, ny, nx, Yp, Yi, Ydeg, Xdeg) ; } #endif } #ifndef NDEBUG DEBUGm4 (("%s singletons: k = "ID"\n", xname, k)) ; for (i = k1 ; i < k ; i++) { DEBUG1 ((" %s: "ID" %s: "ID"\n", xname, Xperm [i], yname, Yperm [i])) ; } ASSERT (k > 0) ; #endif return (k) ; } /* ========================================================================== */ /* === find_any_singletons ================================================== */ /* ========================================================================== */ PRIVATE Int find_any_singletons /* returns # of singletons found */ ( /* input, not modified: */ Int n_row, Int n_col, const Int Ap [ ], /* size n_col+1 */ const Int Ai [ ], /* size nz = Ap [n_col] */ /* input, modified on output: */ Int Cdeg [ ], /* size n_col */ Int Rdeg [ ], /* size n_row */ /* output, not defined on input: */ Int Cperm [ ], /* size n_col */ Int Rperm [ ], /* size n_row */ Int *p_n1r, /* # of row singletons */ Int *p_n1c, /* # of col singletons */ /* workspace, not defined on input or output */ Int Rp [ ], /* size n_row+1 */ Int Ri [ ], /* size nz */ Int W [ ], /* size n_row */ Int Next [ ] /* size MAX (n_row, n_col) */ ) { Int n1, col, row, row_form, head, tail, n1r, n1c ; /* ---------------------------------------------------------------------- */ /* eliminate column singletons */ /* ---------------------------------------------------------------------- */ n1 = 0 ; n1r = 0 ; n1c = 0 ; row_form = FALSE ; head = EMPTY ; tail = EMPTY ; for (col = n_col-1 ; col >= 0 ; col--) { if (Cdeg [col] == 1) { /* put the column singleton in the queue */ if (head == EMPTY) tail = col ; Next [col] = head ; head = col ; DEBUG1 (("Column singleton: "ID"\n", col)) ; } } if (head != EMPTY) { /* ------------------------------------------------------------------ */ /* create the row-form of A */ /* ------------------------------------------------------------------ */ create_row_form (n_row, n_col, Ap, Ai, Rdeg, Rp, Ri, W) ; row_form = TRUE ; /* ------------------------------------------------------------------ */ /* find and order the column singletons */ /* ------------------------------------------------------------------ */ n1 = order_singletons (0, head, tail, Next, Cdeg, Cperm, Ap, Ai, Rdeg, Rperm, Rp, Ri #ifndef NDEBUG , "col", "row", n_col, n_row #endif ) ; n1c = n1 ; } /* ---------------------------------------------------------------------- */ /* eliminate row singletons */ /* ---------------------------------------------------------------------- */ head = EMPTY ; tail = EMPTY ; for (row = n_row-1 ; row >= 0 ; row--) { if (Rdeg [row] == 1) { /* put the row singleton in the queue */ if (head == EMPTY) tail = row ; Next [row] = head ; head = row ; DEBUG1 (("Row singleton: "ID"\n", row)) ; } } if (head != EMPTY) { /* ------------------------------------------------------------------ */ /* create the row-form of A, if not already created */ /* ------------------------------------------------------------------ */ if (!row_form) { create_row_form (n_row, n_col, Ap, Ai, Rdeg, Rp, Ri, W) ; } /* ------------------------------------------------------------------ */ /* find and order the row singletons */ /* ------------------------------------------------------------------ */ n1 = order_singletons (n1, head, tail, Next, Rdeg, Rperm, Rp, Ri, Cdeg, Cperm, Ap, Ai #ifndef NDEBUG , "row", "col", n_row, n_col #endif ) ; n1r = n1 - n1c ; } DEBUG0 (("n1 "ID"\n", n1)) ; *p_n1r = n1r ; *p_n1c = n1c ; return (n1) ; } /* ========================================================================== */ /* === find_user_singletons ================================================= */ /* ========================================================================== */ PRIVATE Int find_user_singletons /* returns # singletons found */ ( /* input, not modified: */ Int n_row, Int n_col, const Int Ap [ ], /* size n_col+1 */ const Int Ai [ ], /* size nz = Ap [n_col] */ const Int Quser [ ], /* size n_col if present */ /* input, modified on output: */ Int Cdeg [ ], /* size n_col */ Int Rdeg [ ], /* size n_row */ /* output, not defined on input */ Int Cperm [ ], /* size n_col */ Int Rperm [ ], /* size n_row */ Int *p_n1r, /* # of row singletons */ Int *p_n1c, /* # of col singletons */ /* workspace, not defined on input or output */ Int Rp [ ], /* size n_row+1 */ Int Ri [ ], /* size nz */ Int W [ ] /* size n_row */ ) { Int n1, col, row, p, p2, pivcol, pivrow, found, k, n1r, n1c ; n1 = 0 ; n1r = 0 ; n1c = 0 ; *p_n1r = 0 ; *p_n1c = 0 ; /* find singletons in the user column permutation, Quser */ pivcol = Quser [0] ; found = (Cdeg [pivcol] == 1) ; DEBUG0 (("Is first col: "ID" a col singleton?: "ID"\n", pivcol, found)) ; if (!found) { /* the first column is not a column singleton, check for a row * singleton in the first column. */ for (p = Ap [pivcol] ; p < Ap [pivcol+1] ; p++) { if (Rdeg [Ai [p]] == 1) { DEBUG0 (("Row singleton in first col: "ID" row: "ID"\n", pivcol, Ai [p])) ; found = TRUE ; break ; } } } if (!found) { /* no singletons in the leading part of A (:,Quser) */ return (0) ; } /* there is at least one row or column singleton. Look for more. */ create_row_form (n_row, n_col, Ap, Ai, Rdeg, Rp, Ri, W) ; n1 = 0 ; for (k = 0 ; k < n_col ; k++) { pivcol = Quser [k] ; pivrow = EMPTY ; /* ------------------------------------------------------------------ */ /* check if col is a column singleton, or contains a row singleton */ /* ------------------------------------------------------------------ */ found = (Cdeg [pivcol] == 1) ; if (found) { /* -------------------------------------------------------------- */ /* pivcol is a column singleton */ /* -------------------------------------------------------------- */ DEBUG0 (("Found a col singleton: k "ID" pivcol "ID"\n", k, pivcol)); /* find the pivrow to match with this pivcol */ #ifndef NDEBUG /* there can only be one pivrow, since the degree of pivcol is 1 */ { Int deg = 0 ; p2 = Ap [pivcol+1] ; for (p = Ap [pivcol] ; p < p2 ; p++) { row = Ai [p] ; DEBUG1 (("row: "ID"\n", row)) ; if (Rdeg [row] >= 0) { /* this is a live index in this column vector */ deg++ ; } } ASSERT (deg == 1) ; } #endif p2 = Ap [pivcol+1] ; for (p = Ap [pivcol] ; p < p2 ; p++) { row = Ai [p] ; DEBUG1 (("row: "ID"\n", row)) ; if (Rdeg [row] >= 0) { /* this is a live index in this pivcol vector */ pivrow = row ; break ; } } DEBUG1 (("Pivot row: "ID"\n", pivrow)) ; ASSERT (pivrow != EMPTY) ; DEBUG1 (("deg "ID"\n", Rdeg [pivrow])) ; ASSERT (Rdeg [pivrow] >= 0) ; /* decrement the degrees after removing this col singleton */ DEBUG1 (("p1 "ID"\n", Rp [pivrow])) ; DEBUG1 (("p2 "ID"\n", Rp [pivrow+1])) ; p2 = Rp [pivrow+1] ; for (p = Rp [pivrow] ; p < p2 ; p++) { col = Ri [p] ; DEBUG1 ((" col: "ID" deg: "ID"\n", col, Cdeg [col])) ; if (Cdeg [col] < 0) continue ; ASSERT (Cdeg [col] > 0) ; Cdeg [col]-- ; ASSERT (Cdeg [col] >= 0) ; } /* flag the pivcol and pivrow by FLIP'ing the degrees */ Cdeg [pivcol] = FLIP (1) ; Rdeg [pivrow] = FLIP (Rdeg [pivrow]) ; n1c++ ; } else { /* -------------------------------------------------------------- */ /* pivcol may contain a row singleton */ /* -------------------------------------------------------------- */ p2 = Ap [pivcol+1] ; for (p = Ap [pivcol] ; p < p2 ; p++) { pivrow = Ai [p] ; if (Rdeg [pivrow] == 1) { DEBUG0 (("Row singleton in pivcol: "ID" row: "ID"\n", pivcol, pivrow)) ; found = TRUE ; break ; } } if (!found) { DEBUG0 (("End of user singletons\n")) ; break ; } #ifndef NDEBUG /* there can only be one pivrow, since the degree of pivcol is 1 */ { Int deg = 0 ; p2 = Rp [pivrow+1] ; for (p = Rp [pivrow] ; p < p2 ; p++) { col = Ri [p] ; DEBUG1 (("col: "ID" cdeg::: "ID"\n", col, Cdeg [col])) ; if (Cdeg [col] >= 0) { /* this is a live index in this column vector */ ASSERT (col == pivcol) ; deg++ ; } } ASSERT (deg == 1) ; } #endif DEBUG1 (("Pivot row: "ID"\n", pivrow)) ; DEBUG1 (("pivcol deg "ID"\n", Cdeg [pivcol])) ; ASSERT (Cdeg [pivcol] > 1) ; /* decrement the degrees after removing this row singleton */ DEBUG1 (("p1 "ID"\n", Ap [pivcol])) ; DEBUG1 (("p2 "ID"\n", Ap [pivcol+1])) ; p2 = Ap [pivcol+1] ; for (p = Ap [pivcol] ; p < p2 ; p++) { row = Ai [p] ; DEBUG1 ((" row: "ID" deg: "ID"\n", row, Rdeg [row])) ; if (Rdeg [row] < 0) continue ; ASSERT (Rdeg [row] > 0) ; Rdeg [row]-- ; ASSERT (Rdeg [row] >= 0) ; } /* flag the pivcol and pivrow by FLIP'ing the degrees */ Cdeg [pivcol] = FLIP (Cdeg [pivcol]) ; Rdeg [pivrow] = FLIP (1) ; n1r++ ; } /* keep track of the pivot row and column */ Cperm [k] = pivcol ; Rperm [k] = pivrow ; n1++ ; #ifndef NDEBUG dump_mat ("col", "row", n_col, n_row, Ap, Ai, Cdeg, Rdeg) ; dump_mat ("row", "col", n_row, n_col, Rp, Ri, Rdeg, Cdeg) ; #endif } DEBUGm4 (("User singletons found: "ID"\n", n1)) ; ASSERT (n1 > 0) ; *p_n1r = n1r ; *p_n1c = n1c ; return (n1) ; } /* ========================================================================== */ /* === finish_permutation =================================================== */ /* ========================================================================== */ /* Complete the permutation for the pruned submatrix. The singletons are * already ordered, but remove their flags. Place rows/columns that are empty * in the pruned submatrix at the end of the output permutation. This can only * occur if the matrix is singular. */ PRIVATE Int finish_permutation ( Int n1, Int nx, Int Xdeg [ ], const Int Xuser [ ], Int Xperm [ ], Int *p_max_deg ) { Int nempty, x, deg, s, max_deg, k ; nempty = 0 ; s = n1 ; max_deg = 0 ; DEBUG0 (("n1 "ID" nempty "ID"\n", n1, nempty)) ; for (k = 0 ; k < nx ; k++) { x = (Xuser != (Int *) NULL) ? Xuser [k] : k ; DEBUG0 (("finish perm k "ID" x "ID" nx "ID"\n", k, x, nx)) ; deg = Xdeg [x] ; if (deg == 0) { /* this row/col is empty in the pruned submatrix */ ASSERT (s < nx - nempty) ; DEBUG0 (("empty k "ID"\n", k)) ; nempty++ ; Xperm [nx - nempty] = x ; } else if (deg > 0) { /* this row/col is nonempty in the pruned submatrix */ ASSERT (s < nx - nempty) ; Xperm [s++] = x ; max_deg = MAX (max_deg, deg) ; } else { /* This is a singleton row/column - it is already ordered. * Just clear the flag. */ Xdeg [x] = FLIP (deg) ; } } ASSERT (s == nx - nempty) ; *p_max_deg = max_deg ; return (nempty) ; } /* ========================================================================== */ /* === UMF_singletons ======================================================= */ /* ========================================================================== */ GLOBAL Int UMF_singletons ( /* input, not modified: */ Int n_row, Int n_col, const Int Ap [ ], /* size n_col+1 */ const Int Ai [ ], /* size nz = Ap [n_col] */ const Int Quser [ ], /* size n_col if present */ Int strategy, /* strategy requested by user */ /* output, not defined on input: */ Int Cdeg [ ], /* size n_col */ Int Cperm [ ], /* size n_col */ Int Rdeg [ ], /* size n_row */ Int Rperm [ ], /* size n_row */ Int InvRperm [ ], /* size n_row, the inverse of Rperm */ Int *p_n1, /* # of col and row singletons */ Int *p_n1c, /* # of col singletons */ Int *p_n1r, /* # of row singletons */ Int *p_nempty_col, /* # of empty columns in pruned submatrix */ Int *p_nempty_row, /* # of empty columns in pruned submatrix */ Int *p_is_sym, /* TRUE if pruned submatrix is square and has been * symmetrically permuted by Cperm and Rperm */ Int *p_max_rdeg, /* maximum Rdeg in pruned submatrix */ /* workspace, not defined on input or output */ Int Rp [ ], /* size n_row+1 */ Int Ri [ ], /* size nz */ Int W [ ], /* size n_row */ Int Next [ ] /* size MAX (n_row, n_col) */ ) { Int n1, s, col, row, p, p1, p2, cdeg, last_row, is_sym, k, nempty_row, nempty_col, max_cdeg, max_rdeg, n1c, n1r ; /* ---------------------------------------------------------------------- */ /* initializations */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG UMF_dump_start ( ) ; DEBUGm4 (("Starting umf_singletons\n")) ; #endif /* ---------------------------------------------------------------------- */ /* scan the columns, check for errors and count row degrees */ /* ---------------------------------------------------------------------- */ if (Ap [0] != 0 || Ap [n_col] < 0) { return (UMFPACK_ERROR_invalid_matrix) ; } for (row = 0 ; row < n_row ; row++) { Rdeg [row] = 0 ; } for (col = 0 ; col < n_col ; col++) { p1 = Ap [col] ; p2 = Ap [col+1] ; cdeg = p2 - p1 ; if (cdeg < 0) { return (UMFPACK_ERROR_invalid_matrix) ; } last_row = EMPTY ; for (p = p1 ; p < p2 ; p++) { row = Ai [p] ; if (row <= last_row || row >= n_row) { return (UMFPACK_ERROR_invalid_matrix) ; } Rdeg [row]++ ; last_row = row ; } Cdeg [col] = cdeg ; } /* ---------------------------------------------------------------------- */ /* find singletons */ /* ---------------------------------------------------------------------- */ if (Quser != (Int *) NULL) { /* user has provided an input column ordering */ if (strategy == UMFPACK_STRATEGY_UNSYMMETRIC) { /* look for singletons, but respect the user's input permutation */ n1 = find_user_singletons (n_row, n_col, Ap, Ai, Quser, Cdeg, Rdeg, Cperm, Rperm, &n1r, &n1c, Rp, Ri, W) ; } else { /* do not look for singletons if Quser given and strategy is * not unsymmetric */ n1 = 0 ; n1r = 0 ; n1c = 0 ; } } else { /* look for singletons anywhere */ n1 = find_any_singletons (n_row, n_col, Ap, Ai, Cdeg, Rdeg, Cperm, Rperm, &n1r, &n1c, Rp, Ri, W, Next) ; } /* ---------------------------------------------------------------------- */ /* eliminate empty columns and complete the column permutation */ /* ---------------------------------------------------------------------- */ nempty_col = finish_permutation (n1, n_col, Cdeg, Quser, Cperm, &max_cdeg) ; /* ---------------------------------------------------------------------- */ /* eliminate empty rows and complete the row permutation */ /* ---------------------------------------------------------------------- */ if (Quser != (Int *) NULL && strategy == UMFPACK_STRATEGY_SYMMETRIC) { /* rows should be symmetrically permuted according to Quser */ ASSERT (n_row == n_col) ; nempty_row = finish_permutation (n1, n_row, Rdeg, Quser, Rperm, &max_rdeg) ; } else { /* rows should not be symmetrically permuted according to Quser */ nempty_row = finish_permutation (n1, n_row, Rdeg, (Int *) NULL, Rperm, &max_rdeg) ; } /* ---------------------------------------------------------------------- */ /* compute the inverse of Rperm */ /* ---------------------------------------------------------------------- */ for (k = 0 ; k < n_row ; k++) { ASSERT (Rperm [k] >= 0 && Rperm [k] < n_row) ; InvRperm [Rperm [k]] = k ; } /* ---------------------------------------------------------------------- */ /* see if pruned submatrix is square and has been symmetrically permuted */ /* ---------------------------------------------------------------------- */ if (n_row == n_col && nempty_row == nempty_col) { /* is_sym is true if the submatrix is square, and * Rperm [n1..n_row-nempty_row-1] = Cperm [n1..n_col-nempty_col-1] */ is_sym = TRUE ; for (s = n1 ; s < n_col - nempty_col ; s++) { if (Cperm [s] != Rperm [s]) { is_sym = FALSE ; break ; } } } else { is_sym = FALSE ; } DEBUGm4 (("Submatrix square and symmetrically permuted? "ID"\n", is_sym)) ; DEBUGm4 (("singletons "ID" row "ID" col "ID"\n", n1, n1r, n1c)) ; DEBUGm4 (("Empty cols "ID" rows "ID"\n", nempty_col, nempty_row)) ; *p_n1 = n1 ; *p_n1r = n1r ; *p_n1c = n1c ; *p_is_sym = is_sym ; *p_nempty_col = nempty_col ; *p_nempty_row = nempty_row ; *p_max_rdeg = max_rdeg ; return (UMFPACK_OK) ; } SuiteSparse/UMFPACK/Source/umf_singletons.h0000644001170100242450000000150210617162411017477 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_singletons ( Int n_row, Int n_col, const Int Ap [ ], const Int Ai [ ], const Int Quser [ ], Int strategy, Int Cdeg [ ], Int Cperm [ ], Int Rdeg [ ], Int Rperm [ ], Int InvRperm [ ], Int *n1, Int *n1c, Int *n1r, Int *nempty_col, Int *nempty_row, Int *is_sym, Int *max_rdeg, Int Rp [ ], Int Ri [ ], Int W [ ], Int Next [ ] ) ; SuiteSparse/UMFPACK/Source/umf_mem_init_memoryspace.c0000644001170100242450000000425410677541760021537 0ustar davisfac/* ========================================================================== */ /* === UMF_mem_init_memoryspace ============================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* The UMF_mem_* routines manage the Numeric->Memory memory space. */ #include "umf_internal.h" #include "umf_mem_init_memoryspace.h" /* initialize the LU and element workspace (Numeric->Memory) */ GLOBAL void UMF_mem_init_memoryspace ( NumericType *Numeric ) { Unit *p ; ASSERT (Numeric != (NumericType *) NULL) ; ASSERT (Numeric->Memory != (Unit *) NULL) ; ASSERT (Numeric->size >= 3) ; DEBUG0 (("Init memory space, size "ID"\n", Numeric->size)) ; Numeric->ngarbage = 0 ; Numeric->nrealloc = 0 ; Numeric->ncostly = 0 ; Numeric->ibig = EMPTY ; Numeric->ihead = 0 ; Numeric->itail = Numeric->size ; #ifndef NDEBUG UMF_allocfail = FALSE ; #endif /* allocate the 2-unit tail marker block and initialize it */ Numeric->itail -= 2 ; p = Numeric->Memory + Numeric->itail ; DEBUG2 (("p "ID" tail "ID"\n", (Int) (p-Numeric->Memory), Numeric->itail)) ; Numeric->tail_usage = 2 ; p->header.prevsize = 0 ; p->header.size = 1 ; /* allocate a 1-unit head marker block at the head of memory */ /* this is done so that an offset of zero is treated as a NULL pointer */ Numeric->ihead++ ; /* initial usage in Numeric->Memory */ Numeric->max_usage = 3 ; Numeric->init_usage = Numeric->max_usage ; /* Note that UMFPACK_*symbolic ensures that Numeric->Memory is of size */ /* at least 3, so this initialization will always succeed. */ #ifndef NDEBUG DEBUG2 (("init_memoryspace, all free (except one unit at head\n")) ; UMF_dump_memory (Numeric) ; #endif } SuiteSparse/UMFPACK/Source/umf_mem_init_memoryspace.h0000644001170100242450000000073210617161777021541 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL void UMF_mem_init_memoryspace ( NumericType *Numeric ) ; SuiteSparse/UMFPACK/Source/umf_row_search.c0000644001170100242450000005520410617162244017455 0ustar davisfac/* ========================================================================== */ /* === UMF_row_search ======================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Find two candidate pivot rows in a column: the best one in the front, and the best one not in the front. Return the two pivot row patterns and their exact degrees. Called by UMF_local_search. Returns UMFPACK_OK if successful, or UMFPACK_WARNING_singular_matrix or UMFPACK_ERROR_different_pattern if not. */ #include "umf_internal.h" #include "umf_row_search.h" GLOBAL Int UMF_row_search ( NumericType *Numeric, WorkType *Work, SymbolicType *Symbolic, Int cdeg0, /* length of column in Front */ Int cdeg1, /* length of column outside Front */ const Int Pattern [ ], /* pattern of column, Pattern [0..cdeg1 -1] */ const Int Pos [ ], /* Pos [Pattern [0..cdeg1 -1]] = 0..cdeg1 -1 */ Int pivrow [2], /* pivrow [IN] and pivrow [OUT] */ Int rdeg [2], /* rdeg [IN] and rdeg [OUT] */ Int W_i [ ], /* pattern of pivrow [IN], */ /* either Fcols or Woi */ Int W_o [ ], /* pattern of pivrow [OUT], */ /* either Wio or Woo */ Int prior_pivrow [2], /* the two other rows just scanned, if any */ const Entry Wxy [ ], /* numerical values Wxy [0..cdeg1-1], either Wx or Wy */ Int pivcol, /* the candidate column being searched */ Int freebie [ ] ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ double maxval, toler, toler2, value, pivot [2] ; Int i, row, deg, col, *Frpos, fnrows, *E, j, ncols, *Cols, *Rows, e, f, Wrpflag, *Fcpos, fncols, tpi, max_rdeg, nans_in_col, was_offdiag, diag_row, prefer_diagonal, *Wrp, found, *Diagonal_map ; Tuple *tp, *tpend, *tp1, *tp2 ; Unit *Memory, *p ; Element *ep ; Int *Row_tuples, *Row_degree, *Row_tlen ; #ifndef NDEBUG Int *Col_degree ; DEBUG2 (("Row_search:\n")) ; for (i = 0 ; i < cdeg1 ; i++) { row = Pattern [i] ; DEBUG4 ((" row: "ID"\n", row)) ; ASSERT (row >= 0 && row < Numeric->n_row) ; ASSERT (i == Pos [row]) ; } /* If row is not in Pattern [0..cdeg1-1], then Pos [row] == EMPTY */ if (UMF_debug > 0 || Numeric->n_row < 1000) { Int cnt = cdeg1 ; DEBUG4 (("Scan all rows:\n")) ; for (row = 0 ; row < Numeric->n_row ; row++) { if (Pos [row] < 0) { cnt++ ; } else { DEBUG4 ((" row: "ID" pos "ID"\n", row, Pos [row])) ; } } ASSERT (cnt == Numeric->n_row) ; } Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro only */ ASSERT (pivcol >= 0 && pivcol < Work->n_col) ; ASSERT (NON_PIVOTAL_COL (pivcol)) ; #endif pivot [IN] = 0. ; pivot [OUT] = 0. ; /* ---------------------------------------------------------------------- */ /* get parameters */ /* ---------------------------------------------------------------------- */ Row_degree = Numeric->Rperm ; Row_tuples = Numeric->Uip ; Row_tlen = Numeric->Uilen ; Wrp = Work->Wrp ; Frpos = Work->Frpos ; E = Work->E ; Memory = Numeric->Memory ; fnrows = Work->fnrows ; prefer_diagonal = Symbolic->prefer_diagonal ; Diagonal_map = Work->Diagonal_map ; if (Diagonal_map) { diag_row = Diagonal_map [pivcol] ; was_offdiag = diag_row < 0 ; if (was_offdiag) { /* the "diagonal" entry in this column was permuted here by an * earlier pivot choice. The tighter off-diagonal tolerance will * be used instead of the symmetric tolerance. */ diag_row = FLIP (diag_row) ; } ASSERT (diag_row >= 0 && diag_row < Numeric->n_row) ; } else { diag_row = EMPTY ; /* unused */ was_offdiag = EMPTY ; /* unused */ } /* pivot row degree cannot exceed max_rdeg */ max_rdeg = Work->fncols_max ; /* ---------------------------------------------------------------------- */ /* scan pivot column for candidate rows */ /* ---------------------------------------------------------------------- */ maxval = 0.0 ; nans_in_col = FALSE ; for (i = 0 ; i < cdeg1 ; i++) { APPROX_ABS (value, Wxy [i]) ; if (SCALAR_IS_NAN (value)) { nans_in_col = TRUE ; maxval = value ; break ; } /* This test can now ignore the NaN case: */ maxval = MAX (maxval, value) ; } /* if maxval is zero, the matrix is numerically singular */ toler = Numeric->relpt * maxval ; toler2 = Numeric->relpt2 * maxval ; toler2 = was_offdiag ? toler : toler2 ; DEBUG5 (("Row_search begins [ maxval %g toler %g %g\n", maxval, toler, toler2)) ; if (SCALAR_IS_NAN (toler) || SCALAR_IS_NAN (toler2)) { nans_in_col = TRUE ; } if (!nans_in_col) { /* look for the diagonal entry, if it exists */ found = FALSE ; ASSERT (!SCALAR_IS_NAN (toler)) ; if (prefer_diagonal) { ASSERT (diag_row != EMPTY) ; i = Pos [diag_row] ; if (i >= 0) { double a ; ASSERT (i < cdeg1) ; ASSERT (diag_row == Pattern [i]) ; APPROX_ABS (a, Wxy [i]) ; ASSERT (!SCALAR_IS_NAN (a)) ; ASSERT (!SCALAR_IS_NAN (toler2)) ; if (SCALAR_IS_NONZERO (a) && a >= toler2) { /* found it! */ DEBUG3 (("Symmetric pivot: "ID" "ID"\n", pivcol, diag_row)); found = TRUE ; if (Frpos [diag_row] >= 0 && Frpos [diag_row] < fnrows) { pivrow [IN] = diag_row ; pivrow [OUT] = EMPTY ; } else { pivrow [IN] = EMPTY ; pivrow [OUT] = diag_row ; } } } } /* either no diagonal found, or we didn't look for it */ if (!found) { if (cdeg0 > 0) { /* this is a column in the front */ for (i = 0 ; i < cdeg0 ; i++) { double a ; APPROX_ABS (a, Wxy [i]) ; ASSERT (!SCALAR_IS_NAN (a)) ; ASSERT (!SCALAR_IS_NAN (toler)) ; if (SCALAR_IS_NONZERO (a) && a >= toler) { row = Pattern [i] ; deg = Row_degree [row] ; #ifndef NDEBUG DEBUG6 ((ID" candidate row "ID" deg "ID" absval %g\n", i, row, deg, a)) ; UMF_dump_rowcol (0, Numeric, Work, row, TRUE) ; #endif ASSERT (Frpos [row] >= 0 && Frpos [row] < fnrows) ; ASSERT (Frpos [row] == i) ; /* row is in the current front */ DEBUG4 ((" in front\n")) ; if (deg < rdeg [IN] /* break ties by picking the largest entry: */ || (deg == rdeg [IN] && a > pivot [IN]) /* break ties by picking the diagonal entry: */ /* || (deg == rdeg [IN] && row == diag_row) */ ) { /* best row in front, so far */ pivrow [IN] = row ; rdeg [IN] = deg ; pivot [IN] = a ; } } } for ( ; i < cdeg1 ; i++) { double a ; APPROX_ABS (a, Wxy [i]) ; ASSERT (!SCALAR_IS_NAN (a)) ; ASSERT (!SCALAR_IS_NAN (toler)) ; if (SCALAR_IS_NONZERO (a) && a >= toler) { row = Pattern [i] ; deg = Row_degree [row] ; #ifndef NDEBUG DEBUG6 ((ID" candidate row "ID" deg "ID" absval %g\n", i, row, deg, a)) ; UMF_dump_rowcol (0, Numeric, Work, row, TRUE) ; #endif ASSERT (Frpos [row] == i) ; /* row is not in the current front */ DEBUG4 ((" NOT in front\n")) ; if (deg < rdeg [OUT] /* break ties by picking the largest entry: */ || (deg == rdeg [OUT] && a > pivot [OUT]) /* break ties by picking the diagonal entry: */ /* || (deg == rdeg [OUT] && row == diag_row) */ ) { /* best row not in front, so far */ pivrow [OUT] = row ; rdeg [OUT] = deg ; pivot [OUT] = a ; } } } } else { /* this column is not in the front */ for (i = 0 ; i < cdeg1 ; i++) { double a ; APPROX_ABS (a, Wxy [i]) ; ASSERT (!SCALAR_IS_NAN (a)) ; ASSERT (!SCALAR_IS_NAN (toler)) ; if (SCALAR_IS_NONZERO (a) && a >= toler) { row = Pattern [i] ; deg = Row_degree [row] ; #ifndef NDEBUG DEBUG6 ((ID" candidate row "ID" deg "ID" absval %g\n", i, row, deg, a)) ; UMF_dump_rowcol (0, Numeric, Work, row, TRUE) ; #endif if (Frpos [row] >= 0 && Frpos [row] < fnrows) { /* row is in the current front */ DEBUG4 ((" in front\n")) ; if (deg < rdeg [IN] /* break ties by picking the largest entry: */ || (deg == rdeg [IN] && a > pivot [IN]) /* break ties by picking the diagonal entry: */ /* || (deg == rdeg [IN] && row == diag_row) */ ) { /* best row in front, so far */ pivrow [IN] = row ; rdeg [IN] = deg ; pivot [IN] = a ; } } else { /* row is not in the current front */ DEBUG4 ((" NOT in front\n")) ; if (deg < rdeg [OUT] /* break ties by picking the largest entry: */ || (deg == rdeg[OUT] && a > pivot [OUT]) /* break ties by picking the diagonal entry: */ /* || (deg == rdeg[OUT] && row == diag_row) */ ) { /* best row not in front, so far */ pivrow [OUT] = row ; rdeg [OUT] = deg ; pivot [OUT] = a ; } } } } } } } /* ---------------------------------------------------------------------- */ /* NaN handling */ /* ---------------------------------------------------------------------- */ /* if cdeg1 > 0 then we must have found a pivot row ... unless NaN's */ /* exist. Try with no numerical tests if no pivot found. */ if (cdeg1 > 0 && pivrow [IN] == EMPTY && pivrow [OUT] == EMPTY) { /* cleanup for the NaN case */ DEBUG0 (("Found a NaN in pivot column!\n")) ; /* grab the first entry in the pivot column, ignoring degree, */ /* numerical stability, and symmetric preference */ row = Pattern [0] ; deg = Row_degree [row] ; if (Frpos [row] >= 0 && Frpos [row] < fnrows) { /* row is in the current front */ DEBUG4 ((" in front\n")) ; pivrow [IN] = row ; rdeg [IN] = deg ; } else { /* row is not in the current front */ DEBUG4 ((" NOT in front\n")) ; pivrow [OUT] = row ; rdeg [OUT] = deg ; } /* We are now guaranteed to have a pivot, no matter how broken */ /* (non-IEEE compliant) the underlying numerical operators are. */ /* This is particularly a problem for Microsoft compilers (they do */ /* not handle NaN's properly). Now try to find a sparser pivot, if */ /* possible. */ for (i = 1 ; i < cdeg1 ; i++) { row = Pattern [i] ; deg = Row_degree [row] ; if (Frpos [row] >= 0 && Frpos [row] < fnrows) { /* row is in the current front */ DEBUG4 ((" in front\n")) ; if (deg < rdeg [IN] || (deg == rdeg [IN] && row == diag_row)) { /* best row in front, so far */ pivrow [IN] = row ; rdeg [IN] = deg ; } } else { /* row is not in the current front */ DEBUG4 ((" NOT in front\n")) ; if (deg < rdeg [OUT] || (deg == rdeg [OUT] && row == diag_row)) { /* best row not in front, so far */ pivrow [OUT] = row ; rdeg [OUT] = deg ; } } } } /* We found a pivot if there are entries (even zero ones) in pivot col */ ASSERT (IMPLIES (cdeg1 > 0, pivrow[IN] != EMPTY || pivrow[OUT] != EMPTY)) ; /* If there are no entries in the pivot column, then no pivot is found */ ASSERT (IMPLIES (cdeg1 == 0, pivrow[IN] == EMPTY && pivrow[OUT] == EMPTY)) ; /* ---------------------------------------------------------------------- */ /* check for singular matrix */ /* ---------------------------------------------------------------------- */ if (cdeg1 == 0) { if (fnrows > 0) { /* Get the pivrow [OUT][IN] from the current front. The frontal matrix looks like this: pivcol[OUT] | v x x x x 0 <- so grab this row as the pivrow [OUT][IN]. x x x x 0 x x x x 0 0 0 0 0 0 The current frontal matrix has some rows in it. The degree of the pivcol[OUT] is zero. The column is empty, and the current front does not contribute to it. */ pivrow [IN] = Work->Frows [0] ; DEBUGm4 (("Got zero pivrow[OUT][IN] "ID" from current front\n", pivrow [IN])) ; } else { /* Get a pivot row from the row-merge tree, use as pivrow [OUT][OUT]. pivrow [IN] remains EMPTY. This can only happen if the current front is 0-by-0. */ Int *Front_leftmostdesc, *Front_1strow, *Front_new1strow, row1, row2, fleftmost, nfr, n_row, frontid ; ASSERT (Work->fncols == 0) ; Front_leftmostdesc = Symbolic->Front_leftmostdesc ; Front_1strow = Symbolic->Front_1strow ; Front_new1strow = Work->Front_new1strow ; nfr = Symbolic->nfr ; n_row = Numeric->n_row ; frontid = Work->frontid ; DEBUGm4 (("Note: pivcol: "ID" is empty front "ID"\n", pivcol, frontid)) ; #ifndef NDEBUG DEBUG1 (("Calling dump rowmerge\n")) ; UMF_dump_rowmerge (Numeric, Symbolic, Work) ; #endif /* Row-merge set is the non-pivotal rows in the range */ /* Front_new1strow [Front_leftmostdesc [frontid]] to */ /* Front_1strow [frontid+1] - 1. */ /* If this is empty, then use the empty rows, in the range */ /* Front_new1strow [nfr] to n_row-1. */ /* If this too is empty, then pivrow [OUT] will be empty. */ /* In both cases, update Front_new1strow [...]. */ fleftmost = Front_leftmostdesc [frontid] ; row1 = Front_new1strow [fleftmost] ; row2 = Front_1strow [frontid+1] - 1 ; DEBUG1 (("Leftmost: "ID" Rows ["ID" to "ID"] srch ["ID" to "ID"]\n", fleftmost, Front_1strow [frontid], row2, row1, row2)) ; /* look in the range row1 ... row2 */ for (row = row1 ; row <= row2 ; row++) { DEBUG3 ((" Row: "ID"\n", row)) ; if (NON_PIVOTAL_ROW (row)) { /* found it */ DEBUG3 ((" Row: "ID" found\n", row)) ; ASSERT (Frpos [row] == EMPTY) ; pivrow [OUT] = row ; DEBUGm4 (("got row merge pivrow %d\n", pivrow [OUT])) ; break ; } } Front_new1strow [fleftmost] = row ; if (pivrow [OUT] == EMPTY) { /* not found, look in empty row set in "dummy" front */ row1 = Front_new1strow [nfr] ; row2 = n_row-1 ; DEBUG3 (("Empty: "ID" Rows ["ID" to "ID"] srch["ID" to "ID"]\n", nfr, Front_1strow [nfr], row2, row1, row2)) ; /* look in the range row1 ... row2 */ for (row = row1 ; row <= row2 ; row++) { DEBUG3 ((" Empty Row: "ID"\n", row)) ; if (NON_PIVOTAL_ROW (row)) { /* found it */ DEBUG3 ((" Empty Row: "ID" found\n", row)) ; ASSERT (Frpos [row] == EMPTY) ; pivrow [OUT] = row ; DEBUGm4 (("got dummy row pivrow %d\n", pivrow [OUT])) ; break ; } } Front_new1strow [nfr] = row ; } if (pivrow [OUT] == EMPTY) { /* Row-merge set is empty. We can just discard */ /* the candidate pivot column. */ DEBUG0 (("Note: row-merge set empty\n")) ; DEBUGm4 (("got no pivrow \n")) ; return (UMFPACK_WARNING_singular_matrix) ; } } } /* ---------------------------------------------------------------------- */ /* construct the candidate row in the front, if any */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG /* check Wrp */ ASSERT (Work->Wrpflag > 0) ; if (UMF_debug > 0 || Work->n_col < 1000) { for (i = 0 ; i < Work->n_col ; i++) { ASSERT (Wrp [i] < Work->Wrpflag) ; } } #endif #ifndef NDEBUG DEBUG4 (("pivrow [IN]: "ID"\n", pivrow [IN])) ; UMF_dump_rowcol (0, Numeric, Work, pivrow [IN], TRUE) ; #endif if (pivrow [IN] != EMPTY) { /* the row merge candidate row is not pivrow [IN] */ freebie [IN] = (pivrow [IN] == prior_pivrow [IN]) && (cdeg1 > 0) ; ASSERT (cdeg1 >= 0) ; if (!freebie [IN]) { /* include current front in the degree of this row */ Fcpos = Work->Fcpos ; fncols = Work->fncols ; Wrpflag = Work->Wrpflag ; /* -------------------------------------------------------------- */ /* construct the pattern of the IN row */ /* -------------------------------------------------------------- */ #ifndef NDEBUG /* check Fcols */ DEBUG5 (("ROW ASSEMBLE: rdeg "ID"\nREDUCE ROW "ID"\n", fncols, pivrow [IN])) ; for (j = 0 ; j < fncols ; j++) { col = Work->Fcols [j] ; ASSERT (col >= 0 && col < Work->n_col) ; ASSERT (Fcpos [col] >= 0) ; } if (UMF_debug > 0 || Work->n_col < 1000) { Int cnt = fncols ; for (col = 0 ; col < Work->n_col ; col++) { if (Fcpos [col] < 0) cnt++ ; } ASSERT (cnt == Work->n_col) ; } #endif rdeg [IN] = fncols ; ASSERT (pivrow [IN] >= 0 && pivrow [IN] < Work->n_row) ; ASSERT (NON_PIVOTAL_ROW (pivrow [IN])) ; /* add the pivot column itself */ ASSERT (Wrp [pivcol] != Wrpflag) ; if (Fcpos [pivcol] < 0) { DEBUG3 (("Adding pivot col to pivrow [IN] pattern\n")) ; if (rdeg [IN] >= max_rdeg) { /* :: pattern change (in) :: */ return (UMFPACK_ERROR_different_pattern) ; } Wrp [pivcol] = Wrpflag ; W_i [rdeg [IN]++] = pivcol ; } tpi = Row_tuples [pivrow [IN]] ; if (tpi) { tp = (Tuple *) (Memory + tpi) ; tp1 = tp ; tp2 = tp ; tpend = tp + Row_tlen [pivrow [IN]] ; for ( ; tp < tpend ; tp++) { e = tp->e ; ASSERT (e > 0 && e <= Work->nel) ; if (!E [e]) { continue ; /* element already deallocated */ } f = tp->f ; p = Memory + E [e] ; ep = (Element *) p ; p += UNITS (Element, 1) ; Cols = (Int *) p ; ncols = ep->ncols ; Rows = Cols + ncols ; if (Rows [f] == EMPTY) { continue ; /* row already assembled */ } ASSERT (pivrow [IN] == Rows [f]) ; for (j = 0 ; j < ncols ; j++) { col = Cols [j] ; ASSERT (col >= EMPTY && col < Work->n_col) ; if ((col >= 0) && (Wrp [col] != Wrpflag) && Fcpos [col] <0) { ASSERT (NON_PIVOTAL_COL (col)) ; if (rdeg [IN] >= max_rdeg) { /* :: pattern change (rdeg in failure) :: */ DEBUGm4 (("rdeg [IN] >= max_rdeg failure\n")) ; return (UMFPACK_ERROR_different_pattern) ; } Wrp [col] = Wrpflag ; W_i [rdeg [IN]++] = col ; } } *tp2++ = *tp ; /* leave the tuple in the list */ } Row_tlen [pivrow [IN]] = tp2 - tp1 ; } #ifndef NDEBUG DEBUG4 (("Reduced IN row:\n")) ; for (j = 0 ; j < fncols ; j++) { DEBUG6 ((" "ID" "ID" "ID"\n", j, Work->Fcols [j], Fcpos [Work->Fcols [j]])) ; ASSERT (Fcpos [Work->Fcols [j]] >= 0) ; } for (j = fncols ; j < rdeg [IN] ; j++) { DEBUG6 ((" "ID" "ID" "ID"\n", j, W_i [j], Wrp [W_i [j]])); ASSERT (W_i [j] >= 0 && W_i [j] < Work->n_col) ; ASSERT (Wrp [W_i [j]] == Wrpflag) ; } /* mark the end of the pattern in case we scan it by mistake */ /* Note that this means W_i must be of size >= fncols_max + 1 */ W_i [rdeg [IN]] = EMPTY ; #endif /* rdeg [IN] is now the exact degree of the IN row */ /* clear Work->Wrp. */ Work->Wrpflag++ ; /* All Wrp [0..n_col] is now < Wrpflag */ } } #ifndef NDEBUG /* check Wrp */ if (UMF_debug > 0 || Work->n_col < 1000) { for (i = 0 ; i < Work->n_col ; i++) { ASSERT (Wrp [i] < Work->Wrpflag) ; } } #endif /* ---------------------------------------------------------------------- */ /* construct the candidate row not in the front, if any */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG DEBUG4 (("pivrow [OUT]: "ID"\n", pivrow [OUT])) ; UMF_dump_rowcol (0, Numeric, Work, pivrow [OUT], TRUE) ; #endif /* If this is a candidate row from the row merge set, force it to be */ /* scanned (ignore prior_pivrow [OUT]). */ if (pivrow [OUT] != EMPTY) { freebie [OUT] = (pivrow [OUT] == prior_pivrow [OUT]) && cdeg1 > 0 ; ASSERT (cdeg1 >= 0) ; if (!freebie [OUT]) { Wrpflag = Work->Wrpflag ; /* -------------------------------------------------------------- */ /* construct the pattern of the row */ /* -------------------------------------------------------------- */ rdeg [OUT] = 0 ; ASSERT (pivrow [OUT] >= 0 && pivrow [OUT] < Work->n_row) ; ASSERT (NON_PIVOTAL_ROW (pivrow [OUT])) ; /* add the pivot column itself */ ASSERT (Wrp [pivcol] != Wrpflag) ; DEBUG3 (("Adding pivot col to pivrow [OUT] pattern\n")) ; if (rdeg [OUT] >= max_rdeg) { /* :: pattern change (out) :: */ return (UMFPACK_ERROR_different_pattern) ; } Wrp [pivcol] = Wrpflag ; W_o [rdeg [OUT]++] = pivcol ; tpi = Row_tuples [pivrow [OUT]] ; if (tpi) { tp = (Tuple *) (Memory + tpi) ; tp1 = tp ; tp2 = tp ; tpend = tp + Row_tlen [pivrow [OUT]] ; for ( ; tp < tpend ; tp++) { e = tp->e ; ASSERT (e > 0 && e <= Work->nel) ; if (!E [e]) { continue ; /* element already deallocated */ } f = tp->f ; p = Memory + E [e] ; ep = (Element *) p ; p += UNITS (Element, 1) ; Cols = (Int *) p ; ncols = ep->ncols ; Rows = Cols + ncols ; if (Rows [f] == EMPTY) { continue ; /* row already assembled */ } ASSERT (pivrow [OUT] == Rows [f]) ; for (j = 0 ; j < ncols ; j++) { col = Cols [j] ; ASSERT (col >= EMPTY && col < Work->n_col) ; if ((col >= 0) && (Wrp [col] != Wrpflag)) { ASSERT (NON_PIVOTAL_COL (col)) ; if (rdeg [OUT] >= max_rdeg) { /* :: pattern change (rdeg out failure) :: */ DEBUGm4 (("rdeg [OUT] failure\n")) ; return (UMFPACK_ERROR_different_pattern) ; } Wrp [col] = Wrpflag ; W_o [rdeg [OUT]++] = col ; } } *tp2++ = *tp ; /* leave the tuple in the list */ } Row_tlen [pivrow [OUT]] = tp2 - tp1 ; } #ifndef NDEBUG DEBUG4 (("Reduced row OUT:\n")) ; for (j = 0 ; j < rdeg [OUT] ; j++) { DEBUG6 ((" "ID" "ID" "ID"\n", j, W_o [j], Wrp [W_o [j]])) ; ASSERT (W_o [j] >= 0 && W_o [j] < Work->n_col) ; ASSERT (Wrp [W_o [j]] == Wrpflag) ; } /* mark the end of the pattern in case we scan it by mistake */ /* Note that this means W_o must be of size >= fncols_max + 1 */ W_o [rdeg [OUT]] = EMPTY ; #endif /* rdeg [OUT] is now the exact degree of the row */ /* clear Work->Wrp. */ Work->Wrpflag++ ; /* All Wrp [0..n] is now < Wrpflag */ } } DEBUG5 (("Row_search end ] \n")) ; #ifndef NDEBUG /* check Wrp */ if (UMF_debug > 0 || Work->n_col < 1000) { for (i = 0 ; i < Work->n_col ; i++) { ASSERT (Wrp [i] < Work->Wrpflag) ; } } #endif return (UMFPACK_OK) ; } SuiteSparse/UMFPACK/Source/umf_row_search.h0000644001170100242450000000152010617162251017450 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_row_search ( NumericType *Numeric, WorkType *Work, SymbolicType *Symbolic, Int cdeg0, Int cdeg1, const Int Pattern [ ], const Int Pos [ ], Int pivrow [2], Int rdeg [2], Int W_i [ ], Int W_o [ ], Int prior_pivrow [2], const Entry Wxy [ ], Int pivcol, Int freebie [2] ) ; #define IN 0 #define OUT 1 #define IN_IN 0 #define IN_OUT 1 #define OUT_IN 2 #define OUT_OUT 3 SuiteSparse/UMFPACK/Source/umf_malloc.c0000644001170100242450000000546710677540752016610 0ustar davisfac/* ========================================================================== */ /* === UMF_malloc =========================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Allocate a block of n objects, each of a given size. This routine does not handle the case when the size is 1 (allocating char's) because of potential integer overflow. UMFPACK never does that. Also maintains the UMFPACK malloc count. */ #include "umf_internal.h" #include "umf_malloc.h" #if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG) /* UMF_malloc_count is a count of the objects malloc'd by UMFPACK. If you suspect a memory leak in your program (caused by not properly destroying the Symbolic and Numeric objects) then compile with -DUMF_MALLOC_COUNT and check value of UMF_malloc_count. By default, UMF_MALLOC_COUNT is not defined, and thus UMFPACK has no global variables. */ GLOBAL Int UMF_malloc_count = 0 ; #endif #ifdef UMF_TCOV_TEST /* For exhaustive statement coverage testing only! */ GLOBAL int umf_fail, umf_fail_lo, umf_fail_hi ; GLOBAL int umf_realloc_fail, umf_realloc_lo, umf_realloc_hi ; #endif GLOBAL void *UMF_malloc ( Int n_objects, size_t size_of_object ) { size_t size ; void *p ; #ifdef UMF_TCOV_TEST /* For exhaustive statement coverage testing only! */ /* Pretend to fail, to test out-of-memory conditions. */ umf_fail-- ; if (umf_fail <= umf_fail_hi && umf_fail >= umf_fail_lo) { DEBUG0 (("umf_malloc: Pretend to fail %d %d %d\n", umf_fail, umf_fail_hi, umf_fail_lo)) ; return ((void *) NULL) ; } #endif DEBUG0 (("UMF_malloc: ")) ; /* make sure that we allocate something */ n_objects = MAX (1, n_objects) ; size = (size_t) n_objects ; ASSERT (size_of_object > 1) ; if (size > Int_MAX / size_of_object) { /* object is too big for integer pointer arithmetic */ return ((void *) NULL) ; } size *= size_of_object ; /* see AMD/Source/amd_global.c for the memory allocator selection */ p = amd_malloc (size) ; DEBUG0 ((ID"\n", (Int) p)) ; #if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG) if (p) { /* One more object has been malloc'ed. Keep track of the count. */ /* (purely for sanity checks). */ UMF_malloc_count++ ; DEBUG0 ((" successful, new malloc count: "ID"\n", UMF_malloc_count)) ; } #endif return (p) ; } SuiteSparse/UMFPACK/Source/umf_malloc.h0000644001170100242450000000124110617161735016571 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ #ifndef _UMF_MALLOC #define _UMF_MALLOC #if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG) #ifndef EXTERN #define EXTERN extern #endif GLOBAL EXTERN Int UMF_malloc_count ; #endif GLOBAL void *UMF_malloc ( Int n_objects, size_t size_of_object ) ; #endif SuiteSparse/UMFPACK/Source/umf_is_permutation.c0000644001170100242450000000274110677540733020372 0ustar davisfac/* ========================================================================== */ /* === UMF_is_permutation =================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Return TRUE if P is a r-permutation vector, FALSE otherwise */ /* P [0..r-1] must be an r-permutation of 0..n-1 */ #include "umf_internal.h" #include "umf_is_permutation.h" GLOBAL Int UMF_is_permutation ( const Int P [ ], /* permutation of size r */ Int W [ ], /* workspace of size n */ Int n, Int r ) { Int i, k ; if (!P) { /* if P is (Int *) NULL, this is the identity permutation */ return (TRUE) ; } ASSERT (W != (Int *) NULL) ; for (i = 0 ; i < n ; i++) { W [i] = FALSE ; } for (k = 0 ; k < r ; k++) { i = P [k] ; DEBUG5 (("k "ID" i "ID"\n", k, i)) ; if (i < 0 || i >= n) { DEBUG0 (("i out of range "ID" "ID"\n", i, n)) ; return (FALSE) ; } if (W [i]) { DEBUG0 (("i duplicate "ID"\n", i)) ; return (FALSE) ; } W [i] = TRUE ; } return (TRUE) ; } SuiteSparse/UMFPACK/Source/umf_is_permutation.h0000644001170100242450000000076310617161646020375 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_is_permutation ( const Int P [ ], Int W [ ], Int n, Int r ) ; SuiteSparse/UMFPACK/Source/umfpack_defaults.c0000644001170100242450000000772410617162034017770 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_defaults ===================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Sets default control parameters. See umfpack_defaults.h for details. */ #include "umf_internal.h" GLOBAL void UMFPACK_defaults ( double Control [UMFPACK_CONTROL] ) { Int i ; if (!Control) { /* silently return if no Control array */ return ; } for (i = 0 ; i < UMFPACK_CONTROL ; i++) { Control [i] = 0 ; } /* ---------------------------------------------------------------------- */ /* default control settings: can be modified at run-time */ /* ---------------------------------------------------------------------- */ /* used in UMFPACK_report_* routines: */ Control [UMFPACK_PRL] = UMFPACK_DEFAULT_PRL ; /* used in UMFPACK_*symbolic: */ Control [UMFPACK_DENSE_ROW] = UMFPACK_DEFAULT_DENSE_ROW ; Control [UMFPACK_DENSE_COL] = UMFPACK_DEFAULT_DENSE_COL ; Control [UMFPACK_AMD_DENSE] = UMFPACK_DEFAULT_AMD_DENSE ; Control [UMFPACK_STRATEGY] = UMFPACK_DEFAULT_STRATEGY ; Control [UMFPACK_2BY2_TOLERANCE] = UMFPACK_DEFAULT_2BY2_TOLERANCE ; Control [UMFPACK_AGGRESSIVE] = UMFPACK_DEFAULT_AGGRESSIVE ; /* used in UMFPACK_numeric: */ Control [UMFPACK_PIVOT_TOLERANCE] = UMFPACK_DEFAULT_PIVOT_TOLERANCE ; Control [UMFPACK_SYM_PIVOT_TOLERANCE] = UMFPACK_DEFAULT_SYM_PIVOT_TOLERANCE; Control [UMFPACK_BLOCK_SIZE] = UMFPACK_DEFAULT_BLOCK_SIZE ; Control [UMFPACK_ALLOC_INIT] = UMFPACK_DEFAULT_ALLOC_INIT ; Control [UMFPACK_FRONT_ALLOC_INIT] = UMFPACK_DEFAULT_FRONT_ALLOC_INIT ; Control [UMFPACK_SCALE] = UMFPACK_DEFAULT_SCALE ; /* used in UMFPACK_*solve: */ Control [UMFPACK_IRSTEP] = UMFPACK_DEFAULT_IRSTEP ; /* ---------------------------------------------------------------------- */ /* compile-time settings: cannot be modified at run-time */ /* ---------------------------------------------------------------------- */ #ifdef NBLAS /* do not use the BLAS - use in-line C code instead */ Control [UMFPACK_COMPILED_WITH_BLAS] = 0 ; #else /* use externally-provided BLAS (dgemm, dger, dgemv, zgemm, zgeru, zgemv) */ Control [UMFPACK_COMPILED_WITH_BLAS] = 1 ; #endif #ifdef MATLAB_MEX_FILE /* compiled as a MATLAB mexFunction */ Control [UMFPACK_COMPILED_FOR_MATLAB] = 1 ; #else #ifdef MATHWORKS /* compiled for internal use in MATLAB */ Control [UMFPACK_COMPILED_FOR_MATLAB] = 2 ; #else /* use ANSI C malloc, free, realloc, and printf */ Control [UMFPACK_COMPILED_FOR_MATLAB] = 0 ; #endif #endif #ifdef NO_TIMER /* no timer used */ Control [UMFPACK_COMPILED_WITH_GETRUSAGE] = 3 ; #ifndef NPOSIX /* uses the POSIX sysconf ( ) and times ( ) routines in UMFPACK_tic, toc */ Control [UMFPACK_COMPILED_WITH_GETRUSAGE] = 2 ; #else #ifdef GETRUSAGE /* uses the non-standard getrusage to get CPU time (Solaris) */ Control [UMFPACK_COMPILED_WITH_GETRUSAGE] = 1 ; #else /* uses the ANSI standard clock routine to get CPU time */ /* this may wrap around */ Control [UMFPACK_COMPILED_WITH_GETRUSAGE] = 0 ; #endif #endif #endif #ifndef NDEBUG /* UMFPACK is compiled in debug mode. */ /* This is exceedingly slow. */ DEBUG0 (("UMFPACK is running in debug mode. This is very slow!\n")) ; Control [UMFPACK_COMPILED_IN_DEBUG_MODE] = 1 ; #else /* UMFPACK is compiled in normal (non-debug) mode */ Control [UMFPACK_COMPILED_IN_DEBUG_MODE] = 0 ; #endif } SuiteSparse/UMFPACK/Source/umf_local_search.c0000644001170100242450000016305010677541666017756 0ustar davisfac/* ========================================================================== */ /* === UMF_local_search ===================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Perform pivot search to find pivot row and pivot column. The pivot column is selected from the candidate set. The candidate set corresponds to a supercolumn from colamd or UMF_analyze. The pivot column is then removed from that set. Constructs the pivot column pattern and values. Called by umf_kernel. Returns UMFPACK_OK if successful, or UMFPACK_WARNING_singular_matrix or UMFPACK_ERROR_different_pattern if not. */ #include "umf_internal.h" #include "umf_local_search.h" #include "umf_row_search.h" #include "umf_mem_free_tail_block.h" /* relaxed amalgamation control parameters are fixed at compile time */ #define RELAX1 0.25 #define SYM_RELAX1 0.0 #define RELAX2 0.1 #define RELAX3 0.125 /* ========================================================================== */ /* === remove_candidate ===================================================== */ /* ========================================================================== */ /* Remove a column from the set of candidate pivot columns. */ PRIVATE void remove_candidate (Int jj, WorkType *Work, SymbolicType *Symbolic) { #ifndef NDEBUG Int j ; DEBUGm2 (("pivot column Candidates before remove: nCand "ID" ncand "ID " lo "ID" hi "ID" jj "ID"\n", Work->nCandidates, Work->ncand, Work->lo, Work->hi, jj)) ; for (j = 0 ; j < Work->nCandidates ; j++) { Int col = Work->Candidates [j] ; DEBUGm2 ((ID" ", col)); ASSERT (col >= 0 && col < Work->n_col) ; /* ASSERT (NON_PIVOTAL_COL (col)) ; */ ASSERT (col >= Work->lo && col <= Work->hi) ; } DEBUGm2 (("\n")) ; #endif if (Symbolic->fixQ) { DEBUGm2 (("FixQ\n")) ; /* do not modify the column ordering */ ASSERT (Work->nCandidates == 1) ; ASSERT (jj == 0) ; if (Work->ncand > 1) { Work->Candidates [0] = Work->nextcand++ ; } else { Work->nCandidates = 0 ; } } else { /* place the next candidate in the set */ if (Work->ncand > MAX_CANDIDATES) { Work->Candidates [jj] = Work->nextcand++ ; } else { ASSERT (Work->nCandidates == Work->ncand) ; Work->Candidates [jj] = Work->Candidates [Work->ncand - 1] ; Work->Candidates [Work->ncand - 1] = EMPTY ; Work->nCandidates-- ; } } Work->ncand-- ; #ifndef NDEBUG DEBUGm2 (("pivot column Candidates after remove: nCand "ID" ncand "ID " lo "ID" hi "ID" jj "ID"\n", Work->nCandidates, Work->ncand, Work->lo, Work->hi, jj)) ; for (j = 0 ; j < Work->nCandidates ; j++) { Int col = Work->Candidates [j] ; DEBUGm2 ((ID" ", col)); ASSERT (col >= 0 && col < Work->n_col) ; /* ASSERT (NON_PIVOTAL_COL (col)) ; */ ASSERT (col >= Work->lo && col <= Work->hi) ; } DEBUGm2 (("\n")) ; ASSERT (Work->ncand >= 0) ; ASSERT (Work->nCandidates <= Work->ncand) ; #endif } /* ========================================================================== */ /* === UMF_local_search ===================================================== */ /* ========================================================================== */ GLOBAL Int UMF_local_search ( NumericType *Numeric, WorkType *Work, SymbolicType *Symbolic ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ double relax1 ; Entry *Flblock, *Fublock, *Fs, *Fcblock, *C, *Wx, *Wy, *Fu, *Flublock, *Flu ; Int pos, nrows, *Cols, *Rows, e, f, status, max_cdeg, fnzeros, nb, j, col, i, row, cdeg_in, rdeg [2][2], fnpiv, nothing [2], new_LUsize, pivrow [2][2], pivcol [2], *Wp, *Fcpos, *Frpos, new_fnzeros, cdeg_out, *Wm, *Wio, *Woi, *Woo, *Frows, *Fcols, fnrows, fncols, *E, deg, nr_in, nc, thiscost, bestcost, nr_out, do_update, extra_cols, extra_rows, extra_zeros, relaxed_front, do_extend, fnr_curr, fnc_curr, tpi, *Col_tuples, *Col_degree, *Col_tlen, jj, jcand [2], freebie [2], did_rowmerge, fnrows_new [2][2], fncols_new [2][2], search_pivcol_out, *Diagonal_map, *Diagonal_imap, row2, col2 ; Unit *Memory, *p ; Tuple *tp, *tpend, *tp1, *tp2 ; Element *ep ; #ifndef NBLAS Int blas_ok = TRUE ; #else #define blas_ok FALSE #endif #ifndef NDEBUG Int debug_ok, n_row, n_col, *Row_degree ; Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro only */ #endif /* ---------------------------------------------------------------------- */ /* get parameters */ /* ---------------------------------------------------------------------- */ Memory = Numeric->Memory ; E = Work->E ; Col_degree = Numeric->Cperm ; Col_tuples = Numeric->Lip ; Col_tlen = Numeric->Lilen ; Wx = Work->Wx ; Wy = Work->Wy ; Wp = Work->Wp ; Wm = Work->Wm ; Woi = Work->Woi ; Wio = Work->Wio ; Woo = Work->Woo ; Fcpos = Work->Fcpos ; Frpos = Work->Frpos ; Frows = Work->Frows ; Fcols = Work->Fcols ; fnrows = Work->fnrows ; fncols = Work->fncols ; nb = Work->nb ; fnr_curr = Work->fnr_curr ; fnc_curr = Work->fnc_curr ; fnpiv = Work->fnpiv ; nothing [0] = EMPTY ; nothing [1] = EMPTY ; relax1 = (Symbolic->prefer_diagonal) ? SYM_RELAX1 : RELAX1 ; fnzeros = Work->fnzeros ; new_fnzeros = fnzeros ; jj = EMPTY ; Fcblock = Work->Fcblock ; /* current contribution block */ Flblock = Work->Flblock ; /* current L block */ Fublock = Work->Fublock ; /* current U block */ Flublock = Work->Flublock ; /* current LU block */ /* The pivot column degree cannot exceed max_cdeg */ max_cdeg = Work->fnrows_max ; ASSERT (Work->fnrows_max <= Symbolic->maxnrows) ; ASSERT (Work->fncols_max <= Symbolic->maxncols) ; if (fnrows == 0 && fncols == 0) { /* frontal matrix is empty */ Work->firstsuper = Work->ksuper ; } #ifndef NDEBUG n_row = Work->n_row ; n_col = Work->n_col ; DEBUG2 (("\n========LOCAL SEARCH: current frontal matrix: ========= \n")) ; UMF_dump_current_front (Numeric, Work, TRUE) ; if (UMF_debug > 0 || MAX (n_row, n_col) < 1000) { for (i = 0 ; i < MAX (n_row, n_col) ; i++) { ASSERT (Wp [i] < 0) ; } } DEBUGm2 ((ID" pivot column Candidates: lo "ID" hi "ID"\n", Work->nCandidates, Work->lo, Work->hi)) ; for (j = 0 ; j < Work->nCandidates ; j++) { col = Work->Candidates [j] ; DEBUGm2 ((ID" ", col)); ASSERT (col >= 0 && col < n_col) ; ASSERT (NON_PIVOTAL_COL (col)) ; ASSERT (col >= Work->lo && col <= Work->hi) ; } DEBUGm2 (("\n")) ; /* there are no 0-by-c or r-by-0 fronts, where c and r are > 0 */ /* a front is either 0-by-0, or r-by-c */ DEBUG2 (("\n\n::: "ID" : Npiv: "ID" + fnpiv "ID" = "ID". " "size "ID"-by-"ID"\n", Work->frontid, Work->npiv, Work->fnpiv, Work->npiv + Work->fnpiv, fnrows, fncols)) ; ASSERT ((fnrows == 0 && fncols == 0) ||(fnrows != 0 && fncols != 0)) ; #endif /* ====================================================================== */ /* === PIVOT SEARCH ===================================================== */ /* ====================================================================== */ /* initialize */ pivcol [IN] = EMPTY ; pivcol [OUT] = EMPTY ; cdeg_in = Int_MAX ; cdeg_out = Int_MAX ; pivrow [IN][IN] = EMPTY ; pivrow [IN][OUT] = EMPTY ; pivrow [OUT][IN] = EMPTY ; pivrow [OUT][OUT] = EMPTY ; rdeg [IN][IN] = Int_MAX ; rdeg [IN][OUT] = Int_MAX ; rdeg [OUT][IN] = Int_MAX ; rdeg [OUT][OUT] = Int_MAX ; freebie [IN] = FALSE ; freebie [OUT] = FALSE ; Work->pivot_case = EMPTY ; bestcost = EMPTY ; nr_out = EMPTY ; nr_in = EMPTY ; jcand [IN] = EMPTY ; jcand [OUT] = EMPTY ; fnrows_new [IN][IN] = EMPTY ; fnrows_new [IN][OUT] = EMPTY ; fnrows_new [OUT][IN] = EMPTY ; fnrows_new [OUT][OUT] = EMPTY ; fncols_new [IN][IN] = EMPTY ; fncols_new [IN][OUT] = EMPTY ; fncols_new [OUT][IN] = EMPTY ; fncols_new [OUT][OUT] = EMPTY ; #ifndef NDEBUG /* check Frpos */ DEBUG4 (("Check Frpos : fnrows "ID" col "ID" maxcdeg "ID"\n", fnrows, pivcol [IN], max_cdeg)) ; for (i = 0 ; i < fnrows ; i++) { row = Frows [i] ; DEBUG4 ((" row: "ID"\n", row)) ; ASSERT (row >= 0 && row < n_row) ; ASSERT (Frpos [row] == i) ; } DEBUG4 (("All:\n")) ; if (UMF_debug > 0 || n_row < 1000) { Int cnt = fnrows ; for (row = 0 ; row < n_row ; row++) { if (Frpos [row] == EMPTY) { cnt++ ; } else { DEBUG4 ((" row: "ID" pos "ID"\n", row, Frpos [row])) ; } } ASSERT (cnt == n_row) ; } #endif /* ---------------------------------------------------------------------- */ /* find shortest column in the front, and shortest column not in the */ /* front, from the candidate pivot column set */ /* ---------------------------------------------------------------------- */ /* If there are too many candidates, then only look at the first */ /* MAX_CANDIDATES of them. Otherwise, if there are O(n) candidates, */ /* this code could take O(n^2) time. */ /* ------------------------------------------------------------------ */ /* look in the candidate set for the best column */ /* ------------------------------------------------------------------ */ DEBUG2 (("Max candidates %d, Work->ncand "ID" jmax "ID"\n", MAX_CANDIDATES, Work->ncand, Work->nCandidates)) ; col = Work->Candidates [0] ; ASSERT (Work->nCandidates > 0) ; DEBUG3 (("Pivot column candidate: "ID" j = "ID"\n", col, j)) ; ASSERT (col >= 0 && col < n_col) ; /* there is no Col_degree if fixQ is true */ deg = Symbolic->fixQ ? EMPTY : Col_degree [col] ; #ifndef NDEBUG DEBUG3 (("Pivot column candidate: "ID" cost: "ID" Fcpos[col] "ID"\n", col, deg, Fcpos [col])) ; UMF_dump_rowcol (1, Numeric, Work, col, !Symbolic->fixQ) ; if (Symbolic->fixQ) { DEBUG1 (("FIXQ: Candidates "ID" pivcol "ID" npiv "ID" fnpiv "ID " ndiscard "ID "\n", Work->nCandidates, col, Work->npiv, Work->fnpiv, Work->ndiscard)) ; ASSERT (Work->nCandidates == 1) ; ASSERT (col == Work->npiv + Work->fnpiv + Work->ndiscard) ; } #endif if (Fcpos [col] >= 0) { /* best column in front, so far */ pivcol [IN] = col ; cdeg_in = deg ; /* ignored, if fixQ is true */ jcand [IN] = 0 ; } else { /* best column not in front, so far */ pivcol [OUT] = col ; cdeg_out = deg ; /* ignored, if fixQ is true */ jcand [OUT] = 0 ; } /* look at the rest of the candidates */ for (j = 1 ; j < Work->nCandidates ; j++) { col = Work->Candidates [j] ; DEBUG3 (("Pivot col candidate: "ID" j = "ID"\n", col, j)) ; ASSERT (col >= 0 && col < n_col) ; ASSERT (!Symbolic->fixQ) ; deg = Col_degree [col] ; #ifndef NDEBUG DEBUG3 (("Pivot col candidate: "ID" cost: "ID" Fcpos[col] "ID"\n", col, deg, Fcpos [col])) ; UMF_dump_rowcol (1, Numeric, Work, col, !Symbolic->fixQ) ; #endif if (Fcpos [col] >= 0) { #ifndef NDEBUG Int fs ; fs = Fcpos [col] / fnr_curr ; ASSERT (fs >= 0 && fs < fncols) ; #endif if (deg < cdeg_in || (deg == cdeg_in && col < pivcol [IN])) { /* best column in front, so far */ pivcol [IN] = col ; cdeg_in = deg ; jcand [IN] = j ; } } else { if (deg < cdeg_out || (deg == cdeg_out && col < pivcol [OUT])) { /* best column not in front, so far */ pivcol [OUT] = col ; cdeg_out = deg ; jcand [OUT] = j ; } } } DEBUG2 (("Pivcol in "ID" out "ID"\n", pivcol [IN], pivcol [OUT])) ; ASSERT ((pivcol [IN] >= 0 && pivcol [IN] < n_col) || (pivcol [OUT] >= 0 && pivcol [OUT] < n_col)) ; cdeg_in = EMPTY ; cdeg_out = EMPTY ; /* ---------------------------------------------------------------------- */ /* construct candidate column in front, and search for pivot rows */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG /* check Frpos */ DEBUG4 (("Prior to col update: fnrows "ID" col "ID" maxcdeg "ID"\n", fnrows, pivcol [IN], max_cdeg)) ; for (i = 0 ; i < fnrows ; i++) { row = Frows [i] ; DEBUG4 ((" row: "ID"\n", row)) ; ASSERT (row >= 0 && row < n_row) ; ASSERT (Frpos [row] == i) ; } DEBUG4 (("All:\n")) ; if (UMF_debug > 0 || n_row < 1000) { Int cnt = fnrows ; for (row = 0 ; row < n_row ; row++) { if (Frpos [row] == EMPTY) { cnt++ ; } else { DEBUG4 ((" row: "ID" pos "ID"\n", row, Frpos [row])) ; } } ASSERT (cnt == n_row) ; } #endif if (pivcol [IN] != EMPTY) { #ifndef NDEBUG DEBUG2 (("col[IN] column "ID" in front at position = "ID"\n", pivcol [IN], Fcpos [pivcol [IN]])) ; UMF_dump_rowcol (1, Numeric, Work, pivcol [IN], !Symbolic->fixQ) ; #endif /* the only way we can have a pivcol[IN] is if the front is not empty */ ASSERT (fnrows > 0 && fncols > 0) ; DEBUG4 (("Update pivot column:\n")) ; Fs = Fcblock + Fcpos [pivcol [IN]] ; Fu = Fublock + (Fcpos [pivcol [IN]] / fnr_curr) ; Flu = Flublock + fnpiv * nb ; /* ------------------------------------------------------------------ */ /* copy the pivot column from the U block into the LU block */ /* ------------------------------------------------------------------ */ /* This copy is permanent if the pivcol [IN] is chosen. */ for (i = 0 ; i < fnpiv ; i++) { Flu [i] = Fu [i*fnc_curr] ; } /* ------------------------------------------------------------------ */ /* update the pivot column in the LU block using a triangular solve */ /* ------------------------------------------------------------------ */ /* This work will be discarded if the pivcol [OUT] is chosen instead. * It is permanent if the pivcol [IN] is chosen. */ if (fnpiv > 1) { /* solve Lx=b, where b = U (:,k), stored in the LU block */ #ifndef NBLAS BLAS_TRSV (fnpiv, Flublock, Flu, nb) ; #endif if (!blas_ok) { /* use plain C code if no BLAS, or on integer overflow */ Entry *Flub = Flublock ; for (j = 0 ; j < fnpiv ; j++) { Entry Fuj = Flu [j] ; #pragma ivdep for (i = j+1 ; i < fnpiv ; i++) { /* Flu [i] -= Flublock [i + j*nb] * Flu [j] ; */ MULT_SUB (Flu [i], Flub [i], Fuj) ; } Flub += nb ; } } } /* ------------------------------------------------------------------ */ /* copy the pivot column from the C block into Wy */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < fnrows ; i++) { Wy [i] = Fs [i] ; } /* ------------------------------------------------------------------ */ /* update the pivot column of L using a matrix-vector multiply */ /* ------------------------------------------------------------------ */ /* this work will be discarded if the pivcol [OUT] is chosen instead */ #ifdef NBLAS /* no BLAS available - use plain C code instead */ for (j = 0 ; j < fnpiv ; j++) { Entry Fuj, *Flub = Flblock + j * fnr_curr ; Fuj = Flu [j] ; if (IS_NONZERO (Fuj)) { #pragma ivdep for (i = 0 ; i < fnrows ; i++) { /* Wy [i] -= Flblock [i+j*fnr_curr] * Fuj ; */ MULT_SUB (Wy [i], Flub [i], Fuj) ; } } /* Flblock += fnr_curr ; */ } #else /* Using 1-based notation: * Wy (1:fnrows) -= Flblock (1:fnrows,1:fnpiv) * Flu (1:fnpiv) */ BLAS_GEMV (fnrows, fnpiv, Flblock, Flu, Wy, fnr_curr) ; #endif /* ------------------------------------------------------------------ */ #ifndef NDEBUG DEBUG2 (("Wy after update: fnrows="ID"\n", fnrows)) ; DEBUG4 ((" fnpiv="ID" \n", fnpiv)) ; for (i = 0 ; i < fnrows ; i++) { DEBUG4 ((ID" "ID" "ID, i, Frows [i], Frpos [Frows [i]])) ; EDEBUG4 (Wy [i]) ; DEBUG4 (("\n")) ; } #endif /* ------------------------------------------------------------------ */ /* construct the candidate column */ /* ------------------------------------------------------------------ */ cdeg_in = fnrows ; #ifndef NDEBUG /* check Frpos */ DEBUG4 (("After col update: fnrows "ID" col "ID" maxcdeg "ID"\n", fnrows, pivcol [IN], max_cdeg)) ; for (i = 0 ; i < fnrows ; i++) { row = Frows [i] ; DEBUG4 ((" row: "ID"\n", row)) ; ASSERT (row >= 0 && row < n_row) ; ASSERT (Frpos [row] == i) ; } DEBUG4 (("All:\n")) ; if (UMF_debug > 0 || n_row < 1000) { Int cnt = fnrows ; for (row = 0 ; row < n_row ; row++) { if (Frpos [row] == EMPTY) { cnt++ ; } else { DEBUG4 ((" row: "ID" pos "ID"\n", row, Frpos [row])) ; } } ASSERT (cnt == n_row) ; } #endif #ifndef NDEBUG /* check Frpos */ DEBUG4 (("COL ASSEMBLE: cdeg "ID"\nREDUCE COL in "ID" max_cdeg "ID"\n", cdeg_in, pivcol [IN], max_cdeg)) ; for (i = 0 ; i < cdeg_in ; i++) { row = Frows [i] ; ASSERT (row >= 0 && row < n_row) ; ASSERT (Frpos [row] == i) ; } if (UMF_debug > 0 || n_row < 1000) { Int cnt = cdeg_in ; for (row = 0 ; row < n_row ; row++) { if (Frpos [row] == EMPTY) cnt++ ; } ASSERT (cnt == n_row) ; } #endif /* assemble column into Wy */ ASSERT (pivcol [IN] >= 0 && pivcol [IN] < n_col) ; ASSERT (NON_PIVOTAL_COL (pivcol [IN])) ; tpi = Col_tuples [pivcol [IN]] ; if (tpi) { tp = (Tuple *) (Memory + tpi) ; tp1 = tp ; tp2 = tp ; tpend = tp + Col_tlen [pivcol [IN]] ; for ( ; tp < tpend ; tp++) { e = tp->e ; ASSERT (e > 0 && e <= Work->nel) ; if (!E [e]) continue ; /* element already deallocated */ f = tp->f ; p = Memory + E [e] ; ep = (Element *) p ; p += UNITS (Element, 1) ; Cols = (Int *) p ; if (Cols [f] == EMPTY) continue ; /* column already assembled */ ASSERT (pivcol [IN] == Cols [f]) ; Rows = Cols + ep->ncols ; nrows = ep->nrows ; p += UNITS (Int, ep->ncols + nrows) ; C = ((Entry *) p) + f * nrows ; for (i = 0 ; i < nrows ; i++) { row = Rows [i] ; if (row >= 0) /* skip this if already gone from element */ { ASSERT (row < n_row) ; pos = Frpos [row] ; if (pos < 0) { /* new entry in the pattern - save Frpos */ ASSERT (cdeg_in < n_row) ; if (cdeg_in >= max_cdeg) { /* :: pattern change (cdeg in failure) :: */ DEBUGm4 (("cdeg_in failure\n")) ; return (UMFPACK_ERROR_different_pattern) ; } Frpos [row] = cdeg_in ; Frows [cdeg_in] = row ; Wy [cdeg_in++] = C [i] ; } else { /* entry already in pattern - sum values in Wy */ /* Wy [pos] += C [i] ; */ ASSERT (pos < max_cdeg) ; ASSEMBLE (Wy [pos], C [i]) ; } } } *tp2++ = *tp ; /* leave the tuple in the list */ } Col_tlen [pivcol [IN]] = tp2 - tp1 ; } /* ------------------------------------------------------------------ */ #ifndef NDEBUG /* check Frpos again */ DEBUG4 (("COL DONE: cdeg "ID"\nREDUCE COL in "ID" max_cdeg "ID"\n", cdeg_in, pivcol [IN], max_cdeg)) ; for (i = 0 ; i < cdeg_in ; i++) { row = Frows [i] ; ASSERT (row >= 0 && row < n_row) ; ASSERT (Frpos [row] == i) ; } if (UMF_debug > 0 || n_row < 1000) { Int cnt = cdeg_in ; for (row = 0 ; row < n_row ; row++) { if (Frpos [row] == EMPTY) cnt++ ; } ASSERT (cnt == n_row) ; } #endif #ifndef NDEBUG DEBUG4 (("Reduced column: cdeg in "ID" fnrows_max "ID"\n", cdeg_in, Work->fnrows_max)) ; for (i = 0 ; i < cdeg_in ; i++) { DEBUG4 ((" "ID" "ID" "ID, i, Frows [i], Frpos [Frows [i]])) ; EDEBUG4 (Wy [i]) ; DEBUG4 (("\n")) ; ASSERT (i == Frpos [Frows [i]]) ; } ASSERT (cdeg_in <= Work->fnrows_max) ; #endif /* ------------------------------------------------------------------ */ /* cdeg_in is now the exact degree of this column */ /* ------------------------------------------------------------------ */ nr_in = cdeg_in - fnrows ; /* since there are no 0-by-x fronts, if there is a pivcol [IN] the */ /* front must have at least one row. */ ASSERT (cdeg_in > 0) ; /* new degree of pivcol [IN], excluding current front is nr_in */ /* column expands by nr_in rows */ /* ------------------------------------------------------------------ */ /* search for two candidate pivot rows */ /* ------------------------------------------------------------------ */ /* for the IN_IN pivot row (if any), */ /* extend the pattern in place, using Fcols */ status = UMF_row_search (Numeric, Work, Symbolic, fnrows, cdeg_in, Frows, Frpos, /* pattern of column to search */ pivrow [IN], rdeg [IN], Fcols, Wio, nothing, Wy, pivcol [IN], freebie) ; ASSERT (!freebie [IN] && !freebie [OUT]) ; /* ------------------------------------------------------------------ */ /* fatal error if matrix pattern has changed since symbolic analysis */ /* ------------------------------------------------------------------ */ if (status == UMFPACK_ERROR_different_pattern) { /* :: pattern change (row search IN failure) :: */ DEBUGm4 (("row search IN failure\n")) ; return (UMFPACK_ERROR_different_pattern) ; } /* ------------------------------------------------------------------ */ /* we now must have a structural pivot */ /* ------------------------------------------------------------------ */ /* Since the pivcol[IN] exists, there must be at least one row in the */ /* current frontal matrix, and so we must have found a structural */ /* pivot. The numerical value might be zero, of course. */ ASSERT (status != UMFPACK_WARNING_singular_matrix) ; /* ------------------------------------------------------------------ */ /* evaluate IN_IN option */ /* ------------------------------------------------------------------ */ if (pivrow [IN][IN] != EMPTY) { /* The current front would become an (implicit) LUson. * Both candidate pivot row and column are in the current front. * Cost is how much the current front would expand */ /* pivrow[IN][IN] candidates are not found via row merge search */ ASSERT (fnrows >= 0 && fncols >= 0) ; ASSERT (cdeg_in > 0) ; nc = rdeg [IN][IN] - fncols ; thiscost = /* each column in front (except pivot column) grows by nr_in: */ (nr_in * (fncols - 1)) + /* new columns not in old front: */ (nc * (cdeg_in - 1)) ; /* no extra cost to relaxed amalgamation */ ASSERT (fnrows + nr_in == cdeg_in) ; ASSERT (fncols + nc == rdeg [IN][IN]) ; /* size of relaxed front (after pivot row column removed): */ fnrows_new [IN][IN] = (fnrows-1) + nr_in ; fncols_new [IN][IN] = (fncols-1) + nc ; /* relaxed_front = fnrows_new [IN][IN] * fncols_new [IN][IN] ; */ do_extend = TRUE ; DEBUG2 (("Evaluating option IN-IN:\n")) ; DEBUG2 (("Work->fnzeros "ID" fnpiv "ID" nr_in "ID" nc "ID"\n", Work->fnzeros, fnpiv, nr_in, nc)) ; DEBUG2 (("fncols "ID" fnrows "ID"\n", fncols, fnrows)) ; /* determine if BLAS-3 update should be applied before extending. */ /* update if too many zero entries accumulate in the LU block */ fnzeros = Work->fnzeros + fnpiv * (nr_in + nc) ; DEBUG2 (("fnzeros "ID"\n", fnzeros)) ; new_LUsize = (fnpiv+1) * (fnrows + nr_in + fncols + nc) ; DEBUG2 (("new_LUsize "ID"\n", new_LUsize)) ; /* There are fnpiv pivots currently in the front. This one * will be the (fnpiv+1)st pivot, if it is extended. */ /* RELAX2 parameter uses a double relop, but ignore NaN case: */ do_update = fnpiv > 0 && (((double) fnzeros) / ((double) new_LUsize)) > RELAX2 ; DEBUG2 (("do_update "ID"\n", do_update)) DEBUG2 (("option IN IN : nr "ID" nc "ID" cost "ID"(0) relax "ID "\n", nr_in, nc, thiscost, do_extend)) ; /* this is the best option seen so far */ Work->pivot_case = IN_IN ; bestcost = thiscost ; /* do the amalgamation and extend the front */ Work->do_extend = do_extend ; Work->do_update = do_update ; new_fnzeros = fnzeros ; } /* ------------------------------------------------------------------ */ /* evaluate IN_OUT option */ /* ------------------------------------------------------------------ */ if (pivrow [IN][OUT] != EMPTY) { /* The current front would become a Uson of the new front. * Candidate pivot column is in the current front, but the * candidate pivot row is not. */ ASSERT (fnrows >= 0 && fncols > 0) ; ASSERT (cdeg_in > 0) ; /* must be at least one row outside the front */ /* (the pivrow [IN][OUT] itself) */ ASSERT (nr_in >= 1) ; /* count columns not in current front */ nc = 0 ; #ifndef NDEBUG debug_ok = FALSE ; #endif for (i = 0 ; i < rdeg [IN][OUT] ; i++) { col = Wio [i] ; DEBUG4 (("counting col "ID" Fcpos[] = "ID"\n", col, Fcpos [col])) ; ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ; if (Fcpos [col] < 0) nc++ ; #ifndef NDEBUG /* we must see the pivot column somewhere */ if (col == pivcol [IN]) { ASSERT (Fcpos [col] >= 0) ; debug_ok = TRUE ; } #endif } ASSERT (debug_ok) ; thiscost = /* each row in front grows by nc: */ (nc * fnrows) + /* new rows not affected by front: */ ((nr_in-1) * (rdeg [IN][OUT]-1)) ; /* check the cost of relaxed IN_OUT amalgamation */ extra_cols = ((fncols-1) + nc ) - (rdeg [IN][OUT] - 1) ; ASSERT (extra_cols >= 0) ; ASSERT (fncols + nc == extra_cols + rdeg [IN][OUT]) ; extra_zeros = (nr_in-1) * extra_cols ; /* symbolic fill-in */ ASSERT (fnrows + nr_in == cdeg_in) ; ASSERT (fncols + nc == rdeg [IN][OUT] + extra_cols) ; /* size of relaxed front (after pivot column removed): */ fnrows_new [IN][OUT] = fnrows + (nr_in-1) ; fncols_new [IN][OUT] = (fncols-1) + nc ; relaxed_front = fnrows_new [IN][OUT] * fncols_new [IN][OUT] ; /* do relaxed amalgamation if the extra zeros are no more */ /* than a fraction (default 0.25) of the relaxed front */ /* if relax = 0: no extra zeros allowed */ /* if relax = +inf: always amalgamate */ /* relax parameter uses a double relop, but ignore NaN case: */ if (extra_zeros == 0) { do_extend = TRUE ; } else { do_extend = ((double) extra_zeros) < (relax1 * (double) relaxed_front) ; } if (do_extend) { /* count the cost of relaxed amalgamation */ thiscost += extra_zeros ; DEBUG2 (("Evaluating option IN-OUT:\n")) ; DEBUG2 (("Work->fnzeros "ID" fnpiv "ID" nr_in "ID" nc "ID"\n", Work->fnzeros, fnpiv, nr_in, nc)) ; DEBUG2 (("fncols "ID" fnrows "ID"\n", fncols, fnrows)) ; /* determine if BLAS-3 update to be applied before extending. */ /* update if too many zero entries accumulate in the LU block */ fnzeros = Work->fnzeros + fnpiv * (nr_in + nc) ; DEBUG2 (("fnzeros "ID"\n", fnzeros)) ; new_LUsize = (fnpiv+1) * (fnrows + nr_in + fncols + nc) ; DEBUG2 (("new_LUsize "ID"\n", new_LUsize)) ; /* RELAX3 parameter uses a double relop, ignore NaN case: */ do_update = fnpiv > 0 && (((double) fnzeros) / ((double) new_LUsize)) > RELAX3 ; DEBUG2 (("do_update "ID"\n", do_update)) } else { /* the current front would not be extended */ do_update = fnpiv > 0 ; fnzeros = 0 ; DEBUG2 (("IN-OUT do_update forced true: "ID"\n", do_update)) ; /* The new front would be just big enough to hold the new * pivot row and column. */ fnrows_new [IN][OUT] = cdeg_in - 1 ; fncols_new [IN][OUT] = rdeg [IN][OUT] - 1 ; } DEBUG2 (("option IN OUT: nr "ID" nc "ID" cost "ID"("ID") relax "ID "\n", nr_in, nc, thiscost, extra_zeros, do_extend)) ; if (bestcost == EMPTY || thiscost < bestcost) { /* this is the best option seen so far */ Work->pivot_case = IN_OUT ; bestcost = thiscost ; Work->do_extend = do_extend ; Work->do_update = do_update ; new_fnzeros = fnzeros ; } } } /* ---------------------------------------------------------------------- */ /* construct candidate column not in front, and search for pivot rows */ /* ---------------------------------------------------------------------- */ search_pivcol_out = (bestcost != 0 && pivcol [OUT] != EMPTY) ; if (Symbolic->prefer_diagonal) { search_pivcol_out = search_pivcol_out && (pivrow [IN][IN] == EMPTY) ; } if (search_pivcol_out) { #ifndef NDEBUG DEBUG2 (("out_col column "ID" NOT in front at position = "ID"\n", pivcol [OUT], Fcpos [pivcol [OUT]])) ; UMF_dump_rowcol (1, Numeric, Work, pivcol [OUT], !Symbolic->fixQ) ; DEBUG2 (("fncols "ID" fncols_max "ID"\n", fncols, Work->fncols_max)) ; ASSERT (fncols < Work->fncols_max) ; #endif /* Use Wx as temporary workspace to construct the pivcol [OUT] */ /* ------------------------------------------------------------------ */ /* construct the candidate column (currently not in the front) */ /* ------------------------------------------------------------------ */ /* Construct the column in Wx, Wm, using Wp for the positions: */ /* Wm [0..cdeg_out-1] list of row indices in the column */ /* Wx [0..cdeg_out-1] list of corresponding numerical values */ /* Wp [0..n-1] starts as all negative, and ends that way too. */ cdeg_out = 0 ; #ifndef NDEBUG /* check Wp */ DEBUG4 (("COL ASSEMBLE: cdeg 0\nREDUCE COL out "ID"\n", pivcol [OUT])) ; if (UMF_debug > 0 || MAX (n_row, n_col) < 1000) { for (i = 0 ; i < MAX (n_row, n_col) ; i++) { ASSERT (Wp [i] < 0) ; } } DEBUG4 (("max_cdeg: "ID"\n", max_cdeg)) ; #endif ASSERT (pivcol [OUT] >= 0 && pivcol [OUT] < n_col) ; ASSERT (NON_PIVOTAL_COL (pivcol [OUT])) ; tpi = Col_tuples [pivcol [OUT]] ; if (tpi) { tp = (Tuple *) (Memory + tpi) ; tp1 = tp ; tp2 = tp ; tpend = tp + Col_tlen [pivcol [OUT]] ; for ( ; tp < tpend ; tp++) { e = tp->e ; ASSERT (e > 0 && e <= Work->nel) ; if (!E [e]) continue ; /* element already deallocated */ f = tp->f ; p = Memory + E [e] ; ep = (Element *) p ; p += UNITS (Element, 1) ; Cols = (Int *) p ; if (Cols [f] == EMPTY) continue ; /* column already assembled */ ASSERT (pivcol [OUT] == Cols [f]) ; Rows = Cols + ep->ncols ; nrows = ep->nrows ; p += UNITS (Int, ep->ncols + nrows) ; C = ((Entry *) p) + f * nrows ; for (i = 0 ; i < nrows ; i++) { row = Rows [i] ; if (row >= 0) /* skip this if already gone from element */ { ASSERT (row < n_row) ; pos = Wp [row] ; if (pos < 0) { /* new entry in the pattern - save Wp */ ASSERT (cdeg_out < n_row) ; if (cdeg_out >= max_cdeg) { /* :: pattern change (cdeg out failure) :: */ DEBUGm4 (("cdeg out failure\n")) ; return (UMFPACK_ERROR_different_pattern) ; } Wp [row] = cdeg_out ; Wm [cdeg_out] = row ; Wx [cdeg_out++] = C [i] ; } else { /* entry already in pattern - sum the values */ /* Wx [pos] += C [i] ; */ ASSEMBLE (Wx [pos], C [i]) ; } } } *tp2++ = *tp ; /* leave the tuple in the list */ } Col_tlen [pivcol [OUT]] = tp2 - tp1 ; } /* ------------------------------------------------------------------ */ #ifndef NDEBUG DEBUG4 (("Reduced column: cdeg out "ID"\n", cdeg_out)) ; for (i = 0 ; i < cdeg_out ; i++) { DEBUG4 ((" "ID" "ID" "ID, i, Wm [i], Wp [Wm [i]])) ; EDEBUG4 (Wx [i]) ; DEBUG4 (("\n")) ; ASSERT (i == Wp [Wm [i]]) ; } #endif /* ------------------------------------------------------------------ */ /* new degree of pivcol [OUT] is cdeg_out */ /* ------------------------------------------------------------------ */ /* search for two candidate pivot rows */ status = UMF_row_search (Numeric, Work, Symbolic, 0, cdeg_out, Wm, Wp, /* pattern of column to search */ pivrow [OUT], rdeg [OUT], Woi, Woo, pivrow [IN], Wx, pivcol [OUT], freebie) ; /* ------------------------------------------------------------------ */ /* fatal error if matrix pattern has changed since symbolic analysis */ /* ------------------------------------------------------------------ */ if (status == UMFPACK_ERROR_different_pattern) { /* :: pattern change detected in umf_local_search :: */ return (UMFPACK_ERROR_different_pattern) ; } /* ------------------------------------------------------------------ */ /* Clear Wp */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < cdeg_out ; i++) { Wp [Wm [i]] = EMPTY ; /* clear Wp */ } /* ------------------------------------------------------------------ */ /* check for rectangular, singular matrix */ /* ------------------------------------------------------------------ */ if (status == UMFPACK_WARNING_singular_matrix) { /* Pivot column is empty, and row-merge set is empty too. The * matrix is structurally singular. The current frontal matrix must * be empty, too. It it weren't, and pivcol [OUT] exists, then * there would be at least one row that could be selected. Since * the current front is empty, pivcol [IN] must also be EMPTY. */ DEBUGm4 (("Note: pivcol [OUT]: "ID" discard\n", pivcol [OUT])) ; ASSERT ((Work->fnrows == 0 && Work->fncols == 0)) ; ASSERT (pivcol [IN] == EMPTY) ; /* remove the failed pivcol [OUT] from candidate set */ ASSERT (pivcol [OUT] == Work->Candidates [jcand [OUT]]) ; remove_candidate (jcand [OUT], Work, Symbolic) ; Work->ndiscard++ ; /* delete all of the tuples, and all contributions to this column */ DEBUG1 (("Prune tuples of dead outcol: "ID"\n", pivcol [OUT])) ; Col_tlen [pivcol [OUT]] = 0 ; UMF_mem_free_tail_block (Numeric, Col_tuples [pivcol [OUT]]) ; Col_tuples [pivcol [OUT]] = 0 ; /* no pivot found at all */ return (UMFPACK_WARNING_singular_matrix) ; } /* ------------------------------------------------------------------ */ if (freebie [IN]) { /* the "in" row is the same as the "in" row for the "in" column */ Woi = Fcols ; rdeg [OUT][IN] = rdeg [IN][IN] ; DEBUG4 (("Freebie in, row "ID"\n", pivrow [IN][IN])) ; } if (freebie [OUT]) { /* the "out" row is the same as the "out" row for the "in" column */ Woo = Wio ; rdeg [OUT][OUT] = rdeg [IN][OUT] ; DEBUG4 (("Freebie out, row "ID"\n", pivrow [IN][OUT])) ; } /* ------------------------------------------------------------------ */ /* evaluate OUT_IN option */ /* ------------------------------------------------------------------ */ if (pivrow [OUT][IN] != EMPTY) { /* The current front would become an Lson of the new front. * The candidate pivot row is in the current front, but the * candidate pivot column is not. */ ASSERT (fnrows > 0 && fncols >= 0) ; did_rowmerge = (cdeg_out == 0) ; if (did_rowmerge) { /* pivrow [OUT][IN] was found via row merge search */ /* it is not (yet) in the pivot column pattern (add it now) */ DEBUGm4 (("did row merge OUT col, IN row\n")) ; Wm [0] = pivrow [OUT][IN] ; CLEAR (Wx [0]) ; cdeg_out = 1 ; ASSERT (nr_out == EMPTY) ; } nc = rdeg [OUT][IN] - fncols ; ASSERT (nc >= 1) ; /* count rows not in current front */ nr_out = 0 ; #ifndef NDEBUG debug_ok = FALSE ; #endif for (i = 0 ; i < cdeg_out ; i++) { row = Wm [i] ; ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ; if (Frpos [row] < 0 || Frpos [row] >= fnrows) nr_out++ ; #ifndef NDEBUG /* we must see the pivot row somewhere */ if (row == pivrow [OUT][IN]) { ASSERT (Frpos [row] >= 0) ; debug_ok = TRUE ; } #endif } ASSERT (debug_ok) ; thiscost = /* each column in front grows by nr_out: */ (nr_out * fncols) + /* new cols not affected by front: */ ((nc-1) * (cdeg_out-1)) ; /* check the cost of relaxed OUT_IN amalgamation */ extra_rows = ((fnrows-1) + nr_out) - (cdeg_out - 1) ; ASSERT (extra_rows >= 0) ; ASSERT (fnrows + nr_out == extra_rows + cdeg_out) ; extra_zeros = (nc-1) * extra_rows ; /* symbolic fill-in */ ASSERT (fnrows + nr_out == cdeg_out + extra_rows) ; ASSERT (fncols + nc == rdeg [OUT][IN]) ; /* size of relaxed front (after pivot row removed): */ fnrows_new [OUT][IN] = (fnrows-1) + nr_out ; fncols_new [OUT][IN] = fncols + (nc-1) ; relaxed_front = fnrows_new [OUT][IN] * fncols_new [OUT][IN] ; /* do relaxed amalgamation if the extra zeros are no more */ /* than a fraction (default 0.25) of the relaxed front */ /* if relax = 0: no extra zeros allowed */ /* if relax = +inf: always amalgamate */ if (did_rowmerge) { do_extend = FALSE ; } else { /* relax parameter uses a double relop, but ignore NaN case: */ if (extra_zeros == 0) { do_extend = TRUE ; } else { do_extend = ((double) extra_zeros) < (relax1 * (double) relaxed_front) ; } } if (do_extend) { /* count the cost of relaxed amalgamation */ thiscost += extra_zeros ; DEBUG2 (("Evaluating option OUT-IN:\n")) ; DEBUG2 ((" Work->fnzeros "ID" fnpiv "ID" nr_out "ID" nc "ID"\n", Work->fnzeros, fnpiv, nr_out, nc)) ; DEBUG2 (("fncols "ID" fnrows "ID"\n", fncols, fnrows)) ; /* determine if BLAS-3 update to be applied before extending. */ /* update if too many zero entries accumulate in the LU block */ fnzeros = Work->fnzeros + fnpiv * (nr_out + nc) ; DEBUG2 (("fnzeros "ID"\n", fnzeros)) ; new_LUsize = (fnpiv+1) * (fnrows + nr_out + fncols + nc) ; DEBUG2 (("new_LUsize "ID"\n", new_LUsize)) ; /* RELAX3 parameter uses a double relop, ignore NaN case: */ do_update = fnpiv > 0 && (((double) fnzeros) / ((double) new_LUsize)) > RELAX3 ; DEBUG2 (("do_update "ID"\n", do_update)) } else { /* the current front would not be extended */ do_update = fnpiv > 0 ; fnzeros = 0 ; DEBUG2 (("OUT-IN do_update forced true: "ID"\n", do_update)) ; /* The new front would be just big enough to hold the new * pivot row and column. */ fnrows_new [OUT][IN] = cdeg_out - 1 ; fncols_new [OUT][IN] = rdeg [OUT][IN] - 1 ; } DEBUG2 (("option OUT IN : nr "ID" nc "ID" cost "ID"("ID") relax "ID "\n", nr_out, nc, thiscost, extra_zeros, do_extend)) ; if (bestcost == EMPTY || thiscost < bestcost) { /* this is the best option seen so far */ Work->pivot_case = OUT_IN ; bestcost = thiscost ; Work->do_extend = do_extend ; Work->do_update = do_update ; new_fnzeros = fnzeros ; } } /* ------------------------------------------------------------------ */ /* evaluate OUT_OUT option */ /* ------------------------------------------------------------------ */ if (pivrow [OUT][OUT] != EMPTY) { /* Neither the candidate pivot row nor the candidate pivot column * are in the current front. */ ASSERT (fnrows >= 0 && fncols >= 0) ; did_rowmerge = (cdeg_out == 0) ; if (did_rowmerge) { /* pivrow [OUT][OUT] was found via row merge search */ /* it is not (yet) in the pivot column pattern (add it now) */ DEBUGm4 (("did row merge OUT col, OUT row\n")) ; Wm [0] = pivrow [OUT][OUT] ; CLEAR (Wx [0]) ; cdeg_out = 1 ; ASSERT (nr_out == EMPTY) ; nr_out = 1 ; } if (fnrows == 0 && fncols == 0) { /* the current front is completely empty */ ASSERT (fnpiv == 0) ; nc = rdeg [OUT][OUT] ; extra_cols = 0 ; nr_out = cdeg_out ; extra_rows = 0 ; extra_zeros = 0 ; thiscost = (nc-1) * (cdeg_out-1) ; /* new columns only */ /* size of new front: */ fnrows_new [OUT][OUT] = nr_out-1 ; fncols_new [OUT][OUT] = nc-1 ; relaxed_front = fnrows_new [OUT][OUT] * fncols_new [OUT][OUT] ; } else { /* count rows not in current front */ if (nr_out == EMPTY) { nr_out = 0 ; #ifndef NDEBUG debug_ok = FALSE ; #endif for (i = 0 ; i < cdeg_out ; i++) { row = Wm [i] ; ASSERT (row >= 0 && row < n_row) ; ASSERT (NON_PIVOTAL_ROW (row)) ; if (Frpos [row] < 0 || Frpos [row] >= fnrows) nr_out++ ; #ifndef NDEBUG /* we must see the pivot row somewhere */ if (row == pivrow [OUT][OUT]) { ASSERT (Frpos [row] < 0 || Frpos [row] >= fnrows) ; debug_ok = TRUE ; } #endif } ASSERT (debug_ok) ; } /* count columns not in current front */ nc = 0 ; #ifndef NDEBUG debug_ok = FALSE ; #endif for (i = 0 ; i < rdeg [OUT][OUT] ; i++) { col = Woo [i] ; ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ; if (Fcpos [col] < 0) nc++ ; #ifndef NDEBUG /* we must see the pivot column somewhere */ if (col == pivcol [OUT]) { ASSERT (Fcpos [col] < 0) ; debug_ok = TRUE ; } #endif } ASSERT (debug_ok) ; extra_cols = (fncols + (nc-1)) - (rdeg [OUT][OUT] - 1) ; extra_rows = (fnrows + (nr_out-1)) - (cdeg_out - 1) ; ASSERT (extra_rows >= 0) ; ASSERT (extra_cols >= 0) ; extra_zeros = ((nc-1) * extra_rows) + ((nr_out-1) * extra_cols); ASSERT (fnrows + nr_out == cdeg_out + extra_rows) ; ASSERT (fncols + nc == rdeg [OUT][OUT] + extra_cols) ; thiscost = /* new columns: */ ((nc-1) * (cdeg_out-1)) + /* old columns in front grow by nr_out-1: */ ((nr_out-1) * (fncols - extra_cols)) ; /* size of relaxed front: */ fnrows_new [OUT][OUT] = fnrows + (nr_out-1) ; fncols_new [OUT][OUT] = fncols + (nc-1) ; relaxed_front = fnrows_new [OUT][OUT] * fncols_new [OUT][OUT] ; } /* do relaxed amalgamation if the extra zeros are no more */ /* than a fraction (default 0.25) of the relaxed front */ /* if relax = 0: no extra zeros allowed */ /* if relax = +inf: always amalgamate */ if (did_rowmerge) { do_extend = FALSE ; } else { /* relax parameter uses a double relop, but ignore NaN case: */ if (extra_zeros == 0) { do_extend = TRUE ; } else { do_extend = ((double) extra_zeros) < (relax1 * (double) relaxed_front) ; } } if (do_extend) { /* count the cost of relaxed amalgamation */ thiscost += extra_zeros ; DEBUG2 (("Evaluating option OUT-OUT:\n")) ; DEBUG2 (("Work->fnzeros "ID" fnpiv "ID" nr_out "ID" nc "ID"\n", Work->fnzeros, fnpiv, nr_out, nc)) ; DEBUG2 (("fncols "ID" fnrows "ID"\n", fncols, fnrows)) ; /* determine if BLAS-3 update to be applied before extending. */ /* update if too many zero entries accumulate in the LU block */ fnzeros = Work->fnzeros + fnpiv * (nr_out + nc) ; DEBUG2 (("fnzeros "ID"\n", fnzeros)) ; new_LUsize = (fnpiv+1) * (fnrows + nr_out + fncols + nc) ; DEBUG2 (("new_LUsize "ID"\n", new_LUsize)) ; /* RELAX3 parameter uses a double relop, ignore NaN case: */ do_update = fnpiv > 0 && (((double) fnzeros) / ((double) new_LUsize)) > RELAX3 ; DEBUG2 (("do_update "ID"\n", do_update)) } else { /* the current front would not be extended */ do_update = fnpiv > 0 ; fnzeros = 0 ; DEBUG2 (("OUT-OUT do_update forced true: "ID"\n", do_update)) ; /* The new front would be just big enough to hold the new * pivot row and column. */ fnrows_new [OUT][OUT] = cdeg_out - 1 ; fncols_new [OUT][OUT] = rdeg [OUT][OUT] - 1 ; } DEBUG2 (("option OUT OUT: nr "ID" nc "ID" cost "ID"\n", rdeg [OUT][OUT], cdeg_out, thiscost)) ; if (bestcost == EMPTY || thiscost < bestcost) { /* this is the best option seen so far */ Work->pivot_case = OUT_OUT ; bestcost = thiscost ; Work->do_extend = do_extend ; Work->do_update = do_update ; new_fnzeros = fnzeros ; } } } /* At this point, a structural pivot has been found. */ /* It may be numerically zero, however. */ ASSERT (Work->pivot_case != EMPTY) ; DEBUG2 (("local search, best option "ID", best cost "ID"\n", Work->pivot_case, bestcost)) ; /* ====================================================================== */ /* Pivot row and column, and extension, now determined */ /* ====================================================================== */ Work->fnzeros = new_fnzeros ; /* ---------------------------------------------------------------------- */ /* finalize the pivot row and column */ /* ---------------------------------------------------------------------- */ switch (Work->pivot_case) { case IN_IN: DEBUG2 (("IN-IN option selected\n")) ; ASSERT (fnrows > 0 && fncols > 0) ; Work->pivcol_in_front = TRUE ; Work->pivrow_in_front = TRUE ; Work->pivcol = pivcol [IN] ; Work->pivrow = pivrow [IN][IN] ; Work->ccdeg = nr_in ; Work->Wrow = Fcols ; Work->rrdeg = rdeg [IN][IN] ; jj = jcand [IN] ; Work->fnrows_new = fnrows_new [IN][IN] ; Work->fncols_new = fncols_new [IN][IN] ; break ; case IN_OUT: DEBUG2 (("IN-OUT option selected\n")) ; ASSERT (fnrows >= 0 && fncols > 0) ; Work->pivcol_in_front = TRUE ; Work->pivrow_in_front = FALSE ; Work->pivcol = pivcol [IN] ; Work->pivrow = pivrow [IN][OUT] ; Work->ccdeg = nr_in ; Work->Wrow = Wio ; Work->rrdeg = rdeg [IN][OUT] ; jj = jcand [IN] ; Work->fnrows_new = fnrows_new [IN][OUT] ; Work->fncols_new = fncols_new [IN][OUT] ; break ; case OUT_IN: DEBUG2 (("OUT-IN option selected\n")) ; ASSERT (fnrows > 0 && fncols >= 0) ; Work->pivcol_in_front = FALSE ; Work->pivrow_in_front = TRUE ; Work->pivcol = pivcol [OUT] ; Work->pivrow = pivrow [OUT][IN] ; Work->ccdeg = cdeg_out ; /* Wrow might be equivalenced to Fcols (Freebie in): */ Work->Wrow = Woi ; Work->rrdeg = rdeg [OUT][IN] ; /* Work->Wrow[0..fncols-1] is not there. See Fcols instead */ jj = jcand [OUT] ; Work->fnrows_new = fnrows_new [OUT][IN] ; Work->fncols_new = fncols_new [OUT][IN] ; break ; case OUT_OUT: DEBUG2 (("OUT-OUT option selected\n")) ; ASSERT (fnrows >= 0 && fncols >= 0) ; Work->pivcol_in_front = FALSE ; Work->pivrow_in_front = FALSE ; Work->pivcol = pivcol [OUT] ; Work->pivrow = pivrow [OUT][OUT] ; Work->ccdeg = cdeg_out ; /* Wrow might be equivalenced to Wio (Freebie out): */ Work->Wrow = Woo ; Work->rrdeg = rdeg [OUT][OUT] ; jj = jcand [OUT] ; Work->fnrows_new = fnrows_new [OUT][OUT] ; Work->fncols_new = fncols_new [OUT][OUT] ; break ; } ASSERT (IMPLIES (fnrows == 0 && fncols == 0, Work->pivot_case == OUT_OUT)) ; if (!Work->pivcol_in_front && pivcol [IN] != EMPTY) { /* clear Frpos if pivcol [IN] was searched, but not selected */ for (i = fnrows ; i < cdeg_in ; i++) { Frpos [Frows [i]] = EMPTY; } } /* ---------------------------------------------------------------------- */ /* Pivot row and column have been found */ /* ---------------------------------------------------------------------- */ /* ---------------------------------------------------------------------- */ /* remove pivot column from candidate pivot column set */ /* ---------------------------------------------------------------------- */ ASSERT (jj >= 0 && jj < Work->nCandidates) ; ASSERT (Work->pivcol == Work->Candidates [jj]) ; remove_candidate (jj, Work, Symbolic) ; /* ---------------------------------------------------------------------- */ /* check for frontal matrix growth */ /* ---------------------------------------------------------------------- */ DEBUG1 (("Check frontal growth:\n")) ; DEBUG1 (("fnrows_new "ID" + 1 = "ID", fnr_curr "ID"\n", Work->fnrows_new, Work->fnrows_new + 1, fnr_curr)) ; DEBUG1 (("fncols_new "ID" + 1 = "ID", fnc_curr "ID"\n", Work->fncols_new, Work->fncols_new + 1, fnc_curr)) ; Work->do_grow = (Work->fnrows_new + 1 > fnr_curr || Work->fncols_new + 1 > fnc_curr) ; if (Work->do_grow) { DEBUG0 (("\nNeed to grow frontal matrix, force do_update true\n")) ; /* If the front must grow, then apply the pending updates and remove * the current pivot rows/columns from the front prior to growing the * front. This frees up as much space as possible for the new front. */ if (!Work->do_update && fnpiv > 0) { /* This update would not have to be done if the current front * was big enough. */ Work->nforced++ ; Work->do_update = TRUE ; } } /* ---------------------------------------------------------------------- */ /* current pivot column */ /* ---------------------------------------------------------------------- */ /* c1) If pivot column index is in the current front: The pivot column pattern is in Frows [0 .. fnrows-1] and the extension is in Frows [fnrows ... fnrows+ccdeg-1]. Frpos [Frows [0 .. fnrows+ccdeg-1]] is equal to 0 .. fnrows+ccdeg-1. Wm is not needed. The values are in Wy [0 .. fnrows+ccdeg-1]. c2) Otherwise, if the pivot column index is not in the current front: c2a) If the front is being extended, old row indices in the the pivot column pattern are in Frows [0 .. fnrows-1]. All entries are in Wm [0 ... ccdeg-1], with values in Wx [0 .. ccdeg-1]. These may include entries already in Frows [0 .. fnrows-1]. Frpos [Frows [0 .. fnrows-1]] is equal to 0 .. fnrows-1. Frpos [Wm [0 .. ccdeg-1]] for new entries is < 0. c2b) If the front is not being extended, then the entire pivot column pattern is in Wm [0 .. ccdeg-1]. It includes the pivot row index. It is does not contain the pattern Frows [0..fnrows-1]. The intersection of these two sets may or may not be empty. The values are in Wx [0..ccdeg-1] In both cases c1 and c2, Frpos [Frows [0 .. fnrows-1]] is equal to 0 .. fnrows-1, which is the pattern of the current front. Any entry of Frpos that is not specified above is < 0. */ #ifndef NDEBUG DEBUG2 (("\n\nSEARCH DONE: Pivot col "ID" in: ("ID") pivot row "ID" in: ("ID ") extend: "ID"\n\n", Work->pivcol, Work->pivcol_in_front, Work->pivrow, Work->pivrow_in_front, Work->do_extend)) ; UMF_dump_rowcol (1, Numeric, Work, Work->pivcol, !Symbolic->fixQ) ; DEBUG2 (("Pivot col "ID": fnrows "ID" ccdeg "ID"\n", Work->pivcol, fnrows, Work->ccdeg)) ; if (Work->pivcol_in_front) /* case c1 */ { Int found = FALSE ; DEBUG3 (("Pivcol in front\n")) ; for (i = 0 ; i < fnrows ; i++) { row = Frows [i] ; DEBUG3 ((ID": row:: "ID" in front ", i, row)) ; ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ; ASSERT (Frpos [row] == i) ; EDEBUG3 (Wy [i]) ; if (row == Work->pivrow) { DEBUG3 ((" <- pivrow")) ; found = TRUE ; } DEBUG3 (("\n")) ; } ASSERT (found == Work->pivrow_in_front) ; found = FALSE ; for (i = fnrows ; i < fnrows + Work->ccdeg ; i++) { row = Frows [i] ; DEBUG3 ((ID": row:: "ID" (new)", i, row)) ; ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ; ASSERT (Frpos [row] == i) ; EDEBUG3 (Wy [i]) ; if (row == Work->pivrow) { DEBUG3 ((" <- pivrow")) ; found = TRUE ; } DEBUG3 (("\n")) ; } ASSERT (found == !Work->pivrow_in_front) ; } else { if (Work->do_extend) { Int found = FALSE ; DEBUG3 (("Pivcol not in front (extend)\n")) ; for (i = 0 ; i < fnrows ; i++) { row = Frows [i] ; DEBUG3 ((ID": row:: "ID" in front ", i, row)) ; ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ; ASSERT (Frpos [row] == i) ; if (row == Work->pivrow) { DEBUG3 ((" <- pivrow")) ; found = TRUE ; } DEBUG3 (("\n")) ; } ASSERT (found == Work->pivrow_in_front) ; found = FALSE ; DEBUG3 (("----\n")) ; for (i = 0 ; i < Work->ccdeg ; i++) { row = Wm [i] ; ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ; DEBUG3 ((ID": row:: "ID" ", i, row)) ; EDEBUG3 (Wx [i]) ; if (Frpos [row] < 0) { DEBUG3 ((" (new) ")) ; } if (row == Work->pivrow) { DEBUG3 ((" <- pivrow")) ; found = TRUE ; /* ... */ if (Work->pivrow_in_front) ASSERT (Frpos [row] >= 0) ; else ASSERT (Frpos [row] < 0) ; } DEBUG3 (("\n")) ; } ASSERT (found) ; } else { Int found = FALSE ; DEBUG3 (("Pivcol not in front (no extend)\n")) ; for (i = 0 ; i < Work->ccdeg ; i++) { row = Wm [i] ; ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ; DEBUG3 ((ID": row:: "ID" ", i, row)) ; EDEBUG3 (Wx [i]) ; DEBUG3 ((" (new) ")) ; if (row == Work->pivrow) { DEBUG3 ((" <- pivrow")) ; found = TRUE ; } DEBUG3 (("\n")) ; } ASSERT (found) ; } } #endif /* ---------------------------------------------------------------------- */ /* current pivot row */ /* ---------------------------------------------------------------------- */ /* r1) If the pivot row index is in the current front: The pivot row pattern is in Fcols [0..fncols-1] and the extenson is in Wrow [fncols .. rrdeg-1]. If the pivot column is in the current front, then Fcols and Wrow are equivalenced. r2) If the pivot row index is not in the current front: r2a) If the front is being extended, the pivot row pattern is in Fcols [0 .. fncols-1]. New entries are in Wrow [0 .. rrdeg-1], but these may include entries already in Fcols [0 .. fncols-1]. r2b) Otherwise, the pivot row pattern is Wrow [0 .. rrdeg-1]. Fcpos [Fcols [0..fncols-1]] is (0..fncols-1) * fnr_curr. All other entries in Fcpos are < 0. These conditions are asserted below. ------------------------------------------------------------------------ Other items in Work structure that are relevant: pivcol: the pivot column index pivrow: the pivot column index rrdeg: ccdeg: fnrows: the number of rows in the currnt contribution block fncols: the number of columns in the current contribution block fnrows_new: the number of rows in the new contribution block fncols_new: the number of rows in the new contribution block ------------------------------------------------------------------------ */ #ifndef NDEBUG UMF_dump_rowcol (0, Numeric, Work, Work->pivrow, TRUE) ; DEBUG2 (("Pivot row "ID":\n", Work->pivrow)) ; if (Work->pivrow_in_front) { Int found = FALSE ; for (i = 0 ; i < fncols ; i++) { col = Fcols [i] ; DEBUG3 ((" col:: "ID" in front\n", col)) ; ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ; ASSERT (Fcpos [col] == i * fnr_curr) ; if (col == Work->pivcol) found = TRUE ; } ASSERT (found == Work->pivcol_in_front) ; found = FALSE ; ASSERT (IMPLIES (Work->pivcol_in_front, Fcols == Work->Wrow)) ; for (i = fncols ; i < Work->rrdeg ; i++) { col = Work->Wrow [i] ; ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ; ASSERT (Fcpos [col] < 0) ; if (col == Work->pivcol) found = TRUE ; else DEBUG3 ((" col:: "ID" (new)\n", col)) ; } ASSERT (found == !Work->pivcol_in_front) ; } else { if (Work->do_extend) { Int found = FALSE ; for (i = 0 ; i < fncols ; i++) { col = Fcols [i] ; DEBUG3 ((" col:: "ID" in front\n", col)) ; ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ; ASSERT (Fcpos [col] == i * fnr_curr) ; if (col == Work->pivcol) found = TRUE ; } ASSERT (found == Work->pivcol_in_front) ; found = FALSE ; for (i = 0 ; i < Work->rrdeg ; i++) { col = Work->Wrow [i] ; ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ; if (Fcpos [col] >= 0) continue ; if (col == Work->pivcol) found = TRUE ; else DEBUG3 ((" col:: "ID" (new, extend)\n", col)) ; } ASSERT (found == !Work->pivcol_in_front) ; } else { Int found = FALSE ; for (i = 0 ; i < Work->rrdeg ; i++) { col = Work->Wrow [i] ; ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ; if (col == Work->pivcol) found = TRUE ; else DEBUG3 ((" col:: "ID" (all new)\n", col)) ; } ASSERT (found) ; } } #endif /* ---------------------------------------------------------------------- */ /* determine whether to do scan2-row and scan2-col */ /* ---------------------------------------------------------------------- */ if (Work->do_extend) { Work->do_scan2row = (fncols > 0) ; Work->do_scan2col = (fnrows > 0) ; } else { Work->do_scan2row = (fncols > 0) && Work->pivrow_in_front ; Work->do_scan2col = (fnrows > 0) && Work->pivcol_in_front ; } /* ---------------------------------------------------------------------- */ DEBUG2 (("LOCAL SEARCH DONE: pivot column "ID" pivot row: "ID"\n", Work->pivcol, Work->pivrow)) ; DEBUG2 (("do_extend: "ID"\n", Work->do_extend)) ; DEBUG2 (("do_update: "ID"\n", Work->do_update)) ; DEBUG2 (("do_grow: "ID"\n", Work->do_grow)) ; /* ---------------------------------------------------------------------- */ /* keep track of the diagonal */ /* ---------------------------------------------------------------------- */ if (Symbolic->prefer_diagonal && Work->pivcol < Work->n_col - Symbolic->nempty_col) { Diagonal_map = Work->Diagonal_map ; Diagonal_imap = Work->Diagonal_imap ; ASSERT (Diagonal_map != (Int *) NULL) ; ASSERT (Diagonal_imap != (Int *) NULL) ; row2 = Diagonal_map [Work->pivcol] ; col2 = Diagonal_imap [Work->pivrow] ; if (row2 < 0) { /* this was an off-diagonal pivot row */ Work->noff_diagonal++ ; row2 = UNFLIP (row2) ; } ASSERT (Diagonal_imap [row2] == Work->pivcol) ; ASSERT (UNFLIP (Diagonal_map [col2]) == Work->pivrow) ; if (row2 != Work->pivrow) { /* swap the diagonal map to attempt to maintain symmetry later on. * Also mark the map for col2 (via FLIP) to denote that the entry * now on the diagonal is not the original entry on the diagonal. */ DEBUG0 (("Unsymmetric pivot\n")) ; Diagonal_map [Work->pivcol] = FLIP (Work->pivrow) ; Diagonal_imap [Work->pivrow] = Work->pivcol ; Diagonal_map [col2] = FLIP (row2) ; Diagonal_imap [row2] = col2 ; } ASSERT (n_row == n_col) ; #ifndef NDEBUG UMF_dump_diagonal_map (Diagonal_map, Diagonal_imap, Symbolic->n1, Symbolic->n_col, Symbolic->nempty_col) ; #endif } return (UMFPACK_OK) ; } SuiteSparse/UMFPACK/Source/umf_local_search.h0000644001170100242450000000100110617161702017725 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_local_search ( NumericType *Numeric, WorkType *Work, SymbolicType *Symbolic ) ; SuiteSparse/UMFPACK/Source/umf_colamd.c0000644001170100242450000026715410617161437016574 0ustar davisfac/* ========================================================================== */ /* === UMF_colamd =========================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* UMF_colamd: an approximate minimum degree column ordering algorithm, used as a preordering for UMFPACK. NOTE: if this routine is used outside of UMFPACK, for a sparse Cholesky factorization of (AQ)'*(AQ) or a QR factorization of A, then one line should be removed (the "&& pivot_row_thickness > 0" expression). See the comment regarding the Cholesky factorization, below. Purpose: Colamd computes a permutation Q such that the Cholesky factorization of (AQ)'(AQ) has less fill-in and requires fewer floating point operations than A'A. This also provides a good ordering for sparse partial pivoting methods, P(AQ) = LU, where Q is computed prior to numerical factorization, and P is computed during numerical factorization via conventional partial pivoting with row interchanges. Colamd is the column ordering method used in SuperLU, part of the ScaLAPACK library. It is also available as built-in function in MATLAB Version 6, available from MathWorks, Inc. (http://www.mathworks.com). This routine can be used in place of colmmd in MATLAB. By default, the \ and / operators in MATLAB perform a column ordering (using colmmd or colamd) prior to LU factorization using sparse partial pivoting, in the built-in MATLAB lu(A) routine. This code is derived from Colamd Version 2.0. Authors: The authors of the COLAMD code itself are Stefan I. Larimore and Timothy A. Davis, University of Florida. The algorithm was developed in collaboration with John Gilbert, Xerox PARC, and Esmond Ng, Oak Ridge National Laboratory. The AMD metric on which this is based is by Patrick Amestoy, T. Davis, and Iain Duff. Date: UMFPACK Version: see above. COLAMD Version 2.0 was released on January 31, 2000. Acknowledgements: This work was supported by the National Science Foundation, under grants DMS-9504974, DMS-9803599, and CCR-0203270. UMFPACK: Copyright (c) 2003 by Timothy A. Davis. All Rights Reserved. See the UMFPACK README file for the License for your use of this code. Availability: Both UMFPACK and the original unmodified colamd/symamd library are available at http://www.cise.ufl.edu/research/sparse. Changes for inclusion in UMFPACK: * symamd, symamd_report, and colamd_report removed * additional terms added to RowInfo, ColInfo, and stats * Frontal matrix information computed for UMFPACK * routines renamed * column elimination tree post-ordering incorporated. In the original version 2.0, this was performed in colamd.m. For more information, see: Amestoy, P. R. and Davis, T. A. and Duff, I. S., An approximate minimum degree ordering algorithm, SIAM J. Matrix Analysis and Applic, vol 17, no 4., pp 886-905, 1996. Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G., A column approximate minimum degree ordering algorithm, Univ. of Florida, CISE Dept., TR-00-005, Gainesville, FL Oct. 2000. Submitted to ACM Trans. Math. Softw. */ /* ========================================================================== */ /* === Description of user-callable routines ================================ */ /* ========================================================================== */ /* ---------------------------------------------------------------------------- colamd_recommended: removed for UMFPACK ---------------------------------------------------------------------------- ---------------------------------------------------------------------------- colamd_set_defaults: ---------------------------------------------------------------------------- C syntax: #include "colamd.h" colamd_set_defaults (double knobs [COLAMD_KNOBS]) ; Purpose: Sets the default parameters. The use of this routine is optional. Arguments: double knobs [COLAMD_KNOBS] ; Output only. Let c = knobs [COLAMD_DENSE_COL], r = knobs [COLAMD_DENSE_ROW]. Colamd: rows with more than max (16, r*16*sqrt(n_col)) entries are removed prior to ordering. Columns with more than max (16, c*16*sqrt(n_row)) entries are removed prior to ordering, and placed last in the output column ordering. Symamd: removed for UMFPACK. COLAMD_DENSE_ROW and COLAMD_DENSE_COL are defined as 0 and 1, respectively, in colamd.h. Default values of these two knobs are both 0.5. Currently, only knobs [0] and knobs [1] are used, but future versions may use more knobs. If so, they will be properly set to their defaults by the future version of colamd_set_defaults, so that the code that calls colamd will not need to change, assuming that you either use colamd_set_defaults, or pass a (double *) NULL pointer as the knobs array to colamd or symamd. knobs [COLAMD_AGGRESSIVE]: if nonzero, then perform aggressive absorption. Otherwise, do not. This version does aggressive absorption by default. COLAMD v2.1 (in MATLAB) always does aggressive absorption (it doesn't have an option to turn it off). ---------------------------------------------------------------------------- colamd: ---------------------------------------------------------------------------- C syntax: #include "colamd.h" Int UMF_colamd (Int n_row, Int n_col, Int Alen, Int *A, Int *p, double knobs [COLAMD_KNOBS], Int stats [COLAMD_STATS]) ; Purpose: Computes a column ordering (Q) of A such that P(AQ)=LU or (AQ)'AQ=LL' have less fill-in and require fewer floating point operations than factorizing the unpermuted matrix A or A'A, respectively. Returns: TRUE (1) if successful, FALSE (0) otherwise. Arguments: Int n_row ; Input argument. Number of rows in the matrix A. Restriction: n_row >= 0. Colamd returns FALSE if n_row is negative. Int n_col ; Input argument. Number of columns in the matrix A. Restriction: n_col >= 0. Colamd returns FALSE if n_col is negative. Int Alen ; Input argument. Restriction (see note): Alen >= 2*nnz + 8*(n_col+1) + 6*(n_row+1) + n_col Colamd returns FALSE if these conditions are not met. Note: this restriction makes an modest assumption regarding the size of the two typedef's structures in colamd.h. We do, however, guarantee that Alen >= UMF_COLAMD_RECOMMENDED (nnz, n_row, n_col) will be sufficient. Int A [Alen] ; Input and output argument. A is an integer array of size Alen. Alen must be at least as large as the bare minimum value given above, but this is very low, and can result in excessive run time. For best performance, we recommend that Alen be greater than or equal to UMF_COLAMD_RECOMMENDED (nnz, n_row, n_col), which adds nnz/5 to the bare minimum value given above. On input, the row indices of the entries in column c of the matrix are held in A [(p [c]) ... (p [c+1]-1)]. The row indices in a given column c need not be in ascending order, and duplicate row indices may be be present. However, colamd will work a little faster if both of these conditions are met (Colamd puts the matrix into this format, if it finds that the the conditions are not met). The matrix is 0-based. That is, rows are in the range 0 to n_row-1, and columns are in the range 0 to n_col-1. Colamd returns FALSE if any row index is out of range. A holds the inverse permutation on output. Int p [n_col+1] ; Both input and output argument. p is an integer array of size n_col+1. On input, it holds the "pointers" for the column form of the matrix A. Column c of the matrix A is held in A [(p [c]) ... (p [c+1]-1)]. The first entry, p [0], must be zero, and p [c] <= p [c+1] must hold for all c in the range 0 to n_col-1. The value p [n_col] is thus the total number of entries in the pattern of the matrix A. Colamd returns FALSE if these conditions are not met. On output, if colamd returns TRUE, the array p holds the column permutation (Q, for P(AQ)=LU or (AQ)'(AQ)=LL'), where p [0] is the first column index in the new ordering, and p [n_col-1] is the last. That is, p [k] = j means that column j of A is the kth pivot column, in AQ, where k is in the range 0 to n_col-1 (p [0] = j means that column j of A is the first column in AQ). If colamd returns FALSE, then no permutation is returned, and p is undefined on output. double knobs [COLAMD_KNOBS] ; Input argument. See colamd_set_defaults for a description. The behavior is undefined if knobs contains NaN's. (UMFPACK does not call umf_colamd with NaN-valued knobs). Int stats [COLAMD_STATS] ; Output argument. Statistics on the ordering, and error status. See colamd.h for related definitions. Colamd returns FALSE if stats is not present. stats [0]: number of dense or empty rows ignored. stats [1]: number of dense or empty columns ignored (and ordered last in the output permutation p) Note that a row can become "empty" if it contains only "dense" and/or "empty" columns, and similarly a column can become "empty" if it only contains "dense" and/or "empty" rows. stats [2]: number of garbage collections performed. This can be excessively high if Alen is close to the minimum required value. stats [3]: status code. < 0 is an error code. > 1 is a warning or notice. 0 OK. Each column of the input matrix contained row indices in increasing order, with no duplicates. -11 Columns of input matrix jumbled (unsorted columns or duplicate entries). stats [4]: the bad column index stats [5]: the bad row index -1 A is a null pointer -2 p is a null pointer -3 n_row is negative stats [4]: n_row -4 n_col is negative stats [4]: n_col -5 number of nonzeros in matrix is negative stats [4]: number of nonzeros, p [n_col] -6 p [0] is nonzero stats [4]: p [0] -7 A is too small stats [4]: required size stats [5]: actual size (Alen) -8 a column has a zero or negative number of entries (changed for UMFPACK) stats [4]: column with <= 0 entries stats [5]: number of entries in col -9 a row index is out of bounds stats [4]: column with bad row index stats [5]: bad row index stats [6]: n_row, # of rows of matrx -10 unused -999 (unused; see symamd.c) Future versions may return more statistics in the stats array. Example: See http://www.cise.ufl.edu/~davis/colamd/example.c for a complete example. To order the columns of a 5-by-4 matrix with 11 nonzero entries in the following nonzero pattern x 0 x 0 x 0 x x 0 x x 0 0 0 x x x x 0 0 with default knobs and no output statistics, do the following: #include "colamd.h" #define ALEN UMF_COLAMD_RECOMMENDED (11, 5, 4) Int A [ALEN] = {1, 2, 5, 3, 5, 1, 2, 3, 4, 2, 4} ; Int p [ ] = {0, 3, 5, 9, 11} ; Int stats [COLAMD_STATS] ; UMF_colamd (5, 4, ALEN, A, p, (double *) NULL, stats) ; The permutation is returned in the array p, and A is destroyed. ---------------------------------------------------------------------------- symamd: does not appear in this version for UMFPACK ---------------------------------------------------------------------------- ---------------------------------------------------------------------------- colamd_report: does not appear in this version for UMFPACK ---------------------------------------------------------------------------- ---------------------------------------------------------------------------- symamd_report: does not appear in this version for UMFPACK ---------------------------------------------------------------------------- */ /* ========================================================================== */ /* === Scaffolding code definitions ======================================== */ /* ========================================================================== */ /* UMFPACK debugging control moved to amd_internal.h */ /* Our "scaffolding code" philosophy: In our opinion, well-written library code should keep its "debugging" code, and just normally have it turned off by the compiler so as not to interfere with performance. This serves several purposes: (1) assertions act as comments to the reader, telling you what the code expects at that point. All assertions will always be true (unless there really is a bug, of course). (2) leaving in the scaffolding code assists anyone who would like to modify the code, or understand the algorithm (by reading the debugging output, one can get a glimpse into what the code is doing). (3) (gasp!) for actually finding bugs. This code has been heavily tested and "should" be fully functional and bug-free ... but you never know... To enable debugging, comment out the "#define NDEBUG" above. For a MATLAB mexFunction, you will also need to modify mexopts.sh to remove the -DNDEBUG definition. The code will become outrageously slow when debugging is enabled. To control the level of debugging output, set an environment variable D to 0 (little), 1 (some), 2, 3, or 4 (lots). When debugging, you should see the following message on the standard output: colamd: debug version, D = 1 (THIS WILL BE SLOW!) or a similar message for symamd. If you don't, then debugging has not been enabled. */ /* ========================================================================== */ /* === Include files ======================================================== */ /* ========================================================================== */ /* ------------------ */ /* modified for UMFPACK: */ #include "umf_internal.h" #include "umf_colamd.h" #include "umf_apply_order.h" #include "umf_fsize.h" /* ------------------ */ /* ========================================================================== */ /* === Definitions ========================================================== */ /* ========================================================================== */ /* ------------------ */ /* UMFPACK: duplicate definitions moved to umf_internal.h */ /* ------------------ */ /* Row and column status */ #define ALIVE (0) #define DEAD (-1) /* Column status */ #define DEAD_PRINCIPAL (-1) #define DEAD_NON_PRINCIPAL (-2) /* Macros for row and column status update and checking. */ #define ROW_IS_DEAD(r) ROW_IS_MARKED_DEAD (Row[r].shared2.mark) #define ROW_IS_MARKED_DEAD(row_mark) (row_mark < ALIVE) #define ROW_IS_ALIVE(r) (Row [r].shared2.mark >= ALIVE) #define COL_IS_DEAD(c) (Col [c].start < ALIVE) #define COL_IS_ALIVE(c) (Col [c].start >= ALIVE) #define COL_IS_DEAD_PRINCIPAL(c) (Col [c].start == DEAD_PRINCIPAL) #define KILL_ROW(r) { Row [r].shared2.mark = DEAD ; } #define KILL_PRINCIPAL_COL(c) { Col [c].start = DEAD_PRINCIPAL ; } #define KILL_NON_PRINCIPAL_COL(c) { Col [c].start = DEAD_NON_PRINCIPAL ; } /* ------------------ */ /* UMFPACK: Colamd reporting mechanism moved to umf_internal.h */ /* ------------------ */ /* ========================================================================== */ /* === Prototypes of PRIVATE routines ======================================= */ /* ========================================================================== */ PRIVATE Int init_rows_cols ( Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int A [], Int p [] /* Int stats [COLAMD_STATS] */ ) ; PRIVATE void init_scoring ( Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int A [], Int head [], double knobs [COLAMD_KNOBS], Int *p_n_row2, Int *p_n_col2, Int *p_max_deg /* ------------------ */ /* added for UMFPACK */ , Int *p_ndense_row /* number of dense rows */ , Int *p_nempty_row /* number of original empty rows */ , Int *p_nnewlyempty_row /* number of newly empty rows */ , Int *p_ndense_col /* number of dense cols (excl "empty" cols) */ , Int *p_nempty_col /* number of original empty cols */ , Int *p_nnewlyempty_col /* number of newly empty cols */ ) ; PRIVATE Int find_ordering ( Int n_row, Int n_col, Int Alen, Colamd_Row Row [], Colamd_Col Col [], Int A [], Int head [], Int n_col2, Int max_deg, Int pfree /* ------------------ */ /* added for UMFPACK: */ , Int Front_npivcol [ ] , Int Front_nrows [ ] , Int Front_ncols [ ] , Int Front_parent [ ] , Int Front_cols [ ] , Int *p_nfr , Int aggressive , Int InFront [ ] /* ------------------ */ ) ; /* ------------------ */ /* order_children deleted for UMFPACK: */ /* ------------------ */ PRIVATE void detect_super_cols ( #ifndef NDEBUG Int n_col, Colamd_Row Row [], #endif /* NDEBUG */ Colamd_Col Col [], Int A [], Int head [], Int row_start, Int row_length ) ; PRIVATE Int garbage_collection ( Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int A [], Int *pfree ) ; PRIVATE Int clear_mark ( Int n_row, Colamd_Row Row [] ) ; /* ------------------ */ /* print_report deleted for UMFPACK */ /* ------------------ */ /* ========================================================================== */ /* === Debugging prototypes and definitions ================================= */ /* ========================================================================== */ #ifndef NDEBUG /* ------------------ */ /* debugging macros moved for UMFPACK */ /* ------------------ */ PRIVATE void debug_deg_lists ( Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int head [], Int min_score, Int should, Int max_deg ) ; PRIVATE void debug_mark ( Int n_row, Colamd_Row Row [], Int tag_mark, Int max_mark ) ; PRIVATE void debug_matrix ( Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int A [] ) ; PRIVATE void debug_structures ( Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int A [], Int n_col2 ) ; /* ------------------ */ /* dump_super added for UMFPACK: */ PRIVATE void dump_super ( Int super_c, Colamd_Col Col [], Int n_col ) ; /* ------------------ */ #endif /* NDEBUG */ /* ========================================================================== */ /* ========================================================================== */ /* === USER-CALLABLE ROUTINES: ============================================== */ /* ========================================================================== */ /* ========================================================================== */ /* === colamd_set_defaults ================================================== */ /* ========================================================================== */ /* The colamd_set_defaults routine sets the default values of the user- controllable parameters for colamd: knobs [0] rows with knobs[0]*n_col entries or more are removed prior to ordering in colamd. Rows and columns with knobs[0]*n_col entries or more are removed prior to ordering in symamd and placed last in the output ordering. knobs [1] columns with knobs[1]*n_row entries or more are removed prior to ordering in colamd, and placed last in the column permutation. Symamd ignores this knob. knobs [2] if nonzero, then perform aggressive absorption. knobs [3..19] unused, but future versions might use this */ GLOBAL void UMF_colamd_set_defaults ( /* === Parameters ======================================================= */ double knobs [COLAMD_KNOBS] /* knob array */ ) { /* === Local variables ================================================== */ Int i ; #if 0 if (!knobs) { return ; /* UMFPACK always passes knobs array */ } #endif for (i = 0 ; i < COLAMD_KNOBS ; i++) { knobs [i] = 0 ; } knobs [COLAMD_DENSE_ROW] = 0.2 ; /* default changed for UMFPACK */ knobs [COLAMD_DENSE_COL] = 0.2 ; /* default changed for UMFPACK */ knobs [COLAMD_AGGRESSIVE] = TRUE ; /* default is to do aggressive * absorption */ } /* ========================================================================== */ /* === symamd removed for UMFPACK =========================================== */ /* ========================================================================== */ /* ========================================================================== */ /* === colamd =============================================================== */ /* ========================================================================== */ /* The colamd routine computes a column ordering Q of a sparse matrix A such that the LU factorization P(AQ) = LU remains sparse, where P is selected via partial pivoting. The routine can also be viewed as providing a permutation Q such that the Cholesky factorization (AQ)'(AQ) = LL' remains sparse. */ /* For UMFPACK: colamd always returns TRUE */ GLOBAL Int UMF_colamd /* returns TRUE if successful, FALSE otherwise*/ ( /* === Parameters ======================================================= */ Int n_row, /* number of rows in A */ Int n_col, /* number of columns in A */ Int Alen, /* length of A */ Int A [], /* row indices of A */ Int p [], /* pointers to columns in A */ double knobs [COLAMD_KNOBS],/* parameters (uses defaults if NULL) */ Int stats [COLAMD_STATS] /* output statistics and error codes */ /* ------------------ */ /* added for UMFPACK: each Front_ array is of size n_col+1 */ , Int Front_npivcol [ ] /* # pivot cols in each front */ , Int Front_nrows [ ] /* # of rows in each front (incl. pivot rows) */ , Int Front_ncols [ ] /* # of cols in each front (incl. pivot cols) */ , Int Front_parent [ ] /* parent of each front */ , Int Front_cols [ ] /* link list of pivot columns for each front */ , Int *p_nfr /* total number of frontal matrices */ , Int InFront [ ] /* InFront [row] = f if the original row was * absorbed into front f. EMPTY if the row was * empty, dense, or not absorbed. This array * has size n_row+1 */ /* ------------------ */ ) { /* === Local variables ================================================== */ Int row ; /* row index */ Int i ; /* loop index */ Int nnz ; /* nonzeros in A */ Int Row_size ; /* size of Row [], in integers */ Int Col_size ; /* size of Col [], in integers */ #if 0 Int need ; /* minimum required length of A */ #endif Colamd_Row *Row ; /* pointer into A of Row [0..n_row] array */ Colamd_Col *Col ; /* pointer into A of Col [0..n_col] array */ Int n_col2 ; /* number of non-dense, non-empty columns */ Int n_row2 ; /* number of non-dense, non-empty rows */ Int ngarbage ; /* number of garbage collections performed */ Int max_deg ; /* maximum row degree */ Int aggressive ; /* TRUE if doing aggressive absorption */ #if 0 double default_knobs [COLAMD_KNOBS] ; /* default knobs array */ #endif /* ------------------ */ /* debugging initializations moved for UMFPACK */ /* ------------------ */ /* ------------------ */ /* added for UMFPACK: */ Int ndense_row, nempty_row, parent, ndense_col, nempty_col, k, col, nfr, *Front_child, *Front_sibling, *Front_stack, *Front_order, *Front_size ; Int nnewlyempty_col, nnewlyempty_row ; /* ------------------ */ /* === Check the input arguments ======================================== */ #if 0 if (!stats) { DEBUG0 (("colamd: stats not present\n")) ; return (FALSE) ; /* UMFPACK: always passes stats [ ] */ } #endif ASSERT (stats != (Int *) NULL) ; for (i = 0 ; i < COLAMD_STATS ; i++) { stats [i] = 0 ; } stats [COLAMD_STATUS] = COLAMD_OK ; stats [COLAMD_INFO1] = -1 ; stats [COLAMD_INFO2] = -1 ; #if 0 if (!A) /* A is not present */ { /* UMFPACK: always passes A [ ] */ DEBUG0 (("colamd: A not present\n")) ; stats [COLAMD_STATUS] = COLAMD_ERROR_A_not_present ; return (FALSE) ; } if (!p) /* p is not present */ { /* UMFPACK: always passes p [ ] */ DEBUG0 (("colamd: p not present\n")) ; stats [COLAMD_STATUS] = COLAMD_ERROR_p_not_present ; return (FALSE) ; } if (n_row < 0) /* n_row must be >= 0 */ { /* UMFPACK: does not call UMF_colamd if n <= 0 */ DEBUG0 (("colamd: nrow negative "ID"\n", n_row)) ; stats [COLAMD_STATUS] = COLAMD_ERROR_nrow_negative ; stats [COLAMD_INFO1] = n_row ; return (FALSE) ; } if (n_col < 0) /* n_col must be >= 0 */ { /* UMFPACK: does not call UMF_colamd if n <= 0 */ DEBUG0 (("colamd: ncol negative "ID"\n", n_col)) ; stats [COLAMD_STATUS] = COLAMD_ERROR_ncol_negative ; stats [COLAMD_INFO1] = n_col ; return (FALSE) ; } #endif ASSERT (A != (Int *) NULL) ; ASSERT (p != (Int *) NULL) ; ASSERT (n_row >= 0) ; ASSERT (n_col >= 0) ; nnz = p [n_col] ; #if 0 if (nnz < 0) /* nnz must be >= 0 */ { /* UMFPACK: does not call UMF_colamd if nnz < 0 */ DEBUG0 (("colamd: number of entries negative "ID"\n", nnz)) ; stats [COLAMD_STATUS] = COLAMD_ERROR_nnz_negative ; stats [COLAMD_INFO1] = nnz ; return (FALSE) ; } if (p [0] != 0) /* p [0] must be exactly zero */ { DEBUG0 (("colamd: p[0] not zero "ID"\n", p [0])) ; stats [COLAMD_STATUS] = COLAMD_ERROR_p0_nonzero ; stats [COLAMD_INFO1] = p [0] ; return (FALSE) ; } #endif ASSERT (nnz >= 0) ; ASSERT (p [0] == 0) ; /* === If no knobs, set default knobs =================================== */ #if 0 if (!knobs) { /* UMFPACK: always passes the knobs */ UMF_colamd_set_defaults (default_knobs) ; knobs = default_knobs ; } #endif ASSERT (knobs != (double *) NULL) ; /* --------------------- */ /* added for UMFPACK v4.1: */ aggressive = (knobs [COLAMD_AGGRESSIVE] != 0) ; /* --------------------- */ /* === Allocate the Row and Col arrays from array A ===================== */ Col_size = UMF_COLAMD_C (n_col) ; Row_size = UMF_COLAMD_R (n_row) ; #if 0 need = MAX (2*nnz, 4*n_col) + n_col + Col_size + Row_size ; if (need > Alen) { /* UMFPACK: always passes enough space */ /* not enough space in array A to perform the ordering */ DEBUG0 (("colamd: Need Alen >= "ID", given only Alen = "ID"\n", need, Alen)) ; stats [COLAMD_STATUS] = COLAMD_ERROR_A_too_small ; stats [COLAMD_INFO1] = need ; stats [COLAMD_INFO2] = Alen ; return (FALSE) ; } #endif Alen -= Col_size + Row_size ; Col = (Colamd_Col *) &A [Alen] ; Row = (Colamd_Row *) &A [Alen + Col_size] ; /* Size of A is now Alen >= MAX (2*nnz, 4*n_col) + n_col. The ordering * requires Alen >= 2*nnz + n_col, and the postorder requires * Alen >= 5*n_col. */ /* === Construct the row and column data structures ===================== */ i = init_rows_cols (n_row, n_col, Row, Col, A, p) ; #if 0 if (!i) { /* input matrix is invalid */ DEBUG0 (("colamd: Matrix invalid\n")) ; return (FALSE) ; } #endif ASSERT (i) ; /* === UMFPACK: Initialize front info =================================== */ for (col = 0 ; col < n_col ; col++) { Front_npivcol [col] = 0 ; Front_nrows [col] = 0 ; Front_ncols [col] = 0 ; Front_parent [col] = EMPTY ; Front_cols [col] = EMPTY ; } /* === Initialize scores, kill dense rows/columns ======================= */ init_scoring (n_row, n_col, Row, Col, A, p, knobs, &n_row2, &n_col2, &max_deg /* ------------------ */ /* added for UMFPACK: */ , &ndense_row, &nempty_row, &nnewlyempty_row , &ndense_col, &nempty_col, &nnewlyempty_col /* ------------------ */ ) ; ASSERT (n_row2 == n_row - nempty_row - nnewlyempty_row - ndense_row) ; ASSERT (n_col2 == n_col - nempty_col - nnewlyempty_col - ndense_col) ; /* === Order the supercolumns =========================================== */ ngarbage = find_ordering (n_row, n_col, Alen, Row, Col, A, p, n_col2, max_deg, 2*nnz /* ------------------ */ /* added for UMFPACK: */ , Front_npivcol, Front_nrows, Front_ncols, Front_parent, Front_cols , &nfr, aggressive, InFront /* ------------------ */ ) ; /* ------------------ */ /* changed for UMFPACK: */ /* A is no longer needed, so use A [0..5*nfr-1] as workspace [ [ */ /* This step requires Alen >= 5*n_col */ Front_child = A ; Front_sibling = Front_child + nfr ; Front_stack = Front_sibling + nfr ; Front_order = Front_stack + nfr ; Front_size = Front_order + nfr ; UMF_fsize (nfr, Front_size, Front_nrows, Front_ncols, Front_parent, Front_npivcol) ; AMD_postorder (nfr, Front_parent, Front_npivcol, Front_size, Front_order, Front_child, Front_sibling, Front_stack) ; /* Front_size, Front_stack, Front_child, Front_sibling no longer needed ] */ /* use A [0..nfr-1] as workspace */ UMF_apply_order (Front_npivcol, Front_order, A, nfr, nfr) ; UMF_apply_order (Front_nrows, Front_order, A, nfr, nfr) ; UMF_apply_order (Front_ncols, Front_order, A, nfr, nfr) ; UMF_apply_order (Front_parent, Front_order, A, nfr, nfr) ; UMF_apply_order (Front_cols, Front_order, A, nfr, nfr) ; /* fix the parent to refer to the new numbering */ for (i = 0 ; i < nfr ; i++) { parent = Front_parent [i] ; if (parent != EMPTY) { Front_parent [i] = Front_order [parent] ; } } /* fix InFront to refer to the new numbering */ for (row = 0 ; row < n_row ; row++) { i = InFront [row] ; ASSERT (i >= EMPTY && i < nfr) ; if (i != EMPTY) { InFront [row] = Front_order [i] ; } } /* Front_order longer needed ] */ /* === Order the columns in the fronts ================================== */ /* use A [0..n_col-1] as inverse permutation */ for (i = 0 ; i < n_col ; i++) { A [i] = EMPTY ; } k = 0 ; for (i = 0 ; i < nfr ; i++) { ASSERT (Front_npivcol [i] > 0) ; for (col = Front_cols [i] ; col != EMPTY ; col = Col [col].nextcol) { ASSERT (col >= 0 && col < n_col) ; DEBUG1 (("Colamd output ordering: k "ID" col "ID"\n", k, col)) ; p [k] = col ; ASSERT (A [col] == EMPTY) ; A [col] = k ; k++ ; } } /* === Order the "dense" and null columns =============================== */ ASSERT (k == n_col2) ; if (n_col2 < n_col) { for (col = 0 ; col < n_col ; col++) { if (A [col] == EMPTY) { k = Col [col].shared2.order ; ASSERT (k >= n_col2 && k < n_col) ; DEBUG1 (("Colamd output ordering: k "ID" col "ID " (dense or null col)\n", k, col)) ; p [k] = col ; A [col] = k ; } } } /* ------------------ */ /* === Return statistics in stats ======================================= */ /* ------------------ */ /* modified for UMFPACK */ stats [COLAMD_DENSE_ROW] = ndense_row ; stats [COLAMD_EMPTY_ROW] = nempty_row ; stats [COLAMD_NEWLY_EMPTY_ROW] = nnewlyempty_row ; stats [COLAMD_DENSE_COL] = ndense_col ; stats [COLAMD_EMPTY_COL] = nempty_col ; stats [COLAMD_NEWLY_EMPTY_COL] = nnewlyempty_col ; ASSERT (ndense_col + nempty_col + nnewlyempty_col == n_col - n_col2) ; /* ------------------ */ stats [COLAMD_DEFRAG_COUNT] = ngarbage ; *p_nfr = nfr ; DEBUG1 (("colamd: done.\n")) ; return (TRUE) ; } /* ========================================================================== */ /* === colamd_report removed for UMFPACK ==================================== */ /* ========================================================================== */ /* ========================================================================== */ /* === symamd_report removed for UMFPACK ==================================== */ /* ========================================================================== */ /* ========================================================================== */ /* === NON-USER-CALLABLE ROUTINES: ========================================== */ /* ========================================================================== */ /* There are no user-callable routines beyond this point in the file */ /* ========================================================================== */ /* === init_rows_cols ======================================================= */ /* ========================================================================== */ /* Takes the column form of the matrix in A and creates the row form of the matrix. Also, row and column attributes are stored in the Col and Row structs. If the columns are un-sorted or contain duplicate row indices, this routine will also sort and remove duplicate row indices from the column form of the matrix. Returns FALSE if the matrix is invalid, TRUE otherwise. Not user-callable. */ /* For UMFPACK, this always returns TRUE */ PRIVATE Int init_rows_cols /* returns TRUE if OK, or FALSE otherwise */ ( /* === Parameters ======================================================= */ Int n_row, /* number of rows of A */ Int n_col, /* number of columns of A */ Colamd_Row Row [], /* of size n_row+1 */ Colamd_Col Col [], /* of size n_col+1 */ Int A [], /* row indices of A, of size Alen */ Int p [] /* pointers to columns in A, of size n_col+1 */ /* Int stats [COLAMD_STATS] colamd statistics, removed for UMFPACK */ ) { /* === Local variables ================================================== */ Int col ; /* a column index */ Int row ; /* a row index */ Int *cp ; /* a column pointer */ Int *cp_end ; /* a pointer to the end of a column */ /* === Initialize columns, and check column pointers ==================== */ for (col = 0 ; col < n_col ; col++) { Col [col].start = p [col] ; Col [col].length = p [col+1] - p [col] ; #if 0 if (Col [col].length < 0) { /* column pointers must be non-decreasing */ stats [COLAMD_STATUS] = COLAMD_ERROR_col_length_negative ; stats [COLAMD_INFO1] = col ; stats [COLAMD_INFO2] = Col [col].length ; DEBUG0 (("colamd: col "ID" length "ID" <= 0\n", col, Col [col].length)); return (FALSE) ; } #endif ASSERT (Col [col].length >= 0) ; /* added for UMFPACK v4.1 */ ASSERT (Col [col].length > 0) ; Col [col].shared1.thickness = 1 ; Col [col].shared2.score = 0 ; Col [col].shared3.prev = EMPTY ; Col [col].shared4.degree_next = EMPTY ; /* ------------------ */ /* added for UMFPACK: */ Col [col].nextcol = EMPTY ; Col [col].lastcol = col ; /* ------------------ */ } /* p [0..n_col] no longer needed, used as "head" in subsequent routines */ /* === Scan columns, compute row degrees, and check row indices ========= */ /* ------------------ */ /* stats [COLAMD_INFO3] = 0 ; */ /* number of duplicate or unsorted row indices - not computed in UMFPACK */ /* ------------------ */ for (row = 0 ; row < n_row ; row++) { Row [row].length = 0 ; /* ------------------ */ /* removed for UMFPACK */ /* Row [row].shared2.mark = -1 ; */ /* ------------------ */ /* ------------------ */ /* added for UMFPACK: */ Row [row].thickness = 1 ; Row [row].front = EMPTY ; /* ------------------ */ } for (col = 0 ; col < n_col ; col++) { #ifndef NDEBUG Int last_row = -1 ; #endif cp = &A [p [col]] ; cp_end = &A [p [col+1]] ; while (cp < cp_end) { row = *cp++ ; #if 0 /* make sure row indices within range */ if (row < 0 || row >= n_row) { stats [COLAMD_STATUS] = COLAMD_ERROR_row_index_out_of_bounds ; stats [COLAMD_INFO1] = col ; stats [COLAMD_INFO2] = row ; /* ------------------ */ /* not needed in UMFPACK: */ /* stats [COLAMD_INFO3] = n_row ; */ /* ------------------ */ DEBUG0 (("colamd: row "ID" col "ID" out of bounds\n", row,col)); return (FALSE) ; } #endif ASSERT (row >= 0 && row < n_row) ; #if 0 /* ------------------ */ /* changed for UMFPACK */ if (row <= last_row) { /* row index are unsorted or repeated (or both), thus col */ /* is jumbled. This is an error condition for UMFPACK */ stats [COLAMD_STATUS] = COLAMD_ERROR_jumbled_matrix ; stats [COLAMD_INFO1] = col ; stats [COLAMD_INFO2] = row ; DEBUG1 (("colamd: row "ID" col "ID" unsorted/duplicate\n", row, col)) ; return (FALSE) ; } /* ------------------ */ #endif ASSERT (row > last_row) ; /* ------------------ */ /* changed for UMFPACK - jumbled columns not tolerated */ Row [row].length++ ; /* ------------------ */ #ifndef NDEBUG last_row = row ; #endif } } /* === Compute row pointers ============================================= */ /* row form of the matrix starts directly after the column */ /* form of matrix in A */ Row [0].start = p [n_col] ; Row [0].shared1.p = Row [0].start ; /* ------------------ */ /* removed for UMFPACK */ /* Row [0].shared2.mark = -1 ; */ /* ------------------ */ for (row = 1 ; row < n_row ; row++) { Row [row].start = Row [row-1].start + Row [row-1].length ; Row [row].shared1.p = Row [row].start ; /* ------------------ */ /* removed for UMFPACK */ /* Row [row].shared2.mark = -1 ; */ /* ------------------ */ } /* === Create row form ================================================== */ /* ------------------ */ /* jumbled matrix case removed for UMFPACK */ /* ------------------ */ for (col = 0 ; col < n_col ; col++) { cp = &A [p [col]] ; cp_end = &A [p [col+1]] ; while (cp < cp_end) { A [(Row [*cp++].shared1.p)++] = col ; } } /* === Clear the row marks and set row degrees ========================== */ for (row = 0 ; row < n_row ; row++) { Row [row].shared2.mark = 0 ; Row [row].shared1.degree = Row [row].length ; } /* ------------------ */ /* recreate columns for jumbled matrix case removed for UMFPACK */ /* ------------------ */ return (TRUE) ; } /* ========================================================================== */ /* === init_scoring ========================================================= */ /* ========================================================================== */ /* Kills dense or empty columns and rows, calculates an initial score for each column, and places all columns in the degree lists. Not user-callable. */ PRIVATE void init_scoring ( /* === Parameters ======================================================= */ Int n_row, /* number of rows of A */ Int n_col, /* number of columns of A */ Colamd_Row Row [], /* of size n_row+1 */ Colamd_Col Col [], /* of size n_col+1 */ Int A [], /* column form and row form of A */ Int head [], /* of size n_col+1 */ double knobs [COLAMD_KNOBS],/* parameters */ Int *p_n_row2, /* number of non-dense, non-empty rows */ Int *p_n_col2, /* number of non-dense, non-empty columns */ Int *p_max_deg /* maximum row degree */ /* ------------------ */ /* added for UMFPACK */ , Int *p_ndense_row /* number of dense rows */ , Int *p_nempty_row /* number of original empty rows */ , Int *p_nnewlyempty_row /* number of newly empty rows */ , Int *p_ndense_col /* number of dense cols (excl "empty" cols) */ , Int *p_nempty_col /* number of original empty cols */ , Int *p_nnewlyempty_col /* number of newly empty cols */ /* ------------------ */ ) { /* === Local variables ================================================== */ Int c ; /* a column index */ Int r, row ; /* a row index */ Int *cp ; /* a column pointer */ Int deg ; /* degree of a row or column */ Int *cp_end ; /* a pointer to the end of a column */ Int *new_cp ; /* new column pointer */ Int col_length ; /* length of pruned column */ Int score ; /* current column score */ Int n_col2 ; /* number of non-dense, non-empty columns */ Int n_row2 ; /* number of non-dense, non-empty rows */ Int dense_row_count ; /* remove rows with more entries than this */ Int dense_col_count ; /* remove cols with more entries than this */ Int min_score ; /* smallest column score */ Int max_deg ; /* maximum row degree */ Int next_col ; /* Used to add to degree list.*/ /* ------------------ */ /* added for UMFPACK */ Int ndense_row ; /* number of dense rows */ Int nempty_row ; /* number of empty rows */ Int nnewlyempty_row ; /* number of newly empty rows */ Int ndense_col ; /* number of dense cols (excl "empty" cols) */ Int nempty_col ; /* number of original empty cols */ Int nnewlyempty_col ; /* number of newly empty cols */ Int ne ; /* ------------------ */ #ifndef NDEBUG Int debug_count ; /* debug only. */ #endif /* NDEBUG */ /* === Extract knobs ==================================================== */ /* --------------------- */ /* old dense row/column knobs: dense_row_count = MAX (0, MIN (knobs [COLAMD_DENSE_ROW] * n_col, n_col)) ; dense_col_count = MAX (0, MIN (knobs [COLAMD_DENSE_COL] * n_row, n_row)) ; */ /* new, for UMFPACK: */ /* Note: if knobs contains a NaN, this is undefined: */ dense_row_count = UMFPACK_DENSE_DEGREE_THRESHOLD (knobs [COLAMD_DENSE_ROW], n_col) ; dense_col_count = UMFPACK_DENSE_DEGREE_THRESHOLD (knobs [COLAMD_DENSE_COL], n_row) ; /* Make sure dense_*_count is between 0 and n: */ dense_row_count = MAX (0, MIN (dense_row_count, n_col)) ; dense_col_count = MAX (0, MIN (dense_col_count, n_row)) ; /* --------------------- */ DEBUG1 (("colamd: densecount: "ID" "ID"\n", dense_row_count, dense_col_count)) ; max_deg = 0 ; n_col2 = n_col ; n_row2 = n_row ; /* --------------------- */ /* added for UMFPACK */ ndense_col = 0 ; nempty_col = 0 ; nnewlyempty_col = 0 ; ndense_row = 0 ; nempty_row = 0 ; nnewlyempty_row = 0 ; /* --------------------- */ /* === Kill empty columns =============================================== */ /* removed for UMFPACK v4.1. prune_singletons has already removed empty * columns and empty rows */ #if 0 /* Put the empty columns at the end in their natural order, so that LU */ /* factorization can proceed as far as possible. */ for (c = n_col-1 ; c >= 0 ; c--) { deg = Col [c].length ; if (deg == 0) { /* this is a empty column, kill and order it last */ Col [c].shared2.order = --n_col2 ; KILL_PRINCIPAL_COL (c) ; /* --------------------- */ /* added for UMFPACK */ nempty_col++ ; /* --------------------- */ } } DEBUG1 (("colamd: null columns killed: "ID"\n", n_col - n_col2)) ; #endif #ifndef NDEBUG for (c = 0 ; c < n_col ; c++) { ASSERT (Col [c].length > 0) ; } #endif /* === Count null rows ================================================== */ #if 0 for (r = 0 ; r < n_row ; r++) { deg = Row [r].shared1.degree ; if (deg == 0) { /* this is an original empty row */ nempty_row++ ; } } #endif #ifndef NDEBUG for (r = 0 ; r < n_row ; r++) { ASSERT (Row [r].shared1.degree > 0) ; ASSERT (Row [r].length > 0) ; } #endif /* === Kill dense columns =============================================== */ /* Put the dense columns at the end, in their natural order */ for (c = n_col-1 ; c >= 0 ; c--) { /* ----------------------------------------------------------------- */ #if 0 /* removed for UMFPACK v4.1: no empty columns */ /* skip any dead columns */ if (COL_IS_DEAD (c)) { continue ; } #endif ASSERT (COL_IS_ALIVE (c)) ; ASSERT (Col [c].length > 0) ; /* ----------------------------------------------------------------- */ deg = Col [c].length ; if (deg > dense_col_count) { /* this is a dense column, kill and order it last */ Col [c].shared2.order = --n_col2 ; /* --------------------- */ /* added for UMFPACK */ ndense_col++ ; /* --------------------- */ /* decrement the row degrees */ cp = &A [Col [c].start] ; cp_end = cp + Col [c].length ; while (cp < cp_end) { Row [*cp++].shared1.degree-- ; } KILL_PRINCIPAL_COL (c) ; } } DEBUG1 (("colamd: Dense and null columns killed: "ID"\n", n_col - n_col2)) ; /* === Kill dense and empty rows ======================================== */ /* Note that there can now be empty rows, since dense columns have * been deleted. These are "newly" empty rows. */ ne = 0 ; for (r = 0 ; r < n_row ; r++) { deg = Row [r].shared1.degree ; ASSERT (deg >= 0 && deg <= n_col) ; /* --------------------- */ /* added for UMFPACK */ if (deg > dense_row_count) { /* There is at least one dense row. Continue ordering, but */ /* symbolic factorization will be redone after UMF_colamd is done.*/ ndense_row++ ; } if (deg == 0) { /* this is a newly empty row, or original empty row */ ne++ ; } /* --------------------- */ if (deg > dense_row_count || deg == 0) { /* kill a dense or empty row */ KILL_ROW (r) ; /* --------------------- */ /* added for UMFPACK */ Row [r].thickness = 0 ; /* --------------------- */ --n_row2 ; } else { /* keep track of max degree of remaining rows */ max_deg = MAX (max_deg, deg) ; } } nnewlyempty_row = ne - nempty_row ; DEBUG1 (("colamd: Dense rows killed: "ID"\n", ndense_row)) ; DEBUG1 (("colamd: Dense and null rows killed: "ID"\n", n_row - n_row2)) ; /* === Compute initial column scores ==================================== */ /* At this point the row degrees are accurate. They reflect the number */ /* of "live" (non-dense) columns in each row. No empty rows exist. */ /* Some "live" columns may contain only dead rows, however. These are */ /* pruned in the code below. */ /* now find the initial matlab score for each column */ for (c = n_col-1 ; c >= 0 ; c--) { /* skip dead column */ if (COL_IS_DEAD (c)) { continue ; } score = 0 ; cp = &A [Col [c].start] ; new_cp = cp ; cp_end = cp + Col [c].length ; while (cp < cp_end) { /* get a row */ row = *cp++ ; /* skip if dead */ if (ROW_IS_DEAD (row)) { continue ; } /* compact the column */ *new_cp++ = row ; /* add row's external degree */ score += Row [row].shared1.degree - 1 ; /* guard against integer overflow */ score = MIN (score, n_col) ; } /* determine pruned column length */ col_length = (Int) (new_cp - &A [Col [c].start]) ; if (col_length == 0) { /* a newly-made null column (all rows in this col are "dense" */ /* and have already been killed) */ DEBUG2 (("Newly null killed: "ID"\n", c)) ; Col [c].shared2.order = --n_col2 ; KILL_PRINCIPAL_COL (c) ; /* --------------------- */ /* added for UMFPACK */ nnewlyempty_col++ ; /* --------------------- */ } else { /* set column length and set score */ ASSERT (score >= 0) ; ASSERT (score <= n_col) ; Col [c].length = col_length ; Col [c].shared2.score = score ; } } DEBUG1 (("colamd: Dense, null, and newly-null columns killed: "ID"\n", n_col-n_col2)) ; /* At this point, all empty rows and columns are dead. All live columns */ /* are "clean" (containing no dead rows) and simplicial (no supercolumns */ /* yet). Rows may contain dead columns, but all live rows contain at */ /* least one live column. */ #ifndef NDEBUG debug_structures (n_row, n_col, Row, Col, A, n_col2) ; #endif /* NDEBUG */ /* === Initialize degree lists ========================================== */ #ifndef NDEBUG debug_count = 0 ; #endif /* NDEBUG */ /* clear the hash buckets */ for (c = 0 ; c <= n_col ; c++) { head [c] = EMPTY ; } min_score = n_col ; /* place in reverse order, so low column indices are at the front */ /* of the lists. This is to encourage natural tie-breaking */ for (c = n_col-1 ; c >= 0 ; c--) { /* only add principal columns to degree lists */ if (COL_IS_ALIVE (c)) { DEBUG4 (("place "ID" score "ID" minscore "ID" ncol "ID"\n", c, Col [c].shared2.score, min_score, n_col)) ; /* === Add columns score to DList =============================== */ score = Col [c].shared2.score ; ASSERT (min_score >= 0) ; ASSERT (min_score <= n_col) ; ASSERT (score >= 0) ; ASSERT (score <= n_col) ; ASSERT (head [score] >= EMPTY) ; /* now add this column to dList at proper score location */ next_col = head [score] ; Col [c].shared3.prev = EMPTY ; Col [c].shared4.degree_next = next_col ; /* if there already was a column with the same score, set its */ /* previous pointer to this new column */ if (next_col != EMPTY) { Col [next_col].shared3.prev = c ; } head [score] = c ; /* see if this score is less than current min */ min_score = MIN (min_score, score) ; #ifndef NDEBUG debug_count++ ; #endif /* NDEBUG */ } } #ifndef NDEBUG DEBUG1 (("colamd: Live cols "ID" out of "ID", non-princ: "ID"\n", debug_count, n_col, n_col-debug_count)) ; ASSERT (debug_count == n_col2) ; debug_deg_lists (n_row, n_col, Row, Col, head, min_score, n_col2, max_deg) ; #endif /* NDEBUG */ /* === Return number of remaining columns, and max row degree =========== */ *p_n_col2 = n_col2 ; *p_n_row2 = n_row2 ; *p_max_deg = max_deg ; /* --------------------- */ /* added for UMFPACK */ *p_ndense_row = ndense_row ; *p_nempty_row = nempty_row ; /* original empty rows */ *p_nnewlyempty_row = nnewlyempty_row ; *p_ndense_col = ndense_col ; *p_nempty_col = nempty_col ; /* original empty cols */ *p_nnewlyempty_col = nnewlyempty_col ; /* --------------------- */ } /* ========================================================================== */ /* === find_ordering ======================================================== */ /* ========================================================================== */ /* Order the principal columns of the supercolumn form of the matrix (no supercolumns on input). Uses a minimum approximate column minimum degree ordering method. Not user-callable. */ PRIVATE Int find_ordering /* return the number of garbage collections */ ( /* === Parameters ======================================================= */ Int n_row, /* number of rows of A */ Int n_col, /* number of columns of A */ Int Alen, /* size of A, 2*nnz + n_col or larger */ Colamd_Row Row [], /* of size n_row+1 */ Colamd_Col Col [], /* of size n_col+1 */ Int A [], /* column form and row form of A */ Int head [], /* of size n_col+1 */ Int n_col2, /* Remaining columns to order */ Int max_deg, /* Maximum row degree */ Int pfree /* index of first free slot (2*nnz on entry) */ /* ------------------ */ /* added for UMFPACK: */ , Int Front_npivcol [ ] , Int Front_nrows [ ] , Int Front_ncols [ ] , Int Front_parent [ ] , Int Front_cols [ ] , Int *p_nfr /* number of fronts */ , Int aggressive , Int InFront [ ] /* ------------------ */ ) { /* === Local variables ================================================== */ Int k ; /* current pivot ordering step */ Int pivot_col ; /* current pivot column */ Int *cp ; /* a column pointer */ Int *rp ; /* a row pointer */ Int pivot_row ; /* current pivot row */ Int *new_cp ; /* modified column pointer */ Int *new_rp ; /* modified row pointer */ Int pivot_row_start ; /* pointer to start of pivot row */ Int pivot_row_degree ; /* number of columns in pivot row */ Int pivot_row_length ; /* number of supercolumns in pivot row */ Int pivot_col_score ; /* score of pivot column */ Int needed_memory ; /* free space needed for pivot row */ Int *cp_end ; /* pointer to the end of a column */ Int *rp_end ; /* pointer to the end of a row */ Int row ; /* a row index */ Int col ; /* a column index */ Int max_score ; /* maximum possible score */ Int cur_score ; /* score of current column */ unsigned Int hash ; /* hash value for supernode detection */ Int head_column ; /* head of hash bucket */ Int first_col ; /* first column in hash bucket */ Int tag_mark ; /* marker value for mark array */ Int row_mark ; /* Row [row].shared2.mark */ Int set_difference ; /* set difference size of row with pivot row */ Int min_score ; /* smallest column score */ Int col_thickness ; /* "thickness" (no. of columns in a supercol) */ Int max_mark ; /* maximum value of tag_mark */ Int pivot_col_thickness ; /* number of columns represented by pivot col */ Int prev_col ; /* Used by Dlist operations. */ Int next_col ; /* Used by Dlist operations. */ Int ngarbage ; /* number of garbage collections performed */ #ifndef NDEBUG Int debug_d ; /* debug loop counter */ Int debug_step = 0 ; /* debug loop counter */ #endif /* NDEBUG */ /* ------------------ */ /* added for UMFPACK: */ Int pivot_row_thickness ; /* number of rows represented by pivot row */ Int nfr = 0 ; /* number of fronts */ Int child ; /* ------------------ */ /* === Initialization and clear mark ==================================== */ max_mark = MAX_MARK (n_col) ; /* defined in umfpack.h */ tag_mark = clear_mark (n_row, Row) ; min_score = 0 ; ngarbage = 0 ; DEBUG1 (("colamd: Ordering, n_col2="ID"\n", n_col2)) ; for (row = 0 ; row < n_row ; row++) { InFront [row] = EMPTY ; } /* === Order the columns ================================================ */ for (k = 0 ; k < n_col2 ; /* 'k' is incremented below */) { #ifndef NDEBUG if (debug_step % 100 == 0) { DEBUG2 (("\n... Step k: "ID" out of n_col2: "ID"\n", k, n_col2)) ; } else { DEBUG3 (("\n-----Step k: "ID" out of n_col2: "ID"\n", k, n_col2)) ; } debug_step++ ; debug_deg_lists (n_row, n_col, Row, Col, head, min_score, n_col2-k, max_deg) ; debug_matrix (n_row, n_col, Row, Col, A) ; #endif /* NDEBUG */ /* === Select pivot column, and order it ============================ */ /* make sure degree list isn't empty */ ASSERT (min_score >= 0) ; ASSERT (min_score <= n_col) ; ASSERT (head [min_score] >= EMPTY) ; #ifndef NDEBUG for (debug_d = 0 ; debug_d < min_score ; debug_d++) { ASSERT (head [debug_d] == EMPTY) ; } #endif /* NDEBUG */ /* get pivot column from head of minimum degree list */ while (head [min_score] == EMPTY && min_score < n_col) { min_score++ ; } pivot_col = head [min_score] ; ASSERT (pivot_col >= 0 && pivot_col <= n_col) ; next_col = Col [pivot_col].shared4.degree_next ; head [min_score] = next_col ; if (next_col != EMPTY) { Col [next_col].shared3.prev = EMPTY ; } ASSERT (COL_IS_ALIVE (pivot_col)) ; DEBUG3 (("Pivot col: "ID"\n", pivot_col)) ; /* remember score for defrag check */ pivot_col_score = Col [pivot_col].shared2.score ; /* the pivot column is the kth column in the pivot order */ Col [pivot_col].shared2.order = k ; /* increment order count by column thickness */ pivot_col_thickness = Col [pivot_col].shared1.thickness ; /* ------------------ */ /* changed for UMFPACK: */ k += pivot_col_thickness ; /* ------------------ */ ASSERT (pivot_col_thickness > 0) ; /* === Garbage_collection, if necessary ============================= */ needed_memory = MIN (pivot_col_score, n_col - k) ; if (pfree + needed_memory >= Alen) { pfree = garbage_collection (n_row, n_col, Row, Col, A, &A [pfree]) ; ngarbage++ ; /* after garbage collection we will have enough */ ASSERT (pfree + needed_memory < Alen) ; /* garbage collection has wiped out the Row[].shared2.mark array */ tag_mark = clear_mark (n_row, Row) ; #ifndef NDEBUG debug_matrix (n_row, n_col, Row, Col, A) ; #endif /* NDEBUG */ } /* === Compute pivot row pattern ==================================== */ /* get starting location for this new merged row */ pivot_row_start = pfree ; /* initialize new row counts to zero */ pivot_row_degree = 0 ; /* ------------------ */ /* added for UMFPACK: */ pivot_row_thickness = 0 ; /* ------------------ */ /* [ tag pivot column as having been visited so it isn't included */ /* in merged pivot row */ Col [pivot_col].shared1.thickness = -pivot_col_thickness ; /* pivot row is the union of all rows in the pivot column pattern */ cp = &A [Col [pivot_col].start] ; cp_end = cp + Col [pivot_col].length ; while (cp < cp_end) { /* get a row */ row = *cp++ ; DEBUG4 (("Pivot col pattern %d "ID"\n", ROW_IS_ALIVE(row), row)) ; /* skip if row is dead */ if (ROW_IS_DEAD (row)) { continue ; } /* ------------------ */ /* added for UMFPACK: */ /* sum the thicknesses of all the rows */ /* ASSERT (Row [row].thickness > 0) ; */ pivot_row_thickness += Row [row].thickness ; /* ------------------ */ rp = &A [Row [row].start] ; rp_end = rp + Row [row].length ; while (rp < rp_end) { /* get a column */ col = *rp++ ; /* add the column, if alive and untagged */ col_thickness = Col [col].shared1.thickness ; if (col_thickness > 0 && COL_IS_ALIVE (col)) { /* tag column in pivot row */ Col [col].shared1.thickness = -col_thickness ; ASSERT (pfree < Alen) ; /* place column in pivot row */ A [pfree++] = col ; pivot_row_degree += col_thickness ; /* ------------------ */ /* added for UMFPACK: */ DEBUG4 (("\t\t\tNew live column in pivot row: "ID"\n",col)); /* ------------------ */ } /* ------------------ */ /* added for UMFPACK */ #ifndef NDEBUG if (col_thickness < 0 && COL_IS_ALIVE (col)) { DEBUG4 (("\t\t\tOld live column in pivot row: "ID"\n",col)); } #endif /* ------------------ */ } } /* ------------------ */ /* added for UMFPACK: */ /* pivot_row_thickness is the number of rows in frontal matrix */ /* both pivotal rows and nonpivotal rows */ /* ------------------ */ /* clear tag on pivot column */ Col [pivot_col].shared1.thickness = pivot_col_thickness ; /* ] */ max_deg = MAX (max_deg, pivot_row_degree) ; #ifndef NDEBUG DEBUG3 (("check2\n")) ; debug_mark (n_row, Row, tag_mark, max_mark) ; #endif /* NDEBUG */ /* === Kill all rows used to construct pivot row ==================== */ /* also kill pivot row, temporarily */ cp = &A [Col [pivot_col].start] ; cp_end = cp + Col [pivot_col].length ; while (cp < cp_end) { /* may be killing an already dead row */ row = *cp++ ; DEBUG2 (("Kill row in pivot col: "ID" alive? %d, front "ID"\n", row, ROW_IS_ALIVE (row), Row [row].front)) ; /* added for UMFPACK: */ if (ROW_IS_ALIVE (row)) { if (Row [row].front != EMPTY) { /* This row represents a frontal matrix. */ /* Row [row].front is a child of current front */ child = Row [row].front ; Front_parent [child] = nfr ; DEBUG1 (("Front "ID" => front "ID", normal\n", child, nfr)); } else { /* This is an original row. Keep track of which front * is its parent in the row-merge tree. */ InFront [row] = nfr ; DEBUG1 (("Row "ID" => front "ID", normal\n", row, nfr)) ; } } KILL_ROW (row) ; /* ------------------ */ /* added for UMFPACK: */ Row [row].thickness = 0 ; /* ------------------ */ } /* === Select a row index to use as the new pivot row =============== */ pivot_row_length = pfree - pivot_row_start ; if (pivot_row_length > 0) { /* pick the "pivot" row arbitrarily (first row in col) */ pivot_row = A [Col [pivot_col].start] ; DEBUG3 (("Pivotal row is "ID"\n", pivot_row)) ; } else { /* there is no pivot row, since it is of zero length */ pivot_row = EMPTY ; ASSERT (pivot_row_length == 0) ; } ASSERT (Col [pivot_col].length > 0 || pivot_row_length == 0) ; /* === Approximate degree computation =============================== */ /* Here begins the computation of the approximate degree. The column */ /* score is the sum of the pivot row "length", plus the size of the */ /* set differences of each row in the column minus the pattern of the */ /* pivot row itself. The column ("thickness") itself is also */ /* excluded from the column score (we thus use an approximate */ /* external degree). */ /* The time taken by the following code (compute set differences, and */ /* add them up) is proportional to the size of the data structure */ /* being scanned - that is, the sum of the sizes of each column in */ /* the pivot row. Thus, the amortized time to compute a column score */ /* is proportional to the size of that column (where size, in this */ /* context, is the column "length", or the number of row indices */ /* in that column). The number of row indices in a column is */ /* monotonically non-decreasing, from the length of the original */ /* column on input to colamd. */ /* === Compute set differences ====================================== */ DEBUG3 (("** Computing set differences phase. **\n")) ; /* pivot row is currently dead - it will be revived later. */ DEBUG3 (("Pivot row: \n")) ; /* for each column in pivot row */ rp = &A [pivot_row_start] ; rp_end = rp + pivot_row_length ; while (rp < rp_end) { col = *rp++ ; ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ; DEBUG3 ((" Col: "ID"\n", col)) ; /* clear tags used to construct pivot row pattern */ col_thickness = -Col [col].shared1.thickness ; ASSERT (col_thickness > 0) ; Col [col].shared1.thickness = col_thickness ; /* === Remove column from degree list =========================== */ cur_score = Col [col].shared2.score ; prev_col = Col [col].shared3.prev ; next_col = Col [col].shared4.degree_next ; ASSERT (cur_score >= 0) ; ASSERT (cur_score <= n_col) ; ASSERT (cur_score >= EMPTY) ; if (prev_col == EMPTY) { head [cur_score] = next_col ; } else { Col [prev_col].shared4.degree_next = next_col ; } if (next_col != EMPTY) { Col [next_col].shared3.prev = prev_col ; } /* === Scan the column ========================================== */ cp = &A [Col [col].start] ; cp_end = cp + Col [col].length ; while (cp < cp_end) { /* get a row */ row = *cp++ ; row_mark = Row [row].shared2.mark ; /* skip if dead */ if (ROW_IS_MARKED_DEAD (row_mark)) { continue ; } ASSERT (row != pivot_row) ; set_difference = row_mark - tag_mark ; /* check if the row has been seen yet */ if (set_difference < 0) { ASSERT (Row [row].shared1.degree <= max_deg) ; set_difference = Row [row].shared1.degree ; } /* subtract column thickness from this row's set difference */ set_difference -= col_thickness ; ASSERT (set_difference >= 0) ; ASSERT (ROW_IS_ALIVE (row)) ; /* absorb this row if the set difference becomes zero */ if (set_difference == 0 && aggressive) { /* v4.1: do aggressive absorption */ DEBUG3 (("aggressive absorption. Row: "ID"\n", row)) ; if (Row [row].front != EMPTY) { /* Row [row].front is a child of current front. */ child = Row [row].front ; Front_parent [child] = nfr ; DEBUG1 (("Front "ID" => front "ID", aggressive\n", child, nfr)) ; } else { /* this is an original row. Keep track of which front * assembles it, for the row-merge tree */ InFront [row] = nfr ; DEBUG1 (("Row "ID" => front "ID", aggressive\n", row, nfr)) ; } KILL_ROW (row) ; /* sum the thicknesses of all the rows */ /* ASSERT (Row [row].thickness > 0) ; */ pivot_row_thickness += Row [row].thickness ; Row [row].thickness = 0 ; } else { /* save the new mark */ Row [row].shared2.mark = set_difference + tag_mark ; } } } #ifndef NDEBUG debug_deg_lists (n_row, n_col, Row, Col, head, min_score, n_col2-k-pivot_row_degree, max_deg) ; #endif /* NDEBUG */ /* === Add up set differences for each column ======================= */ DEBUG3 (("** Adding set differences phase. **\n")) ; /* for each column in pivot row */ rp = &A [pivot_row_start] ; rp_end = rp + pivot_row_length ; while (rp < rp_end) { /* get a column */ col = *rp++ ; ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ; hash = 0 ; cur_score = 0 ; cp = &A [Col [col].start] ; /* compact the column */ new_cp = cp ; cp_end = cp + Col [col].length ; DEBUG4 (("Adding set diffs for Col: "ID".\n", col)) ; while (cp < cp_end) { /* get a row */ row = *cp++ ; ASSERT(row >= 0 && row < n_row) ; row_mark = Row [row].shared2.mark ; /* skip if dead */ if (ROW_IS_MARKED_DEAD (row_mark)) { /* ------------------ */ /* changed for UMFPACK: */ DEBUG4 ((" Row "ID", dead\n", row)) ; /* ------------------ */ continue ; } /* ------------------ */ /* changed for UMFPACK: */ /* ASSERT (row_mark > tag_mark) ; */ DEBUG4 ((" Row "ID", set diff "ID"\n", row, row_mark-tag_mark)); ASSERT (row_mark >= tag_mark) ; /* ------------------ */ /* compact the column */ *new_cp++ = row ; /* compute hash function */ hash += row ; /* add set difference */ cur_score += row_mark - tag_mark ; /* integer overflow... */ cur_score = MIN (cur_score, n_col) ; } /* recompute the column's length */ Col [col].length = (Int) (new_cp - &A [Col [col].start]) ; /* === Further mass elimination ================================= */ if (Col [col].length == 0) { DEBUG4 (("further mass elimination. Col: "ID"\n", col)) ; /* nothing left but the pivot row in this column */ KILL_PRINCIPAL_COL (col) ; pivot_row_degree -= Col [col].shared1.thickness ; ASSERT (pivot_row_degree >= 0) ; /* order it */ Col [col].shared2.order = k ; /* increment order count by column thickness */ k += Col [col].shared1.thickness ; /* ------------------ */ /* added for UMFPACK: */ pivot_col_thickness += Col [col].shared1.thickness ; /* add to column list of front ... */ #ifndef NDEBUG DEBUG1 (("Mass")) ; dump_super (col, Col, n_col) ; #endif Col [Col [col].lastcol].nextcol = Front_cols [nfr] ; Front_cols [nfr] = col ; /* ------------------ */ } else { /* === Prepare for supercolumn detection ==================== */ DEBUG4 (("Preparing supercol detection for Col: "ID".\n", col)); /* save score so far */ Col [col].shared2.score = cur_score ; /* add column to hash table, for supercolumn detection */ /* NOTE: hash is an unsigned Int to avoid a problem in ANSI C. * The sign of the expression a % b is not defined when a and/or * b are negative. Since hash is unsigned and n_col >= 0, * this problem is avoided. */ hash %= n_col + 1 ; DEBUG4 ((" Hash = "ID", n_col = "ID".\n", (Int) hash, n_col)) ; ASSERT (((Int) hash) <= n_col) ; head_column = head [hash] ; if (head_column > EMPTY) { /* degree list "hash" is non-empty, use prev (shared3) of */ /* first column in degree list as head of hash bucket */ first_col = Col [head_column].shared3.headhash ; Col [head_column].shared3.headhash = col ; } else { /* degree list "hash" is empty, use head as hash bucket */ first_col = - (head_column + 2) ; head [hash] = - (col + 2) ; } Col [col].shared4.hash_next = first_col ; /* save hash function in Col [col].shared3.hash */ Col [col].shared3.hash = (Int) hash ; ASSERT (COL_IS_ALIVE (col)) ; } } /* The approximate external column degree is now computed. */ /* === Supercolumn detection ======================================== */ DEBUG3 (("** Supercolumn detection phase. **\n")) ; detect_super_cols ( #ifndef NDEBUG n_col, Row, #endif /* NDEBUG */ Col, A, head, pivot_row_start, pivot_row_length) ; /* === Kill the pivotal column ====================================== */ KILL_PRINCIPAL_COL (pivot_col) ; /* ------------------ */ /* added for UMFPACK: */ /* add columns to column list of front */ #ifndef NDEBUG DEBUG1 (("Pivot")) ; dump_super (pivot_col, Col, n_col) ; #endif Col [Col [pivot_col].lastcol].nextcol = Front_cols [nfr] ; Front_cols [nfr] = pivot_col ; /* ------------------ */ /* === Clear mark =================================================== */ tag_mark += (max_deg + 1) ; if (tag_mark >= max_mark) { DEBUG2 (("clearing tag_mark\n")) ; tag_mark = clear_mark (n_row, Row) ; } #ifndef NDEBUG DEBUG3 (("check3\n")) ; debug_mark (n_row, Row, tag_mark, max_mark) ; #endif /* NDEBUG */ /* === Finalize the new pivot row, and column scores ================ */ DEBUG3 (("** Finalize scores phase. **\n")) ; DEBUG3 (("pivot_row_degree "ID"\n", pivot_row_degree)) ; /* for each column in pivot row */ rp = &A [pivot_row_start] ; /* compact the pivot row */ new_rp = rp ; rp_end = rp + pivot_row_length ; while (rp < rp_end) { col = *rp++ ; DEBUG3 (("Col "ID" \n", col)) ; /* skip dead columns */ if (COL_IS_DEAD (col)) { DEBUG3 (("dead\n")) ; continue ; } *new_rp++ = col ; /* add new pivot row to column */ A [Col [col].start + (Col [col].length++)] = pivot_row ; /* retrieve score so far and add on pivot row's degree. */ /* (we wait until here for this in case the pivot */ /* row's degree was reduced due to mass elimination). */ cur_score = Col [col].shared2.score + pivot_row_degree ; DEBUG3 ((" cur_score "ID" ", cur_score)) ; /* calculate the max possible score as the number of */ /* external columns minus the 'k' value minus the */ /* columns thickness */ max_score = n_col - k - Col [col].shared1.thickness ; DEBUG3 ((" max_score "ID" ", max_score)) ; /* make the score the external degree of the union-of-rows */ cur_score -= Col [col].shared1.thickness ; DEBUG3 ((" cur_score "ID" ", cur_score)) ; /* make sure score is less or equal than the max score */ cur_score = MIN (cur_score, max_score) ; ASSERT (cur_score >= 0) ; /* store updated score */ Col [col].shared2.score = cur_score ; DEBUG3 ((" "ID"\n", cur_score)) ; /* === Place column back in degree list ========================= */ ASSERT (min_score >= 0) ; ASSERT (min_score <= n_col) ; ASSERT (cur_score >= 0) ; ASSERT (cur_score <= n_col) ; ASSERT (head [cur_score] >= EMPTY) ; next_col = head [cur_score] ; Col [col].shared4.degree_next = next_col ; Col [col].shared3.prev = EMPTY ; if (next_col != EMPTY) { Col [next_col].shared3.prev = col ; } head [cur_score] = col ; /* see if this score is less than current min */ min_score = MIN (min_score, cur_score) ; } #ifndef NDEBUG debug_deg_lists (n_row, n_col, Row, Col, head, min_score, n_col2-k, max_deg) ; #endif /* NDEBUG */ /* ------------------ */ /* added for UMFPACK: */ /* frontal matrix can have more pivot cols than pivot rows for */ /* singular matrices. */ /* number of candidate pivot columns */ Front_npivcol [nfr] = pivot_col_thickness ; /* all rows (not just size of contrib. block) */ Front_nrows [nfr] = pivot_row_thickness ; /* all cols */ Front_ncols [nfr] = pivot_col_thickness + pivot_row_degree ; Front_parent [nfr] = EMPTY ; pivot_row_thickness -= pivot_col_thickness ; DEBUG1 (("Front "ID" Pivot_row_thickness after pivot cols elim: "ID"\n", nfr, pivot_row_thickness)) ; pivot_row_thickness = MAX (0, pivot_row_thickness) ; /* ------------------ */ /* === Resurrect the new pivot row ================================== */ if (pivot_row_degree > 0 /* ------------------ */ /* added for UMFPACK. Note that this part of the expression should be * removed if this routine is used outside of UMFPACK, for a Cholesky * factorization of (AQ)'(AQ) */ && pivot_row_thickness > 0 /* ------------------ */ ) { /* update pivot row length to reflect any cols that were killed */ /* during super-col detection and mass elimination */ Row [pivot_row].start = pivot_row_start ; Row [pivot_row].length = (Int) (new_rp - &A[pivot_row_start]) ; ASSERT (Row [pivot_row].length > 0) ; Row [pivot_row].shared1.degree = pivot_row_degree ; Row [pivot_row].shared2.mark = 0 ; /* ------------------ */ /* added for UMFPACK: */ Row [pivot_row].thickness = pivot_row_thickness ; Row [pivot_row].front = nfr ; /* ------------------ */ /* pivot row is no longer dead */ } /* ------------------ */ /* added for UMFPACK: */ #ifndef NDEBUG DEBUG1 (("Front "ID" : "ID" "ID" "ID" ", nfr, Front_npivcol [nfr], Front_nrows [nfr], Front_ncols [nfr])) ; DEBUG1 ((" cols:[ ")) ; debug_d = 0 ; for (col = Front_cols [nfr] ; col != EMPTY ; col = Col [col].nextcol) { DEBUG1 ((" "ID, col)) ; ASSERT (col >= 0 && col < n_col) ; ASSERT (COL_IS_DEAD (col)) ; debug_d++ ; ASSERT (debug_d <= pivot_col_thickness) ; } ASSERT (debug_d == pivot_col_thickness) ; DEBUG1 ((" ]\n ")) ; #endif nfr++ ; /* one more front */ /* ------------------ */ } /* === All principal columns have now been ordered ====================== */ /* ------------------ */ /* added for UMFPACK: */ *p_nfr = nfr ; /* ------------------ */ return (ngarbage) ; } /* ========================================================================== */ /* === order_children deleted for UMFPACK =================================== */ /* ========================================================================== */ /* ========================================================================== */ /* === detect_super_cols ==================================================== */ /* ========================================================================== */ /* Detects supercolumns by finding matches between columns in the hash buckets. Check amongst columns in the set A [row_start ... row_start + row_length-1]. The columns under consideration are currently *not* in the degree lists, and have already been placed in the hash buckets. The hash bucket for columns whose hash function is equal to h is stored as follows: if head [h] is >= 0, then head [h] contains a degree list, so: head [h] is the first column in degree bucket h. Col [head [h]].headhash gives the first column in hash bucket h. otherwise, the degree list is empty, and: -(head [h] + 2) is the first column in hash bucket h. For a column c in a hash bucket, Col [c].shared3.prev is NOT a "previous column" pointer. Col [c].shared3.hash is used instead as the hash number for that column. The value of Col [c].shared4.hash_next is the next column in the same hash bucket. Assuming no, or "few" hash collisions, the time taken by this routine is linear in the sum of the sizes (lengths) of each column whose score has just been computed in the approximate degree computation. Not user-callable. */ PRIVATE void detect_super_cols ( /* === Parameters ======================================================= */ #ifndef NDEBUG /* these two parameters are only needed when debugging is enabled: */ Int n_col, /* number of columns of A */ Colamd_Row Row [], /* of size n_row+1 */ #endif /* NDEBUG */ Colamd_Col Col [], /* of size n_col+1 */ Int A [], /* row indices of A */ Int head [], /* head of degree lists and hash buckets */ Int row_start, /* pointer to set of columns to check */ Int row_length /* number of columns to check */ ) { /* === Local variables ================================================== */ Int hash ; /* hash value for a column */ Int *rp ; /* pointer to a row */ Int c ; /* a column index */ Int super_c ; /* column index of the column to absorb into */ Int *cp1 ; /* column pointer for column super_c */ Int *cp2 ; /* column pointer for column c */ Int length ; /* length of column super_c */ Int prev_c ; /* column preceding c in hash bucket */ Int i ; /* loop counter */ Int *rp_end ; /* pointer to the end of the row */ Int col ; /* a column index in the row to check */ Int head_column ; /* first column in hash bucket or degree list */ Int first_col ; /* first column in hash bucket */ /* === Consider each column in the row ================================== */ rp = &A [row_start] ; rp_end = rp + row_length ; while (rp < rp_end) { col = *rp++ ; if (COL_IS_DEAD (col)) { continue ; } /* get hash number for this column */ hash = Col [col].shared3.hash ; ASSERT (hash <= n_col) ; /* === Get the first column in this hash bucket ===================== */ head_column = head [hash] ; if (head_column > EMPTY) { first_col = Col [head_column].shared3.headhash ; } else { first_col = - (head_column + 2) ; } /* === Consider each column in the hash bucket ====================== */ for (super_c = first_col ; super_c != EMPTY ; super_c = Col [super_c].shared4.hash_next) { ASSERT (COL_IS_ALIVE (super_c)) ; ASSERT (Col [super_c].shared3.hash == hash) ; length = Col [super_c].length ; /* prev_c is the column preceding column c in the hash bucket */ prev_c = super_c ; /* === Compare super_c with all columns after it ================ */ for (c = Col [super_c].shared4.hash_next ; c != EMPTY ; c = Col [c].shared4.hash_next) { ASSERT (c != super_c) ; ASSERT (COL_IS_ALIVE (c)) ; ASSERT (Col [c].shared3.hash == hash) ; /* not identical if lengths or scores are different */ if (Col [c].length != length || Col [c].shared2.score != Col [super_c].shared2.score) { prev_c = c ; continue ; } /* compare the two columns */ cp1 = &A [Col [super_c].start] ; cp2 = &A [Col [c].start] ; for (i = 0 ; i < length ; i++) { /* the columns are "clean" (no dead rows) */ ASSERT (ROW_IS_ALIVE (*cp1)) ; ASSERT (ROW_IS_ALIVE (*cp2)) ; /* row indices will same order for both supercols, */ /* no gather scatter nessasary */ if (*cp1++ != *cp2++) { break ; } } /* the two columns are different if the for-loop "broke" */ if (i != length) { prev_c = c ; continue ; } /* === Got it! two columns are identical =================== */ ASSERT (Col [c].shared2.score == Col [super_c].shared2.score) ; Col [super_c].shared1.thickness += Col [c].shared1.thickness ; Col [c].shared1.parent = super_c ; KILL_NON_PRINCIPAL_COL (c) ; Col [c].shared2.order = EMPTY ; /* remove c from hash bucket */ Col [prev_c].shared4.hash_next = Col [c].shared4.hash_next ; /* ------------------ */ /* added for UMFPACK: */ /* add c to end of list of super_c */ ASSERT (Col [super_c].lastcol >= 0) ; ASSERT (Col [super_c].lastcol < n_col) ; Col [Col [super_c].lastcol].nextcol = c ; Col [super_c].lastcol = Col [c].lastcol ; #ifndef NDEBUG /* dump the supercolumn */ DEBUG1 (("Super")) ; dump_super (super_c, Col, n_col) ; #endif /* ------------------ */ } } /* === Empty this hash bucket ======================================= */ if (head_column > EMPTY) { /* corresponding degree list "hash" is not empty */ Col [head_column].shared3.headhash = EMPTY ; } else { /* corresponding degree list "hash" is empty */ head [hash] = EMPTY ; } } } /* ========================================================================== */ /* === garbage_collection =================================================== */ /* ========================================================================== */ /* Defragments and compacts columns and rows in the workspace A. Used when all avaliable memory has been used while performing row merging. Returns the index of the first free position in A, after garbage collection. The time taken by this routine is linear is the size of the array A, which is itself linear in the number of nonzeros in the input matrix. Not user-callable. */ PRIVATE Int garbage_collection /* returns the new value of pfree */ ( /* === Parameters ======================================================= */ Int n_row, /* number of rows */ Int n_col, /* number of columns */ Colamd_Row Row [], /* row info */ Colamd_Col Col [], /* column info */ Int A [], /* A [0 ... Alen-1] holds the matrix */ Int *pfree /* &A [0] ... pfree is in use */ ) { /* === Local variables ================================================== */ Int *psrc ; /* source pointer */ Int *pdest ; /* destination pointer */ Int j ; /* counter */ Int r ; /* a row index */ Int c ; /* a column index */ Int length ; /* length of a row or column */ #ifndef NDEBUG Int debug_rows ; DEBUG2 (("Defrag..\n")) ; for (psrc = &A[0] ; psrc < pfree ; psrc++) ASSERT (*psrc >= 0) ; debug_rows = 0 ; #endif /* NDEBUG */ /* === Defragment the columns =========================================== */ pdest = &A[0] ; for (c = 0 ; c < n_col ; c++) { if (COL_IS_ALIVE (c)) { psrc = &A [Col [c].start] ; /* move and compact the column */ ASSERT (pdest <= psrc) ; Col [c].start = (Int) (pdest - &A [0]) ; length = Col [c].length ; for (j = 0 ; j < length ; j++) { r = *psrc++ ; if (ROW_IS_ALIVE (r)) { *pdest++ = r ; } } Col [c].length = (Int) (pdest - &A [Col [c].start]) ; } } /* === Prepare to defragment the rows =================================== */ for (r = 0 ; r < n_row ; r++) { if (ROW_IS_ALIVE (r)) { if (Row [r].length == 0) { /* :: defrag row kill :: */ /* This row is of zero length. cannot compact it, so kill it. * NOTE: in the current version, there are no zero-length live * rows when garbage_collection is called. So this code will * never trigger. However, if the code is modified, or if * garbage_collection is called at a different place, then rows * can be of zero length. So this test is kept, just in case. */ DEBUGm4 (("Defrag row kill\n")) ; KILL_ROW (r) ; } else { /* save first column index in Row [r].shared2.first_column */ psrc = &A [Row [r].start] ; Row [r].shared2.first_column = *psrc ; ASSERT (ROW_IS_ALIVE (r)) ; /* flag the start of the row with the one's complement of row */ *psrc = ONES_COMPLEMENT (r) ; #ifndef NDEBUG debug_rows++ ; #endif /* NDEBUG */ } } } /* === Defragment the rows ============================================== */ psrc = pdest ; while (psrc < pfree) { /* find a negative number ... the start of a row */ if (*psrc++ < 0) { psrc-- ; /* get the row index */ r = ONES_COMPLEMENT (*psrc) ; ASSERT (r >= 0 && r < n_row) ; /* restore first column index */ *psrc = Row [r].shared2.first_column ; ASSERT (ROW_IS_ALIVE (r)) ; /* move and compact the row */ ASSERT (pdest <= psrc) ; Row [r].start = (Int) (pdest - &A [0]) ; length = Row [r].length ; for (j = 0 ; j < length ; j++) { c = *psrc++ ; if (COL_IS_ALIVE (c)) { *pdest++ = c ; } } Row [r].length = (Int) (pdest - &A [Row [r].start]) ; #ifndef NDEBUG debug_rows-- ; #endif /* NDEBUG */ } } /* ensure we found all the rows */ ASSERT (debug_rows == 0) ; /* === Return the new value of pfree ==================================== */ return ((Int) (pdest - &A [0])) ; } /* ========================================================================== */ /* === clear_mark =========================================================== */ /* ========================================================================== */ /* Clears the Row [].shared2.mark array, and returns the new tag_mark. Return value is the new tag_mark. Not user-callable. */ PRIVATE Int clear_mark /* return the new value for tag_mark */ ( /* === Parameters ======================================================= */ Int n_row, /* number of rows in A */ Colamd_Row Row [] /* Row [0 ... n-1].shared2.mark is set to zero */ ) { /* === Local variables ================================================== */ Int r ; for (r = 0 ; r < n_row ; r++) { if (ROW_IS_ALIVE (r)) { Row [r].shared2.mark = 0 ; } } /* ------------------ */ return (1) ; /* ------------------ */ } /* ========================================================================== */ /* === print_report removed for UMFPACK ===================================== */ /* ========================================================================== */ /* ========================================================================== */ /* === colamd debugging routines ============================================ */ /* ========================================================================== */ /* When debugging is disabled, the remainder of this file is ignored. */ #ifndef NDEBUG /* ========================================================================== */ /* === debug_structures ===================================================== */ /* ========================================================================== */ /* At this point, all empty rows and columns are dead. All live columns are "clean" (containing no dead rows) and simplicial (no supercolumns yet). Rows may contain dead columns, but all live rows contain at least one live column. */ PRIVATE void debug_structures ( /* === Parameters ======================================================= */ Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int A [], Int n_col2 ) { /* === Local variables ================================================== */ Int i ; Int c ; Int *cp ; Int *cp_end ; Int len ; Int score ; Int r ; Int *rp ; Int *rp_end ; Int deg ; /* === Check A, Row, and Col ============================================ */ for (c = 0 ; c < n_col ; c++) { if (COL_IS_ALIVE (c)) { len = Col [c].length ; score = Col [c].shared2.score ; DEBUG4 (("initial live col "ID" "ID" "ID"\n", c, len, score)) ; ASSERT (len > 0) ; ASSERT (score >= 0) ; ASSERT (Col [c].shared1.thickness == 1) ; cp = &A [Col [c].start] ; cp_end = cp + len ; while (cp < cp_end) { r = *cp++ ; ASSERT (ROW_IS_ALIVE (r)) ; } } else { i = Col [c].shared2.order ; ASSERT (i >= n_col2 && i < n_col) ; } } for (r = 0 ; r < n_row ; r++) { if (ROW_IS_ALIVE (r)) { i = 0 ; len = Row [r].length ; deg = Row [r].shared1.degree ; ASSERT (len > 0) ; ASSERT (deg > 0) ; rp = &A [Row [r].start] ; rp_end = rp + len ; while (rp < rp_end) { c = *rp++ ; if (COL_IS_ALIVE (c)) { i++ ; } } ASSERT (i > 0) ; } } } /* ========================================================================== */ /* === debug_deg_lists ====================================================== */ /* ========================================================================== */ /* Prints the contents of the degree lists. Counts the number of columns in the degree list and compares it to the total it should have. Also checks the row degrees. */ PRIVATE void debug_deg_lists ( /* === Parameters ======================================================= */ Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int head [], Int min_score, Int should, Int max_deg ) { /* === Local variables ================================================== */ Int deg ; Int col ; Int have ; Int row ; /* === Check the degree lists =========================================== */ if (n_col > 10000 && UMF_debug <= 0) { return ; } have = 0 ; DEBUG4 (("Degree lists: "ID"\n", min_score)) ; for (deg = 0 ; deg <= n_col ; deg++) { col = head [deg] ; if (col == EMPTY) { continue ; } DEBUG4 ((ID":", deg)) ; while (col != EMPTY) { DEBUG4 ((" "ID, col)) ; have += Col [col].shared1.thickness ; ASSERT (COL_IS_ALIVE (col)) ; col = Col [col].shared4.degree_next ; } DEBUG4 (("\n")) ; } DEBUG4 (("should "ID" have "ID"\n", should, have)) ; ASSERT (should == have) ; /* === Check the row degrees ============================================ */ if (n_row > 10000 && UMF_debug <= 0) { return ; } for (row = 0 ; row < n_row ; row++) { if (ROW_IS_ALIVE (row)) { ASSERT (Row [row].shared1.degree <= max_deg) ; } } } /* ========================================================================== */ /* === debug_mark =========================================================== */ /* ========================================================================== */ /* Ensures that the tag_mark is less that the maximum and also ensures that each entry in the mark array is less than the tag mark. */ PRIVATE void debug_mark ( /* === Parameters ======================================================= */ Int n_row, Colamd_Row Row [], Int tag_mark, Int max_mark ) { /* === Local variables ================================================== */ Int r ; /* === Check the Row marks ============================================== */ ASSERT (tag_mark > 0 && tag_mark <= max_mark) ; if (n_row > 10000 && UMF_debug <= 0) { return ; } for (r = 0 ; r < n_row ; r++) { ASSERT (Row [r].shared2.mark < tag_mark) ; } } /* ========================================================================== */ /* === debug_matrix ========================================================= */ /* ========================================================================== */ /* Prints out the contents of the columns and the rows. */ PRIVATE void debug_matrix ( /* === Parameters ======================================================= */ Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int A [] ) { /* === Local variables ================================================== */ Int r ; Int c ; Int *rp ; Int *rp_end ; Int *cp ; Int *cp_end ; /* === Dump the rows and columns of the matrix ========================== */ if (UMF_debug < 3) { return ; } DEBUG3 (("DUMP MATRIX:\n")) ; for (r = 0 ; r < n_row ; r++) { DEBUG3 (("Row "ID" alive? %d\n", r, ROW_IS_ALIVE (r))) ; if (ROW_IS_DEAD (r)) { continue ; } /* ------------------ */ /* changed for UMFPACK: */ DEBUG3 (("start "ID" length "ID" degree "ID" thickness "ID"\n", Row [r].start, Row [r].length, Row [r].shared1.degree, Row [r].thickness)) ; /* ------------------ */ rp = &A [Row [r].start] ; rp_end = rp + Row [r].length ; while (rp < rp_end) { c = *rp++ ; DEBUG4 ((" %d col "ID"\n", COL_IS_ALIVE (c), c)) ; } } for (c = 0 ; c < n_col ; c++) { DEBUG3 (("Col "ID" alive? %d\n", c, COL_IS_ALIVE (c))) ; if (COL_IS_DEAD (c)) { continue ; } /* ------------------ */ /* changed for UMFPACK: */ DEBUG3 (("start "ID" length "ID" shared1[thickness,parent] "ID " shared2 [order,score] "ID"\n", Col [c].start, Col [c].length, Col [c].shared1.thickness, Col [c].shared2.score)); /* ------------------ */ cp = &A [Col [c].start] ; cp_end = cp + Col [c].length ; while (cp < cp_end) { r = *cp++ ; DEBUG4 ((" %d row "ID"\n", ROW_IS_ALIVE (r), r)) ; } /* ------------------ */ /* added for UMFPACK: */ DEBUG1 (("Col")) ; dump_super (c, Col, n_col) ; /* ------------------ */ } } /* ------------------ */ /* dump_super added for UMFPACK: */ PRIVATE void dump_super ( Int super_c, Colamd_Col Col [], Int n_col ) { Int col, ncols ; DEBUG1 ((" =[ ")) ; ncols = 0 ; for (col = super_c ; col != EMPTY ; col = Col [col].nextcol) { DEBUG1 ((" "ID, col)) ; ASSERT (col >= 0 && col < n_col) ; if (col != super_c) { ASSERT (COL_IS_DEAD (col)) ; } if (Col [col].nextcol == EMPTY) { ASSERT (col == Col [super_c].lastcol) ; } ncols++ ; ASSERT (ncols <= Col [super_c].shared1.thickness) ; } ASSERT (ncols == Col [super_c].shared1.thickness) ; DEBUG1 (("]\n")) ; } /* ------------------ */ #endif /* NDEBUG */ SuiteSparse/UMFPACK/Source/umf_colamd.h0000644001170100242450000002175710617161444016574 0ustar davisfac/* ========================================================================== */ /* === umf_colamd.h ========================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Authors: The authors of the COLAMD code itself are Stefan I. Larimore and Timothy A. Davis, University of Florida. The algorithm was developed in collaboration with John Gilbert, Xerox PARC, and Esmond Ng, Oak Ridge National Laboratory. Date: UMFPACK Version: see above. COLAMD Version 2.0 was released on January 31, 2000. Acknowledgements: This work was supported by the National Science Foundation, under grants DMS-9504974, DMS-9803599, and CCR-0203270. UMFPACK: Copyright (c) 2003 by Timothy A. Davis. All Rights Reserved. See the UMFPACK README file for the License for your use of this code. Availability: Both UMFPACK and the original unmodified colamd/symamd library are available at http://www.cise.ufl.edu/research/sparse. */ #ifndef COLAMD_H #define COLAMD_H /* ========================================================================== */ /* === Include files ======================================================== */ /* ========================================================================== */ #include /* ========================================================================== */ /* === Knob and statistics definitions ====================================== */ /* ========================================================================== */ /* size of the knobs [ ] array. Only knobs [0..2] are currently used. */ #define COLAMD_KNOBS 20 /* number of output statistics. Only stats [0..8] are currently used. */ #define COLAMD_STATS 20 /* knobs [0] and stats [0]: dense row knob and output statistic. */ #define COLAMD_DENSE_ROW 0 /* knobs [1] and stats [1]: dense column knob and output statistic. */ #define COLAMD_DENSE_COL 1 /* knobs [2]: aggressive absorption option */ #define COLAMD_AGGRESSIVE 2 /* stats [2]: memory defragmentation count output statistic */ #define COLAMD_DEFRAG_COUNT 2 /* stats [3]: colamd status: zero OK, > 0 warning or notice, < 0 error */ #define COLAMD_STATUS 3 /* stats [4..6]: error info, or info on jumbled columns */ #define COLAMD_INFO1 4 #define COLAMD_INFO2 5 #define COLAMD_INFO3 6 /* ------------------ */ /* added for UMFPACK: */ /* stats [7]: number of originally empty rows */ #define COLAMD_EMPTY_ROW 7 /* stats [8]: number of originally empty cols */ #define COLAMD_EMPTY_COL 8 /* stats [9]: number of rows with entries only in dense cols */ #define COLAMD_NEWLY_EMPTY_ROW 9 /* stats [10]: number of cols with entries only in dense rows */ #define COLAMD_NEWLY_EMPTY_COL 10 /* ------------------ */ /* error codes returned in stats [3]: */ #define COLAMD_OK (0) #define COLAMD_ERROR_jumbled_matrix (-11) #define COLAMD_ERROR_A_not_present (-1) #define COLAMD_ERROR_p_not_present (-2) #define COLAMD_ERROR_nrow_negative (-3) #define COLAMD_ERROR_ncol_negative (-4) #define COLAMD_ERROR_nnz_negative (-5) #define COLAMD_ERROR_p0_nonzero (-6) #define COLAMD_ERROR_A_too_small (-7) #define COLAMD_ERROR_col_length_negative (-8) #define COLAMD_ERROR_row_index_out_of_bounds (-9) #define COLAMD_ERROR_out_of_memory (-10) #define COLAMD_ERROR_internal_error (-999) /* ========================================================================== */ /* === Row and Column structures ============================================ */ /* ========================================================================== */ /* User code that makes use of the colamd/symamd routines need not directly */ /* reference these structures. They are used only for the COLAMD_RECOMMENDED */ /* macro. */ typedef struct Colamd_Col_struct { Int start ; /* index for A of first row in this column, or DEAD */ /* if column is dead */ Int length ; /* number of rows in this column */ union { Int thickness ; /* number of original columns represented by this */ /* col, if the column is alive */ Int parent ; /* parent in parent tree super-column structure, if */ /* the column is dead */ } shared1 ; union { Int score ; /* the score used to maintain heap, if col is alive */ Int order ; /* pivot ordering of this column, if col is dead */ } shared2 ; union { Int headhash ; /* head of a hash bucket, if col is at the head of */ /* a degree list */ Int hash ; /* hash value, if col is not in a degree list */ Int prev ; /* previous column in degree list, if col is in a */ /* degree list (but not at the head of a degree list) */ } shared3 ; union { Int degree_next ; /* next column, if col is in a degree list */ Int hash_next ; /* next column, if col is in a hash list */ } shared4 ; /* ------------------ */ /* added for UMFPACK: */ Int nextcol ; /* next column in this supercolumn */ Int lastcol ; /* last column in this supercolumn */ /* ------------------ */ } Colamd_Col ; typedef struct Colamd_Row_struct { Int start ; /* index for A of first col in this row */ Int length ; /* number of principal columns in this row */ union { Int degree ; /* number of principal & non-principal columns in row */ Int p ; /* used as a row pointer in init_rows_cols () */ } shared1 ; union { Int mark ; /* for computing set differences and marking dead rows*/ Int first_column ;/* first column in row (used in garbage collection) */ } shared2 ; /* ------------------ */ /* added for UMFPACK: */ Int thickness ; /* number of original rows represented by this row */ /* that are not yet pivotal */ Int front ; /* -1 if an original row */ /* k if this row represents the kth frontal matrix */ /* where k goes from 0 to at most n_col-1 */ /* ------------------ */ } Colamd_Row ; /* ========================================================================== */ /* === Colamd recommended memory size ======================================= */ /* ========================================================================== */ /* The recommended length Alen of the array A passed to colamd is given by the COLAMD_RECOMMENDED (nnz, n_row, n_col) macro. It returns -1 if any argument is negative. 2*nnz space is required for the row and column indices of the matrix. COLAMD_C (n_col) + COLAMD_R (n_row) space is required for the Col and Row arrays, respectively, which are internal to colamd. An additional n_col space is the minimal amount of "elbow room", and nnz/5 more space is recommended for run time efficiency. This macro is not needed when using symamd. */ /* about 8*(n_col+1) integers: */ #define UMF_COLAMD_C(n_col) ((n_col + 1) * sizeof (Colamd_Col) / sizeof (Int)) /* about 6*(n_row+1) integers: */ #define UMF_COLAMD_R(n_row) ((n_row + 1) * sizeof (Colamd_Row) / sizeof (Int)) /* UMFPACK: make sure Alen is >= 5*n_col + size of Col and Row structures. * Alen is typically about 2.2*nz + 9*n_col + 6*n_row, or 2.2nz+15n for * square matrices. */ #define UMF_COLAMD_RECOMMENDED(nnz, n_row, n_col) \ ( \ ((nnz) < 0 || (n_row) < 0 || (n_col) < 0) \ ? \ (-1) \ : \ (MAX (2 * (nnz), 4 * (n_col)) + \ (Int) UMF_COLAMD_C (n_col) + \ (Int) UMF_COLAMD_R (n_row) + (n_col) + ((nnz) / 5)) \ ) /* ========================================================================== */ /* === Prototypes of user-callable routines ================================= */ /* ========================================================================== */ /* colamd_recommended removed for UMFPACK */ void UMF_colamd_set_defaults /* sets default parameters */ ( /* knobs argument is modified on output */ double knobs [COLAMD_KNOBS] /* parameter settings for colamd */ ) ; Int UMF_colamd /* returns (1) if successful, (0) otherwise*/ ( /* A and p arguments are modified on output */ Int n_row, /* number of rows in A */ Int n_col, /* number of columns in A */ Int Alen, /* size of the array A */ Int A [], /* row indices of A, of size Alen */ Int p [], /* column pointers of A, of size n_col+1 */ double knobs [COLAMD_KNOBS],/* parameter settings for colamd */ Int stats [COLAMD_STATS] /* colamd output statistics and error codes */ /* ------------------ */ /* added for UMFPACK: */ , Int Front_npivcol [ ] , Int Front_nrows [ ] , Int Front_ncols [ ] , Int Front_parent [ ] , Int Front_cols [ ] , Int *p_nfr , Int InFront [ ] /* ------------------ */ ) ; /* symamd deleted for UMFPACK */ /* colamd_report deleted for UMFPACK */ /* symamd_report deleted for UMFPACK */ #endif /* COLAMD_H */ SuiteSparse/UMFPACK/Source/umfpack_report_vector.c0000644001170100242450000000231710617162142021047 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_report_vector ================================================ */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Prints a real or complex vector. See umfpack_report_vector.h for details. */ #include "umf_internal.h" #include "umf_report_vector.h" GLOBAL Int UMFPACK_report_vector ( Int n, const double Xx [ ], #ifdef COMPLEX const double Xz [ ], #endif const double Control [UMFPACK_CONTROL] ) { Int prl ; #ifndef COMPLEX double *Xz = (double *) NULL ; #endif prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ; if (prl <= 2) { return (UMFPACK_OK) ; } return (UMF_report_vector (n, Xx, Xz, prl, TRUE, FALSE)) ; } SuiteSparse/UMFPACK/Source/umfpack_free_numeric.c0000644001170100242450000000360610617162040020614 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_free_numeric ================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Free the entire Numeric object (consists of 11 to 13 * malloc'd objects. See UMFPACK_free_numeric.h for details. */ #include "umf_internal.h" #include "umf_free.h" GLOBAL void UMFPACK_free_numeric ( void **NumericHandle ) { NumericType *Numeric ; if (!NumericHandle) { return ; } Numeric = *((NumericType **) NumericHandle) ; if (!Numeric) { return ; } /* these 9 objects always exist */ (void) UMF_free ((void *) Numeric->D) ; (void) UMF_free ((void *) Numeric->Rperm) ; (void) UMF_free ((void *) Numeric->Cperm) ; (void) UMF_free ((void *) Numeric->Lpos) ; (void) UMF_free ((void *) Numeric->Lilen) ; (void) UMF_free ((void *) Numeric->Lip) ; (void) UMF_free ((void *) Numeric->Upos) ; (void) UMF_free ((void *) Numeric->Uilen) ; (void) UMF_free ((void *) Numeric->Uip) ; /* Rs does not exist if scaling was not performed */ (void) UMF_free ((void *) Numeric->Rs) ; /* Upattern can only exist for singular or rectangular matrices */ (void) UMF_free ((void *) Numeric->Upattern) ; /* these 2 objects always exist */ (void) UMF_free ((void *) Numeric->Memory) ; (void) UMF_free ((void *) Numeric) ; *NumericHandle = (void *) NULL ; } SuiteSparse/UMFPACK/Source/umf_lsolve.c0000644001170100242450000001022410677541674016634 0ustar davisfac/* ========================================================================== */ /* === UMF_lsolve =========================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* solves Lx = b, where L is the lower triangular factor of a matrix */ /* B is overwritten with the solution X. */ /* Returns the floating point operation count */ #include "umf_internal.h" #include "umf_lsolve.h" GLOBAL double UMF_lsolve ( NumericType *Numeric, Entry X [ ], /* b on input, solution x on output */ Int Pattern [ ] /* a work array of size n */ ) { Entry xk ; Entry *xp, *Lval ; Int k, deg, *ip, j, row, *Lpos, *Lilen, *Lip, llen, lp, newLchain, pos, npiv, n1, *Li ; /* ---------------------------------------------------------------------- */ if (Numeric->n_row != Numeric->n_col) return (0.) ; npiv = Numeric->npiv ; Lpos = Numeric->Lpos ; Lilen = Numeric->Lilen ; Lip = Numeric->Lip ; n1 = Numeric->n1 ; #ifndef NDEBUG DEBUG4 (("Lsolve start:\n")) ; for (j = 0 ; j < Numeric->n_row ; j++) { DEBUG4 (("Lsolve start "ID": ", j)) ; EDEBUG4 (X [j]) ; DEBUG4 (("\n")) ; } #endif /* ---------------------------------------------------------------------- */ /* singletons */ /* ---------------------------------------------------------------------- */ for (k = 0 ; k < n1 ; k++) { DEBUG4 (("Singleton k "ID"\n", k)) ; xk = X [k] ; deg = Lilen [k] ; if (deg > 0 && IS_NONZERO (xk)) { lp = Lip [k] ; Li = (Int *) (Numeric->Memory + lp) ; lp += UNITS (Int, deg) ; Lval = (Entry *) (Numeric->Memory + lp) ; for (j = 0 ; j < deg ; j++) { DEBUG4 ((" row "ID" k "ID" value", Li [j], k)) ; EDEBUG4 (Lval [j]) ; DEBUG4 (("\n")) ; /* X [Li [j]] -= xk * Lval [j] ; */ MULT_SUB (X [Li [j]], xk, Lval [j]) ; } } } /* ---------------------------------------------------------------------- */ /* rest of L */ /* ---------------------------------------------------------------------- */ deg = 0 ; for (k = n1 ; k < npiv ; k++) { /* ------------------------------------------------------------------ */ /* make column of L in Pattern [0..deg-1] */ /* ------------------------------------------------------------------ */ lp = Lip [k] ; newLchain = (lp < 0) ; if (newLchain) { lp = -lp ; deg = 0 ; DEBUG4 (("start of chain for column of L\n")) ; } /* remove pivot row */ pos = Lpos [k] ; if (pos != EMPTY) { DEBUG4 ((" k "ID" removing row "ID" at position "ID"\n", k, Pattern [pos], pos)) ; ASSERT (!newLchain) ; ASSERT (deg > 0) ; ASSERT (pos >= 0 && pos < deg) ; ASSERT (Pattern [pos] == k) ; Pattern [pos] = Pattern [--deg] ; } /* concatenate the pattern */ ip = (Int *) (Numeric->Memory + lp) ; llen = Lilen [k] ; for (j = 0 ; j < llen ; j++) { row = *ip++ ; DEBUG4 ((" row "ID" k "ID"\n", row, k)) ; ASSERT (row > k) ; Pattern [deg++] = row ; } /* ------------------------------------------------------------------ */ /* use column k of L */ /* ------------------------------------------------------------------ */ xk = X [k] ; if (IS_NONZERO (xk)) { xp = (Entry *) (Numeric->Memory + lp + UNITS (Int, llen)) ; for (j = 0 ; j < deg ; j++) { DEBUG4 ((" row "ID" k "ID" value", Pattern [j], k)) ; EDEBUG4 (*xp) ; DEBUG4 (("\n")) ; /* X [Pattern [j]] -= xk * (*xp) ; */ MULT_SUB (X [Pattern [j]], xk, *xp) ; xp++ ; } } } #ifndef NDEBUG for (j = 0 ; j < Numeric->n_row ; j++) { DEBUG4 (("Lsolve done "ID": ", j)) ; EDEBUG4 (X [j]) ; DEBUG4 (("\n")) ; } DEBUG4 (("Lsolve done.\n")) ; #endif return (MULTSUB_FLOPS * ((double) Numeric->lnz)) ; } SuiteSparse/UMFPACK/Source/umf_lsolve.h0000644001170100242450000000076410617161712016632 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL double UMF_lsolve ( NumericType *Numeric, Entry X [ ], Int Pattern [ ] ) ; SuiteSparse/UMFPACK/Source/umf_tuple_lengths.c0000644001170100242450000001054010677542460020200 0ustar davisfac/* ========================================================================== */ /* === UMF_tuple_lengths ==================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Determine the tuple list lengths, and the amount of memory required for */ /* them. Return the amount of memory needed to store all the tuples. */ /* This routine assumes that the tuple lists themselves are either already */ /* deallocated, or will be shortly (so Row[ ].tlen and Col[ ].tlen are */ /* overwritten) */ #include "umf_internal.h" #include "umf_tuple_lengths.h" GLOBAL Int UMF_tuple_lengths /* return memory usage */ ( NumericType *Numeric, WorkType *Work, double *p_dusage /* output argument */ ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ double dusage ; Int e, nrows, ncols, nel, i, *Rows, *Cols, row, col, n_row, n_col, *E, *Row_degree, *Row_tlen, *Col_degree, *Col_tlen, usage, n1 ; Element *ep ; Unit *p ; /* ---------------------------------------------------------------------- */ /* get parameters */ /* ---------------------------------------------------------------------- */ E = Work->E ; Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro only */ Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro only */ Row_tlen = Numeric->Uilen ; Col_tlen = Numeric->Lilen ; n_row = Work->n_row ; n_col = Work->n_col ; n1 = Work->n1 ; nel = Work->nel ; DEBUG3 (("TUPLE_LENGTHS: n_row "ID" n_col "ID" nel "ID"\n", n_row, n_col, nel)) ; ASSERT (nel < Work->elen) ; /* tuple list lengths already initialized to zero */ /* ---------------------------------------------------------------------- */ /* scan each element: count tuple list lengths (include element 0) */ /* ---------------------------------------------------------------------- */ for (e = 1 ; e <= nel ; e++) /* for all elements, in any order */ { if (E [e]) { #ifndef NDEBUG UMF_dump_element (Numeric, Work, e, FALSE) ; #endif p = Numeric->Memory + E [e] ; GET_ELEMENT_PATTERN (ep, p, Cols, Rows, ncols) ; nrows = ep->nrows ; for (i = 0 ; i < nrows ; i++) { row = Rows [i] ; ASSERT (row == EMPTY || (row >= n1 && row < n_row)) ; if (row >= n1) { ASSERT (NON_PIVOTAL_ROW (row)) ; Row_tlen [row] ++ ; } } for (i = 0 ; i < ncols ; i++) { col = Cols [i] ; ASSERT (col == EMPTY || (col >= n1 && col < n_col)) ; if (col >= n1) { ASSERT (NON_PIVOTAL_COL (col)) ; Col_tlen [col] ++ ; } } } } /* note: tuple lengths are now modified, but the tuple lists are not */ /* updated to reflect that fact. */ /* ---------------------------------------------------------------------- */ /* determine the required memory to hold all the tuple lists */ /* ---------------------------------------------------------------------- */ DEBUG0 (("UMF_build_tuples_usage\n")) ; usage = 0 ; dusage = 0 ; ASSERT (Col_tlen && Col_degree) ; for (col = n1 ; col < n_col ; col++) { if (NON_PIVOTAL_COL (col)) { usage += 1 + UNITS (Tuple, TUPLES (Col_tlen [col])) ; dusage += 1 + DUNITS (Tuple, TUPLES (Col_tlen [col])) ; DEBUG0 ((" col: "ID" tlen "ID" usage so far: "ID"\n", col, Col_tlen [col], usage)) ; } } ASSERT (Row_tlen && Row_degree) ; for (row = n1 ; row < n_row ; row++) { if (NON_PIVOTAL_ROW (row)) { usage += 1 + UNITS (Tuple, TUPLES (Row_tlen [row])) ; dusage += 1 + DUNITS (Tuple, TUPLES (Row_tlen [row])) ; DEBUG0 ((" row: "ID" tlen "ID" usage so far: "ID"\n", row, Row_tlen [row], usage)) ; } } DEBUG0 (("UMF_build_tuples_usage "ID" %g\n", usage, dusage)) ; *p_dusage = dusage ; return (usage) ; } SuiteSparse/UMFPACK/Source/umf_tuple_lengths.h0000644001170100242450000000077210617162467020212 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_tuple_lengths ( NumericType *Numeric, WorkType *Work, double *dusage ) ; SuiteSparse/UMFPACK/Source/umf_config.h0000644001170100242450000002762710617161450016601 0ustar davisfac/* ========================================================================== */ /* === umf_config.h ========================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* This file controls the compile-time configuration of UMFPACK. Modify the UFconfig/UFconfig.mk file and this file if necessary, to control these options. The following flags may be given as options to your C compiler (as in "cc -DNSUNPERF", for example). These flags are normally placed in your UMFPACK_CONFIG string, defined in the UFconfig/UFconfig.mk file. All of these options, except for the timer, are for accessing the BLAS. -DNSUNPERF Applies only to Sun Solaris. If -DNSUNPERF is set, then the Sun Performance Library BLAS will not be used. The Sun Performance Library BLAS is used by default when compiling the C-callable libumfpack.a library on Sun Solaris. -DLONGBLAS -DNPOSIX If -DNPOSIX is set, then your Unix operating system is not POSIX- compliant, and the POSIX routines sysconf ( ) and times ( ) routines are not used. These routines provide CPU time and wallclock time information. If -DNPOSIX is set, then the ANSI C clock ( ) routine is used. If -DNPOSIX is not set, then sysconf ( ) and times ( ) are used in umfpack_tic and umfpack_toc. See umfpack_tictoc.c for more information. The default is to use the POSIX routines, except for Windows, which is not POSIX-compliant. -DGETRUSAGE If -DGETRUSAGE is set, then your system's getrusage ( ) routine will be used for getting the process CPU time. Otherwise the ANSI C clock ( ) routine will be used. The default is to use getrusage ( ) on Unix systems, and to use clock on all other architectures. -DNO_TIMER If -DNO_TIMER is set, then no timing routines are used at all. -DNRECIPROCAL This option controls a tradeoff between speed and accuracy. Using -DNRECIPROCAL can lead to more accurate results, but with perhaps some cost in performance, particularly if floating-point division is much more costly than floating-point multiplication. This option determines the method used to scale the pivot column. If set, or if the absolute value of the pivot is < 1e-12 (or is a NaN), then the pivot column is divided by the pivot value. Otherwise, the reciprocal of the pivot value is computed, and the pivot column is multiplied by (1/pivot). Multiplying by the reciprocal can be slightly less accurate than dividing by the pivot, but it is often faster. See umf_scale.c. This has a small effect on the performance of UMFPACK, at least on a Pentium 4M. It may have a larger effect on other architectures where floating-point division is much more costly than floating- point multiplication. The RS 6000 is one such example. By default, the method chosen is to multiply by the reciprocal (sacrificing accuracy for speed), except when compiling UMFPACK as a built-in routine in MATLAB, or when gcc is being used. When MATHWORKS is defined, -DNRECIPROCAL is forced on, and the pivot column is divided by the pivot value. The only way of using the other method in this case is to edit this file. If -DNRECIPROCAL is enabled, then the row scaling factors are always applied by dividing each row by the scale factor, rather than multiplying by the reciprocal. If -DNRECIPROCAL is not enabled (the default case), then the scale factors are normally applied by multiplying by the reciprocal. If, however, the smallest scale factor is tiny, then the scale factors are applied via division. -DNO_DIVIDE_BY_ZERO If the pivot is zero, and this flag is set, then no divide-by-zero occurs. The following options are controlled by amd_internal.h: -DMATLAB_MEX_FILE This flag is turned on when compiling the umfpack mexFunction for use in MATLAB. The -DNRECIPROCAL flag is forced on (more accurate, slightly slower). The umfpack mexFunction always returns L*U = P*(R\A)*Q. -DMATHWORKS This flag is turned on when compiling umfpack as a built-in routine in MATLAB. The -DNRECIPROCAL flag is forced on. -DNDEBUG Debugging mode (if NDEBUG is not defined). The default, of course, is no debugging. Turning on debugging takes some work (see below). If you do not edit this file, then debugging is turned off anyway, regardless of whether or not -DNDEBUG is specified in your compiler options. */ /* ========================================================================== */ /* === AMD configuration ==================================================== */ /* ========================================================================== */ /* NDEBUG, PRINTF defined in amd_internal.h */ /* ========================================================================== */ /* === reciprocal option ==================================================== */ /* ========================================================================== */ /* Force the definition NRECIPROCAL when MATHWORKS or MATLAB_MEX_FILE * are defined. Do not multiply by the reciprocal in those cases. */ #ifndef NRECIPROCAL #if defined (MATHWORKS) || defined (MATLAB_MEX_FILE) #define NRECIPROCAL #endif #endif /* ========================================================================== */ /* === Microsoft Windows configuration ====================================== */ /* ========================================================================== */ #if defined (UMF_WINDOWS) || defined (UMF_MINGW) /* Windows isn't Unix. Profound. */ #define NPOSIX #endif /* ========================================================================== */ /* === 0-based or 1-based printing ========================================== */ /* ========================================================================== */ #if defined (MATLAB_MEX_FILE) && defined (NDEBUG) /* In MATLAB, matrices are 1-based to the user, but 0-based internally. */ /* One is added to all row and column indices when printing matrices */ /* for the MATLAB user. The +1 shift is turned off when debugging. */ #define INDEX(i) ((i)+1) #else /* In ANSI C, matrices are 0-based and indices are reported as such. */ /* This mode is also used for debug mode, and if MATHWORKS is defined rather */ /* than MATLAB_MEX_FILE. */ #define INDEX(i) (i) #endif /* ========================================================================== */ /* === Timer ================================================================ */ /* ========================================================================== */ /* If you have the getrusage routine (all Unix systems I've test do), then use that. Otherwise, use the ANSI C clock function. Note that on many systems, the ANSI clock function wraps around after only 2147 seconds, or about 36 minutes. BE CAREFUL: if you compare the run time of UMFPACK with other sparse matrix packages, be sure to use the same timer. See umfpack_tictoc.c for the timer used internally by UMFPACK. See also umfpack_timer.c for the timer used in an earlier version of UMFPACK. That timer is still available as a user-callable routine, but it is no longer used internally by UMFPACK. */ /* Sun Solaris, SGI Irix, Linux, Compaq Alpha, and IBM RS 6000 all have */ /* getrusage. It's in BSD unix, so perhaps all unix systems have it. */ #if defined (UMF_SOL2) || defined (UMF_SGI) || defined (UMF_LINUX) \ || defined (UMF_ALPHA) || defined (UMF_AIX) || defined (UMF_CYGWIN) #define GETRUSAGE #endif /* ========================================================================== */ /* === BLAS ================================================================= */ /* ========================================================================== */ #include "cholmod_blas.h" /* -------------------------------------------------------------------------- */ /* DGEMM */ /* -------------------------------------------------------------------------- */ /* C = C - A*B', where: * A is m-by-k with leading dimension ldac * B is k-by-n with leading dimension ldb * C is m-by-n with leading dimension ldac */ #ifdef COMPLEX #define BLAS_GEMM(m,n,k,A,B,ldb,C,ldac) \ { \ double alpha [2] = {-1,0}, beta [2] = {1,0} ; \ BLAS_zgemm ("N", "T", m, n, k, alpha, (double *) A, ldac, \ (double *) B, ldb, beta, (double *) C, ldac) ; \ } #else #define BLAS_GEMM(m,n,k,A,B,ldb,C,ldac) \ { \ double alpha = -1, beta = 1 ; \ BLAS_dgemm ("N", "T", m, n, k, &alpha, A, ldac, B, ldb, &beta, C, ldac) ; \ } #endif /* -------------------------------------------------------------------------- */ /* GER */ /* -------------------------------------------------------------------------- */ /* A = A - x*y', where: * A is m-by-n with leading dimension d x is a column vector with stride 1 y is a column vector with stride 1 */ #ifdef COMPLEX #define BLAS_GER(m,n,x,y,A,d) \ { \ double alpha [2] = {-1,0} ; \ BLAS_zgeru (m, n, alpha, (double *) x, 1, (double *) y, 1, \ (double *) A, d) ; \ } #else #define BLAS_GER(m,n,x,y,A,d) \ { \ double alpha = -1 ; \ BLAS_dger (m, n, &alpha, x, 1, y, 1, A, d) ; \ } #endif /* -------------------------------------------------------------------------- */ /* GEMV */ /* -------------------------------------------------------------------------- */ /* y = y - A*x, where A is m-by-n with leading dimension d, x is a column vector with stride 1 y is a column vector with stride 1 */ #ifdef COMPLEX #define BLAS_GEMV(m,n,A,x,y,d) \ { \ double alpha [2] = {-1,0}, beta [2] = {1,0} ; \ BLAS_zgemv ("N", m, n, alpha, (double *) A, d, (double *) x, 1, beta, \ (double *) y, 1) ; \ } #else #define BLAS_GEMV(m,n,A,x,y,d) \ { \ double alpha = -1, beta = 1 ; \ BLAS_dgemv ("N", m, n, &alpha, A, d, x, 1, &beta, y, 1) ; \ } #endif /* -------------------------------------------------------------------------- */ /* TRSV */ /* -------------------------------------------------------------------------- */ /* solve Lx=b, where: * B is a column vector (m-by-1) with leading dimension d * A is m-by-m with leading dimension d */ #ifdef COMPLEX #define BLAS_TRSV(m,A,b,d) \ { \ BLAS_ztrsv ("L", "N", "U", m, (double *) A, d, (double *) b, 1) ; \ } #else #define BLAS_TRSV(m,A,b,d) \ { \ BLAS_dtrsv ("L", "N", "U", m, A, d, b, 1) ; \ } #endif /* -------------------------------------------------------------------------- */ /* TRSM */ /* -------------------------------------------------------------------------- */ /* solve XL'=B where: * B is m-by-n with leading dimension ldb * A is n-by-n with leading dimension lda */ #ifdef COMPLEX #define BLAS_TRSM_RIGHT(m,n,A,lda,B,ldb) \ { \ double alpha [2] = {1,0} ; \ BLAS_ztrsm ("R", "L", "T", "U", m, n, alpha, (double *) A, lda, \ (double *) B, ldb) ; \ } #else #define BLAS_TRSM_RIGHT(m,n,A,lda,B,ldb) \ { \ double alpha = 1 ; \ BLAS_dtrsm ("R", "L", "T", "U", m, n, &alpha, A, lda, B, ldb) ; \ } #endif /* -------------------------------------------------------------------------- */ /* SCAL */ /* -------------------------------------------------------------------------- */ /* x = s*x, where x is a stride-1 vector of length n */ #ifdef COMPLEX #define BLAS_SCAL(n,s,x) \ { \ double alpha [2] ; \ alpha [0] = REAL_COMPONENT (s) ; \ alpha [1] = IMAG_COMPONENT (s) ; \ BLAS_zscal (n, alpha, (double *) x, 1) ; \ } #else #define BLAS_SCAL(n,s,x) \ { \ double alpha = REAL_COMPONENT (s) ; \ BLAS_dscal (n, &alpha, (double *) x, 1) ; \ } #endif SuiteSparse/UMFPACK/Source/umfpack_qsymbolic.c0000644001170100242450000023226010617162101020151 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_qsymbolic ==================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Performs a symbolic factorization. See umfpack_qsymbolic.h and umfpack_symbolic.h for details. Dynamic memory usage: about (3.4nz + 8n + n) integers and n double's as workspace (via UMF_malloc, for a square matrix). All of it is free'd via UMF_free if an error occurs. If successful, the Symbolic object contains 12 to 14 objects allocated by UMF_malloc, with a total size of no more than about 13*n integers. */ #include "umf_internal.h" #include "umf_symbolic_usage.h" #include "umf_colamd.h" #include "umf_set_stats.h" #include "umf_analyze.h" #include "umf_transpose.h" #include "umf_is_permutation.h" #include "umf_malloc.h" #include "umf_free.h" #include "umf_2by2.h" #include "umf_singletons.h" typedef struct /* SWType */ { Int *Front_npivcol ; /* size n_col + 1 */ Int *Front_nrows ; /* size n_col */ Int *Front_ncols ; /* size n_col */ Int *Front_parent ; /* size n_col */ Int *Front_cols ; /* size n_col */ Int *InFront ; /* size n_row */ Int *Ci ; /* size Clen */ Int *Cperm1 ; /* size n_col */ Int *Rperm1 ; /* size n_row */ Int *InvRperm1 ; /* size n_row */ Int *Si ; /* size nz */ Int *Sp ; /* size n_col + 1 */ double *Rs ; /* size n_row */ Int *Rperm_2by2 ; /* size n_row */ } SWType ; PRIVATE void free_work ( SWType *SW ) ; PRIVATE void error ( SymbolicType **Symbolic, SWType *SW ) ; /* worst-case usage for SW object */ #define SYM_WORK_USAGE(n_col,n_row,Clen) \ (DUNITS (Int, Clen) + \ DUNITS (Int, nz) + \ 4 * DUNITS (Int, n_row) + \ 4 * DUNITS (Int, n_col) + \ 2 * DUNITS (Int, n_col + 1) + \ DUNITS (double, n_row)) /* required size of Ci for code that calls UMF_transpose and UMF_analyze below*/ #define UMF_ANALYZE_CLEN(nz,n_row,n_col,nn) \ ((n_col) + MAX ((nz),(n_col)) + 3*(nn)+1 + (n_col)) /* size of an element (in Units), including tuples */ #define ELEMENT_SIZE(r,c) \ (DGET_ELEMENT_SIZE (r, c) + 1 + (r + c) * UNITS (Tuple, 1)) #ifndef NDEBUG PRIVATE Int init_count ; #endif /* ========================================================================== */ /* === do_amd =============================================================== */ /* ========================================================================== */ PRIVATE void do_amd ( Int n, const Int Ap [ ], /* size n+1 */ const Int Ai [ ], /* size nz = Ap [n] */ Int Q [ ], /* output permutation, j = Q [k] */ Int Qinv [ ], /* output inverse permutation, Qinv [j] = k */ Int Sdeg [ ], /* degree of A+A', from AMD_aat */ Int Clen, /* size of Ci */ Int Ci [ ], /* size Ci workspace */ double amd_Control [ ], /* AMD control parameters */ double amd_Info [ ], /* AMD info */ SymbolicType *Symbolic, /* Symbolic object */ double Info [ ] /* UMFPACK info */ ) { if (n == 0) { Symbolic->amd_dmax = 0 ; Symbolic->amd_lunz = 0 ; Info [UMFPACK_SYMMETRIC_LUNZ] = 0 ; Info [UMFPACK_SYMMETRIC_FLOPS] = 0 ; Info [UMFPACK_SYMMETRIC_DMAX] = 0 ; Info [UMFPACK_SYMMETRIC_NDENSE] = 0 ; } else { AMD_1 (n, Ap, Ai, Q, Qinv, Sdeg, Clen, Ci, amd_Control, amd_Info) ; /* return estimates computed from AMD on PA+PA' */ Symbolic->amd_dmax = amd_Info [AMD_DMAX] ; Symbolic->amd_lunz = 2 * amd_Info [AMD_LNZ] + n ; Info [UMFPACK_SYMMETRIC_LUNZ] = Symbolic->amd_lunz ; Info [UMFPACK_SYMMETRIC_FLOPS] = DIV_FLOPS * amd_Info [AMD_NDIV] + MULTSUB_FLOPS * amd_Info [AMD_NMULTSUBS_LU] ; Info [UMFPACK_SYMMETRIC_DMAX] = Symbolic->amd_dmax ; Info [UMFPACK_SYMMETRIC_NDENSE] = amd_Info [AMD_NDENSE] ; Info [UMFPACK_SYMBOLIC_DEFRAG] += amd_Info [AMD_NCMPA] ; } } /* ========================================================================== */ /* === prune_singletons ===================================================== */ /* ========================================================================== */ /* Create the submatrix after removing the n1 singletons. The matrix has * row and column indices in the range 0 to n_row-n1 and 0 to n_col-n1, * respectively. */ PRIVATE Int prune_singletons ( Int n1, Int n_col, const Int Ap [ ], const Int Ai [ ], const double Ax [ ], #ifdef COMPLEX const double Az [ ], #endif Int Cperm1 [ ], Int InvRperm1 [ ], Int Si [ ], Int Sp [ ] #ifndef NDEBUG , Int Rperm1 [ ] , Int n_row #endif ) { Int row, k, pp, p, oldcol, newcol, newrow, nzdiag, do_nzdiag ; #ifdef COMPLEX Int split = SPLIT (Az) ; #endif nzdiag = 0 ; do_nzdiag = (Ax != (double *) NULL) ; #ifndef NDEBUG DEBUGm4 (("Prune : S = A (Cperm1 (n1+1:end), Rperm1 (n1+1:end))\n")) ; for (k = 0 ; k < n_row ; k++) { ASSERT (Rperm1 [k] >= 0 && Rperm1 [k] < n_row) ; ASSERT (InvRperm1 [Rperm1 [k]] == k) ; } #endif /* create the submatrix after removing singletons */ pp = 0 ; for (k = n1 ; k < n_col ; k++) { oldcol = Cperm1 [k] ; newcol = k - n1 ; DEBUG5 (("Prune singletons k "ID" oldcol "ID" newcol "ID": "ID"\n", k, oldcol, newcol, pp)) ; Sp [newcol] = pp ; /* load column pointers */ for (p = Ap [oldcol] ; p < Ap [oldcol+1] ; p++) { row = Ai [p] ; DEBUG5 ((" "ID": row "ID, pp, row)) ; ASSERT (row >= 0 && row < n_row) ; newrow = InvRperm1 [row] - n1 ; ASSERT (newrow < n_row - n1) ; if (newrow >= 0) { DEBUG5 ((" newrow "ID, newrow)) ; Si [pp++] = newrow ; if (do_nzdiag) { /* count the number of truly nonzero entries on the * diagonal of S, excluding entries that are present, * but numerically zero */ if (newrow == newcol) { /* this is the diagonal entry */ #ifdef COMPLEX if (split) { if (SCALAR_IS_NONZERO (Ax [p]) || SCALAR_IS_NONZERO (Az [p])) { nzdiag++ ; } } else { if (SCALAR_IS_NONZERO (Ax [2*p ]) || SCALAR_IS_NONZERO (Ax [2*p+1])) { nzdiag++ ; } } #else if (SCALAR_IS_NONZERO (Ax [p])) { nzdiag++ ; } #endif } } } DEBUG5 (("\n")) ; } } Sp [n_col - n1] = pp ; return (nzdiag) ; } /* ========================================================================== */ /* === combine_ordering ===================================================== */ /* ========================================================================== */ PRIVATE void combine_ordering ( Int n1, Int nempty_col, Int n_col, Int Cperm_init [ ], /* output permutation */ Int Cperm1 [ ], /* singleton and empty column ordering */ Int Qinv [ ] /* Qinv from AMD or COLAMD */ ) { Int k, oldcol, newcol, knew ; /* combine the singleton ordering with Qinv */ #ifndef NDEBUG for (k = 0 ; k < n_col ; k++) { Cperm_init [k] = EMPTY ; } #endif for (k = 0 ; k < n1 ; k++) { DEBUG1 ((ID" Initial singleton: "ID"\n", k, Cperm1 [k])) ; Cperm_init [k] = Cperm1 [k] ; } for (k = n1 ; k < n_col - nempty_col ; k++) { /* this is a non-singleton column */ oldcol = Cperm1 [k] ; /* user's name for this column */ newcol = k - n1 ; /* Qinv's name for this column */ knew = Qinv [newcol] ; /* Qinv's ordering for this column */ knew += n1 ; /* shift order, after singletons */ DEBUG1 ((" k "ID" oldcol "ID" newcol "ID" knew "ID"\n", k, oldcol, newcol, knew)) ; ASSERT (knew >= 0 && knew < n_col - nempty_col) ; ASSERT (Cperm_init [knew] == EMPTY) ; Cperm_init [knew] = oldcol ; } for (k = n_col - nempty_col ; k < n_col ; k++) { Cperm_init [k] = Cperm1 [k] ; } #ifndef NDEBUG { Int *W = (Int *) malloc ((n_col + 1) * sizeof (Int)) ; ASSERT (UMF_is_permutation (Cperm_init, W, n_col, n_col)) ; free (W) ; } #endif } /* ========================================================================== */ /* === UMFPACK_qsymbolic ==================================================== */ /* ========================================================================== */ GLOBAL Int UMFPACK_qsymbolic ( Int n_row, Int n_col, const Int Ap [ ], const Int Ai [ ], const double Ax [ ], #ifdef COMPLEX const double Az [ ], #endif const Int Quser [ ], void **SymbolicHandle, const double Control [UMFPACK_CONTROL], double User_Info [UMFPACK_INFO] ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ double knobs [COLAMD_KNOBS], flops, f, r, c, force_fixQ, Info2 [UMFPACK_INFO], drow, dcol, dtail_usage, dlf, duf, dmax_usage, dhead_usage, dlnz, dunz, dmaxfrsize, dClen, dClen_analyze, sym, amd_Info [AMD_INFO], dClen_amd, dr, dc, cr, cc, cp, amd_Control [AMD_CONTROL], stats [2], tol ; double *Info ; Int i, nz, j, newj, status, f1, f2, maxnrows, maxncols, nfr, col, nchains, maxrows, maxcols, p, nb, nn, *Chain_start, *Chain_maxrows, *Chain_maxcols, *Front_npivcol, *Ci, Clen, colamd_stats [COLAMD_STATS], fpiv, n_inner, child, parent, *Link, row, *Front_parent, analyze_compactions, k, chain, is_sym, *Si, *Sp, n2, do_UMF_analyze, fpivcol, fallrows, fallcols, *InFront, *F1, snz, *Front_1strow, f1rows, kk, *Cperm_init, *Rperm_init, newrow, *InvRperm1, *Front_leftmostdesc, Clen_analyze, strategy, Clen_amd, fixQ, prefer_diagonal, nzdiag, nzaat, *Wq, *Sdeg, *Fr_npivcol, nempty, *Fr_nrows, *Fr_ncols, *Fr_parent, *Fr_cols, nempty_row, nempty_col, user_auto_strategy, fail, max_rdeg, head_usage, tail_usage, lnz, unz, esize, *Esize, rdeg, *Cdeg, *Rdeg, *Cperm1, *Rperm1, n1, oldcol, newcol, n1c, n1r, *Rperm_2by2, oldrow, dense_row_threshold, tlen, aggressive, scale, *Rp, *Ri ; SymbolicType *Symbolic ; SWType SWspace, *SW ; #ifndef NDEBUG UMF_dump_start ( ) ; init_count = UMF_malloc_count ; PRINTF (( "**** Debugging enabled (UMFPACK will be exceedingly slow!) *****************\n" )) ; #endif /* ---------------------------------------------------------------------- */ /* get the amount of time used by the process so far */ /* ---------------------------------------------------------------------- */ umfpack_tic (stats) ; /* ---------------------------------------------------------------------- */ /* get control settings and check input parameters */ /* ---------------------------------------------------------------------- */ drow = GET_CONTROL (UMFPACK_DENSE_ROW, UMFPACK_DEFAULT_DENSE_ROW) ; dcol = GET_CONTROL (UMFPACK_DENSE_COL, UMFPACK_DEFAULT_DENSE_COL) ; nb = GET_CONTROL (UMFPACK_BLOCK_SIZE, UMFPACK_DEFAULT_BLOCK_SIZE) ; strategy = GET_CONTROL (UMFPACK_STRATEGY, UMFPACK_DEFAULT_STRATEGY) ; tol = GET_CONTROL (UMFPACK_2BY2_TOLERANCE, UMFPACK_DEFAULT_2BY2_TOLERANCE) ; scale = GET_CONTROL (UMFPACK_SCALE, UMFPACK_DEFAULT_SCALE) ; force_fixQ = GET_CONTROL (UMFPACK_FIXQ, UMFPACK_DEFAULT_FIXQ) ; AMD_defaults (amd_Control) ; amd_Control [AMD_DENSE] = GET_CONTROL (UMFPACK_AMD_DENSE, UMFPACK_DEFAULT_AMD_DENSE) ; aggressive = (GET_CONTROL (UMFPACK_AGGRESSIVE, UMFPACK_DEFAULT_AGGRESSIVE) != 0) ; amd_Control [AMD_AGGRESSIVE] = aggressive ; nb = MAX (2, nb) ; nb = MIN (nb, MAXNB) ; ASSERT (nb >= 0) ; if (nb % 2 == 1) nb++ ; /* make sure nb is even */ DEBUG0 (("UMFPACK_qsymbolic: nb = "ID" aggressive = "ID"\n", nb, aggressive)) ; tol = MAX (0.0, MIN (tol, 1.0)) ; if (scale != UMFPACK_SCALE_NONE && scale != UMFPACK_SCALE_MAX) { scale = UMFPACK_DEFAULT_SCALE ; } if (User_Info != (double *) NULL) { /* return Info in user's array */ Info = User_Info ; } else { /* no Info array passed - use local one instead */ Info = Info2 ; } /* clear all of Info */ for (i = 0 ; i < UMFPACK_INFO ; i++) { Info [i] = EMPTY ; } nn = MAX (n_row, n_col) ; n_inner = MIN (n_row, n_col) ; Info [UMFPACK_STATUS] = UMFPACK_OK ; Info [UMFPACK_NROW] = n_row ; Info [UMFPACK_NCOL] = n_col ; Info [UMFPACK_SIZE_OF_UNIT] = (double) (sizeof (Unit)) ; Info [UMFPACK_SIZE_OF_INT] = (double) (sizeof (int)) ; Info [UMFPACK_SIZE_OF_LONG] = (double) (sizeof (UF_long)) ; Info [UMFPACK_SIZE_OF_POINTER] = (double) (sizeof (void *)) ; Info [UMFPACK_SIZE_OF_ENTRY] = (double) (sizeof (Entry)) ; Info [UMFPACK_SYMBOLIC_DEFRAG] = 0 ; if (!Ai || !Ap || !SymbolicHandle) { Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ; return (UMFPACK_ERROR_argument_missing) ; } *SymbolicHandle = (void *) NULL ; if (n_row <= 0 || n_col <= 0) /* n_row, n_col must be > 0 */ { Info [UMFPACK_STATUS] = UMFPACK_ERROR_n_nonpositive ; return (UMFPACK_ERROR_n_nonpositive) ; } nz = Ap [n_col] ; DEBUG0 (("n_row "ID" n_col "ID" nz "ID"\n", n_row, n_col, nz)) ; Info [UMFPACK_NZ] = nz ; if (nz < 0) { Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_matrix ; return (UMFPACK_ERROR_invalid_matrix) ; } /* ---------------------------------------------------------------------- */ /* get the requested strategy */ /* ---------------------------------------------------------------------- */ if (n_row != n_col) { /* if the matrix is rectangular, the only available strategy is * unsymmetric */ strategy = UMFPACK_STRATEGY_UNSYMMETRIC ; DEBUGm3 (("Rectangular: forcing unsymmetric strategy\n")) ; } if (strategy < UMFPACK_STRATEGY_AUTO || strategy > UMFPACK_STRATEGY_SYMMETRIC) { /* unrecognized strategy */ strategy = UMFPACK_STRATEGY_AUTO ; } if (Quser != (Int *) NULL) { /* when the user provides Q, only symmetric and unsymmetric strategies * are available */ if (strategy == UMFPACK_STRATEGY_2BY2) { strategy = UMFPACK_STRATEGY_SYMMETRIC ; } if (strategy != UMFPACK_STRATEGY_SYMMETRIC) { strategy = UMFPACK_STRATEGY_UNSYMMETRIC ; } } user_auto_strategy = (strategy == UMFPACK_STRATEGY_AUTO) ; /* ---------------------------------------------------------------------- */ /* determine amount of memory required for UMFPACK_symbolic */ /* ---------------------------------------------------------------------- */ /* The size of Clen required for UMF_colamd is always larger than */ /* UMF_analyze, but the max is included here in case that changes in */ /* future versions. */ /* This is about 2.2*nz + 9*n_col + 6*n_row, or nz/5 + 13*n_col + 6*n_row, * whichever is bigger. For square matrices, it works out to * 2.2nz + 15n, or nz/5 + 19n, whichever is bigger (typically 2.2nz+15n). */ dClen = UMF_COLAMD_RECOMMENDED ((double) nz, (double) n_row, (double) n_col) ; /* This is defined above, as max (nz,n_col) + 3*nn+1 + 2*n_col, where * nn = max (n_row,n_col). It is always smaller than the space required * for colamd or amd. */ dClen_analyze = UMF_ANALYZE_CLEN ((double) nz, (double) n_row, (double) n_col, (double) nn) ; dClen = MAX (dClen, dClen_analyze) ; /* The space for AMD can be larger than what's required for colamd: */ dClen_amd = 2.4 * (double) nz + 8 * (double) n_inner ; /* additional space for the 2-by-2 strategy */ dClen_amd += (double) MAX (nn, nz) ; dClen = MAX (dClen, dClen_amd) ; /* worst case total memory usage for UMFPACK_symbolic (revised below) */ Info [UMFPACK_SYMBOLIC_PEAK_MEMORY] = SYM_WORK_USAGE (n_col, n_row, dClen) + UMF_symbolic_usage (n_row, n_col, n_col, n_col, n_col, TRUE) ; if (INT_OVERFLOW (dClen * sizeof (Int))) { /* :: int overflow, Clen too large :: */ /* Problem is too large for array indexing (Ci [i]) with an Int i. */ /* Cannot even analyze the problem to determine upper bounds on */ /* memory usage. Need to use the UF_long version, umfpack_*l_*. */ DEBUGm4 (("out of memory: symbolic int overflow\n")) ; Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; return (UMFPACK_ERROR_out_of_memory) ; } /* repeat the size calculations, in integers */ Clen = UMF_COLAMD_RECOMMENDED (nz, n_row, n_col) ; Clen_analyze = UMF_ANALYZE_CLEN (nz, n_row, n_col, nn) ; Clen = MAX (Clen, Clen_analyze) ; Clen_amd = 2.4 * nz + 8 * n_inner ; Clen_amd += MAX (nn, nz) ; /* for Ri, in UMF_2by2 */ Clen = MAX (Clen, Clen_amd) ; /* ---------------------------------------------------------------------- */ /* allocate the first part of the Symbolic object (header and Cperm_init) */ /* ---------------------------------------------------------------------- */ /* (1) Five calls to UMF_malloc are made, for a total space of * 2 * (n_row + n_col) + 4 integers + sizeof (SymbolicType). * sizeof (SymbolicType) is a small constant. This space is part of the * Symbolic object and is not freed unless an error occurs. If A is square * then this is about 4*n integers. */ Symbolic = (SymbolicType *) UMF_malloc (1, sizeof (SymbolicType)) ; if (!Symbolic) { /* If we fail here, Symbolic is NULL and thus it won't be */ /* dereferenced by UMFPACK_free_symbolic, as called by error ( ). */ DEBUGm4 (("out of memory: symbolic object\n")) ; Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; error (&Symbolic, (SWType *) NULL) ; return (UMFPACK_ERROR_out_of_memory) ; } /* We now know that Symbolic has been allocated */ Symbolic->valid = 0 ; Symbolic->Chain_start = (Int *) NULL ; Symbolic->Chain_maxrows = (Int *) NULL ; Symbolic->Chain_maxcols = (Int *) NULL ; Symbolic->Front_npivcol = (Int *) NULL ; Symbolic->Front_parent = (Int *) NULL ; Symbolic->Front_1strow = (Int *) NULL ; Symbolic->Front_leftmostdesc = (Int *) NULL ; Symbolic->Esize = (Int *) NULL ; Symbolic->esize = 0 ; Symbolic->Cperm_init = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ; Symbolic->Rperm_init = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ; Symbolic->Cdeg = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ; Symbolic->Rdeg = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ; Symbolic->Diagonal_map = (Int *) NULL ; Cperm_init = Symbolic->Cperm_init ; Rperm_init = Symbolic->Rperm_init ; Cdeg = Symbolic->Cdeg ; Rdeg = Symbolic->Rdeg ; if (!Cperm_init || !Rperm_init || !Cdeg || !Rdeg) { DEBUGm4 (("out of memory: symbolic perm\n")) ; Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; error (&Symbolic, (SWType *) NULL) ; return (UMFPACK_ERROR_out_of_memory) ; } Symbolic->n_row = n_row ; Symbolic->n_col = n_col ; Symbolic->nz = nz ; Symbolic->nb = nb ; /* ---------------------------------------------------------------------- */ /* check user's input permutation */ /* ---------------------------------------------------------------------- */ if (Quser != (Int *) NULL) { /* use Cperm_init as workspace to check input permutation */ if (!UMF_is_permutation (Quser, Cperm_init, n_col, n_col)) { Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_permutation ; error (&Symbolic, (SWType *) NULL) ; return (UMFPACK_ERROR_invalid_permutation) ; } } /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* (2) Eleven calls to UMF_malloc are made, for workspace of size * Clen + nz + 7*n_col + 2*n_row + 2 integers. Clen is the larger of * MAX (2*nz, 4*n_col) + 8*n_col + 6*n_row + n_col + nz/5 and * 2.4*nz + 8 * MIN (n_row, n_col) + MAX (n_row, n_col, nz) * If A is square and non-singular, then Clen is * MAX (MAX (2*nz, 4*n) + 7*n + nz/5, 3.4*nz) + 8*n * If A has at least 4*n nonzeros then Clen is * MAX (2.2*nz + 7*n, 3.4*nz) + 8*n * If A has at least (7/1.2)*n nonzeros, (about 5.8*n), then Clen is * 3.4*nz + 8*n * This space will be free'd when this routine finishes. * * Total space thus far is about 3.4nz + 12n integers. * For the double precision, 32-bit integer version, the user's matrix * requires an equivalent space of 3*nz + n integers. So this space is just * slightly larger than the user's input matrix (including the numerical * values themselves). */ SW = &SWspace ; /* used for UMFPACK_symbolic only */ /* Note that SW->Front_* does not include the dummy placeholder front. */ /* This space is accounted for by the SYM_WORK_USAGE macro. */ /* this is free'd early */ SW->Si = (Int *) UMF_malloc (nz, sizeof (Int)) ; SW->Sp = (Int *) UMF_malloc (n_col + 1, sizeof (Int)) ; SW->InvRperm1 = (Int *) UMF_malloc (n_row, sizeof (Int)) ; SW->Cperm1 = (Int *) UMF_malloc (n_col, sizeof (Int)) ; /* this is free'd late */ SW->Ci = (Int *) UMF_malloc (Clen, sizeof (Int)) ; SW->Front_npivcol = (Int *) UMF_malloc (n_col + 1, sizeof (Int)) ; SW->Front_nrows = (Int *) UMF_malloc (n_col, sizeof (Int)) ; SW->Front_ncols = (Int *) UMF_malloc (n_col, sizeof (Int)) ; SW->Front_parent = (Int *) UMF_malloc (n_col, sizeof (Int)) ; SW->Front_cols = (Int *) UMF_malloc (n_col, sizeof (Int)) ; SW->Rperm1 = (Int *) UMF_malloc (n_row, sizeof (Int)) ; SW->InFront = (Int *) UMF_malloc (n_row, sizeof (Int)) ; /* this is allocated later, and free'd after Cperm1 but before Ci */ SW->Rperm_2by2 = (Int *) NULL ; /* will be nn Int's */ /* this is allocated last, and free'd first */ SW->Rs = (double *) NULL ; /* will be n_row double's */ Ci = SW->Ci ; Fr_npivcol = SW->Front_npivcol ; Fr_nrows = SW->Front_nrows ; Fr_ncols = SW->Front_ncols ; Fr_parent = SW->Front_parent ; Fr_cols = SW->Front_cols ; Cperm1 = SW->Cperm1 ; Rperm1 = SW->Rperm1 ; Si = SW->Si ; Sp = SW->Sp ; InvRperm1 = SW->InvRperm1 ; Rperm_2by2 = (Int *) NULL ; InFront = SW->InFront ; if (!Ci || !Fr_npivcol || !Fr_nrows || !Fr_ncols || !Fr_parent || !Fr_cols || !Cperm1 || !Rperm1 || !Si || !Sp || !InvRperm1 || !InFront) { DEBUGm4 (("out of memory: symbolic work\n")) ; Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; error (&Symbolic, SW) ; return (UMFPACK_ERROR_out_of_memory) ; } DEBUG0 (("Symbolic UMF_malloc_count - init_count = "ID"\n", UMF_malloc_count - init_count)) ; ASSERT (UMF_malloc_count == init_count + 17) ; /* ---------------------------------------------------------------------- */ /* find the row and column singletons */ /* ---------------------------------------------------------------------- */ /* [ use first nz + n_row + MAX (n_row, n_col) entries in Ci as workspace, * and use Rperm_init as workspace */ ASSERT (Clen >= nz + n_row + MAX (n_row, n_col)) ; status = UMF_singletons (n_row, n_col, Ap, Ai, Quser, strategy, Cdeg, Cperm1, Rdeg, Rperm1, InvRperm1, &n1, &n1c, &n1r, &nempty_col, &nempty_row, &is_sym, &max_rdeg, /* workspace: */ Rperm_init, Ci, Ci + nz, Ci + nz + n_row) ; /* ] done using Rperm_init and Ci as workspace */ /* InvRperm1 is now the inverse of Rperm1 */ if (status != UMFPACK_OK) { DEBUGm4 (("matrix invalid: UMF_singletons\n")) ; Info [UMFPACK_STATUS] = status ; error (&Symbolic, SW) ; return (status) ; } Info [UMFPACK_NEMPTY_COL] = nempty_col ; Info [UMFPACK_NEMPTY_ROW] = nempty_row ; Info [UMFPACK_NDENSE_COL] = 0 ; /* # dense rows/cols recomputed below */ Info [UMFPACK_NDENSE_ROW] = 0 ; Info [UMFPACK_COL_SINGLETONS] = n1c ; Info [UMFPACK_ROW_SINGLETONS] = n1r ; Info [UMFPACK_S_SYMMETRIC] = is_sym ; nempty = MIN (nempty_col, nempty_row) ; Symbolic->nempty_row = nempty_row ; Symbolic->nempty_col = nempty_col ; /* UMF_singletons has verified that the user's input matrix is valid */ ASSERT (AMD_valid (n_row, n_col, Ap, Ai) == AMD_OK) ; Symbolic->n1 = n1 ; Symbolic->nempty = nempty ; ASSERT (n1 <= n_inner) ; n2 = nn - n1 - nempty ; dense_row_threshold = UMFPACK_DENSE_DEGREE_THRESHOLD (drow, n_col - n1 - nempty_col) ; Symbolic->dense_row_threshold = dense_row_threshold ; if (!is_sym) { /* either the pruned submatrix rectangular, or it is square and * Rperm [n1 .. n-nempty-1] is not the same as Cperm [n1 .. n-nempty-1]. * Switch to the unsymmetric strategy, ignoring user-requested * strategy. */ strategy = UMFPACK_STRATEGY_UNSYMMETRIC ; DEBUGm4 (("Strategy: Unsymmetric singletons\n")) ; } /* ---------------------------------------------------------------------- */ /* determine symmetry, nzdiag, and degrees of S+S' */ /* ---------------------------------------------------------------------- */ /* S is the matrix obtained after removing singletons * = A (Cperm1 [n1..n_col-nempty_col-1], Rperm1 [n1..n_row-nempty_row-1]) */ Wq = Rperm_init ; /* use Rperm_init as workspace for Wq [ */ Sdeg = Cperm_init ; /* use Cperm_init as workspace for Sdeg [ */ sym = EMPTY ; nzaat = EMPTY ; nzdiag = EMPTY ; for (i = 0 ; i < AMD_INFO ; i++) { amd_Info [i] = EMPTY ; } if (strategy != UMFPACK_STRATEGY_UNSYMMETRIC) { /* This also determines the degree of each node in S+S' (Sdeg), which * is needed by the 2-by-2 strategy, the symmetry of S, and the number * of nonzeros on the diagonal of S. */ ASSERT (n_row == n_col) ; ASSERT (nempty_row == nempty_col) ; /* get the count of nonzeros on the diagonal of S, excluding explicitly * zero entries. nzdiag = amd_Info [AMD_NZDIAG] counts the zero entries * in S. */ nzdiag = prune_singletons (n1, nn, Ap, Ai, Ax, #ifdef COMPLEX Az, #endif Cperm1, InvRperm1, Si, Sp #ifndef NDEBUG , Rperm1, nn #endif ) ; /* use Ci as workspace to sort S into R, if needed [ */ if (Quser != (Int *) NULL) { /* need to sort the columns of S first */ Rp = Ci ; Ri = Ci + (n_row) + 1 ; (void) UMF_transpose (n2, n2, Sp, Si, (double *) NULL, (Int *) NULL, (Int *) NULL, 0, Rp, Ri, (double *) NULL, Wq, FALSE #ifdef COMPLEX , (double *) NULL, (double *) NULL, FALSE #endif ) ; } else { /* S already has sorted columns */ Rp = Sp ; Ri = Si ; } ASSERT (AMD_valid (n2, n2, Rp, Ri) == AMD_OK) ; nzaat = AMD_aat (n2, Rp, Ri, Sdeg, Wq, amd_Info) ; sym = amd_Info [AMD_SYMMETRY] ; Info [UMFPACK_N2] = n2 ; /* nzdiag = amd_Info [AMD_NZDIAG] counts the zero entries of S too */ /* done using Ci as workspace to sort S into R ] */ #ifndef NDEBUG for (k = 0 ; k < n2 ; k++) { ASSERT (Sdeg [k] >= 0 && Sdeg [k] < n2) ; } ASSERT (Sp [n2] - n2 <= nzaat && nzaat <= 2 * Sp [n2]) ; DEBUG0 (("Explicit zeros: "ID" %g\n", nzdiag, amd_Info [AMD_NZDIAG])) ; #endif } /* get statistics from amd_aat, if computed */ Symbolic->sym = sym ; Symbolic->nzaat = nzaat ; Symbolic->nzdiag = nzdiag ; Symbolic->amd_dmax = EMPTY ; Info [UMFPACK_PATTERN_SYMMETRY] = sym ; Info [UMFPACK_NZ_A_PLUS_AT] = nzaat ; Info [UMFPACK_NZDIAG] = nzdiag ; /* ---------------------------------------------------------------------- */ /* determine the initial strategy based on symmetry and nnz (diag (S)) */ /* ---------------------------------------------------------------------- */ if (strategy == UMFPACK_STRATEGY_AUTO) { if (sym < 0.10) { /* highly unsymmetric: use the unsymmetric strategy */ strategy = UMFPACK_STRATEGY_UNSYMMETRIC ; DEBUGm4 (("Strategy: select unsymmetric\n")) ; } else if (sym >= 0.7 && nzdiag == n2) { /* mostly symmetric, zero-free diagonal: use symmetric strategy */ strategy = UMFPACK_STRATEGY_SYMMETRIC ; DEBUGm4 (("Strategy: select symmetric\n")) ; } else { /* Evaluate the symmetric 2-by-2 strategy, and select it, or * the unsymmetric strategy if the 2-by-2 strategy doesn't look * promising. */ strategy = UMFPACK_STRATEGY_2BY2 ; DEBUGm4 (("Strategy: try 2-by-2\n")) ; } } /* ---------------------------------------------------------------------- */ /* try the 2-by-2 strategy */ /* ---------------------------------------------------------------------- */ /* (3) If the 2-by-2 strategy is attempted, additional workspace of size * nn integers and nn double's is allocated, where nn = n_row = n_col. * The real workspace is immediately free'd. The integer workspace of * size nn remains until the end of umfpack_qsymbolic. */ /* If the resulting matrix S (Rperm_2by2, :) is too unsymmetric, then the * unsymmetric strategy will be used instead. */ if (strategy == UMFPACK_STRATEGY_2BY2) { double sym2 ; Int *Blen, *W, nz_papat, nzd2, nweak, unmatched, Clen3 ; /* ------------------------------------------------------------------ */ /* get workspace for UMF_2by2 */ /* ------------------------------------------------------------------ */ ASSERT (n_row == n_col && nn == n_row) ; #ifndef NDEBUG for (k = 0 ; k < n2 ; k++) { ASSERT (Sdeg [k] >= 0 && Sdeg [k] < n2) ; } #endif /* allocate Rperm_2by2 */ SW->Rperm_2by2 = (Int *) UMF_malloc (nn, sizeof (Int)) ; Rperm_2by2 = SW->Rperm_2by2 ; if (Rperm_2by2 == (Int *) NULL) { DEBUGm4 (("out of memory: Rperm_2by2\n")) ; Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; error (&Symbolic, SW) ; return (UMFPACK_ERROR_out_of_memory) ; } /* allocate Ri from the tail end of Ci [ */ Clen3 = Clen - (MAX (nn, nz) + 1) ; Ri = Ci + Clen3 ; ASSERT (Clen3 >= nz) ; /* space required for UMF_2by2 */ /* use Fr_* as workspace for Rp, Blen, and W [ */ Rp = Fr_npivcol ; Blen = Fr_ncols ; W = Fr_cols ; if (scale != UMFPACK_SCALE_NONE) { SW->Rs = (double *) UMF_malloc (nn, sizeof (double)) ; if (SW->Rs == (double *) NULL) { DEBUGm4 (("out of memory: scale factors for 2-by-2\n")) ; Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; error (&Symbolic, SW) ; return (UMFPACK_ERROR_out_of_memory) ; } } /* ------------------------------------------------------------------ */ /* find the 2-by-2 row permutation */ /* ------------------------------------------------------------------ */ /* find a row permutation Rperm_2by2 such that S (Rperm_2by2, :) * has a healthy diagonal */ UMF_2by2 (nn, Ap, Ai, Ax, #ifdef COMPLEX Az, #endif tol, scale, Cperm1, #ifndef NDEBUG Rperm1, #endif InvRperm1, n1, nempty, Sdeg, Rperm_2by2, &nweak, &unmatched, Ri, Rp, SW->Rs, Blen, W, Ci, Wq) ; DEBUGm3 (("2by2: nweak "ID" unmatched "ID"\n", nweak, unmatched)) ; Info [UMFPACK_2BY2_NWEAK] = nweak ; Info [UMFPACK_2BY2_UNMATCHED] = unmatched ; SW->Rs = (double *) UMF_free ((void *) SW->Rs) ; /* R = S (Rperm_2by2,:)' */ (void) UMF_transpose (n2, n2, Sp, Si, (double *) NULL, Rperm_2by2, (Int *) NULL, 0, Rp, Ri, (double *) NULL, W, FALSE #ifdef COMPLEX , (double *) NULL, (double *) NULL, FALSE #endif ) ; ASSERT (AMD_valid (n2, n2, Rp, Ri) == AMD_OK) ; /* contents of Si and Sp no longer needed, but the space is * still needed */ /* ------------------------------------------------------------------ */ /* find symmetry of S (Rperm_2by2, :)', and prepare to order with AMD */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < AMD_INFO ; i++) { amd_Info [i] = EMPTY ; } nz_papat = AMD_aat (n2, Rp, Ri, Sdeg, Wq, amd_Info) ; sym2 = amd_Info [AMD_SYMMETRY] ; nzd2 = amd_Info [AMD_NZDIAG] ; Info [UMFPACK_2BY2_PATTERN_SYMMETRY] = sym2 ; Info [UMFPACK_2BY2_NZ_PA_PLUS_PAT] = nz_papat ; Info [UMFPACK_2BY2_NZDIAG] = nzd2 ; DEBUG0 (("2by2: sym2 %g nzd2 "ID" n2 "ID"\n", sym2, nzd2, n2)) ; /* ------------------------------------------------------------------ */ /* evaluate the 2-by-2 results */ /* ------------------------------------------------------------------ */ if (user_auto_strategy) { if ((sym2 > 1.1 * sym) && (nzd2 > 0.9 * n2)) { /* 2-by-2 made it much more symmetric */ DEBUGm4 (("eval Strategy 2by2: much more symmetric: 2by2\n")) ; strategy = UMFPACK_STRATEGY_2BY2 ; } else if (sym2 < 0.7 * sym) { /* 2-by-2 made it much more unsymmetric */ DEBUGm4 (("eval Strategy 2by2: much more UNsymmetric:unsym\n")); strategy = UMFPACK_STRATEGY_UNSYMMETRIC ; } else if (sym2 < 0.25) { DEBUGm4 (("eval Strategy 2by2: is UNsymmetric: unsym\n")); strategy = UMFPACK_STRATEGY_UNSYMMETRIC ; } else if (sym2 >= 0.51) { DEBUGm4 (("eval Strategy 2by2: sym2 >= 0.51: 2by2\n")) ; strategy = UMFPACK_STRATEGY_2BY2 ; } else if (sym2 >= 0.999 * sym) { /* 2-by-2 improved symmetry, or made it only slightly worse */ DEBUGm4 (("eval Strategy 2by2: sym2 >= 0.999 sym: 2by2\n")) ; strategy = UMFPACK_STRATEGY_2BY2 ; } else { /* can't decide what to do, so pick the unsymmetric strategy */ DEBUGm4 (("eval Strategy 2by2: punt: unsym\n")); strategy = UMFPACK_STRATEGY_UNSYMMETRIC ; } } /* ------------------------------------------------------------------ */ /* if the 2-by-2 strategy is selected: */ /* ------------------------------------------------------------------ */ if (strategy == UMFPACK_STRATEGY_2BY2) { if (Quser == (Int *) NULL) { /* 2-by-2 strategy is successful */ /* compute amd (S) */ Int *Qinv = Fr_npivcol ; ASSERT (Clen3 >= (nz_papat + nz_papat/5 + nn) + 7*nn) ; do_amd (n2, Rp, Ri, Wq, Qinv, Sdeg, Clen3, Ci, amd_Control, amd_Info, Symbolic, Info) ; /* combine the singleton ordering and the AMD ordering */ combine_ordering (n1, nempty, nn, Cperm_init, Cperm1, Qinv) ; } /* fix Rperm_2by2 to reflect A, not S */ for (k = 0 ; k < n1 ; k++) { oldcol = Cperm1 [k] ; i = k ; oldrow = Rperm1 [k] ; W [oldcol] = oldrow ; } for (k = n1 ; k < nn - nempty ; k++) { oldcol = Cperm1 [k] ; i = Rperm_2by2 [k - n1] + n1 ; oldrow = Rperm1 [i] ; W [oldcol] = oldrow ; } for (k = nn - nempty ; k < nn ; k++) { oldcol = Cperm1 [k] ; i = k ; oldrow = Rperm1 [k] ; W [oldcol] = oldrow ; } for (k = 0 ; k < nn ; k++) { Rperm_2by2 [k] = W [k] ; } /* Now, the "diagonal" entry in oldcol (where oldcol is the user's * name for a column, is the entry in row oldrow (where oldrow is * the user's name for a row, and oldrow = Rperm_2by2 [oldcol] */ } /* Fr_* no longer needed for Rp, Blen, W ] */ } /* ---------------------------------------------------------------------- */ /* finalize the strategy, including fixQ and prefer_diagonal */ /* ---------------------------------------------------------------------- */ if (strategy == UMFPACK_STRATEGY_SYMMETRIC) { /* use given Quser or AMD (A+A'), fix Q during factorization, * prefer diagonal */ DEBUG0 (("\nStrategy: symmetric\n")) ; ASSERT (n_row == n_col) ; Symbolic->ordering = UMFPACK_ORDERING_AMD ; fixQ = TRUE ; prefer_diagonal = TRUE ; } else if (strategy == UMFPACK_STRATEGY_2BY2) { /* use Q = given Quser or Q = AMD (PA+PA'), fix Q during factorization, * prefer diagonal, and factorize PAQ, where P is found by UMF_2by2. */ DEBUG0 (("\nStrategy: symmetric 2-by-2\n")) ; ASSERT (n_row == n_col) ; Symbolic->ordering = UMFPACK_ORDERING_AMD ; fixQ = TRUE ; prefer_diagonal = TRUE ; } else { /* use given Quser or COLAMD (A), refine Q during factorization, * no diagonal preference */ ASSERT (strategy == UMFPACK_STRATEGY_UNSYMMETRIC) ; DEBUG0 (("\nStrategy: unsymmetric\n")) ; Symbolic->ordering = UMFPACK_ORDERING_COLAMD ; fixQ = FALSE ; prefer_diagonal = FALSE ; } if (Quser != (Int *) NULL) { Symbolic->ordering = UMFPACK_ORDERING_GIVEN ; } if (force_fixQ > 0) { fixQ = TRUE ; DEBUG0 (("Force fixQ true\n")) ; } else if (force_fixQ < 0) { fixQ = FALSE ; DEBUG0 (("Force fixQ false\n")) ; } DEBUG0 (("Strategy: ordering: "ID"\n", Symbolic->ordering)) ; DEBUG0 (("Strategy: fixQ: "ID"\n", fixQ)) ; DEBUG0 (("Strategy: prefer diag "ID"\n", prefer_diagonal)) ; /* get statistics from amd_aat, if computed */ Symbolic->strategy = strategy ; Symbolic->fixQ = fixQ ; Symbolic->prefer_diagonal = prefer_diagonal ; Info [UMFPACK_STRATEGY_USED] = strategy ; Info [UMFPACK_ORDERING_USED] = Symbolic->ordering ; Info [UMFPACK_QFIXED] = fixQ ; Info [UMFPACK_DIAG_PREFERRED] = prefer_diagonal ; /* ---------------------------------------------------------------------- */ /* get the AMD ordering for the symmetric strategy */ /* ---------------------------------------------------------------------- */ if (strategy == UMFPACK_STRATEGY_SYMMETRIC && Quser == (Int *) NULL) { /* symmetric strategy for a matrix with mostly symmetric pattern */ Int *Qinv = Fr_npivcol ; ASSERT (n_row == n_col && nn == n_row) ; ASSERT (Clen >= (nzaat + nzaat/5 + nn) + 7*nn) ; do_amd (n2, Sp, Si, Wq, Qinv, Sdeg, Clen, Ci, amd_Control, amd_Info, Symbolic, Info) ; /* combine the singleton ordering and the AMD ordering */ combine_ordering (n1, nempty, nn, Cperm_init, Cperm1, Qinv) ; } /* Sdeg no longer needed ] */ /* done using Rperm_init as workspace for Wq ] */ /* Contents of Si and Sp no longer needed, but the space is still needed */ /* ---------------------------------------------------------------------- */ /* use the user's input column ordering (already in Cperm1) */ /* ---------------------------------------------------------------------- */ if (Quser != (Int *) NULL) { for (k = 0 ; k < n_col ; k++) { Cperm_init [k] = Cperm1 [k] ; } } /* ---------------------------------------------------------------------- */ /* use COLAMD to order the matrix */ /* ---------------------------------------------------------------------- */ if (strategy == UMFPACK_STRATEGY_UNSYMMETRIC && Quser == (Int *) NULL) { /* ------------------------------------------------------------------ */ /* copy the matrix into colamd workspace (colamd destroys its input) */ /* ------------------------------------------------------------------ */ /* C = A (Cperm1 (n1+1:end), Rperm1 (n1+1:end)), where Ci is used as * the row indices and Cperm_init (on input) is used as the column * pointers. */ (void) prune_singletons (n1, n_col, Ap, Ai, (double *) NULL, #ifdef COMPLEX (double *) NULL, #endif Cperm1, InvRperm1, Ci, Cperm_init #ifndef NDEBUG , Rperm1, n_row #endif ) ; /* ------------------------------------------------------------------ */ /* set UMF_colamd defaults */ /* ------------------------------------------------------------------ */ UMF_colamd_set_defaults (knobs) ; knobs [COLAMD_DENSE_ROW] = drow ; knobs [COLAMD_DENSE_COL] = dcol ; knobs [COLAMD_AGGRESSIVE] = aggressive ; /* ------------------------------------------------------------------ */ /* check input matrix and find the initial column pre-ordering */ /* ------------------------------------------------------------------ */ /* NOTE: umf_colamd is not given any original empty rows or columns. * Those have already been removed via prune_singletons, above. The * umf_colamd routine has been modified to assume that all rows and * columns have at least one entry in them. It will break if it is * given empty rows or columns (an assertion is triggered when running * in debug mode. */ (void) UMF_colamd ( n_row - n1 - nempty_row, n_col - n1 - nempty_col, Clen, Ci, Cperm_init, knobs, colamd_stats, Fr_npivcol, Fr_nrows, Fr_ncols, Fr_parent, Fr_cols, &nfr, InFront) ; ASSERT (colamd_stats [COLAMD_EMPTY_ROW] == 0) ; ASSERT (colamd_stats [COLAMD_EMPTY_COL] == 0) ; /* # of dense rows will be recomputed below */ Info [UMFPACK_NDENSE_ROW] = colamd_stats [COLAMD_DENSE_ROW] ; Info [UMFPACK_NDENSE_COL] = colamd_stats [COLAMD_DENSE_COL] ; Info [UMFPACK_SYMBOLIC_DEFRAG] = colamd_stats [COLAMD_DEFRAG_COUNT] ; /* re-analyze if any "dense" rows or cols ignored by UMF_colamd */ do_UMF_analyze = colamd_stats [COLAMD_DENSE_ROW] > 0 || colamd_stats [COLAMD_DENSE_COL] > 0 ; /* Combine the singleton and colamd ordering into Cperm_init */ /* Note that colamd returns its inverse permutation in Ci */ combine_ordering (n1, nempty_col, n_col, Cperm_init, Cperm1, Ci) ; /* contents of Ci no longer needed */ #ifndef NDEBUG for (col = 0 ; col < n_col ; col++) { DEBUG1 (("Cperm_init ["ID"] = "ID"\n", col, Cperm_init[col])); } /* make sure colamd returned a valid permutation */ ASSERT (Cperm_init != (Int *) NULL) ; ASSERT (UMF_is_permutation (Cperm_init, Ci, n_col, n_col)) ; #endif } else { /* ------------------------------------------------------------------ */ /* do not call colamd - use input Quser or AMD instead */ /* ------------------------------------------------------------------ */ /* The ordering (Quser or Qamd) is already in Cperm_init */ do_UMF_analyze = TRUE ; } Cperm_init [n_col] = EMPTY ; /* unused in Cperm_init */ /* ---------------------------------------------------------------------- */ /* AMD ordering, if it exists, has been copied into Cperm_init */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG DEBUG3 (("Cperm_init column permutation:\n")) ; ASSERT (UMF_is_permutation (Cperm_init, Ci, n_col, n_col)) ; for (k = 0 ; k < n_col ; k++) { DEBUG3 ((ID"\n", Cperm_init [k])) ; } /* ensure that empty columns have been placed last in A (:,Cperm_init) */ for (newj = 0 ; newj < n_col ; newj++) { /* empty columns will be last in A (:, Cperm_init (1:n_col)) */ j = Cperm_init [newj] ; ASSERT (IMPLIES (newj >= n_col-nempty_col, Cdeg [j] == 0)) ; ASSERT (IMPLIES (newj < n_col-nempty_col, Cdeg [j] > 0)) ; } #endif /* ---------------------------------------------------------------------- */ /* symbolic factorization (unless colamd has already done it) */ /* ---------------------------------------------------------------------- */ if (do_UMF_analyze) { Int *W, *Bp, *Bi, *Cperm2, ok, *P, Clen2, bsize, Clen0 ; /* ------------------------------------------------------------------ */ /* construct column pre-ordered, pruned submatrix */ /* ------------------------------------------------------------------ */ /* S = column form submatrix after removing singletons and applying * initial column ordering (includes singleton ordering) */ (void) prune_singletons (n1, n_col, Ap, Ai, (double *) NULL, #ifdef COMPLEX (double *) NULL, #endif Cperm_init, InvRperm1, Si, Sp #ifndef NDEBUG , Rperm1, n_row #endif ) ; /* ------------------------------------------------------------------ */ /* Ci [0 .. Clen-1] holds the following work arrays: first Clen0 entries empty space, where Clen0 = Clen - (nn+1 + 2*nn + n_col) and Clen0 >= nz + n_col next nn+1 entries Bp [0..nn] next nn entries Link [0..nn-1] next nn entries W [0..nn-1] last n_col entries Cperm2 [0..n_col-1] We have Clen >= n_col + MAX (nz,n_col) + 3*nn+1 + n_col, So Clen0 >= 2*n_col as required for AMD_postorder and Clen0 >= n_col + nz as required */ Clen0 = Clen - (nn+1 + 2*nn + n_col) ; Bp = Ci + Clen0 ; Link = Bp + (nn+1) ; W = Link + nn ; Cperm2 = W + nn ; ASSERT (Cperm2 + n_col == Ci + Clen) ; ASSERT (Clen0 >= nz + n_col) ; ASSERT (Clen0 >= 2*n_col) ; /* ------------------------------------------------------------------ */ /* P = order that rows will be used in UMF_analyze */ /* ------------------------------------------------------------------ */ /* use W to mark rows, and use Link for row permutation P [ [ */ for (row = 0 ; row < n_row - n1 ; row++) { W [row] = FALSE ; } P = Link ; k = 0 ; for (col = 0 ; col < n_col - n1 ; col++) { /* empty columns are last in S */ for (p = Sp [col] ; p < Sp [col+1] ; p++) { row = Si [p] ; if (!W [row]) { /* this row has just been seen for the first time */ W [row] = TRUE ; P [k++] = row ; } } } /* If the matrix has truly empty rows, then P will not be */ /* complete, and visa versa. The matrix is structurally singular. */ nempty_row = n_row - n1 - k ; if (k < n_row - n1) { /* complete P by putting empty rows last in their natural order, */ /* rather than declaring an error (the matrix is singular) */ for (row = 0 ; row < n_row - n1 ; row++) { if (!W [row]) { /* W [row] = TRUE ; (not required) */ P [k++] = row ; } } } /* contents of W no longer needed ] */ #ifndef NDEBUG DEBUG3 (("Induced row permutation:\n")) ; ASSERT (k == n_row - n1) ; ASSERT (UMF_is_permutation (P, W, n_row - n1, n_row - n1)) ; for (k = 0 ; k < n_row - n1 ; k++) { DEBUG3 ((ID"\n", P [k])) ; } #endif /* ------------------------------------------------------------------ */ /* B = row-form of the pattern of S (excluding empty columns) */ /* ------------------------------------------------------------------ */ /* Ci [0 .. Clen-1] holds the following work arrays: first Clen2 entries empty space, must be at least >= n_col next max (nz,1) Bi [0..max (nz,1)-1] next nn+1 entries Bp [0..nn] next nn entries Link [0..nn-1] next nn entries W [0..nn-1] last n_col entries Cperm2 [0..n_col-1] This memory usage is accounted for by the UMF_ANALYZE_CLEN macro. */ Clen2 = Clen0 ; snz = Sp [n_col - n1] ; bsize = MAX (snz, 1) ; Clen2 -= bsize ; Bi = Ci + Clen2 ; ASSERT (Clen2 >= n_col) ; (void) UMF_transpose (n_row - n1, n_col - n1 - nempty_col, Sp, Si, (double *) NULL, P, (Int *) NULL, 0, Bp, Bi, (double *) NULL, W, FALSE #ifdef COMPLEX , (double *) NULL, (double *) NULL, FALSE #endif ) ; /* contents of Si and Sp no longer needed */ /* contents of P (same as Link) and W not needed */ /* still need Link and W as work arrays, though ] */ ASSERT (Bp [0] == 0) ; ASSERT (Bp [n_row - n1] == snz) ; /* increment Bp to point into Ci, not Bi */ for (i = 0 ; i <= n_row - n1 ; i++) { Bp [i] += Clen2 ; } ASSERT (Bp [0] == Clen0 - bsize) ; ASSERT (Bp [n_row - n1] <= Clen0) ; /* Ci [0 .. Clen-1] holds the following work arrays: first Clen0 entries Ci [0 .. Clen0-1], where the col indices of B are at the tail end of this part, and Bp [0] = Clen2 >= n_col. Note that Clen0 = Clen2 + max (snz,1). next nn+1 entries Bp [0..nn] next nn entries Link [0..nn-1] next nn entries W [0..nn-1] last n_col entries Cperm2 [0..n_col-1] */ /* ------------------------------------------------------------------ */ /* analyze */ /* ------------------------------------------------------------------ */ /* only analyze the non-empty, non-singleton part of the matrix */ ok = UMF_analyze ( n_row - n1 - nempty_row, n_col - n1 - nempty_col, Ci, Bp, Cperm2, fixQ, W, Link, Fr_ncols, Fr_nrows, Fr_npivcol, Fr_parent, &nfr, &analyze_compactions) ; if (!ok) { /* :: internal error in umf_analyze :: */ Info [UMFPACK_STATUS] = UMFPACK_ERROR_internal_error ; error (&Symbolic, SW) ; return (UMFPACK_ERROR_internal_error) ; } Info [UMFPACK_SYMBOLIC_DEFRAG] += analyze_compactions ; /* ------------------------------------------------------------------ */ /* combine the input permutation and UMF_analyze's permutation */ /* ------------------------------------------------------------------ */ if (!fixQ) { /* Cperm2 is the column etree post-ordering */ ASSERT (UMF_is_permutation (Cperm2, W, n_col-n1-nempty_col, n_col-n1-nempty_col)) ; /* Note that the empty columns remain at the end of Cperm_init */ for (k = 0 ; k < n_col - n1 - nempty_col ; k++) { W [k] = Cperm_init [n1 + Cperm2 [k]] ; } for (k = 0 ; k < n_col - n1 - nempty_col ; k++) { Cperm_init [n1 + k] = W [k] ; } } ASSERT (UMF_is_permutation (Cperm_init, W, n_col, n_col)) ; } /* ---------------------------------------------------------------------- */ /* free some of the workspace */ /* ---------------------------------------------------------------------- */ /* (4) The real workspace, Rs, of size n_row doubles has already been * free'd. An additional workspace of size nz + n_col+1 + n_col integers * is now free'd as well. */ SW->Si = (Int *) UMF_free ((void *) SW->Si) ; SW->Sp = (Int *) UMF_free ((void *) SW->Sp) ; SW->Cperm1 = (Int *) UMF_free ((void *) SW->Cperm1) ; ASSERT (SW->Rs == (double *) NULL) ; /* ---------------------------------------------------------------------- */ /* determine the size of the Symbolic object */ /* ---------------------------------------------------------------------- */ /* ---------------------------------------------------------------------- */ /* determine the size of the Symbolic object */ /* ---------------------------------------------------------------------- */ nchains = 0 ; for (i = 0 ; i < nfr ; i++) { if (Fr_parent [i] != i+1) { nchains++ ; } } Symbolic->nchains = nchains ; Symbolic->nfr = nfr ; Symbolic->esize = (max_rdeg > dense_row_threshold) ? (n_col - n1 - nempty_col) : 0 ; /* true size of Symbolic object */ Info [UMFPACK_SYMBOLIC_SIZE] = UMF_symbolic_usage (n_row, n_col, nchains, nfr, Symbolic->esize, prefer_diagonal) ; /* actual peak memory usage for UMFPACK_symbolic (actual nfr, nchains) */ Info [UMFPACK_SYMBOLIC_PEAK_MEMORY] = SYM_WORK_USAGE (n_col, n_row, Clen) + Info [UMFPACK_SYMBOLIC_SIZE] ; Symbolic->peak_sym_usage = Info [UMFPACK_SYMBOLIC_PEAK_MEMORY] ; DEBUG0 (("Number of fronts: "ID"\n", nfr)) ; /* ---------------------------------------------------------------------- */ /* allocate the second part of the Symbolic object (Front_*, Chain_*) */ /* ---------------------------------------------------------------------- */ /* (5) UMF_malloc is called 7 or 8 times, for a total space of * (4*(nfr+1) + 3*(nchains+1) + esize) integers, where nfr is the total * number of frontal matrices and nchains is the total number of frontal * matrix chains, and where nchains <= nfr <= n_col. esize is zero if there * are no dense rows, or n_col-n1-nempty_col otherwise (n1 is the number of * singletons and nempty_col is the number of empty columns). This space is * part of the Symbolic object and is not free'd unless an error occurs. * This is between 7 and about 8n integers when A is square. */ /* Note that Symbolic->Front_* does include the dummy placeholder front */ Symbolic->Front_npivcol = (Int *) UMF_malloc (nfr+1, sizeof (Int)) ; Symbolic->Front_parent = (Int *) UMF_malloc (nfr+1, sizeof (Int)) ; Symbolic->Front_1strow = (Int *) UMF_malloc (nfr+1, sizeof (Int)) ; Symbolic->Front_leftmostdesc = (Int *) UMF_malloc (nfr+1, sizeof (Int)) ; Symbolic->Chain_start = (Int *) UMF_malloc (nchains+1, sizeof (Int)) ; Symbolic->Chain_maxrows = (Int *) UMF_malloc (nchains+1, sizeof (Int)) ; Symbolic->Chain_maxcols = (Int *) UMF_malloc (nchains+1, sizeof (Int)) ; fail = (!Symbolic->Front_npivcol || !Symbolic->Front_parent || !Symbolic->Front_1strow || !Symbolic->Front_leftmostdesc || !Symbolic->Chain_start || !Symbolic->Chain_maxrows || !Symbolic->Chain_maxcols) ; if (Symbolic->esize > 0) { Symbolic->Esize = (Int *) UMF_malloc (Symbolic->esize, sizeof (Int)) ; fail = fail || !Symbolic->Esize ; } if (fail) { DEBUGm4 (("out of memory: rest of symbolic object\n")) ; Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; error (&Symbolic, SW) ; return (UMFPACK_ERROR_out_of_memory) ; } DEBUG0 (("Symbolic UMF_malloc_count - init_count = "ID"\n", UMF_malloc_count - init_count)) ; ASSERT (UMF_malloc_count == init_count + 21 + (SW->Rperm_2by2 != (Int *) NULL) + (Symbolic->Esize != (Int *) NULL)) ; Front_npivcol = Symbolic->Front_npivcol ; Front_parent = Symbolic->Front_parent ; Front_1strow = Symbolic->Front_1strow ; Front_leftmostdesc = Symbolic->Front_leftmostdesc ; Chain_start = Symbolic->Chain_start ; Chain_maxrows = Symbolic->Chain_maxrows ; Chain_maxcols = Symbolic->Chain_maxcols ; Esize = Symbolic->Esize ; /* ---------------------------------------------------------------------- */ /* assign rows to fronts */ /* ---------------------------------------------------------------------- */ /* find InFront, unless colamd has already computed it */ if (do_UMF_analyze) { DEBUGm4 ((">>>>>>>>>Computing Front_1strow from scratch\n")) ; /* empty rows go to dummy front nfr */ for (row = 0 ; row < n_row ; row++) { InFront [row] = nfr ; } /* assign the singleton pivot rows to the "empty" front */ for (k = 0 ; k < n1 ; k++) { row = Rperm1 [k] ; InFront [row] = EMPTY ; } DEBUG1 (("Front (EMPTY), singleton nrows "ID" ncols "ID"\n", k, k)) ; newj = n1 ; for (i = 0 ; i < nfr ; i++) { fpivcol = Fr_npivcol [i] ; f1rows = 0 ; /* for all pivot columns in front i */ for (kk = 0 ; kk < fpivcol ; kk++, newj++) { j = Cperm_init [newj] ; ASSERT (IMPLIES (newj >= n_col-nempty_col, Ap [j+1] - Ap [j] == 0)); for (p = Ap [j] ; p < Ap [j+1] ; p++) { row = Ai [p] ; if (InFront [row] == nfr) { /* this row belongs to front i */ DEBUG1 ((" Row "ID" in Front "ID"\n", row, i)) ; InFront [row] = i ; f1rows++ ; } } } Front_1strow [i] = f1rows ; DEBUG1 ((" Front "ID" has 1strows: "ID" pivcols "ID"\n", i, f1rows, fpivcol)) ; } } else { /* COLAMD has already computed InFront, but it is not yet * InFront [row] = front i, where row is an original row. It is * InFront [k-n1] = i for k in the range n1 to n_row-nempty_row, * and where row = Rperm1 [k]. Need to permute InFront. Also compute * # of original rows assembled into each front. * [ use Ci as workspace */ DEBUGm4 ((">>>>>>>>>Computing Front_1strow from colamd's InFront\n")) ; for (i = 0 ; i <= nfr ; i++) { Front_1strow [i] = 0 ; } /* assign the singleton pivot rows to "empty" front */ for (k = 0 ; k < n1 ; k++) { row = Rperm1 [k] ; Ci [row] = EMPTY ; } /* assign the non-empty rows to the front that assembled them */ for ( ; k < n_row - nempty_row ; k++) { row = Rperm1 [k] ; i = InFront [k - n1] ; ASSERT (i >= EMPTY && i < nfr) ; if (i != EMPTY) { Front_1strow [i]++ ; } /* use Ci as permuted version of InFront */ Ci [row] = i ; } /* empty rows go to the "dummy" front */ for ( ; k < n_row ; k++) { row = Rperm1 [k] ; Ci [row] = nfr ; } /* permute InFront so that InFront [row] = i if the original row is * in front i */ for (row = 0 ; row < n_row ; row++) { InFront [row] = Ci [row] ; } /* ] no longer need Ci as workspace */ } #ifndef NDEBUG for (row = 0 ; row < n_row ; row++) { if (InFront [row] == nfr) { DEBUG1 ((" Row "ID" in Dummy Front "ID"\n", row, nfr)) ; } else if (InFront [row] == EMPTY) { DEBUG1 ((" singleton Row "ID"\n", row)) ; } else { DEBUG1 ((" Row "ID" in Front "ID"\n", row, nfr)) ; } } #endif /* ---------------------------------------------------------------------- */ /* copy front information into Symbolic object */ /* ---------------------------------------------------------------------- */ k = n1 ; for (i = 0 ; i < nfr ; i++) { fpivcol = Fr_npivcol [i] ; DEBUG1 (("Front "ID" k "ID" npivcol "ID" nrows "ID" ncols "ID"\n", i, k, fpivcol, Fr_nrows [i], Fr_ncols [i])) ; k += fpivcol ; /* copy Front info into Symbolic object from SW */ Front_npivcol [i] = fpivcol ; Front_parent [i] = Fr_parent [i] ; } /* assign empty columns to dummy placehold front nfr */ DEBUG1 (("Dummy Cols in Front "ID" : "ID"\n", nfr, n_col-k)) ; Front_npivcol [nfr] = n_col - k ; Front_parent [nfr] = EMPTY ; /* ---------------------------------------------------------------------- */ /* find initial row permutation */ /* ---------------------------------------------------------------------- */ /* order the singleton pivot rows */ for (k = 0 ; k < n1 ; k++) { Rperm_init [k] = Rperm1 [k] ; } /* determine the first row in each front (in the new row ordering) */ for (i = 0 ; i < nfr ; i++) { f1rows = Front_1strow [i] ; DEBUG1 (("Front "ID" : npivcol "ID" parent "ID, i, Front_npivcol [i], Front_parent [i])) ; DEBUG1 ((" 1st rows in Front "ID" : "ID"\n", i, f1rows)) ; Front_1strow [i] = k ; k += f1rows ; } /* assign empty rows to dummy placehold front nfr */ DEBUG1 (("Rows in Front "ID" (dummy): "ID"\n", nfr, n_row-k)) ; Front_1strow [nfr] = k ; DEBUG1 (("nfr "ID" 1strow[nfr] "ID" nrow "ID"\n", nfr, k, n_row)) ; /* Use Ci as temporary workspace for F1 */ F1 = Ci ; /* [ of size nfr+1 */ ASSERT (Clen >= 2*n_row + nfr+1) ; for (i = 0 ; i <= nfr ; i++) { F1 [i] = Front_1strow [i] ; } for (row = 0 ; row < n_row ; row++) { i = InFront [row] ; if (i != EMPTY) { newrow = F1 [i]++ ; ASSERT (newrow >= n1) ; Rperm_init [newrow] = row ; } } Rperm_init [n_row] = EMPTY ; /* unused */ #ifndef NDEBUG for (k = 0 ; k < n_row ; k++) { DEBUG2 (("Rperm_init ["ID"] = "ID"\n", k, Rperm_init [k])) ; } #endif /* ] done using F1 */ /* ---------------------------------------------------------------------- */ /* find the diagonal map */ /* ---------------------------------------------------------------------- */ /* Rperm_init [newrow] = row gives the row permutation that is implied * by the column permutation, where "row" is a row index of the original * matrix A. It is not dependent on the Rperm_2by2 permutation, which * only redefines the "diagonal". Both are used to construct the * Diagonal_map. Diagonal_map only needs to be defined for * k = n1 to nn - nempty, but go ahead and define it for all of * k = 0 to nn */ if (prefer_diagonal) { Int *Diagonal_map ; ASSERT (n_row == n_col && nn == n_row) ; ASSERT (nempty_row == nempty_col && nempty == nempty_row) ; /* allocate the Diagonal_map */ Symbolic->Diagonal_map = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ; Diagonal_map = Symbolic->Diagonal_map ; if (Diagonal_map == (Int *) NULL) { /* :: out of memory (diagonal map) :: */ DEBUGm4 (("out of memory: Diagonal map\n")) ; Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; error (&Symbolic, SW) ; return (UMFPACK_ERROR_out_of_memory) ; } /* use Ci as workspace to compute the inverse of Rperm_init [ */ for (newrow = 0 ; newrow < nn ; newrow++) { oldrow = Rperm_init [newrow] ; ASSERT (oldrow >= 0 && oldrow < nn) ; Ci [oldrow] = newrow ; } if (strategy == UMFPACK_STRATEGY_2BY2) { ASSERT (Rperm_2by2 != (Int *) NULL) ; for (newcol = 0 ; newcol < nn ; newcol++) { oldcol = Cperm_init [newcol] ; /* 2-by-2 pivoting done in S */ oldrow = Rperm_2by2 [oldcol] ; newrow = Ci [oldrow] ; Diagonal_map [newcol] = newrow ; } } else { for (newcol = 0 ; newcol < nn ; newcol++) { oldcol = Cperm_init [newcol] ; /* no 2-by-2 pivoting in S */ oldrow = oldcol ; newrow = Ci [oldrow] ; Diagonal_map [newcol] = newrow ; } } #ifndef NDEBUG DEBUG1 (("\nDiagonal map:\n")) ; for (newcol = 0 ; newcol < nn ; newcol++) { oldcol = Cperm_init [newcol] ; DEBUG3 (("oldcol "ID" newcol "ID":\n", oldcol, newcol)) ; for (p = Ap [oldcol] ; p < Ap [oldcol+1] ; p++) { Entry aij ; CLEAR (aij) ; oldrow = Ai [p] ; newrow = Ci [oldrow] ; if (Ax != (double *) NULL) { ASSIGN (aij, Ax, Az, p, SPLIT (Az)) ; } if (oldrow == oldcol) { DEBUG2 ((" old diagonal : oldcol "ID" oldrow "ID" ", oldcol, oldrow)) ; EDEBUG2 (aij) ; DEBUG2 (("\n")) ; } if (newrow == Diagonal_map [newcol]) { DEBUG2 ((" MAP diagonal : newcol "ID" MAProw "ID" ", newcol, Diagonal_map [newrow])) ; EDEBUG2 (aij) ; DEBUG2 (("\n")) ; } } } #endif /* done using Ci as workspace ] */ } /* ---------------------------------------------------------------------- */ /* find the leftmost descendant of each front */ /* ---------------------------------------------------------------------- */ for (i = 0 ; i <= nfr ; i++) { Front_leftmostdesc [i] = EMPTY ; } for (i = 0 ; i < nfr ; i++) { /* start at i and walk up the tree */ DEBUG2 (("Walk up front tree from "ID"\n", i)) ; j = i ; while (j != EMPTY && Front_leftmostdesc [j] == EMPTY) { DEBUG3 ((" Leftmost desc of "ID" is "ID"\n", j, i)) ; Front_leftmostdesc [j] = i ; j = Front_parent [j] ; DEBUG3 ((" go to j = "ID"\n", j)) ; } } /* ---------------------------------------------------------------------- */ /* find the frontal matrix chains and max frontal matrix sizes */ /* ---------------------------------------------------------------------- */ maxnrows = 1 ; /* max # rows in any front */ maxncols = 1 ; /* max # cols in any front */ dmaxfrsize = 1 ; /* max frontal matrix size */ /* start the first chain */ nchains = 0 ; /* number of chains */ Chain_start [0] = 0 ; /* front 0 starts a new chain */ maxrows = 1 ; /* max # rows for any front in current chain */ maxcols = 1 ; /* max # cols for any front in current chain */ DEBUG1 (("Constructing chains:\n")) ; for (i = 0 ; i < nfr ; i++) { /* get frontal matrix info */ fpivcol = Front_npivcol [i] ; /* # candidate pivot columns */ fallrows = Fr_nrows [i] ; /* all rows (not just Schur comp) */ fallcols = Fr_ncols [i] ; /* all cols (not just Schur comp) */ parent = Front_parent [i] ; /* parent in column etree */ fpiv = MIN (fpivcol, fallrows) ; /* # pivot rows and cols */ maxrows = MAX (maxrows, fallrows) ; maxcols = MAX (maxcols, fallcols) ; DEBUG1 (("Front: "ID", pivcol "ID", "ID"-by-"ID" parent "ID ", npiv "ID" Chain: maxrows "ID" maxcols "ID"\n", i, fpivcol, fallrows, fallcols, parent, fpiv, maxrows, maxcols)) ; if (parent != i+1) { /* this is the end of a chain */ double s ; DEBUG1 (("\nEnd of chain "ID"\n", nchains)) ; /* make sure maxrows is an odd number */ ASSERT (maxrows >= 0) ; if (maxrows % 2 == 0) maxrows++ ; DEBUG1 (("Chain maxrows "ID" maxcols "ID"\n", maxrows, maxcols)) ; Chain_maxrows [nchains] = maxrows ; Chain_maxcols [nchains] = maxcols ; /* keep track of the maximum front size for all chains */ /* for Info only: */ s = (double) maxrows * (double) maxcols ; dmaxfrsize = MAX (dmaxfrsize, s) ; /* for the subsequent numerical factorization */ maxnrows = MAX (maxnrows, maxrows) ; maxncols = MAX (maxncols, maxcols) ; DEBUG1 (("Chain dmaxfrsize %g\n\n", dmaxfrsize)) ; /* start the next chain */ nchains++ ; Chain_start [nchains] = i+1 ; maxrows = 1 ; maxcols = 1 ; } } /* for Info only: */ dmaxfrsize = ceil (dmaxfrsize) ; DEBUGm1 (("dmaxfrsize %30.20g Int_MAX "ID"\n", dmaxfrsize, Int_MAX)) ; ASSERT (Symbolic->nchains == nchains) ; /* For allocating objects in umfpack_numeric (does not include all possible * pivots, particularly pivots from prior fronts in the chain. Need to add * nb to these to get the # of columns in the L block, for example. This * is the largest row dimension and largest column dimension of any frontal * matrix. maxnrows is always odd. */ Symbolic->maxnrows = maxnrows ; Symbolic->maxncols = maxncols ; DEBUGm3 (("maxnrows "ID" maxncols "ID"\n", maxnrows, maxncols)) ; /* ---------------------------------------------------------------------- */ /* find the initial element sizes */ /* ---------------------------------------------------------------------- */ if (max_rdeg > dense_row_threshold) { /* there are one or more dense rows in the input matrix */ /* count the number of dense rows in each column */ /* use Ci as workspace for inverse of Rperm_init [ */ ASSERT (Esize != (Int *) NULL) ; for (newrow = 0 ; newrow < n_row ; newrow++) { oldrow = Rperm_init [newrow] ; ASSERT (oldrow >= 0 && oldrow < nn) ; Ci [oldrow] = newrow ; } for (col = n1 ; col < n_col - nempty_col ; col++) { oldcol = Cperm_init [col] ; esize = Cdeg [oldcol] ; ASSERT (esize > 0) ; for (p = Ap [oldcol] ; p < Ap [oldcol+1] ; p++) { oldrow = Ai [p] ; newrow = Ci [oldrow] ; if (newrow >= n1 && Rdeg [oldrow] > dense_row_threshold) { esize-- ; } } ASSERT (esize >= 0) ; Esize [col - n1] = esize ; } /* done using Ci as workspace ] */ } /* If there are no dense rows, then Esize [col-n1] is identical to * Cdeg [col], once Cdeg is permuted below */ /* ---------------------------------------------------------------------- */ /* permute Cdeg and Rdeg according to initial column and row permutation */ /* ---------------------------------------------------------------------- */ /* use Ci as workspace [ */ for (k = 0 ; k < n_col ; k++) { Ci [k] = Cdeg [Cperm_init [k]] ; } for (k = 0 ; k < n_col ; k++) { Cdeg [k] = Ci [k] ; } for (k = 0 ; k < n_row ; k++) { Ci [k] = Rdeg [Rperm_init [k]] ; } for (k = 0 ; k < n_row ; k++) { Rdeg [k] = Ci [k] ; } /* done using Ci as workspace ] */ /* ---------------------------------------------------------------------- */ /* simulate UMF_kernel_init */ /* ---------------------------------------------------------------------- */ /* count elements and tuples at tail, LU factors of singletons, and * head and tail markers */ dlnz = n_inner ; /* upper limit of nz in L (incl diag) */ dunz = dlnz ; /* upper limit of nz in U (incl diag) */ /* head marker */ head_usage = 1 ; dhead_usage = 1 ; /* tail markers: */ tail_usage = 2 ; dtail_usage = 2 ; /* allocate the Rpi and Rpx workspace for UMF_kernel_init (incl. headers) */ tail_usage += UNITS (Int *, n_row+1) + UNITS (Entry *, n_row+1) + 2 ; dtail_usage += DUNITS (Int *, n_row+1) + DUNITS (Entry *, n_row+1) + 2 ; DEBUG1 (("Symbolic usage after Rpi/Rpx allocation: head "ID" tail "ID"\n", head_usage, tail_usage)) ; /* LU factors for singletons, at the head of memory */ for (k = 0 ; k < n1 ; k++) { lnz = Cdeg [k] - 1 ; unz = Rdeg [k] - 1 ; dlnz += lnz ; dunz += unz ; DEBUG1 (("singleton k "ID" pivrow "ID" pivcol "ID" lnz "ID" unz "ID"\n", k, Rperm_init [k], Cperm_init [k], lnz, unz)) ; head_usage += UNITS (Int, lnz) + UNITS (Entry, lnz) + UNITS (Int, unz) + UNITS (Entry, unz) ; dhead_usage += DUNITS (Int, lnz) + DUNITS (Entry, lnz) + DUNITS (Int, unz) + DUNITS (Entry, unz) ; } DEBUG1 (("Symbolic init head usage: "ID" for LU singletons\n",head_usage)) ; /* column elements: */ for (k = n1 ; k < n_col - nempty_col; k++) { esize = Esize ? Esize [k-n1] : Cdeg [k] ; DEBUG2 ((" esize: "ID"\n", esize)) ; ASSERT (esize >= 0) ; if (esize > 0) { tail_usage += GET_ELEMENT_SIZE (esize, 1) + 1 ; dtail_usage += DGET_ELEMENT_SIZE (esize, 1) + 1 ; } } /* dense row elements */ if (Esize) { Int nrow_elements = 0 ; for (k = n1 ; k < n_row - nempty_row ; k++) { rdeg = Rdeg [k] ; if (rdeg > dense_row_threshold) { tail_usage += GET_ELEMENT_SIZE (1, rdeg) + 1 ; dtail_usage += GET_ELEMENT_SIZE (1, rdeg) + 1 ; nrow_elements++ ; } } Info [UMFPACK_NDENSE_ROW] = nrow_elements ; } DEBUG1 (("Symbolic usage: "ID" = head "ID" + tail "ID" after els\n", head_usage + tail_usage, head_usage, tail_usage)) ; /* compute the tuple lengths */ if (Esize) { /* row tuples */ for (row = n1 ; row < n_row ; row++) { rdeg = Rdeg [row] ; tlen = (rdeg > dense_row_threshold) ? 1 : rdeg ; tail_usage += 1 + UNITS (Tuple, TUPLES (tlen)) ; dtail_usage += 1 + DUNITS (Tuple, TUPLES (tlen)) ; } /* column tuples */ for (col = n1 ; col < n_col - nempty_col ; col++) { /* tlen is 1 plus the number of dense rows in this column */ esize = Esize [col - n1] ; tlen = (esize > 0) + (Cdeg [col] - esize) ; tail_usage += 1 + UNITS (Tuple, TUPLES (tlen)) ; dtail_usage += 1 + DUNITS (Tuple, TUPLES (tlen)) ; } for ( ; col < n_col ; col++) { tail_usage += 1 + UNITS (Tuple, TUPLES (0)) ; dtail_usage += 1 + DUNITS (Tuple, TUPLES (0)) ; } } else { /* row tuples */ for (row = n1 ; row < n_row ; row++) { tlen = Rdeg [row] ; tail_usage += 1 + UNITS (Tuple, TUPLES (tlen)) ; dtail_usage += 1 + DUNITS (Tuple, TUPLES (tlen)) ; } /* column tuples */ for (col = n1 ; col < n_col ; col++) { tail_usage += 1 + UNITS (Tuple, TUPLES (1)) ; dtail_usage += 1 + DUNITS (Tuple, TUPLES (1)) ; } } Symbolic->num_mem_init_usage = head_usage + tail_usage ; DEBUG1 (("Symbolic usage: "ID" = head "ID" + tail "ID" final\n", Symbolic->num_mem_init_usage, head_usage, tail_usage)) ; ASSERT (UMF_is_permutation (Rperm_init, Ci, n_row, n_row)) ; /* initial head and tail usage in Numeric->Memory */ dmax_usage = dhead_usage + dtail_usage ; dmax_usage = MAX (Symbolic->num_mem_init_usage, ceil (dmax_usage)) ; Info [UMFPACK_VARIABLE_INIT_ESTIMATE] = dmax_usage ; /* In case Symbolic->num_mem_init_usage overflows, keep as a double, too */ Symbolic->dnum_mem_init_usage = dmax_usage ; /* free the Rpi and Rpx workspace */ tail_usage -= UNITS (Int *, n_row+1) + UNITS (Entry *, n_row+1) ; dtail_usage -= DUNITS (Int *, n_row+1) + DUNITS (Entry *, n_row+1) ; /* ---------------------------------------------------------------------- */ /* simulate UMF_kernel, assuming unsymmetric pivoting */ /* ---------------------------------------------------------------------- */ /* Use Ci as temporary workspace for link lists [ */ Link = Ci ; for (i = 0 ; i < nfr ; i++) { Link [i] = EMPTY ; } flops = 0 ; /* flop count upper bound */ for (chain = 0 ; chain < nchains ; chain++) { double fsize ; f1 = Chain_start [chain] ; f2 = Chain_start [chain+1] - 1 ; /* allocate frontal matrix working array (C, L, and U) */ dr = Chain_maxrows [chain] ; dc = Chain_maxcols [chain] ; fsize = nb*nb /* LU is nb-by-nb */ + dr*nb /* L is dr-by-nb */ + nb*dc /* U is nb-by-dc, stored by rows */ + dr*dc ; /* C is dr by dc */ dtail_usage += DUNITS (Entry, fsize) ; dmax_usage = MAX (dmax_usage, dhead_usage + dtail_usage) ; for (i = f1 ; i <= f2 ; i++) { /* get frontal matrix info */ fpivcol = Front_npivcol [i] ; /* # candidate pivot columns */ fallrows = Fr_nrows [i] ; /* all rows (not just Schur comp*/ fallcols = Fr_ncols [i] ; /* all cols (not just Schur comp*/ parent = Front_parent [i] ; /* parent in column etree */ fpiv = MIN (fpivcol, fallrows) ; /* # pivot rows and cols */ f = (double) fpiv ; r = fallrows - fpiv ; /* # rows in Schur comp. */ c = fallcols - fpiv ; /* # cols in Schur comp. */ /* assemble all children of front i in column etree */ for (child = Link [i] ; child != EMPTY ; child = Link [child]) { ASSERT (child >= 0 && child < i) ; ASSERT (Front_parent [child] == i) ; /* free the child element and remove it from tuple lists */ cp = MIN (Front_npivcol [child], Fr_nrows [child]) ; cr = Fr_nrows [child] - cp ; cc = Fr_ncols [child] - cp ; ASSERT (cp >= 0 && cr >= 0 && cc >= 0) ; dtail_usage -= ELEMENT_SIZE (cr, cc) ; } /* The flop count computed here is "canonical". */ /* factorize the frontal matrix */ flops += DIV_FLOPS * (f*r + (f-1)*f/2) /* scale pivot columns */ /* f outer products: */ + MULTSUB_FLOPS * (f*r*c + (r+c)*(f-1)*f/2 + (f-1)*f*(2*f-1)/6); /* count nonzeros and memory usage in double precision */ dlf = (f*f-f)/2 + f*r ; /* nz in L below diagonal */ duf = (f*f-f)/2 + f*c ; /* nz in U above diagonal */ dlnz += dlf ; dunz += duf ; /* store f columns of L and f rows of U */ dhead_usage += DUNITS (Entry, dlf + duf) /* numerical values (excl diag) */ + DUNITS (Int, r + c + f) ; /* indices (compressed) */ if (parent != EMPTY) { /* create new element and place in tuple lists */ dtail_usage += ELEMENT_SIZE (r, c) ; /* place in link list of parent */ Link [i] = Link [parent] ; Link [parent] = i ; } /* keep track of peak Numeric->Memory usage */ dmax_usage = MAX (dmax_usage, dhead_usage + dtail_usage) ; } /* free the current frontal matrix */ dtail_usage -= DUNITS (Entry, fsize) ; } dhead_usage = ceil (dhead_usage) ; dmax_usage = ceil (dmax_usage) ; Symbolic->num_mem_size_est = dhead_usage ; Symbolic->num_mem_usage_est = dmax_usage ; Symbolic->lunz_bound = dlnz + dunz - n_inner ; /* ] done using Ci as workspace for Link array */ /* ---------------------------------------------------------------------- */ /* estimate total memory usage in UMFPACK_numeric */ /* ---------------------------------------------------------------------- */ UMF_set_stats ( Info, Symbolic, dmax_usage, /* estimated peak size of Numeric->Memory */ dhead_usage, /* estimated final size of Numeric->Memory */ flops, /* estimated "true flops" */ dlnz, /* estimated nz in L */ dunz, /* estimated nz in U */ dmaxfrsize, /* estimated largest front size */ (double) n_col, /* worst case Numeric->Upattern size */ (double) n_inner, /* max possible pivots to be found */ (double) maxnrows, /* estimated largest #rows in front */ (double) maxncols, /* estimated largest #cols in front */ TRUE, /* assume scaling is to be performed */ prefer_diagonal, ESTIMATE) ; /* ---------------------------------------------------------------------- */ #ifndef NDEBUG for (i = 0 ; i < nchains ; i++) { DEBUG2 (("Chain "ID" start "ID" end "ID" maxrows "ID" maxcols "ID"\n", i, Chain_start [i], Chain_start [i+1] - 1, Chain_maxrows [i], Chain_maxcols [i])) ; UMF_dump_chain (Chain_start [i], Fr_parent, Fr_npivcol, Fr_nrows, Fr_ncols, nfr) ; } fpivcol = 0 ; for (i = 0 ; i < nfr ; i++) { fpivcol = MAX (fpivcol, Front_npivcol [i]) ; } DEBUG0 (("Max pivot cols in any front: "ID"\n", fpivcol)) ; DEBUG1 (("Largest front: maxnrows "ID" maxncols "ID" dmaxfrsize %g\n", maxnrows, maxncols, dmaxfrsize)) ; #endif /* ---------------------------------------------------------------------- */ /* UMFPACK_symbolic was successful, return the object handle */ /* ---------------------------------------------------------------------- */ Symbolic->valid = SYMBOLIC_VALID ; *SymbolicHandle = (void *) Symbolic ; /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ /* (6) The last of the workspace is free'd. The final Symbolic object * consists of 12 to 14 allocated objects. Its final total size is lies * roughly between 4*n and 13*n for a square matrix, which is all that is * left of the memory allocated by this routine. If an error occurs, the * entire Symbolic object is free'd when this routine returns (the error * return routine, below). */ free_work (SW) ; DEBUG0 (("(3)Symbolic UMF_malloc_count - init_count = "ID"\n", UMF_malloc_count - init_count)) ; ASSERT (UMF_malloc_count == init_count + 12 + (Symbolic->Esize != (Int *) NULL) + (Symbolic->Diagonal_map != (Int *) NULL)) ; /* ---------------------------------------------------------------------- */ /* get the time used by UMFPACK_*symbolic */ /* ---------------------------------------------------------------------- */ umfpack_toc (stats) ; Info [UMFPACK_SYMBOLIC_WALLTIME] = stats [0] ; Info [UMFPACK_SYMBOLIC_TIME] = stats [1] ; return (UMFPACK_OK) ; } /* ========================================================================== */ /* === free_work ============================================================ */ /* ========================================================================== */ PRIVATE void free_work ( SWType *SW ) { if (SW) { SW->Rperm_2by2 = (Int *) UMF_free ((void *) SW->Rperm_2by2) ; SW->InvRperm1 = (Int *) UMF_free ((void *) SW->InvRperm1) ; SW->Rs = (double *) UMF_free ((void *) SW->Rs) ; SW->Si = (Int *) UMF_free ((void *) SW->Si) ; SW->Sp = (Int *) UMF_free ((void *) SW->Sp) ; SW->Ci = (Int *) UMF_free ((void *) SW->Ci) ; SW->Front_npivcol = (Int *) UMF_free ((void *) SW->Front_npivcol); SW->Front_nrows = (Int *) UMF_free ((void *) SW->Front_nrows) ; SW->Front_ncols = (Int *) UMF_free ((void *) SW->Front_ncols) ; SW->Front_parent = (Int *) UMF_free ((void *) SW->Front_parent) ; SW->Front_cols = (Int *) UMF_free ((void *) SW->Front_cols) ; SW->Cperm1 = (Int *) UMF_free ((void *) SW->Cperm1) ; SW->Rperm1 = (Int *) UMF_free ((void *) SW->Rperm1) ; SW->InFront = (Int *) UMF_free ((void *) SW->InFront) ; } } /* ========================================================================== */ /* === error ================================================================ */ /* ========================================================================== */ /* Error return from UMFPACK_symbolic. Free all allocated memory. */ PRIVATE void error ( SymbolicType **Symbolic, SWType *SW ) { free_work (SW) ; UMFPACK_free_symbolic ((void **) Symbolic) ; ASSERT (UMF_malloc_count == init_count) ; } SuiteSparse/UMFPACK/Source/umfpack_load_symbolic.c0000644001170100242450000001272510677543733021015 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_load_symbolic ================================================ */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Loads a Symbolic object from a file created by umfpack_*_save_symbolic. */ #include "umf_internal.h" #include "umf_valid_symbolic.h" #include "umf_malloc.h" #include "umf_free.h" #define READ(object,type,n) \ { \ object = (type *) UMF_malloc (n, sizeof (type)) ; \ if (object == (type *) NULL) \ { \ UMFPACK_free_symbolic ((void **) &Symbolic) ; \ fclose (f) ; \ return (UMFPACK_ERROR_out_of_memory) ; \ } \ if (fread (object, sizeof (type), n, f) != (size_t) n) \ { \ UMFPACK_free_symbolic ((void **) &Symbolic) ; \ fclose (f) ; \ return (UMFPACK_ERROR_file_IO) ; \ } \ if (ferror (f)) \ { \ UMFPACK_free_symbolic ((void **) &Symbolic) ; \ fclose (f) ; \ return (UMFPACK_ERROR_file_IO) ; \ } \ } /* ========================================================================== */ /* === UMFPACK_load_symbolic ================================================ */ /* ========================================================================== */ GLOBAL Int UMFPACK_load_symbolic ( void **SymbolicHandle, char *user_filename ) { SymbolicType *Symbolic ; char *filename ; FILE *f ; *SymbolicHandle = (void *) NULL ; /* ---------------------------------------------------------------------- */ /* get the filename, or use the default name if filename is NULL */ /* ---------------------------------------------------------------------- */ if (user_filename == (char *) NULL) { filename = "symbolic.umf" ; } else { filename = user_filename ; } f = fopen (filename, "rb") ; if (!f) { return (UMFPACK_ERROR_file_IO) ; } /* ---------------------------------------------------------------------- */ /* read the Symbolic header from the file, in binary */ /* ---------------------------------------------------------------------- */ Symbolic = (SymbolicType *) UMF_malloc (1, sizeof (SymbolicType)) ; if (Symbolic == (SymbolicType *) NULL) { fclose (f) ; return (UMFPACK_ERROR_out_of_memory) ; } if (fread (Symbolic, sizeof (SymbolicType), 1, f) != 1) { (void) UMF_free ((void *) Symbolic) ; fclose (f) ; return (UMFPACK_ERROR_file_IO) ; } if (ferror (f)) { (void) UMF_free ((void *) Symbolic) ; fclose (f) ; return (UMFPACK_ERROR_file_IO) ; } if (Symbolic->valid != SYMBOLIC_VALID || Symbolic->n_row <= 0 || Symbolic->n_col <= 0 || Symbolic->nfr < 0 || Symbolic->nchains < 0 || Symbolic->esize < 0) { /* Symbolic does not point to a Symbolic object */ (void) UMF_free ((void *) Symbolic) ; fclose (f) ; return (UMFPACK_ERROR_invalid_Symbolic_object) ; } Symbolic->Cperm_init = (Int *) NULL ; Symbolic->Rperm_init = (Int *) NULL ; Symbolic->Front_npivcol = (Int *) NULL ; Symbolic->Front_parent = (Int *) NULL ; Symbolic->Front_1strow = (Int *) NULL ; Symbolic->Front_leftmostdesc = (Int *) NULL ; Symbolic->Chain_start = (Int *) NULL ; Symbolic->Chain_maxrows = (Int *) NULL ; Symbolic->Chain_maxcols = (Int *) NULL ; Symbolic->Cdeg = (Int *) NULL ; Symbolic->Rdeg = (Int *) NULL ; Symbolic->Esize = (Int *) NULL ; Symbolic->Diagonal_map = (Int *) NULL ; /* umfpack_free_symbolic can now be safely called if an error occurs */ /* ---------------------------------------------------------------------- */ /* read the rest of the Symbolic object */ /* ---------------------------------------------------------------------- */ READ (Symbolic->Cperm_init, Int, Symbolic->n_col+1) ; READ (Symbolic->Rperm_init, Int, Symbolic->n_row+1) ; READ (Symbolic->Front_npivcol, Int, Symbolic->nfr+1) ; READ (Symbolic->Front_parent, Int, Symbolic->nfr+1) ; READ (Symbolic->Front_1strow, Int, Symbolic->nfr+1) ; READ (Symbolic->Front_leftmostdesc, Int, Symbolic->nfr+1) ; READ (Symbolic->Chain_start, Int, Symbolic->nchains+1) ; READ (Symbolic->Chain_maxrows, Int, Symbolic->nchains+1) ; READ (Symbolic->Chain_maxcols, Int, Symbolic->nchains+1) ; READ (Symbolic->Cdeg, Int, Symbolic->n_col+1) ; READ (Symbolic->Rdeg, Int, Symbolic->n_row+1) ; if (Symbolic->esize > 0) { /* only when dense rows are present */ READ (Symbolic->Esize, Int, Symbolic->esize) ; } if (Symbolic->prefer_diagonal) { /* only when diagonal pivoting is prefered */ READ (Symbolic->Diagonal_map, Int, Symbolic->n_col+1) ; } /* close the file */ fclose (f) ; /* make sure the Symbolic object is valid */ if (!UMF_valid_symbolic (Symbolic)) { UMFPACK_free_symbolic ((void **) &Symbolic) ; return (UMFPACK_ERROR_invalid_Symbolic_object) ; } *SymbolicHandle = (void *) Symbolic ; return (UMFPACK_OK) ; } SuiteSparse/UMFPACK/Source/umfpack_report_symbolic.c0000644001170100242450000001566210617162134021376 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_report_symbolic ============================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Prints the Symbolic object. See umfpack_report_symbolic.h for details. Does not print new Cdeg, Rdeg, Esize, and the Diagonal_map. Dynamic memory usage: Allocates a size MAX (n_row,n_col)*sizeof(Int) workspace via a single call to UMF_malloc and then frees all of it via UMF_free on return. The workspace is not allocated if an early error return occurs before the workspace is needed. */ #include "umf_internal.h" #include "umf_valid_symbolic.h" #include "umf_report_perm.h" #include "umf_malloc.h" #include "umf_free.h" GLOBAL Int UMFPACK_report_symbolic ( void *SymbolicHandle, const double Control [UMFPACK_CONTROL] ) { Int n_row, n_col, nz, nchains, nfr, maxnrows, maxncols, prl, k, chain, frontid, frontid1, frontid2, kk, *Chain_start, *W, *Chain_maxrows, *Chain_maxcols, *Front_npivcol, *Front_1strow, *Front_leftmostdesc, *Front_parent, done, status1, status2 ; SymbolicType *Symbolic ; prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ; if (prl <= 2) { return (UMFPACK_OK) ; } PRINTF (("Symbolic object: ")) ; Symbolic = (SymbolicType *) SymbolicHandle ; if (!UMF_valid_symbolic (Symbolic)) { PRINTF (("ERROR: invalid\n")) ; return (UMFPACK_ERROR_invalid_Symbolic_object) ; } n_row = Symbolic->n_row ; n_col = Symbolic->n_col ; nz = Symbolic->nz ; nchains = Symbolic->nchains ; nfr = Symbolic->nfr ; maxnrows = Symbolic->maxnrows ; maxncols = Symbolic->maxncols ; Chain_start = Symbolic->Chain_start ; Chain_maxrows = Symbolic->Chain_maxrows ; Chain_maxcols = Symbolic->Chain_maxcols ; Front_npivcol = Symbolic->Front_npivcol ; Front_1strow = Symbolic->Front_1strow ; Front_leftmostdesc = Symbolic->Front_leftmostdesc ; Front_parent = Symbolic->Front_parent ; if (prl >= 4) { PRINTF (("\n matrix to be factorized:\n")) ; PRINTF (("\tn_row: "ID" n_col: "ID"\n", n_row, n_col)) ; PRINTF (("\tnumber of entries: "ID"\n", nz)) ; PRINTF ((" block size used for dense matrix kernels: "ID"\n", Symbolic->nb)) ; PRINTF ((" strategy used: ")) ; /* strategy cannot be auto */ if (Symbolic->strategy == UMFPACK_STRATEGY_SYMMETRIC) { PRINTF (("symmetric")) ; } else if (Symbolic->strategy == UMFPACK_STRATEGY_UNSYMMETRIC) { PRINTF (("unsymmetric")) ; } else if (Symbolic->strategy == UMFPACK_STRATEGY_2BY2) { PRINTF (("symmetric 2-by-2")) ; } PRINTF (("\n")) ; PRINTF ((" ordering used: ")) ; if (Symbolic->ordering == UMFPACK_ORDERING_COLAMD) { PRINTF (("colamd on A\n")) ; } else if (Symbolic->ordering == UMFPACK_ORDERING_AMD) { PRINTF (("amd on A+A'\n")) ; } else if (Symbolic->ordering == UMFPACK_ORDERING_GIVEN) { PRINTF (("provided by user")) ; } PRINTF (("\n")) ; PRINTF ((" performn column etree postorder: ")) ; if (Symbolic->fixQ) { PRINTF (("no\n")) ; } else { PRINTF (("yes\n")) ; } PRINTF ((" prefer diagonal pivoting (attempt P=Q): ")) ; if (Symbolic->prefer_diagonal) { PRINTF (("yes\n")) ; } else { PRINTF (("no\n")) ; } PRINTF ((" variable-size part of Numeric object:\n")) ; PRINTF (("\tminimum initial size (Units): %.20g (MBytes): %.1f\n", Symbolic->dnum_mem_init_usage, MBYTES (Symbolic->dnum_mem_init_usage))) ; PRINTF (("\testimated peak size (Units): %.20g (MBytes): %.1f\n", Symbolic->num_mem_usage_est, MBYTES (Symbolic->num_mem_usage_est))) ; PRINTF (("\testimated final size (Units): %.20g (MBytes): %.1f\n", Symbolic->num_mem_size_est, MBYTES (Symbolic->num_mem_size_est))) ; PRINTF ((" symbolic factorization memory usage (Units):" " %.20g (MBytes): %.1f\n", Symbolic->peak_sym_usage, MBYTES (Symbolic->peak_sym_usage))) ; PRINTF ((" frontal matrices / supercolumns:\n")) ; PRINTF (("\tnumber of frontal chains: "ID"\n", nchains)) ; PRINTF (("\tnumber of frontal matrices: "ID"\n", nfr)) ; PRINTF (("\tlargest frontal matrix row dimension: "ID"\n", maxnrows)) ; PRINTF (("\tlargest frontal matrix column dimension: "ID"\n",maxncols)); } k = 0 ; done = FALSE ; for (chain = 0 ; chain < nchains ; chain++) { frontid1 = Chain_start [chain] ; frontid2 = Chain_start [chain+1] - 1 ; PRINTF4 (("\n Frontal chain: "ID". Frontal matrices "ID" to "ID"\n", INDEX (chain), INDEX (frontid1), INDEX (frontid2))) ; PRINTF4 (("\tLargest frontal matrix in Frontal chain: "ID"-by-"ID"\n", Chain_maxrows [chain], Chain_maxcols [chain])) ; for (frontid = frontid1 ; frontid <= frontid2 ; frontid++) { kk = Front_npivcol [frontid] ; PRINTF4 (("\tFront: "ID" pivot cols: "ID" (pivot columns "ID" to " ID")\n", INDEX (frontid), kk, INDEX (k), INDEX (k+kk-1))) ; PRINTF4 (("\t pivot row candidates: "ID" to "ID"\n", INDEX (Front_1strow [Front_leftmostdesc [frontid]]), INDEX (Front_1strow [frontid+1]-1))) ; PRINTF4 (("\t leftmost descendant: "ID"\n", INDEX (Front_leftmostdesc [frontid]))) ; PRINTF4 (("\t 1st new candidate row : "ID"\n", INDEX (Front_1strow [frontid]))) ; PRINTF4 (("\t parent:")) ; if (Front_parent [frontid] == EMPTY) { PRINTF4 ((" (none)\n")) ; } else { PRINTF4 ((" "ID"\n", INDEX (Front_parent [frontid]))) ; } done = (frontid == 20 && frontid < nfr-1 && prl == 4) ; if (done) { PRINTF4 (("\t...\n")) ; break ; } k += kk ; } if (Front_npivcol [nfr] != 0) { PRINTF4 (("\tFront: "ID" placeholder for "ID" empty columns\n", INDEX (nfr), Front_npivcol [nfr])) ; } if (done) { break ; } } W = (Int *) UMF_malloc (MAX (n_row, n_col), sizeof (Int)) ; if (!W) { PRINTF (("ERROR: out of memory to check Symbolic object\n\n")) ; return (UMFPACK_ERROR_out_of_memory) ; } PRINTF4 (("\nInitial column permutation, Q1: ")) ; status1 = UMF_report_perm (n_col, Symbolic->Cperm_init, W, prl, 0) ; PRINTF4 (("\nInitial row permutation, P1: ")) ; status2 = UMF_report_perm (n_row, Symbolic->Rperm_init, W, prl, 0) ; (void) UMF_free ((void *) W) ; if (status1 != UMFPACK_OK || status2 != UMFPACK_OK) { return (UMFPACK_ERROR_invalid_Symbolic_object) ; } PRINTF4 ((" Symbolic object: ")) ; PRINTF (("OK\n\n")) ; return (UMFPACK_OK) ; } SuiteSparse/UMFPACK/Source/umf_version.h0000644001170100242450000010121710617162533017010 0ustar davisfac/* ========================================================================== */ /* === umf_version.h ======================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Define routine names, depending on version being compiled. DINT: double precision, int's as integers DLONG: double precision, UF_long's as integers ZLONG: complex double precision, UF_long's as integers ZINT: complex double precision, int's as integers */ /* Set DINT as the default, if nothing is defined */ #if !defined (DLONG) && !defined (DINT) && !defined (ZLONG) && !defined (ZINT) #define DINT #endif /* Determine if this is a real or complex version */ #if defined (ZLONG) || defined (ZINT) #define COMPLEX #endif /* -------------------------------------------------------------------------- */ /* integer type (Int is int or UF_long) now defined in amd_internal.h */ /* -------------------------------------------------------------------------- */ #if defined (DLONG) || defined (ZLONG) #define LONG_INTEGER #endif /* -------------------------------------------------------------------------- */ /* Numerical relop macros for correctly handling the NaN case */ /* -------------------------------------------------------------------------- */ /* SCALAR_IS_NAN(x): True if x is NaN. False otherwise. The commonly-existing isnan(x) function could be used, but it's not in Kernighan & Ritchie 2nd edition (ANSI C). It may appear in , but I'm not certain about portability. The expression x != x is true if and only if x is NaN, according to the IEEE 754 floating-point standard. SCALAR_IS_ZERO(x): True if x is zero. False if x is nonzero, NaN, or +/- Inf. This is (x == 0) if the compiler is IEEE 754 compliant. SCALAR_IS_NONZERO(x): True if x is nonzero, NaN, or +/- Inf. False if x zero. This is (x != 0) if the compiler is IEEE 754 compliant. SCALAR_IS_LTZERO(x): True if x is < zero or -Inf. False if x is >= 0, NaN, or +Inf. This is (x < 0) if the compiler is IEEE 754 compliant. */ #if defined (UMF_WINDOWS) && !defined (MATHWORKS) /* Yes, this is exceedingly ugly. Blame Microsoft, which hopelessly */ /* violates the IEEE 754 floating-point standard in a bizarre way. */ /* If you're using an IEEE 754-compliant compiler, then x != x is true */ /* iff x is NaN. For Microsoft, (x < x) is true iff x is NaN. */ /* So either way, this macro safely detects a NaN. */ #define SCALAR_IS_NAN(x) (((x) != (x)) || (((x) < (x)))) #define SCALAR_IS_ZERO(x) (((x) == 0.) && !SCALAR_IS_NAN(x)) #define SCALAR_IS_NONZERO(x) (((x) != 0.) || SCALAR_IS_NAN(x)) #define SCALAR_IS_LTZERO(x) (((x) < 0.) && !SCALAR_IS_NAN(x)) #else /* These all work properly, according to the IEEE 754 standard ... except on */ /* a PC with windows. Works fine in Linux on the same PC... */ #define SCALAR_IS_NAN(x) ((x) != (x)) #define SCALAR_IS_ZERO(x) ((x) == 0.) #define SCALAR_IS_NONZERO(x) ((x) != 0.) #define SCALAR_IS_LTZERO(x) ((x) < 0.) #endif /* scalar absolute value macro. If x is NaN, the result is NaN: */ #define SCALAR_ABS(x) ((SCALAR_IS_LTZERO (x)) ? -(x) : (x)) /* true if an integer (stored in double x) would overflow (or if x is NaN) */ #define INT_OVERFLOW(x) ((!((x) * (1.0+1e-8) <= (double) Int_MAX)) \ || SCALAR_IS_NAN (x)) /* print a scalar (avoid printing "-0" for negative zero). */ #define PRINT_SCALAR(a) \ { \ if (SCALAR_IS_NONZERO (a)) \ { \ PRINTF ((" (%g)", (a))) ; \ } \ else \ { \ PRINTF ((" (0)")) ; \ } \ } /* -------------------------------------------------------------------------- */ /* Real floating-point arithmetic */ /* -------------------------------------------------------------------------- */ #ifndef COMPLEX #define Entry double #define SPLIT(s) (1) #define REAL_COMPONENT(c) (c) #define IMAG_COMPONENT(c) (0.) #define ASSIGN(c,s1,s2,p,split) { (c) = (s1)[p] ; } #define CLEAR(c) { (c) = 0. ; } #define CLEAR_AND_INCREMENT(p) { *p++ = 0. ; } #define IS_NAN(a) SCALAR_IS_NAN (a) #define IS_ZERO(a) SCALAR_IS_ZERO (a) #define IS_NONZERO(a) SCALAR_IS_NONZERO (a) #define SCALE_DIV(c,s) { (c) /= (s) ; } #define SCALE(c,s) { (c) *= (s) ; } #define ASSEMBLE(c,a) { (c) += (a) ; } #define ASSEMBLE_AND_INCREMENT(c,p) { (c) += *p++ ; } #define DECREMENT(c,a) { (c) -= (a) ; } #define MULT(c,a,b) { (c) = (a) * (b) ; } #define MULT_CONJ(c,a,b) { (c) = (a) * (b) ; } #define MULT_SUB(c,a,b) { (c) -= (a) * (b) ; } #define MULT_SUB_CONJ(c,a,b) { (c) -= (a) * (b) ; } #define DIV(c,a,b) { (c) = (a) / (b) ; } #define DIV_CONJ(c,a,b) { (c) = (a) / (b) ; } #define APPROX_ABS(s,a) { (s) = SCALAR_ABS (a) ; } #define ABS(s,a) { (s) = SCALAR_ABS (a) ; } #define PRINT_ENTRY(a) PRINT_SCALAR (a) /* for flop counts */ #define MULTSUB_FLOPS 2. /* c -= a*b */ #define DIV_FLOPS 1. /* c = a/b */ #define ABS_FLOPS 0. /* c = abs (a) */ #define ASSEMBLE_FLOPS 1. /* c += a */ #define DECREMENT_FLOPS 1. /* c -= a */ #define MULT_FLOPS 1. /* c = a*b */ #define SCALE_FLOPS 1. /* c = a/s */ #else /* -------------------------------------------------------------------------- */ /* Complex floating-point arithmetic */ /* -------------------------------------------------------------------------- */ /* Note: An alternative to this DoubleComplex type would be to use a struct { double r ; double i ; }. The problem with that method (used by the Sun Performance Library, for example) is that ANSI C provides no guarantee about the layout of a struct. It is possible that the sizeof the struct above would be greater than 2 * sizeof (double). This would mean that the complex BLAS could not be used. The method used here avoids that possibility. ANSI C *does* guarantee that an array of structs has the same size as n times the size of one struct. The ANSI C99 version of the C language includes a "double _Complex" type. It should be possible in that case to do the following: #define Entry double _Complex and remove the DoubleComplex struct. The macros, below, could then be replaced with instrinsic operators. Note that the #define Real and #define Imag should also be removed (they only appear in this file). For the MULT, MULT_SUB, MULT_SUB_CONJ, and MULT_CONJ macros, the output argument c cannot be the same as any input argument. */ typedef struct { double component [2] ; /* real and imaginary parts */ } DoubleComplex ; #define Entry DoubleComplex #define Real component [0] #define Imag component [1] /* for flop counts */ #define MULTSUB_FLOPS 8. /* c -= a*b */ #define DIV_FLOPS 9. /* c = a/b */ #define ABS_FLOPS 6. /* c = abs (a), count sqrt as one flop */ #define ASSEMBLE_FLOPS 2. /* c += a */ #define DECREMENT_FLOPS 2. /* c -= a */ #define MULT_FLOPS 6. /* c = a*b */ #define SCALE_FLOPS 2. /* c = a/s or c = a*s */ /* -------------------------------------------------------------------------- */ /* real part of c */ #define REAL_COMPONENT(c) ((c).Real) /* -------------------------------------------------------------------------- */ /* imag part of c */ #define IMAG_COMPONENT(c) ((c).Imag) /* -------------------------------------------------------------------------- */ /* Return TRUE if a complex number is in split form, FALSE if in packed form */ #define SPLIT(sz) ((sz) != (double *) NULL) /* -------------------------------------------------------------------------- */ /* c = (s1) + (s2)*i, if s2 is null, then X is in "packed" format (compatible * with Entry and ANSI C99 double _Complex type). */ #define ASSIGN(c,s1,s2,p,split) \ { \ if (split) \ { \ (c).Real = (s1)[p] ; \ (c).Imag = (s2)[p] ; \ } \ else \ { \ (c) = ((Entry *)(s1))[p] ; \ } \ } /* -------------------------------------------------------------------------- */ /* c = 0 */ #define CLEAR(c) \ { \ (c).Real = 0. ; \ (c).Imag = 0. ; \ } /* -------------------------------------------------------------------------- */ /* *p++ = 0 */ #define CLEAR_AND_INCREMENT(p) \ { \ p->Real = 0. ; \ p->Imag = 0. ; \ p++ ; \ } /* -------------------------------------------------------------------------- */ /* True if a == 0 */ #define IS_ZERO(a) \ (SCALAR_IS_ZERO ((a).Real) && SCALAR_IS_ZERO ((a).Imag)) /* -------------------------------------------------------------------------- */ /* True if a is NaN */ #define IS_NAN(a) \ (SCALAR_IS_NAN ((a).Real) || SCALAR_IS_NAN ((a).Imag)) /* -------------------------------------------------------------------------- */ /* True if a != 0 */ #define IS_NONZERO(a) \ (SCALAR_IS_NONZERO ((a).Real) || SCALAR_IS_NONZERO ((a).Imag)) /* -------------------------------------------------------------------------- */ /* c /= s */ #define SCALE_DIV(c,s) \ { \ (c).Real /= (s) ; \ (c).Imag /= (s) ; \ } /* -------------------------------------------------------------------------- */ /* c *= s */ #define SCALE(c,s) \ { \ (c).Real *= (s) ; \ (c).Imag *= (s) ; \ } /* -------------------------------------------------------------------------- */ /* c += a */ #define ASSEMBLE(c,a) \ { \ (c).Real += (a).Real ; \ (c).Imag += (a).Imag ; \ } /* -------------------------------------------------------------------------- */ /* c += *p++ */ #define ASSEMBLE_AND_INCREMENT(c,p) \ { \ (c).Real += p->Real ; \ (c).Imag += p->Imag ; \ p++ ; \ } /* -------------------------------------------------------------------------- */ /* c -= a */ #define DECREMENT(c,a) \ { \ (c).Real -= (a).Real ; \ (c).Imag -= (a).Imag ; \ } /* -------------------------------------------------------------------------- */ /* c = a*b, assert because c cannot be the same as a or b */ #define MULT(c,a,b) \ { \ ASSERT (&(c) != &(a) && &(c) != &(b)) ; \ (c).Real = (a).Real * (b).Real - (a).Imag * (b).Imag ; \ (c).Imag = (a).Imag * (b).Real + (a).Real * (b).Imag ; \ } /* -------------------------------------------------------------------------- */ /* c = a*conjugate(b), assert because c cannot be the same as a or b */ #define MULT_CONJ(c,a,b) \ { \ ASSERT (&(c) != &(a) && &(c) != &(b)) ; \ (c).Real = (a).Real * (b).Real + (a).Imag * (b).Imag ; \ (c).Imag = (a).Imag * (b).Real - (a).Real * (b).Imag ; \ } /* -------------------------------------------------------------------------- */ /* c -= a*b, assert because c cannot be the same as a or b */ #define MULT_SUB(c,a,b) \ { \ ASSERT (&(c) != &(a) && &(c) != &(b)) ; \ (c).Real -= (a).Real * (b).Real - (a).Imag * (b).Imag ; \ (c).Imag -= (a).Imag * (b).Real + (a).Real * (b).Imag ; \ } /* -------------------------------------------------------------------------- */ /* c -= a*conjugate(b), assert because c cannot be the same as a or b */ #define MULT_SUB_CONJ(c,a,b) \ { \ ASSERT (&(c) != &(a) && &(c) != &(b)) ; \ (c).Real -= (a).Real * (b).Real + (a).Imag * (b).Imag ; \ (c).Imag -= (a).Imag * (b).Real - (a).Real * (b).Imag ; \ } /* -------------------------------------------------------------------------- */ /* c = a/b, using function pointer */ #define DIV(c,a,b) \ { \ (void) umfpack_divcomplex ((a).Real, (a).Imag, (b).Real, (b).Imag, \ &((c).Real), &((c).Imag)) ; \ } /* -------------------------------------------------------------------------- */ /* c = a/conjugate(b), using function pointer */ #define DIV_CONJ(c,a,b) \ { \ (void) umfpack_divcomplex ((a).Real, (a).Imag, (b).Real, (-(b).Imag), \ &((c).Real), &((c).Imag)) ; \ } /* -------------------------------------------------------------------------- */ /* approximate absolute value, s = |r|+|i| */ #define APPROX_ABS(s,a) \ { \ (s) = SCALAR_ABS ((a).Real) + SCALAR_ABS ((a).Imag) ; \ } /* -------------------------------------------------------------------------- */ /* exact absolute value, s = sqrt (a.real^2 + a.imag^2) */ #define ABS(s,a) \ { \ (s) = umfpack_hypot ((a).Real, (a).Imag) ; \ } /* -------------------------------------------------------------------------- */ /* print an entry (avoid printing "-0" for negative zero). */ #define PRINT_ENTRY(a) \ { \ if (SCALAR_IS_NONZERO ((a).Real)) \ { \ PRINTF ((" (%g", (a).Real)) ; \ } \ else \ { \ PRINTF ((" (0")) ; \ } \ if (SCALAR_IS_LTZERO ((a).Imag)) \ { \ PRINTF ((" - %gi)", -(a).Imag)) ; \ } \ else if (SCALAR_IS_ZERO ((a).Imag)) \ { \ PRINTF ((" + 0i)")) ; \ } \ else \ { \ PRINTF ((" + %gi)", (a).Imag)) ; \ } \ } /* -------------------------------------------------------------------------- */ #endif /* #ifndef COMPLEX */ /* -------------------------------------------------------------------------- */ /* Double precision, with int's as integers */ /* -------------------------------------------------------------------------- */ #ifdef DINT #define UMF_analyze umf_i_analyze #define UMF_apply_order umf_i_apply_order #define UMF_assemble umfdi_assemble #define UMF_assemble_fixq umfdi_assemble_fixq #define UMF_blas3_update umfdi_blas3_update #define UMF_build_tuples umfdi_build_tuples #define UMF_build_tuples_usage umfdi_build_tuples_usage #define UMF_colamd umf_i_colamd #define UMF_colamd_set_defaults umf_i_colamd_set_defaults #define UMF_create_element umfdi_create_element #define UMF_extend_front umfdi_extend_front #define UMF_free umf_i_free #define UMF_fsize umf_i_fsize #define UMF_garbage_collection umfdi_garbage_collection #define UMF_get_memory umfdi_get_memory #define UMF_grow_front umfdi_grow_front #define UMF_init_front umfdi_init_front #define UMF_is_permutation umf_i_is_permutation #define UMF_kernel umfdi_kernel #define UMF_kernel_init umfdi_kernel_init #define UMF_kernel_init_usage umfdi_kernel_init_usage #define UMF_kernel_wrapup umfdi_kernel_wrapup #define UMF_local_search umfdi_local_search #define UMF_lsolve umfdi_lsolve #define UMF_ltsolve umfdi_ltsolve #define UMF_lhsolve umfdi_lhsolve #define UMF_malloc umf_i_malloc #define UMF_mem_alloc_element umfdi_mem_alloc_element #define UMF_mem_alloc_head_block umfdi_mem_alloc_head_block #define UMF_mem_alloc_tail_block umfdi_mem_alloc_tail_block #define UMF_mem_free_tail_block umfdi_mem_free_tail_block #define UMF_mem_init_memoryspace umfdi_mem_init_memoryspace #define UMF_realloc umf_i_realloc #define UMF_report_perm umf_i_report_perm #define UMF_report_vector umfdi_report_vector #define UMF_row_search umfdi_row_search #define UMF_scale umfdi_scale #define UMF_scale_column umfdi_scale_column #define UMF_set_stats umf_i_set_stats #define UMF_singletons umf_i_singletons #define UMF_solve umfdi_solve #define UMF_start_front umfdi_start_front #define UMF_store_lu umfdi_store_lu #define UMF_store_lu_drop umfdi_store_lu_drop #define UMF_symbolic_usage umfdi_symbolic_usage #define UMF_transpose umfdi_transpose #define UMF_tuple_lengths umfdi_tuple_lengths #define UMF_usolve umfdi_usolve #define UMF_utsolve umfdi_utsolve #define UMF_uhsolve umfdi_uhsolve #define UMF_valid_numeric umfdi_valid_numeric #define UMF_valid_symbolic umfdi_valid_symbolic #define UMF_triplet_map_x umfdi_triplet_map_x #define UMF_triplet_map_nox umfdi_triplet_map_nox #define UMF_triplet_nomap_x umfdi_triplet_nomap_x #define UMF_triplet_nomap_nox umfdi_triplet_nomap_nox #define UMF_2by2 umfdi_2by2 #define UMFPACK_col_to_triplet umfpack_di_col_to_triplet #define UMFPACK_defaults umfpack_di_defaults #define UMFPACK_free_numeric umfpack_di_free_numeric #define UMFPACK_free_symbolic umfpack_di_free_symbolic #define UMFPACK_get_lunz umfpack_di_get_lunz #define UMFPACK_get_numeric umfpack_di_get_numeric #define UMFPACK_get_symbolic umfpack_di_get_symbolic #define UMFPACK_get_determinant umfpack_di_get_determinant #define UMFPACK_numeric umfpack_di_numeric #define UMFPACK_qsymbolic umfpack_di_qsymbolic #define UMFPACK_report_control umfpack_di_report_control #define UMFPACK_report_info umfpack_di_report_info #define UMFPACK_report_matrix umfpack_di_report_matrix #define UMFPACK_report_numeric umfpack_di_report_numeric #define UMFPACK_report_perm umfpack_di_report_perm #define UMFPACK_report_status umfpack_di_report_status #define UMFPACK_report_symbolic umfpack_di_report_symbolic #define UMFPACK_report_triplet umfpack_di_report_triplet #define UMFPACK_report_vector umfpack_di_report_vector #define UMFPACK_save_numeric umfpack_di_save_numeric #define UMFPACK_save_symbolic umfpack_di_save_symbolic #define UMFPACK_load_numeric umfpack_di_load_numeric #define UMFPACK_load_symbolic umfpack_di_load_symbolic #define UMFPACK_scale umfpack_di_scale #define UMFPACK_solve umfpack_di_solve #define UMFPACK_symbolic umfpack_di_symbolic #define UMFPACK_transpose umfpack_di_transpose #define UMFPACK_triplet_to_col umfpack_di_triplet_to_col #define UMFPACK_wsolve umfpack_di_wsolve /* for debugging only: */ #define UMF_malloc_count umf_i_malloc_count #define UMF_debug umfdi_debug #define UMF_allocfail umfdi_allocfail #define UMF_gprob umfdi_gprob #define UMF_dump_dense umfdi_dump_dense #define UMF_dump_element umfdi_dump_element #define UMF_dump_rowcol umfdi_dump_rowcol #define UMF_dump_matrix umfdi_dump_matrix #define UMF_dump_current_front umfdi_dump_current_front #define UMF_dump_lu umfdi_dump_lu #define UMF_dump_memory umfdi_dump_memory #define UMF_dump_packed_memory umfdi_dump_packed_memory #define UMF_dump_col_matrix umfdi_dump_col_matrix #define UMF_dump_chain umfdi_dump_chain #define UMF_dump_start umfdi_dump_start #define UMF_dump_rowmerge umfdi_dump_rowmerge #define UMF_dump_diagonal_map umfdi_dump_diagonal_map #endif /* -------------------------------------------------------------------------- */ /* Double precision, with UF_long's as integers */ /* -------------------------------------------------------------------------- */ #ifdef DLONG #define UMF_analyze umf_l_analyze #define UMF_apply_order umf_l_apply_order #define UMF_assemble umfdl_assemble #define UMF_assemble_fixq umfdl_assemble_fixq #define UMF_blas3_update umfdl_blas3_update #define UMF_build_tuples umfdl_build_tuples #define UMF_build_tuples_usage umfdl_build_tuples_usage #define UMF_colamd umf_l_colamd #define UMF_colamd_set_defaults umf_l_colamd_set_defaults #define UMF_create_element umfdl_create_element #define UMF_extend_front umfdl_extend_front #define UMF_free umf_l_free #define UMF_fsize umf_l_fsize #define UMF_garbage_collection umfdl_garbage_collection #define UMF_get_memory umfdl_get_memory #define UMF_grow_front umfdl_grow_front #define UMF_init_front umfdl_init_front #define UMF_is_permutation umf_l_is_permutation #define UMF_kernel umfdl_kernel #define UMF_kernel_init umfdl_kernel_init #define UMF_kernel_init_usage umfdl_kernel_init_usage #define UMF_kernel_wrapup umfdl_kernel_wrapup #define UMF_local_search umfdl_local_search #define UMF_lsolve umfdl_lsolve #define UMF_ltsolve umfdl_ltsolve #define UMF_lhsolve umfdl_lhsolve #define UMF_malloc umf_l_malloc #define UMF_mem_alloc_element umfdl_mem_alloc_element #define UMF_mem_alloc_head_block umfdl_mem_alloc_head_block #define UMF_mem_alloc_tail_block umfdl_mem_alloc_tail_block #define UMF_mem_free_tail_block umfdl_mem_free_tail_block #define UMF_mem_init_memoryspace umfdl_mem_init_memoryspace #define UMF_realloc umf_l_realloc #define UMF_report_perm umf_l_report_perm #define UMF_report_vector umfdl_report_vector #define UMF_row_search umfdl_row_search #define UMF_scale umfdl_scale #define UMF_scale_column umfdl_scale_column #define UMF_set_stats umf_l_set_stats #define UMF_singletons umf_l_singletons #define UMF_solve umfdl_solve #define UMF_start_front umfdl_start_front #define UMF_store_lu umfdl_store_lu #define UMF_store_lu_drop umfdl_store_lu_drop #define UMF_symbolic_usage umfdl_symbolic_usage #define UMF_transpose umfdl_transpose #define UMF_tuple_lengths umfdl_tuple_lengths #define UMF_usolve umfdl_usolve #define UMF_utsolve umfdl_utsolve #define UMF_uhsolve umfdl_uhsolve #define UMF_valid_numeric umfdl_valid_numeric #define UMF_valid_symbolic umfdl_valid_symbolic #define UMF_triplet_map_x umfdl_triplet_map_x #define UMF_triplet_map_nox umfdl_triplet_map_nox #define UMF_triplet_nomap_x umfdl_triplet_nomap_x #define UMF_triplet_nomap_nox umfdl_triplet_nomap_nox #define UMF_2by2 umfdl_2by2 #define UMFPACK_col_to_triplet umfpack_dl_col_to_triplet #define UMFPACK_defaults umfpack_dl_defaults #define UMFPACK_free_numeric umfpack_dl_free_numeric #define UMFPACK_free_symbolic umfpack_dl_free_symbolic #define UMFPACK_get_lunz umfpack_dl_get_lunz #define UMFPACK_get_numeric umfpack_dl_get_numeric #define UMFPACK_get_symbolic umfpack_dl_get_symbolic #define UMFPACK_get_determinant umfpack_dl_get_determinant #define UMFPACK_numeric umfpack_dl_numeric #define UMFPACK_qsymbolic umfpack_dl_qsymbolic #define UMFPACK_report_control umfpack_dl_report_control #define UMFPACK_report_info umfpack_dl_report_info #define UMFPACK_report_matrix umfpack_dl_report_matrix #define UMFPACK_report_numeric umfpack_dl_report_numeric #define UMFPACK_report_perm umfpack_dl_report_perm #define UMFPACK_report_status umfpack_dl_report_status #define UMFPACK_report_symbolic umfpack_dl_report_symbolic #define UMFPACK_report_triplet umfpack_dl_report_triplet #define UMFPACK_report_vector umfpack_dl_report_vector #define UMFPACK_save_numeric umfpack_dl_save_numeric #define UMFPACK_save_symbolic umfpack_dl_save_symbolic #define UMFPACK_load_numeric umfpack_dl_load_numeric #define UMFPACK_load_symbolic umfpack_dl_load_symbolic #define UMFPACK_scale umfpack_dl_scale #define UMFPACK_solve umfpack_dl_solve #define UMFPACK_symbolic umfpack_dl_symbolic #define UMFPACK_transpose umfpack_dl_transpose #define UMFPACK_triplet_to_col umfpack_dl_triplet_to_col #define UMFPACK_wsolve umfpack_dl_wsolve /* for debugging only: */ #define UMF_malloc_count umf_l_malloc_count #define UMF_debug umfdl_debug #define UMF_allocfail umfdl_allocfail #define UMF_gprob umfdl_gprob #define UMF_dump_dense umfdl_dump_dense #define UMF_dump_element umfdl_dump_element #define UMF_dump_rowcol umfdl_dump_rowcol #define UMF_dump_matrix umfdl_dump_matrix #define UMF_dump_current_front umfdl_dump_current_front #define UMF_dump_lu umfdl_dump_lu #define UMF_dump_memory umfdl_dump_memory #define UMF_dump_packed_memory umfdl_dump_packed_memory #define UMF_dump_col_matrix umfdl_dump_col_matrix #define UMF_dump_chain umfdl_dump_chain #define UMF_dump_start umfdl_dump_start #define UMF_dump_rowmerge umfdl_dump_rowmerge #define UMF_dump_diagonal_map umfdl_dump_diagonal_map #endif /* -------------------------------------------------------------------------- */ /* Complex double precision, with int's as integers */ /* -------------------------------------------------------------------------- */ #ifdef ZINT #define UMF_analyze umf_i_analyze #define UMF_apply_order umf_i_apply_order #define UMF_assemble umfzi_assemble #define UMF_assemble_fixq umfzi_assemble_fixq #define UMF_blas3_update umfzi_blas3_update #define UMF_build_tuples umfzi_build_tuples #define UMF_build_tuples_usage umfzi_build_tuples_usage #define UMF_colamd umf_i_colamd #define UMF_colamd_set_defaults umf_i_colamd_set_defaults #define UMF_create_element umfzi_create_element #define UMF_extend_front umfzi_extend_front #define UMF_free umf_i_free #define UMF_fsize umf_i_fsize #define UMF_garbage_collection umfzi_garbage_collection #define UMF_get_memory umfzi_get_memory #define UMF_grow_front umfzi_grow_front #define UMF_init_front umfzi_init_front #define UMF_is_permutation umf_i_is_permutation #define UMF_kernel umfzi_kernel #define UMF_kernel_init umfzi_kernel_init #define UMF_kernel_init_usage umfzi_kernel_init_usage #define UMF_kernel_wrapup umfzi_kernel_wrapup #define UMF_local_search umfzi_local_search #define UMF_lsolve umfzi_lsolve #define UMF_ltsolve umfzi_ltsolve #define UMF_lhsolve umfzi_lhsolve #define UMF_malloc umf_i_malloc #define UMF_mem_alloc_element umfzi_mem_alloc_element #define UMF_mem_alloc_head_block umfzi_mem_alloc_head_block #define UMF_mem_alloc_tail_block umfzi_mem_alloc_tail_block #define UMF_mem_free_tail_block umfzi_mem_free_tail_block #define UMF_mem_init_memoryspace umfzi_mem_init_memoryspace #define UMF_realloc umf_i_realloc #define UMF_report_perm umf_i_report_perm #define UMF_report_vector umfzi_report_vector #define UMF_row_search umfzi_row_search #define UMF_scale umfzi_scale #define UMF_scale_column umfzi_scale_column #define UMF_set_stats umfzi_set_stats #define UMF_singletons umf_i_singletons #define UMF_solve umfzi_solve #define UMF_start_front umfzi_start_front #define UMF_store_lu umfzi_store_lu #define UMF_store_lu_drop umfzi_store_lu_drop #define UMF_symbolic_usage umfzi_symbolic_usage #define UMF_transpose umfzi_transpose #define UMF_tuple_lengths umfzi_tuple_lengths #define UMF_usolve umfzi_usolve #define UMF_utsolve umfzi_utsolve #define UMF_uhsolve umfzi_uhsolve #define UMF_valid_numeric umfzi_valid_numeric #define UMF_valid_symbolic umfzi_valid_symbolic #define UMF_triplet_map_x umfzi_triplet_map_x #define UMF_triplet_map_nox umfzi_triplet_map_nox #define UMF_triplet_nomap_x umfzi_triplet_nomap_x #define UMF_triplet_nomap_nox umfzi_triplet_nomap_nox #define UMF_2by2 umfzi_2by2 #define UMFPACK_col_to_triplet umfpack_zi_col_to_triplet #define UMFPACK_defaults umfpack_zi_defaults #define UMFPACK_free_numeric umfpack_zi_free_numeric #define UMFPACK_free_symbolic umfpack_zi_free_symbolic #define UMFPACK_get_lunz umfpack_zi_get_lunz #define UMFPACK_get_numeric umfpack_zi_get_numeric #define UMFPACK_get_symbolic umfpack_zi_get_symbolic #define UMFPACK_get_determinant umfpack_zi_get_determinant #define UMFPACK_numeric umfpack_zi_numeric #define UMFPACK_qsymbolic umfpack_zi_qsymbolic #define UMFPACK_report_control umfpack_zi_report_control #define UMFPACK_report_info umfpack_zi_report_info #define UMFPACK_report_matrix umfpack_zi_report_matrix #define UMFPACK_report_numeric umfpack_zi_report_numeric #define UMFPACK_report_perm umfpack_zi_report_perm #define UMFPACK_report_status umfpack_zi_report_status #define UMFPACK_report_symbolic umfpack_zi_report_symbolic #define UMFPACK_report_triplet umfpack_zi_report_triplet #define UMFPACK_report_vector umfpack_zi_report_vector #define UMFPACK_save_numeric umfpack_zi_save_numeric #define UMFPACK_save_symbolic umfpack_zi_save_symbolic #define UMFPACK_load_numeric umfpack_zi_load_numeric #define UMFPACK_load_symbolic umfpack_zi_load_symbolic #define UMFPACK_scale umfpack_zi_scale #define UMFPACK_solve umfpack_zi_solve #define UMFPACK_symbolic umfpack_zi_symbolic #define UMFPACK_transpose umfpack_zi_transpose #define UMFPACK_triplet_to_col umfpack_zi_triplet_to_col #define UMFPACK_wsolve umfpack_zi_wsolve /* for debugging only: */ #define UMF_malloc_count umf_i_malloc_count #define UMF_debug umfzi_debug #define UMF_allocfail umfzi_allocfail #define UMF_gprob umfzi_gprob #define UMF_dump_dense umfzi_dump_dense #define UMF_dump_element umfzi_dump_element #define UMF_dump_rowcol umfzi_dump_rowcol #define UMF_dump_matrix umfzi_dump_matrix #define UMF_dump_current_front umfzi_dump_current_front #define UMF_dump_lu umfzi_dump_lu #define UMF_dump_memory umfzi_dump_memory #define UMF_dump_packed_memory umfzi_dump_packed_memory #define UMF_dump_col_matrix umfzi_dump_col_matrix #define UMF_dump_chain umfzi_dump_chain #define UMF_dump_start umfzi_dump_start #define UMF_dump_rowmerge umfzi_dump_rowmerge #define UMF_dump_diagonal_map umfzi_dump_diagonal_map #endif /* -------------------------------------------------------------------------- */ /* Complex double precision, with UF_long's as integers */ /* -------------------------------------------------------------------------- */ #ifdef ZLONG #define UMF_analyze umf_l_analyze #define UMF_apply_order umf_l_apply_order #define UMF_assemble umfzl_assemble #define UMF_assemble_fixq umfzl_assemble_fixq #define UMF_blas3_update umfzl_blas3_update #define UMF_build_tuples umfzl_build_tuples #define UMF_build_tuples_usage umfzl_build_tuples_usage #define UMF_colamd umf_l_colamd #define UMF_colamd_set_defaults umf_l_colamd_set_defaults #define UMF_create_element umfzl_create_element #define UMF_extend_front umfzl_extend_front #define UMF_free umf_l_free #define UMF_fsize umf_l_fsize #define UMF_garbage_collection umfzl_garbage_collection #define UMF_get_memory umfzl_get_memory #define UMF_grow_front umfzl_grow_front #define UMF_init_front umfzl_init_front #define UMF_is_permutation umf_l_is_permutation #define UMF_kernel umfzl_kernel #define UMF_kernel_init umfzl_kernel_init #define UMF_kernel_init_usage umfzl_kernel_init_usage #define UMF_kernel_wrapup umfzl_kernel_wrapup #define UMF_local_search umfzl_local_search #define UMF_lsolve umfzl_lsolve #define UMF_ltsolve umfzl_ltsolve #define UMF_lhsolve umfzl_lhsolve #define UMF_malloc umf_l_malloc #define UMF_mem_alloc_element umfzl_mem_alloc_element #define UMF_mem_alloc_head_block umfzl_mem_alloc_head_block #define UMF_mem_alloc_tail_block umfzl_mem_alloc_tail_block #define UMF_mem_free_tail_block umfzl_mem_free_tail_block #define UMF_mem_init_memoryspace umfzl_mem_init_memoryspace #define UMF_realloc umf_l_realloc #define UMF_report_perm umf_l_report_perm #define UMF_report_vector umfzl_report_vector #define UMF_row_search umfzl_row_search #define UMF_scale umfzl_scale #define UMF_scale_column umfzl_scale_column #define UMF_set_stats umfzl_set_stats #define UMF_singletons umf_l_singletons #define UMF_solve umfzl_solve #define UMF_start_front umfzl_start_front #define UMF_store_lu umfzl_store_lu #define UMF_store_lu_drop umfzl_store_lu_drop #define UMF_symbolic_usage umfzl_symbolic_usage #define UMF_transpose umfzl_transpose #define UMF_tuple_lengths umfzl_tuple_lengths #define UMF_usolve umfzl_usolve #define UMF_utsolve umfzl_utsolve #define UMF_uhsolve umfzl_uhsolve #define UMF_valid_numeric umfzl_valid_numeric #define UMF_valid_symbolic umfzl_valid_symbolic #define UMF_triplet_map_x umfzl_triplet_map_x #define UMF_triplet_map_nox umfzl_triplet_map_nox #define UMF_triplet_nomap_x umfzl_triplet_nomap_x #define UMF_triplet_nomap_nox umfzl_triplet_nomap_nox #define UMF_2by2 umfzl_2by2 #define UMFPACK_col_to_triplet umfpack_zl_col_to_triplet #define UMFPACK_defaults umfpack_zl_defaults #define UMFPACK_free_numeric umfpack_zl_free_numeric #define UMFPACK_free_symbolic umfpack_zl_free_symbolic #define UMFPACK_get_lunz umfpack_zl_get_lunz #define UMFPACK_get_numeric umfpack_zl_get_numeric #define UMFPACK_get_symbolic umfpack_zl_get_symbolic #define UMFPACK_get_determinant umfpack_zl_get_determinant #define UMFPACK_numeric umfpack_zl_numeric #define UMFPACK_qsymbolic umfpack_zl_qsymbolic #define UMFPACK_report_control umfpack_zl_report_control #define UMFPACK_report_info umfpack_zl_report_info #define UMFPACK_report_matrix umfpack_zl_report_matrix #define UMFPACK_report_numeric umfpack_zl_report_numeric #define UMFPACK_report_perm umfpack_zl_report_perm #define UMFPACK_report_status umfpack_zl_report_status #define UMFPACK_report_symbolic umfpack_zl_report_symbolic #define UMFPACK_report_triplet umfpack_zl_report_triplet #define UMFPACK_report_vector umfpack_zl_report_vector #define UMFPACK_save_numeric umfpack_zl_save_numeric #define UMFPACK_save_symbolic umfpack_zl_save_symbolic #define UMFPACK_load_numeric umfpack_zl_load_numeric #define UMFPACK_load_symbolic umfpack_zl_load_symbolic #define UMFPACK_scale umfpack_zl_scale #define UMFPACK_solve umfpack_zl_solve #define UMFPACK_symbolic umfpack_zl_symbolic #define UMFPACK_transpose umfpack_zl_transpose #define UMFPACK_triplet_to_col umfpack_zl_triplet_to_col #define UMFPACK_wsolve umfpack_zl_wsolve /* for debugging only: */ #define UMF_malloc_count umf_l_malloc_count #define UMF_debug umfzl_debug #define UMF_allocfail umfzl_allocfail #define UMF_gprob umfzl_gprob #define UMF_dump_dense umfzl_dump_dense #define UMF_dump_element umfzl_dump_element #define UMF_dump_rowcol umfzl_dump_rowcol #define UMF_dump_matrix umfzl_dump_matrix #define UMF_dump_current_front umfzl_dump_current_front #define UMF_dump_lu umfzl_dump_lu #define UMF_dump_memory umfzl_dump_memory #define UMF_dump_packed_memory umfzl_dump_packed_memory #define UMF_dump_col_matrix umfzl_dump_col_matrix #define UMF_dump_chain umfzl_dump_chain #define UMF_dump_start umfzl_dump_start #define UMF_dump_rowmerge umfzl_dump_rowmerge #define UMF_dump_diagonal_map umfzl_dump_diagonal_map #endif SuiteSparse/UMFPACK/Source/umf_assemble.c0000644001170100242450000010220210677541253017112 0ustar davisfac/* ========================================================================== */ /* === UMF_assemble ========================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Degree update and numerical assembly. This is compiled twice (with and * without FIXQ) for each real/complex int/UF_long version, for a total of 8 * versions.*/ #include "umf_internal.h" #include "umf_assemble.h" #include "umf_mem_free_tail_block.h" /* ========================================================================== */ /* === row_assemble ========================================================= */ /* ========================================================================== */ PRIVATE void row_assemble ( Int row, NumericType *Numeric, WorkType *Work ) { Entry *S, *Fcblock, *Frow ; Int tpi, e, *E, *Fcpos, *Frpos, *Row_degree, *Row_tuples, *Row_tlen, rdeg0, f, nrows, ncols, *Rows, *Cols, col, ncolsleft, j ; Tuple *tp, *tp1, *tp2, *tpend ; Unit *Memory, *p ; Element *ep ; #ifndef FIXQ Int *Col_degree ; Col_degree = Numeric->Cperm ; #endif Row_tuples = Numeric->Uip ; tpi = Row_tuples [row] ; if (!tpi) return ; Memory = Numeric->Memory ; E = Work->E ; Fcpos = Work->Fcpos ; Frpos = Work->Frpos ; Row_degree = Numeric->Rperm ; Row_tlen = Numeric->Uilen ; E = Work->E ; Memory = Numeric->Memory ; rdeg0 = Work->rdeg0 ; Fcblock = Work->Fcblock ; #ifndef NDEBUG DEBUG6 (("SCAN2-row: "ID"\n", row)) ; UMF_dump_rowcol (0, Numeric, Work, row, FALSE) ; #endif ASSERT (NON_PIVOTAL_ROW (row)) ; tp = (Tuple *) (Memory + tpi) ; tp1 = tp ; tp2 = tp ; tpend = tp + Row_tlen [row] ; for ( ; tp < tpend ; tp++) { e = tp->e ; ASSERT (e > 0 && e <= Work->nel) ; if (!E [e]) continue ; /* element already deallocated */ f = tp->f ; p = Memory + E [e] ; ep = (Element *) p ; p += UNITS (Element, 1) ; Cols = (Int *) p ; Rows = Cols + ep->ncols ; if (Rows [f] == EMPTY) continue ; /* row already assembled */ ASSERT (row == Rows [f] && row >= 0 && row < Work->n_row) ; if (ep->rdeg == rdeg0) { /* ------------------------------------------------------ */ /* this is an old Lson - assemble just one row */ /* ------------------------------------------------------ */ /* flag the row as assembled from the Lson */ Rows [f] = EMPTY ; nrows = ep->nrows ; ncols = ep->ncols ; p += UNITS (Int, ncols + nrows) ; S = ((Entry *) p) + f ; DEBUG6 (("Old LSON: "ID"\n", e)) ; #ifndef NDEBUG UMF_dump_element (Numeric, Work, e, FALSE) ; #endif ncolsleft = ep->ncolsleft ; Frow = Fcblock + Frpos [row] ; DEBUG6 (("LSON found (in scan2-row): "ID"\n", e)) ; Row_degree [row] -= ncolsleft ; if (ncols == ncolsleft) { /* -------------------------------------------------- */ /* no columns assembled out this Lson yet */ /* -------------------------------------------------- */ #pragma ivdep for (j = 0 ; j < ncols ; j++) { col = Cols [j] ; ASSERT (col >= 0 && col < Work->n_col) ; #ifndef FIXQ Col_degree [col] -- ; #endif /* Frow [Fcpos [col]] += *S ; */ ASSEMBLE (Frow [Fcpos [col]], *S) ; S += nrows ; } } else { /* -------------------------------------------------- */ /* some columns have been assembled out of this Lson */ /* -------------------------------------------------- */ #pragma ivdep for (j = 0 ; j < ncols ; j++) { col = Cols [j] ; if (col >= 0) { ASSERT (col < Work->n_col) ; #ifndef FIXQ Col_degree [col] -- ; #endif /* Frow [Fcpos [col]] += *S ; */ ASSEMBLE (Frow [Fcpos [col]], *S) ; } S += nrows ; } } ep->nrowsleft-- ; ASSERT (ep->nrowsleft > 0) ; } else { *tp2++ = *tp ; /* leave the tuple in the list */ } } Row_tlen [row] = tp2 - tp1 ; #ifndef NDEBUG DEBUG7 (("row assembled in scan2-row: "ID"\n", row)) ; UMF_dump_rowcol (0, Numeric, Work, row, FALSE) ; DEBUG7 (("Current frontal matrix: (scan 1b)\n")) ; UMF_dump_current_front (Numeric, Work, TRUE) ; #endif } /* ========================================================================== */ /* === col_assemble ========================================================= */ /* ========================================================================== */ PRIVATE void col_assemble ( Int col, NumericType *Numeric, WorkType *Work ) { Entry *S, *Fcblock, *Fcol ; Int tpi, e, *E, *Fcpos, *Frpos, *Row_degree, *Col_tuples, *Col_tlen, cdeg0, f, nrows, ncols, *Rows, *Cols, row, nrowsleft, i ; Tuple *tp, *tp1, *tp2, *tpend ; Unit *Memory, *p ; Element *ep ; #if !defined (FIXQ) || !defined (NDEBUG) Int *Col_degree ; Col_degree = Numeric->Cperm ; #endif Col_tuples = Numeric->Lip ; tpi = Col_tuples [col] ; if (!tpi) return ; Memory = Numeric->Memory ; E = Work->E ; Fcpos = Work->Fcpos ; Frpos = Work->Frpos ; Row_degree = Numeric->Rperm ; Col_tlen = Numeric->Lilen ; E = Work->E ; Memory = Numeric->Memory ; cdeg0 = Work->cdeg0 ; Fcblock = Work->Fcblock ; DEBUG6 (("SCAN2-col: "ID"\n", col)) ; #ifndef NDEBUG UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ; #endif ASSERT (NON_PIVOTAL_COL (col)) ; tp = (Tuple *) (Memory + tpi) ; tp1 = tp ; tp2 = tp ; tpend = tp + Col_tlen [col] ; for ( ; tp < tpend ; tp++) { e = tp->e ; ASSERT (e > 0 && e <= Work->nel) ; if (!E [e]) continue ; /* element already deallocated */ f = tp->f ; p = Memory + E [e] ; ep = (Element *) p ; p += UNITS (Element, 1) ; Cols = (Int *) p ; if (Cols [f] == EMPTY) continue ; /* col already assembled */ ASSERT (col == Cols [f] && col >= 0 && col < Work->n_col) ; if (ep->cdeg == cdeg0) { /* ------------------------------------------------------ */ /* this is an old Uson - assemble just one col */ /* ------------------------------------------------------ */ /* flag the col as assembled from the Uson */ Cols [f] = EMPTY ; nrows = ep->nrows ; ncols = ep->ncols ; Rows = Cols + ncols ; p += UNITS (Int, ncols + nrows) ; S = ((Entry *) p) + f * nrows ; DEBUG6 (("Old USON: "ID"\n", e)) ; #ifndef NDEBUG UMF_dump_element (Numeric, Work, e, FALSE) ; #endif nrowsleft = ep->nrowsleft ; Fcol = Fcblock + Fcpos [col] ; DEBUG6 (("USON found (in scan2-col): "ID"\n", e)) ; #ifndef FIXQ Col_degree [col] -= nrowsleft ; #endif if (nrows == nrowsleft) { /* -------------------------------------------------- */ /* no rows assembled out of this Uson yet */ /* -------------------------------------------------- */ #pragma ivdep for (i = 0 ; i < nrows ; i++) { row = Rows [i] ; ASSERT (row >= 0 && row < Work->n_row) ; Row_degree [row]-- ; /* Fcol [Frpos [row]] += S [i] ; */ ASSEMBLE (Fcol [Frpos [row]], S [i]) ; } } else { /* -------------------------------------------------- */ /* some rows have been assembled out of this Uson */ /* -------------------------------------------------- */ #pragma ivdep for (i = 0 ; i < nrows ; i++) { row = Rows [i] ; if (row >= 0) { ASSERT (row < Work->n_row) ; Row_degree [row]-- ; /* Fcol [Frpos [row]] += S [i] ; */ ASSEMBLE (Fcol [Frpos [row]], S [i]) ; } } } ep->ncolsleft-- ; ASSERT (ep->ncolsleft > 0) ; } else { *tp2++ = *tp ; /* leave the tuple in the list */ } } Col_tlen [col] = tp2 - tp1 ; #ifndef NDEBUG DEBUG7 (("Column assembled in scan2-col: "ID"\n", col)) ; UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ; DEBUG7 (("Current frontal matrix: after scan2-col\n")) ; UMF_dump_current_front (Numeric, Work, TRUE) ; #endif } /* ========================================================================== */ /* === UMF_assemble / UMF_assemble_fixq ===================================== */ /* ========================================================================== */ #ifndef FIXQ GLOBAL void UMF_assemble #else GLOBAL void UMF_assemble_fixq #endif ( NumericType *Numeric, WorkType *Work ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Int e, i, row, col, i2, nrows, ncols, f, tpi, extcdeg, extrdeg, rdeg0, cdeg0, son_list, next, nrows_to_assemble, ncols_to_assemble, ngetrows, j, j2, nrowsleft, /* number of rows remaining in S */ ncolsleft, /* number of columns remaining in S */ prior_Lson, prior_Uson, *E, *Cols, *Rows, *Wm, *Woo, *Row_tuples, *Row_degree, *Row_tlen, *Col_tuples, *Col_tlen ; Unit *Memory, *p ; Element *ep ; Tuple *tp, *tp1, *tp2, *tpend ; Entry *S, /* a pointer into the contribution block of a son */ *Fcblock, /* current contribution block */ *Fcol ; /* a column of FC */ Int *Frpos, *Fcpos, fnrows, /* number of rows in contribution block in F */ fncols ; /* number of columns in contribution block in F */ #if !defined (FIXQ) || !defined (NDEBUG) Int *Col_degree ; #endif #ifndef NDEBUG Int n_row, n_col ; n_row = Work->n_row ; n_col = Work->n_col ; DEBUG3 (("::Assemble SCANS 1-4\n")) ; UMF_dump_current_front (Numeric, Work, TRUE) ; #endif #if !defined (FIXQ) || !defined (NDEBUG) Col_degree = Numeric->Cperm ; /* not updated if FIXQ is true */ #endif /* ---------------------------------------------------------------------- */ /* get parameters */ /* ---------------------------------------------------------------------- */ fncols = Work->fncols ; fnrows = Work->fnrows ; Fcpos = Work->Fcpos ; Frpos = Work->Frpos ; Row_degree = Numeric->Rperm ; Row_tuples = Numeric->Uip ; Row_tlen = Numeric->Uilen ; Col_tuples = Numeric->Lip ; Col_tlen = Numeric->Lilen ; E = Work->E ; Memory = Numeric->Memory ; Wm = Work->Wm ; Woo = Work->Woo ; rdeg0 = Work->rdeg0 ; cdeg0 = Work->cdeg0 ; #ifndef NDEBUG DEBUG6 (("============================================\n")) ; DEBUG6 (("Degree update, assembly.\n")) ; DEBUG6 (("pivot row pattern: fncols="ID"\n", fncols)) ; for (j = 0 ; j < fncols ; j++) { col = Work->Fcols [j] ; DEBUG6 ((ID" ", col)) ; ASSERT (Fcpos [col] == j * Work->fnr_curr) ; ASSERT (NON_PIVOTAL_COL (col)) ; } ASSERT (Fcpos [Work->pivcol] >= 0) ; DEBUG6 (("pivcol: "ID" pos "ID" fnr_curr "ID" fncols "ID"\n", Work->pivcol, Fcpos [Work->pivcol], Work->fnr_curr, fncols)) ; ASSERT (Fcpos [Work->pivcol] < fncols * Work->fnr_curr) ; DEBUG6 (("\npivot col pattern: fnrows="ID"\n", fnrows)) ; for (i = 0 ; i < fnrows ; i++) { row = Work->Frows [i] ; DEBUG6 ((ID" ", row)) ; ASSERT (Frpos [row] == i) ; ASSERT (NON_PIVOTAL_ROW (row)) ; } DEBUG6 (("\n")) ; ASSERT (Frpos [Work->pivrow] >= 0) ; ASSERT (Frpos [Work->pivrow] < fnrows) ; ASSERT (Work->Flublock == (Entry *) (Numeric->Memory + E [0])) ; ASSERT (Work->Fcblock == Work->Flublock + Work->nb * (Work->nb + Work->fnr_curr + Work->fnc_curr)) ; #endif Fcblock = Work->Fcblock ; /* ---------------------------------------------------------------------- */ /* determine the largest actual frontal matrix size (for Info only) */ /* ---------------------------------------------------------------------- */ ASSERT (fnrows == Work->fnrows_new + 1) ; ASSERT (fncols == Work->fncols_new + 1) ; Numeric->maxnrows = MAX (Numeric->maxnrows, fnrows) ; Numeric->maxncols = MAX (Numeric->maxncols, fncols) ; /* this is safe from integer overflow, since the current frontal matrix * is already allocated. */ Numeric->maxfrsize = MAX (Numeric->maxfrsize, fnrows * fncols) ; /* ---------------------------------------------------------------------- */ /* assemble from prior elements into the current frontal matrix */ /* ---------------------------------------------------------------------- */ DEBUG2 (("New assemble start [prior_element:"ID"\n", Work->prior_element)) ; /* Currently no rows or columns are marked. No elements are scanned, */ /* that is, (ep->next == EMPTY) is true for all elements */ son_list = 0 ; /* start creating son_list [ */ /* ---------------------------------------------------------------------- */ /* determine if most recent element is Lson or Uson of current front */ /* ---------------------------------------------------------------------- */ if (!Work->do_extend) { prior_Uson = ( Work->pivcol_in_front && !Work->pivrow_in_front) ; prior_Lson = (!Work->pivcol_in_front && Work->pivrow_in_front) ; if (prior_Uson || prior_Lson) { e = Work->prior_element ; if (e != EMPTY) { ASSERT (E [e]) ; p = Memory + E [e] ; ep = (Element *) p ; ep->next = son_list ; son_list = e ; #ifndef NDEBUG DEBUG2 (("e "ID" is Prior son "ID" "ID"\n", e, prior_Uson, prior_Lson)) ; UMF_dump_element (Numeric, Work, e, FALSE) ; #endif ASSERT (E [e]) ; } } } Work->prior_element = EMPTY ; /* ---------------------------------------------------------------------- */ /* SCAN1-row: scan the element lists of each new row in the pivot col */ /* and compute the external column degree for each frontal */ /* ---------------------------------------------------------------------- */ for (i2 = Work->fscan_row ; i2 < fnrows ; i2++) { /* Get a row */ row = Work->NewRows [i2] ; if (row < 0) row = FLIP (row) ; ASSERT (row >= 0 && row < n_row) ; DEBUG6 (("SCAN1-row: "ID"\n", row)) ; #ifndef NDEBUG UMF_dump_rowcol (0, Numeric, Work, row, FALSE) ; #endif ASSERT (NON_PIVOTAL_ROW (row)) ; tpi = Row_tuples [row] ; if (!tpi) continue ; tp = (Tuple *) (Memory + tpi) ; tp1 = tp ; tp2 = tp ; tpend = tp + Row_tlen [row] ; for ( ; tp < tpend ; tp++) { e = tp->e ; ASSERT (e > 0 && e <= Work->nel) ; if (!E [e]) continue ; /* element already deallocated */ f = tp->f ; p = Memory + E [e] ; ep = (Element *) p ; p += UNITS (Element, 1) ; Rows = ((Int *) p) + ep->ncols ; if (Rows [f] == EMPTY) continue ; /* row already assembled */ ASSERT (row == Rows [f]) ; if (ep->cdeg < cdeg0) { /* first time seen in scan1-row */ ep->cdeg = ep->nrowsleft + cdeg0 ; DEBUG6 (("e "ID" First seen: cdeg: "ID" ", e, ep->cdeg-cdeg0)) ; ASSERT (ep->ncolsleft > 0 && ep->nrowsleft > 0) ; } ep->cdeg-- ; /* decrement external column degree */ DEBUG6 (("e "ID" New ext col deg: "ID"\n", e, ep->cdeg - cdeg0)) ; /* this element is not yet in the new son list */ if (ep->cdeg == cdeg0 && ep->next == EMPTY) { /* A new LUson or Uson has been found */ ep->next = son_list ; son_list = e ; } ASSERT (ep->cdeg >= cdeg0) ; *tp2++ = *tp ; /* leave the tuple in the list */ } Row_tlen [row] = tp2 - tp1 ; } /* ---------------------------------------------------------------------- */ /* SCAN1-col: scan the element lists of each new col in the pivot row */ /* and compute the external row degree for each frontal */ /* ---------------------------------------------------------------------- */ for (j2 = Work->fscan_col ; j2 < fncols ; j2++) { /* Get a column */ col = Work->NewCols [j2] ; if (col < 0) col = FLIP (col) ; ASSERT (col >= 0 && col < n_col) ; DEBUG6 (("SCAN 1-col: "ID"\n", col)) ; #ifndef NDEBUG UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ; #endif ASSERT (NON_PIVOTAL_COL (col)) ; tpi = Col_tuples [col] ; if (!tpi) continue ; tp = (Tuple *) (Memory + tpi) ; tp1 = tp ; tp2 = tp ; tpend = tp + Col_tlen [col] ; for ( ; tp < tpend ; tp++) { e = tp->e ; ASSERT (e > 0 && e <= Work->nel) ; if (!E [e]) continue ; /* element already deallocated */ f = tp->f ; p = Memory + E [e] ; ep = (Element *) p ; p += UNITS (Element, 1) ; Cols = (Int *) p ; if (Cols [f] == EMPTY) continue ; /* column already assembled */ ASSERT (col == Cols [f]) ; if (ep->rdeg < rdeg0) { /* first time seen in scan1-col */ ep->rdeg = ep->ncolsleft + rdeg0 ; DEBUG6 (("e "ID" First seen: rdeg: "ID" ", e, ep->rdeg-rdeg0)) ; ASSERT (ep->ncolsleft > 0 && ep->nrowsleft > 0) ; } ep->rdeg-- ; /* decrement external row degree */ DEBUG6 (("e "ID" New ext row degree: "ID"\n", e, ep->rdeg-rdeg0)) ; if (ep->rdeg == rdeg0 && ep->next == EMPTY) { /* A new LUson or Lson has been found */ ep->next = son_list ; son_list = e ; } ASSERT (ep->rdeg >= rdeg0) ; *tp2++ = *tp ; /* leave the tuple in the list */ } Col_tlen [col] = tp2 - tp1 ; } /* ---------------------------------------------------------------------- */ /* assemble new sons via full scans */ /* ---------------------------------------------------------------------- */ next = EMPTY ; for (e = son_list ; e > 0 ; e = next) { ASSERT (e > 0 && e <= Work->nel && E [e]) ; p = Memory + E [e] ; DEBUG2 (("New son: "ID"\n", e)) ; #ifndef NDEBUG UMF_dump_element (Numeric, Work, e, FALSE) ; #endif GET_ELEMENT (ep, p, Cols, Rows, ncols, nrows, S) ; nrowsleft = ep->nrowsleft ; ncolsleft = ep->ncolsleft ; next = ep->next ; ep->next = EMPTY ; extrdeg = (ep->rdeg < rdeg0) ? ncolsleft : (ep->rdeg - rdeg0) ; extcdeg = (ep->cdeg < cdeg0) ? nrowsleft : (ep->cdeg - cdeg0) ; ncols_to_assemble = ncolsleft - extrdeg ; nrows_to_assemble = nrowsleft - extcdeg ; DEBUG2 (("extrdeg "ID" extcdeg "ID"\n", extrdeg, extcdeg)) ; if (extrdeg == 0 && extcdeg == 0) { /* -------------------------------------------------------------- */ /* this is an LUson - assemble an entire contribution block */ /* -------------------------------------------------------------- */ DEBUG6 (("LUson found: "ID"\n", e)) ; if (nrows == nrowsleft) { /* ---------------------------------------------------------- */ /* no rows assembled out of this LUson yet */ /* ---------------------------------------------------------- */ /* compute the compressed column offset vector*/ /* [ use Wm [0..nrows-1] for offsets */ #pragma ivdep for (i = 0 ; i < nrows ; i++) { row = Rows [i] ; Row_degree [row] -= ncolsleft ; Wm [i] = Frpos [row] ; } if (ncols == ncolsleft) { /* ------------------------------------------------------ */ /* no rows or cols assembled out of LUson yet */ /* ------------------------------------------------------ */ for (j = 0 ; j < ncols ; j++) { col = Cols [j] ; #ifndef FIXQ Col_degree [col] -= nrowsleft ; #endif Fcol = Fcblock + Fcpos [col] ; #pragma ivdep for (i = 0 ; i < nrows ; i++) { /* Fcol [Wm [i]] += S [i] ; */ ASSEMBLE (Fcol [Wm [i]], S [i]) ; } S += nrows ; } } else { /* ------------------------------------------------------ */ /* only cols have been assembled out of LUson */ /* ------------------------------------------------------ */ for (j = 0 ; j < ncols ; j++) { col = Cols [j] ; if (col >= 0) { #ifndef FIXQ Col_degree [col] -= nrowsleft ; #endif Fcol = Fcblock + Fcpos [col] ; #pragma ivdep for (i = 0 ; i < nrows ; i++) { /* Fcol [Wm [i]] += S [i] ; */ ASSEMBLE (Fcol [Wm [i]], S [i]) ; } } S += nrows ; } } /* ] done using Wm [0..nrows-1] for offsets */ } else { /* ---------------------------------------------------------- */ /* some rows have been assembled out of this LUson */ /* ---------------------------------------------------------- */ /* compute the compressed column offset vector*/ /* [ use Woo,Wm [0..nrowsleft-1] for offsets */ ngetrows = 0 ; for (i = 0 ; i < nrows ; i++) { row = Rows [i] ; if (row >= 0) { Row_degree [row] -= ncolsleft ; Woo [ngetrows] = i ; Wm [ngetrows++] = Frpos [row] ; } } ASSERT (ngetrows == nrowsleft) ; if (ncols == ncolsleft) { /* ------------------------------------------------------ */ /* only rows have been assembled out of this LUson */ /* ------------------------------------------------------ */ for (j = 0 ; j < ncols ; j++) { col = Cols [j] ; #ifndef FIXQ Col_degree [col] -= nrowsleft ; #endif Fcol = Fcblock + Fcpos [col] ; #pragma ivdep for (i = 0 ; i < nrowsleft ; i++) { /* Fcol [Wm [i]] += S [Woo [i]] ; */ ASSEMBLE (Fcol [Wm [i]], S [Woo [i]]) ; } S += nrows ; } } else { /* ------------------------------------------------------ */ /* both rows and columns have been assembled out of LUson */ /* ------------------------------------------------------ */ for (j = 0 ; j < ncols ; j++) { col = Cols [j] ; if (col >= 0) { #ifndef FIXQ Col_degree [col] -= nrowsleft ; #endif Fcol = Fcblock + Fcpos [col] ; #pragma ivdep for (i = 0 ; i < nrowsleft ; i++) { /* Fcol [Wm [i]] += S [Woo [i]] ; */ ASSEMBLE (Fcol [Wm [i]], S [Woo [i]]) ; } } S += nrows ; } } /* ] done using Woo,Wm [0..nrowsleft-1] */ } /* deallocate the element: remove from ordered list */ UMF_mem_free_tail_block (Numeric, E [e]) ; E [e] = 0 ; } else if (extcdeg == 0) { /* -------------------------------------------------------------- */ /* this is a Uson - assemble all possible columns */ /* -------------------------------------------------------------- */ DEBUG6 (("New USON: "ID"\n", e)) ; ASSERT (extrdeg > 0) ; DEBUG6 (("New uson "ID" cols to do "ID"\n", e, ncols_to_assemble)) ; if (ncols_to_assemble > 0) { Int skip = FALSE ; if (ncols_to_assemble * 16 < ncols && nrows == 1) { /* this is a tall and thin frontal matrix consisting of * only one column (most likely an original column). Do * not assemble it. It cannot be the pivot column, since * the pivot column element would be an LU son, not an Lson, * of the current frontal matrix. */ ASSERT (nrowsleft == 1) ; ASSERT (Rows [0] >= 0 && Rows [0] < Work->n_row) ; skip = TRUE ; Work->any_skip = TRUE ; } if (!skip) { if (nrows == nrowsleft) { /* -------------------------------------------------- */ /* no rows have been assembled out of this Uson yet */ /* -------------------------------------------------- */ /* compute the compressed column offset vector */ /* [ use Wm [0..nrows-1] for offsets */ #pragma ivdep for (i = 0 ; i < nrows ; i++) { row = Rows [i] ; ASSERT (row >= 0 && row < n_row) ; Row_degree [row] -= ncols_to_assemble ; Wm [i] = Frpos [row] ; } for (j = 0 ; j < ncols ; j++) { col = Cols [j] ; if ((col >= 0) && (Fcpos [col] >= 0)) { #ifndef FIXQ Col_degree [col] -= nrowsleft ; #endif Fcol = Fcblock + Fcpos [col] ; #pragma ivdep for (i = 0 ; i < nrows ; i++) { /* Fcol [Wm [i]] += S [i] ; */ ASSEMBLE (Fcol [Wm [i]], S [i]) ; } /* flag the column as assembled from Uson */ Cols [j] = EMPTY ; } S += nrows ; } /* ] done using Wm [0..nrows-1] for offsets */ } else { /* -------------------------------------------------- */ /* some rows have been assembled out of this Uson */ /* -------------------------------------------------- */ /* compute the compressed column offset vector*/ /* [ use Woo,Wm [0..nrows-1] for offsets */ ngetrows = 0 ; for (i = 0 ; i < nrows ; i++) { row = Rows [i] ; if (row >= 0) { Row_degree [row] -= ncols_to_assemble ; ASSERT (row < n_row && Frpos [row] >= 0) ; Woo [ngetrows] = i ; Wm [ngetrows++] = Frpos [row] ; } } ASSERT (ngetrows == nrowsleft) ; for (j = 0 ; j < ncols ; j++) { col = Cols [j] ; if ((col >= 0) && (Fcpos [col] >= 0)) { #ifndef FIXQ Col_degree [col] -= nrowsleft ; #endif Fcol = Fcblock + Fcpos [col] ; #pragma ivdep for (i = 0 ; i < nrowsleft ; i++) { /* Fcol [Wm [i]] += S [Woo [i]] ; */ ASSEMBLE (Fcol [Wm [i]], S [Woo [i]]) ; } /* flag the column as assembled from Uson */ Cols [j] = EMPTY ; } S += nrows ; } /* ] done using Woo,Wm */ } ep->ncolsleft = extrdeg ; } } } else { /* -------------------------------------------------------------- */ /* this is an Lson - assemble all possible rows */ /* -------------------------------------------------------------- */ DEBUG6 (("New LSON: "ID"\n", e)) ; ASSERT (extrdeg == 0 && extcdeg > 0) ; DEBUG6 (("New lson "ID" rows to do "ID"\n", e, nrows_to_assemble)) ; if (nrows_to_assemble > 0) { Int skip = FALSE ; if (nrows_to_assemble * 16 < nrows && ncols == 1) { /* this is a tall and thin frontal matrix consisting of * only one column (most likely an original column). Do * not assemble it. It cannot be the pivot column, since * the pivot column element would be an LU son, not an Lson, * of the current frontal matrix. */ ASSERT (ncolsleft == 1) ; ASSERT (Cols [0] >= 0 && Cols [0] < Work->n_col) ; Work->any_skip = TRUE ; skip = TRUE ; } if (!skip) { /* compute the compressed column offset vector */ /* [ use Woo,Wm [0..nrows-1] for offsets */ ngetrows = 0 ; for (i = 0 ; i < nrows ; i++) { row = Rows [i] ; if ((row >= 0) && (Frpos [row] >= 0)) { ASSERT (row < n_row) ; Row_degree [row] -= ncolsleft ; Woo [ngetrows] = i ; Wm [ngetrows++] = Frpos [row] ; /* flag the row as assembled from the Lson */ Rows [i] = EMPTY ; } } ASSERT (nrowsleft - ngetrows == extcdeg) ; ASSERT (ngetrows == nrows_to_assemble) ; if (ncols == ncolsleft) { /* -------------------------------------------------- */ /* no columns assembled out this Lson yet */ /* -------------------------------------------------- */ for (j = 0 ; j < ncols ; j++) { col = Cols [j] ; ASSERT (col >= 0 && col < n_col) ; #ifndef FIXQ Col_degree [col] -= nrows_to_assemble ; #endif Fcol = Fcblock + Fcpos [col] ; #pragma ivdep for (i = 0 ; i < nrows_to_assemble ; i++) { /* Fcol [Wm [i]] += S [Woo [i]] ; */ ASSEMBLE (Fcol [Wm [i]], S [Woo [i]]) ; } S += nrows ; } } else { /* -------------------------------------------------- */ /* some columns have been assembled out of this Lson */ /* -------------------------------------------------- */ for (j = 0 ; j < ncols ; j++) { col = Cols [j] ; ASSERT (col < n_col) ; if (col >= 0) { #ifndef FIXQ Col_degree [col] -= nrows_to_assemble ; #endif Fcol = Fcblock + Fcpos [col] ; #pragma ivdep for (i = 0 ; i < nrows_to_assemble ; i++) { /* Fcol [Wm [i]] += S [Woo [i]] ; */ ASSEMBLE (Fcol [Wm [i]], S [Woo [i]]) ; } } S += nrows ; } } /* ] done using Woo,Wm */ ep->nrowsleft = extcdeg ; } } } } /* Note that garbage collection, and build tuples */ /* both destroy the son list. */ /* ] son_list now empty */ /* ---------------------------------------------------------------------- */ /* If frontal matrix extended, assemble old L/Usons from new rows/cols */ /* ---------------------------------------------------------------------- */ /* ---------------------------------------------------------------------- */ /* SCAN2-row: assemble rows of old Lsons from the new rows */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG DEBUG7 (("Current frontal matrix: (prior to scan2-row)\n")) ; UMF_dump_current_front (Numeric, Work, TRUE) ; #endif /* rescan the pivot row */ if (Work->any_skip) { row_assemble (Work->pivrow, Numeric, Work) ; } if (Work->do_scan2row) { for (i2 = Work->fscan_row ; i2 < fnrows ; i2++) { /* Get a row */ row = Work->NewRows [i2] ; if (row < 0) row = FLIP (row) ; ASSERT (row >= 0 && row < n_row) ; if (!(row == Work->pivrow && Work->any_skip)) { /* assemble it */ row_assemble (row, Numeric, Work) ; } } } /* ---------------------------------------------------------------------- */ /* SCAN2-col: assemble columns of old Usons from the new columns */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG DEBUG7 (("Current frontal matrix: (prior to scan2-col)\n")) ; UMF_dump_current_front (Numeric, Work, TRUE) ; #endif /* rescan the pivot col */ if (Work->any_skip) { col_assemble (Work->pivcol, Numeric, Work) ; } if (Work->do_scan2col) { for (j2 = Work->fscan_col ; j2 < fncols ; j2++) { /* Get a column */ col = Work->NewCols [j2] ; if (col < 0) col = FLIP (col) ; ASSERT (col >= 0 && col < n_col) ; if (!(col == Work->pivcol && Work->any_skip)) { /* assemble it */ col_assemble (col, Numeric, Work) ; } } } /* ---------------------------------------------------------------------- */ /* done. the remainder of this routine is used only when in debug mode */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG /* ---------------------------------------------------------------------- */ /* when debugging: make sure the assembly did everything that it could */ /* ---------------------------------------------------------------------- */ DEBUG3 (("::Assemble done\n")) ; for (i2 = 0 ; i2 < fnrows ; i2++) { /* Get a row */ row = Work->Frows [i2] ; ASSERT (row >= 0 && row < n_row) ; DEBUG6 (("DEBUG SCAN 1: "ID"\n", row)) ; UMF_dump_rowcol (0, Numeric, Work, row, TRUE) ; ASSERT (NON_PIVOTAL_ROW (row)) ; tpi = Row_tuples [row] ; if (!tpi) continue ; tp = (Tuple *) (Memory + tpi) ; tpend = tp + Row_tlen [row] ; for ( ; tp < tpend ; tp++) { e = tp->e ; ASSERT (e > 0 && e <= Work->nel) ; if (!E [e]) continue ; /* element already deallocated */ f = tp->f ; p = Memory + E [e] ; ep = (Element *) p ; p += UNITS (Element, 1) ; Cols = (Int *) p ; Rows = ((Int *) p) + ep->ncols ; if (Rows [f] == EMPTY) continue ; /* row already assembled */ ASSERT (row == Rows [f]) ; extrdeg = (ep->rdeg < rdeg0) ? ep->ncolsleft : (ep->rdeg - rdeg0) ; extcdeg = (ep->cdeg < cdeg0) ? ep->nrowsleft : (ep->cdeg - cdeg0) ; DEBUG6 (( "e "ID" After assembly ext row deg: "ID" ext col degree "ID"\n", e, extrdeg, extcdeg)) ; if (Work->any_skip) { /* no Lsons in any row, except for very tall and thin ones */ ASSERT (extrdeg >= 0) ; if (extrdeg == 0) { /* this is an unassemble Lson */ ASSERT (ep->ncols == 1) ; ASSERT (ep->ncolsleft == 1) ; col = Cols [0] ; ASSERT (col != Work->pivcol) ; } } else { /* no Lsons in any row */ ASSERT (extrdeg > 0) ; /* Uson external row degree is = number of cols left */ ASSERT (IMPLIES (extcdeg == 0, extrdeg == ep->ncolsleft)) ; } } } /* ---------------------------------------------------------------------- */ for (j2 = 0 ; j2 < fncols ; j2++) { /* Get a column */ col = Work->Fcols [j2] ; ASSERT (col >= 0 && col < n_col) ; DEBUG6 (("DEBUG SCAN 2: "ID"\n", col)) ; #ifndef FIXQ UMF_dump_rowcol (1, Numeric, Work, col, TRUE) ; #else UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ; #endif ASSERT (NON_PIVOTAL_COL (col)) ; tpi = Col_tuples [col] ; if (!tpi) continue ; tp = (Tuple *) (Memory + tpi) ; tpend = tp + Col_tlen [col] ; for ( ; tp < tpend ; tp++) { e = tp->e ; ASSERT (e > 0 && e <= Work->nel) ; if (!E [e]) continue ; /* element already deallocated */ f = tp->f ; p = Memory + E [e] ; ep = (Element *) p ; p += UNITS (Element, 1) ; Cols = (Int *) p ; Rows = ((Int *) p) + ep->ncols ; if (Cols [f] == EMPTY) continue ; /* column already assembled */ ASSERT (col == Cols [f]) ; extrdeg = (ep->rdeg < rdeg0) ? ep->ncolsleft : (ep->rdeg - rdeg0) ; extcdeg = (ep->cdeg < cdeg0) ? ep->nrowsleft : (ep->cdeg - cdeg0) ; DEBUG6 (("e "ID" After assembly ext col deg: "ID"\n", e, extcdeg)) ; if (Work->any_skip) { /* no Usons in any column, except for very tall and thin ones */ ASSERT (extcdeg >= 0) ; if (extcdeg == 0) { /* this is an unassemble Uson */ ASSERT (ep->nrows == 1) ; ASSERT (ep->nrowsleft == 1) ; row = Rows [0] ; ASSERT (row != Work->pivrow) ; } } else { /* no Usons in any column */ ASSERT (extcdeg > 0) ; /* Lson external column degree is = number of rows left */ ASSERT (IMPLIES (extrdeg == 0, extcdeg == ep->nrowsleft)) ; } } } #endif /* NDEBUG */ } SuiteSparse/UMFPACK/Source/umf_assemble.h0000644001170100242450000000106410617161410017106 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL void UMF_assemble ( NumericType *Numeric, WorkType *Work ) ; GLOBAL void UMF_assemble_fixq ( NumericType *Numeric, WorkType *Work ) ; SuiteSparse/UMFPACK/Source/umf_scale.c0000644001170100242450000000451210677542243016413 0ustar davisfac/* ========================================================================== */ /* === UMF_scale ============================================================ */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Divide a vector of stride 1 by the pivot value. */ #include "umf_internal.h" #include "umf_scale.h" GLOBAL void UMF_scale ( Int n, Entry pivot, Entry X [ ] ) { Entry x ; double s ; Int i ; /* ---------------------------------------------------------------------- */ /* compute the approximate absolute value of the pivot, and select method */ /* ---------------------------------------------------------------------- */ APPROX_ABS (s, pivot) ; if (s < RECIPROCAL_TOLERANCE || IS_NAN (pivot)) { /* ------------------------------------------------------------------ */ /* tiny, or zero, pivot case */ /* ------------------------------------------------------------------ */ /* The pivot is tiny, or NaN. Do not divide zero by the pivot value, * and do not multiply by 1/pivot, either. */ for (i = 0 ; i < n ; i++) { /* X [i] /= pivot ; */ x = X [i] ; #ifndef NO_DIVIDE_BY_ZERO if (IS_NONZERO (x)) { DIV (X [i], x, pivot) ; } #else /* Do not divide by zero */ if (IS_NONZERO (x) && IS_NONZERO (pivot)) { DIV (X [i], x, pivot) ; } #endif } } else { /* ------------------------------------------------------------------ */ /* normal case */ /* ------------------------------------------------------------------ */ /* The pivot is not tiny, and is not NaN. Don't bother to check for * zeros in the pivot column, X. This is slightly more accurate than * multiplying by 1/pivot (but slightly slower), particularly if the * pivot column consists of only IEEE subnormals. */ for (i = 0 ; i < n ; i++) { /* X [i] /= pivot ; */ x = X [i] ; DIV (X [i], x, pivot) ; } } } SuiteSparse/UMFPACK/Source/umf_scale_column.c0000644001170100242450000003335110677542354017776 0ustar davisfac/* ========================================================================== */ /* === UMF_scale_column ===================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Scale the current pivot column, move the pivot row and column into place, and log the permutation. */ #include "umf_internal.h" #include "umf_scale_column.h" #include "umf_mem_free_tail_block.h" #include "umf_scale.h" /* ========================================================================== */ /* === shift_pivot_row ====================================================== */ /* ========================================================================== */ /* Except for the BLAS, most of the time is typically spent in the following * shift_pivot_row routine. It copies the pivot row into the U block, and * then fills in the whole in the C block by shifting the last row of C into * the row vacated by the pivot row. */ PRIVATE void shift_pivot_row (Entry *Fd, Entry *Fs, Entry *Fe, Int len, Int d) { Int j ; #pragma ivdep for (j = 0 ; j < len ; j++) { Fd [j] = Fs [j*d] ; Fs [j*d] = Fe [j*d] ; } } /* ========================================================================== */ /* === UMF_scale_column ===================================================== */ /* ========================================================================== */ GLOBAL void UMF_scale_column ( NumericType *Numeric, WorkType *Work ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Entry pivot_value ; Entry *Fcol, *Flublock, *Flblock, *Fublock, *Fcblock ; Int k, k1, fnr_curr, fnrows, fncols, *Frpos, *Fcpos, pivrow, pivcol, *Frows, *Fcols, fnc_curr, fnpiv, *Row_tuples, nb, *Col_tuples, *Rperm, *Cperm, fspos, col2, row2 ; #ifndef NDEBUG Int *Col_degree, *Row_degree ; #endif /* ---------------------------------------------------------------------- */ /* get parameters */ /* ---------------------------------------------------------------------- */ fnrows = Work->fnrows ; fncols = Work->fncols ; fnpiv = Work->fnpiv ; /* ---------------------------------------------------------------------- */ Rperm = Numeric->Rperm ; Cperm = Numeric->Cperm ; /* ---------------------------------------------------------------------- */ Flublock = Work->Flublock ; Flblock = Work->Flblock ; Fublock = Work->Fublock ; Fcblock = Work->Fcblock ; fnr_curr = Work->fnr_curr ; fnc_curr = Work->fnc_curr ; Frpos = Work->Frpos ; Fcpos = Work->Fcpos ; Frows = Work->Frows ; Fcols = Work->Fcols ; pivrow = Work->pivrow ; pivcol = Work->pivcol ; ASSERT (pivrow >= 0 && pivrow < Work->n_row) ; ASSERT (pivcol >= 0 && pivcol < Work->n_col) ; #ifndef NDEBUG Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro */ Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro */ #endif Row_tuples = Numeric->Uip ; Col_tuples = Numeric->Lip ; nb = Work->nb ; #ifndef NDEBUG ASSERT (fnrows == Work->fnrows_new + 1) ; ASSERT (fncols == Work->fncols_new + 1) ; DEBUG1 (("SCALE COL: fnrows "ID" fncols "ID"\n", fnrows, fncols)) ; DEBUG2 (("\nFrontal matrix, including all space:\n" "fnr_curr "ID" fnc_curr "ID" nb "ID"\n" "fnrows "ID" fncols "ID" fnpiv "ID"\n", fnr_curr, fnc_curr, nb, fnrows, fncols, fnpiv)) ; DEBUG2 (("\nJust the active part:\n")) ; DEBUG7 (("C block: ")) ; UMF_dump_dense (Fcblock, fnr_curr, fnrows, fncols) ; DEBUG7 (("L block: ")) ; UMF_dump_dense (Flblock, fnr_curr, fnrows, fnpiv); DEBUG7 (("U' block: ")) ; UMF_dump_dense (Fublock, fnc_curr, fncols, fnpiv) ; DEBUG7 (("LU block: ")) ; UMF_dump_dense (Flublock, nb, fnpiv, fnpiv) ; #endif /* ====================================================================== */ /* === Shift pivot row and column ======================================= */ /* ====================================================================== */ /* ---------------------------------------------------------------------- */ /* move pivot column into place */ /* ---------------------------------------------------------------------- */ /* Note that the pivot column is already in place. Just shift the last * column into the position vacated by the pivot column. */ fspos = Fcpos [pivcol] ; /* one less column in the contribution block */ fncols = --(Work->fncols) ; if (fspos != fncols * fnr_curr) { Int fs = fspos / fnr_curr ; DEBUG6 (("Shift pivot column in front\n")) ; DEBUG6 (("fspos: "ID" flpos: "ID"\n", fspos, fncols * fnr_curr)) ; /* ------------------------------------------------------------------ */ /* move Fe => Fs */ /* ------------------------------------------------------------------ */ /* column of the contribution block: */ { /* Fs: current position of pivot column in contribution block */ /* Fe: position of last column in contribution block */ Int i ; Entry *Fs, *Fe ; Fs = Fcblock + fspos ; Fe = Fcblock + fncols * fnr_curr ; #pragma ivdep for (i = 0 ; i < fnrows ; i++) { Fs [i] = Fe [i] ; } } /* column of the U2 block */ { /* Fs: current position of pivot column in U block */ /* Fe: last column in U block */ Int i ; Entry *Fs, *Fe ; Fs = Fublock + fs ; Fe = Fublock + fncols ; #pragma ivdep for (i = 0 ; i < fnpiv ; i++) { Fs [i * fnc_curr] = Fe [i * fnc_curr] ; } } /* move column Fe to Fs in the Fcols pattern */ col2 = Fcols [fncols] ; Fcols [fs] = col2 ; Fcpos [col2] = fspos ; } /* pivot column is no longer in the frontal matrix */ Fcpos [pivcol] = EMPTY ; #ifndef NDEBUG DEBUG2 (("\nFrontal matrix after col swap, including all space:\n" "fnr_curr "ID" fnc_curr "ID" nb "ID"\n" "fnrows "ID" fncols "ID" fnpiv "ID"\n", fnr_curr, fnc_curr, nb, fnrows, fncols, fnpiv)) ; DEBUG2 (("\nJust the active part:\n")) ; DEBUG7 (("C block: ")) ; UMF_dump_dense (Fcblock, fnr_curr, fnrows, fncols) ; DEBUG7 (("L block: ")) ; UMF_dump_dense (Flblock, fnr_curr, fnrows, fnpiv+1); DEBUG7 (("U' block: ")) ; UMF_dump_dense (Fublock, fnc_curr, fncols, fnpiv) ; DEBUG7 (("LU block: ")) ; UMF_dump_dense (Flublock, nb, fnpiv, fnpiv+1) ; #endif /* ---------------------------------------------------------------------- */ /* move pivot row into place */ /* ---------------------------------------------------------------------- */ fspos = Frpos [pivrow] ; /* one less row in the contribution block */ fnrows = --(Work->fnrows) ; DEBUG6 (("Swap/shift pivot row in front:\n")) ; DEBUG6 (("fspos: "ID" flpos: "ID"\n", fspos, fnrows)) ; if (fspos == fnrows) { /* ------------------------------------------------------------------ */ /* move Fs => Fd */ /* ------------------------------------------------------------------ */ DEBUG6 (("row case 1\n")) ; /* row of the contribution block: */ { Int j ; Entry *Fd, *Fs ; Fd = Fublock + fnpiv * fnc_curr ; Fs = Fcblock + fspos ; #pragma ivdep for (j = 0 ; j < fncols ; j++) { Fd [j] = Fs [j * fnr_curr] ; } } /* row of the L2 block: */ if (Work->pivrow_in_front) { Int j ; Entry *Fd, *Fs ; Fd = Flublock + fnpiv ; Fs = Flblock + fspos ; #pragma ivdep for (j = 0 ; j <= fnpiv ; j++) { Fd [j * nb] = Fs [j * fnr_curr] ; } } else { Int j ; Entry *Fd, *Fs ; Fd = Flublock + fnpiv ; Fs = Flblock + fspos ; #pragma ivdep for (j = 0 ; j < fnpiv ; j++) { ASSERT (IS_ZERO (Fs [j * fnr_curr])) ; CLEAR (Fd [j * nb]) ; } Fd [fnpiv * nb] = Fs [fnpiv * fnr_curr] ; } } else { /* ------------------------------------------------------------------ */ /* move Fs => Fd */ /* move Fe => Fs */ /* ------------------------------------------------------------------ */ DEBUG6 (("row case 2\n")) ; /* this is the most common case, by far */ /* row of the contribution block: */ { /* Fd: destination of pivot row on U block */ /* Fs: current position of pivot row in contribution block */ /* Fe: position of last row in contribution block */ Entry *Fd, *Fs, *Fe ; Fd = Fublock + fnpiv * fnc_curr ; Fs = Fcblock + fspos ; Fe = Fcblock + fnrows ; shift_pivot_row (Fd, Fs, Fe, fncols, fnr_curr) ; } /* row of the L2 block: */ if (Work->pivrow_in_front) { /* Fd: destination of pivot row in LU block */ /* Fs: current position of pivot row in L block */ /* Fe: last row in L block */ Int j ; Entry *Fd, *Fs, *Fe ; Fd = Flublock + fnpiv ; Fs = Flblock + fspos ; Fe = Flblock + fnrows ; #pragma ivdep for (j = 0 ; j <= fnpiv ; j++) { Fd [j * nb] = Fs [j * fnr_curr] ; Fs [j * fnr_curr] = Fe [j * fnr_curr] ; } } else { Int j ; Entry *Fd, *Fs, *Fe ; Fd = Flublock + fnpiv ; Fs = Flblock + fspos ; Fe = Flblock + fnrows ; #pragma ivdep for (j = 0 ; j < fnpiv ; j++) { ASSERT (IS_ZERO (Fs [j * fnr_curr])) ; CLEAR (Fd [j * nb]) ; Fs [j * fnr_curr] = Fe [j * fnr_curr] ; } Fd [fnpiv * nb] = Fs [fnpiv * fnr_curr] ; Fs [fnpiv * fnr_curr] = Fe [fnpiv * fnr_curr] ; } /* move row Fe to Fs in the Frows pattern */ row2 = Frows [fnrows] ; Frows [fspos] = row2 ; Frpos [row2] = fspos ; } /* pivot row is no longer in the frontal matrix */ Frpos [pivrow] = EMPTY ; #ifndef NDEBUG DEBUG2 (("\nFrontal matrix after row swap, including all space:\n" "fnr_curr "ID" fnc_curr "ID" nb "ID"\n" "fnrows "ID" fncols "ID" fnpiv "ID"\n", Work->fnr_curr, Work->fnc_curr, Work->nb, Work->fnrows, Work->fncols, Work->fnpiv)) ; DEBUG2 (("\nJust the active part:\n")) ; DEBUG7 (("C block: ")) ; UMF_dump_dense (Fcblock, fnr_curr, fnrows, fncols) ; DEBUG7 (("L block: ")) ; UMF_dump_dense (Flblock, fnr_curr, fnrows, fnpiv+1); DEBUG7 (("U' block: ")) ; UMF_dump_dense (Fublock, fnc_curr, fncols, fnpiv+1) ; DEBUG7 (("LU block: ")) ; UMF_dump_dense (Flublock, nb, fnpiv+1, fnpiv+1) ; #endif /* ---------------------------------------------------------------------- */ /* Frpos [row] >= 0 for each row in pivot column pattern. */ /* offset into pattern is given by: */ /* Frpos [row] == offset - 1 */ /* Frpos [pivrow] is EMPTY */ /* Fcpos [col] >= 0 for each col in pivot row pattern. */ /* Fcpos [col] == (offset - 1) * fnr_curr */ /* Fcpos [pivcol] is EMPTY */ /* Fcols [0..fncols-1] is the pivot row pattern (excl pivot cols) */ /* Frows [0..fnrows-1] is the pivot col pattern (excl pivot rows) */ /* ====================================================================== */ /* === scale pivot column =============================================== */ /* ====================================================================== */ /* pivot column (except for pivot entry itself) */ Fcol = Flblock + fnpiv * fnr_curr ; /* fnpiv-th pivot in frontal matrix located in Flublock (fnpiv, fnpiv) */ pivot_value = Flublock [fnpiv + fnpiv * nb] ; /* this is the kth global pivot */ k = Work->npiv + fnpiv ; DEBUG4 (("Pivot value: ")) ; EDEBUG4 (pivot_value) ; DEBUG4 (("\n")) ; UMF_scale (fnrows, pivot_value, Fcol) ; /* ---------------------------------------------------------------------- */ /* deallocate the pivot row and pivot column tuples */ /* ---------------------------------------------------------------------- */ UMF_mem_free_tail_block (Numeric, Row_tuples [pivrow]) ; UMF_mem_free_tail_block (Numeric, Col_tuples [pivcol]) ; Row_tuples [pivrow] = 0 ; Col_tuples [pivcol] = 0 ; DEBUG5 (("number of pivots prior to this one: "ID"\n", k)) ; ASSERT (NON_PIVOTAL_ROW (pivrow)) ; ASSERT (NON_PIVOTAL_COL (pivcol)) ; /* save row and column inverse permutation */ k1 = ONES_COMPLEMENT (k) ; Rperm [pivrow] = k1 ; /* aliased with Row_degree */ Cperm [pivcol] = k1 ; /* aliased with Col_degree */ ASSERT (!NON_PIVOTAL_ROW (pivrow)) ; ASSERT (!NON_PIVOTAL_COL (pivcol)) ; /* ---------------------------------------------------------------------- */ /* Keep track of the pivot order. This is the kth pivot row and column. */ /* ---------------------------------------------------------------------- */ /* keep track of pivot rows and columns in the LU, L, and U blocks */ ASSERT (fnpiv < MAXNB) ; Work->Pivrow [fnpiv] = pivrow ; Work->Pivcol [fnpiv] = pivcol ; /* ====================================================================== */ /* === one step in the factorization is done ============================ */ /* ====================================================================== */ /* One more step is done, except for pending updates to the U and C blocks * of this frontal matrix. Those are saved up, and applied by * UMF_blas3_update when enough pivots have accumulated. Also, the * LU factors for these pending pivots have not yet been stored. */ Work->fnpiv++ ; #ifndef NDEBUG DEBUG7 (("Current frontal matrix: (after pivcol scale)\n")) ; UMF_dump_current_front (Numeric, Work, TRUE) ; #endif } SuiteSparse/UMFPACK/Source/umf_scale_column.h0000644001170100242450000000074610617162277020001 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL void UMF_scale_column ( NumericType *Numeric, WorkType *Work ) ; SuiteSparse/UMFPACK/Source/umf_kernel_wrapup.c0000644001170100242450000003035210677541660020205 0ustar davisfac/* ========================================================================== */ /* === UMF_kernel_wrapup ==================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* The matrix is factorized. Finish the LU data structure. */ #include "umf_internal.h" #include "umf_kernel_wrapup.h" GLOBAL void UMF_kernel_wrapup ( NumericType *Numeric, SymbolicType *Symbolic, WorkType *Work ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Entry pivot_value ; double d ; Entry *D ; Int i, k, col, row, llen, ulen, *ip, *Rperm, *Cperm, *Lilen, npiv, lp, *Uilen, *Lip, *Uip, *Cperm_init, up, pivrow, pivcol, *Lpos, *Upos, *Wr, *Wc, *Wp, *Frpos, *Fcpos, *Row_degree, *Col_degree, *Rperm_init, n_row, n_col, n_inner, zero_pivot, nan_pivot, n1 ; #ifndef NDEBUG UMF_dump_matrix (Numeric, Work, FALSE) ; #endif DEBUG0 (("Kernel complete, Starting Kernel wrapup\n")) ; n_row = Symbolic->n_row ; n_col = Symbolic->n_col ; n_inner = MIN (n_row, n_col) ; Rperm = Numeric->Rperm ; Cperm = Numeric->Cperm ; Lilen = Numeric->Lilen ; Uilen = Numeric->Uilen ; Upos = Numeric->Upos ; Lpos = Numeric->Lpos ; Lip = Numeric->Lip ; Uip = Numeric->Uip ; D = Numeric->D ; npiv = Work->npiv ; Numeric->npiv = npiv ; Numeric->ulen = Work->ulen ; ASSERT (n_row == Numeric->n_row) ; ASSERT (n_col == Symbolic->n_col) ; DEBUG0 (("Wrap-up: npiv "ID" ulen "ID"\n", npiv, Numeric->ulen)) ; ASSERT (npiv <= n_inner) ; /* this will be nonzero only if matrix is singular or rectangular */ ASSERT (IMPLIES (npiv == n_col, Work->ulen == 0)) ; /* ---------------------------------------------------------------------- */ /* find the smallest and largest entries in D */ /* ---------------------------------------------------------------------- */ for (k = 0 ; k < npiv ; k++) { pivot_value = D [k] ; ABS (d, pivot_value) ; zero_pivot = SCALAR_IS_ZERO (d) ; nan_pivot = SCALAR_IS_NAN (d) ; if (!zero_pivot) { /* the pivot is nonzero, but might be Inf or NaN */ Numeric->nnzpiv++ ; } if (k == 0) { Numeric->min_udiag = d ; Numeric->max_udiag = d ; } else { /* min (abs (diag (U))) behaves as follows: If any entry is zero, then the result is zero (regardless of the presence of NaN's). Otherwise, if any entry is NaN, then the result is NaN. Otherwise, the result is the smallest absolute value on the diagonal of U. */ if (SCALAR_IS_NONZERO (Numeric->min_udiag)) { if (zero_pivot || nan_pivot) { Numeric->min_udiag = d ; } else if (!SCALAR_IS_NAN (Numeric->min_udiag)) { /* d and min_udiag are both non-NaN */ Numeric->min_udiag = MIN (Numeric->min_udiag, d) ; } } /* max (abs (diag (U))) behaves as follows: If any entry is NaN then the result is NaN. Otherise, the result is the largest absolute value on the diagonal of U. */ if (nan_pivot) { Numeric->max_udiag = d ; } else if (!SCALAR_IS_NAN (Numeric->max_udiag)) { /* d and max_udiag are both non-NaN */ Numeric->max_udiag = MAX (Numeric->max_udiag, d) ; } } } /* ---------------------------------------------------------------------- */ /* check if matrix is singular or rectangular */ /* ---------------------------------------------------------------------- */ Col_degree = Cperm ; /* for NON_PIVOTAL_COL macro */ Row_degree = Rperm ; /* for NON_PIVOTAL_ROW macro */ if (npiv < n_row) { /* finalize the row permutation */ k = npiv ; DEBUGm3 (("Singular pivot rows "ID" to "ID"\n", k, n_row-1)) ; for (row = 0 ; row < n_row ; row++) { if (NON_PIVOTAL_ROW (row)) { Rperm [row] = ONES_COMPLEMENT (k) ; DEBUGm3 (("Singular row "ID" is k: "ID" pivot row\n", row, k)) ; ASSERT (!NON_PIVOTAL_ROW (row)) ; Lpos [row] = EMPTY ; Uip [row] = EMPTY ; Uilen [row] = 0 ; k++ ; } } ASSERT (k == n_row) ; } if (npiv < n_col) { /* finalize the col permutation */ k = npiv ; DEBUGm3 (("Singular pivot cols "ID" to "ID"\n", k, n_col-1)) ; for (col = 0 ; col < n_col ; col++) { if (NON_PIVOTAL_COL (col)) { Cperm [col] = ONES_COMPLEMENT (k) ; DEBUGm3 (("Singular col "ID" is k: "ID" pivot row\n", col, k)) ; ASSERT (!NON_PIVOTAL_COL (col)) ; Upos [col] = EMPTY ; Lip [col] = EMPTY ; Lilen [col] = 0 ; k++ ; } } ASSERT (k == n_col) ; } if (npiv < n_inner) { /* finalize the diagonal of U */ DEBUGm3 (("Diag of U is zero, "ID" to "ID"\n", npiv, n_inner-1)) ; for (k = npiv ; k < n_inner ; k++) { CLEAR (D [k]) ; } } /* save the pattern of the last row of U */ if (Numeric->ulen > 0) { DEBUGm3 (("Last row of U is not empty\n")) ; Numeric->Upattern = Work->Upattern ; Work->Upattern = (Int *) NULL ; } DEBUG2 (("Nnzpiv: "ID" npiv "ID"\n", Numeric->nnzpiv, npiv)) ; ASSERT (Numeric->nnzpiv <= npiv) ; if (Numeric->nnzpiv < n_inner && !SCALAR_IS_NAN (Numeric->min_udiag)) { /* the rest of the diagonal is zero, so min_udiag becomes 0, * unless it is already NaN. */ Numeric->min_udiag = 0.0 ; } /* ---------------------------------------------------------------------- */ /* size n_row, n_col workspaces that can be used here: */ /* ---------------------------------------------------------------------- */ Frpos = Work->Frpos ; /* of size n_row+1 */ Fcpos = Work->Fcpos ; /* of size n_col+1 */ Wp = Work->Wp ; /* of size MAX(n_row,n_col)+1 */ /* Work->Upattern ; cannot be used (in Numeric) */ Wr = Work->Lpattern ; /* of size n_row+1 */ Wc = Work->Wrp ; /* of size n_col+1 or bigger */ /* ---------------------------------------------------------------------- */ /* construct Rperm from inverse permutations */ /* ---------------------------------------------------------------------- */ /* use Frpos for temporary copy of inverse row permutation [ */ for (pivrow = 0 ; pivrow < n_row ; pivrow++) { k = Rperm [pivrow] ; ASSERT (k < 0) ; k = ONES_COMPLEMENT (k) ; ASSERT (k >= 0 && k < n_row) ; Wp [k] = pivrow ; Frpos [pivrow] = k ; } for (k = 0 ; k < n_row ; k++) { Rperm [k] = Wp [k] ; } /* ---------------------------------------------------------------------- */ /* construct Cperm from inverse permutation */ /* ---------------------------------------------------------------------- */ /* use Fcpos for temporary copy of inverse column permutation [ */ for (pivcol = 0 ; pivcol < n_col ; pivcol++) { k = Cperm [pivcol] ; ASSERT (k < 0) ; k = ONES_COMPLEMENT (k) ; ASSERT (k >= 0 && k < n_col) ; Wp [k] = pivcol ; /* save a copy of the inverse column permutation in Fcpos */ Fcpos [pivcol] = k ; } for (k = 0 ; k < n_col ; k++) { Cperm [k] = Wp [k] ; } #ifndef NDEBUG for (k = 0 ; k < n_col ; k++) { col = Cperm [k] ; ASSERT (col >= 0 && col < n_col) ; ASSERT (Fcpos [col] == k) ; /* col is the kth pivot */ } for (k = 0 ; k < n_row ; k++) { row = Rperm [k] ; ASSERT (row >= 0 && row < n_row) ; ASSERT (Frpos [row] == k) ; /* row is the kth pivot */ } #endif #ifndef NDEBUG UMF_dump_lu (Numeric) ; #endif /* ---------------------------------------------------------------------- */ /* permute Lpos, Upos, Lilen, Lip, Uilen, and Uip */ /* ---------------------------------------------------------------------- */ for (k = 0 ; k < npiv ; k++) { pivrow = Rperm [k] ; Wr [k] = Uilen [pivrow] ; Wp [k] = Uip [pivrow] ; } for (k = 0 ; k < npiv ; k++) { Uilen [k] = Wr [k] ; Uip [k] = Wp [k] ; } for (k = 0 ; k < npiv ; k++) { pivrow = Rperm [k] ; Wp [k] = Lpos [pivrow] ; } for (k = 0 ; k < npiv ; k++) { Lpos [k] = Wp [k] ; } for (k = 0 ; k < npiv ; k++) { pivcol = Cperm [k] ; Wc [k] = Lilen [pivcol] ; Wp [k] = Lip [pivcol] ; } for (k = 0 ; k < npiv ; k++) { Lilen [k] = Wc [k] ; Lip [k] = Wp [k] ; } for (k = 0 ; k < npiv ; k++) { pivcol = Cperm [k] ; Wp [k] = Upos [pivcol] ; } for (k = 0 ; k < npiv ; k++) { Upos [k] = Wp [k] ; } /* ---------------------------------------------------------------------- */ /* terminate the last Uchain and last Lchain */ /* ---------------------------------------------------------------------- */ Upos [npiv] = EMPTY ; Lpos [npiv] = EMPTY ; Uip [npiv] = EMPTY ; Lip [npiv] = EMPTY ; Uilen [npiv] = 0 ; Lilen [npiv] = 0 ; /* ---------------------------------------------------------------------- */ /* convert U to the new pivot order */ /* ---------------------------------------------------------------------- */ n1 = Symbolic->n1 ; for (k = 0 ; k < n1 ; k++) { /* this is a singleton row of U */ ulen = Uilen [k] ; DEBUG4 (("K "ID" New U. ulen "ID" Singleton 1\n", k, ulen)) ; if (ulen > 0) { up = Uip [k] ; ip = (Int *) (Numeric->Memory + up) ; for (i = 0 ; i < ulen ; i++) { col = *ip ; DEBUG4 ((" old col "ID" new col "ID"\n", col, Fcpos [col])); ASSERT (col >= 0 && col < n_col) ; *ip++ = Fcpos [col] ; } } } for (k = n1 ; k < npiv ; k++) { up = Uip [k] ; if (up < 0) { /* this is the start of a new Uchain (with a pattern) */ ulen = Uilen [k] ; DEBUG4 (("K "ID" New U. ulen "ID" End_Uchain 1\n", k, ulen)) ; if (ulen > 0) { up = -up ; ip = (Int *) (Numeric->Memory + up) ; for (i = 0 ; i < ulen ; i++) { col = *ip ; DEBUG4 ((" old col "ID" new col "ID"\n", col, Fcpos [col])); ASSERT (col >= 0 && col < n_col) ; *ip++ = Fcpos [col] ; } } } } ulen = Numeric->ulen ; if (ulen > 0) { /* convert last pivot row of U to the new pivot order */ DEBUG4 (("K "ID" (last)\n", k)) ; for (i = 0 ; i < ulen ; i++) { col = Numeric->Upattern [i] ; DEBUG4 ((" old col "ID" new col "ID"\n", col, Fcpos [col])) ; Numeric->Upattern [i] = Fcpos [col] ; } } /* Fcpos no longer needed ] */ /* ---------------------------------------------------------------------- */ /* convert L to the new pivot order */ /* ---------------------------------------------------------------------- */ for (k = 0 ; k < n1 ; k++) { llen = Lilen [k] ; DEBUG4 (("K "ID" New L. llen "ID" Singleton col\n", k, llen)) ; if (llen > 0) { lp = Lip [k] ; ip = (Int *) (Numeric->Memory + lp) ; for (i = 0 ; i < llen ; i++) { row = *ip ; DEBUG4 ((" old row "ID" new row "ID"\n", row, Frpos [row])) ; ASSERT (row >= 0 && row < n_row) ; *ip++ = Frpos [row] ; } } } for (k = n1 ; k < npiv ; k++) { llen = Lilen [k] ; DEBUG4 (("K "ID" New L. llen "ID" \n", k, llen)) ; if (llen > 0) { lp = Lip [k] ; if (lp < 0) { /* this starts a new Lchain */ lp = -lp ; } ip = (Int *) (Numeric->Memory + lp) ; for (i = 0 ; i < llen ; i++) { row = *ip ; DEBUG4 ((" old row "ID" new row "ID"\n", row, Frpos [row])) ; ASSERT (row >= 0 && row < n_row) ; *ip++ = Frpos [row] ; } } } /* Frpos no longer needed ] */ /* ---------------------------------------------------------------------- */ /* combine symbolic and numeric permutations */ /* ---------------------------------------------------------------------- */ Cperm_init = Symbolic->Cperm_init ; Rperm_init = Symbolic->Rperm_init ; for (k = 0 ; k < n_row ; k++) { Rperm [k] = Rperm_init [Rperm [k]] ; } for (k = 0 ; k < n_col ; k++) { Cperm [k] = Cperm_init [Cperm [k]] ; } /* Work object will be freed immediately upon return (to UMF_kernel */ /* and then to UMFPACK_numeric). */ } SuiteSparse/UMFPACK/Source/umf_kernel_wrapup.h0000644001170100242450000000100310617161671020173 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL void UMF_kernel_wrapup ( NumericType *Numeric, SymbolicType *Symbolic, WorkType *Work ) ; SuiteSparse/UMFPACK/Source/umfpack_report_info.c0000644001170100242450000005256410617162112020506 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_report_info ================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Prints the Info array. See umfpack_report_info.h for details. */ #include "umf_internal.h" #define PRINT_INFO(format,x) \ { \ if (SCALAR_IS_NAN (x) || (!SCALAR_IS_LTZERO (x))) \ { \ PRINTF ((format, x)) ; \ } \ } /* RATIO macro uses a double relop, but ignore NaN case: */ #define RATIO(a,b,c) (((b) == 0) ? (c) : (((double) a)/((double) b))) /* ========================================================================== */ /* === print_ratio ========================================================== */ /* ========================================================================== */ PRIVATE void print_ratio ( char *what, char *format, double estimate, double actual ) { if (estimate < 0 && actual < 0) /* double relop, but ignore Nan case */ { return ; } PRINTF ((" %-27s", what)) ; if (estimate >= 0) /* double relop, but ignore Nan case */ { PRINTF ((format, estimate)) ; } else { PRINTF ((" -")) ; } if (actual >= 0) /* double relop, but ignore Nan case */ { PRINTF ((format, actual)) ; } else { PRINTF ((" -")) ; } if (estimate >= 0 && actual >= 0) /* double relop, but ignore Nan case */ { PRINTF ((" %5.0f%%\n", 100 * RATIO (actual, estimate, 1))) ; } else { PRINTF ((" -\n")) ; } } /* ========================================================================== */ /* === UMFPACK_report_info ================================================== */ /* ========================================================================== */ GLOBAL void UMFPACK_report_info ( const double Control [UMFPACK_CONTROL], const double Info [UMFPACK_INFO] ) { double lnz_est, unz_est, lunz_est, lnz, unz, lunz, tsym, tnum, fnum, tsolve, fsolve, ttot, ftot, twsym, twnum, twsolve, twtot, n2 ; Int n_row, n_col, n_inner, prl, is_sym ; /* ---------------------------------------------------------------------- */ /* get control settings and status to determine what to print */ /* ---------------------------------------------------------------------- */ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ; if (!Info || prl < 2) { /* no output generated if Info is (double *) NULL */ /* or if prl is less than 2 */ return ; } /* ---------------------------------------------------------------------- */ /* print umfpack version */ /* ---------------------------------------------------------------------- */ PRINTF (("UMFPACK V%d.%d.%d (%s), Info:\n", UMFPACK_MAIN_VERSION, UMFPACK_SUB_VERSION, UMFPACK_SUBSUB_VERSION, UMFPACK_DATE)) ; #ifndef NDEBUG PRINTF (( "**** Debugging enabled (UMFPACK will be exceedingly slow!) *****************\n" )) ; #endif /* ---------------------------------------------------------------------- */ /* print run-time options */ /* ---------------------------------------------------------------------- */ #ifdef DINT PRINTF ((" matrix entry defined as: double\n")) ; PRINTF ((" Int (generic integer) defined as: int\n")) ; #endif #ifdef DLONG PRINTF ((" matrix entry defined as: double\n")) ; PRINTF ((" Int (generic integer) defined as: UF_long\n")) ; #endif #ifdef ZINT PRINTF ((" matrix entry defined as: double complex\n")) ; PRINTF ((" Int (generic integer) defined as: int\n")) ; #endif #ifdef ZLONG PRINTF ((" matrix entry defined as: double complex\n")) ; PRINTF ((" Int (generic integer) defined as: UF_long\n")) ; #endif /* ---------------------------------------------------------------------- */ /* print compile-time options */ /* ---------------------------------------------------------------------- */ PRINTF ((" BLAS library used: ")) ; #ifdef NBLAS PRINTF (("none. UMFPACK will be slow.\n")) ; #else PRINTF (("Fortran BLAS. size of BLAS integer: "ID"\n", (Int) (sizeof (BLAS_INT)))) ; #endif PRINTF ((" MATLAB: ")) ; #ifdef MATLAB_MEX_FILE PRINTF (("yes.\n")) ; #else #ifdef MATHWORKS PRINTF (("yes.\n")) ; #else PRINTF (("no.\n")) ; #endif #endif PRINTF ((" CPU timer: ")) ; #ifdef NO_TIMER PRINTF (("none.\n")) ; #else #ifndef NPOSIX PRINTF (("POSIX times ( ) routine.\n")) ; #else #ifdef GETRUSAGE PRINTF (("getrusage ( ) routine.\n")) ; #else PRINTF (("ANSI clock ( ) routine.\n")) ; #endif #endif #endif /* ---------------------------------------------------------------------- */ /* print n and nz */ /* ---------------------------------------------------------------------- */ n_row = (Int) Info [UMFPACK_NROW] ; n_col = (Int) Info [UMFPACK_NCOL] ; n_inner = MIN (n_row, n_col) ; PRINT_INFO (" number of rows in matrix A: "ID"\n", n_row) ; PRINT_INFO (" number of columns in matrix A: "ID"\n", n_col) ; PRINT_INFO (" entries in matrix A: "ID"\n", (Int) Info [UMFPACK_NZ]) ; PRINT_INFO (" memory usage reported in: "ID"-byte Units\n", (Int) Info [UMFPACK_SIZE_OF_UNIT]) ; PRINT_INFO (" size of int: "ID" bytes\n", (Int) Info [UMFPACK_SIZE_OF_INT]) ; PRINT_INFO (" size of UF_long: "ID" bytes\n", (Int) Info [UMFPACK_SIZE_OF_LONG]) ; PRINT_INFO (" size of pointer: "ID" bytes\n", (Int) Info [UMFPACK_SIZE_OF_POINTER]) ; PRINT_INFO (" size of numerical entry: "ID" bytes\n", (Int) Info [UMFPACK_SIZE_OF_ENTRY]) ; /* ---------------------------------------------------------------------- */ /* symbolic parameters */ /* ---------------------------------------------------------------------- */ if (Info [UMFPACK_STRATEGY_USED] == UMFPACK_STRATEGY_SYMMETRIC) { PRINTF (("\n strategy used: symmetric\n")) ; } else if (Info [UMFPACK_STRATEGY_USED] == UMFPACK_STRATEGY_UNSYMMETRIC) { PRINTF (("\n strategy used: unsymmetric\n")) ; } else if (Info [UMFPACK_STRATEGY_USED] == UMFPACK_STRATEGY_2BY2) { PRINTF (("\n strategy used: symmetric 2-by-2\n")); } if (Info [UMFPACK_ORDERING_USED] == UMFPACK_ORDERING_AMD) { PRINTF ((" ordering used: amd on A+A'\n")) ; } else if (Info [UMFPACK_ORDERING_USED] == UMFPACK_ORDERING_COLAMD) { PRINTF ((" ordering used: colamd on A\n")) ; } else if (Info [UMFPACK_ORDERING_USED] == UMFPACK_ORDERING_GIVEN) { PRINTF ((" ordering used: provided by user\n")) ; } if (Info [UMFPACK_QFIXED] == 1) { PRINTF ((" modify Q during factorization: no\n")) ; } else if (Info [UMFPACK_QFIXED] == 0) { PRINTF ((" modify Q during factorization: yes\n")) ; } if (Info [UMFPACK_DIAG_PREFERRED] == 0) { PRINTF ((" prefer diagonal pivoting: no\n")) ; } else if (Info [UMFPACK_DIAG_PREFERRED] == 1) { PRINTF ((" prefer diagonal pivoting: yes\n")) ; } /* ---------------------------------------------------------------------- */ /* singleton statistics */ /* ---------------------------------------------------------------------- */ PRINT_INFO (" pivots with zero Markowitz cost: %0.f\n", Info [UMFPACK_COL_SINGLETONS] + Info [UMFPACK_ROW_SINGLETONS]) ; PRINT_INFO (" submatrix S after removing zero-cost pivots:\n" " number of \"dense\" rows: %.0f\n", Info [UMFPACK_NDENSE_ROW]) ; PRINT_INFO (" number of \"dense\" columns: %.0f\n", Info [UMFPACK_NDENSE_COL]) ; PRINT_INFO (" number of empty rows: %.0f\n", Info [UMFPACK_NEMPTY_ROW]) ; PRINT_INFO (" number of empty columns %.0f\n", Info [UMFPACK_NEMPTY_COL]) ; is_sym = Info [UMFPACK_S_SYMMETRIC] ; if (is_sym > 0) { PRINTF ((" submatrix S square and diagonal preserved\n")) ; } else if (is_sym == 0) { PRINTF ((" submatrix S not square or diagonal not preserved\n")); } /* ---------------------------------------------------------------------- */ /* statistics from amd_aat */ /* ---------------------------------------------------------------------- */ n2 = Info [UMFPACK_N2] ; if (n2 >= 0) { PRINTF ((" pattern of square submatrix S:\n")) ; } PRINT_INFO (" number rows and columns %.0f\n", n2) ; PRINT_INFO (" symmetry of nonzero pattern: %.6f\n", Info [UMFPACK_PATTERN_SYMMETRY]) ; PRINT_INFO (" nz in S+S' (excl. diagonal): %.0f\n", Info [UMFPACK_NZ_A_PLUS_AT]) ; PRINT_INFO (" nz on diagonal of matrix S: %.0f\n", Info [UMFPACK_NZDIAG]) ; if (Info [UMFPACK_NZDIAG] >= 0 && n2 > 0) { PRINTF ((" fraction of nz on diagonal: %.6f\n", Info [UMFPACK_NZDIAG] / n2)) ; } /* ---------------------------------------------------------------------- */ /* statistics from 2-by-2 permutation */ /* ---------------------------------------------------------------------- */ PRINT_INFO (" 2-by-2 pivoting to place large entries on diagonal:\n" " # of small diagonal entries of S: %.0f\n", Info [UMFPACK_2BY2_NWEAK]) ; PRINT_INFO (" # unmatched: %.0f\n", Info [UMFPACK_2BY2_UNMATCHED]) ; PRINT_INFO (" symmetry of P2*S: %.6f\n", Info [UMFPACK_2BY2_PATTERN_SYMMETRY]) ; PRINT_INFO (" nz in P2*S+(P2*S)' (excl. diag.): %.0f\n", Info [UMFPACK_2BY2_NZ_PA_PLUS_PAT]) ; PRINT_INFO (" nz on diagonal of P2*S: %.0f\n", Info [UMFPACK_2BY2_NZDIAG]) ; if (Info [UMFPACK_2BY2_NZDIAG] >= 0 && n2 > 0) { PRINTF ((" fraction of nz on diag of P2*S: %.6f\n", Info [UMFPACK_2BY2_NZDIAG] / n2)) ; } /* ---------------------------------------------------------------------- */ /* statistics from AMD */ /* ---------------------------------------------------------------------- */ if (Info [UMFPACK_ORDERING_USED] == UMFPACK_ORDERING_AMD) { double dmax = Info [UMFPACK_SYMMETRIC_DMAX] ; PRINTF ((" AMD statistics, for strict diagonal pivoting:\n")) ; PRINT_INFO (" est. flops for LU factorization: %.5e\n", Info [UMFPACK_SYMMETRIC_FLOPS]) ; PRINT_INFO (" est. nz in L+U (incl. diagonal): %.0f\n", Info [UMFPACK_SYMMETRIC_LUNZ]) ; PRINT_INFO (" est. largest front (# entries): %.0f\n", dmax*dmax) ; PRINT_INFO (" est. max nz in any column of L: %.0f\n", dmax) ; PRINT_INFO ( " number of \"dense\" rows/columns in S+S': %.0f\n", Info [UMFPACK_SYMMETRIC_NDENSE]) ; } /* ---------------------------------------------------------------------- */ /* symbolic factorization */ /* ---------------------------------------------------------------------- */ tsym = Info [UMFPACK_SYMBOLIC_TIME] ; twsym = Info [UMFPACK_SYMBOLIC_WALLTIME] ; PRINT_INFO (" symbolic factorization defragmentations: %.0f\n", Info [UMFPACK_SYMBOLIC_DEFRAG]) ; PRINT_INFO (" symbolic memory usage (Units): %.0f\n", Info [UMFPACK_SYMBOLIC_PEAK_MEMORY]) ; PRINT_INFO (" symbolic memory usage (MBytes): %.1f\n", MBYTES (Info [UMFPACK_SYMBOLIC_PEAK_MEMORY])) ; PRINT_INFO (" Symbolic size (Units): %.0f\n", Info [UMFPACK_SYMBOLIC_SIZE]) ; PRINT_INFO (" Symbolic size (MBytes): %.0f\n", MBYTES (Info [UMFPACK_SYMBOLIC_SIZE])) ; PRINT_INFO (" symbolic factorization CPU time (sec): %.2f\n", tsym) ; PRINT_INFO (" symbolic factorization wallclock time(sec): %.2f\n", twsym) ; /* ---------------------------------------------------------------------- */ /* scaling, from numerical factorization */ /* ---------------------------------------------------------------------- */ if (Info [UMFPACK_WAS_SCALED] == UMFPACK_SCALE_NONE) { PRINTF (("\n matrix scaled: no\n")) ; } else if (Info [UMFPACK_WAS_SCALED] == UMFPACK_SCALE_SUM) { PRINTF (("\n matrix scaled: yes ")) ; PRINTF (("(divided each row by sum of abs values in each row)\n")) ; PRINTF ((" minimum sum (abs (rows of A)): %.5e\n", Info [UMFPACK_RSMIN])) ; PRINTF ((" maximum sum (abs (rows of A)): %.5e\n", Info [UMFPACK_RSMAX])) ; } else if (Info [UMFPACK_WAS_SCALED] == UMFPACK_SCALE_MAX) { PRINTF (("\n matrix scaled: yes ")) ; PRINTF (("(divided each row by max abs value in each row)\n")) ; PRINTF ((" minimum max (abs (rows of A)): %.5e\n", Info [UMFPACK_RSMIN])) ; PRINTF ((" maximum max (abs (rows of A)): %.5e\n", Info [UMFPACK_RSMAX])) ; } /* ---------------------------------------------------------------------- */ /* estimate/actual in symbolic/numeric factorization */ /* ---------------------------------------------------------------------- */ /* double relop, but ignore NaN case: */ if (Info [UMFPACK_SYMBOLIC_DEFRAG] >= 0 /* UMFPACK_*symbolic called */ || Info [UMFPACK_NUMERIC_DEFRAG] >= 0) /* UMFPACK_numeric called */ { PRINTF (("\n symbolic/numeric factorization: upper bound")) ; PRINTF ((" actual %%\n")) ; PRINTF ((" variable-sized part of Numeric object:\n")) ; } print_ratio (" initial size (Units)", " %20.0f", Info [UMFPACK_VARIABLE_INIT_ESTIMATE], Info [UMFPACK_VARIABLE_INIT]) ; print_ratio (" peak size (Units)", " %20.0f", Info [UMFPACK_VARIABLE_PEAK_ESTIMATE], Info [UMFPACK_VARIABLE_PEAK]) ; print_ratio (" final size (Units)", " %20.0f", Info [UMFPACK_VARIABLE_FINAL_ESTIMATE], Info [UMFPACK_VARIABLE_FINAL]) ; print_ratio ("Numeric final size (Units)", " %20.0f", Info [UMFPACK_NUMERIC_SIZE_ESTIMATE], Info [UMFPACK_NUMERIC_SIZE]) ; print_ratio ("Numeric final size (MBytes)", " %20.1f", MBYTES (Info [UMFPACK_NUMERIC_SIZE_ESTIMATE]), MBYTES (Info [UMFPACK_NUMERIC_SIZE])) ; print_ratio ("peak memory usage (Units)", " %20.0f", Info [UMFPACK_PEAK_MEMORY_ESTIMATE], Info [UMFPACK_PEAK_MEMORY]) ; print_ratio ("peak memory usage (MBytes)", " %20.1f", MBYTES (Info [UMFPACK_PEAK_MEMORY_ESTIMATE]), MBYTES (Info [UMFPACK_PEAK_MEMORY])) ; print_ratio ("numeric factorization flops", " %20.5e", Info [UMFPACK_FLOPS_ESTIMATE], Info [UMFPACK_FLOPS]) ; lnz_est = Info [UMFPACK_LNZ_ESTIMATE] ; unz_est = Info [UMFPACK_UNZ_ESTIMATE] ; if (lnz_est >= 0 && unz_est >= 0) /* double relop, but ignore NaN case */ { lunz_est = lnz_est + unz_est - n_inner ; } else { lunz_est = EMPTY ; } lnz = Info [UMFPACK_LNZ] ; unz = Info [UMFPACK_UNZ] ; if (lnz >= 0 && unz >= 0) /* double relop, but ignore NaN case */ { lunz = lnz + unz - n_inner ; } else { lunz = EMPTY ; } print_ratio ("nz in L (incl diagonal)", " %20.0f", lnz_est, lnz) ; print_ratio ("nz in U (incl diagonal)", " %20.0f", unz_est, unz) ; print_ratio ("nz in L+U (incl diagonal)", " %20.0f", lunz_est, lunz) ; print_ratio ("largest front (# entries)", " %20.0f", Info [UMFPACK_MAX_FRONT_SIZE_ESTIMATE], Info [UMFPACK_MAX_FRONT_SIZE]) ; print_ratio ("largest # rows in front", " %20.0f", Info [UMFPACK_MAX_FRONT_NROWS_ESTIMATE], Info [UMFPACK_MAX_FRONT_NROWS]) ; print_ratio ("largest # columns in front", " %20.0f", Info [UMFPACK_MAX_FRONT_NCOLS_ESTIMATE], Info [UMFPACK_MAX_FRONT_NCOLS]) ; /* ---------------------------------------------------------------------- */ /* numeric factorization */ /* ---------------------------------------------------------------------- */ tnum = Info [UMFPACK_NUMERIC_TIME] ; twnum = Info [UMFPACK_NUMERIC_WALLTIME] ; fnum = Info [UMFPACK_FLOPS] ; PRINT_INFO ("\n initial allocation ratio used: %0.3g\n", Info [UMFPACK_ALLOC_INIT_USED]) ; PRINT_INFO (" # of forced updates due to frontal growth: %.0f\n", Info [UMFPACK_FORCED_UPDATES]) ; PRINT_INFO (" number of off-diagonal pivots: %.0f\n", Info [UMFPACK_NOFF_DIAG]) ; PRINT_INFO (" nz in L (incl diagonal), if none dropped %.0f\n", Info [UMFPACK_ALL_LNZ]) ; PRINT_INFO (" nz in U (incl diagonal), if none dropped %.0f\n", Info [UMFPACK_ALL_UNZ]) ; PRINT_INFO (" number of small entries dropped %.0f\n", Info [UMFPACK_NZDROPPED]) ; PRINT_INFO (" nonzeros on diagonal of U: %.0f\n", Info [UMFPACK_UDIAG_NZ]) ; PRINT_INFO (" min abs. value on diagonal of U: %.2e\n", Info [UMFPACK_UMIN]) ; PRINT_INFO (" max abs. value on diagonal of U: %.2e\n", Info [UMFPACK_UMAX]) ; PRINT_INFO (" estimate of reciprocal of condition number: %.2e\n", Info [UMFPACK_RCOND]) ; PRINT_INFO (" indices in compressed pattern: %.0f\n", Info [UMFPACK_COMPRESSED_PATTERN]) ; PRINT_INFO (" numerical values stored in Numeric object: %.0f\n", Info [UMFPACK_LU_ENTRIES]) ; PRINT_INFO (" numeric factorization defragmentations: %.0f\n", Info [UMFPACK_NUMERIC_DEFRAG]) ; PRINT_INFO (" numeric factorization reallocations: %.0f\n", Info [UMFPACK_NUMERIC_REALLOC]) ; PRINT_INFO (" costly numeric factorization reallocations: %.0f\n", Info [UMFPACK_NUMERIC_COSTLY_REALLOC]) ; PRINT_INFO (" numeric factorization CPU time (sec): %.2f\n", tnum) ; PRINT_INFO (" numeric factorization wallclock time (sec): %.2f\n", twnum) ; #define TMIN 0.001 if (tnum > TMIN && fnum > 0) { PRINT_INFO ( " numeric factorization mflops (CPU time): %.2f\n", 1e-6 * fnum / tnum) ; } if (twnum > TMIN && fnum > 0) { PRINT_INFO ( " numeric factorization mflops (wallclock): %.2f\n", 1e-6 * fnum / twnum) ; } ttot = EMPTY ; ftot = fnum ; if (tsym >= TMIN && tnum >= 0) { ttot = tsym + tnum ; PRINT_INFO (" symbolic + numeric CPU time (sec): %.2f\n", ttot) ; if (ftot > 0 && ttot > TMIN) { PRINT_INFO ( " symbolic + numeric mflops (CPU time): %.2f\n", 1e-6 * ftot / ttot) ; } } twtot = EMPTY ; if (twsym >= TMIN && twnum >= TMIN) { twtot = twsym + twnum ; PRINT_INFO (" symbolic + numeric wall clock time (sec): %.2f\n", twtot) ; if (ftot > 0 && twtot > TMIN) { PRINT_INFO ( " symbolic + numeric mflops (wall clock): %.2f\n", 1e-6 * ftot / twtot) ; } } /* ---------------------------------------------------------------------- */ /* solve */ /* ---------------------------------------------------------------------- */ tsolve = Info [UMFPACK_SOLVE_TIME] ; twsolve = Info [UMFPACK_SOLVE_WALLTIME] ; fsolve = Info [UMFPACK_SOLVE_FLOPS] ; PRINT_INFO ("\n solve flops: %.5e\n", fsolve) ; PRINT_INFO (" iterative refinement steps taken: %.0f\n", Info [UMFPACK_IR_TAKEN]) ; PRINT_INFO (" iterative refinement steps attempted: %.0f\n", Info [UMFPACK_IR_ATTEMPTED]) ; PRINT_INFO (" sparse backward error omega1: %.2e\n", Info [UMFPACK_OMEGA1]) ; PRINT_INFO (" sparse backward error omega2: %.2e\n", Info [UMFPACK_OMEGA2]) ; PRINT_INFO (" solve CPU time (sec): %.2f\n", tsolve) ; PRINT_INFO (" solve wall clock time (sec): %.2f\n", twsolve) ; if (fsolve > 0 && tsolve > TMIN) { PRINT_INFO ( " solve mflops (CPU time): %.2f\n", 1e-6 * fsolve / tsolve) ; } if (fsolve > 0 && twsolve > TMIN) { PRINT_INFO ( " solve mflops (wall clock time): %.2f\n", 1e-6 * fsolve / twsolve) ; } if (ftot >= 0 && fsolve >= 0) { ftot += fsolve ; PRINT_INFO ( "\n total symbolic + numeric + solve flops: %.5e\n", ftot) ; } if (tsolve >= TMIN) { if (ttot >= TMIN && ftot >= 0) { ttot += tsolve ; PRINT_INFO ( " total symbolic + numeric + solve CPU time: %.2f\n", ttot) ; if (ftot > 0 && ttot > TMIN) { PRINT_INFO ( " total symbolic + numeric + solve mflops (CPU): %.2f\n", 1e-6 * ftot / ttot) ; } } } if (twsolve >= TMIN) { if (twtot >= TMIN && ftot >= 0) { twtot += tsolve ; PRINT_INFO ( " total symbolic+numeric+solve wall clock time: %.2f\n", twtot) ; if (ftot > 0 && twtot > TMIN) { PRINT_INFO ( " total symbolic+numeric+solve mflops(wallclock) %.2f\n", 1e-6 * ftot / twtot) ; } } } PRINTF (("\n")) ; } SuiteSparse/UMFPACK/Source/umf_valid_symbolic.c0000644001170100242450000000317310677542513020326 0ustar davisfac/* ========================================================================== */ /* === UMF_valid_symbolic =================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ #include "umf_internal.h" #include "umf_valid_symbolic.h" /* Returns TRUE if the Symbolic object is valid, FALSE otherwise. */ /* The UMFPACK_report_symbolic routine does a more thorough check. */ GLOBAL Int UMF_valid_symbolic ( SymbolicType *Symbolic ) { /* This routine does not check the contents of the individual arrays, so */ /* it can miss some errors. All it checks for is the presence of the */ /* arrays, and the Symbolic "valid" entry. */ if (!Symbolic) { return (FALSE) ; } if (Symbolic->valid != SYMBOLIC_VALID) { /* Symbolic does not point to a SymbolicType object */ return (FALSE) ; } if (!Symbolic->Cperm_init || !Symbolic->Rperm_init || !Symbolic->Front_npivcol || !Symbolic->Front_1strow || !Symbolic->Front_leftmostdesc || !Symbolic->Front_parent || !Symbolic->Chain_start || !Symbolic->Chain_maxrows || !Symbolic->Chain_maxcols || Symbolic->n_row <= 0 || Symbolic->n_col <= 0) { return (FALSE) ; } return (TRUE) ; } SuiteSparse/UMFPACK/Source/umf_valid_symbolic.h0000644001170100242450000000072510617162523020324 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_valid_symbolic ( SymbolicType *Symbolic ) ; SuiteSparse/UMFPACK/Source/umfpack_scale.c0000644001170100242450000000672510617162156017255 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_scale ======================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Applies the scale factors computed during numerical factorization to a vector. See umfpack_scale.h for more details. The LU factorization is L*U = P*R*A*Q, where P and Q are permutation matrices, and R is diagonal. This routine computes X = R * B using the matrix R stored in the Numeric object. Returns FALSE if any argument is invalid, TRUE otherwise. If R not present in the Numeric object, then R = I and no floating-point work is done. B is simply copied into X. */ #include "umf_internal.h" #include "umf_valid_numeric.h" GLOBAL Int UMFPACK_scale ( double Xx [ ], #ifdef COMPLEX double Xz [ ], #endif const double Bx [ ], #ifdef COMPLEX const double Bz [ ], #endif void *NumericHandle ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ NumericType *Numeric ; Int n, i ; double *Rs ; #ifdef COMPLEX Int split = SPLIT (Xz) && SPLIT (Bz) ; #endif Numeric = (NumericType *) NumericHandle ; if (!UMF_valid_numeric (Numeric)) { return (UMFPACK_ERROR_invalid_Numeric_object) ; } n = Numeric->n_row ; Rs = Numeric->Rs ; if (!Xx || !Bx) { return (UMFPACK_ERROR_argument_missing) ; } /* ---------------------------------------------------------------------- */ /* X = R*B or R\B */ /* ---------------------------------------------------------------------- */ if (Rs != (double *) NULL) { #ifndef NRECIPROCAL if (Numeric->do_recip) { /* multiply by the scale factors */ #ifdef COMPLEX if (split) { for (i = 0 ; i < n ; i++) { Xx [i] = Bx [i] * Rs [i] ; Xz [i] = Bz [i] * Rs [i] ; } } else { for (i = 0 ; i < n ; i++) { Xx [2*i ] = Bx [2*i ] * Rs [i] ; Xx [2*i+1] = Bx [2*i+1] * Rs [i] ; } } #else for (i = 0 ; i < n ; i++) { Xx [i] = Bx [i] * Rs [i] ; } #endif } else #endif { /* divide by the scale factors */ #ifdef COMPLEX if (split) { for (i = 0 ; i < n ; i++) { Xx [i] = Bx [i] / Rs [i] ; Xz [i] = Bz [i] / Rs [i] ; } } else { for (i = 0 ; i < n ; i++) { Xx [2*i ] = Bx [2*i ] / Rs [i] ; Xx [2*i+1] = Bx [2*i+1] / Rs [i] ; } } #else for (i = 0 ; i < n ; i++) { Xx [i] = Bx [i] / Rs [i] ; } #endif } } else { /* no scale factors, just copy B into X */ #ifdef COMPLEX if (split) { for (i = 0 ; i < n ; i++) { Xx [i] = Bx [i] ; Xz [i] = Bz [i] ; } } else { for (i = 0 ; i < n ; i++) { Xx [2*i ] = Bx [2*i ] ; Xx [2*i+1] = Bx [2*i+1] ; } } #else for (i = 0 ; i < n ; i++) { Xx [i] = Bx [i] ; } #endif } return (UMFPACK_OK) ; } SuiteSparse/UMFPACK/Source/umf_blas3_update.c0000644001170100242450000001031610677542076017675 0ustar davisfac/* ========================================================================== */ /* === UMF_blas3_update ===================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ #include "umf_internal.h" #include "umf_blas3_update.h" GLOBAL void UMF_blas3_update ( WorkType *Work ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Entry *L, *U, *C, *LU ; Int i, j, s, k, m, n, d, nb, dc ; #ifndef NBLAS Int blas_ok = TRUE ; #else #define blas_ok FALSE #endif DEBUG5 (("In UMF_blas3_update "ID" "ID" "ID"\n", Work->fnpiv, Work->fnrows, Work->fncols)) ; k = Work->fnpiv ; if (k == 0) { /* no work to do */ return ; } m = Work->fnrows ; n = Work->fncols ; d = Work->fnr_curr ; dc = Work->fnc_curr ; nb = Work->nb ; ASSERT (d >= 0 && (d % 2) == 1) ; C = Work->Fcblock ; /* ldc is fnr_curr */ L = Work->Flblock ; /* ldl is fnr_curr */ U = Work->Fublock ; /* ldu is fnc_curr, stored by rows */ LU = Work->Flublock ; /* nb-by-nb */ #ifndef NDEBUG DEBUG5 (("DO RANK-NB UPDATE of frontal:\n")) ; DEBUG5 (("DGEMM : "ID" "ID" "ID"\n", k, m, n)) ; DEBUG7 (("C block: ")) ; UMF_dump_dense (C, d, m, n) ; DEBUG7 (("A block: ")) ; UMF_dump_dense (L, d, m, k) ; DEBUG7 (("B' block: ")) ; UMF_dump_dense (U, dc, n, k) ; DEBUG7 (("LU block: ")) ; UMF_dump_dense (LU, nb, k, k) ; #endif if (k == 1) { #ifndef NBLAS BLAS_GER (m, n, L, U, C, d) ; #endif if (!blas_ok) { /* rank-1 outer product to update the C block */ for (j = 0 ; j < n ; j++) { Entry u_j = U [j] ; if (IS_NONZERO (u_j)) { Entry *c_ij, *l_is ; c_ij = & C [j*d] ; l_is = & L [0] ; #pragma ivdep for (i = 0 ; i < m ; i++) { /* C [i+j*d]-= L [i] * U [j] */ MULT_SUB (*c_ij, *l_is, u_j) ; c_ij++ ; l_is++ ; } } } } } else { /* triangular solve to update the U block */ #ifndef NBLAS BLAS_TRSM_RIGHT (n, k, LU, nb, U, dc) ; #endif if (!blas_ok) { /* use plain C code if no BLAS at compile time, or if integer * overflow has occurred */ for (s = 0 ; s < k ; s++) { for (i = s+1 ; i < k ; i++) { Entry l_is = LU [i+s*nb] ; if (IS_NONZERO (l_is)) { Entry *u_ij, *u_sj ; u_ij = & U [i*dc] ; u_sj = & U [s*dc] ; #pragma ivdep for (j = 0 ; j < n ; j++) { /* U [i*dc+j] -= LU [i+s*nb] * U [s*dc+j] ; */ MULT_SUB (*u_ij, l_is, *u_sj) ; u_ij++ ; u_sj++ ; } } } } } /* rank-k outer product to update the C block */ /* C = C - L*U' (U is stored by rows, not columns) */ #ifndef NBLAS BLAS_GEMM (m, n, k, L, U, dc, C, d) ; #endif if (!blas_ok) { /* use plain C code if no BLAS at compile time, or if integer * overflow has occurred */ for (s = 0 ; s < k ; s++) { for (j = 0 ; j < n ; j++) { Entry u_sj = U [j+s*dc] ; if (IS_NONZERO (u_sj)) { Entry *c_ij, *l_is ; c_ij = & C [j*d] ; l_is = & L [s*d] ; #pragma ivdep for (i = 0 ; i < m ; i++) { /* C [i+j*d]-= L [i+s*d] * U [s*dc+j] */ MULT_SUB (*c_ij, *l_is, u_sj) ; c_ij++ ; l_is++ ; } } } } } } #ifndef NDEBUG DEBUG5 (("RANK-NB UPDATE of frontal done:\n")) ; DEBUG5 (("DGEMM : "ID" "ID" "ID"\n", k, m, n)) ; DEBUG7 (("C block: ")) ; UMF_dump_dense (C, d, m, n) ; DEBUG7 (("A block: ")) ; UMF_dump_dense (L, d, m, k) ; DEBUG7 (("B' block: ")) ; UMF_dump_dense (U, dc, n, k) ; DEBUG7 (("LU block: ")) ; UMF_dump_dense (LU, nb, k, k) ; #endif DEBUG2 (("blas3 "ID" "ID" "ID"\n", k, Work->fnrows, Work->fncols)) ; } SuiteSparse/UMFPACK/Source/umf_blas3_update.h0000644001170100242450000000071410617161416017670 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL void UMF_blas3_update ( WorkType *Work ) ; SuiteSparse/UMFPACK/Source/umf_start_front.c0000644001170100242450000002113310677542422017666 0ustar davisfac/* ========================================================================== */ /* === UMF_start_front ====================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Allocate the initial frontal matrix working array for a single chain. The * front does not have to be big enough, since if it's too small it will get * reallocated. The size computed here is just an estimate. */ #include "umf_internal.h" #include "umf_start_front.h" #include "umf_grow_front.h" GLOBAL Int UMF_start_front /* returns TRUE if successful, FALSE otherwise */ ( Int chain, NumericType *Numeric, WorkType *Work, SymbolicType *Symbolic ) { double maxbytes ; Int fnrows_max, fncols_max, fnr2, fnc2, fsize, fcurr_size, maxfrsize, overflow, nb, f, cdeg ; nb = Symbolic->nb ; fnrows_max = Symbolic->Chain_maxrows [chain] ; fncols_max = Symbolic->Chain_maxcols [chain] ; DEBUGm2 (("Start Front for chain "ID". fnrows_max "ID" fncols_max "ID"\n", chain, fnrows_max, fncols_max)) ; Work->fnrows_max = fnrows_max ; Work->fncols_max = fncols_max ; Work->any_skip = FALSE ; maxbytes = sizeof (Entry) * (double) (fnrows_max + nb) * (double) (fncols_max + nb) ; fcurr_size = Work->fcurr_size ; if (Symbolic->prefer_diagonal) { /* Get a rough upper bound on the degree of the first pivot column in * this front. Note that Col_degree is not maintained if diagonal * pivoting is preferred. For most matrices, the first pivot column * of the first frontal matrix of a new chain has only one tuple in * it anyway, so this bound is exact in that case. */ Int col, tpi, e, *E, *Col_tuples, *Col_tlen, *Cols ; Tuple *tp, *tpend ; Unit *Memory, *p ; Element *ep ; E = Work->E ; Memory = Numeric->Memory ; Col_tuples = Numeric->Lip ; Col_tlen = Numeric->Lilen ; col = Work->nextcand ; tpi = Col_tuples [col] ; tp = (Tuple *) Memory + tpi ; tpend = tp + Col_tlen [col] ; cdeg = 0 ; DEBUGm3 (("\n=============== start front: col "ID" tlen "ID"\n", col, Col_tlen [col])) ; for ( ; tp < tpend ; tp++) { DEBUG1 (("Tuple ("ID","ID")\n", tp->e, tp->f)) ; e = tp->e ; if (!E [e]) continue ; f = tp->f ; p = Memory + E [e] ; ep = (Element *) p ; p += UNITS (Element, 1) ; Cols = (Int *) p ; if (Cols [f] == EMPTY) continue ; DEBUG1 ((" nrowsleft "ID"\n", ep->nrowsleft)) ; cdeg += ep->nrowsleft ; } #ifndef NDEBUG DEBUGm3 (("start front cdeg: "ID" col "ID"\n", cdeg, col)) ; UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ; #endif /* cdeg is now the rough upper bound on the degree of the next pivot * column. */ /* If AMD was called, we know the maximum number of nonzeros in any * column of L. Use this as an upper bound for cdeg, but add 2 to * account for a small amount of off-diagonal pivoting. */ if (Symbolic->amd_dmax > 0) { cdeg = MIN (cdeg, Symbolic->amd_dmax) ; } /* Increase it to account for larger columns later on. * Also ensure that it's larger than zero. */ cdeg += 2 ; /* cdeg cannot be larger than fnrows_max */ cdeg = MIN (cdeg, fnrows_max) ; } else { /* don't do the above cdeg computation */ cdeg = 0 ; } DEBUGm2 (("fnrows max "ID" fncols_max "ID"\n", fnrows_max, fncols_max)) ; /* the current frontal matrix is empty */ ASSERT (Work->fnrows == 0 && Work->fncols == 0 && Work->fnpiv == 0) ; /* maximum row dimension is always odd, to avoid bad cache effects */ ASSERT (fnrows_max >= 0) ; ASSERT (fnrows_max % 2 == 1) ; /* ---------------------------------------------------------------------- * allocate working array for current frontal matrix: * minimum size: 1-by-1 * maximum size: fnrows_max-by-fncols_max * desired size: * * if Numeric->front_alloc_init >= 0: * * for unsymmetric matrices: * Numeric->front_alloc_init * (fnrows_max-by-fncols_max) * * for symmetric matrices (diagonal pivoting preference, actually): * Numeric->front_alloc_init * (fnrows_max-by-fncols_max), or * cdeg*cdeg, whichever is smaller. * * if Numeric->front_alloc_init < 0: * allocate a front of size -Numeric->front_alloc_init. * * Allocate the whole thing if it's small (less than 2*nb^2). Make sure the * leading dimension of the frontal matrix is odd. * * Also allocate the nb-by-nb LU block, the dr-by-nb L block, and the * nb-by-dc U block. * ---------------------------------------------------------------------- */ /* get the maximum front size, avoiding integer overflow */ overflow = INT_OVERFLOW (maxbytes) ; if (overflow) { /* :: int overflow, max front size :: */ maxfrsize = Int_MAX / sizeof (Entry) ; } else { maxfrsize = (fnrows_max + nb) * (fncols_max + nb) ; } ASSERT (!INT_OVERFLOW ((double) maxfrsize * sizeof (Entry))) ; if (Numeric->front_alloc_init < 0) { /* allocate a front of -Numeric->front_alloc_init entries */ fsize = -Numeric->front_alloc_init ; fsize = MAX (1, fsize) ; } else { if (INT_OVERFLOW (Numeric->front_alloc_init * maxbytes)) { /* :: int overflow, requested front size :: */ fsize = Int_MAX / sizeof (Entry) ; } else { fsize = Numeric->front_alloc_init * maxfrsize ; } if (cdeg > 0) { /* diagonal pivoting is in use. cdeg was computed above */ Int fsize2 ; /* add the L and U blocks */ cdeg += nb ; if (INT_OVERFLOW (((double) cdeg * (double) cdeg) * sizeof (Entry))) { /* :: int overflow, symmetric front size :: */ fsize2 = Int_MAX / sizeof (Entry) ; } else { fsize2 = MAX (cdeg * cdeg, fcurr_size) ; } fsize = MIN (fsize, fsize2) ; } } fsize = MAX (fsize, 2*nb*nb) ; /* fsize and maxfrsize are now safe from integer overflow. They both * include the size of the pivot blocks. */ ASSERT (!INT_OVERFLOW ((double) fsize * sizeof (Entry))) ; Work->fnrows_new = 0 ; Work->fncols_new = 0 ; /* desired size is fnr2-by-fnc2 (includes L and U blocks): */ DEBUGm2 ((" fsize "ID" fcurr_size "ID"\n", fsize, fcurr_size)) ; DEBUGm2 ((" maxfrsize "ID" fnr_curr "ID" fnc_curr "ID"\n", maxfrsize, Work->fnr_curr, Work->fnc_curr)) ; if (fsize >= maxfrsize && !overflow) { /* max working array is small, allocate all of it */ fnr2 = fnrows_max + nb ; fnc2 = fncols_max + nb ; fsize = maxfrsize ; DEBUGm1 ((" sufficient for ("ID"+"ID")-by-("ID"+"ID")\n", fnrows_max, nb, fncols_max, nb)) ; } else { /* allocate a smaller working array */ if (fnrows_max <= fncols_max) { fnr2 = (Int) sqrt ((double) fsize) ; /* make sure fnr2 is odd */ fnr2 = MAX (fnr2, 1) ; if (fnr2 % 2 == 0) fnr2++ ; fnr2 = MIN (fnr2, fnrows_max + nb) ; fnc2 = fsize / fnr2 ; } else { fnc2 = (Int) sqrt ((double) fsize) ; fnc2 = MIN (fnc2, fncols_max + nb) ; fnr2 = fsize / fnc2 ; /* make sure fnr2 is odd */ fnr2 = MAX (fnr2, 1) ; if (fnr2 % 2 == 0) { fnr2++ ; fnc2 = fsize / fnr2 ; } } DEBUGm1 ((" smaller "ID"-by-"ID"\n", fnr2, fnc2)) ; } fnr2 = MIN (fnr2, fnrows_max + nb) ; fnc2 = MIN (fnc2, fncols_max + nb) ; ASSERT (fnr2 % 2 == 1) ; ASSERT (fnr2 * fnc2 <= fsize) ; fnr2 -= nb ; fnc2 -= nb ; ASSERT (fnr2 >= 0) ; ASSERT (fnc2 >= 0) ; if (fsize > fcurr_size) { DEBUGm1 ((" Grow front \n")) ; Work->do_grow = TRUE ; if (!UMF_grow_front (Numeric, fnr2, fnc2, Work, -1)) { /* since the minimum front size is 1-by-1, it would be nearly * impossible to run out of memory here. */ DEBUGm4 (("out of memory: start front\n")) ; return (FALSE) ; } } else { /* use the existing front */ DEBUGm1 ((" existing front ok\n")) ; Work->fnr_curr = fnr2 ; Work->fnc_curr = fnc2 ; Work->Flblock = Work->Flublock + nb * nb ; Work->Fublock = Work->Flblock + nb * fnr2 ; Work->Fcblock = Work->Fublock + nb * fnc2 ; } ASSERT (Work->Flblock == Work->Flublock + Work->nb*Work->nb) ; ASSERT (Work->Fublock == Work->Flblock + Work->fnr_curr*Work->nb) ; ASSERT (Work->Fcblock == Work->Fublock + Work->nb*Work->fnc_curr) ; return (TRUE) ; } SuiteSparse/UMFPACK/Source/umf_start_front.h0000644001170100242450000000101710617162425017665 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_start_front ( Int chain, NumericType *Numeric, WorkType *Work, SymbolicType *Symbolic ) ; SuiteSparse/UMFPACK/Source/umf_scale.h0000644001170100242450000000073610617162302016410 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL void UMF_scale ( Int n, Entry alpha, Entry X [ ] ) ; SuiteSparse/UMFPACK/Source/umfpack_triplet_to_col.c0000644001170100242450000001465010617162207021201 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_triplet_to_col =============================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User callable. Converts triplet input to column-oriented form. Duplicate entries may exist (they are summed in the output). The columns of the column-oriented form are in sorted order. The input is not modified. Returns 1 if OK, 0 if an error occurred. See umfpack_triplet_to_col.h for details. If Map is present (a non-NULL pointer to an Int array of size nz), then on output it holds the position of the triplets in the column-form matrix. That is, suppose p = Map [k], and the k-th triplet is i=Ti[k], j=Tj[k], and aij=Tx[k]. Then i=Ai[p], and aij will have been summed into Ax[p]. Also, Ap[j] <= p < Ap[j+1]. The Map array is not computed if it is (Int *) NULL. Dynamic memory usage: If numerical values are present, then one (two for complex version) workspace of size (nz+1)*sizeof(double) is allocated via UMF_malloc. Next, 4 calls to UMF_malloc are made to obtain workspace of size ((nz+1) + (n_row+1) + n_row + MAX (n_row,n_col)) * sizeof(Int). All of this workspace (4 to 6 objects) are free'd via UMF_free on return. For the complex version, additional space is allocated. An extra array of size nz*sizeof(Int) is allocated if Map is present. */ #include "umf_internal.h" #include "umf_malloc.h" #include "umf_free.h" #include "umf_triplet.h" #ifndef NDEBUG PRIVATE Int init_count ; #endif /* ========================================================================== */ GLOBAL Int UMFPACK_triplet_to_col ( Int n_row, Int n_col, Int nz, const Int Ti [ ], /* size nz */ const Int Tj [ ], /* size nz */ const double Tx [ ], /* size nz */ #ifdef COMPLEX const double Tz [ ], /* size nz */ #endif Int Ap [ ], /* size n_col + 1 */ Int Ai [ ], /* size nz */ double Ax [ ] /* size nz */ #ifdef COMPLEX , double Az [ ] /* size nz */ #endif , Int Map [ ] /* size nz */ ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ Int *RowCount, *Rp, *Rj, *W, nn, do_values, do_map, *Map2, status ; double *Rx ; #ifdef COMPLEX double *Rz ; Int split ; #endif #ifndef NDEBUG UMF_dump_start ( ) ; init_count = UMF_malloc_count ; #endif /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ if (!Ai || !Ap || !Ti || !Tj) { return (UMFPACK_ERROR_argument_missing) ; } if (n_row <= 0 || n_col <= 0) /* must be > 0 */ { return (UMFPACK_ERROR_n_nonpositive) ; } if (nz < 0) /* nz must be >= 0 (singular matrices are OK) */ { return (UMFPACK_ERROR_invalid_matrix) ; } nn = MAX (n_row, n_col) ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ Rx = (double *) NULL ; do_values = Ax && Tx ; if (do_values) { #ifdef COMPLEX Rx = (double *) UMF_malloc (2*nz+2, sizeof (double)) ; split = SPLIT (Tz) && SPLIT (Az) ; if (split) { Rz = Rx + nz ; } else { Rz = (double *) NULL ; } #else Rx = (double *) UMF_malloc (nz+1, sizeof (double)) ; #endif if (!Rx) { DEBUGm4 (("out of memory: triplet work \n")) ; ASSERT (UMF_malloc_count == init_count) ; return (UMFPACK_ERROR_out_of_memory) ; } } do_map = (Map != (Int *) NULL) ; Map2 = (Int *) NULL ; if (do_map) { DEBUG0 (("Do map:\n")) ; Map2 = (Int *) UMF_malloc (nz+1, sizeof (Int)) ; if (!Map2) { DEBUGm4 (("out of memory: triplet map\n")) ; (void) UMF_free ((void *) Rx) ; ASSERT (UMF_malloc_count == init_count) ; return (UMFPACK_ERROR_out_of_memory) ; } } Rj = (Int *) UMF_malloc (nz+1, sizeof (Int)) ; Rp = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ; RowCount = (Int *) UMF_malloc (n_row, sizeof (Int)) ; W = (Int *) UMF_malloc (nn, sizeof (Int)) ; if (!Rj || !Rp || !RowCount || !W) { DEBUGm4 (("out of memory: triplet work (int)\n")) ; (void) UMF_free ((void *) Rx) ; (void) UMF_free ((void *) Map2) ; (void) UMF_free ((void *) Rp) ; (void) UMF_free ((void *) Rj) ; (void) UMF_free ((void *) RowCount) ; (void) UMF_free ((void *) W) ; ASSERT (UMF_malloc_count == init_count) ; return (UMFPACK_ERROR_out_of_memory) ; } ASSERT (UMF_malloc_count == init_count + 4 + (Rx != (double *) NULL) + do_map) ; /* ---------------------------------------------------------------------- */ /* convert from triplet to column form */ /* ---------------------------------------------------------------------- */ if (do_map) { if (do_values) { status = UMF_triplet_map_x (n_row, n_col, nz, Ti, Tj, Ap, Ai, Rp, Rj, W, RowCount, Tx, Ax, Rx #ifdef COMPLEX , Tz, Az, Rz #endif , Map, Map2) ; } else { status = UMF_triplet_map_nox (n_row, n_col, nz, Ti, Tj, Ap, Ai, Rp, Rj, W, RowCount, Map, Map2) ; } } else { if (do_values) { status = UMF_triplet_nomap_x (n_row, n_col, nz, Ti, Tj, Ap, Ai, Rp, Rj, W, RowCount , Tx, Ax, Rx #ifdef COMPLEX , Tz, Az, Rz #endif ) ; } else { status = UMF_triplet_nomap_nox (n_row, n_col, nz, Ti, Tj, Ap, Ai, Rp, Rj, W, RowCount) ; } } /* ---------------------------------------------------------------------- */ /* free the workspace */ /* ---------------------------------------------------------------------- */ (void) UMF_free ((void *) Rx) ; (void) UMF_free ((void *) Map2) ; (void) UMF_free ((void *) Rp) ; (void) UMF_free ((void *) Rj) ; (void) UMF_free ((void *) RowCount) ; (void) UMF_free ((void *) W) ; ASSERT (UMF_malloc_count == init_count) ; return (status) ; } SuiteSparse/UMFPACK/Source/umfpack_report_matrix.c0000644001170100242450000001225510617162115021053 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_report_matrix ================================================ */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Prints a column or row-oriented matrix. See umfpack_report_matrix.h for details. */ #include "umf_internal.h" GLOBAL Int UMFPACK_report_matrix ( Int n_row, Int n_col, const Int Ap [ ], const Int Ai [ ], const double Ax [ ], #ifdef COMPLEX const double Az [ ], #endif Int col_form, /* 1: column form, 0: row form */ const double Control [UMFPACK_CONTROL] ) { Entry a ; Int prl, i, k, length, ilast, p, nz, prl1, p1, p2, n, n_i, do_values ; char *vector, *index ; #ifdef COMPLEX Int split = SPLIT (Az) ; #endif /* ---------------------------------------------------------------------- */ /* determine the form, and check if inputs exist */ /* ---------------------------------------------------------------------- */ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ; if (prl <= 2) { return (UMFPACK_OK) ; } if (col_form) { vector = "column" ; /* column vectors */ index = "row" ; /* with row indices */ n = n_col ; n_i = n_row ; } else { vector = "row" ; /* row vectors */ index = "column" ; /* with column indices */ n = n_row ; n_i = n_col ; } PRINTF (("%s-form matrix, n_row "ID" n_col "ID", ", vector, n_row, n_col)) ; if (n_row <= 0 || n_col <= 0) { PRINTF (("ERROR: n_row <= 0 or n_col <= 0\n\n")) ; return (UMFPACK_ERROR_n_nonpositive) ; } if (!Ap) { PRINTF (("ERROR: Ap missing\n\n")) ; return (UMFPACK_ERROR_argument_missing) ; } nz = Ap [n] ; PRINTF (("nz = "ID". ", nz)) ; if (nz < 0) { PRINTF (("ERROR: number of entries < 0\n\n")) ; return (UMFPACK_ERROR_invalid_matrix) ; } if (Ap [0] != 0) { PRINTF (("ERROR: Ap ["ID"] = "ID" must be "ID"\n\n", (Int) INDEX (0), INDEX (Ap [0]), (Int) INDEX (0))) ; return (UMFPACK_ERROR_invalid_matrix) ; } if (!Ai) { PRINTF (("ERROR: Ai missing\n\n")) ; return (UMFPACK_ERROR_argument_missing) ; } do_values = Ax != (double *) NULL ; PRINTF4 (("\n")) ; /* ---------------------------------------------------------------------- */ /* check the row/column pointers, Ap */ /* ---------------------------------------------------------------------- */ for (k = 0 ; k < n ; k++) { if (Ap [k] < 0) { PRINTF (("ERROR: Ap ["ID"] < 0\n\n", INDEX (k))) ; return (UMFPACK_ERROR_invalid_matrix) ; } if (Ap [k] > nz) { PRINTF (("ERROR: Ap ["ID"] > size of Ai\n\n", INDEX (k))) ; return (UMFPACK_ERROR_invalid_matrix) ; } } for (k = 0 ; k < n ; k++) { length = Ap [k+1] - Ap [k] ; if (length < 0) { PRINTF (("ERROR: # entries in %s "ID" is < 0\n\n", vector, INDEX (k))) ; return (UMFPACK_ERROR_invalid_matrix) ; } } /* ---------------------------------------------------------------------- */ /* print each vector */ /* ---------------------------------------------------------------------- */ prl1 = prl ; for (k = 0 ; k < n ; k++) { /* if prl is 4, print the first 10 entries of the first 10 vectors */ if (k < 10) { prl = prl1 ; } /* get the vector pointers */ p1 = Ap [k] ; p2 = Ap [k+1] ; length = p2 - p1 ; PRINTF4 (("\n %s "ID": start: "ID" end: "ID" entries: "ID"\n", vector, INDEX (k), p1, p2-1, length)) ; ilast = EMPTY ; for (p = p1 ; p < p2 ; p++) { i = Ai [p] ; PRINTF4 (("\t%s "ID" ", index, INDEX (i))) ; if (do_values && prl >= 4) { PRINTF ((":")) ; ASSIGN (a, Ax, Az, p, split) ; PRINT_ENTRY (a) ; } if (i < 0 || i >= n_i) { PRINTF ((" ERROR: %s index "ID" out of range in %s "ID"\n\n", index, INDEX (i), vector, INDEX (k))) ; return (UMFPACK_ERROR_invalid_matrix) ; } if (i <= ilast) { PRINTF ((" ERROR: %s index "ID" out of order (or duplicate) in " "%s "ID"\n\n", index, INDEX (i), vector, INDEX (k))) ; return (UMFPACK_ERROR_invalid_matrix) ; } PRINTF4 (("\n")) ; /* truncate printout, but continue to check matrix */ if (prl == 4 && (p - p1) == 9 && length > 10) { PRINTF4 (("\t...\n")) ; prl-- ; } ilast = i ; } /* truncate printout, but continue to check matrix */ if (prl == 4 && k == 9 && n > 10) { PRINTF4 (("\n ...\n")) ; prl-- ; } } prl = prl1 ; /* ---------------------------------------------------------------------- */ /* return the status of the matrix */ /* ---------------------------------------------------------------------- */ PRINTF4 ((" %s-form matrix ", vector)) ; PRINTF (("OK\n\n")) ; return (UMFPACK_OK) ; } SuiteSparse/UMFPACK/Source/umfpack_report_perm.c0000644001170100242450000000263710617162125020516 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_report_perm ================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Prints a permutation vector. See umfpack_report_perm.h for details. Dynamic memory usage: Allocates a size max(np,1)*sizeof(Int) workspace via a single call to UMF_malloc and then frees all of it via UMF_free on return. */ #include "umf_internal.h" #include "umf_report_perm.h" #include "umf_malloc.h" #include "umf_free.h" GLOBAL Int UMFPACK_report_perm ( Int np, const Int Perm [ ], const double Control [UMFPACK_CONTROL] ) { Int prl, *W, status ; prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ; if (prl <= 2) { return (UMFPACK_OK) ; } W = (Int *) UMF_malloc (MAX (np,1), sizeof (Int)) ; status = UMF_report_perm (np, Perm, W, prl, 1) ; (void) UMF_free ((void *) W) ; return (status) ; } SuiteSparse/UMFPACK/Source/umf_realloc.c0000644001170100242450000000440510677541004016740 0ustar davisfac/* ========================================================================== */ /* === UMF_realloc ========================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Realloc a block previously allocated by UMF_malloc. Return NULL on failure (in which case the block is still allocated, and will be kept at is present size). This routine is only used for Numeric->Memory. */ #include "umf_internal.h" #include "umf_realloc.h" #if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG) #include "umf_malloc.h" #endif GLOBAL void *UMF_realloc ( void *p, Int n_objects, size_t size_of_object ) { size_t size ; void *p2 ; #ifdef UMF_TCOV_TEST /* For exhaustive statement coverage testing only! */ /* Pretend to fail, to test out-of-memory conditions. */ umf_realloc_fail-- ; if (umf_realloc_fail <= umf_realloc_hi && umf_realloc_fail >= umf_realloc_lo) { return ((void *) NULL) ; } #endif /* make sure that we allocate something */ n_objects = MAX (1, n_objects) ; size = (size_t) n_objects ; ASSERT (size_of_object > 1) ; if (size > Int_MAX / size_of_object) { /* :: int overflow in umf_realloc :: */ return ((void *) NULL) ; } size *= size_of_object ; DEBUG0 (("UMF_realloc: "ID" n_objects "ID" size_of_object "ID"\n", (Int) p, n_objects, (Int) size_of_object)) ; /* see AMD/Source/amd_global.c for the memory allocator selection */ p2 = amd_realloc (p, size) ; #if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG) /* If p didn't exist on input, and p2 exists, then a new object has been * allocated. */ if (p == (void *) NULL && p2 != (void *) NULL) { UMF_malloc_count++ ; } #endif DEBUG0 (("UMF_realloc: "ID" new malloc count "ID"\n", (Int) p2, UMF_malloc_count)) ; return (p2) ; } SuiteSparse/UMFPACK/Source/umf_realloc.h0000644001170100242450000000075710617162216016751 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL void *UMF_realloc ( void *p, Int n_objects, size_t size_of_object ) ; SuiteSparse/UMFPACK/Source/umfpack_free_symbolic.c0000644001170100242450000000365710617162044021005 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_free_symbolic ================================================ */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. See umfpack_free_symbolic.h for details. All 10 objects comprising the Symbolic object are free'd via UMF_free. */ #include "umf_internal.h" #include "umf_free.h" GLOBAL void UMFPACK_free_symbolic ( void **SymbolicHandle ) { SymbolicType *Symbolic ; if (!SymbolicHandle) { return ; } Symbolic = *((SymbolicType **) SymbolicHandle) ; if (!Symbolic) { return ; } (void) UMF_free ((void *) Symbolic->Cperm_init) ; (void) UMF_free ((void *) Symbolic->Rperm_init) ; (void) UMF_free ((void *) Symbolic->Front_npivcol) ; (void) UMF_free ((void *) Symbolic->Front_parent) ; (void) UMF_free ((void *) Symbolic->Front_1strow) ; (void) UMF_free ((void *) Symbolic->Front_leftmostdesc) ; (void) UMF_free ((void *) Symbolic->Chain_start) ; (void) UMF_free ((void *) Symbolic->Chain_maxrows) ; (void) UMF_free ((void *) Symbolic->Chain_maxcols) ; (void) UMF_free ((void *) Symbolic->Cdeg) ; (void) UMF_free ((void *) Symbolic->Rdeg) ; /* only when dense rows are present */ (void) UMF_free ((void *) Symbolic->Esize) ; /* only when diagonal pivoting is prefered */ (void) UMF_free ((void *) Symbolic->Diagonal_map) ; (void) UMF_free ((void *) Symbolic) ; *SymbolicHandle = (void *) NULL ; } SuiteSparse/UMFPACK/Source/umf_mem_alloc_tail_block.c0000644001170100242450000001004410677541740021435 0ustar davisfac/* ========================================================================== */ /* === UMF_mem_alloc_tail_block ============================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* The UMF_mem_* routines manage the Numeric->Memory memory space. */ #include "umf_internal.h" #include "umf_mem_alloc_tail_block.h" /* allocate nunits from tail of Numeric->Memory */ /* (requires nunits+1, for header). */ /* Returns the index into Numeric->Memory if successful, or 0 on failure. */ GLOBAL Int UMF_mem_alloc_tail_block ( NumericType *Numeric, Int nunits ) { Int bigsize, usage ; Unit *p, *pnext, *pbig ; ASSERT (Numeric != (NumericType *) NULL) ; ASSERT (Numeric->Memory != (Unit *) NULL) ; #ifndef NDEBUG if (UMF_allocfail) { /* pretend to fail, to test garbage_collection */ DEBUGm2 (("UMF_mem_alloc_tail_block: pretend to fail\n")) ; UMF_allocfail = FALSE ; /* don't fail the next time */ return (0) ; } DEBUG2 (("UMF_mem_alloc_tail_block, size: "ID" + 1 = "ID": ", nunits, nunits+1)) ; #endif bigsize = 0 ; pbig = (Unit *) NULL ; ASSERT (nunits > 0) ; /* size must be positive */ if (Numeric->ibig != EMPTY) { ASSERT (Numeric->ibig > Numeric->itail) ; ASSERT (Numeric->ibig < Numeric->size) ; pbig = Numeric->Memory + Numeric->ibig ; bigsize = -pbig->header.size ; ASSERT (bigsize > 0) ; /* Numeric->ibig is free */ ASSERT (pbig->header.prevsize >= 0) ; /* prev. is not free */ } if (pbig && bigsize >= nunits) { /* use the biggest block, somewhere in middle of memory */ p = pbig ; pnext = p + 1 + bigsize ; /* next is in range */ ASSERT (pnext < Numeric->Memory + Numeric->size) ; /* prevsize of next = this size */ ASSERT (pnext->header.prevsize == bigsize) ; /* next is not free */ ASSERT (pnext->header.size > 0) ; bigsize -= nunits + 1 ; if (bigsize < 4) { /* internal fragmentation would be too small */ /* allocate the entire free block */ p->header.size = -p->header.size ; DEBUG2 (("GET BLOCK: p: "ID" size: "ID", all of big: "ID" size: " ID"\n", (Int) (p-Numeric->Memory), nunits, Numeric->ibig, p->header.size)) ; /* no more biggest block */ Numeric->ibig = EMPTY ; } else { /* allocate just the first nunits Units of the free block */ p->header.size = nunits ; /* make a new free block */ Numeric->ibig += nunits + 1 ; pbig = Numeric->Memory + Numeric->ibig ; pbig->header.size = -bigsize ; pbig->header.prevsize = nunits ; pnext->header.prevsize = bigsize ; DEBUG2 (("GET BLOCK: p: "ID" size: "ID", some of big: "ID" left: " ID"\n", (Int) (p-Numeric->Memory), nunits, Numeric->ibig, bigsize)) ; } } else { /* allocate from the top of tail */ pnext = Numeric->Memory + Numeric->itail ; DEBUG2 (("GET BLOCK: from tail ")) ; if ((nunits + 1) > (Numeric->itail - Numeric->ihead)) { DEBUG2 (("\n")) ; return (0) ; } Numeric->itail -= (nunits + 1) ; p = Numeric->Memory + Numeric->itail ; p->header.size = nunits ; p->header.prevsize = 0 ; pnext->header.prevsize = nunits ; DEBUG2 (("p: "ID" size: "ID", new tail "ID"\n", (Int) (p-Numeric->Memory), nunits, Numeric->itail)) ; } Numeric->tail_usage += p->header.size + 1 ; usage = Numeric->ihead + Numeric->tail_usage ; Numeric->max_usage = MAX (Numeric->max_usage, usage) ; #ifndef NDEBUG UMF_debug -= 10 ; UMF_dump_memory (Numeric) ; UMF_debug += 10 ; #endif /* p points to the header. Add one to point to the usable block itself. */ /* return the offset into Numeric->Memory */ return ((p - Numeric->Memory) + 1) ; } SuiteSparse/UMFPACK/Source/umf_mem_alloc_tail_block.h0000644001170100242450000000075110617161761021441 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ GLOBAL Int UMF_mem_alloc_tail_block ( NumericType *Numeric, Int nunits ) ; SuiteSparse/UMFPACK/Source/umf_dump.c0000644001170100242450000007743110617161534016275 0ustar davisfac/* ========================================================================== */ /* === UMF_dump ============================================================= */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* These routines, and external variables, are used only when debugging. */ /* If debugging is disabled (for normal operation) then this entire file */ /* becomes empty */ #include "umf_internal.h" #ifndef NDEBUG /* These global debugging variables and arrays do not exist if debugging */ /* is disabled at compile time (which is the default). */ GLOBAL Int UMF_debug = -999 ; GLOBAL Int UMF_allocfail = FALSE ; GLOBAL double UMF_gprob = -1.0 ; /* static debugging arrays used only in UMF_dump_rowcol */ PRIVATE Int UMF_DBflag = 0 ; PRIVATE Int UMF_DBpacked [UMF_DBMAX+1] ; PRIVATE Int UMF_DBscatter [UMF_DBMAX+1] ; /* ========================================================================== */ /* === UMF_DBinit =========================================================== */ /* ========================================================================== */ /* clear the debugging arrays */ PRIVATE void UMF_DBinit ( void ) { Int i ; /* Int_MAX is defined in umfpack.h */ if (UMF_DBflag < 1 || UMF_DBflag == Int_MAX) { /* clear the debugging arrays */ UMF_DBflag = 0 ; for (i = 0 ; i <= UMF_DBMAX ; i++) { UMF_DBscatter [i] = 0 ; UMF_DBpacked [i] = 0 ; } } UMF_DBflag++ ; /* UMF_DBflag > UMF_DBscatter [0...UMF_DBmax] is now true */ } /* ========================================================================== */ /* === UMF_dump_dense ======================================================= */ /* ========================================================================== */ GLOBAL void UMF_dump_dense ( Entry *C, Int dim, Int m, Int n ) { /* dump C [1..m,1..n], with column dimenstion dim */ Int i, j; if (UMF_debug < 7) return ; if (C == (Entry *) NULL) { DEBUG7 (("No dense matrix allocated\n")) ; return ; } DEBUG8 ((" dimension= "ID" rows= "ID" cols= "ID"\n", dim, m, n)) ; for (i = 0 ; i < m ; i++) { DEBUG9 ((ID": ", i)) ; for (j = 0 ; j < n ; j++) { EDEBUG9 (C [i+j*dim]) ; if (j % 6 == 5) DEBUG9 (("\n ")) ; } DEBUG9 (("\n")) ; } for (i = 0 ; i < m ; i++) { for (j = 0 ; j < n ; j++) { if (IS_ZERO (C [i+j*dim])) { DEBUG8 ((".")) ; } else { DEBUG8 (("X")) ; } } DEBUG8 (("\n")) ; } } /* ========================================================================== */ /* === UMF_dump_element ===================================================== */ /* ========================================================================== */ GLOBAL void UMF_dump_element ( NumericType *Numeric, WorkType *Work, Int e, Int clean ) { Int i, j, k, *Rows, *Cols, nrows, ncols, *E, row, col, *Row_degree, *Col_degree ; Entry *C ; Element *ep ; Unit *p ; if (UMF_debug < 7) return ; if (e == 0) { UMF_dump_current_front (Numeric, Work, FALSE) ; return ; } DEBUG7 (("\n====================ELEMENT: "ID" ", e)) ; if (!Numeric || !Work || !Numeric->Memory) { DEBUG7 ((" No Numeric, Work\n")) ; return ; } DEBUG7 ((" nel: "ID" of "ID, e, Work->nel)) ; E = Work->E ; if (!E) { DEBUG7 ((" No elements\n")) ; return ; } if (e < 0 || e > Work->nel) { DEBUG7 (("e out of range!\n")) ; return ; } if (!E [e]) { DEBUG7 ((" deallocated\n")) ; return ; } DEBUG7 (("\n")) ; Col_degree = Numeric->Cperm ; Row_degree = Numeric->Rperm ; p = Numeric->Memory + E [e] ; DEBUG7 (("ep "ID"\n", (Int) (p-Numeric->Memory))) ; GET_ELEMENT (ep, p, Cols, Rows, ncols, nrows, C) ; DEBUG7 (("nrows "ID" nrowsleft "ID"\n", nrows, ep->nrowsleft)) ; DEBUG7 (("ncols "ID" ncolsleft "ID"\n", ncols, ep->ncolsleft)) ; DEBUG7 (("cdeg-cdeg0 "ID" rdeg-rdeg0 "ID" next "ID"\n", ep->cdeg - Work->cdeg0, ep->rdeg - Work->rdeg0, ep->next)) ; DEBUG8 (("rows: ")) ; k = 0 ; for (i = 0 ; i < ep->nrows ; i++) { row = Rows [i] ; if (row >= 0) { DEBUG8 ((" "ID, row)) ; ASSERT (row < Work->n_row) ; if ((k++ % 10) == 9) DEBUG8 (("\n")) ; ASSERT (IMPLIES (clean, NON_PIVOTAL_ROW (row))) ; } } DEBUG8 (("\ncols: ")) ; k = 0 ; for (j = 0 ; j < ep->ncols ; j++) { col = Cols [j] ; if (col >= 0) { DEBUG8 ((" "ID, col)) ; ASSERT (col < Work->n_col) ; if ((k++ % 10) == 9) DEBUG8 (("\n")) ; ASSERT (IMPLIES (clean, NON_PIVOTAL_COL (col))) ; } } DEBUG8 (("\nvalues:\n")) ; if (UMF_debug >= 9) { for (i = 0 ; i < ep->nrows ; i++) { row = Rows [i] ; if (row >= 0) { DEBUG9 ((ID": ", row)) ; k = 0 ; for (j = 0 ; j < ep->ncols ; j++) { col = Cols [j] ; if (col >= 0) { EDEBUG9 (C [i+j*ep->nrows]) ; if (k++ % 6 == 5) DEBUG9 (("\n ")) ; } } DEBUG9 (("\n")) ; } } } DEBUG7 (("====================\n")) ; } /* ========================================================================== */ /* === UMF_dump_rowcol ====================================================== */ /* ========================================================================== */ /* dump a row or a column, from one or more memory spaces */ /* return exact degree */ GLOBAL void UMF_dump_rowcol ( Int dumpwhich, /* 0 for row, 1 for column */ NumericType *Numeric, WorkType *Work, Int dumpindex, /* row or column index to dump */ Int check_degree /* true if degree is to be checked */ ) { Entry value ; Entry *C ; Int f, nrows, j, jj, len, e, deg, index, n_row, n_col, *Cols, *Rows, nn, dumpdeg, ncols, preve, *E, tpi, *Pattern, approx_deg, not_in_use ; Tuple *tp, *tend ; Element *ep ; Int *Row_tuples, *Row_degree, *Row_tlen ; Int *Col_tuples, *Col_degree, *Col_tlen ; Unit *p ; Int is_there ; /* clear the debugging arrays */ UMF_DBinit () ; if (dumpwhich == 0) { DEBUG7 (("\n====================ROW: "ID, dumpindex)) ; } else { DEBUG7 (("\n====================COL: "ID, dumpindex)) ; } if (dumpindex == EMPTY) { DEBUG7 ((" (EMPTY)\n")) ; return ; } deg = 0 ; approx_deg = 0 ; if (!Numeric || !Work) { DEBUG7 ((" No Numeric, Work\n")) ; return ; } n_row = Work->n_row ; n_col = Work->n_col ; nn = MAX (n_row, n_col) ; E = Work->E ; Col_degree = Numeric->Cperm ; Row_degree = Numeric->Rperm ; Row_tuples = Numeric->Uip ; Row_tlen = Numeric->Uilen ; Col_tuples = Numeric->Lip ; Col_tlen = Numeric->Lilen ; if (!E || !Row_tuples || !Row_degree || !Row_tlen || !Col_tuples || !Col_degree || !Col_tlen) { DEBUG7 ((" No E, Rows, Cols\n")) ; return ; } if (dumpwhich == 0) { /* dump a row */ ASSERT (dumpindex >= 0 && dumpindex < n_row) ; if (!NON_PIVOTAL_ROW (dumpindex)) { DEBUG7 ((" Pivotal\n")) ; return ; } len = Row_tlen [dumpindex] ; dumpdeg = Row_degree [dumpindex] ; tpi = Row_tuples [dumpindex] ; } else { /* dump a column */ ASSERT (dumpindex >= 0 && dumpindex < n_col) ; if (!NON_PIVOTAL_COL (dumpindex)) { DEBUG7 ((" Pivotal\n")) ; return ; } len = Col_tlen [dumpindex] ; dumpdeg = Col_degree [dumpindex] ; tpi = Col_tuples [dumpindex] ; } p = Numeric->Memory + tpi ; tp = (Tuple *) p ; if (!tpi) { DEBUG7 ((" Nonpivotal, No tuple list tuples "ID" tlen "ID"\n", tpi, len)) ; return ; } ASSERT (p >= Numeric->Memory + Numeric->itail) ; ASSERT (p < Numeric->Memory + Numeric->size) ; DEBUG7 ((" degree: "ID" len: "ID"\n", dumpdeg, len)) ; not_in_use = (p-1)->header.size - UNITS (Tuple, len) ; DEBUG7 ((" Tuple list: p+1: "ID" size: "ID" units, "ID" not in use\n", (Int) (p-Numeric->Memory), (p-1)->header.size, not_in_use)) ; ASSERT (not_in_use >= 0) ; tend = tp + len ; preve = 0 ; for ( ; tp < tend ; tp++) { /* row/col of element e, offset is f: */ /* DEBUG8 ((" (tp="ID")\n", tp)) ; */ e = tp->e ; f = tp->f ; DEBUG8 ((" (e="ID", f="ID")\n", e, f)) ; ASSERT (e > 0 && e <= Work->nel) ; /* dump the pattern and values */ if (E [e]) { p = Numeric->Memory + E [e] ; GET_ELEMENT (ep, p, Cols, Rows, ncols, nrows, C) ; if (dumpwhich == 0) { Pattern = Cols ; jj = ep->ncols ; is_there = Rows [f] >= 0 ; if (is_there) approx_deg += ep->ncolsleft ; } else { Pattern = Rows ; jj = ep->nrows ; is_there = Cols [f] >= 0 ; if (is_there) approx_deg += ep->nrowsleft ; } if (!is_there) { DEBUG8 (("\t\tnot present\n")) ; } else { for (j = 0 ; j < jj ; j++) { index = Pattern [j] ; value = C [ (dumpwhich == 0) ? (f+nrows*j) : (j+nrows*f) ] ; if (index >= 0) { DEBUG8 (("\t\t"ID":", index)) ; EDEBUG8 (value) ; DEBUG8 (("\n")) ; if (dumpwhich == 0) { /* col must be in the range 0..n_col-1 */ ASSERT (index < n_col) ; } else { /* row must be in the range 0..n_row-1 */ ASSERT (index < n_row) ; } if (nn <= UMF_DBMAX) { if (UMF_DBscatter [index] != UMF_DBflag) { UMF_DBpacked [deg++] = index ; UMF_DBscatter [index] = UMF_DBflag ; } } } } } /* the (e,f) tuples should be in order of their creation */ /* this means that garbage collection will not jumble them */ ASSERT (preve < e) ; preve = e ; } else { DEBUG8 (("\t\tdeallocated\n")) ; } } if (nn <= UMF_DBMAX) { if (deg > 0) { DEBUG7 ((" Assembled, actual deg: "ID" : ", deg)) ; for (j = 0 ; j < deg ; j++) { index = UMF_DBpacked [j] ; DEBUG8 ((ID" ", index)) ; if (j % 20 == 19) DEBUG8 (("\n ")) ; ASSERT (UMF_DBscatter [index] == UMF_DBflag) ; } DEBUG7 (("\n")) ; } } /* Col_degree is not maintained when fixQ is true */ if (check_degree) { DEBUG8 ((" approx_deg "ID" dumpdeg "ID"\n", approx_deg, dumpdeg)) ; ASSERT (approx_deg == dumpdeg) ; } DEBUG7 (("====================\n")) ; /* deg is now the exact degree */ /* if nn <= UMF_DBMAX, then UMF_DBscatter [i] == UMF_DBflag for every i */ /* in the row or col, and != UMF_DBflag if not */ return ; } /* ========================================================================== */ /* === UMF_dump_matrix ====================================================== */ /* ========================================================================== */ GLOBAL void UMF_dump_matrix ( NumericType *Numeric, WorkType *Work, Int check_degree ) { Int e, row, col, intfrag, frag, n_row, n_col, *E, fullsize, actualsize ; Element *ep ; Unit *p ; DEBUG6 (("=================================================== MATRIX:\n")) ; if (!Numeric || !Work) { DEBUG6 (("No Numeric or Work allocated\n")) ; return ; } if (!Numeric->Memory) { DEBUG6 (("No Numeric->Memory\n")) ; return ; } n_row = Work->n_row ; n_col = Work->n_col ; DEBUG6 (("n_row "ID" n_col "ID" nz "ID"\n", n_row, n_col, Work->nz)) ; DEBUG6 (("============================ ELEMENTS: "ID" \n", Work->nel)) ; intfrag = 0 ; E = Work->E ; if (!E) { DEBUG6 (("No elements allocated\n")) ; } else { for (e = 0 ; e <= Work->nel ; e++) { UMF_dump_element (Numeric, Work, e, FALSE) ; if (e > 0 && E [e]) { p = Numeric->Memory + E [e] ; ep = (Element *) p ; ASSERT (ep->nrowsleft > 0 || ep->ncolsleft > 0) ; fullsize = GET_BLOCK_SIZE (p) ; actualsize = GET_ELEMENT_SIZE (ep->nrowsleft,ep->ncolsleft); frag = fullsize - actualsize ; intfrag += frag ; DEBUG7 (("dump el: "ID", full "ID" actual "ID" frag: "ID " intfrag: "ID"\n", e, fullsize, actualsize, frag, intfrag)) ; } } } DEBUG6 (("CURRENT INTERNAL FRAG in elements: "ID" \n", intfrag)) ; DEBUG6 (("======================================== ROWS: "ID"\n", n_row)) ; UMF_debug -= 2 ; for (row = 0 ; row < n_row ; row++) { UMF_dump_rowcol (0, Numeric, Work, row, check_degree) ; } UMF_debug += 2 ; DEBUG6 (("======================================== COLS: "ID"\n", n_col)) ; UMF_debug -= 2 ; for (col = 0 ; col < n_col ; col++) { UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ; } UMF_debug += 2 ; DEBUG6 (("============================================= END OF MATRIX:\n")); } /* ========================================================================== */ /* === UMF_dump_current_front =============================================== */ /* ========================================================================== */ GLOBAL void UMF_dump_current_front ( NumericType *Numeric, WorkType *Work, Int check ) { Entry *Flublock, *Flblock, *Fublock, *Fcblock ; Int fnrows_max, fncols_max, fnrows, fncols, fnpiv, *Frows, *Fcols, i, j, *Fcpos, *Frpos, fnr_curr, fnc_curr, *E ; if (!Work) return ; DEBUG7 (("\n\n========CURRENT FRONTAL MATRIX:\n")) ; Flublock = Work->Flublock ; Flblock = Work->Flblock ; Fublock = Work->Fublock ; Fcblock = Work->Fcblock ; Frows = Work->Frows ; Fcols = Work->Fcols ; Frpos = Work->Frpos ; Fcpos = Work->Fcpos ; fnrows_max = Work->fnrows_max ; fncols_max = Work->fncols_max ; fnr_curr = Work->fnr_curr ; fnc_curr = Work->fnc_curr ; fnrows = Work->fnrows ; fncols = Work->fncols ; fnpiv = Work->fnpiv ; E = Work->E ; DEBUG6 (("=== fnpiv= "ID"\n", fnpiv)) ; DEBUG6 (("fnrows_max fncols_max "ID" "ID"\n",fnrows_max, fncols_max)) ; DEBUG6 (("fnr_curr fnc_curr "ID" "ID"\n",fnr_curr, fnc_curr)) ; DEBUG6 (("fnrows fncols "ID" "ID"\n",fnrows, fncols)) ; ASSERT ((fnr_curr % 2 == 1) || fnr_curr == 0) ; DEBUG6 (("Pivot row pattern:\n")) ; for (j = 0 ; j < fncols ; j++) { DEBUG7 ((ID" "ID" "ID" %d\n", j, Fcols [j], Fcpos [Fcols [j]], j < fncols)) ; if (check) { ASSERT (Fcols [j] >= 0 && Fcols [j] < Work->n_col) ; ASSERT (Fcpos [Fcols [j]] == j * fnr_curr) ; } } DEBUG6 (("Pivot col pattern:\n")) ; for (i = 0 ; i < fnrows ; i++) { DEBUG7 ((ID" "ID" "ID" %d\n", i, Frows [i], Frpos [Frows [i]], i < fnrows)) ; if (check) { ASSERT (Frows [i] >= 0 && Frows [i] < Work->n_row) ; ASSERT (Frpos [Frows [i]] == i) ; } } if (UMF_debug < 7) return ; if (!E [0]) { DEBUG6 (("current front not allocated\n")) ; ASSERT (!Work->Flublock) ; return ; } ASSERT (Work->Flublock == (Entry *) (Numeric->Memory + E [0])) ; DEBUG7 (("C block: ")) ; UMF_dump_dense (Fcblock, fnr_curr, fnrows, fncols) ; DEBUG7 (("L block: ")) ; UMF_dump_dense (Flblock, fnr_curr, fnrows, fnpiv) ; DEBUG7 (("U' block: ")) ; UMF_dump_dense (Fublock, fnc_curr, fncols, fnpiv) ; DEBUG7 (("LU block: ")) ; UMF_dump_dense (Flublock, Work->nb, fnpiv, fnpiv) ; if (fnpiv > 0) { DEBUG7 (("Pivot entry: ")) ; EDEBUG7 (Flublock [(fnpiv-1)+(fnpiv-1)*Work->nb]) ; DEBUG7 (("\n")) ; } } /* ========================================================================== */ /* === UMF_dump_lu ========================================================== */ /* ========================================================================== */ GLOBAL void UMF_dump_lu ( NumericType *Numeric ) { Int i, n_row, n_col, *Cperm, *Rperm ; DEBUG6 (("=============================================== LU factors:\n")) ; if (!Numeric) { DEBUG6 (("No LU factors allocated\n")) ; return ; } n_row = Numeric->n_row ; n_col = Numeric->n_col ; DEBUG6 (("n_row: "ID" n_col: "ID"\n", n_row, n_col)) ; DEBUG6 (("nLentries: "ID" nUentries: "ID"\n", Numeric->nLentries, Numeric->nUentries)) ; if (Numeric->Cperm) { Cperm = Numeric->Cperm ; DEBUG7 (("Column permutations: (new: old)\n")) ; for (i = 0 ; i < n_col ; i++) { if (Cperm [i] != EMPTY) { DEBUG7 ((ID": "ID"\n", i, Cperm [i])) ; } } } else { DEBUG7 (("No Numeric->Cperm allocatated\n")) ; } if (Numeric->Rperm) { Rperm = Numeric->Rperm ; DEBUG7 (("row permutations: (new: old)\n")) ; for (i = 0 ; i < n_row ; i++) { if (Rperm [i] != EMPTY) { DEBUG7 ((ID": "ID"\n", i, Rperm [i])) ; } } } else { DEBUG7 (("No Numeric->Rperm allocatated\n")) ; } DEBUG6 (("========================================= END OF LU factors:\n")); } /* ========================================================================== */ /* === UMF_dump_memory ====================================================== */ /* ========================================================================== */ GLOBAL void UMF_dump_memory ( NumericType *Numeric ) { Unit *p ; Int prevsize, s ; Int found ; if (!Numeric) { DEBUG6 (("No memory space S allocated\n")) ; return ; } DEBUG6 (("\n ============================================== MEMORY:\n")) ; if (!Numeric || !Numeric->Memory) { DEBUG6 (("No memory space Numeric allocated\n")) ; return ; } DEBUG6 (("S: "ID"\n", (Int) Numeric)) ; DEBUG6 (("S->ihead : "ID"\n", Numeric->ihead)) ; DEBUG6 (("S->itail : "ID"\n", Numeric->itail)) ; DEBUG6 (("S->size : "ID"\n", Numeric->size)) ; DEBUG6 (("S->ngarbage : "ID"\n", Numeric->ngarbage)) ; DEBUG6 (("S->nrealloc : "ID"\n", Numeric->nrealloc)) ; DEBUG6 ((" in use at head : "ID"\n", Numeric->ihead)) ; DEBUG6 ((" free space : "ID"\n", Numeric->itail - Numeric->ihead)) ; DEBUG6 ((" blocks in use at tail : "ID"\n", Numeric->size - Numeric->itail)) ; DEBUG6 ((" total in use : "ID"\n", Numeric->size - (Numeric->itail - Numeric->ihead))) ; prevsize = 0 ; found = FALSE ; ASSERT (0 <= Numeric->ihead) ; ASSERT (Numeric->ihead <= Numeric->itail) ; ASSERT (Numeric->itail <= Numeric->size) ; p = Numeric->Memory + Numeric->itail ; while (p < Numeric->Memory + Numeric->size) { DEBUG8 (("p: "ID" p+1: "ID" prevsize: "ID" size: "ID, (Int) (p-Numeric->Memory), (Int) (p+1-Numeric->Memory), p->header.prevsize, p->header.size)) ; if (p->header.size < 0) { DEBUG8 ((" free")) ; } if (p == Numeric->Memory + Numeric->itail) { ASSERT (p->header.prevsize == 0) ; } else { ASSERT (p->header.prevsize > 0) ; } ASSERT (p->header.size != 0) ; s = prevsize >= 0 ? prevsize : -prevsize ; ASSERT (p->header.prevsize == s) ; /* no adjacent free blocks */ ASSERT (p->header.size > 0 || prevsize > 0) ; if (Numeric->ibig != EMPTY) { if (p == Numeric->Memory + Numeric->ibig) { ASSERT (p->header.size < 0) ; DEBUG8 ((" <===== Numeric->ibig")) ; found = TRUE ; } } s = p->header.size ; prevsize = s ; s = s >= 0 ? s : -s ; p = p + 1 + s ; DEBUG8 (("\n")) ; } ASSERT (p == Numeric->Memory + Numeric->size) ; ASSERT (IMPLIES (Numeric->ibig != EMPTY, found)) ; DEBUG6 (("============================================= END OF MEMORY:\n")); } /* ========================================================================== */ /* === UMF_dump_packed_memory =============================================== */ /* ========================================================================== */ GLOBAL void UMF_dump_packed_memory ( NumericType *Numeric, WorkType *Work ) { Unit *p, *p3 ; Int prevsize, col, row, *Rows, *Cols, ncols, nrows, k, esize, *Row_tuples, *Row_degree, *Col_tuples, *Col_degree ; Entry *C ; Element *ep ; Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro */ Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro */ Row_tuples = Numeric->Uip ; Col_tuples = Numeric->Lip ; DEBUG6 (("============================================ PACKED MEMORY:\n")) ; if (!Numeric || !Numeric->Memory) { DEBUG6 (("No memory space S allocated\n")) ; return ; } DEBUG6 (("S: "ID"\n", (Int) Numeric)) ; DEBUG6 (("S->ihead : "ID"\n", Numeric->ihead)) ; DEBUG6 (("S->itail : "ID"\n", Numeric->itail)) ; DEBUG6 (("S->size : "ID"\n", Numeric->size)) ; DEBUG6 (("S->ngarbage : "ID"\n", Numeric->ngarbage)) ; DEBUG6 (("S->nrealloc : "ID"\n", Numeric->nrealloc)) ; DEBUG6 ((" in use at head : "ID"\n", Numeric->ihead)) ; DEBUG6 ((" free space : "ID"\n", Numeric->itail - Numeric->ihead)) ; DEBUG6 ((" blocks in use at tail : "ID"\n", Numeric->size - Numeric->itail)) ; DEBUG6 ((" total in use : "ID"\n", Numeric->size - (Numeric->itail - Numeric->ihead))) ; ASSERT (0 <= Numeric->ihead) ; ASSERT (Numeric->ihead <= Numeric->itail) ; ASSERT (Numeric->itail <= Numeric->size) ; for (row = 0 ; row < Work->n_row ; row++) { ASSERT (IMPLIES (NON_PIVOTAL_ROW (row), !Row_tuples [row])) ; } for (col = 0 ; col < Work->n_col ; col++) { ASSERT (IMPLIES (NON_PIVOTAL_COL (col), !Col_tuples [col])) ; } prevsize = 0 ; p = Numeric->Memory + Numeric->itail ; while (p < Numeric->Memory + Numeric->size) { DEBUG9 (("====================\n")) ; DEBUG7 (("p: "ID" p+1: "ID" prevsize: "ID" size: "ID"\n", (Int) (p-Numeric->Memory), (Int) (p+1-Numeric->Memory), p->header.prevsize, p->header.size)) ; ASSERT (p->header.size > 0) ; if (p == Numeric->Memory + Numeric->itail) { ASSERT (p->header.prevsize == 0) ; } else { ASSERT (p->header.prevsize > 0) ; } ASSERT (p->header.prevsize == prevsize) ; prevsize = p->header.size ; if (p != Numeric->Memory + Numeric->size - 2) { p3 = p + 1 ; if (p3 == Numeric->Memory + Work->E [0]) { /* this is the current frontal matrix */ UMF_dump_current_front (Numeric, Work, FALSE) ; } else { /* this is a packed element */ GET_ELEMENT (ep, p3, Cols, Rows, ncols, nrows, C) ; DEBUG9 (("ep "ID"\n nrows "ID" ncols "ID"\n", (Int) ((p+1)-Numeric->Memory), ep->nrows, ep->ncols)) ; DEBUG9 (("rows:")) ; for (k = 0 ; k < ep->nrows; k++) { row = Rows [k] ; DEBUG9 ((" "ID, row)) ; ASSERT (row >= 0 && row <= Work->n_row) ; if ((k % 10) == 9) DEBUG9 (("\n")) ; } DEBUG9 (("\ncols:")) ; for (k = 0 ; k < ep->ncols; k++) { col = Cols [k] ; DEBUG9 ((" "ID, col)) ; ASSERT (col >= 0 && col <= Work->n_col) ; if ((k % 10) == 9) DEBUG9 (("\n")) ; } DEBUG9 (("\nvalues: ")) ; if (UMF_debug >= 9) { UMF_dump_dense (C, ep->nrows, ep->nrows, ep->ncols) ; } esize = GET_ELEMENT_SIZE (ep->nrows, ep->ncols) ; DEBUG9 (("esize: "ID"\n", esize)) ; ASSERT (esize <= p->header.size) ; } } else { /* this is the final marker block */ ASSERT (p->header.size == 1) ; } p = p + 1 + p->header.size ; } ASSERT (Numeric->ibig == EMPTY) ; ASSERT (p == Numeric->Memory + Numeric->size) ; DEBUG6 (("======================================END OF PACKED MEMORY:\n")) ; } /* ========================================================================== */ /* === UMF_dump_col_matrix ================================================== */ /* ========================================================================== */ /* This code is the same for real or complex matrices. */ GLOBAL void UMF_dump_col_matrix ( const double Ax [ ], /* Ax [0..nz-1]: real values, in column order */ #ifdef COMPLEX const double Az [ ], /* Az [0..nz-1]: imag values, in column order */ #endif const Int Ai [ ], /* Ai [0..nz-1]: row indices, in column order */ const Int Ap [ ], /* Ap [0..n_col]: column pointers */ Int n_row, /* number of rows of A */ Int n_col, /* number of columns of A */ Int nz /* number of entries */ ) { Int col, p, p1, p2, row ; #ifdef COMPLEX Int split = SPLIT (Az) ; #endif if (!Ai || !Ap) return ; DEBUG6 (("============================================ COLUMN FORM:\n")) ; ASSERT (n_col >= 0) ; nz = Ap [n_col] ; DEBUG2 (("UMF_dump_col: nz "ID"\n", nz)) ; DEBUG2 (("n_row "ID" \n", n_row)) ; DEBUG2 (("n_col "ID" \n", n_col)) ; DEBUG6 ((" n_row = "ID", n_col ="ID" nz = "ID" Ap [0] "ID", Ap [n] "ID"\n", n_row, n_col, nz, Ap [0], Ap [n_col])) ; ASSERT (Ap [0] == 0) ; ASSERT (Ap [n_col] == nz) ; for (col = 0 ; col < n_col ; col++) { p1 = Ap [col] ; p2 = Ap [col+1] ; DEBUG6 (("col: "ID", length "ID"\n", col, p2 - p1)) ; ASSERT (p2 >= p1) ; for (p = p1 ; p < p2 ; p++) { row = Ai [p] ; ASSERT (row >= 0 && row < n_row) ; DEBUG6 (("\t"ID" ", row)) ; if (Ax != (double *) NULL) { #ifdef COMPLEX if (split) { DEBUG6 ((" (%e+%ei) ", Ax [p], Az [p])) ; } else { DEBUG6 ((" (%e+%ei) ", Ax [2*p], Ax [2*p+1])) ; } #else DEBUG6 ((" %e", Ax [p])) ; #endif } DEBUG6 (("\n")) ; } } DEBUG6 (("========================================== COLUMN FORM done\n")) ; } /* ========================================================================== */ /* === UMF_dump_chain ======================================================= */ /* ========================================================================== */ GLOBAL void UMF_dump_chain ( Int frontid, Int Front_parent [ ], Int Front_npivcol [ ], Int Front_nrows [ ], Int Front_ncols [ ], Int nfr ) { Int i, len = 0 ; /* print a list of contiguous parents */ i = frontid ; ASSERT (Front_parent [i] == EMPTY || (Front_parent [i] > i && Front_parent [i] < nfr)) ; len++ ; DEBUG3 (("Chain:\n "ID" ["ID","ID"]("ID"-by-"ID")\n", i, Front_npivcol [i], MIN (Front_npivcol [i], Front_nrows [i]), Front_nrows [i], Front_ncols [i])) ; for (i = frontid ; i < nfr ; i++) { ASSERT (Front_parent [i] == EMPTY || (Front_parent [i] > i && Front_parent [i] < nfr)) ; if (Front_parent [i] == i+1) { len++ ; DEBUG3 (("\t"ID" ["ID","ID"]("ID"-by-"ID")\n", i+1, Front_npivcol [i+1], MIN (Front_npivcol [i+1], Front_nrows [i+1]), Front_nrows [i+1], Front_ncols [i+1])) ; } else { DEBUG2 (("Length of chain: "ID"\n", len)) ; return ; } } } /* ========================================================================== */ /* === UMF_dump_start ======================================================= */ /* ========================================================================== */ GLOBAL void UMF_dump_start ( void ) { FILE *ff ; AMD_debug_init ("from umfpack") ; /* get the debug print level from the "debug.umf" file, if it exists */ UMF_debug = -999 ; ff = fopen ("debug.umf", "r") ; if (ff) { (void) fscanf (ff, ID, &UMF_debug) ; (void) fclose (ff) ; } DEBUG0 (("umfpack: debug version (SLOW!) ")) ; DEBUG0 ((" MATLAB: ")) ; #ifdef MATLAB_MEX_FILE DEBUG0 (("mexFunction.\n")) ; #else #ifdef MATHWORKS DEBUG0 (("yes.\n")) ; #else DEBUG0 (("no.\n")) ; #endif #endif UMF_gprob = -1.0 ; ff = fopen ("gprob.umf", "r") ; if (ff) { (void) fscanf (ff, "%lg", &UMF_gprob) ; (void) fclose (ff) ; srand (1) ; /* restart the random number generator */ } if (UMF_gprob > 1.0) UMF_gprob = 1.0 ; DEBUG1 (("factor: UMF_gprob: %e UMF_debug "ID"\n", UMF_gprob, UMF_debug)) ; DEBUG2 (("sizeof: (bytes / int / Units) \n")) ; DEBUG2 (("sizeof (Int) %u %u %u\n", sizeof (Int), sizeof (Int) / sizeof (int), UNITS (Int, 1) )) ; DEBUG2 (("sizeof (int) %u %u %u\n", sizeof (int), sizeof (int) / sizeof (int), UNITS (int, 1) )) ; DEBUG2 (("sizeof (size_t) %u %u %u\n", sizeof (size_t), sizeof (size_t) / sizeof (size_t), UNITS (size_t, 1) )) ; DEBUG2 (("sizeof (UF_long) %u %u %u\n", sizeof (UF_long), sizeof (UF_long) / sizeof (UF_long), UNITS (UF_long, 1))); DEBUG2 (("sizeof (double) %u %u %u\n", sizeof (double), sizeof (double) / sizeof (int), UNITS (double, 1) )) ; DEBUG2 (("sizeof (Unit) %u %u %u\n", sizeof (Unit), sizeof (Unit) / sizeof (int), UNITS (Unit, 1) )) ; DEBUG2 (("sizeof (Entry) %u %u %u\n", sizeof (Entry), sizeof (Entry) / sizeof (int), UNITS (Entry, 1) )) ; DEBUG2 (("sizeof (Tuple) %u %u %u\n", sizeof (Tuple), sizeof (Tuple) / sizeof (int), UNITS (Tuple, 1) )) ; DEBUG2 (("sizeof (Tuple *) %u %u %u\n", sizeof (Tuple *), sizeof (Tuple *) / sizeof (int), UNITS (Tuple *, 1) )) ; DEBUG2 (("sizeof (Element) %u %u %u\n", sizeof (Element), sizeof (Element) / sizeof (int), UNITS (Element, 1) )) ; DEBUG2 (("sizeof (Element *) %u %u %u\n", sizeof (Element *), sizeof (Element *) / sizeof (int), UNITS (Element *, 1) )) ; DEBUG2 (("sizeof (WorkType) %u %u %u\n", sizeof (WorkType), sizeof (WorkType) / sizeof (int), UNITS (WorkType, 1) )) ; DEBUG2 (("sizeof (NumericType) %u %u %u\n", sizeof (NumericType), sizeof (NumericType) / sizeof (int), UNITS (NumericType, 1) )) ; DEBUG2 (("sizeof (SymbolicType) %u %u %u\n", sizeof (SymbolicType), sizeof (SymbolicType) / sizeof (int), UNITS (SymbolicType, 1) )) ; } /* ========================================================================== */ /* === UMF_dump_rowmerge ==================================================== */ /* ========================================================================== */ GLOBAL void UMF_dump_rowmerge ( NumericType *Numeric, SymbolicType *Symbolic, WorkType *Work ) { Int *Front_leftmostdesc, *Front_1strow, *Front_new1strow, row1, row2, fleftmost, nfr, n_row, *Row_degree, i, frontid, row ; nfr = Symbolic->nfr ; DEBUG3 (("\n================== Row merge sets: nfr "ID"\n", nfr)) ; Front_leftmostdesc = Symbolic->Front_leftmostdesc ; Front_1strow = Symbolic->Front_1strow ; Front_new1strow = Work->Front_new1strow ; n_row = Symbolic->n_row ; Row_degree = Numeric->Rperm ; frontid = Work->frontid ; for (i = frontid ; i <= nfr ; i++) { DEBUG3 (("----------------------\n")) ; if (i == nfr) DEBUG3 (("Dummy: ")) ; DEBUG3 (("Front "ID" 1strow "ID" new1strow "ID" leftmostdesc "ID, i, Front_1strow [i], Front_new1strow [i], Front_leftmostdesc [i])) ; DEBUG3 ((" parent "ID" pivcol "ID"\n", Symbolic->Front_parent [i], Symbolic->Front_npivcol [i])) ; if (i == nfr) { fleftmost = -1 ; row1 = Front_new1strow [i] ; row2 = n_row-1 ; } else { fleftmost = Front_leftmostdesc [i] ; row1 = Front_new1strow [fleftmost] ; row2 = Front_1strow [i+1] - 1 ; } DEBUG3 (("Leftmost: "ID" Rows ["ID" to "ID"], search ["ID" to "ID"]\n", fleftmost, Front_1strow [i], row2, row1, row2)) ; for (row = row1 ; row <= row2 ; row++) { ASSERT (row >= 0 && row < n_row) ; DEBUG3 ((" Row "ID" live: %d\n", row, NON_PIVOTAL_ROW (row))) ; } } } /* ========================================================================== */ /* === UMF_dump_diagonal_map ================================================ */ /* ========================================================================== */ GLOBAL void UMF_dump_diagonal_map ( Int Diagonal_map [ ], Int Diagonal_imap [ ], Int n1, Int nn, Int nempty ) { Int row, col ; if (Diagonal_map != (Int *) NULL) { DEBUG2 (("\nDump the Diagonal_map: n1 "ID" nn "ID" nempty "ID"\n", n1, nn, nempty)) ; for (col = n1 ; col < nn - nempty ; col++) { row = Diagonal_map [col] ; DEBUG2 ((" Diagonal_map [col = "ID"] gives "ID": ", col, row)) ; row = UNFLIP (row) ; DEBUG2 ((" row "ID"\n", row)) ; ASSERT (Diagonal_imap [row] == col) ; } } } #endif /* NDEBUG */ SuiteSparse/UMFPACK/Source/umf_dump.h0000644001170100242450000000765310617161540016276 0ustar davisfac/* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* umf_dump.h: debugging definitions. */ #ifndef NDEBUG GLOBAL void UMF_dump_dense ( Entry *C, Int dim, Int m, Int n ) ; GLOBAL void UMF_dump_element ( NumericType *Numeric, WorkType *Work, Int e, Int clean ) ; GLOBAL void UMF_dump_rowcol ( Int dump_which, NumericType *Numeric, WorkType *Work, Int dump_index, Int check_degree ) ; GLOBAL void UMF_dump_matrix ( NumericType *Numeric, WorkType *Work, Int check_degree ) ; GLOBAL void UMF_dump_current_front ( NumericType *Numeric, WorkType *Work, Int check ) ; GLOBAL void UMF_dump_lu ( NumericType *Numeric ) ; GLOBAL void UMF_dump_memory ( NumericType *Numeric ) ; GLOBAL void UMF_dump_packed_memory ( NumericType *Numeric, WorkType *Work ) ; GLOBAL void UMF_dump_col_matrix ( const double Ax [ ], #ifdef COMPLEX const double Az [ ], #endif const Int Ai [ ], const Int Ap [ ], Int n_row, Int n_col, Int nz ) ; GLOBAL void UMF_dump_chain ( Int frontid, Int Front_parent [ ], Int Front_npivcol [ ], Int Front_nrows [ ], Int Front_ncols [ ], Int nfr ) ; GLOBAL void UMF_dump_rowmerge ( NumericType *Numeric, SymbolicType *Symbolic, WorkType *Work ) ; GLOBAL void UMF_dump_start ( void ) ; GLOBAL void UMF_dump_diagonal_map ( Int Diagonal_map [ ], Int Diagonal_imap [ ], Int n1, Int nn, Int nempty ) ; #define UMF_DBMAX 50000 #ifndef EXTERN #define EXTERN extern #endif GLOBAL EXTERN Int UMF_debug ; GLOBAL EXTERN Int UMF_allocfail ; GLOBAL EXTERN double UMF_gprob ; #define DEBUGk(k,params) { if (UMF_debug >= (k)) { PRINTF (params) ; } } #define DEBUGm4(params) DEBUGk (-4, params) #define DEBUGm3(params) DEBUGk (-3, params) #define DEBUGm2(params) DEBUGk (-2, params) #define DEBUGm1(params) DEBUGk (-1, params) #define DEBUG0(params) DEBUGk (0, params) #define DEBUG1(params) DEBUGk (1, params) #define DEBUG2(params) DEBUGk (2, params) #define DEBUG3(params) DEBUGk (3, params) #define DEBUG4(params) DEBUGk (4, params) #define DEBUG5(params) DEBUGk (5, params) #define DEBUG6(params) DEBUGk (6, params) #define DEBUG7(params) DEBUGk (7, params) #define DEBUG8(params) DEBUGk (8, params) #define DEBUG9(params) DEBUGk (9, params) #define EDEBUGk(k,a) { if (UMF_debug >= (k)) { PRINT_ENTRY (a) ; } } #define EDEBUG0(a) EDEBUGk (0, a) #define EDEBUG1(a) EDEBUGk (1, a) #define EDEBUG2(a) EDEBUGk (2, a) #define EDEBUG3(a) EDEBUGk (3, a) #define EDEBUG4(a) EDEBUGk (4, a) #define EDEBUG5(a) EDEBUGk (5, a) #define EDEBUG6(a) EDEBUGk (6, a) #define EDEBUG7(a) EDEBUGk (7, a) #define EDEBUG8(a) EDEBUGk (8, a) #define EDEBUG9(a) EDEBUGk (9, a) /* ASSERT defined in amd_dump.h */ #else /* ========================================================================== */ /* === No debugging ========================================================= */ /* ========================================================================== */ /* turn off all debugging macros */ #define DEBUGk(k,params) #define DEBUGm4(params) #define DEBUGm3(params) #define DEBUGm2(params) #define DEBUGm1(params) #define DEBUG0(params) #define DEBUG1(params) #define DEBUG2(params) #define DEBUG3(params) #define DEBUG4(params) #define DEBUG5(params) #define DEBUG6(params) #define DEBUG7(params) #define DEBUG8(params) #define DEBUG9(params) #define EDEBUGk(k,a) #define EDEBUG0(a) #define EDEBUG1(a) #define EDEBUG2(a) #define EDEBUG3(a) #define EDEBUG4(a) #define EDEBUG5(a) #define EDEBUG6(a) #define EDEBUG7(a) #define EDEBUG8(a) #define EDEBUG9(a) #endif /* NDEBUG */ SuiteSparse/UMFPACK/Source/umfpack_solve.c0000644001170100242450000001515410617162166017313 0ustar davisfac/* ========================================================================== */ /* === UMFPACK_solve ======================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Solves a linear system using the numerical factorization computed by UMFPACK_numeric. See umfpack_solve.h for more details. For umfpack_*_solve: Dynamic memory usage: UMFPACK_solve calls UMF_malloc twice, for workspace of size c*n*sizeof(double) + n*sizeof(Int), where c is defined below. On return, all of this workspace is free'd via UMF_free. For umfpack_*_wsolve: No dynamic memory usage. Input arrays are used for workspace instead. Pattern is a workspace of size n Integers. The double array W must be at least of size c*n, where c is defined below. If iterative refinement is requested, and Ax=b, A'x=b or A.'x=b is being solved, and the matrix A is not singular, then c is 5 for the real version and 10 for the complex version. Otherwise, c is 1 for the real version and 4 for the complex version. */ #include "umf_internal.h" #include "umf_valid_numeric.h" #include "umf_solve.h" #ifndef WSOLVE #include "umf_malloc.h" #include "umf_free.h" #ifndef NDEBUG PRIVATE Int init_count ; #endif #endif GLOBAL Int #ifdef WSOLVE UMFPACK_wsolve #else UMFPACK_solve #endif ( Int sys, const Int Ap [ ], const Int Ai [ ], const double Ax [ ], #ifdef COMPLEX const double Az [ ], #endif double Xx [ ], #ifdef COMPLEX double Xz [ ], #endif const double Bx [ ], #ifdef COMPLEX const double Bz [ ], #endif void *NumericHandle, const double Control [UMFPACK_CONTROL], double User_Info [UMFPACK_INFO] #ifdef WSOLVE , Int Pattern [ ], double W [ ] #endif ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ double Info2 [UMFPACK_INFO], stats [2] ; double *Info ; NumericType *Numeric ; Int n, i, irstep, status ; #ifndef WSOLVE Int *Pattern, wsize ; double *W ; #endif /* ---------------------------------------------------------------------- */ /* get the amount of time used by the process so far */ /* ---------------------------------------------------------------------- */ umfpack_tic (stats) ; #ifndef WSOLVE #ifndef NDEBUG init_count = UMF_malloc_count ; #endif #endif /* ---------------------------------------------------------------------- */ /* get parameters */ /* ---------------------------------------------------------------------- */ irstep = GET_CONTROL (UMFPACK_IRSTEP, UMFPACK_DEFAULT_IRSTEP) ; if (User_Info != (double *) NULL) { /* return Info in user's array */ Info = User_Info ; /* clear the parts of Info that are set by UMFPACK_solve */ for (i = UMFPACK_IR_TAKEN ; i <= UMFPACK_SOLVE_TIME ; i++) { Info [i] = EMPTY ; } } else { /* no Info array passed - use local one instead */ Info = Info2 ; for (i = 0 ; i < UMFPACK_INFO ; i++) { Info [i] = EMPTY ; } } Info [UMFPACK_STATUS] = UMFPACK_OK ; Info [UMFPACK_SOLVE_FLOPS] = 0 ; Numeric = (NumericType *) NumericHandle ; if (!UMF_valid_numeric (Numeric)) { Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_Numeric_object ; return (UMFPACK_ERROR_invalid_Numeric_object) ; } Info [UMFPACK_NROW] = Numeric->n_row ; Info [UMFPACK_NCOL] = Numeric->n_col ; if (Numeric->n_row != Numeric->n_col) { /* only square systems can be handled */ Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_system ; return (UMFPACK_ERROR_invalid_system) ; } n = Numeric->n_row ; if (Numeric->nnzpiv < n || SCALAR_IS_ZERO (Numeric->rcond) || SCALAR_IS_NAN (Numeric->rcond)) { /* turn off iterative refinement if A is singular */ /* or if U has NaN's on the diagonal. */ irstep = 0 ; } if (!Xx || !Bx) { Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ; return (UMFPACK_ERROR_argument_missing) ; } if (sys >= UMFPACK_Pt_L) { /* no iterative refinement except for nonsingular Ax=b, A'x=b, A.'x=b */ irstep = 0 ; } /* ---------------------------------------------------------------------- */ /* allocate or check the workspace */ /* ---------------------------------------------------------------------- */ #ifdef WSOLVE if (!W || !Pattern) { Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ; return (UMFPACK_ERROR_argument_missing) ; } #else #ifdef COMPLEX if (irstep > 0) { wsize = 10*n ; /* W, X, Z, S, Y, B2 */ } else { wsize = 4*n ; /* W, X */ } #else if (irstep > 0) { wsize = 5*n ; /* W, Z, S, Y, B2 */ } else { wsize = n ; /* W */ } #endif Pattern = (Int *) UMF_malloc (n, sizeof (Int)) ; W = (double *) UMF_malloc (wsize, sizeof (double)) ; if (!W || !Pattern) { DEBUGm4 (("out of memory: solve work\n")) ; Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; (void) UMF_free ((void *) W) ; (void) UMF_free ((void *) Pattern) ; return (UMFPACK_ERROR_out_of_memory) ; } #endif /* WSOLVE */ /* ---------------------------------------------------------------------- */ /* solve the system */ /* ---------------------------------------------------------------------- */ status = UMF_solve (sys, Ap, Ai, Ax, Xx, Bx, #ifdef COMPLEX Az, Xz, Bz, #endif Numeric, irstep, Info, Pattern, W) ; /* ---------------------------------------------------------------------- */ /* free the workspace (if allocated) */ /* ---------------------------------------------------------------------- */ #ifndef WSOLVE (void) UMF_free ((void *) W) ; (void) UMF_free ((void *) Pattern) ; ASSERT (UMF_malloc_count == init_count) ; #endif /* ---------------------------------------------------------------------- */ /* get the time used by UMFPACK_*solve */ /* ---------------------------------------------------------------------- */ Info [UMFPACK_STATUS] = status ; if (status >= 0) { umfpack_toc (stats) ; Info [UMFPACK_SOLVE_WALLTIME] = stats [0] ; Info [UMFPACK_SOLVE_TIME] = stats [1] ; } return (status) ; } SuiteSparse/UMFPACK/README.txt0000644001170100242450000004403710677545524014562 0ustar davisfacUMFPACK : a set of routines solving sparse linear systems via LU factorization. Requires three other packages: the BLAS (dense matrix operations), AMD (sparse matrix minimum degree ordering), and UFconfig. Includes a C-callable and MATLAB interface, and a basic FORTRAN 77 interface to a subset of the C-callable routines. Requires AMD Version 2.0 or later. The AMD, UFconfig, and UMFPACK directories must all reside in the same parent directory. Quick start (Unix, or Windows with Cygwin): To compile, test, and install both UMFPACK and AMD, the UMFPACK and AMD directories must be in the same parent directory. To configure, edit the UFconfig/UFconfig.mk file (otherwise, you may get warnings that the BLAS (dgemm, etc) are not found). You may use UMFPACK_CONFIG = -DNBLAS in the UFconfig/UFconfig.mk file, to avoid using the BLAS, but UMFPACK will be slow. Next, cd to this directory (UMFPACK) and type "make". To compile and run a FORTRAN demo program for Harwell/Boeing matrices, type "make hb". To compile a FORTRAN main program that calls the 32-bit C-callable UMFPACK library, type "make fortran". When done, type "make clean" to remove unused *.o files (keeps the compiled libraries and demo programs). See the User Guide (Doc/UserGuide.pdf), or ../UFconfig/UFconfig.mk for more details (including options for compiling in 64-bit mode). Quick start (for MATLAB users): To compile, test, and install the UMFPACK mexFunction, cd to the UMFPACK/MATLAB directory and type umfpack_make at the MATLAB prompt. NOTE: DO NOT ATTEMPT TO USE THIS CODE IN 64-BIT MATLAB (v7.3). It is not yet ported to that version of MATLAB. -------------------------------------------------------------------------------- UMFPACK, Copyright (c) 1995-2006 by Timothy A. Davis. All Rights Reserved. UMFPACK is available under alternate licences; contact T. Davis for details. UMFPACK License: Your use or distribution of UMFPACK or any modified version of UMFPACK implies that you agree to this License. This library is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Permission is hereby granted to use or copy this program under the terms of the GNU GPL, provided that the Copyright, this License, and the Availability of the original version is retained on all copies. User documentation of any code that uses this code or any modified version of this code must cite the Copyright, this License, the Availability note, and "Used by permission." Permission to modify the code and to distribute modified code is granted, provided the Copyright, this License, and the Availability note are retained, and a notice that the code was modified is included. Availability: http://www.cise.ufl.edu/research/sparse/umfpack UMFPACK (including versions 2.2.1 and earlier, in FORTRAN) is available at http://www.cise.ufl.edu/research/sparse. MA38 is available in the Harwell Subroutine Library. This version of UMFPACK includes a modified form of COLAMD Version 2.0, originally released on Jan. 31, 2000, also available at http://www.cise.ufl.edu/research/sparse. COLAMD V2.0 is also incorporated as a built-in function in MATLAB version 6.1, by The MathWorks, Inc. (http://www.mathworks.com). COLAMD V1.0 appears as a column-preordering in SuperLU (SuperLU is available at http://www.netlib.org). UMFPACK v4.0 is a built-in routine in MATLAB 6.5. UMFPACK v4.3 is a built-in routine in MATLAB 7.1. -------------------------------------------------------------------------------- Refer to ../AMD/README for the License for AMD, which is a separate package for ordering sparse matrices that is required by UMFPACK. UMFPACK v4.5 cannot use AMD v1.1 or earlier. UMFPACK 5.x requires AMD v2.0 or later. -------------------------------------------------------------------------------- This is the UMFPACK README.txt file. It is a terse overview of UMFPACK. Refer to the User Guide (Doc/UserGuide.pdf) for how to install and use UMFPACK, or to the Quick Start Guide, QuickStart.pdf. Description: UMFPACK is a set of routines for solving unsymmetric sparse linear systems, Ax=b, using the Unsymmetric MultiFrontal method. Written in ANSI/ISO C, with a MATLAB (Version 6.0 or later) interface. For best performance, UMFPACK requires an optimized BLAS library. It can also be compiled without any BLAS at all. UMFPACK requires AMD Version 2.0. Authors: Timothy A. Davis (davis@cise.ufl.edu), University of Florida. Includes a modified version of COLAMD V2.0, by Stefan I. Larimore and Timothy A. Davis, University of Florida. The COLAMD algorithm was developed in collaboration with John Gilbert, Xerox Palo Alto Research Center, and Esmond Ng, Lawrence Berkeley National Laboratory. Includes AMD, by Timothy A. Davis, Patrick R. Amestoy, and Iain S. Duff. UMFPACK Version 2.2.1 (MA38 in the Harwell Subroutine Library) is co-authored with Iain S. Duff, Rutherford Appleton Laboratory. Acknowledgements: This work was supported by the National Science Foundation, under grants DMS-9504974, DMS-9803599, and CCR-0203270. Portions of this work were done while on sabbatical at Stanford University and Lawrence Berkeley National Laboratory (with funding from the SciDAC program). I would like to thank Gene Golub, Esmond Ng, and Horst Simon for making this sabbatical possible. I would also like to thank the many researchers who provided sparse matrices from a wide range of domains and used earlier versions of UMFPACK/ MA38 in their applications, and thus assisted in the practical development of the algorithm (see http://www.cise.ufl.edu/research/sparse, future contributions of matrices are always welcome). The MathWorks, Inc., provided a pre-release of MATLAB V6 which allowed me to release the first umfpack mexFunction (v3.0) about 6 months earlier than I had originally planned. They also supported the extension of UMFPACK to complex, singular, and rectangular matrices (UMFPACK v4.0). Penny Anderson (The MathWorks, Inc.), Anshul Gupta (IBM), and Friedrich Grund (WAIS) assisted in porting UMFPACK to different platforms. Penny Anderson also incorporated UMFPACK v4.0 into MATLAB, for lu, backslash (\), and forward slash (/). David Bateman (Motorola) wrote the initial version of the packed complex input option, and umfpack_get_determinant. -------------------------------------------------------------------------------- Files and directories in the UMFPACK distribution: -------------------------------------------------------------------------------- ---------------------------------------------------------------------------- Subdirectories of the UMFPACK directory: ---------------------------------------------------------------------------- Doc documentation Source primary source code Include include files for use in your code that calls UMFPACK Demo demo programs. also serves as test of the UMFPACK installation. MATLAB UMFPACK mexFunction for MATLAB, and supporting m-files Lib where the compiled C-callable UMFPACK library is placed. ---------------------------------------------------------------------------- Files in the UMFPACK directory: ---------------------------------------------------------------------------- Makefile top-level Makefile for GNU make or original make. Windows users would require Cygwin to use "make" README.txt this file ---------------------------------------------------------------------------- Doc directory: documentation ---------------------------------------------------------------------------- ChangeLog change log License the UMFPACK License Makefile for creating the documentation QuickStart.tex Quick Start guide (source) QuickStart.pdf Quick Start guide (PDF) UserGuide.bib User Guide (references) UserGuide.sed1 sed script for processing UserGuide.stex UserGuide.sed2 sed script for processing UserGuide.stex UserGuide.stex User Guide (LaTeX) UserGuide.pdf User Guide (PDF) ---------------------------------------------------------------------------- Source directory: ---------------------------------------------------------------------------- cholmod_blas.h an exact copy of CHOLMOD/Include/cholmod_blas.h umfpack_col_to_triplet.c convert col form to triplet umfpack_defaults.c set Control defaults umfpack_free_numeric.c free Numeric object umfpack_free_symbolic.c free Symbolic object umfpack_get_determinant.c compute determinant from Numeric object umfpack_get_lunz.c get nz's in L and U umfpack_get_numeric.c get Numeric object umfpack_get_symbolic.c get Symbolic object umfpack_load_numeric.c load Numeric object from file umfpack_load_symbolic.c load Symbolic object from file umfpack_numeric.c numeric factorization umfpack_qsymbolic.c symbolic factorization, user Q umfpack_report_control.c print Control settings umfpack_report_info.c print Info statistics umfpack_report_matrix.c print col or row-form sparse matrix umfpack_report_numeric.c print Numeric object umfpack_report_perm.c print permutation umfpack_report_status.c print return status umfpack_report_symbolic.c print Symbolic object umfpack_report_triplet.c print triplet matrix umfpack_report_vector.c print dense vector umfpack_save_numeric.c save Numeric object to file umfpack_save_symbolic.c save Symbolic object to file umfpack_scale.c scale a vector umfpack_solve.c solve a linear system umfpack_symbolic.c symbolic factorization umfpack_tictoc.c timer umfpack_timer.c timer umfpack_transpose.c transpose a matrix umfpack_triplet_to_col.c convert triplet to col form umf_config.h configuration file (BLAS, memory, timer) umf_internal.h definitions internal to UMFPACK umf_version.h version definitions (int/UF_long, real/complex) umf_2by2.[ch] umf_analyze.[ch] symbolic factorization of A'*A umf_apply_order.[ch] apply column etree postorder umf_assemble.[ch] assemble elements into current front umf_blas3_update.[ch] rank-k update. Uses level-3 BLAS umf_build_tuples.[ch] construct tuples for elements umf_colamd.[ch] COLAMD pre-ordering, modified for UMFPACK umf_create_element.[ch] create a new element umf_dump.[ch] debugging routines, not normally active umf_extend_front.[ch] extend the current frontal matrix umf_free.[ch] free memory umf_fsize.[ch] determine largest front in each subtree umf_garbage_collection.[ch] compact Numeric->Memory umf_get_memory.[ch] make Numeric->Memory bigger umf_grow_front.[ch] make current frontal matrix bigger umf_init_front.[ch] initialize a new frontal matrix umf_is_permutation.[ch] checks the validity of a permutation vector umf_kernel.[ch] the main numeric factorization kernel umf_kernel_init.[ch] initializations for umf_kernel umf_kernel_wrapup.[ch] wrapup for umf_kernel umf_local_search.[ch] local row and column pivot search umf_lsolve.[ch] solve Lx=b umf_ltsolve.[ch] solve L'x=b and L.'x=b umf_malloc.[ch] malloc some memory umf_mem_alloc_element.[ch] allocate element in Numeric->Memory umf_mem_alloc_head_block.[ch] alloc. block at head of Numeric->Memory umf_mem_alloc_tail_block.[ch] alloc. block at tail of Numeric->Memory umf_mem_free_tail_block.[ch] free block at tail of Numeric->Memory umf_mem_init_memoryspace.[ch] initialize Numeric->Memory umf_realloc.[ch] realloc memory umf_report_perm.[ch] print a permutation vector umf_report_vector.[ch] print a double vector umf_row_search.[ch] look for a pivot row umf_scale.[ch] scale the pivot column umf_scale_column.[ch] move pivot row & column into place, log P and Q umf_set_stats.[ch] set statistics (final or estimates) umf_singletons.[ch] find all zero-cost pivots umf_solve.[ch] solve a linear system umf_start_front.[ch] start a new frontal matrix for one frontal chain umf_store_lu.[ch] store LU factors of current front umf_symbolic_usage.[ch] determine memory usage for Symbolic object umf_transpose.[ch] transpose a matrix in row or col form umf_triplet.[ch] convert triplet to column form umf_tuple_lengths.[ch] determine the tuple list lengths umf_usolve.[ch] solve Ux=b umf_utsolve.[ch] solve U'x=b and U.'x=b umf_valid_numeric.[ch] checks the validity of a Numeric object umf_valid_symbolic.[ch] check the validity of a Symbolic object ---------------------------------------------------------------------------- Include directory: ---------------------------------------------------------------------------- umfpack.h include file for user programs. Includes all of the following files. This serves are source- code level documenation. These files are also used to construct the User Guide. umfpack_col_to_triplet.h umfpack_defaults.h umfpack_free_numeric.h umfpack_free_symbolic.h umfpack_get_determinant.h umfpack_get_lunz.h umfpack_get_numeric.h umfpack_get_symbolic.h umfpack_load_numeric.h umfpack_load_symbolic.h umfpack_numeric.h umfpack_qsymbolic.h umfpack_report_control.h umfpack_report_info.h umfpack_report_matrix.h umfpack_report_numeric.h umfpack_report_perm.h umfpack_report_status.h umfpack_report_symbolic.h umfpack_report_triplet.h umfpack_report_vector.h umfpack_save_numeric.h umfpack_save_symbolic.h umfpack_scale.h umfpack_solve.h umfpack_symbolic.h umfpack_tictoc.h umfpack_timer.h umfpack_transpose.h umfpack_triplet_to_col.h umfpack_wsolve.h note that there is no umfpack_wsolve.c. The umfpack_*_wsolve routines are created from the umfpack_solve.c file. ---------------------------------------------------------------------------- Demo directory: ---------------------------------------------------------------------------- Makefile for GNU make or original make umfpack_simple.c a simple demo umpack_xx_demo.c template to create the demo codes below umfpack_di_demo.sed for creating umfpack_di_demo.c umfpack_dl_demo.sed for creating umfpack_dl_demo.c umfpack_zi_demo.sed for creating umfpack_zi_demo.c umfpack_zl_demo.sed for creating umfpack_zl_demo.c umfpack_di_demo.c a full demo (real/int version) umfpack_dl_demo.c a full demo (real/UF_long version) umfpack_zi_demo.c a full demo (complex/int version) umfpack_zl_demo.c a full demo (complex/UF_long version) umfpack_di_demo.out umfpack_di_demo output umfpack_dl_demo.out umfpack_dl_demo output umfpack_zi_demo.out umfpack_zi_demo output umfpack_zl_demo.out umfpack_zl_demo output umf4.c a demo (real/int) for Harwell/Boeing matrices umf4.out output of "make hb" HB directory of sample Harwell/Boeing matrices readhb.f reads HB matrices, keeps zero entries readhb_nozeros.f reads HB matrices, removes zero entries readhb_size.f reads HB matrix dimension, nnz tmp empty directory for umf4.c demo umf4_f77wrapper.c a simple FORTRAN interface for UMFPACK. compile with "make fortran" umf4hb.f a demo of the FORTRAN interface umf4hb.out output of "make fortran" umf4_f77zwrapper.c a simple FORTRAN interface for the complex UMFPACK routines. compile with "make fortran" umf4zhb.f a demo of the FORTRAN interface (complex) umf4zhb.out output of umf4zhb with HB/qc324.cua umf4hb64.f 64-bit version of umf4hb.f simple_compile a single command that compiles the double/int version of UMFPACK (useful prototype for Microsoft Visual Studio project) ---------------------------------------------------------------------------- MATLAB directory: ---------------------------------------------------------------------------- Contents.m for "help umfpack" listing of toolbox contents GNUmakefile a nice Makefile, for GNU make Makefile an ugly Unix Makefile (for older make's) lu_normest.m 1-norm estimate of A-L*U (by Hager & Davis). luflop.m for "help luflop" luflopmex.c luflop mexFunction, for computing LU flop count umfpack.m for "help umfpack" umfpack_btf.m solve Ax=b using umfpack and dmperm umfpack_demo.m a full umfpack demo umfpack_details.m the details of how to use umfpack umfpack_make.m compile the umfpack mexFunction within MATLAB umfpack_report.m report statistics umfpack_simple.m a simple umfpack demo umfpack_solve.m x=A\b or b/A for arbitrary b umfpack_test.m extensive test, requires UF sparse matrices umfpackmex.c the umfpack mexFunction west0067.mat sparse matrix for umfpack_demo.m umfpack_demo.m.out output of umfpack_demo.m umfpack_simple.m.out output of umfpack_simple lcc_lib/lapacksyms.def LAPACK definitions for lcc compiler (Windows) lcc_lib/libmwlapack.lib LAPACK definitions for lcc compiler (Windows) ---------------------------------------------------------------------------- Lib directory: libumfpack.a library placed here ---------------------------------------------------------------------------- GNUmakefile a nice Makefile, for GNU make Makefile an ugly Unix Makefile (for older make's) libumfpack.def UMPFACK definitions for Windows SuiteSparse/README.txt0000644001170100242450000001134110711427447013454 0ustar davisfacSuiteSparse: A Suite of Sparse matrix packages ------------------ SuiteSparse/README ------------------ ================================================================================ QUICK START FOR MATLAB USERS: unzip the SuiteSparse.zip file, then in the MATLAB Command Window, cd to the SuiteSparse directory and type SuiteSparse_install. All packages will be compiled, and several demos will be run. ================================================================================ Nov 1, 2007. SuiteSparse version 3.1 AMD approximate minimum degree ordering CAMD constrained approximate minimum degree ordering COLAMD column approximate minimum degree ordering CCOLAMD constrained column approximate minimum degree ordering BTF permutation to block triangular form KLU sparse LU factorization, primarily for circuit simulation. Requires AMD, COLAMD, and BTF. Optionally uses CHOLMOD, CAMD, CCOLAMD, and METIS. UMFPACK sparse LU factorization. Requires AMD and the BLAS. CHOLMOD sparse Cholesky factorization. Requires AMD, COLAMD, CCOLAMD, the BLAS, and LAPACK. Optionally uses METIS. UFconfig configuration file for all the above packages. The UFconfig/UFconfig.mk is included in the Makefile's of all packages. CSparse and RBio do not use UFconfig. CSparse a concise sparse matrix package, developed for my upcoming book, "Direct Methods for Sparse Linear Systems", to be published by SIAM. CXSparse CSparse Extended. Includes support for complex matrices and both int or long integers. RBio read/write sparse matrices in Rutherford/Boeing format UFcollection toolbox for managing the UF Sparse Matrix Collection LPDASA LP dual active set algorithm (to appear) MESHND 2D and 3D mesh generation and nested dissection ordering SSMULT sparse matrix multiply for MATLAB LINFACTOR simple m-file demonstrating how to use LU and CHOL in MATLAB to solve Ax=b MATLAB_Tools various simple m-files for use in MATLAB CHOLMOD optionally uses METIS 4.0.1 (http://www-users.cs.umn.edu/~karypis/metis). To use METIS, place a copy of the metis-4.0 directory in the same directory (CHOLMOD_ACM_TOMS) containing this README file. The use of METIS will improve the ordering quality in CHOLMOD. Refer to each package for license, copyright, and author information. All codes are authored or co-authored by Timothy A. Davis, CISE Dept., Univ. of Florida. email: my last name @ cise dot ufl dot edu. ================================================================================ If you use SuiteSparse_install in MATLAB, stop reading here. ================================================================================ ---------------------------- To use "make" in Unix/Linux: ---------------------------- (1) Use the right BLAS and LAPACK libraries See http://www.netlib.org/blas for the Fortran reference BLAS (slow, but they work). See http://www.tacc.utexas.edu/~kgoto/ or http://www.cs.utexas.edu/users/flame/goto/ for an optimized BLAS. See http://www.netlib.org/lapack for LAPACK. The UFconfig/UFconfig.mk file assumes the vanilla BLAS (-lblas). You should use an optimized BLAS; otherwise UMFPACK and CHOLMOD will be slow. Change -lblas to -l(your BLAS library here) in the UFconfig/UFconfig.mk file. (2) Configure METIS (or don't use METIS) cd to metis-4.0 and edit the Makefile.in file. I recommend making these changes to metis-4.0/Makefile.in: CC = gcc OPTFLAGS = -O3 COPTIONS = -fexceptions -D_FILE_OFFSET_BITS=64 -D_LARGEFILE64_SOURCE Next, cd to metis-4.0 and type "make". If you do not wish to use METIS, then edit the UFconfig/UFconfig.mk file, and change the line CHOLMOD_CONFIG = to CHOLMOD_CONFIG = -DNPARTITION Also change the line METIS = ../../metis-4.0/libmetis.a to METIS = (3) Make other changes to UFconfig/UFconfig.mk as needed Edit the UFconfig/UFconfig.mk file as needed. Directions are in that file. If you have compiled SuiteSparse already (partially or completely), then whenever you edit the UFconfig/UFconfig.mk file, you should then type "make purge" (or "make realclean") in this directory. (4) Type "make" in this directory. All packages will be be compiled. METIS will be compiled if you have it. Several demos will be run. The libraries will appear in */Lib/*.a. Include files, as needed by user programs that use CHOLMOD, AMD, CAMD, COLAMD, CCOLAMD, BTF, KLU, UMFPACK, LDL, etc. are in */Include/*.h. The METIS library is in metis-4.0/libmetis.a. METIS Include files (not needed by the end user of SuiteSparse) are in located in metis-4.0/Lib/*.h. SuiteSparse/CXSparse_newfiles/0000755001170100242450000000000010711425626015337 5ustar davisfacSuiteSparse/CXSparse_newfiles/Doc/0000755001170100242450000000000010620606360016037 5ustar davisfacSuiteSparse/CXSparse_newfiles/Doc/License.txt0000644001170100242450000000162210375601211020160 0ustar davisfacCXSparse: a Concise Sparse matrix package - Extended. Copyright (c) 2006, Timothy A. Davis. http://www.cise.ufl.edu/research/sparse/CSparse -------------------------------------------------------------------------------- CXSparse is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. CXSparse is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA SuiteSparse/CXSparse_newfiles/Lib/0000755001170100242450000000000010617166727016056 5ustar davisfacSuiteSparse/CXSparse_newfiles/Lib/Makefile0000644001170100242450000001062010617170455017506 0ustar davisfac# Modify the "-O" optimization option for best performance (-O3 on Linux): CC = cc CFLAGS = -O I = -I../../UFconfig -I../Include AR = ar cr RANLIB = ranlib all: libcxsparse.a CS_SOURCE = cs_add.c cs_amd.c cs_chol.c cs_cholsol.c cs_counts.c cs_cumsum.c \ cs_droptol.c cs_dropzeros.c cs_dupl.c cs_entry.c \ cs_etree.c cs_fkeep.c cs_gaxpy.c cs_happly.c cs_house.c cs_ipvec.c \ cs_lsolve.c cs_ltsolve.c cs_lu.c cs_lusol.c cs_util.c cs_multiply.c \ cs_permute.c cs_pinv.c cs_post.c cs_pvec.c cs_qr.c cs_qrsol.c \ cs_scatter.c cs_schol.c cs_sqr.c cs_symperm.c cs_tdfs.c cs_malloc.c \ cs_transpose.c cs_compress.c cs_usolve.c cs_utsolve.c cs_scc.c \ cs_maxtrans.c cs_dmperm.c cs_updown.c cs_print.c cs_norm.c cs_load.c \ cs_dfs.c cs_reach.c cs_spsolve.c cs_leaf.c cs_ereach.c cs_randperm.c CS_DI_OBJ = cs_add_di.o cs_amd_di.o cs_chol_di.o cs_cholsol_di.o cs_counts_di.o \ cs_cumsum_di.o cs_droptol_di.o cs_dropzeros_di.o cs_dupl_di.o \ cs_entry_di.o cs_etree_di.o cs_fkeep_di.o cs_gaxpy_di.o cs_happly_di.o \ cs_house_di.o cs_ipvec_di.o cs_lsolve_di.o cs_ltsolve_di.o cs_lu_di.o \ cs_lusol_di.o cs_util_di.o cs_multiply_di.o cs_permute_di.o cs_pinv_di.o \ cs_post_di.o cs_pvec_di.o cs_qr_di.o cs_qrsol_di.o cs_scatter_di.o \ cs_schol_di.o cs_sqr_di.o cs_symperm_di.o cs_tdfs_di.o cs_malloc_di.o \ cs_transpose_di.o cs_compress_di.o cs_usolve_di.o cs_utsolve_di.o \ cs_scc_di.o cs_maxtrans_di.o cs_dmperm_di.o cs_updown_di.o cs_print_di.o \ cs_norm_di.o cs_load_di.o cs_dfs_di.o cs_reach_di.o cs_spsolve_di.o \ cs_leaf_di.o cs_ereach_di.o cs_randperm_di.o CS_DL_OBJ = cs_add_dl.o cs_amd_dl.o cs_chol_dl.o cs_cholsol_dl.o cs_counts_dl.o \ cs_cumsum_dl.o cs_droptol_dl.o cs_dropzeros_dl.o cs_dupl_dl.o \ cs_entry_dl.o cs_etree_dl.o cs_fkeep_dl.o cs_gaxpy_dl.o cs_happly_dl.o \ cs_house_dl.o cs_ipvec_dl.o cs_lsolve_dl.o cs_ltsolve_dl.o cs_lu_dl.o \ cs_lusol_dl.o cs_util_dl.o cs_multiply_dl.o cs_permute_dl.o cs_pinv_dl.o \ cs_post_dl.o cs_pvec_dl.o cs_qr_dl.o cs_qrsol_dl.o cs_scatter_dl.o \ cs_schol_dl.o cs_sqr_dl.o cs_symperm_dl.o cs_tdfs_dl.o cs_malloc_dl.o \ cs_transpose_dl.o cs_compress_dl.o cs_usolve_dl.o cs_utsolve_dl.o \ cs_scc_dl.o cs_maxtrans_dl.o cs_dmperm_dl.o cs_updown_dl.o cs_print_dl.o \ cs_norm_dl.o cs_load_dl.o cs_dfs_dl.o cs_reach_dl.o cs_spsolve_dl.o \ cs_leaf_dl.o cs_ereach_dl.o cs_randperm_dl.o CS_CI_OBJ = cs_add_ci.o cs_amd_ci.o cs_chol_ci.o cs_cholsol_ci.o cs_counts_ci.o \ cs_cumsum_ci.o cs_droptol_ci.o cs_dropzeros_ci.o cs_dupl_ci.o \ cs_entry_ci.o cs_etree_ci.o cs_fkeep_ci.o cs_gaxpy_ci.o cs_happly_ci.o \ cs_house_ci.o cs_ipvec_ci.o cs_lsolve_ci.o cs_ltsolve_ci.o cs_lu_ci.o \ cs_lusol_ci.o cs_util_ci.o cs_multiply_ci.o cs_permute_ci.o cs_pinv_ci.o \ cs_post_ci.o cs_pvec_ci.o cs_qr_ci.o cs_qrsol_ci.o cs_scatter_ci.o \ cs_schol_ci.o cs_sqr_ci.o cs_symperm_ci.o cs_tdfs_ci.o cs_malloc_ci.o \ cs_transpose_ci.o cs_compress_ci.o cs_usolve_ci.o cs_utsolve_ci.o \ cs_scc_ci.o cs_maxtrans_ci.o cs_dmperm_ci.o cs_updown_ci.o cs_print_ci.o \ cs_norm_ci.o cs_load_ci.o cs_dfs_ci.o cs_reach_ci.o cs_spsolve_ci.o \ cs_leaf_ci.o cs_ereach_ci.o cs_randperm_ci.o CS_CL_OBJ = cs_add_cl.o cs_amd_cl.o cs_chol_cl.o cs_cholsol_cl.o cs_counts_cl.o \ cs_cumsum_cl.o cs_droptol_cl.o cs_dropzeros_cl.o cs_dupl_cl.o \ cs_entry_cl.o cs_etree_cl.o cs_fkeep_cl.o cs_gaxpy_cl.o cs_happly_cl.o \ cs_house_cl.o cs_ipvec_cl.o cs_lsolve_cl.o cs_ltsolve_cl.o cs_lu_cl.o \ cs_lusol_cl.o cs_util_cl.o cs_multiply_cl.o cs_permute_cl.o cs_pinv_cl.o \ cs_post_cl.o cs_pvec_cl.o cs_qr_cl.o cs_qrsol_cl.o cs_scatter_cl.o \ cs_schol_cl.o cs_sqr_cl.o cs_symperm_cl.o cs_tdfs_cl.o cs_malloc_cl.o \ cs_transpose_cl.o cs_compress_cl.o cs_usolve_cl.o cs_utsolve_cl.o \ cs_scc_cl.o cs_maxtrans_cl.o cs_dmperm_cl.o cs_updown_cl.o cs_print_cl.o \ cs_norm_cl.o cs_load_cl.o cs_dfs_cl.o cs_reach_cl.o cs_spsolve_cl.o \ cs_leaf_cl.o cs_ereach_cl.o cs_randperm_cl.o CS = cs_convert.o $(CS_DI_OBJ) $(CS_DL_OBJ) $(CS_CI_OBJ) $(CS_CL_OBJ) $(CS): ../Include/cs.h Makefile cs_convert.o: ../Source/cs_convert.c $(CC) $(CFLAGS) $(I) -c $< -o $@ %_di.o : ../Source/%.c $(CC) $(CFLAGS) $(I) -c $< -o $@ %_dl.o : ../Source/%.c $(CC) $(CFLAGS) $(I) -DCS_LONG -c $< -o $@ %_ci.o : ../Source/%.c $(CC) $(CFLAGS) $(I) -DCS_COMPLEX -c $< -o $@ %_cl.o : ../Source/%.c $(CC) $(CFLAGS) $(I) -DCS_LONG -DCS_COMPLEX -c $< -o $@ libcxsparse.a: $(CS) $(AR) libcxsparse.a $(CS) $(RANLIB) libcxsparse.a clean: rm -f *.o purge: distclean distclean: clean rm -f *.a SuiteSparse/CXSparse_newfiles/Demo/0000755001170100242450000000000010620626405016220 5ustar davisfacSuiteSparse/CXSparse_newfiles/Demo/Makefile0000644001170100242450000001176510620626640017673 0ustar davisfacCC = cc CFLAGS = -O I = -I../Include -I../../UFconfig CS = ../Lib/libcxsparse.a all: $(CS) cs_demo1 cs_demo2 cs_demo3 \ cs_di_demo1 cs_di_demo2 cs_di_demo3 \ cs_dl_demo1 cs_dl_demo2 cs_dl_demo3 \ cs_ci_demo1 cs_ci_demo2 cs_ci_demo3 \ cs_cl_demo1 cs_cl_demo2 cs_cl_demo3 \ tests cs_idemo tests: test_convert test test_di test_dl test_ci test_cl test: cs_demo1 cs_demo2 cs_demo3 - ./cs_demo1 < ../Matrix/t1 - ./cs_demo2 < ../Matrix/t1 - ./cs_demo2 < ../Matrix/fs_183_1 - ./cs_demo2 < ../Matrix/west0067 - ./cs_demo2 < ../Matrix/lp_afiro - ./cs_demo2 < ../Matrix/ash219 - ./cs_demo2 < ../Matrix/mbeacxc - ./cs_demo2 < ../Matrix/bcsstk01 - ./cs_demo3 < ../Matrix/bcsstk01 - ./cs_demo2 < ../Matrix/bcsstk16 - ./cs_demo3 < ../Matrix/bcsstk16 test_di: cs_di_demo1 cs_di_demo2 cs_di_demo3 - ./cs_di_demo1 < ../Matrix/t1 - ./cs_di_demo2 < ../Matrix/t1 - ./cs_di_demo2 < ../Matrix/fs_183_1 - ./cs_di_demo2 < ../Matrix/west0067 - ./cs_di_demo2 < ../Matrix/lp_afiro - ./cs_di_demo2 < ../Matrix/ash219 - ./cs_di_demo2 < ../Matrix/mbeacxc - ./cs_di_demo2 < ../Matrix/bcsstk01 - ./cs_di_demo3 < ../Matrix/bcsstk01 - ./cs_di_demo2 < ../Matrix/bcsstk16 - ./cs_di_demo3 < ../Matrix/bcsstk16 test_dl: cs_dl_demo1 cs_dl_demo2 cs_dl_demo3 - ./cs_dl_demo1 < ../Matrix/t1 - ./cs_dl_demo2 < ../Matrix/t1 - ./cs_dl_demo2 < ../Matrix/fs_183_1 - ./cs_dl_demo2 < ../Matrix/west0067 - ./cs_dl_demo2 < ../Matrix/lp_afiro - ./cs_dl_demo2 < ../Matrix/ash219 - ./cs_dl_demo2 < ../Matrix/mbeacxc - ./cs_dl_demo2 < ../Matrix/bcsstk01 - ./cs_dl_demo3 < ../Matrix/bcsstk01 - ./cs_dl_demo2 < ../Matrix/bcsstk16 - ./cs_dl_demo3 < ../Matrix/bcsstk16 test_ci: cs_ci_demo1 cs_ci_demo2 cs_ci_demo3 - ./cs_ci_demo1 < ../Matrix/t2 - ./cs_ci_demo2 < ../Matrix/t2 - ./cs_ci_demo2 < ../Matrix/t3 - ./cs_ci_demo2 < ../Matrix/t4 - ./cs_ci_demo2 < ../Matrix/c_west0067 - ./cs_ci_demo2 < ../Matrix/c_mbeacxc - ./cs_ci_demo2 < ../Matrix/young1c - ./cs_ci_demo2 < ../Matrix/qc324 - ./cs_ci_demo2 < ../Matrix/neumann - ./cs_ci_demo2 < ../Matrix/c4 - ./cs_ci_demo3 < ../Matrix/c4 - ./cs_ci_demo2 < ../Matrix/mhd1280b - ./cs_ci_demo3 < ../Matrix/mhd1280b test_cl: cs_cl_demo1 cs_cl_demo2 cs_cl_demo3 - ./cs_cl_demo1 < ../Matrix/t2 - ./cs_cl_demo2 < ../Matrix/t2 - ./cs_cl_demo2 < ../Matrix/t3 - ./cs_cl_demo2 < ../Matrix/t4 - ./cs_cl_demo2 < ../Matrix/c_west0067 - ./cs_cl_demo2 < ../Matrix/c_mbeacxc - ./cs_cl_demo2 < ../Matrix/young1c - ./cs_cl_demo2 < ../Matrix/qc324 - ./cs_cl_demo2 < ../Matrix/neumann - ./cs_cl_demo2 < ../Matrix/c4 - ./cs_cl_demo3 < ../Matrix/c4 - ./cs_cl_demo2 < ../Matrix/mhd1280b - ./cs_cl_demo3 < ../Matrix/mhd1280b test_convert: cs_idemo cs_ldemo - ./cs_idemo < ../Matrix/t2 - ./cs_ldemo < ../Matrix/t2 $(CS): ( cd ../Lib ; $(MAKE) ) cs_demo1: $(CS) cs_demo1.c Makefile $(CS) $(CC) $(I) -o cs_demo1 cs_demo1.c $(CS) -lm cs_demo2: $(CS) cs_demo2.c cs_demo.c cs_demo.h Makefile $(CS) $(CC) $(I) -o cs_demo2 cs_demo2.c cs_demo.c $(CS) -lm cs_demo3: $(CS) cs_demo3.c cs_demo.c cs_demo.h Makefile $(CS) $(CC) $(I) -o cs_demo3 cs_demo3.c cs_demo.c $(CS) -lm cs_di_demo1: $(CS) cs_di_demo1.c Makefile $(CS) $(CC) $(I) -o cs_di_demo1 cs_di_demo1.c $(CS) -lm cs_di_demo2: $(CS) cs_di_demo2.c cs_di_demo.c cs_di_demo.h Makefile $(CS) $(CC) $(I) -o cs_di_demo2 cs_di_demo2.c cs_di_demo.c $(CS) -lm cs_di_demo3: $(CS) cs_di_demo3.c cs_di_demo.c cs_di_demo.h Makefile $(CS) $(CC) $(I) -o cs_di_demo3 cs_di_demo3.c cs_di_demo.c $(CS) -lm cs_ci_demo1: $(CS) cs_ci_demo1.c Makefile $(CS) $(CC) $(I) -o cs_ci_demo1 cs_ci_demo1.c $(CS) -lm cs_ci_demo2: $(CS) cs_ci_demo2.c cs_ci_demo.c cs_ci_demo.h Makefile $(CS) $(CC) $(I) -o cs_ci_demo2 cs_ci_demo2.c cs_ci_demo.c $(CS) -lm cs_ci_demo3: $(CS) cs_ci_demo3.c cs_ci_demo.c cs_ci_demo.h Makefile $(CS) $(CC) $(I) -o cs_ci_demo3 cs_ci_demo3.c cs_ci_demo.c $(CS) -lm cs_dl_demo1: $(CS) cs_dl_demo1.c Makefile $(CS) $(CC) $(I) -o cs_dl_demo1 cs_dl_demo1.c $(CS) -lm cs_dl_demo2: $(CS) cs_dl_demo2.c cs_dl_demo.c cs_dl_demo.h Makefile $(CS) $(CC) $(I) -o cs_dl_demo2 cs_dl_demo2.c cs_dl_demo.c $(CS) -lm cs_dl_demo3: $(CS) cs_dl_demo3.c cs_dl_demo.c cs_dl_demo.h Makefile $(CS) $(CC) $(I) -o cs_dl_demo3 cs_dl_demo3.c cs_dl_demo.c $(CS) -lm cs_cl_demo1: $(CS) cs_cl_demo1.c Makefile $(CS) $(CC) $(I) -o cs_cl_demo1 cs_cl_demo1.c $(CS) -lm cs_cl_demo2: $(CS) cs_cl_demo2.c cs_cl_demo.c cs_cl_demo.h Makefile $(CS) $(CC) $(I) -o cs_cl_demo2 cs_cl_demo2.c cs_cl_demo.c $(CS) -lm cs_cl_demo3: $(CS) cs_cl_demo3.c cs_cl_demo.c cs_cl_demo.h Makefile $(CS) $(CC) $(I) -o cs_cl_demo3 cs_cl_demo3.c cs_cl_demo.c $(CS) -lm cs_idemo: $(CS) cs_idemo.c Makefile $(CS) $(CC) $(I) -o cs_idemo cs_idemo.c $(CS) -lm cs_ldemo: $(CS) cs_ldemo.c Makefile $(CS) $(CC) $(I) -DCS_LONG -o cs_ldemo cs_ldemo.c $(CS) -lm clean: rm -f *.o purge: distclean distclean: clean rm -f cs_demo1 cs_demo2 cs_demo3 *.a rm -f cs_di_demo1 cs_di_demo2 cs_di_demo3 rm -f cs_dl_demo1 cs_dl_demo2 cs_dl_demo3 rm -f cs_ci_demo1 cs_ci_demo2 cs_ci_demo3 rm -f cs_cl_demo1 cs_cl_demo2 cs_cl_demo3 rm -f cs_idemo cs_ldemo SuiteSparse/CXSparse_newfiles/Demo/cs_idemo.c0000644001170100242450000000300610623313303020136 0ustar davisfac#include "cs.h" /* test real/complex conversion routines (int version) */ int main (void) { cs_ci *T, *A, *A1, *A2, *B ; cs_di *C1, *C2, *Treal, *Timag ; printf ("\n--- cs_idemo, size of CS_INT: %d\n", (int) sizeof (CS_INT)) ; T = cs_ci_load (stdin) ; /* load a complex triplet matrix, T */ printf ("\nT:\n") ; cs_ci_print (T, 0) ; Treal = cs_i_real (T, 1) ; /* Treal = real part of T */ printf ("\nTreal:\n") ; cs_di_print (Treal, 0) ; Timag = cs_i_real (T, 0) ; /* Treal = imaginary part of T */ printf ("\nTimag:\n") ; cs_di_print (Timag, 0) ; A = cs_ci_compress (T) ; /* A = compressed-column form of T */ printf ("\nA:\n") ; cs_ci_print (A, 0) ; C1 = cs_i_real (A, 1) ; /* C1 = real (A) */ printf ("\nC1 = real(A):\n") ; cs_di_print (C1, 0) ; C2 = cs_i_real (A, 0) ; /* C2 = imag (A) */ printf ("\nC2 = imag(A):\n") ; cs_di_print (C2, 0) ; A1 = cs_i_complex (C1, 1) ; /* A1 = complex version of C1 */ printf ("\nA1:\n") ; cs_ci_print (A1, 0) ; A2 = cs_i_complex (C2, 0) ; /* A2 = complex version of C2 (imag.) */ printf ("\nA2:\n") ; cs_ci_print (A2, 0) ; B = cs_ci_add (A1, A2, 1., -1.) ; /* B = A1 - A2 */ printf ("\nB = conj(A):\n") ; cs_ci_print (B, 0) ; cs_ci_spfree (T) ; cs_ci_spfree (A) ; cs_ci_spfree (A1) ; cs_ci_spfree (A2) ; cs_ci_spfree (B) ; cs_di_spfree (C1) ; cs_di_spfree (C2) ; cs_di_spfree (Treal) ; cs_di_spfree (Timag) ; return (0) ; } SuiteSparse/CXSparse_newfiles/Demo/cs_ldemo.c0000644001170100242450000000300610623313341020143 0ustar davisfac#include "cs.h" /* test real/complex conversion routines (int version) */ int main (void) { cs_cl *T, *A, *A1, *A2, *B ; cs_dl *C1, *C2, *Treal, *Timag ; printf ("\n--- cs_ldemo, size of CS_INT: %d\n", (int) sizeof (CS_INT)) ; T = cs_cl_load (stdin) ; /* load a complex triplet matrix, T */ printf ("\nT:\n") ; cs_cl_print (T, 0) ; Treal = cs_l_real (T, 1) ; /* Treal = real part of T */ printf ("\nTreal:\n") ; cs_dl_print (Treal, 0) ; Timag = cs_l_real (T, 0) ; /* Treal = imaginary part of T */ printf ("\nTimag:\n") ; cs_dl_print (Timag, 0) ; A = cs_cl_compress (T) ; /* A = compressed-column form of T */ printf ("\nA:\n") ; cs_cl_print (A, 0) ; C1 = cs_l_real (A, 1) ; /* C1 = real (A) */ printf ("\nC1 = real(A):\n") ; cs_dl_print (C1, 0) ; C2 = cs_l_real (A, 0) ; /* C2 = imag (A) */ printf ("\nC2 = imag(A):\n") ; cs_dl_print (C2, 0) ; A1 = cs_l_complex (C1, 1) ; /* A1 = complex version of C1 */ printf ("\nA1:\n") ; cs_cl_print (A1, 0) ; A2 = cs_l_complex (C2, 0) ; /* A2 = complex version of C2 (imag.) */ printf ("\nA2:\n") ; cs_cl_print (A2, 0) ; B = cs_cl_add (A1, A2, 1., -1.) ; /* B = A1 - A2 */ printf ("\nB = conj(A):\n") ; cs_cl_print (B, 0) ; cs_cl_spfree (T) ; cs_cl_spfree (A) ; cs_cl_spfree (A1) ; cs_cl_spfree (A2) ; cs_cl_spfree (B) ; cs_dl_spfree (C1) ; cs_dl_spfree (C2) ; cs_dl_spfree (Treal) ; cs_dl_spfree (Timag) ; return (0) ; } SuiteSparse/CXSparse_newfiles/Demo/README.txt0000644001170100242450000000045410375603510017720 0ustar davisfacCXSparse/Demo: to compile a run the demos, just type "make" in this directory. The printed residuals should all be small, except for the mbeacxc matrix (which is numerically and structurally singular), and ash219 (which is a least-squares problem). See cs_demo.out for the proper output of "make". SuiteSparse/CXSparse_newfiles/Tcov/0000755001170100242450000000000010617167237016260 5ustar davisfacSuiteSparse/CXSparse_newfiles/Tcov/Makefile0000644001170100242450000002751610617167237017733 0ustar davisfac # To run with valgrind: V = # V = valgrind -q # Linux test coverage CC = gcc CFLAGS = -O -g -fprofile-arcs -ftest-coverage \ -Wall -W -Wshadow -Wmissing-prototypes -Wstrict-prototypes \ -Wredundant-decls -Wnested-externs -Wdisabled-optimization -ansi \ -Wno-unused-parameter -Werror -I../Include -I../Demo -I../../UFconfig run: all run_convert run_di run_dl run_ci run_cl ./covall all: cs_demo1_di cs_demo2_di cs_demo3_di cstcov_test_di \ cs_demo1_dl cs_demo2_dl cs_demo3_dl cstcov_test_dl \ cs_demo1_ci cs_demo2_ci cs_demo3_ci cstcov_test_ci \ cs_demo1_cl cs_demo2_cl cs_demo3_cl cstcov_test_cl \ cs_idemo cs_ldemo CS_DI = cs_add_di.o cs_amd_di.o cs_chol_di.o cs_cholsol_di.o cs_counts_di.o \ cs_cumsum_di.o cs_droptol_di.o cs_dropzeros_di.o cs_dupl_di.o \ cs_entry_di.o cs_etree_di.o cs_fkeep_di.o cs_gaxpy_di.o cs_happly_di.o \ cs_house_di.o cs_ipvec_di.o cs_lsolve_di.o cs_ltsolve_di.o cs_lu_di.o \ cs_lusol_di.o cs_util_di.o cs_multiply_di.o cs_permute_di.o \ cs_pinv_di.o cs_post_di.o cs_pvec_di.o cs_qr_di.o cs_qrsol_di.o \ cs_scatter_di.o cs_schol_di.o cs_sqr_di.o cs_symperm_di.o cs_tdfs_di.o \ cs_transpose_di.o cs_compress_di.o cs_usolve_di.o cs_scc_di.o \ cs_maxtrans_di.o cs_dmperm_di.o cs_updown_di.o cs_print_di.o \ cs_norm_di.o cs_load_di.o cs_dfs_di.o cstcov_malloc_test_di.o \ cs_utsolve_di.o cs_reach_di.o cs_spsolve_di.o \ cs_leaf_di.o cs_ereach_di.o cs_randperm_di.o CS_DL = cs_add_dl.o cs_amd_dl.o cs_chol_dl.o cs_cholsol_dl.o cs_counts_dl.o \ cs_cumsum_dl.o cs_droptol_dl.o cs_dropzeros_dl.o cs_dupl_dl.o \ cs_entry_dl.o cs_etree_dl.o cs_fkeep_dl.o cs_gaxpy_dl.o cs_happly_dl.o \ cs_house_dl.o cs_ipvec_dl.o cs_lsolve_dl.o cs_ltsolve_dl.o cs_lu_dl.o \ cs_lusol_dl.o cs_util_dl.o cs_multiply_dl.o cs_permute_dl.o \ cs_pinv_dl.o cs_post_dl.o cs_pvec_dl.o cs_qr_dl.o cs_qrsol_dl.o \ cs_scatter_dl.o cs_schol_dl.o cs_sqr_dl.o cs_symperm_dl.o cs_tdfs_dl.o \ cs_transpose_dl.o cs_compress_dl.o cs_usolve_dl.o cs_scc_dl.o \ cs_maxtrans_dl.o cs_dmperm_dl.o cs_updown_dl.o cs_print_dl.o \ cs_norm_dl.o cs_load_dl.o cs_dfs_dl.o cstcov_malloc_test_dl.o \ cs_utsolve_dl.o cs_reach_dl.o cs_spsolve_dl.o \ cs_leaf_dl.o cs_ereach_dl.o cs_randperm_dl.o CS_CI = cs_add_ci.o cs_amd_ci.o cs_chol_ci.o cs_cholsol_ci.o cs_counts_ci.o \ cs_cumsum_ci.o cs_droptol_ci.o cs_dropzeros_ci.o cs_dupl_ci.o \ cs_entry_ci.o cs_etree_ci.o cs_fkeep_ci.o cs_gaxpy_ci.o cs_happly_ci.o \ cs_house_ci.o cs_ipvec_ci.o cs_lsolve_ci.o cs_ltsolve_ci.o cs_lu_ci.o \ cs_lusol_ci.o cs_util_ci.o cs_multiply_ci.o cs_permute_ci.o \ cs_pinv_ci.o cs_post_ci.o cs_pvec_ci.o cs_qr_ci.o cs_qrsol_ci.o \ cs_scatter_ci.o cs_schol_ci.o cs_sqr_ci.o cs_symperm_ci.o cs_tdfs_ci.o \ cs_transpose_ci.o cs_compress_ci.o cs_usolve_ci.o cs_scc_ci.o \ cs_maxtrans_ci.o cs_dmperm_ci.o cs_updown_ci.o cs_print_ci.o \ cs_norm_ci.o cs_load_ci.o cs_dfs_ci.o cstcov_malloc_test_ci.o \ cs_utsolve_ci.o cs_reach_ci.o cs_spsolve_ci.o \ cs_leaf_ci.o cs_ereach_ci.o cs_randperm_ci.o CS_CL = cs_add_cl.o cs_amd_cl.o cs_chol_cl.o cs_cholsol_cl.o cs_counts_cl.o \ cs_cumsum_cl.o cs_droptol_cl.o cs_dropzeros_cl.o cs_dupl_cl.o \ cs_entry_cl.o cs_etree_cl.o cs_fkeep_cl.o cs_gaxpy_cl.o cs_happly_cl.o \ cs_house_cl.o cs_ipvec_cl.o cs_lsolve_cl.o cs_ltsolve_cl.o cs_lu_cl.o \ cs_lusol_cl.o cs_util_cl.o cs_multiply_cl.o cs_permute_cl.o \ cs_pinv_cl.o cs_post_cl.o cs_pvec_cl.o cs_qr_cl.o cs_qrsol_cl.o \ cs_scatter_cl.o cs_schol_cl.o cs_sqr_cl.o cs_symperm_cl.o cs_tdfs_cl.o \ cs_transpose_cl.o cs_compress_cl.o cs_usolve_cl.o cs_scc_cl.o \ cs_maxtrans_cl.o cs_dmperm_cl.o cs_updown_cl.o cs_print_cl.o \ cs_norm_cl.o cs_load_cl.o cs_dfs_cl.o cstcov_malloc_test_cl.o \ cs_utsolve_cl.o cs_reach_cl.o cs_spsolve_cl.o \ cs_leaf_cl.o cs_ereach_cl.o cs_randperm_cl.o OBJ = $(CS_DI) $(CS_DL) $(CS_CI) $(CS_CL) cs_convert.o $(OBJ): ../Include/cs.h cstcov_malloc_test.h Makefile .PRECIOUS: %demo.c %demo1.c %demo2.c %demo3.c cs_%.c cs_%_ci.c cs_%_cl.c cs_%_di.c cs_%_dl.c cstcov_%.c %demo.c: - ln -s ../Demo/$*demo.c %demo1.c: - ln -s ../Demo/$*demo1.c %demo2.c: - ln -s ../Demo/$*demo2.c %demo3.c: - ln -s ../Demo/$*demo3.c cstcov_%.c: - ln -s cstcov_malloc_test.c cstcov_$*.c cs_convert.c: - ln -s ../Source/cs_convert.c cs_%_ci.c: - ln -s ../Source/cs_$*.c cs_$*_ci.c cs_%_di.c: - ln -s ../Source/cs_$*.c cs_$*_di.c cs_%_dl.c: - ln -s ../Source/cs_$*.c cs_$*_dl.c cs_%_cl.c: - ln -s ../Source/cs_$*.c cs_$*_cl.c %_di.o: %_di.c $(CC) $(CFLAGS) -c $< %_dl.o: %_dl.c $(CC) $(CFLAGS) -DCS_LONG -c $< %_ci.o: %_ci.c $(CC) $(CFLAGS) -DCS_COMPLEX -c $< %_cl.o: %_cl.c $(CC) $(CFLAGS) -DCS_LONG -DCS_COMPLEX -c $< cs_idemo: $(OBJ) cs_idemo.c $(CC) $(CFLAGS) -o cs_idemo cs_idemo.c $(OBJ) -lm cs_ldemo: $(OBJ) cs_ldemo.c $(CC) $(CFLAGS) -o cs_ldemo cs_ldemo.c $(OBJ) -lm cs_demo1_di: $(CS_DI) cs_di_demo1.c $(CC) $(CFLAGS) -o cs_demo1_di cs_di_demo1.c $(CS_DI) -lm cs_demo2_di: $(CS_DI) cs_di_demo2.c cs_di_demo.c $(CC) $(CFLAGS) -o cs_demo2_di cs_di_demo2.c cs_di_demo.c $(CS_DI) -lm cs_demo3_di: $(CS_DI) cs_di_demo3.c cs_di_demo.c $(CC) $(CFLAGS) -o cs_demo3_di cs_di_demo3.c cs_di_demo.c $(CS_DI) -lm cstcov_test_di: $(CS_DI) cstcov_test.c cs_di_demo.c $(CC) $(CFLAGS) -o cstcov_test_di cstcov_test.c cs_di_demo.c $(CS_DI) -lm cs_demo1_dl: $(CS_DL) cs_dl_demo1.c $(CC) $(CFLAGS) -DCS_LONG -o cs_demo1_dl cs_dl_demo1.c $(CS_DL) -lm cs_demo2_dl: $(CS_DL) cs_dl_demo2.c cs_dl_demo.c $(CC) $(CFLAGS) -DCS_LONG -o cs_demo2_dl cs_dl_demo2.c cs_dl_demo.c $(CS_DL) -lm cs_demo3_dl: $(CS_DL) cs_dl_demo3.c cs_dl_demo.c $(CC) $(CFLAGS) -DCS_LONG -o cs_demo3_dl cs_dl_demo3.c cs_dl_demo.c $(CS_DL) -lm cstcov_test_dl: $(CS_DL) cstcov_test.c cs_dl_demo.c $(CC) $(CFLAGS) -DCS_LONG -o cstcov_test_dl cstcov_test.c cs_dl_demo.c $(CS_DL) -lm cs_demo1_ci: $(CS_CI) cs_ci_demo1.c $(CC) $(CFLAGS) -DCS_COMPLEX -o cs_demo1_ci cs_ci_demo1.c $(CS_CI) -lm cs_demo2_ci: $(CS_CI) cs_ci_demo2.c cs_ci_demo.c $(CC) $(CFLAGS) -DCS_COMPLEX -o cs_demo2_ci cs_ci_demo2.c cs_ci_demo.c $(CS_CI) -lm cs_demo3_ci: $(CS_CI) cs_ci_demo3.c cs_ci_demo.c $(CC) $(CFLAGS) -DCS_COMPLEX -o cs_demo3_ci cs_ci_demo3.c cs_ci_demo.c $(CS_CI) -lm cstcov_test_ci: $(CS_CI) cstcov_test.c cs_ci_demo.c $(CC) $(CFLAGS) -DCS_COMPLEX -o cstcov_test_ci cstcov_test.c cs_ci_demo.c $(CS_CI) -lm cs_demo1_cl: $(CS_CL) cs_cl_demo1.c $(CC) $(CFLAGS) -DCS_LONG -DCS_COMPLEX -o cs_demo1_cl cs_cl_demo1.c $(CS_CL) -lm cs_demo2_cl: $(CS_CL) cs_cl_demo2.c cs_cl_demo.c $(CC) $(CFLAGS) -DCS_LONG -DCS_COMPLEX -o cs_demo2_cl cs_cl_demo2.c cs_cl_demo.c $(CS_CL) -lm cs_demo3_cl: $(CS_CL) cs_cl_demo3.c cs_cl_demo.c $(CC) $(CFLAGS) -DCS_LONG -DCS_COMPLEX -o cs_demo3_cl cs_cl_demo3.c cs_cl_demo.c $(CS_CL) -lm cstcov_test_cl: $(CS_CL) cstcov_test.c cs_cl_demo.c $(CC) $(CFLAGS) -DCS_LONG -DCS_COMPLEX -o cstcov_test_cl cstcov_test.c cs_cl_demo.c $(CS_CL) -lm run_convert: cs_idemo cs_ldemo - $(V) ./cs_idemo < ../Matrix/t2 - $(V) ./cs_ldemo < ../Matrix/t2 run_di: cs_demo1_di cs_demo2_di cs_demo3_di cstcov_test_di - $(V) ./cs_demo1_di < ../Matrix/t1 - $(V) ./cs_demo1_di < nil - $(V) ./cs_demo1_di < zero - $(V) ./cs_demo2_di < nil - $(V) ./cs_demo2_di < zero - $(V) ./cs_demo2_di < ../Matrix/t1 - $(V) ./cs_demo2_di < ../Matrix/bcsstk01 - $(V) ./cs_demo2_di < ../Matrix/fs_183_1 - $(V) ./cs_demo2_di < ../Matrix/west0067 - $(V) ./cs_demo2_di < ../Matrix/lp_afiro - $(V) ./cs_demo2_di < ../Matrix/ash219 - $(V) ./cs_demo2_di < ../Matrix/mbeacxc - $(V) ./cs_demo2_di < ../Matrix/bcsstk16 - $(V) ./cs_demo2_di < ../Matrix/ibm32a - $(V) ./cs_demo2_di < ../Matrix/ibm32b - $(V) ./cs_demo3_di < nil - $(V) ./cs_demo3_di < ../Matrix/bcsstk01 - $(V) ./cs_demo3_di < ../Matrix/bcsstk16 - $(V) ./cstcov_test_di nil > test_di_nil.out - $(V) ./cstcov_test_di zero > test_di_zero.out - $(V) ./cstcov_test_di ../Matrix/t1 > test_di_t1.out - $(V) ./cstcov_test_di ../Matrix/bcsstk01 > test_di_k1.out - $(V) ./cstcov_test_di ../Matrix/fs_183_1 > test_di_fs.out - $(V) ./cstcov_test_di ../Matrix/west0067 > test_di_we.out - $(V) ./cstcov_test_di ../Matrix/ash219 > test_di_ash.out - $(V) ./cstcov_test_di ../Matrix/lp_afiro > test_di_afiro.out run_dl: cs_demo1_dl cs_demo2_dl cs_demo3_dl cstcov_test_dl - $(V) ./cs_demo1_dl < ../Matrix/t1 - $(V) ./cs_demo1_dl < nil - $(V) ./cs_demo1_dl < zero - $(V) ./cs_demo2_dl < nil - $(V) ./cs_demo2_dl < zero - $(V) ./cs_demo2_dl < ../Matrix/t1 - $(V) ./cs_demo2_dl < ../Matrix/bcsstk01 - $(V) ./cs_demo2_dl < ../Matrix/fs_183_1 - $(V) ./cs_demo2_dl < ../Matrix/west0067 - $(V) ./cs_demo2_dl < ../Matrix/lp_afiro - $(V) ./cs_demo2_dl < ../Matrix/ash219 - $(V) ./cs_demo2_dl < ../Matrix/mbeacxc - $(V) ./cs_demo2_dl < ../Matrix/bcsstk16 - $(V) ./cs_demo2_dl < ../Matrix/ibm32a - $(V) ./cs_demo2_dl < ../Matrix/ibm32b - $(V) ./cs_demo3_dl < nil - $(V) ./cs_demo3_dl < ../Matrix/bcsstk01 - $(V) ./cs_demo3_dl < ../Matrix/bcsstk16 - $(V) ./cstcov_test_dl nil > test_dl_nil.out - $(V) ./cstcov_test_dl zero > test_dl_zero.out - $(V) ./cstcov_test_dl ../Matrix/t1 > test_dl_t1.out - $(V) ./cstcov_test_dl ../Matrix/bcsstk01 > test_dl_k1.out - $(V) ./cstcov_test_dl ../Matrix/fs_183_1 > test_dl_fs.out - $(V) ./cstcov_test_dl ../Matrix/west0067 > test_dl_we.out - $(V) ./cstcov_test_dl ../Matrix/ash219 > test_dl_ash.out - $(V) ./cstcov_test_dl ../Matrix/lp_afiro > test_dl_afiro.out run_ci: cs_demo1_ci cs_demo2_ci cs_demo3_ci cstcov_test_ci - $(V) ./cs_demo1_ci < ../Matrix/t2 - $(V) ./cs_demo2_ci < ../Matrix/t2 - $(V) ./cs_demo1_ci < czero - $(V) ./cs_demo2_ci < czero - $(V) ./cs_demo1_ci < ../Matrix/t3 - $(V) ./cs_demo2_ci < ../Matrix/t3 - $(V) ./cs_demo1_ci < ../Matrix/t4 - $(V) ./cs_demo2_ci < ../Matrix/t4 - $(V) ./cs_demo2_ci < ../Matrix/c_west0067 - $(V) ./cs_demo2_ci < ../Matrix/c_mbeacxc - $(V) ./cs_demo2_ci < ../Matrix/c_ibm32a - $(V) ./cs_demo2_ci < ../Matrix/c_ibm32b - $(V) ./cs_demo2_ci < ../Matrix/young1c - $(V) ./cs_demo2_ci < ../Matrix/qc324 - $(V) ./cs_demo2_ci < ../Matrix/neumann - $(V) ./cs_demo2_ci < ../Matrix/c4 - $(V) ./cs_demo3_ci < ../Matrix/c4 - $(V) ./cs_demo2_ci < ../Matrix/mhd1280b - $(V) ./cs_demo3_ci < ../Matrix/mhd1280b - $(V) ./cstcov_test_ci ../Matrix/t2 > test_ci_t2.out - $(V) ./cstcov_test_ci ../Matrix/young1c > test_ci_young1c.out - $(V) ./cstcov_test_ci ../Matrix/qc324 > test_ci_qc324.out - $(V) ./cstcov_test_ci ../Matrix/neumann > test_ci_neumann.out - $(V) ./cstcov_test_ci ../Matrix/mhd1280b > test_ci_mhd1280b.out run_cl: cs_demo1_cl cs_demo2_cl cs_demo3_cl cstcov_test_cl - $(V) ./cs_demo1_cl < ../Matrix/t2 - $(V) ./cs_demo2_cl < ../Matrix/t2 - $(V) ./cs_demo1_cl < czero - $(V) ./cs_demo2_cl < czero - $(V) ./cs_demo1_cl < ../Matrix/t3 - $(V) ./cs_demo2_cl < ../Matrix/t3 - $(V) ./cs_demo1_cl < ../Matrix/t4 - $(V) ./cs_demo2_cl < ../Matrix/t4 - $(V) ./cs_demo2_cl < ../Matrix/c_west0067 - $(V) ./cs_demo2_cl < ../Matrix/c_mbeacxc - $(V) ./cs_demo2_cl < ../Matrix/c_ibm32a - $(V) ./cs_demo2_cl < ../Matrix/c_ibm32b - $(V) ./cs_demo2_cl < ../Matrix/young1c - $(V) ./cs_demo2_cl < ../Matrix/qc324 - $(V) ./cs_demo2_cl < ../Matrix/neumann - $(V) ./cs_demo2_cl < ../Matrix/c4 - $(V) ./cs_demo3_cl < ../Matrix/c4 - $(V) ./cs_demo2_cl < ../Matrix/mhd1280b - $(V) ./cs_demo3_cl < ../Matrix/mhd1280b - $(V) ./cstcov_test_cl ../Matrix/t2 > test_cl_t2.out - $(V) ./cstcov_test_cl ../Matrix/young1c > test_cl_young1c.out - $(V) ./cstcov_test_cl ../Matrix/qc324 > test_cl_qc324.out - $(V) ./cstcov_test_cl ../Matrix/neumann > test_cl_neumann.out - $(V) ./cstcov_test_cl ../Matrix/mhd1280b > test_cl_mhd1280b.out readhb: readhb.f f77 -o readhb readhb.f readhb.f: - ln -s ../Demo/readhb.f clean: rm -f *.o *.bbg *.da *.gcov *.gcda *.gcno purge: distclean distclean: clean rm -f readhb *.out *.a cov.sort rm -f cs_demo1_di cs_demo2_di cs_demo3_di cstcov_test_di rm -f cs_demo1_dl cs_demo2_dl cs_demo3_dl cstcov_test_dl rm -f cs_demo1_ci cs_demo2_ci cs_demo3_ci cstcov_test_ci rm -f cs_demo1_cl cs_demo2_cl cs_demo3_cl cstcov_test_cl rm -f cs_idemo cs_ldemo rm -f cs_*.c rm -f cs*_di.c cs*_dl.c cs*_ci.c cs*_cl.c SuiteSparse/CXSparse_newfiles/Tcov/czero0000644001170100242450000000001010376373611017311 0ustar davisfac0 0 0 0 SuiteSparse/CXSparse_newfiles/Tcov/README.txt0000644001170100242450000000131210376376004017747 0ustar davisfacCXSparse/Tcov: comprehensive test coverage for CXSparse. Requires Linux. Type "make" to compile, and then "make run" to run the tests. The test coverage is in cover.out. The test output is printed on stdout, except for cs_test (which prints its output in various *.out files). If the test is successful, the last line printed should be "statements not yet tested: 0", and all printed residuals should be small. Note that you will get warnings about unused parameters for some functions. These warnings can be safely ignored. They are parameters for functions that are passed to cs_fkeep, and all functions used in this manner must have the same calling sequence, even if some of the parameters are not used. SuiteSparse/CXSparse_newfiles/Tcov/cstcov_malloc_test.c0000644001170100242450000000171110473440334022303 0ustar davisfac#include "cstcov_malloc_test.h" int malloc_count = INT_MAX ; /* wrapper for malloc */ void *cs_malloc (CS_INT n, size_t size) { if (--malloc_count < 0) return (NULL) ; /* pretend to fail */ return (malloc (CS_MAX (n,1) * size)) ; } /* wrapper for calloc */ void *cs_calloc (CS_INT n, size_t size) { if (--malloc_count < 0) return (NULL) ; /* pretend to fail */ return (calloc (CS_MAX (n,1), size)) ; } /* wrapper for free */ void *cs_free (void *p) { if (p) free (p) ; /* free p if it is not already NULL */ return (NULL) ; /* return NULL to simplify the use of cs_free */ } /* wrapper for realloc */ void *cs_realloc (void *p, CS_INT n, size_t size, CS_INT *ok) { void *pnew ; *ok = 0 ; if (--malloc_count < 0) return (p) ; /* pretend to fail */ pnew = realloc (p, CS_MAX (n,1) * size) ; /* realloc the block */ *ok = (pnew != NULL) ; return ((*ok) ? pnew : p) ; /* return original p if failure */ } SuiteSparse/CXSparse_newfiles/Tcov/cstcov_malloc_test.h0000644001170100242450000000020410473440334022304 0ustar davisfac#include "cs.h" #define malloc_count CS_NAME (_malloc_count) #ifndef EXTERN #define EXTERN extern #endif EXTERN int malloc_count ; SuiteSparse/CXSparse_newfiles/MATLAB/0000755001170100242450000000000010712370325016273 5ustar davisfacSuiteSparse/CXSparse_newfiles/MATLAB/Demo/0000755001170100242450000000000010620375072017161 5ustar davisfacSuiteSparse/CXSparse_newfiles/MATLAB/Demo/Contents.m0000644001170100242450000000053410620375072021136 0ustar davisfac% CXSparse MATLAB demos. % % cs_demo - run all CXSparse demos. % cs_demo1 - MATLAB version of the CSparse/Demo/cs_demo1.c program. % cs_demo2 - MATLAB version of the CSparse/Demo/cs_demo2.c program. % cs_demo3 - MATLAB version of the CSparse/Demo/cs_demo3.c program. % Example: % help cs_demo % Copyright 2006-2007, Timothy A. Davis SuiteSparse/CXSparse_newfiles/MATLAB/Demo/cs_demo.m0000644001170100242450000000206410620723666020760 0ustar davisfacfunction cs_demo (do_pause, matrixpath) %CS_DEMO run all CXSparse demos. % cs_demo(0) will run all demos without pausing. % % Example: % cs_demo % See also: cs_demo1, cs_demo2, cs_demo3 % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse help cs_demo if (nargin < 1) do_pause = 1 ; end if (nargin < 2) matrixpath = [] ; end figure (1) clf fprintf ('\n\n-------------------------------------------------------\n') ; help cs_demo1 ; cs_demo1 (matrixpath) ; fprintf ('\n\n-------------------------------------------------------\n') ; help cs_demo2 cs_demo2 (do_pause, matrixpath) ; fprintf ('\n\n-------------------------------------------------------\n') ; help cs_demo3 cs_demo3 (do_pause, matrixpath) ; fprintf ('\n\n-------------------------------------------------------\n') ; help ex_1 ex_1 fprintf ('\n\n-------------------------------------------------------\n') ; help ex2 ex2 fprintf ('\n\n-------------------------------------------------------\n') ; help ex3 ex3 fprintf ('\nAll CXSparse demos finished.\n') ; SuiteSparse/CXSparse_newfiles/MATLAB/Demo/README.txt0000644001170100242450000000010510571365661020663 0ustar davisfacDemo for MATLAB interface for CXSparse. See Contents.m for details. SuiteSparse/CXSparse_newfiles/MATLAB/Test/0000755001170100242450000000000010710651265017215 5ustar davisfacSuiteSparse/CXSparse_newfiles/MATLAB/Test/cs_sparse2_mex.c0000644001170100242450000000276610710251214022277 0ustar davisfac#include "cs_mex.h" /* A = cs_sparse2 (i,j,x), removing duplicates and numerically zero entries, * and returning A sorted (test cs_entry) */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT k, m, n, nz, *Ti, *Tj ; if (nargout > 1 || nargin != 3) { mexErrMsgTxt ("Usage: A = cs_sparse2(i,j,x)") ; } nz = mxGetM (pargin [0]) ; Ti = cs_dl_mex_get_int (nz, pargin [0], &m, 1) ; Tj = cs_dl_mex_get_int (nz, pargin [1], &n, 1) ; cs_mex_check (1, nz, 1, 0, 0, 1, pargin [2]) ; if (mxIsComplex (pargin [2])) { #ifdef NCOMPLEX mexErrMsgTxt ("complex case not supported") ; #else cs_complex_t *Tx ; cs_cl *A, *C, *T ; Tx = cs_cl_mex_get_double (nz, pargin [2]) ; T = cs_cl_spalloc (n, m, 1, 1, 1) ; for (k = 0 ; k < nz ; k++) { cs_cl_entry (T, Tj [k], Ti [k], Tx [k]) ; } C = cs_cl_compress (T) ; cs_cl_spfree (T) ; cs_cl_dupl (C) ; cs_cl_dropzeros (C) ; A = cs_cl_transpose (C, -1) ; cs_cl_spfree (C) ; pargout [0] = cs_cl_mex_put_sparse (&A) ; cs_free (Tx) ; #endif } else { double *Tx ; cs_dl *A, *C, *T ; Tx = mxGetPr (pargin [2]) ; T = cs_dl_spalloc (n, m, 1, 1, 1) ; for (k = 0 ; k < nz ; k++) { cs_dl_entry (T, Tj [k], Ti [k], Tx [k]) ; } C = cs_dl_compress (T) ; cs_dl_spfree (T) ; cs_dl_dupl (C) ; cs_dl_dropzeros (C) ; A = cs_dl_transpose (C, 1) ; cs_dl_spfree (C) ; pargout [0] = cs_dl_mex_put_sparse (&A) ; } cs_free (Ti) ; cs_free (Tj) ; } SuiteSparse/CXSparse_newfiles/MATLAB/Test/cs_rowcnt_mex.c0000644001170100242450000000521710571353755022250 0ustar davisfac/* Compute the row counts of the Cholesky factor L of the matrix A. Uses * the lower triangular part of A. */ #include "cs_mex.h" static void firstdesc (CS_INT n, CS_INT *parent, CS_INT *post, CS_INT *first, CS_INT *level) { CS_INT len, i, k, r, s ; for (i = 0 ; i < n ; i++) first [i] = -1 ; for (k = 0 ; k < n ; k++) { i = post [k] ; /* node i of etree is kth postordered node */ len = 0 ; /* traverse from i towards the root */ for (r = i ; r != -1 && first [r] == -1 ; r = parent [r], len++) first [r] = k ; len += (r == -1) ? (-1) : level [r] ; /* root node or end of path */ for (s = i ; s != r ; s = parent [s]) level [s] = len-- ; } } /* return rowcount [0..n-1] */ static CS_INT *rowcnt (cs_dl *A, CS_INT *parent, CS_INT *post) { CS_INT i, j, k, len, s, p, jprev, q, n, sparent, jleaf, *Ap, *Ai, *maxfirst, *ancestor, *prevleaf, *w, *first, *level, *rowcount ; n = A->n ; Ap = A->p ; Ai = A->i ; /* get A */ w = cs_dl_malloc (5*n, sizeof (CS_INT)) ; /* get workspace */ ancestor = w ; maxfirst = w+n ; prevleaf = w+2*n ; first = w+3*n ; level = w+4*n ; rowcount = cs_dl_malloc (n, sizeof (CS_INT)) ; /* allocate result */ firstdesc (n, parent, post, first, level) ; /* find first and level */ for (i = 0 ; i < n ; i++) { rowcount [i] = 1 ; /* count the diagonal of L */ prevleaf [i] = -1 ; /* no previous leaf of the ith row subtree */ maxfirst [i] = -1 ; /* max first[j] for node j in ith subtree */ ancestor [i] = i ; /* every node is in its own set, by itself */ } for (k = 0 ; k < n ; k++) { j = post [k] ; /* j is the kth node in the postordered etree */ for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; q = cs_dl_leaf (i, j, first, maxfirst, prevleaf, ancestor, &jleaf) ; if (jleaf) rowcount [i] += (level [j] - level [q]) ; } if (parent [j] != -1) ancestor [j] = parent [j] ; } cs_dl_free (w) ; return (rowcount) ; } void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs_dl *A, Amatrix ; double *x ; CS_INT i, m, n, *parent, *post, *rowcount ; if (nargout > 1 || nargin != 3) { mexErrMsgTxt ("Usage: r = cs_rowcnt(A,parent,post)") ; } /* get inputs */ A = cs_dl_mex_get_sparse (&Amatrix, 1, 0, pargin [0]) ; n = A->n ; parent = cs_dl_mex_get_int (n, pargin [1], &i, 0) ; post = cs_dl_mex_get_int (n, pargin [2], &i, 1) ; rowcount = rowcnt (A, parent, post) ; pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ; x = mxGetPr (pargout [0]) ; for (i = 0 ; i < n ; i++) x [i] = rowcount [i] ; cs_dl_free (rowcount) ; } SuiteSparse/CXSparse_newfiles/MATLAB/Test/Makefile0000644001170100242450000000235610617732311020661 0ustar davisfacinclude ../../../UFconfig/UFconfig.mk MX = $(MEX) -DCS_LONG AR = ar cr RANLIB = ranlib I = -I../../Include -I../../../UFconfig -I../CSparse all: cs_sparse2.mexglx \ cs_ipvec.mexglx \ cs_pvec.mexglx \ cs_reach.mexglx \ cs_maxtransr.mexglx \ cs_reachr.mexglx \ cs_rowcnt.mexglx \ cs_frand.mexglx mexcsparse: ( cd ../CSparse ; make mexcsparse.a ) cs_ipvec.mexglx: cs_ipvec_mex.c mexcsparse $(MX) -output cs_ipvec $< $(I) ../CSparse/mexcsparse.a cs_pvec.mexglx: cs_pvec_mex.c mexcsparse $(MX) -output cs_pvec $< $(I) ../CSparse/mexcsparse.a cs_reach.mexglx: cs_reach_mex.c mexcsparse $(MX) -output cs_reach $< $(I) ../CSparse/mexcsparse.a cs_sparse2.mexglx: cs_sparse2_mex.c mexcsparse $(MX) -output cs_sparse2 $< $(I) ../CSparse/mexcsparse.a cs_maxtransr.mexglx: cs_maxtransr_mex.c mexcsparse $(MX) -output cs_maxtransr $< $(I) ../CSparse/mexcsparse.a cs_reachr.mexglx: cs_reachr_mex.c mexcsparse $(MX) -output cs_reachr $< $(I) ../CSparse/mexcsparse.a cs_rowcnt.mexglx: cs_rowcnt_mex.c mexcsparse $(MX) -output cs_rowcnt $< $(I) ../CSparse/mexcsparse.a cs_frand.mexglx: cs_frand_mex.c mexcsparse $(MX) -output cs_frand $< $(I) ../CSparse/mexcsparse.a clean: rm -f *.o distclean: clean rm -f *.mex* *.a cs_cl_*.c purge: distclean SuiteSparse/CXSparse_newfiles/MATLAB/Test/cholupdown.m0000644001170100242450000000236210620701365021555 0ustar davisfacfunction L = cholupdown (Lold, sigma, w) %CHOLUPDOWN Cholesky update/downdate (Bischof, Pan, and Tang method) % This version only works for the real case. See chol_updown2 for % a code that handles both the real and complex cases. % Example: % L = cholupdown (Lold, sigma, w) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse beta = 1 ; n = size (Lold,1) ; L = Lold ; % x = weros (n,1) ; % worig = w ; for k = 1:n alpha = w(k) / L(k,k) ; beta_new = sqrt (beta^2 + sigma*alpha^2) ; gamma = alpha / (beta_new * beta) ; if (sigma < 0) % downdate bratio = beta_new / beta ; w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ; L (k,k) = bratio * L (k,k) ; L (k+1:n,k) = bratio * L (k+1:n,k) - gamma*w(k+1:n) ; else % update bratio = beta / beta_new ; % wold = w (k+1:n) ; % w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ; % L (k ,k) = bratio * L (k ,k) + gamma*w(k) ; % L (k+1:n,k) = bratio * L (k+1:n,k) + gamma*wold ; L (k,k) = bratio * L (k,k) + gamma*w(k) ; for i = k+1:n wold = w (i) ; w (i) = w (i) - alpha * L (i,k) ; L (i,k) = bratio * L (i,k) + gamma*wold ; end end w (k) = alpha ; beta = beta_new ; end % norm (w-(Lold\worig)) SuiteSparse/CXSparse_newfiles/MATLAB/Test/cs_reachr_mex.c0000644001170100242450000000332010571353322022157 0ustar davisfac#include "cs_mex.h" /* find nonzero pattern of x=L\sparse(b). L must be sparse and lower * triangular. b must be a sparse vector. */ static void dfsr (CS_INT j, const cs *L, CS_INT *top, CS_INT *xi, CS_INT *w) { CS_INT p ; w [j] = 1 ; /* mark node j */ for (p = L->p [j] ; p < L->p [j+1] ; p++) /* for each i in L(:,j) */ { if (w [L->i [p]] != 1) /* if i is unmarked */ { dfsr (L->i [p], L, top, xi, w) ; /* start a dfs at i */ } } xi [--(*top)] = j ; /* push j onto the stack */ } /* w [0..n-1] == 0 on input, <= 1 on output. size n */ static CS_INT reachr (const cs *L, const cs *B, CS_INT *xi, CS_INT *w) { CS_INT p, n = L->n ; CS_INT top = n ; /* stack is empty */ for (p = B->p [0] ; p < B->p [1] ; p++) /* for each i in pattern of b */ { if (w [B->i [p]] != 1) /* if i is unmarked */ { dfsr (B->i [p], L, &top, xi, w) ; /* start a dfs at i */ } } return (top) ; /* return top of stack */ } void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs_dl Lmatrix, Bmatrix, *L, *B ; double *x ; CS_INT i, j, top, *xi ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_reachr(L,b)") ; } /* get inputs */ L = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ; cs_mex_check (0, L->n, 1, 0, 1, 1, pargin [1]) ; xi = cs_dl_calloc (2*L->n, sizeof (CS_INT)) ; top = reachr (L, B, xi, xi + L->n) ; pargout [0] = mxCreateDoubleMatrix (L->n - top, 1, mxREAL) ; x = mxGetPr (pargout [0]) ; for (j = 0, i = top ; i < L->n ; i++, j++) x [j] = xi [i] ; cs_free (xi) ; } SuiteSparse/CXSparse_newfiles/MATLAB/Test/Contents.m0000644001170100242450000001213510620375605021173 0ustar davisfac% CXSparse testing and "textbook" MATLAB M-files and mexFunctions, related to % CXSparse but not a part of CXSparse itself. % % M-files: % % chol_downdate - downdate a Cholesky factorization. % chol_left - left-looking Cholesky factorization. % chol_left2 - left-looking Cholesky factorization, more details. % chol_right - right-looking Cholesky factorization. % chol_super - left-looking "supernodal" Cholesky factorization. % chol_up - up-looking Cholesky factorization. % chol_update - update a Cholesky factorization. % chol_updown - update or downdate a Cholesky factorization. % chol_updown2 - Cholesky update/downdate (real and complex) % cond1est - 1-norm condition estimate. % cs_fiedler - the Fiedler vector of a connected graph. % givens2 - find a Givens rotation. % house - find a Householder reflection. % lu_left - left-looking LU factorization. % lu_right - right-looking LU factorization. % lu_rightp - right-looking LU factorization, with partial pivoting. % lu_rightpr - recursive right-looking LU, with partial pivoting. % lu_rightr - recursive right-looking LU. % norm1est - 1-norm estimate. % qr_givens - Givens-rotation QR factorization. % qr_givens_full - Givens-rotation QR factorization, for full matrices. % qr_left - left-looking Householder QR factorization. % qr_right - right-looking Householder QR factorization. % % mexFunctions: % % cs_frand - generate a random finite-element matrix % cs_ipvec - x(p)=b % cs_maxtransr - recursive maximum matching algorithm % cs_pvec - x=b(p) % cs_reach - non-recursive reach (interface to CSparse cs_reach) % cs_reachr - recursive reach (interface to CSparse cs_reachr) % cs_rowcnt - row counts for sparse Cholesky % cs_sparse2 - same as cs_sparse, to test cs_entry function % % Extensive test functions, not for normal usage: % % check_if_same - check if two inputs are identical or not % choldn - Cholesky downdate % cholup - Cholesky update, using Given's rotations % cholupdown - Cholesky update/downdate (Bischof, Pan, and Tang method) % cs_q1 - construct Q from Householder vectors % cs_test_make - compiles the CSparse, Demo, and Test mexFunctions. % dmperm_test - test cs_dmperm % chol_example - simple Cholesky factorization example % etree_sample - construct a sample etree and symbolic factorization % gqr3 - QR factorization, based on Givens rotations % happly - apply Householder reflection to a vector % hmake1 - construct a Householder reflection % mynormest1 - estimate norm(A,1), using LU factorization (L*U = P*A*Q). % myqr - QR factorization using Householder reflections % another_colormap - try another color map % cspy_test - test cspy and cs_dmspy % qr2 - QR factorization based on Householder reflections % sample_colormap - try a colormap for use in cspy % signum - compute and display the sign of a column vector x % sqr_example - test cs_sqr % dmspy_test - test cspy, cs_dmspy, and cs_dmperm % test_qr - test various QR factorization methods % test_randperms - test random permutations % testh - test Householder reflections % test_qr1 - test QR factorizations % test_qrsol - test cs_qrsol % test_sep - test cs_sep, and compare with Gilbert's meshpart vtxsep % testall - test all CSparse functions (run tests 1 to 28 below) % test1 - test cs_transpose, cs_gaxpy, cs_sparse, cs_sparse2 % test2 - test cs_sparse, cs_permute, cs_pvec, cs_ipvec, cs_symperm % test3 - test cs_lsolve, cs_ltsolve, cs_usolve, cs_chol % test4 - test cs_multiply % test5 - test cs_add % test6 - test cs_reach, cs_reachr, cs_lsolve, cs_usolve % test7 - test cs_lu % test8 - test cs_cholsol, cs_lusol % test9 - test cs_qr % test10 - test cs_qr % test11 - test cs_rowcnt % test12 - test cs_qr and compare with svd % test13 - test cs_counts, cs_etree % test14 - test cs_droptol % test15 - test cs_amd % test16 - test cs_amd % test17 - test cs_qr, cs_qright, cs_q1, cs_qrleft, cs_qrsol % test18 - test iterative refinement after backslash % test19 - test cs_dmperm, cs_maxtransr, cs_dmspy, cs_scc, cspy % test20 - test chol_updown2 % test21 - test cs_updown, chol_updown2 % test22 - test cond1est % test23 - test cs_dmspy % test24 - test cs_fielder % test25 - test cs_nd % test26 - test cs_dmsol and cs_dmspy % test27 - test cs_qr, cs_utsolve, cs_qrsol % test28 - test cs_randperm, cs_dmperm % Example: % help chol_update % Copyright 2006-2007, Timothy A. Davis SuiteSparse/CXSparse_newfiles/MATLAB/Test/test10.m0000644001170100242450000000371610710254556020524 0ustar davisfacfunction test10 %TEST10 test cs_qr % % Example: % test10 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) ; % f = 185 ; % f = 449 ; clf for trials = 1:100 m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; d = 0.1 * rand (1) ; A = sprandn (m, n, d) ; [m n] = size (A) ; if (m < n) A = A' ; end [m n] = size (A) ; sp = sprank (A) ; % if (sp < n) % continue ; % end for cmplex = 0:double(~ispc) if (cmplex) A = A + 1i * sprand (A) * norm (A,1) / 10 ; end Aorig = A ; % A = A (:, colamd (A)) ; if (cmplex) tic ; R = chol (A'*A + speye (n)) ; t1 = toc ; else tic ; R = qr (A) ; t1 = toc ; end % tic ; % [Q,R] = qr (A) ; % t1 = toc ; [c,h,parent] = symbfact (A, 'col') ; %#ok rnz = sum (c) ; %#ok tic ; [V2,Beta2,p,R2] = cs_qr (sparse(A)) ; t2 = toc ; C = A ; m2 = size (V2,1) ; if (m2 > m) C = [A ; sparse(m2-m, n)] ; end C = C (p,:) ; [H1,R1] = myqr (C) ; err1 = norm (R1-R2,1) / norm (R1) ; disp ('err1 = ') ; disp (err1) ; % [svd(A) svd(R1) svd(full(R2))] s1 = svd (full (A)) ; s2 = svd (full (R2)) ; if (n > 0) err2 = norm (s1 - s2) / s1 (1) ; disp ('err2 = ') ; disp (err2) ; else err2 = 0 ; end fprintf ('%10.6f %10.6f cs speedup %8.3f sprank %d vs %d\n', t1, t2, t1/t2, sp, n) ; % H2 = full (H2) % R2 = full (R2) subplot (2,4,1) ; spy (A) ; title ('A colamd') ; subplot (2,4,4) ; spy (Aorig) ; title ('Aorig') ; subplot (2,4,2) ; spy (C) ; title ('A rperm') ; subplot (2,4,5) ; spy (abs(R2)>0) ; title ('spqr R, no zeros') ; subplot (2,4,6) ; spy (R) ; title ('matlab R') ; subplot (2,4,7) ; spy (R2) ; title ('spqr R') ; subplot (2,4,8) ; spy (V2) ; title ('spqr H') ; drawnow if (err2 > 1e-9) error ('!') ; end if (m2 > m) fprintf ('added %d rows, sprank %d n %d\n', m2-m, sp, n) ; end end end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test11.m0000644001170100242450000000162510710651265020520 0ustar davisfacfunction test11 %TEST11 test cs_rowcnt % % Example: % test11 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:200) ; for i = f Prob = UFget (i, index) ; disp (Prob) ; A = Prob.A ; [m n] = size (A) ; if (m ~= n) continue end A = spones (A) ; A = A+A' + speye(n) ; if (~ispc) if (rand ( ) > .5) A = A + 1i * sprand (A) ; end end [cc h pa po R] = symbfact (A) ; rc1 = full (sum (R)) ; rc2 = cs_rowcnt (A, pa, po) ; if (any (rc1 ~= rc2)) error ('!') ; end try p = amd (A) ; catch p = symamd (A) ; end A = A (p,p) ; [cc h pa po R] = symbfact (A) ; rc1 = full (sum (R)) ; rc2 = cs_rowcnt (A, pa, po) ; if (any (rc1 ~= rc2)) error ('!') ; end end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test12.m0000644001170100242450000000154210710254563020517 0ustar davisfacfunction test12 %TEST12 test cs_qr and compare with svd % % Example: % test12 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse fprintf ('test 12\n') ; rand ('state',0) ; % A = rand (3,4) for trial = 1:100 m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; d = .1 * rand (1) ; A = sprandn (m,n,d) ; if (m < n) continue ; end if (m == 0 | n == 0) %#ok continue ; end for cmplex = 0:double(~ispc) if (cmplex) A = A + 1i * sprand (A) ; end fprintf ('m %d n %d nnz %d\n', m, n, nnz(A)) ; [V,Beta,p,R] = cs_qr (A) ; s1 = svd (full (A)) ; s2 = svd (full (R)) ; s2 = s2 (1:length(s1)) ; err = norm (s1-s2) ; if (length (s1) > 1) err = err / s1 (1) ; end fprintf ('err %g\n', err) ; if (err > 1e-12) error ('!') ; end end end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test13.m0000644001170100242450000000334610710252076020521 0ustar davisfacfunction test13 %TEST13 test cs_counts, cs_etree % % Example: % test13 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions randn ('state',0) ; rand ('state',0) ; for trial = 1:100 m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; d = .1 * rand (1) ; A = sprandn (n,n,d) ; C = sprandn (m,n,d) ; A = A+A' ; fprintf ('m %4d n %4d nnz(A) %6d nnz(C) %6d\n', m, n, nnz(A), nnz(C)) ; if (~ispc) if (rand ( ) > .5) A = A + 1i * sprand (A) ; end end [p1,po1] = etree (A) ; [p2,po2] = cs_etree (A) ; [p3,po3] = cs_etree (A, 'sym') ; % po2 = cs_post (p2) ; check_if_same (p1,p2) ; check_if_same (po1,po2) ; check_if_same (p1,p3) ; check_if_same (po1,po3) ; c1 = symbfact (A) ; c2 = cs_counts (A) ; % A-A' check_if_same (c1,c2) ; c2 = cs_counts (triu (A)) ; check_if_same (c1,c2) ; % pause p0 = etree (A, 'col') ; % p1 = etree2 (A, 'col') ; % CHOLMOD p2 = cs_etree (A, 'col') ; if (~isempty (A)) check_if_same (p0,p2) ; end p0 = etree (C, 'col') ; % p1 = etree2 (C, 'col') ; % CHOLMOD p2 = cs_etree (C, 'col') ; if (~isempty (C)) check_if_same (p0,p2) ; end % find etree of A'A, and postorder it [m n] = size (A) ; %#ok % full (A) [cp0 cpo0] = etree (A, 'col') ; % [cp1 cpo1] = etree2 (A, 'col') ; % CHOLMOD [cp2 cpo2] = cs_etree (A, 'col') ; % cpo2 = cs_post (cp2) ; check_if_same (cp0, cp2) ; check_if_same (cpo0, cpo2) ; c0 = symbfact (A, 'col') ; % c1 = symbfact2 (A, 'col') ; % CHOLMOD c2 = cs_counts (A, 'col') ; check_if_same (c0, c2) ; end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test14.m0000644001170100242450000000153010710254565020520 0ustar davisfacfunction test14 %TEST14 test cs_droptol % % Example: % test14 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) ; for trial = 1:100 m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; d = 0.1*rand (1) ; A = sprandn (m,n,d) ; [i j x] = find (A) ; A = sparse (i,j,2*x-1) ; fprintf ('test14 m %3d n %3d nz %d\n', m, n, nnz (A)) ; for cmplex = 0:double(~ispc) if (cmplex) A = A + 1i * sparse (i,j,2*rand(size(x))-1) ; end % using CSparse tol = 0.5 ; B = cs_droptol (A, tol) ; % using MATLAB C = A .* (abs (A) > tol) ; % [m n] = size (A) ; % s = abs (A) > tol ; % [i j] = find (s) ; % x = A (find (s)) ; % A = sparse (i, j, x, m, n) ; if (norm (C-B,1) > 0) error ('!') ; end end end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test15.m0000644001170100242450000000177410710252146020524 0ustar davisfacfunction test15 %TEST15 test cs_amd % % Example: % test15 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) ; randn ('state', 0) ; clf for trials = 1:100 n = fix (200 * rand (1)) ; d = 0.05 * rand (1) ; A = sprandn (n, n, d) ; % add a randomly placed dense column k = fix (n * rand (1)) ; k = max (1, k) ; k = min (n, k) ; if (n > 0) A (:,k) = 1 ; end if (~ispc) if (rand ( ) > .5) A = A + 1i * sprand (A) ; end end try p0 = amd (A) ; catch p0 = symamd (A) ; end p1 = cs_amd (A) ; if (any (sort (p1) ~= 1:n)) error ('not perm!') ; end C = A+A' + speye (n) ; lnz0 = sum (symbfact (C (p0,p0))) ; lnz1 = sum (symbfact (C (p1,p1))) ; subplot (1,3,1) ; spy (C) subplot (1,3,2) ; spy (C (p0,p0)) subplot (1,3,3) ; spy (C (p1,p1)) fprintf ('n %4d nz %6d lnz %6d %6d\n', n, nnz(A), lnz0, lnz1) ; drawnow end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test16.m0000644001170100242450000000357110710252163020521 0ustar davisfacfunction test16 %TEST16 test cs_amd % % Example: % test16 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) ; randn ('state', 0) ; clf index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:200) ; skip = 811 ; % f = 719 for i = f if (any (i == skip)) continue end Prob = UFget (i) ; A = spones (Prob.A) ; Aorig = A ; [m n] = size (A) ; if (m < n) A = A' ; end [m n] = size (A) ; if (m ~= n) A = A'*A ; end if (~ispc) if (rand ( ) > .5) A = A + 1i * sprand (A) ; end end fprintf ('n %4d nz %d\n', n, nnz (A)) ; try p0 = amd (A) ; catch p0 = symamd (A) ; end fprintf ('symmetric case:\n') ; p1 = cs_amd (A) ; if (any (sort (p1) ~= 1:n)) error ('not perm!') ; end C = A+A' + speye (n) ; lnz0 = sum (symbfact (C (p0,p0))) ; lnz1 = sum (symbfact (C (p1,p1))) ; subplot (2,3,1) ; spy (C) subplot (2,3,2) ; spy (C (p0,p0)) ; title ('amd') ; subplot (2,3,3) ; spy (C (p1,p1)) ; title ('csamd') ; drawnow if (lnz0 ~= lnz1) fprintf ('----------------- lnz %d %d %9.4f\n', ... lnz0, lnz1, 100*(lnz0-lnz1)/max([1 lnz0])) ; end if (1) p0 = colamd (Aorig) ; [m n] = size (Aorig) ; fprintf ('m %d n %d\n', m, n) ; fprintf ('A''A case, no dense rows (for QR):\n') ; p1 = cs_amd (Aorig, 3) ; if (any (sort (p1) ~= 1:n)) error ('not perm!') ; end subplot (2,3,4) ; spy (Aorig) subplot (2,3,5) ; spy (Aorig (:,p0)) ; title ('colamd') ; subplot (2,3,6) ; spy (Aorig (:,p1)) ; title ('cs amd(A''A)') ; lnz0 = sum (symbfact (Aorig (:,p0), 'col')) ; lnz1 = sum (symbfact (Aorig (:,p1), 'col')) ; fprintf (' A''A: %7d %7d %9.4f\n', ... lnz0, lnz1, 100*(lnz0-lnz1)/max([1 lnz0])) ; drawnow % pause end end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test17.m0000644001170100242450000000430310710252200020504 0ustar davisfacfunction test17 %TEST17 test cs_qr, cs_qright, cs_q1, cs_qrleft, cs_qrsol % % Example: % test17 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions clf rand ('state', 0) ; randn ('state', 0) ; for trials = 1:100 m = 1 + fix (10 * rand (1)) ; n = 1 + fix (10 * rand (1)) ; d = rand (1) ; % n = m ; A = sprandn (m, n, d) ; if (m < n) A = A' ; end [m n] = size (A) ; if (~ispc) if (rand ( ) > .5) A = A + 1i * sprand (A) ; end end subplot (3,4,1) ; spy (A) ; [V1, Beta1, p1, R1, q1] = cs_qr (A) ; Q1 = cs_qright (V1, Beta1, p1, speye (size (V1,1))) ; Q1b = cs_q1 (V1, Beta1, p1) ; err = norm (Q1-Q1b,1) ; disp ('err = ') ; disp (err) ; if (err > 1e-12) error ('!') ; end m2 = size (Q1,1) ; A1 = [A ; sparse(m2-m,n)] ; subplot (3,4,5) ; spy (A1 (p1,q1)) ; subplot (3,4,6) ; spy (V1) ; subplot (3,4,7) ; spy (R1) ; subplot (3,4,8) ; spy (Q1) ; [V3, Beta3, R3] = qr2 (A) ; % Q3 = cs_qmake (V3, Beta3) ; Q3 = cs_q1 (V3, Beta3) ; subplot (3,4,9) ; spy (A) ; subplot (3,4,10) ; spy (V3) ; subplot (3,4,11) ; spy (R3) ; subplot (3,4,12) ; spy (Q3) ; err1 = norm (Q1*R1 - A1(:,q1), 1) ; % err2 = norm (Q2*R2 - A (:,q2), 1) ; err3 = norm (Q3*R3 - A, 1) ; fprintf ('m %3d m2 %3d n %3d ::: %3d %6.2e %6.2e\n', ... m, m2, n, m2-m, err1, err3) ; if (err1 > 1e-12) error ('2!') ; end % if (err2 > 1e-12) % error ('!') ; % end if (err3 > 1e-12) error ('3!') ; end try % this fails if A is complex b = rand (m,1) ; [Q,R] = qr (A (:,q1)) ; x = R\(Q'*b) ; x (q1) = x ; r1 = norm (A*x-b) ; x2 = cs_qrsol (A,b) ; r2 = norm (A*x2(1:n)-b) ; qt = cs_qleft (V1, Beta1, p1, speye(size(V1,1))) ; fprintf ('Q''*A-R: %6.2e\n', norm (qt*A1(:,q1)-R1,1)) ; qtb = cs_qleft (V1, Beta1, p1, b) ; % [V1, Beta1, p1, R1, q1] = cs_qr (A) ; x3 = R1 \ qtb ; r3 = norm (A(:,q1)*x3(1:n)-b) ; fprintf ('least sq: %6.2e %6.2e %6.2e diff %6.2e %6.2e\n', ... r1, r2, r3, r1-r2, r1-r3) ; catch end drawnow % pause end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test18.m0000644001170100242450000000112110620667511020517 0ustar davisfacfunction test18 %TEST18 test iterative refinement after backslash % % Example: % test18 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:100) ; clf % f = f(1) for i = f Prob = UFget (i) ; disp (Prob) ; A = Prob.A ; [m n] = size (A) ; if (~isreal (A) | m ~= n) %#ok continue end b = rand (n,1) ; x = A\b ; r = b - A*x ; x = x + A\r ; fprintf ('\n%6.2e to %6.2e\n', norm (r), norm (b-A*x)) ; end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test19.m0000644001170100242450000000704610710252222020521 0ustar davisfacfunction test19 %TEST19 test cs_dmperm, cs_maxtransr, cs_dmspy, cs_scc, cspy % % Example: % test19 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions randn ('state', 0) ; rand ('state', 0) ; clf for trials = 1:100 m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; % d = 0.1 * rand (1) ; d = rand (1) * 4 * max (m,n) / max (m*n,1) ; A = sprandn (m,n,d) ; S = sprandn (m,m,d) + speye (m) ; if (~ispc) if (rand ( ) > .5) A = A + 1i * sprand (A) ; end if (rand ( ) > .5) S = S + 1i * sprand (S) ; end end subplot (2,3,1) ; cspy (A) ; pp = dmperm (A) ; sprnk = sum (pp > 0) ; pp2 = cs_dmperm (A) ; spr2 = sum (pp2 > 0) ; if (spr2 ~= sprnk) error ('!') end pp2 = cs_maxtransr (A) ; spr2 = sum (pp2 > 0) ; if (spr2 ~= sprnk) error ('!') end [p,q,r,s] = dmperm (A) ; C = A (p,q) ; % r % s nk = length (r) - 1 ; fprintf ('sprnk: %d m %d n %d nb: %d\n', sprnk, m, n, nk) ; subplot (2,3,2) ; hold off spy (C) hold on for k = 1:nk r1 = r(k) ; r2 = r(k+1) ; c1 = s(k) ; c2 = s(k+1) ; plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ; end [p2,q2,rr2,ss2,cp,rp] = cs_dmperm (A) ; if (min (m,n) > 0) if (length (rr2) ~= length (r)) error ('# fine blocks!') ; end end if (rp (4) - 1 ~= sprnk) rp %#ok sprnk %#ok error ('!') ; end if (any (sort (p2) ~= 1:m)) error ('p2!') ; end if (any (sort (q2) ~= 1:n)) error ('q2!') ; end if (cp (5) ~= n+1) error ('cp!') ; end if (rp (5) ~= m+1) error ('rp!') ; end C = A (p2,q2) ; subplot (2,3,3) ; cs_dmspy (A,0) ; % hold off % spy (C) ; % hold on % r1 = rp(1) ; % r2 = rp(2) ; % c1 = cp(1) ; % c2 = cp(2) ; % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ; r1 = rp(1) ; r2 = rp(2) ; c1 = cp(2) ; c2 = cp(3) ; % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ; B = C (r1:r2-1, c1:c2-1) ; if (nnz (diag (B)) ~= size (B,1)) error ('C1 diag!') ; end r1 = rp(2) ; r2 = rp(3) ; c1 = cp(3) ; c2 = cp(4) ; % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'r') ; B = C (r1:r2-1, c1:c2-1) ; if (nnz (diag (B)) ~= size (B,1)) error ('C2 diag!') ; end r1 = rp(3) ; r2 = rp(4) ; c1 = cp(4) ; c2 = cp(5) ; % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ; B = C (r1:r2-1, c1:c2-1) ; if (nnz (diag (B)) ~= size (B,1)) error ('C3 diag!') ; end r1 = rp(4) ; %#ok r2 = rp(5) ; %#ok c1 = cp(4) ; %#ok c2 = cp(5) ; %#ok % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ; if (~isempty (S)) [p1,q1,r0,s0] = dmperm (S) ; [p3,r3] = cs_scc (S) ; if (length (r3) ~= length (r0)) error ('scc size!') ; end if (any (sort (p3) ~= 1:m)) error ('scc perm!') ; end nk = length (r0)-1 ; subplot (2,3,4) ; hold off spy (S (p1,q1)) ; hold on for k = 1:nk r1 = r0(k) ; r2 = r0(k+1) ; c1 = s0(k) ; c2 = s0(k+1) ; plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ; end subplot (2,3,5) ; hold off spy (S (p3,p3)) ; hold on for k = 1:nk r1 = r3(k) ; r2 = r3(k+1) ; c1 = r3(k) ; c2 = r3(k+1) ; plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ; end end subplot (2,3,6) ; cs_dmspy (A) ; drawnow % pause end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test20.m0000644001170100242450000000175610710252311020512 0ustar davisfacfunction test20 %TEST20 test chol_updown2 % % Example: % test20 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions rand ('state', 0) ; maxerr = [0 0 0 0] ; for trials = 1:100 n = fix (100 * rand (1)) ; A = rand (n) ; if (~ispc) if (mod (trials, 2) == 0) A = A + 1i*rand(n) ; end end A1 = A*A' + n*eye (n) ; try L1 = chol (A1)' ; catch continue ; end err1 = norm (L1*L1'-A1) ; w = rand (n,1) ; A2 = A1 + w*w' ; L2 = chol (A2)' ; err2 = norm (L2*L2'-A2) ; % try an update L2b = chol_updown2 (L1, +1, w) ; err2b = norm (L2b*L2b'-A2) ; % try a downdate L1b = chol_updown2 (L2, -1, w) ; %#ok err1b = norm (L1b*L1b'-A1) ; fprintf ('%3d: %6.2e %6.2e : %6.2e %6.2e\n', n, err1, err2, err2b, err1b) ; % pause maxerr = max (maxerr, [err1 err2 err2b err1b]) ; end fprintf ('maxerr: %g\n', maxerr) ; SuiteSparse/CXSparse_newfiles/MATLAB/Test/test21.m0000644001170100242450000000360410710252335020513 0ustar davisfacfunction test21 %TEST21 test cs_updown, chol_updown2 % % Example: % test21 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions rand ('state', 0) ; randn ('state', 0) ; clf for trials = 1:100 if (trials <= 1) n = trials ; else n = 1+fix (100 * rand (1)) ; end fprintf ('n: %d\n', n) ; d = 0.1 * rand (1) ; A = sprandn (n,n,d) ; if (~ispc) if (rand ( ) > .5) A = A + 1i * sprand (A) ; end end A = A+A' + 100 * speye (n) ; try p = amd (A) ; catch p = symamd (A) ; end A = sparse (A (p,p)) ; try L = chol (A)' ; catch continue ; end parent = etree (A) ; subplot (1,3,1) ; spy (A) ; if (n > 0) subplot (1,3,2) ; treeplot (parent) ; end subplot (1,3,3) ; spy (L) ; drawnow for trials2 = 1:10 k = 1+fix (n * rand (1)) ; if (k <= 0 | k > n) %#ok k = 1 ; end w = sprandn (L (:,k)) ; Anew = A + w*w' ; Lnew = cs_updown (L, w, parent) ; err6 = norm (Lnew*Lnew' - Anew, 1) ; Lnew = cs_updown (L, w, parent, '+') ; err7 = norm (Lnew*Lnew' - Anew, 1) ; [Lnew, wnew] = chol_updown2 (L, 1, w) ; err2 = norm (Lnew*Lnew' - Anew, 1) ; err10 = norm (wnew - (L\w)) ; L3 = chol_updown2 (L, +1, w) ; err9 = norm (L3*L3' - Anew, 1) ; [L2, wnew] = chol_updown2 (Lnew, -1, w) ; err3 = norm (L2*L2' - A, 1) ; err11 = norm (wnew - (Lnew\w)) ; L2 = cs_updown (Lnew, w, parent, '-') ; err5 = norm (L2*L2' - A, 1) ; L2 = chol_updown2 (Lnew, -1, w) ; err8 = norm (L2*L2' - A, 1) ; err = max ([err2 err3 err5 err6 err7 err9 err8 err10 err11]) ; fprintf (' k %3d %6.2e\n', k, err) ; if (err > 1e-11) err2 %#ok err3 %#ok err5 %#ok err6 %#ok err7 %#ok err8 %#ok err9 %#ok err10 %#ok err11 %#ok pause end end % pause end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test22.m0000644001170100242450000000174610620667553020535 0ustar davisfacfunction test22 %TEST22 test cond1est % % Example: % test22 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:200) ; clf % f = f(1) nprob = length (f) ; C1 = zeros (nprob,1) ; C2 = zeros (nprob,1) ; C3 = zeros (nprob,1) ; for k = 1:length (f) i = f (k) ; Prob = UFget (i) ; disp (Prob) ; A = Prob.A ; [m n] = size (A) ; if (~isreal (A) | m ~= n) %#ok continue end c1 = condest (A) ; c2 = cond1est (A) ; if (c1 == c2) err = 0 ; else err = (c1-c2)/max(1,c1) ; end c3 = cond (full (A), 1) ; fprintf ('%10.4e %10.4e (%10.4e) : %10.4e\n', c1, c2, c3, err) ; C1 (k) = c1 ; C2 (k) = c2 ; C3 (k) = c3 ; subplot (1,2,1) ; loglog (C1, C2, 'x', [1 1e20], [1 1e20], 'r') ; subplot (1,2,2) ; loglog (C3, C2, 'x', [1 1e20], [1 1e20], 'r') ; drawnow end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test23.m0000644001170100242450000000116010710252361020507 0ustar davisfacfunction test23 %TEST23 test cs_dmspy % % Example: % test23 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions randn ('state', 0) ; rand ('state', 0) ; clf for trials = 1:1000 % m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; m = n ; % d = 0.1 * rand (1) ; d = rand (1) * 4 * max (m,n) / max (m*n,1) ; A = sprandn (m,n,d) ; % S = sprandn (m,m,d) + speye (m) ; if (~ispc) if (rand ( ) > .5) A = A + 1i * sprand (A) ; end end cs_dmspy (A) ; drawnow % pause end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test24.m0000644001170100242450000000171410710252400020507 0ustar davisfacfunction test24 %TEST24 test cs_fielder % % Example: % test24 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:200) ; clf % f = f(1) for k = 1:length (f) i = f (k) ; Prob = UFget (i) ; disp (Prob) ; A = real (Prob.A) ; [m n] = size (A) ; if (m ~= n) continue end S = A ; if (~ispc) if (mod (k,2) == 0) S = S + 1i * sprand (A) ; end end tic p1 = symrcm (A) ; t1 = toc ; tic p2 = cs_fiedler (S) ; t2 = toc ; rel = t2 / max (t1,1e-6) ; fprintf ('time: symrcm %8.3f fiedler %8.3f rel %8.2f\n', t1, t2, rel) ; A = A|A' ; subplot (1,3,1) ; spy (A) ; subplot (1,3,2) ; spy (A (p1,p1)) ; subplot (1,3,3) ; spy (A (p2,p2)) ; % evaluate the profile ... drawnow % pause end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test25.m0000644001170100242450000000212310710252417020513 0ustar davisfacfunction test25 %TEST25 test cs_nd % % Example: % test25 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:400) ; clf % f = f(1) for k = 1:length (f) i = f (k) ; Prob = UFget (i) ; disp (Prob) ; A = real (Prob.A) ; [m n] = size (A) ; if (m ~= n) continue end A = A|A' ; S = A ; if (~ispc) if (mod (k,2) == 0) S = S + 1i * sprand (A) ; end end tic ; p1 = symrcm (A) ; t1 = toc ; tic ; p2 = cs_nd (sparse (1)) ; toc ; if (p2 ~= 1) error ('!') ; end tic ; p2 = cs_nd (S) ; t2 = toc ; if (any (sort (p2) ~= 1:n)) error ('!') ; end rel = t2 / max (t1,1e-6) ; fprintf ('time: symrcm %8.3f nd %8.3f rel %8.2f\n', t1, t2, rel) ; subplot (1,3,1) ; spy (A) ; subplot (1,3,2) ; spy (A (p1,p1)) ; subplot (1,3,3) ; spy (A (p2,p2)) ; % evaluate the profile ... drawnow % pause end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test26.m0000644001170100242450000000335310710252502020515 0ustar davisfacfunction test26 %TEST26 test cs_dmsol and cs_dmspy % % Example: % test26 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions randn ('state', 0) ; rand ('state', 0) ; clf ntrials = 1000 ; e1 = zeros (ntrials,1) ; e2 = zeros (ntrials,1) ; for trials = 1:ntrials m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; % d = 0.1 * rand (1) ; d = rand (1) * 4 * max (m,n) / max (m*n,1) ; A = sprandn (m,n,d) ; % S = sprandn (m,m,d) + speye (m) ; if (~ispc) if (rand ( ) > .5) A = A + 1i * sprand (A) ; end end subplot (1,3,2) ; spy (A) ; subplot (1,3,3) ; cs_dmspy (A) ; b = rand (m,1) ; if (~ispc) if (rand ( ) > .5) b = b + 1i * rand (size (b)) ; end end % MATLAB cannot do A\b when A is sparse and rectangular and either % A or b are complex if (m ~= n & isreal (A) & ~isreal (b)) %#ok x1 = (A\real(b)) + 1i * (A\imag(b)) ; err1 = norm (A*x1-b) ; elseif ((m ~= n) & ~isreal (A)) %#ok err1 = 1 ; else x1 = A\b ; err1 = norm (A*x1-b) ; end x2 = cs_dmsol (A,b) ; err2 = norm (A*x2-b) ; lerr1 = log10 (max (err1, eps)) ; lerr2 = log10 (max (err2, eps)) ; fprintf ('rank: %3d %3d err %6.2e %6.2e : %6.1f\n', ... sprank(A), rank(full(A)), err1, err2, lerr1 - lerr2) ; if (isnan (err1)) lerr1 = 10 ; end if (isnan (err2)) lerr2 = 10 ; end if (lerr2 > lerr1 + 5) % pause end e1 (trials) = lerr1 ; e2 (trials) = lerr2 ; subplot (1,3,1) ; plot (e1, e2, 'o', [-16 10], [-16 10], 'r') ; xlabel ('MATLAB error') ; ylabel ('dmsol error') ; drawnow % pause end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test27.m0000644001170100242450000000116710620372664020533 0ustar davisfacfunction test27 %TEST27 test cs_qr, cs_utsolve, cs_qrsol % % Example: % test27 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions rand ('state', 0) ; Prob = UFget ('HB/ibm32') ; A = Prob.A ; A = A (1:10,:) ; [m n] = size (A) ; [V,Beta,p,R,q] = cs_qr (A') ; b = rand (m,1) ; Rm = R (1:m,1:m) ; bq = b (q) ; rtbq = Rm' \ bq ; rt2 = cs_utsolve (Rm, bq) ; norm (rtbq - rt2) x = [rt2 ; zeros(n-m,1)] ; for k = m:-1:1 x = x - V(:,k) * (Beta (k) * (V (:,k)' * x)) ; end x (p) = x ; norm (A*x-b) x2 = cs_qrsol (A,b) ; norm (A*x2-b) norm (x-x2) SuiteSparse/CXSparse_newfiles/MATLAB/Test/test28.m0000644001170100242450000000436310710252523020524 0ustar davisfacfunction test28 %TEST28 test cs_randperm, cs_dmperm % % Example: % test28 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear functions rand ('state', 0) ; for n = 1:100 for trials = 1:1000 p = cs_randperm (n, rand) ; if (any (sort (p) ~= 1:n)) n %#ok p %#ok error ('!') end end end index = UFget ; [ignore f] = sort (index.nnz) ; fprintf ('p=dmperm (std, rand, rev) [p,q,r,s]=dmperm (std, rand, rev)\n') ; nmat = length (f) ; nmat = min (100, nmat) ; T1 = zeros (nmat,1) ; T2 = zeros (nmat,1) ; T3 = zeros (nmat,1) ; D1 = zeros (nmat,1) ; D2 = zeros (nmat,1) ; D3 = zeros (nmat,1) ; for k = 1:nmat i = f (k) ; Prob = UFget (i,index) ; A = Prob.A ; [m n] = size (A) ; fprintf ('%35s: ', Prob.name) ; if (~ispc) if (rand () > .5) A = A + 1i * sprand (A) ; end end tic p = cs_dmperm (A) ; t1 = toc ; sprank1 = sum (p > 0) ; fprintf (' %8.2f', t1) ; T1 (k) = t1 ; tic p = cs_dmperm (A,1) ; t2 = toc ; sprank2 = sum (p > 0) ; fprintf (' %8.2f', t2) ; T2 (k) = t2 ; tic p = cs_dmperm (A,-1) ; t3 = toc ; sprank3 = sum (p > 0) ; fprintf (' %8.2f', t3) ; T3 (k) = t3 ; if (sprank1 ~= sprank2 | sprank1 ~= sprank3) %#ok error ('!') ; end tic [p1,q1,r1,s1,cc1,rr1] = cs_dmperm (A) ; %#ok d1 = toc ; fprintf (' %8.2f', d1) ; D1 (k) = d1 ; tic [p2,q2,r2,s2,cc2,rr2] = cs_dmperm (A,1) ; %#ok d2 = toc ; fprintf (' %8.2f', d2) ; D2 (k) = d2 ; tic [p3,q3,r3,s3,cc3,rr3] = cs_dmperm (A,-1) ; %#ok d3 = toc ; fprintf (' %8.2f\n', d3) ; D3 (k) = d3 ; if (sprank1 == max (m,n)) nz1 = nnz (diag (A (p1,q1))) ; nz2 = nnz (diag (A (p2,q2))) ; nz3 = nnz (diag (A (p3,q3))) ; if (nz1 ~= sprank1 | nz2 ~= sprank2 | nz3 ~= sprank3) %#ok error ('!') end end subplot (1,2,1) loglog (T1 (1:k), T2 (1:k), 'x', ... T1 (1:k), T3 (1:k), 'go', ... [1e-5 1e3], [1e-5 1e3], 'r-') ; axis equal subplot (1,2,2) loglog (D1 (1:k), D2 (1:k), 'x', ... D1 (1:k), D3 (1:k), 'go', ... [1e-5 1e3], [1e-5 1e3], 'r-') ; axis equal drawnow end SuiteSparse/CXSparse_newfiles/MATLAB/Test/cs_frand_mex.c0000644001170100242450000000276210571350365022022 0ustar davisfac#include "cs_mex.h" /* A = cs_frand (n,nel,s) creates an n-by-n sparse matrix consisting of nel * finite elements, each of which are of size s-by-s with random symmetric * nonzero pattern, plus the identity matrix. * See also MATLAB/Demo/private/frand.m */ cs_dl *cs_dl_frand (CS_INT n, CS_INT nel, CS_INT s) { CS_INT ss = s*s, nz = nel*ss, e, i, j, *P ; cs *A, *T = cs_dl_spalloc (n, n, nz, 1, 1) ; if (!T) return (NULL) ; P = cs_dl_malloc (s, sizeof (CS_INT)) ; if (!P) return (cs_dl_spfree (T)) ; for (e = 0 ; e < nel ; e++) { for (i = 0 ; i < s ; i++) P [i] = rand () % n ; for (j = 0 ; j < s ; j++) { for (i = 0 ; i < s ; i++) { cs_dl_entry (T, P [i], P [j], rand () / (double) RAND_MAX) ; } } } for (i = 0 ; i < n ; i++) cs_dl_entry (T, i, i, 1) ; A = cs_dl_compress (T) ; cs_dl_spfree (T) ; return (cs_dl_dupl (A) ? A : cs_dl_spfree (A)) ; } void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT n, nel, s ; cs *A, *AT ; if (nargout > 1 || nargin != 3) { mexErrMsgTxt ("Usage: C = cs_frand(n,nel,s)") ; } n = mxGetScalar (pargin [0]) ; nel = mxGetScalar (pargin [1]) ; s = mxGetScalar (pargin [2]) ; n = CS_MAX (1,n) ; nel = CS_MAX (1,nel) ; s = CS_MAX (1,s) ; AT = cs_dl_frand (n, nel, s) ; A = cs_dl_transpose (AT, 1) ; cs_dl_spfree (AT) ; cs_dl_dropzeros (A) ; pargout [0] = cs_dl_mex_put_sparse (&A) ; } SuiteSparse/CXSparse_newfiles/MATLAB/Test/test1.m0000644001170100242450000000274110710254571020436 0ustar davisfacfunction test1 %TEST1 test cs_transpose, cs_gaxpy, cs_sparse, cs_sparse2 % % Example: % test1 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:100) ; for ii = f Prob = UFget (ii) ; disp (Prob) ; for cmplex = 0:double(~ispc) A = Prob.A ; if (cmplex) A = A + 1i*sprand(A) ; end B = A' ; C = cs_transpose (A) ; if (nnz (B-C) ~= 0) error ('!') end C = cs_transpose (A,0) ; if (nnz (A.'-C) ~= 0) error ('!') end C = cs_transpose (A,1) ; if (nnz (A'-C) ~= 0) error ('!') end [m n] = size (A) ; % if (m == n) x = rand (n,1) ; y = rand (m,1) ; z = y+A*x ; q = cs_gaxpy (A,x,y) ; err = norm (z-q,1) / norm (z,1) ; disp (err) ; if (err > 1e-14) error ('!') end % end if (~ispc) x = x + 1i*rand (n,1) ; y = y + 1i*rand (m,1) ; z = y+A*x ; q = cs_gaxpy (A,x,y) ; err = norm (z-q,1) / norm (z,1) ; disp (err) ; if (err > 1e-14) error ('!') end end [i j x] = find (A) ; p = randperm (length (i)) ; i = i (p) ; j = j (p) ; x = x (p) ; D = sparse (i,j,x) ; E = cs_sparse (i,j,x) ; % [i j x] F = cs_sparse2 (i,j,x) ; if (nnz (D-E) ~= 0) error ('!') end if (nnz (F-E) ~= 0) error ('!') end clear A B C D E F % pause end end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test2.m0000644001170100242450000000371310710252554020436 0ustar davisfacfunction test2 %TEST2 test cs_sparse, cs_permute, cs_pvec, cs_ipvec, cs_symperm % % Example: % test2 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) % clf for trial = 1:100 m = fix (10 * rand (1)) ; n = fix (10 * rand (1)) ; nz = fix (100 * rand (1)) ; i = 1 + fix (m * rand (nz,1)) ; j = 1 + fix (n * rand (nz,1)) ; x = rand (nz,1) ; if (~ispc) if (mod (trial, 2) == 1) x = x + 1i * (2*rand(nz,1)-1) ; end end A = sparse (i,j,x) ; B = cs_sparse (i,j,x) ; D = cs_sparse2 (i,j,x) ; fprintf ('%3d %3d %6d : %6d %6d : %d\n', ... m, n, nz, nnz (A), nnz(B), nz-nnz(A)) ; err = norm (A-B,1) / max (1, norm (A,1)) ; if (err > 0) disp ('err = ') ; disp (err) ; end if (err > 1e-14) error ('!') ; end if (nnz (B-D) > 0) error ('!') ; end if (nnz (A) ~= nnz (B)) error ('nz!') ; end if (max (1,nnz (B)) ~= max (1,nzmax (B))) nnz (B) nzmax (B) error ('nzmax!') ; end % pack [m n] = size (A) ; p = randperm (m) ; q = randperm (n) ; C1 = A (p,q) ; C2 = cs_permute (A,p,q) ; err = norm (C1-C2,1) ; if (err > 0) error ('!') ; end % subplot (1,2,1) ; spy (A) % subplot (1,2,2) ; spy (C2) % drawnow x = rand (m,1) ; if (~ispc) if (mod (trial, 2) == 1) x = x + 1i * (2*rand(m,1)-1) ; end end x1 = x (p) ; x2 = cs_pvec (x, p) ; err = norm (x1-x2,1) ; if (err > 0) error ('!') ; end x1 = zeros (m,1) ; x1 (p) = x ; %#ok x2 = cs_ipvec (x, p) ; %#ok n = min (m,n) ; B = A (1:n, 1:n) ; p = randperm (n) ; B = B+B' ; C1 = triu (B (p,p)) ; C2 = cs_symperm (B,p) ; try pp = amd (C2) ; %#ok catch pp = symamd (C2) ; %#ok end err = norm (C1-C2,1) ; if (err > 0) error ('!') ; end end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test3.m0000644001170100242450000000326610710254574020446 0ustar davisfacfunction test3 %TEST3 test cs_lsolve, cs_ltsolve, cs_usolve, cs_chol % % Example: % test3 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse clear index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:100) ; clf % f = f(1) for i = f Prob = UFget (i) ; disp (Prob) ; for cmplex = 0:double(~ispc) A = Prob.A ; [m n] = size (A) ; if (m ~= n) continue end if (cmplex) A = A + 1i*sprand(A) ; end A = A*A' + 2*n*speye (n) ; try p = amd (A) ; catch p = symamd (A) ; end try L0 = chol (A)' ; catch continue end b = rand (n,1) ; if (~ispc) if (mod (i,2) == 1) b = b + 1i*rand(n,1) ; end end C = A(p,p) ; c = condest (C) ; fprintf ('condest: %g\n', c) ; x1 = L0\b ; x2 = cs_lsolve (L0,b) ; err = norm (x1-x2,1) ; if (err > 1e-12 * c) error ('!') ; end x1 = L0'\b ; x2 = cs_ltsolve (L0,b) ; err = norm (x1-x2,1) ; if (err > 1e-10 * c) error ('!') ; end U = L0' ; x1 = U\b ; x2 = cs_usolve (U,b) ; err = norm (x1-x2,1) ; if (err > 1e-10 * c) error ('!') ; end L2 = cs_chol (A) ; subplot (2,3,1) ; spy (L0) ; subplot (2,3,4) ; spy (L2) ; err = norm (L0-L2,1) ; if (err > 1e-8 * c) error ('!') ; end L1 = chol (C)' ; L2 = cs_chol (C) ; subplot (2,3,2) ; spy (L1) ; subplot (2,3,5) ; spy (L2) ; err = norm (L1-L2,1) ; if (err > 1e-8 * c) error ('!') ; end [L3,p] = cs_chol (A) ; C = A(p,p) ; L4 = chol (C)' ; subplot (2,3,3) ; spy (L4) ; subplot (2,3,6) ; spy (L3) ; err = norm (L4-L3,1) ; if (err > 1e-8 * c) error ('!') ; end drawnow end end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test4.m0000644001170100242450000000156510710252626020443 0ustar davisfacfunction test4 %TEST4 test cs_multiply % % Example: % test4 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) ; for trial = 1:100 m = fix (10 * rand (1)) ; n = fix (10 * rand (1)) ; k = fix (10 * rand (1)) ; d = rand (1) ; A = sprandn (m,n,d) ; B = sprandn (n,k,d) ; if (~ispc) if (mod (trial, 4) == 0) A = A + 1i * sprandn (A) ; end if (mod (trial, 2) == 0) B = B + 1i * sprandn (B) ; end end C = A*B ; D = cs_multiply (A,B) ; err = nnz (spones (C) - spones (D)) ; if (err > 0) error ('nz!') ; end err = norm (C-D,1) ; fprintf ('m %3d n %3d k %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ... m, n, k, nnz(A), nnz(B), nnz(C), err) ; if (err > 1e-12) error ('!') ; end end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test5.m0000644001170100242450000000323410710252655020441 0ustar davisfacfunction test5 %TEST5 test cs_add % % Example: % test5 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) ; for trial = 1:200 m = fix (100 * rand (1)) ; n = fix (100 * rand (1)) ; d = rand (1) ; A = sprandn (m,n,d) ; B = sprandn (m,n,d) ; if (~ispc) if (mod (trial, 4) == 0) A = A + 1i*sprand(A) ; end if (mod (trial, 2) == 0) B = B + 1i*sprand(B) ; end end C = A+B ; D = cs_add (A,B) ; err = nnz (spones (C) - spones (D)) ; if (err > 0) error ('nz!') ; end err = norm (C-D,1) ; fprintf ('m %3d n %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ... m, n, nnz(A), nnz(B), nnz(C), err) ; if (err > 1e-12) error ('!') ; end alpha = pi ; beta = 3 ; if (~ispc) if (rand () > .5) alpha = alpha + rand ( ) * 1i ; end if (rand () > .5) beta = beta + rand ( ) * 1i ; end end C = alpha*A+B ; D = cs_add (A,B,alpha) ; err = nnz (spones (C) - spones (D)) ; if (err > 0) error ('nz!') ; end err = norm (C-D,1) ; fprintf ('m %3d n %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ... m, n, nnz(A), nnz(B), nnz(C), err) ; if (err > 1e-12) error ('!') ; end C = alpha*A + beta*B ; D = cs_add (A,B,alpha,beta) ; err = nnz (spones (C) - spones (D)) ; if (err > 0) error ('nz!') ; end err = norm (C-D,1) ; fprintf ('m %3d n %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ... m, n, nnz(A), nnz(B), nnz(C), err) ; if (err > 1e-12) error ('!') ; end end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test6.m0000644001170100242450000000342710710252671020444 0ustar davisfacfunction test6 %TEST6 test cs_reach, cs_reachr, cs_lsolve, cs_usolve % % Example: % test6 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) maxerr = 0 ; clf for trial = 1:201 n = fix (100 * rand (1)) ; d = 0.1 * rand (1) ; L = tril (sprandn (n,n,d),-1) + sprand (speye (n)) ; b = sprandn (n,1,d) ; if (~ispc) if (rand ( ) > .5) L = L + 1i*sprand(L) ; end if (rand ( ) > .5) b = b + 1i*sprand(b) ; end end for uplo = 0:1 if (uplo == 1) % solve Ux=b instead ; L = L' ; end x = L\b ; sr = 1 + cs_reachr (L,b) ; sz = 1 + cs_reachr (L,b) ; check_if_same (sr,sz) ; s2 = 1 + cs_reach (L,b) ; try if (uplo == 0) x3 = cs_lsolve (L,b) ; else x3 = cs_usolve (L,b) ; end catch if (isreal (L) & isreal (b)) %#ok lasterr error ('!') ; end % punt: sparse(L)\sparse(b) not handled by cs_lsolve or cs_usolve x3 = L\b ; end spy ([L b x x3]) drawnow s = sort (sr) ; [i j xx] = find (x) ; %#ok [i3 j3 xx3] = find (x3) ; %#ok if (isempty (i)) if (~isempty (s)) i %#ok s %#ok error ('!') ; end elseif (any (s ~= i)) i %#ok s %#ok error ('!') ; end if (isempty (i3)) if (~isempty (s)) i3 %#ok s %#ok error ('!') ; end elseif (any (s ~= sort (i3))) s %#ok i3 %#ok error ('!') ; end if (any (s2 ~= sr)) s2 %#ok sr %#ok error ('!') ; end err = norm (x-x3,1) ; if (err > 1e-12) x %#ok x3 %#ok uplo %#ok err %#ok error ('!') end maxerr = max (maxerr, err) ; end drawnow end fprintf ('maxerr = %g\n', maxerr) ; SuiteSparse/CXSparse_newfiles/MATLAB/Test/test7.m0000644001170100242450000000505610620667776020465 0ustar davisfacfunction test7 %TEST7 test cs_lu % % Example: % test7 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:100) ; clf maxerr1 = 0 ; maxerr2 = 0 ; for i = f Prob = UFget (i) ; disp (Prob) ; A = Prob.A ; [m n] = size (A) ; if (m ~= n) continue end for cmplex = 0:1 if (cmplex) A = A + norm(A,1) * sprand (A) / 3 ; end [L,U,P] = lu (A) ; udiag = full (diag (U)) ; umin = min (abs (udiag)) ; fprintf ('umin %g\n', umin) ; if (umin > 1e-14) [L2,U2,p] = cs_lu (A) ; subplot (3,4,1) ; spy (A) ; subplot (3,4,2) ; spy (A(p,:)) ; subplot (3,4,3) ; spy (L2) ; subplot (3,4,4) ; spy (U2) ; err1 = norm (L*U-P*A,1) / norm (A,1) ; err2 = norm (L2*U2-A(p,:),1) / norm (A,1) ; fprintf ('err %g %g\n', err1, err2) ; if (err1 > 1e-10 | err2 > 1e-10) %#ok error ('!') ; end maxerr1 = max (maxerr1, err1) ; maxerr2 = max (maxerr2, err2) ; end q = colamd (A) ; [L,U,P] = lu (A (:,q)) ; udiag = full (diag (U)) ; umin = min (abs (udiag)) ; fprintf ('umin %g with q\n', umin) ; if (umin > 1e-14) [L2,U2,p,q2] = cs_lu (A) ; subplot (3,4,5) ; spy (A) ; subplot (3,4,6) ; spy (A(p,q2)) ; subplot (3,4,7) ; spy (L2) ; subplot (3,4,8) ; spy (U2) ; err1 = norm (L*U-P*A(:,q),1) / norm (A,1) ; err2 = norm (L2*U2-A(p,q2),1) / norm (A,1) ; fprintf ('err %g %g\n', err1, err2) ; if (err1 > 1e-10 | err2 > 1e-10) %#ok error ('!') ; end maxerr1 = max (maxerr1, err1) ; maxerr2 = max (maxerr2, err2) ; end try q = amd (A) ; catch q = symamd (A) ; end tol = 0.01 ; [L,U,P] = lu (A (q,q), tol) ; udiag = full (diag (U)) ; umin = min (abs (udiag)) ; fprintf ('umin %g with amd q\n', umin) ; if (umin > 1e-14) [L2,U2,p,q2] = cs_lu (A,tol) ; subplot (3,4,9) ; spy (A) ; subplot (3,4,10) ; spy (A(p,q2)) ; subplot (3,4,11) ; spy (L2) ; subplot (3,4,12) ; spy (U2) ; err1 = norm (L*U-P*A(q,q),1) / norm (A,1) ; err2 = norm (L2*U2-A(p,q2),1) / norm (A,1) ; lbig = full (max (max (abs (L2)))) ; fprintf ('err %g %g lbig %g\n', err1, err2, lbig) ; if (lbig > 1/tol) error ('L!') ; end if (err1 > 1e-10 | err2 > 1e-10) %#ok error ('!') ; end maxerr1 = max (maxerr1, err1) ; maxerr2 = max (maxerr2, err2) ; end drawnow % pause end end fprintf ('maxerr %g %g\n', maxerr1, maxerr2) ; SuiteSparse/CXSparse_newfiles/MATLAB/Test/test8.m0000644001170100242450000000277110710254600020441 0ustar davisfacfunction test8 %TEST8 test cs_cholsol, cs_lusol % % Example: % test8 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:100) ; % f = f(1) for i = f Prob = UFget (i) ; disp (Prob) ; A = Prob.A ; [m n] = size (A) ; if (m ~= n) continue end for cmplex = 0:double(~ispc) if (cmplex) A = A + 0.1i * (sprand (tril (A,-1) + triu (A,1))) ; end spd = 0 ; if (m == n) if (nnz (A-A') == 0) try p = amd (A) ; catch p = symamd (A) ; end [R,p] = chol (A (p,p)) ; spd = (p == 0) ; end end if (spd) C = A ; else C = A*A' + n*speye (n) ; try p = amd (C) ; catch p = symamd (C) ; end try R = chol (C (p,p)) ; %#ok catch continue end end b = rand (n,1) ; x1 = C\b ; x2 = cs_cholsol (C,b) ; r1 = norm (C*x1-b,1) / norm (C,1) ; r2 = norm (C*x2-b,1) / norm (C,1) ; err = abs (r1-r2) ; fprintf ('err %g\n', err) ; if (err > 1e-10) error ('!') ; end x2 = cs_lusol (C,b, 1, 0.001) ; r2 = norm (C*x2-b,1) / norm (C,1) ; err = abs (r1-r2) ; fprintf ('err %g (lu with amd(A+A'')\n', err) ; if (err > 1e-10) error ('!') ; end if (m ~= n) continue ; end x1 = A\b ; r1 = norm (A*x1-b,1) / norm (A,1) ; if (r1 < 1e-6) x2 = cs_lusol (A,b) ; r2 = norm (A*x2-b,1) / norm (A,1) ; fprintf ('lu resid %g %g\n', r1, r2) ; end end end SuiteSparse/CXSparse_newfiles/MATLAB/Test/test9.m0000644001170100242450000000504110710254603020436 0ustar davisfacfunction test9 %TEST9 test cs_qr % % Example: % test9 % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse rand ('state', 0) ; index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; f = f (1:100) ; clf % f = 185 ; % f = 449 ; % f = 186 for i = f Prob = UFget (i) ; disp (Prob) ; A = Prob.A ; [m n] = size (A) ; if (m < n) A = A' ; end [m n] = size (A) ; sp = sprank (A) ; % if (sprank (A) < min (m,n)) % continue % end for cmplex = 0:double(~ispc) if (cmplex) A = A + 1i * sprand (A) ; end Aorig = A ; A = A (:, colamd (A)) ; s1 = svd (full (A)) ; if (cmplex) try tic ; R = chol (A'*A) ; t1 = toc ; %#ok catch fprintf ('chol (A''*A) failed\n') ; R = [ ] ; end else tic ; R = qr (A) ; t1 = toc ; %#ok end % tic ; % [Q,R] = qr (A) ; % t1 = toc ; [c,h,parent] = symbfact (A, 'col') ; rnz = sum (c) ; %#ok tic ; [V2,Beta2,p,R2] = cs_qr (sparse(A)) ; t2 = toc ; %#ok v2 = full (V2) ; if (any (spones (v2) ~= spones (V2))) error ('got zeros!') ; end C = A ; m2 = size (V2,1) ; if (m2 > m) C = [A ; sparse(m2-m, n)] ; end C = C (p,:) ; % [H1,R1] = myqr (C) ; % err1 = norm (R1-R2,1) / norm (R1) % % [svd(A) svd(R1) svd(full(R2))] % s2 = svd (full (R2)) ; % err2 = norm (s1 - s2) / s1 (1) % fprintf ('%10.6f %10.6f cs speedup %8.3f sprank %d n %d\n', ... % t1, t2, t1/t2, sp, n) ; % err2 % left-looking: [V,Beta3,R3] = qr_left (C) ; %#ok s3 = svd (full (R2)) ; err3 = norm (s1 - s3) / s1 (1) ; disp ('err3 = ') ; disp (err3) ; if (err3 > 1e-12) error ('!') ; end % right-looking: [V,Beta4,R4] = qr_right (C) ; %#ok s4 = svd (full (R2)) ; err4 = norm (s1 - s4) / s1 (1) ; disp ('err4 = ') ; disp (err4) ; if (err4 > 1e-12) error ('!') ; end % H2 = full (H2) % R2 = full (R2) subplot (2,4,1) ; spy (A) ; title ('A colamd') ; subplot (2,4,2) ; spy (C) ; title ('A rperm') ; subplot (2,4,3) ; treeplot (parent) ; subplot (2,4,4) ; spy (Aorig) ; title ('Aorig') ; subplot (2,4,5) ; spy (abs(R2)>0) ; title ('spqr R, no zeros') ; subplot (2,4,6) ; spy (R) ; title ('matlab R') ; subplot (2,4,7) ; spy (R2) ; title ('spqr R') ; subplot (2,4,8) ; spy (V2) ; title ('spqr V') ; drawnow % if (err2 > 1e-9) % error ('!') ; % end if (m2 > m) fprintf ('added %d rows, sprank %d n %d\n', m2-m, sp, n) ; end % pause end end SuiteSparse/CXSparse_newfiles/MATLAB/Test/testh.m0000644001170100242450000000315510620372711020522 0ustar davisfacfunction testh %TESTH test Householder reflections % % Example: % testh % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse format long e fprintf ('-------------------------------------------------\n') ; x = [-3 4 5]' ; disp (x) ; [v, beta, s] = house (x) ; disp ('v = ') ; disp (v) ; disp ('beta = ') ; disp (beta) ; disp ('s = ') ; disp (s) ; x = x - v*(beta*(v'*x)) ; disp (x) ; fprintf ('-------------------------------------------------\n') ; x = [3 4 5]' ; disp (x) ; [v, beta, s] = house (x) ; disp ('v = ') ; disp (v) ; disp ('beta = ') ; disp (beta) ; disp ('s = ') ; disp (s) ; x = x - v*(beta*(v'*x)) ; disp (x) ; fprintf ('-------------------------------------------------\n') ; x = [1 eps]' ; disp (x) ; [v, beta, s] = house (x) ; disp ('v = ') ; disp (v) ; disp ('beta = ') ; disp (beta) ; disp ('s = ') ; disp (s) ; x = x - v*(beta*(v'*x)) ; disp (x) ; fprintf ('-------------------------------------------------\n') ; x = pi ; disp (x) ; [v, beta, s] = house (x) ; disp ('v = ') ; disp (v) ; disp ('beta = ') ; disp (beta) ; disp ('s = ') ; disp (s) ; x = x - v*(beta*(v'*x)) ; disp (x) ; fprintf ('-------------------------------------------------\n') ; x = -pi ; disp (x) ; [v, beta, s] = house (x) ; disp ('v = ') ; disp (v) ; disp ('beta = ') ; disp (beta) ; disp ('s = ') ; disp (s) ; x = x - v*(beta*(v'*x)) ; disp (x) ; fprintf ('-------------------------------------------------\n') ; x = [1 0 0]' ; disp (x) ; [v, beta, s] = house (x) ; %#ok x = x - v*(beta*(v'*x)) ; disp (x) ; fprintf ('-------------------------------------------------\n') ; SuiteSparse/CXSparse_newfiles/MATLAB/Test/cs_pvec_mex.c0000644001170100242450000000215210710251202021637 0ustar davisfac#include "cs_mex.h" /* x = b(p) */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT n, k, *p ; double *xx ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_pvec(b,p)") ; } n = mxGetNumberOfElements (pargin [0]) ; if (n != mxGetNumberOfElements (pargin [1])) { mexErrMsgTxt ("b or p wrong size") ; } xx = mxGetPr (pargin [1]) ; p = cs_dl_malloc (n, sizeof (CS_INT)) ; for (k = 0 ; k < n ; k++) p [k] = xx [k] - 1 ; if (mxIsComplex (pargin [0])) { #ifdef NCOMPLEX mexErrMsgTxt ("complex case not supported") ; #else cs_complex_t *x, *b ; b = cs_cl_mex_get_double (n, pargin [0]) ; x = cs_dl_malloc (n, sizeof (cs_complex_t)) ; cs_cl_pvec (p, b, x, n) ; pargout [0] = cs_cl_mex_put_double (n, x) ; cs_free (b) ; /* free copy of complex values */ #endif } else { double *x, *b ; b = cs_dl_mex_get_double (n, pargin [0]) ; pargout [0] = mxCreateDoubleMatrix (n, 1, mxREAL) ; x = mxGetPr (pargout [0]) ; cs_dl_pvec (p, b, x, n) ; } cs_free (p) ; } SuiteSparse/CXSparse_newfiles/MATLAB/Test/cs_maxtransr_mex.c0000644001170100242450000000556710571351706022755 0ustar davisfac#include "cs_mex.h" /* find an augmenting path starting at column j and extend the match if found */ static CS_INT augment (CS_INT k, cs_dl *A, CS_INT *jmatch, CS_INT *cheap, CS_INT *w, CS_INT j) { CS_INT found = 0, p, i = -1, *Ap = A->p, *Ai = A->i ; /* --- Start depth-first-search at node j ------------------------------- */ w [j] = k ; /* mark j as visited for kth path */ for (p = cheap [j] ; p < Ap [j+1] && !found ; p++) { i = Ai [p] ; /* try a cheap assignment (i,j) */ found = (jmatch [i] == -1) ; } cheap [j] = p ; /* start here next time for j */ /* --- Depth-first-search of neighbors of j ----------------------------- */ for (p = Ap [j] ; p < Ap [j+1] && !found ; p++) { i = Ai [p] ; /* consider row i */ if (w [jmatch [i]] == k) continue ; /* skip col jmatch [i] if marked */ found = augment (k, A, jmatch, cheap, w, jmatch [i]) ; } if (found) jmatch [i] = j ; /* augment jmatch if path found */ return (found) ; } /* find a maximum transveral */ static CS_INT *maxtrans (cs_dl *A) /* returns jmatch [0..m-1] */ { CS_INT i, j, k, n, m, *Ap, *jmatch, *w, *cheap ; if (!A) return (NULL) ; /* check inputs */ n = A->n ; m = A->m ; Ap = A->p ; jmatch = cs_dl_malloc (m, sizeof (CS_INT)) ; /* allocate result */ w = cs_dl_malloc (2*n, sizeof (CS_INT)) ; /* allocate workspace */ if (!w || !jmatch) return (cs_dl_idone (jmatch, NULL, w, 0)) ; cheap = w + n ; for (j = 0 ; j < n ; j++) cheap [j] = Ap [j] ; /* for cheap assignment */ for (j = 0 ; j < n ; j++) w [j] = -1 ; /* all columns unflagged */ for (i = 0 ; i < m ; i++) jmatch [i] = -1 ; /* no rows matched yet */ for (k = 0 ; k < n ; k++) augment (k, A, jmatch, cheap, w, k) ; return (cs_dl_idone (jmatch, NULL, w, 1)) ; } /* invert a maximum matching */ static CS_INT *invmatch (CS_INT *jmatch, CS_INT m, CS_INT n) { CS_INT i, j, *imatch ; if (!jmatch) return (NULL) ; imatch = cs_dl_malloc (n, sizeof (CS_INT)) ; if (!imatch) return (NULL) ; for (j = 0 ; j < n ; j++) imatch [j] = -1 ; for (i = 0 ; i < m ; i++) if (jmatch [i] >= 0) imatch [jmatch [i]] = i ; return (imatch) ; } void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs_dl *A, Amatrix ; double *x ; CS_INT i, m, n, *imatch, *jmatch ; if (nargout > 1 || nargin != 1) { mexErrMsgTxt ("Usage: p = cr_maxtransr(A)") ; } /* get inputs */ A = cs_dl_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ; m = A->m ; n = A->n ; jmatch = maxtrans (A) ; imatch = invmatch (jmatch, m, n) ; /* imatch = inverse of jmatch */ pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ; x = mxGetPr (pargout [0]) ; for (i = 0 ; i < n ; i++) x [i] = imatch [i] + 1 ; cs_free (jmatch) ; cs_free (imatch) ; } SuiteSparse/CXSparse_newfiles/MATLAB/Test/chol_updown2.m0000644001170100242450000000221410620375657022005 0ustar davisfacfunction [L, w] = chol_updown2 (L, sigma, w) %CHOL_UPDOWN2 Cholesky update/downdate (real and complex) % (real or complex) % Example: % [L, w] = chol_updown2 (L, sigma, w) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis, William W. Hager % http://www.cise.ufl.edu/research/sparse beta = 1 ; n = size (L,1) ; if (n == 1) wnew = L\w ; L = sqrt (L*L'+sigma*w*w') ; w = wnew ; return ; end for k = 1:n alpha = w(k) / L(k,k) ; beta2 = sqrt (beta*beta + sigma*alpha*conj(alpha)) ; gamma = sigma * conj(alpha) / (beta2 * beta) ; if (sigma > 0) % update delta = beta / beta2 ; L (k,k) = delta * L (k,k) + gamma * w (k) ; phase = abs (L (k, k))/L (k, k) ; L (k, k) = phase*L (k, k) ; w1 = w (k+1:n) ; w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ; L (k+1:n,k) = phase * (delta * L (k+1:n,k) + gamma * w1) ; else % downdate delta = beta2 / beta ; L (k,k) = delta * L (k,k) ; phase = abs (L (k, k))/L (k, k) ; L (k, k) = phase*L (k, k) ; w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ; L (k+1:n,k) = phase * (delta * L (k+1:n,k) + gamma * w (k+1:n)) ; end w (k) = alpha ; beta = beta2 ; end SuiteSparse/CXSparse_newfiles/MATLAB/Test/cs_ipvec_mex.c0000644001170100242450000000215510710251173022022 0ustar davisfac#include "cs_mex.h" /* x(p) = b */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT n, k, *p ; double *xx ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_ipvec(b,p)") ; } n = mxGetNumberOfElements (pargin [0]) ; if (n != mxGetNumberOfElements (pargin [1])) { mexErrMsgTxt ("b or p wrong size") ; } xx = mxGetPr (pargin [1]) ; p = cs_dl_malloc (n, sizeof (CS_INT)) ; for (k = 0 ; k < n ; k++) p [k] = xx [k] - 1 ; if (mxIsComplex (pargin [0])) { #ifdef NCOMPLEX mexErrMsgTxt ("complex case not supported") ; #else cs_complex_t *x, *b ; b = cs_cl_mex_get_double (n, pargin [0]) ; x = cs_dl_malloc (n, sizeof (cs_complex_t)) ; cs_cl_ipvec (p, b, x, n) ; pargout [0] = cs_cl_mex_put_double (n, x) ; cs_free (b) ; /* free copy of complex values */ #endif } else { double *x, *b ; b = cs_dl_mex_get_double (n, pargin [0]) ; pargout [0] = mxCreateDoubleMatrix (n, 1, mxREAL) ; x = mxGetPr (pargout [0]) ; cs_dl_ipvec (p, b, x, n) ; } cs_free (p) ; } SuiteSparse/CXSparse_newfiles/MATLAB/Test/README.txt0000644001170100242450000000035110571641104020706 0ustar davisfacTest for MATLAB interface for CXSparse. Type "testall" to run all the tests. Also includes "textbook" codes for the book "Direct Methods for Sparse Linear Systems", which are not part of CXSparse proper, but are used in the tests. SuiteSparse/CXSparse_newfiles/MATLAB/Test/cs_test_make.m0000644001170100242450000000221610710251526022031 0ustar davisfacfunction cs_test_make (force) %CS_TEST_MAKE compiles the CSparse, Demo, and Test mexFunctions. % The current directory must be CSparse/MATLAB/Test to use this function. % % Example: % cs_test_make % See also: testall % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse mexcmd = 'mex -DCS_LONG -I../../../UFconfig' ; if (~isempty (strfind (computer, '64'))) mexcmd = [mexcmd ' -largeArrayDims'] ; end if (nargin < 1) force = 0 ; end cd ('../CSparse') ; [object_files timestamp] = cs_make ; cd ('../Test') ; mexfunc = { 'cs_ipvec', 'cs_pvec', 'cs_sparse2', ... 'cs_reach', 'cs_maxtransr', 'cs_reachr', 'cs_rowcnt', 'cs_frand' } ; if (ispc) % Windows does not support ANSI C99 mexcmd = [mexcmd ' -DNCOMPLEX'] ; end for i = 1:length(mexfunc) [s t tobj] = cs_must_compile ('', mexfunc{i}, '_mex', ... ['.' mexext], 'cs_test_make.m', force) ; if (s | tobj < timestamp) %#ok cmd = [mexcmd ' -O -output ' mexfunc{i} ' ' mexfunc{i} '_mex.c -I..' ... filesep '..' filesep 'Include -I..' ... filesep 'CSparse ' object_files] ; fprintf ('%s\n', cmd) ; eval (cmd) ; end end SuiteSparse/CXSparse_newfiles/MATLAB/Test/house.m0000644001170100242450000000067410620372614020523 0ustar davisfacfunction [v,beta,s] = house (x) %HOUSE find a Householder reflection. % real or complex case. % Example: % [v,beta,s] = house (x) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse v = x ; s = norm (x) ; if (s == 0) beta = 0 ; v (1) = 1 ; else if (x (1) ~= 0) s = sign (x (1)) * s ; end v (1) = v (1) + s ; beta = 1 / real (conj (s) * v (1)) ; end s = - s ; SuiteSparse/CXSparse_newfiles/MATLAB/Test/cs_reach_mex.c0000644001170100242450000000200110571352431021770 0ustar davisfac#include "cs_mex.h" /* find nonzero pattern of x=L\sparse(b). L must be sparse and lower * triangular. b must be a sparse vector. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs Lmatrix, Bmatrix, *L, *B ; double *x ; CS_INT k, i, j, top, *xi, *perm ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_reach(L,b)") ; } /* get inputs */ L = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ; cs_mex_check (0, L->n, 1, 0, 1, 1, pargin [1]) ; perm = cs_dl_malloc (L->n, sizeof (CS_INT)) ; for (k = 0 ; k < L->n ; k++) perm [k] = k ; xi = cs_dl_calloc (3*L->n, sizeof (CS_INT)) ; top = cs_dl_reach (L, B, 0, xi, perm) ; pargout [0] = mxCreateDoubleMatrix (L->n - top, 1, mxREAL) ; x = mxGetPr (pargout [0]) ; for (j = 0, i = top ; i < L->n ; i++, j++) x [j] = xi [i] ; cs_free (xi) ; cs_free (perm) ; } SuiteSparse/CXSparse_newfiles/MATLAB/Test/cs_fiedler.m0000644001170100242450000000164410620372610021471 0ustar davisfacfunction [p,v,d] = cs_fiedler (A) %CS_FIEDLER the Fiedler vector of a connected graph. % [p,v,d] = cs_fiedler(A) computes the Fiedler vector v (the eigenvector % corresponding to the 2nd smallest eigenvalue d of the Laplacian of the graph % of A+A'). p is the permutation obtained when v is sorted. A should be a % connected graph. % % Example: % [p,v,d] = cs_fiedler (A) ; % % See also CS_SCC, EIGS, SYMRCM, UNMESH. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (A,1) ; if (n < 2) p = 1 ; v = 1 ; d = 0 ; return ; end opt.disp = 0 ; % turn off printing in eigs opt.tol = sqrt (eps) ; if (~isreal (A)) A = spones (A) ; end S = A | A' | speye (n) ; % compute the Laplacian of A S = diag (sum (S)) - S ; [v,d] = eigs (S, 2, 'SA', opt) ; % find the Fiedler vector v v = v (:,2) ; d = d (2,2) ; [ignore p] = sort (v) ; % sort it to get p SuiteSparse/CXSparse_newfiles/MATLAB/Test/testall.m0000644001170100242450000000302110710513106021026 0ustar davisfacfunction testall %TESTALL test all CSparse functions (run tests 1 to 28 below) % % Example: % testall % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse h = waitbar (0, 'CXSparse') ; cs_test_make % compile all CSparse, Demo, Text, and Test mexFunctions ntests = 29 ; testwait (1, ntests, h) ; test1 ; testwait (2, ntests, h) ; test2 ; testwait (3, ntests, h) ; test3 ; testwait (4, ntests, h) ; test4 ; testwait (5, ntests, h) ; test5 ; testwait (6, ntests, h) ; test6 ; testwait (7, ntests, h) ; test7 ; testwait (8, ntests, h) ; test8 ; testwait (9, ntests, h) ; test9 ; testwait (10, ntests, h) ; test10 ; testwait (11, ntests, h) ; test11 ; testwait (12, ntests, h) ; test12 ; testwait (13, ntests, h) ; test13 ; testwait (14, ntests, h) ; test14 ; testwait (15, ntests, h) ; test15 ; testwait (16, ntests, h) ; test16 ; testwait (17, ntests, h) ; test17 ; testwait (18, ntests, h) ; test18 ; testwait (19, ntests, h) ; test19 ; testwait (20, ntests, h) ; test20 ; testwait (21, ntests, h) ; test21 ; testwait (22, ntests, h) ; test22 ; testwait (23, ntests, h) ; test23 ; testwait (24, ntests, h) ; test24 ; testwait (25, ntests, h) ; test25 ; testwait (26, ntests, h) ; test26 ; testwait (27, ntests, h) ; test27 ; testwait (28, ntests, h) ; test28 ; testwait (29, ntests, h) ; test_qr ; close (h) function testwait (n,ntests,h) fprintf ('\n------------------------ test%d\n', n) ; waitbar (n/(ntests+1), h, sprintf ('CXSparse test %d of %d\n', n, ntests)) ; SuiteSparse/CXSparse_newfiles/MATLAB/Test/norm1est.m0000644001170100242450000000131410620667470021147 0ustar davisfacfunction est = norm1est (L,U,P,Q) %NORM1EST 1-norm estimate. % L and U must be real. % Example: % est = norm1est (L,U,P,Q) % See also: cs_demo % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse n = size (L,1) ; for k = 1:5 if (k == 1) est = 0 ; x = ones (n,1) / n ; jold = -1 ; else j = min (find (abs (x) == norm (x,inf))) ; %#ok if (j == jold) break end ; x = zeros (n,1) ; x (j) = 1 ; jold = j ; end x = Q * (U \ (L \ (P*x))) ; est_old = est ; est = norm (x,1) ; if (k > 1 & est <= est_old) %#ok break end ; s = ones (n,1) ; s (find (x < 0)) = -1 ; %#ok x = P' * (L' \ (U' \ (Q'*s))) ; end SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/0000755001170100242450000000000010634327246017642 5ustar davisfacSuiteSparse/CXSparse_newfiles/MATLAB/CSparse/Makefile0000644001170100242450000000735410617167014021307 0ustar davisfacinclude ../../../UFconfig/UFconfig.mk MX = $(MEX) -DCS_LONG AR = ar cr RANLIB = ranlib I = -I../../Include -I../../../UFconfig all: mexcsparse.a cs_mex.h $(MX) cs_thumb_mex.c $(I) mexcsparse.a -output cs_thumb $(MX) cs_print_mex.c $(I) mexcsparse.a -output cs_print $(MX) cs_updown_mex.c $(I) mexcsparse.a -output cs_updown $(MX) cs_gaxpy_mex.c $(I) mexcsparse.a -output cs_gaxpy $(MX) cs_transpose_mex.c $(I) mexcsparse.a -output cs_transpose $(MX) cs_sparse_mex.c $(I) mexcsparse.a -output cs_sparse $(MX) cs_multiply_mex.c $(I) mexcsparse.a -output cs_multiply $(MX) cs_add_mex.c $(I) mexcsparse.a -output cs_add $(MX) cs_permute_mex.c $(I) mexcsparse.a -output cs_permute $(MX) cs_symperm_mex.c $(I) mexcsparse.a -output cs_symperm $(MX) cs_lsolve_mex.c $(I) mexcsparse.a -output cs_lsolve $(MX) cs_ltsolve_mex.c $(I) mexcsparse.a -output cs_ltsolve $(MX) cs_usolve_mex.c $(I) mexcsparse.a -output cs_usolve $(MX) cs_utsolve_mex.c $(I) mexcsparse.a -output cs_utsolve $(MX) cs_chol_mex.c $(I) mexcsparse.a -output cs_chol $(MX) cs_etree_mex.c $(I) mexcsparse.a -output cs_etree $(MX) cs_counts_mex.c $(I) mexcsparse.a -output cs_counts $(MX) cs_qr_mex.c $(I) mexcsparse.a -output cs_qr $(MX) cs_amd_mex.c $(I) mexcsparse.a -output cs_amd $(MX) cs_lu_mex.c $(I) mexcsparse.a -output cs_lu $(MX) cs_cholsol_mex.c $(I) mexcsparse.a -output cs_cholsol $(MX) cs_lusol_mex.c $(I) mexcsparse.a -output cs_lusol $(MX) cs_droptol_mex.c $(I) mexcsparse.a -output cs_droptol $(MX) cs_qrsol_mex.c $(I) mexcsparse.a -output cs_qrsol $(MX) cs_dmperm_mex.c $(I) mexcsparse.a -output cs_dmperm $(MX) cs_scc_mex.c $(I) mexcsparse.a -output cs_scc $(MX) cs_sqr_mex.c $(I) mexcsparse.a -output cs_sqr $(MX) cs_randperm_mex.c $(I) mexcsparse.a -output cs_randperm CSD = cs_mex.o \ cs_amd.o \ cs_chol.o \ cs_counts.o \ cs_cumsum.o \ cs_fkeep.o \ cs_dfs.o \ cs_dmperm.o \ cs_droptol.o \ cs_dropzeros.o \ cs_dupl.o \ cs_entry.o \ cs_etree.o \ cs_gaxpy.o \ cs_ipvec.o \ cs_lsolve.o \ cs_ltsolve.o \ cs_lu.o \ cs_maxtrans.o \ cs_util.o \ cs_malloc.o \ cs_multiply.o \ cs_add.o \ cs_scatter.o \ cs_permute.o \ cs_pinv.o \ cs_post.o \ cs_tdfs.o \ cs_pvec.o \ cs_qr.o \ cs_happly.o \ cs_house.o \ cs_schol.o \ cs_scc.o \ cs_sqr.o \ cs_symperm.o \ cs_transpose.o \ cs_compress.o \ cs_usolve.o \ cs_utsolve.o \ cs_cholsol.o \ cs_lusol.o \ cs_qrsol.o \ cs_updown.o \ cs_norm.o \ cs_print.o \ cs_load.o \ cs_spsolve.o \ cs_reach.o \ cs_ereach.o \ cs_leaf.o \ cs_randperm.o CSC = \ cs_cl_amd.o \ cs_cl_chol.o \ cs_cl_counts.o \ cs_cl_cumsum.o \ cs_cl_fkeep.o \ cs_cl_dfs.o \ cs_cl_dmperm.o \ cs_cl_droptol.o \ cs_cl_dropzeros.o \ cs_cl_dupl.o \ cs_cl_entry.o \ cs_cl_etree.o \ cs_cl_gaxpy.o \ cs_cl_ipvec.o \ cs_cl_lsolve.o \ cs_cl_ltsolve.o \ cs_cl_lu.o \ cs_cl_maxtrans.o \ cs_cl_util.o \ cs_cl_malloc.o \ cs_cl_multiply.o \ cs_cl_add.o \ cs_cl_scatter.o \ cs_cl_permute.o \ cs_cl_pinv.o \ cs_cl_post.o \ cs_cl_tdfs.o \ cs_cl_pvec.o \ cs_cl_qr.o \ cs_cl_happly.o \ cs_cl_house.o \ cs_cl_schol.o \ cs_cl_scc.o \ cs_cl_sqr.o \ cs_cl_symperm.o \ cs_cl_transpose.o \ cs_cl_compress.o \ cs_cl_usolve.o \ cs_cl_utsolve.o \ cs_cl_cholsol.o \ cs_cl_lusol.o \ cs_cl_qrsol.o \ cs_cl_updown.o \ cs_cl_norm.o \ cs_cl_print.o \ cs_cl_load.o \ cs_cl_spsolve.o \ cs_cl_reach.o \ cs_cl_ereach.o \ cs_cl_leaf.o \ cs_cl_randperm.o CS = $(CSD) $(CSC) mexcsparse.a: $(CS) $(AR) mexcsparse.a $(CS) $(RANLIB) mexcsparse.a $(CS): ../../Include/cs.h cs_mex.o: cs_mex.c cs_mex.h $(MX) -c $(I) $< cs_cl_%.o: ../../Source/cs_%.c cp -f $< cs_cl_$*.c $(MX) -DCS_COMPLEX -c $(I) cs_cl_$*.c cs_%.o: ../../Source/cs_%.c $(MX) -c $(I) $< clean: - rm -f *.o distclean: clean - rm -f *.mex* *.dll *.a cs_cl_*.c purge: distclean SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_amd_mex.c0000644001170100242450000000126310573562345022112 0ustar davisfac#include "cs_mex.h" /* cs_amd: approximate minimum degree ordering */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs_dl Amatrix, *A ; CS_INT *P, order ; if (nargout > 1 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: p = cs_amd(A,order)") ; } A = cs_dl_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ; /* get A */ order = (nargin > 1) ? mxGetScalar (pargin [1]) : 1 ; /* get ordering */ order = CS_MAX (order, 1) ; order = CS_MIN (order, 3) ; P = cs_dl_amd (order, A) ; /* min. degree ordering */ pargout [0] = cs_dl_mex_put_int (P, A->n, 1, 1) ; /* return P */ } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_counts_mex.c0000644001170100242450000000165710573562346022674 0ustar davisfac#include "cs_mex.h" /* cs_counts: column counts for sparse Cholesky factor L. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs_dl Amatrix, *A ; CS_INT n, ata, *parent, *post, *c ; char mode [20] ; if (nargout > 2 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: c = cs_counts(A,mode)") ; } ata = 0 ; /* get mode */ if (nargin > 1 && mxIsChar (pargin [1])) { mxGetString (pargin [1], mode, 8) ; ata = (mode [0] == 'c') ; } A = cs_dl_mex_get_sparse (&Amatrix, !ata, 0, pargin [0]) ; /* get A */ n = A->n ; parent = cs_dl_etree (A, ata) ; /* compute etree */ post = cs_dl_post (parent, n) ; /* postorder the etree*/ c = cs_dl_counts (A, parent, post, ata) ; /* get column counts */ pargout [0] = cs_dl_mex_put_int (c, n, 0, 1) ; /* return counts */ cs_free (parent) ; cs_free (post) ; } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_transpose_mex.c0000644001170100242450000000204110573562353023361 0ustar davisfac#include "cs_mex.h" /* C = cs_transpose (A), computes C=A', where A must be sparse. C = cs_transpose (A,kind) computes C=A.' if kind <= 0, C=A' if kind > 0 */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT values ; if (nargout > 1 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: C = cs_transpose(A,kind)") ; } values = (nargin > 1) ? mxGetScalar (pargin [1]) : 1 ; values = (values <= 0) ? -1 : 1 ; if (mxIsComplex (pargin [0])) { #ifndef NCOMPLEX cs_cl Amatrix, *A, *C ; A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */ C = cs_cl_transpose (A, values) ; /* C = A' */ pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Amatrix, *A, *C ; A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ C = cs_dl_transpose (A, values) ; /* C = A' */ pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */ } } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_permute_mex.c0000644001170100242450000000272410573562351023032 0ustar davisfac#include "cs_mex.h" /* cs_permute: permute a sparse matrix */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT ignore, *P, *Q, *Pinv, m, n ; if (nargout > 1 || nargin != 3) { mexErrMsgTxt ("Usage: C = cs_permute(A,p,q)") ; } m = mxGetM (pargin [0]) ; n = mxGetN (pargin [0]) ; P = cs_dl_mex_get_int (m, pargin [1], &ignore, 1) ; /* get P */ Q = cs_dl_mex_get_int (n, pargin [2], &ignore, 1) ; /* get Q */ Pinv = cs_pinv (P, m) ; /* P = Pinv' */ if (mxIsComplex (pargin [0])) { #ifndef NCOMPLEX cs_cl Amatrix, *A, *C, *D ; A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */ C = cs_cl_permute (A, Pinv, Q, 1) ; /* C = A(p,q) */ cs_cl_free (A->x) ; D = cs_cl_transpose (C, 1) ; /* sort C via double transpose */ cs_cl_spfree (C) ; C = cs_cl_transpose (D, 1) ; cs_cl_spfree (D) ; pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Amatrix, *A, *C, *D ; A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ C = cs_dl_permute (A, Pinv, Q, 1) ; /* C = A(p,q) */ D = cs_dl_transpose (C, 1) ; /* sort C via double transpose */ cs_dl_spfree (C) ; C = cs_dl_transpose (D, 1) ; cs_dl_spfree (D) ; pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */ } cs_free (Pinv) ; cs_free (P) ; cs_free (Q) ; } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/Contents.m0000644001170100242450000000537510620374610021617 0ustar davisfac% CXSparse: a Concise Sparse matrix Package. % % Matrices used in CXSparse must in general be either sparse matrices % or dense vectors. Ordering methods can accept any sparse matrix. % CXsparse allows for complex matrices (CSparse does not). % % cs_add - sparse matrix addition. % cs_amd - approximate minimum degree ordering. % cs_chol - sparse Cholesky factorization. % cs_cholsol - solve A*x=b using a sparse Cholesky factorization. % cs_counts - column counts for sparse Cholesky factor L. % cs_dmperm - maximum matching or Dulmage-Mendelsohn permutation. % cs_dmsol - x=A\b using the coarse Dulmage-Mendelsohn decomposition. % cs_dmspy - plot the Dulmage-Mendelsohn decomposition of a matrix. % cs_droptol - remove small entries from a sparse matrix. % cs_esep - find an edge separator of a symmetric matrix A % cs_etree - elimination tree of A or A'*A. % cs_gaxpy - sparse matrix times vector. % cs_lsolve - solve a sparse lower triangular system L*x=b. % cs_ltsolve - solve a sparse upper triangular system L'*x=b. % cs_lu - sparse LU factorization, with fill-reducing ordering. % cs_lusol - solve Ax=b using LU factorization. % cs_make - compiles CXSparse for use in MATLAB. % cs_multiply - sparse matrix multiply. % cs_nd - generalized nested dissection ordering. % cs_nsep - find a node separator of a symmetric matrix A. % cs_permute - permute a sparse matrix. % cs_print - print the contents of a sparse matrix. % cs_qr - sparse QR factorization (Householder-based). % cs_qleft - apply Householder vectors on the left. % cs_qright - apply Householder vectors on the right. % cs_qrsol - solve a sparse least-squares problem. % cs_randperm - random permutation. % cs_sep - convert an edge separator into a node separator. % cs_scc - strongly-connected components of a square sparse matrix. % cs_scc2 - cs_scc, or connected components of a bipartite graph. % cs_sparse - convert a triplet form into a sparse matrix. % cs_sqr - symbolic sparse QR factorization. % cs_symperm - symmetric permutation of a symmetric matrix. % cs_transpose - transpose a sparse matrix. % cs_updown - rank-1 update/downdate of a sparse Cholesky factorization. % cs_usolve - solve a sparse upper triangular system U*x=b. % cs_utsolve - solve a sparse lower triangular system U'*x=b. % cspy - plot a matrix in color. % ccspy - plot the connected components of a matrix. % Example: % help cs_add % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse % helper function: % cs_must_compile - return 1 if source code f must be compiled, 0 otherwise SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_multiply_mex.c0000644001170100242450000000277010634322566023231 0ustar davisfac#include "cs_mex.h" /* cs_multiply: sparse matrix multiply */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: C = cs_multiply(A,B)") ; } if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { #ifndef NCOMPLEX cs_cl A1matrix, B1matrix, *A, *B, *C, *D, *A1, *B1 ; A1 = cs_cl_mex_get_sparse (&A1matrix, 0, pargin [0]) ; A = cs_cl_transpose (A1, 1) ; cs_cl_free (A1->x) ; /* complex copy no longer needed */ B1 = cs_cl_mex_get_sparse (&B1matrix, 0, pargin [1]) ; B = cs_cl_transpose (B1, 1) ; cs_cl_free (B1->x) ; /* complex copy no longer needed */ D = cs_cl_multiply (B,A) ; /* D = B'*A' */ cs_cl_spfree (A) ; cs_cl_spfree (B) ; cs_cl_dropzeros (D) ; /* drop zeros from D */ C = cs_cl_transpose (D, 1) ; /* C = D', so C is sorted */ cs_cl_spfree (D) ; pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Amatrix, Bmatrix, *A, *B, *C, *D ; A = cs_dl_transpose (cs_dl_mex_get_sparse (&Amatrix, 0,1, pargin[0]),1); B = cs_dl_transpose (cs_dl_mex_get_sparse (&Bmatrix, 0,1, pargin[1]),1); D = cs_dl_multiply (B,A) ; /* D = B'*A' */ cs_dl_spfree (A) ; cs_dl_spfree (B) ; cs_dl_dropzeros (D) ; /* drop zeros from D */ C = cs_dl_transpose (D, 1) ; /* C = D', so C is sorted */ cs_dl_spfree (D) ; pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */ } } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_gaxpy_mex.c0000644001170100242450000000230310634322365022467 0ustar davisfac#include "cs_mex.h" /* z = cs_gaxpy (A,x,y) computes z = A*x+y */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { if (nargout > 1 || nargin != 3) { mexErrMsgTxt ("Usage: z = cs_gaxpy(A,x,y)") ; } if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]) || mxIsComplex (pargin [2])) { #ifndef NCOMPLEX cs_cl Amatrix, *A ; cs_complex_t *x, *z ; A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ;/* get A */ x = cs_cl_mex_get_double (A->n, pargin [1]) ; /* get x */ z = cs_cl_mex_get_double (A->m, pargin [2]) ; /* z = y */ cs_cl_gaxpy (A, x, z) ; /* z = z + A*x */ cs_free (x) ; cs_free (A->x) ; pargout [0] = cs_cl_mex_put_double (A->m, z) ; /* return z */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Amatrix, *A ; double *x, *y, *z ; A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ;/* get A */ x = cs_dl_mex_get_double (A->n, pargin [1]) ; /* get x */ y = cs_dl_mex_get_double (A->m, pargin [2]) ; /* get y */ z = cs_dl_mex_put_double (A->m, y, &(pargout [0])) ; /* z = y */ cs_dl_gaxpy (A, x, z) ; /* z = z + A*x */ } } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_scc_mex.c0000644001170100242450000000215310573562352022116 0ustar davisfac#include "cs_mex.h" /* [p,r] = cs_scc (A) finds the strongly connected components of A */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs_dl Amatrix, *A ; cs_dld *D ; CS_INT n, j, *Ap2 ; if (nargout > 2 || nargin != 1) { mexErrMsgTxt ("Usage: [p,r] = cs_scc(A)") ; } A = cs_dl_mex_get_sparse (&Amatrix, 1, 0, pargin [0]) ; /* get A */ /* cs_scc modifies A->p and then restores it (in cs_dfs). Avoid the issue * of a mexFunction modifying its input (even temporarily) by making a copy * of A->p. This issue does not arise in cs_dmperm, because that function * applies cs_scc to a submatrix C, not to A directly. */ n = A->n ; Ap2 = cs_dl_malloc (n+1, sizeof (CS_INT)) ; for (j = 0 ; j <= n ; j++) Ap2 [j] = A->p [j] ; A->p = Ap2 ; D = cs_dl_scc (A) ; /* find conn. comp. */ pargout [0] = cs_dl_mex_put_int (D->p, n, 1, 0) ; /* return p */ pargout [1] = cs_dl_mex_put_int (D->r, D->nb+1, 1, 0) ; /* return r */ cs_dl_dfree (D) ; cs_free (Ap2) ; /* free the copy of A->p */ } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_lu_mex.c0000644001170100242450000000562610634322545021772 0ustar davisfac#include "cs_mex.h" /* cs_lu: sparse LU factorization, with optional fill-reducing ordering */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT n, order, *p ; double tol ; if (nargout > 4 || nargin > 3 || nargin < 1) { mexErrMsgTxt ("Usage: [L,U,p,q] = cs_lu (A,tol)") ; } if (nargin == 2) /* determine tol and ordering */ { tol = mxGetScalar (pargin [1]) ; order = (nargout == 4) ? 1 : 0 ; /* amd (A+A'), or natural */ } else { tol = 1 ; order = (nargout == 4) ? 2 : 0 ; /* amd(S'*S) w/dense rows or I */ } if (mxIsComplex (pargin [0])) { #ifndef NCOMPLEX cs_cls *S ; cs_cln *N ; cs_cl Amatrix, *A, *D ; A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ; /* get A */ n = A->n ; S = cs_cl_sqr (order, A, 0) ; /* symbolic ordering, no QR bound */ N = cs_cl_lu (A, S, tol) ; /* numeric factorization */ if (!N) mexErrMsgTxt ("cs_lu failed (singular, or out of memory)") ; cs_cl_free (A->x) ; /* complex copy no longer needed */ cs_cl_dropzeros (N->L) ; /* drop zeros from L and sort it */ D = cs_cl_transpose (N->L, 1) ; cs_cl_spfree (N->L) ; N->L = cs_cl_transpose (D, 1) ; cs_cl_spfree (D) ; cs_cl_dropzeros (N->U) ; /* drop zeros from U and sort it */ D = cs_cl_transpose (N->U, 1) ; cs_cl_spfree (N->U) ; N->U = cs_cl_transpose (D, 1) ; cs_cl_spfree (D) ; p = cs_cl_pinv (N->pinv, n) ; /* p=pinv' */ pargout [0] = cs_cl_mex_put_sparse (&(N->L)) ; /* return L */ pargout [1] = cs_cl_mex_put_sparse (&(N->U)) ; /* return U */ pargout [2] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */ /* return Q */ if (nargout == 4) pargout [3] = cs_dl_mex_put_int (S->q, n, 1, 0) ; cs_cl_nfree (N) ; cs_cl_sfree (S) ; #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dls *S ; cs_dln *N ; cs_dl Amatrix, *A, *D ; A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */ n = A->n ; S = cs_dl_sqr (order, A, 0) ; /* symbolic ordering, no QR bound */ N = cs_dl_lu (A, S, tol) ; /* numeric factorization */ if (!N) mexErrMsgTxt ("cs_lu failed (singular, or out of memory)") ; cs_dl_dropzeros (N->L) ; /* drop zeros from L and sort it */ D = cs_dl_transpose (N->L, 1) ; cs_dl_spfree (N->L) ; N->L = cs_dl_transpose (D, 1) ; cs_dl_spfree (D) ; cs_dl_dropzeros (N->U) ; /* drop zeros from U and sort it */ D = cs_dl_transpose (N->U, 1) ; cs_dl_spfree (N->U) ; N->U = cs_dl_transpose (D, 1) ; cs_dl_spfree (D) ; p = cs_dl_pinv (N->pinv, n) ; /* p=pinv' */ pargout [0] = cs_dl_mex_put_sparse (&(N->L)) ; /* return L */ pargout [1] = cs_dl_mex_put_sparse (&(N->U)) ; /* return U */ pargout [2] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */ /* return Q */ if (nargout == 4) pargout [3] = cs_dl_mex_put_int (S->q, n, 1, 0) ; cs_dl_nfree (N) ; cs_dl_sfree (S) ; } } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_chol_mex.c0000644001170100242450000000346710573562345022306 0ustar davisfac#include "cs_mex.h" /* cs_chol: sparse Cholesky factorization */ void mexFunction (int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ]) { CS_INT order, n, drop, *p ; if (nargout > 2 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: [L,p] = cs_chol(A,drop)") ; } drop = (nargin == 1) ? 1 : mxGetScalar (pargin [1]) ; order = (nargout > 1) ? 1 : 0 ; /* determine ordering */ if (mxIsComplex (pargin [0])) { #ifndef NCOMPLEX cs_cl Amatrix, *A ; cs_cls *S ; cs_cln *N ; A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ; /* get A */ n = A->n ; S = cs_cl_schol (order, A) ; /* symbolic Cholesky */ N = cs_cl_chol (A, S) ; /* numeric Cholesky */ if (!N) mexErrMsgTxt ("cs_chol failed: not positive definite\n") ; cs_free (A->x) ; if (drop) cs_cl_dropzeros (N->L) ; /* drop zeros if requested*/ pargout [0] = cs_cl_mex_put_sparse (&(N->L)) ; /* return L */ if (nargout > 1) { p = cs_cl_pinv (S->pinv, n) ; /* p=pinv' */ pargout [1] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */ } cs_cl_nfree (N) ; cs_cl_sfree (S) ; #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Amatrix, *A ; cs_dls *S ; cs_dln *N ; A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */ n = A->n ; S = cs_dl_schol (order, A) ; /* symbolic Cholesky */ N = cs_dl_chol (A, S) ; /* numeric Cholesky */ if (!N) mexErrMsgTxt ("cs_chol failed: not positive definite\n") ; if (drop) cs_dl_dropzeros (N->L) ; /* drop zeros if requested*/ pargout [0] = cs_dl_mex_put_sparse (&(N->L)) ; /* return L */ if (nargout > 1) { p = cs_dl_pinv (S->pinv, n) ; /* p=pinv' */ pargout [1] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */ } cs_dl_nfree (N) ; cs_dl_sfree (S) ; } } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_dmperm_mex.c0000644001170100242450000000240110573562346022631 0ustar davisfac#include "cs_mex.h" /* cs_dmperm: maximum matching or Dulmage-Mendelsohn permutation. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double seed ; cs_dl *A, Amatrix ; cs_dld *D ; CS_INT m, n, *jmatch, iseed ; if (nargin < 1 || nargin > 2 || nargout > 6) { mexErrMsgTxt ("Usage: [p,q,r,s,cc,rr] = cs_dmperm (A,seed)") ; } seed = (nargin > 1) ? mxGetScalar (pargin [1]) : 0 ; /* get seed */ iseed = (seed > 0 && seed < 1) ? (seed * RAND_MAX) : seed ; A = cs_dl_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ; /* get A */ n = A->n ; m = A->m ; if (nargout <= 1) { jmatch = cs_dl_maxtrans (A, iseed) ; /* max. matching */ pargout [0] = cs_dl_mex_put_int (jmatch+m, n, 1, 0) ; /* return imatch */ cs_free (jmatch) ; } else { D = cs_dl_dmperm (A, iseed) ; /* Dulmage-Mendelsohn decomposition */ pargout [0] = cs_dl_mex_put_int (D->p, m, 1, 0) ; pargout [1] = cs_dl_mex_put_int (D->q, n, 1, 0) ; pargout [2] = cs_dl_mex_put_int (D->r, D->nb+1, 1, 0) ; pargout [3] = cs_dl_mex_put_int (D->s, D->nb+1, 1, 0) ; pargout [4] = cs_dl_mex_put_int (D->cc, 5, 1, 0) ; pargout [5] = cs_dl_mex_put_int (D->rr, 5, 1, 0) ; cs_dl_dfree (D) ; } } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_qrsol_mex.c0000644001170100242450000000304110573562351022502 0ustar davisfac#include "cs_mex.h" /* cs_qrsol: solve least squares or underdetermined problem */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT k, order ; if (nargout > 1 || nargin < 2 || nargin > 3) { mexErrMsgTxt ("Usage: x = cs_qrsol(A,b,order)") ; } order = (nargin < 3) ? 3 : mxGetScalar (pargin [2]) ; order = CS_MAX (order, 0) ; order = CS_MIN (order, 3) ; if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { #ifndef NCOMPLEX cs_cl *A, Amatrix ; cs_complex_t *x, *b ; A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */ b = cs_cl_mex_get_double (A->m, pargin [1]) ; /* get b */ x = cs_dl_calloc (CS_MAX (A->m, A->n), sizeof (cs_complex_t)) ; for (k = 0 ; k < A->m ; k++) x [k] = b [k] ; /* x = b */ cs_free (b) ; if (!cs_cl_qrsol (order, A, x)) /* x = A\x */ { mexErrMsgTxt ("QR solve failed") ; } pargout [0] = cs_cl_mex_put_double (A->n, x) ; /* return x */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl *A, Amatrix ; double *x, *b ; A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ b = cs_dl_mex_get_double (A->m, pargin [1]) ; /* get b */ x = cs_dl_calloc (CS_MAX (A->m, A->n), sizeof (double)) ; /* x = b */ for (k = 0 ; k < A->m ; k++) x [k] = b [k] ; if (!cs_dl_qrsol (order, A, x)) /* x = A\x */ { mexErrMsgTxt ("QR solve failed") ; } cs_dl_mex_put_double (A->n, x, &(pargout [0])) ; /* return x */ cs_free (x) ; } } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_droptol_mex.c0000644001170100242450000000255410573562346023041 0ustar davisfac#include "cs_mex.h" /* cs_droptol: remove small entries from A */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT j, k ; double tol ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: C = cs_droptol(A,tol)") ; } tol = mxGetScalar (pargin [1]) ; /* get tol */ if (mxIsComplex (pargin [0])) { #ifndef NCOMPLEX cs_cl Amatrix, *C, *A ; A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */ C = cs_cl_spalloc (A->m, A->n, A->nzmax, 1, 0) ; /* C = A */ for (j = 0 ; j <= A->n ; j++) C->p [j] = A->p [j] ; for (k = 0 ; k < A->nzmax ; k++) C->i [k] = A->i [k] ; for (k = 0 ; k < A->nzmax ; k++) C->x [k] = A->x [k] ; cs_cl_droptol (C, tol) ; /* drop from C */ pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Amatrix, *C, *A ; A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ C = cs_dl_spalloc (A->m, A->n, A->nzmax, 1, 0) ; /* C = A */ for (j = 0 ; j <= A->n ; j++) C->p [j] = A->p [j] ; for (k = 0 ; k < A->nzmax ; k++) C->i [k] = A->i [k] ; for (k = 0 ; k < A->nzmax ; k++) C->x [k] = A->x [k] ; cs_dl_droptol (C, tol) ; /* drop from C */ pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */ } } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_lsolve_mex.c0000644001170100242450000000574210634322432022650 0ustar davisfac#include "cs_mex.h" /* cs_lsolve: x=L\b. L must be sparse and lower triangular. b must be a * full or sparse vector. x is full or sparse, depending on b. * * Time taken is O(flop count), which may be less than n if b is sparse, * depending on L and b. * * This function works with MATLAB 7.2, but is not perfectly compatible with * the requirements of a MATLAB mexFunction when b is sparse. X is returned * as an unsorted sparse vector. Also, this mexFunction temporarily modifies * its input, L, by modifying L->p (in the cs_dfs function) and then restoring * it. This could be corrected by creating a copy of L->p * (see cs_dmperm_mex.c), but this would take O(n) time, destroying the * O(flop count) time complexity of this function. * * Note that b cannot be sparse complex. This function does not support * sparse complex L and b because the sparse x=L\b only accesses part of the * matrix L. Converting L from a MATLAB complex matrix to a CXSparse complex * matrix requires all of L to be accessed, defeating the purpose of this * function. * * L can be sparse complex, but in that case b must be full real or complex, * not sparse. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT top, nz, p, *xi, n ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_lsolve(L,b)") ; } if (mxIsSparse (pargin [1])) { cs_dl Lmatrix, Bmatrix, *L, *B, *X ; double *x ; if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { mexErrMsgTxt ("sparse complex case not supported") ; } L = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ;/* get L */ n = L->n ; B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ;/* get sparse b*/ cs_mex_check (0, n, 1, 0, 1, 1, pargin [1]) ; xi = cs_dl_malloc (2*n, sizeof (CS_INT)) ; /* get workspace */ x = cs_dl_malloc (n, sizeof (double)) ; top = cs_dl_spsolve (L, B, 0, xi, x, NULL, 1) ; /* x = L\b */ X = cs_dl_spalloc (n, 1, n-top, 1, 0) ; /* create sparse x*/ X->p [0] = 0 ; nz = 0 ; for (p = top ; p < n ; p++) { X->i [nz] = xi [p] ; X->x [nz++] = x [xi [p]] ; } X->p [1] = nz ; pargout [0] = cs_dl_mex_put_sparse (&X) ; cs_free (x) ; cs_free (xi) ; } else if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { #ifndef NCOMPLEX cs_cl Lmatrix, *L ; cs_complex_t *x ; L = cs_cl_mex_get_sparse (&Lmatrix, 1, pargin [0]) ; /* get L */ n = L->n ; x = cs_cl_mex_get_double (n, pargin [1]) ; /* x = b */ cs_cl_lsolve (L, x) ; /* x = L\x */ cs_free (L->x) ; pargout [0] = cs_cl_mex_put_double (n, x) ; /* return x */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Lmatrix, *L ; double *x, *b ; L = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; /* get L */ n = L->n ; b = cs_dl_mex_get_double (n, pargin [1]) ; /* get b */ x = cs_dl_mex_put_double (n, b, &(pargout [0])) ; /* x = b */ cs_dl_lsolve (L, x) ; /* x = L\x */ } } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_print_mex.c0000644001170100242450000000147110573562351022503 0ustar davisfac#include "cs_mex.h" /* cs_print: print the contents of a sparse matrix. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT brief ; if (nargout > 0 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: cs_print(A,brief)") ; } brief = (nargin < 2) ? 0 : mxGetScalar (pargin [1]) ; /* get brief */ if (mxIsComplex (pargin [0])) { #ifndef NCOMPLEX cs_cl Amatrix, *A ; A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */ cs_cl_print (A, brief) ; /* print A */ cs_free (A->x) ; #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Amatrix, *A ; A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ;/* get A */ cs_print (A, brief) ; /* print A */ } } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_esep.m0000644001170100242450000000120310620372560021427 0ustar davisfacfunction [a,b] = cs_esep (A) %CS_ESEP find an edge separator of a symmetric matrix A % [a,b] = cs_esep(A) finds a edge separator s that splits the graph of A % into two parts a and b of roughly equal size. The edge separator is the % set of entries in A(a,b). % % Example: % Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; % [a,b] = cs_esep (A) ; % cspy (A (a,b)) ; % % See also CS_NSEP, CS_SEP, CS_ND, SYMRCM. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (~isreal (A)) A = spones (A) ; end p = symrcm (A) ; n2 = fix (size(A,1)/2) ; a = p (1:n2) ; b = p (n2+1:end) ; SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_thumb_mex.c0000644001170100242450000000340610573562353022470 0ustar davisfac#include "cs_mex.h" /* cs_thumb: convert a sparse matrix to a dense 2D thumbnail matrix of size * at most k-by-k. k defaults to 256. A helper mexFunction for cspy. */ #define INDEX(i,j,lda) ((i)+(j)*(lda)) #define ISNAN(x) ((x) != (x)) #ifdef DBL_MAX #define BIG_VALUE DBL_MAX #else #define BIG_VALUE 1.7e308 #endif void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT m, n, mn, m2, n2, k, s, j, ij, sj, si, p, *Ap, *Ai ; double aij, ax, az, *S, *Ax, *Az ; if (nargout > 1 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: S = cs_thumb(A,k)") ; } cs_mex_check (0, -1, -1, 0, 1, 1, pargin [0]) ; m = mxGetM (pargin [0]) ; n = mxGetN (pargin [0]) ; mn = CS_MAX (m,n) ; k = (nargin == 1) ? 256 : mxGetScalar (pargin [1]) ; /* get k */ /* s = size of each submatrix; A(1:s,1:s) maps to S(1,1) */ s = (mn < k) ? 1 : (CS_INT) ceil ((double) mn / (double) k) ; m2 = (CS_INT) ceil ((double) m / (double) s) ; n2 = (CS_INT) ceil ((double) n / (double) s) ; /* create S */ pargout [0] = mxCreateDoubleMatrix (m2, n2, mxREAL) ; S = mxGetPr (pargout [0]) ; Ap = (CS_INT *) mxGetJc (pargin [0]) ; Ai = (CS_INT *) mxGetIr (pargin [0]) ; Ax = mxGetPr (pargin [0]) ; Az = (mxIsComplex (pargin [0])) ? mxGetPi (pargin [0]) : NULL ; for (j = 0 ; j < n ; j++) { sj = j/s ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { si = Ai [p] / s ; ij = INDEX (si,sj,m2) ; ax = Ax [p] ; az = Az ? Az [p] : 0 ; if (az == 0) { aij = fabs (ax) ; } else { aij = sqrt (ax*ax + az*az) ; } if (ISNAN (aij)) aij = BIG_VALUE ; aij = CS_MIN (BIG_VALUE, aij) ; S [ij] = CS_MAX (S [ij], aij) ; } } } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_updown_mex.c0000644001170100242450000000612210634327243022656 0ustar davisfac#include "cs_mex.h" /* cs_updown: sparse Cholesky update/downdate (rank-1 or multiple rank) */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT ignore, j, k, n, lnz, *parent, sigma = 1, cp [2], ok ; char sigma_string [20] ; if (nargout > 1 || nargin < 3 || nargin > 4) { mexErrMsgTxt ("Usage: L = cs_updown(L,C,parent,sigma)") ; } if (nargin > 3 && mxIsChar (pargin [3])) { mxGetString (pargin [3], sigma_string, 8) ; sigma = (sigma_string [0] == '-') ? (-1) : 1 ; } n = mxGetN (pargin [0]) ; parent = cs_dl_mex_get_int (n, pargin [2], &ignore, 0) ; /* get parent*/ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { #ifndef NCOMPLEX cs_cl Lmatrix, *Lin, Cmatrix, *C, *L, Cvector, *Cvec ; /* get input L, and copy MATLAB complex to C complex type */ Lin = cs_cl_mex_get_sparse (&Lmatrix, 1, pargin [0]) ; /* make a copy of L (this can take more work than updating L itself) */ lnz = Lin->p [n] ; L = cs_cl_spalloc (n, n, lnz, 0, 0) ; for (j = 0 ; j <= n ; j++) L->p [j] = Lin->p [j] ; for (k = 0 ; k < lnz ; k++) L->i [k] = Lin->i [k] ; /* complex values already copied into Lin->x, use shallow copy for L */ L->x = Lin->x ; cs_mex_check (0, n, -1, 0, 1, 1, pargin [1]) ; /* get C */ C = cs_cl_mex_get_sparse (&Cmatrix, 0, pargin [1]) ; /* do the update one column at a time */ Cvec = &Cvector ; Cvec->m = n ; Cvec->n = 1 ; Cvec->p = cp ; Cvec->nz = -1 ; cp [0] = 0 ; for (k = 0 ; k < C->n ; k++) { /* extract C(:,k) */ cp [1] = C->p [k+1] - C->p [k] ; Cvec->nzmax = cp [1] ; Cvec->i = C->i + C->p [k] ; Cvec->x = C->x + C->p [k] ; /* update/downdate */ ok = cs_cl_updown (L, sigma, Cvec, parent) ; if (!ok) mexErrMsgTxt ("matrix is not positive definite") ; } /* return new L */ pargout [0] = cs_cl_mex_put_sparse (&L) ; cs_free (C->x) ; /* free complex copy of C */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Lmatrix, *Lin, Cmatrix, *C, *L, Cvector, *Cvec ; /* get input L */ Lin = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; /* make a copy of L (this can take more work than updating L itself) */ lnz = Lin->p [n] ; L = cs_dl_spalloc (n, n, lnz, 1, 0) ; for (j = 0 ; j <= n ; j++) L->p [j] = Lin->p [j] ; for (k = 0 ; k < lnz ; k++) L->i [k] = Lin->i [k] ; for (k = 0 ; k < lnz ; k++) L->x [k] = Lin->x [k] ; cs_mex_check (0, n, -1, 0, 1, 1, pargin [1]) ; /* get C */ C = cs_dl_mex_get_sparse (&Cmatrix, 0, 1, pargin [1]) ; /* do the update one column at a time */ Cvec = &Cvector ; Cvec->m = n ; Cvec->n = 1 ; Cvec->p = cp ; Cvec->nz = -1 ; cp [0] = 0 ; for (k = 0 ; k < C->n ; k++) { /* extract C(:,k) */ cp [1] = C->p [k+1] - C->p [k] ; Cvec->nzmax = cp [1] ; Cvec->i = C->i + C->p [k] ; Cvec->x = C->x + C->p [k] ; /* update/downdate */ ok = cs_dl_updown (L, sigma, Cvec, parent) ; if (!ok) mexErrMsgTxt ("matrix is not positive definite") ; } /* return new L */ pargout [0] = cs_dl_mex_put_sparse (&L) ; } } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_make.m0000644001170100242450000000613110621037031021405 0ustar davisfacfunction [objfiles, timestamp] = cs_make (f, docomplex) %CS_MAKE compiles CXSparse for use in MATLAB. % Usage: % cs_make % [objfiles, timestamp] = cs_make (f, docomplex) % % With no input arguments, or with f=0, only those files needing to be % compiled are compiled (like the Unix/Linux/GNU "make" command, but not % requiring "make"). If f is a nonzero number, all files are compiled. % If f is a string, only that mexFunction is compiled. For example, % cs_make ('cs_add') just compiles the cs_add mexFunction. This option is % useful when developing a single new mexFunction. This function can only be % used if the current directory is CXSparse/MATLAB/CSparse. Returns a list of % the object files in CXSparse, and the latest modification time of any source % codes. % % NOTE: if your compiler does not support the ANSI C99 complex type (most % notably Microsoft Windows), the CXSparse mexFunctions will not support % complex sparse matrices. The complex case is not attempted if docomplex is % zero. % % To add a new function and its MATLAB mexFunction to CXSparse: % % (1) Create a source code file CXSparse/Source/cs_mynewfunc.c. % (2) Create a help file, CXSparse/MATLAB/CSparse/cs_mynewfunc.m. % This is very useful, but not strictly required. % (3) Add the prototype of cs_mynewfunc to CXSparse/Include/cs.h. % (4) Create its MATLAB mexFunction, CXSparse/MATLAB/cs_mynewfunc_mex.c. % (5) Edit cs_make.m, and add 'cs_mynewfunc' to the 'cs' and 'csm' lists. % (6) Type 'cs_make' in the CXSparse/MATLAB/CSparse directory. % If all goes well, your new function is ready for use in MATLAB. % % (7) Optionally add 'cs_mynewfunc' to CXSparse/Source/Makefile % and CXSparse/MATLAB/CSparse/Makefile, if you want to use the % Unix/Linux/GNU make command instead of cs_make.m. See where % 'cs_add' and 'cs_add_mex' appear in those files, and add % 'cs_mynewfunc' accordingly. % (8) Optionally add 'cs_mynewfunc' to Tcov/Makefile, and add additional % test code to cs_test.c, and add MATLAB test code to MATLAB/Test/*. % % Example: % cs_make % compile everything % cs_make ('cs_chol') ; % just compile cs_chol mexFunction % % See also MEX. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse if (nargin < 1) f = 0 ; end if (nargin < 2) docomplex = 1 ; end try % ispc does not appear in MATLAB 5.3 pc = ispc ; catch % if ispc fails, assume we are on a Windows PC if it's not unix pc = ~isunix ; end if (pc) docomplex = 0 ; end if (docomplex == 0) % do not attempt to compile with complex matrices [objfiles, timestamp] = cs_make_helper (f, 0) ; else try % try with complex support [objfiles, timestamp] = cs_make_helper (f, 1) ; catch % oops - that failed, try without complex support fprintf ('retrying without complex matrix support\n') ; [objfiles, timestamp] = cs_make_helper (f, 0) ; end end if (f > 0) fprintf ('CXSparse successfully installed.\n') ; end SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/README.txt0000644001170100242450000000007410571365512021337 0ustar davisfacMATLAB interface for CXSparse. See Contents.m for details. SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_lusol_mex.c0000644001170100242450000000315710573562350022507 0ustar davisfac#include "cs_mex.h" /* cs_lusol: solve A*x=b using a sparse LU factorization */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double tol ; CS_INT order ; if (nargout > 1 || nargin < 2 || nargin > 4) { mexErrMsgTxt ("Usage: x = cs_lusol(A,b,order,tol)") ; } order = (nargin < 3) ? 2 : mxGetScalar (pargin [2]) ; order = CS_MAX (order, 0) ; order = CS_MIN (order, 3) ; if (nargin == 2) { tol = 1 ; /* normal partial pivoting */ } else if (nargin == 3) { tol = (order == 1) ? 0.001 : 1 ; /* tol = 0.001 for amd(A+A') */ } else { tol = mxGetScalar (pargin [3]) ; } if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { #ifndef NCOMPLEX cs_cl *A, Amatrix ; cs_complex_t *x ; A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ; /* get A */ x = cs_cl_mex_get_double (A->n, pargin [1]) ; /* x = b */ if (!cs_cl_lusol (order, A, x, tol)) /* x = A\x */ { mexErrMsgTxt ("failed (singular or out of memory)") ; } cs_cl_free (A->x) ; /* complex copy no longer needed */ pargout [0] = cs_cl_mex_put_double (A->n, x) ; /* return x */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl *A, Amatrix ; double *x, *b ; A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */ b = cs_dl_mex_get_double (A->n, pargin [1]) ; /* get b */ x = cs_dl_mex_put_double (A->n, b, &(pargout [0])) ; /* x = b */ if (!cs_dl_lusol (order, A, x, tol)) /* x = A\x */ { mexErrMsgTxt ("failed (singular or out of memory)") ; } } } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_etree_mex.c0000644001170100242450000000164410573562347022462 0ustar davisfac#include "cs_mex.h" /* cs_etree: elimination tree of A or A'*A */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { cs_dl Amatrix, *A ; CS_INT n, *parent, *post ; int ata ; char mode [20] ; if (nargout > 2 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: [parent,post] = cs_etree(A,mode)") ; } ata = 0 ; /* get mode */ if (nargin > 1 && mxIsChar (pargin [1])) { mxGetString (pargin [1], mode, 8) ; ata = (mode [0] == 'c') ; } A = cs_dl_mex_get_sparse (&Amatrix, !ata, 0, pargin [0]) ; /* get A */ n = A->n ; parent = cs_dl_etree (A, ata) ; /* compute etree */ if (nargout > 1) { post = cs_dl_post (parent, n) ; /* postorder the etree*/ pargout [1] = cs_dl_mex_put_int (post, n, 1, 1) ; /* return post */ } pargout [0] = cs_dl_mex_put_int (parent, n, 1, 1) ; /* return parent */ } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_sparse_mex.c0000644001170100242450000000346110573562352022646 0ustar davisfac#include "cs_mex.h" /* cs_sparse: convert triplet form into compress-column form sparse matrix */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { if (nargout > 1 || nargin != 3) { mexErrMsgTxt ("Usage: A = cs_sparse(i,j,x)") ; } if (mxIsComplex (pargin [2])) { #ifndef NCOMPLEX cs_cl *A, *C, *T, Tmatrix ; T = &Tmatrix ; /* get i,j,x and copy to triplet form */ T->nz = mxGetM (pargin [0]) ; T->p = cs_dl_mex_get_int (T->nz, pargin [0], &(T->n), 1) ; T->i = cs_dl_mex_get_int (T->nz, pargin [1], &(T->m), 1) ; cs_mex_check (1, T->nz, 1, 0, 0, 1, pargin [2]) ; T->x = cs_cl_mex_get_double (T->nz, pargin [2]) ; T->nzmax = T->nz ; C = cs_cl_compress (T) ; /* create sparse matrix C */ cs_cl_dupl (C) ; /* remove duplicates from C */ cs_cl_dropzeros (C) ; /* remove zeros from C */ A = cs_cl_transpose (C, -1) ; /* A=C.' */ cs_cl_spfree (C) ; pargout [0] = cs_cl_mex_put_sparse (&A) ; /* return A */ cs_free (T->p) ; cs_free (T->i) ; cs_free (T->x) ; /* free copy of complex values*/ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl *A, *C, *T, Tmatrix ; T = &Tmatrix ; /* get i,j,x and copy to triplet form */ T->nz = mxGetM (pargin [0]) ; T->p = cs_dl_mex_get_int (T->nz, pargin [0], &(T->n), 1) ; T->i = cs_dl_mex_get_int (T->nz, pargin [1], &(T->m), 1) ; cs_mex_check (1, T->nz, 1, 0, 0, 1, pargin [2]) ; T->x = mxGetPr (pargin [2]) ; T->nzmax = T->nz ; C = cs_dl_compress (T) ; /* create sparse matrix C */ cs_dl_dupl (C) ; /* remove duplicates from C */ cs_dl_dropzeros (C) ; /* remove zeros from C */ A = cs_dl_transpose (C, 1) ; /* A=C' */ cs_dl_spfree (C) ; pargout [0] = cs_dl_mex_put_sparse (&A) ; /* return A */ cs_free (T->p) ; cs_free (T->i) ; } } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_add_mex.c0000644001170100242450000000403210573562344022075 0ustar davisfac#include "cs_mex.h" /* cs_add: sparse matrix addition */ #ifndef NCOMPLEX static cs_complex_t get_complex (const mxArray *a) { cs_complex_t s = mxGetScalar (a) ; if (mxIsComplex (a)) { double *z = mxGetPi (a) ; s += I * z [0] ; } return (s) ; } #endif void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { if (nargout > 1 || nargin < 2 || nargin > 4) { mexErrMsgTxt ("Usage: C = cs_add(A,B,alpha,beta)") ; } if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]) || (nargin > 2 && mxIsComplex (pargin [2])) || (nargin > 3 && mxIsComplex (pargin [3]))) { #ifndef NCOMPLEX cs_complex_t alpha, beta ; cs_cl Amatrix, Bmatrix, *A, *B, *C, *D ; A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */ B = cs_cl_mex_get_sparse (&Bmatrix, 0, pargin [1]) ; /* get B */ alpha = (nargin < 3) ? 1 : get_complex (pargin [2]) ; /* get alpha */ beta = (nargin < 4) ? 1 : get_complex (pargin [3]) ; /* get beta */ C = cs_cl_add (A,B,alpha,beta) ; /* C = alpha*A + beta *B */ cs_cl_dropzeros (C) ; /* drop zeros */ D = cs_cl_transpose (C, 1) ; /* sort result via double transpose */ cs_cl_spfree (C) ; C = cs_cl_transpose (D, 1) ; cs_cl_spfree (D) ; pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { double alpha, beta ; cs_dl Amatrix, Bmatrix, *A, *B, *C, *D ; A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ; /* get B */ alpha = (nargin < 3) ? 1 : mxGetScalar (pargin [2]) ; /* get alpha */ beta = (nargin < 4) ? 1 : mxGetScalar (pargin [3]) ; /* get beta */ C = cs_dl_add (A,B,alpha,beta) ; /* C = alpha*A + beta *B */ cs_dl_dropzeros (C) ; /* drop zeros */ D = cs_dl_transpose (C, 1) ; /* sort result via double transpose */ cs_dl_spfree (C) ; C = cs_dl_transpose (D, 1) ; cs_dl_spfree (D) ; pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */ } } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_ltsolve_mex.c0000644001170100242450000000200610634327040023022 0ustar davisfac#include "cs_mex.h" /* cs_ltsolve: solve an upper triangular system L'*x=b */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_ltsolve(L,b)") ; } if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { #ifndef NCOMPLEX cs_cl Lmatrix, *L ; cs_complex_t *x ; L = cs_cl_mex_get_sparse (&Lmatrix, 1, pargin [0]) ; /* get L */ x = cs_cl_mex_get_double (L->n, pargin [1]) ; /* x = b */ cs_cl_ltsolve (L, x) ; /* x = L'\x */ cs_free (L->x) ; pargout [0] = cs_cl_mex_put_double (L->n, x) ; /* return x */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Lmatrix, *L ; double *x, *b ; L = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; /* get L */ b = cs_dl_mex_get_double (L->n, pargin [1]) ; /* get b */ x = cs_dl_mex_put_double (L->n, b, &(pargout [0])) ; /* x = b */ cs_dl_ltsolve (L, x) ; /* x = L'\x */ } } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_symperm_mex.c0000644001170100242450000000261010634322614023031 0ustar davisfac#include "cs_mex.h" /* cs_symperm: symmetric permutation of a symmetric sparse matrix. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT ignore, n, *P, *Pinv ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: C = cs_symperm(A,p)") ; } if (mxIsComplex (pargin [0])) { #ifndef NCOMPLEX cs_cl Amatrix, *A, *C, *D ; A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ; n = A->n ; P = cs_dl_mex_get_int (n, pargin [1], &ignore, 1) ; /* get P */ Pinv = cs_cl_pinv (P, n) ; /* P=Pinv' */ C = cs_cl_symperm (A, Pinv, 1) ; /* C = A(p,p) */ D = cs_cl_transpose (C, 1) ; /* sort C */ cs_cl_spfree (C) ; C = cs_cl_transpose (D, 1) ; cs_cl_spfree (D) ; pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */ cs_free (P) ; cs_free (Pinv) ; #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Amatrix, *A, *C, *D ; A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; n = A->n ; P = cs_dl_mex_get_int (n, pargin [1], &ignore, 1) ; /* get P */ Pinv = cs_dl_pinv (P, n) ; /* P=Pinv' */ C = cs_dl_symperm (A, Pinv, 1) ; /* C = A(p,p) */ D = cs_dl_transpose (C, 1) ; /* sort C */ cs_dl_spfree (C) ; C = cs_dl_transpose (D, 1) ; cs_dl_spfree (D) ; pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */ cs_free (P) ; cs_free (Pinv) ; } } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_mex.c0000644001170100242450000001451210634322255021262 0ustar davisfac#include "cs_mex.h" /* check MATLAB input argument */ void cs_mex_check (CS_INT nel, CS_INT m, CS_INT n, int square, int sparse, int values, const mxArray *A) { CS_INT nnel, mm = mxGetM (A), nn = mxGetN (A) ; #ifdef NCOMPLEX if (values) { if (mxIsComplex (A)) mexErrMsgTxt ("complex matrices not supported") ; } #endif if (sparse && !mxIsSparse (A)) mexErrMsgTxt ("matrix must be sparse") ; if (!sparse) { if (mxIsSparse (A)) mexErrMsgTxt ("matrix must be full") ; if (values && !mxIsDouble (A)) mexErrMsgTxt ("matrix must be double") ; } if (nel) { /* check number of elements */ nnel = mxGetNumberOfElements (A) ; if (m >= 0 && n >= 0 && m*n != nnel) mexErrMsgTxt ("wrong length") ; } else { /* check row and/or column dimensions */ if (m >= 0 && m != mm) mexErrMsgTxt ("wrong dimension") ; if (n >= 0 && n != nn) mexErrMsgTxt ("wrong dimension") ; } if (square && mm != nn) mexErrMsgTxt ("matrix must be square") ; } /* get a real (or pattern) MATLAB sparse matrix and convert to cs_dl */ cs_dl *cs_dl_mex_get_sparse (cs_dl *A, int square, int values, const mxArray *Amatlab) { cs_mex_check (0, -1, -1, square, 1, values, Amatlab) ; A->m = mxGetM (Amatlab) ; A->n = mxGetN (Amatlab) ; A->p = (CS_INT *) mxGetJc (Amatlab) ; A->i = (CS_INT *) mxGetIr (Amatlab) ; A->x = values ? mxGetPr (Amatlab) : NULL ; A->nzmax = mxGetNzmax (Amatlab) ; A->nz = -1 ; /* denotes a compressed-col matrix, instead of triplet */ return (A) ; } /* return a real sparse matrix to MATLAB */ mxArray *cs_dl_mex_put_sparse (cs_dl **Ahandle) { cs_dl *A ; mxArray *Amatlab ; A = *Ahandle ; if (!A) mexErrMsgTxt ("failed") ; Amatlab = mxCreateSparse (0, 0, 0, mxREAL) ; mxSetM (Amatlab, A->m) ; mxSetN (Amatlab, A->n) ; mxSetNzmax (Amatlab, A->nzmax) ; cs_free (mxGetJc (Amatlab)) ; cs_free (mxGetIr (Amatlab)) ; cs_free (mxGetPr (Amatlab)) ; mxSetJc (Amatlab, (void *) (A->p)) ; /* assign A->p pointer to MATLAB A */ mxSetIr (Amatlab, (void *) (A->i)) ; mxSetPr (Amatlab, A->x) ; cs_free (A) ; /* frees A struct only, not A->p, etc */ *Ahandle = NULL ; return (Amatlab) ; } /* get a real MATLAB dense column vector */ double *cs_dl_mex_get_double (CS_INT n, const mxArray *X) { cs_mex_check (0, n, 1, 0, 0, 1, X) ; return (mxGetPr (X)) ; } /* return a double vector to MATLAB */ double *cs_dl_mex_put_double (CS_INT n, const double *b, mxArray **X) { double *x ; CS_INT k ; *X = mxCreateDoubleMatrix (n, 1, mxREAL) ; /* create x */ x = mxGetPr (*X) ; for (k = 0 ; k < n ; k++) x [k] = b [k] ; /* copy x = b */ return (x) ; } /* get a MATLAB flint array and convert to CS_INT */ CS_INT *cs_dl_mex_get_int (CS_INT n, const mxArray *Imatlab, CS_INT *imax, int lo) { double *p ; CS_INT i, k, *C = cs_dl_malloc (n, sizeof (CS_INT)) ; cs_mex_check (1, n, 1, 0, 0, 1, Imatlab) ; if (mxIsComplex (Imatlab)) { mexErrMsgTxt ("integer input cannot be complex") ; } p = mxGetPr (Imatlab) ; *imax = 0 ; for (k = 0 ; k < n ; k++) { i = p [k] ; C [k] = i - 1 ; if (i < lo) mexErrMsgTxt ("index out of bounds") ; *imax = CS_MAX (*imax, i) ; } return (C) ; } /* return an CS_INT array to MATLAB as a flint row vector */ mxArray *cs_dl_mex_put_int (CS_INT *p, CS_INT n, CS_INT offset, int do_free) { mxArray *X = mxCreateDoubleMatrix (1, n, mxREAL) ; double *x = mxGetPr (X) ; CS_INT k ; for (k = 0 ; k < n ; k++) x [k] = (p ? p [k] : k) + offset ; if (do_free) cs_free (p) ; return (X) ; } #ifndef NCOMPLEX /* copy a MATLAB real or complex vector into a cs_cl complex vector */ static cs_complex_t *cs_cl_get_vector (CS_INT n, CS_INT size, const mxArray *Xmatlab) { CS_INT p ; double *X, *Z ; cs_complex_t *Y ; X = mxGetPr (Xmatlab) ; Z = (mxIsComplex (Xmatlab)) ? mxGetPi (Xmatlab) : NULL ; Y = cs_dl_malloc (size, sizeof (cs_complex_t)) ; for (p = 0 ; p < n ; p++) { Y [p] = X [p] + I * (Z ? Z [p] : 0) ; } return (Y) ; } /* get a real or complex MATLAB sparse matrix and convert to cs_cl */ cs_cl *cs_cl_mex_get_sparse (cs_cl *A, int square, const mxArray *Amatlab) { cs_mex_check (0, -1, -1, square, 1, 1, Amatlab) ; A->m = mxGetM (Amatlab) ; A->n = mxGetN (Amatlab) ; A->p = (CS_INT *) mxGetJc (Amatlab) ; A->i = (CS_INT *) mxGetIr (Amatlab) ; A->nzmax = mxGetNzmax (Amatlab) ; A->x = cs_cl_get_vector (A->p [A->n], A->nzmax, Amatlab) ; A->nz = -1 ; /* denotes a compressed-col matrix, instead of triplet */ return (A) ; } /* return a complex sparse matrix to MATLAB */ mxArray *cs_cl_mex_put_sparse (cs_cl **Ahandle) { cs_cl *A ; double *x, *z ; mxArray *Amatlab ; CS_INT k ; A = *Ahandle ; if (!A) mexErrMsgTxt ("failed") ; Amatlab = mxCreateSparse (0, 0, 0, mxCOMPLEX) ; mxSetM (Amatlab, A->m) ; mxSetN (Amatlab, A->n) ; mxSetNzmax (Amatlab, A->nzmax) ; cs_cl_free (mxGetJc (Amatlab)) ; cs_cl_free (mxGetIr (Amatlab)) ; cs_cl_free (mxGetPr (Amatlab)) ; cs_cl_free (mxGetPi (Amatlab)) ; mxSetJc (Amatlab, (void *) (A->p)) ; /* assign A->p pointer to MATLAB A */ mxSetIr (Amatlab, (void *) (A->i)) ; x = cs_dl_malloc (A->nzmax, sizeof (double)) ; z = cs_dl_malloc (A->nzmax, sizeof (double)) ; for (k = 0 ; k < A->nzmax ; k++) { x [k] = creal (A->x [k]) ; /* copy and split numerical values */ z [k] = cimag (A->x [k]) ; } cs_cl_free (A->x) ; /* free copy of complex values */ mxSetPr (Amatlab, x) ; mxSetPi (Amatlab, z) ; cs_cl_free (A) ; /* frees A struct only, not A->p, etc */ *Ahandle = NULL ; return (Amatlab) ; } /* get a real or complex MATLAB dense column vector, and copy to cs_complex_t */ cs_complex_t *cs_cl_mex_get_double (CS_INT n, const mxArray *X) { cs_mex_check (0, n, 1, 0, 0, 1, X) ; return (cs_cl_get_vector (n, n, X)) ; } /* copy a complex vector back to MATLAB and free it */ mxArray *cs_cl_mex_put_double (CS_INT n, cs_complex_t *b) { double *x, *z ; mxArray *X ; CS_INT k ; X = mxCreateDoubleMatrix (n, 1, mxCOMPLEX) ; /* create x */ x = mxGetPr (X) ; z = mxGetPi (X) ; for (k = 0 ; k < n ; k++) { x [k] = creal (b [k]) ; /* copy x = b */ z [k] = cimag (b [k]) ; } cs_cl_free (b) ; return (X) ; } #endif SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_mex.h0000644001170100242450000000153510573562554021302 0ustar davisfac#include "cs.h" #include "mex.h" void cs_mex_check (CS_INT nel, CS_INT m, CS_INT n, int square, int sparse, int values, const mxArray *A) ; CS_INT *cs_dl_mex_get_int (CS_INT n, const mxArray *Imatlab, CS_INT *imax, int lo); mxArray *cs_dl_mex_put_int (CS_INT *p, CS_INT n, CS_INT offset, int do_free) ; double *cs_dl_mex_get_double (CS_INT n, const mxArray *X) ; cs_dl *cs_dl_mex_get_sparse (cs_dl *A, int square, int values, const mxArray *Amatlab) ; double *cs_dl_mex_put_double (CS_INT n, const double *b, mxArray **X) ; mxArray *cs_dl_mex_put_sparse (cs_dl **A) ; #ifndef NCOMPLEX cs_complex_t *cs_cl_mex_get_double (CS_INT n, const mxArray *X) ; cs_cl *cs_cl_mex_get_sparse (cs_cl *A, int square, const mxArray *Amatlab) ; mxArray *cs_cl_mex_put_double (CS_INT n, cs_complex_t *b) ; mxArray *cs_cl_mex_put_sparse (cs_cl **Ahandle) ; #endif SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_utsolve_mex.c0000644001170100242450000000200510634322660023035 0ustar davisfac#include "cs_mex.h" /* cs_utsolve: solve a lower triangular system U'*x=b */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_utsolve(U,b)") ; } if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { #ifndef NCOMPLEX cs_cl Umatrix, *U ; cs_complex_t *x ; U = cs_cl_mex_get_sparse (&Umatrix, 1, pargin [0]) ; /* get U */ x = cs_cl_mex_get_double (U->n, pargin [1]) ; /* x = b */ cs_cl_utsolve (U, x) ; /* x = U'\x */ cs_free (U->x) ; pargout [0] = cs_cl_mex_put_double (U->n, x) ; /* return x */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Umatrix, *U ; double *x, *b ; U = cs_dl_mex_get_sparse (&Umatrix, 1, 1, pargin [0]) ; /* get U */ b = cs_dl_mex_get_double (U->n, pargin [1]) ; /* get b */ x = cs_dl_mex_put_double (U->n, b, &(pargout [0])) ; /* x = b */ cs_dl_utsolve (U, x) ; /* x = U'\x */ } } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_randperm_mex.c0000644001170100242450000000165110573562351023157 0ustar davisfac#include "cs_mex.h" /* cs_randperm: random permutation. p=cs_randperm(n,0) is 1:n, * p=cs_randperm(n,-1) is n:-1:1. p = cs_randperm (n,seed) is a random * permutation using the given seed (where seed is not 0 or -1). * seed defaults to 1. A single seed always gives a repeatable permutation. * Use p = cs_randperm(n,rand) to get a permutation that varies with each use. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double seed ; CS_INT iseed, n, *p ; if (nargout > 1 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: p = cs_randperm(n,seed)") ; } seed = (nargin > 1) ? mxGetScalar (pargin [1]) : 1 ; iseed = (seed > 0 && seed < 1) ? (seed * RAND_MAX) : seed ; n = mxGetScalar (pargin [0]) ; n = CS_MAX (n, 0) ; p = cs_dl_randperm (n, iseed) ; pargout [0] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */ } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_usolve_mex.c0000644001170100242450000000574210634322644022666 0ustar davisfac#include "cs_mex.h" /* cs_usolve: x=U\b. U must be sparse and upper triangular. b must be a * full or sparse vector. x is full or sparse, depending on b. * * Time taken is O(flop count), which may be less than n if b is sparse, * depending on U and b. * * This function works with MATLAB 7.2, but is not perfectly compatible with * the requirements of a MATLAB mexFunction when b is sparse. X is returned * as an unsorted sparse vector. Also, this mexFunction temporarily modifies * its input, U, by modifying U->p (in the cs_dfs function) and then restoring * it. This could be corrected by creating a copy of U->p * (see cs_dmperm_mex.c), but this would take O(n) time, destroying the * O(flop count) time complexity of this function. * * Note that b cannot be sparse complex. This function does not support * sparse complex U and b because the sparse x=U\b only accesses part of the * matrix U. Converting U from a MATLAB complex matrix to a CXSparse complex * matrix requires all of U to be accessed, defeating the purpose of this * function. * * U can be sparse complex, but in that case b must be full real or complex, * not sparse. */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT top, nz, p, *xi, n ; if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = cs_usolve(U,b)") ; } if (mxIsSparse (pargin [1])) { cs_dl Umatrix, Bmatrix, *U, *B, *X ; double *x ; if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { mexErrMsgTxt ("sparse complex case not supported") ; } U = cs_dl_mex_get_sparse (&Umatrix, 1, 1, pargin [0]) ;/* get U */ n = U->n ; B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ;/* get sparse b*/ cs_mex_check (0, n, 1, 0, 1, 1, pargin [1]) ; xi = cs_dl_malloc (2*n, sizeof (CS_INT)) ; /* get workspace */ x = cs_dl_malloc (n, sizeof (double)) ; top = cs_dl_spsolve (U, B, 0, xi, x, NULL, 0) ; /* x = U\b */ X = cs_dl_spalloc (n, 1, n-top, 1, 0) ; /* create sparse x*/ X->p [0] = 0 ; nz = 0 ; for (p = top ; p < n ; p++) { X->i [nz] = xi [p] ; X->x [nz++] = x [xi [p]] ; } X->p [1] = nz ; pargout [0] = cs_dl_mex_put_sparse (&X) ; cs_free (x) ; cs_free (xi) ; } else if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { #ifndef NCOMPLEX cs_cl Umatrix, *U ; cs_complex_t *x ; U = cs_cl_mex_get_sparse (&Umatrix, 1, pargin [0]) ; /* get U */ n = U->n ; x = cs_cl_mex_get_double (n, pargin [1]) ; /* x = b */ cs_cl_usolve (U, x) ; /* x = U\x */ cs_free (U->x) ; pargout [0] = cs_cl_mex_put_double (n, x) ; /* return x */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl Umatrix, *U ; double *x, *b ; U = cs_dl_mex_get_sparse (&Umatrix, 1, 1, pargin [0]) ; /* get U */ n = U->n ; b = cs_dl_mex_get_double (n, pargin [1]) ; /* get b */ x = cs_dl_mex_put_double (n, b, &(pargout [0])) ; /* x = b */ cs_dl_usolve (U, x) ; /* x = U\x */ } } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_cholsol_mex.c0000644001170100242450000000246510634322337023012 0ustar davisfac#include "cs_mex.h" /* cs_cholsol: solve A*x=b using a sparse Cholesky factorization */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT order ; if (nargout > 1 || nargin < 2 || nargin > 3) { mexErrMsgTxt ("Usage: x = cs_cholsol(A,b,order)") ; } order = (nargin < 3) ? 1 : mxGetScalar (pargin [2]) ; order = CS_MAX (order, 0) ; order = CS_MIN (order, 3) ; if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { #ifndef NCOMPLEX cs_cl *A, Amatrix ; cs_complex_t *x ; A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ; /* get A */ x = cs_cl_mex_get_double (A->n, pargin [1]) ; /* x = b */ if (!cs_cl_cholsol (order, A, x)) /* x = A\x */ { mexErrMsgTxt ("A not positive definite") ; } cs_free (A->x) ; pargout [0] = cs_cl_mex_put_double (A->n, x) ; /* return x */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl *A, Amatrix ; double *x, *b ; A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */ b = cs_dl_mex_get_double (A->n, pargin [1]) ; /* get b */ x = cs_dl_mex_put_double (A->n, b, &(pargout [0])) ; /* x = b */ if (!cs_dl_cholsol (order, A, x)) /* x = A\x */ { mexErrMsgTxt ("A not positive definite") ; } } } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/private/0000755001170100242450000000000010621054722021304 5ustar davisfacSuiteSparse/CXSparse_newfiles/MATLAB/CSparse/private/cs_make_helper.m0000644001170100242450000001545610621054716024441 0ustar davisfacfunction [objfiles, timestamp_out] = cs_make_helper (f, docomplex) %CS_MAKE_HELPER compiles CXSparse for use in MATLAB. % Usage: % [objfiles, timestamp] = cs_make (f, docomplex) % % With f=0, only those files needing to be % compiled are compiled (like the Unix/Linux/GNU "make" command, but not % requiring "make"). If f is a nonzero number, all files are compiled. % If f is a string, only that mexFunction is compiled. For example, % cs_make ('cs_add') just compiles the cs_add mexFunction. This option is % useful when developing a single new mexFunction. This function can only be % used if the current directory is CXSparse/MATLAB/CSparse. Returns a list of % the object files in CXSparse, and the latest modification time of any source % codes. % % NOTE: if your compiler does not support the ANSI C99 complex type, the % CXSparse mexFunctions will not support complex sparse matrices. % % To add a new function and its MATLAB mexFunction to CXSparse: % % (1) Create a source code file CXSparse/Source/cs_mynewfunc.c. % (2) Create a help file, CXSparse/MATLAB/CSparse/cs_mynewfunc.m. % This is very useful, but not strictly required. % (3) Add the prototype of cs_mynewfunc to CXSparse/Include/cs.h. % (4) Create its MATLAB mexFunction, CXSparse/MATLAB/cs_mynewfunc_mex.c. % (5) Edit cs_make.m, and add 'cs_mynewfunc' to the 'cs' and 'csm' lists. % (6) Type 'cs_make' in the CXSparse/MATLAB/CSparse directory. % If all goes well, your new function is ready for use in MATLAB. % % (7) Optionally add 'cs_mynewfunc' to CXSparse/Source/Makefile % and CXSparse/MATLAB/CSparse/Makefile, if you want to use the % Unix/Linux/GNU make command instead of cs_make.m. See where % 'cs_add' and 'cs_add_mex' appear in those files, and add % 'cs_mynewfunc' accordingly. % (8) Optionally add 'cs_mynewfunc' to Tcov/Makefile, and add additional % test code to cs_test.c, and add MATLAB test code to MATLAB/Test/*. % % Example: % cs_make_helper (1,1) ; % compile everything % cs_make ('cs_chol', 1) ; % just compile cs_chol mexFunction % % See also MEX. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse mexcmd = 'mex -DCS_LONG -I../../../UFconfig' ; if (~isempty (strfind (computer, '64'))) mexcmd = [mexcmd ' -largeArrayDims'] ; end if (nargin < 2) docomplex = 1 ; end if (~docomplex) mexcmd = [mexcmd ' -DNCOMPLEX'] ; end % CSparse source files, in ../../Source, such as ../../Source/cs_add.c. % Note that not all CSparse source files have their own mexFunction. cs = { 'cs_add', 'cs_amd', 'cs_chol', 'cs_cholsol', 'cs_counts', ... 'cs_cumsum', 'cs_dfs', 'cs_dmperm', 'cs_droptol', 'cs_dropzeros', ... 'cs_dupl', 'cs_entry', 'cs_etree', 'cs_fkeep', 'cs_gaxpy', 'cs_happly', ... 'cs_house', 'cs_ipvec', 'cs_load', 'cs_lsolve', 'cs_ltsolve', 'cs_lu', ... 'cs_lusol', 'cs_malloc', 'cs_maxtrans', 'cs_multiply', 'cs_norm', ... 'cs_permute', 'cs_pinv', 'cs_post', 'cs_print', 'cs_pvec', 'cs_qr', ... 'cs_qrsol', 'cs_scatter', 'cs_scc', 'cs_schol', 'cs_sqr', 'cs_symperm', ... 'cs_tdfs', 'cs_transpose', 'cs_compress', 'cs_updown', 'cs_usolve', ... 'cs_utsolve', 'cs_util', 'cs_reach', 'cs_spsolve', 'cs_ereach', ... 'cs_leaf', 'cs_randperm' } ; % add cs_mynewfunc to the above list details = 1 ; kk = 0 ; csm = { } ; if (nargin == 0) force = 0 ; elseif (ischar (f)) fprintf ('cs_make: compiling ../../Source files and %s_mex.c\n', f) ; force = 0 ; csm = {f} ; else force = f ; details = details | (force > 1) ; %#ok if (force & details) %#ok fprintf ('cs_make: re-compiling everything\n') ; end end if (isempty (csm)) % mexFunctions, of the form cs_add_mex.c, etc, in this directory csm = { 'cs_add', 'cs_amd', 'cs_chol', 'cs_cholsol', 'cs_counts', ... 'cs_dmperm', 'cs_droptol', 'cs_etree', 'cs_gaxpy', 'cs_lsolve', ... 'cs_ltsolve', 'cs_lu', 'cs_lusol', 'cs_multiply', 'cs_permute', ... 'cs_print', 'cs_qr', 'cs_qrsol', 'cs_scc', 'cs_symperm', 'cs_thumb', ... 'cs_transpose', 'cs_sparse', 'cs_updown', 'cs_usolve', ... 'cs_utsolve', 'cs_randperm', 'cs_sqr' } ; % add cs_mynewfunc to the above list end try % ispc does not appear in MATLAB 5.3 pc = ispc ; catch % if ispc fails, assume we are on a Windows PC if it's not unix pc = ~isunix ; end if (pc) obj = '.obj' ; else obj = '.o' ; end srcdir = '../../Source/' ; hfile = '../../Include/cs.h' ; % compile each CSparse source file [anysrc timestamp kk] = compile_source ('', 'cs_mex', obj, hfile, force, ... mexcmd, kk, details) ; CS = ['cs_mex' obj] ; if (nargout > 0) objfiles = ['..' filesep 'CSparse' filesep 'cs_mex' obj] ; end for i = 1:length (cs) [s t kk] = compile_source (srcdir, cs{i}, obj, hfile, force, mexcmd, ... kk, details) ; timestamp = max (timestamp, t) ; anysrc = anysrc | s ; %#ok CS = [CS ' ' cs{i} obj] ; %#ok if (nargout > 0) objfiles = [objfiles ' ..' filesep 'CSparse' filesep cs{i} obj] ; %#ok end % complex version: if (docomplex) csrc = cs {i} ; csrc = [ 'cs_cl_' csrc(4:end) ] ; CS = [CS ' ' csrc obj] ; %#ok if (nargout > 0) objfiles = [objfiles ' ..' filesep 'CSparse' filesep csrc obj] ;%#ok end if (s) copyfile (['../../Source/' cs{i} '.c'], [csrc '.c'], 'f') ; if (details) fprintf ('%s\n', ['cp -f ../../Source/' cs{i} '.c ' csrc '.c']); end cmd = sprintf ('%s -DCS_COMPLEX -O -c -I../../Include %s.c\n', ... mexcmd, csrc) ; kk = do_cmd (cmd, kk, details) ; end end end % compile each CSparse mexFunction obj = ['.' mexext] ; for i = 1:length (csm) [s t] = cs_must_compile ('', csm{i}, '_mex', obj, hfile, force) ; timestamp = max (timestamp, t) ; if (anysrc | s) %#ok cmd = sprintf ('%s -O -I../../Include %s_mex.c %s -output %s\n', ... mexcmd, csm{i}, CS, csm{i}) ; kk = do_cmd (cmd, kk, details) ; end end if (nargout > 1) timestamp_out = timestamp ; end fprintf ('\n') ; %------------------------------------------------------------------------------- function [s,t,kk] = compile_source (srcdir, f, obj, hfile, force, mexcmd, ... kk, details) % compile a source code file in ../../Source, leaving object file in % this directory. [s t] = cs_must_compile (srcdir, f, '', obj, hfile, force) ; if (s) cmd = sprintf ('%s -O -c -I../../Include %s%s.c\n', mexcmd, srcdir, f) ; kk = do_cmd (cmd, kk, details) ; end %------------------------------------------------------------------------------- function kk = do_cmd (s, kk, details) %DO_CMD: evaluate a command, and either print it or print a "." if (details) fprintf ('%s', s) ; else if (mod (kk, 60) == 0) fprintf ('\n') ; end kk = kk + 1 ; fprintf ('.') ; end eval (s) ; SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_transpose.m0000644001170100242450000000075410620372563022526 0ustar davisfacfunction C = cs_transpose (A) %#ok %CS_TRANSPOSE transpose a sparse matrix. % C = cs_transpose(A), computes C = A' % C = cs_transpose(A,-1) computes C=A.' % C = cs_transpose(A,1) computes C=A' % % Example: % Prob = UFget ('HB/ibm32') ; A = Prob.A ; % C = cs_transpose (A) ; % C-A' % % See also TRANSPOSE, CTRANSPOSE. % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse error ('cs_transpose mexFunction not found') ; SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_sqr_mex.c0000644001170100242450000000260610620711515022144 0ustar davisfac#include "cs_mex.h" /* cs_sqr: symbolic sparse QR factorization */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double s ; cs_dls *S ; cs_dl Amatrix, *A ; CS_INT m, n, order, *p ; if (nargout > 7 || nargin != 1) { mexErrMsgTxt ("Usage: [vnz,rnz,parent,c,leftmost,p,q] = cs_sqr(A)") ; } A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ m = A->m ; n = A->n ; if (m < n) mexErrMsgTxt ("A must have # rows >= # columns") ; order = (nargout == 7) ? 3 : 0 ; /* determine ordering */ S = cs_dl_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/ if (!S) mexErrMsgTxt ("cs_sqr failed") ; s = S->lnz ; cs_dl_mex_put_double (1, &s, &(pargout [0])) ; /* return nnz(V) */ s = S->unz ; cs_dl_mex_put_double (1, &s, &(pargout [1])) ; /* return nnz(R) */ pargout [2] = cs_dl_mex_put_int (S->parent, n, 1, 0) ; /* return parent */ pargout [3] = cs_dl_mex_put_int (S->cp, n, 0, 0) ; /* return c */ pargout [4] = cs_dl_mex_put_int (S->leftmost, m, 1, 0) ;/* return leftmost*/ p = cs_dl_pinv (S->pinv, S->m2) ; /* p = pinv' */ pargout [5] = cs_dl_mex_put_int (p, S->m2, 1, 1) ; /* return p */ if (nargout > 6) { pargout [6] = cs_dl_mex_put_int (S->q, n, 1, 0) ; /* return q */ } cs_dl_sfree (S) ; } SuiteSparse/CXSparse_newfiles/MATLAB/CSparse/cs_qr_mex.c0000644001170100242450000000543410573562351021774 0ustar davisfac#include "cs_mex.h" /* cs_qr: sparse QR factorization */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT m, n, order, *p ; if (nargout > 5 || nargin != 1) { mexErrMsgTxt ("Usage: [V,beta,p,R,q] = cs_qr(A)") ; } order = (nargout == 5) ? 3 : 0 ; /* determine ordering */ m = mxGetM (pargin [0]) ; n = mxGetN (pargin [0]) ; if (m < n) mexErrMsgTxt ("A must have # rows >= # columns") ; if (mxIsComplex (pargin [0])) { #ifndef NCOMPLEX cs_cls *S ; cs_cln *N ; cs_cl Amatrix, *A, *D ; A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */ S = cs_cl_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/ N = cs_cl_qr (A, S) ; /* numeric QR factorization */ cs_free (A->x) ; if (!N) mexErrMsgTxt ("qr failed") ; cs_cl_dropzeros (N->L) ; /* drop zeros from V and sort */ D = cs_cl_transpose (N->L, 1) ; cs_cl_spfree (N->L) ; N->L = cs_cl_transpose (D, 1) ; cs_cl_spfree (D) ; cs_cl_dropzeros (N->U) ; /* drop zeros from R and sort */ D = cs_cl_transpose (N->U, 1) ; cs_cl_spfree (N->U) ; N->U = cs_cl_transpose (D, 1) ; cs_cl_spfree (D) ; m = N->L->m ; /* m may be larger now */ p = cs_cl_pinv (S->pinv, m) ; /* p = pinv' */ pargout [0] = cs_cl_mex_put_sparse (&(N->L)) ; /* return V */ cs_dl_mex_put_double (n, N->B, &(pargout [1])) ; /* return beta */ pargout [2] = cs_dl_mex_put_int (p, m, 1, 1) ; /* return p */ pargout [3] = cs_cl_mex_put_sparse (&(N->U)) ; /* return R */ pargout [4] = cs_dl_mex_put_int (S->q, n, 1, 0) ; /* return q */ cs_cl_nfree (N) ; cs_cl_sfree (S) ; #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dls *S ; cs_dln *N ; cs_dl Amatrix, *A, *D ; A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ S = cs_dl_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/ N = cs_dl_qr (A, S) ; /* numeric QR factorization */ if (!N) mexErrMsgTxt ("qr failed") ; cs_dl_dropzeros (N->L) ; /* drop zeros from V and sort */ D = cs_dl_transpose (N->L, 1) ; cs_dl_spfree (N->L) ; N->L = cs_dl_transpose (D, 1) ; cs_dl_spfree (D) ; cs_dl_dropzeros (N->U) ; /* drop zeros from R and sort */ D = cs_dl_transpose (N->U, 1) ; cs_dl_spfree (N->U) ; N->U = cs_dl_transpose (D, 1) ; cs_dl_spfree (D) ; m = N->L->m ; /* m may be larger now */ p = cs_dl_pinv (S->pinv, m) ; /* p = pinv' */ pargout [0] = cs_dl_mex_put_sparse (&(N->L)) ; /* return V */ cs_dl_mex_put_double (n, N->B, &(pargout [1])) ; /* return beta */ pargout [2] = cs_dl_mex_put_int (p, m, 1, 1) ; /* return p */ pargout [3] = cs_dl_mex_put_sparse (&(N->U)) ; /* return R */ pargout [4] = cs_dl_mex_put_int (S->q, n, 1, 0) ; /* return q */ cs_dl_nfree (N) ; cs_dl_sfree (S) ; } } SuiteSparse/CXSparse_newfiles/MATLAB/README.txt0000644001170100242450000000210610573562200017770 0ustar davisfacCXSparse/MATLAB directory, which contains the MATLAB mexFunction interfaces for CXSparse, demos, and tests. It includes various "textbook" files that are printed in the book, but not a proper part of CSparse itself. It also includes "UFget", a MATLAB interface for the UF Sparse Matrix Collection. Type the command "cs_install" while in this directory. It will compile CSparse, and add the directories: CXSparse/MATLAB/CSparse CXSparse/MATLAB/Demo CXSparse/MATLAB/UFget to your MATLAB path (see the "pathtool" command to add these to your path permanently, for future MATLAB sessions). To run the MATLAB demo programs, run cs_demo in the Demo directory. This demo will work whether or not your compiler supports the complex type. To run the MATLAB test programs, run testall in the Test directory. However, you may run the tests in the Test directory only if your compiler supports the ANSI C99 complex type. If it does not support the ANSI C99 complex type, the tests in the Test directory will fail, since the codes there test both the real and complex cases in CXSparse. SuiteSparse/CXSparse_newfiles/MATLAB/cs_install.m0000644001170100242450000000313110712370323020600 0ustar davisfacfunction cs_install (do_pause) %CS_INSTALL: compile and install CXSparse for use in MATLAB. % Your current working directory must be CXSparse/MATLAB in order to use this % function. % % The directories % % CXSparse/MATLAB/CSparse % CXSparse/MATLAB/Demo % CXSparse/MATLAB/UFget % % are added to your MATLAB path (see the "pathtool" command to add these to % your path permanently, for future MATLAB sessions). % % Next, the MATLAB CXSparse demo program, CXSparse/MATLAB/cs_demo is executed. % To run the demo with pauses so you can see the results, use cs_install(1). % To run the full MATLAB test programs for CXSparse, run testall in the % Test directory. % % Example: % cs_install % install and run demo with no pauses % cs_install(1) % install and run demo with pauses % % See also: cs_demo % % Copyright 2006-2007, Timothy A. Davis. % http://www.cise.ufl.edu/research/sparse fprintf ('Compiling and installing CXSparse\n') ; if (nargin < 1) do_pause = 0 ; end if (do_pause) input ('Hit enter to continue: ') ; end addpath ([pwd filesep 'CSparse']) ; addpath ([pwd filesep 'Demo']) ; v = getversion ; if (v >= 7.0) addpath ([pwd filesep 'UFget']) ; else fprintf ('UFget not installed (MATLAB 7.0 or later required)\n') ; end cd ('CSparse') ; cs_make (1) ; cd ('../Demo') ; cs_demo (do_pause) %------------------------------------------------------------------------------- function v = getversion % determine the MATLAB version, and return it as a double. v = sscanf (version, '%d.%d.%d') ; v = 10.^(0:-1:-(length(v)-1)) * v ; SuiteSparse/CXSparse_newfiles/Matrix/0000755001170100242450000000000010567667105016614 5ustar davisfacSuiteSparse/CXSparse_newfiles/Matrix/c40000644001170100242450000000026110567667105017044 0ustar davisfac0 0 9.27539 0 1 0 14.7693 -1.04429 2 0 7.96934 2.8854 3 0 13.0094 -2.32583 1 1 23.8338 0 2 1 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65 45 1 0.1 65 46 1 0.1 65 47 1 0.1 66 61 1 0.1 66 62 1 0.1 66 63 1 0.1 66 64 1 0.1 66 65 1 0.1 9 17 1 0.1 1 13 1.012658 0.1 37 57 1.118012 0.1 47 63 1.118012 0.1 21 38 1.253918 0.1 0 12 1.265823 0.1 36 56 1.490683 0.1 46 62 1.490683 0.1 20 37 1.567398 0.1 35 55 1.863354 0.1 45 61 1.863354 0.1 SuiteSparse/CXSparse_newfiles/Include/0000755001170100242450000000000010711427651016722 5ustar davisfacSuiteSparse/CXSparse_newfiles/Include/cs.h0000644001170100242450000007406010711425530017501 0ustar davisfac#ifndef _CXS_H #define _CXS_H #include #include #include #include #ifdef MATLAB_MEX_FILE #include "mex.h" #endif #ifdef __cplusplus #ifndef NCOMPLEX #include typedef std::complex cs_complex_t ; #endif extern "C" { #else #ifndef NCOMPLEX #include #define cs_complex_t double _Complex #endif #endif #define CS_VER 2 /* CXSparse Version 2.2.1 */ #define CS_SUBVER 2 #define CS_SUBSUB 1 #define CS_DATE "Nov 1, 2007" /* CXSparse release date */ #define CS_COPYRIGHT "Copyright (c) Timothy A. Davis, 2006-2007" #define CXSPARSE /* define UF_long */ #include "UFconfig.h" /* -------------------------------------------------------------------------- */ /* double/int version of CXSparse */ /* -------------------------------------------------------------------------- */ /* --- primary CSparse routines and data structures ------------------------- */ typedef struct cs_di_sparse /* matrix in compressed-column or triplet form */ { int nzmax ; /* maximum number of entries */ int m ; /* number of rows */ int n ; /* number of columns */ int *p ; /* column pointers (size n+1) or col indices (size nzmax) */ int *i ; /* row indices, size nzmax */ double *x ; /* numerical values, size nzmax */ int nz ; /* # of entries in triplet matrix, -1 for compressed-col */ } cs_di ; cs_di *cs_di_add (const cs_di *A, const cs_di *B, double alpha, double beta) ; int cs_di_cholsol (int order, const cs_di *A, double *b) ; int cs_di_dupl (cs_di *A) ; int cs_di_entry (cs_di *T, int i, int j, double x) ; int cs_di_lusol (int order, const cs_di *A, double *b, double tol) ; int cs_di_gaxpy (const cs_di *A, const double *x, double *y) ; cs_di *cs_di_multiply (const cs_di *A, const cs_di *B) ; int cs_di_qrsol (int order, const cs_di *A, double *b) ; cs_di *cs_di_transpose (const cs_di *A, int values) ; cs_di *cs_di_compress (const cs_di *T) ; double cs_di_norm (const cs_di *A) ; int cs_di_print (const cs_di *A, int brief) ; cs_di *cs_di_load (FILE *f) ; /* utilities */ void *cs_di_calloc (int n, size_t size) ; void *cs_di_free (void *p) ; void *cs_di_realloc (void *p, int n, size_t size, int *ok) ; cs_di *cs_di_spalloc (int m, int n, int nzmax, int values, int t) ; cs_di *cs_di_spfree (cs_di *A) ; int cs_di_sprealloc (cs_di *A, int nzmax) ; void *cs_di_malloc (int n, size_t size) ; /* --- secondary CSparse routines and data structures ----------------------- */ typedef struct cs_di_symbolic /* symbolic Cholesky, LU, or QR analysis */ { int *pinv ; /* inverse row perm. for QR, fill red. perm for Chol */ int *q ; /* fill-reducing column permutation for LU and QR */ int *parent ; /* elimination tree for Cholesky and QR */ int *cp ; /* column pointers for Cholesky, row counts for QR */ int *leftmost ; /* leftmost[i] = min(find(A(i,:))), for QR */ int m2 ; /* # of rows for QR, after adding fictitious rows */ double lnz ; /* # entries in L for LU or Cholesky; in V for QR */ double unz ; /* # entries in U for LU; in R for QR */ } cs_dis ; typedef struct cs_di_numeric /* numeric Cholesky, LU, or QR factorization */ { cs_di *L ; /* L for LU and Cholesky, V for QR */ cs_di *U ; /* U for LU, r for QR, not used for Cholesky */ int *pinv ; /* partial pivoting for LU */ double *B ; /* beta [0..n-1] for QR */ } cs_din ; typedef struct cs_di_dmperm_results /* cs_di_dmperm or cs_di_scc output */ { int *p ; /* size m, row permutation */ int *q ; /* size n, column permutation */ int *r ; /* size nb+1, block k is rows r[k] to r[k+1]-1 in A(p,q) */ int *s ; /* size nb+1, block k is cols s[k] to s[k+1]-1 in A(p,q) */ int nb ; /* # of blocks in fine dmperm decomposition */ int rr [5] ; /* coarse row decomposition */ int cc [5] ; /* coarse column decomposition */ } cs_did ; int *cs_di_amd (int order, const cs_di *A) ; cs_din *cs_di_chol (const cs_di *A, const cs_dis *S) ; cs_did *cs_di_dmperm (const cs_di *A, int seed) ; int cs_di_droptol (cs_di *A, double tol) ; int cs_di_dropzeros (cs_di *A) ; int cs_di_happly (const cs_di *V, int i, double beta, double *x) ; int cs_di_ipvec (const int *p, const double *b, double *x, int n) ; int cs_di_lsolve (const cs_di *L, double *x) ; int cs_di_ltsolve (const cs_di *L, double *x) ; cs_din *cs_di_lu (const cs_di *A, const cs_dis *S, double tol) ; cs_di *cs_di_permute (const cs_di *A, const int *pinv, const int *q, int values) ; int *cs_di_pinv (const int *p, int n) ; int cs_di_pvec (const int *p, const double *b, double *x, int n) ; cs_din *cs_di_qr (const cs_di *A, const cs_dis *S) ; cs_dis *cs_di_schol (int order, const cs_di *A) ; cs_dis *cs_di_sqr (int order, const cs_di *A, int qr) ; cs_di *cs_di_symperm (const cs_di *A, const int *pinv, int values) ; int cs_di_usolve (const cs_di *U, double *x) ; int cs_di_utsolve (const cs_di *U, double *x) ; int cs_di_updown (cs_di *L, int sigma, const cs_di *C, const int *parent) ; /* utilities */ cs_dis *cs_di_sfree (cs_dis *S) ; cs_din *cs_di_nfree (cs_din *N) ; cs_did *cs_di_dfree (cs_did *D) ; /* --- tertiary CSparse routines -------------------------------------------- */ int *cs_di_counts (const cs_di *A, const int *parent, const int *post, int ata) ; double cs_di_cumsum (int *p, int *c, int n) ; int cs_di_dfs (int j, cs_di *G, int top, int *xi, int *pstack, const int *pinv) ; int *cs_di_etree (const cs_di *A, int ata) ; int cs_di_fkeep (cs_di *A, int (*fkeep) (int, int, double, void *), void *other) ; double cs_di_house (double *x, double *beta, int n) ; int *cs_di_maxtrans (const cs_di *A, int seed) ; int *cs_di_post (const int *parent, int n) ; cs_did *cs_di_scc (cs_di *A) ; int cs_di_scatter (const cs_di *A, int j, double beta, int *w, double *x, int mark, cs_di *C, int nz) ; int cs_di_tdfs (int j, int k, int *head, const int *next, int *post, int *stack) ; int cs_di_leaf (int i, int j, const int *first, int *maxfirst, int *prevleaf, int *ancestor, int *jleaf) ; int cs_di_reach (cs_di *G, const cs_di *B, int k, int *xi, const int *pinv) ; int cs_di_spsolve (cs_di *L, const cs_di *B, int k, int *xi, double *x, const int *pinv, int lo) ; int cs_di_ereach (const cs_di *A, int k, const int *parent, int *s, int *w) ; int *cs_di_randperm (int n, int seed) ; /* utilities */ cs_did *cs_di_dalloc (int m, int n) ; cs_di *cs_di_done (cs_di *C, void *w, void *x, int ok) ; int *cs_di_idone (int *p, cs_di *C, void *w, int ok) ; cs_din *cs_di_ndone (cs_din *N, cs_di *C, void *w, void *x, int ok) ; cs_did *cs_di_ddone (cs_did *D, cs_di *C, void *w, int ok) ; /* -------------------------------------------------------------------------- */ /* double/UF_long version of CXSparse */ /* -------------------------------------------------------------------------- */ /* --- primary CSparse routines and data structures ------------------------- */ typedef struct cs_dl_sparse /* matrix in compressed-column or triplet form */ { UF_long nzmax ; /* maximum number of entries */ UF_long m ; /* number of rows */ UF_long n ; /* number of columns */ UF_long *p ; /* column pointers (size n+1) or col indlces (size nzmax) */ UF_long *i ; /* row indices, size nzmax */ double *x ; /* numerical values, size nzmax */ UF_long nz ; /* # of entries in triplet matrix, -1 for compressed-col */ } cs_dl ; cs_dl *cs_dl_add (const cs_dl *A, const cs_dl *B, double alpha, double beta) ; UF_long cs_dl_cholsol (UF_long order, const cs_dl *A, double *b) ; UF_long cs_dl_dupl (cs_dl *A) ; UF_long cs_dl_entry (cs_dl *T, UF_long i, UF_long j, double x) ; UF_long cs_dl_lusol (UF_long order, const cs_dl *A, double *b, double tol) ; UF_long cs_dl_gaxpy (const cs_dl *A, const double *x, double *y) ; cs_dl *cs_dl_multiply (const cs_dl *A, const cs_dl *B) ; UF_long cs_dl_qrsol (UF_long order, const cs_dl *A, double *b) ; cs_dl *cs_dl_transpose (const cs_dl *A, UF_long values) ; cs_dl *cs_dl_compress (const cs_dl *T) ; double cs_dl_norm (const cs_dl *A) ; UF_long cs_dl_print (const cs_dl *A, UF_long brief) ; cs_dl *cs_dl_load (FILE *f) ; /* utilities */ void *cs_dl_calloc (UF_long n, size_t size) ; void *cs_dl_free (void *p) ; void *cs_dl_realloc (void *p, UF_long n, size_t size, UF_long *ok) ; cs_dl *cs_dl_spalloc (UF_long m, UF_long n, UF_long nzmax, UF_long values, UF_long t) ; cs_dl *cs_dl_spfree (cs_dl *A) ; UF_long cs_dl_sprealloc (cs_dl *A, UF_long nzmax) ; void *cs_dl_malloc (UF_long n, size_t size) ; /* --- secondary CSparse routines and data structures ----------------------- */ typedef struct cs_dl_symbolic /* symbolic Cholesky, LU, or QR analysis */ { UF_long *pinv ; /* inverse row perm. for QR, fill red. perm for Chol */ UF_long *q ; /* fill-reducing column permutation for LU and QR */ UF_long *parent ; /* elimination tree for Cholesky and QR */ UF_long *cp ; /* column pointers for Cholesky, row counts for QR */ UF_long *leftmost ; /* leftmost[i] = min(find(A(i,:))), for QR */ UF_long m2 ; /* # of rows for QR, after adding fictitious rows */ double lnz ; /* # entries in L for LU or Cholesky; in V for QR */ double unz ; /* # entries in U for LU; in R for QR */ } cs_dls ; typedef struct cs_dl_numeric /* numeric Cholesky, LU, or QR factorization */ { cs_dl *L ; /* L for LU and Cholesky, V for QR */ cs_dl *U ; /* U for LU, r for QR, not used for Cholesky */ UF_long *pinv ; /* partial pivoting for LU */ double *B ; /* beta [0..n-1] for QR */ } cs_dln ; typedef struct cs_dl_dmperm_results /* cs_dl_dmperm or cs_dl_scc output */ { UF_long *p ; /* size m, row permutation */ UF_long *q ; /* size n, column permutation */ UF_long *r ; /* size nb+1, block k is rows r[k] to r[k+1]-1 in A(p,q) */ UF_long *s ; /* size nb+1, block k is cols s[k] to s[k+1]-1 in A(p,q) */ UF_long nb ; /* # of blocks in fine dmperm decomposition */ UF_long rr [5] ; /* coarse row decomposition */ UF_long cc [5] ; /* coarse column decomposition */ } cs_dld ; UF_long *cs_dl_amd (UF_long order, const cs_dl *A) ; cs_dln *cs_dl_chol (const cs_dl *A, const cs_dls *S) ; cs_dld *cs_dl_dmperm (const cs_dl *A, UF_long seed) ; UF_long cs_dl_droptol (cs_dl *A, double tol) ; UF_long cs_dl_dropzeros (cs_dl *A) ; UF_long cs_dl_happly (const cs_dl *V, UF_long i, double beta, double *x) ; UF_long cs_dl_ipvec (const UF_long *p, const double *b, double *x, UF_long n) ; UF_long cs_dl_lsolve (const cs_dl *L, double *x) ; UF_long cs_dl_ltsolve (const cs_dl *L, double *x) ; cs_dln *cs_dl_lu (const cs_dl *A, const cs_dls *S, double tol) ; cs_dl *cs_dl_permute (const cs_dl *A, const UF_long *pinv, const UF_long *q, UF_long values) ; UF_long *cs_dl_pinv (const UF_long *p, UF_long n) ; UF_long cs_dl_pvec (const UF_long *p, const double *b, double *x, UF_long n) ; cs_dln *cs_dl_qr (const cs_dl *A, const cs_dls *S) ; cs_dls *cs_dl_schol (UF_long order, const cs_dl *A) ; cs_dls *cs_dl_sqr (UF_long order, const cs_dl *A, UF_long qr) ; cs_dl *cs_dl_symperm (const cs_dl *A, const UF_long *pinv, UF_long values) ; UF_long cs_dl_usolve (const cs_dl *U, double *x) ; UF_long cs_dl_utsolve (const cs_dl *U, double *x) ; UF_long cs_dl_updown (cs_dl *L, UF_long sigma, const cs_dl *C, const UF_long *parent) ; /* utilities */ cs_dls *cs_dl_sfree (cs_dls *S) ; cs_dln *cs_dl_nfree (cs_dln *N) ; cs_dld *cs_dl_dfree (cs_dld *D) ; /* --- tertiary CSparse routines -------------------------------------------- */ UF_long *cs_dl_counts (const cs_dl *A, const UF_long *parent, const UF_long *post, UF_long ata) ; double cs_dl_cumsum (UF_long *p, UF_long *c, UF_long n) ; UF_long cs_dl_dfs (UF_long j, cs_dl *G, UF_long top, UF_long *xi, UF_long *pstack, const UF_long *pinv) ; UF_long *cs_dl_etree (const cs_dl *A, UF_long ata) ; UF_long cs_dl_fkeep (cs_dl *A, UF_long (*fkeep) (UF_long, UF_long, double, void *), void *other) ; double cs_dl_house (double *x, double *beta, UF_long n) ; UF_long *cs_dl_maxtrans (const cs_dl *A, UF_long seed) ; UF_long *cs_dl_post (const UF_long *parent, UF_long n) ; cs_dld *cs_dl_scc (cs_dl *A) ; UF_long cs_dl_scatter (const cs_dl *A, UF_long j, double beta, UF_long *w, double *x, UF_long mark,cs_dl *C, UF_long nz) ; UF_long cs_dl_tdfs (UF_long j, UF_long k, UF_long *head, const UF_long *next, UF_long *post, UF_long *stack) ; UF_long cs_dl_leaf (UF_long i, UF_long j, const UF_long *first, UF_long *maxfirst, UF_long *prevleaf, UF_long *ancestor, UF_long *jleaf) ; UF_long cs_dl_reach (cs_dl *G, const cs_dl *B, UF_long k, UF_long *xi, const UF_long *pinv) ; UF_long cs_dl_spsolve (cs_dl *L, const cs_dl *B, UF_long k, UF_long *xi, double *x, const UF_long *pinv, UF_long lo) ; UF_long cs_dl_ereach (const cs_dl *A, UF_long k, const UF_long *parent, UF_long *s, UF_long *w) ; UF_long *cs_dl_randperm (UF_long n, UF_long seed) ; /* utilities */ cs_dld *cs_dl_dalloc (UF_long m, UF_long n) ; cs_dl *cs_dl_done (cs_dl *C, void *w, void *x, UF_long ok) ; UF_long *cs_dl_idone (UF_long *p, cs_dl *C, void *w, UF_long ok) ; cs_dln *cs_dl_ndone (cs_dln *N, cs_dl *C, void *w, void *x, UF_long ok) ; cs_dld *cs_dl_ddone (cs_dld *D, cs_dl *C, void *w, UF_long ok) ; /* -------------------------------------------------------------------------- */ /* complex/int version of CXSparse */ /* -------------------------------------------------------------------------- */ #ifndef NCOMPLEX /* --- primary CSparse routines and data structures ------------------------- */ typedef struct cs_ci_sparse /* matrix in compressed-column or triplet form */ { int nzmax ; /* maximum number of entries */ int m ; /* number of rows */ int n ; /* number of columns */ int *p ; /* column pointers (size n+1) or col indices (size nzmax) */ int *i ; /* row indices, size nzmax */ cs_complex_t *x ; /* numerical values, size nzmax */ int nz ; /* # of entries in triplet matrix, -1 for compressed-col */ } cs_ci ; cs_ci *cs_ci_add (const cs_ci *A, const cs_ci *B, cs_complex_t alpha, cs_complex_t beta) ; int cs_ci_cholsol (int order, const cs_ci *A, cs_complex_t *b) ; int cs_ci_dupl (cs_ci *A) ; int cs_ci_entry (cs_ci *T, int i, int j, cs_complex_t x) ; int cs_ci_lusol (int order, const cs_ci *A, cs_complex_t *b, double tol) ; int cs_ci_gaxpy (const cs_ci *A, const cs_complex_t *x, cs_complex_t *y) ; cs_ci *cs_ci_multiply (const cs_ci *A, const cs_ci *B) ; int cs_ci_qrsol (int order, const cs_ci *A, cs_complex_t *b) ; cs_ci *cs_ci_transpose (const cs_ci *A, int values) ; cs_ci *cs_ci_compress (const cs_ci *T) ; double cs_ci_norm (const cs_ci *A) ; int cs_ci_print (const cs_ci *A, int brief) ; cs_ci *cs_ci_load (FILE *f) ; /* utilities */ void *cs_ci_calloc (int n, size_t size) ; void *cs_ci_free (void *p) ; void *cs_ci_realloc (void *p, int n, size_t size, int *ok) ; cs_ci *cs_ci_spalloc (int m, int n, int nzmax, int values, int t) ; cs_ci *cs_ci_spfree (cs_ci *A) ; int cs_ci_sprealloc (cs_ci *A, int nzmax) ; void *cs_ci_malloc (int n, size_t size) ; /* --- secondary CSparse routines and data structures ----------------------- */ typedef struct cs_ci_symbolic /* symbolic Cholesky, LU, or QR analysis */ { int *pinv ; /* inverse row perm. for QR, fill red. perm for Chol */ int *q ; /* fill-reducing column permutation for LU and QR */ int *parent ; /* elimination tree for Cholesky and QR */ int *cp ; /* column pointers for Cholesky, row counts for QR */ int *leftmost ; /* leftmost[i] = min(find(A(i,:))), for QR */ int m2 ; /* # of rows for QR, after adding fictitious rows */ double lnz ; /* # entries in L for LU or Cholesky; in V for QR */ double unz ; /* # entries in U for LU; in R for QR */ } cs_cis ; typedef struct cs_ci_numeric /* numeric Cholesky, LU, or QR factorization */ { cs_ci *L ; /* L for LU and Cholesky, V for QR */ cs_ci *U ; /* U for LU, r for QR, not used for Cholesky */ int *pinv ; /* partial pivoting for LU */ double *B ; /* beta [0..n-1] for QR */ } cs_cin ; typedef struct cs_ci_dmperm_results /* cs_ci_dmperm or cs_ci_scc output */ { int *p ; /* size m, row permutation */ int *q ; /* size n, column permutation */ int *r ; /* size nb+1, block k is rows r[k] to r[k+1]-1 in A(p,q) */ int *s ; /* size nb+1, block k is cols s[k] to s[k+1]-1 in A(p,q) */ int nb ; /* # of blocks in fine dmperm decomposition */ int rr [5] ; /* coarse row decomposition */ int cc [5] ; /* coarse column decomposition */ } cs_cid ; int *cs_ci_amd (int order, const cs_ci *A) ; cs_cin *cs_ci_chol (const cs_ci *A, const cs_cis *S) ; cs_cid *cs_ci_dmperm (const cs_ci *A, int seed) ; int cs_ci_droptol (cs_ci *A, double tol) ; int cs_ci_dropzeros (cs_ci *A) ; int cs_ci_happly (const cs_ci *V, int i, double beta, cs_complex_t *x) ; int cs_ci_ipvec (const int *p, const cs_complex_t *b, cs_complex_t *x, int n) ; int cs_ci_lsolve (const cs_ci *L, cs_complex_t *x) ; int cs_ci_ltsolve (const cs_ci *L, cs_complex_t *x) ; cs_cin *cs_ci_lu (const cs_ci *A, const cs_cis *S, double tol) ; cs_ci *cs_ci_permute (const cs_ci *A, const int *pinv, const int *q, int values) ; int *cs_ci_pinv (const int *p, int n) ; int cs_ci_pvec (const int *p, const cs_complex_t *b, cs_complex_t *x, int n) ; cs_cin *cs_ci_qr (const cs_ci *A, const cs_cis *S) ; cs_cis *cs_ci_schol (int order, const cs_ci *A) ; cs_cis *cs_ci_sqr (int order, const cs_ci *A, int qr) ; cs_ci *cs_ci_symperm (const cs_ci *A, const int *pinv, int values) ; int cs_ci_usolve (const cs_ci *U, cs_complex_t *x) ; int cs_ci_utsolve (const cs_ci *U, cs_complex_t *x) ; int cs_ci_updown (cs_ci *L, int sigma, const cs_ci *C, const int *parent) ; /* utilities */ cs_cis *cs_ci_sfree (cs_cis *S) ; cs_cin *cs_ci_nfree (cs_cin *N) ; cs_cid *cs_ci_dfree (cs_cid *D) ; /* --- tertiary CSparse routines -------------------------------------------- */ int *cs_ci_counts (const cs_ci *A, const int *parent, const int *post, int ata) ; double cs_ci_cumsum (int *p, int *c, int n) ; int cs_ci_dfs (int j, cs_ci *G, int top, int *xi, int *pstack, const int *pinv) ; int *cs_ci_etree (const cs_ci *A, int ata) ; int cs_ci_fkeep (cs_ci *A, int (*fkeep) (int, int, cs_complex_t, void *), void *other) ; cs_complex_t cs_ci_house (cs_complex_t *x, double *beta, int n) ; int *cs_ci_maxtrans (const cs_ci *A, int seed) ; int *cs_ci_post (const int *parent, int n) ; cs_cid *cs_ci_scc (cs_ci *A) ; int cs_ci_scatter (const cs_ci *A, int j, cs_complex_t beta, int *w, cs_complex_t *x, int mark,cs_ci *C, int nz) ; int cs_ci_tdfs (int j, int k, int *head, const int *next, int *post, int *stack) ; int cs_ci_leaf (int i, int j, const int *first, int *maxfirst, int *prevleaf, int *ancestor, int *jleaf) ; int cs_ci_reach (cs_ci *G, const cs_ci *B, int k, int *xi, const int *pinv) ; int cs_ci_spsolve (cs_ci *L, const cs_ci *B, int k, int *xi, cs_complex_t *x, const int *pinv, int lo) ; int cs_ci_ereach (const cs_ci *A, int k, const int *parent, int *s, int *w) ; int *cs_ci_randperm (int n, int seed) ; /* utilities */ cs_cid *cs_ci_dalloc (int m, int n) ; cs_ci *cs_ci_done (cs_ci *C, void *w, void *x, int ok) ; int *cs_ci_idone (int *p, cs_ci *C, void *w, int ok) ; cs_cin *cs_ci_ndone (cs_cin *N, cs_ci *C, void *w, void *x, int ok) ; cs_cid *cs_ci_ddone (cs_cid *D, cs_ci *C, void *w, int ok) ; /* -------------------------------------------------------------------------- */ /* complex/UF_long version of CXSparse */ /* -------------------------------------------------------------------------- */ /* --- primary CSparse routines and data structures ------------------------- */ typedef struct cs_cl_sparse /* matrix in compressed-column or triplet form */ { UF_long nzmax ; /* maximum number of entries */ UF_long m ; /* number of rows */ UF_long n ; /* number of columns */ UF_long *p ; /* column pointers (size n+1) or col indlces (size nzmax) */ UF_long *i ; /* row indices, size nzmax */ cs_complex_t *x ; /* numerical values, size nzmax */ UF_long nz ; /* # of entries in triplet matrix, -1 for compressed-col */ } cs_cl ; cs_cl *cs_cl_add (const cs_cl *A, const cs_cl *B, cs_complex_t alpha, cs_complex_t beta) ; UF_long cs_cl_cholsol (UF_long order, const cs_cl *A, cs_complex_t *b) ; UF_long cs_cl_dupl (cs_cl *A) ; UF_long cs_cl_entry (cs_cl *T, UF_long i, UF_long j, cs_complex_t x) ; UF_long cs_cl_lusol (UF_long order, const cs_cl *A, cs_complex_t *b, double tol) ; UF_long cs_cl_gaxpy (const cs_cl *A, const cs_complex_t *x, cs_complex_t *y) ; cs_cl *cs_cl_multiply (const cs_cl *A, const cs_cl *B) ; UF_long cs_cl_qrsol (UF_long order, const cs_cl *A, cs_complex_t *b) ; cs_cl *cs_cl_transpose (const cs_cl *A, UF_long values) ; cs_cl *cs_cl_compress (const cs_cl *T) ; double cs_cl_norm (const cs_cl *A) ; UF_long cs_cl_print (const cs_cl *A, UF_long brief) ; cs_cl *cs_cl_load (FILE *f) ; /* utilities */ void *cs_cl_calloc (UF_long n, size_t size) ; void *cs_cl_free (void *p) ; void *cs_cl_realloc (void *p, UF_long n, size_t size, UF_long *ok) ; cs_cl *cs_cl_spalloc (UF_long m, UF_long n, UF_long nzmax, UF_long values, UF_long t) ; cs_cl *cs_cl_spfree (cs_cl *A) ; UF_long cs_cl_sprealloc (cs_cl *A, UF_long nzmax) ; void *cs_cl_malloc (UF_long n, size_t size) ; /* --- secondary CSparse routines and data structures ----------------------- */ typedef struct cs_cl_symbolic /* symbolic Cholesky, LU, or QR analysis */ { UF_long *pinv ; /* inverse row perm. for QR, fill red. perm for Chol */ UF_long *q ; /* fill-reducing column permutation for LU and QR */ UF_long *parent ; /* elimination tree for Cholesky and QR */ UF_long *cp ; /* column pointers for Cholesky, row counts for QR */ UF_long *leftmost ; /* leftmost[i] = min(find(A(i,:))), for QR */ UF_long m2 ; /* # of rows for QR, after adding fictitious rows */ double lnz ; /* # entries in L for LU or Cholesky; in V for QR */ double unz ; /* # entries in U for LU; in R for QR */ } cs_cls ; typedef struct cs_cl_numeric /* numeric Cholesky, LU, or QR factorization */ { cs_cl *L ; /* L for LU and Cholesky, V for QR */ cs_cl *U ; /* U for LU, r for QR, not used for Cholesky */ UF_long *pinv ; /* partial pivoting for LU */ double *B ; /* beta [0..n-1] for QR */ } cs_cln ; typedef struct cs_cl_dmperm_results /* cs_cl_dmperm or cs_cl_scc output */ { UF_long *p ; /* size m, row permutation */ UF_long *q ; /* size n, column permutation */ UF_long *r ; /* size nb+1, block k is rows r[k] to r[k+1]-1 in A(p,q) */ UF_long *s ; /* size nb+1, block k is cols s[k] to s[k+1]-1 in A(p,q) */ UF_long nb ; /* # of blocks in fine dmperm decomposition */ UF_long rr [5] ; /* coarse row decomposition */ UF_long cc [5] ; /* coarse column decomposition */ } cs_cld ; UF_long *cs_cl_amd (UF_long order, const cs_cl *A) ; cs_cln *cs_cl_chol (const cs_cl *A, const cs_cls *S) ; cs_cld *cs_cl_dmperm (const cs_cl *A, UF_long seed) ; UF_long cs_cl_droptol (cs_cl *A, double tol) ; UF_long cs_cl_dropzeros (cs_cl *A) ; UF_long cs_cl_happly (const cs_cl *V, UF_long i, double beta, cs_complex_t *x) ; UF_long cs_cl_ipvec (const UF_long *p, const cs_complex_t *b, cs_complex_t *x, UF_long n) ; UF_long cs_cl_lsolve (const cs_cl *L, cs_complex_t *x) ; UF_long cs_cl_ltsolve (const cs_cl *L, cs_complex_t *x) ; cs_cln *cs_cl_lu (const cs_cl *A, const cs_cls *S, double tol) ; cs_cl *cs_cl_permute (const cs_cl *A, const UF_long *pinv, const UF_long *q, UF_long values) ; UF_long *cs_cl_pinv (const UF_long *p, UF_long n) ; UF_long cs_cl_pvec (const UF_long *p, const cs_complex_t *b, cs_complex_t *x, UF_long n) ; cs_cln *cs_cl_qr (const cs_cl *A, const cs_cls *S) ; cs_cls *cs_cl_schol (UF_long order, const cs_cl *A) ; cs_cls *cs_cl_sqr (UF_long order, const cs_cl *A, UF_long qr) ; cs_cl *cs_cl_symperm (const cs_cl *A, const UF_long *pinv, UF_long values) ; UF_long cs_cl_usolve (const cs_cl *U, cs_complex_t *x) ; UF_long cs_cl_utsolve (const cs_cl *U, cs_complex_t *x) ; UF_long cs_cl_updown (cs_cl *L, UF_long sigma, const cs_cl *C, const UF_long *parent) ; /* utilities */ cs_cls *cs_cl_sfree (cs_cls *S) ; cs_cln *cs_cl_nfree (cs_cln *N) ; cs_cld *cs_cl_dfree (cs_cld *D) ; /* --- tertiary CSparse routines -------------------------------------------- */ UF_long *cs_cl_counts (const cs_cl *A, const UF_long *parent, const UF_long *post, UF_long ata) ; double cs_cl_cumsum (UF_long *p, UF_long *c, UF_long n) ; UF_long cs_cl_dfs (UF_long j, cs_cl *G, UF_long top, UF_long *xi, UF_long *pstack, const UF_long *pinv) ; UF_long *cs_cl_etree (const cs_cl *A, UF_long ata) ; UF_long cs_cl_fkeep (cs_cl *A, UF_long (*fkeep) (UF_long, UF_long, cs_complex_t, void *), void *other) ; cs_complex_t cs_cl_house (cs_complex_t *x, double *beta, UF_long n) ; UF_long *cs_cl_maxtrans (const cs_cl *A, UF_long seed) ; UF_long *cs_cl_post (const UF_long *parent, UF_long n) ; cs_cld *cs_cl_scc (cs_cl *A) ; UF_long cs_cl_scatter (const cs_cl *A, UF_long j, cs_complex_t beta, UF_long *w, cs_complex_t *x, UF_long mark,cs_cl *C, UF_long nz) ; UF_long cs_cl_tdfs (UF_long j, UF_long k, UF_long *head, const UF_long *next, UF_long *post, UF_long *stack) ; UF_long cs_cl_leaf (UF_long i, UF_long j, const UF_long *first, UF_long *maxfirst, UF_long *prevleaf, UF_long *ancestor, UF_long *jleaf) ; UF_long cs_cl_reach (cs_cl *G, const cs_cl *B, UF_long k, UF_long *xi, const UF_long *pinv) ; UF_long cs_cl_spsolve (cs_cl *L, const cs_cl *B, UF_long k, UF_long *xi, cs_complex_t *x, const UF_long *pinv, UF_long lo) ; UF_long cs_cl_ereach (const cs_cl *A, UF_long k, const UF_long *parent, UF_long *s, UF_long *w) ; UF_long *cs_cl_randperm (UF_long n, UF_long seed) ; /* utilities */ cs_cld *cs_cl_dalloc (UF_long m, UF_long n) ; cs_cl *cs_cl_done (cs_cl *C, void *w, void *x, UF_long ok) ; UF_long *cs_cl_idone (UF_long *p, cs_cl *C, void *w, UF_long ok) ; cs_cln *cs_cl_ndone (cs_cln *N, cs_cl *C, void *w, void *x, UF_long ok) ; cs_cld *cs_cl_ddone (cs_cld *D, cs_cl *C, void *w, UF_long ok) ; #endif /* -------------------------------------------------------------------------- */ /* Macros for constructing each version of CSparse */ /* -------------------------------------------------------------------------- */ #ifdef CS_LONG #define CS_INT UF_long #define CS_INT_MAX UF_long_max #define CS_ID UF_long_id #ifdef CS_COMPLEX #define CS_ENTRY cs_complex_t #define CS_NAME(nm) cs_cl ## nm #define cs cs_cl #else #define CS_ENTRY double #define CS_NAME(nm) cs_dl ## nm #define cs cs_dl #endif #else #define CS_INT int #define CS_INT_MAX INT_MAX #define CS_ID "%d" #ifdef CS_COMPLEX #define CS_ENTRY cs_complex_t #define CS_NAME(nm) cs_ci ## nm #define cs cs_ci #else #define CS_ENTRY double #define CS_NAME(nm) cs_di ## nm #define cs cs_di #endif #endif #ifdef CS_COMPLEX #define CS_REAL(x) creal(x) #define CS_IMAG(x) cimag(x) #define CS_CONJ(x) conj(x) #define CS_ABS(x) cabs(x) #else #define CS_REAL(x) (x) #define CS_IMAG(x) (0.) #define CS_CONJ(x) (x) #define CS_ABS(x) fabs(x) #endif #define CS_MAX(a,b) (((a) > (b)) ? (a) : (b)) #define CS_MIN(a,b) (((a) < (b)) ? (a) : (b)) #define CS_FLIP(i) (-(i)-2) #define CS_UNFLIP(i) (((i) < 0) ? CS_FLIP(i) : (i)) #define CS_MARKED(w,j) (w [j] < 0) #define CS_MARK(w,j) { w [j] = CS_FLIP (w [j]) ; } #define CS_CSC(A) (A && (A->nz == -1)) #define CS_TRIPLET(A) (A && (A->nz >= 0)) /* --- primary CSparse routines and data structures ------------------------- */ #define cs_add CS_NAME (_add) #define cs_cholsol CS_NAME (_cholsol) #define cs_dupl CS_NAME (_dupl) #define cs_entry CS_NAME (_entry) #define cs_lusol CS_NAME (_lusol) #define cs_gaxpy CS_NAME (_gaxpy) #define cs_multiply CS_NAME (_multiply) #define cs_qrsol CS_NAME (_qrsol) #define cs_transpose CS_NAME (_transpose) #define cs_compress CS_NAME (_compress) #define cs_norm CS_NAME (_norm) #define cs_print CS_NAME (_print) #define cs_load CS_NAME (_load) /* utilities */ #define cs_calloc CS_NAME (_calloc) #define cs_free CS_NAME (_free) #define cs_realloc CS_NAME (_realloc) #define cs_spalloc CS_NAME (_spalloc) #define cs_spfree CS_NAME (_spfree) #define cs_sprealloc CS_NAME (_sprealloc) #define cs_malloc CS_NAME (_malloc) /* --- secondary CSparse routines and data structures ----------------------- */ #define css CS_NAME (s) #define csn CS_NAME (n) #define csd CS_NAME (d) #define cs_amd CS_NAME (_amd) #define cs_chol CS_NAME (_chol) #define cs_dmperm CS_NAME (_dmperm) #define cs_droptol CS_NAME (_droptol) #define cs_dropzeros CS_NAME (_dropzeros) #define cs_happly CS_NAME (_happly) #define cs_ipvec CS_NAME (_ipvec) #define cs_lsolve CS_NAME (_lsolve) #define cs_ltsolve CS_NAME (_ltsolve) #define cs_lu CS_NAME (_lu) #define cs_permute CS_NAME (_permute) #define cs_pinv CS_NAME (_pinv) #define cs_pvec CS_NAME (_pvec) #define cs_qr CS_NAME (_qr) #define cs_schol CS_NAME (_schol) #define cs_sqr CS_NAME (_sqr) #define cs_symperm CS_NAME (_symperm) #define cs_usolve CS_NAME (_usolve) #define cs_utsolve CS_NAME (_utsolve) #define cs_updown CS_NAME (_updown) /* utilities */ #define cs_sfree CS_NAME (_sfree) #define cs_nfree CS_NAME (_nfree) #define cs_dfree CS_NAME (_dfree) /* --- tertiary CSparse routines -------------------------------------------- */ #define cs_counts CS_NAME (_counts) #define cs_cumsum CS_NAME (_cumsum) #define cs_dfs CS_NAME (_dfs) #define cs_etree CS_NAME (_etree) #define cs_fkeep CS_NAME (_fkeep) #define cs_house CS_NAME (_house) #define cs_invmatch CS_NAME (_invmatch) #define cs_maxtrans CS_NAME (_maxtrans) #define cs_post CS_NAME (_post) #define cs_scc CS_NAME (_scc) #define cs_scatter CS_NAME (_scatter) #define cs_tdfs CS_NAME (_tdfs) #define cs_reach CS_NAME (_reach) #define cs_spsolve CS_NAME (_spsolve) #define cs_ereach CS_NAME (_ereach) #define cs_randperm CS_NAME (_randperm) #define cs_leaf CS_NAME (_leaf) /* utilities */ #define cs_dalloc CS_NAME (_dalloc) #define cs_done CS_NAME (_done) #define cs_idone CS_NAME (_idone) #define cs_ndone CS_NAME (_ndone) #define cs_ddone CS_NAME (_ddone) /* -------------------------------------------------------------------------- */ /* Conversion routines */ /* -------------------------------------------------------------------------- */ #ifndef NCOMPLEX cs_di *cs_i_real (cs_ci *A, int real) ; cs_ci *cs_i_complex (cs_di *A, int real) ; cs_dl *cs_l_real (cs_cl *A, UF_long real) ; cs_cl *cs_l_complex (cs_dl *A, UF_long real) ; #endif #ifdef __cplusplus } #endif #endif SuiteSparse/CXSparse_newfiles/Source/0000755001170100242450000000000010711425510016567 5ustar davisfacSuiteSparse/CXSparse_newfiles/Source/cs_house.c0000644001170100242450000000143610630067063020554 0ustar davisfac#include "cs.h" /* create a Householder reflection [v,beta,s]=house(x), overwrite x with v, * where (I-beta*v*v')*x = s*e1 and e1 = [1 0 ... 0]'. * Note that this CXSparse version is different than CSparse. See Higham, * Accuracy & Stability of Num Algorithms, 2nd ed, 2002, page 357. */ CS_ENTRY cs_house (CS_ENTRY *x, double *beta, CS_INT n) { CS_ENTRY s = 0 ; CS_INT i ; if (!x || !beta) return (-1) ; /* check inputs */ /* s = norm(x) */ for (i = 0 ; i < n ; i++) s += x [i] * CS_CONJ (x [i]) ; s = sqrt (s) ; if (s == 0) { (*beta) = 0 ; x [0] = 1 ; } else { /* s = sign(x[0]) * norm (x) ; */ if (x [0] != 0) { s *= x [0] / CS_ABS (x [0]) ; } x [0] += s ; (*beta) = 1. / CS_REAL (CS_CONJ (s) * x [0]) ; } return (-s) ; } SuiteSparse/CXSparse_newfiles/Source/cs_updown.c0000644001170100242450000000354610571364723020760 0ustar davisfac#include "cs.h" /* sparse Cholesky update/downdate, L*L' + sigma*w*w' (sigma = +1 or -1) */ CS_INT cs_updown (cs *L, CS_INT sigma, const cs *C, const CS_INT *parent) { CS_INT n, p, f, j, *Lp, *Li, *Cp, *Ci ; CS_ENTRY *Lx, *Cx, alpha, gamma, w1, w2, *w ; double beta = 1, beta2 = 1, delta ; #ifdef CS_COMPLEX cs_complex_t phase ; #endif if (!CS_CSC (L) || !CS_CSC (C) || !parent) return (0) ; /* check inputs */ Lp = L->p ; Li = L->i ; Lx = L->x ; n = L->n ; Cp = C->p ; Ci = C->i ; Cx = C->x ; if ((p = Cp [0]) >= Cp [1]) return (1) ; /* return if C empty */ w = cs_malloc (n, sizeof (CS_ENTRY)) ; /* get workspace */ if (!w) return (0) ; /* out of memory */ f = Ci [p] ; for ( ; p < Cp [1] ; p++) f = CS_MIN (f, Ci [p]) ; /* f = min (find (C)) */ for (j = f ; j != -1 ; j = parent [j]) w [j] = 0 ; /* clear workspace w */ for (p = Cp [0] ; p < Cp [1] ; p++) w [Ci [p]] = Cx [p] ; /* w = C */ for (j = f ; j != -1 ; j = parent [j]) /* walk path f up to root */ { p = Lp [j] ; alpha = w [j] / Lx [p] ; /* alpha = w(j) / L(j,j) */ beta2 = beta*beta + sigma*alpha*CS_CONJ(alpha) ; if (beta2 <= 0) break ; /* not positive definite */ beta2 = sqrt (beta2) ; delta = (sigma > 0) ? (beta / beta2) : (beta2 / beta) ; gamma = sigma * CS_CONJ(alpha) / (beta2 * beta) ; Lx [p] = delta * Lx [p] + ((sigma > 0) ? (gamma * w [j]) : 0) ; beta = beta2 ; #ifdef CS_COMPLEX phase = CS_ABS (Lx [p]) / Lx [p] ; /* phase = abs(L(j,j))/L(j,j)*/ Lx [p] *= phase ; /* L(j,j) = L(j,j) * phase */ #endif for (p++ ; p < Lp [j+1] ; p++) { w1 = w [Li [p]] ; w [Li [p]] = w2 = w1 - alpha * Lx [p] ; Lx [p] = delta * Lx [p] + gamma * ((sigma > 0) ? w1 : w2) ; #ifdef CS_COMPLEX Lx [p] *= phase ; /* L(i,j) = L(i,j) * phase */ #endif } } cs_free (w) ; return (beta2 > 0) ; } SuiteSparse/CXSparse_newfiles/Source/cs_convert.c0000644001170100242450000000662010566670105021116 0ustar davisfac#include "cs.h" /* convert from complex to real (int version) */ /* C = real(A) if real is true, imag(A) otherwise */ cs_di *cs_i_real (cs_ci *A, int real) { cs_di *C ; int n, triplet, nn, p, nz, *Ap, *Ai, *Cp, *Ci ; cs_complex_t *Ax ; double *Cx ; if (!A || !A->x) return (NULL) ; /* return if A NULL or pattern-only */ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; triplet = (A->nz >= 0) ; /* true if A is a triplet matrix */ nz = triplet ? A->nz : Ap [n] ; C = cs_di_spalloc (A->m, n, A->nzmax, 1, triplet) ; if (!C) return (NULL) ; Cp = C->p ; Ci = C->i ; Cx = C->x ; nn = triplet ? nz : (n+1) ; for (p = 0 ; p < nz ; p++) Ci [p] = Ai [p] ; for (p = 0 ; p < nn ; p++) Cp [p] = Ap [p] ; for (p = 0 ; p < nz ; p++) Cx [p] = real ? creal (Ax [p]) : cimag (Ax [p]) ; if (triplet) C->nz = nz ; return (C) ; } /* convert from real to complex (int version) */ /* C = A if real is true, or C = i*A otherwise */ cs_ci *cs_i_complex (cs_di *A, int real) { cs_ci *C ; int n, triplet, nn, p, nz, *Ap, *Ai, *Cp, *Ci ; double *Ax ; cs_complex_t *Cx ; if (!A || !A->x) return (NULL) ; /* return if A NULL or pattern-only */ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; triplet = (A->nz >= 0) ; /* true if A is a triplet matrix */ nz = triplet ? A->nz : Ap [n] ; C = cs_ci_spalloc (A->m, n, A->nzmax, 1, triplet) ; if (!C) return (NULL) ; Cp = C->p ; Ci = C->i ; Cx = C->x ; nn = triplet ? nz : (n+1) ; for (p = 0 ; p < nz ; p++) Ci [p] = Ai [p] ; for (p = 0 ; p < nn ; p++) Cp [p] = Ap [p] ; for (p = 0 ; p < nz ; p++) Cx [p] = real ? Ax [p] : (I * Ax [p]) ; if (triplet) C->nz = nz ; return (C) ; } /* convert from complex to real (UF_long version) */ /* C = real(A) if real is true, imag(A) otherwise */ cs_dl *cs_l_real (cs_cl *A, UF_long real) { cs_dl *C ; UF_long n, triplet, nn, p, nz, *Ap, *Ai, *Cp, *Ci ; cs_complex_t *Ax ; double *Cx ; if (!A || !A->x) return (NULL) ; /* return if A NULL or pattern-only */ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; triplet = (A->nz >= 0) ; /* true if A is a triplet matrix */ nz = triplet ? A->nz : Ap [n] ; C = cs_dl_spalloc (A->m, n, A->nzmax, 1, triplet) ; if (!C) return (NULL) ; Cp = C->p ; Ci = C->i ; Cx = C->x ; nn = triplet ? nz : (n+1) ; for (p = 0 ; p < nz ; p++) Ci [p] = Ai [p] ; for (p = 0 ; p < nn ; p++) Cp [p] = Ap [p] ; for (p = 0 ; p < nz ; p++) Cx [p] = real ? creal (Ax [p]) : cimag (Ax [p]) ; if (triplet) C->nz = nz ; return (C) ; } /* convert from real to complex (UF_long version) */ /* C = A if real is true, or C = i*A otherwise */ cs_cl *cs_l_complex (cs_dl *A, UF_long real) { cs_cl *C ; UF_long n, triplet, nn, p, nz, *Ap, *Ai, *Cp, *Ci ; double *Ax ; cs_complex_t *Cx ; if (!A || !A->x) return (NULL) ; /* return if A NULL or pattern-only */ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; triplet = (A->nz >= 0) ; /* true if A is a triplet matrix */ nz = triplet ? A->nz : Ap [n] ; C = cs_cl_spalloc (A->m, n, A->nzmax, 1, triplet) ; if (!C) return (NULL) ; Cp = C->p ; Ci = C->i ; Cx = C->x ; nn = triplet ? nz : (n+1) ; for (p = 0 ; p < nz ; p++) Ci [p] = Ai [p] ; for (p = 0 ; p < nn ; p++) Cp [p] = Ap [p] ; for (p = 0 ; p < nz ; p++) Cx [p] = real ? Ax [p] : (I * Ax [p]) ; if (triplet) C->nz = nz ; return (C) ; } SuiteSparse/CXSparse_newfiles/Source/README.txt0000644001170100242450000000023710375603427020302 0ustar davisfacCXSparse/Source directory: primary ANSI C source code files for CXSparse. To compile the libcxsparse.a C-callable library, just type "make" in this directory. SuiteSparse/CXSparse_newfiles/README.txt0000644001170100242450000005751210711425615017045 0ustar davisfacCXSparse: a Concise Sparse Matrix package - Extended. Version 2.2.0, Copyright (c) 2006-2007, Timothy A. Davis. Derived from CSparse. Conversion originally by David Bateman, Motorola, and then modified by Tim Davis. ANSI C99 is required, with support for the _Complex data type. (if you use a C++ compiler, the C++ complex type is used instead). CXSparse is a version of CSparse that operates on both real and complex matrices, using either int or UF_long integers. A UF_long is normally just a long on most platforms, but becomes __int64 on WIN64. It now includes a MATLAB interface, enabling the use of CXSparse functions on both 32-bit and 64-bit platforms. To install for use in MATLAB, simply type "cs_install" in the MATLAB Command Window, while in the CXSparse/MATLAB directory. (NOTE: Windows users cannot use the "lcc" command; run "mex -setup" first, and select a different compiler). If you use the Unix "make" command in that directory instead and are using a 64-bit platform, then you must edit the CXSparse/MATLAB/Makefile first. Refer to the instructions in that file. Refer to "Direct Methods for Sparse Linear Systems," Timothy A. Davis, SIAM, Philadelphia, 2006. No detailed user guide is included in this package; the user guide is the book itself. To compile the C-library (./Source), C demo programs (./Demo) just type "make" in this directory. To run the exhaustive statement coverage tests, type "make" in the Tcov directory; the Tcov tests assume you are using Linux. To remove all files not in the original distribution, type "make distclean". I recommend that you use a different level of optimization than "cc -O", which was chosen so that the Makefile is portable. See Source/Makefile. If your C compiler does not support the ANSI C99 complex type, the #include statement will fail. If this happens, compile the code with the -DNCOMPLEX flag (the MATLAB cs_install will do this for you). This package is backward compatible with CSparse. That is, user code that uses CSparse may switch to using CXSparse without any changes to the user code. Each CXSparse function has a generic version with the same name as the CSparse function, and four type-specific versions. For example: cs_add same as cs_add_di by default, but can be changed to use UF_long integers if user code is compiled with -DCS_LONG, and/or can be changed to operate on complex matrices with -DCS_COMPLEX. cs_di_add double/int version of cs_add cs_dl_add double/UF_long version of cs_add cs_ci_add complex/int version of cs_add cs_cl_add complex/UF_long version of cs_add The sparse matrix data structures are treated in the same way: cs, css, csn, and csd become cs_di, cs_dis, cs_din, and cs_did for the double/int case, cs_cl, cs_cls, cs_cln, and cs_cld for the complex/UF_long case, and so on. See cs_demo.c for a type-generic user program, and cs_cl_demo.c for a type-specific version of the same program (complex/UF_long). Several macros are available in CXSparse (but not in CSparse) to allow user code to be written in a type-generic manner: CS_INT int by default, UF_long if -DCS_LONG compiler flag is used CS_ENTRY double by default, double complex if -DCS_COMPLEX flag is used. CS_ID "%d" or "%ld", for printf and scanf of the CS_INT type. CS_INT_MAX INT_MAX or LONG_MAX, the largest possible value of CS_INT. CS_REAL(x) x or creal(x) CS_IMAG(x) 0 or cimag(x) CS_CONJ(x) x or conj(x) CS_ABS(x) fabs(x) or cabs(x) Even the name of the include file (cs.h) is the same. To use CXSparse instead of CSparse, simply compile with -ICXSparse/Source instead of -ICSparse/Source, and link against libcxsparse.a instead of the CSparse libcsparse.a library. To determine at compile time if CXSparse or CSparse is being used: #ifdef CXSPARSE CXSparse is in use. The generic functions equivalent to CSparse may be used (cs_add, etc). These generic functions can use different types, depending on the -DCS_LONG and -DCS_COMPLEX compile flags, with the default being double/int. The type-specific functions and data types (cs_di_add, cs_di, CS_INT, etc.) can be used. #else CSparse is in use. Only the generic functions "cs_add", etc., are available, and they are of type double/int. #endif See cs.h for the prototypes of each function, and the book "Direct Methods for Sparse Linear Systems" for full documentation of CSparse and CXSparse. Other changes from CSparse: cs_transpose performs the complex conjugate transpose if values>0 (C=A'), the pattern-only transpose if values=0 (C=spones(A') in MATLAB), and the array transpose if values<0 (C=A.' in MATLAB notation). A set of four conversion routines are included in CXSparse, to convert real matrices to/from complex matrices. The Householder reflection constructed by cs_house.c also differs slightly, to accomodate both the real and complex cases properly. CXSparse is generated automatically from CSparse. Refer to http://www.cise.ufl.edu/research/sparse/CSparse for details. -------------------------------------------------------------------------------- Contents: -------------------------------------------------------------------------------- Demo/ demo C programs that use CXSparse Doc/ license and change log Makefile Makefile for the whole package MATLAB/ MATLAB interface, demos, and tests for CXSparse Matrix/ sample matrices (with extra complex matrices for CXSparse) README.txt this file Source/ primary CXSparse source files Tcov/ CXSparse tests -------------------------------------------------------------------------------- ./Doc: license and change log -------------------------------------------------------------------------------- ChangeLog changes in CSparse since first release lesser.txt the GNU LGPL License.txt license (GNU LGPL) -------------------------------------------------------------------------------- ./Source: Primary source code for CXSparse -------------------------------------------------------------------------------- cs_add.c add sparse matrices cs_amd.c approximate minimum degree cs_chol.c sparse Cholesky cs_cholsol.c x=A\b using sparse Cholesky cs_compress.c convert a compress form to compressed-column form cs_counts.c column counts for Cholesky and QR cs_convert.c convert real to complex and complex to real (not in CSparse) cs_cumsum.c cumulative sum cs_dfs.c depth-first-search cs_dmperm.c Dulmage-Mendelsohn permutation cs_droptol.c drop small entries from a sparse matrix cs_dropzeros.c drop zeros from a sparse matrix cs_dupl.c remove (and sum) duplicates cs_entry.c add an entry to a triplet matrix cs_ereach.c nonzero pattern of Cholesky L(k,:) from etree and triu(A(:,k)) cs_etree.c find elimination tree cs_fkeep.c drop entries from a sparse matrix cs_gaxpy.c sparse matrix times dense matrix cs.h include file for CXSparse cs_happly.c apply Householder reflection cs_house.c Householder reflection (*** NOTE: different algo. from CSparse) cs_ipvec.c x(p)=b cs_leaf.c determine if j is a leaf of the skeleton matrix and find lca cs_load.c load a sparse matrix from a file cs_lsolve.c x=L\b cs_ltsolve.c x=L'\b cs_lu.c sparse LU factorization cs_lusol.c x=A\b using sparse LU factorization cs_malloc.c memory manager cs_maxtrans.c maximum transveral (permutation for zero-free diagonal) cs_multiply.c sparse matrix multiply cs_norm.c sparse matrix norm cs_permute.c permute a sparse matrix cs_pinv.c invert a permutation vector cs_post.c postorder an elimination tree cs_print.c print a sparse matrix cs_pvec.c x=b(p) cs_qr.c sparse QR cs_qrsol.c solve a least-squares problem cs_randperm.c random permutation cs_reach.c find nonzero pattern of x=L\b for sparse L and b cs_scatter.c scatter a sparse vector cs_scc.c strongly-connected components cs_schol.c symbolic Cholesky cs_spsolve.c x=Z\b where Z, x, and b are sparse, and Z upper/lower triangular cs_sqr.c symbolic QR (also can be used for LU) cs_symperm.c symmetric permutation of a sparse matrix cs_tdfs.c depth-first-search of a tree cs_transpose.c transpose a sparse matrix cs_updown.c sparse rank-1 Cholesky update/downate cs_usolve.c x=U\b cs_util.c various utilities (allocate/free matrices, workspace, etc) cs_utsolve.c x=U'\b Makefile Makefile for CXSparse README.txt README file for CXSparse -------------------------------------------------------------------------------- ./Demo: C program demos -------------------------------------------------------------------------------- cs_ci_demo1.c complex/int version of cs_demo1.c cs_ci_demo2.c complex/int version of cs_demo2.c cs_ci_demo3.c complex/int version of cs_demo3.c cs_ci_demo.c complex/int version of cs_demo.c cs_ci_demo.h complex/int version of cs_demo.h cs_cl_demo1.c complex/UF_long version of cs_demo1.c cs_cl_demo2.c complex/UF_long version of cs_demo2.c cs_cl_demo3.c complex/UF_long version of cs_demo3.c cs_cl_demo.c complex/UF_long version of cs_demo.c cs_cl_demo.h complex/UF_long version of cs_demo.h cs_demo1.c read a matrix from a file and perform basic matrix operations cs_demo2.c read a matrix from a file and solve a linear system cs_demo3.c read a matrix, solve a linear system, update/downdate cs_demo.c support routines for cs_demo*.c cs_demo.h include file for demo programs cs_demo.out output of "make", which runs the demos on some matrices cs_di_demo1.c double/int version of cs_demo1.c cs_di_demo2.c double/int version of cs_demo2.c cs_di_demo3.c double/int version of cs_demo3.c cs_di_demo.c double/int version of cs_demo.c cs_di_demo.h double/int version of cs_demo.h cs_dl_demo1.c double/UF_long version of cs_demo1.c cs_dl_demo2.c double/UF_long version of cs_demo2.c cs_dl_demo3.c double/UF_long version of cs_demo3.c cs_dl_demo.c double/UF_long version of cs_demo.c cs_dl_demo.h double/UF_long version of cs_demo.h cs_idemo.c convert real matrices to/from complex (int version) cs_ldemo.c convert real matrices to/from complex (UF_long version) Makefile Makefile for Demo programs readhb.f read a Rutherford-Boeing matrix (real matrices only) README.txt Demo README file -------------------------------------------------------------------------------- ./MATLAB: MATLAB interface, demos, and tests -------------------------------------------------------------------------------- cs_install.m MATLAB function for compiling and installing CSparse for MATLAB CSparse/ MATLAB interface for CSparse Demo/ MATLAB demos for CSparse Makefile MATLAB interface Makefile README.txt MATLAB README file Test/ MATLAB test for CSparse, and "textbook" routines UFget/ MATLAB interface to UF Sparse Matrix Collection -------------------------------------------------------------------------------- ./MATLAB/CSparse: MATLAB interface for CSparse -------------------------------------------------------------------------------- Contents.m Contents of MATLAB interface to CSparse cs_add.m add two sparse matrices cs_add_mex.c cs_amd.m approximate minimum degree cs_amd_mex.c cs_chol.m sparse Cholesky cs_chol_mex.c cs_cholsol.m x=A\b using a sparse Cholesky cs_cholsol_mex.c cs_counts.m column counts for Cholesky or QR (like "symbfact" in MATLAB) cs_counts_mex.c cs_dmperm.m Dulmage-Mendelsohn permutation cs_dmperm_mex.c cs_dmsol.m x=A\b using dmperm cs_dmspy.m plot a picture of a dmperm-permuted matrix cs_droptol.m drop small entries cs_droptol_mex.c cs_esep.m find edge separator cs_etree.m compute elimination tree cs_etree_mex.c cs_gaxpy.m sparse matrix times dense vector cs_gaxpy_mex.c cs_lsolve.m x=L\b where L is lower triangular cs_lsolve_mex.c cs_ltsolve.m x=L'\b where L is lower triangular cs_ltsolve_mex.c cs_lu.m sparse LU factorization cs_lu_mex.c cs_lusol.m x=A\b using sparse LU factorization cs_lusol_mex.c cs_make.m compiles CSparse for use in MATLAB cs_mex.c support routines for CSparse mexFunctions cs_mex.h cs_multiply.m sparse matrix multiply cs_multiply_mex.c cs_must_compile.m determine if a source file needs to be compiled with mex cs_nd.m nested dissection cs_nsep.m find node separator cs_permute.m permute a sparse matrix cs_permute_mex.c cs_print.m print a sparse matrix cs_print_mex.c cs_qleft.m apply Householder vectors to the left cs_qright.m apply Householder vectors to the right cs_qr.m sparse QR factorization cs_qr_mex.c cs_qrsol.m solve a sparse least squares problem cs_qrsol_mex.c cs_randperm.m randdom permutation cs_randperm_mex.c cs_scc.m strongly-connected components cs_scc_mex.c cs_sep.m convert an edge separator into a node separator cs_sparse.m convert a triplet form matrix to a compress-column form cs_sparse_mex.c cs_symperm.m symmetric permutation of a sparse matrix cs_symperm_mex.c cs_sqr.m symbolic QR ordering and analysis cs_sqr_mex.c cs_thumb_mex.c compute small "thumbnail" of a sparse matrix (for cspy). cs_transpose.m transpose a sparse matrix cs_transpose_mex.c cs_updown.m sparse Cholesky update/downdate cs_updown_mex.c cs_usolve.m x=U\b where U is upper triangular cs_usolve_mex.c cs_utsolve.m x=U'\b where U is upper triangular cs_utsolve_mex.c cspy.m a color "spy" Makefile Makefile for CSparse MATLAB interface README.txt README file for CSparse MATLAB interface -------------------------------------------------------------------------------- ./MATLAB/Demo: MATLAB demos for CSparse -------------------------------------------------------------------------------- Contents.m Contents of MATLAB demo for CSparse cs_demo.m run all MATLAB demos for CSparse cs_demo1.m MATLAB version of Demo/cs_demo1.c cs_demo2.m MATLAB version of Demo/cs_demo2.c cs_demo3.m MATLAB version of Demo/cs_demo3.c private/ private functions for MATLAB demos README.txt README file for CSparse MATLAB demo -------------------------------------------------------------------------------- ./MATLAB/Demo/private: private functions for MATLAB demos -------------------------------------------------------------------------------- demo2.m demo 2 demo3.m demo 3 ex_1.m example 1 ex2.m example 2 ex3.m example 3 frand.m generate a random finite-element matrix get_problem.m get a matrix is_sym.m determine if a matrix is symmetric mesh2d1.m construct a 2D mesh (method 1) mesh2d2.m construct a 2D mesh (method 2) mesh3d1.m construct a 3D mesh (method 1) mesh3d2.m construct a 3D mesh (method 2) print_order.m print the ordering method used resid.m compute residual rhs.m create right-hand-side -------------------------------------------------------------------------------- ./MATLAB/Test: Extensive test of CSparse, in MATLAB -------------------------------------------------------------------------------- Makefile Makefile for MATLAB Test directory README.txt README file for MATLAB/Test Contents.m Contents of MATLAB/Test, "textbook" files only chol_downdate.m downdate a Cholesky factorization. chol_left.m left-looking Cholesky factorization. chol_left2.m left-looking Cholesky factorization, more details. chol_right.m right-looking Cholesky factorization. chol_super.m left-looking "supernodal" Cholesky factorization. chol_up.m up-looking Cholesky factorization. chol_update.m update a Cholesky factorization. chol_updown.m update or downdate a Cholesky factorization. cond1est.m 1-norm condition estimate. cs_fiedler.m the Fiedler vector of a connected graph. givens2.m find a Givens rotation. house.m find a Householder reflection. lu_left.m left-looking LU factorization. lu_right.m right-looking LU factorization. lu_rightp.m right-looking LU factorization, with partial pivoting. lu_rightpr.m recursive right-looking LU, with partial pivoting. lu_rightr.m recursive right-looking LU. norm1est.m 1-norm estimate. qr_givens.m Givens-rotation QR factorization. qr_givens_full.m Givens-rotation QR factorization, for full matrices. qr_left.m left-looking Householder QR factorization. qr_right.m right-looking Householder QR factorization. cs_fiedler.m Fiedler vector cs_frand.m generate a random finite-element matrix cs_frand_mex.c cs_ipvec.m x(p)=b cs_ipvec_mex.c cs_maxtransr.m recursive maximum matching algorithm cs_maxtransr_mex.c cs_pvec.m x=b(p) cs_pvec_mex.c interface for cs_pvec cs_reach.m non-recursive reach (interface to CSparse cs_reach) cs_reach_mex.c non-recursive x=spones(L\sparse(b)) cs_reachr.m recursive reach (interface to CSparse cs_reachr) cs_reachr_mex.c cs_rowcnt.m row counts for sparse Cholesky cs_rowcnt_mex.c row counts for sparse Cholesky cs_sparse2.m same as cs_sparse, to test cs_entry function cs_sparse2_mex.c like cs_sparse, but for testing cs_entry cs_test_make.m compiles MATLAB tests check_if_same.m check if two inputs are identical or not choldn.m Cholesky downdate cholup.m Cholesky update, using Given's rotations cholupdown.m Cholesky update/downdate (Bischof, Pan, and Tang method) cs_q1.m construct Q from Householder vectors cs_test_make.m compiles the CSparse, Demo, and Test mexFunctions. dmperm_test.m test cs_dmperm chol_example.m simple Cholesky factorization example etree_sample.m construct a sample etree and symbolic factorization gqr3.m QR factorization, based on Givens rotations happly.m apply Householder reflection to a vector hmake1.m construct a Householder reflection mynormest1.m estimate norm(A,1), using LU factorization (L*U = P*A*Q). myqr.m QR factorization using Householder reflections another_colormap.m try another color map cspy_test.m test cspy and cs_dmspy qr2.m QR factorization based on Householder reflections sample_colormap.m try a colormap for use in cspy signum.m compute and display the sign of a column vector x sqr_example.m test cs_sqr dmspy_test.m test cspy, cs_dmspy, and cs_dmperm test_qr.m test various QR factorization methods test_randperms.m test random permutations testh.m test Householder reflections test_qr1.m test QR factorizations test_qrsol.m test cs_qrsol test_sep.m test cs_sep, and compare with Gilbert's meshpart vtxsep testall.m test all CSparse functions (run tests 1 to 28 below) test1.m test cs_transpose test2.m test cs_sparse test3.m test cs_lsolve, cs_ltsolve, cs_usolve, cs_chol test4.m test cs_multiply test5.m test cs_add test6.m test cs_reach, cs_reachr, cs_lsolve, cs_usolve test7.m test cs_lu test8.m test cs_cholsol, cs_lusol test9.m test cs_qr test10.m test cs_qr test11.m test cs_rowcnt test12.m test cs_qr and compare with svd test13.m test cs_counts, cs_etree test14.m test cs_droptol test15.m test cs_amd test16.m test cs_amd test17.m test cs_qr, cs_qright, cs_q1, cs_qrleft, cs_qrsol test18.m test iterative refinement after backslash test19.m test cs_dmperm, cs_maxtransr, cs_dmspy, cs_scc test20.m test cholupdown test21.m test cs_updown test22.m test cond1est test23.m test cs_dmspy test24.m test cs_fielder test25.m test cs_nd test26.m test cs_dmsol and cs_dmspy test27.m test cs_qr, cs_utsolve, cs_qrsol test28.m test cs_randperm, cs_dmperm -------------------------------------------------------------------------------- ./MATLAB/UFget: MATLAB interface for the UF Sparse Matrix Collection -------------------------------------------------------------------------------- Contents.m Contents of UFget mat/ default directory where downloaded matrices will be put README.txt README file for UFget UFget_defaults.m default parameter settings UFget_example.m example of use UFget_install.m installs UFget temporarily (for current session) UFget_java.class read a url and load it in into MATLAB (compiled Java code) UFget_java.java read a url and load it in into MATLAB (Java source code) UFget_lookup.m look up a matrix in the index UFget.m UFget itself (primary user interface) UFweb.m open url for a matrix or collection mat/UF_Index.mat index of matrices in UF Sparse Matrix Collection -------------------------------------------------------------------------------- ./Matrix: Sample matrices, most from Rutherford/Boeing collection -------------------------------------------------------------------------------- ash219 overdetermined pattern of Holland survey. Ashkenazi, 1974. bcsstk01 stiffness matrix for small generalized eigenvalue problem bcsstk16 stiffness matrix, Corp of Engineers dam fs_183_1 unsymmetric facsimile convergence matrix lp_afiro NETLIB afiro linear programming problem mbeacxc US economy, 1972. Dan Szyld, while at NYU t1 small example used in Chapter 2 west0067 Cavett problem with 5 components (chemical eng., Westerberg) c_mbeacxc complex version of mbeacxc c_west0067 complex version of west0067 mhd1280b Alfven spectra in magnetohydrodynamics (complex) neumann complex matrix qc324 model of H+ in an electromagnetic field (complex) t2 small complex matrix t3 small complex matrix t4 small complex matrix c4 small complex matrix young1c aeronautical problem (complex matrix) -------------------------------------------------------------------------------- ./Tcov: Exhaustive test coverage of CXSparse -------------------------------------------------------------------------------- covall same as covall.linux covall.linux find coverage (Linux) covall.sol find coverage (Solaris) cov.awk coverage summary cover print uncovered lines covs print uncovered lines cstcov_malloc_test.c malloc test cstcov_malloc_test.h cstcov_test.c main program for Tcov tests gcovs run gcov (Linux) Makefile Makefile for Tcov tests nil an empty matrix zero a 1-by-1 zero matrix czero a 1-by-1 complex zero matrix README.txt README file for Tcov directory -------------------------------------------------------------------------------- Change Log: -------------------------------------------------------------------------------- Refer to CSparse for changes in CSparse, which are immediately propagated into CXSparse (those Change Log entries are not repeated here). Nov 1, 2007. version 2.2.1 CXSparse/MATLAB/Test ported to Windows May 31, 2007. version 2.2.0 * back-port to MATLAB 7.2 and earlier (which does not have mwIndex). * more graceful failure in cs_make when attempting complex matrix support (Windows, in particular) * correction to CXSparse/Demo/Makefile * added sizeof(CS_INT) printout to cs_idemo.c, cs_ldemo.c Mar 14, 2007. Version 2.1.0. * MATLAB interface added for CXSparse. * cs_complex_t type added (a #define for "double _Complex", which is the complex type used in CXSparse 2.0.x). When compiling with a C++ compiler, the std::compex type is used for the complex case. * bug fix in complex sparse Cholesky (cs_chol.c). * bug fix in complex sparse Cholesky update/downdate (cs_updown.c). * bug fix in cs_symperm for the complex case. * "beta" changed from complex to real, in sparse QR (cs_house.c, cs_happly.c, cs_qr.c), (a performance/memory improvement, not a bug fix). Similar change to "nz2" in cs_cumsum.c. May 5, 2006. Version 2.0.1 released. * long changed to UF_long, dependency in ../UFconfig/UFconfig.h added. "UF_long" is a #define'd term in UFconfig.h. It is normally defined as "long", but can be redefined as something else if desired. On Windows-64, it becomes __int64. Mar 6, 2006 "double complex" changed to "double _Complex", to avoid conflicts when CXSparse is compiled with a C++ compiler. Other minor changes to cs.h. SuiteSparse/CCOLAMD/0000755001170100242450000000000010620614432013007 5ustar davisfacSuiteSparse/CCOLAMD/Doc/0000755001170100242450000000000010711427601013515 5ustar davisfacSuiteSparse/CCOLAMD/Doc/ChangeLog0000644001170100242450000000153210711427577015304 0ustar davisfacNov 1, 2007: version 2.7.1 * minor changes to MATLAB test code May 31, 2007: version 2.7.0 * ported to 64-bit MATLAB * subdirectories added (Source/, Include/, Lib/, Doc/, MATLAB/, Demo/) Dec 12, 2006, version 2.5.2 * minor MATLAB clean up Apr 30, 2006: version 2.5 * ccolamd_recommended modified. 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SuiteSparse/CCOLAMD/Lib/0000755001170100242450000000000010711435724013523 5ustar davisfacSuiteSparse/CCOLAMD/Lib/Makefile0000644001170100242450000000146110617106661015165 0ustar davisfac#------------------------------------------------------------------------------- # CCOLAMD Makefile #------------------------------------------------------------------------------- default: libccolamd.a include ../../UFconfig/UFconfig.mk I = -I../Include -I../../UFconfig INC = ../Include/ccolamd.h ../../UFconfig/UFconfig.h SRC = ../Source/ccolamd.c ../Source/ccolamd_global.c # creates libccolamd.a, a C-callable COLAMD library libccolamd.a: $(SRC) $(INC) $(CC) $(CFLAGS) $(I) -c ../Source/ccolamd_global.c $(CC) $(CFLAGS) $(I) -c ../Source/ccolamd.c $(CC) $(CFLAGS) $(I) -c ../Source/ccolamd.c -DDLONG -o ccolamd_l.o $(AR) libccolamd.a ccolamd.o ccolamd_l.o ccolamd_global.o ccode: libccolamd.a library: libccolamd.a clean: - $(RM) $(CLEAN) purge: distclean distclean: clean - $(RM) libccolamd.a SuiteSparse/CCOLAMD/Demo/0000755001170100242450000000000010711435724013701 5ustar davisfacSuiteSparse/CCOLAMD/Demo/ccolamd_example.c0000644001170100242450000001430210616375115017163 0ustar davisfac/* ========================================================================== */ /* === ccolamd and csymamd example ========================================== */ /* ========================================================================== */ /* ---------------------------------------------------------------------------- * CCOLAMD Copyright (C), Univ. of Florida. Authors: Timothy A. Davis, * Sivasankaran Rajamanickam, and Stefan Larimore * See License.txt for the Version 2.1 of the GNU Lesser General Public License * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* * ccolamd example of use, to order the columns of a 5-by-4 matrix with * 11 nonzero entries in the following nonzero pattern, with default knobs * and no ordering constraints. * * x 0 x 0 * x 0 x x * 0 x x 0 * 0 0 x x * x x 0 0 * * csymamd example of use, to order the rows and columns of a 5-by-5 * matrix with 13 nonzero entries in the following nonzero pattern, * with default knobs and no ordering constraints. * * x x 0 0 0 * x x x x 0 * 0 x x 0 0 * 0 x 0 x x * 0 0 0 x x * * (where x denotes a nonzero value). */ /* ========================================================================== */ #include #include "ccolamd.h" #define A_NNZ 11 #define A_NROW 5 #define A_NCOL 4 #define ALEN 150 /* size max (2.2*nnz+17*ncol+7*nrow+6, 23*ncol+7*nrow+6) */ #define B_NNZ 4 #define B_N 5 int main (void) { /* ====================================================================== */ /* input matrix A definition */ /* ====================================================================== */ int A [ALEN] = { 0, 1, 4, /* row indices of nonzeros in column 0 */ 2, 4, /* row indices of nonzeros in column 1 */ 0, 1, 2, 3, /* row indices of nonzeros in column 2 */ 1, 3} ; /* row indices of nonzeros in column 3 */ int p [ ] = { 0, /* column 0 is in A [0..2] */ 3, /* column 1 is in A [3..4] */ 5, /* column 2 is in A [5..8] */ 9, /* column 3 is in A [9..10] */ A_NNZ} ; /* number of nonzeros in A */ /* ====================================================================== */ /* input matrix B definition */ /* ====================================================================== */ int B [ ] = { /* Note: only strictly lower triangular part */ /* is included, since symamd ignores the */ /* diagonal and upper triangular part of B. */ 1, /* row indices of nonzeros in column 0 */ 2, 3, /* row indices of nonzeros in column 1 */ /* row indices of nonzeros in column 2 (none) */ 4 /* row indices of nonzeros in column 3 */ } ; /* row indices of nonzeros in column 4 (none) */ int q [ ] = { 0, /* column 0 is in B [0] */ 1, /* column 1 is in B [1..2] */ 3, /* column 2 is empty */ 3, /* column 3 is in B [3] */ 4, /* column 4 is empty */ B_NNZ} ; /* number of nonzeros in strictly lower B */ /* ====================================================================== */ /* other variable definitions */ /* ====================================================================== */ int perm [B_N+1] ; /* note the size is N+1 */ int stats [CCOLAMD_STATS] ; /* for ccolamd and csymamd output statistics */ int row, col, pp, length, ok ; /* ====================================================================== */ /* dump the input matrix A */ /* ====================================================================== */ printf ("ccolamd %d-by-%d input matrix:\n", A_NROW, A_NCOL) ; for (col = 0 ; col < A_NCOL ; col++) { length = p [col+1] - p [col] ; printf ("Column %d, with %d entries:\n", col, length) ; for (pp = p [col] ; pp < p [col+1] ; pp++) { row = A [pp] ; printf (" row %d\n", row) ; } } /* ====================================================================== */ /* order the matrix. Note that this destroys A and overwrites p */ /* ====================================================================== */ ok = ccolamd (A_NROW, A_NCOL, ALEN, A, p, (double *) NULL, stats, NULL) ; ccolamd_report (stats) ; if (!ok) { printf ("ccolamd error!\n") ; exit (1) ; } /* ====================================================================== */ /* print the column ordering */ /* ====================================================================== */ printf ("ccolamd column ordering:\n") ; printf ("1st column: %d\n", p [0]) ; printf ("2nd column: %d\n", p [1]) ; printf ("3rd column: %d\n", p [2]) ; printf ("4th column: %d\n", p [3]) ; /* ====================================================================== */ /* dump the strictly lower triangular part of symmetric input matrix B */ /* ====================================================================== */ printf ("\n\ncsymamd %d-by-%d input matrix:\n", B_N, B_N) ; printf ("Entries in strictly lower triangular part:\n") ; for (col = 0 ; col < B_N ; col++) { length = q [col+1] - q [col] ; printf ("Column %d, with %d entries:\n", col, length) ; for (pp = q [col] ; pp < q [col+1] ; pp++) { row = B [pp] ; printf (" row %d\n", row) ; } } /* ====================================================================== */ /* order the matrix B. Note that this does not modify B or q. */ /* ====================================================================== */ ok = csymamd (B_N, B, q, perm, (double *) NULL, stats, &calloc, &free, NULL, -1) ; csymamd_report (stats) ; if (!ok) { printf ("csymamd error!\n") ; exit (1) ; } /* ====================================================================== */ /* print the symmetric ordering */ /* ====================================================================== */ printf ("csymamd column ordering:\n") ; printf ("1st row/column: %d\n", perm [0]) ; printf ("2nd row/column: %d\n", perm [1]) ; printf ("3rd row/column: %d\n", perm [2]) ; printf ("4th row/column: %d\n", perm [3]) ; printf ("5th row/column: %d\n", perm [4]) ; return (0) ; } SuiteSparse/CCOLAMD/Demo/Makefile0000644001170100242450000000256210617106610015340 0ustar davisfac#----------------------------------------------------------------------------- # compile the CCOLAMD demo #----------------------------------------------------------------------------- default: ccolamd_example ccolamd_l_example include ../../UFconfig/UFconfig.mk I = -I../Include -I../../UFconfig C = $(CC) $(CFLAGS) $(I) library: ( cd ../Lib ; $(MAKE) ) #------------------------------------------------------------------------------ # Create the demo program, run it, and compare the output #------------------------------------------------------------------------------ dist: ccolamd_example: ccolamd_example.c library $(C) -o ccolamd_example ccolamd_example.c ../Lib/libccolamd.a -lm - ./ccolamd_example > my_ccolamd_example.out - diff ccolamd_example.out my_ccolamd_example.out ccolamd_l_example: ccolamd_l_example.c library $(C) -o ccolamd_l_example ccolamd_l_example.c ../Lib/libccolamd.a -lm - ./ccolamd_l_example > my_ccolamd_l_example.out - diff ccolamd_example.out my_ccolamd_example.out #------------------------------------------------------------------------------ # Remove all but the files in the original distribution #------------------------------------------------------------------------------ clean: - $(RM) $(CLEAN) purge: distclean distclean: clean - $(RM) ccolamd_example ccolamd_l_example - $(RM) my_ccolamd_example.out my_ccolamd_l_example.out SuiteSparse/CCOLAMD/Demo/ccolamd_l_example.out0000644001170100242450000000210110711431134020043 0ustar davisfacccolamd 5-by-4 input matrix: Column 0, with 3 entries: row 0 row 1 row 4 Column 1, with 2 entries: row 2 row 4 Column 2, with 4 entries: row 0 row 1 row 2 row 3 Column 3, with 2 entries: row 1 row 3 ccolamd version 2.7, Nov 1, 2007: OK. ccolamd: number of dense or empty rows ignored: 0 ccolamd: number of dense or empty columns ignored: 0 ccolamd: number of garbage collections performed: 0 ccolamd_l column ordering: 1st column: 1 2nd column: 0 3rd column: 3 4th column: 2 csymamd_l 5-by-5 input matrix: Entries in strictly lower triangular part: Column 0, with 1 entries: row 1 Column 1, with 2 entries: row 2 row 3 Column 2, with 0 entries: Column 3, with 1 entries: row 4 Column 4, with 0 entries: csymamd version 2.7, Nov 1, 2007: OK. csymamd: number of dense or empty rows ignored: 0 csymamd: number of dense or empty columns ignored: 0 csymamd: number of garbage collections performed: 0 csymamd_l column ordering: 1st row/column: 0 2nd row/column: 2 3rd row/column: 1 4th row/column: 3 5th row/column: 4 SuiteSparse/CCOLAMD/Demo/ccolamd_example.out0000644001170100242450000000207310711431133017537 0ustar davisfacccolamd 5-by-4 input matrix: Column 0, with 3 entries: row 0 row 1 row 4 Column 1, with 2 entries: row 2 row 4 Column 2, with 4 entries: row 0 row 1 row 2 row 3 Column 3, with 2 entries: row 1 row 3 ccolamd version 2.7, Nov 1, 2007: OK. ccolamd: number of dense or empty rows ignored: 0 ccolamd: number of dense or empty columns ignored: 0 ccolamd: number of garbage collections performed: 0 ccolamd column ordering: 1st column: 1 2nd column: 0 3rd column: 3 4th column: 2 csymamd 5-by-5 input matrix: Entries in strictly lower triangular part: Column 0, with 1 entries: row 1 Column 1, with 2 entries: row 2 row 3 Column 2, with 0 entries: Column 3, with 1 entries: row 4 Column 4, with 0 entries: csymamd version 2.7, Nov 1, 2007: OK. csymamd: number of dense or empty rows ignored: 0 csymamd: number of dense or empty columns ignored: 0 csymamd: number of garbage collections performed: 0 csymamd column ordering: 1st row/column: 0 2nd row/column: 2 3rd row/column: 1 4th row/column: 3 5th row/column: 4 SuiteSparse/CCOLAMD/Demo/ccolamd_l_example.c0000644001170100242450000001444510616375173017512 0ustar davisfac/* ========================================================================== */ /* === ccolamd and csymamd example (UF_long integer version) ================ */ /* ========================================================================== */ /* ---------------------------------------------------------------------------- * CCOLAMD Copyright (C), Univ. of Florida. Authors: Timothy A. Davis, * Sivasankaran Rajamanickam, and Stefan Larimore * See License.txt for the Version 2.1 of the GNU Lesser General Public License * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* * ccolamd example of use, to order the columns of a 5-by-4 matrix with * 11 nonzero entries in the following nonzero pattern, with default knobs * and no ordering constraints. * * x 0 x 0 * x 0 x x * 0 x x 0 * 0 0 x x * x x 0 0 * * csymamd example of use, to order the rows and columns of a 5-by-5 * matrix with 13 nonzero entries in the following nonzero pattern, * with default knobs and no ordering constraints. * * x x 0 0 0 * x x x x 0 * 0 x x 0 0 * 0 x 0 x x * 0 0 0 x x * * (where x denotes a nonzero value). */ /* ========================================================================== */ #include #include "ccolamd.h" #define A_NNZ 11 #define A_NROW 5 #define A_NCOL 4 #define ALEN 150 /* size max (2.2*nnz+17*ncol+7*nrow+6, 23*ncol+7*nrow+6) */ #define B_NNZ 4 #define B_N 5 /* define UF_long */ #include "UFconfig.h" int main (void) { /* ====================================================================== */ /* input matrix A definition */ /* ====================================================================== */ UF_long A [ALEN] = { 0, 1, 4, /* row indices of nonzeros in column 0 */ 2, 4, /* row indices of nonzeros in column 1 */ 0, 1, 2, 3, /* row indices of nonzeros in column 2 */ 1, 3} ; /* row indices of nonzeros in column 3 */ UF_long p [ ] = { 0, /* column 0 is in A [0..2] */ 3, /* column 1 is in A [3..4] */ 5, /* column 2 is in A [5..8] */ 9, /* column 3 is in A [9..10] */ A_NNZ} ; /* number of nonzeros in A */ /* ====================================================================== */ /* input matrix B definition */ /* ====================================================================== */ UF_long B [ ] = { /* Note: only strictly lower triangular part */ /* is included, since symamd ignores the */ /* diagonal and upper triangular part of B. */ 1, /* row indices of nonzeros in column 0 */ 2, 3, /* row indices of nonzeros in column 1 */ /* row indices of nonzeros in column 2 (none) */ 4 /* row indices of nonzeros in column 3 */ } ; /* row indices of nonzeros in column 4 (none) */ UF_long q [ ] = { 0, /* column 0 is in B [0] */ 1, /* column 1 is in B [1..2] */ 3, /* column 2 is empty */ 3, /* column 3 is in B [3] */ 4, /* column 4 is empty */ B_NNZ} ; /* number of nonzeros in strictly lower B */ /* ====================================================================== */ /* other variable definitions */ /* ====================================================================== */ UF_long perm [B_N+1] ; /* note the size is N+1 */ UF_long stats [CCOLAMD_STATS] ; /* for ccolamd and csymamd output stats */ UF_long row, col, pp, length, ok ; /* ====================================================================== */ /* dump the input matrix A */ /* ====================================================================== */ printf ("ccolamd %d-by-%d input matrix:\n", A_NROW, A_NCOL) ; for (col = 0 ; col < A_NCOL ; col++) { length = p [col+1] - p [col] ; printf ("Column %ld, with %ld entries:\n", col, length) ; for (pp = p [col] ; pp < p [col+1] ; pp++) { row = A [pp] ; printf (" row %ld\n", row) ; } } /* ====================================================================== */ /* order the matrix. Note that this destroys A and overwrites p */ /* ====================================================================== */ ok = ccolamd_l (A_NROW, A_NCOL, ALEN, A, p, (double *) NULL, stats, NULL) ; ccolamd_l_report (stats) ; if (!ok) { printf ("ccolamd error!\n") ; exit (1) ; } /* ====================================================================== */ /* print the column ordering */ /* ====================================================================== */ printf ("ccolamd_l column ordering:\n") ; printf ("1st column: %ld\n", p [0]) ; printf ("2nd column: %ld\n", p [1]) ; printf ("3rd column: %ld\n", p [2]) ; printf ("4th column: %ld\n", p [3]) ; /* ====================================================================== */ /* dump the strictly lower triangular part of symmetric input matrix B */ /* ====================================================================== */ printf ("\n\ncsymamd_l %d-by-%d input matrix:\n", B_N, B_N) ; printf ("Entries in strictly lower triangular part:\n") ; for (col = 0 ; col < B_N ; col++) { length = q [col+1] - q [col] ; printf ("Column %ld, with %ld entries:\n", col, length) ; for (pp = q [col] ; pp < q [col+1] ; pp++) { row = B [pp] ; printf (" row %ld\n", row) ; } } /* ====================================================================== */ /* order the matrix B. Note that this does not modify B or q. */ /* ====================================================================== */ ok = csymamd_l (B_N, B, q, perm, (double *) NULL, stats, &calloc, &free, NULL, -1) ; csymamd_l_report (stats) ; if (!ok) { printf ("csymamd error!\n") ; exit (1) ; } /* ====================================================================== */ /* print the symmetric ordering */ /* ====================================================================== */ printf ("csymamd_l column ordering:\n") ; printf ("1st row/column: %ld\n", perm [0]) ; printf ("2nd row/column: %ld\n", perm [1]) ; printf ("3rd row/column: %ld\n", perm [2]) ; printf ("4th row/column: %ld\n", perm [3]) ; printf ("5th row/column: %ld\n", perm [4]) ; return (0) ; } SuiteSparse/CCOLAMD/Makefile0000644001170100242450000000223210617106475014457 0ustar davisfac#------------------------------------------------------------------------------ # CCOLAMD Makefile #------------------------------------------------------------------------------ default: demo include ../UFconfig/UFconfig.mk # Compile all C code, including the C-callable routine and the mexFunctions. # Do not the MATLAB interface. demo: ( cd Lib ; $(MAKE) ) ( cd Demo ; $(MAKE) ) # Compile all C code, including the C-callable routine and the mexFunctions. all: ( cd Lib ; $(MAKE) ) ( cd Demo ; $(MAKE) ) ( cd MATLAB ; $(MAKE) ) # compile just the C-callable libraries (not mexFunctions or Demos) library: ( cd Lib ; $(MAKE) ) # remove object files, but keep the compiled programs and library archives clean: ( cd Lib ; $(MAKE) clean ) ( cd Demo ; $(MAKE) clean ) ( cd MATLAB ; $(MAKE) clean ) # clean, and then remove compiled programs and library archives purge: ( cd Lib ; $(MAKE) purge ) ( cd Demo ; $(MAKE) purge ) ( cd MATLAB ; $(MAKE) purge ) distclean: purge # get ready for distribution dist: purge ( cd Demo ; $(MAKE) dist ) ccode: library lib: library # compile the MATLAB mexFunction mex: ( cd MATLAB ; $(MAKE) ) SuiteSparse/CCOLAMD/MATLAB/0000755001170100242450000000000010711653400013746 5ustar davisfacSuiteSparse/CCOLAMD/MATLAB/ccolamd_demo.m0000644001170100242450000001545510620370041016540 0ustar davisfac%CCOLAMD_DEMO demo for ccolamd and csymamd % minimum degree ordering algorithm. % % Example: % ccolamd_demo % % See also ccolamd % Copyright 1998-2007, Timothy A. Davis, Stefan Larimore, and Siva Rajamanickam % Developed in collaboration with J. Gilbert and E. Ng. %------------------------------------------------------------------------------- % Print the introduction, the help info, and compile the mexFunctions %------------------------------------------------------------------------------- fprintf (1, '\n-----------------------------------------------------------\n') ; fprintf (1, 'ccolamd/csymamd demo.') ; fprintf (1, '\n-----------------------------------------------------------\n') ; help ccolamd_demo ; fprintf (1, '\n-----------------------------------------------------------\n') ; fprintf (1, 'ccolamd help information:') ; fprintf (1, '\n-----------------------------------------------------------\n') ; help ccolamd ; fprintf (1, '\n-----------------------------------------------------------\n') ; fprintf (1, 'csymamd help information:') ; fprintf (1, '\n-----------------------------------------------------------\n') ; help csymamd ; %------------------------------------------------------------------------------- % Solving Ax=b %------------------------------------------------------------------------------- n = 100 ; fprintf (1, '\n-----------------------------------------------------------\n') ; fprintf (1, 'Solving Ax=b for a small %d-by-%d random matrix:', n, n) ; fprintf (1, '\n-----------------------------------------------------------\n') ; fprintf (1, '\nNote: Random sparse matrices are AWFUL test cases.\n') ; fprintf (1, 'They''re just easy to generate in a demo.\n') ; % set up the system rand ('state', 0) ; randn ('state', 0) ; spparms ('default') ; A = sprandn (n, n, 2/n) + speye (n) ; b = (1:n)' ; figure (1) clf ; subplot (2,2,1) spy (A) title ('original matrix') fprintf (1, '\n\nSolving via lu (PAQ = LU), where Q is from ccolamd:\n') ; q = ccolamd (A, 1) ; I = speye (n) ; Q = I (:, q) ; [L,U,P] = lu (A*Q) ; fl = luflops (L, U) ; x = Q * (U \ (L \ (P * b))) ; fprintf (1, '\nFlop count for [L,U,P] = lu (A*Q): %d\n', fl) ; fprintf (1, 'residual: %e\n', norm (A*x-b)); subplot (2,2,2) ; spy (L|U) ; title ('LU with ccolamd') ; try fprintf (1, '\n\nSolving via lu (PAQ = LU), where Q is from colamd:\n') ; q = colamd (A) ; I = speye (n) ; Q = I (:, q) ; [L,U,P] = lu (A*Q) ; fl = luflops (L, U) ; x = Q * (U \ (L \ (P * b))) ; fprintf (1, '\nFlop count for [L,U,P] = lu (A*Q): %d\n', fl) ; fprintf (1, 'residual: %e\n', norm (A*x-b)); subplot (2,2,3) ; spy (L|U) ; title ('LU with colamd') ; catch fprintf (1, 'You have a very old version of MATLAB (no colamd) \n') ; end fprintf (1, '\n\nSolving via lu (PA = LU), without regard for sparsity:\n') ; [L,U,P] = lu (A) ; fl = luflops (L, U) ; x = U \ (L \ (P * b)) ; fprintf (1, '\nFlop count for [L,U,P] = lu (A*Q): %d\n', fl) ; fprintf (1, 'residual: %e\n', norm (A*x-b)); subplot (2,2,4) ; spy (L|U) ; title ('LU with no ordering') ; %------------------------------------------------------------------------------- % Large demo for ccolamd %------------------------------------------------------------------------------- % Since the analysis will be done on the Cholesky factorization of A'A, % set the knob to tell ccolamd to order for Cholesky, not LU. fprintf (1, '\n-----------------------------------------------------------\n') ; fprintf (1, 'Large demo for ccolamd (symbolic analysis only):') ; fprintf (1, '\n-----------------------------------------------------------\n') ; rand ('state', 0) ; randn ('state', 0) ; spparms ('default') ; n = 1000 ; fprintf (1, 'Generating a random %d-by-%d sparse matrix.\n', n, n) ; A = sprandn (n, n, 2/n) + speye (n) ; figure (2) clf ; subplot (2,2,1) spy (A) title ('original matrix') fprintf (1, '\n\nUnordered matrix:\n') ; [lnz,h,parent,post,R] = symbfact (A, 'col') ; fprintf (1, 'nz in Cholesky factors of A''A: %d\n', sum (lnz)) ; fprintf (1, 'flop count for Cholesky of A''A: %d\n', sum (lnz.^2)) ; subplot (2,2,4) ; spy (R) ; title ('Cholesky with no ordering') ; tic ; p = ccolamd (A) ; t = toc ; [lnz,h,parent,post,R] = symbfact (A (:,p), 'col') ; fprintf (1, '\n\nccolamd run time: %f\n', t) ; fprintf (1, 'ccolamd ordering quality: \n') ; fprintf (1, 'nz in Cholesky factors of A(:,p)''A(:,p): %d\n', sum (lnz)) ; fprintf (1, 'flop count for Cholesky of A(:,p)''A(:,p): %d\n', sum (lnz.^2)) ; subplot (2,2,2) ; spy (R) ; title ('Cholesky with ccolamd') ; try tic ; p = colamd (A) ; t = toc ; [lnz,h,parent,post,R] = symbfact (A (:,p), 'col') ; fprintf (1, '\n\ncolamd run time: %f\n', t) ; fprintf (1, 'colamd ordering quality: \n') ; fprintf (1, 'nz in Cholesky factors of A(:,p)''A(:,p): %d\n', sum (lnz)) ; fprintf (1, 'flop count for Cholesky of A(:,p)''A(:,p): %d\n', sum (lnz.^2)) ; subplot (2,2,3) ; spy (R) ; title ('Cholesky with colamd') ; catch fprintf (1, 'You have a very old version of MATLAB (no colamd) \n') ; end %------------------------------------------------------------------------------- % Large demo for csymamd %------------------------------------------------------------------------------- fprintf (1, '\n-----------------------------------------------------------\n') ; fprintf (1, 'Large demo for csymamd (symbolic analysis only):') ; fprintf (1, '\n-----------------------------------------------------------\n') ; fprintf (1, 'Generating a random symmetric %d-by-%d sparse matrix.\n', n, n) ; A = A+A' ; figure (3) clf ; subplot (2,2,1) spy (A) title ('original matrix') fprintf (1, '\n\nUnordered matrix:\n') ; [lnz,h,parent,post,R] = symbfact (A, 'sym') ; fprintf (1, 'nz in Cholesky factors of A: %d\n', sum (lnz)) ; fprintf (1, 'flop count for Cholesky of A: %d\n', sum (lnz.^2)) ; subplot (2,2,4) ; spy (R) ; title ('Cholesky with no ordering') ; tic ; p = csymamd (A) ; t = toc ; [lnz,h,parent,post,R] = symbfact (A (p,p), 'sym') ; fprintf (1, '\n\ncsymamd run time: %f\n', t) ; fprintf (1, 'csymamd ordering quality: \n') ; fprintf (1, 'nz in Cholesky factors of A(p,p): %d\n', sum (lnz)) ; fprintf (1, 'flop count for Cholesky of A(p,p): %d\n', sum (lnz.^2)) ; subplot (2,2,2) ; spy (R) ; title ('Cholesky with csymamd') ; try tic ; p = symamd (A) ; t = toc ; lnz = symbfact (A (p,p), 'sym') ; fprintf (1, '\n\nsymamd run time: %f\n', t) ; fprintf (1, 'symamd ordering quality: \n') ; fprintf (1, 'nz in Cholesky factors of A(p,p): %d\n', sum (lnz)) ; fprintf (1, 'flop count for Cholesky of A(p,p): %d\n', sum (lnz.^2)) ; subplot (2,2,3) ; spy (R) ; title ('Cholesky with symamd') ; catch fprintf (1, 'You have a very old version of MATLAB (no symamd) \n') ; end drawnow SuiteSparse/CCOLAMD/MATLAB/Makefile0000644001170100242450000000134610617240104015410 0ustar davisfac# CCOLAMD Makefile for MATLAB mexFunctions default: ccolamd2 csymamd2 include ../../UFconfig/UFconfig.mk I = -I../../UFconfig -I../Include INC = ../Include/ccolamd.h ../../UFconfig/UFconfig.h SRC = ../Source/ccolamd.c ../Source/ccolamd_global.c MX = $(MEX) -DDLONG $(I) # Compiles the MATLAB-callable routines mex: ccolamd2 csymamd2 csymamd2: csymamdmex.c $(INC) $(SRC) $(MX) -output csymamd csymamdmex.c $(SRC) ccolamd2: ccolamdmex.c $(INC) $(SRC) $(MX) -output ccolamd ccolamdmex.c $(SRC) # Compiles the extensive test code test: mex ccolamdtestmex.c csymamdtestmex.c $(INC) $(SRC) $(MX) ccolamdtestmex.c $(SRC) $(MX) csymamdtestmex.c $(SRC) clean: - $(RM) $(CLEAN) purge: distclean distclean: clean - $(RM) *.mex* *.dll SuiteSparse/CCOLAMD/MATLAB/ccolamd_make.m0000644001170100242450000000144710620370175016535 0ustar davisfacfunction ccolamd_make %CCOLAMD_MAKE compiles CCOLAMD and CSYMAMD for MATLAB % % Example: % ccolamd_make % % See also ccolamd, csymamd % Copyright 1998-2007, Timothy A. Davis, Stefan Larimore, and Siva Rajamanickam % Developed in collaboration with J. Gilbert and E. Ng. details = 0 ; % 1 if details of each command are to be printed d = '' ; if (~isempty (strfind (computer, '64'))) d = '-largeArrayDims' ; end src = '../Source/ccolamd.c ../Source/ccolamd_global.c' ; cmd = sprintf ('mex -DDLONG -O %s -I../../UFconfig -I../Include -output ', d) ; s = [cmd 'ccolamd ccolamdmex.c ' src] ; if (details) fprintf ('%s\n', s) ; end eval (s) ; s = [cmd 'csymamd csymamdmex.c ' src] ; if (details) fprintf ('%s\n', s) ; end eval (s) ; fprintf ('CCOLAMD and CSYMAMD successfully compiled.\n') ; SuiteSparse/CCOLAMD/MATLAB/ccolamdtestmex.c0000644001170100242450000003350710616375256017154 0ustar davisfac/* ========================================================================== */ /* === ccolamdtest mexFunction ============================================== */ /* ========================================================================== */ /* ---------------------------------------------------------------------------- * CCOLAMD Copyright (C), Univ. of Florida. Authors: Timothy A. Davis, * Sivasankaran Rajamanickam, and Stefan Larimore * See License.txt for the Version 2.1 of the GNU Lesser General Public License * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* * This MATLAB mexFunction is for testing only. It is not meant for * production use. See ccolamdmex.c and ccolamd.m instead. * * Usage: * * [ P, stats ] = ccolamdtest (A, knobs) ; * * The stats vector is optional. knobs is required: * * knobs (1) order for LU if nonzero, Cholesky otherwise. default 0 * knobs (2) spumoni, default 0. * knobs (3) dense row control. default 10 * knobs (4) dense column control. default 10 * knobs (5) aggresive absorption if nonzero. default: 1 * * knobs (6) for testing only. Controls the workspace used. * knobs (7) for testing only. Controls how the input matrix is * jumbled prior to calling colamd, to test its error * handling capability. * * see ccolamd.c for a description of the stats array. * */ /* ========================================================================== */ /* === Include files ======================================================== */ /* ========================================================================== */ #include "ccolamd.h" #include "mex.h" #include "matrix.h" #include #include #include "UFconfig.h" /* Here only for testing */ #undef MIN #undef MAX #define MIN(a,b) (((a) < (b)) ? (a) : (b)) #define MAX(a,b) (((a) > (b)) ? (a) : (b)) #define CCOLAMD_MIN_MEMORY(nnz,n_row,n_col) \ (MAX (2 * nnz, 4 * n_col) + \ 8*n_col + 6*n_row + n_col + (nnz / 5) \ + ((3 * n_col) + 1) + 5 * (n_col + 1) + n_row) /* ========================================================================== */ /* === dump_matrix ========================================================== */ /* ========================================================================== */ static void dump_matrix ( UF_long A [ ], UF_long p [ ], UF_long n_row, UF_long n_col, UF_long Alen, UF_long limit ) { UF_long col, k, row ; mexPrintf ("dump matrix: nrow %d ncol %d Alen %d\n", n_row, n_col, Alen) ; for (col = 0 ; col < MIN (n_col, limit) ; col++) { mexPrintf ("column %d, p[col] %d, p [col+1] %d, length %d\n", col, p [col], p [col+1], p [col+1] - p [col]) ; for (k = p [col] ; k < p [col+1] ; k++) { row = A [k] ; mexPrintf (" %d", row) ; } mexPrintf ("\n") ; } } /* ========================================================================== */ /* === ccolamd mexFunction ================================================== */ /* ========================================================================== */ void mexFunction ( /* === Parameters ======================================================= */ int nargout, /* number of left-hand sides */ mxArray *pargout [ ], /* left-hand side matrices */ int nargin, /* number of right--hand sides */ const mxArray *pargin [ ] /* right-hand side matrices */ ) { /* === Local variables ================================================== */ UF_long *A ; /* ccolamd's copy of the matrix and workspace */ UF_long *p ; /* ccolamd's copy of the column pointers */ UF_long Alen ; /* size of A */ UF_long n_col ; /* number of columns of A */ UF_long n_row ; /* number of rows of A */ UF_long nnz ; /* number of entries in A */ UF_long full ; /* TRUE if input matrix full, FALSE if sparse */ double knobs [CCOLAMD_KNOBS] ; /* ccolamd user-controllable parameters */ double *out_perm ; /* output permutation vector */ double *out_stats ; /* output stats vector */ double *in_knobs ; /* input knobs vector */ UF_long i ; /* loop counter */ mxArray *Ainput ; /* input matrix handle */ UF_long spumoni ; /* verbosity variable */ UF_long stats2 [CCOLAMD_STATS] ; /* stats for ccolamd */ UF_long *cp, *cp_end, result, col, length, ok ; UF_long *stats ; stats = stats2 ; /* === Check inputs ===================================================== */ if (nargin != 3 || nargout < 0 || nargout > 2) { mexErrMsgTxt ( "ccolamdtest: incorrect number of input and/or output arguments") ; } /* for testing we require all 7 knobs */ if (mxGetNumberOfElements (pargin [1]) != 7) { mexErrMsgTxt ("ccolamdtest: must have all 7 knobs for testing") ; } /* === Get knobs ======================================================== */ ccolamd_l_set_defaults (knobs) ; spumoni = 0 ; in_knobs = mxGetPr (pargin [1]) ; knobs [CCOLAMD_LU] = (in_knobs [0] != 0) ; knobs [CCOLAMD_DENSE_ROW] = in_knobs [1] ; knobs [CCOLAMD_DENSE_COL] = in_knobs [2] ; knobs [CCOLAMD_AGGRESSIVE] = (in_knobs [3] != 0) ; spumoni = (in_knobs [4] != 0) ; /* print knob settings if spumoni is set */ if (spumoni) { mexPrintf ("\nccolamd version %d.%d, %s:\nknobs(1): %g, order for %s\n", CCOLAMD_MAIN_VERSION, CCOLAMD_SUB_VERSION, CCOLAMD_DATE, in_knobs [0], (knobs [CCOLAMD_LU] != 0) ? "lu(A)" : "chol(A'*A)") ; if (knobs [CCOLAMD_DENSE_ROW] >= 0) { mexPrintf ("knobs(2): %g, rows with > max(16,%g*sqrt(size(A,2)))" " entries removed\n", in_knobs [1], knobs [CCOLAMD_DENSE_ROW]) ; } else { mexPrintf ("knobs(2): %g, no dense rows removed\n", in_knobs [1]) ; } if (knobs [CCOLAMD_DENSE_COL] >= 0) { mexPrintf ("knobs(3): %g, cols with > max(16,%g*sqrt(min(size(A)))" " entries removed\n", in_knobs [2], knobs [CCOLAMD_DENSE_COL]) ; } else { mexPrintf ("knobs(3): no dense columns removed\n", in_knobs [2]) ; } mexPrintf ("knobs(4): %g, aggressive absorption: %s\n", in_knobs [3], (knobs [CCOLAMD_AGGRESSIVE] != 0) ? "yes" : "no") ; mexPrintf ("knobs(5): %g, statistics and knobs printed\n", in_knobs [4]) ; mexPrintf ("Testing: %g %g\n", in_knobs [5], in_knobs[6]) ; } /* === If A is full, convert to a sparse matrix ========================= */ Ainput = (mxArray *) pargin [0] ; if (mxGetNumberOfDimensions (Ainput) != 2) { mexErrMsgTxt ("ccolamd: input matrix must be 2-dimensional") ; } full = !mxIsSparse (Ainput) ; if (full) { mexCallMATLAB (1, &Ainput, 1, (mxArray **) pargin, "sparse") ; } /* === Allocate workspace for ccolamd =================================== */ /* get size of matrix */ n_row = mxGetM (Ainput) ; n_col = mxGetN (Ainput) ; /* get column pointer vector so we can find nnz */ p = (UF_long *) mxCalloc (n_col+1, sizeof (UF_long)) ; (void) memcpy (p, mxGetJc (Ainput), (n_col+1)*sizeof (UF_long)) ; nnz = p [n_col] ; Alen = (UF_long) ccolamd_l_recommended (nnz, n_row, n_col) ; if (Alen == 0) { mexErrMsgTxt ("ccolamd: problem too large") ; } /* === Modify size of Alen if testing =================================== */ /* knobs [5] amount of workspace given to colamd. < 0 : TIGHT memory > 0 : MIN + knob [3] - 1 == 0 : RECOMMENDED memory */ /* get knob [5], if negative */ if (in_knobs [5] < 0) { Alen = CCOLAMD_MIN_MEMORY (nnz, n_row, n_col) + n_col ; } else if (in_knobs [5] > 0) { Alen = CCOLAMD_MIN_MEMORY (nnz, n_row, n_col) + in_knobs [5] - 1 ; } /* otherwise, we use the recommended amount set above */ /* === Copy input matrix into workspace ================================= */ A = (UF_long *) mxCalloc (Alen, sizeof (UF_long)) ; (void) memcpy (A, mxGetIr (Ainput), nnz*sizeof (UF_long)) ; if (full) { mxDestroyArray (Ainput) ; } /* === Jumble matrix ==================================================== */ /* knobs [6] FOR TESTING ONLY: Specifies how to jumble matrix 0 : No jumbling 1 : Make n_row less than zero 2 : Make first pointer non-zero 3 : Make column pointers not non-decreasing 4 : Make a column pointer greater or equal to Alen 5 : Make row indices not strictly increasing 6 : Make a row index greater or equal to n_row 7 : Set A = NULL 8 : Set p = NULL 9 : Repeat row index 10: make row indices not sorted 11: jumble columns massively (note this changes the pattern of the matrix A.) 12: Set stats = NULL 13: Make n_col less than zero */ /* jumble appropriately */ switch ((UF_long) in_knobs [6]) { case 0 : if (spumoni) { mexPrintf ("ccolamdtest: no errors expected\n") ; } result = 1 ; /* no errors */ break ; case 1 : if (spumoni) { mexPrintf ("ccolamdtest: nrow out of range\n") ; } result = 0 ; /* nrow out of range */ n_row = -1 ; break ; case 2 : if (spumoni) { mexPrintf ("ccolamdtest: p [0] nonzero\n") ; } result = 0 ; /* p [0] must be zero */ p [0] = 1 ; break ; case 3 : if (spumoni) { mexPrintf ("colamdtest: negative length last column\n") ; } result = (n_col == 0) ; /* p must be monotonically inc. */ p [n_col] = p [0] ; break ; case 4 : if (spumoni) { mexPrintf ("colamdtest: Alen too small\n") ; } result = 0 ; /* out of memory */ p [n_col] = Alen ; break ; case 5 : if (spumoni) { mexPrintf ("colamdtest: row index out of range (-1)\n") ; } if (nnz > 0) /* row index out of range */ { result = 0 ; A [nnz-1] = -1 ; } else { if (spumoni) { mexPrintf ("Note: no row indices to put out of range\n") ; } result = 1 ; } break ; case 6 : if (spumoni) { mexPrintf ("ccolamdtest: row index out of range (n_row)\n") ; } if (nnz > 0) /* row index out of range */ { if (spumoni) { mexPrintf ("Changing A[nnz-1] from %d to %d\n", A [nnz-1], n_row) ; } result = 0 ; A [nnz-1] = n_row ; } else { if (spumoni) { mexPrintf ("Note: no row indices to put out of range\n") ; } result = 1 ; } break ; case 7 : if (spumoni) { mexPrintf ("ccolamdtest: A not present\n") ; } result = 0 ; /* A not present */ A = (UF_long *) NULL ; break ; case 8 : if (spumoni) { mexPrintf ("ccolamdtest: p not present\n") ; } result = 0 ; /* p not present */ p = (UF_long *) NULL ; break ; case 9 : if (spumoni) { mexPrintf ("ccolamdtest: duplicate row index\n") ; } result = 1 ; /* duplicate row index */ for (col = 0 ; col < n_col ; col++) { length = p [col+1] - p [col] ; if (length > 1) { A [p [col]] = A [p [col] + 1] ; if (spumoni) { mexPrintf ("Made duplicate row %d in col %d\n", A [p [col] + 1], col) ; } break ; } } if (spumoni > 1) { dump_matrix (A, p, n_row, n_col, Alen, col+2) ; } break ; case 10 : if (spumoni) { mexPrintf ("ccolamdtest: unsorted column\n") ; } result = 1 ; /* jumbled columns */ for (col = 0 ; col < n_col ; col++) { length = p [col+1] - p [col] ; if (length > 1) { i = A[p [col]] ; A [p [col]] = A[p [col] + 1] ; A [p [col] + 1] = i ; if (spumoni) { mexPrintf ("Unsorted column %d \n", col) ; } break ; } } if (spumoni > 1) { dump_matrix (A, p, n_row, n_col, Alen, col+2) ; } break ; case 11 : if (spumoni) { mexPrintf ("ccolamdtest: massive jumbling\n") ; } result = 1 ; /* massive jumbling, but no errors */ srand (1) ; for (i = 0 ; i < n_col ; i++) { cp = &A [p [i]] ; cp_end = &A [p [i+1]] ; while (cp < cp_end) { *cp++ = rand() % n_row ; } } if (spumoni > 1) { dump_matrix (A, p, n_row, n_col, Alen, n_col) ; } break ; case 12 : if (spumoni) { mexPrintf ("ccolamdtest: stats not present\n") ; } result = 0 ; /* stats not present */ stats = (UF_long *) NULL ; break ; case 13 : if (spumoni) { mexPrintf ("ccolamdtest: ncol out of range\n") ; } result = 0 ; /* ncol out of range */ n_col = -1 ; break ; } /* === Order the columns (destroys A) =================================== */ ok = ccolamd_l (n_row, n_col, Alen, A, p, knobs, stats, NULL) ; if (spumoni) { ccolamd_l_report (stats) ; } /* === Return the stats vector ========================================== */ if (nargout == 2) { pargout [1] = mxCreateDoubleMatrix (1, CCOLAMD_STATS, mxREAL) ; out_stats = mxGetPr (pargout [1]) ; for (i = 0 ; i < CCOLAMD_STATS ; i++) { out_stats [i] = (stats == NULL) ? (-1) : (stats [i]) ; } /* fix stats (5) and (6), for 1-based information on jumbled matrix. */ /* note that this correction doesn't occur if csymamd returns FALSE */ out_stats [CCOLAMD_INFO1] ++ ; out_stats [CCOLAMD_INFO2] ++ ; } mxFree (A) ; if (ok) { /* === Return the permutation vector ================================ */ pargout [0] = mxCreateDoubleMatrix (1, n_col, mxREAL) ; out_perm = mxGetPr (pargout [0]) ; for (i = 0 ; i < n_col ; i++) { /* ccolamd is 0-based, but MATLAB expects this to be 1-based */ out_perm [i] = p [i] + 1 ; } if (!result) { ccolamd_l_report (stats) ; mexErrMsgTxt ("ccolamd should have returned TRUE\n") ; } } else { /* return p = -1 if ccolamd failed */ pargout [0] = mxCreateDoubleMatrix (1, 1, mxREAL) ; out_perm = mxGetPr (pargout [0]) ; out_perm [0] = -1 ; if (result) { ccolamd_l_report (stats) ; mexErrMsgTxt ("ccolamd should have returned FALSE\n") ; } } mxFree (p) ; } SuiteSparse/CCOLAMD/MATLAB/ccolamdtestmex.m0000644001170100242450000000055410620370214017142 0ustar davisfacfunction [P, stats] = ccolamdtestmex (A, knobs) %#ok % CCOLAMDTESTMEX test function for ccolamd % Example: % [ P, stats ] = ccolamdtest (A, knobs) ; % See also ccolamd % Copyright 1998-2007, Timothy A. Davis, Stefan Larimore, and Siva Rajamanickam % Developed in collaboration with J. Gilbert and E. Ng. error ('ccolamdtestmex mexFunction not found') ; SuiteSparse/CCOLAMD/MATLAB/ccolamd_test.m0000644001170100242450000002703310707726444016610 0ustar davisfacfunction ccolamd_test %CCOLAMD_TEST extensive test of ccolamd and csymamd % % Example: % ccolamd_test % % See also csymamd, ccolamd, ccolamd_make. % Copyright 1998-2007, Timothy A. Davis, Stefan Larimore, and Siva Rajamanickam % Developed in collaboration with J. Gilbert and E. Ng. help ccolamd_test global ccolamd_default_knobs csymamd_default_knobs ccolamd_default_knobs = [0 10 10 1 0] ; csymamd_default_knobs = [10 1 0] ; fprintf ('Compiling ccolamd, csymamd, and test mexFunctions.\n') ; ccolamd_make ; d = '' ; if (~isempty (strfind (computer, '64'))) d = '-largeArrayDims' ; end src = '../Source/ccolamd.c ../Source/ccolamd_global.c' ; cmd = sprintf ('mex -DDLONG -O %s -I../../UFconfig -I../Include ', d) ; eval ([cmd 'ccolamdtestmex.c ' src]) ; eval ([cmd 'csymamdtestmex.c ' src]) ; fprintf ('Done compiling.\n') ; fprintf ('\nThe following codes will be tested:\n') ; which ccolamd which csymamd which ccolamdtestmex which csymamdtestmex fprintf ('\nStarting the tests. Please be patient.\n') ; h = waitbar (0, 'COLAMD test') ; rand ('state', 0) ; randn ('state', 0) ; A = sprandn (500,500,0.4) ; p = ccolamd (A, [0 10 10 1 1]) ; check_perm (p, A) ; p = ccolamd (A, [1 2 7 1 1]) ; check_perm (p, A) ; p = ccolamd (A, [1 2 10 0 1]) ; check_perm (p, A) ; p = ccolamd (A, [9 2 3 1 1]) ; check_perm (p, A) ; p = csymamd (A, [10 1 1]) ; check_perm (p, A) ; p = csymamd (A, [4 1 1]) ; check_perm (p, A) ; p = csymamd (A, [9 0 1]) ; check_perm (p, A) ; fprintf ('Null matrices') ; A = zeros (0,0) ; A = sparse (A) ; p = ccolamd (A) ; check_perm (p, A) ; p = csymamd (A) ; check_perm (p, A) ; A = zeros (0, 100) ; A = sparse (A) ; p = ccolamd (A) ; check_perm (p, A) ; A = zeros (100, 0) ; A = sparse (A) ; p = ccolamd (A) ; check_perm (p, A) ; fprintf (' OK\n') ; fprintf ('Matrices with a few dense row/cols\n') ; for trial = 1:20 waitbar (trial/20, h, 'CCOLAMD: dense rows/cols') ; % random square unsymmetric matrix A = rand_matrix (1000, 1000, 1, 10, 20) ; [m n] = size (A) ; cmember = irand (min (trial,n), n) ; for tol = [0:.1:2 3:20 1e6] B = A + A' ; p = ccolamd (A, [ ]) ; check_perm (p, A) ; p = ccolamd (A, [1 tol tol 1]) ; check_perm (p, A) ; p = ccolamd (A, [0 tol tol 1]) ; check_perm (p, A) ; p = ccolamd (A, [1 tol tol 0]) ; check_perm (p, A) ; p = ccolamd (A, [0 tol tol 1]) ; check_perm (p, A) ; p = csymamd (A, [tol 1]) ; check_perm (p, A) ; p = csymamd (A, tol) ; check_perm (p, A) ; p = csymamd (A, [ ]) ; check_perm (p, A) ; p = csymamd (B, [tol 0]) ; check_perm (p, A) ; p = ccolamd (A, [0 tol -1 1]) ; check_perm (p, A) ; p = ccolamd (A, [0 -1 tol 1]) ; check_perm (p, A) ; % check with non-null cmember p = ccolamd (A, [ ], cmember) ; check_perm (p, A) ; p = ccolamd (A, [1 tol tol 1], cmember) ; check_perm (p, A) ; p = ccolamd (A, [0 tol tol 1], cmember) ; check_perm (p, A) ; p = ccolamd (A, [1 tol tol 0], cmember) ; check_perm (p, A) ; p = ccolamd (A, [0 tol tol 1], cmember) ; check_perm (p, A) ; p = csymamd (A, [tol 1], cmember) ; check_perm (p, A) ; p = csymamd (A, tol, cmember) ; check_perm (p, A) ; p = csymamd (A, [ ], cmember) ; check_perm (p, A) ; p = csymamd (B, [tol 0], cmember) ; check_perm (p, A) ; p = ccolamd (A, [0 tol -1 1], cmember) ; check_perm (p, A) ; p = ccolamd (A, [0 -1 tol 1], cmember) ; check_perm (p, A) ; p = ccolamd (A, [ ], [ ]) ; check_perm (p, A) ; p = ccolamd (A, [1 tol tol 1], [ ]) ; check_perm (p, A) ; p = ccolamd (A, [0 tol tol 1], [ ]) ; check_perm (p, A) ; p = ccolamd (A, [1 tol tol 0], [ ]) ; check_perm (p, A) ; p = ccolamd (A, [0 tol tol 1], [ ]) ; check_perm (p, A) ; p = csymamd (A, [tol 1], [ ]) ; check_perm (p, A) ; p = csymamd (A, tol, [ ]) ; check_perm (p, A) ; p = csymamd (A, [ ], [ ]) ; check_perm (p, A) ; p = csymamd (B, [tol 0], [ ]) ; check_perm (p, A) ; p = ccolamd (A, [0 tol -1 1], [ ]) ; check_perm (p, A) ; p = ccolamd (A, [0 -1 tol 1], [ ]) ; check_perm (p, A) ; end end fprintf (' OK\n') ; fprintf ('General matrices\n') ; for trial = 1:400 waitbar (trial/400, h, 'CCOLAMD: with dense rows/cols') ; % matrix of random mtype mtype = irand (3) ; A = rand_matrix (2000, 2000, mtype, 0, 0) ; p = ccolamd (A) ; check_perm (p, A) ; if (mtype == 3) p = csymamd (A) ; check_perm (p, A) ; end end fprintf (' OK\n') ; fprintf ('Test error handling with invalid inputs\n') ; % Check different erroneous input. for trial = 1:30 waitbar (trial/30, h, 'CCOLAMD: error handling') ; A = rand_matrix (1000, 1000, 2, 0, 0) ; for err = 1:13 p = Tcolamd (A, [ccolamd_default_knobs 1 err], [ ]) ; if (p(1) ~= -1) %#ok check_perm (p, A) ; end if (err == 1) % check different (valid) input args to ccolamd p = Acolamd (A) ; p2 = Acolamd (A, [ccolamd_default_knobs 0 0]) ; if (any (p ~= p2)) error ('ccolamd: mismatch 1!') ; end end B = A'*A ; p = Tsymamd (B, [-1 1 0 err], [ ]) ; if (p(1) ~= -1) %#ok check_perm (p, A) ; end if (err == 1) % check different (valid) input args to csymamd p = Asymamd (B) ; check_perm (p, A) ; p2 = Asymamd (B, [csymamd_default_knobs 0]) ; if (any (p ~= p2)) error ('symamd: mismatch 1!') ; end end end end fprintf (' OK\n') ; fprintf ('Matrices with a few empty columns\n') ; for trial = 1:400 waitbar (trial/400, h, 'CCOLAMD: with empty rows/cols') ; % some are square, some are rectangular n = 0 ; while (n < 5) A = rand_matrix (1000, 1000, irand (2), 0, 0) ; [m n] = size (A) ; end % Add 5 null columns at random locations. null_col = randperm (n) ; A (:, null_col) = 0 ; % Order the matrix and make sure that the null columns are ordered last. p = ccolamd (A, [1 1e6 1e6 0]) ; check_perm (p, A) ; % find all null columns in A null_col = find (sum (spones (A), 1) == 0) ; nnull = length (null_col) ; if (any (null_col ~= p ((n-nnull+1):n))) error ('ccolamd: Null cols are not ordered last in natural order') ; end end fprintf (' OK\n') ; fprintf ('Matrices with a few empty rows and columns\n') ; for trial = 1:400 waitbar (trial/400, h, 'CCOLAMD: with empty rows/cols') ; % symmetric matrices n = 0 ; while (n < 5) A = rand_matrix (1000, 1000, 3, 0, 0) ; [m n] = size (A) ; end % Add 5 null columns and rows at random locations. null_col = randperm (n) ; A (:, null_col) = 0 ; A (null_col, :) = 0 ; % Order the matrix and make sure that the null rows/cols are ordered last. p = csymamd (A, -1) ; check_perm (p, A) ; % find all null rows/columns in A Alo = tril (A, -1) ; null_col = ... find ((sum (spones (Alo), 1) == 0) & (sum (spones (Alo), 2) == 0)') ; nnull = length (null_col) ; if (any (null_col ~= p ((n-nnull+1):n))) error ('csymamd: Null cols are not ordered last in natural order') ; end end fprintf (' OK\n') ; fprintf ('Matrices with a few empty rows\n') ; % Test matrices with null rows inserted. for trial = 1:400 waitbar (trial/400, h, 'CCOLAMD: with null rows') ; m = 0 ; while (m < 5) A = rand_matrix (1000, 1000, 2, 0, 0) ; m = size (A,1) ; end % Add 5 null rows at random locations. null_row = randperm (m) ; null_row = sort (null_row (1:5)) ; A (null_row, :) = 0 ; p = ccolamd (A) ; check_perm (p, A) ; end fprintf (' OK\n') ; fprintf ('\nccolamd and csymamd: all tests passed\n\n') ; close (h) ; %------------------------------------------------------------------------------- function p = Acolamd (S, knobs) % Acolamd: compare ccolamd and Tcolamd results global ccolamd_default_knobs if (nargin < 2) p = ccolamd (S) ; p1 = Tcolamd (S, [ccolamd_default_knobs 0 0], [ ]) ; else p = ccolamd (S, knobs) ; p1 = Tcolamd (S, knobs, [ ]) ; end check_perm (p, S) ; check_perm (p1, S) ; if (any (p1 ~= p)) narg = nargin ; if (nargin == 2) save bad S narg knobs else save bad S narg end error ('Acolamd mismatch!') ; end %------------------------------------------------------------------------------- function p = Asymamd (S, knobs) % Asymamd: compare csymamd and Tsymamd results global csymamd_default_knobs if (nargin < 2) p = csymamd (S) ; p1 = Tsymamd (S, [csymamd_default_knobs 0], [ ]) ; else p = csymamd (S, knobs) ; p1 = Tsymamd (S, knobs, [ ]) ; end if (any (p1 ~= p)) error ('Asymamd mismatch!') ; end %------------------------------------------------------------------------------- function check_perm (p, A, cmember) % check_perm: check for a valid permutation vector if (isempty (A) & isempty (p)) %#ok % empty permutation vectors of empty matrices are OK return end if (isempty (p)) error ('Bad permutation: cannot be empty') ; end [m n] = size (A) ; [p_m p_n] = size (p) ; if (p_n == 1) % force p to be a row vector p = p' ; [p_m p_n] = size (p) ; end if (n ~= p_n) error ('Bad permutation: wrong size') ; end if (p_m ~= 1) ; % p must be a vector error ('Bad permutation: not a vector') ; else if (any (sort (p) - (1:p_n))) error ('Bad permutation') ; end end if (nargin > 2) % check cmember c = cmember (p) ; % c must be monotonically non-decreasing c = diff (c) ; if (any (c < 0)) error ('permutation breaks the cmember constraints') ; end end %------------------------------------------------------------------------------- function i = irand (n,s) % irand: return a random vector of size s, with values between 1 and n if (nargin == 1) s = 1 ; end i = min (n, 1 + floor (rand (1,s) * n)) ; %------------------------------------------------------------------------------- function A = rand_matrix (n_max, m_max, mtype, d_rows, d_cols) % rand_matrix: return a random sparse matrix % % A = rand_matrix (n_max, m_max, mtype, d_rows, d_cols) % % A binary matrix of random size, at most n_max-by-m_max, with d_rows dense rows % and d_cols dense columns. % % mtype 1: square unsymmetric (m_max is ignored) % mtype 2: rectangular % mtype 3: symmetric (m_max is ignored) n = irand (n_max) ; if (mtype ~= 2) % square m = n ; else m = irand (m_max) ; end A = sprand (m, n, 10 / max (m,n)) ; if (d_rows > 0) % add dense rows for k = 1:d_rows i = irand (m) ; nz = irand (n) ; p = randperm (n) ; p = p (1:nz) ; A (i,p) = 1 ; end end if (d_cols > 0) % add dense cols for k = 1:d_cols j = irand (n) ; nz = irand (m) ; p = randperm (m) ; p = p (1:nz) ; A (p,j) = 1 ; end end A = spones (A) ; % ensure that there are no empty columns d = find (full (sum (A,1)) == 0) ; %#ok A (m,d) = 1 ; %#ok % ensure that there are no empty rows d = find (full (sum (A,2)) == 0) ; %#ok A (d,n) = 1 ; %#ok if (mtype == 3) % symmetric A = A + A' + speye (n) ; end A = spones (A) ; %------------------------------------------------------------------------------- % Tcolamd: run ccolamd in a testing mode %------------------------------------------------------------------------------- function p = Tcolamd (S, knobs, cmember) % knobs (5) = 1 ; p = ccolamdtestmex (S, knobs, cmember) ; if (p (1) ~= -1) check_perm (p, S) ; end %------------------------------------------------------------------------------- % Tsymamd: run csymamd in a testing mode %------------------------------------------------------------------------------- function p = Tsymamd (S, knobs, cmember) % knobs (2) = 1 ; p = csymamdtestmex (S, knobs, cmember) ; if (p (1) ~= -1) check_perm (p, S) ; end SuiteSparse/CCOLAMD/MATLAB/ccolamd.m0000644001170100242450000000470010620370165015532 0ustar davisfacfunction [p, stats] = ccolamd (S, knobs, cmember) %#ok %CCOLAMD constrained column approximate minimum degree permutation. % p = CCOLAMD(S) returns the column approximate minimum degree permutation % vector for the sparse matrix S. For a non-symmetric matrix S, S(:,p) % tends to have sparser LU factors than S. chol(S(:,p)'*S(:,p)) also tends % to be sparser than chol(S'*S). p=ccolamd(S,1) optimizes the ordering for % lu(S(:,p)). The ordering is followed by a column elimination tree post- % ordering. % % Example: % p = ccolamd (S) % p = ccolamd (S,knobs,cmember) % % knobs is an optional one- to five-element input vector, with a default % value of [0 10 10 1 0] if not present or empty ([ ]). Entries not present % are set to their defaults. % % knobs(1): if nonzero, the ordering is optimized for lu(S(:,p)). It will % be a poor ordering for chol(S(:,p)'*S(:,p)). This is the most % important knob for ccolamd. % knobs(2): if S is m-by-n, rows with more than max(16,knobs(2)*sqrt(n)) % entries are ignored. % knobs(3): columns with more than max(16,knobs(3)*sqrt(min(m,n))) entries % are ignored and ordered last in the output permutation (subject to the % cmember constraints). % knobs(4): if nonzero, aggressive absorption is performed. % knobs(5): if nonzero, statistics and knobs are printed. % % cmember is an optional vector of length n. It defines the constraints on % the column ordering. If cmember(j)=s, then column j is in constraint set % s (s must be in the range 1 to n). In the output permutation p, all % columns in set 1 appear first, followed by all columns in set 2, and so % on. cmember=ones(1,n) if not present or empty. ccolamd(S,[],1:n) returns % 1:n. % % p = ccolamd(S) is about the same as p = colamd(S). knobs and its default % values differ. colamd always does aggressive absorption, and it finds an % ordering suitable for both lu(S(:,p)) and chol(S(:,p)'*S(:,p)); it cannot % optimize its ordering for lu(S(:,p)) to the extent that ccolamd(S,1) can. % % See also AMD, CSYMAMD, COLAMD, SYMAMD, SYMRCM. % Copyright 1998-2007, Timothy A. Davis, Stefan Larimore, and Siva Rajamanickam % Developed in collaboration with J. Gilbert and E. Ng. % Supported by the National Science Foundation (DMS-9504974, DMS-9803599, % CCR-0203270), and a grant from Sandia National Lab. error ('ccolamd: mexFunction not found') ; SuiteSparse/CCOLAMD/MATLAB/Contents.m0000644001170100242450000000156010620370546015731 0ustar davisfac% CCOLAMD, constrained approximate minimum degree ordering % % Primary functions: % csymamd - constrained symmetric approximate minimum degree permutation % ccolamd - constrained column approximate minimum degree permutation. % % helper and test functions: % ccolamd_demo - demo for ccolamd and csymamd % ccolamd_make - compiles CCOLAMD and CSYMAMD for MATLAB % ccolamd_install - compiles and installs ccolamd and csymamd for MATLAB % ccolamd_test - extensive test of ccolamd and csymamd % luflops - compute the flop count for sparse LU factorization % ccolamdtestmex - test function for ccolamd % csymamdtestmex - test function for csymamd % % Example: % p = ccolamd (S, knobs, cmember) % Copyright 1998-2007, Timothy A. Davis, Stefan Larimore, and Siva Rajamanickam % Developed in collaboration with J. Gilbert and E. Ng. SuiteSparse/CCOLAMD/MATLAB/csymamd.m0000644001170100242450000000457310620370251015571 0ustar davisfacfunction [p, stats] = csymamd (S, knobs, cmember) %#ok %CSYMAMD constrained symmetric approximate minimum degree permutation % P = CSYMAMD(S) for a symmetric positive definite matrix S, returns the % permutation vector p such that S(p,p) tends to have a sparser Cholesky % factor than S. Sometimes CSYMAMD works well for symmetric indefinite % matrices too. The matrix S is assumed to be symmetric; only the % strictly lower triangular part is referenced. S must be square. Note % that p=amd(S) is faster, but does not allow for a constrained ordering. % The ordering is followed by an elimination tree post-ordering. % % See also AMD, CCOLAMD, COLAMD, SYMAMD. % % Example: % p = csymamd (S) % p = csymamd (S,knobs,cmember) % % knobs is an optional one- to three-element input vector, with a default % value of [10 1 0] if present or empty ([ ]). Entries not present are set % to their defaults. % % knobs(1): If S is n-by-n, then rows and columns with more than % max(16,knobs(1)*sqrt(n)) entries are ignored, and ordered last in the % output permutation (subject to the cmember constraints). % knobs(2): if nonzero, aggressive absorption is performed. % knobs(3): if nonzero, statistics and knobs are printed. % % cmember is an optional vector of length n. It defines the constraints on % the ordering. If cmember(j)=s, then row/column j is in constraint set s % (s must be in the range 1 to n). In the output permutation p, % rows/columns in set 1 appear first, followed by all rows/columns in set 2, % and so on. cmember=ones(1,n) if not present or empty. csymamd(S,[],1:n) % returns 1:n. % % p = csymamd(S) is about the same as p = symamd(S). knobs and its default % values differ. % % Authors: S. Larimore, T. Davis (Univ of Florida), and S. Rajamanickam, in % collaboration with J. Gilbert and E. Ng. Supported by the National % Science Foundation (DMS-9504974, DMS-9803599, CCR-0203270), and a grant % from Sandia National Lab. See http://www.cise.ufl.edu/research/sparse % for ccolamd, csymamd, amd, colamd, symamd, and other related orderings. % % See also AMD, CCOLAMD, COLAMD, SYMAMD, SYMRCM. % Copyright 1998-2007, Timothy A. Davis, Stefan Larimore, and Siva Rajamanickam % Developed in collaboration with J. Gilbert and E. Ng. error ('csymamd: mexFunction not found') ; SuiteSparse/CCOLAMD/MATLAB/csymamdmex.c0000644001170100242450000001466210617107036016276 0ustar davisfac/* ========================================================================== */ /* === csymamd mexFunction ================================================== */ /* ========================================================================== */ /* ---------------------------------------------------------------------------- * CCOLAMD, Copyright (C), Univ. of Florida. Authors: Timothy A. Davis, * Sivasankaran Rajamanickam, and Stefan Larimore * See License.txt for the Version 2.1 of the GNU Lesser General Public License * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* * Usage: * p = csymamd (A) ; * [p stats] = csymamd (A, knobs, cmember) ; * * See csymamd.m for a description. */ /* ========================================================================== */ /* === Include files ======================================================== */ /* ========================================================================== */ #include "ccolamd.h" #include "mex.h" #include "matrix.h" #include #include "UFconfig.h" /* ========================================================================== */ /* === csymamd mexFunction ================================================== */ /* ========================================================================== */ void mexFunction ( /* === Parameters ======================================================= */ int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { /* === Local variables ================================================== */ UF_long *A ; /* row indices of input matrix A */ UF_long *perm ; /* column ordering of M and ordering of A */ UF_long *cmember ; /* csymamd's copy of the constraint set */ double *in_cmember ; /* input constraint set */ UF_long *p ; /* column pointers of input matrix A */ UF_long cslen ; /* size of constraint set */ UF_long n_col ; /* number of columns of A */ UF_long n_row ; /* number of rows of A */ UF_long full ; /* TRUE if input matrix full, FALSE if sparse */ double knobs [CCOLAMD_KNOBS] ; /* csymamd user-controllable parameters */ double *out_perm ; /* output permutation vector */ double *out_stats ; /* output stats vector */ double *in_knobs ; /* input knobs vector */ UF_long i ; /* loop counter */ mxArray *Ainput ; /* input matrix handle */ UF_long spumoni ; /* verbosity variable */ UF_long stats [CCOLAMD_STATS] ; /* stats for symamd */ /* === Check inputs ===================================================== */ if (nargin < 1 || nargin > 3 || nargout < 0 || nargout > 2) { mexErrMsgTxt ("Usage: [p stats] = csymamd (S, knobs, cmember)") ; } /* === Get cmember ====================================================== */ cmember = NULL ; cslen = 0 ; if (nargin > 2) { in_cmember = mxGetPr (pargin [2]) ; cslen = mxGetNumberOfElements (pargin [2]) ; if (cslen != 0) { cmember = (UF_long *) mxCalloc (cslen, sizeof (UF_long)) ; for (i = 0 ; i < cslen ; i++) { /* convert cmember from 1-based to 0-based */ cmember[i] = ((UF_long) in_cmember [i] - 1) ; } } } /* === Get knobs ======================================================== */ ccolamd_l_set_defaults (knobs) ; spumoni = 0 ; /* check for user-passed knobs */ i = 0 ; if (nargin > 1) { in_knobs = mxGetPr (pargin [1]) ; i = mxGetNumberOfElements (pargin [1]) ; if (i > 0) knobs [CCOLAMD_DENSE_ROW] = in_knobs [0] ; if (i > 1) knobs [CCOLAMD_AGGRESSIVE] = in_knobs [1] ; if (i > 2) spumoni = (in_knobs [2] != 0) ; } /* print knob settings if spumoni is set */ if (spumoni) { mexPrintf ("\ncsymamd version %d.%d, %s:\n", CCOLAMD_MAIN_VERSION, CCOLAMD_SUB_VERSION, CCOLAMD_DATE) ; if (knobs [CCOLAMD_DENSE_ROW] >= 0) { mexPrintf ("knobs(1): %g, rows/cols with > " "max(16,%g*sqrt(size(A,2))) entries removed\n", in_knobs [0], knobs [CCOLAMD_DENSE_ROW]) ; } else { mexPrintf ("knobs(1): %g, no dense rows removed\n", in_knobs [0]) ; } mexPrintf ("knobs(2): %g, aggressive absorption: %s\n", in_knobs [1], (knobs [CCOLAMD_AGGRESSIVE] != 0) ? "yes" : "no") ; mexPrintf ("knobs(3): %g, statistics and knobs printed\n", in_knobs [2]) ; } /* === If A is full, convert to a sparse matrix ========================= */ Ainput = (mxArray *) pargin [0] ; if (mxGetNumberOfDimensions (Ainput) != 2) { mexErrMsgTxt ("csymamd: input matrix must be 2-dimensional.") ; } full = !mxIsSparse (Ainput) ; if (full) { mexCallMATLAB (1, &Ainput, 1, (mxArray **) pargin, "sparse") ; } /* === Allocate workspace for csymamd =================================== */ /* get size of matrix */ n_row = mxGetM (Ainput) ; n_col = mxGetN (Ainput) ; if (n_col != n_row) { mexErrMsgTxt ("csymamd: matrix must be square.") ; } if (cmember != NULL && cslen != n_col) { mexErrMsgTxt ("csymamd: cmember must be of length equal to #cols of A"); } A = (UF_long *) mxGetIr (Ainput) ; p = (UF_long *) mxGetJc (Ainput) ; perm = (UF_long *) mxCalloc (n_col+1, sizeof (UF_long)) ; /* === Order the rows and columns of A (does not destroy A) ============= */ if (!csymamd_l (n_col, A, p, perm, knobs, stats, &mxCalloc, &mxFree, cmember, -1)) { csymamd_l_report (stats) ; mexErrMsgTxt ("csymamd error!") ; } if (full) { mxDestroyArray (Ainput) ; } /* === Return the permutation vector ==================================== */ pargout [0] = mxCreateDoubleMatrix (1, n_col, mxREAL) ; out_perm = mxGetPr (pargout [0]) ; for (i = 0 ; i < n_col ; i++) { /* symamd is 0-based, but MATLAB expects this to be 1-based */ out_perm [i] = perm [i] + 1 ; } mxFree (perm) ; mxFree (cmember) ; /* === Return the stats vector ========================================== */ /* print stats if spumoni is set */ if (spumoni) { csymamd_l_report (stats) ; } if (nargout == 2) { pargout [1] = mxCreateDoubleMatrix (1, CCOLAMD_STATS, mxREAL) ; out_stats = mxGetPr (pargout [1]) ; for (i = 0 ; i < CCOLAMD_STATS ; i++) { out_stats [i] = stats [i] ; } /* fix stats (5) and (6), for 1-based information on jumbled matrix. */ /* note that this correction doesn't occur if symamd returns FALSE */ out_stats [CCOLAMD_INFO1] ++ ; out_stats [CCOLAMD_INFO2] ++ ; } } SuiteSparse/CCOLAMD/MATLAB/luflops.m0000644001170100242450000000272110620370270015612 0ustar davisfacfunction fl = luflops (L, U) %LUFLOPS compute the flop count for sparse LU factorization % % Example: % fl = luflops (L,U) % % Given a sparse LU factorization (L and U), return the flop count required % by a conventional LU factorization algorithm to compute it. L and U can % be either sparse or full matrices. L must be lower triangular and U must % be upper triangular. Do not attempt to use this on the permuted L from % [L,U] = lu (A). Instead, use [L,U,P] = lu (A) or [L,U,P,Q] = lu (A). % % Note that there is a subtle undercount in this estimate. Suppose A is % completely dense, but during LU factorization exact cancellation occurs, % causing some of the entries in L and U to become identically zero. The % flop count returned by this routine is an undercount. There is a simple % way to fix this (L = spones (L) + spones (tril (A))), but the fix is partial. % It can also occur that some entry in L is a "symbolic" fill-in (zero in % A, but a fill-in entry and thus must be computed), but numerically % zero. The only way to get a reliable LU factorization would be to do a % purely symbolic factorization of A. This cannot be done with % symbfact (A, 'col'). % % See NA Digest, Vol 00, #50, Tuesday, Dec. 5, 2000 % % See also symbfact % Copyright 1998-2007, Timothy A. Davis Lnz = full (sum (spones (L))) - 1 ; % off diagonal nz in cols of L Unz = full (sum (spones (U')))' - 1 ; % off diagonal nz in rows of U fl = 2*Lnz*Unz + sum (Lnz) ; SuiteSparse/CCOLAMD/MATLAB/ccolamd_install.m0000644001170100242450000000110510620370537017257 0ustar davisfacfunction ccolamd_install %CCOLAMD_INSTALL compiles and installs ccolamd and csymamd for MATLAB % Your current directory must be CCOLAMD/MATLAB for this function to work. % % Example: % ccolamd_install % % See also ccolamd, csymamd. % Copyright 1998-2007, Timothy A. Davis, Stefan Larimore, and Siva Rajamanickam % Developed in collaboration with J. Gilbert and E. Ng. ccolamd_make addpath (pwd) fprintf ('\nThe following path has been added. You may wish to add it\n') ; fprintf ('permanently, using the MATLAB pathtool command.\n') ; fprintf ('%s\n\n', pwd) ; ccolamd_demo SuiteSparse/CCOLAMD/MATLAB/csymamdtestmex.c0000644001170100242450000003024210616375416017176 0ustar davisfac/* ========================================================================== */ /* === csymamdtest mexFunction ============================================== */ /* ========================================================================== */ /* ---------------------------------------------------------------------------- * CCOLAMD Copyright (C), Univ. of Florida. Authors: Timothy A. Davis, * Sivasankaran Rajamanickam, and Stefan Larimore * See License.txt for the Version 2.1 of the GNU Lesser General Public License * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* * This MATLAB mexFunction is for testing only. It is not meant for * production use. See csymamdmex.c and csymamd.m instead. * * Usage: * * [ P, stats ] = csymamdtest (A, knobs, cmember) ; * * The knobs and stats vectors are optional: * * knobs (1) dense row/col control. default 10 * knobs (2) spumoni, default 0. * knobs (3) aggresive absorption if nonzero. default 1 * * knobs (4) for testing only. Controls how the input matrix is * jumbled prior to calling colamd, to test its error * handling capability. */ /* ========================================================================== */ /* === Include files ======================================================== */ /* ========================================================================== */ #include "ccolamd.h" #include "mex.h" #include "matrix.h" #include #include #include "UFconfig.h" #ifdef MIN #undef MIN #endif #define MIN(a,b) (((a) < (b)) ? (a) : (b)) static void dump_matrix ( UF_long A [ ], UF_long p [ ], UF_long n_row, UF_long n_col, UF_long Alen, UF_long limit ) { UF_long col, k, row ; mexPrintf ("dump matrix: nrow %d ncol %d Alen %d\n", n_row, n_col, Alen) ; if (!A) { mexPrintf ("A not present\n") ; return ; } if (!p) { mexPrintf ("p not present\n") ; return ; } for (col = 0 ; col < MIN (n_col, limit) ; col++) { mexPrintf ("column %d, p[col] %d, p [col+1] %d, length %d\n", col, p [col], p [col+1], p [col+1] - p [col]) ; for (k = p [col] ; k < p [col+1] ; k++) { row = A [k] ; mexPrintf (" %d", row) ; } mexPrintf ("\n") ; } } /* ========================================================================== */ /* === csymamd mexFunction ================================================== */ /* ========================================================================== */ void mexFunction ( /* === Parameters ======================================================= */ int nargout, /* number of left-hand sides */ mxArray *pargout [ ], /* left-hand side matrices */ int nargin, /* number of right--hand sides */ const mxArray *pargin [ ] /* right-hand side matrices */ ) { /* === Local variables ================================================== */ UF_long *perm ; /* column ordering of M and ordering of A */ UF_long *A ; /* row indices of input matrix A */ UF_long *p ; /* column pointers of input matrix A */ UF_long n_col ; /* number of columns of A */ UF_long n_row ; /* number of rows of A */ UF_long full ; /* TRUE if input matrix full, FALSE if sparse */ double knobs [CCOLAMD_KNOBS] ; /* ccolamd user-controllable parameters */ double *out_perm ; /* output permutation vector */ double *out_stats ; /* output stats vector */ double *in_knobs ; /* input knobs vector */ UF_long i ; /* loop counter */ mxArray *Ainput ; /* input matrix handle */ UF_long spumoni ; /* verbosity variable */ UF_long stats2 [CCOLAMD_STATS] ;/* stats for csymamd */ UF_long *cp, *cp_end, result, nnz, col, length, ok ; UF_long *stats ; stats = stats2 ; /* === Check inputs ===================================================== */ if (nargin != 3 || nargout > 2) { mexErrMsgTxt ( "csymamdtest: incorrect number of input and/or output arguments.") ; } /* for testing we require all 4 knobs */ if (mxGetNumberOfElements (pargin [1]) != 4) { mexErrMsgTxt ("csymamdtest: must have 4 knobs for testing") ; } /* === Get knobs ======================================================== */ ccolamd_l_set_defaults (knobs) ; spumoni = 0 ; in_knobs = mxGetPr (pargin [1]) ; i = mxGetNumberOfElements (pargin [1]) ; knobs [CCOLAMD_DENSE_ROW] = in_knobs [0] ; knobs [CCOLAMD_DENSE_COL] = in_knobs [0] ; knobs [CCOLAMD_AGGRESSIVE] = (in_knobs [1] != 0) ; spumoni = (in_knobs [2] != 0) ; /* print knob settings if spumoni is set */ if (spumoni) { mexPrintf ("\ncsymamd version %d.%d, %s:\n", CCOLAMD_MAIN_VERSION, CCOLAMD_SUB_VERSION, CCOLAMD_DATE) ; if (knobs [CCOLAMD_DENSE_ROW] >= 0) { mexPrintf ("knobs(1): %g, rows/cols with > " "max(16,%g*sqrt(size(A,2))) entries removed\n", in_knobs [0], knobs [CCOLAMD_DENSE_ROW]) ; } else { mexPrintf ("knobs(1): %g, no dense rows removed\n", in_knobs [0]) ; } mexPrintf ("knobs(2): %g, aggressive absorption: %s\n", in_knobs [1], (knobs [CCOLAMD_AGGRESSIVE] != 0) ? "yes" : "no") ; mexPrintf ("knobs(3): %g, statistics and knobs printed\n", in_knobs [2]) ; mexPrintf ("Testing: %g\n", in_knobs [3]) ; } /* === If A is full, convert to a sparse matrix ========================= */ Ainput = (mxArray *) pargin [0] ; if (mxGetNumberOfDimensions (Ainput) != 2) { mexErrMsgTxt ("csymamd: input matrix must be 2-dimensional.") ; } full = !mxIsSparse (Ainput) ; if (full) { mexCallMATLAB (1, &Ainput, 1, (mxArray **) pargin, "sparse") ; } /* === Allocate workspace for csymamd =================================== */ /* get size of matrix */ n_row = mxGetM (Ainput) ; n_col = mxGetN (Ainput) ; if (n_col != n_row) { mexErrMsgTxt ("csymamd: matrix must be square.") ; } /* p = mxGetJc (Ainput) ; */ p = (UF_long *) mxCalloc (n_col+1, sizeof (UF_long)) ; (void) memcpy (p, mxGetJc (Ainput), (n_col+1)*sizeof (UF_long)) ; nnz = p [n_col] ; if (spumoni) { mexPrintf ("csymamdtest: nnz %d\n", nnz) ; } /* A = mxGetIr (Ainput) ; */ A = (UF_long *) mxCalloc (nnz+1, sizeof (UF_long)) ; (void) memcpy (A, mxGetIr (Ainput), nnz*sizeof (UF_long)) ; perm = (UF_long *) mxCalloc (n_col+1, sizeof (UF_long)) ; /* === Jumble matrix ==================================================== */ /* knobs [4] FOR TESTING ONLY: Specifies how to jumble matrix 0 : No jumbling 1 : (no errors) 2 : Make first pointer non-zero 3 : Make column pointers not non-decreasing 4 : (no errors) 5 : Make row indices not strictly increasing 6 : Make a row index greater or equal to n_row 7 : Set A = NULL 8 : Set p = NULL 9 : Repeat row index 10: make row indices not sorted 11: jumble columns massively (note this changes the pattern of the matrix A.) 12: Set stats = NULL 13: Make n_col less than zero */ /* jumble appropriately */ switch ((UF_long) in_knobs [3]) { case 0 : if (spumoni) { mexPrintf ("csymamdtest: no errors expected\n") ; } result = 1 ; /* no errors */ break ; case 1 : if (spumoni) { mexPrintf ("csymamdtest: no errors expected (1)\n") ; } result = 1 ; break ; case 2 : if (spumoni) { mexPrintf ("csymamdtest: p [0] nonzero\n") ; } result = 0 ; /* p [0] must be zero */ p [0] = 1 ; break ; case 3 : if (spumoni) { mexPrintf ("csymamdtest: negative length last column\n") ; } result = (n_col == 0) ; /* p must be monotonically inc. */ p [n_col] = p [0] ; break ; case 4 : if (spumoni) { mexPrintf ("csymamdtest: no errors expected (4)\n") ; } result = 1 ; break ; case 5 : if (spumoni) { mexPrintf ("csymamdtest: row index out of range (-1)\n") ; } if (nnz > 0) /* row index out of range */ { result = 0 ; A [nnz-1] = -1 ; } else { if (spumoni) { mexPrintf ("Note: no row indices to put out of range\n") ; } result = 1 ; } break ; case 6 : if (spumoni) { mexPrintf ("csymamdtest: row index out of range (ncol)\n") ; } if (nnz > 0) /* row index out of range */ { result = 0 ; A [nnz-1] = n_col ; } else { if (spumoni) { mexPrintf ("Note: no row indices to put out of range\n") ; } result = 1 ; } break ; case 7 : if (spumoni) { mexPrintf ("csymamdtest: A not present\n") ; } result = 0 ; /* A not present */ A = (UF_long *) NULL ; break ; case 8 : if (spumoni) { mexPrintf ("csymamdtest: p not present\n") ; } result = 0 ; /* p not present */ p = (UF_long *) NULL ; break ; case 9 : if (spumoni) { mexPrintf ("csymamdtest: duplicate row index\n") ; } result = 1 ; /* duplicate row index */ for (col = 0 ; col < n_col ; col++) { length = p [col+1] - p [col] ; if (length > 1) { A [p [col+1]-2] = A [p [col+1] - 1] ; if (spumoni) { mexPrintf ("Made duplicate row %d in col %d\n", A [p [col+1] - 1], col) ; } break ; } } if (spumoni > 1) { dump_matrix (A, p, n_row, n_col, nnz, col+2) ; } break ; case 10 : if (spumoni) { mexPrintf ("csymamdtest: unsorted column\n") ; } result = 1 ; /* jumbled columns */ for (col = 0 ; col < n_col ; col++) { length = p [col+1] - p [col] ; if (length > 1) { i = A[p [col]] ; A [p [col]] = A[p [col] + 1] ; A [p [col] + 1] = i ; if (spumoni) { mexPrintf ("Unsorted column %d \n", col) ; } break ; } } if (spumoni > 1) { dump_matrix (A, p, n_row, n_col, nnz, col+2) ; } break ; case 11 : if (spumoni) { mexPrintf ("csymamdtest: massive jumbling\n") ; } result = 1 ; /* massive jumbling, but no errors */ srand (1) ; for (i = 0 ; i < n_col ; i++) { cp = &A [p [i]] ; cp_end = &A [p [i+1]] ; while (cp < cp_end) { *cp++ = rand() % n_row ; } } if (spumoni > 1) { dump_matrix (A, p, n_row, n_col, nnz, n_col) ; } break ; case 12 : if (spumoni) { mexPrintf ("csymamdtest: stats not present\n") ; } result = 0 ; /* stats not present */ stats = (UF_long *) NULL ; break ; case 13 : if (spumoni) { mexPrintf ("csymamdtest: ncol out of range\n") ; } result = 0 ; /* ncol out of range */ n_col = -1 ; break ; } /* === Order the rows and columns of A (does not destroy A) ============= */ ok = csymamd_l (n_col, A, p, perm, knobs, stats, &mxCalloc, &mxFree, NULL, -1) ; if (full) { mxDestroyArray (Ainput) ; } if (spumoni) { csymamd_l_report (stats) ; } /* === Return the stats vector ========================================== */ if (nargout == 2) { pargout [1] = mxCreateDoubleMatrix (1, CCOLAMD_STATS, mxREAL) ; out_stats = mxGetPr (pargout [1]) ; for (i = 0 ; i < CCOLAMD_STATS ; i++) { out_stats [i] = (stats == NULL) ? (-1) : (stats [i]) ; } /* fix stats (5) and (6), for 1-based information on jumbled matrix. */ /* note that this correction doesn't occur if csymamd returns FALSE */ out_stats [CCOLAMD_INFO1] ++ ; out_stats [CCOLAMD_INFO2] ++ ; } mxFree (A) ; if (ok) { /* === Return the permutation vector ================================ */ pargout [0] = mxCreateDoubleMatrix (1, n_col, mxREAL) ; out_perm = mxGetPr (pargout [0]) ; for (i = 0 ; i < n_col ; i++) { /* csymamd is 0-based, but MATLAB expects this to be 1-based */ out_perm [i] = perm [i] + 1 ; } if (!result) { csymamd_l_report (stats) ; mexErrMsgTxt ("csymamd should have returned TRUE\n") ; } } else { /* return p = -1 if csymamd failed */ pargout [0] = mxCreateDoubleMatrix (1, 1, mxREAL) ; out_perm = mxGetPr (pargout [0]) ; out_perm [0] = -1 ; if (result) { csymamd_l_report (stats) ; mexErrMsgTxt ("csymamd should have returned FALSE\n") ; } } mxFree (p) ; mxFree (perm) ; } SuiteSparse/CCOLAMD/MATLAB/csymamdtestmex.m0000644001170100242450000000055410620370256017203 0ustar davisfacfunction [P, stats] = csymamdtestmex (A, knobs) %#ok % CSYMAMDTESTMEX test function for csymamd % Example: % [ P, stats ] = csymamdtest (A, knobs) ; % See also csymamd % Copyright 1998-2007, Timothy A. Davis, Stefan Larimore, and Siva Rajamanickam % Developed in collaboration with J. Gilbert and E. Ng. error ('csymamdtestmex mexFunction not found') ; SuiteSparse/CCOLAMD/MATLAB/ccolamdmex.c0000644001170100242450000001640510616372162016243 0ustar davisfac/* ========================================================================== */ /* === ccolamd mexFunction ================================================== */ /* ========================================================================== */ /* ---------------------------------------------------------------------------- * CCOLAMD, Copyright (C), Univ. of Florida. Authors: Timothy A. Davis, * Sivasankaran Rajamanickam, and Stefan Larimore * See License.txt for the Version 2.1 of the GNU Lesser General Public License * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* * Usage: * p = ccolamd (A) ; * [p stats] = ccolamd (A, knobs, cmember) ; * * See ccolamd.m for a description. */ /* ========================================================================== */ /* === Include files ======================================================== */ /* ========================================================================== */ #include "ccolamd.h" #include "mex.h" #include "matrix.h" #include #include #include "UFconfig.h" /* ========================================================================== */ /* === ccolamd mexFunction ================================================== */ /* ========================================================================== */ void mexFunction ( /* === Parameters ======================================================= */ int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { /* === Local variables ================================================== */ UF_long *A ; /* ccolamd's copy of the matrix and workspace */ UF_long *cmember ; /* ccolamd's copy of the constraint set */ double *in_cmember ; /* input constraint set */ UF_long *p ; /* ccolamd's copy of the column pointers */ UF_long Alen ; /* size of A */ UF_long cslen ; /* size of CS */ UF_long n_col ; /* number of columns of A */ UF_long n_row ; /* number of rows of A */ UF_long nnz ; /* number of entries in A */ UF_long full ; /* TRUE if input matrix full, FALSE if sparse */ double knobs [CCOLAMD_KNOBS] ; /* ccolamd user-controllable parameters */ double *out_perm ; /* output permutation vector */ double *out_stats ; /* output stats vector */ double *in_knobs ; /* input knobs vector */ UF_long i ; /* loop counter */ mxArray *Ainput ; /* input matrix handle */ UF_long spumoni ; /* verbosity variable */ UF_long stats [CCOLAMD_STATS] ; /* stats for ccolamd */ /* === Check inputs ===================================================== */ if (nargin < 1 || nargin > 3 || nargout < 0 || nargout > 2) { mexErrMsgTxt ("Usage: [p stats] = ccolamd (A, knobs, cmember)") ; } /* === Get cmember ====================================================== */ cmember = NULL ; cslen = 0 ; if (nargin > 2) { in_cmember = mxGetPr (pargin [2]) ; cslen = mxGetNumberOfElements (pargin [2]) ; if (cslen != 0) { cmember = (UF_long *) mxCalloc (cslen, sizeof (UF_long)) ; for (i = 0 ; i < cslen ; i++) { /* convert cmember from 1-based to 0-based */ cmember[i] = ((UF_long) in_cmember [i] - 1) ; } } } /* === Get knobs ======================================================== */ ccolamd_l_set_defaults (knobs) ; spumoni = 0 ; /* check for user-passed knobs */ if (nargin > 1) { in_knobs = mxGetPr (pargin [1]) ; i = mxGetNumberOfElements (pargin [1]) ; if (i > 0) knobs [CCOLAMD_LU] = (in_knobs [0] != 0) ; if (i > 1) knobs [CCOLAMD_DENSE_ROW] = in_knobs [1] ; if (i > 2) knobs [CCOLAMD_DENSE_COL] = in_knobs [2] ; if (i > 3) knobs [CCOLAMD_AGGRESSIVE] = (in_knobs [3] != 0) ; if (i > 4) spumoni = (in_knobs [4] != 0) ; } /* print knob settings if spumoni is set */ if (spumoni) { mexPrintf ("\nccolamd version %d.%d, %s:\nknobs(1): %g, order for %s\n", CCOLAMD_MAIN_VERSION, CCOLAMD_SUB_VERSION, CCOLAMD_DATE, in_knobs [0], (knobs [CCOLAMD_LU] != 0) ? "lu(A)" : "chol(A'*A)") ; if (knobs [CCOLAMD_DENSE_ROW] >= 0) { mexPrintf ("knobs(2): %g, rows with > max(16,%g*sqrt(size(A,2)))" " entries removed\n", in_knobs [1], knobs [CCOLAMD_DENSE_ROW]) ; } else { mexPrintf ("knobs(2): %g, no dense rows removed\n", in_knobs [1]) ; } if (knobs [CCOLAMD_DENSE_COL] >= 0) { mexPrintf ("knobs(3): %g, cols with > max(16,%g*sqrt(min(size(A)))" " entries removed\n", in_knobs [2], knobs [CCOLAMD_DENSE_COL]) ; } else { mexPrintf ("knobs(3): no dense columns removed\n", in_knobs [2]) ; } mexPrintf ("knobs(4): %g, aggressive absorption: %s\n", in_knobs [3], (knobs [CCOLAMD_AGGRESSIVE] != 0) ? "yes" : "no") ; mexPrintf ("knobs(5): %g, statistics and knobs printed\n", in_knobs [4]) ; } /* === If A is full, convert to a sparse matrix ========================= */ Ainput = (mxArray *) pargin [0] ; if (mxGetNumberOfDimensions (Ainput) != 2) { mexErrMsgTxt ("ccolamd: input matrix must be 2-dimensional") ; } full = !mxIsSparse (Ainput) ; if (full) { mexCallMATLAB (1, &Ainput, 1, (mxArray **) pargin, "sparse") ; } /* === Allocate workspace for ccolamd =================================== */ /* get size of matrix */ n_row = mxGetM (Ainput) ; n_col = mxGetN (Ainput) ; /* get column pointer vector */ p = (UF_long *) mxCalloc (n_col+1, sizeof (UF_long)) ; (void) memcpy (p, mxGetJc (Ainput), (n_col+1)*sizeof (UF_long)) ; nnz = p [n_col] ; Alen = (UF_long) ccolamd_l_recommended (nnz, n_row, n_col) ; if (Alen == 0) { mexErrMsgTxt ("ccolamd: problem too large") ; } /* === Copy input matrix into workspace ================================= */ A = (UF_long *) mxCalloc (Alen, sizeof (UF_long)) ; (void) memcpy (A, mxGetIr (Ainput), nnz*sizeof (UF_long)) ; if (full) { mxDestroyArray (Ainput) ; } /* Check constraint set size */ if (cmember != NULL && cslen != n_col) { mexErrMsgTxt ("ccolamd: cmember must be of length equal to #cols of A"); } /* === Order the columns (destroys A) =================================== */ if (!ccolamd_l (n_row, n_col, Alen, A, p, knobs, stats, cmember)) { ccolamd_l_report (stats) ; mexErrMsgTxt ("ccolamd error!") ; } mxFree (A) ; mxFree (cmember) ; /* === Return the permutation vector ==================================== */ pargout [0] = mxCreateDoubleMatrix (1, n_col, mxREAL) ; out_perm = mxGetPr (pargout [0]) ; for (i = 0 ; i < n_col ; i++) { /* ccolamd is 0-based, but MATLAB expects this to be 1-based */ out_perm [i] = p [i] + 1 ; } mxFree (p) ; /* === Return the stats vector ========================================== */ /* print stats if spumoni is set */ if (spumoni) { ccolamd_l_report (stats) ; } if (nargout == 2) { pargout [1] = mxCreateDoubleMatrix (1, CCOLAMD_STATS, mxREAL) ; out_stats = mxGetPr (pargout [1]) ; for (i = 0 ; i < CCOLAMD_STATS ; i++) { out_stats [i] = stats [i] ; } /* fix stats (5) and (6), for 1-based information on jumbled matrix. */ /* note that this correction doesn't occur if symamd returns FALSE */ out_stats [CCOLAMD_INFO1] ++ ; out_stats [CCOLAMD_INFO2] ++ ; } } SuiteSparse/CCOLAMD/Include/0000755001170100242450000000000010617106414014374 5ustar davisfacSuiteSparse/CCOLAMD/Include/ccolamd.h0000644001170100242450000002473010711427073016157 0ustar davisfac/* ========================================================================== */ /* === CCOLAMD/ccolamd.h ==================================================== */ /* ========================================================================== */ /* ---------------------------------------------------------------------------- * CCOLAMD Copyright (C), Univ. of Florida. Authors: Timothy A. Davis, * Sivasankaran Rajamanickam, and Stefan Larimore * See License.txt for the Version 2.1 of the GNU Lesser General Public License * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* * You must include this file (ccolamd.h) in any routine that uses ccolamd, * csymamd, or the related macros and definitions. */ #ifndef CCOLAMD_H #define CCOLAMD_H /* make it easy for C++ programs to include CCOLAMD */ #ifdef __cplusplus extern "C" { #endif /* for size_t definition: */ #include /* ========================================================================== */ /* === CCOLAMD version ====================================================== */ /* ========================================================================== */ /* All versions of CCOLAMD will include the following definitions. * As an example, to test if the version you are using is 1.3 or later: * * if (CCOLAMD_VERSION >= CCOLAMD_VERSION_CODE (1,3)) ... * * This also works during compile-time: * * #if CCOLAMD_VERSION >= CCOLAMD_VERSION_CODE (1,3) * printf ("This is version 1.3 or later\n") ; * #else * printf ("This is an early version\n") ; * #endif */ #define CCOLAMD_DATE "Nov 1, 2007" #define CCOLAMD_VERSION_CODE(main,sub) ((main) * 1000 + (sub)) #define CCOLAMD_MAIN_VERSION 2 #define CCOLAMD_SUB_VERSION 7 #define CCOLAMD_SUBSUB_VERSION 1 #define CCOLAMD_VERSION \ CCOLAMD_VERSION_CODE(CCOLAMD_MAIN_VERSION,CCOLAMD_SUB_VERSION) /* ========================================================================== */ /* === Knob and statistics definitions ====================================== */ /* ========================================================================== */ /* size of the knobs [ ] array. Only knobs [0..3] are currently used. */ #define CCOLAMD_KNOBS 20 /* number of output statistics. Only stats [0..10] are currently used. */ #define CCOLAMD_STATS 20 /* knobs [0] and stats [0]: dense row knob and output statistic. */ #define CCOLAMD_DENSE_ROW 0 /* knobs [1] and stats [1]: dense column knob and output statistic. */ #define CCOLAMD_DENSE_COL 1 /* knobs [2]: aggressive absorption option */ #define CCOLAMD_AGGRESSIVE 2 /* knobs [3]: LU or Cholesky factorization option */ #define CCOLAMD_LU 3 /* stats [2]: memory defragmentation count output statistic */ #define CCOLAMD_DEFRAG_COUNT 2 /* stats [3]: ccolamd status: zero OK, > 0 warning or notice, < 0 error */ #define CCOLAMD_STATUS 3 /* stats [4..6]: error info, or info on jumbled columns */ #define CCOLAMD_INFO1 4 #define CCOLAMD_INFO2 5 #define CCOLAMD_INFO3 6 /* stats [7]: number of originally empty rows */ #define CCOLAMD_EMPTY_ROW 7 /* stats [8]: number of originally empty cols */ #define CCOLAMD_EMPTY_COL 8 /* stats [9]: number of rows with entries only in dense cols */ #define CCOLAMD_NEWLY_EMPTY_ROW 9 /* stats [10]: number of cols with entries only in dense rows */ #define CCOLAMD_NEWLY_EMPTY_COL 10 /* error codes returned in stats [3]: */ #define CCOLAMD_OK (0) #define CCOLAMD_OK_BUT_JUMBLED (1) #define CCOLAMD_ERROR_A_not_present (-1) #define CCOLAMD_ERROR_p_not_present (-2) #define CCOLAMD_ERROR_nrow_negative (-3) #define CCOLAMD_ERROR_ncol_negative (-4) #define CCOLAMD_ERROR_nnz_negative (-5) #define CCOLAMD_ERROR_p0_nonzero (-6) #define CCOLAMD_ERROR_A_too_small (-7) #define CCOLAMD_ERROR_col_length_negative (-8) #define CCOLAMD_ERROR_row_index_out_of_bounds (-9) #define CCOLAMD_ERROR_out_of_memory (-10) #define CCOLAMD_ERROR_invalid_cmember (-11) #define CCOLAMD_ERROR_internal_error (-999) /* ========================================================================== */ /* === Prototypes of user-callable routines ================================= */ /* ========================================================================== */ /* define UF_long */ #include "UFconfig.h" size_t ccolamd_recommended /* returns recommended value of Alen, */ /* or 0 if input arguments are erroneous */ ( int nnz, /* nonzeros in A */ int n_row, /* number of rows in A */ int n_col /* number of columns in A */ ) ; size_t ccolamd_l_recommended /* returns recommended value of Alen, */ /* or 0 if input arguments are erroneous */ ( UF_long nnz, /* nonzeros in A */ UF_long n_row, /* number of rows in A */ UF_long n_col /* number of columns in A */ ) ; void ccolamd_set_defaults /* sets default parameters */ ( /* knobs argument is modified on output */ double knobs [CCOLAMD_KNOBS] /* parameter settings for ccolamd */ ) ; void ccolamd_l_set_defaults /* sets default parameters */ ( /* knobs argument is modified on output */ double knobs [CCOLAMD_KNOBS] /* parameter settings for ccolamd */ ) ; int ccolamd /* returns (1) if successful, (0) otherwise*/ ( /* A and p arguments are modified on output */ int n_row, /* number of rows in A */ int n_col, /* number of columns in A */ int Alen, /* size of the array A */ int A [ ], /* row indices of A, of size Alen */ int p [ ], /* column pointers of A, of size n_col+1 */ double knobs [CCOLAMD_KNOBS],/* parameter settings for ccolamd */ int stats [CCOLAMD_STATS], /* ccolamd output statistics and error codes */ int cmember [ ] /* Constraint set of A, of size n_col */ ) ; UF_long ccolamd_l /* same as ccolamd, but with UF_long integers */ ( UF_long n_row, UF_long n_col, UF_long Alen, UF_long A [ ], UF_long p [ ], double knobs [CCOLAMD_KNOBS], UF_long stats [CCOLAMD_STATS], UF_long cmember [ ] ) ; int csymamd /* return (1) if OK, (0) otherwise */ ( int n, /* number of rows and columns of A */ int A [ ], /* row indices of A */ int p [ ], /* column pointers of A */ int perm [ ], /* output permutation, size n_col+1 */ double knobs [CCOLAMD_KNOBS],/* parameters (uses defaults if NULL) */ int stats [CCOLAMD_STATS], /* output statistics and error codes */ void * (*allocate) (size_t, size_t), /* pointer to calloc (ANSI C) or */ /* mxCalloc (for MATLAB mexFunction) */ void (*release) (void *), /* pointer to free (ANSI C) or */ /* mxFree (for MATLAB mexFunction) */ int cmember [ ], /* Constraint set of A */ int stype /* 0: use both parts, >0: upper, <0: lower */ ) ; UF_long csymamd_l /* same as csymamd, but with UF_long integers */ ( UF_long n, UF_long A [ ], UF_long p [ ], UF_long perm [ ], double knobs [CCOLAMD_KNOBS], UF_long stats [CCOLAMD_STATS], void * (*allocate) (size_t, size_t), void (*release) (void *), UF_long cmember [ ], UF_long stype ) ; void ccolamd_report ( int stats [CCOLAMD_STATS] ) ; void ccolamd_l_report ( UF_long stats [CCOLAMD_STATS] ) ; void csymamd_report ( int stats [CCOLAMD_STATS] ) ; void csymamd_l_report ( UF_long stats [CCOLAMD_STATS] ) ; /* ========================================================================== */ /* === Prototypes of "expert" routines ====================================== */ /* ========================================================================== */ /* These routines are meant to be used internally, or in a future version of * UMFPACK. They appear here so that UMFPACK can use them, but they should not * be called directly by the user. */ int ccolamd2 ( /* A and p arguments are modified on output */ int n_row, /* number of rows in A */ int n_col, /* number of columns in A */ int Alen, /* size of the array A */ int A [ ], /* row indices of A, of size Alen */ int p [ ], /* column pointers of A, of size n_col+1 */ double knobs [CCOLAMD_KNOBS],/* parameter settings for ccolamd */ int stats [CCOLAMD_STATS], /* ccolamd output statistics and error codes */ /* each Front_ array is of size n_col+1: */ int Front_npivcol [ ], /* # pivot cols in each front */ int Front_nrows [ ], /* # of rows in each front (incl. pivot rows) */ int Front_ncols [ ], /* # of cols in each front (incl. pivot cols) */ int Front_parent [ ], /* parent of each front */ int Front_cols [ ], /* link list of pivot columns for each front */ int *p_nfr, /* total number of frontal matrices */ int InFront [ ], /* InFront [row] = f if row in front f */ int cmember [ ] /* Constraint set of A */ ) ; UF_long ccolamd2_l /* same as ccolamd2, but with UF_long integers */ ( UF_long n_row, UF_long n_col, UF_long Alen, UF_long A [ ], UF_long p [ ], double knobs [CCOLAMD_KNOBS], UF_long stats [CCOLAMD_STATS], UF_long Front_npivcol [ ], UF_long Front_nrows [ ], UF_long Front_ncols [ ], UF_long Front_parent [ ], UF_long Front_cols [ ], UF_long *p_nfr, UF_long InFront [ ], UF_long cmember [ ] ) ; void ccolamd_apply_order ( int Front [ ], const int Order [ ], int Temp [ ], int nn, int nfr ) ; void ccolamd_l_apply_order ( UF_long Front [ ], const UF_long Order [ ], UF_long Temp [ ], UF_long nn, UF_long nfr ) ; void ccolamd_fsize ( int nn, int MaxFsize [ ], int Fnrows [ ], int Fncols [ ], int Parent [ ], int Npiv [ ] ) ; void ccolamd_l_fsize ( UF_long nn, UF_long MaxFsize [ ], UF_long Fnrows [ ], UF_long Fncols [ ], UF_long Parent [ ], UF_long Npiv [ ] ) ; void ccolamd_postorder ( int nn, int Parent [ ], int Npiv [ ], int Fsize [ ], int Order [ ], int Child [ ], int Sibling [ ], int Stack [ ], int Front_cols [ ], int cmember [ ] ) ; void ccolamd_l_postorder ( UF_long nn, UF_long Parent [ ], UF_long Npiv [ ], UF_long Fsize [ ], UF_long Order [ ], UF_long Child [ ], UF_long Sibling [ ], UF_long Stack [ ], UF_long Front_cols [ ], UF_long cmember [ ] ) ; int ccolamd_post_tree ( int root, int k, int Child [ ], const int Sibling [ ], int Order [ ], int Stack [ ] ) ; UF_long ccolamd_l_post_tree ( UF_long root, UF_long k, UF_long Child [ ], const UF_long Sibling [ ], UF_long Order [ ], UF_long Stack [ ] ) ; #ifndef EXTERN #define EXTERN extern #endif EXTERN int (*ccolamd_printf) (const char *, ...) ; #ifdef __cplusplus } #endif #endif SuiteSparse/CCOLAMD/Source/0000755001170100242450000000000010617106440014250 5ustar davisfacSuiteSparse/CCOLAMD/Source/ccolamd_global.c0000644001170100242450000000167410616375133017354 0ustar davisfac/* ========================================================================== */ /* === ccolamd_global.c ===================================================== */ /* ========================================================================== */ /* ---------------------------------------------------------------------------- * CCOLAMD Copyright (C), Univ. of Florida. Authors: Timothy A. Davis, * Sivasankaran Rajamanickam, and Stefan Larimore * See License.txt for the Version 2.1 of the GNU Lesser General Public License * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Global variables for CCOLAMD */ #ifndef NPRINT #ifdef MATLAB_MEX_FILE #include "mex.h" int (*ccolamd_printf) (const char *, ...) = mexPrintf ; #else #include int (*ccolamd_printf) (const char *, ...) = printf ; #endif #else int (*ccolamd_printf) (const char *, ...) = ((void *) 0) ; #endif SuiteSparse/CCOLAMD/Source/ccolamd.c0000644001170100242450000042150310616375043016031 0ustar davisfac/* ========================================================================== */ /* === CCOLAMD/CSYMAMD - a constrained column ordering algorithm ============ */ /* ========================================================================== */ /* ---------------------------------------------------------------------------- * CCOLAMD, Copyright (C) Univ. of Florida. Authors: Timothy A. Davis, * Sivasankaran Rajamanickam, and Stefan Larimore * See License.txt for the Version 2.1 of the GNU Lesser General Public License * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* * ccolamd: a constrained approximate minimum degree column ordering * algorithm, LU factorization of symmetric or unsymmetric matrices, * QR factorization, least squares, interior point methods for * linear programming problems, and other related problems. * * csymamd: a constrained approximate minimum degree ordering algorithm for * Cholesky factorization of symmetric matrices. * * Purpose: * * CCOLAMD computes a permutation Q such that the Cholesky factorization of * (AQ)'(AQ) has less fill-in and requires fewer floating point operations * than A'A. This also provides a good ordering for sparse partial * pivoting methods, P(AQ) = LU, where Q is computed prior to numerical * factorization, and P is computed during numerical factorization via * conventional partial pivoting with row interchanges. CCOLAMD is an * extension of COLAMD, available as built-in function in MATLAB Version 6, * available from MathWorks, Inc. (http://www.mathworks.com). This * routine can be used in place of COLAMD in MATLAB. * * CSYMAMD computes a permutation P of a symmetric matrix A such that the * Cholesky factorization of PAP' has less fill-in and requires fewer * floating point operations than A. CSYMAMD constructs a matrix M such * that M'M has the same nonzero pattern of A, and then orders the columns * of M using colmmd. The column ordering of M is then returned as the * row and column ordering P of A. CSYMAMD is an extension of SYMAMD. * * Authors: * * Timothy A. Davis and S. Rajamanickam wrote CCOLAMD, based directly on * COLAMD by Stefan I. Larimore and Timothy A. Davis, University of * Florida. The algorithm was developed in collaboration with John * Gilbert, (UCSB, then at Xerox PARC), and Esmond Ng, (Lawrence Berkeley * National Lab, then at Oak Ridge National Laboratory). * * Acknowledgements: * * This work was supported by the National Science Foundation, under * grants DMS-9504974 and DMS-9803599, CCR-0203270, and a grant from the * Sandia National Laboratory (Dept. of Energy). * * Copyright and License: * * Copyright (c) 1998-2005 by the University of Florida. * All Rights Reserved. * COLAMD is also available under alternate licenses, contact T. Davis * for details. * * This library is free software; you can redistribute it and/or * modify it under the terms of the GNU Lesser General Public * License as published by the Free Software Foundation; either * version 2.1 of the License, or (at your option) any later version. * * This library is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * Lesser General Public License for more details. * * You should have received a copy of the GNU Lesser General Public * License along with this library; if not, write to the Free Software * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 * USA * * Permission is hereby granted to use or copy this program under the * terms of the GNU LGPL, provided that the Copyright, this License, * and the Availability of the original version is retained on all copies. * User documentation of any code that uses this code or any modified * version of this code must cite the Copyright, this License, the * Availability note, and "Used by permission." Permission to modify * the code and to distribute modified code is granted, provided the * Copyright, this License, and the Availability note are retained, * and a notice that the code was modified is included. * * Availability: * * The CCOLAMD/CSYMAMD library is available at * * http://www.cise.ufl.edu/research/sparse/ccolamd/ * * This is the http://www.cise.ufl.edu/research/sparse/ccolamd/ccolamd.c * file. * * See the ChangeLog file for changes since Version 1.0. */ /* ========================================================================== */ /* === Description of user-callable routines ================================ */ /* ========================================================================== */ /* CCOLAMD includes both int and UF_long versions of all its routines. The * description below is for the int version. For UF_long, all int arguments * become UF_long integers. UF_long is normally defined as long, except for * WIN64 */ /* ---------------------------------------------------------------------------- * ccolamd_recommended: * ---------------------------------------------------------------------------- * * C syntax: * * #include "ccolamd.h" * size_t ccolamd_recommended (int nnz, int n_row, int n_col) ; * size_t ccolamd_l_recommended (UF_long nnz, UF_long n_row, * UF_long n_col) ; * * Purpose: * * Returns recommended value of Alen for use by ccolamd. Returns 0 * if any input argument is negative. The use of this routine * is optional. Not needed for csymamd, which dynamically allocates * its own memory. * * Arguments (all input arguments): * * int nnz ; Number of nonzeros in the matrix A. This must * be the same value as p [n_col] in the call to * ccolamd - otherwise you will get a wrong value * of the recommended memory to use. * * int n_row ; Number of rows in the matrix A. * * int n_col ; Number of columns in the matrix A. * * ---------------------------------------------------------------------------- * ccolamd_set_defaults: * ---------------------------------------------------------------------------- * * C syntax: * * #include "ccolamd.h" * ccolamd_set_defaults (double knobs [CCOLAMD_KNOBS]) ; * ccolamd_l_set_defaults (double knobs [CCOLAMD_KNOBS]) ; * * Purpose: * * Sets the default parameters. The use of this routine is optional. * Passing a (double *) NULL pointer for the knobs results in the * default parameter settings. * * Arguments: * * double knobs [CCOLAMD_KNOBS] ; Output only. * * knobs [0] and knobs [1] behave differently than they did in COLAMD. * The other knobs are new to CCOLAMD. * * knobs [0]: dense row control * * For CCOLAMD, rows with more than * max (16, knobs [CCOLAMD_DENSE_ROW] * sqrt (n_col)) * entries are removed prior to ordering. * * For CSYMAMD, rows and columns with more than * max (16, knobs [CCOLAMD_DENSE_ROW] * sqrt (n)) * entries are removed prior to ordering, and placed last in the * output ordering (subject to the constraints). * * If negative, only completely dense rows are removed. If you * intend to use CCOLAMD for a Cholesky factorization of A*A', set * knobs [CCOLAMD_DENSE_ROW] to -1, which is more appropriate for * that case. * * Default: 10. * * knobs [1]: dense column control * * For CCOLAMD, columns with more than * max (16, knobs [CCOLAMD_DENSE_COL] * sqrt (MIN (n_row,n_col))) * entries are removed prior to ordering, and placed last in the * output column ordering (subject to the constraints). * Not used by CSYMAMD. If negative, only completely dense * columns are removed. Default: 10. * * knobs [2]: aggressive absorption * * knobs [CCOLAMD_AGGRESSIVE] controls whether or not to do * aggressive absorption during the ordering. Default is TRUE * (nonzero). If zero, no aggressive absorption is performed. * * knobs [3]: optimize ordering for LU or Cholesky * * knobs [CCOLAMD_LU] controls an option that optimizes the * ordering for the LU of A or the Cholesky factorization of A'A. * If TRUE (nonzero), an ordering optimized for LU is performed. * If FALSE (zero), an ordering for Cholesky is performed. * Default is FALSE. CSYMAMD ignores this parameter; it always * orders for Cholesky. * * ---------------------------------------------------------------------------- * ccolamd: * ---------------------------------------------------------------------------- * * C syntax: * * #include "ccolamd.h" * int ccolamd (int n_row, int n_col, int Alen, int *A, int *p, * double knobs [CCOLAMD_KNOBS], int stats [CCOLAMD_STATS], * int *cmember) ; * * UF_long ccolamd_l (UF_long n_row, UF_long n_col, UF_long Alen, * UF_long *A, UF_long *p, double knobs [CCOLAMD_KNOBS], * UF_long stats [CCOLAMD_STATS], UF_long *cmember) ; * * Purpose: * * Computes a column ordering (Q) of A such that P(AQ)=LU or * (AQ)'AQ=LL' have less fill-in and require fewer floating point * operations than factorizing the unpermuted matrix A or A'A, * respectively. * * Returns: * * TRUE (1) if successful, FALSE (0) otherwise. * * Arguments (for int version): * * int n_row ; Input argument. * * Number of rows in the matrix A. * Restriction: n_row >= 0. * ccolamd returns FALSE if n_row is negative. * * int n_col ; Input argument. * * Number of columns in the matrix A. * Restriction: n_col >= 0. * ccolamd returns FALSE if n_col is negative. * * int Alen ; Input argument. * * Restriction (see note): * Alen >= MAX (2*nnz, 4*n_col) + 17*n_col + 7*n_row + 7, where * nnz = p [n_col]. ccolamd returns FALSE if this condition is * not met. We recommend about nnz/5 more space for better * efficiency. This restriction makes an modest assumption * regarding the size of two typedef'd structures in ccolamd.h. * We do, however, guarantee that * * Alen >= ccolamd_recommended (nnz, n_row, n_col) * * will work efficiently. * * int A [Alen] ; Input argument, undefined on output. * * A is an integer array of size Alen. Alen must be at least as * large as the bare minimum value given above, but this is very * low, and can result in excessive run time. For best * performance, we recommend that Alen be greater than or equal to * ccolamd_recommended (nnz, n_row, n_col), which adds * nnz/5 to the bare minimum value given above. * * On input, the row indices of the entries in column c of the * matrix are held in A [(p [c]) ... (p [c+1]-1)]. The row indices * in a given column c need not be in ascending order, and * duplicate row indices may be be present. However, ccolamd will * work a little faster if both of these conditions are met * (ccolamd puts the matrix into this format, if it finds that the * the conditions are not met). * * The matrix is 0-based. That is, rows are in the range 0 to * n_row-1, and columns are in the range 0 to n_col-1. ccolamd * returns FALSE if any row index is out of range. * * The contents of A are modified during ordering, and are * undefined on output. * * int p [n_col+1] ; Both input and output argument. * * p is an integer array of size n_col+1. On input, it holds the * "pointers" for the column form of the matrix A. Column c of * the matrix A is held in A [(p [c]) ... (p [c+1]-1)]. The first * entry, p [0], must be zero, and p [c] <= p [c+1] must hold * for all c in the range 0 to n_col-1. The value nnz = p [n_col] * is thus the total number of entries in the pattern of the * matrix A. ccolamd returns FALSE if these conditions are not * met. * * On output, if ccolamd returns TRUE, the array p holds the column * permutation (Q, for P(AQ)=LU or (AQ)'(AQ)=LL'), where p [0] is * the first column index in the new ordering, and p [n_col-1] is * the last. That is, p [k] = j means that column j of A is the * kth pivot column, in AQ, where k is in the range 0 to n_col-1 * (p [0] = j means that column j of A is the first column in AQ). * * If ccolamd returns FALSE, then no permutation is returned, and * p is undefined on output. * * double knobs [CCOLAMD_KNOBS] ; Input argument. * * See ccolamd_set_defaults for a description. * * int stats [CCOLAMD_STATS] ; Output argument. * * Statistics on the ordering, and error status. * See ccolamd.h for related definitions. * ccolamd returns FALSE if stats is not present. * * stats [0]: number of dense or empty rows ignored. * * stats [1]: number of dense or empty columns ignored (and * ordered last in the output permutation p, subject to the * constraints). Note that a row can become "empty" if it * contains only "dense" and/or "empty" columns, and similarly * a column can become "empty" if it only contains "dense" * and/or "empty" rows. * * stats [2]: number of garbage collections performed. This can * be excessively high if Alen is close to the minimum * required value. * * stats [3]: status code. < 0 is an error code. * > 1 is a warning or notice. * * 0 OK. Each column of the input matrix contained row * indices in increasing order, with no duplicates. * * 1 OK, but columns of input matrix were jumbled (unsorted * columns or duplicate entries). CCOLAMD had to do some * extra work to sort the matrix first and remove * duplicate entries, but it still was able to return a * valid permutation (return value of ccolamd was TRUE). * * stats [4]: highest column index of jumbled columns * stats [5]: last seen duplicate or unsorted row index * stats [6]: number of duplicate or unsorted row indices * * -1 A is a null pointer * * -2 p is a null pointer * * -3 n_row is negative. stats [4]: n_row * * -4 n_col is negative. stats [4]: n_col * * -5 number of nonzeros in matrix is negative * * stats [4]: number of nonzeros, p [n_col] * * -6 p [0] is nonzero * * stats [4]: p [0] * * -7 A is too small * * stats [4]: required size * stats [5]: actual size (Alen) * * -8 a column has a negative number of entries * * stats [4]: column with < 0 entries * stats [5]: number of entries in col * * -9 a row index is out of bounds * * stats [4]: column with bad row index * stats [5]: bad row index * stats [6]: n_row, # of rows of matrx * * -10 (unused; see csymamd) * * int cmember [n_col] ; Input argument. * * cmember is new to CCOLAMD. It did not appear in COLAMD. * It places contraints on the output ordering. s = cmember [j] * gives the constraint set s that contains the column j * (Restriction: 0 <= s < n_col). In the output column * permutation, all columns in set 0 appear first, followed by * all columns in set 1, and so on. If NULL, all columns are * treated as if they were in a single constraint set, and you * will obtain the same ordering as COLAMD (with one exception: * the dense row/column threshold and other default knobs in * CCOLAMD and COLAMD are different). * * Example: * * See * http://www.cise.ufl.edu/research/sparse/ccolamd/ccolamd_example.c * for a complete example. * * To order the columns of a 5-by-4 matrix with 11 nonzero entries in * the following nonzero pattern * * x 0 x 0 * x 0 x x * 0 x x 0 * 0 0 x x * x x 0 0 * * with default knobs, no output statistics, and no ordering * constraints, do the following: * * #include "ccolamd.h" * #define ALEN 144 * int A [ALEN] = {0, 1, 4, 2, 4, 0, 1, 2, 3, 1, 3} ; * int p [ ] = {0, 3, 5, 9, 11} ; * int stats [CCOLAMD_STATS] ; * ccolamd (5, 4, ALEN, A, p, (double *) NULL, stats, NULL) ; * * The permutation is returned in the array p, and A is destroyed. * * ---------------------------------------------------------------------------- * csymamd: * ---------------------------------------------------------------------------- * * C syntax: * * #include "ccolamd.h" * * int csymamd (int n, int *A, int *p, int *perm, * double knobs [CCOLAMD_KNOBS], int stats [CCOLAMD_STATS], * void (*allocate) (size_t, size_t), void (*release) (void *), * int *cmember, int stype) ; * * UF_long csymamd_l (UF_long n, UF_long *A, UF_long *p, UF_long *perm, * double knobs [CCOLAMD_KNOBS], UF_long stats [CCOLAMD_STATS], * void (*allocate) (size_t, size_t), void (*release) (void *), * UF_long *cmember, UF_long stype) ; * * Purpose: * * The csymamd routine computes an ordering P of a symmetric sparse * matrix A such that the Cholesky factorization PAP' = LL' remains * sparse. It is based on a column ordering of a matrix M constructed * so that the nonzero pattern of M'M is the same as A. Either the * lower or upper triangular part of A can be used, or the pattern * A+A' can be used. You must pass your selected memory allocator * (usually calloc/free or mxCalloc/mxFree) to csymamd, for it to * allocate memory for the temporary matrix M. * * Returns: * * TRUE (1) if successful, FALSE (0) otherwise. * * Arguments: * * int n ; Input argument. * * Number of rows and columns in the symmetrix matrix A. * Restriction: n >= 0. * csymamd returns FALSE if n is negative. * * int A [nnz] ; Input argument. * * A is an integer array of size nnz, where nnz = p [n]. * * The row indices of the entries in column c of the matrix are * held in A [(p [c]) ... (p [c+1]-1)]. The row indices in a * given column c need not be in ascending order, and duplicate * row indices may be present. However, csymamd will run faster * if the columns are in sorted order with no duplicate entries. * * The matrix is 0-based. That is, rows are in the range 0 to * n-1, and columns are in the range 0 to n-1. csymamd * returns FALSE if any row index is out of range. * * The contents of A are not modified. * * int p [n+1] ; Input argument. * * p is an integer array of size n+1. On input, it holds the * "pointers" for the column form of the matrix A. Column c of * the matrix A is held in A [(p [c]) ... (p [c+1]-1)]. The first * entry, p [0], must be zero, and p [c] <= p [c+1] must hold * for all c in the range 0 to n-1. The value p [n] is * thus the total number of entries in the pattern of the matrix A. * csymamd returns FALSE if these conditions are not met. * * The contents of p are not modified. * * int perm [n+1] ; Output argument. * * On output, if csymamd returns TRUE, the array perm holds the * permutation P, where perm [0] is the first index in the new * ordering, and perm [n-1] is the last. That is, perm [k] = j * means that row and column j of A is the kth column in PAP', * where k is in the range 0 to n-1 (perm [0] = j means * that row and column j of A are the first row and column in * PAP'). The array is used as a workspace during the ordering, * which is why it must be of length n+1, not just n. * * double knobs [CCOLAMD_KNOBS] ; Input argument. * * See colamd_set_defaults for a description. * * int stats [CCOLAMD_STATS] ; Output argument. * * Statistics on the ordering, and error status. * See ccolamd.h for related definitions. * csymand returns FALSE if stats is not present. * * stats [0]: number of dense or empty row and columns ignored * (and ordered last in the output permutation perm, subject * to the constraints). Note that a row/column can become * "empty" if it contains only "dense" and/or "empty" * columns/rows. * * stats [1]: (same as stats [0]) * * stats [2]: number of garbage collections performed. * * stats [3]: status code. < 0 is an error code. * > 1 is a warning or notice. * * 0 to -9: same as ccolamd, with n replacing n_col and n_row, * and -3 and -7 are unused. * * -10 out of memory (unable to allocate temporary workspace * for M or count arrays using the "allocate" routine * passed into csymamd). * * void * (*allocate) (size_t, size_t) * * A pointer to a function providing memory allocation. The * allocated memory must be returned initialized to zero. For a * C application, this argument should normally be a pointer to * calloc. For a MATLAB mexFunction, the routine mxCalloc is * passed instead. * * void (*release) (size_t, size_t) * * A pointer to a function that frees memory allocated by the * memory allocation routine above. For a C application, this * argument should normally be a pointer to free. For a MATLAB * mexFunction, the routine mxFree is passed instead. * * int cmember [n] ; Input argument. * * Same as ccolamd, except that cmember is of size n, and it places * contraints symmetrically, on both the row and column ordering. * Entries in cmember must be in the range 0 to n-1. * * int stype ; Input argument. * * If stype < 0, then only the strictly lower triangular part of * A is accessed. The upper triangular part is assumed to be the * transpose of the lower triangular part. This is the same as * SYMAMD, which did not have an stype parameter. * * If stype > 0, only the strictly upper triangular part of A is * accessed. The lower triangular part is assumed to be the * transpose of the upper triangular part. * * If stype == 0, then the nonzero pattern of A+A' is ordered. * * ---------------------------------------------------------------------------- * ccolamd_report: * ---------------------------------------------------------------------------- * * C syntax: * * #include "ccolamd.h" * ccolamd_report (int stats [CCOLAMD_STATS]) ; * ccolamd_l_report (UF_long stats [CCOLAMD_STATS]) ; * * Purpose: * * Prints the error status and statistics recorded in the stats * array on the standard error output (for a standard C routine) * or on the MATLAB output (for a mexFunction). * * Arguments: * * int stats [CCOLAMD_STATS] ; Input only. Statistics from ccolamd. * * * ---------------------------------------------------------------------------- * csymamd_report: * ---------------------------------------------------------------------------- * * C syntax: * * #include "ccolamd.h" * csymamd_report (int stats [CCOLAMD_STATS]) ; * csymamd_l_report (UF_long stats [CCOLAMD_STATS]) ; * * Purpose: * * Prints the error status and statistics recorded in the stats * array on the standard error output (for a standard C routine) * or on the MATLAB output (for a mexFunction). * * Arguments: * * int stats [CCOLAMD_STATS] ; Input only. Statistics from csymamd. * */ /* ========================================================================== */ /* === Scaffolding code definitions ======================================== */ /* ========================================================================== */ /* Ensure that debugging is turned off: */ #ifndef NDEBUG #define NDEBUG #endif /* turn on debugging by uncommenting the following line #undef NDEBUG */ /* ========================================================================== */ /* === Include files ======================================================== */ /* ========================================================================== */ #include "ccolamd.h" #include #include #include #ifdef MATLAB_MEX_FILE #include "mex.h" #include "matrix.h" #endif #if !defined (NPRINT) || !defined (NDEBUG) #include #endif #ifndef NULL #define NULL ((void *) 0) #endif /* ========================================================================== */ /* === int or UF_long ======================================================= */ /* ========================================================================== */ /* define UF_long */ #include "UFconfig.h" #ifdef DLONG #define Int UF_long #define ID UF_long_id #define Int_MAX UF_long_max #define CCOLAMD_recommended ccolamd_l_recommended #define CCOLAMD_set_defaults ccolamd_l_set_defaults #define CCOLAMD_2 ccolamd2_l #define CCOLAMD_MAIN ccolamd_l #define CCOLAMD_apply_order ccolamd_l_apply_order #define CCOLAMD_postorder ccolamd_l_postorder #define CCOLAMD_post_tree ccolamd_l_post_tree #define CCOLAMD_fsize ccolamd_l_fsize #define CSYMAMD_MAIN csymamd_l #define CCOLAMD_report ccolamd_l_report #define CSYMAMD_report csymamd_l_report #else #define Int int #define ID "%d" #define Int_MAX INT_MAX #define CCOLAMD_recommended ccolamd_recommended #define CCOLAMD_set_defaults ccolamd_set_defaults #define CCOLAMD_2 ccolamd2 #define CCOLAMD_MAIN ccolamd #define CCOLAMD_apply_order ccolamd_apply_order #define CCOLAMD_postorder ccolamd_postorder #define CCOLAMD_post_tree ccolamd_post_tree #define CCOLAMD_fsize ccolamd_fsize #define CSYMAMD_MAIN csymamd #define CCOLAMD_report ccolamd_report #define CSYMAMD_report csymamd_report #endif /* ========================================================================== */ /* === Row and Column structures ============================================ */ /* ========================================================================== */ typedef struct CColamd_Col_struct { /* size of this struct is 8 integers if no padding occurs */ Int start ; /* index for A of first row in this column, or DEAD */ /* if column is dead */ Int length ; /* number of rows in this column */ union { Int thickness ; /* number of original columns represented by this */ /* col, if the column is alive */ Int parent ; /* parent in parent tree super-column structure, if */ /* the column is dead */ } shared1 ; union { Int score ; Int order ; } shared2 ; union { Int headhash ; /* head of a hash bucket, if col is at the head of */ /* a degree list */ Int hash ; /* hash value, if col is not in a degree list */ Int prev ; /* previous column in degree list, if col is in a */ /* degree list (but not at the head of a degree list) */ } shared3 ; union { Int degree_next ; /* next column, if col is in a degree list */ Int hash_next ; /* next column, if col is in a hash list */ } shared4 ; Int nextcol ; /* next column in this supercolumn */ Int lastcol ; /* last column in this supercolumn */ } CColamd_Col ; typedef struct CColamd_Row_struct { /* size of this struct is 6 integers if no padding occurs */ Int start ; /* index for A of first col in this row */ Int length ; /* number of principal columns in this row */ union { Int degree ; /* number of principal & non-principal columns in row */ Int p ; /* used as a row pointer in init_rows_cols () */ } shared1 ; union { Int mark ; /* for computing set differences and marking dead rows*/ Int first_column ;/* first column in row (used in garbage collection) */ } shared2 ; Int thickness ; /* number of original rows represented by this row */ /* that are not yet pivotal */ Int front ; /* -1 if an original row */ /* k if this row represents the kth frontal matrix */ /* where k goes from 0 to at most n_col-1 */ } CColamd_Row ; /* ========================================================================== */ /* === basic definitions ==================================================== */ /* ========================================================================== */ #define EMPTY (-1) #define MAX(a,b) (((a) > (b)) ? (a) : (b)) #define MIN(a,b) (((a) < (b)) ? (a) : (b)) /* Routines are either PUBLIC (user-callable) or PRIVATE (not user-callable) */ #define GLOBAL #define PUBLIC #define PRIVATE static #define DENSE_DEGREE(alpha,n) \ ((Int) MAX (16.0, (alpha) * sqrt ((double) (n)))) #define CMEMBER(c) ((cmember == (Int *) NULL) ? (0) : (cmember [c])) /* True if x is NaN */ #define SCALAR_IS_NAN(x) ((x) != (x)) /* true if an integer (stored in double x) would overflow (or if x is NaN) */ #define INT_OVERFLOW(x) ((!((x) * (1.0+1e-8) <= (double) Int_MAX)) \ || SCALAR_IS_NAN (x)) #define ONES_COMPLEMENT(r) (-(r)-1) #undef TRUE #undef FALSE #define TRUE (1) #define FALSE (0) /* Row and column status */ #define ALIVE (0) #define DEAD (-1) /* Column status */ #define DEAD_PRINCIPAL (-1) #define DEAD_NON_PRINCIPAL (-2) /* Macros for row and column status update and checking. */ #define ROW_IS_DEAD(r) ROW_IS_MARKED_DEAD (Row[r].shared2.mark) #define ROW_IS_MARKED_DEAD(row_mark) (row_mark < ALIVE) #define ROW_IS_ALIVE(r) (Row [r].shared2.mark >= ALIVE) #define COL_IS_DEAD(c) (Col [c].start < ALIVE) #define COL_IS_ALIVE(c) (Col [c].start >= ALIVE) #define COL_IS_DEAD_PRINCIPAL(c) (Col [c].start == DEAD_PRINCIPAL) #define KILL_ROW(r) { Row [r].shared2.mark = DEAD ; } #define KILL_PRINCIPAL_COL(c) { Col [c].start = DEAD_PRINCIPAL ; } #define KILL_NON_PRINCIPAL_COL(c) { Col [c].start = DEAD_NON_PRINCIPAL ; } /* ========================================================================== */ /* === ccolamd reporting mechanism ========================================== */ /* ========================================================================== */ #if defined (MATLAB_MEX_FILE) || defined (MATHWORKS) /* In MATLAB, matrices are 1-based to the user, but 0-based internally */ #define INDEX(i) ((i)+1) #else /* In C, matrices are 0-based and indices are reported as such in *_report */ #define INDEX(i) (i) #endif /* All output goes through the PRINTF macro. */ #define PRINTF(params) { if (ccolamd_printf != NULL) (void) ccolamd_printf params ; } /* ========================================================================== */ /* === Debugging prototypes and definitions ================================= */ /* ========================================================================== */ #ifndef NDEBUG #include /* debug print level, present only when debugging */ PRIVATE Int ccolamd_debug ; /* debug print statements */ #define DEBUG0(params) { PRINTF (params) ; } #define DEBUG1(params) { if (ccolamd_debug >= 1) PRINTF (params) ; } #define DEBUG2(params) { if (ccolamd_debug >= 2) PRINTF (params) ; } #define DEBUG3(params) { if (ccolamd_debug >= 3) PRINTF (params) ; } #define DEBUG4(params) { if (ccolamd_debug >= 4) PRINTF (params) ; } #ifdef MATLAB_MEX_FILE #define ASSERT(expression) (mxAssert ((expression), "")) #else #define ASSERT(expression) (assert (expression)) #endif PRIVATE void ccolamd_get_debug ( char *method ) ; PRIVATE void debug_mark ( Int n_row, CColamd_Row Row [], Int tag_mark, Int max_mark ) ; PRIVATE void debug_matrix ( Int n_row, Int n_col, CColamd_Row Row [], CColamd_Col Col [], Int A [] ) ; PRIVATE void debug_structures ( Int n_row, Int n_col, CColamd_Row Row [], CColamd_Col Col [], Int A [], Int in_cset [], Int cset_start [] ) ; PRIVATE void dump_super ( Int super_c, CColamd_Col Col [], Int n_col ) ; PRIVATE void debug_deg_lists ( Int n_row, Int n_col, CColamd_Row Row [ ], CColamd_Col Col [ ], Int head [ ], Int min_score, Int should, Int max_deg ) ; #else /* === No debugging ========================================================= */ #define DEBUG0(params) ; #define DEBUG1(params) ; #define DEBUG2(params) ; #define DEBUG3(params) ; #define DEBUG4(params) ; #define ASSERT(expression) #endif /* ========================================================================== */ /* === Prototypes of PRIVATE routines ======================================= */ /* ========================================================================== */ PRIVATE Int init_rows_cols ( Int n_row, Int n_col, CColamd_Row Row [ ], CColamd_Col Col [ ], Int A [ ], Int p [ ], Int stats [CCOLAMD_STATS] ) ; PRIVATE void init_scoring ( Int n_row, Int n_col, CColamd_Row Row [ ], CColamd_Col Col [ ], Int A [ ], Int head [ ], double knobs [CCOLAMD_KNOBS], Int *p_n_row2, Int *p_n_col2, Int *p_max_deg, Int cmember [ ], Int n_cset, Int cset_start [ ], Int dead_cols [ ], Int *p_ndense_row, /* number of dense rows */ Int *p_nempty_row, /* number of original empty rows */ Int *p_nnewlyempty_row, /* number of newly empty rows */ Int *p_ndense_col, /* number of dense cols (excl "empty" cols) */ Int *p_nempty_col, /* number of original empty cols */ Int *p_nnewlyempty_col /* number of newly empty cols */ ) ; PRIVATE Int find_ordering ( Int n_row, Int n_col, Int Alen, CColamd_Row Row [ ], CColamd_Col Col [ ], Int A [ ], Int head [ ], #ifndef NDEBUG Int n_col2, #endif Int max_deg, Int pfree, Int cset [ ], Int cset_start [ ], #ifndef NDEBUG Int n_cset, #endif Int cmember [ ], Int Front_npivcol [ ], Int Front_nrows [ ], Int Front_ncols [ ], Int Front_parent [ ], Int Front_cols [ ], Int *p_nfr, Int aggressive, Int InFront [ ], Int order_for_lu ) ; PRIVATE void detect_super_cols ( #ifndef NDEBUG Int n_col, CColamd_Row Row [ ], #endif CColamd_Col Col [ ], Int A [ ], Int head [ ], Int row_start, Int row_length, Int in_set [ ] ) ; PRIVATE Int garbage_collection ( Int n_row, Int n_col, CColamd_Row Row [ ], CColamd_Col Col [ ], Int A [ ], Int *pfree ) ; PRIVATE Int clear_mark ( Int tag_mark, Int max_mark, Int n_row, CColamd_Row Row [ ] ) ; PRIVATE void print_report ( char *method, Int stats [CCOLAMD_STATS] ) ; /* ========================================================================== */ /* === USER-CALLABLE ROUTINES: ============================================== */ /* ========================================================================== */ /* ========================================================================== */ /* === ccolamd_recommended ================================================== */ /* ========================================================================== */ /* * The ccolamd_recommended routine returns the suggested size for Alen. This * value has been determined to provide good balance between the number of * garbage collections and the memory requirements for ccolamd. If any * argument is negative, or if integer overflow occurs, a 0 is returned as * an error condition. * * 2*nnz space is required for the row and column indices of the matrix * (or 4*n_col, which ever is larger). * * CCOLAMD_C (n_col) + CCOLAMD_R (n_row) space is required for the Col and Row * arrays, respectively, which are internal to ccolamd. This is equal to * 8*n_col + 6*n_row if the structures are not padded. * * An additional n_col space is the minimal amount of "elbow room", * and nnz/5 more space is recommended for run time efficiency. * * The remaining (((3 * n_col) + 1) + 5 * (n_col + 1) + n_row) space is * for other workspace used in ccolamd which did not appear in colamd. */ /* add two values of type size_t, and check for integer overflow */ static size_t t_add (size_t a, size_t b, int *ok) { (*ok) = (*ok) && ((a + b) >= MAX (a,b)) ; return ((*ok) ? (a + b) : 0) ; } /* compute a*k where k is a small integer, and check for integer overflow */ static size_t t_mult (size_t a, size_t k, int *ok) { size_t i, s = 0 ; for (i = 0 ; i < k ; i++) { s = t_add (s, a, ok) ; } return (s) ; } /* size of the Col and Row structures */ #define CCOLAMD_C(n_col,ok) \ ((t_mult (t_add (n_col, 1, ok), sizeof (CColamd_Col), ok) / sizeof (Int))) #define CCOLAMD_R(n_row,ok) \ ((t_mult (t_add (n_row, 1, ok), sizeof (CColamd_Row), ok) / sizeof (Int))) /* #define CCOLAMD_RECOMMENDED(nnz, n_row, n_col) \ MAX (2 * nnz, 4 * n_col) + \ CCOLAMD_C (n_col) + CCOLAMD_R (n_row) + n_col + (nnz / 5) \ + ((3 * n_col) + 1) + 5 * (n_col + 1) + n_row */ static size_t ccolamd_need (Int nnz, Int n_row, Int n_col, int *ok) { /* ccolamd_need, compute the following, and check for integer overflow: need = MAX (2*nnz, 4*n_col) + n_col + Col_size + Row_size + (3*n_col+1) + (5*(n_col+1)) + n_row ; */ size_t s, c, r, t ; /* MAX (2*nnz, 4*n_col) */ s = t_mult (nnz, 2, ok) ; /* 2*nnz */ t = t_mult (n_col, 4, ok) ; /* 4*n_col */ s = MAX (s,t) ; s = t_add (s, n_col, ok) ; /* bare minimum elbow room */ /* Col and Row arrays */ c = CCOLAMD_C (n_col, ok) ; /* size of column structures */ r = CCOLAMD_R (n_row, ok) ; /* size of row structures */ s = t_add (s, c, ok) ; s = t_add (s, r, ok) ; c = t_mult (n_col, 3, ok) ; /* 3*n_col + 1 */ c = t_add (c, 1, ok) ; s = t_add (s, c, ok) ; c = t_add (n_col, 1, ok) ; /* 5 * (n_col + 1) */ c = t_mult (c, 5, ok) ; s = t_add (s, c, ok) ; s = t_add (s, n_row, ok) ; /* n_row */ return (ok ? s : 0) ; } PUBLIC size_t CCOLAMD_recommended /* returns recommended value of Alen. */ ( /* === Parameters ======================================================= */ Int nnz, /* number of nonzeros in A */ Int n_row, /* number of rows in A */ Int n_col /* number of columns in A */ ) { size_t s ; int ok = TRUE ; if (nnz < 0 || n_row < 0 || n_col < 0) { return (0) ; } s = ccolamd_need (nnz, n_row, n_col, &ok) ; /* bare minimum needed */ s = t_add (s, nnz/5, &ok) ; /* extra elbow room */ ok = ok && (s < Int_MAX) ; return (ok ? s : 0) ; } /* ========================================================================== */ /* === ccolamd_set_defaults ================================================= */ /* ========================================================================== */ /* * The ccolamd_set_defaults routine sets the default values of the user- * controllable parameters for ccolamd. */ PUBLIC void CCOLAMD_set_defaults ( /* === Parameters ======================================================= */ double knobs [CCOLAMD_KNOBS] /* knob array */ ) { /* === Local variables ================================================== */ Int i ; if (!knobs) { return ; /* no knobs to initialize */ } for (i = 0 ; i < CCOLAMD_KNOBS ; i++) { knobs [i] = 0 ; } knobs [CCOLAMD_DENSE_ROW] = 10 ; knobs [CCOLAMD_DENSE_COL] = 10 ; knobs [CCOLAMD_AGGRESSIVE] = TRUE ; /* default: do aggressive absorption*/ knobs [CCOLAMD_LU] = FALSE ; /* default: order for Cholesky */ } /* ========================================================================== */ /* === symamd =============================================================== */ /* ========================================================================== */ PUBLIC Int CSYMAMD_MAIN /* return TRUE if OK, FALSE otherwise */ ( /* === Parameters ======================================================= */ Int n, /* number of rows and columns of A */ Int A [ ], /* row indices of A */ Int p [ ], /* column pointers of A */ Int perm [ ], /* output permutation, size n+1 */ double knobs [CCOLAMD_KNOBS], /* parameters (uses defaults if NULL) */ Int stats [CCOLAMD_STATS], /* output statistics and error codes */ void * (*allocate) (size_t, size_t),/* pointer to calloc (ANSI C) or */ /* mxCalloc (for MATLAB mexFunction) */ void (*release) (void *), /* pointer to free (ANSI C) or */ /* mxFree (for MATLAB mexFunction) */ Int cmember [ ], /* constraint set */ Int stype /* stype of A */ ) { /* === Local variables ================================================== */ double cknobs [CCOLAMD_KNOBS] ; double default_knobs [CCOLAMD_KNOBS] ; Int *count ; /* length of each column of M, and col pointer*/ Int *mark ; /* mark array for finding duplicate entries */ Int *M ; /* row indices of matrix M */ size_t Mlen ; /* length of M */ Int n_row ; /* number of rows in M */ Int nnz ; /* number of entries in A */ Int i ; /* row index of A */ Int j ; /* column index of A */ Int k ; /* row index of M */ Int mnz ; /* number of nonzeros in M */ Int pp ; /* index into a column of A */ Int last_row ; /* last row seen in the current column */ Int length ; /* number of nonzeros in a column */ Int both ; /* TRUE if ordering A+A' */ Int upper ; /* TRUE if ordering triu(A)+triu(A)' */ Int lower ; /* TRUE if ordering tril(A)+tril(A)' */ #ifndef NDEBUG ccolamd_get_debug ("csymamd") ; #endif both = (stype == 0) ; upper = (stype > 0) ; lower = (stype < 0) ; /* === Check the input arguments ======================================== */ if (!stats) { DEBUG1 (("csymamd: stats not present\n")) ; return (FALSE) ; } for (i = 0 ; i < CCOLAMD_STATS ; i++) { stats [i] = 0 ; } stats [CCOLAMD_STATUS] = CCOLAMD_OK ; stats [CCOLAMD_INFO1] = -1 ; stats [CCOLAMD_INFO2] = -1 ; if (!A) { stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_A_not_present ; DEBUG1 (("csymamd: A not present\n")) ; return (FALSE) ; } if (!p) /* p is not present */ { stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_p_not_present ; DEBUG1 (("csymamd: p not present\n")) ; return (FALSE) ; } if (n < 0) /* n must be >= 0 */ { stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_ncol_negative ; stats [CCOLAMD_INFO1] = n ; DEBUG1 (("csymamd: n negative "ID" \n", n)) ; return (FALSE) ; } nnz = p [n] ; if (nnz < 0) /* nnz must be >= 0 */ { stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_nnz_negative ; stats [CCOLAMD_INFO1] = nnz ; DEBUG1 (("csymamd: number of entries negative "ID" \n", nnz)) ; return (FALSE) ; } if (p [0] != 0) { stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_p0_nonzero ; stats [CCOLAMD_INFO1] = p [0] ; DEBUG1 (("csymamd: p[0] not zero "ID"\n", p [0])) ; return (FALSE) ; } /* === If no knobs, set default knobs =================================== */ if (!knobs) { CCOLAMD_set_defaults (default_knobs) ; knobs = default_knobs ; } /* === Allocate count and mark ========================================== */ count = (Int *) ((*allocate) (n+1, sizeof (Int))) ; if (!count) { stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_out_of_memory ; DEBUG1 (("csymamd: allocate count (size "ID") failed\n", n+1)) ; return (FALSE) ; } mark = (Int *) ((*allocate) (n+1, sizeof (Int))) ; if (!mark) { stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_out_of_memory ; (*release) ((void *) count) ; DEBUG1 (("csymamd: allocate mark (size "ID") failed\n", n+1)) ; return (FALSE) ; } /* === Compute column counts of M, check if A is valid ================== */ stats [CCOLAMD_INFO3] = 0 ; /* number of duplicate or unsorted row indices*/ for (i = 0 ; i < n ; i++) { mark [i] = -1 ; } for (j = 0 ; j < n ; j++) { last_row = -1 ; length = p [j+1] - p [j] ; if (length < 0) { /* column pointers must be non-decreasing */ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_col_length_negative ; stats [CCOLAMD_INFO1] = j ; stats [CCOLAMD_INFO2] = length ; (*release) ((void *) count) ; (*release) ((void *) mark) ; DEBUG1 (("csymamd: col "ID" negative length "ID"\n", j, length)) ; return (FALSE) ; } for (pp = p [j] ; pp < p [j+1] ; pp++) { i = A [pp] ; if (i < 0 || i >= n) { /* row index i, in column j, is out of bounds */ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_row_index_out_of_bounds ; stats [CCOLAMD_INFO1] = j ; stats [CCOLAMD_INFO2] = i ; stats [CCOLAMD_INFO3] = n ; (*release) ((void *) count) ; (*release) ((void *) mark) ; DEBUG1 (("csymamd: row "ID" col "ID" out of bounds\n", i, j)) ; return (FALSE) ; } if (i <= last_row || mark [i] == j) { /* row index is unsorted or repeated (or both), thus col */ /* is jumbled. This is a notice, not an error condition. */ stats [CCOLAMD_STATUS] = CCOLAMD_OK_BUT_JUMBLED ; stats [CCOLAMD_INFO1] = j ; stats [CCOLAMD_INFO2] = i ; (stats [CCOLAMD_INFO3]) ++ ; DEBUG1 (("csymamd: row "ID" col "ID" unsorted/dupl.\n", i, j)) ; } if (mark [i] != j) { if ((both && i != j) || (lower && i > j) || (upper && i < j)) { /* row k of M will contain column indices i and j */ count [i]++ ; count [j]++ ; } } /* mark the row as having been seen in this column */ mark [i] = j ; last_row = i ; } } /* === Compute column pointers of M ===================================== */ /* use output permutation, perm, for column pointers of M */ perm [0] = 0 ; for (j = 1 ; j <= n ; j++) { perm [j] = perm [j-1] + count [j-1] ; } for (j = 0 ; j < n ; j++) { count [j] = perm [j] ; } /* === Construct M ====================================================== */ mnz = perm [n] ; n_row = mnz / 2 ; Mlen = CCOLAMD_recommended (mnz, n_row, n) ; M = (Int *) ((*allocate) (Mlen, sizeof (Int))) ; DEBUG1 (("csymamd: M is "ID"-by-"ID" with "ID" entries, Mlen = %g\n", n_row, n, mnz, (double) Mlen)) ; if (!M) { stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_out_of_memory ; (*release) ((void *) count) ; (*release) ((void *) mark) ; DEBUG1 (("csymamd: allocate M (size %g) failed\n", (double) Mlen)) ; return (FALSE) ; } k = 0 ; if (stats [CCOLAMD_STATUS] == CCOLAMD_OK) { /* Matrix is OK */ for (j = 0 ; j < n ; j++) { ASSERT (p [j+1] - p [j] >= 0) ; for (pp = p [j] ; pp < p [j+1] ; pp++) { i = A [pp] ; ASSERT (i >= 0 && i < n) ; if ((both && i != j) || (lower && i > j) || (upper && i < j)) { /* row k of M contains column indices i and j */ M [count [i]++] = k ; M [count [j]++] = k ; k++ ; } } } } else { /* Matrix is jumbled. Do not add duplicates to M. Unsorted cols OK. */ DEBUG1 (("csymamd: Duplicates in A.\n")) ; for (i = 0 ; i < n ; i++) { mark [i] = -1 ; } for (j = 0 ; j < n ; j++) { ASSERT (p [j+1] - p [j] >= 0) ; for (pp = p [j] ; pp < p [j+1] ; pp++) { i = A [pp] ; ASSERT (i >= 0 && i < n) ; if (mark [i] != j) { if ((both && i != j) || (lower && i > j) || (upper && i= 0 */ { stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_nrow_negative ; stats [CCOLAMD_INFO1] = n_row ; DEBUG1 (("ccolamd: nrow negative "ID"\n", n_row)) ; return (FALSE) ; } if (n_col < 0) /* n_col must be >= 0 */ { stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_ncol_negative ; stats [CCOLAMD_INFO1] = n_col ; DEBUG1 (("ccolamd: ncol negative "ID"\n", n_col)) ; return (FALSE) ; } nnz = p [n_col] ; if (nnz < 0) /* nnz must be >= 0 */ { stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_nnz_negative ; stats [CCOLAMD_INFO1] = nnz ; DEBUG1 (("ccolamd: number of entries negative "ID"\n", nnz)) ; return (FALSE) ; } if (p [0] != 0) { stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_p0_nonzero ; stats [CCOLAMD_INFO1] = p [0] ; DEBUG1 (("ccolamd: p[0] not zero "ID"\n", p [0])) ; return (FALSE) ; } /* === If no knobs, set default knobs =================================== */ if (!knobs) { CCOLAMD_set_defaults (default_knobs) ; knobs = default_knobs ; } aggressive = (knobs [CCOLAMD_AGGRESSIVE] != FALSE) ; order_for_lu = (knobs [CCOLAMD_LU] != FALSE) ; /* === Allocate workspace from array A ================================== */ ok = TRUE ; Col_size = CCOLAMD_C (n_col, &ok) ; Row_size = CCOLAMD_R (n_row, &ok) ; /* min size of A is 2nnz+ncol. cset and cset_start are of size 2ncol+1 */ /* Each of the 5 fronts is of size n_col + 1. InFront is of size nrow. */ /* need = MAX (2*nnz, 4*n_col) + n_col + Col_size + Row_size + (3*n_col+1) + (5*(n_col+1)) + n_row ; */ need = ccolamd_need (nnz, n_row, n_col, &ok) ; if (!ok || need > (size_t) Alen || need > Int_MAX) { /* not enough space in array A to perform the ordering */ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_A_too_small ; stats [CCOLAMD_INFO1] = need ; stats [CCOLAMD_INFO2] = Alen ; DEBUG1 (("ccolamd: Need Alen >= "ID", given "ID"\n", need, Alen)) ; return (FALSE) ; } /* since integer overflow has been check, the following cannot overflow: */ Alen -= Col_size + Row_size + (3*n_col + 1) + 5*(n_col+1) + n_row ; /* Size of A is now Alen >= MAX (2*nnz, 4*n_col) + n_col. The ordering * requires Alen >= 2*nnz + n_col, and the postorder requires * Alen >= 5*n_col. */ ap = Alen ; /* Front array workspace: 5*(n_col+1) + n_row */ if (!Front_npivcol || !Front_nrows || !Front_ncols || !Front_parent || !Front_cols || !Front_cols || !InFront) { Front_npivcol = &A [ap] ; ap += (n_col + 1) ; Front_nrows = &A [ap] ; ap += (n_col + 1) ; Front_ncols = &A [ap] ; ap += (n_col + 1) ; Front_parent = &A [ap] ; ap += (n_col + 1) ; Front_cols = &A [ap] ; ap += (n_col + 1) ; InFront = &A [ap] ; ap += (n_row) ; } else { /* Fronts are present. Leave the additional space as elbow room. */ ap += 5*(n_col+1) + n_row ; ap = Alen ; } /* Workspace for cset management: 3*n_col+1 */ /* cset_start is of size n_col + 1 */ cset_start = &A [ap] ; ap += n_col + 1 ; /* dead_col is of size n_col */ dead_cols = &A [ap] ; ap += n_col ; /* cset is of size n_col */ cset = &A [ap] ; ap += n_col ; /* Col is of size Col_size. The space is shared by temp_cstart and csize */ Col = (CColamd_Col *) &A [ap] ; temp_cstart = (Int *) Col ; /* [ temp_cstart is of size n_col+1 */ csize = temp_cstart + (n_col+1) ; /* csize is of size n_col+1 */ ap += Col_size ; ASSERT (Col_size >= 2*n_col+1) ; /* Row is of size Row_size */ Row = (CColamd_Row *) &A [ap] ; ap += Row_size ; /* Initialize csize & dead_cols to zero */ for (i = 0 ; i < n_col ; i++) { csize [i] = 0 ; dead_cols [i] = 0 ; } /* === Construct the constraint set ===================================== */ if (n_col == 0) { n_cset = 0 ; } else if (cmember == (Int *) NULL) { /* no constraint set; all columns belong to set zero */ n_cset = 1 ; csize [0] = n_col ; DEBUG1 (("no cmember present\n")) ; } else { n_cset = 0 ; for (i = 0 ; i < n_col ; i++) { if (cmember [i] < 0 || cmember [i] > n_col) { stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_invalid_cmember ; DEBUG1 (("ccolamd: malformed cmember \n")) ; return (FALSE) ; } n_cset = MAX (n_cset, cmember [i]) ; csize [cmember [i]]++ ; } /* cset is zero based */ n_cset++ ; } ASSERT ((n_cset >= 0) && (n_cset <= n_col)) ; cset_start [0] = temp_cstart [0] = 0 ; for (i = 1 ; i <= n_cset ; i++) { cset_start [i] = cset_start [i-1] + csize [i-1] ; DEBUG4 ((" cset_start ["ID"] = "ID" \n", i , cset_start [i])) ; temp_cstart [i] = cset_start [i] ; } /* do in reverse order to encourage natural tie-breaking */ if (cmember == (Int *) NULL) { for (i = n_col-1 ; i >= 0 ; i--) { cset [temp_cstart [0]++] = i ; } } else { for (i = n_col-1 ; i >= 0 ; i--) { cset [temp_cstart [cmember [i]]++] = i ; } } /* ] temp_cstart and csize are no longer used */ /* === Construct the row and column data structures ===================== */ if (!init_rows_cols (n_row, n_col, Row, Col, A, p, stats)) { /* input matrix is invalid */ DEBUG1 (("ccolamd: Matrix invalid\n")) ; return (FALSE) ; } /* === Initialize front info ============================================ */ for (col = 0 ; col < n_col ; col++) { Front_npivcol [col] = 0 ; Front_nrows [col] = 0 ; Front_ncols [col] = 0 ; Front_parent [col] = EMPTY ; Front_cols [col] = EMPTY ; } /* === Initialize scores, kill dense rows/columns ======================= */ init_scoring (n_row, n_col, Row, Col, A, p, knobs, &n_row2, &n_col2, &max_deg, cmember, n_cset, cset_start, dead_cols, &ndense_row, &nempty_row, &nnewlyempty_row, &ndense_col, &nempty_col, &nnewlyempty_col) ; ASSERT (n_row2 == n_row - nempty_row - nnewlyempty_row - ndense_row) ; ASSERT (n_col2 == n_col - nempty_col - nnewlyempty_col - ndense_col) ; DEBUG1 (("# dense rows "ID" cols "ID"\n", ndense_row, ndense_col)) ; /* === Order the supercolumns =========================================== */ ngarbage = find_ordering (n_row, n_col, Alen, Row, Col, A, p, #ifndef NDEBUG n_col2, #endif max_deg, 2*nnz, cset, cset_start, #ifndef NDEBUG n_cset, #endif cmember, Front_npivcol, Front_nrows, Front_ncols, Front_parent, Front_cols, &nfr, aggressive, InFront, order_for_lu) ; ASSERT (Alen >= 5*n_col) ; /* === Postorder ======================================================== */ /* A is no longer needed, so use A [0..5*nfr-1] as workspace [ [ */ /* This step requires Alen >= 5*n_col */ Front_child = A ; Front_sibling = Front_child + nfr ; Front_stack = Front_sibling + nfr ; Front_order = Front_stack + nfr ; Front_size = Front_order + nfr ; CCOLAMD_fsize (nfr, Front_size, Front_nrows, Front_ncols, Front_parent, Front_npivcol) ; CCOLAMD_postorder (nfr, Front_parent, Front_npivcol, Front_size, Front_order, Front_child, Front_sibling, Front_stack, Front_cols, cmember) ; /* Front_size, Front_stack, Front_child, Front_sibling no longer needed ] */ /* use A [0..nfr-1] as workspace */ CCOLAMD_apply_order (Front_npivcol, Front_order, A, nfr, nfr) ; CCOLAMD_apply_order (Front_nrows, Front_order, A, nfr, nfr) ; CCOLAMD_apply_order (Front_ncols, Front_order, A, nfr, nfr) ; CCOLAMD_apply_order (Front_parent, Front_order, A, nfr, nfr) ; CCOLAMD_apply_order (Front_cols, Front_order, A, nfr, nfr) ; /* fix the parent to refer to the new numbering */ for (i = 0 ; i < nfr ; i++) { parent = Front_parent [i] ; if (parent != EMPTY) { Front_parent [i] = Front_order [parent] ; } } /* fix InFront to refer to the new numbering */ for (row = 0 ; row < n_row ; row++) { i = InFront [row] ; ASSERT (i >= EMPTY && i < nfr) ; if (i != EMPTY) { InFront [row] = Front_order [i] ; } } /* Front_order longer needed ] */ /* === Order the columns in the fronts ================================== */ /* use A [0..n_col-1] as inverse permutation */ for (i = 0 ; i < n_col ; i++) { A [i] = EMPTY ; } k = 0 ; set1 = 0 ; for (i = 0 ; i < nfr ; i++) { ASSERT (Front_npivcol [i] > 0) ; set2 = CMEMBER (Front_cols [i]) ; while (set1 < set2) { k += dead_cols [set1] ; DEBUG3 (("Skip null/dense columns of set "ID"\n",set1)) ; set1++ ; } set1 = set2 ; for (col = Front_cols [i] ; col != EMPTY ; col = Col [col].nextcol) { ASSERT (col >= 0 && col < n_col) ; DEBUG1 (("ccolamd output ordering: k "ID" col "ID"\n", k, col)) ; p [k] = col ; ASSERT (A [col] == EMPTY) ; cs = CMEMBER (col) ; ASSERT (k >= cset_start [cs] && k < cset_start [cs+1]) ; A [col] = k ; k++ ; } } /* === Order the "dense" and null columns =============================== */ if (n_col2 < n_col) { for (col = 0 ; col < n_col ; col++) { if (A [col] == EMPTY) { k = Col [col].shared2.order ; cs = CMEMBER (col) ; #ifndef NDEBUG dead_cols [cs]-- ; #endif ASSERT (k >= cset_start [cs] && k < cset_start [cs+1]) ; DEBUG1 (("ccolamd output ordering: k "ID" col "ID " (dense or null col)\n", k, col)) ; p [k] = col ; A [col] = k ; } } } #ifndef NDEBUG for (i = 0 ; i < n_cset ; i++) { ASSERT (dead_cols [i] == 0) ; } #endif /* === Return statistics in stats ======================================= */ stats [CCOLAMD_DENSE_ROW] = ndense_row ; stats [CCOLAMD_DENSE_COL] = nempty_row ; stats [CCOLAMD_NEWLY_EMPTY_ROW] = nnewlyempty_row ; stats [CCOLAMD_DENSE_COL] = ndense_col ; stats [CCOLAMD_EMPTY_COL] = nempty_col ; stats [CCOLAMD_NEWLY_EMPTY_COL] = nnewlyempty_col ; ASSERT (ndense_col + nempty_col + nnewlyempty_col == n_col - n_col2) ; if (p_nfr) { *p_nfr = nfr ; } stats [CCOLAMD_DEFRAG_COUNT] = ngarbage ; DEBUG1 (("ccolamd: done.\n")) ; return (TRUE) ; } /* ========================================================================== */ /* === colamd_report ======================================================== */ /* ========================================================================== */ PUBLIC void CCOLAMD_report ( Int stats [CCOLAMD_STATS] ) { print_report ("ccolamd", stats) ; } /* ========================================================================== */ /* === symamd_report ======================================================== */ /* ========================================================================== */ PUBLIC void CSYMAMD_report ( Int stats [CCOLAMD_STATS] ) { print_report ("csymamd", stats) ; } /* ========================================================================== */ /* === NON-USER-CALLABLE ROUTINES: ========================================== */ /* ========================================================================== */ /* There are no user-callable routines beyond this point in the file */ /* ========================================================================== */ /* === init_rows_cols ======================================================= */ /* ========================================================================== */ /* Takes the column form of the matrix in A and creates the row form of the matrix. Also, row and column attributes are stored in the Col and Row structs. If the columns are un-sorted or contain duplicate row indices, this routine will also sort and remove duplicate row indices from the column form of the matrix. Returns FALSE if the matrix is invalid, TRUE otherwise. Not user-callable. */ PRIVATE Int init_rows_cols /* returns TRUE if OK, or FALSE otherwise */ ( /* === Parameters ======================================================= */ Int n_row, /* number of rows of A */ Int n_col, /* number of columns of A */ CColamd_Row Row [ ], /* of size n_row+1 */ CColamd_Col Col [ ], /* of size n_col+1 */ Int A [ ], /* row indices of A, of size Alen */ Int p [ ], /* pointers to columns in A, of size n_col+1 */ Int stats [CCOLAMD_STATS] /* colamd statistics */ ) { /* === Local variables ================================================== */ Int col ; /* a column index */ Int row ; /* a row index */ Int *cp ; /* a column pointer */ Int *cp_end ; /* a pointer to the end of a column */ Int *rp ; /* a row pointer */ Int *rp_end ; /* a pointer to the end of a row */ Int last_row ; /* previous row */ /* === Initialize columns, and check column pointers ==================== */ for (col = 0 ; col < n_col ; col++) { Col [col].start = p [col] ; Col [col].length = p [col+1] - p [col] ; if (Col [col].length < 0) { /* column pointers must be non-decreasing */ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_col_length_negative ; stats [CCOLAMD_INFO1] = col ; stats [CCOLAMD_INFO2] = Col [col].length ; DEBUG1 (("ccolamd: col "ID" length "ID" < 0\n", col, Col [col].length)) ; return (FALSE) ; } Col [col].shared1.thickness = 1 ; Col [col].shared2.score = 0 ; Col [col].shared3.prev = EMPTY ; Col [col].shared4.degree_next = EMPTY ; Col [col].nextcol = EMPTY ; Col [col].lastcol = col ; } /* p [0..n_col] no longer needed, used as "head" in subsequent routines */ /* === Scan columns, compute row degrees, and check row indices ========= */ stats [CCOLAMD_INFO3] = 0 ; /* number of duplicate or unsorted row indices*/ for (row = 0 ; row < n_row ; row++) { Row [row].length = 0 ; Row [row].shared2.mark = -1 ; Row [row].thickness = 1 ; Row [row].front = EMPTY ; } for (col = 0 ; col < n_col ; col++) { DEBUG1 (("\nCcolamd input column "ID":\n", col)) ; last_row = -1 ; cp = &A [p [col]] ; cp_end = &A [p [col+1]] ; while (cp < cp_end) { row = *cp++ ; DEBUG1 (("row: "ID"\n", row)) ; /* make sure row indices within range */ if (row < 0 || row >= n_row) { stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_row_index_out_of_bounds ; stats [CCOLAMD_INFO1] = col ; stats [CCOLAMD_INFO2] = row ; stats [CCOLAMD_INFO3] = n_row ; DEBUG1 (("row "ID" col "ID" out of bounds\n", row, col)) ; return (FALSE) ; } if (row <= last_row || Row [row].shared2.mark == col) { /* row index are unsorted or repeated (or both), thus col */ /* is jumbled. This is a notice, not an error condition. */ stats [CCOLAMD_STATUS] = CCOLAMD_OK_BUT_JUMBLED ; stats [CCOLAMD_INFO1] = col ; stats [CCOLAMD_INFO2] = row ; (stats [CCOLAMD_INFO3]) ++ ; DEBUG1 (("row "ID" col "ID" unsorted/duplicate\n", row, col)) ; } if (Row [row].shared2.mark != col) { Row [row].length++ ; } else { /* this is a repeated entry in the column, */ /* it will be removed */ Col [col].length-- ; } /* mark the row as having been seen in this column */ Row [row].shared2.mark = col ; last_row = row ; } } /* === Compute row pointers ============================================= */ /* row form of the matrix starts directly after the column */ /* form of matrix in A */ Row [0].start = p [n_col] ; Row [0].shared1.p = Row [0].start ; Row [0].shared2.mark = -1 ; for (row = 1 ; row < n_row ; row++) { Row [row].start = Row [row-1].start + Row [row-1].length ; Row [row].shared1.p = Row [row].start ; Row [row].shared2.mark = -1 ; } /* === Create row form ================================================== */ if (stats [CCOLAMD_STATUS] == CCOLAMD_OK_BUT_JUMBLED) { /* if cols jumbled, watch for repeated row indices */ for (col = 0 ; col < n_col ; col++) { cp = &A [p [col]] ; cp_end = &A [p [col+1]] ; while (cp < cp_end) { row = *cp++ ; if (Row [row].shared2.mark != col) { A [(Row [row].shared1.p)++] = col ; Row [row].shared2.mark = col ; } } } } else { /* if cols not jumbled, we don't need the mark (this is faster) */ for (col = 0 ; col < n_col ; col++) { cp = &A [p [col]] ; cp_end = &A [p [col+1]] ; while (cp < cp_end) { A [(Row [*cp++].shared1.p)++] = col ; } } } /* === Clear the row marks and set row degrees ========================== */ for (row = 0 ; row < n_row ; row++) { Row [row].shared2.mark = 0 ; Row [row].shared1.degree = Row [row].length ; } /* === See if we need to re-create columns ============================== */ if (stats [CCOLAMD_STATUS] == CCOLAMD_OK_BUT_JUMBLED) { DEBUG1 (("ccolamd: reconstructing column form, matrix jumbled\n")) ; #ifndef NDEBUG /* make sure column lengths are correct */ for (col = 0 ; col < n_col ; col++) { p [col] = Col [col].length ; } for (row = 0 ; row < n_row ; row++) { rp = &A [Row [row].start] ; rp_end = rp + Row [row].length ; while (rp < rp_end) { p [*rp++]-- ; } } for (col = 0 ; col < n_col ; col++) { ASSERT (p [col] == 0) ; } /* now p is all zero (different than when debugging is turned off) */ #endif /* === Compute col pointers ========================================= */ /* col form of the matrix starts at A [0]. */ /* Note, we may have a gap between the col form and the row */ /* form if there were duplicate entries, if so, it will be */ /* removed upon the first garbage collection */ Col [0].start = 0 ; p [0] = Col [0].start ; for (col = 1 ; col < n_col ; col++) { /* note that the lengths here are for pruned columns, i.e. */ /* no duplicate row indices will exist for these columns */ Col [col].start = Col [col-1].start + Col [col-1].length ; p [col] = Col [col].start ; } /* === Re-create col form =========================================== */ for (row = 0 ; row < n_row ; row++) { rp = &A [Row [row].start] ; rp_end = rp + Row [row].length ; while (rp < rp_end) { A [(p [*rp++])++] = row ; } } } /* === Done. Matrix is not (or no longer) jumbled ====================== */ return (TRUE) ; } /* ========================================================================== */ /* === init_scoring ========================================================= */ /* ========================================================================== */ /* Kills dense or empty columns and rows, calculates an initial score for each column, and places all columns in the degree lists. Not user-callable. */ PRIVATE void init_scoring ( /* === Parameters ======================================================= */ Int n_row, /* number of rows of A */ Int n_col, /* number of columns of A */ CColamd_Row Row [ ], /* of size n_row+1 */ CColamd_Col Col [ ], /* of size n_col+1 */ Int A [ ], /* column form and row form of A */ Int head [ ], /* of size n_col+1 */ double knobs [CCOLAMD_KNOBS],/* parameters */ Int *p_n_row2, /* number of non-dense, non-empty rows */ Int *p_n_col2, /* number of non-dense, non-empty columns */ Int *p_max_deg, /* maximum row degree */ Int cmember [ ], Int n_cset, Int cset_start [ ], Int dead_cols [ ], Int *p_ndense_row, /* number of dense rows */ Int *p_nempty_row, /* number of original empty rows */ Int *p_nnewlyempty_row, /* number of newly empty rows */ Int *p_ndense_col, /* number of dense cols (excl "empty" cols) */ Int *p_nempty_col, /* number of original empty cols */ Int *p_nnewlyempty_col /* number of newly empty cols */ ) { /* === Local variables ================================================== */ Int c ; /* a column index */ Int r, row ; /* a row index */ Int *cp ; /* a column pointer */ Int deg ; /* degree of a row or column */ Int *cp_end ; /* a pointer to the end of a column */ Int *new_cp ; /* new column pointer */ Int col_length ; /* length of pruned column */ Int score ; /* current column score */ Int n_col2 ; /* number of non-dense, non-empty columns */ Int n_row2 ; /* number of non-dense, non-empty rows */ Int dense_row_count ; /* remove rows with more entries than this */ Int dense_col_count ; /* remove cols with more entries than this */ Int max_deg ; /* maximum row degree */ Int s ; /* a cset index */ Int ndense_row ; /* number of dense rows */ Int nempty_row ; /* number of empty rows */ Int nnewlyempty_row ; /* number of newly empty rows */ Int ndense_col ; /* number of dense cols (excl "empty" cols) */ Int nempty_col ; /* number of original empty cols */ Int nnewlyempty_col ; /* number of newly empty cols */ Int ne ; #ifndef NDEBUG Int debug_count ; /* debug only. */ #endif /* === Extract knobs ==================================================== */ /* Note: if knobs contains a NaN, this is undefined: */ if (knobs [CCOLAMD_DENSE_ROW] < 0) { /* only remove completely dense rows */ dense_row_count = n_col-1 ; } else { dense_row_count = DENSE_DEGREE (knobs [CCOLAMD_DENSE_ROW], n_col) ; } if (knobs [CCOLAMD_DENSE_COL] < 0) { /* only remove completely dense columns */ dense_col_count = n_row-1 ; } else { dense_col_count = DENSE_DEGREE (knobs [CCOLAMD_DENSE_COL], MIN (n_row, n_col)) ; } DEBUG1 (("densecount: "ID" "ID"\n", dense_row_count, dense_col_count)) ; max_deg = 0 ; n_col2 = n_col ; n_row2 = n_row ; /* Set the head array for bookkeeping of dense and empty columns. */ /* This will be used as hash buckets later. */ for (s = 0 ; s < n_cset ; s++) { head [s] = cset_start [s+1] ; } ndense_col = 0 ; nempty_col = 0 ; nnewlyempty_col = 0 ; ndense_row = 0 ; nempty_row = 0 ; nnewlyempty_row = 0 ; /* === Kill empty columns =============================================== */ /* Put the empty columns at the end in their natural order, so that LU */ /* factorization can proceed as far as possible. */ for (c = n_col-1 ; c >= 0 ; c--) { deg = Col [c].length ; if (deg == 0) { /* this is a empty column, kill and order it last of its cset */ Col [c].shared2.order = --head [CMEMBER (c)] ; --n_col2 ; dead_cols [CMEMBER (c)] ++ ; nempty_col++ ; KILL_PRINCIPAL_COL (c) ; } } DEBUG1 (("ccolamd: null columns killed: "ID"\n", n_col - n_col2)) ; /* === Kill dense columns =============================================== */ /* Put the dense columns at the end, in their natural order */ for (c = n_col-1 ; c >= 0 ; c--) { /* skip any dead columns */ if (COL_IS_DEAD (c)) { continue ; } deg = Col [c].length ; if (deg > dense_col_count) { /* this is a dense column, kill and order it last of its cset */ Col [c].shared2.order = --head [CMEMBER (c)] ; --n_col2 ; dead_cols [CMEMBER (c)] ++ ; ndense_col++ ; /* decrement the row degrees */ cp = &A [Col [c].start] ; cp_end = cp + Col [c].length ; while (cp < cp_end) { Row [*cp++].shared1.degree-- ; } KILL_PRINCIPAL_COL (c) ; } } DEBUG1 (("Dense and null columns killed: "ID"\n", n_col - n_col2)) ; /* === Kill dense and empty rows ======================================== */ /* Note that there can now be empty rows, since dense columns have * been deleted. These are "newly" empty rows. */ ne = 0 ; for (r = 0 ; r < n_row ; r++) { deg = Row [r].shared1.degree ; ASSERT (deg >= 0 && deg <= n_col) ; if (deg > dense_row_count) { /* There is at least one dense row. Continue ordering, but */ /* symbolic factorization will be redone after ccolamd is done.*/ ndense_row++ ; } if (deg == 0) { /* this is a newly empty row, or original empty row */ ne++ ; } if (deg > dense_row_count || deg == 0) { /* kill a dense or empty row */ KILL_ROW (r) ; Row [r].thickness = 0 ; --n_row2 ; } else { /* keep track of max degree of remaining rows */ max_deg = MAX (max_deg, deg) ; } } nnewlyempty_row = ne - nempty_row ; DEBUG1 (("ccolamd: Dense and null rows killed: "ID"\n", n_row - n_row2)) ; /* === Compute initial column scores ==================================== */ /* At this point the row degrees are accurate. They reflect the number */ /* of "live" (non-dense) columns in each row. No empty rows exist. */ /* Some "live" columns may contain only dead rows, however. These are */ /* pruned in the code below. */ /* now find the initial COLMMD score for each column */ for (c = n_col-1 ; c >= 0 ; c--) { /* skip dead column */ if (COL_IS_DEAD (c)) { continue ; } score = 0 ; cp = &A [Col [c].start] ; new_cp = cp ; cp_end = cp + Col [c].length ; while (cp < cp_end) { /* get a row */ row = *cp++ ; /* skip if dead */ if (ROW_IS_DEAD (row)) { continue ; } /* compact the column */ *new_cp++ = row ; /* add row's external degree */ score += Row [row].shared1.degree - 1 ; /* guard against integer overflow */ score = MIN (score, n_col) ; } /* determine pruned column length */ col_length = (Int) (new_cp - &A [Col [c].start]) ; if (col_length == 0) { /* a newly-made null column (all rows in this col are "dense" */ /* and have already been killed) */ DEBUG1 (("Newly null killed: "ID"\n", c)) ; Col [c].shared2.order = -- head [CMEMBER (c)] ; --n_col2 ; dead_cols [CMEMBER (c)] ++ ; nnewlyempty_col++ ; KILL_PRINCIPAL_COL (c) ; } else { /* set column length and set score */ ASSERT (score >= 0) ; ASSERT (score <= n_col) ; Col [c].length = col_length ; Col [c].shared2.score = score ; } } DEBUG1 (("ccolamd: Dense, null, and newly-null columns killed: "ID"\n", n_col-n_col2)) ; /* At this point, all empty rows and columns are dead. All live columns */ /* are "clean" (containing no dead rows) and simplicial (no supercolumns */ /* yet). Rows may contain dead columns, but all live rows contain at */ /* least one live column. */ #ifndef NDEBUG debug_count = 0 ; #endif /* clear the hash buckets */ for (c = 0 ; c <= n_col ; c++) { head [c] = EMPTY ; } #ifndef NDEBUG debug_structures (n_row, n_col, Row, Col, A, cmember, cset_start) ; #endif /* === Return number of remaining columns, and max row degree =========== */ *p_n_col2 = n_col2 ; *p_n_row2 = n_row2 ; *p_max_deg = max_deg ; *p_ndense_row = ndense_row ; *p_nempty_row = nempty_row ; /* original empty rows */ *p_nnewlyempty_row = nnewlyempty_row ; *p_ndense_col = ndense_col ; *p_nempty_col = nempty_col ; /* original empty cols */ *p_nnewlyempty_col = nnewlyempty_col ; } /* ========================================================================== */ /* === find_ordering ======================================================== */ /* ========================================================================== */ /* * Order the principal columns of the supercolumn form of the matrix * (no supercolumns on input). Uses a minimum approximate column minimum * degree ordering method. Not user-callable. */ PRIVATE Int find_ordering /* return the number of garbage collections */ ( /* === Parameters ======================================================= */ Int n_row, /* number of rows of A */ Int n_col, /* number of columns of A */ Int Alen, /* size of A, 2*nnz + n_col or larger */ CColamd_Row Row [ ], /* of size n_row+1 */ CColamd_Col Col [ ], /* of size n_col+1 */ Int A [ ], /* column form and row form of A */ Int head [ ], /* of size n_col+1 */ #ifndef NDEBUG Int n_col2, /* Remaining columns to order */ #endif Int max_deg, /* Maximum row degree */ Int pfree, /* index of first free slot (2*nnz on entry) */ Int cset [ ], /* constraint set of A */ Int cset_start [ ], /* pointer to the start of every cset */ #ifndef NDEBUG Int n_cset, /* number of csets */ #endif Int cmember [ ], /* col -> cset mapping */ Int Front_npivcol [ ], Int Front_nrows [ ], Int Front_ncols [ ], Int Front_parent [ ], Int Front_cols [ ], Int *p_nfr, /* number of fronts */ Int aggressive, Int InFront [ ], Int order_for_lu ) { /* === Local variables ================================================== */ Int k ; /* current pivot ordering step */ Int pivot_col ; /* current pivot column */ Int *cp ; /* a column pointer */ Int *rp ; /* a row pointer */ Int pivot_row ; /* current pivot row */ Int *new_cp ; /* modified column pointer */ Int *new_rp ; /* modified row pointer */ Int pivot_row_start ; /* pointer to start of pivot row */ Int pivot_row_degree ; /* number of columns in pivot row */ Int pivot_row_length ; /* number of supercolumns in pivot row */ Int pivot_col_score ; /* score of pivot column */ Int needed_memory ; /* free space needed for pivot row */ Int *cp_end ; /* pointer to the end of a column */ Int *rp_end ; /* pointer to the end of a row */ Int row ; /* a row index */ Int col ; /* a column index */ Int max_score ; /* maximum possible score */ Int cur_score ; /* score of current column */ unsigned Int hash ; /* hash value for supernode detection */ Int head_column ; /* head of hash bucket */ Int first_col ; /* first column in hash bucket */ Int tag_mark ; /* marker value for mark array */ Int row_mark ; /* Row [row].shared2.mark */ Int set_difference ; /* set difference size of row with pivot row */ Int min_score ; /* smallest column score */ Int col_thickness ; /* "thickness" (no. of columns in a supercol) */ Int max_mark ; /* maximum value of tag_mark */ Int pivot_col_thickness ; /* number of columns represented by pivot col */ Int prev_col ; /* Used by Dlist operations. */ Int next_col ; /* Used by Dlist operations. */ Int ngarbage ; /* number of garbage collections performed */ Int current_set ; /* consraint set that is being ordered */ Int score ; /* score of a column */ Int colstart ; /* pointer to first column in current cset */ Int colend ; /* pointer to last column in current cset */ Int deadcol ; /* number of dense & null columns in a cset */ #ifndef NDEBUG Int debug_d ; /* debug loop counter */ Int debug_step = 0 ; /* debug loop counter */ Int cols_thickness = 0 ; /* the thickness of the columns in current */ /* cset degreelist and in pivot row pattern. */ #endif Int pivot_row_thickness ; /* number of rows represented by pivot row */ Int nfr = 0 ; /* number of fronts */ Int child ; /* === Initialization and clear mark ==================================== */ max_mark = Int_MAX - n_col ; /* Int_MAX defined in */ tag_mark = clear_mark (0, max_mark, n_row, Row) ; min_score = 0 ; ngarbage = 0 ; current_set = -1 ; deadcol = 0 ; DEBUG1 (("ccolamd: Ordering, n_col2="ID"\n", n_col2)) ; for (row = 0 ; row < n_row ; row++) { InFront [row] = EMPTY ; } /* === Order the columns ================================================ */ for (k = 0 ; k < n_col ; /* 'k' is incremented below */) { /* make sure degree list isn't empty */ ASSERT (min_score >= 0) ; ASSERT (min_score <= n_col) ; ASSERT (head [min_score] >= EMPTY) ; #ifndef NDEBUG for (debug_d = 0 ; debug_d < min_score ; debug_d++) { ASSERT (head [debug_d] == EMPTY) ; } #endif /* Initialize the degree list with columns from next non-empty cset */ while ((k+deadcol) == cset_start [current_set+1]) { current_set++ ; DEBUG1 (("\n\n\n============ CSET: "ID"\n", current_set)) ; k += deadcol ; /* jump to start of next cset */ deadcol = 0 ; /* reset dead column count */ ASSERT ((current_set == n_cset) == (k == n_col)) ; /* return if all columns are ordered. */ if (k == n_col) { *p_nfr = nfr ; return (ngarbage) ; } #ifndef NDEBUG for (col = 0 ; col <= n_col ; col++) { ASSERT (head [col] == EMPTY) ; } #endif min_score = n_col ; colstart = cset_start [current_set] ; colend = cset_start [current_set+1] ; while (colstart < colend) { col = cset [colstart++] ; if (COL_IS_DEAD(col)) { DEBUG1 (("Column "ID" is dead\n", col)) ; /* count dense and null columns */ if (Col [col].shared2.order != EMPTY) { deadcol++ ; } continue ; } /* only add principal columns in current set to degree lists */ ASSERT (CMEMBER (col) == current_set) ; score = Col [col].shared2.score ; DEBUG1 (("Column "ID" is alive, score "ID"\n", col, score)) ; ASSERT (min_score >= 0) ; ASSERT (min_score <= n_col) ; ASSERT (score >= 0) ; ASSERT (score <= n_col) ; ASSERT (head [score] >= EMPTY) ; /* now add this column to dList at proper score location */ next_col = head [score] ; Col [col].shared3.prev = EMPTY ; Col [col].shared4.degree_next = next_col ; /* if there already was a column with the same score, set its */ /* previous pointer to this new column */ if (next_col != EMPTY) { Col [next_col].shared3.prev = col ; } head [score] = col ; /* see if this score is less than current min */ min_score = MIN (min_score, score) ; } #ifndef NDEBUG DEBUG1 (("degree lists initialized \n")) ; debug_deg_lists (n_row, n_col, Row, Col, head, min_score, ((cset_start [current_set+1]-cset_start [current_set])-deadcol), max_deg) ; #endif } #ifndef NDEBUG if (debug_step % 100 == 0) { DEBUG2 (("\n... Step k: "ID" out of n_col2: "ID"\n", k, n_col2)) ; } else { DEBUG3 (("\n------Step k: "ID" out of n_col2: "ID"\n", k, n_col2)) ; } debug_step++ ; DEBUG1 (("start of step k="ID": ", k)) ; debug_deg_lists (n_row, n_col, Row, Col, head, min_score, cset_start [current_set+1]-(k+deadcol), max_deg) ; debug_matrix (n_row, n_col, Row, Col, A) ; #endif /* === Select pivot column, and order it ============================ */ while (head [min_score] == EMPTY && min_score < n_col) { min_score++ ; } pivot_col = head [min_score] ; ASSERT (pivot_col >= 0 && pivot_col <= n_col) ; next_col = Col [pivot_col].shared4.degree_next ; head [min_score] = next_col ; if (next_col != EMPTY) { Col [next_col].shared3.prev = EMPTY ; } ASSERT (COL_IS_ALIVE (pivot_col)) ; /* remember score for defrag check */ pivot_col_score = Col [pivot_col].shared2.score ; /* the pivot column is the kth column in the pivot order */ Col [pivot_col].shared2.order = k ; /* increment order count by column thickness */ pivot_col_thickness = Col [pivot_col].shared1.thickness ; k += pivot_col_thickness ; ASSERT (pivot_col_thickness > 0) ; DEBUG3 (("Pivot col: "ID" thick "ID"\n", pivot_col, pivot_col_thickness)) ; /* === Garbage_collection, if necessary ============================= */ needed_memory = MIN (pivot_col_score, n_col - k) ; if (pfree + needed_memory >= Alen) { pfree = garbage_collection (n_row, n_col, Row, Col, A, &A [pfree]) ; ngarbage++ ; /* after garbage collection we will have enough */ ASSERT (pfree + needed_memory < Alen) ; /* garbage collection has wiped out Row [ ].shared2.mark array */ tag_mark = clear_mark (0, max_mark, n_row, Row) ; #ifndef NDEBUG debug_matrix (n_row, n_col, Row, Col, A) ; #endif } /* === Compute pivot row pattern ==================================== */ /* get starting location for this new merged row */ pivot_row_start = pfree ; /* initialize new row counts to zero */ pivot_row_degree = 0 ; pivot_row_thickness = 0 ; /* tag pivot column as having been visited so it isn't included */ /* in merged pivot row */ Col [pivot_col].shared1.thickness = -pivot_col_thickness ; /* pivot row is the union of all rows in the pivot column pattern */ cp = &A [Col [pivot_col].start] ; cp_end = cp + Col [pivot_col].length ; while (cp < cp_end) { /* get a row */ row = *cp++ ; ASSERT (row >= 0 && row < n_row) ; DEBUG4 (("Pivcol pattern "ID" "ID"\n", ROW_IS_ALIVE (row), row)) ; /* skip if row is dead */ if (ROW_IS_ALIVE (row)) { /* sum the thicknesses of all the rows */ pivot_row_thickness += Row [row].thickness ; rp = &A [Row [row].start] ; rp_end = rp + Row [row].length ; while (rp < rp_end) { /* get a column */ col = *rp++ ; /* add the column, if alive and untagged */ col_thickness = Col [col].shared1.thickness ; if (col_thickness > 0 && COL_IS_ALIVE (col)) { /* tag column in pivot row */ Col [col].shared1.thickness = -col_thickness ; ASSERT (pfree < Alen) ; /* place column in pivot row */ A [pfree++] = col ; pivot_row_degree += col_thickness ; DEBUG4 (("\t\t\tNew live col in pivrow: "ID"\n",col)) ; } #ifndef NDEBUG if (col_thickness < 0 && COL_IS_ALIVE (col)) { DEBUG4 (("\t\t\tOld live col in pivrow: "ID"\n",col)) ; } #endif } } } /* pivot_row_thickness is the number of rows in frontal matrix */ /* including both pivotal rows and nonpivotal rows */ /* clear tag on pivot column */ Col [pivot_col].shared1.thickness = pivot_col_thickness ; max_deg = MAX (max_deg, pivot_row_degree) ; #ifndef NDEBUG DEBUG3 (("check2\n")) ; debug_mark (n_row, Row, tag_mark, max_mark) ; #endif /* === Kill all rows used to construct pivot row ==================== */ /* also kill pivot row, temporarily */ cp = &A [Col [pivot_col].start] ; cp_end = cp + Col [pivot_col].length ; while (cp < cp_end) { /* may be killing an already dead row */ row = *cp++ ; DEBUG3 (("Kill row in pivot col: "ID"\n", row)) ; ASSERT (row >= 0 && row < n_row) ; if (ROW_IS_ALIVE (row)) { if (Row [row].front != EMPTY) { /* This row represents a frontal matrix. */ /* Row [row].front is a child of current front */ child = Row [row].front ; Front_parent [child] = nfr ; DEBUG1 (("Front "ID" => front "ID", normal\n", child, nfr)); } else { /* This is an original row. Keep track of which front * is its parent in the row-merge tree. */ InFront [row] = nfr ; DEBUG1 (("Row "ID" => front "ID", normal\n", row, nfr)) ; } } KILL_ROW (row) ; Row [row].thickness = 0 ; } /* === Select a row index to use as the new pivot row =============== */ pivot_row_length = pfree - pivot_row_start ; if (pivot_row_length > 0) { /* pick the "pivot" row arbitrarily (first row in col) */ pivot_row = A [Col [pivot_col].start] ; DEBUG3 (("Pivotal row is "ID"\n", pivot_row)) ; } else { /* there is no pivot row, since it is of zero length */ pivot_row = EMPTY ; ASSERT (pivot_row_length == 0) ; } ASSERT (Col [pivot_col].length > 0 || pivot_row_length == 0) ; /* === Approximate degree computation =============================== */ /* Here begins the computation of the approximate degree. The column */ /* score is the sum of the pivot row "length", plus the size of the */ /* set differences of each row in the column minus the pattern of the */ /* pivot row itself. The column ("thickness") itself is also */ /* excluded from the column score (we thus use an approximate */ /* external degree). */ /* The time taken by the following code (compute set differences, and */ /* add them up) is proportional to the size of the data structure */ /* being scanned - that is, the sum of the sizes of each column in */ /* the pivot row. Thus, the amortized time to compute a column score */ /* is proportional to the size of that column (where size, in this */ /* context, is the column "length", or the number of row indices */ /* in that column). The number of row indices in a column is */ /* monotonically non-decreasing, from the length of the original */ /* column on input to colamd. */ /* === Compute set differences ====================================== */ DEBUG3 (("** Computing set differences phase. **\n")) ; /* pivot row is currently dead - it will be revived later. */ DEBUG3 (("Pivot row: ")) ; /* for each column in pivot row */ rp = &A [pivot_row_start] ; rp_end = rp + pivot_row_length ; while (rp < rp_end) { col = *rp++ ; ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ; DEBUG3 (("Col: "ID"\n", col)) ; /* clear tags used to construct pivot row pattern */ col_thickness = -Col [col].shared1.thickness ; ASSERT (col_thickness > 0) ; Col [col].shared1.thickness = col_thickness ; /* === Remove column from degree list =========================== */ /* only columns in current_set will be in degree list */ if (CMEMBER (col) == current_set) { #ifndef NDEBUG cols_thickness += col_thickness ; #endif cur_score = Col [col].shared2.score ; prev_col = Col [col].shared3.prev ; next_col = Col [col].shared4.degree_next ; DEBUG3 ((" cur_score "ID" prev_col "ID" next_col "ID"\n", cur_score, prev_col, next_col)) ; ASSERT (cur_score >= 0) ; ASSERT (cur_score <= n_col) ; ASSERT (cur_score >= EMPTY) ; if (prev_col == EMPTY) { head [cur_score] = next_col ; } else { Col [prev_col].shared4.degree_next = next_col ; } if (next_col != EMPTY) { Col [next_col].shared3.prev = prev_col ; } } /* === Scan the column ========================================== */ cp = &A [Col [col].start] ; cp_end = cp + Col [col].length ; while (cp < cp_end) { /* get a row */ row = *cp++ ; row_mark = Row [row].shared2.mark ; /* skip if dead */ if (ROW_IS_MARKED_DEAD (row_mark)) { continue ; } ASSERT (row != pivot_row) ; set_difference = row_mark - tag_mark ; /* check if the row has been seen yet */ if (set_difference < 0) { ASSERT (Row [row].shared1.degree <= max_deg) ; set_difference = Row [row].shared1.degree ; } /* subtract column thickness from this row's set difference */ set_difference -= col_thickness ; ASSERT (set_difference >= 0) ; /* absorb this row if the set difference becomes zero */ if (set_difference == 0 && aggressive) { DEBUG3 (("aggressive absorption. Row: "ID"\n", row)) ; if (Row [row].front != EMPTY) { /* Row [row].front is a child of current front. */ child = Row [row].front ; Front_parent [child] = nfr ; DEBUG1 (("Front "ID" => front "ID", aggressive\n", child, nfr)) ; } else { /* this is an original row. Keep track of which front * assembles it, for the row-merge tree */ InFront [row] = nfr ; DEBUG1 (("Row "ID" => front "ID", aggressive\n", row, nfr)) ; } KILL_ROW (row) ; /* sum the thicknesses of all the rows */ pivot_row_thickness += Row [row].thickness ; Row [row].thickness = 0 ; } else { /* save the new mark */ Row [row].shared2.mark = set_difference + tag_mark ; } } } #ifndef NDEBUG debug_deg_lists (n_row, n_col, Row, Col, head, min_score, cset_start [current_set+1]-(k+deadcol)-(cols_thickness), max_deg) ; cols_thickness = 0 ; #endif /* === Add up set differences for each column ======================= */ DEBUG3 (("** Adding set differences phase. **\n")) ; /* for each column in pivot row */ rp = &A [pivot_row_start] ; rp_end = rp + pivot_row_length ; while (rp < rp_end) { /* get a column */ col = *rp++ ; ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ; hash = 0 ; cur_score = 0 ; cp = &A [Col [col].start] ; /* compact the column */ new_cp = cp ; cp_end = cp + Col [col].length ; DEBUG4 (("Adding set diffs for Col: "ID".\n", col)) ; while (cp < cp_end) { /* get a row */ row = *cp++ ; ASSERT (row >= 0 && row < n_row) ; row_mark = Row [row].shared2.mark ; /* skip if dead */ if (ROW_IS_MARKED_DEAD (row_mark)) { DEBUG4 ((" Row "ID", dead\n", row)) ; continue ; } DEBUG4 ((" Row "ID", set diff "ID"\n", row, row_mark-tag_mark)); ASSERT (row_mark >= tag_mark) ; /* compact the column */ *new_cp++ = row ; /* compute hash function */ hash += row ; /* add set difference */ cur_score += row_mark - tag_mark ; /* integer overflow... */ cur_score = MIN (cur_score, n_col) ; } /* recompute the column's length */ Col [col].length = (Int) (new_cp - &A [Col [col].start]) ; /* === Further mass elimination ================================= */ if (Col [col].length == 0 && CMEMBER (col) == current_set) { DEBUG4 (("further mass elimination. Col: "ID"\n", col)) ; /* nothing left but the pivot row in this column */ KILL_PRINCIPAL_COL (col) ; pivot_row_degree -= Col [col].shared1.thickness ; ASSERT (pivot_row_degree >= 0) ; /* order it */ Col [col].shared2.order = k ; /* increment order count by column thickness */ k += Col [col].shared1.thickness ; pivot_col_thickness += Col [col].shared1.thickness ; /* add to column list of front */ #ifndef NDEBUG DEBUG1 (("Mass")) ; dump_super (col, Col, n_col) ; #endif Col [Col [col].lastcol].nextcol = Front_cols [nfr] ; Front_cols [nfr] = col ; } else { /* === Prepare for supercolumn detection ==================== */ DEBUG4 (("Preparing supercol detection for Col: "ID".\n", col)); /* save score so far */ Col [col].shared2.score = cur_score ; /* add column to hash table, for supercolumn detection */ hash %= n_col + 1 ; DEBUG4 ((" Hash = "ID", n_col = "ID".\n", hash, n_col)) ; ASSERT (((Int) hash) <= n_col) ; head_column = head [hash] ; if (head_column > EMPTY) { /* degree list "hash" is non-empty, use prev (shared3) of */ /* first column in degree list as head of hash bucket */ first_col = Col [head_column].shared3.headhash ; Col [head_column].shared3.headhash = col ; } else { /* degree list "hash" is empty, use head as hash bucket */ first_col = - (head_column + 2) ; head [hash] = - (col + 2) ; } Col [col].shared4.hash_next = first_col ; /* save hash function in Col [col].shared3.hash */ Col [col].shared3.hash = (Int) hash ; ASSERT (COL_IS_ALIVE (col)) ; } } /* The approximate external column degree is now computed. */ /* === Supercolumn detection ======================================== */ DEBUG3 (("** Supercolumn detection phase. **\n")) ; detect_super_cols ( #ifndef NDEBUG n_col, Row, #endif Col, A, head, pivot_row_start, pivot_row_length, cmember) ; /* === Kill the pivotal column ====================================== */ DEBUG1 ((" KILLING column detect supercols "ID" \n", pivot_col)) ; KILL_PRINCIPAL_COL (pivot_col) ; /* add columns to column list of front */ #ifndef NDEBUG DEBUG1 (("Pivot")) ; dump_super (pivot_col, Col, n_col) ; #endif Col [Col [pivot_col].lastcol].nextcol = Front_cols [nfr] ; Front_cols [nfr] = pivot_col ; /* === Clear mark =================================================== */ tag_mark = clear_mark (tag_mark+max_deg+1, max_mark, n_row, Row) ; #ifndef NDEBUG DEBUG3 (("check3\n")) ; debug_mark (n_row, Row, tag_mark, max_mark) ; #endif /* === Finalize the new pivot row, and column scores ================ */ DEBUG3 (("** Finalize scores phase. **\n")) ; /* for each column in pivot row */ rp = &A [pivot_row_start] ; /* compact the pivot row */ new_rp = rp ; rp_end = rp + pivot_row_length ; while (rp < rp_end) { col = *rp++ ; /* skip dead columns */ if (COL_IS_DEAD (col)) { continue ; } *new_rp++ = col ; /* add new pivot row to column */ A [Col [col].start + (Col [col].length++)] = pivot_row ; /* retrieve score so far and add on pivot row's degree. */ /* (we wait until here for this in case the pivot */ /* row's degree was reduced due to mass elimination). */ cur_score = Col [col].shared2.score + pivot_row_degree ; /* calculate the max possible score as the number of */ /* external columns minus the 'k' value minus the */ /* columns thickness */ max_score = n_col - k - Col [col].shared1.thickness ; /* make the score the external degree of the union-of-rows */ cur_score -= Col [col].shared1.thickness ; /* make sure score is less or equal than the max score */ cur_score = MIN (cur_score, max_score) ; ASSERT (cur_score >= 0) ; /* store updated score */ Col [col].shared2.score = cur_score ; /* === Place column back in degree list ========================= */ if (CMEMBER (col) == current_set) { ASSERT (min_score >= 0) ; ASSERT (min_score <= n_col) ; ASSERT (cur_score >= 0) ; ASSERT (cur_score <= n_col) ; ASSERT (head [cur_score] >= EMPTY) ; next_col = head [cur_score] ; Col [col].shared4.degree_next = next_col ; Col [col].shared3.prev = EMPTY ; if (next_col != EMPTY) { Col [next_col].shared3.prev = col ; } head [cur_score] = col ; /* see if this score is less than current min */ min_score = MIN (min_score, cur_score) ; } else { Col [col].shared4.degree_next = EMPTY ; Col [col].shared3.prev = EMPTY ; } } #ifndef NDEBUG debug_deg_lists (n_row, n_col, Row, Col, head, min_score, cset_start [current_set+1]-(k+deadcol), max_deg) ; #endif /* frontal matrix can have more pivot cols than pivot rows for */ /* singular matrices. */ /* number of candidate pivot columns */ Front_npivcol [nfr] = pivot_col_thickness ; /* all rows (not just size of contrib. block) */ Front_nrows [nfr] = pivot_row_thickness ; /* all cols */ Front_ncols [nfr] = pivot_col_thickness + pivot_row_degree ; Front_parent [nfr] = EMPTY ; pivot_row_thickness -= pivot_col_thickness ; DEBUG1 (("Front "ID" Pivot_row_thickness after pivot cols elim: "ID"\n", nfr, pivot_row_thickness)) ; pivot_row_thickness = MAX (0, pivot_row_thickness) ; /* === Resurrect the new pivot row ================================== */ if ((pivot_row_degree > 0 && pivot_row_thickness > 0 && (order_for_lu)) || (pivot_row_degree > 0 && (!order_for_lu))) { /* update pivot row length to reflect any cols that were killed */ /* during super-col detection and mass elimination */ Row [pivot_row].start = pivot_row_start ; Row [pivot_row].length = (Int) (new_rp - &A[pivot_row_start]) ; Row [pivot_row].shared1.degree = pivot_row_degree ; Row [pivot_row].shared2.mark = 0 ; Row [pivot_row].thickness = pivot_row_thickness ; Row [pivot_row].front = nfr ; /* pivot row is no longer dead */ DEBUG1 (("Resurrect Pivot_row "ID" deg: "ID"\n", pivot_row, pivot_row_degree)) ; } #ifndef NDEBUG DEBUG1 (("Front "ID" : "ID" "ID" "ID" ", nfr, Front_npivcol [nfr], Front_nrows [nfr], Front_ncols [nfr])) ; DEBUG1 ((" cols:[ ")) ; debug_d = 0 ; for (col = Front_cols [nfr] ; col != EMPTY ; col = Col [col].nextcol) { DEBUG1 ((" "ID, col)) ; ASSERT (col >= 0 && col < n_col) ; ASSERT (COL_IS_DEAD (col)) ; debug_d++ ; ASSERT (debug_d <= pivot_col_thickness) ; } ASSERT (debug_d == pivot_col_thickness) ; DEBUG1 ((" ]\n ")) ; #endif nfr++ ; /* one more front */ } /* === All principal columns have now been ordered ====================== */ *p_nfr = nfr ; return (ngarbage) ; } /* ========================================================================== */ /* === detect_super_cols ==================================================== */ /* ========================================================================== */ /* * Detects supercolumns by finding matches between columns in the hash buckets. * Check amongst columns in the set A [row_start ... row_start + row_length-1]. * The columns under consideration are currently *not* in the degree lists, * and have already been placed in the hash buckets. * * The hash bucket for columns whose hash function is equal to h is stored * as follows: * * if head [h] is >= 0, then head [h] contains a degree list, so: * * head [h] is the first column in degree bucket h. * Col [head [h]].headhash gives the first column in hash bucket h. * * otherwise, the degree list is empty, and: * * -(head [h] + 2) is the first column in hash bucket h. * * For a column c in a hash bucket, Col [c].shared3.prev is NOT a "previous * column" pointer. Col [c].shared3.hash is used instead as the hash number * for that column. The value of Col [c].shared4.hash_next is the next column * in the same hash bucket. * * Assuming no, or "few" hash collisions, the time taken by this routine is * linear in the sum of the sizes (lengths) of each column whose score has * just been computed in the approximate degree computation. * Not user-callable. */ PRIVATE void detect_super_cols ( /* === Parameters ======================================================= */ #ifndef NDEBUG /* these two parameters are only needed when debugging is enabled: */ Int n_col, /* number of columns of A */ CColamd_Row Row [ ], /* of size n_row+1 */ #endif CColamd_Col Col [ ], /* of size n_col+1 */ Int A [ ], /* row indices of A */ Int head [ ], /* head of degree lists and hash buckets */ Int row_start, /* pointer to set of columns to check */ Int row_length, /* number of columns to check */ Int cmember [ ] /* col -> cset mapping */ ) { /* === Local variables ================================================== */ Int hash ; /* hash value for a column */ Int *rp ; /* pointer to a row */ Int c ; /* a column index */ Int super_c ; /* column index of the column to absorb into */ Int *cp1 ; /* column pointer for column super_c */ Int *cp2 ; /* column pointer for column c */ Int length ; /* length of column super_c */ Int prev_c ; /* column preceding c in hash bucket */ Int i ; /* loop counter */ Int *rp_end ; /* pointer to the end of the row */ Int col ; /* a column index in the row to check */ Int head_column ; /* first column in hash bucket or degree list */ Int first_col ; /* first column in hash bucket */ /* === Consider each column in the row ================================== */ rp = &A [row_start] ; rp_end = rp + row_length ; while (rp < rp_end) { col = *rp++ ; if (COL_IS_DEAD (col)) { continue ; } /* get hash number for this column */ hash = Col [col].shared3.hash ; ASSERT (hash <= n_col) ; /* === Get the first column in this hash bucket ===================== */ head_column = head [hash] ; if (head_column > EMPTY) { first_col = Col [head_column].shared3.headhash ; } else { first_col = - (head_column + 2) ; } /* === Consider each column in the hash bucket ====================== */ for (super_c = first_col ; super_c != EMPTY ; super_c = Col [super_c].shared4.hash_next) { ASSERT (COL_IS_ALIVE (super_c)) ; ASSERT (Col [super_c].shared3.hash == hash) ; length = Col [super_c].length ; /* prev_c is the column preceding column c in the hash bucket */ prev_c = super_c ; /* === Compare super_c with all columns after it ================ */ for (c = Col [super_c].shared4.hash_next ; c != EMPTY ; c = Col [c].shared4.hash_next) { ASSERT (c != super_c) ; ASSERT (COL_IS_ALIVE (c)) ; ASSERT (Col [c].shared3.hash == hash) ; /* not identical if lengths or scores are different, */ /* or if in different constraint sets */ if (Col [c].length != length || Col [c].shared2.score != Col [super_c].shared2.score || CMEMBER (c) != CMEMBER (super_c)) { prev_c = c ; continue ; } /* compare the two columns */ cp1 = &A [Col [super_c].start] ; cp2 = &A [Col [c].start] ; for (i = 0 ; i < length ; i++) { /* the columns are "clean" (no dead rows) */ ASSERT (ROW_IS_ALIVE (*cp1)) ; ASSERT (ROW_IS_ALIVE (*cp2)) ; /* row indices will same order for both supercols, */ /* no gather scatter nessasary */ if (*cp1++ != *cp2++) { break ; } } /* the two columns are different if the for-loop "broke" */ /* super columns should belong to the same constraint set */ if (i != length) { prev_c = c ; continue ; } /* === Got it! two columns are identical =================== */ ASSERT (Col [c].shared2.score == Col [super_c].shared2.score) ; Col [super_c].shared1.thickness += Col [c].shared1.thickness ; Col [c].shared1.parent = super_c ; KILL_NON_PRINCIPAL_COL (c) ; /* order c later, in order_children() */ Col [c].shared2.order = EMPTY ; /* remove c from hash bucket */ Col [prev_c].shared4.hash_next = Col [c].shared4.hash_next ; /* add c to end of list of super_c */ ASSERT (Col [super_c].lastcol >= 0) ; ASSERT (Col [super_c].lastcol < n_col) ; Col [Col [super_c].lastcol].nextcol = c ; Col [super_c].lastcol = Col [c].lastcol ; #ifndef NDEBUG /* dump the supercolumn */ DEBUG1 (("Super")) ; dump_super (super_c, Col, n_col) ; #endif } } /* === Empty this hash bucket ======================================= */ if (head_column > EMPTY) { /* corresponding degree list "hash" is not empty */ Col [head_column].shared3.headhash = EMPTY ; } else { /* corresponding degree list "hash" is empty */ head [hash] = EMPTY ; } } } /* ========================================================================== */ /* === garbage_collection =================================================== */ /* ========================================================================== */ /* * Defragments and compacts columns and rows in the workspace A. Used when * all avaliable memory has been used while performing row merging. Returns * the index of the first free position in A, after garbage collection. The * time taken by this routine is linear is the size of the array A, which is * itself linear in the number of nonzeros in the input matrix. * Not user-callable. */ PRIVATE Int garbage_collection /* returns the new value of pfree */ ( /* === Parameters ======================================================= */ Int n_row, /* number of rows */ Int n_col, /* number of columns */ CColamd_Row Row [ ], /* row info */ CColamd_Col Col [ ], /* column info */ Int A [ ], /* A [0 ... Alen-1] holds the matrix */ Int *pfree /* &A [0] ... pfree is in use */ ) { /* === Local variables ================================================== */ Int *psrc ; /* source pointer */ Int *pdest ; /* destination pointer */ Int j ; /* counter */ Int r ; /* a row index */ Int c ; /* a column index */ Int length ; /* length of a row or column */ #ifndef NDEBUG Int debug_rows ; DEBUG2 (("Defrag..\n")) ; for (psrc = &A[0] ; psrc < pfree ; psrc++) ASSERT (*psrc >= 0) ; debug_rows = 0 ; #endif /* === Defragment the columns =========================================== */ pdest = &A[0] ; for (c = 0 ; c < n_col ; c++) { if (COL_IS_ALIVE (c)) { psrc = &A [Col [c].start] ; /* move and compact the column */ ASSERT (pdest <= psrc) ; Col [c].start = (Int) (pdest - &A [0]) ; length = Col [c].length ; for (j = 0 ; j < length ; j++) { r = *psrc++ ; if (ROW_IS_ALIVE (r)) { *pdest++ = r ; } } Col [c].length = (Int) (pdest - &A [Col [c].start]) ; } } /* === Prepare to defragment the rows =================================== */ for (r = 0 ; r < n_row ; r++) { if (ROW_IS_DEAD (r) || (Row [r].length == 0)) { /* This row is already dead, or is of zero length. Cannot compact * a row of zero length, so kill it. NOTE: in the current version, * there are no zero-length live rows. Kill the row (for the first * time, or again) just to be safe. */ KILL_ROW (r) ; } else { /* save first column index in Row [r].shared2.first_column */ psrc = &A [Row [r].start] ; Row [r].shared2.first_column = *psrc ; ASSERT (ROW_IS_ALIVE (r)) ; /* flag the start of the row with the one's complement of row */ *psrc = ONES_COMPLEMENT (r) ; #ifndef NDEBUG debug_rows++ ; #endif } } /* === Defragment the rows ============================================== */ psrc = pdest ; while (psrc < pfree) { /* find a negative number ... the start of a row */ if (*psrc++ < 0) { psrc-- ; /* get the row index */ r = ONES_COMPLEMENT (*psrc) ; ASSERT (r >= 0 && r < n_row) ; /* restore first column index */ *psrc = Row [r].shared2.first_column ; ASSERT (ROW_IS_ALIVE (r)) ; /* move and compact the row */ ASSERT (pdest <= psrc) ; Row [r].start = (Int) (pdest - &A [0]) ; length = Row [r].length ; for (j = 0 ; j < length ; j++) { c = *psrc++ ; if (COL_IS_ALIVE (c)) { *pdest++ = c ; } } Row [r].length = (Int) (pdest - &A [Row [r].start]) ; #ifndef NDEBUG debug_rows-- ; #endif } } /* ensure we found all the rows */ ASSERT (debug_rows == 0) ; /* === Return the new value of pfree ==================================== */ return ((Int) (pdest - &A [0])) ; } /* ========================================================================== */ /* === clear_mark =========================================================== */ /* ========================================================================== */ /* * Clears the Row [ ].shared2.mark array, and returns the new tag_mark. * Return value is the new tag_mark. Not user-callable. */ PRIVATE Int clear_mark /* return the new value for tag_mark */ ( /* === Parameters ======================================================= */ Int tag_mark, /* new value of tag_mark */ Int max_mark, /* max allowed value of tag_mark */ Int n_row, /* number of rows in A */ CColamd_Row Row [ ] /* Row [0 ... n_row-1].shared2.mark is set to zero */ ) { /* === Local variables ================================================== */ Int r ; if (tag_mark <= 0 || tag_mark >= max_mark) { for (r = 0 ; r < n_row ; r++) { if (ROW_IS_ALIVE (r)) { Row [r].shared2.mark = 0 ; } } tag_mark = 1 ; } return (tag_mark) ; } /* ========================================================================== */ /* === print_report ========================================================= */ /* ========================================================================== */ /* No printing occurs if NPRINT is defined at compile time. */ PRIVATE void print_report ( char *method, Int stats [CCOLAMD_STATS] ) { Int i1, i2, i3 ; PRINTF (("\n%s version %d.%d, %s: ", method, CCOLAMD_MAIN_VERSION, CCOLAMD_SUB_VERSION, CCOLAMD_DATE)) ; if (!stats) { PRINTF (("No statistics available.\n")) ; return ; } i1 = stats [CCOLAMD_INFO1] ; i2 = stats [CCOLAMD_INFO2] ; i3 = stats [CCOLAMD_INFO3] ; if (stats [CCOLAMD_STATUS] >= 0) { PRINTF(("OK. ")) ; } else { PRINTF(("ERROR. ")) ; } switch (stats [CCOLAMD_STATUS]) { case CCOLAMD_OK_BUT_JUMBLED: PRINTF(("Matrix has unsorted or duplicate row indices.\n")) ; PRINTF(("%s: duplicate or out-of-order row indices: "ID"\n", method, i3)) ; PRINTF(("%s: last seen duplicate or out-of-order row: "ID"\n", method, INDEX (i2))) ; PRINTF(("%s: last seen in column: "ID"", method, INDEX (i1))) ; /* no break - fall through to next case instead */ case CCOLAMD_OK: PRINTF(("\n")) ; PRINTF(("%s: number of dense or empty rows ignored: "ID"\n", method, stats [CCOLAMD_DENSE_ROW])) ; PRINTF(("%s: number of dense or empty columns ignored: "ID"\n", method, stats [CCOLAMD_DENSE_COL])) ; PRINTF(("%s: number of garbage collections performed: "ID"\n", method, stats [CCOLAMD_DEFRAG_COUNT])) ; break ; case CCOLAMD_ERROR_A_not_present: PRINTF(("Array A (row indices of matrix) not present.\n")) ; break ; case CCOLAMD_ERROR_p_not_present: PRINTF(("Array p (column pointers for matrix) not present.\n")) ; break ; case CCOLAMD_ERROR_nrow_negative: PRINTF(("Invalid number of rows ("ID").\n", i1)) ; break ; case CCOLAMD_ERROR_ncol_negative: PRINTF(("Invalid number of columns ("ID").\n", i1)) ; break ; case CCOLAMD_ERROR_nnz_negative: PRINTF(("Invalid number of nonzero entries ("ID").\n", i1)) ; break ; case CCOLAMD_ERROR_p0_nonzero: PRINTF(("Invalid column pointer, p [0] = "ID", must be 0.\n", i1)) ; break ; case CCOLAMD_ERROR_A_too_small: PRINTF(("Array A too small.\n")) ; PRINTF((" Need Alen >= "ID", but given only Alen = "ID".\n", i1, i2)) ; break ; case CCOLAMD_ERROR_col_length_negative: PRINTF(("Column "ID" has a negative number of entries ("ID").\n", INDEX (i1), i2)) ; break ; case CCOLAMD_ERROR_row_index_out_of_bounds: PRINTF(("Row index (row "ID") out of bounds ("ID" to "ID") in" "column "ID".\n", INDEX (i2), INDEX (0), INDEX (i3-1), INDEX (i1))) ; break ; case CCOLAMD_ERROR_out_of_memory: PRINTF(("Out of memory.\n")) ; break ; case CCOLAMD_ERROR_invalid_cmember: PRINTF(("cmember invalid\n")) ; break ; } } /* ========================================================================= */ /* === "Expert" routines =================================================== */ /* ========================================================================= */ /* The following routines are visible outside this routine, but are not meant * to be called by the user. They are meant for a future version of UMFPACK, * to replace UMFPACK internal routines with a similar name. */ /* ========================================================================== */ /* === CCOLAMD_apply_order ================================================== */ /* ========================================================================== */ /* * Apply post-ordering of supernodal elimination tree. */ GLOBAL void CCOLAMD_apply_order ( Int Front [ ], /* of size nn on input, size nfr on output */ const Int Order [ ], /* Order [i] = k, i in the range 0..nn-1, * and k in the range 0..nfr-1, means that node * i is the kth node in the postordered tree. */ Int Temp [ ], /* workspace of size nfr */ Int nn, /* nodes are numbered in the range 0..nn-1 */ Int nfr /* the number of nodes actually in use */ ) { Int i, k ; for (i = 0 ; i < nn ; i++) { k = Order [i] ; ASSERT (k >= EMPTY && k < nfr) ; if (k != EMPTY) { Temp [k] = Front [i] ; } } for (k = 0 ; k < nfr ; k++) { Front [k] = Temp [k] ; } } /* ========================================================================== */ /* === CCOLAMD_fsize ======================================================== */ /* ========================================================================== */ /* Determine the largest frontal matrix size for each subtree. * Only required to sort the children of each * node prior to postordering the column elimination tree. */ GLOBAL void CCOLAMD_fsize ( Int nn, Int Fsize [ ], Int Fnrows [ ], Int Fncols [ ], Int Parent [ ], Int Npiv [ ] ) { double dr, dc ; Int j, parent, frsize, r, c ; for (j = 0 ; j < nn ; j++) { Fsize [j] = EMPTY ; } /* ---------------------------------------------------------------------- */ /* find max front size for tree rooted at node j, for each front j */ /* ---------------------------------------------------------------------- */ DEBUG1 (("\n\n========================================FRONTS:\n")) ; for (j = 0 ; j < nn ; j++) { if (Npiv [j] > 0) { /* this is a frontal matrix */ parent = Parent [j] ; r = Fnrows [j] ; c = Fncols [j] ; /* avoid integer overflow */ dr = (double) r ; dc = (double) c ; frsize = (INT_OVERFLOW (dr * dc)) ? Int_MAX : (r * c) ; DEBUG1 ((""ID" : npiv "ID" size "ID" parent "ID" ", j, Npiv [j], frsize, parent)) ; Fsize [j] = MAX (Fsize [j], frsize) ; DEBUG1 (("Fsize [j = "ID"] = "ID"\n", j, Fsize [j])) ; if (parent != EMPTY) { /* find the maximum frontsize of self and children */ ASSERT (Npiv [parent] > 0) ; ASSERT (parent > j) ; Fsize [parent] = MAX (Fsize [parent], Fsize [j]) ; DEBUG1 (("Fsize [parent = "ID"] = "ID"\n", parent, Fsize [parent])); } } } DEBUG1 (("fsize done\n")) ; } /* ========================================================================= */ /* === CCOLAMD_postorder =================================================== */ /* ========================================================================= */ /* Perform a postordering (via depth-first search) of an assembly tree. */ GLOBAL void CCOLAMD_postorder ( /* inputs, not modified on output: */ Int nn, /* nodes are in the range 0..nn-1 */ Int Parent [ ], /* Parent [j] is the parent of j, or EMPTY if root */ Int Nv [ ], /* Nv [j] > 0 number of pivots represented by node j, * or zero if j is not a node. */ Int Fsize [ ], /* Fsize [j]: size of node j */ /* output, not defined on input: */ Int Order [ ], /* output post-order */ /* workspaces of size nn: */ Int Child [ ], Int Sibling [ ], Int Stack [ ], Int Front_cols [ ], /* input, not modified on output: */ Int cmember [ ] ) { Int i, j, k, parent, frsize, f, fprev, maxfrsize, bigfprev, bigf, fnext ; for (j = 0 ; j < nn ; j++) { Child [j] = EMPTY ; Sibling [j] = EMPTY ; } /* --------------------------------------------------------------------- */ /* place the children in link lists - bigger elements tend to be last */ /* --------------------------------------------------------------------- */ for (j = nn-1 ; j >= 0 ; j--) { if (Nv [j] > 0) { /* this is an element */ parent = Parent [j] ; if (parent != EMPTY) { /* place the element in link list of the children its parent */ /* bigger elements will tend to be at the end of the list */ Sibling [j] = Child [parent] ; if (CMEMBER (Front_cols[parent]) == CMEMBER (Front_cols[j])) { Child [parent] = j ; } } } } #ifndef NDEBUG { Int nels, ff, nchild ; DEBUG1 (("\n\n================================ ccolamd_postorder:\n")); nels = 0 ; for (j = 0 ; j < nn ; j++) { if (Nv [j] > 0) { DEBUG1 ((""ID" : nels "ID" npiv "ID" size "ID " parent "ID" maxfr "ID"\n", j, nels, Nv [j], Fsize [j], Parent [j], Fsize [j])) ; /* this is an element */ /* dump the link list of children */ nchild = 0 ; DEBUG1 ((" Children: ")) ; for (ff = Child [j] ; ff != EMPTY ; ff = Sibling [ff]) { DEBUG1 ((ID" ", ff)) ; nchild++ ; ASSERT (nchild < nn) ; } DEBUG1 (("\n")) ; parent = Parent [j] ; nels++ ; } } } #endif /* --------------------------------------------------------------------- */ /* place the largest child last in the list of children for each node */ /* --------------------------------------------------------------------- */ for (i = 0 ; i < nn ; i++) { if (Nv [i] > 0 && Child [i] != EMPTY) { #ifndef NDEBUG Int nchild ; DEBUG1 (("Before partial sort, element "ID"\n", i)) ; nchild = 0 ; for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) { DEBUG1 ((" f: "ID" size: "ID"\n", f, Fsize [f])) ; nchild++ ; } #endif /* find the biggest element in the child list */ fprev = EMPTY ; maxfrsize = EMPTY ; bigfprev = EMPTY ; bigf = EMPTY ; for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) { frsize = Fsize [f] ; if (frsize >= maxfrsize) { /* this is the biggest seen so far */ maxfrsize = frsize ; bigfprev = fprev ; bigf = f ; } fprev = f ; } fnext = Sibling [bigf] ; DEBUG1 (("bigf "ID" maxfrsize "ID" bigfprev "ID" fnext "ID " fprev " ID"\n", bigf, maxfrsize, bigfprev, fnext, fprev)) ; if (fnext != EMPTY) { /* if fnext is EMPTY then bigf is already at the end of list */ if (bigfprev == EMPTY) { /* delete bigf from the element of the list */ Child [i] = fnext ; } else { /* delete bigf from the middle of the list */ Sibling [bigfprev] = fnext ; } /* put bigf at the end of the list */ Sibling [bigf] = EMPTY ; Sibling [fprev] = bigf ; } #ifndef NDEBUG DEBUG1 (("After partial sort, element "ID"\n", i)) ; for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) { DEBUG1 ((" "ID" "ID"\n", f, Fsize [f])) ; nchild-- ; } #endif } } /* --------------------------------------------------------------------- */ /* postorder the assembly tree */ /* --------------------------------------------------------------------- */ for (i = 0 ; i < nn ; i++) { Order [i] = EMPTY ; } k = 0 ; for (i = 0 ; i < nn ; i++) { if ((Parent [i] == EMPTY || (CMEMBER (Front_cols [Parent [i]]) != CMEMBER (Front_cols [i]))) && Nv [i] > 0) { DEBUG1 (("Root of assembly tree "ID"\n", i)) ; k = CCOLAMD_post_tree (i, k, Child, Sibling, Order, Stack) ; } } } /* ========================================================================= */ /* === CCOLAMD_post_tree =================================================== */ /* ========================================================================= */ /* Post-ordering of a supernodal column elimination tree. */ GLOBAL Int CCOLAMD_post_tree ( Int root, /* root of the tree */ Int k, /* start numbering at k */ Int Child [ ], /* input argument of size nn, undefined on * output. Child [i] is the head of a link * list of all nodes that are children of node * i in the tree. */ const Int Sibling [ ], /* input argument of size nn, not modified. * If f is a node in the link list of the * children of node i, then Sibling [f] is the * next child of node i. */ Int Order [ ], /* output order, of size nn. Order [i] = k * if node i is the kth node of the reordered * tree. */ Int Stack [ ] /* workspace of size nn */ ) { Int f, head, h, i ; #if 0 /* --------------------------------------------------------------------- */ /* recursive version (Stack [ ] is not used): */ /* --------------------------------------------------------------------- */ /* this is simple, but can cause stack overflow if nn is large */ i = root ; for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) { k = CCOLAMD_post_tree (f, k, Child, Sibling, Order, Stack, nn) ; } Order [i] = k++ ; return (k) ; #endif /* --------------------------------------------------------------------- */ /* non-recursive version, using an explicit stack */ /* --------------------------------------------------------------------- */ /* push root on the stack */ head = 0 ; Stack [0] = root ; while (head >= 0) { /* get head of stack */ i = Stack [head] ; DEBUG1 (("head of stack "ID" \n", i)) ; if (Child [i] != EMPTY) { /* the children of i are not yet ordered */ /* push each child onto the stack in reverse order */ /* so that small ones at the head of the list get popped first */ /* and the biggest one at the end of the list gets popped last */ for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) { head++ ; } h = head ; for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) { ASSERT (h > 0) ; Stack [h--] = f ; DEBUG1 (("push "ID" on stack\n", f)) ; } ASSERT (Stack [h] == i) ; /* delete child list so that i gets ordered next time we see it */ Child [i] = EMPTY ; } else { /* the children of i (if there were any) are already ordered */ /* remove i from the stack and order it. Front i is kth front */ head-- ; DEBUG1 (("pop "ID" order "ID"\n", i, k)) ; Order [i] = k++ ; } #ifndef NDEBUG DEBUG1 (("\nStack:")) ; for (h = head ; h >= 0 ; h--) { Int j = Stack [h] ; DEBUG1 ((" "ID, j)) ; } DEBUG1 (("\n\n")) ; #endif } return (k) ; } /* ========================================================================== */ /* === CCOLAMD debugging routines =========================================== */ /* ========================================================================== */ /* When debugging is disabled, the remainder of this file is ignored. */ #ifndef NDEBUG /* ========================================================================== */ /* === debug_structures ===================================================== */ /* ========================================================================== */ /* * At this point, all empty rows and columns are dead. All live columns * are "clean" (containing no dead rows) and simplicial (no supercolumns * yet). Rows may contain dead columns, but all live rows contain at * least one live column. */ PRIVATE void debug_structures ( /* === Parameters ======================================================= */ Int n_row, Int n_col, CColamd_Row Row [ ], CColamd_Col Col [ ], Int A [ ], Int cmember [ ], Int cset_start [ ] ) { /* === Local variables ================================================== */ Int i ; Int c ; Int *cp ; Int *cp_end ; Int len ; Int score ; Int r ; Int *rp ; Int *rp_end ; Int deg ; Int cs ; /* === Check A, Row, and Col ============================================ */ for (c = 0 ; c < n_col ; c++) { if (COL_IS_ALIVE (c)) { len = Col [c].length ; score = Col [c].shared2.score ; DEBUG4 (("initial live col %5d %5d %5d\n", c, len, score)) ; ASSERT (len > 0) ; ASSERT (score >= 0) ; ASSERT (Col [c].shared1.thickness == 1) ; cp = &A [Col [c].start] ; cp_end = cp + len ; while (cp < cp_end) { r = *cp++ ; ASSERT (ROW_IS_ALIVE (r)) ; } } else { i = Col [c].shared2.order ; cs = CMEMBER (c) ; ASSERT (i >= cset_start [cs] && i < cset_start [cs+1]) ; } } for (r = 0 ; r < n_row ; r++) { if (ROW_IS_ALIVE (r)) { i = 0 ; len = Row [r].length ; deg = Row [r].shared1.degree ; ASSERT (len > 0) ; ASSERT (deg > 0) ; rp = &A [Row [r].start] ; rp_end = rp + len ; while (rp < rp_end) { c = *rp++ ; if (COL_IS_ALIVE (c)) { i++ ; } } ASSERT (i > 0) ; } } } /* ========================================================================== */ /* === debug_deg_lists ====================================================== */ /* ========================================================================== */ /* * Prints the contents of the degree lists. Counts the number of columns * in the degree list and compares it to the total it should have. Also * checks the row degrees. */ PRIVATE void debug_deg_lists ( /* === Parameters ======================================================= */ Int n_row, Int n_col, CColamd_Row Row [ ], CColamd_Col Col [ ], Int head [ ], Int min_score, Int should, Int max_deg ) { /* === Local variables ================================================== */ Int deg ; Int col ; Int have ; Int row ; /* === Check the degree lists =========================================== */ if (n_col > 10000 && ccolamd_debug <= 0) { return ; } have = 0 ; DEBUG4 (("Degree lists: "ID"\n", min_score)) ; for (deg = 0 ; deg <= n_col ; deg++) { col = head [deg] ; if (col == EMPTY) { continue ; } DEBUG4 (("%d:", deg)) ; ASSERT (Col [col].shared3.prev == EMPTY) ; while (col != EMPTY) { DEBUG4 ((" "ID"", col)) ; have += Col [col].shared1.thickness ; ASSERT (COL_IS_ALIVE (col)) ; col = Col [col].shared4.degree_next ; } DEBUG4 (("\n")) ; } DEBUG4 (("should "ID" have "ID"\n", should, have)) ; ASSERT (should == have) ; /* === Check the row degrees ============================================ */ if (n_row > 10000 && ccolamd_debug <= 0) { return ; } for (row = 0 ; row < n_row ; row++) { if (ROW_IS_ALIVE (row)) { ASSERT (Row [row].shared1.degree <= max_deg) ; } } } /* ========================================================================== */ /* === debug_mark =========================================================== */ /* ========================================================================== */ /* * Ensures that the tag_mark is less that the maximum and also ensures that * each entry in the mark array is less than the tag mark. */ PRIVATE void debug_mark ( /* === Parameters ======================================================= */ Int n_row, CColamd_Row Row [ ], Int tag_mark, Int max_mark ) { /* === Local variables ================================================== */ Int r ; /* === Check the Row marks ============================================== */ ASSERT (tag_mark > 0 && tag_mark <= max_mark) ; if (n_row > 10000 && ccolamd_debug <= 0) { return ; } for (r = 0 ; r < n_row ; r++) { ASSERT (Row [r].shared2.mark < tag_mark) ; } } /* ========================================================================== */ /* === debug_matrix ========================================================= */ /* ========================================================================== */ /* Prints out the contents of the columns and the rows. */ PRIVATE void debug_matrix ( /* === Parameters ======================================================= */ Int n_row, Int n_col, CColamd_Row Row [ ], CColamd_Col Col [ ], Int A [ ] ) { /* === Local variables ================================================== */ Int r ; Int c ; Int *rp ; Int *rp_end ; Int *cp ; Int *cp_end ; /* === Dump the rows and columns of the matrix ========================== */ if (ccolamd_debug < 3) { return ; } DEBUG3 (("DUMP MATRIX:\n")) ; for (r = 0 ; r < n_row ; r++) { DEBUG3 (("Row "ID" alive? "ID"\n", r, ROW_IS_ALIVE (r))) ; if (ROW_IS_DEAD (r)) { continue ; } DEBUG3 (("start "ID" length "ID" degree "ID"\nthickness "ID"\n", Row [r].start, Row [r].length, Row [r].shared1.degree, Row [r].thickness)) ; rp = &A [Row [r].start] ; rp_end = rp + Row [r].length ; while (rp < rp_end) { c = *rp++ ; DEBUG4 ((" "ID" col "ID"\n", COL_IS_ALIVE (c), c)) ; } } for (c = 0 ; c < n_col ; c++) { DEBUG3 (("Col "ID" alive? "ID"\n", c, COL_IS_ALIVE (c))) ; if (COL_IS_DEAD (c)) { continue ; } DEBUG3 (("start "ID" length "ID" shared1 "ID" shared2 "ID"\n", Col [c].start, Col [c].length, Col [c].shared1.thickness, Col [c].shared2.score)) ; cp = &A [Col [c].start] ; cp_end = cp + Col [c].length ; while (cp < cp_end) { r = *cp++ ; DEBUG4 ((" "ID" row "ID"\n", ROW_IS_ALIVE (r), r)) ; } } } /* ========================================================================== */ /* === dump_super =========================================================== */ /* ========================================================================== */ PRIVATE void dump_super ( Int super_c, CColamd_Col Col [ ], Int n_col ) { Int col, ncols ; DEBUG1 ((" =[ ")) ; ncols = 0 ; for (col = super_c ; col != EMPTY ; col = Col [col].nextcol) { DEBUG1 ((" "ID, col)) ; ASSERT (col >= 0 && col < n_col) ; if (col != super_c) { ASSERT (COL_IS_DEAD (col)) ; } if (Col [col].nextcol == EMPTY) { ASSERT (col == Col [super_c].lastcol) ; } ncols++ ; ASSERT (ncols <= Col [super_c].shared1.thickness) ; } ASSERT (ncols == Col [super_c].shared1.thickness) ; DEBUG1 (("]\n")) ; } /* ========================================================================== */ /* === ccolamd_get_debug ==================================================== */ /* ========================================================================== */ PRIVATE void ccolamd_get_debug ( char *method ) { FILE *debug_file ; ccolamd_debug = 0 ; /* no debug printing */ /* Read debug info from the debug file. */ debug_file = fopen ("debug", "r") ; if (debug_file) { (void) fscanf (debug_file, ""ID"", &ccolamd_debug) ; (void) fclose (debug_file) ; } DEBUG0 ((":")) ; DEBUG1 (("%s: debug version, D = "ID" (THIS WILL BE SLOW!)\n", method, ccolamd_debug)) ; DEBUG1 ((" Debug printing level: "ID"\n", ccolamd_debug)) ; } #endif SuiteSparse/CCOLAMD/README.txt0000644001170100242450000001430410617111303014502 0ustar davisfacCCOLAMD version 2.7: constrained column approximate minimum degree ordering Copyright (C) 2005-2007, Univ. of Florida. Authors: Timothy A. Davis, Sivasankaran Rajamanickam, and Stefan Larimore. Closely based on COLAMD by Davis, Stefan Larimore, in collaboration with Esmond Ng, and John Gilbert. http://www.cise.ufl.edu/research/sparse ------------------------------------------------------------------------------- The CCOLAMD column approximate minimum degree ordering algorithm computes a permutation vector P such that the LU factorization of A (:,P) tends to be sparser than that of A. The Cholesky factorization of (A (:,P))'*(A (:,P)) will also tend to be sparser than that of A'*A. CSYMAMD is a symmetric minimum degree ordering method based on CCOLAMD, also available as a MATLAB-callable function. It constructs a matrix M such that M'*M has the same pattern as A, and then uses CCOLAMD to compute a column ordering of M. Requires UFconfig, in the ../UFconfig directory relative to this directory. To compile and install the ccolamd m-files and mexFunctions, just cd to CCOLAMD/MATLAB and type ccolamd_install in the MATLAB command window. A short demo will run. Optionally, type ccolamd_test to run an extensive tests. Type "make" in Unix in the CCOLAMD directory to compile the C-callable library and to run a short demo. If you have MATLAB 7.2 or earlier, you must first edit UFconfig/UFconfig.h to remove the "-largeArrayDims" option from the MEX command (or just use ccolamd_install.m inside MATLAB). Other "make" targets: make mex compiles MATLAB mexFunctions only make libccolamd.a compiles a C-callable library containing ccolamd make clean removes all files not in the distribution, except for libccolamd.a make distclean removes all files not in the distribution To use ccolamd and csymamd within an application written in C, all you need are ccolamd.c and ccolamd.h, which are the C-callable ccolamd/csymamd codes. See ccolamd.c for more information on how to call ccolamd from a C program. It contains a complete description of the C-interface to CCOLAMD and CSYMAMD. Copyright (c) 1998-2007 by the University of Florida. All Rights Reserved. Licensed under the GNU LESSER GENERAL PUBLIC LICENSE. ------------------------------------------------------------------------------- This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA ------------------------------------------------------------------------------- Related papers: T. A. Davis and W. W. Hager, Rajamanickam, Multiple-rank updates to a supernodal sparse Cholesky factorization, submitted. T. A. Davis, W. W. Hager, S. Rajamanickam, and Y. Chen, CHOLMOD: a sparse Cholesky update/downdate package, submitted. CHOLMOD's nested dissection ordering relies on CCOLAMD and CSYMAMD to order the matrix after graph partitioning is used to find the ordering constraints. T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, An approximate column minimum degree ordering algorithm, ACM Transactions on Mathematical Software, vol. 30, no. 3., pp. 353-376, 2004. T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, Algorithm 836: COLAMD, an approximate column minimum degree ordering algorithm, ACM Transactions on Mathematical Software, vol. 30, no. 3., pp. 377-380, 2004. "An approximate minimum degree column ordering algorithm", S. I. Larimore, MS Thesis, Dept. of Computer and Information Science and Engineering, University of Florida, Gainesville, FL, 1998. CISE Tech Report TR-98-016. Available at ftp://ftp.cise.ufl.edu/cis/tech-reports/tr98/tr98-016.ps via anonymous ftp. Approximate Deficiency for Ordering the Columns of a Matrix, J. L. Kern, Senior Thesis, Dept. of Computer and Information Science and Engineering, University of Florida, Gainesville, FL, 1999. Available at http://www.cise.ufl.edu/~davis/Kern/kern.ps Authors: Timothy A. Davis, Sivasankaran Rajamanickam, and Stefan Larimore. Closely based on COLAMD by Stefan I. Larimore and Timothy A. Davis, University of Florida, in collaboration with John Gilbert, Xerox PARC (now at UC Santa Barbara), and Esmong Ng, Lawrence Berkeley National Laboratory (much of this work he did while at Oak Ridge National Laboratory). CCOLAMD files: Demo simple demo Doc additional documentation (see ccolamd.c for more) Include include file Lib compiled C-callable library Makefile primary Unix Makefile MATLAB MATLAB functions README.txt this file Source C source code ./Demo: ccolamd_example.c simple example ccolamd_example.out output of colamd_example.c ccolamd_l_example.c simple example, long integers ccolamd_l_example.out output of colamd_l_example.c Makefile Makefile for C demos ./Doc: ChangeLog change log lesser.txt license ./Include: ccolamd.h include file ./Lib: Makefile Makefile for C-callable library ./MATLAB: ccolamd.m MATLAB interface for ccolamd ccolamd_demo.m simple demo ccolamd_install.m compile and install ccolamd and csymamd ccolamd_make.m compile colamd2 and symamd2 ccolamdmex.c MATLAB mexFunction for ccolamd ccolamd_test.m extensive test ccolamdtestmex.c test function for ccolamd Contents.m contents of the MATLAB directory luflops.m test code Makefile Makefile for MATLAB functions csymamd.m MATLAB interface for csymamd csymamdmex.c MATLAB mexFunction for csymamd symamdtestmex.c test function for csymamd ./Source: ccolamd.c primary source code ccolamd_global.c globally defined function pointers (malloc, free, ...) SuiteSparse/CHOLMOD/0000755001170100242450000000000010711425430013031 5ustar davisfacSuiteSparse/CHOLMOD/Doc/0000755001170100242450000000000010711441430013534 5ustar davisfacSuiteSparse/CHOLMOD/Doc/Makefile0000644001170100242450000004014210616452406015206 0ustar davisfacdefault: all include ../../UFconfig/UFconfig.mk all: UserGuide.pdf I = \ ../Include/cholmod.h \ ../Include/cholmod_blas.h \ ../Include/cholmod_check.h \ ../Include/cholmod_cholesky.h \ ../Include/cholmod_complexity.h \ ../Include/cholmod_config.h \ ../Include/cholmod_core.h \ ../Include/cholmod_internal.h \ ../Include/cholmod_matrixops.h \ ../Include/cholmod_modify.h \ ../Include/cholmod_partition.h \ ../Include/cholmod_supernodal.h \ ../Include/cholmod_template.h C = ../Demo/cholmod_simple.c M = \ ../MATLAB/analyze.m \ ../MATLAB/bisect.m \ ../MATLAB/chol2.m \ ../MATLAB/cholmod2.m \ ../MATLAB/cholmod_demo.m \ ../MATLAB/cholmod_make.m \ ../MATLAB/etree2.m \ ../MATLAB/graph_demo.m \ ../MATLAB/lchol.m \ ../MATLAB/ldlchol.m \ ../MATLAB/ldl_normest.m \ ../MATLAB/ldlsolve.m \ ../MATLAB/ldlsplit.m \ ../MATLAB/ldlupdate.m \ ../MATLAB/metis.m \ ../MATLAB/nesdis.m \ ../MATLAB/resymbol.m \ ../MATLAB/sdmult.m \ ../MATLAB/sparse2.m \ ../MATLAB/spsym.m \ ../MATLAB/mread.m \ ../MATLAB/mwrite.m \ ../MATLAB/symbfact2.m UserGuide.pdf: UserGuide.tex UserGuide.bib $(I) $(C) $(M) Makefile getproto rule.awk header.tex footer.tex getmproto mfooter.tex mheader.tex mfile.awk ./getmproto ../MATLAB/analyze.m > _analyze_m.tex ./getmproto ../MATLAB/bisect.m > _bisect_m.tex ./getmproto ../MATLAB/chol2.m > _chol2_m.tex ./getmproto ../MATLAB/cholmod2.m > _cholmod2_m.tex ./getmproto ../MATLAB/cholmod_demo.m > _cholmod_demo_m.tex ./getmproto ../MATLAB/cholmod_make.m > _cholmod_make_m.tex ./getmproto ../MATLAB/etree2.m > _etree2_m.tex ./getmproto ../MATLAB/graph_demo.m > _graph_demo_m.tex ./getmproto ../MATLAB/lchol.m > _lchol_m.tex ./getmproto ../MATLAB/ldlchol.m > _ldlchol_m.tex ./getmproto ../MATLAB/ldl_normest.m > _ldl_normest_m.tex ./getmproto ../MATLAB/ldlsolve.m > _ldlsolve_m.tex ./getmproto ../MATLAB/ldlsplit.m > _ldlsplit_m.tex ./getmproto ../MATLAB/ldlupdate.m > _ldlupdate_m.tex ./getmproto ../MATLAB/metis.m > _metis_m.tex ./getmproto ../MATLAB/mread.m > _mread_m.tex ./getmproto ../MATLAB/spsym.m > _spsym_m.tex ./getmproto ../MATLAB/mwrite.m > _mwrite_m.tex ./getmproto ../MATLAB/nesdis.m > _nesdis_m.tex ./getmproto ../MATLAB/resymbol.m > _resymbol_m.tex ./getmproto ../MATLAB/sdmult.m > _sdmult_m.tex ./getmproto ../MATLAB/sparse2.m > _sparse2_m.tex ./getmproto ../MATLAB/symbfact2.m > _symbfact2_m.tex ./getproto '/include/, /^}/' ../Demo/cholmod_simple.c > _simple.tex ./getproto '/typedef struct cholmod_common/, /^}/' ../Include/cholmod_core.h > _common.tex ./getproto '/int cholmod_start/, /\*\) ;/' ../Include/cholmod_core.h > _start.tex ./getproto '/int cholmod_finish/, /\*\) ;/' ../Include/cholmod_core.h > _finish.tex ./getproto '/int cholmod_defaults/, /\*\) ;/' ../Include/cholmod_core.h > _defaults.tex ./getproto '/size_t cholmod_maxrank/, /\*\) ;/' ../Include/cholmod_core.h > _maxrank.tex ./getproto '/int cholmod_allocate_work/, /\*\) ;/' ../Include/cholmod_core.h > _allocate_work.tex ./getproto '/int cholmod_free_work/, /\*\) ;/' ../Include/cholmod_core.h > _free_work.tex ./getproto '/long cholmod_clear_flag/, /\*\) ;/' ../Include/cholmod_core.h > _clear_flag.tex ./getproto '/int cholmod_error/, /\*\) ;/' ../Include/cholmod_core.h > _error.tex ./getproto '/double cholmod_dbound/, /\*\) ;/' ../Include/cholmod_core.h > _dbound.tex ./getproto '/double cholmod_hypot/, /double\) ;/' ../Include/cholmod_core.h > _hypot.tex ./getproto '/int cholmod_divcomplex/, /\*\) ;/' ../Include/cholmod_core.h > _divcomplex.tex ./getproto '/typedef struct cholmod_sparse/, /^}/' ../Include/cholmod_core.h > _sparse.tex ./getproto '/cholmod_sparse \*cholmod_allocate_sparse/, /\*\) ;/' ../Include/cholmod_core.h > _allocate_sparse.tex ./getproto '/int cholmod_free_sparse/, /\*\) ;/' ../Include/cholmod_core.h > _free_sparse.tex ./getproto '/int cholmod_reallocate_sparse/, /\*\) ;/' ../Include/cholmod_core.h > _reallocate_sparse.tex ./getproto '/long cholmod_nnz/, /\*\) ;/' ../Include/cholmod_core.h > _nnz.tex ./getproto '/cholmod_sparse \*cholmod_speye/, /\*\) ;/' ../Include/cholmod_core.h > _speye.tex ./getproto '/cholmod_sparse \*cholmod_spzeros/, /\*\) ;/' ../Include/cholmod_core.h > _spzeros.tex ./getproto '/cholmod_sparse \*cholmod_transpose/, /\*\) ;/' ../Include/cholmod_core.h > _transpose.tex ./getproto '/int cholmod_transpose_unsym/, /\*\) ;/' ../Include/cholmod_core.h > _transpose_unsym.tex ./getproto '/int cholmod_transpose_sym/, /\*\) ;/' ../Include/cholmod_core.h > _transpose_sym.tex ./getproto '/cholmod_sparse \*cholmod_ptranspose/, /\*\) ;/' ../Include/cholmod_core.h > _ptranspose.tex ./getproto '/int cholmod_sort/, /\*\) ;/' ../Include/cholmod_core.h > _sort.tex ./getproto '/cholmod_sparse \*cholmod_band/, /\*\) ;/' ../Include/cholmod_core.h > _band.tex ./getproto '/int cholmod_band_inplace/, /\*\) ;/' ../Include/cholmod_core.h > _band_inplace.tex ./getproto '/cholmod_sparse \*cholmod_aat/, /\*\) ;/' ../Include/cholmod_core.h > _aat.tex ./getproto '/cholmod_sparse \*cholmod_copy_sparse/, /\*\) ;/' ../Include/cholmod_core.h > _copy_sparse.tex ./getproto '/cholmod_sparse \*cholmod_copy /, /\*\) ;/' ../Include/cholmod_core.h > _copy.tex ./getproto '/cholmod_sparse \*cholmod_add/, /\*\) ;/' ../Include/cholmod_core.h > _add.tex ./getproto '/int cholmod_sparse_xtype/, /\*\) ;/' ../Include/cholmod_core.h > _sparse_xtype.tex ./getproto '/typedef struct cholmod_factor/, /^}/' ../Include/cholmod_core.h > _factor.tex ./getproto '/cholmod_factor \*cholmod_allocate_factor/, /\*\) ;/' ../Include/cholmod_core.h > _allocate_factor.tex ./getproto '/int cholmod_free_factor/, /\*\) ;/' ../Include/cholmod_core.h > _free_factor.tex ./getproto '/int cholmod_reallocate_factor/, /\*\) ;/' ../Include/cholmod_core.h > _reallocate_factor.tex ./getproto '/int cholmod_change_factor/, /\*\) ;/' ../Include/cholmod_core.h > _change_factor.tex ./getproto '/int cholmod_pack_factor/, /\*\) ;/' ../Include/cholmod_core.h > _pack_factor.tex ./getproto '/int cholmod_reallocate_column/, /\*\) ;/' ../Include/cholmod_core.h > _reallocate_column.tex ./getproto '/cholmod_sparse \*cholmod_factor_to_sparse/, /\*\) ;/' ../Include/cholmod_core.h > _factor_to_sparse.tex ./getproto '/cholmod_factor \*cholmod_copy_factor/, /\*\) ;/' ../Include/cholmod_core.h > _copy_factor.tex ./getproto '/int cholmod_factor_xtype/, /\*\) ;/' ../Include/cholmod_core.h > _factor_xtype.tex ./getproto '/typedef struct cholmod_dense/, /^}/' ../Include/cholmod_core.h > _dense.tex ./getproto '/cholmod_dense \*cholmod_allocate_dense/, /\*\) ;/' ../Include/cholmod_core.h > _allocate_dense.tex ./getproto '/cholmod_dense \*cholmod_zeros/, /\*\) ;/' ../Include/cholmod_core.h > _zeros.tex ./getproto '/cholmod_dense \*cholmod_ones/, /\*\) ;/' ../Include/cholmod_core.h > _ones.tex ./getproto '/cholmod_dense \*cholmod_eye/, /\*\) ;/' ../Include/cholmod_core.h > _eye.tex ./getproto '/int cholmod_free_dense/, /\*\) ;/' ../Include/cholmod_core.h > _free_dense.tex ./getproto '/cholmod_dense \*cholmod_sparse_to_dense/, /\*\) ;/' ../Include/cholmod_core.h > _sparse_to_dense.tex ./getproto '/cholmod_sparse \*cholmod_dense_to_sparse/, /\*\) ;/' ../Include/cholmod_core.h > _dense_to_sparse.tex ./getproto '/cholmod_dense \*cholmod_copy_dense/, /\*\) ;/' ../Include/cholmod_core.h > _copy_dense.tex ./getproto '/int cholmod_copy_dense2/, /\*\) ;/' ../Include/cholmod_core.h > _copy_dense2.tex ./getproto '/int cholmod_dense_xtype/, /\*\) ;/' ../Include/cholmod_core.h > _dense_xtype.tex ./getproto '/typedef struct cholmod_triplet/, /^}/' ../Include/cholmod_core.h > _triplet.tex ./getproto '/cholmod_triplet \*cholmod_allocate_triplet/, /\*\) ;/' ../Include/cholmod_core.h > _allocate_triplet.tex ./getproto '/int cholmod_free_triplet/, /\*\) ;/' ../Include/cholmod_core.h > _free_triplet.tex ./getproto '/int cholmod_reallocate_triplet/, /\*\) ;/' ../Include/cholmod_core.h > _reallocate_triplet.tex ./getproto '/cholmod_triplet \*cholmod_sparse_to_triplet/, /\*\) ;/' ../Include/cholmod_core.h > _sparse_to_triplet.tex ./getproto '/cholmod_sparse \*cholmod_triplet_to_sparse/, /\*\) ;/' ../Include/cholmod_core.h > _triplet_to_sparse.tex ./getproto '/cholmod_triplet \*cholmod_copy_triplet/, /\*\) ;/' ../Include/cholmod_core.h > _copy_triplet.tex ./getproto '/int cholmod_triplet_xtype/, /\*\) ;/' ../Include/cholmod_core.h > _triplet_xtype.tex ./getproto '/void \*cholmod_malloc/, /\*\) ;/' ../Include/cholmod_core.h > _malloc.tex ./getproto '/void \*cholmod_calloc/, /\*\) ;/' ../Include/cholmod_core.h > _calloc.tex ./getproto '/void \*cholmod_free/, /\*\) ;/' ../Include/cholmod_core.h > _free.tex ./getproto '/void \*cholmod_realloc/, /\*\) ;/' ../Include/cholmod_core.h > _realloc.tex ./getproto '/int cholmod_realloc_multiple/, /\*\) ;/' ../Include/cholmod_core.h > _realloc_multiple.tex ./getproto '/itype defines the/, /define CHOLMOD_SUPERNODAL/' ../Include/cholmod_core.h > _defn.tex ./getproto '/int cholmod_check_common/, /\*\) ;/' ../Include/cholmod_check.h > _check_common.tex ./getproto '/int cholmod_print_common/, /\*\) ;/' ../Include/cholmod_check.h > _print_common.tex ./getproto '/int cholmod_check_sparse/, /\*\) ;/' ../Include/cholmod_check.h > _check_sparse.tex ./getproto '/int cholmod_print_sparse/, /\*\) ;/' ../Include/cholmod_check.h > _print_sparse.tex ./getproto '/int cholmod_check_dense/, /\*\) ;/' ../Include/cholmod_check.h > _check_dense.tex ./getproto '/int cholmod_print_dense/, /\*\) ;/' ../Include/cholmod_check.h > _print_dense.tex ./getproto '/int cholmod_check_factor/, /\*\) ;/' ../Include/cholmod_check.h > _check_factor.tex ./getproto '/int cholmod_print_factor/, /\*\) ;/' ../Include/cholmod_check.h > _print_factor.tex ./getproto '/int cholmod_check_triplet/, /\*\) ;/' ../Include/cholmod_check.h > _check_triplet.tex ./getproto '/int cholmod_print_triplet/, /\*\) ;/' ../Include/cholmod_check.h > _print_triplet.tex ./getproto '/int cholmod_check_subset/, /\*\) ;/' ../Include/cholmod_check.h > _check_subset.tex ./getproto '/int cholmod_print_subset/, /\*\) ;/' ../Include/cholmod_check.h > _print_subset.tex ./getproto '/int cholmod_check_perm/, /\*\) ;/' ../Include/cholmod_check.h > _check_perm.tex ./getproto '/int cholmod_print_perm/, /\*\) ;/' ../Include/cholmod_check.h > _print_perm.tex ./getproto '/int cholmod_check_parent/, /\*\) ;/' ../Include/cholmod_check.h > _check_parent.tex ./getproto '/int cholmod_print_parent/, /\*\) ;/' ../Include/cholmod_check.h > _print_parent.tex ./getproto '/cholmod_triplet \*cholmod_read_triplet/, /\*\) ;/' ../Include/cholmod_check.h > _read_triplet.tex ./getproto '/cholmod_sparse \*cholmod_read_sparse/, /\*\) ;/' ../Include/cholmod_check.h > _read_sparse.tex ./getproto '/cholmod_dense \*cholmod_read_dense/, /\*\) ;/' ../Include/cholmod_check.h > _read_dense.tex ./getproto '/void \*cholmod_read_matrix/, /\*\) ;/' ../Include/cholmod_check.h > _read_matrix.tex ./getproto '/int cholmod_write_sparse/, /\*\) ;/' ../Include/cholmod_check.h > _write_sparse.tex ./getproto '/int cholmod_write_dense/, /\*\) ;/' ../Include/cholmod_check.h > _write_dense.tex ./getproto '/cholmod_factor \*cholmod_analyze /, /\*\) ;/' ../Include/cholmod_cholesky.h > _analyze.tex ./getproto '/cholmod_factor \*cholmod_analyze_p/, /\*\) ;/' ../Include/cholmod_cholesky.h > _analyze_p.tex ./getproto '/int cholmod_factorize /, /\*\) ;/' ../Include/cholmod_cholesky.h > _factorize.tex ./getproto '/int cholmod_factorize_p/, /\*\) ;/' ../Include/cholmod_cholesky.h > _factorize_p.tex ./getproto '/cholmod_dense \*cholmod_solve/, /\*\) ;/' ../Include/cholmod_cholesky.h > _solve.tex ./getproto '/cholmod_sparse \*cholmod_spsolve/, /\*\) ;/' ../Include/cholmod_cholesky.h > _spsolve.tex ./getproto '/int cholmod_etree/, /\*\) ;/' ../Include/cholmod_cholesky.h > _etree.tex ./getproto '/int cholmod_rowcolcounts/, /\*\) ;/' ../Include/cholmod_cholesky.h > _rowcolcounts.tex ./getproto '/int cholmod_analyze_ordering/, /\*\) ;/' ../Include/cholmod_cholesky.h > _analyze_ordering.tex ./getproto '/int cholmod_amd/, /\*\) ;/' ../Include/cholmod_cholesky.h > _amd.tex ./getproto '/int cholmod_colamd/, /\*\) ;/' ../Include/cholmod_cholesky.h > _colamd.tex ./getproto '/int cholmod_rowfac/, /\*\) ;/' ../Include/cholmod_cholesky.h > _rowfac.tex ./getproto '/int cholmod_rowfac_mask/, /\*\) ;/' ../Include/cholmod_cholesky.h > _rowfac_mask.tex ./getproto '/int cholmod_row_subtree/, /\*\) ;/' ../Include/cholmod_cholesky.h > _row_subtree.tex ./getproto '/int cholmod_row_lsubtree/, /\*\) ;/' ../Include/cholmod_cholesky.h > _row_lsubtree.tex ./getproto '/int cholmod_resymbol /, /\*\) ;/' ../Include/cholmod_cholesky.h > _resymbol.tex ./getproto '/int cholmod_resymbol_noperm/, /\*\) ;/' ../Include/cholmod_cholesky.h > _resymbol_noperm.tex ./getproto '/double cholmod_rcond/, /\*\) ;/' ../Include/cholmod_cholesky.h > _rcond.tex ./getproto '/long cholmod_postorder/, /\*\) ;/' ../Include/cholmod_cholesky.h > _postorder.tex ./getproto '/int cholmod_updown /, /\*\) ;/' ../Include/cholmod_modify.h > _updown.tex ./getproto '/int cholmod_updown_solve/, /\*\) ;/' ../Include/cholmod_modify.h > _updown_solve.tex ./getproto '/int cholmod_updown_mark/, /\*\) ;/' ../Include/cholmod_modify.h > _updown_mark.tex ./getproto '/int cholmod_updown_mask/, /\*\) ;/' ../Include/cholmod_modify.h > _updown_mask.tex ./getproto '/int cholmod_rowadd /, /\*\) ;/' ../Include/cholmod_modify.h > _rowadd.tex ./getproto '/int cholmod_rowadd_solve/, /\*\) ;/' ../Include/cholmod_modify.h > _rowadd_solve.tex ./getproto '/int cholmod_rowadd_mark/, /\*\) ;/' ../Include/cholmod_modify.h > _rowadd_mark.tex ./getproto '/int cholmod_rowdel /, /\*\) ;/' ../Include/cholmod_modify.h > _rowdel.tex ./getproto '/int cholmod_rowdel_solve/, /\*\) ;/' ../Include/cholmod_modify.h > _rowdel_solve.tex ./getproto '/int cholmod_rowdel_mark/, /\*\) ;/' ../Include/cholmod_modify.h > _rowdel_mark.tex ./getproto '/int cholmod_drop/, /\*\) ;/' ../Include/cholmod_matrixops.h > _drop.tex ./getproto '/double cholmod_norm_dense/, /\*\) ;/' ../Include/cholmod_matrixops.h > _norm_dense.tex ./getproto '/double cholmod_norm_sparse/, /\*\) ;/' ../Include/cholmod_matrixops.h > _norm_sparse.tex ./getproto '/cholmod_sparse \*cholmod_horzcat/, /\*\) ;/' ../Include/cholmod_matrixops.h > _horzcat.tex ./getproto '/define CHOLMOD_SCALAR/, /\*\) ;/' ../Include/cholmod_matrixops.h > _scale.tex ./getproto '/int cholmod_sdmult/, /\*\) ;/' ../Include/cholmod_matrixops.h > _sdmult.tex ./getproto '/cholmod_sparse \*cholmod_ssmult/, /\*\) ;/' ../Include/cholmod_matrixops.h > _ssmult.tex ./getproto '/cholmod_sparse \*cholmod_submatrix/, /\*\) ;/' ../Include/cholmod_matrixops.h > _submatrix.tex ./getproto '/cholmod_sparse \*cholmod_vertcat/, /\*\) ;/' ../Include/cholmod_matrixops.h > _vertcat.tex ./getproto '/int cholmod_symmetry/, /\*\) ;/' ../Include/cholmod_matrixops.h > _symmetry.tex ./getproto '/int cholmod_super_symbolic/, /\*\) ;/' ../Include/cholmod_supernodal.h > _super_symbolic.tex ./getproto '/int cholmod_super_numeric/, /\*\) ;/' ../Include/cholmod_supernodal.h > _super_numeric.tex ./getproto '/int cholmod_super_lsolve/, /\*\) ;/' ../Include/cholmod_supernodal.h > _super_lsolve.tex ./getproto '/int cholmod_super_ltsolve/, /\*\) ;/' ../Include/cholmod_supernodal.h > _super_ltsolve.tex ./getproto '/long cholmod_nested_dissection/, /\*\) ;/' ../Include/cholmod_partition.h > _nested_dissection.tex ./getproto '/int cholmod_metis/, /\*\) ;/' ../Include/cholmod_partition.h > _metis.tex ./getproto '/int cholmod_ccolamd/, /\*\) ;/' ../Include/cholmod_partition.h > _ccolamd.tex ./getproto '/int cholmod_camd/, /\*\) ;/' ../Include/cholmod_partition.h > _camd.tex ./getproto '/int cholmod_csymamd/, /\*\) ;/' ../Include/cholmod_partition.h > _csymamd.tex ./getproto '/int cholmod_csymamd/, /\*\) ;/' ../Include/cholmod_partition.h > _csymamd.tex ./getproto '/long cholmod_bisect/, /\*\) ;/' ../Include/cholmod_partition.h > _bisect.tex ./getproto '/long cholmod_metis_bisector/, /\*\) ;/' ../Include/cholmod_partition.h > _metis_bisector.tex ./getproto '/long cholmod_collapse_septree/, /\*\) ;/' ../Include/cholmod_partition.h > _collapse_septree.tex pdflatex UserGuide bibtex UserGuide pdflatex UserGuide pdflatex UserGuide distclean: purge purge: clean - $(RM) _temp.awk _*.tex *.dvi *.aux *.log *.lof *.lot *.toc *.bak *.bbl *.blg clean: - $(RM) $(CLEAN) SuiteSparse/CHOLMOD/Doc/mfooter.tex0000644001170100242450000000012410304300375015726 0ustar davisfac\end{verbatim} } \noindent\hspace{0.85in}\rule[0.25in]{5.2in}{1pt} \vspace{-0.15in} SuiteSparse/CHOLMOD/Doc/rule.awk0000644001170100242450000000003510304303017015201 0ustar davisfac{ print " ", $0 } SuiteSparse/CHOLMOD/Doc/UserGuide.bib0000644001170100242450000001212110533334034016106 0ustar davisfac@string{SIMAX = "{SIAM} J. Matrix Anal. Applic."} @string{TOMS = "{ACM} Trans. Math. Softw."} @string{SIAMJSC = "{SIAM} J. Sci. Comput."} @article{DavisHager06, author={Davis, T. A. and Hager, W. W.}, title={Dynamic supernodes in sparse {Cholesky} update/downdate and triangular solves}, journal=TOMS, year={submitted in 2006} } @article{ChenDavisHagerRajamanickam06, author={Chen, Y. and Davis, T. A. and Hager, W. W. and Rajamanickam, S.}, title={Algorithm 8xx: {CHOLMOD}, supernodal sparse {Cholesky} factorization and update/downdate}, journal=TOMS, year={submitted in 2006} } @article{DavisHager99, author={Davis, T. A. and Hager, W. W.}, title={Modifying a sparse {C}holesky factorization}, journal=SIMAX, year={1999} ,volume={20} ,number={3} ,pages={606--627} } @article{DavisHager01, author={Davis, T. A. and Hager, W. W.}, title={Multiple-Rank Modifications of a Sparse {C}holesky Factorization}, journal=SIMAX, year={2001} ,volume={22} ,number={4} ,pages={997--1013} } @article{DavisHager05, author={Davis, T. A. and Hager, W. W.}, title={Row modifications of a sparse {Cholesky} factorization}, journal=SIMAX, year={2005} ,volume={26} ,number={3} ,pages={621--639} } @article{AmestoyDavisDuff96, author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.}, title={An approximate minimum degree ordering algorithm}, journal=SIMAX, year={1996} ,volume={17} ,number={4} ,pages={886--905} } @article{Davis05, author={Davis, T. A.}, title={Algorithm 849: A concise sparse {Cholesky} algorithm}, journal=TOMS, year={2005},volume={31},number={4},pages={587--591}} @article{DavisGilbertLarimoreNg00, author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.}, title={A column approximate minimum degree ordering algorithm}, journal=TOMS, year={2004} ,volume={30} ,number={3} ,pages={353--376}} @article{DavisGilbertLarimoreNg00_algo, author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.}, title={Algorithm 836: {COLAMD}, a column approximate minimum degree ordering algorithm}, journal=TOMS, year={2004} ,volume={30} ,number={3} ,pages={377--380}} @article{NgPeyton91b, author={Ng, E. and Peyton, B.}, title={Block sparse {C}holesky algorithms on advanced uniprocessor computers}, journal=SIAMJSC, year={1993} ,volume={14} ,pages={1034--1056} } @article{Liu86c, author={Liu, J. W. H.}, title={A Compact Row Storage Scheme for {C}holesky Factors Using Elimination Trees}, journal=TOMS, year={1986}, volume={12}, number={2}, pages={127--148}, } @article{Liu90a, author={Liu, J. W. H.}, title={The Role of Elimination Trees in Sparse Factorization}, journal=SIMAX, year={1990} ,volume={11} ,number={1} ,pages={134--172} } @article{GilbertNgPeyton94, author={Gilbert, J. R. and Ng, E. G. and Peyton, B. W.}, title={An efficient algorithm to compute row and column counts for sparse {C}holesky factorization}, journal=SIMAX, year={1994} ,volume={15} ,number={4} ,pages={1075--1091} } @article{GilbertLiNgPeyton01, author={Gilbert, J. R. and Li, X. S. and Ng, E. G. and Peyton, B. W.}, title={Computing row and column counts for sparse {QR} and {LU} factorization}, journal={{BIT}}, year={2001} ,volume={41} ,number={4} ,pages={693--710} } @book{LAPACK, author={Anderson, E. and Bai, Z. and Bischof, C. and Blackford, S. and Demmel, J. and Dongarra, J. and {Du Croz}, J. and Greenbaum, A. and Hammarling, S. and McKenny, A. and Sorensen, D.}, title={{LAPACK} Users' Guide, 3rd ed.}, publisher={{SIAM}}, year={1999} } @article{ACM679a, author={Dongarra, J. J. and {Du Croz}, J. and Duff, I. S. and Hammarling, S.}, title={A set of level-3 basic linear algebra subprograms}, journal=TOMS, year={1990} ,volume={16} ,number={1} ,pages={1--17} } @article{KarypisKumar98, author={Karypis, G. and Kumar, V.}, title={A fast and high quality multilevel scheme for partitioning irregular graphs}, journal=SIAMJSC, year=1998 ,volume={20} ,number={1} ,pages={359--392} } @article{GilbertMolerSchreiber, author={Gilbert, J. R. and Moler, C. and Schreiber, R.}, title={Sparse matrices in {MATLAB}: design and implementation}, journal=SIMAX, year={1992} ,volume={13} ,number={1} ,pages={333--356} } @article{AmestoyDavisDuff03, author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.}, title={Algorithm 837: {AMD}, an approximate minimum degree ordering algorithm}, journal=TOMS, year={2004} ,volume={30} ,number={3} ,pages={381-388}} @article{GouldHuScott05, author={Gould, N. I. M. and Hu, Y. and Scott, J. A.}, title={A numerical evaluation of sparse direct solvers for the solution of large sparse, symmetric linear systems of equations}, journal=TOMS, year={to appear} } @techreport{GouldHuScott05b, author={Gould, N. I. M. and Hu, Y. and Scott, J. A.}, title={Complete results from a numerical evaluation of sparse direct solvers for the solution of large sparse, symmetric linear systems of equations}, institution={CCLRC, Rutherford Appleton Laboratory}, number={Internal report 2005-1 (revision 1)}, year={2005}, howpublished={www.numerical.rl.ac.uk/reports/reports.shtml} } SuiteSparse/CHOLMOD/Doc/UserGuide.pdf0000644001170100242450000160123510711441355016141 0ustar davisfac%PDF-1.4 3 0 obj << /Length 2278 /Filter /FlateDecode >> stream xڍXIw6WLHf^^N˴ՓC-R6)Q!)_ZtX BW t\6P` R%&8X߻Le;ő owUQ2j2t?}G2y!~MuI2;Yȹɾ{* ~ k}lM1{[ Qd0SRd2IIu3)Hjܿ{n,z0,Q$X# $3F5.KEnz8U ir.~&4|:Rp&e$lPtrMW]fɌ rQQ-1|ܬk ݲ*7˒c_7xjS*R6J7ճWiG鴪ĭ$=#];>/" 6SZ(MSP ߎ !VxdOžR6Df$K-oe}&m&R3R!Sa 7% Ȓ8-&2OR<@d uXFSH5|fG'" #fJ[ ,`kY}[-yj MW3qdIH +"J^@,YVQPzKF DSI%R)rNej# 9pB S\,Vqh2gaLqҴ!M 6y(/C>|ktv+Ha 煑G98ɹ'95A֥(Z'ݞ5}1|l uR1X2MzwȾ6̌ "6zJA3NAĀ؋3PBځsHƃT1Ȼ6)h *`=aQd8hRo\)>5>Tȃ"uϧ5`%bW(p/ p6⌊igpF.S.?9O& ?U˶UγPs7f;^{^el]Eqa ߡq*m!Eu֥5fel@i8@`68Y3d׌?D2 ?C{ ÿ"XEd|jj?c>PAYy`㌻mTFHùͷGYKsw:Gk%0P9`zާ#V=N 3]7myZOڢCc3Qc&Lw4FXJbWI }׬Kf';e.a :s>/p|y6ToA_#o?rҷl)[D?${ghonhWF[7ѡGGY7$' pyM;%G ^YЋ%Bc-2ԎePIҿtZHhf dC7xx1Z)<YZ?AaGC{=f'bUݵ3~ Hl9e`5gf| .8cl3uP )x.D\ X9C)endstream endobj 2 0 obj << /Type /Page /Contents 3 0 R /Resources 1 0 R /MediaBox [0 0 595.2756 841.8898] /Parent 34 0 R >> endobj 1 0 obj << /Font << /F16 6 0 R /F17 9 0 R /F26 12 0 R /F8 15 0 R /F7 18 0 R /F33 21 0 R /F35 24 0 R /F36 27 0 R /F19 30 0 R /F27 33 0 R >> /ProcSet [ /PDF /Text ] >> endobj 37 0 obj << /Length 2391 /Filter /FlateDecode >> stream x[[o~ׯT9Q>mE셦$J9]Ƚ.盙^1gc0t<[) VN:u,5,Ӑ'\ "dt:j&qVZ~[5%)q2Ӧu4[fyM菿bXo%$TÊ#ߗ5 iDmmJE\yѥ [oKuP` o\?WτQwя}3~J[$>&3@x <8jA[}++ '޽1O_ՋoZi:'K-]5!94P("s)^,tR0T<5׫#8mSHG֌{=`DfMoRH ~M0e t3DI}yr`;*ѻwn)Zήb8C54dh Lyd>&XM1D/ˉ32kD"*[8A!hc.l R}*l%7>l4?C):ΪX~L48@|ɪpp)\KJ%9Oc~"c&Cb 1˒̾ПoˬS;3vpMϳ>jκ؂(Jk^̴imnH=-i#O*&Y}}χf~gqIj @Xdu\*5]Ϊ,2/!0wWiey:. 2˭)Ss|(X޻¤ύm4gѤ9իEYk{{i(>)gCj88/:5 3iݴhӖx/xWL5͌>J(ZM|sI:3T= cSE$b]Zh@ 0sKt!jEfb]AjLElJ(:Vti.\- (wt}mq_uߗa\sպkYO@̭ Φ#}dIƂW`eW/g3.}P8G-w1y=.5Xy 6UUtC,lA$jVC޴66v*m&J\t vo)=DcєffVA|$4}sSyYɅx4lYQ nrV_$@l'5LPm\bqb;X7->ώ]v3 ocMrL x6.k _b5 U<:q ?8!@lnlc%_>~,# {`aOiQL|'.sz^2mq{񁟛qZl~5qh EB&)l<wP4挼c>CP ΕCRIĕԧDE(~YuMtq'Эsl$ TXqHDHRZ$JlLI/2R.l.ՅK)PiC%S4/0 xQ(ɕ<5V D@_Doi> endobj 35 0 obj << /Font << /F38 40 0 R /F26 12 0 R /F8 15 0 R /F36 27 0 R /F33 21 0 R >> /ProcSet [ /PDF /Text ] >> endobj 43 0 obj << /Length 3045 /Filter /FlateDecode >> stream x\Ks6W(e#rKJ%ܒhh# % hPHzd\fhjv@?o޼NHԐۻ LI*qmwLT$xZo#l&Wt?%UvAbI_-GX`[fc l~NE6~$'H1ʼn 1T9[-O%a𿡕,֛.1cXN7x],`v՛98JX*cNeRy31Tn:;&DB4Cj͎>=⧹7.oRzu~@/`:@XiT -|Q9џy/ٶC/NhPuªBs[a?;B[~jk(" Wh$4)psMAM'+O+'cPE;TYTφ̣ -L$f܂fV"''ܒf}M@?$Z(6y5eȲyDDJyeTG;Q3SeNb*\l$?`helUy3_ ke|I*ͦ[[A2j^k{:S:M!a4msr>43gWvL D9'>'Jh^x:nߍK8@@ a_L7 Mie=ʹﲇ+"D# C2}[ PN^ t34B*b=`kvOr2eclѴKqYw.sZڬhU&lnN~5܀E;4V !$jL5C9XZi)MК㐠4AISEIJ\[[8`qTF1t6('iyءrAx<˼\`CL Bt(继C1q*Ѫv;?ӯHxOpI:j ^1:.6d OgϛU;lǮVN9F+>y Ϫիu659>||r& Yu>k:{iO|J'I")Ote̍ݘ\eÁߔu{b۷v8~MG{$B/" hؐeakQuh>v 1_]kbaE^5F /5龞)(d1E kv !pGvWw^>=04U-`NW1h YODH$$59)1I*9oո#rXoq&0b#:&`t(~Сp-nvm8J6t2mVKM+2Zr 4fxŁs9_4#մঞ'vت9>:T]If:Ayc^DZOوjmaDe3`m$,{PS폇ӹ p~ ޏ9A=+=:{srͦ&Z)< m 8ޓ^w>/S=nxKz?e"jڬTDK3 YZٳ螆vq-V,87v;jn}8 %#TAdP/dkO:ޛ7pijIZst@OA駟Ev;Kb՘,UI9*emW*D<,{F,%}X(i7\+'hVjLNu pkӫ㑩cF!^y:6tkU7z<}HOFd*}e+`s1k,xg>u~@B_%[F񰬟*Te4;pP?BʢAAURMW,{l#3;-4ҧ96JKl0s" RyJlYS-mX󣲊%)UZӨ1|k=|x|E>B!_ֺt{Ⱐ׌ǼcE_c5@?j)dϚ.Xmw F}n/G Wt 0^C&'\ј!^x: I(BWHהq(Ps!d Ot 1a('㠘Fb6,b>;#b蚠fի-Tݔ0 2u}m!y,}k:;hfߍ)%4¸/A #=4<ݹ:p *U5AK_[{qJXU˪+öi-epȲתnp2u2$O[B^ި ${Y 0l;Yb֓}PdcI> endobj 41 0 obj << /Font << /F8 15 0 R /F36 27 0 R /F26 12 0 R /F33 21 0 R >> /ProcSet [ /PDF /Text ] >> endobj 46 0 obj << /Length 2912 /Filter /FlateDecode >> stream x\Ks7WHU0ޏZR-WbŤPt_<LbToO>|3F>ͬ%B 33g'O|(t.h#tylo?>]͘ .o6W^^/WgmB~}%q.< n\73E4 jXʙ_Kمzowa;$%Ѯ )eŮΛoB|ys`s `9qE%Qx_V+ B%a=[죖("Le*r?0*L SJwaǼkn=w8/~z2)jI,2y˛/E5VAZI e BIޥ$|k/{`疙7|oO1_YX#9ږr* hD$`H(wOFz'w⓷}Dn0!%s/{m,ӆX&2EEx0spDIc "g!zթs?5,o7Go7c? 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00000 n 0000448262 00000 n 0000448315 00000 n trailer << /Size 537 /Root 535 0 R /Info 536 0 R /ID [<0AF0B355A3F6134800C6E81B7120BC6D> <0AF0B355A3F6134800C6E81B7120BC6D>] >> startxref 448519 %%EOF SuiteSparse/CHOLMOD/Doc/UserGuide.tex0000644001170100242450000047510010711441317016165 0ustar davisfac%------------------------------------------------------------------------------- % The CHOLMOD/Doc/UserGuide.tex file. %------------------------------------------------------------------------------- \documentclass[11pt]{article} \newcommand{\m}[1]{{\bf{#1}}} % for matrices and vectors \newcommand{\tr}{^{\sf T}} % transpose \newcommand{\new}[1]{\overline{#1}} \topmargin 0in \textheight 9in \oddsidemargin 0pt \evensidemargin 0pt \textwidth 6.5in \begin{document} \author{Timothy A. Davis \\ Dept. of Computer and Information Science and Engineering \\ Univ. of Florida, Gainesville, FL} \title{User Guide for CHOLMOD: a sparse Cholesky factorization and modification package} \date{Version 1.6, Nov 1, 2007} \maketitle %------------------------------------------------------------------------------- \begin{abstract} CHOLMOD\footnote{CHOLMOD is short for CHOLesky MODification, since a key feature of the package is its ability to update/downdate a sparse Cholesky factorization} is a set of routines for factorizing sparse symmetric positive definite matrices of the form $\m{A}$ or $\m{AA}\tr$, updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system $\m{Lx}=\m{b}$, and many other sparse matrix functions for both symmetric and unsymmetric matrices. Its supernodal Cholesky factorization relies on LAPACK and the Level-3 BLAS, and obtains a substantial fraction of the peak performance of the BLAS. Both real and complex matrices are supported. CHOLMOD is written in ANSI/ISO C, with both C and MATLAB interfaces. This code works on Microsoft Windows and many versions of Unix and Linux. \end{abstract} %------------------------------------------------------------------------------- CHOLMOD Copyright\copyright 2005-2006 by Timothy A. Davis. Portions are also copyrighted by William W. Hager (the {\tt Modify} Module), and the University of Florida (the {\tt Partition} and {\tt Core} Modules). All Rights Reserved. Some of CHOLMOD's Modules are distributed under the GNU General Public License, and others under the GNU Lesser General Public License. Refer to each Module for details. CHOLMOD is also available under other licenses that permit its use in proprietary applications; contact the authors for details. See http://www.cise.ufl.edu/research/sparse for the code and all documentation, including this User Guide. \newpage \tableofcontents %------------------------------------------------------------------------------- \newpage \section{Overview} %------------------------------------------------------------------------------- CHOLMOD is a set of ANSI C routines for solving systems of linear equations, $\m{Ax}=\m{b}$, when $\m{A}$ is sparse and symmetric positive definite, and $\m{x}$ and $\m{b}$ can be either sparse or dense.\footnote{Some support is provided for symmetric indefinite matrices.} Complex matrices are supported, in two different formats. CHOLMOD includes high-performance left-looking supernodal factorization and solve methods \cite{NgPeyton91b}, based on LAPACK \cite{LAPACK} and the BLAS \cite{ACM679a}. After a matrix is factorized, its factors can be updated or downdated using the techniques described by Davis and Hager in \cite{DavisHager99,DavisHager01,DavisHager05}. Many additional sparse matrix operations are provided, for both symmetric and unsymmetric matrices (square or rectangular), including sparse matrix multiply, add, transpose, permutation, scaling, norm, concatenation, sub-matrix access, and converting to alternate data structures. Interfaces to many ordering methods are provided, including minimum degree (AMD \cite{AmestoyDavisDuff96,AmestoyDavisDuff03}, COLAMD \cite{DavisGilbertLarimoreNg00_algo,DavisGilbertLarimoreNg00}), constrained minimum degree (CSYMAMD, CCOLAMD, CAMD), and graph-partitioning-based nested dissection (METIS \cite{KarypisKumar98}). Most of its operations are available within MATLAB via mexFunction interfaces. A pair of articles on CHOLMOD has been submitted to the ACM Transactions on Mathematical Softare: \cite{ChenDavisHagerRajamanickam06,DavisHager06}. CHOLMOD 1.0 replaces {\tt chol} (the sparse case), {\tt symbfact}, and {\tt etree} in MATLAB 7.2 (R2006a), and is used for {\tt x=A}$\backslash${\tt b} when {\tt A} is symmetric positive definite \cite{GilbertMolerSchreiber}. It will replace {\tt sparse} in a future version of MATLAB. The C-callable CHOLMOD library consists of 133 user-callable routines and one include file. Each routine comes in two versions, one for {\tt int} integers and another for {\tt long}. Many of the routines can support either real or complex matrices, simply by passing a matrix of the appropriate type. Nick Gould, Yifan Hu, and Jennifer Scott have independently tested CHOLMOD's performance, comparing it with nearly a dozen or so other solvers \cite{GouldHuScott05,GouldHuScott05b}. Its performance was quite competitive. %------------------------------------------------------------------------------- \newpage \section{Primary routines and data structures} %------------------------------------------------------------------------------- Five primary CHOLMOD routines are required to factorize $\m{A}$ or $\m{AA}\tr$ and solve the related system $\m{Ax}=\m{b}$ or $\m{AA}\tr\m{x}=\m{b}$, for either the real or complex cases: \begin{enumerate} \item {\tt cholmod\_start}: This must be the first call to CHOLMOD. \item {\tt cholmod\_analyze}: Finds a fill-reducing ordering, and performs the symbolic factorization, either simplicial (non-supernodal) or supernodal. \item {\tt cholmod\_factorize}: Numerical factorization, either simplicial or supernodal, $\m{LL}\tr$ or $\m{LDL}\tr$ using either the symbolic factorization from {\tt cholmod\_analyze} or the numerical factorization from a prior call to {\tt cholmod\_factorize}. \item {\tt cholmod\_solve}: Solves $\m{Ax}=\m{b}$, or many other related systems, where $\m{x}$ and $\m{b}$ are dense matrices. The {\tt cholmod\_spsolve} routine handles the sparse case. Any mixture of real and complex $\m{A}$ and $\m{b}$ are allowed. \item {\tt cholmod\_finish}: This must be the last call to CHOLMOD. \end{enumerate} Additional routines are also required to create and destroy the matrices $\m{A}$, $\m{x}$, $\m{b}$, and the $\m{LL}\tr$ or $\m{LDL}\tr$ factorization. CHOLMOD has five kinds of data structures, referred to as objects and implemented as pointers to {\tt struct}'s: \begin{enumerate} \item {\tt cholmod\_common}: parameter settings, statistics, and workspace used internally by CHOLMOD. See Section~\ref{cholmod_common} for details. \item {\tt cholmod\_sparse}: a sparse matrix in compressed-column form, either pattern-only, real, complex, or ``zomplex.'' In its basic form, the matrix {\tt A} contains: \begin{itemize} \item {\tt A->p}, an integer array of size {\tt A->ncol+1}. \item {\tt A->i}, an integer array of size {\tt A->nzmax}. \item {\tt A->x}, a {\tt double} array of size {\tt A->nzmax} or twice that for the complex case. This is compatible with the Fortran and ANSI C99 complex data type. \item {\tt A->z}, a {\tt double} array of size {\tt A->nzmax} if {\tt A} is zomplex. A zomplex matrix has a {\tt z} array, thus the name. This is compatible with the MATLAB representation of complex matrices. \end{itemize} For all four types of matrices, the row indices of entries of column {\tt j} are located in {\tt A->i [A->p [j] ... A->p [j+1]-1]}. For a real matrix, the corresponding numerical values are in {\tt A->x} at the same location. For a complex matrix, the entry whose row index is {\tt A->i [p]} is contained in {\tt A->x [2*p]} (the real part) and {\tt A->x [2*p+1]} (the imaginary part). For a zomplex matrix, the real part is in {\tt A->x [p]} and imaginary part is in {\tt A->z [p]}. See Section~\ref{cholmod_sparse} for more details. \item {\tt cholmod\_factor}: A symbolic or numeric factorization, either real, complex, or zomplex. It can be either an $\m{LL}\tr$ or $\m{LDL}\tr$ factorization, and either simplicial or supernodal. You will normally not need to examine its contents. See Section~\ref{cholmod_factor} for more details. \item {\tt cholmod\_dense}: A dense matrix, either real, complex or zomplex, in column-major order. This differs from the row-major convention used in C. A dense matrix {\tt X} contains \begin{itemize} \item {\tt X->x}, a double array of size {\tt X->nzmax} or twice that for the complex case. \item {\tt X->z}, a double array of size {\tt X->nzmax} if {\tt X} is zomplex. \end{itemize} For a real dense matrix $x_{ij}$ is {\tt X->x [i+j*d]} where {\tt d = X->d} is the leading dimension of {\tt X}. For a complex dense matrix, the real part of $x_{ij}$ is {\tt X->x [2*(i+j*d)]} and the imaginary part is {\tt X->x [2*(i+j*d)+1]}. For a zomplex dense matrix, the real part of $x_{ij}$ is {\tt X->x [i+j*d]} and the imaginary part is {\tt X->z [i+j*d]}. Real and complex dense matrices can be passed to LAPACK and the BLAS. See Section~\ref{cholmod_dense} for more details. \item {\tt cholmod\_triplet}: CHOLMOD's sparse matrix ({\tt cholmod\_sparse}) is the primary input for nearly all CHOLMOD routines, but it can be difficult for the user to construct. A simpler method of creating a sparse matrix is to first create a {\tt cholmod\_triplet} matrix, and then convert it to a {\tt cholmod\_sparse} matrix via the {\tt cholmod\_triplet\_to\_sparse} routine. In its basic form, the triplet matrix {\tt T} contains \begin{itemize} \item {\tt T->i} and {\tt T->j}, integer arrays of size {\tt T->nzmax}. \item {\tt T->x}, a double array of size {\tt T->nzmax} or twice that for the complex case. \item {\tt T->z}, a double array of size {\tt T->nzmax} if {\tt T} is zomplex. \end{itemize} The {\tt k}th entry in the data structure has row index {\tt T->i [k]} and column index {\tt T->j [k]}. For a real triplet matrix, its numerical value is {\tt T->x [k]}. For a complex triplet matrix, its real part is {\tt T->x [2*k]} and its imaginary part is {\tt T->x [2*k+1]}. For a zomplex matrix, the real part is {\tt T->x [k]} and imaginary part is {\tt T->z [k]}. The entries can be in any order, and duplicates are permitted. See Section~\ref{cholmod_triplet} for more details. \end{enumerate} Each of the five objects has a routine in CHOLMOD to create and destroy it. CHOLMOD provides many other operations on these objects as well. A few of the most important ones are illustrated in the sample program in the next section. %------------------------------------------------------------------------------- \newpage \section{Simple example program} %------------------------------------------------------------------------------- \input{_simple.tex} The {\tt Demo/cholmod\_simple.c} program illustrates the basic usage of CHOLMOD. It reads a triplet matrix from a file (in Matrix Market format), converts it into a sparse matrix, creates a linear system, solves it, and prints the norm of the residual. See the {\tt CHOLMOD/Demo/cholmod\_demo.c} program for a more elaborate example, and \newline {\tt CHOLMOD/Demo/cholmod\_l\_demo.c} for its {\tt long} integer version. %------------------------------------------------------------------------------- \newpage \section{Installation of the C-callable library} \label{Install} %------------------------------------------------------------------------------- CHOLMOD requires a suite of external packages, many of which are distributed along with CHOLMOD, but three of which are not. Those included with CHOLMOD are: \begin{itemize} \item AMD: an approximate minimum degree ordering algorithm, by Tim Davis, Patrick Amestoy, and Iain Duff \cite{AmestoyDavisDuff96,AmestoyDavisDuff03}. \item COLAMD: an approximate column minimum degree ordering algorithm, by Tim Davis, Stefan Larimore, John Gilbert, and Esmond Ng \cite{DavisGilbertLarimoreNg00_algo,DavisGilbertLarimoreNg00}. \item CCOLAMD: a constrained approximate column minimum degree ordering algorithm, by Tim Davis and Siva Rajamanickam, based directly on COLAMD. This package is not required if CHOLMOD is compiled with the {\tt -DNPARTITION} flag. \item CAMD: a constrained approximate minimum degree ordering algorithm, by Tim Davis and Yanqing Chen, based directly on AMD. This package is not required if CHOLMOD is compiled with the {\tt -DNPARTITION} flag. \item {\tt UFconfig}: a single place where all sparse matrix packages authored or co-authored by Davis are configured. Also includes a version of the {\tt xerbla} routine for the BLAS. \end{itemize} Three other packages are required for optimal performance: \begin{itemize} \item {\tt METIS 4.0.1}: a graph partitioning package by George Karypis, Univ. of Minnesota. Not needed if {\tt -DNPARTITION} is used. See http://www-users.cs.umn.edu/$\sim$karypis/metis. \item BLAS: the Basic Linear Algebra Subprograms. Not needed if {\tt -DNSUPERNODAL} is used. See http://www.netlib.org for the reference BLAS (not meant for production use). For Kazushige Goto's optimized BLAS (highly recommended for CHOLMOD) see \newline http://www.tacc.utexas.edu/$\sim$kgoto/ or http://www.cs.utexas.edu/users/flame/goto/. I recommend that you avoid the Intel MKL BLAS; one recent version returns NaN's, where both the Goto BLAS and the standard Fortran reference BLAS return the correct answer. See {\tt CHOLMOD/README} for more information. \item LAPACK: the Basic Linear Algebra Subprograms. Not needed if {\tt -DNSUPERNODAL} is used. See http://www.netlib.org. \end{itemize} You must first obtain and install METIS, LAPACK, and the BLAS. Next edit the system-dependent configurations in the {\tt UFconfig/UFconfig.mk} file. Sample configurations are provided for Linux, Macintosh, Sun Solaris, SGI IRIX, IBM AIX, and the DEC/Compaq Alpha. The most important configuration is the location of the BLAS, LAPACK, and METIS packages, since in its default configuration CHOLMOD cannot be compiled without them. \noindent Here are the various parameters that you can control in your {\tt UFconfig/UFconfig.mk} file: \begin{itemize} \item {\tt CC = } your C compiler, such as {\tt cc}. \item {\tt CFLAGS = } optimization flags, such as {\tt -O}. \item {\tt RANLIB = } your system's {\tt ranlib} program, if needed. \item {\tt AR =} the command to create a library (such as {\tt ar}). \item {\tt RM =} the command to delete a file. \item {\tt MV =} the command to rename a file. \item {\tt F77 =} the command to compile a Fortran program (optional). \item {\tt F77FLAGS =} the Fortran compiler flags (optional). \item {\tt F77LIB =} the Fortran libraries (optional). \item {\tt LIB = } basic libraries, such as {\tt -lm}. \item {\tt MEX =} the command to compile a MATLAB mexFunction. \item {\tt BLAS =} your BLAS library. \item {\tt LAPACK =} your LAPACK library. \item {\tt XERBLA =} a library containing the BLAS {\tt xerbla} routine, if required. \item {\tt METIS\_PATH =} the path to your copy of the METIS 4.0.1 source code. \item {\tt METIS =} your METIS library. \item {\tt CHOLMOD\_CONFIG = } configuration settings specific to CHOLMOD. \end{itemize} \noindent CHOLMOD's specific settings are given by the {\tt CHOLMOD\_CONFIG} string: \begin{itemize} \item {\tt -DNCHECK}: do not include the Check module. License: GNU LGPL. \item {\tt -DNCHOLESKY}: do not include the Cholesky module. License: GNU LGPL. \item {\tt -DNPARTITION}: do not include the Partition module. License: GNU LGPL. \item {\tt -DNGPL}: do not include any GNU GPL Modules in the CHOLMOD library. \item {\tt -DNMATRIXOPS}: do not include the MatrixOps module. License: GNU GPL. \item {\tt -DNMODIFY}: do not include the Modify module. License: GNU GPL. \item {\tt -DNSUPERNODAL}: do not include the Supernodal module. License: GNU GPL. \item {\tt -DNPRINT}: do not print anything. \item {\tt -D'LONGBLAS=long'} or {\tt -DLONGBLAS='long long'} defines the integers used by LAPACK and the BLAS (defaults to {\tt int}). \item {\tt -DNSUNPERF}: for Solaris only. If defined, do not use the Sun Performance Library. \item {\tt -DNLARGEFILE}: CHOLMOD now assumes support for large files (2GB or larger). If this causes problems, you can compile CHOLMOD with -DNLARGEFILE. To use large files, you should {\tt \#include "cholmod.h"} (or at least {\tt \#include "cholmod\_io64.h"}) before any other {\tt \#include} statements, in your application that uses CHOLMOD. You may need to use {\tt fopen64} to create a file pointer to pass to CHOLMOD, if you are using a non-gcc compiler. \end{itemize} Type {\tt make} in the {\tt CHOLMOD} directory. The AMD, COLAMD, CAMD, CCOLAMD, and {\tt CHOLMOD} libraries will be compiled, as will the C version of the null-output {\tt xerbla} routine in case you need it. No Fortran compiler is required in this case. A short demo program will be compiled and tested on a few matrices. The residuals should all be small. Compare your output with the {\tt CHOLMOD/Demo/make.out} file. CHOLMOD is now ready for use in your own applications. You must link your programs with the {\tt CHOLMOD/Lib/libcholmod.a}, {\tt AMD/Lib/libamd.a}, {\tt COLAMD/libcolamd.a}, {\tt CAMD/libcamd.a}, \newline {\tt CCOLAMD/libccolamd.a}, {\tt metis-4.0/libmetis.a}, LAPACK, and BLAS libraries, as well as the {\tt xerbla} library if you need it ({\tt UFconfig/xerlib/libcerbla.a} for the C version or \newline {\tt UFconfig/xerlib/libxerbla.a} for the Fortran version). Your compiler needs to know the location of the CHOLMOD {\tt Include} directory, so that it can find the {\tt cholmod.h} include file, by adding the {\tt -ICHOLMOD/Include} to your C compiler options (modified appropriately to reflect the location of your copy of CHOLMOD). %------------------------------------------------------------------------------- \newpage \section{Using CHOLMOD in MATLAB} %------------------------------------------------------------------------------- CHOLMOD includes a set of m-files and mexFunctions in the CHOLMOD/MATLAB directory. The following functions are provided: \vspace{0.1in} \begin{tabular}{ll} \hline {\tt analyze} & order and analyze a matrix \\ {\tt bisect} & find a node separator \\ {\tt chol2} & same as {\tt chol} \\ {\tt cholmod2} & same as {\tt x=A}$\backslash${\tt b} if {\tt A} is symmetric positive definite \\ {\tt cholmod\_demo} & a short demo program \\ {\tt cholmod\_make} & compiles CHOLMOD for use in MATLAB \\ {\tt etree2} & same as {\tt etree} \\ {\tt graph\_demo} & graph partitioning demo \\ {\tt lchol} & {\tt L*L'} factorization \\ {\tt ldlchol} & {\tt L*D*L'} factorization \\ {\tt ldl\_normest} & estimate {\tt norm(A-L*D*L')} \\ {\tt ldlsolve} & {\tt x = L'}$\backslash${\tt (D}$\backslash${\tt (L}$\backslash${\tt b))} \\ {\tt ldlsplit} & split the output of {\tt ldlchol} into {\tt L} and {\tt D} \\ {\tt ldlupdate} & update/downdate an {\tt L*D*L'} factorization \\ {\tt metis} & interface to {\tt METIS\_NodeND} ordering \\ {\tt mread} & read a sparse or dense Matrix Market file \\ {\tt mwrite} & write a sparse or dense Matrix Market file \\ {\tt nesdis} & CHOLMOD's nested dissection ordering \\ {\tt resymbol} & recomputes the symbolic factorization \\ {\tt sdmult} & {\tt S*F} where {\tt S} is sparse and {\tt F} is dense \\ {\tt spsym} & determine symmetry \\ {\tt sparse2} & same as {\tt sparse} \\ {\tt symbfact2} & same as {\tt symbfact} \\ \hline \end{tabular} \vspace{0.1in}\noindent Each function is described in the next sections. \newpage \subsection{{\tt analyze}: order and analyze} \input{_analyze_m.tex} \subsection{{\tt bisect}: find a node separator} \input{_bisect_m.tex} \subsection{{\tt chol2}: same as {\tt chol}} \input{_chol2_m.tex} \newpage \subsection{{\tt cholmod2}: supernodal backslash} \input{_cholmod2_m.tex} \newpage \subsection{{\tt cholmod\_demo}: a short demo program} \input{_cholmod_demo_m.tex} \subsection{{\tt cholmod\_make}: compile CHOLMOD in MATLAB} \input{_cholmod_make_m.tex} \newpage \subsection{{\tt etree2}: same as {\tt etree}} \input{_etree2_m.tex} \subsection{{\tt graph\_demo}: graph partitioning demo} \input{_graph_demo_m.tex} \newpage \subsection{{\tt lchol}: $\m{LL}\tr$ factorization} \input{_lchol_m.tex} \subsection{{\tt ldlchol}: $\m{LDL}\tr$ factorization} \input{_ldlchol_m.tex} \newpage \subsection{{\tt ldlsolve}: solve using an $\m{LDL}\tr$ factorization} \input{_ldlsolve_m.tex} \subsection{{\tt ldlsplit}: split an $\m{LDL}\tr$ factorization} \input{_ldlsplit_m.tex} \newpage \subsection{{\tt ldlupdate}: update/downdate an $\m{LDL}\tr$ factorization} \input{_ldlupdate_m.tex} \newpage \subsection{{\tt mread}: read a sparse or dense matrix from a Matrix Market file}\input{_mread_m.tex} \subsection{{\tt mwrite}: write a sparse or densematrix to a Matrix Market file} \input{_mwrite_m.tex} \newpage \subsection{{\tt metis}: order with METIS} \input{_metis_m.tex} \newpage \subsection{{\tt nesdis}: order with CHOLMOD nested dissection} \input{_nesdis_m.tex} \newpage \subsection{{\tt resymbol}: re-do symbolic factorization} \input{_resymbol_m.tex} \subsection{{\tt sdmult}: sparse matrix times dense matrix} \input{_sdmult_m.tex} \newpage \subsection{{\tt spsym}: determine symmetry} \input{_spsym_m.tex} \newpage \subsection{{\tt sparse2}: same as {\tt sparse}} \input{_sparse2_m.tex} \newpage \subsection{{\tt symbfact2}: same as {\tt symbfact}} \input{_symbfact2_m.tex} %------------------------------------------------------------------------------- \newpage \section{Installation for use in MATLAB} %------------------------------------------------------------------------------- If you wish to use METIS within CHOLMOD, you should first obtain a copy of METIS 4.0.1. See http://www-users.cs.umn.edu/$\sim$karypis/metis. Place your copy of the {\tt metis-4.0} directory (folder, for Windows users) in the same directory that contains your copy of the {\tt CHOLMOD} directory. If you do not have METIS, however, you can still use CHOLMOD. Some of the CHOLMOD functions will not be available ({\tt metis}, {\tt bisect}, and {\tt nesdis}), and you may experience higher fill-in for large matrices (particularly those arising in 3D finite-element problems) when using {\tt analyze}, {\tt chol2}, {\tt cholmod2}, {\tt lchol}, and {\tt ldlchol}. There are two methods for compiling CHOLMOD for use in MATLAB; both are described below. %------------------------------------------------------------------------------- \subsection{{\tt cholmod\_make}: compiling CHOLMOD in MATLAB} %------------------------------------------------------------------------------- This is the preferred method, since it allows METIS to be reconfigured to use the MATLAB memory-management functions instead of {\tt malloc} and {\tt free}; this avoids the issue of METIS terminating MATLAB if it runs out of memory. It is also simpler for Windows users, who do not have the {\tt make} command (unless you obtain a copy of {\tt Cygwin}). Start MATLAB, {\tt cd} to the {\tt CHOLMOD/MATLAB} directory, and type {\tt cholmod\_make} in the MATLAB command window. This will compile the MATLAB interfaces for AMD, COLAMD, CAMD, CCOLAMD, METIS, and CHOLMOD. If you do not have METIS, type {\tt cholmod\_make('')}. If your copy of METIS is in another location, type {\tt cholmod\_make ('path')} where {\tt path} is the pathname of your copy of the {\tt metis-4.0} directory. When METIS is compiled {\tt malloc}, {\tt free}, {\tt calloc}, and {\tt realloc} are redefined to the MATLAB-equivalents ({\tt mxMalloc}, ...). These memory-management functions safely terminate a mexFunction if they fail, and will free all memory allocated by the mexFunction. Thus, METIS will safely abort without terminating MATLAB, if it runs out of memory. The {\tt cholmod\_make} handles this redefinition without making any changes to your METIS source code. %------------------------------------------------------------------------------- \subsection{Unix {\tt make} for compiling CHOLMOD} %------------------------------------------------------------------------------- You can also compile the CHOLMOD mexFunctions using the Unix/Linux {\tt make} command. When using the {\tt gcc} compiler, I strongly recommend editing the {\tt metis-4.0/Makefile.in} file and changing {\tt COPTIONS} to \begin{verbatim} COPTIONS = -fexceptions \end{verbatim} Also ensure {\tt -fexceptions} is in the {\tt CFLAGS} option in the {\tt UFconfig/UFconfig.mk} file that comes with CHOLMOD. If you do not make these modifications, the CHOLMOD mexFunctions will terminate MATLAB if they encounter an error. If you have MATLAB 7.2 or earlier and use {\tt make mex} in the {\tt CHOLMOD} directory (equivalently, {\tt make} in {\tt CHOLMOD/MATLAB}), you must first edit {\tt UFconfig/UFconfig.h} to remove the {\tt -largeArrayDims} option from the MEX command (or just use {\tt cholmod\_make.m} inside MATLAB). Next, compile your METIS 4.0.1 library by typing {\tt make} in the {\tt metis-4.0} directory. Then type {\tt make} in the {\tt CHOLMOD/MATLAB} directory. This will compile the C-callable libraries for AMD, COLAMD, CAMD, CCOLAMD, METIS, and CHOLMOD, and then compile the mexFunction interfaces to those libraries. If METIS tries {\tt malloc} and encounters an out-of-memory condition, it calls {\tt abort}, which will terminate MATLAB. This problem does not occur using the method described in the previous section. %------------------------------------------------------------------------------- \newpage \section{Integer and floating-point types, and notation used} %------------------------------------------------------------------------------- CHOLMOD supports both {\tt int} and {\tt long} integers. CHOLMOD routines with the prefix {\tt cholmod\_} use {\tt int} integers, {\tt cholmod\_l\_} routines use {\tt long}. All floating-point values are {\tt double}. The {\tt long} integer is redefinable, via {\tt UFconfig.h}. That file defines a C preprocessor token {\tt UF\_long} which is {\tt long} on all systems except for Windows-64, in which case it is defined as {\tt \_\_int64}. The intent is that with suitable compile-time switches, {\tt int} is a 32-bit integer and {\tt UF\_long} is a 64-bit integer. The term {\tt long} is used to describe the latter integer throughout this document (except in the prototypes). Two kinds of complex matrices are supported: complex and zomplex. A complex matrix is held in a manner that is compatible with the Fortran and ANSI C99 complex data type. A complex array of size {\tt n} is a {\tt double} array {\tt x} of size {\tt 2*n}, with the real and imaginary parts interleaved (the real part comes first, as a {\tt double}, followed the imaginary part, also as a {\tt double}. Thus, the real part of the {\tt k}th entry is {\tt x[2*k]} and the imaginary part is {\tt x[2*k+1]}. A zomplex matrix of size {\tt n} stores its real part in one {\tt double} array of size {\tt n} called {\tt x} and its imaginary part in another {\tt double} array of size {\tt n} called {\tt z} (thus the name ``zomplex''). This also how MATLAB stores its complex matrices. The real part of the {\tt k}th entry is {\tt x[k]} and the imaginary part is {\tt z[k]}. Unlike {\tt UMFPACK}, the same routine name in CHOLMOD is used for pattern-only, real, complex, and zomplex matrices. For example, the statement \begin{verbatim} C = cholmod_copy_sparse (A, &Common) ; \end{verbatim} creates a copy of a pattern, real, complex, or zomplex sparse matrix {\tt A}. The xtype (pattern, real, complex, or zomplex) of the resulting sparse matrix {\tt C} is the same as {\tt A} (a pattern-only sparse matrix contains no floating-point values). In the above case, {\tt C} and {\tt A} use {\tt int} integers. For {\tt long} integers, the statement would become: \begin{verbatim} C = cholmod_l_copy_sparse (A, &Common) ; \end{verbatim} The last parameter of all CHOLMOD routines is always {\tt \&Common}, a pointer to the {\tt cholmod\_common} object, which contains parameters, statistics, and workspace used throughout CHOLMOD. The {\tt xtype} of a CHOLMOD object (sparse matrix, triplet matrix, dense matrix, or factorization) determines whether it is pattern-only, real, complex, or zomplex. The names of the {\tt int} versions are primarily used in this document. To obtain the name of the {\tt long} version of the same routine, simply replace {\tt cholmod\_} with {\tt cholmod\_l\_}. MATLAB matrix notation is used throughout this document and in the comments in the CHOLMOD code itself. If you are not familiar with MATLAB, here is a short introduction to the notation, and a few minor variations used in CHOLMOD: \begin{itemize} \item {\tt C=A+B} and {\tt C=A*B}, respectively are a matrix add and multiply if both {\tt A} and {\tt B} are matrices of appropriate size. If {\tt A} is a scalar, then it is added to or multiplied with every entry in {\tt B}. \item {\tt a:b} where {\tt a} and {\tt b} are integers refers to the sequence {\tt a}, {\tt a+1}, ... {\tt b}. \item {\tt [A B]} and {\tt [A,B]} are the horizontal concatenation of {\tt A} and {\tt B}. \item {\tt [A;B]} is the vertical concatenation of {\tt A} and {\tt B}. \item {\tt A(i,j)} can refer either to a scalar or a submatrix. For example: \newline \vspace{0.05in} \begin{tabular}{ll} \hline {\tt A(1,1)} & a scalar. \\ {\tt A(:,j)} & column {\tt j} of {\tt A}. \\ {\tt A(i,:)} & row {\tt i} of {\tt A}. \\ {\tt A([1 2], [1 2])} & a 2-by-2 matrix containing the 2-by-2 leading minor of {\tt A}. \\ \hline \end{tabular} \newline \vspace{0.1in} If {\tt p} is a permutation of {\tt 1:n}, and {\tt A} is {\tt n}-by-{\tt n}, then {\tt A(p,p)} corresponds to the permuted matrix $\m{PAP}\tr$. \item {\tt tril(A)} is the lower triangular part of {\tt A}, including the diagonal. \item {\tt tril(A,k)} is the lower triangular part of {\tt A}, including entries on and below the $k$th diagonal. \item {\tt triu(A)} is the upper triangular part of {\tt A}, including the diagonal. \item {\tt triu(A,k)} is the upper triangular part of {\tt A}, including entries on and above the $k$th diagonal. \item {\tt size(A)} returns the dimensions of {\tt A}. \item {\tt find(x)} if {\tt x} is a vector returns a list of indices {\tt i} for which {\tt x(i)} is nonzero. \item {\tt A'} is the transpose of {\tt A} if {\tt A} is real, or the complex conjugate transpose if {\tt A} is complex. \item {\tt A.'} is the array transpose of {\tt A}. \item {\tt diag(A)} is the diagonal of {\tt A} if {\tt A} is a matrix. \item {\tt C=diag(s)} is a diagonal matrix if {\tt s} is a vector, with the values of {\tt s} on the diagonal of {\tt C}. \item {\tt S=spones(A)} returns a binary matrix {\tt S} with the same nonzero pattern of {\tt A}. \item {\tt nnz(A)} is the number of nonzero entries in {\tt A}. \end{itemize} \noindent Variations to MATLAB notation used in this document: \begin{itemize} \item CHOLMOD uses 0-based notation (the first entry in the matrix is {\tt A(0,0)}). MATLAB is 1-based. The context is usually clear. \item {\tt I} is the identity matrix. \item {\tt A(:,f)}, where {\tt f} is a set of columns, is interpreted differently in CHOLMOD, but just for the set named {\tt f}. See {\tt cholmod\_transpose\_unsym} for details. \end{itemize} %------------------------------------------------------------------------------- \newpage \section{The CHOLMOD Modules, objects, and functions} \label{Modules} %------------------------------------------------------------------------------- CHOLMOD contains a total of 133 {\tt int}-based routines (and the same number of {\tt long} routines), divided into a set of inter-related Modules. Each Module contains a set of related functions. The functions are divided into two types: Primary and Secondary, to reflect how a user will typically use CHOLMOD. Most users will find the Primary routines to be sufficient to use CHOLMOD in their programs. Each Module exists as a sub-directory (a folder for Windows users) within the CHOLMOD directory (or folder). \vspace{0.1in} \noindent There are seven Modules that provide user-callable routines for CHOLMOD. \begin{enumerate} \item {\tt Core}: basic data structures and definitions \item {\tt Check}: prints/checks each of CHOLMOD's objects \item {\tt Cholesky}: sparse Cholesky factorization \item {\tt Modify}: sparse Cholesky update/downdate and row-add/row-delete \item {\tt MatrixOps}: sparse matrix operators (add, multiply, norm, scale) \item {\tt Supernodal}: supernodal sparse Cholesky factorization \item {\tt Partition}: graph-partitioning-based orderings \end{enumerate} \noindent Two additional Modules are required to compile the CHOLMOD library: \begin{enumerate} \item {\tt Include}: include files for CHOLMOD and programs that use CHOLMOD \item {\tt Lib}: where the CHOLMOD library is built \end{enumerate} \noindent Five additional Modules provide support functions and documentation: \begin{enumerate} \item {\tt Demo}: simple programs that illustrate the use of CHOLMOD \item {\tt Doc}: documentation (including this document) \item {\tt MATLAB}: CHOLMOD's interface to MATLAB \item {\tt Tcov}: an exhaustive test coverage (requires Linux or Solaris) \item {\tt Valgrind}: runs the {\tt Tcov} test under {\tt valgrind} (requires Linux) \end{enumerate} The following Modules are licensed under the GNU Lesser General Public License: {\tt Check}, {\tt Cholesky}, {\tt Core}, and {\tt Partition}. The following Modules are licensed under the GNU General Public License: {\tt Demo}, {\tt Modify}, {\tt MatrixOps}, {\tt Supernodal}, the {\tt MATLAB} Module (not MATLAB itself!), {\tt Tcov}, and {\tt Valgrind}. The files in the {\tt Include} Module are licensed according to their respective Modules. The {\tt Lib} and {\tt Doc} Modules need no license; the compiled binaries are licensed the same as their source code. %------------------------------------------------------------------------------- \newpage \subsection{{\tt Core} Module: basic data structures and definitions} %------------------------------------------------------------------------------- CHOLMOD includes five basic objects, defined in the {\tt Core} Module. The {\tt Core Module} provides basic operations for these objects and is required by all six other CHOLMOD library Modules: \subsubsection{{\tt cholmod\_common}: parameters, statistics, and workspace} You must call {\tt cholmod\_start} before calling any other CHOLMOD routine, and you must call {\tt cholmod\_finish} as your last call to CHOLMOD (with the exception of {\tt cholmod\_print\_common} and {\tt cholmod\_check\_common} in the {\tt Check} Module). Once the {\tt cholmod\_common} object is initialized, the user may modify CHOLMOD's parameters held in this object, and obtain statistics on CHOLMOD's activity. \vspace{0.1in} \noindent Primary routines for the {\tt cholmod\_common} object: % 2 \begin{itemize} \item {\tt cholmod\_start}: the first call to CHOLMOD. \item {\tt cholmod\_finish}: the last call to CHOLMOD (frees workspace in the {\tt cholmod\_common} object). \end{itemize} \noindent Secondary routines for the {\tt cholmod\_common} object: % 9 \begin{itemize} \item {\tt cholmod\_defaults}: restores default parameters \item {\tt cholmod\_maxrank}: determine maximum rank for update/downdate. \item {\tt cholmod\_allocate\_work}: allocate workspace. \item {\tt cholmod\_free\_work}: free workspace. \item {\tt cholmod\_clear\_flag}: clear {\tt Flag} array. \item {\tt cholmod\_error}: called when CHOLMOD encounters and error. \item {\tt cholmod\_dbound}: bounds the diagonal of $\m{L}$ or $\m{D}$. \item {\tt cholmod\_hypot}: compute {\tt sqrt(x*x+y*y)} accurately. \item {\tt cholmod\_divcomplex}: complex divide. \end{itemize} %------------------------------------------------------------------------------- \newpage \subsubsection{{\tt cholmod\_sparse}: a sparse matrix in compressed column form} %------------------------------------------------------------------------------- A sparse matrix {\tt A} is held in compressed column form. In the basic type (``packed,'' which corresponds to how MATLAB stores its sparse matrices), and {\tt nrow}-by-{\tt ncol} matrix with {\tt nzmax} entries is held in three arrays: {\tt p} of size {\tt ncol+1}, {\tt i} of size {\tt nzmax}, and {\tt x} of size {\tt nzmax}. Row indices of nonzero entries in column {\tt j} are held in {\tt i [p[j] ... p[j+1]-1]}, and their corresponding numerical values are held in {\tt x [p[j] ... p[j+1]-1]}. The first column starts at location zero ({\tt p[0]=0}). There may be no duplicate entries. Row indices in each column may be sorted or unsorted (the {\tt A->sorted} flag must be false if the columns are unsorted). The {\tt A->stype} determines the storage mode: 0 if the matrix is unsymmetric, 1 if the matrix is symmetric with just the upper triangular part stored, and -1 if the matrix is symmetric with just the lower triangular part stored. In ``unpacked'' form, an additional array {\tt nz} of size {\tt ncol} is used. The end of column {\tt j} in {\tt i} and {\tt x} is given by {\tt p[j]+nz[j]}. Columns not need be in any particular order ({\tt p[0]} need not be zero), and there may be gaps between the columns. \vspace{0.1in} \noindent Primary routines for the {\tt cholmod\_sparse} object: % 2 \begin{itemize} \item {\tt cholmod\_allocate\_sparse}: allocate a sparse matrix \item {\tt cholmod\_free\_sparse}: free a sparse matrix \end{itemize} \noindent Secondary routines for the {\tt cholmod\_sparse} object: % 16 \begin{itemize} \item {\tt cholmod\_reallocate\_sparse}: change the size (number of entries) of a sparse matrix. \item {\tt cholmod\_nnz}: number of nonzeros in a sparse matrix. \item {\tt cholmod\_speye}: sparse identity matrix. \item {\tt cholmod\_spzeros}: sparse zero matrix. \item {\tt cholmod\_transpose}: transpose a sparse matrix. \item {\tt cholmod\_ptranspose}: transpose/permute a sparse matrix. \item {\tt cholmod\_transpose\_unsym}: transpose/permute an unsymmetric sparse matrix. \item {\tt cholmod\_transpose\_sym}: transpose/permute a symmetric sparse matrix. \item {\tt cholmod\_sort}: sort row indices in each column of a sparse matrix. \item {\tt cholmod\_band}: extract a band of a sparse matrix. \item {\tt cholmod\_band\_inplace}: remove entries not with a band. \item {\tt cholmod\_aat}: {\tt C = A*A'}. \item {\tt cholmod\_copy\_sparse}: {\tt C = A}, create an exact copy of a sparse matrix. \item {\tt cholmod\_copy}: {\tt C = A}, with possible change of {\tt stype}. \item {\tt cholmod\_add}: {\tt C = alpha*A + beta*B}. \item {\tt cholmod\_sparse\_xtype}: change the {\tt xtype} of a sparse matrix. \end{itemize} %------------------------------------------------------------------------------- \newpage \subsubsection{{\tt cholmod\_factor}: a symbolic or numeric factorization} %------------------------------------------------------------------------------- A factor can be in $\m{LL}\tr$ or $\m{LDL}\tr$ form, and either supernodal or simplicial form. In simplicial form, this is very much like a packed or unpacked {\tt cholmod\_sparse} matrix. In supernodal form, adjacent columns with similar nonzero pattern are stored as a single block (a supernode). \vspace{0.1in} \noindent Primary routine for the {\tt cholmod\_factor} object: % 1 \begin{itemize} \item {\tt cholmod\_free\_factor}: free a factor \end{itemize} \noindent Secondary routines for the {\tt cholmod\_factor} object: % 8 \begin{itemize} \item {\tt cholmod\_allocate\_factor}: allocate a factor. You will normally use {\tt cholmod\_analyze} to create a factor. \item {\tt cholmod\_reallocate\_factor}: change the number of entries in a factor. \item {\tt cholmod\_change\_factor}: change the type of a factor ($\m{LDL}\tr$ to $\m{LL}\tr$, supernodal to simplicial, etc.). \item {\tt cholmod\_pack\_factor}: pack the columns of a factor. \item {\tt cholmod\_reallocate\_column}: resize a single column of a factor. \item {\tt cholmod\_factor\_to\_sparse}: create a sparse matrix copy of a factor. \item {\tt cholmod\_copy\_factor}: create a copy of a factor. \item {\tt cholmod\_factor\_xtype}: change the xtype of a factor. \end{itemize} %------------------------------------------------------------------------------- \subsubsection{{\tt cholmod\_dense}: a dense matrix} %------------------------------------------------------------------------------- This consists of a dense array of numerical values and its dimensions. \vspace{0.1in} \noindent Primary routines for the {\tt cholmod\_dense} object: % 2 \begin{itemize} \item {\tt cholmod\_allocate\_dense}: allocate a dense matrix. \item {\tt cholmod\_free\_dense}: free a dense matrix. \end{itemize} \vspace{0.1in} \noindent Secondary routines for the {\tt cholmod\_dense} object: % 8 \begin{itemize} \item {\tt cholmod\_zeros}: allocate a dense matrix of all zeros. \item {\tt cholmod\_ones}: allocate a dense matrix of all ones. \item {\tt cholmod\_eye}: allocate a dense identity matrix . \item {\tt cholmod\_sparse\_to\_dense}: create a dense matrix copy of a sparse matrix. \item {\tt cholmod\_dense\_to\_sparse}: create a sparse matrix copy of a dense matrix. \item {\tt cholmod\_copy\_dense}: create a copy of a dense matrix. \item {\tt cholmod\_copy\_dense2}: copy a dense matrix (pre-allocated). \item {\tt cholmod\_dense\_xtype}: change the {\tt xtype} of a dense matrix. \end{itemize} %------------------------------------------------------------------------------- \newpage \subsubsection{{\tt cholmod\_triplet}: a sparse matrix in ``triplet'' form} %------------------------------------------------------------------------------- The {\tt cholmod\_sparse} matrix is the basic sparse matrix used in CHOLMOD, but it can be difficult for the user to construct. It also does not easily support the inclusion of new entries in the matrix. The {\tt cholmod\_triplet} matrix is provided to address these issues. A sparse matrix in triplet form consists of three arrays of size {\tt nzmax}: {\tt i}, {\tt j}, and {\tt x}, and a {\tt z} array for the zomplex case. \vspace{0.1in} \noindent Primary routines for the {\tt cholmod\_triplet} object: % 3 \begin{itemize} \item {\tt cholmod\_allocate\_triplet}: allocate a triplet matrix. \item {\tt cholmod\_free\_triplet}: free a triplet matrix. \item {\tt cholmod\_triplet\_to\_sparse}: create a sparse matrix copy of a triplet matrix. \end{itemize} \noindent Secondary routines for the {\tt cholmod\_triplet} object: % 4 \begin{itemize} \item {\tt cholmod\_reallocate\_triplet}: change the number of entries in a triplet matrix. \item {\tt cholmod\_sparse\_to\_triplet}: create a triplet matrix copy of a sparse matrix. \item {\tt cholmod\_copy\_triplet}: create a copy of a triplet matrix. \item {\tt cholmod\_triplet\_xtype}: change the {\tt xtype} of a triplet matrix. \end{itemize} %------------------------------------------------------------------------------- \subsubsection{Memory management routines} %------------------------------------------------------------------------------- By default, CHOLMOD uses the ANSI C {\tt malloc}, {\tt free}, {\tt calloc}, and {\tt realloc} routines. You may use different routines by modifying function pointers in the {\tt cholmod\_common} object. \vspace{0.1in} \noindent Primary routines: % 2 \begin{itemize} \item {\tt cholmod\_malloc}: {\tt malloc} wrapper. \item {\tt cholmod\_free}: {\tt free} wrapper. \end{itemize} \noindent Secondary routines: % 3 \begin{itemize} \item {\tt cholmod\_calloc}: {\tt calloc} wrapper. \item {\tt cholmod\_realloc}: {\tt realloc} wrapper. \item {\tt cholmod\_realloc\_multiple}: {\tt realloc} wrapper for multiple objects. \end{itemize} %------------------------------------------------------------------------------- \newpage \subsection{{\tt Check} Module: print/check the CHOLMOD objects} %------------------------------------------------------------------------------- The {\tt Check} Module contains routines that check and print the five basic objects in CHOLMOD, and three kinds of integer vectors (a set, a permutation, and a tree). It also provides a routine to read a sparse matrix from a file in Matrix Market format (http://www.nist.gov/MatrixMarket). Requires the {\tt Core} Module. \vspace{0.1in} \noindent Primary routines: % 4 \begin{itemize} \item {\tt cholmod\_print\_common}: print the {\tt cholmod\_common} object, including statistics on CHOLMOD's behavior (fill-in, flop count, ordering methods used, and so on). \item {\tt cholmod\_write\_sparse}: write a sparse matrix to a file in Matrix Market format. \item {\tt cholmod\_write\_dense}: write a sparse matrix to a file in Matrix Market format. \item {\tt cholmod\_read\_matrix}: read a sparse or dense matrix from a file in Matrix Market format. \end{itemize} \vspace{0.1in} \noindent Secondary routines: % 18 \begin{itemize} \item {\tt cholmod\_check\_common}: check the {\tt cholmod\_common} object \item {\tt cholmod\_check\_sparse}: check a sparse matrix \item {\tt cholmod\_print\_sparse}: print a sparse matrix \item {\tt cholmod\_check\_dense}: check a dense matrix \item {\tt cholmod\_print\_dense}: print a dense matrix \item {\tt cholmod\_check\_factor}: check a Cholesky factorization \item {\tt cholmod\_print\_factor}: print a Cholesky factorization \item {\tt cholmod\_check\_triplet}: check a triplet matrix \item {\tt cholmod\_print\_triplet}: print a triplet matrix \item {\tt cholmod\_check\_subset}: check a subset (integer vector in given range) \item {\tt cholmod\_print\_subset}: print a subset (integer vector in given range) \item {\tt cholmod\_check\_perm}: check a permutation (an integer vector) \item {\tt cholmod\_print\_perm}: print a permutation (an integer vector) \item {\tt cholmod\_check\_parent}: check an elimination tree (an integer vector) \item {\tt cholmod\_print\_parent}: print an elimination tree (an integer vector) \item {\tt cholmod\_read\_triplet}: read a triplet matrix from a file \item {\tt cholmod\_read\_sparse}: read a sparse matrix from a file \item {\tt cholmod\_read\_dense}: read a dense matrix from a file \end{itemize} %------------------------------------------------------------------------------- \newpage \subsection{{\tt Cholesky} Module: sparse Cholesky factorization} %------------------------------------------------------------------------------- The primary routines are all that a user requires to order, analyze, and factorize a sparse symmetric positive definite matrix $\m{A}$ (or $\m{AA}\tr$), and to solve $\m{Ax}=\m{b}$ (or $\m{AA}\tr\m{x}=\m{b}$). The primary routines rely on the secondary routines, the {\tt Core} Module, and the AMD and COLAMD packages. They make optional use of the {\tt Supernodal} and {\tt Partition} Modules, the METIS package, the CAMD package, and the CCOLAMD package. The {\tt Cholesky} Module is required by the {\tt Partition} Module. \vspace{0.1in} \noindent Primary routines: % 4 \begin{itemize} \item {\tt cholmod\_analyze}: order and analyze (simplicial or supernodal). \item {\tt cholmod\_factorize}: simplicial or supernodal Cholesky factorization. \item {\tt cholmod\_solve}: solve a linear system (simplicial or supernodal, dense $\m{x}$ and $\m{b}$). \item {\tt cholmod\_spsolve}: solve a linear system (simplicial or supernodal, sparse $\m{x}$ and $\m{b}$ ). \end{itemize} \noindent Secondary routines: % 15 \begin{itemize} \item {\tt cholmod\_analyze\_p}: analyze, with user-provided permutation or $\m{f}$ set. \item {\tt cholmod\_factorize\_p}: factorize, with user-provided permutation or $\m{f}$. \item {\tt cholmod\_analyze\_ordering}: analyze a permutation \item {\tt cholmod\_etree}: find the elimination tree. \item {\tt cholmod\_rowcolcounts}: compute the row/column counts of $\m{L}$. \item {\tt cholmod\_amd}: order using AMD. \item {\tt cholmod\_colamd}: order using COLAMD. \item {\tt cholmod\_rowfac}: incremental simplicial factorization. \item {\tt cholmod\_row\_subtree}: find the nonzero pattern of a row of $\m{L}$. \item {\tt cholmod\_row\_lsubtree}: find the nonzero pattern of a row of $\m{L}$. \item {\tt cholmod\_resymbol}: recompute the symbolic pattern of $\m{L}$. \item {\tt cholmod\_resymbol\_noperm}: recompute the symbolic pattern of $\m{L}$, no permutation. \item {\tt cholmod\_postorder}: postorder a tree. \item {\tt cholmod\_rcond}: compute the reciprocal condition number estimate. \item {\tt cholmod\_rowfac\_mask}: for use in LPDASA only. \end{itemize} %------------------------------------------------------------------------------- \newpage \subsection{{\tt Modify} Module: update/downdate a sparse Cholesky factorization} %------------------------------------------------------------------------------- The {\tt Modify} Module contains sparse Cholesky modification routines: update, downdate, row-add, and row-delete. It can also modify a corresponding solution to $\m{Lx}=\m{b}$ when L is modified. This module is most useful when applied on a Cholesky factorization computed by the {\tt Cholesky} module, but it does not actually require the {\tt Cholesky} module. The {\tt Core} module can create an identity Cholesky factorization ($\m{LDL}\tr$ where $\m{L}=\m{D}=\m{I}$) that can then be modified by these routines. Requires the {\tt Core} module. Not required by any other CHOLMOD Module. \vspace{0.1in} \noindent Primary routine: % 1 \begin{itemize} \item {\tt cholmod\_updown}: multiple rank update/downdate \end{itemize} \noindent Secondary routines: % 8 \begin{itemize} \item {\tt cholmod\_updown\_solve}: update/downdate, and modify solution to $\m{Lx=b}$ \item {\tt cholmod\_updown\_mark}: update/downdate, and modify solution to partial $\m{Lx=b}$ \item {\tt cholmod\_updown\_mask}: for use in LPDASA only. \item {\tt cholmod\_rowadd}: add a row to an $\m{LDL}\tr$ factorization \item {\tt cholmod\_rowadd\_solve}: add a row, and update solution to $\m{Lx=b}$ \item {\tt cholmod\_rowadd\_mark}: add a row, and update solution to partial $\m{Lx=b}$ \item {\tt cholmod\_rowdel}: delete a row from an $\m{LDL}\tr$ factorization \item {\tt cholmod\_rowdel\_solve}: delete a row, and downdate $\m{Lx=b}$ \item {\tt cholmod\_rowdel\_mark}: delete a row, and downdate solution to partial $\m{Lx=b}$ \end{itemize} %------------------------------------------------------------------------------- \subsection{{\tt MatrixOps} Module: basic sparse matrix operations} %------------------------------------------------------------------------------- The {\tt MatrixOps} Module provides basic operations on sparse and dense matrices. Requires the {\tt Core} module. Not required by any other CHOLMOD module. In the descriptions below, {\tt A}, {\tt B}, and {\tt C:} are sparse matrices ({\tt cholmod\_sparse}), {\tt X} and {\tt Y} are dense matrices ({\tt cholmod\_dense}), {\tt s} is a scalar or vector, and {\tt alpha} {\tt beta} are scalars. % 10 \begin{itemize} \item {\tt cholmod\_drop}: drop entries from A with absolute value $\ge$ a given tolerance. \item {\tt cholmod\_norm\_dense}: {\tt s = norm (X)}, 1-norm, infinity-norm, or 2-norm \item {\tt cholmod\_norm\_sparse}: {\tt s = norm (A)}, 1-norm or infinity-norm \item {\tt cholmod\_horzcat}: {\tt C = [A,B]} \item {\tt cholmod\_scale}: {\tt A = diag(s)*A}, {\tt A*diag(s)}, {\tt s*A} or {\tt diag(s)*A*diag(s)}. \item {\tt cholmod\_sdmult}: {\tt Y = alpha*(A*X) + beta*Y} or {\tt alpha*(A'*X) + beta*Y}. \item {\tt cholmod\_ssmult}: {\tt C = A*B} \item {\tt cholmod\_submatrix}: {\tt C = A (i,j)}, where {\tt i} and {\tt j} are arbitrary integer vectors. \item {\tt cholmod\_vertcat}: {\tt C = [A ; B]}. \item {\tt cholmod\_symmetry}: determine symmetry of a matrix. \end{itemize} %------------------------------------------------------------------------------- \newpage \subsection{{\tt Supernodal} Module: supernodal sparse Cholesky factorization} %------------------------------------------------------------------------------- The {\tt Supernodal} Module performs supernodal analysis, factorization, and solve. The simplest way to use these routines is via the {\tt Cholesky} Module. This Module does not provide any fill-reducing orderings. It normally operates on matrices ordered by the {\tt Cholesky} Module. It does not require the {\tt Cholesky} Module itself, however. Requires the {\tt Core} Module, and two external packages: LAPACK and the BLAS. Optionally used by the {\tt Cholesky} Module. All are secondary routines since these functions are more easily used via the {\tt Cholesky} Module. \vspace{0.1in} \noindent Secondary routines: % 4 \begin{itemize} \item {\tt cholmod\_super\_symbolic}: supernodal symbolic analysis \item {\tt cholmod\_super\_numeric}: supernodal numeric factorization \item {\tt cholmod\_super\_lsolve}: supernodal $\m{Lx}=\m{b}$ solve \item {\tt cholmod\_super\_ltsolve}: supernodal $\m{L}\tr\m{x}=\m{b}$ solve \end{itemize} %------------------------------------------------------------------------------- \subsection{{\tt Partition} Module: graph-partitioning-based orderings} %------------------------------------------------------------------------------- The {\tt Partition} Module provides graph partitioning and graph-partition-based orderings. It includes an interface to CAMD, CCOLAMD, and CSYMAMD, constrained minimum degree ordering methods which order a matrix following constraints determined via nested dissection. Requires the {\tt Core} and {\tt Cholesky} Modules, and two packages: {\tt METIS 4.0.1}, CAMD, and CCOLAMD. Optionally used by the {\tt Cholesky} Module. All are secondary routines since these are more easily used by the {\tt Cholesky} Module. Note that METIS does not have a version that uses {\tt long} integers. If you try to use these routines (except the CAMD, CCOLAMD, and CSYMAMD interfaces) on a matrix that is too large, an error code will be returned. \vspace{0.1in} \noindent Secondary routines: % 8 \begin{itemize} \item {\tt cholmod\_nested\_dissection}: CHOLMOD nested dissection ordering \item {\tt cholmod\_metis}: METIS nested dissection ordering ({\tt METIS\_NodeND}) \item {\tt cholmod\_camd}: interface to CAMD ordering \item {\tt cholmod\_ccolamd}: interface to CCOLAMD ordering \item {\tt cholmod\_csymamd}: interface to CSYMAMD ordering \item {\tt cholmod\_bisect}: graph partitioner (currently based on METIS) \item {\tt cholmod\_metis\_bisector}: direct interface to {\tt METIS\_NodeComputeSeparator}. \item {\tt cholmod\_collapse\_septree}: pruned a separator tree from {\tt cholmod\_nested\_dissection}. \end{itemize} %------------------------------------------------------------------------------- \newpage \section{CHOLMOD naming convention, parameters, and return values} %------------------------------------------------------------------------------- All routine names, data types, and CHOLMOD library files use the {\tt cholmod\_} prefix. All macros and other {\tt \#define} statements visible to the user program use the {\tt CHOLMOD} prefix. The {\tt cholmod.h} file must be included in user programs that use CHOLMOD: {\footnotesize \begin{verbatim} #include "cholmod.h" \end{verbatim} } \noindent All CHOLMOD routines (in all modules) use the following protocol for return values: \begin{itemize} \item {\tt int}: {\tt TRUE} (1) if successful, or {\tt FALSE} (0) otherwise. (exception: {\tt cholmod\_divcomplex}). \item {\tt long}: a value $\ge 0$ if successful, or -1 otherwise. \item {\tt double}: a value $\ge 0$ if successful, or -1 otherwise. \item {\tt size\_t}: a value $>$ 0 if successful, or 0 otherwise. \item {\tt void *}: a non-{\tt NULL} pointer to newly allocated memory if successful, or {\tt NULL} otherwise. \item {\tt cholmod\_sparse *}: a non-{\tt NULL} pointer to a newly allocated sparse matrix if successful, or {\tt NULL} otherwise. \item {\tt cholmod\_factor *}: a non-{\tt NULL} pointer to a newly allocated factor if successful, or {\tt NULL} otherwise. \item {\tt cholmod\_triplet *}: a non-{\tt NULL} pointer to a newly allocated triplet matrix if successful, or {\tt NULL} otherwise. \item {\tt cholmod\_dense *}: a non-{\tt NULL} pointer to a newly allocated dense matrix if successful, or {\tt NULL} otherwise. \end{itemize} {\tt TRUE} and {\tt FALSE} are not defined in {\tt cholmod.h}, since they may conflict with the user program. A routine that described here returning {\tt TRUE} or {\tt FALSE} returns 1 or 0, respectively. Any {\tt TRUE}/{\tt FALSE} parameter is true if nonzero, false if zero. \noindent Input, output, and input/output parameters: \begin{itemize} \item Input parameters appear first in the parameter lists of all CHOLMOD routines. They are not modified by CHOLMOD. \item Input/output parameters (except for {\tt Common}) appear next. They must be defined on input, and are modified on output. \item Output parameters are listed next. If they are pointers, they must point to allocated space on input, but their contents are not defined on input. \item Workspace parameters appear next. They are used in only two routines in the Supernodal module. \item The {\tt cholmod\_common *Common} parameter always appears as the last parameter (with two exceptions: {\tt cholmod\_hypot} and {\tt cholmod\_divcomplex}). It is always an input/output parameter. \end{itemize} A floating-point scalar is passed to CHOLMOD as a pointer to a {\tt double} array of size two. The first entry in this array is the real part of the scalar, and the second entry is the imaginary part. The imaginary part is only accessed if the other inputs are complex or zomplex. In some cases the imaginary part is always ignored ({\tt cholmod\_factor\_p}, for example). %------------------------------------------------------------------------------- \newpage \section{{\tt Core} Module: {\tt cholmod\_common} object} \label{cholmod_common} %------------------------------------------------------------------------------- %--------------------------------------- \subsection{Constant definitions} %--------------------------------------- \input{_defn.tex} These definitions are used within the {\tt cholmod\_common} object, called {\tt Common} both here and throughout the code. %--------------------------------------- \newpage \subsection{{\tt cholmod\_common}: parameters, statistics, and workspace} %--------------------------------------- \input{_common.tex} The {\tt cholmod\_common Common} object contains parameters, statistics, and workspace used within CHOLMOD. The first call to CHOLMOD must be {\tt cholmod\_start}, which initializes this object. %--------------------------------------- \newpage \subsection{{\tt cholmod\_start}: start CHOLMOD} %--------------------------------------- \input{_start.tex} Sets the default parameters, clears the statistics, and initializes all workspace pointers to {\tt NULL}. The {\tt int}/{\tt long} type is set in {\tt Common->itype}. %--------------------------------------- \subsection{{\tt cholmod\_finish}: finish CHOLMOD} %--------------------------------------- \input{_finish.tex} This must be the last call to CHOLMOD. %--------------------------------------- \subsection{{\tt cholmod\_defaults}: set default parameters} %--------------------------------------- \input{_defaults.tex} Sets the default parameters. %--------------------------------------- \subsection{{\tt cholmod\_maxrank}: maximum update/downdate rank} %--------------------------------------- \input{_maxrank.tex} Returns the maximum rank for an update/downdate. %--------------------------------------- \subsection{{\tt cholmod\_allocate\_work}: allocate workspace} %--------------------------------------- \input{_allocate_work.tex} Allocates workspace in {\tt Common}. The workspace consists of the integer {\tt Head}, {\tt Flag}, and {\tt Iwork} arrays, of size {\tt nrow+1}, {\tt nrow}, and {\tt iworksize}, respectively, and a {\tt double} array {\tt Xwork} of size {\tt xworksize}. The {\tt Head} array is normally equal to -1 when it is cleared. If the {\tt Flag} array is cleared, all entries are less than {\tt Common->mark}. The {\tt Iwork} array is not kept in any particular state. The integer type is {\tt int} or {\tt long}, depending on whether the {\tt cholmod\_} or {\tt cholmod\_l\_} routines are used. %--------------------------------------- \subsection{{\tt cholmod\_free\_work}: free workspace} %--------------------------------------- \input{_free_work.tex} Frees the workspace in {\tt Common}. %--------------------------------------- \subsection{{\tt cholmod\_clear\_flag}: clear Flag array} %--------------------------------------- \input{_clear_flag.tex} Increments {\tt Common->mark} so that the {\tt Flag} array is now cleared. %--------------------------------------- \newpage \subsection{{\tt cholmod\_error}: report error} %--------------------------------------- \input{_error.tex} This routine is called when CHOLMOD encounters an error. It prints a message (if printing is enabled), sets {\tt Common->status}. It then calls the user error handler routine {\tt Common->error\_handler}, if it is not {\tt NULL}. %--------------------------------------- \subsection{{\tt cholmod\_dbound}: bound diagonal of $\m{L}$} %--------------------------------------- \input{_dbound.tex} Ensures that entries on the diagonal of $\m{L}$ for an $\m{LL}\tr$ factorization are greater than or equal to {\tt Common->dbound}. For an $\m{LDL}\tr$ factorization, it ensures that the magnitude of the entries of $\m{D}$ are greater than or equal to {\tt Common->dbound}. %--------------------------------------- \subsection{{\tt cholmod\_hypot}: {\tt sqrt(x*x+y*y)}} %--------------------------------------- \input{_hypot.tex} Computes the magnitude of a complex number. This routine is the default value for the {\tt Common->hypotenuse} function pointer. See also {\tt hypot}, in the standard {\tt math.h} header. If you have the ANSI C99 {\tt hypot}, you can use {\tt Common->hypotenuse = hypot}. The {\tt cholmod\_hypot} routine is provided in case you are using the ANSI C89 standard, which does not have {\tt hypot}. %--------------------------------------- \subsection{{\tt cholmod\_divcomplex}: complex divide} %--------------------------------------- \input{_divcomplex.tex} Divides two complex numbers. It returns 1 if a divide-by-zero occurred, or 0 otherwise. This routine is the default value for the {\tt Common->complex\_divide} function pointer. This return value is the single exception to the CHOLMOD rule that states all {\tt int} return values are {\tt TRUE} if successful or {\tt FALSE} otherwise. The exception is made to match the return value of a different complex divide routine that is not a part of CHOLMOD, but can be used via the function pointer. %------------------------------------------------------------------------------- \newpage \section{{\tt Core} Module: {\tt cholmod\_sparse} object} \label{cholmod_sparse} %------------------------------------------------------------------------------- %--------------------------------------- \subsection{{\tt cholmod\_sparse}: compressed-column sparse matrix} %--------------------------------------- \input{_sparse.tex} Stores a sparse matrix in compressed-column form. %--------------------------------------- \newpage \subsection{{\tt cholmod\_allocate\_sparse}: allocate sparse matrix} %--------------------------------------- \input{_allocate_sparse.tex} Allocates a sparse matrix. {\tt A->i}, {\tt A->x}, and {\tt A->z} are not initialized. The matrix returned is all zero, but it contains space enough for {\tt nzmax} entries. %--------------------------------------- \subsection{{\tt cholmod\_free\_sparse}: free sparse matrix} %--------------------------------------- \input{_free_sparse.tex} Frees a sparse matrix. %--------------------------------------- \subsection{{\tt cholmod\_reallocate\_sparse}: reallocate sparse matrix} %--------------------------------------- \input{_reallocate_sparse.tex} Reallocates a sparse matrix, so that it can contain {\tt nznew} entries. %--------------------------------------- \newpage \subsection{{\tt cholmod\_nnz}: number of entries in sparse matrix} %--------------------------------------- \input{_nnz.tex} Returns the number of entries in a sparse matrix. %--------------------------------------- \subsection{{\tt cholmod\_speye}: sparse identity matrix} %--------------------------------------- \input{_speye.tex} Returns the sparse identity matrix. %--------------------------------------- \subsection{{\tt cholmod\_spzeros}: sparse zero matrix} %--------------------------------------- \input{_spzeros.tex} Returns the sparse zero matrix. This is another name for {\tt cholmod\_allocate\_sparse}, but with fewer parameters (the matrix is packed, sorted, and unsymmetric). %--------------------------------------- \newpage \subsection{{\tt cholmod\_transpose}: transpose sparse matrix} %--------------------------------------- \input{_transpose.tex} Returns the transpose or complex conjugate transpose of a sparse matrix. %--------------------------------------- \subsection{{\tt cholmod\_ptranspose}: transpose/permute sparse matrix} %--------------------------------------- \input{_ptranspose.tex} Returns {\tt A'} or {\tt A(p,p)'} if {\tt A} is symmetric. Returns {\tt A'}, {\tt A(:,f)'}, or {\tt A(p,f)'} if {\tt A} is unsymmetric. See {\tt cholmod\_transpose\_unsym} for a discussion of how {\tt f} is used; this usage deviates from the MATLAB notation. Can also return the array transpose. %--------------------------------------- \subsection{{\tt cholmod\_sort}: sort columns of a sparse matrix} %--------------------------------------- \input{_sort.tex} Sorts the columns of the matrix {\tt A}. Returns {\tt A} in packed form, even if it starts as unpacked. Removes entries in the ignored part of a symmetric matrix. %--------------------------------------- \newpage \subsection{{\tt cholmod\_transpose\_unsym}: transpose/permute unsymmetric sparse matrix} %--------------------------------------- \input{_transpose_unsym.tex} Transposes and optionally permutes an unsymmetric sparse matrix. The output matrix must be preallocated before calling this routine. Computes {\tt F=A'}, {\tt F=A(:,f)'} or {\tt F=A(p,f)'}, except that the indexing by {\tt f} does not work the same as the MATLAB notation (see below). {\tt A->stype} is zero, which denotes that both the upper and lower triangular parts of A are present (and used). The matrix {\tt A} may in fact be symmetric in pattern and/or value; {\tt A->stype} just denotes which part of {\tt A} are stored. {\tt A} may be rectangular. The integer vector {\tt p} is a permutation of {\tt 0:m-1}, and {\tt f} is a subset of {\tt 0:n-1}, where A is {\tt m}-by-{\tt n}. There can be no duplicate entries in {\tt p} or {\tt f}. \noindent Three kinds of transposes are available, depending on the {\tt values} parameter: \begin{itemize} \item 0: do not transpose the numerical values; create a {\tt CHOLMOD\_PATTERN} matrix \item 1: array transpose \item 2: complex conjugate transpose (same as 2 if input is real or pattern) \end{itemize} \noindent The set {\tt f} is held in fset and fsize: \begin{itemize} \item {\tt fset = NULL} means ``{\tt :}'' in MATLAB. {\tt fset} is ignored. \item {\tt fset != NULL} means {\tt f = fset [0..fsize-1]}. \item {\tt fset != NULL} and {\tt fsize = 0} means {\tt f} is the empty set. \end{itemize} Columns not in the set {\tt f} are considered to be zero. That is, if {\tt A} is 5-by-10 then {\tt F=A(:,[3 4])'} is not 2-by-5, but 10-by-5, and rows 3 and 4 of {\tt F} are equal to columns 3 and 4 of {\tt A} (the other rows of {\tt F} are zero). More precisely, in MATLAB notation: \begin{verbatim} [m n] = size (A) F = A notf = ones (1,n) notf (f) = 0 F (:, find (notf)) = 0 F = F' \end{verbatim} If you want the MATLAB equivalent {\tt F=A(p,f)} operation, use {\tt cholmod\_submatrix} instead (which does not compute the transpose). {\tt F->nzmax} must be large enough to hold the matrix {\tt F}. If {\tt F->nz} is present then {\tt F->nz [j]} is equal to the number of entries in column {\tt j} of {\tt F}. {\tt A} can be sorted or unsorted, with packed or unpacked columns. If {\tt f} is present and not sorted in ascending order, then {\tt F} is unsorted (that is, it may contain columns whose row indices do not appear in ascending order). Otherwise, {\tt F} is sorted (the row indices in each column of {\tt F} appear in strictly ascending order). {\tt F} is returned in packed or unpacked form, depending on {\tt F->packed} on input. If {\tt F->packed} is {\tt FALSE}, then {\tt F} is returned in unpacked form ({\tt F->nz} must be present). Each row {\tt i} of {\tt F} is large enough to hold all the entries in row {\tt i} of {\tt A}, even if {\tt f} is provided. That is, {\tt F->i} and {\tt F->x [F->p [i] .. F->p [i] + F->nz [i] - 1]} contain all entries in {\tt A(i,f)}, but {\tt F->p [i+1] - F->p [i]} is equal to the number of nonzeros in {\tt A (i,:)}, not just {\tt A (i,f)}. The {\tt cholmod\_transpose\_unsym} routine is the only operation in CHOLMOD that can produce an unpacked matrix. %--------------------------------------- \subsection{{\tt cholmod\_transpose\_sym}: transpose/permute symmetric sparse matrix} %--------------------------------------- \input{_transpose_sym.tex} Computes {\tt F = A'} or {\tt F = A(p,p)'}, the transpose or permuted transpose, where {\tt A->stype} is nonzero. {\tt A} must be square and symmetric. If {\tt A->stype} $> 0$, then {\tt A} is a symmetric matrix where just the upper part of the matrix is stored. Entries in the lower triangular part may be present, but are ignored. If {\tt A->stype} $< 0$, then {\tt A} is a symmetric matrix where just the lower part of the matrix is stored. Entries in the upper triangular part may be present, but are ignored. If {\tt F=A'}, then {\tt F} is returned sorted; otherwise {\tt F} is unsorted for the {\tt F=A(p,p)'} case. There can be no duplicate entries in {\tt p}. Three kinds of transposes are available, depending on the {\tt values} parameter: \begin{itemize} \item 0: do not transpose the numerical values; create a {\tt CHOLMOD\_PATTERN} matrix \item 1: array transpose \item 2: complex conjugate transpose (same as 2 if input is real or pattern) \end{itemize} For {\tt cholmod\_transpose\_unsym} and {\tt cholmod\_transpose\_sym}, the output matrix {\tt F} must already be pre-allocated by the caller, with the correct dimensions. If {\tt F} is not valid or has the wrong dimensions, it is not modified. Otherwise, if {\tt F} is too small, the transpose is not computed; the contents of {\tt F->p} contain the column pointers of the resulting matrix, where {\tt F->p [F->ncol] > F->nzmax}. In this case, the remaining contents of {\tt F} are not modified. {\tt F} can still be properly freed with {\tt cholmod\_free\_sparse}. %--------------------------------------- \newpage \subsection{{\tt cholmod\_band}: extract band of a sparse matrix} %--------------------------------------- \input{_band.tex} Returns {\tt C = tril (triu (A,k1), k2)}. {\tt C} is a matrix consisting of the diagonals of A from {\tt k1} to {\tt k2}. {\tt k=0} is the main diagonal of {\tt A}, {\tt k=1} is the superdiagonal, {\tt k=-1} is the subdiagonal, and so on. If {\tt A} is {\tt m}-by-{\tt n}, then: \begin{itemize} \item {\tt k1=-m} means {\tt C = tril (A,k2)} \item {\tt k2=n} means {\tt C = triu (A,k1)} \item {\tt k1=0} and {\tt k2=0} means {\tt C = diag(A)}, except {\tt C} is a matrix, not a vector \end{itemize} Values of {\tt k1} and {\tt k2} less than {\tt -m} are treated as {\tt -m}, and values greater than {\tt n} are treated as {\tt n}. {\tt A} can be of any symmetry (upper, lower, or unsymmetric); {\tt C} is returned in the same form, and packed. If {\tt A->stype} $> 0$, entries in the lower triangular part of {\tt A} are ignored, and the opposite is true if {\tt A->stype} $< 0$. If {\tt A} has sorted columns, then so does {\tt C}. {\tt C} has the same size as {\tt A}. {\tt C} can be returned as a numerical valued matrix (if {\tt A} has numerical values and {\tt mode} $> 0$), as a pattern-only ({\tt mode} $=0$), or as a pattern-only but with the diagonal entries removed ({\tt mode} $< 0$). The xtype of {\tt A} can be pattern or real. Complex or zomplex cases are supported only if {\tt mode} is $\le 0$ (in which case the numerical values are ignored). %--------------------------------------- \subsection{{\tt cholmod\_band\_inplace}: extract band, in place} %--------------------------------------- \input{_band_inplace.tex} Same as {\tt cholmod\_band}, except that it always operates in place. Only packed matrices can be converted in place. %--------------------------------------- \newpage \subsection{{\tt cholmod\_aat}: compute $\m{AA}\tr$} %--------------------------------------- \input{_aat.tex} Computes {\tt C = A*A'} or {\tt C = A(:,f)*A(:,f)'}. {\tt A} can be packed or unpacked, sorted or unsorted, but must be stored with both upper and lower parts ({\tt A->stype} of zero). {\tt C} is returned as packed, {\tt C->stype} of zero (both upper and lower parts present), and unsorted. See {\tt cholmod\_ssmult} in the {\tt MatrixOps} Module for a more general matrix-matrix multiply. The xtype of {\tt A} can be pattern or real. Complex or zomplex cases are supported only if {\tt mode} is $\le 0$ (in which case the numerical values are ignored). You can trivially convert {\tt C} to a symmetric upper/lower matrix by changing {\tt C->stype} to 1 or -1, respectively, after calling this routine. %--------------------------------------- \subsection{{\tt cholmod\_copy\_sparse}: copy sparse matrix} %--------------------------------------- \input{_copy_sparse.tex} Returns an exact copy of the input sparse matrix {\tt A}. %--------------------------------------- \newpage \subsection{{\tt cholmod\_copy}: copy (and change) sparse matrix} %--------------------------------------- \input{_copy.tex} {\tt C = A}, which allocates {\tt C} and copies {\tt A} into {\tt C}, with possible change of {\tt stype}. The diagonal can optionally be removed. The numerical entries can optionally be copied. This routine differs from {\tt cholmod\_copy\_sparse}, which makes an exact copy of a sparse matrix. {\tt A} can be of any type (packed/unpacked, upper/lower/unsymmetric). {\tt C} is packed and can be of any stype (upper/lower/unsymmetric), except that if {\tt A} is rectangular {\tt C} can only be unsymmetric. If the stype of A and C differ, then the appropriate conversion is made. \noindent There are three cases for {\tt A->stype}: \begin{itemize} \item $<0$, lower: assume {\tt A} is symmetric with just {\tt tril(A)} stored; the rest of {\tt A} is ignored \item $ 0$, unsymmetric: assume {\tt A} is unsymmetric; consider all entries in A \item $>0$, upper: assume {\tt A} is symmetric with just {\tt triu(A)} stored; the rest of {\tt A} is ignored \end{itemize} \noindent There are three cases for the requested symmetry of {\tt C} ({\tt stype} parameter): \begin{itemize} \item $<0$, lower: return just {\tt tril(C)} \item $0$, unsymmetric: return all of {\tt C} \item $>0$, upper: return just {\tt triu(C)} \end{itemize} \noindent This gives a total of nine combinations: \newline \begin{tabular}{ll} \hline Equivalent MATLAB statements & Using {\tt cholmod\_copy} \\ \hline {\tt C = A ; }& {\tt A} unsymmetric, {\tt C} unsymmetric \\ {\tt C = tril (A) ; }& {\tt A} unsymmetric, {\tt C} lower \\ {\tt C = triu (A) ; }& {\tt A} unsymmetric, {\tt C} upper \\ {\tt U = triu (A) ; L = tril (U',-1) ; C = L+U ; }& {\tt A} upper, {\tt C} unsymmetric \\ {\tt C = triu (A)' ; }& {\tt A} upper, {\tt C} lower \\ {\tt C = triu (A) ; }& {\tt A} upper, {\tt C} upper \\ {\tt L = tril (A) ; U = triu (L',1) ; C = L+U ; }& {\tt A} lower, {\tt C} unsymmetric \\ {\tt C = tril (A) ; }& {\tt A} lower, {\tt C} lower \\ {\tt C = tril (A)' ; }& {\tt A} lower, {\tt C} upper \\ \hline \end{tabular} \vspace{0.1in} The xtype of {\tt A} can be pattern or real. Complex or zomplex cases are supported only if {\tt values} is {\tt FALSE} (in which case the numerical values are ignored). %--------------------------------------- \newpage \subsection{{\tt cholmod\_add}: add sparse matrices} %--------------------------------------- \input{_add.tex} Returns {\tt C = alpha*A + beta*B}. If the {\tt stype} of {\tt A} and {\tt B} match, then {\tt C} has the same {\tt stype}. Otherwise, {\tt C->stype} is zero ({\tt C} is unsymmetric). %--------------------------------------- \subsection{{\tt cholmod\_sparse\_xtype}: change sparse xtype} %--------------------------------------- \input{_sparse_xtype.tex} Changes the {\tt xtype} of a sparse matrix, to pattern, real, complex, or zomplex. Changing from complex or zomplex to real discards the imaginary part. %------------------------------------------------------------------------------- \newpage \section{{\tt Core} Module: {\tt cholmod\_factor} object} \label{cholmod_factor} %------------------------------------------------------------------------------- %--------------------------------------- \subsection{{\tt cholmod\_factor} object: a sparse Cholesky factorization} %--------------------------------------- \input{_factor.tex} An $\m{LL}\tr$ or $\m{LDL}\tr$ factorization in simplicial or supernodal form. A simplicial factor is very similar to a {\tt cholmod\_sparse} matrix. For an $\m{LDL}\tr$ factorization, the diagonal matrix $\m{D}$ is stored as the diagonal of $\m{L}$; the unit-diagonal of $\m{L}$ is not stored. %--------------------------------------- \newpage \subsection{{\tt cholmod\_free\_factor}: free factor} %--------------------------------------- \input{_free_factor.tex} Frees a factor. %--------------------------------------- \subsection{{\tt cholmod\_allocate\_factor}: allocate factor} %--------------------------------------- \input{_allocate_factor.tex} Allocates a factor and sets it to identity. %--------------------------------------- \subsection{{\tt cholmod\_reallocate\_factor}: reallocate factor} %--------------------------------------- \input{_reallocate_factor.tex} Reallocates a simplicial factor so that it can contain {\tt nznew} entries. %--------------------------------------- \newpage \subsection{{\tt cholmod\_change\_factor}: change factor} %--------------------------------------- \input{_change_factor.tex} Change the numeric or symbolic, $\m{LL}\tr$ or $\m{LDL}\tr$, simplicial or super, packed or unpacked, and monotonic or non-monotonic status of a {\tt cholmod\_factor} object. There are four basic classes of factor types: \begin{enumerate} \item simplicial symbolic: Consists of two size-{\tt n} arrays: the fill-reducing permutation ({\tt L->Perm}) and the nonzero count for each column of L ({\tt L->ColCount}). All other factor types also include this information. {\tt L->ColCount} may be exact (obtained from the analysis routines), or it may be a guess. During factorization, and certainly after update/downdate, the columns of {\tt L} can have a different number of nonzeros. {\tt L->ColCount} is used to allocate space. {\tt L->ColCount} is exact for the supernodal factorizations. The nonzero pattern of {\tt L} is not kept. \item simplicial numeric: These represent {\tt L} in a compressed column form. The variants of this type are: \begin{itemize} \item $\m{LDL}\tr$: {\tt L} is unit diagonal. Row indices in column {\tt j} are located in {\tt L->i [L->p [j] ... L->p [j] + L->nz [j]]}, and corresponding numeric values are in the same locations in {\tt L->x}. The total number of entries is the sum of {\tt L->nz [j]}. The unit diagonal is not stored; {\tt D} is stored on the diagonal of {\tt L} instead. {\tt L->p} may or may not be monotonic. The order of storage of the columns in {\tt L->i} and {\tt L->x} is given by a doubly-linked list ({\tt L->prev} and {\tt L->next}). {\tt L->p} is of size {\tt n+1}, but only the first {\tt n} entries are used. For the complex case, {\tt L->x} is stored interleaved with real and imaginary parts, and is of size {\tt 2*lnz*sizeof(double)}. For the zomplex case, {\tt L->x} is of size {\tt lnz*sizeof(double)} and holds the real part; {\tt L->z} is the same size and holds the imaginary part. \item $\m{LL}\tr$: This is identical to the $\m{LDL}\tr$ form, except that the non-unit diagonal of {\tt L} is stored as the first entry in each column of {\tt L}. \end{itemize} \item supernodal symbolic: A representation of the nonzero pattern of the supernodes for a supernodal factorization. There are {\tt L->nsuper} supernodes. Columns {\tt L->super [k]} to {\tt L->super [k+1]-1} are in the {\tt k}th supernode. The row indices for the {\tt k}th supernode are in {\tt L->s [L->pi [k] ... L->pi [k+1]-1]}. The numerical values are not allocated ({\tt L->x}), but when they are they will be located in {\tt L->x [L->px [k] ... L->px [k+1]-1]}, and the {\tt L->px} array is defined in this factor type. For the complex case, {\tt L->x} is stored interleaved with real/imaginary parts, and is of size \newline {\tt 2*L->xsize*sizeof(double)}. The zomplex supernodal case is not supported, since it is not compatible with LAPACK and the BLAS. \item supernodal numeric: Always an $\m{LL}\tr$ factorization. {\tt L} has a non-unit diagonal. {\tt L->x} contains the numerical values of the supernodes, as described above for the supernodal symbolic factor. For the complex case, {\tt L->x} is stored interleaved, and is of size {\tt 2*L->xsize*sizeof(double)}. The zomplex supernodal case is not supported, since it is not compatible with LAPACK and the BLAS. \end{enumerate} In all cases, the row indices in each column ({\tt L->i} for simplicial {\tt L} and {\tt L->s} for supernodal {\tt L}) are kept sorted from low indices to high indices. This means the diagonal of {\tt L} (or {\tt D} for a $\m{LDL}\tr$ factorization) is always kept as the first entry in each column. The elimination tree is not kept. The parent of node {\tt j} can be found as the second row index in the {\tt j}th column. If column {\tt j} has no off-diagonal entries then node {\tt j} is a root of the elimination tree. The {\tt cholmod\_change\_factor} routine can do almost all possible conversions. It cannot do the following conversions: \begin{itemize} \item Simplicial numeric types cannot be converted to a supernodal symbolic type. This would simultaneously deallocate the simplicial pattern and numeric values and reallocate uninitialized space for the supernodal pattern. This isn't useful for the user, and not needed by CHOLMOD's own routines either. \item Only a symbolic factor (simplicial to supernodal) can be converted to a supernodal numeric factor. \end{itemize} Some conversions are meant only to be used internally by other CHOLMOD routines, and should not be performed by the end user. They allocate space whose contents are undefined: \begin{itemize} \item converting from simplicial symbolic to supernodal symbolic. \item converting any factor to supernodal numeric. \end{itemize} Supports all xtypes, except that there is no supernodal zomplex L. The {\tt to\_xtype} parameter is used only when converting from symbolic to numeric or numeric to symbolic. It cannot be used to convert a numeric xtype (real, complex, or zomplex) to a different numeric xtype. For that conversion, use {\tt cholmod\_factor\_xtype} instead. %--------------------------------------- \newpage \subsection{{\tt cholmod\_pack\_factor}: pack the columns of a factor} %--------------------------------------- \input{_pack_factor.tex} Pack the columns of a simplicial $\m{LDL}\tr$ or $\m{LL}\tr$ factorization. This can be followed by a call to {\tt cholmod\_reallocate\_factor} to reduce the size of {\tt L} to the exact size required by the factor, if desired. Alternatively, you can leave the size of {\tt L->i} and {\tt L->x} the same, to allow space for future updates/rowadds. Each column is reduced in size so that it has at most {\tt Common->grow2} free space at the end of the column. Does nothing and returns silently if given any other type of factor. Does not force the columns of {\tt L} to be monotonic. It thus differs from \begin{verbatim} cholmod_change_factor (xtype, L->is_ll, FALSE, TRUE, TRUE, L, Common) \end{verbatim} which packs the columns and ensures that they appear in monotonic order. %--------------------------------------- \subsection{{\tt cholmod\_reallocate\_column}: reallocate one column of a factor} %--------------------------------------- \input{_reallocate_column.tex} Reallocates the space allotted to a single column of $\m{L}$. %--------------------------------------- \newpage \subsection{{\tt cholmod\_factor\_to\_sparse}: sparse matrix copy of a factor} %--------------------------------------- \input{_factor_to_sparse.tex} Returns a column-oriented sparse matrix containing the pattern and values of a simplicial or supernodal numerical factor, and then converts the factor into a simplicial symbolic factor. If {\tt L} is already packed, monotonic, and simplicial (which is the case when {\tt cholmod\_factorize} uses the simplicial Cholesky factorization algorithm) then this routine requires only a small amount of time and memory, independent of {\tt n}. It only operates on numeric factors (real, complex, or zomplex). It does not change {\tt L->xtype} (the resulting sparse matrix has the same {\tt xtype} as {\tt L}). If this routine fails, {\tt L} is left unmodified. %--------------------------------------- \subsection{{\tt cholmod\_copy\_factor}: copy factor} %--------------------------------------- \input{_copy_factor.tex} Returns an exact copy of a factor. %--------------------------------------- \subsection{{\tt cholmod\_factor\_xtype}: change factor xtype} %--------------------------------------- \input{_factor_xtype.tex} Changes the {\tt xtype} of a factor, to pattern, real, complex, or zomplex. Changing from complex or zomplex to real discards the imaginary part. You cannot change a supernodal factor to the zomplex xtype. %------------------------------------------------------------------------------- \newpage \section{{\tt Core} Module: {\tt cholmod\_dense} object} \label{cholmod_dense} %------------------------------------------------------------------------------- %--------------------------------------- \subsection{{\tt cholmod\_dense} object: a dense matrix} %--------------------------------------- \input{_dense.tex} Contains a dense matrix. %--------------------------------------- \subsection{{\tt cholmod\_allocate\_dense}: allocate dense matrix} %--------------------------------------- \input{_allocate_dense.tex} Allocates a dense matrix. %--------------------------------------- \subsection{{\tt cholmod\_free\_dense}: free dense matrix} %--------------------------------------- \input{_free_dense.tex} Frees a dense matrix. %--------------------------------------- \newpage \subsection{{\tt cholmod\_zeros}: dense zero matrix} %--------------------------------------- \input{_zeros.tex} Returns an all-zero dense matrix. %--------------------------------------- \subsection{{\tt cholmod\_ones}: dense matrix, all ones} %--------------------------------------- \input{_ones.tex} Returns a dense matrix with each entry equal to one. %--------------------------------------- \subsection{{\tt cholmod\_eye}: dense identity matrix} %--------------------------------------- \input{_eye.tex} Returns a dense identity matrix. %--------------------------------------- \newpage \subsection{{\tt cholmod\_sparse\_to\_dense}: dense matrix copy of a sparse matrix} %--------------------------------------- \input{_sparse_to_dense.tex} Returns a dense copy of a sparse matrix. %--------------------------------------- \subsection{{\tt cholmod\_dense\_to\_sparse}: sparse matrix copy of a dense matrix} %--------------------------------------- \input{_dense_to_sparse.tex} Returns a sparse copy of a dense matrix. %--------------------------------------- \subsection{{\tt cholmod\_copy\_dense}: copy dense matrix} %--------------------------------------- \input{_copy_dense.tex} Returns a copy of a dense matrix. %--------------------------------------- \newpage \subsection{{\tt cholmod\_copy\_dense2}: copy dense matrix (preallocated)} %--------------------------------------- \input{_copy_dense2.tex} Returns a copy of a dense matrix, placing the result in a preallocated matrix {\tt Y}. %--------------------------------------- \subsection{{\tt cholmod\_dense\_xtype}: change dense matrix xtype} %--------------------------------------- \input{_dense_xtype.tex} Changes the {\tt xtype} of a dense matrix, to real, complex, or zomplex. Changing from complex or zomplex to real discards the imaginary part. %------------------------------------------------------------------------------- \newpage \section{{\tt Core} Module: {\tt cholmod\_triplet} object} \label{cholmod_triplet} %------------------------------------------------------------------------------- %--------------------------------------- \subsection{{\tt cholmod\_triplet} object: sparse matrix in triplet form} %--------------------------------------- \input{_triplet.tex} Contains a sparse matrix in triplet form. %--------------------------------------- \subsection{{\tt cholmod\_allocate\_triplet}: allocate triplet matrix} %--------------------------------------- \input{_allocate_triplet.tex} Allocates a triplet matrix. %--------------------------------------- \subsection{{\tt cholmod\_free\_triplet}: free triplet matrix} %--------------------------------------- \input{_free_triplet.tex} Frees a triplet matrix. %--------------------------------------- \newpage \subsection{{\tt cholmod\_reallocate\_triplet}: reallocate triplet matrix} %--------------------------------------- \input{_reallocate_triplet.tex} Reallocates a triplet matrix so that it can hold {\tt nznew} entries. %--------------------------------------- \subsection{{\tt cholmod\_sparse\_to\_triplet}: triplet matrix copy of a sparse matrix} %--------------------------------------- \input{_sparse_to_triplet.tex} Returns a triplet matrix copy of a sparse matrix. %--------------------------------------- \subsection{{\tt cholmod\_triplet\_to\_sparse}: sparse matrix copy of a triplet matrix} %--------------------------------------- \input{_triplet_to_sparse.tex} Returns a sparse matrix copy of a triplet matrix. If the triplet matrix is symmetric with just the lower part present ({\tt T->stype} $< 0$), then entries in the upper part are transposed and placed in the lower part when converting to a sparse matrix. Similarly, if the triplet matrix is symmetric with just the upper part present ({\tt T->stype} $> 0$), then entries in the lower part are transposed and placed in the upper part when converting to a sparse matrix. Any duplicate entries are summed. %--------------------------------------- \newpage \subsection{{\tt cholmod\_copy\_triplet}: copy triplet matrix} %--------------------------------------- \input{_copy_triplet.tex} Returns an exact copy of a triplet matrix. %--------------------------------------- \subsection{{\tt cholmod\_triplet\_xtype}: change triplet xtype} %--------------------------------------- \input{_triplet_xtype.tex} Changes the {\tt xtype} of a dense matrix, to real, complex, or zomplex. Changing from complex or zomplex to real discards the imaginary part. %------------------------------------------------------------------------------- \newpage \section{{\tt Core} Module: memory management} %------------------------------------------------------------------------------- %--------------------------------------- \subsection{{\tt cholmod\_malloc}: allocate memory} %--------------------------------------- \input{_malloc.tex} Allocates a block of memory of size {\tt n*size}, using the {\tt Common->malloc\_memory} function pointer (default is to use the ANSI C {\tt malloc} routine). A value of {\tt n=0} is treated as {\tt n=1}. If not successful, {\tt NULL} is returned and {\tt Common->status} is set to {\tt CHOLMOD\_OUT\_OF\_MEMORY}. %--------------------------------------- \subsection{{\tt cholmod\_calloc}: allocate and clear memory} %--------------------------------------- \input{_calloc.tex} Allocates a block of memory of size {\tt n*size}, using the {\tt Common->calloc\_memory} function pointer (default is to use the ANSI C {\tt calloc} routine). A value of {\tt n=0} is treated as {\tt n=1}. If not successful, {\tt NULL} is returned and {\tt Common->status} is set to {\tt CHOLMOD\_OUT\_OF\_MEMORY}. %--------------------------------------- \newpage \subsection{{\tt cholmod\_free}: free memory} %--------------------------------------- \input{_free.tex} Frees a block of memory of size {\tt n*size}, using the {\tt Common->free\_memory} function pointer (default is to use the ANSI C {\tt free} routine). The size of the block ({\tt n} and {\tt size}) is only required so that CHOLMOD can keep track of its current and peak memory usage. This is a useful statistic, and it can also help in tracking down memory leaks. After the call to {\tt cholmod\_finish}, the count of allocated blocks ({\tt Common->malloc\_count}) should be zero, and the count of bytes in use ({\tt Common->memory\_inuse}) also should be zero. If you allocate a block with one size and free it with another, the {\tt Common->memory\_inuse} count will be wrong, but CHOLMOD will not have a memory leak. %--------------------------------------- \subsection{{\tt cholmod\_realloc}: reallocate memory} %--------------------------------------- \input{_realloc.tex} Reallocates a block of memory whose current size {\tt n*size}, and whose new size will be {\tt nnew*size} if successful, using the {\tt Common->calloc\_memory} function pointer (default is to use the ANSI C {\tt realloc} routine). If the reallocation is not successful, {\tt p} is returned unchanged and {\tt Common->status} is set to {\tt CHOLMOD\_OUT\_OF\_MEMORY}. The value of {\tt n} is set to {\tt nnew} if successful, or left unchanged otherwise. A value of {\tt nnew=0} is treated as {\tt nnew=1}. %--------------------------------------- \newpage \subsection{{\tt cholmod\_realloc\_multiple}: reallocate memory} %--------------------------------------- \input{_realloc_multiple.tex} Reallocates multiple blocks of memory, all with the same number of items (but with different item sizes). Either all reallocations succeed, or all are returned to their original size. %------------------------------------------------------------------------------- \newpage \section{{\tt Check} Module routines} %------------------------------------------------------------------------------- No CHOLMOD routines print anything, except for the {\tt cholmod\_print\_*} routines in the {\tt Check} Module, and the {\tt cholmod\_error} routine. The {\tt Common->print\_function} is a pointer to {\tt printf} by default; you can redirect the output of CHOLMOD by redefining this pointer. If {\tt Common->print\_function} is {\tt NULL}, CHOLMOD does not print anything. The {\tt Common->print} parameter determines how much detail is printed. Each value of {\tt Common->print} listed below also prints the items listed for smaller values of {\tt Common->print}: \begin{itemize} \item 0: print nothing; check the data structures and return {\tt TRUE} or {\tt FALSE}. \item 1: print error messages. \item 2: print warning messages. \item 3: print a one-line summary of the object. \item 4: print a short summary of the object (first and last few entries). \item 5: print the entire contents of the object. \end{itemize} Values less than zero are treated as zero, and values greater than five are treated as five. %--------------------------------------- \subsection{{\tt cholmod\_check\_common}: check Common object} %--------------------------------------- \input{_check_common.tex} Check if the {\tt Common} object is valid. %--------------------------------------- \subsection{{\tt cholmod\_print\_common}: print Common object} %--------------------------------------- \input{_print_common.tex} Print the {\tt Common} object and check if it is valid. This prints the CHOLMOD parameters and statistics. %--------------------------------------- \newpage \subsection{{\tt cholmod\_check\_sparse}: check sparse matrix} %--------------------------------------- \input{_check_sparse.tex} Check if a sparse matrix is valid. %--------------------------------------- \subsection{{\tt cholmod\_print\_sparse}: print sparse matrix} %--------------------------------------- \input{_print_sparse.tex} Print a sparse matrix and check if it is valid. %--------------------------------------- \newpage \subsection{{\tt cholmod\_check\_dense}: check dense matrix} %--------------------------------------- \input{_check_dense.tex} Check if a dense matrix is valid. %--------------------------------------- \subsection{{\tt cholmod\_print\_dense}: print dense matrix} %--------------------------------------- \input{_print_dense.tex} Print a dense matrix and check if it is valid. %--------------------------------------- \newpage \subsection{{\tt cholmod\_check\_factor}: check factor} %--------------------------------------- \input{_check_factor.tex} Check if a factor is valid. %--------------------------------------- \subsection{{\tt cholmod\_print\_factor}: print factor} %--------------------------------------- \input{_print_factor.tex} Print a factor and check if it is valid. %--------------------------------------- \newpage \subsection{{\tt cholmod\_check\_triplet}: check triplet matrix} %--------------------------------------- \input{_check_triplet.tex} Check if a triplet matrix is valid. %--------------------------------------- \subsection{{\tt cholmod\_print\_triplet}: print triplet matrix} %--------------------------------------- \input{_print_triplet.tex} Print a triplet matrix and check if it is valid. %--------------------------------------- \newpage \subsection{{\tt cholmod\_check\_subset}: check subset} %--------------------------------------- \input{_check_subset.tex} Check if a subset is valid. %--------------------------------------- \subsection{{\tt cholmod\_print\_subset}: print subset} %--------------------------------------- \input{_print_subset.tex} Print a subset and check if it is valid. %--------------------------------------- \newpage \subsection{{\tt cholmod\_check\_perm}: check permutation} %--------------------------------------- \input{_check_perm.tex} Check if a permutation is valid. %--------------------------------------- \subsection{{\tt cholmod\_print\_perm}: print permutation} %--------------------------------------- \input{_print_perm.tex} Print a permutation and check if it is valid. %--------------------------------------- \newpage \subsection{{\tt cholmod\_check\_parent}: check elimination tree} %--------------------------------------- \input{_check_parent.tex} Check if an elimination tree is valid. %--------------------------------------- \subsection{{\tt cholmod\_print\_parent}: print elimination tree} %--------------------------------------- \input{_print_parent.tex} Print an elimination tree and check if it is valid. %--------------------------------------- \newpage \subsection{{\tt cholmod\_read\_triplet}: read triplet matrix from file} %--------------------------------------- \input{_read_triplet.tex} Read a sparse matrix in triplet form, using the the {\tt coord} Matrix Market format (http://www.nist.gov/MatrixMarket). Skew-symmetric and complex symmetric matrices are returned with both upper and lower triangular parts present (an stype of zero). Real symmetric and complex Hermitian matrices are returned with just their upper or lower triangular part, depending on their stype. The Matrix Market {\tt array} data type for dense matrices is not supported (use {\tt cholmod\_read\_dense} for that case). If the first line of the file starts with {\tt \%\%MatrixMarket}, then it is interpreted as a file in Matrix Market format. The header line is optional. If present, this line must have the following format: \vspace{0.1in} {\tt \%\%MatrixMarket matrix coord} {\em type storage} \vspace{0.1in} \noindent where {\em type} is one of: {\tt real}, {\tt complex}, {\tt pattern}, or {\tt integer}, and {\em storage} is one of: {\tt general}, {\tt hermitian}, {\tt symmetric}, or {\tt skew-symmetric}. In CHOLMOD, these roughly correspond to the {\tt xtype} (pattern, real, complex, or zomplex) and {\tt stype} (unsymmetric, symmetric/upper, and symmetric/lower). The strings are case-insensitive. Only the first character (or the first two for skew-symmetric) is significant. The {\tt coord} token can be replaced with {\tt array} in the Matrix Market format, but this format not supported by {\tt cholmod\_read\_triplet}. The {\tt integer} type is converted to real. The {\em type} is ignored; the actual type (real, complex, or pattern) is inferred from the number of tokens in each line of the file (2: pattern, 3: real, 4: complex). This is compatible with the Matrix Market format. A storage of {\tt general} implies an stype of zero (see below). A storage of {\tt symmetric} and {\tt hermitian} imply an stype of -1. Skew-symmetric and complex symmetric matrices are returned with an stype of 0. Blank lines, any other lines starting with ``{\tt \%}'' are treated as comments, and are ignored. The first non-comment line contains 3 or 4 integers: \vspace{0.1in} {\em nrow ncol nnz stype} \vspace{0.1in} \noindent where {\em stype} is optional (stype does not appear in the Matrix Market format). The matrix is {\em nrow}-by-{\em ncol}. The following {\em nnz} lines (excluding comments) each contain a single entry. Duplicates are permitted, and are summed in the output matrix. If stype is present, it denotes the storage format for the matrix. \begin{itemize} \item stype = 0 denotes an unsymmetric matrix (same as Matrix Market {\tt general}). \item stype = -1 denotes a symmetric or Hermitian matrix whose lower triangular entries are stored. Entries may be present in the upper triangular part, but these are ignored (same as Matrix Market {\tt symmetric} for the real case, {\tt hermitian} for the complex case). \item stype = 1 denotes a symmetric or Hermitian matrix whose upper triangular entries are stored. Entries may be present in the lower triangular part, but these are ignored. This format is not available in the Matrix Market format. \end{itemize} If neither the stype nor the Matrix Market header are present, then the stype is inferred from the rest of the data. If the matrix is rectangular, or has entries in both the upper and lower triangular parts, then it is assumed to be unsymmetric (stype=0). If only entries in the lower triangular part are present, the matrix is assumed to have stype = -1. If only entries in the upper triangular part are present, the matrix is assumed to have stype = 1. Each nonzero consists of one line with 2, 3, or 4 entries. All lines must have the same number of entries. The first two entries are the row and column indices of the nonzero. If 3 entries are present, the 3rd entry is the numerical value, and the matrix is real. If 4 entries are present, the 3rd and 4th entries in the line are the real and imaginary parts of a complex value. The matrix can be either 0-based or 1-based. It is first assumed to be one-based (compatible with Matrix Market), with row indices in the range 1 to ncol and column indices in the range 1 to nrow. If a row or column index of zero is found, the matrix is assumed to be zero-based (with row indices in the range 0 to ncol-1 and column indices in the range 0 to nrow-1). This test correctly determines that all Matrix Market matrices are in 1-based form. For symmetric pattern-only matrices, the kth diagonal (if present) is set to one plus the degree of the row k or column k (whichever is larger), and the off-diagonals are set to -1. A symmetric pattern-only matrix with a zero-free diagonal is thus converted into a symmetric positive definite matrix. All entries are set to one for an unsymmetric pattern-only matrix. This differs from the MatrixMarket format ({\tt A = mmread ('file')} returns a binary pattern for A for symmetric pattern-only matrices). To return a binary format for all pattern-only matrices, use {\tt A = mread('file',1)}. Example matrices that follow this format can be found in the {\tt CHOLMOD/Demo/Matrix} and \newline {\tt CHOLMOD/Tcov/Matrix} directories. You can also try any of the matrices in the Matrix Market collection at http://www.nist.gov/MatrixMarket. %--------------------------------------- \subsection{{\tt cholmod\_read\_sparse}: read sparse matrix from file} %--------------------------------------- \input{_read_sparse.tex} Read a sparse matrix in triplet form from a file (using {\tt cholmod\_read\_triplet}) and convert to a CHOLMOD sparse matrix. The Matrix Market format is used. If {\tt Common->prefer\_upper} is {\tt TRUE} (the default case), a symmetric matrix is returned stored in upper-triangular form ({\tt A->stype} is 1). Otherwise, it is left in its original form, either upper or lower. %--------------------------------------- \newpage \subsection{{\tt cholmod\_read\_dense}: read dense matrix from file} %--------------------------------------- \input{_read_dense.tex} Read a dense matrix from a file, using the the {\tt array} Matrix Market format \newline (http://www.nist.gov/MatrixMarket). %--------------------------------------- \subsection{{\tt cholmod\_read\_matrix}: read a matrix from file} %--------------------------------------- \input{_read_matrix.tex} Read a sparse or dense matrix from a file, in Matrix Market format. Returns a {\tt void} pointer to either a {\tt cholmod\_triplet}, {\tt cholmod\_sparse}, or {\tt cholmod\_dense} object. %--------------------------------------- \newpage \subsection{{\tt cholmod\_write\_sparse}: write a sparse matrix to a file} %--------------------------------------- \input{_write_sparse.tex} Write a sparse matrix to a file in Matrix Market format. Optionally include comments, and print explicit zero entries given by the pattern of the {\tt Z} matrix. If not NULL, the {\tt Z} matrix must have the same dimensions and stype as {\tt A}. Returns the symmetry in which the matrix was printed (1 to 7) or -1 on failure. See the {\tt cholmod\_symmetry} function for a description of the return codes. If {\tt A} and {\tt Z} are sorted on input, and either unsymmetric (stype = 0) or symmetric-lower (stype < 0), and if {\tt A} and {\tt Z} do not overlap, then the triplets are sorted, first by column and then by row index within each column, with no duplicate entries. If all the above holds except stype > 0, then the triplets are sorted by row first and then column. %--------------------------------------- \subsection{{\tt cholmod\_write\_dense}: write a dense matrix to a file} %--------------------------------------- \input{_write_dense.tex} Write a dense matrix to a file in Matrix Market format. Optionally include comments. Returns > 0 if successful, -1 otherwise (1 if rectangular, 2 if square). A dense matrix is written in "general" format; symmetric formats in the Matrix Market standard are not exploited. %------------------------------------------------------------------------------- \newpage \section{{\tt Cholesky} Module routines} %------------------------------------------------------------------------------- %--------------------------------------- \subsection{{\tt cholmod\_analyze}: symbolic factorization} %--------------------------------------- \input{_analyze.tex} Orders and analyzes a matrix (either simplicial or supernodal), in preparation for numerical factorization via {\tt cholmod\_factorize} or via the ``expert'' routines {\tt cholmod\_rowfac} and {\tt cholmod\_super\_numeric}. In the symmetric case, {\tt A} or {\tt A(p,p)} is analyzed, where {\tt p} is the fill-reducing ordering. In the unsymmetric case, {\tt A*A'} or {\tt A(p,:)*A(p,:)'} is analyzed. The {\tt cholmod\_analyze\_p} routine can be given a user-provided permutation {\tt p} (see below). The default ordering strategy is to first try AMD. The ordering quality is analyzed, and if AMD obtains an ordering where {\tt nnz(L)} is greater than or equal to {\tt 5*nnz(tril(A))} (or {\tt 5*nnz(tril(A*A'))} if {\tt A} is unsymmetric) and the floating-point operation count for the subsequent factorization is greater than or equal to {\tt 500*nnz(L)}, then METIS is tried (if installed). For {\tt cholmod\_analyze\_p}, the user-provided ordering is also tried. This default behavior is obtained when {\tt Common->nmethods} is zero. In this case, methods 0, 1, and 2 in {\tt Common->method[...]} are reset to user-provided, AMD, and METIS, respectively. The ordering with the smallest {\tt nnz(L)} is kept. If {\tt Common->default\_nesdis} is true (nonzero), then CHOLMOD's nested dissection (NESDIS) is used for the default strategy described above, in place of METIS. Other ordering options can be requested. These include: \begin{enumerate} \item natural: A is not permuted to reduce fill-in. \item user-provided: a permutation can be provided to {\tt cholmod\_analyze\_p}. \item AMD: approximate minimum degree (AMD for the symmetric case, COLAMD for the {\tt A*A'} case). \item METIS: nested dissection with {\tt METIS\_NodeND} \item {\tt NESDIS}: CHOLMOD's nested dissection using {\tt METIS\_NodeComputeSeparator}, followed by a constrained minimum degree (CAMD or CSYMAMD for the symmetric case, CCOLAMD for the {\tt A*A'} case). This is typically slower than METIS, but typically provides better orderings. \end{enumerate} Multiple ordering options can be tried (up to 9 of them), and the best one is selected (the one that gives the smallest number of nonzeros in the simplicial factor L). If one method fails, {\tt cholmod\_analyze} keeps going, and picks the best among the methods that succeeded. This routine fails (and returns {\tt NULL}) if either the initial memory allocation fails, all ordering methods fail, or the supernodal analysis (if requested) fails. Change {\tt Common->nmethods} to the number of methods you wish to try. By default, the 9 methods available are: \begin{enumerate} \item user-provided permutation (only for {\tt cholmod\_analyze\_p}). \item AMD with default parameters. \item METIS with default parameters. \item {\tt NESDIS} with default parameters: stopping the partitioning when the graph is of size {\tt nd\_small} = 200 or less, remove nodes with more than {\tt max (16, prune\_dense * sqrt (n))} nodes where {\tt prune\_dense} = 10, and follow partitioning with constrained minimum degree ordering (CAMD for the symmetric case, CCOLAMD for the unsymmetric case). \item natural ordering (with weighted postorder). \item NESDIS, {\tt nd\_small} = 20000, {\tt prune\_dense} = 10. \item NESDIS, {\tt nd\_small} = 4, {\tt prune\_dense} = 10, no constrained minimum degree. \item NESDIS, {\tt nd\_small} = 200, {\tt prune\_dense} = 0. \item COLAMD for {\tt A*A'} or AMD for {\tt A} \end{enumerate} You can modify these 9 methods and the number of methods tried by changing parameters in the {\tt Common} argument. If you know the best ordering for your matrix, set {\tt Common->nmethods} to 1 and set {\tt Common->method[0].ordering} to the requested ordering method. Parameters for each method can also be modified (refer to the description of {\tt cholmod\_common} for details). Note that it is possible for METIS to terminate your program if it runs out of memory. This is not the case for any CHOLMOD or minimum degree ordering routine (AMD, COLAMD, CAMD, CCOLAMD, or CSYMAMD). Since {\tt NESDIS} relies on METIS, it too can terminate your program. The selected ordering is followed by a weighted postorder of the elimination tree by default (see {\tt cholmod\_postorder} for details), unless {\tt Common->postorder} is set to {\tt FALSE}. The postorder does not change the number of nonzeros in $\m{L}$ or the floating-point operation count. It does improve performance, particularly for the supernodal factorization. If you truly want the natural ordering with no postordering, you must set {\tt Common->postorder} to {\tt FALSE}. The factor {\tt L} is returned as simplicial symbolic if {\tt Common->supernodal} is {\tt CHOLMOD\_SIMPLICIAL} (zero) or as supernodal symbolic if {\tt Common->supernodal} is {\tt CHOLMOD\_SUPERNODAL} (two). If \newline {\tt Common->supernodal} is {\tt CHOLMOD\_AUTO} (one), then {\tt L} is simplicial if the flop count per nonzero in {\tt L} is less than {\tt Common->supernodal\_switch} (default: 40), and supernodal otherwise. In both cases, {\tt L->xtype} is {\tt CHOLMOD\_PATTERN}. A subsequent call to {\tt cholmod\_factorize} will perform a simplicial or supernodal factorization, depending on the type of {\tt L}. For the simplicial case, {\tt L} contains the fill-reducing permutation ({\tt L->Perm}) and the counts of nonzeros in each column of {\tt L} ({\tt L->ColCount}). For the supernodal case, {\tt L} also contains the nonzero pattern of each supernode. If a simplicial factorization is selected, it will be $\m{LDL}\tr$ by default, since this is the kind required by the {\tt Modify} Module. CHOLMOD does not include a supernodal $\m{LDL}\tr$ factorization, so if a supernodal factorization is selected, it will be in the form $\m{LL}\tr$. The $\m{LDL}\tr$ method can be used to factorize positive definite matrices and indefinite matrices whose leading minors are well-conditioned (2-by-2 pivoting is not supported). The $\m{LL}\tr$ method is restricted to positive definite matrices. To factorize a large indefinite matrix, set {\tt Common->supernodal} to {\tt CHOLMOD\_SIMPLICIAL}, and the simplicial $\m{LDL}\tr$ method will always be used. This will be significantly slower than a supernodal $\m{LL}\tr$ factorization, however. Refer to {\tt cholmod\_transpose\_unsym} for a description of {\tt f}. %--------------------------------------- \newpage \subsection{{\tt cholmod\_factorize}: numeric factorization} %--------------------------------------- \input{_factorize.tex} Computes the numerical factorization of a symmetric matrix. The % primary inputs to this routine are a sparse matrix {\tt A} and the symbolic factor {\tt L} from {\tt cholmod\_analyze} or a prior numerical factor {\tt L}. If {\tt A} is symmetric, this routine factorizes {\tt A(p,p)}. %+beta*I (beta can be zero), where p is the fill-reducing permutation ({\tt L->Perm}). If {\tt A} is unsymmetric, % either {\tt A(p,:)*A(p,:)'} % +beta*I or A(p,f)*A(p,f)'+beta*I is factorized. % The set f and The nonzero pattern of the matrix {\tt A} must be the same as the matrix passed to {\tt cholmod\_analyze} for the supernodal case. For the simplicial case, it can be different, but it should be the same for best performance. % beta is real. A simplicial factorization or supernodal factorization is chosen, based on the type of the factor {\tt L}. If {\tt L->is\_super} is {\tt TRUE}, a supernodal $\m{LL}\tr$ factorization is computed. Otherwise, a simplicial numeric factorization is computed, either $\m{LL}\tr$ or $\m{LDL}\tr$, depending on {\tt Common->final\_ll} (the default for the simplicial case is to compute an $\m{LDL}\tr$ factorization). Once the factorization is complete, it can be left as is or optionally converted into any simplicial numeric type, depending on the {\tt Common->final\_*} parameters. If converted from a supernodal to simplicial type, and {\tt Common->final\_resymbol} is {\tt TRUE}, then numerically zero entries in {\tt L} due to relaxed supernodal amalgamation are removed from the simplicial factor (they are always left in the supernodal form of {\tt L}). Entries that are numerically zero but present in the simplicial symbolic pattern of {\tt L} are left in place (the graph of {\tt L} remains chordal). This is required for the update/downdate/rowadd/rowdel routines to work properly. If the matrix is not positive definite the routine returns {\tt TRUE}, but {\tt Common->status} is set to {\tt CHOLMOD\_NOT\_POSDEF} and {\tt L->minor} is set to the column at which the failure occurred. Columns {\tt L->minor} to {\tt L->n-1} are set to zero. Supports any xtype (pattern, real, complex, or zomplex), except that the input matrix {\tt A} cannot be pattern-only. If {\tt L} is simplicial, its numeric xtype matches {\tt A} on output. If {\tt L} is supernodal, its xtype is real if {\tt A} is real, or complex if {\tt A} is complex or zomplex. CHOLMOD does not provide a supernodal zomplex factor, since it is incompatible with how complex numbers are stored in LAPACK and the BLAS. %--------------------------------------- \newpage \subsection{{\tt cholmod\_analyze\_p}: symbolic factorization, given permutation} %--------------------------------------- \input{_analyze_p.tex} Identical to {\tt cholmod\_analyze}, except that a user-provided permutation {\tt p} can be provided, and the set {\tt f} for the unsymmetric case can be provided. The matrices {\tt A(:,f)*A(:,f)'} or {\tt A(p,f)*A(p,f)'} can be analyzed in the the unsymmetric case. %--------------------------------------- \subsection{{\tt cholmod\_factorize\_p}: numeric factorization, given permutation} %--------------------------------------- \input{_factorize_p.tex} Identical to {\tt cholmod\_factorize}, but with additional options. The set {\tt f} can be provided for the unsymmetric case; {\tt A(p,f)*A(p,f)'} is factorized. The term {\tt beta*I} can be added to the matrix before it is factorized, where {\tt beta} is real. Only the real part, {\tt beta[0]}, is used. %--------------------------------------- \newpage \subsection{{\tt cholmod\_solve}: solve a linear system} %--------------------------------------- \input{_solve.tex} Returns a solution {\tt X} that solves one of the following systems: \begin{tabular}{ll|ll} \hline system & {\tt sys} parameter & system & {\tt sys} parameter \\ $\m{Ax}=\m{b}$ & 0: {\tt CHOLMOD\_A} & & \\ $\m{LDL}\tr\m{x}=\m{b}$ & 1: {\tt CHOLMOD\_LDLt} & $\m{L}\tr\m{x}=\m{b}$ & 5: {\tt CHOLMOD\_Lt} \\ $\m{LDx}=\m{b}$ & 2: {\tt CHOLMOD\_LD} & $\m{Dx}=\m{b}$ & 6: {\tt CHOLMOD\_D} \\ $\m{DL}\tr\m{x}=\m{b}$ & 3: {\tt CHOLMOD\_DLt} & $\m{x}=\m{Pb}$ & 7: {\tt CHOLMOD\_P} \\ $\m{Lx}=\m{b}$ & 4: {\tt CHOLMOD\_L} & $\m{x}=\m{P}\tr\m{b}$ & 8: {\tt CHOLMOD\_Pt} \\ \hline \end{tabular} The factorization can be simplicial $\m{LDL}\tr$, simplicial $\m{LL}\tr$, or supernodal $\m{LL}\tr$. For an $\m{LL}\tr$ factorization, $\m{D}$ is the identity matrix. Thus {\tt CHOLMOD\_LD} and {\tt CHOLMOD\_L} solve the same system if an $\m{LL}\tr$ factorization was performed, for example. This is one of the few routines in CHOLMOD for which the xtype of the input arguments need not match. If both {\tt L} and {\tt B} are real, then {\tt X} is returned real. If either is complex or zomplex, {\tt X} is returned as either complex or zomplex, depending on the {\tt Common->prefer\_zomplex} parameter (default is complex). This routine does not check to see if the diagonal of $\m{L}$ or $\m{D}$ is zero, because sometimes a partial solve can be done with an indefinite or singular matrix. If you wish to check in your own code, test {\tt L->minor}. If {\tt L->minor == L->n}, then the matrix has no zero diagonal entries. If {\tt k = L->minor < L->n}, then {\tt L(k,k)} is zero for an $\m{LL}\tr$ factorization, or {\tt D(k,k)} is zero for an $\m{LDL}\tr$ factorization. Iterative refinement is not performed, but this can be easily done with the {\tt MatrixOps} Module. See {\tt Demo/cholmod\_demo.c} for an example. %--------------------------------------- \subsection{{\tt cholmod\_spsolve}: solve a linear system} %--------------------------------------- \input{_spsolve.tex} Identical to {\tt cholmod\_spsolve}, except that {\tt B} and {\tt X} are sparse. %--------------------------------------- \newpage \subsection{{\tt cholmod\_etree}: find elimination tree} %--------------------------------------- \input{_etree.tex} Computes the elimination tree of {\tt A} or {\tt A'*A}. In the symmetric case, the upper triangular part of {\tt A} is used. Entries not in this part of the matrix are ignored. Computing the etree of a symmetric matrix from just its lower triangular entries is not supported. In the unsymmetric case, all of {\tt A} is used, and the etree of {\tt A'*A} is computed. Refer to \cite{Liu90a} for a discussion of the elimination tree and its use in sparse Cholesky factorization. % J. Liu, "The role of elimination trees in sparse factorization", SIAM J. % Matrix Analysis \& Applic., vol 11, 1990, pp. 134-172. %--------------------------------------- \subsection{{\tt cholmod\_rowcolcounts}: nonzeros counts of a factor} %--------------------------------------- \input{_rowcolcounts.tex} Compute the row and column counts of the Cholesky factor {\tt L} of the matrix {\tt A} or {\tt A*A'}. The etree and its postordering must already be computed (see {\tt cholmod\_etree} and {\tt cholmod\_postorder}) and given as inputs to this routine. For the symmetric case ($\m{LL}\tr=\m{A}$), {\tt A} must be stored in symmetric/lower form ({\tt A->stype = -1}). In the unsymmetric case, {\tt A*A'} or {\tt A(:,f)*A(:,f)'} can be analyzed. The fundamental floating-point operation count is returned in {\tt Common->fl} (this excludes extra flops due to relaxed supernodal amalgamation). Refer to {\tt cholmod\_transpose\_unsym} for a description of {\tt f}. The algorithm is described in \cite{GilbertLiNgPeyton01,GilbertNgPeyton94}. % J. Gilbert, E. Ng, B. Peyton, "An efficient algorithm to compute row and % column counts for sparse Cholesky factorization", SIAM J. Matrix Analysis \& % Applic., vol 15, 1994, pp. 1075-1091. % % J. Gilbert, X. Li, E. Ng, B. Peyton, "Computing row and column counts for % sparse QR and LU factorization", BIT, vol 41, 2001, pp. 693-710. %--------------------------------------- \newpage \subsection{{\tt cholmod\_analyze\_ordering}: analyze a permutation} %--------------------------------------- \input{_analyze_ordering.tex} Given a matrix {\tt A} and its fill-reducing permutation, compute the elimination tree, its (non-weighted) postordering, and the number of nonzeros in each column of {\tt L}. Also computes the flop count, the total nonzeros in {\tt L}, and the nonzeros in {\tt tril(A)} ({\tt Common->fl}, {\tt Common->lnz}, and {\tt Common->anz}). In the unsymmetric case, {\tt A(p,f)*A(p,f)'} is analyzed, and {\tt Common->anz} is the number of nonzero entries in the lower triangular part of the product, not in {\tt A} itself. Refer to {\tt cholmod\_transpose\_unsym} for a description of {\tt f}. The column counts of {\tt L}, flop count, and other statistics from {\tt cholmod\_rowcolcounts} are not computed if {\tt ColCount} is {\tt NULL}. %--------------------------------------- \newpage \subsection{{\tt cholmod\_amd}: interface to AMD} %--------------------------------------- \input{_amd.tex} CHOLMOD interface to the AMD ordering package. Orders {\tt A} if the matrix is symmetric. On output, {\tt Perm [k] = i} if row/column {\tt i} of {\tt A} is the {\tt k}th row/column of {\tt P*A*P'}. This corresponds to {\tt A(p,p)} in MATLAB notation. If A is unsymmetric, {\tt cholmod\_amd} orders {\tt A*A'} or {\tt A(:,f)*A(:,f)'}. On output, {\tt Perm [k] = i} if row/column {\tt i} of {\tt A*A'} is the {\tt k}th row/column of {\tt P*A*A'*P'}. This corresponds to {\tt A(p,:)*A(p,:)'} in MATLAB notation. If {\tt f} is present, {\tt A(p,f)*A(p,f)'} is the permuted matrix. Refer to {\tt cholmod\_transpose\_unsym} for a description of {\tt f}. Computes the flop count for a subsequent $\m{LL}\tr$ factorization, the number of nonzeros in {\tt L}, and the number of nonzeros in the matrix ordered ({\tt A}, {\tt A*A'} or {\tt A(:,f)*A(:,f)'}). These statistics are returned in {\tt Common->fl}, {\tt Common->lnz}, and {\tt Common->anz}, respectively. %--------------------------------------- \subsection{{\tt cholmod\_colamd}: interface to COLAMD} %--------------------------------------- \input{_colamd.tex} CHOLMOD interface to the COLAMD ordering package. Finds a permutation {\tt p} such that the Cholesky factorization of {\tt P*A*A'*P'} is sparser than {\tt A*A'}, using COLAMD. If the {\tt postorder} input parameter is {\tt TRUE}, the column elimination tree is found and postordered, and the COLAMD ordering is then combined with its postordering (COLAMD itself does not perform this postordering). {\tt A} must be unsymmetric ({\tt A->stype = 0}). %--------------------------------------- \newpage \subsection{{\tt cholmod\_rowfac}: row-oriented Cholesky factorization} %--------------------------------------- \input{_rowfac.tex} Full or incremental numerical $\m{LDL}\tr$ or $\m{LL}\tr$ factorization (simplicial, not supernodal). {\tt cholmod\_factorize} is the ``easy'' wrapper for this code, but it does not provide access to incremental factorization. The algorithm is the row-oriented, up-looking method described in \cite{Davis05}. See also \cite{Liu86c}. No 2-by-2 pivoting (or any other pivoting) is performed. {\tt cholmod\_rowfac} computes the full or incremental $\m{LDL}\tr$ or $\m{LL}\tr$ factorization of {\tt A+beta*I} (where {\tt A} is symmetric) or {\tt A*F+beta*I} (where {\tt A} and {\tt F} are unsymmetric and only the upper triangular part of {\tt A*F+beta*I} is used). It computes {\tt L} (and {\tt D}, for $\m{LDL}\tr$) one row at a time. The input scalar {\tt beta} is real; only the real part ({\tt beta[0]}) is used. {\tt L} can be a simplicial symbolic or numeric ({\tt L->is\_super} must be {\tt FALSE}). A symbolic factor is converted immediately into a numeric factor containing the identity matrix. For a full factorization, use {\tt kstart = 0} and {\tt kend = nrow}. The existing nonzero entries (numerical values in {\tt L->x} and {\tt L->z} for the zomplex case, and indices in {\tt L->i}) are overwritten. To compute an incremental factorization, select {\tt kstart} and {\tt kend} as the range of rows of {\tt L} you wish to compute. Rows {\tt kstart} to {\tt kend-1} of {\tt L} will be computed. A correct factorization will be computed only if all descendants of all nodes {\tt kstart} to {\tt kend-1} in the elimination tree have been factorized by a prior call to this routine, and if rows {\tt kstart} to {\tt kend-1} have not been factorized. This condition is {\bf not} checked on input. In the symmetric case, {\tt A} must be stored in upper form ({\tt A->stype} is greater than zero). The matrix {\tt F} is not accessed and may be {\tt NULL}. Only columns {\tt kstart} to {\tt kend-1} of {\tt A} are accessed. In the unsymmetric case, the typical case is {\tt F=A'}. Alternatively, if {\tt F=A(:,f)'}, then this routine factorizes the matrix {\tt S = beta*I + A(:,f)*A(:,f)'}. The product {\tt A*F} is assumed to be symmetric; only the upper triangular part of {\tt A*F} is used. {\tt F} must be of size {\tt A->ncol} by {\tt A->nrow}. % J. Liu, "A compact row storage scheme for Cholesky factors", ACM Trans. % Math. Software, vol 12, 1986, pp. 127-148. %--------------------------------------- \subsection{{\tt cholmod\_rowfac\_mask}: row-oriented Cholesky factorization} %--------------------------------------- \input{_rowfac_mask.tex} For use in LPDASA only. %--------------------------------------- \newpage \subsection{{\tt cholmod\_row\_subtree}: pattern of row of a factor} %--------------------------------------- \input{_row_subtree.tex} Compute the nonzero pattern of the solution to the lower triangular system \begin{verbatim} L(0:k-1,0:k-1) * x = A (0:k-1,k) \end{verbatim} if {\tt A} is symmetric, or \begin{verbatim} L(0:k-1,0:k-1) * x = A (0:k-1,:) * A (:,k)' \end{verbatim} if {\tt A} is unsymmetric. This gives the nonzero pattern of row {\tt k} of {\tt L} (excluding the diagonal). The pattern is returned postordered, according to the subtree of the elimination tree rooted at node {\tt k}. The symmetric case requires {\tt A} to be in symmetric-upper form. The result is returned in {\tt R}, a pre-allocated sparse matrix of size {\tt nrow}-by-1, with {\tt R->nzmax >= nrow}. {\tt R} is assumed to be packed ({\tt Rnz [0]} is not updated); the number of entries in {\tt R} is given by {\tt Rp [0]}. %--------------------------------------- \newpage \subsection{{\tt cholmod\_row\_lsubtree}: pattern of row of a factor} %--------------------------------------- \input{_row_lsubtree.tex} Identical to {\tt cholmod\_row\_subtree}, except the elimination tree is found from {\tt L} itself, not {\tt Parent}. Also, {\tt F=A'} is not provided; the nonzero pattern of the {\tt k}th column of {\tt F} is given by {\tt Fi} and {\tt fnz} instead. %--------------------------------------- \newpage \subsection{{\tt cholmod\_resymbol}: re-do symbolic factorization} %--------------------------------------- \input{_resymbol.tex} Recompute the symbolic pattern of {\tt L}. Entries not in the symbolic pattern of the factorization of {\tt A(p,p)} or {\tt F*F'}, where {\tt F=A(p,f)} or {\tt F=A(:,f)}, are dropped, where {\tt p = L->Perm} is used to permute the input matrix {\tt A}. Refer to {\tt cholmod\_transpose\_unsym} for a description of {\tt f}. If an entry in {\tt L} is kept, its numerical value does not change. This routine is used after a supernodal factorization is converted into a simplicial one, to remove zero entries that were added due to relaxed supernode amalgamation. It can also be used after a series of downdates to remove entries that would no longer be present if the matrix were factorized from scratch. A downdate ({\tt cholmod\_updown}) does not remove any entries from {\tt L}. %--------------------------------------- \subsection{{\tt cholmod\_resymbol\_noperm}: re-do symbolic factorization} %--------------------------------------- \input{_resymbol_noperm.tex} Identical to {\tt cholmod\_resymbol}, except that the fill-reducing ordering {\tt L->Perm} is not used. %--------------------------------------- \newpage \subsection{{\tt cholmod\_postorder}: tree postorder} %--------------------------------------- \input{_postorder.tex} Postorder a tree. The tree is either an elimination tree (the output from {\tt cholmod\_etree}) or a component tree (from {\tt cholmod\_nested\_dissection}). An elimination tree is a complete tree of {\tt n} nodes with {\tt Parent [j] > j} or {\tt Parent [j] = -1} if j is a root. On output {\tt Post [0..n-1]} is a complete permutation vector; {\tt Post [k] = j} if node {\tt j} is the {\tt k}th node in the postordered elimination tree, where {\tt k} is in the range 0 to {\tt n-1}. A component tree is a subset of {\tt 0:n-1}. {\tt Parent [j] = -2} if node {\tt j} is not in the component tree. {\tt Parent [j] = -1} if {\tt j} is a root of the component tree, and {\tt Parent [j]} is in the range 0 to {\tt n-1} if {\tt j} is in the component tree but not a root. On output, {\tt Post [k]} is defined only for nodes in the component tree. {\tt Post [k] = j} if node {\tt j} is the {\tt k}th node in the postordered component tree, where {\tt k} is in the range 0 to the number of components minus 1. Node {\tt j} is ignored and not included in the postorder if {\tt Parent [j] < -1}. As a result, {\tt cholmod\_check\_parent (Parent, ...)} and {\tt cholmod\_check\_perm (Post, ...)} fail if used for a component tree and its postordering. An optional node weight can be given. When starting a postorder at node {\tt j}, the children of {\tt j} are ordered in decreasing order of their weight. If no weights are given ({\tt Weight} is {\tt NULL}) then children are ordered in decreasing order of their node number. The weight of a node must be in the range 0 to {\tt n-1}. Weights outside that range are silently converted to that range (weights $<$ 0 are treated as zero, and weights $\ge$ {\tt n} are treated as {\tt n-1}). %--------------------------------------- \subsection{{\tt cholmod\_rcond}: reciprocal condition number} %--------------------------------------- \input{_rcond.tex} Returns a rough estimate of the reciprocal of the condition number: the minimum entry on the diagonal of {\tt L} (or absolute entry of {\tt D} for an $\m{LDL}\tr$ factorization) divided by the maximum entry. {\tt L} can be real, complex, or zomplex. Returns -1 on error, 0 if the matrix is singular or has a zero or NaN entry on the diagonal of {\tt L}, 1 if the matrix is 0-by-0, or {\tt min(diag(L))/max(diag(L))} otherwise. Never returns NaN; if {\tt L} has a NaN on the diagonal it returns zero instead. %------------------------------------------------------------------------------- \newpage \section{{\tt Modify} Module routines} %------------------------------------------------------------------------------- %--------------------------------------- \subsection{{\tt cholmod\_updown}: update/downdate} %--------------------------------------- \input{_updown.tex} Updates/downdates the $\m{LDL}\tr$ factorization (symbolic, then numeric), by computing a new factorization of \[ \new{\m{L}}\new{\m{D}}\new{\m{L}}\tr = \m{LDL}\tr \pm \m{CC}\tr \] where $\new{\m{L}}$ denotes the new factor. {\tt C} must be sorted. It can be either packed or unpacked. As in all CHOLMOD routines, the columns of {\tt L} are sorted on input, and also on output. If {\tt L} does not contain a simplicial numeric $\m{LDL}\tr$ factorization, it is converted into one. Thus, a supernodal $\m{LL}\tr$ factorization can be passed to {\tt cholmod\_updown}. A symbolic {\tt L} is converted into a numeric identity matrix. If the initial conversion fails, the factor is returned unchanged. If memory runs out during the update, the factor is returned as a simplicial symbolic factor. That is, everything is freed except for the fill-reducing ordering and its corresponding column counts (typically computed by {\tt cholmod\_analyze}). Note that the fill-reducing permutation {\tt L->Perm} is not used. The row indices of {\tt C} refer to the rows of {\tt L}, not {\tt A}. If your original system is $\m{LDL}\tr = \m{PAP}\tr$ (where $\m{P} =$ {\tt L->Perm}), and you want to compute the $\m{LDL}\tr$ factorization of $\m{A}+\m{CC}\tr$, then you must permute $\m{C}$ first. That is, if \[ \m{PAP}\tr = \m{LDL}\tr \] is the initial factorization, then \[ \m{P}(\m{A}+\m{CC}\tr)\m{P}\tr = \m{PAP}\tr+\m{PCC}\tr\m{P}\tr = \m{LDL}\tr + (\m{PC})(\m{PC})\tr = \m{LDL}\tr + \new{\m{C}}\new{\m{C}}\tr \] where $\new{\m{C}} = \m{PC}$. You can use the {\tt cholmod\_submatrix} routine in the {\tt MatrixOps} Module to permute {\tt C}, with: \begin{verbatim} Cnew = cholmod_submatrix (C, L->Perm, L->n, NULL, -1, TRUE, TRUE, Common) ; \end{verbatim} Note that the {\tt sorted} input parameter to {\tt cholmod\_submatrix} must be {\tt TRUE}, because {\tt cholmod\_updown} requires {\tt C} with sorted columns. Only real matrices are supported. The algorithms are described in \cite{DavisHager99,DavisHager01}. %--------------------------------------- \subsection{{\tt cholmod\_updown\_solve}: update/downdate} %--------------------------------------- \input{_updown_solve.tex} Identical to {\tt cholmod\_updown}, except the system $\m{Lx}=\m{b}$ is also updated/downdated. The new system is $\new{\m{L}}\new{\m{x}}=\m{b} + \Delta \m{b}$. The old solution $\m{x}$ is overwritten with $\new{\m{x}}$. Note that as in the update/downdate of $\m{L}$ itself, the fill- reducing permutation {\tt L->Perm} is not used. The vectors $\m{x}$ and $\m{b}$ are in the permuted ordering, not your original ordering. This routine does not handle multiple right-hand-sides. %--------------------------------------- \newpage \subsection{{\tt cholmod\_updown\_mark}: update/downdate} %--------------------------------------- \input{_updown_mark.tex} Identical to {\tt cholmod\_updown\_solve}, except that only part of $\m{L}$ is used in the update of the solution to $\m{Lx}=\m{b}$. For more details, see the source code file {\tt CHOLMOD/Modify/cholmod\_updown.c}. This routine is meant for use in the {\tt LPDASA} linear program solver only, by Hager and Davis. %--------------------------------------- \subsection{{\tt cholmod\_updown\_mask}: update/downdate} %--------------------------------------- \input{_updown_mask.tex} For use in LPDASA only. %--------------------------------------- \newpage \subsection{{\tt cholmod\_rowadd}: add row to factor} %--------------------------------------- \input{_rowadd.tex} Adds a row and column to an $\m{LDL}\tr$ factorization. The {\tt k}th row and column of {\tt L} must be equal to the {\tt k}th row and column of the identity matrix on input. Only real matrices are supported. The algorithm is described in \cite{DavisHager05}. %--------------------------------------- \subsection{{\tt cholmod\_rowadd\_solve}: add row to factor} %--------------------------------------- \input{_rowadd_solve.tex} Identical to {\tt cholmod\_rowadd}, except the system $\m{Lx}=\m{b}$ is also updated/downdated, just like {\tt cholmod\_updown\_solve}. %--------------------------------------- \newpage \subsection{{\tt cholmod\_rowdel}: delete row from factor} %--------------------------------------- \input{_rowdel.tex} Deletes a row and column from an $\m{LDL}\tr$ factorization. The {\tt k}th row and column of {\tt L} is equal to the {\tt k}th row and column of the identity matrix on output. Only real matrices are supported. %--------------------------------------- \subsection{{\tt cholmod\_rowdel\_solve}: delete row from factor} %--------------------------------------- \input{_rowdel_solve.tex} Identical to {\tt cholmod\_rowdel}, except the system $\m{Lx}=\m{b}$ is also updated/downdated, just like {\tt cholmod\_updown\_solve}. When row/column $k$ of $\m{A}$ is deleted from the system $\m{Ay}=\m{b}$, this can induce a change to $\m{x}$, in addition to changes arising when $\m{L}$ and $\m{b}$ are modified. If this is the case, the kth entry of $\m{y}$ is required as input ({\tt yk}). The algorithm is described in \cite{DavisHager05}. %--------------------------------------- \newpage \subsection{{\tt cholmod\_rowadd\_mark}: add row to factor} %--------------------------------------- \input{_rowadd_mark.tex} Identical to {\tt cholmod\_rowadd\_solve}, except that only part of $\m{L}$ is used in the update of the solution to $\m{Lx}=\m{b}$. For more details, see the source code file {\tt CHOLMOD/Modify/cholmod\_rowadd.c}. This routine is meant for use in the {\tt LPDASA} linear program solver only. %--------------------------------------- \subsection{{\tt cholmod\_rowdel\_mark}: delete row from factor} %--------------------------------------- \input{_rowdel_mark.tex} Identical to {\tt cholmod\_rowadd\_solve}, except that only part of $\m{L}$ is used in the update of the solution to $\m{Lx}=\m{b}$. For more details, see the source code file {\tt CHOLMOD/Modify/cholmod\_rowdel.c}. This routine is meant for use in the {\tt LPDASA} linear program solver only. %------------------------------------------------------------------------------- \newpage \section{{\tt MatrixOps} Module routines} %------------------------------------------------------------------------------- %--------------------------------------- \subsection{{\tt cholmod\_drop}: drop small entries} %--------------------------------------- \input{_drop.tex} Drop small entries from {\tt A}, and entries in the ignored part of {\tt A} if {\tt A} is symmetric. No CHOLMOD routine drops small numerical entries from a matrix, except for this one. NaN's and Inf's are kept. Supports pattern and real matrices; complex and zomplex matrices are not supported. %--------------------------------------- \subsection{{\tt cholmod\_norm\_dense}: dense matrix norm} %--------------------------------------- \input{_norm_dense.tex} Returns the infinity-norm, 1-norm, or 2-norm of a dense matrix. Can compute the 2-norm only for a dense column vector. All xtypes are supported. %--------------------------------------- \subsection{{\tt cholmod\_norm\_sparse}: sparse matrix norm} %--------------------------------------- \input{_norm_sparse.tex} Returns the infinity-norm or 1-norm of a sparse matrix. All xtypes are supported. %--------------------------------------- \newpage \subsection{{\tt cholmod\_scale}: scale sparse matrix} %--------------------------------------- \input{_scale.tex} Scales a matrix: {\tt A = diag(s)*A}, {\tt A*diag(s)}, {\tt s*A}, or {\tt diag(s)*A*diag(s)}. {\tt A} can be of any type (packed/unpacked, upper/lower/unsymmetric). The symmetry of {\tt A} is ignored; all entries in the matrix are modified. If {\tt A} is {\tt m}-by-{\tt n} unsymmetric but scaled symmetrically, the result is \begin{verbatim} A = diag (s (1:m)) * A * diag (s (1:n)) \end{verbatim} Row or column scaling of a symmetric matrix still results in a symmetric matrix, since entries are still ignored by other routines. For example, when row-scaling a symmetric matrix where just the upper triangular part is stored (and lower triangular entries ignored) {\tt A = diag(s)*triu(A)} is performed, where the result {\tt A} is also symmetric-upper. This has the effect of modifying the implicit lower triangular part. In MATLAB notation: \begin{verbatim} U = diag(s)*triu(A) ; L = tril (U',-1) A = L + U ; \end{verbatim} The scale parameter determines the kind of scaling to perform and the size of {\tt S}: \begin{tabular}{lll} \hline {\tt scale} & operation & size of {\tt S} \\ \hline {\tt CHOLMOD\_SCALAR} & {\tt s[0]*A} & 1 \\ {\tt CHOLMOD\_ROW} & {\tt diag(s)*A} & {\tt nrow}-by-1 or 1-by-{\tt nrow} \\ {\tt CHOLMOD\_COL} & {\tt A*diag(s)} & {\tt ncol}-by-1 or 1-by-{\tt ncol} \\ {\tt CHOLMOD\_SYM} & {\tt diag(s)*A*diag(s)} & {\tt max(nrow,ncol)}-by-1, or 1-by-{\tt max(nrow,ncol)} \\ \hline \end{tabular} Only real matrices are supported. %--------------------------------------- \newpage \subsection{{\tt cholmod\_sdmult}: sparse-times-dense matrix} %--------------------------------------- \input{_sdmult.tex} Sparse matrix times dense matrix: {\tt Y = alpha*(A*X) + beta*Y} or {\tt Y = alpha*(A'*X) + beta*Y}, where {\tt A} is sparse and {\tt X} and {\tt Y} are dense. When using {\tt A}, {\tt X} has {\tt A->ncol} columns and {\tt Y} has {\tt A->nrow} rows. When using {\tt A'}, {\tt X} has {\tt A->nrow} columns and {\tt Y} has {\tt A->ncol} rows. If {\tt transpose = 0}, then {\tt A} is used; otherwise, {\tt A'} is used (the complex conjugate transpose). The {\tt transpose} parameter is ignored if the matrix is symmetric or Hermitian. (the array transpose {\tt A.'} is not supported). Supports real, complex, and zomplex matrices, but the xtypes of {\tt A}, {\tt X}, and {\tt Y} must all match. %--------------------------------------- \subsection{{\tt cholmod\_ssmult}: sparse-times-sparse matrix} %--------------------------------------- \input{_ssmult.tex} Computes {\tt C = A*B}; multiplying two sparse matrices. {\tt C} is returned as packed, and either unsorted or sorted, depending on the {\tt sorted} input parameter. If {\tt C} is returned sorted, then either {\tt C = (B'*A')'} or {\tt C = (A*B)''} is computed, depending on the number of nonzeros in {\tt A}, {\tt B}, and {\tt C}. The stype of {\tt C} is determined by the {\tt stype} parameter. Only pattern and real matrices are supported. Complex and zomplex matrices are supported only when the numerical values are not computed ({\tt values} is {\tt FALSE}). %--------------------------------------- \newpage \subsection{{\tt cholmod\_submatrix}: sparse submatrix} %--------------------------------------- \input{_submatrix.tex} Returns {\tt C = A (rset,cset)}, where {\tt C} becomes {\tt length(rset)}-by-{\tt length(cset)} in dimension. {\tt rset} and {\tt cset} can have duplicate entries. {\tt A} must be unsymmetric. {\tt C} unsymmetric and is packed. If {\tt sorted} is {\tt TRUE} on input, or {\tt rset} is sorted and {\tt A} is sorted, then {\tt C} is sorted; otherwise {\tt C} is unsorted. If {\tt rset} is {\tt NULL}, it means ``{\tt [ ]}'' in MATLAB notation, the empty set. The number of rows in the result {\tt C} will be zero if {\tt rset} is {\tt NULL}. Likewise if {\tt cset} means the empty set; the number of columns in the result {\tt C} will be zero if {\tt cset} is {\tt NULL}. If {\tt rsize} or {\tt csize} is negative, it denotes ``{\tt :}'' in MATLAB notation. Thus, if both {\tt rsize} and {\tt csize} are negative {\tt C = A(:,:) = A} is returned. For permuting a matrix, this routine is an alternative to {\tt cholmod\_ptranspose} (which permutes and transposes a matrix and can work on symmetric matrices). The time taken by this routine is O({\tt A->nrow}) if the {\tt Common} workspace needs to be initialized, plus O({\tt C->nrow + C->ncol + nnz (A (:,cset))}). Thus, if {\tt C} is small and the workspace is not initialized, the time can be dominated by the call to {\tt cholmod\_allocate\_work}. However, once the workspace is allocated, subsequent calls take less time. Only pattern and real matrices are supported. Complex and zomplex matrices are supported only when {\tt values} is {\tt FALSE}. %--------------------------------------- \newpage \subsection{{\tt cholmod\_horzcat}: horizontal concatenation} %--------------------------------------- \input{_horzcat.tex} Horizontal concatenation, returns {\tt C = [A,B]} in MATLAB notation. {\tt A} and {\tt B} can have any stype. {\tt C} is returned unsymmetric and packed. {\tt A} and {\tt B} must have the same number of rows. {\tt C} is sorted if both {\tt A} and {\tt B} are sorted. {\tt A} and {\tt B} must have the same numeric xtype, unless {\tt values} is {\tt FALSE}. {\tt A} and {\tt B} cannot be complex or zomplex, unless {\tt values} is {\tt FALSE}. %--------------------------------------- \subsection{{\tt cholmod\_vertcat}: vertical concatenation} %--------------------------------------- \input{_vertcat.tex} Vertical concatenation, returns {\tt C = [A;B]} in MATLAB notation. {\tt A} and {\tt B} can have any stype. {\tt C} is returned unsymmetric and packed. {\tt A} and {\tt B} must have the same number of columns. {\tt C} is sorted if both {\tt A} and {\tt B} are sorted. {\tt A} and {\tt B} must have the same numeric xtype, unless {\tt values} is {\tt FALSE}. {\tt A} and {\tt B} cannot be complex or zomplex, unless {\tt values} is {\tt FALSE}. %--------------------------------------- \newpage \subsection{{\tt cholmod\_symmetry}: compute the symmetry of a matrix} %--------------------------------------- \input{_symmetry.tex} Determines if a sparse matrix is rectangular, unsymmetric, symmetric, skew-symmetric, or Hermitian. It does so by looking at its numerical values of both upper and lower triangular parts of a CHOLMOD "unsymmetric" matrix, where A->stype == 0. The transpose of A is NOT constructed. If not unsymmetric, it also determines if the matrix has a diagonal whose entries are all real and positive (and thus a candidate for sparse Cholesky if A->stype is changed to a nonzero value). Note that a Matrix Market "general" matrix is either rectangular or unsymmetric. The row indices in the column of each matrix MUST be sorted for this function to work properly (A->sorted must be TRUE). This routine returns EMPTY if A->stype is not zero, or if A->sorted is FALSE. The exception to this rule is if A is rectangular. If option == 0, then this routine returns immediately when it finds a non-positive diagonal entry (or one with nonzero imaginary part). If the matrix is not a candidate for sparse Cholesky, it returns the value {\tt CHOLMOD\_MM\_UNSYMMETRIC}, even if the matrix might in fact be symmetric or Hermitian. This routine is useful inside the MATLAB backslash, which must look at an arbitrary matrix (A->stype == 0) and determine if it is a candidate for sparse Cholesky. In that case, option should be 0. This routine is also useful when writing a MATLAB matrix to a file in Rutherford/Boeing or Matrix Market format. Those formats require a determination as to the symmetry of the matrix, and thus this routine should not return upon encountering the first non-positive diagonal. In this case, option should be 1. If option is 2, this function can be used to compute the numerical and pattern symmetry, where 0 is a completely unsymmetric matrix, and 1 is a perfectly symmetric matrix. This option is used when computing the following statistics for the matrices in the UF Sparse Matrix Collection. numerical symmetry: number of matched offdiagonal nonzeros over the total number of offdiagonal entries. A real entry $a_{ij}$, $i \ne j$, is matched if $a_{ji} = a_{ij}$, but this is only counted if both $a_{ji}$ and $a_{ij}$ are nonzero. This does not depend on {\tt Z}. (If A is complex, then the above test is modified; $a_{ij}$ is matched if $\mbox{conj}(a_{ji}) = a_{ij}$. Then numeric symmetry = xmatched / nzoffdiag, or 1 if nzoffdiag = 0. pattern symmetry: number of matched offdiagonal entries over the total number of offdiagonal entries. An entry $a_{ij}$, $i \ne j$, is matched if $a_{ji}$ is also an entry. Then pattern symmetry = pmatched / nzoffdiag, or 1 if nzoffdiag = 0. The symmetry of a matrix with no offdiagonal entries is equal to 1. A workspace of size ncol integers is allocated; EMPTY is returned if this allocation fails. Summary of return values: \begin{tabular}{ll} {\tt EMPTY (-1)} & out of memory, stype not zero, A not sorted \\ {\tt CHOLMOD\_MM\_RECTANGULAR 1} & A is rectangular \\ {\tt CHOLMOD\_MM\_UNSYMMETRIC 2} & A is unsymmetric \\ {\tt CHOLMOD\_MM\_SYMMETRIC 3} & A is symmetric, but with non-pos. diagonal \\ {\tt CHOLMOD\_MM\_HERMITIAN 4} & A is Hermitian, but with non-pos. diagonal \\ {\tt CHOLMOD\_MM\_SKEW\_SYMMETRIC 5} & A is skew symmetric \\ {\tt CHOLMOD\_MM\_SYMMETRIC\_POSDIAG 6} & A is symmetric with positive diagonal \\ {\tt CHOLMOD\_MM\_HERMITIAN\_POSDIAG 7} & A is Hermitian with positive diagonal \\ \end{tabular} See also the {\tt spsym} mexFunction, which is a MATLAB interface for this code. If the matrix is a candidate for sparse Cholesky, it will return a result \newline {\tt CHOLMOD\_MM\_SYMMETRIC\_POSDIAG} if real, or {\tt CHOLMOD\_MM\_HERMITIAN\_POSDIAG} if complex. Otherwise, it will return a value less than this. This is true regardless of the value of the option parameter. %------------------------------------------------------------------------------- \newpage \section{{\tt Supernodal} Module routines} %------------------------------------------------------------------------------- %--------------------------------------- \subsection{{\tt cholmod\_super\_symbolic}: supernodal symbolic factorization} %--------------------------------------- \input{_super_symbolic.tex} Supernodal symbolic analysis of the $\m{LL}\tr$ factorization of {\tt A}, {\tt A*A'}, or {\tt A(:,f)*A(:,f)'}. This routine must be preceded by a simplicial symbolic analysis ({\tt cholmod\_rowcolcounts}). See {\tt Cholesky/cholmod\_analyze.c} for an example of how to use this routine. The user need not call this directly; {\tt cholmod\_analyze} is a ``simple'' wrapper for this routine. {\tt A} can be symmetric (upper), or unsymmetric. The symmetric/lower form is not supported. In the unsymmetric case {\tt F} is the normally transpose of {\tt A}. Alternatively, if {\tt F=A(:,f)'} then {\tt F*F'} is analyzed. Requires {\tt Parent} and {\tt L->ColCount} to be defined on input; these are the simplicial {\tt Parent} and {\tt ColCount} arrays as computed by {\tt cholmod\_rowcolcounts}. Does not use {\tt L->Perm}; the input matrices {\tt A} and {\tt F} must already be properly permuted. Allocates and computes the supernodal pattern of {\tt L} ({\tt L->super}, {\tt L->pi}, {\tt L->px}, and {\tt L->s}). Does not allocate the real part ({\tt L->x}). %--------------------------------------- \newpage \subsection{{\tt cholmod\_super\_numeric}: supernodal numeric factorization} %--------------------------------------- \input{_super_numeric.tex} Computes the numerical Cholesky factorization of {\tt A+beta*I} or {\tt A*F+beta*I}. Only the lower triangular part of {\tt A+beta*I} or {\tt A*F+beta*I} is accessed. The matrices {\tt A} and {\tt F} must already be permuted according to the fill-reduction permutation {\tt L->Perm}. {\tt cholmod\_factorize} is an "easy" wrapper for this code which applies that permutation. The input scalar {\tt beta} is real; only the real part ({\tt beta[0]} is used. Symmetric case: {\tt A} is a symmetric (lower) matrix. {\tt F} is not accessed and may be {\tt NULL}. With a fill-reducing permutation, {\tt A(p,p)} should be passed for {\tt A}, where is {\tt p} is {\tt L->Perm}. Unsymmetric case: {\tt A} is unsymmetric, and {\tt F} must be present. Normally, {\tt F=A'}. With a fill-reducing permutation, {\tt A(p,f)} and {\tt A(p,f)'} should be passed as the parameters {\tt A} and {\tt F}, respectively, where {\tt f} is a list of the subset of the columns of {\tt A}. The input factorization {\tt L} must be supernodal ({\tt L->is\_super} is {\tt TRUE}). It can either be symbolic or numeric. In the first case, {\tt L} has been analyzed by {\tt cholmod\_analyze} or {\tt cholmod\_super\_symbolic}, but the matrix has not yet been numerically factorized. The numerical values are allocated here and the factorization is computed. In the second case, a prior matrix has been analyzed and numerically factorized, and a new matrix is being factorized. The numerical values of {\tt L} are replaced with the new numerical factorization. {\tt L->is\_ll} is ignored on input, and set to {\tt TRUE} on output. This routine always computes an $\m{LL}\tr$ factorization. Supernodal $\m{LDL}\tr$ factorization is not supported. If the matrix is not positive definite the routine returns {\tt TRUE}, but sets {\tt Common->status} to {\tt CHOLMOD\_NOT\_POSDEF} and {\tt L->minor} is set to the column at which the failure occurred. Columns {\tt L->minor} to {\tt L->n-1} are set to zero. If {\tt L} is supernodal symbolic on input, it is converted to a supernodal numeric factor on output, with an xtype of real if {\tt A} is real, or complex if {\tt A} is complex or zomplex. If {\tt L} is supernodal numeric on input, its xtype must match {\tt A} (except that {\tt L} can be complex and {\tt A} zomplex). The xtype of {\tt A} and {\tt F} must match. %--------------------------------------- \newpage \subsection{{\tt cholmod\_super\_lsolve}: supernodal forward solve} %--------------------------------------- \input{_super_lsolve.tex} Solve $\m{Lx}=\m{b}$ for a supernodal factorization. This routine does not apply the permutation {\tt L->Perm}. See {\tt cholmod\_solve} for a more general interface that performs that operation. Only real and complex xtypes are supported. {\tt L}, {\tt X}, and {\tt E} must have the same xtype. %--------------------------------------- \subsection{{\tt cholmod\_super\_ltsolve}: supernodal backsolve} %--------------------------------------- \input{_super_ltsolve.tex} Solve $\m{L}\tr\m{x}=\m{b}$ for a supernodal factorization. This routine does not apply the permutation {\tt L->Perm}. See {\tt cholmod\_solve} for a more general interface that performs that operation. Only real and complex xtypes are supported. {\tt L}, {\tt X}, and {\tt E} must have the same xtype. %------------------------------------------------------------------------------- \newpage \section{{\tt Partition} Module routines} %------------------------------------------------------------------------------- %--------------------------------------- \subsection{{\tt cholmod\_nested\_dissection}: nested dissection ordering} %--------------------------------------- \input{_nested_dissection.tex} CHOLMOD's nested dissection algorithm: using its own compression and connected-components algorithms, an external graph partitioner (METIS), and a constrained minimum degree ordering algorithm (CAMD, CCOLAMD, or CSYMAMD). Typically gives better orderings than {\tt METIS\_NodeND} (about 5\% to 10\% fewer nonzeros in {\tt L}). This method uses a node bisector, applied recursively (but using a non-recursive implementation). Once the graph is partitioned, it calls a constrained minimum degree code (CAMD or CSYMAMD for {\tt A+A'}, and CCOLAMD for {\tt A*A'}) to order all the nodes in the graph - but obeying the constraints determined by the separators. This routine is similar to {\tt METIS\_NodeND}, except for how it treats the leaf nodes. {\tt METIS\_NodeND} orders the leaves of the separator tree with {\tt MMD}, ignoring the rest of the matrix when ordering a single leaf. This routine orders the whole matrix with CAMD, CSYMAMD, or CCOLAMD, all at once, when the graph partitioning is done. %--------------------------------------- \newpage \subsection{{\tt cholmod\_metis}: interface to METIS nested dissection} %--------------------------------------- \input{_metis.tex} CHOLMOD wrapper for the {\tt METIS\_NodeND} ordering routine. Creates {\tt A+A'}, {\tt A*A'} or {\tt A(:,f)*A(:,f)'} and then calls {\tt METIS\_NodeND} on the resulting graph. This routine is comparable to {\tt cholmod\_nested\_dissection}, except that it calls {\tt METIS\_NodeND} directly, and it does not return the separator tree. %--------------------------------------- \newpage \subsection{{\tt cholmod\_camd}: interface to CAMD} %--------------------------------------- \input{_camd.tex} CHOLMOD interface to the CAMD ordering routine. Finds a permutation {\tt p} such that the Cholesky factorization of {\tt A(p,p)} is sparser than {\tt A}. If {\tt A} is unsymmetric, {\tt A*A'} is ordered. If {\tt Cmember[i]=c} then node {\tt i} is in set {\tt c}. All nodes in set 0 are ordered first, followed by all nodes in set 1, and so on. %--------------------------------------- \newpage \subsection{{\tt cholmod\_ccolamd}: interface to CCOLAMD} %--------------------------------------- \input{_ccolamd.tex} CHOLMOD interface to the CCOLAMD ordering routine. Finds a permutation {\tt p} such that the Cholesky factorization of {\tt A(p,:)*A(p,:)'} is sparser than {\tt A*A'}. The column elimination is found and postordered, and the CCOLAMD ordering is then combined with its postordering. {\tt A} must be unsymmetric. If {\tt Cmember[i]=c} then node {\tt i} is in set {\tt c}. All nodes in set 0 are ordered first, followed by all nodes in set 1, and so on. %--------------------------------------- \subsection{{\tt cholmod\_csymamd}: interface to CSYMAMD} %--------------------------------------- \input{_csymamd.tex} CHOLMOD interface to the CSYMAMD ordering routine. Finds a permutation {\tt p} such that the Cholesky factorization of {\tt A(p,p)} is sparser than {\tt A}. The elimination tree is found and postordered, and the CSYMAMD ordering is then combined with its postordering. If {\tt A} is unsymmetric, {\tt A+A'} is ordered ({\tt A} must be square). If {\tt Cmember[i]=c} then node {\tt i} is in set {\tt c}. All nodes in set 0 are ordered first, followed by all nodes in set 1, and so on. %--------------------------------------- \newpage \subsection{{\tt cholmod\_bisect}: graph bisector} %--------------------------------------- \input{_bisect.tex} Finds a node bisector of {\tt A}, {\tt A*A'}, {\tt A(:,f)*A(:,f)'}: a set of nodes that partitions the graph into two parts. Compresses the graph first, and then calls METIS. %--------------------------------------- \subsection{{\tt cholmod\_metis\_bisector}: interface to METIS node bisector} %--------------------------------------- \input{_metis_bisector.tex} Finds a set of nodes that bisects the graph of {\tt A} or {\tt A*A'} (a direct interface to \newline {\tt METIS\_NodeComputeSeparator}). The input matrix {\tt A} must be square, symmetric (with both upper and lower parts present) and with no diagonal entries. These conditions are not checked. %--------------------------------------- \newpage \subsection{{\tt cholmod\_collapse\_septree}: prune a separator tree} %--------------------------------------- \input{_collapse_septree.tex} Prunes a separator tree obtained from {\tt cholmod\_nested\_dissection}. \newpage \bibliographystyle{plain} \bibliography{UserGuide} \end{document} SuiteSparse/CHOLMOD/Doc/mheader.tex0000644001170100242450000000014410304303215015656 0ustar davisfac \noindent\hspace{0.85in}\rule[0.05in]{5.2in}{1pt} \vspace{-0.15in} {\footnotesize \begin{verbatim} SuiteSparse/CHOLMOD/Doc/getmproto0000755001170100242450000000011210304300351015466 0ustar davisfac#!/bin/sh cat mheader.tex expand -8 $1 | awk -f mfile.awk cat mfooter.tex SuiteSparse/CHOLMOD/Doc/getproto0000755001170100242450000000017110304102345015321 0ustar davisfac#!/bin/sh echo -n $1 > _temp.awk cat rule.awk >> _temp.awk cat header.tex expand -8 $2 | awk -f _temp.awk cat footer.tex SuiteSparse/CHOLMOD/Doc/footer.tex0000644001170100242450000000015610304131374015557 0ustar davisfac\end{verbatim} } \noindent\hspace{0.85in}\rule[0.25in]{5.2in}{1pt} \vspace{-0.15in} \noindent {\bf Purpose:} SuiteSparse/CHOLMOD/Doc/mfile.awk0000644001170100242450000000005510304303052015327 0ustar davisfac/^%/ { print " ", substr ($0,2) } SuiteSparse/CHOLMOD/Doc/ChangeLog0000644001170100242450000001471210711427606015324 0ustar davisfacNov 1, 2007, version 1.6.0 * minor lint cleanup (no bugs) * new CHOLMOD_CLEAR_FLAG macro, which speeds up the calls to cholmod_clear_flag, avoiding the function call if not needed. Note that this leads to untested lines in the Tcov test, but the lines of the macro are tested in several places, just not everywhere it appers. * port to MATLAB 7.5 (mex -lmwblas option now required for Linux) * minor bug fix to cholmod_add.c to avoid potential Int overflow * extra option added to cholmod2 mexFunction * sparse2 mexFunction modified to ensure nnz(A) == nzmax(A) always holds (It didn't in v1.5.0 if numerically zero entries were dropped in A). * correction to Help comments for spsym function * bug fix to cholmod_symmetry.c: determination of Hermitian vs non-Hermitian matrices was incorrect if the diagonal was imaginary. * performance fix for cholmod_nesdis.c and nesdis mexFunction May 31, 2007, version 1.5.0 * 64-bit MATLAB interface * MATLAB interface back-ported to MATLAB 6.1. * bug fix: solving Dx=b using a supernodal factorization, in cholmod_l_solve, when sizeof(UF_long) > sizeof(BLAS integer) * changes to Makefiles to reflect directory changes in COLAMD and CCOLAMD v2.7.0 directory structure (CHOLMOD v1.5 requires v2.7.0 of those two packages) * update to Modify/cholmod_updown.c, to allow input vector R to be packed or unpacked. * bug fix to Tcov/huge.c test code, for 64-bit case (this has no effect on the CHOLMOD library itself, just the test code) Dec 12, 2006, version 1.4.0 * added support for large files (larger than 2GB) * minor MATLAB cleanup * renamed MATLAB function from cholmod to cholmod2, to avoid filename clash with itself (the built-in version of cholmod). Dec 2, 2006, version 1.3.0 * Major modification to cholmod_read.c; now fully supports all forms of the Matrix Market format. Added cholmod_read_dense and cholmod_read_matrix functions to cholmod_read.c. Major changes to mread MATLAB function. Added Common->prefer_binary option for cholmod_read. * Added cholmod_write.c (cholmod_write_sparse and cholmod_write_dense functions). Added mwrite MATLAB function. * Added 2nd output argument to sparse2 (Z, binary pattern of explicit zero entries). * Added the function cholmod_symmetry to the MatrixOps module. Added spsym MATLAB function. * 2nd argument to cholmod_triplet_to_sparse changed from int to size_t. * minor correction to cholmod_analyze_ordering, cholmod_dense.c * minor change to cholmod_rowfac.c, cholmod_solve.c, ... to allow for easier testing. Sept 28, 2006, version 1.2.1 * bug fix to cholmod_matlab.c, when working with sparse INT64 matrices in the "sparse2" function Aug 31, 2006, version 1.2 * Common->default_nesdis parameter and Common->called_nd statistic added. Otherwise, no change to user interface. v1.2 is fully upward compatible with v1.1 (even binary compatible). * non-supernodal Lx=b and L'x=b solves simplified, slight increase in performance. * update/downdate performance improved. * ordering options and output statistics added to MATLAB/cholmod mexFunction. July 27, 2006, version 1.1.1 * bug fix for cholmod_rowfac_mask, for the complex case. Has no effect on MATLAB. June 27, 2006: * trivial changes to nested dissection code, and cholmod_read.c (for debugging, and to add explicit typecasts so compilers don't complain). May, 2006: * Added new routines for LPDASA: cholmod_rowfac_mask, cholmod_updown_mask. Added cholmod_collapse_septree. Added nd_oksep, nd_components parameters to Common. Apr 30, 2006: version 1.1 * added interface to CAMD. cholmod_nested_dissection can now call CCOLAMD, CSYMAMD, and CAMD. Common->nd_camd usage extended. New argument added to nesdis mexFunction. New cholmod_camd function added. No other changes to CHOLMOD user interface. * more careful integer overflow checks. Added non-user-callable functions to add and multiply size_t integers, with overflow checks. * added Common->no_workspace_reallocate * flop count is now correct for A*A' case (Common->rowfacfl). Jan 18, 2006: version 1.0.2 * bug fix: MATLAB interface incorrect for full logical matrices. * Tcov tests modified to generate fewer intentional nan's, to make it easier to look for errors in BLAS libraries that incorrectly generate nan's. Dec 16, 2005: version 1.0.1 * bug fix: cholmod_amd allocated too small of a workspace when ordering A*A' Dec 8, 2005: version 1.0 * no real changes. Version 1.0 is the same as version 0.8. Version 1.0 is simply the formal stable release. * known issue: the floating point operation count, Common->rowfacfl, is statistic is incorrect when factorizing A*A'. This will be fixed in version 1.1. Nov 15, 2005: version 0.8 * bug fix in t_cholmod_super_numeric, for [R,p]=chol(A) usage. * Common->quick_return_if_not_posdef added. * Added cholmod_row_lsubtree (required for LPDASA) * bug fix: cholmod_rcond returned sqrt(1/cond) for an LL' factorization; 1/cond is required. * new statistics added: flop counts for cholmod_rowfac, # of factor column reallocations, # of factor reallocations due to column reallocations, and # of times the (non-default) bounds on diag(L) are hit. * factor column reallocation skipped if space already big enough. * bug fix: cholmod_copy_factor did not copy L->is_monotonic. * bug fix: cholmod_change_factor (diagonal entry was wrong in one case) * rcond added to cholmod mexFunction ([x,rcond] = cholmod(A,b)). * cholmod_rowadd, cholmod_rowdel modified. rowdel no longer removes entries from the matrix; it sets them to zero instead. Oct 10, 2005: version 0.7 * minor changes: minor change to Check/cholmod_check.c (coerce sizeof(...) to (int) when printing. Less strict check on A->p for unpacked matrices) , removed a few unused variables in Check/cholmod_read.c and Demo/cholmod*demo.c, changed "exit(0)" to "return(0)" in Demo/cholmod_simple.c. Changed Makefile so that "." is not assumed to be on the $path. Added Cygwin to architecture detection in Include/cholmod_blas.h. Added cparent and cmember to nesdis.m. Space for future expansion added to cholmod_common. * removed "rowmark" from the Modify module, which affects how partial updates to Lx=b solves are done during update/downdate. Should only affect LPDASA. * added CHOLMOD_SUBSUB_VERSION Aug 31, 2005: version 0.6 released. SuiteSparse/CHOLMOD/Doc/header.tex0000644001170100242450000000014310304131166015504 0ustar davisfac\noindent\hspace{0.85in}\rule[0.05in]{5.2in}{1pt} \vspace{-0.15in} {\footnotesize \begin{verbatim} SuiteSparse/CHOLMOD/Lib/0000755001170100242450000000000010711435726013550 5ustar davisfacSuiteSparse/CHOLMOD/Lib/Makefile0000644001170100242450000003327710617113210015206 0ustar davisfac#=============================================================================== # CHOLOMD/Lib/Makefile: for compiling the CHOLMOD library #=============================================================================== default: all ccode: all include ../../UFconfig/UFconfig.mk C = $(CC) $(CFLAGS) $(CHOLMOD_CONFIG) all: libcholmod.a library: libcholmod.a purge: distclean distclean: clean - $(RM) libcholmod.a clean: - $(RM) $(CLEAN) #------------------------------------------------------------------------------- # ../Include/ directory contains all include files: #------------------------------------------------------------------------------- INC = ../Include/cholmod.h \ ../Include/cholmod_blas.h \ ../Include/cholmod_check.h \ ../Include/cholmod_cholesky.h \ ../Include/cholmod_complexity.h \ ../Include/cholmod_config.h \ ../Include/cholmod_core.h \ ../Include/cholmod_internal.h \ ../Include/cholmod_matrixops.h \ ../Include/cholmod_modify.h \ ../Include/cholmod_partition.h \ ../Include/cholmod_supernodal.h \ ../Include/cholmod_template.h #------------------------------------------------------------------------------- # The 7 CHOLMOD library modules (int, double) #------------------------------------------------------------------------------- CORE = cholmod_aat.o cholmod_add.o cholmod_band.o \ cholmod_change_factor.o cholmod_common.o cholmod_complex.o \ cholmod_copy.o cholmod_dense.o cholmod_error.o cholmod_factor.o \ cholmod_memory.o cholmod_sparse.o \ cholmod_transpose.o cholmod_triplet.o CHECK = cholmod_check.o cholmod_read.o cholmod_write.o CHOLESKY = cholmod_amd.o cholmod_analyze.o cholmod_colamd.o \ cholmod_etree.o cholmod_factorize.o cholmod_postorder.o \ cholmod_rcond.o cholmod_resymbol.o cholmod_rowcolcounts.o \ cholmod_rowfac.o cholmod_solve.o cholmod_spsolve.o MATRIXOPS = cholmod_drop.o cholmod_horzcat.o cholmod_norm.o \ cholmod_scale.o cholmod_sdmult.o cholmod_ssmult.o \ cholmod_submatrix.o cholmod_vertcat.o cholmod_symmetry.o PARTITION = cholmod_ccolamd.o cholmod_csymamd.o \ cholmod_metis.o cholmod_nesdis.o cholmod_camd.o MODIFY = cholmod_rowadd.o cholmod_rowdel.o cholmod_updown.o SUPERNODAL = cholmod_super_numeric.o cholmod_super_solve.o \ cholmod_super_symbolic.o DI = $(CORE) $(CHECK) $(CHOLESKY) $(MATRIXOPS) $(MODIFY) $(SUPERNODAL) \ $(PARTITION) #------------------------------------------------------------------------------- # CHOLMOD library modules (long, double) #------------------------------------------------------------------------------- LCORE = cholmod_l_aat.o cholmod_l_add.o cholmod_l_band.o \ cholmod_l_change_factor.o cholmod_l_common.o cholmod_l_complex.o \ cholmod_l_copy.o cholmod_l_dense.o cholmod_l_error.o \ cholmod_l_factor.o cholmod_l_memory.o \ cholmod_l_sparse.o cholmod_l_transpose.o cholmod_l_triplet.o LCHECK = cholmod_l_check.o cholmod_l_read.o cholmod_l_write.o LCHOLESKY = cholmod_l_amd.o cholmod_l_analyze.o cholmod_l_colamd.o \ cholmod_l_etree.o cholmod_l_factorize.o cholmod_l_postorder.o \ cholmod_l_rcond.o cholmod_l_resymbol.o cholmod_l_rowcolcounts.o \ cholmod_l_rowfac.o cholmod_l_solve.o cholmod_l_spsolve.o LMATRIXOPS = cholmod_l_drop.o cholmod_l_horzcat.o cholmod_l_norm.o \ cholmod_l_scale.o cholmod_l_sdmult.o cholmod_l_ssmult.o \ cholmod_l_submatrix.o cholmod_l_vertcat.o cholmod_l_symmetry.o LPARTITION = cholmod_l_ccolamd.o cholmod_l_csymamd.o \ cholmod_l_metis.o cholmod_l_nesdis.o cholmod_l_camd.o LMODIFY = cholmod_l_rowadd.o cholmod_l_rowdel.o cholmod_l_updown.o LSUPERNODAL = cholmod_l_super_numeric.o cholmod_l_super_solve.o \ cholmod_l_super_symbolic.o DL = $(LCORE) $(LCHECK) $(LCHOLESKY) $(LMATRIXOPS) $(LMODIFY) $(LSUPERNODAL) \ $(LPARTITION) #------------------------------------------------------------------------------- # to compile just the double/int version, use OBJ = $(DI) OBJ = $(DI) $(DL) libcholmod.a: $(OBJ) $(AR) libcholmod.a $(OBJ) $(RANLIB) libcholmod.a $(OBJ): $(INC) I = -I../../AMD/Include -I../../AMD/Source -I../../COLAMD/Include \ -I$(METIS_PATH)/Lib -I../../CCOLAMD/Include -I../../CAMD/Include \ -I../Include -I../../UFconfig #------------------------------------------------------------------------------- # Check Module: #------------------------------------------------------------------------------- cholmod_check.o: ../Check/cholmod_check.c $(C) -c $(I) $< cholmod_read.o: ../Check/cholmod_read.c $(C) -c $(I) $< cholmod_write.o: ../Check/cholmod_write.c $(C) -c $(I) $< #------------------------------------------------------------------------------- cholmod_l_check.o: ../Check/cholmod_check.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_read.o: ../Check/cholmod_read.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_write.o: ../Check/cholmod_write.c $(C) -DDLONG -c $(I) $< -o $@ #------------------------------------------------------------------------------- # Core Module: #------------------------------------------------------------------------------- cholmod_common.o: ../Core/cholmod_common.c $(C) -c $(I) $< cholmod_dense.o: ../Core/cholmod_dense.c ../Core/t_cholmod_dense.c $(C) -c $(I) $< cholmod_factor.o: ../Core/cholmod_factor.c $(C) -c $(I) $< cholmod_change_factor.o: ../Core/cholmod_change_factor.c \ ../Core/t_cholmod_change_factor.c $(C) -c $(I) $< cholmod_memory.o: ../Core/cholmod_memory.c $(C) -c $(I) $< cholmod_sparse.o: ../Core/cholmod_sparse.c $(C) -c $(I) $< cholmod_complex.o: ../Core/cholmod_complex.c $(C) -c $(I) $< cholmod_transpose.o: ../Core/cholmod_transpose.c ../Core/t_cholmod_transpose.c $(C) -c $(I) $< cholmod_band.o: ../Core/cholmod_band.c $(C) -c $(I) $< cholmod_copy.o: ../Core/cholmod_copy.c $(C) -c $(I) $< cholmod_triplet.o: ../Core/cholmod_triplet.c ../Core/t_cholmod_triplet.c $(C) -c $(I) $< cholmod_error.o: ../Core/cholmod_error.c $(C) -c $(I) $< cholmod_aat.o: ../Core/cholmod_aat.c $(C) -c $(I) $< cholmod_add.o: ../Core/cholmod_add.c $(C) -c $(I) $< #------------------------------------------------------------------------------- cholmod_l_common.o: ../Core/cholmod_common.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_dense.o: ../Core/cholmod_dense.c ../Core/t_cholmod_dense.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_factor.o: ../Core/cholmod_factor.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_change_factor.o: ../Core/cholmod_change_factor.c \ ../Core/t_cholmod_change_factor.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_memory.o: ../Core/cholmod_memory.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_sparse.o: ../Core/cholmod_sparse.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_complex.o: ../Core/cholmod_complex.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_transpose.o: ../Core/cholmod_transpose.c ../Core/t_cholmod_transpose.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_band.o: ../Core/cholmod_band.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_copy.o: ../Core/cholmod_copy.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_triplet.o: ../Core/cholmod_triplet.c ../Core/t_cholmod_triplet.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_error.o: ../Core/cholmod_error.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_aat.o: ../Core/cholmod_aat.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_add.o: ../Core/cholmod_add.c $(C) -DDLONG -c $(I) $< -o $@ #------------------------------------------------------------------------------- # Cholesky Module: #------------------------------------------------------------------------------- cholmod_amd.o: ../Cholesky/cholmod_amd.c $(C) -c $(I) $< cholmod_analyze.o: ../Cholesky/cholmod_analyze.c $(C) -c $(I) $< cholmod_colamd.o: ../Cholesky/cholmod_colamd.c $(C) -c $(I) $< cholmod_etree.o: ../Cholesky/cholmod_etree.c $(C) -c $(I) $< cholmod_factorize.o: ../Cholesky/cholmod_factorize.c $(C) -c $(I) $< cholmod_postorder.o: ../Cholesky/cholmod_postorder.c $(C) -c $(I) $< cholmod_rcond.o: ../Cholesky/cholmod_rcond.c $(C) -c $(I) $< cholmod_resymbol.o: ../Cholesky/cholmod_resymbol.c $(C) -c $(I) $< cholmod_rowcolcounts.o: ../Cholesky/cholmod_rowcolcounts.c $(C) -c $(I) $< cholmod_solve.o: ../Cholesky/cholmod_solve.c ../Cholesky/t_cholmod_lsolve.c \ ../Cholesky/t_cholmod_ltsolve.c ../Cholesky/t_cholmod_solve.c $(C) -c $(I) $< cholmod_spsolve.o: ../Cholesky/cholmod_spsolve.c $(C) -c $(I) $< cholmod_rowfac.o: ../Cholesky/cholmod_rowfac.c ../Cholesky/t_cholmod_rowfac.c $(C) -c $(I) $< #------------------------------------------------------------------------------- cholmod_l_amd.o: ../Cholesky/cholmod_amd.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_analyze.o: ../Cholesky/cholmod_analyze.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_colamd.o: ../Cholesky/cholmod_colamd.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_etree.o: ../Cholesky/cholmod_etree.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_factorize.o: ../Cholesky/cholmod_factorize.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_postorder.o: ../Cholesky/cholmod_postorder.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_rcond.o: ../Cholesky/cholmod_rcond.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_resymbol.o: ../Cholesky/cholmod_resymbol.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_rowcolcounts.o: ../Cholesky/cholmod_rowcolcounts.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_solve.o: ../Cholesky/cholmod_solve.c ../Cholesky/t_cholmod_lsolve.c \ ../Cholesky/t_cholmod_ltsolve.c ../Cholesky/t_cholmod_solve.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_spsolve.o: ../Cholesky/cholmod_spsolve.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_rowfac.o: ../Cholesky/cholmod_rowfac.c ../Cholesky/t_cholmod_rowfac.c $(C) -DDLONG -c $(I) $< -o $@ #------------------------------------------------------------------------------- # Partition Module: #------------------------------------------------------------------------------- cholmod_ccolamd.o: ../Partition/cholmod_ccolamd.c $(C) -c $(I) $< cholmod_csymamd.o: ../Partition/cholmod_csymamd.c $(C) -c $(I) $< cholmod_camd.o: ../Partition/cholmod_camd.c $(C) -c $(I) $< cholmod_metis.o: ../Partition/cholmod_metis.c $(C) -c $(I) $< cholmod_nesdis.o: ../Partition/cholmod_nesdis.c $(C) -c $(I) $< #------------------------------------------------------------------------------- cholmod_l_ccolamd.o: ../Partition/cholmod_ccolamd.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_csymamd.o: ../Partition/cholmod_csymamd.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_camd.o: ../Partition/cholmod_camd.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_metis.o: ../Partition/cholmod_metis.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_nesdis.o: ../Partition/cholmod_nesdis.c $(C) -DDLONG -c $(I) $< -o $@ #------------------------------------------------------------------------------- # MatrixOps Module: #------------------------------------------------------------------------------- cholmod_horzcat.o: ../MatrixOps/cholmod_horzcat.c $(C) -c $(I) $< cholmod_norm.o: ../MatrixOps/cholmod_norm.c $(C) -c $(I) $< cholmod_scale.o: ../MatrixOps/cholmod_scale.c $(C) -c $(I) $< cholmod_drop.o: ../MatrixOps/cholmod_drop.c $(C) -c $(I) $< cholmod_sdmult.o: ../MatrixOps/cholmod_sdmult.c \ ../MatrixOps/t_cholmod_sdmult.c $(C) -c $(I) $< cholmod_ssmult.o: ../MatrixOps/cholmod_ssmult.c $(C) -c $(I) $< cholmod_submatrix.o: ../MatrixOps/cholmod_submatrix.c $(C) -c $(I) $< cholmod_vertcat.o: ../MatrixOps/cholmod_vertcat.c $(C) -c $(I) $< cholmod_symmetry.o: ../MatrixOps/cholmod_symmetry.c $(C) -c $(I) $< #------------------------------------------------------------------------------- cholmod_l_horzcat.o: ../MatrixOps/cholmod_horzcat.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_norm.o: ../MatrixOps/cholmod_norm.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_scale.o: ../MatrixOps/cholmod_scale.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_drop.o: ../MatrixOps/cholmod_drop.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_sdmult.o: ../MatrixOps/cholmod_sdmult.c \ ../MatrixOps/t_cholmod_sdmult.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_ssmult.o: ../MatrixOps/cholmod_ssmult.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_submatrix.o: ../MatrixOps/cholmod_submatrix.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_vertcat.o: ../MatrixOps/cholmod_vertcat.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_symmetry.o: ../MatrixOps/cholmod_symmetry.c $(C) -DDLONG -c $(I) $< -o $@ #------------------------------------------------------------------------------- # Modify Module: #------------------------------------------------------------------------------- cholmod_rowadd.o: ../Modify/cholmod_rowadd.c $(C) -c $(I) $< cholmod_rowdel.o: ../Modify/cholmod_rowdel.c $(C) -c $(I) $< cholmod_updown.o: ../Modify/cholmod_updown.c \ ../Modify/t_cholmod_updown.c ../Modify/t_cholmod_updown_numkr.c $(C) -c $(I) $< #------------------------------------------------------------------------------- cholmod_l_rowadd.o: ../Modify/cholmod_rowadd.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_rowdel.o: ../Modify/cholmod_rowdel.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_updown.o: ../Modify/cholmod_updown.c \ ../Modify/t_cholmod_updown.c ../Modify/t_cholmod_updown_numkr.c $(C) -DDLONG -c $(I) $< -o $@ #------------------------------------------------------------------------------- # Supernodal Module: #------------------------------------------------------------------------------- cholmod_super_numeric.o: ../Supernodal/cholmod_super_numeric.c \ ../Supernodal/t_cholmod_super_numeric.c $(C) -c $(I) $< cholmod_super_symbolic.o: ../Supernodal/cholmod_super_symbolic.c $(C) -c $(I) $< cholmod_super_solve.o: ../Supernodal/cholmod_super_solve.c \ ../Supernodal/t_cholmod_super_solve.c $(C) -c $(I) $< #------------------------------------------------------------------------------- cholmod_l_super_numeric.o: ../Supernodal/cholmod_super_numeric.c \ ../Supernodal/t_cholmod_super_numeric.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_super_symbolic.o: ../Supernodal/cholmod_super_symbolic.c $(C) -DDLONG -c $(I) $< -o $@ cholmod_l_super_solve.o: ../Supernodal/cholmod_super_solve.c \ ../Supernodal/t_cholmod_super_solve.c $(C) -DDLONG -c $(I) $< -o $@ SuiteSparse/CHOLMOD/Core/0000755001170100242450000000000010677524360013736 5ustar davisfacSuiteSparse/CHOLMOD/Core/t_cholmod_triplet.c0000644001170100242450000001115610537777460017627 0ustar davisfac/* ========================================================================== */ /* === Core/t_cholmod_triplet =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Template routine for cholmod_triplet. All xtypes supported */ #include "cholmod_template.h" /* ========================================================================== */ /* === t_cholmod_triplet_to_sparse ========================================== */ /* ========================================================================== */ static size_t TEMPLATE (cholmod_triplet_to_sparse) ( /* ---- input ---- */ cholmod_triplet *T, /* matrix to copy */ /* ---- in/out --- */ cholmod_sparse *R, /* output matrix */ /* --------------- */ cholmod_common *Common ) { double *Rx, *Rz, *Tx, *Tz ; Int *Wj, *Rp, *Ri, *Rnz, *Ti, *Tj ; Int i, j, p, p1, p2, pdest, pj, k, stype, nrow, ncol, nz ; size_t anz ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ /* Wj contains a copy of Rp on input [ */ Wj = Common->Iwork ; /* size MAX (nrow,ncol). (i/l/l) */ Rp = R->p ; Ri = R->i ; Rnz = R->nz ; Rx = R->x ; Rz = R->z ; Ti = T->i ; Tj = T->j ; Tx = T->x ; Tz = T->z ; nz = T->nnz ; nrow = T->nrow ; ncol = T->ncol ; stype = SIGN (T->stype) ; /* ---------------------------------------------------------------------- */ /* construct the row form */ /* ---------------------------------------------------------------------- */ /* if Ti is jumbled, this part dominates the run time */ if (stype > 0) { for (k = 0 ; k < nz ; k++) { i = Ti [k] ; j = Tj [k] ; if (i < j) { /* place triplet (j,i,x) in column i of R */ p = Wj [i]++ ; Ri [p] = j ; } else { /* place triplet (i,j,x) in column j of R */ p = Wj [j]++ ; Ri [p] = i ; } ASSIGN (Rx, Rz, p, Tx, Tz, k) ; } } else if (stype < 0) { for (k = 0 ; k < nz ; k++) { i = Ti [k] ; j = Tj [k] ; if (i > j) { /* place triplet (j,i,x) in column i of R */ p = Wj [i]++ ; Ri [p] = j ; } else { /* place triplet (i,j,x) in column j of R */ p = Wj [j]++ ; Ri [p] = i ; } ASSIGN (Rx, Rz, p, Tx, Tz, k) ; } } else { for (k = 0 ; k < nz ; k++) { /* place triplet (i,j,x) in column i of R */ p = Wj [Ti [k]]++ ; Ri [p] = Tj [k] ; ASSIGN (Rx, Rz, p, Tx, Tz, k) ; } } /* done using Wj (i/l/l) as temporary row pointers ] */ /* ---------------------------------------------------------------------- */ /* sum up duplicates */ /* ---------------------------------------------------------------------- */ /* use Wj (i/l/l) of size ncol to keep track of duplicates in each row [ */ for (j = 0 ; j < ncol ; j++) { Wj [j] = EMPTY ; } anz = 0 ; for (i = 0 ; i < nrow ; i++) { p1 = Rp [i] ; p2 = Rp [i+1] ; pdest = p1 ; /* at this point Wj [j] < p1 holds true for all columns j, because * Ri/Rx is stored in row oriented manner */ for (p = p1 ; p < p2 ; p++) { j = Ri [p] ; pj = Wj [j] ; if (pj >= p1) { /* this column index j is already in row i at position pj; * sum up the duplicate entry */ /* Rx [pj] += Rx [p] ; */ ASSEMBLE (Rx, Rz, pj, Rx, Rz, p) ; } else { /* keep the entry and keep track in Wj [j] for case above */ Wj [j] = pdest ; if (pdest != p) { Ri [pdest] = j ; ASSIGN (Rx, Rz, pdest, Rx, Rz, p) ; } pdest++ ; } } Rnz [i] = pdest - p1 ; anz += (pdest - p1) ; } /* done using Wj to keep track of duplicate entries in each row ] */ /* ---------------------------------------------------------------------- */ /* return number of entries after summing up duplicates */ /* ---------------------------------------------------------------------- */ return (anz) ; } #undef PATTERN #undef REAL #undef COMPLEX #undef ZOMPLEX SuiteSparse/CHOLMOD/Core/cholmod_aat.c0000644001170100242450000002077010635770614016361 0ustar davisfac/* ========================================================================== */ /* === Core/cholmod_aat ===================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* C = A*A' or C = A(:,f)*A(:,f)' * * A can be packed or unpacked, sorted or unsorted, but must be stored with * both upper and lower parts (A->stype of zero). C is returned as packed, * C->stype of zero (both upper and lower parts present), and unsorted. See * cholmod_ssmult in the MatrixOps Module for a more general matrix-matrix * multiply. * * You can trivially convert C into a symmetric upper/lower matrix by * changing C->stype = 1 or -1 after calling this routine. * * workspace: * Flag (A->nrow), * Iwork (max (A->nrow, A->ncol)) if fset present, * Iwork (A->nrow) if no fset, * W (A->nrow) if mode > 0, * allocates temporary copy for A'. * * A can be pattern or real. Complex or zomplex cases are supported only * if the mode is <= 0 (in which case the numerical values are ignored). */ #include "cholmod_internal.h" #include "cholmod_core.h" cholmod_sparse *CHOLMOD(aat) ( /* ---- input ---- */ cholmod_sparse *A, /* input matrix; C=A*A' is constructed */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) * -2: pattern only, no diagonal, add 50% + n extra * space to C */ /* --------------- */ cholmod_common *Common ) { double fjt ; double *Ax, *Fx, *Cx, *W ; Int *Ap, *Anz, *Ai, *Fp, *Fi, *Cp, *Ci, *Flag ; cholmod_sparse *C, *F ; Int packed, j, i, pa, paend, pf, pfend, n, mark, cnz, t, p, values, diag, extra ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; values = (mode > 0) && (A->xtype != CHOLMOD_PATTERN) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; if (A->stype) { ERROR (CHOLMOD_INVALID, "matrix cannot be symmetric") ; return (NULL) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ diag = (mode >= 0) ; n = A->nrow ; CHOLMOD(allocate_work) (n, MAX (A->ncol, A->nrow), values ? n : 0, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n : 0, Common)) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_sparse) (A, "A", Common) >= 0) ; /* get the A matrix */ Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; packed = A->packed ; /* get workspace */ W = Common->Xwork ; /* size n, unused if values is FALSE */ Flag = Common->Flag ; /* size n, Flag [0..n-1] < mark on input*/ /* ---------------------------------------------------------------------- */ /* F = A' or A(:,f)' */ /* ---------------------------------------------------------------------- */ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/ F = CHOLMOD(ptranspose) (A, values, NULL, fset, fsize, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } Fp = F->p ; Fi = F->i ; Fx = F->x ; /* ---------------------------------------------------------------------- */ /* count the number of entries in the result C */ /* ---------------------------------------------------------------------- */ cnz = 0 ; for (j = 0 ; j < n ; j++) { /* clear the Flag array */ /* mark = CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; /* exclude the diagonal, if requested */ if (!diag) { Flag [j] = mark ; } /* for each nonzero F(t,j) in column j, do: */ pfend = Fp [j+1] ; for (pf = Fp [j] ; pf < pfend ; pf++) { /* F(t,j) is nonzero */ t = Fi [pf] ; /* add the nonzero pattern of A(:,t) to the pattern of C(:,j) */ pa = Ap [t] ; paend = (packed) ? (Ap [t+1]) : (pa + Anz [t]) ; for ( ; pa < paend ; pa++) { i = Ai [pa] ; if (Flag [i] != mark) { Flag [i] = mark ; cnz++ ; } } } if (cnz < 0) { break ; /* integer overflow case */ } } extra = (mode == -2) ? (cnz/2 + n) : 0 ; mark = CHOLMOD(clear_flag) (Common) ; /* ---------------------------------------------------------------------- */ /* check for integer overflow */ /* ---------------------------------------------------------------------- */ if (cnz < 0 || (cnz + extra) < 0) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; CHOLMOD(clear_flag) (Common) ; CHOLMOD(free_sparse) (&F, Common) ; return (NULL) ; /* problem too large */ } /* ---------------------------------------------------------------------- */ /* allocate C */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(allocate_sparse) (n, n, cnz + extra, FALSE, TRUE, 0, values ? A->xtype : CHOLMOD_PATTERN, Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_sparse) (&F, Common) ; return (NULL) ; /* out of memory */ } Cp = C->p ; Ci = C->i ; Cx = C->x ; /* ---------------------------------------------------------------------- */ /* C = A*A' */ /* ---------------------------------------------------------------------- */ cnz = 0 ; if (values) { /* pattern and values */ for (j = 0 ; j < n ; j++) { /* clear the Flag array */ mark = CHOLMOD(clear_flag) (Common) ; /* start column j of C */ Cp [j] = cnz ; /* for each nonzero F(t,j) in column j, do: */ pfend = Fp [j+1] ; for (pf = Fp [j] ; pf < pfend ; pf++) { /* F(t,j) is nonzero */ t = Fi [pf] ; fjt = Fx [pf] ; /* add the nonzero pattern of A(:,t) to the pattern of C(:,j) * and scatter the values into W */ pa = Ap [t] ; paend = (packed) ? (Ap [t+1]) : (pa + Anz [t]) ; for ( ; pa < paend ; pa++) { i = Ai [pa] ; if (Flag [i] != mark) { Flag [i] = mark ; Ci [cnz++] = i ; } W [i] += Ax [pa] * fjt ; } } /* gather the values into C(:,j) */ for (p = Cp [j] ; p < cnz ; p++) { i = Ci [p] ; Cx [p] = W [i] ; W [i] = 0 ; } } } else { /* pattern only */ for (j = 0 ; j < n ; j++) { /* clear the Flag array */ mark = CHOLMOD(clear_flag) (Common) ; /* exclude the diagonal, if requested */ if (!diag) { Flag [j] = mark ; } /* start column j of C */ Cp [j] = cnz ; /* for each nonzero F(t,j) in column j, do: */ pfend = Fp [j+1] ; for (pf = Fp [j] ; pf < pfend ; pf++) { /* F(t,j) is nonzero */ t = Fi [pf] ; /* add the nonzero pattern of A(:,t) to the pattern of C(:,j) */ pa = Ap [t] ; paend = (packed) ? (Ap [t+1]) : (pa + Anz [t]) ; for ( ; pa < paend ; pa++) { i = Ai [pa] ; if (Flag [i] != mark) { Flag [i] = mark ; Ci [cnz++] = i ; } } } } } Cp [n] = cnz ; ASSERT (IMPLIES (mode != -2, MAX (1,cnz) == C->nzmax)) ; /* ---------------------------------------------------------------------- */ /* clear workspace and free temporary matrices and return result */ /* ---------------------------------------------------------------------- */ CHOLMOD(free_sparse) (&F, Common) ; CHOLMOD(clear_flag) (Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n : 0, Common)) ; DEBUG (i = CHOLMOD(dump_sparse) (C, "aat", Common)) ; ASSERT (IMPLIES (mode < 0, i == 0)) ; return (C) ; } SuiteSparse/CHOLMOD/Core/cholmod_add.c0000644001170100242450000002031310677524356016343 0ustar davisfac/* ========================================================================== */ /* === Core/cholmod_add ===================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* C = alpha*A + beta*B, or spones(A+B). Result is packed, with sorted or * unsorted columns. This routine is much faster and takes less memory if C * is allowed to have unsorted columns. * * If A and B are both symmetric (in upper form) then C is the same. Likewise, * if A and B are both symmetric (in lower form) then C is the same. * Otherwise, C is unsymmetric. A and B must have the same dimension. * * workspace: Flag (nrow), W (nrow) if values, Iwork (max (nrow,ncol)). * allocates temporary copies for A and B if they are symmetric. * allocates temporary copy of C if it is to be returned sorted. * * A and B can have an xtype of pattern or real. Complex or zomplex cases * are supported only if the "values" input parameter is FALSE. */ #include "cholmod_internal.h" #include "cholmod_core.h" cholmod_sparse *CHOLMOD(add) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to add */ cholmod_sparse *B, /* matrix to add */ double alpha [2], /* scale factor for A */ double beta [2], /* scale factor for B */ int values, /* if TRUE compute the numerical values of C */ int sorted, /* if TRUE, sort columns of C */ /* --------------- */ cholmod_common *Common ) { double *Ax, *Bx, *Cx, *W ; Int apacked, up, lo, nrow, ncol, bpacked, nzmax, pa, paend, pb, pbend, i, j, p, mark, nz ; Int *Ap, *Ai, *Anz, *Bp, *Bi, *Bnz, *Flag, *Cp, *Ci ; cholmod_sparse *A2, *B2, *C ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; RETURN_IF_NULL (B, NULL) ; values = values && (A->xtype != CHOLMOD_PATTERN) && (B->xtype != CHOLMOD_PATTERN) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; RETURN_IF_XTYPE_INVALID (B, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; if (A->nrow != B->nrow || A->ncol != B->ncol) { /* A and B must have the same dimensions */ ERROR (CHOLMOD_INVALID, "A and B dimesions do not match") ; return (NULL) ; } /* A and B must have the same numerical type if values is TRUE (both must * be CHOLMOD_REAL, this is implicitly checked above) */ Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ nrow = A->nrow ; ncol = A->ncol ; CHOLMOD(allocate_work) (nrow, MAX (nrow,ncol), values ? nrow : 0, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if (nrow <= 1) { /* C will be implicitly sorted, so no need to sort it here */ sorted = FALSE ; } /* convert A or B to unsymmetric, if necessary */ A2 = NULL ; B2 = NULL ; if (A->stype != B->stype) { if (A->stype) { /* workspace: Iwork (max (nrow,ncol)) */ A2 = CHOLMOD(copy) (A, 0, values, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } A = A2 ; } if (B->stype) { /* workspace: Iwork (max (nrow,ncol)) */ B2 = CHOLMOD(copy) (B, 0, values, Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_sparse) (&A2, Common) ; return (NULL) ; /* out of memory */ } B = B2 ; } } /* get the A matrix */ ASSERT (A->stype == B->stype) ; up = (A->stype > 0) ; lo = (A->stype < 0) ; Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; apacked = A->packed ; /* get the B matrix */ Bp = B->p ; Bnz = B->nz ; Bi = B->i ; Bx = B->x ; bpacked = B->packed ; /* get workspace */ W = Common->Xwork ; /* size nrow, used if values is TRUE */ Flag = Common->Flag ; /* size nrow, Flag [0..nrow-1] < mark on input */ /* ---------------------------------------------------------------------- */ /* allocate the result C */ /* ---------------------------------------------------------------------- */ /* If integer overflow occurs, nzmax < 0 and the allocate fails properly * (likewise in most other matrix manipulation routines). */ nzmax = CHOLMOD(nnz) (A, Common) + CHOLMOD(nnz) (B, Common) ; C = CHOLMOD(allocate_sparse) (nrow, ncol, nzmax, FALSE, TRUE, SIGN (A->stype), values ? A->xtype : CHOLMOD_PATTERN, Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; return (NULL) ; /* out of memory */ } Cp = C->p ; Ci = C->i ; Cx = C->x ; /* ---------------------------------------------------------------------- */ /* compute C = alpha*A + beta*B */ /* ---------------------------------------------------------------------- */ nz = 0 ; for (j = 0 ; j < ncol ; j++) { Cp [j] = nz ; /* clear the Flag array */ /* mark = CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; /* scatter B into W */ pb = Bp [j] ; pbend = (bpacked) ? (Bp [j+1]) : (pb + Bnz [j]) ; for (p = pb ; p < pbend ; p++) { i = Bi [p] ; if ((up && i > j) || (lo && i < j)) { continue ; } Flag [i] = mark ; if (values) { W [i] = beta [0] * Bx [p] ; } } /* add A and gather from W into C(:,j) */ pa = Ap [j] ; paend = (apacked) ? (Ap [j+1]) : (pa + Anz [j]) ; for (p = pa ; p < paend ; p++) { i = Ai [p] ; if ((up && i > j) || (lo && i < j)) { continue ; } Flag [i] = EMPTY ; Ci [nz] = i ; if (values) { Cx [nz] = W [i] + alpha [0] * Ax [p] ; W [i] = 0 ; } nz++ ; } /* gather remaining entries into C(:,j), using pattern of B */ for (p = pb ; p < pbend ; p++) { i = Bi [p] ; if ((up && i > j) || (lo && i < j)) { continue ; } if (Flag [i] == mark) { Ci [nz] = i ; if (values) { Cx [nz] = W [i] ; W [i] = 0 ; } nz++ ; } } } Cp [ncol] = nz ; /* ---------------------------------------------------------------------- */ /* reduce C in size and free temporary matrices */ /* ---------------------------------------------------------------------- */ ASSERT (MAX (1,nz) <= C->nzmax) ; CHOLMOD(reallocate_sparse) (nz, C, Common) ; ASSERT (Common->status >= CHOLMOD_OK) ; /* clear the Flag array */ mark = CHOLMOD(clear_flag) (Common) ; CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; /* ---------------------------------------------------------------------- */ /* sort C, if requested */ /* ---------------------------------------------------------------------- */ if (sorted) { /* workspace: Iwork (max (nrow,ncol)) */ if (!CHOLMOD(sort) (C, Common)) { CHOLMOD(free_sparse) (&C, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } } } /* ---------------------------------------------------------------------- */ /* return result */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_sparse) (C, "add", Common) >= 0) ; return (C) ; } SuiteSparse/CHOLMOD/Core/cholmod_complex.c0000644001170100242450000003757510537777416017306 0ustar davisfac/* ========================================================================== */ /* === Core/cholmod_complex ================================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* If you convert a matrix that contains uninitialized data, valgrind will * complain. This can occur in a factor L which has gaps (a partial * factorization, or after updates that change the nonzero pattern), an * unpacked sparse matrix, a dense matrix with leading dimension d > # of rows, * or any matrix (dense, sparse, triplet, or factor) with more space allocated * than is used. You can safely ignore any of these complaints by valgrind. */ #include "cholmod_internal.h" #include "cholmod_core.h" /* ========================================================================== */ /* === cholmod_hypot ======================================================== */ /* ========================================================================== */ /* There is an equivalent routine called hypot in , which conforms * to ANSI C99. However, CHOLMOD does not assume that ANSI C99 is available. * You can use the ANSI C99 hypot routine with: * * #include * Common->hypotenuse = hypot ; * * Default value of the Common->hypotenuse pointer is cholmod_hypot. * * s = hypot (x,y) computes s = sqrt (x*x + y*y) but does so more accurately. * The NaN cases for the double relops x >= y and x+y == x are safely ignored. */ double CHOLMOD(hypot) (double x, double y) { double s, r ; x = fabs (x) ; y = fabs (y) ; if (x >= y) { if (x + y == x) { s = x ; } else { r = y / x ; s = x * sqrt (1.0 + r*r) ; } } else { if (y + x == y) { s = y ; } else { r = x / y ; s = y * sqrt (1.0 + r*r) ; } } return (s) ; } /* ========================================================================== */ /* === cholmod_divcomplex =================================================== */ /* ========================================================================== */ /* c = a/b where c, a, and b are complex. The real and imaginary parts are * passed as separate arguments to this routine. The NaN case is ignored * for the double relop br >= bi. Returns 1 if the denominator is zero, * 0 otherwise. Note that this return value is the single exception to the * rule that all CHOLMOD routines that return int return TRUE if successful * or FALSE otherise. * * This uses ACM Algo 116, by R. L. Smith, 1962, which tries to avoid * underflow and overflow. * * c can be the same variable as a or b. * * Default value of the Common->complex_divide pointer is cholmod_divcomplex. */ int CHOLMOD(divcomplex) ( double ar, double ai, /* real and imaginary parts of a */ double br, double bi, /* real and imaginary parts of b */ double *cr, double *ci /* real and imaginary parts of c */ ) { double tr, ti, r, den ; if (fabs (br) >= fabs (bi)) { r = bi / br ; den = br + r * bi ; tr = (ar + ai * r) / den ; ti = (ai - ar * r) / den ; } else { r = br / bi ; den = r * br + bi ; tr = (ar * r + ai) / den ; ti = (ai * r - ar) / den ; } *cr = tr ; *ci = ti ; return (IS_ZERO (den)) ; } /* ========================================================================== */ /* === change_complexity ==================================================== */ /* ========================================================================== */ /* X and Z represent an array of size nz, with numeric xtype given by xtype_in. * * If xtype_in is: * CHOLMOD_PATTERN: X and Z must be NULL. * CHOLMOD_REAL: X is of size nz, Z must be NULL. * CHOLMOD_COMPLEX: X is of size 2*nz, Z must be NULL. * CHOLMOD_ZOMPLEX: X is of size nz, Z is of size nz. * * The array is changed into the numeric xtype given by xtype_out, with the * same definitions of X and Z above. Note that the input conditions, above, * are not checked. These are checked in the caller routine. * * Returns TRUE if successful, FALSE otherwise. X and Z are not modified if * not successful. */ static int change_complexity ( /* ---- input ---- */ Int nz, /* size of X and/or Z */ int xtype_in, /* xtype of X and Z on input */ int xtype_out, /* requested xtype of X and Z on output */ int xtype1, /* xtype_out must be in the range [xtype1 .. xtype2] */ int xtype2, /* ---- in/out --- */ void **XX, /* old X on input, new X on output */ void **ZZ, /* old Z on input, new Z on output */ /* --------------- */ cholmod_common *Common ) { double *Xold, *Zold, *Xnew, *Znew ; Int k ; size_t nz2 ; if (xtype_out < xtype1 || xtype_out > xtype2) { ERROR (CHOLMOD_INVALID, "invalid xtype") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; Xold = *XX ; Zold = *ZZ ; switch (xtype_in) { /* ------------------------------------------------------------------ */ /* converting from pattern */ /* ------------------------------------------------------------------ */ case CHOLMOD_PATTERN: switch (xtype_out) { /* ---------------------------------------------------------- */ /* pattern -> real */ /* ---------------------------------------------------------- */ case CHOLMOD_REAL: /* allocate X and set to all ones */ Xnew = CHOLMOD(malloc) (nz, sizeof (double), Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } for (k = 0 ; k < nz ; k++) { Xnew [k] = 1 ; } *XX = Xnew ; break ; /* ---------------------------------------------------------- */ /* pattern -> complex */ /* ---------------------------------------------------------- */ case CHOLMOD_COMPLEX: /* allocate X and set to all ones */ Xnew = CHOLMOD(malloc) (nz, 2*sizeof (double), Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } for (k = 0 ; k < nz ; k++) { Xnew [2*k ] = 1 ; Xnew [2*k+1] = 0 ; } *XX = Xnew ; break ; /* ---------------------------------------------------------- */ /* pattern -> zomplex */ /* ---------------------------------------------------------- */ case CHOLMOD_ZOMPLEX: /* allocate X and Z and set to all ones */ Xnew = CHOLMOD(malloc) (nz, sizeof (double), Common) ; Znew = CHOLMOD(malloc) (nz, sizeof (double), Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free) (nz, sizeof (double), Xnew, Common) ; CHOLMOD(free) (nz, sizeof (double), Znew, Common) ; return (FALSE) ; } for (k = 0 ; k < nz ; k++) { Xnew [k] = 1 ; Znew [k] = 0 ; } *XX = Xnew ; *ZZ = Znew ; break ; } break ; /* ------------------------------------------------------------------ */ /* converting from real */ /* ------------------------------------------------------------------ */ case CHOLMOD_REAL: switch (xtype_out) { /* ---------------------------------------------------------- */ /* real -> pattern */ /* ---------------------------------------------------------- */ case CHOLMOD_PATTERN: /* free X */ *XX = CHOLMOD(free) (nz, sizeof (double), *XX, Common) ; break ; /* ---------------------------------------------------------- */ /* real -> complex */ /* ---------------------------------------------------------- */ case CHOLMOD_COMPLEX: /* allocate a new X and copy the old X */ Xnew = CHOLMOD(malloc) (nz, 2*sizeof (double), Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } for (k = 0 ; k < nz ; k++) { Xnew [2*k ] = Xold [k] ; Xnew [2*k+1] = 0 ; } CHOLMOD(free) (nz, sizeof (double), *XX, Common) ; *XX = Xnew ; break ; /* ---------------------------------------------------------- */ /* real -> zomplex */ /* ---------------------------------------------------------- */ case CHOLMOD_ZOMPLEX: /* allocate a new Z and set it to zero */ Znew = CHOLMOD(malloc) (nz, sizeof (double), Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } for (k = 0 ; k < nz ; k++) { Znew [k] = 0 ; } *ZZ = Znew ; break ; } break ; /* ------------------------------------------------------------------ */ /* converting from complex */ /* ------------------------------------------------------------------ */ case CHOLMOD_COMPLEX: switch (xtype_out) { /* ---------------------------------------------------------- */ /* complex -> pattern */ /* ---------------------------------------------------------- */ case CHOLMOD_PATTERN: /* free X */ *XX = CHOLMOD(free) (nz, 2*sizeof (double), *XX, Common) ; break ; /* ---------------------------------------------------------- */ /* complex -> real */ /* ---------------------------------------------------------- */ case CHOLMOD_REAL: /* pack the real part of X, discarding the imaginary part */ for (k = 0 ; k < nz ; k++) { Xold [k] = Xold [2*k] ; } /* shrink X in half (this cannot fail) */ nz2 = 2*nz ; *XX = CHOLMOD(realloc) (nz, sizeof (double), *XX, &nz2, Common) ; break ; /* ---------------------------------------------------------- */ /* complex -> zomplex */ /* ---------------------------------------------------------- */ case CHOLMOD_ZOMPLEX: /* allocate X and Z and copy the old X into them */ Xnew = CHOLMOD(malloc) (nz, sizeof (double), Common) ; Znew = CHOLMOD(malloc) (nz, sizeof (double), Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free) (nz, sizeof (double), Xnew, Common) ; CHOLMOD(free) (nz, sizeof (double), Znew, Common) ; return (FALSE) ; } for (k = 0 ; k < nz ; k++) { Xnew [k] = Xold [2*k ] ; Znew [k] = Xold [2*k+1] ; } CHOLMOD(free) (nz, 2*sizeof (double), *XX, Common) ; *XX = Xnew ; *ZZ = Znew ; break ; } break ; /* ------------------------------------------------------------------ */ /* converting from zomplex */ /* ------------------------------------------------------------------ */ case CHOLMOD_ZOMPLEX: switch (xtype_out) { /* ---------------------------------------------------------- */ /* zomplex -> pattern */ /* ---------------------------------------------------------- */ case CHOLMOD_PATTERN: /* free X and Z */ *XX = CHOLMOD(free) (nz, sizeof (double), *XX, Common) ; *ZZ = CHOLMOD(free) (nz, sizeof (double), *ZZ, Common) ; break ; /* ---------------------------------------------------------- */ /* zomplex -> real */ /* ---------------------------------------------------------- */ case CHOLMOD_REAL: /* free the imaginary part */ *ZZ = CHOLMOD(free) (nz, sizeof (double), *ZZ, Common) ; break ; /* ---------------------------------------------------------- */ /* zomplex -> complex */ /* ---------------------------------------------------------- */ case CHOLMOD_COMPLEX: Xnew = CHOLMOD(malloc) (nz, 2*sizeof (double), Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } for (k = 0 ; k < nz ; k++) { Xnew [2*k ] = Xold [k] ; Xnew [2*k+1] = Zold [k] ; } CHOLMOD(free) (nz, sizeof (double), *XX, Common) ; CHOLMOD(free) (nz, sizeof (double), *ZZ, Common) ; *XX = Xnew ; *ZZ = NULL ; break ; } break ; } return (TRUE) ; } /* ========================================================================== */ /* === cholmod_sparse_xtype ================================================= */ /* ========================================================================== */ /* Change the numeric xtype of a sparse matrix. Supports any type on input * and output (pattern, real, complex, or zomplex). */ int CHOLMOD(sparse_xtype) ( /* ---- input ---- */ int to_xtype, /* requested xtype */ /* ---- in/out --- */ cholmod_sparse *A, /* sparse matrix to change */ /* --------------- */ cholmod_common *Common ) { Int ok ; RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; ok = change_complexity (A->nzmax, A->xtype, to_xtype, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, &(A->x), &(A->z), Common) ; if (ok) { A->xtype = to_xtype ; } return (ok) ; } /* ========================================================================== */ /* === cholmod_triplet_xtype ================================================ */ /* ========================================================================== */ /* Change the numeric xtype of a triplet matrix. Supports any type on input * and output (pattern, real, complex, or zomplex). */ int CHOLMOD(triplet_xtype) ( /* ---- input ---- */ int to_xtype, /* requested xtype */ /* ---- in/out --- */ cholmod_triplet *T, /* triplet matrix to change */ /* --------------- */ cholmod_common *Common ) { Int ok ; RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (T, FALSE) ; RETURN_IF_XTYPE_INVALID (T, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; ok = change_complexity (T->nzmax, T->xtype, to_xtype, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, &(T->x), &(T->z), Common) ; if (ok) { T->xtype = to_xtype ; } return (ok) ; } /* ========================================================================== */ /* === cholmod_dense_xtype ================================================= */ /* ========================================================================== */ /* Change the numeric xtype of a dense matrix. Supports real, complex or * zomplex on input and output */ int CHOLMOD(dense_xtype) ( /* ---- input ---- */ int to_xtype, /* requested xtype */ /* ---- in/out --- */ cholmod_dense *X, /* dense matrix to change */ /* --------------- */ cholmod_common *Common ) { Int ok ; RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (X, FALSE) ; RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; ok = change_complexity (X->nzmax, X->xtype, to_xtype, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, &(X->x), &(X->z), Common) ; if (ok) { X->xtype = to_xtype ; } return (ok) ; } /* ========================================================================== */ /* === cholmod_factor_xtype ================================================= */ /* ========================================================================== */ /* Change the numeric xtype of a factor. Supports real, complex or zomplex on * input and output. Supernodal zomplex factors are not supported. */ int CHOLMOD(factor_xtype) ( /* ---- input ---- */ int to_xtype, /* requested xtype */ /* ---- in/out --- */ cholmod_factor *L, /* factor to change */ /* --------------- */ cholmod_common *Common ) { Int ok ; RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; if (L->is_super && (L->xtype == CHOLMOD_ZOMPLEX || to_xtype == CHOLMOD_ZOMPLEX)) { ERROR (CHOLMOD_INVALID, "invalid xtype for supernodal L") ; return (FALSE) ; } ok = change_complexity ((L->is_super ? L->xsize : L->nzmax), L->xtype, to_xtype, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, &(L->x), &(L->z), Common) ; if (ok) { L->xtype = to_xtype ; } return (ok) ; } SuiteSparse/CHOLMOD/Core/cholmod_triplet.c0000644001170100242450000005612410537777446017314 0ustar davisfac/* ========================================================================== */ /* === Core/cholmod_triplet ================================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Core utility routines for the cholmod_triplet object: * * A sparse matrix held in triplet form is the simplest one for a user to * create. It consists of a list of nz entries in arbitrary order, held in * three arrays: i, j, and x, each of length nk. The kth entry is in row i[k], * column j[k], with value x[k]. There may be duplicate values; if A(i,j) * appears more than once, its value is the sum of the entries with those row * and column indices. * * Primary routines: * ----------------- * cholmod_allocate_triplet allocate a triplet matrix * cholmod_free_triplet free a triplet matrix * * Secondary routines: * ------------------- * cholmod_reallocate_triplet reallocate a triplet matrix * cholmod_sparse_to_triplet create a triplet matrix copy of a sparse matrix * cholmod_triplet_to_sparse create a sparse matrix copy of a triplet matrix * cholmod_copy_triplet create a copy of a triplet matrix * * The relationship between an m-by-n cholmod_sparse matrix A and a * cholmod_triplet matrix (i, j, and x) is identical to how they are used in * the MATLAB "sparse" and "find" functions: * * [i j x] = find (A) * [m n] = size (A) * A = sparse (i,j,x,m,n) * * with the exception that the cholmod_sparse matrix may be "unpacked", may * have either sorted or unsorted columns (depending on the option selected), * and may be symmetric with just the upper or lower triangular part stored. * Likewise, the cholmod_triplet matrix may contain just the entries in the * upper or lower triangular part of a symmetric matrix. * * MATLAB sparse matrices are always "packed", always have sorted columns, * and always store both parts of a symmetric matrix. In some cases, MATLAB * behaves like CHOLMOD by ignoring entries in the upper or lower triangular * part of a matrix that is otherwise assumed to be symmetric (such as the * input to chol). In CHOLMOD, that option is a characteristic of the object. * In MATLAB, that option is based on how a matrix is used as the input to * a function. * * The triplet matrix is provided to give the user a simple way of constructing * a sparse matrix. There are very few operations supported for triplet * matrices. The assumption is that they will be converted to cholmod_sparse * matrix form first. * * Adding two triplet matrices simply involves concatenating the contents of * the three arrays (i, j, and x). To permute a triplet matrix, just replace * the row and column indices with their permuted values. For example, if * P is a permutation vector, then P [k] = j means row/column j is the kth * row/column in C=P*A*P'. In MATLAB notation, C=A(p,p). If Pinv is an array * of size n and T is the triplet form of A, then: * * Ti = T->i ; * Tj = T->j ; * for (k = 0 ; k < n ; k++) Pinv [P [k]] = k ; * for (k = 0 ; k < nz ; k++) Ti [k] = Pinv [Ti [k]] ; * for (k = 0 ; k < nz ; k++) Tj [k] = Pinv [Tj [k]] ; * * overwrites T with the triplet form of C=P*A*P'. The conversion * * C = cholmod_triplet_to_sparse (T, 0, &Common) ; * * will then return the matrix C = P*A*P'. * * Note that T->stype > 0 means that entries in the lower triangular part of * T are transposed into the upper triangular part when T is converted to * sparse matrix (cholmod_sparse) form with cholmod_triplet_to_sparse. The * opposite is true for T->stype < 0. * * Since the triplet matrix T is so simple to generate, it's quite easy * to remove entries that you do not want, prior to converting T to the * cholmod_sparse form. So if you include these entries in T, CHOLMOD * assumes that there must be a reason (such as the one above). Thus, * no entry in a triplet matrix is ever ignored. * * Other operations, such as extacting a submatrix, horizontal and vertical * concatenation, multiply a triplet matrix times a dense matrix, are also * simple. Multiplying two triplet matrices is not trivial; the simplest * method is to convert them to cholmod_sparse matrices first. * * Supports all xtypes (pattern, real, complex, and zomplex). */ #include "cholmod_internal.h" #include "cholmod_core.h" /* ========================================================================== */ /* === TEMPLATE ============================================================= */ /* ========================================================================== */ #define PATTERN #include "t_cholmod_triplet.c" #define REAL #include "t_cholmod_triplet.c" #define COMPLEX #include "t_cholmod_triplet.c" #define ZOMPLEX #include "t_cholmod_triplet.c" /* ========================================================================== */ /* === cholmod_allocate_triplet ============================================= */ /* ========================================================================== */ /* allocate space for a triplet matrix * * workspace: none */ cholmod_triplet *CHOLMOD(allocate_triplet) ( /* ---- input ---- */ size_t nrow, /* # of rows of T */ size_t ncol, /* # of columns of T */ size_t nzmax, /* max # of nonzeros of T */ int stype, /* stype of T */ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) { cholmod_triplet *T ; size_t nzmax0 ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; if (xtype < CHOLMOD_PATTERN || xtype > CHOLMOD_ZOMPLEX) { ERROR (CHOLMOD_INVALID, "xtype invalid") ; return (NULL) ; } /* ensure the dimensions do not cause integer overflow */ (void) CHOLMOD(add_size_t) (ncol, 2, &ok) ; if (!ok || nrow > Int_max || ncol > Int_max || nzmax > Int_max) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (NULL) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate header */ /* ---------------------------------------------------------------------- */ T = CHOLMOD(malloc) (sizeof (cholmod_triplet), 1, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } PRINT1 (("cholmod_allocate_triplet %d-by-%d nzmax %d xtype %d\n", nrow, ncol, nzmax, xtype)) ; nzmax = MAX (1, nzmax) ; T->nrow = nrow ; T->ncol = ncol ; T->nzmax = nzmax ; T->nnz = 0 ; T->stype = stype ; T->itype = ITYPE ; T->xtype = xtype ; T->dtype = DTYPE ; T->j = NULL ; T->i = NULL ; T->x = NULL ; T->z = NULL ; /* ---------------------------------------------------------------------- */ /* allocate the matrix itself */ /* ---------------------------------------------------------------------- */ nzmax0 = 0 ; CHOLMOD(realloc_multiple) (nzmax, 2, xtype, &(T->i), &(T->j), &(T->x), &(T->z), &nzmax0, Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_triplet) (&T, Common) ; return (NULL) ; /* out of memory */ } return (T) ; } /* ========================================================================== */ /* === cholmod_free_triplet ================================================= */ /* ========================================================================== */ /* free a triplet matrix * * workspace: none */ int CHOLMOD(free_triplet) ( /* ---- in/out --- */ cholmod_triplet **THandle, /* matrix to deallocate, NULL on output */ /* --------------- */ cholmod_common *Common ) { Int nz ; cholmod_triplet *T ; RETURN_IF_NULL_COMMON (FALSE) ; if (THandle == NULL) { /* nothing to do */ return (TRUE) ; } T = *THandle ; if (T == NULL) { /* nothing to do */ return (TRUE) ; } nz = T->nzmax ; T->j = CHOLMOD(free) (nz, sizeof (Int), T->j, Common) ; T->i = CHOLMOD(free) (nz, sizeof (Int), T->i, Common) ; if (T->xtype == CHOLMOD_REAL) { T->x = CHOLMOD(free) (nz, sizeof (double), T->x, Common) ; } else if (T->xtype == CHOLMOD_COMPLEX) { T->x = CHOLMOD(free) (nz, 2*sizeof (double), T->x, Common) ; } else if (T->xtype == CHOLMOD_ZOMPLEX) { T->x = CHOLMOD(free) (nz, sizeof (double), T->x, Common) ; T->z = CHOLMOD(free) (nz, sizeof (double), T->z, Common) ; } *THandle = CHOLMOD(free) (1, sizeof (cholmod_triplet), (*THandle), Common) ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_reallocate_triplet =========================================== */ /* ========================================================================== */ /* Change the size of T->i, T->j, and T->x, or allocate them if their current * size is zero. T->x is not modified if T->xtype is CHOLMOD_PATTERN. * * workspace: none */ int CHOLMOD(reallocate_triplet) ( /* ---- input ---- */ size_t nznew, /* new # of entries in T */ /* ---- in/out --- */ cholmod_triplet *T, /* triplet matrix to modify */ /* --------------- */ cholmod_common *Common ) { /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (T, FALSE) ; RETURN_IF_XTYPE_INVALID (T, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; Common->status = CHOLMOD_OK ; PRINT1 (("realloc triplet %d to %d, xtype: %d\n", T->nzmax, nznew, T->xtype)) ; /* ---------------------------------------------------------------------- */ /* resize the matrix */ /* ---------------------------------------------------------------------- */ CHOLMOD(realloc_multiple) (MAX (1,nznew), 2, T->xtype, &(T->i), &(T->j), &(T->x), &(T->z), &(T->nzmax), Common) ; return (Common->status == CHOLMOD_OK) ; } /* ========================================================================== */ /* === cholmod_triplet_to_sparse ============================================ */ /* ========================================================================== */ /* Convert a set of triplets into a cholmod_sparse matrix. In MATLAB notation, * for unsymmetric matrices: * * A = sparse (Ti, Tj, Tx, nrow, ncol, nzmax) ; * * For the symmetric upper case: * * A = sparse (min(Ti,Tj), max(Ti,Tj), Tx, nrow, ncol, nzmax) ; * * For the symmetric lower case: * * A = sparse (max(Ti,Tj), min(Ti,Tj), Tx, nrow, ncol, nzmax) ; * * If Tx is NULL, then A->x is not allocated, and only the pattern of A is * computed. A is returned in packed form, and can be of any stype * (upper/lower/unsymmetric). It has enough space to hold the values in T, * or nzmax, whichever is larger. * * workspace: Iwork (max (nrow,ncol)) * allocates a temporary copy of its output matrix. * * The resulting sparse matrix has the same xtype as the input triplet matrix. */ cholmod_sparse *CHOLMOD(triplet_to_sparse) ( /* ---- input ---- */ cholmod_triplet *T, /* matrix to copy */ size_t nzmax, /* allocate at least this much space in output matrix */ /* --------------- */ cholmod_common *Common ) { cholmod_sparse *R, *A = NULL ; Int *Wj, *Rp, *Ri, *Rnz, *Ti, *Tj ; Int i, j, p, k, stype, nrow, ncol, nz, ok ; size_t anz = 0 ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (T, NULL) ; Ti = T->i ; Tj = T->j ; RETURN_IF_NULL (Ti, NULL) ; RETURN_IF_NULL (Tj, NULL) ; RETURN_IF_XTYPE_INVALID (T, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ; stype = SIGN (T->stype) ; if (stype && T->nrow != T->ncol) { /* inputs invalid */ ERROR (CHOLMOD_INVALID, "matrix invalid") ; return (NULL) ; } Common->status = CHOLMOD_OK ; DEBUG (CHOLMOD(dump_triplet) (T, "T", Common)) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nrow = T->nrow ; ncol = T->ncol ; nz = T->nnz ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ CHOLMOD(allocate_work) (0, MAX (nrow, ncol), 0, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } /* ---------------------------------------------------------------------- */ /* allocate temporary matrix R */ /* ---------------------------------------------------------------------- */ R = CHOLMOD(allocate_sparse) (ncol, nrow, nz, FALSE, FALSE, -stype, T->xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } Rp = R->p ; Ri = R->i ; Rnz = R->nz ; /* ---------------------------------------------------------------------- */ /* count the entries in each row of A (also counting duplicates) */ /* ---------------------------------------------------------------------- */ for (i = 0 ; i < nrow ; i++) { Rnz [i] = 0 ; } if (stype > 0) { for (k = 0 ; k < nz ; k++) { i = Ti [k] ; j = Tj [k] ; if (i < 0 || i >= nrow || j < 0 || j >= ncol) { ERROR (CHOLMOD_INVALID, "index out of range") ; break ; } /* A will be symmetric with just the upper triangular part stored. * Create a matrix R that is lower triangular. Entries in the * upper part of R are transposed to the lower part. */ Rnz [MIN (i,j)]++ ; } } else if (stype < 0) { for (k = 0 ; k < nz ; k++) { i = Ti [k] ; j = Tj [k] ; if (i < 0 || i >= nrow || j < 0 || j >= ncol) { ERROR (CHOLMOD_INVALID, "index out of range") ; break ; } /* A will be symmetric with just the lower triangular part stored. * Create a matrix R that is upper triangular. Entries in the * lower part of R are transposed to the upper part. */ Rnz [MAX (i,j)]++ ; } } else { for (k = 0 ; k < nz ; k++) { i = Ti [k] ; j = Tj [k] ; if (i < 0 || i >= nrow || j < 0 || j >= ncol) { ERROR (CHOLMOD_INVALID, "index out of range") ; break ; } /* constructing an unsymmetric matrix */ Rnz [i]++ ; } } if (Common->status < CHOLMOD_OK) { /* triplet matrix is invalid */ CHOLMOD(free_sparse) (&R, Common) ; return (NULL) ; } /* ---------------------------------------------------------------------- */ /* construct the row pointers */ /* ---------------------------------------------------------------------- */ p = 0 ; for (i = 0 ; i < nrow ; i++) { Rp [i] = p ; p += Rnz [i] ; } Rp [nrow] = p ; /* use Wj (i/l/l) as temporary row pointers */ Wj = Common->Iwork ; /* size MAX (nrow,ncol) FUTURE WORK: (i/l/l) */ for (i = 0 ; i < nrow ; i++) { Wj [i] = Rp [i] ; } /* ---------------------------------------------------------------------- */ /* construct triplet matrix, using template routine */ /* ---------------------------------------------------------------------- */ switch (T->xtype) { case CHOLMOD_PATTERN: anz = p_cholmod_triplet_to_sparse (T, R, Common) ; break ; case CHOLMOD_REAL: anz = r_cholmod_triplet_to_sparse (T, R, Common) ; break ; case CHOLMOD_COMPLEX: anz = c_cholmod_triplet_to_sparse (T, R, Common) ; break ; case CHOLMOD_ZOMPLEX: anz = z_cholmod_triplet_to_sparse (T, R, Common) ; break ; } /* ---------------------------------------------------------------------- */ /* A = R' (array transpose, not complex conjugate transpose) */ /* ---------------------------------------------------------------------- */ /* workspace: Iwork (R->nrow), which is A->ncol */ ASSERT (CHOLMOD(dump_sparse) (R, "R", Common) >= 0) ; A = CHOLMOD(allocate_sparse) (nrow, ncol, MAX (anz, nzmax), TRUE, TRUE, stype, T->xtype, Common) ; if (stype) { ok = CHOLMOD(transpose_sym) (R, 1, NULL, A, Common) ; } else { ok = CHOLMOD(transpose_unsym) (R, 1, NULL, NULL, 0, A, Common) ; } CHOLMOD(free_sparse) (&R, Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_sparse) (&A, Common) ; } /* ---------------------------------------------------------------------- */ /* return result */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_sparse) (A, "A = triplet(T) result", Common) >= 0) ; return (A) ; } /* ========================================================================== */ /* === cholmod_sparse_to_triplet ============================================ */ /* ========================================================================== */ /* Converts a sparse column-oriented matrix to triplet form. * The resulting triplet matrix has the same xtype as the sparse matrix. * * workspace: none */ cholmod_triplet *CHOLMOD(sparse_to_triplet) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) { double *Ax, *Az, *Tx, *Tz ; Int *Ap, *Ai, *Ti, *Tj, *Anz ; cholmod_triplet *T ; Int i, xtype, p, pend, k, j, nrow, ncol, nz, stype, packed, up, lo, both ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ; stype = SIGN (A->stype) ; nrow = A->nrow ; ncol = A->ncol ; if (stype && nrow != ncol) { /* inputs invalid */ ERROR (CHOLMOD_INVALID, "matrix invalid") ; return (NULL) ; } Ax = A->x ; Az = A->z ; xtype = A->xtype ; Common->status = CHOLMOD_OK ; ASSERT (CHOLMOD(dump_sparse) (A, "A", Common) >= 0) ; /* ---------------------------------------------------------------------- */ /* allocate triplet matrix */ /* ---------------------------------------------------------------------- */ nz = CHOLMOD(nnz) (A, Common) ; T = CHOLMOD(allocate_triplet) (nrow, ncol, nz, A->stype, A->xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } /* ---------------------------------------------------------------------- */ /* convert to a sparse matrix */ /* ---------------------------------------------------------------------- */ Ap = A->p ; Ai = A->i ; Anz = A->nz ; packed = A->packed ; Ti = T->i ; Tj = T->j ; Tx = T->x ; Tz = T->z ; T->stype = A->stype ; both = (A->stype == 0) ; up = (A->stype > 0) ; lo = (A->stype < 0) ; k = 0 ; for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (both || (up && i <= j) || (lo && i >= j)) { Ti [k] = Ai [p] ; Tj [k] = j ; if (xtype == CHOLMOD_REAL) { Tx [k] = Ax [p] ; } else if (xtype == CHOLMOD_COMPLEX) { Tx [2*k ] = Ax [2*p ] ; Tx [2*k+1] = Ax [2*p+1] ; } else if (xtype == CHOLMOD_ZOMPLEX) { Tx [k] = Ax [p] ; Tz [k] = Az [p] ; } k++ ; ASSERT (k <= nz) ; } } } T->nnz = k ; /* ---------------------------------------------------------------------- */ /* return result */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_triplet) (T, "T", Common)) ; return (T) ; } /* ========================================================================== */ /* === cholmod_copy_triplet ================================================= */ /* ========================================================================== */ /* Create an exact copy of a triplet matrix, except that entries in unused * space are not copied (they might not be initialized, and copying them would * cause program checkers such as purify and valgrind to complain). * The output triplet matrix has the same xtype as the input triplet matrix. */ cholmod_triplet *CHOLMOD(copy_triplet) ( /* ---- input ---- */ cholmod_triplet *T, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) { double *Tx, *Tz, *Cx, *Cz ; Int *Ci, *Cj, *Ti, *Tj ; cholmod_triplet *C ; Int xtype, k, nz ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (T, NULL) ; RETURN_IF_XTYPE_INVALID (T, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ; nz = T->nnz ; Ti = T->i ; Tj = T->j ; Tx = T->x ; Tz = T->z ; xtype = T->xtype ; RETURN_IF_NULL (Ti, NULL) ; RETURN_IF_NULL (Tj, NULL) ; Common->status = CHOLMOD_OK ; DEBUG (CHOLMOD(dump_triplet) (T, "T input", Common)) ; /* ---------------------------------------------------------------------- */ /* allocate copy */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(allocate_triplet) (T->nrow, T->ncol, T->nzmax, T->stype, xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } /* ---------------------------------------------------------------------- */ /* copy the triplet matrix */ /* ---------------------------------------------------------------------- */ Ci = C->i ; Cj = C->j ; Cx = C->x ; Cz = C->z ; C->nnz = nz ; for (k = 0 ; k < nz ; k++) { Ci [k] = Ti [k] ; } for (k = 0 ; k < nz ; k++) { Cj [k] = Tj [k] ; } if (xtype == CHOLMOD_REAL) { for (k = 0 ; k < nz ; k++) { Cx [k] = Tx [k] ; } } else if (xtype == CHOLMOD_COMPLEX) { for (k = 0 ; k < nz ; k++) { Cx [2*k ] = Tx [2*k ] ; Cx [2*k+1] = Tx [2*k+1] ; } } else if (xtype == CHOLMOD_ZOMPLEX) { for (k = 0 ; k < nz ; k++) { Cx [k] = Tx [k] ; Cz [k] = Tz [k] ; } } /* ---------------------------------------------------------------------- */ /* return the result */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_triplet) (C, "C triplet copy", Common)) ; return (C) ; } SuiteSparse/CHOLMOD/Core/cholmod_change_factor.c0000644001170100242450000011343010537777411020376 0ustar davisfac/* ========================================================================== */ /* === Core/cholmod_change_factor =========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Change the numeric/symbolic, LL/LDL, simplicial/super, packed/unpacked, * monotonic/non-monotonic status of a cholmod_factor object. * * There are four basic classes of factor types: * * (1) simplicial symbolic: Consists of two size-n arrays: the fill-reducing * permutation (L->Perm) and the nonzero count for each column of L * (L->ColCount). All other factor types also include this information. * L->ColCount may be exact (obtained from the analysis routines), or * it may be a guess. During factorization, and certainly after update/ * downdate, the columns of L can have a different number of nonzeros. * L->ColCount is used to allocate space. L->ColCount is exact for the * supernodal factorizations. The nonzero pattern of L is not kept. * * (2) simplicial numeric: These represent L in a compressed column form. The * variants of this type are: * * LDL': L is unit diagonal. Row indices in column j are located in * L->i [L->p [j] ... L->p [j] + L->nz [j]], and corresponding numeric * values are in the same locations in L->x. The total number of * entries is the sum of L->nz [j]. The unit diagonal is not stored; * D is stored on the diagonal of L instead. L->p may or may not be * monotonic. The order of storage of the columns in L->i and L->x is * given by a doubly-linked list (L->prev and L->next). L->p is of * size n+1, but only the first n entries are used (it is used if L * is converted to a sparse matrix via cholmod_factor_to_sparse). * * For the complex case, L->x is stored interleaved with real/imag * parts, and is of size 2*lnz*sizeof(double). For the zomplex case, * L->x is of size lnz*sizeof(double) and holds the real part; L->z * is the same size and holds the imaginary part. * * LL': This is identical to the LDL' form, except that the non-unit * diagonal of L is stored as the first entry in each column of L. * * (3) supernodal symbolic: A representation of the nonzero pattern of the * supernodes for a supernodal factorization. There are L->nsuper * supernodes. Columns L->super [k] to L->super [k+1]-1 are in the kth * supernode. The row indices for the kth supernode are in * L->s [L->pi [k] ... L->pi [k+1]-1]. The numerical values are not * allocated (L->x), but when they are they will be located in * L->x [L->px [k] ... L->px [k+1]-1], and the L->px array is defined * in this factor type. * * For the complex case, L->x is stored interleaved with real/imag parts, * and is of size 2*L->xsize*sizeof(double). The zomplex supernodal case * is not supported, since it is not compatible with LAPACK and the BLAS. * * (4) supernodal numeric: Always an LL' factorization. L is non-unit * diagonal. L->x contains the numerical values of the supernodes, as * described above for the supernodal symbolic factor. * For the complex case, L->x is stored interleaved, and is of size * 2*L->xsize*sizeof(double). The zomplex supernodal case is not * supported, since it is not compatible with LAPACK and the BLAS. * * FUTURE WORK: support a supernodal LDL' factor. * * * In all cases, the row indices in each column (L->i for simplicial L and * L->s for supernodal L) are kept sorted from low indices to high indices. * This means the diagonal of L (or D for LDL' factors) is always kept as the * first entry in each column. * * The cholmod_change_factor routine can do almost all possible conversions. * It cannot do the following conversions: * * (1) Simplicial numeric types cannot be converted to a supernodal * symbolic type. This would simultaneously deallocate the * simplicial pattern and numeric values and reallocate uninitialized * space for the supernodal pattern. This isn't useful for the user, * and not needed by CHOLMOD's own routines either. * * (2) Only a symbolic factor (simplicial to supernodal) can be converted * to a supernodal numeric factor. * * Some conversions are meant only to be used internally by other CHOLMOD * routines, and should not be performed by the end user. They allocate space * whose contents are undefined: * * (1) converting from simplicial symbolic to supernodal symbolic. * (2) converting any factor to supernodal numeric. * * workspace: no conversion routine uses workspace in Common. No temporary * workspace is allocated. * * Supports all xtypes, except that there is no supernodal zomplex L. * * The to_xtype parameter is used only when converting from symbolic to numeric * or numeric to symbolic. It cannot be used to convert a numeric xtype (real, * complex, or zomplex) to a different numeric xtype. For that conversion, * use cholmod_factor_xtype instead. */ #include "cholmod_internal.h" #include "cholmod_core.h" static void natural_list (cholmod_factor *L) ; /* ========================================================================== */ /* === TEMPLATE ============================================================= */ /* ========================================================================== */ #define REAL #include "t_cholmod_change_factor.c" #define COMPLEX #include "t_cholmod_change_factor.c" #define ZOMPLEX #include "t_cholmod_change_factor.c" /* ========================================================================== */ /* === L_is_packed ========================================================== */ /* ========================================================================== */ /* Return TRUE if the columns of L are packed, FALSE otherwise. For debugging * only. */ #ifndef NDEBUG static int L_is_packed (cholmod_factor *L, cholmod_common *Common) { Int j ; Int *Lnz = L->nz ; Int *Lp = L->p ; Int n = L->n ; if (L->xtype == CHOLMOD_PATTERN || L->is_super) { return (TRUE) ; } if (Lnz == NULL || Lp == NULL) { return (TRUE) ; } for (j = 0 ; j < n ; j++) { PRINT3 (("j: "ID" Lnz "ID" Lp[j+1] "ID" Lp[j] "ID"\n", j, Lnz [j], Lp [j+1], Lp [j])) ; if (Lnz [j] != (Lp [j+1] - Lp [j])) { PRINT2 (("L is not packed\n")) ; return (FALSE) ; } } return (TRUE) ; } #endif /* ========================================================================== */ /* === natural_list ========================================================= */ /* ========================================================================== */ /* Create a naturally-ordered doubly-linked list of columns. */ static void natural_list (cholmod_factor *L) { Int head, tail, n, j ; Int *Lnext, *Lprev ; Lnext = L->next ; Lprev = L->prev ; ASSERT (Lprev != NULL && Lnext != NULL) ; n = L->n ; head = n+1 ; tail = n ; Lnext [head] = 0 ; Lprev [head] = EMPTY ; Lnext [tail] = EMPTY ; Lprev [tail] = n-1 ; for (j = 0 ; j < n ; j++) { Lnext [j] = j+1 ; Lprev [j] = j-1 ; } Lprev [0] = head ; L->is_monotonic = TRUE ; } /* ========================================================================== */ /* === allocate_simplicial_numeric ========================================== */ /* ========================================================================== */ /* Allocate O(n) arrays for simplicial numeric factorization. Initializes * the link lists only. Does not allocate the L->i, L->x, or L->z arrays. */ static int allocate_simplicial_numeric ( cholmod_factor *L, cholmod_common *Common ) { Int n ; Int *Lp, *Lnz, *Lprev, *Lnext ; size_t n1, n2 ; PRINT1 (("Allocate simplicial\n")) ; ASSERT (L->xtype == CHOLMOD_PATTERN || L->is_super) ; ASSERT (L->p == NULL) ; ASSERT (L->nz == NULL) ; ASSERT (L->prev == NULL) ; ASSERT (L->next == NULL) ; n = L->n ; /* this cannot cause size_t overflow */ n1 = ((size_t) n) + 1 ; n2 = ((size_t) n) + 2 ; Lp = CHOLMOD(malloc) (n1, sizeof (Int), Common) ; Lnz = CHOLMOD(malloc) (n, sizeof (Int), Common) ; Lprev = CHOLMOD(malloc) (n2, sizeof (Int), Common) ; Lnext = CHOLMOD(malloc) (n2, sizeof (Int), Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free) (n1, sizeof (Int), Lp, Common) ; CHOLMOD(free) (n, sizeof (Int), Lnz, Common) ; CHOLMOD(free) (n2, sizeof (Int), Lprev, Common) ; CHOLMOD(free) (n2, sizeof (Int), Lnext, Common) ; PRINT1 (("Allocate simplicial failed\n")) ; return (FALSE) ; /* out of memory */ } /* ============================================== commit the changes to L */ L->p = Lp ; L->nz = Lnz ; L->prev = Lprev ; L->next = Lnext ; /* initialize a doubly linked list for columns in natural order */ natural_list (L) ; PRINT1 (("Allocate simplicial done\n")) ; return (TRUE) ; } /* ========================================================================== */ /* === simplicial_symbolic_to_super_symbolic ================================ */ /* ========================================================================== */ /* Convert a simplicial symbolic factor supernodal symbolic factor. Does not * initialize the new space. */ static int simplicial_symbolic_to_super_symbolic ( cholmod_factor *L, cholmod_common *Common ) { Int nsuper, xsize, ssize ; Int *Lsuper, *Lpi, *Lpx, *Ls ; size_t nsuper1 ; ASSERT (L->xtype == CHOLMOD_PATTERN && !(L->is_super)) ; xsize = L->xsize ; ssize = L->ssize ; nsuper = L->nsuper ; nsuper1 = ((size_t) nsuper) + 1 ; PRINT1 (("simple sym to super sym: ssize "ID" xsize "ID" nsuper "ID"" " status %d\n", ssize, xsize, nsuper, Common->status)) ; /* O(nsuper) arrays, where nsuper <= n */ Lsuper = CHOLMOD(malloc) (nsuper1, sizeof (Int), Common) ; Lpi = CHOLMOD(malloc) (nsuper1, sizeof (Int), Common) ; Lpx = CHOLMOD(malloc) (nsuper1, sizeof (Int), Common) ; /* O(ssize) array, where ssize <= nnz(L), and usually much smaller */ Ls = CHOLMOD(malloc) (ssize, sizeof (Int), Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free) (nsuper1, sizeof (Int), Lsuper, Common) ; CHOLMOD(free) (nsuper1, sizeof (Int), Lpi, Common) ; CHOLMOD(free) (nsuper1, sizeof (Int), Lpx, Common) ; CHOLMOD(free) (ssize, sizeof (Int), Ls, Common) ; return (FALSE) ; /* out of memory */ } /* ============================================== commit the changes to L */ ASSERT (Lsuper != NULL && Lpi != NULL && Lpx != NULL && Ls != NULL) ; L->maxcsize = 0 ; L->maxesize = 0 ; L->super = Lsuper ; L->pi = Lpi ; L->px = Lpx ; L->s = Ls ; Ls [0] = EMPTY ; /* supernodal pattern undefined */ L->is_super = TRUE ; L->is_ll = TRUE ; /* supernodal LDL' not supported */ L->xtype = CHOLMOD_PATTERN ; L->dtype = DTYPE ; L->minor = L->n ; return (TRUE) ; } /* ========================================================================== */ /* === any_to_simplicial_symbolic =========================================== */ /* ========================================================================== */ /* Convert any factor L to a simplicial symbolic factor, leaving only L->Perm * and L->ColCount. Cannot fail. Any of the components of L (except Perm and * ColCount) may already be free'd. */ static void any_to_simplicial_symbolic ( cholmod_factor *L, int to_ll, cholmod_common *Common ) { Int n, lnz, xs, ss, s, e ; size_t n1, n2 ; /* ============================================== commit the changes to L */ n = L->n ; lnz = L->nzmax ; s = L->nsuper + 1 ; xs = (L->is_super) ? ((Int) (L->xsize)) : (lnz) ; e = (L->xtype == CHOLMOD_COMPLEX ? 2 : 1) ; ss = L->ssize ; /* this cannot cause size_t overflow */ n1 = ((size_t) n) + 1 ; n2 = ((size_t) n) + 2 ; /* free all but the symbolic analysis (Perm and ColCount) */ L->p = CHOLMOD(free) (n1, sizeof (Int), L->p, Common) ; L->i = CHOLMOD(free) (lnz, sizeof (Int), L->i, Common) ; L->x = CHOLMOD(free) (xs, e*sizeof (double), L->x, Common) ; L->z = CHOLMOD(free) (lnz, sizeof (double), L->z, Common) ; L->nz = CHOLMOD(free) (n, sizeof (Int), L->nz, Common) ; L->next = CHOLMOD(free) (n2, sizeof (Int), L->next, Common) ; L->prev = CHOLMOD(free) (n2, sizeof (Int), L->prev, Common) ; L->super = CHOLMOD(free) (s, sizeof (Int), L->super, Common) ; L->pi = CHOLMOD(free) (s, sizeof (Int), L->pi, Common) ; L->px = CHOLMOD(free) (s, sizeof (Int), L->px, Common) ; L->s = CHOLMOD(free) (ss, sizeof (Int), L->s, Common) ; L->nzmax = 0 ; L->is_super = FALSE ; L->xtype = CHOLMOD_PATTERN ; L->dtype = DTYPE ; L->minor = n ; L->is_ll = to_ll ; } /* ========================================================================== */ /* === ll_super_to_super_symbolic =========================================== */ /* ========================================================================== */ /* Convert a numerical supernodal L to symbolic supernodal. Cannot fail. */ static void ll_super_to_super_symbolic ( cholmod_factor *L, cholmod_common *Common ) { /* ============================================== commit the changes to L */ /* free all but the supernodal numerical factor */ ASSERT (L->xtype != CHOLMOD_PATTERN && L->is_super && L->is_ll) ; DEBUG (CHOLMOD(dump_factor) (L, "start to super symbolic", Common)) ; L->x = CHOLMOD(free) (L->xsize, (L->xtype == CHOLMOD_COMPLEX ? 2 : 1) * sizeof (double), L->x, Common) ; L->xtype = CHOLMOD_PATTERN ; L->dtype = DTYPE ; L->minor = L->n ; L->is_ll = TRUE ; /* supernodal LDL' not supported */ DEBUG (CHOLMOD(dump_factor) (L, "done to super symbolic", Common)) ; } /* ========================================================================== */ /* === simplicial_symbolic_to_simplicial_numeric ============================ */ /* ========================================================================== */ /* Convert a simplicial symbolic L to a simplicial numeric L; allocate space * for L using L->ColCount from symbolic analysis, and set L to identity. * * If packed < 0, then this routine is creating a copy of another factor * (via cholmod_copy_factor). In this case, the space is not initialized. */ static void simplicial_symbolic_to_simplicial_numeric ( cholmod_factor *L, int to_ll, int packed, int to_xtype, cholmod_common *Common ) { double grow0, grow1, xlen, xlnz ; double *Lx, *Lz ; Int *Li, *Lp, *Lnz, *ColCount ; Int n, grow, grow2, p, j, lnz, len, ok, e ; ASSERT (L->xtype == CHOLMOD_PATTERN && !(L->is_super)) ; if (!allocate_simplicial_numeric (L, Common)) { PRINT1 (("out of memory, allocate simplicial numeric\n")) ; return ; /* out of memory */ } ASSERT (L->ColCount != NULL && L->nz != NULL && L->p != NULL) ; ASSERT (L->x == NULL && L->z == NULL && L->i == NULL) ; ColCount = L->ColCount ; Lnz = L->nz ; Lp = L->p ; ok = TRUE ; n = L->n ; if (packed < 0) { /* ------------------------------------------------------------------ */ /* used by cholmod_copy_factor to allocate a copy of a factor object */ /* ------------------------------------------------------------------ */ lnz = L->nzmax ; L->nzmax = 0 ; } else if (packed) { /* ------------------------------------------------------------------ */ /* LDL' or LL' packed */ /* ------------------------------------------------------------------ */ PRINT1 (("convert to packed LL' or LDL'\n")) ; lnz = 0 ; for (j = 0 ; ok && j < n ; j++) { /* ensure len is in the range 1 to n-j */ len = ColCount [j] ; len = MAX (1, len) ; len = MIN (len, n-j) ; lnz += len ; ok = (lnz >= 0) ; } for (j = 0 ; j <= n ; j++) { Lp [j] = j ; } for (j = 0 ; j < n ; j++) { Lnz [j] = 1 ; } } else { /* ------------------------------------------------------------------ */ /* LDL' unpacked */ /* ------------------------------------------------------------------ */ PRINT1 (("convert to unpacked\n")) ; /* compute new lnzmax */ /* if any parameter is NaN, grow is false */ grow0 = Common->grow0 ; grow1 = Common->grow1 ; grow2 = Common->grow2 ; grow0 = IS_NAN (grow0) ? 1 : grow0 ; grow1 = IS_NAN (grow1) ? 1 : grow1 ; /* fl.pt. compare, but no NaN's: */ grow = (grow0 >= 1.0) && (grow1 >= 1.0) && (grow2 > 0) ; PRINT1 (("init, grow1 %g grow2 "ID"\n", grow1, grow2)) ; /* initialize Lp and Lnz for each column */ lnz = 0 ; for (j = 0 ; ok && j < n ; j++) { Lp [j] = lnz ; Lnz [j] = 1 ; /* ensure len is in the range 1 to n-j */ len = ColCount [j] ; len = MAX (1, len) ; len = MIN (len, n-j) ; /* compute len in double to avoid integer overflow */ PRINT1 (("ColCount ["ID"] = "ID"\n", j, len)) ; if (grow) { xlen = (double) len ; xlen = grow1 * xlen + grow2 ; xlen = MIN (xlen, n-j) ; len = (Int) xlen ; } ASSERT (len >= 1 && len <= n-j) ; lnz += len ; ok = (lnz >= 0) ; } if (ok) { Lp [n] = lnz ; if (grow) { /* add extra space */ xlnz = (double) lnz ; xlnz *= grow0 ; xlnz = MIN (xlnz, Size_max) ; xlnz = MIN (xlnz, ((double) n * (double) n + (double) n) / 2) ; lnz = (Int) xlnz ; } } } lnz = MAX (1, lnz) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; } /* allocate L->i, L->x, and L->z */ PRINT1 (("resizing from zero size to lnz "ID"\n", lnz)) ; ASSERT (L->nzmax == 0) ; e = (to_xtype == CHOLMOD_COMPLEX ? 2 : 1) ; if (!ok || !CHOLMOD(realloc_multiple) (lnz, 1, to_xtype, &(L->i), NULL, &(L->x), &(L->z), &(L->nzmax), Common)) { L->p = CHOLMOD(free) (n+1, sizeof (Int), L->p, Common) ; L->nz = CHOLMOD(free) (n, sizeof (Int), L->nz, Common) ; L->prev = CHOLMOD(free) (n+2, sizeof (Int), L->prev, Common) ; L->next = CHOLMOD(free) (n+2, sizeof (Int), L->next, Common) ; L->i = CHOLMOD(free) (lnz, sizeof (Int), L->i, Common) ; L->x = CHOLMOD(free) (lnz, e*sizeof (double), L->x, Common) ; L->z = CHOLMOD(free) (lnz, sizeof (double), L->z, Common) ; PRINT1 (("cannot realloc simplicial numeric\n")) ; return ; /* out of memory */ } /* ============================================== commit the changes to L */ /* initialize L to be the identity matrix */ L->xtype = to_xtype ; L->dtype = DTYPE ; L->minor = n ; Li = L->i ; Lx = L->x ; Lz = L->z ; #if 0 if (lnz == 1) { /* the user won't expect to access this entry, but some CHOLMOD * routines may. Set it to zero so that valgrind doesn't complain. */ switch (to_xtype) { case CHOLMOD_REAL: Lx [0] = 0 ; break ; case CHOLMOD_COMPLEX: Lx [0] = 0 ; Lx [1] = 0 ; break ; case CHOLMOD_ZOMPLEX: Lx [0] = 0 ; Lz [0] = 0 ; break ; } } #endif if (packed >= 0) { /* create the unit diagonal for either the LL' or LDL' case */ switch (L->xtype) { case CHOLMOD_REAL: for (j = 0 ; j < n ; j++) { ASSERT (Lp [j] < Lp [j+1]) ; p = Lp [j] ; Li [p] = j ; Lx [p] = 1 ; } break ; case CHOLMOD_COMPLEX: for (j = 0 ; j < n ; j++) { ASSERT (Lp [j] < Lp [j+1]) ; p = Lp [j] ; Li [p] = j ; Lx [2*p ] = 1 ; Lx [2*p+1] = 0 ; } break ; case CHOLMOD_ZOMPLEX: for (j = 0 ; j < n ; j++) { ASSERT (Lp [j] < Lp [j+1]) ; p = Lp [j] ; Li [p] = j ; Lx [p] = 1 ; Lz [p] = 0 ; } break ; } } L->is_ll = to_ll ; PRINT1 (("done convert simplicial symbolic to numeric\n")) ; } /* ========================================================================== */ /* === change_simplicial_numeric ============================================ */ /* ========================================================================== */ /* Change LL' to LDL', LDL' to LL', or leave as-is. * * If to_packed is TRUE, then the columns of L are packed and made monotonic * (to_monotonic is ignored; it is implicitly TRUE). * * If to_monotonic is TRUE but to_packed is FALSE, the columns of L are made * monotonic but not packed. * * If both to_packed and to_monotonic are FALSE, then the columns of L are * left as-is, and the conversion is done in place. * * If L is already monotonic, or if it is to be left non-monotonic, then this * conversion always succeeds. * * When converting an LDL' to LL' factorization, any column with a negative * or zero diagonal entry is not modified so that conversion back to LDL' will * succeed. This can result in a matrix L with a negative entry on the diagonal * If the kth entry on the diagonal of D is negative, it and the kth column of * L are left unchanged. A subsequent conversion back to an LDL' form will also * leave the column unchanged, so the correct LDL' factorization will be * restored. L->minor is set to the smallest k for which D (k,k) is negative. */ static void change_simplicial_numeric ( cholmod_factor *L, int to_ll, int to_packed, int to_monotonic, cholmod_common *Common ) { double grow0, grow1, xlen, xlnz ; void *newLi, *newLx, *newLz ; double *Lx, *Lz ; Int *Lp, *Li, *Lnz ; Int make_monotonic, grow2, n, j, lnz, len, grow, ok, make_ll, make_ldl ; size_t nzmax0 ; PRINT1 (("\n===Change simplicial numeric: %d %d %d\n", to_ll, to_packed, to_monotonic)) ; DEBUG (CHOLMOD(dump_factor) (L, "change simplicial numeric", Common)) ; ASSERT (L->xtype != CHOLMOD_PATTERN && !(L->is_super)) ; make_monotonic = ((to_packed || to_monotonic) && !(L->is_monotonic)) ; make_ll = (to_ll && !(L->is_ll)) ; make_ldl = (!to_ll && L->is_ll) ; n = L->n ; Lp = L->p ; Li = L->i ; Lx = L->x ; Lz = L->z ; Lnz = L->nz ; grow = FALSE ; grow0 = Common->grow0 ; grow1 = Common->grow1 ; grow2 = Common->grow2 ; grow0 = IS_NAN (grow0) ? 1 : grow0 ; grow1 = IS_NAN (grow1) ? 1 : grow1 ; ok = TRUE ; newLi = NULL ; newLx = NULL ; newLz = NULL ; lnz = 0 ; if (make_monotonic) { /* ------------------------------------------------------------------ */ /* Columns out of order, but will be reordered and optionally packed. */ /* ------------------------------------------------------------------ */ PRINT1 (("L is non-monotonic\n")) ; /* compute new L->nzmax */ if (!to_packed) { /* if any parameter is NaN, grow is false */ /* fl.pt. comparisons below are false if any parameter is NaN */ grow = (grow0 >= 1.0) && (grow1 >= 1.0) && (grow2 > 0) ; } for (j = 0 ; ok && j < n ; j++) { len = Lnz [j] ; ASSERT (len >= 1 && len <= n-j) ; /* compute len in double to avoid integer overflow */ if (grow) { xlen = (double) len ; xlen = grow1 * xlen + grow2 ; xlen = MIN (xlen, n-j) ; len = (Int) xlen ; } ASSERT (len >= Lnz [j] && len <= n-j) ; PRINT2 (("j: "ID" Lnz[j] "ID" len "ID" p "ID"\n", j, Lnz [j], len, lnz)) ; lnz += len ; ok = (lnz >= 0) ; } if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return ; } if (grow) { xlnz = (double) lnz ; xlnz *= grow0 ; xlnz = MIN (xlnz, Size_max) ; xlnz = MIN (xlnz, ((double) n * (double) n + (double) n) / 2) ; lnz = (Int) xlnz ; } lnz = MAX (1, lnz) ; PRINT1 (("final lnz "ID"\n", lnz)) ; nzmax0 = 0 ; CHOLMOD(realloc_multiple) (lnz, 1, L->xtype, &newLi, NULL, &newLx, &newLz, &nzmax0, Common) ; if (Common->status < CHOLMOD_OK) { return ; /* out of memory */ } } /* ============================================== commit the changes to L */ /* ---------------------------------------------------------------------- */ /* convert the simplicial L, using template routine */ /* ---------------------------------------------------------------------- */ switch (L->xtype) { case CHOLMOD_REAL: r_change_simplicial_numeric (L, to_ll, to_packed, newLi, newLx, newLz, lnz, grow, grow1, grow2, make_ll, make_monotonic, make_ldl, Common) ; break ; case CHOLMOD_COMPLEX: c_change_simplicial_numeric (L, to_ll, to_packed, newLi, newLx, newLz, lnz, grow, grow1, grow2, make_ll, make_monotonic, make_ldl, Common) ; break ; case CHOLMOD_ZOMPLEX: z_change_simplicial_numeric (L, to_ll, to_packed, newLi, newLx, newLz, lnz, grow, grow1, grow2, make_ll, make_monotonic, make_ldl, Common) ; break ; } DEBUG (CHOLMOD(dump_factor) (L, "L simplicial changed", Common)) ; } /* ========================================================================== */ /* === ll_super_to_simplicial_numeric ======================================= */ /* ========================================================================== */ /* Convert a supernodal numeric factorization to any simplicial numeric one. * Leaves L->xtype unchanged (real or complex, not zomplex since there is * no supernodal zomplex L). */ static void ll_super_to_simplicial_numeric ( cholmod_factor *L, int to_packed, int to_ll, cholmod_common *Common ) { Int *Ls, *Lpi, *Lpx, *Super, *Li ; Int n, lnz, s, nsuper, psi, psend, nsrow, nscol, k1, k2, erows ; DEBUG (CHOLMOD(dump_factor) (L, "start LL super to simplicial", Common)) ; PRINT1 (("super -> simplicial (%d %d)\n", to_packed, to_ll)) ; ASSERT (L->xtype != CHOLMOD_PATTERN && L->is_ll && L->is_super) ; ASSERT (L->x != NULL && L->i == NULL) ; n = L->n ; nsuper = L->nsuper ; Lpi = L->pi ; Lpx = L->px ; Ls = L->s ; Super = L->super ; /* Int overflow cannot occur since supernodal L already exists */ if (to_packed) { /* count the number of nonzeros in L. Each supernode is of the form * * l . . . For this example, nscol = 4 (# columns). nsrow = 9. * l l . . The "." entries are allocated in the supernodal * l l l . factor, but not used. They are not copied to the * l l l l simplicial factor. Some "l" and "e" entries may be * e e e e numerically zero and even symbolically zero if a * e e e e tight simplicial factorization or resymbol were * e e e e done, because of numerical cancellation and relaxed * e e e e supernode amalgamation, respectively. * e e e e */ lnz = 0 ; for (s = 0 ; s < nsuper ; s++) { k1 = Super [s] ; k2 = Super [s+1] ; psi = Lpi [s] ; psend = Lpi [s+1] ; nsrow = psend - psi ; nscol = k2 - k1 ; ASSERT (nsrow >= nscol) ; erows = nsrow - nscol ; /* lower triangular part, including the diagonal, * counting the "l" terms in the figure above. */ lnz += nscol * (nscol+1) / 2 ; /* rectangular part, below the diagonal block (the "e" terms) */ lnz += nscol * erows ; } ASSERT (lnz <= (Int) (L->xsize)) ; } else { /* Li will be the same size as Lx */ lnz = L->xsize ; } ASSERT (lnz >= 0) ; PRINT1 (("simplicial lnz = "ID" to_packed: %d to_ll: %d L->xsize %g\n", lnz, to_ll, to_packed, (double) L->xsize)) ; Li = CHOLMOD(malloc) (lnz, sizeof (Int), Common) ; if (Common->status < CHOLMOD_OK) { return ; /* out of memory */ } if (!allocate_simplicial_numeric (L, Common)) { CHOLMOD(free) (lnz, sizeof (Int), Li, Common) ; return ; /* out of memory */ } /* ============================================== commit the changes to L */ L->i = Li ; L->nzmax = lnz ; /* ---------------------------------------------------------------------- */ /* convert the supernodal L, using template routine */ /* ---------------------------------------------------------------------- */ switch (L->xtype) { case CHOLMOD_REAL: r_ll_super_to_simplicial_numeric (L, to_packed, to_ll, Common) ; break ; case CHOLMOD_COMPLEX: c_ll_super_to_simplicial_numeric (L, to_packed, to_ll, Common) ; break ; } /* ---------------------------------------------------------------------- */ /* free unused parts of L */ /* ---------------------------------------------------------------------- */ L->super = CHOLMOD(free) (nsuper+1, sizeof (Int), L->super, Common) ; L->pi = CHOLMOD(free) (nsuper+1, sizeof (Int), L->pi, Common) ; L->px = CHOLMOD(free) (nsuper+1, sizeof (Int), L->px, Common) ; L->s = CHOLMOD(free) (L->ssize, sizeof (Int), L->s, Common) ; L->ssize = 0 ; L->xsize = 0 ; L->nsuper = 0 ; L->maxesize = 0 ; L->maxcsize = 0 ; L->is_super = FALSE ; DEBUG (CHOLMOD(dump_factor) (L, "done LL super to simplicial", Common)) ; } /* ========================================================================== */ /* === super_symbolic_to_ll_super =========================================== */ /* ========================================================================== */ /* Convert a supernodal symbolic factorization to a supernodal numeric * factorization by allocating L->x. Contents of L->x are undefined. */ static int super_symbolic_to_ll_super ( int to_xtype, cholmod_factor *L, cholmod_common *Common ) { double *Lx ; Int wentry = (to_xtype == CHOLMOD_REAL) ? 1 : 2 ; PRINT1 (("convert super sym to num\n")) ; ASSERT (L->xtype == CHOLMOD_PATTERN && L->is_super) ; Lx = CHOLMOD(malloc) (L->xsize, wentry * sizeof (double), Common) ; PRINT1 (("xsize %g\n", (double) L->xsize)) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; /* out of memory */ } /* ============================================== commit the changes to L */ if (L->xsize == 1) { /* the caller won't expect to access this entry, but some CHOLMOD * routines may. Set it to zero so that valgrind doesn't complain. */ switch (to_xtype) { case CHOLMOD_REAL: Lx [0] = 0 ; break ; case CHOLMOD_COMPLEX: Lx [0] = 0 ; Lx [1] = 0 ; break ; } } L->x = Lx ; L->xtype = to_xtype ; L->dtype = DTYPE ; L->minor = L->n ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_change_factor ================================================ */ /* ========================================================================== */ /* Convert a factor L. Some conversions simply allocate uninitialized space * that meant to be filled later. * * If the conversion fails, the factor is left in its original form, with one * exception. Converting a supernodal symbolic factor to a simplicial numeric * one (with L=D=I) may leave the factor in simplicial symbolic form. * * Memory allocated for each conversion is listed below. */ int CHOLMOD(change_factor) ( /* ---- input ---- */ int to_xtype, /* convert to CHOLMOD_PATTERN, _REAL, _COMPLEX, or * _ZOMPLEX */ int to_ll, /* TRUE: convert to LL', FALSE: LDL' */ int to_super, /* TRUE: convert to supernodal, FALSE: simplicial */ int to_packed, /* TRUE: pack simplicial columns, FALSE: do not pack */ int to_monotonic, /* TRUE: put simplicial columns in order, FALSE: not */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) { /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; if (to_xtype < CHOLMOD_PATTERN || to_xtype > CHOLMOD_ZOMPLEX) { ERROR (CHOLMOD_INVALID, "xtype invalid") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; PRINT1 (("-----convert from (%d,%d,%d,%d,%d) to (%d,%d,%d,%d,%d)\n", L->xtype, L->is_ll, L->is_super, L_is_packed (L, Common), L->is_monotonic, to_xtype, to_ll, to_super, to_packed, to_monotonic)) ; /* ensure all parameters are TRUE/FALSE */ to_ll = BOOLEAN (to_ll) ; to_super = BOOLEAN (to_super) ; ASSERT (BOOLEAN (L->is_ll) == L->is_ll) ; ASSERT (BOOLEAN (L->is_super) == L->is_super) ; if (to_super && to_xtype == CHOLMOD_ZOMPLEX) { ERROR (CHOLMOD_INVALID, "supernodal zomplex L not supported") ; return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* convert */ /* ---------------------------------------------------------------------- */ if (to_xtype == CHOLMOD_PATTERN) { /* ------------------------------------------------------------------ */ /* convert to symbolic */ /* ------------------------------------------------------------------ */ if (!to_super) { /* -------------------------------------------------------------- */ /* convert any factor into a simplicial symbolic factor */ /* -------------------------------------------------------------- */ any_to_simplicial_symbolic (L, to_ll, Common) ; /* cannot fail */ } else { /* -------------------------------------------------------------- */ /* convert to a supernodal symbolic factor */ /* -------------------------------------------------------------- */ if (L->xtype != CHOLMOD_PATTERN && L->is_super) { /* convert from supernodal numeric to supernodal symbolic. * this preserves symbolic pattern of L, discards numeric * values */ ll_super_to_super_symbolic (L, Common) ; /* cannot fail */ } else if (L->xtype == CHOLMOD_PATTERN && !(L->is_super)) { /* convert from simplicial symbolic to supernodal symbolic. * contents of supernodal pattern are uninitialized. Not meant * for the end user. */ simplicial_symbolic_to_super_symbolic (L, Common) ; } else { /* cannot convert from simplicial numeric to supernodal * symbolic */ ERROR (CHOLMOD_INVALID, "cannot convert L to supernodal symbolic") ; } } } else { /* ------------------------------------------------------------------ */ /* convert to numeric */ /* ------------------------------------------------------------------ */ if (to_super) { /* -------------------------------------------------------------- */ /* convert to supernodal numeric factor */ /* -------------------------------------------------------------- */ if (L->xtype == CHOLMOD_PATTERN) { if (L->is_super) { /* Convert supernodal symbolic to supernodal numeric. * Contents of supernodal numeric values are uninitialized. * This is used by cholmod_super_numeric. Not meant for * the end user. */ super_symbolic_to_ll_super (to_xtype, L, Common) ; } else { /* Convert simplicial symbolic to supernodal numeric. * Contents not defined. This is used by * Core/cholmod_copy_factor only. Not meant for the end * user. */ if (!simplicial_symbolic_to_super_symbolic (L, Common)) { /* failure, convert back to simplicial symbolic */ any_to_simplicial_symbolic (L, to_ll, Common) ; } else { /* conversion to super symbolic OK, allocate numeric * part */ super_symbolic_to_ll_super (to_xtype, L, Common) ; } } } else { /* nothing to do if L is already in supernodal numeric form */ if (!(L->is_super)) { ERROR (CHOLMOD_INVALID, "cannot convert simplicial L to supernodal") ; } /* FUTURE WORK: convert to/from supernodal LL' and LDL' */ } } else { /* -------------------------------------------------------------- */ /* convert any factor to simplicial numeric */ /* -------------------------------------------------------------- */ if (L->xtype == CHOLMOD_PATTERN && !(L->is_super)) { /* ---------------------------------------------------------- */ /* convert simplicial symbolic to simplicial numeric (L=I,D=I)*/ /* ---------------------------------------------------------- */ simplicial_symbolic_to_simplicial_numeric (L, to_ll, to_packed, to_xtype, Common) ; } else if (L->xtype != CHOLMOD_PATTERN && L->is_super) { /* ---------------------------------------------------------- */ /* convert a supernodal LL' to simplicial numeric */ /* ---------------------------------------------------------- */ ll_super_to_simplicial_numeric (L, to_packed, to_ll, Common) ; } else if (L->xtype == CHOLMOD_PATTERN && L->is_super) { /* ---------------------------------------------------------- */ /* convert a supernodal symbolic to simplicial numeric (L=D=I)*/ /* ---------------------------------------------------------- */ any_to_simplicial_symbolic (L, to_ll, Common) ; /* if the following fails, it leaves the factor in simplicial * symbolic form */ simplicial_symbolic_to_simplicial_numeric (L, to_ll, to_packed, to_xtype, Common) ; } else { /* ---------------------------------------------------------- */ /* change a simplicial numeric factor */ /* ---------------------------------------------------------- */ /* change LL' to LDL', LDL' to LL', or leave as-is. pack the * columns of L, or leave as-is. Ensure the columns are * monotonic, or leave as-is. */ change_simplicial_numeric (L, to_ll, to_packed, to_monotonic, Common) ; } } } /* ---------------------------------------------------------------------- */ /* return result */ /* ---------------------------------------------------------------------- */ return (Common->status >= CHOLMOD_OK) ; } SuiteSparse/CHOLMOD/Core/cholmod_transpose.c0000644001170100242450000007541210616661511017627 0ustar davisfac/* ========================================================================== */ /* === Core/cholmod_transpose =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Core utility routines for the cholmod_sparse object to * compute the transpose or permuted transpose of a matrix: * * Primary routines: * ----------------- * cholmod_transpose transpose sparse matrix * cholmod_ptranspose transpose and permute sparse matrix * cholmod_sort sort row indices in each column of sparse matrix * * Secondary routines: * ------------------- * cholmod_transpose_unsym transpose unsymmetric sparse matrix * cholmod_transpose_sym transpose symmetric sparse matrix * * All xtypes (pattern, real, complex, and zomplex) are supported. * * --------------------------------------- * Unsymmetric case: A->stype is zero. * --------------------------------------- * * Computes F = A', F = A (:,f)' or F = A (p,f)', except that the indexing by * f does not work the same as the MATLAB notation (see below). A->stype * is zero, which denotes that both the upper and lower triangular parts of * A are present (and used). A may in fact be symmetric in pattern and/or * value; A->stype just denotes which part of A are stored. A may be * rectangular. * * p is a permutation of 0:m-1, and f is a subset of 0:n-1, where A is m-by-n. * There can be no duplicate entries in p or f. * * The set f is held in fset and fsize. * fset = NULL means ":" in MATLAB. fsize is ignored. * fset != NULL means f = fset [0..fsize-1]. * fset != NULL and fsize = 0 means f is the empty set. * * Columns not in the set f are considered to be zero. That is, * if A is 5-by-10 then F = A (:,[3 4])' is not 2-by-5, but 10-by-5, and rows * 3 and 4 of F are equal to columns 3 and 4 of A (the other rows of F are * zero). More precisely, in MATLAB notation: * * [m n] = size (A) ; * F = A ; * notf = ones (1,n) ; * notf (f) = 0 ; * F (:, find (notf)) = 0 * F = F' * * If you want the MATLAB equivalent F=A(p,f) operation, use cholmod_submatrix * instead (which does not compute the transpose). * * F->nzmax must be large enough to hold the matrix F. It is not modified. * If F->nz is present then F->nz [j] = # of entries in column j of F. * * A can be sorted or unsorted, with packed or unpacked columns. * * If f is present and not sorted in ascending order, then F is unsorted * (that is, it may contain columns whose row indices do not appear in * ascending order). Otherwise, F is sorted (the row indices in each * column of F appear in strictly ascending order). * * F is returned in packed or unpacked form, depending on F->packed on input. * If F->packed is false, then F is returned in unpacked form (F->nz must be * present). Each row i of F is large enough to hold all the entries in row i * of A, even if f is provided. That is, F->i and * F->x [F->p [i] .. F->p [i] + F->nz [i] - 1] contain all entries in A (i,f), * but F->p [i+1] - F->p [i] is equal to the number of nonzeros in A (i,:), * not just A (i,f). * * The cholmod_transpose_unsym routine is the only operation in CHOLMOD that * can produce an unpacked matrix. * * --------------------------------------- * Symmetric case: A->stype is nonzero. * --------------------------------------- * * Computes F = A' or F = A(p,p)', the transpose or permuted transpose, where * A->stype is nonzero. * * If A->stype > 0, then A is a symmetric matrix where just the upper part * of the matrix is stored. Entries in the lower triangular part may be * present, but are ignored. A must be square. If F=A', then F is returned * sorted; otherwise F is unsorted for the F=A(p,p)' case. * * There can be no duplicate entries in p. * The fset and fsize parameters are not used. * * Three kinds of transposes are available, depending on the "values" parameter: * 0: do not transpose the numerical values; create a CHOLMOD_PATTERN matrix * 1: array transpose * 2: complex conjugate transpose (same as 2 if input is real or pattern) * * ----------------------------------------------------------------------------- * * For cholmod_transpose_unsym and cholmod_transpose_sym, the output matrix * F must already be pre-allocated by the caller, with the correct dimensions. * If F is not valid or has the wrong dimensions, it is not modified. * Otherwise, if F is too small, the transpose is not computed; the contents * of F->p contain the column pointers of the resulting matrix, where * F->p [F->ncol] > F->nzmax. In this case, the remaining contents of F are * not modified. F can still be properly free'd with cholmod_free_sparse. */ #include "cholmod_internal.h" #include "cholmod_core.h" /* ========================================================================== */ /* === TEMPLATE ============================================================= */ /* ========================================================================== */ #define PATTERN #include "t_cholmod_transpose.c" #define REAL #include "t_cholmod_transpose.c" #define COMPLEX #include "t_cholmod_transpose.c" #define COMPLEX #define NCONJUGATE #include "t_cholmod_transpose.c" #define ZOMPLEX #include "t_cholmod_transpose.c" #define ZOMPLEX #define NCONJUGATE #include "t_cholmod_transpose.c" /* ========================================================================== */ /* === cholmod_transpose_unsym ============================================== */ /* ========================================================================== */ /* Compute F = A', A (:,f)', or A (p,f)', where A is unsymmetric and F is * already allocated. See cholmod_transpose for a simpler routine. * * workspace: * Iwork (MAX (nrow,ncol)) if fset is present * Iwork (nrow) if fset is NULL * * The xtype of A and F must match, unless values is zero or F->xtype is * CHOLMOD_PATTERN (in which case only the pattern of A is transpose into F). */ int CHOLMOD(transpose_unsym) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to transpose */ int values, /* 2: complex conj. transpose, 1: array transpose, 0: do not transpose the numerical values */ Int *Perm, /* size nrow, if present (can be NULL) */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- output --- */ cholmod_sparse *F, /* F = A', A(:,f)', or A(p,f)' */ /* --------------- */ cholmod_common *Common ) { Int *Fp, *Fnz, *Ap, *Ai, *Anz, *Wi ; Int nrow, ncol, permute, use_fset, Apacked, Fpacked, p, pend, i, j, k, Fsorted, nf, jj, jlast ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (F, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (F, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; if (A->nrow != F->ncol || A->ncol != F->nrow) { ERROR (CHOLMOD_INVALID, "F has the wrong dimensions") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nf = fsize ; use_fset = (fset != NULL) ; nrow = A->nrow ; ncol = A->ncol ; Ap = A->p ; /* size A->ncol+1, column pointers of A */ Ai = A->i ; /* size nz = Ap [A->ncol], row indices of A */ Anz = A->nz ; Apacked = A->packed ; ASSERT (IMPLIES (!Apacked, Anz != NULL)) ; permute = (Perm != NULL) ; Fp = F->p ; /* size A->nrow+1, row pointers of F */ Fnz = F->nz ; Fpacked = F->packed ; ASSERT (IMPLIES (!Fpacked, Fnz != NULL)) ; nf = (use_fset) ? nf : ncol ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = nrow + ((fset != NULL) ? ncol : 0) */ s = CHOLMOD(add_size_t) (nrow, ((fset != NULL) ? ncol : 0), &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (0, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; /* out of memory */ } Wi = Common->Iwork ; /* size nrow (i/l/l) */ /* ---------------------------------------------------------------------- */ /* check Perm and fset */ /* ---------------------------------------------------------------------- */ if (permute) { for (i = 0 ; i < nrow ; i++) { Wi [i] = 1 ; } for (k = 0 ; k < nrow ; k++) { i = Perm [k] ; if (i < 0 || i > nrow || Wi [i] == 0) { ERROR (CHOLMOD_INVALID, "invalid permutation") ; return (FALSE) ; } Wi [i] = 0 ; } } if (use_fset) { for (j = 0 ; j < ncol ; j++) { Wi [j] = 1 ; } for (k = 0 ; k < nf ; k++) { j = fset [k] ; if (j < 0 || j > ncol || Wi [j] == 0) { ERROR (CHOLMOD_INVALID, "invalid fset") ; return (FALSE) ; } Wi [j] = 0 ; } } /* Perm and fset are now valid */ ASSERT (CHOLMOD(dump_perm) (Perm, nrow, nrow, "Perm", Common)) ; ASSERT (CHOLMOD(dump_perm) (fset, nf, ncol, "fset", Common)) ; /* ---------------------------------------------------------------------- */ /* count the entries in each row of A or A(:,f) */ /* ---------------------------------------------------------------------- */ for (i = 0 ; i < nrow ; i++) { Wi [i] = 0 ; } jlast = EMPTY ; Fsorted = TRUE ; if (use_fset) { /* count entries in each row of A(:,f) */ for (jj = 0 ; jj < nf ; jj++) { j = fset [jj] ; if (j <= jlast) { Fsorted = FALSE ; } p = Ap [j] ; pend = (Apacked) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { Wi [Ai [p]]++ ; } jlast = j ; } /* save the nz counts if F is unpacked, and recount all of A */ if (!Fpacked) { if (permute) { for (i = 0 ; i < nrow ; i++) { Fnz [i] = Wi [Perm [i]] ; } } else { for (i = 0 ; i < nrow ; i++) { Fnz [i] = Wi [i] ; } } for (i = 0 ; i < nrow ; i++) { Wi [i] = 0 ; } /* count entries in each row of A */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (Apacked) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { Wi [Ai [p]]++ ; } } } } else { /* count entries in each row of A */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (Apacked) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { Wi [Ai [p]]++ ; } } /* save the nz counts if F is unpacked */ if (!Fpacked) { if (permute) { for (i = 0 ; i < nrow ; i++) { Fnz [i] = Wi [Perm [i]] ; } } else { for (i = 0 ; i < nrow ; i++) { Fnz [i] = Wi [i] ; } } } } /* ---------------------------------------------------------------------- */ /* compute the row pointers */ /* ---------------------------------------------------------------------- */ p = 0 ; if (permute) { for (i = 0 ; i < nrow ; i++) { Fp [i] = p ; p += Wi [Perm [i]] ; } for (i = 0 ; i < nrow ; i++) { Wi [Perm [i]] = Fp [i] ; } } else { for (i = 0 ; i < nrow ; i++) { Fp [i] = p ; p += Wi [i] ; } for (i = 0 ; i < nrow ; i++) { Wi [i] = Fp [i] ; } } Fp [nrow] = p ; if (p > (Int) (F->nzmax)) { ERROR (CHOLMOD_INVALID, "F is too small") ; return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* transpose matrix, using template routine */ /* ---------------------------------------------------------------------- */ ok = FALSE ; if (values == 0 || F->xtype == CHOLMOD_PATTERN) { ok = p_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ; } else if (F->xtype == CHOLMOD_REAL) { ok = r_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ; } else if (F->xtype == CHOLMOD_COMPLEX) { if (values == 1) { /* array transpose */ ok = ct_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ; } else { /* complex conjugate transpose */ ok = c_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ; } } else if (F->xtype == CHOLMOD_ZOMPLEX) { if (values == 1) { /* array transpose */ ok = zt_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ; } else { /* complex conjugate transpose */ ok = z_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ; } } /* ---------------------------------------------------------------------- */ /* finalize result F */ /* ---------------------------------------------------------------------- */ if (ok) { F->sorted = Fsorted ; } ASSERT (CHOLMOD(dump_sparse) (F, "output F unsym", Common) >= 0) ; return (ok) ; } /* ========================================================================== */ /* === cholmod_transpose_sym ================================================ */ /* ========================================================================== */ /* Compute F = A' or A (p,p)', where A is symmetric and F is already allocated. * See cholmod_transpose for a simpler routine. * * workspace: Iwork (nrow) if Perm NULL, Iwork (2*nrow) if Perm non-NULL. */ int CHOLMOD(transpose_sym) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to transpose */ int values, /* 2: complex conj. transpose, 1: array transpose, 0: do not transpose the numerical values */ Int *Perm, /* size nrow, if present (can be NULL) */ /* ---- output --- */ cholmod_sparse *F, /* F = A' or A(p,p)' */ /* --------------- */ cholmod_common *Common ) { Int *Ap, *Anz, *Ai, *Fp, *Wi, *Pinv, *Iwork ; Int p, pend, packed, upper, permute, jold, n, i, j, k, iold ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (F, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (F, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; if (A->nrow != A->ncol || A->stype == 0) { /* this routine handles square symmetric matrices only */ ERROR (CHOLMOD_INVALID, "matrix must be symmetric") ; return (FALSE) ; } if (A->nrow != F->ncol || A->ncol != F->nrow) { ERROR (CHOLMOD_INVALID, "F has the wrong dimensions") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ permute = (Perm != NULL) ; n = A->nrow ; Ap = A->p ; /* size A->ncol+1, column pointers of A */ Ai = A->i ; /* size nz = Ap [A->ncol], row indices of A */ Anz = A->nz ; packed = A->packed ; ASSERT (IMPLIES (!packed, Anz != NULL)) ; upper = (A->stype > 0) ; Fp = F->p ; /* size A->nrow+1, row pointers of F */ /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = (Perm != NULL) ? 2*n : n */ s = CHOLMOD(add_size_t) (n, ((Perm != NULL) ? n : 0), &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (0, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; /* out of memory */ } /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Iwork = Common->Iwork ; Wi = Iwork ; /* size n (i/l/l) */ Pinv = Iwork + n ; /* size n (i/i/l) , unused if Perm NULL */ /* ---------------------------------------------------------------------- */ /* check Perm and construct inverse permutation */ /* ---------------------------------------------------------------------- */ if (permute) { for (i = 0 ; i < n ; i++) { Pinv [i] = EMPTY ; } for (k = 0 ; k < n ; k++) { i = Perm [k] ; if (i < 0 || i > n || Pinv [i] != EMPTY) { ERROR (CHOLMOD_INVALID, "invalid permutation") ; return (FALSE) ; } Pinv [i] = k ; } } /* Perm is now valid */ ASSERT (CHOLMOD(dump_perm) (Perm, n, n, "Perm", Common)) ; /* ---------------------------------------------------------------------- */ /* count the entries in each row of F */ /* ---------------------------------------------------------------------- */ for (i = 0 ; i < n ; i++) { Wi [i] = 0 ; } if (packed) { if (permute) { if (upper) { /* packed, permuted, upper */ for (j = 0 ; j < n ; j++) { jold = Perm [j] ; pend = Ap [jold+1] ; for (p = Ap [jold] ; p < pend ; p++) { iold = Ai [p] ; if (iold <= jold) { i = Pinv [iold] ; Wi [MIN (i, j)]++ ; } } } } else { /* packed, permuted, lower */ for (j = 0 ; j < n ; j++) { jold = Perm [j] ; pend = Ap [jold+1] ; for (p = Ap [jold] ; p < pend ; p++) { iold = Ai [p] ; if (iold >= jold) { i = Pinv [iold] ; Wi [MAX (i, j)]++ ; } } } } } else { if (upper) { /* packed, unpermuted, upper */ for (j = 0 ; j < n ; j++) { pend = Ap [j+1] ; for (p = Ap [j] ; p < pend ; p++) { i = Ai [p] ; if (i <= j) { Wi [i]++ ; } } } } else { /* packed, unpermuted, lower */ for (j = 0 ; j < n ; j++) { pend = Ap [j+1] ; for (p = Ap [j] ; p < pend ; p++) { i = Ai [p] ; if (i >= j) { Wi [i]++ ; } } } } } } else { if (permute) { if (upper) { /* unpacked, permuted, upper */ for (j = 0 ; j < n ; j++) { jold = Perm [j] ; p = Ap [jold] ; pend = p + Anz [jold] ; for ( ; p < pend ; p++) { iold = Ai [p] ; if (iold <= jold) { i = Pinv [iold] ; Wi [MIN (i, j)]++ ; } } } } else { /* unpacked, permuted, lower */ for (j = 0 ; j < n ; j++) { jold = Perm [j] ; p = Ap [jold] ; pend = p + Anz [jold] ; for ( ; p < pend ; p++) { iold = Ai [p] ; if (iold >= jold) { i = Pinv [iold] ; Wi [MAX (i, j)]++ ; } } } } } else { if (upper) { /* unpacked, unpermuted, upper */ for (j = 0 ; j < n ; j++) { p = Ap [j] ; pend = p + Anz [j] ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i <= j) { Wi [i]++ ; } } } } else { /* unpacked, unpermuted, lower */ for (j = 0 ; j < n ; j++) { p = Ap [j] ; pend = p + Anz [j] ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i >= j) { Wi [i]++ ; } } } } } } /* ---------------------------------------------------------------------- */ /* compute the row pointers */ /* ---------------------------------------------------------------------- */ p = 0 ; for (i = 0 ; i < n ; i++) { Fp [i] = p ; p += Wi [i] ; } Fp [n] = p ; for (i = 0 ; i < n ; i++) { Wi [i] = Fp [i] ; } if (p > (Int) (F->nzmax)) { ERROR (CHOLMOD_INVALID, "F is too small") ; return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* transpose matrix, using template routine */ /* ---------------------------------------------------------------------- */ ok = FALSE ; if (values == 0 || F->xtype == CHOLMOD_PATTERN) { PRINT2 (("\n:::: p_transpose_sym Perm %p\n", Perm)) ; ok = p_cholmod_transpose_sym (A, Perm, F, Common) ; } else if (F->xtype == CHOLMOD_REAL) { PRINT2 (("\n:::: r_transpose_sym Perm %p\n", Perm)) ; ok = r_cholmod_transpose_sym (A, Perm, F, Common) ; } else if (F->xtype == CHOLMOD_COMPLEX) { if (values == 1) { /* array transpose */ PRINT2 (("\n:::: ct_transpose_sym Perm %p\n", Perm)) ; ok = ct_cholmod_transpose_sym (A, Perm, F, Common) ; } else { /* complex conjugate transpose */ PRINT2 (("\n:::: c_transpose_sym Perm %p\n", Perm)) ; ok = c_cholmod_transpose_sym (A, Perm, F, Common) ; } } else if (F->xtype == CHOLMOD_ZOMPLEX) { if (values == 1) { /* array transpose */ PRINT2 (("\n:::: zt_transpose_sym Perm %p\n", Perm)) ; ok = zt_cholmod_transpose_sym (A, Perm, F, Common) ; } else { /* complex conjugate transpose */ PRINT2 (("\n:::: z_transpose_sym Perm %p\n", Perm)) ; ok = z_cholmod_transpose_sym (A, Perm, F, Common) ; } } /* ---------------------------------------------------------------------- */ /* finalize result F */ /* ---------------------------------------------------------------------- */ /* F is sorted if there is no permutation vector */ if (ok) { F->sorted = !permute ; F->packed = TRUE ; F->stype = - SIGN (A->stype) ; /* flip the stype */ ASSERT (CHOLMOD(dump_sparse) (F, "output F sym", Common) >= 0) ; } return (ok) ; } /* ========================================================================== */ /* === cholmod_transpose ==================================================== */ /* ========================================================================== */ /* Returns A'. See also cholmod_ptranspose below. */ cholmod_sparse *CHOLMOD(transpose) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to transpose */ int values, /* 2: complex conj. transpose, 1: array transpose, 0: do not transpose the numerical values (returns its result as CHOLMOD_PATTERN) */ /* --------------- */ cholmod_common *Common ) { return (CHOLMOD(ptranspose) (A, values, NULL, NULL, 0, Common)) ; } /* ========================================================================== */ /* === cholmod_ptranspose =================================================== */ /* ========================================================================== */ /* Return A' or A(p,p)' if A is symmetric. Return A', A(:,f)', or A(p,f)' if * A is unsymmetric. * * workspace: * Iwork (MAX (nrow,ncol)) if unsymmetric and fset is non-NULL * Iwork (nrow) if unsymmetric and fset is NULL * Iwork (2*nrow) if symmetric and Perm is non-NULL. * Iwork (nrow) if symmetric and Perm is NULL. * * A simple worst-case upper bound on the workspace is nrow+ncol. */ cholmod_sparse *CHOLMOD(ptranspose) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to transpose */ int values, /* 2: complex conj. transpose, 1: array transpose, 0: do not transpose the numerical values */ Int *Perm, /* if non-NULL, F = A(p,f) or A(p,p) */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* --------------- */ cholmod_common *Common ) { Int *Ap, *Anz ; cholmod_sparse *F ; Int nrow, ncol, use_fset, j, jj, fnz, packed, stype, nf, xtype ; size_t ineed ; int ok = TRUE ; nf = fsize ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ; stype = A->stype ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ nrow = A->nrow ; ncol = A->ncol ; if (stype != 0) { use_fset = FALSE ; if (Perm != NULL) { ineed = CHOLMOD(mult_size_t) (A->nrow, 2, &ok) ; } else { ineed = A->nrow ; } } else { use_fset = (fset != NULL) ; if (use_fset) { ineed = MAX (A->nrow, A->ncol) ; } else { ineed = A->nrow ; } } if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (NULL) ; } CHOLMOD(allocate_work) (0, ineed, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Ap = A->p ; Anz = A->nz ; packed = A->packed ; ASSERT (IMPLIES (!packed, Anz != NULL)) ; xtype = values ? A->xtype : CHOLMOD_PATTERN ; /* ---------------------------------------------------------------------- */ /* allocate F */ /* ---------------------------------------------------------------------- */ /* determine # of nonzeros in F */ if (stype != 0) { /* F=A' or F=A(p,p)', fset is ignored */ fnz = CHOLMOD(nnz) (A, Common) ; } else { nf = (use_fset) ? nf : ncol ; if (use_fset) { fnz = 0 ; /* F=A(:,f)' or F=A(p,f)' */ for (jj = 0 ; jj < nf ; jj++) { /* The fset is not yet checked; it will be thoroughly checked * in cholmod_transpose_unsym. For now, just make sure we don't * access Ap and Anz out of bounds. */ j = fset [jj] ; if (j >= 0 && j < ncol) { fnz += packed ? (Ap [j+1] - Ap [j]) : MAX (0, Anz [j]) ; } } } else { /* F=A' or F=A(p,:)' */ fnz = CHOLMOD(nnz) (A, Common) ; } } /* F is ncol-by-nrow, fnz nonzeros, sorted unless f is present and unsorted, * packed, of opposite stype as A, and with/without numerical values */ F = CHOLMOD(allocate_sparse) (ncol, nrow, fnz, TRUE, TRUE, -SIGN(stype), xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } /* ---------------------------------------------------------------------- */ /* transpose and optionally permute the matrix A */ /* ---------------------------------------------------------------------- */ if (stype != 0) { /* F = A (p,p)', using upper or lower triangular part of A only */ ok = CHOLMOD(transpose_sym) (A, values, Perm, F, Common) ; } else { /* F = A (p,f)' */ ok = CHOLMOD(transpose_unsym) (A, values, Perm, fset, nf, F, Common) ; } /* ---------------------------------------------------------------------- */ /* return the matrix F, or NULL if an error occured */ /* ---------------------------------------------------------------------- */ if (!ok) { CHOLMOD(free_sparse) (&F, Common) ; } return (F) ; } /* ========================================================================== */ /* === cholmod_sort ========================================================= */ /* ========================================================================== */ /* Sort the columns of A, in place. Returns A in packed form, even if it * starts as unpacked. Removes entries in the ignored part of a symmetric * matrix. * * workspace: Iwork (max (nrow,ncol)). Allocates additional workspace for a * temporary copy of A'. */ int CHOLMOD(sort) ( /* ---- in/out --- */ cholmod_sparse *A, /* matrix to sort */ /* --------------- */ cholmod_common *Common ) { Int *Ap ; cholmod_sparse *F ; Int anz, ncol, nrow, stype ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; Common->status = CHOLMOD_OK ; nrow = A->nrow ; if (nrow <= 1) { /* a 1-by-n sparse matrix must be sorted */ A->sorted = TRUE ; return (TRUE) ; } /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ ncol = A->ncol ; CHOLMOD(allocate_work) (0, MAX (nrow, ncol), 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; /* out of memory */ } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ anz = CHOLMOD(nnz) (A, Common) ; stype = A->stype ; /* ---------------------------------------------------------------------- */ /* sort the columns of the matrix */ /* ---------------------------------------------------------------------- */ /* allocate workspace for transpose: ncol-by-nrow, same # of nonzeros as A, * sorted, packed, same stype as A, and of the same numeric type as A. */ F = CHOLMOD(allocate_sparse) (ncol, nrow, anz, TRUE, TRUE, stype, A->xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; /* out of memory */ } if (stype != 0) { /* F = A', upper or lower triangular part only */ CHOLMOD(transpose_sym) (A, 1, NULL, F, Common) ; A->packed = TRUE ; /* A = F' */ CHOLMOD(transpose_sym) (F, 1, NULL, A, Common) ; } else { /* F = A' */ CHOLMOD(transpose_unsym) (A, 1, NULL, NULL, 0, F, Common) ; A->packed = TRUE ; /* A = F' */ CHOLMOD(transpose_unsym) (F, 1, NULL, NULL, 0, A, Common) ; } ASSERT (A->sorted && A->packed) ; ASSERT (CHOLMOD(dump_sparse) (A, "Asorted", Common) >= 0) ; /* ---------------------------------------------------------------------- */ /* reduce A in size, if needed. This must succeed. */ /* ---------------------------------------------------------------------- */ Ap = A->p ; anz = Ap [ncol] ; ASSERT ((size_t) anz <= A->nzmax) ; CHOLMOD(reallocate_sparse) (anz, A, Common) ; ASSERT (Common->status >= CHOLMOD_OK) ; /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ CHOLMOD(free_sparse) (&F, Common) ; return (TRUE) ; } SuiteSparse/CHOLMOD/Core/cholmod_memory.c0000644001170100242450000004137710664627223017131 0ustar davisfac/* ========================================================================== */ /* === Core/cholmod_memory ================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Core memory management routines: * * Primary routines: * ----------------- * cholmod_malloc malloc wrapper * cholmod_free free wrapper * * Secondary routines: * ------------------- * cholmod_calloc calloc wrapper * cholmod_realloc realloc wrapper * cholmod_realloc_multiple realloc wrapper for multiple objects * * The user may make use of these, just like malloc and free. You can even * malloc an object and safely free it with cholmod_free, and visa versa * (except that the memory usage statistics will be corrupted). These routines * do differ from malloc and free. If cholmod_free is given a NULL pointer, * for example, it does nothing (unlike the ANSI free). cholmod_realloc does * not return NULL if given a non-NULL pointer and a nonzero size, even if it * fails (it sets an error code in Common->status instead). * * CHOLMOD keeps track of the amount of memory it has allocated, and so the * cholmod_free routine includes as a parameter the size of the object being * freed. This is only used for memory usage statistics, which are very useful * in finding memory leaks in your program. If you, the user of CHOLMOD, pass * the wrong size, the only consequence is that the memory usage statistics * will be invalid. This will causes assertions to fail if CHOLMOD is * compiled with debugging enabled, but otherwise it will cause no errors. * * The cholmod_free_* routines for each CHOLMOD object keep track of the size * of the blocks they free, so they do not require you to pass their sizes * as a parameter. * * If a block of size zero is requested, these routines allocate a block of * size one instead. */ #include "cholmod_internal.h" #include "cholmod_core.h" /* ========================================================================== */ /* === cholmod_add_size_t =================================================== */ /* ========================================================================== */ /* Safely compute a+b, and check for integer overflow. If overflow occurs, * return 0 and set OK to FALSE. Also return 0 if OK is FALSE on input. */ size_t CHOLMOD(add_size_t) (size_t a, size_t b, int *ok) { size_t s = a + b ; (*ok) = (*ok) && (s >= a) ; return ((*ok) ? s : 0) ; } /* ========================================================================== */ /* === cholmod_mult_size_t ================================================== */ /* ========================================================================== */ /* Safely compute a*k, where k should be small, and check for integer overflow. * If overflow occurs, return 0 and set OK to FALSE. Also return 0 if OK is * FALSE on input. */ size_t CHOLMOD(mult_size_t) (size_t a, size_t k, int *ok) { size_t p = 0, s ; while (*ok) { if (k % 2) { p = p + a ; (*ok) = (*ok) && (p >= a) ; } k = k / 2 ; if (!k) return (p) ; s = a + a ; (*ok) = (*ok) && (s >= a) ; a = s ; } return (0) ; } /* ========================================================================== */ /* === cholmod_malloc ======================================================= */ /* ========================================================================== */ /* Wrapper around malloc routine. Allocates space of size MAX(1,n)*size, where * size is normally a sizeof (...). * * This routine, cholmod_calloc, and cholmod_realloc do not set Common->status * to CHOLMOD_OK on success, so that a sequence of cholmod_malloc's, _calloc's, * or _realloc's can be used. If any of them fails, the Common->status will * hold the most recent error status. * * Usage, for a pointer to int: * * p = cholmod_malloc (n, sizeof (int), Common) * * Uses a pointer to the malloc routine (or its equivalent) defined in Common. */ void *CHOLMOD(malloc) /* returns pointer to the newly malloc'd block */ ( /* ---- input ---- */ size_t n, /* number of items */ size_t size, /* size of each item */ /* --------------- */ cholmod_common *Common ) { void *p ; size_t s ; int ok = TRUE ; RETURN_IF_NULL_COMMON (NULL) ; if (size == 0) { ERROR (CHOLMOD_INVALID, "sizeof(item) must be > 0") ; p = NULL ; } else if (n >= (Size_max / size) || n >= Int_max) { /* object is too big to allocate without causing integer overflow */ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; p = NULL ; } else { /* call malloc, or its equivalent */ s = CHOLMOD(mult_size_t) (MAX (1,n), size, &ok) ; p = ok ? ((Common->malloc_memory) (s)) : NULL ; if (p == NULL) { /* failure: out of memory */ ERROR (CHOLMOD_OUT_OF_MEMORY, "out of memory") ; } else { /* success: increment the count of objects allocated */ Common->malloc_count++ ; Common->memory_inuse += (n * size) ; Common->memory_usage = MAX (Common->memory_usage, Common->memory_inuse) ; PRINTM (("cholmod_malloc %p %d cnt: %d inuse %d\n", p, n*size, Common->malloc_count, Common->memory_inuse)) ; } } return (p) ; } /* ========================================================================== */ /* === cholmod_free ========================================================= */ /* ========================================================================== */ /* Wrapper around free routine. Returns NULL, which can be assigned to the * pointer being freed, as in: * * p = cholmod_free (n, sizeof (int), p, Common) ; * * In CHOLMOD, the syntax: * * cholmod_free (n, sizeof (int), p, Common) ; * * is used if p is a local pointer and the routine is returning shortly. * Uses a pointer to the free routine (or its equivalent) defined in Common. * Nothing is freed if the pointer is NULL. */ void *CHOLMOD(free) /* always returns NULL */ ( /* ---- input ---- */ size_t n, /* number of items */ size_t size, /* size of each item */ /* ---- in/out --- */ void *p, /* block of memory to free */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (NULL) ; if (p != NULL) { /* only free the object if the pointer is not NULL */ /* call free, or its equivalent */ (Common->free_memory) (p) ; Common->malloc_count-- ; Common->memory_inuse -= (n * size) ; PRINTM (("cholmod_free %p %d cnt: %d inuse %d\n", p, n*size, Common->malloc_count, Common->memory_inuse)) ; /* This assertion will fail if the user calls cholmod_malloc and * cholmod_free with mismatched memory sizes. It shouldn't fail * otherwise. */ ASSERT (IMPLIES (Common->malloc_count == 0, Common->memory_inuse == 0)); } /* return NULL, and the caller should assign this to p. This avoids * freeing the same pointer twice. */ return (NULL) ; } /* ========================================================================== */ /* === cholmod_calloc ======================================================= */ /* ========================================================================== */ /* Wrapper around calloc routine. * * Uses a pointer to the calloc routine (or its equivalent) defined in Common. * This routine is identical to malloc, except that it zeros the newly allocated * block to zero. */ void *CHOLMOD(calloc) /* returns pointer to the newly calloc'd block */ ( /* ---- input ---- */ size_t n, /* number of items */ size_t size, /* size of each item */ /* --------------- */ cholmod_common *Common ) { void *p ; RETURN_IF_NULL_COMMON (NULL) ; if (size == 0) { ERROR (CHOLMOD_INVALID, "sizeof(item) must be > 0") ; p = NULL ; } else if (n >= (Size_max / size) || n >= Int_max) { /* object is too big to allocate without causing integer overflow */ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; p = NULL ; } else { /* call calloc, or its equivalent */ p = (Common->calloc_memory) (MAX (1,n), size) ; if (p == NULL) { /* failure: out of memory */ ERROR (CHOLMOD_OUT_OF_MEMORY, "out of memory") ; } else { /* success: increment the count of objects allocated */ Common->malloc_count++ ; Common->memory_inuse += (n * size) ; Common->memory_usage = MAX (Common->memory_usage, Common->memory_inuse) ; PRINTM (("cholmod_calloc %p %d cnt: %d inuse %d\n", p, n*size, Common->malloc_count, Common->memory_inuse)) ; } } return (p) ; } /* ========================================================================== */ /* === cholmod_realloc ====================================================== */ /* ========================================================================== */ /* Wrapper around realloc routine. Given a pointer p to a block of size * (*n)*size memory, it changes the size of the block pointed to by p to be * MAX(1,nnew)*size in size. It may return a pointer different than p. This * should be used as (for a pointer to int): * * p = cholmod_realloc (nnew, sizeof (int), p, *n, Common) ; * * If p is NULL, this is the same as p = cholmod_malloc (...). * A size of nnew=0 is treated as nnew=1. * * If the realloc fails, p is returned unchanged and Common->status is set * to CHOLMOD_OUT_OF_MEMORY. If successful, Common->status is not modified, * and p is returned (possibly changed) and pointing to a large block of memory. * * Uses a pointer to the realloc routine (or its equivalent) defined in Common. */ void *CHOLMOD(realloc) /* returns pointer to reallocated block */ ( /* ---- input ---- */ size_t nnew, /* requested # of items in reallocated block */ size_t size, /* size of each item */ /* ---- in/out --- */ void *p, /* block of memory to realloc */ size_t *n, /* current size on input, nnew on output if successful*/ /* --------------- */ cholmod_common *Common ) { size_t nold = (*n) ; void *pnew ; size_t s ; int ok = TRUE ; RETURN_IF_NULL_COMMON (NULL) ; if (size == 0) { ERROR (CHOLMOD_INVALID, "sizeof(item) must be > 0") ; p = NULL ; } else if (p == NULL) { /* A fresh object is being allocated. */ PRINT1 (("realloc fresh: %d %d\n", nnew, size)) ; p = CHOLMOD(malloc) (nnew, size, Common) ; *n = (p == NULL) ? 0 : nnew ; } else if (nold == nnew) { /* Nothing to do. Do not change p or n. */ PRINT1 (("realloc nothing: %d %d\n", nnew, size)) ; } else if (nnew >= (Size_max / size) || nnew >= Int_max) { /* failure: nnew is too big. Do not change p or n. */ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; } else { /* The object exists, and is changing to some other nonzero size. */ /* call realloc, or its equivalent */ PRINT1 (("realloc : %d to %d, %d\n", nold, nnew, size)) ; pnew = NULL ; s = CHOLMOD(mult_size_t) (MAX (1,nnew), size, &ok) ; pnew = ok ? ((Common->realloc_memory) (p, s)) : NULL ; if (pnew == NULL) { /* Do not change p, since it still points to allocated memory */ if (nnew <= nold) { /* The attempt to reduce the size of the block from n to * nnew has failed. The current block is not modified, so * pretend to succeed, but do not change p. Do change * CHOLMOD's notion of the size of the block, however. */ *n = nnew ; PRINTM (("nnew <= nold failed, pretend to succeed\n")) ; PRINTM (("cholmod_realloc_old: %p %d cnt: %d inuse %d\n" "cholmod_realloc_new: %p %d cnt: %d inuse %d\n", p, nold*size, Common->malloc_count-1, Common->memory_inuse - nold*size, p, nnew*size, Common->malloc_count, Common->memory_inuse + (nnew-nold)*size)) ; Common->memory_inuse += ((nnew-nold) * size) ; } else { /* Increasing the size of the block has failed. * Do not change n. */ ERROR (CHOLMOD_OUT_OF_MEMORY, "out of memory") ; } } else { /* success: return revised p and change the size of the block */ PRINTM (("cholmod_realloc_old: %p %d cnt: %d inuse %d\n" "cholmod_realloc_new: %p %d cnt: %d inuse %d\n", p, nold*size, Common->malloc_count-1, Common->memory_inuse - nold*size, pnew, nnew*size, Common->malloc_count, Common->memory_inuse + (nnew-nold)*size)) ; p = pnew ; *n = nnew ; Common->memory_inuse += ((nnew-nold) * size) ; } Common->memory_usage = MAX (Common->memory_usage, Common->memory_inuse); } return (p) ; } /* ========================================================================== */ /* === cholmod_realloc_multiple ============================================= */ /* ========================================================================== */ /* reallocate multiple blocks of memory, all of the same size (up to two integer * and two real blocks). Either reallocations all succeed, or all are returned * in the original size (they are freed if the original size is zero). The nnew * blocks are of size 1 or more. */ int CHOLMOD(realloc_multiple) ( /* ---- input ---- */ size_t nnew, /* requested # of items in reallocated blocks */ int nint, /* number of int/UF_long blocks */ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */ /* ---- in/out --- */ void **I, /* int or UF_long block */ void **J, /* int or UF_long block */ void **X, /* complex or double block */ void **Z, /* zomplex case only: double block */ size_t *nold_p, /* current size of the I,J,X,Z blocks on input, * nnew on output if successful */ /* --------------- */ cholmod_common *Common ) { double *xx, *zz ; size_t i, j, x, z, nold ; RETURN_IF_NULL_COMMON (FALSE) ; if (xtype < CHOLMOD_PATTERN || xtype > CHOLMOD_ZOMPLEX) { ERROR (CHOLMOD_INVALID, "invalid xtype") ; return (FALSE) ; } nold = *nold_p ; if (nint < 1 && xtype == CHOLMOD_PATTERN) { /* nothing to do */ return (TRUE) ; } i = nold ; j = nold ; x = nold ; z = nold ; if (nint > 0) { *I = CHOLMOD(realloc) (nnew, sizeof (Int), *I, &i, Common) ; } if (nint > 1) { *J = CHOLMOD(realloc) (nnew, sizeof (Int), *J, &j, Common) ; } switch (xtype) { case CHOLMOD_REAL: *X = CHOLMOD(realloc) (nnew, sizeof (double), *X, &x, Common) ; break ; case CHOLMOD_COMPLEX: *X = CHOLMOD(realloc) (nnew, 2*sizeof (double), *X, &x, Common) ; break ; case CHOLMOD_ZOMPLEX: *X = CHOLMOD(realloc) (nnew, sizeof (double), *X, &x, Common) ; *Z = CHOLMOD(realloc) (nnew, sizeof (double), *Z, &z, Common) ; break ; } if (Common->status < CHOLMOD_OK) { /* one or more realloc's failed. Resize all back down to nold. */ if (nold == 0) { if (nint > 0) { *I = CHOLMOD(free) (i, sizeof (Int), *I, Common) ; } if (nint > 1) { *J = CHOLMOD(free) (j, sizeof (Int), *J, Common) ; } switch (xtype) { case CHOLMOD_REAL: *X = CHOLMOD(free) (x, sizeof (double), *X, Common) ; break ; case CHOLMOD_COMPLEX: *X = CHOLMOD(free) (x, 2*sizeof (double), *X, Common) ; break ; case CHOLMOD_ZOMPLEX: *X = CHOLMOD(free) (x, sizeof (double), *X, Common) ; *Z = CHOLMOD(free) (x, sizeof (double), *Z, Common) ; break ; } } else { if (nint > 0) { *I = CHOLMOD(realloc) (nold, sizeof (Int), *I, &i, Common) ; } if (nint > 1) { *J = CHOLMOD(realloc) (nold, sizeof (Int), *J, &j, Common) ; } switch (xtype) { case CHOLMOD_REAL: *X = CHOLMOD(realloc) (nold, sizeof (double), *X, &x, Common) ; break ; case CHOLMOD_COMPLEX: *X = CHOLMOD(realloc) (nold, 2*sizeof (double), *X, &x, Common) ; break ; case CHOLMOD_ZOMPLEX: *X = CHOLMOD(realloc) (nold, sizeof (double), *X, &x, Common) ; *Z = CHOLMOD(realloc) (nold, sizeof (double), *Z, &z, Common) ; break ; } } return (FALSE) ; } if (nold == 0) { /* New space was allocated. Clear the first entry so that valgrind * doesn't complain about its access in change_complexity * (Core/cholmod_complex.c). */ xx = *X ; zz = *Z ; switch (xtype) { case CHOLMOD_REAL: xx [0] = 0 ; break ; case CHOLMOD_COMPLEX: xx [0] = 0 ; xx [1] = 0 ; break ; case CHOLMOD_ZOMPLEX: xx [0] = 0 ; zz [0] = 0 ; break ; } } /* all realloc's succeeded, change size to reflect realloc'ed size. */ *nold_p = nnew ; return (TRUE) ; } SuiteSparse/CHOLMOD/Core/t_cholmod_change_factor.c0000644001170100242450000003756610537777450020743 0ustar davisfac/* ========================================================================== */ /* === Core/t_cholmod_change_factor ========================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Template routine for cholmod_change_factor. All xtypes supported. */ #include "cholmod_template.h" /* ========================================================================== */ /* === t_change_simplicial_numeric ========================================== */ /* ========================================================================== */ static void TEMPLATE (change_simplicial_numeric) ( cholmod_factor *L, Int to_ll, Int to_packed, Int *newLi, double *newLx, double *newLz, Int lnz, Int grow, double grow1, Int grow2, Int make_ll, Int make_monotonic, Int make_ldl, cholmod_common *Common ) { double xlen, dj [1], ljj [1], lj2 [1] ; double *Lx, *Lz ; Int *Lp, *Li, *Lnz ; Int n, j, len, pnew, pold, k, p, pend ; n = L->n ; Lp = L->p ; Li = L->i ; Lx = L->x ; Lz = L->z ; Lnz = L->nz ; if (make_ll) { L->minor = n ; } if (make_monotonic) { /* ------------------------------------------------------------------ */ /* reorder the columns to make them monotonic */ /* ------------------------------------------------------------------ */ pnew = 0 ; for (j = 0 ; j < n ; j++) { /* copy and pack column j */ len = Lnz [j] ; PRINT2 (("j: "ID" Lnz[j] "ID" len "ID" p "ID"\n", j, Lnz [j], len, pnew)) ; pold = Lp [j] ; ASSERT (Li [pold] == j) ; if (make_ll) { /* ---------------------------------------------------------- */ /* copy and convert LDL' to LL' */ /* ---------------------------------------------------------- */ /* dj = Lx [pold] ; */ ASSIGN_REAL (dj,0, Lx,pold) ; if (IS_LE_ZERO (dj [0])) { /* Conversion has failed; matrix is not positive definite. * Do not modify the column so that the LDL' factorization * can be restored if desired, by converting back to LDL'. * Continue the conversion, but flag the error. */ if (L->minor == (size_t) n) { ERROR (CHOLMOD_NOT_POSDEF, "L not positive definite") ; L->minor = j ; } for (k = 0 ; k < len ; k++) { newLi [pnew + k] = Li [pold + k] ; /* newLx [pnew + k] = Lx [pold + k] ; */ ASSIGN (newLx, newLz, pnew+k, Lx, Lz, pold+k) ; } } else { ljj [0] = sqrt (dj [0]) ; newLi [pnew] = j ; /* newLx [pnew] = ljj ; */ ASSIGN_REAL (newLx, pnew, ljj, 0) ; CLEAR_IMAG (newLx, newLz, pnew) ; for (k = 1 ; k < len ; k++) { newLi [pnew + k] = Li [pold + k] ; /* newLx [pnew + k] = Lx [pold + k] * ljj ; */ MULT_REAL (newLx, newLz, pnew+k, Lx, Lz, pold+k, ljj,0); } } } else if (make_ldl) { /* ---------------------------------------------------------- */ /* copy and convert LL' to LDL' */ /* ---------------------------------------------------------- */ /* ljj = Lx [pold] ; */ ASSIGN_REAL (ljj, 0, Lx, pold) ; if (ljj [0] <= 0) { /* matrix is not positive-definite; copy column as-is */ for (k = 0 ; k < len ; k++) { newLi [pnew + k] = Li [pold + k] ; /* newLx [pnew + k] = Lx [pold + k] ; */ ASSIGN (newLx, newLz, pnew+k, Lx, Lz, pold+k) ; } } else { newLi [pnew] = j ; /* newLx [pnew] = ljj*ljj ; */ lj2 [0] = ljj [0] * ljj [0] ; ASSIGN_REAL (newLx, pnew, lj2, 0) ; CLEAR_IMAG (newLx, newLz, pnew) ; for (k = 1 ; k < len ; k++) { newLi [pnew + k] = Li [pold + k] ; /* newLx [pnew + k] = Lx [pold + k] / ljj ; */ DIV_REAL (newLx, newLz, pnew+k, Lx, Lz, pold+k, ljj,0) ; } } } else { /* ---------------------------------------------------------- */ /* copy and leave LL' or LDL' as-is */ /* ---------------------------------------------------------- */ for (k = 0 ; k < len ; k++) { newLi [pnew + k] = Li [pold + k] ; /* newLx [pnew + k] = Lx [pold + k] ; */ ASSIGN (newLx, newLz, pnew+k, Lx, Lz, pold+k) ; } } Lp [j] = pnew ; /* compute len in double to avoid integer overflow */ if (grow) { xlen = (double) len ; xlen = grow1 * xlen + grow2 ; xlen = MIN (xlen, n-j) ; len = (Int) xlen ; } ASSERT (len >= Lnz [j] && len <= n-j) ; pnew += len ; ASSERT (pnew > 0) ; /* integer overflow case already covered */ } Lp [n] = pnew ; PRINT1 (("final pnew = "ID", lnz "ID" lnzmax %g\n", pnew, lnz, (double) L->nzmax)) ; ASSERT (pnew <= lnz) ; /* free the old L->i and L->x and replace with the new ones */ CHOLMOD(free) (L->nzmax, sizeof (Int), L->i, Common) ; #ifdef REAL CHOLMOD(free) (L->nzmax, sizeof (double), L->x, Common) ; #elif defined (COMPLEX) CHOLMOD(free) (L->nzmax, 2*sizeof (double), L->x, Common) ; #else CHOLMOD(free) (L->nzmax, sizeof (double), L->x, Common) ; CHOLMOD(free) (L->nzmax, sizeof (double), L->z, Common) ; #endif L->i = newLi ; L->x = newLx ; L->z = newLz ; L->nzmax = lnz ; /* reconstruct the link list */ natural_list (L) ; } else if (to_packed) { /* ------------------------------------------------------------------ */ /* already monotonic, just pack the columns of L */ /* ------------------------------------------------------------------ */ pnew = 0 ; if (make_ll) { /* -------------------------------------------------------------- */ /* pack and convert LDL' to LL' */ /* -------------------------------------------------------------- */ for (j = 0 ; j < n ; j++) { /* pack column j */ pold = Lp [j] ; len = Lnz [j] ; ASSERT (len > 0) ; ASSERT (Li [pold] == j) ; PRINT2 (("col "ID" pnew "ID" pold "ID"\n", j, pnew, pold)) ; /* dj = Lx [pold] ; */ ASSIGN_REAL (dj,0, Lx,pold) ; if (IS_LE_ZERO (dj [0])) { /* Conversion has failed; matrix is not positive definite. * Do not modify the column so that the LDL' factorization * can be restored if desired, by converting back to LDL'. * Continue the conversion, but flag the error. */ if (L->minor == (size_t) n) { ERROR (CHOLMOD_NOT_POSDEF, "L not positive definite") ; L->minor = j ; } for (k = 0 ; k < len ; k++) { Li [pnew + k] = Li [pold + k] ; /* Lx [pnew + k] = Lx [pold + k] ; */ ASSIGN (Lx, Lz, pnew+k, Lx, Lz, pold+k) ; } } else { ljj [0] = sqrt (dj [0]) ; Li [pnew] = j ; /* Lx [pnew] = ljj ; */ ASSIGN_REAL (Lx, pnew, ljj, 0) ; CLEAR_IMAG (Lx, Lz, pnew) ; for (k = 1 ; k < len ; k++) { Li [pnew + k] = Li [pold + k] ; /* Lx [pnew + k] = Lx [pold + k] * ljj ; */ MULT_REAL (Lx, Lz, pnew+k, Lx, Lz, pold+k, ljj,0) ; } } Lp [j] = pnew ; pnew += len ; } } else if (make_ldl) { /* -------------------------------------------------------------- */ /* pack and convert LL' to LDL' */ /* -------------------------------------------------------------- */ for (j = 0 ; j < n ; j++) { /* pack column j */ pold = Lp [j] ; len = Lnz [j] ; /* ljj = Lx [pold] ; */ ASSIGN_REAL (ljj, 0, Lx, pold) ; ASSERT (len > 0) ; PRINT2 (("col "ID" pnew "ID" pold "ID"\n", j, pnew, pold)) ; if (ljj [0] <= 0) { /* matrix is not positive-definite; pack column as-is */ for (k = 0 ; k < len ; k++) { Li [pnew + k] = Li [pold + k] ; /* Lx [pnew + k] = Lx [pold + k] ; */ ASSIGN (Lx, Lz, pnew+k, Lx, Lz, pold+k) ; } } else { Li [pnew] = Li [pold] ; /* Lx [pnew] = ljj*ljj ; */ lj2 [0] = ljj [0] * ljj [0] ; ASSIGN_REAL (Lx, pnew, lj2, 0) ; CLEAR_IMAG (Lx, Lz, pnew) ; for (k = 1 ; k < len ; k++) { Li [pnew + k] = Li [pold + k] ; /* Lx [pnew + k] = Lx [pold + k] / ljj ; */ DIV_REAL (Lx, Lz, pnew+k, Lx, Lz, pold+k, ljj,0) ; } } Lp [j] = pnew ; pnew += len ; } } else { /* ---------------------------------------------------------- */ /* pack and leave LL' or LDL' as-is */ /* ---------------------------------------------------------- */ for (j = 0 ; j < n ; j++) { /* pack column j */ pold = Lp [j] ; len = Lnz [j] ; ASSERT (len > 0) ; PRINT2 (("col "ID" pnew "ID" pold "ID"\n", j, pnew, pold)) ; if (pnew < pold) { PRINT2 ((" pack this column\n")) ; for (k = 0 ; k < len ; k++) { Li [pnew + k] = Li [pold + k] ; /* Lx [pnew + k] = Lx [pold + k] ; */ ASSIGN (Lx, Lz, pnew+k, Lx, Lz, pold+k) ; } Lp [j] = pnew ; } pnew += len ; } } Lp [n] = pnew ; PRINT2 (("Lp [n] = "ID"\n", pnew)) ; } else if (make_ll) { /* ------------------------------------------------------------------ */ /* convert LDL' to LL', but do so in-place */ /* ------------------------------------------------------------------ */ for (j = 0 ; j < n ; j++) { p = Lp [j] ; pend = p + Lnz [j] ; /* dj = Lx [p] ; */ ASSIGN_REAL (dj,0, Lx,p) ; if (IS_LE_ZERO (dj [0])) { /* Conversion has failed; matrix is not positive definite. * Do not modify the column so that the LDL' factorization * can be restored if desired, by converting back to LDL'. * Continue the conversion, but flag the error. */ if (L->minor == (size_t) n) { ERROR (CHOLMOD_NOT_POSDEF, "L not positive definite") ; L->minor = j ; } } else { ljj [0] = sqrt (dj [0]) ; /* Lx [p] = ljj ; */ ASSIGN_REAL (Lx,p, ljj,0) ; CLEAR_IMAG (Lx, Lz, p) ; for (p++ ; p < pend ; p++) { /* Lx [p] *= ljj ; */ MULT_REAL (Lx,Lz,p, Lx,Lz,p, ljj,0) ; } } } } else if (make_ldl) { /* ------------------------------------------------------------------ */ /* convert LL' to LDL', but do so in-place */ /* ------------------------------------------------------------------ */ for (j = 0 ; j < n ; j++) { p = Lp [j] ; pend = p + Lnz [j] ; /* ljj = Lx [p] ; */ ASSIGN_REAL (ljj, 0, Lx, p) ; if (ljj [0] > 0) { /* Lx [p] = ljj*ljj ; */ lj2 [0] = ljj [0] * ljj [0] ; ASSIGN_REAL (Lx, p, lj2, 0) ; CLEAR_IMAG (Lx, Lz, p) ; for (p++ ; p < pend ; p++) { /* Lx [p] /= ljj ; */ DIV_REAL (Lx,Lz,p, Lx,Lz,p, ljj,0) ; } } } } L->is_ll = to_ll ; DEBUG (CHOLMOD(dump_factor) (L, "done change simplicial numeric", Common)) ; } /* ========================================================================== */ /* === t_ll_super_to_simplicial_numeric ===================================== */ /* ========================================================================== */ /* A supernodal L can only be real or complex, not zomplex */ #ifndef ZOMPLEX static void TEMPLATE (ll_super_to_simplicial_numeric) ( cholmod_factor *L, Int to_packed, Int to_ll, cholmod_common *Common ) { double ljj [1], lj2 [1] ; double *Lx ; Int *Ls, *Lpi, *Lpx, *Super, *Lp, *Li, *Lnz ; Int n, lnz, s, nsuper, p, psi, psx, psend, nsrow, nscol, ii, jj, j, k1, k2, q ; L->is_ll = to_ll ; Lp = L->p ; Li = L->i ; Lx = L->x ; Lnz = L->nz ; lnz = L->nzmax ; n = L->n ; nsuper = L->nsuper ; Lpi = L->pi ; Lpx = L->px ; Ls = L->s ; Super = L->super ; p = 0 ; for (s = 0 ; s < nsuper ; s++) { k1 = Super [s] ; k2 = Super [s+1] ; psi = Lpi [s] ; psend = Lpi [s+1] ; psx = Lpx [s] ; nsrow = psend - psi ; nscol = k2 - k1 ; for (jj = 0 ; jj < nscol ; jj++) { /* column j of L starts here */ j = jj + k1 ; if (to_ll) { if (to_packed) { /* ------------------------------------------------------ */ /* convert to LL' packed */ /* ------------------------------------------------------ */ Lp [j] = p ; PRINT2 (("Col j "ID" p "ID"\n", j, p)) ; for (ii = jj ; ii < nsrow ; ii++) { /* get L(i,j) from supernode and store in column j */ ASSERT (p < (Int) (L->xsize) && p <= psx+ii+jj*nsrow) ; Li [p] = Ls [psi + ii] ; /* Lx [p] = Lx [psx + ii + jj*nsrow] ; */ q = psx + ii + jj*nsrow ; ASSIGN (Lx,-,p, Lx,-,q) ; PRINT2 ((" i "ID" ", Li [p])) ; XPRINT2 (Lx,-,q) ; PRINT2 (("\n")) ; p++ ; } Lnz [j] = p - Lp [j] ; } else { /* ------------------------------------------------------ */ /* convert to LL' unpacked */ /* ------------------------------------------------------ */ p = psx + jj + jj*nsrow ; Lp [j] = p ; Li [p] = j ; Lnz [j] = nsrow - jj ; p++ ; for (ii = jj + 1 ; ii < nsrow ; ii++) { /* get L(i,j) from supernode and store in column j */ Li [psx + ii + jj*nsrow] = Ls [psi + ii] ; } } } else { if (to_packed) { /* ------------------------------------------------------ */ /* convert to LDL' packed */ /* ------------------------------------------------------ */ Lp [j] = p ; PRINT2 (("Col j "ID" p "ID"\n", Lp [j], p)) ; /* ljj = Lx [psx + jj + jj*nsrow] ; */ ASSIGN_REAL (ljj, 0, Lx, psx + jj + jj*nsrow) ; if (ljj [0] <= 0) { /* the matrix is not positive definite; do not divide */ /* Lx [p] = ljj ; */ ASSIGN_REAL (Lx, p, ljj, 0) ; CLEAR_IMAG (Lx, Lz, p) ; ljj [0] = 1 ; } else { lj2 [0] = ljj [0] * ljj [0] ; /* Lx [p] = ljj*ljj ; */ ASSIGN_REAL (Lx, p, lj2, 0) ; CLEAR_IMAG (Lx, Lz, p) ; } Li [p] = j ; p++ ; for (ii = jj + 1 ; ii < nsrow ; ii++) { /* get L(i,j) from supernode and store in column j */ ASSERT (p < (Int) (L->xsize) && p <= psx+ii+jj*nsrow) ; Li [p] = Ls [psi + ii] ; /* Lx [p] = Lx [psx + ii + jj*nsrow] / ljj ; */ q = psx + ii + jj*nsrow ; DIV_REAL (Lx, Lz, p, Lx, Lz, q, ljj,0) ; PRINT2 ((" i "ID" %g\n", Li [p], Lx [p])) ; p++ ; } Lnz [j] = p - Lp [j] ; } else { /* ------------------------------------------------------ */ /* convert to LDL' unpacked */ /* ------------------------------------------------------ */ p = psx + jj + jj*nsrow ; Lp [j] = p ; /* ljj = Lx [p] ; */ ASSIGN_REAL (ljj,0, Lx,p) ; if (ljj [0] <= 0) { /* the matrix is not positive definite; do not divide */ /* Lx [p] = ljj ; */ ASSIGN_REAL (Lx, p, ljj, 0) ; CLEAR_IMAG (Lx, Lz, p) ; ljj [0] = 1 ; } else { lj2 [0] = ljj [0] * ljj [0] ; /* Lx [p] = ljj*ljj ; */ ASSIGN_REAL (Lx, p, lj2, 0) ; CLEAR_IMAG (Lx, Lz, p) ; } Li [p] = j ; Lnz [j] = nsrow - jj ; p++ ; for (ii = jj + 1 ; ii < nsrow ; ii++) { /* get L(i,j) from supernode and store in column j */ Li [psx + ii + jj*nsrow] = Ls [psi + ii] ; /* Lx [psx + ii + jj*nsrow] /= ljj ; */ q = psx + ii + jj*nsrow ; DIV_REAL (Lx, Lz, q, Lx, Lz, q, ljj,0) ; } } } } } if (to_packed) { Lp [n] = p ; PRINT1 (("Final Lp "ID" n "ID" lnz "ID"\n", p, n, lnz)) ; ASSERT (Lp [n] == lnz) ; ASSERT (lnz <= (Int) (L->xsize)) ; /* reduce size of L->x to match L->i. This cannot fail. */ L->x = CHOLMOD(realloc) (lnz, #ifdef COMPLEX 2 * #endif sizeof (double), L->x, &(L->xsize), Common) ; ASSERT (lnz == (Int) (L->xsize)) ; Common->status = CHOLMOD_OK ; } else { Lp [n] = Lpx [nsuper] ; ASSERT (MAX (1,Lp [n]) == (Int) (L->xsize)) ; ASSERT (MAX (1,Lp [n]) == (Int) (L->nzmax)) ; } } #endif #undef PATTERN #undef REAL #undef COMPLEX #undef ZOMPLEX SuiteSparse/CHOLMOD/Core/cholmod_band.c0000644001170100242450000002327710537777406016534 0ustar davisfac/* ========================================================================== */ /* === Core/cholmod_band ==================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* C = tril (triu (A,k1), k2) * * C is a matrix consisting of the diagonals of A from k1 to k2. * * k=0 is the main diagonal of A, k=1 is the superdiagonal, k=-1 is the * subdiagonal, and so on. If A is m-by-n, then: * * k1=-m C = tril (A,k2) * k2=n C = triu (A,k1) * k1=0 and k2=0 C = diag(A), except C is a matrix, not a vector * * Values of k1 and k2 less than -m are treated as -m, and values greater * than n are treated as n. * * A can be of any symmetry (upper, lower, or unsymmetric); C is returned in * the same form, and packed. If A->stype > 0, entries in the lower * triangular part of A are ignored, and the opposite is true if * A->stype < 0. If A has sorted columns, then so does C. * C has the same size as A. * * If inplace is TRUE, then the matrix A is modified in place. * Only packed matrices can be converted in place. * * C can be returned as a numerical valued matrix (if A has numerical values * and mode > 0), as a pattern-only (mode == 0), or as a pattern-only but with * the diagonal entries removed (mode < 0). * * workspace: none * * A can have an xtype of pattern or real. Complex and zomplex cases supported * only if mode <= 0 (in which case the numerical values are ignored). */ #include "cholmod_internal.h" #include "cholmod_core.h" static cholmod_sparse *band /* returns C, or NULL if failure */ ( /* ---- input or in/out if inplace is TRUE --- */ cholmod_sparse *A, /* ---- input ---- */ UF_long k1, /* ignore entries below the k1-st diagonal */ UF_long k2, /* ignore entries above the k2-nd diagonal */ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diagonal) */ int inplace, /* if TRUE, then convert A in place */ /* --------------- */ cholmod_common *Common ) { double *Ax, *Cx ; Int packed, nz, j, p, pend, i, ncol, nrow, jlo, jhi, ilo, ihi, sorted, values, diag ; Int *Ap, *Anz, *Ai, *Cp, *Ci ; cholmod_sparse *C ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; values = (mode > 0) && (A->xtype != CHOLMOD_PATTERN) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; packed = A->packed ; diag = (mode >= 0) ; if (inplace && !packed) { /* cannot operate on an unpacked matrix in place */ ERROR (CHOLMOD_INVALID, "cannot operate on unpacked matrix in-place") ; return (NULL) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ PRINT1 (("k1 %ld k2 %ld\n", k1, k2)) ; Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; sorted = A->sorted ; if (A->stype > 0) { /* ignore any entries in strictly lower triangular part of A */ k1 = MAX (k1, 0) ; } if (A->stype < 0) { /* ignore any entries in strictly upper triangular part of A */ k2 = MIN (k2, 0) ; } ncol = A->ncol ; nrow = A->nrow ; /* ensure k1 and k2 are in the range -nrow to +ncol to * avoid possible integer overflow if k1 and k2 are huge */ k1 = MAX (-nrow, k1) ; k1 = MIN (k1, ncol) ; k2 = MAX (-nrow, k2) ; k2 = MIN (k2, ncol) ; /* consider columns jlo to jhi. columns outside this range are empty */ jlo = MAX (k1, 0) ; jhi = MIN (k2+nrow, ncol) ; if (k1 > k2) { /* nothing to do */ jlo = ncol ; jhi = ncol ; } /* ---------------------------------------------------------------------- */ /* allocate C, or operate on A in place */ /* ---------------------------------------------------------------------- */ if (inplace) { /* convert A in place */ C = A ; } else { /* count the number of entries in the result C */ nz = 0 ; if (sorted) { for (j = jlo ; j < jhi ; j++) { ilo = j-k2 ; ihi = j-k1 ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i > ihi) { break ; } if (i >= ilo && (diag || i != j)) { nz++ ; } } } } else { for (j = jlo ; j < jhi ; j++) { ilo = j-k2 ; ihi = j-k1 ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i >= ilo && i <= ihi && (diag || i != j)) { nz++ ; } } } } /* allocate C; A will not be modified. C is sorted if A is sorted */ C = CHOLMOD(allocate_sparse) (A->nrow, ncol, nz, sorted, TRUE, A->stype, values ? A->xtype : CHOLMOD_PATTERN, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } } Cp = C->p ; Ci = C->i ; Cx = C->x ; /* ---------------------------------------------------------------------- */ /* construct C */ /* ---------------------------------------------------------------------- */ /* columns 0 to jlo-1 are empty */ for (j = 0 ; j < jlo ; j++) { Cp [j] = 0 ; } nz = 0 ; if (sorted) { if (values) { /* pattern and values */ ASSERT (diag) ; for (j = jlo ; j < jhi ; j++) { ilo = j-k2 ; ihi = j-k1 ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; Cp [j] = nz ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i > ihi) { break ; } if (i >= ilo) { Ci [nz] = i ; Cx [nz] = Ax [p] ; nz++ ; } } } } else { /* pattern only, perhaps with no diagonal */ for (j = jlo ; j < jhi ; j++) { ilo = j-k2 ; ihi = j-k1 ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; Cp [j] = nz ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i > ihi) { break ; } if (i >= ilo && (diag || i != j)) { Ci [nz++] = i ; } } } } } else { if (values) { /* pattern and values */ ASSERT (diag) ; for (j = jlo ; j < jhi ; j++) { ilo = j-k2 ; ihi = j-k1 ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; Cp [j] = nz ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i >= ilo && i <= ihi) { Ci [nz] = i ; Cx [nz] = Ax [p] ; nz++ ; } } } } else { /* pattern only, perhaps with no diagonal */ for (j = jlo ; j < jhi ; j++) { ilo = j-k2 ; ihi = j-k1 ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; Cp [j] = nz ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i >= ilo && i <= ihi && (diag || i != j)) { Ci [nz++] = i ; } } } } } /* columns jhi to ncol-1 are empty */ for (j = jhi ; j <= ncol ; j++) { Cp [j] = nz ; } /* ---------------------------------------------------------------------- */ /* reduce A in size if done in place */ /* ---------------------------------------------------------------------- */ if (inplace) { /* free the unused parts of A, and reduce A->i and A->x in size */ ASSERT (MAX (1,nz) <= A->nzmax) ; CHOLMOD(reallocate_sparse) (nz, A, Common) ; ASSERT (Common->status >= CHOLMOD_OK) ; } /* ---------------------------------------------------------------------- */ /* return the result C */ /* ---------------------------------------------------------------------- */ DEBUG (i = CHOLMOD(dump_sparse) (C, "band", Common)) ; ASSERT (IMPLIES (mode < 0, i == 0)) ; return (C) ; } /* ========================================================================== */ /* === cholmod_band ========================================================= */ /* ========================================================================== */ cholmod_sparse *CHOLMOD(band) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to extract band matrix from */ UF_long k1, /* ignore entries below the k1-st diagonal */ UF_long k2, /* ignore entries above the k2-nd diagonal */ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */ /* --------------- */ cholmod_common *Common ) { return (band (A, k1, k2, mode, FALSE, Common)) ; } /* ========================================================================== */ /* === cholmod_band_inplace ================================================= */ /* ========================================================================== */ int CHOLMOD(band_inplace) ( /* ---- input ---- */ UF_long k1, /* ignore entries below the k1-st diagonal */ UF_long k2, /* ignore entries above the k2-nd diagonal */ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */ /* ---- in/out --- */ cholmod_sparse *A, /* matrix from which entries not in band are removed */ /* --------------- */ cholmod_common *Common ) { return (band (A, k1, k2, mode, TRUE, Common) != NULL) ; } SuiteSparse/CHOLMOD/Core/cholmod_copy.c0000644001170100242450000002737010537777421016575 0ustar davisfac/* ========================================================================== */ /* === Core/cholmod_copy ==================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* C = A, which allocates C and copies A into C, with possible change of * stype. The diagonal can optionally be removed. The numerical entries * can optionally be copied. This routine differs from cholmod_copy_sparse, * which makes an exact copy of a sparse matrix. * * A can be of any type (packed/unpacked, upper/lower/unsymmetric). C is * packed and can be of any stype (upper/lower/unsymmetric), except that if * A is rectangular C can only be unsymmetric. If the stype of A and C * differ, then the appropriate conversion is made. * * Symmetry of A (A->stype): * <0: lower: assume A is symmetric with just tril(A); the rest of A is ignored * 0 unsym: assume A is unsymmetric; consider all entries in A * >0 upper: assume A is symmetric with just triu(A); the rest of A is ignored * * Symmetry of C (stype parameter): * <0 lower: return just tril(C) * 0 unsym: return all of C * >0 upper: return just triu(C) * * In MATLAB: Using cholmod_copy: * ---------- ---------------------------- * C = A ; A unsymmetric, C unsymmetric * C = tril (A) ; A unsymmetric, C lower * C = triu (A) ; A unsymmetric, C upper * U = triu (A) ; L = tril (U',-1) ; C = L+U ; A upper, C unsymmetric * C = triu (A)' ; A upper, C lower * C = triu (A) ; A upper, C upper * L = tril (A) ; U = triu (L',1) ; C = L+U ; A lower, C unsymmetric * C = tril (A) ; A lower, C lower * C = tril (A)' ; A lower, C upper * * workspace: Iwork (max (nrow,ncol)) * * A can have an xtype of pattern or real. Complex and zomplex cases only * supported when mode <= 0 (in which case the numerical values are ignored). */ #include "cholmod_internal.h" #include "cholmod_core.h" /* ========================================================================== */ /* === copy_sym_to_unsym ==================================================== */ /* ========================================================================== */ /* Construct an unsymmetric copy of a symmetric sparse matrix. This does the * work for as C = cholmod_copy (A, 0, mode, Common) when A is symmetric. * In this case, extra space can be added to C. */ static cholmod_sparse *copy_sym_to_unsym ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to copy */ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) * -2: pattern only, no diagonal, add 50% + n extra * space to C */ /* --------------- */ cholmod_common *Common ) { double aij ; double *Ax, *Cx ; Int *Ap, *Ai, *Anz, *Cp, *Ci, *Wj, *Iwork ; cholmod_sparse *C ; Int nrow, ncol, nz, packed, j, p, pend, i, pc, up, lo, values, diag, astype, extra ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nrow = A->nrow ; ncol = A->ncol ; Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; packed = A->packed ; values = (mode > 0) && (A->xtype != CHOLMOD_PATTERN) ; diag = (mode >= 0) ; astype = SIGN (A->stype) ; up = (astype > 0) ; lo = (astype < 0) ; ASSERT (astype != 0) ; /* ---------------------------------------------------------------------- */ /* create an unsymmetric copy of a symmetric matrix */ /* ---------------------------------------------------------------------- */ Iwork = Common->Iwork ; Wj = Iwork ; /* size ncol (i/i/l) */ /* In MATLAB notation, for converting a symmetric/upper matrix: * U = triu (A) ; * L = tril (U',-1) ; * C = L + U ; * * For converting a symmetric/lower matrix to unsymmetric: * L = tril (A) ; * U = triu (L',1) ; * C = L + U ; */ ASSERT (up || lo) ; PRINT1 (("copy: convert symmetric to unsym\n")) ; /* count the number of entries in each column of C */ for (j = 0 ; j < ncol ; j++) { Wj [j] = 0 ; } for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i == j) { /* the diagonal entry A(i,i) will appear just once * (unless it is excluded with mode < 0) */ if (diag) { Wj [j]++ ; } } else if ((up && i < j) || (lo && i > j)) { /* upper case: A(i,j) is in the strictly upper part; * A(j,i) will be added to the strictly lower part of C. * lower case is the opposite. */ Wj [j]++ ; Wj [i]++ ; } } } nz = 0 ; for (j = 0 ; j < ncol ; j++) { nz += Wj [j] ; } extra = (mode == -2) ? (nz/2 + ncol) : 0 ; /* allocate C. C is sorted if and only if A is sorted */ C = CHOLMOD(allocate_sparse) (nrow, ncol, nz + extra, A->sorted, TRUE, 0, values ? A->xtype : CHOLMOD_PATTERN, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; } Cp = C->p ; Ci = C->i ; Cx = C->x ; /* construct the column pointers for C */ p = 0 ; for (j = 0 ; j < ncol ; j++) { Cp [j] = p ; p += Wj [j] ; } Cp [ncol] = p ; for (j = 0 ; j < ncol ; j++) { Wj [j] = Cp [j] ; } /* construct C */ if (values) { /* pattern and values */ ASSERT (diag) ; for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; aij = Ax [p] ; if (i == j) { /* add diagonal entry A(i,i) to column i */ pc = Wj [i]++ ; Ci [pc] = i ; Cx [pc] = aij ; } else if ((up && i < j) || (lo && i > j)) { /* add A(i,j) to column j */ pc = Wj [j]++ ; Ci [pc] = i ; Cx [pc] = aij ; /* add A(j,i) to column i */ pc = Wj [i]++ ; Ci [pc] = j ; Cx [pc] = aij ; } } } } else { /* pattern only, possibly excluding the diagonal */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i == j) { /* add diagonal entry A(i,i) to column i * (unless it is excluded with mode < 0) */ if (diag) { Ci [Wj [i]++] = i ; } } else if ((up && i < j) || (lo && i > j)) { /* add A(i,j) to column j */ Ci [Wj [j]++] = i ; /* add A(j,i) to column i */ Ci [Wj [i]++] = j ; } } } } /* ---------------------------------------------------------------------- */ /* return the result */ /* ---------------------------------------------------------------------- */ DEBUG (i = CHOLMOD(dump_sparse) (C, "copy_sym_to_unsym", Common)) ; PRINT1 (("mode %d nnzdiag "ID"\n", mode, i)) ; ASSERT (IMPLIES (mode < 0, i == 0)) ; return (C) ; } /* ========================================================================== */ /* === cholmod_copy ========================================================= */ /* ========================================================================== */ cholmod_sparse *CHOLMOD(copy) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to copy */ int stype, /* requested stype of C */ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */ /* --------------- */ cholmod_common *Common ) { cholmod_sparse *C ; Int nrow, ncol, up, lo, values, diag, astype ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; values = (mode > 0) && (A->xtype != CHOLMOD_PATTERN) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; nrow = A->nrow ; ncol = A->ncol ; if ((stype || A->stype) && nrow != ncol) { /* inputs invalid */ ERROR (CHOLMOD_INVALID, "matrix invalid") ; return (NULL) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ CHOLMOD(allocate_work) (0, MAX (nrow,ncol), 0, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ diag = (mode >= 0) ; astype = SIGN (A->stype) ; stype = SIGN (stype) ; up = (astype > 0) ; lo = (astype < 0) ; /* ---------------------------------------------------------------------- */ /* copy the matrix */ /* ---------------------------------------------------------------------- */ if (astype == stype) { /* ------------------------------------------------------------------ */ /* symmetry of A and C are the same */ /* ------------------------------------------------------------------ */ /* copy A into C, keeping the same symmetry. If A is symmetric * entries in the ignored part of A are not copied into C */ C = CHOLMOD(band) (A, -nrow, ncol, mode, Common) ; } else if (!astype) { /* ------------------------------------------------------------------ */ /* convert unsymmetric matrix A into a symmetric matrix C */ /* ------------------------------------------------------------------ */ if (stype > 0) { /* C = triu (A) */ C = CHOLMOD(band) (A, 0, ncol, mode, Common) ; } else { /* C = tril (A) */ C = CHOLMOD(band) (A, -nrow, 0, mode, Common) ; } if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } C->stype = stype ; } else if (astype == -stype) { /* ------------------------------------------------------------------ */ /* transpose a symmetric matrix */ /* ------------------------------------------------------------------ */ /* converting upper to lower or lower to upper */ /* workspace: Iwork (nrow) */ C = CHOLMOD(transpose) (A, values, Common) ; if (!diag) { /* remove diagonal, if requested */ CHOLMOD(band_inplace) (-nrow, ncol, -1, C, Common) ; } } else { /* ------------------------------------------------------------------ */ /* create an unsymmetric copy of a symmetric matrix */ /* ------------------------------------------------------------------ */ C = copy_sym_to_unsym (A, mode, Common) ; } /* ---------------------------------------------------------------------- */ /* return if error */ /* ---------------------------------------------------------------------- */ if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } /* ---------------------------------------------------------------------- */ /* return the result */ /* ---------------------------------------------------------------------- */ DEBUG (diag = CHOLMOD(dump_sparse) (C, "copy", Common)) ; PRINT1 (("mode %d nnzdiag "ID"\n", mode, diag)) ; ASSERT (IMPLIES (mode < 0, diag == 0)) ; return (C) ; } SuiteSparse/CHOLMOD/Core/cholmod_factor.c0000644001170100242450000006536210677222357017102 0ustar davisfac/* ========================================================================== */ /* === Core/cholmod_factor ================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Core utility routines for the cholmod_factor object: * * The data structure for an LL' or LDL' factorization is too complex to * describe in one sentence. This object can hold the symbolic analysis alone, * or in combination with a "simplicial" (similar to a sparse matrix) or * "supernodal" form of the numerical factorization. Only the routine to free * a factor is primary, since a factor object is created by the factorization * routine (cholmod_factorize). It must be freed with cholmod_free_factor. * * Primary routine: * ---------------- * cholmod_free_factor free a factor * * Secondary routines: * ------------------- * cholmod_allocate_factor allocate a symbolic factor (LL' or LDL') * cholmod_reallocate_factor change the # entries in a factor * cholmod_change_factor change the type of factor (e.g., LDL' to LL') * cholmod_pack_factor pack the columns of a factor * cholmod_reallocate_column resize a single column of a factor * cholmod_factor_to_sparse create a sparse matrix copy of a factor * cholmod_copy_factor create a copy of a factor * * Note that there is no cholmod_sparse_to_factor routine to create a factor * as a copy of a sparse matrix. It could be done, after a fashion, but a * lower triangular sparse matrix would not necessarily have a chordal graph, * which would break the many CHOLMOD routines that rely on this property. * * The cholmod_factor_to_sparse routine is provided so that matrix operations * in the MatrixOps module may be applied to L. Those operations operate on * cholmod_sparse objects, and they are not guaranteed to maintain the chordal * property of L. Such a modified L cannot be safely converted back to a * cholmod_factor object. */ #include "cholmod_internal.h" #include "cholmod_core.h" /* ========================================================================== */ /* === cholmod_allocate_factor ============================================== */ /* ========================================================================== */ /* Allocate a simplicial symbolic factor, with L->Perm and L->ColCount allocated * and initialized to "empty" values (Perm [k] = k, and ColCount[k] = 1). * The integer and numerical parts of L are not allocated. L->xtype is returned * as CHOLMOD_PATTERN and L->is_super are returned as FALSE. L->is_ll is also * returned FALSE, but this may be modified when the matrix is factorized. * * This is sufficient (but far from ideal) for input to cholmod_factorize, * since the simplicial LL' or LDL' factorization (cholmod_rowfac) can * reallocate the columns of L as needed. The primary purpose of this routine * is to allocate space for a symbolic factorization, for the "expert" user to * do his or her own symbolic analysis. The typical user should use * cholmod_analyze instead of this routine. * * workspace: none */ cholmod_factor *CHOLMOD(allocate_factor) ( /* ---- input ---- */ size_t n, /* L is n-by-n */ /* --------------- */ cholmod_common *Common ) { Int j ; Int *Perm, *ColCount ; cholmod_factor *L ; int ok = TRUE ; RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; /* ensure the dimension does not cause integer overflow */ (void) CHOLMOD(add_size_t) (n, 2, &ok) ; if (!ok || n > Int_max) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (NULL) ; } L = CHOLMOD(malloc) (sizeof (cholmod_factor), 1, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } L->n = n ; L->is_ll = FALSE ; L->is_super = FALSE ; L->is_monotonic = TRUE ; L->itype = ITYPE ; L->xtype = CHOLMOD_PATTERN ; L->dtype = DTYPE ; /* allocate the purely symbolic part of L */ L->ordering = CHOLMOD_NATURAL ; L->Perm = CHOLMOD(malloc) (n, sizeof (Int), Common) ; L->ColCount = CHOLMOD(malloc) (n, sizeof (Int), Common) ; /* simplicial part of L is empty */ L->nzmax = 0 ; L->p = NULL ; L->i = NULL ; L->x = NULL ; L->z = NULL ; L->nz = NULL ; L->next = NULL ; L->prev = NULL ; /* supernodal part of L is also empty */ L->nsuper = 0 ; L->ssize = 0 ; L->xsize = 0 ; L->maxesize = 0 ; L->maxcsize = 0 ; L->super = NULL ; L->pi = NULL ; L->px = NULL ; L->s = NULL ; /* L has not been factorized */ L->minor = n ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_factor) (&L, Common) ; return (NULL) ; /* out of memory */ } /* initialize Perm and ColCount */ Perm = L->Perm ; for (j = 0 ; j < ((Int) n) ; j++) { Perm [j] = j ; } ColCount = L->ColCount ; for (j = 0 ; j < ((Int) n) ; j++) { ColCount [j] = 1 ; } return (L) ; } /* ========================================================================== */ /* === cholmod_free_factor ================================================== */ /* ========================================================================== */ /* Free a factor object. * * workspace: none */ int CHOLMOD(free_factor) ( /* ---- in/out --- */ cholmod_factor **LHandle, /* factor to free, NULL on output */ /* --------------- */ cholmod_common *Common ) { Int n, lnz, xs, ss, s ; cholmod_factor *L ; RETURN_IF_NULL_COMMON (FALSE) ; if (LHandle == NULL) { /* nothing to do */ return (TRUE) ; } L = *LHandle ; if (L == NULL) { /* nothing to do */ return (TRUE) ; } n = L->n ; lnz = L->nzmax ; s = L->nsuper + 1 ; xs = (L->is_super) ? ((Int) (L->xsize)) : (lnz) ; ss = L->ssize ; /* symbolic part of L */ CHOLMOD(free) (n, sizeof (Int), L->Perm, Common) ; CHOLMOD(free) (n, sizeof (Int), L->ColCount, Common) ; /* simplicial form of L */ CHOLMOD(free) (n+1, sizeof (Int), L->p, Common) ; CHOLMOD(free) (lnz, sizeof (Int), L->i, Common) ; CHOLMOD(free) (n, sizeof (Int), L->nz, Common) ; CHOLMOD(free) (n+2, sizeof (Int), L->next, Common) ; CHOLMOD(free) (n+2, sizeof (Int), L->prev, Common) ; /* supernodal form of L */ CHOLMOD(free) (s, sizeof (Int), L->pi, Common) ; CHOLMOD(free) (s, sizeof (Int), L->px, Common) ; CHOLMOD(free) (s, sizeof (Int), L->super, Common) ; CHOLMOD(free) (ss, sizeof (Int), L->s, Common) ; /* numerical values for both simplicial and supernodal L */ if (L->xtype == CHOLMOD_REAL) { CHOLMOD(free) (xs, sizeof (double), L->x, Common) ; } else if (L->xtype == CHOLMOD_COMPLEX) { CHOLMOD(free) (xs, 2*sizeof (double), L->x, Common) ; } else if (L->xtype == CHOLMOD_ZOMPLEX) { CHOLMOD(free) (xs, sizeof (double), L->x, Common) ; CHOLMOD(free) (xs, sizeof (double), L->z, Common) ; } *LHandle = CHOLMOD(free) (1, sizeof (cholmod_factor), (*LHandle), Common) ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_reallocate_factor ============================================ */ /* ========================================================================== */ /* Change the size of L->i and L->x, or allocate them if their current size * is zero. L must be simplicial. * * workspace: none */ int CHOLMOD(reallocate_factor) ( /* ---- input ---- */ size_t nznew, /* new # of entries in L */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) { /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; PRINT1 (("realloc factor: xtype %d\n", L->xtype)) ; if (L->is_super) { /* L must be simplicial, and not symbolic */ ERROR (CHOLMOD_INVALID, "L invalid") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; PRINT1 (("realloc factor %g to %g\n", (double) L->nzmax, (double) nznew)) ; /* ---------------------------------------------------------------------- */ /* resize (or allocate) the L->i and L->x components of the factor */ /* ---------------------------------------------------------------------- */ CHOLMOD(realloc_multiple) (nznew, 1, L->xtype, &(L->i), NULL, &(L->x), &(L->z), &(L->nzmax), Common) ; return (Common->status == CHOLMOD_OK) ; } /* ========================================================================== */ /* === cholmod_reallocate_column =========================================== */ /* ========================================================================== */ /* Column j needs more space, reallocate it at the end of L->i and L->x. * If the reallocation fails, the factor is converted to a simplicial * symbolic factor (no pattern, just L->Perm and L->ColCount). * * workspace: none */ int CHOLMOD(reallocate_column) ( /* ---- input ---- */ size_t j, /* the column to reallocate */ size_t need, /* required size of column j */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) { double xneed ; double *Lx, *Lz ; Int *Lp, *Lprev, *Lnext, *Li, *Lnz ; Int n, pold, pnew, len, k, tail ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; if (L->is_super) { ERROR (CHOLMOD_INVALID, "L must be simplicial") ; return (FALSE) ; } n = L->n ; if (j >= L->n || need == 0) { ERROR (CHOLMOD_INVALID, "j invalid") ; return (FALSE) ; /* j out of range */ } Common->status = CHOLMOD_OK ; DEBUG (CHOLMOD(dump_factor) (L, "start colrealloc", Common)) ; /* ---------------------------------------------------------------------- */ /* increase the size of L if needed */ /* ---------------------------------------------------------------------- */ /* head = n+1 ; */ tail = n ; Lp = L->p ; Lnz = L->nz ; Lprev = L->prev ; Lnext = L->next ; ASSERT (Lnz != NULL) ; ASSERT (Lnext != NULL && Lprev != NULL) ; PRINT1 (("col %g need %g\n", (double) j, (double) need)) ; /* column j cannot have more than n-j entries if all entries are present */ need = MIN (need, n-j) ; /* compute need in double to avoid integer overflow */ if (Common->grow1 >= 1.0) { xneed = (double) need ; xneed = Common->grow1 * xneed + Common->grow2 ; xneed = MIN (xneed, n-j) ; need = (Int) xneed ; } PRINT1 (("really new need %g current %g\n", (double) need, (double) (Lp [Lnext [j]] - Lp [j]))) ; ASSERT (need >= 1 && need <= n-j) ; if (Lp [Lnext [j]] - Lp [j] >= (Int) need) { /* no need to reallocate the column, it's already big enough */ PRINT1 (("colrealloc: quick return %g %g\n", (double) (Lp [Lnext [j]] - Lp [j]), (double) need)) ; return (TRUE) ; } if (Lp [tail] + need > L->nzmax) { /* use double to avoid integer overflow */ xneed = (double) need ; if (Common->grow0 < 1.2) /* fl. pt. compare, false if NaN */ { /* if grow0 is less than 1.2 or NaN, don't use it */ xneed = 1.2 * (((double) L->nzmax) + xneed + 1) ; } else { xneed = Common->grow0 * (((double) L->nzmax) + xneed + 1) ; } if (xneed > Size_max || !CHOLMOD(reallocate_factor) ((Int) xneed, L, Common)) { /* out of memory, convert to simplicial symbolic */ CHOLMOD(change_factor) (CHOLMOD_PATTERN, L->is_ll, FALSE, TRUE, TRUE, L, Common) ; ERROR (CHOLMOD_OUT_OF_MEMORY, "out of memory; L now symbolic") ; return (FALSE) ; /* out of memory */ } PRINT1 (("\n=== GROW L from %g to %g\n", (double) L->nzmax, (double) xneed)) ; /* pack all columns so that each column has at most grow2 free space */ CHOLMOD(pack_factor) (L, Common) ; ASSERT (Common->status == CHOLMOD_OK) ; Common->nrealloc_factor++ ; } /* ---------------------------------------------------------------------- */ /* reallocate the column */ /* ---------------------------------------------------------------------- */ Common->nrealloc_col++ ; Li = L->i ; Lx = L->x ; Lz = L->z ; /* remove j from its current position in the list */ Lnext [Lprev [j]] = Lnext [j] ; Lprev [Lnext [j]] = Lprev [j] ; /* place j at the end of the list */ Lnext [Lprev [tail]] = j ; Lprev [j] = Lprev [tail] ; Lnext [j] = n ; Lprev [tail] = j ; /* L is no longer monotonic; columns are out-of-order */ L->is_monotonic = FALSE ; /* allocate space for column j */ pold = Lp [j] ; pnew = Lp [tail] ; Lp [j] = pnew ; Lp [tail] += need ; /* copy column j to the new space */ len = Lnz [j] ; for (k = 0 ; k < len ; k++) { Li [pnew + k] = Li [pold + k] ; } if (L->xtype == CHOLMOD_REAL) { for (k = 0 ; k < len ; k++) { Lx [pnew + k] = Lx [pold + k] ; } } else if (L->xtype == CHOLMOD_COMPLEX) { for (k = 0 ; k < len ; k++) { Lx [2*(pnew + k) ] = Lx [2*(pold + k) ] ; Lx [2*(pnew + k)+1] = Lx [2*(pold + k)+1] ; } } else if (L->xtype == CHOLMOD_ZOMPLEX) { for (k = 0 ; k < len ; k++) { Lx [pnew + k] = Lx [pold + k] ; Lz [pnew + k] = Lz [pold + k] ; } } DEBUG (CHOLMOD(dump_factor) (L, "colrealloc done", Common)) ; /* successful reallocation of column j of L */ return (TRUE) ; } /* ========================================================================== */ /* === cholmod_pack_factor ================================================== */ /* ========================================================================== */ /* Pack the columns of a simplicial LDL' or LL' factor. This can be followed * by a call to cholmod_reallocate_factor to reduce the size of L to the exact * size required by the factor, if desired. Alternatively, you can leave the * size of L->i and L->x the same, to allow space for future updates/rowadds. * * Each column is reduced in size so that it has at most Common->grow2 free * space at the end of the column. * * Does nothing and returns silently if given any other type of factor. * * Does NOT force the columns of L to be monotonic. It thus differs from * cholmod_change_factor (xtype, -, FALSE, TRUE, TRUE, L, Common), which * packs the columns and ensures that they appear in monotonic order. */ int CHOLMOD(pack_factor) ( /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) { double *Lx, *Lz ; Int *Lp, *Li, *Lnz, *Lnext ; Int pnew, j, k, pold, len, n, head, tail, grow2 ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; Common->status = CHOLMOD_OK ; DEBUG (CHOLMOD(dump_factor) (L, "start pack", Common)) ; PRINT1 (("PACK factor %d\n", L->is_super)) ; if (L->xtype == CHOLMOD_PATTERN || L->is_super) { /* nothing to do unless L is simplicial numeric */ return (TRUE) ; } /* ---------------------------------------------------------------------- */ /* pack */ /* ---------------------------------------------------------------------- */ grow2 = Common->grow2 ; PRINT1 (("\nPACK grow2 "ID"\n", grow2)) ; pnew = 0 ; n = L->n ; Lp = L->p ; Li = L->i ; Lx = L->x ; Lz = L->z ; Lnz = L->nz ; Lnext = L->next ; head = n+1 ; tail = n ; for (j = Lnext [head] ; j != tail ; j = Lnext [j]) { /* pack column j */ pold = Lp [j] ; len = Lnz [j] ; ASSERT (len > 0) ; PRINT2 (("col "ID" pnew "ID" pold "ID"\n", j, pnew, pold)) ; if (pnew < pold) { PRINT2 ((" pack this column\n")) ; for (k = 0 ; k < len ; k++) { Li [pnew + k] = Li [pold + k] ; } if (L->xtype == CHOLMOD_REAL) { for (k = 0 ; k < len ; k++) { Lx [pnew + k] = Lx [pold + k] ; } } else if (L->xtype == CHOLMOD_COMPLEX) { for (k = 0 ; k < len ; k++) { Lx [2*(pnew + k) ] = Lx [2*(pold + k) ] ; Lx [2*(pnew + k)+1] = Lx [2*(pold + k)+1] ; } } else if (L->xtype == CHOLMOD_ZOMPLEX) { for (k = 0 ; k < len ; k++) { Lx [pnew + k] = Lx [pold + k] ; Lz [pnew + k] = Lz [pold + k] ; } } Lp [j] = pnew ; } len = MIN (len + grow2, n - j) ; pnew = MIN (Lp [j] + len, Lp [Lnext [j]]) ; } PRINT2 (("final pnew = "ID"\n", pnew)) ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_factor_to_sparse ============================================= */ /* ========================================================================== */ /* Constructs a column-oriented sparse matrix containing the pattern and values * of a simplicial or supernodal numerical factor, and then converts the factor * into a simplicial symbolic factor. If L is already packed, monotonic, * and simplicial (which is the case when cholmod_factorize uses the simplicial * Cholesky factorization algorithm) then this routine requires only O(1) * memory and takes O(1) time. * * Only operates on numeric factors (real, complex, or zomplex). Does not * change the numeric L->xtype (the resulting sparse matrix has the same xtype * as L). If this routine fails, L is left unmodified. */ cholmod_sparse *CHOLMOD(factor_to_sparse) ( /* ---- in/out --- */ cholmod_factor *L, /* factor to copy, converted to symbolic on output */ /* --------------- */ cholmod_common *Common ) { cholmod_sparse *Lsparse ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (L, NULL) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ; Common->status = CHOLMOD_OK ; DEBUG (CHOLMOD(dump_factor) (L, "start convert to matrix", Common)) ; /* ---------------------------------------------------------------------- */ /* convert to packed, monotonic, simplicial, numeric */ /* ---------------------------------------------------------------------- */ /* leave as LL or LDL' */ if (!CHOLMOD(change_factor) (L->xtype, L->is_ll, FALSE, TRUE, TRUE, L, Common)) { ERROR (CHOLMOD_INVALID, "cannot convert L") ; return (NULL) ; } /* ---------------------------------------------------------------------- */ /* create Lsparse */ /* ---------------------------------------------------------------------- */ /* allocate the header for Lsparse, the sparse matrix version of L */ Lsparse = CHOLMOD(malloc) (sizeof (cholmod_sparse), 1, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } /* transfer the contents from L to Lsparse */ Lsparse->nrow = L->n ; Lsparse->ncol = L->n ; Lsparse->p = L->p ; Lsparse->i = L->i ; Lsparse->x = L->x ; Lsparse->z = L->z ; Lsparse->nz = NULL ; Lsparse->stype = 0 ; Lsparse->itype = L->itype ; Lsparse->xtype = L->xtype ; Lsparse->dtype = L->dtype ; Lsparse->sorted = TRUE ; Lsparse->packed = TRUE ; Lsparse->nzmax = L->nzmax ; ASSERT (CHOLMOD(dump_sparse) (Lsparse, "Lsparse", Common) >= 0) ; /* ---------------------------------------------------------------------- */ /* convert L to symbolic, but do not free contents transfered to Lsparse */ /* ---------------------------------------------------------------------- */ L->p = NULL ; L->i = NULL ; L->x = NULL ; L->z = NULL ; L->xtype = CHOLMOD_PATTERN ; CHOLMOD(change_factor) (CHOLMOD_PATTERN, FALSE, FALSE, TRUE, TRUE, L, Common) ; return (Lsparse) ; } /* ========================================================================== */ /* === cholmod_copy_factor ================================================== */ /* ========================================================================== */ /* Create an exact copy of a factor, with one exception: * * Entries in unused space are not copied (they might not be initialized, * and copying them would cause program checkers such as purify and * valgrind to complain). * * Note that a supernodal L cannot be zomplex. */ cholmod_factor *CHOLMOD(copy_factor) ( /* ---- input ---- */ cholmod_factor *L, /* factor to copy */ /* --------------- */ cholmod_common *Common ) { cholmod_factor *L2 ; double *Lx, *L2x, *Lz, *L2z ; Int *Perm, *ColCount, *Lp, *Li, *Lnz, *Lnext, *Lprev, *Lsuper, *Lpi, *Lpx, *Ls, *Perm2, *ColCount2, *L2p, *L2i, *L2nz, *L2next, *L2prev, *L2super, *L2pi, *L2px, *L2s ; Int n, j, p, pend, s, xsize, ssize, nsuper ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (L, NULL) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ; Common->status = CHOLMOD_OK ; DEBUG (CHOLMOD(dump_factor) (L, "start copy", Common)) ; n = L->n ; /* ---------------------------------------------------------------------- */ /* allocate a simplicial symbolic factor */ /* ---------------------------------------------------------------------- */ /* allocates L2->Perm and L2->ColCount */ L2 = CHOLMOD(allocate_factor) (n, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } ASSERT (L2->xtype == CHOLMOD_PATTERN && !(L2->is_super)) ; Perm = L->Perm ; ColCount = L->ColCount ; Perm2 = L2->Perm ; ColCount2 = L2->ColCount ; L2->ordering = L->ordering ; for (j = 0 ; j < n ; j++) { Perm2 [j] = Perm [j] ; } for (j = 0 ; j < n ; j++) { ColCount2 [j] = ColCount [j] ; } L2->is_ll = L->is_ll ; /* ---------------------------------------------------------------------- */ /* copy the rest of the factor */ /* ---------------------------------------------------------------------- */ if (L->xtype != CHOLMOD_PATTERN && !(L->super)) { /* ------------------------------------------------------------------ */ /* allocate a simplicial numeric factor */ /* ------------------------------------------------------------------ */ /* allocate L2->p, L2->nz, L2->prev, L2->next, L2->i, and L2->x. * packed = -1 so that cholmod_change_factor allocates space of * size L2->nzmax */ L2->nzmax = L->nzmax ; if (!CHOLMOD(change_factor) (L->xtype, L->is_ll, FALSE, -1, TRUE, L2, Common)) { CHOLMOD(free_factor) (&L2, Common) ; return (NULL) ; /* out of memory */ } ASSERT (MAX (1, L->nzmax) == L2->nzmax) ; /* ------------------------------------------------------------------ */ /* copy the contents of a simplicial numeric factor */ /* ------------------------------------------------------------------ */ Lp = L->p ; Li = L->i ; Lx = L->x ; Lz = L->z ; Lnz = L->nz ; Lnext = L->next ; Lprev = L->prev ; L2p = L2->p ; L2i = L2->i ; L2x = L2->x ; L2z = L2->z ; L2nz = L2->nz ; L2next = L2->next ; L2prev = L2->prev ; L2->xtype = L->xtype ; L2->dtype = L->dtype ; for (j = 0 ; j <= n ; j++) { L2p [j] = Lp [j] ; } for (j = 0 ; j < n+2 ; j++) { L2prev [j] = Lprev [j] ; } for (j = 0 ; j < n+2 ; j++) { L2next [j] = Lnext [j] ; } for (j = 0 ; j < n ; j++) { L2nz [j] = Lnz [j] ; } for (j = 0 ; j < n ; j++) { p = Lp [j] ; pend = p + Lnz [j] ; for ( ; p < pend ; p++) { L2i [p] = Li [p] ; } p = Lp [j] ; if (L->xtype == CHOLMOD_REAL) { for ( ; p < pend ; p++) { L2x [p] = Lx [p] ; } } else if (L->xtype == CHOLMOD_COMPLEX) { for ( ; p < pend ; p++) { L2x [2*p ] = Lx [2*p ] ; L2x [2*p+1] = Lx [2*p+1] ; } } else if (L->xtype == CHOLMOD_ZOMPLEX) { for ( ; p < pend ; p++) { L2x [p] = Lx [p] ; L2z [p] = Lz [p] ; } } } } else if (L->is_super) { /* ------------------------------------------------------------------ */ /* copy a supernodal factor */ /* ------------------------------------------------------------------ */ xsize = L->xsize ; ssize = L->ssize ; nsuper = L->nsuper ; L2->xsize = xsize ; L2->ssize = ssize ; L2->nsuper = nsuper ; /* allocate L2->super, L2->pi, L2->px, and L2->s. Allocate L2->x if * L is numeric */ if (!CHOLMOD(change_factor) (L->xtype, TRUE, TRUE, TRUE, TRUE, L2, Common)) { CHOLMOD(free_factor) (&L2, Common) ; return (NULL) ; /* out of memory */ } ASSERT (L2->s != NULL) ; /* ------------------------------------------------------------------ */ /* copy the contents of a supernodal factor */ /* ------------------------------------------------------------------ */ Lsuper = L->super ; Lpi = L->pi ; Lpx = L->px ; Ls = L->s ; Lx = L->x ; L2super = L2->super ; L2pi = L2->pi ; L2px = L2->px ; L2s = L2->s ; L2x = L2->x ; L2->maxcsize = L->maxcsize ; L2->maxesize = L->maxesize ; for (s = 0 ; s <= nsuper ; s++) { L2super [s] = Lsuper [s] ; } for (s = 0 ; s <= nsuper ; s++) { L2pi [s] = Lpi [s] ; } for (s = 0 ; s <= nsuper ; s++) { L2px [s] = Lpx [s] ; } L2s [0] = 0 ; for (p = 0 ; p < ssize ; p++) { L2s [p] = Ls [p] ; } if (L->xtype == CHOLMOD_REAL) { for (p = 0 ; p < xsize ; p++) { L2x [p] = Lx [p] ; } } else if (L->xtype == CHOLMOD_COMPLEX) { for (p = 0 ; p < 2*xsize ; p++) { L2x [p] = Lx [p] ; } } } L2->minor = L->minor ; L2->is_monotonic = L->is_monotonic ; DEBUG (CHOLMOD(dump_factor) (L2, "L2 got copied", Common)) ; ASSERT (L2->xtype == L->xtype && L2->is_super == L->is_super) ; return (L2) ; } SuiteSparse/CHOLMOD/Core/cholmod_sparse.c0000644001170100242450000004303410665025300017073 0ustar davisfac/* ========================================================================== */ /* === Core/cholmod_sparse ================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Core utility routines for the cholmod_sparse object: * * A sparse matrix is held in compressed column form. In the basic type * ("packed", which corresponds to a MATLAB sparse matrix), an n-by-n matrix * with nz entries is held in three arrays: p of size n+1, i of size nz, and x * of size nz. Row indices of column j are held in i [p [j] ... p [j+1]-1] and * in the same locations in x. There may be no duplicate entries in a column. * Row indices in each column may be sorted or unsorted (CHOLMOD keeps track). * * Primary routines: * ----------------- * cholmod_allocate_sparse allocate a sparse matrix * cholmod_free_sparse free a sparse matrix * * Secondary routines: * ------------------- * cholmod_reallocate_sparse change the size (# entries) of sparse matrix * cholmod_nnz number of nonzeros in a sparse matrix * cholmod_speye sparse identity matrix * cholmod_spzeros sparse zero matrix * cholmod_copy_sparse create a copy of a sparse matrix * * All xtypes are supported (pattern, real, complex, and zomplex) */ #include "cholmod_internal.h" #include "cholmod_core.h" /* ========================================================================== */ /* === cholmod_allocate_sparse ============================================== */ /* ========================================================================== */ /* Allocate space for a matrix. A->i and A->x are not initialized. A->p * (and A->nz if A is not packed) are set to zero, so a matrix containing no * entries (all zero) is returned. See also cholmod_spzeros. * * workspace: none */ cholmod_sparse *CHOLMOD(allocate_sparse) ( /* ---- input ---- */ size_t nrow, /* # of rows of A */ size_t ncol, /* # of columns of A */ size_t nzmax, /* max # of nonzeros of A */ int sorted, /* TRUE if columns of A sorted, FALSE otherwise */ int packed, /* TRUE if A will be packed, FALSE otherwise */ int stype, /* stype of A */ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) { cholmod_sparse *A ; Int *Ap, *Anz ; size_t nzmax0 ; Int j ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; if (stype != 0 && nrow != ncol) { ERROR (CHOLMOD_INVALID, "rectangular matrix with stype != 0 invalid") ; return (NULL) ; } if (xtype < CHOLMOD_PATTERN || xtype > CHOLMOD_ZOMPLEX) { ERROR (CHOLMOD_INVALID, "xtype invalid") ; return (NULL) ; } /* ensure the dimensions do not cause integer overflow */ (void) CHOLMOD(add_size_t) (ncol, 2, &ok) ; if (!ok || nrow > Int_max || ncol > Int_max || nzmax > Int_max) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (NULL) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate header */ /* ---------------------------------------------------------------------- */ A = CHOLMOD(malloc) (sizeof (cholmod_sparse), 1, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } PRINT1 (("cholmod_allocate_sparse %d-by-%d nzmax %d sorted %d packed %d" " xtype %d\n", nrow, ncol, nzmax, sorted, packed, xtype)) ; nzmax = MAX (1, nzmax) ; A->nrow = nrow ; A->ncol = ncol ; A->nzmax = nzmax ; A->packed = packed ; /* default is packed (A->nz not present) */ A->stype = stype ; A->itype = ITYPE ; A->xtype = xtype ; A->dtype = DTYPE ; A->nz = NULL ; A->p = NULL ; A->i = NULL ; A->x = NULL ; A->z = NULL ; /* A 1-by-m matrix always has sorted columns */ A->sorted = (nrow <= 1) ? TRUE : sorted ; /* ---------------------------------------------------------------------- */ /* allocate the matrix itself */ /* ---------------------------------------------------------------------- */ /* allocate O(ncol) space */ A->p = CHOLMOD(malloc) (((size_t) ncol)+1, sizeof (Int), Common) ; if (!packed) { A->nz = CHOLMOD(malloc) (ncol, sizeof (Int), Common) ; } /* allocate O(nz) space */ nzmax0 = 0 ; CHOLMOD(realloc_multiple) (nzmax, 1, xtype, &(A->i), NULL, &(A->x), &(A->z), &nzmax0, Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_sparse) (&A, Common) ; return (NULL) ; /* out of memory */ } /* ---------------------------------------------------------------------- */ /* initialize A->p and A->nz so that A is an empty matrix */ /* ---------------------------------------------------------------------- */ Ap = A->p ; for (j = 0 ; j <= (Int) ncol ; j++) { Ap [j] = 0 ; } if (!packed) { Anz = A->nz ; for (j = 0 ; j < (Int) ncol ; j++) { Anz [j] = 0 ; } } return (A) ; } /* ========================================================================== */ /* === cholmod_free_sparse ================================================== */ /* ========================================================================== */ /* free a sparse matrix * * workspace: none */ int CHOLMOD(free_sparse) ( /* ---- in/out --- */ cholmod_sparse **AHandle, /* matrix to deallocate, NULL on output */ /* --------------- */ cholmod_common *Common ) { Int n, nz ; cholmod_sparse *A ; RETURN_IF_NULL_COMMON (FALSE) ; if (AHandle == NULL) { /* nothing to do */ return (TRUE) ; } A = *AHandle ; if (A == NULL) { /* nothing to do */ return (TRUE) ; } n = A->ncol ; nz = A->nzmax ; A->p = CHOLMOD(free) (n+1, sizeof (Int), A->p, Common) ; A->i = CHOLMOD(free) (nz, sizeof (Int), A->i, Common) ; A->nz = CHOLMOD(free) (n, sizeof (Int), A->nz, Common) ; switch (A->xtype) { case CHOLMOD_REAL: A->x = CHOLMOD(free) (nz, sizeof (double), A->x, Common) ; break ; case CHOLMOD_COMPLEX: A->x = CHOLMOD(free) (nz, 2*sizeof (double), A->x, Common) ; break ; case CHOLMOD_ZOMPLEX: A->x = CHOLMOD(free) (nz, sizeof (double), A->x, Common) ; A->z = CHOLMOD(free) (nz, sizeof (double), A->z, Common) ; break ; } *AHandle = CHOLMOD(free) (1, sizeof (cholmod_sparse), (*AHandle), Common) ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_reallocate_sparse ============================================ */ /* ========================================================================== */ /* Change the size of A->i, A->x, and A->z, or allocate them if their current * size is zero. A->x and A->z are not modified if A->xtype is CHOLMOD_PATTERN. * A->z is not modified unless A->xtype is CHOLMOD_ZOMPLEX. * * workspace: none */ int CHOLMOD(reallocate_sparse) ( /* ---- input ---- */ size_t nznew, /* new # of entries in A */ /* ---- in/out --- */ cholmod_sparse *A, /* matrix to reallocate */ /* --------------- */ cholmod_common *Common ) { /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; Common->status = CHOLMOD_OK ; PRINT1 (("realloc matrix %d to %d, xtype: %d\n", A->nzmax, nznew, A->xtype)) ; /* ---------------------------------------------------------------------- */ /* resize the matrix */ /* ---------------------------------------------------------------------- */ CHOLMOD(realloc_multiple) (MAX (1,nznew), 1, A->xtype, &(A->i), NULL, &(A->x), &(A->z), &(A->nzmax), Common) ; return (Common->status == CHOLMOD_OK) ; } /* ========================================================================== */ /* === cholmod_speye ======================================================== */ /* ========================================================================== */ /* Return a sparse identity matrix. */ cholmod_sparse *CHOLMOD(speye) ( /* ---- input ---- */ size_t nrow, /* # of rows of A */ size_t ncol, /* # of columns of A */ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) { double *Ax, *Az ; cholmod_sparse *A ; Int *Ap, *Ai ; Int j, n ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate the matrix */ /* ---------------------------------------------------------------------- */ n = MIN (nrow, ncol) ; A = CHOLMOD(allocate_sparse) (nrow, ncol, n, TRUE, TRUE, 0, xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory or inputs invalid */ } /* ---------------------------------------------------------------------- */ /* create the identity matrix */ /* ---------------------------------------------------------------------- */ Ap = A->p ; Ai = A->i ; Ax = A->x ; Az = A->z ; for (j = 0 ; j < n ; j++) { Ap [j] = j ; } for (j = n ; j <= ((Int) ncol) ; j++) { Ap [j] = n ; } for (j = 0 ; j < n ; j++) { Ai [j] = j ; } switch (xtype) { case CHOLMOD_REAL: for (j = 0 ; j < n ; j++) { Ax [j] = 1 ; } break ; case CHOLMOD_COMPLEX: for (j = 0 ; j < n ; j++) { Ax [2*j ] = 1 ; Ax [2*j+1] = 0 ; } break ; case CHOLMOD_ZOMPLEX: for (j = 0 ; j < n ; j++) { Ax [j] = 1 ; } for (j = 0 ; j < n ; j++) { Az [j] = 0 ; } break ; } return (A) ; } /* ========================================================================== */ /* === cholmod_spzeros ====================================================== */ /* ========================================================================== */ /* Return a sparse zero matrix. */ cholmod_sparse *CHOLMOD(spzeros) ( /* ---- input ---- */ size_t nrow, /* # of rows of A */ size_t ncol, /* # of columns of A */ size_t nzmax, /* max # of nonzeros of A */ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) { /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate the matrix */ /* ---------------------------------------------------------------------- */ return (CHOLMOD(allocate_sparse) (nrow, ncol, nzmax, TRUE, TRUE, 0, xtype, Common)) ; } /* ========================================================================== */ /* === cholmod_nnz ========================================================== */ /* ========================================================================== */ /* Return the number of entries in a sparse matrix. * * workspace: none * integer overflow cannot occur, since the matrix is already allocated. */ UF_long CHOLMOD(nnz) ( /* ---- input ---- */ cholmod_sparse *A, /* --------------- */ cholmod_common *Common ) { Int *Ap, *Anz ; size_t nz ; Int j, ncol ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (A, EMPTY) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* return nnz (A) */ /* ---------------------------------------------------------------------- */ ncol = A->ncol ; if (A->packed) { Ap = A->p ; RETURN_IF_NULL (Ap, EMPTY) ; nz = Ap [ncol] ; } else { Anz = A->nz ; RETURN_IF_NULL (Anz, EMPTY) ; nz = 0 ; for (j = 0 ; j < ncol ; j++) { nz += MAX (0, Anz [j]) ; } } return (nz) ; } /* ========================================================================== */ /* === cholmod_copy_sparse ================================================== */ /* ========================================================================== */ /* C = A. Create an exact copy of a sparse matrix, with one exception. * Entries in unused space are not copied (they might not be initialized, * and copying them would cause program checkers such as purify and * valgrind to complain). The xtype of the resulting matrix C is the same as * the xtype of the input matrix A. * * See also Core/cholmod_copy, which copies a matrix with possible changes * in stype, presence of diagonal entries, pattern vs. numerical values, * real and/or imaginary parts, and so on. */ cholmod_sparse *CHOLMOD(copy_sparse) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) { double *Ax, *Cx, *Az, *Cz ; Int *Ap, *Ai, *Anz, *Cp, *Ci, *Cnz ; cholmod_sparse *C ; Int p, pend, j, ncol, packed, nzmax, nz, xtype ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ; if (A->stype != 0 && A->nrow != A->ncol) { ERROR (CHOLMOD_INVALID, "rectangular matrix with stype != 0 invalid") ; return (NULL) ; } Common->status = CHOLMOD_OK ; ASSERT (CHOLMOD(dump_sparse) (A, "A original", Common) >= 0) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ ncol = A->ncol ; nzmax = A->nzmax ; packed = A->packed ; Ap = A->p ; Ai = A->i ; Ax = A->x ; Az = A->z ; Anz = A->nz ; xtype = A->xtype ; /* ---------------------------------------------------------------------- */ /* allocate the copy */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(allocate_sparse) (A->nrow, A->ncol, A->nzmax, A->sorted, A->packed, A->stype, A->xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } Cp = C->p ; Ci = C->i ; Cx = C->x ; Cz = C->z ; Cnz = C->nz ; /* ---------------------------------------------------------------------- */ /* copy the matrix */ /* ---------------------------------------------------------------------- */ for (j = 0 ; j <= ncol ; j++) { Cp [j] = Ap [j] ; } if (packed) { nz = Ap [ncol] ; for (p = 0 ; p < nz ; p++) { Ci [p] = Ai [p] ; } switch (xtype) { case CHOLMOD_REAL: for (p = 0 ; p < nz ; p++) { Cx [p] = Ax [p] ; } break ; case CHOLMOD_COMPLEX: for (p = 0 ; p < 2*nz ; p++) { Cx [p] = Ax [p] ; } break ; case CHOLMOD_ZOMPLEX: for (p = 0 ; p < nz ; p++) { Cx [p] = Ax [p] ; Cz [p] = Az [p] ; } break ; } } else { for (j = 0 ; j < ncol ; j++) { Cnz [j] = Anz [j] ; } switch (xtype) { case CHOLMOD_PATTERN: for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = p + Anz [j] ; for ( ; p < pend ; p++) { Ci [p] = Ai [p] ; } } break ; case CHOLMOD_REAL: for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = p + Anz [j] ; for ( ; p < pend ; p++) { Ci [p] = Ai [p] ; Cx [p] = Ax [p] ; } } break ; case CHOLMOD_COMPLEX: for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = p + Anz [j] ; for ( ; p < pend ; p++) { Ci [p] = Ai [p] ; Cx [2*p ] = Ax [2*p ] ; Cx [2*p+1] = Ax [2*p+1] ; } } break ; case CHOLMOD_ZOMPLEX: for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = p + Anz [j] ; for ( ; p < pend ; p++) { Ci [p] = Ai [p] ; Cx [p] = Ax [p] ; Cz [p] = Az [p] ; } } break ; } } /* ---------------------------------------------------------------------- */ /* return the result */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_sparse) (C, "C copy", Common) >= 0) ; return (C) ; } SuiteSparse/CHOLMOD/Core/License.txt0000644001170100242450000000210710540000266016040 0ustar davisfacCHOLMOD/Core Module. Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis CHOLMOD is also available under other licenses; contact authors for details. http://www.cise.ufl.edu/research/sparse Note that this license is for the CHOLMOD/Core module only. All CHOLMOD modules are licensed separately. -------------------------------------------------------------------------------- This Module is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This Module is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA SuiteSparse/CHOLMOD/Core/cholmod_dense.c0000644001170100242450000004440610537777424016723 0ustar davisfac/* ========================================================================== */ /* === Core/cholmod_dense =================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Core utility routines for the cholmod_dense object: * * The solve routines and some of the MatrixOps and Modify routines use dense * matrices as inputs. These are held in column-major order. With a leading * dimension of d, the entry in row i and column j is held in x [i+j*d]. * * Primary routines: * ----------------- * cholmod_allocate_dense allocate a dense matrix * cholmod_free_dense free a dense matrix * * Secondary routines: * ------------------- * cholmod_zeros allocate a dense matrix of all zeros * cholmod_ones allocate a dense matrix of all ones * cholmod_eye allocate a dense identity matrix * cholmod_sparse_to_dense create a dense matrix copy of a sparse matrix * cholmod_dense_to_sparse create a sparse matrix copy of a dense matrix * cholmod_copy_dense create a copy of a dense matrix * cholmod_copy_dense2 copy a dense matrix (pre-allocated) * * All routines in this file can handle the real, complex, and zomplex cases. * Pattern-only dense matrices are not supported. cholmod_sparse_to_dense can * take a pattern-only input sparse matrix, however, and cholmod_dense_to_sparse * can generate a pattern-only output sparse matrix. */ #include "cholmod_internal.h" #include "cholmod_core.h" /* ========================================================================== */ /* === TEMPLATE ============================================================= */ /* ========================================================================== */ #define PATTERN #include "t_cholmod_dense.c" #define REAL #include "t_cholmod_dense.c" #define COMPLEX #include "t_cholmod_dense.c" #define ZOMPLEX #include "t_cholmod_dense.c" /* ========================================================================== */ /* === cholmod_allocate_dense =============================================== */ /* ========================================================================== */ /* Allocate a dense matrix with leading dimension d. The space is not * initialized. */ cholmod_dense *CHOLMOD(allocate_dense) ( /* ---- input ---- */ size_t nrow, /* # of rows of matrix */ size_t ncol, /* # of columns of matrix */ size_t d, /* leading dimension */ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) { cholmod_dense *X ; size_t nzmax, nzmax0 ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; if (d < nrow) { ERROR (CHOLMOD_INVALID, "leading dimension invalid") ; return (NULL) ; } if (xtype < CHOLMOD_REAL || xtype > CHOLMOD_ZOMPLEX) { ERROR (CHOLMOD_INVALID, "xtype invalid") ; return (NULL) ; } /* ensure the dimensions do not cause integer overflow */ (void) CHOLMOD(add_size_t) (ncol, 2, &ok) ; /* nzmax = MAX (1, d*ncol) ; */ nzmax = CHOLMOD(mult_size_t) (d, ncol, &ok) ; nzmax = MAX (1, nzmax) ; if (!ok || nrow > Int_max || ncol > Int_max || nzmax > Int_max) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (NULL) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate header */ /* ---------------------------------------------------------------------- */ X = CHOLMOD(malloc) (sizeof (cholmod_dense), 1, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } PRINT1 (("cholmod_allocate_dense %d-by-%d nzmax %d xtype %d\n", nrow, ncol, nzmax, xtype)) ; X->nrow = nrow ; X->ncol = ncol ; X->nzmax = nzmax ; X->xtype = xtype ; X->dtype = DTYPE ; X->x = NULL ; X->z = NULL ; X->d = d ; /* ---------------------------------------------------------------------- */ /* allocate the matrix itself */ /* ---------------------------------------------------------------------- */ nzmax0 = 0 ; CHOLMOD(realloc_multiple) (nzmax, 0, xtype, NULL, NULL, &(X->x), &(X->z), &nzmax0, Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_dense) (&X, Common) ; return (NULL) ; /* out of memory */ } return (X) ; } /* ========================================================================== */ /* === cholmod_zeros ======================================================== */ /* ========================================================================== */ /* Allocate a dense matrix and set it to zero */ cholmod_dense *CHOLMOD(zeros) ( /* ---- input ---- */ size_t nrow, /* # of rows of matrix */ size_t ncol, /* # of columns of matrix */ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) { cholmod_dense *X ; double *Xx, *Xz ; Int i, nz ; /* ---------------------------------------------------------------------- */ /* allocate a dense matrix and set it to zero */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; X = CHOLMOD(allocate_dense) (nrow, ncol, nrow, xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* NULL Common, out of memory, or inputs invalid */ } Xx = X->x ; Xz = X->z ; nz = MAX (1, X->nzmax) ; switch (xtype) { case CHOLMOD_REAL: for (i = 0 ; i < nz ; i++) { Xx [i] = 0 ; } break ; case CHOLMOD_COMPLEX: for (i = 0 ; i < 2*nz ; i++) { Xx [i] = 0 ; } break ; case CHOLMOD_ZOMPLEX: for (i = 0 ; i < nz ; i++) { Xx [i] = 0 ; } for (i = 0 ; i < nz ; i++) { Xz [i] = 0 ; } break ; } return (X) ; } /* ========================================================================== */ /* === cholmod_ones ========================================================= */ /* ========================================================================== */ /* Allocate a dense matrix and set it to zero */ cholmod_dense *CHOLMOD(ones) ( /* ---- input ---- */ size_t nrow, /* # of rows of matrix */ size_t ncol, /* # of columns of matrix */ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) { cholmod_dense *X ; double *Xx, *Xz ; Int i, nz ; /* ---------------------------------------------------------------------- */ /* allocate a dense matrix and set it to all ones */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; X = CHOLMOD(allocate_dense) (nrow, ncol, nrow, xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* NULL Common, out of memory, or inputs invalid */ } Xx = X->x ; Xz = X->z ; nz = MAX (1, X->nzmax) ; switch (xtype) { case CHOLMOD_REAL: for (i = 0 ; i < nz ; i++) { Xx [i] = 1 ; } break ; case CHOLMOD_COMPLEX: for (i = 0 ; i < nz ; i++) { Xx [2*i ] = 1 ; Xx [2*i+1] = 0 ; } break ; case CHOLMOD_ZOMPLEX: for (i = 0 ; i < nz ; i++) { Xx [i] = 1 ; } for (i = 0 ; i < nz ; i++) { Xz [i] = 0 ; } break ; } return (X) ; } /* ========================================================================== */ /* === cholmod_eye ========================================================== */ /* ========================================================================== */ /* Allocate a dense matrix and set it to the identity matrix */ cholmod_dense *CHOLMOD(eye) ( /* ---- input ---- */ size_t nrow, /* # of rows of matrix */ size_t ncol, /* # of columns of matrix */ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) { cholmod_dense *X ; double *Xx, *Xz ; Int i, n, nz ; /* ---------------------------------------------------------------------- */ /* allocate a dense matrix and set it to the identity matrix */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; X = CHOLMOD(zeros) (nrow, ncol, xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* NULL Common, out of memory, or inputs invalid */ } nz = MAX (1, nrow*ncol) ; Xx = X->x ; Xz = X->z ; n = MIN (nrow, ncol) ; switch (xtype) { case CHOLMOD_REAL: case CHOLMOD_ZOMPLEX: for (i = 0 ; i < n ; i++) { Xx [i + i*nrow] = 1 ; } break ; case CHOLMOD_COMPLEX: for (i = 0 ; i < n ; i++) { Xx [2 * (i + i*nrow)] = 1 ; } break ; } return (X) ; } /* ========================================================================== */ /* === cholmod_free_dense =================================================== */ /* ========================================================================== */ /* free a dense matrix * * workspace: none */ int CHOLMOD(free_dense) ( /* ---- in/out --- */ cholmod_dense **XHandle, /* dense matrix to deallocate, NULL on output */ /* --------------- */ cholmod_common *Common ) { cholmod_dense *X ; RETURN_IF_NULL_COMMON (FALSE) ; if (XHandle == NULL) { /* nothing to do */ return (TRUE) ; } X = *XHandle ; if (X == NULL) { /* nothing to do */ return (TRUE) ; } switch (X->xtype) { case CHOLMOD_REAL: X->x = CHOLMOD(free) (X->nzmax, sizeof (double), X->x, Common) ; break ; case CHOLMOD_COMPLEX: X->x = CHOLMOD(free) (X->nzmax, 2*sizeof (double), X->x, Common) ; break ; case CHOLMOD_ZOMPLEX: X->x = CHOLMOD(free) (X->nzmax, sizeof (double), X->x, Common) ; X->z = CHOLMOD(free) (X->nzmax, sizeof (double), X->z, Common) ; break ; } *XHandle = CHOLMOD(free) (1, sizeof (cholmod_dense), (*XHandle), Common) ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_sparse_to_dense ============================================== */ /* ========================================================================== */ /* Convert a sparse matrix to a dense matrix. * The output dense matrix has the same xtype as the input sparse matrix, * except that a pattern-only sparse matrix A is converted into a real dense * matrix X, with 1's and 0's. All xtypes are supported. */ cholmod_dense *CHOLMOD(sparse_to_dense) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) { cholmod_dense *X = NULL ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ; if (A->stype && A->nrow != A->ncol) { ERROR (CHOLMOD_INVALID, "matrix invalid") ; return (NULL) ; } Common->status = CHOLMOD_OK ; ASSERT (CHOLMOD(dump_sparse) (A, "A", Common) >= 0) ; /* ---------------------------------------------------------------------- */ /* convert the matrix, using template routine */ /* ---------------------------------------------------------------------- */ switch (A->xtype) { case CHOLMOD_PATTERN: X = p_cholmod_sparse_to_dense (A, Common) ; break ; case CHOLMOD_REAL: X = r_cholmod_sparse_to_dense (A, Common) ; break ; case CHOLMOD_COMPLEX: X = c_cholmod_sparse_to_dense (A, Common) ; break ; case CHOLMOD_ZOMPLEX: X = z_cholmod_sparse_to_dense (A, Common) ; break ; } return (X) ; } /* ========================================================================== */ /* === cholmod_dense_to_sparse ============================================== */ /* ========================================================================== */ /* Convert a dense matrix to a sparse matrix, similar to the MATLAB statements: * * C = sparse (X) values = TRUE * C = spones (sparse (X)) values = FALSE * * except that X must be double (it can be of many different types in MATLAB) * * The resulting sparse matrix C has the same numeric xtype as the input dense * matrix X, unless "values" is FALSE (in which case C is real, where C(i,j)=1 * if (i,j) is an entry in X. */ cholmod_sparse *CHOLMOD(dense_to_sparse) ( /* ---- input ---- */ cholmod_dense *X, /* matrix to copy */ int values, /* TRUE if values to be copied, FALSE otherwise */ /* --------------- */ cholmod_common *Common ) { cholmod_sparse *C = NULL ; DEBUG (CHOLMOD(dump_dense) (X, "X", Common)) ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (X, NULL) ; RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ; if (X->d < X->nrow) { ERROR (CHOLMOD_INVALID, "matrix invalid") ; return (NULL) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* convert the matrix, using template routine */ /* ---------------------------------------------------------------------- */ switch (X->xtype) { case CHOLMOD_REAL: C = r_cholmod_dense_to_sparse (X, values, Common) ; break ; case CHOLMOD_COMPLEX: C = c_cholmod_dense_to_sparse (X, values, Common) ; break ; case CHOLMOD_ZOMPLEX: C = z_cholmod_dense_to_sparse (X, values, Common) ; break ; } return (C) ; } /* ========================================================================== */ /* === cholmod_copy_dense2 ================================================== */ /* ========================================================================== */ /* Y = X, where X and Y are both already allocated. The leading dimensions of * X and Y may differ, but both must be >= the # of rows in X and Y. * Entries in rows nrow to d-1 are not copied from X, since the space might not * be initialized. Y->nzmax is unchanged. X->nzmax is typically * (X->d)*(X->ncol), but a user might modify that condition outside of any * CHOLMOD routine. * * The two dense matrices X and Y must have the same numeric xtype. */ int CHOLMOD(copy_dense2) ( /* ---- input ---- */ cholmod_dense *X, /* matrix to copy */ /* ---- output --- */ cholmod_dense *Y, /* copy of matrix X */ /* --------------- */ cholmod_common *Common ) { /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (X, FALSE) ; RETURN_IF_NULL (Y, FALSE) ; RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (Y, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; if (X->nrow != Y->nrow || X->ncol != Y->ncol || X->xtype != Y->xtype) { ERROR (CHOLMOD_INVALID, "X and Y must have same dimensions and xtype") ; return (FALSE) ; } if (X->d < X->nrow || Y->d < Y->nrow || (X->d * X->ncol) > X->nzmax || (Y->d * Y->ncol) > Y->nzmax) { ERROR (CHOLMOD_INVALID, "X and/or Y invalid") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* copy the matrix, using template routine */ /* ---------------------------------------------------------------------- */ switch (X->xtype) { case CHOLMOD_REAL: r_cholmod_copy_dense2 (X, Y) ; break ; case CHOLMOD_COMPLEX: c_cholmod_copy_dense2 (X, Y) ; break ; case CHOLMOD_ZOMPLEX: z_cholmod_copy_dense2 (X, Y) ; break ; } return (TRUE) ; } /* ========================================================================== */ /* === cholmod_copy_dense =================================================== */ /* ========================================================================== */ /* Y = X, copy a dense matrix */ cholmod_dense *CHOLMOD(copy_dense) ( /* ---- input ---- */ cholmod_dense *X, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) { cholmod_dense *Y ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (X, NULL) ; RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate result */ /* ---------------------------------------------------------------------- */ Y = CHOLMOD(allocate_dense) (X->nrow, X->ncol, X->d, X->xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory or X invalid */ } /* ---------------------------------------------------------------------- */ /* Y = X */ /* ---------------------------------------------------------------------- */ /* This cannot fail (X and Y are allocated, and have the same nrow, ncol * d, and xtype) */ CHOLMOD(copy_dense2) (X, Y, Common) ; /* ---------------------------------------------------------------------- */ /* return result */ /* ---------------------------------------------------------------------- */ return (Y) ; } SuiteSparse/CHOLMOD/Core/t_cholmod_transpose.c0000644001170100242450000002131710537777456020167 0ustar davisfac/* ========================================================================== */ /* === Core/t_cholmod_transpose ============================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Template routine for cholmod_transpose. All xtypes are supported. For * complex matrices, either the array tranpose or complex conjugate transpose * can be computed. */ #include "cholmod_template.h" /* ========================================================================== */ /* === t_cholmod_transpose_unsym ============================================ */ /* ========================================================================== */ /* Compute F = A', A (:,f)', or A (p,f)', where A is unsymmetric and F is * already allocated. The complex case performs either the array transpose * or complex conjugate transpose. * * workspace: * Iwork (MAX (nrow,ncol)) if fset is present * Iwork (nrow) if fset is NULL */ static int TEMPLATE (cholmod_transpose_unsym) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to transpose */ Int *Perm, /* size nrow, if present (can be NULL) */ Int *fset, /* subset of 0:(A->ncol)-1 */ Int nf, /* size of fset */ /* ---- output --- */ cholmod_sparse *F, /* F = A', A(:,f)', or A(p,f)' */ /* --------------- */ cholmod_common *Common ) { double *Ax, *Az, *Fx, *Fz ; Int *Ap, *Anz, *Ai, *Fp, *Fnz, *Fj, *Wi, *Iwork ; Int j, p, pend, nrow, ncol, Apacked, use_fset, fp, Fpacked, jj, permute ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ /* ensure the xtype of A and F match (ignored if this is pattern version) */ if (!XTYPE_OK (A->xtype)) { ERROR (CHOLMOD_INVALID, "real/complex mismatch") ; return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ use_fset = (fset != NULL) ; nrow = A->nrow ; ncol = A->ncol ; Ap = A->p ; /* size A->ncol+1, column pointers of A */ Ai = A->i ; /* size nz = Ap [A->ncol], row indices of A */ Ax = A->x ; /* size nz, real values of A */ Az = A->z ; /* size nz, imag values of A */ Anz = A->nz ; Apacked = A->packed ; ASSERT (IMPLIES (!Apacked, Anz != NULL)) ; permute = (Perm != NULL) ; Fp = F->p ; /* size A->nrow+1, row pointers of F */ Fj = F->i ; /* size nz, column indices of F */ Fx = F->x ; /* size nz, real values of F */ Fz = F->z ; /* size nz, imag values of F */ Fnz = F->nz ; Fpacked = F->packed ; ASSERT (IMPLIES (!Fpacked, Fnz != NULL)) ; nf = (use_fset) ? nf : ncol ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Iwork = Common->Iwork ; Wi = Iwork ; /* size nrow (i/l/l) */ /* ---------------------------------------------------------------------- */ /* construct the transpose */ /* ---------------------------------------------------------------------- */ for (jj = 0 ; jj < nf ; jj++) { j = (use_fset) ? (fset [jj]) : jj ; p = Ap [j] ; pend = (Apacked) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { fp = Wi [Ai [p]]++ ; Fj [fp] = j ; #ifdef NCONJUGATE ASSIGN (Fx, Fz, fp, Ax, Az, p) ; #else ASSIGN_CONJ (Fx, Fz, fp, Ax, Az, p) ; #endif } } return (TRUE) ; } /* ========================================================================== */ /* === t_cholmod_transpose_sym ============================================== */ /* ========================================================================== */ /* Compute F = A' or A (p,p)', where A is symmetric and F is already allocated. * The complex case performs either the array transpose or complex conjugate * transpose. * * workspace: Iwork (nrow) if Perm NULL, Iwork (2*nrow) if Perm non-NULL. */ static int TEMPLATE (cholmod_transpose_sym) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to transpose */ Int *Perm, /* size n, if present (can be NULL) */ /* ---- output --- */ cholmod_sparse *F, /* F = A' or A(p,p)' */ /* --------------- */ cholmod_common *Common ) { double *Ax, *Az, *Fx, *Fz ; Int *Ap, *Anz, *Ai, *Fp, *Fj, *Wi, *Pinv, *Iwork ; Int p, pend, packed, fp, upper, permute, jold, n, i, j, iold ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ /* ensure the xtype of A and F match (ignored if this is pattern version) */ if (!XTYPE_OK (A->xtype)) { ERROR (CHOLMOD_INVALID, "real/complex mismatch") ; return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ permute = (Perm != NULL) ; n = A->nrow ; Ap = A->p ; /* size A->ncol+1, column pointers of A */ Ai = A->i ; /* size nz = Ap [A->ncol], row indices of A */ Ax = A->x ; /* size nz, real values of A */ Az = A->z ; /* size nz, imag values of A */ Anz = A->nz ; packed = A->packed ; ASSERT (IMPLIES (!packed, Anz != NULL)) ; upper = (A->stype > 0) ; Fp = F->p ; /* size A->nrow+1, row pointers of F */ Fj = F->i ; /* size nz, column indices of F */ Fx = F->x ; /* size nz, real values of F */ Fz = F->z ; /* size nz, imag values of F */ /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Iwork = Common->Iwork ; Wi = Iwork ; /* size n (i/l/l) */ Pinv = Iwork + n ; /* size n (i/i/l) , unused if Perm NULL */ /* ---------------------------------------------------------------------- */ /* construct the transpose */ /* ---------------------------------------------------------------------- */ if (permute) { if (upper) { /* permuted, upper */ for (j = 0 ; j < n ; j++) { jold = Perm [j] ; p = Ap [jold] ; pend = (packed) ? Ap [jold+1] : p + Anz [jold] ; for ( ; p < pend ; p++) { iold = Ai [p] ; if (iold <= jold) { i = Pinv [iold] ; if (i < j) { fp = Wi [i]++ ; Fj [fp] = j ; #ifdef NCONJUGATE ASSIGN (Fx, Fz, fp, Ax, Az, p) ; #else ASSIGN_CONJ (Fx, Fz, fp, Ax, Az, p) ; #endif } else { fp = Wi [j]++ ; Fj [fp] = i ; ASSIGN (Fx, Fz, fp, Ax, Az, p) ; } } } } } else { /* permuted, lower */ for (j = 0 ; j < n ; j++) { jold = Perm [j] ; p = Ap [jold] ; pend = (packed) ? Ap [jold+1] : p + Anz [jold] ; for ( ; p < pend ; p++) { iold = Ai [p] ; if (iold >= jold) { i = Pinv [iold] ; if (i > j) { fp = Wi [i]++ ; Fj [fp] = j ; #ifdef NCONJUGATE ASSIGN (Fx, Fz, fp, Ax, Az, p) ; #else ASSIGN_CONJ (Fx, Fz, fp, Ax, Az, p) ; #endif } else { fp = Wi [j]++ ; Fj [fp] = i ; ASSIGN (Fx, Fz, fp, Ax, Az, p) ; } } } } } } else { if (upper) { /* unpermuted, upper */ for (j = 0 ; j < n ; j++) { p = Ap [j] ; pend = (packed) ? Ap [j+1] : p + Anz [j] ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i <= j) { fp = Wi [i]++ ; Fj [fp] = j ; #ifdef NCONJUGATE ASSIGN (Fx, Fz, fp, Ax, Az, p) ; #else ASSIGN_CONJ (Fx, Fz, fp, Ax, Az, p) ; #endif } } } } else { /* unpermuted, lower */ for (j = 0 ; j < n ; j++) { p = Ap [j] ; pend = (packed) ? Ap [j+1] : p + Anz [j] ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i >= j) { fp = Wi [i]++ ; Fj [fp] = j ; #ifdef NCONJUGATE ASSIGN (Fx, Fz, fp, Ax, Az, p) ; #else ASSIGN_CONJ (Fx, Fz, fp, Ax, Az, p) ; #endif } } } } } return (TRUE) ; } #undef PATTERN #undef REAL #undef COMPLEX #undef ZOMPLEX #undef NCONJUGATE SuiteSparse/CHOLMOD/Core/t_cholmod_dense.c0000644001170100242450000001626410537777454017252 0ustar davisfac/* ========================================================================== */ /* === Core/t_cholmod_dense ================================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Template routine for cholmod_dense. All xtypes supported, except that there * are no dense matrices with an xtype of pattern. */ #include "cholmod_template.h" /* ========================================================================== */ /* === t_cholmod_sparse_to_dense ============================================ */ /* ========================================================================== */ static cholmod_dense *TEMPLATE (cholmod_sparse_to_dense) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) { double *Ax, *Xx, *Az, *Xz ; Int *Ap, *Ai, *Anz ; cholmod_dense *X ; Int i, j, p, pend, nrow, ncol, packed ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nrow = A->nrow ; ncol = A->ncol ; packed = A->packed ; Ap = A->p ; Ai = A->i ; Ax = A->x ; Az = A->z ; Anz = A->nz ; /* ---------------------------------------------------------------------- */ /* allocate result */ /* ---------------------------------------------------------------------- */ X = CHOLMOD(zeros) (nrow, ncol, XTYPE2, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } Xx = X->x ; Xz = X->z ; /* ---------------------------------------------------------------------- */ /* copy into dense matrix */ /* ---------------------------------------------------------------------- */ if (A->stype < 0) { /* A is symmetric with lower stored, but both parts of X are present */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i >= j) { ASSIGN2 (Xx, Xz, i+j*nrow, Ax, Az, p) ; ASSIGN2_CONJ (Xx, Xz, j+i*nrow, Ax, Az, p) ; } } } } else if (A->stype > 0) { /* A is symmetric with upper stored, but both parts of X are present */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i <= j) { ASSIGN2 (Xx, Xz, i+j*nrow, Ax, Az, p) ; ASSIGN2_CONJ (Xx, Xz, j+i*nrow, Ax, Az, p) ; } } } } else { /* both parts of A and X are present */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; ASSIGN2 (Xx, Xz, i+j*nrow, Ax, Az, p) ; } } } return (X) ; } #ifndef PATTERN /* There are no dense matrices of xtype CHOLMOD_PATTERN */ /* ========================================================================== */ /* === t_cholmod_dense_to_sparse ============================================ */ /* ========================================================================== */ static cholmod_sparse *TEMPLATE (cholmod_dense_to_sparse) ( /* ---- input ---- */ cholmod_dense *X, /* matrix to copy */ int values, /* TRUE if values to be copied, FALSE otherwise */ /* --------------- */ cholmod_common *Common ) { double *Xx, *Cx, *Xz, *Cz ; Int *Ci, *Cp ; cholmod_sparse *C ; Int i, j, p, d, nrow, ncol, nz ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nrow = X->nrow ; ncol = X->ncol ; d = X->d ; Xx = X->x ; Xz = X->z ; /* ---------------------------------------------------------------------- */ /* count the number of nonzeros in the result */ /* ---------------------------------------------------------------------- */ nz = 0 ; for (j = 0 ; j < ncol ; j++) { for (i = 0 ; i < nrow ; i++) { if (ENTRY_IS_NONZERO (Xx, Xz, i+j*d)) { nz++ ; } } } /* ---------------------------------------------------------------------- */ /* allocate the result C */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(allocate_sparse) (nrow, ncol, nz, TRUE, TRUE, 0, values ? XTYPE : CHOLMOD_PATTERN, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } Cp = C->p ; Ci = C->i ; Cx = C->x ; Cz = C->z ; /* ---------------------------------------------------------------------- */ /* copy the dense matrix X into the sparse matrix C */ /* ---------------------------------------------------------------------- */ p = 0 ; for (j = 0 ; j < ncol ; j++) { Cp [j] = p ; for (i = 0 ; i < nrow ; i++) { if (ENTRY_IS_NONZERO (Xx, Xz, i+j*d)) { Ci [p] = i ; if (values) { ASSIGN (Cx, Cz, p, Xx, Xz, i+j*d) ; } p++ ; } } } ASSERT (p == nz) ; Cp [ncol] = nz ; /* ---------------------------------------------------------------------- */ /* return result */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_sparse) (C, "C", Common) >= 0) ; return (C) ; } /* ========================================================================== */ /* === t_cholmod_copy_dense2 ================================================ */ /* ========================================================================== */ /* Y = X, where X and Y are both already allocated. */ static int TEMPLATE (cholmod_copy_dense2) ( /* ---- input ---- */ cholmod_dense *X, /* matrix to copy */ /* ---- output --- */ cholmod_dense *Y /* copy of matrix X */ ) { double *Xx, *Xz, *Yx, *Yz ; Int i, j, nrow, ncol, dy, dx ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Xx = X->x ; Xz = X->z ; Yx = Y->x ; Yz = Y->z ; dx = X->d ; dy = Y->d ; nrow = X->nrow ; ncol = X->ncol ; /* ---------------------------------------------------------------------- */ /* copy */ /* ---------------------------------------------------------------------- */ CLEAR (Yx, Yz, 0) ; for (j = 0 ; j < ncol ; j++) { for (i = 0 ; i < nrow ; i++) { ASSIGN (Yx, Yz, i+j*dy, Xx, Xz, i+j*dx) ; } } return (TRUE) ; } #endif #undef PATTERN #undef REAL #undef COMPLEX #undef ZOMPLEX SuiteSparse/CHOLMOD/Core/cholmod_error.c0000644001170100242450000000535110537777426016754 0ustar davisfac/* ========================================================================== */ /* === Core/cholmod_error =================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* CHOLMOD error-handling routine. */ #include "cholmod_internal.h" #include "cholmod_core.h" /* ========================================================================== */ /* ==== cholmod_error ======================================================= */ /* ========================================================================== */ /* An error has occurred. Set the status, optionally print an error message, * and call the user error-handling routine (if it exists). If * Common->try_catch is TRUE, then CHOLMOD is inside a try/catch block. * The status is set, but no message is printed and the user error handler * is not called. This is not (yet) an error, since CHOLMOD may recover. * * In the current version, this try/catch mechanism is used internally only in * cholmod_analyze, which tries multiple ordering methods and picks the best * one. If one or more ordering method fails, it keeps going. Only one * ordering needs to succeed for cholmod_analyze to succeed. */ int CHOLMOD(error) ( /* ---- input ---- */ int status, /* error status */ char *file, /* name of source code file where error occured */ int line, /* line number in source code file where error occured*/ char *message, /* error message */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = status ; if (!(Common->try_catch)) { #ifndef NPRINT /* print a warning or error message */ if (Common->print_function != NULL) { if (status > 0 && Common->print > 1) { (Common->print_function) ("CHOLMOD warning: %s\n", message) ; fflush (stdout) ; fflush (stderr) ; } else if (Common->print > 0) { (Common->print_function) ("CHOLMOD error: %s\n", message) ; fflush (stdout) ; fflush (stderr) ; } } #endif /* call the user error handler, if it exists */ if (Common->error_handler != NULL) { Common->error_handler (status, file, line, message) ; } } return (TRUE) ; } SuiteSparse/CHOLMOD/Core/cholmod_common.c0000644001170100242450000005114510664623514017102 0ustar davisfac/* ========================================================================== */ /* === Core/cholmod_common ================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Core Module. Copyright (C) 2005-2006, * Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Core utility routines for the cholmod_common object: * * Primary routines: * ----------------- * cholmod_start the first call to CHOLMOD * cholmod_finish the last call to CHOLMOD * * Secondary routines: * ------------------- * cholmod_defaults restore (most) default control parameters * cholmod_allocate_work allocate (or reallocate) workspace in Common * cholmod_free_work free workspace in Common * cholmod_clear_flag clear Common->Flag in workspace * cholmod_maxrank column dimension of Common->Xwork workspace * * The Common object is unique. It cannot be allocated or deallocated by * CHOLMOD, since it contains the definition of the memory management routines * used (pointers to malloc, free, realloc, and calloc, or their equivalent). * The Common object contains workspace that is used between calls to * CHOLMOD routines. This workspace allocated by CHOLMOD as needed, by * cholmod_allocate_work and cholmod_free_work. */ #include "cholmod_internal.h" #include "cholmod_core.h" /* ========================================================================== */ /* === cholmod_start ======================================================== */ /* ========================================================================== */ /* Initialize Common default parameters and statistics. Sets workspace * pointers to NULL. * * This routine must be called just once, prior to calling any other CHOLMOD * routine. Do not call this routine after any other CHOLMOD routine (except * cholmod_finish, to start a new CHOLMOD session), or a memory leak will * occur. * * workspace: none */ int CHOLMOD(start) ( cholmod_common *Common ) { if (Common == NULL) { return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* user error handling routine */ /* ---------------------------------------------------------------------- */ Common->error_handler = NULL ; /* ---------------------------------------------------------------------- */ /* integer and numerical types */ /* ---------------------------------------------------------------------- */ Common->itype = ITYPE ; Common->dtype = DTYPE ; /* ---------------------------------------------------------------------- */ /* default control parameters */ /* ---------------------------------------------------------------------- */ CHOLMOD(defaults) (Common) ; Common->try_catch = FALSE ; /* ---------------------------------------------------------------------- */ /* memory management routines */ /* ---------------------------------------------------------------------- */ /* The user can replace cholmod's memory management routines by redefining * these function pointers. */ #ifndef NMALLOC /* stand-alone ANSI C program */ Common->malloc_memory = malloc ; Common->free_memory = free ; Common->realloc_memory = realloc ; Common->calloc_memory = calloc ; #else /* no memory manager defined at compile-time; MUST define one at run-time */ Common->malloc_memory = NULL ; Common->free_memory = NULL ; Common->realloc_memory = NULL ; Common->calloc_memory = NULL ; #endif /* ---------------------------------------------------------------------- */ /* complex arithmetic routines */ /* ---------------------------------------------------------------------- */ Common->complex_divide = CHOLMOD(divcomplex) ; Common->hypotenuse = CHOLMOD(hypot) ; /* ---------------------------------------------------------------------- */ /* print routine */ /* ---------------------------------------------------------------------- */ #ifndef NPRINT /* stand-alone ANSI C program */ Common->print_function = printf ; #else /* printing disabled */ Common->print_function = NULL ; #endif /* ---------------------------------------------------------------------- */ /* workspace */ /* ---------------------------------------------------------------------- */ /* This code assumes the workspace held in Common is not initialized. If * it is, then a memory leak will occur because the pointers are * overwritten with NULL. */ Common->nrow = 0 ; Common->mark = EMPTY ; Common->xworksize = 0 ; Common->iworksize = 0 ; Common->Flag = NULL ; Common->Head = NULL ; Common->Iwork = NULL ; Common->Xwork = NULL ; Common->no_workspace_reallocate = FALSE ; /* ---------------------------------------------------------------------- */ /* statistics */ /* ---------------------------------------------------------------------- */ /* fl and lnz are computed in cholmod_analyze and cholmod_rowcolcounts */ Common->fl = EMPTY ; Common->lnz = EMPTY ; /* modfl is computed in cholmod_updown, cholmod_rowadd, and cholmod_rowdel*/ Common->modfl = EMPTY ; /* all routines use status as their error-report code */ Common->status = CHOLMOD_OK ; Common->malloc_count = 0 ; /* # calls to malloc minus # calls to free */ Common->memory_usage = 0 ; /* peak memory usage (in bytes) */ Common->memory_inuse = 0 ; /* current memory in use (in bytes) */ Common->nrealloc_col = 0 ; Common->nrealloc_factor = 0 ; Common->ndbounds_hit = 0 ; Common->rowfacfl = 0 ; Common->aatfl = EMPTY ; /* Common->called_nd is TRUE if cholmod_analyze called or NESDIS */ Common->called_nd = FALSE ; DEBUG_INIT ("cholmod start", Common) ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_defaults ===================================================== */ /* ========================================================================== */ /* Set Common default parameters, except for the function pointers. * * workspace: none */ int CHOLMOD(defaults) ( cholmod_common *Common ) { Int i ; RETURN_IF_NULL_COMMON (FALSE) ; /* ---------------------------------------------------------------------- */ /* default control parameters */ /* ---------------------------------------------------------------------- */ Common->dbound = 0.0 ; Common->grow0 = 1.2 ; Common->grow1 = 1.2 ; Common->grow2 = 5 ; Common->maxrank = 8 ; Common->final_asis = TRUE ; Common->final_super = TRUE ; Common->final_ll = FALSE ; Common->final_pack = TRUE ; Common->final_monotonic = TRUE ; Common->final_resymbol = FALSE ; /* use simplicial factorization if flop/nnz(L) < 40, supernodal otherwise */ Common->supernodal = CHOLMOD_AUTO ; Common->supernodal_switch = 40 ; Common->nrelax [0] = 4 ; Common->nrelax [1] = 16 ; Common->nrelax [2] = 48 ; Common->zrelax [0] = 0.8 ; Common->zrelax [1] = 0.1 ; Common->zrelax [2] = 0.05 ; Common->prefer_zomplex = FALSE ; Common->prefer_upper = TRUE ; Common->prefer_binary = FALSE ; Common->quick_return_if_not_posdef = FALSE ; /* METIS workarounds */ Common->metis_memory = 0.0 ; /* > 0 for memory guard (2 is reasonable) */ Common->metis_nswitch = 3000 ; Common->metis_dswitch = 0.66 ; Common->print = 3 ; Common->precise = FALSE ; /* ---------------------------------------------------------------------- */ /* default ordering methods */ /* ---------------------------------------------------------------------- */ /* Note that if the Partition module is not installed, the CHOLMOD_METIS * and CHOLMOD_NESDIS methods will not be available. cholmod_analyze will * report the CHOLMOD_NOT_INSTALLED error, and safely skip over them. */ #if (CHOLMOD_MAXMETHODS < 9) #error "CHOLMOD_MAXMETHODS must be 9 or more (defined in cholmod_core.h)." #endif /* default strategy: try given, AMD, and then METIS if AMD reports high * fill-in. NESDIS can be used instead, if Common->default_nesdis is TRUE. */ Common->nmethods = 0 ; /* use default strategy */ Common->default_nesdis = FALSE ; /* use METIS in default strategy */ Common->current = 0 ; /* current method being tried */ Common->selected = 0 ; /* the best method selected */ /* first, fill each method with default parameters */ for (i = 0 ; i <= CHOLMOD_MAXMETHODS ; i++) { /* CHOLMOD's default method is AMD for A or AA' */ Common->method [i].ordering = CHOLMOD_AMD ; /* CHOLMOD nested dissection and minimum degree parameter */ Common->method [i].prune_dense = 10.0 ; /* dense row/col control */ /* min degree parameters (AMD, COLAMD, SYMAMD, CAMD, CCOLAMD, CSYMAMD)*/ Common->method [i].prune_dense2 = -1 ; /* COLAMD dense row control */ Common->method [i].aggressive = TRUE ; /* aggressive absorption */ Common->method [i].order_for_lu = FALSE ;/* order for Cholesky not LU */ /* CHOLMOD's nested dissection (METIS + constrained AMD) */ Common->method [i].nd_small = 200 ; /* small graphs aren't cut */ Common->method [i].nd_compress = TRUE ; /* compress graph & subgraphs */ Common->method [i].nd_camd = 1 ; /* use CAMD */ Common->method [i].nd_components = FALSE ; /* lump connected comp. */ Common->method [i].nd_oksep = 1.0 ; /* sep ok if < oksep*n */ /* statistics for each method are not yet computed */ Common->method [i].fl = EMPTY ; Common->method [i].lnz = EMPTY ; } Common->postorder = TRUE ; /* follow ordering with weighted postorder */ /* Next, define some methods. The first five use default parameters. */ Common->method [0].ordering = CHOLMOD_GIVEN ; /* skip if UserPerm NULL */ Common->method [1].ordering = CHOLMOD_AMD ; Common->method [2].ordering = CHOLMOD_METIS ; Common->method [3].ordering = CHOLMOD_NESDIS ; Common->method [4].ordering = CHOLMOD_NATURAL ; /* CHOLMOD's nested dissection with large leaves of separator tree */ Common->method [5].ordering = CHOLMOD_NESDIS ; Common->method [5].nd_small = 20000 ; /* CHOLMOD's nested dissection with tiny leaves, and no AMD ordering */ Common->method [6].ordering = CHOLMOD_NESDIS ; Common->method [6].nd_small = 4 ; Common->method [6].nd_camd = 0 ; /* no CSYMAMD or CAMD */ /* CHOLMOD's nested dissection with no dense node removal */ Common->method [7].ordering = CHOLMOD_NESDIS ; Common->method [7].prune_dense = -1. ; /* COLAMD for A*A', AMD for A */ Common->method [8].ordering = CHOLMOD_COLAMD ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_finish ======================================================= */ /* ========================================================================== */ /* The last call to CHOLMOD must be cholmod_finish. You may call this routine * more than once, and can safely call any other CHOLMOD routine after calling * it (including cholmod_start). * * The statistics and parameter settings in Common are preserved. The * workspace in Common is freed. This routine is just another name for * cholmod_free_work. */ int CHOLMOD(finish) ( cholmod_common *Common ) { return (CHOLMOD(free_work) (Common)) ; } /* ========================================================================== */ /* === cholmod_allocate_work ================================================ */ /* ========================================================================== */ /* Allocate and initialize workspace for CHOLMOD routines, or increase the size * of already-allocated workspace. If enough workspace is already allocated, * then nothing happens. * * workspace: Flag (nrow), Head (nrow+1), Iwork (iworksize), Xwork (xworksize) */ int CHOLMOD(allocate_work) ( /* ---- input ---- */ size_t nrow, /* # of rows in the matrix A */ size_t iworksize, /* size of Iwork */ size_t xworksize, /* size of Xwork */ /* --------------- */ cholmod_common *Common ) { double *W ; Int *Head ; Int i ; size_t nrow1 ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* Allocate Flag (nrow) and Head (nrow+1) */ /* ---------------------------------------------------------------------- */ nrow = MAX (1, nrow) ; /* nrow1 = nrow + 1 */ nrow1 = CHOLMOD(add_size_t) (nrow, 1, &ok) ; if (!ok) { /* nrow+1 causes size_t overflow ; problem is too large */ Common->status = CHOLMOD_TOO_LARGE ; CHOLMOD(free_work) (Common) ; return (FALSE) ; } if (nrow > Common->nrow) { if (Common->no_workspace_reallocate) { /* CHOLMOD is not allowed to change the workspace here */ Common->status = CHOLMOD_INVALID ; return (FALSE) ; } /* free the old workspace (if any) and allocate new space */ Common->Flag = CHOLMOD(free) (Common->nrow, sizeof (Int), Common->Flag, Common) ; Common->Head = CHOLMOD(free) (Common->nrow+1,sizeof (Int), Common->Head, Common) ; Common->Flag = CHOLMOD(malloc) (nrow, sizeof (Int), Common) ; Common->Head = CHOLMOD(malloc) (nrow1, sizeof (Int), Common) ; /* record the new size of Flag and Head */ Common->nrow = nrow ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_work) (Common) ; return (FALSE) ; } /* initialize Flag and Head */ Common->mark = EMPTY ; CHOLMOD(clear_flag) (Common) ; Head = Common->Head ; for (i = 0 ; i <= (Int) (nrow) ; i++) { Head [i] = EMPTY ; } } /* ---------------------------------------------------------------------- */ /* Allocate Iwork (iworksize) */ /* ---------------------------------------------------------------------- */ iworksize = MAX (1, iworksize) ; if (iworksize > Common->iworksize) { if (Common->no_workspace_reallocate) { /* CHOLMOD is not allowed to change the workspace here */ Common->status = CHOLMOD_INVALID ; return (FALSE) ; } /* free the old workspace (if any) and allocate new space. * integer overflow safely detected in cholmod_malloc */ CHOLMOD(free) (Common->iworksize, sizeof (Int), Common->Iwork, Common) ; Common->Iwork = CHOLMOD(malloc) (iworksize, sizeof (Int), Common) ; /* record the new size of Iwork */ Common->iworksize = iworksize ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_work) (Common) ; return (FALSE) ; } /* note that Iwork does not need to be initialized */ } /* ---------------------------------------------------------------------- */ /* Allocate Xwork (xworksize) and set it to ((double) 0.) */ /* ---------------------------------------------------------------------- */ /* make sure xworksize is >= 1 */ xworksize = MAX (1, xworksize) ; if (xworksize > Common->xworksize) { if (Common->no_workspace_reallocate) { /* CHOLMOD is not allowed to change the workspace here */ Common->status = CHOLMOD_INVALID ; return (FALSE) ; } /* free the old workspace (if any) and allocate new space */ CHOLMOD(free) (Common->xworksize, sizeof (double), Common->Xwork, Common) ; Common->Xwork = CHOLMOD(malloc) (xworksize, sizeof (double), Common) ; /* record the new size of Xwork */ Common->xworksize = xworksize ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_work) (Common) ; return (FALSE) ; } /* initialize Xwork */ W = Common->Xwork ; for (i = 0 ; i < (Int) xworksize ; i++) { W [i] = 0. ; } } return (TRUE) ; } /* ========================================================================== */ /* === cholmod_free_work ==================================================== */ /* ========================================================================== */ /* Deallocate the CHOLMOD workspace. * * workspace: deallocates all workspace in Common */ int CHOLMOD(free_work) ( cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->Flag = CHOLMOD(free) (Common->nrow, sizeof (Int), Common->Flag, Common) ; Common->Head = CHOLMOD(free) (Common->nrow+1, sizeof (Int), Common->Head, Common) ; Common->Iwork = CHOLMOD(free) (Common->iworksize, sizeof (Int), Common->Iwork, Common) ; Common->Xwork = CHOLMOD(free) (Common->xworksize, sizeof (double), Common->Xwork, Common) ; Common->nrow = 0 ; Common->iworksize = 0 ; Common->xworksize = 0 ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_clear_flag =================================================== */ /* ========================================================================== */ /* Increment mark to ensure Flag [0..nrow-1] < mark. If integer overflow * occurs, or mark was initially negative, reset the entire array. This is * not an error condition, but an intended function of the Flag workspace. * * workspace: Flag (nrow). Does not modify Flag if nrow is zero. */ UF_long CHOLMOD(clear_flag) ( cholmod_common *Common ) { Int i, nrow, *Flag ; RETURN_IF_NULL_COMMON (-1) ; Common->mark++ ; if (Common->mark <= 0) { nrow = Common->nrow ; Flag = Common->Flag ; PRINT2 (("reset Flag: nrow "ID"\n", nrow)) ; PRINT2 (("reset Flag: mark %ld\n", Common->mark)) ; for (i = 0 ; i < nrow ; i++) { Flag [i] = EMPTY ; } Common->mark = 0 ; } return (Common->mark) ; } /* ========================================================================== */ /* ==== cholmod_maxrank ===================================================== */ /* ========================================================================== */ /* Find a valid value of Common->maxrank. Returns 0 if error, or 2, 4, or 8 * if successful. */ size_t CHOLMOD(maxrank) /* returns validated value of Common->maxrank */ ( /* ---- input ---- */ size_t n, /* A and L will have n rows */ /* --------------- */ cholmod_common *Common ) { size_t maxrank ; RETURN_IF_NULL_COMMON (0) ; maxrank = Common->maxrank ; if (n > 0) { /* Ensure maxrank*n*sizeof(double) does not result in integer overflow. * If n is so large that 2*n*sizeof(double) results in integer overflow * (n = 268,435,455 if an Int is 32 bits), then maxrank will be 0 or 1, * but maxrank will be set to 2 below. 2*n will not result in integer * overflow, and CHOLMOD will run out of memory or safely detect integer * overflow elsewhere. */ maxrank = MIN (maxrank, Size_max / (n * sizeof (double))) ; } if (maxrank <= 2) { maxrank = 2 ; } else if (maxrank <= 4) { maxrank = 4 ; } else { maxrank = 8 ; } return (maxrank) ; } /* ========================================================================== */ /* === cholmod_dbound ======================================================= */ /* ========================================================================== */ /* Ensure the absolute value of a diagonal entry, D (j,j), is greater than * Common->dbound. This routine is not meant for the user to call. It is used * by the various LDL' factorization and update/downdate routines. The * default value of Common->dbound is zero, and in that case this routine is not * called at all. No change is made if D (j,j) is NaN. CHOLMOD does not call * this routine if Common->dbound is NaN. */ double CHOLMOD(dbound) /* returns modified diagonal entry of D */ ( /* ---- input ---- */ double dj, /* diagonal entry of D, for LDL' factorization */ /* --------------- */ cholmod_common *Common ) { double dbound ; RETURN_IF_NULL_COMMON (0) ; if (!IS_NAN (dj)) { dbound = Common->dbound ; if (dj < 0) { if (dj > -dbound) { dj = -dbound ; Common->ndbounds_hit++ ; if (Common->status == CHOLMOD_OK) { ERROR (CHOLMOD_DSMALL, "diagonal below threshold") ; } } } else { if (dj < dbound) { dj = dbound ; Common->ndbounds_hit++ ; if (Common->status == CHOLMOD_OK) { ERROR (CHOLMOD_DSMALL, "diagonal below threshold") ; } } } } return (dj) ; } SuiteSparse/CHOLMOD/Core/lesser.txt0000644001170100242450000006350010253404164015765 0ustar davisfac GNU LESSER GENERAL PUBLIC LICENSE Version 2.1, February 1999 Copyright (C) 1991, 1999 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. 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SuiteSparse/CHOLMOD/Demo/0000755001170100242450000000000010711435726013726 5ustar davisfacSuiteSparse/CHOLMOD/Demo/Makefile0000644001170100242450000000527210617113272015366 0ustar davisfac#=============================================================================== # CHOLMOD/Demo/Makefile #=============================================================================== # If you compile CHOLMOD with -DNPARTITION, then you do not need METIS or # CCOLAMD. default: all include ../../UFconfig/UFconfig.mk #------------------------------------------------------------------------------- # With METIS, CCOLAMD, CAMD, and the Partition Module: LIB2 = ../Lib/libcholmod.a ../../AMD/Lib/libamd.a ../../COLAMD/Lib/libcolamd.a \ ../../CCOLAMD/Lib/libccolamd.a ../../CAMD/Lib/libcamd.a \ $(METIS) $(LAPACK) $(BLAS) $(XERBLA) $(LIB) # Use this instead, if you compile with -DNPARTITION: # LIB2 = ../Lib/libcholmod.a ../../AMD/Lib/libamd.a ../../COLAMD/libcolamd.a \ $(LAPACK) $(BLAS) $(XERBLA) $(LIB) #------------------------------------------------------------------------------- C = $(CC) $(CFLAGS) $(CHOLMOD_CONFIG) code: library cholmod_demo cholmod_l_demo cholmod_simple fortran: readhb readhb2 reade all: code ./cholmod_demo < Matrix/bcsstk01.tri ./cholmod_l_demo < Matrix/bcsstk01.tri ./cholmod_demo < Matrix/lp_afiro.tri ./cholmod_l_demo < Matrix/lp_afiro.tri ./cholmod_demo < Matrix/can___24.mtx ./cholmod_l_demo < Matrix/can___24.mtx ./cholmod_demo < Matrix/c.tri ./cholmod_l_demo < Matrix/c.tri ./cholmod_simple < Matrix/c.tri ./cholmod_simple < Matrix/can___24.mtx ./cholmod_simple < Matrix/bcsstk01.tri distclean: purge purge: clean - $(RM) cholmod_demo cholmod_l_demo readhb readhb2 reade - $(RM) cholmod_simple clean: - $(RM) $(CLEAN) #------------------------------------------------------------------------------- # See below if you compile with -DNPARTITION library: ( cd ../../UFconfig/xerbla ; $(MAKE) ) ( cd ../Lib ; $(MAKE) ) ( cd ../../AMD ; $(MAKE) library ) ( cd ../../CAMD ; $(MAKE) library ) ( cd ../../COLAMD ; $(MAKE) library ) ( cd ../../CCOLAMD ; $(MAKE) library ) # use this rule instead, if you compile with -DNPARTITION: # library: # ( cd ../../UFconfig/xerbla ; $(MAKE) ) # ( cd ../Lib ; $(MAKE) ) # ( cd ../../AMD ; $(MAKE) library ) # ( cd ../../COLAMD ; $(MAKE) ) #------------------------------------------------------------------------------- I = -I../Include -I../../UFconfig cholmod_demo: library cholmod_demo.c cholmod_demo.h $(C) -o cholmod_demo $(I) cholmod_demo.c $(LIB2) cholmod_simple: library cholmod_simple.c $(C) -o cholmod_simple $(I) cholmod_simple.c $(LIB2) cholmod_l_demo: library cholmod_l_demo.c cholmod_demo.h $(C) -o cholmod_l_demo $(I) cholmod_l_demo.c $(LIB2) readhb: readhb.f $(F77) $(FFLAGS) -o readhb readhb.f readhb2: readhb2.f $(F77) $(FFLAGS) -O -o readhb2 readhb2.f reade: reade.f $(F77) $(FFLAGS) -O -o reade reade.f SuiteSparse/CHOLMOD/Demo/reade.f0000644001170100242450000001227710277474236015174 0ustar davisfacc----------------------------------------------------------------------- c Read a sparse matrix in the Harwell/Boeing format and output a c matrix in triplet format. c c not for: **A c use for: RSE and PSE c----------------------------------------------------------------------- integer nzmax, nmax parameter (nzmax = 50000000, nmax = 1000000) integer Ptr (nmax), Index (nzmax), n, nz, totcrd, ptrcrd, $ indcrd, valcrd, rhscrd, ncol, nrow, nrhs, row, col, p, $ nguess, nexact, nrhsix, nrhsvl character title*72, key*30, type*3, ptrfmt*16, $ indfmt*16, valfmt*20, rhsfmt*20 logical sym, unsorted double precision Value (nzmax) double precision skew character rhstyp*3 integer nel integer lastrow integer prow, el, pval, hasval integer stype c----------------------------------------------------------------------- c read header information from Harwell/Boeing matrix c----------------------------------------------------------------------- nrhs = 0 nrhsix = 0 read (5, 10, err = 998) $ title, key, $ totcrd, ptrcrd, indcrd, valcrd, rhscrd, $ type, nrow, ncol, nz, nel, $ ptrfmt, indfmt, valfmt, rhsfmt if (rhscrd .gt. 0) then c new Harwell/Boeing format: read (5, 20, err = 998) rhstyp,nrhs,nrhsix endif 10 format (a72, a8 / 5i14 / a3, 11x, 4i14 / 2a16, 2a20) 20 format (a3, 11x, 2i14) skew = 0.0 if (type (2:2) .eq. 'Z' .or. type (2:2) .eq. 'z') then write (0, *) '*ZE not supported!' stop endif if (type (2:2) .eq. 'S' .or. type (2:2) .eq. 's') skew = 1.0 if (type (2:2) .eq. 'H' .or. type (2:2) .eq. 'h') then write (0, *) '*HE not supported!' stop endif sym = skew .ne. 0.0 c write (0, 30) title, key, type, nrow, ncol, nz if (rhscrd .gt. 0) then c new Harwell/Boeing format: c write (0, 40) rhstyp,nrhs,nzrhs endif 30 format ( $ ' title: ', a72 / $ ' key: ', a8 / $ ' type: ', a3, ' nrow: ', i14, ' ncol: ', i14 / $ ' nz: ', i14) 40 format (' rhstyp: ', a3, ' nrhs: ', i14, ' nzrhs: ', i14) n = max (nrow, ncol) if (n .ge. nmax .or. nz .gt. nzmax) then write (0, *) 'Matrix too big!' stop endif if (type (3:3) .ne. 'E' .and. type (3:3) .ne. 'a') then write (0, *) 'Can only handle **E types!' stop endif if (.not. ( $ type (1:1) .eq. 'P' .or. $ type (1:1) .eq. 'p' .or. $ type (1:1) .eq. 'R' .or. $ type (1:1) .eq. 'r')) then write (0, *) 'Can only handle R*E or P*E types!' stop endif c----------------------------------------------------------------------- c read the pattern c----------------------------------------------------------------------- read (5, ptrfmt, err = 998) (Ptr (p), p = 1, ncol+1) read (5, indfmt, err = 998) (Index (p), p = 1, nz) c----------------------------------------------------------------------- c check if the columns are sorted c----------------------------------------------------------------------- unsorted = .false. do 101 col = 1, ncol lastrow = 0 do 91 p = Ptr (col), Ptr (col+1) - 1 row = Index (p) if (row .lt. lastrow) then unsorted = .true. write (0,*) ' ********* Columns are unsorted' goto 102 endif lastrow = row 91 continue 101 continue 102 continue c----------------------------------------------------------------------- c read the values c----------------------------------------------------------------------- if (valcrd .gt. 0) then read (5, valfmt, err = 998) (Value (p), p = 1, nel) endif c----------------------------------------------------------------------- c write the triplet form of the input matrix c----------------------------------------------------------------------- c stype = 0: unsymmetric c stype = -1: symmetric, lower triangular part present stype = -1 nz = 0 do 300 el = 1, ncol do 390 p = Ptr (el), Ptr (el+1) - 1 do 392 prow = p, Ptr (el+1) - 1 nz = nz + 1 392 continue 390 continue 300 continue write (6, 701) title write (6, 702) key 701 format ('% title:', a72) 702 format ('% key: ', a8) write (6, 710) nrow, nrow, nz, stype 710 format (2i8, i12, i3) pval = 0 do 100 el = 1, ncol do 90 p = Ptr (el), Ptr (el+1) - 1 col = Index (p) do 92 prow = p, Ptr (el+1) - 1 row = Index (prow) if (row .lt. col) then write (0, *) 'bad format!' stop endif if (valcrd .gt. 0) then pval = pval + 1 if (pval .gt. nel) then write (0, *) 'bad format!' stop endif write (6, 200) row, col, Value (pval) else write (6, 201) row, col endif 92 continue 90 continue 100 continue 200 format (2i8, e30.18e3) 201 format (2i8) c----------------------------------------------------------------------- stop 998 write (0,*) 'Read error: Harwell/Boeing matrix' stop end SuiteSparse/CHOLMOD/Demo/Matrix/0000755001170100242450000000000010424737163015173 5ustar davisfacSuiteSparse/CHOLMOD/Demo/Matrix/n50000644001170100242450000011122710302115724015430 0ustar davisfac210 210 4060 1 1 1 5 2 1 1 3 1 1 4 1 1 25 1 1 45 1 1 65 1 1 85 1 1 101 1 2 102 1 2 103 1 2 104 1 2 152 1 1 158 1 1 169 1 1 185 1 1 201 1 -1 206 1 -1 1 2 1 2 2 5 3 2 1 4 2 1 29 2 1 49 2 1 69 2 1 89 2 1 101 2 2 102 2 2 103 2 2 104 2 2 153 2 1 160 2 1 172 2 1 189 2 1 201 2 -1 206 2 -1 1 3 1 2 3 1 3 3 5 4 3 1 33 3 1 53 3 1 73 3 1 93 3 1 101 3 2 102 3 2 103 3 2 104 3 2 154 3 1 162 3 1 175 3 1 193 3 1 201 3 -1 206 3 -1 1 4 1 2 4 1 3 4 1 4 4 5 37 4 1 57 4 1 77 4 1 97 4 1 101 4 2 102 4 2 103 4 2 104 4 2 155 4 1 164 4 1 178 4 1 197 4 1 201 4 -1 206 4 -1 5 5 5 6 5 1 7 5 1 8 5 1 21 5 1 41 5 1 61 5 1 81 5 1 105 5 2 106 5 2 107 5 2 108 5 2 151 5 1 156 5 1 166 5 1 181 5 1 202 5 -1 206 5 -1 5 6 1 6 6 5 7 6 1 8 6 1 30 6 1 50 6 1 70 6 1 90 6 1 105 6 2 106 6 2 107 6 2 108 6 2 153 6 1 160 6 1 172 6 1 189 6 1 202 6 -1 206 6 -1 5 7 1 6 7 1 7 7 5 8 7 1 34 7 1 54 7 1 74 7 1 94 7 1 105 7 2 106 7 2 107 7 2 108 7 2 154 7 1 162 7 1 175 7 1 193 7 1 202 7 -1 206 7 -1 5 8 1 6 8 1 7 8 1 8 8 5 38 8 1 58 8 1 78 8 1 98 8 1 105 8 2 106 8 2 107 8 2 108 8 2 155 8 1 164 8 1 178 8 1 197 8 1 202 8 -1 206 8 -1 9 9 5 10 9 1 11 9 1 12 9 1 22 9 1 42 9 1 62 9 1 82 9 1 109 9 2 110 9 2 111 9 2 112 9 2 151 9 1 156 9 1 166 9 1 181 9 1 203 9 -1 206 9 -1 9 10 1 10 10 5 11 10 1 12 10 1 26 10 1 46 10 1 66 10 1 86 10 1 109 10 2 110 10 2 111 10 2 112 10 2 152 10 1 158 10 1 169 10 1 185 10 1 203 10 -1 206 10 -1 9 11 1 10 11 1 11 11 5 12 11 1 35 11 1 55 11 1 75 11 1 95 11 1 109 11 2 110 11 2 111 11 2 112 11 2 154 11 1 162 11 1 175 11 1 193 11 1 203 11 -1 206 11 -1 9 12 1 10 12 1 11 12 1 12 12 5 39 12 1 59 12 1 79 12 1 99 12 1 109 12 2 110 12 2 111 12 2 112 12 2 155 12 1 164 12 1 178 12 1 197 12 1 203 12 -1 206 12 -1 13 13 5 14 13 1 15 13 1 16 13 1 23 13 1 43 13 1 63 13 1 83 13 1 113 13 2 114 13 2 115 13 2 116 13 2 151 13 1 156 13 1 166 13 1 181 13 1 204 13 -1 206 13 -1 13 14 1 14 14 5 15 14 1 16 14 1 27 14 1 47 14 1 67 14 1 87 14 1 113 14 2 114 14 2 115 14 2 116 14 2 152 14 1 158 14 1 169 14 1 185 14 1 204 14 -1 206 14 -1 13 15 1 14 15 1 15 15 5 16 15 1 31 15 1 51 15 1 71 15 1 91 15 1 113 15 2 114 15 2 115 15 2 116 15 2 153 15 1 160 15 1 172 15 1 189 15 1 204 15 -1 206 15 -1 13 16 1 14 16 1 15 16 1 16 16 5 40 16 1 60 16 1 80 16 1 100 16 1 113 16 2 114 16 2 115 16 2 116 16 2 155 16 1 164 16 1 178 16 1 197 16 1 204 16 -1 206 16 -1 17 17 5 18 17 1 19 17 1 20 17 1 24 17 1 44 17 1 64 17 1 84 17 1 117 17 2 118 17 2 119 17 2 120 17 2 151 17 1 156 17 1 166 17 1 181 17 1 205 17 -1 206 17 -1 17 18 1 18 18 5 19 18 1 20 18 1 28 18 1 48 18 1 68 18 1 88 18 1 117 18 2 118 18 2 119 18 2 120 18 2 152 18 1 158 18 1 169 18 1 185 18 1 205 18 -1 206 18 -1 17 19 1 18 19 1 19 19 5 20 19 1 32 19 1 52 19 1 72 19 1 92 19 1 117 19 2 118 19 2 119 19 2 120 19 2 153 19 1 160 19 1 172 19 1 189 19 1 205 19 -1 206 19 -1 17 20 1 18 20 1 19 20 1 20 20 5 36 20 1 56 20 1 76 20 1 96 20 1 117 20 2 118 20 2 119 20 2 120 20 2 154 20 1 162 20 1 175 20 1 193 20 1 205 20 -1 206 20 -1 5 21 1 21 21 5 22 21 1 23 21 1 24 21 1 45 21 1 65 21 1 85 21 1 105 21 1 121 21 2 122 21 2 123 21 2 151 21 2 159 21 1 170 21 1 186 21 1 201 21 -1 207 21 -1 9 22 1 21 22 1 22 22 5 23 22 1 24 22 1 49 22 1 69 22 1 89 22 1 109 22 1 121 22 2 122 22 2 123 22 2 151 22 2 161 22 1 173 22 1 190 22 1 201 22 -1 207 22 -1 13 23 1 21 23 1 22 23 1 23 23 5 24 23 1 53 23 1 73 23 1 93 23 1 113 23 1 121 23 2 122 23 2 123 23 2 151 23 2 163 23 1 176 23 1 194 23 1 201 23 -1 207 23 -1 17 24 1 21 24 1 22 24 1 23 24 1 24 24 5 57 24 1 77 24 1 97 24 1 117 24 1 121 24 2 122 24 2 123 24 2 151 24 2 165 24 1 179 24 1 198 24 1 201 24 -1 207 24 -1 1 25 1 25 25 5 26 25 1 27 25 1 28 25 1 41 25 1 61 25 1 81 25 1 101 25 1 124 25 2 125 25 2 126 25 2 152 25 2 157 25 1 167 25 1 182 25 1 202 25 -1 207 25 -1 10 26 1 25 26 1 26 26 5 27 26 1 28 26 1 50 26 1 70 26 1 90 26 1 109 26 1 124 26 2 125 26 2 126 26 2 152 26 2 161 26 1 173 26 1 190 26 1 202 26 -1 207 26 -1 14 27 1 25 27 1 26 27 1 27 27 5 28 27 1 54 27 1 74 27 1 94 27 1 113 27 1 124 27 2 125 27 2 126 27 2 152 27 2 163 27 1 176 27 1 194 27 1 202 27 -1 207 27 -1 18 28 1 25 28 1 26 28 1 27 28 1 28 28 5 58 28 1 78 28 1 98 28 1 117 28 1 124 28 2 125 28 2 126 28 2 152 28 2 165 28 1 179 28 1 198 28 1 202 28 -1 207 28 -1 2 29 1 29 29 5 30 29 1 31 29 1 32 29 1 42 29 1 62 29 1 82 29 1 101 29 1 127 29 2 128 29 2 129 29 2 153 29 2 157 29 1 167 29 1 182 29 1 203 29 -1 207 29 -1 6 30 1 29 30 1 30 30 5 31 30 1 32 30 1 46 30 1 66 30 1 86 30 1 105 30 1 127 30 2 128 30 2 129 30 2 153 30 2 159 30 1 170 30 1 186 30 1 203 30 -1 207 30 -1 15 31 1 29 31 1 30 31 1 31 31 5 32 31 1 55 31 1 75 31 1 95 31 1 113 31 1 127 31 2 128 31 2 129 31 2 153 31 2 163 31 1 176 31 1 194 31 1 203 31 -1 207 31 -1 19 32 1 29 32 1 30 32 1 31 32 1 32 32 5 59 32 1 79 32 1 99 32 1 117 32 1 127 32 2 128 32 2 129 32 2 153 32 2 165 32 1 179 32 1 198 32 1 203 32 -1 207 32 -1 3 33 1 33 33 5 34 33 1 35 33 1 36 33 1 43 33 1 63 33 1 83 33 1 101 33 1 130 33 2 131 33 2 132 33 2 154 33 2 157 33 1 167 33 1 182 33 1 204 33 -1 207 33 -1 7 34 1 33 34 1 34 34 5 35 34 1 36 34 1 47 34 1 67 34 1 87 34 1 105 34 1 130 34 2 131 34 2 132 34 2 154 34 2 159 34 1 170 34 1 186 34 1 204 34 -1 207 34 -1 11 35 1 33 35 1 34 35 1 35 35 5 36 35 1 51 35 1 71 35 1 91 35 1 109 35 1 130 35 2 131 35 2 132 35 2 154 35 2 161 35 1 173 35 1 190 35 1 204 35 -1 207 35 -1 20 36 1 33 36 1 34 36 1 35 36 1 36 36 5 60 36 1 80 36 1 100 36 1 117 36 1 130 36 2 131 36 2 132 36 2 154 36 2 165 36 1 179 36 1 198 36 1 204 36 -1 207 36 -1 4 37 1 37 37 5 38 37 1 39 37 1 40 37 1 44 37 1 64 37 1 84 37 1 101 37 1 133 37 2 134 37 2 135 37 2 155 37 2 157 37 1 167 37 1 182 37 1 205 37 -1 207 37 -1 8 38 1 37 38 1 38 38 5 39 38 1 40 38 1 48 38 1 68 38 1 88 38 1 105 38 1 133 38 2 134 38 2 135 38 2 155 38 2 159 38 1 170 38 1 186 38 1 205 38 -1 207 38 -1 12 39 1 37 39 1 38 39 1 39 39 5 40 39 1 52 39 1 72 39 1 92 39 1 109 39 1 133 39 2 134 39 2 135 39 2 155 39 2 161 39 1 173 39 1 190 39 1 205 39 -1 207 39 -1 16 40 1 37 40 1 38 40 1 39 40 1 40 40 5 56 40 1 76 40 1 96 40 1 113 40 1 133 40 2 134 40 2 135 40 2 155 40 2 163 40 1 176 40 1 194 40 1 205 40 -1 207 40 -1 5 41 1 25 41 1 41 41 5 42 41 1 43 41 1 44 41 1 65 41 1 85 41 1 106 41 1 124 41 1 136 41 2 137 41 2 156 41 2 157 41 2 171 41 1 187 41 1 201 41 -1 208 41 -1 9 42 1 29 42 1 41 42 1 42 42 5 43 42 1 44 42 1 69 42 1 89 42 1 110 42 1 127 42 1 136 42 2 137 42 2 156 42 2 157 42 2 174 42 1 191 42 1 201 42 -1 208 42 -1 13 43 1 33 43 1 41 43 1 42 43 1 43 43 5 44 43 1 73 43 1 93 43 1 114 43 1 130 43 1 136 43 2 137 43 2 156 43 2 157 43 2 177 43 1 195 43 1 201 43 -1 208 43 -1 17 44 1 37 44 1 41 44 1 42 44 1 43 44 1 44 44 5 77 44 1 97 44 1 118 44 1 133 44 1 136 44 2 137 44 2 156 44 2 157 44 2 180 44 1 199 44 1 201 44 -1 208 44 -1 1 45 1 21 45 1 45 45 5 46 45 1 47 45 1 48 45 1 61 45 1 81 45 1 102 45 1 121 45 1 138 45 2 139 45 2 158 45 2 159 45 2 168 45 1 183 45 1 202 45 -1 208 45 -1 10 46 1 30 46 1 45 46 1 46 46 5 47 46 1 48 46 1 70 46 1 90 46 1 110 46 1 127 46 1 138 46 2 139 46 2 158 46 2 159 46 2 174 46 1 191 46 1 202 46 -1 208 46 -1 14 47 1 34 47 1 45 47 1 46 47 1 47 47 5 48 47 1 74 47 1 94 47 1 114 47 1 130 47 1 138 47 2 139 47 2 158 47 2 159 47 2 177 47 1 195 47 1 202 47 -1 208 47 -1 18 48 1 38 48 1 45 48 1 46 48 1 47 48 1 48 48 5 78 48 1 98 48 1 118 48 1 133 48 1 138 48 2 139 48 2 158 48 2 159 48 2 180 48 1 199 48 1 202 48 -1 208 48 -1 2 49 1 22 49 1 49 49 5 50 49 1 51 49 1 52 49 1 62 49 1 82 49 1 102 49 1 121 49 1 140 49 2 141 49 2 160 49 2 161 49 2 168 49 1 183 49 1 203 49 -1 208 49 -1 6 50 1 26 50 1 49 50 1 50 50 5 51 50 1 52 50 1 66 50 1 86 50 1 106 50 1 124 50 1 140 50 2 141 50 2 160 50 2 161 50 2 171 50 1 187 50 1 203 50 -1 208 50 -1 15 51 1 35 51 1 49 51 1 50 51 1 51 51 5 52 51 1 75 51 1 95 51 1 114 51 1 130 51 1 140 51 2 141 51 2 160 51 2 161 51 2 177 51 1 195 51 1 203 51 -1 208 51 -1 19 52 1 39 52 1 49 52 1 50 52 1 51 52 1 52 52 5 79 52 1 99 52 1 118 52 1 133 52 1 140 52 2 141 52 2 160 52 2 161 52 2 180 52 1 199 52 1 203 52 -1 208 52 -1 3 53 1 23 53 1 53 53 5 54 53 1 55 53 1 56 53 1 63 53 1 83 53 1 102 53 1 121 53 1 142 53 2 143 53 2 162 53 2 163 53 2 168 53 1 183 53 1 204 53 -1 208 53 -1 7 54 1 27 54 1 53 54 1 54 54 5 55 54 1 56 54 1 67 54 1 87 54 1 106 54 1 124 54 1 142 54 2 143 54 2 162 54 2 163 54 2 171 54 1 187 54 1 204 54 -1 208 54 -1 11 55 1 31 55 1 53 55 1 54 55 1 55 55 5 56 55 1 71 55 1 91 55 1 110 55 1 127 55 1 142 55 2 143 55 2 162 55 2 163 55 2 174 55 1 191 55 1 204 55 -1 208 55 -1 20 56 1 40 56 1 53 56 1 54 56 1 55 56 1 56 56 5 80 56 1 100 56 1 118 56 1 133 56 1 142 56 2 143 56 2 162 56 2 163 56 2 180 56 1 199 56 1 204 56 -1 208 56 -1 4 57 1 24 57 1 57 57 5 58 57 1 59 57 1 60 57 1 64 57 1 84 57 1 102 57 1 121 57 1 144 57 2 145 57 2 164 57 2 165 57 2 168 57 1 183 57 1 205 57 -1 208 57 -1 8 58 1 28 58 1 57 58 1 58 58 5 59 58 1 60 58 1 68 58 1 88 58 1 106 58 1 124 58 1 144 58 2 145 58 2 164 58 2 165 58 2 171 58 1 187 58 1 205 58 -1 208 58 -1 12 59 1 32 59 1 57 59 1 58 59 1 59 59 5 60 59 1 72 59 1 92 59 1 110 59 1 127 59 1 144 59 2 145 59 2 164 59 2 165 59 2 174 59 1 191 59 1 205 59 -1 208 59 -1 16 60 1 36 60 1 57 60 1 58 60 1 59 60 1 60 60 5 76 60 1 96 60 1 114 60 1 130 60 1 144 60 2 145 60 2 164 60 2 165 60 2 177 60 1 195 60 1 205 60 -1 208 60 -1 5 61 1 25 61 1 45 61 1 61 61 5 62 61 1 63 61 1 64 61 1 85 61 1 107 61 1 125 61 1 138 61 1 146 61 2 166 61 2 167 61 2 168 61 2 188 61 1 201 61 -1 209 61 -1 9 62 1 29 62 1 49 62 1 61 62 1 62 62 5 63 62 1 64 62 1 89 62 1 111 62 1 128 62 1 140 62 1 146 62 2 166 62 2 167 62 2 168 62 2 192 62 1 201 62 -1 209 62 -1 13 63 1 33 63 1 53 63 1 61 63 1 62 63 1 63 63 5 64 63 1 93 63 1 115 63 1 131 63 1 142 63 1 146 63 2 166 63 2 167 63 2 168 63 2 196 63 1 201 63 -1 209 63 -1 17 64 1 37 64 1 57 64 1 61 64 1 62 64 1 63 64 1 64 64 5 97 64 1 119 64 1 134 64 1 144 64 1 146 64 2 166 64 2 167 64 2 168 64 2 200 64 1 201 64 -1 209 64 -1 1 65 1 21 65 1 41 65 1 65 65 5 66 65 1 67 65 1 68 65 1 81 65 1 103 65 1 122 65 1 136 65 1 147 65 2 169 65 2 170 65 2 171 65 2 184 65 1 202 65 -1 209 65 -1 10 66 1 30 66 1 50 66 1 65 66 1 66 66 5 67 66 1 68 66 1 90 66 1 111 66 1 128 66 1 140 66 1 147 66 2 169 66 2 170 66 2 171 66 2 192 66 1 202 66 -1 209 66 -1 14 67 1 34 67 1 54 67 1 65 67 1 66 67 1 67 67 5 68 67 1 94 67 1 115 67 1 131 67 1 142 67 1 147 67 2 169 67 2 170 67 2 171 67 2 196 67 1 202 67 -1 209 67 -1 18 68 1 38 68 1 58 68 1 65 68 1 66 68 1 67 68 1 68 68 5 98 68 1 119 68 1 134 68 1 144 68 1 147 68 2 169 68 2 170 68 2 171 68 2 200 68 1 202 68 -1 209 68 -1 2 69 1 22 69 1 42 69 1 69 69 5 70 69 1 71 69 1 72 69 1 82 69 1 103 69 1 122 69 1 136 69 1 148 69 2 172 69 2 173 69 2 174 69 2 184 69 1 203 69 -1 209 69 -1 6 70 1 26 70 1 46 70 1 69 70 1 70 70 5 71 70 1 72 70 1 86 70 1 107 70 1 125 70 1 138 70 1 148 70 2 172 70 2 173 70 2 174 70 2 188 70 1 203 70 -1 209 70 -1 15 71 1 35 71 1 55 71 1 69 71 1 70 71 1 71 71 5 72 71 1 95 71 1 115 71 1 131 71 1 142 71 1 148 71 2 172 71 2 173 71 2 174 71 2 196 71 1 203 71 -1 209 71 -1 19 72 1 39 72 1 59 72 1 69 72 1 70 72 1 71 72 1 72 72 5 99 72 1 119 72 1 134 72 1 144 72 1 148 72 2 172 72 2 173 72 2 174 72 2 200 72 1 203 72 -1 209 72 -1 3 73 1 23 73 1 43 73 1 73 73 5 74 73 1 75 73 1 76 73 1 83 73 1 103 73 1 122 73 1 136 73 1 149 73 2 175 73 2 176 73 2 177 73 2 184 73 1 204 73 -1 209 73 -1 7 74 1 27 74 1 47 74 1 73 74 1 74 74 5 75 74 1 76 74 1 87 74 1 107 74 1 125 74 1 138 74 1 149 74 2 175 74 2 176 74 2 177 74 2 188 74 1 204 74 -1 209 74 -1 11 75 1 31 75 1 51 75 1 73 75 1 74 75 1 75 75 5 76 75 1 91 75 1 111 75 1 128 75 1 140 75 1 149 75 2 175 75 2 176 75 2 177 75 2 192 75 1 204 75 -1 209 75 -1 20 76 1 40 76 1 60 76 1 73 76 1 74 76 1 75 76 1 76 76 5 100 76 1 119 76 1 134 76 1 144 76 1 149 76 2 175 76 2 176 76 2 177 76 2 200 76 1 204 76 -1 209 76 -1 4 77 1 24 77 1 44 77 1 77 77 5 78 77 1 79 77 1 80 77 1 84 77 1 103 77 1 122 77 1 136 77 1 150 77 2 178 77 2 179 77 2 180 77 2 184 77 1 205 77 -1 209 77 -1 8 78 1 28 78 1 48 78 1 77 78 1 78 78 5 79 78 1 80 78 1 88 78 1 107 78 1 125 78 1 138 78 1 150 78 2 178 78 2 179 78 2 180 78 2 188 78 1 205 78 -1 209 78 -1 12 79 1 32 79 1 52 79 1 77 79 1 78 79 1 79 79 5 80 79 1 92 79 1 111 79 1 128 79 1 140 79 1 150 79 2 178 79 2 179 79 2 180 79 2 192 79 1 205 79 -1 209 79 -1 16 80 1 36 80 1 56 80 1 77 80 1 78 80 1 79 80 1 80 80 5 96 80 1 115 80 1 131 80 1 142 80 1 150 80 2 178 80 2 179 80 2 180 80 2 196 80 1 205 80 -1 209 80 -1 5 81 1 25 81 1 45 81 1 65 81 1 81 81 5 82 81 1 83 81 1 84 81 1 108 81 1 126 81 1 139 81 1 147 81 1 181 81 2 182 81 2 183 81 2 184 81 2 201 81 -1 210 81 -1 9 82 1 29 82 1 49 82 1 69 82 1 81 82 1 82 82 5 83 82 1 84 82 1 112 82 1 129 82 1 141 82 1 148 82 1 181 82 2 182 82 2 183 82 2 184 82 2 201 82 -1 210 82 -1 13 83 1 33 83 1 53 83 1 73 83 1 81 83 1 82 83 1 83 83 5 84 83 1 116 83 1 132 83 1 143 83 1 149 83 1 181 83 2 182 83 2 183 83 2 184 83 2 201 83 -1 210 83 -1 17 84 1 37 84 1 57 84 1 77 84 1 81 84 1 82 84 1 83 84 1 84 84 5 120 84 1 135 84 1 145 84 1 150 84 1 181 84 2 182 84 2 183 84 2 184 84 2 201 84 -1 210 84 -1 1 85 1 21 85 1 41 85 1 61 85 1 85 85 5 86 85 1 87 85 1 88 85 1 104 85 1 123 85 1 137 85 1 146 85 1 185 85 2 186 85 2 187 85 2 188 85 2 202 85 -1 210 85 -1 10 86 1 30 86 1 50 86 1 70 86 1 85 86 1 86 86 5 87 86 1 88 86 1 112 86 1 129 86 1 141 86 1 148 86 1 185 86 2 186 86 2 187 86 2 188 86 2 202 86 -1 210 86 -1 14 87 1 34 87 1 54 87 1 74 87 1 85 87 1 86 87 1 87 87 5 88 87 1 116 87 1 132 87 1 143 87 1 149 87 1 185 87 2 186 87 2 187 87 2 188 87 2 202 87 -1 210 87 -1 18 88 1 38 88 1 58 88 1 78 88 1 85 88 1 86 88 1 87 88 1 88 88 5 120 88 1 135 88 1 145 88 1 150 88 1 185 88 2 186 88 2 187 88 2 188 88 2 202 88 -1 210 88 -1 2 89 1 22 89 1 42 89 1 62 89 1 89 89 5 90 89 1 91 89 1 92 89 1 104 89 1 123 89 1 137 89 1 146 89 1 189 89 2 190 89 2 191 89 2 192 89 2 203 89 -1 210 89 -1 6 90 1 26 90 1 46 90 1 66 90 1 89 90 1 90 90 5 91 90 1 92 90 1 108 90 1 126 90 1 139 90 1 147 90 1 189 90 2 190 90 2 191 90 2 192 90 2 203 90 -1 210 90 -1 15 91 1 35 91 1 55 91 1 75 91 1 89 91 1 90 91 1 91 91 5 92 91 1 116 91 1 132 91 1 143 91 1 149 91 1 189 91 2 190 91 2 191 91 2 192 91 2 203 91 -1 210 91 -1 19 92 1 39 92 1 59 92 1 79 92 1 89 92 1 90 92 1 91 92 1 92 92 5 120 92 1 135 92 1 145 92 1 150 92 1 189 92 2 190 92 2 191 92 2 192 92 2 203 92 -1 210 92 -1 3 93 1 23 93 1 43 93 1 63 93 1 93 93 5 94 93 1 95 93 1 96 93 1 104 93 1 123 93 1 137 93 1 146 93 1 193 93 2 194 93 2 195 93 2 196 93 2 204 93 -1 210 93 -1 7 94 1 27 94 1 47 94 1 67 94 1 93 94 1 94 94 5 95 94 1 96 94 1 108 94 1 126 94 1 139 94 1 147 94 1 193 94 2 194 94 2 195 94 2 196 94 2 204 94 -1 210 94 -1 11 95 1 31 95 1 51 95 1 71 95 1 93 95 1 94 95 1 95 95 5 96 95 1 112 95 1 129 95 1 141 95 1 148 95 1 193 95 2 194 95 2 195 95 2 196 95 2 204 95 -1 210 95 -1 20 96 1 40 96 1 60 96 1 80 96 1 93 96 1 94 96 1 95 96 1 96 96 5 120 96 1 135 96 1 145 96 1 150 96 1 193 96 2 194 96 2 195 96 2 196 96 2 204 96 -1 210 96 -1 4 97 1 24 97 1 44 97 1 64 97 1 97 97 5 98 97 1 99 97 1 100 97 1 104 97 1 123 97 1 137 97 1 146 97 1 197 97 2 198 97 2 199 97 2 200 97 2 205 97 -1 210 97 -1 8 98 1 28 98 1 48 98 1 68 98 1 97 98 1 98 98 5 99 98 1 100 98 1 108 98 1 126 98 1 139 98 1 147 98 1 197 98 2 198 98 2 199 98 2 200 98 2 205 98 -1 210 98 -1 12 99 1 32 99 1 52 99 1 72 99 1 97 99 1 98 99 1 99 99 5 100 99 1 112 99 1 129 99 1 141 99 1 148 99 1 197 99 2 198 99 2 199 99 2 200 99 2 205 99 -1 210 99 -1 16 100 1 36 100 1 56 100 1 76 100 1 97 100 1 98 100 1 99 100 1 100 100 5 116 100 1 132 100 1 143 100 1 149 100 1 197 100 2 198 100 2 199 100 2 200 100 2 205 100 -1 210 100 -1 1 101 2 2 101 2 3 101 2 4 101 2 25 101 1 29 101 1 33 101 1 37 101 1 101 101 5 102 101 1 103 101 1 104 101 1 152 101 1 153 101 1 154 101 1 155 101 1 201 101 -1 206 101 -1 1 102 2 2 102 2 3 102 2 4 102 2 45 102 1 49 102 1 53 102 1 57 102 1 101 102 1 102 102 5 103 102 1 104 102 1 158 102 1 160 102 1 162 102 1 164 102 1 201 102 -1 206 102 -1 1 103 2 2 103 2 3 103 2 4 103 2 65 103 1 69 103 1 73 103 1 77 103 1 101 103 1 102 103 1 103 103 5 104 103 1 169 103 1 172 103 1 175 103 1 178 103 1 201 103 -1 206 103 -1 1 104 2 2 104 2 3 104 2 4 104 2 85 104 1 89 104 1 93 104 1 97 104 1 101 104 1 102 104 1 103 104 1 104 104 5 185 104 1 189 104 1 193 104 1 197 104 1 201 104 -1 206 104 -1 5 105 2 6 105 2 7 105 2 8 105 2 21 105 1 30 105 1 34 105 1 38 105 1 105 105 5 106 105 1 107 105 1 108 105 1 151 105 1 153 105 1 154 105 1 155 105 1 202 105 -1 206 105 -1 5 106 2 6 106 2 7 106 2 8 106 2 41 106 1 50 106 1 54 106 1 58 106 1 105 106 1 106 106 5 107 106 1 108 106 1 156 106 1 160 106 1 162 106 1 164 106 1 202 106 -1 206 106 -1 5 107 2 6 107 2 7 107 2 8 107 2 61 107 1 70 107 1 74 107 1 78 107 1 105 107 1 106 107 1 107 107 5 108 107 1 166 107 1 172 107 1 175 107 1 178 107 1 202 107 -1 206 107 -1 5 108 2 6 108 2 7 108 2 8 108 2 81 108 1 90 108 1 94 108 1 98 108 1 105 108 1 106 108 1 107 108 1 108 108 5 181 108 1 189 108 1 193 108 1 197 108 1 202 108 -1 206 108 -1 9 109 2 10 109 2 11 109 2 12 109 2 22 109 1 26 109 1 35 109 1 39 109 1 109 109 5 110 109 1 111 109 1 112 109 1 151 109 1 152 109 1 154 109 1 155 109 1 203 109 -1 206 109 -1 9 110 2 10 110 2 11 110 2 12 110 2 42 110 1 46 110 1 55 110 1 59 110 1 109 110 1 110 110 5 111 110 1 112 110 1 156 110 1 158 110 1 162 110 1 164 110 1 203 110 -1 206 110 -1 9 111 2 10 111 2 11 111 2 12 111 2 62 111 1 66 111 1 75 111 1 79 111 1 109 111 1 110 111 1 111 111 5 112 111 1 166 111 1 169 111 1 175 111 1 178 111 1 203 111 -1 206 111 -1 9 112 2 10 112 2 11 112 2 12 112 2 82 112 1 86 112 1 95 112 1 99 112 1 109 112 1 110 112 1 111 112 1 112 112 5 181 112 1 185 112 1 193 112 1 197 112 1 203 112 -1 206 112 -1 13 113 2 14 113 2 15 113 2 16 113 2 23 113 1 27 113 1 31 113 1 40 113 1 113 113 5 114 113 1 115 113 1 116 113 1 151 113 1 152 113 1 153 113 1 155 113 1 204 113 -1 206 113 -1 13 114 2 14 114 2 15 114 2 16 114 2 43 114 1 47 114 1 51 114 1 60 114 1 113 114 1 114 114 5 115 114 1 116 114 1 156 114 1 158 114 1 160 114 1 164 114 1 204 114 -1 206 114 -1 13 115 2 14 115 2 15 115 2 16 115 2 63 115 1 67 115 1 71 115 1 80 115 1 113 115 1 114 115 1 115 115 5 116 115 1 166 115 1 169 115 1 172 115 1 178 115 1 204 115 -1 206 115 -1 13 116 2 14 116 2 15 116 2 16 116 2 83 116 1 87 116 1 91 116 1 100 116 1 113 116 1 114 116 1 115 116 1 116 116 5 181 116 1 185 116 1 189 116 1 197 116 1 204 116 -1 206 116 -1 17 117 2 18 117 2 19 117 2 20 117 2 24 117 1 28 117 1 32 117 1 36 117 1 117 117 5 118 117 1 119 117 1 120 117 1 151 117 1 152 117 1 153 117 1 154 117 1 205 117 -1 206 117 -1 17 118 2 18 118 2 19 118 2 20 118 2 44 118 1 48 118 1 52 118 1 56 118 1 117 118 1 118 118 5 119 118 1 120 118 1 156 118 1 158 118 1 160 118 1 162 118 1 205 118 -1 206 118 -1 17 119 2 18 119 2 19 119 2 20 119 2 64 119 1 68 119 1 72 119 1 76 119 1 117 119 1 118 119 1 119 119 5 120 119 1 166 119 1 169 119 1 172 119 1 175 119 1 205 119 -1 206 119 -1 17 120 2 18 120 2 19 120 2 20 120 2 84 120 1 88 120 1 92 120 1 96 120 1 117 120 1 118 120 1 119 120 1 120 120 5 181 120 1 185 120 1 189 120 1 193 120 1 205 120 -1 206 120 -1 21 121 2 22 121 2 23 121 2 24 121 2 45 121 1 49 121 1 53 121 1 57 121 1 121 121 5 122 121 1 123 121 1 151 121 1 159 121 1 161 121 1 163 121 1 165 121 1 201 121 -1 207 121 -1 21 122 2 22 122 2 23 122 2 24 122 2 65 122 1 69 122 1 73 122 1 77 122 1 121 122 1 122 122 5 123 122 1 151 122 1 170 122 1 173 122 1 176 122 1 179 122 1 201 122 -1 207 122 -1 21 123 2 22 123 2 23 123 2 24 123 2 85 123 1 89 123 1 93 123 1 97 123 1 121 123 1 122 123 1 123 123 5 151 123 1 186 123 1 190 123 1 194 123 1 198 123 1 201 123 -1 207 123 -1 25 124 2 26 124 2 27 124 2 28 124 2 41 124 1 50 124 1 54 124 1 58 124 1 124 124 5 125 124 1 126 124 1 152 124 1 157 124 1 161 124 1 163 124 1 165 124 1 202 124 -1 207 124 -1 25 125 2 26 125 2 27 125 2 28 125 2 61 125 1 70 125 1 74 125 1 78 125 1 124 125 1 125 125 5 126 125 1 152 125 1 167 125 1 173 125 1 176 125 1 179 125 1 202 125 -1 207 125 -1 25 126 2 26 126 2 27 126 2 28 126 2 81 126 1 90 126 1 94 126 1 98 126 1 124 126 1 125 126 1 126 126 5 152 126 1 182 126 1 190 126 1 194 126 1 198 126 1 202 126 -1 207 126 -1 29 127 2 30 127 2 31 127 2 32 127 2 42 127 1 46 127 1 55 127 1 59 127 1 127 127 5 128 127 1 129 127 1 153 127 1 157 127 1 159 127 1 163 127 1 165 127 1 203 127 -1 207 127 -1 29 128 2 30 128 2 31 128 2 32 128 2 62 128 1 66 128 1 75 128 1 79 128 1 127 128 1 128 128 5 129 128 1 153 128 1 167 128 1 170 128 1 176 128 1 179 128 1 203 128 -1 207 128 -1 29 129 2 30 129 2 31 129 2 32 129 2 82 129 1 86 129 1 95 129 1 99 129 1 127 129 1 128 129 1 129 129 5 153 129 1 182 129 1 186 129 1 194 129 1 198 129 1 203 129 -1 207 129 -1 33 130 2 34 130 2 35 130 2 36 130 2 43 130 1 47 130 1 51 130 1 60 130 1 130 130 5 131 130 1 132 130 1 154 130 1 157 130 1 159 130 1 161 130 1 165 130 1 204 130 -1 207 130 -1 33 131 2 34 131 2 35 131 2 36 131 2 63 131 1 67 131 1 71 131 1 80 131 1 130 131 1 131 131 5 132 131 1 154 131 1 167 131 1 170 131 1 173 131 1 179 131 1 204 131 -1 207 131 -1 33 132 2 34 132 2 35 132 2 36 132 2 83 132 1 87 132 1 91 132 1 100 132 1 130 132 1 131 132 1 132 132 5 154 132 1 182 132 1 186 132 1 190 132 1 198 132 1 204 132 -1 207 132 -1 37 133 2 38 133 2 39 133 2 40 133 2 44 133 1 48 133 1 52 133 1 56 133 1 133 133 5 134 133 1 135 133 1 155 133 1 157 133 1 159 133 1 161 133 1 163 133 1 205 133 -1 207 133 -1 37 134 2 38 134 2 39 134 2 40 134 2 64 134 1 68 134 1 72 134 1 76 134 1 133 134 1 134 134 5 135 134 1 155 134 1 167 134 1 170 134 1 173 134 1 176 134 1 205 134 -1 207 134 -1 37 135 2 38 135 2 39 135 2 40 135 2 84 135 1 88 135 1 92 135 1 96 135 1 133 135 1 134 135 1 135 135 5 155 135 1 182 135 1 186 135 1 190 135 1 194 135 1 205 135 -1 207 135 -1 41 136 2 42 136 2 43 136 2 44 136 2 65 136 1 69 136 1 73 136 1 77 136 1 136 136 5 137 136 1 156 136 1 157 136 1 171 136 1 174 136 1 177 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64 209 -1 65 209 -1 66 209 -1 67 209 -1 68 209 -1 69 209 -1 70 209 -1 71 209 -1 72 209 -1 73 209 -1 74 209 -1 75 209 -1 76 209 -1 77 209 -1 78 209 -1 79 209 -1 80 209 -1 146 209 -1 147 209 -1 148 209 -1 149 209 -1 150 209 -1 166 209 -1 167 209 -1 168 209 -1 169 209 -1 170 209 -1 171 209 -1 172 209 -1 173 209 -1 174 209 -1 175 209 -1 176 209 -1 177 209 -1 178 209 -1 179 209 -1 180 209 -1 201 209 1 202 209 1 203 209 1 204 209 1 205 209 1 209 209 5 81 210 -1 82 210 -1 83 210 -1 84 210 -1 85 210 -1 86 210 -1 87 210 -1 88 210 -1 89 210 -1 90 210 -1 91 210 -1 92 210 -1 93 210 -1 94 210 -1 95 210 -1 96 210 -1 97 210 -1 98 210 -1 99 210 -1 100 210 -1 181 210 -1 182 210 -1 183 210 -1 184 210 -1 185 210 -1 186 210 -1 187 210 -1 188 210 -1 189 210 -1 190 210 -1 191 210 -1 192 210 -1 193 210 -1 194 210 -1 195 210 -1 196 210 -1 197 210 -1 198 210 -1 199 210 -1 200 210 -1 201 210 1 202 210 1 203 210 1 204 210 1 205 210 1 210 210 5 SuiteSparse/CHOLMOD/Demo/Matrix/0.tri0000644001170100242450000000001010276441214016033 0ustar davisfac0 0 0 0 SuiteSparse/CHOLMOD/Demo/Matrix/c.mtx0000644001170100242450000000016610276435764016161 0ustar davisfac%%MatrixMarket matrix coordinate complex hermitian 3 3 5 1 1 1. 0. 3 1 2. -1. 2 2 1. 0. 3 2 3. 0. 3 3 42. 0. SuiteSparse/CHOLMOD/Demo/Matrix/c.tri0000644001170100242450000000010610271566637016140 0ustar davisfac3 3 5 -1 1 1 1. 0. 3 1 2. -1. 2 2 1. 0. 3 2 3. 0. 3 3 42. 0. SuiteSparse/CHOLMOD/Demo/Matrix/d.tri0000644001170100242450000000010510276436737016142 0ustar davisfac3 3 5 0 1 1 1. 0. 3 1 2. -1. 2 2 1. 0. 3 2 3. 0. 3 3 42. 0. SuiteSparse/CHOLMOD/Demo/Matrix/pts5ldd03.mtx0000644001170100242450000003446710253621647017464 0ustar davisfac%%MatrixMarket matrix coordinate real general %Laplacian of uniform grid on L-shaped domain of 3 unit squares %(interior points only have non-zero values,) matrix order N=3*n^2+2*n %meshsize h=1/(n+1), count begins from rectangle corner furthest from %attached square, (thus long columns first). Function value %is 1 except over attached square where f=M1, and f=(1+M1)/2 %on boundary between rectangle and square. Here let M1=1 and n=7, %and eigmin = 9.69316221355115459. 161 161 745 1 1 256 2 2 256 3 3 256 4 4 256 5 5 256 6 6 256 7 7 256 8 8 256 9 9 256 10 10 256 11 11 256 12 12 256 13 13 256 14 14 256 15 15 256 16 16 256 17 17 256 18 18 256 19 19 256 20 20 256 21 21 256 22 22 256 23 23 256 24 24 256 25 25 256 26 26 256 27 27 256 28 28 256 29 29 256 30 30 256 31 31 256 32 32 256 33 33 256 34 34 256 35 35 256 36 36 256 37 37 256 38 38 256 39 39 256 40 40 256 41 41 256 42 42 256 43 43 256 44 44 256 45 45 256 46 46 256 47 47 256 48 48 256 49 49 256 50 50 256 51 51 256 52 52 256 53 53 256 54 54 256 55 55 256 56 56 256 57 57 256 58 58 256 59 59 256 60 60 256 61 61 256 62 62 256 63 63 256 64 64 256 65 65 256 66 66 256 67 67 256 68 68 256 69 69 256 70 70 256 71 71 256 72 72 256 73 73 256 74 74 256 75 75 256 76 76 256 77 77 256 78 78 256 79 79 256 80 80 256 81 81 256 82 82 256 83 83 256 84 84 256 85 85 256 86 86 256 87 87 256 88 88 256 89 89 256 90 90 256 91 91 256 92 92 256 93 93 256 94 94 256 95 95 256 96 96 256 97 97 256 98 98 256 99 99 256 100 100 256 101 101 256 102 102 256 103 103 256 104 104 256 105 105 256 106 106 256 107 107 256 108 108 256 109 109 256 110 110 256 111 111 256 112 112 256 113 113 256 114 114 256 115 115 256 116 116 256 117 117 256 118 118 256 119 119 256 120 120 256 121 121 256 122 122 256 123 123 256 124 124 256 125 125 256 126 126 256 127 127 256 128 128 256 129 129 256 130 130 256 131 131 256 132 132 256 133 133 256 134 134 256 135 135 256 136 136 256 137 137 256 138 138 256 139 139 256 140 140 256 141 141 256 142 142 256 143 143 256 144 144 256 145 145 256 146 146 256 147 147 256 148 148 256 149 149 256 150 150 256 151 151 256 152 152 256 153 153 256 154 154 256 155 155 256 156 156 256 157 157 256 158 158 256 159 159 256 160 160 256 161 161 256 1 2 -64 2 3 -64 3 4 -64 4 5 -64 5 6 -64 6 7 -64 7 8 -64 8 9 -64 9 10 -64 10 11 -64 11 12 -64 12 13 -64 13 14 -64 14 15 -64 2 1 -64 3 2 -64 4 3 -64 5 4 -64 6 5 -64 7 6 -64 8 7 -64 9 8 -64 10 9 -64 11 10 -64 12 11 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real general SuiteSparse/CHOLMOD/Demo/Matrix/mangle3.mtx0000644001170100242450000000005610276435407017255 0ustar davisfac%%MatrixMarket matrix coordinate junk general SuiteSparse/CHOLMOD/Demo/Matrix/mangle4.mtx0000644001170100242450000000005310276435423017251 0ustar davisfac%%MatrixMarket matrix coordinate real junk SuiteSparse/CHOLMOD/Demo/Matrix/mangle5.tri0000644001170100242450000000010610276437171017241 0ustar davisfac-3 3 5 1 1 1 1. 0. 1 3 2. -1. 2 2 1. 0. 2 3 3. 0. 3 3 42. 0. SuiteSparse/CHOLMOD/Demo/Matrix/mangle6.tri0000644001170100242450000000001210276441400017224 0ustar davisfac3 3 1 0 5 SuiteSparse/CHOLMOD/Demo/Matrix/mangle7.tri0000644001170100242450000000002510276442051017234 0ustar davisfac3 3 1 0 999 999 3.14 SuiteSparse/CHOLMOD/Demo/Matrix/mangle8.tri0000644001170100242450000000002610276443007017240 0ustar davisfac3 3 1 0 -999 999 3.14 SuiteSparse/CHOLMOD/Demo/Matrix/empty.tri0000644001170100242450000000000010276435100017026 0ustar davisfacSuiteSparse/CHOLMOD/Demo/Matrix/up.tri0000644001170100242450000000010510276437074016336 0ustar davisfac3 3 5 1 1 1 1. 0. 1 3 2. -1. 2 2 1. 0. 2 3 3. 0. 3 3 42. 0. SuiteSparse/CHOLMOD/Demo/Matrix/can___24.mtx0000644001170100242450000000103610253622164017263 0ustar davisfac%%MatrixMarket matrix coordinate pattern symmetric 24 24 92 1 1 6 1 7 1 13 1 14 1 18 1 19 1 20 1 22 1 2 2 9 2 10 2 14 2 15 2 18 2 3 3 7 3 12 3 21 3 22 3 23 3 4 4 8 4 11 4 16 4 19 4 20 4 5 5 8 5 10 5 15 5 16 5 17 5 6 6 7 6 13 6 14 6 18 6 7 7 12 7 13 7 20 7 22 7 24 7 8 8 10 8 15 8 16 8 17 8 18 8 19 8 9 9 10 9 15 9 10 10 14 10 15 10 18 10 19 10 11 11 19 11 20 11 21 11 22 11 12 12 13 12 22 12 24 12 13 13 24 13 14 14 18 14 15 15 16 16 17 16 19 16 17 17 18 18 19 18 20 18 19 19 20 19 20 20 21 20 22 20 21 21 22 21 23 21 22 22 23 22 23 23 24 24 SuiteSparse/CHOLMOD/Demo/Matrix/lp_afiro.rra0000644001170100242450000001023610253407300017461 0ustar davisfacLP problem: min c'*x, where Ax=b, l<=x<=u (c,l,u,z0 in lp_afiro.clu )AFIRO 58 3 4 34 17 RRA 27 51 102 0 (20i4) (26i3) (3e26.18) (3e26.18) F 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 24 26 28 30 34 38 42 46 48 50 52 54 56 58 60 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49 -0.100000000000000000E+001 15 50 0.100000000000000000E+001 27 50 0.100000000000000000E+001 16 51 0.100000000000000000E+001 SuiteSparse/CHOLMOD/Demo/Matrix/one.tri0000644001170100242450000000006610276443271016475 0ustar davisfac%%MatrixMarket matrix coord pattern general 1 1 1 1 1 SuiteSparse/CHOLMOD/Demo/make.out0000644001170100242450000001621510711432450015370 0ustar davisfac./cholmod_demo < Matrix/bcsstk01.tri ---------------------------------- cholmod_demo: norm (A,inf) = 3.57095e+09 norm (A,1) = 3.57095e+09 CHOLMOD sparse: A: 48-by-48, nz 224, upper. OK CHOLMOD dense: B: 48-by-1, OK bnorm 1.97917 Analyze: flop 6009 lnz 489 Factorizing A CHOLMOD factor: L: 48-by-48 simplicial, LDL'. nzmax 489. nz 489 OK Ordering: AMD fl/lnz 12.3 lnz/anz 2.2 ints in L: 782, doubles in L: 489 factor flops 6009 nnz(L) 489 (w/no amalgamation) nnz(A*A'): 224 flops / nnz(L): 12.3 nnz(L) / nnz(A): 2.2 analyze cputime: 0.0000 factor cputime: 0.0000 mflop: 0.0 solve cputime: 0.0000 mflop: 0.0 overall cputime: 0.0000 mflop: 0.0 peak memory usage: 0 (MB) residual 2.5e-19 (|Ax-b|/(|A||x|+|b|)) residual 1.3e-19 (|Ax-b|/(|A||x|+|b|)) after iterative refinement rcond 9.5e-06 ./cholmod_l_demo < Matrix/bcsstk01.tri ---------------------------------- cholmod_l_demo: norm (A,inf) = 3.57095e+09 norm (A,1) = 3.57095e+09 CHOLMOD sparse: A: 48-by-48, nz 224, upper. OK CHOLMOD dense: B: 48-by-1, OK bnorm 1.97917 Analyze: flop 6009 lnz 489 Factorizing A CHOLMOD factor: L: 48-by-48 simplicial, LDL'. nzmax 489. nz 489 OK Ordering: AMD fl/lnz 12.3 lnz/anz 2.2 ints in L: 782, doubles in L: 489 factor flops 6009 nnz(L) 489 (w/no amalgamation) nnz(A*A'): 224 flops / nnz(L): 12.3 nnz(L) / nnz(A): 2.2 analyze cputime: 0.0000 factor cputime: 0.0000 mflop: 0.0 solve cputime: 0.0000 mflop: 0.0 overall cputime: 0.0000 mflop: 0.0 peak memory usage: 0 (MB) residual 2.5e-19 (|Ax-b|/(|A||x|+|b|)) residual 1.3e-19 (|Ax-b|/(|A||x|+|b|)) after iterative refinement rcond 9.5e-06 ./cholmod_demo < Matrix/lp_afiro.tri ---------------------------------- cholmod_demo: norm (A,inf) = 20.525 norm (A,1) = 3.429 CHOLMOD sparse: A: 27-by-51, nz 102, up/lo. OK CHOLMOD dense: B: 27-by-1, OK bnorm 1.96296 Analyze: flop 529 lnz 113 Factorizing A*A'+beta*I CHOLMOD factor: L: 27-by-27 simplicial, LDL'. nzmax 113. nz 113 OK Ordering: AMD fl/lnz 4.7 lnz/anz 1.3 ints in L: 280, doubles in L: 113 factor flops 529 nnz(L) 113 (w/no amalgamation) nnz(A): 90 flops / nnz(L): 4.7 nnz(L) / nnz(A): 1.3 analyze cputime: 0.0000 factor cputime: 0.0000 mflop: 0.0 solve cputime: 0.0000 mflop: 0.0 overall cputime: 0.0000 mflop: 0.0 peak memory usage: 0 (MB) residual 7.4e-17 (|Ax-b|/(|A||x|+|b|)) rcond 3.0e-02 ./cholmod_l_demo < Matrix/lp_afiro.tri ---------------------------------- cholmod_l_demo: norm (A,inf) = 20.525 norm (A,1) = 3.429 CHOLMOD sparse: A: 27-by-51, nz 102, up/lo. OK CHOLMOD dense: B: 27-by-1, OK bnorm 1.96296 Analyze: flop 529 lnz 113 Factorizing A*A'+beta*I CHOLMOD factor: L: 27-by-27 simplicial, LDL'. nzmax 113. nz 113 OK Ordering: AMD fl/lnz 4.7 lnz/anz 1.3 ints in L: 280, doubles in L: 113 factor flops 529 nnz(L) 113 (w/no amalgamation) nnz(A): 90 flops / nnz(L): 4.7 nnz(L) / nnz(A): 1.3 analyze cputime: 0.0000 factor cputime: 0.0000 mflop: 0.0 solve cputime: 0.0000 mflop: 0.0 overall cputime: 0.0000 mflop: 0.0 peak memory usage: 0 (MB) residual 7.4e-17 (|Ax-b|/(|A||x|+|b|)) rcond 3.0e-02 ./cholmod_demo < Matrix/can___24.mtx ---------------------------------- cholmod_demo: norm (A,inf) = 17 norm (A,1) = 17 CHOLMOD sparse: A: 24-by-24, nz 92, upper. OK CHOLMOD dense: B: 24-by-1, OK bnorm 1.95833 Analyze: flop 656 lnz 120 Factorizing A CHOLMOD factor: L: 24-by-24 simplicial, LDL'. nzmax 120. nz 120 OK Ordering: AMD fl/lnz 5.5 lnz/anz 1.3 ints in L: 269, doubles in L: 120 factor flops 656 nnz(L) 120 (w/no amalgamation) nnz(A*A'): 92 flops / nnz(L): 5.5 nnz(L) / nnz(A): 1.3 analyze cputime: 0.0000 factor cputime: 0.0000 mflop: 0.0 solve cputime: 0.0000 mflop: 0.0 overall cputime: 0.0000 mflop: 0.0 peak memory usage: 0 (MB) residual 1.3e-16 (|Ax-b|/(|A||x|+|b|)) residual 7.5e-17 (|Ax-b|/(|A||x|+|b|)) after iterative refinement rcond 5.0e-01 ./cholmod_l_demo < Matrix/can___24.mtx ---------------------------------- cholmod_l_demo: norm (A,inf) = 17 norm (A,1) = 17 CHOLMOD sparse: A: 24-by-24, nz 92, upper. OK CHOLMOD dense: B: 24-by-1, OK bnorm 1.95833 Analyze: flop 656 lnz 120 Factorizing A CHOLMOD factor: L: 24-by-24 simplicial, LDL'. nzmax 120. nz 120 OK Ordering: AMD fl/lnz 5.5 lnz/anz 1.3 ints in L: 269, doubles in L: 120 factor flops 656 nnz(L) 120 (w/no amalgamation) nnz(A*A'): 92 flops / nnz(L): 5.5 nnz(L) / nnz(A): 1.3 analyze cputime: 0.0000 factor cputime: 0.0000 mflop: 0.0 solve cputime: 0.0000 mflop: 0.0 overall cputime: 0.0000 mflop: 0.0 peak memory usage: 0 (MB) residual 1.3e-16 (|Ax-b|/(|A||x|+|b|)) residual 7.5e-17 (|Ax-b|/(|A||x|+|b|)) after iterative refinement rcond 5.0e-01 ./cholmod_demo < Matrix/c.tri ---------------------------------- cholmod_demo: norm (A,inf) = 47.2361 norm (A,1) = 47.2361 CHOLMOD sparse: A: 3-by-3, nz 5, upper. OK CHOLMOD dense: B: 3-by-1, OK bnorm 1.66759 Analyze: flop 9 lnz 5 Factorizing A CHOLMOD factor: L: 3-by-3 simplicial, LDL'. nzmax 5. nz 5 OK Ordering: AMD fl/lnz 1.8 lnz/anz 1.0 ints in L: 28, doubles in L: 5 factor flops 9 nnz(L) 5 (w/no amalgamation) nnz(A*A'): 5 flops / nnz(L): 1.8 nnz(L) / nnz(A): 1.0 analyze cputime: 0.0000 factor cputime: 0.0000 mflop: 0.0 solve cputime: 0.0000 mflop: 0.0 overall cputime: 0.0000 mflop: 0.0 peak memory usage: 0 (MB) residual 2.0e-17 (|Ax-b|/(|A||x|+|b|)) rcond 3.6e-02 ./cholmod_l_demo < Matrix/c.tri ---------------------------------- cholmod_l_demo: norm (A,inf) = 47.2361 norm (A,1) = 47.2361 CHOLMOD sparse: A: 3-by-3, nz 5, upper. OK CHOLMOD dense: B: 3-by-1, OK bnorm 1.66759 Analyze: flop 9 lnz 5 Factorizing A CHOLMOD factor: L: 3-by-3 simplicial, LDL'. nzmax 5. nz 5 OK Ordering: AMD fl/lnz 1.8 lnz/anz 1.0 ints in L: 28, doubles in L: 5 factor flops 9 nnz(L) 5 (w/no amalgamation) nnz(A*A'): 5 flops / nnz(L): 1.8 nnz(L) / nnz(A): 1.0 analyze cputime: 0.0000 factor cputime: 0.0000 mflop: 0.0 solve cputime: 0.0000 mflop: 0.0 overall cputime: 0.0000 mflop: 0.0 peak memory usage: 0 (MB) residual 2.0e-17 (|Ax-b|/(|A||x|+|b|)) rcond 3.6e-02 ./cholmod_simple < Matrix/c.tri CHOLMOD sparse: A: 3-by-3, nz 5, upper. OK norm(b-Ax) 5.6e-17 ./cholmod_simple < Matrix/can___24.mtx CHOLMOD sparse: A: 24-by-24, nz 92, upper. OK norm(b-Ax) 2.0e-15 ./cholmod_simple < Matrix/bcsstk01.tri CHOLMOD sparse: A: 48-by-48, nz 224, upper. OK norm(b-Ax) 2.7e-13 SuiteSparse/CHOLMOD/Demo/cholmod_demo.c0000644001170100242450000002777510537777464016563 0ustar davisfac/* ========================================================================== */ /* === Demo/cholmod_demo ==================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Demo Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Demo Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Read in a matrix from a file, and use CHOLMOD to solve Ax=b if A is * symmetric, or (AA'+beta*I)x=b otherwise. The file format is a simple * triplet format, compatible with most files in the Matrix Market format. * See cholmod_read.c for more details. The readhb.f program reads a * Harwell/Boeing matrix (excluding element-types) and converts it into the * form needed by this program. reade.f reads a matrix in Harwell/Boeing * finite-element form. * * Usage: * cholmod_demo matrixfile * cholmod_demo < matrixfile * * The matrix is assumed to be positive definite (a supernodal LL' or simplicial * LDL' factorization is used). * * Requires the Core, Cholesky, MatrixOps, and Check Modules. * Optionally uses the Partition and Supernodal Modules. * Does not use the Modify Module. * * See cholmod_simple.c for a simpler demo program. */ #include "cholmod_demo.h" /* ff is a global variable so that it can be closed by my_handler */ FILE *ff ; /* halt if an error occurs */ static void my_handler (int status, char *file, int line, char *message) { printf ("cholmod error: file: %s line: %d status: %d: %s\n", file, line, status, message) ; if (status < 0) { if (ff != NULL) fclose (ff) ; exit (0) ; } } int main (int argc, char **argv) { double resid, t, ta, tf, ts, tot, bnorm, xnorm, anorm, rnorm, fl, anz, axbnorm, rnorm2, resid2 ; FILE *f ; cholmod_sparse *A ; cholmod_dense *X, *B, *W, *R ; double one [2], zero [2], minusone [2], beta [2], xlnz ; cholmod_common Common, *cm ; cholmod_factor *L ; double *Bx, *Rx, *Xx ; int i, n, isize, xsize, ordering, xtype, s, ss, lnz ; /* ---------------------------------------------------------------------- */ /* get the file containing the input matrix */ /* ---------------------------------------------------------------------- */ ff = NULL ; if (argc > 1) { if ((f = fopen (argv [1], "r")) == NULL) { my_handler (CHOLMOD_INVALID, __FILE__, __LINE__, "unable to open file") ; } ff = f ; } else { f = stdin ; } /* ---------------------------------------------------------------------- */ /* start CHOLMOD and set parameters */ /* ---------------------------------------------------------------------- */ cm = &Common ; cholmod_start (cm) ; /* use default parameter settings, except for the error handler. This * demo program terminates if an error occurs (out of memory, not positive * definite, ...). It makes the demo program simpler (no need to check * CHOLMOD error conditions). This non-default parameter setting has no * effect on performance. */ cm->error_handler = my_handler ; /* Note that CHOLMOD will do a supernodal LL' or a simplicial LDL' by * default, automatically selecting the latter if flop/nnz(L) < 40. */ /* ---------------------------------------------------------------------- */ /* create basic scalars */ /* ---------------------------------------------------------------------- */ zero [0] = 0 ; zero [1] = 0 ; one [0] = 1 ; one [1] = 0 ; minusone [0] = -1 ; minusone [1] = 0 ; beta [0] = 1e-6 ; beta [1] = 0 ; /* ---------------------------------------------------------------------- */ /* read in a matrix */ /* ---------------------------------------------------------------------- */ printf ("\n---------------------------------- cholmod_demo:\n") ; A = cholmod_read_sparse (f, cm) ; if (ff != NULL) fclose (ff) ; anorm = cholmod_norm_sparse (A, 0, cm) ; xtype = A->xtype ; printf ("norm (A,inf) = %g\n", anorm) ; printf ("norm (A,1) = %g\n", cholmod_norm_sparse (A, 1, cm)) ; cholmod_print_sparse (A, "A", cm) ; if (A->nrow > A->ncol) { /* Transpose A so that A'A+beta*I will be factorized instead */ cholmod_sparse *C = cholmod_transpose (A, 2, cm) ; cholmod_free_sparse (&A, cm) ; A = C ; printf ("transposing input matrix\n") ; } /* ---------------------------------------------------------------------- */ /* create an arbitrary right-hand-side */ /* ---------------------------------------------------------------------- */ n = A->nrow ; B = cholmod_zeros (n, 1, xtype, cm) ; Bx = B->x ; #if GHS { /* b = A*ones(n,1), used by Gould, Hu, and Scott in their experiments */ cholmod_dense *X0 ; X0 = cholmod_ones (A->ncol, 1, xtype, cm) ; cholmod_sdmult (A, 0, one, zero, X0, B, cm) ; cholmod_free_dense (&X0, cm) ; } #else if (xtype == CHOLMOD_REAL) { /* real case */ for (i = 0 ; i < n ; i++) { double x = n ; Bx [i] = 1 + i / x ; } } else { /* complex case */ for (i = 0 ; i < n ; i++) { double x = n ; Bx [2*i ] = 1 + i / x ; /* real part of B(i) */ Bx [2*i+1] = (x/2 - i) / (3*x) ; /* imag part of B(i) */ } } #endif cholmod_print_dense (B, "B", cm) ; bnorm = cholmod_norm_dense (B, 0, cm) ; /* max norm */ printf ("bnorm %g\n", bnorm) ; /* ---------------------------------------------------------------------- */ /* analyze, factorize, and solve */ /* ---------------------------------------------------------------------- */ t = CPUTIME ; L = cholmod_analyze (A, cm) ; ta = CPUTIME - t ; ta = MAX (ta, 0) ; printf ("Analyze: flop %g lnz %g\n", cm->fl, cm->lnz) ; if (A->stype == 0) { printf ("Factorizing A*A'+beta*I\n") ; t = CPUTIME ; cholmod_factorize_p (A, beta, NULL, 0, L, cm) ; tf = CPUTIME - t ; tf = MAX (tf, 0) ; } else { printf ("Factorizing A\n") ; t = CPUTIME ; cholmod_factorize (A, L, cm) ; tf = CPUTIME - t ; tf = MAX (tf, 0) ; } t = CPUTIME ; X = cholmod_solve (CHOLMOD_A, L, B, cm) ; ts = CPUTIME - t ; ts = MAX (ts, 0) ; tot = ta + tf + ts ; /* ---------------------------------------------------------------------- */ /* compute the residual */ /* ---------------------------------------------------------------------- */ if (A->stype == 0) { /* (AA'+beta*I)x=b is the linear system that was solved */ /* W = A'*X */ W = cholmod_allocate_dense (A->ncol, 1, A->ncol, xtype, cm) ; cholmod_sdmult (A, 2, one, zero, X, W, cm) ; /* R = B - beta*X */ R = cholmod_zeros (n, 1, xtype, cm) ; Rx = R->x ; Xx = X->x ; if (xtype == CHOLMOD_REAL) { for (i = 0 ; i < n ; i++) { Rx [i] = Bx [i] - beta [0] * Xx [i] ; } } else { /* complex case */ for (i = 0 ; i < n ; i++) { Rx [2*i ] = Bx [2*i ] - beta [0] * Xx [2*i ] ; Rx [2*i+1] = Bx [2*i+1] - beta [0] * Xx [2*i+1] ; } } /* R = A*W - R */ cholmod_sdmult (A, 0, one, minusone, W, R, cm) ; cholmod_free_dense (&W, cm) ; } else { /* Ax=b was factorized and solved, R = B-A*X */ R = cholmod_copy_dense (B, cm) ; cholmod_sdmult (A, 0, minusone, one, X, R, cm) ; } rnorm = cholmod_norm_dense (R, 0, cm) ; /* max abs. entry */ xnorm = cholmod_norm_dense (X, 0, cm) ; /* max abs. entry */ axbnorm = (anorm * xnorm + bnorm + ((n == 0) ? 1 : 0)) ; resid = rnorm / axbnorm ; /* ---------------------------------------------------------------------- */ /* iterative refinement (real symmetric case only) */ /* ---------------------------------------------------------------------- */ resid2 = -1 ; if (A->stype != 0 && A->xtype == CHOLMOD_REAL) { cholmod_dense *R2 ; /* R2 = A\(B-A*X) */ R2 = cholmod_solve (CHOLMOD_A, L, R, cm) ; /* compute X = X + A\(B-A*X) */ Xx = X->x ; Rx = R2->x ; for (i = 0 ; i < n ; i++) { Xx [i] = Xx [i] + Rx [i] ; } cholmod_free_dense (&R2, cm) ; cholmod_free_dense (&R, cm) ; /* compute the new residual, R = B-A*X */ R = cholmod_copy_dense (B, cm) ; cholmod_sdmult (A, 0, minusone, one, X, R, cm) ; rnorm2 = cholmod_norm_dense (R, 0, cm) ; resid2 = rnorm2 / axbnorm ; } cholmod_free_dense (&R, cm) ; /* ---------------------------------------------------------------------- */ /* print results */ /* ---------------------------------------------------------------------- */ cholmod_print_factor (L, "L", cm) ; /* determine the # of integers's and reals's in L. See cholmod_free */ if (L->is_super) { s = L->nsuper + 1 ; xsize = L->xsize ; ss = L->ssize ; isize = n /* L->Perm */ + n /* L->ColCount, nz in each column of 'pure' L */ + s /* L->pi, column pointers for L->s */ + s /* L->px, column pointers for L->x */ + s /* L->super, starting column index of each supernode */ + ss ; /* L->s, the pattern of the supernodes */ } else { /* this space can increase if you change parameters to their non- * default values (cm->final_pack, for example). */ lnz = L->nzmax ; xsize = lnz ; isize = n /* L->Perm */ + n /* L->ColCount, nz in each column of 'pure' L */ + n+1 /* L->p, column pointers */ + lnz /* L->i, integer row indices */ + n /* L->nz, nz in each column of L */ + n+2 /* L->next, link list */ + n+2 ; /* L->prev, link list */ } anz = cm->anz ; for (i = 0 ; i < CHOLMOD_MAXMETHODS ; i++) { fl = cm->method [i].fl ; xlnz = cm->method [i].lnz ; cm->method [i].fl = -1 ; cm->method [i].lnz = -1 ; ordering = cm->method [i].ordering ; if (fl >= 0) { printf ("Ordering: ") ; if (ordering == CHOLMOD_POSTORDERED) printf ("postordered ") ; if (ordering == CHOLMOD_NATURAL) printf ("natural ") ; if (ordering == CHOLMOD_GIVEN) printf ("user ") ; if (ordering == CHOLMOD_AMD) printf ("AMD ") ; if (ordering == CHOLMOD_METIS) printf ("METIS ") ; if (ordering == CHOLMOD_NESDIS) printf ("NESDIS ") ; if (xlnz > 0) { printf ("fl/lnz %10.1f", fl / xlnz) ; } if (anz > 0) { printf (" lnz/anz %10.1f", xlnz / anz) ; } printf ("\n") ; } } printf ("ints in L: %d, doubles in L: %d\n", isize, xsize) ; printf ("factor flops %g nnz(L) %15.0f (w/no amalgamation)\n", cm->fl, cm->lnz) ; if (A->stype == 0) { printf ("nnz(A): %15.0f\n", cm->anz) ; } else { printf ("nnz(A*A'): %15.0f\n", cm->anz) ; } if (cm->lnz > 0) { printf ("flops / nnz(L): %8.1f\n", cm->fl / cm->lnz) ; } if (anz > 0) { printf ("nnz(L) / nnz(A): %8.1f\n", cm->lnz / cm->anz) ; } printf ("analyze cputime: %12.4f\n", ta) ; printf ("factor cputime: %12.4f mflop: %8.1f\n", tf, (tf == 0) ? 0 : (1e-6*cm->fl / tf)) ; printf ("solve cputime: %12.4f mflop: %8.1f\n", ts, (ts == 0) ? 0 : (1e-6*4*cm->lnz / ts)) ; printf ("overall cputime: %12.4f mflop: %8.1f\n", tot, (tot == 0) ? 0 : (1e-6 * (cm->fl + 4 * cm->lnz) / tot)) ; printf ("peak memory usage: %12.0f (MB)\n", (double) (cm->memory_usage) / 1048576.) ; printf ("residual %8.1e (|Ax-b|/(|A||x|+|b|))\n", resid) ; if (resid2 >= 0) { printf ("residual %8.1e (|Ax-b|/(|A||x|+|b|))" " after iterative refinement\n", resid2) ; } printf ("rcond %8.1e\n\n", cholmod_rcond (L, cm)) ; cholmod_free_factor (&L, cm) ; cholmod_free_dense (&X, cm) ; /* ---------------------------------------------------------------------- */ /* free matrices and finish CHOLMOD */ /* ---------------------------------------------------------------------- */ cholmod_free_sparse (&A, cm) ; cholmod_free_dense (&B, cm) ; cholmod_finish (cm) ; return (0) ; } SuiteSparse/CHOLMOD/Demo/cholmod_demo.h0000644001170100242450000000172610537777466016556 0ustar davisfac/* ========================================================================== */ /* === Demo/cholmod_demo.h ================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Demo Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Demo Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ #include "cholmod.h" #include #include #include #include #include #define TRUE 1 #define FALSE 0 #define CPUTIME ((double) (clock ( )) / CLOCKS_PER_SEC) #define MAX(a,b) (((a) > (b)) ? (a) : (b)) SuiteSparse/CHOLMOD/Demo/License.txt0000644001170100242450000000203310540000270016025 0ustar davisfacCHOLMOD/Demo Module. Copyright (C) 2005-2006, Timothy A. Davis CHOLMOD is also available under other licenses; contact authors for details. http://www.cise.ufl.edu/research/sparse Note that this license is for the CHOLMOD/Demo module only. All CHOLMOD modules are licensed separately. -------------------------------------------------------------------------------- This Module is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This Module is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. SuiteSparse/CHOLMOD/Demo/cholmod_simple.c0000644001170100242450000000423610537777472017112 0ustar davisfac/* ========================================================================== */ /* === Demo/cholmod_simple ================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Demo Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Demo Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Read in a real symmetric or complex Hermitian matrix from stdin in * MatrixMarket format, solve Ax=b where b=[1 1 ... 1]', and print the residual. * Usage: cholmod_simple < matrixfile */ #include "cholmod.h" int main (void) { cholmod_sparse *A ; cholmod_dense *x, *b, *r ; cholmod_factor *L ; double one [2] = {1,0}, m1 [2] = {-1,0} ; /* basic scalars */ cholmod_common c ; cholmod_start (&c) ; /* start CHOLMOD */ A = cholmod_read_sparse (stdin, &c) ; /* read in a matrix */ cholmod_print_sparse (A, "A", &c) ; /* print the matrix */ if (A == NULL || A->stype == 0) /* A must be symmetric */ { cholmod_free_sparse (&A, &c) ; cholmod_finish (&c) ; return (0) ; } b = cholmod_ones (A->nrow, 1, A->xtype, &c) ; /* b = ones(n,1) */ L = cholmod_analyze (A, &c) ; /* analyze */ cholmod_factorize (A, L, &c) ; /* factorize */ x = cholmod_solve (CHOLMOD_A, L, b, &c) ; /* solve Ax=b */ r = cholmod_copy_dense (b, &c) ; /* r = b */ cholmod_sdmult (A, 0, m1, one, x, r, &c) ; /* r = r-Ax */ printf ("norm(b-Ax) %8.1e\n", cholmod_norm_dense (r, 0, &c)) ; /* print norm(r) */ cholmod_free_factor (&L, &c) ; /* free matrices */ cholmod_free_sparse (&A, &c) ; cholmod_free_dense (&r, &c) ; cholmod_free_dense (&x, &c) ; cholmod_free_dense (&b, &c) ; cholmod_finish (&c) ; /* finish CHOLMOD */ return (0) ; } SuiteSparse/CHOLMOD/Demo/gpl.txt0000644001170100242450000004313310253411077015247 0ustar davisfac GNU GENERAL PUBLIC LICENSE Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. 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SuiteSparse/CHOLMOD/Demo/cholmod_l_demo.c0000644001170100242450000003022510537777470017053 0ustar davisfac/* ========================================================================== */ /* === Demo/cholmod_l_demo ================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Demo Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Demo Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Read in a matrix from a file, and use CHOLMOD to solve Ax=b if A is * symmetric, or (AA'+beta*I)x=b otherwise. The file format is a simple * triplet format, compatible with most files in the Matrix Market format. * See cholmod_read.c for more details. The readhb.f format reads a * Harwell/Boeing matrix (excluding element-types) and converts it into the * form needed by this program. reade.f reads a matrix in Harwell/Boeing * finite-element form. * * Usage: * cholmod_l_demo matrixfile * cholmod_l_demo < matrixfile * * The matrix is assumed to be positive definite (a supernodal LL' or simplicial * LDL' factorization is used). * * Requires the Core, Cholesky, MatrixOps, and Check Modules. * Optionally uses the Partition and Supernodal Modules. * Does not use the Modify Module. * * See cholmod_simple.c for a simpler demo program. * * UF_long is normally defined as long, except for WIN64. */ #include "cholmod_demo.h" /* ff is a global variable so that it can be closed by my_handler */ FILE *ff ; /* halt if an error occurs */ static void my_handler (int status, char *file, int line, char *message) { printf ("cholmod error: file: %s line: %d status: %d: %s\n", file, line, status, message) ; if (status < 0) { if (ff != NULL) fclose (ff) ; exit (0) ; } } int main (int argc, char **argv) { double resid, t, ta, tf, ts, tot, bnorm, xnorm, anorm, rnorm, fl, anz, axbnorm, rnorm2, resid2 ; FILE *f ; cholmod_sparse *A ; cholmod_dense *X, *B, *W, *R ; double one [2], zero [2], minusone [2], beta [2], xlnz ; cholmod_common Common, *cm ; cholmod_factor *L ; double *Bx, *Rx, *Xx ; UF_long i, n, isize, xsize, ordering, xtype, s, ss, lnz ; /* ---------------------------------------------------------------------- */ /* get the file containing the input matrix */ /* ---------------------------------------------------------------------- */ ff = NULL ; if (argc > 1) { if ((f = fopen (argv [1], "r")) == NULL) { my_handler (CHOLMOD_INVALID, __FILE__, __LINE__, "unable to open file") ; } ff = f ; } else { f = stdin ; } /* ---------------------------------------------------------------------- */ /* start CHOLMOD and set parameters */ /* ---------------------------------------------------------------------- */ cm = &Common ; cholmod_l_start (cm) ; /* use default parameter settings, except for the error handler. This * demo program terminates if an error occurs (out of memory, not positive * definite, ...). It makes the demo program simpler (no need to check * CHOLMOD error conditions). This non-default parameter setting has no * effect on performance. */ cm->error_handler = my_handler ; /* Note that CHOLMOD will do a supernodal LL' or a simplicial LDL' by * default, automatically selecting the latter if flop/nnz(L) < 40. */ /* ---------------------------------------------------------------------- */ /* create basic scalars */ /* ---------------------------------------------------------------------- */ zero [0] = 0 ; zero [1] = 0 ; one [0] = 1 ; one [1] = 0 ; minusone [0] = -1 ; minusone [1] = 0 ; beta [0] = 1e-6 ; beta [1] = 0 ; /* ---------------------------------------------------------------------- */ /* read in a matrix */ /* ---------------------------------------------------------------------- */ printf ("\n---------------------------------- cholmod_l_demo:\n") ; A = cholmod_l_read_sparse (f, cm) ; if (ff != NULL) fclose (ff) ; anorm = cholmod_l_norm_sparse (A, 0, cm) ; xtype = A->xtype ; printf ("norm (A,inf) = %g\n", anorm) ; printf ("norm (A,1) = %g\n", cholmod_l_norm_sparse (A, 1, cm)) ; cholmod_l_print_sparse (A, "A", cm) ; if (A->nrow > A->ncol) { /* Transpose A so that A'A+beta*I will be factorized instead */ cholmod_sparse *C = cholmod_l_transpose (A, 2, cm) ; cholmod_l_free_sparse (&A, cm) ; A = C ; printf ("transposing input matrix\n") ; } /* ---------------------------------------------------------------------- */ /* create an arbitrary right-hand-side */ /* ---------------------------------------------------------------------- */ n = A->nrow ; B = cholmod_l_zeros (n, 1, xtype, cm) ; Bx = B->x ; #if GHS { /* b = A*ones(n,1), used by Gould, Hu, and Scott in their experiments */ cholmod_dense *X0 ; X0 = cholmod_l_ones (A->ncol, 1, xtype, cm) ; cholmod_l_sdmult (A, 0, one, zero, X0, B, cm) ; cholmod_l_free_dense (&X0, cm) ; } #else if (xtype == CHOLMOD_REAL) { /* real case */ for (i = 0 ; i < n ; i++) { double x = n ; Bx [i] = 1 + i / x ; } } else { /* complex case */ for (i = 0 ; i < n ; i++) { double x = n ; Bx [2*i ] = 1 + i / x ; /* real part of B(i) */ Bx [2*i+1] = (x/2 - i) / (3*x) ; /* imag part of B(i) */ } } #endif cholmod_l_print_dense (B, "B", cm) ; bnorm = cholmod_l_norm_dense (B, 0, cm) ; /* max norm */ printf ("bnorm %g\n", bnorm) ; /* ---------------------------------------------------------------------- */ /* analyze, factorize, and solve */ /* ---------------------------------------------------------------------- */ t = CPUTIME ; L = cholmod_l_analyze (A, cm) ; ta = CPUTIME - t ; ta = MAX (ta, 0) ; printf ("Analyze: flop %g lnz %g\n", cm->fl, cm->lnz) ; if (A->stype == 0) { printf ("Factorizing A*A'+beta*I\n") ; t = CPUTIME ; cholmod_l_factorize_p (A, beta, NULL, 0, L, cm) ; tf = CPUTIME - t ; tf = MAX (tf, 0) ; } else { printf ("Factorizing A\n") ; t = CPUTIME ; cholmod_l_factorize (A, L, cm) ; tf = CPUTIME - t ; tf = MAX (tf, 0) ; } t = CPUTIME ; X = cholmod_l_solve (CHOLMOD_A, L, B, cm) ; ts = CPUTIME - t ; ts = MAX (ts, 0) ; tot = ta + tf + ts ; /* ---------------------------------------------------------------------- */ /* compute the residual */ /* ---------------------------------------------------------------------- */ if (A->stype == 0) { /* (AA'+beta*I)x=b is the linear system that was solved */ /* W = A'*X */ W = cholmod_l_allocate_dense (A->ncol, 1, A->ncol, xtype, cm) ; cholmod_l_sdmult (A, 2, one, zero, X, W, cm) ; /* R = B - beta*X */ R = cholmod_l_zeros (n, 1, xtype, cm) ; Rx = R->x ; Xx = X->x ; if (xtype == CHOLMOD_REAL) { for (i = 0 ; i < n ; i++) { Rx [i] = Bx [i] - beta [0] * Xx [i] ; } } else { /* complex case */ for (i = 0 ; i < n ; i++) { Rx [2*i ] = Bx [2*i ] - beta [0] * Xx [2*i ] ; Rx [2*i+1] = Bx [2*i+1] - beta [0] * Xx [2*i+1] ; } } /* R = A*W - R */ cholmod_l_sdmult (A, 0, one, minusone, W, R, cm) ; cholmod_l_free_dense (&W, cm) ; } else { /* Ax=b was factorized and solved, R = B-A*X */ R = cholmod_l_copy_dense (B, cm) ; cholmod_l_sdmult (A, 0, minusone, one, X, R, cm) ; } rnorm = cholmod_l_norm_dense (R, 0, cm) ; /* max abs. entry */ xnorm = cholmod_l_norm_dense (X, 0, cm) ; /* max abs. entry */ axbnorm = (anorm * xnorm + bnorm + ((n == 0) ? 1 : 0)) ; resid = rnorm / axbnorm ; /* ---------------------------------------------------------------------- */ /* iterative refinement (real symmetric case only) */ /* ---------------------------------------------------------------------- */ resid2 = -1 ; if (A->stype != 0 && A->xtype == CHOLMOD_REAL) { cholmod_dense *R2 ; /* R2 = A\(B-A*X) */ R2 = cholmod_l_solve (CHOLMOD_A, L, R, cm) ; /* compute X = X + A\(B-A*X) */ Xx = X->x ; Rx = R2->x ; for (i = 0 ; i < n ; i++) { Xx [i] = Xx [i] + Rx [i] ; } cholmod_l_free_dense (&R2, cm) ; cholmod_l_free_dense (&R, cm) ; /* compute the new residual, R = B-A*X */ R = cholmod_l_copy_dense (B, cm) ; cholmod_l_sdmult (A, 0, minusone, one, X, R, cm) ; rnorm2 = cholmod_l_norm_dense (R, 0, cm) ; resid2 = rnorm2 / axbnorm ; } cholmod_l_free_dense (&R, cm) ; /* ---------------------------------------------------------------------- */ /* print results */ /* ---------------------------------------------------------------------- */ cholmod_l_print_factor (L, "L", cm) ; /* determine the # of integers's and reals's in L. See cholmod_free */ if (L->is_super) { s = L->nsuper + 1 ; xsize = L->xsize ; ss = L->ssize ; isize = n /* L->Perm */ + n /* L->ColCount, nz in each column of 'pure' L */ + s /* L->pi, column pointers for L->s */ + s /* L->px, column pointers for L->x */ + s /* L->super, starting column index of each supernode */ + ss ; /* L->s, the pattern of the supernodes */ } else { /* this space can increase if you change parameters to their non- * default values (cm->final_pack, for example). */ lnz = L->nzmax ; xsize = lnz ; isize = n /* L->Perm */ + n /* L->ColCount, nz in each column of 'pure' L */ + n+1 /* L->p, column pointers */ + lnz /* L->i, integer row indices */ + n /* L->nz, nz in each column of L */ + n+2 /* L->next, link list */ + n+2 ; /* L->prev, link list */ } anz = cm->anz ; for (i = 0 ; i < CHOLMOD_MAXMETHODS ; i++) { fl = cm->method [i].fl ; xlnz = cm->method [i].lnz ; cm->method [i].fl = -1 ; cm->method [i].lnz = -1 ; ordering = cm->method [i].ordering ; if (fl >= 0) { printf ("Ordering: ") ; if (ordering == CHOLMOD_POSTORDERED) printf ("postordered ") ; if (ordering == CHOLMOD_NATURAL) printf ("natural ") ; if (ordering == CHOLMOD_GIVEN) printf ("user ") ; if (ordering == CHOLMOD_AMD) printf ("AMD ") ; if (ordering == CHOLMOD_METIS) printf ("METIS ") ; if (ordering == CHOLMOD_NESDIS) printf ("NESDIS ") ; if (xlnz > 0) { printf ("fl/lnz %10.1f", fl / xlnz) ; } if (anz > 0) { printf (" lnz/anz %10.1f", xlnz / anz) ; } printf ("\n") ; } } printf ("ints in L: %ld, doubles in L: %ld\n", isize, xsize) ; printf ("factor flops %g nnz(L) %15.0f (w/no amalgamation)\n", cm->fl, cm->lnz) ; if (A->stype == 0) { printf ("nnz(A): %15.0f\n", cm->anz) ; } else { printf ("nnz(A*A'): %15.0f\n", cm->anz) ; } if (cm->lnz > 0) { printf ("flops / nnz(L): %8.1f\n", cm->fl / cm->lnz) ; } if (anz > 0) { printf ("nnz(L) / nnz(A): %8.1f\n", cm->lnz / cm->anz) ; } printf ("analyze cputime: %12.4f\n", ta) ; printf ("factor cputime: %12.4f mflop: %8.1f\n", tf, (tf == 0) ? 0 : (1e-6*cm->fl / tf)) ; printf ("solve cputime: %12.4f mflop: %8.1f\n", ts, (ts == 0) ? 0 : (1e-6*4*cm->lnz / ts)) ; printf ("overall cputime: %12.4f mflop: %8.1f\n", tot, (tot == 0) ? 0 : (1e-6 * (cm->fl + 4 * cm->lnz) / tot)) ; printf ("peak memory usage: %12.0f (MB)\n", (double) (cm->memory_usage) / 1048576.) ; printf ("residual %8.1e (|Ax-b|/(|A||x|+|b|))\n", resid) ; if (resid2 >= 0) { printf ("residual %8.1e (|Ax-b|/(|A||x|+|b|))" " after iterative refinement\n", resid2) ; } printf ("rcond %8.1e\n\n", cholmod_l_rcond (L, cm)) ; cholmod_l_free_factor (&L, cm) ; cholmod_l_free_dense (&X, cm) ; /* ---------------------------------------------------------------------- */ /* free matrices and finish CHOLMOD */ /* ---------------------------------------------------------------------- */ cholmod_l_free_sparse (&A, cm) ; cholmod_l_free_dense (&B, cm) ; cholmod_l_finish (cm) ; return (0) ; } SuiteSparse/CHOLMOD/Demo/readhb.f0000644001170100242450000000647310277474252015340 0ustar davisfacc----------------------------------------------------------------------- c Read a sparse matrix in the Harwell/Boeing format and output a c matrix in triplet format. Only the lower triangular part of a c symmetric matrix is provided. Does not handle skew-symmetric c matrices. c----------------------------------------------------------------------- integer nzmax, nmax parameter (nzmax = 100000000, nmax = 1000000) integer Ptr (nmax), Index (nzmax), n, nz, totcrd, ptrcrd, $ indcrd, valcrd, rhscrd, ncol, nrow, nrhs, row, col, p character title*72, key*30, type*3, ptrfmt*16, $ indfmt*16, valfmt*20, rhsfmt*20 logical sym double precision Value (nzmax), skew character rhstyp*3 integer nzrhs, nel, stype c----------------------------------------------------------------------- c read header information from Harwell/Boeing matrix read (5, 10, err = 998) $ title, key, $ totcrd, ptrcrd, indcrd, valcrd, rhscrd, $ type, nrow, ncol, nz, nel, $ ptrfmt, indfmt, valfmt, rhsfmt if (rhscrd .gt. 0) then c new Harwell/Boeing format: read (5, 20, err = 998) rhstyp,nrhs,nzrhs endif 10 format (a72, a8 / 5i14 / a3, 11x, 4i14 / 2a16, 2a20) 20 format (a3, 11x, 2i14) skew = 0.0 if (type (2:2) .eq. 'Z' .or. type (2:2) .eq. 'z') skew = -1.0 if (type (2:2) .eq. 'S' .or. type (2:2) .eq. 's') skew = 1.0 sym = skew .ne. 0.0 c write (0, 30) title, key, type, nrow, ncol, nz if (rhscrd .gt. 0) then c new Harwell/Boeing format: c write (0, 40) rhstyp,nrhs,nzrhs endif 30 format ( $ ' title: ', a72 / $ ' key: ', a8 / $ ' type: ', a3, ' nrow: ', i14, ' ncol: ', i14 / $ ' nz: ', i14) 40 format (' rhstyp: ', a3, ' nrhs: ', i14, ' nzrhs: ', i14) * write (0, *) ' sym: ', sym, ' skew: ', skew if (skew .eq. -1) then write (0, *) 'Cannot handle skew-symmetric matrices' stop endif n = max (nrow, ncol) if (ncol .ge. nmax .or. nz .gt. nzmax) then write (0, *) ' Matrix too big!' stop endif read (5, ptrfmt, err = 998) (Ptr (p), p = 1, ncol+1) read (5, indfmt, err = 998) (Index (p), p = 1, nz) c read the values if (valcrd .gt. 0) then read (5, valfmt, err = 998) (Value (p), p = 1, nz) endif c create the triplet form of the input matrix c stype = 0: unsymmetric c stype = -1: symmetric, lower triangular part present stype = -skew write (6, 101) title write (6, 102) key 101 format ('% title:', a72) 102 format ('% key: ', a8) write (6, 110) nrow, ncol, nz, stype 110 format (2i8, i12, i3) do 100 col = 1, ncol do 90 p = Ptr (col), Ptr (col+1) - 1 row = Index (p) if (valcrd .gt. 0) then write (6, 200) row, col, Value (p) c if (sym .and. row .ne. col) then c write (6, 200) col, row, skew * Value (p) c endif else write (6, 201) row, col endif 90 continue 100 continue 200 format (2i8, e30.18e3) 201 format (2i8) stop 998 write (0,*) 'Read error: Harwell/Boeing matrix' stop end SuiteSparse/CHOLMOD/Demo/readhb2.f0000644001170100242450000000725210277474247015422 0ustar davisfacc----------------------------------------------------------------------- c Read a sparse matrix in the Harwell/Boeing format and output a c matrix in triplet format. Only the lower triangular part of a c symmetric matrix is provided. Does not handle skew-symmetric c matrices. c c This version assumes the matrix is symmetric. Only the c lower triangular part is printed. c----------------------------------------------------------------------- integer nzmax, nmax parameter (nzmax = 100000000, nmax = 1000000) integer Ptr (nmax), Index (nzmax), n, nz, totcrd, ptrcrd, $ indcrd, valcrd, rhscrd, ncol, nrow, nrhs, row, col, p character title*72, key*30, type*3, ptrfmt*16, $ indfmt*16, valfmt*20, rhsfmt*20 logical sym double precision Value (nzmax), skew character rhstyp*3 integer nzrhs, nel, stype c----------------------------------------------------------------------- c read header information from Harwell/Boeing matrix read (5, 10, err = 998) $ title, key, $ totcrd, ptrcrd, indcrd, valcrd, rhscrd, $ type, nrow, ncol, nz, nel, $ ptrfmt, indfmt, valfmt, rhsfmt if (rhscrd .gt. 0) then c new Harwell/Boeing format: read (5, 20, err = 998) rhstyp,nrhs,nzrhs endif 10 format (a72, a8 / 5i14 / a3, 11x, 4i14 / 2a16, 2a20) 20 format (a3, 11x, 2i14) skew = 0.0 if (type (2:2) .eq. 'Z' .or. type (2:2) .eq. 'z') skew = -1.0 if (type (2:2) .eq. 'S' .or. type (2:2) .eq. 's') skew = 1.0 sym = skew .ne. 0.0 c write (0, 30) title, key, type, nrow, ncol, nz if (rhscrd .gt. 0) then c new Harwell/Boeing format: c write (0, 40) rhstyp,nrhs,nzrhs endif 30 format ( $ ' title: ', a72 / $ ' key: ', a8 / $ ' type: ', a3, ' nrow: ', i14, ' ncol: ', i14 / $ ' nz: ', i14) 40 format (' rhstyp: ', a3, ' nrhs: ', i14, ' nzrhs: ', i14) * write (0, *) ' sym: ', sym, ' skew: ', skew if (skew .eq. -1) then write (0, *) 'Cannot handle skew-symmetric matrices' stop endif n = max (nrow, ncol) if (ncol .ge. nmax .or. nz .gt. nzmax) then write (0, *) ' Matrix too big!' stop endif read (5, ptrfmt, err = 998) (Ptr (p), p = 1, ncol+1) read (5, indfmt, err = 998) (Index (p), p = 1, nz) c read the values if (valcrd .gt. 0) then read (5, valfmt, err = 998) (Value (p), p = 1, nz) endif c create the triplet form of the input matrix c stype = 0: unsymmetric c stype = -1: symmetric, lower triangular part present c stype = -skew stype = -1 nz = 0 ; do 300 col = 1, ncol do 390 p = Ptr (col), Ptr (col+1) - 1 row = Index (p) if (row .ge. col) then nz = nz + 1 endif 390 continue 300 continue write (6, 101) title write (6, 102) key 101 format ('% title:', a72) 102 format ('% key: ', a8) write (6, 110) nrow, ncol, nz, stype 110 format (2i8, i12, i3) do 100 col = 1, ncol do 90 p = Ptr (col), Ptr (col+1) - 1 row = Index (p) if (row .ge. col) then if (valcrd .gt. 0) then write (6, 200) row, col, Value (p) c if (sym .and. row .ne. col) then c write (6, 200) col, row, skew * Value (p) c endif else write (6, 201) row, col endif endif 90 continue 100 continue 200 format (2i8, e30.18e3) 201 format (2i8) stop 998 write (0,*) 'Read error: Harwell/Boeing matrix' stop end SuiteSparse/CHOLMOD/Tcov/0000755001170100242450000000000010711175717013756 5ustar davisfacSuiteSparse/CHOLMOD/Tcov/tmp/0000755001170100242450000000000010711175716014555 5ustar davisfacSuiteSparse/CHOLMOD/Tcov/cm.c0000644001170100242450000013070210540000037014502 0ustar davisfac/* ========================================================================== */ /* === Tcov/cm ============================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* A program for exhaustive statement-coverage for CHOLMOD, AMD, COLAMD, and * CCOLAMD. It tests every line of code in all three packages. * * For a complete test, all CHOLMOD modules, AMD, COLAMD, CCOLAMD, METIS, * LAPACK, and the BLAS are required. A partial test can be performed without * the Supernodal and/or Partition modules. METIS is not required if the * Partition module is not installed. LAPACK and the BLAS are not required * if the Supernodal module is not installed. * * Usage: * * cm < input > output * * where "input" contains a sparse matrix in triplet form. The first line of * the file contains four or five integers: * * nrow ncol nnz stype complex * * where the matrix is nrow-by-ncol. nnz is the number of (i,j,aij) triplets * in the rest of the file, one triplet per line. stype is -1 (symmetric * with entries in lower triangular part provided), 0 (unsymmetric), or 1 * (symmetric upper). If the 5th entry is missing, or 0, then the matrix is * real; if 1 the matrix is complex, if 2 the matrix is zomplex. Each * subsequent line contains * * i j aij * * for the row index, column index, and value of A(i,j). Duplicate entries * are summed. If stype is 2 or 3, the rest of the file is ignored, and a * special test matrix is constructed (2: arrowhead, 3: tridiagonal plus a * dense row). Test matrices are located in the Matrix/ subdirectory. * * For complex matrices, each line consists of * * i j xij zij * * where xij is the real part of A(i,j) and zij is the imaginary part. * * cm takes one optional parameter. If present (it does not matter what the * argument is, actually) then extension memory-failure tests are performed. */ #include "cm.h" /* ========================================================================== */ /* === global variables ===================================================== */ /* ========================================================================== */ double zero [2], one [2], minusone [2] ; cholmod_common Common, *cm ; cholmod_dense *M1 ; Int dot = 0 ; double Zero [2] ; /* ========================================================================== */ /* === my_rand ============================================================== */ /* ========================================================================== */ /* The POSIX example of rand, duplicated here so that the same sequence will * be generated on different machines. */ static unsigned long next = 1 ; /* RAND_MAX assumed to be 32767 */ Int my_rand (void) { next = next * 1103515245 + 12345 ; return ((unsigned)(next/65536) % /* 32768 */ (MY_RAND_MAX + 1)) ; } void my_srand (unsigned seed) { next = seed ; } unsigned long my_seed (void) { return (next) ; } /* ========================================================================== */ /* === progress ============================================================= */ /* ========================================================================== */ /* print a "." on stderr to indicate progress */ #define LINEWIDTH 70 #define COUNT 100 void progress (Int force, char s) { dot++ ; if (force) { dot += (COUNT - (dot % COUNT)) ; } if (dot % COUNT == 0) { fprintf (stderr, "%c", s) ; } if (dot % (COUNT*LINEWIDTH) == 0) { fprintf (stderr, "\n") ; } fflush (stdout) ; fflush (stderr) ; } /* ========================================================================== */ /* === my_handler =========================================================== */ /* ========================================================================== */ /* An error occurred that should not have occurred */ void my_handler (int status, char *file, int line, char *msg) { printf ("Error handler: file %s line %d status %d: %s\n", file, line, status, msg) ; if (status < CHOLMOD_OK || status > CHOLMOD_DSMALL) { fprintf (stderr, "\n\n************************************************" "********************************\n" "*** Test failure: file: %s line: %d\n" "*** status: %d message: %s\n" "***********************************************************" "*********************\n", file, line, status, msg); fflush (stderr) ; fflush (stdout) ; abort ( ) ; } } /* ========================================================================== */ /* === Assert =============================================================== */ /* ========================================================================== */ void Assert (int truth, char *file, int line) { if (!truth) { my_handler (-1, file, line, "") ; } } /* ========================================================================== */ /* === nrand ================================================================ */ /* ========================================================================== */ /* return a random Int between 0 and n-1 */ Int nrand (Int n) { return ((n <= 0) ? (0) : (rand ( ) % n)) ; } /* ========================================================================== */ /* === xrand ================================================================ */ /* ========================================================================== */ /* return a random double between 0 and x */ double xrand (double range) { return ((range * (double) (my_rand ( ))) / MY_RAND_MAX) ; } /* ========================================================================== */ /* === prand ================================================================ */ /* ========================================================================== */ /* allocate and construct a random permutation of 0:n-1 */ Int *prand (Int n) { Int *P ; Int t, j, k ; P = CHOLMOD(malloc) (n, sizeof (Int), cm) ; if (P == NULL) { ERROR (CHOLMOD_INVALID, "cannot create random perm") ; return (NULL) ; } for (k = 0 ; k < n ; k++) { P [k] = k ; } for (k = 0 ; k < n-1 ; k++) { j = k + nrand (n-k) ; t = P [j] ; P [j] = P [k] ; P [k] = t ; } CHOLMOD(print_perm) (P, n, n, "Prandom", cm) ; return (P) ; } /* ========================================================================== */ /* === rand_set ============================================================= */ /* ========================================================================== */ /* allocate and construct a random set of 0:n-1, possibly with duplicates */ Int *rand_set (Int len, Int n) { Int *cset ; Int k ; cset = CHOLMOD(malloc) (len, sizeof (Int), cm) ; if (cset == NULL) { ERROR (CHOLMOD_INVALID, "cannot create random set") ; return (NULL) ; } for (k = 0 ; k < len ; k++) { cset [k] = nrand (n) ; } CHOLMOD(print_subset) (cset, len, n, "random cset", cm) ; return (cset) ; } /* ========================================================================== */ /* === read_triplet ========================================================= */ /* ========================================================================== */ /* Read a triplet matrix from a file. */ #define MAXLINE 1024 cholmod_triplet *read_triplet ( FILE *f ) { cholmod_triplet *T ; double *Tx, *Tz ; long long x1, x2, x3, x4, x5 ; Int *Ti, *Tj ; Int n, j, k, nrow, ncol, nz, stype, arrowhead, tridiag_plus_denserow, xtype, is_complex ; char s [MAXLINE] ; /* ---------------------------------------------------------------------- */ /* read in a triplet matrix from a file */ /* ---------------------------------------------------------------------- */ dot = 0 ; xtype = 0 ; if (fgets (s, MAXLINE, f) == NULL) { return (NULL) ; } x1 = 0 ; x2 = 0 ; x3 = 0 ; x4 = 0 ; x5 = 0 ; k = sscanf (s, "%lld %lld %lld %lld %lld\n", &x1, &x2, &x3, &x4, &x5) ; nrow = x1 ; ncol = x2 ; nz = x3 ; stype = x4 ; xtype = x5 ; xtype++ ; is_complex = (xtype != CHOLMOD_REAL) ; printf ("read_triplet: nrow "ID" ncol "ID" nz "ID" stype "ID" xtype "ID"\n", nrow, ncol, nz, stype, xtype) ; arrowhead = FALSE ; tridiag_plus_denserow = FALSE ; n = MAX (nrow, ncol) ; if (stype == 2) { /* ignore nz and the rest of the file, and create an arrowhead matrix */ arrowhead = TRUE ; nz = nrow + ncol + 1 ; stype = (nrow == ncol) ? (1) : (0) ; } else if (stype == 3) { tridiag_plus_denserow = TRUE ; nrow = n ; ncol = n ; nz = 4*n + 4 ; stype = 0 ; } T = CHOLMOD(allocate_triplet) (nrow, ncol, nz, stype, is_complex ? CHOLMOD_ZOMPLEX : CHOLMOD_REAL, cm) ; if (T == NULL) { ERROR (CHOLMOD_INVALID, "cannot create triplet matrix") ; return (NULL) ; } Ti = T->i ; Tj = T->j ; Tx = T->x ; Tz = T->z ; if (arrowhead) { for (k = 0 ; k < MIN (nrow,ncol) ; k++) { Ti [k] = k ; Tj [k] = k ; Tx [k] = nrow + xrand (1) ; /* RAND */ if (is_complex) { Tz [k] = nrow + xrand (1) ; /* RAND */ } } for (j = 0 ; j < ncol ; j++) { Ti [k] = 0 ; Tj [k] = j ; Tx [k] = - xrand (1) ; /* RAND */ if (is_complex) { Tz [k] = - xrand (1) ; /* RAND */ } k++ ; } T->nnz = k ; } else if (tridiag_plus_denserow) { /* dense row, except for the last column */ for (k = 0 ; k < n-1 ; k++) { Ti [k] = 0 ; Tj [k] = k ; Tx [k] = xrand (1) ; /* RAND */ if (is_complex) { Tz [k] = xrand (1) ; /* RAND */ } } /* diagonal */ for (j = 0 ; j < n ; j++) { Ti [k] = j ; Tj [k] = j ; Tx [k] = nrow + xrand (1) ; /* RAND */ if (is_complex) { Tz [k] = nrow + xrand (1) ; /* RAND */ } k++ ; } /* superdiagonal */ for (j = 1 ; j < n ; j++) { Ti [k] = j-1 ; Tj [k] = j ; Tx [k] = xrand (1) ; /* RAND */ if (is_complex) { Tz [k] = xrand (1) ; /* RAND */ } k++ ; } /* subdiagonal */ for (j = 0 ; j < n-1 ; j++) { Ti [k] = j+1 ; Tj [k] = j ; Tx [k] = xrand (1) ; /* RAND */ if (is_complex) { Tz [k] = xrand (1) ; /* RAND */ } k++ ; } /* a few extra terms in the last column */ Ti [k] = MAX (0, n-3) ; Tj [k] = n-1 ; Tx [k] = xrand (1) ; /* RAND */ if (is_complex) { Tz [k] = xrand (1) ; /* RAND */ } k++ ; Ti [k] = MAX (0, n-4) ; Tj [k] = n-1 ; Tx [k] = xrand (1) ; /* RAND */ if (is_complex) { Tz [k] = xrand (1) ; /* RAND */ } k++ ; Ti [k] = MAX (0, n-5) ; Tj [k] = n-1 ; Tx [k] = xrand (1) ; /* RAND */ if (is_complex) { Tz [k] = xrand (1) ; /* RAND */ } k++ ; T->nnz = k ; } else { if (is_complex) { for (k = 0 ; k < nz ; k++) { if (fscanf (f,""ID" "ID" %lg %lg\n", Ti+k, Tj+k, Tx+k, Tz+k) == EOF) { ERROR (CHOLMOD_INVALID, "Error reading triplet matrix\n") ; } } } else { for (k = 0 ; k < nz ; k++) { if (fscanf (f, ""ID" "ID" %lg\n", Ti+k, Tj+k, Tx+k) == EOF) { ERROR (CHOLMOD_INVALID, "Error reading triplet matrix\n") ; } } } T->nnz = nz ; } CHOLMOD(triplet_xtype) (xtype, T, cm) ; /* ---------------------------------------------------------------------- */ /* print the triplet matrix */ /* ---------------------------------------------------------------------- */ cm->print = 4 ; CHOLMOD(print_triplet) (T, "T input", cm) ; cm->print = 1 ; fprintf (stderr, "Test matrix: "ID"-by-"ID" with "ID" entries, stype: "ID "\n", (Int) T->nrow, (Int) T->ncol, (Int) T->nnz, (Int) T->stype) ; printf ("\n\n======================================================\n" "Test matrix: "ID"-by-"ID" with "ID" entries, stype: "ID"\n", (Int) T->nrow, (Int) T->ncol, (Int) T->nnz, (Int) T->stype) ; if (MAX (nrow, ncol) > NLARGE) { fprintf (stderr, "Please wait, this will take a while ...") ; dot = 39*LINEWIDTH ; } return (T) ; } /* ========================================================================== */ /* === zeros ================================================================ */ /* ========================================================================== */ /* Same as cholmod_zeros or cholmod_l_zeros, except it allows for a leading * dimension that is different than nrow */ cholmod_dense *zeros (Int nrow, Int ncol, Int d, Int xtype) { cholmod_dense *X ; double *Xx, *Xz ; Int i, nz ; X = CHOLMOD(allocate_dense) (nrow, ncol, d, xtype, cm) ; if (X == NULL) { return (NULL) ; } Xx = X->x ; Xz = X->z ; nz = MAX (1, X->nzmax) ; switch (X->xtype) { case CHOLMOD_REAL: for (i = 0 ; i < nz ; i++) { Xx [i] = 0 ; } break ; case CHOLMOD_COMPLEX: for (i = 0 ; i < 2*nz ; i++) { Xx [i] = 0 ; } break ; case CHOLMOD_ZOMPLEX: for (i = 0 ; i < nz ; i++) { Xx [i] = 0 ; } for (i = 0 ; i < nz ; i++) { Xz [i] = 0 ; } break ; } return (X) ; } /* ========================================================================== */ /* === xtrue ================================================================ */ /* ========================================================================== */ /* Allocate and construct a dense matrix, X(i,j) = i+j*d+1 */ cholmod_dense *xtrue (Int nrow, Int ncol, Int d, Int xtype) { double *x, *z ; cholmod_dense *X ; Int j, i ; X = zeros (nrow, ncol, d, xtype) ; if (X == NULL) { ERROR (CHOLMOD_INVALID, "cannot create dense matrix") ; return (NULL) ; } x = X->x ; z = X->z ; if (xtype == CHOLMOD_REAL) { for (j = 0 ; j < ncol ; j++) { for (i = 0 ; i < nrow ; i++) { x [i+j*d] = i+j*d + 1 ; } } } else if (xtype == CHOLMOD_COMPLEX) { for (j = 0 ; j < ncol ; j++) { for (i = 0 ; i < nrow ; i++) { x [2*(i+j*d) ] = i+j*d + 1 ; x [2*(i+j*d)+1] = ((double) (j+i*d + 1))/10 ; } } } else { for (j = 0 ; j < ncol ; j++) { for (i = 0 ; i < nrow ; i++) { x [i+j*d] = i+j*d + 1 ; z [i+j*d] = ((double) (j+i*d + 1))/10 ; } } } return (X) ; } /* ========================================================================== */ /* === rhs ================================================================== */ /* ========================================================================== */ /* Create a right-hand-side, b = A*x, where x is a known solution */ cholmod_dense *rhs (cholmod_sparse *A, Int nrhs, Int d) { Int n ; cholmod_dense *W, *Z, *B ; if (A == NULL) { ERROR (CHOLMOD_INVALID, "cannot compute rhs") ; return (NULL) ; } n = A->nrow ; /* B = zeros (n,rhs) but with leading dimension d */ B = zeros (n, nrhs, d, A->xtype) ; /* ---------------------------------------------------------------------- */ /* create a known solution */ /* ---------------------------------------------------------------------- */ Z = xtrue (n, nrhs, d, A->xtype) ; /* ---------------------------------------------------------------------- */ /* compute B = A*Z or A*A'*Z */ /* ---------------------------------------------------------------------- */ if (A->stype == 0) { /* W = A'*Z */ W = CHOLMOD(zeros) (A->ncol, nrhs, A->xtype, cm) ; CHOLMOD(sdmult) (A, TRUE, one, zero, Z, W, cm) ; /* B = A*W */ CHOLMOD(sdmult) (A, FALSE, one, zero, W, B, cm) ; CHOLMOD(free_dense) (&W, cm) ; } else { /* B = A*Z */ CHOLMOD(sdmult) (A, FALSE, one, zero, Z, B, cm) ; } CHOLMOD(free_dense) (&Z, cm) ; return (B) ; } /* ========================================================================== */ /* === resid ================================================================ */ /* ========================================================================== */ /* compute r = norm (A*x-b)/norm(b) or r = norm (A*A'*x-b)/norm(b) */ double resid (cholmod_sparse *A, cholmod_dense *X, cholmod_dense *B) { double r, bnorm ; cholmod_dense *R, *X2, *B2 ; cholmod_sparse *C, *A2 ; Int d, n, nrhs, xtype ; if (A == NULL || X == NULL || B == NULL) { ERROR (CHOLMOD_INVALID, "cannot compute resid") ; return (1) ; } cm->status = CHOLMOD_OK ; n = B->nrow ; /* ---------------------------------------------------------------------- */ /* convert all inputs to an identical xtype */ /* ---------------------------------------------------------------------- */ xtype = MAX (A->xtype, X->xtype) ; xtype = MAX (xtype, B->xtype) ; A2 = NULL ; B2 = NULL ; X2 = NULL ; if (A->xtype != xtype) { A2 = CHOLMOD(copy_sparse) (A, cm) ; CHOLMOD(sparse_xtype) (xtype, A2, cm) ; A = A2 ; } if (X->xtype != xtype) { X2 = CHOLMOD(copy_dense) (X, cm) ; CHOLMOD(dense_xtype) (xtype, X2, cm) ; X = X2 ; } if (B->xtype != xtype) { B2 = CHOLMOD(copy_dense) (B, cm) ; CHOLMOD(dense_xtype) (xtype, B2, cm) ; B = B2 ; } if (cm->status < CHOLMOD_OK) { ERROR (CHOLMOD_INVALID, "cannot compute resid") ; CHOLMOD(free_sparse) (&A2, cm) ; CHOLMOD(free_dense) (&B2, cm) ; CHOLMOD(free_dense) (&X2, cm) ; return (1) ; } /* ---------------------------------------------------------------------- */ /* get the right-hand-side, B, and its norm */ /* ---------------------------------------------------------------------- */ nrhs = B->ncol ; d = B->d ; if (nrhs == 1) { /* inf-norm, 1-norm, or 2-norm (random choice) */ bnorm = CHOLMOD(norm_dense) (B, nrand (2), cm) ; } else { /* inf-norm or 1-norm (random choice) */ bnorm = CHOLMOD(norm_dense) (B, nrand (1), cm) ; } /* ---------------------------------------------------------------------- */ /* compute the residual */ /* ---------------------------------------------------------------------- */ if (A->stype == 0) { if (n < 10 && A->xtype == CHOLMOD_REAL) { /* test cholmod_aat, C = A*A' */ C = CHOLMOD(aat) (A, NULL, 0, 1, cm) ; /* R = B */ R = CHOLMOD(copy_dense) (B, cm) ; /* R = C*X - R */ CHOLMOD(sdmult) (C, FALSE, one, minusone, X, R, cm) ; CHOLMOD(free_sparse) (&C, cm) ; } else { /* W = A'*X */ cholmod_dense *W ; W = CHOLMOD(zeros) (A->ncol, nrhs, A->xtype, cm) ; CHOLMOD(sdmult) (A, TRUE, one, zero, X, W, cm) ; /* R = B */ R = CHOLMOD(copy_dense) (B, cm) ; /* R = A*W - R */ CHOLMOD(sdmult) (A, FALSE, one, minusone, W, R, cm) ; CHOLMOD(free_dense) (&W, cm) ; } } else { /* R = B */ R = CHOLMOD(copy_dense) (B, cm) ; /* R = A*X - R */ CHOLMOD(sdmult) (A, FALSE, one, minusone, X, R, cm) ; } /* ---------------------------------------------------------------------- */ /* r = norm (R) / norm (B) */ /* ---------------------------------------------------------------------- */ r = CHOLMOD(norm_dense) (R, 1, cm) ; CHOLMOD(free_dense) (&R, cm) ; CHOLMOD(free_sparse) (&A2, cm) ; CHOLMOD(free_dense) (&B2, cm) ; CHOLMOD(free_dense) (&X2, cm) ; if (bnorm > 0) { r /= bnorm ; } return (r) ; } /* ========================================================================== */ /* === resid_sparse ========================================================= */ /* ========================================================================== */ /* compute r = norm (A*x-b)/norm(b) or r = norm (A*A'*x-b)/norm(b) */ double resid_sparse (cholmod_sparse *A, cholmod_sparse *X, cholmod_sparse *B) { double r, bnorm ; cholmod_sparse *R, *W, *AT, *W2 ; cholmod_dense *X2, *B2 ; Int n, nrhs, xtype ; if (A == NULL || X == NULL || B == NULL) { ERROR (CHOLMOD_INVALID, "cannot compute resid") ; return (1) ; } /* ---------------------------------------------------------------------- */ /* compute the residual */ /* ---------------------------------------------------------------------- */ xtype = MAX (A->xtype, X->xtype) ; xtype = MAX (xtype, B->xtype) ; if (xtype > CHOLMOD_REAL) { /* ------------------------------------------------------------------ */ /* convert X and B to dense if any is complex or zomplex */ /* ------------------------------------------------------------------ */ X2 = CHOLMOD(sparse_to_dense) (X, cm) ; B2 = CHOLMOD(sparse_to_dense) (B, cm) ; r = resid (A, X2, B2) ; CHOLMOD(free_dense) (&X2, cm) ; CHOLMOD(free_dense) (&B2, cm) ; } else { /* ------------------------------------------------------------------ */ /* all inputs are real */ /* ------------------------------------------------------------------ */ n = B->nrow ; nrhs = B->ncol ; /* inf-norm or 1-norm (random choice) */ bnorm = CHOLMOD(norm_sparse) (B, nrand (1), cm) ; if (A->stype == 0) { /* W = A'*X */ AT = CHOLMOD(transpose) (A, 1, cm) ; W = CHOLMOD(ssmult) (AT, X, 0, TRUE, FALSE, cm) ; CHOLMOD(free_sparse) (&AT, cm) ; /* W2 = A*W */ W2 = CHOLMOD(ssmult) (A, W, 0, TRUE, FALSE, cm) ; CHOLMOD(free_sparse) (&W, cm) ; /* R = W2 - B */ R = CHOLMOD(add) (W2, B, one, minusone, TRUE, FALSE, cm) ; CHOLMOD(free_sparse) (&W2, cm) ; } else { /* W = A*X */ W = CHOLMOD(ssmult) (A, X, 0, TRUE, FALSE, cm) ; /* R = W - B */ R = CHOLMOD(add) (W, B, one, minusone, TRUE, FALSE, cm) ; CHOLMOD(free_sparse) (&W, cm) ; } r = CHOLMOD(norm_sparse) (R, 1, cm) ; CHOLMOD(free_sparse) (&R, cm) ; if (bnorm > 0) { r /= bnorm ; } } return (r) ; } /* ========================================================================== */ /* === resid3 =============================================================== */ /* ========================================================================== */ /* r = norm (A1*A2*A3*x - b) / norm (b) */ double resid3 (cholmod_sparse *A1, cholmod_sparse *A2, cholmod_sparse *A3, cholmod_dense *X, cholmod_dense *B) { double r, bnorm ; cholmod_dense *R, *W1, *W2, *X2, *B2 ; cholmod_sparse *C1, *C2, *C3 ; Int n, nrhs, d, xtype ; if (A1 == NULL || X == NULL || B == NULL) { ERROR (CHOLMOD_INVALID, "cannot compute resid3") ; return (1) ; } cm->status = CHOLMOD_OK ; n = B->nrow ; /* ---------------------------------------------------------------------- */ /* convert all inputs to an identical xtype */ /* ---------------------------------------------------------------------- */ xtype = MAX (A1->xtype, X->xtype) ; xtype = MAX (xtype, B->xtype) ; if (A2 != NULL) { xtype = MAX (xtype, A2->xtype) ; } if (A3 != NULL) { xtype = MAX (xtype, A3->xtype) ; } C1 = NULL ; C2 = NULL ; C3 = NULL ; B2 = NULL ; X2 = NULL ; if (A1->xtype != xtype) { C1 = CHOLMOD(copy_sparse) (A1, cm) ; CHOLMOD(sparse_xtype) (xtype, C1, cm) ; A1 = C1 ; } if (A2 != NULL && A2->xtype != xtype) { C2 = CHOLMOD(copy_sparse) (A2, cm) ; CHOLMOD(sparse_xtype) (xtype, C2, cm) ; A2 = C2 ; } if (A3 != NULL && A3->xtype != xtype) { C3 = CHOLMOD(copy_sparse) (A3, cm) ; CHOLMOD(sparse_xtype) (xtype, C3, cm) ; A3 = C3 ; } if (X->xtype != xtype) { X2 = CHOLMOD(copy_dense) (X, cm) ; CHOLMOD(dense_xtype) (xtype, X2, cm) ; X = X2 ; } if (B->xtype != xtype) { B2 = CHOLMOD(copy_dense) (B, cm) ; CHOLMOD(dense_xtype) (xtype, B2, cm) ; B = B2 ; } if (cm->status < CHOLMOD_OK) { ERROR (CHOLMOD_INVALID, "cannot compute resid3") ; CHOLMOD(free_sparse) (&C1, cm) ; CHOLMOD(free_sparse) (&C2, cm) ; CHOLMOD(free_sparse) (&C3, cm) ; CHOLMOD(free_dense) (&B2, cm) ; CHOLMOD(free_dense) (&X2, cm) ; return (1) ; } /* ---------------------------------------------------------------------- */ /* get B and its norm */ /* ---------------------------------------------------------------------- */ nrhs = B->ncol ; d = B->d ; bnorm = CHOLMOD(norm_dense) (B, 1, cm) ; /* ---------------------------------------------------------------------- */ /* compute the residual */ /* ---------------------------------------------------------------------- */ if (A3 != NULL) { /* W1 = A3*X */ W1 = CHOLMOD(zeros) (n, nrhs, xtype, cm) ; CHOLMOD(sdmult) (A3, FALSE, one, zero, X, W1, cm) ; } else { W1 = X ; } if (A2 != NULL) { /* W2 = A2*W1 */ W2 = CHOLMOD(eye) (n, nrhs, xtype, cm) ; CHOLMOD(sdmult) (A2, FALSE, one, zero, W1, W2, cm) ; } else { W2 = W1 ; } /* R = B */ R = CHOLMOD(copy_dense) (B, cm) ; /* R = A1*W2 - R */ CHOLMOD(sdmult) (A1, FALSE, one, minusone, W2, R, cm) ; /* ---------------------------------------------------------------------- */ /* r = norm (R) / norm (B) */ /* ---------------------------------------------------------------------- */ r = CHOLMOD(norm_dense) (R, 1, cm) ; CHOLMOD(free_dense) (&R, cm) ; CHOLMOD(free_sparse) (&C1, cm) ; CHOLMOD(free_sparse) (&C2, cm) ; CHOLMOD(free_sparse) (&C3, cm) ; CHOLMOD(free_dense) (&B2, cm) ; CHOLMOD(free_dense) (&X2, cm) ; if (A3 != NULL) { CHOLMOD(free_dense) (&W1, cm) ; } if (A2 != NULL) { CHOLMOD(free_dense) (&W2, cm) ; } if (bnorm > 0) { r /= bnorm ; } return (r) ; } /* ========================================================================== */ /* === pnorm ================================================================ */ /* ========================================================================== */ /* r = norm (x-Pb) or r = norm(x-P'b). This is lengthy because CHOLMOD does * not provide any operations on dense matrices, and because it used to test * the sparse-to-dense conversion routine. Multiple methods are used to compute * the same thing. */ double pnorm (cholmod_dense *X, Int *P, cholmod_dense *B, Int inv) { cholmod_dense *R, *X2, *B2 ; cholmod_factor *L ; double *xx, *xz, *bx, *bz, *rx, *rz ; Int *Pinv, *Perm ; double rnorm, r ; Int i, j, k, n, nrhs, xtype, ok, save, lxtype ; if (X == NULL || P == NULL || B == NULL) { ERROR (CHOLMOD_INVALID, "cannot compute pnorm") ; return (1) ; } save = cm->prefer_zomplex ; n = X->nrow ; nrhs = X->ncol ; rnorm = 0 ; Pinv = CHOLMOD(malloc) (n, sizeof (Int), cm) ; if (Pinv != NULL) { for (k = 0 ; k < n ; k++) { Pinv [P [k]] = k ; } } xtype = MAX (X->xtype, B->xtype) ; R = CHOLMOD(zeros) (n, nrhs, CHOLMOD_ZOMPLEX, cm) ; B2 = CHOLMOD(copy_dense) (B, cm) ; ok = R != NULL && B2 != NULL ; ok = ok && CHOLMOD(dense_xtype) (CHOLMOD_ZOMPLEX, B2, cm) ; for (lxtype = CHOLMOD_REAL ; ok && lxtype <= CHOLMOD_ZOMPLEX ; lxtype++) { /* create a fake factor object */ L = CHOLMOD(allocate_factor) (n, cm) ; CHOLMOD(change_factor) (lxtype, TRUE, FALSE, TRUE, TRUE, L, cm) ; ok = ok && (L != NULL && L->Perm != NULL && Pinv != NULL) ; if (ok) { L->ordering = CHOLMOD_GIVEN ; Perm = L->Perm ; for (k = 0 ; k < n ; k++) { Perm [k] = Pinv [k] ; } } for (k = 0 ; k <= 1 ; k++) { /* solve the inverse permutation system, X2 = P*X or X2 = P'*X */ cm->prefer_zomplex = k ; X2 = CHOLMOD(solve) (inv ? CHOLMOD_Pt : CHOLMOD_P, L, X, cm) ; ok = ok && CHOLMOD(dense_xtype) (CHOLMOD_ZOMPLEX, X2, cm) ; if (ok && X2 != NULL) { rx = R->x ; rz = R->z ; xx = X2->x ; xz = X2->z ; bx = B2->x ; bz = B2->z ; for (j = 0 ; j < nrhs ; j++) { for (i = 0 ; i < n ; i++) { rx [i+j*n] = xx [i+j*n] - bx [i+j*n] ; rz [i+j*n] = xz [i+j*n] - bz [i+j*n] ; } } } r = CHOLMOD(norm_dense) (R, 0, cm) ; rnorm = MAX (r, rnorm) ; CHOLMOD(free_dense) (&X2, cm) ; } CHOLMOD(free_factor) (&L, cm) ; } CHOLMOD(free_dense) (&B2, cm) ; CHOLMOD(free_dense) (&R, cm) ; if (xtype == CHOLMOD_REAL) { /* X and B are both real */ cholmod_sparse *Bs, *Pb ; Bs = CHOLMOD(dense_to_sparse) (B, TRUE, cm) ; Pb = CHOLMOD(submatrix) (Bs, inv ? Pinv : P, n, NULL, -1, TRUE, TRUE,cm); X2 = CHOLMOD(sparse_to_dense) (Pb, cm) ; R = CHOLMOD(zeros) (n, nrhs, CHOLMOD_REAL, cm) ; if (R != NULL && X != NULL && X2 != NULL) { rx = R->x ; xx = X->x ; bx = X2->x ; for (j = 0 ; j < nrhs ; j++) { for (i = 0 ; i < n ; i++) { rx [i+j*n] = xx [i+j*n] - bx [i+j*n] ; } } } CHOLMOD(free_sparse) (&Bs, cm) ; CHOLMOD(free_sparse) (&Pb, cm) ; CHOLMOD(free_dense) (&X2, cm) ; r = CHOLMOD(norm_dense) (R, 1, cm) ; rnorm = MAX (rnorm, r) ; CHOLMOD(free_dense) (&R, cm) ; } CHOLMOD(free) (n, sizeof (Int), Pinv, cm) ; cm->prefer_zomplex = save ; return (rnorm) ; } /* ========================================================================== */ /* === prune_row ============================================================ */ /* ========================================================================== */ /* Set row k and column k of a packed matrix A to zero. Set A(k,k) to 1 * if space is available. */ void prune_row (cholmod_sparse *A, Int k) { double *Ax ; Int *Ap, *Ai ; Int ncol, p, i, j, nz ; if (A == NULL) { ERROR (CHOLMOD_INVALID, "nothing to prune") ; return ; } Ap = A->p ; Ai = A->i ; Ax = A->x ; nz = 0 ; ncol = A->ncol ; for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; Ap [j] = nz ; if (j == k && nz < Ap [j+1]) { Ai [nz] = k ; Ax [nz] = 1 ; nz++ ; } else { for ( ; p < Ap [j+1] ; p++) { i = Ai [p] ; if (i != k) { Ai [nz] = i ; Ax [nz] = Ax [p] ; nz++ ; } } } } Ap [ncol] = nz ; } /* ========================================================================== */ /* === do_matrix =========================================================== */ /* ========================================================================== */ double do_matrix (cholmod_sparse *A) { double err, maxerr = 0 ; Int print, precise, maxprint, minprint, nmethods ; if (A == NULL) { ERROR (CHOLMOD_INVALID, "no matrix") ; return (1) ; } /* ---------------------------------------------------------------------- */ /* determine print level, based on matrix size */ /* ---------------------------------------------------------------------- */ if (A->nrow <= 4) { minprint = 5 ; maxprint = 5 ; } else if (A->nrow <= 8) { minprint = 4 ; maxprint = 4 ; } else { minprint = 1 ; maxprint = 1 ; } /* ---------------------------------------------------------------------- */ /* for all print levels and precisions, do: */ /* ---------------------------------------------------------------------- */ for (print = minprint ; print <= maxprint ; print++) { for (precise = 0 ; precise <= (print >= 4) ? 1 : 0 ; precise++) { Int save1, save2 ; maxerr = 0 ; my_srand (42) ; /* RAND reset */ cm->print = print ; cm->precise = precise ; printf ("\n----------Print level %d precise: %d\n", cm->print, cm->precise) ; save1 = cm->final_asis ; save2 = cm->final_super ; cm->final_asis = FALSE ; cm->final_super = TRUE ; OK (CHOLMOD(print_common) ("cm", cm)) ; cm->final_asis = save1 ; cm->final_super = save2 ; /* -------------------------------------------------------------- */ /* test various matrix operations */ /* -------------------------------------------------------------- */ err = test_ops (A) ; /* RAND */ MAXERR (maxerr, err, 1) ; /* -------------------------------------------------------------- */ /* solve the augmented system */ /* -------------------------------------------------------------- */ err = aug (A) ; /* no random number use */ MAXERR (maxerr, err, 1) ; /* -------------------------------------------------------------- */ /* solve using different methods */ /* -------------------------------------------------------------- */ printf ("test_solver (1)\n") ; cm->nmethods = 9 ; cm->final_asis = TRUE ; err = test_solver (A) ; /* RAND reset */ MAXERR (maxerr, err, 1) ; printf ("test_solver (2)\n") ; cm->final_asis = TRUE ; cm->method [0].ordering = CHOLMOD_NATURAL ; for (nmethods = 0 ; nmethods < 7 ; nmethods++) { cm->nmethods = nmethods ; err = test_solver (A) ; /* RAND reset */ MAXERR (maxerr, err, 1) ; } printf ("test_solver (3)\n") ; cm->nmethods = 1 ; cm->method [0].ordering = CHOLMOD_NESDIS ; err = test_solver (A) ; /* RAND reset */ MAXERR (maxerr, err, 1) ; printf ("test_solver (3b)\n") ; cm->nmethods = 1 ; cm->method [0].ordering = CHOLMOD_NESDIS ; cm->method [0].nd_camd = 2 ; err = test_solver (A) ; /* RAND reset */ MAXERR (maxerr, err, 1) ; printf ("test_solver (3c)\n") ; cm->nmethods = 1 ; cm->method [0].ordering = CHOLMOD_NATURAL ; err = test_solver (A) ; /* RAND reset */ MAXERR (maxerr, err, 1) ; printf ("test_solver (4)\n") ; cm->nmethods = 1 ; cm->method[0].ordering = CHOLMOD_METIS ; err = test_solver (A) ; /* RAND reset */ MAXERR (maxerr, err, 1) ; printf ("test_solver (5)\n") ; cm->nmethods = 1 ; cm->method [0].ordering = CHOLMOD_AMD ; CHOLMOD(free_work) (cm) ; err = test_solver (A) ; /* RAND reset */ MAXERR (maxerr, err, 1) ; printf ("test_solver (6)\n") ; cm->nmethods = 1 ; cm->method[0].ordering = CHOLMOD_COLAMD ; err = test_solver (A) ; /* RAND reset */ MAXERR (maxerr, err, 1) ; /* -------------------------------------------------------------- */ /* restore default control parameters */ /* -------------------------------------------------------------- */ OK (CHOLMOD(print_common) ("cm", cm)) ; CHOLMOD(defaults) (cm) ; } } printf ("do_matrix max error %.1g\n", maxerr) ; return (maxerr) ; } /* ========================================================================== */ /* === main ================================================================= */ /* ========================================================================== */ /* Usage: * cm < matrix do not perform intensive memory-failure tests * cm -m < matrix do perform memory tests * cm -s < matrix matrix is singular, nan error expected * * (The memory tests are performed if any argument is given to cm). */ int main (int argc, char **argv) { cholmod_triplet *T ; cholmod_sparse *A, *C, *AT ; char *s ; double err = 0, maxerr = 0 ; Int n = 0, nmin = 0, nrow = 0, ncol = 0, save ; int singular, do_memory, i, do_nantests ; double v = CHOLMOD_VERSION ; printf ("Testing CHOLMOD (%g)\n", v) ; printf ("%s: argc: %d\n", argv [0], argc) ; my_srand (42) ; /* RAND */ fflush (stdout) ; singular = FALSE ; do_memory = FALSE ; do_nantests = FALSE ; for (i = 1 ; i < argc ; i++) { s = argv [i] ; if (s [0] == '-' && s [1] == 'm') do_memory = TRUE ; if (s [0] == '-' && s [1] == 's') singular = TRUE ; if (s [0] == '-' && s [1] == 'n') do_nantests = TRUE ; } printf ("do_memory: %d singular: %d\n", do_memory, singular) ; /* ---------------------------------------------------------------------- */ /* initialize CHOLMOD */ /* ---------------------------------------------------------------------- */ cm = &Common ; OK (CHOLMOD(start) (cm)) ; /* ---------------------------------------------------------------------- */ /* test all methods with NULL common */ /* ---------------------------------------------------------------------- */ /* no user error handler, since lots of errors will be raised here */ cm->error_handler = NULL ; null_test (NULL) ; save = cm->itype ; cm->itype = -999 ; null_test (cm) ; cm->itype = save ; null_test2 ( ) ; CHOLMOD(finish) (cm) ; OK (cm->malloc_count == 0) ; OK (CHOLMOD(start) (cm)) ; /* ---------------------------------------------------------------------- */ /* create basic scalars */ /* ---------------------------------------------------------------------- */ Zero [0] = 0 ; Zero [1] = 0 ; zero [0] = 0 ; zero [1] = 0 ; one [0] = 1 ; one [1] = 0 ; minusone [0] = -1 ; minusone [1] = 0 ; M1 = CHOLMOD(ones) (1, 1, CHOLMOD_REAL, cm) ; if (M1 != NULL) { ((double *) (M1->x)) [0] = -1 ; } /* ---------------------------------------------------------------------- */ /* read in a triplet matrix and use it to test CHOLMOD */ /* ---------------------------------------------------------------------- */ for ( ; (T = read_triplet (stdin)) != NULL ; ) /* RAND */ { if (T->nrow > 1000000) { /* do huge-problem tests only */ huge ( ) ; CHOLMOD(free_triplet) (&T, cm) ; continue ; } maxerr = 0 ; CHOLMOD(defaults) (cm) ; cm->error_handler = my_handler ; cm->print = 4 ; cm->precise = FALSE ; cm->nmethods = 8 ; /* ------------------------------------------------------------------ */ /* convert triplet to sparse matrix */ /* ------------------------------------------------------------------ */ A = CHOLMOD(triplet_to_sparse) (T, 0, cm) ; AT = CHOLMOD(transpose) (A, 0, cm) ; OK (CHOLMOD(print_sparse) (A, "Test matrix, A", cm)) ; C = unpack (A) ; /* RAND */ OK (CHOLMOD(print_sparse) (C, "Unpacked/unsorted version of A", cm)) ; cm->print = 1 ; if (T != NULL) { nrow = T->nrow ; ncol = T->ncol ; n = MAX (nrow, ncol) ; nmin = MIN (nrow, ncol) ; } /* ------------------------------------------------------------------ */ /* basic error tests */ /* ------------------------------------------------------------------ */ null2 (T, do_nantests) ; /* RAND */ printf ("Null2 OK : no error\n") ; if (do_nantests) { maxerr = 0 ; goto done ; /* yes, this is ugly */ } /* ------------------------------------------------------------------ */ /* raw factorization tests */ /* ------------------------------------------------------------------ */ cm->error_handler = NULL ; err = raw_factor (A, 2) ; /* RAND */ cm->error_handler = my_handler ; MAXERR (maxerr, err, 1) ; printf ("raw factorization error %.1g\n", err) ; err = raw_factor2 (A, 0., 0) ; MAXERR (maxerr, err, 1) ; printf ("raw factorization error2 %.1g\n", err) ; err = raw_factor2 (A, 1e-16, 0) ; MAXERR (maxerr, err, 1) ; printf ("raw factorization error3 %.1g\n", err) ; if (n < 1000 && A && T && A->stype == 1) { /* factorize a symmetric matrix (upper part stored), possibly * with ignored entries in lower triangular part. */ cholmod_sparse *F ; int save = T->stype ; T->stype = 0 ; F = CHOLMOD(triplet_to_sparse) (T, 0, cm) ; T->stype = save ; /* ET = CHOLMOD(transpose) (E, 2, cm) ; if (E) E->stype = 0 ; if (ET) ET->stype = 0 ; F = CHOLMOD(add) (E, ET, one, one, 1, 1, cm) ; */ if (F) F->stype = 1 ; err = raw_factor2 (F, 0., 0) ; MAXERR (maxerr, err, 1) ; printf ("raw factorization error4 %.1g\n", err) ; err = raw_factor2 (F, 1e-16, 0) ; MAXERR (maxerr, err, 1) ; printf ("raw factorization error5 %.1g\n", err) ; cm->dbound = 1e-15 ; err = raw_factor2 (F, 0., 0) ; MAXERR (maxerr, err, 1) ; printf ("raw factorization error6 %.1g\n", err) ; err = raw_factor2 (F, 1e-16, 0) ; MAXERR (maxerr, err, 1) ; printf ("raw factorization error7 %.1g\n", err) ; err = raw_factor2 (F, 1e-16, 1) ; MAXERR (maxerr, err, 1) ; printf ("raw factorization error8 %.1g\n", err) ; cm->dbound = 0 ; /* CHOLMOD(free_sparse) (&E, cm) ; CHOLMOD(free_sparse) (&ET, cm) ; */ CHOLMOD(free_sparse) (&F, cm) ; } /* ------------------------------------------------------------------ */ /* matrix ops */ /* ------------------------------------------------------------------ */ err = test_ops (A) ; /* RAND */ MAXERR (maxerr, err, 1) ; printf ("initial testops error %.1g\n", err) ; /* ------------------------------------------------------------------ */ /* analyze, factorize, solve */ /* ------------------------------------------------------------------ */ err = solve (A) ; /* RAND */ MAXERR (maxerr, err, 1) ; printf ("initial solve error %.1g\n", err) ; /* ------------------------------------------------------------------ */ /* CCOLAMD tests */ /* ------------------------------------------------------------------ */ cctest (A) ; /* RAND reset */ cctest (AT) ; /* RAND reset */ /* ------------------------------------------------------------------ */ /* COLAMD tests */ /* ------------------------------------------------------------------ */ ctest (A) ; ctest (AT) ; /* ------------------------------------------------------------------ */ /* AMD tests */ /* ------------------------------------------------------------------ */ if (n < NLARGE || A->stype) { /* for unsymmetric matrices, this forms A*A' and A'*A, which can * fail if A has a dense row or column. So it is only done for * modest-sized unsymmetric matrices. */ amdtest (A) ; amdtest (AT) ; camdtest (A) ; /* RAND */ camdtest (AT) ; /* RAND */ } if (n < NSMALL) { /* -------------------------------------------------------------- */ /* do_matrix with an unpacked matrix */ /* -------------------------------------------------------------- */ /* try with an unpacked matrix, and a non-default dbound */ cm->dbound = 1e-15 ; err = do_matrix (C) ; /* RAND reset */ MAXERR (maxerr, err, 1) ; cm->dbound = 0 ; /* -------------------------------------------------------------- */ /* do_matrix: analyze, factorize, and solve, with many options */ /* -------------------------------------------------------------- */ err = do_matrix (A) ; /* RAND reset */ MAXERR (maxerr, err, 1) ; /* -------------------------------------------------------------- */ /* pretend to solve an LP */ /* -------------------------------------------------------------- */ if (nrow != ncol) { cm->print = 2 ; err = lpdemo (T) ; /* RAND */ cm->print = 1 ; MAXERR (maxerr, err, 1) ; cm->print = 5; CHOLMOD(print_common) ("Common", cm);cm->print=1; cm->nmethods = 1 ; cm->method [0].ordering = CHOLMOD_COLAMD ; err = lpdemo (T) ; /* RAND */ MAXERR (maxerr, err, 1) ; printf ("initial lp error %.1g, dbound %g\n", err, cm->dbound) ; cm->nmethods = 0 ; cm->method [0].ordering = CHOLMOD_GIVEN ; } } progress (1, '|') ; if (n < NSMALL && do_memory) { /* -------------------------------------------------------------- */ /* Exhaustive memory-error handling */ /* -------------------------------------------------------------- */ memory_tests (T) ; /* RAND */ } /* ------------------------------------------------------------------ */ /* free matrices and print results */ /* ------------------------------------------------------------------ */ done: /* an ugly "goto" target; added to minimize code changes * when added "do_nantests", for version 1.0.2 */ CHOLMOD(free_sparse) (&C, cm) ; CHOLMOD(free_sparse) (&AT, cm) ; CHOLMOD(free_sparse) (&A, cm) ; CHOLMOD(free_triplet) (&T, cm) ; fprintf (stderr, "\n " " Test OK") ; if (nrow <= ncol && !singular) { /* maxerr should be NaN if nrow > ncol, so don't print it */ fprintf (stderr, ", maxerr %.1g", maxerr) ; } fprintf (stderr, "\n") ; my_srand (42) ; /* RAND reset */ } /* ---------------------------------------------------------------------- */ /* finalize CHOLMOD */ /* ---------------------------------------------------------------------- */ CHOLMOD(free_dense) (&M1, cm) ; CHOLMOD(finish) (cm) ; cm->print = 5 ; OK (CHOLMOD(print_common) ("cm", cm)) ; printf ("malloc count "ID" inuse "ID"\n", (Int) cm->malloc_count, (Int) cm->memory_inuse) ; OK (cm->malloc_count == 0) ; OK (cm->memory_inuse == 0) ; if (nrow > ncol) { /* maxerr should be NaN, so don't print it */ printf ("All tests successful\n") ; } else { printf ("All tests successful: max error %.1g\n", maxerr) ; } return (0) ; } SuiteSparse/CHOLMOD/Tcov/cm.h0000644001170100242450000002040510462167317014527 0ustar davisfac#include "cholmod.h" #include #include #include #include #define Size_max ((size_t) (-1)) /* -------------------------------------------------------------------------- */ /* double, UF_long */ /* -------------------------------------------------------------------------- */ #ifdef DLONG #define Real double #define Int UF_long #define Int_max UF_long_max #define CHOLMOD(name) cholmod_l_ ## name #define LONG #define DOUBLE #define ITYPE CHOLMOD_LONG #define DTYPE CHOLMOD_DOUBLE /* -------------------------------------------------------------------------- */ /* double, int: this is the default */ /* -------------------------------------------------------------------------- */ #else #ifndef DINT #define DINT #endif #define INT #define DOUBLE #define Real double #define Int int #define Int_max INT_MAX #define CHOLMOD(name) cholmod_ ## name #define ITYPE CHOLMOD_INT #define DTYPE CHOLMOD_DOUBLE #endif /* -------------------------------------------------------------------------- */ #include "cholmod_blas.h" #define EMPTY (-1) #define TRUE 1 #define FALSE 0 #define MAX(a,b) (((a) > (b)) ? (a) : (b)) #define MIN(a,b) (((a) < (b)) ? (a) : (b)) #define IMPLIES(p,q) (!(p) || (q)) #if defined(WIN32) || defined(_WIN32) #define ISNAN(x) (((x) != (x)) || (((x) < (x)))) #else #define ISNAN(x) ((x) != (x)) #endif #define MY_RAND_MAX 32767 #define MAXERR(maxerr,err,anorm) \ { \ if (ISNAN (maxerr)) \ { \ /* do nothing */ ; \ } \ else if (ISNAN (err)) \ { \ maxerr = err ; \ } \ else if (anorm > 0) \ { \ if ((err/anorm) > maxerr) maxerr = (err/anorm) ; \ } \ else \ { \ if (err > maxerr) maxerr = err ; \ } \ /* printf ("MAXERR: %7.2e %7.2e %7.2e in %d : %s\n", \ maxerr, err, (double) anorm, __LINE__, __FILE__ ) ; */ \ } #define OKP(p) Assert ((p) != NULL, __FILE__, __LINE__) #define OK(truth) Assert (truth, __FILE__, __LINE__) #define NOT(truth) Assert (!(truth), __FILE__, __LINE__) #define NOP(p) Assert ((p) == NULL, __FILE__, __LINE__) #define NSMALL 200 #define NLARGE 1000 #define ERROR(status,message) \ CHOLMOD(error) (status, __FILE__, __LINE__, message, cm) /* -------------------------------------------------------------------------- */ /* global variables */ /* -------------------------------------------------------------------------- */ #ifndef EXTERN #define EXTERN extern #endif EXTERN double zero [2], one [2], minusone [2] ; EXTERN cholmod_common Common, *cm ; EXTERN cholmod_dense *M1 ; EXTERN Int my_tries ; EXTERN double Zero [2] ; /* -------------------------------------------------------------------------- */ /* prototypes */ /* -------------------------------------------------------------------------- */ void null_test (cholmod_common *) ; void null_test2 (void) ; void Assert (int truth, char *file, int line) ; Int nrand (Int n) ; Int *prand (Int n) ; cholmod_triplet *read_triplet (FILE *f) ; double test_ops (cholmod_sparse *A) ; cholmod_dense *xtrue (Int nrow, Int ncol, Int d, Int xtype) ; double resid (cholmod_sparse *A, cholmod_dense *X, cholmod_dense *B) ; double solve (cholmod_sparse *A) ; double aug (cholmod_sparse *A) ; double do_matrix (cholmod_sparse *A) ; cholmod_dense *rhs (cholmod_sparse *A, Int nrhs, Int d) ; void prune_row (cholmod_sparse *A, Int k) ; double pnorm (cholmod_dense *X, Int *P, cholmod_dense *B, Int inv) ; double test_solver (cholmod_sparse *A) ; Int *rand_set (Int len, Int n) ; void my_handler (int status, char *file, int line, char *msg) ; void my_handler2 (int status, char *file, int line, char *msg) ; double resid3 (cholmod_sparse *A1, cholmod_sparse *A2, cholmod_sparse *A3, cholmod_dense *X, cholmod_dense *B) ; double xrand (double range) ; double lp_resid (cholmod_sparse *A, Int *rflag, Int *fset, Int fsize, double beta [2], cholmod_dense *X, cholmod_dense *B) ; double lpdemo (cholmod_triplet *T) ; cholmod_sparse *lp_prune ( cholmod_sparse *A, Int *rflag, Int *fset, Int fsize); void null2 (cholmod_triplet *Tok, int do_nantests) ; void *my_malloc2 (size_t size) ; void *my_calloc2 (size_t n, size_t size) ; void *my_realloc2 (void *p, size_t size) ; void my_free2 (void *p) ; void memory_tests (cholmod_triplet *T) ; void progress (Int force, char s) ; void test_memory_handler ( void ) ; void normal_memory_handler ( void ) ; cholmod_sparse *unpack (cholmod_sparse *A) ; Int nzdiag (cholmod_sparse *A) ; Int check_partition (cholmod_sparse *A, Int *Part) ; double raw_factor (cholmod_sparse *A, Int errors) ; double raw_factor2 (cholmod_sparse *A, double alpha, int domask) ; cholmod_sparse *get_row (cholmod_sparse *A, Int i, Int *rflag, Int *fset, Int fsize, double beta [2]) ; Int my_rand (void) ; void my_srand (unsigned seed) ; unsigned long my_seed (void) ; void cctest (cholmod_sparse *A) ; Int check_constraints (Int *P, Int *Cmember, Int n) ; void ctest (cholmod_sparse *A) ; void amdtest (cholmod_sparse *A) ; double resid_sparse (cholmod_sparse *A, cholmod_sparse *X, cholmod_sparse *B) ; cholmod_dense *zeros (Int nrow, Int ncol, Int d, Int xtype) ; /* -------------------------------------------------------------------------- */ /* AMD, COLAMD, and CCOLAMD */ /* -------------------------------------------------------------------------- */ #ifdef LONG #define ID "%ld" #define AMD_order amd_l_order #define AMD_defaults amd_l_defaults #define AMD_control amd_l_control #define AMD_info amd_l_info #define AMD_1 amd_l1 #define AMD_2 amd_l2 #define AMD_valid amd_l_valid #define AMD_aat amd_l_aat #define AMD_postorder amd_l_postorder #define AMD_post_tree amd_l_post_tree #define AMD_dump amd_l_dump #define AMD_debug amd_l_debug #define AMD_debug_init amd_l_debug_init #define AMD_preprocess amd_l_preprocess #define CAMD_order camd_l_order #define CAMD_defaults camd_l_defaults #define CAMD_control camd_l_control #define CAMD_info camd_l_info #define CAMD_1 camd_l1 #define CAMD_2 camd_l2 #define CAMD_valid camd_l_valid #define CAMD_cvalid camd_l_cvalid #define CAMD_aat camd_l_aat #define CAMD_postorder camd_l_postorder #define CAMD_dump camd_l_dump #define CAMD_debug camd_l_debug #define CAMD_debug_init camd_l_debug_init #define CAMD_preprocess camd_l_preprocess #define CCOLAMD_recommended ccolamd_l_recommended #define CCOLAMD_set_defaults ccolamd_l_set_defaults #define CCOLAMD_2 ccolamd2_l #define CCOLAMD_MAIN ccolamd_l #define CCOLAMD_apply_order ccolamd_l_apply_order #define CCOLAMD_postorder ccolamd_l_postorder #define CCOLAMD_post_tree ccolamd_l_post_tree #define CCOLAMD_fsize ccolamd_l_fsize #define CSYMAMD_MAIN csymamd_l #define CCOLAMD_report ccolamd_l_report #define CSYMAMD_report csymamd_l_report #define COLAMD_recommended colamd_l_recommended #define COLAMD_set_defaults colamd_l_set_defaults #define COLAMD_MAIN colamd_l #define SYMAMD_MAIN symamd_l #define COLAMD_report colamd_l_report #define SYMAMD_report symamd_l_report #else #define ID "%d" #define AMD_order amd_order #define AMD_defaults amd_defaults #define AMD_control amd_control #define AMD_info amd_info #define AMD_1 amd_1 #define AMD_2 amd_2 #define AMD_valid amd_valid #define AMD_aat amd_aat #define AMD_postorder amd_postorder #define AMD_post_tree amd_post_tree #define AMD_dump amd_dump #define AMD_debug amd_debug #define AMD_debug_init amd_debug_init #define AMD_preprocess amd_preprocess #define CAMD_order camd_order #define CAMD_defaults camd_defaults #define CAMD_control camd_control #define CAMD_info camd_info #define CAMD_1 camd_1 #define CAMD_2 camd_2 #define CAMD_valid camd_valid #define CAMD_cvalid camd_cvalid #define CAMD_aat camd_aat #define CAMD_postorder camd_postorder #define CAMD_dump camd_dump #define CAMD_debug camd_debug #define CAMD_debug_init camd_debug_init #define CAMD_preprocess camd_preprocess #define CCOLAMD_recommended ccolamd_recommended #define CCOLAMD_set_defaults ccolamd_set_defaults #define CCOLAMD_2 ccolamd2 #define CCOLAMD_MAIN ccolamd #define CCOLAMD_apply_order ccolamd_apply_order #define CCOLAMD_postorder ccolamd_postorder #define CCOLAMD_post_tree ccolamd_post_tree #define CCOLAMD_fsize ccolamd_fsize #define CSYMAMD_MAIN csymamd #define CCOLAMD_report ccolamd_report #define CSYMAMD_report csymamd_report #define COLAMD_recommended colamd_recommended #define COLAMD_set_defaults colamd_set_defaults #define COLAMD_MAIN colamd #define SYMAMD_MAIN symamd #define COLAMD_report colamd_report #define SYMAMD_report symamd_report #endif SuiteSparse/CHOLMOD/Tcov/covs0000755001170100242450000000046610533127615014660 0ustar davisfac#!/bin/csh # usage: covs echo '=================================================================' foreach file (*.?cov) echo $file grep "#####" $file | grep -v "__dev" | grep -v "__major" | \ grep -v "#####:[ ]*[0-9]*:[{}]" echo '=================================================================' end SuiteSparse/CHOLMOD/Tcov/cov.awk0000644001170100242450000000026610276530600015245 0ustar davisfac/cannot/ /function/ { f = $8 } /file/ { f = $8 } /lines/ { k = match ($1, "%") ; p = substr ($1, 1, k-1) ; if ((p+0) != 100) { printf "%8s %s\n", p, f } } SuiteSparse/CHOLMOD/Tcov/test_ops.c0000644001170100242450000007156610540000072015756 0ustar davisfac/* ========================================================================== */ /* === Tcov/test_ops ======================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Test CHOLMOD matrix operators. */ #include "cm.h" /* ========================================================================== */ /* === nzdiag =============================================================== */ /* ========================================================================== */ /* Count the entries on the diagonal */ Int nzdiag (cholmod_sparse *A) { Int *Ap, *Ai, *Anz ; Int nnzdiag, packed, j, p, i, pend, ncol ; if (A == NULL) { return (EMPTY) ; } nnzdiag = 0 ; ncol = A->ncol ; Ap = A->p ; Ai = A->i ; Anz = A->nz ; packed = A->packed ; for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i == j) { nnzdiag++ ; } } } return (nnzdiag) ; } /* ========================================================================== */ /* === check_partition ====================================================== */ /* ========================================================================== */ /* Check a node separator, and return the # of nodes in the node separator or * -1 if the separater is invalid. A node j is in the left part if * Part [j] = 0, in the right part if Part [j] = 1, and in the separator if * Part [j] = 2. */ Int check_partition (cholmod_sparse *A, Int *Part) { Int *Ap, *Ai, *Anz ; Int chek [3], which, i, j, p, n, pend, packed ; if (A == NULL || Part == NULL || A->nrow != A->ncol) { return (EMPTY) ; } n = A->nrow ; Ap = A->p ; Ai = A->i ; Anz = A->nz ; packed = A->packed ; chek [0] = 0 ; chek [1] = 0 ; chek [2] = 0 ; for (j = 0 ; j < n ; j++) { which = Part [j] ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (which == 0) { if (Part [i] == 1) { return (EMPTY) ; } } else if (which == 1) { if (Part [i] == 0) { return (EMPTY) ; } } } if (which < 0 || which > 2) { return (EMPTY) ; } chek [which]++ ; } return (chek [2]) ; } /* ========================================================================== */ /* === check_equality ======================================================= */ /* ========================================================================== */ /* Ensure two sparse matrices are identical. */ static void check_equality (cholmod_sparse *E, cholmod_sparse *D, Int xtype) { double *Ex, *Ez, *Dx, *Dz ; Int *Ep, *Ei, *Dp, *Di ; Int j, nz, p, ncol ; if (E == NULL || D == NULL || D->xtype != xtype || E->xtype != xtype) { return ; } Ep = E->p ; Ei = E->i ; Ex = E->x ; Ez = E->z ; Dp = D->p ; Di = D->i ; Dx = D->x ; Dz = D->z ; OK (E->ncol == D->ncol) ; OK (E->nrow == D->nrow) ; ncol = E->ncol ; for (j = 0 ; j <= ncol ; j++) { OK (Ep [j] == Dp [j]) ; } nz = Ep [ncol] ; for (p = 0 ; p < nz ; p++) { OK (Ei [p] == Di [p]) ; } if (xtype == CHOLMOD_REAL) { for (p = 0 ; p < nz ; p++) { OK (Ex [p] == Dx [p]) ; } } else if (xtype == CHOLMOD_COMPLEX) { for (p = 0 ; p < 2*nz ; p++) { OK (Ex [p] == Dx [p]) ; } } else if (xtype == CHOLMOD_ZOMPLEX) { for (p = 0 ; p < nz ; p++) { OK (Ex [p] == Dx [p]) ; OK (Ez [p] == Dz [p]) ; } } } /* ========================================================================== */ /* === test_ops ============================================================= */ /* ========================================================================== */ /* Test various matrix operations. */ double test_ops (cholmod_sparse *A) { double maxerr = 0, r, x, anorm, r1, rinf ; double *Sx, *Sz ; Int *Pinv, *P, *Si, *Sj, *Q, *Qinv, *fset, *Partition ; cholmod_triplet *S ; cholmod_sparse *C, *D, *E, *F, *G, *H, *AT, *Zs ; cholmod_dense *X, *Y ; Int n, kk, k, nrow, ncol, len, nz, ok, i, j, stype, nmin, mode, isreal, xtype, xtype2, mtype, asym, xmatched, pmatched, nzoffdiag, nz_diag ; size_t nz1, nz2 ; void (*save) (int, char *, int, char *) ; double alpha [2], beta [2], *Xx ; FILE *f ; int option, save3 ; if (A == NULL) { ERROR (CHOLMOD_INVALID, "nothing for test_ops") ; return (1) ; } nrow = A->nrow ; ncol = A->ncol ; H = NULL ; n = MAX (nrow, ncol) ; nmin = MIN (nrow, ncol) ; xtype = A->xtype ; isreal = (A->xtype == CHOLMOD_REAL) ; /* ---------------------------------------------------------------------- */ /* norm */ /* ---------------------------------------------------------------------- */ CHOLMOD(print_sparse) (A, "A for testops", cm) ; r1 = CHOLMOD(norm_sparse) (A, 1, cm) ; rinf = CHOLMOD(norm_sparse) (A, 0, cm) ; anorm = r1 ; /* E = pattern of A */ E = CHOLMOD(copy) (A, 0, 0, cm) ; CHOLMOD(print_sparse) (E, "E = pattern of A", cm) ; r1 = CHOLMOD(norm_sparse) (E, 1, cm) ; rinf = CHOLMOD(norm_sparse) (E, 0, cm) ; OK (r1 <= nrow) ; OK (rinf <= ncol) ; CHOLMOD(free_sparse) (&E, cm) ; /* E = pattern of A, but exclude the diagonal */ E = CHOLMOD(copy) (A, 0, -1, cm) ; CHOLMOD(print_sparse) (E, "E = spones (A), excl diag", cm) ; r1 = CHOLMOD(norm_sparse) (E, 1, cm) ; rinf = CHOLMOD(norm_sparse) (E, 0, cm) ; if (nrow < ncol) { OK (r1 <= nrow) ; OK (rinf < MAX (1,ncol)) ; } else { OK (r1 < MAX (1,nrow)) ; OK (rinf <= ncol) ; } CHOLMOD(free_sparse) (&E, cm) ; /* ---------------------------------------------------------------------- */ /* copy */ /* ---------------------------------------------------------------------- */ if (A->stype) { /* E = tril (A), no diagonal */ E = CHOLMOD(copy) (A, -1, -1, cm) ; CHOLMOD(print_sparse) (E, "E, lower and no diagonal", cm) ; CHOLMOD(band_inplace) (0, n, 0, E, cm) ; CHOLMOD(print_sparse) (E, "E Empty", cm) ; nz = CHOLMOD(nnz) (E, cm) ; if (E != NULL) { OK (nz == 0) ; } CHOLMOD(free_sparse) (&E, cm) ; } /* ---------------------------------------------------------------------- */ /* read/write */ /* ---------------------------------------------------------------------- */ /* i = cm->print ; cm->print = 4 ; CHOLMOD(print_sparse) (A, "A for read/write", cm) ; cm->print = i ; */ /* delete the contents of the temp1.mtx and temp2.mtx file */ f = fopen ("temp1.mtx", "w") ; fprintf (f, "temp1\n") ; fclose (f) ; f = fopen ("temp3.mtx", "w") ; fprintf (f, "temp3\n") ; fclose (f) ; CHOLMOD(free_work) (cm) ; f = fopen ("temp1.mtx", "w") ; asym = CHOLMOD(write_sparse) (f, A, NULL, "comments.txt", cm) ; fclose (f) ; printf ("write_sparse, asym: %d\n", asym) ; OK (IMPLIES (A != NULL, asym > EMPTY)) ; f = fopen ("temp1.mtx", "r") ; C = CHOLMOD(read_sparse) (f, cm) ; fclose (f) ; printf ("got_sparse\n") ; CHOLMOD(free_sparse) (&C, cm) ; save3 = A->xtype ; A->xtype = CHOLMOD_PATTERN ; f = fopen ("temp3.mtx", "w") ; asym = CHOLMOD(write_sparse) (f, A, NULL, "comments.txt", cm) ; A->xtype = save3 ; fclose (f) ; printf ("write_sparse3, asym: %d\n", asym) ; f = fopen ("temp3.mtx", "r") ; C = CHOLMOD(read_sparse) (f, cm) ; fclose (f) ; printf ("got_sparse3\n") ; CHOLMOD(free_sparse) (&C, cm) ; for (i = 0 ; i <= 1 ; i++) { f = fopen ("temp2.mtx", "w") ; fprintf (f, "temp2\n") ; fclose (f) ; X = CHOLMOD(ones) (4, 4, CHOLMOD_REAL, cm) ; if (X != NULL) { Xx = X->x ; Xx [0] = (i == 0) ? 1.1e308 : -1.1e308 ; } f = fopen ("temp2.mtx", "w") ; ok = CHOLMOD(write_dense) (f, X, "comments.txt", cm) ; fclose (f) ; printf ("wrote dense\n") ; f = fopen ("temp2.mtx", "r") ; Y = CHOLMOD(read_dense) (f, cm) ; fclose (f) ; printf ("got dense\n") ; CHOLMOD(free_dense) (&X, cm) ; CHOLMOD(free_dense) (&Y, cm) ; } /* ---------------------------------------------------------------------- */ /* symmetry */ /* ---------------------------------------------------------------------- */ CHOLMOD(free_work) (cm) ; xmatched = 0 ; pmatched = 0 ; nzoffdiag = 0 ; nz_diag = 0 ; for (option = 0 ; option <= 2 ; option++) { asym = CHOLMOD(symmetry) (A, option, &xmatched, &pmatched, &nzoffdiag, &nz_diag, cm); printf ("symmetry, asym: %d matched %d %d offdiag %d diag %d\n", asym, xmatched, pmatched, nzoffdiag, nz_diag) ; } /* ---------------------------------------------------------------------- */ /* transpose */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(allocate_sparse) (A->ncol, A->nrow, A->nzmax, TRUE, TRUE, -(A->stype), A->xtype, cm) ; D = CHOLMOD(allocate_sparse) (A->nrow, A->ncol, A->nzmax, TRUE, TRUE, A->stype, A->xtype, cm) ; CHOLMOD(free_work) (cm) ; ok = (C != NULL && D != NULL) ; /* C = A' */ if (ok) { if (A->stype) { ok = CHOLMOD(transpose_sym) (A, 2, NULL, C, cm) ; } else { ok = CHOLMOD(transpose_unsym) (A, 2, NULL, NULL, 0, C, cm) ; } OK (ok || cm->status == CHOLMOD_OUT_OF_MEMORY) ; } /* D = C' */ if (ok) { if (A->stype) { ok = CHOLMOD(transpose_sym) (C, 2, NULL, D, cm) ; } else { ok = CHOLMOD(transpose_unsym) (C, 2, NULL, NULL, 0, D, cm) ; } OK (ok || cm->status == CHOLMOD_OUT_OF_MEMORY) ; } if (ok) { ok = CHOLMOD(check_sparse) (D, cm) ; OK (ok || cm->status == CHOLMOD_OUT_OF_MEMORY) ; } CHOLMOD(free_sparse) (&C, cm) ; CHOLMOD(free_sparse) (&D, cm) ; /* ---------------------------------------------------------------------- */ /* C = A with jumbled triplets */ /* ---------------------------------------------------------------------- */ S = CHOLMOD(sparse_to_triplet) (A, cm) ; /* [ */ if (S != NULL && nmin > 0) { /* double the number of entries in S */ nz1 = S->nzmax ; nz2 = 2*nz1 ; ok = CHOLMOD(reallocate_triplet) (nz2, S, cm) ; if (ok) { /* add duplicate entries, but keep the matrix the same */ OK (S->nzmax == nz2) ; Si = S->i ; Sj = S->j ; Sx = S->x ; Sz = S->z ; for (k = nz1 ; k < ((Int) nz2) ; k++) { kk = nrand (k) ; /* RAND */ Si [k] = Si [kk] ; Sj [k] = Sj [kk] ; if (S->xtype == CHOLMOD_REAL) { x = Sx [kk] * (xrand (4.) - 2) ; /* RAND */ Sx [k] = x ; Sx [kk] -= x ; } else if (S->xtype == CHOLMOD_COMPLEX) { x = Sx [2*kk] * (xrand (4.) - 2) ; /* RAND */ Sx [2*k] = x ; Sx [2*kk] -= x ; x = Sx [2*kk+1] * (xrand (4.) - 2) ; /* RAND */ Sx [2*k+1] = x ; Sx [2*kk+1] -= x ; } else { x = Sx [kk] * (xrand (4.) - 2) ; /* RAND */ Sx [k] = x ; Sx [kk] -= x ; x = Sz [kk] * (xrand (4.) - 2) ; /* RAND */ Sz [k] = x ; Sz [kk] -= x ; } } /* randomly jumble the entries */ for (k = 0 ; k < ((Int) (nz2-1)) ; k++) { kk = k + nrand (nz2-k) ; /* RAND */ i = Si [k] ; Si [k] = Si [kk] ; Si [kk] = i ; j = Sj [k] ; Sj [k] = Sj [kk] ; Sj [kk] = j ; if (S->xtype == CHOLMOD_REAL) { x = Sx [k] ; Sx [k] = Sx [kk] ; Sx [kk] = x ; } else if (S->xtype == CHOLMOD_COMPLEX) { x = Sx [2*k] ; Sx [2*k] = Sx [2*kk] ; Sx [2*kk] = x ; x = Sx [2*k+1] ; Sx [2*k+1] = Sx [2*kk+1] ; Sx [2*kk+1] = x ; } else { x = Sx [k] ; Sx [k] = Sx [kk] ; Sx [kk] = x ; x = Sz [k] ; Sz [k] = Sz [kk] ; Sz [kk] = x ; } } S->nnz = nz2 ; } else { OK (S->nzmax == nz1) ; OK (S->nnz == nz1) ; } } CHOLMOD(print_triplet) (S, "S jumbled", cm) ; C = CHOLMOD(triplet_to_sparse) (S, 0, cm) ; /* [ */ CHOLMOD(print_sparse) (A, "A", cm) ; CHOLMOD(print_sparse) (C, "C", cm) ; Zs = CHOLMOD(spzeros) (nrow, ncol, 1, xtype, cm) ; /* [ */ G = NULL ; F = NULL ; if (isreal) { /* G=A+0 */ G = CHOLMOD(add) (A, Zs, one, one, TRUE, TRUE, cm) ; /* [ */ /* F = G-C */ F = CHOLMOD(add) (G, C, one, minusone, TRUE, TRUE, cm) ; /* [ */ CHOLMOD(print_sparse) (F, "F", cm) ; r = CHOLMOD(norm_sparse) (F, 1, cm) ; MAXERR (maxerr, r, anorm) ; r = CHOLMOD(norm_sparse) (F, 0, cm) ; CHOLMOD(drop) (0, F, cm) ; rinf = CHOLMOD(norm_sparse) (F, 0, cm) ; if (F != NULL) { OK (r == rinf) ; } MAXERR (maxerr, r, anorm) ; MAXERR (maxerr, rinf, anorm) ; /* E = F, with change of type and dropping small entries */ for (stype = -1 ; stype <= 1 ; stype++) { if (stype != 0 && (F != NULL && F->nrow != F->ncol)) { continue ; } for (mode = 0 ; mode <= 1 ; mode++) { E = CHOLMOD(copy) (F, stype, mode, cm) ; /* [ */ CHOLMOD(drop) (1e-16, E, cm) ; r1 = CHOLMOD(norm_sparse) (E, 1, cm) ; rinf = CHOLMOD(norm_sparse) (E, 0, cm) ; if (E != NULL) { if (mode == 0) { /* pattern only */ OK (r1 <= nrow) ; OK (rinf <= ncol) ; } else { MAXERR (maxerr, r1, anorm) ; MAXERR (maxerr, rinf, anorm) ; } } CHOLMOD(free_sparse) (&E, cm) ; /* ] */ } } CHOLMOD(free_sparse) (&F, cm) ; /* ] */ CHOLMOD(free_sparse) (&G, cm) ; /* ] */ } Y = CHOLMOD(ones) (nrow, 1, xtype, cm) ; /* [ */ X = CHOLMOD(ones) (ncol, 1, xtype, cm) ; /* [ */ alpha [0] = 0 ; alpha [1] = 0 ; beta [0] = 2 ; beta [1] = 0 ; /* Y = 0*A*X + 2*Y */ CHOLMOD(sdmult) (A, FALSE, alpha, beta, X, Y, cm) ; r = CHOLMOD(norm_dense) (Y, 0, cm) ; if (Y != NULL && X != NULL && A != NULL) { OK ((nrow == 0) ? (r == 0) : (r == 2)) ; } alpha [0] = 1 ; /* Y = 1*(0)*X + 2*Y */ CHOLMOD(sdmult) (Zs, FALSE, alpha, beta, X, Y, cm) ; r = CHOLMOD(norm_dense) (Y, 0, cm) ; if (Y != NULL && X != NULL && A != NULL) { OK ((nrow == 0) ? (r == 0) : (r == 4)) ; } CHOLMOD(free_dense) (&X, cm) ; /* ] */ CHOLMOD(free_dense) (&Y, cm) ; /* ] */ CHOLMOD(free_sparse) (&Zs, cm) ; /* ] */ CHOLMOD(free_sparse) (&C, cm) ; /* ] */ CHOLMOD(free_triplet) (&S, cm) ; /* ] */ /* ---------------------------------------------------------------------- */ /* C = P*A*Q in triplet form */ /* ---------------------------------------------------------------------- */ S = CHOLMOD(sparse_to_triplet) (A, cm) ; P = prand (nrow) ; /* RAND */ if (A->stype == 0) { Q = prand (ncol) ; /* RAND */ } else { /* if A is symmetric, and stored in either upper or lower form, then * the following code only works if P = Q */ Q = P ; } Pinv = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ; Qinv = CHOLMOD(malloc) (ncol, sizeof (Int), cm) ; Partition = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ; if (Pinv != NULL && Qinv != NULL && P != NULL && Q != NULL && S != NULL) { Si = S->i ; Sj = S->j ; nz = S->nnz ; for (k = 0 ; k < nrow ; k++) { Pinv [P [k]] = k ; } for (k = 0 ; k < ncol ; k++) { Qinv [Q [k]] = k ; } for (k = 0 ; k < nz ; k++) { Si [k] = Pinv [Si [k]] ; } for (k = 0 ; k < nz ; k++) { Sj [k] = Qinv [Sj [k]] ; } } C = CHOLMOD(triplet_to_sparse) (S, 0, cm) ; D = NULL ; E = NULL ; F = NULL ; G = NULL ; if (isreal) { /* ------------------------------------------------------------------ */ /* E = P*A*Q in sparse form */ /* ------------------------------------------------------------------ */ D = CHOLMOD(copy) (A, 0, 1, cm) ; E = CHOLMOD(submatrix) (D, P, nrow, Q, ncol, TRUE, FALSE, cm) ; CHOLMOD(sort) (E, cm) ; /* ------------------------------------------------------------------ */ /* F = E-G */ /* ------------------------------------------------------------------ */ G = CHOLMOD(copy) (C, 0, 1, cm) ; F = CHOLMOD(add) (E, G, one, minusone, TRUE, TRUE, cm) ; CHOLMOD(drop) (0, F, cm) ; nz = CHOLMOD(nnz) (F, cm) ; if (F != NULL) { OK (nz == 0) ; } } CHOLMOD(free_sparse) (&F, cm) ; CHOLMOD(free_sparse) (&G, cm) ; CHOLMOD(free_sparse) (&D, cm) ; CHOLMOD(free_sparse) (&E, cm) ; CHOLMOD(free_sparse) (&H, cm) ; CHOLMOD(free_sparse) (&C, cm) ; CHOLMOD(free_triplet) (&S, cm) ; /* ---------------------------------------------------------------------- */ /* submatrix */ /* ---------------------------------------------------------------------- */ if (A->stype == 0 && isreal) { /* E = A(:,:) */ E = CHOLMOD(submatrix) (A, NULL, -1, NULL, -1, TRUE, TRUE, cm) ; /* C = A-E */ C = CHOLMOD(add) (A, E, one, minusone, TRUE, TRUE, cm) ; ok = CHOLMOD(drop) (0., C, cm) ; nz = CHOLMOD(nnz) (C, cm) ; if (C != NULL) { OK (nz == 0) ; } CHOLMOD(free_sparse) (&C, cm) ; CHOLMOD(free_sparse) (&E, cm) ; } /* ---------------------------------------------------------------------- */ /* test band and add, unsymmetric */ /* ---------------------------------------------------------------------- */ if (isreal) { CHOLMOD(print_sparse) (A, "A for do triplet", cm) ; /* E = A */ E = CHOLMOD(copy) (A, 0, 1, cm) ; CHOLMOD(print_sparse) (E, "E=triu(A)", cm) ; /* E = triu (E) */ CHOLMOD(band_inplace) (0, ncol, 1, E, cm) ; /* F = A */ F = CHOLMOD(copy) (A, 0, 1, cm) ; CHOLMOD(print_sparse) (F, "F=tril(A)", cm) ; /* F = tril(F,-1) */ CHOLMOD(band_inplace) (-nrow, -1, 1, F, cm) ; CHOLMOD(print_sparse) (F, "Ftril", cm) ; /* G = E+F */ G = CHOLMOD(add) (E, F, one, one, TRUE, TRUE, cm) ; CHOLMOD(print_sparse) (G, "G=E+F", cm) ; /* D = A-G, which should be empty */ D = CHOLMOD(add) (G, A, one, minusone, TRUE, TRUE, cm) ; CHOLMOD(print_sparse) (D, "D=A-G", cm) ; CHOLMOD(drop) (0, D, cm) ; CHOLMOD(print_sparse) (D, "D drop", cm) ; nz = CHOLMOD(nnz) (D, cm) ; if (D != NULL) { OK (nz == 0) ; } CHOLMOD(free_sparse) (&F, cm) ; CHOLMOD(free_sparse) (&D, cm) ; CHOLMOD(free_sparse) (&E, cm) ; CHOLMOD(free_sparse) (&G, cm) ; D = CHOLMOD(band) (A, 1, -1, 0, cm) ; nz = CHOLMOD(nnz) (D, cm) ; if (D != NULL) { OK (nz == 0) ; } CHOLMOD(free_sparse) (&D, cm) ; D = CHOLMOD(band) (A, 0, 0, 0, cm) ; nz = CHOLMOD(nnz) (D, cm) ; if (D != NULL) { OK (nz == nzdiag (D)) ; } CHOLMOD(free_sparse) (&D, cm) ; } /* ---------------------------------------------------------------------- */ /* test band, add and copy_sparse (symmetric) */ /* ---------------------------------------------------------------------- */ if (A->stype && isreal) { /* E = A, in symmetric/upper form */ E = CHOLMOD(copy) (A, 1, 1, cm) ; CHOLMOD(print_sparse) (E, "E=A in sym/upper form", cm) ; /* E = -E */ CHOLMOD(scale) (M1, CHOLMOD_SCALAR, E, cm) ; /* F = A, in symmetric/lower form */ F = CHOLMOD(copy) (A, -1, 1, cm) ; CHOLMOD(print_sparse) (F, "F=A in sym/lower form", cm) ; /* C = F (exact copy) */ C = CHOLMOD(copy_sparse) (F, cm) ; /* G = E+C */ G = CHOLMOD(add) (E, C, one, one, TRUE, FALSE, cm) ; CHOLMOD(print_sparse) (G, "G=E+F", cm) ; CHOLMOD(sort) (G, cm) ; CHOLMOD(drop) (0, G, cm) ; CHOLMOD(print_sparse) (G, "G drop", cm) ; nz = CHOLMOD(nnz) (G, cm) ; if (G != NULL) { OK (nz == 0) ; } CHOLMOD(free_sparse) (&C, cm) ; CHOLMOD(free_sparse) (&F, cm) ; CHOLMOD(free_sparse) (&E, cm) ; CHOLMOD(free_sparse) (&G, cm) ; } /* ---------------------------------------------------------------------- */ /* try a dense identity matrix */ /* ---------------------------------------------------------------------- */ X = CHOLMOD(eye) (3, 4, CHOLMOD_REAL, cm) ; CHOLMOD(print_dense) (X, "Dense identity", cm) ; CHOLMOD(free_dense) (&X, cm) ; /* ---------------------------------------------------------------------- */ /* bisector and nested_dissection */ /* ---------------------------------------------------------------------- */ #ifndef NPARTITION if (A != NULL && A->nrow == A->ncol) { UF_long nc, nc_new ; Int cnz, csep, save2 ; Int *Cnw, *Cew, *Cmember, *CParent, *Perm ; double save1 ; /* try CHOLMOD's interface to METIS_NodeComputeSeparator */ cm->metis_memory = 2.0 ; CHOLMOD(print_sparse) (A, "A for bisect", cm) ; csep = CHOLMOD(bisect) (A, NULL, 0, TRUE, Partition, cm) ; if (csep != EMPTY) { OK (csep == check_partition (A, Partition)) ; } /* try the raw interface to METIS_NodeComputeSeparator */ CHOLMOD(print_sparse) (A, "A for metis bisect", cm) ; /* C = A+A', remove the diagonal */ AT = CHOLMOD(transpose) (A, 0, cm) ; E = CHOLMOD(add) (A, AT, one, one, FALSE, TRUE, cm) ; CHOLMOD(free_sparse) (&AT, cm) ; C = CHOLMOD(copy) (E, 0, -1, cm) ; CHOLMOD(print_sparse) (C, "C for metis bisect", cm) ; cnz = (C != NULL) ? (C->nzmax) : 0 ; Cew = CHOLMOD(malloc) (cnz, sizeof (Int), cm) ; Cnw = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ; if (Cnw != NULL) { for (j = 0 ; j < (Int) (A->nrow) ; j++) { Cnw [j] = 1 ; } } if (Cew != NULL) { for (j = 0 ; j < cnz ; j++) { Cew [j] = 1 ; } } csep = CHOLMOD(metis_bisector) (C, Cnw, Cew, Partition, cm) ; if (csep != EMPTY) { OK (csep == check_partition (C, Partition)) ; } CHOLMOD(free) (nrow, sizeof (Int), Cnw, cm) ; CHOLMOD(free) (cnz, sizeof (Int), Cew, cm) ; CHOLMOD(free_sparse) (&C, cm) ; CHOLMOD(free_sparse) (&E, cm) ; Cmember = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ; CParent = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ; Perm = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ; save1 = cm->method [cm->current].nd_small ; save2 = cm->method [cm->current].nd_oksep ; cm->method [cm->current].nd_small = 1 ; cm->method [cm->current].nd_oksep = 1.0 ; nc = CHOLMOD(nested_dissection) (A, NULL, 0, Perm, CParent, Cmember, cm); if (nc > 0) { OK (CHOLMOD(check_perm) (Perm, n, n, cm)) ; } CHOLMOD(free_work) (cm) ; /* collapse the septree */ if (nc > 0 && n > 0) { nc_new = CHOLMOD(collapse_septree) (n, nc, 0.1, 400, CParent, Cmember, cm) ; /* error checks */ save = cm->error_handler ; cm->error_handler = NULL ; nc_new = CHOLMOD(collapse_septree) (n, nc, 0.1, 400, CParent, Cmember, NULL) ; OK (nc_new == EMPTY) ; nc_new = CHOLMOD(collapse_septree) (n, nc, 0.1, 400, NULL, Cmember, cm) ; OK (nc_new == EMPTY) ; nc_new = CHOLMOD(collapse_septree) (n, nc, 0.1, 400, CParent, NULL, cm) ; OK (nc_new == EMPTY) ; nc_new = CHOLMOD(collapse_septree) (0, 1, 0.1, 400, CParent, Cmember, cm) ; OK (nc_new == EMPTY) ; nc_new = CHOLMOD(collapse_septree) (1, 1, 0.1, 400, CParent, Cmember, cm) ; OK (nc_new == 1 || nc_new == EMPTY) ; nc_new = CHOLMOD(collapse_septree) (Int_max, Int_max, 0.1, 400, CParent, Cmember, cm) ; OK (nc_new == EMPTY) ; cm->error_handler = save ; } CHOLMOD(free) (nrow, sizeof (Int), Cmember, cm) ; CHOLMOD(free) (nrow, sizeof (Int), CParent, cm) ; CHOLMOD(free) (nrow, sizeof (Int), Perm, cm) ; cm->method [cm->current].nd_small = save1 ; cm->method [cm->current].nd_oksep = save2 ; } #endif /* ---------------------------------------------------------------------- */ /* dense to/from sparse conversions */ /* ---------------------------------------------------------------------- */ /* convert A to real, remove zero entries, and then convert to pattern */ if (MAX (nrow, ncol) < 1000) { C = CHOLMOD(copy_sparse) (A, cm) ; CHOLMOD(sparse_xtype) (CHOLMOD_REAL, C, cm) ; CHOLMOD(drop) (0., C, cm) ; D = CHOLMOD(copy) (C, 0, 0, cm) ; CHOLMOD(sort) (D, cm) ; /* X = dense copy of C */ CHOLMOD(sparse_xtype) (CHOLMOD_PATTERN, C, cm) ; X = CHOLMOD(sparse_to_dense) (C, cm) ; CHOLMOD(free_sparse) (&C, cm) ; /* change X to sparse pattern and then real/complex/zomplex, it should * equal D */ for (xtype2 = CHOLMOD_REAL ; xtype2 <= CHOLMOD_ZOMPLEX ; xtype2++) { E = CHOLMOD(dense_to_sparse) (X, FALSE, cm) ; ok = CHOLMOD(sparse_xtype) (xtype2, E, cm) ; ok = CHOLMOD(sparse_xtype) (xtype2, D, cm) ; if (xtype2 == CHOLMOD_REAL) { F = CHOLMOD(add) (E, D, one, minusone, TRUE, TRUE, cm) ; r = CHOLMOD(norm_sparse) (F, 0, cm) ; if (F != NULL) { OK (r == 0) ; } CHOLMOD(free_sparse) (&F, cm) ; } else { check_equality (E, D, xtype2) ; } CHOLMOD(free_sparse) (&E, cm) ; } CHOLMOD(free_sparse) (&D, cm) ; CHOLMOD(free_dense) (&X, cm) ; } /* ---------------------------------------------------------------------- */ /* unsymmetric transpose */ /* ---------------------------------------------------------------------- */ len = ncol/2 ; fset = prand (ncol) ; /* RAND */ CHOLMOD(print_perm) (P, nrow, nrow, "P", cm) ; CHOLMOD(print_subset) (fset, ncol, ncol, "fset", cm) ; if (isreal) { C = CHOLMOD(copy) (A, 0, 1, cm) ; D = CHOLMOD(ptranspose) (C, 1, P, fset, len, cm) ; E = CHOLMOD(transpose) (D, 1, cm) ; F = CHOLMOD(transpose) (E, 1, cm) ; G = CHOLMOD(add) (D, F, one, minusone, TRUE, FALSE, cm) ; r = CHOLMOD(norm_sparse) (G, 0, cm) ; if (G != NULL) { OK (r == 0) ; } CHOLMOD(drop) (0, G, cm) ; r = CHOLMOD(norm_sparse) (G, 0, cm) ; nz = CHOLMOD(nnz) (G, cm) ; if (G != NULL) { OK (r == 0) ; OK (nz == 0) ; } CHOLMOD(free_sparse) (&C, cm) ; CHOLMOD(free_sparse) (&D, cm) ; CHOLMOD(free_sparse) (&E, cm) ; CHOLMOD(free_sparse) (&F, cm) ; CHOLMOD(free_sparse) (&G, cm) ; } /* ---------------------------------------------------------------------- */ /* symmetric array transpose */ /* ---------------------------------------------------------------------- */ if (A->stype != 0) { /* C = A(p,p).' */ C = CHOLMOD(ptranspose) (A, 1, P, NULL, 0, cm) ; /* D = C(pinv,pinv).' */ D = CHOLMOD(ptranspose) (C, 1, Pinv, NULL, 0, cm) ; CHOLMOD(sort) (D, cm) ; CHOLMOD(free_sparse) (&C, cm) ; /* C = A, sorted */ C = CHOLMOD(copy_sparse) (A, cm) ; CHOLMOD(sort) (C, cm) ; /* C and D should be equal */ check_equality (C, D, xtype) ; CHOLMOD(free_sparse) (&C, cm) ; CHOLMOD(free_sparse) (&D, cm) ; /* C = A.' */ C = CHOLMOD(transpose) (A, 1, cm) ; /* D = C.' */ D = CHOLMOD(transpose) (C, 1, cm) ; CHOLMOD(sort) (D, cm) ; CHOLMOD(free_sparse) (&C, cm) ; /* C = A, sorted */ C = CHOLMOD(copy_sparse) (A, cm) ; CHOLMOD(sort) (C, cm) ; /* C and D should be equal */ check_equality (C, D, xtype) ; CHOLMOD(free_sparse) (&C, cm) ; CHOLMOD(free_sparse) (&D, cm) ; } /* ---------------------------------------------------------------------- */ /* matrix multiply */ /* ---------------------------------------------------------------------- */ if (isreal) { /* this fails for a large arrowhead matrix, so turn off error hanlder */ save = cm->error_handler ; cm->error_handler = NULL ; AT = CHOLMOD(transpose) (A, 1, cm) ; D = CHOLMOD(copy) (A, 0, 1, cm) ; if (n > NLARGE) progress (1, '.') ; C = CHOLMOD(aat) (D, NULL, 0, 1, cm) ; if (n > NLARGE) progress (1, '.') ; CHOLMOD(print_common) ("After A*A'", cm) ; for (stype = -1 ; stype <= 1 ; stype++) { if (n > NLARGE) progress (1, '.') ; E = CHOLMOD(ssmult) (A, AT, stype, TRUE, TRUE, cm) ; if (n > NLARGE) progress (1, '.') ; G = CHOLMOD(add) (C, E, one, minusone, TRUE, FALSE, cm) ; if (n > NLARGE) progress (1, '.') ; r = CHOLMOD(norm_sparse) (G, 0, cm) ; if (G != NULL) { MAXERR (maxerr, r, anorm) ; } CHOLMOD(drop) (0, G, cm) ; r = CHOLMOD(norm_sparse) (G, 0, cm) ; if (G != NULL) { MAXERR (maxerr, r, anorm) ; } CHOLMOD(free_sparse) (&E, cm) ; CHOLMOD(free_sparse) (&G, cm) ; } if (nrow == ncol) { /* E = pattern of A */ E = CHOLMOD(copy) (A, 0, 0, cm) ; /* G = E*E */ if (n > NLARGE) progress (1, '.') ; G = CHOLMOD(ssmult) (E, E, 0, FALSE, FALSE, cm) ; if (n > NLARGE) progress (1, '.') ; CHOLMOD(free_sparse) (&E, cm) ; CHOLMOD(free_sparse) (&G, cm) ; } cm->error_handler = save ; CHOLMOD(free_sparse) (&D, cm) ; CHOLMOD(free_sparse) (&C, cm) ; CHOLMOD(free_sparse) (&AT, cm) ; } /* ---------------------------------------------------------------------- */ /* free P, Q, and their inverses */ /* ---------------------------------------------------------------------- */ CHOLMOD(free) (ncol, sizeof (Int), fset, cm) ; CHOLMOD(free) (nrow, sizeof (Int), P, cm) ; CHOLMOD(free) (nrow, sizeof (Int), Pinv, cm) ; if (A->stype == 0) { CHOLMOD(free) (ncol, sizeof (Int), Q, cm) ; } CHOLMOD(free) (ncol, sizeof (Int), Qinv, cm) ; CHOLMOD(free) (nrow, sizeof (Int), Partition, cm) ; progress (0, '.') ; return (maxerr) ; } SuiteSparse/CHOLMOD/Tcov/Make.inc0000644001170100242450000000015710533351163015322 0ustar davisfac# valgrind is not used V = # covall is used COVER = ./covall # with test coverage CFLAGS = -O0 -g --coverage SuiteSparse/CHOLMOD/Tcov/Makefile0000644001170100242450000011426310617135416015422 0ustar davisfac#=============================================================================== # CHOLMOD/Tcov/Makefile #=============================================================================== # If you compile CHOLMOD with -DNPARTITION, then you do not need METIS, # CCOLAMD, or the Partition module. include ../../UFconfig/UFconfig.mk include Make.inc # Tcov requires gcc CC = gcc C = $(CC) $(CFLAGS) $(CHOLMOD_CONFIG) $(NANTESTS) # optimized LAPACK and BLAS # LIB = $(METIS) -lm $(LAPACK) $(BLAS) $(XERBLA) # LAPACK and the Fortran reference BLAS, compiled with gfortran -g -O: # LIB = $(METIS) -lm -llapack_plain -lblas_plain -lg2c LIB = $(METIS) -lm -llapack_plain -lblas_plain -lgfortran -lgfortranbegin LIB = $(METIS) -lm -llapack -lblas -lgfortran -lgfortranbegin # Solaris # LIB = $(METIS) -xlic_lib=sunperf # Use "grep" only, if you do not have "indent" PRETTY = grep -v "^\#" | indent -bl -nce -ss -bli0 -i4 -sob -l120 # PRETTY = grep -v "^\#" | ssh persimmon indent -bl -nce -ss -bli0 -i4 -sob -l120 # PRETTY = grep -v "^\#" I = -I../../AMD/Include -I../../COLAMD/Include \ -I$(METIS_PATH)/Lib -I../../CCOLAMD/Include -I../../CAMD/Include \ -I../Include -I../../UFconfig default: cm cl z_demo l_demo cmread clread TEST = cm.c test_ops.c null.c null2.c lpdemo.c memory.c solve.c aug.c unpack.c \ raw_factor.c cctest.c ctest.c amdtest.c camdtest.c huge.c INC = ../Include/cholmod.h \ ../Include/cholmod_blas.h \ ../Include/cholmod_check.h \ ../Include/cholmod_cholesky.h \ ../Include/cholmod_complexity.h \ ../Include/cholmod_config.h \ ../Include/cholmod_core.h \ ../Include/cholmod_internal.h \ ../Include/cholmod_matrixops.h \ ../Include/cholmod_modify.h \ ../Include/cholmod_partition.h \ ../Include/cholmod_supernodal.h \ ../Include/cholmod_template.h AMDSRC = ../../AMD/Source/amd_1.c \ ../../AMD/Source/amd_2.c \ ../../AMD/Source/amd_aat.c \ ../../AMD/Source/amd_control.c \ ../../AMD/Source/amd_defaults.c \ ../../AMD/Source/amd_global.c \ ../../AMD/Source/amd_info.c \ ../../AMD/Source/amd_order.c \ ../../AMD/Source/amd_postorder.c \ ../../AMD/Source/amd_post_tree.c \ ../../AMD/Source/amd_preprocess.c \ ../../AMD/Source/amd_valid.c \ ../../AMD/Include/amd.h \ ../../AMD/Include/amd_internal.h AMDOBJ = \ zz_amd_1.o \ zz_amd_2.o \ zz_amd_aat.o \ zz_amd_control.o \ zz_amd_defaults.o \ zz_amd_global.o \ zz_amd_info.o \ zz_amd_dump.o \ zz_amd_order.o \ zz_amd_postorder.o \ zz_amd_post_tree.o \ zz_amd_preprocess.o \ zz_amd_valid.o LAMDOBJ = \ zl_amd_1.o \ zl_amd_2.o \ zl_amd_aat.o \ zl_amd_control.o \ zl_amd_defaults.o \ zl_amd_global.o \ zl_amd_info.o \ zl_amd_dump.o \ zl_amd_order.o \ zl_amd_postorder.o \ zl_amd_post_tree.o \ zl_amd_preprocess.o \ zl_amd_valid.o COLAMDSRC = ../../COLAMD/Source/colamd.c ../../COLAMD/Source/colamd_global.c COLAMDOBJ = zz_colamd.o yz_colamd_global.o LCOLAMDOBJ = zl_colamd.o yl_colamd_global.o #------------------------------------------------------------------------------- # When using the Partition Module: CCOLAMDSRC = \ ../../CCOLAMD/Source/ccolamd.c \ ../../CCOLAMD/Source/ccolamd_global.c \ ../../CCOLAMD/Include/ccolamd.h CCOLAMDOBJ = zz_ccolamd.o yz_ccolamd_global.o LCCOLAMDOBJ = zl_ccolamd.o yl_ccolamd_global.o $(CCOLAMDOBJ): $(CCOLAMDSRC) $(LCCOLAMDOBJ): $(CCOLAMDSRC) IPARTITION_OBJ = \ z_ccolamd.o \ z_csymamd.o \ z_camd.o \ z_metis.o \ z_nesdis.o LPARTITION_OBJ = \ l_ccolamd.o \ l_csymamd.o \ l_camd.o \ l_metis.o \ l_nesdis.o CAMDSRC = ../../CAMD/Source/camd_1.c \ ../../CAMD/Source/camd_2.c \ ../../CAMD/Source/camd_aat.c \ ../../CAMD/Source/camd_control.c \ ../../CAMD/Source/camd_defaults.c \ ../../CAMD/Source/camd_global.c \ ../../CAMD/Source/camd_info.c \ ../../CAMD/Source/camd_order.c \ ../../CAMD/Source/camd_postorder.c \ ../../CAMD/Source/camd_preprocess.c \ ../../CAMD/Source/camd_valid.c \ ../../CAMD/Include/camd.h \ ../../CAMD/Include/camd_internal.h CAMDOBJ = \ zz_camd_1.o \ zz_camd_2.o \ zz_camd_aat.o \ zz_camd_control.o \ zz_camd_defaults.o \ zz_camd_global.o \ zz_camd_info.o \ zz_camd_order.o \ zz_camd_postorder.o \ zz_camd_preprocess.o \ zz_camd_valid.o \ zz_camd_dump.o LCAMDOBJ = \ zl_camd_1.o \ zl_camd_2.o \ zl_camd_aat.o \ zl_camd_control.o \ zl_camd_defaults.o \ zl_camd_global.o \ zl_camd_info.o \ zl_camd_order.o \ zl_camd_postorder.o \ zl_camd_preprocess.o \ zl_camd_valid.o \ zl_camd_dump.o $(CAMDOBJ): $(CAMDSRC) $(LCAMDOBJ): $(CAMDSRC) #------------------------------------------------------------------------------- # If you compile with -DNPARTITION, you may replace the above definitions # with empty ones (see immediately below), and then you do not need a copy of # CCOLAMD: # CCOLAMDSRC = # CCOLAMDOBJ = # LCCOLAMDOBJ = # IPARTITION_OBJ = # LPARTITION_OBJ = # CAMDSRC = # CAMDOBJ = # LCAMDOBJ = #------------------------------------------------------------------------------- IOBJ = \ z_common.o \ z_dense.o \ z_factor.o \ z_change_factor.o \ z_memory.o \ z_sparse.o \ z_complex.o \ z_transpose.o \ z_band.o \ z_copy.o \ z_triplet.o \ z_error.o \ z_aat.o \ z_add.o \ z_check.o \ z_read.o \ z_write.o \ z_amd.o \ z_analyze.o \ z_colamd.o \ z_etree.o \ z_factorize.o \ z_postorder.o \ z_rcond.o \ z_resymbol.o \ z_rowcolcounts.o \ z_rowfac.o \ z_solve.o \ z_spsolve.o \ z_drop.o \ z_horzcat.o \ z_norm.o \ z_scale.o \ z_sdmult.o \ z_ssmult.o \ z_submatrix.o \ z_vertcat.o \ z_symmetry.o \ z_rowadd.o \ z_rowdel.o \ z_updown.o \ z_super_numeric.o \ z_super_solve.o \ z_super_symbolic.o \ $(IPARTITION_OBJ) LOBJ = \ l_common.o \ l_dense.o \ l_factor.o \ l_change_factor.o \ l_memory.o \ l_sparse.o \ l_complex.o \ l_transpose.o \ l_band.o \ l_copy.o \ l_triplet.o \ l_error.o \ l_aat.o \ l_add.o \ l_check.o \ l_read.o \ l_write.o \ l_amd.o \ l_analyze.o \ l_colamd.o \ l_etree.o \ l_factorize.o \ l_postorder.o \ l_rcond.o \ l_resymbol.o \ l_rowcolcounts.o \ l_rowfac.o \ l_solve.o \ l_spsolve.o \ l_drop.o \ l_horzcat.o \ l_norm.o \ l_scale.o \ l_sdmult.o \ l_ssmult.o \ l_submatrix.o \ l_vertcat.o \ l_symmetry.o \ l_rowadd.o \ l_rowdel.o \ l_updown.o \ l_super_numeric.o \ l_super_solve.o \ l_super_symbolic.o \ $(LPARTITION_OBJ) IALL = $(IOBJ) $(AMDOBJ) $(COLAMDOBJ) $(CCOLAMDOBJ) $(CAMDOBJ) LALL = $(LOBJ) $(LAMDOBJ) $(LCOLAMDOBJ) $(LCCOLAMDOBJ) $(LCAMDOBJ) cm: $(IALL) $(TEST) cm.h Makefile $(C) $(I) $(TEST) -o cm $(IALL) $(LIB) cl: $(LALL) $(TEST) cm.h Makefile $(C) -DDLONG $(I) $(TEST) -o cl $(LALL) $(LIB) cmread: $(IALL) cmread.c Makefile $(C) $(I) cmread.c -o cmread $(IALL) $(LIB) clread: $(LALL) cmread.c Makefile $(C) -DDLONG $(I) cmread.c -o clread $(LALL) $(LIB) z_demo: $(IALL) ../Demo/cholmod_demo.c cm.h Makefile \ ../Demo/cholmod_demo.h cat ../Demo/cholmod_demo.c > z_demo.c $(C) $(I) -I../Demo z_demo.c -o z_demo $(IALL) $(LIB) l_demo: $(LALL) ../Demo/cholmod_l_demo.c cm.h Makefile \ ../Demo/cholmod_demo.h cat ../Demo/cholmod_l_demo.c > l_demo.c $(C) -DDLONG $(I) -I../Demo l_demo.c -o l_demo $(LALL) $(LIB) go: z_demo l_demo cmread clread cm cl $(V) ./z_demo ../Demo/Matrix/bcsstk01.tri > tmp/demo_k1.out $(V) ./z_demo ../Demo/Matrix/bcsstk02.tri > tmp/demo_k2.out $(V) ./z_demo < ../Demo/Matrix/lp_afiro.tri > tmp/demo_afiro.out $(V) ./z_demo < ../Demo/Matrix/can___24.mtx > tmp/demo_can24.out $(V) ./z_demo < ../Demo/Matrix/c.tri > tmp/demo_c.out $(V) ./z_demo < ../Demo/Matrix/d.tri > tmp/demo_d.out $(V) ./z_demo < ../Demo/Matrix/up.tri > tmp/demo_up.out $(V) ./z_demo < ../Demo/Matrix/c.mtx > tmp/demo_c_mtx.out $(V) ./z_demo < ../Demo/Matrix/0.tri > tmp/demo_0.out $(V) ./z_demo < Matrix/3_2 > tmp/demo_3_2.out $(V) ./z_demo < Matrix/c5lo > tmp/demo_c5lo.out $(V) ./z_demo < Matrix/c10 > tmp/demo_c10.out $(V) ./z_demo no_such_file > tmp/demo_no_such_file.out $(V) ./z_demo ../Demo/Matrix/mangle1.mtx > tmp/demo_mangle1.out $(V) ./z_demo ../Demo/Matrix/mangle2.mtx > tmp/demo_mangle2.out $(V) ./z_demo ../Demo/Matrix/mangle3.mtx > tmp/demo_mangle3.out $(V) ./z_demo ../Demo/Matrix/mangle4.mtx > tmp/demo_mangle4.out $(V) ./z_demo ../Demo/Matrix/pts5ldd03.mtx > tmp/demo_pts5ldd03.out $(V) ./l_demo ../Demo/Matrix/bcsstk01.tri > tmp/ldemo_k1.out $(V) ./l_demo ../Demo/Matrix/bcsstk02.tri > tmp/ldemo_k2.out $(V) ./l_demo < ../Demo/Matrix/lp_afiro.tri > tmp/ldemo_afiro.out $(V) ./l_demo < ../Demo/Matrix/can___24.mtx > tmp/ldemo_can24.out $(V) ./l_demo < ../Demo/Matrix/c.tri > tmp/ldemo_c.out $(V) ./l_demo < ../Demo/Matrix/d.tri > tmp/ldemo_d.out $(V) ./l_demo < ../Demo/Matrix/up.tri > tmp/ldemo_up.out $(V) ./l_demo < ../Demo/Matrix/c.mtx > tmp/ldemo_c_mtx.out $(V) ./l_demo < ../Demo/Matrix/0.tri > tmp/ldemo_0.out $(V) ./l_demo < Matrix/3_2 > tmp/ldemo_3_2.out $(V) ./l_demo < Matrix/c5lo > tmp/ldemo_c5lo.out $(V) ./l_demo < Matrix/c10 > tmp/ldemo_c10.out $(V) ./l_demo no_such_file > tmp/ldemo_no_such_file.out $(V) ./l_demo ../Demo/Matrix/mangle1.mtx > tmp/ldemo_mangle1.out $(V) ./l_demo ../Demo/Matrix/mangle2.mtx > tmp/ldemo_mangle2.out $(V) ./l_demo ../Demo/Matrix/mangle3.mtx > tmp/ldemo_mangle3.out $(V) ./l_demo ../Demo/Matrix/mangle4.mtx > tmp/ldemo_mangle4.out $(V) ./l_demo ../Demo/Matrix/pts5ldd03.mtx > tmp/ldemo_pts5ldd03.out - grep resid tmp/demo* $(V) ./cmread no_such_file > tmp/no_such_file.out $(V) ./cmread Matrix/crud1 > tmp/crud1.out $(V) ./cmread Matrix/crud2 > tmp/crud2.out $(V) ./cmread Matrix/fullcrud.mtx > tmp/fullcrud.out $(V) ./cmread Matrix/fullcrud1.mtx > tmp/fullcrud1.out $(V) ./cmread Matrix/fullcrud2.mtx > tmp/fullcrud2.out $(V) ./cmread Matrix/3by0.mtx > tmp/3by0.out $(V) ./cmread Matrix/fullrza.mtx > tmp/fullrza.out $(V) ./cmread Matrix/fullrsa.mtx > tmp/fullrsa.out $(V) ./cmread Matrix/fullcsa.mtx > tmp/fullcsa.out $(V) ./cmread Matrix/fullcza.mtx > tmp/fullcza.out $(V) ./cmread Matrix/fullcha.mtx > tmp/fullcha.out $(V) ./cmread Matrix/cha.mtx > tmp/cha.out $(V) ./cmread Matrix/cza.mtx > tmp/cza.out $(V) ./cmread Matrix/csa.mtx > tmp/csa.out $(V) ./cmread Matrix/one > tmp/one.out $(V) ./cmread Matrix/rza.mtx > tmp/rza.out $(V) ./cmread ../Demo/Matrix/mangle5.tri > tmp/mangle5.out $(V) ./cmread ../Demo/Matrix/mangle6.tri > tmp/mangle6.out $(V) ./cmread ../Demo/Matrix/mangle7.tri > tmp/mangle6.out $(V) ./cmread ../Demo/Matrix/mangle8.tri > tmp/mangle8.out $(V) ./cmread ../Demo/Matrix/empty.tri > tmp/empty.out $(V) ./cmread ../Demo/Matrix/one.tri > tmp/one.out $(V) ./cmread Matrix/plskz362.mtx > tmp/plskz363.out $(V) ./cmread Matrix/2diag.tri > tmp/2diag.out $(V) ./cmread Matrix/r5lo > tmp/r5lo.out $(V) ./cmread Matrix/r5lo2 > tmp/r5lo2.out - diff tmp/r5lo.out tmp/r5lo2.out $(V) ./cmread Matrix/cs.mtx > tmp/cs.out $(V) ./cmread Matrix/2lo.tri > tmp/2lo.out $(V) ./cmread Matrix/2.tri > tmp/2.out $(V) ./cmread Matrix/2up.tri > tmp/2up.out $(V) ./cmread Matrix/huge.tri > tmp/huge.out $(V) ./cmread Matrix/1e99 > tmp/1e99.out $(V) ./clread no_such_file > tmp/l_no_such_file.out $(V) ./clread Matrix/crud1 > tmp/l_crud1.out $(V) ./clread Matrix/crud2 > tmp/l_crud2.out $(V) ./clread Matrix/fullcrud.mtx > tmp/l_fullcrud.out $(V) ./clread Matrix/fullcrud1.mtx > tmp/l_fullcrud1.out $(V) ./clread Matrix/fullcrud2.mtx > tmp/l_fullcrud2.out $(V) ./clread Matrix/3by0.mtx > tmp/l_3by0.out $(V) ./clread Matrix/fullrza.mtx > tmp/l_fullrza.out $(V) ./clread Matrix/fullrsa.mtx > tmp/l_fullrsa.out $(V) ./clread Matrix/fullcsa.mtx > tmp/l_fullcsa.out $(V) ./clread Matrix/fullcza.mtx > tmp/l_fullcza.out $(V) ./clread Matrix/fullcha.mtx > tmp/l_fullcha.out $(V) ./clread Matrix/cha.mtx > tmp/l_cha.out $(V) ./clread Matrix/cza.mtx > tmp/l_cza.out $(V) ./clread Matrix/csa.mtx > tmp/l_csa.out $(V) ./clread Matrix/one > tmp/l_one.out $(V) ./clread Matrix/rza.mtx > tmp/l_rza.out $(V) ./clread ../Demo/Matrix/mangle5.tri > tmp/l_mangle5.out $(V) ./clread ../Demo/Matrix/mangle6.tri > tmp/l_mangle6.out $(V) ./clread ../Demo/Matrix/mangle7.tri > tmp/l_mangle6.out $(V) ./clread ../Demo/Matrix/mangle8.tri > tmp/l_mangle8.out $(V) ./clread ../Demo/Matrix/empty.tri > tmp/l_empty.out $(V) ./clread ../Demo/Matrix/one.tri > tmp/l_one.out $(V) ./clread Matrix/plskz362.mtx > tmp/l_plskz363.out $(V) ./clread Matrix/2diag.tri > tmp/l_2diag.out $(V) ./clread Matrix/r5lo > tmp/l_r5lo.out $(V) ./clread Matrix/r5lo2 > tmp/l_r5lo2.out - diff tmp/r5lo.out tmp/r5lo2.out $(V) ./clread Matrix/cs.mtx > tmp/l_cs.out $(V) ./clread Matrix/2lo.tri > tmp/l_l_2lo.out $(V) ./clread Matrix/2.tri > tmp/l_2.out $(V) ./clread Matrix/2up.tri > tmp/l_2up.out $(V) ./clread Matrix/huge.tri > tmp/l_huge.out $(V) ./clread Matrix/1e99 > tmp/l_1e99.out $(V) ./cm < Matrix/galenet > tmp/galenet.out $(V) ./cl < Matrix/galenet > tmp/l_galenet.out - $(COVER) $(V) ./cm < Matrix/5by50 > tmp/5by50.out $(V) ./cl < Matrix/5by50 > tmp/l_5by50.out - $(COVER) $(V) ./cm < Matrix/r5lo > tmp/r5lo.out $(V) ./cl < Matrix/r5lo > tmp/l_r5lo.out $(V) ./cm < Matrix/r5up > tmp/r5up.out $(V) ./cl < Matrix/r5up > tmp/l_r5up.out $(V) ./cm < Matrix/r5up2 > tmp/r5up2.out $(V) ./cl < Matrix/r5up2 > tmp/l_r5up2.out $(V) ./cm < Matrix/c5up2 > tmp/c5up2.out $(V) ./cl < Matrix/c5up2 > tmp/l_c5up2.out $(V) ./cm < Matrix/z5up2 > tmp/z5up2.out $(V) ./cl < Matrix/z5up2 > tmp/l_z5up2.out $(V) ./cm -m < Matrix/z5lo > tmp/z5lo.out $(V) ./cl -m < Matrix/z5lo > tmp/l_z5lo.out $(V) ./cm < Matrix/ibm32 > tmp/ibm.out $(V) ./cl < Matrix/ibm32 > tmp/l_ibm.out - $(COVER) $(V) ./cm -m < Matrix/c5lo > tmp/c5lo.out $(V) ./cl -m < Matrix/c5lo > tmp/l_c5lo.out $(V) ./cm -m < Matrix/z10 > tmp/z10.out $(V) ./cl -m < Matrix/z10 > tmp/l_z10.out $(V) ./cm -m < Matrix/z5up > tmp/z5up.out $(V) ./cl -m < Matrix/z5up > tmp/l_z5up.out - $(COVER) $(V) ./cm -s < Matrix/3singular > tmp/3singular.out $(V) ./cl -s < Matrix/3singular > tmp/l_3singular.out $(V) ./cm -s < Matrix/z3singular > tmp/z3singular.out $(V) ./cl -s < Matrix/z3singular > tmp/l_z3singular.out $(V) ./cm -s < Matrix/c3singular > tmp/c3singular.out $(V) ./cl -s < Matrix/c3singular > tmp/l_c3singular.out $(V) ./cm -m < Matrix/0 > tmp/0.out $(V) ./cl -m < Matrix/0 > tmp/l_0.out $(V) ./cm -m < Matrix/afiro > tmp/afiro.out $(V) ./cl -m < Matrix/afiro > tmp/l_afiro.out - $(COVER) $(V) ./cm -m < Matrix/k01up > tmp/k01up.out $(V) ./cl -m < Matrix/k01up > tmp/l_k01up.out - $(COVER) $(V) ./cm < Matrix/diag > tmp/diag.out $(V) ./cl < Matrix/diag > tmp/l_diag.out $(V) ./cm -m < Matrix/ex5lo > tmp/ex5lo.out $(V) ./cl -m < Matrix/ex5lo > tmp/l_ex5lo.out - $(COVER) $(V) ./cm < Matrix/20lo > tmp/20lo.out $(V) ./cl < Matrix/20lo > tmp/l_20lo.out $(V) ./cm < Matrix/z30lo > tmp/z30lo.out $(V) ./cl < Matrix/z30lo > tmp/l_z30lo.out - $(COVER) $(V) ./cm -m < Matrix/z30up > tmp/z30up.out $(V) ./cl -m < Matrix/z30up > tmp/l_z30up.out $(V) ./cm < Matrix/c10 > tmp/c10.out $(V) ./cl < Matrix/c10 > tmp/l_c10.out $(V) ./cm < Matrix/c30lo > tmp/c30lo.out $(V) ./cl < Matrix/c30lo > tmp/l_c30lo.out - $(COVER) $(V) ./cm -m < Matrix/c30up > tmp/c30up.out $(V) ./cl -m < Matrix/c30up > tmp/l_c30up.out $(V) ./cm < Matrix/pi > tmp/pi.out $(V) ./cl < Matrix/pi > tmp/l_pi.out $(V) ./cm < Matrix/cpi > tmp/cpi.out $(V) ./cl < Matrix/cpi > tmp/l_cpi.out $(V) ./cm < Matrix/1_0 > tmp/1_0.out $(V) ./cl < Matrix/1_0 > tmp/l_1_0.out $(V) ./cm -s < Matrix/3b > tmp/3b.out $(V) ./cl -s < Matrix/3b > tmp/l_3b.out $(V) ./cm -s < Matrix/cza > tmp/cza2.out $(V) ./cl -s < Matrix/cza > tmp/l_cza2.out $(V) ./cm < Matrix/0_1 > tmp/0_1.out $(V) ./cl < Matrix/0_1 > tmp/l_0_1.out - $(COVER) $(V) ./cm -n < Matrix/galenet > tmp/galenet_nan.out - $(COVER) $(V) ./cl -n < Matrix/galenet > tmp/l_galenet_nan.out - $(COVER) $(V) ./cm < Matrix/a1 > tmp/a1.out - $(COVER) $(V) ./cl < Matrix/a1 > tmp/l_a1.out - $(COVER) $(V) ./cm < Matrix/zero > tmp/zero.out $(V) ./cl < Matrix/zero > tmp/zero.out - $(COVER) cov: - $(COVER) purge: distclean distclean: clean - $(RM) cm cl cmread clread *.c.gcov *.out tmp/*.out z_demo l_demo - $(RM) leak zz_*.c z_*.c *.a l_*.c zl_*.c cov.sort yl_*.c yz_*.c - $(RM) -r cm.profile cmread.profile z_demo.profile - $(RM) -r cl.profile clread.profile l_demo.profile - $(RM) *.gcda *.gcno - $(RM) temp*.mtx clean: - $(RM) $(CLEAN) $(AMDOBJ): $(AMDSRC) $(LAMDOBJ): $(AMDSRC) $(IOBJ): $(INC) $(LOBJ): $(INC) .c.o: $(C) -c $(I) $*.c #------------------------------------------------------------------------------- # AMD #------------------------------------------------------------------------------- zz_amd_1.o: ../../AMD/Source/amd_1.c $(C) -E $(I) $< | $(PRETTY) > zz_amd_1.c $(C) -c $(I) zz_amd_1.c zz_amd_2.o: ../../AMD/Source/amd_2.c $(C) -E $(I) $< | $(PRETTY) > zz_amd_2.c $(C) -c $(I) zz_amd_2.c zz_amd_aat.o: ../../AMD/Source/amd_aat.c $(C) -E $(I) $< | $(PRETTY) > zz_amd_aat.c $(C) -c $(I) zz_amd_aat.c zz_amd_control.o: ../../AMD/Source/amd_control.c $(C) -E $(I) $< | $(PRETTY) > zz_amd_control.c $(C) -c $(I) zz_amd_control.c zz_amd_defaults.o: ../../AMD/Source/amd_defaults.c $(C) -E $(I) $< | $(PRETTY) > zz_amd_defaults.c $(C) -c $(I) zz_amd_defaults.c zz_amd_global.o: ../../AMD/Source/amd_global.c $(C) -E $(I) $< | $(PRETTY) > zz_amd_global.c $(C) -c $(I) zz_amd_global.c zz_amd_dump.o: ../../AMD/Source/amd_dump.c $(C) -E $(I) $< | $(PRETTY) > zz_amd_dump.c $(C) -c $(I) zz_amd_dump.c zz_amd_info.o: ../../AMD/Source/amd_info.c $(C) -E $(I) $< | $(PRETTY) > zz_amd_info.c $(C) -c $(I) zz_amd_info.c zz_amd_order.o: ../../AMD/Source/amd_order.c $(C) -E $(I) $< | $(PRETTY) > zz_amd_order.c $(C) -c $(I) zz_amd_order.c zz_amd_postorder.o: ../../AMD/Source/amd_postorder.c $(C) -E $(I) $< | $(PRETTY) > zz_amd_postorder.c $(C) -c $(I) zz_amd_postorder.c zz_amd_post_tree.o: ../../AMD/Source/amd_post_tree.c $(C) -E $(I) $< | $(PRETTY) > zz_amd_post_tree.c $(C) -c $(I) zz_amd_post_tree.c zz_amd_preprocess.o: ../../AMD/Source/amd_preprocess.c $(C) -E $(I) $< | $(PRETTY) > zz_amd_preprocess.c $(C) -c $(I) zz_amd_preprocess.c zz_amd_valid.o: ../../AMD/Source/amd_valid.c $(C) -E $(I) $< | $(PRETTY) > zz_amd_valid.c $(C) -c $(I) zz_amd_valid.c #------------------------------------------------------------------------------- zl_amd_1.o: ../../AMD/Source/amd_1.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_1.c $(C) -c $(I) zl_amd_1.c zl_amd_2.o: ../../AMD/Source/amd_2.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_2.c $(C) -c $(I) zl_amd_2.c zl_amd_aat.o: ../../AMD/Source/amd_aat.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_aat.c $(C) -c $(I) zl_amd_aat.c zl_amd_control.o: ../../AMD/Source/amd_control.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_control.c $(C) -c $(I) zl_amd_control.c zl_amd_defaults.o: ../../AMD/Source/amd_defaults.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_defaults.c $(C) -c $(I) zl_amd_defaults.c zl_amd_global.o: ../../AMD/Source/amd_global.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_global.c $(C) -c $(I) zl_amd_global.c zl_amd_dump.o: ../../AMD/Source/amd_dump.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_dump.c $(C) -c $(I) zl_amd_dump.c zl_amd_info.o: ../../AMD/Source/amd_info.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_info.c $(C) -c $(I) zl_amd_info.c zl_amd_order.o: ../../AMD/Source/amd_order.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_order.c $(C) -c $(I) zl_amd_order.c zl_amd_postorder.o: ../../AMD/Source/amd_postorder.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_postorder.c $(C) -c $(I) zl_amd_postorder.c zl_amd_post_tree.o: ../../AMD/Source/amd_post_tree.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_post_tree.c $(C) -c $(I) zl_amd_post_tree.c zl_amd_preprocess.o: ../../AMD/Source/amd_preprocess.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_preprocess.c $(C) -c $(I) zl_amd_preprocess.c zl_amd_valid.o: ../../AMD/Source/amd_valid.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_valid.c $(C) -c $(I) zl_amd_valid.c #------------------------------------------------------------------------------- # CAMD #------------------------------------------------------------------------------- zz_camd_1.o: ../../CAMD/Source/camd_1.c $(C) -E $(I) $< | $(PRETTY) > zz_camd_1.c $(C) -c $(I) zz_camd_1.c zz_camd_2.o: ../../CAMD/Source/camd_2.c $(C) -E $(I) $< | $(PRETTY) > zz_camd_2.c $(C) -c $(I) zz_camd_2.c zz_camd_aat.o: ../../CAMD/Source/camd_aat.c $(C) -E $(I) $< | $(PRETTY) > zz_camd_aat.c $(C) -c $(I) zz_camd_aat.c zz_camd_control.o: ../../CAMD/Source/camd_control.c $(C) -E $(I) $< | $(PRETTY) > zz_camd_control.c $(C) -c $(I) zz_camd_control.c zz_camd_defaults.o: ../../CAMD/Source/camd_defaults.c $(C) -E $(I) $< | $(PRETTY) > zz_camd_defaults.c $(C) -c $(I) zz_camd_defaults.c zz_camd_global.o: ../../CAMD/Source/camd_global.c $(C) -E $(I) $< | $(PRETTY) > zz_camd_global.c $(C) -c $(I) zz_camd_global.c zz_camd_dump.o: ../../CAMD/Source/camd_dump.c $(C) -E $(I) $< | $(PRETTY) > zz_camd_dump.c $(C) -c $(I) zz_camd_dump.c zz_camd_info.o: ../../CAMD/Source/camd_info.c $(C) -E $(I) $< | $(PRETTY) > zz_camd_info.c $(C) -c $(I) zz_camd_info.c zz_camd_order.o: ../../CAMD/Source/camd_order.c $(C) -E $(I) $< | $(PRETTY) > zz_camd_order.c $(C) -c $(I) zz_camd_order.c zz_camd_postorder.o: ../../CAMD/Source/camd_postorder.c $(C) -E $(I) $< | $(PRETTY) > zz_camd_postorder.c $(C) -c $(I) zz_camd_postorder.c zz_camd_preprocess.o: ../../CAMD/Source/camd_preprocess.c $(C) -E $(I) $< | $(PRETTY) > zz_camd_preprocess.c $(C) -c $(I) zz_camd_preprocess.c zz_camd_valid.o: ../../CAMD/Source/camd_valid.c $(C) -E $(I) $< | $(PRETTY) > zz_camd_valid.c $(C) -c $(I) zz_camd_valid.c #------------------------------------------------------------------------------- zl_camd_1.o: ../../CAMD/Source/camd_1.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_1.c $(C) -c $(I) zl_camd_1.c zl_camd_2.o: ../../CAMD/Source/camd_2.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_2.c $(C) -c $(I) zl_camd_2.c zl_camd_aat.o: ../../CAMD/Source/camd_aat.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_aat.c $(C) -c $(I) zl_camd_aat.c zl_camd_control.o: ../../CAMD/Source/camd_control.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_control.c $(C) -c $(I) zl_camd_control.c zl_camd_defaults.o: ../../CAMD/Source/camd_defaults.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_defaults.c $(C) -c $(I) zl_camd_defaults.c zl_camd_global.o: ../../CAMD/Source/camd_global.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_global.c $(C) -c $(I) zl_camd_global.c zl_camd_dump.o: ../../CAMD/Source/camd_dump.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_dump.c $(C) -c $(I) zl_camd_dump.c zl_camd_info.o: ../../CAMD/Source/camd_info.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_info.c $(C) -c $(I) zl_camd_info.c zl_camd_order.o: ../../CAMD/Source/camd_order.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_order.c $(C) -c $(I) zl_camd_order.c zl_camd_postorder.o: ../../CAMD/Source/camd_postorder.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_postorder.c $(C) -c $(I) zl_camd_postorder.c zl_camd_preprocess.o: ../../CAMD/Source/camd_preprocess.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_preprocess.c $(C) -c $(I) zl_camd_preprocess.c zl_camd_valid.o: ../../CAMD/Source/camd_valid.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_valid.c $(C) -c $(I) zl_camd_valid.c #------------------------------------------------------------------------------- zz_colamd.o: ../../COLAMD/Source/colamd.c $(C) -E $(I) $< | $(PRETTY) > zz_colamd.c $(C) -c $(I) zz_colamd.c yz_colamd_global.o: ../../COLAMD/Source/colamd_global.c $(C) -E $(I) $< | $(PRETTY) > yz_colamd_global.c $(C) -c $(I) yz_colamd_global.c zl_colamd.o: ../../COLAMD/Source/colamd.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_colamd.c $(C) -c $(I) zl_colamd.c yl_colamd_global.o: ../../COLAMD/Source/colamd_global.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > yl_colamd_global.c $(C) -c $(I) yl_colamd_global.c #------------------------------------------------------------------------------- zz_ccolamd.o: ../../CCOLAMD/Source/ccolamd.c $(C) -E $(I) $< | $(PRETTY) > zz_ccolamd.c $(C) -c $(I) zz_ccolamd.c yz_ccolamd_global.o: ../../CCOLAMD/Source/ccolamd_global.c $(C) -E $(I) $< | $(PRETTY) > yz_ccolamd_global.c $(C) -c $(I) yz_ccolamd_global.c zl_ccolamd.o: ../../CCOLAMD/Source/ccolamd.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_ccolamd.c $(C) -c $(I) zl_ccolamd.c yl_ccolamd_global.o: ../../CCOLAMD/Source/ccolamd_global.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > yl_ccolamd_global.c $(C) -c $(I) yl_ccolamd_global.c #------------------------------------------------------------------------------- z_check.o: ../Check/cholmod_check.c $(C) -E $(I) $< | $(PRETTY) > z_check.c $(C) -c $(I) z_check.c z_read.o: ../Check/cholmod_read.c $(C) -E $(I) $< | $(PRETTY) > z_read.c $(C) -c $(I) z_read.c z_write.o: ../Check/cholmod_write.c $(C) -E $(I) $< | $(PRETTY) > z_write.c $(C) -c $(I) z_write.c #------------------------------------------------------------------------------- z_common.o: ../Core/cholmod_common.c $(C) -E $(I) $< | $(PRETTY) > z_common.c $(C) -c $(I) z_common.c z_dense.o: ../Core/cholmod_dense.c ../Core/t_cholmod_dense.c $(C) -E $(I) $< | $(PRETTY) > z_dense.c $(C) -c $(I) z_dense.c z_factor.o: ../Core/cholmod_factor.c $(C) -E $(I) $< | $(PRETTY) > z_factor.c $(C) -c $(I) z_factor.c z_change_factor.o: ../Core/cholmod_change_factor.c \ ../Core/t_cholmod_change_factor.c $(C) -E $(I) $< | $(PRETTY) > z_change_factor.c $(C) -c $(I) z_change_factor.c z_memory.o: ../Core/cholmod_memory.c $(C) -E $(I) $< | $(PRETTY) > z_memory.c $(C) -c $(I) z_memory.c z_sparse.o: ../Core/cholmod_sparse.c $(C) -E $(I) $< | $(PRETTY) > z_sparse.c $(C) -c $(I) z_sparse.c z_complex.o: ../Core/cholmod_complex.c $(C) -E $(I) $< | $(PRETTY) > z_complex.c $(C) -c $(I) z_complex.c z_transpose.o: ../Core/cholmod_transpose.c ../Core/t_cholmod_transpose.c $(C) -E $(I) $< | $(PRETTY) > z_transpose.c $(C) -c $(I) z_transpose.c z_band.o: ../Core/cholmod_band.c $(C) -E $(I) $< | $(PRETTY) > z_band.c $(C) -c $(I) z_band.c z_copy.o: ../Core/cholmod_copy.c $(C) -E $(I) $< | $(PRETTY) > z_copy.c $(C) -c $(I) z_copy.c z_triplet.o: ../Core/cholmod_triplet.c ../Core/t_cholmod_triplet.c $(C) -E $(I) $< | $(PRETTY) > z_triplet.c $(C) -c $(I) z_triplet.c z_error.o: ../Core/cholmod_error.c $(C) -E $(I) $< | $(PRETTY) > z_error.c $(C) -c $(I) z_error.c z_aat.o: ../Core/cholmod_aat.c $(C) -E $(I) $< | $(PRETTY) > z_aat.c $(C) -c $(I) z_aat.c z_add.o: ../Core/cholmod_add.c $(C) -E $(I) $< | $(PRETTY) > z_add.c $(C) -c $(I) z_add.c #------------------------------------------------------------------------------- z_amd.o: ../Cholesky/cholmod_amd.c $(C) -E $(I) $< | $(PRETTY) > z_amd.c $(C) -c $(I) z_amd.c z_analyze.o: ../Cholesky/cholmod_analyze.c $(C) -E $(I) $< | $(PRETTY) > z_analyze.c $(C) -c $(I) z_analyze.c z_colamd.o: ../Cholesky/cholmod_colamd.c $(C) -E $(I) $< | $(PRETTY) > z_colamd.c $(C) -c $(I) z_colamd.c z_etree.o: ../Cholesky/cholmod_etree.c $(C) -E $(I) $< | $(PRETTY) > z_etree.c $(C) -c $(I) z_etree.c z_factorize.o: ../Cholesky/cholmod_factorize.c $(C) -E $(I) $< | $(PRETTY) > z_factorize.c $(C) -c $(I) z_factorize.c z_postorder.o: ../Cholesky/cholmod_postorder.c $(C) -E $(I) $< | $(PRETTY) > z_postorder.c $(C) -c $(I) z_postorder.c z_rcond.o: ../Cholesky/cholmod_rcond.c $(C) -E $(I) $< | $(PRETTY) > z_rcond.c $(C) -c $(I) z_rcond.c z_resymbol.o: ../Cholesky/cholmod_resymbol.c $(C) -E $(I) $< | $(PRETTY) > z_resymbol.c $(C) -c $(I) z_resymbol.c z_rowcolcounts.o: ../Cholesky/cholmod_rowcolcounts.c $(C) -E $(I) $< | $(PRETTY) > z_rowcolcounts.c $(C) -c $(I) z_rowcolcounts.c z_solve.o: ../Cholesky/cholmod_solve.c ../Cholesky/t_cholmod_lsolve.c \ ../Cholesky/t_cholmod_ltsolve.c ../Cholesky/t_cholmod_solve.c $(C) -E $(I) $< | $(PRETTY) > z_solve.c $(C) -c $(I) z_solve.c z_spsolve.o: ../Cholesky/cholmod_spsolve.c $(C) -E $(I) $< | $(PRETTY) > z_spsolve.c $(C) -c $(I) z_spsolve.c z_rowfac.o: ../Cholesky/cholmod_rowfac.c ../Cholesky/t_cholmod_rowfac.c $(C) -E $(I) $< | $(PRETTY) > z_rowfac.c $(C) -c $(I) z_rowfac.c #------------------------------------------------------------------------------- z_ccolamd.o: ../Partition/cholmod_ccolamd.c $(C) -E $(I) $< | $(PRETTY) > z_ccolamd.c $(C) -c $(I) z_ccolamd.c z_csymamd.o: ../Partition/cholmod_csymamd.c $(C) -E $(I) $< | $(PRETTY) > z_csymamd.c $(C) -c $(I) z_csymamd.c z_camd.o: ../Partition/cholmod_camd.c $(C) -E $(I) $< | $(PRETTY) > z_camd.c $(C) -c $(I) z_camd.c z_metis.o: ../Partition/cholmod_metis.c $(C) -E $(I) $< | $(PRETTY) > z_metis.c $(C) -c $(I) z_metis.c z_nesdis.o: ../Partition/cholmod_nesdis.c $(C) -E $(I) $< | $(PRETTY) > z_nesdis.c $(C) -c $(I) z_nesdis.c #------------------------------------------------------------------------------- z_horzcat.o: ../MatrixOps/cholmod_horzcat.c $(C) -E $(I) $< | $(PRETTY) > z_horzcat.c $(C) -c $(I) z_horzcat.c z_norm.o: ../MatrixOps/cholmod_norm.c $(C) -E $(I) $< | $(PRETTY) > z_norm.c $(C) -c $(I) z_norm.c z_scale.o: ../MatrixOps/cholmod_scale.c $(C) -E $(I) $< | $(PRETTY) > z_scale.c $(C) -c $(I) z_scale.c z_drop.o: ../MatrixOps/cholmod_drop.c $(C) -E $(I) $< | $(PRETTY) > z_drop.c $(C) -c $(I) z_drop.c z_sdmult.o: ../MatrixOps/cholmod_sdmult.c ../MatrixOps/t_cholmod_sdmult.c $(C) -E $(I) $< | $(PRETTY) > z_sdmult.c $(C) -c $(I) z_sdmult.c z_ssmult.o: ../MatrixOps/cholmod_ssmult.c $(C) -E $(I) $< | $(PRETTY) > z_ssmult.c $(C) -c $(I) z_ssmult.c z_submatrix.o: ../MatrixOps/cholmod_submatrix.c $(C) -E $(I) $< | $(PRETTY) > z_submatrix.c $(C) -c $(I) z_submatrix.c z_vertcat.o: ../MatrixOps/cholmod_vertcat.c $(C) -E $(I) $< | $(PRETTY) > z_vertcat.c $(C) -c $(I) z_vertcat.c z_symmetry.o: ../MatrixOps/cholmod_symmetry.c $(C) -E $(I) $< | $(PRETTY) > z_symmetry.c $(C) -c $(I) z_symmetry.c #------------------------------------------------------------------------------- z_rowadd.o: ../Modify/cholmod_rowadd.c $(C) -E $(I) $< | $(PRETTY) > z_rowadd.c $(C) -c $(I) z_rowadd.c z_rowdel.o: ../Modify/cholmod_rowdel.c $(C) -E $(I) $< | $(PRETTY) > z_rowdel.c $(C) -c $(I) z_rowdel.c z_updown.o: ../Modify/cholmod_updown.c \ ../Modify/t_cholmod_updown.c ../Modify/t_cholmod_updown_numkr.c $(C) -E $(I) $< | $(PRETTY) > z_updown.c $(C) -c $(I) z_updown.c #------------------------------------------------------------------------------- z_super_numeric.o: ../Supernodal/cholmod_super_numeric.c \ ../Supernodal/t_cholmod_super_numeric.c $(C) -E $(I) $< | $(PRETTY) > z_super_numeric.c $(C) -c $(I) z_super_numeric.c z_super_symbolic.o: ../Supernodal/cholmod_super_symbolic.c $(C) -E $(I) $< | $(PRETTY) > z_super_symbolic.c $(C) -c $(I) z_super_symbolic.c z_super_solve.o: ../Supernodal/cholmod_super_solve.c $(C) -E $(I) $< | $(PRETTY) > z_super_solve.c $(C) -c $(I) z_super_solve.c #------------------------------------------------------------------------------- #------------------------------------------------------------------------------- l_check.o: ../Check/cholmod_check.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_check.c $(C) -c $(I) l_check.c l_read.o: ../Check/cholmod_read.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_read.c $(C) -c $(I) l_read.c l_write.o: ../Check/cholmod_write.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_write.c $(C) -c $(I) l_write.c #------------------------------------------------------------------------------- l_common.o: ../Core/cholmod_common.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_common.c $(C) -c $(I) l_common.c l_dense.o: ../Core/cholmod_dense.c ../Core/t_cholmod_dense.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_dense.c $(C) -c $(I) l_dense.c l_factor.o: ../Core/cholmod_factor.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_factor.c $(C) -c $(I) l_factor.c l_change_factor.o: ../Core/cholmod_change_factor.c \ ../Core/t_cholmod_change_factor.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_change_factor.c $(C) -c $(I) l_change_factor.c l_memory.o: ../Core/cholmod_memory.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_memory.c $(C) -c $(I) l_memory.c l_sparse.o: ../Core/cholmod_sparse.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_sparse.c $(C) -c $(I) l_sparse.c l_complex.o: ../Core/cholmod_complex.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_complex.c $(C) -c $(I) l_complex.c l_transpose.o: ../Core/cholmod_transpose.c ../Core/t_cholmod_transpose.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_transpose.c $(C) -c $(I) l_transpose.c l_band.o: ../Core/cholmod_band.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_band.c $(C) -c $(I) l_band.c l_copy.o: ../Core/cholmod_copy.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_copy.c $(C) -c $(I) l_copy.c l_triplet.o: ../Core/cholmod_triplet.c ../Core/t_cholmod_triplet.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_triplet.c $(C) -c $(I) l_triplet.c l_error.o: ../Core/cholmod_error.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_error.c $(C) -c $(I) l_error.c l_aat.o: ../Core/cholmod_aat.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_aat.c $(C) -c $(I) l_aat.c l_add.o: ../Core/cholmod_add.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_add.c $(C) -c $(I) l_add.c #------------------------------------------------------------------------------- l_amd.o: ../Cholesky/cholmod_amd.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_amd.c $(C) -c $(I) l_amd.c l_analyze.o: ../Cholesky/cholmod_analyze.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_analyze.c $(C) -c $(I) l_analyze.c l_colamd.o: ../Cholesky/cholmod_colamd.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_colamd.c $(C) -c $(I) l_colamd.c l_etree.o: ../Cholesky/cholmod_etree.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_etree.c $(C) -c $(I) l_etree.c l_factorize.o: ../Cholesky/cholmod_factorize.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_factorize.c $(C) -c $(I) l_factorize.c l_postorder.o: ../Cholesky/cholmod_postorder.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_postorder.c $(C) -c $(I) l_postorder.c l_rcond.o: ../Cholesky/cholmod_rcond.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_rcond.c $(C) -c $(I) l_rcond.c l_resymbol.o: ../Cholesky/cholmod_resymbol.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_resymbol.c $(C) -c $(I) l_resymbol.c l_rowcolcounts.o: ../Cholesky/cholmod_rowcolcounts.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_rowcolcounts.c $(C) -c $(I) l_rowcolcounts.c l_solve.o: ../Cholesky/cholmod_solve.c ../Cholesky/t_cholmod_lsolve.c \ ../Cholesky/t_cholmod_ltsolve.c ../Cholesky/t_cholmod_solve.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_solve.c $(C) -c $(I) l_solve.c l_spsolve.o: ../Cholesky/cholmod_spsolve.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_spsolve.c $(C) -c $(I) l_spsolve.c l_rowfac.o: ../Cholesky/cholmod_rowfac.c ../Cholesky/t_cholmod_rowfac.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_rowfac.c $(C) -c $(I) l_rowfac.c #------------------------------------------------------------------------------- l_ccolamd.o: ../Partition/cholmod_ccolamd.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_ccolamd.c $(C) -c $(I) l_ccolamd.c l_csymamd.o: ../Partition/cholmod_csymamd.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_csymamd.c $(C) -c $(I) l_csymamd.c l_camd.o: ../Partition/cholmod_camd.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_camd.c $(C) -c $(I) l_camd.c l_metis.o: ../Partition/cholmod_metis.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_metis.c $(C) -c $(I) l_metis.c l_nesdis.o: ../Partition/cholmod_nesdis.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_nesdis.c $(C) -c $(I) l_nesdis.c #------------------------------------------------------------------------------- l_horzcat.o: ../MatrixOps/cholmod_horzcat.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_horzcat.c $(C) -c $(I) l_horzcat.c l_norm.o: ../MatrixOps/cholmod_norm.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_norm.c $(C) -c $(I) l_norm.c l_scale.o: ../MatrixOps/cholmod_scale.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_scale.c $(C) -c $(I) l_scale.c l_drop.o: ../MatrixOps/cholmod_drop.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_drop.c $(C) -c $(I) l_drop.c l_sdmult.o: ../MatrixOps/cholmod_sdmult.c ../MatrixOps/t_cholmod_sdmult.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_sdmult.c $(C) -c $(I) l_sdmult.c l_ssmult.o: ../MatrixOps/cholmod_ssmult.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_ssmult.c $(C) -c $(I) l_ssmult.c l_submatrix.o: ../MatrixOps/cholmod_submatrix.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_submatrix.c $(C) -c $(I) l_submatrix.c l_vertcat.o: ../MatrixOps/cholmod_vertcat.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_vertcat.c $(C) -c $(I) l_vertcat.c l_symmetry.o: ../MatrixOps/cholmod_symmetry.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_symmetry.c $(C) -c $(I) l_symmetry.c #------------------------------------------------------------------------------- l_rowadd.o: ../Modify/cholmod_rowadd.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_rowadd.c $(C) -c $(I) l_rowadd.c l_rowdel.o: ../Modify/cholmod_rowdel.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_rowdel.c $(C) -c $(I) l_rowdel.c l_updown.o: ../Modify/cholmod_updown.c \ ../Modify/t_cholmod_updown.c ../Modify/t_cholmod_updown_numkr.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_updown.c $(C) -c $(I) l_updown.c #------------------------------------------------------------------------------- l_super_numeric.o: ../Supernodal/cholmod_super_numeric.c \ ../Supernodal/t_cholmod_super_numeric.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_super_numeric.c $(C) -c $(I) l_super_numeric.c l_super_symbolic.o: ../Supernodal/cholmod_super_symbolic.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_super_symbolic.c $(C) -c $(I) l_super_symbolic.c l_super_solve.o: ../Supernodal/cholmod_super_solve.c $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_super_solve.c $(C) -c $(I) l_super_solve.c #------------------------------------------------------------------------------- SuiteSparse/CHOLMOD/Tcov/ctest.c0000644001170100242450000002304510540000045015225 0ustar davisfac/* ========================================================================== */ /* === Tcov/ctest =========================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Test for colamd v2.4 */ #include "cm.h" #include "colamd.h" /* ========================================================================== */ /* === ctest ================================================================ */ /* ========================================================================== */ void ctest (cholmod_sparse *A) { double knobs [COLAMD_KNOBS], knobs2 [COLAMD_KNOBS] ; Int *P, *Cp, *Ci, *Si, *Sp ; cholmod_sparse *C, *A2, *B, *S, *BT ; Int nrow, ncol, alen, ok, stats [COLAMD_STATS], i, p, trial ; size_t s ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ printf ("\nCOLAMD test\n") ; if (A == NULL) { return ; } if (A->stype) { A2 = CHOLMOD(copy) (A, 0, 0, cm) ; B = A2 ; } else { A2 = NULL ; B = A ; } nrow = B->nrow ; ncol = B->ncol ; S = NULL ; /* ---------------------------------------------------------------------- */ /* allocate workspace colamd */ /* ---------------------------------------------------------------------- */ P = CHOLMOD(malloc) (nrow+1, sizeof (Int), cm) ; COLAMD_set_defaults (knobs) ; COLAMD_set_defaults (knobs2) ; COLAMD_set_defaults (NULL) ; COLAMD_report (NULL) ; SYMAMD_report (NULL) ; alen = COLAMD_recommended (B->nzmax, ncol, nrow) ; C = CHOLMOD(allocate_sparse) (ncol, nrow, alen, TRUE, TRUE, 0, CHOLMOD_PATTERN, cm) ; Cp = C->p ; Ci = C->i ; /* ---------------------------------------------------------------------- */ /* order with colamd */ /* ---------------------------------------------------------------------- */ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ; CHOLMOD(print_sparse) (C, "C for colamd", cm) ; ok = COLAMD_MAIN (ncol, nrow, alen, Ci, Cp, NULL, stats) ; COLAMD_report (stats) ; OK (ok) ; ok = stats [COLAMD_STATUS] ; ok = (ok == COLAMD_OK || ok == COLAMD_OK_BUT_JUMBLED) ; OK (ok) ; /* permutation returned in C->p, if the ordering succeeded */ /* make sure P obeys the constraints */ OK (CHOLMOD(print_perm) (Cp, nrow, nrow, "colamd perm", cm)) ; /* ---------------------------------------------------------------------- */ /* with different dense thresholds */ /* ---------------------------------------------------------------------- */ printf ("\nall dense rows:\n") ; knobs2 [COLAMD_DENSE_ROW] = 0 ; knobs2 [COLAMD_DENSE_COL] = 0.5 ; ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ; ok = COLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs2, stats) ; COLAMD_report (stats) ; OK (CHOLMOD(print_perm) (Cp, nrow, nrow, "colamd perm", cm)) ; printf ("\nall dense cols:\n") ; knobs2 [COLAMD_DENSE_ROW] = 0.5 ; knobs2 [COLAMD_DENSE_COL] = 0 ; ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ; ok = COLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs2, stats) ; COLAMD_report (stats) ; OK (CHOLMOD(print_perm) (Cp, nrow, nrow, "colamd perm", cm)) ; printf ("\nno dense rows/cols:\n") ; knobs2 [COLAMD_DENSE_ROW] = -1 ; knobs2 [COLAMD_DENSE_COL] = -1 ; ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ; ok = COLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs2, stats) ; COLAMD_report (stats) ; OK (CHOLMOD(print_perm) (Cp, nrow, nrow, "colamd perm", cm)) ; knobs2 [COLAMD_DENSE_ROW] = 0.5 ; knobs2 [COLAMD_DENSE_COL] = 0.5 ; /* ---------------------------------------------------------------------- */ /* duplicate entries */ /* ---------------------------------------------------------------------- */ if (ncol > 2 && nrow > 2) { ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ; if (Cp [1] - Cp [0] > 2) { Ci [0] = Ci [1] ; } ok = COLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs2, stats) ; COLAMD_report (stats) ; OK (CHOLMOD(print_perm) (Cp, nrow, nrow, "colamd perm", cm)) ; } /* ---------------------------------------------------------------------- */ /* symamd */ /* ---------------------------------------------------------------------- */ if (nrow == ncol) { Int n = nrow ; BT = CHOLMOD(transpose) (B, 0, cm) ; OKP(BT); S = CHOLMOD(add) (B, BT, one, one, FALSE, FALSE, cm) ; CHOLMOD(free_sparse) (&BT, cm) ; Si = S->i ; Sp = S->p ; ok = SYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory, cm->free_memory) ; OK (ok) ; OK (CHOLMOD(print_perm) (P, n, n, "symamd perm", cm)) ; SYMAMD_report (stats) ; /* ------------------------------------------------------------------ */ /* symamd errors */ /* ------------------------------------------------------------------ */ test_memory_handler ( ) ; for (trial = 0 ; trial < 3 ; trial++) { my_tries = trial ; ok = SYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory, cm->free_memory) ; NOT (ok) ; } my_tries = 3 ; ok = SYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory, cm->free_memory) ; OK (ok) ; normal_memory_handler ( ) ; ok = SYMAMD_MAIN (n, Si, Sp, P, NULL, NULL, cm->calloc_memory, cm->free_memory) ; NOT (ok); ok = SYMAMD_MAIN (n, NULL, Sp, P, NULL, stats, cm->calloc_memory, cm->free_memory) ; NOT (ok); SYMAMD_report (stats) ; ok = SYMAMD_MAIN (n, Si, NULL, P, NULL, stats, cm->calloc_memory, cm->free_memory) ; NOT (ok); SYMAMD_report (stats) ; ok = SYMAMD_MAIN (-1, Si, Sp, P, NULL, stats, cm->calloc_memory, cm->free_memory) ; NOT (ok); SYMAMD_report (stats) ; p = Sp [n] ; Sp [n] = -1 ; ok = SYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory, cm->free_memory) ; NOT (ok); SYMAMD_report (stats) ; Sp [n] = p ; Sp [0] = -1 ; ok = SYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory, cm->free_memory) ; NOT (ok); SYMAMD_report (stats) ; Sp [0] = 0 ; if (n > 2 && Sp [n] > 3) { p = Sp [1] ; Sp [1] = -1 ; ok = SYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory, cm->free_memory) ; NOT (ok); SYMAMD_report (stats) ; Sp [1] = p ; i = Si [0] ; Si [0] = -1 ; ok = SYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory, cm->free_memory) ; NOT (ok); SYMAMD_report (stats) ; Si [0] = i ; /* ok, but jumbled */ i = Si [0] ; Si [0] = Si [1] ; Si [1] = i ; ok = SYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory, cm->free_memory) ; OK (ok); SYMAMD_report (stats) ; OK (CHOLMOD(print_perm) (P, nrow, nrow, "symamd perm", cm)) ; i = Si [0] ; Si [0] = Si [1] ; Si [1] = i ; test_memory_handler ( ) ; ok = SYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory, cm->free_memory) ; NOT (ok); SYMAMD_report (stats) ; normal_memory_handler ( ) ; } } /* ---------------------------------------------------------------------- */ /* error tests */ /* ---------------------------------------------------------------------- */ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ; ok = COLAMD_MAIN (ncol, nrow, 0, Ci, Cp, knobs, stats) ; NOT (ok) ; COLAMD_report (stats) ; ok = COLAMD_MAIN (ncol, nrow, alen, NULL, Cp, knobs, stats); NOT (ok) ; COLAMD_report (stats) ; ok = COLAMD_MAIN (ncol, nrow, alen, Ci, NULL, knobs, stats); NOT (ok) ; COLAMD_report (stats) ; ok = COLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, NULL) ; NOT (ok) ; COLAMD_report (stats) ; ok = COLAMD_MAIN (-1, nrow, alen, Ci, Cp, knobs, stats) ; NOT (ok) ; COLAMD_report (stats) ; ok = COLAMD_MAIN (ncol, -1, alen, Ci, Cp, knobs, stats) ; NOT (ok) ; COLAMD_report (stats) ; ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ; Cp [nrow] = -1 ; ok = COLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, stats) ; NOT (ok) ; COLAMD_report (stats) ; Cp [0] = 1 ; ok = COLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, stats) ; NOT (ok) ; COLAMD_report (stats) ; ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ; if (nrow > 0 && alen > 0 && Cp [1] > 0) { p = Cp [1] ; Cp [1] = -1 ; ok = COLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, stats) ; NOT(ok); COLAMD_report (stats) ; Cp [1] = p ; i = Ci [0] ; Ci [0] = -1 ; ok = COLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, stats) ; NOT(ok); COLAMD_report (stats) ; Ci [0] = i ; } s = COLAMD_recommended (-1, 0, 0) ; OK (s == 0) ; /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ CHOLMOD(free) (nrow+1, sizeof (Int), P, cm) ; CHOLMOD(free_sparse) (&S, cm) ; CHOLMOD(free_sparse) (&A2, cm) ; CHOLMOD(free_sparse) (&C, cm) ; } SuiteSparse/CHOLMOD/Tcov/aug.c0000644001170100242450000001650110540000027014656 0ustar davisfac/* ========================================================================== */ /* === Tcov/aug ============================================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Create the augmented system S = [-I A' ; A alpha*I], solve Sx=b, and return * the residual. The system solved is (alpha*I + A*A')*x=b. * * r1 = norm (Sx-b) * r2 = norm ((alpha*I+AA')x-b) * alpha = norm(A) */ #include "cm.h" /* ========================================================================== */ /* === aug ================================================================== */ /* ========================================================================== */ double aug (cholmod_sparse *A) { double r, maxerr = 0, bnorm, anorm ; cholmod_sparse *S, *Im, *In, *At, *A1, *A2, *Sup ; cholmod_dense *Alpha, *B, *Baug, *X, *W1, *W2, *R, *X2, X2mat ; cholmod_factor *L ; double *b, *baug, *rx, *w, *x ; Int nrow, ncol, nrhs, i, j, d, d2, save, save2, save3 ; if (A == NULL) { ERROR (CHOLMOD_INVALID, "cm: no A for aug") ; return (1) ; } if (A->xtype != CHOLMOD_REAL) { return (0) ; } /* ---------------------------------------------------------------------- */ /* A is m-by-n, B must be m-by-nrhs */ /* ---------------------------------------------------------------------- */ nrow = A->nrow ; ncol = A->ncol ; B = rhs (A, 5, A->nrow + 7) ; /* ---------------------------------------------------------------------- */ /* create scalars */ /* ---------------------------------------------------------------------- */ bnorm = CHOLMOD(norm_dense) (B, 0, cm) ; anorm = CHOLMOD(norm_sparse) (A, 1, cm) ; Alpha = CHOLMOD(eye) (1, 1, CHOLMOD_REAL, cm) ; if (Alpha != NULL) { ((double *) (Alpha->x)) [0] = anorm ; } CHOLMOD(print_dense) (M1, "MinusOne", cm) ; CHOLMOD(print_dense) (Alpha, "Alpha = norm(A)", cm) ; /* ---------------------------------------------------------------------- */ /* create augmented system, S = [-I A' ; A anorm*I] */ /* ---------------------------------------------------------------------- */ Im = CHOLMOD(speye) (nrow, nrow, CHOLMOD_REAL, cm) ; In = CHOLMOD(speye) (ncol, ncol, CHOLMOD_REAL, cm) ; CHOLMOD(scale) (Alpha, CHOLMOD_SCALAR, Im, cm) ; CHOLMOD(scale) (M1, CHOLMOD_SCALAR, In, cm) ; At = CHOLMOD(transpose) (A, 2, cm) ; /* use one of two equivalent methods */ if (nrow % 2) { /* S = [[-In A'] ; [A alpha*Im]] */ A1 = CHOLMOD(horzcat) (In, At, TRUE, cm) ; A2 = CHOLMOD(horzcat) (A, Im, TRUE, cm) ; S = CHOLMOD(vertcat) (A1, A2, TRUE, cm) ; } else { /* S = [[-In ; A] [A' ; alpha*Im]] */ A1 = CHOLMOD(vertcat) (In, A, TRUE, cm) ; A2 = CHOLMOD(vertcat) (At, Im, TRUE, cm) ; S = CHOLMOD(horzcat) (A1, A2, TRUE, cm) ; } CHOLMOD(free_sparse) (&Im, cm) ; CHOLMOD(free_sparse) (&In, cm) ; CHOLMOD(print_sparse) (S, "S, augmented system", cm) ; /* make a symmetric (upper) copy of S */ Sup = CHOLMOD(copy) (S, 1, 1, cm) ; CHOLMOD(print_sparse) (S, "S, augmented system (upper)", cm) ; CHOLMOD(print_sparse) (Sup, "Sup", cm) ; /* ---------------------------------------------------------------------- */ /* create augmented right-hand-side, Baug = [ zeros(ncol,nrhs) ; B ] */ /* ---------------------------------------------------------------------- */ b = NULL ; d = 0 ; nrhs = 0 ; d2 = 0 ; if (B != NULL) { nrhs = B->ncol ; d = B->d ; b = B->x ; Baug = CHOLMOD(zeros) (nrow+ncol, nrhs, CHOLMOD_REAL, cm) ; if (Baug != NULL) { d2 = Baug->d ; baug = Baug->x ; for (j = 0 ; j < nrhs ; j++) { for (i = 0 ; i < nrow ; i++) { baug [(i+ncol)+j*d2] = b [i+j*d] ; } } } } else { Baug = NULL ; } /* ---------------------------------------------------------------------- */ /* solve Sx=baug */ /* ---------------------------------------------------------------------- */ /* S is symmetric indefinite, so do not use a supernodal LL' */ save = cm->supernodal ; save2 = cm->final_asis ; cm->supernodal = CHOLMOD_SIMPLICIAL ; cm->final_asis = TRUE ; save3 = cm->metis_memory ; cm->metis_memory = 2.0 ; L = CHOLMOD(analyze) (Sup, cm) ; CHOLMOD(factorize) (Sup, L, cm) ; X = CHOLMOD(solve) (CHOLMOD_A, L, Baug, cm) ; cm->supernodal = save ; cm->final_asis = save2 ; cm->metis_memory = save3 ; /* ---------------------------------------------------------------------- */ /* compute the residual */ /* ---------------------------------------------------------------------- */ r = resid (Sup, X, Baug) ; MAXERR (maxerr, r, 1) ; /* ---------------------------------------------------------------------- */ /* create a shallow submatrix of X, X2 = X (ncol:end, :) */ /* ---------------------------------------------------------------------- */ if (X == NULL) { X2 = NULL ; } else { X2 = &X2mat ; X2->nrow = nrow ; X2->ncol = nrhs ; X2->nzmax = X->nzmax ; X2->d = X->d ; X2->x = ((double *) X->x) + ncol ; X2->z = NULL ; X2->xtype = X->xtype ; X2->dtype = X->dtype ; } CHOLMOD(print_dense) (X, "X", cm) ; CHOLMOD(print_dense) (X2, "X2 = X (ncol:end,:)", cm) ; /* ---------------------------------------------------------------------- */ /* compute norm ((alpha*I + A*A')*x-b) */ /* ---------------------------------------------------------------------- */ /* W1 = A'*X2 */ W1 = CHOLMOD(zeros) (ncol, nrhs, CHOLMOD_REAL, cm) ; CHOLMOD(sdmult) (A, TRUE, one, zero, X2, W1, cm) ; /* W2 = A*W1 */ W2 = CHOLMOD(zeros) (nrow, nrhs, CHOLMOD_REAL, cm) ; CHOLMOD(sdmult) (A, FALSE, one, zero, W1, W2, cm) ; /* R = alpha*x + w2 - b */ R = CHOLMOD(zeros) (nrow, nrhs, CHOLMOD_REAL, cm) ; if (R != NULL && W2 != NULL && X != NULL) { w = W2->x ; rx = R->x ; x = X2->x ; for (j = 0 ; j < nrhs ; j++) { for (i = 0 ; i < nrow ; i++) { rx [i+j*nrow] = anorm * x [i+j*d2] + w [i+j*nrow] - b [i+j*d] ; } } } r = CHOLMOD(norm_dense) (R, 1, cm) ; MAXERR (maxerr, r, bnorm) ; /* ---------------------------------------------------------------------- */ /* free everything */ /* ---------------------------------------------------------------------- */ CHOLMOD(free_sparse) (&At, cm) ; CHOLMOD(free_sparse) (&A1, cm) ; CHOLMOD(free_sparse) (&A2, cm) ; CHOLMOD(free_sparse) (&S, cm) ; CHOLMOD(free_sparse) (&Sup, cm) ; CHOLMOD(free_factor) (&L, cm) ; CHOLMOD(free_dense) (&R, cm) ; CHOLMOD(free_dense) (&W1, cm) ; CHOLMOD(free_dense) (&W2, cm) ; CHOLMOD(free_dense) (&B, cm) ; CHOLMOD(free_dense) (&Baug, cm) ; CHOLMOD(free_dense) (&X, cm) ; CHOLMOD(free_dense) (&Alpha, cm) ; progress (0, '.') ; return (maxerr) ; } SuiteSparse/CHOLMOD/Tcov/cover0000755001170100242450000000050310222045704015005 0ustar davisfac#!/bin/csh # usage: cover files echo '=================================================================' foreach file ($argv[1-]) echo $file echo '=================================================================' grep "#####" -A5 -B5 $file echo '=================================================================' end SuiteSparse/CHOLMOD/Tcov/gcovs0000755001170100242450000000011310533127672015017 0ustar davisfac# usage: gcovs files foreach file ($argv[1-]) gcov $file > /dev/null end SuiteSparse/CHOLMOD/Tcov/Matrix/0000755001170100242450000000000010616503231015210 5ustar davisfacSuiteSparse/CHOLMOD/Tcov/Matrix/00000644001170100242450000000001010223043054015255 0ustar davisfac0 0 0 0 SuiteSparse/CHOLMOD/Tcov/Matrix/40000644001170100242450000000075110217161252015301 0ustar davisfac4 4 16 0 0 0 8.4472150190817474e-01 1 0 3.6775288246828447e-01 2 0 6.2080133182114383e-01 3 0 7.3127726446634478e-01 0 1 1.9389317998466821e-01 1 1 9.0481233416635698e-01 2 1 5.6920574967174709e-01 3 1 6.3178992922175603e-01 0 2 2.3441295540825388e-01 1 2 5.4878212553858818e-01 2 2 9.3158335257969060e-01 3 2 3.3519743020639464e-01 0 3 6.5553105501201447e-01 1 3 3.9190420688900335e-01 2 3 6.2731478808399666e-01 3 3 6.9908013774533750e-01 SuiteSparse/CHOLMOD/Tcov/Matrix/50000644001170100242450000000071310220353342015275 0ustar davisfac5 5 15 1 0 0 2.3128893423956103e+00 0 1 2.0414504875924515e+00 1 1 2.3404148406122136e+00 0 2 1.3087150593318868e+00 1 2 1.0697105858626588e+00 2 2 1.1518495146909449e+00 0 3 1.8412759629133451e+00 1 3 1.6127622826156847e+00 2 3 9.9254946878554184e-01 3 3 1.5263467772586621e+00 0 4 1.1506154116930891e+00 1 4 8.5366433729208291e-01 2 4 5.8985415046641843e-01 3 4 8.4135254506414192e-01 4 4 9.2240833463986371e-01 SuiteSparse/CHOLMOD/Tcov/Matrix/3b0000644001170100242450000000003610533071742015443 0ustar davisfac3 3 4 0 0 1 2 0 1 0 1 1 0 2 1 SuiteSparse/CHOLMOD/Tcov/Matrix/a10000644001170100242450000000002010222746161015430 0ustar davisfac70000 70000 0 2 SuiteSparse/CHOLMOD/Tcov/Matrix/a20000644001170100242450000000001410222741537015436 0ustar davisfac200 200 0 2 SuiteSparse/CHOLMOD/Tcov/Matrix/pi0000644001170100242450000000004610222534234015543 0ustar davisfac1 1 1 0 0 0 3.1415926535897931e+00 SuiteSparse/CHOLMOD/Tcov/Matrix/0_10000644001170100242450000000001010223112143015471 0ustar davisfac0 1 0 0 SuiteSparse/CHOLMOD/Tcov/Matrix/1_00000644001170100242450000000001010223113430015471 0ustar davisfac1 0 0 0 SuiteSparse/CHOLMOD/Tcov/Matrix/2_30000644001170100242450000000027410223241074015517 0ustar davisfac2 3 6 0 0 0 9.4423471389861624e-01 1 0 8.3855545301913648e-01 0 1 2.5842740296885991e-01 1 1 4.2898125196177306e-02 0 2 5.8847897639891693e-03 1 2 5.7441796740690909e-01 SuiteSparse/CHOLMOD/Tcov/Matrix/3_20000644001170100242450000000027410223242504015516 0ustar davisfac3 2 6 0 0 0 9.4423471389861624e-01 1 0 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10 0.0324186 0.445355 9 10 0.733926 0.0129578 0 11 0.536517 0.308742 2 11 0.27603 0.875351 8 11 0.368458 0.835259 1 12 0.0128863 0.333095 2 12 0.889206 0.880705 8 12 0.866021 0.479687 9 12 0.254247 0.560817 0 13 0.569481 0.615909 2 13 0.159265 0.661899 3 13 0.594364 0.616633 7 13 0.3311 0.68514 9 13 0.658613 0.510153 5 14 0.863634 0.713961 8 14 0.567623 0.515208 SuiteSparse/CHOLMOD/Tcov/Matrix/tri0000644001170100242450000000001310226465556015741 0ustar davisfac10 10 44 3 SuiteSparse/CHOLMOD/Tcov/Matrix/20lo0000644001170100242450000001457310222536154015724 0ustar davisfac20 20 210 -1 0 0 1.0828864476260923e+01 1 0 1.6627011669737349e-01 2 0 3.9390600531964565e-01 3 0 5.2075748437407210e-01 4 0 7.1812397228036695e-01 5 0 5.6918951876742652e-01 6 0 4.6080617332598611e-01 7 0 4.4530705340682281e-01 8 0 8.7744606123989974e-02 9 0 4.4348321523342715e-01 10 0 3.6629984599465693e-01 11 0 3.0253381852374750e-01 12 0 8.5184469733234425e-01 13 0 7.5947938787995917e-01 14 0 9.4975928462912151e-01 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SuiteSparse/CHOLMOD/Tcov/Matrix/z5up0000644001170100242450000000032710276203372016045 0ustar davisfac5 5 11 1 2 0 0 2.43872 0 0 1 0.261819 0.16627 1 1 4.21742 0 0 2 0.724062 -0.804517 1 2 1.69463 0.324218 2 2 4.77818 0 1 3 1.23492 -0.0754504 2 3 0.902819 -0.460806 3 3 3.51267 0 0 4 0.281634 -0.828864 4 4 6.25922 0 SuiteSparse/CHOLMOD/Tcov/Matrix/zero0000644001170100242450000000003210424430515016106 0ustar davisfac1100000000 1100000000 0 0 SuiteSparse/CHOLMOD/Tcov/Matrix/2.tri0000644001170100242450000000003710276443556016110 0ustar davisfac2 2 4 0 0 1 0 1 2 1 0 -2 1 1 3 SuiteSparse/CHOLMOD/Tcov/Matrix/rename.h0000644001170100242450000000037710532641534016645 0ustar davisfac/* do not edit this file; generated by cholmod_make */ #undef log2 #include "../../metis-4.0/Lib/rename.h" #undef log2 #define log2 METIS__log2 #include "mex.h" #define malloc mxMalloc #define free mxFree #define calloc mxCalloc #define realloc mxRealloc 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SuiteSparse/CHOLMOD/Tcov/Matrix/3singular0000644001170100242450000000020010247366654017052 0ustar davisfac3 3 4 1 0 0 9.4423471389861624e-01 0 1 8.3855545301913648e-01 1 1 4.2898125196177306e-02 1 2 5.7441796740690909e-01 SuiteSparse/CHOLMOD/Tcov/Matrix/itest20000644001170100242450000000144210226306574016356 0ustar davisfac9 13 26 0 0 0 -1.0000000000000000e+00 1 1 -1.0000000000000000e+00 2 2 1.0000000000000000e+00 3 3 1.0000000000000000e+00 4 4 1.0000000000000000e+00 5 5 -1.0000000000000000e+00 6 6 1.0000000000000000e+00 7 7 1.0000000000000000e+00 8 8 -1.0000000000000000e+00 0 9 -5.0000000000000000e-01 1 9 2.0000000000000000e+00 2 9 3.0000000000000000e+00 6 9 1.0000000000000000e+00 7 9 1.0000000000000000e+00 0 10 1.0000000000000000e+00 1 10 -1.0000000000000000e+00 2 10 1.0000000000000000e+00 7 10 2.0000000000000000e+00 8 10 1.0000000000000000e+00 4 11 3.0000000000000000e+00 5 11 1.0000000000000000e+00 7 11 1.0000000000000000e+00 8 11 1.0000000000000000e+00 3 12 1.0000000000000000e+00 4 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SuiteSparse/CHOLMOD/Tcov/Matrix/c3singular0000644001170100242450000000022410276425215017212 0ustar davisfac3 3 4 1 1 0 0 9.4423471389861624e-01 0.1 0 1 8.3855545301913648e-01 0.2 1 1 4.2898125196177306e-02 0.03 1 2 5.7441796740690909e-01 0.04 SuiteSparse/CHOLMOD/Tcov/Matrix/tribig0000644001170100242450000000002410226475650016421 0ustar davisfac1000000 1000000 0 3 SuiteSparse/CHOLMOD/Tcov/Matrix/3by0.mtx0000644001170100242450000000005510532672276016534 0ustar davisfac%%MatrixMarket matrix array real general 3 0 SuiteSparse/CHOLMOD/Tcov/Matrix/2diag.tri0000644001170100242450000000002210276443527016725 0ustar davisfac2 2 2 0 0 1 1 1 3 SuiteSparse/CHOLMOD/Tcov/Matrix/fullcrud.mtx0000644001170100242450000000011310532711245017560 0ustar davisfac%%MatrixMarket matrix array real general 2 2 1.3 3.4 7.7 % too few entries SuiteSparse/CHOLMOD/Tcov/Matrix/2lo.tri0000644001170100242450000000003010276443470016427 0ustar davisfac2 2 3 0 0 1 1 0 2 1 1 3 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SuiteSparse/CHOLMOD/Tcov/unpack.c0000644001170100242450000000754010540000074015370 0ustar davisfac/* ========================================================================== */ /* === Tcov/unpack ========================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Create an unpacked, unsorted version of a matrix, with random-sized gaps in * each column. */ #include "cm.h" /* ========================================================================== */ /* === unpack =============================================================== */ /* ========================================================================== */ cholmod_sparse *unpack (cholmod_sparse *A) { double x ; double *Ax, *Cx, *Az, *Cz ; Int *Ap, *Ai, *Anz, *Cp, *Ci, *Cnz ; cholmod_sparse *C ; Int i, j, p, q, pdest, pend, nrow, ncol, nzmax, sorted, packed, stype, extra ; if (A == NULL) { return (NULL) ; } extra = 10 ; nrow = A->nrow ; ncol = A->ncol ; nzmax = A->nzmax ; sorted = A->sorted ; packed = A->packed ; stype = A->stype ; C = CHOLMOD(allocate_sparse) (nrow, ncol, nzmax + extra*ncol, FALSE, FALSE, stype, A->xtype, cm) ; if (C == NULL) { return (NULL) ; } Ap = A->p ; Ai = A->i ; Ax = A->x ; Az = A->z ; Anz = A->nz ; Cp = C->p ; Ci = C->i ; Cx = C->x ; Cz = C->z ; Cnz = C->nz ; nzmax = C->nzmax ; nzmax = MAX (1, nzmax) ; for (p = 0 ; p < nzmax ; p++) { Ci [p] = 0 ; } if (A->xtype == CHOLMOD_REAL) { for (p = 0 ; p < nzmax ; p++) { Cx [p] = 0 ; } } else if (A->xtype == CHOLMOD_COMPLEX) { for (p = 0 ; p < 2*nzmax ; p++) { Cx [p] = 0 ; } } else if (A->xtype == CHOLMOD_ZOMPLEX) { for (p = 0 ; p < nzmax ; p++) { Cx [p] = 0 ; Cz [p] = 0 ; } } pdest = 0 ; for (j = 0 ; j < ncol ; j++) { /* copy the column into C */ p = Ap [j] ; Cp [j] = pdest ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; Cnz [j] = pend - p ; for ( ; p < pend ; p++) { Ci [pdest] = Ai [p] ; if (A->xtype == CHOLMOD_REAL) { Cx [pdest] = Ax [p] ; } else if (A->xtype == CHOLMOD_COMPLEX) { Cx [2*pdest ] = Ax [2*p] ; Cx [2*pdest+1] = Ax [2*p+1] ; } else if (A->xtype == CHOLMOD_ZOMPLEX) { Cx [pdest] = Ax [p] ; Cz [pdest] = Az [p] ; } pdest++ ; } /* jumble the column */ p = Cp [j] ; pend = p + Cnz [j] ; for ( ; p < pend-1 ; p++) { q = p + nrand (pend-p) ; /* RAND */ i = Ci [p] ; Ci [p] = Ci [q] ; Ci [q] = i ; if (A->xtype == CHOLMOD_REAL) { x = Cx [p] ; Cx [p] = Cx [q] ; Cx [q] = x ; } else if (A->xtype == CHOLMOD_COMPLEX) { x = Cx [2*p] ; Cx [2*p] = Cx [2*q] ; Cx [2*q] = x ; x = Cx [2*p+1] ; Cx [2*p+1] = Cx [2*q+1] ; Cx [2*q+1] = x ; } else if (A->xtype == CHOLMOD_ZOMPLEX) { x = Cx [p] ; Cx [p] = Cx [q] ; Cx [q] = x ; x = Cz [p] ; Cz [p] = Cz [q] ; Cz [q] = x ; } } /* add some random blank space */ pdest += nrand (extra) ; /* RAND */ for (p = pend ; p < pdest ; p++) { Ci [p] = 0 ; if (A->xtype == CHOLMOD_REAL) { Cx [p] = 0 ; } else if (A->xtype == CHOLMOD_COMPLEX) { Cx [2*p] = 0 ; Cx [2*p+1] = 0 ; } else if (A->xtype == CHOLMOD_ZOMPLEX) { Cx [p] = 0 ; Cz [p] = 0 ; } } } Cp [ncol] = pdest ; return (C) ; } SuiteSparse/CHOLMOD/Tcov/cmread.c0000644001170100242450000000647310540000042015341 0ustar davisfac/* ========================================================================== */ /* === Tcov/cmread ========================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Read in a matrix from a file and print it out. * * Usage: * cmread matrixfile * cmread < matrixfile */ #include "cholmod.h" #ifdef DLONG #define CHOLMOD(routine) cholmod_l_ ## routine #define Int UF_long #else #define CHOLMOD(routine) cholmod_ ## routine #define Int int #endif int main (int argc, char **argv) { cholmod_sparse *A, *C, *Z ; cholmod_dense *X ; cholmod_triplet *T ; void *V ; FILE *f, *f2 ; cholmod_common Common, *cm ; int mtype, prefer, option ; /* ---------------------------------------------------------------------- */ /* get the file containing the input matrix */ /* ---------------------------------------------------------------------- */ if (argc > 1) { if ((f = fopen (argv [1], "r")) == NULL) { printf ("cannot open file: %s\n", argv [1]) ; return (0) ; } } else { f = stdin ; } /* ---------------------------------------------------------------------- */ /* start CHOLMOD, read the matrix, print it, and free it */ /* ---------------------------------------------------------------------- */ cm = &Common ; CHOLMOD (start) (cm) ; cm->print = 5 ; A = CHOLMOD (read_sparse) (f, cm) ; if (argc > 1) fclose (f) ; CHOLMOD (print_sparse) (A, "A", cm) ; if (argc > 1) { for (prefer = 0 ; prefer <= 2 ; prefer++) { printf ("\n---------------------- Prefer: %d\n", prefer) ; f = fopen (argv [1], "r") ; V = CHOLMOD (read_matrix) (f, prefer, &mtype, cm) ; if (V != NULL) switch (mtype) { case CHOLMOD_TRIPLET: T = V ; CHOLMOD (print_triplet) (T, "T", cm) ; CHOLMOD (free_triplet) (&T, cm) ; break ; case CHOLMOD_SPARSE: C = V ; CHOLMOD (print_sparse) (C, "C", cm) ; Z = CHOLMOD (speye) (C->nrow, C->ncol, CHOLMOD_PATTERN, cm); for (option = 0 ; option <= 2 ; option++) { int asym ; Int xmatch = 0, pmatch = 0, nzoff = 0, nzd = 0 ; asym = CHOLMOD (symmetry) (C, option, &xmatch, &pmatch, &nzoff, &nzd, cm) ; f2 = fopen ("temp5.mtx", "w") ; CHOLMOD (write_sparse) (f2, C, Z, NULL, cm) ; fclose (f2) ; printf ("asym %d\n", asym) ; } CHOLMOD (free_sparse) (&C, cm) ; CHOLMOD (free_sparse) (&Z, cm) ; break ; case CHOLMOD_DENSE: X = V ; CHOLMOD (print_dense) (X, "X", cm) ; f2 = fopen ("temp5.mtx", "w") ; CHOLMOD (write_dense) (f2, X, NULL, cm) ; fclose (f2) ; CHOLMOD (free_dense) (&X, cm) ; break ; } fclose (f) ; } } CHOLMOD (free_sparse) (&A, cm) ; CHOLMOD (finish) (cm) ; return (0) ; } SuiteSparse/CHOLMOD/Tcov/solve.c0000644001170100242450000011035210616474637015263 0ustar davisfac/* ========================================================================== */ /* === Tcov/solve =========================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Test CHOLMOD for solving various systems of linear equations. */ #include "cm.h" #define NFTYPES 17 Int ll_types [NFTYPES] = { 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0 } ; Int pk_types [NFTYPES] = { 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0 } ; Int mn_types [NFTYPES] = { 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0 } ; Int co_types [NFTYPES] = { 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1 } ; #define NRHS 9 #ifndef NDEBUG #ifndef EXTERN #define EXTERN extern #endif EXTERN int cholmod_dump, cholmod_l_dump ; #endif /* ========================================================================== */ /* === test_solver ========================================================== */ /* ========================================================================== */ /* Test solve(A) with various control parameters */ double test_solver (cholmod_sparse *A) { double err, maxerr = 0 ; int save ; for (cm->postorder = 0 ; cm->postorder <= 1 ; cm->postorder++) { my_srand (42) ; /* RAND reset */ /* simplicial, no extra memory */ printf ("test_solver: simplicial, no extra memory\n") ; cm->supernodal = CHOLMOD_SIMPLICIAL ; cm->grow2 = 0 ; err = solve (A) ; MAXERR (maxerr, err, 1) ; printf ("test_solver err: %6.2e\n", err) ; /* simplicial, extra space in columns of L */ printf ("test_solver: simplicial, extra space in columns of L\n") ; cm->grow2 = 5 ; err = solve (A) ; MAXERR (maxerr, err, 1) ; printf ("test_solver err: %6.2e\n", err) ; /* supernodal */ printf ("test_solver: supernodal\n") ; cm->supernodal = CHOLMOD_SUPERNODAL ; err = solve (A) ; MAXERR (maxerr, err, 1) ; printf ("test_solver err: %6.2e\n", err) ; /* supernodal, without final resymbol */ printf ("test_solver: supernodal, without final resymbol\n") ; cm->final_resymbol = FALSE ; err = solve (A) ; MAXERR (maxerr, err, 1) ; printf ("test_solver err: %6.2e\n", err) ; /* supernodal, with resymbol, final_super false */ printf ("test_solver: supernodal, with resymbol\n") ; cm->supernodal = CHOLMOD_SUPERNODAL ; cm->final_asis = FALSE ; cm->final_resymbol = TRUE ; cm->final_super = FALSE ; err = solve (A) ; MAXERR (maxerr, err, 1) ; printf ("test_solver err: %6.2e\n", err) ; /* supernodal, with resymbol, final_super tree */ printf ("test_solver: supernodal, with resymbol\n") ; cm->supernodal = CHOLMOD_SUPERNODAL ; cm->final_asis = FALSE ; cm->final_resymbol = TRUE ; cm->final_super = TRUE ; err = solve (A) ; MAXERR (maxerr, err, 1) ; printf ("test_solver err: %6.2e\n", err) ; /* simplicial LL' */ printf ("test_solver: simplicial LL', try NESDIS instead of METIS\n") ; cm->supernodal = CHOLMOD_SIMPLICIAL ; cm->final_ll = TRUE ; cm->default_nesdis = TRUE ; err = solve (A) ; cm->default_nesdis = FALSE ; MAXERR (maxerr, err, 1) ; cm->final_ll = FALSE ; printf ("test_solver err: %6.2e\n", err) ; /* supernodal, without final resymbol, and no relaxed supernodes */ printf ( "test_solver: supernodal, without final resymbol, and no relaxed supernodes\n") ; cm->supernodal = CHOLMOD_SUPERNODAL ; cm->final_asis = TRUE ; cm->nrelax [0] = 0 ; cm->nrelax [1] = 0 ; cm->nrelax [2] = 0 ; cm->zrelax [0] = 0 ; cm->zrelax [1] = 0 ; cm->zrelax [2] = 0 ; cm->grow0 = 1 ; cm->grow1 = 1 ; cm->grow2 = 0 ; err = solve (A) ; MAXERR (maxerr, err, 1) ; printf ("test_solver err: %6.2e\n", err) ; /* ------------------------------------------------------------------ */ /* restore defaults */ /* ------------------------------------------------------------------ */ cm->dbound = 0.0 ; cm->grow0 = 1.2 ; cm->grow1 = 1.2 ; cm->grow2 = 5 ; cm->final_asis = TRUE ; cm->final_super = TRUE ; cm->final_ll = FALSE ; cm->final_pack = TRUE ; cm->final_monotonic = TRUE ; cm->final_resymbol = FALSE ; cm->supernodal = CHOLMOD_AUTO ; cm->nrelax [0] = 4 ; cm->nrelax [1] = 16 ; cm->nrelax [2] = 48 ; cm->zrelax [0] = 0.8 ; cm->zrelax [1] = 0.1 ; cm->zrelax [2] = 0.05 ; /* do not restore these defaults: */ /* cm->maxrank = ... cm->metis_memory = 2.0 cm->metis_nswitch = 3000 cm->metis_dswitch = 0.66 cm->print = 3 cm->precise = FALSE */ } progress (1, '.') ; return (maxerr) ; } /* ========================================================================== */ /* === solve ================================================================ */ /* ========================================================================== */ /* solve Ax=b or AA'x=b, systems involving just L, D, or L', and update/downdate * the system. Returns the worst-case residual. This routine keeps going if * it runs out of memory (unless the error handler terminates it), because * it is used both normally and in the memory tests. */ double solve (cholmod_sparse *A) { double r, enorm, snorm, maxerr = 0, gnorm, anorm, bnorm, xnorm, norm, rcond; cholmod_factor *L, *Lcopy, *L2 ; cholmod_sparse *Lmat, *Lo, *D, *Up, *S, *LD, *LDL, *E, *I, *C, *CC, *Ct, *Ssym, *Cperm, *C2, *S2, *H, *F, *Lo1, *Aboth ; cholmod_dense *X, *Cdense, *B, *Bcomplex, *Bzomplex, *Breal, *W, *R, *A3, *C3, *E3 ; cholmod_sparse *AFt, *AF, *G, *RowK, *Bsparse, *Xsparse ; double *Cx ; Int *P, *cset, *fset, *Parent, *Post, *RowCount, *ColCount, *First, *Level, *rcount, *ccount, *Lp, *Li ; Int p, i, j, k, n, nrhs, save, save2, csize, rank, nrow, ncol, is_ll, xtype, isreal, prefer_zomplex, Lxtype, xtype2, save3 ; int blas_ok = TRUE ; if (cm->print > 1) { printf ("============================================== in solve:\n") ; } if (A == NULL) { ERROR (CHOLMOD_INVALID, "nothing to solve") ; return (1) ; } /* ---------------------------------------------------------------------- */ /* construct right-hand-side (Ax=b if symmetric, AA'x=b otherwise) */ /* ---------------------------------------------------------------------- */ n = A->nrow ; nrow = A->nrow ; ncol = A->ncol ; xtype = A->xtype ; isreal = (xtype == CHOLMOD_REAL) ; B = rhs (A, NRHS, n) ; anorm = CHOLMOD(norm_sparse) (A, 1, cm) ; save = cm->final_asis ; cm->final_asis = TRUE ; /* contents of these will be revised later */ Bzomplex = CHOLMOD(copy_dense) (B, cm) ; Bcomplex = CHOLMOD(copy_dense) (Bzomplex, cm) ; Breal = CHOLMOD(copy_dense) (Bzomplex, cm) ; /* ---------------------------------------------------------------------- */ /* analyze */ /* ---------------------------------------------------------------------- */ if (n < 100 && cm->nmethods == 1 && cm->method[0].ordering == CHOLMOD_GIVEN) { Int *UserPerm = prand (nrow) ; /* RAND */ L = CHOLMOD(analyze_p) (A, UserPerm, NULL, 0, cm) ; OK (CHOLMOD(print_common) ("with UserPerm", cm)) ; CHOLMOD(free) (nrow, sizeof (Int), UserPerm, cm) ; } else { L = CHOLMOD(analyze) (A, cm) ; } /* test rowadd on a symbolic factor */ if (isreal) { RowK = CHOLMOD(spzeros) (n, 1, 0, CHOLMOD_REAL, cm) ; Lcopy = CHOLMOD(copy_factor) (L, cm) ; if (n > 0) { CHOLMOD(rowadd) (0, RowK, Lcopy, cm) ; CHOLMOD(check_factor) (Lcopy, cm) ; CHOLMOD(print_factor) (Lcopy, "Lcopy, now numeric", cm) ; } CHOLMOD(free_sparse) (&RowK, cm) ; CHOLMOD(free_factor) (&Lcopy, cm) ; } /* ---------------------------------------------------------------------- */ /* factorize */ /* ---------------------------------------------------------------------- */ CHOLMOD(factorize) (A, L, cm) ; /* ---------------------------------------------------------------------- */ /* various solves */ /* ---------------------------------------------------------------------- */ if (B != NULL) { /* B->ncol = 1 ; */ prefer_zomplex = (B->xtype == CHOLMOD_ZOMPLEX) ; } else { prefer_zomplex = FALSE ; } for (k = 0 ; k <= 1 ; k++) { cm->prefer_zomplex = k ; /* compute the residual, X complex if L or B not real */ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ; r = resid (A, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; /* zomplex right-hand-side */ CHOLMOD(dense_xtype) (CHOLMOD_ZOMPLEX, Bzomplex, cm) ; if (Bzomplex != NULL && B != NULL && B->xtype == CHOLMOD_REAL && Bzomplex->xtype == CHOLMOD_ZOMPLEX) { /* add an arbitrary imaginary part */ double *Bz = Bzomplex->z ; for (j = 0 ; j < NRHS ; j++) { for (i = 0 ; i < n ; i++) { Bz [i+j*n] = (double) (i+j*n) ; } } } X = CHOLMOD(solve) (CHOLMOD_A, L, Bzomplex, cm) ; r = resid (A, X, Bzomplex) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; /* complex right-hand-side */ CHOLMOD(dense_xtype) (CHOLMOD_COMPLEX, Bcomplex, cm) ; X = CHOLMOD(solve) (CHOLMOD_A, L, Bcomplex, cm) ; r = resid (A, X, Bcomplex) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; /* real right-hand-side */ CHOLMOD(dense_xtype) (CHOLMOD_REAL, Breal, cm) ; X = CHOLMOD(solve) (CHOLMOD_A, L, Breal, cm) ; r = resid (A, X, Breal) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; /* sparse solve of Ax=b, b real */ Bsparse = CHOLMOD(dense_to_sparse) (Breal, TRUE, cm) ; Xsparse = CHOLMOD(spsolve) (CHOLMOD_A, L, Bsparse, cm) ; r = resid_sparse (A, Xsparse, Bsparse) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_sparse) (&Bsparse, cm) ; CHOLMOD(free_sparse) (&Xsparse, cm) ; /* sparse solve of Ax=b, b complex */ Bsparse = CHOLMOD(dense_to_sparse) (Bcomplex, TRUE, cm) ; Xsparse = CHOLMOD(spsolve) (CHOLMOD_A, L, Bsparse, cm) ; r = resid_sparse (A, Xsparse, Bsparse) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_sparse) (&Bsparse, cm) ; CHOLMOD(free_sparse) (&Xsparse, cm) ; /* sparse solve of Ax=b, b zomplex */ Bsparse = CHOLMOD(dense_to_sparse) (Bzomplex, TRUE, cm) ; Xsparse = CHOLMOD(spsolve) (CHOLMOD_A, L, Bsparse, cm) ; r = resid_sparse (A, Xsparse, Bsparse) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_sparse) (&Bsparse, cm) ; CHOLMOD(free_sparse) (&Xsparse, cm) ; } cm->prefer_zomplex = FALSE ; /* ---------------------------------------------------------------------- */ /* sparse solve to compute inv(A) */ /* ---------------------------------------------------------------------- */ CHOLMOD(print_sparse) (A, "A", cm) ; CHOLMOD(print_factor) (L, "L", cm) ; rcond = CHOLMOD(rcond) (L, cm) ; if (cm->print > 1) { printf ("rcond: %g\n", rcond) ; } if (n < 100 && A->stype != 0) { /* solve A*C=I, so C should equal A inverse */ I = CHOLMOD(speye) (n, n, CHOLMOD_REAL, cm) ; C = CHOLMOD(spsolve) (CHOLMOD_A, L, I, cm) ; /* compute norm of A*C-I */ if (isreal && n > 10) { /* A and C are large and real */ E = CHOLMOD(ssmult) (A, C, 0, TRUE, FALSE, cm) ; F = CHOLMOD(add) (E, I, minusone, one, TRUE, FALSE, cm) ; r = CHOLMOD(norm_sparse) (F, 1, cm) ; CHOLMOD(free_sparse) (&E, cm) ; CHOLMOD(free_sparse) (&F, cm) ; } else { /* There is no complex ssmult or add, so use the BLAS. * Also test sparse_to_dense for small symmetric matrices. */ A3 = CHOLMOD(sparse_to_dense) (A, cm) ; C3 = CHOLMOD(sparse_to_dense) (C, cm) ; xtype2 = isreal ? CHOLMOD_REAL : CHOLMOD_COMPLEX ; CHOLMOD(dense_xtype) (xtype2, A3, cm) ; CHOLMOD(dense_xtype) (xtype2, C3, cm) ; E3 = CHOLMOD(eye) (n, n, xtype2, cm) ; if (A3 != NULL && C3 != NULL && E3 != NULL) { /* E3 = A3*C3-I */ if (isreal) { BLAS_dgemm ("N", "N", n, n, n, one, A3->x, n, C3->x, n, minusone, E3->x, n) ; } else { BLAS_zgemm ("N", "N", n, n, n, one, A3->x, n, C3->x, n, minusone, E3->x, n) ; } OK (blas_ok) ; } r = CHOLMOD(norm_dense) (E3, 1, cm) ; CHOLMOD(free_dense) (&A3, cm) ; CHOLMOD(free_dense) (&C3, cm) ; CHOLMOD(free_dense) (&E3, cm) ; } MAXERR (maxerr, r, 1) ; CHOLMOD(free_sparse) (&I, cm) ; CHOLMOD(free_sparse) (&C, cm) ; } /* ---------------------------------------------------------------------- */ /* change complexity of L and solve again; test copy/change routines */ /* ---------------------------------------------------------------------- */ /* change to complex, otherwise leave as */ Lcopy = CHOLMOD(copy_factor) (L, cm) ; CHOLMOD(factor_xtype) (CHOLMOD_COMPLEX, Lcopy, cm) ; X = CHOLMOD(solve) (CHOLMOD_A, Lcopy, B, cm) ; r = resid (A, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; CHOLMOD(free_factor) (&Lcopy, cm) ; /* change to zomplex LDL' */ Lxtype = (L == NULL) ? CHOLMOD_REAL : (L->xtype) ; Lcopy = CHOLMOD(copy_factor) (L, cm) ; CHOLMOD(check_factor) (L, cm) ; CHOLMOD(print_factor) (Lcopy, "Lcopy", cm) ; CHOLMOD(change_factor) (Lxtype, FALSE, FALSE, TRUE, TRUE, Lcopy, cm) ; CHOLMOD(factor_xtype) (CHOLMOD_ZOMPLEX, Lcopy, cm) ; X = CHOLMOD(solve) (CHOLMOD_A, Lcopy, B, cm) ; r = resid (A, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; CHOLMOD(free_factor) (&Lcopy, cm) ; Lcopy = CHOLMOD(copy_factor) (L, cm) ; CHOLMOD(change_factor) (Lxtype, TRUE, FALSE, FALSE, FALSE, Lcopy, cm) ; CHOLMOD(check_factor) (L, cm) ; CHOLMOD(print_factor) (Lcopy, "Lcopy LL unpacked", cm) ; CHOLMOD(free_factor) (&Lcopy, cm) ; CHOLMOD(free_factor) (&L, cm) ; cm->final_asis = save ; /* ---------------------------------------------------------------------- */ /* solve again, but use cm->final_asis as given */ /* ---------------------------------------------------------------------- */ if (n < 100 && cm->nmethods == 1 && cm->method[0].ordering == CHOLMOD_GIVEN) { Int *UserPerm = prand (nrow) ; /* RAND */ L = CHOLMOD(analyze_p) (A, UserPerm, NULL, 0, cm) ; CHOLMOD(free) (nrow, sizeof (Int), UserPerm, cm) ; } else { L = CHOLMOD(analyze) (A, cm) ; } CHOLMOD(print_factor) (L, "Lsymbolic", cm) ; CHOLMOD(factorize) (A, L, cm) ; /* turn off memory tests [ */ save3 = my_tries ; my_tries = -1 ; CHOLMOD(print_factor) (L, "Lnumeric for solver tests", cm) ; CHOLMOD(print_dense) (B, "B for solver tests", cm) ; CHOLMOD(print_dense) (Breal, "Breal for solver tests", cm) ; CHOLMOD(print_dense) (Bcomplex, "Bcomplex for solver tests", cm) ; CHOLMOD(print_dense) (Bzomplex, "Bzomplex for solver tests", cm) ; if (B != NULL && Breal != NULL && Bcomplex != NULL && Bzomplex != NULL) { for (nrhs = 1 ; nrhs <= NRHS ; nrhs++) { for (cm->prefer_zomplex = 0 ; cm->prefer_zomplex <= 1 ; cm->prefer_zomplex++) { B->ncol = nrhs ; Breal->ncol = nrhs ; Bcomplex->ncol = nrhs ; Bzomplex->ncol = nrhs ; X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ; r = resid (A, X, B) ; CHOLMOD(free_dense) (&X, cm) ; MAXERR (maxerr, r, 1) ; X = CHOLMOD(solve) (CHOLMOD_A, L, Breal, cm) ; r = resid (A, X, Breal) ; CHOLMOD(free_dense) (&X, cm) ; MAXERR (maxerr, r, 1) ; X = CHOLMOD(solve) (CHOLMOD_A, L, Bcomplex, cm) ; r = resid (A, X, Bcomplex) ; CHOLMOD(free_dense) (&X, cm) ; MAXERR (maxerr, r, 1) ; X = CHOLMOD(solve) (CHOLMOD_A, L, Bzomplex, cm) ; r = resid (A, X, Bzomplex) ; CHOLMOD(free_dense) (&X, cm) ; MAXERR (maxerr, r, 1) ; } } } cm->prefer_zomplex = FALSE ; /* turn memory tests back on, where we left off ] */ my_tries = save3 ; Lcopy = CHOLMOD(copy_factor) (L, cm) ; /* ---------------------------------------------------------------------- */ /* convert L to LDL' packed or LL packed */ /* ---------------------------------------------------------------------- */ printf ("before change factor : %d\n", L ? L->is_super : -1) ; is_ll = (L == NULL) ? FALSE : (L->is_ll) ; Lxtype = (L == NULL) ? CHOLMOD_REAL : (L->xtype) ; CHOLMOD(change_factor) (Lxtype, is_ll, FALSE, TRUE, TRUE, Lcopy, cm) ; printf ("after change factor : %d\n", L ? L->is_super : -1) ; /* ---------------------------------------------------------------------- */ /* extract L, D, and L' as matrices from Lcopy */ /* ---------------------------------------------------------------------- */ CHOLMOD(resymbol) (A, NULL, 0, TRUE, Lcopy, cm) ; Lmat = CHOLMOD(factor_to_sparse) (Lcopy, cm) ; CHOLMOD(check_sparse) (Lmat, cm) ; I = CHOLMOD(speye) (n, n, CHOLMOD_REAL, cm) ; Lo = NULL ; D = NULL ; Lxtype = (Lmat == NULL) ? CHOLMOD_REAL : (Lmat->xtype) ; if (isreal) { /* use band and add */ if (!is_ll) { /* factorization is LDL' = Lo*D*Up */ Lo1 = CHOLMOD(band) (Lmat, -n, -1, 1, cm) ; Lo = CHOLMOD(add) (Lo1, I, one, one, TRUE, TRUE, cm) ; CHOLMOD(free_sparse) (&Lo1, cm) ; D = CHOLMOD(band) (Lmat, 0, 0, 1, cm) ; } else { /* factorization is LL' = Lo*D*Up */ Lo = CHOLMOD(band) (Lmat, -n, 0, 1, cm) ; D = CHOLMOD(speye) (n, n, Lxtype, cm) ; } } else { /* band and add do not work for c/zomplex matrices*/ D = CHOLMOD(speye) (n, n, Lxtype, cm) ; Lo = CHOLMOD(copy_sparse) (Lmat, cm) ; if (!is_ll && D != NULL && Lo != NULL) { /* factorization is LDL' = Lo*D*Up */ double *Dx = D->x ; double *Lx = Lo->x ; Lp = Lo->p ; for (k = 0 ; k < n ; k++) { p = Lp [k] ; if (Lxtype == CHOLMOD_COMPLEX) { Dx [2*k] = Lx [2*p] ; Lx [2*p] = 1 ; } else { Dx [k] = Lx [p] ; Lx [p] = 1 ; } } } } Up = CHOLMOD(transpose) (Lo, 2, cm) ; /* ---------------------------------------------------------------------- */ /* compute 1-norm of (Lo*D*Up - PAP') or (Lo*D*Up - PAA'P') */ /* ---------------------------------------------------------------------- */ P = (L != NULL) ? (L->Perm) : NULL ; S = NULL ; G = NULL ; if (isreal) { if (A->stype == 0) { /* G = A*A', try with fset = prand (ncol) */ fset = prand (ncol) ; /* RAND */ AFt = CHOLMOD(ptranspose) (A, 1, NULL, fset, ncol, cm) ; AF = CHOLMOD(transpose) (AFt, 1, cm) ; CHOLMOD(free) (ncol, sizeof (Int), fset, cm) ; G = CHOLMOD(ssmult) (AF, AFt, 0, TRUE, TRUE, cm) ; /* also try aat */ H = CHOLMOD(aat) (AF, NULL, 0, 1, cm) ; E = CHOLMOD(add) (G, H, one, minusone, TRUE, FALSE, cm) ; enorm = CHOLMOD(norm_sparse) (E, 0, cm) ; gnorm = CHOLMOD(norm_sparse) (G, 0, cm) ; MAXERR (maxerr, enorm, gnorm) ; if (cm->print > 1) { printf ("enorm %g gnorm %g hnorm %g\n", enorm, gnorm, CHOLMOD(norm_sparse) (H, 0, cm)) ; } if (gnorm > 0) { enorm /= gnorm ; } OK (enorm < 1e-8) ; CHOLMOD(free_sparse) (&AFt, cm) ; CHOLMOD(free_sparse) (&AF, cm) ; CHOLMOD(free_sparse) (&E, cm) ; CHOLMOD(free_sparse) (&H, cm) ; } else { /* G = A */ G = CHOLMOD(copy) (A, 0, 1, cm) ; } if (A->stype == 0) { /* S = PAA'P' */ S = CHOLMOD(submatrix) (G, P, n, P, n, TRUE, FALSE, cm) ; } else { /* S = PAP' */ Aboth = CHOLMOD(copy) (A, 0, 1, cm) ; S = CHOLMOD(submatrix) (Aboth, P, n, P, n, TRUE, FALSE, cm) ; CHOLMOD(free_sparse) (&Aboth, cm) ; } if (n < NSMALL) { /* only do this for small test matrices, since L*D*L' can have many * nonzero entries */ /* E = L*D*L' - S */ LD = CHOLMOD(ssmult) (Lo, D, 0, TRUE, FALSE, cm) ; LDL = CHOLMOD(ssmult) (LD, Up, 0, TRUE, FALSE, cm) ; CHOLMOD(free_sparse) (&LD, cm) ; E = CHOLMOD(add) (LDL, S, one, minusone, TRUE, FALSE, cm) ; CHOLMOD(free_sparse) (&LDL, cm) ; /* e = norm (E) / norm (S) */ enorm = CHOLMOD(norm_sparse) (E, 1, cm) ; snorm = CHOLMOD(norm_sparse) (S, 0, cm) ; MAXERR (maxerr, enorm, snorm) ; CHOLMOD(free_sparse) (&E, cm) ; } /* check the row/col counts */ RowCount = CHOLMOD(malloc) (n, sizeof (Int), cm) ; ColCount = CHOLMOD(malloc) (n, sizeof (Int), cm) ; Parent = CHOLMOD(malloc) (n, sizeof (Int), cm) ; Post = CHOLMOD(malloc) (n, sizeof (Int), cm) ; First = CHOLMOD(malloc) (n, sizeof (Int), cm) ; Level = CHOLMOD(malloc) (n, sizeof (Int), cm) ; rcount = CHOLMOD(calloc) (n, sizeof (Int), cm) ; ccount = CHOLMOD(calloc) (n, sizeof (Int), cm) ; if (S != NULL && Lmat != NULL && RowCount != NULL && ColCount != NULL && Parent != NULL && Post != NULL && First != NULL && Level != NULL && rcount != NULL && ccount != NULL) { S->stype = 1 ; CHOLMOD(etree) (S, Parent, cm) ; CHOLMOD(print_parent) (Parent, n, "Parent", cm) ; CHOLMOD(postorder) (Parent, n, NULL, Post, cm) ; CHOLMOD(print_perm) (Post, n, n, "Post", cm) ; S->stype = -1 ; CHOLMOD(rowcolcounts) (S, NULL, 0, Parent, Post, RowCount, ColCount, First, Level, cm) ; Lp = Lmat->p ; Li = Lmat->i ; OK (Lmat->packed) ; for (j = 0 ; j < n ; j++) { for (p = Lp [j] ; p < Lp [j+1] ; p++) { i = Li [p] ; rcount [i]++ ; ccount [j]++ ; } } /* a singular matrix will only be partially factorized */ if (L->minor == (size_t) n) { for (j = 0 ; j < n ; j++) { OK (ccount [j] == ColCount [j]) ; } } for (i = 0 ; i < (Int) (L->minor) ; i++) { OK (rcount [i] == RowCount [i]) ; } } CHOLMOD(free) (n, sizeof (Int), RowCount, cm) ; CHOLMOD(free) (n, sizeof (Int), ColCount, cm) ; CHOLMOD(free) (n, sizeof (Int), Parent, cm) ; CHOLMOD(free) (n, sizeof (Int), Post, cm) ; CHOLMOD(free) (n, sizeof (Int), First, cm) ; CHOLMOD(free) (n, sizeof (Int), Level, cm) ; CHOLMOD(free) (n, sizeof (Int), rcount, cm) ; CHOLMOD(free) (n, sizeof (Int), ccount, cm) ; CHOLMOD(free_sparse) (&S, cm) ; } CHOLMOD(free_factor) (&Lcopy, cm) ; /* ---------------------------------------------------------------------- */ /* solve other systems */ /* ---------------------------------------------------------------------- */ /* turn off memory tests [ */ save3 = my_tries ; my_tries = -1 ; for (nrhs = 1 ; nrhs <= 4 ; nrhs++) /* reduced here (6 to 4) */ { if (B == NULL) { break ; } B->ncol = nrhs ; /* solve LDL'x=b */ X = CHOLMOD(solve) (CHOLMOD_LDLt, L, B, cm) ; /* printf ("LDL'x=b %p %p %p\n", Lo, X, B) ; */ r = resid3 (Lo, D, Up, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; /* solve LDx=b */ X = CHOLMOD(solve) (CHOLMOD_LD, L, B, cm) ; /* printf ("LDx=b %p %p %p\n", Lo, X, B) ; */ r = resid3 (Lo, D, NULL, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; /* solve DL'x=b */ X = CHOLMOD(solve) (CHOLMOD_DLt, L, B, cm) ; /* printf ("DL'x=b %p %p %p\n", D, X, B) ; */ r = resid3 (D, Up, NULL, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; /* solve Lx=b */ X = CHOLMOD(solve) (CHOLMOD_L, L, B, cm) ; /* printf ("Lx=b %p %p %p\n", Lo, X, B) ; */ r = resid3 (Lo, NULL, NULL, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; /* solve L'x=b */ X = CHOLMOD(solve) (CHOLMOD_Lt, L, B, cm) ; /* printf ("L'x=b %p %p %p\n", Up, X, B) ; */ r = resid3 (Up, NULL, NULL, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; /* solve Dx=b */ X = CHOLMOD(solve) (CHOLMOD_D, L, B, cm) ; /* printf ("Dx=b %p %p %p\n", D, X, B) ; */ r = resid3 (D, NULL, NULL, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; save2 = cm->prefer_zomplex ; for (k = 0 ; k <= 1 ; k++) { cm->prefer_zomplex = k ; /* x=Pb */ X = CHOLMOD(solve) (CHOLMOD_P, L, B, cm) ; r = pnorm (X, P, B, FALSE) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; /* x=P'b */ X = CHOLMOD(solve) (CHOLMOD_Pt, L, B, cm) ; r = pnorm (X, P, B, TRUE) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; } cm->prefer_zomplex = save2 ; } /* turn memory tests back on, where we left off ] */ my_tries = save3 ; CHOLMOD(free_dense) (&B, cm) ; CHOLMOD(free_sparse) (&I, cm) ; CHOLMOD(free_sparse) (&D, cm) ; CHOLMOD(free_sparse) (&Lo, cm) ; CHOLMOD(free_sparse) (&Up, cm) ; CHOLMOD(free_sparse) (&Lmat, cm) ; /* ---------------------------------------------------------------------- */ /* update the factorization */ /* ---------------------------------------------------------------------- */ /* turn off memory tests [ */ save3 = my_tries ; my_tries = -1 ; B = rhs (A, 1, n) ; for (rank = 1 ; isreal && rank <= ((n < 100) ? 33 : 2) ; rank++) { /* pick a random C */ Cdense = CHOLMOD(zeros) (n, rank, CHOLMOD_REAL, cm) ; if (Cdense != NULL) { Cx = Cdense->x ; for (k = 0 ; k < 10*rank ; k++) { i = nrand (n) ; /* RAND */ j = nrand (rank) ; /* RAND */ Cx [i+j*n] += xrand (1.) ; /* RAND */ } } C = CHOLMOD(dense_to_sparse) (Cdense, TRUE, cm) ; CHOLMOD(free_dense) (&Cdense, cm) ; /* permute the rows according to L->Perm */ Cperm = CHOLMOD(submatrix) (C, P, n, NULL, -1, TRUE, TRUE, cm) ; /* update */ CHOLMOD(updown) (TRUE, Cperm, L, cm) ; CHOLMOD(free_sparse) (&Cperm, cm) ; /* solve (G+C*C')x=b */ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ; /* an alternative method would be to compute (G*x + C*(C'*x) - b) */ /* compute S = G+C*C', with no sort */ Ct = CHOLMOD(transpose) (C, 1, cm) ; CC = CHOLMOD(ssmult) (C, Ct, 0, TRUE, FALSE, cm) ; S = CHOLMOD(add) (G, CC, one, one, TRUE, TRUE, cm) ; Ssym = CHOLMOD(copy) (S, 1, 1, cm) ; CHOLMOD(free_sparse) (&CC, cm) ; CHOLMOD(free_sparse) (&Ct, cm) ; /* compute norm (S*x-b) */ r = resid (Ssym, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; /* ------------------------------------------------------------------ */ /* factor A+CC' from scratch, using same permutation */ /* ------------------------------------------------------------------ */ if (rank == 1) { save = cm->nmethods ; save2 = cm->method [0].ordering ; cm->nmethods = 1 ; cm->method [0].ordering = CHOLMOD_GIVEN ; L2 = CHOLMOD(analyze_p) (Ssym, P, NULL, 0, cm) ; cm->nmethods = save ; cm->method [0].ordering = save2 ; CHOLMOD(factorize) (Ssym, L2, cm) ; X = CHOLMOD(solve) (CHOLMOD_A, L2, B, cm) ; r = resid (Ssym, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; CHOLMOD(free_factor) (&L2, cm) ; } CHOLMOD(free_sparse) (&Ssym, cm) ; /* ------------------------------------------------------------------ */ /* downdate, with just the first half of C */ /* ------------------------------------------------------------------ */ csize = MAX (1, rank / 2) ; cset = CHOLMOD(malloc) (csize, sizeof (Int), cm) ; if (cset != NULL) { for (i = 0 ; i < csize ; i++) { cset [i] = i ; } } C2 = CHOLMOD(submatrix) (C, NULL, -1, cset, csize, TRUE, TRUE, cm) ; Cperm = CHOLMOD(submatrix) (C2, P, n, NULL, -1, TRUE, TRUE, cm) ; CHOLMOD(free) (csize, sizeof (Int), cset, cm) ; CHOLMOD(updown) (FALSE, Cperm, L, cm) ; CHOLMOD(free_sparse) (&Cperm, cm) ; /* solve (G+C*C'-C2*C2')x=b */ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ; /* This is an expensive way to compute the residual. A better * method would be to compute (G*x + C*(C'*x) - C2*(C2'*x) - b), * using sdmult. It is done just to test the ssmult * routine. */ /* compute S2 = G+C*C'-C2*C2', with no sort */ Ct = CHOLMOD(transpose) (C2, 1, cm) ; CC = CHOLMOD(ssmult) (C2, Ct, 0, TRUE, FALSE, cm) ; S2 = CHOLMOD(add) (S, CC, one, minusone, TRUE, FALSE, cm) ; CHOLMOD(free_sparse) (&CC, cm) ; CHOLMOD(free_sparse) (&Ct, cm) ; CHOLMOD(free_sparse) (&C2, cm) ; /* Ssym is a symmetric/upper copy of S2 */ Ssym = CHOLMOD(copy) (S2, 1, 1, cm) ; CHOLMOD(free_sparse) (&S2, cm) ; /* compute norm (S2*x-b) */ r = resid (Ssym, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; /* ------------------------------------------------------------------ */ /* factor S2 scratch, using same permutation */ /* ------------------------------------------------------------------ */ if (rank == 1) { save = cm->nmethods ; save2 = cm->method [0].ordering ; cm->nmethods = 1 ; cm->method [0].ordering = CHOLMOD_GIVEN ; L2 = CHOLMOD(analyze_p) (Ssym, P, NULL, 0, cm) ; cm->nmethods = save ; cm->method [0].ordering = save2 ; CHOLMOD(factorize) (Ssym, L2, cm) ; X = CHOLMOD(solve) (CHOLMOD_A, L2, B, cm) ; r = resid (Ssym, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; CHOLMOD(free_factor) (&L2, cm) ; } /* ------------------------------------------------------------------ */ /* re-do the symbolic factorization on L */ /* ------------------------------------------------------------------ */ CHOLMOD(resymbol) (Ssym, NULL, 0, TRUE, L, cm) ; /* solve (G+C*C'-C2*C2')x=b again */ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ; /* compute norm (S2*x-b) */ r = resid (Ssym, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; CHOLMOD(free_sparse) (&Ssym, cm) ; /* ------------------------------------------------------------------ */ /* downdate, with the remaining part of C, to get original L */ /* ------------------------------------------------------------------ */ if (rank > csize) { cset = CHOLMOD(malloc) (rank-csize, sizeof (Int), cm) ; if (cset != NULL) { for (i = csize ; i < rank ; i++) { cset [i-csize] = i ; } } if (rank - csize == 4) { /* test the subset print/check routine */ CHOLMOD(print_subset) (cset, rank-csize, rank, "cset", cm) ; } C2 = CHOLMOD(submatrix) (C, NULL, -1, cset, rank-csize, TRUE, TRUE, cm) ; Cperm = CHOLMOD(submatrix) (C2, P, n, NULL, -1, TRUE, TRUE, cm) ; CHOLMOD(free) (rank-csize, sizeof (Int), cset, cm) ; CHOLMOD(updown) (FALSE, Cperm, L, cm) ; CHOLMOD(free_sparse) (&Cperm, cm) ; CHOLMOD(free_sparse) (&C2, cm) ; /* solve the original system */ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ; /* compute the residual */ r = resid (A, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; } CHOLMOD(free_sparse) (&C, cm) ; CHOLMOD(free_sparse) (&S, cm) ; } /* turn memory tests back on, where we left off ] */ my_tries = save3 ; CHOLMOD(free_dense) (&B, cm) ; CHOLMOD(free_sparse) (&G, cm) ; CHOLMOD(free_factor) (&L, cm) ; /* ---------------------------------------------------------------------- */ /* factor again, then change the factor type many times */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(copy_sparse) (A, cm) ; if (C != NULL) { C->sorted = FALSE ; } L = CHOLMOD(analyze) (C, cm) ; CHOLMOD(factorize) (C, L, cm) ; if (L != NULL && !(L->is_super)) { CHOLMOD(resymbol) (C, NULL, 0, TRUE, L, cm) ; } B = rhs (C, 1, n) ; cm->prefer_zomplex = prefer_zomplex ; X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ; cm->prefer_zomplex = FALSE ; r = resid (C, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; for (k = 0 ; k < NFTYPES ; k++) { if (co_types [k] && n > 1) { /* reallocate column zero of L, to make it non-monotonic */ CHOLMOD(reallocate_column) (0, n, L, cm) ; } Lxtype = (L == NULL) ? CHOLMOD_REAL : (L->xtype) ; CHOLMOD(change_factor) (Lxtype, ll_types [k], FALSE, pk_types [k], mn_types [k], L, cm) ; cm->prefer_zomplex = prefer_zomplex ; X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ; cm->prefer_zomplex = FALSE ; r = resid (C, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; } /* reallocate a column and solve again */ if (n > 3) { CHOLMOD(change_factor) (CHOLMOD_REAL, FALSE, FALSE, TRUE, TRUE, L, cm) ; CHOLMOD(reallocate_column) (0, n, L, cm) ; cm->prefer_zomplex = prefer_zomplex ; X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ; cm->prefer_zomplex = FALSE ; r = resid (C, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; } CHOLMOD(free_sparse) (&C, cm) ; CHOLMOD(free_factor) (&L, cm) ; CHOLMOD(free_dense) (&B, cm) ; CHOLMOD(free_dense) (&Breal, cm) ; CHOLMOD(free_dense) (&Bcomplex, cm) ; CHOLMOD(free_dense) (&Bzomplex, cm) ; /* ---------------------------------------------------------------------- */ /* factorize and solve (A*A'+beta*I)x=b or A'x=b */ /* ---------------------------------------------------------------------- */ if (A->stype == 0) { double *Rx, *Rz, *Xx, *Xz ; double beta [2] ; beta [0] = 3.14159 ; beta [1] = 0 ; L = CHOLMOD(analyze) (A, cm) ; CHOLMOD(factorize_p) (A, beta, NULL, 0, L, cm) ; B = rhs (A, 1, n) ; cm->prefer_zomplex = prefer_zomplex ; X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ; cm->prefer_zomplex = FALSE ; /* compute the residual */ /* W = A'*X */ W = CHOLMOD(zeros) (ncol, 1, xtype, cm) ; CHOLMOD(sdmult) (A, 2, one, zero, X, W, cm) ; /* R = B */ R = CHOLMOD(copy_dense) (B, cm) ; /* R = A*W - R */ CHOLMOD(sdmult) (A, 0, one, minusone, W, R, cm) ; /* R = R + beta*X */ if (R != NULL && X != NULL) { Rx = R->x ; Rz = R->z ; Xx = X->x ; Xz = X->z ; for (i = 0 ; i < nrow ; i++) { switch (xtype) { case CHOLMOD_REAL: Rx [i] += beta [0] * Xx [i] ; break ; case CHOLMOD_COMPLEX: Rx [2*i ] += beta [0] * Xx [2*i ] ; Rx [2*i+1] += beta [0] * Xx [2*i+1] ; break ; case CHOLMOD_ZOMPLEX: Rx [i] += beta [0] * Xx [i] ; Rz [i] += beta [0] * Xz [i] ; break ; } } } r = CHOLMOD(norm_dense) (R, 2, cm) ; bnorm = CHOLMOD(norm_dense) (B, 2, cm) ; xnorm = CHOLMOD(norm_dense) (X, 2, cm) ; norm = MAX (r, xnorm) ; if (norm > 0) { r /= norm ; } MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; CHOLMOD(free_dense) (&R, cm) ; CHOLMOD(free_dense) (&W, cm) ; CHOLMOD(free_factor) (&L, cm) ; CHOLMOD(free_dense) (&B, cm) ; } /* ---------------------------------------------------------------------- */ /* test rowdel and updown */ /* ---------------------------------------------------------------------- */ if (isreal && A->stype == 1 && n > 0 && n < NLARGE) { Int save4, save5, save6 ; save4 = cm->nmethods ; save5 = cm->method [0].ordering ; save6 = cm->supernodal ; cm->nmethods = 1 ; cm->method [0].ordering = CHOLMOD_NATURAL ; cm->supernodal = CHOLMOD_SUPERNODAL ; B = rhs (A, 1, n) ; L = CHOLMOD(analyze) (A, cm) ; CHOLMOD(factorize) (A, L, cm) ; /* solve Ax=b */ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ; r = resid (A, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; /* determine the new system with row/column k missing */ k = n/2 ; S = CHOLMOD(copy) (A, 0, 1, cm) ; RowK = CHOLMOD(submatrix) (S, NULL, -1, &k, 1, TRUE, TRUE, cm) ; CHOLMOD(print_sparse) (S, "S", cm) ; CHOLMOD(print_sparse) (RowK, "RowK of S", cm) ; CHOLMOD(free_sparse) (&RowK, cm) ; prune_row (S, k) ; if (S != NULL) { S->stype = 1 ; } /* delete row k of L (converts to LDL') */ /* printf ("rowdel here:\n") ; */ CHOLMOD(rowdel) (k, NULL, L, cm) ; CHOLMOD(resymbol) (S, NULL, 0, TRUE, L, cm) ; /* solve with row k missing */ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ; r = resid (S, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; CHOLMOD(free_sparse) (&S, cm) ; /* factorize again */ CHOLMOD(free_factor) (&L, cm) ; L = CHOLMOD(analyze) (A, cm) ; CHOLMOD(factorize) (A, L, cm) ; /* rank-3 update (converts to LDL') and solve */ C = CHOLMOD(speye) (n, 3, CHOLMOD_REAL, cm) ; CC = CHOLMOD(aat) (C, NULL, 0, 1, cm) ; S = CHOLMOD(add) (A, CC, one, one, TRUE, TRUE, cm) ; if (S != NULL) { S->stype = 1 ; } CHOLMOD(updown) (TRUE, C, L, cm) ; X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ; r = resid (S, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; /* free everything */ CHOLMOD(free_sparse) (&S, cm) ; CHOLMOD(free_sparse) (&CC, cm) ; CHOLMOD(free_sparse) (&C, cm) ; CHOLMOD(free_sparse) (&S, cm) ; CHOLMOD(free_factor) (&L, cm) ; CHOLMOD(free_dense) (&B, cm) ; cm->nmethods = save4 ; cm->method [0].ordering = save5 ; cm->supernodal = save6 ; } /* ---------------------------------------------------------------------- */ /* free remaining workspace */ /* ---------------------------------------------------------------------- */ OK (CHOLMOD(print_common) ("cm", cm)) ; progress (0, '.') ; return (maxerr) ; } SuiteSparse/CHOLMOD/Tcov/covall0000755001170100242450000000015510533542223015155 0ustar davisfac#!/bin/csh ./gcovs z*.c l_*c ./covs > covs.out echo -n "statments not yet tested: " grep -c "#####" covs.out SuiteSparse/CHOLMOD/Tcov/raw_factor.c0000644001170100242450000005607610540000065016246 0ustar davisfac/* ========================================================================== */ /* === Tcov/raw_factor ====================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Factorize A using cholmod_rowfac for the simplicial case, and the * cholmod_super_* routines for the supernodal case, and test the solution to * linear systems. */ #include "cm.h" /* ========================================================================== */ /* === icomp ================================================================ */ /* ========================================================================== */ /* for sorting by qsort */ static int icomp (Int *i, Int *j) { if (*i < *j) { return (-1) ; } else { return (1) ; } } /* ========================================================================== */ /* === add_gunk ============================================================= */ /* ========================================================================== */ static cholmod_sparse *add_gunk (cholmod_sparse *A) { cholmod_sparse *S ; double *Sx, *Sz ; Int *Sp, *Si, nz, p, save3, j, n ; if (A == NULL) return (NULL) ; /* save3 = cm->print ; cm->print = 5 ; */ A->nzmax++ ; S = CHOLMOD(copy_sparse) (A, cm) ; A->nzmax-- ; /* add a S(n,1)=1 entry to the matrix */ if (S != NULL) { S->sorted = FALSE ; Sx = S->x ; Si = S->i ; Sp = S->p ; Sz = S->z ; n = S->ncol ; nz = Sp [n] ; for (j = 1 ; j <= n ; j++) { Sp [j]++ ; } if (S->xtype == CHOLMOD_REAL) { for (p = nz-1 ; p >= 0 ; p--) { Si [p+1] = Si [p] ; Sx [p+1] = Sx [p] ; } Si [0] = n-1 ; Sx [0] = 99999 ; } else if (S->xtype == CHOLMOD_COMPLEX) { for (p = nz-1 ; p >= 0 ; p--) { Si [p+1] = Si [p] ; Sx [2*p+2] = Sx [2*p] ; Sx [2*p+3] = Sx [2*p+1] ; } Si [0] = n-1 ; Sx [0] = 99999 ; Sx [1] = 0 ; } else if (S->xtype == CHOLMOD_ZOMPLEX) { for (p = nz-1 ; p >= 0 ; p--) { Si [p+1] = Si [p] ; Sx [p+1] = Sx [p] ; Sz [p+1] = Sz [p] ; } Si [0] = n-1 ; Sx [0] = 99999 ; Sz [0] = 0 ; } } /* CHOLMOD(print_sparse) (A, "A for gunk", cm) ; */ /* CHOLMOD(print_sparse) (S, "S with gunk", cm) ; */ /* cm->print = save3 ; */ return (S) ; } /* ========================================================================== */ /* === raw_factor =========================================================== */ /* ========================================================================== */ /* Factor A, without using any fill-reducing permutation. This may fail due * to catastrophic fill-in (which is the desired test result for a large * arrowhead matrix). */ double raw_factor (cholmod_sparse *A, Int check_errors) { double maxerr = 0, r, anorm ; cholmod_sparse *AT, *C, *LT, *Lsparse, *S, *ST, *R, *A1 ; cholmod_factor *L, *Lcopy ; cholmod_dense *X, *W, *B, *X2 ; Int i, k, n, ok, ok1, ok2, trial, rnz, lnz, Lxtype, Axtype, posdef, prefer_zomplex, Bxtype ; Int *Parent, *Post, *First, *Level, *Ri, *Rp, *LTp = NULL, *LTi = NULL, *P, *mask, *RLinkUp ; UF_long lr ; double beta [2] ; unsigned UF_long save ; /* ---------------------------------------------------------------------- */ /* create the problem */ /* ---------------------------------------------------------------------- */ if (A == NULL || A->stype != 1) { return (0) ; } W = NULL ; X2 = NULL ; L = NULL ; n = A->nrow ; B = rhs (A, 1, n) ; AT = CHOLMOD(transpose) (A, 2, cm) ; Parent = CHOLMOD(malloc) (n, sizeof (Int), cm) ; Post = CHOLMOD(malloc) (n, sizeof (Int), cm) ; First = CHOLMOD(malloc) (n, sizeof (Int), cm) ; Level = CHOLMOD(malloc) (n, sizeof (Int), cm) ; beta [0] = 0 ; beta [1] = 0 ; anorm = CHOLMOD(norm_sparse) (A, 1, cm) ; prefer_zomplex = (A->xtype == CHOLMOD_ZOMPLEX) ; Bxtype = A->xtype ; /* ---------------------------------------------------------------------- */ /* supernodal factorization */ /* ---------------------------------------------------------------------- */ L = CHOLMOD(allocate_factor) (n, cm) ; ok1 = CHOLMOD(etree) (A, Parent, cm) ; lr = CHOLMOD(postorder) (Parent, n, NULL, Post, cm) ; ok2 = CHOLMOD(rowcolcounts) (AT, NULL, 0, Parent, Post, NULL, (L != NULL) ? (L->ColCount) : NULL, First, Level, cm) ; if (ok2) { printf ("raw_factor: cm->fl %g cm->lnz %g\n", cm->fl, cm->lnz) ; } if (check_errors) { OKP (AT) ; OKP (Parent) ; OKP (Post) ; OKP (First) ; OKP (Level) ; OK (AT->stype == -1) ; OKP (L) ; OK (ok1) ; OK (ok2) ; OK (lr >= 0) ; /* rowcolcounts requires A in symmetric lower form */ ok = CHOLMOD(rowcolcounts) (A, NULL, 0, Parent, Post, NULL, L->ColCount, First, Level, cm) ; NOT (ok) ; } /* super_symbolic needs A in upper form, so this will succeed * unless the problem is huge */ ok = CHOLMOD(super_symbolic) (A, NULL, Parent, L, cm) ; /* super_symbolic should fail if lnz is too large */ if (cm->lnz > Size_max / 2) { printf ("raw_factor: problem is huge\n") ; NOT (ok) ; OK (L->xtype == CHOLMOD_PATTERN && !(L->is_super)) ; /* try changing to LDL packed, which should also fail */ ok = CHOLMOD(change_factor) (CHOLMOD_REAL, FALSE, FALSE, TRUE, TRUE, L, cm) ; NOT (ok) ; CHOLMOD(free_factor) (&L, cm) ; CHOLMOD(free_sparse) (&AT, cm) ; CHOLMOD(free_dense) (&B, cm) ; CHOLMOD(free) (n, sizeof (Int), First, cm) ; CHOLMOD(free) (n, sizeof (Int), Level, cm) ; CHOLMOD(free) (n, sizeof (Int), Parent, cm) ; CHOLMOD(free) (n, sizeof (Int), Post, cm) ; return (0) ; } if (check_errors) { if (cm->status == CHOLMOD_OUT_OF_MEMORY || cm->status == CHOLMOD_TOO_LARGE) { /* no test case will reach here, but check just to be safe */ printf ("raw_factor: out of memory for symbolic case %d\n", cm->status) ; CHOLMOD(free_factor) (&L, cm) ; CHOLMOD(free_sparse) (&AT, cm) ; CHOLMOD(free_dense) (&B, cm) ; CHOLMOD(free) (n, sizeof (Int), First, cm) ; CHOLMOD(free) (n, sizeof (Int), Level, cm) ; CHOLMOD(free) (n, sizeof (Int), Parent, cm) ; CHOLMOD(free) (n, sizeof (Int), Post, cm) ; return (0) ; } OK (ok) ; ok = CHOLMOD(super_symbolic)(A, NULL, Parent, L, cm) ; NOT (ok) ; ok = CHOLMOD(super_symbolic)(AT, NULL, Parent, L, cm) ; NOT (ok) ; ok = CHOLMOD(super_symbolic)(NULL, NULL, Parent, L, cm) ; NOT (ok) ; ok = CHOLMOD(super_symbolic)(A, NULL, NULL, L, cm) ; NOT (ok) ; ok = CHOLMOD(super_symbolic)(A, NULL, Parent, NULL, cm) ; NOT (ok) ; } /* super_numeric needs A in lower form, so this will succeed unless * the problem is huge */ ok = CHOLMOD(super_numeric) (AT, NULL, Zero, L, cm) ; if (check_errors) { if (cm->status == CHOLMOD_OUT_OF_MEMORY) { /* For the 64-bit case, the Matrix/a1 problem will reach here */ printf ("raw_factor: out of memory for numeric case\n") ; CHOLMOD(free_factor) (&L, cm) ; CHOLMOD(free_sparse) (&AT, cm) ; CHOLMOD(free_dense) (&B, cm) ; CHOLMOD(free) (n, sizeof (Int), First, cm) ; CHOLMOD(free) (n, sizeof (Int), Level, cm) ; CHOLMOD(free) (n, sizeof (Int), Parent, cm) ; CHOLMOD(free) (n, sizeof (Int), Post, cm) ; return (0) ; } OK (ok) ; ok = CHOLMOD(super_numeric)(A, NULL, Zero, L, cm) ; NOT (ok) ; ok = CHOLMOD(super_numeric)(NULL, NULL, Zero, L, cm) ; NOT (ok) ; ok = CHOLMOD(super_numeric)(AT, NULL, Zero, NULL, cm) ; NOT (ok) ; } /* solve */ Lxtype = (L == NULL) ? CHOLMOD_REAL : L->xtype ; W = CHOLMOD(zeros) (n, 1, Lxtype, cm) ; X = CHOLMOD(copy_dense) (B, cm) ; if (Bxtype == CHOLMOD_ZOMPLEX) { CHOLMOD(dense_xtype) (CHOLMOD_COMPLEX, X, cm) ; } CHOLMOD(print_factor) (L, "L for super l/ltsolve", cm) ; CHOLMOD(print_dense) (W, "W", cm) ; CHOLMOD(print_dense) (X, "X", cm) ; ok1 = CHOLMOD(super_lsolve) (L, X, W, cm) ; CHOLMOD(print_dense) (X, "X", cm) ; ok2 = CHOLMOD(super_ltsolve) (L, X, W, cm) ; CHOLMOD(print_dense) (X, "X", cm) ; if (Bxtype == CHOLMOD_ZOMPLEX) { CHOLMOD(dense_xtype) (CHOLMOD_ZOMPLEX, X, cm) ; } r = resid (A, X, B) ; MAXERR (maxerr, r, 1) ; if (Bxtype == CHOLMOD_ZOMPLEX) { CHOLMOD(dense_xtype) (CHOLMOD_COMPLEX, X, cm) ; } if (check_errors) { OKP (W) ; OKP (X) ; OK (ok1) ; OK (ok2) ; ok = CHOLMOD(super_lsolve) (NULL, X, W, cm) ; NOT (ok) ; ok = CHOLMOD(super_ltsolve) (NULL, X, W, cm) ; NOT (ok) ; ok = CHOLMOD(super_lsolve) (L, NULL, W, cm) ; NOT (ok) ; ok = CHOLMOD(super_ltsolve) (L, NULL, W, cm) ; NOT (ok) ; ok = CHOLMOD(super_lsolve) (L, X, NULL, cm) ; NOT (ok) ; ok = CHOLMOD(super_ltsolve) (L, X, NULL, cm) ; NOT (ok) ; if (L != NULL && L->maxesize > 1) { /* W is too small */ ok = CHOLMOD(free_dense) (&W, cm) ; OK (ok) ; W = CHOLMOD(zeros) (1, 1, Lxtype, cm) ; OKP (W) ; ok = CHOLMOD(super_lsolve) (L, X, W, cm) ; NOT (ok) ; ok = CHOLMOD(super_ltsolve) (L, X, W, cm) ; NOT (ok) ; ok = CHOLMOD(free_dense) (&W, cm) ; OK (ok) ; W = CHOLMOD(zeros) (n, 1, Lxtype, cm) ; OKP (W) ; } /* X2 has the wrong dimensions */ X2 = CHOLMOD(zeros) (n+1, 1, Lxtype, cm) ; OKP (X2) ; ok = CHOLMOD(super_lsolve) (L, X2, W, cm) ; NOT (ok) ; ok = CHOLMOD(super_ltsolve) (L, X2, W, cm) ; NOT (ok) ; CHOLMOD(free_dense) (&X2, cm) ; } CHOLMOD(free_dense) (&X, cm) ; /* X2 is n-by-0, which is OK */ X2 = CHOLMOD(zeros) (n, 0, Lxtype, cm) ; ok1 = CHOLMOD(super_lsolve) (L, X2, W, cm) ; ok2 = CHOLMOD(super_ltsolve) (L, X2, W, cm) ; CHOLMOD(free_dense) (&W, cm) ; CHOLMOD(free_dense) (&X2, cm) ; if (check_errors) { OK (ok1) ; OK (ok2) ; test_memory_handler ( ) ; my_tries = 0 ; ok = CHOLMOD(super_symbolic) (A, NULL, Parent, L, cm) ; NOT (ok) ; ok = CHOLMOD(super_numeric) (AT, NULL, Zero, L, cm) ; NOT (ok) ; normal_memory_handler ( ) ; cm->error_handler = NULL ; } /* R = space for result of row_subtree and row_lsubtree */ R = CHOLMOD(allocate_sparse)(n, 1, n, FALSE, TRUE, 0, CHOLMOD_PATTERN, cm) ; /* ---------------------------------------------------------------------- */ /* erroneous factorization */ /* ---------------------------------------------------------------------- */ /* cannot use rowfac or row_lsubtree on a supernodal factorization */ if (check_errors && n > 0) { ok = CHOLMOD(rowfac) (A, NULL, beta, 0, 0, L, cm) ; NOT (ok) ; ok = CHOLMOD(row_lsubtree) (A, &i, 0, n-1, L, R, cm) ; NOT (ok) ; } /* ---------------------------------------------------------------------- */ /* convert to simplicial LDL' */ /* ---------------------------------------------------------------------- */ CHOLMOD(change_factor) (Lxtype, FALSE, FALSE, TRUE, TRUE, L, cm) ; /* remove entries due to relaxed supernodal amalgamation */ CHOLMOD(resymbol) (A, NULL, 0, TRUE, L, cm) ; /* refactorize a numeric factor */ posdef = 0 ; /* unknown */ if (A != NULL && A->stype >= 0) { if (A->stype > 0 && A->packed) { S = add_gunk (A) ; CHOLMOD(rowfac) (S, NULL, beta, 0, n, L, cm) ; if (S && S->xtype == CHOLMOD_COMPLEX) { CHOLMOD(sparse_xtype) (CHOLMOD_ZOMPLEX, S, cm) ; } ok = CHOLMOD(free_sparse) (&S, cm) ; OK (ok) ; } else { CHOLMOD(rowfac) (A, NULL, beta, 0, n, L, cm) ; } posdef = (cm->status == CHOLMOD_OK) ; } /* convert to a sparse matrix, and transpose L */ Lcopy = CHOLMOD(copy_factor)(L, cm) ; Lsparse = CHOLMOD(factor_to_sparse) (L, cm) ; LT = CHOLMOD(transpose) (Lsparse, 0, cm) ; CHOLMOD(free_sparse) (&Lsparse, cm) ; if (LT != NULL) { LTp = LT->p ; LTi = LT->i ; OK (LT->packed) ; } /* remove the unit diagonal of LT */ CHOLMOD(band_inplace) (1, n, -1, LT, cm) ; /* ST = pattern of A(p,p)' */ P = (L == NULL) ? NULL : L->Perm ; ST = CHOLMOD(ptranspose) (A, 0, P, NULL, 0, cm) ; /* S = pattern of A(p,p) */ S = CHOLMOD(transpose) (ST, 0, cm) ; ok = CHOLMOD(free_sparse) (&ST, cm) ; if (R != NULL && LT != NULL && posdef && A != NULL && A->stype >= 0 && S != NULL && Lcopy != NULL) { LTp = LT->p ; LTi = LT->i ; Ri = R->i ; Rp = R->p ; save = my_seed ( ) ; /* RAND */ for (trial = 0 ; trial < 30 ; trial++) { /* pick a row at random */ i = nrand (n) ; /* RAND */ /* compute R = pattern of L(i,0:i-1), using row subtrees */ ok = CHOLMOD(row_subtree) (S, NULL, i, Parent, R, cm) ; if (!ok) { break ; } rnz = Rp [1] ; /* sort R */ qsort (Ri, rnz, sizeof (Int), (int (*) (const void *, const void *)) icomp) ; /* compare with ith column of L transpose */ lnz = LTp [i+1] - LTp [i] ; ok = TRUE ; for (k = 0 ; k < MIN (rnz,lnz) ; k++) { /* printf ("%d vs %d\n", Ri [k], LTi [LTp [i] + k]) ; */ ok = ok && (Ri [k] == LTi [LTp [i] + k]) ; } OK (ok) ; OK (rnz == lnz) ; /* compute R = pattern of L(i,0:i-1), using row lsubtrees */ ok = CHOLMOD(row_lsubtree) (S, NULL, 0, i, Lcopy, R, cm) ; if (!ok) { break ; } rnz = Rp [1] ; /* sort R */ qsort (Ri, rnz, sizeof (Int), (int (*) (const void *, const void *)) icomp) ; /* compare with ith column of L transpose */ lnz = LTp [i+1] - LTp [i] ; ok = TRUE ; for (k = 0 ; k < MIN (rnz,lnz) ; k++) { /* printf ("%d vs %d\n", Ri [k], LTi [LTp [i] + k]) ; */ ok = ok && (Ri [k] == LTi [LTp [i] + k]) ; } OK (ok) ; OK (rnz == lnz) ; /* L is symbolic, so cholmod_lsubtree will fail */ if (check_errors) { ok = CHOLMOD(row_lsubtree) (S, NULL, 0, i, L, R, cm) ; NOT (ok) ; } } my_srand (save) ; /* RAND */ } ok = CHOLMOD(free_factor) (&L, cm) ; OK (ok) ; ok = CHOLMOD(free_factor) (&Lcopy, cm) ; OK (ok) ; ok = CHOLMOD(free_sparse) (<, cm) ; OK (ok) ; ok = CHOLMOD(free_sparse) (&R, cm) ; OK (ok) ; ok = CHOLMOD(free_sparse) (&S, cm) ; OK (ok) ; /* ---------------------------------------------------------------------- */ /* simplicial LDL' or LL' factorization with no analysis */ /* ---------------------------------------------------------------------- */ for (trial = 0 ; trial <= check_errors ; trial++) { /* create a simplicial symbolic factor */ L = CHOLMOD(allocate_factor) (n, cm) ; ok = TRUE ; Axtype = (A == NULL) ? CHOLMOD_REAL : A->xtype ; if (check_errors) { OKP (L) ; if (trial == 0) { /* convert to packed LDL' first, then unpacked */ ok = CHOLMOD(change_factor) (Axtype, FALSE, FALSE, TRUE, TRUE, L, cm) ; OK (ok); ok = CHOLMOD(change_factor) (Axtype, FALSE, FALSE, FALSE, TRUE, L, cm) ; OK (ok) ; } else if (trial == 1) { ok = CHOLMOD(rowfac)(NULL, NULL, beta, 0, 0, L, cm) ; NOT (ok) ; ok = CHOLMOD(rowfac)(A, NULL, beta, 0, 0, NULL, cm) ; NOT (ok) ; ok = CHOLMOD(rowfac)(AT, NULL, beta, 0, 0, L, cm) ; NOT (ok) ; if (n > 1) { A1 = CHOLMOD(allocate_sparse)(1, 1, 1, TRUE, TRUE, 1, CHOLMOD_PATTERN, cm) ; OKP (A1) ; ok = CHOLMOD(rowfac)(A1, NULL, beta, 0, 0, L, cm); NOT (ok); ok = CHOLMOD(free_sparse)(&A1, cm) ; OK (ok); } } else { /* convert to symbolic LL' */ ok = CHOLMOD(change_factor) (CHOLMOD_PATTERN, TRUE, FALSE, TRUE, TRUE, L, cm) ; OK (ok) ; OK (L->is_ll) ; } } /* factor */ CHOLMOD(print_factor) (L, "L for rowfac", cm) ; CHOLMOD(print_sparse) (A, "A for rowfac", cm) ; cm->dbound = 1e-15 ; for (k = 0 ; ok && k < n ; k++) { if (!CHOLMOD(rowfac) (A, NULL, beta, k, k+1, L, cm)) { ok = FALSE ; } if (cm->status == CHOLMOD_NOT_POSDEF) { /* LL' factorization failed; subsequent rowfac's should fail */ k++ ; ok = CHOLMOD(rowfac) (A, NULL, beta, k, k+1, L, cm) ; NOT (ok) ; ok = TRUE ; } } cm->dbound = 0 ; if (check_errors) { OK (ok) ; ok = CHOLMOD(rowfac) (A, NULL, beta, n, n+1, L, cm) ; NOT (ok) ; ok = TRUE ; } /* solve */ if (ok) { /* int saveit = cm->print ; int saveit2 = cm->precise ; cm->print = 5 ; cm->precise = TRUE ; CHOLMOD (print_sparse) (A, "A here", cm) ; CHOLMOD (print_factor) (L, "L here", cm) ; CHOLMOD (print_dense) (B, "B here", cm) ; */ cm->prefer_zomplex = prefer_zomplex ; X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ; /* CHOLMOD (print_dense) (X, "X here", cm) ; */ cm->prefer_zomplex = FALSE ; r = resid (A, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_dense) (&X, cm) ; /* cm->print = saveit ; cm->precise = saveit2 ; fprintf (stderr, "solve %8.2e\n", r) ; */ } CHOLMOD(free_factor) (&L, cm) ; } /* ---------------------------------------------------------------------- */ /* factor again with entries in the (ignored) lower part A */ /* ---------------------------------------------------------------------- */ if (A->packed) { L = CHOLMOD(allocate_factor) (n, cm) ; C = add_gunk (A) ; /* C = CHOLMOD(copy) (A, 0, 1, cm) ; if (C != NULL) { C->stype = 1 ; } */ CHOLMOD(rowfac) (C, NULL, beta, 0, n, L, cm) ; X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ; r = resid (A, X, B) ; MAXERR (maxerr, r, 1) ; CHOLMOD(free_sparse) (&C, cm) ; CHOLMOD(free_factor) (&L, cm) ; CHOLMOD(free_dense) (&X, cm) ; } /* ---------------------------------------------------------------------- */ /* factor again using rowfac_mask (for LPDASA only) */ /* ---------------------------------------------------------------------- */ r = raw_factor2 (A, 0., 0) ; MAXERR (maxerr, r, 1) ; r = raw_factor2 (A, 1e-16, 0) ; MAXERR (maxerr, r, 1) ; /* ---------------------------------------------------------------------- */ /* free the problem */ /* ---------------------------------------------------------------------- */ CHOLMOD(free_sparse) (&AT, cm) ; CHOLMOD(free_dense) (&B, cm) ; CHOLMOD(free) (n, sizeof (Int), First, cm) ; CHOLMOD(free) (n, sizeof (Int), Level, cm) ; CHOLMOD(free) (n, sizeof (Int), Parent, cm) ; CHOLMOD(free) (n, sizeof (Int), Post, cm) ; progress (0, '.') ; return (maxerr) ; } /* ========================================================================== */ /* === raw_factor2 ========================================================== */ /* ========================================================================== */ /* A->stype can be 0 (lower), 1 (upper) or 0 (unsymmetric). In the first two * cases, Ax=b is solved. In the third, A*A'x=b is solved. No analysis and no * fill-reducing ordering is used. Both simplicial LL' and LDL' factorizations * are used (testing rowfac_mask, for LPDASA only). */ double raw_factor2 (cholmod_sparse *A, double alpha, int domask) { Int n, i, prefer_zomplex, is_ll, xtype, sorted, axtype, stype ; Int *mask = NULL, *RLinkUp = NULL, nz = 0 ; Int *Cp = NULL, added_gunk ; double maxerr = 0, r = 0 ; cholmod_sparse *AT = NULL, *C = NULL, *CT = NULL, *CC = NULL, *C2 = NULL ; cholmod_factor *L = NULL ; cholmod_dense *B = NULL, *X = NULL ; double beta [2] ; /* int saveit = cm->print ; int saveit2 = cm->precise ; cm->print = 5 ; cm->precise = TRUE ; */ if (A == NULL) { return (0) ; } n = A->nrow ; if (n > 1000) { printf ("\nSkipping rowfac, matrix too large\n") ; return (0) ; } axtype = A->xtype ; beta [0] = alpha ; beta [1] = 0 ; prefer_zomplex = (A->xtype == CHOLMOD_ZOMPLEX) ; AT = CHOLMOD(transpose) (A, 2, cm) ; /* ensure C has stype of 0 or 1. Do not prune any entries */ stype = A->stype ; if (stype >= 0) { A->stype = 0 ; C = CHOLMOD(copy_sparse) (A, cm) ; A->stype = stype ; if (C) C->stype = stype ; /* C = CHOLMOD(copy) (A, 0, 1, cm) ; if (C) C->stype = A->stype ; */ CT = AT ; } else { C = AT ; /* CT = CHOLMOD(copy_sparse) (A, cm) ; */ /* CT = CHOLMOD(copy) (A, 0, 1, cm) ; if (CT) CT->stype = A->stype ; */ A->stype = 0 ; CT = CHOLMOD(copy_sparse) (A, cm) ; A->stype = stype ; if (CT) CT->stype = stype ; /* only domask if C is symmetric and upper part stored */ domask = FALSE ; } mask = CHOLMOD(malloc) (n, sizeof (Int), cm) ; RLinkUp = CHOLMOD(malloc) (n, sizeof (Int), cm) ; if (C && cm->status == CHOLMOD_OK) { for (i = 0 ; i < n ; i++) { mask [i] = -1 ; RLinkUp [i] = i+1 ; } } else { domask = FALSE ; } if (C && !(C->packed) && !(C->sorted)) { /* do not do the unpacked or unsorted cases */ domask = FALSE ; } /* make a copy of C and add some gunk if stype > 0 */ added_gunk = (C && C->stype > 0) ; if (added_gunk) { C2 = add_gunk (C) ; } else { C2 = CHOLMOD(copy_sparse) (C, cm) ; } CC = CHOLMOD(copy_sparse) (C2, cm) ; if (CC && domask) { Int *Cp, *Ci, p ; double *Cx, *Cz ; /* this implicitly sets the first row/col of C to zero, except diag. */ mask [0] = 1 ; /* CC = C2, and then set the first row/col to zero, except diagonal */ Cp = CC->p ; Ci = CC->i ; Cx = CC->x ; Cz = CC->z ; nz = Cp [n] ; switch (C->xtype) { case CHOLMOD_REAL: for (p = 1 ; p < nz ; p++) { if (Ci [p] == 0) Cx [p] = 0 ; } break ; case CHOLMOD_COMPLEX: for (p = 1 ; p < nz ; p++) { if (Ci [p] == 0) { Cx [2*p ] = 0 ; Cx [2*p+1] = 0 ; } } break ; case CHOLMOD_ZOMPLEX: for (p = 1 ; p < nz ; p++) { if (Ci [p] == 0) { Cx [p] = 0 ; Cz [p] = 0 ; } } break ; } } B = rhs (CC, 1, n) ; for (sorted = 1 ; sorted >= 0 ; sorted--) { if (!sorted) { if (C2 && !added_gunk) C2->sorted = FALSE ; if (C) C->sorted = FALSE ; if (CT) CT->sorted = FALSE ; } for (is_ll = 0 ; is_ll <= 1 ; is_ll++) { for (xtype = 0 ; xtype <= 1 ; xtype++) { L = CHOLMOD(allocate_factor) (n, cm) ; if (L) L->is_ll = is_ll ; if (xtype) { CHOLMOD (change_factor) (axtype, is_ll, 0, 0, 1, L, cm) ; } CHOLMOD(rowfac_mask) (sorted ? C : C2, CT, beta, 0, n, mask, RLinkUp, L, cm) ; cm->prefer_zomplex = prefer_zomplex ; X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ; cm->prefer_zomplex = FALSE ; r = resid (CC, X, B) ; MAXERR (maxerr, r, 1) ; printf ("rowfac mask: resid is %g\n", r) ; CHOLMOD(free_factor) (&L, cm) ; CHOLMOD(free_dense) (&X, cm) ; } } } CHOLMOD(free) (n, sizeof (Int), mask, cm) ; CHOLMOD(free) (n, sizeof (Int), RLinkUp, cm) ; CHOLMOD(free_sparse) (&C2, cm) ; CHOLMOD(free_sparse) (&CC, cm) ; CHOLMOD(free_sparse) (&CT, cm) ; CHOLMOD(free_sparse) (&C, cm) ; CHOLMOD(free_dense) (&B, cm) ; return (maxerr) ; } SuiteSparse/CHOLMOD/Tcov/License.txt0000644001170100242450000000203310540000310016047 0ustar davisfacCHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis CHOLMOD is also available under other licenses; contact authors for details. http://www.cise.ufl.edu/research/sparse Note that this license is for the CHOLMOD/Tcov module only. All CHOLMOD modules are licensed separately. -------------------------------------------------------------------------------- This Module is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This Module is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. SuiteSparse/CHOLMOD/Tcov/huge.c0000644001170100242450000001562410616503636015061 0ustar davisfac/* ========================================================================== */ /* === Tcov/huge ============================================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Tests on huge matrices */ #include "cm.h" #include "amd.h" #ifndef NPARTITION #include "camd.h" #endif /* ========================================================================== */ /* === huge ================================================================= */ /* ========================================================================== */ void huge ( ) { cholmod_sparse *A, *C ; cholmod_triplet *T ; cholmod_factor *L ; cholmod_dense *X ; size_t n, nbig ; int ok = TRUE, save ; Int junk ; FILE *f ; double beta [2] ; n = Size_max ; CHOLMOD (free_work) (cm) ; CHOLMOD (allocate_work) (n, 0, 0, cm) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; n = CHOLMOD(add_size_t) (n, 1, &ok) ; NOT (ok) ; /* create a fake zero sparse matrix, with huge dimensions */ A = CHOLMOD (spzeros) (1, 1, 0, CHOLMOD_REAL, cm) ; A->nrow = Size_max ; A->ncol = Size_max ; A->stype = 0 ; /* create a fake factor, with huge dimensions. */ L = CHOLMOD (allocate_factor) (1, cm) ; OKP (L) ; L->n = Size_max ; CHOLMOD (factorize) (A, L, cm) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; /* free the fake factor */ L->n = 1 ; CHOLMOD (free_factor) (&L, cm) ; /* create a valid factor to test resymbol */ C = CHOLMOD (speye) (1, 1, CHOLMOD_REAL, cm) ; C->stype = 1 ; L = CHOLMOD (analyze) (C, cm) ; OKP (L) ; CHOLMOD (factorize) (C, L, cm) ; ok = CHOLMOD (resymbol) (C, NULL, 0, 0, L, cm) ; OK (ok) ; C->nrow = Size_max ; C->ncol = Size_max ; L->n = Size_max ; ok = CHOLMOD (resymbol) (C, NULL, 0, 0, L, cm) ; NOT (ok) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; printf ("rowfac:\n") ; beta [0] = 1 ; beta [1] = 0 ; C->xtype = CHOLMOD_COMPLEX ; L->xtype = CHOLMOD_COMPLEX ; ok = CHOLMOD (rowfac) (C, NULL, beta, 0, 0, L, cm) ; printf ("rowfac %d\n", cm->status) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; C->xtype = CHOLMOD_REAL ; L->xtype = CHOLMOD_REAL ; printf ("rowfac done:\n") ; C->stype = -1 ; ok = CHOLMOD (resymbol_noperm) (C, NULL, 0, 0, L, cm) ; NOT (ok) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; C->ncol = 1 ; CHOLMOD (rowadd) (0, C, L, cm) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; CHOLMOD (rowdel) (0, C, L, cm) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; C->ncol = 4 ; CHOLMOD (updown) (1, C, L, cm) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; C->nrow = 1 ; C->ncol = 1 ; L->n = 1 ; CHOLMOD (free_sparse) (&C, cm) ; CHOLMOD (free_factor) (&L, cm) ; C = CHOLMOD (allocate_sparse) (Size_max, Size_max, Size_max, 0, 0, 0, 0, cm); NOP (C) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; CHOLMOD (rowcolcounts) (A, NULL, 0, &junk, &junk, &junk, &junk, &junk, &junk, cm) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; C = CHOLMOD (submatrix) (A, &junk, Size_max/2, &junk, Size_max/2, 0, 0, cm) ; NOP (C) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; ok = CHOLMOD (transpose_unsym) (A, 0, &junk, &junk, Size_max, A, cm) ; NOT (ok) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; A->stype = 1 ; ok = CHOLMOD (transpose_sym) (A, 0, &junk, A, cm) ; NOT (ok) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; C = CHOLMOD (ptranspose) (A, 0, &junk, NULL, 0, cm) ; NOP (C) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; A->stype = 0 ; CHOLMOD (amd) (A, NULL, 0, &junk, cm) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; L = CHOLMOD (analyze) (A, cm) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; NOP (L) ; #ifndef NPARTITION CHOLMOD (camd) (A, NULL, 0, &junk, NULL, cm) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; #endif printf ("calling colamd\n") ; CHOLMOD (colamd) (A, NULL, 0, 0, &junk, cm) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; #ifndef NPARTITION printf ("calling ccolamd\n") ; CHOLMOD (ccolamd) (A, NULL, 0, NULL, &junk, cm) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; #endif CHOLMOD (etree) (A, &junk, cm) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; L = CHOLMOD (allocate_factor) (Size_max, cm) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; NOP (L) ; #ifndef NPARTITION CHOLMOD (metis) (A, NULL, 0, 0, &junk, cm) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; CHOLMOD (bisect) (A, NULL, 0, 0, &junk, cm) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; CHOLMOD (nested_dissection) (A, NULL, 0, &junk, &junk, &junk, cm) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; #endif CHOLMOD (postorder) (&junk, Size_max, &junk, &junk, cm) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; /* causes overflow in 32-bit version, but not 64-bit */ f = fopen ("../Tcov/Matrix/mega.tri", "r") ; T = CHOLMOD (read_triplet) (f, cm) ; if (sizeof (Int) == sizeof (int)) { NOP (T) ; OK (cm->status != CHOLMOD_OK) ; } CHOLMOD (free_triplet) (&T, cm) ; fclose (f) ; n = Size_max ; X = CHOLMOD (allocate_dense) (n, 1, n, CHOLMOD_REAL, cm) ; NOP (X) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; /* supernodal symbolic test */ C = CHOLMOD (speye) (1, 1, CHOLMOD_REAL, cm) ; C->stype = 1 ; save = cm->supernodal ; cm->supernodal = CHOLMOD_SIMPLICIAL ; L = CHOLMOD (analyze) (C, cm) ; OKP (L) ; junk = 0 ; C->nrow = Size_max ; C->ncol = Size_max ; L->n = Size_max ; CHOLMOD (super_symbolic) (C, C, &junk, L, cm) ; OK (cm->status == CHOLMOD_TOO_LARGE) ; cm->supernodal = save ; C->nrow = 1 ; C->ncol = 1 ; L->n = 1 ; CHOLMOD (free_sparse) (&C, cm) ; CHOLMOD (free_factor) (&L, cm) ; /* supernodal numeric test */ C = CHOLMOD (speye) (1, 1, CHOLMOD_REAL, cm) ; C->stype = -1 ; save = cm->supernodal ; cm->supernodal = CHOLMOD_SUPERNODAL ; L = CHOLMOD (analyze) (C, cm) ; OKP (L) ; OK (cm->status == CHOLMOD_OK) ; C->nrow = Size_max ; C->ncol = Size_max ; L->n = Size_max ; CHOLMOD (super_numeric) (C, C, beta, L, cm) ; cm->supernodal = save ; C->nrow = 1 ; C->ncol = 1 ; L->n = 1 ; CHOLMOD (free_sparse) (&C, cm) ; CHOLMOD (free_factor) (&L, cm) ; /* free the fake matrix */ A->nrow = 1 ; A->ncol = 1 ; CHOLMOD (free_sparse) (&A, cm) ; fprintf (stderr, "\n") ; } SuiteSparse/CHOLMOD/Tcov/leak.c0000644001170100242450000000553710540000052015023 0ustar davisfac/* ========================================================================== */ /* === Tcov/leak ============================================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Look for CHOLMOD memory leaks. Run cm with * cholmod_dump >= cholmod_dump_malloc (see Check/cholmod_check.c), * to get output file. Then grep "cnt:" output | leak */ #include #include #include #define LEN 2048 char line [LEN] ; char operation [LEN] ; char s_cnt [LEN] ; char s_inuse [LEN] ; int block [LEN] ; int blocksize [LEN] ; #define FALSE 0 #define TRUE 1 int main (void) { int p, size, cnt2, inuse2, nblocks, found, b, bfound, nlines ; nblocks = 0 ; nlines = 0 ; while (fgets (line, LEN, stdin) != NULL) { sscanf (line, "%s %x %d %s %d %s %d\n", operation, &p, &size, s_cnt, &cnt2, s_inuse, &inuse2) ; nlines++ ; printf ("%d:: %s %x %d %s %d %s %d\n", nlines, operation, p, size, s_cnt, cnt2, s_inuse, inuse2) ; /* determine operation */ if (strcmp (operation, "cholmod_malloc") == 0 || strcmp (operation, "cholmod_realloc_new:") == 0 || strcmp (operation, "cholmod_calloc") == 0) { /* p = malloc (size) */ for (b = 0 ; b < nblocks ; b++) { if (p == block [b]) { printf ("duplicate!\n") ; abort ( ) ; } } if (nblocks >= LEN) { printf ("out of space!\n") ; abort ( ) ; } /* add the new block to the list */ block [nblocks] = p ; blocksize [nblocks] = size ; nblocks++ ; } else if (strcmp (operation, "cholmod_free") == 0 || strcmp (operation, "cholmod_realloc_old:") == 0) { /* p = free (size) */ found = FALSE ; for (b = 0 ; !found && b < nblocks ; b++) { if (p == block [b]) { bfound = b ; found = TRUE ; } } if (!found) { printf ("not found!\n") ; abort ( ) ; } if (size != blocksize [bfound]) { printf ("wrong size! %x : %d vs %d\n", p, size, blocksize[bfound]) ; abort ( ) ; } /* remove the block from the list */ --nblocks ; block [bfound] = block [nblocks] ; blocksize [bfound] = blocksize [nblocks] ; } else { printf ("unrecognized!\n") ; abort ( ) ; } if (cnt2 != nblocks) { printf ("nblocks wrong! %d %d\n", nblocks, cnt2) ; } } return (0) ; } SuiteSparse/CHOLMOD/Tcov/null.c0000644001170100242450000003736210540000063015064 0ustar davisfac/* ========================================================================== */ /* === Tcov/null ============================================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Test CHOLMOD with NULL pointers, and other error cases. */ #include "cm.h" /* ========================================================================== */ /* === my_hander2 =========================================================== */ /* ========================================================================== */ void my_handler2 (int status, char *file, int line, char *msg) { printf ("This ERROR is expected: file %s line %d\n%d: %s\n", file, line, status, msg) ; } /* ========================================================================== */ /* === null_test ============================================================ */ /* ========================================================================== */ /* This routine is not called during memory testing */ void null_test (cholmod_common *cn) { cholmod_sparse *A = NULL, *F = NULL, *C = NULL, *R = NULL, *B = NULL ; cholmod_factor *L = NULL ; cholmod_triplet *T = NULL ; cholmod_dense *X = NULL, *DeltaB = NULL, *S = NULL, *Y = NULL, *E = NULL ; void *p = NULL, *ii = NULL, *jj = NULL, *xx = NULL, *zz = NULL ; Int *Perm = NULL, *fset = NULL, *Parent = NULL, *Post = NULL, *RowCount = NULL, *ColCount = NULL, *First = NULL, *Level = NULL, *UserPerm = NULL, *colmark = NULL, *Constraints = NULL, *r = NULL, *c = NULL, *Set = NULL ; char *name = NULL ; double alpha [2], beta [2], bk [2], yk [2], rcond ; double dj = 1, nm = 0, tol = 0 ; int ok, stype = 0, xtype = 0, sorted = 0, packed = 0, nint = 0, update = 0, postorder = 0, pack = 0, values = 0, mode = 0, sys = 0, norm = 0, to_xtype = 0, to_ll = 0, to_super = 0, to_packed = 0, to_monotonic = 0, scale = 0, transpose = 0, option = 0, ordering = 0, prefer = 0, mtype = 0, asym = 0 ; UF_long lr = 0, k1 = 0, k2 = 0 ; size_t j = 0, need = 0, n = 0, mr = 0, nrow = 0, ncol = 0, iworksize = 0, newsize = 0, fsize = 0, d = 0, nzmax = 0, nnew = 0, size = 0, nold = 0, xwork = 0, kstart = 0, kend = 0, nr = 0, nc = 0, len = 0, krow = 0, k = 0 ; #ifndef NPARTITION Int *Anw = NULL, *Aew = NULL, *Partition = NULL, *CParent = NULL, *Cmember = NULL ; Int compress = 0 ; #endif /* ---------------------------------------------------------------------- */ /* Core */ /* ---------------------------------------------------------------------- */ if (cn == NULL) { ok = CHOLMOD(start)(cn) ; NOT (ok) ; } ok = CHOLMOD(finish)(cn) ; NOT (ok) ; ok = CHOLMOD(defaults)(cn) ; NOT (ok) ; mr = CHOLMOD(maxrank)(n, cn) ; NOT (mr>0) ; ok = CHOLMOD(allocate_work)(nrow, iworksize, xwork, cn) ; NOT (ok) ; ok = CHOLMOD(free_work)(cn) ; NOT (ok) ; lr = CHOLMOD(clear_flag)(cn) ; NOT (lr>=0) ; dj = CHOLMOD(dbound)(dj, cn) ; OK (dj==0) ; ok = CHOLMOD(error)(CHOLMOD_INVALID, __FILE__, __LINE__, "oops", cn) ; NOT (ok) ; A = CHOLMOD(allocate_sparse)(nrow, ncol, nzmax, sorted, packed, stype, xtype, cn) ; NOP (A) ; ok = CHOLMOD(free_sparse)(&A, cn) ; NOT (ok) ; ok = CHOLMOD(reallocate_sparse)(newsize, A, cn) ; NOT (ok) ; lr = CHOLMOD(nnz)(A, cn) ; NOT (lr>=0) ; A = CHOLMOD(speye)(nrow, ncol, xtype, cn) ; NOP (A) ; A = CHOLMOD(spzeros)(nrow, ncol, 0, xtype, cn) ; NOP (A) ; A = CHOLMOD(ptranspose)(A, values, Perm, fset, fsize, cn); NOP (A) ; A = CHOLMOD(transpose)(A, values, cn) ; NOP (A) ; ok = CHOLMOD(transpose_unsym)(A, values, Perm, fset, fsize, F, cn) ; NOT (ok) ; ok = CHOLMOD(transpose_sym)(A, values, Perm, F, cn) ; NOT (ok) ; ok = CHOLMOD(sort)(A, cn) ; NOT (ok) ; A = CHOLMOD(copy_sparse)(A, cn) ; NOP (A) ; C = CHOLMOD(aat)(A, fset, fsize, mode, cn) ; NOP (C) ; L = CHOLMOD(allocate_factor)(n, cn) ; NOP (L) ; ok = CHOLMOD(free_factor)(&L, cn) ; NOT (ok) ; ok = CHOLMOD(reallocate_factor)(newsize, L, cn) ; NOT (ok) ; ok = CHOLMOD(change_factor)(0, 0, 0, 0, 0, L, cn) ; NOT (ok) ; ok = CHOLMOD(pack_factor)(L, cn) ; NOT (ok) ; ok = CHOLMOD(change_factor)(to_xtype, to_ll, to_super, to_packed, to_monotonic, L, cn) ; NOT (ok) ; ok = CHOLMOD(reallocate_column)(j, need, L, cn) ; NOT (ok) ; A = CHOLMOD(factor_to_sparse)(L, cn) ; NOP (A) ; L = CHOLMOD(copy_factor)(L, cn) ; NOP (L) ; X = CHOLMOD(allocate_dense)(nrow, ncol, d, xtype, cn) ; NOP (X) ; X = CHOLMOD(zeros)(nrow, ncol, xtype, cn) ; NOP (X) ; X = CHOLMOD(ones)(nrow, ncol, xtype, cn) ; NOP (X) ; X = CHOLMOD(eye)(nrow, ncol, xtype, cn) ; NOP (X) ; ok = CHOLMOD(free_dense)(&X, cn) ; NOT (ok) ; X = CHOLMOD(sparse_to_dense)(A, cn) ; NOP (X) ; A = CHOLMOD(dense_to_sparse)(X, values, cn) ; NOP (A) ; Y = CHOLMOD(copy_dense)(X, cn) ; NOP (X) ; ok = CHOLMOD(copy_dense2)(X, Y, cn) ; NOT (ok) ; T = CHOLMOD(allocate_triplet)(nrow, ncol, nzmax, stype, xtype, cn) ; NOP (T) ; ok = CHOLMOD(free_triplet)(&T, cn) ; NOT (ok) ; T = CHOLMOD(sparse_to_triplet)(A, cn) ; NOP (T) ; A = CHOLMOD(triplet_to_sparse)(T, 0, cn) ; NOP (A) ; T = CHOLMOD(copy_triplet)(T, cn) ; NOP (T) ; ok = CHOLMOD(reallocate_triplet)(nzmax, T, cn) ; NOT (ok) ; lr = CHOLMOD(postorder)(Parent, nrow, NULL, Post, cn) ; NOT (lr>=0) ; p = CHOLMOD(malloc)(n, size, cn) ; NOP (p) ; p = CHOLMOD(calloc)(n, size, cn) ; NOP (p) ; p = CHOLMOD(free)(n, size, p, cn) ; NOP (p) ; p = CHOLMOD(realloc)(nnew, size, p, &n, cn) ; NOP (p) ; ok = CHOLMOD(realloc_multiple)(nnew, nint, xtype, &ii, &jj, &xx, &zz, &nold, cn) ; NOT (ok) ; C = CHOLMOD(band)(A, k1, k2, mode, cn) ; NOP (C) ; ok = CHOLMOD(band_inplace)(k1, k2, mode, A, cn) ; NOT (ok) ; ok = CHOLMOD(factor_xtype)(CHOLMOD_REAL, L, cn) ; NOT (ok) ; ok = CHOLMOD(sparse_xtype)(CHOLMOD_REAL, A, cn) ; NOT (ok) ; ok = CHOLMOD(dense_xtype)(CHOLMOD_REAL, X, cn) ; NOT (ok) ; ok = CHOLMOD(triplet_xtype)(CHOLMOD_REAL, T, cn) ; NOT (ok) ; /* ---------------------------------------------------------------------- */ /* Cholesky */ /* ---------------------------------------------------------------------- */ L = CHOLMOD(analyze)(A, cn) ; NOP (L) ; L = CHOLMOD(analyze_p)(A, UserPerm, fset, fsize, cn) ; NOP (L) ; ok = CHOLMOD(factorize)(A, L, cn) ; NOT (ok) ; ok = CHOLMOD(factorize_p)(A, beta, fset, fsize, L, cn) ; NOT (ok) ; rcond = CHOLMOD(rcond)(L, cn) ; NOT (rcond>=0) ; X = CHOLMOD(solve)(sys, L, Y, cn) ; NOP (X) ; C = CHOLMOD(spsolve)(sys, L, B, cn) ; NOP (C) ; ok = CHOLMOD(etree)(A, Parent, cn) ; NOT (ok) ; ok = CHOLMOD(rowcolcounts)(A, fset, fsize, Parent, Post, RowCount, ColCount, First, Level, cn) ; NOT (ok) ; ok = CHOLMOD(amd)(A, fset, fsize, Perm, cn) ; NOT (ok) ; ok = CHOLMOD(camd)(A, fset, fsize, Constraints, Perm, cn) ; NOT (ok) ; ok = CHOLMOD(colamd)(A, fset, fsize, postorder, Perm, cn) ; NOT (ok) ; ok = CHOLMOD(rowfac)(A, F, beta, kstart, kend, L, cn) ; NOT (ok) ; ok = CHOLMOD(row_subtree)(A, F, krow, Parent, R, cn) ; NOT (ok) ; ok = CHOLMOD(row_lsubtree)(A, c, 0, krow, L, R, cn) ; NOT (ok) ; ok = CHOLMOD(resymbol)(A, fset, fsize, pack, L, cn) ; NOT (ok) ; ok = CHOLMOD(resymbol_noperm)(A, fset, fsize, pack, L, cn) ;NOT (ok) ; ok = CHOLMOD(analyze_ordering)(A, ordering, Perm, fset, fsize, Parent, Post, ColCount, First, Level, cn) ; NOT (ok) ; /* ---------------------------------------------------------------------- */ /* Modify */ /* ---------------------------------------------------------------------- */ ok = CHOLMOD(updown)(update, C, L, cn) ; NOT (ok) ; ok = CHOLMOD(updown_solve)(update, C, L, X, DeltaB, cn) ; NOT (ok) ; ok = CHOLMOD(updown_mark)(update, C, colmark, L, X, DeltaB, cn) ; NOT (ok) ; ok = CHOLMOD(rowadd)(k, R, L, cn) ; NOT (ok) ; ok = CHOLMOD(rowadd_solve)(k, R, bk, L, X, DeltaB, cn) ; NOT (ok) ; ok = CHOLMOD(rowadd_mark)(k, R, bk, colmark, L, X, DeltaB, cn) ; NOT (ok) ; ok = CHOLMOD(rowdel)(k, R, L, cn) ; NOT (ok) ; ok = CHOLMOD(rowdel_solve)(k, R, yk, L, X, DeltaB, cn) ; NOT (ok) ; ok = CHOLMOD(rowdel_mark)(k, R, yk, colmark, L, X, DeltaB, cn) ; NOT (ok) ; /* ---------------------------------------------------------------------- */ /* MatrixOps */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(add)(A, B, alpha, beta, values, sorted, cn) ; NOP (C) ; C = CHOLMOD(copy)(A, stype, mode, cn) ; NOP (C) ; ok = CHOLMOD(drop)(tol, A, cn) ; NOT (ok) ; nm = CHOLMOD(norm_dense)(X, norm, cn) ; NOT (nm>=0) ; nm = CHOLMOD(norm_sparse)(A, norm, cn) ; NOT (nm>=0) ; C = CHOLMOD(horzcat)(A, B, values, cn) ; NOP (C) ; ok = CHOLMOD(scale)(S, scale, A, cn) ; NOT (ok) ; ok = CHOLMOD(sdmult)(A, transpose, alpha, beta, X, Y, cn) ; NOT (ok) ; C = CHOLMOD(ssmult)(A, B, stype, values, sorted, cn) ; NOP (C) ; C = CHOLMOD(submatrix)(A, r, nr, c, nc, values, sorted, cn) ; NOP (C) ; C = CHOLMOD(vertcat)(A, B, values, cn) ; NOP (C) ; asym = CHOLMOD(symmetry)(A, option, NULL, NULL, NULL, NULL, cn) ; NOT(asym>=0) ; /* ---------------------------------------------------------------------- */ /* Supernodal */ /* ---------------------------------------------------------------------- */ ok = CHOLMOD(super_symbolic)(A, F, Parent, L, cn) ; NOT (ok) ; ok = CHOLMOD(super_numeric)(A, F, beta, L, cn) ; NOT (ok) ; ok = CHOLMOD(super_lsolve)(L, X, E, cn) ; NOT (ok) ; ok = CHOLMOD(super_ltsolve)(L, X, E, cn) ; NOT (ok) ; /* ---------------------------------------------------------------------- */ /* Check */ /* ---------------------------------------------------------------------- */ ok = CHOLMOD(check_common)(cn) ; NOT (ok) ; ok = CHOLMOD(print_common)(name, cn) ; NOT (ok) ; ok = CHOLMOD(check_sparse)(A, cn) ; NOT (ok) ; ok = CHOLMOD(print_sparse)(A, name, cn) ; NOT (ok) ; ok = CHOLMOD(check_dense)(X, cn) ; NOT (ok) ; ok = CHOLMOD(print_dense)(X, name, cn) ; NOT (ok) ; ok = CHOLMOD(check_factor)(L, cn) ; NOT (ok) ; ok = CHOLMOD(print_factor)(L, name, cn) ; NOT (ok) ; ok = CHOLMOD(check_triplet)(T, cn) ; NOT (ok) ; ok = CHOLMOD(print_triplet)(T, name, cn) ; NOT (ok) ; ok = CHOLMOD(check_subset)(Set, len, n, cn) ; NOT (ok) ; ok = CHOLMOD(print_subset)(Set, len, n, name, cn) ; NOT (ok) ; ok = CHOLMOD(check_perm)(Perm, n, n, cn) ; NOT (ok) ; ok = CHOLMOD(print_perm)(Perm, n, n, name, cn) ; NOT (ok) ; ok = CHOLMOD(check_parent)(Parent, n, cn) ; NOT (ok) ; ok = CHOLMOD(print_parent)(Parent, n, name, cn) ; NOT (ok) ; A = CHOLMOD(read_sparse)(NULL, cn) ; NOP (A) ; p = CHOLMOD(read_matrix)(NULL, prefer, &mtype, cn) ; NOP (p) ; X = CHOLMOD(read_dense)(NULL, cn) ; NOP (X) ; T = CHOLMOD(read_triplet)(NULL, cn) ; NOP (T) ; asym = CHOLMOD(write_dense) (NULL, NULL, NULL, cn) ; NOT (asym>=0) ; asym = CHOLMOD(write_dense) ((FILE *) 1, NULL, NULL, cn) ; NOT (asym>=0) ; asym = CHOLMOD(write_sparse)(NULL, NULL, NULL, NULL, cn) ; NOT (asym>=0) ; asym = CHOLMOD(write_sparse)((FILE *) 1, NULL, NULL, NULL, cn) ; NOT (asym>=0) ; /* ---------------------------------------------------------------------- */ /* Partition */ /* ---------------------------------------------------------------------- */ #ifndef NPARTITION lr = CHOLMOD(nested_dissection)(A, fset, fsize, Perm, CParent, Cmember, cn) ; NOT (lr >= 0) ; lr = CHOLMOD(collapse_septree) (n, n, 1., 4, CParent, Cmember, cn) ; NOT (lr >= 0) ; ok = CHOLMOD(metis)(A, fset, fsize, postorder, Perm, cn) ; NOT (ok) ; ok = CHOLMOD(ccolamd)(A, fset, fsize, Cmember, Perm, cn) ; NOT (ok) ; ok = CHOLMOD(csymamd)(A, Cmember, Perm, cn) ; NOT (ok) ; lr = CHOLMOD(bisect)(A, fset, fsize, compress, Partition, cn) ; NOT (lr >= 0) ; lr = CHOLMOD(metis_bisector)(A, Anw, Aew, Partition, cn) ; NOT (lr >= 0) ; #endif } /* ========================================================================== */ /* === null_test2 =========================================================== */ /* ========================================================================== */ void null_test2 (void) { cholmod_dense *X, *Xbad = NULL ; cholmod_sparse *Sbad = NULL, *A ; int ok ; /* ---------------------------------------------------------------------- */ /* Test Core Common */ /* ---------------------------------------------------------------------- */ ok = CHOLMOD(allocate_work)(Size_max, 1, 1, cm) ; NOT (ok) ; ok = CHOLMOD(allocate_work)(1, Size_max, 1, cm) ; NOT (ok) ; ok = CHOLMOD(allocate_work)(1, 1, Size_max, cm) ; NOT (ok) ; /* free a NULL pointer */ CHOLMOD(free)(42, sizeof (char), NULL, cm) ; cm->print = 5 ; CHOLMOD(print_common)("cm", cm) ; cm->print = 3 ; cm->maxrank = 3 ; cm->maxrank = CHOLMOD(maxrank)(5, cm) ; OK (cm->maxrank == 4) ; cm->maxrank = 1 ; cm->maxrank = CHOLMOD(maxrank)(5, cm) ; OK (cm->maxrank == 2) ; cm->maxrank = 8 ; /* test the error handler */ cm->error_handler = my_handler2 ; CHOLMOD(drop)(0., NULL, cm) ; cm->error_handler = NULL ; /* ---------------------------------------------------------------------- */ /* dense */ /* ---------------------------------------------------------------------- */ X = CHOLMOD(allocate_dense)(5, 4, 1, CHOLMOD_REAL, cm) ; NOP (X) ; X = CHOLMOD(allocate_dense)(1, Int_max, 1, CHOLMOD_REAL, cm) ; NOP (X) ; X = CHOLMOD(allocate_dense)(1, 1, 1, -1, cm) ; NOP (X) ; CHOLMOD(free_dense)(&X, cm) ; /* free a NULL dense matrix */ ok = CHOLMOD(free_dense)(&X, cm) ; OK (ok) ; ok = CHOLMOD(free_dense)(NULL, cm) ; OK (ok) ; /* make an invalid sparse matrix */ Sbad = CHOLMOD(speye)(2, 3, CHOLMOD_REAL, cm) ; OKP (Sbad) ; Sbad->stype = 1 ; ok = CHOLMOD(check_sparse)(Sbad, cm) ; NOT (ok) ; X = CHOLMOD(sparse_to_dense)(Sbad, cm) ; NOP (X) ; ok = CHOLMOD(free_sparse)(&Sbad, cm) ; OK (ok) ; /* make an invalid dense matrix */ Xbad = CHOLMOD(eye)(4, 4, CHOLMOD_REAL, cm) ; OKP (Xbad) ; Xbad->d = 1 ; ok = CHOLMOD(check_dense)(Xbad, cm) ; NOT (ok) ; A = CHOLMOD(dense_to_sparse)(Xbad, TRUE, cm) ; ok = CHOLMOD(free_dense)(&Xbad, cm) ; OK (ok) ; CHOLMOD(print_common)("cm", cm) ; cm->print = 5 ; CHOLMOD(print_sparse)(A, "Bad A", cm) ; cm->print = 3 ; NOP (A) ; /* ---------------------------------------------------------------------- */ /* sparse */ /* ---------------------------------------------------------------------- */ /* free a NULL sparse matrix */ ok = CHOLMOD(free_sparse)(&A, cm) ; OK (ok) ; ok = CHOLMOD(free_sparse)(NULL, cm) ; OK (ok) ; A = CHOLMOD(copy_sparse)(NULL, cm) ; NOP (A) ; /* ---------------------------------------------------------------------- */ /* error tests done */ /* ---------------------------------------------------------------------- */ printf ("------------------ null tests done\n") ; } SuiteSparse/CHOLMOD/Tcov/covall.sol0000755001170100242450000000020610533351347015753 0ustar davisfac#!/bin/csh tcov -x cm.profile z*.c >& /dev/null echo -n "statments not yet tested: " ./covs > covs.out grep "#####" *tcov | wc -l SuiteSparse/CHOLMOD/Tcov/README.txt0000644001170100242450000000453110540513363015450 0ustar davisfacTcov directory: Torture test for CHOLMOD, with statement coverage. -------------------------------------------------------------------------------- This test suite is not required to compile and use CHOLMOD. It is thus not ported to all architectures. Linux is assumed; see the Makefile for running on Solaris. Use tcov instead of gcov in the "covall" script. Edit the Makefile and change the definition of CC. You may need to change PRETTY as well. You will need to edit LIB to reflect the proper LAPACK and BLAS libraries. Requires all CHOLMOD modules except the Partition Module, which it can optionally use (and test). Also acts as a statement coverage test for AMD, COLAMD, and CCOLAMD. Type "make" in this directory to compile CHOLMOMD with statement coverage testing. Then type "make go" to run the tests. Note that about 500MB of disk space is required, mostly in the tmp/ directory. Every line of AMD, CAMD, COLAMD, CCOLAMD, and CHOLMOD will be exercised, and their results checked. The line "All tests passed" should be printed for each test on stderr. Some matrices will report NaN as their maximum error; these are the four singular test matrices (Matrix/1_0, Matrix/3singular, Matrix/c3singluar, and Matrix/z3singular). These test results are expected. Nan's will also appear in tmp/galenet_nan.out and tmp/l_galenet_nan.out; these are generated intentionally, to test the code's NaN-handling features. The source code files are first preprocessed with cc -E, and the resulting file (z_*.c, zz_*.c, l_*.c, or zl_*.c) is then compiled. This is to ensure that all lines within macros and included *.c files are tested (take a look at z_updown.c and z_solve.c if you'd like to see how loop-unrolling and real/complex templates are done in CHOLMOD, and compare those files with their source files in ../Modify and ../Cholesky). Note that many, many error messages will appear in the test output itself (tmp/*.out), because all of CHOLMOD's error handling is checked as well. These errors are expected. Any unexpected error will cause the test to fail. The last line of each output file should be "All tests successful". To remove all but the original source files and output files from this directory, type "make clean". To remove all but the files in the original distribution, type "make distclean". The output of "make go" is in the "make_go.output" file. SuiteSparse/CHOLMOD/Tcov/amdtest.c0000644001170100242450000002612010540000024015536 0ustar davisfac/* ========================================================================== */ /* === Tcov/amdtest ========================================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Test for amd v2.0 */ #include "cm.h" #include "amd.h" /* ========================================================================== */ /* === amdtest ============================================================== */ /* ========================================================================== */ void amdtest (cholmod_sparse *A) { double Control [AMD_CONTROL], Info [AMD_INFO], alpha ; Int *P, *Cp, *Ci, *Sp, *Si, *Bp, *Bi, *Ep, *Ei, *Fp, *Fi, *Len, *Nv, *Next, *Head, *Elen, *Deg, *Wi, *W, *Flag ; cholmod_sparse *C, *B, *S, *E, *F ; Int i, j, n, nrow, ncol, ok, cnz, bnz, p, trial, sorted ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ printf ("\nAMD test\n") ; if (A == NULL) { return ; } if (A->stype) { B = CHOLMOD(copy) (A, 0, 0, cm) ; } else { B = CHOLMOD(aat) (A, NULL, 0, 0, cm) ; } if (A->nrow != A->ncol) { F = CHOLMOD(copy_sparse) (B, cm) ; OK (F->nrow == F->ncol) ; CHOLMOD(sort) (F, cm) ; } else { /* A is square and unsymmetric, and may have entries in A+A' that * are not in A */ F = CHOLMOD(copy_sparse) (A, cm) ; CHOLMOD(sort) (F, cm) ; } C = CHOLMOD(copy_sparse) (B, cm) ; nrow = C->nrow ; ncol = C->ncol ; n = nrow ; OK (nrow == ncol) ; Cp = C->p ; Ci = C->i ; Bp = B->p ; Bi = B->i ; /* ---------------------------------------------------------------------- */ /* S = sorted form of B, using AMD_preprocess */ /* ---------------------------------------------------------------------- */ cnz = CHOLMOD(nnz) (C, cm) ; S = CHOLMOD(allocate_sparse) (n, n, cnz, TRUE, TRUE, 0, CHOLMOD_PATTERN, cm); Sp = S->p ; Si = S->i ; W = CHOLMOD(malloc) (n, sizeof (Int), cm) ; Flag = CHOLMOD(malloc) (n, sizeof (Int), cm) ; AMD_preprocess (n, Bp, Bi, Sp, Si, W, Flag) ; /* ---------------------------------------------------------------------- */ /* allocate workspace for amd */ /* ---------------------------------------------------------------------- */ P = CHOLMOD(malloc) (n+1, sizeof (Int), cm) ; Len = CHOLMOD(malloc) (n, sizeof (Int), cm) ; Nv = CHOLMOD(malloc) (n, sizeof (Int), cm) ; Next = CHOLMOD(malloc) (n, sizeof (Int), cm) ; Head = CHOLMOD(malloc) (n+1, sizeof (Int), cm) ; Elen = CHOLMOD(malloc) (n, sizeof (Int), cm) ; Deg = CHOLMOD(malloc) (n, sizeof (Int), cm) ; Wi = CHOLMOD(malloc) (n, sizeof (Int), cm) ; /* ---------------------------------------------------------------------- */ for (sorted = 0 ; sorted <= 1 ; sorted++) { if (sorted) CHOLMOD(sort) (C, cm) ; Cp = C->p ; Ci = C->i ; /* ------------------------------------------------------------------ */ /* order C with AMD_order */ /* ------------------------------------------------------------------ */ AMD_defaults (Control) ; AMD_defaults (NULL) ; AMD_control (Control) ; AMD_control (NULL) ; AMD_info (NULL) ; ok = AMD_order (n, Cp, Ci, P, Control, Info) ; printf ("amd return value: "ID"\n", ok) ; AMD_info (Info) ; OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ; OK (CHOLMOD(print_perm) (P, n, n, "AMD permutation", cm)) ; /* no dense rows/cols */ alpha = Control [AMD_DENSE] ; Control [AMD_DENSE] = -1 ; AMD_control (Control) ; ok = AMD_order (n, Cp, Ci, P, Control, Info) ; printf ("amd return value: "ID"\n", ok) ; AMD_info (Info) ; OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ; OK (CHOLMOD(print_perm) (P, n, n, "AMD permutation (alpha=-1)", cm)) ; /* many dense rows/cols */ Control [AMD_DENSE] = 0 ; AMD_control (Control) ; ok = AMD_order (n, Cp, Ci, P, Control, Info) ; printf ("amd return value: "ID"\n", ok) ; AMD_info (Info) ; OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ; OK (CHOLMOD(print_perm) (P, n, n, "AMD permutation (alpha=0)", cm)) ; Control [AMD_DENSE] = alpha ; /* no aggressive absorption */ Control [AMD_AGGRESSIVE] = FALSE ; AMD_control (Control) ; ok = AMD_order (n, Cp, Ci, P, Control, Info) ; printf ("amd return value: "ID"\n", ok) ; AMD_info (Info) ; OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ; OK (CHOLMOD(print_perm) (P, n, n, "AMD permutation (no agg) ", cm)) ; Control [AMD_AGGRESSIVE] = TRUE ; /* ------------------------------------------------------------------ */ /* order F with AMD_order */ /* ------------------------------------------------------------------ */ Fp = F->p ; Fi = F->i ; ok = AMD_order (n, Fp, Fi, P, Control, Info) ; printf ("amd return value: "ID"\n", ok) ; AMD_info (Info) ; OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ; OK (CHOLMOD(print_perm) (P, n, n, "F: AMD permutation", cm)) ; /* ------------------------------------------------------------------ */ /* order S with AMD_order */ /* ------------------------------------------------------------------ */ ok = AMD_order (n, Sp, Si, P, Control, Info) ; printf ("amd return value: "ID"\n", ok) ; AMD_info (Info) ; OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ; OK (CHOLMOD(print_perm) (P, n, n, "AMD permutation", cm)) ; /* ------------------------------------------------------------------ */ /* order E with AMD_2, which destroys its contents */ /* ------------------------------------------------------------------ */ E = CHOLMOD(copy) (B, 0, -1, cm) ; /* remove diagonal entries */ bnz = CHOLMOD(nnz) (E, cm) ; /* add the bare minimum extra space to E */ ok = CHOLMOD(reallocate_sparse) (bnz + n, E, cm) ; OK (ok) ; Ep = E->p ; Ei = E->i ; for (j = 0 ; j < n ; j++) { Len [j] = Ep [j+1] - Ep [j] ; } printf ("calling AMD_2:\n") ; if (n > 0) { AMD_2 (n, Ep, Ei, Len, E->nzmax, Ep [n], Nv, Next, P, Head, Elen, Deg, Wi, Control, Info) ; AMD_info (Info) ; OK (CHOLMOD(print_perm) (P, n, n, "AMD2 permutation", cm)) ; } /* ------------------------------------------------------------------ */ /* error tests */ /* ------------------------------------------------------------------ */ ok = AMD_order (n, Cp, Ci, P, Control, Info) ; OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ; ok = AMD_order (-1, Cp, Ci, P, Control, Info) ; OK (ok == AMD_INVALID); ok = AMD_order (0, Cp, Ci, P, Control, Info) ; OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ; ok = AMD_order (n, NULL, Ci, P, Control, Info) ; OK (ok == AMD_INVALID); ok = AMD_order (n, Cp, NULL, P, Control, Info) ; OK (ok == AMD_INVALID); ok = AMD_order (n, Cp, Ci, NULL, Control, Info) ; OK (ok == AMD_INVALID); if (n > 0) { printf ("AMD error tests:\n") ; p = Cp [n] ; Cp [n] = -1 ; ok = AMD_order (n, Cp, Ci, P, Control, Info) ; OK (ok == AMD_INVALID) ; if (Size_max/2 == Int_max) { Cp [n] = Int_max ; ok = AMD_order (n, Cp, Ci, P, Control, Info) ; printf ("AMD status is %d\n", ok) ; OK (ok == AMD_OUT_OF_MEMORY) ; } Cp [n] = p ; ok = AMD_order (n, Cp, Ci, P, Control, Info) ; OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ; if (Cp [n] > 0) { printf ("Mangle column zero:\n") ; i = Ci [0] ; Ci [0] = -1 ; ok = AMD_order (n, Cp, Ci, P, Control, Info) ; AMD_info (Info) ; OK (ok == AMD_INVALID) ; Ci [0] = i ; } } ok = AMD_valid (n, n, Sp, Si) ; OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ; ok = AMD_valid (-1, n, Sp, Si) ; OK (ok == AMD_INVALID) ; ok = AMD_valid (n, -1, Sp, Si) ; OK (ok == AMD_INVALID) ; ok = AMD_valid (n, n, NULL, Si) ; OK (ok == AMD_INVALID) ; ok = AMD_valid (n, n, Sp, NULL) ; OK (ok == AMD_INVALID) ; if (n > 0 && Sp [n] > 0) { p = Sp [n] ; Sp [n] = -1 ; ok = AMD_valid (n, n, Sp, Si) ; OK (ok == AMD_INVALID) ; Sp [n] = p ; p = Sp [0] ; Sp [0] = -1 ; ok = AMD_valid (n, n, Sp, Si) ; OK (ok == AMD_INVALID) ; Sp [0] = p ; p = Sp [1] ; Sp [1] = -1 ; ok = AMD_valid (n, n, Sp, Si) ; OK (ok == AMD_INVALID) ; Sp [1] = p ; i = Si [0] ; Si [0] = -1 ; ok = AMD_valid (n, n, Sp, Si) ; OK (ok == AMD_INVALID) ; Si [0] = i ; } ok = AMD_valid (n, n, Sp, Si) ; OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ; AMD_preprocess (n, Bp, Bi, Sp, Si, W, Flag) ; ok = AMD_valid (n, n, Sp, Si) ; OK (ok == AMD_OK) ; if (n > 0 && Bp [n] > 0) { p = Bp [n] ; Bp [n] = -1 ; ok = AMD_valid (n, n, Bp, Bi) ; OK (ok == AMD_INVALID) ; Bp [n] = p ; p = Bp [1] ; Bp [1] = -1 ; ok = AMD_valid (n, n, Bp, Bi) ; OK (ok == AMD_INVALID) ; Bp [1] = p ; i = Bi [0] ; Bi [0] = -1 ; ok = AMD_valid (n, n, Bp, Bi) ; OK (ok == AMD_INVALID) ; Bi [0] = i ; } AMD_preprocess (n, Bp, Bi, Sp, Si, W, Flag) ; Info [AMD_STATUS] = 777 ; AMD_info (Info) ; /* ------------------------------------------------------------------ */ /* memory tests */ /* ------------------------------------------------------------------ */ if (n > 0) { amd_malloc = cm->malloc_memory ; amd_free = cm->free_memory ; ok = AMD_order (n, Cp, Ci, P, Control, Info) ; OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ; test_memory_handler ( ) ; amd_malloc = cm->malloc_memory ; amd_free = cm->free_memory ; for (trial = 0 ; trial < 6 ; trial++) { my_tries = trial ; printf ("AMD memory trial "ID"\n", trial) ; ok = AMD_order (n, Cp, Ci, P, Control, Info) ; AMD_info (Info) ; OK (ok == AMD_OUT_OF_MEMORY || (sorted ? (ok == AMD_OK) : (ok >= AMD_OK))) ; } normal_memory_handler ( ) ; OK (CHOLMOD(print_perm) (P, n, n, "AMD2 permutation", cm)) ; amd_malloc = cm->malloc_memory ; amd_free = cm->free_memory ; } CHOLMOD(free_sparse) (&E, cm) ; } /* ---------------------------------------------------------------------- */ /* free everything */ /* ---------------------------------------------------------------------- */ CHOLMOD(free) (n, sizeof (Int), Len, cm) ; CHOLMOD(free) (n, sizeof (Int), Nv, cm) ; CHOLMOD(free) (n, sizeof (Int), Next, cm) ; CHOLMOD(free) (n+1, sizeof (Int), Head, cm) ; CHOLMOD(free) (n, sizeof (Int), Elen, cm) ; CHOLMOD(free) (n, sizeof (Int), Deg, cm) ; CHOLMOD(free) (n, sizeof (Int), Wi, cm) ; CHOLMOD(free) (n+1, sizeof (Int), P, cm) ; CHOLMOD(free) (n, sizeof (Int), W, cm) ; CHOLMOD(free) (n, sizeof (Int), Flag, cm) ; CHOLMOD(free_sparse) (&S, cm) ; CHOLMOD(free_sparse) (&B, cm) ; CHOLMOD(free_sparse) (&C, cm) ; CHOLMOD(free_sparse) (&F, cm) ; } SuiteSparse/CHOLMOD/Tcov/gpl.txt0000644001170100242450000004313310253411071015270 0ustar davisfac GNU GENERAL PUBLIC LICENSE Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. 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It is safest to attach them to the start of each source file to most effectively convey the exclusion of warranty; and each file should have at least the "copyright" line and a pointer to where the full notice is found. Copyright (C) This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Also add information on how to contact you by electronic and paper mail. If the program is interactive, make it output a short notice like this when it starts in an interactive mode: Gnomovision version 69, Copyright (C) year name of author Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the program `Gnomovision' (which makes passes at compilers) written by James Hacker. , 1 April 1989 Ty Coon, President of Vice This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Library General Public License instead of this License. SuiteSparse/CHOLMOD/Tcov/comments.txt0000644001170100242450000000006410532617404016337 0ustar davisfac Comments for testing cholmod_read/write functions. SuiteSparse/CHOLMOD/Tcov/null2.c0000644001170100242450000032626410540000061015146 0ustar davisfac/* ========================================================================== */ /* === Tcov/null2 =========================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Null and error tests, continued. */ #include "cm.h" #include "amd.h" #ifndef NPARTITION #include "camd.h" #endif #define CSETSIZE 5 /* ========================================================================== */ /* === null2 ================================================================ */ /* ========================================================================== */ void null2 (cholmod_triplet *Tok, int do_nantests) { double nm, gsave0, gsave1, r, anorm, beta [2], maxerr, xnan, rcond, ax, az, bx, bz, cx, cz, dx, dz, ex, ez ; cholmod_sparse *A, *C, *AT, *E, *F, *G, *Sok, *R0, *R1, *Aboth, *Axbad, *I1, *Abad, *R, *Acopy, *R3, *Abad2, *I, *I3, *Abad3, *AA, *Rt, *AF, *AFT, *I7, *C2, *R2, *Z ; cholmod_dense *Xok, *Bok, *Two, *X, *W, *XX, *YY, *Xbad2, *B, *Scale, *Y, *X1, *B1, *B2, *X7, *B7 ; cholmod_factor *L, *L2, *L3, *L4, *L5, *L6, *Lcopy, *Lbad, *L7 ; cholmod_triplet *T, *T2, *Tz, *T3 ; Int *fsetok, *Pok, *Flag, *Head, *Cp, *Ci, *P2, *Parent, *Lperm, *Lp, *Li, *Lnz, *Lprev, *Lnext, *Ls, *Lpi, *Lpx, *Super, *Tj, *Ti, *Enz, *Ep, *Post, *Cmember, *CParent, *Partition, *Pinv, *ATi, *ATp, *LColCount, *ColCount, *First, *Level, *fsetbad, *Pbad, *Lz, *R2p, *R2i ; double *Xwork, *Cx, *x, *Lx, *Tx, *Az, *R2x ; size_t size, nznew, gsave2 ; UF_long lr ; void *pp, *ii, *jj, *xx ; Int p, i, j, d, nrhs, nrow, ncol, stype, fsizeok, nz, ok, n2, trial, anz, nzmax, cset [CSETSIZE], Axbad_type, isreal, xtype, enz, Lxtype, Cxtype, Xxtype, Txtype, Abad2xtype, k, xtype2, Abad3xtype, save1, save2, save3, save4, ok1, fnz ; int option, asym ; FILE *f ; beta [0] = 1e-6 ; beta [1] = 0 ; xnan = 0 ; xtype = Tok->xtype ; isreal = (xtype == CHOLMOD_REAL) ; /* ---------------------------------------------------------------------- */ /* hypot and divcomplex */ /* ---------------------------------------------------------------------- */ maxerr = 0 ; ax = 4.3 ; az = 9.2 ; for (i = 0 ; i <= 1 ; i++) { if (i == 0) { bx = 3.14159 ; bz = -1.2 ; } else { bx = 0.9 ; bz = -1.2 ; } /* c = a/b */ CHOLMOD(divcomplex)(ax, az, bx, bz, &cx, &cz) ; /* d = c*b */ dx = cx * bx - cz * bz ; dz = cz * bx + cx * bz ; /* e = d-a, which should be zero */ ex = dx - ax ; ez = dz - az ; r = CHOLMOD(hypot)(ex, ez) ; MAXERR (maxerr, r, 1) ; OK (r < 1e-14) ; } /* ---------------------------------------------------------------------- */ /* create objects to test */ /* ---------------------------------------------------------------------- */ printf ("\n------------------------null2 tests:\n") ; cm->error_handler = my_handler ; CHOLMOD(check_triplet)(Tok, cm) ; nrhs = 5 ; nrow = Tok->nrow ; ncol = Tok->ncol ; d = nrow + 2 ; A = CHOLMOD(triplet_to_sparse)(Tok, 0, cm) ; /* [ */ anorm = CHOLMOD(norm_sparse)(A, 1, cm) ; anz = A->nzmax ; AT = CHOLMOD(transpose)(A, 2, cm) ; /* [ */ printf ("xtrue:\n") ; Xok = xtrue (nrow, nrhs, d, xtype) ; /* [ */ printf ("rhs:\n") ; Bok = rhs (A, nrhs, d) ; /* [ */ printf ("fset:\n") ; fsetok = prand (ncol) ; /* [ */ /* RAND */ fsetbad = prand (ncol) ; /* [ */ /* RAND */ if (ncol > 0) { fsetbad [0] = -1 ; } Pbad = prand (nrow) ; /* [ */ /* RAND */ if (nrow > 0) { Pbad [0] = -1 ; } I1 = CHOLMOD(speye)(nrow+1, nrow+1, xtype, cm) ; /* [ */ fsizeok = (ncol < 2) ? ncol : (ncol/2) ; Pok = prand (nrow) ; /* [ */ /* RAND */ R2 = CHOLMOD(allocate_sparse)(nrow, 1, nrow, FALSE, TRUE, 0, /* [ */ CHOLMOD_REAL, cm) ; OKP (R2) ; R2p = R2->p ; R2i = R2->i ; R2x = R2->x ; for (i = 0 ; i < nrow ; i++) { R2i [i] = Pok [i] ; R2x [i] = 1 ; } R2p [0] = 0 ; R2p [1] = nrow ; stype = A->stype ; Two = CHOLMOD(zeros)(1, 1, xtype, cm) ; /* [ */ *((double *)(Two->x)) = 2 ; Pinv = CHOLMOD(malloc)(nrow, sizeof (Int), cm) ; /* [ */ Parent = CHOLMOD(malloc)(nrow, sizeof (Int), cm) ; Post = CHOLMOD(malloc)(nrow, sizeof (Int), cm) ; Cmember = CHOLMOD(malloc)(nrow, sizeof (Int), cm) ; CParent = CHOLMOD(malloc)(nrow, sizeof (Int), cm) ; Partition = CHOLMOD(malloc)(nrow, sizeof (Int), cm) ; ColCount = CHOLMOD(malloc)(nrow, sizeof (Int), cm) ; First = CHOLMOD(malloc)(nrow, sizeof (Int), cm) ; Level = CHOLMOD(malloc)(nrow, sizeof (Int), cm) ; printf ("etree:\n") ; if (AT->stype >= 0) { /* AT is unsymmetric, or symmetric/upper */ CHOLMOD(etree)(AT, Parent, cm) ; } else { /* A is symmetric/upper */ CHOLMOD(etree)(A, Parent, cm) ; } CHOLMOD(check_parent)(Parent, nrow, cm) ; for (cm->print = 0 ; cm->print <= ((nrow <= 30) ? 5 : 4) ; cm->print++) { CHOLMOD(print_parent)(Parent, nrow, "Parent", cm) ; } cm->print = 1 ; /* get row 0 and row 1 of A */ R0 = NULL ; R1 = NULL ; Aboth = NULL ; Sok = NULL ; if (isreal) { Aboth = CHOLMOD(copy)(A, 0, 1, cm) ; /* [ */ Sok = CHOLMOD(copy)(A, 0, 0, cm) ; Aboth->sorted = FALSE ; } if (isreal) /* [ */ { if (nrow > 1) { cm->print = 4 ; if (nrow < 10) { ok = CHOLMOD(print_sparse)(Aboth, "Aboth", cm) ; OK (ok) ; } i = 0 ; R0 = CHOLMOD(submatrix)(Aboth, &i, 1, NULL, -1, TRUE, TRUE, cm) ; ok = CHOLMOD(print_sparse)(R0, "Row zero", cm) ; OK (ok) ; i = 1 ; R1 = CHOLMOD(submatrix)(Aboth, &i, 1, NULL, -1, TRUE, TRUE, cm) ; ok = CHOLMOD(print_sparse)(R1, "Row one", cm) ; OK (ok) ; Rt = CHOLMOD(transpose)(R1, 1, cm) ; C = CHOLMOD(ssmult)(R0, Rt, 0, TRUE, TRUE, cm) ; OKP (C) ; ok = CHOLMOD(print_sparse)(C, "(Row zero)*(Row one)'", cm) ;OK (ok); ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; ok = CHOLMOD(free_sparse)(&Rt, cm) ; OK (ok) ; cm->print = 1 ; } } /* Abad: symmetric but not square, or null if A is square */ if (A->nrow != A->ncol) { Abad = CHOLMOD(copy_sparse)(A, cm) ; /* [ */ Abad->stype = 1 ; } else { Abad = NULL ; } /* Abad2: sparse matrix with invalid xtype */ printf ("allocate Abad2:\n") ; Abad2 = CHOLMOD(copy_sparse)(A, cm) ; /* [ */ cm->print = 4 ; CHOLMOD(print_sparse)(Abad2, "Abad2", cm) ; cm->print = 1 ; Abad2xtype = Abad2->xtype ; Abad2->xtype = -999 ; /* Xbad2: dense matrix with invalid xtype */ printf ("allocate Xbad2:\n") ; Xbad2 = CHOLMOD(zeros)(2, 2, CHOLMOD_REAL, cm) ; /* [ */ Xbad2->xtype = -911 ; /* ---------------------------------------------------------------------- */ /* expect lots of errors */ /* ---------------------------------------------------------------------- */ printf ("\n------------------------null2 tests: ERRORs will occur\n") ; cm->error_handler = NULL ; /* ---------------------------------------------------------------------- */ /* transpose */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(transpose)(Abad2, 1, cm) ; NOP (C) ; ok = CHOLMOD(sort)(Abad2, cm) ; NOT (ok) ; ok = CHOLMOD(sort)(NULL, cm) ; NOT (ok) ; if (nrow > 0) { C = CHOLMOD(ptranspose)(A, 1, Pbad, NULL, 0, cm) ; NOP (C) ; } C = CHOLMOD(allocate_sparse)(ncol, nrow, anz, TRUE, TRUE, -(A->stype), xtype, cm) ; OKP (C) ; ok = CHOLMOD(transpose_unsym)(A, 1, NULL, NULL, 0, C, cm) ; OK (ok); ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; C = CHOLMOD(allocate_sparse)(ncol, nrow, anz, TRUE, FALSE, -(A->stype), xtype, cm) ; OKP (C) ; ok = CHOLMOD(transpose_unsym)(A, 1, NULL, NULL, 0, C, cm) ; OK (ok); ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; C = CHOLMOD(allocate_sparse)(ncol, nrow, anz, TRUE, FALSE, -(A->stype), xtype, cm) ; OKP (C) ; ok = CHOLMOD(transpose_unsym)(A, 1, Pok, NULL, 0, C, cm) ; OK (ok); ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; C = CHOLMOD(allocate_sparse)(ncol, nrow, anz, TRUE, FALSE, -(A->stype), xtype, cm) ; OKP (C) ; ok = CHOLMOD(transpose_unsym)(A, 1, Pok, fsetok, fsizeok, C, cm) ; OK (ok); ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; C = CHOLMOD(allocate_sparse)(ncol, nrow, anz, TRUE, FALSE, -(A->stype), xtype, cm) ; OKP (C) ; ok = CHOLMOD(transpose_unsym)(A, 1, NULL, fsetok, fsizeok, C, cm) ; OK (ok); ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; C = CHOLMOD(allocate_sparse)(ncol, nrow, anz, TRUE, FALSE, -(A->stype), CHOLMOD_PATTERN, cm) ; OKP (C) ; ok = CHOLMOD(transpose_unsym)(A, 1, NULL, fsetok, fsizeok, C, cm) ; OK (ok); E = CHOLMOD(allocate_sparse)(nrow, ncol, anz, TRUE, FALSE, (A->stype), CHOLMOD_PATTERN, cm) ; OKP (C) ; enz = CHOLMOD(nnz)(E, cm) ; OK (enz == 0) ; ok = CHOLMOD(transpose_unsym)(C, 1, NULL, Pok, nrow, E, cm) ; OK (ok); ok = CHOLMOD(free_sparse)(&E, cm) ; OK (ok) ; if (A->nrow != A->ncol) { ok = CHOLMOD(transpose_sym)(A, 1, NULL, C, cm) ; NOT (ok) ; } ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; /* Abad3: sparse matrix with invalid xtype [ */ printf ("allocate Abad3:\n") ; C = CHOLMOD(copy_sparse)(A, cm) ; Abad3 = CHOLMOD(transpose)(A, 1, cm) ; OKP (Abad3) ; E = CHOLMOD(transpose)(A, 1, cm) ; OKP (E) ; Abad3xtype = Abad3->xtype ; Abad3->xtype = -999 ; ok = CHOLMOD(transpose_sym)(C, 1, NULL, Abad3, cm) ; NOT (ok) ; ok = CHOLMOD(transpose_sym)(Abad3, 1, NULL, C, cm) ; NOT (ok) ; ok = CHOLMOD(transpose_unsym)(C, 1, NULL, NULL, 0, Abad3, cm) ;NOT (ok); ok = CHOLMOD(transpose_unsym)(Abad3, 1, NULL, NULL, 0, C, cm) ;NOT (ok); switch (xtype) { case CHOLMOD_REAL: CHOLMOD(sparse_xtype)(CHOLMOD_COMPLEX, E, cm) ; break ; case CHOLMOD_COMPLEX: CHOLMOD(sparse_xtype)(CHOLMOD_ZOMPLEX, E, cm) ; break ; case CHOLMOD_ZOMPLEX: CHOLMOD(sparse_xtype)(CHOLMOD_COMPLEX, E, cm) ; break ; } printf ("mismatch start [:\n") ; ok = CHOLMOD(transpose_sym)(C, 1, NULL, E, cm) ; NOT (ok) ; ok = CHOLMOD(transpose_sym)(E, 1, NULL, C, cm) ; NOT (ok) ; ok = CHOLMOD(transpose_sym)(C, 2, NULL, E, cm) ; NOT (ok) ; ok = CHOLMOD(transpose_sym)(E, 2, NULL, C, cm) ; NOT (ok) ; ok = CHOLMOD(transpose_unsym)(C, 1, NULL, NULL, 0, E, cm) ; NOT (ok); ok = CHOLMOD(transpose_unsym)(E, 1, NULL, NULL, 0, C, cm) ; NOT (ok); ok = CHOLMOD(transpose_unsym)(C, 2, NULL, NULL, 0, E, cm) ; NOT (ok); ok = CHOLMOD(transpose_unsym)(E, 2, NULL, NULL, 0, C, cm) ; NOT (ok); printf ("mismatch done ]\n") ; printf ("wrong dim [:\n") ; ok = CHOLMOD(transpose_sym)(C, 1, NULL, I1, cm) ; NOT (ok) ; ok = CHOLMOD(transpose_sym)(I1, 1, NULL, C, cm) ; NOT (ok) ; ok = CHOLMOD(transpose_unsym)(C, 1, NULL, NULL, 0, I1, cm) ; NOT (ok); ok = CHOLMOD(transpose_unsym)(I1, 1, NULL, NULL, 0, C, cm) ; NOT (ok); ok = CHOLMOD(transpose_unsym)(C, 2, NULL, NULL, 0, I1, cm) ; NOT (ok); ok = CHOLMOD(transpose_unsym)(I1, 2, NULL, NULL, 0, C, cm) ; NOT (ok); printf ("wrong dim ]\n") ; nz = CHOLMOD(nnz)(C, cm) ; if (nz > 10) { printf ("F too small [:\n") ; F = CHOLMOD(allocate_sparse)(C->ncol, C->nrow, C->nzmax-5, TRUE, TRUE, -(C->stype), C->xtype, cm) ; OKP (F) ; ok = CHOLMOD(transpose_sym)(C, 1, NULL, F, cm) ; NOT (ok) ; ok = CHOLMOD(transpose_unsym)(C, 1, NULL, NULL, 0, F, cm) ; NOT (ok); CHOLMOD(free_sparse)(&F, cm) ; printf ("F too small ]\n") ; } ok = CHOLMOD(transpose_unsym)(C, 1, NULL, NULL, 0, NULL, cm) ; NOT (ok); ok = CHOLMOD(transpose_unsym)(NULL, 1, NULL, NULL, 0, C, cm) ; NOT (ok); ok = CHOLMOD(transpose_sym)(C, 1, NULL, NULL, cm) ; NOT (ok); ok = CHOLMOD(transpose_sym)(NULL, 1, NULL, C, cm) ; NOT (ok); CHOLMOD(free_sparse)(&C, cm) ; CHOLMOD(free_sparse)(&E, cm) ; Abad3->xtype = Abad3xtype ; CHOLMOD(free_sparse)(&Abad3, cm) ; /* ] */ cm->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* aat */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(aat)(NULL, NULL, 0, 0, cm) ; NOP (C) ; if (stype) { C = CHOLMOD(aat)(A, fsetok, fsizeok, 0, cm) ; NOP (C) ; } else { C = CHOLMOD(aat)(A, fsetok, fsizeok, 0, cm) ; OKP (C) ; CHOLMOD(free_sparse)(&C, cm) ; C = CHOLMOD(aat)(Abad2, fsetok, fsizeok, 0, cm) ; NOP (C) ; } /* ---------------------------------------------------------------------- */ /* add */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(add)(A, NULL, one, one, TRUE, TRUE, cm) ; NOP (C) ; C = CHOLMOD(add)(NULL, AT, one, one, TRUE, TRUE, cm) ; NOP (C) ; C = CHOLMOD(add)(A, AT, one, one, TRUE, TRUE, cm) ; if (A->nrow == A->ncol && isreal) { OKP (C) ; /* C should equal 2*A if A=A' */ if (stype) { double *s ; E = CHOLMOD(copy_sparse)(A, cm) ; CHOLMOD(scale)(Two, CHOLMOD_SCALAR, E, cm) ; F = CHOLMOD(add)(C, E, one, minusone, TRUE, TRUE, cm) ; CHOLMOD(drop)(0., F, cm) ; nz = CHOLMOD(nnz)(F, cm) ; OK (nz == 0) ; CHOLMOD(free_sparse)(&E, cm) ; CHOLMOD(free_sparse)(&F, cm) ; Scale = CHOLMOD(zeros)(nrow, 1, CHOLMOD_REAL, cm) ; s = Scale->x ; for (i = 0 ; i < nrow ; i++) { s [i] = 2 ; } E = CHOLMOD(copy_sparse)(A, cm) ; CHOLMOD(scale)(Scale, CHOLMOD_ROW, E, cm) ; F = CHOLMOD(add)(C, E, one, minusone, TRUE, TRUE, cm) ; CHOLMOD(drop)(0., F, cm) ; nz = CHOLMOD(nnz)(F, cm) ; r = CHOLMOD(norm_sparse)(F, 0, cm) ; OK (nz == 0) ; CHOLMOD(free_sparse)(&E, cm) ; CHOLMOD(free_sparse)(&F, cm) ; E = CHOLMOD(copy_sparse)(A, cm) ; CHOLMOD(scale)(Scale, CHOLMOD_COL, E, cm) ; F = CHOLMOD(add)(C, E, one, minusone, TRUE, TRUE, cm) ; CHOLMOD(drop)(0., F, cm) ; nz = CHOLMOD(nnz)(F, cm) ; r = CHOLMOD(norm_sparse)(F, 0, cm) ; OK (nz == 0) ; CHOLMOD(free_sparse)(&E, cm) ; CHOLMOD(free_sparse)(&F, cm) ; for (i = 0 ; i < nrow ; i++) { s [i] = sqrt (2) ; } E = CHOLMOD(copy_sparse)(A, cm) ; CHOLMOD(scale)(Scale, CHOLMOD_SYM, E, cm) ; F = CHOLMOD(add)(C, E, one, minusone, TRUE, TRUE, cm) ; CHOLMOD(drop)(0., F, cm) ; nz = CHOLMOD(nnz)(F, cm) ; r = CHOLMOD(norm_sparse)(F, 0, cm) ; OK (r < 1e-12*anorm) ; Scale->x = NULL ; CHOLMOD(scale)(Scale, CHOLMOD_SYM, E, cm) ; Scale->x = s ; OKP (E) ; OKP (cm) ; ok = CHOLMOD(scale)(NULL, CHOLMOD_ROW, E, cm) ; NOT (ok) ; ok = CHOLMOD(scale)(Scale, CHOLMOD_SYM, NULL, cm) ; NOT (ok) ; ok = CHOLMOD(scale)(NULL, CHOLMOD_SYM, NULL, cm) ; NOT (ok) ; ok = CHOLMOD(scale)(Scale, -1, E, cm) ; NOT (ok) ; CHOLMOD(free_sparse)(&E, cm) ; CHOLMOD(free_sparse)(&F, cm) ; CHOLMOD(free_dense)(&Scale, cm) ; } CHOLMOD(free_sparse)(&C, cm) ; } else { NOP (C) ; } Axbad = CHOLMOD(copy_sparse)(A, cm) ; /* [ */ Axbad_type = Axbad->xtype ; Axbad->xtype = CHOLMOD_COMPLEX ; C = CHOLMOD(add)(A, Axbad, one, one, TRUE, TRUE, cm) ; NOP (C) ; if (nrow > 1 && xtype == CHOLMOD_REAL) { /* C = A (0,:) + A (1,:) */ C = CHOLMOD(add)(R0, R1, one, one, TRUE, TRUE, cm) ; OKP (C) ; OK (CHOLMOD(check_sparse)(C, cm)) ; ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; } ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; ok = CHOLMOD(free_sparse)(NULL, cm) ; OK (ok) ; /* ---------------------------------------------------------------------- */ /* sparse */ /* ---------------------------------------------------------------------- */ cm->print = 4 ; ok = CHOLMOD(reallocate_sparse)(10, NULL, cm) ; NOT (ok) ; C = CHOLMOD(allocate_sparse)(10, 10, 10, TRUE, TRUE, 0, -1, cm) ; NOP (C) ; ok = CHOLMOD(reallocate_sparse)(Abad2->nzmax, Abad2, cm) ; NOT (ok) ; C = CHOLMOD(copy_sparse)(Abad2, cm) ; NOP (C) ; C = CHOLMOD(allocate_sparse)(2, 3, 6, TRUE, TRUE, 1, 0, cm) ; NOP (C) ; C = CHOLMOD(copy)(A, 0, -1, cm) ; OKP (C) ; E = unpack (C) ; OKP (E) ; F = CHOLMOD(copy_sparse)(E, cm) ; OKP (F) ; ok = CHOLMOD(sparse_xtype)(CHOLMOD_REAL, C, cm) ; OK (ok) ; ok = CHOLMOD(sparse_xtype)(CHOLMOD_REAL, F, cm) ; OK (ok) ; /* G = C-F */ G = CHOLMOD(add)(C, F, one, minusone, TRUE, FALSE, cm) ; OKP (G) ; ok = CHOLMOD(drop)(0., G, cm) ; OK (ok) ; nz = CHOLMOD(nnz)(G, cm) ; CHOLMOD(print_sparse)(C, "C", cm) ; CHOLMOD(print_sparse)(E, "E", cm) ; CHOLMOD(print_sparse)(F, "F", cm) ; CHOLMOD(print_sparse)(G, "G", cm) ; OK (nz == 0) ; CHOLMOD(free_sparse)(&C, cm) ; CHOLMOD(free_sparse)(&E, cm) ; CHOLMOD(free_sparse)(&F, cm) ; CHOLMOD(free_sparse)(&G, cm) ; cm->print = 1 ; /* ---------------------------------------------------------------------- */ /* scale */ /* ---------------------------------------------------------------------- */ ok = CHOLMOD(scale)(Two, -1, C, cm) ; NOT (ok) ; if (nrow > 1) { E = CHOLMOD(copy_sparse)(A, cm) ; OKP (E) ; CHOLMOD(scale)(Two, CHOLMOD_ROW, E, cm) ; NOT (ok) ; ok = CHOLMOD(free_sparse)(&E, cm) ; OK (ok) ; } /* ---------------------------------------------------------------------- */ /* amd */ /* ---------------------------------------------------------------------- */ ok = CHOLMOD(amd)(NULL, NULL, 0, NULL, cm) ; NOT (ok) ; ok = CHOLMOD(amd)(A, NULL, 0, NULL, cm) ; NOT (ok) ; ok = CHOLMOD(amd)(NULL, NULL, 0, Pok, cm) ; NOT (ok) ; ok = CHOLMOD(amd)(A, NULL, 0, Pok, cm) ; OK (ok) ; cm->current = -1 ; ok = CHOLMOD(amd)(A, NULL, 0, Pok, cm) ; OK (ok) ; cm->current = 0 ; ok = CHOLMOD(print_perm)(Pok, nrow, nrow, "AMD perm", cm) ; OK (ok) ; i = cm->print ; cm->print = 4 ; if (A->nrow < 1000 && isreal) { CHOLMOD(print_sparse)(Aboth, "Aboth", cm) ; ok = CHOLMOD(amd)(Aboth, NULL, 0, Pok, cm) ; OK (ok) ; } cm->print = i ; ok = CHOLMOD(amd)(Abad2, NULL, 0, Pok, cm) ; NOT (ok) ; /* ---------------------------------------------------------------------- */ /* camd */ /* ---------------------------------------------------------------------- */ #ifndef NPARTITION ok = CHOLMOD(camd)(NULL, NULL, 0, NULL, NULL, cm) ; NOT (ok) ; ok = CHOLMOD(camd)(A, NULL, 0, NULL, NULL, cm) ; NOT (ok) ; ok = CHOLMOD(camd)(NULL, NULL, 0, NULL, Pok, cm) ; NOT (ok) ; ok = CHOLMOD(camd)(A, NULL, 0, NULL, Pok, cm) ; OK (ok) ; cm->current = -1 ; ok = CHOLMOD(camd)(A, NULL, 0, NULL, Pok, cm) ; OK (ok) ; cm->current = 0 ; ok = CHOLMOD(print_perm)(Pok, nrow, nrow, "CAMD perm", cm) ; OK (ok) ; i = cm->print ; cm->print = 4 ; if (A->nrow < 1000 && isreal) { CHOLMOD(print_sparse)(Aboth, "Aboth", cm) ; ok = CHOLMOD(camd)(Aboth, NULL, 0, NULL, Pok, cm) ; OK (ok) ; } cm->print = i ; ok = CHOLMOD(camd)(Abad2, NULL, 0, NULL, Pok, cm) ; NOT (ok) ; #endif /* ---------------------------------------------------------------------- */ /* analyze */ /* ---------------------------------------------------------------------- */ cm->nmethods = 1 ; cm->method [0].ordering = -1 ; ok = CHOLMOD(print_common)("Bad cm", cm) ; NOT (ok) ; ok = CHOLMOD(analyze_ordering)(NULL, 0, NULL, NULL, 0, NULL, NULL, NULL, NULL, NULL, cm) ; NOT (ok) ; L = CHOLMOD(analyze)(NULL, cm) ; NOP (L) ; L = CHOLMOD(analyze)(Abad2, cm) ; NOP (L) ; L = CHOLMOD(analyze)(A, cm) ; OKP (L) ; cm->nmethods = 0 ; /* restore defaults */ cm->method [0].ordering = CHOLMOD_GIVEN ; cm->print = 4 ; ok = CHOLMOD(print_common)("OKcm", cm) ; OK (ok) ; ok = CHOLMOD(print_factor)(L, "L symbolic", cm) ; OK (ok) ; cm->print = 1 ; ok = CHOLMOD(free_factor)(&L, cm) ; OK (ok) ; ok = CHOLMOD(free_factor)(&L, cm) ; OK (ok) ; ok = CHOLMOD(free_factor)(NULL, cm) ; OK (ok) ; /* ---------------------------------------------------------------------- */ /* band */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(band)(NULL, 0, 0, 0, cm) ; NOP (C) ; C = CHOLMOD(band)(Abad2, 0, 0, 0, cm) ; NOP (C) ; /* ---------------------------------------------------------------------- */ /* ccolamd */ /* ---------------------------------------------------------------------- */ #ifndef NPARTITION ok = CHOLMOD(ccolamd)(NULL, fsetok, fsizeok, NULL, Pok, cm) ; NOT (ok) ; ok = CHOLMOD(ccolamd)(A, fsetok, fsizeok, NULL, NULL, cm) ; NOT (ok) ; ok = CHOLMOD(ccolamd)(A, fsetok, fsizeok, NULL, Pok, cm) ; if (stype) { NOT (ok) ; } else { OK (ok) ; } cm->current = -1 ; ok = CHOLMOD(ccolamd)(A, fsetok, fsizeok, NULL, Pok, cm) ; cm->current = 0 ; if (stype) { NOT (ok) ; } else { OK (ok) ; } #endif /* ---------------------------------------------------------------------- */ /* copy */ /* ---------------------------------------------------------------------- */ CHOLMOD(print_sparse)(Abad, "Abad", cm) ; C = CHOLMOD(copy)(Abad, 0, 1, cm) ; CHOLMOD(print_sparse)(C, "copy of Abad", cm) ; NOP (C) ; C = CHOLMOD(copy_sparse)(Abad, cm) ; CHOLMOD(print_sparse)(C, "another copy of Abad", cm) ; NOP (C) ; C = CHOLMOD(copy)(A, 0, -1, cm) ; OKP (C) ; OK (nzdiag (C) == 0) ; ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; /* ---------------------------------------------------------------------- */ /* submatrix */ /* ---------------------------------------------------------------------- */ if (A->nrow == A->ncol) { /* submatrix cannot operation on symmetric matrices */ C = CHOLMOD(copy)(A, 1, 0, cm) ; OKP (C) ; E = CHOLMOD(submatrix)(C, NULL, -1, NULL, -1, TRUE, TRUE, cm); NOP (E) ; ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; } E = CHOLMOD(submatrix)(Abad2, NULL, -1, NULL, -1, TRUE, TRUE, cm) ; NOP(E) ; if (A->stype == 0 && isreal) { /* E = A(:,:) */ E = CHOLMOD(submatrix)(NULL, NULL,-1, NULL,-1, TRUE, TRUE, cm) ; NOP(E); E = CHOLMOD(submatrix)(A, NULL, -1, NULL, -1, TRUE, TRUE, cm) ; OKP(E) ; /* C = A-E */ C = CHOLMOD(add)(A, E, one, minusone, TRUE, TRUE, cm) ; OKP (C) ; ok = CHOLMOD(drop)(0., C, cm) ; OK (ok) ; ok = CHOLMOD(drop)(0., Abad2, cm) ; NOT(ok) ; nz = CHOLMOD(nnz)(C, cm) ; OK (nz == 0) ; ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; ok = CHOLMOD(free_sparse)(&E, cm) ; OK (ok) ; i = -1 ; E = CHOLMOD(submatrix)(A, &i, 1, NULL, -1, TRUE, TRUE, cm) ; NOP(E) ; E = CHOLMOD(submatrix)(A, NULL, -1, &i, 1, TRUE, TRUE, cm) ; NOP(E) ; E = CHOLMOD(submatrix)(A, &i, 1, &i, 1, TRUE, TRUE, cm) ; NOP(E) ; i = 0 ; j = -1 ; E = CHOLMOD(submatrix)(A, &i, 1, &j, 1, TRUE, TRUE, cm) ; NOP(E) ; } /* ---------------------------------------------------------------------- */ /* read */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(read_sparse)(NULL, cm) ; NOP (C) ; X = CHOLMOD(read_dense)(NULL, cm) ; NOP (X) ; pp = CHOLMOD(read_matrix)(NULL, 1, NULL, cm) ; NOP (pp) ; pp = CHOLMOD(read_matrix)((FILE *) 1, 1, NULL, cm) ; NOP (pp) ; T3 = CHOLMOD(read_triplet)(NULL, cm) ; NOP (T3) ; /* ---------------------------------------------------------------------- */ /* write */ /* ---------------------------------------------------------------------- */ asym = CHOLMOD(write_sparse) (NULL, NULL, NULL, NULL, cm) ; NOT (asym>=0); asym = CHOLMOD(write_sparse) ((FILE *) 1, NULL, NULL, NULL, cm) ; NOT (asym>=0); asym = CHOLMOD(write_dense) (NULL, NULL, NULL, cm) ; NOT (asym>=0); asym = CHOLMOD(write_dense) ((FILE *) 1, NULL, NULL, cm) ; NOT (asym>=0); f = fopen ("temp4.mtx", "w") ; asym = CHOLMOD(write_sparse) (f, A, NULL, "garbage.txt", cm) ; fclose (f) ; printf ("write_sparse, asym: %d\n", asym) ; OK (asym == EMPTY) ; if (A != NULL) { save1 = A->xtype ; A->xtype = 999 ; f = fopen ("temp4.mtx", "w") ; asym = CHOLMOD(write_sparse) (f, A, NULL, NULL, cm) ; fclose (f) ; printf ("write_sparse, asym: %d\n", asym) ; OK (asym == EMPTY) ; A->xtype = save1 ; } Z = CHOLMOD(speye) (nrow+1, ncol+1, CHOLMOD_PATTERN, cm) ; f = fopen ("temp4.mtx", "w") ; asym = CHOLMOD(write_sparse) (f, A, Z, NULL, cm) ; fclose (f) ; printf ("write_sparse, asym: %d with Z\n", asym) ; OK (asym == EMPTY) ; Z->xtype = 999 ; f = fopen ("temp4.mtx", "w") ; asym = CHOLMOD(write_sparse) (f, A, Z, NULL, cm) ; fclose (f) ; printf ("write_sparse, asym: %d with Z2\n", asym) ; OK (asym == EMPTY) ; Z->xtype = CHOLMOD_PATTERN ; CHOLMOD(free_sparse) (&Z, cm) ; Z = CHOLMOD(speye) (0, ncol+1, CHOLMOD_PATTERN, cm) ; f = fopen ("temp4.mtx", "w") ; asym = CHOLMOD(write_sparse) (f, A, Z, NULL, cm) ; fclose (f) ; printf ("write_sparse, asym: %d with Z\n", asym) ; if (A == NULL) { OK (asym == EMPTY) ; } else { OK (asym > EMPTY) ; } CHOLMOD(free_sparse) (&Z, cm) ; X = CHOLMOD(ones) (4, 4, CHOLMOD_REAL, cm) ; f = fopen ("temp6.mtx", "w") ; asym = CHOLMOD(write_dense) (f, X, "garbage.txt", cm) ; fclose (f) ; OK (asym == EMPTY) ; X->xtype = 999 ; f = fopen ("temp6.mtx", "w") ; asym = CHOLMOD(write_dense) (f, X, NULL, cm) ; fclose (f) ; OK (asym == EMPTY) ; X->xtype = CHOLMOD_REAL ; CHOLMOD(free_dense) (&X, cm) ; /* ---------------------------------------------------------------------- */ /* print_common */ /* ---------------------------------------------------------------------- */ cm->print = 4 ; ok = CHOLMOD(print_common)("Null", NULL) ; NOT (ok) ; for (cm->status = CHOLMOD_INVALID ; cm->status <= CHOLMOD_DSMALL ; cm->status++) { ok = CHOLMOD(print_common)("status", cm) ; OK (ok) ; } cm->status = 999 ; ok = CHOLMOD(print_common)("bad status", cm) ; NOT (ok) ; cm->status = CHOLMOD_OK ; Flag = cm->Flag ; cm->Flag = NULL ; ok = CHOLMOD(print_common)("bad Flag", cm) ; NOT (ok) ; cm->Flag = Flag ; ok = CHOLMOD(print_common)("ok Flag", cm) ; OK (ok) ; Flag [0] = Int_max ; ok = CHOLMOD(print_common)("bad Flag", cm) ; NOT (ok) ; Flag [0] = -1 ; ok = CHOLMOD(print_common)("ok Flag", cm) ; OK (ok) ; Head = cm->Head ; cm->Head = NULL ; ok = CHOLMOD(print_common)("bad Head", cm) ; NOT (ok) ; cm->Head = Head ; ok = CHOLMOD(print_common)("ok Head", cm) ; OK (ok) ; Head [0] = Int_max ; ok = CHOLMOD(print_common)("bad Head", cm) ; NOT (ok) ; Head [0] = -1 ; ok = CHOLMOD(print_common)("ok Head", cm) ; OK (ok) ; Xwork = cm->Xwork ; cm->Xwork = NULL ; ok = CHOLMOD(print_common)("bad Xwork", cm) ; NOT (ok) ; cm->Xwork = Xwork ; ok = CHOLMOD(print_common)("ok Xwork", cm) ; OK (ok) ; Xwork [0] = 1 ; ok = CHOLMOD(print_common)("bad Xwork", cm) ; NOT (ok) ; Xwork [0] = 0 ; ok = CHOLMOD(print_common)("ok Xwork", cm) ; OK (ok) ; p = cm->nmethods ; i = cm->method [0].ordering ; cm->nmethods = 1 ; cm->method [0].ordering = 999 ; ok = CHOLMOD(print_common)("bad method", cm) ; NOT (ok) ; cm->nmethods = p ; cm->method [0].ordering = i ; /* ---------------------------------------------------------------------- */ /* print_sparse */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(copy_sparse)(A, cm) ; OKP (C) ; cm->print = 3 ; C->itype = EMPTY ; ok = CHOLMOD(print_sparse)(C, "CIbad", cm) ; NOT (ok) ; C->itype = CHOLMOD_INTLONG ; ok = CHOLMOD(print_sparse)(C, "Cibad", cm) ; NOT (ok) ; C->itype = cm->itype ; cm->print = 1 ; cm->print = 4 ; #ifdef LONG C->itype = CHOLMOD_INT ; #else C->itype = CHOLMOD_LONG ; #endif ok = CHOLMOD(print_sparse)(C, "Cibad2", cm) ; NOT (ok) ; C->itype = cm->itype ; cm->print = 1 ; C->dtype = CHOLMOD_SINGLE ; ok = CHOLMOD(print_sparse)(C, "Cdbad", cm) ; NOT (ok) ; C->dtype = EMPTY ; ok = CHOLMOD(print_sparse)(C, "CDbad", cm) ; NOT (ok) ; C->dtype = CHOLMOD_DOUBLE ; Cxtype = C->xtype ; C->xtype = EMPTY ; ok = CHOLMOD(print_sparse)(C, "CXbad", cm) ; NOT (ok) ; C->xtype = Cxtype ; ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ; Cp = C->p ; Ci = C->i ; Cx = C->x ; C->p = NULL ; ok = CHOLMOD(print_sparse)(C, "Cp bad", cm) ; NOT (ok) ; C->p = Cp ; ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ; C->i = NULL ; ok = CHOLMOD(print_sparse)(C, "Ci bad", cm) ; NOT (ok) ; C->i = Ci ; ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ; C->x = NULL ; ok = CHOLMOD(print_sparse)(C, "Cx bad", cm) ; NOT (ok) ; C->x = Cx ; ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ; Cp [0] = 42 ; ok = CHOLMOD(print_sparse)(C, "Cp [0] bad", cm) ; NOT (ok) ; Cp [0] = 0 ; ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ; p = Cp [ncol] ; Cp [ncol] = C->nzmax + 10 ; ok = CHOLMOD(print_sparse)(C, "Cp [ncol] bad", cm) ; NOT (ok) ; Cp [ncol] = p ; ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ; p = Cp [ncol] ; Cp [ncol] = -1 ; ok = CHOLMOD(print_sparse)(C, "Cp [ncol] neg", cm) ; NOT (ok) ; Cp [ncol] = p ; ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ; if (ncol > 0) { p = Cp [1] ; Cp [1] = 2*nrow + 1 ; ok = CHOLMOD(print_sparse)(C, "Cp [1] bad", cm) ; NOT (ok) ; Cp [1] = p ; ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ; } if (ncol > 2) { p = Cp [2] ; Cp [2] = Cp [1] - 1 ; ok = CHOLMOD(print_sparse)(C, "Cp [2] bad", cm) ; NOT (ok) ; Cp [2] = p ; ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ; } if (Cp [ncol] > 0) { i = Ci [0] ; Ci [0] = -1 ; ok = CHOLMOD(print_sparse)(C, "Ci [0] neg", cm) ; NOT (ok) ; Ci [0] = i ; ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ; } if (ncol > 0 && C->sorted && Cp [1] - Cp [0] > 2) { i = Ci [0] ; Ci [0] = nrow-1 ; ok = CHOLMOD(print_sparse)(C, "Ci [0] unsorted", cm) ; NOT (ok) ; Ci [0] = i ; ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ; } if (ncol > 0 && C->sorted && ncol > 2 && Cp [1] - Cp [0] > 2) { /* swap the first two entries */ p = Ci [0] ; Ci [0] = Ci [1] ; Ci [1] = p ; ok = CHOLMOD(print_sparse)(C, "Ci [0] unsorted", cm) ; NOT (ok) ; C->sorted = FALSE ; ok = CHOLMOD(print_sparse)(C, "Ci [0] unsorted", cm) ; OK (ok) ; Ci [1] = Ci [0] ; ok = CHOLMOD(print_sparse)(C, "Ci [0] duplicate", cm) ; NOT (ok) ; Ci [1] = p ; ok = CHOLMOD(print_sparse)(C, "Ci [0] unsorted", cm) ; OK (ok) ; p = Ci [0] ; Ci [0] = Ci [1] ; Ci [1] = p ; ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ; C->sorted = TRUE ; ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ; } E = CHOLMOD(copy_sparse)(C, cm) ; OKP (E) ; Enz = CHOLMOD(malloc)(ncol, sizeof (Int), cm) ; OKP (Enz) ; E->nz = Enz ; Ep = E->p ; for (j = 0 ; j < ncol ; j++) { Enz [j] = Ep [j+1] - Ep [j] ; } E->packed = FALSE ; ok = CHOLMOD(print_sparse)(E, "E unpacked ok", cm) ; OK (ok) ; ok = CHOLMOD(band_inplace)(0, 0, 0, E, cm) ; NOT (ok) ; E->nz = NULL ; ok = CHOLMOD(print_sparse)(E, "E unpacked bad", cm) ; NOT (ok) ; E->nz = Enz ; ok = CHOLMOD(print_sparse)(E, "E unpacked ok", cm) ; OK (ok) ; F = CHOLMOD(copy)(E, 0, 0, cm) ; cm->print = 4 ; ok = CHOLMOD(print_sparse)(F, "F pattern ok", cm) ; OK (ok) ; cm->print = 1 ; CHOLMOD(free_sparse)(&F, cm) ; CHOLMOD(free_sparse)(&E, cm) ; CHOLMOD(free_sparse)(&C, cm) ; /* ---------------------------------------------------------------------- */ /* print_dense */ /* ---------------------------------------------------------------------- */ X = CHOLMOD(sparse_to_dense)(NULL, cm) ; NOP (X) ; X = CHOLMOD(sparse_to_dense)(Abad2, cm) ; NOP (X) ; C = CHOLMOD(dense_to_sparse)(NULL, TRUE, cm) ; NOP (C) ; X = CHOLMOD(copy_dense)(Xok, cm) ; ok = CHOLMOD(print_dense)(NULL, "null", cm) ; NOT (ok) ; x = X->x ; X->x = NULL ; ok = CHOLMOD(print_dense)(X, "Xnull", cm) ; NOT (ok) ; X->x = x ; ok = CHOLMOD(print_dense)(X, "X OK", cm) ; OK (ok) ; X->nzmax = 1 ; ok = CHOLMOD(print_dense)(X, "X nzmax too small", cm) ; NOT (ok) ; X->nzmax = Xok->nzmax ; ok = CHOLMOD(print_dense)(X, "X OK", cm) ; OK (ok) ; X->d = -1 ; ok = CHOLMOD(print_dense)(X, "X d too small", cm) ; NOT (ok) ; X->d = Xok->d ; ok = CHOLMOD(print_dense)(X, "X OK", cm) ; OK (ok) ; Xxtype = X->xtype ; X->xtype = CHOLMOD_PATTERN ; ok = CHOLMOD(print_dense)(X, "X pattern", cm) ; NOT (ok) ; X->xtype = -1 ; ok = CHOLMOD(print_dense)(X, "X unknown", cm) ; NOT (ok) ; X->xtype = Xxtype ; ok = CHOLMOD(print_dense)(X, "X OK", cm) ; OK (ok) ; X->dtype = CHOLMOD_SINGLE ; ok = CHOLMOD(print_dense)(X, "X float", cm) ; NOT (ok) ; X->dtype = -1 ; ok = CHOLMOD(print_dense)(X, "X unknown", cm) ; NOT (ok) ; X->dtype = CHOLMOD_DOUBLE ; ok = CHOLMOD(print_dense)(X, "X OK", cm) ; OK (ok) ; CHOLMOD(free_dense)(&X, cm) ; /* ---------------------------------------------------------------------- */ /* print_subset */ /* ---------------------------------------------------------------------- */ ok = CHOLMOD(check_subset)(NULL, 0, 0, cm) ; OK (ok) ; ok = CHOLMOD(print_subset)(NULL, 0, 0, "null", cm) ; OK (ok) ; for (i = 0 ; i < CSETSIZE ; i++) { cset [i] = i ; } for (cm->print = 0 ; cm->print <= 5 ; cm->print++) { ok = CHOLMOD(print_subset)(NULL, -1, 10, "[0:9]", cm) ; OK (ok) ; ok = CHOLMOD(print_subset)(cset, CSETSIZE, CSETSIZE, "cset OK", cm) ; OK (ok) ; cset [0] = -1 ; ok = CHOLMOD(print_subset)(cset, CSETSIZE, CSETSIZE, "cset bad", cm) ; NOT (ok) ; cset [0] = CSETSIZE-1 ; ok = CHOLMOD(print_subset)(cset, CSETSIZE, CSETSIZE, "cset OK", cm) ; OK (ok) ; } cm->print = 1 ; /* ---------------------------------------------------------------------- */ /* print_perm */ /* ---------------------------------------------------------------------- */ ok = CHOLMOD(check_perm)(NULL, 0, 0, cm) ; OK (ok) ; for (cm->print = 3 ; cm->print <= 4 ; cm->print++) { ok = CHOLMOD(print_perm)(Pok, nrow, nrow, "P OK", cm) ; OK (ok) ; if (nrow > 0) { p = Pok [0] ; Pok [0] = 2*ncol + 1 ; ok = CHOLMOD(print_perm)(Pok, nrow, nrow, "P bad", cm) ; NOT (ok) ; Pok [0] = p ; ok = CHOLMOD(print_perm)(Pok, nrow, nrow, "P OK", cm) ; } OK (ok) ; } cm->print = 1 ; n2 = 2 * cm->nrow ; P2 = prand (n2) ; /* RAND */ for (cm->print = 3 ; cm->print <= 4 ; cm->print++) { ok = CHOLMOD(print_perm)(P2, n2, n2, "P2 OK", cm) ; OK (ok) ; p = P2 [0] ; P2 [0] = -1 ; ok = CHOLMOD(print_perm)(P2, n2, n2, "P2 bad", cm) ; NOT (ok) ; P2 [0] = p ; ok = CHOLMOD(print_perm)(P2, n2, n2, "P2 OK", cm) ; OK (ok) ; } cm->print = 1 ; CHOLMOD(free)(2 * (cm->nrow), sizeof (Int), P2, cm) ; /* ---------------------------------------------------------------------- */ /* print_parent */ /* ---------------------------------------------------------------------- */ ok = CHOLMOD(print_parent)(NULL, 0, "null", cm) ; NOT (ok) ; if (nrow > 0) { i = Parent [0] ; Parent [0] = -2 ; ok = CHOLMOD(print_parent)(Parent, nrow, "bad Parent", cm) ; NOT (ok) ; Parent [0] = i ; ok = CHOLMOD(print_parent)(Parent, nrow, "OK Parent", cm) ; OK (ok) ; } /* ---------------------------------------------------------------------- */ /* print_factor */ /* ---------------------------------------------------------------------- */ if (A->stype == 0) { L = CHOLMOD(allocate_factor)(nrow, cm) ; OKP (L) ; ok = CHOLMOD(super_symbolic)(A, NULL, Parent, L, cm) ; NOT (ok) ; CHOLMOD(free_factor)(&L, cm) ; } ok = CHOLMOD(print_factor)(NULL, "L null", cm) ; NOT (ok) ; /* create a valid symbolic supernodal L */ cm->supernodal = CHOLMOD_SUPERNODAL ; cm->final_asis = TRUE ; L = CHOLMOD(analyze)(A, cm) ; /* [ */ OKP (L) ; ok = CHOLMOD(print_factor)(L, "L ok", cm) ; OK (ok) ; ok = CHOLMOD(change_factor)(CHOLMOD_ZOMPLEX, TRUE, TRUE, TRUE, TRUE, L, cm); NOT (ok) ; OK (L->xtype == CHOLMOD_PATTERN) ; OK (L->is_super) ; L->itype = CHOLMOD_INTLONG ; ok = CHOLMOD(print_factor)(L, "L int/UF_long", cm) ; NOT (ok) ; L->itype = -1 ; ok = CHOLMOD(print_factor)(L, "L int unknown", cm) ; NOT (ok) ; L->itype = cm->itype ; ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ; cm->print = 4 ; #ifdef LONG L->itype = CHOLMOD_INT ; #else L->itype = CHOLMOD_LONG ; #endif ok = CHOLMOD(print_factor)(L, "L bad itype", cm) ; NOT (ok) ; L->itype = cm->itype ; cm->print = 1 ; cm->print = 4 ; i = L->ordering ; L->ordering = -1 ; ok = CHOLMOD(print_factor)(L, "L bad ordering", cm) ; NOT (ok) ; L->ordering = CHOLMOD_GIVEN ; ok = CHOLMOD(print_factor)(L, "L given ordering", cm) ; OK (ok) ; L->ordering = i ; Lxtype = L->xtype ; L->xtype = CHOLMOD_REAL ; ok = CHOLMOD(print_factor)(L, "L real", cm) ; NOT (ok) ; L->xtype = CHOLMOD_COMPLEX ; ok = CHOLMOD(print_factor)(L, "L complex", cm) ; NOT (ok) ; L->xtype = CHOLMOD_ZOMPLEX ; ok = CHOLMOD(print_factor)(L, "L zomplex", cm) ; NOT (ok) ; L->xtype = -1 ; ok = CHOLMOD(print_factor)(L, "L unknown", cm) ; NOT (ok) ; L->xtype = CHOLMOD_PATTERN ; ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ; L->xtype = Lxtype ; /* ---------------------------------------------------------------------- */ /* supernodal factor */ /* ---------------------------------------------------------------------- */ /* create a valid supernodal numeric L (simplicial if Supernodal * module not installed) */ ok = CHOLMOD(factorize)(A, L, cm) ; OK (ok || cm->status == CHOLMOD_NOT_POSDEF) ; if (L->is_super) { /* there is no supernodal zomplex L */ ok = CHOLMOD(factor_xtype)(CHOLMOD_ZOMPLEX, L, cm) ; NOT (ok) ; } /* pack the simplicial factor, or return silently if supernodal */ ok = CHOLMOD(pack_factor)(L, cm) ; OK (ok) ; Lbad = CHOLMOD(copy_factor)(L, cm) ; /* [ */ Lxtype = L->xtype ; Lbad->xtype = -1 ; OK (L->is_super && L->xtype != CHOLMOD_PATTERN && L->is_ll) ; if (A->stype == 0) { ok = CHOLMOD(super_symbolic)(A, NULL, Parent, L, cm) ; NOT (ok) ; } ok = CHOLMOD(super_symbolic)(A, Abad2, Parent, L, cm) ; NOT (ok) ; ok = CHOLMOD(super_symbolic)(Abad2, A, Parent, L, cm) ; NOT (ok) ; W = CHOLMOD(zeros)(nrow, 1, L->xtype, cm) ; OKP (W) ; X = CHOLMOD(ones)(nrow, 1, L->xtype, cm) ; OKP (X) ; ok = CHOLMOD(super_lsolve)(L, X, W, cm) ; OK (ok) ; ok = CHOLMOD(super_ltsolve)(L, X, W, cm) ; OK (ok) ; ok = CHOLMOD(super_lsolve)(Lbad, X, W, cm) ; NOT (ok) ; ok = CHOLMOD(super_ltsolve)(Lbad, X, W, cm) ; NOT (ok) ; XX = CHOLMOD(zeros)(nrow, 1, L->xtype == CHOLMOD_REAL ? CHOLMOD_COMPLEX : CHOLMOD_REAL, cm) ; ok = CHOLMOD(super_lsolve)(L, X, XX, cm) ; NOT (ok) ; ok = CHOLMOD(super_ltsolve)(L, X, XX, cm) ; NOT (ok) ; CHOLMOD(free_dense)(&XX, cm) ; ok = CHOLMOD(super_lsolve)(L, X, W, cm) ; OK (ok) ; ok = CHOLMOD(super_ltsolve)(L, X, W, cm) ; OK (ok) ; x = X->x ; X->x = NULL ; ok = CHOLMOD(super_lsolve)(L, X, W, cm) ; NOT (ok) ; ok = CHOLMOD(super_ltsolve)(L, X, W, cm) ; NOT (ok) ; X->x = x ; x = W->x ; W->x = NULL ; ok = CHOLMOD(super_lsolve)(L, X, W, cm) ; NOT (ok) ; ok = CHOLMOD(super_ltsolve)(L, X, W, cm) ; NOT (ok) ; W->x = x ; CHOLMOD(free_dense)(&X, cm) ; CHOLMOD(free_dense)(&W, cm) ; cm->precise = TRUE ; ok = CHOLMOD(print_factor)(L, "L supernodal (precise)", cm) ; OK (ok) ; cm->precise = FALSE ; ok = CHOLMOD(print_factor)(L, "L supernodal", cm) ; OK (ok) ; cm->print = 1 ; /* cannot realloc a supernodal L */ ok = CHOLMOD(reallocate_factor)(10000, L, cm) ; NOT (ok) ; ok = CHOLMOD(reallocate_factor)(10000, NULL, cm) ; NOT (ok) ; ok = CHOLMOD(pack_factor)(NULL, cm) ; NOT (ok) ; /* ---------------------------------------------------------------------- */ /* print factor */ /* ---------------------------------------------------------------------- */ Lxtype = L->xtype ; i = cm->print ; cm->print = 4 ; L->xtype = CHOLMOD_PATTERN ; ok = CHOLMOD(print_factor)(L, "L pattern", cm) ; OK (ok) ; C = CHOLMOD(factor_to_sparse)(L, cm) ; NOP (C) ; L->xtype = Lxtype ; cm->print = i ; /* check with bad L factor */ ok = CHOLMOD(print_factor)(Lbad, "L unknown", cm) ; NOT (ok) ; ok = CHOLMOD(reallocate_factor)(999, Lbad, cm) ; NOT (ok) ; ok = CHOLMOD(pack_factor)(Lbad, cm) ; NOT (ok) ; C = CHOLMOD(factor_to_sparse)(Lbad, cm) ; NOP (C) ; L2 = CHOLMOD(copy_factor)(Lbad, cm) ; NOP (L2) ; ok = CHOLMOD(factorize)(A, Lbad, cm) ; NOT (ok) ; ok = CHOLMOD(resymbol)(A, NULL, 0, TRUE, Lbad, cm) ; NOT (ok) ; ok = CHOLMOD(resymbol_noperm)(A, NULL, 0, TRUE, Lbad, cm) ; NOT (ok) ; ok = CHOLMOD(rowadd)(nrow-2, A, Lbad, cm) ; NOT (ok) ; ok = CHOLMOD(rowdel)(nrow-2, NULL, Lbad, cm) ; NOT (ok) ; ok = CHOLMOD(rowfac)(A, AT, beta, 1, 2, Lbad, cm) ; NOT (ok) ; ok = CHOLMOD(updown)(+1, A, Lbad, cm) ; NOT (ok) ; ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ; L->dtype = CHOLMOD_SINGLE ; ok = CHOLMOD(print_factor)(L, "L float", cm) ; NOT (ok) ; L->dtype = -1 ; ok = CHOLMOD(print_factor)(L, "L unknown", cm) ; NOT (ok) ; L->dtype = CHOLMOD_DOUBLE ; ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ; if (nrow > 0) { Lperm = L->Perm ; p = Lperm [0] ; Lperm [0] = -1 ; ok = CHOLMOD(print_factor)(L, "L perm invalid", cm) ; NOT (ok) ; Lperm [0] = p ; ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ; } LColCount = L->ColCount ; L->ColCount = NULL ; ok = CHOLMOD(print_factor)(L, "L no colcount", cm) ; NOT (ok) ; L->ColCount = LColCount ; ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ; if (nrow > 0) { LColCount = L->ColCount ; p = LColCount [0] ; LColCount [0] = -1 ; ok = CHOLMOD(print_factor)(L, "L colcount vad", cm) ; NOT (ok) ; LColCount [0] = p ; ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ; } /* ---------------------------------------------------------------------- */ /* print simplicial factor */ /* ---------------------------------------------------------------------- */ /* check LDL' unpacked */ ok = CHOLMOD(print_factor)(L, "L OK for L2 copy", cm) ; OK (ok) ; L2 = CHOLMOD(copy_factor)(L, cm) ; /* [ */ OKP (L2) ; ok = CHOLMOD(change_factor)(L->xtype, FALSE, FALSE, FALSE, TRUE, L2, cm) ; /* check LDL' packed */ L3 = CHOLMOD(copy_factor)(L, cm) ; OKP (L3) ; ok = CHOLMOD(change_factor)(L->xtype, FALSE, FALSE, TRUE, TRUE, L3, cm) ; ok = CHOLMOD(print_factor)(L3, "L3 OK", cm) ; OK (ok) ; CHOLMOD(free_factor)(&L3, cm) ; OK (ok) ; ok = CHOLMOD(print_factor)(L2, "L2 OK", cm) ; OK (ok) ; ok = CHOLMOD(pack_factor)(L2, cm) ; OK (ok) ; ok = CHOLMOD(print_factor)(L2, "L2 OK packed", cm) ; OK (ok) ; /* create a simplicial factor from scratch */ cm->supernodal = CHOLMOD_SIMPLICIAL ; cm->final_asis = TRUE ; L6 = CHOLMOD(analyze)(A, cm) ; /* [ */ OKP (L6) ; ok = CHOLMOD(factorize)(A, L6, cm) ; OK (cm->status >= CHOLMOD_OK) ; cm->supernodal = CHOLMOD_AUTO ; ok = CHOLMOD(print_sparse)(A, "A OK", cm) ; OK (ok) ; ok = CHOLMOD(print_factor)(L6, "L6 OK", cm) ; OK (ok) ; Lz = L6->z ; L6->z = NULL ; ok = CHOLMOD(print_factor)(L6, "L6 no z", cm) ; if (L6->xtype == CHOLMOD_ZOMPLEX) { NOT (ok) ; } else { OK (ok) ; } L6->z = Lz ; CHOLMOD(free_factor)(&L6, cm) ; /* ] */ Az = A->z ; A->z = NULL ; ok = CHOLMOD(print_sparse)(A, "A no z", cm) ; if (A->xtype == CHOLMOD_ZOMPLEX) { NOT (ok) ; } else { OK (ok) ; } A->z = Az ; Lp = L2->p ; Li = L2->i ; Lx = L2->x ; Lnz = L2->nz ; Lnext = L2->next ; Lprev = L2->prev ; OK (Lp [0] == 0) ; L2->p = NULL ; ok = CHOLMOD(print_factor)(L2, "L no p", cm) ; NOT (ok) ; L2->p = Lp ; ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ; L2->i = NULL ; ok = CHOLMOD(print_factor)(L2, "L no i", cm) ; NOT (ok) ; L2->i = Li ; ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ; L2->x = NULL ; ok = CHOLMOD(print_factor)(L2, "L no x", cm) ; NOT (ok) ; L2->x = Lx ; ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ; L2->nz = NULL ; ok = CHOLMOD(print_factor)(L2, "L no nz", cm) ; NOT (ok) ; L2->nz = Lnz ; ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ; L2->next = NULL ; ok = CHOLMOD(print_factor)(L2, "L no next", cm) ; NOT (ok) ; L2->next = Lnext ; ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ; L2->prev = NULL ; ok = CHOLMOD(print_factor)(L2, "L no prev", cm) ; NOT (ok) ; L2->prev = Lprev ; ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ; if (nrow > 0) { p = Lp [0] ; Lp [0] = -1 ; ok = CHOLMOD(print_factor)(L2, "Lp bad", cm) ; NOT (ok) ; Lp [0] = p ; ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ; p = Li [0] ; Li [0] = -1 ; ok = CHOLMOD(print_factor)(L2, "Li bad", cm) ; NOT (ok) ; Li [0] = p ; ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ; p = Lnz [0] ; Lnz [0] = -1 ; ok = CHOLMOD(print_factor)(L2, "Lnz bad", cm) ; NOT (ok) ; Lnz [0] = p ; } ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ; OK (Lnz != NULL) ; if (nrow > 0 && Lnz [0] > 3) { ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ; p = Li [1] ; Li [1] = nrow ; ok = CHOLMOD(print_factor)(L2, "Li bad", cm) ; NOT (ok) ; Li [1] = p ; ok = CHOLMOD(print_factor)(L2, "L OK again", cm) ; OK (ok) ; p = Li [2] ; Li [2] = Li [1] ; ok = CHOLMOD(print_factor)(L2, "Li bad", cm) ; NOT (ok) ; Li [2] = p ; ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ; } /* check LDL' dynamic link list */ ok = CHOLMOD(change_factor)(L->xtype, FALSE, FALSE, FALSE, FALSE, L2, cm) ; OK (ok) ; ok = CHOLMOD(print_factor)(L2, "L2 OK", cm) ; OK (ok) ; OK (L2->xtype != CHOLMOD_PATTERN && !(L2->is_ll) && !(L2->is_super)) ; /* cannot do a supernodal factorization on a dynamic LDL' factor */ ok = CHOLMOD(super_numeric)(AT, NULL, Zero, L2, cm) ; NOT (ok) ; ok = CHOLMOD(super_numeric)(I1, NULL, Zero, L2, cm) ; NOT (ok) ; ok = CHOLMOD(super_numeric)(I1, I1, Zero, L2, cm) ; NOT (ok) ; G = CHOLMOD(copy)(I1, 1, 0, cm) ; OKP (G) ; ok = CHOLMOD(super_numeric)(G, NULL, Zero, L2, cm) ; NOT (ok) ; ok = CHOLMOD(free_sparse)(&G, cm) ; OK (ok) ; G = CHOLMOD(copy)(I1, -1, 0, cm) ; OKP (G) ; ok = CHOLMOD(super_numeric)(G, NULL, Zero, L2, cm) ; NOT (ok) ; ok = CHOLMOD(free_sparse)(&G, cm) ; OK (ok) ; ok = CHOLMOD(super_numeric)(AT, I1, Zero, L2, cm) ; NOT (ok) ; W = CHOLMOD(zeros)(nrow, 1, CHOLMOD_REAL, cm) ; OKP (W) ; X = CHOLMOD(ones)(nrow, 1, CHOLMOD_REAL, cm) ; OKP (X) ; ok = CHOLMOD(super_lsolve)(L2, X, W, cm) ; NOT (ok) ; ok = CHOLMOD(super_ltsolve)(L2, X, W, cm) ; NOT (ok) ; ok = CHOLMOD(free_dense)(&W, cm) ; OK (ok) ; ok = CHOLMOD(free_dense)(&X, cm) ; OK (ok) ; Lnext = L2->next ; Lprev = L2->prev ; if (nrow > 3) { p = Lnext [nrow+1] ; Lnext [nrow+1] = -1 ; ok = CHOLMOD(print_factor)(L2, "Lnext bad", cm) ; NOT (ok) ; Lnext [nrow+1] = -p ; ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ; p = Lnext [2] ; Lnext [2] = 2 ; ok = CHOLMOD(print_factor)(L2, "Lnext bad", cm) ; NOT (ok) ; Lnext [2] = p ; ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ; p = Lnext [2] ; Lnext [2] = -1 ; ok = CHOLMOD(print_factor)(L2, "Lnext bad", cm) ; NOT (ok) ; Lnext [2] = p ; ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ; p = Lprev [2] ; Lprev [2] = -9 ; ok = CHOLMOD(print_factor)(L2, "Lprev bad", cm) ; NOT (ok) ; Lprev [2] = p ; ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ; p = Lnext [nrow] ; Lnext [nrow] = 0 ; ok = CHOLMOD(print_factor)(L2, "Lnext/prev bad", cm) ; NOT (ok) ; Lnext [nrow] = p ; ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ; /* make a non-monotonic copy of L2 and then mangle it */ L6 = CHOLMOD(copy_factor)(L2, cm) ; ok = CHOLMOD(reallocate_column)(0, nrow, L6, cm) ; if (ok && !(L6->is_monotonic)) { ok = CHOLMOD(print_factor)(L6, "L6 monotonic OK ", cm) ; OK (ok) ; L6->is_monotonic = TRUE ; ok = CHOLMOD(print_factor)(L6, "L6 monotonic bad", cm) ; NOT (ok) ; } CHOLMOD(free_factor)(&L6, cm) ; } L6 = CHOLMOD(copy_factor)(L, cm) ; OKP (L6) ; I = CHOLMOD(speye)(nrow, nrow, L->xtype, cm) ; OKP (I) ; I3 = CHOLMOD(speye)(nrow, nrow, L->xtype-1, cm) ; OKP (I3) ; ok = CHOLMOD(super_numeric)(I, I, beta, L6, cm) ; OK (ok) ; ok = CHOLMOD(super_numeric)(I, I3, beta, L6, cm) ; NOT (ok) ; ok = CHOLMOD(super_numeric)(I, Abad2, beta, L6, cm) ; NOT (ok) ; ok = CHOLMOD(super_numeric)(I, I, beta, Lbad, cm) ; NOT (ok) ; I->stype = -1 ; ok = CHOLMOD(super_numeric)(I, I, beta, L6, cm) ; OK (ok) ; ok = CHOLMOD(super_numeric)(I, NULL, beta, L6, cm) ; OK (ok) ; I3->stype = -1 ; cm->print = 4 ; CHOLMOD(print_sparse)(I3, "I3", cm) ; CHOLMOD(print_factor)(L6, "L6", cm) ; cm->print = 1 ; ok = CHOLMOD(super_numeric)(I3, NULL, beta, L6, cm) ; NOT (ok) ; CHOLMOD(free_sparse)(&I, cm) ; I = CHOLMOD(speye)(nrow+1, nrow+1, L->xtype, cm) ; OKP (I) ; I->stype = -1 ; ok = CHOLMOD(super_numeric)(I, I, beta, L6, cm) ; NOT (ok) ; CHOLMOD(free_sparse)(&I, cm) ; CHOLMOD(free_sparse)(&I3, cm) ; ok = CHOLMOD(free_factor)(&L6, cm) ; OK (ok) ; /* check the supernodal L */ Ls = L->s ; Lpi = L->pi ; Lpx = L->px ; Super = L->super ; Lx = L->x ; ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ; L->s = NULL ; ok = CHOLMOD(print_factor)(L, "L no s", cm) ; NOT (ok) ; L->s = Ls ; ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ; L->pi = NULL ; ok = CHOLMOD(print_factor)(L, "L no pi", cm) ; NOT (ok) ; L->pi = Lpi ; ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ; L->px = NULL ; ok = CHOLMOD(print_factor)(L, "L no px", cm) ; NOT (ok) ; L->px = Lpx ; ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ; L->super = NULL ; ok = CHOLMOD(print_factor)(L, "L no super", cm) ; NOT (ok) ; L->super = Super ; ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ; L->x = NULL ; ok = CHOLMOD(print_factor)(L, "L no x", cm) ; NOT (ok) ; L->x = Lx ; ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ; p = Ls [0] ; Ls [0] = -1 ; ok = CHOLMOD(print_factor)(L, "L bad s", cm) ; NOT (ok) ; Ls [0] = p ; ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ; p = Lpi [0] ; Lpi [0] = -1 ; ok = CHOLMOD(print_factor)(L, "L bad pi", cm) ; NOT (ok) ; Lpi [0] = p ; ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ; p = Lpx [0] ; Lpx [0] = -1 ; ok = CHOLMOD(print_factor)(L, "L bad px", cm) ; NOT (ok) ; Lpx [0] = p ; ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ; if (nrow > 0) { p = Super [0] ; Super [0] = -1 ; ok = CHOLMOD(print_factor)(L, "L bad super", cm) ; NOT (ok) ; Super [0] = p ; ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ; p = Ls [0] ; Ls [0] = 42 ; ok = CHOLMOD(print_factor)(L, "L bad s", cm) ; NOT (ok) ; Ls [0] = p ; ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ; } if (nrow > 0 && Lpi [1] - Lpi [0] > 3) { p = Ls [2] ; Ls [2] = Ls [1] ; ok = CHOLMOD(print_factor)(L, "L unsorted s", cm) ; NOT (ok) ; Ls [2] = p ; ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ; } /* ---------------------------------------------------------------------- */ /* Cholesky */ /* ---------------------------------------------------------------------- */ /* test the supernodal symbolic L */ L3 = CHOLMOD(copy_factor)(L, cm) ; OKP (L3) ; ok = CHOLMOD(change_factor)(CHOLMOD_PATTERN, TRUE, TRUE, TRUE, TRUE, L3, cm) ; OK (ok) ; Ls = L3->s ; Lpi = L3->pi ; Super = L3->super ; if (nrow > 0) { p = Ls [0] ; Ls [0] = 42 ; ok = CHOLMOD(print_factor)(L3, "Lsym bad s", cm) ; NOT (ok) ; Ls [0] = p ; ok = CHOLMOD(print_factor)(L3, "Lsym OK", cm) ; OK (ok) ; } if (nrow > 0 && Lpi [1] - Lpi [0] > 3) { p = Ls [2] ; Ls [2] = Ls [1] ; ok = CHOLMOD(print_factor)(L3, "Lsym unsorted s", cm) ; NOT (ok) ; Ls [2] = p ; ok = CHOLMOD(print_factor)(L3, "Lsym OK", cm) ; OK (ok) ; } if (nrow > 0 && L->nsuper > 0) { Int nscol = Super [1] ; Int nsrow = Lpi [1] - Lpi [0] ; if (nsrow > nscol + 1) { p = Ls [nscol] ; Ls [nscol] = Ls [nscol+1] ; ok = CHOLMOD(print_factor)(L3, "Lsym unsorted s2", cm) ; NOT (ok) ; Ls [nscol] = p ; ok = CHOLMOD(print_factor)(L3, "Lsym OK", cm) ; OK (ok) ; } } CHOLMOD(free_factor)(&L3, cm) ; /* (re)factorize as LL' */ L5 = CHOLMOD(copy_factor)(L, cm) ; /* [ */ OKP (L5) ; ok = CHOLMOD(factor_xtype)(-1, L, cm) ; NOT (ok) ; ok = CHOLMOD(factor_xtype)(CHOLMOD_REAL, NULL, cm) ; NOT (ok) ; L3 = CHOLMOD(copy_factor)(L, cm) ; OKP (L3) ; CHOLMOD(print_factor)(L3, "L3 before factorize", cm) ; ok = CHOLMOD(change_factor)(L3->xtype, TRUE, FALSE, TRUE, TRUE, L3, cm) ; OK (ok) ; Acopy = CHOLMOD(copy_sparse)(A, cm) ; /* [ */ CHOLMOD(sparse_xtype)(L3->xtype, Acopy, cm) ; CHOLMOD(print_sparse)(Acopy, "Acopy for factorize", cm) ; ok = CHOLMOD(factorize)(Acopy, L3, cm) ; OK (ok || cm->status >= CHOLMOD_OK) ; ok = CHOLMOD(free_factor)(&L3, cm) ; OK (ok) ; CHOLMOD(print_sparse)(A, "A for factorize", cm) ; CHOLMOD(print_factor)(L3, "L3 for factorize", cm) ; /* refactor, but with wrong-sized A */ ok = CHOLMOD(print_sparse)(I1, "I1", cm) ; OK (ok) ; ok = CHOLMOD(factorize)(I1, L, cm) ; NOT (ok) ; ok = CHOLMOD(factorize)(Abad2, L, cm) ; NOT (ok) ; C = CHOLMOD(transpose)(I1, 0, cm) ; OKP (C) ; ok = CHOLMOD(print_sparse)(C, "C = I1'", cm) ; OK (ok) ; ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; ok = CHOLMOD(print_factor)(L, "L OK ", cm) ; OK (ok) ; /* refactor, with invalid A (NULL, or symmetric but not square) */ ok = CHOLMOD(print_sparse)(Abad, "Abad", cm) ; NOT (ok) ; ok = CHOLMOD(factorize)(Abad, L, cm) ; NOT (ok) ; /* refactorize supernodal LL' */ printf ("refactorize here\n") ; ok = CHOLMOD(print_sparse)(Acopy, "Acopy refactorize", cm) ; OK (ok) ; ok = CHOLMOD(print_factor)(L, "L for refactorize", cm) ; OK (ok) ; printf ("L->xtype for refactorize %d\n", L->xtype) ; ok = CHOLMOD(factorize)(Acopy, L, cm) ; OK (ok || cm->status == CHOLMOD_NOT_POSDEF) ; ok = CHOLMOD(print_factor)(L, "L ok, here", cm) ; OK (ok) ; ok = CHOLMOD(factorize)(Acopy, L, cm) ; OK (ok || cm->status == CHOLMOD_NOT_POSDEF) ; ok = CHOLMOD(print_factor)(L, "L ok, here2", cm) ; OK (ok) ; /* solve */ B = CHOLMOD(ones)(nrow, 0, CHOLMOD_REAL, cm) ; OKP (B) ; X = CHOLMOD(solve)(CHOLMOD_A, L, B, cm) ; OKP (X) ; ok = CHOLMOD(free_dense)(&X, cm) ; OK (ok) ; X = CHOLMOD(solve)(-1, L, B, cm) ; NOP (X) ; ok = CHOLMOD(free_dense)(&B, cm) ; OK (ok) ; B = CHOLMOD(zeros)(nrow+1, 0, CHOLMOD_REAL, cm) ; OKP (B) ; X = CHOLMOD(solve)(CHOLMOD_A, L, B, cm) ; NOP (X) ; B->xtype = 0 ; X = CHOLMOD(solve)(CHOLMOD_A, L, B, cm) ; NOP (X) ; B->xtype = CHOLMOD_REAL ; ok = CHOLMOD(free_dense)(&B, cm) ; OK (ok) ; /* sparse solve */ if (nrow < 100 && A->stype != 0) { /* solve A*C=I, so C should equal A inverse */ I = CHOLMOD(speye)(nrow, nrow, CHOLMOD_REAL, cm) ; OKP (I) ; C = CHOLMOD(spsolve)(CHOLMOD_A, L, I, cm) ; OKP (C) ; /* compute norm of A*C-I */ if (xtype == CHOLMOD_REAL) { E = CHOLMOD(ssmult)(A, C, 0, TRUE, FALSE, cm) ; OKP (E) ; F = CHOLMOD(add)(E, I, minusone, one, TRUE, FALSE, cm) ;OKP (F) ; cm->print = 4 ; ok = CHOLMOD(print_sparse)(F, "A*inv(A)-I", cm) ; OK (ok) ; cm->print = 1 ; r = CHOLMOD(norm_sparse)(F, 1, cm) ; OK (! (r < 0)) ; MAXERR (maxerr, r, 1) ; ok = CHOLMOD(free_sparse)(&E, cm) ; OK (ok) ; ok = CHOLMOD(free_sparse)(&F, cm) ; OK (ok) ; } CHOLMOD(free_sparse)(&C, cm) ; /* check error cases for sparse solve */ C = CHOLMOD(spsolve)(CHOLMOD_A, NULL, I, cm) ; NOP (C) ; C = CHOLMOD(spsolve)(CHOLMOD_A, Lbad, I, cm) ; NOP (C) ; C = CHOLMOD(spsolve)(CHOLMOD_A, L, NULL, cm) ; NOP (C) ; I->xtype = 0 ; C = CHOLMOD(spsolve)(CHOLMOD_A, L, I, cm) ; NOP (C) ; I->xtype = CHOLMOD_REAL ; I->stype = -1 ; C = CHOLMOD(spsolve)(CHOLMOD_A, L, I, cm) ; NOP (C) ; ok = CHOLMOD(free_sparse)(&I, cm) ; OK (ok) ; I = CHOLMOD(speye)(nrow+1, nrow+1, CHOLMOD_REAL, cm) ; OKP (I) ; C = CHOLMOD(spsolve)(CHOLMOD_A, L, I, cm) ; NOP (C) ; ok = CHOLMOD(free_sparse)(&I, cm) ; OK (ok) ; } /* resymbol */ ok = CHOLMOD(resymbol)(I1, NULL, 0, TRUE, L, cm) ; NOT (ok) ; ok = CHOLMOD(resymbol_noperm)(I1, NULL, 0, TRUE, L, cm) ; NOT (ok) ; ok = CHOLMOD(change_factor)(L->xtype, FALSE, FALSE, FALSE, FALSE, L, cm) ; OK (ok) ; ok = CHOLMOD(resymbol)(I1, NULL, 0, TRUE, L, cm) ; NOT (ok) ; ok = CHOLMOD(resymbol_noperm)(I1, NULL, 0, TRUE, L, cm) ; NOT (ok) ; ok = CHOLMOD(change_factor)(-1, FALSE, FALSE, FALSE, FALSE, L, cm) ; NOT (ok) ; ok = CHOLMOD(change_factor)(L->xtype, FALSE, FALSE, FALSE, FALSE, Lbad, cm); NOT (ok) ; ok = CHOLMOD(resymbol_noperm)(Acopy, NULL, 0, TRUE, L2, cm) ; if (Acopy->stype <= 0) { OK (ok) ; } else { NOT (ok) ; } ok = CHOLMOD(resymbol_noperm)(Abad2, NULL, 0, TRUE, L2, cm) ; NOT (ok) ; ok = CHOLMOD(resymbol)(Abad2, NULL, 0, TRUE, L2, cm) ; NOT (ok) ; ok = CHOLMOD(resymbol_noperm)(Acopy, NULL, 0, TRUE, NULL, cm) ; NOT (ok) ; ok = CHOLMOD(resymbol)(Acopy, NULL, 0, TRUE, L2, cm) ; OK (ok) ; if (ncol > 0) { ok = CHOLMOD(print_perm)(fsetbad, ncol, ncol, "bad fset", cm) ; NOT (ok) ; } if (ncol > 1) { ok = CHOLMOD(resymbol)(Acopy, fsetok, ncol/2, TRUE, L2, cm) ; OK (ok) ; ok = CHOLMOD(resymbol)(Acopy, fsetbad, ncol/2, TRUE, L2, cm) ; if (Acopy->stype) { /* fset is ignored */ OK (ok) ; } else { NOT (ok) ; ok = CHOLMOD(resymbol_noperm)(Acopy, fsetbad, ncol/2, TRUE, L2, cm); NOT (ok) ; } Acopy->sorted = FALSE ; ok = CHOLMOD(resymbol)(Acopy, fsetok, ncol/2, TRUE, L2, cm) ; OK (ok) ; Acopy->sorted = TRUE ; } cm->print = 4 ; gsave0 = cm->grow0 ; gsave1 = cm->grow1 ; gsave2 = cm->grow2 ; /* reallocate column */ L4 = NULL ; if (nrow > 0) { ok = CHOLMOD(print_factor)(L, "L ok, for colrealloc", cm) ; OK (ok) ; L4 = CHOLMOD(copy_factor)(L, cm) ; ok = CHOLMOD(print_factor)(L4, "L4 ok, for colrealloc", cm) ; OK (ok) ; OK (nrow == (Int)(L->n)) ; ok = CHOLMOD(reallocate_column)(nrow, 1, L4, cm) ; NOT (ok) ; ok = CHOLMOD(reallocate_column)(nrow-1, 0, L4, cm) ; NOT (ok) ; ok = CHOLMOD(reallocate_column)(nrow-1, 10, L4, cm) ; OK (ok) ; cm->grow0 = 2e10 ; cm->grow1 = 2 ; /* this may or may not fail */ ok = CHOLMOD(reallocate_column)(0, 10, L4, cm) ; CHOLMOD(print_common)("OK or too large", cm) ; ok = CHOLMOD(free_factor)(&L4, cm) ; OK (ok) ; } cm->grow0 = gsave0 ; cm->grow1 = gsave1 ; cm->grow2 = gsave2 ; if (ok && nrow > 2) { L4 = CHOLMOD(copy_factor)(L, cm) ; ok = CHOLMOD(resymbol)(A, NULL, 0, TRUE, L4, cm) ; OK (ok) ; /* make it non-monotonic and then monotonic (LDL' unpacked) */ ok = CHOLMOD(reallocate_column)(0, nrow-1, L4, cm) ; OK (ok) ; /* this should be OK for small matrices, but fail for large ones */ cm->grow0 = nrow ; cm->grow1 = nrow ; cm->grow2 = nrow ; ok = CHOLMOD(change_factor)(CHOLMOD_REAL, FALSE, FALSE, FALSE, TRUE, L4, cm) ; ok = CHOLMOD(free_factor)(&L4, cm) ; OK (ok) ; L4 = CHOLMOD(copy_factor)(L, cm) ; ok = CHOLMOD(resymbol)(A, NULL, 0, TRUE, L4, cm) ; OK (ok) ; ok = CHOLMOD(pack_factor)(L4, cm) ; OK (ok) ; /* now try to make L4 really huge */ /* cm->print = 5 ; CHOLMOD(print_sparse) (A, "A for huge", cm) ; CHOLMOD(print_factor) (L4, "L4 for huge", cm) ; */ if (ok && !(L->is_super) && L->xtype != CHOLMOD_PATTERN) { cm->grow0 = gsave0 ; cm->grow1 = gsave1 ; cm->grow2 = gsave2 ; ok = CHOLMOD(reallocate_column)(0, nrow-1, L4, cm) ; OK (ok) ; cm->grow0 = nrow ; cm->grow1 = nrow ; cm->grow2 = nrow ; /* CHOLMOD(print_factor) (L4, "L4 for huge, realloced", cm) ; printf ("L4 for huge is monotonic: %d\n", L4->is_monotonic) ; */ if (!(L4->is_monotonic)) { /* printf ("Make L4 really huge: ") ; */ ok = CHOLMOD(change_factor)(CHOLMOD_REAL, TRUE, FALSE, FALSE, TRUE, L4, cm) ; printf ("L4 huge ok: "ID"\n", ok) ; } } ok = CHOLMOD(free_factor)(&L4, cm) ; OK (ok) ; } cm->grow0 = gsave0 ; cm->grow1 = gsave1 ; cm->grow2 = gsave2 ; cm->print = 1 ; /* ---------------------------------------------------------------------- */ /* more error tests */ /* ---------------------------------------------------------------------- */ cm->error_handler = NULL ; /* ---------------------------------------------------------------------- */ /* modify */ /* ---------------------------------------------------------------------- */ X = CHOLMOD(ones)(nrow, 1, CHOLMOD_REAL, cm) ; OKP (X) ; R = CHOLMOD(dense_to_sparse)(X, TRUE, cm) ; /* [ */ OKP (R) ; if (isreal) { C = CHOLMOD(speye)(nrow, 1, CHOLMOD_REAL, cm) ; OKP (C) ; ok = CHOLMOD(updown)(+1, C, L, cm) ; OK (ok) ; X1 = CHOLMOD(ones)(nrow, 1, CHOLMOD_REAL, cm) ; B1 = CHOLMOD(eye)(nrow, 1, CHOLMOD_REAL, cm) ; ok = CHOLMOD(updown_solve)(+1, C, L, X1, B1, cm) ; OK (ok) ; B1->xtype = -999 ; ok = CHOLMOD(updown_solve)(+1, C, L, X1, B1, cm) ; NOT (ok) ; ok = CHOLMOD(rowadd_solve)(0, R, beta, L, X1, B1, cm) ; NOT (ok) ; ok = CHOLMOD(rowdel_solve)(0, R, beta, L, X1, B1, cm) ; NOT (ok) ; B1->xtype = CHOLMOD_REAL ; CHOLMOD(free_dense)(&B1, cm) ; B2 = CHOLMOD(ones)(nrow, 2, CHOLMOD_REAL, cm) ; ok = CHOLMOD(updown_solve)(+1, C, L, X1, B2, cm) ; NOT (ok) ; ok = CHOLMOD(rowadd_solve)(0, R, beta, L, X1, B2, cm) ; NOT (ok) ; ok = CHOLMOD(rowdel_solve)(0, R, beta, L, X1, B2, cm) ; NOT (ok) ; CHOLMOD(free_dense)(&B2, cm) ; CHOLMOD(free_dense)(&X1, cm) ; ok = CHOLMOD(updown)(+1, Abad2, L, cm) ; NOT (ok) ; ok = CHOLMOD(updown)(+1, C, NULL, cm) ; NOT (ok) ; C->sorted = FALSE ; ok = CHOLMOD(updown)(+1, C, L, cm) ; NOT (ok) ; ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; ok = CHOLMOD(updown)(+1, NULL, L, cm) ; NOT (ok) ; if (nrow > 0) { C = CHOLMOD(speye)(nrow-1, 1, CHOLMOD_REAL, cm) ; OKP (C) ; ok = CHOLMOD(updown)(+1, C, L, cm) ; NOT (ok) ; ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; } C = CHOLMOD(speye)(nrow, 0, CHOLMOD_REAL, cm) ; OKP (C) ; ok = CHOLMOD(updown)(+1, C, L, cm) ; OK (ok) ; ok = CHOLMOD(rowdel)(0, C, L, cm) ; NOT (ok) ; ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; } /* ---------------------------------------------------------------------- */ /* rowfac, rcond */ /* ---------------------------------------------------------------------- */ cm->nmethods = 1 ; cm->method [0].ordering = CHOLMOD_NATURAL ; cm->postorder = FALSE ; cm->print = 5 ; cm->final_ll = TRUE ; for (xtype2 = CHOLMOD_REAL ; xtype2 <= CHOLMOD_ZOMPLEX ; xtype2++) { cm->supernodal = CHOLMOD_SIMPLICIAL ; /* factor a singular matrix (C=LL') */ printf ("start singular LL'\n") ; XX = CHOLMOD(ones)(4, 4, xtype2, cm) ; OKP (X) ; C = CHOLMOD(dense_to_sparse)(XX, TRUE, cm) ; OKP (C) ; CHOLMOD(free_dense)(&XX, cm) ; C->stype = 1 ; CHOLMOD(print_sparse)(C, "C ones", cm) ; L6 = CHOLMOD(analyze)(C, cm) ; OKP (L6) ; ok = CHOLMOD(factorize)(C, L6, cm) ; OK (ok) ; printf ("status %d\n", cm->status) ; ok1 = (cm->status == CHOLMOD_NOT_POSDEF) ; ok = CHOLMOD(print_factor)(L6, "L6 singular", cm) ; OK (ok) ; OK (ok1) ; rcond = CHOLMOD(rcond) (L6, cm) ; OK (rcond == 0) ; /* now make C positive definite */ CHOLMOD(free_sparse)(&C, cm) ; XX = CHOLMOD(ones)(4, 4, xtype2, cm) ; OKP (X) ; x = XX->x ; for (i = 0 ; i < 4 ; i++) { if (xtype2 == CHOLMOD_REAL || xtype2 == CHOLMOD_ZOMPLEX) { x [i + 4*i] = 42 ; } else /* complex */ { x [2*(i + 4*i)] = 42 ; } } C = CHOLMOD(dense_to_sparse)(XX, TRUE, cm) ; OKP (C) ; CHOLMOD(free_dense)(&XX, cm) ; C->stype = 1 ; CHOLMOD(print_sparse)(C, "C ok", cm) ; ok = CHOLMOD(factorize)(C, L6, cm) ; OK (ok) ; ok1 = (cm->status == CHOLMOD_OK) ; ok = CHOLMOD(print_factor)(L6, "L6 ok", cm) ; OK (ok) ; OK (ok1) ; rcond = CHOLMOD(rcond) (L6, cm) ; OK (rcond > 0) ; /* generate intentional nan's, to test the nan-handling of cholmod_rcond */ if (do_nantests) { xnan = xnan/xnan ; /* C(2,2) = nan */ x = C->x ; i = 2 ; if (xtype2 == CHOLMOD_REAL || xtype2 == CHOLMOD_ZOMPLEX) { x [i + 4*i] = xnan ; } else /* complex */ { x [2*(i + 4*i)] = xnan ; } ok = CHOLMOD(factorize)(C, L6, cm) ; OK (ok) ; ok1 = (cm->status == CHOLMOD_OK) ; ok = CHOLMOD(print_factor)(L6, "L6 nan2", cm) ; OK (ok) ; printf ("rcond %g\n", rcond) ; OK (ok1) ; rcond = CHOLMOD(rcond) (L6, cm) ; OK (rcond == 0) ; CHOLMOD(free_factor)(&L6, cm) ; /* C(2,2) = nan, LDL' */ cm->supernodal = CHOLMOD_SIMPLICIAL ; cm->final_ll = TRUE ; L6 = CHOLMOD(analyze)(C, cm) ; OKP (L6) ; ok = CHOLMOD(factorize)(C, L6, cm) ; OK (ok) ; ok1 = (cm->status == CHOLMOD_OK) ; ok = CHOLMOD(print_factor)(L6, "LDL6 nan2", cm) ; OK (ok) ; OK (ok1) ; rcond = CHOLMOD(rcond) (L6, cm) ; OK (rcond == 0) ; CHOLMOD(free_factor)(&L6, cm) ; /* C(2,2) = nan, supernodal */ cm->supernodal = CHOLMOD_SUPERNODAL ; cm->final_ll = FALSE ; L6 = CHOLMOD(analyze)(C, cm) ; OKP (L6) ; ok = CHOLMOD(factorize)(C, L6, cm) ; OK (ok) ; ok1 = (cm->status == CHOLMOD_OK) ; ok = CHOLMOD(print_factor)(L6, "L6 supernan2", cm) ; OK (ok) ; OK (ok1) ; rcond = CHOLMOD(rcond) (L6, cm) ; OK (rcond == 0) ; CHOLMOD(free_factor)(&L6, cm) ; /* C(0,0) = nan */ cm->supernodal = CHOLMOD_SIMPLICIAL ; cm->final_ll = FALSE ; x [0] = xnan ; L6 = CHOLMOD(analyze)(C, cm) ; OKP (L6) ; ok = CHOLMOD(factorize)(C, L6, cm) ; OK (ok) ; ok1 = (cm->status == CHOLMOD_OK) ; ok = CHOLMOD(print_factor)(L6, "L6 nan0", cm) ; OK (ok) ; OK (ok1) ; rcond = CHOLMOD(rcond) (L6, cm) ; OK (rcond == 0) ; CHOLMOD(free_factor)(&L6, cm) ; /* C(0,0) = nan, LDL' */ cm->supernodal = CHOLMOD_SIMPLICIAL ; cm->final_ll = TRUE ; L6 = CHOLMOD(analyze)(C, cm) ; OKP (L6) ; ok = CHOLMOD(factorize)(C, L6, cm) ; OK (ok) ; ok1 = (cm->status == CHOLMOD_OK) ; ok = CHOLMOD(print_factor)(L6, "LDL6 nan0", cm) ; OK (ok) ; OK (ok1) ; rcond = CHOLMOD(rcond) (L6, cm) ; OK (rcond == 0) ; CHOLMOD(free_factor)(&L6, cm) ; /* C(0,0) = nan, supernodal */ cm->supernodal = CHOLMOD_SUPERNODAL ; cm->final_ll = FALSE ; L6 = CHOLMOD(analyze)(C, cm) ; OKP (L6) ; ok = CHOLMOD(factorize)(C, L6, cm) ; OK (ok) ; ok1 = (cm->status == CHOLMOD_OK) ; ok = CHOLMOD(print_factor)(L6, "L6 supernan0", cm) ; OK (ok) ; OK (ok1) ; rcond = CHOLMOD(rcond) (L6, cm) ; OK (rcond == 0) ; } CHOLMOD(free_factor)(&L6, cm) ; CHOLMOD(free_sparse)(&C, cm) ; } cm->supernodal = CHOLMOD_AUTO ; cm->final_ll = FALSE ; cm->print = 1 ; /* ---------------------------------------------------------------------- */ /* refactorize simplicial LDL' */ /* ---------------------------------------------------------------------- */ if (nrow < NLARGE) { L7 = CHOLMOD(analyze) (A, cm) ; OKP (L7) ; ok = CHOLMOD(factorize) (A, L7, cm) ; OK (ok) ; ok = CHOLMOD(factorize) (A, L7, cm) ; OK (ok) ; B7 = CHOLMOD(ones) (nrow, 1, xtype, cm) ; OKP (B7) ; X7 = CHOLMOD(solve) (CHOLMOD_A, L7, B7, cm) ; OKP (X7) ; ok = CHOLMOD(free_dense) (&X7, cm) ; OK (ok) ; ok = CHOLMOD(free_dense) (&B7, cm) ; OK (ok) ; if (A->stype > 0) { ok = CHOLMOD(rowfac) (A, NULL, zero, 0, nrow, L7, cm) ; OK (ok) ; ok = CHOLMOD(rowfac) (A, NULL, zero, 0, nrow, L7, cm) ; OK (ok) ; printf ("I7 :::\n") ; I7 = CHOLMOD(speye) (nrow+1, 1, xtype, cm) ; OKP (I7) ; I7->stype = 1 ; ok = CHOLMOD(rowfac) (I7,NULL, zero, 0, nrow, L7, cm) ; NOT(ok) ; printf ("I7 ::: done\n") ; CHOLMOD(free_sparse) (&I7, cm) ; } ok = CHOLMOD(free_factor) (&L7, cm) ; OK (ok) ; } cm->nmethods = 0 ; /* restore defaults */ cm->method [0].ordering = CHOLMOD_GIVEN ; cm->postorder = TRUE ; /* ---------------------------------------------------------------------- */ /* row subtree */ /* ---------------------------------------------------------------------- */ i = nrow / 2 ; C = CHOLMOD(allocate_sparse)(nrow, 1, nrow, TRUE, TRUE, 0, CHOLMOD_REAL, cm) ; OKP (C) ; C2 = CHOLMOD(allocate_sparse)(nrow, 1, nrow, TRUE, TRUE, 0, CHOLMOD_REAL, cm) ; OKP (C) ; ok = CHOLMOD(row_subtree)(NULL, NULL, i, Parent, C, cm) ; NOT (ok) ; ok = CHOLMOD(row_lsubtree)(NULL, NULL, 0, i, L, C2, cm) ; NOT (ok) ; if (A->stype == 0 && nrow > 0 && AT != NULL) { ok = CHOLMOD(row_subtree)(A, AT, i, Parent, C, cm) ; OK (ok) ; ATp = AT->p ; ATi = AT->i ; fnz = ATp [i+1] - ATp [i] ; ok = CHOLMOD(row_lsubtree)(A, ATi, fnz, i, L, C2, cm) ; OK (ok) ; ok = CHOLMOD(row_lsubtree)(Abad2, ATi, fnz, i, L, C2, cm) ; NOT (ok) ; ok = CHOLMOD(row_lsubtree)(A, NULL, fnz, i, L, C2, cm) ; NOT (ok) ; ok = CHOLMOD(row_lsubtree)(A, ATi, fnz, i, L, Abad2, cm) ; NOT (ok) ; ok = CHOLMOD(row_lsubtree)(A, ATi, fnz, i, NULL, C2, cm) ; NOT (ok) ; ok = CHOLMOD(row_lsubtree)(A, ATi, fnz, nrow+1, L, C2, cm) ;NOT (ok) ; ok = CHOLMOD(row_subtree)(Abad2, AT, i, Parent, C, cm) ; NOT (ok) ; ok = CHOLMOD(row_subtree)(A, Abad2, i, Parent, C, cm) ; NOT (ok) ; ok = CHOLMOD(row_subtree)(A, AT, i, Parent, Abad2, cm) ; NOT (ok) ; ok = CHOLMOD(row_subtree)(A, NULL, i, Parent, C, cm) ; NOT (ok) ; ok = CHOLMOD(row_subtree)(A, AT, nrow+1, Parent, C, cm) ; NOT (ok) ; } else if (A->stype == 1 && nrow > 0) { ok = CHOLMOD(row_subtree)(A, NULL, i, Parent, C, cm) ; OK (ok) ; ok = CHOLMOD(row_lsubtree)(A, NULL, 0, i, L, C2, cm) ; OK (ok) ; } else { ok = CHOLMOD(row_subtree)(A, NULL, i, Parent, C, cm) ; NOT (ok) ; ok = CHOLMOD(row_lsubtree)(A, NULL, 0, i, L, C2, cm) ; NOT (ok) ; } ok = CHOLMOD(row_subtree)(A, NULL, i, Parent, NULL, cm) ; NOT (ok) ; ok = CHOLMOD(row_subtree)(A, NULL, i, NULL, C, cm) ; NOT (ok) ; ok = CHOLMOD(row_lsubtree)(A, NULL, 0, i, L, NULL, cm) ; NOT (ok) ; if (A->stype == 1 && nrow > 0) { /* add extra entries in the (ignored) lower triangular part to AA */ if (!(A->sorted)) { ok = CHOLMOD(sort)(A, cm) ; OK (ok) ; } AA = CHOLMOD(copy)(A, 0, 0, cm) ; OK (AA->sorted) ; AA->stype = 1 ; ok = CHOLMOD(row_subtree)(AA, NULL, i, Parent, C, cm) ; OK (ok) ; ok = CHOLMOD(row_lsubtree)(AA, NULL, 0, i, L, C2, cm) ; OK (ok) ; ok = CHOLMOD(free_sparse)(&AA, cm) ; OK (ok) ; } ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; ok = CHOLMOD(free_sparse)(&C2, cm) ; OK (ok) ; C = CHOLMOD(speye)(nrow, 0, CHOLMOD_REAL, cm) ; OKP (C) ; if (A->stype == 0 && AT != NULL && nrow > 0) { ok = CHOLMOD(row_subtree)(A, AT, i, Parent, C, cm) ; NOT (ok) ; ATp = AT->p ; ATi = AT->i ; fnz = ATp [i+1] - ATp [i] ; ok = CHOLMOD(row_lsubtree)(A, ATi, fnz, i, L, C, cm) ; NOT (ok) ; } ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; L6 = CHOLMOD(allocate_factor)(nrow, cm) ; OKP (L6) ; if (A->stype == 0 && nrow > 2) { ok = CHOLMOD(rowfac)(A, AT, beta, 0, 1, L6, cm) ; OK (ok) ; OK (cm->status == CHOLMOD_OK) ; ok = CHOLMOD(rowfac)(A, NULL, beta, 1, 2, L6, cm) ; NOT (ok) ; ok = CHOLMOD(rowfac)(A, AT, beta, 1, 2, L6, cm) ; OK (ok) ; ok = CHOLMOD(rowfac)(Abad2, AT, beta, 1, 2, L6, cm) ; NOT (ok) ; ok = CHOLMOD(rowfac)(A, Abad2, beta, 1, 2, L6, cm) ; NOT (ok) ; } ok = CHOLMOD(free_factor)(&L6, cm) ; OK (ok) ; /* ---------------------------------------------------------------------- */ /* horzcat, vertcat */ /* ---------------------------------------------------------------------- */ if (A->nrow != A->ncol) { C = CHOLMOD(horzcat)(A, AT, TRUE, cm) ; NOP (C) ; C = CHOLMOD(vertcat)(A, AT, TRUE, cm) ; NOP (C) ; } C = CHOLMOD(horzcat)(A, Axbad, TRUE, cm) ; NOP (C) ; C = CHOLMOD(vertcat)(A, Axbad, TRUE, cm) ; NOP (C) ; C = CHOLMOD(vertcat)(A, NULL, TRUE, cm) ; NOP (C) ; C = CHOLMOD(vertcat)(NULL, AT, TRUE, cm) ; NOP (C) ; C = CHOLMOD(horzcat)(A, NULL, TRUE, cm) ; NOP (C) ; C = CHOLMOD(horzcat)(NULL, AT, TRUE, cm) ; NOP (C) ; /* ---------------------------------------------------------------------- */ /* print_triplet */ /* ---------------------------------------------------------------------- */ cm->print = 4 ; ok = CHOLMOD(print_triplet)(Tok, "T ok", cm) ; OK (ok) ; T = CHOLMOD(copy_triplet)(Tok, cm) ; /* [ */ OKP (T) ; Tz = T->z ; T->z = NULL ; ok = CHOLMOD(print_triplet)(T, "T no z", cm) ; if (T->xtype == CHOLMOD_ZOMPLEX) { NOT (ok) ; } else { OK (ok) ; } T->z = Tz ; cm->print = 1 ; ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ; ok = CHOLMOD(print_triplet)(NULL, "null", cm) ; NOT (ok) ; p = T->nzmax ; T->nzmax = T->nnz - 1 ; ok = CHOLMOD(print_triplet)(T, "T nzmax too small", cm) ; NOT (ok) ; T->nzmax = p ; ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ; T->itype = -1 ; ok = CHOLMOD(print_triplet)(T, "T itype bad", cm) ; NOT (ok) ; T->itype = CHOLMOD_INTLONG ; ok = CHOLMOD(print_triplet)(T, "T itype bad", cm) ; NOT (ok) ; T->itype = cm->itype ; ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ; cm->print = 4 ; #ifdef LONG T->itype = CHOLMOD_INT ; #else T->itype = CHOLMOD_LONG ; #endif ok = CHOLMOD(print_triplet)(T, "T bad itype", cm) ; NOT (ok) ; T->itype = cm->itype ; cm->print = 1 ; Txtype = T->xtype ; T->xtype = -1 ; ok = CHOLMOD(print_triplet)(T, "T xtype bad", cm) ; NOT (ok) ; T->xtype = Txtype ; ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ; T->dtype = -1 ; ok = CHOLMOD(print_triplet)(T, "T dtype bad", cm) ; NOT (ok) ; T->dtype = CHOLMOD_SINGLE ; ok = CHOLMOD(print_triplet)(T, "T dtype bad", cm) ; NOT (ok) ; T->dtype = CHOLMOD_DOUBLE ; ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ; Tj = T->j ; Ti = T->i ; Tx = T->x ; T->j = NULL ; ok = CHOLMOD(print_triplet)(T, "Tj null", cm) ; NOT (ok) ; T->j = Tj ; ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ; T->i = NULL ; ok = CHOLMOD(print_triplet)(T, "Ti null", cm) ; NOT (ok) ; T->i = Ti ; ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ; T->x = NULL ; ok = CHOLMOD(print_triplet)(T, "Tx null", cm) ; NOT (ok) ; T->x = Tx ; ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ; if (T->nnz > 0) { p = Ti [0] ; Ti [0] = -1 ; ok = CHOLMOD(print_triplet)(T, "Ti bad", cm) ; NOT (ok) ; C = CHOLMOD(triplet_to_sparse)(T, 0, cm) ; NOP (C) ; Ti [0] = p ; ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ; p = Tj [0] ; Tj [0] = -1 ; ok = CHOLMOD(print_triplet)(T, "Tj bad", cm) ; NOT (ok) ; C = CHOLMOD(triplet_to_sparse)(T, 0, cm) ; NOP (C) ; Tj [0] = p ; ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ; } cm->print = 4 ; CHOLMOD(triplet_xtype)(CHOLMOD_PATTERN, T, cm) ; ok = CHOLMOD(print_triplet)(T, "T pattern ok", cm) ; OK (ok) ; cm->print = 1 ; /* ---------------------------------------------------------------------- */ /* triplet, realloc_multiple */ /* ---------------------------------------------------------------------- */ ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ; OK (cm->status == CHOLMOD_OK) ; cm->print = 4 ; if (T->nrow != T->ncol) { OK (T->stype == 0) ; CHOLMOD(print_triplet)(T, "T ok", cm) ; C = CHOLMOD(triplet_to_sparse)(T, 0, cm) ; CHOLMOD(print_sparse)(C, "C ok", cm) ; OKP (C) ; ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; Ti = T->i ; T->i = NULL ; C = CHOLMOD(triplet_to_sparse)(T, 0, cm) ; NOP (C) ; T->i = Ti ; Tj = T->j ; T->j = NULL ; C = CHOLMOD(triplet_to_sparse)(T, 0, cm) ; NOP (C) ; T->j = Tj ; T->stype = 1 ; ok = CHOLMOD(print_triplet)(T, "T bad", cm) ; NOT (ok) ; C = CHOLMOD(triplet_to_sparse)(T, 0, cm) ; NOP (C) ; T->stype = 0 ; ok = CHOLMOD(print_triplet)(T, "T pattern ok", cm) ; OK (ok) ; } OK (cm->status == CHOLMOD_OK) ; cm->print = 1 ; ok = CHOLMOD(reallocate_triplet)(1, NULL, cm) ; NOT (ok) ; CHOLMOD(print_triplet)(T, "T before realloc", cm) ; ok = CHOLMOD(reallocate_triplet)(1+(T->nzmax), T, cm) ; OK (ok) ; CHOLMOD(print_triplet)(T, "T after realloc", cm) ; nznew = 10 + T->nzmax ; pp = NULL ; ok = CHOLMOD(realloc_multiple)(Size_max/2, 2, T->xtype, &(T->i), &(T->j), &(T->x), &(T->z), &(T->nzmax), cm) ; NOT (ok) ; size = 0 ; ii = NULL ; jj = NULL ; xx = NULL ; ok = CHOLMOD(realloc_multiple)(Size_max, 2, CHOLMOD_REAL, &ii, &jj, &xx, NULL, &size, cm) ; NOT (ok) ; ok = CHOLMOD(realloc_multiple)(0, 0, CHOLMOD_PATTERN, &ii, &jj, &xx, NULL, &size, cm) ; OK (ok) ; ok = CHOLMOD(realloc_multiple)(0, 0, -1, &ii, &jj, &xx, NULL, &size, cm) ; NOT (ok) ; /* change to pattern-only */ CHOLMOD(triplet_xtype)(CHOLMOD_PATTERN, T, cm) ; ok = CHOLMOD(reallocate_triplet)(1+(T->nzmax), T, cm) ; OK (ok) ; ok = CHOLMOD(free_triplet)(&T, cm) ; /* ] */ OK (ok) ; T = CHOLMOD(allocate_triplet)(nrow, ncol, Size_max, 0, CHOLMOD_REAL, cm); NOP (T) ; T2 = CHOLMOD(allocate_triplet)(4, 4, 8, 0, CHOLMOD_REAL, cm); OKP (T2) ; ok = CHOLMOD(reallocate_triplet)(12, T2, cm) ; OK (ok) ; T = CHOLMOD(copy_triplet)(T2, cm) ; OKP (T) ; CHOLMOD(free_triplet)(&T, cm) ; T = CHOLMOD(sparse_to_triplet)(A, cm) ; OKP (T) ; C = CHOLMOD(triplet_to_sparse)(T, 100, cm) ; OKP (C) ; CHOLMOD(free_sparse)(&C, cm) ; CHOLMOD(free_triplet)(&T, cm) ; T2->xtype = -1 ; ok = CHOLMOD(reallocate_triplet)(16, T2, cm) ; NOT (ok) ; T = CHOLMOD(copy_triplet)(T2, cm) ; NOP (T) ; C = CHOLMOD(triplet_to_sparse)(T2, 100, cm) ; NOP (C) ; T2->xtype = CHOLMOD_REAL ; CHOLMOD(free_triplet)(&T2, cm) ; T = CHOLMOD(allocate_triplet)(4, 4, 16, 0, -1, cm); NOP (T) ; T = CHOLMOD(sparse_to_triplet)(Abad2, cm) ; NOP (T) ; for (stype = -1 ; stype <= 1 ; stype++) { T = CHOLMOD(allocate_triplet)(4, 4, 16, stype, CHOLMOD_PATTERN, cm) ; OKP (T) ; Ti = T->i ; Tj = T->j ; k = 0 ; for (i = 0 ; i < 4 ; i++) { for (j = 0 ; j < 4 ; j++) { Ti [k] = i ; Tj [k] = j ; k++ ; } } T->nnz = k ; C = CHOLMOD(triplet_to_sparse)(T, 0, cm) ; cm->print = 4 ; printf ("stype "ID"\n", stype) ; CHOLMOD(print_triplet)(T, "T from triplet", cm) ; CHOLMOD(print_sparse)(C, "C from triplet", cm) ; cm->print = 1 ; OKP (C) ; CHOLMOD(free_sparse)(&C, cm) ; CHOLMOD(free_triplet)(&T, cm) ; } /* ---------------------------------------------------------------------- */ /* sparse_to_triplet */ /* ---------------------------------------------------------------------- */ if (A->nrow != A->ncol) { OK (A->stype == 0) ; T = CHOLMOD(sparse_to_triplet)(A, cm) ; OKP (T) ; ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ; T2 = CHOLMOD(copy_triplet)(NULL, cm) ; NOP (T2) ; Ti = T->i ; T->i = NULL ; T2 = CHOLMOD(copy_triplet)(T, cm) ; NOP (T2) ; T->i = Ti ; Tj = T->j ; T->j = NULL ; T2 = CHOLMOD(copy_triplet)(T, cm) ; NOP (T2) ; T->j = Tj ; ok = CHOLMOD(free_triplet)(&T, cm) ; OK (ok) ; A->stype = 1 ; T = CHOLMOD(sparse_to_triplet)(A, cm) ; NOP (T) ; A->stype = 0 ; T = CHOLMOD(sparse_to_triplet)(NULL, cm) ; NOP (T) ; } /* ---------------------------------------------------------------------- */ /* colamd */ /* ---------------------------------------------------------------------- */ ok = CHOLMOD(colamd)(A, fsetok, fsizeok, TRUE, NULL, cm) ; NOT (ok) ; ok = CHOLMOD(colamd)(NULL, fsetok, fsizeok, TRUE, Pok, cm) ; NOT (ok) ; cm->current = 0 ; save1 = cm->method [0].prune_dense2 ; save2 = cm->method [0].ordering ; save4 = cm->nmethods ; cm->method [0].prune_dense2 = 0.5 ; cm->method [0].ordering = CHOLMOD_COLAMD ; cm->nmethods = 1 ; ok = CHOLMOD(colamd)(A, fsetok, fsizeok, TRUE, Pok, cm) ; if (A->stype == 0) { save3 = cm->print ; cm->print = 5 ; ok = CHOLMOD(print_common) ("colamd dense2", cm) ; OK (ok) ; cm->print = save3 ; OK (ok) ; } else { NOT (ok) ; } cm->method [0].prune_dense2 = save1 ; cm->method [0].ordering = save2 ; cm->nmethods = save4 ; cm->current = -1 ; ok = CHOLMOD(colamd)(A, fsetok, fsizeok, TRUE, Pok, cm) ; if (A->stype == 0) { OK (ok) ; } else { NOT (ok) ; } cm->current = 0 ; ok = CHOLMOD(colamd)(Abad2, NULL, 0, TRUE, Pok, cm) ; NOT (ok) ; if (ncol > 0) { ok = CHOLMOD(colamd)(A, fsetbad, ncol, TRUE, Pok, cm) ; NOT (ok) ; } /* mangle the matrix to test integer overflow in colamd */ if (A->stype == 0) { nzmax = A->nzmax ; A->nzmax = Size_max/2 ; ok = CHOLMOD(colamd)(A, fsetok, fsizeok, TRUE, Pok, cm) ; NOT (ok) ; A->nzmax = nzmax ; } /* ---------------------------------------------------------------------- */ /* ccolamd/csymamd */ /* ---------------------------------------------------------------------- */ #ifndef NPARTITION ok = CHOLMOD(ccolamd)(A, fsetok, fsizeok, NULL, NULL, cm) ; NOT (ok) ; ok = CHOLMOD(ccolamd)(A, fsetok, fsizeok, NULL, Pok, cm) ; if (A->stype == 0) { OK (ok) ; } else { NOT (ok) ; } ok = CHOLMOD(ccolamd)(Abad2, NULL, 0, NULL, Pok, cm) ; NOT (ok) ; ok = CHOLMOD(csymamd)(A, NULL, Pok, cm) ; if (A->nrow == A->ncol) { OK (ok) ; } else { NOT (ok) ; } ok = CHOLMOD(csymamd)(Abad2, NULL, Pok, cm) ; NOT (ok) ; ok = CHOLMOD(csymamd)(NULL, NULL, Pok, cm) ; NOT (ok) ; ok = CHOLMOD(csymamd)(A, NULL, NULL, cm) ; NOT (ok) ; /* mangle the matrix to test integer overflow in colamd */ if (A->stype == 0) { nzmax = A->nzmax ; A->nzmax = Size_max/2 ; ok = CHOLMOD(ccolamd)(A, fsetok, fsizeok, NULL, Pok, cm) ; NOT (ok) ; A->nzmax = nzmax ; } #endif /* ---------------------------------------------------------------------- */ /* amd */ /* ---------------------------------------------------------------------- */ ok = CHOLMOD(amd)(A, NULL, 0, Pok, cm) ; OK (ok) ; /* ---------------------------------------------------------------------- */ /* metis */ /* ---------------------------------------------------------------------- */ #ifndef NPARTITION /* no METIS memory guard */ cm->metis_memory = 0 ; if (A->stype) { E = CHOLMOD(copy)(A, 0, -1, cm) ; } else { E = CHOLMOD(aat)(A, NULL, 0, -1, cm) ; } enz = CHOLMOD(nnz)(E, cm) ; CHOLMOD(print_sparse)(A, "A for metis", cm) ; if (A != NULL && Pok != NULL) { ok = CHOLMOD(metis)(A, NULL, 0, TRUE, Pok, cm) ; /* memory guard triggered */ if (nrow > 0) { double density ; cm->metis_memory = Size_max ; ok = CHOLMOD(metis)(A, NULL, 0, FALSE, Pok, cm) ; OK (ok) ; /* Pok should be identity */ for (j = 0 ; j < nrow ; j++) { OK (Pok [j] == j) ; } /* memory guard triggered */ cm->metis_memory = 2 ; cm->metis_nswitch = 10 ; ok = CHOLMOD(metis)(A, NULL, 0, FALSE, Pok, cm) ; OK (ok) ; /* Pok should be identity if the matrix is dense */ density = ((double) enz) / (((double) nrow) * ((double) nrow)) ; if (nrow > 10 && density > cm->metis_dswitch) { for (j = 0 ; j < nrow ; j++) { OK (Pok [j] == j) ; } } } } /* restore METIS default memory guard */ cm->metis_memory = 2 ; cm->metis_nswitch = 3000 ; /* check metis bisector error handling */ if (E != NULL && enz > 0) { Int *Anw, *Aew ; Anw = CHOLMOD(malloc)(nrow, sizeof (Int), cm) ; Aew = CHOLMOD(malloc)(MAX (anz,enz), sizeof (Int), cm) ; for (j = 0 ; j < nrow ; j++) { Anw [j] = 1 ; } for (j = 0 ; j < enz ; j++) { Aew [j] = 1 ; } lr = CHOLMOD(metis_bisector)(E, Anw, Aew, Pok, cm) ; if (E->stype || E->nrow != E->ncol) { NOT (lr >= 0) ; } else { OK (lr >= 0) ; } lr = CHOLMOD(metis_bisector)(Abad2, Anw, Aew, Pok, cm) ;NOT (lr >= 0); lr = CHOLMOD(metis_bisector)(NULL, Anw, Aew, Pok, cm) ; NOT (lr >= 0); lr = CHOLMOD(metis_bisector)(A, NULL, Aew, Pok, cm) ; NOT (lr >= 0); lr = CHOLMOD(metis_bisector)(A, Anw, NULL, Pok, cm) ; NOT (lr >= 0); lr = CHOLMOD(metis_bisector)(A, Anw, Aew, NULL, cm) ; NOT (lr >= 0); if (A->stype) { lr = CHOLMOD(metis_bisector)(A, Anw, Aew, Pok, cm) ; NOT (lr>=0) ; } CHOLMOD(free)(nrow, sizeof (Int), Anw, cm) ; CHOLMOD(free)(MAX (anz,enz), sizeof (Int), Aew, cm) ; } CHOLMOD(free_sparse)(&E, cm) ; CHOLMOD(print_sparse)(Abad, "Abad", cm) ; lr = CHOLMOD(bisect)(Abad, NULL, 0, TRUE, Partition, cm) ; if (Abad != NULL && Abad->nrow == 0) { OK (lr == 0) ; } else { NOT (lr >= 0) ; } lr = CHOLMOD(bisect)(A, NULL, 0, TRUE, NULL, cm) ; NOT (lr >= 0); lr = CHOLMOD(bisect)(NULL, NULL, 0, TRUE, Partition, cm) ; NOT (lr >= 0); lr = CHOLMOD(nested_dissection)(NULL, NULL, 0, Pok, CParent, Cmember, cm) ; NOT (lr>=0) ; lr = CHOLMOD(nested_dissection)(A, NULL, 0, NULL, CParent, Cmember, cm) ; NOT (lr>=0) ; lr = CHOLMOD(nested_dissection)(A, NULL, 0, Pok, NULL, Cmember, cm) ; NOT (lr>=0) ; lr = CHOLMOD(nested_dissection)(A, NULL, 0, Pok, CParent, NULL, cm) ; NOT (lr>=0) ; ok = CHOLMOD(metis)(NULL, NULL, 0, TRUE, Pok, cm) ; NOT (ok) ; ok = CHOLMOD(metis)(A, NULL, 0, TRUE, NULL, cm) ; NOT (ok) ; ok = CHOLMOD(metis)(Abad2, NULL, 0, FALSE, Pok, cm) ; NOT (ok) ; lr = CHOLMOD(bisect)(Abad2, NULL, 0, TRUE, Partition, cm) ; NOT (lr >= 0); #endif /* ---------------------------------------------------------------------- */ /* etree */ /* ---------------------------------------------------------------------- */ if (A->stype < 0) { ok = CHOLMOD(etree)(A, Parent, cm) ; NOT (ok) ; } ok = CHOLMOD(etree)(Abad2, Parent, cm) ; NOT (ok) ; /* ---------------------------------------------------------------------- */ /* etree, postorder, rowcolcount */ /* ---------------------------------------------------------------------- */ if (A->stype == 0 && ncol > 0) { AFT = CHOLMOD(ptranspose)(A, 1, NULL, fsetok, fsizeok, cm) ; OKP(AFT); AF = CHOLMOD(transpose)(AFT, 1, cm) ; OKP(AF); ok = CHOLMOD(etree)(NULL, Parent, cm) ; NOT(ok); ok = CHOLMOD(etree)(AFT, NULL, cm) ; NOT(ok); ok = CHOLMOD(etree)(AFT, Parent, cm) ; OK (ok); lr = CHOLMOD(postorder)(Parent, nrow, NULL, Post, cm) ; OK (lr>=0) ; lr = CHOLMOD(postorder)(NULL, nrow, NULL, Post, cm) ; NOT (lr>=0) ; lr = CHOLMOD(postorder)(Parent, nrow, NULL, NULL, cm) ; NOT (lr>=0) ; ok = CHOLMOD(rowcolcounts)(A, fsetok, fsizeok, Parent, Post, NULL, ColCount, First, Level, cm) ; OK (ok); ok = CHOLMOD(rowcolcounts)(Abad2, fsetok, fsizeok, Parent, Post, NULL, ColCount, First, Level, cm) ; NOT(ok); ok = CHOLMOD(rowcolcounts)(NULL, fsetok, fsizeok, Parent, Post, NULL, ColCount, First, Level, cm) ; NOT(ok); ok = CHOLMOD(rowcolcounts)(A, fsetok, fsizeok, NULL, Post, NULL, ColCount, First, Level, cm) ; NOT(ok); ok = CHOLMOD(rowcolcounts)(A, fsetok, fsizeok, Parent, NULL, NULL, ColCount, First, Level, cm) ; NOT(ok); ok = CHOLMOD(rowcolcounts)(A, fsetok, fsizeok, Parent, Post, NULL, NULL, First, Level, cm) ; NOT(ok); ok = CHOLMOD(rowcolcounts)(A, fsetok, fsizeok, Parent, Post, NULL, ColCount, NULL, Level, cm) ; NOT(ok); ok = CHOLMOD(rowcolcounts)(A, fsetok, fsizeok, Parent, Post, NULL, ColCount, First, NULL, cm) ; NOT(ok); ok = CHOLMOD(rowcolcounts)(A, fsetbad, ncol, Parent, Post, NULL, ColCount, First, Level, cm) ; NOT(ok); ok = CHOLMOD(rowcolcounts)(A, fsetok, fsizeok, Parent, Post, NULL, ColCount, First, NULL, cm) ; NOT(ok); CHOLMOD(free_sparse)(&AF, cm) ; CHOLMOD(free_sparse)(&AFT, cm) ; } /* ---------------------------------------------------------------------- */ /* norm */ /* ---------------------------------------------------------------------- */ nm = CHOLMOD(norm_sparse)(A, 2, cm) ; NOT (nm>=0) ; nm = CHOLMOD(norm_sparse)(Abad, 0, cm) ; NOT (nm>=0) ; nm = CHOLMOD(norm_sparse)(Abad2, 2, cm) ; NOT (nm>=0) ; nm = CHOLMOD(norm_dense)(Bok, 3, cm) ; NOT (nm>=0) ; nm = CHOLMOD(norm_dense)(Bok, 2, cm) ; NOT (nm>=0) ; nm = CHOLMOD(norm_dense)(Xbad2, 1, cm) ; NOT (nm>=0) ; /* ---------------------------------------------------------------------- */ /* copy dense */ /* ---------------------------------------------------------------------- */ ok = CHOLMOD(copy_dense2)(NULL, Bok, cm) ; NOT (ok) ; ok = CHOLMOD(copy_dense2)(Bok, NULL, cm) ; NOT (ok) ; ok = CHOLMOD(copy_dense2)(Bok, Xbad2, cm) ; NOT (ok) ; ok = CHOLMOD(copy_dense2)(Xbad2, Xbad2, cm) ; NOT (ok) ; if (nrow > 1) { /* wrong dimensions */ ok = CHOLMOD(copy_dense2)(Two, Bok, cm) ; NOT (ok) ; /* mangled matrix */ Y = CHOLMOD(copy_dense)(Bok, cm) ; OKP (Y) ; Y->d = 0 ; ok = CHOLMOD(copy_dense2)(Bok, Y, cm) ; NOT (ok) ; CHOLMOD(free_dense)(&Y, cm) ; Y = CHOLMOD(copy_dense)(Xbad2, cm) ; NOP (Y) ; Y = CHOLMOD(copy_dense)(NULL, cm) ; NOP (Y) ; } /* ---------------------------------------------------------------------- */ /* complex */ /* ---------------------------------------------------------------------- */ W = CHOLMOD(eye)(4, 4, CHOLMOD_COMPLEX, cm) ; OKP (W) ; ok = CHOLMOD(dense_xtype)(0, W, cm) ; NOT (ok) ; ok = CHOLMOD(dense_xtype)(CHOLMOD_REAL, W, cm) ; OK (ok) ; ok = CHOLMOD(dense_xtype)(CHOLMOD_REAL, NULL, cm) ; NOT (ok) ; k = W->xtype ; W->xtype = -1 ; ok = CHOLMOD(dense_xtype)(CHOLMOD_REAL, W, cm) ; NOT (ok) ; W->xtype = k ; ok = CHOLMOD(free_dense)(&W, cm) ; OK (ok) ; C = CHOLMOD(speye)(4, 4, CHOLMOD_COMPLEX, cm) ; OKP (C) ; ok = CHOLMOD(sparse_xtype)(-1, C, cm) ; NOT (ok) ; ok = CHOLMOD(sparse_xtype)(CHOLMOD_ZOMPLEX, C, cm) ; OK (ok) ; ok = CHOLMOD(sparse_xtype)(CHOLMOD_ZOMPLEX, NULL, cm) ; NOT (ok) ; T = CHOLMOD(sparse_to_triplet)(C, cm) ; OKP (T) ; ok = CHOLMOD(triplet_xtype)(-1, T, cm) ; NOT (ok) ; ok = CHOLMOD(triplet_xtype)(CHOLMOD_ZOMPLEX, T, cm) ; OK (ok) ; ok = CHOLMOD(triplet_xtype)(CHOLMOD_ZOMPLEX, NULL, cm) ; NOT (ok) ; k = T->xtype ; T->xtype = -1 ; ok = CHOLMOD(triplet_xtype)(CHOLMOD_REAL, T, cm) ; NOT (ok) ; T->xtype = k ; k = C->xtype ; C->xtype = -1 ; ok = CHOLMOD(sparse_xtype)(CHOLMOD_REAL, C, cm) ; NOT (ok) ; C->xtype = k ; ok = CHOLMOD(free_triplet)(&T, cm) ; OK (ok) ; ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; ok = CHOLMOD(factor_xtype)(CHOLMOD_REAL, Lbad, cm) ; NOT (ok) ; /* ---------------------------------------------------------------------- */ /* rowadd */ /* ---------------------------------------------------------------------- */ x = X->x ; X->x = NULL ; C = CHOLMOD(dense_to_sparse)(X, TRUE, cm) ; NOP (C) ; if (nrow > 3 && isreal) { ok = CHOLMOD(rowadd)(1, I1, L, cm) ; NOT (ok) ; ok = CHOLMOD(rowadd)(nrow+1, R, L, cm) ; NOT (ok) ; ok = CHOLMOD(rowadd)(nrow+1, R, L, cm) ; NOT (ok) ; ok = CHOLMOD(rowdel)(nrow+1, NULL, L5, cm) ; NOT (ok) ; ok = CHOLMOD(rowdel)(nrow-2, NULL, L5, cm) ; OK (ok) ; ok = CHOLMOD(rowdel)(nrow-2, NULL, L5, cm) ; OK (ok) ; ok = CHOLMOD(rowdel)(nrow-2, Abad2, L5, cm) ; NOT (ok) ; ok = CHOLMOD(rowdel)(nrow-1, R, L5, cm) ; NOT (ok) ; ok = CHOLMOD(change_factor)(CHOLMOD_REAL, TRUE, FALSE, TRUE, TRUE, L5, cm) ; OK (ok) ; ok = CHOLMOD(rowadd)(nrow-2, NULL, L5, cm) ; NOT (ok) ; ok = CHOLMOD(rowadd)(nrow-2, R, NULL, cm) ; NOT (ok) ; ok = CHOLMOD(rowadd)(nrow-2, R, L5, cm) ; OK (ok) ; ok = CHOLMOD(rowadd)(nrow-2, Abad2, L5, cm) ; NOT (ok) ; /* ok = CHOLMOD(rowadd)(nrow-2, R, L5, cm) ; NOT (ok) ; */ ok = CHOLMOD(rowdel)(nrow-2, NULL, L5, cm) ; OK (ok) ; ok = CHOLMOD(change_factor)(CHOLMOD_PATTERN, TRUE, TRUE, TRUE, TRUE, L5, cm) ; NOT (ok) ; ok = CHOLMOD(change_factor)(CHOLMOD_REAL, TRUE, TRUE, TRUE, TRUE, L5, cm) ; NOT (ok) ; ok = CHOLMOD(rowadd_solve)(nrow-2, R, beta, L5, X, X, cm) ; NOT (ok) ; ok = CHOLMOD(rowdel_solve)(nrow-2, R, beta, L5, X, X, cm) ; NOT (ok) ; ok = CHOLMOD(updown_solve)(TRUE, R, L5, X, X, cm) ; NOT (ok) ; if (nrow < 200 && L5 != NULL && R2 != NULL) { cholmod_factor *L8 ; Int *L8p, *L8i, *L8nz, rnz ; double *L8x ; L8 = CHOLMOD(copy_factor) (L5, cm) ; ok = TRUE ; for (k = nrow-1 ; ok && L8 != NULL && L8->xtype == CHOLMOD_REAL && k >= 0 ; k--) { for (rnz = 0 ; rnz < nrow ; rnz++) { /* first, ensure row i is zero */ for (j = 0 ; j < nrow ; j++) { L8p = L8->p ; L8i = L8->i ; L8nz = L8->nz ; L8x = L8->x ; for (p = L8p [j] ; p < L8p [j] + L8nz [j] ; p++) { i = L8i [p] ; if (i == k) L8x [p] = 0 ; } } R2p [1] = rnz ; ok = CHOLMOD(rowadd)(k, R2, L8, cm) ; OK (ok) ; ok = CHOLMOD(rowdel)(k, NULL, L8, cm) ; OK (ok) ; ok = CHOLMOD(rowadd)(k, R2, L8, cm) ; OK (ok) ; } } CHOLMOD(free_factor) (&L8, cm) ; } } X->x = x ; ok = CHOLMOD(free_dense)(&X, cm) ; OK (ok) ; /* ---------------------------------------------------------------------- */ /* ssmult */ /* ---------------------------------------------------------------------- */ if (nrow < 100) { C = CHOLMOD(ssmult)(A, A, 0, TRUE, TRUE, cm) ; if (A->nrow != A->ncol || !isreal) { NOP (C) ; } else { OKP (C) ; ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; } C = CHOLMOD(ssmult)(NULL, A, 0, TRUE, TRUE, cm) ; NOP (C) ; C = CHOLMOD(ssmult)(A, NULL, 0, TRUE, TRUE, cm) ; NOP (C) ; C = CHOLMOD(ssmult)(A, Axbad, 0, TRUE, TRUE, cm) ; NOP (C) ; } /* ---------------------------------------------------------------------- */ /* sdmult */ /* ---------------------------------------------------------------------- */ if (nrow > 1) { ok = CHOLMOD(sdmult)(A, FALSE, one, one, Two, Two, cm) ; NOT (ok) ; } YY = CHOLMOD(ones)(A->nrow, 1, xtype, cm) ; OKP (YY) ; XX = CHOLMOD(ones)(A->ncol, 1, xtype, cm) ; OKP (XX) ; cm->print = 4 ; ok = CHOLMOD(print_dense)(XX, "XX", cm) ; OK (ok) ; cm->print = 1 ; ok = CHOLMOD(sdmult)(A, FALSE, one, one, XX, YY, cm) ; OK (ok) ; ok = CHOLMOD(sdmult)(NULL, FALSE, one, one, XX, YY, cm) ; NOT (ok) ; ok = CHOLMOD(sdmult)(A, FALSE, one, one, NULL, YY, cm) ; NOT (ok) ; ok = CHOLMOD(sdmult)(A, FALSE, one, one, XX, NULL, cm) ; NOT (ok) ; ok = CHOLMOD(sdmult)(Abad2, FALSE, one, one, XX, YY, cm) ; NOT (ok) ; XX->xtype++ ; ok = CHOLMOD(sdmult)(A, FALSE, one, one, XX, YY, cm) ; NOT (ok) ; XX->xtype-- ; YY->xtype++ ; ok = CHOLMOD(sdmult)(A, FALSE, one, one, XX, YY, cm) ; NOT (ok) ; YY->xtype-- ; CHOLMOD(free_dense)(&YY, cm) ; CHOLMOD(free_dense)(&XX, cm) ; /* ---------------------------------------------------------------------- */ /* symmetry */ /* ---------------------------------------------------------------------- */ for (option = 0 ; option <= 2 ; option++) { Int xmatched = 0, pmatched = 0, nzoffdiag = 0, nz_diag = 0 ; int asym ; printf ("test symmetry: option %d\n", option) ; save1 = cm->print ; cm->print = 5 ; CHOLMOD(print_sparse) (A, "A", cm) ; cm->print = save1 ; asym = CHOLMOD(symmetry) (A, option, &xmatched, &pmatched, &nzoffdiag, &nz_diag, cm) ; printf ("asym: %d\n", asym) ; OK (A->stype != 0 || asym >= 0) ; save1 = A->xtype ; A->xtype = CHOLMOD_PATTERN ; asym = CHOLMOD(symmetry) (A, option, &xmatched, &pmatched, &nzoffdiag, &nz_diag, cm) ; printf ("asym: %d pattern\n", asym) ; OK (A->stype != 0 || asym >= 0) ; A->xtype = save1 ; C = CHOLMOD(copy_sparse) (A, cm) ; OKP (C) ; ok = CHOLMOD(sparse_xtype) (CHOLMOD_ZOMPLEX, C, cm) ; OK (ok) ; asym = CHOLMOD(symmetry) (C, option, &xmatched, &pmatched, &nzoffdiag, &nz_diag, cm) ; OK (A->stype != 0 || asym >= 0) ; printf ("asym: %d zomplex\n", asym) ; asym = CHOLMOD(symmetry) (NULL, option, &xmatched, &pmatched, &nzoffdiag, &nz_diag, cm) ; NOT (asym >= 0) ; C->xtype = 999 ; asym = CHOLMOD(symmetry) (C, option, &xmatched, &pmatched, &nzoffdiag, &nz_diag, cm) ; NOT (asym >= 0) ; C->xtype = CHOLMOD_ZOMPLEX ; ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; C = CHOLMOD(copy) (A, 0, (A->xtype == CHOLMOD_REAL), cm) ; OKP (C) ; asym = CHOLMOD(symmetry) (C, option, &xmatched, &pmatched, &nzoffdiag, &nz_diag, cm) ; OK (asym >= 0) ; ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ; } /* ---------------------------------------------------------------------- */ /* memory tests */ /* ---------------------------------------------------------------------- */ R3 = CHOLMOD(speye)(nrow, 1, CHOLMOD_PATTERN, cm) ; /* [ */ OKP (R3) ; test_memory_handler ( ) ; ok = CHOLMOD(amd)(A, NULL, 0, Pok, cm) ; if (A->nrow == 0) { OK (ok) ; } else { NOT (ok) ; } #ifndef NPARTITION ok = CHOLMOD(camd)(A, NULL, 0, NULL, Pok, cm) ; if (A->nrow == 0) { OK (ok) ; } else { NOT (ok) ; } #endif C = CHOLMOD(aat)(A, NULL, 0, 0, cm) ; NOP (C) ; A->sorted = FALSE ; ok = CHOLMOD(check_sparse)(A, cm) ; NOT (ok) ; A->sorted = TRUE ; CHOLMOD(free_work)(cm) ; if (A->stype == 0) { for (trial = 0 ; !ok && trial < 20 ; trial++) { my_tries = trial ; printf ("--------------------- trial "ID"\n", my_tries) ; ok = CHOLMOD(colamd)(A, NULL, 0, TRUE, Pok, cm) ; } OK (ok) ; } #ifndef NPARTITION test_memory_handler ( ) ; ok = CHOLMOD(ccolamd)(A, fsetok, fsizeok, NULL, Pok, cm) ; NOT (ok) ; ok = CHOLMOD(csymamd)(A, NULL, Pok, cm) ; NOT (ok) ; for (trial = 0 ; trial < 7 ; trial++) { test_memory_handler ( ) ; my_tries = trial ; ok = CHOLMOD(csymamd)(A, NULL, Pok, cm) ; NOT (ok) ; } if (A->nrow == A->ncol && A->packed) { test_memory_handler ( ) ; my_tries = 8 ; ok = CHOLMOD(csymamd)(A, NULL, Pok, cm) ; OK (ok) ; test_memory_handler ( ) ; ok = CHOLMOD(csymamd)(A, NULL, Pok, cm) ; NOT (ok) ; OK (cm->status == CHOLMOD_OUT_OF_MEMORY) ; } for (trial = 0 ; trial < 5 ; trial++) { test_memory_handler ( ) ; my_tries = trial ; ok = CHOLMOD(camd)(A, NULL, 0, NULL, Pok, cm) ; if (A->nrow == 0) { OK (ok) ; } else { NOT (ok) ; } } #endif test_memory_handler ( ) ; ok = CHOLMOD(etree)(A, Parent, cm) ; NOT (ok) ; ok = CHOLMOD(factorize)(A, L, cm) ; NOT (ok) ; pp = CHOLMOD(malloc)(4, 0, cm) ; NOP (pp) ; pp = CHOLMOD(calloc)(4, 0, cm) ; NOP (pp) ; pp = CHOLMOD(calloc)(Size_max, 1, cm) ; NOP (pp) ; pp = NULL ; size = 0 ; pp = CHOLMOD(realloc)(4, 0, pp, &size, cm) ; NOP (pp) ; pp = CHOLMOD(realloc)(Size_max, 1, pp, &size, cm) ; NOP (pp) ; normal_memory_handler ( ) ; OK (CHOLMOD(print_sparse)(A, "A ok", cm)) ; OK (CHOLMOD(print_factor)(L, "L ok", cm)) ; /* test no_workspace_reallocate flag */ CHOLMOD (free_work) (cm) ; CHOLMOD (allocate_work) (1, 1, 1, cm) ; OK (cm->status == CHOLMOD_OK) ; cm->no_workspace_reallocate = TRUE ; ok = CHOLMOD (allocate_work) (2, 1, 1, cm) ; NOT (ok) ; ok = CHOLMOD (allocate_work) (1, 2, 1, cm) ; NOT (ok) ; ok = CHOLMOD (allocate_work) (1, 1, 2, cm) ; NOT (ok) ; cm->no_workspace_reallocate = FALSE ; ok = CHOLMOD (allocate_work) (1, 1, 2, cm) ; OK (ok) ; cm->print = 4 ; ok = CHOLMOD(print_factor)(L, "L for copy", cm) ; OK (ok) ; ok = FALSE ; test_memory_handler ( ) ; for (trial = 0 ; !ok && trial < 100 ; trial++) { my_tries = trial ; Lcopy = CHOLMOD(copy_factor)(L, cm) ; ok = (Lcopy != NULL) ; } normal_memory_handler ( ) ; ok = CHOLMOD(print_factor)(Lcopy, "Lcopy", cm) ; OK (ok) ; CHOLMOD(free_factor)(&Lcopy, cm) ; cm->print = 1 ; test_memory_handler ( ) ; ok = CHOLMOD(resymbol)(A, NULL, 0, TRUE, L, cm) ; NOT (ok) ; ok = CHOLMOD(resymbol_noperm)(A, NULL, 0, TRUE, L, cm) ; NOT (ok) ; lr = CHOLMOD(postorder)(Parent, nrow, NULL, Post, cm) ; NOT (lr>=0) ; T = CHOLMOD(copy_triplet)(Tok, cm) ; NOT (ok) ; #ifndef NPARTITION lr = CHOLMOD(nested_dissection)(A, NULL, 0, Pok, CParent, Cmember, cm) ; if (nrow == 0) { OK (lr >= 0) ; } else { NOT (lr >= 0) ; } lr = CHOLMOD(nested_dissection)(Abad2, NULL, 0, Pok, CParent, Cmember, cm) ; NOT (lr >= 0) ; ok = CHOLMOD(metis)(A, NULL, 0, TRUE, Pok, cm) ; if (nrow == 0) { OK (ok) ; } else { NOT (ok) ; } lr = CHOLMOD(bisect)(A, NULL, 0, TRUE, Partition, cm) ; if (nrow == 0) { OK (lr == 0) ; } else { NOT (lr >= 0) ; } lr = CHOLMOD(bisect)(Abad2, NULL, 0, TRUE, Partition, cm) ; NOT (lr >= 0) ; #endif if (nrow > 3) { ok = CHOLMOD(rowdel)(nrow-2, NULL, L5, cm) ; NOT (ok) ; ok = CHOLMOD(rowadd)(nrow-2, R, L5, cm) ; NOT (ok) ; ok = CHOLMOD(updown)(+1, A, L, cm) ; NOT (ok) ; } C = CHOLMOD(add)(A, A, one, one, TRUE, TRUE, cm) ; NOP (C) ; C = CHOLMOD(ssmult)(A, A, 0, TRUE, TRUE, cm) ; NOP (C) ; ok = CHOLMOD(rowcolcounts)(A, NULL, 0, Parent, Post, NULL, ColCount, First, Level, cm) ; NOT (ok) ; ok = CHOLMOD(rowfac)(A, NULL, beta, 0, 0, L, cm) ; NOT (ok) ; ok = CHOLMOD(transpose_unsym)(A, 1, Pok, NULL, 0, R, cm) ; NOT (ok) ; ok = CHOLMOD(transpose_sym)(A, 1, Pok, R, cm) ; NOT (ok) ; if (nrow > 1) { ok = CHOLMOD(sort)(A, cm) ; NOT (ok) ; } ok = CHOLMOD(row_subtree)(A, AT, 0, Parent, R3, cm) ; NOT (ok) ; ATi = (AT == NULL) ? NULL : AT->i ; ok = CHOLMOD(row_lsubtree)(A, ATi, 0, 0, L, R3, cm) ; NOT (ok) ; normal_memory_handler ( ) ; /* ---------------------------------------------------------------------- */ /* free the valid objects */ /* ---------------------------------------------------------------------- */ cm->status = CHOLMOD_OK ; CHOLMOD(free_triplet)(NULL, cm) ; CHOLMOD(free_sparse)(&R3, cm) ; /* ] */ CHOLMOD(free_sparse)(&R, cm) ; /* ] */ CHOLMOD(free_sparse)(&Acopy, cm) ; /* ] */ CHOLMOD(free_factor)(&L5, cm) ; /* ] */ CHOLMOD(free_factor)(&L2, cm) ; /* ] */ Lbad->xtype = Lxtype ; CHOLMOD(free_factor)(&Lbad, cm) ; /* ] */ CHOLMOD(free_factor)(&L, cm) ; /* ] */ CHOLMOD(free_triplet)(&T, cm) ; Axbad->xtype = Axbad_type ; CHOLMOD(free_sparse)(&Axbad, cm) ; /* ] */ cm->error_handler = my_handler ; Xbad2->xtype = CHOLMOD_REAL ; CHOLMOD(free_dense)(&Xbad2, cm) ; /* ] */ Abad2->xtype = Abad2xtype ; CHOLMOD(free_sparse)(&Abad2, cm) ; /* ] */ CHOLMOD(free_sparse)(&Abad, cm) ; /* ] */ CHOLMOD(free_sparse)(&R0, cm) ; CHOLMOD(free_sparse)(&R1, cm) ; /* ] */ CHOLMOD(free_sparse)(&Aboth, cm) ; /* ] */ CHOLMOD(free_sparse)(&Sok, cm) ; CHOLMOD(free)(nrow, sizeof (Int), Pinv, cm) ; CHOLMOD(free)(nrow, sizeof (Int), Parent, cm) ; CHOLMOD(free)(nrow, sizeof (Int), Post, cm) ; CHOLMOD(free)(nrow, sizeof (Int), Cmember, cm) ; CHOLMOD(free)(nrow, sizeof (Int), CParent, cm) ; CHOLMOD(free)(nrow, sizeof (Int), Partition, cm) ; CHOLMOD(free)(nrow, sizeof (Int), ColCount, cm) ; CHOLMOD(free)(nrow, sizeof (Int), First, cm) ; CHOLMOD(free)(nrow, sizeof (Int), Level, cm) ; /* ] */ CHOLMOD(free_dense)(&Two, cm) ; /* ] */ CHOLMOD(free_sparse)(&R2, cm) ; /* ] */ CHOLMOD(free)(nrow, sizeof (Int), Pok, cm) ; /* ] */ CHOLMOD(free_sparse)(&I1, cm) ; /* ] */ CHOLMOD(free)(nrow, sizeof (Int), Pbad, cm) ; /* ] */ CHOLMOD(free)(ncol, sizeof (Int), fsetbad, cm) ; /* ] */ CHOLMOD(free)(ncol, sizeof (Int), fsetok, cm) ; /* ] */ CHOLMOD(free_dense)(&Bok, cm) ; /* ] */ CHOLMOD(free_dense)(&Xok, cm) ; /* ] */ CHOLMOD(free_sparse)(&AT, cm) ; /* ] */ CHOLMOD(free_sparse)(&A, cm) ; /* ] */ OK (cm->status == CHOLMOD_OK) ; printf ("\n------------------------null2 tests: All OK\n") ; } SuiteSparse/CHOLMOD/Tcov/camdtest.c0000644001170100242450000003044110540000032015701 0ustar davisfac/* ========================================================================== */ /* === Tcov/camdtest ======================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Test for camd v2.0 */ #include "cm.h" #ifndef NPARTITION #include "camd.h" /* ========================================================================== */ /* === camdtest ============================================================= */ /* ========================================================================== */ void camdtest (cholmod_sparse *A) { double Control [CAMD_CONTROL], Info [CAMD_INFO], alpha ; Int *P, *Cp, *Ci, *Sp, *Si, *Bp, *Bi, *Ep, *Ei, *Fp, *Fi, *Len, *Nv, *Next, *Head, *Elen, *Deg, *Wi, *W, *Flag, *BucketSet, *Constraint ; cholmod_sparse *C, *B, *S, *E, *F ; Int i, j, n, nrow, ncol, ok, cnz, bnz, p, trial, sorted ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ printf ("\nCAMD test\n") ; if (A == NULL) { return ; } if (A->stype) { B = CHOLMOD(copy) (A, 0, 0, cm) ; } else { B = CHOLMOD(aat) (A, NULL, 0, 0, cm) ; } if (A->nrow != A->ncol) { F = CHOLMOD(copy_sparse) (B, cm) ; OK (F->nrow == F->ncol) ; CHOLMOD(sort) (F, cm) ; } else { /* A is square and unsymmetric, and may have entries in A+A' that * are not in A */ F = CHOLMOD(copy_sparse) (A, cm) ; CHOLMOD(sort) (F, cm) ; } C = CHOLMOD(copy_sparse) (B, cm) ; nrow = C->nrow ; ncol = C->ncol ; n = nrow ; OK (nrow == ncol) ; Cp = C->p ; Ci = C->i ; Bp = B->p ; Bi = B->i ; /* ---------------------------------------------------------------------- */ /* S = sorted form of B, using CAMD_preprocess */ /* ---------------------------------------------------------------------- */ cnz = CHOLMOD(nnz) (C, cm) ; S = CHOLMOD(allocate_sparse) (n, n, cnz, TRUE, TRUE, 0, CHOLMOD_PATTERN, cm); Sp = S->p ; Si = S->i ; W = CHOLMOD(malloc) (n, sizeof (Int), cm) ; Flag = CHOLMOD(malloc) (n, sizeof (Int), cm) ; CAMD_preprocess (n, Bp, Bi, Sp, Si, W, Flag) ; /* ---------------------------------------------------------------------- */ /* allocate workspace for camd */ /* ---------------------------------------------------------------------- */ P = CHOLMOD(malloc) (n+1, sizeof (Int), cm) ; Constraint = CHOLMOD(malloc) (n, sizeof (Int), cm) ; for (i = 0 ; i < n ; i++) { Constraint [i] = my_rand () % (MIN (n,6)) ; } ok = CAMD_cvalid (n, Constraint) ; OK (ok) ; if (n > 0) { Constraint [0] = -1 ; ok = CAMD_cvalid (n, Constraint) ; OK (!ok) ; Constraint [0] = 0 ; } ok = CAMD_cvalid (n, Constraint) ; OK (ok) ; ok = CAMD_cvalid (n, NULL) ; OK (ok) ; Len = CHOLMOD(malloc) (n, sizeof (Int), cm) ; Nv = CHOLMOD(malloc) (n, sizeof (Int), cm) ; Next = CHOLMOD(malloc) (n, sizeof (Int), cm) ; Head = CHOLMOD(malloc) (n+1, sizeof (Int), cm) ; Elen = CHOLMOD(malloc) (n, sizeof (Int), cm) ; Deg = CHOLMOD(malloc) (n, sizeof (Int), cm) ; Wi = CHOLMOD(malloc) (n+1, sizeof (Int), cm) ; BucketSet = CHOLMOD(malloc) (n, sizeof (Int), cm) ; /* ---------------------------------------------------------------------- */ for (sorted = 0 ; sorted <= 1 ; sorted++) { if (sorted) CHOLMOD(sort) (C, cm) ; Cp = C->p ; Ci = C->i ; /* ------------------------------------------------------------------ */ /* order C with CAMD_order */ /* ------------------------------------------------------------------ */ CAMD_defaults (Control) ; CAMD_defaults (NULL) ; CAMD_control (Control) ; CAMD_control (NULL) ; CAMD_info (NULL) ; ok = CAMD_order (n, Cp, Ci, P, Control, Info, Constraint) ; printf ("camd return value: "ID"\n", ok) ; CAMD_info (Info) ; OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ; OK (CHOLMOD(print_perm) (P, n, n, "CAMD permutation", cm)) ; ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ; printf ("camd return value: "ID"\n", ok) ; CAMD_info (Info) ; OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ; OK (CHOLMOD(print_perm) (P, n, n, "CAMD permutation", cm)) ; /* no dense rows/cols */ alpha = Control [CAMD_DENSE] ; Control [CAMD_DENSE] = -1 ; CAMD_control (Control) ; ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ; printf ("camd return value: "ID"\n", ok) ; CAMD_info (Info) ; OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ; OK (CHOLMOD(print_perm) (P, n, n, "CAMD permutation (alpha=-1)", cm)) ; /* many dense rows/cols */ Control [CAMD_DENSE] = 0 ; CAMD_control (Control) ; ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ; printf ("camd return value: "ID"\n", ok) ; CAMD_info (Info) ; OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ; OK (CHOLMOD(print_perm) (P, n, n, "CAMD permutation (alpha=0)", cm)) ; Control [CAMD_DENSE] = alpha ; /* no aggressive absorption */ Control [CAMD_AGGRESSIVE] = FALSE ; CAMD_control (Control) ; ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ; printf ("camd return value: "ID"\n", ok) ; CAMD_info (Info) ; OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ; OK (CHOLMOD(print_perm) (P, n, n, "CAMD permutation (no agg) ", cm)) ; Control [CAMD_AGGRESSIVE] = TRUE ; /* ------------------------------------------------------------------ */ /* order F with CAMD_order */ /* ------------------------------------------------------------------ */ Fp = F->p ; Fi = F->i ; ok = CAMD_order (n, Fp, Fi, P, Control, Info, NULL) ; printf ("camd return value: "ID"\n", ok) ; CAMD_info (Info) ; OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ; OK (CHOLMOD(print_perm) (P, n, n, "F: CAMD permutation", cm)) ; /* ------------------------------------------------------------------ */ /* order S with CAMD_order */ /* ------------------------------------------------------------------ */ ok = CAMD_order (n, Sp, Si, P, Control, Info, NULL) ; printf ("camd return value: "ID"\n", ok) ; CAMD_info (Info) ; OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ; OK (CHOLMOD(print_perm) (P, n, n, "CAMD permutation", cm)) ; /* ------------------------------------------------------------------ */ /* order E with CAMD_2, which destroys its contents */ /* ------------------------------------------------------------------ */ E = CHOLMOD(copy) (B, 0, -1, cm) ; /* remove diagonal entries */ bnz = CHOLMOD(nnz) (E, cm) ; /* add the bare minimum extra space to E */ ok = CHOLMOD(reallocate_sparse) (bnz + n, E, cm) ; OK (ok) ; Ep = E->p ; Ei = E->i ; for (j = 0 ; j < n ; j++) { Len [j] = Ep [j+1] - Ep [j] ; } printf ("calling CAMD_2:\n") ; if (n > 0) { CAMD_2 (n, Ep, Ei, Len, E->nzmax, Ep [n], Nv, Next, P, Head, Elen, Deg, Wi, NULL, Info, NULL, BucketSet) ; CAMD_info (Info) ; OK (CHOLMOD(print_perm) (P, n, n, "CAMD2 permutation", cm)) ; } /* ------------------------------------------------------------------ */ /* error tests */ /* ------------------------------------------------------------------ */ ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ; OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ; ok = CAMD_order (-1, Cp, Ci, P, Control, Info, NULL) ; OK (ok == CAMD_INVALID); ok = CAMD_order (0, Cp, Ci, P, Control, Info, NULL) ; OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ; ok = CAMD_order (n, NULL, Ci, P, Control, Info, NULL) ; OK (ok == CAMD_INVALID); ok = CAMD_order (n, Cp, NULL, P, Control, Info, NULL) ; OK (ok == CAMD_INVALID); ok = CAMD_order (n, Cp, Ci, NULL, Control, Info, NULL) ; OK (ok == CAMD_INVALID); if (n > 0) { printf ("CAMD error tests:\n") ; p = Cp [n] ; Cp [n] = -1 ; ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ; OK (ok == CAMD_INVALID) ; if (Size_max/2 == Int_max) { Cp [n] = Int_max ; ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ; printf ("CAMD status is %d\n", ok) ; OK (ok == CAMD_OUT_OF_MEMORY) ; } Cp [n] = p ; ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ; OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ; if (Cp [n] > 0) { printf ("Mangle column zero:\n") ; i = Ci [0] ; Ci [0] = -1 ; ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ; CAMD_info (Info) ; OK (ok == CAMD_INVALID) ; Ci [0] = i ; } } ok = CAMD_valid (n, n, Sp, Si) ; OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ; ok = CAMD_valid (-1, n, Sp, Si) ; OK (ok == CAMD_INVALID) ; ok = CAMD_valid (n, -1, Sp, Si) ; OK (ok == CAMD_INVALID) ; ok = CAMD_valid (n, n, NULL, Si) ; OK (ok == CAMD_INVALID) ; ok = CAMD_valid (n, n, Sp, NULL) ; OK (ok == CAMD_INVALID) ; if (n > 0 && Sp [n] > 0) { p = Sp [n] ; Sp [n] = -1 ; ok = CAMD_valid (n, n, Sp, Si) ; OK (ok == CAMD_INVALID) ; Sp [n] = p ; p = Sp [0] ; Sp [0] = -1 ; ok = CAMD_valid (n, n, Sp, Si) ; OK (ok == CAMD_INVALID) ; Sp [0] = p ; p = Sp [1] ; Sp [1] = -1 ; ok = CAMD_valid (n, n, Sp, Si) ; OK (ok == CAMD_INVALID) ; Sp [1] = p ; i = Si [0] ; Si [0] = -1 ; ok = CAMD_valid (n, n, Sp, Si) ; OK (ok == CAMD_INVALID) ; Si [0] = i ; } ok = CAMD_valid (n, n, Sp, Si) ; OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ; CAMD_preprocess (n, Bp, Bi, Sp, Si, W, Flag) ; ok = CAMD_valid (n, n, Sp, Si) ; OK (ok == CAMD_OK) ; if (n > 0 && Bp [n] > 0) { p = Bp [n] ; Bp [n] = -1 ; ok = CAMD_valid (n, n, Bp, Bi) ; OK (ok == CAMD_INVALID) ; Bp [n] = p ; p = Bp [1] ; Bp [1] = -1 ; ok = CAMD_valid (n, n, Bp, Bi) ; OK (ok == CAMD_INVALID) ; Bp [1] = p ; i = Bi [0] ; Bi [0] = -1 ; ok = CAMD_valid (n, n, Bp, Bi) ; OK (ok == CAMD_INVALID) ; Bi [0] = i ; } CAMD_preprocess (n, Bp, Bi, Sp, Si, W, Flag) ; Info [CAMD_STATUS] = 777 ; CAMD_info (Info) ; /* ------------------------------------------------------------------ */ /* memory tests */ /* ------------------------------------------------------------------ */ if (n > 0) { camd_malloc = cm->malloc_memory ; camd_free = cm->free_memory ; ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ; OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ; test_memory_handler ( ) ; camd_malloc = cm->malloc_memory ; camd_free = cm->free_memory ; for (trial = 0 ; trial < 6 ; trial++) { my_tries = trial ; printf ("CAMD memory trial "ID"\n", trial) ; ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ; CAMD_info (Info) ; OK (ok == CAMD_OUT_OF_MEMORY || (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK))) ; } normal_memory_handler ( ) ; OK (CHOLMOD(print_perm) (P, n, n, "CAMD2 permutation", cm)) ; camd_malloc = cm->malloc_memory ; camd_free = cm->free_memory ; } CHOLMOD(free_sparse) (&E, cm) ; } /* ---------------------------------------------------------------------- */ /* free everything */ /* ---------------------------------------------------------------------- */ CHOLMOD(free) (n, sizeof (Int), Len, cm) ; CHOLMOD(free) (n, sizeof (Int), Nv, cm) ; CHOLMOD(free) (n, sizeof (Int), Next, cm) ; CHOLMOD(free) (n+1, sizeof (Int), Head, cm) ; CHOLMOD(free) (n, sizeof (Int), Elen, cm) ; CHOLMOD(free) (n, sizeof (Int), Deg, cm) ; CHOLMOD(free) (n+1, sizeof (Int), Wi, cm) ; CHOLMOD(free) (n, sizeof (Int), BucketSet, cm) ; CHOLMOD(free) (n+1, sizeof (Int), P, cm) ; CHOLMOD(free) (n, sizeof (Int), Constraint, cm) ; CHOLMOD(free) (n, sizeof (Int), W, cm) ; CHOLMOD(free) (n, sizeof (Int), Flag, cm) ; CHOLMOD(free_sparse) (&S, cm) ; CHOLMOD(free_sparse) (&B, cm) ; CHOLMOD(free_sparse) (&C, cm) ; CHOLMOD(free_sparse) (&F, cm) ; } #else void camdtest (cholmod_sparse *A) { if (A == NULL) { return ; } cm->print = 1 ; } #endif SuiteSparse/CHOLMOD/Tcov/cctest.c0000644001170100242450000002736110540000034015373 0ustar davisfac/* ========================================================================== */ /* === Tcov/cctest ========================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Test for ccolamd v1.0. Not used if NPARTITION defined at compile time. */ #include "cm.h" #ifndef NPARTITION #include "ccolamd.h" /* ========================================================================== */ /* === check_constraints ==================================================== */ /* ========================================================================== */ /* Check to see if P obeys the constraints */ Int check_constraints (Int *P, Int *Cmember, Int n) { Int c, clast, k, i ; if ((P == NULL) || !CHOLMOD(print_perm) (P, n, n, "ccolamd perm", cm)) { printf ("cctest: Perm is bad\n") ; return (FALSE) ; } clast = EMPTY ; for (k = 0 ; k < n ; k++) { i = P [k] ; c = Cmember [i] ; if (c < clast) { printf ("cctest: constraints are incorrect\n") ; return (FALSE) ; } clast = c ; } return (TRUE) ; } /* ========================================================================== */ /* === cctest =============================================================== */ /* ========================================================================== */ void cctest (cholmod_sparse *A) { double knobs [CCOLAMD_KNOBS], knobs2 [CCOLAMD_KNOBS] ; Int *P, *Cmember, *Cp, *Ci, *Front_npivcol, *Front_nrows, *Front_ncols, *Front_parent, *Front_cols, *InFront, *Si, *Sp ; cholmod_sparse *C, *A2, *B, *S ; Int nrow, ncol, alen, ok, stats [CCOLAMD_STATS], csets, i, nfr, c, p ; size_t s ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ my_srand (42) ; /* RAND reset */ printf ("\nCCOLAMD test\n") ; if (A == NULL) { return ; } if (A->stype) { A2 = CHOLMOD(copy) (A, 0, 0, cm) ; B = A2 ; } else { A2 = NULL ; B = A ; } S = CHOLMOD(copy_sparse) (A, cm) ; nrow = B->nrow ; ncol = B->ncol ; Si = S->i ; Sp = S->p ; /* ---------------------------------------------------------------------- */ /* allocate workspace and Cmember for ccolamd */ /* ---------------------------------------------------------------------- */ P = CHOLMOD(malloc) (nrow+1, sizeof (Int), cm) ; Cmember = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ; Front_npivcol = CHOLMOD(malloc) (nrow+1, sizeof (Int), cm) ; Front_nrows = CHOLMOD(malloc) (nrow+1, sizeof (Int), cm) ; Front_ncols = CHOLMOD(malloc) (nrow+1, sizeof (Int), cm) ; Front_parent = CHOLMOD(malloc) (nrow+1, sizeof (Int), cm) ; Front_cols = CHOLMOD(malloc) (nrow+1, sizeof (Int), cm) ; InFront = CHOLMOD(malloc) (ncol, sizeof (Int), cm) ; csets = MIN (6, nrow) ; for (i = 0 ; i < nrow ; i++) { Cmember [i] = nrand (csets) ; } CCOLAMD_set_defaults (knobs) ; CCOLAMD_set_defaults (knobs2) ; CCOLAMD_set_defaults (NULL) ; CCOLAMD_report (NULL) ; CSYMAMD_report (NULL) ; alen = CCOLAMD_recommended (B->nzmax, ncol, nrow) ; C = CHOLMOD(allocate_sparse) (ncol, nrow, alen, TRUE, TRUE, 0, CHOLMOD_PATTERN, cm) ; Cp = C->p ; Ci = C->i ; /* ---------------------------------------------------------------------- */ /* order with ccolamd */ /* ---------------------------------------------------------------------- */ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ; CHOLMOD(print_sparse) (C, "C for ccolamd", cm) ; ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, NULL, stats, Cmember) ; CCOLAMD_report (stats) ; OK (ok) ; ok = stats [CCOLAMD_STATUS] ; ok = (ok == CCOLAMD_OK || ok == CCOLAMD_OK_BUT_JUMBLED) ; OK (ok) ; /* permutation returned in C->p, if the ordering succeeded */ /* make sure P obeys the constraints */ OK (check_constraints (Cp, Cmember, nrow)) ; /* ---------------------------------------------------------------------- */ /* order with ccolamd2 */ /* ---------------------------------------------------------------------- */ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ; ok = CCOLAMD_2 (ncol, nrow, alen, Ci, Cp, NULL, stats, Front_npivcol, Front_nrows, Front_ncols, Front_parent, Front_cols, &nfr, InFront, Cmember) ; CCOLAMD_report (stats) ; OK (check_constraints (Cp, Cmember, nrow)) ; /* ---------------------------------------------------------------------- */ /* with a small dense-row threshold */ /* ---------------------------------------------------------------------- */ knobs2 [CCOLAMD_DENSE_ROW] = 0 ; ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ; ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs2, stats, Cmember) ; CCOLAMD_report (stats) ; knobs2 [CCOLAMD_DENSE_ROW] = 0.625 ; knobs2 [CCOLAMD_DENSE_COL] = 0 ; ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ; ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs2, stats, Cmember) ; CCOLAMD_report (stats) ; knobs2 [CCOLAMD_DENSE_ROW] = 0.625 ; knobs2 [CCOLAMD_DENSE_COL] = -1 ; ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ; ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs2, stats, Cmember) ; CCOLAMD_report (stats) ; knobs2 [CCOLAMD_DENSE_COL] = 0 ; /* ---------------------------------------------------------------------- */ /* duplicate entries */ /* ---------------------------------------------------------------------- */ if (ncol > 2 && nrow > 2) { ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ; if (Cp [1] - Cp [0] > 2) { Ci [0] = Ci [1] ; } ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs2, stats, Cmember) ; CCOLAMD_report (stats) ; OK (CHOLMOD(print_perm) (Cp, nrow, nrow, "ccolamd perm", cm)) ; } /* ---------------------------------------------------------------------- */ /* csymamd */ /* ---------------------------------------------------------------------- */ if (nrow == ncol) { Int n = nrow ; ok = CSYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory, cm->free_memory, Cmember, A->stype) ; OK (ok) ; OK (check_constraints (P, Cmember, n)) ; CSYMAMD_report (stats) ; /* ------------------------------------------------------------------ */ /* csymamd errors */ /* ------------------------------------------------------------------ */ ok = CSYMAMD_MAIN (n, Si, Sp, P, NULL, NULL, cm->calloc_memory, cm->free_memory, Cmember, A->stype) ; NOT (ok); ok = CSYMAMD_MAIN (n, NULL, Sp, P, NULL, stats, cm->calloc_memory, cm->free_memory, Cmember, A->stype) ; NOT (ok); CSYMAMD_report (stats) ; ok = CSYMAMD_MAIN (n, Si, NULL, P, NULL, stats, cm->calloc_memory, cm->free_memory, Cmember, A->stype) ; NOT (ok); CSYMAMD_report (stats) ; ok = CSYMAMD_MAIN (-1, Si, Sp, P, NULL, stats, cm->calloc_memory, cm->free_memory, Cmember, A->stype) ; NOT (ok); CSYMAMD_report (stats) ; p = Sp [n] ; Sp [n] = -1 ; ok = CSYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory, cm->free_memory, Cmember, A->stype) ; NOT (ok); CSYMAMD_report (stats) ; Sp [n] = p ; Sp [0] = -1 ; ok = CSYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory, cm->free_memory, Cmember, A->stype) ; NOT (ok); CSYMAMD_report (stats) ; Sp [0] = 0 ; if (n > 2 && Sp [n] > 3) { p = Sp [1] ; Sp [1] = -1 ; ok = CSYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory, cm->free_memory, Cmember, A->stype) ; NOT (ok); CSYMAMD_report (stats) ; Sp [1] = p ; i = Si [0] ; Si [0] = -1 ; ok = CSYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory, cm->free_memory, Cmember, A->stype) ; NOT (ok); CSYMAMD_report (stats) ; Si [0] = i ; /* ok, but jumbled */ i = Si [0] ; Si [0] = Si [1] ; Si [1] = i ; ok = CSYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory, cm->free_memory, Cmember, A->stype) ; OK (ok); CSYMAMD_report (stats) ; i = Si [0] ; Si [0] = Si [1] ; Si [1] = i ; test_memory_handler ( ) ; ok = CSYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory, cm->free_memory, Cmember, A->stype) ; NOT(ok); CSYMAMD_report (stats) ; normal_memory_handler ( ) ; } } /* ---------------------------------------------------------------------- */ /* error tests */ /* ---------------------------------------------------------------------- */ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ; ok = CCOLAMD_MAIN (ncol, nrow, 0, Ci, Cp, knobs, stats, Cmember) ; NOT (ok) ; CCOLAMD_report (stats) ; ok = CCOLAMD_MAIN (ncol, nrow, alen, NULL, Cp, knobs, stats, Cmember); NOT (ok) ; CCOLAMD_report (stats) ; ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, NULL, knobs, stats, Cmember); NOT (ok) ; CCOLAMD_report (stats) ; ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, NULL, Cmember) ; NOT (ok) ; CCOLAMD_report (stats) ; ok = CCOLAMD_MAIN (-1, nrow, alen, Ci, Cp, knobs, stats, Cmember) ; NOT (ok) ; CCOLAMD_report (stats) ; ok = CCOLAMD_MAIN (ncol, -1, alen, Ci, Cp, knobs, stats, Cmember) ; NOT (ok) ; CCOLAMD_report (stats) ; ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ; Cp [nrow] = -1 ; ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, stats, Cmember) ; NOT (ok) ; CCOLAMD_report (stats) ; Cp [0] = 1 ; ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, stats, Cmember) ; NOT (ok) ; CCOLAMD_report (stats) ; ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ; if (nrow > 0 && alen > 0 && Cp [1] > 0) { c = Cmember [0] ; Cmember [0] = -1 ; ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, stats, Cmember) ;NOT(ok); CCOLAMD_report (stats) ; Cmember [0] = c ; p = Cp [1] ; Cp [1] = -1 ; ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, stats, Cmember) ;NOT(ok); CCOLAMD_report (stats) ; Cp [1] = p ; i = Ci [0] ; Ci [0] = -1 ; ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, stats, Cmember) ;NOT(ok); CCOLAMD_report (stats) ; Ci [0] = i ; } s = CCOLAMD_recommended (-1, 0, 0) ; OK (s == 0) ; /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ CHOLMOD(free) (nrow+1, sizeof (Int), Front_npivcol, cm) ; CHOLMOD(free) (nrow+1, sizeof (Int), Front_nrows, cm) ; CHOLMOD(free) (nrow+1, sizeof (Int), Front_ncols, cm) ; CHOLMOD(free) (nrow+1, sizeof (Int), Front_parent, cm) ; CHOLMOD(free) (nrow+1, sizeof (Int), Front_cols, cm) ; CHOLMOD(free) (nrow+1, sizeof (Int), P, cm) ; CHOLMOD(free) (nrow, sizeof (Int), Cmember, cm) ; CHOLMOD(free) (ncol, sizeof (Int), InFront, cm) ; CHOLMOD(free_sparse) (&S, cm) ; CHOLMOD(free_sparse) (&A2, cm) ; CHOLMOD(free_sparse) (&C, cm) ; cm->print = 1 ; } #else void cctest (cholmod_sparse *A) { if (A == NULL) { return ; } cm->print = 1 ; } #endif SuiteSparse/CHOLMOD/Tcov/lpdemo.c0000644001170100242450000006310310540000054015362 0ustar davisfac/* ========================================================================== */ /* === Tcov/lpdemo ========================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* A rectangular matrix is being tested (# nrows < # cols). This is a * linear programming problem. Process the system using the same kind of * operations that occur in an LP solver (the LP Dual Active Set Algorithm). * This routine does not actually solve the LP. It simply mimics the kind * of matrix operations that occur in LPDASA. * * The active set f is held in fset [0..fsize-1]. It is a subset of the columns * of A. Columns not in the fset are in the list fnot [0..ncol-fsize-1]. * * Rows can be added and deleted from A as well. A "dead" row is one that has * been (temporarily) set to zero in A. If row i is dead, rflag [i] is 0, * and 1 otherwise. * * The list r of "live" rows is kept in rset [0..rsize-1]. The list of "dead" * rows is kept in rnot [0..nrow-rsize-1]. * * The system to solve as r and/or f change is (beta*I + A(r,f)*A(r,f)') x = b. * If a row i is deleted from A, it is set to zero. Row i of L and D are set * to the ith row of the identity matrix. */ #include "cm.h" #define MAXCOLS 8 /* ========================================================================== */ /* === Lcheck =============================================================== */ /* ========================================================================== */ /* Testing only: make sure there are no dead rows in L (excluding diagonal) */ static void Lcheck (cholmod_factor *L, Int *rflag) { Int *Lp, *Li, *Lnz ; Int i, n, j, p, pend ; double *Lx ; if (L == NULL) { return ; } Lp = L->p ; Li = L->i ; Lx = L->x ; Lnz = L->nz ; n = L->n ; for (j = 0 ; j < n ; j++) { p = Lp [j] ; pend = p + Lnz [j] ; for (p++ ; p < pend ; p++) { i = Li [p] ; OK (IMPLIES (!rflag [i], Lx [p] == 0)) ; } } } /* ========================================================================== */ /* === lp_prune ============================================================= */ /* ========================================================================== */ /* C = A (r,f), except that C and A have the same row dimension. Row i of C * and A(:,f) are equal if row i is in the rset. Row i of C is zero * otherwise. C has as many columns as the size of f. */ cholmod_sparse *lp_prune ( cholmod_sparse *A, Int *rflag, Int *fset, Int fsize ) { cholmod_sparse *C ; double *Ax, *Cx ; Int *Ai, *Ap, *Ci, *Cp ; Int i, kk, j, p, nz, nf, ncol ; if (A == NULL) { ERROR (CHOLMOD_INVALID, "nothing to prune") ; return (NULL) ; } Ap = A->p ; Ai = A->i ; Ax = A->x ; ncol = A->ncol ; nf = (fset == NULL) ? ncol : fsize ; OK (fsize >= 0) ; C = CHOLMOD(allocate_sparse) (A->nrow, nf, A->nzmax, A->sorted, TRUE, 0, CHOLMOD_REAL, cm) ; if (C == NULL) { ERROR (CHOLMOD_INVALID, "cannot create pruned C") ; return (NULL) ; } Cp = C->p ; Ci = C->i ; Cx = C->x ; nz = 0 ; for (kk = 0 ; kk < nf ; kk++) { j = (fset == NULL) ? (kk) : (fset [kk]) ; Cp [kk] = nz ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { i = Ai [p] ; if (rflag [i]) { Ci [nz] = i ; Cx [nz] = Ax [p] ; nz++ ; } } } Cp [nf] = nz ; return (C) ; } /* ========================================================================== */ /* === lp_resid ============================================================= */ /* ========================================================================== */ /* Compute the 2-norm of the residual. * norm ((beta*I + C*C')y(r) - b(r)), where C = A (r,f). */ double lp_resid ( cholmod_sparse *A, Int *rflag, Int *fset, Int fsize, double beta [2], cholmod_dense *Y, cholmod_dense *B ) { cholmod_dense *R ; double *Rx, *Yx ; double rnorm, bnorm, ynorm, norm ; cholmod_sparse *C ; cholmod_dense *W ; Int i, nrow ; if (A == NULL) { ERROR (CHOLMOD_INVALID, "cannot compute LP resid") ; return (1) ; } nrow = A->nrow ; R = CHOLMOD(zeros) (nrow, 1, CHOLMOD_REAL, cm) ; /* C = A(r,f). In LPDASA, we do this in place, without making a copy. */ C = lp_prune (A, rflag, fset, fsize) ; /* W = C'*Y */ OK (fsize >= 0) ; W = CHOLMOD(zeros) (fsize, 1, CHOLMOD_REAL, cm) ; CHOLMOD(sdmult) (C, TRUE, one, zero, Y, W, cm) ; /* R = B */ CHOLMOD(copy_dense2) (B, R, cm) ; /* R = C*W - R */ CHOLMOD(sdmult) (C, FALSE, one, minusone, W, R, cm) ; /* R = R + beta*Y, (beta = 1 for dropped rows) */ if (R != NULL && Y != NULL) { Rx = R->x ; Yx = Y->x ; for (i = 0 ; i < nrow ; i++) { if (rflag [i]) { Rx [i] += beta [0] * Yx [i] ; } else { Rx [i] += Yx [i] ; } } } /* rnorm = norm (R) */ rnorm = CHOLMOD(norm_dense) (R, 2, cm) ; bnorm = CHOLMOD(norm_dense) (B, 2, cm) ; ynorm = CHOLMOD(norm_dense) (Y, 2, cm) ; norm = MAX (bnorm, ynorm) ; if (norm > 0) { rnorm /= norm ; } CHOLMOD(print_dense) (R, "R, resid", cm) ; CHOLMOD(free_sparse) (&C, cm) ; CHOLMOD(free_dense) (&W, cm) ; CHOLMOD(free_dense) (&R, cm) ; return (rnorm) ; } /* ========================================================================== */ /* === get_row ============================================================== */ /* ========================================================================== */ /* S = column i of beta*I + A(r,f)*A(r,f)' */ cholmod_sparse *get_row ( cholmod_sparse *A, Int i, Int *rflag, Int *fset, Int fsize, double beta [2] ) { cholmod_sparse *Ri, *R, *C, *S ; double *Sx ; Int *Sp, *Si ; Int p, ii, found ; if (rflag [i] == 0) { S = CHOLMOD(speye) (A->nrow, A->nrow, CHOLMOD_REAL, cm) ; CHOLMOD(print_sparse) (S, "S identity", cm) ; return (S) ; } OK (fsize >= 0) ; /* Getting row i of A is expensive. In LPDASA, we maintain * a copy of A(r,f)', and extact row i as column i of that * matrix. We compute S = A(r,f)*A(i,f)' and S(i) += beta * in a single pass. This is a simpler but slower method. */ /* R = A (i,f)' */ Ri = CHOLMOD(submatrix) (A, &i, 1, fset, fsize, TRUE, FALSE, cm) ; R = CHOLMOD(transpose) (Ri, 1, cm) ; CHOLMOD(free_sparse) (&Ri, cm) ; /* C = A (r,f) */ C = lp_prune (A, rflag, fset, fsize) ; /* S = C*R */ S = CHOLMOD(ssmult) (C, R, 0, TRUE, TRUE, cm) ; CHOLMOD(free_sparse) (&C, cm) ; CHOLMOD(free_sparse) (&R, cm) ; if (S == NULL) { return (NULL) ; } /* S (i) += beta */ found = FALSE ; Sp = S->p ; Si = S->i ; Sx = S->x ; for (p = Sp [0] ; p < Sp [1] ; p++) { ii = Si [p] ; if (ii == i) { found = TRUE ; Sx [p] += beta [0] ; break ; } } if (!found) { /* oops, row index i is not present in S. Add it. */ CHOLMOD(reallocate_sparse) (S->nzmax+1, S, cm) ; OK (Sp [1] < (Int) (S->nzmax)) ; Si = S->i ; Sx = S->x ; Si [Sp [1]] = i ; Sx [Sp [1]] = beta [0] ; Sp [1]++ ; S->sorted = FALSE ; } CHOLMOD(print_sparse) (S, "S", cm) ; return (S) ; } /* ========================================================================== */ /* === lpdemo =============================================================== */ /* ========================================================================== */ double lpdemo (cholmod_triplet *T) { double r, maxerr = 0, anorm, bnorm, norm, xnorm, ynorm ; double *b = NULL, *Yx = NULL, *Xx = NULL, *Sx ; cholmod_sparse *A, *AT, *Apermuted, *C, *S, *Row ; cholmod_dense *X, *B, *Y, *DeltaB, *R ; cholmod_factor *L ; Int *init, *rset, *rnot, *fset, *fnot, *rflag, *P, *Pinv, *Lperm, *fflag, *Sp, *Si, *StaticParent ; Int i, j, k, nrow, ncol, fsize, cols [MAXCOLS+1], trial, rank, kk, rsize, p, op, ok ; double beta [2], bk [2], yk [2] ; /* ---------------------------------------------------------------------- */ /* convert T into a sparse matrix A */ /* ---------------------------------------------------------------------- */ if (T == NULL || T->ncol == 0) { /* nothing to do */ return (0) ; } if (T->xtype != CHOLMOD_REAL) { return (0) ; } A = CHOLMOD(triplet_to_sparse) (T, 0, cm) ; if (A == NULL) { ERROR (CHOLMOD_INVALID, "cannot continue LP demo") ; return (1) ; } nrow = A->nrow ; ncol = A->ncol ; anorm = CHOLMOD(norm_sparse) (A, 1, cm) ; /* switch for afiro, but not galenet */ cm->supernodal_switch = 5 ; /* ---------------------------------------------------------------------- */ /* select a random initial row and column basis */ /* ---------------------------------------------------------------------- */ /* select an initial fset of size nrow */ init = prand (ncol) ; /* RAND */ fset = CHOLMOD(malloc) (ncol, sizeof (Int), cm) ; fnot = CHOLMOD(malloc) (ncol, sizeof (Int), cm) ; fflag = CHOLMOD(malloc) (ncol, sizeof (Int), cm) ; fsize = MIN (nrow, ncol) ; if (init != NULL && fset != NULL && fflag != NULL) { for (k = 0 ; k < fsize ; k++) { j = init [k] ; fset [k] = j ; fflag [j] = 1 ; } for ( ; k < ncol ; k++) { j = init [k] ; fnot [k-fsize] = j ; fflag [j] = 0 ; } } CHOLMOD(free) (ncol, sizeof (Int), init, cm) ; /* all rows are live */ rsize = nrow ; rflag = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ; rset = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ; rnot = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ; if (rset != NULL && rflag != NULL) { for (i = 0 ; i < nrow ; i++) { rflag [i] = 1 ; rset [i] = i ; } } /* ---------------------------------------------------------------------- */ /* factorize the first matrix, beta*I + A(p,f)*A(p,f)' */ /* ---------------------------------------------------------------------- */ beta [0] = 1e-6 ; beta [1] = 0 ; /* Need to prune entries due to relaxed amalgamation, or else * cholmod_row_subtree will not be able to find all the entries in row * k of L. */ cm->final_resymbol = TRUE ; cm->final_asis = FALSE ; cm->final_super = FALSE ; cm->final_ll = FALSE ; cm->final_pack = FALSE ; cm->final_monotonic = FALSE ; L = CHOLMOD(analyze_p) (A, NULL, fset, fsize, cm) ; CHOLMOD(factorize_p) (A, beta, fset, fsize, L, cm) ; /* get a copy of the fill-reducing permutation P and compute its inverse */ Lperm = (L != NULL) ? (L->Perm) : NULL ; P = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ; Pinv = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ; if (P != NULL && Pinv != NULL && Lperm != NULL) { for (k = 0 ; k < nrow ; k++) { P [k] = Lperm [k] ; Pinv [P [k]] = k ; } } else { P = CHOLMOD(free) (nrow, sizeof (Int), P, cm) ; Pinv = CHOLMOD(free) (nrow, sizeof (Int), Pinv, cm) ; } if (cm->print > 1) { k = cm->print ; cm->print = 5 ; CHOLMOD(print_common) ("cm for lpdemo", cm) ; cm->print = k ; } /* ---------------------------------------------------------------------- */ /* A=P*A: permute the rows of A according to P */ /* ---------------------------------------------------------------------- */ /* This is done just once, since the system will be solved and modified * many times. It's faster, and easier, to work in the permuted ordering * rather than the original ordering. */ /* A will become unsorted later on; don't bother to sort it here */ Apermuted = CHOLMOD(submatrix) (A, P, nrow, NULL, -1, TRUE, TRUE, cm) ; CHOLMOD(free_sparse) (&A, cm) ; A = Apermuted ; /* ---------------------------------------------------------------------- */ /* find the etree of A*A' */ /* ---------------------------------------------------------------------- */ /* Since the fset is a subset of 0:ncol-1, and rset is a subset of 0:nrow-1, * the nonzero pattern of the Cholesky factorization of A(r,f)*A(r,f)' is a * subset of the Cholesky factorization of A*A'. After many updates/ * downdates/rowadds/rowdels, any given row i of L may have entries that * are not in the factorization of A (r,f)*A(r,f)'. To drop a row using * cholmod_rowdel, we either need to know the pattern of the ith row of L, * we can pass NULL and have cholmod_rowdel look at each column 0 to i-1. * The StaticParent array is the etree of A*A', and it suffices to compute * the pattern of the ith row of L based on that etree, and A and A' * (ignoring the fset and rset). This gives us an upper bound on the * nonzero pattern of the ith row of the current L (the factorization * of A(r,f)*A(r,f)'. */ /* AT = nonzero pattern of A', used for row-subtree computations */ AT = CHOLMOD(transpose) (A, 0, cm) ; /* Row = cholmod_row_subtree workspace (unsorted, packed, unsym, pattern) */ Row = CHOLMOD(allocate_sparse) (nrow, 1, nrow, FALSE, TRUE, 0, CHOLMOD_PATTERN, cm) ; /* Compute the "static" etree; the etree of A*A' */ StaticParent = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ; CHOLMOD(etree) (AT, StaticParent, cm) ; /* ---------------------------------------------------------------------- */ /* compute initial right-hand-side */ /* ---------------------------------------------------------------------- */ /* If row i of the original A and B is row k of the permuted P*A and P*B, * then P [k] = i and Pinv [i] = k. Row indices of A now refer to the * permuted form of A, not the original A. Likewise, row k of B will * refer to the permuted row k = Pinv [i], not the original row i. In a * real program, this would affect how B is computed. This program just * creates a random B anyway, so the order of B does not matter. It does * use Pinv [i], just to show you how you would do it. */ B = CHOLMOD(zeros) (nrow, 1, CHOLMOD_REAL, cm) ; if (B != NULL && Pinv != NULL) { b = B->x ; for (i = 0 ; i < nrow ; i++) { /* row i of the original B is row k of the permuted B */ k = Pinv [i] ; b [k] = xrand (1.) ; /* RAND */ } } /* ---------------------------------------------------------------------- */ /* solve the system */ /* ---------------------------------------------------------------------- */ /* Solve the system (beta*I + A(:,f)*A(:,f)')y=b without using L->Perm, * since A and B have already been permuted according to L->Perm. */ DeltaB = CHOLMOD(zeros) (nrow, 1, CHOLMOD_REAL, cm) ; /* solve Lx=b */ X = CHOLMOD(solve) (CHOLMOD_L, L, B, cm) ; /* solve DL'y=x */ Y = CHOLMOD(solve) (CHOLMOD_DLt, L, X, cm) ; r = lp_resid (A, rflag, fset, fsize, beta, Y, B) ; MAXERR (maxerr, r, 1) ; bk [0] = 0 ; bk [1] = 0 ; yk [0] = 0 ; yk [1] = 0 ; bnorm = CHOLMOD(norm_dense) (B, 1, cm) ; /* ---------------------------------------------------------------------- */ /* modify the system */ /* ---------------------------------------------------------------------- */ ok = (fset != NULL && fnot != NULL && fflag != NULL && rset != NULL && rnot != NULL && rflag != NULL && B != NULL && Y != NULL && X != NULL && Row != NULL && A != NULL && AT != NULL && StaticParent != NULL && DeltaB != NULL && L != NULL && L->xtype != CHOLMOD_PATTERN && !(L->is_ll) && !(L->is_super)) ; for (trial = 1 ; ok && trial < MAX (64, 2*ncol) ; trial++) { /* select an operation at random */ op = nrand (6) ; /* RAND */ Xx = X->x ; Yx = Y->x ; switch (op) { /* -------------------------------------------------------------- */ case 0: /* update */ /* -------------------------------------------------------------- */ /* pick some columns at random, but not all columns */ rank = 1 + nrand (MAXCOLS+4) ; /* RAND */ rank = MIN (rank, MAXCOLS) ; rank = MIN (rank, ncol-fsize-1) ; if (rank <= 0) { continue ; } /* remove the columns from fnot and add them to fset */ for (k = 0 ; k < rank ; k++) { kk = nrand (ncol-fsize) ; /* RAND */ j = fnot [kk] ; fnot [kk] = fnot [ncol-fsize-1] ; fset [fsize++] = j ; OK (fsize < ncol) ; cols [k] = j ; fflag [j] = 1 ; } /* update L, and the solution to Lx=b+deltaB */ C = lp_prune (A, rflag, cols, rank) ; ok = CHOLMOD(updown_solve) (TRUE, C, L, X, DeltaB, cm) ; CHOLMOD(free_sparse) (&C, cm) ; break ; /* -------------------------------------------------------------- */ case 1: /* downdate */ /* -------------------------------------------------------------- */ /* pick some columns at random, but not all columns */ rank = 1 + nrand (MAXCOLS+4) ; /* RAND */ rank = MIN (rank, MAXCOLS) ; rank = MIN (rank, fsize-1) ; if (rank <= 0) { continue ; } /* remove the columns from fset and add them to fnot */ for (k = 0 ; k < rank ; k++) { kk = nrand (fsize) ; /* RAND */ j = fset [kk] ; fset [kk] = fset [fsize-1] ; fnot [ncol-fsize] = j ; fsize-- ; OK (fsize > 0) ; cols [k] = j ; fflag [j] = 0 ; } /* downdate L, and the solution to Lx=b+deltaB */ C = lp_prune (A, rflag, cols, rank) ; ok = CHOLMOD(updown_solve) (FALSE, C, L, X, DeltaB, cm) ; CHOLMOD(free_sparse) (&C, cm) ; break ; /* -------------------------------------------------------------- */ case 2: /* resymbol (no change to numerical values) */ /* -------------------------------------------------------------- */ /* let resymbol handle the fset */ C = lp_prune (A, rflag, NULL, 0) ; ok = CHOLMOD(resymbol_noperm) (C, fset, fsize, TRUE, L, cm) ; CHOLMOD(free_sparse) (&C, cm) ; break; /* -------------------------------------------------------------- */ case 3: /* add row */ /* -------------------------------------------------------------- */ /* remove a row from rnot and add to rset */ if (nrow == rsize) { continue ; } kk = nrand (nrow-rsize) ; /* RAND */ i = rnot [kk] ; OK (rflag [i] == 0) ; rnot [kk] = rnot [nrow-rsize-1] ; rset [rsize++] = i ; rflag [i] = 1 ; /* S = column i of beta*I + A(r,f)*A(r,f)' */ S = get_row (A, i, rflag, fset, fsize, beta) ; ok = (S != NULL) ; if (ok) { /* pick a random right-hand-side for this new row */ b [i] = 1 ; /* xrand (1) */ /* was RAND */ bk [0] = b [i] ; bk [1] = 0 ; ok = CHOLMOD(rowadd_solve) (i, S, bk, L, X, DeltaB, cm) ; } CHOLMOD(free_sparse) (&S, cm) ; break ; /* -------------------------------------------------------------- */ case 4: /* delete row */ /* -------------------------------------------------------------- */ /* remove a row from rset and add to rnot */ if (rsize == 0) { continue ; } kk = nrand (rsize) ; /* RAND */ i = rset [kk] ; OK (rflag [i] == 1) ; rset [kk] = rset [rsize-1] ; rnot [nrow-rsize] = i ; rsize-- ; /* S = column i of beta*I + A(r,f)*A(r,f)' */ S = get_row (A, i, rflag, fset, fsize, beta) ; ok = (S != NULL) ; if (ok) { /* B = B - S * y(i) */ Sp = S->p ; Si = S->i ; Sx = S->x ; for (p = 0 ; p < Sp [1] ; p++) { b [Si [p]] -= Sx [p] * Yx [i] ; } /* B(i) = y(i) */ b [i] = Yx [i] ; yk [0] = Yx [i] ; yk [1] = 0 ; /* pick a method arbitrarily */ if (trial % 2) { /* get upper bound nonzero pattern of L(i,0:i-1) */ CHOLMOD(row_subtree) (A, AT, i, StaticParent, Row, cm) ; ok = CHOLMOD(rowdel_solve) (i, Row, yk, L, X, DeltaB, cm) ; } else { /* Look in all cols 0 to i-1 for entries in L(i,0:i-1). * This is more costly, but requires no knowledge of * an upper bound on the pattern of L. */ ok = CHOLMOD(rowdel_solve) (i, NULL, yk, L, X, DeltaB, cm) ; } /* for testing only, to ensure cholmod_row_subtree worked */ if (ok) { rflag [i] = 0 ; Lcheck (L, rflag) ; } } if (ok) { /* let resymbol handle the fset */ C = lp_prune (A, rflag, NULL, 0) ; ok = CHOLMOD(resymbol_noperm) (C, fset, fsize, TRUE, L, cm) ; CHOLMOD(free_sparse) (&C, cm) ; } CHOLMOD(free_sparse) (&S, cm) ; break ; /* -------------------------------------------------------------- */ case 5: /* convert, just for testing */ /* -------------------------------------------------------------- */ /* convert to LDL', optionally packed */ if (trial % 2) { ok = CHOLMOD(change_factor) (CHOLMOD_REAL, FALSE, FALSE, TRUE, TRUE, L, cm) ; } else { ok = CHOLMOD(change_factor) (CHOLMOD_REAL, FALSE, FALSE, FALSE, TRUE, L, cm) ; } break ; } if (ok) { /* scale B and X if their norm is getting large */ ynorm = CHOLMOD(norm_dense) (Y, 1, cm) ; bnorm = CHOLMOD(norm_dense) (B, 1, cm) ; xnorm = CHOLMOD(norm_dense) (X, 1, cm) ; norm = MAX (bnorm, xnorm) ; norm = MAX (norm, ynorm) ; if (norm > 1e10) { for (i = 0 ; i < nrow ; i++) { Xx [i] /= norm ; b [i] /= norm ; } } CHOLMOD(free_dense) (&Y, cm) ; Y = CHOLMOD(solve) (CHOLMOD_DLt, L, X, cm) ; r = lp_resid (A, rflag, fset, fsize, beta, Y, B) ; OK (!ISNAN (r)) ; MAXERR (maxerr, r, 1) ; if (r > 1e-6 && cm->print > 1) { printf ("lp err %.1g operation: "ID" ok "ID"\n", r, op, ok) ; } ok = (Y != NULL) ; } } CHOLMOD(free_dense) (&Y, cm) ; OK (CHOLMOD(print_common) ("cm in lpdemo", cm)) ; /* ---------------------------------------------------------------------- */ /* convert to LDL packed, LDL unpacked or LL packed and solve again */ /* ---------------------------------------------------------------------- */ /* solve the new system and check the residual */ CHOLMOD(print_factor) (L, "L final, for convert", cm) ; if (ok) { switch (nrand (3)) /* RAND */ { /* pick one at random */ case 0: { ok = CHOLMOD(change_factor) (CHOLMOD_REAL, FALSE, FALSE, TRUE, TRUE, L, cm) ; Y = CHOLMOD(solve) (CHOLMOD_DLt, L, X, cm) ; break ; } case 1: { ok = CHOLMOD(change_factor) (CHOLMOD_REAL, FALSE, FALSE, FALSE, TRUE, L, cm) ; Y = CHOLMOD(solve) (CHOLMOD_DLt, L, X, cm) ; break ; } case 2: { ok = CHOLMOD(change_factor) (CHOLMOD_REAL, TRUE, FALSE, TRUE, TRUE, L, cm) ; Y = CHOLMOD(solve) (CHOLMOD_LDLt, L, B, cm) ; break ; } } r = lp_resid (A, rflag, fset, fsize, beta, Y, B) ; OK (!ISNAN (r)) ; MAXERR (maxerr, r, 1) ; CHOLMOD(print_factor) (L, "L after convert", cm) ; } /* ---------------------------------------------------------------------- */ /* rank-1 update, but only partial Lx=b update */ /* ---------------------------------------------------------------------- */ if (ok && fsize < ncol && nrow > 3) { Int colmark [1] ; j = fnot [0] ; fnot [0] = fnot [ncol-fsize-1] ; fset [fsize++] = j ; OK (fsize <= ncol) ; cols [0] = j ; fflag [j] = 1 ; for (colmark [0] = 0 ; colmark [0] <= nrow ; colmark [0]++) { cholmod_factor *L2 ; cholmod_dense *X2 ; double *X2x ; L2 = CHOLMOD(copy_factor) (L, cm) ; X2 = CHOLMOD(copy_dense) (X, cm) ; X2x = (X2 == NULL) ? NULL : X2->x ; /* fprintf (stderr, "check colmark "ID"\n", colmark [0]) ; */ printf ("check cholmark "ID"\n", colmark [0]) ; /* colmark [0] = 3 ; */ /* update L, and the solution to Lx=b+deltaB, * but only update solution in rows 0 to colmark[0] */ C = lp_prune (A, rflag, cols, 1) ; ok = CHOLMOD(updown_mark) (TRUE, C, colmark, L2, X2, DeltaB, cm) ; CHOLMOD(free_sparse) (&C, cm) ; /* compare with Lr=b+deltaB */ R = CHOLMOD(solve) (CHOLMOD_L, L2, B, cm) ; r = -1 ; if (ok && R != NULL) { double *Rx ; Rx = R->x ; r = 0 ; for (i = 0 ; i < colmark [0] ; i++) { r = MAX (r, fabs (X2x [i] - Rx [i])) ; } MAXERR (maxerr, r, 1) ; } printf ("check cholmark resid %6.2e\n", r) ; CHOLMOD(free_dense) (&R, cm) ; CHOLMOD(free_dense) (&X2, cm) ; CHOLMOD(free_factor) (&L2, cm) ; } } /* ---------------------------------------------------------------------- */ /* free everything */ /* ---------------------------------------------------------------------- */ /* restore defaults */ cm->final_resymbol = FALSE ; cm->final_asis = TRUE ; cm->supernodal_switch = 40 ; CHOLMOD(free) (nrow, sizeof (Int), StaticParent, cm) ; CHOLMOD(free) (nrow, sizeof (Int), Pinv, cm) ; CHOLMOD(free) (nrow, sizeof (Int), P, cm) ; CHOLMOD(free) (nrow, sizeof (Int), rflag, cm) ; CHOLMOD(free) (nrow, sizeof (Int), rset, cm) ; CHOLMOD(free) (nrow, sizeof (Int), rnot, cm) ; CHOLMOD(free) (ncol, sizeof (Int), fset, cm) ; CHOLMOD(free) (ncol, sizeof (Int), fnot, cm) ; CHOLMOD(free) (ncol, sizeof (Int), fflag, cm) ; CHOLMOD(free_factor) (&L, cm) ; CHOLMOD(free_sparse) (&Row, cm) ; CHOLMOD(free_sparse) (&AT, cm) ; CHOLMOD(free_sparse) (&A, cm) ; CHOLMOD(free_dense) (&B, cm) ; CHOLMOD(free_dense) (&X, cm) ; CHOLMOD(free_dense) (&Y, cm) ; CHOLMOD(free_dense) (&DeltaB, cm) ; progress (0, '.') ; return (maxerr) ; } SuiteSparse/CHOLMOD/Tcov/make_go.output0000644001170100242450000004644310474145232016650 0ustar davisfac./z_demo ../Demo/Matrix/bcsstk01.tri > tmp/demo_k1.out ./z_demo ../Demo/Matrix/bcsstk02.tri > tmp/demo_k2.out ./z_demo < ../Demo/Matrix/lp_afiro.tri > tmp/demo_afiro.out ./z_demo < ../Demo/Matrix/can___24.mtx > tmp/demo_can24.out ./z_demo < ../Demo/Matrix/c.tri > tmp/demo_c.out ./z_demo < ../Demo/Matrix/d.tri > tmp/demo_d.out ./z_demo < ../Demo/Matrix/up.tri > tmp/demo_up.out ./z_demo < ../Demo/Matrix/c.mtx > tmp/demo_c_mtx.out ./z_demo < ../Demo/Matrix/0.tri > tmp/demo_0.out ./z_demo < Matrix/3_2 > tmp/demo_3_2.out ./z_demo < Matrix/c5lo > tmp/demo_c5lo.out ./z_demo < Matrix/c10 > tmp/demo_c10.out ./z_demo no_such_file > tmp/demo_no_such_file.out ./z_demo ../Demo/Matrix/mangle1.mtx > tmp/demo_mangle1.out ./z_demo ../Demo/Matrix/mangle2.mtx > tmp/demo_mangle2.out ./z_demo ../Demo/Matrix/mangle3.mtx > tmp/demo_mangle3.out ./z_demo ../Demo/Matrix/mangle4.mtx > tmp/demo_mangle4.out ./z_demo ../Demo/Matrix/pts5ldd03.mtx > tmp/demo_pts5ldd03.out ./l_demo ../Demo/Matrix/bcsstk01.tri > tmp/ldemo_k1.out ./l_demo ../Demo/Matrix/bcsstk02.tri > tmp/ldemo_k2.out ./l_demo < ../Demo/Matrix/lp_afiro.tri > tmp/ldemo_afiro.out ./l_demo < ../Demo/Matrix/can___24.mtx > tmp/ldemo_can24.out ./l_demo < ../Demo/Matrix/c.tri > tmp/ldemo_c.out ./l_demo < ../Demo/Matrix/d.tri > tmp/ldemo_d.out ./l_demo < ../Demo/Matrix/up.tri > tmp/ldemo_up.out ./l_demo < ../Demo/Matrix/c.mtx > tmp/ldemo_c_mtx.out ./l_demo < ../Demo/Matrix/0.tri > tmp/ldemo_0.out ./l_demo < Matrix/3_2 > tmp/ldemo_3_2.out ./l_demo < Matrix/c5lo > tmp/ldemo_c5lo.out ./l_demo < Matrix/c10 > tmp/ldemo_c10.out ./l_demo no_such_file > tmp/ldemo_no_such_file.out ./l_demo ../Demo/Matrix/mangle1.mtx > tmp/ldemo_mangle1.out ./l_demo ../Demo/Matrix/mangle2.mtx > tmp/ldemo_mangle2.out ./l_demo ../Demo/Matrix/mangle3.mtx > tmp/ldemo_mangle3.out ./l_demo ../Demo/Matrix/mangle4.mtx > tmp/ldemo_mangle4.out ./l_demo ../Demo/Matrix/pts5ldd03.mtx > tmp/ldemo_pts5ldd03.out grep resid tmp/demo* tmp/demo_0.out:residual 0.0e+00 (|Ax-b|/(|A||x|+|b|)) tmp/demo_3_2.out:residual 9.4e-17 (|Ax-b|/(|A||x|+|b|)) tmp/demo_afiro.out:residual 6.5e-17 (|Ax-b|/(|A||x|+|b|)) tmp/demo_c10.out:residual 5.6e-17 (|Ax-b|/(|A||x|+|b|)) tmp/demo_c5lo.out:residual 6.3e-17 (|Ax-b|/(|A||x|+|b|)) tmp/demo_can24.out:residual 8.2e-17 (|Ax-b|/(|A||x|+|b|)) tmp/demo_can24.out:residual 1.0e-16 (|Ax-b|/(|A||x|+|b|)) after iterative refinement tmp/demo_c_mtx.out:residual 2.0e-17 (|Ax-b|/(|A||x|+|b|)) tmp/demo_c.out:residual 2.0e-17 (|Ax-b|/(|A||x|+|b|)) tmp/demo_d.out:residual 8.5e-18 (|Ax-b|/(|A||x|+|b|)) tmp/demo_k1.out:residual 1.5e-19 (|Ax-b|/(|A||x|+|b|)) tmp/demo_k1.out:residual 1.2e-19 (|Ax-b|/(|A||x|+|b|)) after iterative refinement tmp/demo_k2.out:residual 7.4e-17 (|Ax-b|/(|A||x|+|b|)) tmp/demo_k2.out:residual 4.0e-17 (|Ax-b|/(|A||x|+|b|)) after iterative refinement tmp/demo_pts5ldd03.out:residual 6.1e-14 (|Ax-b|/(|A||x|+|b|)) tmp/demo_up.out:residual 1.1e-17 (|Ax-b|/(|A||x|+|b|)) ./cmread no_such_file > tmp/no_such_file.out ./cmread ../Demo/Matrix/mangle5.tri > tmp/mangle5.out ./cmread ../Demo/Matrix/mangle6.tri > tmp/mangle6.out ./cmread ../Demo/Matrix/mangle7.tri > tmp/mangle6.out ./cmread ../Demo/Matrix/mangle8.tri > tmp/mangle8.out ./cmread ../Demo/Matrix/empty.tri > tmp/empty.out ./cmread ../Demo/Matrix/one.tri > tmp/one.out ./cmread Matrix/plskz362.mtx > tmp/plskz363.out ./cmread Matrix/2diag.tri > tmp/2diag.out ./cmread Matrix/r5lo > tmp/r5lo.out ./cmread Matrix/r5lo2 > tmp/r5lo2.out diff tmp/r5lo.out tmp/r5lo2.out ./cmread Matrix/cs.mtx > tmp/cs.out ./cmread Matrix/2lo.tri > tmp/2lo.out ./cmread Matrix/2.tri > tmp/2.out ./cmread Matrix/2up.tri > tmp/2up.out ./cmread Matrix/huge.tri > tmp/huge.out ./clread no_such_file > tmp/l_no_such_file.out ./clread ../Demo/Matrix/mangle5.tri > tmp/l_mangle5.out ./clread ../Demo/Matrix/mangle6.tri > tmp/l_mangle6.out ./clread ../Demo/Matrix/mangle7.tri > tmp/l_mangle6.out ./clread ../Demo/Matrix/mangle8.tri > tmp/l_mangle8.out ./clread ../Demo/Matrix/empty.tri > tmp/l_empty.out ./clread ../Demo/Matrix/one.tri > tmp/l_one.out ./clread Matrix/plskz362.mtx > tmp/l_plskz363.out ./clread Matrix/2diag.tri > tmp/l_2diag.out ./clread Matrix/r5lo > tmp/l_r5lo.out ./clread Matrix/r5lo2 > tmp/l_r5lo2.out diff tmp/r5lo.out tmp/r5lo2.out ./clread Matrix/cs.mtx > tmp/l_cs.out ./clread Matrix/2lo.tri > tmp/l_l_2lo.out ./clread Matrix/2.tri > tmp/l_2.out ./clread Matrix/2up.tri > tmp/l_2up.out ./clread Matrix/huge.tri > tmp/l_huge.out ./cm < Matrix/galenet > tmp/galenet.out Test matrix: 8-by-14 with 22 entries, stype: 0 ........................................................| Test OK, maxerr 1e-11 ./cl < Matrix/galenet > tmp/l_galenet.out ; ./covall Test matrix: 8-by-14 with 22 entries, stype: 0 ........................................................| Test OK, maxerr 1e-11 statments not yet tested: 10734 ./cm < Matrix/5by50 > tmp/5by50.out Test matrix: 5-by-50 with 68 entries, stype: 0 ........................................................| Test OK, maxerr 4e-12 ./cl < Matrix/5by50 > tmp/l_5by50.out ; ./covall Test matrix: 5-by-50 with 68 entries, stype: 0 ........................................................| Test OK, maxerr 4e-12 statments not yet tested: 10358 ./cm < Matrix/r5lo > tmp/r5lo.out Test matrix: 5-by-5 with 10 entries, stype: -1 ........................................................| Test OK, maxerr 2e-13 ./cl < Matrix/r5lo > tmp/l_r5lo.out Test matrix: 5-by-5 with 10 entries, stype: -1 ........................................................| Test OK, maxerr 2e-13 ./cm < Matrix/r5up > tmp/r5up.out Test matrix: 5-by-5 with 10 entries, stype: 1 ........................................................| Test OK, maxerr 2e-13 ./cl < Matrix/r5up > tmp/l_r5up.out Test matrix: 5-by-5 with 10 entries, stype: 1 ........................................................| Test OK, maxerr 2e-13 ./cm < Matrix/r5up2 > tmp/r5up2.out Test matrix: 5-by-5 with 10 entries, stype: 1 ........................................................| Test OK, maxerr 2e-13 ./cl < Matrix/r5up2 > tmp/l_r5up2.out Test matrix: 5-by-5 with 10 entries, stype: 1 ........................................................| Test OK, maxerr 2e-13 ./cm < Matrix/c5up2 > tmp/c5up2.out Test matrix: 5-by-5 with 11 entries, stype: 1 ........................................................| Test OK, maxerr 6e-16 ./cl < Matrix/c5up2 > tmp/l_c5up2.out Test matrix: 5-by-5 with 11 entries, stype: 1 ........................................................| Test OK, maxerr 6e-16 ./cm < Matrix/z5up2 > tmp/z5up2.out Test matrix: 5-by-5 with 11 entries, stype: 1 ........................................................| Test OK, maxerr 6e-16 ./cl < Matrix/z5up2 > tmp/l_z5up2.out Test matrix: 5-by-5 with 11 entries, stype: 1 ........................................................| Test OK, maxerr 6e-16 ./cm -m < Matrix/z5lo > tmp/z5lo.out Test matrix: 5-by-5 with 11 entries, stype: -1 ........................................................|...........| Test OK, maxerr 6e-16 ./cl -m < Matrix/z5lo > tmp/l_z5lo.out Test matrix: 5-by-5 with 11 entries, stype: -1 ........................................................|...........| Test OK, maxerr 6e-16 ./cm < Matrix/ibm32 > tmp/ibm.out Test matrix: 32-by-32 with 126 entries, stype: 0 ............................| Test OK, maxerr 9e-13 ./cl < Matrix/ibm32 > tmp/l_ibm.out ; ./covall Test matrix: 32-by-32 with 126 entries, stype: 0 ............................| Test OK, maxerr 9e-13 statments not yet tested: 1238 ./cm -m < Matrix/c5lo > tmp/c5lo.out Test matrix: 5-by-5 with 11 entries, stype: -1 ........................................................|...........| Test OK, maxerr 6e-16 ./cl -m < Matrix/c5lo > tmp/l_c5lo.out Test matrix: 5-by-5 with 11 entries, stype: -1 ........................................................|...........| Test OK, maxerr 6e-16 ./cm -m < Matrix/z10 > tmp/z10.out Test matrix: 10-by-15 with 60 entries, stype: 0 ............................|............| Test OK, maxerr 3e-15 ./cl -m < Matrix/z10 > tmp/l_z10.out Test matrix: 10-by-15 with 60 entries, stype: 0 ............................|............| Test OK, maxerr 3e-15 ./cm -m < Matrix/z5up > tmp/z5up.out Test matrix: 5-by-5 with 11 entries, stype: 1 ........................................................|............. ...| Test OK, maxerr 6e-16 ./cl -m < Matrix/z5up > tmp/l_z5up.out ; ./covall Test matrix: 5-by-5 with 11 entries, stype: 1 ........................................................|............. ...| Test OK, maxerr 6e-16 statments not yet tested: 968 ./cm -s < Matrix/3singular > tmp/3singular.out Test matrix: 3-by-3 with 4 entries, stype: 1 ........................................................| Test OK ./cl -s < Matrix/3singular > tmp/l_3singular.out Test matrix: 3-by-3 with 4 entries, stype: 1 ........................................................| Test OK ./cm -s < Matrix/z3singular > tmp/z3singular.out Test matrix: 3-by-3 with 4 entries, stype: 1 ........................................................| Test OK ./cl -s < Matrix/z3singular > tmp/l_z3singular.out Test matrix: 3-by-3 with 4 entries, stype: 1 ........................................................| Test OK ./cm -s < Matrix/c3singular > tmp/c3singular.out Test matrix: 3-by-3 with 4 entries, stype: 1 ........................................................| Test OK ./cl -s < Matrix/c3singular > tmp/l_c3singular.out Test matrix: 3-by-3 with 4 entries, stype: 1 ........................................................| Test OK ./cm -m < Matrix/0 > tmp/0.out Test matrix: 0-by-0 with 0 entries, stype: 0 ........................................................|............. .| Test OK, maxerr 0 ./cl -m < Matrix/0 > tmp/l_0.out Test matrix: 0-by-0 with 0 entries, stype: 0 ........................................................|............. .| Test OK, maxerr 0 ./cm -m < Matrix/afiro > tmp/afiro.out Test matrix: 27-by-51 with 102 entries, stype: 0 ............................|......................................... ...| Test OK, maxerr 2e-10 ./cl -m < Matrix/afiro > tmp/l_afiro.out ; ./covall Test matrix: 27-by-51 with 102 entries, stype: 0 ............................|......................................... ...| Test OK, maxerr 2e-10 statments not yet tested: 412 ./cm -m < Matrix/k01up > tmp/k01up.out Test matrix: 48-by-48 with 224 entries, stype: 1 ............................|........................| Test OK, maxerr 8e-07 ./cl -m < Matrix/k01up > tmp/l_k01up.out ; ./covall Test matrix: 48-by-48 with 224 entries, stype: 1 ............................|........................| Test OK, maxerr 8e-07 statments not yet tested: 346 ./cm < Matrix/diag > tmp/diag.out Test matrix: 20-by-20 with 20 entries, stype: 1 ............................| Test OK, maxerr 7e-13 ./cl < Matrix/diag > tmp/l_diag.out Test matrix: 20-by-20 with 20 entries, stype: 1 ............................| Test OK, maxerr 7e-13 ./cm -m < Matrix/ex5lo > tmp/ex5lo.out Test matrix: 27-by-27 with 153 entries, stype: -1 ............................|.................| Test OK, maxerr 4e-09 ./cl -m < Matrix/ex5lo > tmp/l_ex5lo.out ; ./covall Test matrix: 27-by-27 with 153 entries, stype: -1 ............................|.................| Test OK, maxerr 4e-09 statments not yet tested: 332 ./cm < Matrix/20lo > tmp/20lo.out Test matrix: 20-by-20 with 210 entries, stype: -1 ............................| Test OK, maxerr 6e-14 ./cl < Matrix/20lo > tmp/l_20lo.out Test matrix: 20-by-20 with 210 entries, stype: -1 ............................| Test OK, maxerr 6e-14 ./cm < Matrix/z30lo > tmp/z30lo.out Test matrix: 30-by-30 with 114 entries, stype: -1 ............................| Test OK, maxerr 6e-15 ./cl < Matrix/z30lo > tmp/l_z30lo.out ; ./covall Test matrix: 30-by-30 with 114 entries, stype: -1 ............................| Test OK, maxerr 6e-15 statments not yet tested: 298 ./cm -m < Matrix/z30up > tmp/z30up.out Test matrix: 30-by-30 with 114 entries, stype: 1 ............................|..................| Test OK, maxerr 6e-15 ./cl -m < Matrix/z30up > tmp/l_z30up.out Test matrix: 30-by-30 with 114 entries, stype: 1 ............................|..................| Test OK, maxerr 6e-15 ./cm < Matrix/c10 > tmp/c10.out Test matrix: 10-by-15 with 60 entries, stype: 0 ............................| Test OK, maxerr 3e-15 ./cl < Matrix/c10 > tmp/l_c10.out Test matrix: 10-by-15 with 60 entries, stype: 0 ............................| Test OK, maxerr 3e-15 ./cm < Matrix/c30lo > tmp/c30lo.out Test matrix: 30-by-30 with 114 entries, stype: -1 ............................| Test OK, maxerr 6e-15 ./cl < Matrix/c30lo > tmp/l_c30lo.out ; ./covall Test matrix: 30-by-30 with 114 entries, stype: -1 ............................| Test OK, maxerr 6e-15 statments not yet tested: 192 ./cm -m < Matrix/c30up > tmp/c30up.out Test matrix: 30-by-30 with 114 entries, stype: 1 ............................|................| Test OK, maxerr 6e-15 ./cl -m < Matrix/c30up > tmp/l_c30up.out Test matrix: 30-by-30 with 114 entries, stype: 1 ............................|................| Test OK, maxerr 6e-15 ./cm < Matrix/pi > tmp/pi.out Test matrix: 1-by-1 with 1 entries, stype: 0 ........................................................| Test OK, maxerr 3e-13 ./cl < Matrix/pi > tmp/l_pi.out Test matrix: 1-by-1 with 1 entries, stype: 0 ........................................................| Test OK, maxerr 3e-13 ./cm < Matrix/cpi > tmp/cpi.out Test matrix: 1-by-1 with 1 entries, stype: 0 ........................................................| Test OK, maxerr 2e-15 ./cl < Matrix/cpi > tmp/l_cpi.out Test matrix: 1-by-1 with 1 entries, stype: 0 ........................................................| Test OK, maxerr 2e-15 ./cm < Matrix/1_0 > tmp/1_0.out Test matrix: 1-by-0 with 0 entries, stype: 0 ........................................................| Test OK ./cl < Matrix/1_0 > tmp/l_1_0.out Test matrix: 1-by-0 with 0 entries, stype: 0 ........................................................| Test OK ./cm < Matrix/0_1 > tmp/0_1.out Test matrix: 0-by-1 with 0 entries, stype: 0 ........................................................| Test OK, maxerr 0 ./cl < Matrix/0_1 > tmp/l_0_1.out ; ./covall Test matrix: 0-by-1 with 0 entries, stype: 0 ........................................................| Test OK, maxerr 0 statments not yet tested: 154 ./cm -n < Matrix/galenet > tmp/galenet_nan.out ; ./covall Test matrix: 8-by-14 with 22 entries, stype: 0 Test OK, maxerr 0 statments not yet tested: 148 ./cl -n < Matrix/galenet > tmp/l_galenet_nan.out ; ./covall Test matrix: 8-by-14 with 22 entries, stype: 0 Test OK, maxerr 0 statments not yet tested: 142 ./cm < Matrix/a1 > tmp/a1.out ; ./covall Test matrix: 70000-by-70000 with 140000 entries, stype: 1 Please wait, this will take a while ................| Test OK, maxerr 5e-12 statments not yet tested: 124 ./cl < Matrix/a1 > tmp/l_a1.out ; ./covall Test matrix: 70000-by-70000 with 140000 entries, stype: 1 Please wait, this will take a while ................| Test OK, maxerr 5e-12 statments not yet tested: 106 ./cm < Matrix/zero > tmp/zero.out Test matrix: 1100000000-by-1100000000 with 0 entries, stype: 0 Please wait, this will take a while ... ./cl < Matrix/zero > tmp/zero.out ; ./covall Test matrix: 1100000000-by-1100000000 with 0 entries, stype: 0 Please wait, this will take a while ... statments not yet tested: 0 SuiteSparse/CHOLMOD/Tcov/memory.c0000644001170100242450000002721210540000056015415 0ustar davisfac/* ========================================================================== */ /* === Tcov/memory ========================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Extensive memory-failure testing for CHOLMOD. * * my_malloc2, my_calloc2, and my_realloc2 pretend to fail if my_tries goes to * zero, to test CHOLMOD's memory error handling. No failure occurs if * my_tries is negative. */ #include "cm.h" /* ========================================================================== */ /* === my_tries ============================================================= */ /* ========================================================================== */ Int my_tries = -1 ; /* a global variable */ /* ========================================================================== */ /* === my_malloc2 =========================================================== */ /* ========================================================================== */ void *my_malloc2 (size_t size) { void *p ; if (my_tries == 0) { /* pretend to fail */ /* printf ("p 0 (pretend to fail)\n") ; */ return (NULL) ; } if (my_tries > 0) { my_tries-- ; } p = malloc (size) ; /* printf ("p %p\n", p) ; */ return (p) ; } /* ========================================================================== */ /* === my_calloc2 =========================================================== */ /* ========================================================================== */ void *my_calloc2 (size_t n, size_t size) { void *p ; if (my_tries == 0) { /* pretend to fail */ /* printf ("p 0 (pretend to fail)\n") ; */ return (NULL) ; } if (my_tries > 0) { my_tries-- ; } p = calloc (n, size) ; /* printf ("p %p\n", p) ; */ return (p) ; } /* ========================================================================== */ /* === my_realloc2 ========================================================== */ /* ========================================================================== */ void *my_realloc2 (void *p, size_t size) { void *p2 ; if (my_tries == 0) { /* pretend to fail */ /* printf ("p2 0 (pretend to fail)\n") ; */ return (NULL) ; } if (my_tries > 0) { my_tries-- ; } p2 = realloc (p, size) ; /* printf ("p2 %p\n", p2) ; */ return (p2) ; } /* ========================================================================== */ /* === my_free2 ============================================================= */ /* ========================================================================== */ void my_free2 (void *p) { free (p) ; } /* ========================================================================== */ /* === normal_memory_handler ================================================ */ /* ========================================================================== */ void normal_memory_handler ( void ) { cm->malloc_memory = malloc ; cm->calloc_memory = calloc ; cm->realloc_memory = realloc ; cm->free_memory = free ; cm->error_handler = my_handler ; CHOLMOD(free_work) (cm) ; } /* ========================================================================== */ /* === test_memory_handler ================================================== */ /* ========================================================================== */ void test_memory_handler ( void ) { cm->malloc_memory = my_malloc2 ; cm->calloc_memory = my_calloc2 ; cm->realloc_memory = my_realloc2 ; cm->free_memory = my_free2 ; cm->error_handler = NULL ; CHOLMOD(free_work) (cm) ; my_tries = 0 ; } /* ========================================================================== */ /* === memory tests ========================================================= */ /* ========================================================================== */ void memory_tests (cholmod_triplet *T) { double err ; cholmod_sparse *A ; Int trial ; size_t count, inuse ; test_memory_handler ( ) ; inuse = cm->memory_inuse ; cm->nmethods = 8 ; cm->print = 0 ; cm->final_resymbol = TRUE ; cm->final_asis = FALSE ; cm->final_super = FALSE ; cm->final_ll = FALSE ; cm->final_pack = FALSE ; cm->final_monotonic = FALSE ; /* ---------------------------------------------------------------------- */ /* test raw factorizations */ /* ---------------------------------------------------------------------- */ printf ("==================================== fac memory test\n") ; count = cm->malloc_count ; my_tries = -1 ; for (trial = 0 ; my_tries <= 0 ; trial++) { cm->print = 0 ; fflush (stdout) ; my_tries = trial ; A = CHOLMOD(triplet_to_sparse) (T, 0, cm) ; my_srand (trial+1) ; /* RAND reset */ err = raw_factor (A, FALSE) ; /* RAND */ CHOLMOD(free_sparse) (&A, cm) ; OK (CHOLMOD(print_common) ("cm", cm)) ; CHOLMOD(free_work) (cm) ; OK (count == cm->malloc_count) ; OK (inuse == cm->memory_inuse) ; } CHOLMOD(free_work) (cm) ; printf ("memory test: fac error %.1g trials "ID"\n", err, trial) ; printf ("initial count: "ID" final count "ID"\n", (Int) count, (Int) cm->malloc_count) ; printf ("initial inuse: "ID" final inuse "ID"\n", (Int) inuse, (Int) cm->memory_inuse) ; OK (count == cm->malloc_count) ; OK (inuse == cm->memory_inuse) ; /* ---------------------------------------------------------------------- */ /* test raw factorizations (rowfac_mask) */ /* ---------------------------------------------------------------------- */ printf ("==================================== fac memory test2\n") ; count = cm->malloc_count ; my_tries = -1 ; for (trial = 0 ; my_tries <= 0 ; trial++) { cm->print = 0 ; fflush (stdout) ; my_tries = trial ; A = CHOLMOD(triplet_to_sparse) (T, 0, cm) ; my_srand (trial+1) ; /* RAND reset */ err = raw_factor2 (A, 0., 0) ; /* RAND */ CHOLMOD(free_sparse) (&A, cm) ; OK (CHOLMOD(print_common) ("cm", cm)) ; CHOLMOD(free_work) (cm) ; OK (count == cm->malloc_count) ; OK (inuse == cm->memory_inuse) ; } CHOLMOD(free_work) (cm) ; printf ("memory test: fac error %.1g trials "ID"\n", err, trial) ; printf ("initial count: "ID" final count "ID"\n", (Int) count, (Int) cm->malloc_count) ; printf ("initial inuse: "ID" final inuse "ID"\n", (Int) inuse, (Int) cm->memory_inuse) ; OK (count == cm->malloc_count) ; OK (inuse == cm->memory_inuse) ; /* ---------------------------------------------------------------------- */ /* test augmented system solver */ /* ---------------------------------------------------------------------- */ printf ("==================================== aug memory test\n") ; count = cm->malloc_count ; my_tries = -1 ; for (trial = 0 ; my_tries <= 0 ; trial++) { cm->print = 0 ; fflush (stdout) ; my_tries = trial ; A = CHOLMOD(triplet_to_sparse) (T, 0, cm) ; err = aug (A) ; /* no random number use */ CHOLMOD(free_sparse) (&A, cm) ; OK (CHOLMOD(print_common) ("cm", cm)) ; CHOLMOD(free_work) (cm) ; OK (count == cm->malloc_count) ; OK (inuse == cm->memory_inuse) ; } CHOLMOD(free_work) (cm) ; printf ("memory test: aug error %.1g trials "ID"\n", err, trial) ; printf ("initial count: "ID" final count "ID"\n", (Int) count, (Int) cm->malloc_count) ; printf ("initial inuse: "ID" final inuse "ID"\n", (Int) inuse, (Int) cm->memory_inuse) ; OK (count == cm->malloc_count) ; OK (inuse == cm->memory_inuse) ; /* ---------------------------------------------------------------------- */ /* test ops */ /* ---------------------------------------------------------------------- */ printf ("==================================== test_ops memory test\n") ; count = cm->malloc_count ; my_tries = -1 ; for (trial = 0 ; my_tries <= 0 ; trial++) { cm->print = 0 ; fflush (stdout) ; my_tries = trial ; A = CHOLMOD(triplet_to_sparse) (T, 0, cm) ; my_srand (trial+1) ; /* RAND reset */ err = test_ops (A) ; /* RAND */ CHOLMOD(free_sparse) (&A, cm) ; OK (CHOLMOD(print_common) ("cm", cm)) ; CHOLMOD(free_work) (cm) ; printf ("inuse "ID" "ID"\n", inuse, cm->memory_inuse) ; OK (count == cm->malloc_count) ; OK (inuse == cm->memory_inuse) ; } printf ("memory test: testops error %.1g trials "ID"\n", err, trial) ; printf ("initial count: "ID" final count "ID"\n", (Int) count, (Int) cm->malloc_count) ; printf ("initial inuse: "ID" final inuse "ID"\n", (Int) inuse, (Int) cm->memory_inuse) ; OK (count == cm->malloc_count) ; OK (inuse == cm->memory_inuse) ; /* ---------------------------------------------------------------------- */ /* test lpdemo */ /* ---------------------------------------------------------------------- */ if (T == NULL || T->nrow != T->ncol) { printf ("==================================== lpdemo memory test\n") ; count = cm->malloc_count ; my_tries = -1 ; for (trial = 0 ; my_tries <= 0 ; trial++) { cm->print = 0 ; fflush (stdout) ; my_tries = trial ; my_srand (trial+1) ; /* RAND reset */ err = lpdemo (T) ; /* RAND */ OK (CHOLMOD(print_common) ("cm", cm)) ; CHOLMOD(free_work) (cm) ; OK (count == cm->malloc_count) ; OK (inuse == cm->memory_inuse) ; } CHOLMOD(free_work) (cm) ; printf ("memory test: lpdemo error %.1g trials "ID"\n", err, trial) ; printf ("initial count: "ID" final count "ID"\n", (Int) count, (Int) cm->malloc_count) ; printf ("initial inuse: "ID" final inuse "ID"\n", (Int) inuse, (Int) cm->memory_inuse) ; OK (count == cm->malloc_count) ; OK (inuse == cm->memory_inuse) ; } /* ---------------------------------------------------------------------- */ /* test solver */ /* ---------------------------------------------------------------------- */ printf ("==================================== solve memory test\n") ; count = cm->malloc_count ; my_tries = -1 ; for (trial = 0 ; my_tries <= 0 ; trial++) { CHOLMOD(defaults) (cm) ; cm->supernodal = CHOLMOD_SUPERNODAL ; cm->metis_memory = 2.0 ; cm->nmethods = 4 ; cm->print = 0 ; fflush (stdout) ; my_tries = trial ; A = CHOLMOD(triplet_to_sparse) (T, 0, cm) ; my_srand (trial+1) ; /* RAND reset */ err = solve (A) ; /* RAND */ CHOLMOD(free_sparse) (&A, cm) ; OK (CHOLMOD(print_common) ("cm", cm)) ; CHOLMOD(free_work) (cm) ; OK (count == cm->malloc_count) ; OK (inuse == cm->memory_inuse) ; } CHOLMOD(free_work) (cm) ; printf ("memory test: solve error %.1g trials "ID"\n", err, trial) ; printf ("initial count: "ID" final count "ID"\n", (Int) count, (Int) cm->malloc_count) ; printf ("initial inuse: "ID" final inuse "ID"\n", (Int) inuse, (Int) cm->memory_inuse) ; OK (count == cm->malloc_count) ; OK (inuse == cm->memory_inuse) ; cm->supernodal = CHOLMOD_AUTO ; progress (1, '|') ; /* ---------------------------------------------------------------------- */ /* restore original memory handler */ /* ---------------------------------------------------------------------- */ normal_memory_handler ( ) ; cm->print = 1 ; printf ("All memory tests OK, no error\n") ; } SuiteSparse/CHOLMOD/Makefile0000644001170100242450000000300310533604550014471 0ustar davisfac#------------------------------------------------------------------------------- # CHOLMOD Makefile #------------------------------------------------------------------------------- # Note: If you do not have METIS, or do not wish to use it in CHOLMOD, you must # compile CHOLMOD with the -DNPARTITION flag. See ../UFconfig/UFconfig.mk. default: all include ../UFconfig/UFconfig.mk # Compile the C-callable libraries and the Demo programs. all: ( cd Lib ; $(MAKE) ) ( cd Demo ; $(MAKE) ) # Compile the C-callable libraries only. library: ( cd Lib ; $(MAKE) ) # Remove all files not in the original distribution purge: ( cd MATLAB ; $(MAKE) purge ) ( cd Tcov ; $(MAKE) purge ) ( cd Lib ; $(MAKE) purge ) # ( cd Valgrind ; $(MAKE) purge ) ( cd Demo ; $(MAKE) purge ) ( cd Doc ; $(MAKE) purge ) # Remove all files not in the original distribution, except keep the # compiled libraries. clean: ( cd MATLAB ; $(MAKE) clean ) ( cd Tcov ; $(MAKE) clean ) ( cd Lib ; $(MAKE) clean ) ( cd Valgrind ; $(MAKE) clean ) ( cd Demo ; $(MAKE) clean ) distclean: purge ccode: all # Compile the MATLAB mexFunctions (you can also use cholmod_make.m in MATLAB) mex: ( cd MATLAB ; $(MAKE) ) # Run the test coverage suite. Takes about 40 minutes on a 3.2GHz Pentium. # Requires Linux (gcc, gcov). cov: ( cd Tcov ; $(MAKE) go ) # Run the test coverage suite using Valgrind. This takes a *** long *** time. valgrind: ( cd Valgrind ; $(MAKE) ) # Compile the C-callable libraries and the Demo programs. demo: ( cd Demo ; $(MAKE) ) SuiteSparse/CHOLMOD/Check/0000755001170100242450000000000010677523707014067 5ustar davisfacSuiteSparse/CHOLMOD/Check/cholmod_check.c0000644001170100242450000017365310616661402017020 0ustar davisfac/* ========================================================================== */ /* === Check/cholmod_check ================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Check Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Check Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Routines to check and print the contents of the 5 CHOLMOD objects: * * No CHOLMOD routine calls the check or print routines. If a user wants to * check CHOLMOD's input parameters, a separate call to the appropriate check * routine should be used before calling other CHOLMOD routines. * * cholmod_check_common check statistics and workspace in Common * cholmod_check_sparse check sparse matrix in compressed column form * cholmod_check_dense check dense matrix * cholmod_check_factor check factorization * cholmod_check_triplet check sparse matrix in triplet form * * cholmod_print_common print statistics in Common * cholmod_print_sparse print sparse matrix in compressed column form * cholmod_print_dense print dense matrix * cholmod_print_factor print factorization * cholmod_print_triplet print sparse matrix in triplet form * * In addition, this file contains routines to check and print three types of * integer vectors: * * cholmod_check_perm check a permutation of 0:n-1 (no duplicates) * cholmod_check_subset check a subset of 0:n-1 (duplicates OK) * cholmod_check_parent check an elimination tree * * cholmod_print_perm print a permutation * cholmod_print_subset print a subset * cholmod_print_parent print an elimination tree * * Each Common->print level prints the items at or below the given level: * * 0: print nothing; just check the data structures and return TRUE/FALSE * 1: error messages * 2: warning messages * 3: one-line summary of each object printed * 4: short summary of each object (first and last few entries) * 5: entire contents of the object * * No CHOLMOD routine calls these routines, so no printing occurs unless * the user specifically calls a cholmod_print_* routine. Thus, the default * print level is 3. * * Common->precise controls the # of digits printed for numerical entries * (5 if FALSE, 15 if TRUE). * * If Common->print_function is NULL, then no printing occurs. The * cholmod_check_* and cholmod_print_* routines still check their inputs and * return TRUE/FALSE if the object is valid or not. * * This file also includes debugging routines that are enabled only when * NDEBUG is defined in cholmod_internal.h (cholmod_dump_*). */ #ifndef NCHECK #include "cholmod_internal.h" #include "cholmod_check.h" /* ========================================================================== */ /* === printing definitions ================================================= */ /* ========================================================================== */ #ifdef LONG #define I8 "%8ld" #define I_8 "%-8ld" #else #define I8 "%8d" #define I_8 "%-8d" #endif #define PR(i,format,arg) \ { \ if (print >= i && Common->print_function != NULL) \ { \ (Common->print_function) (format, arg) ; \ } \ } #define P1(format,arg) PR(1,format,arg) #define P2(format,arg) PR(2,format,arg) #define P3(format,arg) PR(3,format,arg) #define P4(format,arg) PR(4,format,arg) #define ERR(msg) \ { \ P1 ("\nCHOLMOD ERROR: %s: ", type) ; \ if (name != NULL) \ { \ P1 ("%s", name) ; \ } \ P1 (": %s\n", msg) ; \ ERROR (CHOLMOD_INVALID, "invalid") ; \ return (FALSE) ; \ } /* print a numerical value */ #define PRINTVALUE(value) \ { \ if (Common->precise) \ { \ P4 (" %23.15e", value) ; \ } \ else \ { \ P4 (" %.5g", value) ; \ } \ } /* start printing */ #define ETC_START(count,limit) \ { \ count = (init_print == 4) ? (limit) : (-1) ; \ } /* re-enable printing if condition is met */ #define ETC_ENABLE(condition,count,limit) \ { \ if ((condition) && init_print == 4) \ { \ count = limit ; \ print = 4 ; \ } \ } /* turn off printing if limit is reached */ #define ETC_DISABLE(count) \ { \ if ((count >= 0) && (count-- == 0) && print == 4) \ { \ P4 ("%s", " ...\n") ; \ print = 3 ; \ } \ } /* re-enable printing, or turn if off after limit is reached */ #define ETC(condition,count,limit) \ { \ ETC_ENABLE (condition, count, limit) ; \ ETC_DISABLE (count) ; \ } #define BOOLSTR(x) ((x) ? "true " : "false") /* ========================================================================== */ /* === print_value ========================================================== */ /* ========================================================================== */ static void print_value ( Int print, Int xtype, double *Xx, double *Xz, Int p, cholmod_common *Common) { if (xtype == CHOLMOD_REAL) { PRINTVALUE (Xx [p]) ; } else if (xtype == CHOLMOD_COMPLEX) { P4 ("%s", "(") ; PRINTVALUE (Xx [2*p ]) ; P4 ("%s", " , ") ; PRINTVALUE (Xx [2*p+1]) ; P4 ("%s", ")") ; } else if (xtype == CHOLMOD_ZOMPLEX) { P4 ("%s", "(") ; PRINTVALUE (Xx [p]) ; P4 ("%s", " , ") ; PRINTVALUE (Xz [p]) ; P4 ("%s", ")") ; } } /* ========================================================================== */ /* === cholmod_check_common ================================================= */ /* ========================================================================== */ /* Print and verify the contents of Common */ static int check_common ( Int print, char *name, cholmod_common *Common ) { double fl, lnz ; double *Xwork ; Int *Flag, *Head ; UF_long mark ; Int i, nrow, nmethods, ordering, xworksize, amd_printed, init_print ; char *type = "common" ; /* ---------------------------------------------------------------------- */ /* print control parameters and statistics */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; init_print = print ; P2 ("%s", "\n") ; P1 ("CHOLMOD version %d", CHOLMOD_MAIN_VERSION) ; P1 (".%d", CHOLMOD_SUB_VERSION) ; P1 (".%d", CHOLMOD_SUBSUB_VERSION) ; P1 (", %s: ", CHOLMOD_DATE) ; if (name != NULL) { P1 ("%s: ", name) ; } switch (Common->status) { case CHOLMOD_OK: P1 ("%s", "status: OK\n") ; break ; case CHOLMOD_OUT_OF_MEMORY: P1 ("%s", "status: ERROR, out of memory\n") ; break ; case CHOLMOD_INVALID: P1 ("%s", "status: ERROR, invalid parameter\n") ; break ; case CHOLMOD_TOO_LARGE: P1 ("%s", "status: ERROR, problem too large\n") ; break ; case CHOLMOD_NOT_INSTALLED: P1 ("%s", "status: ERROR, method not installed\n") ; break ; case CHOLMOD_NOT_POSDEF: P1 ("%s", "status: warning, matrix not positive definite\n") ; break ; case CHOLMOD_DSMALL: P1 ("%s", "status: warning, diagonal entry has tiny abs. value\n") ; break ; default: ERR ("unknown status") ; } P2 (" Architecture: %s\n", CHOLMOD_ARCHITECTURE) ; P3 (" sizeof(int): %d\n", (int) sizeof (int)) ; P3 (" sizeof(UF_long): %d\n", (int) sizeof (UF_long)) ; P3 (" sizeof(void *): %d\n", (int) sizeof (void *)) ; P3 (" sizeof(double): %d\n", (int) sizeof (double)) ; P3 (" sizeof(Int): %d (CHOLMOD's basic integer)\n", (int) sizeof (Int)) ; P3 (" sizeof(BLAS_INT): %d (integer used in the BLAS)\n", (int) sizeof (BLAS_INT)) ; if (Common->fl != EMPTY) { P2 ("%s", " Results from most recent analysis:\n") ; P2 (" Cholesky flop count: %.5g\n", Common->fl) ; P2 (" Nonzeros in L: %.5g\n", Common->lnz) ; } if (Common->modfl != EMPTY) { P2 (" Update/downdate flop count: %.5g\n", Common->modfl) ; } P2 (" memory blocks in use: %8.0f\n", (double) (Common->malloc_count)) ; P2 (" memory in use (MB): %8.1f\n", (double) (Common->memory_inuse) / 1048576.) ; P2 (" peak memory usage (MB): %8.1f\n", (double) (Common->memory_usage) / 1048576.) ; /* ---------------------------------------------------------------------- */ /* primary control parameters and related ordering statistics */ /* ---------------------------------------------------------------------- */ P3 (" maxrank: update/downdate rank: "ID"\n", (Int) CHOLMOD(maxrank) (0, Common)) ; P3 (" supernodal control: %d", Common->supernodal) ; P3 (" %g ", Common->supernodal_switch) ; if (Common->supernodal <= CHOLMOD_SIMPLICIAL) { P3 ("%s", "(always do simplicial)\n") ; } else if (Common->supernodal == CHOLMOD_AUTO) { P3 ("(supernodal if flops/lnz >= %g)\n", Common->supernodal_switch) ; } else { P3 ("%s", "(always do supernodal)\n") ; } nmethods = MIN (Common->nmethods, CHOLMOD_MAXMETHODS) ; nmethods = MAX (0, nmethods) ; if (nmethods > 0) { P3 ("%s", " nmethods: number of ordering methods to try: ") ; P3 (""ID"\n", nmethods) ; } else { P3 ("%s", " nmethods=0: default strategy: Try user permutation if " "given. Try AMD.\n") ; #ifndef NPARTITION if (Common->default_nesdis) { P3 ("%s", " Try NESDIS if AMD reports flops/nnz(L) >= 500 and " "nnz(L)/nnz(A) >= 5.\n") ; } else { P3 ("%s", " Try METIS if AMD reports flops/nnz(L) >= 500 and " "nnz(L)/nnz(A) >= 5.\n") ; } #endif P3 ("%s", " Select best ordering tried.\n") ; Common->method [0].ordering = CHOLMOD_GIVEN ; Common->method [1].ordering = CHOLMOD_AMD ; Common->method [2].ordering = CHOLMOD_METIS ; #ifndef NPARTITION nmethods = 3 ; #else nmethods = 2 ; #endif } amd_printed = FALSE ; for (i = 0 ; i < nmethods ; i++) { P3 (" method "ID": ", i) ; ordering = Common->method [i].ordering ; fl = Common->method [i].fl ; lnz = Common->method [i].lnz ; switch (ordering) { case CHOLMOD_NATURAL: P3 ("%s", "natural\n") ; break ; case CHOLMOD_GIVEN: P3 ("%s", "user permutation (if given)\n") ; break ; case CHOLMOD_AMD: P3 ("%s", "AMD (or COLAMD if factorizing AA')\n") ; amd_printed = TRUE ; break ; case CHOLMOD_COLAMD: P3 ("%s", "AMD if factorizing A, COLAMD if factorizing AA')\n"); amd_printed = TRUE ; break ; case CHOLMOD_METIS: P3 ("%s", "METIS_NodeND nested dissection\n") ; break ; case CHOLMOD_NESDIS: P3 ("%s", "CHOLMOD nested dissection\n") ; P3 (" nd_small: # nodes in uncut subgraph: "ID"\n", (Int) (Common->method [i].nd_small)) ; P3 (" nd_compress: compress the graph: %s\n", BOOLSTR (Common->method [i].nd_compress)) ; P3 (" nd_camd: use constrained min degree: %s\n", BOOLSTR (Common->method [i].nd_camd)) ; break ; default: P3 (ID, ordering) ; ERR ("unknown ordering method") ; break ; } if (!(ordering == CHOLMOD_NATURAL || ordering == CHOLMOD_GIVEN)) { if (Common->method [i].prune_dense < 0) { P3 (" prune_dense: for pruning dense nodes: %s\n", " none pruned") ; } else { P3 (" prune_dense: for pruning dense nodes: " "%.5g\n", Common->method [i].prune_dense) ; P3 (" a dense node has degree " ">= max(16,(%.5g)*sqrt(n))\n", Common->method [i].prune_dense) ; } } if (ordering == CHOLMOD_COLAMD || ordering == CHOLMOD_NESDIS) { if (Common->method [i].prune_dense2 < 0) { P3 (" prune_dense2: for pruning dense rows for AA':" " %s\n", " none pruned") ; } else { P3 (" prune_dense2: for pruning dense rows for AA':" " %.5g\n", Common->method [i].prune_dense2) ; P3 (" a dense row has degree " ">= max(16,(%.5g)*sqrt(ncol))\n", Common->method [i].prune_dense2) ; } } if (fl != EMPTY) P3 (" flop count: %.5g\n", fl) ; if (lnz != EMPTY) P3 (" nnz(L): %.5g\n", lnz) ; } /* backup AMD results, if any */ if (!amd_printed) { P3 ("%s", " backup method: ") ; P3 ("%s", "AMD (or COLAMD if factorizing AA')\n") ; fl = Common->method [nmethods].fl ; lnz = Common->method [nmethods].lnz ; if (fl != EMPTY) P3 (" AMD flop count: %.5g\n", fl) ; if (lnz != EMPTY) P3 (" AMD nnz(L): %.5g\n", lnz) ; } /* ---------------------------------------------------------------------- */ /* arcane control parameters */ /* ---------------------------------------------------------------------- */ if (Common->final_asis) { P4 ("%s", " final_asis: TRUE, leave as is\n") ; } else { P4 ("%s", " final_asis: FALSE, convert when done\n") ; if (Common->final_super) { P4 ("%s", " final_super: TRUE, leave in supernodal form\n") ; } else { P4 ("%s", " final_super: FALSE, convert to simplicial form\n") ; } if (Common->final_ll) { P4 ("%s", " final_ll: TRUE, convert to LL' form\n") ; } else { P4 ("%s", " final_ll: FALSE, convert to LDL' form\n") ; } if (Common->final_pack) { P4 ("%s", " final_pack: TRUE, pack when done\n") ; } else { P4 ("%s", " final_pack: FALSE, do not pack when done\n") ; } if (Common->final_monotonic) { P4 ("%s", " final_monotonic: TRUE, ensure L is monotonic\n") ; } else { P4 ("%s", " final_monotonic: FALSE, do not ensure L is monotonic\n") ; } P4 (" final_resymbol: remove zeros from amalgamation: %s\n", BOOLSTR (Common->final_resymbol)) ; } P4 (" dbound: LDL' diagonal threshold: % .5g\n Entries with abs. value" " less than dbound are replaced with +/- dbound.\n", Common->dbound) ; P4 (" grow0: memory reallocation: % .5g\n", Common->grow0) ; P4 (" grow1: memory reallocation: % .5g\n", Common->grow1) ; P4 (" grow2: memory reallocation: %g\n", (double) (Common->grow2)) ; P4 ("%s", " nrelax, zrelax: supernodal amalgamation rule:\n") ; P4 ("%s", " s = # columns in two adjacent supernodes\n") ; P4 ("%s", " z = % of zeros in new supernode if they are merged.\n") ; P4 ("%s", " Two supernodes are merged if") ; P4 (" (s <= %g) or (no new zero entries) or\n", (double) (Common->nrelax [0])) ; P4 (" (s <= %g and ", (double) (Common->nrelax [1])) ; P4 ("z < %.5g%%) or", Common->zrelax [0] * 100) ; P4 (" (s <= %g and ", (double) (Common->nrelax [2])) ; P4 ("z < %.5g%%) or", Common->zrelax [1] * 100) ; P4 (" (z < %.5g%%)\n", Common->zrelax [2] * 100) ; /* ---------------------------------------------------------------------- */ /* check workspace */ /* ---------------------------------------------------------------------- */ mark = Common->mark ; nrow = Common->nrow ; Flag = Common->Flag ; Head = Common->Head ; if (nrow > 0) { if (mark < 0 || Flag == NULL || Head == NULL) { ERR ("workspace corrupted (Flag and/or Head missing)") ; } for (i = 0 ; i < nrow ; i++) { if (Flag [i] >= mark) { PRINT0 (("Flag ["ID"]="ID", mark = %ld\n", i, Flag [i], mark)) ; ERR ("workspace corrupted (Flag)") ; } } for (i = 0 ; i <= nrow ; i++) { if (Head [i] != EMPTY) { PRINT0 (("Head ["ID"] = "ID",\n", i, Head [i])) ; ERR ("workspace corrupted (Head)") ; } } } xworksize = Common->xworksize ; Xwork = Common->Xwork ; if (xworksize > 0) { if (Xwork == NULL) { ERR ("workspace corrupted (Xwork missing)") ; } for (i = 0 ; i < xworksize ; i++) { if (Xwork [i] != 0.) { PRINT0 (("Xwork ["ID"] = %g\n", i, Xwork [i])) ; ERR ("workspace corrupted (Xwork)") ; } } } /* workspace and parameters are valid */ P3 ("%s", " OK\n") ; P4 ("%s", "\n") ; return (TRUE) ; } int CHOLMOD(check_common) ( cholmod_common *Common ) { return (check_common (0, NULL, Common)) ; } int CHOLMOD(print_common) ( /* ---- input ---- */ char *name, /* printed name of Common object */ /* --------------- */ cholmod_common *Common ) { Int print = (Common == NULL) ? 3 : (Common->print) ; return (check_common (print, name, Common)) ; } /* ========================================================================== */ /* === cholmod_check_sparse ================================================= */ /* ========================================================================== */ /* Ensure that a sparse matrix in column-oriented form is valid, and optionally * print it. Returns the number of entries on the diagonal or -1 if error. * * workspace: Iwork (nrow) */ static UF_long check_sparse ( Int *Wi, Int print, char *name, cholmod_sparse *A, UF_long *nnzdiag, cholmod_common *Common ) { double *Ax, *Az ; Int *Ap, *Ai, *Anz ; Int nrow, ncol, nzmax, sorted, packed, j, p, pend, i, nz, ilast, space, init_print, dnz, count, xtype ; char *type = "sparse" ; /* ---------------------------------------------------------------------- */ /* print header information */ /* ---------------------------------------------------------------------- */ P4 ("%s", "\n") ; P3 ("%s", "CHOLMOD sparse: ") ; if (name != NULL) { P3 ("%s: ", name) ; } if (A == NULL) { ERR ("null") ; } nrow = A->nrow ; ncol = A->ncol ; nzmax = A->nzmax ; sorted = A->sorted ; packed = A->packed ; xtype = A->xtype ; Ap = A->p ; Ai = A->i ; Ax = A->x ; Az = A->z ; Anz = A->nz ; nz = CHOLMOD(nnz) (A, Common) ; P3 (" "ID"", nrow) ; P3 ("-by-"ID", ", ncol) ; P3 ("nz "ID",", nz) ; if (A->stype > 0) { P3 ("%s", " upper.") ; } else if (A->stype < 0) { P3 ("%s", " lower.") ; } else { P3 ("%s", " up/lo.") ; } P4 ("\n nzmax "ID", ", nzmax) ; if (nz > nzmax) { ERR ("nzmax too small") ; } if (!sorted) { P4 ("%s", "un") ; } P4 ("%s", "sorted, ") ; if (!packed) { P4 ("%s", "un") ; } P4 ("%s", "packed, ") ; switch (A->itype) { case CHOLMOD_INT: P4 ("%s", "\n scalar types: int, ") ; break ; case CHOLMOD_INTLONG: ERR ("mixed int/UF_long type unsupported") ; case CHOLMOD_LONG: P4 ("%s", "\n scalar types: UF_long, ") ; break ; default: ERR ("unknown itype") ; } switch (A->xtype) { case CHOLMOD_PATTERN: P4 ("%s", "pattern") ; break ; case CHOLMOD_REAL: P4 ("%s", "real") ; break ; case CHOLMOD_COMPLEX: P4 ("%s", "complex") ; break ; case CHOLMOD_ZOMPLEX: P4 ("%s", "zomplex") ; break ; default: ERR ("unknown xtype") ; } switch (A->dtype) { case CHOLMOD_DOUBLE: P4 ("%s", ", double\n") ; break ; case CHOLMOD_SINGLE: ERR ("float unsupported") ; default: ERR ("unknown dtype") ; } if (A->itype != ITYPE || A->dtype != DTYPE) { ERR ("integer and real type must match routine") ; } if (A->stype && nrow != ncol) { ERR ("symmetric but not square") ; } /* check for existence of Ap, Ai, Anz, Ax, and Az arrays */ if (Ap == NULL) { ERR ("p array not present") ; } if (Ai == NULL) { ERR ("i array not present") ; } if (!packed && Anz == NULL) { ERR ("nz array not present") ; } if (xtype != CHOLMOD_PATTERN && Ax == NULL) { ERR ("x array not present") ; } if (xtype == CHOLMOD_ZOMPLEX && Az == NULL) { ERR ("z array not present") ; } /* packed matrices must start at Ap [0] = 0 */ if (packed && Ap [0] != 0) { ERR ("p [0] must be zero") ; } if (packed && (Ap [ncol] < Ap [0] || Ap [ncol] > nzmax)) { ERR ("p [ncol] invalid") ; } /* ---------------------------------------------------------------------- */ /* allocate workspace if needed */ /* ---------------------------------------------------------------------- */ if (!sorted) { if (Wi == NULL) { CHOLMOD(allocate_work) (0, nrow, 0, Common) ; Wi = Common->Iwork ; /* size nrow, (i/i/l) */ } if (Common->status < CHOLMOD_OK) { return (FALSE) ; /* out of memory */ } for (i = 0 ; i < nrow ; i++) { Wi [i] = EMPTY ; } } /* ---------------------------------------------------------------------- */ /* check and print each column */ /* ---------------------------------------------------------------------- */ init_print = print ; dnz = 0 ; ETC_START (count, 8) ; for (j = 0 ; j < ncol ; j++) { ETC (j == ncol-1, count, 4) ; p = Ap [j] ; if (packed) { pend = Ap [j+1] ; nz = pend - p ; } else { /* Note that Anz [j] < 0 is treated as zero */ nz = MAX (0, Anz [j]) ; pend = p + nz ; } /* Note that space can be negative if the matrix is non-monotonic */ space = Ap [j+1] - p ; P4 (" col "ID":", j) ; P4 (" nz "ID"", nz) ; P4 (" start "ID"", p) ; P4 (" end "ID"", pend) ; if (!packed) { P4 (" space "ID"", space) ; } P4 ("%s", ":\n") ; if (p < 0 || pend > nzmax) { ERR ("pointer invalid") ; } if (nz < 0 || nz > nrow) { ERR ("nz invalid") ; } ilast = EMPTY ; for ( ; p < pend ; p++) { ETC (j == ncol-1 && p >= pend-4, count, -1) ; i = Ai [p] ; P4 (" "I8":", i) ; print_value (print, xtype, Ax, Az, p, Common) ; if (i == j) { dnz++ ; } if (i < 0 || i >= nrow) { ERR ("row index out of range") ; } if (sorted && i <= ilast) { ERR ("row indices out of order") ; } if (!sorted && Wi [i] == j) { ERR ("duplicate row index") ; } P4 ("%s", "\n") ; ilast = i ; if (!sorted) { Wi [i] = j ; } } } /* matrix is valid */ P4 (" nnz on diagonal: "ID"\n", dnz) ; P3 ("%s", " OK\n") ; P4 ("%s", "\n") ; *nnzdiag = dnz ; return (TRUE) ; } int CHOLMOD(check_sparse) ( /* ---- input ---- */ cholmod_sparse *A, /* sparse matrix to check */ /* --------------- */ cholmod_common *Common ) { UF_long nnzdiag ; RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_sparse (NULL, 0, NULL, A, &nnzdiag, Common)) ; } int CHOLMOD(print_sparse) ( /* ---- input ---- */ cholmod_sparse *A, /* sparse matrix to print */ char *name, /* printed name of sparse matrix */ /* --------------- */ cholmod_common *Common ) { UF_long nnzdiag ; RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_sparse (NULL, Common->print, name, A, &nnzdiag, Common)) ; } /* ========================================================================== */ /* === cholmod_check_dense ================================================== */ /* ========================================================================== */ /* Ensure a dense matrix is valid, and optionally print it. */ static int check_dense ( Int print, char *name, cholmod_dense *X, cholmod_common *Common ) { double *Xx, *Xz ; Int i, j, d, nrow, ncol, nzmax, nz, init_print, count, xtype ; char *type = "dense" ; /* ---------------------------------------------------------------------- */ /* print header information */ /* ---------------------------------------------------------------------- */ P4 ("%s", "\n") ; P3 ("%s", "CHOLMOD dense: ") ; if (name != NULL) { P3 ("%s: ", name) ; } if (X == NULL) { ERR ("null") ; } nrow = X->nrow ; ncol = X->ncol ; nzmax = X->nzmax ; d = X->d ; Xx = X->x ; Xz = X->z ; xtype = X->xtype ; P3 (" "ID"", nrow) ; P3 ("-by-"ID", ", ncol) ; P4 ("\n leading dimension "ID", ", d) ; P4 ("nzmax "ID", ", nzmax) ; if (d * ncol > nzmax) { ERR ("nzmax too small") ; } if (d < nrow) { ERR ("leading dimension must be >= # of rows") ; } if (Xx == NULL) { ERR ("null") ; } switch (X->xtype) { case CHOLMOD_PATTERN: ERR ("pattern unsupported") ; break ; case CHOLMOD_REAL: P4 ("%s", "real") ; break ; case CHOLMOD_COMPLEX: P4 ("%s", "complex") ; break ; case CHOLMOD_ZOMPLEX: P4 ("%s", "zomplex") ; break ; default: ERR ("unknown xtype") ; } switch (X->dtype) { case CHOLMOD_DOUBLE: P4 ("%s", ", double\n") ; break ; case CHOLMOD_SINGLE: ERR ("single unsupported") ; default: ERR ("unknown dtype") ; } /* ---------------------------------------------------------------------- */ /* check and print each entry */ /* ---------------------------------------------------------------------- */ if (print >= 4) { init_print = print ; ETC_START (count, 9) ; nz = nrow * ncol ; for (j = 0 ; j < ncol ; j++) { ETC (j == ncol-1, count, 5) ; P4 (" col "ID":\n", j) ; for (i = 0 ; i < nrow ; i++) { ETC (j == ncol-1 && i >= nrow-4, count, -1) ; P4 (" "I8":", i) ; print_value (print, xtype, Xx, Xz, i+j*d, Common) ; P4 ("%s", "\n") ; } } } /* dense is valid */ P3 ("%s", " OK\n") ; P4 ("%s", "\n") ; return (TRUE) ; } int CHOLMOD(check_dense) ( /* ---- input ---- */ cholmod_dense *X, /* dense matrix to check */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_dense (0, NULL, X, Common)) ; } int CHOLMOD(print_dense) ( /* ---- input ---- */ cholmod_dense *X, /* dense matrix to print */ char *name, /* printed name of dense matrix */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_dense (Common->print, name, X, Common)) ; } /* ========================================================================== */ /* === cholmod_check_subset ================================================= */ /* ========================================================================== */ /* Ensure S (0:len-1) is a subset of 0:n-1. Duplicates are allowed. S may be * NULL. A negative len denotes the set 0:n-1. * * To check the rset and cset for A(rset,cset), where nc and nr are the length * of cset and rset respectively: * * cholmod_check_subset (cset, nc, A->ncol, Common) ; * cholmod_check_subset (rset, nr, A->nrow, Common) ; * * workspace: none */ static int check_subset ( Int *S, UF_long len, size_t n, Int print, char *name, cholmod_common *Common ) { Int i, k, init_print, count ; char *type = "subset" ; init_print = print ; if (S == NULL) { /* zero len denotes S = [ ], negative len denotes S = 0:n-1 */ len = (len < 0) ? (-1) : 0 ; } P4 ("%s", "\n") ; P3 ("%s", "CHOLMOD subset: ") ; if (name != NULL) { P3 ("%s: ", name) ; } P3 (" len: %ld ", len) ; if (len < 0) { P3 ("%s", "(denotes 0:n-1) ") ; } P3 ("n: "ID"", (Int) n) ; P4 ("%s", "\n") ; if (len <= 0 || S == NULL) { P3 ("%s", " OK\n") ; P4 ("%s", "\n") ; return (TRUE) ; } if (print >= 4) { ETC_START (count, 8) ; for (k = 0 ; k < ((Int) len) ; k++) { ETC (k == ((Int) len) - 4, count, -1) ; i = S [k] ; P4 (" "I8":", k) ; P4 (" "ID"\n", i) ; if (i < 0 || i >= ((Int) n)) { ERR ("entry out range") ; } } } else { for (k = 0 ; k < ((Int) len) ; k++) { i = S [k] ; if (i < 0 || i >= ((Int) n)) { ERR ("entry out range") ; } } } P3 ("%s", " OK\n") ; P4 ("%s", "\n") ; return (TRUE) ; } int CHOLMOD(check_subset) ( /* ---- input ---- */ Int *Set, /* Set [0:len-1] is a subset of 0:n-1. Duplicates OK */ UF_long len, /* size of Set (an integer array), or < 0 if 0:n-1 */ size_t n, /* 0:n-1 is valid range */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_subset (Set, len, n, 0, NULL, Common)) ; } int CHOLMOD(print_subset) ( /* ---- input ---- */ Int *Set, /* Set [0:len-1] is a subset of 0:n-1. Duplicates OK */ UF_long len, /* size of Set (an integer array), or < 0 if 0:n-1 */ size_t n, /* 0:n-1 is valid range */ char *name, /* printed name of Set */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_subset (Set, len, n, Common->print, name, Common)) ; } /* ========================================================================== */ /* === cholmod_check_perm =================================================== */ /* ========================================================================== */ /* Ensure that Perm [0..len-1] is a permutation of a subset of 0:n-1. Perm * may be NULL, which is interpreted as the identity permutation. There can * be no duplicate entries (len must be <= n). * * If n <= Common->nrow, then this routine takes O(len) time and does not * allocate any memory, by using Common->Flag. Otherwise, it takes O(n) time * and ensures that Common->Iwork is at least n*sizeof(Int) in size. * * To check the fset: cholmod_check_perm (fset, fsize, ncol, Common) ; * To check a permutation: cholmod_check_perm (Perm, n, n, Common) ; * * workspace: Flag (n) if n <= Common->nrow, Iwork (n) otherwise. */ static int check_perm ( Int *Wi, Int print, char *name, Int *Perm, size_t len, size_t n, cholmod_common *Common ) { Int *Flag ; Int i, k, mark, init_print, count ; char *type = "perm" ; /* ---------------------------------------------------------------------- */ /* checks that take O(1) time */ /* ---------------------------------------------------------------------- */ if (Perm == NULL || n == 0) { /* Perm is valid implicit identity, or empty */ return (TRUE) ; } /* ---------------------------------------------------------------------- */ /* checks that take O(n) time or require memory allocation */ /* ---------------------------------------------------------------------- */ init_print = print ; ETC_START (count, 8) ; if (Wi == NULL && n <= Common->nrow) { /* use the Common->Flag array if it's big enough */ mark = CHOLMOD(clear_flag) (Common) ; Flag = Common->Flag ; ASSERT (CHOLMOD(dump_work) (TRUE, FALSE, 0, Common)) ; if (print >= 4) { for (k = 0 ; k < ((Int) len) ; k++) { ETC (k >= ((Int) len) - 4, count, -1) ; i = Perm [k] ; P4 (" "I8":", k) ; P4 (""ID"\n", i) ; if (i < 0 || i >= ((Int) n) || Flag [i] == mark) { CHOLMOD(clear_flag) (Common) ; ERR ("invalid permutation") ; } Flag [i] = mark ; } } else { for (k = 0 ; k < ((Int) len) ; k++) { i = Perm [k] ; if (i < 0 || i >= ((Int) n) || Flag [i] == mark) { CHOLMOD(clear_flag) (Common) ; ERR ("invalid permutation") ; } Flag [i] = mark ; } } CHOLMOD(clear_flag) (Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, FALSE, 0, Common)) ; } else { if (Wi == NULL) { /* use Common->Iwork instead, but initialize it first */ CHOLMOD(allocate_work) (0, n, 0, Common) ; Wi = Common->Iwork ; /* size n, (i/i/i) is OK */ } if (Common->status < CHOLMOD_OK) { return (FALSE) ; /* out of memory */ } for (i = 0 ; i < ((Int) n) ; i++) { Wi [i] = FALSE ; } if (print >= 4) { for (k = 0 ; k < ((Int) len) ; k++) { ETC (k >= ((Int) len) - 4, count, -1) ; i = Perm [k] ; P4 (" "I8":", k) ; P4 (""ID"\n", i) ; if (i < 0 || i >= ((Int) n) || Wi [i]) { ERR ("invalid permutation") ; } Wi [i] = TRUE ; } } else { for (k = 0 ; k < ((Int) len) ; k++) { i = Perm [k] ; if (i < 0 || i >= ((Int) n) || Wi [i]) { ERR ("invalid permutation") ; } Wi [i] = TRUE ; } } } /* perm is valid */ return (TRUE) ; } int CHOLMOD(check_perm) ( /* ---- input ---- */ Int *Perm, /* Perm [0:len-1] is a permutation of subset of 0:n-1 */ size_t len, /* size of Perm (an integer array) */ size_t n, /* 0:n-1 is valid range */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_perm (NULL, 0, NULL, Perm, len, n, Common)) ; } int CHOLMOD(print_perm) ( /* ---- input ---- */ Int *Perm, /* Perm [0:len-1] is a permutation of subset of 0:n-1 */ size_t len, /* size of Perm (an integer array) */ size_t n, /* 0:n-1 is valid range */ char *name, /* printed name of Perm */ /* --------------- */ cholmod_common *Common ) { Int ok, print ; RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; print = Common->print ; P4 ("%s", "\n") ; P3 ("%s", "CHOLMOD perm: ") ; if (name != NULL) { P3 ("%s: ", name) ; } P3 (" len: "ID"", (Int) len) ; P3 (" n: "ID"", (Int) n) ; P4 ("%s", "\n") ; ok = check_perm (NULL, print, name, Perm, len, n, Common) ; if (ok) { P3 ("%s", " OK\n") ; P4 ("%s", "\n") ; } return (ok) ; } /* ========================================================================== */ /* === cholmod_check_parent ================================================= */ /* ========================================================================== */ /* Ensure that Parent is a valid elimination tree of nodes 0 to n-1. * If j is a root of the tree then Parent [j] is EMPTY (-1). * * NOTE: this check will fail if applied to the component tree (CParent) in * cholmod_nested_dissection, unless it has been postordered and renumbered. * * workspace: none */ static int check_parent ( Int *Parent, size_t n, Int print, char *name, cholmod_common *Common ) { Int j, p, init_print, count ; char *type = "parent" ; init_print = print ; P4 ("%s", "\n") ; P3 ("%s", "CHOLMOD parent: ") ; if (name != NULL) { P3 ("%s: ", name) ; } P3 (" n: "ID"", (Int) n) ; P4 ("%s", "\n") ; if (Parent == NULL) { ERR ("null") ; } /* ---------------------------------------------------------------------- */ /* checks that take O(n) time */ /* ---------------------------------------------------------------------- */ ETC_START (count, 8) ; for (j = 0 ; j < ((Int) n) ; j++) { ETC (j == ((Int) n) - 4, count, -1) ; p = Parent [j] ; P4 (" "I8":", j) ; P4 (" "ID"\n", p) ; if (!(p == EMPTY || p > j)) { ERR ("invalid") ; } } P3 ("%s", " OK\n") ; P4 ("%s", "\n") ; return (TRUE) ; } int CHOLMOD(check_parent) ( /* ---- input ---- */ Int *Parent, /* Parent [0:n-1] is an elimination tree */ size_t n, /* size of Parent */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_parent (Parent, n, 0, NULL, Common)) ; } int CHOLMOD(print_parent) ( /* ---- input ---- */ Int *Parent, /* Parent [0:n-1] is an elimination tree */ size_t n, /* size of Parent */ char *name, /* printed name of Parent */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_parent (Parent, n, Common->print, name, Common)) ; } /* ========================================================================== */ /* === cholmod_check_factor ================================================= */ /* ========================================================================== */ static int check_factor ( Int *Wi, Int print, char *name, cholmod_factor *L, cholmod_common *Common ) { double *Lx, *Lz ; Int *Lp, *Li, *Lnz, *Lnext, *Lprev, *Perm, *ColCount, *Lpi, *Lpx, *Super, *Ls ; Int n, nzmax, j, p, pend, i, nz, ordering, space, is_monotonic, minor, count, precise, init_print, ilast, lnz, head, tail, jprev, plast, jnext, examine_super, nsuper, s, k1, k2, psi, psend, psx, nsrow, nscol, ps2, psxend, ssize, xsize, maxcsize, maxesize, nsrow2, jj, ii, xtype ; char *type = "factor" ; /* ---------------------------------------------------------------------- */ /* print header information */ /* ---------------------------------------------------------------------- */ P4 ("%s", "\n") ; P3 ("%s", "CHOLMOD factor: ") ; if (name != NULL) { P3 ("%s: ", name) ; } if (L == NULL) { ERR ("null") ; } n = L->n ; minor = L->minor ; ordering = L->ordering ; xtype = L->xtype ; Perm = L->Perm ; ColCount = L->ColCount ; lnz = 0 ; precise = Common->precise ; P3 (" "ID"", n) ; P3 ("-by-"ID"", n) ; if (minor < n) { P3 (" not positive definite (column "ID")", minor) ; } switch (L->itype) { case CHOLMOD_INT: P4 ("%s", "\n scalar types: int, ") ; break ; case CHOLMOD_INTLONG: ERR ("mixed int/UF_long type unsupported") ; case CHOLMOD_LONG: P4 ("%s", "\n scalar types: UF_long, ") ; break ; default: ERR ("unknown itype") ; } switch (L->xtype) { case CHOLMOD_PATTERN: P4 ("%s", "pattern") ; break ; case CHOLMOD_REAL: P4 ("%s", "real") ; break ; case CHOLMOD_COMPLEX: P4 ("%s", "complex") ; break ; case CHOLMOD_ZOMPLEX: P4 ("%s", "zomplex") ; break ; default: ERR ("unknown xtype") ; } switch (L->dtype) { case CHOLMOD_DOUBLE: P4 ("%s", ", double\n") ; break ; case CHOLMOD_SINGLE: ERR ("single unsupported") ; default: ERR ("unknown dtype") ; } if (L->itype != ITYPE || L->dtype != DTYPE) { ERR ("integer and real type must match routine") ; } if (L->is_super) { P3 ("%s", " supernodal") ; } else { P3 ("%s", " simplicial") ; } if (L->is_ll) { P3 ("%s", ", LL'.") ; } else { P3 ("%s", ", LDL'.") ; } P4 ("%s", "\n ordering method used: ") ; switch (L->ordering) { case CHOLMOD_POSTORDERED:P4 ("%s", "natural (postordered)") ; break ; case CHOLMOD_NATURAL: P4 ("%s", "natural") ; break ; case CHOLMOD_GIVEN: P4 ("%s", "user-provided") ; break ; case CHOLMOD_AMD: P4 ("%s", "AMD") ; break ; case CHOLMOD_COLAMD: P4 ("%s", "AMD for A, COLAMD for A*A'") ;break ; #ifndef NPARTITION case CHOLMOD_METIS: P4 ("%s", "METIS NodeND") ; break ; case CHOLMOD_NESDIS: P4 ("%s", "CHOLMOD nested dissection") ; break ; #endif default: ERR ("unknown ordering") ; } P4 ("%s", "\n") ; init_print = print ; if (L->is_super && L->xtype == CHOLMOD_ZOMPLEX) { ERR ("Supernodal zomplex L not supported") ; } /* ---------------------------------------------------------------------- */ /* check L->Perm */ /* ---------------------------------------------------------------------- */ if (!check_perm (Wi, print, name, Perm, n, n, Common)) { return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* check L->ColCount */ /* ---------------------------------------------------------------------- */ if (ColCount == NULL) { ERR ("ColCount vector invalid") ; } ETC_START (count, 8) ; for (j = 0 ; j < n ; j++) { ETC (j >= n-4, count, -1) ; P4 (" col: "ID" ", j) ; nz = ColCount [j] ; P4 ("colcount: "ID"\n", nz) ; if (nz < 0 || nz > n-j) { ERR ("ColCount out of range") ; } } /* ---------------------------------------------------------------------- */ /* check factor */ /* ---------------------------------------------------------------------- */ if (L->xtype == CHOLMOD_PATTERN && !(L->is_super)) { /* ------------------------------------------------------------------ */ /* check simplicial symbolic factor */ /* ------------------------------------------------------------------ */ /* nothing else to do */ ; } else if (L->xtype != CHOLMOD_PATTERN && !(L->is_super)) { /* ------------------------------------------------------------------ */ /* check simplicial numerical factor */ /* ------------------------------------------------------------------ */ P4 ("monotonic: %d\n", L->is_monotonic) ; nzmax = L->nzmax ; P3 (" nzmax "ID".", nzmax) ; P4 ("%s", "\n") ; Lp = L->p ; Li = L->i ; Lx = L->x ; Lz = L->z ; Lnz = L->nz ; Lnext = L->next ; Lprev = L->prev ; /* check for existence of Lp, Li, Lnz, Lnext, Lprev, and Lx arrays */ if (Lp == NULL) { ERR ("p array not present") ; } if (Li == NULL) { ERR ("i array not present") ; } if (Lnz == NULL) { ERR ("nz array not present") ; } if (Lx == NULL) { ERR ("x array not present") ; } if (xtype == CHOLMOD_ZOMPLEX && Lz == NULL) { ERR ("z array not present") ; } if (Lnext == NULL) { ERR ("next array not present") ; } if (Lprev == NULL) { ERR ("prev array not present") ; } ETC_START (count, 8) ; /* check each column of L */ plast = 0 ; is_monotonic = TRUE ; for (j = 0 ; j < n ; j++) { ETC (j >= n-3, count, -1) ; p = Lp [j] ; nz = Lnz [j] ; pend = p + nz ; lnz += nz ; P4 (" col "ID":", j) ; P4 (" nz "ID"", nz) ; P4 (" start "ID"", p) ; P4 (" end "ID"", pend) ; if (Lnext [j] < 0 || Lnext [j] > n) { ERR ("invalid link list") ; } space = Lp [Lnext [j]] - p ; P4 (" space "ID"", space) ; P4 (" free "ID":\n", space - nz) ; if (p < 0 || pend > nzmax || space < 1) { ERR ("pointer invalid") ; } if (nz < 1 || nz > (n-j) || nz > space) { ERR ("nz invalid") ; } ilast = j-1 ; if (p < plast) { is_monotonic = FALSE ; } plast = p ; i = Li [p] ; P4 (" "I8":", i) ; if (i != j) { ERR ("diagonal missing") ; } print_value (print, xtype, Lx, Lz, p, Common) ; P4 ("%s", "\n") ; ilast = j ; for (p++ ; p < pend ; p++) { ETC_DISABLE (count) ; i = Li [p] ; P4 (" "I8":", i) ; if (i < j || i >= n) { ERR ("row index out of range") ; } if (i <= ilast) { ERR ("row indices out of order") ; } print_value (print, xtype, Lx, Lz, p, Common) ; P4 ("%s", "\n") ; ilast = i ; } } if (L->is_monotonic && !is_monotonic) { ERR ("columns not monotonic") ; } /* check the link list */ head = n+1 ; tail = n ; j = head ; jprev = EMPTY ; count = 0 ; for ( ; ; ) { if (j < 0 || j > n+1 || count > n+2) { ERR ("invalid link list") ; } jnext = Lnext [j] ; if (j >= 0 && j < n) { if (jprev != Lprev [j]) { ERR ("invalid link list") ; } } count++ ; if (j == tail) { break ; } jprev = j ; j = jnext ; } if (Lnext [tail] != EMPTY || count != n+2) { ERR ("invalid link list") ; } } else { /* ------------------------------------------------------------------ */ /* check supernodal numeric or symbolic factor */ /* ------------------------------------------------------------------ */ nsuper = L->nsuper ; ssize = L->ssize ; xsize = L->xsize ; maxcsize = L->maxcsize ; maxesize = L->maxesize ; Ls = L->s ; Lpi = L->pi ; Lpx = L->px ; Super = L->super ; Lx = L->x ; ETC_START (count, 8) ; P4 (" ssize "ID" ", ssize) ; P4 ("xsize "ID" ", xsize) ; P4 ("maxcsize "ID" ", maxcsize) ; P4 ("maxesize "ID"\n", maxesize) ; if (Ls == NULL) { ERR ("invalid: L->s missing") ; } if (Lpi == NULL) { ERR ("invalid: L->pi missing") ; } if (Lpx == NULL) { ERR ("invalid: L->px missing") ; } if (Super == NULL) { ERR ("invalid: L->super missing") ; } if (L->xtype != CHOLMOD_PATTERN) { /* numerical supernodal factor */ if (Lx == NULL) { ERR ("invalid: L->x missing") ; } if (Ls [0] == EMPTY) { ERR ("invalid: L->s not defined") ; } examine_super = TRUE ; } else { /* symbolic supernodal factor, but only if it has been computed */ examine_super = (Ls [0] != EMPTY) ; } if (examine_super) { if (Lpi [0] != 0 || MAX (1, Lpi [nsuper]) != ssize) { PRINT0 (("Lpi [0] "ID", Lpi [nsuper = "ID"] = "ID"\n", Lpi [0], nsuper, Lpi [nsuper])) ; ERR ("invalid: L->pi invalid") ; } if (Lpx [0] != 0 || MAX (1, Lpx [nsuper]) != xsize) { ERR ("invalid: L->px invalid") ; } /* check and print each supernode */ for (s = 0 ; s < nsuper ; s++) { k1 = Super [s] ; k2 = Super [s+1] ; psi = Lpi [s] ; psend = Lpi [s+1] ; psx = Lpx [s] ; nsrow = psend - psi ; nscol = k2 - k1 ; nsrow2 = nsrow - nscol ; ps2 = psi + nscol ; psxend = Lpx [s+1] ; ETC (s == nsuper-1, count, 4) ; P4 (" supernode "ID", ", s) ; P4 ("col "ID" ", k1) ; P4 ("to "ID". ", k2-1) ; P4 ("nz in first col: "ID".\n", nsrow) ; P4 (" values start "ID", ", psx) ; P4 ("end "ID"\n", psxend) ; if (k1 > k2 || k1 < 0 || k2 > n || nsrow < nscol || nsrow2 < 0 || psxend - psx != nsrow * nscol) { ERR ("invalid supernode") ; } lnz += nscol * nsrow - (nscol*nscol - nscol)/2 ; if (L->xtype != CHOLMOD_PATTERN) { /* print each column of the supernode */ for (jj = 0 ; jj < nscol ; jj++) { ETC_ENABLE (s == nsuper-1 && jj >= nscol-3, count, -1) ; j = k1 + jj ; P4 (" col "ID"\n", j) ; ilast = j ; i = Ls [psi + jj] ; P4 (" "I8":", i) ; if (i != j) { ERR ("row index invalid") ; } /* PRINTVALUE (Lx [psx + jj + jj*nsrow]) ; */ print_value (print, xtype, Lx, NULL, psx + jj + jj*nsrow, Common) ; P4 ("%s", "\n") ; for (ii = jj + 1 ; ii < nsrow ; ii++) { ETC_DISABLE (count) ; i = Ls [psi + ii] ; P4 (" "I8":", i) ; if (i <= ilast || i > n) { ERR ("row index out of range") ; } /* PRINTVALUE (Lx [psx + ii + jj*nsrow]) ; */ print_value (print, xtype, Lx, NULL, psx + ii + jj*nsrow, Common) ; P4 ("%s", "\n") ; ilast = i ; } } } else { /* just print the leading column of the supernode */ P4 (" col "ID"\n", k1) ; for (jj = 0 ; jj < nscol ; jj++) { ETC (s == nsuper-1 && jj >= nscol-3, count, -1) ; j = k1 + jj ; i = Ls [psi + jj] ; P4 (" "I8"", i) ; if (i != j) { ERR ("row index invalid") ; } P4 ("%s", "\n") ; } ilast = j ; for (ii = nscol ; ii < nsrow ; ii++) { ETC_DISABLE (count) ; i = Ls [psi + ii] ; P4 (" "I8"", i) ; if (i <= ilast || i > n) { ERR ("row index out of range") ; } P4 ("%s", "\n") ; ilast = i ; } } } } } /* factor is valid */ P3 (" nz "ID"", lnz) ; P3 ("%s", " OK\n") ; P4 ("%s", "\n") ; return (TRUE) ; } int CHOLMOD(check_factor) ( /* ---- input ---- */ cholmod_factor *L, /* factor to check */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_factor (NULL, 0, NULL, L, Common)) ; } int CHOLMOD(print_factor) ( /* ---- input ---- */ cholmod_factor *L, /* factor to print */ char *name, /* printed name of factor */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_factor (NULL, Common->print, name, L, Common)) ; } /* ========================================================================== */ /* === cholmod_check_triplet ================================================ */ /* ========================================================================== */ /* Ensure a triplet matrix is valid, and optionally print it. */ static int check_triplet ( Int print, char *name, cholmod_triplet *T, cholmod_common *Common ) { double *Tx, *Tz ; Int *Ti, *Tj ; Int i, j, p, nrow, ncol, nzmax, nz, xtype, init_print, count ; char *type = "triplet" ; /* ---------------------------------------------------------------------- */ /* print header information */ /* ---------------------------------------------------------------------- */ P4 ("%s", "\n") ; P3 ("%s", "CHOLMOD triplet: ") ; if (name != NULL) { P3 ("%s: ", name) ; } if (T == NULL) { ERR ("null") ; } nrow = T->nrow ; ncol = T->ncol ; nzmax = T->nzmax ; nz = T->nnz ; Ti = T->i ; Tj = T->j ; Tx = T->x ; Tz = T->z ; xtype = T->xtype ; P3 (" "ID"", nrow) ; P3 ("-by-"ID", ", ncol) ; P3 ("nz "ID",", nz) ; if (T->stype > 0) { P3 ("%s", " upper.") ; } else if (T->stype < 0) { P3 ("%s", " lower.") ; } else { P3 ("%s", " up/lo.") ; } P4 ("\n nzmax "ID", ", nzmax) ; if (nz > nzmax) { ERR ("nzmax too small") ; } switch (T->itype) { case CHOLMOD_INT: P4 ("%s", "\n scalar types: int, ") ; break ; case CHOLMOD_INTLONG: ERR ("mixed int/UF_long type unsupported") ; case CHOLMOD_LONG: P4 ("%s", "\n scalar types: UF_long, ") ; break ; default: ERR ("unknown itype") ; } switch (T->xtype) { case CHOLMOD_PATTERN: P4 ("%s", "pattern") ; break ; case CHOLMOD_REAL: P4 ("%s", "real") ; break ; case CHOLMOD_COMPLEX: P4 ("%s", "complex") ; break ; case CHOLMOD_ZOMPLEX: P4 ("%s", "zomplex") ; break ; default: ERR ("unknown xtype") ; } switch (T->dtype) { case CHOLMOD_DOUBLE: P4 ("%s", ", double\n") ; break ; case CHOLMOD_SINGLE: ERR ("single unsupported") ; default: ERR ("unknown dtype") ; } if (T->itype != ITYPE || T->dtype != DTYPE) { ERR ("integer and real type must match routine") ; } if (T->stype && nrow != ncol) { ERR ("symmetric but not square") ; } /* check for existence of Ti, Tj, Tx arrays */ if (Tj == NULL) { ERR ("j array not present") ; } if (Ti == NULL) { ERR ("i array not present") ; } if (xtype != CHOLMOD_PATTERN && Tx == NULL) { ERR ("x array not present") ; } if (xtype == CHOLMOD_ZOMPLEX && Tz == NULL) { ERR ("z array not present") ; } /* ---------------------------------------------------------------------- */ /* check and print each entry */ /* ---------------------------------------------------------------------- */ init_print = print ; ETC_START (count, 8) ; for (p = 0 ; p < nz ; p++) { ETC (p >= nz-4, count, -1) ; i = Ti [p] ; P4 (" "I8":", p) ; P4 (" "I_8"", i) ; if (i < 0 || i >= nrow) { ERR ("row index out of range") ; } j = Tj [p] ; P4 (" "I_8"", j) ; if (j < 0 || j >= ncol) { ERR ("column index out of range") ; } print_value (print, xtype, Tx, Tz, p, Common) ; P4 ("%s", "\n") ; } /* triplet matrix is valid */ P3 ("%s", " OK\n") ; P4 ("%s", "\n") ; return (TRUE) ; } int CHOLMOD(check_triplet) ( /* ---- input ---- */ cholmod_triplet *T, /* triplet matrix to check */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_triplet (0, NULL, T, Common)) ; } int CHOLMOD(print_triplet) ( /* ---- input ---- */ cholmod_triplet *T, /* triplet matrix to print */ char *name, /* printed name of triplet matrix */ /* --------------- */ cholmod_common *Common ) { RETURN_IF_NULL_COMMON (FALSE) ; Common->status = CHOLMOD_OK ; return (check_triplet (Common->print, name, T, Common)) ; } /* ========================================================================== */ /* === CHOLMOD debugging routines =========================================== */ /* ========================================================================== */ #ifndef NDEBUG /* The global variables present only when debugging enabled. */ int CHOLMOD(dump) = 0 ; int CHOLMOD(dump_malloc) = -1 ; /* workspace: no debug routines use workspace in Common */ /* ========================================================================== */ /* === cholmod_dump_init ==================================================== */ /* ========================================================================== */ void CHOLMOD(dump_init) (char *s, cholmod_common *Common) { FILE *f ; f = fopen ("debug", "r") ; if (f == NULL) { CHOLMOD(dump) = 0 ; } else { fscanf (f, "%d", &CHOLMOD(dump)) ; fclose (f) ; } PRINT1 (("%s: cholmod_dump_init, D = %d\n", s, CHOLMOD(dump))) ; } /* ========================================================================== */ /* === cholmod_dump_sparse ================================================== */ /* ========================================================================== */ UF_long CHOLMOD(dump_sparse) /* returns nnz (diag (A)) or EMPTY if error */ ( cholmod_sparse *A, char *name, cholmod_common *Common ) { Int *Wi ; UF_long nnzdiag ; Int ok ; if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return (0) ; } RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; Wi = malloc (MAX (1, A->nrow) * sizeof (Int)) ; ok = check_sparse (Wi, CHOLMOD(dump), name, A, &nnzdiag, Common) ; if (Wi != NULL) free (Wi) ; return (ok ? nnzdiag : EMPTY) ; } /* ========================================================================== */ /* === cholmod_dump_factor ================================================== */ /* ========================================================================== */ int CHOLMOD(dump_factor) ( cholmod_factor *L, char *name, cholmod_common *Common ) { Int *Wi ; int ok ; if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return (TRUE) ; } RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; Wi = malloc (MAX (1, L->n) * sizeof (Int)) ; ok = check_factor (Wi, CHOLMOD(dump), name, L, Common) ; if (Wi != NULL) free (Wi) ; return (ok) ; } /* ========================================================================== */ /* === cholmod_dump_perm ==================================================== */ /* ========================================================================== */ int CHOLMOD(dump_perm) ( Int *Perm, size_t len, size_t n, char *name, cholmod_common *Common ) { Int *Wi ; int ok ; if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return (TRUE) ; } RETURN_IF_NULL_COMMON (FALSE) ; Wi = malloc (MAX (1, n) * sizeof (Int)) ; ok = check_perm (Wi, CHOLMOD(dump), name, Perm, len, n,Common) ; if (Wi != NULL) free (Wi) ; return (ok) ; } /* ========================================================================== */ /* === cholmod_dump_dense =================================================== */ /* ========================================================================== */ int CHOLMOD(dump_dense) ( cholmod_dense *X, char *name, cholmod_common *Common ) { if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return (TRUE) ; } RETURN_IF_NULL_COMMON (FALSE) ; return (check_dense (CHOLMOD(dump), name, X, Common)) ; } /* ========================================================================== */ /* === cholmod_dump_triplet ================================================= */ /* ========================================================================== */ int CHOLMOD(dump_triplet) ( cholmod_triplet *T, char *name, cholmod_common *Common ) { if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return (TRUE) ; } RETURN_IF_NULL_COMMON (FALSE) ; return (check_triplet (CHOLMOD(dump), name, T, Common)) ; } /* ========================================================================== */ /* === cholmod_dump_subset ================================================== */ /* ========================================================================== */ int CHOLMOD(dump_subset) ( Int *S, size_t len, size_t n, char *name, cholmod_common *Common ) { if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return (TRUE) ; } RETURN_IF_NULL_COMMON (FALSE) ; return (check_subset (S, len, n, CHOLMOD(dump), name, Common)) ; } /* ========================================================================== */ /* === cholmod_dump_parent ================================================== */ /* ========================================================================== */ int CHOLMOD(dump_parent) ( Int *Parent, size_t n, char *name, cholmod_common *Common ) { if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return (TRUE) ; } RETURN_IF_NULL_COMMON (FALSE) ; return (check_parent (Parent, n, CHOLMOD(dump), name, Common)) ; } /* ========================================================================== */ /* === cholmod_dump_real ==================================================== */ /* ========================================================================== */ void CHOLMOD(dump_real) ( char *name, Real *X, UF_long nrow, UF_long ncol, int lower, int xentry, cholmod_common *Common ) { /* dump an nrow-by-ncol real dense matrix */ UF_long i, j ; double x, z ; if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return ; } PRINT1 (("%s: dump_real, nrow: %ld ncol: %ld lower: %d\n", name, nrow, ncol, lower)) ; for (j = 0 ; j < ncol ; j++) { PRINT2 ((" col %ld\n", j)) ; for (i = 0 ; i < nrow ; i++) { /* X is stored in column-major form */ if (lower && i < j) { PRINT2 ((" %5ld: -", i)) ; } else { x = *X ; PRINT2 ((" %5ld: %e", i, x)) ; if (xentry == 2) { z = *(X+1) ; PRINT2 ((", %e", z)) ; } } PRINT2 (("\n")) ; X += xentry ; } } } /* ========================================================================== */ /* === cholmod_dump_super =================================================== */ /* ========================================================================== */ void CHOLMOD(dump_super) ( UF_long s, Int *Super, Int *Lpi, Int *Ls, Int *Lpx, double *Lx, int xentry, cholmod_common *Common ) { Int k1, k2, do_values, psi, psx, nsrow, nscol, psend, ilast, p, i ; if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return ; } k1 = Super [s] ; k2 = Super [s+1] ; nscol = k2 - k1 ; do_values = (Lpx != NULL) && (Lx != NULL) ; psi = Lpi [s] ; psend = Lpi [s+1] ; nsrow = psend - psi ; PRINT1 (("\nSuper %ld, columns "ID" to "ID", "ID" rows "ID" cols\n", s, k1, k2-1, nsrow, nscol)) ; ilast = -1 ; for (p = psi ; p < psend ; p++) { i = Ls [p] ; PRINT2 ((" "ID" : p-psi "ID"\n", i, p-psi)) ; ASSERT (IMPLIES (p-psi < nscol, i == k1 + (p-psi))) ; if (p-psi == nscol-1) PRINT2 (("------\n")) ; ASSERT (i > ilast) ; ilast = i ; } if (do_values) { psx = Lpx [s] ; CHOLMOD(dump_real) ("Supernode", Lx + xentry*psx, nsrow, nscol, TRUE, xentry, Common) ; } } /* ========================================================================== */ /* === cholmod_dump_mem ===================================================== */ /* ========================================================================== */ int CHOLMOD(dump_mem) (char *where, UF_long should, cholmod_common *Common) { UF_long diff = should - Common->memory_inuse ; if (diff != 0) { PRINT0 (("mem: %-15s peak %10g inuse %10g should %10g\n", where, (double) Common->memory_usage, (double) Common->memory_inuse, (double) should)) ; PRINT0 (("mem: %s diff %ld !\n", where, diff)) ; } return (diff == 0) ; } /* ========================================================================== */ /* === cholmod_dump_partition =============================================== */ /* ========================================================================== */ /* make sure we have a proper separator (for debugging only) * * workspace: none */ int CHOLMOD(dump_partition) ( UF_long n, Int *Cp, Int *Ci, Int *Cnw, Int *Part, UF_long sepsize, cholmod_common *Common ) { Int chek [3], which, ok, i, j, p ; PRINT1 (("bisect sepsize %ld\n", sepsize)) ; ok = TRUE ; chek [0] = 0 ; chek [1] = 0 ; chek [2] = 0 ; for (j = 0 ; j < n ; j++) { PRINT2 (("--------j "ID" in part "ID" nw "ID"\n", j, Part [j], Cnw[j])); which = Part [j] ; for (p = Cp [j] ; p < Cp [j+1] ; p++) { i = Ci [p] ; PRINT3 (("i "ID", part "ID"\n", i, Part [i])) ; if (which == 0) { if (Part [i] == 1) { PRINT0 (("Error! "ID" "ID"\n", i, j)) ; ok = FALSE ; } } else if (which == 1) { if (Part [i] == 0) { PRINT0 (("Error! "ID" "ID"\n", i, j)) ; ok = FALSE ; } } } if (which < 0 || which > 2) { PRINT0 (("Part out of range\n")) ; ok = FALSE ; } chek [which] += Cnw [j] ; } PRINT1 (("sepsize %ld check "ID" "ID" "ID"\n", sepsize, chek[0], chek[1],chek[2])); if (sepsize != chek[2]) { PRINT0 (("mismatch!\n")) ; ok = FALSE ; } return (ok) ; } /* ========================================================================== */ /* === cholmod_dump_work ==================================================== */ /* ========================================================================== */ int CHOLMOD(dump_work) (int flag, int head, UF_long wsize, cholmod_common *Common) { double *W ; Int *Flag, *Head ; Int k, nrow, mark ; if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return (TRUE) ; } RETURN_IF_NULL_COMMON (FALSE) ; nrow = Common->nrow ; Flag = Common->Flag ; Head = Common->Head ; W = Common->Xwork ; mark = Common->mark ; if (wsize < 0) { /* check all of Xwork */ wsize = Common->xworksize ; } else { /* check on the first wsize doubles in Xwork */ wsize = MIN (wsize, (Int) (Common->xworksize)) ; } if (flag) { for (k = 0 ; k < nrow ; k++) { if (Flag [k] >= mark) { PRINT0 (("Flag invalid, Flag ["ID"] = "ID", mark = "ID"\n", k, Flag [k], mark)) ; ASSERT (0) ; return (FALSE) ; } } } if (head) { for (k = 0 ; k < nrow ; k++) { if (Head [k] != EMPTY) { PRINT0 (("Head invalid, Head ["ID"] = "ID"\n", k, Head [k])) ; ASSERT (0) ; return (FALSE) ; } } } for (k = 0 ; k < wsize ; k++) { if (W [k] != 0.) { PRINT0 (("W invalid, W ["ID"] = %g\n", k, W [k])) ; ASSERT (0) ; return (FALSE) ; } } return (TRUE) ; } #endif #endif SuiteSparse/CHOLMOD/Check/cholmod_write.c0000644001170100242450000005122210634317313017057 0ustar davisfac/* ========================================================================== */ /* === Check/cholmod_write ================================================== */ /* ========================================================================== */ /* Write a matrix to a file in Matrix Market form. * * A can be sparse or full. * * If present and non-empty, A and Z must have the same dimension. Z contains * the explicit zero entries in the matrix (which MATLAB drops). The entries * of Z appear as explicit zeros in the output file. Z is optional. If it is * an empty matrix it is ignored. Z must be sparse or empty, if present. * It is ignored if A is full. * * filename is the name of the output file. comments is file whose * contents are include after the Matrix Market header and before the first * data line. Ignored if an empty string or not present. * * Except for the workspace used by cholmod_symmetry (ncol integers) for * the sparse case, these routines use no workspace at all. */ #ifndef NCHECK #include "cholmod_internal.h" #include "cholmod_check.h" #include "cholmod_matrixops.h" #include #include #define MMLEN 1024 #define MAXLINE MMLEN+6 /* ========================================================================== */ /* === include_comments ===================================================== */ /* ========================================================================== */ /* Read in the comments file, if it exists, and copy it to the Matrix Market * file. A "%" is prepended to each line. Returns TRUE if successful, FALSE * otherwise. */ static int include_comments (FILE *f, char *comments) { FILE *cf = NULL ; char buffer [MAXLINE] ; int ok = TRUE ; if (comments != NULL && comments [0] != '\0') { cf = fopen (comments, "r") ; if (cf == NULL) { return (FALSE) ; } while (ok && fgets (buffer, MAXLINE, cf) != NULL) { /* ensure the line is not too long */ buffer [MMLEN-1] = '\0' ; buffer [MMLEN-2] = '\n' ; ok = ok && (fprintf (f, "%%%s", buffer) > 0) ; } fclose (cf) ; } return (ok) ; } /* ========================================================================== */ /* === get_value ============================================================ */ /* ========================================================================== */ /* Get the pth value in the matrix. */ static void get_value ( double *Ax, /* real values, or real/imag. for CHOLMOD_COMPLEX type */ double *Az, /* imaginary values for CHOLMOD_ZOMPLEX type */ Int p, /* get the pth entry */ Int xtype, /* A->xtype: pattern, real, complex, or zomplex */ double *x, /* the real part */ double *z /* the imaginary part */ ) { switch (xtype) { case CHOLMOD_PATTERN: *x = 1 ; *z = 0 ; break ; case CHOLMOD_REAL: *x = Ax [p] ; *z = 0 ; break ; case CHOLMOD_COMPLEX: *x = Ax [2*p] ; *z = Ax [2*p+1] ; break ; case CHOLMOD_ZOMPLEX: *x = Ax [p] ; *z = Az [p] ; break ; } } /* ========================================================================== */ /* === print_value ========================================================== */ /* ========================================================================== */ /* Print a numeric value to the file, using the shortest format that ensures * the value is written precisely. Returns TRUE if successful, FALSE otherwise. */ static int print_value ( FILE *f, /* file to print to */ double x, /* value to print */ Int is_integer /* TRUE if printing as an integer */ ) { double y ; char s [MAXLINE], *p ; Int i, dest = 0, src = 0 ; int width, ok ; if (is_integer) { i = (Int) x ; ok = (fprintf (f, ID, i) > 0) ; return (ok) ; } /* ---------------------------------------------------------------------- */ /* handle Inf and NaN */ /* ---------------------------------------------------------------------- */ /* change -inf to -HUGE_DOUBLE, and change +inf and nan to +HUGE_DOUBLE */ if (CHOLMOD_IS_NAN (x) || x >= HUGE_DOUBLE) { x = HUGE_DOUBLE ; } else if (x <= -HUGE_DOUBLE) { x = -HUGE_DOUBLE ; } /* ---------------------------------------------------------------------- */ /* find the smallest acceptable precision */ /* ---------------------------------------------------------------------- */ for (width = 6 ; width < 20 ; width++) { sprintf (s, "%.*g", width, x) ; sscanf (s, "%lg", &y) ; if (x == y) break ; } /* ---------------------------------------------------------------------- */ /* shorten the string */ /* ---------------------------------------------------------------------- */ /* change "e+0" to "e", change "e+" to "e", and change "e-0" to "e-" */ for (i = 0 ; i < MAXLINE && s [i] != '\0' ; i++) { if (s [i] == 'e') { if (s [i+1] == '+') { dest = i+1 ; if (s [i+2] == '0') { /* delete characters s[i+1] and s[i+2] */ src = i+3 ; } else { /* delete characters s[i+1] */ src = i+2 ; } } else if (s [i+1] == '-') { dest = i+2 ; if (s [i+2] == '0') { /* delete character s[i+2] */ src = i+3 ; } else { /* no change */ break ; } } while (s [src] != '\0') { s [dest++] = s [src++] ; } s [dest] = '\0' ; break ; } } /* delete the leading "0" if present and not necessary */ p = s ; s [MAXLINE-1] = '\0' ; i = strlen (s) ; if (i > 2 && s [0] == '0' && s [1] == '.') { /* change "0.x" to ".x" */ p = s + 1 ; } else if (i > 3 && s [0] == '-' && s [1] == '0' && s [2] == '.') { /* change "-0.x" to "-.x" */ s [1] = '-' ; p = s + 1 ; } #if 0 /* double-check */ i = sscanf (p, "%lg", &z) ; if (i != 1 || y != z) { /* oops! something went wrong in the "e+0" edit, above. */ /* this "cannot" happen */ sprintf (s, "%.*g", width, x) ; p = s ; } #endif /* ---------------------------------------------------------------------- */ /* print the value to the file */ /* ---------------------------------------------------------------------- */ ok = (fprintf (f, "%s", p) > 0) ; return (ok) ; } /* ========================================================================== */ /* === print_triplet ======================================================== */ /* ========================================================================== */ /* Print a triplet, converting it to one-based. Returns TRUE if successful, * FALSE otherwise. */ static int print_triplet ( FILE *f, /* file to print to */ Int is_binary, /* TRUE if file is "pattern" */ Int is_complex, /* TRUE if file is "complex" */ Int is_integer, /* TRUE if file is "integer" */ Int i, /* row index (zero-based) */ Int j, /* column index (zero-based) */ double x, /* real part */ double z /* imaginary part */ ) { int ok ; ok = (fprintf (f, ID " " ID, 1+i, 1+j) > 0) ; if (!is_binary) { fprintf (f, " ") ; ok = ok && print_value (f, x, is_integer) ; if (is_complex) { fprintf (f, " ") ; ok = ok && print_value (f, z, is_integer) ; } } ok = ok && (fprintf (f, "\n") > 0) ; return (ok) ; } /* ========================================================================== */ /* === ntriplets ============================================================ */ /* ========================================================================== */ /* Compute the number of triplets that will be printed to the file * from the matrix A. */ static Int ntriplets ( cholmod_sparse *A, /* matrix that will be printed */ Int is_sym /* TRUE if the file is symmetric (lower part only)*/ ) { Int *Ap, *Ai, *Anz, packed, i, j, p, pend, ncol, stype, nz = 0 ; if (A == NULL) { /* the Z matrix is NULL */ return (0) ; } stype = A->stype ; Ap = A->p ; Ai = A->i ; Anz = A->nz ; packed = A->packed ; ncol = A->ncol ; for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? Ap [j+1] : p + Anz [j] ; for ( ; p < pend ; p++) { i = Ai [p] ; if ((stype < 0 && i >= j) || (stype == 0 && (i >= j || !is_sym))) { /* CHOLMOD matrix is symmetric-lower (and so is the file); * or CHOLMOD matrix is unsymmetric and either A(i,j) is in * the lower part or the file is unsymmetric. */ nz++ ; } else if (stype > 0 && i <= j) { /* CHOLMOD matrix is symmetric-upper, but the file is * symmetric-lower. Need to transpose the entry. */ nz++ ; } } } return (nz) ; } /* ========================================================================== */ /* === cholmod_write_sparse ================================================= */ /* ========================================================================== */ /* Write a sparse matrix to a file in Matrix Market format. Optionally include * comments, and print explicit zero entries given by the pattern of the Z * matrix. If not NULL, the Z matrix must have the same dimensions and stype * as A. * * Returns the symmetry in which the matrix was printed (1 to 7, see the * CHOLMOD_MM_* codes in CHOLMOD/Include/cholmod_core.h), or -1 on failure. * * If A and Z are sorted on input, and either unsymmetric (stype = 0) or * symmetric-lower (stype < 0), and if A and Z do not overlap, then the triplets * are sorted, first by column and then by row index within each column, with * no duplicate entries. If all the above holds except stype > 0, then the * triplets are sorted by row first and then column. */ int CHOLMOD(write_sparse) ( /* ---- input ---- */ FILE *f, /* file to write to, must already be open */ cholmod_sparse *A, /* matrix to print */ cholmod_sparse *Z, /* optional matrix with pattern of explicit zeros */ char *comments, /* optional filename of comments to include */ /* --------------- */ cholmod_common *Common ) { double x = 0, z = 0 ; double *Ax, *Az ; Int *Ap, *Ai, *Anz, *Zp, *Zi, *Znz ; Int nrow, ncol, is_complex, symmetry, i, j, q, iz, p, nz, is_binary, stype, is_integer, asym, is_sym, xtype, apacked, zpacked, pend, qend, zsym ; int ok ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (f, EMPTY) ; RETURN_IF_NULL (A, EMPTY) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ; if (Z != NULL && (Z->nrow == 0 || Z->ncol == 0)) { /* Z is non-NULL but empty, so treat it as a NULL matrix */ Z = NULL ; } if (Z != NULL) { RETURN_IF_XTYPE_INVALID (Z, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ; if (Z->nrow != A->nrow || Z->ncol != A->ncol || Z->stype != A->stype) { ERROR (CHOLMOD_INVALID, "dimension or type of A and Z mismatch") ; return (EMPTY) ; } } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* get the A matrix */ /* ---------------------------------------------------------------------- */ Ap = A->p ; Ai = A->i ; Ax = A->x ; Az = A->z ; Anz = A->nz ; nrow = A->nrow ; ncol = A->ncol ; xtype = A->xtype ; apacked = A->packed ; if (xtype == CHOLMOD_PATTERN) { /* a CHOLMOD pattern matrix is printed as "pattern" in the file */ is_binary = TRUE ; is_integer = FALSE ; is_complex = FALSE ; } else if (xtype == CHOLMOD_REAL) { /* determine if a real matrix is in fact binary or integer */ is_binary = TRUE ; is_integer = TRUE ; is_complex = FALSE ; for (j = 0 ; (is_binary || is_integer) && j < ncol ; j++) { p = Ap [j] ; pend = (apacked) ? Ap [j+1] : p + Anz [j] ; for ( ; (is_binary || is_integer) && p < pend ; p++) { x = Ax [p] ; if (x != 1) { is_binary = FALSE ; } /* convert to Int and then back to double */ i = (Int) x ; z = (double) i ; if (z != x) { is_integer = FALSE ; } } } } else { /* a CHOLMOD complex matrix is printed as "complex" in the file */ is_binary = FALSE ; is_integer = FALSE ; is_complex = TRUE ; } /* ---------------------------------------------------------------------- */ /* get the Z matrix (only consider the pattern) */ /* ---------------------------------------------------------------------- */ Zp = NULL ; Zi = NULL ; Znz = NULL ; zpacked = TRUE ; if (Z != NULL) { Zp = Z->p ; Zi = Z->i ; Znz = Z->nz ; zpacked = Z->packed ; } /* ---------------------------------------------------------------------- */ /* determine the symmetry of A and Z */ /* ---------------------------------------------------------------------- */ stype = A->stype ; if (A->nrow != A->ncol) { asym = CHOLMOD_MM_RECTANGULAR ; } else if (stype != 0) { /* CHOLMOD's A and Z matrices have a symmetric (and matching) stype. * Note that the diagonal is not checked. */ asym = is_complex ? CHOLMOD_MM_HERMITIAN : CHOLMOD_MM_SYMMETRIC ; } else if (!A->sorted) { /* A is in unsymmetric storage, but unsorted */ asym = CHOLMOD_MM_UNSYMMETRIC ; } else { /* CHOLMOD's stype is zero (stored in unsymmetric form) */ asym = EMPTY ; zsym = EMPTY ; #ifndef NMATRIXOPS /* determine if the matrices are in fact symmetric or Hermitian */ asym = CHOLMOD(symmetry) (A, 1, NULL, NULL, NULL, NULL, Common) ; zsym = (Z == NULL) ? 999 : CHOLMOD(symmetry) (Z, 1, NULL, NULL, NULL, NULL, Common) ; #endif if (asym == EMPTY || zsym <= CHOLMOD_MM_UNSYMMETRIC) { /* not computed, out of memory, or Z is unsymmetric */ asym = CHOLMOD_MM_UNSYMMETRIC ; } } /* ---------------------------------------------------------------------- */ /* write the Matrix Market header */ /* ---------------------------------------------------------------------- */ ok = fprintf (f, "%%%%MatrixMarket matrix coordinate") > 0 ; if (is_complex) { ok = ok && (fprintf (f, " complex") > 0) ; } else if (is_binary) { ok = ok && (fprintf (f, " pattern") > 0) ; } else if (is_integer) { ok = ok && (fprintf (f, " integer") > 0) ; } else { ok = ok && (fprintf (f, " real") > 0) ; } is_sym = FALSE ; switch (asym) { case CHOLMOD_MM_RECTANGULAR: case CHOLMOD_MM_UNSYMMETRIC: /* A is rectangular or unsymmetric */ ok = ok && (fprintf (f, " general\n") > 0) ; is_sym = FALSE ; symmetry = CHOLMOD_MM_UNSYMMETRIC ; break ; case CHOLMOD_MM_SYMMETRIC: case CHOLMOD_MM_SYMMETRIC_POSDIAG: /* A is symmetric */ ok = ok && (fprintf (f, " symmetric\n") > 0) ; is_sym = TRUE ; symmetry = CHOLMOD_MM_SYMMETRIC ; break ; case CHOLMOD_MM_HERMITIAN: case CHOLMOD_MM_HERMITIAN_POSDIAG: /* A is Hermitian */ ok = ok && (fprintf (f, " Hermitian\n") > 0) ; is_sym = TRUE ; symmetry = CHOLMOD_MM_HERMITIAN ; break ; case CHOLMOD_MM_SKEW_SYMMETRIC: /* A is skew symmetric */ ok = ok && (fprintf (f, " skew-symmetric\n") > 0) ; is_sym = TRUE ; symmetry = CHOLMOD_MM_SKEW_SYMMETRIC ; break ; } /* ---------------------------------------------------------------------- */ /* include the comments if present */ /* ---------------------------------------------------------------------- */ ok = ok && include_comments (f, comments) ; /* ---------------------------------------------------------------------- */ /* write a sparse matrix (A and Z) */ /* ---------------------------------------------------------------------- */ nz = ntriplets (A, is_sym) + ntriplets (Z, is_sym) ; /* write the first data line, with nrow, ncol, and # of triplets */ ok = ok && (fprintf (f, ID " " ID " " ID "\n", nrow, ncol, nz) > 0) ; for (j = 0 ; ok && j < ncol ; j++) { /* merge column of A and Z */ p = Ap [j] ; pend = (apacked) ? Ap [j+1] : p + Anz [j] ; q = (Z == NULL) ? 0 : Zp [j] ; qend = (Z == NULL) ? 0 : ((zpacked) ? Zp [j+1] : q + Znz [j]) ; while (ok) { /* get the next row index from A and Z */ i = (p < pend) ? Ai [p] : (nrow+1) ; iz = (q < qend) ? Zi [q] : (nrow+2) ; if (i <= iz) { /* get A(i,j), or quit if both A and Z are exhausted */ if (i == nrow+1) break ; get_value (Ax, Az, p, xtype, &x, &z) ; p++ ; } else { /* get Z(i,j) */ i = iz ; x = 0 ; z = 0 ; q++ ; } if ((stype < 0 && i >= j) || (stype == 0 && (i >= j || !is_sym))) { /* CHOLMOD matrix is symmetric-lower (and so is the file); * or CHOLMOD matrix is unsymmetric and either A(i,j) is in * the lower part or the file is unsymmetric. */ ok = ok && print_triplet (f, is_binary, is_complex, is_integer, i,j, x,z) ; } else if (stype > 0 && i <= j) { /* CHOLMOD matrix is symmetric-upper, but the file is * symmetric-lower. Need to transpose the entry. If the * matrix is real, the complex part is ignored. If the matrix * is complex, it Hermitian. */ ASSERT (IMPLIES (is_complex, asym == CHOLMOD_MM_HERMITIAN)) ; if (z != 0) { z = -z ; } ok = ok && print_triplet (f, is_binary, is_complex, is_integer, j,i, x,z) ; } } } if (!ok) { ERROR (CHOLMOD_INVALID, "error reading/writing file") ; return (EMPTY) ; } return (asym) ; } /* ========================================================================== */ /* === cholmod_write_dense ================================================== */ /* ========================================================================== */ /* Write a dense matrix to a file in Matrix Market format. Optionally include * comments. Returns > 0 if successful, -1 otherwise (1 if rectangular, 2 if * square). Future versions may return 1 to 7 on success (a CHOLMOD_MM_* code, * just as cholmod_write_sparse does). * * A dense matrix is written in "general" format; symmetric formats in the * Matrix Market standard are not exploited. */ int CHOLMOD(write_dense) ( /* ---- input ---- */ FILE *f, /* file to write to, must already be open */ cholmod_dense *X, /* matrix to print */ char *comments, /* optional filename of comments to include */ /* --------------- */ cholmod_common *Common ) { double x = 0, z = 0 ; double *Xx, *Xz ; Int nrow, ncol, is_complex, i, j, xtype, p ; int ok ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (f, EMPTY) ; RETURN_IF_NULL (X, EMPTY) ; RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, EMPTY) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* get the X matrix */ /* ---------------------------------------------------------------------- */ Xx = X->x ; Xz = X->z ; nrow = X->nrow ; ncol = X->ncol ; xtype = X->xtype ; is_complex = (xtype == CHOLMOD_COMPLEX) || (xtype == CHOLMOD_ZOMPLEX) ; /* ---------------------------------------------------------------------- */ /* write the Matrix Market header */ /* ---------------------------------------------------------------------- */ ok = (fprintf (f, "%%%%MatrixMarket matrix array") > 0) ; if (is_complex) { ok = ok && (fprintf (f, " complex general\n") > 0) ; } else { ok = ok && (fprintf (f, " real general\n") > 0) ; } /* ---------------------------------------------------------------------- */ /* include the comments if present */ /* ---------------------------------------------------------------------- */ ok = ok && include_comments (f, comments) ; /* ---------------------------------------------------------------------- */ /* write a dense matrix */ /* ---------------------------------------------------------------------- */ /* write the first data line, with nrow and ncol */ ok = ok && (fprintf (f, ID " " ID "\n", nrow, ncol) > 0) ; Xx = X->x ; Xz = X->z ; for (j = 0 ; ok && j < ncol ; j++) { for (i = 0 ; ok && i < nrow ; i++) { p = i + j*nrow ; get_value (Xx, Xz, p, xtype, &x, &z) ; ok = ok && print_value (f, x, FALSE) ; if (is_complex) { ok = ok && (fprintf (f, " ") > 0) ; ok = ok && print_value (f, z, FALSE) ; } ok = ok && (fprintf (f, "\n") > 0) ; } } if (!ok) { ERROR (CHOLMOD_INVALID, "error reading/writing file") ; return (EMPTY) ; } return ((nrow == ncol) ? CHOLMOD_MM_UNSYMMETRIC : CHOLMOD_MM_RECTANGULAR) ; } #endif SuiteSparse/CHOLMOD/Check/License.txt0000644001170100242450000000205710540000255016167 0ustar davisfacCHOLMOD/Check Module. Copyright (C) 2005-2006, Timothy A. Davis CHOLMOD is also available under other licenses; contact authors for details. http://www.cise.ufl.edu/research/sparse Note that this license is for the CHOLMOD/Check module only. All CHOLMOD modules are licensed separately. -------------------------------------------------------------------------------- This Module is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This Module is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA SuiteSparse/CHOLMOD/Check/cholmod_read.c0000644001170100242450000011745410564125252016653 0ustar davisfac/* ========================================================================== */ /* === Check/cholmod_read =================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Check Module. Copyright (C) 2005-2006, Timothy A. Davis. * The CHOLMOD/Check Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Read a sparse matrix in triplet or dense form. A triplet matrix can be * returned as compressed-column sparse matrix. The file format is compatible * with all variations of the Matrix Market "coordinate" and "array" format * (http://www.nist.gov/MatrixMarket). The format supported by these routines * also allow other formats, where the Matrix Market header is optional. * * Although the Matrix Market header is optional, I recommend that users stick * with the strict Matrix Market format. The optional format appears here to * support the reading of symmetric matrices stored with just their upper * triangular parts present, for testing and development of the A->stype > 0 * format in CHOLMOD. That format is not included in the Matrix Market format. * * If the first line of the file starts with %%MatrixMarket, then it is * interpretted as a file in Matrix Market format. This line must have * the following format: * * %%MatrixMarket matrix * * is one of: coordinate or array. The former is a sparse matrix in * triplet form. The latter is a dense matrix in column-major form. * * is one of: real, complex, pattern, or integer. * The functions here convert the "integer" and "pattern" types to real. * * is one of: general, hermitian, symmetric, or skew-symmetric * * The strings are case-insensitive. Only the first character is * significant (or the first two for skew-symmetric). * * is ignored for all matrices; the actual type (real, complex, * or pattern) is inferred from the number of tokens in each line of the * file. For a "coordinate" matrix: 2: pattern, 3: real, 4: complex; for * a dense "array" matrix: 1: real, 2: complex. This is compatible with * the Matrix Market format, since pattern matrices must have two tokens * per line, real matrices must have 3, and complex matrices must have 4. * A storage of "general" implies an stype of zero (see below). * "symmetric" and "hermitian" imply an stype of -1. Skew-symmetric and * complex symmetric matrices are always returned with both upper and lower * triangular parts present, with an stype of zero, since CHOLMOD does not * have a method for representing skew-symmetric and complex symmetric * matrices. Real symmetric and complex Hermitian matrices may optionally * be returned with both parts present. * * Any other lines starting with "%" are treated as comments, and are ignored. * Blank lines are ignored. The Matrix Market header is optional in this * routine (it is not optional in the Matrix Market format). * * Note that complex matrices are always returned in CHOLMOD_COMPLEX format, * not CHOLMOD_ZOMPLEX. * * ----------------------------------------------------------------------------- * Triplet matrices: * ----------------------------------------------------------------------------- * * The first data line of a triplet matrix contains 3 or 4 integers: * * nrow ncol nnz stype * * where stype is optional (stype does not appear in the Matrix Market format). * The matrix is nrow-by-ncol. The following nnz lines (excluding comments * and blank lines) each contain a single entry. Duplicates are permitted, * and are summed in the output matrix. * * The stype is first derived from the Matrix Market header. If the stype * appears as the fourth integer in the first data line, it is determined from * that line. * * If stype is present, it denotes the storage format for the matrix. * stype = 0 denotes an unsymmetric matrix (same as Matrix Market "general"). * stype = -1 denotes a real symmetric or complex Hermitian matrix whose lower * triangular entries are stored. Entries may be present in the upper * triangular part, but these are ignored (same as Matrix Market * "real symmetric" and "complex Hermitian"). * stype = 1 denotes a real symmetric or complex Hermitian matrix whose upper * triangular entries are stored. Entries may be present in the lower * triangular part, but these are ignored. This option is not present * in the Matrix Market format. * * If stype is not present (no Matrix Market header and not in the first data * line) it is inferred from the rest of the data. If the matrix is * rectangular, or has entries in both the upper and lower triangular parts, * then it is assumed to be unsymmetric (stype=0). If only entries in the * lower triangular part are present, the matrix is assumed to have stype = -1. * If only entries in the upper triangular part are present, the matrix is * assumed to have stype = 1. * * After the first data line (with nrow, ncol, nnz, and optionally stype), * each nonzero consists of one line with 2, 3, or 4 entries. All lines must * have the same number of entries. The first two entries are the row and * column indices of the nonzero. If 3 entries are present, the 3rd entry is * the numerical value, and the matrix is real. If 4 entries are present, * the 3rd and 4th entries in the line are the real and imaginary parts of * a complex value. * * The matrix can be either 0-based or 1-based. It is first assumed to be * one-based (all matrices in the Matrix Market are one-based), with row indices * in the range 1 to ncol and column indices in the range 1 to nrow. If a row * or column index of zero is found, the matrix is assumed to be zero-based * (with row indices in the range 0 to ncol-1 and column indices in the range 0 * to nrow-1). * * If Common->prefer_binary is set to its default value of FALSE, then * for symmetric pattern-only matrices, the kth diagonal (if present) is set to * one plus the degree of the row/column k, and the off-diagonal entries are set * to -1. A symmetric pattern-only matrix with a zero-free diagonal is thus * converted into a symmetric positive definite matrix. All entries are set to * one for an unsymmetric pattern-only matrix. This differs from the * Matrix Market format (A = mmread ('file') returns a binary pattern for A for * symmetric pattern-only matrices). If Common->prefer_binary is TRUE, then * this function returns a binary matrix (just like mmread('file')). * * ----------------------------------------------------------------------------- * Dense matrices: * ----------------------------------------------------------------------------- * * A dense matrix is specified by the Matrix Market "array" format. The * Matrix Market header is optional; if not present, the matrix is assumed to * be in the Matrix Market "general" format. The first data line contains just * two integers: * * nrow ncol * * The can be real, integer, or complex (not pattern). These functions * convert an integer type to real. The entries in the matrix are stored in * column-major format, with one line per entry. Two entries are present in * each line for complex matrices, one for real and integer matrices. In * rectangular and unsymmetric matrices, all entries are present. For real * symmetric or complex Hermitian matrices, only entries in the lower triangular * part appear. For skew-symmetric matrices, only entries in the strictly * lower triangular part appear. * * Since CHOLMOD does not have a data structure for presenting dense symmetric/ * Hermitian matrices, these functions always return a dense matrix in its * general form, with both upper and lower parts present. */ #ifndef NCHECK #include "cholmod_internal.h" #include "cholmod_check.h" #include #include /* The MatrixMarket format specificies a maximum line length of 1024 */ #define MAXLINE 1030 /* ========================================================================== */ /* === get_line ============================================================= */ /* ========================================================================== */ /* Read one line of the file, return TRUE if successful, FALSE if EOF. */ static int get_line (FILE *f, char *buf) { buf [0] = '\0' ; buf [1] = '\0' ; buf [MAXLINE] = '\0' ; return (fgets (buf, MAXLINE, f) != NULL) ; } /* ========================================================================== */ /* === fix_inf ============================================================== */ /* ========================================================================== */ /* Replace huge values with +/- Inf's, since scanf and printf don't deal * with Inf's properly. */ static double fix_inf (double x) { if ((x >= HUGE_DOUBLE) || (x <= -HUGE_DOUBLE)) { /* treat this as +/- Inf (assume 2*x leads to overflow) */ x = 2*x ; } return (x) ; } /* ========================================================================== */ /* === is_blank_line ======================================================== */ /* ========================================================================== */ /* TRUE if s is a blank line or comment, FALSE otherwise */ static int is_blank_line ( char *s ) { int c, k ; if (s [0] == '%') { /* a comment line */ return (TRUE) ; } for (k = 0 ; k <= MAXLINE ; k++) { c = s [k] ; if (c == '\0') { /* end of line */ break ; } if (!isspace (c)) { /* non-space character */ return (FALSE) ; } } return (TRUE) ; } /* ========================================================================== */ /* === read_header ========================================================== */ /* ========================================================================== */ /* Read the header. This consists of zero or more comment lines (blank, or * starting with a "%" in the first column), followed by a single data line * containing up to four numerical values. * * The first line may optionally be a Matrix Market header line, of the form * * %%MatrixMarket matrix * * The first data line of a sparse matrix in triplet form consists of 3 or 4 * numerical values: * * nrow ncol nnz stype * * where stype is optional (it does not appear in the Matrix Market file * format). The first line of a dense matrix in column-major form consists of * two numerical values: * * nrow ncol * * The stype of the matrix is determine either from the Matrix Market header, * or (optionally) from the first data line. stypes of 0 to -3 directly * correlate with the Matrix Market format; stype = 1 is an extension to that * format. * * 999: unknown (will be inferred from the data) * 1: real symmetric or complex Hermitian with upper part stored * (not in the Matrix Market format) * 0: unsymmetric (same as Matrix Market "general") * -1: real symmetric or complex Hermitian, with lower part stored * (Matrix Market "real symmetric" or "complex hermitian") * -2: real or complex skew symmetric (lower part stored, can only be * specified by Matrix Market header) * -3: complex symmetric (lower part stored) * specified by Matrix Market header) * * The Matrix Market header is optional. If stype appears in the first data * line, it is determine by that data line. Otherwise, if the Matrix Market * header appears, stype is determined from that header. If stype does not * appear, it is set to "unknown" (999). */ #define STYPE_UNKNOWN 999 #define STYPE_SYMMETRIC_UPPER 1 #define STYPE_UNSYMMETRIC 0 #define STYPE_SYMMETRIC_LOWER -1 #define STYPE_SKEW_SYMMETRIC -2 #define STYPE_COMPLEX_SYMMETRIC_LOWER -3 static int read_header /* returns TRUE if successful, FALSE on error */ ( /* ---- input ---- */ FILE *f, /* file to read from */ /* ---- output --- */ char *buf, /* a character array of size MAXLINE+1 */ int *mtype, /* CHOLMOD_TRIPLET or CHOLMOD_DENSE */ size_t *nrow, /* number of rows in the matrix */ size_t *ncol, /* number of columns in the matrix */ size_t *nnz, /* number of entries in a triplet matrix (0 for dense)*/ int *stype /* stype (see above) */ ) { char *p ; int first = TRUE, got_mm_header = FALSE, c, c2, is_complex, nitems ; double l1, l2, l3, l4 ; *mtype = CHOLMOD_TRIPLET ; *nrow = 0 ; *ncol = 0 ; *nnz = 0 ; *stype = STYPE_UNKNOWN ; for ( ; ; ) { /* ------------------------------------------------------------------ */ /* get the next line */ /* ------------------------------------------------------------------ */ if (!get_line (f, buf)) { /* premature end of file */ return (FALSE) ; } if (first && (strncmp (buf, "%%MatrixMarket", 14) == 0)) { /* -------------------------------------------------------------- */ /* read a Matrix Market header */ /* -------------------------------------------------------------- */ got_mm_header = TRUE ; p = buf ; /* -------------------------------------------------------------- */ /* get "matrix" token */ /* -------------------------------------------------------------- */ while (*p && !isspace (*p)) p++ ; while (*p && isspace (*p)) p++ ; c = tolower (*p) ; if (c != 'm') { /* bad format */ return (FALSE) ; } /* -------------------------------------------------------------- */ /* get the fmt token ("coord" or "array") */ /* -------------------------------------------------------------- */ while (*p && !isspace (*p)) p++ ; while (*p && isspace (*p)) p++ ; c = tolower (*p) ; if (c == 'c') { *mtype = CHOLMOD_TRIPLET ; } else if (c == 'a') { *mtype = CHOLMOD_DENSE ; } else { /* bad format, neither "coordinate" nor "array" */ return (FALSE) ; } /* -------------------------------------------------------------- */ /* get type token (real, pattern, complex, integer) */ /* -------------------------------------------------------------- */ while (*p && !isspace (*p)) p++ ; while (*p && isspace (*p)) p++ ; c = tolower (*p) ; if (!(c == 'r' || c == 'p' || c == 'c' || c == 'i')) { /* bad format */ return (FALSE) ; } is_complex = (c == 'c') ; /* -------------------------------------------------------------- */ /* get storage token (general, hermitian, symmetric, skew) */ /* -------------------------------------------------------------- */ while (*p && !isspace (*p)) p++ ; while (*p && isspace (*p)) p++ ; c = tolower (*p) ; c2 = tolower (*(p+1)) ; if (c == 'g') { /* "general" storage (unsymmetric matrix), both parts present */ *stype = STYPE_UNSYMMETRIC ; } else if (c == 's' && c2 == 'y') { /* "symmetric" */ if (is_complex) { /* complex symmetric, lower triangular part present */ *stype = STYPE_COMPLEX_SYMMETRIC_LOWER ; } else { /* real symmetric, lower triangular part present */ *stype = STYPE_SYMMETRIC_LOWER ; } } else if (c == 'h') { /* "hermitian" matrix, lower triangular part present */ *stype = STYPE_SYMMETRIC_LOWER ; } else if (c == 's' && c2 == 'k') { /* "skew-symmetric" (real or complex), lower part present */ *stype = STYPE_SKEW_SYMMETRIC ; } else { /* bad format */ return (FALSE) ; } } else if (is_blank_line (buf)) { /* -------------------------------------------------------------- */ /* blank line or comment line */ /* -------------------------------------------------------------- */ continue ; } else { /* -------------------------------------------------------------- */ /* read the first data line and return */ /* -------------------------------------------------------------- */ /* format: nrow ncol nnz stype */ l1 = EMPTY ; l2 = EMPTY ; l3 = 0 ; l4 = 0 ; nitems = sscanf (buf, "%lg %lg %lg %lg\n", &l1, &l2, &l3, &l4) ; if (nitems < 2 || nitems > 4 || l1 > Int_max || l2 > Int_max) { /* invalid matrix */ return (FALSE) ; } *nrow = l1 ; *ncol = l2 ; if (nitems == 2) { /* a dense matrix */ if (!got_mm_header) { *mtype = CHOLMOD_DENSE ; *stype = STYPE_UNSYMMETRIC ; } } if (nitems == 3 || nitems == 4) { /* a sparse triplet matrix */ *nnz = l3 ; if (!got_mm_header) { *mtype = CHOLMOD_TRIPLET ; } } if (nitems == 4) { /* an stype specified here can only be 1, 0, or -1 */ if (l4 < 0) { *stype = STYPE_SYMMETRIC_LOWER ; } else if (l4 > 0) { *stype = STYPE_SYMMETRIC_UPPER ; } else { *stype = STYPE_UNSYMMETRIC ; } } if (*nrow != *ncol) { /* a rectangular matrix must be unsymmetric */ *stype = STYPE_UNSYMMETRIC ; } return (TRUE) ; } first = FALSE ; } } /* ========================================================================== */ /* === read_triplet ========================================================= */ /* ========================================================================== */ /* Header has already been read in, including first line (nrow ncol nnz stype). * Read the triplets. */ static cholmod_triplet *read_triplet ( /* ---- input ---- */ FILE *f, /* file to read from, must already be open */ size_t nrow, /* number of rows */ size_t ncol, /* number of columns */ size_t nnz, /* number of triplets in file to read */ int stype, /* stype from header, or "unknown" */ int prefer_unsym, /* if TRUE, always return T->stype of zero */ /* ---- workspace */ char *buf, /* of size MAXLINE+1 */ /* --------------- */ cholmod_common *Common ) { double x, z ; double *Tx ; Int *Ti, *Tj, *Rdeg, *Cdeg ; cholmod_triplet *T ; double l1, l2 ; Int nitems, xtype, unknown, k, nshould, is_lower, is_upper, one_based, i, j, imax, jmax, skew_symmetric, p, complex_symmetric ; size_t s, nnz2, extra ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* quick return for empty matrix */ /* ---------------------------------------------------------------------- */ if (nrow == 0 || ncol == 0 || nnz == 0) { /* return an empty matrix */ return (CHOLMOD(allocate_triplet) (nrow, ncol, 0, 0, CHOLMOD_REAL, Common)) ; } /* ---------------------------------------------------------------------- */ /* special stype cases: unknown, skew symmetric, and complex symmetric */ /* ---------------------------------------------------------------------- */ unknown = (stype == STYPE_UNKNOWN) ; skew_symmetric = (stype == STYPE_SKEW_SYMMETRIC) ; complex_symmetric = (stype == STYPE_COMPLEX_SYMMETRIC_LOWER) ; extra = 0 ; if (stype < STYPE_SYMMETRIC_LOWER || (prefer_unsym && stype != STYPE_UNSYMMETRIC)) { /* 999: unknown might be converted to unsymmetric */ /* 1: symmetric upper converted to unsym. if prefer_unsym is TRUE */ /* -1: symmetric lower converted to unsym. if prefer_unsym is TRUE */ /* -2: real or complex skew symmetric converted to unsymmetric */ /* -3: complex symmetric converted to unsymmetric */ stype = STYPE_UNSYMMETRIC ; extra = nnz ; } nnz2 = CHOLMOD(add_size_t) (nnz, extra, &ok) ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = nrow + ncol */ s = CHOLMOD(add_size_t) (nrow, ncol, &ok) ; if (!ok || nrow > Int_max || ncol > Int_max || nnz > Int_max) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (NULL) ; } CHOLMOD(allocate_work) (0, s, 0, Common) ; Rdeg = Common->Iwork ; /* size nrow */ Cdeg = Rdeg + nrow ; /* size ncol */ /* ---------------------------------------------------------------------- */ /* read the triplets */ /* ---------------------------------------------------------------------- */ is_lower = TRUE ; is_upper = TRUE ; one_based = TRUE ; imax = 0 ; jmax = 0 ; Tx = NULL ; Ti = NULL ; Tj = NULL ; xtype = 999 ; nshould = 0 ; for (k = 0 ; k < (Int) nnz ; k++) { /* ------------------------------------------------------------------ */ /* get the next triplet, skipping blank lines and comment lines */ /* ------------------------------------------------------------------ */ l1 = EMPTY ; l2 = EMPTY ; x = 0 ; z = 0 ; for ( ; ; ) { if (!get_line (f, buf)) { /* premature end of file - not enough triplets read in */ ERROR (CHOLMOD_INVALID, "premature EOF") ; return (NULL) ; } if (is_blank_line (buf)) { /* blank line or comment */ continue ; } nitems = sscanf (buf, "%lg %lg %lg %lg\n", &l1, &l2, &x, &z) ; x = fix_inf (x) ; z = fix_inf (z) ; break ; } nitems = (nitems == EOF) ? 0 : nitems ; i = l1 ; j = l2 ; /* ------------------------------------------------------------------ */ /* for first triplet: determine type and allocate triplet matrix */ /* ------------------------------------------------------------------ */ if (k == 0) { if (nitems < 2 || nitems > 4) { /* invalid matrix */ ERROR (CHOLMOD_INVALID, "invalid format") ; return (NULL) ; } else if (nitems == 2) { /* this will be converted into a real matrix later */ xtype = CHOLMOD_PATTERN ; } else if (nitems == 3) { xtype = CHOLMOD_REAL ; } else if (nitems == 4) { xtype = CHOLMOD_COMPLEX ; } /* the rest of the lines should have the same number of entries */ nshould = nitems ; /* allocate triplet matrix */ T = CHOLMOD(allocate_triplet) (nrow, ncol, nnz2, stype, (xtype == CHOLMOD_PATTERN ? CHOLMOD_REAL : xtype), Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } Ti = T->i ; Tj = T->j ; Tx = T->x ; T->nnz = nnz ; } /* ------------------------------------------------------------------ */ /* save the entry in the triplet matrix */ /* ------------------------------------------------------------------ */ if (nitems != nshould || i < 0 || j < 0) { /* wrong format, premature end-of-file, or negative indices */ CHOLMOD(free_triplet) (&T, Common) ; ERROR (CHOLMOD_INVALID, "invalid matrix file") ; return (NULL) ; } Ti [k] = i ; Tj [k] = j ; if (i < j) { /* this entry is in the upper triangular part */ is_lower = FALSE ; } if (i > j) { /* this entry is in the lower triangular part */ is_upper = FALSE ; } if (xtype == CHOLMOD_REAL) { Tx [k] = x ; } else if (xtype == CHOLMOD_COMPLEX) { Tx [2*k ] = x ; /* real part */ Tx [2*k+1] = z ; /* imaginary part */ } if (i == 0 || j == 0) { one_based = FALSE ; } imax = MAX (i, imax) ; jmax = MAX (j, jmax) ; } /* ---------------------------------------------------------------------- */ /* convert to zero-based */ /* ---------------------------------------------------------------------- */ if (one_based) { /* input matrix is one-based; convert matrix to zero-based */ for (k = 0 ; k < (Int) nnz ; k++) { Ti [k]-- ; Tj [k]-- ; } } if (one_based ? (imax > (Int) nrow || jmax > (Int) ncol) : (imax >= (Int) nrow || jmax >= (Int) ncol)) { /* indices out of range */ CHOLMOD(free_triplet) (&T, Common) ; ERROR (CHOLMOD_INVALID, "indices out of range") ; return (NULL) ; } /* ---------------------------------------------------------------------- */ /* determine the stype, if not yet known */ /* ---------------------------------------------------------------------- */ if (unknown) { if (is_lower && is_upper) { /* diagonal matrix, symmetric with upper part present */ stype = STYPE_SYMMETRIC_UPPER ; } else if (is_lower && !is_upper) { /* symmetric, lower triangular part present */ stype = STYPE_SYMMETRIC_LOWER ; } else if (!is_lower && is_upper) { /* symmetric, upper triangular part present */ stype = STYPE_SYMMETRIC_UPPER ; } else { /* unsymmetric */ stype = STYPE_UNSYMMETRIC ; extra = 0 ; } } /* ---------------------------------------------------------------------- */ /* add the remainder of symmetric, skew-symmetric or Hermitian matrices */ /* ---------------------------------------------------------------------- */ /* note that this step is not done for real symmetric or complex Hermitian * matrices, unless prefer_unsym is TRUE */ if (extra > 0) { p = nnz ; for (k = 0 ; k < (Int) nnz ; k++) { i = Ti [k] ; j = Tj [k] ; if (i != j) { Ti [p] = j ; Tj [p] = i ; if (xtype == CHOLMOD_REAL) { if (skew_symmetric) { Tx [p] = -Tx [k] ; } else { Tx [p] = Tx [k] ; } } else if (xtype == CHOLMOD_COMPLEX) { if (skew_symmetric) { Tx [2*p ] = -Tx [2*k ] ; Tx [2*p+1] = -Tx [2*k+1] ; } else if (complex_symmetric) { Tx [2*p ] = Tx [2*k ] ; Tx [2*p+1] = Tx [2*k+1] ; } else /* Hermitian */ { Tx [2*p ] = Tx [2*k ] ; Tx [2*p+1] = -Tx [2*k+1] ; } } p++ ; } } T->nnz = p ; nnz = p ; } T->stype = stype ; /* ---------------------------------------------------------------------- */ /* create values for a pattern-only matrix */ /* ---------------------------------------------------------------------- */ if (xtype == CHOLMOD_PATTERN) { if (stype == STYPE_UNSYMMETRIC || Common->prefer_binary) { /* unsymmetric case, or binary case */ for (k = 0 ; k < (Int) nnz ; k++) { Tx [k] = 1 ; } } else { /* compute the row and columm degrees (excluding the diagonal) */ for (i = 0 ; i < (Int) nrow ; i++) { Rdeg [i] = 0 ; } for (j = 0 ; j < (Int) ncol ; j++) { Cdeg [j] = 0 ; } for (k = 0 ; k < (Int) nnz ; k++) { i = Ti [k] ; j = Tj [k] ; if ((stype < 0 && i > j) || (stype > 0 && i < j)) { /* both a(i,j) and a(j,i) appear in the matrix */ Rdeg [i]++ ; Cdeg [j]++ ; Rdeg [j]++ ; Cdeg [i]++ ; } } /* assign the numerical values */ for (k = 0 ; k < (Int) nnz ; k++) { i = Ti [k] ; j = Tj [k] ; Tx [k] = (i == j) ? (1 + MAX (Rdeg [i], Cdeg [j])) : (-1) ; } } } /* ---------------------------------------------------------------------- */ /* return the new triplet matrix */ /* ---------------------------------------------------------------------- */ return (T) ; } /* ========================================================================== */ /* === read_dense =========================================================== */ /* ========================================================================== */ /* Header has already been read in, including first line (nrow ncol). * Read a dense matrix. */ static cholmod_dense *read_dense ( /* ---- input ---- */ FILE *f, /* file to read from, must already be open */ size_t nrow, /* number of rows */ size_t ncol, /* number of columns */ int stype, /* stype from header */ /* ---- workspace */ char *buf, /* of size MAXLINE+1 */ /* --------------- */ cholmod_common *Common ) { double x, z ; double *Xx = NULL ; cholmod_dense *X ; Int nitems, xtype = -1, nshould = 0, i, j, k, kup, first ; /* ---------------------------------------------------------------------- */ /* quick return for empty matrix */ /* ---------------------------------------------------------------------- */ if (nrow == 0 || ncol == 0) { /* return an empty dense matrix */ return (CHOLMOD(zeros) (nrow, ncol, CHOLMOD_REAL, Common)) ; } /* ---------------------------------------------------------------------- */ /* read the entries */ /* ---------------------------------------------------------------------- */ first = TRUE ; for (j = 0 ; j < (Int) ncol ; j++) { /* ------------------------------------------------------------------ */ /* get the row index of the first entry in the file for column j */ /* ------------------------------------------------------------------ */ if (stype == STYPE_UNSYMMETRIC) { i = 0 ; } else if (stype == STYPE_SKEW_SYMMETRIC) { i = j+1 ; } else /* real symmetric or complex Hermitian lower */ { i = j ; } /* ------------------------------------------------------------------ */ /* get column j */ /* ------------------------------------------------------------------ */ for ( ; i < (Int) nrow ; i++) { /* -------------------------------------------------------------- */ /* get the next entry, skipping blank lines and comment lines */ /* -------------------------------------------------------------- */ x = 0 ; z = 0 ; for ( ; ; ) { if (!get_line (f, buf)) { /* premature end of file - not enough entries read in */ ERROR (CHOLMOD_INVALID, "premature EOF") ; return (NULL) ; } if (is_blank_line (buf)) { /* blank line or comment */ continue ; } nitems = sscanf (buf, "%lg %lg\n", &x, &z) ; x = fix_inf (x) ; z = fix_inf (z) ; break ; } nitems = (nitems == EOF) ? 0 : nitems ; /* -------------------------------------------------------------- */ /* for first entry: determine type and allocate dense matrix */ /* -------------------------------------------------------------- */ if (first) { first = FALSE ; if (nitems < 1 || nitems > 2) { /* invalid matrix */ ERROR (CHOLMOD_INVALID, "invalid format") ; return (NULL) ; } else if (nitems == 1) { /* a real matrix */ xtype = CHOLMOD_REAL ; } else if (nitems == 2) { /* a complex matrix */ xtype = CHOLMOD_COMPLEX ; } /* the rest of the lines should have same number of entries */ nshould = nitems ; /* allocate the result */ X = CHOLMOD(zeros) (nrow, ncol, xtype, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } Xx = X->x ; } /* -------------------------------------------------------------- */ /* save the entry in the dense matrix */ /* -------------------------------------------------------------- */ if (nitems != nshould) { /* wrong format or premature end-of-file */ CHOLMOD(free_dense) (&X, Common) ; ERROR (CHOLMOD_INVALID, "invalid matrix file") ; return (NULL) ; } k = i + j*nrow ; kup = j + i*nrow ; if (xtype == CHOLMOD_REAL) { /* real matrix */ Xx [k] = x ; if (k != kup) { if (stype == STYPE_SYMMETRIC_LOWER) { /* real symmetric matrix */ Xx [kup] = x ; } else if (stype == STYPE_SKEW_SYMMETRIC) { /* real skew symmetric matrix */ Xx [kup] = -x ; } } } else if (xtype == CHOLMOD_COMPLEX) { Xx [2*k ] = x ; /* real part */ Xx [2*k+1] = z ; /* imaginary part */ if (k != kup) { if (stype == STYPE_SYMMETRIC_LOWER) { /* complex Hermitian */ Xx [2*kup ] = x ; /* real part */ Xx [2*kup+1] = -z ; /* imaginary part */ } else if (stype == STYPE_SKEW_SYMMETRIC) { /* complex skew symmetric */ Xx [2*kup ] = -x ; /* real part */ Xx [2*kup+1] = -z ; /* imaginary part */ } if (stype == STYPE_COMPLEX_SYMMETRIC_LOWER) { /* complex symmetric */ Xx [2*kup ] = x ; /* real part */ Xx [2*kup+1] = z ; /* imaginary part */ } } } } } /* ---------------------------------------------------------------------- */ /* return the new dense matrix */ /* ---------------------------------------------------------------------- */ return (X) ; } /* ========================================================================== */ /* === cholmod_read_triplet ================================================= */ /* ========================================================================== */ /* Read in a triplet matrix from a file. */ cholmod_triplet *CHOLMOD(read_triplet) ( /* ---- input ---- */ FILE *f, /* file to read from, must already be open */ /* --------------- */ cholmod_common *Common ) { char buf [MAXLINE+1] ; size_t nrow, ncol, nnz ; int stype, mtype ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (f, NULL) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* read the header and first data line */ /* ---------------------------------------------------------------------- */ if (!read_header (f, buf, &mtype, &nrow, &ncol, &nnz, &stype) || mtype != CHOLMOD_TRIPLET) { /* invalid matrix - this function can only read in a triplet matrix */ ERROR (CHOLMOD_INVALID, "invalid format") ; return (NULL) ; } /* ---------------------------------------------------------------------- */ /* read the triplet matrix */ /* ---------------------------------------------------------------------- */ return (read_triplet (f, nrow, ncol, nnz, stype, FALSE, buf, Common)) ; } /* ========================================================================== */ /* === cholmod_read_sparse ================================================== */ /* ========================================================================== */ /* Read a sparse matrix from a file. See cholmod_read_triplet for a discussion * of the file format. * * If Common->prefer_upper is TRUE (the default case), a symmetric matrix is * returned stored in upper-triangular form (A->stype == 1). */ cholmod_sparse *CHOLMOD(read_sparse) ( /* ---- input ---- */ FILE *f, /* file to read from, must already be open */ /* --------------- */ cholmod_common *Common ) { cholmod_sparse *A, *A2 ; cholmod_triplet *T ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (f, NULL) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* convert to a sparse matrix in compressed-column form */ /* ---------------------------------------------------------------------- */ T = CHOLMOD(read_triplet) (f, Common) ; A = CHOLMOD(triplet_to_sparse) (T, 0, Common) ; CHOLMOD(free_triplet) (&T, Common) ; if (Common->prefer_upper && A != NULL && A->stype == -1) { /* A=A' */ A2 = CHOLMOD(transpose) (A, 2, Common) ; CHOLMOD(free_sparse) (&A, Common) ; A = A2 ; } return (A) ; } /* ========================================================================== */ /* === cholmod_read_dense =================================================== */ /* ========================================================================== */ /* Read a dense matrix from a file. */ cholmod_dense *CHOLMOD(read_dense) ( /* ---- input ---- */ FILE *f, /* file to read from, must already be open */ /* --------------- */ cholmod_common *Common ) { char buf [MAXLINE+1] ; size_t nrow, ncol, nnz ; int stype, mtype ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (f, NULL) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* read the header and first data line */ /* ---------------------------------------------------------------------- */ if (!read_header (f, buf, &mtype, &nrow, &ncol, &nnz, &stype) || mtype != CHOLMOD_DENSE) { /* invalid matrix - this function can only read in a dense matrix */ ERROR (CHOLMOD_INVALID, "invalid format") ; return (NULL) ; } /* ---------------------------------------------------------------------- */ /* read the dense matrix */ /* ---------------------------------------------------------------------- */ return (read_dense (f, nrow, ncol, stype, buf, Common)) ; } /* ========================================================================== */ /* === cholmod_read_matrix ================================================== */ /* ========================================================================== */ /* Read a triplet matrix, sparse matrix or a dense matrix from a file. Returns * a void pointer to either a cholmod_triplet, cholmod_sparse, or cholmod_dense * object. The type of object is passed back to the caller as the mtype * argument. */ void *CHOLMOD(read_matrix) ( /* ---- input ---- */ FILE *f, /* file to read from, must already be open */ int prefer, /* If 0, a sparse matrix is always return as a * cholmod_triplet form. It can have any stype * (symmetric-lower, unsymmetric, or * symmetric-upper). * If 1, a sparse matrix is returned as an unsymmetric * cholmod_sparse form (A->stype == 0), with both * upper and lower triangular parts present. * This is what the MATLAB mread mexFunction does, * since MATLAB does not have an stype. * If 2, a sparse matrix is returned with an stype of 0 * or 1 (unsymmetric, or symmetric with upper part * stored). * This argument has no effect for dense matrices. */ /* ---- output---- */ int *mtype, /* CHOLMOD_TRIPLET, CHOLMOD_SPARSE or CHOLMOD_DENSE */ /* --------------- */ cholmod_common *Common ) { void *G = NULL ; cholmod_sparse *A, *A2 ; cholmod_triplet *T ; char buf [MAXLINE+1] ; size_t nrow, ncol, nnz ; int stype ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (f, NULL) ; RETURN_IF_NULL (mtype, NULL) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* read the header to determine the mtype */ /* ---------------------------------------------------------------------- */ if (!read_header (f, buf, mtype, &nrow, &ncol, &nnz, &stype)) { /* invalid matrix */ ERROR (CHOLMOD_INVALID, "invalid format") ; return (NULL) ; } /* ---------------------------------------------------------------------- */ /* read a matrix */ /* ---------------------------------------------------------------------- */ if (*mtype == CHOLMOD_TRIPLET) { /* read in the triplet matrix, converting to unsymmetric format if * prefer == 1 */ T = read_triplet (f, nrow, ncol, nnz, stype, prefer == 1, buf, Common) ; if (prefer == 0) { /* return matrix in its original triplet form */ G = T ; } else { /* return matrix in a compressed-column form */ A = CHOLMOD(triplet_to_sparse) (T, 0, Common) ; CHOLMOD(free_triplet) (&T, Common) ; if (A != NULL && prefer == 2 && A->stype == -1) { /* convert A from symmetric-lower to symmetric-upper */ A2 = CHOLMOD(transpose) (A, 2, Common) ; CHOLMOD(free_sparse) (&A, Common) ; A = A2 ; } *mtype = CHOLMOD_SPARSE ; G = A ; } } else if (*mtype == CHOLMOD_DENSE) { /* return a dense matrix */ G = read_dense (f, nrow, ncol, stype, buf, Common) ; } return (G) ; } #endif SuiteSparse/CHOLMOD/Check/lesser.txt0000644001170100242450000006350010253404155016112 0ustar davisfac GNU LESSER GENERAL PUBLIC LICENSE Version 2.1, February 1999 Copyright (C) 1991, 1999 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. 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SuiteSparse/CHOLMOD/MATLAB/0000755001170100242450000000000010712370267014001 5ustar davisfacSuiteSparse/CHOLMOD/MATLAB/Test/0000755001170100242450000000000010712150660014711 5ustar davisfacSuiteSparse/CHOLMOD/MATLAB/Test/dg.m0000644001170100242450000000311210710406255015460 0ustar davisfacfunction dg(A) %DG order and plot A*A', using CHOLMOD's nested dissection % used by test27.m % Example: % dg(A) % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida A = spones (A) ; [p cp cm] = nesdis (A, 'row') ; % get the corresponding column ordering. Order the columns % in increasing order of min(find(A(:,j))) [m n] = size (A) ; C = A (p,:) ; qmin = zeros (1,n) ; for j = 1:n qmin (j) = min (find (C (:,j))) ; %#ok end [ignore q] = sort (qmin) ; C = C (:,q) ; % figure (1) clf subplot (2,3,1) ; treeplot (cp) drawnow subplot (2,3,2) ; spy (C) drawnow % axis off subplot (2,3,3) ; spy (C*C') drawnow % axis off ncomp = max(cm) ; fprintf ('# of components: %d\n', ncomp) % cs = [cm(p) n+1] ; % cboundaries = find (diff (cs)) ; fprintf ('size of root %d out of %d rows\n', length (find (cm == ncomp)), m); [cnt h pa po R] = symbfact2 (A (p,:), 'row') ; % rc = full (sum (R)) ; for k = 1:ncomp fprintf ('node %4d : parent %4d size %6d work %g\n', ... k, cp (k), length (find (cm == k)), sum (cnt (find (cm == k)).^2) ) ; %#ok end subplot (2,3,4) ; spy (A*A') ; drawnow subplot (2,3,5) ; spy (R+R') ; drawnow pamd = amd2 (A*A') ; % use AMD from SuiteSparse, not built-in [cnt h pa po R] = symbfact2 (A (pamd,:), 'row') ; subplot (2,3,6) ; spy (R+R') ; drawnow % s = bisect (A, 'row') ; % [ignore pp] = sort (s) ; % E = A(pp,:) ; % subplot (2,3,4) ; spy (E*E') % fprintf ('bisect: %d\n', length (find (s == 2))) ; % figure (2) % spy (C*C') % hold on % for j = cboundaries % plot ([1 n], [j j], 'r', [j j], [1 n], 'r') ; % end SuiteSparse/CHOLMOD/MATLAB/Test/n2.m0000644001170100242450000000260210620371276015414 0ustar davisfac%N2 script to test CHOLMOD septree function % Example: % n2 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida index = UFget ; f = find ((index.amd_lnz > 0) & (index.nrows > 200)) ; [ignore i] = sort (index.amd_lnz (f)) ; f = f (i) ; nmat = length (f) ; for i = f Prob = UFget (i, index) ; disp (Prob) ; A = spones (Prob.A) ; [m n] = size (A) ; name = Prob.name ; clear Prob if (m == n) mode = 'sym' ; A = A + A' ; len = n ; elseif (m < n) mode = 'row' ; len = m ; else mode = 'col' ; len = n ; end [p cp cmem] = nesdis (A, mode) ; subplot (2,4,1) ; treeplot (cp) ; [cp2 cmem2] = septree (cp, cmem, 0.5, 200) ; %#ok subplot (2,4,2) ; treeplot (cp2) ; [cp3 cmem3] = septree (cp, cmem, 0.2, 300) ; %#ok subplot (2,4,3) ; treeplot (cp3) ; [cp4 cmem4] = septree (cp, cmem, 0.12, 500) ; %#ok subplot (2,4,4) ; treeplot (cp4) ; [p cp cmem] = nesdis (A, mode, [200 1]) ; subplot (2,4,5) ; treeplot (cp) ; [cp2 cmem2] = septree (cp, cmem, 0.5, 200) ; %#ok subplot (2,4,6) ; treeplot (cp2) ; [cp3 cmem3] = septree (cp, cmem, 0.2, 300) ; %#ok subplot (2,4,7) ; treeplot (cp3) ; [cp4 cmem4] = septree (cp, cmem, 0.12, 500) ; %#ok subplot (2,4,8) ; treeplot (cp4) ; drawnow % pause end SuiteSparse/CHOLMOD/MATLAB/Test/nn.m0000644001170100242450000000764310620371300015506 0ustar davisfac%NN Compare nesdis with metis, in both quality and run time % % Example: % nn % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida index = UFget ; f = find (index.amd_lnz > 0) ; [ignore i] = sort (index.amd_lnz (f)) ; f = f (i) ; nmat = length (f) ; T1 = zeros (1,nmat) ; T2 = zeros (1,nmat) ; TM = zeros (1,nmat) ; Lnz1 = zeros (1,nmat) ; Lnz2 = zeros (1,nmat) ; LnzM = zeros (1,nmat) ; Fl1 = zeros (1,nmat) ; Fl2 = zeros (1,nmat) ; FlM = zeros (1,nmat) ; for k = 1:nmat i = f (k) ; Prob = UFget (i,index) ; A = Prob.A ; [m n] = size (A) ; if (m ~= n) continue ; end fprintf ('%35s: ', Prob.name) ; if (m == n) mode = 'sym' ; A = A + A' ; len = n ; elseif (m < n) mode = 'row' ; len = m ; else mode = 'col' ; len = n ; end fprintf (' %s ', mode) ; % try nesdis using camd, and splitting connected components tic [p2 cparent2 cmember2] = nesdis (A, mode, [200 1]) ; t2 = toc ; % subplot (3,3,7) ; treeplot (cparent2) ; % try nesdis using camd tic [p1 cparent1 cmember1] = nesdis (A, mode) ; t1 = toc ; % subplot (3,3,8) ; treeplot (cparent1) ; % try metis tic pm = metis (A, mode) ; tm = toc ; if (any (sort (p1) ~= 1:len)) error ('p1!') ; end if (any (sort (p2) ~= 1:len)) error ('p2!') ; end % compare ordering quality if (m == n) c2 = symbfact2 (A (p2,p2), mode) ; fl2 = sum (c2.^2) ; c2 = sum (c2) ; c1 = symbfact2 (A (p1,p1), mode) ; fl1 = sum (c1.^2) ; c1 = sum (c1) ; cm = symbfact2 (A (pm,pm), mode) ; flm = sum (cm.^2) ; cm = sum (cm) ; elseif (m < n) c2 = symbfact2 (A (p2, :), mode) ; fl2 = sum (c2.^2) ; c2 = sum (c2) ; c1 = symbfact2 (A (p1, :), mode) ; fl1 = sum (c1.^2) ; c1 = sum (c1) ; cm = symbfact2 (A (pm, :), mode) ; flm = sum (cm.^2) ; cm = sum (cm) ; else c2 = symbfact2 (A ( :,p2), mode) ; fl2 = sum (c2.^2) ; c2 = sum (c2) ; c1 = symbfact2 (A ( :,p1), mode) ; fl1 = sum (c1.^2) ; c1 = sum (c1) ; cm = symbfact2 (A ( :,pm), mode) ; flm = sum (cm.^2) ; cm = sum (cm) ; end T1 (k) = t1 ; T2 (k) = t2 ; TM (k) = tm ; Lnz1 (k) = c1 ; Lnz2 (k) = c2 ; LnzM (k) = cm ; Fl1 (k) = fl1 ; Fl2 (k) = fl2 ; FlM (k) = flm ; tmax = max ([max(T1 (1:k)) max(T2 (1:k)) max(TM (1:k))]) ; tmin = min ([min(T1 (1:k)) min(T2 (1:k)) min(TM (1:k))]) ; cmax = max ([max(Lnz1 (1:k)) max(Lnz2 (1:k)) max(LnzM (1:k))]) ; flmax =max ([max(Fl1 (1:k)) max(Fl2 (1:k)) max(FlM (1:k))]) ; fprintf (... 'time %8.2f %8.2f %8.2f speedup %8.2f flop %8.2e %8.2e %8.2e ratio %8.2f\n', ... t2, t1, tm, tm/t1, fl2, fl1, flm, flm/fl1) ; if (mod (k, 20) ~= 0) continue end subplot (3,3,1) ; x = T1 (1:k) ./ T2 (1:k) ; semilogy (1:k, x, 'o', [1 k], [1 1], 'r-') ; axis tight title (sprintf ('(nesdis default)/(with split) time, median: %g', ... median (x))) ; subplot (3,3,2) ; x = (Lnz1 (1:k) ./ Lnz2 (1:k)) ; semilogy (1:k, x, 'o', [1 k], [1 1], 'r-') ; axis tight title (sprintf ('(nesdis default)/(with split) lnz, median: %g', ... median (x))) ; subplot (3,3,3) ; x = (Fl1 (1:k) ./ Fl2 (1:k)) ; semilogy (1:k, x, 'o', [1 k], [1 1], 'r-') ; axis tight title (sprintf ('(nesdis default)/(with split) flops, median: %g', ... median (x))) ; subplot (3,3,4) ; x = T1 (1:k) ./ TM (1:k) ; semilogy (1:k, x, 'o', [1 k], [1 1], 'r-') ; axis tight title (sprintf ('(nesdis default)/metis time, median %g', median (x))) ; subplot (3,3,5) ; x = (Lnz1 (1:k) ./ LnzM (1:k)) ; semilogy (1:k, x, 'o', [1 k], [1 1], 'r-') ; axis tight title (sprintf ('(nesdis default)/metis lnz, median: %g', median (x))) ; subplot (3,3,6) ; x = (Fl1 (1:k) ./ FlM (1:k)) ; semilogy (1:k, x, 'o', [1 k], [1 1], 'r-') ; axis tight title (sprintf ('(nesdis default)/metis flops, median: %g', median (x))) ; drawnow % pause end SuiteSparse/CHOLMOD/MATLAB/Test/Contents.m0000644001170100242450000000426410620371266016677 0ustar davisfac% CHOLMOD TEST functions % % cholmod_test - test the CHOLMOD mexFunctions % dg - order and plot A*A', using CHOLMOD's nested dissection % n2 - script to test CHOLMOD septree function % nn - Compare nesdis with metis, in both quality and run time % test0 - test most CHOLMOD functions % test1 - test sparse2 % test2 - test sparse2 % test3 - test sparse on int8, int16, and logical % test4 - test cholmod2 with multiple and sparse right-hand-sides % test5 - test sparse2 % test6 - test sparse with large matrix, both real and complex % test7 - test sparse2 % test8 - order a large range of sparse matrices, test symbfact2 % test9 - test metis, etree, bisect, nesdis % test10 - test cholmod2's backslash on real and complex matrices % test11 - compare CHOLMOD and MATLAB, save results in Results.mat % test11results - analyze results from test11.m % test12 - test etree2 and compare with etree % test13 - test cholmod2 and MATLAB on large tridiagonal matrices % test14 - test metis, symbfact2, and etree2 % test15 - test symbfact2 vs MATLAB % test16 - test cholmod2 on a large matrix % test17 - test lchol on a few large matrices % test18 - test cholmod2 on a few large matrices % test19 - look for NaN's from lchol (caused by Intel MKL 7.x bug) % test20 - test symbfact2, cholmod2, and lu on a few large matrices % test21 - test cholmod2 on diagonal or ill-conditioned matrices % test22 - test pos.def and indef. matrices % test23 - test chol and cholmod2 on the sparse matrix used in "bench" % test24 - test sdmult % test25 - test sdmult on a large matrix % test26 - test logical full and sparse matrices % test27 - test nesdis with one matrix (HB/west0479) % test28 - test nesdis % testmm - compare mread and mmread for entire Matrix Market collection % testsolve - test CHOLMOD and compare with x=A\b % % Example: % cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida SuiteSparse/CHOLMOD/MATLAB/Test/test10.m0000644001170100242450000000431110620371303016203 0ustar davisfacfunction test10 (nmat) %TEST10 test cholmod2's backslash on real and complex matrices % Example: % test10(nmat) % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test10: test cholmod2''s backslash\n') ; rand ('state',0) ; randn ('state',0) ; index = UFget ; f = find (index.posdef) ; [ignore i] = sort (index.nrows (f)) ; f = f (i) ; % start after nd6k % f = f ((find (f == 937) + 1):end) ; skip = [937:939 1202:1211] ; if (nargin > 0) nmat = max (0,nmat) ; nmat = min (nmat, length (f)) ; f = f (1:nmat) ; end fprintf ('test matrices sorted by dimension:\n') ; for i = f if (any (i == skip)) continue end fprintf ('%4d: %-20s %-20s %12d %d\n', i, ... index.Group {i}, index.Name {i}, index.nrows (i), index.posdef (i)) ; end for nn = f % for nn = 23 if (any (nn == skip)) continue end % try for complexity = 0:1 if nn < 0 n = -nn ; A = rand (n) + (complexity * rand(n) * 1i) ; A=A*A' ; full (A) A = sparse (A) ; elseif (nn == 0) i = 1i ; A = [ 11 4-i 1+i 2+2*i 4+i 22 0 0 1-i 0 33 0 2-2*i 0 0 44 ] ; A = sparse (A) ; p = [4 3 2 1] ; %#ok full (A) A = sparse (A) ; else if (~complexity) nn %#ok Prob = UFget (nn) %#ok end A = Prob.A ; if (complexity) A = A / norm(A,1) ; Z = .1 * sprandn (A) * 1i ; Z = Z+Z' ; A = A + Z ; A = A + norm(A,1) * speye (size(A,1)) ; end n = size (A,1) ; end for sparsity = 0:1 if (sparsity) b = sprandn (n,4,0.1) ; else b = rand (n,4) ; end b1 = b (:,1) ; [x1,x2,e1,e2] = testsolve (A,b1) ; %#ok [x1,x2,e1,e2] = testsolve (A,b) ; %#ok if (sparsity) b = sprandn (n,9,0.1) ; else b = rand (n,9) ; end [x1,x2,e1,e2] = testsolve (A,b) ; %#ok if (sparsity) b = sprandn (n,9,0.1) + sprandn (n,9,0.1)*1i ; else b = rand (n,9) + rand(n,9)*1i ; end b1 = b (:,1) ; [x1,x2,e1,e2] = testsolve (A,b1) ; %#ok [x1,x2,e1,e2] = testsolve (A,b) ; %#ok end end % catch % fprintf (' failed\n') ; % end end SuiteSparse/CHOLMOD/MATLAB/Test/test11.m0000644001170100242450000000521710710415764016224 0ustar davisfacfunction test11 (nmat) %TEST11 compare CHOLMOD and MATLAB, save results in Results.mat % also tests analyze % Example: % test11(nmat) % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test11 : compare CHOLMOD and MATLAB, save results in Results.mat\n'); rand ('state',0) ; randn ('state',0) ; index = UFget ; f = find (index.posdef) ; [ignore i] = sort (index.nrows (f)) ; f = f (i) ; clear ignore % start after nd6k % f = f ((find (f == 937) + 1):end) ; skip = [937:939 1202:1211] ; if (nargin > 0) nmat = max (0,nmat) ; nmat = min (nmat, length (f)) ; f = f (1:nmat) ; end fprintf ('test matrices sorted by dimension:\n') ; for i = f if (any (i == skip)) continue end fprintf ('%4d: %-20s %-20s %12d %d\n', i, ... index.Group {i}, index.Name {i}, index.nrows (i), index.posdef (i)) ; end kk = 0 ; nmat = length (f) ; T1 = zeros (1,nmat) ; % matlab time T2 = zeros (1,nmat) ; % cholmod2 time E1 = zeros (1,nmat) ; % matlab residual E2 = zeros (1,nmat) ; % cholmod2 residual FL = zeros (1,nmat) ; % cholmod2 flop count LNZ = zeros (1,nmat) ; % cholmod2 lnz for kkk = 1:length(f) nn = f (kkk) ; if (any (nn == skip)) continue end % try fprintf ('\n%3d: %s/%s\n', nn, index.Group {nn}, index.Name {nn}) ; Prob = UFget (nn) ; A = Prob.A ; clear Prob n = size (A,1) ; b = rand (n,1) ; % analyze [p count] = analyze (A) ; % LDL' flop count % fl = sum ((count-1).*(count-1) + 2*(count-1)) ; % LL' flop count fl = sum (count.^2) ; lnz = sum (count) ; fprintf ('n %d lnz %g fl %g\n', n, lnz, fl) ; clear p count % try k2 = 0 ; t2 = 0 ; while (t2 < 1) tic x = cholmod2 (A,b) ; t = toc ; t2 = t2 + t ; k2 = k2 + 1 ; end t2 = t2 / k2 ; e2 = norm (A*x-b,1) ; % catch % e2 = Inf ; % k2 = Inf ; % t2 = Inf ; % end fprintf ('cholmod2: t: %10.5f e: %6.1e mflop %6.0f\n', ... t2, e2, 1e-6 * fl / t2) ; % try k1 = 0 ; t1 = 0 ; while (t1 < 1) tic x = A\b ; t = toc ; t1 = t1 + t ; k1 = k1 + 1 ; end t1 = t1 / k1 ; e1 = norm (A*x-b,1) ; % catch % e1 = Inf ; % k1 = Inf ; % t1 = Inf ; % end fprintf ('matlab: t: %10.5f e: %6.1e mflop %6.0f', ... t1, e1, 1e-6 * fl / t1) ; fprintf (' cholmod2 speedup: %5.1f\n', t1/t2) ; kk = kk + 1 ; T1 (kk) = t1 ; T2 (kk) = t2 ; E1 (kk) = e1 ; E2 (kk) = e2 ; FL (kk) = fl ; LNZ (kk) = lnz ; save Results T1 T2 E1 E2 FL LNZ f kkk % catch % fprintf (' failed\n') ; % end clear A x b end % test11results fprintf ('test11 passed\n') ; SuiteSparse/CHOLMOD/MATLAB/Test/test12.m0000644001170100242450000001116710710406332016215 0ustar davisfacfunction test12 (nmat) %TEST12 test etree2 and compare with etree % Example: % test12(nmat) % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test12: test etree2 and compare with etree\n') ; index = UFget ; % only test matrices with nrows = 109000 or less. large ones nearly always % cause a MATLAB segfault. % f = find (index.nrows < 109000) ; f = 1:length (index.nrows) ; % sort by row dimension [ignore i] = sort (index.nrows (f)) ; f = f (i) ; if (nargin > 0) nmat = max (0,nmat) ; nmat = min (nmat, length (f)) ; f = f (1:nmat) ; end % MATLAB 7.0 (R14, sp2, linux) etree gives a segfault for these matrices: s_skip = [ 803 374 1287 1311 1308 957 958 1257 955 761 1282 1230 1256 ... 924 1302 537 820 821 822 1258 ... 844 845 1238 804 939 1270 1305 1208 1209 290 879 928 1307 1244 ... 1275 1276 1296 885 1269 959 542 1290 ] ; sym_skip = s_skip ; p_sym_skip = 1296 ; p_symt_skip = 1296 ; symt_skip= [ s_skip 592 593 809 ] ; rowcol_skip = [ 646 ... 1224 803 588 589 374 1287 562 563 801 1311 1246 951 1308 950 ... 957 958 800 1257 564 565 955 761 1282 590 591 1230 1256 952 566 ... 567 924 1302 1293 1294 537 820 821 822 1306 849 1258 592 593 ... 1225 844 845 1226 1238 1227 804 939 1270 752 753 1305 809 1228 ... 1208 1209 1291 1292 1300 856 1229 290 879 928 1307 857 1244 ... 1275 1276 1296 885 858 859 1269 1263 959 542 1290 ] ; col_skip = [ rowcol_skip 647 612 610 648 799 651 652 750 751 640 ] ; row_skip= [ rowcol_skip 903 373 ] ; % f = f (find (f == 1290) : end) ; fprintf ('Matrices to test: %d\n', length (f)) ; for i = f % try Problem = UFget (i) ; A = spones (Problem.A) ; [m n] = size (A) ; fprintf ('\n%4d: %-20s nrow: %6d ncol: %6d nnz: %10d\n', ... i, Problem.name, m, n, nnz(A)) ; % if (max (m,n) < 500) % A = full (A) ; % end % warmup, for accurate timing etree (sparse (1)) ; etree2 (sparse (1)) ; amd2 (sparse (1)) ; % test column etree skip = any (i == col_skip) | m > 109000 ; %#ok if (~skip) tic ; [parent post] = etree (A, 'col') ; t1 = toc ; else t1 = Inf ; end tic ; [my_parent my_post] = etree2 (A, 'col') ; t2 = toc ; if (~skip) if (any (parent ~= my_parent)) error ('parent invalid!') ; end end fprintf ('etree(A,''col''): %8.4f %8.4f speedup %8.2f ',... t1, t2, t1/t2); if (~skip) if (any (post ~= my_post)) fprintf ('postorder differs') ; end end fprintf ('\n') ; % test row etree skip = any (i == row_skip) | m > 109000 ; %#ok if (~skip) tic ; [parent post] = etree (A', 'col') ; t1 = toc ; else t1 = Inf ; end tic ; [my_parent my_post] = etree2 (A, 'row') ; t2 = toc ; if (~skip) if (any (parent ~= my_parent)) error ('parent invalid!') ; end end fprintf ('etree(A,''row''): %8.4f %8.4f speedup %8.2f ',... t1, t2, t1/t2); if (~skip) if (any (post ~= my_post)) fprintf ('postorder differs') ; end end fprintf ('\n') ; if (m == n) for trial = 1:2 if (trial == 1) skip1 = any (i == sym_skip) | m > 109000 ; %#ok skip2 = any (i == symt_skip) | m > 109000 ; %#ok else skip1 = any (i == p_sym_skip) | m > 109000 ; %#ok skip2 = any (i == p_symt_skip) | m > 109000 ; %#ok fprintf ('after amd:\n') ; p = amd2 (A) ; % use AMD from SuiteSparse A = A (p,p) ; end % test symmetric etree, using triu(A) if (~skip1) tic ; [parent post] = etree (A) ; t1 = toc ; else t1 = Inf ; end tic ; [my_parent my_post] = etree2 (A) ; t2 = toc ; if (~skip1) if (any (parent ~= my_parent)) error ('parent invalid!') ; end end fprintf ('etree(A): %8.4f %8.4f speedup %8.2f ',... t1, t2, t1/t2); if (~skip1) if (any (post ~= my_post)) fprintf ('postorder differs') ; end end fprintf ('\n') ; % test symmetric etree, using tril(A) if (~skip2) tic ; [parent post] = etree (A') ; t1 = toc ; else t1 = Inf ; end tic ; [my_parent my_post] = etree2 (A, 'lo') ; t2 = toc ; if (~skip2) if (any (parent ~= my_parent)) error ('parent invalid!') ; end end fprintf('etree(A''): %8.4f %8.4f speedup %8.2f ',... t1, t2, t1/t2); if (~skip2) if (any (post ~= my_post)) fprintf ('postorder differs') ; end end fprintf ('\n') ; end end % catch % fprintf ('%d: failed\n', i) ; % end end fprintf ('test12 passed\n') ; SuiteSparse/CHOLMOD/MATLAB/Test/test13.m0000644001170100242450000000137610620371311016215 0ustar davisfacfunction test13 %TEST13 test cholmod2 and MATLAB on large tridiagonal matrices % Example: % test13 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test13: test cholmod2 and MATLAB on large tridiagonal matrices\n') ; for n = [10000 1e4 1e5 1e6] e = ones (n,1) ; A = spdiags ([e 4*e e], -1:1, n, n) ; clear e b = rand (n,1) ; tic ; x = cholmod2 (A,b) ; t2 = toc ; e = norm (A*x-b,1) ; fprintf ('n %9d cholmod2 %8.2f err %6.1e\n', n, t2, e) ; tic ; x = A\b ; t1 = toc ; e = norm (A*x-b,1) ; fprintf ('n %9d matlab %8.2f err %6.1e\n', n, t1, e) ; clear A b end SuiteSparse/CHOLMOD/MATLAB/Test/test14.m0000644001170100242450000000531210620371312016211 0ustar davisfacfunction test14 (nmat) %TEST14 test metis, symbfact2, and etree2 % Example: % test14(nmat) % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test14: test metis, symbfact2, and etree2\n') ; index = UFget ; [ignore f] = sort (max (index.nrows, index.ncols)) ; % f1 = find (max (index.nrows (f), index.ncols (f)) > 55500) ; % f1 = f1 (1) ; % f = f (f1:end) ; % These bugs show up when Common->metis_memory is set to zero: % skip = [ 1298 ] ; % runs out of memory in metis(A,'row') skip = 1257 ; %#ok % GHS_psdef/crankseg_1: segfault in metis(A,'row') ; skip = 850 ; %#ok % Chen/pkustk04: segfault in metis(A,'row') ; skip = [ ] ; %#ok if (nargin > 0) nmat = max (0,nmat) ; nmat = min (nmat, length (f)) ; f = f (1:nmat) ; end for i = f fprintf ('%d:\n', i) ; if (any (skip == i)) fprintf ('skip %s / %s\n', index.Group {i}, index.Name {i}) ; continue end % try Prob = UFget (i) %#ok A = Prob.A ; [m n] = size (A) ; if (m == n) S = spones (A) ; else n = min (m,n) ; S = spones (A (1:n,1:n)) ; end try % compute nnz(S*S') nzaat = nnz (S*S') ; catch nzaat = -1 ; end try % compute nnz(S'*S) nzata = nnz (S'*S) ; catch nzata = -1 ; end S = S | S' ; fprintf ('nnz(A) %d\n', nnz (A)) ; fprintf ('nnz(S) %d\n', nnz (S)) ; fprintf ('nnz(A*A'') %d\n', nzaat) ; fprintf ('nnz(A''*A) %d\n', nzata) ; fprintf ('metis (S):\n') ; p1 = metis (S) ; fprintf ('metis (A,row):\n') ; p2 = metis (A, 'row') ; fprintf ('metis (A,col):\n') ; p3 = metis (A, 'col') ; fprintf ('turning off postorder:\n') ; fprintf ('metis (S):\n') ; n1 = metis (S, 'sym', 'no postorder') ; fprintf ('metis (A,row):\n') ; n2 = metis (A, 'row', 'no postorder') ; fprintf ('metis (A,col):\n') ; n3 = metis (A, 'col', 'no postorder') ; fprintf ('analyzing results:\n') ; [pa1 po1] = etree2 (S (n1,n1)) ; [pa2 po2] = etree2 (A (n2,:), 'row') ; [pa3 po3] = etree2 (A (:,n3), 'col') ; q1 = n1 (po1) ; q2 = n2 (po2) ; q3 = n3 (po3) ; if (any (p1 ~= q1)) error ('1!') ; end if (any (p2 ~= q2)) error ('2!') ; end if (any (p3 ~= q3)) error ('3!') ; end s1 = symbfact2 (S (p1,p1)) ; s2 = symbfact2 (A (p2,:), 'row') ; s3 = symbfact2 (A (:,p3), 'col') ; t1 = symbfact2 (S (n1,n1)) ; t2 = symbfact2 (A (n2,:), 'row') ; t3 = symbfact2 (A (:,n3), 'col') ; if (any (s1 ~= t1 (po1))) error ('s1!') ; end if (any (s2 ~= t2 (po2))) error ('s2!') ; end if (any (s3 ~= t3 (po3))) error ('s3!') ; end % catch % fprintf ('%d failed\n') ; % end end fprintf ('test14 passed\n') ; SuiteSparse/CHOLMOD/MATLAB/Test/test15.m0000644001170100242450000000723610710406337016227 0ustar davisfacfunction test15 (nmat) %TEST15 test symbfact2 vs MATLAB % Example: % test15(nmat) % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); index = UFget ; % only test matrices with nrows = 109000 or less. large ones nearly always % cause a MATLAB segfault. f = find (index.nrows < 109000 & index.ncols < 109000) ; % sort by row /col dimension s = max (index.nrows, index.ncols) ; [ignore i] = sort (s (f)) ; f = f (i) ; if (nargin > 0) nmat = max (0,nmat) ; nmat = min (nmat, length (f)) ; f = f (1:nmat) ; end fprintf ('Matrices to test: %d\n', length (f)) ; for i = f % try Problem = UFget (i) ; A = spones (Problem.A) ; [m n] = size (A) ; fprintf ('\n%4d: %-20s nrow: %6d ncol: %6d nnz: %10d\n', ... i, Problem.name, m, n, nnz(A)) ; % warmup, for accurate timing etree (sparse (1)) ; etree2 (sparse (1)) ; amd2 (sparse (1)) ; symbfact (sparse (1)) ; symbfact2 (sparse (1)) ; % test symmetric case if (m == n) % permute the matrix first p = amd2 (A) ; A = A (p,p) ; % test with triu(A) tic co = symbfact (A) ; t1 = toc ; tic co2 = symbfact2 (A) ; t2 = toc ; fprintf ('c=symbfact(A): %10.4f %10.4f speedup %8.2f lnz %d\n', ... t1, t2, t1/t2, sum (co)) ; if (any (co ~= co2)) error ('!') ; end tic [co h parent post R] = symbfact (A) ; t1 = toc ; tic [co2 h2 parent2 post2 R2] = symbfact2 (A) ; t2 = toc ; fprintf ('R=symbfact(A): %10.4f %10.4f speedup %8.2f\n',... t1, t2, t1/t2) ; checkem(co,co2,parent,parent2,post,post2,R,R2,h,h2) ; % test with tril(A) tic co = symbfact (A') ; t1 = toc ; tic co2 = symbfact2 (A,'lo') ; t2 = toc ; fprintf (... 'c=symbfact(A''): %10.4f %10.4f speedup %8.2f lnz %d\n',... t1, t2, t1/t2, sum (co)) ; if (any (co ~= co2)) error ('!') ; end tic [co h parent post R] = symbfact (A') ; t1 = toc ; tic [co2 h2 parent2 post2 R2] = symbfact2 (A,'lo') ; t2 = toc ; fprintf (... 'R=symbfact(A''): %10.4f %10.4f speedup %8.2f\n',... t1, t2, t1/t2) ; checkem(co,co2,parent,parent2,post,post2,R,R2,h,h2) ; end % permute the matrix first p = colamd (A) ; [parent post] = etree2 (A (:,p), 'col') ; p = p (post) ; A = A (:,p) ; % test column case tic co = symbfact (A,'col') ; t1 = toc ; tic co2 = symbfact2 (A,'col') ; t2 = toc ; fprintf ('c=symbfact(A,''col''): %10.4f %10.4f speedup %8.2f lnz %d\n', ... t1, t2, t1/t2, sum (co)) ; if (any (co ~= co2)) error ('!') ; end tic [co h parent post R] = symbfact (A,'col') ; t1 = toc ; tic [co2 h2 parent2 post2 R2] = symbfact2 (A,'col') ; t2 = toc ; fprintf ('R=symbfact(A,''col''): %10.4f %10.4f speedup %8.2f\n', ... t1, t2, t1/t2) ; checkem(co,co2,parent,parent2,post,post2,R,R2,h,h2) ; % catch % fprintf ('%d failed\n', i) ; % end end fprintf ('test15 passed\n') ; %------------------------------------------------------------------------------- function checkem(co,co2,parent,parent2,post,post2,R,R2,h,h2) % checkem compare results from symbfact and symbfact2 if (any (co ~= co2)) error ('count!') ; end if (any (parent ~= parent2)) error ('parent!') ; end if (any (post ~= post2)) error ('post!') ; end if (nnz (R2) ~= nnz (R)) error ('lnz!') ; end if (h ~= h2) error ('h!') ; end % this may run out of memory try % compute nnz(R-R2) err = nnz (R-R2) ; catch err = -1 ; fprintf ('nnz(R-R2) not computed\n') ; end if (err > 0) error ('R!') ; end SuiteSparse/CHOLMOD/MATLAB/Test/test16.m0000644001170100242450000000116510620371316016221 0ustar davisfacfunction test16 %TEST16 test cholmod2 on a large matrix % Example: % test16 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test16: test cholmod2 on a large matrix\n') ; rand ('state',1) ; randn ('state',1) ; Prob = UFget (936) %#ok A = Prob.A ; % tic % [L,s,p] = lchol (A) ; % toc % norm (L,1) n = size (A,1) ; b = rand (n,1) ; tic x = cholmod2(A,b) ; t = toc ; fprintf ('time %g\n', t) ; err = norm (A*x-b) ; if (err > 1e-5) error ('!') ; end fprintf ('test16 passed\n') ; SuiteSparse/CHOLMOD/MATLAB/Test/test17.m0000644001170100242450000000122410620371320016211 0ustar davisfacfunction test17 %TEST17 test lchol on a few large matrices % Example: % test17 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test17: test lchol on a few large matrices\n') ; rand ('state',1) ; randn ('state',1) ; Prob = UFget (887) %#ok A = Prob.A ; [L,s,p] = lchol (A) ; %#ok norm (L,1) clear all Prob = UFget (936) %#ok A = Prob.A ; [L,s,p] = lchol (A) ; %#ok norm (L,1) %#ok clear all Prob = UFget (887) %#ok A = Prob.A ; [L,s,p] = lchol (A) ; %#ok norm (L,1) %#ok SuiteSparse/CHOLMOD/MATLAB/Test/test18.m0000644001170100242450000000137310620371322016221 0ustar davisfacfunction test18 %TEST18 test cholmod2 on a few large matrices % Example: % test18 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test18: test cholmod2 on a few large matrices\n') ; rand ('state',1) ; randn ('state',1) ; Prob = UFget (887) %#ok A = Prob.A ; n = size (A,1) ; b = rand (n,1) ; x = cholmod2 (A,b) ; norm (A*x-b,1) clear all Prob = UFget (936) %#ok A = Prob.A ; n = size (A,1) ; b = rand (n,1) ; x = cholmod2 (A,b) ; norm (A*x-b,1) clear all Prob = UFget (887) %#ok A = Prob.A ; n = size (A,1) ; b = rand (n,1) ; x = cholmod2 (A,b) ; norm (A*x-b,1) fprintf ('test18 passed\n') ; SuiteSparse/CHOLMOD/MATLAB/Test/test19.m0000644001170100242450000000132610620371323016221 0ustar davisfacfunction test19 %TEST19 look for NaN's from lchol (caused by Intel MKL 7.x bug) % Example: % test19 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test19: look for NaN''s from lchol (caused by Intel MKL 7.x bug)\n') ; Prob = UFget (936) %#ok A = Prob.A ; [p count] = analyze (A) ; A = A (p,p) ; tic L = lchol (A) ; t = toc ; fl = sum (count.^2) ; fprintf ('mflop rate: %8.2f\n', 1e-6*fl/t) ; n = size (L,1) ; for k = 1:n if (any (isnan (L (:,k)))) k %#ok error ('!') ; end end fprintf ('test19 passed; you have a NaN-free BLAS (must not be MKL 7.x...)\n') ; SuiteSparse/CHOLMOD/MATLAB/Test/test20.m0000644001170100242450000000243610710406342016214 0ustar davisfacfunction test20 %TEST20 test symbfact2, cholmod2, and lu on a few large matrices % Example: % test20 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test20: test symbfact2, cholmod2, and lu on a few large matrices\n') ; unsym = [409 899 901 291 827] ; %#ok spd = [813 817] ; % f = [ unsym spd ] ; f = spd ; spparms ('spumoni',0) ; for i = f Prob = UFget (i) %#ok A = Prob.A ; clear Prob ; n = size (A,1) ; b = A*ones (n,1) ; if (any (i == spd)) p = amd2 (A) ; count = symbfact2 (A (p,p)) ; count2 = symbfact (A (p,p)) ; if (any (count ~= count2)) error ('!') ; end fl = sum (count.^2) ; lnz = sum (count) ; unz = lnz ; tic x = cholmod2 (A,b) ; t = toc ; else % spparms ('spumoni',2) ; [L, U, P, Q] = lu (A) ; %#ok % fl = luflop (L,U) ; Lnz = full (sum (spones (L))) - 1 ; Unz = full (sum (spones (U')))' - 1 ; fl = 2*Lnz*Unz + sum (Lnz) ; lnz = nnz(L) ; unz = nnz(U) ; tic x=A\b ; t = toc ; end err = norm (A*x-b,1) ; clear L U P Q A x b fprintf ('lnz %d unz %d nnz(L+U) %d fl %g gflop %g\n t %g err %e\n', ... lnz, unz, lnz+unz-n, fl, 1e-9*fl/t, t, err) ; % pause end SuiteSparse/CHOLMOD/MATLAB/Test/test21.m0000644001170100242450000000205410620371330016207 0ustar davisfacfunction test21 %TEST21 test cholmod2 on diagonal or ill-conditioned matrices % Example: % test21 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test21: test cholmod2 on diagonal or ill-conditioned matrices\n') ; f = [ 72 % HB/bcsstm22 315 % Bai/mhdb416 64 % HB/bcsstm09 71 % HB/bcsstm21 1207 % Oberwolfach/t2dal_e 354 % Boeing/crystm02 1211 % Oberwolfach/t3dl_e ]' ; for i = f Prob = UFget (i) %#ok A = Prob.A ; n = size (A,1) ; x = ones (n,2) ; b = A*x ; fprintf ('nnz: %d\n', nnz (A)) ; x1 = A\b ; x2 = cholmod2 (A,b) ; s = norm (A,1) * norm (x,1) + norm (b,1) ; resid1 = norm (A*x1-b,1) / s ; resid2 = norm (A*x2-b,1) / s ; err1 = norm (x-x1,1) ; err2 = norm (x-x2,1) ; fprintf ('MATLAB resid %6.1e err %6.1e\n', resid1, err1) ; fprintf ('CHOLMOD resid %6.1e err %6.1e\n', resid2, err2) ; fprintf ('condest %6.1e\n', condest (A)) ; end SuiteSparse/CHOLMOD/MATLAB/Test/test22.m0000644001170100242450000001101510710406346016213 0ustar davisfacfunction test22(nmat) %TEST22 test pos.def and indef. matrices % Example: % test22(nmat) % % if nmat <= 0, just test problematic matrices % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test22: test pos.def and indef. matrices\n') ; index = UFget ; [ignore f] = sort (index.nrows) ; if (nargin > 0) problematic = (nmat <= 0) ; if (problematic) % Matrices for which MATLAB and CHOLMOD differ, for which the error % is high, or other issues arose during debugging fprintf ('testing matrices for which MATLAB and CHOLMOD differ\n') ; f = [ 186 % HB/jgl011 109 % HB/curtis54 793 % Qaplib/lp_nug05 607 % LPnetlib/lp_brandy 707 % LPnetlib/lp_bore3d 231 % HB/plskz362 794 % Qaplib/lp_nug06 673 % LPnetlib/lp_scorpion 1156 % Sandia/oscil_dcop_45 (also 1157:1168) 795 % Qaplib/lp_nug07 796 % Qaplib/lp_nug08 260 % HB/well1033 261 % HB/well1850 230 % HB/plsk1919 649 % LPnetlib/lp_pds_02 660 % LPnetlib/lp_qap12 609 % LPnetlib/lp_cre_a 619 % LPnetlib/lp_dfl001 661 % LPnetlib/lp_qap15 650 % LPnetlib/lp_pds_06 379 % Cote/vibrobox 638 % LPnetlib/lp_ken_11 799 % Qaplib/lp_nug20 ]' ; else nmat = max (0,nmat) ; nmat = min (nmat, length (f)) ; f = f (1:nmat) ; end end skip = [ 811, ... % Simon/appu, which is a random matrix 937:939, ... % large ND/ problems 1157:1168 ... % duplicates 799 % rather large: Qaplib/lp_nug20 ] ; tlimit = 0.1 ; fprintf ('test22: chol and chol2 are repeated so each take >= %g sec\n',tlimit); klimit = 1 ; % warmup, for more accurate timing [R,p] = chol (sparse (1)) ; %#ok [R,p] = chol2 (sparse (1)) ; %#ok clear R p for i = f if (any (i == skip)) continue ; end Problem = UFget (i) ; A = Problem.A ; [m n] = size (A) ; fprintf ('\n================== %4d: Problem: %s m: %d n: %d nnz: %d', ... i, Problem.name, m, n, nnz (A)) ; clear Problem ; try % create a symmetric version of the matrix if (m == n) if (nnz (A-A') > 0) A = A+A' ; end else A = A*A' ; end catch fprintf ('skip\n') ; continue end fprintf (' %d\n', nnz (A)) ; p = amd2 (A) ; A = A (p,p) ; anorm = norm (A,1) ; % Run each code for at least 'tlimit' seconds % MATLAB k = 0 ; t1 = 0 ; while (t1 < tlimit & k < klimit) %#ok tic ; [R1,p1] = chol (A) ; t = toc ; t1 = t1 + t ; k = k + 1 ; end t1 = t1 / k ; % CHOLMOD k = 0 ; t2 = 0 ; while (t2 < tlimit & k < klimit) %#ok tic ; [R2,p2] = chol2 (A) ; t = toc ; t2 = t2 + t ; k = k + 1 ; end t2 = t2 / k ; if (klimit == 1) rmin = full (min (abs (diag (R2)))) ; rmax = full (max (abs (diag (R2)))) ; if (p2 ~= 0 | isnan (rmin) | isnan (rmax) | rmax == 0) %#ok rcond = 0 ; else rcond = rmin / rmax ; end fprintf ('rcond: %30.20e\n', rcond) ; end if (p1 == 1) % MATLAB does not follow its own definitions. If p is 1, then R is % supposed to be 0-by-n, not 0-by-0. CHOLMOD fixes this bug. % Here, A is m-by-m R1 = sparse (0,m) ; end kerr = 0 ; if (p1 ~= p2) % MATLAB and CHOLMOD don't agree. See if both are correct, % because differences in roundoff errors can make one go % a little farther than the other. % if p1 is zero, it means MATLAB was fully successful k1 = p1 ; if (k1 == 0) k1 = n ; end % if p2 is zero, it means CHOLMOD was fully successful k2 = p2 ; if (k2 == 0) k2 = n ; end if (k1 > k2) % MATLAB went further than CHOLMOD. This is OK if MATLAB found % a small entry where CHOLMOD stopped. k = k2 ; kerr = R1 (k,k) ; % now reduce R1 in size, to compare with R2 R1 = R1 (1:k2-1,:) ; else % CHOLMOD went further than MATLAB. This is OK if CHOLMOD found % a small entry where MATLAB stopped. k = k1 ; kerr = R2 (k,k) ; % now reduce R2 in size, to compare with R1 R2 = R2 (1:k1-1,:) ; end end err = norm (R1-R2,1) / max (anorm,1) ; fprintf ('p: %6d %6d MATLAB: %10.4f CHOLMOD: %10.4f speedup %6.2f err:', ... p1, p2, t1, t2, t1/t2) ; if (err == 0) fprintf (' 0') ; else fprintf (' %6.0e', err) ; end if (kerr == 0) fprintf (' 0\n') ; else fprintf (' %6.0e\n', kerr) ; end % if (err > 1e-6) % error ('!') ; % end % pause clear R1 R2 p1 p2 p A end fprintf ('test22: all tests passed\n') ; SuiteSparse/CHOLMOD/MATLAB/Test/test23.m0000644001170100242450000000557210710406363016226 0ustar davisfacfunction test23 %TEST23 test chol and cholmod2 on the sparse matrix used in "bench" % Example: % test23 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test23: test chol & cholmod2 on the sparse matrix used in "bench"\n'); n = 120 ; A = delsq (numgrid ('L', n)) ; b = sum (A)' ; fprintf ('Using each method''s internal fill-reducing ordering:\n') ; tic ; x = A\b ; t1 = toc ; e1 = norm (A*x-b) ; tic ; x = cholmod2 (A,b) ; t2 = toc ; e2 = norm (A*x-b) ; fprintf ('MATLAB x=A\\b time: %8.4f resid: %8.0e\n', t1, e1) ; fprintf ('CHOLMOD x=A\\b time: %8.4f resid: %8.0e\n', t2, e2) ; fprintf ('CHOLMOD speedup: %8.2f\n', t1/t2) ; % get CHOLMOD's ordering (best of AMD and METIS) p = analyze (A) ; S = A (p,p) ; tic ; R = chol (S) ; t1 = toc ; x = R \ (R' \ b (p)) ; x (p) = x ; e1 = norm (A*x-b) ; tic ; L = lchol (S) ; t2 = toc ; x = L' \ (L \ b (p)) ; x (p) = x ; e2 = norm (A*x-b) ; fprintf ('\nS = A(p,p) where p is CHOLMOD''s ordering:\n') ; fprintf ('MATLAB R=chol(S) time: %8.4f resid: %8.0e\n', t1, e1) ; fprintf ('CHOLMOD L=lchol(S) time: %8.4f resid: %8.0e\n', t2, e2) ; fprintf ('CHOLMOD speedup: %8.2f\n', t1/t2) ; % get MATLABS's ordering (symmmd in v7.0.4). If that fails then use amd. % A future version of MATLAB will remove symmmd, since it is declared % "deprecated" in v7.0.4. try % symmmd, use amd if it fails method = 'symmmd' ; p = symmmd (A) ; catch % use AMD from SuiteSparse method = 'amd' ; fprintf ('\nsymmmd not available, using amd instead.\n') ; p = amd2 (A) ; end S = A (p,p) ; tic ; R = chol (S) ; t1 = toc ; x = R \ (R' \ b (p)) ; x (p) = x ; e1 = norm (A*x-b) ; tic ; L = lchol (S) ; t2 = toc ; x = L' \ (L \ b (p)) ; x (p) = x ; e2 = norm (A*x-b) ; fprintf ('\nS = A(p,p) where p is MATLAB''s ordering in x=A\\b (%s):\n',method); fprintf ('MATLAB R=chol(S) time: %8.4f resid: %8.0e\n', t1, e1) ; fprintf ('CHOLMOD L=lchol(S) time: %8.4f resid: %8.0e\n', t2, e2) ; fprintf ('CHOLMOD speedup: %8.2f\n', t1/t2) ; fprintf ('\n\nWith no fill-reducing orderings:\n') ; tic ; R = chol (A) ; t1 = toc ; x = R \ (R' \ b) ; e1 = norm (A*x-b) ; tic ; L = lchol (A) ; t2 = toc ; x = L' \ (L \ b) ; e2 = norm (A*x-b) ; fprintf ('MATLAB R=chol(A) time: %8.4f resid: %8.0e\n', t1, e1) ; fprintf ('CHOLMOD L=lchol(A) time: %8.4f resid: %8.0e\n', t2, e2) ; fprintf ('CHOLMOD speedup: %8.2f\n', t1/t2) ; fprintf ('\n\nWith no fill-reducing orderings (as used in "bench"):\n') ; spparms ('autommd',0) ; tic ; x = A\b ; t1 = toc ; e1 = norm (A*x-b) ; tic ; x = cholmod2 (A,b,0) ; t2 = toc ; e2 = norm (A*x-b) ; fprintf ('MATLAB x=A\\b time: %8.4f resid: %8.0e\n', t1, e1) ; fprintf ('CHOLMOD x=A\\b time: %8.4f resid: %8.0e\n', t2, e2) ; fprintf ('CHOLMOD speedup: %8.2f\n', t1/t2) ; spparms ('default') ; SuiteSparse/CHOLMOD/MATLAB/Test/test24.m0000644001170100242450000000213610620665327016227 0ustar davisfacfunction test24 %TEST24 test sdmult % Example: % test24 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test24: test sdmult\n') ; rand ('state', 0) ; randn ('state', 0) ; maxerr = 0 ; for trials = 1:1000 sm = fix (20 * rand (1)) ; sn = fix (20 * rand (1)) ; fn = fix (20 * rand (1)) ; for complexity = 0:1 for transpose = 0:1 if (transpose) fm = sm ; else fm = sn ; end S = sprand (sm,sn,0.5) ; F = rand (fm,fn) ; if (complexity) S = S + 1i * sprand (S) ; F = F + 1i * rand (fm,fn) ; end % MATLAB does not support empty complex matrices if (isempty (S) | isempty (F)) %#ok S = sparse (real (S)) ; F = real (F) ; end C = sdmult (S,F,transpose) ; if (transpose) D = S'*F ; else D = S*F ; end err = norm (C-D,1) ; maxerr = max (err, maxerr) ; if (err > 1e-13) error ('!') ; end end end end fprintf ('test 24 passed, maxerr %g\n', maxerr) ; SuiteSparse/CHOLMOD/MATLAB/Test/test25.m0000644001170100242450000000256510620371336016230 0ustar davisfacfunction test25 %TEST25 test sdmult on a large matrix % Example: % test25 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test25: test sdmult on a large matrix\n') ; Prob = UFget (936) ; A = Prob.A ; n = size (A,1) ; nz = nnz (A) ; fprintf ('\nTest matrix: %d-by-%d, nnz %d\n', n, n, nz) ; Z = rand (n, 500) ; fprintf ('\nA*X where X is %d-by-k\n', n) ; for k = [0:10 10:10:50 100:100:500] X = Z (:, 1:k) ; tic ; D = A*X ; t1 = toc ; tic ; C = sdmult (A,X) ; t2 = toc ; err = norm (C-D,1) ; fprintf (... 'k: %3d time: MATLAB %8.2f CHOLMOD %8.2f speedup %8.2f err %6.0e',... k, t1, t2, t1/t2, err) ; fl = 2*nz*k ; fprintf (' mflop: MATLAB %8.1f CHOLMOD %8.1f\n', 1e-6*fl/t1, 1e-6*fl/t2) ; clear C D X end fprintf ('\nFor comparison, here is CHOLMOD''s x=A\\b time:\n') ; for k = [1 100:100:500] B = Z (:, 1:k) ; tic x = cholmod2 (A,B) ; t2 = toc ; err2 = norm (sdmult(A,x)-B,1) ; fprintf (... 'CHOLMOD x=A\\b time: %8.2f (b is n-by-%d) resid %6.0e\n', t2, k, err2) ; clear x B end b = Z (:,1) ; clear Z tic x = A\b ; t1 = toc ; err1 = norm (A*x-b,1) ; fprintf ('\nMATLAB x=A\\b time: %8.2f (b is n-by-1) resid %6.0e\n', t1, err1) ; fprintf ('test25 passed\n') ; SuiteSparse/CHOLMOD/MATLAB/Test/test26.m0000644001170100242450000000357710710406367016240 0ustar davisfacfunction test26 (do_metis) %TEST26 test logical full and sparse matrices % Example: % test26 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test26: test logical full and sparse matrices\n') ; if (nargin < 1) do_metis = 1 ; end Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; p = amd2 (A) ; n = size (A,1) ; A = A (p,p) + 10*speye (n) ; C = logical (A ~= 0) ; test26b (A,C,do_metis) ; test26b (full (A),C,do_metis) ; test26b (full (A), full (C),do_metis) ; test26b (A, full(C),do_metis) ; A = A + 0.001 * (spones (tril (A,-1) + triu (A,1))) * 1i ; test26b (A,C,do_metis) ; test26b (full (A),C,do_metis) ; test26b (full (A), full (C),do_metis) ; test26b (A, full(C),do_metis) ; fprintf ('test26 passed\n') ; %------------------------------------------------------------------------------- function test26b (A,C,do_metis) % test26b test bisect, analyze, etree2, metis, nesdis, symbfact2, and resymbol p1 = analyze (A) ; p2 = analyze (C) ; if (any (p1 ~= p2)) error ('test 26 failed (analyze)!') ; end p1 = etree2 (A) ; p2 = etree2 (C) ; if (any (p1 ~= p2)) error ('test 26 failed (etree2)!') ; end if (do_metis) s1 = bisect (A) ; s2 = bisect (C) ; if (any (s1 ~= s2)) error ('test 26 failed (bisect)!') ; end p1 = metis (A) ; p2 = metis (C) ; if (any (p1 ~= p2)) error ('test 26 failed (metis)!') ; end p1 = nesdis (A) ; p2 = nesdis (C) ; if (any (p1 ~= p2)) error ('test 26 failed (nesdis)!') ; end end c1 = symbfact2 (A) ; c2 = symbfact2 (C) ; if (any (c1 ~= c2)) error ('test 26 failed (symbfact2)!') ; end A (1,2) = 0 ; A (2,1) = 0 ; C = logical (A ~= 0) ; L = chol (sparse (A))' ; L1 = resymbol (L, A) ; L2 = resymbol (L, C) ; if (norm (L1 - L2, 1) ~= 0) error ('test 26 failed (resymbol)!') ; end SuiteSparse/CHOLMOD/MATLAB/Test/test27.m0000644001170100242450000000056310620371342016223 0ustar davisfacfunction test27 %TEST27 test nesdis with one matrix (HB/west0479) % Example: % test27 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test27: test nesdis\n') ; Prob = UFget ('HB/west0479') ; dg (Prob.A) ; fprintf ('test27 passed\n') ; SuiteSparse/CHOLMOD/MATLAB/Test/test28.m0000644001170100242450000000221410620665342016225 0ustar davisfacfunction test28 %TEST28 test nesdis % Example: % test28 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida index = UFget ; [ignore f] = sort (index.nnz) ; % f = find (index.nrows < index.ncols) ; % [ignore i] = sort (index.nnz (f)) ; % f = f (i) ; f = f (1:100) ; for i = f try Prob = UFget (i, index) ; A = spones (Prob.A) ; [m n] = size (A) ; if (m < n) A = A*A' ; elseif (m > n) ; A = A'*A ; else A = A+A' ; end % default: do not split connected components [p1 cp1 cmem1] = nesdis (A) ; %#ok % order connected components separately [p2 cp2 cmem2] = nesdis (A, 'sym', [200 1]) ; %#ok c1 = symbfact (A (p1,p1)) ; c2 = symbfact (A (p2,p2)) ; lnz1 = sum (c1) ; lnz2 = sum (c2) ; fprintf ('%35s %8d %8d ', Prob.name, lnz1, lnz2) if (lnz1 == lnz2) fprintf (' 1\n') ; else fprintf (' %8.3f\n', lnz1/lnz2) ; end subplot (2,3,1) ; spy (A) ; subplot (2,3,2) ; spy (A (p1,p1)) ; subplot (2,3,3) ; treeplot (cp1) ; subplot (2,3,5) ; spy (A (p2,p2)) ; subplot (2,3,6) ; treeplot (cp2) ; drawnow catch fprintf ('%4d failed\n', i) ; end end SuiteSparse/CHOLMOD/MATLAB/Test/testmm.m0000644001170100242450000005562510620371363016420 0ustar davisfac%TESTMM compare mread and mmread for entire Matrix Market collection % Example: % testmm % See also mread. % Requires the mmread MATLAB m-file from http://www.nist.gov % Copyright 2006-2007, Timothy A. Davis, University of Florida matrices = { 'M/Harwell-Boeing/acoust/young1c.mtx', ... 'M/Harwell-Boeing/acoust/young2c.mtx', ... 'M/Harwell-Boeing/acoust/young3c.mtx', ... 'M/Harwell-Boeing/acoust/young4c.mtx', ... 'M/Harwell-Boeing/airtfc/zenios.mtx', ... 'M/Harwell-Boeing/astroph/mcca.mtx', ... 'M/Harwell-Boeing/astroph/mcfe.mtx', ... 'M/Harwell-Boeing/bcspwr/bcspwr01.mtx', ... 'M/Harwell-Boeing/bcspwr/bcspwr02.mtx', ... 'M/Harwell-Boeing/bcspwr/bcspwr03.mtx', ... 'M/Harwell-Boeing/bcspwr/bcspwr04.mtx', ... 'M/Harwell-Boeing/bcspwr/bcspwr05.mtx', ... 'M/Harwell-Boeing/bcspwr/bcspwr06.mtx', ... 'M/Harwell-Boeing/bcspwr/bcspwr07.mtx', ... 'M/Harwell-Boeing/bcspwr/bcspwr08.mtx', ... 'M/Harwell-Boeing/bcspwr/bcspwr09.mtx', ... 'M/Harwell-Boeing/bcspwr/bcspwr10.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstk01.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstk02.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstk03.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstk04.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstk05.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstk06.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstk07.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstk08.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstk09.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstk10.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstk11.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstk12.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstk13.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstm01.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstm02.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstm03.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstm04.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstm05.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstm06.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstm07.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstm08.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstm09.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstm10.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstm11.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstm12.mtx', ... 'M/Harwell-Boeing/bcsstruc1/bcsstm13.mtx', ... 'M/Harwell-Boeing/bcsstruc2/bcsstk14.mtx', ... 'M/Harwell-Boeing/bcsstruc2/bcsstk15.mtx', ... 'M/Harwell-Boeing/bcsstruc2/bcsstk16.mtx', ... 'M/Harwell-Boeing/bcsstruc2/bcsstk17.mtx', ... 'M/Harwell-Boeing/bcsstruc2/bcsstk18.mtx', ... 'M/Harwell-Boeing/bcsstruc3/bcsstk19.mtx', ... 'M/Harwell-Boeing/bcsstruc3/bcsstk20.mtx', ... 'M/Harwell-Boeing/bcsstruc3/bcsstk21.mtx', ... 'M/Harwell-Boeing/bcsstruc3/bcsstk22.mtx', ... 'M/Harwell-Boeing/bcsstruc3/bcsstk23.mtx', ... 'M/Harwell-Boeing/bcsstruc3/bcsstk24.mtx', ... 'M/Harwell-Boeing/bcsstruc3/bcsstk25.mtx', ... 'M/Harwell-Boeing/bcsstruc3/bcsstm19.mtx', ... 'M/Harwell-Boeing/bcsstruc3/bcsstm20.mtx', ... 'M/Harwell-Boeing/bcsstruc3/bcsstm21.mtx', ... 'M/Harwell-Boeing/bcsstruc3/bcsstm22.mtx', ... 'M/Harwell-Boeing/bcsstruc3/bcsstm23.mtx', ... 'M/Harwell-Boeing/bcsstruc3/bcsstm24.mtx', ... 'M/Harwell-Boeing/bcsstruc3/bcsstm25.mtx', ... 'M/Harwell-Boeing/bcsstruc4/bcsstk26.mtx', ... 'M/Harwell-Boeing/bcsstruc4/bcsstk27.mtx', ... 'M/Harwell-Boeing/bcsstruc4/bcsstk28.mtx', ... 'M/Harwell-Boeing/bcsstruc4/bcsstm26.mtx', ... 'M/Harwell-Boeing/bcsstruc4/bcsstm27.mtx', ... 'M/Harwell-Boeing/bcsstruc5/bcsstk29.mtx', ... 'M/Harwell-Boeing/bcsstruc5/bcsstk30.mtx', ... 'M/Harwell-Boeing/bcsstruc5/bcsstk31.mtx', ... 'M/Harwell-Boeing/bcsstruc5/bcsstk32.mtx', ... 'M/Harwell-Boeing/bcsstruc5/bcsstk33.mtx', ... 'M/Harwell-Boeing/bcsstruc6/blckhole.mtx', ... 'M/Harwell-Boeing/bcsstruc6/sstmodel.mtx', ... 'M/Harwell-Boeing/cannes/can_1054.mtx', ... 'M/Harwell-Boeing/cannes/can_1072.mtx', ... 'M/Harwell-Boeing/cannes/can__144.mtx', ... 'M/Harwell-Boeing/cannes/can__161.mtx', ... 'M/Harwell-Boeing/cannes/can__187.mtx', ... 'M/Harwell-Boeing/cannes/can__229.mtx', ... 'M/Harwell-Boeing/cannes/can___24.mtx', ... 'M/Harwell-Boeing/cannes/can__256.mtx', ... 'M/Harwell-Boeing/cannes/can__268.mtx', ... 'M/Harwell-Boeing/cannes/can__292.mtx', ... 'M/Harwell-Boeing/cannes/can__445.mtx', ... 'M/Harwell-Boeing/cannes/can___61.mtx', ... 'M/Harwell-Boeing/cannes/can___62.mtx', ... 'M/Harwell-Boeing/cannes/can__634.mtx', ... 'M/Harwell-Boeing/cannes/can__715.mtx', ... 'M/Harwell-Boeing/cannes/can___73.mtx', ... 'M/Harwell-Boeing/cannes/can__838.mtx', ... 'M/Harwell-Boeing/cannes/can___96.mtx', ... 'M/Harwell-Boeing/chemimp/impcol_a.mtx', ... 'M/Harwell-Boeing/chemimp/impcol_b.mtx', ... 'M/Harwell-Boeing/chemimp/impcol_c.mtx', ... 'M/Harwell-Boeing/chemimp/impcol_d.mtx', ... 'M/Harwell-Boeing/chemimp/impcol_e.mtx', ... 'M/Harwell-Boeing/chemwest/west0067.mtx', ... 'M/Harwell-Boeing/chemwest/west0132.mtx', ... 'M/Harwell-Boeing/chemwest/west0156.mtx', ... 'M/Harwell-Boeing/chemwest/west0167.mtx', ... 'M/Harwell-Boeing/chemwest/west0381.mtx', ... 'M/Harwell-Boeing/chemwest/west0479.mtx', ... 'M/Harwell-Boeing/chemwest/west0497.mtx', ... 'M/Harwell-Boeing/chemwest/west0655.mtx', ... 'M/Harwell-Boeing/chemwest/west0989.mtx', ... 'M/Harwell-Boeing/chemwest/west1505.mtx', ... 'M/Harwell-Boeing/chemwest/west2021.mtx', ... 'M/Harwell-Boeing/cirphys/jpwh_991.mtx', ... 'M/Harwell-Boeing/counterx/jgl009.mtx', ... 'M/Harwell-Boeing/counterx/jgl011.mtx', ... 'M/Harwell-Boeing/counterx/rgg010.mtx', ... 'M/Harwell-Boeing/dwt/dwt_1005.mtx', ... 'M/Harwell-Boeing/dwt/dwt_1007.mtx', ... 'M/Harwell-Boeing/dwt/dwt_1242.mtx', ... 'M/Harwell-Boeing/dwt/dwt__162.mtx', ... 'M/Harwell-Boeing/dwt/dwt__193.mtx', ... 'M/Harwell-Boeing/dwt/dwt__198.mtx', ... 'M/Harwell-Boeing/dwt/dwt__209.mtx', ... 'M/Harwell-Boeing/dwt/dwt__221.mtx', ... 'M/Harwell-Boeing/dwt/dwt__234.mtx', ... 'M/Harwell-Boeing/dwt/dwt__245.mtx', ... 'M/Harwell-Boeing/dwt/dwt_2680.mtx', ... 'M/Harwell-Boeing/dwt/dwt__307.mtx', ... 'M/Harwell-Boeing/dwt/dwt__310.mtx', ... 'M/Harwell-Boeing/dwt/dwt__346.mtx', ... 'M/Harwell-Boeing/dwt/dwt__361.mtx', ... 'M/Harwell-Boeing/dwt/dwt__419.mtx', ... 'M/Harwell-Boeing/dwt/dwt__492.mtx', ... 'M/Harwell-Boeing/dwt/dwt__503.mtx', ... 'M/Harwell-Boeing/dwt/dwt__512.mtx', ... 'M/Harwell-Boeing/dwt/dwt__592.mtx', ... 'M/Harwell-Boeing/dwt/dwt___59.mtx', ... 'M/Harwell-Boeing/dwt/dwt__607.mtx', ... 'M/Harwell-Boeing/dwt/dwt___66.mtx', ... 'M/Harwell-Boeing/dwt/dwt___72.mtx', ... 'M/Harwell-Boeing/dwt/dwt__758.mtx', ... 'M/Harwell-Boeing/dwt/dwt__869.mtx', ... 'M/Harwell-Boeing/dwt/dwt__878.mtx', ... 'M/Harwell-Boeing/dwt/dwt___87.mtx', ... 'M/Harwell-Boeing/dwt/dwt__918.mtx', ... 'M/Harwell-Boeing/dwt/dwt__992.mtx', ... 'M/Harwell-Boeing/econaus/mahindas.mtx', ... 'M/Harwell-Boeing/econaus/orani678.mtx', ... 'M/Harwell-Boeing/econiea/beacxc.mtx', ... 'M/Harwell-Boeing/econiea/beaflw.mtx', ... 'M/Harwell-Boeing/econiea/beause.mtx', ... 'M/Harwell-Boeing/econiea/mbeacxc.mtx', ... 'M/Harwell-Boeing/econiea/mbeaflw.mtx', ... 'M/Harwell-Boeing/econiea/mbeause.mtx', ... 'M/Harwell-Boeing/econiea/wm1.mtx', ... 'M/Harwell-Boeing/econiea/wm2.mtx', ... 'M/Harwell-Boeing/econiea/wm3.mtx', ... 'M/Harwell-Boeing/facsimile/fs_183_1.mtx', ... 'M/Harwell-Boeing/facsimile/fs_183_3.mtx', ... 'M/Harwell-Boeing/facsimile/fs_183_4.mtx', ... 'M/Harwell-Boeing/facsimile/fs_183_6.mtx', ... 'M/Harwell-Boeing/facsimile/fs_680_1.mtx', ... 'M/Harwell-Boeing/facsimile/fs_680_2.mtx', ... 'M/Harwell-Boeing/facsimile/fs_680_3.mtx', ... 'M/Harwell-Boeing/facsimile/fs_760_1.mtx', ... 'M/Harwell-Boeing/facsimile/fs_760_2.mtx', ... 'M/Harwell-Boeing/facsimile/fs_760_3.mtx', ... 'M/Harwell-Boeing/gemat/gemat11.mtx', ... 'M/Harwell-Boeing/gemat/gemat12.mtx', ... 'M/Harwell-Boeing/gemat/gemat1.mtx', ... 'M/Harwell-Boeing/grenoble/gre_1107.mtx', ... 'M/Harwell-Boeing/grenoble/gre__115.mtx', ... 'M/Harwell-Boeing/grenoble/gre__185.mtx', ... 'M/Harwell-Boeing/grenoble/gre_216a.mtx', ... 'M/Harwell-Boeing/grenoble/gre_216b.mtx', ... 'M/Harwell-Boeing/grenoble/gre__343.mtx', ... 'M/Harwell-Boeing/grenoble/gre__512.mtx', ... 'M/Harwell-Boeing/jagmesh/jagmesh1.mtx', ... 'M/Harwell-Boeing/jagmesh/jagmesh2.mtx', ... 'M/Harwell-Boeing/jagmesh/jagmesh3.mtx', ... 'M/Harwell-Boeing/jagmesh/jagmesh4.mtx', ... 'M/Harwell-Boeing/jagmesh/jagmesh5.mtx', ... 'M/Harwell-Boeing/jagmesh/jagmesh6.mtx', ... 'M/Harwell-Boeing/jagmesh/jagmesh7.mtx', ... 'M/Harwell-Boeing/jagmesh/jagmesh8.mtx', ... 'M/Harwell-Boeing/jagmesh/jagmesh9.mtx', ... 'M/Harwell-Boeing/lanpro/nos1.mtx', ... 'M/Harwell-Boeing/lanpro/nos2.mtx', ... 'M/Harwell-Boeing/lanpro/nos3.mtx', ... 'M/Harwell-Boeing/lanpro/nos4.mtx', ... 'M/Harwell-Boeing/lanpro/nos5.mtx', ... 'M/Harwell-Boeing/lanpro/nos6.mtx', ... 'M/Harwell-Boeing/lanpro/nos7.mtx', ... 'M/Harwell-Boeing/laplace/gr_30_30.mtx', ... 'M/Harwell-Boeing/lns/lns__131.mtx', ... 'M/Harwell-Boeing/lns/lns_3937.mtx', ... 'M/Harwell-Boeing/lns/lns__511.mtx', ... 'M/Harwell-Boeing/lns/lnsp_131.mtx', ... 'M/Harwell-Boeing/lns/lnsp3937.mtx', ... 'M/Harwell-Boeing/lns/lnsp_511.mtx', ... 'M/Harwell-Boeing/lshape/lshp1009.mtx', ... 'M/Harwell-Boeing/lshape/lshp1270.mtx', ... 'M/Harwell-Boeing/lshape/lshp1561.mtx', ... 'M/Harwell-Boeing/lshape/lshp1882.mtx', ... 'M/Harwell-Boeing/lshape/lshp2233.mtx', ... 'M/Harwell-Boeing/lshape/lshp2614.mtx', ... 'M/Harwell-Boeing/lshape/lshp_265.mtx', ... 'M/Harwell-Boeing/lshape/lshp3025.mtx', ... 'M/Harwell-Boeing/lshape/lshp3466.mtx', ... 'M/Harwell-Boeing/lshape/lshp_406.mtx', ... 'M/Harwell-Boeing/lshape/lshp_577.mtx', ... 'M/Harwell-Boeing/lshape/lshp_778.mtx', ... 'M/Harwell-Boeing/lsq/illc1033.mtx', ... 'M/Harwell-Boeing/lsq/illc1850.mtx', ... 'M/Harwell-Boeing/lsq/well1033.mtx', ... 'M/Harwell-Boeing/lsq/well1850.mtx', ... 'M/Harwell-Boeing/nnceng/hor__131.mtx', ... 'M/Harwell-Boeing/nucl/nnc1374.mtx', ... 'M/Harwell-Boeing/nucl/nnc261.mtx', ... 'M/Harwell-Boeing/nucl/nnc666.mtx', ... 'M/Harwell-Boeing/oilgen/orsirr_1.mtx', ... 'M/Harwell-Boeing/oilgen/orsirr_2.mtx', ... 'M/Harwell-Boeing/oilgen/orsreg_1.mtx', ... 'M/Harwell-Boeing/platz/plat1919.mtx', ... 'M/Harwell-Boeing/platz/plat362.mtx', ... 'M/Harwell-Boeing/platz/plsk1919.mtx', ... 'M/Harwell-Boeing/platz/plskz362.mtx', ... 'M/Harwell-Boeing/pores/pores_1.mtx', ... 'M/Harwell-Boeing/pores/pores_2.mtx', ... 'M/Harwell-Boeing/pores/pores_3.mtx', ... 'M/Harwell-Boeing/psadmit/1138_bus.mtx', ... 'M/Harwell-Boeing/psadmit/494_bus.mtx', ... 'M/Harwell-Boeing/psadmit/662_bus.mtx', ... 'M/Harwell-Boeing/psadmit/685_bus.mtx', ... 'M/Harwell-Boeing/psmigr/psmigr_1.mtx', ... 'M/Harwell-Boeing/psmigr/psmigr_2.mtx', ... 'M/Harwell-Boeing/psmigr/psmigr_3.mtx', ... 'M/Harwell-Boeing/saylor/saylr1.mtx', ... 'M/Harwell-Boeing/saylor/saylr3.mtx', ... 'M/Harwell-Boeing/saylor/saylr4.mtx', ... 'M/Harwell-Boeing/sherman/sherman1.mtx', ... 'M/Harwell-Boeing/sherman/sherman2.mtx', ... 'M/Harwell-Boeing/sherman/sherman3.mtx', ... 'M/Harwell-Boeing/sherman/sherman4.mtx', ... 'M/Harwell-Boeing/sherman/sherman5.mtx', ... 'M/Harwell-Boeing/smtape/abb313.mtx', ... 'M/Harwell-Boeing/smtape/arc130.mtx', ... 'M/Harwell-Boeing/smtape/ash219.mtx', ... 'M/Harwell-Boeing/smtape/ash292.mtx', ... 'M/Harwell-Boeing/smtape/ash331.mtx', ... 'M/Harwell-Boeing/smtape/ash608.mtx', ... 'M/Harwell-Boeing/smtape/ash85.mtx', ... 'M/Harwell-Boeing/smtape/bp_____0.mtx', ... 'M/Harwell-Boeing/smtape/bp__1000.mtx', ... 'M/Harwell-Boeing/smtape/bp__1200.mtx', ... 'M/Harwell-Boeing/smtape/bp__1400.mtx', ... 'M/Harwell-Boeing/smtape/bp__1600.mtx', ... 'M/Harwell-Boeing/smtape/bp___200.mtx', ... 'M/Harwell-Boeing/smtape/bp___400.mtx', ... 'M/Harwell-Boeing/smtape/bp___600.mtx', ... 'M/Harwell-Boeing/smtape/bp___800.mtx', ... 'M/Harwell-Boeing/smtape/curtis54.mtx', ... 'M/Harwell-Boeing/smtape/eris1176.mtx', ... 'M/Harwell-Boeing/smtape/fs_541_1.mtx', ... 'M/Harwell-Boeing/smtape/fs_541_2.mtx', ... 'M/Harwell-Boeing/smtape/fs_541_3.mtx', ... 'M/Harwell-Boeing/smtape/fs_541_4.mtx', ... 'M/Harwell-Boeing/smtape/gent113.mtx', ... 'M/Harwell-Boeing/smtape/ibm32.mtx', ... 'M/Harwell-Boeing/smtape/lund_a.mtx', ... 'M/Harwell-Boeing/smtape/lund_b.mtx', ... 'M/Harwell-Boeing/smtape/shl____0.mtx', ... 'M/Harwell-Boeing/smtape/shl__200.mtx', ... 'M/Harwell-Boeing/smtape/shl__400.mtx', ... 'M/Harwell-Boeing/smtape/str____0.mtx', ... 'M/Harwell-Boeing/smtape/str__200.mtx', ... 'M/Harwell-Boeing/smtape/str__400.mtx', ... 'M/Harwell-Boeing/smtape/str__600.mtx', ... 'M/Harwell-Boeing/smtape/will199.mtx', ... 'M/Harwell-Boeing/smtape/will57.mtx', ... 'M/Harwell-Boeing/steam/steam1.mtx', ... 'M/Harwell-Boeing/steam/steam2.mtx', ... 'M/Harwell-Boeing/steam/steam3.mtx', ... 'M/Harwell-Boeing/watt/watt__1.mtx', ... 'M/Harwell-Boeing/watt/watt__2.mtx', ... 'M/misc/cylshell/s1rmq4m1.mtx', ... 'M/misc/cylshell/s1rmt3m1.mtx', ... 'M/misc/cylshell/s2rmq4m1.mtx', ... 'M/misc/cylshell/s3dkq4m2.mtx', ... 'M/misc/cylshell/s3dkt3m2.mtx', ... 'M/misc/cylshell/s3rmq4m1.mtx', ... 'M/misc/cylshell/s3rmt3m1.mtx', ... 'M/misc/cylshell/s3rmt3m3.mtx', ... 'M/misc/hamm/add20.mtx', ... 'M/misc/hamm/add32.mtx', ... 'M/misc/hamm/memplus.mtx', ... 'M/misc/pts5ldd0/pts5ldd03.mtx', ... 'M/misc/pts5ldd0/pts5ldd04.mtx', ... 'M/misc/pts5ldd0/pts5ldd05.mtx', ... 'M/misc/pts5ldd0/pts5ldd06.mtx', ... 'M/misc/pts5ldd0/pts5ldd07.mtx', ... 'M/misc/pts5ldd1/pts5ldd13.mtx', ... 'M/misc/pts5ldd1/pts5ldd14.mtx', ... 'M/misc/pts5ldd1/pts5ldd15.mtx', ... 'M/misc/pts5ldd1/pts5ldd16.mtx', ... 'M/misc/pts5ldd1/pts5ldd17.mtx', ... 'M/misc/pts5ldd2/pts5ldd23.mtx', ... 'M/misc/pts5ldd2/pts5ldd24.mtx', ... 'M/misc/pts5ldd2/pts5ldd25.mtx', ... 'M/misc/pts5ldd2/pts5ldd26.mtx', ... 'M/misc/pts5ldd2/pts5ldd27.mtx', ... 'M/misc/qcd/conf5.0-00l4x4-1000.mtx', ... 'M/misc/qcd/conf5.0-00l4x4-1400.mtx', ... 'M/misc/qcd/conf5.0-00l4x4-1800.mtx', ... 'M/misc/qcd/conf5.0-00l4x4-2200.mtx', ... 'M/misc/qcd/conf5.0-00l4x4-2600.mtx', ... 'M/misc/qcd/conf5.4-00l8x8-0500.mtx', ... 'M/misc/qcd/conf5.4-00l8x8-1000.mtx', ... 'M/misc/qcd/conf5.4-00l8x8-1500.mtx', ... 'M/misc/qcd/conf5.4-00l8x8-2000.mtx', ... 'M/misc/qcd/conf6.0-00l4x4-2000.mtx', ... 'M/misc/qcd/conf6.0-00l4x4-3000.mtx', ... 'M/misc/qcd/conf6.0-00l8x8-2000.mtx', ... 'M/misc/qcd/conf6.0-00l8x8-3000.mtx', ... 'M/misc/qcd/conf6.0-00l8x8-8000.mtx', ... 'M/NEP/airfoil/af23560.mtx', ... 'M/NEP/bfwave/bfw398a.mtx', ... 'M/NEP/bfwave/bfw398b.mtx', ... 'M/NEP/bfwave/bfw62a.mtx', ... 'M/NEP/bfwave/bfw62b.mtx', ... 'M/NEP/bfwave/bfw782a.mtx', ... 'M/NEP/bfwave/bfw782b.mtx', ... 'M/NEP/brussel/rdb1250l.mtx', ... 'M/NEP/brussel/rdb1250.mtx', ... 'M/NEP/brussel/rdb200l.mtx', ... 'M/NEP/brussel/rdb200.mtx', ... 'M/NEP/brussel/rdb2048l.mtx', ... 'M/NEP/brussel/rdb2048.mtx', ... 'M/NEP/brussel/rdb3200l.mtx', ... 'M/NEP/brussel/rdb450l.mtx', ... 'M/NEP/brussel/rdb450.mtx', ... 'M/NEP/brussel/rdb800l.mtx', ... 'M/NEP/brussel/rdb968.mtx', ... 'M/NEP/chuck/ck104.mtx', ... 'M/NEP/chuck/ck400.mtx', ... 'M/NEP/chuck/ck656.mtx', ... 'M/NEP/crystal/cry10000.mtx', ... 'M/NEP/crystal/cry2500.mtx', ... 'M/NEP/dwave/dw2048.mtx', ... 'M/NEP/dwave/dw8192.mtx', ... 'M/NEP/dwave/dwa512.mtx', ... 'M/NEP/dwave/dwb512.mtx', ... 'M/NEP/gedney/dwg961a.mtx', ... 'M/NEP/gedney/dwg961b.mtx', ... 'M/NEP/h2plus/qc2534.mtx', ... 'M/NEP/h2plus/qc324.mtx', ... 'M/NEP/matpde/pde225.mtx', ... 'M/NEP/matpde/pde2961.mtx', ... 'M/NEP/matpde/pde900.mtx', ... 'M/NEP/mhd/mhd1280a.mtx', ... 'M/NEP/mhd/mhd1280b.mtx', ... 'M/NEP/mhd/mhd3200a.mtx', ... 'M/NEP/mhd/mhd3200b.mtx', ... 'M/NEP/mhd/mhd416a.mtx', ... 'M/NEP/mhd/mhd416b.mtx', ... 'M/NEP/mhd/mhd4800a.mtx', ... 'M/NEP/mhd/mhd4800b.mtx', ... 'M/NEP/mvmbwm/bwm2000.mtx', ... 'M/NEP/mvmbwm/bwm200.mtx', ... 'M/NEP/mvmmcd/cdde1.mtx', ... 'M/NEP/mvmmcd/cdde2.mtx', ... 'M/NEP/mvmmcd/cdde3.mtx', ... 'M/NEP/mvmmcd/cdde4.mtx', ... 'M/NEP/mvmmcd/cdde5.mtx', ... 'M/NEP/mvmmcd/cdde6.mtx', ... 'M/NEP/mvmode/odep400a.mtx', ... 'M/NEP/mvmode/odep400b.mtx', ... 'M/NEP/mvmrwk/rw136.mtx', ... 'M/NEP/mvmrwk/rw496.mtx', ... 'M/NEP/mvmrwk/rw5151.mtx', ... 'M/NEP/mvmtls/tols1090.mtx', ... 'M/NEP/mvmtls/tols2000.mtx', ... 'M/NEP/mvmtls/tols340.mtx', ... 'M/NEP/mvmtls/tols4000.mtx', ... 'M/NEP/mvmtls/tols90.mtx', ... 'M/NEP/olmstead/olm1000.mtx', ... 'M/NEP/olmstead/olm100.mtx', ... 'M/NEP/olmstead/olm2000.mtx', ... 'M/NEP/olmstead/olm5000.mtx', ... 'M/NEP/olmstead/olm500.mtx', ... 'M/NEP/quebec/qh1484.mtx', ... 'M/NEP/quebec/qh768.mtx', ... 'M/NEP/quebec/qh882.mtx', ... 'M/NEP/robotics/rbs480a.mtx', ... 'M/NEP/robotics/rbs480b.mtx', ... 'M/NEP/stoch/lop163.mtx', ... 'M/NEP/tubular/tub1000.mtx', ... 'M/NEP/tubular/tub100.mtx', ... 'M/SPARSKIT/drivcav/e05r0000.mtx', ... 'M/SPARSKIT/drivcav/e05r0100.mtx', ... 'M/SPARSKIT/drivcav/e05r0200.mtx', ... 'M/SPARSKIT/drivcav/e05r0300.mtx', ... 'M/SPARSKIT/drivcav/e05r0400.mtx', ... 'M/SPARSKIT/drivcav/e05r0500.mtx', ... 'M/SPARSKIT/drivcav/e20r0000.mtx', ... 'M/SPARSKIT/drivcav/e20r0100.mtx', ... 'M/SPARSKIT/drivcav/e20r0500.mtx', ... 'M/SPARSKIT/drivcav/e20r1000.mtx', ... 'M/SPARSKIT/drivcav/e20r2000.mtx', ... 'M/SPARSKIT/drivcav/e20r3000.mtx', ... 'M/SPARSKIT/drivcav/e20r4000.mtx', ... 'M/SPARSKIT/drivcav/e20r5000.mtx', ... 'M/SPARSKIT/drivcav/e30r0000.mtx', ... 'M/SPARSKIT/drivcav/e30r0100.mtx', ... 'M/SPARSKIT/drivcav/e30r0500.mtx', ... 'M/SPARSKIT/drivcav/e30r1000.mtx', ... 'M/SPARSKIT/drivcav/e30r2000.mtx', ... 'M/SPARSKIT/drivcav/e30r3000.mtx', ... 'M/SPARSKIT/drivcav/e30r4000.mtx', ... 'M/SPARSKIT/drivcav/e30r5000.mtx', ... 'M/SPARSKIT/drivcav/e40r0000.mtx', ... 'M/SPARSKIT/drivcav/e40r0100.mtx', ... 'M/SPARSKIT/drivcav/e40r0500.mtx', ... 'M/SPARSKIT/drivcav/e40r1000.mtx', ... 'M/SPARSKIT/drivcav/e40r2000.mtx', ... 'M/SPARSKIT/drivcav/e40r3000.mtx', ... 'M/SPARSKIT/drivcav/e40r4000.mtx', ... 'M/SPARSKIT/drivcav/e40r5000.mtx', ... 'M/SPARSKIT/drivcav_old/cavity01.mtx', ... 'M/SPARSKIT/drivcav_old/cavity02.mtx', ... 'M/SPARSKIT/drivcav_old/cavity03.mtx', ... 'M/SPARSKIT/drivcav_old/cavity04.mtx', ... 'M/SPARSKIT/drivcav_old/cavity05.mtx', ... 'M/SPARSKIT/drivcav_old/cavity06.mtx', ... 'M/SPARSKIT/drivcav_old/cavity07.mtx', ... 'M/SPARSKIT/drivcav_old/cavity08.mtx', ... 'M/SPARSKIT/drivcav_old/cavity09.mtx', ... 'M/SPARSKIT/drivcav_old/cavity10.mtx', ... 'M/SPARSKIT/drivcav_old/cavity11.mtx', ... 'M/SPARSKIT/drivcav_old/cavity12.mtx', ... 'M/SPARSKIT/drivcav_old/cavity13.mtx', ... 'M/SPARSKIT/drivcav_old/cavity14.mtx', ... 'M/SPARSKIT/drivcav_old/cavity15.mtx', ... 'M/SPARSKIT/drivcav_old/cavity16.mtx', ... 'M/SPARSKIT/drivcav_old/cavity17.mtx', ... 'M/SPARSKIT/drivcav_old/cavity18.mtx', ... 'M/SPARSKIT/drivcav_old/cavity19.mtx', ... 'M/SPARSKIT/drivcav_old/cavity20.mtx', ... 'M/SPARSKIT/drivcav_old/cavity21.mtx', ... 'M/SPARSKIT/drivcav_old/cavity22.mtx', ... 'M/SPARSKIT/drivcav_old/cavity23.mtx', ... 'M/SPARSKIT/drivcav_old/cavity24.mtx', ... 'M/SPARSKIT/drivcav_old/cavity25.mtx', ... 'M/SPARSKIT/drivcav_old/cavity26.mtx', ... 'M/SPARSKIT/fidap/fidap001.mtx', ... 'M/SPARSKIT/fidap/fidap002.mtx', ... 'M/SPARSKIT/fidap/fidap003.mtx', ... 'M/SPARSKIT/fidap/fidap004.mtx', ... 'M/SPARSKIT/fidap/fidap005.mtx', ... 'M/SPARSKIT/fidap/fidap006.mtx', ... 'M/SPARSKIT/fidap/fidap007.mtx', ... 'M/SPARSKIT/fidap/fidap008.mtx', ... 'M/SPARSKIT/fidap/fidap009.mtx', ... 'M/SPARSKIT/fidap/fidap010.mtx', ... 'M/SPARSKIT/fidap/fidap011.mtx', ... 'M/SPARSKIT/fidap/fidap012.mtx', ... 'M/SPARSKIT/fidap/fidap013.mtx', ... 'M/SPARSKIT/fidap/fidap014.mtx', ... 'M/SPARSKIT/fidap/fidap015.mtx', ... 'M/SPARSKIT/fidap/fidap018.mtx', ... 'M/SPARSKIT/fidap/fidap019.mtx', ... 'M/SPARSKIT/fidap/fidap020.mtx', ... 'M/SPARSKIT/fidap/fidap021.mtx', ... 'M/SPARSKIT/fidap/fidap022.mtx', ... 'M/SPARSKIT/fidap/fidap023.mtx', ... 'M/SPARSKIT/fidap/fidap024.mtx', ... 'M/SPARSKIT/fidap/fidap025.mtx', ... 'M/SPARSKIT/fidap/fidap026.mtx', ... 'M/SPARSKIT/fidap/fidap027.mtx', ... 'M/SPARSKIT/fidap/fidap028.mtx', ... 'M/SPARSKIT/fidap/fidap029.mtx', ... 'M/SPARSKIT/fidap/fidap031.mtx', ... 'M/SPARSKIT/fidap/fidap032.mtx', ... 'M/SPARSKIT/fidap/fidap033.mtx', ... 'M/SPARSKIT/fidap/fidap035.mtx', ... 'M/SPARSKIT/fidap/fidap036.mtx', ... 'M/SPARSKIT/fidap/fidap037.mtx', ... 'M/SPARSKIT/fidap/fidapm02.mtx', ... 'M/SPARSKIT/fidap/fidapm03.mtx', ... 'M/SPARSKIT/fidap/fidapm05.mtx', ... 'M/SPARSKIT/fidap/fidapm07.mtx', ... 'M/SPARSKIT/fidap/fidapm08.mtx', ... 'M/SPARSKIT/fidap/fidapm09.mtx', ... 'M/SPARSKIT/fidap/fidapm10.mtx', ... 'M/SPARSKIT/fidap/fidapm11.mtx', ... 'M/SPARSKIT/fidap/fidapm13.mtx', ... 'M/SPARSKIT/fidap/fidapm15.mtx', ... 'M/SPARSKIT/fidap/fidapm29.mtx', ... 'M/SPARSKIT/fidap/fidapm33.mtx', ... 'M/SPARSKIT/fidap/fidapm37.mtx', ... 'M/SPARSKIT/tokamak/utm1700a.mtx', ... 'M/SPARSKIT/tokamak/utm1700b.mtx', ... 'M/SPARSKIT/tokamak/utm300.mtx', ... 'M/SPARSKIT/tokamak/utm3060.mtx', ... 'M/SPARSKIT/tokamak/utm5940.mtx', ... } ; for i = 1:length(matrices) filename = matrices {i} ; fprintf ('\nfile: %s\n', filename) ; tic [A,rows,cols,entries,rep,field,symm] = mmread(filename) ; t1 = toc ; fprintf (' %d by %d, nz %d %s %s %s\n', ... rows, cols, entries, rep, field, symm) ; % try tic B = mread (filename) ; t2 = toc ; % catch % B = [ ] ; % end fprintf ('speedup %6.2f nnz %d\n', t1/t2, nnz(A)) ; % mread add values to a pattern-only matrix. Remove them if (strcmp (field, 'pattern')) B = spones (B) ; end if (isempty (B)) fprintf ('============================ could not read with CHOLMOD\n') ; error ('!') ; else err = norm (A-B,1) ; if (err ~= 0) fprintf ('=================================== %8.1e\n', err) ; error ('!') ; end end end SuiteSparse/CHOLMOD/MATLAB/Test/Results.mat0000644001170100242450000000456310711454700017066 0ustar davisfacMATLAB 5.0 MAT-file, Platform: GLNXA64, Created on: Mon Oct 29 18:08:00 2007 IMx-9 `@7Xٺ:bN\+q9CkwccaJL1\ 5o$eX+tyPjtqB>WӵnKO40I)9梼b(o|&$ܸLjkJxc``89 4B@)#0b dO lx >&|,;d}]duXUGI_,JQW4T:h\a`_O'v+St+ސlj0}3?{F@?~7؊^6]sQs\W~w׮yC>#b77Pυ[edlIfoY65~vO𤒿}ԬRIIAG^δ׷0,f?~|t{˝;Jd:yKZMj槝AEek=}b{Dm`nK_*2I1Ҟ_软}[ǝ˞bˆnwcKB$9|͍smT,n/>`yG{}1yVgv:ʵO$y. _Q+foG}r ~~Ǿ{'K{֨^t߲ij܎H;}B~J_S셵^+>)wm }]~}Hkn5vI_h?Qm3ųyxc``89 4B@)#0j dO 2ih؂K3@9IvG)Xa'0B<k֛ wdR^nwA! @; 024cd [f jufrځ3TA-k K[[^1wm9Y?jF=N^ff4%ļl@a/SԖi֔`Z~:Tm'ؖaƧ=vb?c3_b#vzni k-6nw%픬nfz-SO@3(lxxc``89 4B@)#0 dpdlAw=;'?(3d~Bg6_3"^ѽw_XlJWaXQoÆaL@ńr[f ,ﰄ_)?CUdڲ u9玶m~9'_`GiK[̌K:) ;uKmjjM6ߡFh_Gԡ"n;AŶ, 3>˘p/ߌlk-WDЯ;1 ֦?m hUk-6nw%픬~fz-SO%Уo>Éfpxc``l@Agb#0?@| 230T30q!:F'\ CPã K@|nL Тܰ D33 30ʱCΤ2 0hX3t`f# ]FCT )30h23ϖf0ba`Z` )xM? Aa"72*IEPe$ddX`XFPFk}K租yCdjRYD^CE?6j,)8`"_ ; eٌ#ҲFf9U3wQn2&\BsS 7v&xc``0b6 313Cvv6e!SuiteSparse/CHOLMOD/MATLAB/Test/test0.m0000644001170100242450000001454010710415761016136 0ustar davisfacfunction test0 (nmat) %TEST0 test most CHOLMOD functions % Example: % test0(nmat) % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test0: test most CHOLMOD functions\n') ; % This test requires UFget, the MATLAB interface to the UF sparse matrix % collection. You can obtain UFget from % http://www.cise.ufl.edu/research/sparse/matrices. try % load UF index index = UFget ; catch error ('Test aborted. UF sparse matrix collection not available.\n') ; end f = find (index.posdef) ; [ignore i] = sort (index.nrows (f)) ; f = f (i) ; rand ('state', 0) ; randn ('state', 0) ; doplots = 0 ; if (doplots) clf end % skip = [937:939 1202:1211] ; skip = 937:939 ; if (nargin > 0) nmat = max (0,nmat) ; nmat = min (nmat, length (f)) ; f = f (1:nmat) ; end % f= 229 fprintf ('test matrices sorted by dimension:\n') ; for i = f if (any (i == skip)) continue end fprintf ('%4d: %-20s %-20s %12d %d\n', i, ... index.Group {i}, index.Name {i}, index.nrows (i), index.posdef (i)) ; end % pause for i = f if (any (i == skip)) continue end % try Problem = UFget (i) ; A = Problem.A ; fprintf ('\n================== Problem: %d: %s n: %d nnz: %d\n', ... i, Problem.name, size (A,1), nnz (A)) ; fprintf ('title: %s\n', Problem.title) ; clear Problem n = size (A,1) ; % use AMD from SuiteSparse tic p = amd2 (A) ; t0 = toc ; fprintf ('time: amd %10.4f\n', t0) ; S = A (p,p) ; if (doplots) subplot (3,2,1) ; spy (A) ; title ('A original') ; subplot (3,2,2) ; spy (S) ; title ('A permuted') ; drawnow ; end % ensure chol, chol2, and lchol are loaded, for more accurate timing R = chol2 (sparse (1)) ; %#ok R = chol (sparse (1)) ; %#ok R = lchol (sparse (1)) ; %#ok R = ldlchol (sparse (1)) ; %#ok R = ldlupdate (sparse (1), sparse (1)) ; %#ok c = symbfact (sparse (1)) ; %#ok tic ; L = lchol (S) ; t3 = toc ; if (doplots) subplot (3,2,5) ; spy (L) ; title ('L=lchol') ; drawnow ; end fprintf ('CHOLMOD time: L=lchol %10.4f nnz(L): %d\n', t3, nnz (L)) ; lnorm = norm (L, 1) ; err = ldl_normest (S, L) / lnorm ; if (err > 1e-6) error ('!') ; end clear L tic ; R = chol2 (S) ; t2 = toc ; if (doplots) subplot (3,2,3) ; spy (R) ; title ('R=chol2') ; drawnow ; end fprintf ('CHOLMOD time: R=chol2 %10.4f nnz(R): %d\n', t2, nnz (R)) ; err = ldl_normest (S, R') / lnorm ; if (err > 1e-6) error ('!') ; end clear R tic ; R = chol (S) ; t1 = toc ; fprintf ('MATLAB time: R=chol %10.4f nnz(R): %d\n', t1, nnz (R)) ; if (doplots) subplot (3,2,4) ; spy (R) ; title ('chol') ; drawnow ; end err = ldl_normest (S, R') / lnorm ; if (err > 1e-6) error ('!') ; end clear R tic ; [count,h,parent,post,R] = symbfact (S) ; t7 = toc ; fprintf ('MATLAB [..,R]=symbfact %10.4f nnz(R): %d\n', t7, nnz (R)) ; fprintf ('\nCHOLMOD speedup vs MATLAB chol: R: %8.2f L: %8.2f\n\n', ... t1/t2, t1/t3) ; fprintf ('\nCHOLMOD numeric lchol vs MATLAB symbfact: %8.2f\n', t7/t3) ; clear R S % use AMD or METIS, doing the ordering in CHOLMOD tic [L,p,q] = lchol (A) ; t4 = toc ; fprintf ('CHOLMOD time: [L,,q]=lchol %10.4f nnz(L): %d\n', ... t4, nnz (L)) ; if (doplots) subplot (3,2,6) ; spy (L) ; title ('[L,p,q]=lchol') ; drawnow ; end err = ldl_normest (A (q,q), L) / lnorm ; if (err > 1e-6) error ('!') ; end clear L % try an LDL' factorization, LD has LDL' factorization of S = A(q,q) tic [LD,p,q] = ldlchol (A) ; t5 = toc ; fprintf ('CHOLMOD time: [L,,q]=ldlchol %10.4f nnz(L): %d\n', ... t5, nnz (LD)) ; [L,D] = ldlsplit (LD) ; S = A (q,q) ; err = ldl_normest (S, L, D) / lnorm ; if (err > 1e-6) error ('!') ; end clear L D A % update the LDL' factorization (rank 1 to 8). Pick a C that has % the same pattern as a random set of columns of L, so no fill-in % occurs. Then add one arbitrary entry, to add some fill-in to L. k = 1 + floor (rand (1) * 8) ; cols = randperm (n) ; cols = cols (1:k) ; C = sprandn (LD (:,cols)) ; row = 1 + floor (rand (1) * n) ; C (row,1) = 1 ; if (~isreal (C) | ~isreal (LD)) %#ok fprintf ('skip update/downdate of complex matrix ...\n') ; continue ; end tic LD2 = ldlupdate (LD, C) ; t = toc ; fprintf ('\nCHOLMOD time: rank-%d ldlupdate %10.4f nnz(L) %d', ... k, t, nnz (LD2)) ; if (nnz (LD2) > nnz (LD)) fprintf (' with fill-in\n') ; else fprintf (' no fill-in\n') ; end clear LD % check the factorization, LD2 has LDL' factorization of S+C*C' [L,D] = ldlsplit (LD2) ; err = ldl_normest (S + C*C', L, D) / lnorm ; if (err > 1e-6) error ('!') ; end clear L D % downate the LDL' factorization, with just part of C % no change to the pattern occurs. k = max (1, floor (k/2)) ; C1 = C (:, 1:k) ; C2 = C (:, k+1:end) ; %#ok tic LD3 = ldlupdate (LD2, C1, '-') ; t = toc ; clear LD2 fprintf ('CHOLMOD time: rank-%d ldldowndate %10.4f nnz(L) %d', ... k, t, nnz (LD3)) ; fprintf (' no fill-in\n') ; % check the factorization, LD3 has LDL' factorization of A(q,q)+C2*C2' [L,D] = ldlsplit (LD3) ; S2 = S + C*C' - C1*C1' ; err = ldl_normest (S2, L, D) / lnorm ; if (err > 1e-6) error ('!') ; end % now test resymbol LD4 = resymbol (LD3, S2) ; [L,D] = ldlsplit (LD4) ; err = ldl_normest (S2, L, D) / lnorm ; if (err > 1e-6) error ('!') ; end fprintf ('after resymbol: %d\n', nnz (LD4)) ; % compare resymbol with ldlchol LD5 = ldlchol (S2) ; if (nnz (LD5) ~= nnz (LD4)) error ('!') ; end if (nnz (spones (LD5) - spones (LD4)) ~= 0) error ('!') ; end b = rand (n,2) ; x = ldlsolve (LD4, b) ; err1 = norm (S2*x-b,1) / norm (S,1) ; fprintf ('CHOLMOD residual: %6.1e\n', err1) ; x = S2\b ; err2 = norm (S2*x-b,1) / norm (S,1) ; fprintf ('MATLAB residual: %6.1e\n', err2) ; b = sprandn (n,3,0.4) ; x = ldlsolve (LD4, b) ; err1 = norm (S2*x-b,1) / norm (S,1) ; fprintf ('CHOLMOD residual: %6.1e (sparse b)\n', err1) ; x = S2\b ; err2 = norm (S2*x-b,1) / norm (S,1) ; fprintf ('MATLAB residual: %6.1e (sparse b)\n', err2) ; % catch % fprintf ('failed\n') ; % end clear A S C L R LD LD2 LD3 D p q C1 C2 LD3 S2 LD4 b x LD5 end fprintf ('test0 passed\n') ; SuiteSparse/CHOLMOD/MATLAB/Test/test1.m0000644001170100242450000000420210620665232016131 0ustar davisfacfunction test1 (wait) %TEST1 test sparse2 % Example: % test1 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test1: test sparse2\n') ; if (nargin == 0) wait = 0 ; end m = 3 ; n = 4 ; ii = { 1, [2 3]', 2, [ ] } ; jj = { 1, [2 3]', 3, [ ] } ; ss = { 1, [2 3]', pi, [ ] } ; for ki = 1:length (ii) for kj = 1:length (jj) for ks = 1:length (ss) fprintf ('\n-----------------------------------------------\n') ; i = ii {ki} %#ok j = jj {kj} %#ok s = ss {ks} %#ok m %#ok n %#ok clear A1 A2 B1 B2 fprintf ('\nA1 = sparse (i,j,s,m,n)\n') ; try % sparse, possibly with invalid inputs A1 = sparse (i,j,s,m,n) %#ok fprintf ('size A1: %d %d\n', size (A1)) ; catch A1 = 'A failed' ; fprintf ('sparse failed\n') ; end fprintf ('\nA2 = sparse2 (i,j,s,m,n)\n') ; try % sparse2, possibly with invalid inputs A2 = sparse2 (i,j,s,m,n) %#ok fprintf ('size A2: %d %d\n', size (A2)) ; catch A2 = 'A failed' ; fprintf ('sparse2 failed\n') ; end fprintf ('\nB1 = sparse (i,j,s)\n') ; try % sparse, possibly with invalid inputs B1 = sparse (i,j,s) %#ok fprintf ('size B1: %d %d\n', size (B1)) ; catch B1 = 'B failed' ; fprintf ('sparse failed\n') ; end fprintf ('\nB2 = sparse2 (i,j,s)\n') ; try % sparse2, possibly with invalid inputs B2 = sparse2 (i,j,s) %#ok fprintf ('size B2: %d %d\n', size (B2)) ; catch B2 = 'B failed' ; fprintf ('sparse2 failed\n') ; end if (wait) pause end if (~isequal (A1,A2) | ~isequal (B1,B2)) %#ok fprintf (... '========================== SPARSE AND SPARSE2 DIFFER\n') ; end end end end fprintf ('test1 passed (review the above results)\n') ; SuiteSparse/CHOLMOD/MATLAB/Test/test2.m0000644001170100242450000000152610620371346016140 0ustar davisfacfunction test2 %TEST2 test sparse2 % Example: % test2 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test2: test sparse2\n') ; i = [ 2 3 ] %#ok j = [ 3 4 ] %#ok s = [11.4 9.2] + 1i * [3.4 1.2] %#ok sparse (i,j,s) %#ok sparse2 (i,j,s) %#ok n = 100 ; nz = 4000 ; i = fix (n * rand (nz,1)) + 1 ; j = fix (n * rand (nz,1)) + 1 ; s = rand (nz,1) + 1i * rand (nz,1) ; A = sparse (i,j,s,n,n) ; B = sparse2 (i,j,s,n,n) ; nnz(A) if (norm (A-B,1) > 1e-14) A_minus_B = A-B %#ok error ('!') ; end C = sparse (A) ; D = sparse2 (B) ; if (norm (C-D,1) > 1e-14) C_minus_D = C-D %#ok error ('!') ; end % spy(C) fprintf ('test2 passed\n') ; SuiteSparse/CHOLMOD/MATLAB/Test/test3.m0000644001170100242450000000141410620371347016136 0ustar davisfacfunction test3 %TEST3 test sparse on int8, int16, and logical % Example: % test3 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test3: test sparse on int8, int16, and logical\n') ; clear all c = ['a' 'b' 0 'd'] %#ok sparse(c) sparse2(c) sparse(c') sparse2(c') whos nzmax(ans) %#ok try % this will fail sparse(int8(c)) catch fprintf ('sparse(int8(c)) fails in MATLAB\n') ; end sparse2(int8(c)) sparse2 (int16(c)) whos s = logical(rand(4) > .5) %#ok sparse (s) whos sparse2(s) whos x = rand(4) %#ok sparse (x > .5) %#ok whos sparse2 (x > .5) %#ok whos fprintf ('test3 passed\n') ; SuiteSparse/CHOLMOD/MATLAB/Test/test4.m0000644001170100242450000000223610620665354016146 0ustar davisfacfunction test4 %TEST4 test cholmod2 with multiple and sparse right-hand-sides % Example: % test4 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test4: test cholmod2 with multiple and sparse right-hand-sides\n') ; Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; n = size (A,1) ; b = rand (n,1) ; x = cholmod2 (A,b) ; m2 = norm (A*x-b,1) ; b = sparse (b) ; x = cholmod2 (A,b) ; m2 = max (m2, norm (A*x-b,1)) ; m1 = 0 ; for nrhs = 1:80 b = sparse (rand (n,nrhs)) ; x = A\b ; e1 = norm (A*x-b,1) ; x = cholmod2 (A,b) ; e2 = norm (A*x-b,1) ; if (e2 > 1e-11) error ('!') ; end m1 = max (m1, e1) ; m2 = max (m2, e2) ; end for nrhs = 1:80 b = sprandn (n, nrhs, 0.01) ; x = A\b ; % nnz (x) / (n*nrhs) e1 = norm (A*x-b,1) ; x = cholmod2 (A,b) ; e2 = norm (A*x-b,1) ; if (e2 > 1e-11) error ('!') ; end m1 = max (m1, e1) ; m2 = max (m2, e2) ; end fprintf ('maxerr %e %e\n', m1, m2) ; if (m1 > 1e-11 | m2 > 1e-11) %#ok error ('!') ; end fprintf ('test4 passed\n') ; SuiteSparse/CHOLMOD/MATLAB/Test/test5.m0000644001170100242450000000330610620371352016136 0ustar davisfacfunction test5 %TEST5 test sparse2 % Example: % test5 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test5: test sparse2\n') ; randn ('state', 0) ; rand ('state', 0) ; A = sprandn (10,20,0.2) ; [m n ] = size (A) ; [i j x] = find (A) ; % [i2 j2 x2] = cholmod_find (A) ; % if (any (i ~= i2)) % error ('i!') ; %end %if (any (j ~= j2)) % error ('j!') ; %end %if (any (x ~= x2)) % error ('x!') ; %end % full (sum (spones (A'))) C = sparse (i,j,x,m,n) ; B = sparse2 (i,j,x,m,n) ; err = norm(A-B,1) ; if (err > 0) error ('dtri 1') ; end err = norm(C-B,1) ; if (err > 0) error ('dtri 1b') ; end nz = length (x) ; p = randperm (nz) ; i2 = i(p) ; j2 = j(p) ; x2 = x(p) ; %#ok B = sparse2 (i,j,x,m,n) ; err = norm(A-B,1) ; if (err > 0) error ('dtri 2') ; end ii = [i2 ; i2] ; jj = [j2 ; j2] ; xx = rand (2*nz,1) ; C = sparse (ii,jj,xx,m,n) ; D = sparse2 (ii,jj,xx,m,n) ; err = norm (C-D,1) ; if (err > 0) error ('dtri 3') ; end % E = sparse2 (ii,jj,xx,n,n,+1) ; E = sparse (min(ii,jj), max(ii,jj), xx, n, n) ; F = sparse (min(ii,jj), max(ii,jj), xx, n, n) ; err = norm (E-F,1) ; if (err > 0) error ('dtri 4') ; end % E = sparse2 (ii,jj,xx,n,n,-1) ; E = sparse (max(ii,jj), min(ii,jj), xx, n, n) ; F = sparse (max(ii,jj), min(ii,jj), xx, n, n) ; err = norm (E-F,1) ; if (err > 0) error ('dtri 5') ; end [i1 j1 x1] = find (F) ; %#ok % [i2 j2 x2] = cholmod_find (F) ; % if (any (i1 ~= i2)) % error ('i!') ; % end % if (any (j1 ~= j2)) % error ('j!') ; % end % if (any (x1 ~= x2)) % error ('x!') ; % end fprintf ('test5 passed\n') ; SuiteSparse/CHOLMOD/MATLAB/Test/test6.m0000644001170100242450000000656010710152476016150 0ustar davisfacfunction test6 %TEST6 test sparse with large matrix, both real and complex % compare times with MATLAB % Example: % test6 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test6: test sparse with large matrix, both real and complex\n') ; for do_complex = 0:1 fprintf ('do_complex = %d\n', do_complex) ; randn ('state', 0) ; rand ('state', 0) ; % Prob = UFget (437) Prob = UFget (749) %#ok A = Prob.A ; [m n] = size (A) ; %#ok if (do_complex) % A = A + 1i*sprand(A) ; % patch for MATLAB 7.2 A = A + sparse(1:m,1:m,1i)*sprand(A) ; end tic [i j x] = find (A) ; t = toc ; fprintf ('find time %8.4f\n', t) ; % tic % [i1 j1 x1] = cholmod_find (A) ; % t = toc ; % fprintf ('cholmod_find time %8.4f (for testing only, it should be slow)\n', t) ; % if (any (i ~= i1)) % error ('i!') ; % end % if (any (j ~= j1)) % error ('j!') ; % end % if (any (x ~= x1)) % error ('x!') ; % end [m n ] = size (A) ; tic ; B = sparse2 (i,j,x,m,n) ; t1 = toc ; tic ; C = sparse (i,j,x,m,n) ; t2 = toc ; fprintf ('dtri time: cholmod2 %8.6f matlab %8.6f\n', t1, t2) ; err = norm(A-B,1) ; if (err > 0) error ('dtri2 1') ; end err = norm(A-C,1) ; if (err > 0) error ('dtri2 1') ; end nz = length (x) ; p = randperm (nz) ; i2 = i(p) ; j2 = j(p) ; x2 = x(p) ; %#ok tic ; B = sparse2 (i,j,x,m,n) ; t1 = toc ; tic ; C = sparse (i,j,x,m,n) ; t2 = toc ; fprintf ('dtri time: cholmod2 %8.6f matlab %8.6f (jumbled)\n', t1, t2) ; err = norm(A-B,1) ; if (err > 0) error ('dtri2 2') ; end err = norm(A-C,1) ; if (err > 0) error ('dtri2 1') ; end ii = [i2 ; i2] ; jj = [j2 ; j2] ; xx = rand (2*nz,1) ; if (do_complex) xx = xx + 1i* rand (2*nz,1) ; end tic ; D = sparse2 (ii,jj,xx,m,n) ; t1 = toc ; tic ; C = sparse (ii,jj,xx,m,n) ; t2 = toc ; err = norm (C-D,1) ; if (err > 0) error ('dtri2 3') ; end fprintf ('dtri time: cholmod2 %8.6f matlab %8.6f (duplicates)\n', t1, t2) ; fprintf ('length %d nz %d\n', length (xx), nnz(D)) ; i2 = min (ii,jj) ; j2 = max (ii,jj) ; tic ; E = sparse2 (i2,j2,xx,n,n) ; t1 = toc ; tic ; F = sparse (i2, j2, xx, n, n) ; t2 = toc ; err = norm (E-F,1) %#ok if (err > 1e-13) error ('dtri2 4') ; end fprintf ('dtri time: cholmod2 %8.6f matlab %8.6f (upper)\n', t1, t2) ; i2 = max (ii,jj) ; j2 = min (ii,jj) ; tic ; E = sparse2 (i2,j2,xx,n,n) ; t1 = toc ; tic ; F = sparse (i2, j2, xx, n, n) ; t2 = toc ; err = norm (E-F,1) %#ok if (err > 1e-13) error ('dtri2 5') ; end fprintf ('dtri time: cholmod2 %8.6f matlab %8.6f (lower)\n', t1, t2) ; [ignore, i] = sort (ii) ; ii = ii (i) ; jj = jj (i) ; xx = xx (i) ; tic ; D = sparse2 (ii,jj,xx,m,n) ; t1 = toc ; tic ; C = sparse (ii,jj,xx,m,n) ; t2 = toc ; err = norm (C-D,1) ; if (err > 0) error ('dtri2 6') ; end fprintf ('dtri time: cholmod2 %8.6f matlab %8.6f (sorted, dupl)\n', t1, t2) ; end fprintf ('test6 passed\n') ; SuiteSparse/CHOLMOD/MATLAB/Test/test7.m0000644001170100242450000000214710620371356016146 0ustar davisfacfunction test7 %TEST7 test sparse2 % Example: % test7 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test7: test sparse2\n') ; randn ('state', 0) ; rand ('state', 0) ; % Prob = UFget (437) Prob = UFget (750) %#ok A = Prob.A ; [m n] = size (A) ; tic [i j x] = find (A) ; t = toc ; fprintf ('find time %8.4f\n', t) ; tic ; B = sparse2 (i,j,x,m,n) ; %#ok t1 = toc ; fprintf ('tot: %8.6f\n', t1) tic ; B = sparse2 (i,j,x,m,n) ; %#ok t1 = toc ; fprintf ('tot: %8.6f again \n', t1) ; tic ; B1 = sparse2 (i,j,x) ; %#ok t1 = toc ; fprintf ('tot: %8.6f (i,j,x)\n', t1) ; nz = length (x) ; p = randperm (nz) ; i2 = i(p) ; j2 = j(p) ; x2 = x(p) ; %#ok tic ; B = sparse2 (i,j,x,m,n) ; %#ok t1 = toc ; fprintf ('tot: %8.6f (jumbled)\n', t1) ; ii = [i2 ; i2] ; jj = [j2 ; j2] ; xx = rand (2*nz,1) ; tic ; D = sparse2 (ii,jj,xx,m,n) ; %#ok t1 = toc ; fprintf ('tot %8.6f (duplicates)\n', t1) ; fprintf ('test7 passed\n') ; SuiteSparse/CHOLMOD/MATLAB/Test/test8.m0000644001170100242450000000601310710406406016136 0ustar davisfacfunction test8 (nmat) %TEST8 order a large range of sparse matrices, test symbfact2 % compare AMD and METIS % Example: % test8(nmat) % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test8: factorize a large range of sparse matrices\n') ; % get list of test matrices index = UFget ; % GHS posdef test set (more or less) f = find (... ((index.numerical_symmetry == 1 & index.isBinary) | (index.posdef)) ... & (index.nnzdiag == index.nrows) ... & (index.nrows > 10000 | index.nrows == 9000) ... & (index.nrows < 600000) & (index.nnz > index.nrows)) ; %#ok % include small matrices f = find (... ((index.numerical_symmetry == 1 & index.isBinary) | (index.posdef)) ... & (index.nnzdiag == index.nrows) ... & (index.nrows < 600000) & (index.nnz > index.nrows)) ; for k = 1:length (f) names {k} = index.Name {f(k)} ; %#ok end [ignore i] = sort (names) ; f = f (i) ; % fprintf ('test matrices sorted by name:\n') ; % for i = f % fprintf ('%4d: %-20s %-20s %12d %d\n', i, ... % index.Group {i}, index.Name {i}, index.nrows (i), index.posdef (i)) ; % end [ignore i] = sort (index.nrows (f)) ; f = f (i) ; if (nargin > 0) nmat = max (0,nmat) ; nmat = min (nmat, length (f)) ; f = f (1:nmat) ; end fprintf ('test matrices sorted by dimension:\n') ; for i = f fprintf ('%4d: %-20s %-20s %12d %d\n', i, ... index.Group {i}, index.Name {i}, index.nrows (i), index.posdef (i)) ; end junk = sparse (1) ; % input ('hit enter to continue: ') ; for k = 1:length (f) Problem = UFget (f(k)) ; A = Problem.A ; fprintf ('\n================== Problem: %s n: %d nnz: %d\n', ... Problem.name, size (A,1), nnz (A)) ; fprintf ('title: %s\n\n', Problem.title) ; clear Problem n = size (A,1) ; %#ok amd2 (junk) ; metis (junk) ; tic ; [p1,info] = amd2 (A) ; %#ok t1 = toc ; S1 = A (p1,p1) ; tic ; c1 = symbfact (S1) ; ts1 = toc ; tic ; d1 = symbfact (S1) ; ts2 = toc ; if (any (c1 ~= d1)) error ('!') end fprintf ('symbfact time: MATLAB %9.4f CHOLMOD %9.4f speedup %8.2f\n', ... ts1, ts2, ts1/ts2) ; lnz1 = sum (c1) ; fl1 = sum (c1.^2) ; fprintf ('time: amd %10.4f mnnz(L) %8.1f mfl %8.0f fl/nnz(L) %8.1f\n', ... t1, lnz1/1e6, fl1 /1e6, fl1/lnz1) ; tic ; p2 = metis (A) ; t2 = toc ; S2 = A (p2,p2) ; c2 = symbfact (S2) ; lnz2 = sum (c2) ; fl2 = sum (c2.^2) ; fprintf ('time: metis %10.4f mnnz(L) %8.1f mfl %8.0f fl/nnz(L) %8.1f\n', ... t2, lnz2/1e6, fl2/1e6, fl2/lnz2) ; r = lnz2 / lnz1 ; %#ok fprintf ('\nmetis/amd time: %8.4f nnz(L): %8.4f\n', t2/t1, lnz2/lnz1) ; % save results lnz (k,1) = lnz1 ; %#ok lnz (k,2) = lnz2 ; %#ok fl1 (k,1) = fl1 ; %#ok fl2 (k,2) = fl2 ; %#ok t (k,1) = t1 ; %#ok t (k,2) = t2 ; %#ok end fprintf ('test8 passed\n') ; SuiteSparse/CHOLMOD/MATLAB/Test/test9.m0000644001170100242450000000431410710406412016136 0ustar davisfacfunction test9 %TEST9 test metis, etree, bisect, nesdis % Example: % test9 % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('=================================================================\n'); fprintf ('test9: test metis, etree, bisect, nesdis\n') ; % Prob = UFget ('LPnetlib/lp_qap15') ; Prob = UFget ('HB/bcsstk15') %#ok A = Prob.A ; C = A'*A ; R = A*A' ; fprintf ('\nmetis:\n') ; tic ; p0 = metis (R) ; toc %#ok % [pa po] = etree2 (R (p0,p0)) ; sparse (po - (1:size(R,1))) tic ; p1 = metis (C) ; toc %#ok % [pa po] = etree2 (C (p1,p1)) ; sparse (po - (1:size(C,1))) tic ; p2 = metis (C, 'sym') ; toc %#ok % [pa po] = etree2 (C (p1,p1)) ; sparse (po - (1:size(C,1))) tic ; p3 = metis (A, 'row') ; toc %#ok % [pa po] = etree2 (A (p1,:), 'row') ; sparse (po - (1:size(A,1))) tic ; p4 = metis (A, 'col') ; toc %#ok % [pa po] = etree2 (A (:,p1), 'col') ; sparse (po - (1:size(A,2))) fprintf ('\nmetis(A):\n') ; [m n] = size(A) ; if (m == n) if (nnz (A-A') == 0) tic ; p5 = metis (A) ; toc % figure (1) % spy (A (p5,p5)) ; [ignore q] = etree (A(p5,p5)) ; p5post = p5 (q) ; %#ok % figure (2) % spy (A (p5post,p5post)) ; lnz0 = sum (symbfact (A (p5,p5))) %#ok end end fprintf ('\namd:\n') ; if (m == n) if (nnz (A-A') == 0) tic ; z0 = amd2 (A) ; toc %#ok lnz = sum (symbfact (A (z0,z0))) %#ok end end fprintf ('\nbisect:\n') ; tic ; s0 = bisect (R) ; toc %#ok tic ; s1 = bisect (C) ; toc %#ok tic ; s2 = bisect (C, 'sym') ; toc %#ok tic ; s3 = bisect (A, 'row') ; toc %#ok tic ; s4 = bisect (A, 'col') ; toc %#ok fprintf ('\nnested dissection:\n') ; tic ; [c0 cp0 cmem0] = nesdis (R) ; toc %#ok tic ; [c1 cp1 cmem1] = nesdis (C) ; toc %#ok tic ; [c2 cp2 cmem2] = nesdis (C, 'sym') ; toc %#ok tic ; [c3 cp3 cmem3] = nesdis (A, 'row') ; toc %#ok tic ; [c4 cp4 cmem4] = nesdis (A, 'col') ; toc %#ok fprintf ('\nnested_dissection(A):\n') ; if (m == n) if (nnz (A-A') == 0) tic ; c5 = nesdis (A) ; toc %#ok lnz1 = sum (symbfact (A (c5,c5))) %#ok end end fprintf ('test9 passed\n') ; SuiteSparse/CHOLMOD/MATLAB/Test/testsolve.m0000644001170100242450000000174610620665473017142 0ustar davisfacfunction [x1,x2,e1,e2] = testsolve (A,b) %TESTSOLVE test CHOLMOD and compare with x=A\b % [x1,x2,e1,e2] = testsolve (A,b) ; % Compare CHOLMOD and MATLAB's x=A\b % x1 = A\b, x2 = cholmod2(A,b), e1 = norm(A*x1-b), e2 = norm(A*x2-b) % Example: % [x1,x2,e1,e2] = testsolve (A,b) ; % See also cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida fprintf ('A: [n %6d real %d] B: [sp:%d nrhs %d real %d] ', ... size(A,1), isreal(A), issparse(b), size(b,2), isreal(b)) ; tic x1 = A\b ; t1 = toc ; tic x2 = cholmod2(A,b) ; t2 = toc ; tic e1 = norm (A*x1-b,1) ; t3 = toc ; e2 = norm (A*x2-b,1) ; if (e2 == 0 | e1 == 0) %#ok e12 = 0 ; else e12 = log2 (e1/e2) ; end if (t2 == 0) t12 = 1 ; else t12 = t1 / t2 ; end if (t2 == 0) t32 = 1 ; %#ok else t32 = t3 / t2 ; %#ok end fprintf (' [e1: %5.0e : %5.1f] [t1: %8.2f t2 %8.2f : %5.1f]\n', ... e1, e12, t1, t2, t12) ; if (e2 > max (1e-8, 1e3*e1)) error ('!') ; end SuiteSparse/CHOLMOD/MATLAB/Test/cholmod_test.m0000644001170100242450000001414410712150653017561 0ustar davisfacfunction cholmod_test (nmat, do_diary) %CHOLMOD_TEST test the CHOLMOD mexFunctions % % Example: % cholmod_test(nmat,do_diary) % % The UFget interface to the UF sparse matrix collection is required. % % nmat is optional. If present, it is the # of matrices used in % tests 0, 8, 10, 11, 12, and 12. tests 14 and 15 use 2*nmat matrices. % default nmat is 50. % % do_diary: 1 to save results in a diary, 0 otherwise. Default 0. % % cholmod_demo: run tests on a few random matrices % graph_demo: graph partitioning demo % test0: test most CHOLMOD functions % test1: test sparse2 % test2: test sparse2 % test3: test sparse on int8, int16, and logical % test4: test cholmod2 with multiple and sparse right-hand-sides % test5: test sparse2 % test6: test sparse with large matrix, both real and complex, compare w/MATLAB % test7: test sparse2 % test8: order many sparse matrices, test symbfact2, compare amd and metis % test9: test metis, etree, bisect, nesdis % test10: test cholmod2's backslash on real and complex matrices % test11: test analyze, compare CHOLMOD and MATLAB, save results in Results.mat % test12: test etree2 and compare with etree % test13: test cholmod2 and MATLAB on large tridiagonal matrices % test14: test metis, symbfact2, and etree2 % test15: test symbfact2 vs MATLAB % test16: test cholmod2 on a large matrix % test17: test lchol on a few large matrices % test18: test cholmod2 on a few large matrices % test19: look for NaN's from lchol (caused by Intel MKL 7.x bug) % test20: test symbfact2, cholmod2, and lu on a few large matrices % test21: test cholmod2 on diagonal or ill-conditioned matrices % test22: test chol and chol2 and singular and indefinite matrices % test23: test chol and cholmod2 on the sparse matrix used in "bench" % test24: test sdmult % test25: test sdmult on a large matrix % test26: test logical full and sparse matrices % test27: test nesdis % % See also test0, test1, ... test28. % This extensive test is not included: % test28: test nesdis % Copyright 2006-2007, Timothy A. Davis, University of Florida if (nargin < 2) do_diary = 0 ; end if (do_diary) diary off s = date ; t = clock ; s = sprintf ('diary cholmod_test_%s_%d-%d-%d.txt\n', s, t (4), t(5), fix(t(6))); eval (s) ; end fprintf ('Running CHOLMOD tests.\n') ; help cholmod_test test_path = pwd ; % addpath (test_path) ; cd ('..') ; cholmod_path = pwd ; addpath (cholmod_path) cd ('../../AMD/MATLAB') ; amd_path = pwd ; addpath (amd_path) cd ('../../COLAMD') ; colamd_path = pwd ; addpath (colamd_path) cd ('../CCOLAMD') ; ccolamd_path = pwd ; addpath (ccolamd_path) cd ('../CAMD/MATLAB') ; camd_path = pwd ; addpath (camd_path) cd (test_path) fprintf ('Added the following paths. You may wish to add them\n') ; fprintf ('permanently using the MATLAB pathtool command.\n') ; fprintf ('%s\n', cholmod_path) ; fprintf ('%s\n', amd_path) ; fprintf ('%s\n', colamd_path) ; fprintf ('%s\n', ccolamd_path) ; fprintf ('%s\n', camd_path) ; if (nargin < 1) nmat = 50 ; end try s = metis (sparse (1)) ; do_metis = 1 ; catch fprintf ('METIS not installed\n') ; do_metis = 0 ; end h = waitbar (0.5/32, 'CHOLMOD demo:') ; try cholmod_demo ; waitbar ( 1/32, h, 'CHOLMOD graph demo'); if (do_metis) graph_demo ; end waitbar ( 2/32, h, 'CHOLMOD test0') ; test0 (nmat) ; waitbar ( 3/32, h, 'CHOLMOD test1') ; test1 ; waitbar ( 4/32, h, 'CHOLMOD test2') ; test2 ; waitbar ( 5/32, h, 'CHOLMOD test3') ; test3 ; waitbar ( 6/32, h, 'CHOLMOD test4') ; test4 ; waitbar ( 7/32, h, 'CHOLMOD test5') ; test5 ; waitbar ( 8/32, h, 'CHOLMOD test6') ; test6 ; waitbar ( 9/32, h, 'CHOLMOD test7') ; test7 ; waitbar (10/32, h, 'CHOLMOD test8') ; if (do_metis) % these tests require METIS test8 (nmat) ; waitbar (11/32, h, 'CHOLMOD test9') ; test9 ; end waitbar (12/32, h, 'CHOLMOD test10') ; test10 (nmat) ; waitbar (13/32, h, 'CHOLMOD test11') ; test11 (nmat) ; waitbar (14/32, h, 'CHOLMOD test12') ; test12 (nmat) ; waitbar (15/32, h, 'CHOLMOD test13') ; test13 ; waitbar (16/32, h, 'CHOLMOD test14') ; if (do_metis) % this test requires METIS test14 (2*nmat) ; end waitbar (17/32, h, 'CHOLMOD test15') ; test15 (2*nmat) ; waitbar (18/32, h, 'CHOLMOD test16') ; test16 ; waitbar (19/32, h, 'CHOLMOD test17') ; test17 ; waitbar (20/32, h, 'CHOLMOD test18') ; test18 ; waitbar (21/32, h, 'CHOLMOD test19') ; test19 ; waitbar (22/32, h, 'CHOLMOD test20') ; test20 ; waitbar (23/32, h, 'CHOLMOD test21') ; test21 ; waitbar (24/32, h, 'CHOLMOD test22a') ; test22 (nmat) ; waitbar (25/32, h, 'CHOLMOD test22b') ; test22 (0) ; waitbar (26/32, h, 'CHOLMOD test23') ; test23 ; waitbar (27/32, h, 'CHOLMOD test24') ; test24 ; waitbar (28/32, h, 'CHOLMOD test25') ; test25 ; waitbar (29/32, h, 'CHOLMOD test26') ; test26 (do_metis) ; waitbar (31/32, h, 'CHOLMOD test27') ; if (do_metis) test27 ; end % this test requires METIS % test28 ; % (disabled) waitbar (32/32, h, 'CHOLMOD test done') ; fprintf ('=============================================================\n'); fprintf ('all tests passed\n') ; catch % out-of-memory is OK, other errors are not disp (lasterr) ; if (isempty (strfind (lasterr, 'Out of memory'))) error (lasterr) ; %#ok else fprintf ('test terminated early, but otherwise OK\n') ; end end close (h) ; if (do_diary) diary off end SuiteSparse/CHOLMOD/MATLAB/Test/test11results.m0000644001170100242450000000245410620371306017637 0ustar davisfacfunction test11results %TEST11RESULTS analyze results from test11.m % Example: % test11results % See also test11, cholmod_test % Copyright 2006-2007, Timothy A. Davis, University of Florida load Results index = UFget ; c = E1(1:kkk) < 1 & T1(1:kkk) > 0 ; m = E2(1:kkk) < 1 & T2(1:kkk) > 0 ; cgood = find (c) ; %#ok mgood = find (m) ; %#ok good = find (c | m) ; bad = find (~(c|m)) ; fl_per_lnz = FL(1:kkk) ./ LNZ(1:kkk) ; speedup = T1(1:kkk) ./ T2(1:kkk) ; [ignore ii] = sort (fl_per_lnz (good)) ; good = good (ii) ; fprintf ('MATLABtime CHOLMOD(time,flop,nnz(L)) speedup problem\n') ; for k = good i = f (k) ; % fprintf ('%4d: t1 %10.2f t2 %10.2f fl %6.1e lnz %6.1e %s/%s\n', ... % i, T1(k), T2(k), FL(k), LNZ(k), index.Group{i}, index.Name{i}) ; fprintf ('%10.4f %10.4f %6.1e %6.1e %5.2f %s/%s\n', ... T1(k), T2(k), FL(k), LNZ(k), speedup(k), ... index.Group{i}, index.Name{i}) ; end fprintf ('\nfailed in both:\n') ; for k = bad i = f (k) ; fprintf ('%10.4f %10.4f %6.1e %6.1e %5.2f %s/%s\n', ... T1(k), T2(k), FL(k), LNZ(k), speedup(k), ... index.Group{i}, index.Name{i}) ; end % figure (3) clf loglog (fl_per_lnz (good), speedup (good), 'x') ; axis ([1 4000 .1 50]) ; xlabel ('Cholesky flop count / nnz(L)') ; ylabel ('(MATLAB x=A\\b time) / (CHOLMOD time)') ; drawnow SuiteSparse/CHOLMOD/MATLAB/Test/cholmod_test_11-May-2007_13-29-15.txt0000644001170100242450000134544310621125342022543 0ustar davisfacRunning CHOLMOD tests. diary cholmod_test_11-May-2007_13-29-15.txt CHOLMOD_TEST test the CHOLMOD mexFunctions Example: cholmod_test(nmat) The UFget interface to the UF sparse matrix collection is required. nmat is optional. If present, it is the # of matrices used in tests 0, 8, 10, 11, 12, and 12. tests 14 and 15 use 2*nmat matrices. default nmat is 50. cholmod_demo: run tests on a few random matrices graph_demo: graph partitioning demo test0: test most CHOLMOD functions test1: test sparse2 test2: test sparse2 test3: test sparse on int8, int16, and logical test4: test cholmod2 with multiple and sparse right-hand-sides test5: test sparse2 test6: test sparse with large matrix, both real and complex, compare w/MATLAB test7: test sparse2 test8: order many sparse matrices, test symbfact2, compare amd and metis test9: test metis, etree, bisect, nesdis test10: test cholmod2's backslash on real and complex matrices test11: test analyze, compare CHOLMOD and MATLAB, save results in Results.mat test12: test etree2 and compare with etree test13: test cholmod2 and MATLAB on large tridiagonal matrices test14: test metis, symbfact2, and etree2 test15: test symbfact2 vs MATLAB test16: test cholmod2 on a large matrix test17: test lchol on a few large matrices test18: test cholmod2 on a few large matrices test19: look for NaN's from lchol (caused by Intel MKL 7.x bug) test20: test symbfact2, cholmod2, and lu on a few large matrices test21: test cholmod2 on diagonal or ill-conditioned matrices test22: test chol and chol2 and singular and indefinite matrices test23: test chol and cholmod2 on the sparse matrix used in "bench" test24: test sdmult test25: test sdmult on a large matrix test26: test logical full and sparse matrices test27: test nesdis See also test0, test1, ... test28. Added the following paths. You may wish to add them permanently using the MATLAB pathtool command. /amd/birch/export/research07/sparse/SuiteSparse/CHOLMOD/MATLAB /amd/birch/export/research07/sparse/SuiteSparse/AMD/MATLAB /amd/birch/export/research07/sparse/SuiteSparse/COLAMD /amd/birch/export/research07/sparse/SuiteSparse/CCOLAMD /amd/birch/export/research07/sparse/SuiteSparse/CAMD/MATLAB --------- Hit enter to contine: CHOLMOD_DEMO a demo for CHOLMOD Tests CHOLMOD with various randomly-generated matrices, and the west0479 matrix distributed with MATLAB. Random matrices are not good test cases, but they are easily generated. It also compares CHOLMOD and MATLAB on the sparse matrix problem used in the MATLAB BENCH command. See CHOLMOD/MATLAB/Test/test_all.m for a lengthy test using matrices from the UF sparse matrix collection. Example: cholmod_demo See also BENCH -------------------------------------------------------------- cholmod_demo: sparse matrix, n 479 nnz 7551 CHOLMOD lchol(sparse(A)) time: 0.00 mflop 83.4 CHOLMOD ldlchol(sparse(A)) time: 0.00 mflop 78.5 CHOLMOD ldlupdate(sparse(A),C) time: 0.01 (rank-1, C dense) err: 8.87659e-16 MATLAB chol(sparse(A)) time: 0.00 mflop 133.1 MATLAB chol(full(A)) time: 0.02 mflop 16.0 MATLAB cholupdate(full(A),C) time: 0.00 (rank-1) err: 2.78134e-16 CHOLMOD lchol(sparse(A)) speedup over chol(sparse(A)): 0.6 CHOLMOD sparse update speedup vs MATLAB DENSE update: 0.3 -------------------------------------------------------------- cholmod_demo: sparse matrix, n 2000 nnz 17946 CHOLMOD lchol(sparse(A)) time: 0.13 mflop 1720.7 CHOLMOD ldlchol(sparse(A)) time: 0.13 mflop 1697.2 CHOLMOD ldlupdate(sparse(A),C) time: 0.16 (rank-1, C dense) err: 1.10497e-14 MATLAB chol(sparse(A)) time: 0.43 mflop 518.5 MATLAB chol(full(A)) time: 1.61 mflop 138.4 MATLAB cholupdate(full(A),C) time: 0.16 (rank-1) err: 2.58727e-14 CHOLMOD lchol(sparse(A)) speedup over chol(sparse(A)): 3.3 CHOLMOD sparse update speedup vs MATLAB DENSE update: 1.0 -------------------------------------------------------------- cholmod_demo: dense matrix, n 100 CHOLMOD lchol(sparse(A)) time: 0.00 mflop 419.8 CHOLMOD ldlchol(sparse(A)) time: 0.00 mflop 373.9 CHOLMOD ldlupdate(sparse(A),C) time: 0.00 (rank-1, C dense) err: 2.67101e-16 MATLAB chol(sparse(A)) time: 0.00 mflop 313.0 MATLAB chol(full(A)) time: 0.00 mflop 735.5 MATLAB cholupdate(full(A),C) time: 0.00 (rank-1) err: 2.63339e-16 CHOLMOD lchol(sparse(A)) speedup over chol(sparse(A)): 1.3 CHOLMOD sparse update speedup vs MATLAB DENSE update: 1.0 -------------------------------------------------------------- cholmod_demo: dense matrix, n 2000 CHOLMOD lchol(sparse(A)) time: 2.21 mflop 1208.8 CHOLMOD ldlchol(sparse(A)) time: 2.24 mflop 1192.4 CHOLMOD ldlupdate(sparse(A),C) time: 0.15 (rank-1, C dense) err: 1.45631e-15 MATLAB chol(sparse(A)) time: 2.66 mflop 1004.9 MATLAB chol(full(A)) time: 1.60 mflop 1672.4 MATLAB cholupdate(full(A),C) time: 0.16 (rank-1) err: 1.42948e-15 CHOLMOD lchol(sparse(A)) speedup over chol(sparse(A)): 1.2 CHOLMOD sparse update speedup vs MATLAB DENSE update: 1.1 -------------------------------------------------------------- With the matrix used in the MATLAB 7.2 "bench" program. No fill-reducing orderings are used; type "help bench" for more information. MATLAB x=A\b time: 4.4297 resid: 2e-13 CHOLMOD x=A\b time: 2.3991 resid: 2e-13 CHOLMOD speedup: 1.85 cholmod_demo finished: all tests passed For more accurate timings, run this test again. ================================================================= test0: test most CHOLMOD functions Testing CHOLMOD with AMD and the UF sparse matrix collection test matrices sorted by dimension: 1440: Oberwolfach LFAT5 14 1 1438: Oberwolfach LF10 18 1 436: FIDAP ex5 27 1 23: HB bcsstk01 48 1 872: Pothen mesh1e1 48 1 873: Pothen mesh1em1 48 1 874: Pothen mesh1em6 48 1 24: HB bcsstk02 66 1 57: HB bcsstm02 66 1 220: HB nos4 100 1 25: HB bcsstk03 112 1 1506: Pajek Journals 124 1 26: HB bcsstk04 132 1 44: HB bcsstk22 138 1 72: HB bcsstm22 138 1 206: HB lund_a 147 1 207: HB lund_b 147 1 27: HB bcsstk05 153 1 60: HB bcsstm05 153 1 217: HB nos1 237 1 877: Pothen mesh3e1 289 1 878: Pothen mesh3em5 289 1 875: Pothen mesh2e1 306 1 876: Pothen mesh2em5 306 1 229: HB plat362 362 1 315: Bai mhdb416 416 1 28: HB bcsstk06 420 1 29: HB bcsstk07 420 1 61: HB bcsstm06 420 1 62: HB bcsstm07 420 1 221: HB nos5 468 1 42: HB bcsstk20 485 1 70: HB bcsstm20 485 1 2: HB 494_bus 494 1 339: Boeing bcsstk34 588 1 3: HB 662_bus 662 1 222: HB nos6 675 1 4: HB 685_bus 685 1 357: Boeing msc00726 726 1 223: HB nos7 729 1 41: HB bcsstk19 817 1 69: HB bcsstm19 817 1 159: HB gr_30_30 900 1 218: HB nos2 957 1 219: HB nos3 960 1 358: Boeing msc01050 1050 1 30: HB bcsstk08 1074 1 63: HB bcsstm08 1074 1 31: HB bcsstk09 1083 1 64: HB bcsstm09 1083 1 ================== Problem: 1440: Oberwolfach/LFAT5 n: 14 nnz: 46 title: Oberwolfach: linear 1D beam time: amd 0.0002 CHOLMOD time: L=lchol 0.0002 nnz(L): 33 CHOLMOD time: R=chol2 0.0002 nnz(R): 33 MATLAB time: R=chol 0.0002 nnz(R): 33 MATLAB [..,R]=symbfact 0.0004 nnz(R): 33 CHOLMOD speedup vs MATLAB chol: R: 0.88 L: 0.91 CHOLMOD numeric lchol vs MATLAB symbfact: 1.79 CHOLMOD time: [L,,q]=lchol 0.0002 nnz(L): 33 CHOLMOD time: [L,,q]=ldlchol 0.0002 nnz(L): 33 CHOLMOD time: rank-8 ldlupdate 0.0002 nnz(L) 33 no fill-in CHOLMOD time: rank-4 ldldowndate 0.0002 nnz(L) 33 no fill-in after resymbol: 33 CHOLMOD residual: 2.3e-21 MATLAB residual: 6.0e-21 CHOLMOD residual: 6.7e-21 (sparse b) MATLAB residual: 1.1e-20 (sparse b) ================== Problem: 1438: Oberwolfach/LF10 n: 18 nnz: 82 title: Oberwolfach: linear 1D beam time: amd 0.0000 CHOLMOD time: L=lchol 0.0000 nnz(L): 58 CHOLMOD time: R=chol2 0.0000 nnz(R): 58 MATLAB time: R=chol 0.0000 nnz(R): 58 MATLAB [..,R]=symbfact 0.0002 nnz(R): 58 CHOLMOD speedup vs MATLAB chol: R: 0.84 L: 1.09 CHOLMOD numeric lchol vs MATLAB symbfact: 4.67 CHOLMOD time: [L,,q]=lchol 0.0001 nnz(L): 58 CHOLMOD time: [L,,q]=ldlchol 0.0001 nnz(L): 58 CHOLMOD time: rank-6 ldlupdate 0.0001 nnz(L) 65 with fill-in CHOLMOD time: rank-3 ldldowndate 0.0000 nnz(L) 65 no fill-in after resymbol: 58 CHOLMOD residual: 5.8e-18 MATLAB residual: 3.3e-18 CHOLMOD residual: 8.9e-18 (sparse b) MATLAB residual: 3.0e-18 (sparse b) ================== Problem: 436: FIDAP/ex5 n: 27 nnz: 279 title: TEST MATRIX FROM FIDAP: EX5.MAT time: amd 0.0000 CHOLMOD time: L=lchol 0.0000 nnz(L): 153 CHOLMOD time: R=chol2 0.0001 nnz(R): 153 MATLAB time: R=chol 0.0001 nnz(R): 153 MATLAB [..,R]=symbfact 0.0002 nnz(R): 153 CHOLMOD speedup vs MATLAB chol: R: 0.91 L: 1.11 CHOLMOD numeric lchol vs MATLAB symbfact: 3.83 CHOLMOD time: [L,,q]=lchol 0.0001 nnz(L): 153 CHOLMOD time: [L,,q]=ldlchol 0.0001 nnz(L): 153 CHOLMOD time: rank-4 ldlupdate 0.0001 nnz(L) 213 with fill-in CHOLMOD time: rank-2 ldldowndate 0.0000 nnz(L) 213 no fill-in after resymbol: 153 CHOLMOD residual: 2.0e-15 MATLAB residual: 2.0e-15 CHOLMOD residual: 1.5e-15 (sparse b) MATLAB residual: 1.2e-15 (sparse b) ================== Problem: 23: HB/bcsstk01 n: 48 nnz: 400 title: SYMMETRIC STIFFNESS MATRIX SMALL GENERALIZED EIGENVALUE PROBLEM time: amd 0.0001 CHOLMOD time: L=lchol 0.0001 nnz(L): 489 CHOLMOD time: R=chol2 0.0001 nnz(R): 489 MATLAB time: R=chol 0.0001 nnz(R): 489 MATLAB [..,R]=symbfact 0.0002 nnz(R): 489 CHOLMOD speedup vs MATLAB chol: R: 0.93 L: 1.04 CHOLMOD numeric lchol vs MATLAB symbfact: 2.45 CHOLMOD time: [L,,q]=lchol 0.0002 nnz(L): 489 CHOLMOD time: [L,,q]=ldlchol 0.0002 nnz(L): 489 CHOLMOD time: rank-3 ldlupdate 0.0001 nnz(L) 518 with fill-in CHOLMOD time: rank-1 ldldowndate 0.0000 nnz(L) 518 no fill-in after resymbol: 489 CHOLMOD residual: 4.9e-22 MATLAB residual: 3.8e-22 CHOLMOD residual: 2.8e-22 (sparse b) MATLAB residual: 3.7e-22 (sparse b) ================== Problem: 872: Pothen/mesh1e1 n: 48 nnz: 306 title: mesh1e1, with coordinates. From NASA, collected by Alex Pothen time: amd 0.0001 CHOLMOD time: L=lchol 0.0001 nnz(L): 336 CHOLMOD time: R=chol2 0.0001 nnz(R): 336 MATLAB time: R=chol 0.0001 nnz(R): 336 MATLAB [..,R]=symbfact 0.0002 nnz(R): 336 CHOLMOD speedup vs MATLAB chol: R: 0.87 L: 1.02 CHOLMOD numeric lchol vs MATLAB symbfact: 2.80 CHOLMOD time: [L,,q]=lchol 0.0001 nnz(L): 336 CHOLMOD time: [L,,q]=ldlchol 0.0001 nnz(L): 336 CHOLMOD time: rank-1 ldlupdate 0.0001 nnz(L) 337 with fill-in CHOLMOD time: rank-1 ldldowndate 0.0000 nnz(L) 337 no fill-in after resymbol: 336 CHOLMOD residual: 3.1e-16 MATLAB residual: 4.4e-16 CHOLMOD residual: 3.9e-16 (sparse b) MATLAB residual: 4.1e-16 (sparse b) ================== Problem: 873: Pothen/mesh1em1 n: 48 nnz: 306 title: mesh1em1, with coordinates. From NASA, collected by Alex Pothen time: amd 0.0001 CHOLMOD time: L=lchol 0.0001 nnz(L): 336 CHOLMOD time: R=chol2 0.0001 nnz(R): 336 MATLAB time: R=chol 0.0001 nnz(R): 336 MATLAB [..,R]=symbfact 0.0002 nnz(R): 336 CHOLMOD speedup vs MATLAB chol: R: 0.87 L: 0.99 CHOLMOD numeric lchol vs MATLAB symbfact: 2.82 CHOLMOD time: [L,,q]=lchol 0.0001 nnz(L): 336 CHOLMOD time: [L,,q]=ldlchol 0.0001 nnz(L): 336 CHOLMOD time: rank-2 ldlupdate 0.0001 nnz(L) 370 with fill-in CHOLMOD time: rank-1 ldldowndate 0.0000 nnz(L) 370 no fill-in after resymbol: 336 CHOLMOD residual: 1.7e-16 MATLAB residual: 1.4e-16 CHOLMOD residual: 1.5e-16 (sparse b) MATLAB residual: 1.9e-16 (sparse b) ================== Problem: 874: Pothen/mesh1em6 n: 48 nnz: 306 title: mesh1em6, with coordinates. From NASA, collected by Alex Pothen time: amd 0.0001 CHOLMOD time: L=lchol 0.0001 nnz(L): 336 CHOLMOD time: R=chol2 0.0001 nnz(R): 336 MATLAB time: R=chol 0.0001 nnz(R): 336 MATLAB [..,R]=symbfact 0.0002 nnz(R): 336 CHOLMOD speedup vs MATLAB chol: R: 0.87 L: 0.68 CHOLMOD numeric lchol vs MATLAB symbfact: 1.89 CHOLMOD time: [L,,q]=lchol 0.0001 nnz(L): 336 CHOLMOD time: [L,,q]=ldlchol 0.0001 nnz(L): 336 CHOLMOD time: rank-4 ldlupdate 0.0001 nnz(L) 371 with fill-in CHOLMOD time: rank-2 ldldowndate 0.0000 nnz(L) 371 no fill-in after resymbol: 336 CHOLMOD residual: 4.8e-16 MATLAB residual: 4.8e-16 CHOLMOD residual: 5.3e-16 (sparse b) MATLAB residual: 4.4e-16 (sparse b) ================== Problem: 24: HB/bcsstk02 n: 66 nnz: 4356 title: SYMMETRIC STIFFNESS MATRIX, SMALL OIL RIG, STATICALLY CONDENSED time: amd 0.0001 CHOLMOD time: L=lchol 0.0003 nnz(L): 2211 CHOLMOD time: R=chol2 0.0004 nnz(R): 2211 MATLAB time: R=chol 0.0004 nnz(R): 2211 MATLAB [..,R]=symbfact 0.0004 nnz(R): 2211 CHOLMOD speedup vs MATLAB chol: R: 0.93 L: 1.12 CHOLMOD numeric lchol vs MATLAB symbfact: 1.16 CHOLMOD time: [L,,q]=lchol 0.0005 nnz(L): 2211 CHOLMOD time: [L,,q]=ldlchol 0.0005 nnz(L): 2211 CHOLMOD time: rank-4 ldlupdate 0.0001 nnz(L) 2211 no fill-in CHOLMOD time: rank-2 ldldowndate 0.0001 nnz(L) 2211 no fill-in after resymbol: 2211 CHOLMOD residual: 9.8e-17 MATLAB residual: 1.0e-16 CHOLMOD residual: 4.3e-17 (sparse b) MATLAB residual: 3.8e-17 (sparse b) ================== Problem: 57: HB/bcsstm02 n: 66 nnz: 66 title: SYMMETRIC MASS MATRIX, SMALL OIL RIG, STATICALLY CONDENSED time: amd 0.0000 CHOLMOD time: L=lchol 0.0000 nnz(L): 66 CHOLMOD time: R=chol2 0.0000 nnz(R): 66 MATLAB time: R=chol 0.0000 nnz(R): 66 MATLAB [..,R]=symbfact 0.0002 nnz(R): 66 CHOLMOD speedup vs MATLAB chol: R: 0.84 L: 1.06 CHOLMOD numeric lchol vs MATLAB symbfact: 5.44 CHOLMOD time: [L,,q]=lchol 0.0001 nnz(L): 66 CHOLMOD time: [L,,q]=ldlchol 0.0001 nnz(L): 66 CHOLMOD time: rank-7 ldlupdate 0.0001 nnz(L) 67 with fill-in CHOLMOD time: rank-3 ldldowndate 0.0000 nnz(L) 67 no fill-in after resymbol: 66 CHOLMOD residual: 2.4e-14 MATLAB residual: 3.2e-15 CHOLMOD residual: 1.0e-14 (sparse b) MATLAB residual: 6.4e-16 (sparse b) ================== Problem: 220: HB/nos4 n: 100 nnz: 594 title: SYMMETRIC MATRIX OF BEAM STRUCTURE, NOVEMBER 1982. time: amd 0.0001 CHOLMOD time: L=lchol 0.0001 nnz(L): 630 CHOLMOD time: R=chol2 0.0001 nnz(R): 630 MATLAB time: R=chol 0.0001 nnz(R): 630 MATLAB [..,R]=symbfact 0.0002 nnz(R): 632 CHOLMOD speedup vs MATLAB chol: R: 0.89 L: 0.99 CHOLMOD numeric lchol vs MATLAB symbfact: 2.13 CHOLMOD time: [L,,q]=lchol 0.0002 nnz(L): 632 CHOLMOD time: [L,,q]=ldlchol 0.0002 nnz(L): 632 CHOLMOD time: rank-3 ldlupdate 0.0001 nnz(L) 654 with fill-in CHOLMOD time: rank-1 ldldowndate 0.0000 nnz(L) 654 no fill-in after resymbol: 632 CHOLMOD residual: 9.2e-13 MATLAB residual: 8.5e-13 CHOLMOD residual: 3.2e-13 (sparse b) MATLAB residual: 2.4e-13 (sparse b) ================== Problem: 25: HB/bcsstk03 n: 112 nnz: 640 title: SYMMETRIC STIFFNESS MATRIX, SMALL TEST STRUCTURE time: amd 0.0001 CHOLMOD time: L=lchol 0.0001 nnz(L): 380 CHOLMOD time: R=chol2 0.0001 nnz(R): 380 MATLAB time: R=chol 0.0001 nnz(R): 380 MATLAB [..,R]=symbfact 0.0002 nnz(R): 384 CHOLMOD speedup vs MATLAB chol: R: 0.88 L: 0.96 CHOLMOD numeric lchol vs MATLAB symbfact: 2.86 CHOLMOD time: [L,,q]=lchol 0.0002 nnz(L): 380 CHOLMOD time: [L,,q]=ldlchol 0.0001 nnz(L): 384 CHOLMOD time: rank-6 ldlupdate 0.0001 nnz(L) 445 with fill-in CHOLMOD time: rank-3 ldldowndate 0.0000 nnz(L) 445 no fill-in after resymbol: 384 CHOLMOD residual: 1.4e-22 MATLAB residual: 2.2e-22 CHOLMOD residual: 9.8e-23 (sparse b) MATLAB residual: 2.2e-22 (sparse b) ================== Problem: 1506: Pajek/Journals n: 124 nnz: 12068 title: Pajek network: Slovenian journals 1999-2000 time: amd 0.0003 CHOLMOD time: L=lchol 0.0010 nnz(L): 6990 CHOLMOD time: R=chol2 0.0013 nnz(R): 6990 MATLAB time: R=chol 0.0013 nnz(R): 6990 MATLAB [..,R]=symbfact 0.0009 nnz(R): 6990 CHOLMOD speedup vs MATLAB chol: R: 1.04 L: 1.25 CHOLMOD numeric lchol vs MATLAB symbfact: 0.84 CHOLMOD time: [L,,q]=lchol 0.0017 nnz(L): 6990 CHOLMOD time: [L,,q]=ldlchol 0.0017 nnz(L): 6990 CHOLMOD time: rank-8 ldlupdate 0.0002 nnz(L) 6990 no fill-in CHOLMOD time: rank-4 ldldowndate 0.0002 nnz(L) 6990 no fill-in after resymbol: 6990 CHOLMOD residual: 5.1e-19 MATLAB residual: 5.3e-19 CHOLMOD residual: 2.5e-19 (sparse b) MATLAB residual: 2.7e-19 (sparse b) ================== Problem: 26: HB/bcsstk04 n: 132 nnz: 3648 title: SYMMETRIC STIFFNESS MATRIX, OIL RIG, NOT CONDENSED (SAME MODEL AS X02) time: amd 0.0002 CHOLMOD time: L=lchol 0.0005 nnz(L): 3291 CHOLMOD time: R=chol2 0.0005 nnz(R): 3291 MATLAB time: R=chol 0.0005 nnz(R): 3291 MATLAB [..,R]=symbfact 0.0004 nnz(R): 3293 CHOLMOD speedup vs MATLAB chol: R: 1.02 L: 1.01 CHOLMOD numeric lchol vs MATLAB symbfact: 0.85 CHOLMOD time: [L,,q]=lchol 0.0007 nnz(L): 3291 CHOLMOD time: [L,,q]=ldlchol 0.0007 nnz(L): 3293 CHOLMOD time: rank-1 ldlupdate 0.0002 nnz(L) 3570 with fill-in CHOLMOD time: rank-1 ldldowndate 0.0001 nnz(L) 3570 no fill-in after resymbol: 3293 CHOLMOD residual: 1.4e-18 MATLAB residual: 1.6e-18 CHOLMOD residual: 4.2e-19 (sparse b) MATLAB residual: 3.5e-19 (sparse b) ================== Problem: 44: HB/bcsstk22 n: 138 nnz: 696 title: SYMMETRIC STIFFNESS MATRIX - TEXTILE LOOM FRAME time: amd 0.0001 CHOLMOD time: L=lchol 0.0001 nnz(L): 680 CHOLMOD time: R=chol2 0.0001 nnz(R): 680 MATLAB time: R=chol 0.0001 nnz(R): 680 MATLAB [..,R]=symbfact 0.0002 nnz(R): 680 CHOLMOD speedup vs MATLAB chol: R: 0.91 L: 0.99 CHOLMOD numeric lchol vs MATLAB symbfact: 2.08 CHOLMOD time: [L,,q]=lchol 0.0002 nnz(L): 680 CHOLMOD time: [L,,q]=ldlchol 0.0002 nnz(L): 680 CHOLMOD time: rank-6 ldlupdate 0.0001 nnz(L) 685 with fill-in CHOLMOD time: rank-3 ldldowndate 0.0001 nnz(L) 685 no fill-in after resymbol: 680 CHOLMOD residual: 1.3e-18 MATLAB residual: 1.2e-18 CHOLMOD residual: 2.3e-19 (sparse b) MATLAB residual: 2.2e-19 (sparse b) ================== Problem: 72: HB/bcsstm22 n: 138 nnz: 138 title: SYMMETRIC MASS MATRIX - TEXTILE LOOM FRAME time: amd 0.0000 CHOLMOD time: L=lchol 0.0000 nnz(L): 138 CHOLMOD time: R=chol2 0.0001 nnz(R): 138 MATLAB time: R=chol 0.0001 nnz(R): 138 MATLAB [..,R]=symbfact 0.0002 nnz(R): 138 CHOLMOD speedup vs MATLAB chol: R: 0.90 L: 1.08 CHOLMOD numeric lchol vs MATLAB symbfact: 3.65 CHOLMOD time: [L,,q]=lchol 0.0001 nnz(L): 138 CHOLMOD time: [L,,q]=ldlchol 0.0001 nnz(L): 138 CHOLMOD time: rank-5 ldlupdate 0.0001 nnz(L) 139 with fill-in CHOLMOD time: rank-2 ldldowndate 0.0000 nnz(L) 139 no fill-in after resymbol: 138 CHOLMOD residual: 5.7e-10 MATLAB residual: 1.2e-13 CHOLMOD residual: 1.5e-11 (sparse b) MATLAB residual: 6.7e-14 (sparse b) ================== Problem: 206: HB/lund_a n: 147 nnz: 2449 title: SYMMETRIC MATRIX A OF LUND EIGENVALUE PROBLEM, MAY 1974 time: amd 0.0002 CHOLMOD time: L=lchol 0.0003 nnz(L): 2339 CHOLMOD time: R=chol2 0.0003 nnz(R): 2339 MATLAB time: R=chol 0.0003 nnz(R): 2339 MATLAB [..,R]=symbfact 0.0003 nnz(R): 2339 CHOLMOD speedup vs MATLAB chol: R: 0.99 L: 0.96 CHOLMOD numeric lchol vs MATLAB symbfact: 1.09 CHOLMOD time: [L,,q]=lchol 0.0004 nnz(L): 2339 CHOLMOD time: [L,,q]=ldlchol 0.0004 nnz(L): 2339 CHOLMOD time: rank-5 ldlupdate 0.0001 nnz(L) 2354 with fill-in CHOLMOD time: rank-2 ldldowndate 0.0001 nnz(L) 2354 no fill-in after resymbol: 2339 CHOLMOD residual: 1.1e-18 MATLAB residual: 8.2e-19 CHOLMOD residual: 5.8e-20 (sparse b) MATLAB residual: 6.4e-20 (sparse b) ================== Problem: 207: HB/lund_b n: 147 nnz: 2441 title: SYMMETRIC MATRIX B OF LUND EIGENVALUE PROBLEM, MAY 1974 time: amd 0.0001 CHOLMOD time: L=lchol 0.0003 nnz(L): 2340 CHOLMOD time: R=chol2 0.0003 nnz(R): 2340 MATLAB time: R=chol 0.0003 nnz(R): 2340 MATLAB [..,R]=symbfact 0.0003 nnz(R): 2340 CHOLMOD speedup vs MATLAB chol: R: 1.07 L: 1.07 CHOLMOD numeric lchol vs MATLAB symbfact: 1.12 CHOLMOD time: [L,,q]=lchol 0.0004 nnz(L): 2340 CHOLMOD time: [L,,q]=ldlchol 0.0004 nnz(L): 2340 CHOLMOD time: rank-6 ldlupdate 0.0001 nnz(L) 2481 with fill-in CHOLMOD time: rank-3 ldldowndate 0.0001 nnz(L) 2481 no fill-in after resymbol: 2340 CHOLMOD residual: 1.2e-16 MATLAB residual: 1.2e-16 CHOLMOD residual: 8.7e-17 (sparse b) MATLAB residual: 8.7e-17 (sparse b) ================== Problem: 27: HB/bcsstk05 n: 153 nnz: 2423 title: SYMMETRIC STIFFNESS MATRIX, TRANSMISSION TOWER, LUMPED MASSES time: amd 0.0002 CHOLMOD time: L=lchol 0.0003 nnz(L): 2326 CHOLMOD time: R=chol2 0.0003 nnz(R): 2326 MATLAB time: R=chol 0.0003 nnz(R): 2326 MATLAB [..,R]=symbfact 0.0003 nnz(R): 2326 CHOLMOD speedup vs MATLAB chol: R: 0.97 L: 0.90 CHOLMOD numeric lchol vs MATLAB symbfact: 1.05 CHOLMOD time: [L,,q]=lchol 0.0005 nnz(L): 2326 CHOLMOD time: [L,,q]=ldlchol 0.0005 nnz(L): 2326 CHOLMOD time: rank-4 ldlupdate 0.0002 nnz(L) 2572 with fill-in CHOLMOD time: rank-2 ldldowndate 0.0001 nnz(L) 2572 no fill-in after resymbol: 2326 CHOLMOD residual: 1.5e-18 MATLAB residual: 1.2e-18 CHOLMOD residual: 3.8e-19 (sparse b) MATLAB residual: 3.3e-19 (sparse b) ================== Problem: 60: HB/bcsstm05 n: 153 nnz: 153 title: SYMMETRIC MASS MATRIX, TRANSMISSION TOWER, LUMPED MASSES time: amd 0.0000 CHOLMOD time: L=lchol 0.0001 nnz(L): 153 CHOLMOD time: R=chol2 0.0001 nnz(R): 153 MATLAB time: R=chol 0.0001 nnz(R): 153 MATLAB [..,R]=symbfact 0.0002 nnz(R): 153 CHOLMOD speedup vs MATLAB chol: R: 0.81 L: 0.94 CHOLMOD numeric lchol vs MATLAB symbfact: 3.33 CHOLMOD time: [L,,q]=lchol 0.0001 nnz(L): 153 CHOLMOD time: [L,,q]=ldlchol 0.0001 nnz(L): 153 CHOLMOD time: rank-1 ldlupdate 0.0001 nnz(L) 154 with fill-in CHOLMOD time: rank-1 ldldowndate 0.0000 nnz(L) 154 no fill-in after resymbol: 153 CHOLMOD residual: 1.8e-15 MATLAB residual: 1.7e-15 CHOLMOD residual: 8.8e-16 (sparse b) MATLAB residual: 8.8e-16 (sparse b) ================== Problem: 217: HB/nos1 n: 237 nnz: 1017 title: SYMMETRIC MATRIX, FE APPROXIMATION TO BIHARMONIC OPERATOR ON BEAM. time: amd 0.0001 CHOLMOD time: L=lchol 0.0001 nnz(L): 704 CHOLMOD time: R=chol2 0.0001 nnz(R): 704 MATLAB time: R=chol 0.0001 nnz(R): 704 MATLAB [..,R]=symbfact 0.0002 nnz(R): 704 CHOLMOD speedup vs MATLAB chol: R: 0.88 L: 0.92 CHOLMOD numeric lchol vs MATLAB symbfact: 2.11 CHOLMOD time: [L,,q]=lchol 0.0002 nnz(L): 704 CHOLMOD time: [L,,q]=ldlchol 0.0002 nnz(L): 704 CHOLMOD time: rank-3 ldlupdate 0.0001 nnz(L) 896 with fill-in CHOLMOD time: rank-1 ldldowndate 0.0001 nnz(L) 896 no fill-in after resymbol: 704 CHOLMOD residual: 2.1e-18 MATLAB residual: 2.2e-18 CHOLMOD residual: 2.5e-19 (sparse b) MATLAB residual: 2.7e-19 (sparse b) ================== Problem: 877: Pothen/mesh3e1 n: 289 nnz: 1377 title: mesh3e1, with coordinates. From NASA, collected by Alex Pothen time: amd 0.0002 CHOLMOD time: L=lchol 0.0003 nnz(L): 2433 CHOLMOD time: R=chol2 0.0003 nnz(R): 2433 MATLAB time: R=chol 0.0003 nnz(R): 2433 MATLAB [..,R]=symbfact 0.0003 nnz(R): 2433 CHOLMOD speedup vs MATLAB chol: R: 0.92 L: 0.94 CHOLMOD numeric lchol vs MATLAB symbfact: 1.18 CHOLMOD time: [L,,q]=lchol 0.0006 nnz(L): 2433 CHOLMOD time: [L,,q]=ldlchol 0.0005 nnz(L): 2433 CHOLMOD time: rank-4 ldlupdate 0.0001 nnz(L) 2433 no fill-in CHOLMOD time: rank-2 ldldowndate 0.0001 nnz(L) 2433 no fill-in after resymbol: 2433 CHOLMOD residual: 2.8e-15 MATLAB residual: 2.9e-15 CHOLMOD residual: 3.9e-15 (sparse b) MATLAB residual: 3.8e-15 (sparse b) ================== Problem: 878: Pothen/mesh3em5 n: 289 nnz: 1377 title: mesh3em5, with coordinates. From NASA, collected by Alex Pothen time: amd 0.0002 CHOLMOD time: L=lchol 0.0003 nnz(L): 2433 CHOLMOD time: R=chol2 0.0003 nnz(R): 2433 MATLAB time: R=chol 0.0003 nnz(R): 2433 MATLAB [..,R]=symbfact 0.0003 nnz(R): 2433 CHOLMOD speedup vs MATLAB chol: R: 0.92 L: 0.93 CHOLMOD numeric lchol vs MATLAB symbfact: 1.17 CHOLMOD time: [L,,q]=lchol 0.0006 nnz(L): 2433 CHOLMOD time: [L,,q]=ldlchol 0.0006 nnz(L): 2433 CHOLMOD time: rank-7 ldlupdate 0.0002 nnz(L) 2538 with fill-in CHOLMOD time: rank-3 ldldowndate 0.0001 nnz(L) 2538 no fill-in after resymbol: 2433 CHOLMOD residual: 4.7e-15 MATLAB residual: 4.9e-15 CHOLMOD residual: 5.3e-15 (sparse b) MATLAB residual: 5.1e-15 (sparse b) ================== Problem: 875: Pothen/mesh2e1 n: 306 nnz: 2018 title: mesh2e1, with coordinates. From NASA, collected by Alex Pothen time: amd 0.0003 CHOLMOD time: L=lchol 0.0004 nnz(L): 3224 CHOLMOD time: R=chol2 0.0004 nnz(R): 3224 MATLAB time: R=chol 0.0004 nnz(R): 3224 MATLAB [..,R]=symbfact 0.0004 nnz(R): 3224 CHOLMOD speedup vs MATLAB chol: R: 0.96 L: 0.96 CHOLMOD numeric lchol vs MATLAB symbfact: 1.06 CHOLMOD time: [L,,q]=lchol 0.0007 nnz(L): 3224 CHOLMOD time: [L,,q]=ldlchol 0.0007 nnz(L): 3224 CHOLMOD time: rank-7 ldlupdate 0.0002 nnz(L) 3508 with fill-in CHOLMOD time: rank-3 ldldowndate 0.0001 nnz(L) 3508 no fill-in after resymbol: 3224 CHOLMOD residual: 1.8e-16 MATLAB residual: 2.2e-16 CHOLMOD residual: 4.0e-16 (sparse b) MATLAB residual: 3.9e-16 (sparse b) ================== Problem: 876: Pothen/mesh2em5 n: 306 nnz: 2018 title: mesh2em5, with coordinates. From NASA, collected by Alex Pothen time: amd 0.0003 CHOLMOD time: L=lchol 0.0004 nnz(L): 3224 CHOLMOD time: R=chol2 0.0004 nnz(R): 3224 MATLAB time: R=chol 0.0004 nnz(R): 3224 MATLAB [..,R]=symbfact 0.0004 nnz(R): 3224 CHOLMOD speedup vs MATLAB chol: R: 1.03 L: 1.04 CHOLMOD numeric lchol vs MATLAB symbfact: 1.01 CHOLMOD time: [L,,q]=lchol 0.0007 nnz(L): 3224 CHOLMOD time: [L,,q]=ldlchol 0.0007 nnz(L): 3224 CHOLMOD time: rank-7 ldlupdate 0.0001 nnz(L) 3224 no fill-in CHOLMOD time: rank-3 ldldowndate 0.0001 nnz(L) 3224 no fill-in after resymbol: 3224 CHOLMOD residual: 1.7e-16 MATLAB residual: 2.2e-16 CHOLMOD residual: 2.2e-16 (sparse b) MATLAB residual: 3.0e-16 (sparse b) ================== Problem: 229: HB/plat362 n: 362 nnz: 5786 title: SPLATZMAN FINITE DIFFERENCE MODEL OF ATLANTICOCEAN time: amd 0.0004 CHOLMOD time: L=lchol 0.0010 nnz(L): 8060 CHOLMOD time: R=chol2 0.0010 nnz(R): 8060 MATLAB time: R=chol 0.0011 nnz(R): 8060 MATLAB [..,R]=symbfact 0.0007 nnz(R): 8060 CHOLMOD speedup vs MATLAB chol: R: 1.07 L: 1.12 CHOLMOD numeric lchol vs MATLAB symbfact: 0.70 CHOLMOD time: [L,,q]=lchol 0.0015 nnz(L): 8060 CHOLMOD time: [L,,q]=ldlchol 0.0015 nnz(L): 8060 CHOLMOD time: rank-5 ldlupdate 0.0007 nnz(L) 9872 with fill-in CHOLMOD time: rank-2 ldldowndate 0.0002 nnz(L) 9872 no fill-in after resymbol: 8060 CHOLMOD residual: 3.5e-05 MATLAB residual: 1.4e-05 CHOLMOD residual: 2.6e-05 (sparse b) MATLAB residual: 1.0e-05 (sparse b) ================== Problem: 315: Bai/mhdb416 n: 416 nnz: 2312 title: MAGNETO-HYDRO-DYNAMICS ALFVEN SPECTRAL PROBLEM time: amd 0.0001 CHOLMOD time: L=lchol 0.0002 nnz(L): 1364 CHOLMOD time: R=chol2 0.0002 nnz(R): 1364 MATLAB time: R=chol 0.0002 nnz(R): 1364 MATLAB [..,R]=symbfact 0.0003 nnz(R): 1364 CHOLMOD speedup vs MATLAB chol: R: 0.87 L: 0.85 CHOLMOD numeric lchol vs MATLAB symbfact: 1.53 CHOLMOD time: [L,,q]=lchol 0.0004 nnz(L): 1364 CHOLMOD time: [L,,q]=ldlchol 0.0004 nnz(L): 1364 CHOLMOD time: rank-5 ldlupdate 0.0001 nnz(L) 1369 with fill-in CHOLMOD time: rank-2 ldldowndate 0.0001 nnz(L) 1369 no fill-in after resymbol: 1364 CHOLMOD residual: 6.7e-11 MATLAB residual: 7.0e-11 CHOLMOD residual: 3.4e-11 (sparse b) MATLAB residual: 1.6e-11 (sparse b) ================== Problem: 28: HB/bcsstk06 n: 420 nnz: 7860 title: SYMMETRIC STIFFNESS MATRIX, MEDIUM TEST PROBLEM, LUMPED MASSES time: amd 0.0004 CHOLMOD time: L=lchol 0.0015 nnz(L): 11345 CHOLMOD time: R=chol2 0.0016 nnz(R): 11345 MATLAB time: R=chol 0.0017 nnz(R): 11345 MATLAB [..,R]=symbfact 0.0009 nnz(R): 11345 CHOLMOD speedup vs MATLAB chol: R: 1.06 L: 1.10 CHOLMOD numeric lchol vs MATLAB symbfact: 0.58 CHOLMOD time: [L,,q]=lchol 0.0021 nnz(L): 11345 CHOLMOD time: [L,,q]=ldlchol 0.0020 nnz(L): 11345 CHOLMOD time: rank-5 ldlupdate 0.0008 nnz(L) 12897 with fill-in CHOLMOD time: rank-2 ldldowndate 0.0003 nnz(L) 12897 no fill-in after resymbol: 11345 CHOLMOD residual: 4.8e-20 MATLAB residual: 4.8e-20 CHOLMOD residual: 2.4e-20 (sparse b) MATLAB residual: 2.6e-20 (sparse b) ================== Problem: 29: HB/bcsstk07 n: 420 nnz: 7860 title: SYMMETRIC STIFFNESS MATRIX, MEDIUM TEST PROBLEM, CONSISTENT MASSES time: amd 0.0004 CHOLMOD time: L=lchol 0.0015 nnz(L): 11345 CHOLMOD time: R=chol2 0.0016 nnz(R): 11345 MATLAB time: R=chol 0.0017 nnz(R): 11345 MATLAB [..,R]=symbfact 0.0009 nnz(R): 11345 CHOLMOD speedup vs MATLAB chol: R: 1.11 L: 1.17 CHOLMOD numeric lchol vs MATLAB symbfact: 0.60 CHOLMOD time: [L,,q]=lchol 0.0021 nnz(L): 11345 CHOLMOD time: [L,,q]=ldlchol 0.0020 nnz(L): 11345 CHOLMOD time: rank-1 ldlupdate 0.0006 nnz(L) 11385 with fill-in CHOLMOD time: rank-1 ldldowndate 0.0002 nnz(L) 11385 no fill-in after resymbol: 11345 CHOLMOD residual: 3.9e-20 MATLAB residual: 4.1e-20 CHOLMOD residual: 1.5e-20 (sparse b) MATLAB residual: 1.4e-20 (sparse b) ================== Problem: 61: HB/bcsstm06 n: 420 nnz: 420 title: SYMMETRIC MASS MATRIX, MEDIUM TEST PROBLEM, LUMPED MASSES time: amd 0.0001 CHOLMOD time: L=lchol 0.0001 nnz(L): 420 CHOLMOD time: R=chol2 0.0001 nnz(R): 420 MATLAB time: R=chol 0.0001 nnz(R): 420 MATLAB [..,R]=symbfact 0.0003 nnz(R): 420 CHOLMOD speedup vs MATLAB chol: R: 0.83 L: 0.90 CHOLMOD numeric lchol vs MATLAB symbfact: 2.86 CHOLMOD time: [L,,q]=lchol 0.0002 nnz(L): 420 CHOLMOD time: [L,,q]=ldlchol 0.0002 nnz(L): 420 CHOLMOD time: rank-5 ldlupdate 0.0001 nnz(L) 421 with fill-in CHOLMOD time: rank-2 ldldowndate 0.0000 nnz(L) 421 no fill-in after resymbol: 420 CHOLMOD residual: 4.2e-19 MATLAB residual: 4.0e-19 CHOLMOD residual: 2.0e-19 (sparse b) MATLAB residual: 2.0e-19 (sparse b) ================== Problem: 62: HB/bcsstm07 n: 420 nnz: 7252 title: SYMMETRIC MASS MATRIX, MEDIUM TEST PROBLEM, CONSISTENT MASSES time: amd 0.0004 CHOLMOD time: L=lchol 0.0014 nnz(L): 10654 CHOLMOD time: R=chol2 0.0015 nnz(R): 10654 MATLAB time: R=chol 0.0015 nnz(R): 10654 MATLAB [..,R]=symbfact 0.0009 nnz(R): 10654 CHOLMOD speedup vs MATLAB chol: R: 1.03 L: 1.08 CHOLMOD numeric lchol vs MATLAB symbfact: 0.61 CHOLMOD time: [L,,q]=lchol 0.0020 nnz(L): 10654 CHOLMOD time: [L,,q]=ldlchol 0.0019 nnz(L): 10654 CHOLMOD time: rank-6 ldlupdate 0.0005 nnz(L) 10730 with fill-in CHOLMOD time: rank-3 ldldowndate 0.0003 nnz(L) 10730 no fill-in after resymbol: 10654 CHOLMOD residual: 2.0e-16 MATLAB residual: 1.8e-16 CHOLMOD residual: 1.7e-16 (sparse b) MATLAB residual: 1.4e-16 (sparse b) ================== Problem: 221: HB/nos5 n: 468 nnz: 5172 title: SYMMETRIC MATRIX, FE APPROXIMATION OF BUILDING. time: amd 0.0008 CHOLMOD time: L=lchol 0.0024 nnz(L): 18436 CHOLMOD time: R=chol2 0.0028 nnz(R): 18436 MATLAB time: R=chol 0.0028 nnz(R): 18436 MATLAB [..,R]=symbfact 0.0012 nnz(R): 18437 CHOLMOD speedup vs MATLAB chol: R: 1.00 L: 1.20 CHOLMOD numeric lchol vs MATLAB symbfact: 0.53 CHOLMOD time: [L,,q]=lchol 0.0036 nnz(L): 18436 CHOLMOD time: [L,,q]=ldlchol 0.0038 nnz(L): 18437 CHOLMOD time: rank-7 ldlupdate 0.0016 nnz(L) 19563 with fill-in CHOLMOD time: rank-3 ldldowndate 0.0004 nnz(L) 19563 no fill-in after resymbol: 18437 CHOLMOD residual: 2.0e-17 MATLAB residual: 1.8e-17 CHOLMOD residual: 3.2e-18 (sparse b) MATLAB residual: 3.8e-18 (sparse b) ================== Problem: 42: HB/bcsstk20 n: 485 nnz: 3135 title: SYMMETRIC STIFFNESS MATRIX - FRAME WITHIN A SUSPENSION BRIDGE time: amd 0.0002 CHOLMOD time: L=lchol 0.0003 nnz(L): 2310 CHOLMOD time: R=chol2 0.0003 nnz(R): 2310 MATLAB time: R=chol 0.0003 nnz(R): 2310 MATLAB [..,R]=symbfact 0.0004 nnz(R): 2336 CHOLMOD speedup vs MATLAB chol: R: 0.91 L: 0.90 CHOLMOD numeric lchol vs MATLAB symbfact: 1.31 CHOLMOD time: [L,,q]=lchol 0.0006 nnz(L): 2310 CHOLMOD time: [L,,q]=ldlchol 0.0006 nnz(L): 2336 CHOLMOD time: rank-7 ldlupdate 0.0002 nnz(L) 2548 with fill-in CHOLMOD time: rank-3 ldldowndate 0.0001 nnz(L) 2548 no fill-in after resymbol: 2336 CHOLMOD residual: 7.4e-22 MATLAB residual: 7.1e-22 CHOLMOD residual: 5.6e-23 (sparse b) MATLAB residual: 9.0e-23 (sparse b) ================== Problem: 70: HB/bcsstm20 n: 485 nnz: 485 title: SYMMETRIC MASS MATRIX - FRAME WITHIN A SUSPENSION BRIDGE time: amd 0.0004 CHOLMOD time: L=lchol 0.0001 nnz(L): 485 CHOLMOD time: R=chol2 0.0001 nnz(R): 485 MATLAB time: R=chol 0.0001 nnz(R): 485 MATLAB [..,R]=symbfact 0.0002 nnz(R): 485 CHOLMOD speedup vs MATLAB chol: R: 0.83 L: 0.81 CHOLMOD numeric lchol vs MATLAB symbfact: 2.04 CHOLMOD time: [L,,q]=lchol 0.0002 nnz(L): 485 CHOLMOD time: [L,,q]=ldlchol 0.0002 nnz(L): 485 CHOLMOD time: rank-8 ldlupdate 0.0001 nnz(L) 486 with fill-in CHOLMOD time: rank-4 ldldowndate 0.0000 nnz(L) 486 no fill-in after resymbol: 485 CHOLMOD residual: 1.0e-22 MATLAB residual: 9.8e-23 CHOLMOD residual: 5.0e-23 (sparse b) MATLAB residual: 4.5e-23 (sparse b) ================== Problem: 2: HB/494_bus n: 494 nnz: 1666 title: S ADMITTANCE MATRIX 494 BUS POWER SYSTEM, D.J.TYLAVSKY, JULY 1985. time: amd 0.0002 CHOLMOD time: L=lchol 0.0002 nnz(L): 1414 CHOLMOD time: R=chol2 0.0002 nnz(R): 1414 MATLAB time: R=chol 0.0002 nnz(R): 1414 MATLAB [..,R]=symbfact 0.0004 nnz(R): 1414 CHOLMOD speedup vs MATLAB chol: R: 0.88 L: 0.87 CHOLMOD numeric lchol vs MATLAB symbfact: 1.46 CHOLMOD time: [L,,q]=lchol 0.0006 nnz(L): 1414 CHOLMOD time: [L,,q]=ldlchol 0.0005 nnz(L): 1414 CHOLMOD time: rank-6 ldlupdate 0.0001 nnz(L) 1499 with fill-in CHOLMOD time: rank-3 ldldowndate 0.0001 nnz(L) 1499 no fill-in after resymbol: 1414 CHOLMOD residual: 2.5e-14 MATLAB residual: 2.0e-14 CHOLMOD residual: 1.4e-15 (sparse b) MATLAB residual: 1.8e-15 (sparse b) ================== Problem: 339: Boeing/bcsstk34 n: 588 nnz: 21418 title: NASTRAN BUCKLING PROBLEM STIFFNESS MATRIX time: amd 0.0010 CHOLMOD time: L=lchol 0.0055 nnz(L): 43351 CHOLMOD time: R=chol2 0.0069 nnz(R): 43351 MATLAB time: R=chol 0.0070 nnz(R): 43351 MATLAB [..,R]=symbfact 0.0036 nnz(R): 43366 CHOLMOD speedup vs MATLAB chol: R: 1.02 L: 1.28 CHOLMOD numeric lchol vs MATLAB symbfact: 0.65 CHOLMOD time: [L,,q]=lchol 0.0073 nnz(L): 43351 CHOLMOD time: [L,,q]=ldlchol 0.0076 nnz(L): 43366 CHOLMOD time: rank-4 ldlupdate 0.0036 nnz(L) 48749 with fill-in CHOLMOD time: rank-2 ldldowndate 0.0012 nnz(L) 48749 no fill-in after resymbol: 43366 CHOLMOD residual: 2.9e-20 MATLAB residual: 3.0e-20 CHOLMOD residual: 2.6e-20 (sparse b) MATLAB residual: 2.6e-20 (sparse b) ================== Problem: 3: HB/662_bus n: 662 nnz: 2474 title: S ADMITTANCE MATRIX 662 BUS POWER SYSTEM, D.J.TYLAVSKY, JULY 1985. time: amd 0.0004 CHOLMOD time: L=lchol 0.0004 nnz(L): 2549 CHOLMOD time: R=chol2 0.0004 nnz(R): 2549 MATLAB time: R=chol 0.0003 nnz(R): 2549 MATLAB [..,R]=symbfact 0.0005 nnz(R): 2549 CHOLMOD speedup vs MATLAB chol: R: 0.89 L: 0.88 CHOLMOD numeric lchol vs MATLAB symbfact: 1.20 CHOLMOD time: [L,,q]=lchol 0.0009 nnz(L): 2549 CHOLMOD time: [L,,q]=ldlchol 0.0008 nnz(L): 2549 CHOLMOD time: rank-6 ldlupdate 0.0002 nnz(L) 2589 with fill-in CHOLMOD time: rank-3 ldldowndate 0.0001 nnz(L) 2589 no fill-in after resymbol: 2549 CHOLMOD residual: 1.4e-13 MATLAB residual: 2.0e-13 CHOLMOD residual: 7.1e-15 (sparse b) MATLAB residual: 8.7e-15 (sparse b) ================== Problem: 222: HB/nos6 n: 675 nnz: 3255 title: SYMMETRIC MATRIX, POISSON'S EQUATION IN L SHAPE, MIXED BC. time: amd 0.0005 CHOLMOD time: L=lchol 0.0007 nnz(L): 6453 CHOLMOD time: R=chol2 0.0007 nnz(R): 6453 MATLAB time: R=chol 0.0007 nnz(R): 6453 MATLAB [..,R]=symbfact 0.0006 nnz(R): 6453 CHOLMOD speedup vs MATLAB chol: R: 1.01 L: 1.00 CHOLMOD numeric lchol vs MATLAB symbfact: 0.85 CHOLMOD time: [L,,q]=lchol 0.0013 nnz(L): 6453 CHOLMOD time: [L,,q]=ldlchol 0.0013 nnz(L): 6453 CHOLMOD time: rank-2 ldlupdate 0.0004 nnz(L) 6600 with fill-in CHOLMOD time: rank-1 ldldowndate 0.0001 nnz(L) 6600 no fill-in after resymbol: 6453 CHOLMOD residual: 3.3e-15 MATLAB residual: 3.6e-15 CHOLMOD residual: 2.1e-16 (sparse b) MATLAB residual: 2.1e-16 (sparse b) ================== Problem: 4: HB/685_bus n: 685 nnz: 3249 title: S ADMITTANCE MATRIX 685 BUS POWER SYSTEM, D.J.TYLAVSKY, JULY 1985. time: amd 0.0005 CHOLMOD time: L=lchol 0.0005 nnz(L): 3650 CHOLMOD time: R=chol2 0.0005 nnz(R): 3650 MATLAB time: R=chol 0.0005 nnz(R): 3650 MATLAB [..,R]=symbfact 0.0005 nnz(R): 3650 CHOLMOD speedup vs MATLAB chol: R: 0.98 L: 0.98 CHOLMOD numeric lchol vs MATLAB symbfact: 1.07 CHOLMOD time: [L,,q]=lchol 0.0011 nnz(L): 3650 CHOLMOD time: [L,,q]=ldlchol 0.0011 nnz(L): 3650 CHOLMOD time: rank-1 ldlupdate 0.0002 nnz(L) 3717 with fill-in CHOLMOD time: rank-1 ldldowndate 0.0001 nnz(L) 3717 no fill-in after resymbol: 3650 CHOLMOD residual: 4.5e-15 MATLAB residual: 6.8e-15 CHOLMOD residual: 2.4e-16 (sparse b) MATLAB residual: 3.3e-16 (sparse b) ================== Problem: 357: Boeing/msc00726 n: 726 nnz: 34518 title: SYMMETRIC TEST MATRIX FROM MSC/NASTRAN BC4F8.OUT2 time: amd 0.0021 CHOLMOD time: L=lchol 0.0173 nnz(L): 110707 CHOLMOD time: R=chol2 0.0214 nnz(R): 110707 MATLAB time: R=chol 0.0218 nnz(R): 110707 MATLAB [..,R]=symbfact 0.0085 nnz(R): 110707 CHOLMOD speedup vs MATLAB chol: R: 1.02 L: 1.26 CHOLMOD numeric lchol vs MATLAB symbfact: 0.49 CHOLMOD time: [L,,q]=lchol 0.0213 nnz(L): 110707 CHOLMOD time: [L,,q]=ldlchol 0.1228 nnz(L): 110707 CHOLMOD time: rank-6 ldlupdate 0.0058 nnz(L) 110715 with fill-in CHOLMOD time: rank-3 ldldowndate 0.0028 nnz(L) 110715 no fill-in after resymbol: 110707 CHOLMOD residual: 2.7e-21 MATLAB residual: 2.8e-21 CHOLMOD residual: 3.9e-22 (sparse b) MATLAB residual: 3.9e-22 (sparse b) ================== Problem: 223: HB/nos7 n: 729 nnz: 4617 title: SYMMETRIC MATRIX, POISSON'S EQUATION IN UNIT CUBE. time: amd 0.0008 CHOLMOD time: L=lchol 0.0027 nnz(L): 18945 CHOLMOD time: R=chol2 0.0035 nnz(R): 18945 MATLAB time: R=chol 0.0034 nnz(R): 18945 MATLAB [..,R]=symbfact 0.0013 nnz(R): 18945 CHOLMOD speedup vs MATLAB chol: R: 0.99 L: 1.24 CHOLMOD numeric lchol vs MATLAB symbfact: 0.48 CHOLMOD time: [L,,q]=lchol 0.0042 nnz(L): 18945 CHOLMOD time: [L,,q]=ldlchol 0.0044 nnz(L): 18945 CHOLMOD time: rank-3 ldlupdate 0.0012 nnz(L) 19170 with fill-in CHOLMOD time: rank-1 ldldowndate 0.0005 nnz(L) 19170 no fill-in after resymbol: 18945 CHOLMOD residual: 2.2e-13 MATLAB residual: 2.6e-13 CHOLMOD residual: 9.3e-15 (sparse b) MATLAB residual: 9.4e-15 (sparse b) ================== Problem: 41: HB/bcsstk19 n: 817 nnz: 6853 title: SYMMETRIC STIFFNESS MATRIX - PART OF A SUSPENSION BRIDGE time: amd 0.0005 CHOLMOD time: L=lchol 0.0009 nnz(L): 7528 CHOLMOD time: R=chol2 0.0009 nnz(R): 7528 MATLAB time: R=chol 0.0009 nnz(R): 7528 MATLAB [..,R]=symbfact 0.0008 nnz(R): 7528 CHOLMOD speedup vs MATLAB chol: R: 0.98 L: 0.95 CHOLMOD numeric lchol vs MATLAB symbfact: 0.90 CHOLMOD time: [L,,q]=lchol 0.0016 nnz(L): 7528 CHOLMOD time: [L,,q]=ldlchol 0.0016 nnz(L): 7528 CHOLMOD time: rank-6 ldlupdate 0.0006 nnz(L) 7558 with fill-in CHOLMOD time: rank-3 ldldowndate 0.0002 nnz(L) 7558 no fill-in after resymbol: 7528 CHOLMOD residual: 2.8e-20 MATLAB residual: 3.2e-20 CHOLMOD residual: 7.6e-21 (sparse b) MATLAB residual: 5.7e-21 (sparse b) ================== Problem: 69: HB/bcsstm19 n: 817 nnz: 817 title: SYMMETRIC MASS MATRIX - PART OF A SUSPENSION BRIDGE time: amd 0.0001 CHOLMOD time: L=lchol 0.0002 nnz(L): 817 CHOLMOD time: R=chol2 0.0002 nnz(R): 817 MATLAB time: R=chol 0.0002 nnz(R): 817 MATLAB [..,R]=symbfact 0.0003 nnz(R): 817 CHOLMOD speedup vs MATLAB chol: R: 0.81 L: 0.79 CHOLMOD numeric lchol vs MATLAB symbfact: 1.67 CHOLMOD time: [L,,q]=lchol 0.0003 nnz(L): 817 CHOLMOD time: [L,,q]=ldlchol 0.0003 nnz(L): 817 CHOLMOD time: rank-2 ldlupdate 0.0001 nnz(L) 818 with fill-in CHOLMOD time: rank-1 ldldowndate 0.0001 nnz(L) 818 no fill-in after resymbol: 817 CHOLMOD residual: 2.0e-22 MATLAB residual: 2.0e-22 CHOLMOD residual: 1.0e-22 (sparse b) MATLAB residual: 1.0e-22 (sparse b) ================== Problem: 159: HB/gr_30_30 n: 900 nnz: 7744 title: SYMMETRIC MATRIX FROM NINE POINT START ON A 30 X 30 GRID. time: amd 0.0007 CHOLMOD time: L=lchol 0.0020 nnz(L): 16348 CHOLMOD time: R=chol2 0.0021 nnz(R): 16348 MATLAB time: R=chol 0.0022 nnz(R): 16348 MATLAB [..,R]=symbfact 0.0012 nnz(R): 16348 CHOLMOD speedup vs MATLAB chol: R: 1.02 L: 1.10 CHOLMOD numeric lchol vs MATLAB symbfact: 0.61 CHOLMOD time: [L,,q]=lchol 0.0030 nnz(L): 16348 CHOLMOD time: [L,,q]=ldlchol 0.0029 nnz(L): 16348 CHOLMOD time: rank-8 ldlupdate 0.0013 nnz(L) 17998 with fill-in CHOLMOD time: rank-4 ldldowndate 0.0004 nnz(L) 17998 no fill-in after resymbol: 16348 CHOLMOD residual: 4.1e-13 MATLAB residual: 4.4e-13 CHOLMOD residual: 2.4e-14 (sparse b) MATLAB residual: 2.7e-14 (sparse b) ================== Problem: 218: HB/nos2 n: 957 nnz: 4137 title: SYMMETRIC MATRIX, FE APPROXIMATION TO BIHARMONIC OPERATOR ON BEAM. time: amd 0.0003 CHOLMOD time: L=lchol 0.0004 nnz(L): 2864 CHOLMOD time: R=chol2 0.0004 nnz(R): 2864 MATLAB time: R=chol 0.0003 nnz(R): 2864 MATLAB [..,R]=symbfact 0.0005 nnz(R): 2864 CHOLMOD speedup vs MATLAB chol: R: 0.88 L: 0.83 CHOLMOD numeric lchol vs MATLAB symbfact: 1.25 CHOLMOD time: [L,,q]=lchol 0.0008 nnz(L): 2864 CHOLMOD time: [L,,q]=ldlchol 0.0008 nnz(L): 2864 CHOLMOD time: rank-8 ldlupdate 0.0003 nnz(L) 3124 with fill-in CHOLMOD time: rank-4 ldldowndate 0.0002 nnz(L) 3124 no fill-in after resymbol: 2864 CHOLMOD residual: 3.5e-17 MATLAB residual: 3.8e-17 CHOLMOD residual: 4.8e-18 (sparse b) MATLAB residual: 4.6e-18 (sparse b) ================== Problem: 219: HB/nos3 n: 960 nnz: 15844 title: SYMMETRIC MATRIX, FE APPROXIMATION TO BIHARMONIC OPERATOR ON PLATE time: amd 0.0009 CHOLMOD time: L=lchol 0.0039 nnz(L): 31309 CHOLMOD time: R=chol2 0.0049 nnz(R): 31309 MATLAB time: R=chol 0.0049 nnz(R): 31309 MATLAB [..,R]=symbfact 0.0027 nnz(R): 31314 CHOLMOD speedup vs MATLAB chol: R: 0.99 L: 1.24 CHOLMOD numeric lchol vs MATLAB symbfact: 0.70 CHOLMOD time: [L,,q]=lchol 0.0055 nnz(L): 31311 CHOLMOD time: [L,,q]=ldlchol 0.0057 nnz(L): 31314 CHOLMOD time: rank-7 ldlupdate 0.0026 nnz(L) 36618 with fill-in CHOLMOD time: rank-3 ldldowndate 0.0010 nnz(L) 36618 no fill-in after resymbol: 31314 CHOLMOD residual: 1.9e-13 MATLAB residual: 1.9e-13 CHOLMOD residual: 7.0e-15 (sparse b) MATLAB residual: 7.0e-15 (sparse b) ================== Problem: 358: Boeing/msc01050 n: 1050 nnz: 26198 title: SYMMETRIC TEST MATRIX FROM MSC/NASTRAN STARF8.OUT2 time: amd 0.0019 CHOLMOD time: L=lchol 0.0051 nnz(L): 28305 CHOLMOD time: R=chol2 0.0054 nnz(R): 28305 MATLAB time: R=chol 0.0057 nnz(R): 28305 MATLAB [..,R]=symbfact 0.0032 nnz(R): 28305 CHOLMOD speedup vs MATLAB chol: R: 1.06 L: 1.13 CHOLMOD numeric lchol vs MATLAB symbfact: 0.64 CHOLMOD time: [L,,q]=lchol 0.0074 nnz(L): 28305 CHOLMOD time: [L,,q]=ldlchol 0.0072 nnz(L): 28305 CHOLMOD time: rank-5 ldlupdate 0.0016 nnz(L) 28411 with fill-in CHOLMOD time: rank-2 ldldowndate 0.0007 nnz(L) 28411 no fill-in after resymbol: 28305 CHOLMOD residual: 5.3e-14 MATLAB residual: 5.1e-14 CHOLMOD residual: 4.3e-15 (sparse b) MATLAB residual: 4.3e-15 (sparse b) ================== Problem: 30: HB/bcsstk08 n: 1074 nnz: 12960 title: SYMMETRIC STIFFNESS MATRIX, FRAME BUILDING (TV STUDIO) time: amd 0.0024 CHOLMOD time: L=lchol 0.0056 nnz(L): 31150 CHOLMOD time: R=chol2 0.0068 nnz(R): 31150 MATLAB time: R=chol 0.0070 nnz(R): 31150 MATLAB [..,R]=symbfact 0.0027 nnz(R): 31153 CHOLMOD speedup vs MATLAB chol: R: 1.04 L: 1.25 CHOLMOD numeric lchol vs MATLAB symbfact: 0.48 CHOLMOD time: [L,,q]=lchol 0.0089 nnz(L): 31150 CHOLMOD time: [L,,q]=ldlchol 0.0092 nnz(L): 31153 CHOLMOD time: rank-8 ldlupdate 0.0021 nnz(L) 31639 with fill-in CHOLMOD time: rank-4 ldldowndate 0.0009 nnz(L) 31639 no fill-in after resymbol: 31153 CHOLMOD residual: 4.0e-22 MATLAB residual: 3.0e-22 CHOLMOD residual: 4.3e-22 (sparse b) MATLAB residual: 2.7e-22 (sparse b) ================== Problem: 63: HB/bcsstm08 n: 1074 nnz: 1074 title: SYMMETRIC MASS MATRIX, FRAME BUILDING (TV STUDIO) time: amd 0.0001 CHOLMOD time: L=lchol 0.0002 nnz(L): 1074 CHOLMOD time: R=chol2 0.0002 nnz(R): 1074 MATLAB time: R=chol 0.0002 nnz(R): 1074 MATLAB [..,R]=symbfact 0.0004 nnz(R): 1074 CHOLMOD speedup vs MATLAB chol: R: 0.83 L: 0.81 CHOLMOD numeric lchol vs MATLAB symbfact: 1.81 CHOLMOD time: [L,,q]=lchol 0.0004 nnz(L): 1074 CHOLMOD time: [L,,q]=ldlchol 0.0004 nnz(L): 1074 CHOLMOD time: rank-8 ldlupdate 0.0001 nnz(L) 1075 with fill-in CHOLMOD time: rank-4 ldldowndate 0.0001 nnz(L) 1075 no fill-in after resymbol: 1074 CHOLMOD residual: 3.2e-21 MATLAB residual: 3.0e-21 CHOLMOD residual: 1.4e-21 (sparse b) MATLAB residual: 1.2e-21 (sparse b) ================== Problem: 31: HB/bcsstk09 n: 1083 nnz: 18437 title: SYMMETRIC STIFFNESS MATRIX, SQUARE PLATE CLAMPED time: amd 0.0018 CHOLMOD time: L=lchol 0.0076 nnz(L): 58341 CHOLMOD time: R=chol2 0.0095 nnz(R): 58341 MATLAB time: R=chol 0.0095 nnz(R): 58341 MATLAB [..,R]=symbfact 0.0045 nnz(R): 58416 CHOLMOD speedup vs MATLAB chol: R: 1.01 L: 1.26 CHOLMOD numeric lchol vs MATLAB symbfact: 0.60 CHOLMOD time: [L,,q]=lchol 0.0103 nnz(L): 58339 CHOLMOD time: [L,,q]=ldlchol 0.0107 nnz(L): 58416 CHOLMOD time: rank-1 ldlupdate 0.0040 nnz(L) 64019 with fill-in CHOLMOD time: rank-1 ldldowndate 0.0015 nnz(L) 64019 no fill-in after resymbol: 58416 CHOLMOD residual: 1.7e-18 MATLAB residual: 1.3e-18 CHOLMOD residual: 1.1e-19 (sparse b) MATLAB residual: 8.9e-20 (sparse b) ================== Problem: 64: HB/bcsstm09 n: 1083 nnz: 1083 title: SYMMETRIC MASS MATRIX, SQUARE PLATE CLAMPED time: amd 0.0001 CHOLMOD time: L=lchol 0.0002 nnz(L): 1083 CHOLMOD time: R=chol2 0.0002 nnz(R): 1083 MATLAB time: R=chol 0.0002 nnz(R): 1083 MATLAB [..,R]=symbfact 0.0004 nnz(R): 1083 CHOLMOD speedup vs MATLAB chol: R: 0.86 L: 0.84 CHOLMOD numeric lchol vs MATLAB symbfact: 1.61 CHOLMOD time: [L,,q]=lchol 0.0004 nnz(L): 1083 CHOLMOD time: [L,,q]=ldlchol 0.0004 nnz(L): 1083 CHOLMOD time: rank-7 ldlupdate 0.0001 nnz(L) 1084 with fill-in CHOLMOD time: rank-3 ldldowndate 0.0001 nnz(L) 1084 no fill-in after resymbol: 1083 CHOLMOD residual: 1.5e-05 MATLAB residual: 3.4e-11 CHOLMOD residual: 1.2e-06 (sparse b) MATLAB residual: 1.8e-11 (sparse b) test0 passed ================================================================= test1: test sparse2 ----------------------------------------------- i = 1 j = 1 s = 1 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (1,1) 1 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (1,1) 1 size A2: 3 4 B1 = sparse (i,j,s) B1 = (1,1) 1 size B1: 1 1 B2 = sparse2 (i,j,s) B2 = (1,1) 1 size B2: 1 1 ----------------------------------------------- i = 1 j = 1 s = 2 3 m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) A2 = (1,1) 5 size A2: 3 4 B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) B2 = (1,1) 5 size B2: 1 1 ========================== SPARSE AND SPARSE2 DIFFER ----------------------------------------------- i = 1 j = 1 s = 3.1416 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (1,1) 3.1416 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (1,1) 3.1416 size A2: 3 4 B1 = sparse (i,j,s) B1 = (1,1) 3.1416 size B1: 1 1 B2 = sparse2 (i,j,s) B2 = (1,1) 3.1416 size B2: 1 1 ----------------------------------------------- i = 1 j = 1 s = [] m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) A2 = All zero sparse: 3-by-4 size A2: 3 4 B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) B2 = All zero sparse: 1-by-1 size B2: 1 1 ========================== SPARSE AND SPARSE2 DIFFER ----------------------------------------------- i = 1 j = 2 3 s = 1 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (1,2) 1 (1,3) 1 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (1,2) 1 (1,3) 1 size A2: 3 4 B1 = sparse (i,j,s) B1 = (1,2) 1 (1,3) 1 size B1: 1 3 B2 = sparse2 (i,j,s) B2 = (1,2) 1 (1,3) 1 size B2: 1 3 ----------------------------------------------- i = 1 j = 2 3 s = 2 3 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (1,2) 2 (1,3) 3 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (1,2) 2 (1,3) 3 size A2: 3 4 B1 = sparse (i,j,s) B1 = (1,2) 2 (1,3) 3 size B1: 1 3 B2 = sparse2 (i,j,s) B2 = (1,2) 2 (1,3) 3 size B2: 1 3 ----------------------------------------------- i = 1 j = 2 3 s = 3.1416 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (1,2) 3.1416 (1,3) 3.1416 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (1,2) 3.1416 (1,3) 3.1416 size A2: 3 4 B1 = sparse (i,j,s) B1 = (1,2) 3.1416 (1,3) 3.1416 size B1: 1 3 B2 = sparse2 (i,j,s) B2 = (1,2) 3.1416 (1,3) 3.1416 size B2: 1 3 ----------------------------------------------- i = 1 j = 2 3 s = [] m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) sparse2 failed B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) sparse2 failed ----------------------------------------------- i = 1 j = 3 s = 1 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (1,3) 1 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (1,3) 1 size A2: 3 4 B1 = sparse (i,j,s) B1 = (1,3) 1 size B1: 1 3 B2 = sparse2 (i,j,s) B2 = (1,3) 1 size B2: 1 3 ----------------------------------------------- i = 1 j = 3 s = 2 3 m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) A2 = (1,3) 5 size A2: 3 4 B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) B2 = (1,3) 5 size B2: 1 3 ========================== SPARSE AND SPARSE2 DIFFER ----------------------------------------------- i = 1 j = 3 s = 3.1416 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (1,3) 3.1416 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (1,3) 3.1416 size A2: 3 4 B1 = sparse (i,j,s) B1 = (1,3) 3.1416 size B1: 1 3 B2 = sparse2 (i,j,s) B2 = (1,3) 3.1416 size B2: 1 3 ----------------------------------------------- i = 1 j = 3 s = [] m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) A2 = All zero sparse: 3-by-4 size A2: 3 4 B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) B2 = All zero sparse: 1-by-3 size B2: 1 3 ========================== SPARSE AND SPARSE2 DIFFER ----------------------------------------------- i = 1 j = [] s = 1 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = All zero sparse: 3-by-4 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = All zero sparse: 3-by-4 size A2: 3 4 B1 = sparse (i,j,s) B1 = All zero sparse: 0-by-0 size B1: 0 0 B2 = sparse2 (i,j,s) B2 = All zero sparse: 1-by-0 size B2: 1 0 ========================== SPARSE AND SPARSE2 DIFFER ----------------------------------------------- i = 1 j = [] s = 2 3 m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) sparse2 failed B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) sparse2 failed ----------------------------------------------- i = 1 j = [] s = 3.1416 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = All zero sparse: 3-by-4 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = All zero sparse: 3-by-4 size A2: 3 4 B1 = sparse (i,j,s) B1 = All zero sparse: 0-by-0 size B1: 0 0 B2 = sparse2 (i,j,s) B2 = All zero sparse: 1-by-0 size B2: 1 0 ========================== SPARSE AND SPARSE2 DIFFER ----------------------------------------------- i = 1 j = [] s = [] m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = All zero sparse: 3-by-4 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = All zero sparse: 3-by-4 size A2: 3 4 B1 = sparse (i,j,s) B1 = All zero sparse: 0-by-0 size B1: 0 0 B2 = sparse2 (i,j,s) B2 = All zero sparse: 1-by-0 size B2: 1 0 ========================== SPARSE AND SPARSE2 DIFFER ----------------------------------------------- i = 2 3 j = 1 s = 1 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (2,1) 1 (3,1) 1 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (2,1) 1 (3,1) 1 size A2: 3 4 B1 = sparse (i,j,s) B1 = (2,1) 1 (3,1) 1 size B1: 3 1 B2 = sparse2 (i,j,s) B2 = (2,1) 1 (3,1) 1 size B2: 3 1 ----------------------------------------------- i = 2 3 j = 1 s = 2 3 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (2,1) 2 (3,1) 3 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (2,1) 2 (3,1) 3 size A2: 3 4 B1 = sparse (i,j,s) B1 = (2,1) 2 (3,1) 3 size B1: 3 1 B2 = sparse2 (i,j,s) B2 = (2,1) 2 (3,1) 3 size B2: 3 1 ----------------------------------------------- i = 2 3 j = 1 s = 3.1416 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (2,1) 3.1416 (3,1) 3.1416 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (2,1) 3.1416 (3,1) 3.1416 size A2: 3 4 B1 = sparse (i,j,s) B1 = (2,1) 3.1416 (3,1) 3.1416 size B1: 3 1 B2 = sparse2 (i,j,s) B2 = (2,1) 3.1416 (3,1) 3.1416 size B2: 3 1 ----------------------------------------------- i = 2 3 j = 1 s = [] m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) sparse2 failed B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) sparse2 failed ----------------------------------------------- i = 2 3 j = 2 3 s = 1 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (2,2) 1 (3,3) 1 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (2,2) 1 (3,3) 1 size A2: 3 4 B1 = sparse (i,j,s) B1 = (2,2) 1 (3,3) 1 size B1: 3 3 B2 = sparse2 (i,j,s) B2 = (2,2) 1 (3,3) 1 size B2: 3 3 ----------------------------------------------- i = 2 3 j = 2 3 s = 2 3 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (2,2) 2 (3,3) 3 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (2,2) 2 (3,3) 3 size A2: 3 4 B1 = sparse (i,j,s) B1 = (2,2) 2 (3,3) 3 size B1: 3 3 B2 = sparse2 (i,j,s) B2 = (2,2) 2 (3,3) 3 size B2: 3 3 ----------------------------------------------- i = 2 3 j = 2 3 s = 3.1416 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (2,2) 3.1416 (3,3) 3.1416 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (2,2) 3.1416 (3,3) 3.1416 size A2: 3 4 B1 = sparse (i,j,s) B1 = (2,2) 3.1416 (3,3) 3.1416 size B1: 3 3 B2 = sparse2 (i,j,s) B2 = (2,2) 3.1416 (3,3) 3.1416 size B2: 3 3 ----------------------------------------------- i = 2 3 j = 2 3 s = [] m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) sparse2 failed B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) sparse2 failed ----------------------------------------------- i = 2 3 j = 3 s = 1 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (2,3) 1 (3,3) 1 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (2,3) 1 (3,3) 1 size A2: 3 4 B1 = sparse (i,j,s) B1 = (2,3) 1 (3,3) 1 size B1: 3 3 B2 = sparse2 (i,j,s) B2 = (2,3) 1 (3,3) 1 size B2: 3 3 ----------------------------------------------- i = 2 3 j = 3 s = 2 3 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (2,3) 2 (3,3) 3 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (2,3) 2 (3,3) 3 size A2: 3 4 B1 = sparse (i,j,s) B1 = (2,3) 2 (3,3) 3 size B1: 3 3 B2 = sparse2 (i,j,s) B2 = (2,3) 2 (3,3) 3 size B2: 3 3 ----------------------------------------------- i = 2 3 j = 3 s = 3.1416 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (2,3) 3.1416 (3,3) 3.1416 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (2,3) 3.1416 (3,3) 3.1416 size A2: 3 4 B1 = sparse (i,j,s) B1 = (2,3) 3.1416 (3,3) 3.1416 size B1: 3 3 B2 = sparse2 (i,j,s) B2 = (2,3) 3.1416 (3,3) 3.1416 size B2: 3 3 ----------------------------------------------- i = 2 3 j = 3 s = [] m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) sparse2 failed B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) sparse2 failed ----------------------------------------------- i = 2 3 j = [] s = 1 m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) sparse2 failed B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) sparse2 failed ----------------------------------------------- i = 2 3 j = [] s = 2 3 m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) sparse2 failed B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) sparse2 failed ----------------------------------------------- i = 2 3 j = [] s = 3.1416 m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) sparse2 failed B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) sparse2 failed ----------------------------------------------- i = 2 3 j = [] s = [] m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) sparse2 failed B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) sparse2 failed ----------------------------------------------- i = 2 j = 1 s = 1 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (2,1) 1 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (2,1) 1 size A2: 3 4 B1 = sparse (i,j,s) B1 = (2,1) 1 size B1: 2 1 B2 = sparse2 (i,j,s) B2 = (2,1) 1 size B2: 2 1 ----------------------------------------------- i = 2 j = 1 s = 2 3 m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) A2 = (2,1) 5 size A2: 3 4 B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) B2 = (2,1) 5 size B2: 2 1 ========================== SPARSE AND SPARSE2 DIFFER ----------------------------------------------- i = 2 j = 1 s = 3.1416 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (2,1) 3.1416 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (2,1) 3.1416 size A2: 3 4 B1 = sparse (i,j,s) B1 = (2,1) 3.1416 size B1: 2 1 B2 = sparse2 (i,j,s) B2 = (2,1) 3.1416 size B2: 2 1 ----------------------------------------------- i = 2 j = 1 s = [] m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) A2 = All zero sparse: 3-by-4 size A2: 3 4 B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) B2 = All zero sparse: 2-by-1 size B2: 2 1 ========================== SPARSE AND SPARSE2 DIFFER ----------------------------------------------- i = 2 j = 2 3 s = 1 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (2,2) 1 (2,3) 1 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (2,2) 1 (2,3) 1 size A2: 3 4 B1 = sparse (i,j,s) B1 = (2,2) 1 (2,3) 1 size B1: 2 3 B2 = sparse2 (i,j,s) B2 = (2,2) 1 (2,3) 1 size B2: 2 3 ----------------------------------------------- i = 2 j = 2 3 s = 2 3 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (2,2) 2 (2,3) 3 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (2,2) 2 (2,3) 3 size A2: 3 4 B1 = sparse (i,j,s) B1 = (2,2) 2 (2,3) 3 size B1: 2 3 B2 = sparse2 (i,j,s) B2 = (2,2) 2 (2,3) 3 size B2: 2 3 ----------------------------------------------- i = 2 j = 2 3 s = 3.1416 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (2,2) 3.1416 (2,3) 3.1416 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (2,2) 3.1416 (2,3) 3.1416 size A2: 3 4 B1 = sparse (i,j,s) B1 = (2,2) 3.1416 (2,3) 3.1416 size B1: 2 3 B2 = sparse2 (i,j,s) B2 = (2,2) 3.1416 (2,3) 3.1416 size B2: 2 3 ----------------------------------------------- i = 2 j = 2 3 s = [] m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) sparse2 failed B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) sparse2 failed ----------------------------------------------- i = 2 j = 3 s = 1 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (2,3) 1 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (2,3) 1 size A2: 3 4 B1 = sparse (i,j,s) B1 = (2,3) 1 size B1: 2 3 B2 = sparse2 (i,j,s) B2 = (2,3) 1 size B2: 2 3 ----------------------------------------------- i = 2 j = 3 s = 2 3 m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) A2 = (2,3) 5 size A2: 3 4 B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) B2 = (2,3) 5 size B2: 2 3 ========================== SPARSE AND SPARSE2 DIFFER ----------------------------------------------- i = 2 j = 3 s = 3.1416 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = (2,3) 3.1416 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = (2,3) 3.1416 size A2: 3 4 B1 = sparse (i,j,s) B1 = (2,3) 3.1416 size B1: 2 3 B2 = sparse2 (i,j,s) B2 = (2,3) 3.1416 size B2: 2 3 ----------------------------------------------- i = 2 j = 3 s = [] m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) A2 = All zero sparse: 3-by-4 size A2: 3 4 B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) B2 = All zero sparse: 2-by-3 size B2: 2 3 ========================== SPARSE AND SPARSE2 DIFFER ----------------------------------------------- i = 2 j = [] s = 1 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = All zero sparse: 3-by-4 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = All zero sparse: 3-by-4 size A2: 3 4 B1 = sparse (i,j,s) B1 = All zero sparse: 0-by-0 size B1: 0 0 B2 = sparse2 (i,j,s) B2 = All zero sparse: 2-by-0 size B2: 2 0 ========================== SPARSE AND SPARSE2 DIFFER ----------------------------------------------- i = 2 j = [] s = 2 3 m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) sparse2 failed B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) sparse2 failed ----------------------------------------------- i = 2 j = [] s = 3.1416 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = All zero sparse: 3-by-4 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = All zero sparse: 3-by-4 size A2: 3 4 B1 = sparse (i,j,s) B1 = All zero sparse: 0-by-0 size B1: 0 0 B2 = sparse2 (i,j,s) B2 = All zero sparse: 2-by-0 size B2: 2 0 ========================== SPARSE AND SPARSE2 DIFFER ----------------------------------------------- i = 2 j = [] s = [] m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = All zero sparse: 3-by-4 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = All zero sparse: 3-by-4 size A2: 3 4 B1 = sparse (i,j,s) B1 = All zero sparse: 0-by-0 size B1: 0 0 B2 = sparse2 (i,j,s) B2 = All zero sparse: 2-by-0 size B2: 2 0 ========================== SPARSE AND SPARSE2 DIFFER ----------------------------------------------- i = [] j = 1 s = 1 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = All zero sparse: 3-by-4 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = All zero sparse: 3-by-4 size A2: 3 4 B1 = sparse (i,j,s) B1 = All zero sparse: 0-by-0 size B1: 0 0 B2 = sparse2 (i,j,s) B2 = All zero sparse: 0-by-1 size B2: 0 1 ========================== SPARSE AND SPARSE2 DIFFER ----------------------------------------------- i = [] j = 1 s = 2 3 m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) sparse2 failed B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) sparse2 failed ----------------------------------------------- i = [] j = 1 s = 3.1416 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = All zero sparse: 3-by-4 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = All zero sparse: 3-by-4 size A2: 3 4 B1 = sparse (i,j,s) B1 = All zero sparse: 0-by-0 size B1: 0 0 B2 = sparse2 (i,j,s) B2 = All zero sparse: 0-by-1 size B2: 0 1 ========================== SPARSE AND SPARSE2 DIFFER ----------------------------------------------- i = [] j = 1 s = [] m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = All zero sparse: 3-by-4 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = All zero sparse: 3-by-4 size A2: 3 4 B1 = sparse (i,j,s) B1 = All zero sparse: 0-by-0 size B1: 0 0 B2 = sparse2 (i,j,s) B2 = All zero sparse: 0-by-1 size B2: 0 1 ========================== SPARSE AND SPARSE2 DIFFER ----------------------------------------------- i = [] j = 2 3 s = 1 m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) sparse2 failed B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) sparse2 failed ----------------------------------------------- i = [] j = 2 3 s = 2 3 m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) sparse2 failed B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) sparse2 failed ----------------------------------------------- i = [] j = 2 3 s = 3.1416 m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) sparse2 failed B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) sparse2 failed ----------------------------------------------- i = [] j = 2 3 s = [] m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) sparse2 failed B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) sparse2 failed ----------------------------------------------- i = [] j = 3 s = 1 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = All zero sparse: 3-by-4 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = All zero sparse: 3-by-4 size A2: 3 4 B1 = sparse (i,j,s) B1 = All zero sparse: 0-by-0 size B1: 0 0 B2 = sparse2 (i,j,s) B2 = All zero sparse: 0-by-3 size B2: 0 3 ========================== SPARSE AND SPARSE2 DIFFER ----------------------------------------------- i = [] j = 3 s = 2 3 m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) sparse2 failed B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) sparse2 failed ----------------------------------------------- i = [] j = 3 s = 3.1416 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = All zero sparse: 3-by-4 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = All zero sparse: 3-by-4 size A2: 3 4 B1 = sparse (i,j,s) B1 = All zero sparse: 0-by-0 size B1: 0 0 B2 = sparse2 (i,j,s) B2 = All zero sparse: 0-by-3 size B2: 0 3 ========================== SPARSE AND SPARSE2 DIFFER ----------------------------------------------- i = [] j = 3 s = [] m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = All zero sparse: 3-by-4 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = All zero sparse: 3-by-4 size A2: 3 4 B1 = sparse (i,j,s) B1 = All zero sparse: 0-by-0 size B1: 0 0 B2 = sparse2 (i,j,s) B2 = All zero sparse: 0-by-3 size B2: 0 3 ========================== SPARSE AND SPARSE2 DIFFER ----------------------------------------------- i = [] j = [] s = 1 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = All zero sparse: 3-by-4 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = All zero sparse: 3-by-4 size A2: 3 4 B1 = sparse (i,j,s) B1 = All zero sparse: 0-by-0 size B1: 0 0 B2 = sparse2 (i,j,s) B2 = All zero sparse: 0-by-0 size B2: 0 0 ----------------------------------------------- i = [] j = [] s = 2 3 m = 3 n = 4 A1 = sparse (i,j,s,m,n) sparse failed A2 = sparse2 (i,j,s,m,n) sparse2 failed B1 = sparse (i,j,s) sparse failed B2 = sparse2 (i,j,s) sparse2 failed ----------------------------------------------- i = [] j = [] s = 3.1416 m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = All zero sparse: 3-by-4 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = All zero sparse: 3-by-4 size A2: 3 4 B1 = sparse (i,j,s) B1 = All zero sparse: 0-by-0 size B1: 0 0 B2 = sparse2 (i,j,s) B2 = All zero sparse: 0-by-0 size B2: 0 0 ----------------------------------------------- i = [] j = [] s = [] m = 3 n = 4 A1 = sparse (i,j,s,m,n) A1 = All zero sparse: 3-by-4 size A1: 3 4 A2 = sparse2 (i,j,s,m,n) A2 = All zero sparse: 3-by-4 size A2: 3 4 B1 = sparse (i,j,s) B1 = All zero sparse: 0-by-0 size B1: 0 0 B2 = sparse2 (i,j,s) B2 = All zero sparse: 0-by-0 size B2: 0 0 test1 passed (review the above results) ================================================================= test2: test sparse2 i = 2 3 j = 3 4 s = 11.4000 + 3.4000i 9.2000 + 1.2000i ans = (2,3) 11.4000 + 3.4000i (3,4) 9.2000 + 1.2000i ans = (2,3) 11.4000 + 3.4000i (3,4) 9.2000 + 1.2000i ans = 3290 test2 passed ================================================================= test3: test sparse on int8, int16, and logical c = ab d Warning: SPARSE with a character array input returns a sparse double result. This behavior will change in a future release. > In test3 at 14 In cholmod_test at 100 ans = (1,1) 97 (1,2) 98 (1,4) 100 ans = (1,1) 97 (1,2) 98 (1,4) 100 Warning: SPARSE with a character array input returns a sparse double result. This behavior will change in a future release. > In test3 at 16 In cholmod_test at 100 ans = (1,1) 97 (2,1) 98 (4,1) 100 ans = (1,1) 97 (2,1) 98 (4,1) 100 Name Size Bytes Class Attributes ans 4x1 64 double sparse c 1x4 8 char ans = 3 sparse(int8(c)) fails in MATLAB ans = (1,1) 97 (1,2) 98 (1,4) 100 ans = (1,1) 97 (1,2) 98 (1,4) 100 Name Size Bytes Class Attributes ans 1x4 88 double sparse c 1x4 8 char s = 1 0 1 1 0 0 0 1 0 1 1 1 1 0 0 0 ans = (1,1) 1 (4,1) 1 (3,2) 1 (1,3) 1 (3,3) 1 (1,4) 1 (2,4) 1 (3,4) 1 Name Size Bytes Class Attributes ans 4x4 112 logical sparse c 1x4 8 char s 4x4 16 logical ans = (1,1) 1 (4,1) 1 (3,2) 1 (1,3) 1 (3,3) 1 (1,4) 1 (2,4) 1 (3,4) 1 Name Size Bytes Class Attributes ans 4x4 112 logical sparse c 1x4 8 char s 4x4 16 logical x = 0.1013 0.2280 0.1095 0.9468 0.2648 0.0281 0.8211 0.8138 0.2595 0.6996 0.4195 0.7779 0.5345 0.8071 0.8422 0.8768 ans = (4,1) 1 (3,2) 1 (4,2) 1 (2,3) 1 (4,3) 1 (1,4) 1 (2,4) 1 (3,4) 1 (4,4) 1 Name Size Bytes Class Attributes ans 4x4 121 logical sparse c 1x4 8 char s 4x4 16 logical x 4x4 128 double ans = (4,1) 1 (3,2) 1 (4,2) 1 (2,3) 1 (4,3) 1 (1,4) 1 (2,4) 1 (3,4) 1 (4,4) 1 Name Size Bytes Class Attributes ans 4x4 121 logical sparse c 1x4 8 char s 4x4 16 logical x 4x4 128 double test3 passed ================================================================= test4: test cholmod2 with multiple and sparse right-hand-sides maxerr 2.363058e-12 2.350665e-12 test4 passed ================================================================= test5: test sparse2 test5 passed ================================================================= test6: test sparse with large matrix, both real and complex do_complex = 0 Prob = title: 'Light hydrocarbon recovery. OK if illconditioned,from a nonlinear solvr' A: [70304x70304 double] Zeros: [70304x70304 double] b: [70304x1 double] name: 'Mallya/lhr71' id: 750 date: '1994' author: 'J. Mallya' ed: 'T. Davis' kind: 'chemical process simulation problem' find time 0.0573 dtri time: cholmod2 0.154045 matlab 0.143959 dtri time: cholmod2 0.155702 matlab 0.144404 (jumbled) dtri time: cholmod2 0.740039 matlab 3.960841 (duplicates) length 2988012 nz 1494006 err = 0 dtri time: cholmod2 1.054730 matlab 3.971992 (upper) err = 0 dtri time: cholmod2 1.170586 matlab 3.867817 (lower) dtri time: cholmod2 0.564294 matlab 3.392247 (sorted, dupl) do_complex = 1 Prob = title: 'Light hydrocarbon recovery. OK if illconditioned,from a nonlinear solvr' A: [70304x70304 double] Zeros: [70304x70304 double] b: [70304x1 double] name: 'Mallya/lhr71' id: 750 date: '1994' author: 'J. Mallya' ed: 'T. Davis' kind: 'chemical process simulation problem' find time 0.0776 dtri time: cholmod2 0.205535 matlab 0.171580 dtri time: cholmod2 0.396889 matlab 0.269580 (jumbled) dtri time: cholmod2 1.634356 matlab 4.170549 (duplicates) length 2988012 nz 1494006 err = 0 dtri time: cholmod2 1.754138 matlab 4.164494 (upper) err = 0 dtri time: cholmod2 1.633999 matlab 4.168737 (lower) dtri time: cholmod2 0.635309 matlab 3.554928 (sorted, dupl) test6 passed ================================================================= test7: test sparse2 Prob = title: 'Light hydrocarbon recovery. OK if illconditioned,from a nonlinear solvr' A: [70304x70304 double] Zeros: [70304x70304 double] b: [70304x1 double] name: 'Mallya/lhr71' id: 750 date: '1994' author: 'J. Mallya' ed: 'T. Davis' kind: 'chemical process simulation problem' find time 0.0574 tot: 0.154660 tot: 0.156477 again tot: 0.153834 (i,j,x) tot: 0.156731 (jumbled) tot 0.634492 (duplicates) test7 passed ================================================================= test8: factorize a large range of sparse matrices test matrices sorted by dimension: 1440: Oberwolfach LFAT5 14 1 1438: Oberwolfach LF10 18 1 97: HB can_24 24 0 1177: HB lap_25 25 0 436: FIDAP ex5 27 1 13: HB bcspwr01 39 0 23: HB bcsstk01 48 1 872: Pothen mesh1e1 48 1 873: Pothen mesh1em1 48 1 874: Pothen mesh1em6 48 1 14: HB bcspwr02 49 0 129: HB dwt_59 59 0 102: HB can_61 61 0 103: HB can_62 62 0 24: HB bcsstk02 66 1 132: HB dwt_66 66 0 883: Pothen sphere2 66 0 133: HB dwt_72 72 0 106: HB can_73 73 0 11: HB ash85 85 0 136: HB dwt_87 87 0 108: HB can_96 96 0 220: HB nos4 100 1 25: HB bcsstk03 112 1 15: HB bcspwr03 118 0 1506: Pajek Journals 124 1 26: HB bcsstk04 132 1 44: HB bcsstk22 138 1 93: HB can_144 144 0 206: HB lund_a 147 1 207: HB lund_b 147 1 27: HB bcsstk05 153 1 94: HB can_161 161 0 113: HB dwt_162 162 0 95: HB can_187 187 0 114: HB dwt_193 193 0 115: HB dwt_198 198 0 116: HB dwt_209 209 0 117: HB dwt_221 221 0 96: HB can_229 229 0 118: HB dwt_234 234 0 217: HB nos1 237 1 119: HB dwt_245 245 0 98: HB can_256 256 0 884: Pothen sphere3 258 0 202: HB lshp_265 265 0 99: HB can_268 268 0 16: HB bcspwr04 274 0 877: Pothen mesh3e1 289 1 878: Pothen mesh3em5 289 1 ================== Problem: Oberwolfach/LFAT5 n: 14 nnz: 46 title: Oberwolfach: linear 1D beam symbfact time: MATLAB 0.0133 CHOLMOD 0.0005 speedup 27.72 time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 2.8 time: metis 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 2.8 metis/amd time: 1.5023 nnz(L): 1.0000 ================== Problem: Oberwolfach/LF10 n: 18 nnz: 82 title: Oberwolfach: linear 1D beam symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.64 time: amd 0.0000 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.4 time: metis 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 4.4 metis/amd time: 4.7692 nnz(L): 1.2414 ================== Problem: HB/can_24 n: 24 nnz: 160 title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981. symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.66 time: amd 0.0000 mnnz(L) 0.0 mfl 0 fl/nnz(L) 5.5 time: metis 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 5.8 metis/amd time: 5.4865 nnz(L): 1.0417 ================== Problem: HB/lap_25 n: 25 nnz: 169 title: FINITE ELEMENT PROBLEM. LAPLACIAN ON A 5 BY 5 GRID. symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.86 time: amd 0.0000 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.3 time: metis 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 5.7 metis/amd time: 4.8421 nnz(L): 0.9493 ================== Problem: FIDAP/ex5 n: 27 nnz: 279 title: TEST MATRIX FROM FIDAP: EX5.MAT symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.73 time: amd 0.0000 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.4 time: metis 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.4 metis/amd time: 3.0526 nnz(L): 1.0000 ================== Problem: HB/bcspwr01 n: 39 nnz: 131 title: SYMMETRIC STRUCTURE (STANDARD TEST POWER SYSTEM - NEW ENGLAND) symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.65 time: amd 0.0000 mnnz(L) 0.0 mfl 0 fl/nnz(L) 2.8 time: metis 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.0 metis/amd time: 3.8750 nnz(L): 1.0385 ================== Problem: HB/bcsstk01 n: 48 nnz: 400 title: SYMMETRIC STIFFNESS MATRIX SMALL GENERALIZED EIGENVALUE PROBLEM symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.84 time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 12.3 time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 12.0 metis/amd time: 6.5909 nnz(L): 0.9898 ================== Problem: Pothen/mesh1e1 n: 48 nnz: 306 title: mesh1e1, with coordinates. From NASA, collected by Alex Pothen symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.65 time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 8.0 time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 8.3 metis/amd time: 5.4697 nnz(L): 1.0357 ================== Problem: Pothen/mesh1em1 n: 48 nnz: 306 title: mesh1em1, with coordinates. From NASA, collected by Alex Pothen symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.53 time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 8.0 time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 8.3 metis/amd time: 5.9667 nnz(L): 1.0357 ================== Problem: Pothen/mesh1em6 n: 48 nnz: 306 title: mesh1em6, with coordinates. From NASA, collected by Alex Pothen symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.56 time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 8.0 time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 8.3 metis/amd time: 5.8361 nnz(L): 1.0357 ================== Problem: HB/bcspwr02 n: 49 nnz: 167 title: SYMMETRIC STRUCTURE OF A SMALL TEST POWER SYSTEM symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.59 time: amd 0.0000 mnnz(L) 0.0 mfl 0 fl/nnz(L) 2.8 time: metis 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.2 metis/amd time: 5.7907 nnz(L): 1.0775 ================== Problem: HB/dwt_59 n: 59 nnz: 267 title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.59 time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 4.5 time: metis 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 4.7 metis/amd time: 3.8286 nnz(L): 1.0492 ================== Problem: HB/can_61 n: 61 nnz: 557 title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981. symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.83 time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.2 time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 7.0 metis/amd time: 6.6721 nnz(L): 1.0997 ================== Problem: HB/can_62 n: 62 nnz: 218 title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981. symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.57 time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.2 time: metis 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.5 metis/amd time: 5.4118 nnz(L): 1.0870 ================== Problem: HB/bcsstk02 n: 66 nnz: 4356 title: SYMMETRIC STIFFNESS MATRIX, SMALL OIL RIG, STATICALLY CONDENSED symbfact time: MATLAB 0.0004 CHOLMOD 0.0002 speedup 1.89 time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 44.3 time: metis 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 44.3 metis/amd time: 2.6044 nnz(L): 1.0000 ================== Problem: HB/dwt_66 n: 66 nnz: 320 title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.58 time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.0 time: metis 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 4.6 metis/amd time: 4.5455 nnz(L): 1.4767 ================== Problem: Pothen/sphere2 n: 66 nnz: 450 title: sphere2, with coordinates. From NASA, collected by Alex Pothen symbfact time: MATLAB 0.0004 CHOLMOD 0.0001 speedup 3.69 time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 12.6 time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 11.8 metis/amd time: 5.2329 nnz(L): 0.9736 ================== Problem: HB/dwt_72 n: 72 nnz: 222 title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.69 time: amd 0.0000 mnnz(L) 0.0 mfl 0 fl/nnz(L) 2.7 time: metis 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 2.9 metis/amd time: 5.6383 nnz(L): 1.0924 ================== Problem: HB/can_73 n: 73 nnz: 377 title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981. symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.59 time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.9 time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 7.4 metis/amd time: 5.5857 nnz(L): 1.0434 ================== Problem: HB/ash85 n: 85 nnz: 523 title: SYMMETRIC PATTERN OF NORMAL MATRIX OF HOLLAND SURVEY. ASHKENAZI, 1974 symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.45 time: amd 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.6 time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 7.6 metis/amd time: 1.4360 nnz(L): 1.1089 ================== Problem: HB/dwt_87 n: 87 nnz: 541 title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.19 time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 5.3 time: metis 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.8 metis/amd time: 3.2791 nnz(L): 1.1739 ================== Problem: HB/can_96 n: 96 nnz: 768 title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981. symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.36 time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 11.6 time: metis 0.0005 mnnz(L) 0.0 mfl 0 fl/nnz(L) 12.3 metis/amd time: 4.6700 nnz(L): 1.0467 ================== Problem: HB/nos4 n: 100 nnz: 594 title: SYMMETRIC MATRIX OF BEAM STRUCTURE, NOVEMBER 1982. symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.40 time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 7.0 time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 9.7 metis/amd time: 3.6610 nnz(L): 1.2168 ================== Problem: HB/bcsstk03 n: 112 nnz: 640 title: SYMMETRIC STIFFNESS MATRIX, SMALL TEST STRUCTURE symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.44 time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.5 time: metis 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 4.9 metis/amd time: 2.9107 nnz(L): 1.3385 ================== Problem: HB/bcspwr03 n: 118 nnz: 476 title: SYMMETRIC STRUCTURE OF 118 BUS IEEE STANDARD TEST CASE POWER NETWORK symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.40 time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.4 time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.9 metis/amd time: 4.0326 nnz(L): 1.0862 ================== Problem: Pajek/Journals n: 124 nnz: 12068 title: Pajek network: Slovenian journals 1999-2000 symbfact time: MATLAB 0.0006 CHOLMOD 0.0004 speedup 1.71 time: amd 0.0003 mnnz(L) 0.0 mfl 1 fl/nnz(L) 72.3 time: metis 0.0020 mnnz(L) 0.0 mfl 0 fl/nnz(L) 70.1 metis/amd time: 5.8776 nnz(L): 0.9744 ================== Problem: HB/bcsstk04 n: 132 nnz: 3648 title: SYMMETRIC STIFFNESS MATRIX, OIL RIG, NOT CONDENSED (SAME MODEL AS X02) symbfact time: MATLAB 0.0004 CHOLMOD 0.0002 speedup 2.05 time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 27.5 time: metis 0.0008 mnnz(L) 0.0 mfl 0 fl/nnz(L) 32.2 metis/amd time: 3.8689 nnz(L): 1.1072 ================== Problem: HB/bcsstk22 n: 138 nnz: 696 title: SYMMETRIC STIFFNESS MATRIX - TEXTILE LOOM FRAME symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.34 time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.2 time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.7 metis/amd time: 2.3333 nnz(L): 1.0632 ================== Problem: HB/can_144 n: 144 nnz: 1296 title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981. symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.27 time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.6 time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 7.2 metis/amd time: 3.3840 nnz(L): 1.0706 ================== Problem: HB/lund_a n: 147 nnz: 2449 title: SYMMETRIC MATRIX A OF LUND EIGENVALUE PROBLEM, MAY 1974 symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 2.12 time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 18.1 time: metis 0.0005 mnnz(L) 0.0 mfl 0 fl/nnz(L) 21.2 metis/amd time: 4.4622 nnz(L): 1.1475 ================== Problem: HB/lund_b n: 147 nnz: 2441 title: SYMMETRIC MATRIX B OF LUND EIGENVALUE PROBLEM, MAY 1974 symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 2.11 time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 18.1 time: metis 0.0006 mnnz(L) 0.0 mfl 0 fl/nnz(L) 22.1 metis/amd time: 4.4160 nnz(L): 1.1833 ================== Problem: HB/bcsstk05 n: 153 nnz: 2423 title: SYMMETRIC STIFFNESS MATRIX, TRANSMISSION TOWER, LUMPED MASSES symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 2.02 time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 16.8 time: metis 0.0007 mnnz(L) 0.0 mfl 0 fl/nnz(L) 21.7 metis/amd time: 4.0545 nnz(L): 1.2055 ================== Problem: HB/can_161 n: 161 nnz: 1377 title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981. symbfact time: MATLAB 0.0003 CHOLMOD 0.0003 speedup 0.93 time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 19.1 time: metis 0.0005 mnnz(L) 0.0 mfl 0 fl/nnz(L) 15.9 metis/amd time: 2.7914 nnz(L): 0.8795 ================== Problem: HB/dwt_162 n: 162 nnz: 1182 title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.17 time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 9.2 time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 9.5 metis/amd time: 2.6013 nnz(L): 1.0291 ================== Problem: HB/can_187 n: 187 nnz: 1491 title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981. symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 2.16 time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 13.8 time: metis 0.0006 mnnz(L) 0.0 mfl 0 fl/nnz(L) 12.8 metis/amd time: 3.7267 nnz(L): 0.9683 ================== Problem: HB/dwt_193 n: 193 nnz: 3493 title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON symbfact time: MATLAB 0.0004 CHOLMOD 0.0002 speedup 2.01 time: amd 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 28.3 time: metis 0.0011 mnnz(L) 0.0 mfl 0 fl/nnz(L) 29.6 metis/amd time: 4.1051 nnz(L): 1.0422 ================== Problem: HB/dwt_198 n: 198 nnz: 1392 title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 2.11 time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 7.4 time: metis 0.0005 mnnz(L) 0.0 mfl 0 fl/nnz(L) 7.1 metis/amd time: 2.9815 nnz(L): 0.9694 ================== Problem: HB/dwt_209 n: 209 nnz: 1743 title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 2.09 time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 11.0 time: metis 0.0008 mnnz(L) 0.0 mfl 0 fl/nnz(L) 13.6 metis/amd time: 3.5598 nnz(L): 1.1378 ================== Problem: HB/dwt_221 n: 221 nnz: 1629 title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 2.11 time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 9.1 time: metis 0.0007 mnnz(L) 0.0 mfl 0 fl/nnz(L) 10.7 metis/amd time: 2.7893 nnz(L): 1.1089 ================== Problem: HB/can_229 n: 229 nnz: 1777 title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981. symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 2.08 time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 17.2 time: metis 0.0008 mnnz(L) 0.0 mfl 0 fl/nnz(L) 18.8 metis/amd time: 3.7621 nnz(L): 1.0619 ================== Problem: HB/dwt_234 n: 234 nnz: 834 title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.26 time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.5 time: metis 0.0005 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.9 metis/amd time: 3.5515 nnz(L): 1.0641 ================== Problem: HB/nos1 n: 237 nnz: 1017 title: SYMMETRIC MATRIX, FE APPROXIMATION TO BIHARMONIC OPERATOR ON BEAM. symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.22 time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.2 time: metis 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 4.4 metis/amd time: 3.7444 nnz(L): 1.3537 ================== Problem: HB/dwt_245 n: 245 nnz: 1461 title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 2.14 time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 7.3 time: metis 0.0006 mnnz(L) 0.0 mfl 0 fl/nnz(L) 9.0 metis/amd time: 2.7129 nnz(L): 1.1176 ================== Problem: HB/can_256 n: 256 nnz: 2916 title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981. symbfact time: MATLAB 0.0004 CHOLMOD 0.0002 speedup 1.94 time: amd 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 17.7 time: metis 0.0008 mnnz(L) 0.0 mfl 0 fl/nnz(L) 20.2 metis/amd time: 2.9789 nnz(L): 1.0937 ================== Problem: Pothen/sphere3 n: 258 nnz: 1794 title: sphere3, with coordinates. From NASA, collected by Alex Pothen symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 1.97 time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 24.5 time: metis 0.0007 mnnz(L) 0.0 mfl 0 fl/nnz(L) 21.5 metis/amd time: 2.8970 nnz(L): 0.9353 ================== Problem: HB/lshp_265 n: 265 nnz: 1753 title: SYMMETRIC MATRIX FROM ALAN GEORGE'S L-SHAPE PROBLEMS, 1978. symbfact time: MATLAB 0.0004 CHOLMOD 0.0002 speedup 2.02 time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 14.4 time: metis 0.0006 mnnz(L) 0.0 mfl 0 fl/nnz(L) 17.5 metis/amd time: 2.8216 nnz(L): 1.1213 ================== Problem: HB/can_268 n: 268 nnz: 3082 title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981. symbfact time: MATLAB 0.0004 CHOLMOD 0.0002 speedup 1.96 time: amd 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 18.1 time: metis 0.0009 mnnz(L) 0.0 mfl 0 fl/nnz(L) 21.3 metis/amd time: 3.2102 nnz(L): 1.0960 ================== Problem: HB/bcspwr04 n: 274 nnz: 1612 title: SYMMETRIC STRUCTURE EQUIVALENCED REPRESENTATION OF U.S. POWER NETWORK symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 1.99 time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.2 time: metis 0.0006 mnnz(L) 0.0 mfl 0 fl/nnz(L) 7.1 metis/amd time: 3.2887 nnz(L): 1.0819 ================== Problem: Pothen/mesh3e1 n: 289 nnz: 1377 title: mesh3e1, with coordinates. From NASA, collected by Alex Pothen symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 2.11 time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 11.3 time: metis 0.0006 mnnz(L) 0.0 mfl 0 fl/nnz(L) 12.7 metis/amd time: 2.3906 nnz(L): 1.0908 ================== Problem: Pothen/mesh3em5 n: 289 nnz: 1377 title: mesh3em5, with coordinates. From NASA, collected by Alex Pothen symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 1.71 time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 11.3 time: metis 0.0006 mnnz(L) 0.0 mfl 0 fl/nnz(L) 12.7 metis/amd time: 2.4410 nnz(L): 1.0908 test8 passed ================================================================= test9: test metis, etree, bisect, nesdis Prob = title: 'S STIFFNESS MATRIX - MODULE OF AN OFFSHORE PLATFORM' A: [3948x3948 double] name: 'HB/bcsstk15' id: 37 date: '1985' author: 'M. Will' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' metis: Elapsed time is 0.100277 seconds. Elapsed time is 0.100283 seconds. Elapsed time is 0.101989 seconds. Elapsed time is 0.113528 seconds. Elapsed time is 0.115154 seconds. metis(A): Elapsed time is 0.058451 seconds. lnz0 = 492391 amd: Elapsed time is 0.009234 seconds. lnz = 614590 bisect: Elapsed time is 0.040865 seconds. Elapsed time is 0.039559 seconds. Elapsed time is 0.040628 seconds. Elapsed time is 0.061155 seconds. Elapsed time is 0.063285 seconds. nested dissection: Elapsed time is 0.137077 seconds. Elapsed time is 0.135862 seconds. Elapsed time is 0.136597 seconds. Elapsed time is 0.174602 seconds. Elapsed time is 0.175804 seconds. nested_dissection(A): Elapsed time is 0.078392 seconds. lnz1 = 485679 test9 passed ================================================================= test10: test cholmod2's backslash test matrices sorted by dimension: 1440: Oberwolfach LFAT5 14 1 1438: Oberwolfach LF10 18 1 436: FIDAP ex5 27 1 23: HB bcsstk01 48 1 872: Pothen mesh1e1 48 1 873: Pothen mesh1em1 48 1 874: Pothen mesh1em6 48 1 24: HB bcsstk02 66 1 57: HB bcsstm02 66 1 220: HB nos4 100 1 25: HB bcsstk03 112 1 1506: Pajek Journals 124 1 26: HB bcsstk04 132 1 44: HB bcsstk22 138 1 72: HB bcsstm22 138 1 206: HB lund_a 147 1 207: HB lund_b 147 1 27: HB bcsstk05 153 1 60: HB bcsstm05 153 1 217: HB nos1 237 1 877: Pothen mesh3e1 289 1 878: Pothen mesh3em5 289 1 875: Pothen mesh2e1 306 1 876: Pothen mesh2em5 306 1 229: HB plat362 362 1 315: Bai mhdb416 416 1 28: HB bcsstk06 420 1 29: HB bcsstk07 420 1 61: HB bcsstm06 420 1 62: HB bcsstm07 420 1 221: HB nos5 468 1 42: HB bcsstk20 485 1 70: HB bcsstm20 485 1 2: HB 494_bus 494 1 339: Boeing bcsstk34 588 1 3: HB 662_bus 662 1 222: HB nos6 675 1 4: HB 685_bus 685 1 357: Boeing msc00726 726 1 223: HB nos7 729 1 41: HB bcsstk19 817 1 69: HB bcsstm19 817 1 159: HB gr_30_30 900 1 218: HB nos2 957 1 219: HB nos3 960 1 358: Boeing msc01050 1050 1 30: HB bcsstk08 1074 1 63: HB bcsstm08 1074 1 31: HB bcsstk09 1083 1 64: HB bcsstm09 1083 1 nn = 1440 Prob = name: 'Oberwolfach/LFAT5' title: 'Oberwolfach: linear 1D beam' A: [14x14 double] id: 1440 notes: 'Primary matrix in this model reduction problem is the Oberwolfach K matrix' aux: [1x1 struct] date: '2004' author: 'J. Lienemann, A. Greiner, J. Korvink' ed: 'E. Rudnyi' kind: 'model reduction problem' A: [n 14 real 1] B: [sp:0 nrhs 1 real 1] [e1: 4e-14 : -0.6] [t1: 0.00 t2 0.00 : 0.8] A: [n 14 real 1] B: [sp:0 nrhs 4 real 1] [e1: 4e-14 : -1.2] [t1: 0.00 t2 0.00 : 1.1] A: [n 14 real 1] B: [sp:0 nrhs 9 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 14 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 14 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-13 : -0.3] [t1: 0.00 t2 0.00 : 1.1] A: [n 14 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 14 real 1] B: [sp:1 nrhs 4 real 1] [e1: 6e-14 : 0.5] [t1: 0.00 t2 0.00 : 1.1] A: [n 14 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 14 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 14 real 1] B: [sp:1 nrhs 9 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 14 real 0] B: [sp:0 nrhs 1 real 1] [e1: 1e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 14 real 0] B: [sp:0 nrhs 4 real 1] [e1: 1e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 14 real 0] B: [sp:0 nrhs 9 real 1] [e1: 1e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 14 real 0] B: [sp:0 nrhs 1 real 0] [e1: 1e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 14 real 0] B: [sp:0 nrhs 9 real 0] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.8] A: [n 14 real 0] B: [sp:1 nrhs 1 real 1] [e1: 4e-18 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 14 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-16 : 0.0] [t1: 0.00 t2 0.00 : 0.8] A: [n 14 real 0] B: [sp:1 nrhs 9 real 1] [e1: 7e-16 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 14 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-16 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 14 real 0] B: [sp:1 nrhs 9 real 0] [e1: 1e-15 : 0.0] [t1: 0.00 t2 0.00 : 2.4] nn = 1438 Prob = name: 'Oberwolfach/LF10' title: 'Oberwolfach: linear 1D beam' A: [18x18 double] id: 1438 notes: 'Primary matrix in this model reduction problem is the Oberwolfach K matrix' aux: [1x1 struct] date: '2004' author: 'J. Lienemann, A. Greiner, J. Korvink' ed: 'E. Rudnyi' kind: 'model reduction problem' A: [n 18 real 1] B: [sp:0 nrhs 1 real 1] [e1: 5e-13 : -2.6] [t1: 0.00 t2 0.00 : 0.5] A: [n 18 real 1] B: [sp:0 nrhs 4 real 1] [e1: 4e-12 : -1.0] [t1: 0.00 t2 0.00 : 0.5] A: [n 18 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-12 : -1.3] [t1: 0.00 t2 0.00 : 0.5] A: [n 18 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-12 : -0.6] [t1: 0.00 t2 0.00 : 0.5] A: [n 18 real 1] B: [sp:0 nrhs 9 real 0] [e1: 4e-12 : -1.2] [t1: 0.00 t2 0.00 : 0.7] A: [n 18 real 1] B: [sp:1 nrhs 1 real 1] [e1: 2e-12 : -0.7] [t1: 0.00 t2 0.00 : 0.5] A: [n 18 real 1] B: [sp:1 nrhs 4 real 1] [e1: 2e-12 : -0.7] [t1: 0.00 t2 0.00 : 0.5] A: [n 18 real 1] B: [sp:1 nrhs 9 real 1] [e1: 4e-12 : 0.1] [t1: 0.00 t2 0.00 : 0.5] A: [n 18 real 1] B: [sp:1 nrhs 1 real 0] [e1: 4e-12 : -1.3] [t1: 0.00 t2 0.00 : 0.5] A: [n 18 real 1] B: [sp:1 nrhs 9 real 0] [e1: 5e-12 : -0.8] [t1: 0.00 t2 0.00 : 0.5] A: [n 18 real 0] B: [sp:0 nrhs 1 real 1] [e1: 9e-16 : -0.2] [t1: 0.00 t2 0.00 : 0.6] A: [n 18 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-15 : -0.5] [t1: 0.00 t2 0.00 : 0.7] A: [n 18 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-15 : -0.3] [t1: 0.00 t2 0.00 : 0.6] A: [n 18 real 0] B: [sp:0 nrhs 1 real 0] [e1: 2e-15 : 0.1] [t1: 0.00 t2 0.00 : 0.5] A: [n 18 real 0] B: [sp:0 nrhs 9 real 0] [e1: 3e-15 : -0.2] [t1: 0.00 t2 0.00 : 0.8] A: [n 18 real 0] B: [sp:1 nrhs 1 real 1] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.5] A: [n 18 real 0] B: [sp:1 nrhs 4 real 1] [e1: 6e-16 : 0.3] [t1: 0.00 t2 0.00 : 0.6] A: [n 18 real 0] B: [sp:1 nrhs 9 real 1] [e1: 5e-16 : 0.1] [t1: 0.00 t2 0.00 : 0.6] A: [n 18 real 0] B: [sp:1 nrhs 1 real 0] [e1: 1e-16 : 0.8] [t1: 0.00 t2 0.00 : 0.5] A: [n 18 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-15 : 0.1] [t1: 0.00 t2 0.00 : 0.8] nn = 436 Prob = title: ' TEST MATRIX FROM FIDAP: EX5.MAT' A: [27x27 double] name: 'FIDAP/ex5' id: 436 date: '1994' author: 'A. Baggag, Y. Saad' ed: 'A. Baggag, Y. Saad' kind: 'computational fluid dynamics problem' A: [n 27 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-08 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 27 real 1] B: [sp:0 nrhs 4 real 1] [e1: 3e-08 : -0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 27 real 1] B: [sp:0 nrhs 9 real 1] [e1: 4e-08 : 0.3] [t1: 0.00 t2 0.00 : 1.0] A: [n 27 real 1] B: [sp:0 nrhs 1 real 0] [e1: 5e-08 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 27 real 1] B: [sp:0 nrhs 9 real 0] [e1: 5e-08 : -0.0] [t1: 0.00 t2 0.00 : 0.6] A: [n 27 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-09 : 0.1] [t1: 0.00 t2 0.00 : 1.0] A: [n 27 real 1] B: [sp:1 nrhs 4 real 1] [e1: 2e-09 : -0.7] [t1: 0.00 t2 0.00 : 0.9] A: [n 27 real 1] B: [sp:1 nrhs 9 real 1] [e1: 7e-09 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 27 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 27 real 1] B: [sp:1 nrhs 9 real 0] [e1: 8e-09 : -0.1] [t1: 0.00 t2 0.00 : 0.9] A: [n 27 real 0] B: [sp:0 nrhs 1 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 27 real 0] B: [sp:0 nrhs 4 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 27 real 0] B: [sp:0 nrhs 9 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 27 real 0] B: [sp:0 nrhs 1 real 0] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 27 real 0] B: [sp:0 nrhs 9 real 0] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 27 real 0] B: [sp:1 nrhs 1 real 1] [e1: 1e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 27 real 0] B: [sp:1 nrhs 4 real 1] [e1: 1e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 27 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 27 real 0] B: [sp:1 nrhs 1 real 0] [e1: 6e-16 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 27 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] nn = 23 Prob = title: 'SYMMETRIC STIFFNESS MATRIX SMALL GENERALIZED EIGENVALUE PROBLEM' A: [48x48 double] name: 'HB/bcsstk01' id: 23 date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 48 real 1] B: [sp:0 nrhs 1 real 1] [e1: 1e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 48 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-12 : 0.1] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 0.7] A: [n 48 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 48 real 1] B: [sp:1 nrhs 4 real 1] [e1: 3e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:1 nrhs 9 real 1] [e1: 6e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:1 nrhs 1 real 0] [e1: 8e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 48 real 1] B: [sp:1 nrhs 9 real 0] [e1: 8e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 0] B: [sp:0 nrhs 1 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 0] B: [sp:0 nrhs 4 real 1] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 0] B: [sp:0 nrhs 9 real 1] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 0] B: [sp:0 nrhs 1 real 0] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 0] B: [sp:0 nrhs 9 real 0] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 48 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-16 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 48 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 48 real 0] B: [sp:1 nrhs 9 real 0] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] nn = 872 Prob = A: [48x48 double] title: 'mesh1e1, with coordinates. From NASA, collected by Alex Pothen' name: 'Pothen/mesh1e1' id: 872 aux: [1x1 struct] date: '2003' author: 'NASA' ed: 'G. Kumfert, A. Pothen' kind: 'structural problem' A: [n 48 real 1] B: [sp:0 nrhs 1 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:0 nrhs 4 real 1] [e1: 4e-15 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:0 nrhs 9 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 1] B: [sp:0 nrhs 1 real 0] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:0 nrhs 9 real 0] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 1] B: [sp:1 nrhs 1 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:1 nrhs 4 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-15 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:1 nrhs 9 real 0] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 0] B: [sp:0 nrhs 1 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.8] A: [n 48 real 0] B: [sp:0 nrhs 4 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 0] B: [sp:0 nrhs 9 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 0] B: [sp:0 nrhs 1 real 0] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 0] B: [sp:0 nrhs 9 real 0] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 0] B: [sp:1 nrhs 1 real 1] [e1: 7e-16 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 48 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] nn = 873 Prob = A: [48x48 double] title: 'mesh1em1, with coordinates. From NASA, collected by Alex Pothen' name: 'Pothen/mesh1em1' id: 873 aux: [1x1 struct] date: '2003' author: 'NASA' ed: 'G. Kumfert, A. Pothen' kind: 'structural problem' A: [n 48 real 1] B: [sp:0 nrhs 1 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:0 nrhs 4 real 1] [e1: 7e-15 : 0.1] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 1] B: [sp:0 nrhs 9 real 1] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 1] B: [sp:0 nrhs 1 real 0] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.2] A: [n 48 real 1] B: [sp:1 nrhs 1 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:1 nrhs 4 real 1] [e1: 4e-15 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:1 nrhs 9 real 1] [e1: 6e-15 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:1 nrhs 1 real 0] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.8] A: [n 48 real 1] B: [sp:1 nrhs 9 real 0] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 0] B: [sp:0 nrhs 1 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 0] B: [sp:0 nrhs 4 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 0] B: [sp:0 nrhs 9 real 1] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 0] B: [sp:0 nrhs 1 real 0] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 0] B: [sp:0 nrhs 9 real 0] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 0] B: [sp:1 nrhs 1 real 1] [e1: 4e-16 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 0] B: [sp:1 nrhs 9 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 0] B: [sp:1 nrhs 1 real 0] [e1: 1e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 0] B: [sp:1 nrhs 9 real 0] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] nn = 874 Prob = A: [48x48 double] title: 'mesh1em6, with coordinates. From NASA, collected by Alex Pothen' name: 'Pothen/mesh1em6' id: 874 aux: [1x1 struct] date: '2003' author: 'NASA' ed: 'G. Kumfert, A. Pothen' kind: 'structural problem' A: [n 48 real 1] B: [sp:0 nrhs 1 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:0 nrhs 4 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 1] B: [sp:0 nrhs 9 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 48 real 1] B: [sp:0 nrhs 1 real 0] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:0 nrhs 9 real 0] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:1 nrhs 1 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:1 nrhs 4 real 1] [e1: 3e-15 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-15 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 1] B: [sp:1 nrhs 1 real 0] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 48 real 1] B: [sp:1 nrhs 9 real 0] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 0] B: [sp:0 nrhs 1 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 0] B: [sp:0 nrhs 4 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 0] B: [sp:0 nrhs 9 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 0] B: [sp:0 nrhs 1 real 0] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 0] B: [sp:0 nrhs 9 real 0] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 48 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 48 real 0] B: [sp:1 nrhs 9 real 0] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] nn = 24 Prob = title: 'SYMMETRIC STIFFNESS MATRIX, SMALL OIL RIG, STATICALLY CONDENSED' A: [66x66 double] name: 'HB/bcsstk02' id: 24 date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 66 real 1] B: [sp:0 nrhs 1 real 1] [e1: 4e-12 : -0.3] [t1: 0.00 t2 0.00 : 0.6] A: [n 66 real 1] B: [sp:0 nrhs 4 real 1] [e1: 5e-12 : -0.2] [t1: 0.00 t2 0.00 : 0.5] A: [n 66 real 1] B: [sp:0 nrhs 9 real 1] [e1: 5e-12 : -0.1] [t1: 0.00 t2 0.00 : 0.5] A: [n 66 real 1] B: [sp:0 nrhs 1 real 0] [e1: 7e-12 : -0.1] [t1: 0.00 t2 0.00 : 0.5] A: [n 66 real 1] B: [sp:0 nrhs 9 real 0] [e1: 7e-12 : -0.1] [t1: 0.00 t2 0.00 : 0.7] A: [n 66 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-13 : 0.2] [t1: 0.00 t2 0.00 : 0.6] A: [n 66 real 1] B: [sp:1 nrhs 4 real 1] [e1: 7e-13 : -0.1] [t1: 0.00 t2 0.00 : 0.5] A: [n 66 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-12 : -0.3] [t1: 0.00 t2 0.00 : 0.5] A: [n 66 real 1] B: [sp:1 nrhs 1 real 0] [e1: 1e-12 : -0.0] [t1: 0.00 t2 0.00 : 0.6] A: [n 66 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-12 : -0.2] [t1: 0.00 t2 0.00 : 0.6] A: [n 66 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-14 : 0.3] [t1: 0.00 t2 0.00 : 1.2] A: [n 66 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-14 : 0.2] [t1: 0.00 t2 0.00 : 0.8] A: [n 66 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-14 : 0.1] [t1: 0.00 t2 0.00 : 0.9] A: [n 66 real 0] B: [sp:0 nrhs 1 real 0] [e1: 2e-14 : 0.2] [t1: 0.00 t2 0.00 : 1.1] A: [n 66 real 0] B: [sp:0 nrhs 9 real 0] [e1: 2e-14 : -0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 66 real 0] B: [sp:1 nrhs 1 real 1] [e1: 9e-16 : -0.1] [t1: 0.00 t2 0.00 : 1.2] A: [n 66 real 0] B: [sp:1 nrhs 4 real 1] [e1: 3e-15 : 0.2] [t1: 0.00 t2 0.00 : 0.8] A: [n 66 real 0] B: [sp:1 nrhs 9 real 1] [e1: 5e-15 : 0.2] [t1: 0.00 t2 0.00 : 0.8] A: [n 66 real 0] B: [sp:1 nrhs 1 real 0] [e1: 4e-15 : 0.1] [t1: 0.00 t2 0.00 : 1.2] A: [n 66 real 0] B: [sp:1 nrhs 9 real 0] [e1: 7e-15 : 0.2] [t1: 0.00 t2 0.00 : 0.8] nn = 57 Prob = title: 'SYMMETRIC MASS MATRIX, SMALL OIL RIG, STATICALLY CONDENSED' A: [66x66 double] name: 'HB/bcsstm02' id: 57 date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 66 real 1] B: [sp:0 nrhs 1 real 1] [e1: 6e-16 : -2.2] [t1: 0.00 t2 0.00 : 0.2] A: [n 66 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e-15 : -1.8] [t1: 0.00 t2 0.00 : 0.3] A: [n 66 real 1] B: [sp:0 nrhs 9 real 1] [e1: 6e-16 : -2.5] [t1: 0.00 t2 0.00 : 0.2] A: [n 66 real 1] B: [sp:0 nrhs 1 real 0] [e1: 1e-15 : -2.0] [t1: 0.00 t2 0.00 : 0.2] A: [n 66 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-15 : -2.5] [t1: 0.00 t2 0.00 : 0.3] A: [n 66 real 1] B: [sp:1 nrhs 1 real 1] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.2] A: [n 66 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-17 : -5.7] [t1: 0.00 t2 0.00 : 0.1] A: [n 66 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-16 : -1.7] [t1: 0.00 t2 0.00 : 0.1] A: [n 66 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-16 : -2.2] [t1: 0.00 t2 0.00 : 0.2] A: [n 66 real 1] B: [sp:1 nrhs 9 real 0] [e1: 3e-16 : -2.0] [t1: 0.00 t2 0.00 : 0.2] A: [n 66 real 1] B: [sp:0 nrhs 1 real 1] [e1: 7e-16 : -2.1] [t1: 0.00 t2 0.00 : 0.2] A: [n 66 real 1] B: [sp:0 nrhs 4 real 1] [e1: 7e-16 : -2.4] [t1: 0.00 t2 0.00 : 0.2] A: [n 66 real 1] B: [sp:0 nrhs 9 real 1] [e1: 8e-16 : -2.3] [t1: 0.00 t2 0.00 : 0.3] A: [n 66 real 1] B: [sp:0 nrhs 1 real 0] [e1: 6e-16 : -3.3] [t1: 0.00 t2 0.00 : 0.2] A: [n 66 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-15 : -2.4] [t1: 0.00 t2 0.00 : 0.4] A: [n 66 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-16 : -2.1] [t1: 0.00 t2 0.00 : 0.2] A: [n 66 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-16 : -2.3] [t1: 0.00 t2 0.00 : 0.2] A: [n 66 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-16 : -2.1] [t1: 0.00 t2 0.00 : 0.2] A: [n 66 real 1] B: [sp:1 nrhs 1 real 0] [e1: 4e-16 : -1.1] [t1: 0.00 t2 0.00 : 0.2] A: [n 66 real 1] B: [sp:1 nrhs 9 real 0] [e1: 4e-16 : -1.9] [t1: 0.00 t2 0.00 : 0.3] nn = 220 Prob = title: 'SYMMETRIC MATRIX OF BEAM STRUCTURE, NOVEMBER 1982.' A: [100x100 double] name: 'HB/nos4' id: 220 date: '1982' author: 'H. Simon' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 100 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 100 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-12 : 0.1] [t1: 0.00 t2 0.00 : 1.0] A: [n 100 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 0.8] A: [n 100 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 100 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 100 real 1] B: [sp:1 nrhs 1 real 1] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 100 real 1] B: [sp:1 nrhs 4 real 1] [e1: 6e-14 : -0.1] [t1: 0.00 t2 0.00 : 1.0] A: [n 100 real 1] B: [sp:1 nrhs 9 real 1] [e1: 3e-13 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 100 real 1] B: [sp:1 nrhs 1 real 0] [e1: 3e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 100 real 1] B: [sp:1 nrhs 9 real 0] [e1: 4e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 100 real 0] B: [sp:0 nrhs 1 real 1] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 100 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 100 real 0] B: [sp:0 nrhs 9 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 100 real 0] B: [sp:0 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 100 real 0] B: [sp:0 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 100 real 0] B: [sp:1 nrhs 1 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 100 real 0] B: [sp:1 nrhs 4 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 100 real 0] B: [sp:1 nrhs 9 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 100 real 0] B: [sp:1 nrhs 1 real 0] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 100 real 0] B: [sp:1 nrhs 9 real 0] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] nn = 25 Prob = title: 'SYMMETRIC STIFFNESS MATRIX, SMALL TEST STRUCTURE' A: [112x112 double] name: 'HB/bcsstk03' id: 25 date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 112 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.2] A: [n 112 real 1] B: [sp:0 nrhs 4 real 1] [e1: 4e-11 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 112 real 1] B: [sp:0 nrhs 9 real 1] [e1: 5e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 112 real 1] B: [sp:0 nrhs 1 real 0] [e1: 4e-11 : 0.0] [t1: 0.00 t2 0.00 : 0.8] A: [n 112 real 1] B: [sp:0 nrhs 9 real 0] [e1: 6e-11 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 112 real 1] B: [sp:1 nrhs 1 real 1] [e1: 9e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 112 real 1] B: [sp:1 nrhs 4 real 1] [e1: 9e-12 : 0.1] [t1: 0.00 t2 0.00 : 0.9] A: [n 112 real 1] B: [sp:1 nrhs 9 real 1] [e1: 8e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 112 real 1] B: [sp:1 nrhs 1 real 0] [e1: 3e-12 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 112 real 1] B: [sp:1 nrhs 9 real 0] [e1: 3e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 112 real 0] B: [sp:0 nrhs 1 real 1] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 112 real 0] B: [sp:0 nrhs 4 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.8] A: [n 112 real 0] B: [sp:0 nrhs 9 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 112 real 0] B: [sp:0 nrhs 1 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 112 real 0] B: [sp:0 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 112 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 112 real 0] B: [sp:1 nrhs 4 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 112 real 0] B: [sp:1 nrhs 9 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 112 real 0] B: [sp:1 nrhs 1 real 0] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 112 real 0] B: [sp:1 nrhs 9 real 0] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] nn = 1506 Prob = name: 'Pajek/Journals' title: 'Pajek network: Slovenian journals 1999-2000' A: [124x124 double] id: 1506 kind: 'undirected weighted graph' notes: [14x78 char] aux: [1x1 struct] date: '2000' author: 'CATI Center Ljubljana' ed: 'V. Batagelj' A: [n 124 real 1] B: [sp:0 nrhs 1 real 1] [e1: 5e-14 : -0.2] [t1: 0.00 t2 0.00 : 0.7] A: [n 124 real 1] B: [sp:0 nrhs 4 real 1] [e1: 5e-14 : -0.2] [t1: 0.10 t2 0.00 : 57.8] A: [n 124 real 1] B: [sp:0 nrhs 9 real 1] [e1: 5e-14 : -0.2] [t1: 0.00 t2 0.00 : 0.8] A: [n 124 real 1] B: [sp:0 nrhs 1 real 0] [e1: 8e-14 : 0.2] [t1: 0.00 t2 0.00 : 0.7] A: [n 124 real 1] B: [sp:0 nrhs 9 real 0] [e1: 8e-14 : -0.0] [t1: 0.00 t2 0.00 : 0.8] A: [n 124 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-14 : 0.5] [t1: 0.00 t2 0.00 : 0.7] A: [n 124 real 1] B: [sp:1 nrhs 4 real 1] [e1: 2e-14 : -0.0] [t1: 0.00 t2 0.00 : 0.7] A: [n 124 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-14 : 0.1] [t1: 0.00 t2 0.00 : 0.6] A: [n 124 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-14 : 0.1] [t1: 0.00 t2 0.00 : 0.7] A: [n 124 real 1] B: [sp:1 nrhs 9 real 0] [e1: 3e-14 : 0.1] [t1: 0.00 t2 0.00 : 0.7] A: [n 124 real 0] B: [sp:0 nrhs 1 real 1] [e1: 3e-14 : 0.1] [t1: 0.00 t2 0.00 : 0.9] A: [n 124 real 0] B: [sp:0 nrhs 4 real 1] [e1: 3e-14 : 0.1] [t1: 0.00 t2 0.00 : 0.8] A: [n 124 real 0] B: [sp:0 nrhs 9 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.8] A: [n 124 real 0] B: [sp:0 nrhs 1 real 0] [e1: 5e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 124 real 0] B: [sp:0 nrhs 9 real 0] [e1: 5e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.8] A: [n 124 real 0] B: [sp:1 nrhs 1 real 1] [e1: 4e-15 : -0.4] [t1: 0.00 t2 0.00 : 1.0] A: [n 124 real 0] B: [sp:1 nrhs 4 real 1] [e1: 1e-14 : 0.3] [t1: 0.00 t2 0.10 : 0.0] A: [n 124 real 0] B: [sp:1 nrhs 9 real 1] [e1: 1e-14 : -0.2] [t1: 0.00 t2 0.01 : 0.7] A: [n 124 real 0] B: [sp:1 nrhs 1 real 0] [e1: 1e-14 : -0.1] [t1: 0.00 t2 0.00 : 1.0] A: [n 124 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-14 : 0.2] [t1: 0.00 t2 0.01 : 0.7] nn = 26 Prob = title: 'SYMMETRIC STIFFNESS MATRIX, OIL RIG, NOT CONDENSED (SAME MODEL AS X02)' A: [132x132 double] name: 'HB/bcsstk04' id: 26 date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 132 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.2] A: [n 132 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-11 : -0.1] [t1: 0.00 t2 0.00 : 1.1] A: [n 132 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-11 : 0.4] [t1: 0.00 t2 0.00 : 1.1] A: [n 132 real 1] B: [sp:0 nrhs 1 real 0] [e1: 3e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 132 real 1] B: [sp:0 nrhs 9 real 0] [e1: 3e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 132 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 132 real 1] B: [sp:1 nrhs 4 real 1] [e1: 4e-12 : 0.1] [t1: 0.00 t2 0.00 : 0.9] A: [n 132 real 1] B: [sp:1 nrhs 9 real 1] [e1: 6e-12 : -0.1] [t1: 0.00 t2 0.00 : 1.1] A: [n 132 real 1] B: [sp:1 nrhs 1 real 0] [e1: 4e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 132 real 1] B: [sp:1 nrhs 9 real 0] [e1: 4e-12 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 132 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 132 real 0] B: [sp:0 nrhs 4 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 132 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 132 real 0] B: [sp:0 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 132 real 0] B: [sp:0 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 132 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 132 real 0] B: [sp:1 nrhs 4 real 1] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 132 real 0] B: [sp:1 nrhs 9 real 1] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.2] A: [n 132 real 0] B: [sp:1 nrhs 1 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 132 real 0] B: [sp:1 nrhs 9 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] nn = 44 Prob = title: 'SYMMETRIC STIFFNESS MATRIX - TEXTILE LOOM FRAME' A: [138x138 double] name: 'HB/bcsstk22' id: 44 date: '1984' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 138 real 1] B: [sp:0 nrhs 1 real 1] [e1: 1e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.3] A: [n 138 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e-11 : -0.1] [t1: 0.00 t2 0.00 : 1.0] A: [n 138 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e-11 : 0.2] [t1: 0.00 t2 0.00 : 1.0] A: [n 138 real 1] B: [sp:0 nrhs 1 real 0] [e1: 1e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 138 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 138 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 138 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 138 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 138 real 1] B: [sp:1 nrhs 1 real 0] [e1: 8e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 138 real 1] B: [sp:1 nrhs 9 real 0] [e1: 3e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 138 real 0] B: [sp:0 nrhs 1 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 138 real 0] B: [sp:0 nrhs 4 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 138 real 0] B: [sp:0 nrhs 9 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 138 real 0] B: [sp:0 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 138 real 0] B: [sp:0 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 138 real 0] B: [sp:1 nrhs 1 real 1] [e1: 4e-16 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 138 real 0] B: [sp:1 nrhs 4 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 138 real 0] B: [sp:1 nrhs 9 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 138 real 0] B: [sp:1 nrhs 1 real 0] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 138 real 0] B: [sp:1 nrhs 9 real 0] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] nn = 72 Prob = title: 'SYMMETRIC MASS MATRIX - TEXTILE LOOM FRAME' A: [138x138 double] name: 'HB/bcsstm22' id: 72 date: '1984' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 138 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-15 : -1.8] [t1: 0.00 t2 0.00 : 0.2] A: [n 138 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-15 : -1.9] [t1: 0.00 t2 0.00 : 0.2] A: [n 138 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-15 : -2.0] [t1: 0.00 t2 0.00 : 0.2] A: [n 138 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-15 : -2.0] [t1: 0.00 t2 0.00 : 0.2] A: [n 138 real 1] B: [sp:0 nrhs 9 real 0] [e1: 3e-15 : -1.9] [t1: 0.00 t2 0.00 : 0.3] A: [n 138 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-16 : -1.1] [t1: 0.00 t2 0.00 : 0.1] A: [n 138 real 1] B: [sp:1 nrhs 4 real 1] [e1: 3e-16 : -1.1] [t1: 0.00 t2 0.00 : 0.1] A: [n 138 real 1] B: [sp:1 nrhs 9 real 1] [e1: 3e-16 : -1.9] [t1: 0.00 t2 0.00 : 0.1] A: [n 138 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-16 : -3.7] [t1: 0.00 t2 0.00 : 0.1] A: [n 138 real 1] B: [sp:1 nrhs 9 real 0] [e1: 9e-16 : -1.7] [t1: 0.00 t2 0.00 : 0.1] A: [n 138 real 1] B: [sp:0 nrhs 1 real 1] [e1: 7e-16 : -3.5] [t1: 0.00 t2 0.00 : 0.2] A: [n 138 real 1] B: [sp:0 nrhs 4 real 1] [e1: 7e-16 : -3.5] [t1: 0.00 t2 0.00 : 0.1] A: [n 138 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e-15 : -3.0] [t1: 0.00 t2 0.00 : 0.2] A: [n 138 real 1] B: [sp:0 nrhs 1 real 0] [e1: 1e-15 : -3.7] [t1: 0.00 t2 0.00 : 0.2] A: [n 138 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-15 : -2.9] [t1: 0.00 t2 0.00 : 0.3] A: [n 138 real 1] B: [sp:1 nrhs 1 real 1] [e1: 7e-16 : -1.4] [t1: 0.00 t2 0.00 : 0.1] A: [n 138 real 1] B: [sp:1 nrhs 4 real 1] [e1: 7e-16 : -1.4] [t1: 0.00 t2 0.00 : 0.1] A: [n 138 real 1] B: [sp:1 nrhs 9 real 1] [e1: 4e-16 : -2.5] [t1: 0.00 t2 0.00 : 0.1] A: [n 138 real 1] B: [sp:1 nrhs 1 real 0] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1] A: [n 138 real 1] B: [sp:1 nrhs 9 real 0] [e1: 5e-16 : -2.3] [t1: 0.00 t2 0.00 : 0.1] nn = 206 Prob = title: 'SYMMETRIC MATRIX A OF LUND EIGENVALUE PROBLEM, MAY 1974' A: [147x147 double] name: 'HB/lund_a' id: 206 date: '1974' author: 'T. Johansson' ed: 'A. Curtis, I. Duff, J. Reid' kind: 'structural problem' A: [n 147 real 1] B: [sp:0 nrhs 1 real 1] [e1: 3e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 147 real 1] B: [sp:0 nrhs 4 real 1] [e1: 3e-10 : -0.1] [t1: 0.00 t2 0.00 : 1.4] A: [n 147 real 1] B: [sp:0 nrhs 9 real 1] [e1: 3e-10 : 0.1] [t1: 0.00 t2 0.00 : 1.0] A: [n 147 real 1] B: [sp:0 nrhs 1 real 0] [e1: 4e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 147 real 1] B: [sp:0 nrhs 9 real 0] [e1: 5e-10 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 147 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 147 real 1] B: [sp:1 nrhs 4 real 1] [e1: 5e-11 : 0.1] [t1: 0.00 t2 0.00 : 1.3] A: [n 147 real 1] B: [sp:1 nrhs 9 real 1] [e1: 3e-11 : 0.2] [t1: 0.00 t2 0.00 : 1.1] A: [n 147 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 147 real 1] B: [sp:1 nrhs 9 real 0] [e1: 4e-11 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 147 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 147 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.8] A: [n 147 real 0] B: [sp:0 nrhs 9 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 147 real 0] B: [sp:0 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 147 real 0] B: [sp:0 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 147 real 0] B: [sp:1 nrhs 1 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 147 real 0] B: [sp:1 nrhs 4 real 1] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 147 real 0] B: [sp:1 nrhs 9 real 1] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 147 real 0] B: [sp:1 nrhs 1 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 147 real 0] B: [sp:1 nrhs 9 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] nn = 207 Prob = title: 'SYMMETRIC MATRIX B OF LUND EIGENVALUE PROBLEM, MAY 1974' A: [147x147 double] name: 'HB/lund_b' id: 207 date: '1974' author: 'T. Johansson' ed: 'A. Curtis, I. Duff, J. Reid' kind: 'structural problem' A: [n 147 real 1] B: [sp:0 nrhs 1 real 1] [e1: 8e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.2] A: [n 147 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e-12 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 147 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 147 real 1] B: [sp:0 nrhs 1 real 0] [e1: 1e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 147 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 147 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 147 real 1] B: [sp:1 nrhs 4 real 1] [e1: 6e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 147 real 1] B: [sp:1 nrhs 9 real 1] [e1: 4e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 147 real 1] B: [sp:1 nrhs 1 real 0] [e1: 3e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 147 real 1] B: [sp:1 nrhs 9 real 0] [e1: 5e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 147 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 147 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 147 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 147 real 0] B: [sp:0 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 147 real 0] B: [sp:0 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 147 real 0] B: [sp:1 nrhs 1 real 1] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 147 real 0] B: [sp:1 nrhs 4 real 1] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 147 real 0] B: [sp:1 nrhs 9 real 1] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 147 real 0] B: [sp:1 nrhs 1 real 0] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 147 real 0] B: [sp:1 nrhs 9 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] nn = 27 Prob = title: 'SYMMETRIC STIFFNESS MATRIX, TRANSMISSION TOWER, LUMPED MASSES' A: [153x153 double] name: 'HB/bcsstk05' id: 27 date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 153 real 1] B: [sp:0 nrhs 1 real 1] [e1: 9e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 153 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e-11 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 153 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e-11 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 153 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 153 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 153 real 1] B: [sp:1 nrhs 1 real 1] [e1: 4e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 153 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-12 : 0.1] [t1: 0.00 t2 0.00 : 1.0] A: [n 153 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 153 real 1] B: [sp:1 nrhs 1 real 0] [e1: 1e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 153 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 153 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 153 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 153 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 153 real 0] B: [sp:0 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 153 real 0] B: [sp:0 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 153 real 0] B: [sp:1 nrhs 1 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 153 real 0] B: [sp:1 nrhs 4 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 153 real 0] B: [sp:1 nrhs 9 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 153 real 0] B: [sp:1 nrhs 1 real 0] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 153 real 0] B: [sp:1 nrhs 9 real 0] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] nn = 60 Prob = title: 'SYMMETRIC MASS MATRIX, TRANSMISSION TOWER, LUMPED MASSES' A: [153x153 double] name: 'HB/bcsstm05' id: 60 date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 153 real 1] B: [sp:0 nrhs 1 real 1] [e1: 1e-15 : -2.8] [t1: 0.00 t2 0.00 : 0.2] A: [n 153 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-15 : -2.5] [t1: 0.00 t2 0.00 : 0.2] A: [n 153 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-15 : -2.1] [t1: 0.00 t2 0.00 : 0.2] A: [n 153 real 1] B: [sp:0 nrhs 1 real 0] [e1: 3e-15 : -2.3] [t1: 0.00 t2 0.00 : 0.5] A: [n 153 real 1] B: [sp:0 nrhs 9 real 0] [e1: 3e-15 : -2.2] [t1: 0.00 t2 0.00 : 0.3] A: [n 153 real 1] B: [sp:1 nrhs 1 real 1] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1] A: [n 153 real 1] B: [sp:1 nrhs 4 real 1] [e1: 4e-16 : -2.3] [t1: 0.00 t2 0.00 : 0.1] A: [n 153 real 1] B: [sp:1 nrhs 9 real 1] [e1: 9e-16 : -1.6] [t1: 0.00 t2 0.00 : 0.1] A: [n 153 real 1] B: [sp:1 nrhs 1 real 0] [e1: 1e-17 : -8.1] [t1: 0.00 t2 0.00 : 0.1] A: [n 153 real 1] B: [sp:1 nrhs 9 real 0] [e1: 5e-16 : -2.6] [t1: 0.00 t2 0.00 : 0.1] A: [n 153 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-15 : -2.0] [t1: 0.00 t2 0.00 : 0.2] A: [n 153 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-15 : -2.1] [t1: 0.00 t2 0.00 : 0.2] A: [n 153 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-15 : -2.6] [t1: 0.00 t2 0.00 : 0.2] A: [n 153 real 1] B: [sp:0 nrhs 1 real 0] [e1: 3e-15 : -2.1] [t1: 0.00 t2 0.00 : 0.2] A: [n 153 real 1] B: [sp:0 nrhs 9 real 0] [e1: 3e-15 : -2.0] [t1: 0.00 t2 0.00 : 0.3] A: [n 153 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-16 : -3.1] [t1: 0.00 t2 0.00 : 0.1] A: [n 153 real 1] B: [sp:1 nrhs 4 real 1] [e1: 2e-16 : -2.1] [t1: 0.00 t2 0.00 : 0.1] A: [n 153 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-16 : -3.9] [t1: 0.00 t2 0.00 : 0.1] A: [n 153 real 1] B: [sp:1 nrhs 1 real 0] [e1: 5e-16 : -2.2] [t1: 0.00 t2 0.00 : 0.1] A: [n 153 real 1] B: [sp:1 nrhs 9 real 0] [e1: 9e-16 : -1.6] [t1: 0.00 t2 0.00 : 0.1] nn = 217 Prob = title: 'SYMMETRIC MATRIX, FE APPROXIMATION TO BIHARMONIC OPERATOR ON BEAM.' A: [237x237 double] name: 'HB/nos1' id: 217 date: '1982' author: 'H. Simon' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 237 real 1] B: [sp:0 nrhs 1 real 1] [e1: 5e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 237 real 1] B: [sp:0 nrhs 4 real 1] [e1: 5e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 237 real 1] B: [sp:0 nrhs 9 real 1] [e1: 5e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 237 real 1] B: [sp:0 nrhs 1 real 0] [e1: 8e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 237 real 1] B: [sp:0 nrhs 9 real 0] [e1: 8e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 237 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 237 real 1] B: [sp:1 nrhs 4 real 1] [e1: 9e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 237 real 1] B: [sp:1 nrhs 9 real 1] [e1: 7e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 237 real 1] B: [sp:1 nrhs 1 real 0] [e1: 7e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 237 real 1] B: [sp:1 nrhs 9 real 0] [e1: 7e-10 : 0.0] [t1: 0.00 t2 0.00 : 0.8] A: [n 237 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 237 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 237 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 237 real 0] B: [sp:0 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 237 real 0] B: [sp:0 nrhs 9 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 237 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.2] A: [n 237 real 0] B: [sp:1 nrhs 4 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 237 real 0] B: [sp:1 nrhs 9 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 237 real 0] B: [sp:1 nrhs 1 real 0] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 237 real 0] B: [sp:1 nrhs 9 real 0] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] nn = 877 Prob = A: [289x289 double] title: 'mesh3e1, with coordinates. From NASA, collected by Alex Pothen' name: 'Pothen/mesh3e1' Zeros: [289x289 double] id: 877 aux: [1x1 struct] date: '2003' author: 'NASA' ed: 'G. Kumfert, A. Pothen' kind: 'structural problem' A: [n 289 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.8] A: [n 289 real 1] B: [sp:0 nrhs 4 real 1] [e1: 3e-14 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 289 real 1] B: [sp:0 nrhs 9 real 1] [e1: 3e-14 : -0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 289 real 1] B: [sp:0 nrhs 1 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 289 real 1] B: [sp:0 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 289 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 289 real 1] B: [sp:1 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 289 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 289 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 289 real 1] B: [sp:1 nrhs 9 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 289 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 289 real 0] B: [sp:0 nrhs 4 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 289 real 0] B: [sp:0 nrhs 9 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 289 real 0] B: [sp:0 nrhs 1 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 289 real 0] B: [sp:0 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 289 real 0] B: [sp:1 nrhs 1 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 289 real 0] B: [sp:1 nrhs 4 real 1] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 289 real 0] B: [sp:1 nrhs 9 real 1] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 289 real 0] B: [sp:1 nrhs 1 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 289 real 0] B: [sp:1 nrhs 9 real 0] [e1: 1e-14 : 0.0] [t1: 0.10 t2 0.00 : 96.1] nn = 878 Prob = A: [289x289 double] title: 'mesh3em5, with coordinates. From NASA, collected by Alex Pothen' name: 'Pothen/mesh3em5' Zeros: [289x289 double] id: 878 aux: [1x1 struct] date: '2003' author: 'NASA' ed: 'G. Kumfert, A. Pothen' kind: 'structural problem' A: [n 289 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 289 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-14 : -0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 289 real 1] B: [sp:0 nrhs 9 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 289 real 1] B: [sp:0 nrhs 1 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 289 real 1] B: [sp:0 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 289 real 1] B: [sp:1 nrhs 1 real 1] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 289 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 289 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-14 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 289 real 1] B: [sp:1 nrhs 1 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 289 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 289 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.10 : 0.0] A: [n 289 real 0] B: [sp:0 nrhs 4 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 289 real 0] B: [sp:0 nrhs 9 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.8] A: [n 289 real 0] B: [sp:0 nrhs 1 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 289 real 0] B: [sp:0 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 289 real 0] B: [sp:1 nrhs 1 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 289 real 0] B: [sp:1 nrhs 4 real 1] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 289 real 0] B: [sp:1 nrhs 9 real 1] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 289 real 0] B: [sp:1 nrhs 1 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 289 real 0] B: [sp:1 nrhs 9 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] nn = 875 Prob = A: [306x306 double] title: 'mesh2e1, with coordinates. From NASA, collected by Alex Pothen' name: 'Pothen/mesh2e1' id: 875 aux: [1x1 struct] date: '2003' author: 'NASA' ed: 'G. Kumfert, A. Pothen' kind: 'structural problem' A: [n 306 real 1] B: [sp:0 nrhs 1 real 1] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.10 : 0.0] A: [n 306 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e-13 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 306 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e-13 : -0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 306 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 306 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 306 real 1] B: [sp:1 nrhs 1 real 1] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 306 real 1] B: [sp:1 nrhs 4 real 1] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 306 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-13 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 306 real 1] B: [sp:1 nrhs 1 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 306 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 306 real 0] B: [sp:0 nrhs 1 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 306 real 0] B: [sp:0 nrhs 4 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 306 real 0] B: [sp:0 nrhs 9 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 306 real 0] B: [sp:0 nrhs 1 real 0] [e1: 5e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 306 real 0] B: [sp:0 nrhs 9 real 0] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 306 real 0] B: [sp:1 nrhs 1 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 306 real 0] B: [sp:1 nrhs 4 real 1] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 306 real 0] B: [sp:1 nrhs 9 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 306 real 0] B: [sp:1 nrhs 1 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 306 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] nn = 876 Prob = A: [306x306 double] title: 'mesh2em5, with coordinates. From NASA, collected by Alex Pothen' name: 'Pothen/mesh2em5' id: 876 aux: [1x1 struct] date: '2003' author: 'NASA' ed: 'G. Kumfert, A. Pothen' kind: 'structural problem' A: [n 306 real 1] B: [sp:0 nrhs 1 real 1] [e1: 5e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 306 real 1] B: [sp:0 nrhs 4 real 1] [e1: 5e-14 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 306 real 1] B: [sp:0 nrhs 9 real 1] [e1: 5e-14 : -0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 306 real 1] B: [sp:0 nrhs 1 real 0] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 306 real 1] B: [sp:0 nrhs 9 real 0] [e1: 9e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 306 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 306 real 1] B: [sp:1 nrhs 4 real 1] [e1: 2e-14 : -0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 306 real 1] B: [sp:1 nrhs 9 real 1] [e1: 4e-14 : -0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 306 real 1] B: [sp:1 nrhs 1 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 306 real 1] B: [sp:1 nrhs 9 real 0] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 306 real 0] B: [sp:0 nrhs 1 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 306 real 0] B: [sp:0 nrhs 4 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 306 real 0] B: [sp:0 nrhs 9 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.5] A: [n 306 real 0] B: [sp:0 nrhs 1 real 0] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 306 real 0] B: [sp:0 nrhs 9 real 0] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 306 real 0] B: [sp:1 nrhs 1 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 306 real 0] B: [sp:1 nrhs 4 real 1] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 306 real 0] B: [sp:1 nrhs 9 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 306 real 0] B: [sp:1 nrhs 1 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 306 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] nn = 229 Prob = title: 'SPLATZMAN FINITE DIFFERENCE MODEL OF ATLANTICOCEAN' A: [362x362 double] name: 'HB/plat362' id: 229 date: '1975' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: '2D/3D problem' A: [n 362 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-05 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 362 real 1] B: [sp:0 nrhs 4 real 1] [e1: 8e-05 : -0.2] [t1: 0.00 t2 0.00 : 1.0] A: [n 362 real 1] B: [sp:0 nrhs 9 real 1] [e1: 8e-05 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 362 real 1] B: [sp:0 nrhs 1 real 0] [e1: 9e-05 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 362 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-04 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 362 real 1] B: [sp:1 nrhs 1 real 1] [e1: 4e-05 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 362 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-04 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 362 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-04 : -0.1] [t1: 0.00 t2 0.00 : 1.1] A: [n 362 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-04 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 362 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-04 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 362 real 0] B: [sp:0 nrhs 1 real 1] [e1: 5e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 362 real 0] B: [sp:0 nrhs 4 real 1] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 362 real 0] B: [sp:0 nrhs 9 real 1] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 362 real 0] B: [sp:0 nrhs 1 real 0] [e1: 9e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 362 real 0] B: [sp:0 nrhs 9 real 0] [e1: 9e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 362 real 0] B: [sp:1 nrhs 1 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 362 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 362 real 0] B: [sp:1 nrhs 9 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 362 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 362 real 0] B: [sp:1 nrhs 9 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] nn = 315 Prob = title: 'MAGNETO-HYDRO-DYNAMICS ALFVEN SPECTRAL PROBLEM' A: [416x416 double] name: 'Bai/mhdb416' id: 315 date: '1994' author: 'A. Booten, M. Kooper, H. van der Vorst, S. Poedts, J. Goedbloed' ed: 'Z. Bai, D. Day, J. Demmel, J. Dongarra' kind: 'electromagnetics problem' A: [n 416 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 416 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-12 : -0.1] [t1: 0.00 t2 0.00 : 1.1] A: [n 416 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-12 : -0.1] [t1: 0.00 t2 0.00 : 1.0] A: [n 416 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 416 real 1] B: [sp:0 nrhs 9 real 0] [e1: 3e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 416 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 416 real 1] B: [sp:1 nrhs 4 real 1] [e1: 5e-13 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 416 real 1] B: [sp:1 nrhs 9 real 1] [e1: 6e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 416 real 1] B: [sp:1 nrhs 1 real 0] [e1: 3e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 416 real 1] B: [sp:1 nrhs 9 real 0] [e1: 7e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 416 real 0] B: [sp:0 nrhs 1 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 416 real 0] B: [sp:0 nrhs 4 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 416 real 0] B: [sp:0 nrhs 9 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 416 real 0] B: [sp:0 nrhs 1 real 0] [e1: 5e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 416 real 0] B: [sp:0 nrhs 9 real 0] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 416 real 0] B: [sp:1 nrhs 1 real 1] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 416 real 0] B: [sp:1 nrhs 4 real 1] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.3] A: [n 416 real 0] B: [sp:1 nrhs 9 real 1] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 416 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.10 t2 0.00 : 206.5] A: [n 416 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] nn = 28 Prob = title: 'SYMMETRIC STIFFNESS MATRIX, MEDIUM TEST PROBLEM, LUMPED MASSES' A: [420x420 double] name: 'HB/bcsstk06' id: 28 date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 420 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.2] A: [n 420 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-10 : 0.1] [t1: 0.00 t2 0.00 : 1.1] A: [n 420 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 420 real 1] B: [sp:0 nrhs 1 real 0] [e1: 3e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.2] A: [n 420 real 1] B: [sp:0 nrhs 9 real 0] [e1: 3e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 1] B: [sp:1 nrhs 1 real 1] [e1: 8e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 420 real 1] B: [sp:1 nrhs 4 real 1] [e1: 3e-11 : -0.1] [t1: 0.00 t2 0.00 : 1.1] A: [n 420 real 1] B: [sp:1 nrhs 9 real 1] [e1: 5e-11 : -0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 420 real 1] B: [sp:1 nrhs 1 real 0] [e1: 4e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 420 real 1] B: [sp:1 nrhs 9 real 0] [e1: 8e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 420 real 0] B: [sp:0 nrhs 1 real 1] [e1: 7e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 0] B: [sp:0 nrhs 4 real 1] [e1: 7e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 0] B: [sp:0 nrhs 9 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 0] B: [sp:0 nrhs 1 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 0] B: [sp:0 nrhs 9 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 420 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.10 : 0.0] A: [n 420 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 420 real 0] B: [sp:1 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 420 real 0] B: [sp:1 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] nn = 29 Prob = title: 'SYMMETRIC STIFFNESS MATRIX, MEDIUM TEST PROBLEM, CONSISTENT MASSES' A: [420x420 double] name: 'HB/bcsstk07' id: 29 kind: 'duplicate structural problem' notes: 'duplicate of HB/bcsstk06' date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' A: [n 420 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.2] A: [n 420 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.2] A: [n 420 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-10 : 0.1] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 1] B: [sp:0 nrhs 1 real 0] [e1: 3e-10 : -0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 420 real 1] B: [sp:0 nrhs 9 real 0] [e1: 3e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 1] B: [sp:1 nrhs 1 real 1] [e1: 4e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 420 real 1] B: [sp:1 nrhs 4 real 1] [e1: 6e-11 : 0.1] [t1: 0.00 t2 0.00 : 1.1] A: [n 420 real 1] B: [sp:1 nrhs 9 real 1] [e1: 6e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 420 real 1] B: [sp:1 nrhs 1 real 0] [e1: 3e-11 : -0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 420 real 1] B: [sp:1 nrhs 9 real 0] [e1: 8e-11 : -0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 420 real 0] B: [sp:0 nrhs 1 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 0] B: [sp:0 nrhs 4 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 0] B: [sp:0 nrhs 9 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.10 : 0.0] A: [n 420 real 0] B: [sp:0 nrhs 1 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 0] B: [sp:0 nrhs 9 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 420 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 420 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 420 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 0] B: [sp:1 nrhs 9 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] nn = 61 Prob = title: 'SYMMETRIC MASS MATRIX, MEDIUM TEST PROBLEM, LUMPED MASSES' A: [420x420 double] name: 'HB/bcsstm06' id: 61 date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 420 real 1] B: [sp:0 nrhs 1 real 1] [e1: 3e-15 : -2.8] [t1: 0.00 t2 0.00 : 0.1] A: [n 420 real 1] B: [sp:0 nrhs 4 real 1] [e1: 3e-15 : -2.7] [t1: 0.00 t2 0.00 : 0.2] A: [n 420 real 1] B: [sp:0 nrhs 9 real 1] [e1: 4e-15 : -2.6] [t1: 0.00 t2 0.00 : 0.2] A: [n 420 real 1] B: [sp:0 nrhs 1 real 0] [e1: 6e-15 : -2.6] [t1: 0.00 t2 0.00 : 0.1] A: [n 420 real 1] B: [sp:0 nrhs 9 real 0] [e1: 6e-15 : -2.5] [t1: 0.00 t2 0.00 : 0.3] A: [n 420 real 1] B: [sp:1 nrhs 1 real 1] [e1: 2e-16 : -3.9] [t1: 0.00 t2 0.00 : 0.1] A: [n 420 real 1] B: [sp:1 nrhs 4 real 1] [e1: 3e-16 : -3.9] [t1: 0.00 t2 0.00 : 0.1] A: [n 420 real 1] B: [sp:1 nrhs 9 real 1] [e1: 9e-16 : -2.1] [t1: 0.00 t2 0.00 : 0.1] A: [n 420 real 1] B: [sp:1 nrhs 1 real 0] [e1: 3e-16 : -4.4] [t1: 0.00 t2 0.00 : 0.1] A: [n 420 real 1] B: [sp:1 nrhs 9 real 0] [e1: 1e-15 : -2.8] [t1: 0.00 t2 0.00 : 0.1] A: [n 420 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-15 : -3.9] [t1: 0.00 t2 0.00 : 0.1] A: [n 420 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-15 : -3.8] [t1: 0.00 t2 0.00 : 0.2] A: [n 420 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-15 : -3.7] [t1: 0.00 t2 0.00 : 0.2] A: [n 420 real 1] B: [sp:0 nrhs 1 real 0] [e1: 4e-15 : -3.5] [t1: 0.00 t2 0.00 : 0.3] A: [n 420 real 1] B: [sp:0 nrhs 9 real 0] [e1: 4e-15 : -3.3] [t1: 0.00 t2 0.00 : 0.3] A: [n 420 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-16 : -4.8] [t1: 0.00 t2 0.00 : 0.1] A: [n 420 real 1] B: [sp:1 nrhs 4 real 1] [e1: 3e-16 : -3.7] [t1: 0.00 t2 0.00 : 0.1] A: [n 420 real 1] B: [sp:1 nrhs 9 real 1] [e1: 3e-16 : -4.0] [t1: 0.00 t2 0.00 : 0.1] A: [n 420 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-16 : -4.5] [t1: 0.00 t2 0.00 : 0.1] A: [n 420 real 1] B: [sp:1 nrhs 9 real 0] [e1: 7e-16 : -4.0] [t1: 0.00 t2 0.00 : 0.1] nn = 62 Prob = title: 'SYMMETRIC MASS MATRIX, MEDIUM TEST PROBLEM, CONSISTENT MASSES' A: [420x420 double] name: 'HB/bcsstm07' id: 62 date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 420 real 1] B: [sp:0 nrhs 1 real 1] [e1: 5e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 420 real 1] B: [sp:0 nrhs 4 real 1] [e1: 6e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 420 real 1] B: [sp:0 nrhs 9 real 1] [e1: 6e-13 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 1] B: [sp:0 nrhs 1 real 0] [e1: 7e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.2] A: [n 420 real 1] B: [sp:0 nrhs 9 real 0] [e1: 9e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 420 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 420 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-13 : -0.1] [t1: 0.00 t2 0.00 : 1.2] A: [n 420 real 1] B: [sp:1 nrhs 9 real 1] [e1: 3e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 420 real 1] B: [sp:1 nrhs 1 real 0] [e1: 3e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 1] B: [sp:1 nrhs 9 real 0] [e1: 3e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 0] B: [sp:0 nrhs 1 real 1] [e1: 7e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 0] B: [sp:0 nrhs 4 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 0] B: [sp:0 nrhs 9 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 420 real 0] B: [sp:0 nrhs 1 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 0] B: [sp:0 nrhs 9 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 420 real 0] B: [sp:1 nrhs 1 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 420 real 0] B: [sp:1 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 420 real 0] B: [sp:1 nrhs 9 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] nn = 221 Prob = title: 'SYMMETRIC MATRIX, FE APPROXIMATION OF BUILDING.' A: [468x468 double] name: 'HB/nos5' id: 221 date: '1982' author: 'H. Simon' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 468 real 1] B: [sp:0 nrhs 1 real 1] [e1: 1e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 468 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 468 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 468 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 468 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 468 real 1] B: [sp:1 nrhs 1 real 1] [e1: 5e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 468 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 468 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.01 : 1.0] A: [n 468 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 468 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 468 real 0] B: [sp:0 nrhs 1 real 1] [e1: 6e-14 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 468 real 0] B: [sp:0 nrhs 4 real 1] [e1: 9e-14 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 468 real 0] B: [sp:0 nrhs 9 real 1] [e1: 8e-14 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 468 real 0] B: [sp:0 nrhs 1 real 0] [e1: 1e-13 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 468 real 0] B: [sp:0 nrhs 9 real 0] [e1: 1e-13 : 0.0] [t1: 0.01 t2 0.01 : 1.1] A: [n 468 real 0] B: [sp:1 nrhs 1 real 1] [e1: 1e-14 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 468 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 468 real 0] B: [sp:1 nrhs 9 real 1] Warning: Matrix is indefinite or singular to working precision [e1: 2e-14 : NaN] [t1: 0.02 t2 0.02 : 1.0] A: [n 468 real 0] B: [sp:1 nrhs 1 real 0] Warning: Matrix is singular to working precision. > In testsolve at 15 In test10 at 116 In cholmod_test at 112 Warning: Matrix is indefinite or singular to working precision [e1: NaN : NaN] [t1: 0.01 t2 0.01 : 1.0] A: [n 468 real 0] B: [sp:1 nrhs 9 real 0] Warning: Matrix is singular to working precision. > In testsolve at 15 In test10 at 117 In cholmod_test at 112 Warning: Matrix is indefinite or singular to working precision [e1: NaN : NaN] [t1: 0.02 t2 0.02 : 1.0] nn = 42 Prob = title: 'SYMMETRIC STIFFNESS MATRIX - FRAME WITHIN A SUSPENSION BRIDGE' A: [485x485 double] name: 'HB/bcsstk20' id: 42 date: '1984' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 485 real 1] B: [sp:0 nrhs 1 real 1] [e1: 9e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 485 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e-05 : 0.4] [t1: 0.00 t2 0.00 : 1.0] A: [n 485 real 1] B: [sp:0 nrhs 9 real 1] [e1: 9e-06 : -0.3] [t1: 0.00 t2 0.00 : 1.3] A: [n 485 real 1] B: [sp:0 nrhs 1 real 0] [e1: 9e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 485 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-05 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 485 real 1] B: [sp:1 nrhs 1 real 1] [e1: 2e-07 : 0.0] [t1: 0.00 t2 0.00 : 1.2] A: [n 485 real 1] B: [sp:1 nrhs 4 real 1] [e1: 8e-07 : 0.4] [t1: 0.00 t2 0.00 : 1.0] A: [n 485 real 1] B: [sp:1 nrhs 9 real 1] [e1: 7e-07 : 0.1] [t1: 0.00 t2 0.00 : 1.0] A: [n 485 real 1] B: [sp:1 nrhs 1 real 0] [e1: 1e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 485 real 1] B: [sp:1 nrhs 9 real 0] [e1: 1e-06 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 485 real 0] B: [sp:0 nrhs 1 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 485 real 0] B: [sp:0 nrhs 4 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 485 real 0] B: [sp:0 nrhs 9 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 485 real 0] B: [sp:0 nrhs 1 real 0] [e1: 7e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 485 real 0] B: [sp:0 nrhs 9 real 0] [e1: 7e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 485 real 0] B: [sp:1 nrhs 1 real 1] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 485 real 0] B: [sp:1 nrhs 4 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 485 real 0] B: [sp:1 nrhs 9 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 485 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 485 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] nn = 70 Prob = title: 'SYMMETRIC MASS MATRIX - FRAME WITHIN A SUSPENSION BRIDGE' A: [485x485 double] name: 'HB/bcsstm20' id: 70 date: '1984' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 485 real 1] B: [sp:0 nrhs 1 real 1] [e1: 5e-15 : -2.2] [t1: 0.00 t2 0.00 : 0.1] A: [n 485 real 1] B: [sp:0 nrhs 4 real 1] [e1: 6e-15 : -2.1] [t1: 0.00 t2 0.00 : 0.2] A: [n 485 real 1] B: [sp:0 nrhs 9 real 1] [e1: 6e-15 : -2.1] [t1: 0.00 t2 0.00 : 0.2] A: [n 485 real 1] B: [sp:0 nrhs 1 real 0] [e1: 9e-15 : -2.2] [t1: 0.00 t2 0.00 : 0.1] A: [n 485 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-14 : -1.8] [t1: 0.00 t2 0.00 : 0.3] A: [n 485 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-16 : -3.1] [t1: 0.00 t2 0.00 : 0.1] A: [n 485 real 1] B: [sp:1 nrhs 4 real 1] [e1: 8e-16 : -2.6] [t1: 0.00 t2 0.00 : 0.1] A: [n 485 real 1] B: [sp:1 nrhs 9 real 1] [e1: 9e-16 : -2.3] [t1: 0.00 t2 0.00 : 0.1] A: [n 485 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-15 : -2.1] [t1: 0.00 t2 0.00 : 0.1] A: [n 485 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-15 : -2.1] [t1: 0.00 t2 0.00 : 0.1] A: [n 485 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-16 : -7.4] [t1: 0.00 t2 0.00 : 0.1] A: [n 485 real 1] B: [sp:0 nrhs 4 real 1] [e1: 4e-16 : -6.3] [t1: 0.00 t2 0.00 : 0.2] A: [n 485 real 1] B: [sp:0 nrhs 9 real 1] [e1: 4e-16 : -6.2] [t1: 0.00 t2 0.00 : 0.2] A: [n 485 real 1] B: [sp:0 nrhs 1 real 0] [e1: 6e-16 : -6.2] [t1: 0.00 t2 0.00 : 0.1] A: [n 485 real 1] B: [sp:0 nrhs 9 real 0] [e1: 7e-16 : -6.2] [t1: 0.00 t2 0.00 : 0.3] A: [n 485 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-16 : -5.6] [t1: 0.00 t2 0.00 : 0.1] A: [n 485 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-16 : -5.6] [t1: 0.00 t2 0.00 : 0.1] A: [n 485 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-17 : -8.7] [t1: 0.00 t2 0.00 : 0.1] A: [n 485 real 1] B: [sp:1 nrhs 1 real 0] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1] A: [n 485 real 1] B: [sp:1 nrhs 9 real 0] [e1: 7e-16 : -4.1] [t1: 0.00 t2 0.00 : 0.1] nn = 2 Prob = title: 'S ADMITTANCE MATRIX 494 BUS POWER SYSTEM, D.J.TYLAVSKY, JULY 1985.' A: [494x494 double] name: 'HB/494_bus' id: 2 date: '1985' author: 'D. Tylavsky' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'power network problem' A: [n 494 real 1] B: [sp:0 nrhs 1 real 1] [e1: 1e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 494 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e-09 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 494 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 494 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 494 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 494 real 1] B: [sp:1 nrhs 1 real 1] [e1: 6e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 494 real 1] B: [sp:1 nrhs 4 real 1] [e1: 3e-11 : -0.1] [t1: 0.00 t2 0.00 : 0.9] A: [n 494 real 1] B: [sp:1 nrhs 9 real 1] [e1: 3e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 494 real 1] B: [sp:1 nrhs 1 real 0] [e1: 4e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 494 real 1] B: [sp:1 nrhs 9 real 0] [e1: 7e-11 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 494 real 0] B: [sp:0 nrhs 1 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 494 real 0] B: [sp:0 nrhs 4 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 494 real 0] B: [sp:0 nrhs 9 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 494 real 0] B: [sp:0 nrhs 1 real 0] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 494 real 0] B: [sp:0 nrhs 9 real 0] [e1: 7e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 494 real 0] B: [sp:1 nrhs 1 real 1] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 494 real 0] B: [sp:1 nrhs 4 real 1] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 494 real 0] B: [sp:1 nrhs 9 real 1] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 494 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 494 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] nn = 339 Prob = title: 'NASTRAN BUCKLING PROBLEM STIFFNESS MATRIX' A: [588x588 double] name: 'Boeing/bcsstk34' id: 339 date: '1995' author: 'R. Grimes' ed: 'T. Davis' kind: 'structural problem' A: [n 588 real 1] B: [sp:0 nrhs 1 real 1] [e1: 1e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 588 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 588 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 588 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 588 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 588 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-13 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 588 real 1] B: [sp:1 nrhs 4 real 1] [e1: 4e-13 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 588 real 1] B: [sp:1 nrhs 9 real 1] [e1: 6e-13 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 588 real 1] B: [sp:1 nrhs 1 real 0] [e1: 4e-13 : 0.0] [t1: 0.01 t2 0.01 : 1.1] A: [n 588 real 1] B: [sp:1 nrhs 9 real 0] [e1: 9e-13 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 588 real 0] B: [sp:0 nrhs 1 real 1] [e1: 1e-13 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 588 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-13 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 588 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-13 : 0.0] [t1: 0.03 t2 0.03 : 1.0] A: [n 588 real 0] B: [sp:0 nrhs 1 real 0] [e1: 2e-13 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 588 real 0] B: [sp:0 nrhs 9 real 0] [e1: 2e-13 : 0.0] [t1: 0.03 t2 0.03 : 1.0] A: [n 588 real 0] B: [sp:1 nrhs 1 real 1] [e1: 3e-14 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 588 real 0] B: [sp:1 nrhs 4 real 1] [e1: 4e-14 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 588 real 0] B: [sp:1 nrhs 9 real 1] [e1: 4e-14 : 0.0] [t1: 0.03 t2 0.03 : 1.0] A: [n 588 real 0] B: [sp:1 nrhs 1 real 0] [e1: 4e-14 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 588 real 0] B: [sp:1 nrhs 9 real 0] [e1: 7e-14 : 0.0] [t1: 0.03 t2 0.03 : 1.0] nn = 3 Prob = title: 'S ADMITTANCE MATRIX 662 BUS POWER SYSTEM, D.J.TYLAVSKY, JULY 1985.' A: [662x662 double] name: 'HB/662_bus' id: 3 date: '1985' author: 'D. Tylavsky' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'power network problem' A: [n 662 real 1] B: [sp:0 nrhs 1 real 1] [e1: 9e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 662 real 1] B: [sp:0 nrhs 4 real 1] [e1: 9e-10 : -0.1] [t1: 0.00 t2 0.00 : 0.9] A: [n 662 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e-09 : -0.1] [t1: 0.00 t2 0.00 : 1.0] A: [n 662 real 1] B: [sp:0 nrhs 1 real 0] [e1: 1e-09 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 662 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-09 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 662 real 1] B: [sp:1 nrhs 1 real 1] [e1: 2e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 662 real 1] B: [sp:1 nrhs 4 real 1] [e1: 3e-11 : -0.1] [t1: 0.00 t2 0.00 : 1.0] A: [n 662 real 1] B: [sp:1 nrhs 9 real 1] [e1: 3e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 662 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 662 real 1] B: [sp:1 nrhs 9 real 0] [e1: 5e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 662 real 0] B: [sp:0 nrhs 1 real 1] [e1: 5e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 662 real 0] B: [sp:0 nrhs 4 real 1] [e1: 5e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 662 real 0] B: [sp:0 nrhs 9 real 1] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 662 real 0] B: [sp:0 nrhs 1 real 0] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 662 real 0] B: [sp:0 nrhs 9 real 0] [e1: 9e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 662 real 0] B: [sp:1 nrhs 1 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 662 real 0] B: [sp:1 nrhs 4 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 662 real 0] B: [sp:1 nrhs 9 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 662 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 662 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] nn = 222 Prob = title: 'SYMMETRIC MATRIX, POISSON'S EQUATION IN L SHAPE, MIXED BC.' A: [675x675 double] name: 'HB/nos6' id: 222 date: '1982' author: 'H. Simon' ed: 'I. Duff, R. Grimes, J. Lewis' kind: '2D/3D problem' A: [n 675 real 1] B: [sp:0 nrhs 1 real 1] [e1: 3e-08 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 675 real 1] B: [sp:0 nrhs 4 real 1] [e1: 3e-08 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 675 real 1] B: [sp:0 nrhs 9 real 1] [e1: 3e-08 : -0.1] [t1: 0.00 t2 0.00 : 1.0] A: [n 675 real 1] B: [sp:0 nrhs 1 real 0] [e1: 4e-08 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 675 real 1] B: [sp:0 nrhs 9 real 0] [e1: 4e-08 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 675 real 1] B: [sp:1 nrhs 1 real 1] [e1: 9e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 675 real 1] B: [sp:1 nrhs 4 real 1] [e1: 2e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 675 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-09 : 0.1] [t1: 0.00 t2 0.00 : 1.0] A: [n 675 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 675 real 1] B: [sp:1 nrhs 9 real 0] [e1: 3e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 675 real 0] B: [sp:0 nrhs 1 real 1] [e1: 7e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 675 real 0] B: [sp:0 nrhs 4 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 675 real 0] B: [sp:0 nrhs 9 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 675 real 0] B: [sp:0 nrhs 1 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 675 real 0] B: [sp:0 nrhs 9 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 675 real 0] B: [sp:1 nrhs 1 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 675 real 0] B: [sp:1 nrhs 4 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 675 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 675 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 675 real 0] B: [sp:1 nrhs 9 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] nn = 4 Prob = title: 'S ADMITTANCE MATRIX 685 BUS POWER SYSTEM, D.J.TYLAVSKY, JULY 1985.' A: [685x685 double] name: 'HB/685_bus' id: 4 date: '1985' author: 'D. Tylavsky' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'power network problem' A: [n 685 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 685 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-10 : -0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 685 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-10 : -0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 685 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 685 real 1] B: [sp:0 nrhs 9 real 0] [e1: 3e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 685 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 685 real 1] B: [sp:1 nrhs 4 real 1] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 685 real 1] B: [sp:1 nrhs 9 real 1] [e1: 5e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 685 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 685 real 1] B: [sp:1 nrhs 9 real 0] [e1: 9e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 685 real 0] B: [sp:0 nrhs 1 real 1] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 685 real 0] B: [sp:0 nrhs 4 real 1] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 685 real 0] B: [sp:0 nrhs 9 real 1] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 685 real 0] B: [sp:0 nrhs 1 real 0] [e1: 9e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 685 real 0] B: [sp:0 nrhs 9 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 685 real 0] B: [sp:1 nrhs 1 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 685 real 0] B: [sp:1 nrhs 4 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 685 real 0] B: [sp:1 nrhs 9 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 685 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 685 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] nn = 357 Prob = title: 'SYMMETRIC TEST MATRIX FROM MSC/NASTRAN BC4F8.OUT2' A: [726x726 double] name: 'Boeing/msc00726' id: 357 date: '1995' author: 'R. Grimes' ed: 'T. Davis' kind: 'structural problem' A: [n 726 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-11 : 0.0] [t1: 0.02 t2 0.02 : 1.1] A: [n 726 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-11 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 726 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-11 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 726 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-11 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 726 real 1] B: [sp:0 nrhs 9 real 0] [e1: 3e-11 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 726 real 1] B: [sp:1 nrhs 1 real 1] [e1: 5e-13 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 726 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-12 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 726 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-12 : 0.0] [t1: 0.03 t2 0.03 : 1.0] A: [n 726 real 1] B: [sp:1 nrhs 1 real 0] [e1: 1e-12 : 0.0] [t1: 0.12 t2 0.02 : 5.4] A: [n 726 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-12 : 0.0] [t1: 0.03 t2 0.03 : 1.0] A: [n 726 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-13 : 0.0] [t1: 0.06 t2 0.16 : 0.4] A: [n 726 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-13 : 0.0] [t1: 0.17 t2 0.07 : 2.3] A: [n 726 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-13 : 0.0] [t1: 0.18 t2 0.18 : 1.0] A: [n 726 real 0] B: [sp:0 nrhs 1 real 0] [e1: 3e-13 : 0.0] [t1: 0.16 t2 0.06 : 2.6] A: [n 726 real 0] B: [sp:0 nrhs 9 real 0] [e1: 4e-13 : 0.0] [t1: 0.18 t2 0.18 : 1.0] A: [n 726 real 0] B: [sp:1 nrhs 1 real 1] [e1: 5e-14 : 0.0] [t1: 0.16 t2 0.06 : 2.6] A: [n 726 real 0] B: [sp:1 nrhs 4 real 1] [e1: 6e-14 : 0.0] [t1: 0.18 t2 0.17 : 1.0] A: [n 726 real 0] B: [sp:1 nrhs 9 real 1] [e1: 5e-14 : 0.0] [t1: 0.19 t2 0.09 : 2.2] A: [n 726 real 0] B: [sp:1 nrhs 1 real 0] [e1: 7e-14 : 0.0] [t1: 0.06 t2 0.16 : 0.4] A: [n 726 real 0] B: [sp:1 nrhs 9 real 0] [e1: 1e-13 : 0.0] [t1: 0.19 t2 0.19 : 1.0] nn = 223 Prob = title: 'SYMMETRIC MATRIX, POISSON'S EQUATION IN UNIT CUBE.' A: [729x729 double] name: 'HB/nos7' id: 223 date: '1982' author: 'H. Simon' ed: 'I. Duff, R. Grimes, J. Lewis' kind: '2D/3D problem' A: [n 729 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 729 real 1] B: [sp:0 nrhs 4 real 1] [e1: 3e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 729 real 1] B: [sp:0 nrhs 9 real 1] [e1: 3e-06 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 729 real 1] B: [sp:0 nrhs 1 real 0] [e1: 4e-06 : 0.0] [t1: 0.00 t2 0.01 : 0.9] A: [n 729 real 1] B: [sp:0 nrhs 9 real 0] [e1: 4e-06 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 729 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 729 real 1] B: [sp:1 nrhs 4 real 1] [e1: 6e-08 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 729 real 1] B: [sp:1 nrhs 9 real 1] [e1: 9e-08 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 729 real 1] B: [sp:1 nrhs 1 real 0] [e1: 1e-07 : 0.0] [t1: 0.10 t2 0.01 : 18.0] A: [n 729 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-07 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 729 real 0] B: [sp:0 nrhs 1 real 1] [e1: 9e-14 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 729 real 0] B: [sp:0 nrhs 4 real 1] [e1: 1e-13 : 0.0] [t1: 0.02 t2 0.12 : 0.2] A: [n 729 real 0] B: [sp:0 nrhs 9 real 1] [e1: 1e-13 : 0.0] [t1: 0.03 t2 0.03 : 1.0] A: [n 729 real 0] B: [sp:0 nrhs 1 real 0] [e1: 1e-13 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 729 real 0] B: [sp:0 nrhs 9 real 0] [e1: 2e-13 : 0.0] [t1: 0.13 t2 0.03 : 5.0] A: [n 729 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 729 real 0] B: [sp:1 nrhs 4 real 1] [e1: 3e-14 : 0.0] [t1: 0.02 t2 0.12 : 0.2] A: [n 729 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.04 t2 0.04 : 1.0] A: [n 729 real 0] B: [sp:1 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.11 t2 0.01 : 8.6] A: [n 729 real 0] B: [sp:1 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.04 t2 0.04 : 1.0] nn = 41 Prob = title: 'SYMMETRIC STIFFNESS MATRIX - PART OF A SUSPENSION BRIDGE' A: [817x817 double] name: 'HB/bcsstk19' id: 41 date: '1984' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 817 real 1] B: [sp:0 nrhs 1 real 1] [e1: 7e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 817 real 1] B: [sp:0 nrhs 4 real 1] [e1: 7e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 817 real 1] B: [sp:0 nrhs 9 real 1] [e1: 7e-06 : -0.2] [t1: 0.00 t2 0.00 : 1.0] A: [n 817 real 1] B: [sp:0 nrhs 1 real 0] [e1: 1e-05 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 817 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-05 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 817 real 1] B: [sp:1 nrhs 1 real 1] [e1: 4e-07 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 817 real 1] B: [sp:1 nrhs 4 real 1] [e1: 5e-07 : -0.1] [t1: 0.00 t2 0.00 : 0.9] A: [n 817 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-06 : -0.2] [t1: 0.00 t2 0.00 : 1.0] A: [n 817 real 1] B: [sp:1 nrhs 1 real 0] [e1: 1e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 817 real 1] B: [sp:1 nrhs 9 real 0] [e1: 1e-06 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 817 real 0] B: [sp:0 nrhs 1 real 1] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 817 real 0] B: [sp:0 nrhs 4 real 1] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 817 real 0] B: [sp:0 nrhs 9 real 1] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 817 real 0] B: [sp:0 nrhs 1 real 0] [e1: 2e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 817 real 0] B: [sp:0 nrhs 9 real 0] [e1: 2e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 817 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 817 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 817 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 817 real 0] B: [sp:1 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 817 real 0] B: [sp:1 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.8] nn = 69 Prob = title: 'SYMMETRIC MASS MATRIX - PART OF A SUSPENSION BRIDGE' A: [817x817 double] name: 'HB/bcsstm19' id: 69 date: '1984' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 817 real 1] B: [sp:0 nrhs 1 real 1] [e1: 8e-15 : -2.1] [t1: 0.00 t2 0.00 : 0.1] A: [n 817 real 1] B: [sp:0 nrhs 4 real 1] [e1: 8e-15 : -2.2] [t1: 0.00 t2 0.00 : 0.1] A: [n 817 real 1] B: [sp:0 nrhs 9 real 1] [e1: 9e-15 : -2.0] [t1: 0.00 t2 0.00 : 0.2] A: [n 817 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-14 : -2.0] [t1: 0.00 t2 0.00 : 0.1] A: [n 817 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-14 : -1.9] [t1: 0.00 t2 0.00 : 0.3] A: [n 817 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-15 : -2.8] [t1: 0.00 t2 0.00 : 0.1] A: [n 817 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-15 : -2.9] [t1: 0.00 t2 0.00 : 0.1] A: [n 817 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-15 : -2.0] [t1: 0.00 t2 0.00 : 0.1] A: [n 817 real 1] B: [sp:1 nrhs 1 real 0] [e1: 3e-15 : -1.8] [t1: 0.00 t2 0.00 : 0.1] A: [n 817 real 1] B: [sp:1 nrhs 9 real 0] [e1: 3e-15 : -1.9] [t1: 0.00 t2 0.00 : 0.1] A: [n 817 real 1] B: [sp:0 nrhs 1 real 1] [e1: 9e-16 : -5.8] [t1: 0.00 t2 0.00 : 0.1] A: [n 817 real 1] B: [sp:0 nrhs 4 real 1] [e1: 9e-16 : -5.8] [t1: 0.00 t2 0.00 : 0.2] A: [n 817 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-15 : -4.9] [t1: 0.00 t2 0.00 : 0.2] A: [n 817 real 1] B: [sp:0 nrhs 1 real 0] [e1: 3e-15 : -4.9] [t1: 0.00 t2 0.00 : 0.1] A: [n 817 real 1] B: [sp:0 nrhs 9 real 0] [e1: 3e-15 : -5.0] [t1: 0.00 t2 0.00 : 0.3] A: [n 817 real 1] B: [sp:1 nrhs 1 real 1] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1] A: [n 817 real 1] B: [sp:1 nrhs 4 real 1] [e1: 2e-16 : -5.6] [t1: 0.00 t2 0.00 : 0.1] A: [n 817 real 1] B: [sp:1 nrhs 9 real 1] [e1: 4e-16 : -4.5] [t1: 0.00 t2 0.00 : 0.1] A: [n 817 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-16 : -6.1] [t1: 0.00 t2 0.00 : 0.1] A: [n 817 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-16 : -6.3] [t1: 0.00 t2 0.00 : 0.1] nn = 159 Prob = title: 'SYMMETRIC MATRIX FROM NINE POINT START ON A 30 X 30 GRID.' A: [900x900 double] name: 'HB/gr_30_30' id: 159 date: '1983' author: 'R. Grimes' ed: 'I. Duff, R. Grimes, J. Lewis' kind: '2D/3D problem' A: [n 900 real 1] B: [sp:0 nrhs 1 real 1] [e1: 9e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 900 real 1] B: [sp:0 nrhs 4 real 1] [e1: 9e-12 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 900 real 1] B: [sp:0 nrhs 9 real 1] [e1: 9e-12 : -0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 900 real 1] B: [sp:0 nrhs 1 real 0] [e1: 1e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 900 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 900 real 1] B: [sp:1 nrhs 1 real 1] [e1: 2e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 900 real 1] B: [sp:1 nrhs 4 real 1] [e1: 4e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 900 real 1] B: [sp:1 nrhs 9 real 1] [e1: 4e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 900 real 1] B: [sp:1 nrhs 1 real 0] [e1: 4e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 900 real 1] B: [sp:1 nrhs 9 real 0] [e1: 6e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 900 real 0] B: [sp:0 nrhs 1 real 1] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 900 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 900 real 0] B: [sp:0 nrhs 9 real 1] [e1: 1e-13 : 0.0] [t1: 0.01 t2 0.01 : 0.7] A: [n 900 real 0] B: [sp:0 nrhs 1 real 0] [e1: 2e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 900 real 0] B: [sp:0 nrhs 9 real 0] [e1: 2e-13 : 0.0] [t1: 0.01 t2 0.01 : 0.9] A: [n 900 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 900 real 0] B: [sp:1 nrhs 4 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 900 real 0] B: [sp:1 nrhs 9 real 1] [e1: 3e-14 : 0.0] [t1: 0.01 t2 0.01 : 0.9] A: [n 900 real 0] B: [sp:1 nrhs 1 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 900 real 0] B: [sp:1 nrhs 9 real 0] [e1: 5e-14 : 0.0] [t1: 0.01 t2 0.01 : 0.9] nn = 218 Prob = title: 'SYMMETRIC MATRIX, FE APPROXIMATION TO BIHARMONIC OPERATOR ON BEAM.' A: [957x957 double] name: 'HB/nos2' id: 218 date: '1982' author: 'H. Simon' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 957 real 1] B: [sp:0 nrhs 1 real 1] [e1: 5e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 957 real 1] B: [sp:0 nrhs 4 real 1] [e1: 5e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 957 real 1] B: [sp:0 nrhs 9 real 1] [e1: 5e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 957 real 1] B: [sp:0 nrhs 1 real 0] [e1: 7e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 957 real 1] B: [sp:0 nrhs 9 real 0] [e1: 8e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 957 real 1] B: [sp:1 nrhs 1 real 1] [e1: 2e-07 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 957 real 1] B: [sp:1 nrhs 4 real 1] [e1: 3e-07 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 957 real 1] B: [sp:1 nrhs 9 real 1] [e1: 3e-07 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 957 real 1] B: [sp:1 nrhs 1 real 0] [e1: 9e-08 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 957 real 1] B: [sp:1 nrhs 9 real 0] [e1: 6e-07 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 957 real 0] B: [sp:0 nrhs 1 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 957 real 0] B: [sp:0 nrhs 4 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0] A: [n 957 real 0] B: [sp:0 nrhs 9 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 957 real 0] B: [sp:0 nrhs 1 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 957 real 0] B: [sp:0 nrhs 9 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 957 real 0] B: [sp:1 nrhs 1 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 957 real 0] B: [sp:1 nrhs 4 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 957 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] A: [n 957 real 0] B: [sp:1 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1] A: [n 957 real 0] B: [sp:1 nrhs 9 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9] nn = 219 Prob = title: 'SYMMETRIC MATRIX, FE APPROXIMATION TO BIHARMONIC OPERATOR ON PLATE' A: [960x960 double] name: 'HB/nos3' id: 219 date: '1982' author: 'H. Simon' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 960 real 1] B: [sp:0 nrhs 1 real 1] [e1: 4e-10 : 0.0] [t1: 0.01 t2 0.00 : 1.0] A: [n 960 real 1] B: [sp:0 nrhs 4 real 1] [e1: 4e-10 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 960 real 1] B: [sp:0 nrhs 9 real 1] [e1: 4e-10 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 960 real 1] B: [sp:0 nrhs 1 real 0] [e1: 6e-10 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 960 real 1] B: [sp:0 nrhs 9 real 0] [e1: 7e-10 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 960 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-11 : 0.0] [t1: 0.00 t2 0.01 : 1.0] A: [n 960 real 1] B: [sp:1 nrhs 4 real 1] [e1: 3e-11 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 960 real 1] B: [sp:1 nrhs 9 real 1] [e1: 3e-11 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 960 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-11 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 960 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-11 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 960 real 0] B: [sp:0 nrhs 1 real 1] [e1: 1e-13 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 960 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-13 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 960 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-13 : 0.0] [t1: 0.03 t2 0.03 : 1.0] A: [n 960 real 0] B: [sp:0 nrhs 1 real 0] [e1: 2e-13 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 960 real 0] B: [sp:0 nrhs 9 real 0] [e1: 3e-13 : 0.0] [t1: 0.03 t2 0.02 : 1.0] A: [n 960 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 960 real 0] B: [sp:1 nrhs 4 real 1] [e1: 4e-14 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 960 real 0] B: [sp:1 nrhs 9 real 1] [e1: 3e-14 : 0.0] [t1: 0.03 t2 0.03 : 1.0] A: [n 960 real 0] B: [sp:1 nrhs 1 real 0] [e1: 5e-14 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 960 real 0] B: [sp:1 nrhs 9 real 0] [e1: 7e-14 : 0.0] [t1: 0.03 t2 0.03 : 1.0] nn = 358 Prob = title: 'SYMMETRIC TEST MATRIX FROM MSC/NASTRAN STARF8.OUT2' A: [1050x1050 double] Zeros: [1050x1050 double] name: 'Boeing/msc01050' id: 358 date: '1995' author: 'R. Grimes' ed: 'T. Davis' kind: 'structural problem' A: [n 1050 real 1] B: [sp:0 nrhs 1 real 1] [e1: 1e-00 : 0.0] [t1: 0.01 t2 0.01 : 1.1] A: [n 1050 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e+00 : -0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 1050 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e+00 : -0.0] [t1: 0.01 t2 0.01 : 1.1] A: [n 1050 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e+00 : -0.0] [t1: 0.01 t2 0.01 : 1.1] A: [n 1050 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e+00 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 1050 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-02 : 0.0] [t1: 0.01 t2 0.01 : 1.1] A: [n 1050 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-01 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 1050 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-01 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 1050 real 1] B: [sp:1 nrhs 1 real 0] [e1: 3e-02 : 0.0] [t1: 0.01 t2 0.01 : 1.1] A: [n 1050 real 1] B: [sp:1 nrhs 9 real 0] [e1: 1e-01 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 1050 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-13 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 1050 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-13 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 1050 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-13 : 0.0] [t1: 0.03 t2 0.03 : 1.0] A: [n 1050 real 0] B: [sp:0 nrhs 1 real 0] [e1: 3e-13 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 1050 real 0] B: [sp:0 nrhs 9 real 0] [e1: 3e-13 : 0.0] [t1: 0.03 t2 0.12 : 0.2] A: [n 1050 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 1050 real 0] B: [sp:1 nrhs 4 real 1] [e1: 5e-14 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 1050 real 0] B: [sp:1 nrhs 9 real 1] [e1: 4e-14 : 0.0] [t1: 0.03 t2 0.03 : 0.9] A: [n 1050 real 0] B: [sp:1 nrhs 1 real 0] [e1: 5e-14 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 1050 real 0] B: [sp:1 nrhs 9 real 0] [e1: 6e-14 : 0.0] [t1: 0.03 t2 0.03 : 0.9] nn = 30 Prob = title: 'SYMMETRIC STIFFNESS MATRIX, FRAME BUILDING (TV STUDIO)' A: [1074x1074 double] name: 'HB/bcsstk08' id: 30 date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 1074 real 1] B: [sp:0 nrhs 1 real 1] [e1: 3e-11 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 1074 real 1] B: [sp:0 nrhs 4 real 1] [e1: 4e-11 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 1074 real 1] B: [sp:0 nrhs 9 real 1] [e1: 4e-11 : 0.0] [t1: 0.01 t2 0.11 : 0.1] A: [n 1074 real 1] B: [sp:0 nrhs 1 real 0] [e1: 5e-11 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 1074 real 1] B: [sp:0 nrhs 9 real 0] [e1: 7e-11 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 1074 real 1] B: [sp:1 nrhs 1 real 1] [e1: 2e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 1074 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-11 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 1074 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-11 : 0.0] [t1: 0.11 t2 0.01 : 8.7] A: [n 1074 real 1] B: [sp:1 nrhs 1 real 0] [e1: 8e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 1074 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-11 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 1074 real 0] B: [sp:0 nrhs 1 real 1] [e1: 1e-13 : 0.0] [t1: 0.13 t2 0.03 : 4.9] A: [n 1074 real 0] B: [sp:0 nrhs 4 real 1] [e1: 1e-13 : 0.0] [t1: 0.04 t2 0.14 : 0.3] A: [n 1074 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-13 : 0.0] [t1: 0.05 t2 0.15 : 0.3] A: [n 1074 real 0] B: [sp:0 nrhs 1 real 0] [e1: 2e-13 : 0.0] [t1: 0.03 t2 0.03 : 1.0] A: [n 1074 real 0] B: [sp:0 nrhs 9 real 0] [e1: 3e-13 : 0.0] [t1: 0.15 t2 0.05 : 3.2] A: [n 1074 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.13 t2 0.03 : 4.9] A: [n 1074 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.04 t2 0.14 : 0.3] A: [n 1074 real 0] B: [sp:1 nrhs 9 real 1] [e1: 3e-14 : 0.0] [t1: 0.06 t2 0.16 : 0.4] A: [n 1074 real 0] B: [sp:1 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.03 t2 0.03 : 1.0] A: [n 1074 real 0] B: [sp:1 nrhs 9 real 0] [e1: 5e-14 : 0.0] [t1: 0.06 t2 0.16 : 0.4] nn = 63 Prob = title: 'SYMMETRIC MASS MATRIX, FRAME BUILDING (TV STUDIO)' A: [1074x1074 double] name: 'HB/bcsstm08' id: 63 date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 1074 real 1] B: [sp:0 nrhs 1 real 1] [e1: 3e-15 : -3.5] [t1: 0.00 t2 0.00 : 0.1] A: [n 1074 real 1] B: [sp:0 nrhs 4 real 1] [e1: 5e-15 : -2.8] [t1: 0.00 t2 0.00 : 0.2] A: [n 1074 real 1] B: [sp:0 nrhs 9 real 1] [e1: 5e-15 : -3.0] [t1: 0.00 t2 0.00 : 0.2] A: [n 1074 real 1] B: [sp:0 nrhs 1 real 0] [e1: 8e-15 : -2.9] [t1: 0.00 t2 0.00 : 0.1] A: [n 1074 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-14 : -2.7] [t1: 0.00 t2 0.00 : 0.3] A: [n 1074 real 1] B: [sp:1 nrhs 1 real 1] [e1: 5e-16 : -3.2] [t1: 0.00 t2 0.00 : 0.1] A: [n 1074 real 1] B: [sp:1 nrhs 4 real 1] [e1: 5e-16 : -3.5] [t1: 0.00 t2 0.00 : 0.1] A: [n 1074 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-15 : -2.5] [t1: 0.00 t2 0.00 : 0.1] A: [n 1074 real 1] B: [sp:1 nrhs 1 real 0] [e1: 7e-16 : -3.8] [t1: 0.00 t2 0.00 : 0.1] A: [n 1074 real 1] B: [sp:1 nrhs 9 real 0] [e1: 1e-15 : -3.2] [t1: 0.00 t2 0.00 : 0.1] A: [n 1074 real 1] B: [sp:0 nrhs 1 real 1] [e1: 6e-17 : -9.2] [t1: 0.00 t2 0.00 : 0.1] A: [n 1074 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-16 : -7.3] [t1: 0.00 t2 0.00 : 0.2] A: [n 1074 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-16 : -7.7] [t1: 0.00 t2 0.00 : 0.2] A: [n 1074 real 1] B: [sp:0 nrhs 1 real 0] [e1: 7e-18 : -13.0] [t1: 0.00 t2 0.00 : 0.1] A: [n 1074 real 1] B: [sp:0 nrhs 9 real 0] [e1: 6e-16 : -6.8] [t1: 0.00 t2 0.00 : 0.4] A: [n 1074 real 1] B: [sp:1 nrhs 1 real 1] [e1: 6e-17 : -6.1] [t1: 0.00 t2 0.00 : 0.1] A: [n 1074 real 1] B: [sp:1 nrhs 4 real 1] [e1: 6e-17 : -6.6] [t1: 0.00 t2 0.00 : 0.1] A: [n 1074 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-16 : -6.1] [t1: 0.00 t2 0.00 : 0.1] A: [n 1074 real 1] B: [sp:1 nrhs 1 real 0] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1] A: [n 1074 real 1] B: [sp:1 nrhs 9 real 0] [e1: 4e-16 : -4.6] [t1: 0.00 t2 0.00 : 0.1] nn = 31 Prob = title: 'SYMMETRIC STIFFNESS MATRIX, SQUARE PLATE CLAMPED' A: [1083x1083 double] name: 'HB/bcsstk09' id: 31 date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 1083 real 1] B: [sp:0 nrhs 1 real 1] [e1: 1e-10 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 1083 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e-10 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 1083 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e-10 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 1083 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-10 : 0.0] [t1: 0.01 t2 0.11 : 0.1] A: [n 1083 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-10 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 1083 real 1] B: [sp:1 nrhs 1 real 1] [e1: 5e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 1083 real 1] B: [sp:1 nrhs 4 real 1] [e1: 5e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 1083 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-11 : 0.0] [t1: 0.01 t2 0.11 : 0.1] A: [n 1083 real 1] B: [sp:1 nrhs 1 real 0] [e1: 9e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0] A: [n 1083 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-11 : 0.0] [t1: 0.02 t2 0.02 : 1.0] A: [n 1083 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-13 : 0.0] [t1: 0.13 t2 0.03 : 4.6] A: [n 1083 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-13 : 0.0] [t1: 0.04 t2 0.14 : 0.3] A: [n 1083 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-13 : 0.0] [t1: 0.04 t2 0.14 : 0.3] A: [n 1083 real 0] B: [sp:0 nrhs 1 real 0] [e1: 3e-13 : 0.0] [t1: 0.03 t2 0.03 : 1.0] A: [n 1083 real 0] B: [sp:0 nrhs 9 real 0] [e1: 4e-13 : 0.0] [t1: 0.14 t2 0.04 : 3.3] A: [n 1083 real 0] B: [sp:1 nrhs 1 real 1] [e1: 3e-14 : 0.0] [t1: 0.03 t2 0.13 : 0.2] A: [n 1083 real 0] B: [sp:1 nrhs 4 real 1] [e1: 5e-14 : 0.0] [t1: 0.04 t2 0.14 : 0.3] A: [n 1083 real 0] B: [sp:1 nrhs 9 real 1] [e1: 5e-14 : 0.0] [t1: 0.05 t2 0.15 : 0.4] A: [n 1083 real 0] B: [sp:1 nrhs 1 real 0] [e1: 8e-14 : 0.0] [t1: 0.03 t2 0.03 : 1.0] A: [n 1083 real 0] B: [sp:1 nrhs 9 real 0] [e1: 1e-13 : 0.0] [t1: 0.16 t2 0.05 : 2.9] nn = 64 Prob = title: 'SYMMETRIC MASS MATRIX, SQUARE PLATE CLAMPED' A: [1083x1083 double] name: 'HB/bcsstm09' id: 64 date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' A: [n 1083 real 1] B: [sp:0 nrhs 1 real 1] [e1: 7e-15 : -3.4] [t1: 0.00 t2 0.00 : 0.2] A: [n 1083 real 1] B: [sp:0 nrhs 4 real 1] [e1: 8e-15 : -3.2] [t1: 0.00 t2 0.00 : 0.2] A: [n 1083 real 1] B: [sp:0 nrhs 9 real 1] [e1: 9e-15 : -3.1] [t1: 0.00 t2 0.00 : 0.2] A: [n 1083 real 1] B: [sp:0 nrhs 1 real 0] [e1: 1e-14 : -3.1] [t1: 0.00 t2 0.00 : 0.1] A: [n 1083 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-14 : -2.9] [t1: 0.00 t2 0.00 : 0.3] A: [n 1083 real 1] B: [sp:1 nrhs 1 real 1] [e1: 7e-16 : -4.3] [t1: 0.00 t2 0.00 : 0.1] A: [n 1083 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-15 : -3.7] [t1: 0.00 t2 0.00 : 0.1] A: [n 1083 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-15 : -3.0] [t1: 0.00 t2 0.00 : 0.1] A: [n 1083 real 1] B: [sp:1 nrhs 1 real 0] [e1: 8e-16 : -4.8] [t1: 0.00 t2 0.00 : 0.1] A: [n 1083 real 1] B: [sp:1 nrhs 9 real 0] [e1: 3e-15 : -3.6] [t1: 0.00 t2 0.00 : 0.1] A: [n 1083 real 1] B: [sp:0 nrhs 1 real 1] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1] A: [n 1083 real 1] B: [sp:0 nrhs 4 real 1] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1] A: [n 1083 real 1] B: [sp:0 nrhs 9 real 1] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.2] A: [n 1083 real 1] B: [sp:0 nrhs 1 real 0] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1] A: [n 1083 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-16 : -10.4] [t1: 0.00 t2 0.00 : 0.3] A: [n 1083 real 1] B: [sp:1 nrhs 1 real 1] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1] A: [n 1083 real 1] B: [sp:1 nrhs 4 real 1] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1] A: [n 1083 real 1] B: [sp:1 nrhs 9 real 1] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1] A: [n 1083 real 1] B: [sp:1 nrhs 1 real 0] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1] A: [n 1083 real 1] B: [sp:1 nrhs 9 real 0] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1] ================================================================= test11 : compare CHOLMOD and MATLAB, save results in Results.mat test matrices sorted by dimension: 1440: Oberwolfach LFAT5 14 1 1438: Oberwolfach LF10 18 1 436: FIDAP ex5 27 1 23: HB bcsstk01 48 1 872: Pothen mesh1e1 48 1 873: Pothen mesh1em1 48 1 874: Pothen mesh1em6 48 1 24: HB bcsstk02 66 1 57: HB bcsstm02 66 1 220: HB nos4 100 1 25: HB bcsstk03 112 1 1506: Pajek Journals 124 1 26: HB bcsstk04 132 1 44: HB bcsstk22 138 1 72: HB bcsstm22 138 1 206: HB lund_a 147 1 207: HB lund_b 147 1 27: HB bcsstk05 153 1 60: HB bcsstm05 153 1 217: HB nos1 237 1 877: Pothen mesh3e1 289 1 878: Pothen mesh3em5 289 1 875: Pothen mesh2e1 306 1 876: Pothen mesh2em5 306 1 229: HB plat362 362 1 315: Bai mhdb416 416 1 28: HB bcsstk06 420 1 29: HB bcsstk07 420 1 61: HB bcsstm06 420 1 62: HB bcsstm07 420 1 221: HB nos5 468 1 42: HB bcsstk20 485 1 70: HB bcsstm20 485 1 2: HB 494_bus 494 1 339: Boeing bcsstk34 588 1 3: HB 662_bus 662 1 222: HB nos6 675 1 4: HB 685_bus 685 1 357: Boeing msc00726 726 1 223: HB nos7 729 1 41: HB bcsstk19 817 1 69: HB bcsstm19 817 1 159: HB gr_30_30 900 1 218: HB nos2 957 1 219: HB nos3 960 1 358: Boeing msc01050 1050 1 30: HB bcsstk08 1074 1 63: HB bcsstm08 1074 1 31: HB bcsstk09 1083 1 64: HB bcsstm09 1083 1 1440: Oberwolfach/LFAT5 n 14 lnz 33 fl 91 cholmod2: t: 0.00003 e: 6.4e-14 mflop 3 matlab: t: 0.00003 e: 4.3e-14 mflop 3 cholmod2 speedup: 1.1 1438: Oberwolfach/LF10 n 18 lnz 58 fl 198 cholmod2: t: 0.00003 e: 1.8e-12 mflop 6 matlab: t: 0.00002 e: 1.1e-12 mflop 9 cholmod2 speedup: 0.6 436: FIDAP/ex5 n 27 lnz 153 fl 981 cholmod2: t: 0.00009 e: 3.5e-08 mflop 11 matlab: t: 0.00012 e: 3.5e-08 mflop 8 cholmod2 speedup: 1.3 23: HB/bcsstk01 n 48 lnz 489 fl 6009 cholmod2: t: 0.00027 e: 1.2e-12 mflop 22 matlab: t: 0.00023 e: 1.2e-12 mflop 26 cholmod2 speedup: 0.8 872: Pothen/mesh1e1 n 48 lnz 336 fl 2678 cholmod2: t: 0.00011 e: 4.1e-15 mflop 25 matlab: t: 0.00009 e: 4.1e-15 mflop 28 cholmod2 speedup: 0.9 873: Pothen/mesh1em1 n 48 lnz 336 fl 2678 cholmod2: t: 0.00021 e: 5.7e-15 mflop 13 matlab: t: 0.00018 e: 5.7e-15 mflop 15 cholmod2 speedup: 0.8 874: Pothen/mesh1em6 n 48 lnz 336 fl 2678 cholmod2: t: 0.00023 e: 2.5e-15 mflop 12 matlab: t: 0.00019 e: 2.5e-15 mflop 14 cholmod2 speedup: 0.8 24: HB/bcsstk02 n 66 lnz 2211 fl 98021 cholmod2: t: 0.00071 e: 5.7e-12 mflop 138 matlab: t: 0.00032 e: 5.7e-12 mflop 302 cholmod2 speedup: 0.5 57: HB/bcsstm02 n 66 lnz 66 fl 66 cholmod2: t: 0.00004 e: 3.3e-15 mflop 2 matlab: t: 0.00001 e: 2.5e-16 mflop 7 cholmod2 speedup: 0.2 220: HB/nos4 n 100 lnz 632 fl 4438 cholmod2: t: 0.00040 e: 1.3e-12 mflop 11 matlab: t: 0.00037 e: 1.3e-12 mflop 12 cholmod2 speedup: 0.9 25: HB/bcsstk03 n 112 lnz 384 fl 1360 cholmod2: t: 0.00027 e: 2.4e-11 mflop 5 matlab: t: 0.00021 e: 2.4e-11 mflop 7 cholmod2 speedup: 0.8 1506: Pajek/Journals n 124 lnz 6990 fl 505314 cholmod2: t: 0.00131 e: 4.2e-14 mflop 386 matlab: t: 0.00087 e: 4.1e-14 mflop 580 cholmod2 speedup: 0.7 26: HB/bcsstk04 n 132 lnz 3293 fl 90567 cholmod2: t: 0.00092 e: 1.5e-11 mflop 98 matlab: t: 0.00132 e: 1.5e-11 mflop 68 cholmod2 speedup: 1.4 44: HB/bcsstk22 n 138 lnz 680 fl 4224 cholmod2: t: 0.00040 e: 8.2e-12 mflop 10 matlab: t: 0.00037 e: 8.2e-12 mflop 11 cholmod2 speedup: 0.9 72: HB/bcsstm22 n 138 lnz 138 fl 138 cholmod2: t: 0.00013 e: 5.4e-15 mflop 1 matlab: t: 0.00002 e: 1.1e-15 mflop 7 cholmod2 speedup: 0.1 206: HB/lund_a n 147 lnz 2339 fl 42287 cholmod2: t: 0.00040 e: 3.4e-10 mflop 105 matlab: t: 0.00041 e: 3.4e-10 mflop 104 cholmod2 speedup: 1.0 207: HB/lund_b n 147 lnz 2340 fl 42320 cholmod2: t: 0.00066 e: 1.4e-12 mflop 65 matlab: t: 0.00076 e: 1.4e-12 mflop 56 cholmod2 speedup: 1.2 27: HB/bcsstk05 n 153 lnz 2326 fl 39118 cholmod2: t: 0.00091 e: 9.7e-12 mflop 43 matlab: t: 0.00090 e: 9.7e-12 mflop 44 cholmod2 speedup: 1.0 60: HB/bcsstm05 n 153 lnz 153 fl 153 cholmod2: t: 0.00015 e: 7.8e-15 mflop 1 matlab: t: 0.00002 e: 1.3e-15 mflop 7 cholmod2 speedup: 0.1 217: HB/nos1 n 237 lnz 704 fl 2254 cholmod2: t: 0.00020 e: 4.0e-09 mflop 11 matlab: t: 0.00018 e: 4.0e-09 mflop 12 cholmod2 speedup: 0.9 877: Pothen/mesh3e1 n 289 lnz 2433 fl 27549 cholmod2: t: 0.00077 e: 2.8e-14 mflop 36 matlab: t: 0.00096 e: 2.8e-14 mflop 29 cholmod2 speedup: 1.3 878: Pothen/mesh3em5 n 289 lnz 2433 fl 27549 cholmod2: t: 0.00108 e: 2.6e-14 mflop 25 matlab: t: 0.00096 e: 2.6e-14 mflop 29 cholmod2 speedup: 0.9 875: Pothen/mesh2e1 n 306 lnz 3224 fl 43648 cholmod2: t: 0.00148 e: 1.5e-13 mflop 29 matlab: t: 0.00124 e: 1.5e-13 mflop 35 cholmod2 speedup: 0.8 876: Pothen/mesh2em5 n 306 lnz 3224 fl 43648 cholmod2: t: 0.00068 e: 4.9e-14 mflop 65 matlab: t: 0.00062 e: 4.9e-14 mflop 70 cholmod2 speedup: 0.9 229: HB/plat362 n 362 lnz 8060 fl 220156 cholmod2: t: 0.00242 e: 2.1e-05 mflop 91 matlab: t: 0.00298 e: 2.1e-05 mflop 74 cholmod2 speedup: 1.2 315: Bai/mhdb416 n 416 lnz 1364 fl 4998 cholmod2: t: 0.00076 e: 2.0e-12 mflop 7 matlab: t: 0.00081 e: 2.0e-12 mflop 6 cholmod2 speedup: 1.1 28: HB/bcsstk06 n 420 lnz 11345 fl 400973 cholmod2: t: 0.00396 e: 1.9e-10 mflop 101 matlab: t: 0.00423 e: 1.9e-10 mflop 95 cholmod2 speedup: 1.1 29: HB/bcsstk07 n 420 lnz 11345 fl 400973 cholmod2: t: 0.00200 e: 1.9e-10 mflop 201 matlab: t: 0.00211 e: 1.9e-10 mflop 190 cholmod2 speedup: 1.1 61: HB/bcsstm06 n 420 lnz 420 fl 420 cholmod2: t: 0.00027 e: 2.1e-14 mflop 2 matlab: t: 0.00003 e: 3.0e-15 mflop 14 cholmod2 speedup: 0.1 62: HB/bcsstm07 n 420 lnz 10654 fl 353996 cholmod2: t: 0.00375 e: 5.7e-13 mflop 94 matlab: t: 0.00392 e: 5.7e-13 mflop 90 cholmod2 speedup: 1.0 221: HB/nos5 n 468 lnz 18437 fl 1.07298e+06 cholmod2: t: 0.00672 e: 9.8e-12 mflop 160 matlab: t: 0.00647 e: 9.8e-12 mflop 166 cholmod2 speedup: 1.0 42: HB/bcsstk20 n 485 lnz 2336 fl 13864 cholmod2: t: 0.00056 e: 5.6e-06 mflop 25 matlab: t: 0.00053 e: 5.6e-06 mflop 26 cholmod2 speedup: 0.9 70: HB/bcsstm20 n 485 lnz 485 fl 485 cholmod2: t: 0.00034 e: 2.7e-14 mflop 1 matlab: t: 0.00004 e: 5.7e-15 mflop 13 cholmod2 speedup: 0.1 2: HB/494_bus n 494 lnz 1414 fl 4812 cholmod2: t: 0.00105 e: 8.0e-10 mflop 5 matlab: t: 0.00098 e: 8.0e-10 mflop 5 cholmod2 speedup: 0.9 339: Boeing/bcsstk34 n 588 lnz 43366 fl 3.91893e+06 cholmod2: t: 0.01322 e: 1.1e-12 mflop 296 matlab: t: 0.01341 e: 1.1e-12 mflop 292 cholmod2 speedup: 1.0 3: HB/662_bus n 662 lnz 2549 fl 12937 cholmod2: t: 0.00185 e: 9.6e-10 mflop 7 matlab: t: 0.00156 e: 9.6e-10 mflop 8 cholmod2 speedup: 0.8 222: HB/nos6 n 675 lnz 6453 fl 85577 cholmod2: t: 0.00129 e: 2.7e-08 mflop 66 matlab: t: 0.00117 e: 2.7e-08 mflop 73 cholmod2 speedup: 0.9 4: HB/685_bus n 685 lnz 3650 fl 25150 cholmod2: t: 0.00158 e: 1.6e-10 mflop 16 matlab: t: 0.00200 e: 1.6e-10 mflop 13 cholmod2 speedup: 1.3 357: Boeing/msc00726 n 726 lnz 110707 fl 2.31244e+07 cholmod2: t: 0.02436 e: 1.8e-11 mflop 949 matlab: t: 0.03762 e: 1.8e-11 mflop 615 cholmod2 speedup: 1.5 223: HB/nos7 n 729 lnz 18945 fl 1.0875e+06 cholmod2: t: 0.00748 e: 2.5e-06 mflop 145 matlab: t: 0.00720 e: 2.5e-06 mflop 151 cholmod2 speedup: 1.0 41: HB/bcsstk19 n 817 lnz 7528 fl 77096 cholmod2: t: 0.00342 e: 6.7e-06 mflop 23 matlab: t: 0.00297 e: 6.7e-06 mflop 26 cholmod2 speedup: 0.9 69: HB/bcsstm19 n 817 lnz 817 fl 817 cholmod2: t: 0.00030 e: 3.8e-14 mflop 3 matlab: t: 0.00003 e: 6.0e-15 mflop 31 cholmod2 speedup: 0.1 159: HB/gr_30_30 n 900 lnz 16348 fl 405796 cholmod2: t: 0.00557 e: 8.7e-12 mflop 73 matlab: t: 0.00560 e: 8.7e-12 mflop 73 cholmod2 speedup: 1.0 218: HB/nos2 n 957 lnz 2864 fl 9214 cholmod2: t: 0.00152 e: 4.4e-06 mflop 6 matlab: t: 0.00144 e: 4.4e-06 mflop 6 cholmod2 speedup: 0.9 219: HB/nos3 n 960 lnz 31314 fl 1.38676e+06 cholmod2: t: 0.00953 e: 4.3e-10 mflop 145 matlab: t: 0.00984 e: 4.3e-10 mflop 141 cholmod2 speedup: 1.0 358: Boeing/msc01050 n 1050 lnz 28305 fl 1.01711e+06 cholmod2: t: 0.00768 e: 1.1e+00 mflop 133 matlab: t: 0.00809 e: 1.1e+00 mflop 126 cholmod2 speedup: 1.1 30: HB/bcsstk08 n 1074 lnz 31153 fl 1.80924e+06 cholmod2: t: 0.01337 e: 4.5e-11 mflop 135 matlab: t: 0.01572 e: 4.5e-11 mflop 115 cholmod2 speedup: 1.2 63: HB/bcsstm08 n 1074 lnz 1074 fl 1074 cholmod2: t: 0.00086 e: 3.6e-14 mflop 1 matlab: t: 0.00005 e: 4.4e-15 mflop 22 cholmod2 speedup: 0.1 31: HB/bcsstk09 n 1083 lnz 58416 fl 4.50027e+06 cholmod2: t: 0.01767 e: 1.3e-10 mflop 255 matlab: t: 0.01763 e: 1.3e-10 mflop 255 cholmod2 speedup: 1.0 64: HB/bcsstm09 n 1083 lnz 1083 fl 1083 cholmod2: t: 0.00040 e: 8.1e-14 mflop 3 matlab: t: 0.00003 e: 8.2e-15 mflop 34 cholmod2 speedup: 0.1 test11 passed ================================================================= test12: test etree2 and compare with etree Matrices to test: 50 904: vanHeukelum/cage3 nrow: 5 ncol: 5 nnz: 19 etree(A,'col'): 0.0004 0.0003 speedup 1.36 etree(A,'row'): 0.0003 0.0003 speedup 1.12 etree(A): 0.0003 0.0003 speedup 1.24 etree(A'): 0.0003 0.0003 speedup 0.96 after amd: etree(A): 0.0002 0.0000 speedup 10.05 etree(A'): 0.0001 0.0000 speedup 5.48 449: Grund/b1_ss nrow: 7 ncol: 7 nnz: 15 etree(A,'col'): 0.0001 0.0000 speedup 7.28 etree(A,'row'): 0.0001 0.0000 speedup 3.83 etree(A): 0.0001 0.0000 speedup 8.14 etree(A'): 0.0001 0.0000 speedup 5.74 after amd: etree(A): 0.0001 0.0000 speedup 7.71 etree(A'): 0.0001 0.0000 speedup 6.41 1710: Meszaros/farm nrow: 7 ncol: 17 nnz: 41 etree(A,'col'): 0.0002 0.0000 speedup 7.70 etree(A,'row'): 0.0001 0.0000 speedup 3.93 715: LPnetlib/lpi_galenet nrow: 8 ncol: 14 nnz: 22 etree(A,'col'): 0.0001 0.0000 speedup 6.39 etree(A,'row'): 0.0001 0.0000 speedup 5.57 1817: Meszaros/kleemin nrow: 8 ncol: 16 nnz: 44 etree(A,'col'): 0.0001 0.0000 speedup 5.80 etree(A,'row'): 0.0001 0.0000 speedup 5.45 185: HB/jgl009 nrow: 9 ncol: 9 nnz: 50 etree(A,'col'): 0.0001 0.0000 speedup 6.39 etree(A,'row'): 0.0001 0.0000 speedup 4.07 etree(A): 0.0001 0.0000 speedup 7.47 etree(A'): 0.0001 0.0000 speedup 5.45 after amd: etree(A): 0.0001 0.0000 speedup 7.93 etree(A'): 0.0001 0.0000 speedup 6.06 719: LPnetlib/lpi_itest2 nrow: 9 ncol: 13 nnz: 26 etree(A,'col'): 0.0001 0.0000 speedup 6.05 etree(A,'row'): 0.0001 0.0000 speedup 5.60 905: vanHeukelum/cage4 nrow: 9 ncol: 9 nnz: 49 etree(A,'col'): 0.0001 0.0000 speedup 6.11 etree(A,'row'): 0.0001 0.0000 speedup 5.36 etree(A): 0.0001 0.0000 speedup 7.79 etree(A'): 0.0001 0.0000 speedup 5.50 after amd: etree(A): 0.0001 0.0000 speedup 7.79 etree(A'): 0.0001 0.0000 speedup 8.11 238: HB/rgg010 nrow: 10 ncol: 10 nnz: 76 etree(A,'col'): 0.0001 0.0000 speedup 6.37 etree(A,'row'): 0.0001 0.0000 speedup 5.55 etree(A): 0.0001 0.0000 speedup 5.10 etree(A'): 0.0001 0.0000 speedup 5.14 after amd: etree(A): 0.0001 0.0000 speedup 7.79 etree(A'): 0.0001 0.0000 speedup 5.63 1524: Pajek/Stranke94 nrow: 10 ncol: 10 nnz: 90 etree(A,'col'): 0.0001 0.0000 speedup 6.21 etree(A,'row'): 0.0001 0.0000 speedup 3.97 etree(A): 0.0001 0.0000 speedup 7.53 etree(A'): 0.0001 0.0000 speedup 5.43 after amd: etree(A): 0.0001 0.0000 speedup 7.36 etree(A'): 0.0001 0.0000 speedup 5.58 186: HB/jgl011 nrow: 11 ncol: 11 nnz: 76 etree(A,'col'): 0.0001 0.0000 speedup 6.21 etree(A,'row'): 0.0001 0.0000 speedup 5.55 etree(A): 0.0001 0.0000 speedup 7.40 etree(A'): 0.0001 0.0000 speedup 4.00 after amd: etree(A): 0.0001 0.0000 speedup 7.64 etree(A'): 0.0001 0.0000 speedup 4.42 720: LPnetlib/lpi_itest6 nrow: 11 ncol: 17 nnz: 29 etree(A,'col'): 0.0001 0.0000 speedup 6.11 etree(A,'row'): 0.0001 0.0000 speedup 5.48 1525: Pajek/Tina_AskCal nrow: 11 ncol: 11 nnz: 29 etree(A,'col'): 0.0001 0.0000 speedup 6.11 etree(A,'row'): 0.0001 0.0000 speedup 5.62 etree(A): 0.0001 0.0000 speedup 7.33 etree(A'): 0.0001 0.0000 speedup 5.53 after amd: etree(A): 0.0001 0.0000 speedup 7.79 etree(A'): 0.0001 0.0000 speedup 5.72 1526: Pajek/Tina_AskCog nrow: 11 ncol: 11 nnz: 36 etree(A,'col'): 0.0001 0.0000 speedup 6.60 etree(A,'row'): 0.0001 0.0000 speedup 5.27 etree(A): 0.0001 0.0000 speedup 7.67 etree(A'): 0.0001 0.0000 speedup 5.70 after amd: etree(A): 0.0001 0.0000 speedup 7.64 etree(A'): 0.0001 0.0000 speedup 5.79 1527: Pajek/Tina_DisCal nrow: 11 ncol: 11 nnz: 41 etree(A,'col'): 0.0001 0.0000 speedup 6.50 etree(A,'row'): 0.0001 0.0000 speedup 5.62 etree(A): 0.0001 0.0000 speedup 7.00 etree(A'): 0.0001 0.0000 speedup 4.28 after amd: etree(A): 0.0001 0.0000 speedup 7.86 etree(A'): 0.0001 0.0000 speedup 4.42 1528: Pajek/Tina_DisCog nrow: 11 ncol: 11 nnz: 48 etree(A,'col'): 0.0001 0.0000 speedup 6.11 etree(A,'row'): 0.0001 0.0000 speedup 4.91 etree(A): 0.0001 0.0000 speedup 9.87 etree(A'): 0.0001 0.0000 speedup 5.00 after amd: etree(A): 0.0001 0.0000 speedup 8.31 etree(A'): 0.0001 0.0000 speedup 5.67 1755: Meszaros/problem nrow: 12 ncol: 46 nnz: 86 etree(A,'col'): 0.0001 0.0000 speedup 5.30 etree(A,'row'): 0.0001 0.0000 speedup 5.17 1440: Oberwolfach/LFAT5 nrow: 14 ncol: 14 nnz: 46 etree(A,'col'): 0.0001 0.0000 speedup 6.39 etree(A,'row'): 0.0001 0.0000 speedup 5.29 etree(A): 0.0002 0.0000 speedup 15.20 etree(A'): 0.0001 0.0000 speedup 5.48 after amd: etree(A): 0.0001 0.0000 speedup 5.10 etree(A'): 0.0001 0.0000 speedup 6.11 1741: Meszaros/p0033 nrow: 15 ncol: 48 nnz: 113 etree(A,'col'): 0.0001 0.0000 speedup 5.43 etree(A,'row'): 0.0001 0.0000 speedup 3.87 1438: Oberwolfach/LF10 nrow: 18 ncol: 18 nnz: 82 etree(A,'col'): 0.0001 0.0000 speedup 6.00 etree(A,'row'): 0.0001 0.0000 speedup 4.88 etree(A): 0.0001 0.0000 speedup 7.73 etree(A'): 0.0001 0.0000 speedup 4.95 after amd: etree(A): 0.0001 0.0000 speedup 5.75 etree(A'): 0.0001 0.0000 speedup 5.14 1479: Pajek/GD01_b nrow: 18 ncol: 18 nnz: 37 etree(A,'col'): 0.0001 0.0000 speedup 5.80 etree(A,'row'): 0.0001 0.0000 speedup 5.18 etree(A): 0.0001 0.0000 speedup 7.47 etree(A'): 0.0001 0.0000 speedup 5.33 after amd: etree(A): 0.0001 0.0000 speedup 7.27 etree(A'): 0.0002 0.0000 speedup 9.05 706: LPnetlib/lpi_bgprtr nrow: 20 ncol: 40 nnz: 70 etree(A,'col'): 0.0001 0.0000 speedup 5.48 etree(A,'row'): 0.0001 0.0000 speedup 5.21 1481: Pajek/GD02_a nrow: 23 ncol: 23 nnz: 87 etree(A,'col'): 0.0001 0.0000 speedup 5.71 etree(A,'row'): 0.0001 0.0000 speedup 5.12 etree(A): 0.0001 0.0000 speedup 7.56 etree(A'): 0.0001 0.0000 speedup 5.23 after amd: etree(A): 0.0001 0.0000 speedup 7.47 etree(A'): 0.0001 0.0000 speedup 5.70 1516: Pajek/Ragusa18 nrow: 23 ncol: 23 nnz: 64 etree(A,'col'): 0.0001 0.0000 speedup 6.00 etree(A,'row'): 0.0001 0.0000 speedup 5.12 etree(A): 0.0001 0.0000 speedup 4.70 etree(A'): 0.0001 0.0000 speedup 5.27 after amd: etree(A): 0.0001 0.0000 speedup 7.27 etree(A'): 0.0001 0.0000 speedup 5.60 1742: Meszaros/p0040 nrow: 23 ncol: 63 nnz: 133 etree(A,'col'): 0.0001 0.0000 speedup 5.39 etree(A,'row'): 0.0001 0.0000 speedup 3.94 97: HB/can_24 nrow: 24 ncol: 24 nnz: 160 etree(A,'col'): 0.0001 0.0000 speedup 6.10 etree(A,'row'): 0.0001 0.0000 speedup 3.72 etree(A): 0.0001 0.0000 speedup 6.88 etree(A'): 0.0001 0.0000 speedup 5.13 after amd: etree(A): 0.0001 0.0000 speedup 7.06 etree(A'): 0.0001 0.0000 speedup 5.24 624: LPnetlib/lp_fit1d nrow: 24 ncol: 1049 nnz: 13427 etree(A,'col'): 0.0004 0.0002 speedup 2.25 etree(A,'row'): 0.0008 0.0002 speedup 3.34 1515: Pajek/Ragusa16 nrow: 24 ncol: 24 nnz: 81 etree(A,'col'): 0.0001 0.0000 speedup 5.71 etree(A,'row'): 0.0001 0.0000 speedup 5.08 etree(A): 0.0001 0.0000 speedup 4.95 etree(A'): 0.0001 0.0000 speedup 4.96 after amd: etree(A): 0.0001 0.0000 speedup 7.60 etree(A'): 0.0001 0.0000 speedup 5.60 626: LPnetlib/lp_fit2d nrow: 25 ncol: 10524 nnz: 129042 etree(A,'col'): 0.0056 0.0020 speedup 2.74 etree(A,'row'): 0.0107 0.0032 speedup 3.33 1177: HB/lap_25 nrow: 25 ncol: 25 nnz: 169 etree(A,'col'): 0.0001 0.0000 speedup 5.76 etree(A,'row'): 0.0001 0.0000 speedup 3.53 etree(A): 0.0001 0.0000 speedup 7.44 etree(A'): 0.0001 0.0000 speedup 5.18 after amd: etree(A): 0.0001 0.0000 speedup 7.93 etree(A'): 0.0001 0.0000 speedup 5.19 436: FIDAP/ex5 nrow: 27 ncol: 27 nnz: 279 etree(A,'col'): 0.0001 0.0000 speedup 5.59 etree(A,'row'): 0.0001 0.0000 speedup 5.04 etree(A): 0.0001 0.0000 speedup 6.59 etree(A'): 0.0001 0.0000 speedup 4.88 after amd: etree(A): 0.0001 0.0000 speedup 6.59 etree(A'): 0.0001 0.0000 speedup 5.45 597: LPnetlib/lp_afiro nrow: 27 ncol: 51 nnz: 102 etree(A,'col'): 0.0001 0.0000 speedup 5.21 etree(A,'row'): 0.0002 0.0000 speedup 6.27 1759: Meszaros/refine nrow: 29 ncol: 62 nnz: 153 etree(A,'col'): 0.0001 0.0000 speedup 4.96 etree(A,'row'): 0.0001 0.0000 speedup 5.08 232: HB/pores_1 nrow: 30 ncol: 30 nnz: 180 etree(A,'col'): 0.0001 0.0000 speedup 5.76 etree(A,'row'): 0.0001 0.0000 speedup 5.04 etree(A): 0.0001 0.0000 speedup 6.82 etree(A'): 0.0001 0.0000 speedup 5.35 after amd: etree(A): 0.0001 0.0000 speedup 7.06 etree(A'): 0.0001 0.0000 speedup 4.11 168: HB/ibm32 nrow: 32 ncol: 32 nnz: 126 etree(A,'col'): 0.0001 0.0000 speedup 5.76 etree(A,'row'): 0.0001 0.0000 speedup 4.58 etree(A): 0.0001 0.0000 speedup 6.82 etree(A'): 0.0001 0.0000 speedup 5.23 after amd: etree(A): 0.0001 0.0000 speedup 7.33 etree(A'): 0.0001 0.0000 speedup 5.29 1199: Hamrle/Hamrle1 nrow: 32 ncol: 32 nnz: 98 etree(A,'col'): 0.0001 0.0000 speedup 5.71 etree(A,'row'): 0.0001 0.0000 speedup 5.17 etree(A): 0.0001 0.0000 speedup 6.88 etree(A'): 0.0001 0.0000 speedup 5.00 after amd: etree(A): 0.0001 0.0000 speedup 6.41 etree(A'): 0.0001 0.0000 speedup 5.65 1480: Pajek/GD01_c nrow: 33 ncol: 33 nnz: 135 etree(A,'col'): 0.0001 0.0000 speedup 5.81 etree(A,'row'): 0.0001 0.0000 speedup 4.70 etree(A): 0.0001 0.0000 speedup 6.44 etree(A'): 0.0001 0.0000 speedup 5.05 after amd: etree(A): 0.0001 0.0000 speedup 7.06 etree(A'): 0.0001 0.0000 speedup 3.93 731: LPnetlib/lpi_woodinfe nrow: 35 ncol: 89 nnz: 140 etree(A,'col'): 0.0001 0.0000 speedup 5.00 etree(A,'row'): 0.0001 0.0000 speedup 5.12 1474: Pajek/football nrow: 35 ncol: 35 nnz: 118 etree(A,'col'): 0.0001 0.0000 speedup 5.68 etree(A,'row'): 0.0001 0.0000 speedup 4.74 etree(A): 0.0001 0.0000 speedup 6.21 etree(A'): 0.0001 0.0000 speedup 5.16 after amd: etree(A): 0.0001 0.0000 speedup 6.33 etree(A'): 0.0001 0.0000 speedup 4.15 1485: Pajek/GD95_a nrow: 36 ncol: 36 nnz: 57 etree(A,'col'): 0.0001 0.0000 speedup 5.50 etree(A,'row'): 0.0001 0.0000 speedup 5.00 etree(A): 0.0001 0.0000 speedup 6.33 etree(A'): 0.0001 0.0000 speedup 4.83 after amd: etree(A): 0.0001 0.0000 speedup 6.53 etree(A'): 0.0001 0.0000 speedup 4.04 906: vanHeukelum/cage5 nrow: 37 ncol: 37 nnz: 233 etree(A,'col'): 0.0001 0.0000 speedup 5.25 etree(A,'row'): 0.0001 0.0000 speedup 4.78 etree(A): 0.0001 0.0000 speedup 6.00 etree(A'): 0.0001 0.0000 speedup 4.73 after amd: etree(A): 0.0001 0.0000 speedup 6.65 etree(A'): 0.0001 0.0000 speedup 5.00 1495: Pajek/GD98_a nrow: 38 ncol: 38 nnz: 50 etree(A,'col'): 0.0001 0.0000 speedup 5.45 etree(A,'row'): 0.0001 0.0000 speedup 4.88 etree(A): 0.0001 0.0000 speedup 6.44 etree(A'): 0.0001 0.0000 speedup 5.04 after amd: etree(A): 0.0001 0.0000 speedup 6.71 etree(A'): 0.0001 0.0000 speedup 5.48 13: HB/bcspwr01 nrow: 39 ncol: 39 nnz: 131 etree(A,'col'): 0.0001 0.0000 speedup 5.25 etree(A,'row'): 0.0001 0.0000 speedup 4.89 etree(A): 0.0001 0.0000 speedup 6.26 etree(A'): 0.0001 0.0000 speedup 3.80 after amd: etree(A): 0.0001 0.0000 speedup 6.53 etree(A'): 0.0001 0.0000 speedup 5.17 636: LPnetlib/lp_kb2 nrow: 43 ncol: 68 nnz: 313 etree(A,'col'): 0.0001 0.0000 speedup 4.67 etree(A,'row'): 0.0001 0.0000 speedup 3.39 1493: Pajek/GD97_b nrow: 47 ncol: 47 nnz: 264 etree(A,'col'): 0.0001 0.0000 speedup 5.08 etree(A,'row'): 0.0001 0.0000 speedup 4.13 etree(A): 0.0001 0.0000 speedup 6.32 etree(A'): 0.0001 0.0000 speedup 4.58 after amd: etree(A): 0.0001 0.0000 speedup 6.11 etree(A'): 0.0002 0.0000 speedup 6.08 23: HB/bcsstk01 nrow: 48 ncol: 48 nnz: 400 etree(A,'col'): 0.0001 0.0000 speedup 4.92 etree(A,'row'): 0.0001 0.0000 speedup 4.28 etree(A): 0.0001 0.0000 speedup 5.86 etree(A'): 0.0001 0.0000 speedup 4.54 after amd: etree(A): 0.0001 0.0000 speedup 5.33 etree(A'): 0.0001 0.0000 speedup 4.70 56: HB/bcsstm01 nrow: 48 ncol: 48 nnz: 24 etree(A,'col'): 0.0001 0.0000 speedup 5.86 etree(A,'row'): 0.0001 0.0000 speedup 5.17 etree(A): 0.0001 0.0000 speedup 4.58 etree(A'): 0.0001 0.0000 speedup 5.32 after amd: etree(A): 0.0001 0.0000 speedup 5.15 etree(A'): 0.0001 0.0000 speedup 5.48 872: Pothen/mesh1e1 nrow: 48 ncol: 48 nnz: 306 etree(A,'col'): 0.0001 0.0000 speedup 5.12 etree(A,'row'): 0.0001 0.0000 speedup 3.51 etree(A): 0.0001 0.0000 speedup 5.81 etree(A'): 0.0002 0.0000 speedup 5.67 after amd: etree(A): 0.0001 0.0000 speedup 5.95 etree(A'): 0.0001 0.0000 speedup 5.04 873: Pothen/mesh1em1 nrow: 48 ncol: 48 nnz: 306 etree(A,'col'): 0.0001 0.0000 speedup 4.88 etree(A,'row'): 0.0001 0.0000 speedup 4.63 etree(A): 0.0001 0.0000 speedup 6.00 etree(A'): 0.0001 0.0000 speedup 3.67 after amd: etree(A): 0.0001 0.0000 speedup 6.53 etree(A'): 0.0001 0.0000 speedup 5.12 874: Pothen/mesh1em6 nrow: 48 ncol: 48 nnz: 306 etree(A,'col'): 0.0001 0.0000 speedup 5.16 etree(A,'row'): 0.0001 0.0000 speedup 4.53 etree(A): 0.0001 0.0000 speedup 6.00 etree(A'): 0.0001 0.0000 speedup 4.25 after amd: etree(A): 0.0001 0.0000 speedup 6.26 etree(A'): 0.0001 0.0000 speedup 5.00 test12 passed ================================================================= test13: test cholmod2 and MATLAB on large tridiagonal matrices n 10000 cholmod2 0.01 err 3.5e-13 n 10000 matlab 0.00 err 2.6e-13 n 10000 cholmod2 0.01 err 3.6e-13 n 10000 matlab 0.00 err 2.6e-13 n 100000 cholmod2 0.14 err 3.6e-12 n 100000 matlab 0.01 err 2.6e-12 n 1000000 cholmod2 2.84 err 3.6e-11 n 1000000 matlab 0.18 err 2.6e-11 ================================================================= test14: test metis, symbfact2, and etree2 904: Prob = title: 'DNA electrophoresis, 3 monomers in polymer. A. van Heukelum, Utrecht U.' A: [5x5 double] name: 'vanHeukelum/cage3' id: 904 date: '2003' author: 'A. van Heukelum' ed: 'T. Davis' kind: 'directed weighted graph' nnz(A) 19 nnz(S) 19 nnz(A*A') 25 nnz(A'*A) 25 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 449: Prob = title: 'Unsymmetric Matrix b1_ss, F. Grund, Dec 1994.' A: [7x7 double] b: [7x1 double] name: 'Grund/b1_ss' id: 449 date: '1997' author: 'F. Grund' ed: 'F. Grund' kind: 'chemical process simulation problem' nnz(A) 15 nnz(S) 24 nnz(A*A') 25 nnz(A'*A) 25 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 185: Prob = title: 'U JOHN G. LEWIS P4 COUNTEREXAMPLE WHICH REQUIRES FILL IN SPIKES' A: [9x9 double] name: 'HB/jgl009' id: 185 date: '1983' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'counter-example problem' nnz(A) 50 nnz(S) 72 nnz(A*A') 81 nnz(A'*A) 81 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 905: Prob = title: 'DNA electrophoresis, 4 monomers in polymer. A. van Heukelum, Utrecht U.' A: [9x9 double] name: 'vanHeukelum/cage4' id: 905 date: '2003' author: 'A. van Heukelum' ed: 'T. Davis' kind: 'directed weighted graph' nnz(A) 49 nnz(S) 49 nnz(A*A') 81 nnz(A'*A) 81 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 238: Prob = title: 'S EXAMPLE TO DEMONSTRATE THE CHIMNEY EFFECT IN P4 - BY R.G. GRIMES' A: [10x10 double] name: 'HB/rgg010' id: 238 date: '1983' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'counter-example problem' nnz(A) 76 nnz(S) 100 nnz(A*A') 100 nnz(A'*A) 100 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1524: Prob = name: 'Pajek/Stranke94' title: 'Pajek network: Slovene Parliamentary Parties 1994' A: [10x10 double] id: 1524 kind: 'undirected weighted graph' notes: [22x78 char] aux: [1x1 struct] date: '1994' author: 'V. Batagelj' ed: 'V. Batagelj' nnz(A) 90 nnz(S) 90 nnz(A*A') 100 nnz(A'*A) 100 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 186: Prob = title: 'U JOHN G. LEWIS P4 COUNTEREXAMPLE WHICH REQUIRES FILL IN SPIKES' A: [11x11 double] name: 'HB/jgl011' id: 186 date: '1983' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'counter-example problem' nnz(A) 76 nnz(S) 108 nnz(A*A') 115 nnz(A'*A) 121 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1525: Prob = name: 'Pajek/Tina_AskCal' title: 'Pajek network: student govt, Univ. Ljubljana, 1992 (ask opin., recall)' A: [11x11 double] id: 1525 kind: 'directed graph' notes: [7x78 char] aux: [1x1 struct] date: '1992' author: 'V. Batagelj' ed: 'V. Batagelj' nnz(A) 29 nnz(S) 50 nnz(A*A') 85 nnz(A'*A) 58 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1526: Prob = name: 'Pajek/Tina_AskCog' title: 'Pajek network: student govt, Univ. Ljubljana, 1992 (ask, recognized)' A: [11x11 double] id: 1526 kind: 'directed graph' notes: [7x78 char] aux: [1x1 struct] date: '1992' author: 'V. Batagelj' ed: 'V. Batagelj' nnz(A) 36 nnz(S) 54 nnz(A*A') 95 nnz(A'*A) 75 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1527: Prob = name: 'Pajek/Tina_DisCal' title: 'Pajek network: student govt, Univ. Ljubljana, 1992 (discuss, recall)' A: [11x11 double] id: 1527 kind: 'directed graph' notes: [7x78 char] aux: [1x1 struct] date: '1992' author: 'V. Batagelj' ed: 'V. Batagelj' nnz(A) 41 nnz(S) 64 nnz(A*A') 103 nnz(A'*A) 76 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1528: Prob = name: 'Pajek/Tina_DisCog' title: 'Pajek network: student govt, Univ. Ljubljana, 1992 (discuss, recog.)' A: [11x11 double] id: 1528 kind: 'directed graph' notes: [7x78 char] aux: [1x1 struct] date: '1992' author: 'V. Batagelj' ed: 'V. Batagelj' nnz(A) 48 nnz(S) 72 nnz(A*A') 109 nnz(A'*A) 97 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 719: Prob = title: 'Netlib LP problem itest2: minimize c'*x, where Ax=b, lo<=x<=hi' name: 'LPnetlib/lpi_itest2' A: [9x13 double] b: [9x1 double] id: 719 aux: [1x1 struct] kind: 'linear programming problem' date: '1991' author: 'J. Chinneck, E. Dravnieks' ed: 'J. Chinneck' notes: [33x76 char] nnz(A) 26 nnz(S) 9 nnz(A*A') 9 nnz(A'*A) 9 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 715: Prob = title: 'Netlib LP problem galenet: minimize c'*x, where Ax=b, lo<=x<=hi' name: 'LPnetlib/lpi_galenet' A: [8x14 double] b: [8x1 double] id: 715 aux: [1x1 struct] kind: 'linear programming problem' date: '' author: 'H. Greenberg' ed: 'J. Chinneck' notes: [19x76 char] nnz(A) 22 nnz(S) 17 nnz(A*A') 11 nnz(A'*A) 14 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1440: Prob = name: 'Oberwolfach/LFAT5' title: 'Oberwolfach: linear 1D beam' A: [14x14 double] id: 1440 notes: 'Primary matrix in this model reduction problem is the Oberwolfach K matrix' aux: [1x1 struct] date: '2004' author: 'J. Lienemann, A. Greiner, J. Korvink' ed: 'E. Rudnyi' kind: 'model reduction problem' nnz(A) 46 nnz(S) 46 nnz(A*A') 72 nnz(A'*A) 72 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1817: Prob = name: 'Meszaros/kleemin' title: 'LP sequence: kleemin3, 4, 5, 6, 7, 8' id: 1817 kind: 'linear programming problem sequence' date: '2004' author: '' ed: 'C. Meszaros' A: [8x16 double] notes: [3x57 char] aux: [1x1 struct] nnz(A) 44 nnz(S) 8 nnz(A*A') 8 nnz(A'*A) 8 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 720: Prob = title: 'Netlib LP problem itest6: minimize c'*x, where Ax=b, lo<=x<=hi' name: 'LPnetlib/lpi_itest6' A: [11x17 double] b: [11x1 double] id: 720 aux: [1x1 struct] kind: 'linear programming problem' date: '1991' author: 'J. Chinneck, E. Dravnieks' ed: 'J. Chinneck' notes: [33x76 char] nnz(A) 29 nnz(S) 19 nnz(A*A') 31 nnz(A'*A) 19 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1710: Prob = name: 'Meszaros/farm' title: 'linear programming problem, C. Meszaros test set' id: 1710 kind: 'linear programming problem' date: '2004' author: '' ed: 'C. Meszaros' A: [7x17 double] b: [7x1 double] aux: [1x1 struct] notes: [3x57 char] nnz(A) 41 nnz(S) 21 nnz(A*A') 18 nnz(A'*A) 21 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1438: Prob = name: 'Oberwolfach/LF10' title: 'Oberwolfach: linear 1D beam' A: [18x18 double] id: 1438 notes: 'Primary matrix in this model reduction problem is the Oberwolfach K matrix' aux: [1x1 struct] date: '2004' author: 'J. Lienemann, A. Greiner, J. Korvink' ed: 'E. Rudnyi' kind: 'model reduction problem' nnz(A) 82 nnz(S) 82 nnz(A*A') 154 nnz(A'*A) 154 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1479: Prob = name: 'Pajek/GD01_b' title: 'Pajek network: Graph Drawing contest 2001' A: [18x18 double] id: 1479 kind: 'directed graph' notes: [7x78 char] aux: [1x1 struct] date: '2001' author: 'Graph Drawing Contest' ed: 'V. Batagelj' nnz(A) 37 nnz(S) 54 nnz(A*A') 62 nnz(A'*A) 56 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1481: Prob = name: 'Pajek/GD02_a' title: 'Pajek network: Graph Drawing contest 2002' A: [23x23 double] id: 1481 kind: 'directed graph' notes: [7x78 char] aux: [1x1 struct] date: '2002' author: 'Graph Drawing Contest' ed: 'V. Batagelj' nnz(A) 87 nnz(S) 118 nnz(A*A') 272 nnz(A'*A) 376 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1516: Prob = name: 'Pajek/Ragusa18' title: 'Pajek network: Ragusa set' A: [23x23 double] id: 1516 kind: 'directed weighted graph' notes: [5x78 char] aux: [1x1 struct] date: '2006' author: 'V. Batagelj' ed: 'V. Batagelj' nnz(A) 64 nnz(S) 105 nnz(A*A') 263 nnz(A'*A) 158 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 97: Prob = title: 'SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.' A: [24x24 double] name: 'HB/can_24' id: 97 date: '1981' author: 'L. Marro' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' nnz(A) 160 nnz(S) 160 nnz(A*A') 336 nnz(A'*A) 336 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1515: Prob = name: 'Pajek/Ragusa16' title: 'Pajek network: Ragusa set' A: [24x24 double] id: 1515 kind: 'directed weighted graph' notes: [5x78 char] aux: [1x1 struct] date: '2006' author: 'V. Batagelj' ed: 'V. Batagelj' nnz(A) 81 nnz(S) 126 nnz(A*A') 271 nnz(A'*A) 250 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1177: Prob = title: 'FINITE ELEMENT PROBLEM. LAPLACIAN ON A 5 BY 5 GRID.' A: [25x25 double] name: 'HB/lap_25' id: 1177 date: '1980' author: 'I. Duff' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' nnz(A) 169 nnz(S) 169 nnz(A*A') 361 nnz(A'*A) 361 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 436: Prob = title: ' TEST MATRIX FROM FIDAP: EX5.MAT' A: [27x27 double] name: 'FIDAP/ex5' id: 436 date: '1994' author: 'A. Baggag, Y. Saad' ed: 'A. Baggag, Y. Saad' kind: 'computational fluid dynamics problem' nnz(A) 279 nnz(S) 279 nnz(A*A') 495 nnz(A'*A) 495 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 232: Prob = title: 'UNSYMMETRIC MATRIX FROM PORES' A: [30x30 double] name: 'HB/pores_1' id: 232 date: '1980' author: 'J. Appleyard' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'computational fluid dynamics problem' nnz(A) 180 nnz(S) 236 nnz(A*A') 476 nnz(A'*A) 388 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 168: Prob = title: 'UNSYMMETRIC PATTERN ON LEAFLET ADVERTISING IBM 1971 CONFERENCE' A: [32x32 double] name: 'HB/ibm32' id: 168 date: '1971' author: 'IBM' ed: 'A. Curtis, I. Duff, J. Reid' kind: 'directed graph' nnz(A) 126 nnz(S) 212 nnz(A*A') 392 nnz(A'*A) 390 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1199: Prob = name: 'Hamrle/Hamrle1' title: 'Hamrle/Hamrle1 circuit simulation matrix' A: [32x32 double] b: [32x1 double] id: 1199 date: '2004' author: 'J. Hamrle' ed: 'T. Davis' kind: 'circuit simulation problem' nnz(A) 98 nnz(S) 185 nnz(A*A') 222 nnz(A'*A) 220 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1480: Prob = name: 'Pajek/GD01_c' title: 'Pajek network: Graph Drawing contest 2001' A: [33x33 double] id: 1480 kind: 'directed multigraph' notes: [7x78 char] aux: [1x1 struct] date: '2001' author: 'Graph Drawing Contest' ed: 'V. Batagelj' nnz(A) 135 nnz(S) 270 nnz(A*A') 312 nnz(A'*A) 374 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1474: Prob = name: 'Pajek/football' title: 'Pajek network: World Soccer, Paris 1998' A: [35x35 double] id: 1474 kind: 'directed weighted graph' notes: [7x78 char] aux: [1x1 struct] date: '1998' author: 'L. Krempel' ed: 'V. Batagelj' nnz(A) 118 nnz(S) 236 nnz(A*A') 568 nnz(A'*A) 234 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1485: Prob = name: 'Pajek/GD95_a' title: 'Pajek network: Graph Drawing contest 1995' A: [36x36 double] id: 1485 kind: 'directed graph' notes: [7x78 char] aux: [1x1 struct] date: '1995' author: 'Graph Drawing Contest' ed: 'V. Batagelj' nnz(A) 57 nnz(S) 112 nnz(A*A') 80 nnz(A'*A) 101 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 906: Prob = title: 'DNA electrophoresis, 5 monomers in polymer. A. van Heukelum, Utrecht U.' A: [37x37 double] name: 'vanHeukelum/cage5' id: 906 date: '2003' author: 'A. van Heukelum' ed: 'T. Davis' kind: 'directed weighted graph' nnz(A) 233 nnz(S) 233 nnz(A*A') 653 nnz(A'*A) 653 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1495: Prob = name: 'Pajek/GD98_a' title: 'Pajek network: Graph Drawing contest 1998' A: [38x38 double] id: 1495 kind: 'directed graph' notes: [7x78 char] aux: [1x1 struct] date: '1998' author: 'Graph Drawing Contest' ed: 'V. Batagelj' nnz(A) 50 nnz(S) 92 nnz(A*A') 78 nnz(A'*A) 241 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 13: Prob = title: 'SYMMETRIC STRUCTURE (STANDARD TEST POWER SYSTEM - NEW ENGLAND)' A: [39x39 double] name: 'HB/bcspwr01' id: 13 date: '1981' author: 'B. Dembart, J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'power network problem' nnz(A) 131 nnz(S) 131 nnz(A*A') 275 nnz(A'*A) 275 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 706: Prob = title: 'Netlib LP problem bgprtr: minimize c'*x, where Ax=b, lo<=x<=hi' name: 'LPnetlib/lpi_bgprtr' A: [20x40 double] b: [20x1 double] id: 706 aux: [1x1 struct] kind: 'linear programming problem' date: '1993' author: 'L. Schrage' ed: 'J. Chinneck' notes: [23x76 char] nnz(A) 70 nnz(S) 52 nnz(A*A') 37 nnz(A'*A) 44 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1755: Prob = name: 'Meszaros/problem' title: 'linear programming problem, C. Meszaros test set' id: 1755 kind: 'linear programming problem' date: '2004' author: '' ed: 'C. Meszaros' A: [12x46 double] b: [12x1 double] aux: [1x1 struct] notes: [3x57 char] nnz(A) 86 nnz(S) 44 nnz(A*A') 14 nnz(A'*A) 80 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1493: Prob = name: 'Pajek/GD97_b' title: 'Pajek network: Graph Drawing contest 1997' A: [47x47 double] id: 1493 kind: 'undirected weighted graph' notes: [12x78 char] aux: [1x1 struct] date: '1997' author: 'Graph Drawing Contest' ed: 'V. Batagelj' nnz(A) 264 nnz(S) 264 nnz(A*A') 1274 nnz(A'*A) 1274 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 23: Prob = title: 'SYMMETRIC STIFFNESS MATRIX SMALL GENERALIZED EIGENVALUE PROBLEM' A: [48x48 double] name: 'HB/bcsstk01' id: 23 date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' nnz(A) 400 nnz(S) 400 nnz(A*A') 1292 nnz(A'*A) 1292 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 56: Prob = title: 'SYMMETRIC MASS MATRIX SMALL GENERALIZED EIGENVALUE PROBLEM, B MATRIX' A: [48x48 double] Zeros: [48x48 double] name: 'HB/bcsstm01' id: 56 date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' nnz(A) 24 nnz(S) 24 nnz(A*A') 24 nnz(A'*A) 24 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 872: Prob = A: [48x48 double] title: 'mesh1e1, with coordinates. From NASA, collected by Alex Pothen' name: 'Pothen/mesh1e1' id: 872 aux: [1x1 struct] date: '2003' author: 'NASA' ed: 'G. Kumfert, A. Pothen' kind: 'structural problem' nnz(A) 306 nnz(S) 306 nnz(A*A') 772 nnz(A'*A) 772 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 873: Prob = A: [48x48 double] title: 'mesh1em1, with coordinates. From NASA, collected by Alex Pothen' name: 'Pothen/mesh1em1' id: 873 aux: [1x1 struct] date: '2003' author: 'NASA' ed: 'G. Kumfert, A. Pothen' kind: 'structural problem' nnz(A) 306 nnz(S) 306 nnz(A*A') 772 nnz(A'*A) 772 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 874: Prob = A: [48x48 double] title: 'mesh1em6, with coordinates. From NASA, collected by Alex Pothen' name: 'Pothen/mesh1em6' id: 874 aux: [1x1 struct] date: '2003' author: 'NASA' ed: 'G. Kumfert, A. Pothen' kind: 'structural problem' nnz(A) 306 nnz(S) 306 nnz(A*A') 772 nnz(A'*A) 772 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1741: Prob = name: 'Meszaros/p0033' title: 'linear programming problem, C. Meszaros test set' id: 1741 kind: 'linear programming problem' date: '2004' author: '' ed: 'C. Meszaros' A: [15x48 double] b: [15x1 double] aux: [1x1 struct] notes: [3x57 char] nnz(A) 113 nnz(S) 15 nnz(A*A') 15 nnz(A'*A) 15 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 14: Prob = title: 'SYMMETRIC STRUCTURE OF A SMALL TEST POWER SYSTEM' A: [49x49 double] name: 'HB/bcspwr02' id: 14 date: '1981' author: 'B. Dembart, J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'power network problem' nnz(A) 167 nnz(S) 167 nnz(A*A') 403 nnz(A'*A) 403 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1460: Prob = name: 'Pajek/divorce' title: 'Pajek network: divorce laws in the 50 US states' A: [50x9 double] id: 1460 kind: 'bipartite graph' notes: [6x78 char] aux: [1x1 struct] date: '2006' author: '' ed: 'V. Batagelj' nnz(A) 225 nnz(S) 57 nnz(A*A') 77 nnz(A'*A) 81 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 597: Prob = title: 'Netlib LP problem afiro: minimize c'*x, where Ax=b, lo<=x<=hi' name: 'LPnetlib/lp_afiro' A: [27x51 double] b: [27x1 double] id: 597 aux: [1x1 struct] kind: 'linear programming problem' date: '' author: 'M. Saunders' ed: 'D. Gay' notes: [48x78 char] nnz(A) 102 nnz(S) 88 nnz(A*A') 71 nnz(A'*A) 73 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 464: Prob = title: 'Unsymmetric Matrix d_ss, F. Grund, Dec 1994.' A: [53x53 double] Zeros: [53x53 double] b: [53x1 double] name: 'Grund/d_ss' id: 464 date: '1997' author: 'F. Grund' ed: 'F. Grund' kind: 'chemical process simulation problem' nnz(A) 144 nnz(S) 278 nnz(A*A') 311 nnz(A'*A) 315 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 109: Prob = title: 'UNSYMMETRIC PATTERN OF CURTIS, 1971' A: [54x54 double] name: 'HB/curtis54' id: 109 date: '1971' author: 'A. Curtis' ed: 'A. Curtis, I. Duff, J. Reid' kind: '2D/3D problem' nnz(A) 291 nnz(S) 302 nnz(A*A') 794 nnz(A'*A) 728 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1457: Prob = name: 'Pajek/Cities' title: 'Pajek network: www.lboro.ac.uk/gawc, data set 6' A: [55x46 double] id: 1457 kind: 'weighted bipartite graph' notes: [10x78 char] aux: [1x1 struct] date: '2001' author: 'P. Taylor, D. Walker' ed: 'V. Batagelj' nnz(A) 1342 nnz(S) 1626 nnz(A*A') 2116 nnz(A'*A) 2114 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 274: Prob = title: 'UNSYMMETRIC PATTERN OF ORDER 57 GIVEN BY WILLOUGHBY IN REID, 1970' A: [57x57 double] name: 'HB/will57' id: 274 date: '1970' author: 'R. Willoughby' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'semiconductor device problem' nnz(A) 281 nnz(S) 311 nnz(A*A') 647 nnz(A'*A) 665 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 129: Prob = title: 'SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON' A: [59x59 double] name: 'HB/dwt_59' id: 129 date: '1980' author: 'G. Everstine, D. Taylor' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' nnz(A) 267 nnz(S) 267 nnz(A*A') 571 nnz(A'*A) 571 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 172: Prob = title: 'UNSYMMETRIC MATRIX - CAVETT'S PROCESS (CHEM ENG),1982' A: [59x59 double] Zeros: [59x59 double] name: 'HB/impcol_b' id: 172 date: '1982' author: 'D. Bogle' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'chemical process simulation problem' nnz(A) 271 nnz(S) 497 nnz(A*A') 783 nnz(A'*A) 627 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 102: Prob = title: 'SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.' A: [61x61 double] name: 'HB/can_61' id: 102 date: '1981' author: 'L. Marro' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' nnz(A) 557 nnz(S) 557 nnz(A*A') 1793 nnz(A'*A) 1793 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 103: Prob = title: 'SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.' A: [62x62 double] name: 'HB/can_62' id: 103 date: '1981' author: 'L. Marro' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' nnz(A) 218 nnz(S) 218 nnz(A*A') 482 nnz(A'*A) 482 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 293: Prob = title: 'BOUNDED FINLINE WAVEGUIDE EIGENMODES B SHULTZ AND S GEDNEY' A: [62x62 double] name: 'Bai/bfwa62' id: 293 date: '1994' author: 'B. Schultz, S. Gedney' ed: 'Z. Bai, D. Day, J. Demmel, J. Dongarra' kind: 'electromagnetics problem' nnz(A) 450 nnz(S) 462 nnz(A*A') 1306 nnz(A'*A) 1340 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 296: Prob = title: 'BOUNDED FINLINE WAVEGUIDE EIGENMODES B SHULTZ AND S GEDNEY' A: [62x62 double] name: 'Bai/bfwb62' id: 296 date: '1994' author: 'B. Schultz, S. Gedney' ed: 'Z. Bai, D. Day, J. Demmel, J. Dongarra' kind: 'electromagnetics problem' nnz(A) 342 nnz(S) 342 nnz(A*A') 992 nnz(A'*A) 992 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1487: Prob = name: 'Pajek/GD95_c' title: 'Pajek network: Graph Drawing contest 1995' A: [62x62 double] id: 1487 kind: 'directed graph' notes: [7x78 char] aux: [1x1 struct] date: '1995' author: 'Graph Drawing Contest' ed: 'V. Batagelj' nnz(A) 287 nnz(S) 288 nnz(A*A') 998 nnz(A'*A) 996 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1759: Prob = name: 'Meszaros/refine' title: 'linear programming problem, C. Meszaros test set' id: 1759 kind: 'linear programming problem' date: '2004' author: '' ed: 'C. Meszaros' A: [29x62 double] b: [29x1 double] aux: [1x1 struct] notes: [3x57 char] nnz(A) 153 nnz(S) 29 nnz(A*A') 29 nnz(A'*A) 29 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1742: Prob = name: 'Meszaros/p0040' title: 'linear programming problem, C. Meszaros test set' id: 1742 kind: 'linear programming problem' date: '2004' author: '' ed: 'C. Meszaros' A: [23x63 double] b: [23x1 double] aux: [1x1 struct] notes: [3x57 char] nnz(A) 133 nnz(S) 23 nnz(A*A') 23 nnz(A'*A) 23 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1498: Prob = name: 'Pajek/GD99_b' title: 'Pajek network: Graph Drawing contest 1999' A: [64x64 double] id: 1498 kind: 'undirected multigraph' notes: [5x78 char] aux: [1x1 struct] date: '1999' author: 'Graph Drawing Contest' ed: 'V. Batagelj' nnz(A) 252 nnz(S) 252 nnz(A*A') 668 nnz(A'*A) 668 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1490: Prob = name: 'Pajek/GD96_c' title: 'Pajek network: Graph Drawing contest 1996' A: [65x65 double] id: 1490 kind: 'undirected graph' notes: [7x78 char] aux: [1x1 struct] date: '1996' author: 'Graph Drawing Contest' ed: 'V. Batagelj' nnz(A) 250 nnz(S) 250 nnz(A*A') 695 nnz(A'*A) 695 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 24: Prob = title: 'SYMMETRIC STIFFNESS MATRIX, SMALL OIL RIG, STATICALLY CONDENSED' A: [66x66 double] name: 'HB/bcsstk02' id: 24 date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' nnz(A) 4356 nnz(S) 4356 nnz(A*A') 4356 nnz(A'*A) 4356 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 57: Prob = title: 'SYMMETRIC MASS MATRIX, SMALL OIL RIG, STATICALLY CONDENSED' A: [66x66 double] name: 'HB/bcsstm02' id: 57 date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' nnz(A) 66 nnz(S) 66 nnz(A*A') 66 nnz(A'*A) 66 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 132: Prob = title: 'SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON' A: [66x66 double] name: 'HB/dwt_66' id: 132 date: '1980' author: 'G. Everstine, D. Taylor' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' nnz(A) 320 nnz(S) 320 nnz(A*A') 576 nnz(A'*A) 576 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 883: Prob = A: [66x66 double] title: 'sphere2, with coordinates. From NASA, collected by Alex Pothen' name: 'Pothen/sphere2' id: 883 aux: [1x1 struct] date: '2003' author: 'NASA' ed: 'G. Kumfert, A. Pothen' kind: 'structural problem' nnz(A) 450 nnz(S) 450 nnz(A*A') 1170 nnz(A'*A) 1170 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 262: Prob = title: 'U CAVETT PROBLEM WITH 5 COMPONENTS ( CHEM. ENG. FROM WESTERBERG )' A: [67x67 double] name: 'HB/west0067' id: 262 date: '1983' author: 'A. Westerberg' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'chemical process simulation problem' nnz(A) 294 nnz(S) 576 nnz(A*A') 1041 nnz(A'*A) 889 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 636: Prob = title: 'Netlib LP problem kb2: minimize c'*x, where Ax=b, lo<=x<=hi' name: 'LPnetlib/lp_kb2' A: [43x68 double] b: [43x1 double] id: 636 aux: [1x1 struct] kind: 'linear programming problem' date: '1989' author: 'J. Tomlin' ed: 'D. Gay' notes: [39x74 char] nnz(A) 313 nnz(S) 318 nnz(A*A') 513 nnz(A'*A) 355 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 133: Prob = title: 'SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON' A: [72x72 double] name: 'HB/dwt_72' id: 133 date: '1980' author: 'G. Everstine, D. Taylor' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' nnz(A) 222 nnz(S) 222 nnz(A*A') 412 nnz(A'*A) 412 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1501: Prob = name: 'Pajek/GlossGT' title: 'Pajek network: graph and digraph glossary' A: [72x72 double] id: 1501 kind: 'directed graph' notes: [10x78 char] aux: [1x1 struct] date: '2001' author: 'W. Cherowitzo' ed: 'V. Batagelj' nnz(A) 122 nnz(S) 236 nnz(A*A') 798 nnz(A'*A) 161 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 106: Prob = title: 'SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.' A: [73x73 double] name: 'HB/can_73' id: 106 date: '1981' author: 'L. Marro' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' nnz(A) 377 nnz(S) 377 nnz(A*A') 1377 nnz(A'*A) 1377 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1486: Prob = name: 'Pajek/GD95_b' title: 'Pajek network: Graph Drawing contest 1995' A: [73x73 double] id: 1486 kind: 'directed graph' notes: [7x78 char] aux: [1x1 struct] date: '1995' author: 'Graph Drawing Contest' ed: 'V. Batagelj' nnz(A) 96 nnz(S) 191 nnz(A*A') 148 nnz(A'*A) 875 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 666: Prob = title: 'Netlib LP problem sc50a: minimize c'*x, where Ax=b, lo<=x<=hi' name: 'LPnetlib/lp_sc50a' A: [50x78 double] b: [50x1 double] id: 666 aux: [1x1 struct] kind: 'linear programming problem' date: '1989' author: 'N. Gould' ed: 'D. Gay' notes: [30x74 char] nnz(A) 160 nnz(S) 163 nnz(A*A') 136 nnz(A'*A) 174 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 667: Prob = title: 'Netlib LP problem sc50b: minimize c'*x, where Ax=b, lo<=x<=hi' name: 'LPnetlib/lp_sc50b' A: [50x78 double] b: [50x1 double] id: 667 aux: [1x1 struct] kind: 'linear programming problem' date: '1989' author: 'N. Gould' ed: 'D. Gay' notes: [30x74 char] nnz(A) 148 nnz(S) 155 nnz(A*A') 132 nnz(A'*A) 162 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 253: Prob = title: 'UNSYMMETRIC - 1D STEAM MODEL OF OIL RES. - 20 POINTS - 4 DOF MAY 1983' A: [80x80 double] Zeros: [80x80 double] name: 'HB/steam3' id: 253 date: '1983' author: 'R. Grimes' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'computational fluid dynamics problem' nnz(A) 314 nnz(S) 392 nnz(A*A') 688 nnz(A'*A) 768 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1482: Prob = name: 'Pajek/GD02_b' title: 'Pajek network: Graph Drawing contest 2002' A: [80x80 double] id: 1482 kind: 'directed graph' notes: [7x78 char] aux: [1x1 struct] date: '2002' author: 'Graph Drawing Contest' ed: 'V. Batagelj' nnz(A) 232 nnz(S) 464 nnz(A*A') 570 nnz(A'*A) 630 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1492: Prob = name: 'Pajek/GD97_a' title: 'Pajek network: Graph Drawing contest 1997' A: [84x84 double] id: 1492 kind: 'directed graph' notes: [5x78 char] aux: [1x1 struct] date: '1997' author: 'Graph Drawing Contest' ed: 'V. Batagelj' nnz(A) 332 nnz(S) 332 nnz(A*A') 860 nnz(A'*A) 860 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 11: Prob = title: 'SYMMETRIC PATTERN OF NORMAL MATRIX OF HOLLAND SURVEY. ASHKENAZI, 1974' A: [85x85 double] name: 'HB/ash85' id: 11 date: '1974' author: 'V. Askenazi' ed: 'A. Curtis, I. Duff, J. Reid' kind: 'least squares problem' nnz(A) 523 nnz(S) 523 nnz(A*A') 1317 nnz(A'*A) 1317 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1519: Prob = name: 'Pajek/Sandi_authors' title: 'Pajek network: Klavzar bibliography' A: [86x86 double] id: 1519 kind: 'undirected weighted graph' notes: [7x78 char] aux: [1x1 struct] date: '1999' author: 'I. Klavzar' ed: 'V. Batagelj' nnz(A) 248 nnz(S) 248 nnz(A*A') 908 nnz(A'*A) 908 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 136: Prob = title: 'SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON' A: [87x87 double] name: 'HB/dwt_87' id: 136 date: '1980' author: 'G. Everstine, D. Taylor' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' nnz(A) 541 nnz(S) 541 nnz(A*A') 1539 nnz(A'*A) 1539 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 462: Prob = title: 'Unsymmetric Matrix d_dyn, F. Grund, Dec 1994.' A: [87x87 double] Zeros: [87x87 double] b: [87x1 double] name: 'Grund/d_dyn' id: 462 date: '1997' author: 'F. Grund' ed: 'F. Grund' kind: 'chemical process simulation problem' nnz(A) 230 nnz(S) 438 nnz(A*A') 497 nnz(A'*A) 525 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 463: Prob = title: 'Unsymmetric Matrix d_dyn1, F. Grund, Oct 1995.' A: [87x87 double] Zeros: [87x87 double] name: 'Grund/d_dyn1' id: 463 date: '1997' author: 'F. Grund' ed: 'F. Grund' kind: 'chemical process simulation problem' nnz(A) 232 nnz(S) 442 nnz(A*A') 503 nnz(A'*A) 535 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 731: Prob = title: 'Netlib LP problem woodinfe: minimize c'*x, where Ax=b, lo<=x<=hi' name: 'LPnetlib/lpi_woodinfe' A: [35x89 double] b: [35x1 double] id: 731 aux: [1x1 struct] kind: 'linear programming problem' date: '1989' author: 'H. Greenberg' ed: 'J. Chinneck' notes: [35x76 char] nnz(A) 140 nnz(S) 67 nnz(A*A') 32 nnz(A'*A) 41 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1641: Prob = name: 'Bai/tols90' title: 'TOLOSA MATRIX' A: [90x90 double] id: 1641 date: '1991' author: 'S. Godet-Thobie' ed: 'Z. Bai, D. Day, J. Demmel, J. Dongarra' kind: 'computational fluid dynamics problem' nnz(A) 1746 nnz(S) 2970 nnz(A*A') 3204 nnz(A'*A) 8100 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 907: Prob = title: 'DNA electrophoresis, 6 monomers in polymer. A. van Heukelum, Utrecht U.' A: [93x93 double] name: 'vanHeukelum/cage6' id: 907 date: '2003' author: 'A. van Heukelum' ed: 'T. Davis' kind: 'directed weighted graph' nnz(A) 785 nnz(S) 785 nnz(A*A') 2849 nnz(A'*A) 2849 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 108: Prob = title: 'SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.' A: [96x96 double] name: 'HB/can_96' id: 108 date: '1981' author: 'L. Marro' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' nnz(A) 768 nnz(S) 768 nnz(A*A') 1920 nnz(A'*A) 1920 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 220: Prob = title: 'SYMMETRIC MATRIX OF BEAM STRUCTURE, NOVEMBER 1982.' A: [100x100 double] name: 'HB/nos4' id: 220 date: '1982' author: 'H. Simon' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' nnz(A) 594 nnz(S) 594 nnz(A*A') 1802 nnz(A'*A) 1802 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 318: Prob = title: 'OLMSTEAD FLOW MODEL' A: [100x100 double] name: 'Bai/olm100' id: 318 date: '1994' author: 'K. Meerbergen' ed: 'Z. Bai, D. Day, J. Demmel, J. Dongarra' kind: 'computational fluid dynamics problem' nnz(A) 396 nnz(S) 494 nnz(A*A') 590 nnz(A'*A) 976 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 337: Prob = title: 'TUBULAR REACTOR MODEL' A: [100x100 double] name: 'Bai/tub100' id: 337 date: '1994' author: 'K. Meerbergen, D. Roose' ed: 'Z. Bai, D. Day, J. Demmel, J. Dongarra' kind: 'computational fluid dynamics problem' nnz(A) 396 nnz(S) 396 nnz(A*A') 784 nnz(A'*A) 784 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1326: Prob = name: 'Morandini/rotor1' title: 'Marco Morandini, small helicoptor rotor model' A: [100x100 double] id: 1326 date: '2006' author: 'M. Morandini' ed: 'T. Davis' kind: 'structural problem' nnz(A) 708 nnz(S) 1020 nnz(A*A') 3346 nnz(A'*A) 3634 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1484: Prob = name: 'Pajek/GD06_theory' title: 'Pajek network: Graph Drawing contest 2006' A: [101x101 double] id: 1484 kind: 'undirected graph' notes: [9x78 char] date: '2006' author: 'Graph Drawing Contest' ed: 'V. Batagelj' nnz(A) 380 nnz(S) 380 nnz(A*A') 3341 nnz(A'*A) 3341 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 861: Prob = A: [102x102 double] b: [102x3 double] title: 'Spline toolbox. Pivot tol 0.1 fails, needs >= 0.26. MathWorks,Inc' name: 'MathWorks/pivtol' id: 861 date: '2002' author: 'B. Cheng' ed: 'T. Davis' kind: 'statistical/mathematical problem' nnz(A) 306 nnz(S) 308 nnz(A*A') 510 nnz(A'*A) 512 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 306: Prob = title: 'CHUCK MATRIX (MULTIPLE EIGENVALUES) J. CULLUM' A: [104x104 double] name: 'Bai/ck104' id: 306 date: '1986' author: 'J. Cullum' ed: 'Z. Bai, D. Day, J. Demmel, J. Dongarra' kind: '2D/3D problem' nnz(A) 992 nnz(S) 992 nnz(A*A') 1712 nnz(A'*A) 1712 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1499: Prob = name: 'Pajek/GD99_c' title: 'Pajek network: Graph Drawing contest 1999' A: [105x105 double] id: 1499 kind: 'directed graph' notes: [7x78 char] aux: [1x1 struct] date: '1999' author: 'Graph Drawing Contest' ed: 'V. Batagelj' nnz(A) 149 nnz(S) 240 nnz(A*A') 177 nnz(A'*A) 352 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 721: Prob = title: 'Netlib LP problem klein1: minimize c'*x, where Ax=b, lo<=x<=hi' name: 'LPnetlib/lpi_klein1' A: [54x108 double] b: [54x1 double] id: 721 aux: [1x1 struct] kind: 'linear programming problem' date: '' author: 'E. Klotz' ed: 'J. Chinneck' notes: [19x76 char] nnz(A) 750 nnz(S) 54 nnz(A*A') 54 nnz(A'*A) 54 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1489: Prob = name: 'Pajek/GD96_b' title: 'Pajek network: Graph Drawing contest 1996' A: [111x111 double] id: 1489 kind: 'directed graph' notes: [7x78 char] aux: [1x1 struct] date: '1996' author: 'Graph Drawing Contest' ed: 'V. Batagelj' nnz(A) 193 nnz(S) 386 nnz(A*A') 3021 nnz(A'*A) 100 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 25: Prob = title: 'SYMMETRIC STIFFNESS MATRIX, SMALL TEST STRUCTURE' A: [112x112 double] name: 'HB/bcsstk03' id: 25 date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' nnz(A) 640 nnz(S) 640 nnz(A*A') 1072 nnz(A'*A) 1072 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 58: Prob = title: 'SYMMETRIC MASS MATRIX, SMALL TEST STRUCTURE' A: [112x112 double] Zeros: [112x112 double] name: 'HB/bcsstm03' id: 58 date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' nnz(A) 72 nnz(S) 72 nnz(A*A') 72 nnz(A'*A) 72 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 1497: Prob = name: 'Pajek/GD98_c' title: 'Pajek network: Graph Drawing contest 1998' A: [112x112 double] id: 1497 kind: 'undirected graph' notes: [7x78 char] aux: [1x1 struct] date: '1998' author: 'Graph Drawing Contest' ed: 'V. Batagelj' nnz(A) 336 nnz(S) 336 nnz(A*A') 784 nnz(A'*A) 784 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 158: Prob = title: 'UNSYMMETRIC PATTERN SUPPLIED BY MORVEN GENTLEMAN, SUMMER 1973' A: [113x113 double] name: 'HB/gent113' id: 158 date: '1973' author: 'W. Gentleman' ed: 'A. Curtis, I. Duff, J. Reid' kind: 'statistical/mathematical problem' nnz(A) 655 nnz(S) 1188 nnz(A*A') 2683 nnz(A'*A) 2351 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: 603: Prob = title: 'Netlib LP problem blend: minimize c'*x, where Ax=b, lo<=x<=hi' name: 'LPnetlib/lp_blend' A: [74x114 double] b: [74x1 double] id: 603 aux: [1x1 struct] kind: 'linear programming problem' date: '1989' author: 'N. Gould' ed: 'D. Gay' notes: [36x76 char] nnz(A) 522 nnz(S) 749 nnz(A*A') 1319 nnz(A'*A) 1062 metis (S): metis (A,row): metis (A,col): turning off postorder: metis (S): metis (A,row): metis (A,col): analyzing results: test14 passed ================================================================= Matrices to test: 100 904: vanHeukelum/cage3 nrow: 5 ncol: 5 nnz: 19 c=symbfact(A): 0.0003 0.0001 speedup 2.57 lnz 12 R=symbfact(A): 0.0004 0.0002 speedup 2.66 c=symbfact(A'): 0.0004 0.0001 speedup 2.89 lnz 12 R=symbfact(A'): 0.0004 0.0002 speedup 2.77 c=symbfact(A,'col'): 0.0004 0.0002 speedup 2.38 lnz 15 R=symbfact(A,'col'): 0.0004 0.0002 speedup 2.86 449: Grund/b1_ss nrow: 7 ncol: 7 nnz: 15 c=symbfact(A): 0.0001 0.0000 speedup 6.25 lnz 13 R=symbfact(A): 0.0001 0.0000 speedup 4.36 c=symbfact(A'): 0.0001 0.0000 speedup 5.84 lnz 10 R=symbfact(A'): 0.0001 0.0000 speedup 5.04 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.80 lnz 19 R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.77 185: HB/jgl009 nrow: 9 ncol: 9 nnz: 50 c=symbfact(A): 0.0001 0.0000 speedup 5.61 lnz 23 R=symbfact(A): 0.0001 0.0000 speedup 3.74 c=symbfact(A'): 0.0001 0.0000 speedup 5.52 lnz 39 R=symbfact(A'): 0.0003 0.0000 speedup 8.63 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.90 lnz 45 R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.07 905: vanHeukelum/cage4 nrow: 9 ncol: 9 nnz: 49 c=symbfact(A): 0.0001 0.0000 speedup 5.94 lnz 36 R=symbfact(A): 0.0001 0.0000 speedup 3.50 c=symbfact(A'): 0.0001 0.0000 speedup 5.52 lnz 36 R=symbfact(A'): 0.0001 0.0000 speedup 4.57 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.67 lnz 45 R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.55 238: HB/rgg010 nrow: 10 ncol: 10 nnz: 76 c=symbfact(A): 0.0001 0.0000 speedup 5.37 lnz 31 R=symbfact(A): 0.0001 0.0000 speedup 4.55 c=symbfact(A'): 0.0001 0.0000 speedup 3.93 lnz 55 R=symbfact(A'): 0.0001 0.0000 speedup 3.57 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.62 lnz 55 R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.37 1524: Pajek/Stranke94 nrow: 10 ncol: 10 nnz: 90 c=symbfact(A): 0.0001 0.0000 speedup 5.37 lnz 55 R=symbfact(A): 0.0001 0.0000 speedup 4.65 c=symbfact(A'): 0.0002 0.0000 speedup 6.65 lnz 55 R=symbfact(A'): 0.0001 0.0000 speedup 4.69 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.76 lnz 55 R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.22 186: HB/jgl011 nrow: 11 ncol: 11 nnz: 76 c=symbfact(A): 0.0001 0.0000 speedup 5.72 lnz 31 R=symbfact(A): 0.0001 0.0000 speedup 4.47 c=symbfact(A'): 0.0001 0.0000 speedup 3.96 lnz 59 R=symbfact(A'): 0.0001 0.0000 speedup 3.57 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.45 lnz 66 R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.32 1525: Pajek/Tina_AskCal nrow: 11 ncol: 11 nnz: 29 c=symbfact(A): 0.0001 0.0000 speedup 5.44 lnz 33 R=symbfact(A): 0.0001 0.0000 speedup 4.48 c=symbfact(A'): 0.0001 0.0000 speedup 5.65 lnz 25 R=symbfact(A'): 0.0001 0.0000 speedup 5.04 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.62 lnz 35 R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.21 1526: Pajek/Tina_AskCog nrow: 11 ncol: 11 nnz: 36 c=symbfact(A): 0.0001 0.0000 speedup 5.61 lnz 36 R=symbfact(A): 0.0001 0.0000 speedup 3.69 c=symbfact(A'): 0.0001 0.0000 speedup 5.36 lnz 35 R=symbfact(A'): 0.0001 0.0000 speedup 4.36 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.50 lnz 44 R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.23 1527: Pajek/Tina_DisCal nrow: 11 ncol: 11 nnz: 41 c=symbfact(A): 0.0001 0.0000 speedup 5.61 lnz 47 R=symbfact(A): 0.0001 0.0000 speedup 4.32 c=symbfact(A'): 0.0001 0.0000 speedup 5.36 lnz 34 R=symbfact(A'): 0.0001 0.0000 speedup 4.54 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.71 lnz 46 R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.33 1528: Pajek/Tina_DisCog nrow: 11 ncol: 11 nnz: 48 c=symbfact(A): 0.0001 0.0000 speedup 5.61 lnz 45 R=symbfact(A): 0.0001 0.0000 speedup 4.55 c=symbfact(A'): 0.0001 0.0000 speedup 5.14 lnz 39 R=symbfact(A'): 0.0001 0.0000 speedup 4.43 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.45 lnz 55 R=symbfact(A,'col'): 0.0002 0.0000 speedup 4.78 719: LPnetlib/lpi_itest2 nrow: 9 ncol: 13 nnz: 26 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.64 lnz 35 R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.09 715: LPnetlib/lpi_galenet nrow: 8 ncol: 14 nnz: 22 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.64 lnz 37 R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.09 1440: Oberwolfach/LFAT5 nrow: 14 ncol: 14 nnz: 46 c=symbfact(A): 0.0001 0.0000 speedup 5.61 lnz 33 R=symbfact(A): 0.0001 0.0000 speedup 3.57 c=symbfact(A'): 0.0001 0.0000 speedup 5.52 lnz 33 R=symbfact(A'): 0.0001 0.0000 speedup 4.61 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.50 lnz 43 R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.26 1817: Meszaros/kleemin nrow: 8 ncol: 16 nnz: 44 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.77 lnz 86 R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.03 720: LPnetlib/lpi_itest6 nrow: 11 ncol: 17 nnz: 29 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.48 lnz 38 R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.12 1710: Meszaros/farm nrow: 7 ncol: 17 nnz: 41 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.61 lnz 101 R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.89 1438: Oberwolfach/LF10 nrow: 18 ncol: 18 nnz: 82 c=symbfact(A): 0.0001 0.0000 speedup 5.00 lnz 58 R=symbfact(A): 0.0001 0.0000 speedup 4.24 c=symbfact(A'): 0.0001 0.0000 speedup 5.32 lnz 58 R=symbfact(A'): 0.0001 0.0000 speedup 4.03 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.17 lnz 86 R=symbfact(A,'col'): 0.0002 0.0000 speedup 4.78 1479: Pajek/GD01_b nrow: 18 ncol: 18 nnz: 37 c=symbfact(A): 0.0001 0.0000 speedup 5.47 lnz 43 R=symbfact(A): 0.0001 0.0001 speedup 0.92 c=symbfact(A'): 0.0001 0.0000 speedup 4.03 lnz 37 R=symbfact(A'): 0.0001 0.0000 speedup 3.50 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.43 lnz 43 R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.06 1481: Pajek/GD02_a nrow: 23 ncol: 23 nnz: 87 c=symbfact(A): 0.0001 0.0000 speedup 5.05 lnz 83 R=symbfact(A): 0.0001 0.0000 speedup 4.14 c=symbfact(A'): 0.0001 0.0000 speedup 3.65 lnz 83 R=symbfact(A'): 0.0001 0.0000 speedup 3.25 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.92 lnz 208 R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.38 1516: Pajek/Ragusa18 nrow: 23 ncol: 23 nnz: 64 c=symbfact(A): 0.0001 0.0000 speedup 5.05 lnz 69 R=symbfact(A): 0.0001 0.0001 speedup 2.10 c=symbfact(A'): 0.0001 0.0000 speedup 3.74 lnz 61 R=symbfact(A'): 0.0001 0.0000 speedup 3.28 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.25 lnz 96 R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.83 97: HB/can_24 nrow: 24 ncol: 24 nnz: 160 c=symbfact(A): 0.0001 0.0000 speedup 4.65 lnz 120 R=symbfact(A): 0.0001 0.0000 speedup 3.09 c=symbfact(A'): 0.0001 0.0000 speedup 4.73 lnz 120 R=symbfact(A'): 0.0001 0.0001 speedup 1.96 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.93 lnz 196 R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.36 1515: Pajek/Ragusa16 nrow: 24 ncol: 24 nnz: 81 c=symbfact(A): 0.0001 0.0000 speedup 5.05 lnz 71 R=symbfact(A): 0.0001 0.0000 speedup 3.36 c=symbfact(A'): 0.0001 0.0000 speedup 5.04 lnz 70 R=symbfact(A'): 0.0001 0.0000 speedup 4.00 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.12 lnz 144 R=symbfact(A,'col'): 0.0002 0.0000 speedup 5.54 1177: HB/lap_25 nrow: 25 ncol: 25 nnz: 169 c=symbfact(A): 0.0001 0.0000 speedup 4.65 lnz 138 R=symbfact(A): 0.0002 0.0000 speedup 3.87 c=symbfact(A'): 0.0001 0.0000 speedup 3.62 lnz 138 R=symbfact(A'): 0.0001 0.0000 speedup 3.86 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.44 lnz 235 R=symbfact(A,'col'): 0.0002 0.0000 speedup 3.21 436: FIDAP/ex5 nrow: 27 ncol: 27 nnz: 279 c=symbfact(A): 0.0001 0.0000 speedup 4.58 lnz 153 R=symbfact(A): 0.0002 0.0000 speedup 3.80 c=symbfact(A'): 0.0001 0.0000 speedup 4.64 lnz 153 R=symbfact(A'): 0.0001 0.0000 speedup 3.92 c=symbfact(A,'col'): 0.0002 0.0000 speedup 6.69 lnz 261 R=symbfact(A,'col'): 0.0002 0.0001 speedup 3.21 232: HB/pores_1 nrow: 30 ncol: 30 nnz: 180 c=symbfact(A): 0.0005 0.0000 speedup 20.28 lnz 133 R=symbfact(A): 0.0002 0.0001 speedup 3.04 c=symbfact(A'): 0.0001 0.0000 speedup 5.04 lnz 183 R=symbfact(A'): 0.0001 0.0000 speedup 3.16 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.82 lnz 253 R=symbfact(A,'col'): 0.0001 0.0001 speedup 2.65 168: HB/ibm32 nrow: 32 ncol: 32 nnz: 126 c=symbfact(A): 0.0001 0.0000 speedup 4.70 lnz 155 R=symbfact(A): 0.0001 0.0000 speedup 3.00 c=symbfact(A'): 0.0001 0.0000 speedup 5.00 lnz 135 R=symbfact(A'): 0.0001 0.0000 speedup 3.75 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.66 lnz 325 R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.08 1199: Hamrle/Hamrle1 nrow: 32 ncol: 32 nnz: 98 c=symbfact(A): 0.0001 0.0000 speedup 4.86 lnz 173 R=symbfact(A): 0.0001 0.0002 speedup 0.88 c=symbfact(A'): 0.0001 0.0000 speedup 4.96 lnz 112 R=symbfact(A'): 0.0001 0.0000 speedup 3.12 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.93 lnz 176 R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.34 1480: Pajek/GD01_c nrow: 33 ncol: 33 nnz: 135 c=symbfact(A): 0.0001 0.0000 speedup 4.50 lnz 139 R=symbfact(A): 0.0962 0.0000 speedup 1963.43 c=symbfact(A'): 0.0002 0.0000 speedup 6.00 lnz 144 R=symbfact(A'): 0.0001 0.0000 speedup 3.87 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.82 lnz 214 R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.04 1474: Pajek/football nrow: 35 ncol: 35 nnz: 118 c=symbfact(A): 0.0001 0.0000 speedup 4.40 lnz 144 R=symbfact(A): 0.0002 0.0000 speedup 3.49 c=symbfact(A'): 0.0002 0.0000 speedup 5.72 lnz 97 R=symbfact(A'): 0.0001 0.0000 speedup 3.09 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.63 lnz 146 R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.13 1485: Pajek/GD95_a nrow: 36 ncol: 36 nnz: 57 c=symbfact(A): 0.0001 0.0000 speedup 4.42 lnz 69 R=symbfact(A): 0.0001 0.0000 speedup 2.96 c=symbfact(A'): 0.0001 0.0000 speedup 4.73 lnz 71 R=symbfact(A'): 0.0001 0.0011 speedup 0.12 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.07 lnz 69 R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.72 906: vanHeukelum/cage5 nrow: 37 ncol: 37 nnz: 233 c=symbfact(A): 0.0001 0.0000 speedup 4.19 lnz 198 R=symbfact(A): 0.0002 0.0001 speedup 2.00 c=symbfact(A'): 0.0001 0.0000 speedup 4.67 lnz 198 R=symbfact(A'): 0.0001 0.0000 speedup 3.36 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.38 lnz 472 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.37 1495: Pajek/GD98_a nrow: 38 ncol: 38 nnz: 50 c=symbfact(A): 0.0001 0.0000 speedup 4.65 lnz 59 R=symbfact(A): 0.0001 0.0000 speedup 3.69 c=symbfact(A'): 0.0001 0.0000 speedup 5.19 lnz 74 R=symbfact(A'): 0.0001 0.0000 speedup 3.16 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.04 lnz 144 R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.49 13: HB/bcspwr01 nrow: 39 ncol: 39 nnz: 131 c=symbfact(A): 0.0001 0.0000 speedup 4.40 lnz 104 R=symbfact(A): 0.0001 0.0001 speedup 2.92 c=symbfact(A'): 0.0001 0.0000 speedup 4.70 lnz 104 R=symbfact(A'): 0.0001 0.0000 speedup 3.54 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.47 lnz 190 R=symbfact(A,'col'): 0.0001 0.0001 speedup 2.65 706: LPnetlib/lpi_bgprtr nrow: 20 ncol: 40 nnz: 70 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.96 lnz 155 R=symbfact(A,'col'): 0.0001 0.0001 speedup 2.72 1755: Meszaros/problem nrow: 12 ncol: 46 nnz: 86 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.93 lnz 377 R=symbfact(A,'col'): 0.0002 0.0001 speedup 3.04 1493: Pajek/GD97_b nrow: 47 ncol: 47 nnz: 264 c=symbfact(A): 0.0001 0.0000 speedup 3.87 lnz 211 R=symbfact(A): 0.0002 0.0001 speedup 2.71 c=symbfact(A'): 0.0001 0.0000 speedup 4.25 lnz 211 R=symbfact(A'): 0.0002 0.0001 speedup 2.75 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.19 lnz 713 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.17 23: HB/bcsstk01 nrow: 48 ncol: 48 nnz: 400 c=symbfact(A): 0.0001 0.0000 speedup 3.75 lnz 489 R=symbfact(A): 0.0002 0.0001 speedup 2.56 c=symbfact(A'): 0.0001 0.0000 speedup 4.45 lnz 489 R=symbfact(A'): 0.0002 0.0001 speedup 2.98 c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.98 lnz 944 R=symbfact(A,'col'): 0.0002 0.0001 speedup 1.97 56: HB/bcsstm01 nrow: 48 ncol: 48 nnz: 24 c=symbfact(A): 0.0001 0.0000 speedup 4.73 lnz 48 R=symbfact(A): 0.0001 0.0000 speedup 4.00 c=symbfact(A'): 0.0001 0.0000 speedup 4.96 lnz 48 R=symbfact(A'): 0.0002 0.0001 speedup 3.67 c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.33 lnz 48 R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.74 872: Pothen/mesh1e1 nrow: 48 ncol: 48 nnz: 306 c=symbfact(A): 0.0001 0.0000 speedup 4.30 lnz 336 R=symbfact(A): 0.0002 0.0001 speedup 3.04 c=symbfact(A'): 0.0001 0.0000 speedup 4.34 lnz 336 R=symbfact(A'): 0.0002 0.0001 speedup 2.72 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.11 lnz 769 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.40 873: Pothen/mesh1em1 nrow: 48 ncol: 48 nnz: 306 c=symbfact(A): 0.0001 0.0000 speedup 3.90 lnz 336 R=symbfact(A): 0.0002 0.0001 speedup 3.13 c=symbfact(A'): 0.0001 0.0000 speedup 4.27 lnz 336 R=symbfact(A'): 0.0002 0.0001 speedup 2.70 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.19 lnz 769 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.45 874: Pothen/mesh1em6 nrow: 48 ncol: 48 nnz: 306 c=symbfact(A): 0.0001 0.0000 speedup 3.90 lnz 336 R=symbfact(A): 0.0002 0.0001 speedup 3.17 c=symbfact(A'): 0.0002 0.0000 speedup 5.35 lnz 336 R=symbfact(A'): 0.0002 0.0001 speedup 3.04 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.08 lnz 769 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.30 1741: Meszaros/p0033 nrow: 15 ncol: 48 nnz: 113 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.61 lnz 364 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.91 14: HB/bcspwr02 nrow: 49 ncol: 49 nnz: 167 c=symbfact(A): 0.0001 0.0000 speedup 4.04 lnz 129 R=symbfact(A): 0.0002 0.0001 speedup 3.06 c=symbfact(A'): 0.0001 0.0000 speedup 4.59 lnz 129 R=symbfact(A'): 0.0001 0.0000 speedup 2.92 c=symbfact(A,'col'): 0.0002 0.0000 speedup 4.97 lnz 275 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.50 1460: Pajek/divorce nrow: 50 ncol: 9 nnz: 225 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.96 lnz 45 R=symbfact(A,'col'): 0.0001 0.0001 speedup 2.71 597: LPnetlib/lp_afiro nrow: 27 ncol: 51 nnz: 102 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.68 lnz 293 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.52 464: Grund/d_ss nrow: 53 ncol: 53 nnz: 144 c=symbfact(A): 0.0001 0.0000 speedup 4.15 lnz 238 R=symbfact(A): 0.0002 0.0001 speedup 2.74 c=symbfact(A'): 0.0001 0.0000 speedup 4.29 lnz 243 R=symbfact(A'): 0.0003 0.0000 speedup 5.36 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.39 lnz 259 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.96 109: HB/curtis54 nrow: 54 ncol: 54 nnz: 291 c=symbfact(A): 0.0001 0.0000 speedup 3.81 lnz 222 R=symbfact(A): 0.0002 0.0001 speedup 3.11 c=symbfact(A'): 0.0001 0.0001 speedup 2.09 lnz 208 R=symbfact(A'): 0.0002 0.0001 speedup 3.34 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.13 lnz 556 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.22 1457: Pajek/Cities nrow: 55 ncol: 46 nnz: 1342 c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.76 lnz 1081 R=symbfact(A,'col'): 0.0003 0.0002 speedup 1.78 274: HB/will57 nrow: 57 ncol: 57 nnz: 281 c=symbfact(A): 0.0001 0.0000 speedup 4.03 lnz 179 R=symbfact(A): 0.0002 0.0001 speedup 3.30 c=symbfact(A'): 0.0001 0.0000 speedup 4.15 lnz 178 R=symbfact(A'): 0.0002 0.0000 speedup 4.41 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.11 lnz 450 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.17 129: HB/dwt_59 nrow: 59 ncol: 59 nnz: 267 c=symbfact(A): 0.0001 0.0000 speedup 3.77 lnz 244 R=symbfact(A): 0.0002 0.0001 speedup 3.13 c=symbfact(A'): 0.0001 0.0001 speedup 2.22 lnz 244 R=symbfact(A'): 0.0002 0.0001 speedup 3.30 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.03 lnz 492 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.25 172: HB/impcol_b nrow: 59 ncol: 59 nnz: 271 c=symbfact(A): 0.0001 0.0000 speedup 3.75 lnz 394 R=symbfact(A): 0.0002 0.0001 speedup 2.52 c=symbfact(A'): 0.0002 0.0000 speedup 6.14 lnz 269 R=symbfact(A'): 0.0002 0.0001 speedup 2.78 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.19 lnz 468 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.25 102: HB/can_61 nrow: 61 ncol: 61 nnz: 557 c=symbfact(A): 0.0001 0.0000 speedup 3.50 lnz 361 R=symbfact(A): 0.0002 0.0001 speedup 2.07 c=symbfact(A'): 0.0002 0.0000 speedup 3.92 lnz 361 R=symbfact(A'): 0.0002 0.0001 speedup 2.54 c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.84 lnz 966 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.09 103: HB/can_62 nrow: 62 ncol: 62 nnz: 218 c=symbfact(A): 0.0001 0.0000 speedup 3.87 lnz 184 R=symbfact(A): 0.0002 0.0001 speedup 2.64 c=symbfact(A'): 0.0001 0.0000 speedup 4.13 lnz 184 R=symbfact(A'): 0.0001 0.0000 speedup 3.19 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.19 lnz 358 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.74 293: Bai/bfwa62 nrow: 62 ncol: 62 nnz: 450 c=symbfact(A): 0.0001 0.0000 speedup 3.43 lnz 317 R=symbfact(A): 0.0002 0.0001 speedup 3.02 c=symbfact(A'): 0.0001 0.0000 speedup 3.97 lnz 327 R=symbfact(A'): 0.0002 0.0001 speedup 3.00 c=symbfact(A,'col'): 0.0002 0.0000 speedup 3.57 lnz 743 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.24 296: Bai/bfwb62 nrow: 62 ncol: 62 nnz: 342 c=symbfact(A): 0.0001 0.0000 speedup 3.64 lnz 288 R=symbfact(A): 0.0002 0.0001 speedup 2.98 c=symbfact(A'): 0.0001 0.0000 speedup 4.00 lnz 288 R=symbfact(A'): 0.0002 0.0001 speedup 2.62 c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.72 lnz 589 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.64 1487: Pajek/GD95_c nrow: 62 ncol: 62 nnz: 287 c=symbfact(A): 0.0002 0.0000 speedup 4.67 lnz 234 R=symbfact(A): 0.0002 0.0001 speedup 3.27 c=symbfact(A'): 0.0001 0.0000 speedup 4.03 lnz 234 R=symbfact(A'): 0.0002 0.0001 speedup 3.13 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.05 lnz 598 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.49 1759: Meszaros/refine nrow: 29 ncol: 62 nnz: 153 c=symbfact(A,'col'): 0.0002 0.0000 speedup 6.03 lnz 628 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.74 1742: Meszaros/p0040 nrow: 23 ncol: 63 nnz: 133 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.71 lnz 515 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.71 1498: Pajek/GD99_b nrow: 64 ncol: 64 nnz: 252 c=symbfact(A): 0.0001 0.0000 speedup 3.75 lnz 461 R=symbfact(A): 0.0002 0.0001 speedup 2.82 c=symbfact(A'): 0.0002 0.0000 speedup 4.46 lnz 461 R=symbfact(A'): 0.0002 0.0001 speedup 2.98 c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.95 lnz 1001 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.81 1490: Pajek/GD96_c nrow: 65 ncol: 65 nnz: 250 c=symbfact(A): 0.0001 0.0000 speedup 3.69 lnz 341 R=symbfact(A): 0.0002 0.0001 speedup 3.00 c=symbfact(A'): 0.0001 0.0000 speedup 4.06 lnz 341 R=symbfact(A'): 0.0002 0.0001 speedup 3.00 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.00 lnz 626 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.16 24: HB/bcsstk02 nrow: 66 ncol: 66 nnz: 4356 c=symbfact(A): 0.0002 0.0001 speedup 2.47 lnz 2211 R=symbfact(A): 0.0934 0.0002 speedup 411.51 c=symbfact(A'): 0.0004 0.0001 speedup 4.48 lnz 2211 R=symbfact(A'): 0.0004 0.0002 speedup 2.47 c=symbfact(A,'col'): 0.0002 0.0001 speedup 2.09 lnz 2211 R=symbfact(A,'col'): 0.0010 0.0008 speedup 1.27 57: HB/bcsstm02 nrow: 66 ncol: 66 nnz: 66 c=symbfact(A): 0.0001 0.0000 speedup 4.82 lnz 66 R=symbfact(A): 0.0001 0.0000 speedup 3.57 c=symbfact(A'): 0.0001 0.0000 speedup 4.92 lnz 66 R=symbfact(A'): 0.0001 0.0001 speedup 1.07 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.96 lnz 66 R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.60 132: HB/dwt_66 nrow: 66 ncol: 66 nnz: 320 c=symbfact(A): 0.0001 0.0000 speedup 4.11 lnz 193 R=symbfact(A): 0.0002 0.0000 speedup 3.59 c=symbfact(A'): 0.0001 0.0000 speedup 4.77 lnz 193 R=symbfact(A'): 0.0002 0.0001 speedup 2.96 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.17 lnz 321 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.89 883: Pothen/sphere2 nrow: 66 ncol: 66 nnz: 450 c=symbfact(A): 0.0001 0.0000 speedup 3.44 lnz 682 R=symbfact(A): 0.0002 0.0001 speedup 2.76 c=symbfact(A'): 0.0002 0.0000 speedup 4.63 lnz 682 R=symbfact(A'): 0.0002 0.0001 speedup 2.82 c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.91 lnz 1368 R=symbfact(A,'col'): 0.0002 0.0001 speedup 1.89 262: HB/west0067 nrow: 67 ncol: 67 nnz: 294 c=symbfact(A): 0.0001 0.0000 speedup 3.56 lnz 701 R=symbfact(A): 0.0002 0.0001 speedup 2.56 c=symbfact(A'): 0.0001 0.0000 speedup 4.11 lnz 569 R=symbfact(A'): 0.0002 0.0001 speedup 2.80 c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.83 lnz 872 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.36 636: LPnetlib/lp_kb2 nrow: 43 ncol: 68 nnz: 313 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.00 lnz 589 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.39 133: HB/dwt_72 nrow: 72 ncol: 72 nnz: 222 c=symbfact(A): 0.0001 0.0000 speedup 4.00 lnz 184 R=symbfact(A): 0.0002 0.0001 speedup 2.78 c=symbfact(A'): 0.0001 0.0000 speedup 4.35 lnz 184 R=symbfact(A'): 0.0002 0.0001 speedup 3.12 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.14 lnz 329 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.76 1501: Pajek/GlossGT nrow: 72 ncol: 72 nnz: 122 c=symbfact(A): 0.0001 0.0000 speedup 3.66 lnz 219 R=symbfact(A): 0.0002 0.0001 speedup 3.09 c=symbfact(A'): 0.0001 0.0000 speedup 3.32 lnz 96 R=symbfact(A'): 0.0001 0.0000 speedup 3.44 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.36 lnz 147 R=symbfact(A,'col'): 0.0002 0.0001 speedup 3.06 106: HB/can_73 nrow: 73 ncol: 73 nnz: 377 c=symbfact(A): 0.0001 0.0000 speedup 3.62 lnz 392 R=symbfact(A): 0.0002 0.0001 speedup 2.60 c=symbfact(A'): 0.0002 0.0000 speedup 4.21 lnz 392 R=symbfact(A'): 0.0002 0.0001 speedup 2.73 c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.90 lnz 1438 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.05 1486: Pajek/GD95_b nrow: 73 ncol: 73 nnz: 96 c=symbfact(A): 0.0001 0.0000 speedup 4.04 lnz 105 R=symbfact(A): 0.0002 0.0000 speedup 3.29 c=symbfact(A'): 0.0001 0.0000 speedup 4.00 lnz 147 R=symbfact(A'): 0.0002 0.0000 speedup 3.30 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.41 lnz 476 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.76 666: LPnetlib/lp_sc50a nrow: 50 ncol: 78 nnz: 160 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.08 lnz 332 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.62 667: LPnetlib/lp_sc50b nrow: 50 ncol: 78 nnz: 148 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.59 lnz 316 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.70 253: HB/steam3 nrow: 80 ncol: 80 nnz: 314 c=symbfact(A): 0.0001 0.0000 speedup 4.00 lnz 208 R=symbfact(A): 0.0002 0.0001 speedup 3.20 c=symbfact(A'): 0.0001 0.0000 speedup 4.09 lnz 205 R=symbfact(A'): 0.0002 0.0001 speedup 3.20 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.11 lnz 424 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.49 1482: Pajek/GD02_b nrow: 80 ncol: 80 nnz: 232 c=symbfact(A): 0.0001 0.0000 speedup 3.56 lnz 326 R=symbfact(A): 0.0002 0.0001 speedup 2.88 c=symbfact(A'): 0.0002 0.0000 speedup 4.31 lnz 317 R=symbfact(A'): 0.0002 0.0001 speedup 2.93 c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.88 lnz 497 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.53 1492: Pajek/GD97_a nrow: 84 ncol: 84 nnz: 332 c=symbfact(A): 0.0001 0.0000 speedup 3.41 lnz 677 R=symbfact(A): 0.0002 0.0001 speedup 2.60 c=symbfact(A'): 0.0002 0.0000 speedup 3.87 lnz 677 R=symbfact(A'): 0.0002 0.0001 speedup 2.75 c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.71 lnz 1608 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.29 11: HB/ash85 nrow: 85 ncol: 85 nnz: 523 c=symbfact(A): 0.0001 0.0000 speedup 3.26 lnz 505 R=symbfact(A): 0.0002 0.0001 speedup 2.73 c=symbfact(A'): 0.0002 0.0000 speedup 3.74 lnz 505 R=symbfact(A'): 0.0002 0.0001 speedup 2.71 c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.59 lnz 1109 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.13 1519: Pajek/Sandi_authors nrow: 86 ncol: 86 nnz: 248 c=symbfact(A): 0.0001 0.0000 speedup 3.46 lnz 221 R=symbfact(A): 0.0002 0.0001 speedup 2.37 c=symbfact(A'): 0.0001 0.0000 speedup 3.94 lnz 221 R=symbfact(A'): 0.0002 0.0001 speedup 2.52 c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.95 lnz 533 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.43 136: HB/dwt_87 nrow: 87 ncol: 87 nnz: 541 c=symbfact(A): 0.0001 0.0000 speedup 3.37 lnz 414 R=symbfact(A): 0.0002 0.0001 speedup 2.64 c=symbfact(A'): 0.0002 0.0000 speedup 4.42 lnz 414 R=symbfact(A'): 0.0002 0.0001 speedup 2.46 c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.65 lnz 921 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.08 462: Grund/d_dyn nrow: 87 ncol: 87 nnz: 230 c=symbfact(A): 0.0001 0.0000 speedup 3.33 lnz 442 R=symbfact(A): 0.0002 0.0001 speedup 2.74 c=symbfact(A'): 0.0001 0.0000 speedup 3.84 lnz 450 R=symbfact(A'): 0.0002 0.0001 speedup 2.85 c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.81 lnz 432 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.01 463: Grund/d_dyn1 nrow: 87 ncol: 87 nnz: 232 c=symbfact(A): 0.0001 0.0000 speedup 3.43 lnz 476 R=symbfact(A): 0.0002 0.0001 speedup 2.64 c=symbfact(A'): 0.0001 0.0000 speedup 3.74 lnz 441 R=symbfact(A'): 0.0002 0.0001 speedup 2.38 c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.74 lnz 439 R=symbfact(A,'col'): 0.0002 0.0001 speedup 1.80 731: LPnetlib/lpi_woodinfe nrow: 35 ncol: 89 nnz: 140 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.11 lnz 402 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.58 1641: Bai/tols90 nrow: 90 ncol: 90 nnz: 1746 c=symbfact(A): 0.0001 0.0000 speedup 3.33 lnz 315 R=symbfact(A): 0.0002 0.0001 speedup 2.75 c=symbfact(A'): 0.0002 0.0001 speedup 2.96 lnz 1539 R=symbfact(A'): 0.0003 0.0001 speedup 2.25 c=symbfact(A,'col'): 0.0002 0.0001 speedup 2.33 lnz 4095 R=symbfact(A,'col'): 0.0007 0.0005 speedup 1.46 907: vanHeukelum/cage6 nrow: 93 ncol: 93 nnz: 785 c=symbfact(A): 0.0001 0.0000 speedup 3.07 lnz 1170 R=symbfact(A): 0.0002 0.0001 speedup 2.27 c=symbfact(A'): 0.0002 0.0000 speedup 3.65 lnz 1170 R=symbfact(A'): 0.0002 0.0001 speedup 2.42 c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.34 lnz 2665 R=symbfact(A,'col'): 0.0003 0.0002 speedup 1.82 108: HB/can_96 nrow: 96 ncol: 96 nnz: 768 c=symbfact(A): 0.0002 0.0000 speedup 3.42 lnz 984 R=symbfact(A): 0.0002 0.0001 speedup 2.26 c=symbfact(A'): 0.0002 0.0001 speedup 1.20 lnz 984 R=symbfact(A'): 0.0002 0.0001 speedup 2.57 c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.46 lnz 2620 R=symbfact(A,'col'): 0.0003 0.0002 speedup 1.78 220: HB/nos4 nrow: 100 ncol: 100 nnz: 594 c=symbfact(A): 0.0001 0.0000 speedup 3.02 lnz 632 R=symbfact(A): 0.0002 0.0001 speedup 2.39 c=symbfact(A'): 0.0002 0.0000 speedup 3.50 lnz 632 R=symbfact(A'): 0.0002 0.0001 speedup 2.59 c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.53 lnz 1414 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.05 318: Bai/olm100 nrow: 100 ncol: 100 nnz: 396 c=symbfact(A): 0.0001 0.0000 speedup 3.67 lnz 247 R=symbfact(A): 0.0002 0.0001 speedup 3.04 c=symbfact(A'): 0.0001 0.0000 speedup 4.15 lnz 249 R=symbfact(A'): 0.0002 0.0001 speedup 3.18 c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.95 lnz 538 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.10 337: Bai/tub100 nrow: 100 ncol: 100 nnz: 396 c=symbfact(A): 0.0001 0.0000 speedup 3.73 lnz 297 R=symbfact(A): 0.0002 0.0001 speedup 2.55 c=symbfact(A'): 0.0001 0.0000 speedup 4.11 lnz 297 R=symbfact(A'): 0.0002 0.0001 speedup 3.05 c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.93 lnz 490 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.55 1326: Morandini/rotor1 nrow: 100 ncol: 100 nnz: 708 c=symbfact(A): 0.0001 0.0000 speedup 3.02 lnz 551 R=symbfact(A): 0.0002 0.0001 speedup 2.44 c=symbfact(A'): 0.0002 0.0000 speedup 4.18 lnz 714 R=symbfact(A'): 0.0002 0.0001 speedup 2.52 c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.41 lnz 2049 R=symbfact(A,'col'): 0.0003 0.0002 speedup 1.76 1484: Pajek/GD06_theory nrow: 101 ncol: 101 nnz: 380 c=symbfact(A): 0.0001 0.0000 speedup 3.61 lnz 336 R=symbfact(A): 0.0002 0.0001 speedup 2.89 c=symbfact(A'): 0.0001 0.0000 speedup 3.94 lnz 336 R=symbfact(A'): 0.0002 0.0001 speedup 2.56 c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.75 lnz 3401 R=symbfact(A,'col'): 0.0003 0.0001 speedup 1.99 861: MathWorks/pivtol nrow: 102 ncol: 102 nnz: 306 c=symbfact(A): 0.0001 0.0000 speedup 3.93 lnz 302 R=symbfact(A): 0.0002 0.0001 speedup 2.57 c=symbfact(A'): 0.0001 0.0000 speedup 4.12 lnz 303 R=symbfact(A'): 0.0002 0.0001 speedup 3.00 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.03 lnz 500 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.62 306: Bai/ck104 nrow: 104 ncol: 104 nnz: 992 c=symbfact(A): 0.0001 0.0000 speedup 3.11 lnz 548 R=symbfact(A): 0.0002 0.0001 speedup 2.61 c=symbfact(A'): 0.0002 0.0000 speedup 3.71 lnz 548 R=symbfact(A'): 0.0002 0.0001 speedup 3.12 c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.48 lnz 912 R=symbfact(A,'col'): 0.0002 0.0001 speedup 1.89 1499: Pajek/GD99_c nrow: 105 ncol: 105 nnz: 149 c=symbfact(A): 0.0002 0.0000 speedup 5.75 lnz 166 R=symbfact(A): 0.0002 0.0001 speedup 3.15 c=symbfact(A'): 0.0001 0.0000 speedup 3.76 lnz 221 R=symbfact(A'): 0.0002 0.0001 speedup 2.61 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.08 lnz 231 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.83 721: LPnetlib/lpi_klein1 nrow: 54 ncol: 108 nnz: 750 c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.35 lnz 2132 R=symbfact(A,'col'): 0.0003 0.0002 speedup 1.82 1489: Pajek/GD96_b nrow: 111 ncol: 111 nnz: 193 c=symbfact(A): 0.0001 0.0000 speedup 3.49 lnz 303 R=symbfact(A): 0.0003 0.0001 speedup 4.68 c=symbfact(A'): 0.0001 0.0000 speedup 4.45 lnz 132 R=symbfact(A'): 0.0001 0.0001 speedup 2.68 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.14 lnz 168 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.83 25: HB/bcsstk03 nrow: 112 ncol: 112 nnz: 640 c=symbfact(A): 0.0002 0.0000 speedup 4.18 lnz 384 R=symbfact(A): 0.0002 0.0001 speedup 2.46 c=symbfact(A'): 0.0002 0.0000 speedup 3.72 lnz 384 R=symbfact(A'): 0.0002 0.0001 speedup 2.88 c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.65 lnz 592 R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.13 58: HB/bcsstm03 nrow: 112 ncol: 112 nnz: 72 c=symbfact(A): 0.0001 0.0000 speedup 4.19 lnz 112 R=symbfact(A): 0.0002 0.0000 speedup 3.40 c=symbfact(A'): 0.0001 0.0000 speedup 4.86 lnz 112 R=symbfact(A'): 0.0001 0.0000 speedup 3.31 c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.52 lnz 112 R=symbfact(A,'col'): 0.0002 0.0000 speedup 3.23 1497: Pajek/GD98_c nrow: 112 ncol: 112 nnz: 336 c=symbfact(A): 0.0001 0.0000 speedup 3.12 lnz 967 R=symbfact(A): 0.0002 0.0001 speedup 2.43 c=symbfact(A'): 0.0002 0.0000 speedup 3.58 lnz 967 R=symbfact(A'): 0.0002 0.0001 speedup 2.43 c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.63 lnz 2064 R=symbfact(A,'col'): 0.0003 0.0001 speedup 2.16 158: HB/gent113 nrow: 113 ncol: 113 nnz: 655 c=symbfact(A): 0.0001 0.0000 speedup 2.94 lnz 791 R=symbfact(A): 0.0002 0.0001 speedup 2.33 c=symbfact(A'): 0.0002 0.0000 speedup 3.73 lnz 643 R=symbfact(A'): 0.0002 0.0001 speedup 2.56 c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.36 lnz 1433 R=symbfact(A,'col'): 0.0003 0.0001 speedup 2.06 603: LPnetlib/lp_blend nrow: 74 ncol: 114 nnz: 522 c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.57 lnz 1459 R=symbfact(A,'col'): 0.0002 0.0002 speedup 1.14 test15 passed ================================================================= test16: test cholmod2 on a large matrix Prob = A: [9000x9000 double] name: 'ND/nd3k' title: 'ND problem set, matrix nd3k' id: 936 date: '2003' author: 'author unknown' ed: 'T. Davis' kind: '2D/3D problem' time 17.5518 test16 passed ================================================================= test17: test lchol on a few large matrices Prob = title: 'S.Norris, Univ. Auckland. FEM, Laplace eqn 2D 100x100 mesh' A: [9604x9604 double] name: 'Norris/fv1' id: 887 date: '2003' author: 'S. Norris' ed: 'T. Davis' kind: '2D/3D problem' ans = 3.4748 Prob = A: [9000x9000 double] name: 'ND/nd3k' title: 'ND problem set, matrix nd3k' id: 936 date: '2003' author: 'author unknown' ed: 'T. Davis' kind: '2D/3D problem' ans = 30.1030 Prob = title: 'S.Norris, Univ. Auckland. FEM, Laplace eqn 2D 100x100 mesh' A: [9604x9604 double] name: 'Norris/fv1' id: 887 date: '2003' author: 'S. Norris' ed: 'T. Davis' kind: '2D/3D problem' ans = 3.4748 ================================================================= test18: test cholmod2 on a few large matrices Prob = title: 'S.Norris, Univ. Auckland. FEM, Laplace eqn 2D 100x100 mesh' A: [9604x9604 double] name: 'Norris/fv1' id: 887 date: '2003' author: 'S. Norris' ed: 'T. Davis' kind: '2D/3D problem' ans = 4.9310e-12 Prob = A: [9000x9000 double] name: 'ND/nd3k' title: 'ND problem set, matrix nd3k' id: 936 date: '2003' author: 'author unknown' ed: 'T. Davis' kind: '2D/3D problem' ans = 1.6330e-05 Prob = title: 'S.Norris, Univ. Auckland. FEM, Laplace eqn 2D 100x100 mesh' A: [9604x9604 double] name: 'Norris/fv1' id: 887 date: '2003' author: 'S. Norris' ed: 'T. Davis' kind: '2D/3D problem' ans = 4.9453e-12 test18 passed ================================================================= test19: look for NaN's from lchol (caused by Intel MKL 7.x bug) Prob = A: [9000x9000 double] name: 'ND/nd3k' title: 'ND problem set, matrix nd3k' id: 936 date: '2003' author: 'author unknown' ed: 'T. Davis' kind: '2D/3D problem' mflop rate: 1287.30 test19 passed; you have a NaN-free BLAS (must not be MKL 7.x...) ================================================================= test20: test symbfact2, cholmod2, and lu on a few large matrices Prob = title: 'STRUCTURE FROM NASA LANGLEY, ACCURACY PROBLEM ON Y-MP' A: [16146x16146 double] b: [16146x1 double] name: 'Simon/olafu' id: 813 date: '1993' author: 'H. Simon' ed: 'H. Simon' kind: 'structural problem' lnz 3095636 unz 3095636 nnz(L+U) 6175126 fl 1.13063e+09 gflop 1.84307 t 0.613446 err 5.225120e-04 Prob = title: 'BUCKLING PROBLEM FOR CONTAINER MODEL, ARTHUR RAEFSKY, CENTRIC ENG.' A: [19779x19779 double] Zeros: [19779x19779 double] b: [19779x1 double] name: 'Simon/raefsky4' id: 817 date: '1993' author: 'A. Raefsky' ed: 'H. Simon' kind: 'structural problem' lnz 7304797 unz 7304797 nnz(L+U) 14589815 fl 5.30769e+09 gflop 4.02389 t 1.31904 err 6.031010e-03 ================================================================= test21: test cholmod2 on diagonal or ill-conditioned matrices Prob = title: 'SYMMETRIC MASS MATRIX - TEXTILE LOOM FRAME' A: [138x138 double] name: 'HB/bcsstm22' id: 72 date: '1984' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' nnz: 138 MATLAB resid 0.0e+00 err 0.0e+00 CHOLMOD resid 1.1e-17 err 1.3e-14 condest 9.4e+02 Prob = title: 'MAGNETO-HYDRO-DYNAMICS ALFVEN SPECTRAL PROBLEM' A: [416x416 double] name: 'Bai/mhdb416' id: 315 date: '1994' author: 'A. Booten, M. Kooper, H. van der Vorst, S. Poedts, J. Goedbloed' ed: 'Z. Bai, D. Day, J. Demmel, J. Dongarra' kind: 'electromagnetics problem' nnz: 2312 MATLAB resid 2.3e-18 err 2.8e-12 CHOLMOD resid 2.3e-18 err 2.8e-12 condest 5.1e+09 Prob = title: 'SYMMETRIC MASS MATRIX, SQUARE PLATE CLAMPED' A: [1083x1083 double] name: 'HB/bcsstm09' id: 64 date: '1982' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' nnz: 1083 MATLAB resid 0.0e+00 err 0.0e+00 CHOLMOD resid 5.2e-17 err 2.4e-13 condest 1.0e+04 Prob = title: 'SYMMETRIC MASS MATRIX - CLAMPED SQUARE PLATE' A: [3600x3600 double] name: 'HB/bcsstm21' id: 71 date: '1984' author: 'J. Lewis' ed: 'I. Duff, R. Grimes, J. Lewis' kind: 'structural problem' nnz: 3600 MATLAB resid 0.0e+00 err 0.0e+00 CHOLMOD resid 2.5e-18 err 2.7e-13 condest 2.4e+01 Prob = name: 'Oberwolfach/t2dal_e' title: 'Oberwolfach: micropyros thruster, E matrix' A: [4257x4257 double] id: 1207 kind: 'duplicate model reduction problem' date: '2004' author: 'E. Rudnyi' ed: 'E. Rudnyi' nnz: 4257 MATLAB resid 0.0e+00 err 0.0e+00 CHOLMOD resid 1.3e-17 err 3.9e-13 condest 3.8e+07 Prob = title: 'FEM CRYSTAL FREE VIBRATION MASS MATRIX' A: [13965x13965 double] name: 'Boeing/crystm02' id: 354 date: '1995' author: 'R. Grimes' ed: 'T. Davis' kind: 'materials problem' nnz: 322905 MATLAB resid 9.5e-17 err 2.3e-11 CHOLMOD resid 9.5e-17 err 2.3e-11 condest 4.5e+02 Prob = name: 'Oberwolfach/t3dl_e' title: 'Oberwolfach: micropyros thruster, E matrix' A: [20360x20360 double] id: 1211 kind: 'duplicate model reduction problem' date: '2004' author: 'E. Rudnyi' ed: 'E. Rudnyi' nnz: 20360 MATLAB resid 0.0e+00 err 0.0e+00 CHOLMOD resid 3.2e-17 err 2.0e-12 condest 6.0e+03 ================================================================= test22: test pos.def and indef. matrices test22: chol and chol2 are repeated so each take >= 0.1 sec ================== 904: Problem: vanHeukelum/cage3 m: 5 n: 5 nnz: 19 19 rcond: 4.25263103233630423983e-01 p: 0 0 MATLAB: 0.0003 CHOLMOD: 0.0003 speedup 1.08 err: 0 0 ================== 449: Problem: Grund/b1_ss m: 7 n: 7 nnz: 15 24 rcond: 0.00000000000000000000e+00 p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.76 err: 0 0 ================== 1710: Problem: Meszaros/farm m: 7 n: 17 nnz: 41 39 rcond: 2.52948218857096309570e-03 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.88 err: 0 0 ================== 715: Problem: LPnetlib/lpi_galenet m: 8 n: 14 nnz: 22 24 rcond: 8.16496580927726145482e-01 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.75 err: 0 0 ================== 1817: Problem: Meszaros/kleemin m: 8 n: 16 nnz: 44 64 rcond: 9.94982371447397095920e-02 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.91 err: 0 0 ================== 185: Problem: HB/jgl009 m: 9 n: 9 nnz: 50 72 rcond: 0.00000000000000000000e+00 p: 3 3 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.78 err: 0 0 ================== 719: Problem: LPnetlib/lpi_itest2 m: 9 n: 13 nnz: 26 51 rcond: 4.47109297966382157608e-01 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.73 err: 0 0 ================== 905: Problem: vanHeukelum/cage4 m: 9 n: 9 nnz: 49 49 rcond: 4.78114120908413264832e-01 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.92 err: 0 0 ================== 238: Problem: HB/rgg010 m: 10 n: 10 nnz: 76 100 rcond: 0.00000000000000000000e+00 p: 3 3 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.90 err: 0 0 ================== 1524: Problem: Pajek/Stranke94 m: 10 n: 10 nnz: 90 90 rcond: 0.00000000000000000000e+00 p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.76 err: 0 0 ================== 186: Problem: HB/jgl011 m: 11 n: 11 nnz: 76 108 rcond: 0.00000000000000000000e+00 p: 6 6 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.80 err: 0 0 ================== 720: Problem: LPnetlib/lpi_itest6 m: 11 n: 17 nnz: 29 51 rcond: 9.45751723210471600956e-03 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.87 err: 0 0 ================== 1525: Problem: Pajek/Tina_AskCal m: 11 n: 11 nnz: 29 50 rcond: 0.00000000000000000000e+00 p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.91 err: 0 0 ================== 1526: Problem: Pajek/Tina_AskCog m: 11 n: 11 nnz: 36 54 rcond: 0.00000000000000000000e+00 p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.79 err: 0 0 ================== 1527: Problem: Pajek/Tina_DisCal m: 11 n: 11 nnz: 41 64 rcond: 0.00000000000000000000e+00 p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.84 err: 0 0 ================== 1528: Problem: Pajek/Tina_DisCog m: 11 n: 11 nnz: 48 72 rcond: 0.00000000000000000000e+00 p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.85 err: 0 0 ================== 1755: Problem: Meszaros/problem m: 12 n: 46 nnz: 86 42 rcond: 5.37847998878130950651e-01 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 1.08 err: 0 0 ================== 1440: Problem: Oberwolfach/LFAT5 m: 14 n: 14 nnz: 46 46 rcond: 1.55639238128393175712e-04 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.76 err: 0 0 ================== 1741: Problem: Meszaros/p0033 m: 15 n: 48 nnz: 113 95 rcond: 1.48172008456599587148e-03 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.78 err: 0 0 ================== 1438: Problem: Oberwolfach/LF10 m: 18 n: 18 nnz: 82 82 rcond: 5.27046276694730000262e-03 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.91 err: 0 0 ================== 1479: Problem: Pajek/GD01_b m: 18 n: 18 nnz: 37 54 rcond: 0.00000000000000000000e+00 p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.92 err: 0 0 ================== 706: Problem: LPnetlib/lpi_bgprtr m: 20 n: 40 nnz: 70 96 rcond: 1.25918385245936273811e-03 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.76 err: 0 0 ================== 1481: Problem: Pajek/GD02_a m: 23 n: 23 nnz: 87 118 rcond: 0.00000000000000000000e+00 p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.78 err: 0 0 ================== 1516: Problem: Pajek/Ragusa18 m: 23 n: 23 nnz: 64 105 rcond: 0.00000000000000000000e+00 p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.93 err: 0 0 ================== 1742: Problem: Meszaros/p0040 m: 23 n: 63 nnz: 133 163 rcond: 2.52390925692451309308e-04 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.91 err: 0 0 ================== 97: Problem: HB/can_24 m: 24 n: 24 nnz: 160 160 rcond: 0.00000000000000000000e+00 p: 2 2 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.82 err: 0 0 ================== 624: Problem: LPnetlib/lp_fit1d m: 24 n: 1049 nnz: 13427 558 rcond: 7.36202451773845909129e-04 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.98 err: 0 0 ================== 1515: Problem: Pajek/Ragusa16 m: 24 n: 24 nnz: 81 126 rcond: 0.00000000000000000000e+00 p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.92 err: 0 0 ================== 626: Problem: LPnetlib/lp_fit2d m: 25 n: 10524 nnz: 129042 617 rcond: 2.18529247214663312551e-03 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.95 err: 0 0 ================== 1177: Problem: HB/lap_25 m: 25 n: 25 nnz: 169 169 rcond: 0.00000000000000000000e+00 p: 2 2 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.80 err: 0 0 ================== 436: Problem: FIDAP/ex5 m: 27 n: 27 nnz: 279 279 rcond: 8.27464239340425602477e-04 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.86 err: 0 0 ================== 597: Problem: LPnetlib/lp_afiro m: 27 n: 51 nnz: 102 153 rcond: 1.72386001683099310267e-01 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.83 err: 0 0 ================== 1759: Problem: Meszaros/refine m: 29 n: 62 nnz: 153 217 rcond: 1.81514831282913007005e-02 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.91 err: 0 0 ================== 232: Problem: HB/pores_1 m: 30 n: 30 nnz: 180 236 rcond: 0.00000000000000000000e+00 p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.91 err: 0 0 ================== 168: Problem: HB/ibm32 m: 32 n: 32 nnz: 126 212 rcond: 0.00000000000000000000e+00 p: 18 18 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.84 err: 0 0 ================== 1199: Problem: Hamrle/Hamrle1 m: 32 n: 32 nnz: 98 181 rcond: 0.00000000000000000000e+00 p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.79 err: 0 0 ================== 1480: Problem: Pajek/GD01_c m: 33 n: 33 nnz: 135 270 rcond: 0.00000000000000000000e+00 p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.92 err: 0 0 ================== 731: Problem: LPnetlib/lpi_woodinfe m: 35 n: 89 nnz: 140 137 rcond: 4.26401432711220829130e-01 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.86 err: 0 0 ================== 1474: Problem: Pajek/football m: 35 n: 35 nnz: 118 236 rcond: 0.00000000000000000000e+00 p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.84 err: 0 0 ================== 1485: Problem: Pajek/GD95_a m: 36 n: 36 nnz: 57 112 rcond: 0.00000000000000000000e+00 p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.80 err: 0 0 ================== 906: Problem: vanHeukelum/cage5 m: 37 n: 37 nnz: 233 233 rcond: 2.54392381006308010427e-01 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.82 err: 0 0 ================== 1495: Problem: Pajek/GD98_a m: 38 n: 38 nnz: 50 92 rcond: 0.00000000000000000000e+00 p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.91 err: 0 0 ================== 13: Problem: HB/bcspwr01 m: 39 n: 39 nnz: 131 131 rcond: 0.00000000000000000000e+00 p: 2 2 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.83 err: 0 0 ================== 636: Problem: LPnetlib/lp_kb2 m: 43 n: 68 nnz: 313 847 rcond: 4.57208742551626703965e-04 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.93 err: 0 0 ================== 1493: Problem: Pajek/GD97_b m: 47 n: 47 nnz: 264 264 rcond: 0.00000000000000000000e+00 p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.99 err: 0 0 ================== 23: Problem: HB/bcsstk01 m: 48 n: 48 nnz: 400 400 rcond: 3.07546526042088742836e-03 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.88 err: 0 0 ================== 56: Problem: HB/bcsstm01 m: 48 n: 48 nnz: 24 24 rcond: 0.00000000000000000000e+00 p: 4 4 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.79 err: 0 0 ================== 872: Problem: Pothen/mesh1e1 m: 48 n: 48 nnz: 306 306 rcond: 5.92447279051849906573e-01 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 1.07 err: 0 0 ================== 873: Problem: Pothen/mesh1em1 m: 48 n: 48 nnz: 306 306 rcond: 2.99182771005118530727e-01 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.88 err: 0 0 ================== 874: Problem: Pothen/mesh1em6 m: 48 n: 48 nnz: 306 306 rcond: 5.98061003584390182830e-01 p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.88 err: 0 0 test22: all tests passed ================================================================= test22: test pos.def and indef. matrices testing matrices for which MATLAB and CHOLMOD differ test22: chol and chol2 are repeated so each take >= 0.1 sec ================== 186: Problem: HB/jgl011 m: 11 n: 11 nnz: 76 108 rcond: 0.00000000000000000000e+00 p: 6 6 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.78 err: 0 0 ================== 109: Problem: HB/curtis54 m: 54 n: 54 nnz: 291 302 rcond: 0.00000000000000000000e+00 p: 4 4 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.96 err: 0 0 ================== 793: Problem: Qaplib/lp_nug05 m: 210 n: 225 nnz: 1050 4060 rcond: 0.00000000000000000000e+00 p: 75 75 MATLAB: 0.0015 CHOLMOD: 0.0014 speedup 1.12 err: 0 0 ================== 607: Problem: LPnetlib/lp_brandy m: 220 n: 303 nnz: 2202 5275 rcond: 0.00000000000000000000e+00 p: 1 1 MATLAB: 0.0004 CHOLMOD: 0.0003 speedup 1.18 err: 0 0 ================== 707: Problem: LPnetlib/lpi_box1 m: 231 n: 261 nnz: 651 1401 rcond: 0.00000000000000000000e+00 p: 22 22 MATLAB: 0.0003 CHOLMOD: 0.0002 speedup 1.80 err: 0 0 ================== 231: Problem: HB/plskz362 m: 362 n: 362 nnz: 1760 0 rcond: 0.00000000000000000000e+00 p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.87 err: 0 0 ================== 794: Problem: Qaplib/lp_nug06 m: 372 n: 486 nnz: 2232 8724 rcond: 0.00000000000000000000e+00 p: 260 260 MATLAB: 0.0089 CHOLMOD: 0.1089 speedup 0.08 err: 0 0 ================== 673: Problem: LPnetlib/lp_scorpion m: 388 n: 466 nnz: 1534 3814 rcond: 0.00000000000000000000e+00 p: 35 35 MATLAB: 0.0003 CHOLMOD: 0.0004 speedup 0.79 err: 0 0 ================== 1156: Problem: Sandia/oscil_dcop_45 m: 430 n: 430 nnz: 1544 1572 rcond: 0.00000000000000000000e+00 p: 31 31 MATLAB: 0.0002 CHOLMOD: 0.0002 speedup 0.90 err: 0 0 ================== 795: Problem: Qaplib/lp_nug07 m: 602 n: 931 nnz: 4214 16576 rcond: 0.00000000000000000000e+00 p: 218 218 MATLAB: 0.0171 CHOLMOD: 0.0170 speedup 1.01 err: 0 0 ================== 796: Problem: Qaplib/lp_nug08 m: 912 n: 1632 nnz: 7296 28816 rcond: 0.00000000000000000000e+00 p: 388 388 MATLAB: 0.1514 CHOLMOD: 0.0512 speedup 2.96 err: 0 0 ================== 260: Problem: HB/well1033 m: 1033 n: 320 nnz: 4732 182679 rcond: 0.00000000000000000000e+00 p: 15 15 MATLAB: 0.0148 CHOLMOD: 0.0149 speedup 0.99 err: 0 0 ================== 261: Problem: HB/well1850 m: 1850 n: 712 nnz: 8755 522902 rcond: 0.00000000000000000000e+00 p: 6 6 MATLAB: 0.0454 CHOLMOD: 0.0440 speedup 1.03 err: 0 0 ================== 230: Problem: HB/plsk1919 m: 1919 n: 1919 nnz: 9662 0 rcond: 0.00000000000000000000e+00 p: 1 1 MATLAB: 0.0003 CHOLMOD: 0.0003 speedup 0.92 err: 0 0 ================== 649: Problem: LPnetlib/lp_pds_02 m: 2953 n: 7716 nnz: 16571 23281 rcond: 2.12687604726321055632e-08 p: 0 0 MATLAB: 0.0140 CHOLMOD: 0.0144 speedup 0.97 err: 0 0 ================== 660: Problem: LPnetlib/lp_qap12 m: 3192 n: 8856 nnz: 38304 152376 rcond: 0.00000000000000000000e+00 p: 1424 1424 MATLAB: 0.9041 CHOLMOD: 1.2285 speedup 0.74 err: 0 0 ================== 609: Problem: LPnetlib/lp_cre_a m: 3516 n: 7248 nnz: 18168 44866 rcond: 0.00000000000000000000e+00 p: 3407 3407 MATLAB: 0.0077 CHOLMOD: 0.0069 speedup 1.11 err: 0 0 ================== 619: Problem: LPnetlib/lp_dfl001 m: 6071 n: 12230 nnz: 35632 81917 rcond: 0.00000000000000000000e+00 p: 5652 5652 MATLAB: 1.0070 CHOLMOD: 1.3922 speedup 0.72 err: 0 0 ================== 661: Problem: LPnetlib/lp_qap15 m: 6330 n: 22275 nnz: 94950 378480 rcond: 0.00000000000000000000e+00 p: 617 617 MATLAB: 0.3764 CHOLMOD: 0.7196 speedup 0.52 err: 0 0 ================== 650: Problem: LPnetlib/lp_pds_06 m: 9881 n: 29351 nnz: 63220 88003 rcond: 0.00000000000000000000e+00 p: 9316 9316 MATLAB: 0.1965 CHOLMOD: 0.1951 speedup 1.01 err: 0 0 ================== 379: Problem: Cote/vibrobox m: 12328 n: 12328 nnz: 301700 301700 rcond: 0.00000000000000000000e+00 p: 11561 11561 MATLAB: 0.6442 CHOLMOD: 0.6420 speedup 1.00 err: 0 0 ================== 638: Problem: LPnetlib/lp_ken_11 m: 14694 n: 21349 nnz: 49058 82454 rcond: 0.00000000000000000000e+00 p: 14626 14626 MATLAB: 0.0411 CHOLMOD: 0.0413 speedup 0.99 err: 0 0 test22: all tests passed ================================================================= test23: test chol & cholmod2 on the sparse matrix used in "bench" Using each method's internal fill-reducing ordering: MATLAB x=A\b time: 0.0467 resid: 6e-14 CHOLMOD x=A\b time: 0.0472 resid: 6e-14 CHOLMOD speedup: 0.99 S = A(p,p) where p is CHOLMOD's ordering: MATLAB R=chol(S) time: 0.0434 resid: 5e-14 CHOLMOD L=lchol(S) time: 0.0363 resid: 5e-14 CHOLMOD speedup: 1.20 Warning: SYMMMD is obsolete and will be removed in a future version. Use SYMAMD instead. > In symmmd at 16 In test23 at 60 In cholmod_test at 131 S = A(p,p) where p is MATLAB's ordering in x=A\b (symmmd): MATLAB R=chol(S) time: 0.0449 resid: 5e-14 CHOLMOD L=lchol(S) time: 0.0369 resid: 5e-14 CHOLMOD speedup: 1.22 With no fill-reducing orderings: MATLAB R=chol(A) time: 0.1380 resid: 1e-13 CHOLMOD L=lchol(A) time: 0.1098 resid: 1e-13 CHOLMOD speedup: 1.26 With no fill-reducing orderings (as used in "bench"): MATLAB x=A\b time: 0.0822 resid: 6e-14 CHOLMOD x=A\b time: 0.0899 resid: 8e-14 CHOLMOD speedup: 0.91 ================================================================= test24: test sdmult test 24 passed, maxerr 0 ================================================================= test25: test sdmult on a large matrix Test matrix: 9000-by-9000, nnz 3279690 A*X where X is 9000-by-k k: 0 time: MATLAB 0.00 CHOLMOD 0.00 speedup 0.90 err 0e+00 mflop: MATLAB 0.0 CHOLMOD 0.0 k: 1 time: MATLAB 0.02 CHOLMOD 0.02 speedup 1.00 err 0e+00 mflop: MATLAB 402.6 CHOLMOD 403.3 k: 2 time: MATLAB 0.02 CHOLMOD 0.02 speedup 0.72 err 0e+00 mflop: MATLAB 740.2 CHOLMOD 535.8 k: 3 time: MATLAB 0.12 CHOLMOD 0.03 speedup 4.51 err 0e+00 mflop: MATLAB 163.9 CHOLMOD 739.9 k: 4 time: MATLAB 0.02 CHOLMOD 0.16 speedup 0.15 err 0e+00 mflop: MATLAB 1132.3 CHOLMOD 165.1 k: 5 time: MATLAB 0.04 CHOLMOD 0.18 speedup 0.23 err 0e+00 mflop: MATLAB 828.0 CHOLMOD 187.1 k: 6 time: MATLAB 0.04 CHOLMOD 0.18 speedup 0.22 err 0e+00 mflop: MATLAB 960.9 CHOLMOD 213.6 k: 7 time: MATLAB 0.14 CHOLMOD 0.09 speedup 1.68 err 0e+00 mflop: MATLAB 320.6 CHOLMOD 537.6 k: 8 time: MATLAB 0.05 CHOLMOD 0.22 speedup 0.21 err 0e+00 mflop: MATLAB 1127.1 CHOLMOD 240.8 k: 9 time: MATLAB 0.16 CHOLMOD 0.23 speedup 0.69 err 0e+00 mflop: MATLAB 363.5 CHOLMOD 251.4 k: 10 time: MATLAB 0.16 CHOLMOD 0.24 speedup 0.68 err 0e+00 mflop: MATLAB 398.6 CHOLMOD 271.1 k: 10 time: MATLAB 0.16 CHOLMOD 0.24 speedup 0.68 err 0e+00 mflop: MATLAB 398.1 CHOLMOD 270.3 k: 20 time: MATLAB 0.32 CHOLMOD 0.59 speedup 0.53 err 0e+00 mflop: MATLAB 412.6 CHOLMOD 220.7 k: 30 time: MATLAB 0.28 CHOLMOD 0.94 speedup 0.30 err 0e+00 mflop: MATLAB 696.3 CHOLMOD 210.1 k: 40 time: MATLAB 0.43 CHOLMOD 1.19 speedup 0.37 err 0e+00 mflop: MATLAB 604.7 CHOLMOD 220.8 k: 50 time: MATLAB 0.60 CHOLMOD 1.43 speedup 0.42 err 0e+00 mflop: MATLAB 549.5 CHOLMOD 229.5 k: 100 time: MATLAB 1.08 CHOLMOD 2.97 speedup 0.36 err 0e+00 mflop: MATLAB 606.6 CHOLMOD 221.0 k: 200 time: MATLAB 2.26 CHOLMOD 5.95 speedup 0.38 err 0e+00 mflop: MATLAB 579.4 CHOLMOD 220.6 k: 300 time: MATLAB 3.55 CHOLMOD 8.80 speedup 0.40 err 0e+00 mflop: MATLAB 554.7 CHOLMOD 223.5 k: 400 time: MATLAB 4.65 CHOLMOD 12.36 speedup 0.38 err 0e+00 mflop: MATLAB 564.5 CHOLMOD 212.3 k: 500 time: MATLAB 5.81 CHOLMOD 14.75 speedup 0.39 err 0e+00 mflop: MATLAB 564.7 CHOLMOD 222.3 For comparison, here is CHOLMOD's x=A\b time: CHOLMOD x=A\b time: 18.82 (b is n-by-1) resid 2e-05 CHOLMOD x=A\b time: 22.40 (b is n-by-100) resid 2e-05 CHOLMOD x=A\b time: 26.86 (b is n-by-200) resid 2e-05 CHOLMOD x=A\b time: 29.62 (b is n-by-300) resid 2e-05 CHOLMOD x=A\b time: 33.93 (b is n-by-400) resid 2e-05 CHOLMOD x=A\b time: 38.16 (b is n-by-500) resid 2e-05 MATLAB x=A\b time: 24.45 (b is n-by-1) resid 1e-05 test25 passed ================================================================= test26: test logical full and sparse matrices test26 passed ================================================================= test27: test nesdis # of components: 7 size of root 32 out of 479 rows node 1 : parent 3 size 105 work 40598 node 2 : parent 3 size 99 work 32753 node 3 : parent 7 size 11 work 2584 node 4 : parent 6 size 108 work 99359 node 5 : parent 6 size 105 work 54811 node 6 : parent 7 size 19 work 8846 node 7 : parent 0 size 32 work 15983 test27 passed ================================================================= all tests passed SuiteSparse/CHOLMOD/MATLAB/Makefile0000644001170100242450000003712510617134775015457 0ustar davisfac#=============================================================================== # CHOLMOD/MATLAB/Makefile #=============================================================================== default: all include ../../UFconfig/UFconfig.mk I = -I. -I../../AMD/Include -I../../COLAMD/Include -I../../CCOLAMD/Include \ -I../../CAMD/Include -I../Include -I../../UFconfig -I$(METIS_PATH)/Lib all: mread sdmult ldlsolve resymbol symbfact2 chol2 lchol \ ldlchol cholmod2 ldlupdate metis bisect nesdis etree2 sparse2 analyze \ septree spsym mwrite other MX = $(MEX) $(CHOLMOD_CONFIG) -DDLONG -D_FILE_OFFSET_BITS=64 -D_LARGEFILE64_SOURCE $(I) distclean: purge purge: clean - $(RM) *.mex* *.dll clean: - $(RM) $(CLEAN) #=============================================================================== AMD_INC = ../../AMD/Include/amd.h ../../AMD/Include/amd_internal.h AMD = \ amd_1.o \ amd_2.o \ amd_aat.o \ amd_control.o \ amd_defaults.o \ amd_dump.o \ amd_global.o \ amd_info.o \ amd_order.o \ amd_postorder.o \ amd_post_tree.o \ amd_preprocess.o \ amd_valid.o amd_1.o: ../../AMD/Source/amd_1.c $(AMD_INC) $(MX) -c $< amd_2.o: ../../AMD/Source/amd_2.c $(AMD_INC) $(MX) -c $< amd_aat.o: ../../AMD/Source/amd_aat.c $(AMD_INC) $(MX) -c $< amd_control.o: ../../AMD/Source/amd_control.c $(AMD_INC) $(MX) -c $< amd_defaults.o: ../../AMD/Source/amd_defaults.c $(AMD_INC) $(MX) -c $< amd_dump.o: ../../AMD/Source/amd_dump.c $(AMD_INC) $(MX) -c $< amd_global.o: ../../AMD/Source/amd_global.c $(AMD_INC) $(MX) -c $< amd_info.o: ../../AMD/Source/amd_info.c $(AMD_INC) $(MX) -c $< amd_order.o: ../../AMD/Source/amd_order.c $(AMD_INC) $(MX) -c $< amd_postorder.o: ../../AMD/Source/amd_postorder.c $(AMD_INC) $(MX) -c $< amd_post_tree.o: ../../AMD/Source/amd_post_tree.c $(AMD_INC) $(MX) -c $< amd_preprocess.o: ../../AMD/Source/amd_preprocess.c $(AMD_INC) $(MX) -c $< amd_valid.o: ../../AMD/Source/amd_valid.c $(AMD_INC) $(MX) -c $< #=============================================================================== CAMD_INC = ../../CAMD/Include/camd.h ../../CAMD/Include/camd_internal.h CAMD = \ camd_1.o \ camd_2.o \ camd_aat.o \ camd_control.o \ camd_defaults.o \ camd_dump.o \ camd_global.o \ camd_info.o \ camd_order.o \ camd_postorder.o \ camd_preprocess.o \ camd_valid.o camd_1.o: ../../CAMD/Source/camd_1.c $(CAMD_INC) $(MX) -c $< camd_2.o: ../../CAMD/Source/camd_2.c $(CAMD_INC) $(MX) -c $< camd_aat.o: ../../CAMD/Source/camd_aat.c $(CAMD_INC) $(MX) -c $< camd_control.o: ../../CAMD/Source/camd_control.c $(CAMD_INC) $(MX) -c $< camd_defaults.o: ../../CAMD/Source/camd_defaults.c $(CAMD_INC) $(MX) -c $< camd_dump.o: ../../CAMD/Source/camd_dump.c $(CAMD_INC) $(MX) -c $< camd_global.o: ../../CAMD/Source/camd_global.c $(CAMD_INC) $(MX) -c $< camd_info.o: ../../CAMD/Source/camd_info.c $(CAMD_INC) $(MX) -c $< camd_order.o: ../../CAMD/Source/camd_order.c $(CAMD_INC) $(MX) -c $< camd_postorder.o: ../../CAMD/Source/camd_postorder.c $(CAMD_INC) $(MX) -c $< camd_post_tree.o: ../../CAMD/Source/camd_post_tree.c $(CAMD_INC) $(MX) -c $< camd_preprocess.o: ../../CAMD/Source/camd_preprocess.c $(CAMD_INC) $(MX) -c $< camd_valid.o: ../../CAMD/Source/camd_valid.c $(CAMD_INC) $(MX) -c $< #=============================================================================== COLAMD_INC = ../../COLAMD/Include/colamd.h COLAMD = colamd.o colamd_global.o colamd.o: ../../COLAMD/Source/colamd.c $(COLAMD_INC) $(MX) -c $< colamd_global.o: ../../COLAMD/Source/colamd_global.c $(COLAMD_INC) $(MX) -c $< #=============================================================================== CCOLAMD_INC = ../../CCOLAMD/Include/ccolamd.h CCOLAMD = ccolamd.o ccolamd_global.o ccolamd.o: ../../CCOLAMD/Source/ccolamd.c $(CCOLAMD_INC) $(MX) -c $< ccolamd_global.o: ../../CCOLAMD/Source/ccolamd_global.c $(CCOLAMD_INC) $(MX) -c $< #=============================================================================== # patch METIS 4.0.1 rename.h: Makefile $(METIS_PATH)/Lib/rename.h echo '/* do not edit this file; generated by CHOLMOD/MATLAB/Makefile */' > rename.h echo '#undef log2' >> rename.h echo '#include "$(METIS_PATH)/Lib/rename.h"' >> rename.h echo '#undef log2' >> rename.h echo '#define log2 METIS__log2' >> rename.h echo '#include "mex.h"' >> rename.h echo '#define malloc mxMalloc' >> rename.h echo '#define free mxFree' >> rename.h echo '#define calloc mxCalloc' >> rename.h echo '#define realloc mxRealloc' >> rename.h METIS_INC = rename.h \ $(METIS_PATH)/Lib/defs.h \ $(METIS_PATH)/Lib/macros.h \ $(METIS_PATH)/Lib/metis.h \ $(METIS_PATH)/Lib/proto.h \ $(METIS_PATH)/Lib/rename.h \ $(METIS_PATH)/Lib/struct.h METIS = \ balance.o \ bucketsort.o \ ccgraph.o \ coarsen.o \ compress.o \ debug.o \ estmem.o \ fm.o \ fortran.o \ frename.o \ graph.o \ initpart.o \ kmetis.o \ kvmetis.o \ kwayfm.o \ kwayrefine.o \ kwayvolfm.o \ kwayvolrefine.o \ match.o \ mbalance2.o \ mbalance.o \ mcoarsen.o \ memory.o \ mesh.o \ meshpart.o \ mfm2.o \ mfm.o \ mincover.o \ minitpart2.o \ minitpart.o \ mkmetis.o \ mkwayfmh.o \ mkwayrefine.o \ mmatch.o \ mmd.o \ mpmetis.o \ mrefine2.o \ mrefine.o \ mutil.o \ myqsort.o \ ometis.o \ parmetis.o \ pmetis.o \ pqueue.o \ refine.o \ separator.o \ sfm.o \ srefine.o \ stat.o \ subdomains.o \ timing.o \ util.o balance.o: $(METIS_PATH)/Lib/balance.c $(METIS_INC) $(MX) -c $< bucketsort.o: $(METIS_PATH)/Lib/bucketsort.c $(METIS_INC) $(MX) -c $< ccgraph.o: $(METIS_PATH)/Lib/ccgraph.c $(METIS_INC) $(MX) -c $< coarsen.o: $(METIS_PATH)/Lib/coarsen.c $(METIS_INC) $(MX) -c $< compress.o: $(METIS_PATH)/Lib/compress.c $(METIS_INC) $(MX) -c $< debug.o: $(METIS_PATH)/Lib/debug.c $(METIS_INC) $(MX) -c $< estmem.o: $(METIS_PATH)/Lib/estmem.c $(METIS_INC) $(MX) -c $< fm.o: $(METIS_PATH)/Lib/fm.c $(METIS_INC) $(MX) -c $< fortran.o: $(METIS_PATH)/Lib/fortran.c $(METIS_INC) $(MX) -c $< frename.o: $(METIS_PATH)/Lib/frename.c $(METIS_INC) $(MX) -c $< graph.o: $(METIS_PATH)/Lib/graph.c $(METIS_INC) $(MX) -c $< initpart.o: $(METIS_PATH)/Lib/initpart.c $(METIS_INC) $(MX) -c $< kmetis.o: $(METIS_PATH)/Lib/kmetis.c $(METIS_INC) $(MX) -c $< kvmetis.o: $(METIS_PATH)/Lib/kvmetis.c $(METIS_INC) $(MX) -c $< kwayfm.o: $(METIS_PATH)/Lib/kwayfm.c $(METIS_INC) $(MX) -c $< kwayrefine.o: $(METIS_PATH)/Lib/kwayrefine.c $(METIS_INC) $(MX) -c $< kwayvolfm.o: $(METIS_PATH)/Lib/kwayvolfm.c $(METIS_INC) $(MX) -c $< kwayvolrefine.o: $(METIS_PATH)/Lib/kwayvolrefine.c $(METIS_INC) $(MX) -c $< match.o: $(METIS_PATH)/Lib/match.c $(METIS_INC) $(MX) -c $< mbalance2.o: $(METIS_PATH)/Lib/mbalance2.c $(METIS_INC) $(MX) -c $< mbalance.o: $(METIS_PATH)/Lib/mbalance.c $(METIS_INC) $(MX) -c $< mcoarsen.o: $(METIS_PATH)/Lib/mcoarsen.c $(METIS_INC) $(MX) -c $< memory.o: $(METIS_PATH)/Lib/memory.c $(METIS_INC) $(MX) -c $< mesh.o: $(METIS_PATH)/Lib/mesh.c $(METIS_INC) $(MX) -c $< meshpart.o: $(METIS_PATH)/Lib/meshpart.c $(METIS_INC) $(MX) -c $< mfm2.o: $(METIS_PATH)/Lib/mfm2.c $(METIS_INC) $(MX) -c $< mfm.o: $(METIS_PATH)/Lib/mfm.c $(METIS_INC) $(MX) -c $< mincover.o: $(METIS_PATH)/Lib/mincover.c $(METIS_INC) $(MX) -c $< minitpart2.o: $(METIS_PATH)/Lib/minitpart2.c $(METIS_INC) $(MX) -c $< minitpart.o: $(METIS_PATH)/Lib/minitpart.c $(METIS_INC) $(MX) -c $< mkmetis.o: $(METIS_PATH)/Lib/mkmetis.c $(METIS_INC) $(MX) -c $< mkwayfmh.o: $(METIS_PATH)/Lib/mkwayfmh.c $(METIS_INC) $(MX) -c $< mkwayrefine.o: $(METIS_PATH)/Lib/mkwayrefine.c $(METIS_INC) $(MX) -c $< mmatch.o: $(METIS_PATH)/Lib/mmatch.c $(METIS_INC) $(MX) -c $< mmd.o: $(METIS_PATH)/Lib/mmd.c $(METIS_INC) $(MX) -c $< mpmetis.o: $(METIS_PATH)/Lib/mpmetis.c $(METIS_INC) $(MX) -c $< mrefine2.o: $(METIS_PATH)/Lib/mrefine2.c $(METIS_INC) $(MX) -c $< mrefine.o: $(METIS_PATH)/Lib/mrefine.c $(METIS_INC) $(MX) -c $< mutil.o: $(METIS_PATH)/Lib/mutil.c $(METIS_INC) $(MX) -c $< myqsort.o: $(METIS_PATH)/Lib/myqsort.c $(METIS_INC) $(MX) -c $< ometis.o: $(METIS_PATH)/Lib/ometis.c $(METIS_INC) $(MX) -c $< parmetis.o: $(METIS_PATH)/Lib/parmetis.c $(METIS_INC) $(MX) -c $< pmetis.o: $(METIS_PATH)/Lib/pmetis.c $(METIS_INC) $(MX) -c $< pqueue.o: $(METIS_PATH)/Lib/pqueue.c $(METIS_INC) $(MX) -c $< refine.o: $(METIS_PATH)/Lib/refine.c $(METIS_INC) $(MX) -c $< separator.o: $(METIS_PATH)/Lib/separator.c $(METIS_INC) $(MX) -c $< sfm.o: $(METIS_PATH)/Lib/sfm.c $(METIS_INC) $(MX) -c $< srefine.o: $(METIS_PATH)/Lib/srefine.c $(METIS_INC) $(MX) -c $< stat.o: $(METIS_PATH)/Lib/stat.c $(METIS_INC) $(MX) -c $< subdomains.o: $(METIS_PATH)/Lib/subdomains.c $(METIS_INC) $(MX) -c $< timing.o: $(METIS_PATH)/Lib/timing.c $(METIS_INC) $(MX) -c $< util.o: $(METIS_PATH)/Lib/util.c $(METIS_INC) $(MX) -c $< #=============================================================================== CHOLMOD_INC = \ cholmod_matlab.h \ ../Include/cholmod_blas.h \ ../Include/cholmod_check.h \ ../Include/cholmod_cholesky.h \ ../Include/cholmod_complexity.h \ ../Include/cholmod_config.h \ ../Include/cholmod_core.h \ ../Include/cholmod.h \ ../Include/cholmod_internal.h \ ../Include/cholmod_io64.h \ ../Include/cholmod_matrixops.h \ ../Include/cholmod_modify.h \ ../Include/cholmod_partition.h \ ../Include/cholmod_supernodal.h \ ../Include/cholmod_template.h CHOLMOD = \ cholmod_matlab.o \ cholmod_check.o \ cholmod_read.o \ cholmod_write.o \ cholmod_amd.o \ cholmod_analyze.o \ cholmod_colamd.o \ cholmod_etree.o \ cholmod_factorize.o \ cholmod_postorder.o \ cholmod_rcond.o \ cholmod_resymbol.o \ cholmod_rowcolcounts.o \ cholmod_rowfac.o \ cholmod_solve.o \ cholmod_spsolve.o \ cholmod_aat.o \ cholmod_add.o \ cholmod_band.o \ cholmod_change_factor.o \ cholmod_common.o \ cholmod_complex.o \ cholmod_copy.o \ cholmod_dense.o \ cholmod_error.o \ cholmod_factor.o \ cholmod_memory.o \ cholmod_sparse.o \ cholmod_transpose.o \ cholmod_triplet.o \ cholmod_drop.o \ cholmod_horzcat.o \ cholmod_norm.o \ cholmod_scale.o \ cholmod_sdmult.o \ cholmod_ssmult.o \ cholmod_submatrix.o \ cholmod_symmetry.o \ cholmod_vertcat.o \ cholmod_rowadd.o \ cholmod_rowdel.o \ cholmod_updown.o \ cholmod_camd.o \ cholmod_ccolamd.o \ cholmod_csymamd.o \ cholmod_metis.o \ cholmod_nesdis.o \ cholmod_super_numeric.o \ cholmod_super_solve.o \ cholmod_super_symbolic.o cholmod_matlab.o: cholmod_matlab.c $(CHOLMOD_INC) $(MX) -c $< cholmod_check.o: ../Check/cholmod_check.c $(CHOLMOD_INC) $(MX) -c $< cholmod_read.o: ../Check/cholmod_read.c $(CHOLMOD_INC) $(MX) -c $< cholmod_write.o: ../Check/cholmod_write.c $(CHOLMOD_INC) $(MX) -c $< cholmod_amd.o: ../Cholesky/cholmod_amd.c $(CHOLMOD_INC) $(MX) -c $< cholmod_analyze.o: ../Cholesky/cholmod_analyze.c $(CHOLMOD_INC) $(MX) -c $< cholmod_colamd.o: ../Cholesky/cholmod_colamd.c $(CHOLMOD_INC) $(MX) -c $< cholmod_etree.o: ../Cholesky/cholmod_etree.c $(CHOLMOD_INC) $(MX) -c $< cholmod_factorize.o: ../Cholesky/cholmod_factorize.c $(CHOLMOD_INC) $(MX) -c $< cholmod_postorder.o: ../Cholesky/cholmod_postorder.c $(CHOLMOD_INC) $(MX) -c $< cholmod_rcond.o: ../Cholesky/cholmod_rcond.c $(CHOLMOD_INC) $(MX) -c $< cholmod_resymbol.o: ../Cholesky/cholmod_resymbol.c $(CHOLMOD_INC) $(MX) -c $< cholmod_rowcolcounts.o: ../Cholesky/cholmod_rowcolcounts.c $(CHOLMOD_INC) $(MX) -c $< cholmod_rowfac.o: ../Cholesky/cholmod_rowfac.c \ ../Cholesky/t_cholmod_rowfac.c $(CHOLMOD_INC) $(MX) -c $< cholmod_solve.o: ../Cholesky/cholmod_solve.c \ ../Cholesky/t_cholmod_lsolve.c \ ../Cholesky/t_cholmod_ltsolve.c \ ../Cholesky/t_cholmod_solve.c $(CHOLMOD_INC) $(MX) -c $< cholmod_spsolve.o: ../Cholesky/cholmod_spsolve.c $(CHOLMOD_INC) $(MX) -c $< cholmod_aat.o: ../Core/cholmod_aat.c $(CHOLMOD_INC) $(MX) -c $< cholmod_add.o: ../Core/cholmod_add.c $(CHOLMOD_INC) $(MX) -c $< cholmod_band.o: ../Core/cholmod_band.c $(CHOLMOD_INC) $(MX) -c $< cholmod_change_factor.o: ../Core/cholmod_change_factor.c \ ../Core/t_cholmod_change_factor.c $(CHOLMOD_INC) $(MX) -c $< cholmod_common.o: ../Core/cholmod_common.c $(CHOLMOD_INC) $(MX) -c $< cholmod_complex.o: ../Core/cholmod_complex.c $(CHOLMOD_INC) $(MX) -c $< cholmod_copy.o: ../Core/cholmod_copy.c $(CHOLMOD_INC) $(MX) -c $< cholmod_dense.o: ../Core/cholmod_dense.c \ ../Core/t_cholmod_dense.c $(CHOLMOD_INC) $(MX) -c $< cholmod_error.o: ../Core/cholmod_error.c $(CHOLMOD_INC) $(MX) -c $< cholmod_factor.o: ../Core/cholmod_factor.c $(CHOLMOD_INC) $(MX) -c $< cholmod_memory.o: ../Core/cholmod_memory.c $(CHOLMOD_INC) $(MX) -c $< cholmod_sparse.o: ../Core/cholmod_sparse.c $(CHOLMOD_INC) $(MX) -c $< cholmod_transpose.o: ../Core/cholmod_transpose.c \ ../Core/t_cholmod_transpose.c $(CHOLMOD_INC) $(MX) -c $< cholmod_triplet.o: ../Core/cholmod_triplet.c \ ../Core/t_cholmod_triplet.c $(CHOLMOD_INC) $(MX) -c $< cholmod_drop.o: ../MatrixOps/cholmod_drop.c $(CHOLMOD_INC) $(MX) -c $< cholmod_horzcat.o: ../MatrixOps/cholmod_horzcat.c $(CHOLMOD_INC) $(MX) -c $< cholmod_norm.o: ../MatrixOps/cholmod_norm.c $(CHOLMOD_INC) $(MX) -c $< cholmod_scale.o: ../MatrixOps/cholmod_scale.c $(CHOLMOD_INC) $(MX) -c $< cholmod_sdmult.o: ../MatrixOps/cholmod_sdmult.c \ ../MatrixOps/t_cholmod_sdmult.c $(CHOLMOD_INC) $(MX) -c $< cholmod_ssmult.o: ../MatrixOps/cholmod_ssmult.c $(CHOLMOD_INC) $(MX) -c $< cholmod_submatrix.o: ../MatrixOps/cholmod_submatrix.c $(CHOLMOD_INC) $(MX) -c $< cholmod_symmetry.o: ../MatrixOps/cholmod_symmetry.c $(CHOLMOD_INC) $(MX) -c $< cholmod_vertcat.o: ../MatrixOps/cholmod_vertcat.c $(CHOLMOD_INC) $(MX) -c $< cholmod_rowadd.o: ../Modify/cholmod_rowadd.c $(CHOLMOD_INC) $(MX) -c $< cholmod_rowdel.o: ../Modify/cholmod_rowdel.c $(CHOLMOD_INC) $(MX) -c $< cholmod_updown.o: ../Modify/cholmod_updown.c \ ../Modify/t_cholmod_updown.c \ ../Modify/t_cholmod_updown_numkr.c $(CHOLMOD_INC) $(MX) -c $< cholmod_camd.o: ../Partition/cholmod_camd.c $(CHOLMOD_INC) $(MX) -c $< cholmod_ccolamd.o: ../Partition/cholmod_ccolamd.c $(CHOLMOD_INC) $(MX) -c $< cholmod_csymamd.o: ../Partition/cholmod_csymamd.c $(CHOLMOD_INC) $(MX) -c $< cholmod_metis.o: ../Partition/cholmod_metis.c $(CHOLMOD_INC) $(MX) -c $< cholmod_nesdis.o: ../Partition/cholmod_nesdis.c $(CHOLMOD_INC) $(MX) -c $< cholmod_super_numeric.o: ../Supernodal/cholmod_super_numeric.c \ ../Supernodal/t_cholmod_super_numeric.c $(CHOLMOD_INC) $(MX) -c $< cholmod_super_solve.o: ../Supernodal/cholmod_super_solve.c \ ../Supernodal/t_cholmod_super_solve.c $(CHOLMOD_INC) $(MX) -c $< cholmod_super_symbolic.o: ../Supernodal/cholmod_super_symbolic.c $(CHOLMOD_INC) $(MX) -c $< #=============================================================================== OBJ = $(AMD) $(CAMD) $(COLAMD) $(CCOLAMD) $(METIS) $(CHOLMOD) analyze: analyze.c $(OBJ) $(MX) analyze.c $(OBJ) mread: mread.c $(OBJ) $(MX) mread.c $(OBJ) mwrite: mwrite.c $(OBJ) $(MX) mwrite.c $(OBJ) spsym: spsym.c $(OBJ) $(MX) spsym.c $(OBJ) chol2: chol2.c $(OBJ) $(MX) chol2.c $(OBJ) lchol: lchol.c $(OBJ) $(MX) lchol.c $(OBJ) ldlchol: ldlchol.c $(OBJ) $(MX) ldlchol.c $(OBJ) ldlupdate: ldlupdate.c $(OBJ) $(MX) ldlupdate.c $(OBJ) ldlsolve: ldlsolve.c $(OBJ) $(MX) ldlsolve.c $(OBJ) sdmult: sdmult.c $(OBJ) $(MX) sdmult.c $(OBJ) resymbol: resymbol.c $(OBJ) $(MX) resymbol.c $(OBJ) cholmod2: cholmod2.c $(OBJ) $(MX) cholmod2.c $(OBJ) nesdis: nesdis.c $(OBJ) $(MX) nesdis.c $(OBJ) septree: septree.c $(OBJ) $(MX) septree.c $(OBJ) metis: metis.c $(OBJ) $(MX) metis.c $(OBJ) etree2: etree2.c $(OBJ) $(MX) etree2.c $(OBJ) bisect: bisect.c $(OBJ) $(MX) bisect.c $(OBJ) symbfact2: symbfact2.c $(OBJ) $(MX) symbfact2.c $(OBJ) sparse2: sparse2.c $(OBJ) $(MX) sparse2.c $(OBJ) #------------------------------------------------------------------------------- other: ( cd ../../AMD ; $(MAKE) mex ) ( cd ../../CAMD ; $(MAKE) mex ) ( cd ../../COLAMD ; $(MAKE) mex ) ( cd ../../CCOLAMD ; $(MAKE) mex ) SuiteSparse/CHOLMOD/MATLAB/bisect.c0000644001170100242450000001174010616446175015426 0ustar davisfac/* ========================================================================== */ /* === CHOLMOD/MATLAB/bisect mexFunction ==================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * MATLAB(tm) is a Trademark of The MathWorks, Inc. * METIS (Copyright 1998, G. Karypis) is not distributed with CHOLMOD. * -------------------------------------------------------------------------- */ /* Find an node separator of an undirected graph, using * METIS_NodeComputeSeparator. * * Usage: * * s = bisect (A) bisects A, uses tril(A) * s = bisect (A, 'sym') bisects A, uses tril(A) * s = bisect (A, 'row') bisects A*A' * s = bisect (A, 'col') bisects A'*A * * Node i of the graph is in the left graph if s(i)=0, the right graph if * s(i)=1, and in the separator if s(i)=2. * * Requirse METIS and the CHOLMOD Partition Module. */ #include "cholmod_matlab.h" void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { #ifndef NPARTITION double dummy = 0 ; Int *Partition ; cholmod_sparse *A, Amatrix, *C, *S ; cholmod_common Common, *cm ; Int n, transpose, c ; char buf [LEN] ; /* ---------------------------------------------------------------------- */ /* start CHOLMOD and set defaults */ /* ---------------------------------------------------------------------- */ cm = &Common ; cholmod_l_start (cm) ; sputil_config (SPUMONI, cm) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if (nargout > 1 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: p = bisect (A, mode)") ; } /* ---------------------------------------------------------------------- */ /* get input matrix A */ /* ---------------------------------------------------------------------- */ A = sputil_get_sparse_pattern (pargin [0], &Amatrix, &dummy, cm) ; S = (A == &Amatrix) ? NULL : A ; /* ---------------------------------------------------------------------- */ /* get A->stype, default is to use tril(A) */ /* ---------------------------------------------------------------------- */ A->stype = -1 ; transpose = FALSE ; if (nargin > 1) { buf [0] = '\0' ; if (mxIsChar (pargin [1])) { mxGetString (pargin [1], buf, LEN) ; } c = buf [0]; if (tolower (c) == 'r') { /* unsymmetric case (A*A') if string starts with 'r' */ transpose = FALSE ; A->stype = 0 ; } else if (tolower (c) == 'c') { /* unsymmetric case (A'*A) if string starts with 'c' */ transpose = TRUE ; A->stype = 0 ; } else if (tolower (c) == 's') { /* symmetric case (A) if string starts with 's' */ transpose = FALSE ; A->stype = -1 ; } else { mexErrMsgTxt ("bisect: p=bisect(A,mode) ; unrecognized mode") ; } } if (A->stype && A->nrow != A->ncol) { mexErrMsgTxt ("bisect: A must be square") ; } C = NULL ; if (transpose) { /* C = A', and then bisect C*C' */ C = cholmod_l_transpose (A, 0, cm) ; if (C == NULL) { mexErrMsgTxt ("bisect failed") ; } A = C ; } n = A->nrow ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Partition = cholmod_l_malloc (n, sizeof (Int), cm) ; /* ---------------------------------------------------------------------- */ /* order the matrix with CHOLMOD's interface to METIS_NodeND */ /* ---------------------------------------------------------------------- */ if (cholmod_l_bisect (A, NULL, 0, TRUE, Partition, cm) < 0) { mexErrMsgTxt ("bisect failed") ; } /* ---------------------------------------------------------------------- */ /* return Partition */ /* ---------------------------------------------------------------------- */ pargout [0] = sputil_put_int (Partition, n, 0) ; /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ cholmod_l_free (n, sizeof (Int), Partition, cm) ; cholmod_l_free_sparse (&C, cm) ; cholmod_l_free_sparse (&S, cm) ; cholmod_l_finish (cm) ; cholmod_l_print_common (" ", cm) ; /* if (cm->malloc_count != 0) mexErrMsgTxt ("!") ; */ #else mexErrMsgTxt ("METIS and the CHOLMOD Partition Module not installed\n") ; #endif } SuiteSparse/CHOLMOD/MATLAB/bisect.m0000644001170100242450000000163610620370721015427 0ustar davisfacfunction p = bisect (A, mode) %#ok %BISECT computes a node separator based on METIS_NodeComputeSeparator. % % Example: % s = bisect(A) bisects A. Uses tril(A) and assumes A is symmetric. % s = bisect(A,'sym') the same as p=bisect(A). % s = bisect(A,'col') bisects A'*A. % s = bisect(A,'row') bisects A*A'. % % A must be square for p=bisect(A) and bisect(A,'sym'). % % s is a vector of length equal to the dimension of A, A'*A, or A*A', % depending on the matrix bisected. s(i)=0 if node i is in the left subgraph, % s(i)=1 if it is in the right subgraph, and s(i)=2 if node i is in the node % separator. % % Requires METIS, authored by George Karypis, Univ. of Minnesota. This % MATLAB interface, via CHOLMOD, is by Tim Davis. % % See also METIS, NESDIS % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse error ('bisect mexFunction not found') ; SuiteSparse/CHOLMOD/MATLAB/rename.h0000644001170100242450000000037710711436461015426 0ustar davisfac/* do not edit this file; generated by cholmod_make */ #undef log2 #include "../../metis-4.0/Lib/rename.h" #undef log2 #define log2 METIS__log2 #include "mex.h" #define malloc mxMalloc #define free mxFree #define calloc mxCalloc #define realloc mxRealloc SuiteSparse/CHOLMOD/MATLAB/lcc_lib/0000755001170100242450000000000010006260712015355 5ustar davisfacSuiteSparse/CHOLMOD/MATLAB/lcc_lib/lapacksyms.def0000644001170100242450000001145310006260712020210 0ustar davisfacLIBRARY liblapack.dll EXPORTS dasum daxpy dbdsdc dbdsqr dcopy ddisna ddot dgbbrd dgbcon dgbequ dgbmv dgbrfs dgbsv dgbsvx dgbtf2 dgbtrf dgbtrs dgebak dgebal dgebd2 dgebrd dgecon dgeequ dgees dgeesx dgeev dgeevx dgegs dgegv dgehd2 dgehrd dgelq2 dgelqf dgels dgelsd dgelss dgelsx dgelsy dgemm dgemv dgeql2 dgeqlf dgeqp3 dgeqpf dgeqr2 dgeqrf dger dgerfs dgerq2 dgerqf dgesc2 dgesdd dgesv dgesvd dgesvx dgetc2 dgetf2 dgetrf dgetri dgetrs dggbak dggbal dgges dggesx dggev dggevx dggglm dgghrd dgglse dggqrf dggrqf dggsvd dggsvp dgtcon dgtrfs dgtsv dgtsvx dgttrf dgttrs dgtts2 dhgeqz dhsein dhseqr dlabad dlabrd dlacon dlacpy dladiv dlae2 dlaebz dlaed0 dlaed1 dlaed2 dlaed3 dlaed4 dlaed5 dlaed6 dlaed7 dlaed8 dlaed9 dlaeda dlaein dlaev2 dlaexc dlag2 dlags2 dlagtf dlagtm dlagts dlagv2 dlahqr dlahrd dlaic1 dlaln2 dlals0 dlalsa dlalsd dlamch dlamrg dlangb dlange dlangt dlanhs dlansb dlansp dlanst dlansy dlantb dlantp dlantr dlanv2 dlapll dlapmt dlapy2 dlapy3 dlaqgb dlaqge dlaqp2 dlaqps dlaqsb dlaqsp dlaqsy dlaqtr dlar1v dlar2v dlarf dlarfb dlarfg dlarft dlarfx dlargv dlarnv dlarrb dlarre dlarrf dlarrv dlartg dlartv dlaruv dlarz dlarzb dlarzt dlas2 dlascl dlasd0 dlasd1 dlasd2 dlasd3 dlasd4 dlasd5 dlasd6 dlasd7 dlasd8 dlasd9 dlasda dlasdq dlasdt dlaset dlasq1 dlasq2 dlasq3 dlasq4 dlasq5 dlasq6 dlasr dlasrt dlassq dlasv2 dlaswp dlasy2 dlasyf 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dtgsna dtgsy2 dtgsyl dtpcon dtpmv dtprfs dtpsv dtptri dtptrs dtrcon dtrevc dtrexc dtrmm dtrmv dtrrfs dtrsen dtrsm dtrsna dtrsv dtrsyl dtrti2 dtrtri dtrtrs dtzrqf dtzrzf dzasum dznrm2 dzsum1 idamax ieeeck ilaenv izamax izmax1 lsame lsamen xerbla zaxpy zbdsqr zcopy zdotc zdotu zdrot zdrscl zdscal zgbbrd zgbcon zgbequ zgbmv zgbrfs zgbsv zgbsvx zgbtf2 zgbtrf zgbtrs zgebak zgebal zgebd2 zgebrd zgecon zgeequ zgees zgeesx zgeev zgeevx zgegs zgegv zgehd2 zgehrd zgelq2 zgelqf zgels zgelsd zgelss zgelsx zgelsy zgemm zgemv zgeql2 zgeqlf zgeqp3 zgeqpf zgeqr2 zgeqrf zgerc zgerfs zgerq2 zgerqf zgeru zgesc2 zgesdd zgesv zgesvd zgesvx zgetc2 zgetf2 zgetrf zgetri zgetrs zggbak zggbal zgges zggesx zggev zggevx zggglm zgghrd zgglse zggqrf zggrqf zggsvd zggsvp zgtcon zgtrfs zgtsv zgtsvx zgttrf zgttrs zgtts2 zhbev zhbevd zhbevx zhbgst zhbgv zhbgvd zhbgvx zhbmv zhbtrd zhecon zheev zheevd zheevr zheevx zhegs2 zhegst zhegv zhegvd zhegvx zhemm zhemv zher zher2 zher2k zherfs zherk zhesv zhesvx zhetd2 zhetf2 zhetrd zhetrf zhetri zhetrs zhgeqz zhpcon zhpev zhpevd zhpevx zhpgst zhpgv zhpgvd zhpgvx zhpmv zhpr zhpr2 zhprfs zhpsv zhpsvx zhptrd zhptrf zhptri zhptrs zhsein zhseqr zlabrd zlacgv zlacon zlacp2 zlacpy zlacrm zlacrt zladiv zlaed0 zlaed7 zlaed8 zlaein zlaesy zlaev2 zlags2 zlagtm zlahef zlahqr zlahrd zlaic1 zlals0 zlalsa zlalsd zlangb zlange zlangt zlanhb zlanhe zlanhp zlanhs zlanht zlansb zlansp zlansy zlantb zlantp zlantr zlapll zlapmt zlaqgb zlaqge zlaqhb zlaqhe zlaqhp zlaqp2 zlaqps zlaqsb zlaqsp zlaqsy zlar1v zlar2v zlarcm zlarf zlarfb zlarfg zlarft zlarfx zlargv zlarnv zlarrv zlartg zlartv zlarz zlarzb zlarzt zlascl zlaset zlasr zlassq zlaswp zlasyf zlatbs zlatdf zlatps zlatrd zlatrs zlatrz zlatzm zlauu2 zlauum zpbcon zpbequ zpbrfs zpbstf zpbsv zpbsvx zpbtf2 zpbtrf zpbtrs zpocon zpoequ zporfs zposv zposvx zpotf2 zpotrf zpotri zpotrs zppcon zppequ zpprfs zppsv zppsvx zpptrf zpptri zpptrs zptcon zpteqr zptrfs zptsv zptsvx zpttrf zpttrs zptts2 zrot zrotg zscal zspcon zspmv zspr zsprfs 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Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * MATLAB(tm) is a Trademark of The MathWorks, Inc. * -------------------------------------------------------------------------- */ /* Numeric LL' factorization. Note that LL' and LDL' are faster than R'R * and use less memory. The LL' factorization methods use tril(A). * * L = lchol (A) same as L = chol (A)', just faster * [L,p] = lchol (A) save as [R,p] = chol(A) ; L=R', just faster * [L,p,q] = lchol (A) factorizes A(q,q) into L*L' * * A must be sparse. It can be complex or real. * * L is returned with no explicit zero entries. This means it might not be * chordal, and L cannot be passed back to CHOLMOD for an update/downdate or * for a fast simplicial solve. spones (L) will be equal to the L returned * by symbfact2 if no numerically zero entries are dropped, or a subset * otherwise. */ #include "cholmod_matlab.h" void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double dummy = 0, *px ; cholmod_sparse Amatrix, *A, *Lsparse ; cholmod_factor *L ; cholmod_common Common, *cm ; Int n, minor ; /* ---------------------------------------------------------------------- */ /* start CHOLMOD and set parameters */ /* ---------------------------------------------------------------------- */ cm = &Common ; cholmod_l_start (cm) ; sputil_config (SPUMONI, cm) ; /* convert to packed LL' when done */ cm->final_asis = FALSE ; cm->final_super = FALSE ; cm->final_ll = TRUE ; cm->final_pack = TRUE ; cm->final_monotonic = TRUE ; /* no need to prune entries due to relaxed supernodal amalgamation, since * zeros are dropped with sputil_drop_zeros instead */ cm->final_resymbol = FALSE ; cm->quick_return_if_not_posdef = (nargout < 2) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if (nargin != 1 || nargout > 3) { mexErrMsgTxt ("usage: [L,p,q] = lchol (A)") ; } n = mxGetN (pargin [0]) ; if (!mxIsSparse (pargin [0]) || n != mxGetM (pargin [0])) { mexErrMsgTxt ("A must be square and sparse") ; } /* get sparse matrix A, use tril(A) */ A = sputil_get_sparse (pargin [0], &Amatrix, &dummy, -1) ; /* use natural ordering if no q output parameter */ if (nargout < 3) { cm->nmethods = 1 ; cm->method [0].ordering = CHOLMOD_NATURAL ; cm->postorder = FALSE ; } /* ---------------------------------------------------------------------- */ /* analyze and factorize */ /* ---------------------------------------------------------------------- */ L = cholmod_l_analyze (A, cm) ; cholmod_l_factorize (A, L, cm) ; if (nargout < 2 && cm->status != CHOLMOD_OK) { mexErrMsgTxt ("matrix is not positive definite") ; } /* ---------------------------------------------------------------------- */ /* convert L to a sparse matrix */ /* ---------------------------------------------------------------------- */ /* the conversion sets L->minor back to n, so get a copy of it first */ minor = L->minor ; Lsparse = cholmod_l_factor_to_sparse (L, cm) ; if (Lsparse->xtype == CHOLMOD_COMPLEX) { /* convert Lsparse from complex to zomplex */ cholmod_l_sparse_xtype (CHOLMOD_ZOMPLEX, Lsparse, cm) ; } if (minor < n) { /* remove columns minor to n-1 from Lsparse */ sputil_trim (Lsparse, minor, cm) ; } /* drop zeros from Lsparse */ sputil_drop_zeros (Lsparse) ; /* ---------------------------------------------------------------------- */ /* return results to MATLAB */ /* ---------------------------------------------------------------------- */ /* return L as a sparse matrix */ pargout [0] = sputil_put_sparse (&Lsparse, cm) ; /* return minor (translate to MATLAB convention) */ if (nargout > 1) { pargout [1] = mxCreateDoubleMatrix (1, 1, mxREAL) ; px = mxGetPr (pargout [1]) ; px [0] = ((minor == n) ? 0 : (minor+1)) ; } /* return permutation */ if (nargout > 2) { pargout [2] = sputil_put_int (L->Perm, n, 1) ; } /* ---------------------------------------------------------------------- */ /* free workspace and the CHOLMOD L, except for what is copied to MATLAB */ /* ---------------------------------------------------------------------- */ cholmod_l_free_factor (&L, cm) ; cholmod_l_finish (cm) ; cholmod_l_print_common (" ", cm) ; /* if (cm->malloc_count != 3 + mxIsComplex (pargout[0])) mexErrMsgTxt ("!") ; */ } SuiteSparse/CHOLMOD/MATLAB/lchol.m0000644001170100242450000000134710620370761015262 0ustar davisfacfunction [L,p,q] = lchol (A) %#ok %LCHOL sparse A=L*L' factorization. % Note that L*L' (LCHOL) and L*D*L' (LDLCHOL) factorizations are faster than % R'*R (CHOL2 and CHOL) and use less memory. The LL' and LDL' factorization % methods use tril(A). A must be sparse. % % Example: % L = lchol (A) same as L = chol (A')', just faster % [L,p] = lchol (A) save as [R,p] = chol(A') ; L=R', just faster % [L,p,q] = lchol (A) factorizes A(q,q) into L*L', where q is a % fill-reducing ordering % % See also CHOL2, LDLCHOL, CHOL. % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse error ('lchol mexFunction not found') ; SuiteSparse/CHOLMOD/MATLAB/ldlsolve.c0000644001170100242450000001252010621027712015762 0ustar davisfac/* ========================================================================== */ /* === CHOLMOD/MATLAB/ldlsolve mexFunction ================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * MATLAB(tm) is a Trademark of The MathWorks, Inc. * -------------------------------------------------------------------------- */ /* Solve LDL'x=b given an LDL' factorization computed by ldlchol. * * Usage: * * x = ldlsolve (LD,b) * * b can be dense or sparse. */ #include "cholmod_matlab.h" void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double dummy = 0, rcond ; Int *Lp, *Lnz, *Lprev, *Lnext ; cholmod_sparse *Bs, Bspmatrix, *Xs ; cholmod_dense *B, Bmatrix, *X ; cholmod_factor *L ; cholmod_common Common, *cm ; Int j, k, n, B_is_sparse, head, tail ; /* ---------------------------------------------------------------------- */ /* start CHOLMOD and set parameters */ /* ---------------------------------------------------------------------- */ cm = &Common ; cholmod_l_start (cm) ; sputil_config (SPUMONI, cm) ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("Usage: x = ldlsolve (LD, b)") ; } n = mxGetN (pargin [0]) ; k = mxGetN (pargin [1]) ; if (!mxIsSparse (pargin [0]) || n != mxGetM (pargin [0])) { mexErrMsgTxt ("ldlsolve: LD must be sparse and square") ; } if (n != mxGetM (pargin [1])) { mexErrMsgTxt ("ldlsolve: b wrong dimension") ; } /* ---------------------------------------------------------------------- */ /* get b */ /* ---------------------------------------------------------------------- */ /* get sparse or dense matrix B */ B = NULL ; Bs = NULL ; B_is_sparse = mxIsSparse (pargin [1]) ; if (B_is_sparse) { /* get sparse matrix B (unsymmetric) */ Bs = sputil_get_sparse (pargin [1], &Bspmatrix, &dummy, 0) ; } else { /* get dense matrix B */ B = sputil_get_dense (pargin [1], &Bmatrix, &dummy) ; } /* ---------------------------------------------------------------------- */ /* construct a shallow copy of the input sparse matrix L */ /* ---------------------------------------------------------------------- */ /* the construction of the CHOLMOD takes O(n) time and memory */ /* allocate the CHOLMOD symbolic L */ L = cholmod_l_allocate_factor (n, cm) ; L->ordering = CHOLMOD_NATURAL ; /* get the MATLAB L */ L->p = mxGetJc (pargin [0]) ; L->i = mxGetIr (pargin [0]) ; L->x = mxGetPr (pargin [0]) ; L->z = mxGetPi (pargin [0]) ; /* allocate and initialize the rest of L */ L->nz = cholmod_l_malloc (n, sizeof (Int), cm) ; Lp = L->p ; Lnz = L->nz ; for (j = 0 ; j < n ; j++) { Lnz [j] = Lp [j+1] - Lp [j] ; } L->prev = cholmod_l_malloc (n+2, sizeof (Int), cm) ; L->next = cholmod_l_malloc (n+2, sizeof (Int), cm) ; Lprev = L->prev ; Lnext = L->next ; head = n+1 ; tail = n ; Lnext [head] = 0 ; Lprev [head] = -1 ; Lnext [tail] = -1 ; Lprev [tail] = n-1 ; for (j = 0 ; j < n ; j++) { Lnext [j] = j+1 ; Lprev [j] = j-1 ; } Lprev [0] = head ; L->xtype = (mxIsComplex (pargin [0])) ? CHOLMOD_ZOMPLEX : CHOLMOD_REAL ; L->nzmax = Lp [n] ; /* ---------------------------------------------------------------------- */ /* solve and return solution to MATLAB */ /* ---------------------------------------------------------------------- */ if (B_is_sparse) { /* solve LDL'X=B with sparse X and B; return sparse X to MATLAB */ Xs = cholmod_l_spsolve (CHOLMOD_LDLt, L, Bs, cm) ; pargout [0] = sputil_put_sparse (&Xs, cm) ; } else { /* solve AX=B with dense X and B; return dense X to MATLAB */ X = cholmod_l_solve (CHOLMOD_LDLt, L, B, cm) ; pargout [0] = sputil_put_dense (&X, cm) ; } rcond = cholmod_l_rcond (L, cm) ; if (rcond == 0) { mexWarnMsgTxt ("Matrix is indefinite or singular to working precision"); } else if (rcond < DBL_EPSILON) { mexWarnMsgTxt ("Matrix is close to singular or badly scaled.") ; mexPrintf (" Results may be inaccurate. RCOND = %g.\n", rcond) ; } /* ---------------------------------------------------------------------- */ /* free workspace and the CHOLMOD L, except for what is copied to MATLAB */ /* ---------------------------------------------------------------------- */ L->p = NULL ; L->i = NULL ; L->x = NULL ; L->z = NULL ; cholmod_l_free_factor (&L, cm) ; cholmod_l_finish (cm) ; cholmod_l_print_common (" ", cm) ; /* if (cm->malloc_count != (mxIsComplex (pargout [0]) + (mxIsSparse (pargout[0]) ? 3:1))) mexErrMsgTxt ("!") ; */ } SuiteSparse/CHOLMOD/MATLAB/ldlsolve.m0000644001170100242450000000117110620370773016003 0ustar davisfacfunction x = ldlsolve (LD,b) %#ok %LDLSOLVE solve LDL'x=b using a sparse LDL' factorization % % Example: % x = ldlsolve (LD,b) % % solves the system L*D*L'*x=b for x. This is equivalent to % % [L,D] = ldlsplit (LD) ; % x = L' \ (D \ (L \ b)) ; % % LD is from ldlchol, or as updated by ldlupdate. You must not modify LD as % obtained from ldlchol or ldlupdate prior to passing it to this function. % See ldlupdate for more details. % % See also LDLCHOL, LDLUPDATE, LDLSPLIT % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse error ('ldlsolve mexFunction not found') ; SuiteSparse/CHOLMOD/MATLAB/Windows/0000755001170100242450000000000010462205215015423 5ustar davisfacSuiteSparse/CHOLMOD/MATLAB/Windows/strings.h0000644001170100242450000000074010301373206017264 0ustar davisfac/* ========================================================================== */ /* === MATLAB/strings.h ===================================================== */ /* ========================================================================== */ /* This is an empty strings.h file, for compiling METIS 4.0.1 properly. METIS * does not need the Unix , but includes it in metis.h anyway. * This empty file is needed to successfully compile METIS using cholmod_make. */ SuiteSparse/CHOLMOD/MATLAB/Windows/rand48.c0000644001170100242450000000146410301415547016677 0ustar davisfac/* ========================================================================== */ /* === MATLAB/rand48.c ====================================================== */ /* ========================================================================== */ /* METIS uses drand48 and srand48, which conform to the SVID standard. The * lcc compiler for Windows shipped with MATLAB does not include the drand48 * and srand48 routines. This file is a cheap replacement using the * more-common rand and srand instead (which lcc does have). * * This file is only used when compiling CHOLMOD with the cholmod_make.m, * on the PC, with the lcc compiler. */ #include double drand48 (void) { return (((double) (rand ( ))) / ((double) RAND_MAX)) ; } void srand48 (long int seed) { srand ((unsigned int) seed) ; } SuiteSparse/CHOLMOD/MATLAB/Windows/README.txt0000644001170100242450000000006210301415444017116 0ustar davisfacThese files are need to compile METIS on Windows. SuiteSparse/CHOLMOD/MATLAB/ldlsplit.m0000644001170100242450000000115710620370775016014 0ustar davisfacfunction [L,D] = ldlsplit (LD) %#ok %LDLSPLIT split an LDL' factorization into L and D. % % Example: % [L,D] = ldlsplit (LD) % % LD contains an LDL' factorization, computed with LD = ldlchol(A), % for example. The diagonal of LD contains D, and the entries below % the diagonal contain L (which has a unit diagonal). This function % splits LD into its two components L and D so that L*D*L' = A. % % See also LDLCHOL, LDLSOLVE, LDLUPDATE. % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse n = size (LD,1) ; D = diag (diag (LD)) ; L = tril (LD,-1) + speye (n) ; SuiteSparse/CHOLMOD/MATLAB/ldl_normest.m0000644001170100242450000000501110620664112016467 0ustar davisfacfunction rho = ldl_normest (A, L, D) %LDL_NORMEST estimate the 1-norm of A-L*D*L' without computing L*D*L' % % Example: % % rho = ldl_normest (A, L, D) % % which estimates the computation of the 1-norm: % % rho = norm (A-L*D*L', 1) % % Authors: William W. Hager, Math Dept., Univ. of Florida % Timothy A. Davis, CISE Dept., Univ. of Florida % Gainesville, FL, 32611, USA. % based on normest1, contributed on November, 1997 % % See also condest, normest % Copyright 2006-2007, William W. Hager and Timothy A. Davis % http://www.cise.ufl.edu/research/sparse [m n] = size (A) ; if (m ~= n) error ('A must be square') ; end if (nnz (A-A') ~= 0) error ('A must be symmetric') ; end if (nargin < 3) D = speye (n) ; end notvisited = ones (m, 1) ; % nonvisited(j) is zero if j is visited, 1 otherwise rho = 0 ; % the global rho for trial = 1:3 % { x = notvisited ./ sum (notvisited) ; rho1 = 0 ; % the current rho for this trial %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% COMPUTE Ex1 = E*x EFFICIENTLY: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Ex1 = (A*x) - L*(U*x) ; Ex1 = (A*x) - L*(D*(L'*x)) ; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% rho2 = norm (Ex1, 1) ; while rho2 > rho1 % { rho1 = rho2 ; y = 2*(Ex1 >= 0) - 1 ; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% COMPUTE z = E'*y EFFICIENTLY: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % z = (A'*y) - U'*(L'*y) ; z = (A*y) - L*(D*(L'*x)) ; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% [zj, j] = max (abs (z .* notvisited)) ; j = j (1) ; if (abs (z (j)) > z'*x) % { x = zeros (m, 1) ; x (j) = 1 ; notvisited (j) = 0 ; else % } { break ; end % } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% COMPUTE Ex1 = E*x EFFICIENTLY: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Ex1 = (A*x) - L*(D*(L'*x)) ; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% rho2 = norm (Ex1, 1) ; end % } rho = max (rho, rho1) ; end % } SuiteSparse/CHOLMOD/MATLAB/Contents.m0000644001170100242450000000363610620371147015760 0ustar davisfac% CHOLMOD: a sparse supernodal Cholesky update/downdate package % % cholmod2 - supernodal sparse Cholesky backslash, x = A\b % chol2 - sparse Cholesky factorization, A=R'R. % lchol - sparse A=L*L' factorization. % ldlchol - sparse A=LDL' factorization % ldlupdate - multiple-rank update or downdate of a sparse LDL' factorization. % resymbol - recomputes the symbolic Cholesky factorization of the matrix A. % ldlsolve - solve LDL'x=b using a sparse LDL' factorization % ldlsplit - split an LDL' factorization into L and D. % metis - nested dissection ordering via METIS_NodeND. % nesdis - nested dissection ordering via CHOLMOD's nested dissection. % septree - prune a separator tree. % bisect - computes a node separator based on METIS_NodeComputeSeparator. % analyze - order and analyze a matrix using CHOLMOD's best-effort ordering. % etree2 - sparse elimination tree. % sparse2 - replacement for SPARSE % symbfact2 - symbolic factorization % sdmult - sparse matrix times dense matrix % mread - read a sparse matrix from a file in Matrix Market format. % mwrite - write a matrix to a file in Matrix Market form. % spsym - determine if a sparse matrix is symmetric, Hermitian, or skew-symmetric. % ldl_normest - estimate the 1-norm of A-L*D*L' without computing L*D*L' % cholmod_demo - a demo for CHOLMOD % cholmod_install - compile and install CHOLMOD, AMD, COLAMD, CCOLAMD, CAMD % cholmod_make - compiles the CHOLMOD mexFunctions % graph_demo - graph partitioning demo % % % Example: % x = cholmod2(A,b) % Note: cholmod has been renamed cholmod2, so as not to conflict with itself % (the MATLAB built-in cholmod function). % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse SuiteSparse/CHOLMOD/MATLAB/metis.c0000644001170100242450000001166410616447253015301 0ustar davisfac/* ========================================================================== */ /* === CHOLMOD/MATLAB/metis mexFunction ===================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * MATLAB(tm) is a Trademark of The MathWorks, Inc. * METIS (Copyright 1998, G. Karypis) is not distributed with CHOLMOD. * -------------------------------------------------------------------------- */ /* Nested dissection using METIS_NodeND * * Usage: * * p = metis (A) orders A, using just tril(A) * p = metis (A,'sym') orders A, using just tril(A) * p = metis (A,'row') orders A*A' * p = metis (A,'col') orders A'*A * * METIS_NodeND's ordering is followed by CHOLMOD's etree or column etree * postordering. Requires METIS and the CHOLMOD Partition Module. */ #include "cholmod_matlab.h" void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { #ifndef NPARTITION double dummy = 0 ; Int *Perm ; cholmod_sparse *A, Amatrix, *C, *S ; cholmod_common Common, *cm ; Int n, transpose, c, postorder ; char buf [LEN] ; /* ---------------------------------------------------------------------- */ /* start CHOLMOD and set defaults */ /* ---------------------------------------------------------------------- */ cm = &Common ; cholmod_l_start (cm) ; sputil_config (SPUMONI, cm) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if (nargout > 1 || nargin < 1 || nargin > 3) { mexErrMsgTxt ("Usage: p = metis (A, mode)") ; } /* ---------------------------------------------------------------------- */ /* get input matrix A */ /* ---------------------------------------------------------------------- */ A = sputil_get_sparse_pattern (pargin [0], &Amatrix, &dummy, cm) ; S = (A == &Amatrix) ? NULL : A ; /* ---------------------------------------------------------------------- */ /* get A->stype, default is to use tril(A) */ /* ---------------------------------------------------------------------- */ A->stype = -1 ; transpose = FALSE ; if (nargin > 1) { buf [0] = '\0' ; if (mxIsChar (pargin [1])) { mxGetString (pargin [1], buf, LEN) ; } c = buf [0] ; if (tolower (c) == 'r') { /* unsymmetric case (A*A') if string starts with 'r' */ transpose = FALSE ; A->stype = 0 ; } else if (tolower (c) == 'c') { /* unsymmetric case (A'*A) if string starts with 'c' */ transpose = TRUE ; A->stype = 0 ; } else if (tolower (c) == 's') { /* symmetric case (A) if string starts with 's' */ transpose = FALSE ; A->stype = -1 ; } else { mexErrMsgTxt ("metis: p=metis(A,mode) ; unrecognized mode") ; } } if (A->stype && A->nrow != A->ncol) { mexErrMsgTxt ("metis: A must be square") ; } C = NULL ; if (transpose) { /* C = A', and then order C*C' with METIS */ C = cholmod_l_transpose (A, 0, cm) ; if (C == NULL) { mexErrMsgTxt ("metis failed") ; } A = C ; } n = A->nrow ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Perm = cholmod_l_malloc (n, sizeof (Int), cm) ; /* ---------------------------------------------------------------------- */ /* order the matrix with CHOLMOD's interface to METIS_NodeND */ /* ---------------------------------------------------------------------- */ postorder = (nargin < 3) ; if (!cholmod_l_metis (A, NULL, 0, postorder, Perm, cm)) { mexErrMsgTxt ("metis failed") ; return ; } /* ---------------------------------------------------------------------- */ /* return Perm */ /* ---------------------------------------------------------------------- */ pargout [0] = sputil_put_int (Perm, n, 1) ; /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ cholmod_l_free (n, sizeof (Int), Perm, cm) ; cholmod_l_free_sparse (&C, cm) ; cholmod_l_free_sparse (&S, cm) ; cholmod_l_finish (cm) ; cholmod_l_print_common (" ", cm) ; /* if (cm->malloc_count != 0) mexErrMsgTxt ("!") ; */ #else mexErrMsgTxt ("METIS and the CHOLMOD Partition Module not installed\n") ; #endif } SuiteSparse/CHOLMOD/MATLAB/metis.m0000644001170100242450000000160710620371016015273 0ustar davisfacfunction p = metis (A, mode) %#ok %METIS nested dissection ordering via METIS_NodeND. % % Example: % p = metis(A) returns p such chol(A(p,p)) is typically sparser than % chol(A). Uses tril(A) and assumes A is symmetric. % p = metis(A,'sym') the same as p=metis(A). % p = metis(A,'col') returns p so that chol(A(:,p)'*A(:,p)) is typically % sparser than chol(A'*A). % p = metis(A,'row') returns p so that chol(A(p,:)*A(p,:)') is typically % sparser than chol(A'*A). % % A must be square for p=metis(A) or metis(A,'sym') % % Requires METIS, authored by George Karypis, Univ. of Minnesota. This % MATLAB interface, via CHOLMOD, is by Tim Davis. % % See also NESDIS, BISECT % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse error ('metis mexFunction not found') ; SuiteSparse/CHOLMOD/MATLAB/graph_demo.m0000644001170100242450000000465410620640443016267 0ustar davisfacfunction graph_demo (n) %GRAPH_DEMO graph partitioning demo % graph_demo(n) constructs an set of n-by-n 2D grids, partitions them, and % plots them in one-second intervals. n is optional; it defaults to 60. % % Example: % graph_demo % % See also DELSQ, NUMGRID, GPLOT, TREEPLOT % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse if (nargin < 1) % construct a 60-by-60 grid n = 60 ; end figure (1) clf for regions = {'Square', 'C' 'Disc', 'Annulus', 'Heart', 'Butterfly', 'L'} % construct the grid region = regions {1} ; g = numgrid (region (1), n) ; x = repmat (0:n-1, n, 1) ; y = repmat (((n-1):-1:0)', 1, n) ; A = delsq (g) ; x = x (find (g)) ; %#ok y = y (find (g)) ; %#ok % plot the original grid clf subplot (2,2,1) my_gplot (A, x, y) title (sprintf ('%s-shaped 2D grid', region)) ; axis equal axis off % bisect the graph s = bisect (A) ; [i j] = find (A) ; subplot (2,2,2) my_gplot (sparse (i, j, s(i) == s(j)), x, y) ; title ('node bisection') ; axis equal axis off % nested dissection nsmall = floor (size (A,1) / 2) ; defaults = 0 ; while (1) if (defaults) % use defaults [p cp cmember] = nesdis (A) ; else [p cp cmember] = nesdis (A, 'sym', nsmall) ; end % plot the components subplot (2,2,3) my_gplot (sparse (i, j, cmember(i) == cmember (j)), x, y) ; if (defaults) title ('nested dissection (defaults)') ; else title (sprintf ('nested dissection, nsmall %d', nsmall)) ; end axis equal axis off % plot the separator tree subplot (2,2,4) treeplot (cp, 'ko') title ('separator tree') ; axis equal axis off drawnow pause (0.1) if (defaults) break ; end nsmall = floor (nsmall / 2) ; if (nsmall < 20) defaults = 1 ; pause (0.2) end end end %------------------------------------------------------------------------------- function my_gplot (A, x, y) % my_gplot : like gplot, just a lot faster [i, j] = find (A) ; [ignore, p] = sort (max(i, j)) ; i = i (p) ; j = j (p) ; nans = repmat (NaN, size (i)) ; x = [ x(i) x(j) nans ]' ; y = [ y(i) y(j) nans ]' ; plot (x (:), y (:)) ; SuiteSparse/CHOLMOD/MATLAB/sparse2.c0000644001170100242450000000077510301355376015533 0ustar davisfac/* ========================================================================== */ /* === MATLAB/sparse2 mexFunction =========================================== */ /* ========================================================================== */ /* Identical to the "sparse" function in MATLAB, just faster. */ #include "cholmod_matlab.h" void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { sputil_sparse (nargout, pargout, nargin, pargin) ; } SuiteSparse/CHOLMOD/MATLAB/sparse2.m0000644001170100242450000000175510620371040015532 0ustar davisfacfunction S = sparse2 (i,j,s,m,n,nzmax) %#ok %SPARSE2 replacement for SPARSE % % Example: % S = sparse2 (i,j,s,m,n,nzmax) % % Identical to the MATLAB sparse function (just faster). % An additional feature is added that is not part of the MATLAB sparse % function, the Z matrix. With an extra output, % % [S Z] = sparse2 (i,j,s,m,n,nzmax) % % the matrix Z is a binary real matrix whose nonzero pattern contains the % explicit zero entries that were dropped from S. Z only contains entries % for the sparse2(i,j,s,...) usage. [S Z]=sparse2(X) where X is full always % returns Z with nnz(Z) = 0, as does [S Z]=sparse2(m,n). More precisely, % Z is the following matrix (where ... means the optional m, n, and nzmax % parameters). % % S = sparse (i,j,s, ...) % Z = spones (sparse (i,j,1, ...)) - spones (S) % % See also sparse. % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse error ('sparse2 mexFunction not found') ; SuiteSparse/CHOLMOD/MATLAB/spsym.c0000644001170100242450000000652010621030000015274 0ustar davisfac/* ========================================================================== */ /* === CHOLMOD/MATLAB/spsym mexFunction ===================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * MATLAB(tm) is a Trademark of The MathWorks, Inc. * -------------------------------------------------------------------------- */ /* [result xmatched pmatched nzoffdiag nzdiag] = spsym (A, quick). * See the spsym.m file for a description of what it computes. */ #include "cholmod_matlab.h" void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double dummy = 0 ; cholmod_sparse Amatrix, *A ; cholmod_common Common, *cm ; Int result, quick, option, xmatched, pmatched, nzoffdiag, nzdiag ; /* ---------------------------------------------------------------------- */ /* start CHOLMOD and set parameters */ /* ---------------------------------------------------------------------- */ cm = &Common ; cholmod_l_start (cm) ; sputil_config (SPUMONI, cm) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if (nargin > 2 || nargin < 1 || nargout > 5) { mexErrMsgTxt ("usage: [s xmatch pmatch nzoff nzd] = spsym (A,quick)") ; } if (!mxIsSparse (pargin [0])) { mexErrMsgTxt ("A must be sparse and double") ; } /* get sparse matrix A */ A = sputil_get_sparse (pargin [0], &Amatrix, &dummy, 0) ; /* get the "quick" parameter */ quick = (nargin > 1) ? (mxGetScalar (pargin [1]) != 0) : FALSE ; if (nargout > 1) { option = 2 ; } else if (quick) { option = 0 ; } else { option = 1 ; } /* ---------------------------------------------------------------------- */ /* determine symmetry */ /* ---------------------------------------------------------------------- */ xmatched = 0 ; pmatched = 0 ; nzoffdiag = 0 ; nzdiag = 0 ; result = cholmod_l_symmetry (A, option, &xmatched, &pmatched, &nzoffdiag, &nzdiag, cm) ; /* ---------------------------------------------------------------------- */ /* return results to MATLAB */ /* ---------------------------------------------------------------------- */ pargout [0] = sputil_put_int (&result, 1, 0) ; if (nargout > 1) pargout [1] = sputil_put_int (&xmatched, 1, 0) ; if (nargout > 2) pargout [2] = sputil_put_int (&pmatched, 1, 0) ; if (nargout > 3) pargout [3] = sputil_put_int (&nzoffdiag, 1, 0) ; if (nargout > 4) pargout [4] = sputil_put_int (&nzdiag, 1, 0) ; /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ cholmod_l_finish (cm) ; cholmod_l_print_common (" ", cm) ; } SuiteSparse/CHOLMOD/MATLAB/spsym.m0000644001170100242450000000611010635513364015331 0ustar davisfacfunction result = spsym (A, quick) %#ok %SPSYM determine if a sparse matrix is symmetric, Hermitian, or skew-symmetric. % If so, also determine if its diagonal has all positive real entries. % A must be sparse. % % Example: % result = spsym (A) ; % result = spsym (A,quick) ; % % If quick = 0, or is not present, then this routine returns: % % 1: if A is rectangular % 2: if A is unsymmetric % 3: if A is symmetric, but with one or more A(j,j) <= 0 % 4: if A is Hermitian, but with one or more A(j,j) <= 0 or with % nonzero imaginary part % 5: if A is skew symmetric (and thus the diagonal is all zero as well) % 6: if A is symmetric with real positive diagonal % 7: if A is Hermitian with real positive diagonal % % If quick is nonzero, then the function can return more quickly, as soon as % it finds a diagonal entry that is <= 0 or with a nonzero imaginary part. In % this case, it returns 1, even if the matrix might otherwise be symmetric or % Hermitian. % % Regardless of the value of "quick", this function returns 6 or 7 if A is % a candidate for sparse Cholesky. % % For an MATLAB M-file function that computes the same thing as this % mexFunction (but much slower), see the get_symmetry function by typing % "type spsym". % % This spsym function does not compute the transpose of A, nor does it need % to examine the entire matrix if it is unsymmetric. It uses very little % memory as well (just size-n workspace, where n = size (A,1)). % % Examples: % load west0479 % A = west0479 ; % spsym (A) % spsym (A+A') % spsym (A-A') % spsym (A+A'+3*speye(size(A,1))) % % See also mldivide. % function result = get_symmetry (A,quick) % %GET_SYMMETRY: does the same thing as the spsym mexFunction. % % It's just a lot slower and uses much more memory. This function % % is meant for testing and documentation only. % [m n] = size (A) ; % if (m ~= n) % result = 1 ; % rectangular % return % end % if (nargin < 2) % quick = 0 ; % end % d = diag (A) ; % posdiag = all (real (d) > 0) & all (imag (d) == 0) ; % if (quick & ~posdiag) % result = 2 ; % Not a candidate for sparse Cholesky. % elseif (~isreal (A) & nnz (A-A') == 0) % if (posdiag) % result = 7 ; % complex Hermitian, with positive diagonal % else % result = 4 ; % complex Hermitian, nonpositive diagonal % end % elseif (nnz (A-A.') == 0) % if (posdiag) % result = 6 ; % symmetric with positive diagonal % else % result = 3 ; % symmetric, nonpositive diagonal % end % elseif (nnz (A+A.') == 0) % result = 5 ; % skew symmetric % else % result = 2 ; % unsymmetric % end % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse error ('spsym mexFunction not found') ; SuiteSparse/CHOLMOD/MATLAB/symbfact2.c0000644001170100242450000002257010621027116016034 0ustar davisfac/* ========================================================================== */ /* === CHOLMOD/MATLAB/symbfact2 mexFunction ================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * MATLAB(tm) is a Trademark of The MathWorks, Inc. * -------------------------------------------------------------------------- */ /* Usage: * * count = symbfact2 (A) returns row counts of R=chol(A) * count = symbfact2 (A,'col') returns row counts of R=chol(A'*A) * count = symbfact2 (A,'sym') same as symbfact2(A) * count = symbfact2 (A,'lo') same as symbfact2(A'), uses tril(A) * count = symbfact2 (A,'row') returns row counts of R=chol(A*A') * * [count, h, parent, post, R] = symbfact2 (...) * * h: height of the elimination tree * parent: the elimination tree itself * post: postordering of the elimination tree * R: a 0-1 matrix whose structure is that of chol(A) or chol(A'*A) * for the 'col' case * * symbfact2(A) and symbfact2(A,'sym') uses triu(A). * symbfact2(A,'lo') uses tril(A). * * These forms return L = R' instead of R. They are faster and take less * memory. They return the same count, h, parent, and post outputs. * * [count, h, parent, post, L] = symbfact2 (A,'col','L') * [count, h, parent, post, L] = symbfact2 (A,'sym','L') * [count, h, parent, post, L] = symbfact2 (A,'lo', 'L') * [count, h, parent, post, L] = symbfact2 (A,'row','L') */ #include "cholmod_matlab.h" void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double dummy = 0 ; double *Lx, *px ; Int *Parent, *Post, *ColCount, *First, *Level, *Rp, *Ri, *Lp, *Li, *W ; cholmod_sparse *A, Amatrix, *F, *Aup, *Alo, *R, *A1, *A2, *L, *S ; cholmod_common Common, *cm ; Int n, i, coletree, j, lnz, p, k, height, c ; char buf [LEN] ; /* ---------------------------------------------------------------------- */ /* start CHOLMOD and set defaults */ /* ---------------------------------------------------------------------- */ cm = &Common ; cholmod_l_start (cm) ; sputil_config (SPUMONI, cm) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if (nargout > 5 || nargin < 1 || nargin > 3) { mexErrMsgTxt ( "Usage: [count h parent post R] = symbfact2 (A, mode, Lmode)") ; } /* ---------------------------------------------------------------------- */ /* get input matrix A */ /* ---------------------------------------------------------------------- */ A = sputil_get_sparse_pattern (pargin [0], &Amatrix, &dummy, cm) ; S = (A == &Amatrix) ? NULL : A ; /* ---------------------------------------------------------------------- */ /* get A->stype, default is to use triu(A) */ /* ---------------------------------------------------------------------- */ A->stype = 1 ; n = A->nrow ; coletree = FALSE ; if (nargin > 1) { buf [0] = '\0' ; if (mxIsChar (pargin [1])) { mxGetString (pargin [1], buf, LEN) ; } c = buf [0] ; if (tolower (c) == 'r') { /* unsymmetric case (A*A') if string starts with 'r' */ A->stype = 0 ; } else if (tolower (c) == 'c') { /* unsymmetric case (A'*A) if string starts with 'c' */ n = A->ncol ; coletree = TRUE ; A->stype = 0 ; } else if (tolower (c) == 's') { /* symmetric upper case (A) if string starts with 's' */ A->stype = 1 ; } else if (tolower (c) == 'l') { /* symmetric lower case (A) if string starts with 'l' */ A->stype = -1 ; } else { mexErrMsgTxt ("symbfact2: unrecognized mode") ; } } if (A->stype && A->nrow != A->ncol) { mexErrMsgTxt ("symbfact2: A must be square") ; } /* ---------------------------------------------------------------------- */ /* compute the etree, its postorder, and the row/column counts */ /* ---------------------------------------------------------------------- */ Parent = cholmod_l_malloc (n, sizeof (Int), cm) ; Post = cholmod_l_malloc (n, sizeof (Int), cm) ; ColCount = cholmod_l_malloc (n, sizeof (Int), cm) ; First = cholmod_l_malloc (n, sizeof (Int), cm) ; Level = cholmod_l_malloc (n, sizeof (Int), cm) ; /* F = A' */ F = cholmod_l_transpose (A, 0, cm) ; if (A->stype == 1 || coletree) { /* symmetric upper case: find etree of A, using triu(A) */ /* column case: find column etree of A, which is etree of A'*A */ Aup = A ; Alo = F ; } else { /* symmetric lower case: find etree of A, using tril(A) */ /* row case: find row etree of A, which is etree of A*A' */ Aup = F ; Alo = A ; } cholmod_l_etree (Aup, Parent, cm) ; if (cm->status < CHOLMOD_OK) { /* out of memory or matrix invalid */ mexErrMsgTxt ("symbfact2 failed: matrix corrupted!") ; } if (cholmod_l_postorder (Parent, n, NULL, Post, cm) != n) { /* out of memory or Parent invalid */ mexErrMsgTxt ("symbfact2 postorder failed!") ; } /* symmetric upper case: analyze tril(F), which is triu(A) */ /* column case: analyze F*F', which is A'*A */ /* symmetric lower case: analyze tril(A) */ /* row case: analyze A*A' */ cholmod_l_rowcolcounts (Alo, NULL, 0, Parent, Post, NULL, ColCount, First, Level, cm) ; if (cm->status < CHOLMOD_OK) { /* out of memory or matrix invalid */ mexErrMsgTxt ("symbfact2 failed: matrix corrupted!") ; } /* ---------------------------------------------------------------------- */ /* return results to MATLAB: count, h, parent, and post */ /* ---------------------------------------------------------------------- */ pargout [0] = sputil_put_int (ColCount, n, 0) ; if (nargout > 1) { /* compute the elimination tree height */ height = 0 ; for (i = 0 ; i < n ; i++) { height = MAX (height, Level [i]) ; } height++ ; pargout [1] = mxCreateDoubleMatrix (1, 1, mxREAL) ; px = mxGetPr (pargout [1]) ; px [0] = height ; } if (nargout > 2) { pargout [2] = sputil_put_int (Parent, n, 1) ; } if (nargout > 3) { pargout [3] = sputil_put_int (Post, n, 1) ; } /* ---------------------------------------------------------------------- */ /* construct L, if requested */ /* ---------------------------------------------------------------------- */ if (nargout > 4) { if (A->stype == 1) { /* symmetric upper case: use triu(A) only, A2 not needed */ A1 = A ; A2 = NULL ; } else if (A->stype == -1) { /* symmetric lower case: use tril(A) only, A2 not needed */ A1 = F ; A2 = NULL ; } else if (coletree) { /* column case: analyze F*F' */ A1 = F ; A2 = A ; } else { /* row case: analyze A*A' */ A1 = A ; A2 = F ; } /* count the total number of entries in L */ lnz = 0 ; for (j = 0 ; j < n ; j++) { lnz += ColCount [j] ; } /* allocate the output matrix L (pattern-only) */ L = cholmod_l_allocate_sparse (n, n, lnz, TRUE, TRUE, 0, CHOLMOD_PATTERN, cm) ; Lp = L->p ; Li = L->i ; /* initialize column pointers */ lnz = 0 ; for (j = 0 ; j < n ; j++) { Lp [j] = lnz ; lnz += ColCount [j] ; } Lp [j] = lnz ; /* create a copy of the column pointers */ W = First ; for (j = 0 ; j < n ; j++) { W [j] = Lp [j] ; } /* get workspace for computing one row of L */ R = cholmod_l_allocate_sparse (n, 1, n, FALSE, TRUE, 0, CHOLMOD_PATTERN, cm) ; Rp = R->p ; Ri = R->i ; /* compute L one row at a time */ for (k = 0 ; k < n ; k++) { /* get the kth row of L and store in the columns of L */ cholmod_l_row_subtree (A1, A2, k, Parent, R, cm) ; for (p = 0 ; p < Rp [1] ; p++) { Li [W [Ri [p]]++] = k ; } /* add the diagonal entry */ Li [W [k]++] = k ; } /* free workspace */ cholmod_l_free_sparse (&R, cm) ; /* transpose L to get R, or leave as is */ if (nargin < 3) { /* R = L' */ R = cholmod_l_transpose (L, 0, cm) ; cholmod_l_free_sparse (&L, cm) ; L = R ; } /* fill numerical values of L with one's (only MATLAB needs this...) */ L->x = cholmod_l_malloc (lnz, sizeof (double), cm) ; Lx = L->x ; for (p = 0 ; p < lnz ; p++) { Lx [p] = 1 ; } L->xtype = CHOLMOD_REAL ; /* return L (or R) to MATLAB */ pargout [4] = sputil_put_sparse (&L, cm) ; } /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ cholmod_l_free (n, sizeof (Int), Parent, cm) ; cholmod_l_free (n, sizeof (Int), Post, cm) ; cholmod_l_free (n, sizeof (Int), ColCount, cm) ; cholmod_l_free (n, sizeof (Int), First, cm) ; cholmod_l_free (n, sizeof (Int), Level, cm) ; cholmod_l_free_sparse (&F, cm) ; cholmod_l_free_sparse (&S, cm) ; cholmod_l_finish (cm) ; cholmod_l_print_common (" ", cm) ; /* if (cm->malloc_count != ((nargout == 5) ? 3:0)) mexErrMsgTxt ("!") ; */ } SuiteSparse/CHOLMOD/MATLAB/symbfact2.m0000644001170100242450000000410710620371044016043 0ustar davisfacfunction [count, h, parent, post, L] = symbfact2 (A, mode, Lmode) %#ok %SYMBFACT2 symbolic factorization % % Analyzes the Cholesky factorization of A, A'*A, or A*A'. % % Example: % count = symbfact2 (A) returns row counts of R=chol(A) % count = symbfact2 (A,'col') returns row counts of R=chol(A'*A) % count = symbfact2 (A,'sym') same as symbfact2(A) % count = symbfact2 (A,'lo') same as symbfact2(A'), uses tril(A) % count = symbfact2 (A,'row') returns row counts of R=chol(A*A') % % The flop count for a subsequent LL' factorization is sum(count.^2) % % [count, h, parent, post, R] = symbfact2 (...) returns: % % h: height of the elimination tree % parent: the elimination tree itself % post: postordering of the elimination tree % R: a 0-1 matrix whose structure is that of chol(A) for the symmetric % case, chol(A'*A) for the 'col' case, or chol(A*A') for the % 'row' case. % % symbfact2(A) and symbfact2(A,'sym') uses the upper triangular part of A % (triu(A)) and assumes the lower triangular part is the transpose of % the upper triangular part. symbfact2(A,'lo') uses tril(A) instead. % % With one to four output arguments, symbfact2 takes time almost proportional % to nnz(A)+n where n is the dimension of R, and memory proportional to % nnz(A). Computing the 5th argument takes more time and memory, both % O(nnz(L)). Internally, the pattern of L is computed and R=L' is returned. % % The following forms return L = R' instead of R. They are faster and take % less memory than the forms above. They return the same count, h, parent, % and post outputs. % % [count, h, parent, post, L] = symbfact2 (A,'col','L') % [count, h, parent, post, L] = symbfact2 (A,'sym','L') % [count, h, parent, post, L] = symbfact2 (A,'lo', 'L') % [count, h, parent, post, L] = symbfact2 (A,'row','L') % % See also CHOL, ETREE, TREELAYOUT, SYMBFACT % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse error ('symbfact2 mexFunction not found!') ; SuiteSparse/CHOLMOD/MATLAB/cholmod_demo.m0000644001170100242450000000714410712143743016613 0ustar davisfacfunction cholmod_demo %CHOLMOD_DEMO a demo for CHOLMOD % % Tests CHOLMOD with various randomly-generated matrices, and the west0479 % matrix distributed with MATLAB. Random matrices are not good test cases, % but they are easily generated. It also compares CHOLMOD and MATLAB on the % sparse matrix problem used in the MATLAB BENCH command. % % See CHOLMOD/MATLAB/Test/cholmod_test.m for a lengthy test using matrices from % the UF sparse matrix collection. % % Example: % cholmod_demo % % See also BENCH % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse help cholmod_demo rand ('state', 0) ; randn ('state', 0) ; load west0479 A = west0479 ; n = size (A,1) ; A = A*A'+100*speye (n) ; try_matrix (A) ; clear A n = 2000 ; A = sprandn (n, n, 0.002) ; A = A+A'+100*speye (n) ; try_matrix (A) ; clear A for n = [100 2000] A = rand (n) ; A = A*A' + 10 * eye (n) ; try_matrix (A) ; clear A end fprintf ('\n--------------------------------------------------------------\n') ; fprintf ('\nWith the matrix used in the MATLAB 7.2 "bench" program.\n') ; fprintf ('No fill-reducing orderings are used; type "help bench" for more') ; fprintf (' information.\n') ; n = 300 ; A = delsq (numgrid ('L', n)) ; b = sum (A)' ; spparms ('default') ; spparms ('autommd',0) ; spparms ('autoamd',0) ; tic ; x = A\b ; t1 = toc ; e1 = norm (A*x-b) ; tic ; x = cholmod2 (A,b,0) ; t2 = toc ; e2 = norm (A*x-b) ; fprintf ('MATLAB x=A\\b time: %8.4f resid: %8.0e\n', t1, e1) ; fprintf ('CHOLMOD x=A\\b time: %8.4f resid: %8.0e\n', t2, e2) ; fprintf ('CHOLMOD speedup: %8.2f\n', t1/t2) ; spparms ('default') ; fprintf ('\ncholmod_demo finished: all tests passed\n') ; fprintf ('\nFor more accurate timings, run this test again.\n') ; function try_matrix (A) % try_matrix: try a matrix with CHOLMOD n = size (A,1) ; S = sparse (A) ; fprintf ('\n--------------------------------------------------------------\n') ; if (issparse (A)) fprintf ('cholmod_demo: sparse matrix, n %d nnz %d\n', n, nnz (A)) ; else fprintf ('cholmod_demo: dense matrix, n %d\n', n) ; end X = rand (n,1) ; C = sparse (X) ; try % use built-in AMD p = amd (S) ; catch try % use AMD from SuiteSparse (../../AMD) p = amd2 (S) ; catch % use SYMAMD p = symamd (S) ; end end S = S (p,p) ; lnz = symbfact2 (S) ; fl = sum (lnz.^2) ; tic L = lchol (S) ; %#ok t1 = toc ; fprintf ('CHOLMOD lchol(sparse(A)) time: %6.2f mflop %8.1f\n', ... t1, 1e-6 * fl / t1) ; tic LD = ldlchol (S) ; %#ok t2 = toc ; fprintf ('CHOLMOD ldlchol(sparse(A)) time: %6.2f mflop %8.1f\n', ... t2, 1e-6 * fl / t2) ; tic LD = ldlupdate (LD,C) ; t3 = toc ; fprintf ('CHOLMOD ldlupdate(sparse(A),C) time: %6.2f (rank-1, C dense)\n', t3) ; [L,D] = ldlsplit (LD) ; L = full (L) ; err = norm ((S+C*C') - L*D*L', 1) / norm (S,1) ; fprintf ('err: %g\n', err) ; tic R = chol (S) ; %#ok s1 = toc ; fprintf ('MATLAB chol(sparse(A)) time: %6.2f mflop %8.1f\n', ... s1, 1e-6 * fl / s1) ; E = full (A) ; tic R = chol (E) ; s2 = toc ; fprintf ('MATLAB chol(full(A)) time: %6.2f mflop %8.1f\n', ... s2, 1e-6 * fl / s2) ; Z = full (R) ; tic Z = cholupdate (Z,X) ; s3 = toc ; fprintf ('MATLAB cholupdate(full(A),C) time: %6.2f (rank-1)\n', s3) ; err = norm ((E+X*X') - Z'*Z, 1) / norm (E,1) ; fprintf ('err: %g\n', err) ; fprintf ('CHOLMOD lchol(sparse(A)) speedup over chol(sparse(A)): %6.1f\n', ... s1 / t1) ; fprintf ('CHOLMOD sparse update speedup vs MATLAB DENSE update: %6.1f\n', ... s3 / t3) ; clear E S L R LD X C D Z clear err s1 s2 s3 t1 t2 t3 n SuiteSparse/CHOLMOD/MATLAB/ldlchol.c0000644001170100242450000001565010621027704015567 0ustar davisfac/* ========================================================================== */ /* === CHOLMOD/MATLAB/ldlchol mexFunction =================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * MATLAB(tm) is a Trademark of The MathWorks, Inc. * -------------------------------------------------------------------------- */ /* Numeric LDL' factorization. Note that LL' and LDL' are faster than R'R * and use less memory. The LDL' factorization methods use tril(A). * The unit diagonal L can be obtained with tril(LD,-1)+speye(n) and the * diagonal D can be obtained with D = diag(diag(LD)) ; * * LD = ldlchol (A) return the LDL' factorization of A * [LD,p] = ldlchol (A) like [R,p] = chol(A), except LD is always square * [LD,p,q] = ldlchol (A) factorizes A(q,q) into L*D*L' * * LD = ldlchol (A,beta) return the LDL' factorization of A*A'+beta*I * [LD,p] = ldlchol (A,beta) like [R,p] = chol(A*A'+beta+I) * [LD,p,q] = ldlchol (A,beta) factorizes A(q,:)*A(q,:)'+beta*I into L*D*L' * * Explicit zeros may appear in the LD matrix. The pattern of LD matches the * pattern of L as computed by symbfact2, even if some entries in LD are * explicitly zero. This is to ensure that ldlupdate works properly. You must * NOT modify LD in MATLAB itself and then use ldlupdate if LD contains * explicit zero entries; ldlupdate will fail catastrophically in this case. * * You MAY modify LD in MATLAB if you do not pass it back to ldlupdate. Just be * aware that LD contains explicit zero entries, contrary to the standard * practice in MATLAB of removing those entries from all sparse matrices. * * Note that CHOLMOD uses a supernodal LL' factorization and then converts it * to LDL' for large matrices, and a simplicial LDL' factorization otherwise. * Two-by-two block pivoting is not performed, in any case. Thus, ldlchol * will not be able to perform an LDL' factorization of an arbitrary indefinite * matrix. The matrix * * 0 1 * 1 0 * * will fail, for example. You can tell CHOLMOD to always use its simplicial * LDL' factorization by adding the statement * * cm->supernodal = CHOLMOD_SIMPLICIAL ; * * but ldlchol will be much slower for large matrices. It still will not be * able to handle the above matrix, but it can then handle matrices such as * * -2 1 * 1 -2 * * or any other symmetric matrix for which all leading minors are * well-conditioned. */ #include "cholmod_matlab.h" void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double dummy = 0, beta [2], *px ; cholmod_sparse Amatrix, *A, *Lsparse ; cholmod_factor *L ; cholmod_common Common, *cm ; Int n, minor ; /* ---------------------------------------------------------------------- */ /* start CHOLMOD and set parameters */ /* ---------------------------------------------------------------------- */ cm = &Common ; cholmod_l_start (cm) ; sputil_config (SPUMONI, cm) ; /* convert to packed LDL' when done */ cm->final_asis = FALSE ; cm->final_super = FALSE ; cm->final_ll = FALSE ; cm->final_pack = TRUE ; cm->final_monotonic = TRUE ; /* since numerically zero entries are NOT dropped from the symbolic * pattern, we DO need to drop entries that result from supernodal * amalgamation. */ cm->final_resymbol = TRUE ; cm->quick_return_if_not_posdef = (nargout < 2) ; /* This will disable the supernodal LL', which will be slow. */ /* cm->supernodal = CHOLMOD_SIMPLICIAL ; */ /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if (nargin > 2 || nargout > 3) { mexErrMsgTxt ("usage: [L,p,q] = ldlchol (A,beta)") ; } n = mxGetM (pargin [0]) ; if (!mxIsSparse (pargin [0])) { mexErrMsgTxt ("A must be sparse") ; } if (nargin == 1 && n != mxGetN (pargin [0])) { mexErrMsgTxt ("A must be square") ; } /* get sparse matrix A, use tril(A) */ A = sputil_get_sparse (pargin [0], &Amatrix, &dummy, -1) ; if (nargin == 1) { A->stype = -1 ; /* use lower part of A */ beta [0] = 0 ; beta [1] = 0 ; } else { A->stype = 0 ; /* use all of A, factorizing A*A' */ beta [0] = mxGetScalar (pargin [1]) ; beta [1] = 0 ; } /* use natural ordering if no q output parameter */ if (nargout < 3) { cm->nmethods = 1 ; cm->method [0].ordering = CHOLMOD_NATURAL ; cm->postorder = FALSE ; } /* ---------------------------------------------------------------------- */ /* analyze and factorize */ /* ---------------------------------------------------------------------- */ L = cholmod_l_analyze (A, cm) ; cholmod_l_factorize_p (A, beta, NULL, 0, L, cm) ; if (nargout < 2 && cm->status != CHOLMOD_OK) { mexErrMsgTxt ("matrix is not positive definite") ; } /* ---------------------------------------------------------------------- */ /* convert L to a sparse matrix */ /* ---------------------------------------------------------------------- */ /* the conversion sets L->minor back to n, so get a copy of it first */ minor = L->minor ; Lsparse = cholmod_l_factor_to_sparse (L, cm) ; if (Lsparse->xtype == CHOLMOD_COMPLEX) { /* convert Lsparse from complex to zomplex */ cholmod_l_sparse_xtype (CHOLMOD_ZOMPLEX, Lsparse, cm) ; } /* ---------------------------------------------------------------------- */ /* return results to MATLAB */ /* ---------------------------------------------------------------------- */ /* return L as a sparse matrix (it may contain numerically zero entries) */ pargout [0] = sputil_put_sparse (&Lsparse, cm) ; /* return minor (translate to MATLAB convention) */ if (nargout > 1) { pargout [1] = mxCreateDoubleMatrix (1, 1, mxREAL) ; px = mxGetPr (pargout [1]) ; px [0] = ((minor == n) ? 0 : (minor+1)) ; } /* return permutation */ if (nargout > 2) { pargout [2] = sputil_put_int (L->Perm, n, 1) ; } /* ---------------------------------------------------------------------- */ /* free workspace and the CHOLMOD L, except for what is copied to MATLAB */ /* ---------------------------------------------------------------------- */ cholmod_l_free_factor (&L, cm) ; cholmod_l_finish (cm) ; cholmod_l_print_common (" ", cm) ; /* if (cm->malloc_count != 3 + mxIsComplex (pargout[0])) mexErrMsgTxt ("!") ; */ } SuiteSparse/CHOLMOD/MATLAB/ldlchol.m0000644001170100242450000000375610620370767015616 0ustar davisfacfunction [LD,p,q] = ldlchol (A,beta) %#ok %LDLCHOL sparse A=LDL' factorization % Note that L*L' (LCHOL) and L*D*L' (LDLCHOL) factorizations are faster than % R'*R (CHOL2 and CHOL) and use less memory. The LL' and LDL' factorization % methods use tril(A). A must be sparse. % % Example: % LD = ldlchol (A) return the LDL' factorization of A % [LD,p] = ldlchol (A) similar [R,p] = chol(A), but for L*D*L' % [LD,p,q] = ldlchol (A) factorizes A(q,q) into L*D*L', where q is a % fill-reducing ordering % % LD = ldlchol (A,beta) return the LDL' factorization of A*A'+beta*I % [LD,p] = ldlchol (A,beta) like [R,p] = chol(A*A'+beta+I) % [LD,p,q] = ldlchol (A,beta) factorizes A(q,:)*A(q,:)'+beta*I into L*D*L' % % The output matrix LD contains both L and D. D is on the diagonal of LD, and % L is contained in the strictly lower triangular part of LD. The unit- % diagonal of L is not stored. You can obtain the L and D matrices with % [L,D] = ldlsplit (LD). LD is in the form needed by ldlupdate. % % Explicit zeros may appear in the LD matrix. The pattern of LD matches the % pattern of L as computed by symbfact2, even if some entries in LD are % explicitly zero. This is to ensure that ldlupdate and ldlsolve work % properly. You must NOT modify LD in MATLAB itself and then use ldlupdate % or ldlsolve if LD contains explicit zero entries; ldlupdate and ldlsolve % will fail catastrophically in this case. % % You MAY modify LD in MATLAB if you do not pass it back to ldlupdate or % ldlsolve. Just be aware that LD contains explicit zero entries, contrary % to the standard practice in MATLAB of removing those entries from all % sparse matrices. LD = sparse2 (LD) will remove any zero entries in LD. % % See also LDLUPDATE, LDLSOLVE, LDLSPLIT, CHOL2, LCHOL, CHOL, SPARSE2 % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse error ('ldlchol mexFunction not found') ; SuiteSparse/CHOLMOD/MATLAB/ldlupdate.c0000644001170100242450000001322410617610225016120 0ustar davisfac/* ========================================================================== */ /* === CHOLMOD/MATLAB/ldlupdate mexFunction ================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * MATLAB(tm) is a Trademark of The MathWorks, Inc. * -------------------------------------------------------------------------- */ /* Multiple-rank update or downdate of a sparse LDL' factorization. * * Usage: * * LD = ldlupdate (LD,C) update an LDL' factorization * LD = ldlupdate (LD,C,'+') update an LDL' factorization * LD = ldlupdate (LD,C,'-') downdate an LDL' factorization * * See ldlupdate.m for details. LD and C must be real and sparse. * * The bulk of the time is spent copying the input LD to the output LD. This * mexFunction could be much faster if it could safely modify its input LD. */ #include "cholmod_matlab.h" void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double dummy = 0 ; double *Lx, *Lx2 ; Int *Li, *Lp, *Li2, *Lp2, *Lnz2, *ColCount ; cholmod_sparse Cmatrix, *C, *Lsparse ; cholmod_factor *L ; cholmod_common Common, *cm ; Int j, k, s, update, n, lnz ; char buf [LEN] ; /* ---------------------------------------------------------------------- */ /* start CHOLMOD and set parameters */ /* ---------------------------------------------------------------------- */ cm = &Common ; cholmod_l_start (cm) ; sputil_config (SPUMONI, cm) ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ if (nargout > 1 || nargin < 2 || nargin > 3) { mexErrMsgTxt ("Usage: L = ldlupdate (L, C, '+')") ; } n = mxGetN (pargin [0]) ; k = mxGetN (pargin [1]) ; if (!mxIsSparse (pargin [0]) || !mxIsSparse (pargin [1]) || n != mxGetM (pargin [0]) || n != mxGetM (pargin [1]) || mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])) { mexErrMsgTxt ("ldlupdate: C and/or L not sparse, complex, or wrong" " dimensions") ; } /* ---------------------------------------------------------------------- */ /* determine if we're doing an update or downdate */ /* ---------------------------------------------------------------------- */ update = TRUE ; if (nargin > 2 && mxIsChar (pargin [2])) { mxGetString (pargin [2], buf, LEN) ; if (buf [0] == '-') { update = FALSE ; } else if (buf [0] != '+') { mexErrMsgTxt ("ldlupdate: update string must be '+' or '-'") ; } } /* ---------------------------------------------------------------------- */ /* get C: sparse matrix of incoming/outgoing columns */ /* ---------------------------------------------------------------------- */ C = sputil_get_sparse (pargin [1], &Cmatrix, &dummy, 0) ; /* ---------------------------------------------------------------------- */ /* construct a copy of the input sparse matrix L */ /* ---------------------------------------------------------------------- */ /* get the MATLAB L */ Lp = (Int *) mxGetJc (pargin [0]) ; Li = (Int *) mxGetIr (pargin [0]) ; Lx = mxGetPr (pargin [0]) ; /* allocate the CHOLMOD symbolic L */ L = cholmod_l_allocate_factor (n, cm) ; L->ordering = CHOLMOD_NATURAL ; ColCount = L->ColCount ; for (j = 0 ; j < n ; j++) { ColCount [j] = Lp [j+1] - Lp [j] ; } /* allocate space for a CHOLMOD LDL' packed factor */ cholmod_l_change_factor (CHOLMOD_REAL, FALSE, FALSE, TRUE, TRUE, L, cm) ; /* copy MATLAB L into CHOLMOD L */ Lp2 = L->p ; Li2 = L->i ; Lx2 = L->x ; Lnz2 = L->nz ; lnz = L->nzmax ; for (j = 0 ; j <= n ; j++) { Lp2 [j] = Lp [j] ; } for (j = 0 ; j < n ; j++) { Lnz2 [j] = Lp [j+1] - Lp [j] ; } for (s = 0 ; s < lnz ; s++) { Li2 [s] = Li [s] ; } for (s = 0 ; s < lnz ; s++) { Lx2 [s] = Lx [s] ; } /* ---------------------------------------------------------------------- */ /* update/downdate the LDL' factorization */ /* ---------------------------------------------------------------------- */ if (!cholmod_l_updown (update, C, L, cm)) { mexErrMsgTxt ("ldlupdate failed\n") ; } /* ---------------------------------------------------------------------- */ /* copy the results back to MATLAB */ /* ---------------------------------------------------------------------- */ /* change L back to packed LDL' (it may have become unpacked if the * sparsity pattern changed). This change takes O(n) time if the pattern * of L wasn't updated. */ Lsparse = cholmod_l_factor_to_sparse (L, cm) ; /* return L as a sparse matrix */ pargout [0] = sputil_put_sparse (&Lsparse, cm) ; /* ---------------------------------------------------------------------- */ /* free workspace and the CHOLMOD L, except for what is copied to MATLAB */ /* ---------------------------------------------------------------------- */ cholmod_l_free_factor (&L, cm) ; cholmod_l_finish (cm) ; cholmod_l_print_common (" ", cm) ; /* if (cm->malloc_count != 3 + mxIsComplex (pargout[0])) mexErrMsgTxt ("!") ; */ } SuiteSparse/CHOLMOD/MATLAB/ldlupdate.m0000644001170100242450000000475310620371011016130 0ustar davisfacfunction LD = ldlupdate (LD,C,updown) %#ok %LDLUPDATE multiple-rank update or downdate of a sparse LDL' factorization. % % On input, LD contains the LDL' factorization of A (L*D*L'=A or A(q,q)). % The unit-diagonal of L is not stored. In its place is the diagonal matrix % D. LD can be computed using the CHOLMOD mexFunctions: % % LD = ldlchol (A) ; % or % [LD,p,q] = ldlchol (A) ; % % With this LD, either of the following MATLAB statements, % % Example: % LD = ldlupdate (LD,C) % LD = ldlupdate (LD,C,'+') % % return the LDL' factorization of A+C*C' or A(q,q)-C*C' if LD holds the LDL' % factorization of A(q,q) on input. For a downdate: % % LD = ldlupdate (LD,C,'-') % % returns the LDL' factorization of A-C*C' or A(q,q)-C*C'. % % LD and C must be sparse and real. LD must be square, and C must have the % same number of rows as LD. You must not modify LD in MATLAB (see the % WARNING below). % % Note that if C is sparse with few columns, most of the time spent in this % routine is taken by copying the input LD to the output LD. If MATLAB % allowed mexFunctions to safely modify its inputs, this mexFunction would % be much faster, since not all of LD changes. % % See also LDLCHOL, LDLSPLIT, LDLSOLVE, CHOLUPDATE % % =========================================================================== % =============================== WARNING =================================== % =========================================================================== % MATLAB drops zero entries from its sparse matrices. LD can contain % numerically zero entries that are symbolically present in the sparse matrix % data structure. These are essential for ldlupdate and ldlsolve to work % properly, since they exploit the graph-theoretic structure of a sparse % Cholesky factorization. If you modify LD in MATLAB, those zero entries may % get dropped and the required graph property will be destroyed. In this % case, ldlupdate and ldlsolve will fail catastrophically (possibly with a % segmentation fault, terminating MATLAB). It takes much more time to ensure % this property holds than the time it takes to do the update/downdate or the % solve, so ldlupdate and ldlsolve simply assume the propertly holds. % =========================================================================== % Copyright 2006-2007, Timothy A. Davis, William W. Hager % http://www.cise.ufl.edu/research/sparse error ('ldlupdate mexFunction not found') ; SuiteSparse/CHOLMOD/MATLAB/resymbol.c0000644001170100242450000001236110621027746016004 0ustar davisfac/* ========================================================================== */ /* === CHOLMOD/MATLAB/resymbol mexFunction ================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * MATLAB(tm) is a Trademark of The MathWorks, Inc. * -------------------------------------------------------------------------- */ /* Usage: * L = resymbol (L, A) * * Recompute the symbolic Cholesky factorization of the matrix A. A must be * symmetric. Only tril(A) is used. Entries in L that are not in the Cholesky * factorization of A are removed from L. L can be from an LL' or LDL' * factorization. The numerical values of A are ignored; only its nonzero * pattern is used. */ /* ========================================================================== */ #include "cholmod_matlab.h" void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double dummy = 0 ; double *Lx, *Lx2, *Lz, *Lz2 ; Int *Li, *Lp, *Lnz2, *Li2, *Lp2, *ColCount ; cholmod_sparse *A, Amatrix, *Lsparse, *S ; cholmod_factor *L ; cholmod_common Common, *cm ; Int j, s, n, lnz, is_complex ; /* ---------------------------------------------------------------------- */ /* start CHOLMOD and set parameters */ /* ---------------------------------------------------------------------- */ cm = &Common ; cholmod_l_start (cm) ; sputil_config (SPUMONI, cm) ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ if (nargout > 1 || nargin != 2) { mexErrMsgTxt ("usage: L = resymbol (L, A)\n") ; } n = mxGetN (pargin [0]) ; if (!mxIsSparse (pargin [0]) || n != mxGetM (pargin [0])) { mexErrMsgTxt ("resymbol: L must be sparse and square") ; } if (n != mxGetM (pargin [1]) || n != mxGetN (pargin [1])) { mexErrMsgTxt ("resymbol: A and L must have same dimensions") ; } /* ---------------------------------------------------------------------- */ /* get the sparse matrix A */ /* ---------------------------------------------------------------------- */ A = sputil_get_sparse_pattern (pargin [1], &Amatrix, &dummy, cm) ; S = (A == &Amatrix) ? NULL : A ; A->stype = -1 ; /* A = sputil_get_sparse (pargin [1], &Amatrix, &dummy, -1) ; */ /* ---------------------------------------------------------------------- */ /* construct a copy of the input sparse matrix L */ /* ---------------------------------------------------------------------- */ /* get the MATLAB L */ Lp = (Int *) mxGetJc (pargin [0]) ; Li = (Int *) mxGetIr (pargin [0]) ; Lx = mxGetPr (pargin [0]) ; Lz = mxGetPi (pargin [0]) ; is_complex = mxIsComplex (pargin [0]) ; /* allocate the CHOLMOD symbolic L */ L = cholmod_l_allocate_factor (n, cm) ; L->ordering = CHOLMOD_NATURAL ; ColCount = L->ColCount ; for (j = 0 ; j < n ; j++) { ColCount [j] = Lp [j+1] - Lp [j] ; } /* allocate space for a CHOLMOD LDL' packed factor */ /* (LL' and LDL' are treated identically) */ cholmod_l_change_factor (is_complex ? CHOLMOD_ZOMPLEX : CHOLMOD_REAL, FALSE, FALSE, TRUE, TRUE, L, cm) ; /* copy MATLAB L into CHOLMOD L */ Lp2 = L->p ; Li2 = L->i ; Lx2 = L->x ; Lz2 = L->z ; Lnz2 = L->nz ; lnz = L->nzmax ; for (j = 0 ; j <= n ; j++) { Lp2 [j] = Lp [j] ; } for (j = 0 ; j < n ; j++) { Lnz2 [j] = Lp [j+1] - Lp [j] ; } for (s = 0 ; s < lnz ; s++) { Li2 [s] = Li [s] ; } for (s = 0 ; s < lnz ; s++) { Lx2 [s] = Lx [s] ; } if (is_complex) { for (s = 0 ; s < lnz ; s++) { Lz2 [s] = Lz [s] ; } } /* ---------------------------------------------------------------------- */ /* resymbolic factorization */ /* ---------------------------------------------------------------------- */ cholmod_l_resymbol (A, NULL, 0, TRUE, L, cm) ; /* ---------------------------------------------------------------------- */ /* copy the results back to MATLAB */ /* ---------------------------------------------------------------------- */ Lsparse = cholmod_l_factor_to_sparse (L, cm) ; /* return L as a sparse matrix */ pargout [0] = sputil_put_sparse (&Lsparse, cm) ; /* ---------------------------------------------------------------------- */ /* free workspace and the CHOLMOD L, except for what is copied to MATLAB */ /* ---------------------------------------------------------------------- */ cholmod_l_free_factor (&L, cm) ; cholmod_l_free_sparse (&S, cm) ; cholmod_l_finish (cm) ; cholmod_l_print_common (" ", cm) ; /* if (cm->malloc_count != 3 + mxIsComplex (pargout[0])) mexErrMsgTxt ("!") ; */ } SuiteSparse/CHOLMOD/MATLAB/resymbol.m0000644001170100242450000000140110620371033015775 0ustar davisfacfunction L = resymbol (L, A) %#ok %RESYMBOL recomputes the symbolic Cholesky factorization of the matrix A. % % Example: % L = resymbol (L, A) % % Recompute the symbolic Cholesky factorization of the matrix A. A must be % symmetric. Only tril(A) is used. Entries in L that are not in the Cholesky % factorization of A are removed from L. L can be from an LL' or LDL' % factorization (lchol or ldlchol). resymbol is useful after a series of % downdates via ldlupdate, since downdates do not remove any entries in L. % The numerical values of A are ignored; only its nonzero pattern is used. % % See also LCHOL, LDLUPDATE % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse error ('resymbol not found') ; SuiteSparse/CHOLMOD/MATLAB/etree2.c0000644001170100242450000001316410616450160015332 0ustar davisfac/* ========================================================================== */ /* === CHOLMOD/MATLAB/etree2 mexFunction ==================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * MATLAB(tm) is a Trademark of The MathWorks, Inc. * -------------------------------------------------------------------------- */ /* Usage: * * parent = etree2 (A) returns etree of A, uses triu(A) * parent = etree2 (A, 'col') returns etree of A'*A * parent = etree2 (A, 'sym') same as etree2 (A) * parent = etree2 (A, 'row') same as etree2 (A', 'col') * parent = etree2 (A, 'lo') returns etree of A, uses tril(A) * * [parent post] = etree2(...) also returns a postorder of the tree * * etree2 (A, 'col') does not form A'*A and is thus faster than etree2 (A'*A) * and takes less memory. Likewise, etree (A, 'row') does not * form A*A', and is thus faster than etree2 (A*A') and takes less memory. */ #include "cholmod_matlab.h" void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double dummy = 0 ; Int *Parent ; cholmod_sparse *A, Amatrix, *S ; cholmod_common Common, *cm ; Int n, coletree, c ; char buf [LEN] ; /* ---------------------------------------------------------------------- */ /* start CHOLMOD and set defaults */ /* ---------------------------------------------------------------------- */ cm = &Common ; cholmod_l_start (cm) ; sputil_config (SPUMONI, cm) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if (nargout > 2 || nargin < 1 || nargin > 2) { mexErrMsgTxt ("Usage: [parent post] = etree2 (A, mode)") ; } /* ---------------------------------------------------------------------- */ /* get input matrix A */ /* ---------------------------------------------------------------------- */ A = sputil_get_sparse_pattern (pargin [0], &Amatrix, &dummy, cm) ; S = (A == &Amatrix) ? NULL : A ; /* ---------------------------------------------------------------------- */ /* get A->stype, default is to use triu(A) */ /* ---------------------------------------------------------------------- */ A->stype = 1 ; n = A->nrow ; coletree = FALSE ; if (nargin > 1) { buf [0] = '\0' ; if (mxIsChar (pargin [1])) { mxGetString (pargin [1], buf, LEN) ; } c = buf [0] ; if (tolower (c) == 'r') { /* unsymmetric case (A*A') if string starts with 'r' */ A->stype = 0 ; } else if (tolower (c) == 'c') { /* unsymmetric case (A'*A) if string starts with 'c' */ n = A->ncol ; coletree = TRUE ; A->stype = 0 ; } else if (tolower (c) == 's') { /* symmetric upper case (A) if string starts with 's' */ A->stype = 1 ; } else if (tolower (c) == 'l') { /* symmetric lower case (A) if string starts with 'l' */ A->stype = -1 ; } else { mexErrMsgTxt ("etree2: unrecognized mode") ; } } if (A->stype && A->nrow != A->ncol) { mexErrMsgTxt ("etree2: A must be square") ; } /* ---------------------------------------------------------------------- */ /* compute the etree */ /* ---------------------------------------------------------------------- */ Parent = cholmod_l_malloc (n, sizeof (Int), cm) ; if (A->stype == 1 || coletree) { /* symmetric case: find etree of A, using triu(A) */ /* column case: find column etree of A, which is etree of A'*A */ cholmod_l_etree (A, Parent, cm) ; } else { /* symmetric case: find etree of A, using tril(A) */ /* row case: find row etree of A, which is etree of A*A' */ /* R = A' */ cholmod_sparse *R ; R = cholmod_l_transpose (A, 0, cm) ; cholmod_l_etree (R, Parent, cm) ; cholmod_l_free_sparse (&R, cm) ; } if (cm->status < CHOLMOD_OK) { /* out of memory or matrix invalid */ mexErrMsgTxt ("etree2 failed: matrix corrupted!") ; } /* ---------------------------------------------------------------------- */ /* return Parent to MATLAB */ /* ---------------------------------------------------------------------- */ pargout [0] = sputil_put_int (Parent, n, 1) ; /* ---------------------------------------------------------------------- */ /* postorder the tree and return results to MATLAB */ /* ---------------------------------------------------------------------- */ if (nargout > 1) { Int *Post ; Post = cholmod_l_malloc (n, sizeof (Int), cm) ; if (cholmod_l_postorder (Parent, n, NULL, Post, cm) != n) { /* out of memory or Parent invalid */ mexErrMsgTxt ("etree2 postorder failed!") ; } pargout [1] = sputil_put_int (Post, n, 1) ; cholmod_l_free (n, sizeof (Int), Post, cm) ; } /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ cholmod_l_free (n, sizeof (Int), Parent, cm) ; cholmod_l_free_sparse (&S, cm) ; cholmod_l_finish (cm) ; cholmod_l_print_common (" ", cm) ; /* if (cm->malloc_count != 0) mexErrMsgTxt ("!") ; */ } SuiteSparse/CHOLMOD/MATLAB/etree2.m0000644001170100242450000000324710711661233015346 0ustar davisfacfunction [parent, post] = etree2 (A, mode) %#ok %ETREE2 sparse elimination tree. % Finds the elimination tree of A, A'*A, or A*A', and optionaly postorders % the tree. parent(j) is the parent of node j in the tree, or 0 if j is a % root. The symmetric case uses only the upper or lower triangular part of % A (etree2(A) uses the upper part, and etree2(A,'lo') uses the lower part). % % Example: % parent = etree2 (A) finds the elimination tree of A, using triu(A) % parent = etree2 (A,'sym') same as etree2(A) % parent = etree2 (A,'col') finds the elimination tree of A'*A % parent = etree2 (A,'row') finds the elimination tree of A*A' % parent = etree2 (A,'lo') finds the elimination tree of A, using tril(A) % % [parent,post] = etree2 (...) also returns a post-ordering of the tree. % % If you have a fill-reducing permutation p, you can combine it with an % elimination tree post-ordering using the following code. Post-ordering has % no effect on fill-in (except for lu), but it does improve the performance % of the subsequent factorization. % % For the symmetric case, suitable for chol(A(p,p)): % % [parent post] = etree2 (A (p,p)) ; % p = p (post) ; % % For the column case, suitable for qr(A(:,p)) or lu(A(:,p)): % % [parent post] = etree2 (A (:,p), 'col') ; % p = p (post) ; % % For the row case, suitable for qr(A(p,:)') or chol(A(p,:)*A(p,:)'): % % [parent post] = etree2 (A (p,:), 'row') ; % p = p (post) ; % % See also TREELAYOUT, TREEPLOT, ETREEPLOT, ETREE % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse error ('etree2 mexFunction not found') ; SuiteSparse/CHOLMOD/MATLAB/License.txt0000644001170100242450000000213210540000244016102 0ustar davisfacCHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis CHOLMOD is also available under other licenses; contact authors for details. MATLAB(tm) is a Registered Trademark of The MathWorks, Inc. http://www.cise.ufl.edu/research/sparse Note that this license is for the CHOLMOD/MATLAB module only. All CHOLMOD modules are licensed separately. -------------------------------------------------------------------------------- This Module is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This Module is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. SuiteSparse/CHOLMOD/MATLAB/mread.c0000644001170100242450000001423110634320673015235 0ustar davisfac/* ========================================================================== */ /* === CHOLMOD/MATLAB/mread mexFunction ===================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * MATLAB(tm) is a Trademark of The MathWorks, Inc. * -------------------------------------------------------------------------- */ /* [A Z] = mread (filename, prefer_binary) * * Read a sparse or dense matrix from a file in Matrix Market format. * * All MatrixMarket formats are supported. * The Matrix Market "integer" format is converted into real, but the values * are preserved. The "pattern" format is converted into real. If a pattern * matrix is unsymmetric, all of its values are equal to one. If a pattern is * symmetric, the kth diagonal entry is set to one plus the number of * off-diagonal nonzeros in row/column k, and off-diagonal entries are set to * -1. * * Explicit zero entries are returned as the binary pattern of the matrix Z. */ #include "cholmod_matlab.h" /* maximum file length */ #define MAXLEN 1030 void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { void *G ; cholmod_dense *X = NULL ; cholmod_sparse *A = NULL, *Z = NULL ; cholmod_common Common, *cm ; Int *Ap = NULL, *Ai ; double *Ax, *Az = NULL ; char filename [MAXLEN] ; Int nz, k, is_complex = FALSE, nrow = 0, ncol = 0, allzero ; int mtype ; /* ---------------------------------------------------------------------- */ /* start CHOLMOD and set parameters */ /* ---------------------------------------------------------------------- */ cm = &Common ; cholmod_l_start (cm) ; sputil_config (SPUMONI, cm) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if (nargin > 2 || nargout > 2) { mexErrMsgTxt ("usage: [A Z] = mread (filename, prefer_binary)") ; } if (!mxIsChar (pargin [0])) { mexErrMsgTxt ("mread requires a filename") ; } mxGetString (pargin [0], filename, MAXLEN) ; sputil_file = fopen (filename, "r") ; if (sputil_file == NULL) { mexErrMsgTxt ("cannot open file") ; } if (nargin > 1) { cm->prefer_binary = (mxGetScalar (pargin [1]) != 0) ; } /* ---------------------------------------------------------------------- */ /* read the matrix, as either a dense or sparse matrix */ /* ---------------------------------------------------------------------- */ G = cholmod_l_read_matrix (sputil_file, 1, &mtype, cm) ; fclose (sputil_file) ; sputil_file = NULL ; if (G == NULL) { mexErrMsgTxt ("could not read file") ; } /* get the specific matrix (A or X), and change to ZOMPLEX if needed */ if (mtype == CHOLMOD_SPARSE) { A = (cholmod_sparse *) G ; nrow = A->nrow ; ncol = A->ncol ; is_complex = (A->xtype == CHOLMOD_COMPLEX) ; Ap = A->p ; Ai = A->i ; if (is_complex) { /* if complex, ensure A is ZOMPLEX */ cholmod_l_sparse_xtype (CHOLMOD_ZOMPLEX, A, cm) ; } Ax = A->x ; Az = A->z ; } else if (mtype == CHOLMOD_DENSE) { X = (cholmod_dense *) G ; nrow = X->nrow ; ncol = X->ncol ; is_complex = (X->xtype == CHOLMOD_COMPLEX) ; if (is_complex) { /* if complex, ensure X is ZOMPLEX */ cholmod_l_dense_xtype (CHOLMOD_ZOMPLEX, X, cm) ; } Ax = X->x ; Az = X->z ; } else { mexErrMsgTxt ("invalid file") ; } /* ---------------------------------------------------------------------- */ /* if requested, extract the zero entries and place them in Z */ /* ---------------------------------------------------------------------- */ if (nargout > 1) { if (mtype == CHOLMOD_SPARSE) { /* A is a sparse real/zomplex double matrix */ Z = sputil_extract_zeros (A, cm) ; } else { /* input is full; just return an empty Z matrix */ Z = cholmod_l_spzeros (nrow, ncol, 0, CHOLMOD_REAL, cm) ; } } /* ---------------------------------------------------------------------- */ /* prune the zero entries from A and set nzmax(A) to nnz(A) */ /* ---------------------------------------------------------------------- */ if (mtype == CHOLMOD_SPARSE) { sputil_drop_zeros (A) ; cholmod_l_reallocate_sparse (cholmod_l_nnz (A, cm), A, cm) ; } /* ---------------------------------------------------------------------- */ /* change a complex matrix to real if its imaginary part is all zero */ /* ---------------------------------------------------------------------- */ if (is_complex) { if (mtype == CHOLMOD_SPARSE) { nz = Ap [ncol] ; } else { nz = nrow * ncol ; } allzero = TRUE ; for (k = 0 ; k < nz ; k++) { if (Az [k] != 0) { allzero = FALSE ; break ; } } if (allzero) { /* discard the all-zero imaginary part */ if (mtype == CHOLMOD_SPARSE) { cholmod_l_sparse_xtype (CHOLMOD_REAL, A, cm) ; } else { cholmod_l_dense_xtype (CHOLMOD_REAL, X, cm) ; } } } /* ---------------------------------------------------------------------- */ /* return results to MATLAB */ /* ---------------------------------------------------------------------- */ if (mtype == CHOLMOD_SPARSE) { pargout [0] = sputil_put_sparse (&A, cm) ; } else { pargout [0] = sputil_put_dense (&X, cm) ; } if (nargout > 1) { pargout [1] = sputil_put_sparse (&Z, cm) ; } /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ cholmod_l_finish (cm) ; cholmod_l_print_common (" ", cm) ; } SuiteSparse/CHOLMOD/MATLAB/mread.m0000644001170100242450000000170610711661246015252 0ustar davisfacfunction [A, Z] = mread (filename,prefer_binary) %#ok %MREAD read a sparse matrix from a file in Matrix Market format. % % Example: % A = mread (filename) % [A Z] = mread (filename, prefer_binary) % % Unlike MMREAD, only the matrix is returned; the file format is not % returned. Explicit zero entries can be present in the file; these are not % included in A. They appear as the nonzero pattern of the binary matrix Z. % % If prefer_binary is not present, or zero, a symmetric pattern-only matrix % is returned with A(i,i) = 1+length(find(A(:,i))) if it is present in the % pattern, and A(i,j) = -1 for off-diagonal entries. If you want the original % Matrix Market matrix in this case, simply use A = mread (filename,1). % % Compare with mmread.m at http://math.nist.gov/MatrixMarket % % See also load % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse error ('mread mexFunction not found') ; SuiteSparse/CHOLMOD/MATLAB/cholmod_make.m0000644001170100242450000002446710712370265016614 0ustar davisfacfunction cholmod_make (metis_path) %CHOLMOD_MAKE compiles the CHOLMOD mexFunctions % % Example: % cholmod_make % % CHOLMOD relies on AMD and COLAMD, and optionally CCOLAMD, CAMD, and METIS. % All but METIS are distributed with CHOLMOD. To compile CHOLMOD to use METIS % you must first place a copy of the metis-4.0 directory (METIS version 4.0.1) % in same directory that contains the AMD, COLAMD, CCOLAMD, and CHOLMOD % directories. Next, type % % cholmod_make % % in the MATLAB command window. Alternatively, use this command: % % cholmod_make ('path to your copy of metis-4.0 here') ; % % See http://www-users.cs.umn.edu/~karypis/metis for a copy of % METIS 4.0.1. If you do not have METIS, use either of the following: % % cholmod_make ('') % cholmod_make ('no metis') % % You must type the cholmod_make command while in the CHOLMOD/MATLAB directory. % % See also analyze, bisect, chol2, cholmod2, etree2, lchol, ldlchol, ldlsolve, % ldlupdate, metis, spsym, nesdis, septree, resymbol, sdmult, sparse2, % symbfact2, mread, mwrite % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse details = 0 ; % 1 if details of each command are to be printed v = getversion ; try % ispc does not appear in MATLAB 5.3 pc = ispc ; catch % if ispc fails, assume we are on a Windows PC if it's not unix pc = ~isunix ; end d = '' ; if (~isempty (strfind (computer, '64'))) % 64-bit MATLAB d = '-largeArrayDims' ; end include = '-I. -I../../AMD/Include -I../../COLAMD/Include -I../../CCOLAMD/Include -I../../CAMD/Include -I../Include -I../../UFconfig' ; if (v < 7.0) % do not attempt to compile CHOLMOD with large file support include = [include ' -DNLARGEFILE'] ; elseif (~pc) % Linux/Unix require these flags for large file support include = [include ' -D_FILE_OFFSET_BITS=64 -D_LARGEFILE64_SOURCE'] ; end if (v < 6.5) % logical class does not exist in MATLAB 6.1 or earlie include = [include ' -DMATLAB6p1_OR_EARLIER'] ; end % Determine the METIS path, and whether or not METIS is available if (nargin == 0) metis_path = '../../metis-4.0' ; end if (strcmp (metis_path, 'no metis')) metis_path = '' ; end have_metis = (~isempty (metis_path)) ; % fix the METIS 4.0.1 rename.h file if (have_metis) fprintf ('Compiling CHOLMOD with METIS on MATLAB Version %g\n', v) ; f = fopen ('rename.h', 'w') ; if (f == -1) error ('unable to create rename.h in current directory') ; end fprintf (f, '/* do not edit this file; generated by cholmod_make */\n') ; fprintf (f, '#undef log2\n') ; fprintf (f, '#include "%s/Lib/rename.h"\n', metis_path) ; fprintf (f, '#undef log2\n') ; fprintf (f, '#define log2 METIS__log2\n') ; fprintf (f, '#include "mex.h"\n') ; fprintf (f, '#define malloc mxMalloc\n') ; fprintf (f, '#define free mxFree\n') ; fprintf (f, '#define calloc mxCalloc\n') ; fprintf (f, '#define realloc mxRealloc\n') ; fclose (f) ; include = [include ' -I' metis_path '/Lib'] ; else fprintf ('Compiling CHOLMOD without METIS on MATLAB Version %g\n', v) ; include = ['-DNPARTITION ' include] ; end %------------------------------------------------------------------------------- % BLAS option %------------------------------------------------------------------------------- % This is exceedingly ugly. The MATLAB mex command needs to be told where to % fine the LAPACK and BLAS libraries, which is a real portability nightmare. if (pc) if (v < 6.5) % MATLAB 6.1 and earlier: use the version supplied here lapack = 'lcc_lib/libmwlapack.lib' ; elseif (v < 7.5) lapack = 'libmwlapack.lib' ; else lapack = 'libmwlapack.lib libmwblas.lib' ; end else if (v < 7.5) lapack = '-lmwlapack' ; else lapack = '-lmwlapack -lmwblas' ; end end %------------------------------------------------------------------------------- include = strrep (include, '/', filesep) ; amd_src = { ... '../../AMD/Source/amd_1', ... '../../AMD/Source/amd_2', ... '../../AMD/Source/amd_aat', ... '../../AMD/Source/amd_control', ... '../../AMD/Source/amd_defaults', ... '../../AMD/Source/amd_dump', ... '../../AMD/Source/amd_global', ... '../../AMD/Source/amd_info', ... '../../AMD/Source/amd_order', ... '../../AMD/Source/amd_postorder', ... '../../AMD/Source/amd_post_tree', ... '../../AMD/Source/amd_preprocess', ... '../../AMD/Source/amd_valid' } ; camd_src = { ... '../../CAMD/Source/camd_1', ... '../../CAMD/Source/camd_2', ... '../../CAMD/Source/camd_aat', ... '../../CAMD/Source/camd_control', ... '../../CAMD/Source/camd_defaults', ... '../../CAMD/Source/camd_dump', ... '../../CAMD/Source/camd_global', ... '../../CAMD/Source/camd_info', ... '../../CAMD/Source/camd_order', ... '../../CAMD/Source/camd_postorder', ... '../../CAMD/Source/camd_preprocess', ... '../../CAMD/Source/camd_valid' } ; colamd_src = { '../../COLAMD/Source/colamd', ... '../../COLAMD/Source/colamd_global' } ; ccolamd_src = { '../../CCOLAMD/Source/ccolamd', ... '../../CCOLAMD/Source/ccolamd_global' } ; metis_src = { 'Lib/balance', ... 'Lib/bucketsort', ... 'Lib/ccgraph', ... 'Lib/coarsen', ... 'Lib/compress', ... 'Lib/debug', ... 'Lib/estmem', ... 'Lib/fm', ... 'Lib/fortran', ... 'Lib/frename', ... 'Lib/graph', ... 'Lib/initpart', ... 'Lib/kmetis', ... 'Lib/kvmetis', ... 'Lib/kwayfm', ... 'Lib/kwayrefine', ... 'Lib/kwayvolfm', ... 'Lib/kwayvolrefine', ... 'Lib/match', ... 'Lib/mbalance2', ... 'Lib/mbalance', ... 'Lib/mcoarsen', ... 'Lib/memory', ... 'Lib/mesh', ... 'Lib/meshpart', ... 'Lib/mfm2', ... 'Lib/mfm', ... 'Lib/mincover', ... 'Lib/minitpart2', ... 'Lib/minitpart', ... 'Lib/mkmetis', ... 'Lib/mkwayfmh', ... 'Lib/mkwayrefine', ... 'Lib/mmatch', ... 'Lib/mmd', ... 'Lib/mpmetis', ... 'Lib/mrefine2', ... 'Lib/mrefine', ... 'Lib/mutil', ... 'Lib/myqsort', ... 'Lib/ometis', ... 'Lib/parmetis', ... 'Lib/pmetis', ... 'Lib/pqueue', ... 'Lib/refine', ... 'Lib/separator', ... 'Lib/sfm', ... 'Lib/srefine', ... 'Lib/stat', ... 'Lib/subdomains', ... 'Lib/timing', ... 'Lib/util' } ; for i = 1:length (metis_src) metis_src {i} = [metis_path '/' metis_src{i}] ; end cholmod_matlab = { 'cholmod_matlab' } ; cholmod_src = { '../Core/cholmod_aat', ... '../Core/cholmod_add', ... '../Core/cholmod_band', ... '../Core/cholmod_change_factor', ... '../Core/cholmod_common', ... '../Core/cholmod_complex', ... '../Core/cholmod_copy', ... '../Core/cholmod_dense', ... '../Core/cholmod_error', ... '../Core/cholmod_factor', ... '../Core/cholmod_memory', ... '../Core/cholmod_sparse', ... '../Core/cholmod_transpose', ... '../Core/cholmod_triplet', ... '../Check/cholmod_check', ... '../Check/cholmod_read', ... '../Check/cholmod_write', ... '../Cholesky/cholmod_amd', ... '../Cholesky/cholmod_analyze', ... '../Cholesky/cholmod_colamd', ... '../Cholesky/cholmod_etree', ... '../Cholesky/cholmod_factorize', ... '../Cholesky/cholmod_postorder', ... '../Cholesky/cholmod_rcond', ... '../Cholesky/cholmod_resymbol', ... '../Cholesky/cholmod_rowcolcounts', ... '../Cholesky/cholmod_rowfac', ... '../Cholesky/cholmod_solve', ... '../Cholesky/cholmod_spsolve', ... '../MatrixOps/cholmod_drop', ... '../MatrixOps/cholmod_horzcat', ... '../MatrixOps/cholmod_norm', ... '../MatrixOps/cholmod_scale', ... '../MatrixOps/cholmod_sdmult', ... '../MatrixOps/cholmod_ssmult', ... '../MatrixOps/cholmod_submatrix', ... '../MatrixOps/cholmod_vertcat', ... '../MatrixOps/cholmod_symmetry', ... '../Modify/cholmod_rowadd', ... '../Modify/cholmod_rowdel', ... '../Modify/cholmod_updown', ... '../Supernodal/cholmod_super_numeric', ... '../Supernodal/cholmod_super_solve', ... '../Supernodal/cholmod_super_symbolic', ... '../Partition/cholmod_ccolamd', ... '../Partition/cholmod_csymamd', ... '../Partition/cholmod_camd', ... '../Partition/cholmod_metis', ... '../Partition/cholmod_nesdis' } ; cholmod_mex_src = { ... 'analyze', ... 'bisect', ... 'chol2', ... 'cholmod2', ... 'etree2', ... 'lchol', ... 'ldlchol', ... 'ldlsolve', ... 'ldlupdate', ... 'metis', ... 'spsym', ... 'nesdis', ... 'septree', ... 'resymbol', ... 'sdmult', ... 'sparse2', ... 'symbfact2', ... 'mread', ... 'mwrite' } ; if (pc) % Windows does not have drand48 and srand48, required by METIS. Use % drand48 and srand48 in CHOLMOD/MATLAB/Windows/rand48.c instead. obj_extension = '.obj' ; cholmod_matlab = [cholmod_matlab {'Windows/rand48'}] ; include = [include ' -IWindows'] ; else obj_extension = '.o' ; end % compile each library source file obj = '' ; source = [amd_src colamd_src ccolamd_src camd_src cholmod_src cholmod_matlab] ; if (have_metis) source = [metis_src source] ; end kk = 0 ; for f = source ff = strrep (f {1}, '/', filesep) ; slash = strfind (ff, filesep) ; if (isempty (slash)) slash = 1 ; else slash = slash (end) + 1 ; end o = ff (slash:end) ; obj = [obj ' ' o obj_extension] ; %#ok s = sprintf ('mex %s -DDLONG -O %s -c %s.c', d, include, ff) ; kk = do_cmd (s, kk, details) ; end % compile each mexFunction for f = cholmod_mex_src s = sprintf ('mex %s -DDLONG -O %s %s.c', d, include, f{1}) ; s = [s obj ' ' lapack] ; %#ok kk = do_cmd (s, kk, details) ; end % clean up s = ['delete ' obj] ; do_cmd (s, kk, details) ; fprintf ('\nCHOLMOD successfully compiled\n') ; %------------------------------------------------------------------------------- function kk = do_cmd (s, kk, details) %DO_CMD: evaluate a command, and either print it or print a "." if (details) fprintf ('%s\n', s) ; else if (mod (kk, 60) == 0) fprintf ('\n') ; end kk = kk + 1 ; fprintf ('.') ; end eval (s) ; %------------------------------------------------------------------------------- function v = getversion % determine the MATLAB version, and return it as a double. v = sscanf (version, '%d.%d.%d') ; v = 10.^(0:-1:-(length(v)-1)) * v ; SuiteSparse/CHOLMOD/MATLAB/sdmult.c0000644001170100242450000000672310634230157015461 0ustar davisfac/* ========================================================================== */ /* === CHOLMOD/MATLAB/sdmult mexFunction ==================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * MATLAB(tm) is a Trademark of The MathWorks, Inc. * -------------------------------------------------------------------------- */ /* Compute C = S*F or S'*F where S is sparse and F is full (C is also sparse). * S and F must both be real or both be complex. * * Usage: * * C = sdmult (S,F) ; C = S*F * C = sdmult (S,F,0) ; C = S*F * C = sdmult (S,F,1) ; C = S'*F */ #include "cholmod_matlab.h" void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double dummy = 0, one [2] = {1,0}, zero [2] = {0,0} ; cholmod_sparse *S, Smatrix ; cholmod_dense *F, Fmatrix, *C ; cholmod_common Common, *cm ; Int srow, scol, frow, fcol, crow, transpose ; /* ---------------------------------------------------------------------- */ /* start CHOLMOD and set parameters */ /* ---------------------------------------------------------------------- */ cm = &Common ; cholmod_l_start (cm) ; sputil_config (SPUMONI, cm) ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ if (nargout > 1 || nargin < 2 || nargin > 3) { mexErrMsgTxt ("Usage: C = sdmult (S,F,transpose)") ; } srow = mxGetM (pargin [0]) ; scol = mxGetN (pargin [0]) ; frow = mxGetM (pargin [1]) ; fcol = mxGetN (pargin [1]) ; transpose = !((nargin == 2) || (mxGetScalar (pargin [2]) == 0)) ; if (frow != (transpose ? srow : scol)) { mexErrMsgTxt ("invalid inner dimensions") ; } if (!mxIsSparse (pargin [0]) || mxIsSparse (pargin [1])) { mexErrMsgTxt ("sdmult (S,F): S must be sparse, F must be full") ; } /* ---------------------------------------------------------------------- */ /* get S and F */ /* ---------------------------------------------------------------------- */ S = sputil_get_sparse (pargin [0], &Smatrix, &dummy, 0) ; F = sputil_get_dense (pargin [1], &Fmatrix, &dummy) ; /* ---------------------------------------------------------------------- */ /* C = S*F or S'*F */ /* ---------------------------------------------------------------------- */ crow = transpose ? scol : srow ; C = cholmod_l_allocate_dense (crow, fcol, crow, F->xtype, cm) ; cholmod_l_sdmult (S, transpose, one, zero, F, C, cm) ; pargout [0] = sputil_put_dense (&C, cm) ; /* ---------------------------------------------------------------------- */ /* free workspace and the CHOLMOD L, except for what is copied to MATLAB */ /* ---------------------------------------------------------------------- */ cholmod_l_finish (cm) ; cholmod_l_print_common (" ", cm) ; /* if (cm->malloc_count != (mxIsComplex (pargout [0]) + 1)) mexErrMsgTxt ("!"); */ } SuiteSparse/CHOLMOD/MATLAB/sdmult.m0000644001170100242450000000115110620371034015454 0ustar davisfacfunction C = sdmult (S,F,transpose) %#ok %SDMULT sparse matrix times dense matrix % Compute C = S*F or S'*F where S is sparse and F is full (C is also sparse). % S and F must both be real or both be complex. This function is % substantially faster than the MATLAB expression C=S*F when F has many % columns. % % Example: % C = sdmult (S,F) ; C = S*F % C = sdmult (S,F,0) ; C = S*F % C = sdmult (S,F,1) ; C = S'*F % % See also MTIMES % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse error ('sdmult mexFunction not found') ; SuiteSparse/CHOLMOD/MATLAB/README.txt0000644001170100242450000000614610533335376015511 0ustar davisfac----------------------- Using CHOLMOD in MATLAB ----------------------- See Contents.m for a description of each CHOLMOD function. To compile CHOLMOD for use in MATLAB, you may optionally use METIS. If you do not use METIS, compile CHOLMOD with the -DNPARTITION flag. There are two ways of compiling the CHOLMOD mexFunctions. The 2nd one is best. (1) Using the Unix "make" command. This will compile the AMD, COLAMD, CCOLAMD, and CHOLMOD libraries (*.a). You must first add -fexceptions to the CFLAGS definition in UFconfig/UFconfig.mk first (for Linux). Otherwise, MATLAB will not be able to handle exceptions properly (CHOLMOD may terminate MATLAB if it encounters an error). The METIS library must also be compiled with -fexceptions (see metis-4.0/Makefile.in). For other operating systems, see your default MATLAB mexopts.sh file (type "mex -v"). Next, simply type "make" in the operating system command window in this directory. On Linux (with gcc), you must compile all codes with the -fexceptions flag. See option (2) if you have problems compiling METIS. (2) using the "cholmod_make" m-file in MATLAB. First, place a copy of METIS 4.0.1 in the ../../metis-4.0 directory (the same directory that contains AMD, COLAMD, CCOLAMD, and CHOLMOD). Then, type "cholmod_make" in the MATLAB command window. All source files (including METIS) will be compiled with the MATLAB mex commnand. This works on all operating systems, including Windows. You can use an alternate location for METIS, if you pass the pathname as the first argument to cholmod_make, as in cholmod_make ('path to your copy of metis-4.0 goes here') ; Option (2) is better because it allows for several workarounds for METIS. With Option (1), METIS terminates MATLAB if it runs out of memory. That does not happen with Option (2). You should also add CHOLMOD/MATLAB to your MATLAB path. cholmod_demo is a short demo program for CHOLMOD. Type "cholmod_demo" in your MATLAB command window to test your newly compiling CHOLMOD functions. Test/cholmod_test.m runs the test suite for the MATLAB interface to CHOLMOD. It requires the "UFget" interface to the UF sparse matrix collection, but provides a more extensive test for CHOLMOD. To obtain a copy of UFget, see http://www.cise.ufl.edu/research/sparse . ---------------------------------------- Using AMD, CCOLAMD, and COLAMD in MATLAB ---------------------------------------- The following steps are not required to use CHOLMOD in MATLAB. To use AMD in MATLAB, go to the AMD/MATLAB directory and either type "amd_make" in the MATLAB command window, or type "make" in the Unix shell. Add AMD/MATLAB to your MATLAB path. To use CCOLAMD in MATLAB, go to the CCOLAMD directory and either type "ccolamd_demo" in the MATLAB command window, or type "make" in the Unix shell. Add CCOLAMD to your MATLAB path. COLAMD is already an integral part of MATLAB, but you can upgrade to the most recent version. Go to the COLAMD directory and either type "colamd_demo" in the MATLAB command window, or type "make" in the Unix shell. Add COLAMD to your MATLAB path. SuiteSparse/CHOLMOD/MATLAB/gpl.txt0000644001170100242450000004313310253404115015316 0ustar davisfac GNU GENERAL PUBLIC LICENSE Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users. This General Public License applies to most of the Free Software Foundation's software and to any other program whose authors commit to using it. (Some other Free Software Foundation software is covered by the GNU Library General Public License instead.) You can apply it to your programs, too. 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SuiteSparse/CHOLMOD/MATLAB/nesdis.c0000644001170100242450000001577110665074061015445 0ustar davisfac/* ========================================================================== */ /* === CHOLMOD/MATLAB/nesdis mexFunction ==================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * MATLAB(tm) is a Trademark of The MathWorks, Inc. * METIS (Copyright 1998, G. Karypis) is not distributed with CHOLMOD. * -------------------------------------------------------------------------- */ /* CHOLMOD's nested dissection, based on METIS_NodeComputerSeparator, CAMD, and * CCOLAMD. * * Usage: * * [p, cp, cmember] = nesdis (A) orders A, using tril(A) * [p, cp, cmember] = nesdis (A,'sym') orders A, using tril(A) * [p, cp, cmember] = nesdis (A,'row') orders A*A' * [p, cp, cmember] = nesdis (A,'col') orders A'*A * * Nested dissection ordering. Returns a permutation p such that the Cholesky * factorization of A(p,p), A(p,:)*A(p,:)', or A(:,p)'*A(:,p) is sparser than * the unpermuted system. 'mode' defaults to 'sym'. * * An optional 3rd input argument: * * nesdis (A,mode,opts) * * specifies control parameters. opts(1) is the smallest subgraph that should * not be partitioned (default is 200), opts(2) is 1 if connected components are * to be split independently (default is 0). opts(3) controls when a separator * is kept; it is kept if nsep < opts(3)*n, where nsep is the number of nodes in * the separator and n is the number of nodes in the graph being cut (default is * 1). * * opts(4) is 0 if the smallest subgraphs are not to be ordered. For the 'sym' * case, or if mode is not present: 1 if to be ordered by CAMD, or 2 if to be * ordered with CSYMAMD (default is 1). For the other cases: 0 for natural * ordering, 1 if to be ordered by CCOLAMD. * * cp and cmember are optional. cmember(i)=c means that node i is in component * c, where c is in the range of 1 to the number of components. length(cp) is * the number of components found. cp is the separator tree; cp(c) is the * parent of component c, or 0 if c is a root. There can be anywhere from * 1 to n components, where n is the number of rows of A, A*A', or A'*A. * * Requires METIS and the CHOLMOD Partition Module. */ #include "cholmod_matlab.h" void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { #ifndef NPARTITION double dummy = 0 ; Int *Perm, *Cmember, *CParent ; cholmod_sparse *A, Amatrix, *C, *S ; cholmod_common Common, *cm ; Int n, transpose, c, ncomp ; char buf [LEN] ; /* ---------------------------------------------------------------------- */ /* start CHOLMOD and set defaults */ /* ---------------------------------------------------------------------- */ cm = &Common ; cholmod_l_start (cm) ; sputil_config (SPUMONI, cm) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if (nargout > 3 || nargin < 1 || nargin > 3) { mexErrMsgTxt ("Usage: [p cp cmember] = nesdis (A, mode, opts)") ; } if (nargin > 2) { double *x = mxGetPr (pargin [2]) ; n = mxGetNumberOfElements (pargin [2]) ; if (n > 0) cm->method [0].nd_small = x [0] ; if (n > 1) cm->method [0].nd_components = x [1] ; if (n > 2) cm->method [0].nd_oksep = x [2] ; if (n > 3) cm->method [0].nd_camd = x [3] ; } /* ---------------------------------------------------------------------- */ /* get input matrix A */ /* ---------------------------------------------------------------------- */ A = sputil_get_sparse_pattern (pargin [0], &Amatrix, &dummy, cm) ; S = (A == &Amatrix) ? NULL : A ; /* ---------------------------------------------------------------------- */ /* get A->stype, default is to use tril(A) */ /* ---------------------------------------------------------------------- */ A->stype = -1 ; transpose = FALSE ; if (nargin > 1) { buf [0] = '\0' ; if (mxIsChar (pargin [1])) { mxGetString (pargin [1], buf, LEN) ; } c = buf [0] ; if (tolower (c) == 'r') { /* unsymmetric case (A*A') if string starts with 'r' */ transpose = FALSE ; A->stype = 0 ; } else if (tolower (c) == 'c') { /* unsymmetric case (A'*A) if string starts with 'c' */ transpose = TRUE ; A->stype = 0 ; } else if (tolower (c) == 's') { /* symmetric case (A) if string starts with 's' */ transpose = FALSE ; A->stype = -1 ; } else { mexErrMsgTxt ("nesdis: unrecognized mode") ; } } if (A->stype && A->nrow != A->ncol) { mexErrMsgTxt ("nesdis: A must be square") ; } C = NULL ; if (transpose) { /* C = A', and then order C*C' with cholmod_l_nested_dissection */ C = cholmod_l_transpose (A, 0, cm) ; if (C == NULL) { mexErrMsgTxt ("nesdis failed") ; } A = C ; } n = A->nrow ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ CParent = cholmod_l_malloc (n, sizeof (Int), cm) ; Cmember = cholmod_l_malloc (n, sizeof (Int), cm) ; Perm = cholmod_l_malloc (n, sizeof (Int), cm) ; /* ---------------------------------------------------------------------- */ /* order the matrix with CHOLMOD's nested dissection */ /* ---------------------------------------------------------------------- */ ncomp = cholmod_l_nested_dissection (A, NULL, 0, Perm, CParent, Cmember,cm); if (ncomp < 0) { mexErrMsgTxt ("nesdis failed") ; return ; } /* ---------------------------------------------------------------------- */ /* return Perm, CParent, and Cmember */ /* ---------------------------------------------------------------------- */ pargout [0] = sputil_put_int (Perm, n, 1) ; if (nargout > 1) { pargout [1] = sputil_put_int (CParent, ncomp, 1) ; } if (nargout > 2) { pargout [2] = sputil_put_int (Cmember, n, 1) ; } /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ cholmod_l_free (n, sizeof (Int), Perm, cm) ; cholmod_l_free (n, sizeof (Int), CParent, cm) ; cholmod_l_free (n, sizeof (Int), Cmember, cm) ; cholmod_l_free_sparse (&C, cm) ; cholmod_l_free_sparse (&S, cm) ; cholmod_l_finish (cm) ; cholmod_l_print_common (" ", cm) ; /* if (cm->malloc_count != 0) mexErrMsgTxt ("!") ; */ #else mexErrMsgTxt ("METIS and the CHOLMOD Partition Module not installed\n") ; #endif } SuiteSparse/CHOLMOD/MATLAB/nesdis.m0000644001170100242450000000537210711661262015450 0ustar davisfacfunction [p, cparent, cmember] = nesdis (A, mode, opts) %#ok %NESDIS nested dissection ordering via CHOLMOD's nested dissection. % % Example: % p = nesdis(A) returns p such chol(A(p,p)) is typically sparser than % chol(A). Uses tril(A) and assumes A is symmetric. % p = nesdis(A,'sym') the same as p=nesdis(A). % p = nesdis(A,'col') returns p so that chol(A(:,p)'*A(:,p)) is typically % sparser than chol(A'*A). % p = nesdis(A,'row') returns p so that chol(A(p,:)*A(p,:)') is typically % sparser than chol(A'*A). % % A must be square for p=nesdis(A) or nesdis(A,'sym'). % % With three output arguments, [p cp cmember] = nesdis(...), the separator % tree and node-to-component mapping is returned. cmember(i)=c means that % node i is in component c, where c is in the range of 1 to the number of % components. length(cp) is the number of components found. cp is the % separator tree; cp(c) is the parent of component c, or 0 if c is a root. % There can be anywhere from 1 to n components, where n is dimension of A, % A*A', or A'*A. cmember is a vector of length n. % % An optional 3rd input argument, nesdis (A,mode,opts), modifies the default % parameters. opts(1) specifies the smallest subgraph that should not be % partitioned (default is 200). opts(2) is 0 by default; if nonzero, % connected components (formed after the node separator is removed) are % partitioned independently. The default value tends to lead to a more % balanced separator tree, cp. opts(3) defines when a separator is kept; it % is kept if the separator size is < opts(3) times the number of nodes in the % graph being cut (valid range is 0 to 1, default is 1). % % opts(4) specifies graph is to be ordered after it is dissected. For the % 'sym' case: 0: natural ordering, 1: CAMD, 2: CSYMAMD. For other cases: % 0: natural ordering, nonzero: CCOLAMD. The default is 1, to use CAMD for % the symmetric case and CCOLAMD for the other cases. % % If opts is shorter than length 4, defaults are used for entries % that are not present. % % NESDIS uses METIS' node separator algorithm to recursively partition the % graph. This gives a set of constraints (cmember) that is then passed to % CCOLAMD, CSYMAMD, or CAMD, constrained minimum degree ordering algorithms. % NESDIS typically takes slightly more time than METIS (METIS_NodeND), but % tends to produce better orderings. % % Requires METIS, authored by George Karypis, Univ. of Minnesota. This % MATLAB interface, via CHOLMOD, is by Tim Davis. % % See also METIS, BISECT, AMD % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse error ('nesdis mexFunction not found') ; SuiteSparse/CHOLMOD/MATLAB/mwrite.c0000644001170100242450000001264710621027740015460 0ustar davisfac/* ========================================================================== */ /* === CHOLMOD/MATLAB/mwrite mexFunction ==================================== */ /* ========================================================================== */ /* Write a matrix to a file in Matrix Market form. * * symmetry = mwrite (filename, A, Z, comments_filename) * * A can be sparse or full. * * If present and non-empty, A and Z must have the same dimension. Z contains * the explicit zero entries in the matrix (which MATLAB drops). The entries * of Z appear as explicit zeros in the output file. Z is optional. If it is * an empty matrix it is ignored. Z must be sparse or empty, if present. * It is ignored if A is full. * * filename is the name of the output file. comments_file is file whose * contents are include after the Matrix Market header and before the first * data line. Ignored if an empty string or not present. */ #include "cholmod_matlab.h" #define MAXLEN 1030 /* -------------------------------------------------------------------------- */ /* mwrite mexFunction */ /* -------------------------------------------------------------------------- */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double dummy = 0 ; cholmod_sparse Amatrix, Zmatrix, *A, *Z ; cholmod_dense Xmatrix, *X ; cholmod_common Common, *cm ; Int arg_z, arg_comments, sym ; char filename [MAXLEN], comments [MAXLEN] ; /* ---------------------------------------------------------------------- */ /* start CHOLMOD and set parameters */ /* ---------------------------------------------------------------------- */ cm = &Common ; cholmod_l_start (cm) ; sputil_config (SPUMONI, cm) ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ if (nargin < 2 || nargin > 4 || nargout > 1) { mexErrMsgTxt ("Usage: mwrite (filename, A, Z, comments_filename)") ; } /* ---------------------------------------------------------------------- */ /* get the output filename */ /* ---------------------------------------------------------------------- */ if (!mxIsChar (pargin [0])) { mexErrMsgTxt ("first parameter must be a filename") ; } mxGetString (pargin [0], filename, MAXLEN) ; /* ---------------------------------------------------------------------- */ /* get the A matrix (sparse or dense) */ /* ---------------------------------------------------------------------- */ if (mxIsSparse (pargin [1])) { A = sputil_get_sparse (pargin [1], &Amatrix, &dummy, 0) ; X = NULL ; } else { X = sputil_get_dense (pargin [1], &Xmatrix, &dummy) ; A = NULL ; } /* ---------------------------------------------------------------------- */ /* determine if the Z matrix and comments_file are present */ /* ---------------------------------------------------------------------- */ if (nargin == 3) { if (mxIsChar (pargin [2])) { /* mwrite (file, A, comments) */ arg_z = -1 ; arg_comments = 2 ; } else { /* mwrite (file, A, Z). Ignore Z if A is full */ arg_z = (A == NULL) ? -1 : 2 ; arg_comments = -1 ; } } else if (nargin == 4) { /* mwrite (file, A, Z, comments). Ignore Z is A is full */ arg_z = (A == NULL) ? -1 : 2 ; arg_comments = 3 ; } else { arg_z = -1 ; arg_comments = -1 ; } /* ---------------------------------------------------------------------- */ /* get the Z matrix */ /* ---------------------------------------------------------------------- */ if (arg_z == -1 || mxGetM (pargin [arg_z]) == 0 || mxGetN (pargin [arg_z]) == 0) { /* A is dense, Z is not present, or Z is empty. Ignore Z. */ Z = NULL ; } else { /* A is sparse and Z is present and not empty */ if (!mxIsSparse (pargin [arg_z])) { mexErrMsgTxt ("Z must be sparse") ; } Z = sputil_get_sparse (pargin [arg_z], &Zmatrix, &dummy, 0) ; } /* ---------------------------------------------------------------------- */ /* get the comments filename */ /* ---------------------------------------------------------------------- */ comments [0] = '\0' ; if (arg_comments != -1) { if (!mxIsChar (pargin [arg_comments])) { mexErrMsgTxt ("comments filename must be a string") ; } mxGetString (pargin [arg_comments], comments, MAXLEN) ; } /* ---------------------------------------------------------------------- */ /* write the matrix to the file */ /* ---------------------------------------------------------------------- */ sputil_file = fopen (filename, "w") ; if (sputil_file == NULL) { mexErrMsgTxt ("error opening file") ; } if (A != NULL) { sym = cholmod_l_write_sparse (sputil_file, A, Z, comments, cm) ; } else { sym = cholmod_l_write_dense (sputil_file, X, comments, cm) ; } fclose (sputil_file) ; sputil_file = NULL ; if (sym < 0) { mexErrMsgTxt ("mwrite failed") ; } /* ---------------------------------------------------------------------- */ /* free workspace and return symmetry */ /* ---------------------------------------------------------------------- */ pargout [0] = sputil_put_int (&sym, 1, 0) ; cholmod_l_finish (cm) ; cholmod_l_print_common (" ", cm) ; } SuiteSparse/CHOLMOD/MATLAB/mwrite.m0000644001170100242450000000156510622674124015474 0ustar davisfacfunction mtype = mwrite (filename, A, Z, comments_filename) %#ok %MWRITE write a matrix to a file in Matrix Market form. % % Example: % mtype = mwrite (filename, A, Z, comments_filename) % % A can be sparse or full. % % If present and non-empty, A and Z must have the same dimension. Z contains % the explicit zero entries in the matrix (which MATLAB drops). The entries % of Z appear as explicit zeros in the output file. Z is optional. If it is % an empty matrix it is ignored. Z must be sparse or empty, if present. % It is ignored if A is full. % % filename is the name of the output file. comments_filename is the file % whose contents are include after the Matrix Market header and before the % first data line. Ignored if an empty string or not present. % % See also mread. % Copyright 2006-2007, Timothy A. Davis error ('mwrite mexFunction not found') ; SuiteSparse/CHOLMOD/MATLAB/analyze.c0000644001170100242450000001263210616446163015616 0ustar davisfac/* ========================================================================== */ /* === CHOLMOD/MATLAB/analyze mexFunction =================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * MATLAB(tm) is a Trademark of The MathWorks, Inc. * -------------------------------------------------------------------------- */ /* Order a matrix and then analyze it, using CHOLMOD's best-effort ordering. * Returns the count of the number of nonzeros in each column of L for the * permuted matrix A. * * Usage: * * [p count] = analyze (A) orders A, using just tril(A) * [p count] = analyze (A,'sym') orders A, using just tril(A) * [p count] = analyze (A,'row') orders A*A' * [p count] = analyze (A,'col') orders A'*A * * with an optional 3rd parameter: * * [p count] = analyze (A,'sym',k) orders A, using just tril(A) * [p count] = analyze (A,'row',k) orders A*A' * [p count] = analyze (A,'col',k) orders A'*A * * k=0 is the default. k != 0 selects the ordering strategy. * * See analyze.m for more details. */ #include "cholmod_matlab.h" void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double dummy = 0 ; cholmod_factor *L ; cholmod_sparse *A, Amatrix, *C, *S ; cholmod_common Common, *cm ; Int n, transpose, c ; char buf [LEN] ; /* ---------------------------------------------------------------------- */ /* start CHOLMOD and set defaults */ /* ---------------------------------------------------------------------- */ cm = &Common ; cholmod_l_start (cm) ; sputil_config (SPUMONI, cm) ; /* only do the simplicial analysis (L->Perm and L->ColCount) */ cm->supernodal = CHOLMOD_SIMPLICIAL ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if (nargout > 2 || nargin < 1 || nargin > 3) { mexErrMsgTxt ("Usage: [p count] = analyze (A, mode)") ; } if (nargin == 3) { cm->nmethods = mxGetScalar (pargin [2]) ; if (cm->nmethods == -1) { /* use AMD only */ cm->nmethods = 1 ; cm->method [0].ordering = CHOLMOD_AMD ; cm->postorder = TRUE ; } else if (cm->nmethods == -2) { /* use METIS only */ cm->nmethods = 1 ; cm->method [0].ordering = CHOLMOD_METIS ; cm->postorder = TRUE ; } else if (cm->nmethods == -3) { /* use NESDIS only */ cm->nmethods = 1 ; cm->method [0].ordering = CHOLMOD_NESDIS ; cm->postorder = TRUE ; } } /* ---------------------------------------------------------------------- */ /* get input matrix A */ /* ---------------------------------------------------------------------- */ A = sputil_get_sparse_pattern (pargin [0], &Amatrix, &dummy, cm) ; S = (A == &Amatrix) ? NULL : A ; /* ---------------------------------------------------------------------- */ /* get A->stype, default is to use tril(A) */ /* ---------------------------------------------------------------------- */ A->stype = -1 ; transpose = FALSE ; if (nargin > 1) { buf [0] = '\0' ; if (mxIsChar (pargin [1])) { mxGetString (pargin [1], buf, LEN) ; } c = buf [0] ; if (tolower (c) == 'r') { /* unsymmetric case (A*A') if string starts with 'r' */ transpose = FALSE ; A->stype = 0 ; } else if (tolower (c) == 'c') { /* unsymmetric case (A'*A) if string starts with 'c' */ transpose = TRUE ; A->stype = 0 ; } else if (tolower (c) == 's') { /* symmetric case (A) if string starts with 's' */ transpose = FALSE ; A->stype = -1 ; } else { mexErrMsgTxt ("analyze: unrecognized mode") ; } } if (A->stype && A->nrow != A->ncol) { mexErrMsgTxt ("analyze: A must be square") ; } C = NULL ; if (transpose) { /* C = A', and then order C*C' */ C = cholmod_l_transpose (A, 0, cm) ; if (C == NULL) { mexErrMsgTxt ("analyze failed") ; } A = C ; } n = A->nrow ; /* ---------------------------------------------------------------------- */ /* analyze and order the matrix */ /* ---------------------------------------------------------------------- */ L = cholmod_l_analyze (A, cm) ; /* ---------------------------------------------------------------------- */ /* return Perm */ /* ---------------------------------------------------------------------- */ pargout [0] = sputil_put_int (L->Perm, n, 1) ; if (nargout > 1) { pargout [1] = sputil_put_int (L->ColCount, n, 0) ; } /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ cholmod_l_free_factor (&L, cm) ; cholmod_l_free_sparse (&C, cm) ; cholmod_l_free_sparse (&S, cm) ; cholmod_l_finish (cm) ; cholmod_l_print_common (" ", cm) ; /* if (cm->malloc_count != 0) mexErrMsgTxt ("!") ; */ } SuiteSparse/CHOLMOD/MATLAB/analyze.m0000644001170100242450000000534110711661214015617 0ustar davisfacfunction [p, count] = analyze (A, mode, k) %#ok %ANALYZE order and analyze a matrix using CHOLMOD's best-effort ordering. % % Example: % [p count] = analyze (A) orders A, using just tril(A) % [p count] = analyze (A,'sym') orders A, using just tril(A) % [p count] = analyze (A,'row') orders A*A' % [p count] = analyze (A,'col') orders A'*A % % an optional 3rd parameter modifies the ordering strategy: % % [p count] = analyze (A,'sym',k) orders A, using just tril(A) % [p count] = analyze (A,'row',k) orders A*A' % [p count] = analyze (A,'col',k) orders A'*A % % Returns a permutation and the count of the number of nonzeros in each % column of L for the permuted matrix A. That is, count is returned as: % % count = symbfact2 (A (p,p)) if ordering A % count = symbfact2 (A (p,:),'row') if ordering A*A' % count = symbfact2 (A (:,p),'col') if ordering A'*A % % CHOLMOD uses the following ordering strategy: % % k = 0: Try AMD. If that ordering gives a flop count >= 500 * nnz(L) % and a fill-in of nnz(L) >= 5*nnz(C), then try METIS_NodeND (where % C = A, A*A', or A'*A is the matrix being ordered. Selects the best % ordering tried. This is the default. % % if k > 0, then multiple orderings are attempted. % % k = 1 or 2: just try AMD % k = 3: also try METIS_NodeND % k = 4: also try NESDIS, CHOLMOD's nested dissection (NESDIS), with % default parameters. Uses METIS's node bisector and CCOLAMD. % k = 5: also try the natural ordering (p = 1:n) % k = 6: also try NESDIS with large leaves of the separator tree % k = 7: also try NESDIS with tiny leaves and no CCOLAMD ordering % k = 8: also try NESDIS with no dense-node removal % k = 9: also try COLAMD if ordering A'*A or A*A', (AMD if ordering A). % k > 9 is treated as k = 9 % % k = -1: just use AMD % k = -2: just use METIS % k = -3: just use NESDIS % % The method returning the smallest nnz(L) is used for p and count. % k = 4 takes much longer than (say) k = 0, but it can reduce nnz(L) by % a typical 5% to 10%. k = 5 to 9 is getting extreme, but if you have % lots of time and want to find the best ordering possible, set k = 9. % % If METIS is not installed for use in CHOLMOD, then the strategy is % different: % % k = 1 to 4: just try AMD % k = 5 to 8: also try the natural ordering (p = 1:n) % k = 9: also try COLAMD if ordering A'*A or A*A', (AMD if ordering A). % k > 9 is treated as k = 9 % % See also METIS, NESDIS, BISECT, SYMBFACT, AMD % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse error ('analyze mexFunction not found') ; SuiteSparse/CHOLMOD/MATLAB/cholmod_matlab.c0000644001170100242450000015161410634324646017125 0ustar davisfac/* ========================================================================== */ /* === MATLAB/cholmod_matlab ================================================ */ /* ========================================================================== */ /* Utility routines for the CHOLMOD MATLAB mexFunctions. * * If CHOLMOD runs out of memory, MATLAB will terminate the mexFunction * immediately since it uses mxMalloc (see sputil_config, below). Likewise, * if mxCreate* or mxMalloc (as called in this file) fails, MATLAB will also * terminate the mexFunction. When this occurs, MATLAB frees all allocated * memory, so we don't have to worry about memory leaks. If this were not the * case, the routines in this file would suffer from memory leaks whenever an * error occurred. */ #include "cholmod_matlab.h" #ifndef INT64_T #define INT64_T long long #endif /* This file pointer is used for the mread and mwrite mexFunctions. It must * be a global variable, because the file pointer is not passed to the * sputil_error_handler function when an error occurs. */ FILE *sputil_file = NULL ; /* ========================================================================== */ /* === sputil_config ======================================================== */ /* ========================================================================== */ /* Define function pointers and other parameters for a mexFunction */ void sputil_config (Int spumoni, cholmod_common *cm) { /* cholmod_l_solve must return a real or zomplex X for MATLAB */ cm->prefer_zomplex = TRUE ; /* use mxMalloc and related memory management routines */ cm->malloc_memory = mxMalloc ; cm->free_memory = mxFree ; cm->realloc_memory = mxRealloc ; cm->calloc_memory = mxCalloc ; /* printing and error handling */ if (spumoni == 0) { /* do not print anything from within CHOLMOD */ cm->print = -1 ; cm->print_function = NULL ; } else { /* spumoni = 1: print warning and error messages. cholmod_l_print_* * routines will print a one-line summary of each object printed. * spumoni = 2: also print a short summary of each object. */ cm->print = spumoni + 2 ; cm->print_function = mexPrintf ; } /* error handler */ cm->error_handler = sputil_error_handler ; /* complex arithmetic */ cm->complex_divide = cholmod_l_divcomplex ; cm->hypotenuse = cholmod_l_hypot ; #ifndef NPARTITION #if defined(METIS_VERSION) #if (METIS_VERSION >= METIS_VER(4,0,2)) /* METIS 4.0.2 uses function pointers for malloc and free */ METIS_malloc = cm->malloc_memory ; METIS_free = cm->free_memory ; #endif #endif #endif /* Turn off METIS memory guard. It is not needed, because mxMalloc will * safely terminate the mexFunction and free any workspace without killing * all of MATLAB. This assumes cholmod_make was used to compile CHOLMOD * for MATLAB. */ cm->metis_memory = 0.0 ; } /* ========================================================================== */ /* === sputil_error_handler ================================================= */ /* ========================================================================== */ void sputil_error_handler (int status, char *file, int line, char *message) { if (status < CHOLMOD_OK) { /* mexPrintf ("ERROR: file %s line %d, status %d\n", file, line, status) ; */ if (sputil_file != NULL) { fclose (sputil_file) ; sputil_file = NULL ; } mexErrMsgTxt (message) ; } /* else { mexPrintf ("Warning: file %s line %d, status %d\n", file, line, status); } */ } /* ========================================================================== */ /* === sputil_get_sparse ==================================================== */ /* ========================================================================== */ /* Create a shallow CHOLMOD copy of a MATLAB sparse matrix. No memory is * allocated. The resulting matrix A must not be modified. */ cholmod_sparse *sputil_get_sparse ( const mxArray *Amatlab, /* MATLAB version of the matrix */ cholmod_sparse *A, /* CHOLMOD version of the matrix */ double *dummy, /* a pointer to a valid scalar double */ Int stype /* -1: lower, 0: unsymmetric, 1: upper */ ) { Int *Ap ; A->nrow = mxGetM (Amatlab) ; A->ncol = mxGetN (Amatlab) ; A->p = (Int *) mxGetJc (Amatlab) ; A->i = (Int *) mxGetIr (Amatlab) ; Ap = A->p ; A->nzmax = Ap [A->ncol] ; A->packed = TRUE ; A->sorted = TRUE ; A->nz = NULL ; A->itype = CHOLMOD_INT ; A->dtype = CHOLMOD_DOUBLE ; A->stype = stype ; #ifndef MATLAB6p1_OR_EARLIER if (mxIsLogical (Amatlab)) { A->x = NULL ; A->z = NULL ; A->xtype = CHOLMOD_PATTERN ; } else if (mxIsEmpty (Amatlab)) { /* this is not dereferenced, but the existence (non-NULL) of these * pointers is checked in CHOLMOD */ A->x = dummy ; A->z = dummy ; A->xtype = mxIsComplex (Amatlab) ? CHOLMOD_ZOMPLEX : CHOLMOD_REAL ; } else if (mxIsDouble (Amatlab)) { A->x = mxGetPr (Amatlab) ; A->z = mxGetPi (Amatlab) ; A->xtype = mxIsComplex (Amatlab) ? CHOLMOD_ZOMPLEX : CHOLMOD_REAL ; } else { /* only logical and complex/real double matrices supported */ sputil_error (ERROR_INVALID_TYPE, 0) ; } #else if (mxIsEmpty (Amatlab)) { /* this is not dereferenced, but the existence (non-NULL) of these * pointers is checked in CHOLMOD */ A->x = dummy ; A->z = dummy ; A->xtype = mxIsComplex (Amatlab) ? CHOLMOD_ZOMPLEX : CHOLMOD_REAL ; } else { /* in MATLAB 6.1, the matrix is sparse, so it must be double */ A->x = mxGetPr (Amatlab) ; A->z = mxGetPi (Amatlab) ; A->xtype = mxIsComplex (Amatlab) ? CHOLMOD_ZOMPLEX : CHOLMOD_REAL ; } #endif return (A) ; } /* ========================================================================== */ /* === sputil_get_dense ===================================================== */ /* ========================================================================== */ /* Create a shallow CHOLMOD copy of a MATLAB dense matrix. No memory is * allocated. Only double (real and zomplex) matrices are supported. The * resulting matrix B must not be modified. */ cholmod_dense *sputil_get_dense ( const mxArray *Amatlab, /* MATLAB version of the matrix */ cholmod_dense *A, /* CHOLMOD version of the matrix */ double *dummy /* a pointer to a valid scalar double */ ) { A->nrow = mxGetM (Amatlab) ; A->ncol = mxGetN (Amatlab) ; A->d = A->nrow ; A->nzmax = A->nrow * A->ncol ; A->dtype = CHOLMOD_DOUBLE ; if (mxIsEmpty (Amatlab)) { A->x = dummy ; A->z = dummy ; } else if (mxIsDouble (Amatlab)) { A->x = mxGetPr (Amatlab) ; A->z = mxGetPi (Amatlab) ; } else { /* only full double matrices supported by sputil_get_dense */ sputil_error (ERROR_INVALID_TYPE, 0) ; } A->xtype = mxIsComplex (Amatlab) ? CHOLMOD_ZOMPLEX : CHOLMOD_REAL ; return (A) ; } /* ========================================================================== */ /* === sputil_get_sparse_pattern ============================================ */ /* ========================================================================== */ /* Create a CHOLMOD_PATTERN sparse matrix for a MATLAB matrix, depending on the * type: * * (1) MATLAB full real double: duplicate CHOLMOD_REAL sparse matrix. * (2) MATLAB full complex double: duplicate CHOLMOD_ZOMPLEX sparse matrix. * (3) MATLAB full logical: duplicate CHOLMOD_PATTERN sparse matrix. * (4) MATLAB sparse real double: shallow CHOLMOD_REAL copy. * (5) MATLAB sparse complex double: shallow CHOLMOD_ZOMPLEX copy. * (6) MATLAB sparse logical: shallow CHOLMOD_PATTERN copy. * * A shallow copy or duplicate is returned; the shallow copy must not be freed. * For a shallow copy, the return value A is the same as Ashallow. For a * complete duplicate, A and Ashallow will differ. */ cholmod_sparse *sputil_get_sparse_pattern ( const mxArray *Amatlab, /* MATLAB version of the matrix */ cholmod_sparse *Ashallow, /* shallow CHOLMOD version of the matrix */ double *dummy, /* a pointer to a valid scalar double */ cholmod_common *cm ) { cholmod_sparse *A = NULL ; if (!mxIsSparse (Amatlab)) { /* ------------------------------------------------------------------ */ /* A = sparse (X) where X is full */ /* ------------------------------------------------------------------ */ if (mxIsDouble (Amatlab)) { /* -------------------------------------------------------------- */ /* convert full double X into sparse matrix A (pattern only) */ /* -------------------------------------------------------------- */ cholmod_dense Xmatrix, *X ; X = sputil_get_dense (Amatlab, &Xmatrix, dummy) ; A = cholmod_l_dense_to_sparse (X, FALSE, cm) ; } #ifndef MATLAB6p1_OR_EARLIER else if (mxIsLogical (Amatlab)) { /* -------------------------------------------------------------- */ /* convert full logical MATLAB matrix into CHOLMOD_PATTERN */ /* -------------------------------------------------------------- */ /* (this is copied and modified from t_cholmod_dense.c) */ char *x ; Int *Ap, *Ai ; Int nrow, ncol, i, j, nz, nzmax, p ; /* -------------------------------------------------------------- */ /* count the number of nonzeros in the result */ /* -------------------------------------------------------------- */ nrow = mxGetM (Amatlab) ; ncol = mxGetN (Amatlab) ; x = (char *) mxGetData (Amatlab) ; nzmax = nrow * ncol ; for (nz = 0, j = 0 ; j < nzmax ; j++) { if (x [j]) { nz++ ; } } /* -------------------------------------------------------------- */ /* allocate the result A */ /* -------------------------------------------------------------- */ A = cholmod_l_allocate_sparse (nrow, ncol, nz, TRUE, TRUE, 0, CHOLMOD_PATTERN, cm) ; if (cm->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } Ap = A->p ; Ai = A->i ; /* -------------------------------------------------------------- */ /* copy the full logical matrix into the sparse matrix A */ /* -------------------------------------------------------------- */ p = 0 ; for (j = 0 ; j < ncol ; j++) { Ap [j] = p ; for (i = 0 ; i < nrow ; i++) { if (x [i+j*nrow]) { Ai [p++] = i ; } } } /* ASSERT (p == nz) ; */ Ap [ncol] = nz ; } #endif else { /* only double and logical matrices supported */ sputil_error (ERROR_INVALID_TYPE, 0) ; } } else { /* ------------------------------------------------------------------ */ /* create a shallow copy of sparse matrix A (default stype is zero) */ /* ------------------------------------------------------------------ */ A = sputil_get_sparse (Amatlab, Ashallow, dummy, 0) ; A->x = NULL ; A->z = NULL ; A->xtype = CHOLMOD_PATTERN ; } return (A) ; } /* ========================================================================== */ /* === sputil_put_sparse ==================================================== */ /* ========================================================================== */ /* Creates a true MATLAB version of a CHOLMOD sparse matrix. The CHOLMOD sparse * matrix is destroyed. Both real and zomplex matrices are supported. */ mxArray *sputil_put_sparse ( cholmod_sparse **Ahandle, /* CHOLMOD version of the matrix */ cholmod_common *cm ) { mxArray *Amatlab ; cholmod_sparse *A ; A = *Ahandle ; Amatlab = mxCreateSparse (0, 0, 0, (A->xtype != CHOLMOD_REAL) ? mxCOMPLEX: mxREAL) ; mxSetM (Amatlab, A->nrow) ; mxSetN (Amatlab, A->ncol) ; mxSetNzmax (Amatlab, A->nzmax) ; mxFree (mxGetJc (Amatlab)) ; mxFree (mxGetIr (Amatlab)) ; mxFree (mxGetPr (Amatlab)) ; mxSetJc (Amatlab, A->p) ; mxSetIr (Amatlab, A->i) ; mxSetPr (Amatlab, A->x) ; mexMakeMemoryPersistent (A->p) ; mexMakeMemoryPersistent (A->i) ; mexMakeMemoryPersistent (A->x) ; if (A->xtype != CHOLMOD_REAL) { mxFree (mxGetPi (Amatlab)) ; mxSetPi (Amatlab, A->z) ; mexMakeMemoryPersistent (A->z) ; } A->p = NULL ; A->i = NULL ; A->x = NULL ; A->z = NULL ; cholmod_l_free_sparse (Ahandle, cm) ; return (Amatlab) ; } /* ========================================================================== */ /* === sputil_put_dense ===================================================== */ /* ========================================================================== */ /* Creates a true MATLAB version of a CHOLMOD dense matrix. The CHOLMOD dense * matrix is destroyed. Both real and zomplex matrices are supported. */ mxArray *sputil_put_dense ( cholmod_dense **Ahandle, /* CHOLMOD version of the matrix */ cholmod_common *cm ) { mxArray *Amatlab ; cholmod_dense *A ; A = *Ahandle ; Amatlab = mxCreateDoubleMatrix (0, 0, (A->xtype != CHOLMOD_REAL) ? mxCOMPLEX: mxREAL) ; mxSetM (Amatlab, A->nrow) ; mxSetN (Amatlab, A->ncol) ; mxFree (mxGetPr (Amatlab)) ; mxSetPr (Amatlab, A->x) ; mexMakeMemoryPersistent (A->x) ; if (A->xtype != CHOLMOD_REAL) { mxFree (mxGetPi (Amatlab)) ; mxSetPi (Amatlab, A->z) ; mexMakeMemoryPersistent (A->z) ; } A->x = NULL ; A->z = NULL ; cholmod_l_free_dense (Ahandle, cm) ; return (Amatlab) ; } /* ========================================================================== */ /* === sputil_put_int ======================================================= */ /* ========================================================================== */ /* Convert an Int vector into a double mxArray */ mxArray *sputil_put_int ( Int *P, /* vector to convert */ Int n, /* length of P */ Int one_based /* 1 if convert from 0-based to 1-based, 0 otherwise */ ) { double *p ; mxArray *Q ; Int i ; Q = mxCreateDoubleMatrix (1, n, mxREAL) ; p = mxGetPr (Q) ; for (i = 0 ; i < n ; i++) { p [i] = (double) (P [i] + one_based) ; } return (Q) ; } /* ========================================================================== */ /* === sputil_error ========================================================= */ /* ========================================================================== */ /* An integer is out of range, or other error has occurred. */ void sputil_error ( Int error, /* kind of error */ Int is_index /* TRUE if a matrix index, FALSE if a matrix dimension */ ) { if (error == ERROR_TOO_SMALL) { mexErrMsgTxt (is_index ? "sparse: index into matrix must be positive" : "sparse: sparse matrix sizes must be non-negative integers") ; } else if (error == ERROR_HUGE) { mexErrMsgTxt (is_index ? "sparse: index into matrix is too large" : "sparse: sparse matrix size is too large") ; } else if (error == ERROR_NOT_INTEGER) { mexErrMsgTxt (is_index ? "sparse: index into matrix must be an integer" : "sparse: sparse matrix size must be an integer") ; } else if (error == ERROR_TOO_LARGE) { mexErrMsgTxt ("sparse: index exceeds matrix dimensions") ; } else if (error == ERROR_USAGE) { mexErrMsgTxt ( "Usage:\n" "A = sparse (S)\n" "A = sparse (i,j,s,m,n,nzmax)\n" "A = sparse (i,j,s,m,n)\n" "A = sparse (i,j,s)\n" "A = sparse (m,n)\n") ; } else if (error == ERROR_LENGTH) { mexErrMsgTxt ("sparse: vectors must be the same lengths") ; } else if (error == ERROR_INVALID_TYPE) { mexErrMsgTxt ("matrix class not supported") ; } } /* ========================================================================== */ /* === sputil_double_to_int ================================================= */ /* ========================================================================== */ /* convert a double into an integer */ Int sputil_double_to_int /* returns integer value of x */ ( double x, /* double value to convert */ Int is_index, /* TRUE if a matrix index, FALSE if a matrix dimension */ Int n /* if a matrix index, x cannot exceed this dimension, * except that -1 is treated as infinity */ ) { Int i ; if (x > INT_MAX) { /* x is way too big for an integer */ sputil_error (ERROR_HUGE, is_index) ; } else if (x < 0) { /* x must be non-negative */ sputil_error (ERROR_TOO_SMALL, is_index) ; } i = (Int) x ; if (x != (double) i) { /* x must be an integer */ sputil_error (ERROR_NOT_INTEGER, is_index) ; } if (is_index) { if (i < 1) { sputil_error (ERROR_TOO_SMALL, is_index) ; } else if (i > n && n != EMPTY) { sputil_error (ERROR_TOO_LARGE, is_index) ; } } return (i) ; } /* ========================================================================== */ /* === sputil_nelements ===================================================== */ /* ========================================================================== */ /* return the number of elements in an mxArray. Trigger an error on integer * overflow (in case the argument is sparse) */ Int sputil_nelements (const mxArray *arg) { double size ; const Int *dims ; Int k, ndims ; ndims = mxGetNumberOfDimensions (arg) ; dims = (Int *) mxGetDimensions (arg) ; size = 1 ; for (k = 0 ; k < ndims ; k++) { size *= dims [k] ; } return (sputil_double_to_int (size, FALSE, 0)) ; } /* ========================================================================== */ /* === sputil_get_double ==================================================== */ /* ========================================================================== */ double sputil_get_double (const mxArray *arg) { if (sputil_nelements (arg) < 1) { /* [] is not a scalar, but its value is zero so that * sparse ([],[],[]) is a 0-by-0 matrix */ return (0) ; } return (mxGetScalar (arg)) ; } /* ========================================================================== */ /* === sputil_get_integer =================================================== */ /* ========================================================================== */ /* return an argument as a non-negative integer scalar, or -1 if error */ Int sputil_get_integer ( const mxArray *arg, /* MATLAB argument to convert */ Int is_index, /* TRUE if an index, FALSE if a matrix dimension */ Int n /* maximum value, if an index */ ) { double x = sputil_get_double (arg) ; if (mxIsInf (x) || mxIsNaN (x)) { /* arg is Inf or NaN, return -1 */ return (EMPTY) ; } return (sputil_double_to_int (x, is_index, n)) ; } /* ========================================================================== */ /* === sputil_trim ========================================================== */ /* ========================================================================== */ /* Remove columns k to n-1 from a sparse matrix S, leaving columns 0 to k-1. * S must be packed (there can be no S->nz array). This condition is not * checked, since only packed matrices are passed to this routine. */ void sputil_trim ( cholmod_sparse *S, Int k, cholmod_common *cm ) { Int *Sp ; Int ncol ; size_t n1, nznew ; if (S == NULL) { return ; } ncol = S->ncol ; if (k < 0 || k >= ncol) { /* do not modify S */ return ; } /* reduce S->p in size. This cannot fail. */ n1 = ncol + 1 ; S->p = cholmod_l_realloc (k+1, sizeof (Int), S->p, &n1, cm) ; /* get the new number of entries in S */ Sp = S->p ; nznew = Sp [k] ; /* reduce S->i, S->x, and S->z (if present) to size nznew */ cholmod_l_reallocate_sparse (nznew, S, cm) ; /* S now has only k columns */ S->ncol = k ; } /* ========================================================================== */ /* === sputil_extract_zeros ================================================= */ /* ========================================================================== */ /* Create a sparse binary (real double) matrix Z that contains the pattern * of explicit zeros in the sparse real/zomplex double matrix A. */ cholmod_sparse *sputil_extract_zeros ( cholmod_sparse *A, cholmod_common *cm ) { Int *Ap, *Ai, *Zp, *Zi ; double *Ax, *Az, *Zx ; Int j, p, nzeros = 0, is_complex, pz, nrow, ncol ; cholmod_sparse *Z ; if (A == NULL || A->xtype == CHOLMOD_PATTERN || A->xtype == CHOLMOD_COMPLEX) { /* only sparse real/zomplex double matrices supported */ sputil_error (ERROR_INVALID_TYPE, 0) ; } Ap = A->p ; Ai = A->i ; Ax = A->x ; Az = A->z ; ncol = A->ncol ; nrow = A->nrow ; is_complex = (A->xtype == CHOLMOD_ZOMPLEX) ; /* count the number of zeros in a sparse matrix A */ for (j = 0 ; j < ncol ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { if (CHOLMOD_IS_ZERO (Ax [p]) && ((is_complex) ? CHOLMOD_IS_ZERO (Az [p]) : TRUE)) { nzeros++ ; } } } /* allocate the Z matrix with space for all the zero entries */ Z = cholmod_l_spzeros (nrow, ncol, nzeros, CHOLMOD_REAL, cm) ; /* extract the zeros from A and store them in Z as binary values */ if (nzeros > 0) { Zp = Z->p ; Zi = Z->i ; Zx = Z->x ; pz = 0 ; for (j = 0 ; j < ncol ; j++) { Zp [j] = pz ; for (p = Ap [j] ; p < Ap [j+1] ; p++) { if (CHOLMOD_IS_ZERO (Ax [p]) && ((is_complex) ? CHOLMOD_IS_ZERO (Az [p]) : TRUE)) { Zi [pz] = Ai [p] ; Zx [pz] = 1 ; pz++ ; } } } Zp [ncol] = pz ; } return (Z) ; } /* ========================================================================== */ /* === sputil_drop_zeros ==================================================== */ /* ========================================================================== */ /* Drop zeros from a packed CHOLMOD sparse matrix (zomplex or real). This is * very similar to CHOLMOD/MatrixOps/cholmod_drop, except that this routine has * no tolerance parameter and it can handle zomplex matrices. NaN's are left * in the matrix. If this is used on the sparse matrix version of the factor * L, then the update/downdate methods cannot be applied to L (ldlupdate). * Returns the number of entries dropped. */ Int sputil_drop_zeros ( cholmod_sparse *S ) { double sik, zik ; Int *Sp, *Si ; double *Sx, *Sz ; Int pdest, k, ncol, p, pend, nz ; if (S == NULL) { return (0) ; } Sp = S->p ; Si = S->i ; Sx = S->x ; Sz = S->z ; pdest = 0 ; ncol = S->ncol ; nz = Sp [ncol] ; if (S->xtype == CHOLMOD_ZOMPLEX) { for (k = 0 ; k < ncol ; k++) { p = Sp [k] ; pend = Sp [k+1] ; Sp [k] = pdest ; for ( ; p < pend ; p++) { sik = Sx [p] ; zik = Sz [p] ; if (CHOLMOD_IS_NONZERO (sik) || CHOLMOD_IS_NONZERO (zik)) { if (p != pdest) { Si [pdest] = Si [p] ; Sx [pdest] = sik ; Sz [pdest] = zik ; } pdest++ ; } } } } else { for (k = 0 ; k < ncol ; k++) { p = Sp [k] ; pend = Sp [k+1] ; Sp [k] = pdest ; for ( ; p < pend ; p++) { sik = Sx [p] ; if (CHOLMOD_IS_NONZERO (sik)) { if (p != pdest) { Si [pdest] = Si [p] ; Sx [pdest] = sik ; } pdest++ ; } } } } Sp [ncol] = pdest ; return (nz - pdest) ; } /* ========================================================================== */ /* === sputil_copy_ij ======================================================= */ /* ========================================================================== */ /* copy i or j arguments into an Int vector. For small integer types, i and * and j can be returned with negative entries; this error condition is caught * later, in cholmod_triplet_to_sparse. * * TODO: if the mxClassID matches the default Int integer (INT32 for 32-bit * MATLAB and INT64 for 64-bit), then it would save memory to patch in the * vector with a pointer copy, rather than making a copy of the whole vector. * This would require that the 1-based i and j vectors be converted on the fly * to 0-based vectors in cholmod_triplet_to_sparse. */ Int sputil_copy_ij /* returns the dimension, n */ ( Int is_scalar, /* TRUE if argument is a scalar, FALSE otherwise */ Int scalar, /* scalar value of the argument */ void *vector, /* vector value of the argument */ mxClassID category, /* type of vector */ Int nz, /* length of output vector I */ Int n, /* maximum dimension, EMPTY if not yet known */ Int *I /* vector of length nz to copy into */ ) { Int i, k, ok, ok2, ok3, n2 ; if (is_scalar) { n2 = scalar ; if (n == EMPTY) { n = scalar ; } i = scalar - 1 ; for (k = 0 ; k < nz ; k++) { I [k] = i ; } } else { /* copy double input into Int vector (convert to 0-based) */ ok = TRUE ; ok2 = TRUE ; ok3 = TRUE ; n2 = 0 ; switch (category) { #ifndef MATLAB6p1_OR_EARLIER /* MATLAB 6.1 or earlier do not have mxLOGICAL_CLASS */ case mxLOGICAL_CLASS: for (k = 0 ; k < nz ; k++) { i = (Int) (((mxLogical *) vector) [k]) ; I [k] = i - 1 ; n2 = MAX (n2, i) ; } break ; #endif case mxCHAR_CLASS: for (k = 0 ; k < nz ; k++) { i = (Int) (((mxChar *) vector) [k]) ; I [k] = i - 1 ; n2 = MAX (n2, i) ; } break ; case mxINT8_CLASS: for (k = 0 ; k < nz ; k++) { i = (Int) (((INT8_T *) vector) [k]) ; I [k] = i - 1 ; n2 = MAX (n2, i) ; } break ; case mxUINT8_CLASS: for (k = 0 ; k < nz ; k++) { i = (Int) (((UINT8_T *) vector) [k]) ; I [k] = i - 1 ; n2 = MAX (n2, i) ; } break ; case mxINT16_CLASS: for (k = 0 ; k < nz ; k++) { i = (Int) (((INT16_T *) vector) [k]) ; I [k] = i - 1 ; n2 = MAX (n2, i) ; } break ; case mxUINT16_CLASS: for (k = 0 ; k < nz ; k++) { i = (Int) (((UINT16_T *) vector) [k]) ; I [k] = i - 1 ; n2 = MAX (n2, i) ; } break ; case mxINT32_CLASS: for (k = 0 ; k < nz ; k++) { i = (Int) (((INT32_T *) vector) [k]) ; I [k] = i - 1 ; n2 = MAX (n2, i) ; } break ; case mxUINT32_CLASS: for (k = 0 ; ok3 && k < nz ; k++) { double y = (((UINT32_T *) vector) [k]) ; i = (Int) y ; ok3 = (y < Int_max) ; I [k] = i - 1 ; n2 = MAX (n2, i) ; } break ; case mxINT64_CLASS: for (k = 0 ; ok2 && ok3 && k < nz ; k++) { INT64_T y = ((INT64_T *) vector) [k] ; i = (Int) y ; ok2 = (y > 0) ; ok3 = (y < Int_max) ; I [k] = i - 1 ; n2 = MAX (n2, i) ; } break ; case mxUINT64_CLASS: for (k = 0 ; ok2 && ok3 && k < nz ; k++) { unsigned INT64_T y = ((unsigned INT64_T *) vector) [k] ; i = (Int) y ; ok2 = (y > 0) ; ok3 = (y < Int_max) ; I [k] = i - 1 ; n2 = MAX (n2, i) ; } break ; case mxSINGLE_CLASS: for (k = 0 ; ok && ok2 && ok3 && k < nz ; k++) { float y = ((float *) vector) [k] ; i = (Int) y ; ok = (y == (float) i) ; ok2 = (y > 0) ; ok3 = (y < Int_max) ; I [k] = i - 1 ; n2 = MAX (n2, i) ; } break ; case mxDOUBLE_CLASS: for (k = 0 ; ok && ok2 && ok3 && k < nz ; k++) { double y = ((double *) vector) [k] ; i = (Int) y ; ok = (y == (double) i) ; ok2 = (y > 0) ; ok3 = (y < Int_max) ; I [k] = i - 1 ; n2 = MAX (n2, i) ; } break ; default: sputil_error (ERROR_INVALID_TYPE, FALSE) ; break ; } if (!ok) { sputil_error (ERROR_NOT_INTEGER, TRUE) ; } if (!ok2) { sputil_error (ERROR_TOO_SMALL, TRUE) ; } if (!ok3) { sputil_error (ERROR_HUGE, TRUE) ; } } return ((n == EMPTY) ? n2 : n) ; } /* ========================================================================== */ /* === sputil_dense_to_sparse =============================================== */ /* ========================================================================== */ /* Convert a dense matrix of any numeric type into a * sparse double or sparse logical matrix. */ #define COUNT_NZ \ { \ for (j = 0 ; j < ncol ; j++) \ { \ for (i = 0 ; i < nrow ; i++) \ { \ xij = X [i + j*nrow] ; \ if (CHOLMOD_IS_NONZERO (xij)) \ { \ nz++ ; \ } \ } \ } \ } #define COPY_DENSE_TO_SPARSE(stype) \ { \ stype *Sx ; \ Sp = (Int *) mxGetJc (S) ; \ Si = (Int *) mxGetIr (S) ; \ Sx = (stype *) mxGetData (S) ; \ nz = 0 ; \ for (j = 0 ; j < ncol ; j++) \ { \ Sp [j] = nz ; \ for (i = 0 ; i < nrow ; i++) \ { \ xij = X [i + j*nrow] ; \ if (CHOLMOD_IS_NONZERO (xij)) \ { \ Si [nz] = i ; \ Sx [nz] = (stype) xij ; \ nz++ ; \ } \ } \ } \ Sp [ncol] = nz ; \ } #define DENSE_TO_SPARSE(type) \ { \ type *X, xij ; \ X = (type *) mxGetData (arg) ; \ COUNT_NZ ; \ S = mxCreateSparse (nrow, ncol, nz, mxREAL) ; \ COPY_DENSE_TO_SPARSE (double) ; \ } mxArray *sputil_dense_to_sparse (const mxArray *arg) { mxArray *S = NULL ; Int *Sp, *Si ; Int nrow, ncol, nz, i, j ; nrow = mxGetM (arg) ; ncol = mxGetN (arg) ; nz = 0 ; if (mxIsComplex (arg)) { /* ------------------------------------------------------------------ */ /* convert a complex dense matrix into a complex sparse matrix */ /* ------------------------------------------------------------------ */ double xij, zij ; double *X, *Z, *Sx, *Sz ; if (mxGetClassID (arg) != mxDOUBLE_CLASS) { /* A complex matrix can have any class (int8, int16, single, etc), * but this function only supports complex double. This condition * is not checked in the caller. */ sputil_error (ERROR_INVALID_TYPE, FALSE) ; } X = mxGetPr (arg) ; Z = mxGetPi (arg) ; for (j = 0 ; j < ncol ; j++) { for (i = 0 ; i < nrow ; i++) { xij = X [i + j*nrow] ; zij = Z [i + j*nrow] ; if (CHOLMOD_IS_NONZERO (xij) || CHOLMOD_IS_NONZERO (zij)) { nz++ ; } } } S = mxCreateSparse (nrow, ncol, nz, mxCOMPLEX) ; Sp = (Int *) mxGetJc (S) ; Si = (Int *) mxGetIr (S) ; Sx = mxGetPr (S) ; Sz = mxGetPi (S) ; nz = 0 ; for (j = 0 ; j < ncol ; j++) { Sp [j] = nz ; for (i = 0 ; i < nrow ; i++) { xij = X [i + j*nrow] ; zij = Z [i + j*nrow] ; if (CHOLMOD_IS_NONZERO (xij) || CHOLMOD_IS_NONZERO (zij)) { Si [nz] = i ; Sx [nz] = xij ; Sz [nz] = zij ; nz++ ; } } } Sp [ncol] = nz ; } else { /* ------------------------------------------------------------------ */ /* convert real matrix (any class) to sparse double or logical */ /* ------------------------------------------------------------------ */ switch (mxGetClassID (arg)) { #ifndef MATLAB6p1_OR_EARLIER /* MATLAB 6.1 or earlier do not have mxLOGICAL_CLASS */ case mxLOGICAL_CLASS: { mxLogical *X, xij ; X = (mxLogical *) mxGetData (arg) ; COUNT_NZ ; S = mxCreateSparseLogicalMatrix (nrow, ncol, nz) ; COPY_DENSE_TO_SPARSE (mxLogical) ; } break ; #endif case mxCHAR_CLASS: DENSE_TO_SPARSE (mxChar) ; break ; case mxINT8_CLASS: DENSE_TO_SPARSE (char) ; break ; case mxUINT8_CLASS: DENSE_TO_SPARSE (unsigned char) ; break ; case mxINT16_CLASS: DENSE_TO_SPARSE (short) ; break ; case mxUINT16_CLASS: DENSE_TO_SPARSE (unsigned short) ; break ; case mxINT32_CLASS: DENSE_TO_SPARSE (INT32_T) ; break ; case mxUINT32_CLASS: DENSE_TO_SPARSE (unsigned INT32_T) ; break ; case mxINT64_CLASS: DENSE_TO_SPARSE (INT64_T) ; break ; case mxUINT64_CLASS: DENSE_TO_SPARSE (unsigned INT64_T) ; break ; case mxSINGLE_CLASS: DENSE_TO_SPARSE (float) ; break ; case mxDOUBLE_CLASS: DENSE_TO_SPARSE (double) ; break ; default: sputil_error (ERROR_INVALID_TYPE, FALSE) ; break ; } } return (S) ; } /* ========================================================================== */ /* === sputil_triplet_to_sparse ============================================= */ /* ========================================================================== */ /* Convert a triplet form into a sparse matrix. If complex, s must be double. * If real, s can be of any class. */ cholmod_sparse *sputil_triplet_to_sparse ( Int nrow, Int ncol, Int nz, Int nzmax, Int i_is_scalar, Int i, void *i_vector, mxClassID i_class, Int j_is_scalar, Int j, void *j_vector, mxClassID j_class, Int s_is_scalar, double x, double z, void *x_vector, double *z_vector, mxClassID s_class, Int s_complex, cholmod_common *cm ) { double dummy = 0 ; cholmod_triplet *T ; cholmod_sparse *S ; double *Tx, *Tz ; Int *Ti, *Tj ; Int k, x_patch ; /* ---------------------------------------------------------------------- */ /* allocate the triplet form */ /* ---------------------------------------------------------------------- */ /* Note that nrow and ncol may be EMPTY; this is not an error condition. * Allocate the numerical part of T only if s is a scalar. */ x_patch = (!s_is_scalar && (s_class == mxDOUBLE_CLASS || s_complex)) ; T = cholmod_l_allocate_triplet (MAX (0,nrow), MAX (0,ncol), nz, 0, x_patch ? CHOLMOD_PATTERN : (s_complex ? CHOLMOD_ZOMPLEX : CHOLMOD_REAL), cm) ; Ti = T->i ; Tj = T->j ; Tx = T->x ; Tz = T->z ; /* ---------------------------------------------------------------------- */ /* fill the triplet form */ /* ---------------------------------------------------------------------- */ if (s_is_scalar) { /* ------------------------------------------------------------------ */ /* fill T->x and T->z with a scalar value */ /* ------------------------------------------------------------------ */ for (k = 0 ; k < nz ; k++) { Tx [k] = x ; } if (s_complex) { for (k = 0 ; k < nz ; k++) { Tz [k] = z ; } } } else { /* ------------------------------------------------------------------ */ /* copy x/z_vector into T->x and T->z, and convert to double */ /* ------------------------------------------------------------------ */ if (s_complex) { /* Patch in s as the numerical values of the triplet matrix. * Note that T->x and T->z must not be free'd when done. */ T->x = (x_vector == NULL) ? &dummy : x_vector ; T->z = (z_vector == NULL) ? &dummy : z_vector ; T->xtype = CHOLMOD_ZOMPLEX ; } else switch (s_class) { #ifndef MATLAB6p1_OR_EARLIER /* MATLAB 6.1 or earlier do not have mxLOGICAL_CLASS */ case mxLOGICAL_CLASS: for (k = 0 ; k < nz ; k++) { Tx [k] = (double) (((mxLogical *) x_vector) [k]) ; } break ; #endif case mxCHAR_CLASS: for (k = 0 ; k < nz ; k++) { Tx [k] = (double) (((mxChar *) x_vector) [k]) ; } break ; case mxINT8_CLASS: for (k = 0 ; k < nz ; k++) { Tx [k] = (double) (((INT8_T *) x_vector) [k]) ; } break ; case mxUINT8_CLASS: for (k = 0 ; k < nz ; k++) { Tx [k] = (double) (((UINT8_T *) x_vector) [k]) ; } break ; case mxINT16_CLASS: for (k = 0 ; k < nz ; k++) { Tx [k] = (double) (((INT16_T *) x_vector) [k]) ; } break ; case mxUINT16_CLASS: for (k = 0 ; k < nz ; k++) { Tx [k] = (double) (((UINT16_T *) x_vector) [k]) ; } break ; case mxINT32_CLASS: for (k = 0 ; k < nz ; k++) { Tx [k] = (double) (((INT32_T *) x_vector) [k]) ; } break ; case mxUINT32_CLASS: for (k = 0 ; k < nz ; k++) { Tx [k] = (double) (((UINT32_T *) x_vector) [k]) ; } break ; case mxINT64_CLASS: for (k = 0 ; k < nz ; k++) { Tx [k] = (double) (((INT64_T *) x_vector) [k]) ; } break ; case mxUINT64_CLASS: for (k = 0 ; k < nz ; k++) { Tx [k] = (double) (((unsigned INT64_T *) x_vector) [k]) ; } break ; case mxSINGLE_CLASS: for (k = 0 ; k < nz ; k++) { Tx [k] = (double) (((float *) x_vector) [k]) ; } break ; case mxDOUBLE_CLASS: /* Patch in s as the numerical values of the triplet matrix. * Note that T->x must not be free'd when done. */ T->x = (x_vector == NULL) ? &dummy : x_vector ; T->xtype = CHOLMOD_REAL ; break ; default: sputil_error (ERROR_INVALID_TYPE, FALSE) ; break ; } } /* copy i in to the integer vector T->i */ nrow = sputil_copy_ij (i_is_scalar, i, i_vector, i_class, nz, nrow, Ti) ; /* copy j in to the integer vector T->j */ ncol = sputil_copy_ij (j_is_scalar, j, j_vector, j_class, nz, ncol, Tj) ; /* nrow and ncol are known */ T->nrow = nrow ; T->ncol = ncol ; T->nnz = nz ; /* ---------------------------------------------------------------------- */ /* convert triplet to sparse matrix */ /* ---------------------------------------------------------------------- */ /* If the triplet matrix T is invalid, or if CHOLMOD runs out of memory, * then S is NULL. */ S = cholmod_l_triplet_to_sparse (T, nzmax, cm) ; /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ /* do not free T->x or T->z if it points to input x_vector */ if (x_patch) { T->x = NULL ; T->z = NULL ; T->xtype = CHOLMOD_PATTERN ; } cholmod_l_free_triplet (&T, cm) ; return (S) ; } /* ========================================================================== */ /* === sputil_copy_sparse =================================================== */ /* ========================================================================== */ /* copy a sparse matrix, S = sparse(A), dropping any zero entries and ensuring * the nzmax(S) == nnz(S). Explicit zero entries in A "cannot" occur, in * the current version of MATLAB ... but a user mexFunction might generate a * matrix with explicit zeros. This function ensures S=sparse(A) drops those * explicit zeros. */ mxArray *sputil_copy_sparse (const mxArray *A) { double aij, zij ; mxArray *S ; double *Ax, *Az, *Sx, *Sz ; Int *Ap, *Ai, *Sp, *Si ; Int anz, snz, p, j, nrow, ncol, pend ; #ifndef MATLAB6p1_OR_EARLIER /* MATLAB 6.1 or earlier : all sparse matrices are OK */ if (! (mxGetClassID (A) == mxLOGICAL_CLASS || mxGetClassID (A) == mxDOUBLE_CLASS)) { /* Only sparse logical and real/complex double matrices supported. * This condition is not checked in the caller. */ sputil_error (ERROR_INVALID_TYPE, 0) ; } #endif nrow = mxGetM (A) ; ncol = mxGetN (A) ; Ap = (Int *) mxGetJc (A) ; Ai = (Int *) mxGetIr (A) ; anz = Ap [ncol] ; snz = 0 ; #ifndef MATLAB6p1_OR_EARLIER /* MATLAB 6.1 or earlier do not have mxLOGICAL_CLASS */ if (mxIsLogical (A)) { /* ------------------------------------------------------------------ */ /* copy a sparse logical matrix */ /* ------------------------------------------------------------------ */ /* count the number of nonzeros in A */ mxLogical *Al, *Sl ; Al = mxGetLogicals (A) ; for (p = 0 ; p < anz ; p++) { if (Al [p]) { snz++ ; } } /* allocate S */ S = mxCreateSparseLogicalMatrix (nrow, ncol, snz) ; Sp = (Int *) mxGetJc (S) ; Si = (Int *) mxGetIr (S) ; Sl = mxGetLogicals (S) ; /* copy A into S, dropping zero entries */ snz = 0 ; for (j = 0 ; j < ncol ; j++) { Sp [j] = snz ; pend = Ap [j+1] ; for (p = Ap [j] ; p < pend ; p++) { if (Al [p]) { Si [snz] = Ai [p] ; Sl [snz] = 1 ; snz++ ; } } } } else #endif if (mxIsComplex (A)) { /* ------------------------------------------------------------------ */ /* copy a sparse complex double matrix */ /* ------------------------------------------------------------------ */ /* count the number of nonzeros in A */ Ax = mxGetPr (A) ; Az = mxGetPi (A) ; for (p = 0 ; p < anz ; p++) { aij = Ax [p] ; zij = Az [p] ; if (CHOLMOD_IS_NONZERO (aij) || CHOLMOD_IS_NONZERO (zij)) { snz++ ; } } /* allocate S */ S = mxCreateSparse (nrow, ncol, snz, mxCOMPLEX) ; Sp = (Int *) mxGetJc (S) ; Si = (Int *) mxGetIr (S) ; Sx = mxGetPr (S) ; Sz = mxGetPi (S) ; /* copy A into S, dropping zero entries */ snz = 0 ; for (j = 0 ; j < ncol ; j++) { Sp [j] = snz ; pend = Ap [j+1] ; for (p = Ap [j] ; p < pend ; p++) { aij = Ax [p] ; zij = Az [p] ; if (CHOLMOD_IS_NONZERO (aij) || CHOLMOD_IS_NONZERO (zij)) { Si [snz] = Ai [p] ; Sx [snz] = aij ; Sz [snz] = zij ; snz++ ; } } } } else { /* ------------------------------------------------------------------ */ /* copy a sparse real double matrix */ /* ------------------------------------------------------------------ */ /* count the number of nonzeros in A */ Ax = mxGetPr (A) ; for (p = 0 ; p < anz ; p++) { aij = Ax [p] ; if (CHOLMOD_IS_NONZERO (aij)) { snz++ ; } } /* allocate S */ S = mxCreateSparse (nrow, ncol, snz, mxREAL) ; Sp = (Int *) mxGetJc (S) ; Si = (Int *) mxGetIr (S) ; Sx = mxGetPr (S) ; /* copy A into S, dropping zero entries */ snz = 0 ; for (j = 0 ; j < ncol ; j++) { Sp [j] = snz ; pend = Ap [j+1] ; for (p = Ap [j] ; p < pend ; p++) { aij = Ax [p] ; if (CHOLMOD_IS_NONZERO (aij)) { Si [snz] = Ai [p] ; Sx [snz] = aij ; snz++ ; } } } } Sp [ncol] = snz ; return (S) ; } /* ========================================================================== */ /* === sputil_sparse_to_dense =============================================== */ /* ========================================================================== */ /* convert a sparse double or logical array to a dense double array */ mxArray *sputil_sparse_to_dense (const mxArray *S) { mxArray *X ; double *Sx, *Sz, *Xx, *Xz ; Int *Sp, *Si ; Int nrow, ncol, i, j, p, pend, j2 ; #ifndef MATLAB6p1_OR_EARLIER /* MATLAB 6.1 or earlier : all sparse matrices are OK */ if (! (mxGetClassID (S) == mxLOGICAL_CLASS || mxGetClassID (S) == mxDOUBLE_CLASS)) { /* only sparse logical and real/complex double matrices supported */ sputil_error (ERROR_INVALID_TYPE, 0) ; } #endif nrow = mxGetM (S) ; ncol = mxGetN (S) ; Sp = (Int *) mxGetJc (S) ; Si = (Int *) mxGetIr (S) ; #ifndef MATLAB6p1_OR_EARLIER /* MATLAB 6.1 or earlier do not have mxLOGICAL_CLASS */ if (mxIsLogical (S)) { /* logical */ mxLogical *Sl ; Sl = (mxLogical *) mxGetData (S) ; X = mxCreateDoubleMatrix (nrow, ncol, mxREAL) ; Xx = mxGetPr (X) ; for (j = 0 ; j < ncol ; j++) { pend = Sp [j+1] ; j2 = j*nrow ; for (p = Sp [j] ; p < pend ; p++) { Xx [Si [p] + j2] = (double) (Sl [p]) ; } } } else #endif if (mxIsComplex (S)) { /* complex */ Sx = mxGetPr (S) ; Sz = mxGetPi (S) ; X = mxCreateDoubleMatrix (nrow, ncol, mxCOMPLEX) ; Xx = mxGetPr (X) ; Xz = mxGetPi (X) ; for (j = 0 ; j < ncol ; j++) { pend = Sp [j+1] ; j2 = j*nrow ; for (p = Sp [j] ; p < pend ; p++) { i = Si [p] ; Xx [i + j2] = Sx [p] ; Xz [i + j2] = Sz [p] ; } } } else { /* real */ Sx = mxGetPr (S) ; X = mxCreateDoubleMatrix (nrow, ncol, mxREAL) ; Xx = mxGetPr (X) ; for (j = 0 ; j < ncol ; j++) { pend = Sp [j+1] ; j2 = j*nrow ; for (p = Sp [j] ; p < pend ; p++) { Xx [Si [p] + j2] = Sx [p] ; } } } return (X) ; } /* ========================================================================== */ /* === sputil_check_ijvector ================================================ */ /* ========================================================================== */ /* Check a sparse i or j input argument */ void sputil_check_ijvector (const mxArray *arg) { if (mxIsComplex (arg)) { /* i and j cannot be complex */ sputil_error (ERROR_NOT_INTEGER, TRUE) ; } if (mxIsSparse (arg)) { /* the i and j arguments for sparse(i,j,s,...) can be sparse, but if so * they must have no zero entries. */ double mn, m, nz ; Int *p, n ; m = (double) mxGetM (arg) ; n = mxGetN (arg) ; mn = m*n ; p = (Int *) mxGetJc (arg) ; nz = p [n] ; if (mn != nz) { /* i or j contains at least one zero, which is invalid */ sputil_error (ERROR_TOO_SMALL, TRUE) ; } } } /* ========================================================================== */ /* === sputil_sparse ======================================================== */ /* ========================================================================== */ /* Implements the sparse2 mexFunction */ void sputil_sparse ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double x, z ; double *z_vector ; void *i_vector, *j_vector, *x_vector ; mxArray *s_array ; cholmod_sparse *S, *Z ; cholmod_common Common, *cm ; Int nrow, ncol, k, nz, i_is_scalar, j_is_scalar, s_is_sparse, s_is_scalar, ilen, jlen, slen, nzmax, i, j, s_complex, ndropped ; mxClassID i_class, j_class, s_class ; /* ---------------------------------------------------------------------- */ /* start CHOLMOD and set defaults */ /* ---------------------------------------------------------------------- */ cm = &Common ; cholmod_l_start (cm) ; sputil_config (SPUMONI, cm) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if (nargout > 2 || nargin > 6 || nargin == 4 || nargin == 0) { sputil_error (ERROR_USAGE, FALSE) ; } /* ---------------------------------------------------------------------- */ /* convert inputs into a sparse matrix S */ /* ---------------------------------------------------------------------- */ S = NULL ; Z = NULL ; if (nargin == 1) { /* ------------------------------------------------------------------ */ /* S = sparse (A) where A is sparse or full */ /* ------------------------------------------------------------------ */ nrow = mxGetM (pargin [0]) ; ncol = mxGetN (pargin [0]) ; if (mxIsSparse (pargin [0])) { /* -------------------------------------------------------------- */ /* S = sparse (A) where A is sparse (double, complex, or logical) */ /* -------------------------------------------------------------- */ pargout [0] = sputil_copy_sparse (pargin [0]) ; } else { /* -------------------------------------------------------------- */ /* S = sparse (A) where A is full (real or complex) */ /* -------------------------------------------------------------- */ /* A can be of any numeric type (mxLogical, int8, ..., double), * except that if A is complex, it must also be double. */ pargout [0] = sputil_dense_to_sparse (pargin [0]) ; } } else if (nargin == 2) { /* ------------------------------------------------------------------ */ /* S = sparse (m,n) */ /* ------------------------------------------------------------------ */ Int *Sp ; nrow = sputil_get_integer (pargin [0], FALSE, 0) ; ncol = sputil_get_integer (pargin [1], FALSE, 0) ; pargout [0] = mxCreateSparse (nrow, ncol, 1, mxREAL) ; Sp = (Int *) mxGetJc (pargout [0]) ; Sp [0] = 0 ; } else { /* ------------------------------------------------------------------ */ /* S = sparse (i,j,s), sparse (i,j,s,m,n) or sparse (i,j,s,m,n,nzmax) */ /* ------------------------------------------------------------------ */ /* i, j, and s can be of any numeric type */ /* ensure i and j are valid (i and j cannot be complex) */ sputil_check_ijvector (pargin [0]) ; sputil_check_ijvector (pargin [1]) ; /* convert s from sparse to dense (double), if necessary */ s_is_sparse = mxIsSparse (pargin [2]) ; if (s_is_sparse) { /* s must be double (real/complex) or logical */ s_array = sputil_sparse_to_dense (pargin [2]) ; } else { s_array = (mxArray *) pargin [2] ; } /* s is now full. It can be any class, except if complex it must also * be double */ s_class = mxGetClassID (s_array) ; s_complex = mxIsComplex (s_array) ; if (s_complex && s_class != mxDOUBLE_CLASS) { /* for complex case, only double class is supported */ sputil_error (ERROR_INVALID_TYPE, 0) ; } /* get sizes of inputs */ ilen = sputil_nelements (pargin [0]) ; jlen = sputil_nelements (pargin [1]) ; slen = sputil_nelements (s_array) ; /* if i, j, s are scalars, they "float" to sizes of non-scalar args */ i_is_scalar = (ilen == 1) ; j_is_scalar = (jlen == 1) ; s_is_scalar = (slen == 1) ; /* find the length */ if (!i_is_scalar) { /* if i is not a scalar, let it determine the length */ nz = ilen ; } else if (!j_is_scalar) { /* otherwise, if j is not a scalar, let it determine the length */ nz = jlen ; } else { /* finally, i and j are both scalars, so let s determine length */ nz = slen ; } /* make sure the sizes are compatible */ if (!((i_is_scalar || ilen == nz) && (j_is_scalar || jlen == nz) && (s_is_scalar || slen == nz))) { sputil_error (ERROR_LENGTH, FALSE) ; } if (nargin > 4) { nrow = sputil_get_integer (pargin [3], FALSE, 0) ; ncol = sputil_get_integer (pargin [4], FALSE, 0) ; } else { /* nrow and ncol will be discovered by scanning i and j */ nrow = EMPTY ; ncol = EMPTY ; } if (nargin > 5) { nzmax = sputil_get_integer (pargin [5], FALSE, 0) ; nzmax = MAX (nzmax, nz) ; } else { nzmax = nz ; } /* ------------------------------------------------------------------ */ /* convert triplet form to sparse form */ /* ------------------------------------------------------------------ */ i = i_is_scalar ? sputil_get_integer (pargin [0], TRUE, nrow) : 0 ; i_vector = mxGetData (pargin [0]) ; i_class = mxGetClassID (pargin [0]) ; j = j_is_scalar ? sputil_get_integer (pargin [1], TRUE, ncol) : 0 ; j_vector = mxGetData (pargin [1]) ; j_class = mxGetClassID (pargin [1]) ; x_vector = mxGetData (s_array) ; z_vector = mxGetPi (s_array) ; x = sputil_get_double (s_array) ; z = (s_complex && z_vector != NULL) ? (z_vector [0]) : 0 ; S = sputil_triplet_to_sparse (nrow, ncol, nz, nzmax, i_is_scalar, i, i_vector, i_class, j_is_scalar, j, j_vector, j_class, s_is_scalar, x, z, x_vector, z_vector, s_class, s_complex, cm) ; /* set nzmax(S) to nnz(S), unless nzmax is specified on input */ if (nargin <= 5 && S != NULL) { cholmod_l_reallocate_sparse (cholmod_l_nnz (S, cm), S, cm) ; } if (nargout > 1) { /* return a binary pattern of the explicit zero entries, for the * [S Z] = sparse(i,j,x, ...) form. */ Z = sputil_extract_zeros (S, cm) ; } /* drop explicit zeros from S */ ndropped = sputil_drop_zeros (S) ; /* if entries dropped, set nzmax(S) to nnz(S), unless nzmax specified */ if (ndropped > 0 && nargin <= 5 && S != NULL) { cholmod_l_reallocate_sparse (cholmod_l_nnz (S, cm), S, cm) ; } if (s_is_sparse) { mxDestroyArray (s_array) ; } } /* ---------------------------------------------------------------------- */ /* convert S into a MATLAB sparse matrix */ /* ---------------------------------------------------------------------- */ k = 0 ; if (S != NULL) { #ifndef MATLAB6p1_OR_EARLIER /* MATLAB 6.1 or earlier do not have mxLOGICAL_CLASS */ if (mxIsLogical (pargin [2])) { /* copy S into a MATLAB sparse logical matrix */ mxLogical *s_logical ; pargout [0] = mxCreateSparseLogicalMatrix (0, 0, 0) ; s_logical = cholmod_l_malloc (S->nzmax, sizeof (mxLogical), cm) ; for (k = 0 ; k < (Int) (S->nzmax) ; k++) { s_logical [k] = 1 ; } mxFree (mxGetData (pargout [0])) ; mxSetData (pargout [0], s_logical) ; mexMakeMemoryPersistent (s_logical) ; k++ ; } else #endif if (mxIsComplex (pargin [2])) { /* copy S into a MATLAB sparse complex double matrix */ pargout [0] = mxCreateSparse (0, 0, 0, mxCOMPLEX) ; mxFree (mxGetPr (pargout [0])) ; mxFree (mxGetPi (pargout [0])) ; mxSetPr (pargout [0], S->x) ; mxSetPi (pargout [0], S->z) ; mexMakeMemoryPersistent (S->x) ; mexMakeMemoryPersistent (S->z) ; k += 2 ; S->x = NULL ; S->z = NULL ; } else { /* copy S into a MATLAB sparse real double matrix */ pargout [0] = mxCreateSparse (0, 0, 0, mxREAL) ; mxSetPr (pargout [0], S->x) ; mexMakeMemoryPersistent (S->x) ; k++ ; S->x = NULL ; } mxSetM (pargout [0], S->nrow) ; mxSetN (pargout [0], S->ncol) ; mxSetNzmax (pargout [0], S->nzmax) ; mxFree (mxGetJc (pargout [0])) ; mxFree (mxGetIr (pargout [0])) ; mxSetJc (pargout [0], S->p) ; mxSetIr (pargout [0], S->i) ; mexMakeMemoryPersistent (S->p) ; mexMakeMemoryPersistent (S->i) ; k += 2 ; /* free cholmod_sparse S, except for what has been given to MATLAB */ S->p = NULL ; S->i = NULL ; cholmod_l_free_sparse (&S, cm) ; } /* ---------------------------------------------------------------------- */ /* return Z to MATLAB, if requested */ /* ---------------------------------------------------------------------- */ if (nargout > 1) { if (Z == NULL) { /* Z not computed; return an empty matrix */ Z = cholmod_l_spzeros (nrow, ncol, 0, CHOLMOD_REAL, cm) ; } pargout [1] = sputil_put_sparse (&Z, cm) ; } cholmod_l_finish (cm) ; cholmod_l_print_common (" ", cm) ; /* if (cm->malloc_count != k) mexErrMsgTxt ("!") ; */ } SuiteSparse/CHOLMOD/MATLAB/cholmod_matlab.h0000644001170100242450000001177010634300157017117 0ustar davisfac/* ========================================================================== */ /* === MATLAB/cholmod_matlab.h ============================================== */ /* ========================================================================== */ /* Shared prototypes and definitions for CHOLMOD mexFunctions */ #include "UFconfig.h" #ifndef DLONG #define DLONG #endif #define Int UF_long #define Int_max UF_long_max /* Ensure cholmod_read_* and cholmod_write_* work for large files. This * requires MATLAB 7.0 or later. If you are using MATLAB 6.5 or earlier, * you must delete the following line, or compile CHOLMOD with -DNLARGEFILE */ #include "cholmod_io64.h" #ifndef NPARTITION #include "metis.h" #endif #undef ASSERT #include "cholmod.h" #include #include #include #include #include "mex.h" #define EMPTY (-1) #define TRUE 1 #define FALSE 0 #define MAX(a,b) (((a) > (b)) ? (a) : (b)) #define LEN 16 #define ERROR_TOO_SMALL 0 #define ERROR_HUGE 1 #define ERROR_NOT_INTEGER 2 #define ERROR_TOO_LARGE 3 #define ERROR_USAGE 4 #define ERROR_LENGTH 5 #define ERROR_INVALID_TYPE 6 #define ERROR_OUT_OF_MEMORY 7 /* getting spumoni at run-time takes way too much time */ #ifndef SPUMONI #define SPUMONI 0 #endif /* closed by sputil_error_handler if not NULL */ extern FILE *sputil_file ; void sputil_error /* reports an error */ ( Int error, /* kind of error */ Int is_index /* TRUE if a matrix index, FALSE if a matrix dimension */ ) ; Int sputil_double_to_int /* returns integer value of x */ ( double x, /* double value to convert */ Int is_index, /* TRUE if a matrix index, FALSE if a matrix dimension */ Int n /* if a matrix index, x cannot exceed this dimension */ ) ; double sputil_get_double (const mxArray *arg) ; /* like mxGetScalar */ Int sputil_get_integer /* returns the integer value of a MATLAB argument */ ( const mxArray *arg, /* MATLAB argument to convert */ Int is_index, /* TRUE if an index, FALSE if a matrix dimension */ Int n /* maximum value, if an index */ ) ; Int sputil_copy_ij /* returns the dimension, n */ ( Int is_scalar, /* TRUE if argument is a scalar, FALSE otherwise */ Int scalar, /* scalar value of the argument */ void *vector, /* vector value of the argument */ mxClassID category, /* type of vector */ Int nz, /* length of output vector I */ Int n, /* maximum dimension, EMPTY if not yet known */ Int *I /* vector of length nz to copy into */ ) ; /* converts a triplet matrix to a compressed-column matrix */ cholmod_sparse *sputil_triplet_to_sparse ( Int nrow, Int ncol, Int nz, Int nzmax, Int i_is_scalar, Int i, void *i_vector, mxClassID i_class, Int j_is_scalar, Int j, void *j_vector, mxClassID j_class, Int s_is_scalar, double x, double z, void *x_vector, double *z_vector, mxClassID s_class, Int s_complex, cholmod_common *cm ) ; mxArray *sputil_copy_sparse (const mxArray *A) ; /* copy a sparse matrix */ Int sputil_nelements (const mxArray *arg) ; /* like mxGetNumberOfElements */ void sputil_sparse /* top-level wrapper for "sparse" function */ ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) ; void sputil_error_handler (int status, char *file, int line, char *message) ; void sputil_config (Int spumoni, cholmod_common *cm) ; mxArray *sputil_sparse_to_dense (const mxArray *S) ; cholmod_sparse *sputil_get_sparse ( const mxArray *Amatlab, /* MATLAB version of the matrix */ cholmod_sparse *A, /* CHOLMOD version of the matrix */ double *dummy, /* a pointer to a valid scalar double */ Int stype /* -1: lower, 0: unsymmetric, 1: upper */ ) ; cholmod_dense *sputil_get_dense ( const mxArray *Amatlab, /* MATLAB version of the matrix */ cholmod_dense *A, /* CHOLMOD version of the matrix */ double *dummy /* a pointer to a valid scalar double */ ) ; mxArray *sputil_put_dense /* returns the MATLAB version */ ( cholmod_dense **Ahandle, /* CHOLMOD version of the matrix */ cholmod_common *cm ) ; mxArray *sputil_put_sparse ( cholmod_sparse **Ahandle, /* CHOLMOD version of the matrix */ cholmod_common *cm ) ; Int sputil_drop_zeros /* drop numerical zeros from a CHOLMOD matrix */ ( cholmod_sparse *S ) ; mxArray *sputil_put_int /* copy Int vector to mxArray */ ( Int *P, /* vector to convert */ Int n, /* length of P */ Int one_based /* 1 if convert from 0-based to 1-based, 0 otherwise */ ) ; mxArray *sputil_dense_to_sparse (const mxArray *arg) ; void sputil_check_ijvector (const mxArray *arg) ; void sputil_trim ( cholmod_sparse *S, Int k, cholmod_common *cm ) ; cholmod_sparse *sputil_get_sparse_pattern ( const mxArray *Amatlab, /* MATLAB version of the matrix */ cholmod_sparse *Ashallow, /* shallow CHOLMOD version of the matrix */ double *dummy, /* a pointer to a valid scalar double */ cholmod_common *cm ) ; cholmod_sparse *sputil_extract_zeros ( cholmod_sparse *A, cholmod_common *cm ) ; SuiteSparse/CHOLMOD/MATLAB/septree.c0000644001170100242450000001072710616447344015627 0ustar davisfac/* ========================================================================== */ /* === CHOLMOD/MATLAB/septree mexFunction =================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * MATLAB(tm) is a Trademark of The MathWorks, Inc. * METIS (Copyright 1998, G. Karypis) is not distributed with CHOLMOD. * -------------------------------------------------------------------------- */ /* Prune a separator tree. * * Usage: * * [cp_new, cmember_new] = septree (cp, cmember, nd_oksep, nd_small) ; * * cp and cmember are outputs of the nesdis mexFunction. * * cmember(i)=c means that node i is in component * c, where c is in the range of 1 to the number of components. length(cp) is * the number of components found. cp is the separator tree; cp(c) is the * parent of component c, or 0 if c is a root. There can be anywhere from * 1 to n components, where n is the number of rows of A, A*A', or A'*A. * * On output, cp_new and cmember_new are the new tree and graph-to-tree mapping. * A subtree is collapsed into a single node if the number of nodes in the * separator is > nd_oksep times the total size of the subtree, or if the * subtree has fewer than nd_small nodes. * * Requires the CHOLMOD Partition Module. */ #include "cholmod_matlab.h" void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { #ifndef NPARTITION double *p ; Int *Cmember, *CParent ; cholmod_common Common, *cm ; double nd_oksep ; Int nd_small, nc, n, c, j, nc_new ; /* ---------------------------------------------------------------------- */ /* start CHOLMOD and set defaults */ /* ---------------------------------------------------------------------- */ cm = &Common ; cholmod_l_start (cm) ; sputil_config (SPUMONI, cm) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if (nargout > 2 || nargin != 4) { mexErrMsgTxt ("Usage: [cp_new, cmember_new] = " "septree (cp, cmember, nd_oksep, nd_small)") ; } nc = mxGetNumberOfElements (pargin [0]) ; n = mxGetNumberOfElements (pargin [1]) ; nd_oksep = mxGetScalar (pargin [2]) ; nd_small = mxGetScalar (pargin [3]) ; if (n < nc) { mexErrMsgTxt ("invalid inputs") ; } CParent = cholmod_l_malloc (nc, sizeof (Int), cm) ; Cmember = cholmod_l_malloc (n, sizeof (Int), cm) ; p = mxGetPr (pargin [0]) ; for (c = 0 ; c < nc ; c++) { CParent [c] = p [c] - 1 ; if (CParent [c] < EMPTY || CParent [c] > nc) { mexErrMsgTxt ("cp invalid") ; } } p = mxGetPr (pargin [1]) ; for (j = 0 ; j < n ; j++) { Cmember [j] = p [j] - 1 ; if (Cmember [j] < 0 || Cmember [j] > nc) { mexErrMsgTxt ("cmember invalid") ; } } /* ---------------------------------------------------------------------- */ /* collapse the tree */ /* ---------------------------------------------------------------------- */ nc_new = cholmod_l_collapse_septree (n, nc, nd_oksep, nd_small, CParent, Cmember, cm) ; if (nc_new < 0) { mexErrMsgTxt ("septree failed") ; return ; } /* ---------------------------------------------------------------------- */ /* return CParent and Cmember */ /* ---------------------------------------------------------------------- */ pargout [0] = sputil_put_int (CParent, nc_new, 1) ; if (nargout > 1) { pargout [1] = sputil_put_int (Cmember, n, 1) ; } /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ cholmod_l_free (nc, sizeof (Int), CParent, cm) ; cholmod_l_free (n, sizeof (Int), Cmember, cm) ; cholmod_l_finish (cm) ; cholmod_l_print_common (" ", cm) ; /* if (cm->malloc_count != 0) mexErrMsgTxt ("!") ; */ #else mexErrMsgTxt ("CHOLMOD Partition Module not installed\n") ; #endif } SuiteSparse/CHOLMOD/MATLAB/septree.m0000644001170100242450000000206710620371036015624 0ustar davisfacfunction [cp_new, cmember_new] = septree (cp, cmember, nd_oksep, nd_small) %#ok %SEPTREE prune a separator tree. % % Example: % [cp_new, cmember_new] = septree (cp, cmember, nd_oksep, nd_small) ; % % cp and cmember are outputs of nesdis. cmember(i)=c means that node i is in % component c, where c is in the range of 1 to the number of components. % length(cp) is the number of components found. cp is the separator tree; % cp(c) is the parent of component c, or 0 if c is a root. There can be % anywhere from 1 to n components, where n is the number of rows of A, A*A', % or A'*A. % % On output, cp_new and cmember_new are the new tree and graph-to-tree % mapping. A subtree is collapsed into a single node if the number of nodes % in the separator is > nd_oksep times the total size of the subtree, or if % the subtree has fewer than nd_small nodes. % % Requires the CHOLMOD Partition Module. % % See also NESDIS. % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse error ('septree mexFunction not found') ; SuiteSparse/CHOLMOD/MATLAB/chol2.c0000644001170100242450000001261210621027617015153 0ustar davisfac/* ========================================================================== */ /* === CHOLMOD/MATLAB/chol2 mexFunction ===================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * MATLAB(tm) is a Trademark of The MathWorks, Inc. * -------------------------------------------------------------------------- */ /* Numeric R'R factorization. Note that LL' and LDL' are faster than R'R * and use less memory. The R'R factorization methods use triu(A), just like * MATLAB's built-in chol. * * R = chol2 (A) same as R = chol (A), just faster * [R,p] = chol2 (A) save as [R,p] = chol(A), just faster * [R,p,q] = chol2 (A) factorizes A(q,q) into R'*R * * A must be sparse. It can be complex or real. * * R is returned with no explicit zero entries. This means it might not be * chordal, and R cannot be passed back to CHOLMOD for an update/downdate or * for a fast simplicial solve. spones (R) will be equal to the R returned * by symbfact2 if no numerically zero entries are dropped, or a subset * otherwise. */ #include "cholmod_matlab.h" void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double dummy = 0, *px ; cholmod_sparse Amatrix, *A, *Lsparse, *R ; cholmod_factor *L ; cholmod_common Common, *cm ; Int n, minor ; /* ---------------------------------------------------------------------- */ /* start CHOLMOD and set parameters */ /* ---------------------------------------------------------------------- */ cm = &Common ; cholmod_l_start (cm) ; sputil_config (SPUMONI, cm) ; /* convert to packed LL' when done */ cm->final_asis = FALSE ; cm->final_super = FALSE ; cm->final_ll = TRUE ; cm->final_pack = TRUE ; cm->final_monotonic = TRUE ; /* no need to prune entries due to relaxed supernodal amalgamation, since * zeros are dropped with sputil_drop_zeros instead */ cm->final_resymbol = FALSE ; cm->quick_return_if_not_posdef = (nargout < 2) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if (nargin != 1 || nargout > 3) { mexErrMsgTxt ("usage: [R,p,q] = chol2 (A)") ; } n = mxGetN (pargin [0]) ; if (!mxIsSparse (pargin [0]) || n != mxGetM (pargin [0])) { mexErrMsgTxt ("A must be square and sparse") ; } /* get input sparse matrix A. Use triu(A) only */ A = sputil_get_sparse (pargin [0], &Amatrix, &dummy, 1) ; /* use natural ordering if no q output parameter */ if (nargout < 3) { cm->nmethods = 1 ; cm->method [0].ordering = CHOLMOD_NATURAL ; cm->postorder = FALSE ; } /* ---------------------------------------------------------------------- */ /* analyze and factorize */ /* ---------------------------------------------------------------------- */ L = cholmod_l_analyze (A, cm) ; cholmod_l_factorize (A, L, cm) ; if (nargout < 2 && cm->status != CHOLMOD_OK) { mexErrMsgTxt ("matrix is not positive definite") ; } /* ---------------------------------------------------------------------- */ /* convert L to a sparse matrix */ /* ---------------------------------------------------------------------- */ /* the conversion sets L->minor back to n, so get a copy of it first */ minor = L->minor ; Lsparse = cholmod_l_factor_to_sparse (L, cm) ; if (Lsparse->xtype == CHOLMOD_COMPLEX) { /* convert Lsparse from complex to zomplex */ cholmod_l_sparse_xtype (CHOLMOD_ZOMPLEX, Lsparse, cm) ; } if (minor < n) { /* remove columns minor to n-1 from Lsparse */ sputil_trim (Lsparse, minor, cm) ; } /* drop zeros from Lsparse */ sputil_drop_zeros (Lsparse) ; /* Lsparse is lower triangular; conjugate transpose to get R */ R = cholmod_l_transpose (Lsparse, 2, cm) ; cholmod_l_free_sparse (&Lsparse, cm) ; /* ---------------------------------------------------------------------- */ /* return results to MATLAB */ /* ---------------------------------------------------------------------- */ /* return R */ pargout [0] = sputil_put_sparse (&R, cm) ; /* return minor (translate to MATLAB convention) */ if (nargout > 1) { pargout [1] = mxCreateDoubleMatrix (1, 1, mxREAL) ; px = mxGetPr (pargout [1]) ; px [0] = ((minor == n) ? 0 : (minor+1)) ; } /* return permutation */ if (nargout > 2) { pargout [2] = sputil_put_int (L->Perm, n, 1) ; } /* ---------------------------------------------------------------------- */ /* free workspace and the CHOLMOD L, except for what is copied to MATLAB */ /* ---------------------------------------------------------------------- */ cholmod_l_free_factor (&L, cm) ; cholmod_l_finish (cm) ; cholmod_l_print_common (" ", cm) ; /* if (cm->malloc_count != (3 + mxIsComplex (pargout[0]))) mexErrMsgTxt ("!") ; */ } SuiteSparse/CHOLMOD/MATLAB/chol2.m0000644001170100242450000000146610620370724015171 0ustar davisfacfunction [R,p,q] = chol2 (A) %#ok %CHOL2 sparse Cholesky factorization, A=R'R. % Note that A=L*L' (LCHOL) and A=L*D*L' (LDLCHOL) factorizations are faster % than R'*R (CHOL2 and CHOL) and use less memory. The LL' and LDL' % factorization methods use tril(A). This method uses triu(A), just like % the built-in CHOL. % % Example: % R = chol2 (A) same as R = chol (A), just faster % [R,p] = chol2 (A) save as [R,p] = chol(A), just faster % [R,p,q] = chol2 (A) factorizes A(q,q) into R'*R, where q is % a fill-reducing ordering % % A must be sparse. % % See also LCHOL, LDLCHOL, CHOL, LDLUPDATE. % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse error ('chol2 mexFunction not found') ; SuiteSparse/CHOLMOD/MATLAB/cholmod_install.m0000644001170100242450000000414210620371142017322 0ustar davisfacfunction cholmod_install (metis_path) %CHOLMOD_INSTALL compile and install CHOLMOD, AMD, COLAMD, CCOLAMD, CAMD % % Example: % cholmod_install % compiles using ../../metis-4.0 % cholmod_install ('/my/metis') % using non-default path to METIS % cholmod_install ('no metis') % do not use METIS at all % % CHOLMOD relies on AMD and COLAMD, for its ordering options, and can % optionally use CCOLAMD, CAMD, and METIS as well. By default, CCOLAMD, CAMD, % and METIS are used. METIS is assumed to be in the ../../metis-4.0 directory. % % See http://www-users.cs.umn.edu/~karypis/metis for a copy of METIS 4.0.1. % % You can only use cholmod_install while in the CHOLMOD/MATLAB directory. % % See also analyze, bisect, chol2, cholmod2, etree2, lchol, ldlchol, ldlsolve, % ldlupdate, metis, spsym, nesdis, septree, resymbol, sdmult, sparse2, % symbfact2, mread, mwrite, amd2, colamd2, camd, ccolamd % Copyright 2006-2007, Timothy A. Davis if (nargin < 1) metis_path = '../../metis-4.0' ; end % compile CHOLMOD and add to the path cholmod_make (metis_path) ; cholmod_path = pwd ; addpath (cholmod_path) fprintf ('\nNow compiling the AMD, COLAMD, CCOLAMD, and CAMD mexFunctions:\n') ; % compile AMD and add to the path cd ../../AMD/MATLAB amd_make amd_path = pwd ; addpath (amd_path) % compile COLAMD and add to the path cd ../../COLAMD/MATLAB colamd_make colamd_path = pwd ; addpath (colamd_path) % compile CCOLAMD and add to the path cd ../../CCOLAMD/MATLAB ccolamd_make ccolamd_path = pwd ; addpath (ccolamd_path) % compile CAMD and add to the path cd ../../CAMD/MATLAB camd_make camd_path = pwd ; addpath (camd_path) cd (cholmod_path) fprintf ('\nThe following paths have been added. You may wish to add them\n') ; fprintf ('permanently, using the MATLAB pathtool command.\n') ; fprintf ('%s\n', cholmod_path) ; fprintf ('%s\n', amd_path) ; fprintf ('%s\n', colamd_path) ; fprintf ('%s\n', ccolamd_path) ; fprintf ('%s\n', camd_path) ; fprintf ('\nTo try your new mexFunctions, cut-and-paste this command:\n') ; fprintf ('amd_demo, colamd_demo, ccolamd_demo, camd_demo, graph_demo, cholmod_demo\n') ; SuiteSparse/CHOLMOD/MATLAB/cholmod2.c0000644001170100242450000002014510674023661015656 0ustar davisfac/* ========================================================================== */ /* === CHOLMOD/MATLAB/cholmod mexFunction =================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * MATLAB(tm) is a Trademark of The MathWorks, Inc. * -------------------------------------------------------------------------- */ /* Supernodal sparse Cholesky backslash, x = A\b. Factorizes PAP' in LL' then * solves a sparse linear system. Uses the diagonal and upper triangular part * of A only. A must be sparse. b can be sparse or dense. * * Usage: * * x = cholmod2 (A, b) * [x stats] = cholmod2 (A, b, ordering) % a scalar: 0,-1,-2, or -3 * [x stats] = cholmod2 (A, b, p) % a permutation vector * * The 3rd argument select the ordering method to use. If not present or -1, * the default ordering strategy is used (AMD, and then try METIS if AMD finds * an ordering with high fill-in, and use the best method tried). * * Other options for the ordering parameter: * * 0 natural (no etree postordering) * -1 use CHOLMOD's default ordering strategy (AMD, then try METIS) * -2 AMD, and then try NESDIS (not METIS) if AMD has high fill-in * -3 use AMD only * -4 use METIS only * -5 use NESDIS only * -6 natural, but with etree postordering * p user permutation (vector of size n, with a permutation of 1:n) * * stats(1) estimate of the reciprocal of the condition number * stats(2) ordering used: * 0: natural, 1: given, 2:amd, 3:metis, 4:nesdis, 5:colamd, * 6: natural but postordered. * stats(3) nnz(L) * stats(4) flop count in Cholesky factorization. Excludes solution * of upper/lower triangular systems, which can be easily * computed from stats(3) (roughly 4*nnz(L)*size(b,2)). * stats(5) memory usage in MB. */ #include "cholmod_matlab.h" void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { double dummy = 0, rcond, *p ; cholmod_sparse Amatrix, Bspmatrix, *A, *Bs, *Xs ; cholmod_dense Bmatrix, *X, *B ; cholmod_factor *L ; cholmod_common Common, *cm ; Int n, B_is_sparse, ordering, k, *Perm ; /* ---------------------------------------------------------------------- */ /* start CHOLMOD and set parameters */ /* ---------------------------------------------------------------------- */ cm = &Common ; cholmod_l_start (cm) ; sputil_config (SPUMONI, cm) ; /* There is no supernodal LDL'. If cm->final_ll = FALSE (the default), then * this mexFunction will use a simplicial LDL' when flops/lnz < 40, and a * supernodal LL' otherwise. This may give suprising results to the MATLAB * user, so always perform an LL' factorization by setting cm->final_ll * to TRUE. */ cm->final_ll = TRUE ; cm->quick_return_if_not_posdef = TRUE ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if (nargout > 2 || nargin < 2 || nargin > 3) { mexErrMsgTxt ("usage: [x,rcond] = cholmod2 (A,b,ordering)") ; } n = mxGetM (pargin [0]) ; if (!mxIsSparse (pargin [0]) || (n != mxGetN (pargin [0]))) { mexErrMsgTxt ("A must be square and sparse") ; } if (n != mxGetM (pargin [1])) { mexErrMsgTxt ("# of rows of A and B must match") ; } /* get sparse matrix A. Use triu(A) only. */ A = sputil_get_sparse (pargin [0], &Amatrix, &dummy, 1) ; /* get sparse or dense matrix B */ B = NULL ; Bs = NULL ; B_is_sparse = mxIsSparse (pargin [1]) ; if (B_is_sparse) { /* get sparse matrix B (unsymmetric) */ Bs = sputil_get_sparse (pargin [1], &Bspmatrix, &dummy, 0) ; } else { /* get dense matrix B */ B = sputil_get_dense (pargin [1], &Bmatrix, &dummy) ; } /* get the ordering option */ if (nargin < 3) { /* use default ordering */ ordering = -1 ; } else { /* use a non-default option */ ordering = mxGetScalar (pargin [2]) ; } p = NULL ; Perm = NULL ; if (ordering == 0) { /* natural ordering */ cm->nmethods = 1 ; cm->method [0].ordering = CHOLMOD_NATURAL ; cm->postorder = FALSE ; } else if (ordering == -1) { /* default strategy ... nothing to change */ } else if (ordering == -2) { /* default strategy, but with NESDIS in place of METIS */ cm->default_nesdis = TRUE ; } else if (ordering == -3) { /* use AMD only */ cm->nmethods = 1 ; cm->method [0].ordering = CHOLMOD_AMD ; cm->postorder = TRUE ; } else if (ordering == -4) { /* use METIS only */ cm->nmethods = 1 ; cm->method [0].ordering = CHOLMOD_METIS ; cm->postorder = TRUE ; } else if (ordering == -5) { /* use NESDIS only */ cm->nmethods = 1 ; cm->method [0].ordering = CHOLMOD_NESDIS ; cm->postorder = TRUE ; } else if (ordering == -6) { /* natural ordering, but with etree postordering */ cm->nmethods = 1 ; cm->method [0].ordering = CHOLMOD_NATURAL ; cm->postorder = TRUE ; } else if (ordering == -7) { /* always try both AMD and METIS, and pick the best */ cm->nmethods = 2 ; cm->method [0].ordering = CHOLMOD_AMD ; cm->method [1].ordering = CHOLMOD_METIS ; cm->postorder = TRUE ; } else if (ordering >= 1) { /* assume the 3rd argument is a user-provided permutation of 1:n */ if (mxGetNumberOfElements (pargin [2]) != n) { mexErrMsgTxt ("invalid input permutation") ; } /* copy from double to integer, and convert to 0-based */ p = mxGetPr (pargin [2]) ; Perm = cholmod_l_malloc (n, sizeof (Int), cm) ; for (k = 0 ; k < n ; k++) { Perm [k] = p [k] - 1 ; } /* check the permutation */ if (!cholmod_l_check_perm (Perm, n, n, cm)) { mexErrMsgTxt ("invalid input permutation") ; } /* use only the given permutation */ cm->nmethods = 1 ; cm->method [0].ordering = CHOLMOD_GIVEN ; cm->postorder = FALSE ; } else { mexErrMsgTxt ("invalid ordering option") ; } /* ---------------------------------------------------------------------- */ /* analyze and factorize */ /* ---------------------------------------------------------------------- */ L = cholmod_l_analyze_p (A, Perm, NULL, 0, cm) ; cholmod_l_free (n, sizeof (Int), Perm, cm) ; cholmod_l_factorize (A, L, cm) ; rcond = cholmod_l_rcond (L, cm) ; if (rcond == 0) { mexWarnMsgTxt ("Matrix is indefinite or singular to working precision"); } else if (rcond < DBL_EPSILON) { mexWarnMsgTxt ("Matrix is close to singular or badly scaled.") ; mexPrintf (" Results may be inaccurate. RCOND = %g.\n", rcond) ; } /* ---------------------------------------------------------------------- */ /* solve and return solution to MATLAB */ /* ---------------------------------------------------------------------- */ if (B_is_sparse) { /* solve AX=B with sparse X and B; return sparse X to MATLAB */ Xs = cholmod_l_spsolve (CHOLMOD_A, L, Bs, cm) ; pargout [0] = sputil_put_sparse (&Xs, cm) ; } else { /* solve AX=B with dense X and B; return dense X to MATLAB */ X = cholmod_l_solve (CHOLMOD_A, L, B, cm) ; pargout [0] = sputil_put_dense (&X, cm) ; } /* return statistics, if requested */ if (nargout > 1) { pargout [1] = mxCreateDoubleMatrix (1, 5, mxREAL) ; p = mxGetPr (pargout [1]) ; p [0] = rcond ; p [1] = L->ordering ; p [2] = cm->lnz ; p [3] = cm->fl ; p [4] = cm->memory_usage / 1048576. ; } cholmod_l_free_factor (&L, cm) ; cholmod_l_finish (cm) ; cholmod_l_print_common (" ", cm) ; /* if (cm->malloc_count != (mxIsComplex (pargout [0]) + (mxIsSparse (pargout[0]) ? 3:1))) mexErrMsgTxt ("memory leak!") ; */ } SuiteSparse/CHOLMOD/MATLAB/cholmod2.m0000644001170100242450000000342510620370733015666 0ustar davisfacfunction [x,stats] = cholmod2 (A, b, ordering) %#ok %CHOLMOD2 supernodal sparse Cholesky backslash, x = A\b % % Example: % x = cholmod2 (A,b) % % Computes the LL' factorization of A(p,p), where p is a fill-reducing % ordering, then solves a sparse linear system Ax=b. A must be sparse, % symmetric, and positive definite). Uses only the upper triangular part % of A. A second output, [x,stats]=cholmod2(A,b), returns statistics: % % stats(1) estimate of the reciprocal of the condition number % stats(2) ordering used: % 0: natural, 1: given, 2:amd, 3:metis, 4:nesdis, % 5:colamd, 6: natural but postordered. % stats(3) nnz(L) % stats(4) flop count in Cholesky factorization. Excludes solution % of upper/lower triangular systems, which can be easily % computed from stats(3) (roughly 4*nnz(L)*size(b,2)). % stats(5) memory usage in MB. % % The 3rd argument select the ordering method to use. If not present or -1, % the default ordering strategy is used (AMD, and then try METIS if AMD finds % an ordering with high fill-in, and use the best method tried). % % Other options for the ordering parameter: % % 0 natural (no etree postordering) % -1 use CHOLMOD's default ordering strategy (AMD, then try METIS) % -2 AMD, and then try NESDIS (not METIS) if AMD has high fill-in % -3 use AMD only % -4 use METIS only % -5 use NESDIS only % -6 natural, but with etree postordering % p user permutation (vector of size n, with a permutation of 1:n) % % See also CHOL, MLDIVIDE. % Copyright 2006-2007, Timothy A. Davis % http://www.cise.ufl.edu/research/sparse error ('cholmod2 mexFunction not found\n') ; SuiteSparse/CHOLMOD/Supernodal/0000755001170100242450000000000010677540316015161 5ustar davisfacSuiteSparse/CHOLMOD/Supernodal/cholmod_super_solve.c0000644001170100242450000001601410616475366021407 0ustar davisfac/* ========================================================================== */ /* === Supernodal/cholmod_super_solve ======================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Supernodal Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Supernodal Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Solve Lx=b or L'x=b for a supernodal factorization. These routines do not * apply the permutation L->Perm. See cholmod_solve for a more general * interface that performs that operation. */ #ifndef NSUPERNODAL #include "cholmod_internal.h" #include "cholmod_supernodal.h" /* ========================================================================== */ /* === TEMPLATE ============================================================= */ /* ========================================================================== */ #define REAL #include "t_cholmod_super_solve.c" #define COMPLEX #include "t_cholmod_super_solve.c" /* ========================================================================== */ /* === cholmod_super_lsolve ================================================= */ /* ========================================================================== */ /* Solve Lx=b where x and b are of size n-by-nrhs. b is overwritten by the * solution x. On input, b is stored in col-major order with leading dimension * of d, and on output x is stored in the same manner. * * The contents of the workspace E are undefined on both input and output. * * workspace: none */ int CHOLMOD(super_lsolve) /* TRUE if OK, FALSE if BLAS overflow occured */ ( /* ---- input ---- */ cholmod_factor *L, /* factor to use for the forward solve */ /* ---- output ---- */ cholmod_dense *X, /* b on input, solution to Lx=b on output */ /* ---- workspace ---- */ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */ /* --------------- */ cholmod_common *Common ) { int blas_ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_NULL (X, FALSE) ; RETURN_IF_NULL (E, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (E, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ; if (L->xtype != X->xtype) { ERROR (CHOLMOD_INVALID, "L and X must have the same xtype") ; return (FALSE) ; } if (L->xtype != E->xtype) { ERROR (CHOLMOD_INVALID, "L and E must have the same xtype") ; return (FALSE) ; } if (X->d < X->nrow || L->n != X->nrow) { ERROR (CHOLMOD_INVALID, "X and L dimensions must match") ; return (FALSE) ; } if (E->nzmax < X->ncol * (L->maxesize)) { ERROR (CHOLMOD_INVALID, "workspace E not large enough") ; return (FALSE) ; } if (!(L->is_ll) || !(L->is_super)) { ERROR (CHOLMOD_INVALID, "L not supernodal") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; ASSERT (IMPLIES (L->n == 0, L->nsuper == 0)) ; if (L->n == 0 || X->ncol == 0) { /* nothing to do */ return (TRUE) ; } /* ---------------------------------------------------------------------- */ /* solve Lx=b using template routine */ /* ---------------------------------------------------------------------- */ switch (L->xtype) { case CHOLMOD_REAL: blas_ok = r_cholmod_super_lsolve (L, X, E, Common) ; break ; case CHOLMOD_COMPLEX: blas_ok = c_cholmod_super_lsolve (L, X, E, Common) ; break ; } if (CHECK_BLAS_INT && !blas_ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large for the BLAS") ; } return (blas_ok) ; } /* ========================================================================== */ /* === cholmod_super_ltsolve ================================================ */ /* ========================================================================== */ /* Solve L'x=b where x and b are of size n-by-nrhs. b is overwritten by the * solution x. On input, b is stored in col-major order with leading dimension * of d, and on output x is stored in the same manner. * * The contents of the workspace E are undefined on both input and output. * * workspace: none */ int CHOLMOD(super_ltsolve) /* TRUE if OK, FALSE if BLAS overflow occured */ ( /* ---- input ---- */ cholmod_factor *L, /* factor to use for the backsolve */ /* ---- output ---- */ cholmod_dense *X, /* b on input, solution to L'x=b on output */ /* ---- workspace ---- */ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */ /* --------------- */ cholmod_common *Common ) { int blas_ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_NULL (X, FALSE) ; RETURN_IF_NULL (E, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (E, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ; if (L->xtype != X->xtype) { ERROR (CHOLMOD_INVALID, "L and X must have the same xtype") ; return (FALSE) ; } if (L->xtype != E->xtype) { ERROR (CHOLMOD_INVALID, "L and E must have the same xtype") ; return (FALSE) ; } if (X->d < X->nrow || L->n != X->nrow) { ERROR (CHOLMOD_INVALID, "X and L dimensions must match") ; return (FALSE) ; } if (E->nzmax < X->ncol * (L->maxesize)) { ERROR (CHOLMOD_INVALID, "workspace E not large enough") ; return (FALSE) ; } if (!(L->is_ll) || !(L->is_super)) { ERROR (CHOLMOD_INVALID, "L not supernodal") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; ASSERT (IMPLIES (L->n == 0, L->nsuper == 0)) ; if (L->n == 0 || X->ncol == 0) { /* nothing to do */ return (TRUE) ; } /* ---------------------------------------------------------------------- */ /* solve Lx=b using template routine */ /* ---------------------------------------------------------------------- */ switch (L->xtype) { case CHOLMOD_REAL: blas_ok = r_cholmod_super_ltsolve (L, X, E, Common) ; break ; case CHOLMOD_COMPLEX: blas_ok = c_cholmod_super_ltsolve (L, X, E, Common) ; break ; } if (CHECK_BLAS_INT && !blas_ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large for the BLAS") ; } return (blas_ok) ; } #endif SuiteSparse/CHOLMOD/Supernodal/t_cholmod_super_solve.c0000644001170100242450000002627710540000020021705 0ustar davisfac/* ========================================================================== */ /* === Supernodal/t_cholmod_super_solve ===================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Supernodal Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Supernodal Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Template routine for cholmod_super_solve. Supports real or complex L. */ #include "cholmod_template.h" static int TEMPLATE (cholmod_super_lsolve) ( /* ---- input ---- */ cholmod_factor *L, /* factor to use for the forward solve */ /* ---- output ---- */ cholmod_dense *X, /* b on input, solution to Lx=b on output */ /* ---- workspace ---- */ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */ /* --------------- */ cholmod_common *Common ) { double *Lx, *Xx, *Ex ; double minus_one [2], one [2] ; Int *Lpi, *Lpx, *Ls, *Super ; Int nsuper, k1, k2, psi, psend, psx, nsrow, nscol, ii, s, nsrow2, n, ps2, j, i, d, nrhs ; /* If integer overflow occurs in the BLAS, Common->status is set to * CHOLMOD_TOO_LARGE in the caller, and the contents of X are undefined. */ int blas_ok = TRUE ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nrhs = X->ncol ; Ex = E->x ; Xx = X->x ; n = L->n ; d = X->d ; nsuper = L->nsuper ; Lpi = L->pi ; Lpx = L->px ; Ls = L->s ; Super = L->super ; Lx = L->x ; minus_one [0] = -1.0 ; minus_one [1] = 0 ; one [0] = 1.0 ; one [1] = 0 ; /* ---------------------------------------------------------------------- */ /* solve Lx=b */ /* ---------------------------------------------------------------------- */ if (nrhs == 1) { for (s = 0 ; s < nsuper ; s++) { k1 = Super [s] ; k2 = Super [s+1] ; psi = Lpi [s] ; psend = Lpi [s+1] ; psx = Lpx [s] ; nsrow = psend - psi ; nscol = k2 - k1 ; nsrow2 = nsrow - nscol ; ps2 = psi + nscol ; ASSERT ((size_t) nsrow2 <= L->maxesize) ; /* L1 is nscol-by-nscol, lower triangular with non-unit diagonal. * L2 is nsrow2-by-nscol. L1 and L2 have leading dimension of * nsrow. x1 is nscol-by-nsrow, with leading dimension n. * E is nsrow2-by-1, with leading dimension nsrow2. */ /* gather X into E */ for (ii = 0 ; ii < nsrow2 ; ii++) { /* Ex [ii] = Xx [Ls [ps2 + ii]] ; */ ASSIGN (Ex,-,ii, Xx,-,Ls [ps2 + ii]) ; } #ifdef REAL /* solve L1*x1 (that is, x1 = L1\x1) */ BLAS_dtrsv ("L", "N", "N", nscol, /* N: L1 is nscol-by-nscol */ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */ Xx + ENTRY_SIZE*k1, 1) ; /* X, INCX: x1 */ /* E = E - L2*x1 */ BLAS_dgemv ("N", nsrow2, nscol, /* M, N: L2 is nsrow2-by-nscol */ minus_one, /* ALPHA: -1 */ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */ nsrow, Xx + ENTRY_SIZE*k1, 1, /* X, INCX: x1 */ one, /* BETA: 1 */ Ex, 1) ; /* Y, INCY: E */ #else /* solve L1*x1 (that is, x1 = L1\x1) */ BLAS_ztrsv ("L", "N", "N", nscol, /* N: L1 is nscol-by-nscol */ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */ Xx + ENTRY_SIZE*k1, 1) ; /* X, INCX: x1 */ /* E = E - L2*x1 */ BLAS_zgemv ("N", nsrow2, nscol, /* M, N: L2 is nsrow2-by-nscol */ minus_one, /* ALPHA: -1 */ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */ nsrow, Xx + ENTRY_SIZE*k1, 1, /* X, INCX: x1 */ one, /* BETA: 1 */ Ex, 1) ; /* Y, INCY: E */ #endif /* scatter E back into X */ for (ii = 0 ; ii < nsrow2 ; ii++) { /* Xx [Ls [ps2 + ii]] = Ex [ii] ; */ ASSIGN (Xx,-,Ls [ps2 + ii], Ex,-,ii) ; } } } else { for (s = 0 ; s < nsuper ; s++) { k1 = Super [s] ; k2 = Super [s+1] ; psi = Lpi [s] ; psend = Lpi [s+1] ; psx = Lpx [s] ; nsrow = psend - psi ; nscol = k2 - k1 ; nsrow2 = nsrow - nscol ; ps2 = psi + nscol ; ASSERT ((size_t) nsrow2 <= L->maxesize) ; /* E is nsrow2-by-nrhs, with leading dimension nsrow2. */ /* gather X into E */ for (ii = 0 ; ii < nsrow2 ; ii++) { i = Ls [ps2 + ii] ; for (j = 0 ; j < nrhs ; j++) { /* Ex [ii + j*nsrow2] = Xx [i + j*d] ; */ ASSIGN (Ex,-,ii+j*nsrow2, Xx,-,i+j*d) ; } } #ifdef REAL /* solve L1*x1 */ BLAS_dtrsm ("L", "L", "N", "N", nscol, nrhs, /* M, N: x1 is nscol-by-nrhs */ one, /* ALPHA: 1 */ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */ Xx + ENTRY_SIZE*k1, d) ; /* B, LDB: x1 */ /* E = E - L2*x1 */ if (nsrow2 > 0) { BLAS_dgemm ("N", "N", nsrow2, nrhs, nscol, /* M, N, K */ minus_one, /* ALPHA: -1 */ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */ nsrow, Xx + ENTRY_SIZE*k1, d, /* B, LDB: X1 */ one, /* BETA: 1 */ Ex, nsrow2) ; /* C, LDC: E */ } #else /* solve L1*x1 */ BLAS_ztrsm ("L", "L", "N", "N", nscol, nrhs, /* M, N: x1 is nscol-by-nrhs */ one, /* ALPHA: 1 */ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */ Xx + ENTRY_SIZE*k1, d) ; /* B, LDB: x1 */ /* E = E - L2*x1 */ if (nsrow2 > 0) { BLAS_zgemm ("N", "N", nsrow2, nrhs, nscol, /* M, N, K */ minus_one, /* ALPHA: -1 */ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */ nsrow, Xx + ENTRY_SIZE*k1, d, /* B, LDB: X1 */ one, /* BETA: 1 */ Ex, nsrow2) ; /* C, LDC: E */ } #endif /* scatter E back into X */ for (ii = 0 ; ii < nsrow2 ; ii++) { i = Ls [ps2 + ii] ; for (j = 0 ; j < nrhs ; j++) { /* Xx [i + j*d] = Ex [ii + j*nsrow2] ; */ ASSIGN (Xx,-,i+j*d, Ex,-,ii+j*nsrow2) ; } } } } Common->status = CHOLMOD_OK ; return (blas_ok) ; } static int TEMPLATE (cholmod_super_ltsolve) ( /* ---- input ---- */ cholmod_factor *L, /* factor to use for the forward solve */ /* ---- output ---- */ cholmod_dense *X, /* b on input, solution to Lx=b on output */ /* ---- workspace ---- */ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */ /* --------------- */ cholmod_common *Common ) { double *Lx, *Xx, *Ex ; double minus_one [2], one [2] ; Int *Lpi, *Lpx, *Ls, *Super ; Int nsuper, k1, k2, psi, psend, psx, nsrow, nscol, ii, s, nsrow2, n, ps2, j, i, d, nrhs ; int blas_ok = TRUE ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nrhs = X->ncol ; Ex = E->x ; Xx = X->x ; n = L->n ; d = X->d ; nsuper = L->nsuper ; Lpi = L->pi ; Lpx = L->px ; Ls = L->s ; Super = L->super ; Lx = L->x ; minus_one [0] = -1.0 ; minus_one [1] = 0 ; one [0] = 1.0 ; one [1] = 0 ; /* ---------------------------------------------------------------------- */ /* solve L'x=b */ /* ---------------------------------------------------------------------- */ if (nrhs == 1) { for (s = nsuper-1 ; s >= 0 ; s--) { k1 = Super [s] ; k2 = Super [s+1] ; psi = Lpi [s] ; psend = Lpi [s+1] ; psx = Lpx [s] ; nsrow = psend - psi ; nscol = k2 - k1 ; nsrow2 = nsrow - nscol ; ps2 = psi + nscol ; ASSERT ((size_t) nsrow2 <= L->maxesize) ; /* L1 is nscol-by-nscol, lower triangular with non-unit diagonal. * L2 is nsrow2-by-nscol. L1 and L2 have leading dimension of * nsrow. x1 is nscol-by-nsrow, with leading dimension n. * E is nsrow2-by-1, with leading dimension nsrow2. */ /* gather X into E */ for (ii = 0 ; ii < nsrow2 ; ii++) { /* Ex [ii] = Xx [Ls [ps2 + ii]] ; */ ASSIGN (Ex,-,ii, Xx,-,Ls [ps2 + ii]) ; } #ifdef REAL /* x1 = x1 - L2'*E */ BLAS_dgemv ("C", nsrow2, nscol, /* M, N: L2 is nsrow2-by-nscol */ minus_one, /* ALPHA: -1 */ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */ nsrow, Ex, 1, /* X, INCX: Ex */ one, /* BETA: 1 */ Xx + ENTRY_SIZE*k1, 1) ; /* Y, INCY: x1 */ /* solve L1'*x1 */ BLAS_dtrsv ("L", "C", "N", nscol, /* N: L1 is nscol-by-nscol */ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */ Xx + ENTRY_SIZE*k1, 1) ; /* X, INCX: x1 */ #else /* x1 = x1 - L2'*E */ BLAS_zgemv ("C", nsrow2, nscol, /* M, N: L2 is nsrow2-by-nscol */ minus_one, /* ALPHA: -1 */ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */ nsrow, Ex, 1, /* X, INCX: Ex */ one, /* BETA: 1 */ Xx + ENTRY_SIZE*k1, 1) ; /* Y, INCY: x1 */ /* solve L1'*x1 */ BLAS_ztrsv ("L", "C", "N", nscol, /* N: L1 is nscol-by-nscol */ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */ Xx + ENTRY_SIZE*k1, 1) ; /* X, INCX: x1 */ #endif } } else { for (s = nsuper-1 ; s >= 0 ; s--) { k1 = Super [s] ; k2 = Super [s+1] ; psi = Lpi [s] ; psend = Lpi [s+1] ; psx = Lpx [s] ; nsrow = psend - psi ; nscol = k2 - k1 ; nsrow2 = nsrow - nscol ; ps2 = psi + nscol ; ASSERT ((size_t) nsrow2 <= L->maxesize) ; /* E is nsrow2-by-nrhs, with leading dimension nsrow2. */ /* gather X into E */ for (ii = 0 ; ii < nsrow2 ; ii++) { i = Ls [ps2 + ii] ; for (j = 0 ; j < nrhs ; j++) { /* Ex [ii + j*nsrow2] = Xx [i + j*d] ; */ ASSIGN (Ex,-,ii+j*nsrow2, Xx,-,i+j*d) ; } } #ifdef REAL /* x1 = x1 - L2'*E */ if (nsrow2 > 0) { BLAS_dgemm ("C", "N", nscol, nrhs, nsrow2, /* M, N, K */ minus_one, /* ALPHA: -1 */ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */ nsrow, Ex, nsrow2, /* B, LDB: E */ one, /* BETA: 1 */ Xx + ENTRY_SIZE*k1, d) ; /* C, LDC: x1 */ } /* solve L1'*x1 */ BLAS_dtrsm ("L", "L", "C", "N", nscol, nrhs, /* M, N: x1 is nscol-by-nrhs */ one, /* ALPHA: 1 */ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */ Xx + ENTRY_SIZE*k1, d) ; /* B, LDB: x1 */ #else /* x1 = x1 - L2'*E */ if (nsrow2 > 0) { BLAS_zgemm ("C", "N", nscol, nrhs, nsrow2, /* M, N, K */ minus_one, /* ALPHA: -1 */ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */ nsrow, Ex, nsrow2, /* B, LDB: E */ one, /* BETA: 1 */ Xx + ENTRY_SIZE*k1, d) ; /* C, LDC: x1 */ } /* solve L1'*x1 */ BLAS_ztrsm ("L", "L", "C", "N", nscol, nrhs, /* M, N: x1 is nscol-by-nrhs */ one, /* ALPHA: 1 */ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */ Xx + ENTRY_SIZE*k1, d) ; /* B, LDB: x1 */ #endif } } Common->status = CHOLMOD_OK ; return (blas_ok) ; } #undef PATTERN #undef REAL #undef COMPLEX #undef ZOMPLEX SuiteSparse/CHOLMOD/Supernodal/License.txt0000644001170100242450000000204610540000306017261 0ustar davisfacCHOLMOD/Supernodal Module. Copyright (C) 2005-2006, Timothy A. Davis CHOLMOD is also available under other licenses; contact authors for details. http://www.cise.ufl.edu/research/sparse Note that this license is for the CHOLMOD/Supernodal module only. All CHOLMOD modules are licensed separately. -------------------------------------------------------------------------------- This Module is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This Module is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. SuiteSparse/CHOLMOD/Supernodal/cholmod_super_numeric.c0000644001170100242450000002516610635771110021714 0ustar davisfac/* ========================================================================== */ /* === Supernodal/cholmod_super_numeric ===================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Supernodal Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Supernodal Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Computes the Cholesky factorization of A+beta*I or A*F+beta*I. Only the * the lower triangular part of A+beta*I or A*F+beta*I is accessed. The * matrices A and F must already be permuted according to the fill-reduction * permutation L->Perm. cholmod_factorize is an "easy" wrapper for this code * which applies that permutation. beta is real. * * Symmetric case: A is a symmetric (lower) matrix. F is not accessed. * With a fill-reducing permutation, A(p,p) should be passed instead, where is * p is L->Perm. * * Unsymmetric case: A is unsymmetric, and F must be present. Normally, F=A'. * With a fill-reducing permutation, A(p,f) and A(p,f)' should be passed as A * and F, respectively, where f is a list of the subset of the columns of A. * * The input factorization L must be supernodal (L->is_super is TRUE). It can * either be symbolic or numeric. In the first case, L has been analyzed by * cholmod_analyze or cholmod_super_symbolic, but the matrix has not yet been * numerically factorized. The numerical values are allocated here and the * factorization is computed. In the second case, a prior matrix has been * analyzed and numerically factorized, and a new matrix is being factorized. * The numerical values of L are replaced with the new numerical factorization. * * L->is_ll is ignored, and set to TRUE. This routine always computes an LL' * factorization. Supernodal LDL' factorization is not (yet) supported. * FUTURE WORK: perform a supernodal LDL' factorization if L->is_ll is FALSE. * * Uses BLAS routines dsyrk, dgemm, dtrsm, and the LAPACK routine dpotrf. * The supernodal solver uses BLAS routines dtrsv, dgemv, dtrsm, and dgemm. * * If the matrix is not positive definite the routine returns TRUE, but sets * Common->status to CHOLMOD_NOT_POSDEF and L->minor is set to the column at * which the failure occurred. The supernode containing the non-positive * diagonal entry is set to zero (this includes columns to the left of L->minor * in the same supernode), as are all subsequent supernodes. * * workspace: Flag (nrow), Head (nrow+1), Iwork (2*nrow + 4*nsuper). * Allocates temporary space of size L->maxcsize * sizeof(double) * (twice that for the complex/zomplex case). * * If L is supernodal symbolic on input, it is converted to a supernodal numeric * factor on output, with an xtype of real if A is real, or complex if A is * complex or zomplex. If L is supernodal numeric on input, its xtype must * match A (except that L can be complex and A zomplex). The xtype of A and F * must match. */ #ifndef NSUPERNODAL #include "cholmod_internal.h" #include "cholmod_supernodal.h" /* ========================================================================== */ /* === TEMPLATE ============================================================= */ /* ========================================================================== */ #define REAL #include "t_cholmod_super_numeric.c" #define COMPLEX #include "t_cholmod_super_numeric.c" #define ZOMPLEX #include "t_cholmod_super_numeric.c" /* ========================================================================== */ /* === cholmod_super_numeric ================================================ */ /* ========================================================================== */ /* Returns TRUE if successful, or if the matrix is not positive definite. * Returns FALSE if out of memory, inputs are invalid, or other fatal error * occurs. */ int CHOLMOD(super_numeric) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ cholmod_sparse *F, /* F = A' or A(:,f)' */ double beta [2], /* beta*I is added to diagonal of matrix to factorize */ /* ---- in/out --- */ cholmod_factor *L, /* factorization */ /* --------------- */ cholmod_common *Common ) { cholmod_dense *C ; Int *Super, *Map, *SuperMap ; size_t maxcsize ; Int nsuper, n, i, k, s, stype, nrow ; int ok = TRUE, symbolic ; size_t t, w ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_COMPLEX, FALSE) ; stype = A->stype ; if (stype < 0) { if (A->nrow != A->ncol || A->nrow != L->n) { ERROR (CHOLMOD_INVALID, "invalid dimensions") ; return (FALSE) ; } } else if (stype == 0) { if (A->nrow != L->n) { ERROR (CHOLMOD_INVALID, "invalid dimensions") ; return (FALSE) ; } RETURN_IF_NULL (F, FALSE) ; RETURN_IF_XTYPE_INVALID (F, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; if (A->nrow != F->ncol || A->ncol != F->nrow || F->stype != 0) { ERROR (CHOLMOD_INVALID, "F invalid") ; return (FALSE) ; } if (A->xtype != F->xtype) { ERROR (CHOLMOD_INVALID, "A and F must have same xtype") ; return (FALSE) ; } } else { /* symmetric upper case not suppored */ ERROR (CHOLMOD_INVALID, "symmetric upper case not supported") ; return (FALSE) ; } if (!(L->is_super)) { ERROR (CHOLMOD_INVALID, "L not supernodal") ; return (FALSE) ; } if (L->xtype != CHOLMOD_PATTERN) { if (! ((A->xtype == CHOLMOD_REAL && L->xtype == CHOLMOD_REAL) || (A->xtype == CHOLMOD_COMPLEX && L->xtype == CHOLMOD_COMPLEX) || (A->xtype == CHOLMOD_ZOMPLEX && L->xtype == CHOLMOD_COMPLEX))) { ERROR (CHOLMOD_INVALID, "complex type mismatch") ; return (FALSE) ; } } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace in Common */ /* ---------------------------------------------------------------------- */ nsuper = L->nsuper ; maxcsize = L->maxcsize ; nrow = A->nrow ; n = nrow ; PRINT1 (("nsuper "ID" maxcsize %g\n", nsuper, (double) maxcsize)) ; ASSERT (nsuper >= 0 && maxcsize > 0) ; /* w = 2*n + 4*nsuper */ w = CHOLMOD(mult_size_t) (n, 2, &ok) ; t = CHOLMOD(mult_size_t) (nsuper, 4, &ok) ; w = CHOLMOD(add_size_t) (w, t, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (n, w, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* get the current factor L and allocate numerical part, if needed */ /* ---------------------------------------------------------------------- */ Super = L->super ; symbolic = (L->xtype == CHOLMOD_PATTERN) ; if (symbolic) { /* convert to supernodal numeric by allocating L->x */ CHOLMOD(change_factor) ( (A->xtype == CHOLMOD_REAL) ? CHOLMOD_REAL : CHOLMOD_COMPLEX, TRUE, TRUE, TRUE, TRUE, L, Common) ; if (Common->status < CHOLMOD_OK) { /* the factor L remains in symbolic supernodal form */ return (FALSE) ; } } ASSERT (L->dtype == DTYPE) ; ASSERT (L->xtype == CHOLMOD_REAL || L->xtype == CHOLMOD_COMPLEX) ; /* supernodal LDL' is not supported */ L->is_ll = TRUE ; /* ---------------------------------------------------------------------- */ /* get more workspace */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(allocate_dense) (maxcsize, 1, maxcsize, L->xtype, Common) ; if (Common->status < CHOLMOD_OK) { int status = Common->status ; if (symbolic) { /* Change L back to symbolic, since the numeric values are not * initialized. This cannot fail. */ CHOLMOD(change_factor) (CHOLMOD_PATTERN, TRUE, TRUE, TRUE, TRUE, L, Common) ; } /* the factor L is now back to the form it had on input */ Common->status = status ; return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ SuperMap = Common->Iwork ; /* size n (i/i/l) */ Map = Common->Flag ; /* size n, use Flag as workspace for Map array */ for (i = 0 ; i < n ; i++) { Map [i] = EMPTY ; } /* ---------------------------------------------------------------------- */ /* find the mapping of nodes to relaxed supernodes */ /* ---------------------------------------------------------------------- */ /* SuperMap [k] = s if column k is contained in supernode s */ for (s = 0 ; s < nsuper ; s++) { PRINT1 (("Super ["ID"] "ID" ncols "ID"\n", s, Super[s], Super[s+1]-Super[s])); for (k = Super [s] ; k < Super [s+1] ; k++) { SuperMap [k] = s ; PRINT2 (("relaxed SuperMap ["ID"] = "ID"\n", k, SuperMap [k])) ; } } /* ---------------------------------------------------------------------- */ /* supernodal numerical factorization, using template routine */ /* ---------------------------------------------------------------------- */ switch (A->xtype) { case CHOLMOD_REAL: ok = r_cholmod_super_numeric (A, F, beta, L, C, Common) ; break ; case CHOLMOD_COMPLEX: ok = c_cholmod_super_numeric (A, F, beta, L, C, Common) ; break ; case CHOLMOD_ZOMPLEX: /* This operates on complex L, not zomplex */ ok = z_cholmod_super_numeric (A, F, beta, L, C, Common) ; break ; } /* ---------------------------------------------------------------------- */ /* clear Common workspace, free temp workspace C, and return */ /* ---------------------------------------------------------------------- */ /* Flag array was used as workspace, clear it */ Common->mark = EMPTY ; /* CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; CHOLMOD(free_dense) (&C, Common) ; return (ok) ; } #endif SuiteSparse/CHOLMOD/Supernodal/t_cholmod_super_numeric.c0000644001170100242450000006104610540000015022214 0ustar davisfac/* ========================================================================== */ /* === Supernodal/t_cholmod_super_numeric =================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Supernodal Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Supernodal Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Template routine for cholmod_super_numeric. All xtypes supported, except * that a zomplex A and F result in a complex L (there is no supernodal * zomplex L). */ /* ========================================================================== */ /* === complex arithmetic =================================================== */ /* ========================================================================== */ #include "cholmod_template.h" #undef L_ENTRY #undef L_CLEAR #undef L_ASSIGN #undef L_MULTADD #undef L_ASSEMBLE #undef L_ASSEMBLESUB #ifdef REAL /* -------------------------------------------------------------------------- */ /* A, F, and L are all real */ /* -------------------------------------------------------------------------- */ #define L_ENTRY 1 #define L_CLEAR(Lx,p) Lx [p] = 0 #define L_ASSIGN(Lx,q, Ax,Az,p) Lx [q] = Ax [p] #define L_MULTADD(Lx,q, Ax,Az,p, f) Lx [q] += Ax [p] * f [0] #define L_ASSEMBLE(Lx,q,b) Lx [q] += b [0] #define L_ASSEMBLESUB(Lx,q,C,p) Lx [q] -= C [p] #else /* -------------------------------------------------------------------------- */ /* A and F are complex or zomplex, L and C are complex */ /* -------------------------------------------------------------------------- */ #define L_ENTRY 2 #define L_CLEAR(Lx,p) Lx [2*(p)] = 0 ; Lx [2*(p)+1] = 0 #define L_ASSEMBLE(Lx,q,b) Lx [2*(q)] += b [0] ; #define L_ASSEMBLESUB(Lx,q,C,p) \ Lx [2*(q) ] -= C [2*(p) ] ; \ Lx [2*(q)+1] -= C [2*(p)+1] ; #ifdef COMPLEX /* -------------------------------------------------------------------------- */ /* A, F, L, and C are all complex */ /* -------------------------------------------------------------------------- */ #define L_ASSIGN(Lx,q, Ax,Az,p) \ Lx [2*(q) ] = Ax [2*(p) ] ; \ Lx [2*(q)+1] = Ax [2*(p)+1] #define L_MULTADD(Lx,q, Ax,Az,p, f) \ Lx [2*(q) ] += Ax [2*(p) ] * f [0] - Ax [2*(p)+1] * f [1] ; \ Lx [2*(q)+1] += Ax [2*(p)+1] * f [0] + Ax [2*(p) ] * f [1] #else /* -------------------------------------------------------------------------- */ /* A and F are zomplex, L and C is complex */ /* -------------------------------------------------------------------------- */ #define L_ASSIGN(Lx,q, Ax,Az,p) \ Lx [2*(q) ] = Ax [p] ; \ Lx [2*(q)+1] = Az [p] ; #define L_MULTADD(Lx,q, Ax,Az,p, f) \ Lx [2*(q) ] += Ax [p] * f [0] - Az [p] * f [1] ; \ Lx [2*(q)+1] += Az [p] * f [0] + Ax [p] * f [1] #endif #endif /* ========================================================================== */ /* === t_cholmod_super_numeric ============================================== */ /* ========================================================================== */ /* This function returns FALSE only if integer overflow occurs in the BLAS. * It returns TRUE otherwise whether or not the matrix is positive definite. */ static int TEMPLATE (cholmod_super_numeric) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ cholmod_sparse *F, /* F = A' or A(:,f)' */ double beta [2], /* beta*I is added to diagonal of matrix to factorize */ /* ---- in/out --- */ cholmod_factor *L, /* factorization */ /* -- workspace -- */ cholmod_dense *Cwork, /* size (L->maxcsize)-by-1 */ /* --------------- */ cholmod_common *Common ) { double one [2], zero [2], fjk [2] ; double *Lx, *Ax, *Fx, *Az, *Fz, *C ; Int *Super, *Head, *Ls, *Lpi, *Lpx, *Map, *SuperMap, *RelativeMap, *Next, *Lpos, *Fp, *Fi, *Fnz, *Ap, *Ai, *Anz, *Iwork, *Next_save, *Lpos_save ; Int nsuper, n, j, i, k, s, p, pend, k1, k2, nscol, psi, psx, psend, nsrow, pj, d, kd1, kd2, info, ndcol, ndrow, pdi, pdx, pdend, pdi1, pdi2, pdx1, ndrow1, ndrow2, px, dancestor, sparent, dnext, nsrow2, ndrow3, pk, pf, pfend, stype, Apacked, Fpacked, q, imap, repeat_supernode, nscol2, ss, nscol_new = 0 ; /* If integer overflow occurs in the BLAS, Common->status is set to * CHOLMOD_TOO_LARGE, and the contents of Lx are undefined. */ int blas_ok = TRUE ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nsuper = L->nsuper ; n = L->n ; C = Cwork->x ; /* workspace of size L->maxcsize */ one [0] = 1.0 ; /* ALPHA for *syrk, *herk, *gemm, and *trsm */ one [1] = 0. ; zero [0] = 0. ; /* BETA for *syrk, *herk, and *gemm */ zero [1] = 0. ; Iwork = Common->Iwork ; SuperMap = Iwork ; /* size n (i/i/l) */ RelativeMap = Iwork + n ; /* size n (i/i/l) */ Next = Iwork + 2*((size_t) n) ; /* size nsuper*/ Lpos = Iwork + 2*((size_t) n) + nsuper ; /* size nsuper*/ Next_save = Iwork + 2*((size_t) n) + 2*((size_t) nsuper) ;/* size nsuper*/ Lpos_save = Iwork + 2*((size_t) n) + 3*((size_t) nsuper) ;/* size nsuper*/ Map = Common->Flag ; /* size n, use Flag as workspace for Map array */ Head = Common->Head ; /* size n+1, only Head [0..nsuper-1] used */ Ls = L->s ; Lpi = L->pi ; Lpx = L->px ; Super = L->super ; Lx = L->x ; stype = A->stype ; if (stype != 0) { /* F not accessed */ Fp = NULL ; Fi = NULL ; Fx = NULL ; Fz = NULL ; Fnz = NULL ; Fpacked = TRUE ; } else { Fp = F->p ; Fi = F->i ; Fx = F->x ; Fz = F->z ; Fnz = F->nz ; Fpacked = F->packed ; } Ap = A->p ; Ai = A->i ; Ax = A->x ; Az = A->z ; Anz = A->nz ; Apacked = A->packed ; /* clear the Map so that changes in the pattern of A can be detected */ for (i = 0 ; i < n ; i++) { Map [i] = EMPTY ; } /* If the matrix is not positive definite, the supernode s containing the * first zero or negative diagonal entry of L is repeated (but factorized * only up to just before the problematic diagonal entry). The purpose is * to provide MATLAB with [R,p]=chol(A); columns 1 to p-1 of L=R' are * required, where L(p,p) is the problematic diagonal entry. The * repeat_supernode flag tells us whether this is the repeated supernode. * Once supernode s is repeated, the factorization is terminated. */ repeat_supernode = FALSE ; /* ---------------------------------------------------------------------- */ /* supernodal numerical factorization */ /* ---------------------------------------------------------------------- */ for (s = 0 ; s < nsuper ; s++) { /* ------------------------------------------------------------------ */ /* get the size of supernode s */ /* ------------------------------------------------------------------ */ k1 = Super [s] ; /* s contains columns k1 to k2-1 of L */ k2 = Super [s+1] ; nscol = k2 - k1 ; /* # of columns in all of s */ psi = Lpi [s] ; /* pointer to first row of s in Ls */ psx = Lpx [s] ; /* pointer to first row of s in Lx */ psend = Lpi [s+1] ; /* pointer just past last row of s in Ls */ nsrow = psend - psi ; /* # of rows in all of s */ PRINT1 (("====================================================\n" "S "ID" k1 "ID" k2 "ID" nsrow "ID" nscol "ID" psi "ID" psend " ""ID" psx "ID"\n", s, k1, k2, nsrow, nscol, psi, psend, psx)) ; /* ------------------------------------------------------------------ */ /* zero the supernode s */ /* ------------------------------------------------------------------ */ ASSERT ((size_t) (psx + nsrow*nscol) <= L->xsize) ; pend = psx + nsrow * nscol ; /* s is nsrow-by-nscol */ for (p = psx ; p < pend ; p++) { /* Lx [p] = 0 ; */ L_CLEAR (Lx,p) ; } /* ------------------------------------------------------------------ */ /* construct the scattered Map for supernode s */ /* ------------------------------------------------------------------ */ /* If row i is the kth row in s, then Map [i] = k. Similarly, if * column j is the kth column in s, then Map [j] = k. */ for (k = 0 ; k < nsrow ; k++) { PRINT1 ((" "ID" map "ID"\n", Ls [psi+k], k)) ; Map [Ls [psi + k]] = k ; } /* ------------------------------------------------------------------ */ /* copy matrix into supernode s (lower triangular part only) */ /* ------------------------------------------------------------------ */ pk = psx ; for (k = k1 ; k < k2 ; k++) { if (stype != 0) { /* copy the kth column of A into the supernode */ p = Ap [k] ; pend = (Apacked) ? (Ap [k+1]) : (p + Anz [k]) ; for ( ; p < pend ; p++) { /* row i of L is located in row Map [i] of s */ i = Ai [p] ; if (i >= k) { /* This test is here simply to avoid a segfault. If * the test is false, the numeric factorization of A * is undefined. It does not detect all invalid * entries, only some of them (when debugging is * enabled, and Map is cleared after each step, then * all entries not in the pattern of L are detected). */ imap = Map [i] ; if (imap >= 0 && imap < nsrow) { /* Lx [Map [i] + pk] = Ax [p] ; */ L_ASSIGN (Lx,(imap+pk), Ax,Az,p) ; } } } } else { /* copy the kth column of A*F into the supernode */ pf = Fp [k] ; pfend = (Fpacked) ? (Fp [k+1]) : (p + Fnz [k]) ; for ( ; pf < pfend ; pf++) { j = Fi [pf] ; /* fjk = Fx [pf] ; */ L_ASSIGN (fjk,0, Fx,Fz,pf) ; p = Ap [j] ; pend = (Apacked) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i >= k) { /* See the discussion of imap above. */ imap = Map [i] ; if (imap >= 0 && imap < nsrow) { /* Lx [Map [i] + pk] += Ax [p] * fjk ; */ L_MULTADD (Lx,(imap+pk), Ax,Az,p, fjk) ; } } } } } pk += nsrow ; /* advance to the next column of the supernode */ } /* add beta to the diagonal of the supernode, if nonzero */ if (beta [0] != 0.0) { /* note that only the real part of beta is used */ pk = psx ; for (k = k1 ; k < k2 ; k++) { /* Lx [pk] += beta [0] ; */ L_ASSEMBLE (Lx,pk, beta) ; pk += nsrow + 1 ; /* advance to the next diagonal entry */ } } PRINT1 (("Supernode with just A: repeat: "ID"\n", repeat_supernode)) ; DEBUG (CHOLMOD(dump_super) (s, Super, Lpi, Ls, Lpx, Lx, L_ENTRY, Common)) ; PRINT1 (("\n\n")) ; /* ------------------------------------------------------------------ */ /* save/restore the list of supernodes */ /* ------------------------------------------------------------------ */ if (!repeat_supernode) { /* Save the list of pending descendants in case s is not positive * definite. Also save Lpos for each descendant d, so that we can * find which part of d is used to update s. */ for (d = Head [s] ; d != EMPTY ; d = Next [d]) { Lpos_save [d] = Lpos [d] ; Next_save [d] = Next [d] ; } } else { /* s is not positive definite, and is being repeated. Restore * the list of supernodes. This can be done with pointer assignment * because all 4 arrays are held within Common->Iwork. */ Lpos = Lpos_save ; Next = Next_save ; } /* ------------------------------------------------------------------ */ /* update supernode s with each pending descendant d */ /* ------------------------------------------------------------------ */ #ifndef NDEBUG for (d = Head [s] ; d != EMPTY ; d = Next [d]) { PRINT1 (("\nWill update "ID" with Child: "ID"\n", s, d)) ; DEBUG (CHOLMOD(dump_super) (d, Super, Lpi, Ls, Lpx, Lx, L_ENTRY, Common)) ; } PRINT1 (("\nNow factorizing supernode "ID":\n", s)) ; #endif for (d = Head [s] ; d != EMPTY ; d = dnext) { /* -------------------------------------------------------------- */ /* get the size of supernode d */ /* -------------------------------------------------------------- */ kd1 = Super [d] ; /* d contains cols kd1 to kd2-1 of L */ kd2 = Super [d+1] ; ndcol = kd2 - kd1 ; /* # of columns in all of d */ pdi = Lpi [d] ; /* pointer to first row of d in Ls */ pdx = Lpx [d] ; /* pointer to first row of d in Lx */ pdend = Lpi [d+1] ; /* pointer just past last row of d in Ls */ ndrow = pdend - pdi ; /* # rows in all of d */ PRINT1 (("Child: ")) ; DEBUG (CHOLMOD(dump_super) (d, Super, Lpi, Ls, Lpx, Lx, L_ENTRY, Common)) ; /* -------------------------------------------------------------- */ /* find the range of rows of d that affect rows k1 to k2-1 of s */ /* -------------------------------------------------------------- */ p = Lpos [d] ; /* offset of 1st row of d affecting s */ pdi1 = pdi + p ; /* ptr to 1st row of d affecting s in Ls */ pdx1 = pdx + p ; /* ptr to 1st row of d affecting s in Lx */ /* there must be at least one row remaining in d to update s */ ASSERT (pdi1 < pdend) ; PRINT1 (("Lpos[d] "ID" pdi1 "ID" Ls[pdi1] "ID"\n", Lpos[d], pdi1, Ls [pdi1])) ; ASSERT (Ls [pdi1] >= k1 && Ls [pdi1] < k2) ; for (pdi2 = pdi1 ; pdi2 < pdend && Ls [pdi2] < k2 ; pdi2++) ; ndrow1 = pdi2 - pdi1 ; /* # rows in first part of d */ ndrow2 = pdend - pdi1 ; /* # rows in remaining d */ /* rows Ls [pdi1 ... pdi2-1] are in the range k1 to k2-1. Since d * affects s, this set cannot be empty. */ ASSERT (pdi1 < pdi2 && pdi2 <= pdend) ; PRINT1 (("ndrow1 "ID" ndrow2 "ID"\n", ndrow1, ndrow2)) ; DEBUG (for (p = pdi1 ; p < pdi2 ; p++) PRINT1 (("Ls["ID"] "ID"\n", p, Ls[p]))) ; /* -------------------------------------------------------------- */ /* construct the update matrix C for this supernode d */ /* -------------------------------------------------------------- */ /* C = L (k1:n-1, kd1:kd2-1) * L (k1:k2-1, kd1:kd2-1)', except * that k1:n-1 refers to all of the rows in L, but many of the * rows are all zero. Supernode d holds columns kd1 to kd2-1 of L. * Nonzero rows in the range k1:k2-1 are in the list * Ls [pdi1 ... pdi2-1], of size ndrow1. Nonzero rows in the range * k2:n-1 are in the list Ls [pdi2 ... pdend], of size ndrow2. Let * L1 = L (Ls [pdi1 ... pdi2-1], kd1:kd2-1), and let * L2 = L (Ls [pdi2 ... pdend], kd1:kd2-1). C is ndrow2-by-ndcol. * Let C1 be the first ndrow1 rows of C and let C2 be the last * ndrow2-ndrow1 rows of C. Only the lower triangular part of C1 * needs to be computed since C1 is symmetric. */ /* maxcsize is the largest size of C for all pairs (d,s) */ ASSERT (ndrow2 * ndrow1 <= ((Int) L->maxcsize)) ; /* compute leading ndrow1-by-ndrow1 lower triangular block of C, * C1 = L1*L1' */ #ifdef REAL BLAS_dsyrk ("L", "N", ndrow1, ndcol, /* N, K: L1 is ndrow1-by-ndcol*/ one, /* ALPHA: 1 */ Lx + L_ENTRY*pdx1, ndrow, /* A, LDA: L1, ndrow */ zero, /* BETA: 0 */ C, ndrow2) ; /* C, LDC: C1 */ #else BLAS_zherk ("L", "N", ndrow1, ndcol, /* N, K: L1 is ndrow1-by-ndcol*/ one, /* ALPHA: 1 */ Lx + L_ENTRY*pdx1, ndrow, /* A, LDA: L1, ndrow */ zero, /* BETA: 0 */ C, ndrow2) ; /* C, LDC: C1 */ #endif /* compute remaining (ndrow3-ndrow1)-by-ndrow1 block of C, * C2 = L2*L1' */ ndrow3 = ndrow2 - ndrow1 ; if (ndrow3 > 0) { #ifdef REAL BLAS_dgemm ("N", "C", ndrow3, ndrow1, ndcol, /* M, N, K */ one, /* ALPHA: 1 */ Lx + L_ENTRY*(pdx1 + ndrow1),/* A, LDA: L2, ndrow */ ndrow, Lx + L_ENTRY*pdx1, /* B, LDB: L1, ndrow */ ndrow, zero, /* BETA: 0 */ C + L_ENTRY*ndrow1, /* C, LDC: C2 */ ndrow2) ; #else BLAS_zgemm ("N", "C", ndrow3, ndrow1, ndcol, /* M, N, K */ one, /* ALPHA: 1 */ Lx + L_ENTRY*(pdx1 + ndrow1),/* A, LDA: L2, ndrow */ ndrow, Lx + L_ENTRY*pdx1, /* B, LDB: L1, ndrow */ ndrow, zero, /* BETA: 0 */ C + L_ENTRY*ndrow1, /* C, LDC: C2 */ ndrow2) ; #endif } DEBUG (CHOLMOD(dump_real) ("C", C, ndrow2, ndrow1, TRUE, L_ENTRY, Common)) ; /* -------------------------------------------------------------- */ /* construct relative map to assemble d into s */ /* -------------------------------------------------------------- */ for (i = 0 ; i < ndrow2 ; i++) { RelativeMap [i] = Map [Ls [pdi1 + i]] ; ASSERT (RelativeMap [i] >= 0 && RelativeMap [i] < nsrow) ; } /* -------------------------------------------------------------- */ /* assemble C into supernode s using the relative map */ /* -------------------------------------------------------------- */ pj = 0 ; for (j = 0 ; j < ndrow1 ; j++) /* cols k1:k2-1 */ { ASSERT (RelativeMap [j] == Map [Ls [pdi1 + j]]) ; ASSERT (RelativeMap [j] >= 0 && RelativeMap [j] < nscol) ; px = psx + RelativeMap [j] * nsrow ; for (i = j ; i < ndrow2 ; i++) /* rows k1:n-1 */ { ASSERT (RelativeMap [i] == Map [Ls [pdi1 + i]]) ; ASSERT (RelativeMap [i] >= j && RelativeMap [i] < nsrow) ; /* Lx [px + RelativeMap [i]] -= C [i + pj] ; */ q = px + RelativeMap [i] ; L_ASSEMBLESUB (Lx,q, C, i+pj) ; } pj += ndrow2 ; } /* -------------------------------------------------------------- */ /* prepare this supernode d for its next ancestor */ /* -------------------------------------------------------------- */ dnext = Next [d] ; if (!repeat_supernode) { /* If node s is being repeated, Head [dancestor] has already * been cleared (set to EMPTY). It must remain EMPTY. The * dancestor will not be factorized since the factorization * terminates at node s. */ Lpos [d] = pdi2 - pdi ; if (Lpos [d] < ndrow) { dancestor = SuperMap [Ls [pdi2]] ; ASSERT (dancestor > s && dancestor < nsuper) ; /* place d in the link list of its next ancestor */ Next [d] = Head [dancestor] ; Head [dancestor] = d ; } } } PRINT1 (("\nSupernode with contributions A: repeat: "ID"\n", repeat_supernode)) ; DEBUG (CHOLMOD(dump_super) (s, Super, Lpi, Ls, Lpx, Lx, L_ENTRY, Common)) ; PRINT1 (("\n\n")) ; /* ------------------------------------------------------------------ */ /* factorize diagonal block of supernode s in LL' */ /* ------------------------------------------------------------------ */ /* The current supernode s is ready to factorize. It has been updated * by all descendant supernodes. Let S = the current supernode, which * holds rows k1:n-1 and columns k1:k2-1 of the updated matrix. It * splits into two parts: the square diagonal block S1, and the * rectangular part S2. Here, S1 is factorized into L1*L1' and * overwritten by S1. * * If supernode s is being repeated, only factorize it up to but not * including the column containing the problematic entry. */ nscol2 = (repeat_supernode) ? (nscol_new) : (nscol) ; #ifdef REAL LAPACK_dpotrf ("L", nscol2, /* N: nscol2 */ Lx + L_ENTRY*psx, nsrow, /* A, LDA: S1, nsrow */ info) ; /* INFO */ #else LAPACK_zpotrf ("L", nscol2, /* N: nscol2 */ Lx + L_ENTRY*psx, nsrow, /* A, LDA: S1, nsrow */ info) ; /* INFO */ #endif /* ------------------------------------------------------------------ */ /* check if the matrix is not positive definite */ /* ------------------------------------------------------------------ */ if (repeat_supernode) { /* the leading part has been refactorized; it must have succeeded */ info = 0 ; /* zero out the rest of this supernode */ p = psx + nsrow * nscol_new ; pend = psx + nsrow * nscol ; /* s is nsrow-by-nscol */ for ( ; p < pend ; p++) { /* Lx [p] = 0 ; */ L_CLEAR (Lx,p) ; } } /* info is set to one in LAPACK_*potrf if blas_ok is FALSE. It is * set to zero in dpotrf/zpotrf if the factorization was successful. */ if (CHECK_BLAS_INT && !blas_ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large for the BLAS") ; } if (info != 0) { /* Matrix is not positive definite. dpotrf/zpotrf do NOT report an * error if the diagonal of L has NaN's, only if it has a zero. */ if (Common->status == CHOLMOD_OK) { ERROR (CHOLMOD_NOT_POSDEF, "matrix not positive definite") ; } /* L->minor is the column of L that contains a zero or negative * diagonal term. */ L->minor = k1 + info - 1 ; /* clear the link lists of all subsequent supernodes */ for (ss = s+1 ; ss < nsuper ; ss++) { Head [ss] = EMPTY ; } /* zero this supernode, and all remaining supernodes */ pend = L->xsize ; for (p = psx ; p < pend ; p++) { /* Lx [p] = 0. ; */ L_CLEAR (Lx,p) ; } /* If L is indefinite, it still contains useful information. * Supernodes 0 to s-1 are valid, similar to MATLAB [R,p]=chol(A), * where the 1-based p is identical to the 0-based L->minor. Since * L->minor is in the current supernode s, it and any columns to the * left of it in supernode s are also all zero. This differs from * [R,p]=chol(A), which contains nonzero rows 1 to p-1. Fix this * by setting repeat_supernode to TRUE, and repeating supernode s. * * If Common->quick_return_if_not_posdef is true, then the entire * supernode s is not factorized; it is left as all zero. */ if (info == 1 || Common->quick_return_if_not_posdef) { /* If the first column of supernode s contains a zero or * negative diagonal entry, then it is already properly set to * zero. Also, info will be 1 if integer overflow occured in * the BLAS. */ Head [s] = EMPTY ; return (Common->status >= CHOLMOD_OK) ; } else { /* Repeat supernode s, but only factorize it up to but not * including the column containing the problematic diagonal * entry. */ repeat_supernode = TRUE ; s-- ; nscol_new = info - 1 ; continue ; } } /* ------------------------------------------------------------------ */ /* compute the subdiagonal block and prepare supernode for its parent */ /* ------------------------------------------------------------------ */ nsrow2 = nsrow - nscol2 ; if (nsrow2 > 0) { /* The current supernode is columns k1 to k2-1 of L. Let L1 be the * diagonal block (factorized by dpotrf/zpotrf above; rows/cols * k1:k2-1), and L2 be rows k2:n-1 and columns k1:k2-1 of L. The * triangular system to solve is L2*L1' = S2, where S2 is * overwritten with L2. More precisely, L2 = S2 / L1' in MATLAB * notation. */ #ifdef REAL BLAS_dtrsm ("R", "L", "C", "N", nsrow2, nscol2, /* M, N */ one, /* ALPHA: 1 */ Lx + L_ENTRY*psx, nsrow, /* A, LDA: L1, nsrow */ Lx + L_ENTRY*(psx + nscol2), /* B, LDB, L2, nsrow */ nsrow) ; #else BLAS_ztrsm ("R", "L", "C", "N", nsrow2, nscol2, /* M, N */ one, /* ALPHA: 1 */ Lx + L_ENTRY*psx, nsrow, /* A, LDA: L1, nsrow */ Lx + L_ENTRY*(psx + nscol2), /* B, LDB, L2, nsrow */ nsrow) ; #endif if (CHECK_BLAS_INT && !blas_ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large for the BLAS") ; } if (!repeat_supernode) { /* Lpos [s] is offset of first row of s affecting its parent */ Lpos [s] = nscol ; sparent = SuperMap [Ls [psi + nscol]] ; ASSERT (sparent != EMPTY) ; ASSERT (Ls [psi + nscol] >= Super [sparent]) ; ASSERT (Ls [psi + nscol] < Super [sparent+1]) ; ASSERT (SuperMap [Ls [psi + nscol]] == sparent) ; ASSERT (sparent > s && sparent < nsuper) ; /* place s in link list of its parent */ Next [s] = Head [sparent] ; Head [sparent] = s ; } } Head [s] = EMPTY ; /* link list for supernode s no longer needed */ /* clear the Map (debugging only, to detect changes in pattern of A) */ DEBUG (for (k = 0 ; k < nsrow ; k++) Map [Ls [psi + k]] = EMPTY) ; DEBUG (CHOLMOD(dump_super) (s, Super, Lpi, Ls, Lpx, Lx, L_ENTRY, Common)) ; if (repeat_supernode) { /* matrix is not positive definite; finished clean-up for supernode * containing negative diagonal */ return (Common->status >= CHOLMOD_OK) ; } } /* success; matrix is positive definite */ L->minor = n ; return (Common->status >= CHOLMOD_OK) ; } #undef PATTERN #undef REAL #undef COMPLEX #undef ZOMPLEX SuiteSparse/CHOLMOD/Supernodal/gpl.txt0000644001170100242450000004313310471712206016477 0ustar davisfac GNU GENERAL PUBLIC LICENSE Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. 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SuiteSparse/CHOLMOD/Supernodal/cholmod_super_symbolic.c0000644001170100242450000006333410677243407022103 0ustar davisfac/* ========================================================================== */ /* === Supernodal/cholmod_super_symbolic ==================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Supernodal Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Supernodal Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Supernodal symbolic analysis of the LL' factorization of A, A*A', * A(:,f)*A(:,f)'. * * This routine must be preceded by a simplicial symbolic analysis * (cholmod_rowcolcounts). See cholmod_analyze.c for an example of how to use * this routine. * * The user need not call this directly; cholmod_analyze is a "simple" wrapper * for this routine. * * Symmetric case: * * A is stored in column form, with entries stored in the upper triangular * part. Entries in the lower triangular part are ignored. * * Unsymmetric case: * * A is stored in column form. If F is equal to the transpose of A, then * A*A' is analyzed. F can include a subset of the columns of A * (F=A(:,f)'), in which case F*F' is analyzed. * * Requires Parent and L->ColCount to be defined on input; these are the * simplicial Parent and ColCount arrays as computed by cholmod_rowcolcounts. * Does not use L->Perm; the input matrices A and F must already be properly * permuted. Allocates and computes the supernodal pattern of L (L->super, * L->pi, L->px, and L->s). Does not allocate the real part (L->x). * * Supports any xtype (pattern, real, complex, or zomplex). */ #ifndef NSUPERNODAL #include "cholmod_internal.h" #include "cholmod_supernodal.h" /* ========================================================================== */ /* === subtree ============================================================== */ /* ========================================================================== */ /* In the symmetric case, traverse the kth row subtree from the nonzeros in * A (0:k,k) and add the new entries found to the pattern of the kth row of L. * * In the unsymmetric case, the nonzero pattern of A*F is computed one column at * one column at a time. The kth column is A*F(:,k), or the set union of all * columns A(:,j) for which F(j,k) is nonzero. This routine is called once * for each entry j. Only the upper triangular part is needed, so only * A (0:k,j) is accessed. * * Only adds column indices corresponding to the leading columns of each * relaxed supernode. */ static void subtree ( /* inputs, not modified: */ Int j, /* j = k for symmetric case */ Int k, Int Ap [ ], Int Ai [ ], Int Anz [ ], Int SuperMap [ ], Int Sparent [ ], Int mark, /* input/output: */ Int Flag [ ], Int Ls [ ], Int Lpi2 [ ] ) { Int p, pend, i, si ; p = Ap [j] ; pend = (Anz == NULL) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i < k) { /* (i,k) is an entry in the upper triangular part of A or A*F'. * symmetric case: A(i,k) is nonzero (j=k). * unsymmetric case: A(i,j) and F(j,k) are both nonzero. * * Column i is in supernode si = SuperMap [i]. Follow path from si * to root of supernodal etree, stopping at the first flagged * supernode. The root of the row subtree is supernode SuperMap[k], * which is flagged already. This traversal will stop there, or it * might stop earlier if supernodes have been flagged by previous * calls to this routine for the same k. */ for (si = SuperMap [i] ; Flag [si] < mark ; si = Sparent [si]) { ASSERT (si <= SuperMap [k]) ; Ls [Lpi2 [si]++] = k ; Flag [si] = mark ; } } } } /* clear workspace used by cholmod_super_symbolic */ #define FREE_WORKSPACE \ { \ /* CHOLMOD(clear_flag) (Common) ; */ \ CHOLMOD_CLEAR_FLAG (Common) ; \ for (k = 0 ; k <= nfsuper ; k++) \ { \ Head [k] = EMPTY ; \ } \ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; \ } \ /* ========================================================================== */ /* === cholmod_super_symbolic =============================================== */ /* ========================================================================== */ /* Analyzes A, AA', or A(:,f)*A(:,f)' in preparation for a supernodal numeric * factorization. The user need not call this directly; cholmod_analyze is * a "simple" wrapper for this routine. * * workspace: Flag (nrow), Head (nrow), Iwork (2*nrow), * and temporary space of size 3*nfsuper*sizeof(Int), where nfsuper <= n * is the number of fundamental supernodes. */ int CHOLMOD(super_symbolic) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ cholmod_sparse *F, /* F = A' or A(:,f)' */ Int *Parent, /* elimination tree */ /* ---- in/out --- */ cholmod_factor *L, /* simplicial symbolic on input, * supernodal symbolic on output */ /* --------------- */ cholmod_common *Common ) { double zrelax0, zrelax1, zrelax2, xxsize ; Int *Wi, *Wj, *Super, *Snz, *Ap, *Ai, *Flag, *Head, *Ls, *Lpi, *Lpx, *Fnz, *Sparent, *Anz, *SuperMap, *Merged, *Nscol, *Zeros, *Fp, *Fj, *ColCount, *Lpi2, *Lsuper, *Iwork ; Int nsuper, d, n, j, k, s, mark, parent, p, pend, k1, k2, packed, nscol, nsrow, ndrow1, ndrow2, stype, ssize, xsize, sparent, plast, slast, csize, maxcsize, ss, nscol0, nscol1, ns, nfsuper, newzeros, totzeros, merge, snext, esize, maxesize, nrelax0, nrelax1, nrelax2 ; size_t w ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_NULL (Parent, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_PATTERN, FALSE) ; stype = A->stype ; if (stype < 0) { /* invalid symmetry; symmetric lower form not supported */ ERROR (CHOLMOD_INVALID, "symmetric lower not supported") ; return (FALSE) ; } if (stype == 0) { /* F must be present in the unsymmetric case */ RETURN_IF_NULL (F, FALSE) ; } if (L->is_super) { /* L must be a simplicial symbolic factor */ ERROR (CHOLMOD_INVALID, "L must be symbolic on input") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ n = A->nrow ; /* w = 5*n */ w = CHOLMOD(mult_size_t) (n, 5, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (n, w, 0, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (FALSE) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ /* A is now either A or triu(A(p,p)) for the symmetric case. It is either * A or A(p,f) for the unsymmetric case (both in column form). It can be * either packed or unpacked, and either sorted or unsorted. Entries in * the lower triangular part may be present if A is symmetric, but these * are ignored. */ Ap = A->p ; Ai = A->i ; Anz = A->nz ; if (stype != 0) { /* F not accessed */ Fp = NULL ; Fj = NULL ; Fnz = NULL ; packed = TRUE ; } else { /* F = A(:,f) or A(p,f) in packed row form, either sorted or unsorted */ Fp = F->p ; Fj = F->i ; Fnz = F->nz ; packed = F->packed ; } ColCount = L->ColCount ; nrelax0 = Common->nrelax [0] ; nrelax1 = Common->nrelax [1] ; nrelax2 = Common->nrelax [2] ; zrelax0 = Common->zrelax [0] ; zrelax1 = Common->zrelax [1] ; zrelax2 = Common->zrelax [2] ; zrelax0 = IS_NAN (zrelax0) ? 0 : zrelax0 ; zrelax1 = IS_NAN (zrelax1) ? 0 : zrelax1 ; zrelax2 = IS_NAN (zrelax2) ? 0 : zrelax2 ; ASSERT (CHOLMOD(dump_parent) (Parent, n, "Parent", Common)) ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ /* Sparent, Snz, and Merged could be allocated later, of size nfsuper */ Iwork = Common->Iwork ; Wi = Iwork ; /* size n (i/l/l). Lpi2 is i/l/l */ Wj = Iwork + n ; /* size n (i/l/l). Zeros is i/l/l */ Sparent = Iwork + 2*((size_t) n) ; /* size nfsuper <= n [ */ Snz = Iwork + 3*((size_t) n) ; /* size nfsuper <= n [ */ Merged = Iwork + 4*((size_t) n) ; /* size nfsuper <= n [ */ Flag = Common->Flag ; /* size n */ Head = Common->Head ; /* size n+1 */ /* ---------------------------------------------------------------------- */ /* find the fundamental supernodes */ /* ---------------------------------------------------------------------- */ /* count the number of children of each node, using Wi [ */ for (j = 0 ; j < n ; j++) { Wi [j] = 0 ; } for (j = 0 ; j < n ; j++) { parent = Parent [j] ; if (parent != EMPTY) { Wi [parent]++ ; } } Super = Head ; /* use Head [0..nfsuper] as workspace for Super list ( */ /* column 0 always starts a new supernode */ nfsuper = (n == 0) ? 0 : 1 ; /* number of fundamental supernodes */ Super [0] = 0 ; for (j = 1 ; j < n ; j++) { /* check if j starts new supernode, or in the same supernode as j-1 */ if (Parent [j-1] != j /* parent of j-1 is not j */ || (ColCount [j-1] != ColCount [j] + 1) /* j-1 not subset of j*/ || Wi [j] > 1) /* j has more than one child */ { /* j is the leading node of a supernode */ Super [nfsuper++] = j ; } } Super [nfsuper] = n ; /* contents of Wi no longer needed for child count ] */ Nscol = Wi ; /* use Wi as size-nfsuper workspace for Nscol [ */ /* ---------------------------------------------------------------------- */ /* find the mapping of fundamental nodes to supernodes */ /* ---------------------------------------------------------------------- */ SuperMap = Wj ; /* use Wj as workspace for SuperMap [ */ /* SuperMap [k] = s if column k is contained in supernode s */ for (s = 0 ; s < nfsuper ; s++) { for (k = Super [s] ; k < Super [s+1] ; k++) { SuperMap [k] = s ; } } /* ---------------------------------------------------------------------- */ /* construct the fundamental supernodal etree */ /* ---------------------------------------------------------------------- */ for (s = 0 ; s < nfsuper ; s++) { j = Super [s+1] - 1 ; /* last node in supernode s */ parent = Parent [j] ; /* parent of last node */ Sparent [s] = (parent == EMPTY) ? EMPTY : SuperMap [parent] ; PRINT1 (("Sparent ["ID"] = "ID"\n", s, Sparent [s])) ; } /* contents of Wj no longer needed as workspace for SuperMap ] * SuperMap will be recomputed below, for the relaxed supernodes. */ Zeros = Wj ; /* use Wj for Zeros, workspace of size nfsuper [ */ /* ---------------------------------------------------------------------- */ /* relaxed amalgamation */ /* ---------------------------------------------------------------------- */ for (s = 0 ; s < nfsuper ; s++) { Merged [s] = EMPTY ; /* s not merged into another */ Nscol [s] = Super [s+1] - Super [s] ; /* # of columns in s */ Zeros [s] = 0 ; /* # of zero entries in s */ ASSERT (s <= Super [s]) ; Snz [s] = ColCount [Super [s]] ; /* # of entries in leading col of s */ PRINT2 (("lnz ["ID"] "ID"\n", s, Snz [s])) ; } for (s = nfsuper-2 ; s >= 0 ; s--) { /* should supernodes s and s+1 merge into a new node s? */ PRINT1 (("\n========= Check relax of s "ID" and s+1 "ID"\n", s, s+1)) ; ss = Sparent [s] ; if (ss == EMPTY) { PRINT1 (("s "ID" is a root, no merge with s+1 = "ID"\n", s, s+1)) ; continue ; } /* find the current parent of s (perform path compression as needed) */ for (ss = Sparent [s] ; Merged [ss] != EMPTY ; ss = Merged [ss]) ; sparent = ss ; PRINT2 (("Current sparent of s "ID" is "ID"\n", s, sparent)) ; /* ss is the current parent of s */ for (ss = Sparent [s] ; Merged [ss] != EMPTY ; ss = snext) { snext = Merged [ss] ; PRINT2 (("ss "ID" is dead, merged into snext "ID"\n", ss, snext)) ; Merged [ss] = sparent ; } /* if s+1 is not the current parent of s, do not merge */ if (sparent != s+1) { continue ; } nscol0 = Nscol [s] ; /* # of columns in s */ nscol1 = Nscol [s+1] ; /* # of columns in s+1 */ ns = nscol0 + nscol1 ; PRINT2 (("ns "ID" nscol0 "ID" nscol1 "ID"\n", ns, nscol0, nscol1)) ; totzeros = Zeros [s+1] ; /* current # of zeros in s+1 */ /* determine if supernodes s and s+1 should merge */ if (ns <= nrelax0) { PRINT2 (("ns is tiny ("ID"), so go ahead and merge\n", ns)) ; merge = TRUE ; } else { /* use double to avoid integer overflow */ double lnz0 = Snz [s] ; /* # entries in leading column of s */ double lnz1 = Snz [s+1] ; /* # entries in leading column of s+1 */ double xnewzeros = nscol0 * (lnz1 + nscol0 - lnz0) ; /* use Int for the final update of Zeros [s] below */ newzeros = nscol0 * (Snz [s+1] + nscol0 - Snz [s]) ; ASSERT (newzeros == xnewzeros) ; PRINT2 (("lnz0 %g lnz1 %g xnewzeros %g\n", lnz0, lnz1, xnewzeros)) ; if (xnewzeros == 0) { /* no new zeros, so go ahead and merge */ PRINT2 (("no new fillin, so go ahead and merge\n")) ; merge = TRUE ; } else { /* # of zeros if merged */ double xtotzeros = ((double) totzeros) + xnewzeros ; /* xtotsize: total size of merged supernode, if merged: */ double xns = (double) ns ; double xtotsize = (xns * (xns+1) / 2) + xns * (lnz1 - nscol1) ; double z = xtotzeros / xtotsize ; Int totsize ; totsize = (ns * (ns+1) / 2) + ns * (Snz [s+1] - nscol1) ; PRINT2 (("oldzeros "ID" newzeros "ID" xtotsize %g z %g\n", Zeros [s+1], newzeros, xtotsize, z)) ; /* use Int for the final update of Zeros [s] below */ totzeros += newzeros ; /* do not merge if supernode would become too big * (Int overflow). Continue computing; not (yet) an error. */ /* fl.pt. compare, but no NaN's can occur here */ merge = ((ns <= nrelax1 && z < zrelax0) || (ns <= nrelax2 && z < zrelax1) || (z < zrelax2)) && (xtotsize < Int_max / sizeof (double)) ; } } if (merge) { PRINT1 (("Merge node s ("ID") and s+1 ("ID")\n", s, s+1)) ; Zeros [s] = totzeros ; Merged [s+1] = s ; Snz [s] = nscol0 + Snz [s+1] ; Nscol [s] += Nscol [s+1] ; } } /* contents of Wj no longer needed for Zeros ] */ /* contents of Wi no longer needed for Nscol ] */ /* contents of Sparent no longer needed (recomputed below) */ /* ---------------------------------------------------------------------- */ /* construct the relaxed supernode list */ /* ---------------------------------------------------------------------- */ nsuper = 0 ; for (s = 0 ; s < nfsuper ; s++) { if (Merged [s] == EMPTY) { PRINT1 (("live supernode: "ID" snz "ID"\n", s, Snz [s])) ; Super [nsuper] = Super [s] ; Snz [nsuper] = Snz [s] ; nsuper++ ; } } Super [nsuper] = n ; PRINT1 (("Fundamental supernodes: "ID" relaxed "ID"\n", nfsuper, nsuper)) ; /* Merged no longer needed ] */ /* ---------------------------------------------------------------------- */ /* find the mapping of relaxed nodes to supernodes */ /* ---------------------------------------------------------------------- */ /* use Wj as workspace for SuperMap { */ /* SuperMap [k] = s if column k is contained in supernode s */ for (s = 0 ; s < nsuper ; s++) { for (k = Super [s] ; k < Super [s+1] ; k++) { SuperMap [k] = s ; } } /* ---------------------------------------------------------------------- */ /* construct the relaxed supernodal etree */ /* ---------------------------------------------------------------------- */ for (s = 0 ; s < nsuper ; s++) { j = Super [s+1] - 1 ; /* last node in supernode s */ parent = Parent [j] ; /* parent of last node */ Sparent [s] = (parent == EMPTY) ? EMPTY : SuperMap [parent] ; PRINT1 (("new Sparent ["ID"] = "ID"\n", s, Sparent [s])) ; } /* ---------------------------------------------------------------------- */ /* determine the size of L->s and L->x */ /* ---------------------------------------------------------------------- */ ssize = 0 ; xsize = 0 ; xxsize = 0 ; for (s = 0 ; s < nsuper ; s++) { nscol = Super [s+1] - Super [s] ; nsrow = Snz [s] ; ASSERT (nscol > 0) ; ssize += nsrow ; xsize += nscol * nsrow ; /* also compute xsize in double to guard against Int overflow */ xxsize += ((double) nscol) * ((double) nsrow) ; if (xxsize > Int_max) { /* Int overflow, clear workspace and return */ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; FREE_WORKSPACE ; return (FALSE) ; } ASSERT (ssize > 0 && xsize > 0) ; } xsize = MAX (1, xsize) ; ssize = MAX (1, ssize) ; PRINT1 (("ix sizes: "ID" "ID" nsuper "ID"\n", ssize, xsize, nsuper)) ; /* ---------------------------------------------------------------------- */ /* allocate L (all except real part L->x) */ /* ---------------------------------------------------------------------- */ L->ssize = ssize ; L->xsize = xsize ; L->nsuper = nsuper ; CHOLMOD(change_factor) (CHOLMOD_PATTERN, TRUE, TRUE, TRUE, TRUE, L, Common); if (Common->status < CHOLMOD_OK) { /* out of memory; L is still a valid simplicial symbolic factor */ FREE_WORKSPACE ; return (FALSE) ; } DEBUG (CHOLMOD(dump_factor) (L, "L to symbolic super", Common)) ; ASSERT (L->is_ll && L->xtype == CHOLMOD_PATTERN && L->is_super) ; Lpi = L->pi ; Lpx = L->px ; Ls = L->s ; Ls [0] = 0 ; /* flag for cholmod_check_factor; supernodes are defined */ Lsuper = L->super ; /* copy the list of relaxed supernodes into the final list in L */ for (s = 0 ; s <= nsuper ; s++) { Lsuper [s] = Super [s] ; } /* Head no longer needed as workspace for fundamental Super list ) */ Super = Lsuper ; /* Super is now the list of relaxed supernodes */ /* ---------------------------------------------------------------------- */ /* construct column pointers of relaxed supernodal pattern (L->pi) */ /* ---------------------------------------------------------------------- */ p = 0 ; for (s = 0 ; s < nsuper ; s++) { Lpi [s] = p ; p += Snz [s] ; PRINT1 (("Snz ["ID"] = "ID", Super ["ID"] = "ID"\n", s, Snz [s], s, Super[s])) ; } Lpi [nsuper] = p ; ASSERT ((Int) (L->ssize) == MAX (1,p)) ; /* ---------------------------------------------------------------------- */ /* construct pointers for supernodal values (L->px) */ /* ---------------------------------------------------------------------- */ p = 0 ; for (s = 0 ; s < nsuper ; s++) { nscol = Super [s+1] - Super [s] ; /* number of columns in s */ nsrow = Snz [s] ; /* # of rows, incl triangular part*/ Lpx [s] = p ; /* pointer to numerical part of s */ p += nscol * nsrow ; } Lpx [s] = p ; ASSERT ((Int) (L->xsize) == MAX (1,p)) ; /* Snz no longer needed ] */ /* ---------------------------------------------------------------------- */ /* symbolic analysis to construct the relaxed supernodal pattern (L->s) */ /* ---------------------------------------------------------------------- */ Lpi2 = Wi ; /* copy Lpi into Lpi2, using Wi as workspace for Lpi2 [ */ for (s = 0 ; s < nsuper ; s++) { Lpi2 [s] = Lpi [s] ; } for (s = 0 ; s < nsuper ; s++) { /* sth supernode is in columns k1 to k2-1. * compute nonzero pattern of L (k1:k2-1,:). */ /* place rows k1 to k2-1 in leading column of supernode s */ k1 = Super [s] ; k2 = Super [s+1] ; PRINT1 (("=========>>> Supernode "ID" k1 "ID" k2-1 "ID"\n", s, k1, k2-1)) ; for (k = k1 ; k < k2 ; k++) { Ls [Lpi2 [s]++] = k ; } /* compute nonzero pattern each row k1 to k2-1 */ for (k = k1 ; k < k2 ; k++) { /* compute row k of L. In the symmetric case, the pattern of L(k,:) * is the set of nodes reachable in the supernodal etree from any * row i in the nonzero pattern of A(0:k,k). In the unsymmetric * case, the pattern of the kth column of A*A' is the set union * of all columns A(0:k,j) for each nonzero F(j,k). */ /* clear the Flag array and mark the current supernode */ /* mark = CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; Flag [s] = mark ; ASSERT (s == SuperMap [k]) ; /* traverse the row subtree for each nonzero in A or AA' */ if (stype != 0) { subtree (k, k, Ap, Ai, Anz, SuperMap, Sparent, mark, Flag, Ls, Lpi2) ; } else { /* for each nonzero in F (k,:) do */ p = Fp [k] ; pend = (packed) ? (Fp [k+1]) : (p + Fnz [k]) ; for ( ; p < pend ; p++) { subtree (Fj [p], k, Ap, Ai, Anz, SuperMap, Sparent, mark, Flag, Ls, Lpi2) ; } } } } #ifndef NDEBUG for (s = 0 ; s < nsuper ; s++) { PRINT1 (("Lpi2[s] "ID" Lpi[s+1] "ID"\n", Lpi2 [s], Lpi [s+1])) ; ASSERT (Lpi2 [s] == Lpi [s+1]) ; CHOLMOD(dump_super) (s, Super, Lpi, Ls, NULL, NULL, 0, Common) ; } #endif /* contents of Wi no longer needed for Lpi2 ] */ /* Sparent no longer needed ] */ /* ---------------------------------------------------------------------- */ /* determine the largest update matrix (L->maxcsize) */ /* ---------------------------------------------------------------------- */ /* maxcsize could be determined before L->s is allocated and defined, which * would mean that all memory requirements for both the symbolic and numeric * factorizations could be computed using O(nnz(A)+O(n)) space. However, it * would require a lot of extra work. The analysis phase, above, would need * to be duplicated, but with Ls not kept; instead, the algorithm would keep * track of the current s and slast for each supernode d, and update them * when a new row index appears in supernode d. An alternative would be to * do this computation only if the allocation of L->s failed, in which case * the following code would be skipped. * * The csize for a supernode is the size of its largest contribution to * a subsequent ancestor supernode. For example, suppose the rows of #'s * in the figure below correspond to the columns of a subsequent supernode, * and the dots are the entries in that ancestore. * * c * c c * c c c * x x x * x x x * # # # . * # # # . . * * * * . . * * * * . . * * * * . . * . . * * Then for this update, the csize is 3-by-2, or 6, because there are 3 * rows of *'s which is the number of rows in the update, and there are * 2 rows of #'s, which is the number columns in the update. The csize * of a supernode is the largest such contribution for any ancestor * supernode. maxcsize, for the whole matrix, has a rough upper bound of * the maximum size of any supernode. This bound is loose, because the * the contribution must be less than the size of the ancestor supernodal * that it's updating. maxcsize of a completely dense matrix, with one * supernode, is zero. * * maxesize is the column dimension for the workspace E needed for the * solve. E is of size nrhs-by-maxesize, where the nrhs is the number of * columns in the right-hand-side. The maxesize is the largest esize of * any supernode. The esize of a supernode is the number of row indices * it contains, excluding the column indices of the supernode itself. * For the following example, esize is 4: * * c * c c * c c c * x x x * x x x * x x x * x x x * * maxesize can be no bigger than n. */ maxcsize = 1 ; maxesize = 1 ; /* do not need to guard csize against Int overflow if xsize is OK */ for (d = 0 ; d < nsuper ; d++) { nscol = Super [d+1] - Super [d] ; p = Lpi [d] + nscol ; plast = p ; pend = Lpi [d+1] ; esize = pend - p ; maxesize = MAX (maxesize, esize) ; slast = (p == pend) ? (EMPTY) : (SuperMap [Ls [p]]) ; for ( ; p <= pend ; p++) { s = (p == pend) ? (EMPTY) : (SuperMap [Ls [p]]) ; if (s != slast) { /* row i is the start of a new supernode */ ndrow1 = p - plast ; ndrow2 = pend - plast ; csize = ndrow2 * ndrow1 ; PRINT1 (("Supernode "ID" ancestor "ID" C: "ID"-by-"ID" csize " ""ID"\n", d, slast, ndrow1, ndrow2, csize)) ; maxcsize = MAX (maxcsize, csize) ; plast = p ; slast = s ; } } } PRINT1 (("max csize "ID"\n", maxcsize)) ; /* Wj no longer needed for SuperMap } */ L->maxcsize = maxcsize ; L->maxesize = maxesize ; L->is_super = TRUE ; ASSERT (L->xtype == CHOLMOD_PATTERN && L->is_ll) ; /* ---------------------------------------------------------------------- */ /* supernodal symbolic factorization is complete */ /* ---------------------------------------------------------------------- */ FREE_WORKSPACE ; return (TRUE) ; } #endif SuiteSparse/CHOLMOD/Modify/0000755001170100242450000000000010671565460014275 5ustar davisfacSuiteSparse/CHOLMOD/Modify/cholmod_rowadd.c0000644001170100242450000004644510635770727017447 0ustar davisfac/* ========================================================================== */ /* === Modify/cholmod_rowadd ================================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Modify Module. * Copyright (C) 2005-2006, Timothy A. Davis and William W. Hager. * The CHOLMOD/Modify Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Adds a row and column to an LDL' factorization, and optionally updates the * solution to Lx=b. * * workspace: Flag (nrow), Head (nrow+1), W (2*nrow), Iwork (2*nrow) * * Only real matrices are supported. A symbolic L is converted into a * numeric identity matrix before the row is added. */ #ifndef NMODIFY #include "cholmod_internal.h" #include "cholmod_modify.h" /* ========================================================================== */ /* === cholmod_rowadd ======================================================= */ /* ========================================================================== */ /* cholmod_rowadd adds a row to the LDL' factorization. It computes the kth * row and kth column of L, and then updates the submatrix L (k+1:n,k+1:n) * accordingly. The kth row and column of L should originally be equal to the * kth row and column of the identity matrix (they are treated as such, if they * are not). The kth row/column of L is computed as the factorization of the * kth row/column of the matrix to factorize, which is provided as a single * n-by-1 sparse matrix R. The sparse vector R need not be sorted. */ int CHOLMOD(rowadd) ( /* ---- input ---- */ size_t k, /* row/column index to add */ cholmod_sparse *R, /* row/column of matrix to factorize (n-by-1) */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) { double bk [2] ; bk [0] = 0. ; bk [1] = 0. ; return (CHOLMOD(rowadd_mark) (k, R, bk, NULL, L, NULL, NULL, Common)) ; } /* ========================================================================== */ /* === cholmod_rowadd_solve ================================================= */ /* ========================================================================== */ /* Does the same as cholmod_rowadd, and also updates the solution to Lx=b * See cholmod_updown for a description of how Lx=b is updated. There is on * additional parameter: bk specifies the new kth entry of b. */ int CHOLMOD(rowadd_solve) ( /* ---- input ---- */ size_t k, /* row/column index to add */ cholmod_sparse *R, /* row/column of matrix to factorize (n-by-1) */ double bk [2], /* kth entry of the right-hand-side b */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) { return (CHOLMOD(rowadd_mark) (k, R, bk, NULL, L, X, DeltaB, Common)) ; } /* ========================================================================== */ /* === icomp ================================================================ */ /* ========================================================================== */ /* for sorting by qsort */ static int icomp (Int *i, Int *j) { if (*i < *j) { return (-1) ; } else { return (1) ; } } /* ========================================================================== */ /* === cholmod_rowadd_mark ================================================== */ /* ========================================================================== */ /* Does the same as cholmod_rowadd_solve, except only part of L is used in * the update/downdate of the solution to Lx=b. This routine is an "expert" * routine. It is meant for use in LPDASA only. */ int CHOLMOD(rowadd_mark) ( /* ---- input ---- */ size_t kadd, /* row/column index to add */ cholmod_sparse *R, /* row/column of matrix to factorize (n-by-1) */ double bk [2], /* kth entry of the right hand side, b */ Int *colmark, /* Int array of size 1. See cholmod_updown.c */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) { double dk, yj, l_kj, lx, l_ij, sqrt_dk, dj, xk, rnz, fl ; double *Lx, *W, *Cx, *Rx, *Xx, *Nx ; Int *Li, *Lp, *Lnz, *Flag, *Stack, *Ci, *Rj, *Rp, *Lnext, *Iwork, *Rnz ; cholmod_sparse *C, Cmatrix ; Int i, j, p, pend, top, len, kk, li, lnz, mark, k, n, parent, Cp [2], do_solve, do_update ; size_t s ; int ok = TRUE ; DEBUG (Int lastrow) ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_NULL (R, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_REAL, FALSE) ; RETURN_IF_XTYPE_INVALID (R, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ; n = L->n ; k = kadd ; if (kadd >= L->n || k < 0) { ERROR (CHOLMOD_INVALID, "k invalid") ; return (FALSE) ; } if (R->ncol != 1 || R->nrow != L->n) { ERROR (CHOLMOD_INVALID, "R invalid") ; return (FALSE) ; } Rj = R->i ; Rx = R->x ; Rp = R->p ; Rnz = R->nz ; rnz = (R->packed) ? (Rp [1]) : (Rnz [0]) ; do_solve = (X != NULL) && (DeltaB != NULL) ; if (do_solve) { RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ; RETURN_IF_XTYPE_INVALID (DeltaB, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ; Xx = X->x ; Nx = DeltaB->x ; if (X->nrow != L->n || X->ncol != 1 || DeltaB->nrow != L->n || DeltaB->ncol != 1 || Xx == NULL || Nx == NULL) { ERROR (CHOLMOD_INVALID, "X and/or DeltaB invalid") ; return (FALSE) ; } } else { Xx = NULL ; Nx = NULL ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = 2*n */ s = CHOLMOD(mult_size_t) (n, 2, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (n, s, s, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, s, Common)) ; /* ---------------------------------------------------------------------- */ /* convert to simplicial numeric LDL' factor, if not already */ /* ---------------------------------------------------------------------- */ if (L->xtype == CHOLMOD_PATTERN || L->is_super || L->is_ll) { /* can only update/downdate a simplicial LDL' factorization */ CHOLMOD(change_factor) (CHOLMOD_REAL, FALSE, FALSE, FALSE, FALSE, L, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory, L is returned unchanged */ return (FALSE) ; } } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ /* inputs, not modified on output: */ Lp = L->p ; /* size n+1. input, not modified on output */ /* outputs, contents defined on input for incremental case only: */ Lnz = L->nz ; /* size n */ Li = L->i ; /* size L->nzmax. Can change in size. */ Lx = L->x ; /* size L->nzmax. Can change in size. */ Lnext = L->next ; /* size n+2 */ ASSERT (L->nz != NULL) ; PRINT1 (("rowadd:\n")) ; fl = 0 ; #if 0 #ifndef NDEBUG /* column k of L should be zero, except for the diagonal. This test is * overly cautious. */ for (p = Lp [k] + 1 ; p < Lp [k] + Lnz [k] ; p++) ASSERT (Lx [p] == 0) ; #endif #endif /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Flag = Common->Flag ; /* size n */ W = Common->Xwork ; /* size n */ Cx = W + n ; /* size n (use 2nd column of Xwork for C) */ Iwork = Common->Iwork ; Stack = Iwork ; /* size n (i/i/l), also in cholmod_updown */ Ci = Iwork + n ; /* size n (i/i/l) */ /* NOTE: cholmod_updown uses Iwork [0..n-1] (i/i/l) as Stack as well */ mark = Common->mark ; /* copy Rj/Rx into W/Ci */ for (p = 0 ; p < rnz ; p++) { i = Rj [p] ; ASSERT (i >= 0 && i < n) ; W [i] = Rx [p] ; Ci [p] = i ; } /* At this point, W [Ci [0..rnz-1]] holds the sparse vector to add */ /* The nonzero pattern of column W is held in Ci (it may be unsorted). */ /* ---------------------------------------------------------------------- */ /* symbolic factorization to get pattern of kth row of L */ /* ---------------------------------------------------------------------- */ DEBUG (for (p = 0 ; p < rnz ; p++) PRINT1 (("C ("ID",%g)\n", Ci [p], W [Ci [p]]))) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* flag the diagonal */ Flag [k] = mark ; /* find the union of all the paths */ top = n ; lnz = 0 ; /* # of nonzeros in column k of L, excluding diagonal */ for (p = 0 ; p < rnz ; p++) { i = Ci [p] ; if (i < k) { /* walk from i = entry in Ci to root (and stop if i marked)*/ PRINT2 (("\nwalk from i = "ID" towards k = "ID"\n", i, k)) ; len = 0 ; /* walk up tree, but stop if we go below the diagonal */ while (i < k && i != EMPTY && Flag [i] < mark) { PRINT2 ((" Add "ID" to path\n", i)) ; ASSERT (i >= 0 && i < k) ; Stack [len++] = i ; /* place i on the stack */ Flag [i] = mark ; /* mark i as visited */ /* parent is the first entry in the column after the diagonal */ ASSERT (Lnz [i] > 0) ; parent = (Lnz [i] > 1) ? (Li [Lp [i] + 1]) : EMPTY ; PRINT2 ((" parent: "ID"\n", parent)) ; i = parent ; /* go up the tree */ } ASSERT (len <= top) ; /* move the path down to the bottom of the stack */ /* this shifts Stack [0..len-1] down to [ ... oldtop-1] */ while (len > 0) { Stack [--top] = Stack [--len] ; } } else if (i > k) { /* prune the diagonal and upper triangular entries from Ci */ Ci [lnz++] = i ; Flag [i] = mark ; } } #ifndef NDEBUG PRINT1 (("length of S after prune: "ID"\n", lnz)) ; for (p = 0 ; p < lnz ; p++) { PRINT1 (("After prune Ci ["ID"] = "ID"\n", p, Ci [p])) ; ASSERT (Ci [p] > k) ; } #endif /* ---------------------------------------------------------------------- */ /* ensure each column of L has enough space to grow */ /* ---------------------------------------------------------------------- */ for (kk = top ; kk < n ; kk++) { /* could skip this if we knew column j already included row k */ j = Stack [kk] ; if (Lp [j] + Lnz [j] >= Lp [Lnext [j]]) { PRINT1 (("Col "ID" realloc, old Lnz "ID"\n", j, Lnz [j])) ; if (!CHOLMOD(reallocate_column) (j, Lnz [j] + 1, L, Common)) { /* out of memory, L is now simplicial symbolic */ /* CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; for (i = 0 ; i < n ; i++) { W [i] = 0 ; } return (FALSE) ; } /* L->i and L->x may have moved */ Li = L->i ; Lx = L->x ; } ASSERT (Lp [j] + Lnz [j] < Lp [Lnext [j]] || (Lp [Lnext [j]] - Lp [j] == n-j)) ; } /* ---------------------------------------------------------------------- */ /* compute kth row of L and store in column form */ /* ---------------------------------------------------------------------- */ /* solve L (1:k-1, 1:k-1) * y (1:k-1) = b (1:k-1) */ /* where b (1:k) is in W and Ci */ /* L (k, 1:k-1) = y (1:k-1) ./ D (1:k-1) */ /* D (k) = B (k,k) - L (k, 1:k-1) * y (1:k-1) */ PRINT2 (("\nForward solve: "ID" to "ID"\n", top, n)) ; ASSERT (Lnz [k] >= 1 && Li [Lp [k]] == k) ; DEBUG (for (i = top ; i < n ; i++) PRINT2 ((" Path: "ID"\n", Stack [i]))) ; dk = W [k] ; W [k] = 0.0 ; /* if do_solve: compute x (k) = b (k) - L (k, 1:k-1) * x (1:k-1) */ xk = bk [0] ; PRINT2 (("B [k] = %g\n", xk)) ; for (kk = top ; kk < n ; kk++) { j = Stack [kk] ; i = j ; PRINT2 (("Forward solve col j = "ID":\n", j)) ; ASSERT (j >= 0 && j < k) ; /* forward solve using L (j+1:k-1,j) */ yj = W [j] ; W [j] = 0.0 ; p = Lp [j] ; pend = p + Lnz [j] ; ASSERT (Lnz [j] > 0) ; dj = Lx [p++] ; for ( ; p < pend ; p++) { i = Li [p] ; PRINT2 ((" row "ID"\n", i)) ; ASSERT (i > j) ; ASSERT (i < n) ; /* stop at row k */ if (i >= k) { break ; } W [i] -= Lx [p] * yj ; } /* each iteration of the above for loop did 2 flops, and 3 flops * are done below. so: fl += 2 * (Lp [j] - p - 1) + 3 becomes: */ fl += 2 * (Lp [j] - p) + 1 ; /* scale L (k,1:k-1) and compute dot product for D (k,k) */ l_kj = yj / dj ; dk -= l_kj * yj ; /* compute dot product for X(k) */ if (do_solve) { xk -= l_kj * Xx [j] ; } /* store l_kj in the jth column of L */ /* and shift the rest of the column down */ li = k ; lx = l_kj ; if (i == k) { /* no need to modify the nonzero pattern of L, since it already * contains row index k. */ ASSERT (Li [p] == k) ; Lx [p] = l_kj ; for (p++ ; p < pend ; p++) { i = Li [p] ; l_ij = Lx [p] ; ASSERT (i > k && i < n) ; PRINT2 ((" apply to row "ID" of column k of L\n", i)) ; /* add to the pattern of the kth column of L */ if (Flag [i] < mark) { PRINT2 ((" add Ci["ID"] = "ID"\n", lnz, i)) ; ASSERT (i > k) ; Ci [lnz++] = i ; Flag [i] = mark ; } /* apply the update to the kth column of L */ /* yj is equal to l_kj * d_j */ W [i] -= l_ij * yj ; } } else { PRINT2 (("Shift col j = "ID", apply saxpy to col k of L\n", j)) ; for ( ; p < pend ; p++) { /* swap (Li [p],Lx [p]) with (li,lx) */ i = Li [p] ; l_ij = Lx [p] ; Li [p] = li ; Lx [p] = lx ; li = i ; lx = l_ij ; ASSERT (i > k && i < n) ; PRINT2 ((" apply to row "ID" of column k of L\n", i)) ; /* add to the pattern of the kth column of L */ if (Flag [i] < mark) { PRINT2 ((" add Ci["ID"] = "ID"\n", lnz, i)) ; ASSERT (i > k) ; Ci [lnz++] = i ; Flag [i] = mark ; } /* apply the update to the kth column of L */ /* yj is equal to l_kj * d_j */ W [i] -= l_ij * yj ; } /* store the last value in the jth column of L */ Li [p] = li ; Lx [p] = lx ; Lnz [j]++ ; } } /* ---------------------------------------------------------------------- */ /* merge C with the pattern of the existing column of L */ /* ---------------------------------------------------------------------- */ /* This column should be zero, but it may contain explicit zero entries. * These entries should be kept, not dropped. */ p = Lp [k] ; pend = p + Lnz [k] ; for (p++ ; p < pend ; p++) { i = Li [p] ; /* add to the pattern of the kth column of L */ if (Flag [i] < mark) { PRINT2 ((" add Ci["ID"] = "ID" from existing col k\n", lnz, i)) ; ASSERT (i > k) ; Ci [lnz++] = i ; Flag [i] = mark ; } } /* ---------------------------------------------------------------------- */ if (do_solve) { Xx [k] = xk ; PRINT2 (("Xx [k] = %g\n", Xx [k])) ; } /* ---------------------------------------------------------------------- */ /* ensure abs (dk) >= dbound, if dbound is given */ /* ---------------------------------------------------------------------- */ dk = (IS_GT_ZERO (Common->dbound)) ? (CHOLMOD(dbound) (dk, Common)) : dk ; PRINT2 (("D [k = "ID"] = %g\n", k, dk)) ; /* ---------------------------------------------------------------------- */ /* store the kth column of L */ /* ---------------------------------------------------------------------- */ /* ensure the new column of L has enough space */ if (Lp [k] + lnz + 1 > Lp [Lnext [k]]) { PRINT1 (("New Col "ID" realloc, old Lnz "ID"\n", k, Lnz [k])) ; if (!CHOLMOD(reallocate_column) (k, lnz + 1, L, Common)) { /* out of memory, L is now simplicial symbolic */ CHOLMOD(clear_flag) (Common) ; for (i = 0 ; i < n ; i++) { W [i] = 0 ; } return (FALSE) ; } /* L->i and L->x may have moved */ Li = L->i ; Lx = L->x ; } ASSERT (Lp [k] + lnz + 1 <= Lp [Lnext [k]]) ; #ifndef NDEBUG PRINT2 (("\nPrior to sort: lnz "ID" (excluding diagonal)\n", lnz)) ; for (kk = 0 ; kk < lnz ; kk++) { i = Ci [kk] ; PRINT2 (("L ["ID"] kept: "ID" %e\n", kk, i, W [i] / dk)) ; } #endif /* sort Ci */ qsort (Ci, lnz, sizeof (Int), (int (*) (const void *, const void *)) icomp); /* store the kth column of L */ DEBUG (lastrow = k) ; p = Lp [k] ; Lx [p++] = dk ; Lnz [k] = lnz + 1 ; fl += lnz ; for (kk = 0 ; kk < lnz ; kk++, p++) { i = Ci [kk] ; PRINT2 (("L ["ID"] after sort: "ID", %e\n", kk, i, W [i] / dk)) ; ASSERT (i > lastrow) ; Li [p] = i ; Lx [p] = W [i] / dk ; W [i] = 0.0 ; DEBUG (lastrow = i) ; } /* compute DeltaB for updown (in DeltaB) */ if (do_solve) { p = Lp [k] ; pend = p + Lnz [k] ; for (p++ ; p < pend ; p++) { ASSERT (Li [p] > k) ; Nx [Li [p]] -= Lx [p] * xk ; } } /* clear the flag for the update */ mark = CHOLMOD(clear_flag) (Common) ; /* workspaces are now cleared */ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 2*n, Common)) ; /* ---------------------------------------------------------------------- */ /* update/downdate */ /* ---------------------------------------------------------------------- */ /* update or downdate L (k+1:n, k+1:n) with the vector * C = L (:,k) * sqrt (abs (D [k])). * Do a numeric update if D[k] < 0, numeric downdate otherwise. */ ok = TRUE ; Common->modfl = 0 ; PRINT1 (("rowadd update lnz = "ID"\n", lnz)) ; if (lnz > 0) { do_update = IS_LT_ZERO (dk) ; if (do_update) { dk = -dk ; } sqrt_dk = sqrt (dk) ; p = Lp [k] + 1 ; for (kk = 0 ; kk < lnz ; kk++, p++) { Cx [kk] = Lx [p] * sqrt_dk ; } fl += lnz + 1 ; /* create a n-by-1 sparse matrix to hold the single column */ C = &Cmatrix ; C->nrow = n ; C->ncol = 1 ; C->nzmax = lnz ; C->sorted = TRUE ; C->packed = TRUE ; C->p = Cp ; C->i = Ci ; C->x = Cx ; C->nz = NULL ; C->itype = L->itype ; C->xtype = L->xtype ; C->dtype = L->dtype ; C->z = NULL ; C->stype = 0 ; Cp [0] = 0 ; Cp [1] = lnz ; /* numeric downdate if dk > 0, and optional Lx=b change */ /* workspace: Flag (nrow), Head (nrow+1), W (nrow), Iwork (2*nrow) */ ok = CHOLMOD(updown_mark) (do_update ? (1) : (0), C, colmark, L, X, DeltaB, Common) ; /* clear workspace */ for (kk = 0 ; kk < lnz ; kk++) { Cx [kk] = 0 ; } } Common->modfl += fl ; DEBUG (CHOLMOD(dump_factor) (L, "LDL factorization, L:", Common)) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 2*n, Common)) ; return (ok) ; } #endif SuiteSparse/CHOLMOD/Modify/cholmod_rowdel.c0000644001170100242450000003174510537777751017465 0ustar davisfac/* ========================================================================== */ /* === Modify/cholmod_rowdel ================================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Modify Module. * Copyright (C) 2005-2006, Timothy A. Davis and William W. Hager. * The CHOLMOD/Modify Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Deletes a row and column from an LDL' factorization. The row and column k * is set to the kth row and column of the identity matrix. Optionally * downdates the solution to Lx=b. * * workspace: Flag (nrow), Head (nrow+1), W (nrow*2), Iwork (2*nrow) * * Only real matrices are supported (exception: since only the pattern of R * is used, it can have any valid xtype). */ #ifndef NMODIFY #include "cholmod_internal.h" #include "cholmod_modify.h" /* ========================================================================== */ /* === cholmod_rowdel ======================================================= */ /* ========================================================================== */ /* Sets the kth row and column of L to be the kth row and column of the identity * matrix, and updates L(k+1:n,k+1:n) accordingly. To reduce the running time, * the caller can optionally provide the nonzero pattern (or an upper bound) of * kth row of L, as the sparse n-by-1 vector R. Provide R as NULL if you want * CHOLMOD to determine this itself, which is easier for the caller, but takes * a little more time. */ int CHOLMOD(rowdel) ( /* ---- input ---- */ size_t k, /* row/column index to delete */ cholmod_sparse *R, /* NULL, or the nonzero pattern of kth row of L */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) { double yk [2] ; yk [0] = 0. ; yk [1] = 0. ; return (CHOLMOD(rowdel_mark) (k, R, yk, NULL, L, NULL, NULL, Common)) ; } /* ========================================================================== */ /* === cholmod_rowdel_solve ================================================= */ /* ========================================================================== */ /* Does the same as cholmod_rowdel, but also downdates the solution to Lx=b. * When row/column k of A is "deleted" from the system A*y=b, this can induce * a change to x, in addition to changes arising when L and b are modified. * If this is the case, the kth entry of y is required as input (yk) */ int CHOLMOD(rowdel_solve) ( /* ---- input ---- */ size_t k, /* row/column index to delete */ cholmod_sparse *R, /* NULL, or the nonzero pattern of kth row of L */ double yk [2], /* kth entry in the solution to A*y=b */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) { return (CHOLMOD(rowdel_mark) (k, R, yk, NULL, L, X, DeltaB, Common)) ; } /* ========================================================================== */ /* === cholmod_rowdel_mark ================================================== */ /* ========================================================================== */ /* Does the same as cholmod_rowdel_solve, except only part of L is used in * the update/downdate of the solution to Lx=b. This routine is an "expert" * routine. It is meant for use in LPDASA only. * * if R == NULL then columns 0:k-1 of L are searched for row k. Otherwise, it * searches columns in the set defined by the pattern of the first column of R. * This is meant to be the pattern of row k of L (a superset of that pattern is * OK too). R must be a permutation of a subset of 0:k-1. */ int CHOLMOD(rowdel_mark) ( /* ---- input ---- */ size_t kdel, /* row/column index to delete */ cholmod_sparse *R, /* NULL, or the nonzero pattern of kth row of L */ double yk [2], /* kth entry in the solution to A*y=b */ Int *colmark, /* Int array of size 1. See cholmod_updown.c */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) { double dk, sqrt_dk, xk, dj, fl ; double *Lx, *Cx, *W, *Xx, *Nx ; Int *Li, *Lp, *Lnz, *Ci, *Rj, *Rp, *Iwork ; cholmod_sparse *C, Cmatrix ; Int j, p, pend, kk, lnz, n, Cp [2], do_solve, do_update, left, k, right, middle, i, klast, given_row, rnz ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_REAL, FALSE) ; n = L->n ; k = kdel ; if (kdel >= L->n || k < 0) { ERROR (CHOLMOD_INVALID, "k invalid") ; return (FALSE) ; } if (R == NULL) { Rj = NULL ; rnz = EMPTY ; } else { RETURN_IF_XTYPE_INVALID (R, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; if (R->ncol != 1 || R->nrow != L->n) { ERROR (CHOLMOD_INVALID, "R invalid") ; return (FALSE) ; } Rj = R->i ; Rp = R->p ; rnz = Rp [1] ; } do_solve = (X != NULL) && (DeltaB != NULL) ; if (do_solve) { RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ; RETURN_IF_XTYPE_INVALID (DeltaB, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ; Xx = X->x ; Nx = DeltaB->x ; if (X->nrow != L->n || X->ncol != 1 || DeltaB->nrow != L->n || DeltaB->ncol != 1 || Xx == NULL || Nx == NULL) { ERROR (CHOLMOD_INVALID, "X and/or DeltaB invalid") ; return (FALSE) ; } } else { Xx = NULL ; Nx = NULL ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = 2*n */ s = CHOLMOD(mult_size_t) (n, 2, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (n, s, s, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 2*n, Common)) ; /* ---------------------------------------------------------------------- */ /* convert to simplicial numeric LDL' factor, if not already */ /* ---------------------------------------------------------------------- */ if (L->xtype == CHOLMOD_PATTERN || L->is_super || L->is_ll) { /* can only update/downdate a simplicial LDL' factorization */ CHOLMOD(change_factor) (CHOLMOD_REAL, FALSE, FALSE, FALSE, FALSE, L, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory, L is returned unchanged */ return (FALSE) ; } } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ /* inputs, not modified on output: */ Lp = L->p ; /* size n+1 */ /* outputs, contents defined on input for incremental case only: */ Lnz = L->nz ; /* size n */ Li = L->i ; /* size L->nzmax. Can change in size. */ Lx = L->x ; /* size L->nzmax. Can change in size. */ ASSERT (L->nz != NULL) ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ W = Common->Xwork ; /* size n, used only in cholmod_updown */ Cx = W + n ; /* use 2nd column of Xwork for C (size n) */ Iwork = Common->Iwork ; Ci = Iwork + n ; /* size n (i/i/l) */ /* NOTE: cholmod_updown uses Iwork [0..n-1] (i/i/l) as Stack */ /* ---------------------------------------------------------------------- */ /* prune row k from all columns of L */ /* ---------------------------------------------------------------------- */ given_row = (rnz >= 0) ; klast = given_row ? rnz : k ; PRINT2 (("given_row "ID"\n", given_row)) ; for (kk = 0 ; kk < klast ; kk++) { /* either search j = 0:k-1 or j = Rj [0:rnz-1] */ j = given_row ? (Rj [kk]) : (kk) ; if (j < 0 || j >= k) { ERROR (CHOLMOD_INVALID, "R invalid") ; return (FALSE) ; } PRINT2 (("Prune col j = "ID":\n", j)) ; lnz = Lnz [j] ; dj = Lx [Lp [j]] ; ASSERT (Lnz [j] > 0 && Li [Lp [j]] == j) ; if (lnz > 1) { left = Lp [j] ; pend = left + lnz ; right = pend - 1 ; i = Li [right] ; if (i < k) { /* row k is not in column j */ continue ; } else if (i == k) { /* k is the last row index in this column (quick delete) */ if (do_solve) { Xx [j] -= yk [0] * dj * Lx [right] ; } Lx [right] = 0 ; } else { /* binary search for row k in column j */ PRINT2 (("\nBinary search: lnz "ID" k = "ID"\n", lnz, k)) ; while (left < right) { middle = (left + right) / 2 ; PRINT2 (("left "ID" right "ID" middle "ID": ["ID" "ID"" ""ID"]\n", left, right, middle, Li [left], Li [middle], Li [right])) ; if (k > Li [middle]) { left = middle + 1 ; } else { right = middle ; } } ASSERT (left >= Lp [j] && left < pend) ; #ifndef NDEBUG /* brute force, linear-time search */ { Int p3 = Lp [j] ; i = EMPTY ; PRINT2 (("Brute force:\n")) ; for ( ; p3 < pend ; p3++) { i = Li [p3] ; PRINT2 (("p "ID" ["ID"]\n", p3, i)) ; if (i >= k) { break ; } } if (i == k) { ASSERT (k == Li [p3]) ; ASSERT (p3 == left) ; } } #endif if (k == Li [left]) { if (do_solve) { Xx [j] -= yk [0] * dj * Lx [left] ; } /* found row k in column j. Prune it from the column.*/ Lx [left] = 0 ; } } } } #ifndef NDEBUG /* ensure that row k has been deleted from the matrix L */ for (j = 0 ; j < k ; j++) { Int lasti ; lasti = EMPTY ; p = Lp [j] ; pend = p + Lnz [j] ; /* look for row k in column j */ PRINT1 (("Pruned column "ID"\n", j)) ; for ( ; p < pend ; p++) { i = Li [p] ; PRINT2 ((" "ID"", i)) ; PRINT2 ((" %g\n", Lx [p])) ; ASSERT (IMPLIES (i == k, Lx [p] == 0)) ; ASSERT (i > lasti) ; lasti = i ; } PRINT1 (("\n")) ; } #endif /* ---------------------------------------------------------------------- */ /* set diagonal and clear column k of L */ /* ---------------------------------------------------------------------- */ lnz = Lnz [k] - 1 ; ASSERT (Lnz [k] > 0) ; /* ---------------------------------------------------------------------- */ /* update/downdate */ /* ---------------------------------------------------------------------- */ /* update or downdate L (k+1:n, k+1:n) with the vector * C = L (:,k) * sqrt (abs (D [k])) * Do a numeric update if D[k] > 0, numeric downdate otherwise. */ PRINT1 (("rowdel downdate lnz = "ID"\n", lnz)) ; /* store the new unit diagonal */ p = Lp [k] ; pend = p + lnz + 1 ; dk = Lx [p] ; Lx [p++] = 1 ; PRINT2 (("D [k = "ID"] = %g\n", k, dk)) ; ok = TRUE ; fl = 0 ; if (lnz > 0) { /* compute DeltaB for updown (in DeltaB) */ if (do_solve) { xk = Xx [k] - yk [0] * dk ; for ( ; p < pend ; p++) { Nx [Li [p]] += Lx [p] * xk ; } } do_update = IS_GT_ZERO (dk) ; if (!do_update) { dk = -dk ; } sqrt_dk = sqrt (dk) ; p = Lp [k] + 1 ; for (kk = 0 ; kk < lnz ; kk++, p++) { Ci [kk] = Li [p] ; Cx [kk] = Lx [p] * sqrt_dk ; Lx [p] = 0 ; /* clear column k */ } fl = lnz + 1 ; /* create a n-by-1 sparse matrix to hold the single column */ C = &Cmatrix ; C->nrow = n ; C->ncol = 1 ; C->nzmax = lnz ; C->sorted = TRUE ; C->packed = TRUE ; C->p = Cp ; C->i = Ci ; C->x = Cx ; C->nz = NULL ; C->itype = L->itype ; C->xtype = L->xtype ; C->dtype = L->dtype ; C->z = NULL ; C->stype = 0 ; Cp [0] = 0 ; Cp [1] = lnz ; /* numeric update if dk > 0, and with Lx=b change */ /* workspace: Flag (nrow), Head (nrow+1), W (nrow), Iwork (2*nrow) */ ok = CHOLMOD(updown_mark) (do_update ? (1) : (0), C, colmark, L, X, DeltaB, Common) ; /* clear workspace */ for (kk = 0 ; kk < lnz ; kk++) { Cx [kk] = 0 ; } } Common->modfl += fl ; if (do_solve) { /* kth equation becomes identity, so X(k) is now Y(k) */ Xx [k] = yk [0] ; } DEBUG (CHOLMOD(dump_factor) (L, "LDL factorization, L:", Common)) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 2*n, Common)) ; return (ok) ; } #endif SuiteSparse/CHOLMOD/Modify/t_cholmod_updown_numkr.c0000644001170100242450000005166710537777761021252 0ustar davisfac/* ========================================================================== */ /* === Modify/t_cholmod_updown_numkr ======================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Modify Module. Copyright (C) 2005-2006, * Timothy A. Davis and William W. Hager. * The CHOLMOD/Modify Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Supernodal numerical update/downdate of rank K = RANK, along a single path. * This routine operates on a simplicial factor, but operates on adjacent * columns of L that would fit within a single supernode. "Adjacent" means * along a single path in the elimination tree; they may or may not be * adjacent in the matrix L. * * external defines: NUMERIC, WDIM, RANK. * * WDIM is 1, 2, 4, or 8. RANK can be 1 to WDIM. * * A simple method is included (#define SIMPLE). The code works, but is slow. * It is meant only to illustrate what this routine is doing. * * A rank-K update proceeds along a single path, using single-column, dual- * column, or quad-column updates of L. If a column j and the next column * in the path (its parent) do not have the same nonzero pattern, a single- * column update is used. If they do, but the 3rd and 4th column from j do * not have the same pattern, a dual-column update is used, in which the two * columns are treated as if they were a single supernode of two columns. If * there are 4 columns in the path that all have the same nonzero pattern, then * a quad-column update is used. All three kinds of updates can be used along * a single path, in a single call to this function. * * Single-column update: * * When updating a single column of L, each iteration of the for loop, * below, processes four rows of W (all columns involved) and one column * of L. Suppose we have a rank-5 update, and columns 2 through 6 of W * are involved. In this case, W in this routine is a pointer to column * 2 of the matrix W in the caller. W (in the caller, shown as 'W') is * held in row-major order, and is 8-by-n (a dense matrix storage format), * but shown below in column form to match the column of L. Suppose there * are 13 nonzero entries in column 27 of L, with row indices 27 (the * diagonal, D), 28, 30, 31, 42, 43, 44, 50, 51, 67, 81, 83, and 84. This * pattern is held in Li [Lp [27] ... Lp [27 + Lnz [27] - 1], where * Lnz [27] = 13. The modification of the current column j of L is done * in the following order. A dot (.) means the entry of W is not accessed. * * W0 points to row 27 of W, and G is a 1-by-8 temporary vector. * * G[0] G[4] * G x x x x x . . . * * W0 * | * v * 27 . . x x x x x . W0 points to W (27,2) * * * row 'W' W column j = 27 * | | | of L * v v v | * first iteration of for loop: v * * 28 . . 1 5 9 13 17 . x * 30 . . 2 6 10 14 18 . x * 31 . . 3 7 11 15 19 . x * 42 . . 4 8 12 16 20 . x * * second iteration of for loop: * * 43 . . 1 5 9 13 17 . x * 44 . . 2 6 10 14 18 . x * 50 . . 3 7 11 15 19 . x * 51 . . 4 8 12 16 20 . x * * third iteration of for loop: * * 67 . . 1 5 9 13 17 . x * 81 . . 2 6 10 14 18 . x * 83 . . 3 7 11 15 19 . x * 84 . . 4 8 12 16 20 . x * * If the number of offdiagonal nonzeros in column j of L is not divisible * by 4, then the switch-statement does the work for the first nz % 4 rows. * * Dual-column update: * * In this case, two columns of L that are adjacent in the path are being * updated, by 1 to 8 columns of W. Suppose columns j=27 and j=28 are * adjacent columns in the path (they need not be j and j+1). Two rows * of G and W are used as coefficients during the update: (G0, G1) and * (W0, W1). * * G0 x x x x x . . . * G1 x x x x x . . . * * 27 . . x x x x x . W0 points to W (27,2) * 28 . . x x x x x . W1 points to W (28,2) * * * row 'W' W0,W1 column j = 27 * | | | of L * v v v | * | |-- column j = 28 of L * v v * update L (j1,j): * * 28 . . 1 2 3 4 5 . x - ("-" is not stored in L) * * cleanup iteration since length is odd: * * 30 . . 1 2 3 4 5 . x x * * then each iteration does two rows of both columns of L: * * 31 . . 1 3 5 7 9 . x x * 42 . . 2 4 6 8 10 . x x * * 43 . . 1 3 5 7 9 . x x * 44 . . 2 4 6 8 10 . x x * * 50 . . 1 3 5 7 9 . x x * 51 . . 2 4 6 8 10 . x x * * 67 . . 1 3 5 7 9 . x x * 81 . . 2 4 6 8 10 . x x * * 83 . . 1 3 5 7 9 . x x * 84 . . 2 4 6 8 10 . x x * * If the number of offdiagonal nonzeros in column j of L is not even, * then the cleanup iteration does the work for the first row. * * Quad-column update: * * In this case, four columns of L that are adjacent in the path are being * updated, by 1 to 8 columns of W. Suppose columns j=27, 28, 30, and 31 * are adjacent columns in the path (they need not be j, j+1, ...). Four * rows of G and W are used as coefficients during the update: (G0 through * G3) and (W0 through W3). j=27, j1=28, j2=30, and j3=31. * * G0 x x x x x . . . * G1 x x x x x . . . * G3 x x x x x . . . * G4 x x x x x . . . * * 27 . . x x x x x . W0 points to W (27,2) * 28 . . x x x x x . W1 points to W (28,2) * 30 . . x x x x x . W2 points to W (30,2) * 31 . . x x x x x . W3 points to W (31,2) * * * row 'W' W0,W1,.. column j = 27 * | | | of L * v v v | * | |-- column j = 28 of L * | | |-- column j = 30 of L * | | | |-- column j = 31 of L * v v v v * update L (j1,j): * 28 . . 1 2 3 4 5 . x - - - * * update L (j2,j): * 30 . . 1 2 3 4 5 . # x - - (# denotes modified) * * update L (j2,j1) * 30 . . 1 2 3 4 5 . x # - - * * update L (j3,j) * 31 . . 1 2 3 4 5 . # x x - * * update L (j3,j1) * 31 . . 1 2 3 4 5 . x # x - * * update L (j3,j2) * 31 . . 1 2 3 4 5 . x x # - * * cleanup iteration since length is odd: * 42 . . 1 2 3 4 5 . x x x x * * * ----- CHOLMOD v1.1.1 did the following -------------------------------------- * then each iteration does two rows of all four colummns of L: * * 43 . . 1 3 5 7 9 . x x x x * 44 . . 2 4 6 8 10 . x x x x * * 50 . . 1 3 5 7 9 . x x x x * 51 . . 2 4 6 8 10 . x x x x * * 67 . . 1 3 5 7 9 . x x x x * 81 . . 2 4 6 8 10 . x x x x * * 83 . . 1 3 5 7 9 . x x x x * 84 . . 2 4 6 8 10 . x x x x * * ----- CHOLMOD v1.2.0 does the following ------------------------------------- * then each iteration does one rows of all four colummns of L: * * 43 . . 1 2 3 4 5 . x x x x * 44 . . 1 2 3 4 5 . x x x x * 50 . . 1 3 5 4 5 . x x x x * 51 . . 1 2 3 4 5 . x x x x * 67 . . 1 3 5 4 5 . x x x x * 81 . . 1 2 3 4 5 . x x x x * 83 . . 1 3 5 4 5 . x x x x * 84 . . 1 2 3 4 5 . x x x x * * This file is included in t_cholmod_updown.c, only. * It is not compiled separately. It contains no user-callable routines. * * workspace: Xwork (WDIM*nrow) */ /* ========================================================================== */ /* === loop unrolling macros ================================================ */ /* ========================================================================== */ #undef RANK1 #undef RANK2 #undef RANK3 #undef RANK4 #undef RANK5 #undef RANK6 #undef RANK7 #undef RANK8 #define RANK1(statement) statement #if RANK < 2 #define RANK2(statement) #else #define RANK2(statement) statement #endif #if RANK < 3 #define RANK3(statement) #else #define RANK3(statement) statement #endif #if RANK < 4 #define RANK4(statement) #else #define RANK4(statement) statement #endif #if RANK < 5 #define RANK5(statement) #else #define RANK5(statement) statement #endif #if RANK < 6 #define RANK6(statement) #else #define RANK6(statement) statement #endif #if RANK < 7 #define RANK7(statement) #else #define RANK7(statement) statement #endif #if RANK < 8 #define RANK8(statement) #else #define RANK8(statement) statement #endif #define FOR_ALL_K \ RANK1 (DO (0)) \ RANK2 (DO (1)) \ RANK3 (DO (2)) \ RANK4 (DO (3)) \ RANK5 (DO (4)) \ RANK6 (DO (5)) \ RANK7 (DO (6)) \ RANK8 (DO (7)) /* ========================================================================== */ /* === alpha/gamma ========================================================== */ /* ========================================================================== */ #undef ALPHA_GAMMA #define ALPHA_GAMMA(Dj,Alpha,Gamma,W) \ { \ double dj = Dj ; \ if (update) \ { \ for (k = 0 ; k < RANK ; k++) \ { \ double w = W [k] ; \ double alpha = Alpha [k] ; \ double a = alpha + (w * w) / dj ; \ dj *= a ; \ Alpha [k] = a ; \ Gamma [k] = (- w / dj) ; \ dj /= alpha ; \ } \ } \ else \ { \ for (k = 0 ; k < RANK ; k++) \ { \ double w = W [k] ; \ double alpha = Alpha [k] ; \ double a = alpha - (w * w) / dj ; \ dj *= a ; \ Alpha [k] = a ; \ Gamma [k] = w / dj ; \ dj /= alpha ; \ } \ } \ Dj = ((use_dbound) ? (CHOLMOD(dbound) (dj, Common)) : (dj)) ; \ } /* ========================================================================== */ /* === numeric update/downdate along one path =============================== */ /* ========================================================================== */ static void NUMERIC (WDIM, RANK) ( int update, /* TRUE for update, FALSE for downdate */ Int j, /* first column in the path */ Int e, /* last column in the path */ double Alpha [ ], /* alpha, for each column of W */ double W [ ], /* W is an n-by-WDIM array, stored in row-major order */ cholmod_factor *L, /* with unit diagonal (diagonal not stored) */ cholmod_common *Common ) { #ifdef SIMPLE #define w(row,col) W [WDIM*(row) + (col)] /* ---------------------------------------------------------------------- */ /* concise but slow version for illustration only */ /* ---------------------------------------------------------------------- */ double Gamma [WDIM] ; double *Lx ; Int *Li, *Lp, *Lnz ; Int p, k ; Int use_dbound = IS_GT_ZERO (Common->dbound) ; Li = L->i ; Lx = L->x ; Lp = L->p ; Lnz = L->nz ; /* walk up the etree from node j to its ancestor e */ for ( ; j <= e ; j = (Lnz [j] > 1) ? (Li [Lp [j] + 1]) : Int_max) { /* update the diagonal entry D (j,j) with each column of W */ ALPHA_GAMMA (Lx [Lp [j]], Alpha, Gamma, (&(w (j,0)))) ; /* update column j of L */ for (p = Lp [j] + 1 ; p < Lp [j] + Lnz [j] ; p++) { /* update row Li [p] of column j of L with each column of W */ Int i = Li [p] ; for (k = 0 ; k < RANK ; k++) { w (i,k) -= w (j,k) * Lx [p] ; Lx [p] -= Gamma [k] * w (i,k) ; } } /* clear workspace W */ for (k = 0 ; k < RANK ; k++) { w (j,k) = 0 ; } } #else /* ---------------------------------------------------------------------- */ /* dynamic supernodal version: supernodes detected dynamically */ /* ---------------------------------------------------------------------- */ double G0 [RANK], G1 [RANK], G2 [RANK], G3 [RANK] ; double Z0 [RANK], Z1 [RANK], Z2 [RANK], Z3 [RANK] ; double *W0, *W1, *W2, *W3, *Lx ; Int *Li, *Lp, *Lnz ; Int j1, j2, j3, p0, p1, p2, p3, parent, lnz, pend, k ; Int use_dbound = IS_GT_ZERO (Common->dbound) ; Li = L->i ; Lx = L->x ; Lp = L->p ; Lnz = L->nz ; /* walk up the etree from node j to its ancestor e */ for ( ; j <= e ; j = parent) { p0 = Lp [j] ; /* col j is Li,Lx [p0 ... p0+lnz-1] */ lnz = Lnz [j] ; W0 = W + WDIM * j ; /* pointer to row j of W */ pend = p0 + lnz ; /* for k = 0 to RANK-1 do: */ #define DO(k) Z0 [k] = W0 [k] ; FOR_ALL_K #undef DO /* for k = 0 to RANK-1 do: */ #define DO(k) W0 [k] = 0 ; FOR_ALL_K #undef DO /* update D (j,j) */ ALPHA_GAMMA (Lx [p0], Alpha, G0, Z0) ; p0++ ; /* determine how many columns of L to update at the same time */ parent = (lnz > 1) ? (Li [p0]) : Int_max ; if (parent <= e && lnz == Lnz [parent] + 1) { /* -------------------------------------------------------------- */ /* node j and its parent j1 can be updated at the same time */ /* -------------------------------------------------------------- */ j1 = parent ; j2 = (lnz > 2) ? (Li [p0+1]) : Int_max ; j3 = (lnz > 3) ? (Li [p0+2]) : Int_max ; W1 = W + WDIM * j1 ; /* pointer to row j1 of W */ p1 = Lp [j1] ; /* for k = 0 to RANK-1 do: */ #define DO(k) Z1 [k] = W1 [k] ; FOR_ALL_K #undef DO /* for k = 0 to RANK-1 do: */ #define DO(k) W1 [k] = 0 ; FOR_ALL_K #undef DO /* update L (j1,j) */ { double lx = Lx [p0] ; /* for k = 0 to RANK-1 do: */ #define DO(k) \ Z1 [k] -= Z0 [k] * lx ; \ lx -= G0 [k] * Z1 [k] ; FOR_ALL_K #undef DO Lx [p0++] = lx ; } /* update D (j1,j1) */ ALPHA_GAMMA (Lx [p1], Alpha, G1, Z1) ; p1++ ; /* -------------------------------------------------------------- */ /* update 2 or 4 columns of L */ /* -------------------------------------------------------------- */ if ((j2 <= e) && /* j2 in the current path */ (j3 <= e) && /* j3 in the current path */ (lnz == Lnz [j2] + 2) && /* column j2 matches */ (lnz == Lnz [j3] + 3)) /* column j3 matches */ { /* ---------------------------------------------------------- */ /* update 4 columns of L */ /* ---------------------------------------------------------- */ /* p0 and p1 currently point to row j2 in cols j and j1 of L */ parent = (lnz > 4) ? (Li [p0+2]) : Int_max ; W2 = W + WDIM * j2 ; /* pointer to row j2 of W */ W3 = W + WDIM * j3 ; /* pointer to row j3 of W */ p2 = Lp [j2] ; p3 = Lp [j3] ; /* for k = 0 to RANK-1 do: */ #define DO(k) Z2 [k] = W2 [k] ; FOR_ALL_K #undef DO /* for k = 0 to RANK-1 do: */ #define DO(k) Z3 [k] = W3 [k] ; FOR_ALL_K #undef DO /* for k = 0 to RANK-1 do: */ #define DO(k) W2 [k] = 0 ; FOR_ALL_K #undef DO /* for k = 0 to RANK-1 do: */ #define DO(k) W3 [k] = 0 ; FOR_ALL_K #undef DO /* update L (j2,j) and update L (j2,j1) */ { double lx [2] ; lx [0] = Lx [p0] ; lx [1] = Lx [p1] ; /* for k = 0 to RANK-1 do: */ #define DO(k) \ Z2 [k] -= Z0 [k] * lx [0] ; lx [0] -= G0 [k] * Z2 [k] ; \ Z2 [k] -= Z1 [k] * lx [1] ; lx [1] -= G1 [k] * Z2 [k] ; FOR_ALL_K #undef DO Lx [p0++] = lx [0] ; Lx [p1++] = lx [1] ; } /* update D (j2,j2) */ ALPHA_GAMMA (Lx [p2], Alpha, G2, Z2) ; p2++ ; /* update L (j3,j), L (j3,j1), and L (j3,j2) */ { double lx [3] ; lx [0] = Lx [p0] ; lx [1] = Lx [p1] ; lx [2] = Lx [p2] ; /* for k = 0 to RANK-1 do: */ #define DO(k) \ Z3 [k] -= Z0 [k] * lx [0] ; lx [0] -= G0 [k] * Z3 [k] ; \ Z3 [k] -= Z1 [k] * lx [1] ; lx [1] -= G1 [k] * Z3 [k] ; \ Z3 [k] -= Z2 [k] * lx [2] ; lx [2] -= G2 [k] * Z3 [k] ; FOR_ALL_K #undef DO Lx [p0++] = lx [0] ; Lx [p1++] = lx [1] ; Lx [p2++] = lx [2] ; } /* update D (j3,j3) */ ALPHA_GAMMA (Lx [p3], Alpha, G3, Z3) ; p3++ ; /* each iteration updates L (i, [j j1 j2 j3]) */ for ( ; p0 < pend ; p0++, p1++, p2++, p3++) { double lx [4], *w0 ; lx [0] = Lx [p0] ; lx [1] = Lx [p1] ; lx [2] = Lx [p2] ; lx [3] = Lx [p3] ; w0 = W + WDIM * Li [p0] ; /* for k = 0 to RANK-1 do: */ #define DO(k) \ w0 [k] -= Z0 [k] * lx [0] ; lx [0] -= G0 [k] * w0 [k] ; \ w0 [k] -= Z1 [k] * lx [1] ; lx [1] -= G1 [k] * w0 [k] ; \ w0 [k] -= Z2 [k] * lx [2] ; lx [2] -= G2 [k] * w0 [k] ; \ w0 [k] -= Z3 [k] * lx [3] ; lx [3] -= G3 [k] * w0 [k] ; FOR_ALL_K #undef DO Lx [p0] = lx [0] ; Lx [p1] = lx [1] ; Lx [p2] = lx [2] ; Lx [p3] = lx [3] ; } } else { /* ---------------------------------------------------------- */ /* update 2 columns of L */ /* ---------------------------------------------------------- */ parent = j2 ; /* cleanup iteration if length is odd */ if ((lnz - 2) % 2) { double lx [2] , *w0 ; lx [0] = Lx [p0] ; lx [1] = Lx [p1] ; w0 = W + WDIM * Li [p0] ; /* for k = 0 to RANK-1 do: */ #define DO(k) \ w0 [k] -= Z0 [k] * lx [0] ; lx [0] -= G0 [k] * w0 [k] ; \ w0 [k] -= Z1 [k] * lx [1] ; lx [1] -= G1 [k] * w0 [k] ; FOR_ALL_K #undef DO Lx [p0++] = lx [0] ; Lx [p1++] = lx [1] ; } for ( ; p0 < pend ; p0 += 2, p1 += 2) { double lx [2][2], w [2], *w0, *w1 ; lx [0][0] = Lx [p0 ] ; lx [1][0] = Lx [p0+1] ; lx [0][1] = Lx [p1 ] ; lx [1][1] = Lx [p1+1] ; w0 = W + WDIM * Li [p0 ] ; w1 = W + WDIM * Li [p0+1] ; /* for k = 0 to RANK-1 do: */ #define DO(k) \ w [0] = w0 [k] - Z0 [k] * lx [0][0] ; \ w [1] = w1 [k] - Z0 [k] * lx [1][0] ; \ lx [0][0] -= G0 [k] * w [0] ; \ lx [1][0] -= G0 [k] * w [1] ; \ w0 [k] = w [0] -= Z1 [k] * lx [0][1] ; \ w1 [k] = w [1] -= Z1 [k] * lx [1][1] ; \ lx [0][1] -= G1 [k] * w [0] ; \ lx [1][1] -= G1 [k] * w [1] ; FOR_ALL_K #undef DO Lx [p0 ] = lx [0][0] ; Lx [p0+1] = lx [1][0] ; Lx [p1 ] = lx [0][1] ; Lx [p1+1] = lx [1][1] ; } } } else { /* -------------------------------------------------------------- */ /* update one column of L */ /* -------------------------------------------------------------- */ /* cleanup iteration if length is not a multiple of 4 */ switch ((lnz - 1) % 4) { case 1: { double lx , *w0 ; lx = Lx [p0] ; w0 = W + WDIM * Li [p0] ; /* for k = 0 to RANK-1 do: */ #define DO(k) \ w0 [k] -= Z0 [k] * lx ; lx -= G0 [k] * w0 [k] ; FOR_ALL_K #undef DO Lx [p0++] = lx ; } break ; case 2: { double lx [2], *w0, *w1 ; lx [0] = Lx [p0 ] ; lx [1] = Lx [p0+1] ; w0 = W + WDIM * Li [p0 ] ; w1 = W + WDIM * Li [p0+1] ; /* for k = 0 to RANK-1 do: */ #define DO(k) \ w0 [k] -= Z0 [k] * lx [0] ; \ w1 [k] -= Z0 [k] * lx [1] ; \ lx [0] -= G0 [k] * w0 [k] ; \ lx [1] -= G0 [k] * w1 [k] ; FOR_ALL_K #undef DO Lx [p0++] = lx [0] ; Lx [p0++] = lx [1] ; } break ; case 3: { double lx [3], *w0, *w1, *w2 ; lx [0] = Lx [p0 ] ; lx [1] = Lx [p0+1] ; lx [2] = Lx [p0+2] ; w0 = W + WDIM * Li [p0 ] ; w1 = W + WDIM * Li [p0+1] ; w2 = W + WDIM * Li [p0+2] ; /* for k = 0 to RANK-1 do: */ #define DO(k) \ w0 [k] -= Z0 [k] * lx [0] ; \ w1 [k] -= Z0 [k] * lx [1] ; \ w2 [k] -= Z0 [k] * lx [2] ; \ lx [0] -= G0 [k] * w0 [k] ; \ lx [1] -= G0 [k] * w1 [k] ; \ lx [2] -= G0 [k] * w2 [k] ; FOR_ALL_K #undef DO Lx [p0++] = lx [0] ; Lx [p0++] = lx [1] ; Lx [p0++] = lx [2] ; } } for ( ; p0 < pend ; p0 += 4) { double lx [4], *w0, *w1, *w2, *w3 ; lx [0] = Lx [p0 ] ; lx [1] = Lx [p0+1] ; lx [2] = Lx [p0+2] ; lx [3] = Lx [p0+3] ; w0 = W + WDIM * Li [p0 ] ; w1 = W + WDIM * Li [p0+1] ; w2 = W + WDIM * Li [p0+2] ; w3 = W + WDIM * Li [p0+3] ; /* for k = 0 to RANK-1 do: */ #define DO(k) \ w0 [k] -= Z0 [k] * lx [0] ; \ w1 [k] -= Z0 [k] * lx [1] ; \ w2 [k] -= Z0 [k] * lx [2] ; \ w3 [k] -= Z0 [k] * lx [3] ; \ lx [0] -= G0 [k] * w0 [k] ; \ lx [1] -= G0 [k] * w1 [k] ; \ lx [2] -= G0 [k] * w2 [k] ; \ lx [3] -= G0 [k] * w3 [k] ; FOR_ALL_K #undef DO Lx [p0 ] = lx [0] ; Lx [p0+1] = lx [1] ; Lx [p0+2] = lx [2] ; Lx [p0+3] = lx [3] ; } } } #endif } /* prepare this file for another inclusion in t_cholmod_updown.c: */ #undef RANK SuiteSparse/CHOLMOD/Modify/License.txt0000644001170100242450000000206310540000301016366 0ustar davisfacCHOLMOD/Modify Module. Copyright (C) 2005-2006, Timothy A. Davis and William W. Hager CHOLMOD is also available under other licenses; contact authors for details. http://www.cise.ufl.edu/research/sparse Note that this license is for the CHOLMOD/Modify module only. All CHOLMOD modules are licensed separately. -------------------------------------------------------------------------------- This Module is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This Module is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. 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If the program is interactive, make it output a short notice like this when it starts in an interactive mode: Gnomovision version 69, Copyright (C) year name of author Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the program `Gnomovision' (which makes passes at compilers) written by James Hacker. , 1 April 1989 Ty Coon, President of Vice This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Library General Public License instead of this License. SuiteSparse/CHOLMOD/Modify/t_cholmod_updown.c0000644001170100242450000001506210537777757020030 0ustar davisfac/* ========================================================================== */ /* === Modify/t_cholmod_updown ============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Modify Module. Copyright (C) 2005-2006, * Timothy A. Davis and William W. Hager. * The CHOLMOD/Modify Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Updates/downdates the LDL' factorization, by computing a new factorization of * * Lnew * Dnew * Lnew' = Lold * Dold * Lold' +/- C*C' * * This file is not compiled separately. It is included into * cholmod_updown.c. There are no user-callable routines in this file. * * The next include statements, below, create the numerical update/downdate * kernels from t_cholmod_updown_numkr.c. There are 4 compiled versions of this * file, one for each value of WDIM in the set 1, 2, 4, and 8. Each calls * multiple versions of t_cholmod_updown_numkr; the number of versions of each * is equal to WDIM. Each t_cholmod_updown_numkr version is included as a * static function within its t_cholmod_updown.c caller routine. Thus: * * t*_updown.c creates these versions of t_cholmod_updown_numkr.c: * --------- --------------------------------------------------- * * updown_1_r updown_1_1 * * updown_2_r updown_2_1 updown_2_2 * * updown_4_r updown_4_1 updown_4_2 updown_4_3 updown_4_4 * * updown_8_r updown_8_1 updown_8_2 updown_8_3 updown_8_4 * updown_8_5 updown_8_6 updown_8_7 updown_8_8 * * workspace: Xwork (nrow*wdim) */ /* ========================================================================== */ /* === routines for numeric update/downdate along one path ================== */ /* ========================================================================== */ #undef FORM_NAME #undef NUMERIC #define FORM_NAME(k,rank) updown_ ## k ## _ ## rank #define NUMERIC(k,rank) FORM_NAME(k,rank) #define RANK 1 #include "t_cholmod_updown_numkr.c" #if WDIM >= 2 #define RANK 2 #include "t_cholmod_updown_numkr.c" #endif #if WDIM >= 4 #define RANK 3 #include "t_cholmod_updown_numkr.c" #define RANK 4 #include "t_cholmod_updown_numkr.c" #endif #if WDIM == 8 #define RANK 5 #include "t_cholmod_updown_numkr.c" #define RANK 6 #include "t_cholmod_updown_numkr.c" #define RANK 7 #include "t_cholmod_updown_numkr.c" #define RANK 8 #include "t_cholmod_updown_numkr.c" #endif /* ========================================================================== */ /* === numeric update/downdate for all paths ================================ */ /* ========================================================================== */ static void NUMERIC (WDIM, r) ( int update, /* TRUE for update, FALSE for downdate */ cholmod_sparse *C, /* in packed or unpacked, and sorted form */ /* no empty columns */ Int rank, /* rank of the update/downdate */ cholmod_factor *L, /* with unit diagonal (diagonal not stored) */ /* temporary workspaces: */ double W [ ], /* n-by-WDIM dense matrix, initially zero */ Path_type Path [ ], Int npaths, Int mask [ ], /* size n */ cholmod_common *Common ) { double Alpha [8] ; double *Cx, *Wpath, *W1, *a ; Int i, j, p, ccol, pend, wfirst, e, path, packed ; Int *Ci, *Cp, *Cnz ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Ci = C->i ; Cx = C->x ; Cp = C->p ; Cnz = C->nz ; packed = C->packed ; ASSERT (IMPLIES (!packed, Cnz != NULL)) ; ASSERT (L->n == C->nrow) ; DEBUG (CHOLMOD(dump_real) ("num_d: in W:", W, WDIM, L->n, FALSE, 1,Common)); /* ---------------------------------------------------------------------- */ /* scatter C into W */ /* ---------------------------------------------------------------------- */ for (path = 0 ; path < rank ; path++) { /* W (:, path) = C (:, Path [path].col) */ ccol = Path [path].ccol ; Wpath = W + path ; PRINT1 (("Ordered Columns [path = "ID"] = "ID"\n", path, ccol)) ; p = Cp [ccol] ; pend = (packed) ? (Cp [ccol+1]) : (p + Cnz [ccol]) ; /* column C can be empty */ for ( ; p < pend ; p++) { i = Ci [p] ; ASSERT (i >= 0 && i < (Int) (C->nrow)) ; if (mask == NULL || mask [i] < 0) { Wpath [WDIM * i] = Cx [p] ; } PRINT1 ((" row "ID" : %g mask "ID"\n", i, Cx [p], (mask) ? mask [i] : 0)) ; } Alpha [path] = 1.0 ; } DEBUG (CHOLMOD(dump_real) ("num_d: W:", W, WDIM, L->n, FALSE, 1,Common)) ; /* ---------------------------------------------------------------------- */ /* numeric update/downdate of the paths */ /* ---------------------------------------------------------------------- */ /* for each disjoint subpath in Tbar in DFS order do */ for (path = rank ; path < npaths ; path++) { /* determine which columns of W to use */ wfirst = Path [path].wfirst ; e = Path [path].end ; j = Path [path].start ; ASSERT (e >= 0 && e < (Int) (L->n)) ; ASSERT (j >= 0 && j < (Int) (L->n)) ; W1 = W + wfirst ; /* pointer to row 0, column wfirst of W */ a = Alpha + wfirst ; /* pointer to Alpha [wfirst] */ PRINT1 (("Numerical update/downdate of path "ID"\n", path)) ; PRINT1 (("start "ID" end "ID" wfirst "ID" rank "ID" ccol "ID"\n", j, e, wfirst, Path [path].rank, Path [path].ccol)) ; #if WDIM == 1 NUMERIC (WDIM,1) (update, j, e, a, W1, L, Common) ; #else switch (Path [path].rank) { case 1: NUMERIC (WDIM,1) (update, j, e, a, W1, L, Common) ; break ; #if WDIM >= 2 case 2: NUMERIC (WDIM,2) (update, j, e, a, W1, L, Common) ; break ; #endif #if WDIM >= 4 case 3: NUMERIC (WDIM,3) (update, j, e, a, W1, L, Common) ; break ; case 4: NUMERIC (WDIM,4) (update, j, e, a, W1, L, Common) ; break ; #endif #if WDIM == 8 case 5: NUMERIC (WDIM,5) (update, j, e, a, W1, L, Common) ; break ; case 6: NUMERIC (WDIM,6) (update, j, e, a, W1, L, Common) ; break ; case 7: NUMERIC (WDIM,7) (update, j, e, a, W1, L, Common) ; break ; case 8: NUMERIC (WDIM,8) (update, j, e, a, W1, L, Common) ; break ; #endif } #endif } } /* prepare for the next inclusion of this file in cholmod_updown.c */ #undef WDIM SuiteSparse/CHOLMOD/Modify/cholmod_updown.c0000644001170100242450000014337610635770737017505 0ustar davisfac/* ========================================================================== */ /* === Modify/cholmod_updown ================================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Modify Module. * Copyright (C) 2005-2006, Timothy A. Davis and William W. Hager. * The CHOLMOD/Modify Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Updates/downdates the LDL' factorization (symbolic, then numeric), by * computing a new factorization of * * Lnew * Dnew * Lnew' = Lold * Dold * Lold' +/- C*C' * * C must be sorted. It can be either packed or unpacked. As in all CHOLMOD * routines, the columns of L are sorted on input, and also on output. * * If the factor is not an unpacked LDL' or dynamic LDL', it is converted * to an LDL' dynamic factor. An unpacked LDL' factor may be updated, but if * any one column runs out of space, the factor is converted to an LDL' * dynamic one. If the initial conversion fails, the factor is returned * unchanged. * * If memory runs out during the update, the factor is returned as a simplicial * symbolic factor. That is, everything is freed except for the fill-reducing * ordering and its corresponding column counts (typically computed by * cholmod_analyze). * * Note that the fill-reducing permutation L->Perm is NOT used. The row * indices of C refer to the rows of L, not A. If your original system is * LDL' = PAP' (where P = L->Perm), and you want to compute the LDL' * factorization of A+CC', then you must permute C first. That is: * * PAP' = LDL' * P(A+CC')P' = PAP'+PCC'P' = LDL' + (PC)(PC)' = LDL' + Cnew*Cnew' * where Cnew = P*C. * * You can use the cholmod_submatrix routine in the MatrixOps module * to permute C, with: * * Cnew = cholmod_submatrix (C, L->Perm, L->n, NULL, -1, TRUE, TRUE, Common) ; * * Note that the sorted input parameter to cholmod_submatrix must be TRUE, * because cholmod_updown requires C with sorted columns. * * The system Lx=b can also be updated/downdated. The old system was Lold*x=b. * The new system is Lnew*xnew = b + deltab. The old solution x is overwritten * with xnew. Note that as in the update/downdate of L itself, the fill- * reducing permutation L->Perm is not used. x and b are in the permuted * ordering, not your original ordering. x and b are n-by-1; this routine * does not handle multiple right-hand-sides. * * workspace: Flag (nrow), Head (nrow+1), W (maxrank*nrow), Iwork (nrow), * where maxrank is 2, 4, or 8. * * Only real matrices are supported. A symbolic L is converted into a * numeric identity matrix. */ #ifndef NMODIFY #include "cholmod_internal.h" #include "cholmod_modify.h" /* ========================================================================== */ /* === cholmod_updown ======================================================= */ /* ========================================================================== */ /* Compute the new LDL' factorization of LDL'+CC' (an update) or LDL'-CC' * (a downdate). The factor object L need not be an LDL' factorization; it * is converted to one if it isn't. */ int CHOLMOD(updown) ( /* ---- input ---- */ int update, /* TRUE for update, FALSE for downdate */ cholmod_sparse *C, /* the incoming sparse update */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) { return (CHOLMOD(updown_mask) (update, C, NULL, NULL, L, NULL, NULL, Common)) ; } /* ========================================================================== */ /* === cholmod_updown_solve ================================================= */ /* ========================================================================== */ /* Does the same as cholmod_updown, except that it also updates/downdates the * solution to Lx=b+DeltaB. x and b must be n-by-1 dense matrices. b is not * need as input to this routine, but a sparse change to b is (DeltaB). Only * entries in DeltaB corresponding to columns modified in L are accessed; the * rest are ignored. */ int CHOLMOD(updown_solve) ( /* ---- input ---- */ int update, /* TRUE for update, FALSE for downdate */ cholmod_sparse *C, /* the incoming sparse update */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) { return (CHOLMOD(updown_mask) (update, C, NULL, NULL, L, X, DeltaB, Common)) ; } /* ========================================================================== */ /* === Power2 =============================================================== */ /* ========================================================================== */ /* Power2 [i] is smallest power of 2 that is >= i (for i in range 0 to 8) */ static Int Power2 [ ] = { /* 0 1 2 3 4 5 6 7 8 */ 0, 1, 2, 4, 4, 8, 8, 8, 8 } ; /* ========================================================================== */ /* === debug routines ======================================================= */ /* ========================================================================== */ #ifndef NDEBUG static void dump_set (Int s, Int **Set_ps1, Int **Set_ps2, Int j, Int n, cholmod_common *Common) { Int *p, len, i, ilast ; if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return ; } len = Set_ps2 [s] - Set_ps1 [s] ; PRINT2 (("Set s: "ID" len: "ID":", s, len)) ; ASSERT (len > 0) ; ilast = j ; for (p = Set_ps1 [s] ; p < Set_ps2 [s] ; p++) { i = *p ; PRINT3 ((" "ID"", i)) ; ASSERT (i > ilast && i < n) ; ilast = i ; } PRINT3 (("\n")) ; } static void dump_col ( char *w, Int j, Int p1, Int p2, Int *Li, double *Lx, Int n, cholmod_common *Common ) { Int p, row, lastrow ; if (CHOLMOD(dump) < -1) { /* no checks if debug level is -2 or less */ return ; } PRINT3 (("\n\nDUMP COL==== j = "ID" %s: p1="ID" p2="ID" \n", j, w, p1,p2)); lastrow = -1 ; for (p = p1 ; p < p2 ; p++) { PRINT3 ((" "ID": ", p)) ; row = Li [p] ; PRINT3 ((""ID" ", Li [p])) ; PRINT3 (("%g ", Lx [p])) ; PRINT3 (("\n")) ; ASSERT (row > lastrow && row < n) ; lastrow = row ; } ASSERT (p1 < p2) ; ASSERT (Li [p1] == j) ; PRINT3 (("\n")) ; } #endif /* ========================================================================== */ /* === a path =============================================================== */ /* ========================================================================== */ /* A path is a set of nodes of the etree which are all affected by the same * columns of C. */ typedef struct Path_struct { Int start ; /* column at which to start, or EMPTY if initial */ Int end ; /* column at which to end, or EMPTY if initial */ Int ccol ; /* column of C to which path refers */ Int parent ; /* parent path */ Int c ; /* child of j along this path */ Int next ; /* next path in link list */ Int rank ; /* number of rank-1 paths merged onto this path */ Int order ; /* dfs order of this path */ Int wfirst ; /* first column of W to affect this path */ Int pending ; /* column at which the path is pending */ Int botrow ; /* for partial update/downdate of solution to Lx=b */ } Path_type ; /* ========================================================================== */ /* === dfs ================================================================== */ /* ========================================================================== */ /* Compute the DFS order of the set of paths. This can be recursive because * there are at most 23 paths to sort: one for each column of C (8 at most), * and one for each node in a balanced binary tree with 8 leaves (15). * Stack overflow is thus not a problem. */ static void dfs ( Path_type *Path, /* the set of Paths */ Int k, /* the rank of the update/downdate */ Int path, /* which path to work on */ Int *path_order, /* the current path order */ Int *w_order, /* the current order of the columns of W */ Int depth, Int npaths /* total number of paths */ ) { Int c ; /* child path */ ASSERT (path >= 0 && path < npaths) ; if (path < k) { /* this is a leaf node, corresponding to column W (:,path) */ /* and column C (:, Path [path].ccol) */ ASSERT (Path [path].ccol >= 0) ; Path [path].wfirst = *w_order ; Path [path].order = *w_order ; (*w_order)++ ; } else { /* this is a non-leaf path, within the tree */ ASSERT (Path [path].c != EMPTY) ; ASSERT (Path [path].ccol == EMPTY) ; /* order each child path */ for (c = Path [path].c ; c != EMPTY ; c = Path [c].next) { dfs (Path, k, c, path_order, w_order, depth+1, npaths) ; if (Path [path].wfirst == EMPTY) { Path [path].wfirst = Path [c].wfirst ; } } /* order this path next */ Path [path].order = (*path_order)++ ; } } /* ========================================================================== */ /* === numeric update/downdate routines ===================================== */ /* ========================================================================== */ #define WDIM 1 #include "t_cholmod_updown.c" #define WDIM 2 #include "t_cholmod_updown.c" #define WDIM 4 #include "t_cholmod_updown.c" #define WDIM 8 #include "t_cholmod_updown.c" /* ========================================================================== */ /* === cholmod_updown_mark ================================================== */ /* ========================================================================== */ /* Update/downdate LDL' +/- C*C', and update/downdate selected portions of the * solution to Lx=b. * * The original system is L*x = b. The new system is Lnew*xnew = b + deltab. * deltab(i) can be nonzero only if column i of L is modified by the update/ * downdate. If column i is not modified, the deltab(i) is not accessed. * * The solution to Lx=b is not modified if either X or DeltaB are NULL. * * Rowmark and colmark: * -------------------- * * rowmark and colmark affect which portions of L take part in the update/ * downdate of the solution to Lx=b. They do not affect how L itself is * updated/downdated. They are both ignored if X or DeltaB are NULL. * * If not NULL, rowmark is an integer array of size n where L is n-by-n. * rowmark [j] defines the part of column j of L that takes part in the update/ * downdate of the forward solve, Lx=b. Specifically, if i = rowmark [j], * then L(j:i-1,j) is used, and L(i:end,j) is ignored. * * If not NULL, colmark is an integer array of size C->ncol. colmark [ccol] * for a column C(:,ccol) redefines those parts of L that take part in the * update/downdate of Lx=b. Each column of C affects a set of columns of L. * If column ccol of C affects column j of L, then the new rowmark [j] of * column j of L is defined as colmark [ccol]. In a multiple-rank update/ * downdate, if two or more columns of C affect column j, its new rowmark [j] * is the colmark of the least-numbered column of C. colmark is ignored if * it is NULL, in which case rowmark is not modified. If colmark [ccol] is * EMPTY (-1), then rowmark is not modified for that particular column of C. * colmark is ignored if it is NULL, or rowmark, X, or DeltaB are NULL. * * The algorithm for modifying the solution to Lx=b when rowmark and colmark * are NULL is as follows: * * for each column j of L that is modified: * deltab (j:end) += L (j:end,j) * x(j) * modify L * for each column j of L that is modified: * x (j) = deltab (j) * deltab (j) = 0 * deltab (j+1:end) -= L (j+1:end,j) * x(j) * * If rowmark is non-NULL but colmark is NULL: * * for each column j of L that is modified: * deltab (j:rowmark(j)-1) += L (j:rowmark(j)-1,j) * x(j) * modify L * for each column j of L that is modified: * x (j) = deltab (j) * deltab (j) = 0 * deltab (j+1:rowmark(j)-1) -= L (j+1:rowmark(j)-1,j) * x(j) * * If both rowmark and colmark are non-NULL: * * for each column j of L that is modified: * deltab (j:rowmark(j)-1) += L (j:rowmark(j)-1,j) * x(j) * modify L * for each column j of L that is modified: * modify rowmark (j) according to colmark * for each column j of L that is modified: * x (j) = deltab (j) * deltab (j) = 0 * deltab (j+1:rowmark(j)-1) -= L (j+1:rowmark(j)-1,j) * x(j) * * Note that if the rank of C exceeds k = Common->maxrank (which is 2, 4, or 8), * then the update/downdate is done as a series of rank-k updates. In this * case, the above algorithm is repeated for each block of k columns of C. * * Unless it leads to no changes in rowmark, colmark should be used only if * C->ncol <= Common->maxrank, because the update/downdate is done with maxrank * columns at a time. Otherwise, the results are undefined. * * This routine is an "expert" routine. It is meant for use in LPDASA only. */ int CHOLMOD(updown_mark) ( /* ---- input ---- */ int update, /* TRUE for update, FALSE for downdate */ cholmod_sparse *C, /* the incoming sparse update */ Int *colmark, /* Int array of size n. */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) { return (CHOLMOD(updown_mask) (update, C, colmark, NULL, L, X, DeltaB, Common)) ; } /* ========================================================================== */ /* === cholmod_updown_mask ================================================== */ /* ========================================================================== */ int CHOLMOD(updown_mask) ( /* ---- input ---- */ int update, /* TRUE for update, FALSE for downdate */ cholmod_sparse *C, /* the incoming sparse update */ Int *colmark, /* Int array of size n. See cholmod_updown.c */ Int *mask, /* size n */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) { double xj, fl ; double *Lx, *W, *Xx, *Nx ; Int *Li, *Lp, *Lnz, *Cp, *Ci, *Cnz, *Head, *Flag, *Stack, *Lnext, *Iwork, *Set_ps1 [32], *Set_ps2 [32], *ps1, *ps2 ; size_t maxrank ; Path_type OrderedPath [32], Path [32] ; Int n, wdim, k1, k2, npaths, i, j, row, packed, ccol, p, cncol, do_solve, mark, jj, j2, kk, nextj, p1, p2, c, use_colmark, newlnz, k, newpath, path_order, w_order, scattered, path, newparent, pp1, pp2, smax, maxrow, row1, nsets, s, p3, newlnz1, Set [32], top, len, lnz, m, botrow ; size_t w ; int ok = TRUE ; DEBUG (Int oldparent) ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (C, FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_REAL, FALSE) ; RETURN_IF_XTYPE_INVALID (C, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ; n = L->n ; cncol = C->ncol ; if (!(C->sorted)) { ERROR (CHOLMOD_INVALID, "C must have sorted columns") ; return (FALSE) ; } if (n != (Int) (C->nrow)) { ERROR (CHOLMOD_INVALID, "C and L dimensions do not match") ; return (FALSE) ; } do_solve = (X != NULL) && (DeltaB != NULL) ; if (do_solve) { RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ; RETURN_IF_XTYPE_INVALID (DeltaB, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ; Xx = X->x ; Nx = DeltaB->x ; if (X->nrow != L->n || X->ncol != 1 || DeltaB->nrow != L->n || DeltaB->ncol != 1 || Xx == NULL || Nx == NULL) { ERROR (CHOLMOD_INVALID, "X and/or DeltaB invalid") ; return (FALSE) ; } } else { Xx = NULL ; Nx = NULL ; } Common->status = CHOLMOD_OK ; Common->modfl = 0 ; fl = 0 ; use_colmark = (colmark != NULL) ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* Note: cholmod_rowadd and cholmod_rowdel use the second n doubles in * Common->Xwork for Cx, and then perform a rank-1 update here, which uses * the first n doubles in Common->Xwork. Both the rowadd and rowdel * routines allocate enough workspace so that Common->Xwork isn't destroyed * below. Also, both cholmod_rowadd and cholmod_rowdel use the second n * ints in Common->Iwork for Ci. */ /* make sure maxrank is in the proper range */ maxrank = CHOLMOD(maxrank) (n, Common) ; k = MIN (cncol, (Int) maxrank) ; /* maximum k is wdim */ wdim = Power2 [k] ; /* number of columns needed in W */ ASSERT (wdim <= (Int) maxrank) ; PRINT1 (("updown wdim final "ID" k "ID"\n", wdim, k)) ; /* w = wdim * n */ w = CHOLMOD(mult_size_t) (n, wdim, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (n, n, w, Common) ; if (Common->status < CHOLMOD_OK || maxrank == 0) { /* out of memory, L is returned unchanged */ return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* convert to simplicial numeric LDL' factor, if not already */ /* ---------------------------------------------------------------------- */ if (L->xtype == CHOLMOD_PATTERN || L->is_super || L->is_ll) { /* can only update/downdate a simplicial LDL' factorization */ CHOLMOD(change_factor) (CHOLMOD_REAL, FALSE, FALSE, FALSE, FALSE, L, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory, L is returned unchanged */ return (FALSE) ; } } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ /* mark = CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; PRINT1 (("updown, rank %g update %d\n", (double) C->ncol, update)) ; DEBUG (CHOLMOD(dump_factor) (L, "input L for updown", Common)) ; ASSERT (CHOLMOD(dump_sparse) (C, "input C for updown", Common) >= 0) ; Ci = C->i ; Cp = C->p ; Cnz = C->nz ; packed = C->packed ; ASSERT (IMPLIES (!packed, Cnz != NULL)) ; /* ---------------------------------------------------------------------- */ /* quick return */ /* ---------------------------------------------------------------------- */ if (cncol <= 0 || n == 0) { /* nothing to do */ return (TRUE) ; } /* ---------------------------------------------------------------------- */ /* get L */ /* ---------------------------------------------------------------------- */ Li = L->i ; Lx = L->x ; Lp = L->p ; Lnz = L->nz ; Lnext = L->next ; ASSERT (Lnz != NULL) ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Flag = Common->Flag ; /* size n, Flag [i] <= mark must hold */ Head = Common->Head ; /* size n, Head [i] == EMPTY must hold */ W = Common->Xwork ; /* size n-by-wdim, zero on input and output*/ /* note that Iwork [n .. 2*n-1] (i/i/l) may be in use in rowadd/rowdel: */ Iwork = Common->Iwork ; Stack = Iwork ; /* size n, uninitialized (i/i/l) */ /* ---------------------------------------------------------------------- */ /* entire rank-cncol update, done as a sequence of rank-k updates */ /* ---------------------------------------------------------------------- */ ps1 = NULL ; ps2 = NULL ; for (k1 = 0 ; k1 < cncol ; k1 += k) { /* ------------------------------------------------------------------ */ /* get the next k columns of C for the update/downdate */ /* ------------------------------------------------------------------ */ /* the last update/downdate might be less than rank-k */ if (k > cncol - k1) { k = cncol - k1 ; wdim = Power2 [k] ; } k2 = k1 + k - 1 ; /* workspaces are in the following state, on input and output */ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, wdim, Common)) ; /* ------------------------------------------------------------------ */ /* create a zero-length path for each column of W */ /* ------------------------------------------------------------------ */ nextj = n ; path = 0 ; for (ccol = k1 ; ccol <= k2 ; ccol++) { PRINT1 (("Column ["ID"]: "ID"\n", path, ccol)) ; ASSERT (ccol >= 0 && ccol <= cncol) ; pp1 = Cp [ccol] ; pp2 = (packed) ? (Cp [ccol+1]) : (pp1 + Cnz [ccol]) ; /* get the row index j of the first entry in C (:,ccol) */ if (pp2 > pp1) { /* Column ccol of C has at least one entry. */ j = Ci [pp1] ; } else { /* Column ccol of C is empty. Pretend it has one entry in * the last column with numerical value of zero. */ j = n-1 ; } ASSERT (j >= 0 && j < n) ; /* find first column to work on */ nextj = MIN (nextj, j) ; Path [path].ccol = ccol ; /* which column of C this path is for */ Path [path].start = EMPTY ; /* paths for C have zero length */ Path [path].end = EMPTY ; Path [path].parent = EMPTY ; /* no parent yet */ Path [path].rank = 1 ; /* one column of W */ Path [path].c = EMPTY ; /* no child of this path (case A) */ Path [path].next = Head [j] ; /* this path is pending at col j */ Path [path].pending = j ; /* this path is pending at col j */ Head [j] = path ; /* this path is pending at col j */ PRINT1(("Path "ID" starts: start "ID" end "ID" parent "ID" c "ID"" "j "ID" ccol "ID"\n", path, Path [path].start, Path [path].end, Path [path].parent, Path [path].c, j, ccol)) ; /* initialize botrow for this path */ Path [path].botrow = (use_colmark) ? colmark [ccol] : n ; path++ ; } /* we start with paths 0 to k-1. Next one (now unused) is npaths */ npaths = k ; j = nextj ; ASSERT (j < n) ; scattered = FALSE ; /* ------------------------------------------------------------------ */ /* symbolic update of columns of L */ /* ------------------------------------------------------------------ */ while (j < n) { ASSERT (j >= 0 && j < n && Lnz [j] > 0) ; /* the old column, Li [p1..p2-1]. D (j,j) is stored in Lx [p1] */ p1 = Lp [j] ; newlnz = Lnz [j] ; p2 = p1 + newlnz ; #ifndef NDEBUG PRINT1 (("\n=========Column j="ID" p1 "ID" p2 "ID" lnz "ID" \n", j, p1, p2, newlnz)) ; dump_col ("Old", j, p1, p2, Li, Lx, n, Common) ; oldparent = (Lnz [j] > 1) ? (Li [p1 + 1]) : EMPTY ; ASSERT (CHOLMOD(dump_work) (TRUE, FALSE, 0, Common)) ; ASSERT (!scattered) ; PRINT1 (("Col "ID": Checking paths, npaths: "ID"\n", j, npaths)) ; for (kk = 0 ; kk < npaths ; kk++) { Int kk2, found, j3 = Path [kk].pending ; PRINT2 (("Path "ID" pending at "ID".\n", kk, j3)) ; if (j3 != EMPTY) { /* Path kk must be somewhere in link list for column j3 */ ASSERT (Head [j3] != EMPTY) ; PRINT3 ((" List at "ID": ", j3)) ; found = FALSE ; for (kk2 = Head [j3] ; kk2 != EMPTY ; kk2 = Path [kk2].next) { PRINT3 ((""ID" ", kk2)) ; ASSERT (Path [kk2].pending == j3) ; found = found || (kk2 == kk) ; } PRINT3 (("\n")) ; ASSERT (found) ; } } PRINT1 (("\nCol "ID": Paths at this column, head "ID"\n", j, Head [j])); ASSERT (Head [j] != EMPTY) ; for (kk = Head [j] ; kk != EMPTY ; kk = Path [kk].next) { PRINT1 (("path "ID": (c="ID" j="ID") npaths "ID"\n", kk, Path[kk].c, j, npaths)) ; ASSERT (kk >= 0 && kk < npaths) ; ASSERT (Path [kk].pending == j) ; } #endif /* -------------------------------------------------------------- */ /* determine the path we're on */ /* -------------------------------------------------------------- */ /* get the first old path at column j */ path = Head [j] ; /* -------------------------------------------------------------- */ /* update/downdate of forward solve, Lx=b */ /* -------------------------------------------------------------- */ if (do_solve) { xj = Xx [j] ; if (IS_NONZERO (xj)) { xj = Xx [j] ; /* This is first time column j has been seen for entire */ /* rank-k update/downdate. */ /* DeltaB += Lold (j:botrow-1,j) * X (j) */ Nx [j] += xj ; /* diagonal of L */ /* find the botrow for this column */ botrow = (use_colmark) ? Path [path].botrow : n ; for (p = p1 + 1 ; p < p2 ; p++) { i = Li [p] ; if (i >= botrow) { break ; } Nx [i] += Lx [p] * xj ; } /* clear X[j] to flag col j of Lold as having been seen. If * X (j) was initially zero, then the above code is never * executed for column j. This is safe, since if xj=0 the * code above does not do anything anyway. */ Xx [j] = 0.0 ; } } /* -------------------------------------------------------------- */ /* start a new path at this column if two or more paths merge */ /* -------------------------------------------------------------- */ newpath = /* start a new path if paths have merged */ (Path [path].next != EMPTY) /* or if j is the first node on a path (case A). */ || (Path [path].c == EMPTY) ; if (newpath) { /* get the botrow of the first path at column j */ botrow = (use_colmark) ? Path [path].botrow : n ; path = npaths++ ; ASSERT (npaths <= 3*k) ; Path [path].ccol = EMPTY ; /* no single col of C for this path*/ Path [path].start = j ; /* path starts at this column j */ Path [path].end = EMPTY ; /* don't know yet where it ends */ Path [path].parent = EMPTY ;/* don't know parent path yet */ Path [path].rank = 0 ; /* rank is sum of child path ranks */ PRINT1 (("Path "ID" starts: start "ID" end "ID" parent "ID"\n", path, Path [path].start, Path [path].end, Path [path].parent)) ; /* set the botrow of the new path */ Path [path].botrow = (use_colmark) ? botrow : n ; } /* -------------------------------------------------------------- */ /* for each path kk pending at column j */ /* -------------------------------------------------------------- */ /* make a list of the sets that need to be merged into column j */ nsets = 0 ; for (kk = Head [j] ; kk != EMPTY ; kk = Path [kk].next) { /* ---------------------------------------------------------- */ /* path kk is at (c,j) */ /* ---------------------------------------------------------- */ c = Path [kk].c ; ASSERT (c < j) ; PRINT1 (("TUPLE on path "ID" (c="ID" j="ID")\n", kk, c, j)) ; ASSERT (Path [kk].pending == j) ; if (newpath) { /* finalize path kk and find rank of this path */ Path [kk].end = c ; /* end of old path is previous node c */ Path [kk].parent = path ; /* parent is this path */ Path [path].rank += Path [kk].rank ; /* sum up ranks */ Path [kk].pending = EMPTY ; PRINT1 (("Path "ID" done:start "ID" end "ID" parent "ID"\n", kk, Path [kk].start, Path [kk].end, Path [kk].parent)) ; } if (c == EMPTY) { /* ------------------------------------------------------ */ /* CASE A: first node in path */ /* ------------------------------------------------------ */ /* update: add pattern of incoming column */ /* Column ccol of C is in Ci [pp1 ... pp2-1] */ ccol = Path [kk].ccol ; pp1 = Cp [ccol] ; pp2 = (packed) ? (Cp [ccol+1]) : (pp1 + Cnz [ccol]) ; PRINT1 (("Case A, ccol = "ID" len "ID"\n", ccol, pp2-pp1)) ; ASSERT (IMPLIES (pp2 > pp1, Ci [pp1] == j)) ; if (!scattered) { /* scatter the original pattern of column j of L */ for (p = p1 ; p < p2 ; p++) { Flag [Li [p]] = mark ; } scattered = TRUE ; } /* scatter column ccol of C (skip first entry, j) */ newlnz1 = newlnz ; for (p = pp1 + 1 ; p < pp2 ; p++) { row = Ci [p] ; if (Flag [row] < mark) { /* this is a new entry in Lj' */ Flag [row] = mark ; newlnz++ ; } } if (newlnz1 != newlnz) { /* column ccol of C adds something to column j of L */ Set [nsets++] = FLIP (ccol) ; } } else if (Head [c] == 1) { /* ------------------------------------------------------ */ /* CASE B: c is old, but changed, child of j */ /* CASE C: new child of j */ /* ------------------------------------------------------ */ /* Head [c] is 1 if col c of L has new entries, * EMPTY otherwise */ Flag [c] = 0 ; Head [c] = EMPTY ; /* update: add Lc' */ /* column c of L is in Li [pp1 .. pp2-1] */ pp1 = Lp [c] ; pp2 = pp1 + Lnz [c] ; PRINT1 (("Case B/C: c = "ID"\n", c)) ; DEBUG (dump_col ("Child", c, pp1, pp2, Li, Lx, n, Common)) ; ASSERT (j == Li [pp1 + 1]) ; /* j is new parent of c */ if (!scattered) { /* scatter the original pattern of column j of L */ for (p = p1 ; p < p2 ; p++) { Flag [Li [p]] = mark ; } scattered = TRUE ; } /* scatter column c of L (skip first two entries, c and j)*/ newlnz1 = newlnz ; for (p = pp1 + 2 ; p < pp2 ; p++) { row = Li [p] ; if (Flag [row] < mark) { /* this is a new entry in Lj' */ Flag [row] = mark ; newlnz++ ; } } PRINT2 (("\n")) ; if (newlnz1 != newlnz) { /* column c of L adds something to column j of L */ Set [nsets++] = c ; } } } /* -------------------------------------------------------------- */ /* update the pattern of column j of L */ /* -------------------------------------------------------------- */ /* Column j of L will be in Li/Lx [p1 .. p3-1] */ p3 = p1 + newlnz ; ASSERT (IMPLIES (nsets == 0, newlnz == Lnz [j])) ; PRINT1 (("p1 "ID" p2 "ID" p3 "ID" nsets "ID"\n", p1, p2, p3,nsets)); /* -------------------------------------------------------------- */ /* ensure we have enough space for the longer column */ /* -------------------------------------------------------------- */ if (nsets > 0 && p3 > Lp [Lnext [j]]) { PRINT1 (("Col realloc: j "ID" newlnz "ID"\n", j, newlnz)) ; if (!CHOLMOD(reallocate_column) (j, newlnz, L, Common)) { /* out of memory, L is now simplicial symbolic */ CHOLMOD(clear_flag) (Common) ; for (j = 0 ; j <= n ; j++) { Head [j] = EMPTY ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, wdim, Common)) ; return (FALSE) ; } /* L->i and L->x may have moved. Column j has moved too */ Li = L->i ; Lx = L->x ; p1 = Lp [j] ; p2 = p1 + Lnz [j] ; p3 = p1 + newlnz ; } /* -------------------------------------------------------------- */ /* create set pointers */ /* -------------------------------------------------------------- */ for (s = 0 ; s < nsets ; s++) { /* Pattern of Set s is *(Set_ps1 [s] ... Set_ps2 [s]-1) */ c = Set [s] ; if (c < EMPTY) { /* column ccol of C, skip first entry (j) */ ccol = FLIP (c) ; pp1 = Cp [ccol] ; pp2 = (packed) ? (Cp [ccol+1]) : (pp1 + Cnz [ccol]) ; ASSERT (pp2 - pp1 > 1) ; Set_ps1 [s] = &(Ci [pp1 + 1]) ; Set_ps2 [s] = &(Ci [pp2]) ; PRINT1 (("set "ID" is ccol "ID"\n", s, ccol)) ; } else { /* column c of L, skip first two entries (c and j) */ pp1 = Lp [c] ; pp2 = pp1 + Lnz [c] ; ASSERT (Lnz [c] > 2) ; Set_ps1 [s] = &(Li [pp1 + 2]) ; Set_ps2 [s] = &(Li [pp2]) ; PRINT1 (("set "ID" is L "ID"\n", s, c)) ; } DEBUG (dump_set (s, Set_ps1, Set_ps2, j, n, Common)) ; } /* -------------------------------------------------------------- */ /* multiset merge */ /* -------------------------------------------------------------- */ /* Merge the sets into a single sorted set, Lj'. Before the merge * starts, column j is located in Li/Lx [p1 ... p2-1] and the * space Li/Lx [p2 ... p3-1] is empty. p1 is Lp [j], p2 is * Lp [j] + Lnz [j] (the old length of the column), and p3 is * Lp [j] + newlnz (the new and longer length of the column). * * The sets 0 to nsets-1 are defined by the Set_ps1 and Set_ps2 * pointers. Set s is located in *(Set_ps1 [s] ... Set_ps2 [s]-1). * It may be a column of C, or a column of L. All row indices i in * the sets are in the range i > j and i < n. All sets are sorted. * * The merge into column j of L is done in place. * * During the merge, p2 and p3 are updated. Li/Lx [p1..p2-1] * reflects the indices of the old column j of L that are yet to * be merged into the new column. Entries in their proper place in * the new column j of L are located in Li/Lx [p3 ... p1+newlnz-1]. * The merge finishes when p2 == p3. * * During the merge, set s consumed as it is merged into column j of * L. Its unconsumed contents are *(Set_ps1 [s] ... Set_ps2 [s]-1). * When a set is completely consumed, it is removed from the set of * sets, and nsets is decremented. * * The multiset merge and 2-set merge finishes when p2 == p3. */ PRINT1 (("Multiset merge p3 "ID" p2 "ID" nsets "ID"\n", p3, p2, nsets)) ; while (p3 > p2 && nsets > 1) { #ifndef NDEBUG PRINT2 (("\nMultiset merge. nsets = "ID"\n", nsets)) ; PRINT2 (("Source col p1 = "ID", p2 = "ID", p3= "ID"\n", p1, p2, p3)) ; for (p = p1 + 1 ; p < p2 ; p++) { PRINT2 ((" p: "ID" source row "ID" %g\n", p, Li[p], Lx[p])) ; ASSERT (Li [p] > j && Li [p] < n) ; } PRINT2 (("---\n")) ; for (p = p3 ; p < p1 + newlnz ; p++) { PRINT2 ((" p: "ID" target row "ID" %g\n", p, Li[p], Lx[p])) ; ASSERT (Li [p] > j && Li [p] < n) ; } for (s = 0 ; s < nsets ; s++) { dump_set (s, Set_ps1, Set_ps2, j, n, Common) ; } #endif /* get the entry at the tail end of source column Lj */ row1 = Li [p2 - 1] ; ASSERT (row1 >= j && p2 >= p1) ; /* find the largest row in all the sets */ maxrow = row1 ; smax = EMPTY ; for (s = nsets-1 ; s >= 0 ; s--) { ASSERT (Set_ps1 [s] < Set_ps2 [s]) ; row = *(Set_ps2 [s] - 1) ; if (row == maxrow) { /* skip past this entry in set s (it is a duplicate) */ Set_ps2 [s]-- ; if (Set_ps1 [s] == Set_ps2 [s]) { /* nothing more in this set */ nsets-- ; Set_ps1 [s] = Set_ps1 [nsets] ; Set_ps2 [s] = Set_ps2 [nsets] ; if (smax == nsets) { /* Set smax redefined; it is now this set */ smax = s ; } } } else if (row > maxrow) { maxrow = row ; smax = s ; } } ASSERT (maxrow > j) ; /* move the row onto the stack of the target column */ if (maxrow == row1) { /* next entry is in Lj, move to the bottom of Lj' */ ASSERT (smax == EMPTY) ; p2-- ; p3-- ; Li [p3] = maxrow ; Lx [p3] = Lx [p2] ; } else { /* new entry in Lj' */ ASSERT (smax >= 0 && smax < nsets) ; Set_ps2 [smax]-- ; p3-- ; Li [p3] = maxrow ; Lx [p3] = 0.0 ; if (Set_ps1 [smax] == Set_ps2 [smax]) { /* nothing more in this set */ nsets-- ; Set_ps1 [smax] = Set_ps1 [nsets] ; Set_ps2 [smax] = Set_ps2 [nsets] ; PRINT1 (("Set "ID" now empty\n", smax)) ; } } } /* -------------------------------------------------------------- */ /* 2-set merge: */ /* -------------------------------------------------------------- */ /* This the same as the multi-set merge, except there is only one * set s = 0 left. The source column j and the set 0 are being * merged into the target column j. */ if (nsets > 0) { ps1 = Set_ps1 [0] ; ps2 = Set_ps2 [0] ; } while (p3 > p2) { #ifndef NDEBUG PRINT2 (("\n2-set merge.\n")) ; ASSERT (nsets == 1) ; PRINT2 (("Source col p1 = "ID", p2 = "ID", p3= "ID"\n", p1, p2, p3)) ; for (p = p1 + 1 ; p < p2 ; p++) { PRINT2 ((" p: "ID" source row "ID" %g\n", p, Li[p], Lx[p])) ; ASSERT (Li [p] > j && Li [p] < n) ; } PRINT2 (("---\n")) ; for (p = p3 ; p < p1 + newlnz ; p++) { PRINT2 ((" p: "ID" target row "ID" %g\n", p, Li[p], Lx[p])) ; ASSERT (Li [p] > j && Li [p] < n) ; } dump_set (0, Set_ps1, Set_ps2, j, n, Common) ; #endif if (p2 == p1 + 1) { /* the top of Lj is empty; copy the set and quit */ while (p3 > p2) { /* new entry in Lj' */ row = *(--ps2) ; p3-- ; Li [p3] = row ; Lx [p3] = 0.0 ; } } else { /* get the entry at the tail end of Lj */ row1 = Li [p2 - 1] ; ASSERT (row1 > j && row1 < n) ; /* get the entry at the tail end of the incoming set */ ASSERT (ps1 < ps2) ; row = *(ps2-1) ; ASSERT (row > j && row1 < n) ; /* move the larger of the two entries to the target set */ if (row1 >= row) { /* next entry is in Lj, move to the bottom */ if (row1 == row) { /* skip past this entry in the set */ ps2-- ; } p2-- ; p3-- ; Li [p3] = row1 ; Lx [p3] = Lx [p2] ; } else { /* new entry in Lj' */ ps2-- ; p3-- ; Li [p3] = row ; Lx [p3] = 0.0 ; } } } /* -------------------------------------------------------------- */ /* The new column j of L is now in Li/Lx [p1 ... p2-1] */ /* -------------------------------------------------------------- */ p2 = p1 + newlnz ; DEBUG (dump_col ("After merge: ", j, p1, p2, Li, Lx, n, Common)) ; fl += Path [path].rank * (6 + 4 * (double) newlnz) ; /* -------------------------------------------------------------- */ /* clear Flag; original pattern of column j L no longer marked */ /* -------------------------------------------------------------- */ mark = CHOLMOD(clear_flag) (Common) ; scattered = FALSE ; /* -------------------------------------------------------------- */ /* find the new parent */ /* -------------------------------------------------------------- */ newparent = (newlnz > 1) ? (Li [p1 + 1]) : EMPTY ; PRINT1 (("\nNew parent, Lnz: "ID": "ID" "ID"\n", j, newparent,newlnz)); ASSERT (oldparent == EMPTY || newparent <= oldparent) ; /* -------------------------------------------------------------- */ /* go to the next node in the path */ /* -------------------------------------------------------------- */ /* path moves to (j,nextj) unless j is a root */ nextj = (newparent == EMPTY) ? n : newparent ; /* place path at head of list for nextj, or terminate the path */ PRINT1 (("\n j = "ID" nextj = "ID"\n\n", j, nextj)) ; Path [path].c = j ; if (nextj < n) { /* put path on link list of pending paths at column nextj */ Path [path].next = Head [nextj] ; Path [path].pending = nextj ; Head [nextj] = path ; PRINT1 (("Path "ID" continues to ("ID","ID"). Rank "ID"\n", path, Path [path].c, nextj, Path [path].rank)) ; } else { /* path has ended here, at a root */ Path [path].next = EMPTY ; Path [path].pending = EMPTY ; Path [path].end = j ; PRINT1 (("Path "ID" ends at root ("ID"). Rank "ID"\n", path, Path [path].end, Path [path].rank)) ; } /* The link list Head [j] can now be emptied. Set Head [j] to 1 * if column j has changed (it is no longer used as a link list). */ PRINT1 (("column "ID", oldlnz = "ID"\n", j, Lnz [j])) ; Head [j] = (Lnz [j] != newlnz) ? 1 : EMPTY ; Lnz [j] = newlnz ; PRINT1 (("column "ID", newlnz = "ID"\n", j, newlnz)) ; DEBUG (dump_col ("New", j, p1, p2, Li, Lx, n, Common)) ; /* move to the next column */ if (k == Path [path].rank) { /* only one path left */ j = nextj ; } else { /* The current path is moving from column j to column nextj * (nextj is n if the path has ended). However, there may be * other paths pending in columns j+1 to nextj-1. There are * two methods for looking for the next column with a pending * update. The first one looks at all columns j+1 to nextj-1 * for a non-empty link list. This can be costly if j and * nextj differ by a large amount (it can be O(n), but this * entire routine may take Omega(1) time). The second method * looks at all paths and finds the smallest column at which any * path is pending. It takes O(# of paths), which is bounded * by 23: one for each column of C (up to 8), and then 15 for a * balanced binary tree with 8 leaves. However, if j and * nextj differ by a tiny amount (nextj is often j+1 near * the end of the matrix), looking at columns j+1 to nextj * would be faster. Both methods give the same answer. */ if (nextj - j < npaths) { /* there are fewer columns to search than paths */ PRINT1 (("check j="ID" to nextj="ID"\n", j, nextj)) ; for (j2 = j + 1 ; j2 < nextj ; j2++) { PRINT1 (("check j="ID" "ID"\n", j2, Head [j2])) ; if (Head [j2] != EMPTY) { PRINT1 (("found, j="ID"\n", j2)) ; ASSERT (Path [Head [j2]].pending == j2) ; break ; } } } else { /* there are fewer paths than columns to search */ j2 = nextj ; for (kk = 0 ; kk < npaths ; kk++) { jj = Path [kk].pending ; PRINT2 (("Path "ID" pending at "ID"\n", kk, jj)) ; if (jj != EMPTY) j2 = MIN (j2, jj) ; } } j = j2 ; } } /* ensure workspaces are back to the values required on input */ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, TRUE, Common)) ; /* ------------------------------------------------------------------ */ /* depth-first-search of tree to order the paths */ /* ------------------------------------------------------------------ */ /* create lists of child paths */ PRINT1 (("\n\nDFS search:\n\n")) ; for (path = 0 ; path < npaths ; path++) { Path [path].c = EMPTY ; /* first child of path */ Path [path].next = EMPTY ; /* next sibling of path */ Path [path].order = EMPTY ; /* path is not ordered yet */ Path [path].wfirst = EMPTY ; /* 1st column of W not found yet */ #ifndef NDEBUG j = Path [path].start ; PRINT1 (("Path "ID" : start "ID" end "ID" parent "ID" ccol "ID"\n", path, j, Path [path].end, Path [path].parent, Path [path].ccol)) ; for ( ; ; ) { PRINT1 ((" column "ID"\n", j)) ; ASSERT (j == EMPTY || (j >= 0 && j < n)) ; if (j == Path [path].end) { break ; } ASSERT (j >= 0 && j < n) ; j = (Lnz [j] > 1) ? (Li [Lp [j] + 1]) : EMPTY ; } #endif } for (path = 0 ; path < npaths ; path++) { p = Path [path].parent ; /* add path to child list of parent */ if (p != EMPTY) { ASSERT (p < npaths) ; Path [path].next = Path [p].c ; Path [p].c = path ; } } path_order = k ; w_order = 0 ; for (path = npaths-1 ; path >= 0 ; path--) { if (Path [path].order == EMPTY) { /* this path is the root of a subtree of Tbar */ PRINT1 (("Root path "ID"\n", path)) ; ASSERT (path >= k) ; dfs (Path, k, path, &path_order, &w_order, 0, npaths) ; } } ASSERT (path_order == npaths) ; ASSERT (w_order == k) ; /* reorder the paths */ for (path = 0 ; path < npaths ; path++) { /* old order is path, new order is Path [path].order */ OrderedPath [Path [path].order] = Path [path] ; } #ifndef NDEBUG for (path = 0 ; path < npaths ; path++) { PRINT1 (("Ordered Path "ID": start "ID" end "ID" wfirst "ID" rank " ""ID" ccol "ID"\n", path, OrderedPath [path].start, OrderedPath [path].end, OrderedPath [path].wfirst, OrderedPath [path].rank, OrderedPath [path].ccol)) ; if (path < k) { ASSERT (OrderedPath [path].ccol >= 0) ; } else { ASSERT (OrderedPath [path].ccol == EMPTY) ; } } #endif /* ------------------------------------------------------------------ */ /* numeric update/downdate for all paths */ /* ------------------------------------------------------------------ */ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, wdim, Common)) ; switch (wdim) { case 1: updown_1_r (update, C, k, L, W, OrderedPath, npaths, mask, Common) ; break ; case 2: updown_2_r (update, C, k, L, W, OrderedPath, npaths, mask, Common) ; break ; case 4: updown_4_r (update, C, k, L, W, OrderedPath, npaths, mask, Common) ; break ; case 8: updown_8_r (update, C, k, L, W, OrderedPath, npaths, mask, Common) ; break ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, wdim, Common)) ; } /* ---------------------------------------------------------------------- */ /* update/downdate the forward solve */ /* ---------------------------------------------------------------------- */ if (do_solve) { /* We now have DeltaB += Lold (:,j) * X (j) for all columns j in union * of all paths seen during the entire rank-cncol update/downdate. For * each j in path, do DeltaB -= Lnew (:,j)*DeltaB(j) * in topological order. */ #ifndef NDEBUG PRINT1 (("\ndo_solve, DeltaB + Lold(:,Path)*X(Path):\n")) ; for (i = 0 ; i < n ; i++) { PRINT1 (("do_solve: "ID" %30.20e\n", i, Nx [i])) ; } #endif /* Note that the downdate, if it deleted entries, would need to compute * the Stack prior to doing any downdates. */ /* find the union of all the paths in the new L */ top = n ; /* "top" is stack pointer, not a row or column index */ for (ccol = 0 ; ccol < cncol ; ccol++) { /* -------------------------------------------------------------- */ /* j = first row index of C (:,ccol) */ /* -------------------------------------------------------------- */ pp1 = Cp [ccol] ; pp2 = (packed) ? (Cp [ccol+1]) : (pp1 + Cnz [ccol]) ; if (pp2 > pp1) { /* Column ccol of C has at least one entry. */ j = Ci [pp1] ; } else { /* Column ccol of C is empty */ j = n-1 ; } PRINT1 (("\ndo_solve: ccol= "ID"\n", ccol)) ; ASSERT (j >= 0 && j < n) ; len = 0 ; /* -------------------------------------------------------------- */ /* find the new rowmark */ /* -------------------------------------------------------------- */ /* Each column of C can redefine the region of L that takes part in * the update/downdate of the triangular solve Lx=b. If * i = colmark [ccol] for column C(:,ccol), then i = rowmark [j] is * redefined for all columns along the path modified by C(:,ccol). * If more than one column modifies any given column j of L, then * the rowmark of j is determined by the colmark of the least- * numbered column that affects column j. That is, if both * C(:,ccol1) and C(:,ccol2) affect column j of L, then * rowmark [j] = colmark [MIN (ccol1, ccol2)]. * * rowmark [j] is not modified if rowmark or colmark are NULL, * or if colmark [ccol] is EMPTY. */ botrow = (use_colmark) ? (colmark [ccol]) : EMPTY ; /* -------------------------------------------------------------- */ /* traverse from j towards root, stopping if node already visited */ /* -------------------------------------------------------------- */ while (j != EMPTY && Flag [j] < mark) { PRINT1 (("do_solve: subpath j= "ID"\n", j)) ; ASSERT (j >= 0 && j < n) ; Stack [len++] = j ; /* place j on the stack */ Flag [j] = mark ; /* flag j as visited */ /* if using colmark, mark column j with botrow */ ASSERT (Li [Lp [j]] == j) ; /* diagonal is always present */ if (use_colmark) { Li [Lp [j]] = botrow ; /* use the space for botrow */ } /* go up the tree, to the parent of j */ j = (Lnz [j] > 1) ? (Li [Lp [j] + 1]) : EMPTY ; } /* -------------------------------------------------------------- */ /* move the path down to the bottom of the stack */ /* -------------------------------------------------------------- */ ASSERT (len <= top) ; while (len > 0) { Stack [--top] = Stack [--len] ; } } #ifndef NDEBUG /* Union of paths now in Stack [top..n-1] in topological order */ PRINT1 (("\nTopological order:\n")) ; for (i = top ; i < n ; i++) { PRINT1 (("column "ID" in full path\n", Stack [i])) ; } #endif /* Do the forward solve for the full path part of L */ for (m = top ; m < n ; m++) { j = Stack [m] ; ASSERT (j >= 0 && j < n) ; PRINT1 (("do_solve: path j= "ID"\n", j)) ; p1 = Lp [j] ; lnz = Lnz [j] ; p2 = p1 + lnz ; xj = Nx [j] ; /* copy new solution onto old one, for all cols in full path */ Xx [j] = xj ; Nx [j] = 0. ; /* DeltaB -= Lnew (j+1:botrow-1,j) * deltab(j) */ if (use_colmark) { botrow = Li [p1] ; /* get botrow */ Li [p1] = j ; /* restore diagonal entry */ for (p = p1 + 1 ; p < p2 ; p++) { i = Li [p] ; if (i >= botrow) break ; Nx [i] -= Lx [p] * xj ; } } else { for (p = p1 + 1 ; p < p2 ; p++) { Nx [Li [p]] -= Lx [p] * xj ; } } } /* clear the Flag */ mark = CHOLMOD(clear_flag) (Common) ; } /* ---------------------------------------------------------------------- */ /* successful update/downdate */ /* ---------------------------------------------------------------------- */ Common->modfl = fl ; DEBUG (for (j = 0 ; j < n ; j++) ASSERT (IMPLIES (do_solve, Nx[j] == 0.))) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, TRUE, Common)) ; DEBUG (CHOLMOD(dump_factor) (L, "output L for updown", Common)) ; return (TRUE) ; } #endif SuiteSparse/CHOLMOD/Cholesky/0000755001170100242450000000000010674020565014622 5ustar davisfacSuiteSparse/CHOLMOD/Cholesky/cholmod_rowfac.c0000644001170100242450000005243710635770574020000 0ustar davisfac/* ========================================================================== */ /* === Cholesky/cholmod_rowfac ============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Full or incremental numerical LDL' or LL' factorization (simplicial, not * supernodal) cholmod_factorize is the "easy" wrapper for this code, but it * does not provide access to incremental factorization. * * cholmod_rowfac computes the full or incremental LDL' or LL' factorization of * A+beta*I (where A is symmetric) or A*F+beta*I (where A and F are unsymmetric * and only the upper triangular part of A*F+beta*I is used). It computes * L (and D, for LDL') one row at a time. beta is real. * * A is nrow-by-ncol or nrow-by-nrow. In "packed" form it is a conventional * column-oriented sparse matrix. Row indices of column j are in * Ai [Ap [j] ... Ap [j+1]-1] and values in the same locations of Ax. * will be faster if A has sorted columns. In "unpacked" form the column * of A ends at Ap [j] + Anz [j] - 1 instead of Ap [j+1] - 1. * * Row indices in each column of A can be sorted or unsorted, but the routine * routine works fastest if A is sorted, or if only triu(A) is provided * for the symmetric case. * * The unit-diagonal nrow-by-nrow output matrix L is returned in "unpacked" * column form, with row indices of column j in Li [Lp [j] ... * Lp [j] + Lnz [j] - 1] and values in the same location in Lx. The row * indices in each column of L are in sorted order. The unit diagonal of L * is not stored. * * L can be a simplicial symbolic or numeric (L->is_super must be FALSE). * A symbolic factor is converted immediately into a numeric factor containing * the identity matrix. * * For a full factorization, kstart = 0 and kend = nrow. The existing nonzero * entries (numerical values in L->x and L->z for the zomplex case, and indices * in L->i), if any, are overwritten. * * To compute an incremental factorization, select kstart and kend as the range * of rows of L you wish to compute. A correct factorization will be computed * only if all descendants of all nodes k = kstart to kend-1 in the etree have * been factorized by a prior call to this routine, and if rows kstart to kend-1 * have not been factorized. This condition is NOT checked on input. * * --------------- * Symmetric case: * --------------- * * The factorization (in MATLAB notation) is: * * S = beta*I + A * S = triu (S) + triu (S,1)' * L*D*L' = S, or L*L' = S * * A is a conventional sparse matrix in compressed column form. Only the * diagonal and upper triangular part of A is accessed; the lower * triangular part is ignored and assumed to be equal to the upper * triangular part. For an incremental factorization, only columns kstart * to kend-1 of A are accessed. F is not used. * * --------------- * Unsymmetric case: * --------------- * * The factorization (in MATLAB notation) is: * * S = beta*I + A*F * S = triu (S) + triu (S,1)' * L*D*L' = S, or L*L' = S * * The typical case is F=A'. Alternatively, if F=A(:,f)', then this * routine factorizes S = beta*I + A(:,f)*A(:,f)'. * * All of A and F are accessed, but only the upper triangular part of A*F * is used. F must be of size A->ncol by A->nrow. F is used for the * unsymmetric case only. F can be packed or unpacked and it need not be * sorted. * * For a complete factorization of beta*I + A*A', * this routine performs a number of flops exactly equal to: * * sum (for each column j of A) of (Anz (j)^2 + Anz (j)), to form S * + * sum (for each column j of L) of (Lnz (j)^2 + 3*Lnz (j)), to factorize S * * where Anz (j) is the number of nonzeros in column j of A, and Lnz (j) * is the number of nonzero in column j of L below the diagonal. * * * workspace: Flag (nrow), W (nrow if real, 2*nrow if complex/zomplex), * Iwork (nrow) * * Supports any xtype, except a pattern-only input matrix A cannot be * factorized. */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "cholmod_cholesky.h" /* ========================================================================== */ /* === subtree ============================================================== */ /* ========================================================================== */ /* Compute the nonzero pattern of the sparse triangular solve Lx=b, where L in * this case is L(0:k-1,0:k-1), and b is a column of A. This is done by * traversing the kth row-subtree of the elimination tree of L, starting from * each nonzero entry in b. The pattern is returned postordered, and is valid * for a subsequent numerical triangular solve of Lx=b. The elimination tree * can be provided in a Parent array, or extracted from the pattern of L itself. * * The pattern of x = inv(L)*b is returned in Stack [top...]. * Also scatters b, or a multiple of b, into the work vector W. * * The SCATTER macro is defines how the numerical values of A or A*A' are to be * scattered. * * PARENT(i) is a macro the defines how the etree is accessed. It is either: * #define PARENT(i) Parent [i] * #define PARENT(i) (Lnz [i] > 1) ? (Li [Lp [i] + 1]) : EMPTY */ #define SUBTREE \ for ( ; p < pend ; p++) \ { \ i = Ai [p] ; \ if (i <= k) \ { \ /* scatter the column of A, or A*A' into Wx and Wz */ \ SCATTER ; \ /* start at node i and traverse up the subtree, stop at node k */ \ for (len = 0 ; i < k && i != EMPTY && Flag [i] < mark ; i = parent) \ { \ /* L(k,i) is nonzero, and seen for the first time */ \ Stack [len++] = i ; /* place i on the stack */ \ Flag [i] = mark ; /* mark i as visited */ \ parent = PARENT (i) ; /* traverse up the etree to the parent */ \ } \ /* move the path down to the bottom of the stack */ \ while (len > 0) \ { \ Stack [--top] = Stack [--len] ; \ } \ } \ else if (sorted) \ { \ break ; \ } \ } /* ========================================================================== */ /* === TEMPLATE ============================================================= */ /* ========================================================================== */ #define REAL #include "t_cholmod_rowfac.c" #define COMPLEX #include "t_cholmod_rowfac.c" #define ZOMPLEX #include "t_cholmod_rowfac.c" #define MASK #define REAL #include "t_cholmod_rowfac.c" #define COMPLEX #include "t_cholmod_rowfac.c" #define ZOMPLEX #include "t_cholmod_rowfac.c" #undef MASK /* ========================================================================== */ /* === cholmod_row_subtree ================================================== */ /* ========================================================================== */ /* Compute the nonzero pattern of the solution to the lower triangular system * L(0:k-1,0:k-1) * x = A (0:k-1,k) if A is symmetric, or * L(0:k-1,0:k-1) * x = A (0:k-1,:) * A (:,k)' if A is unsymmetric. * This gives the nonzero pattern of row k of L (excluding the diagonal). * The pattern is returned postordered. * * The symmetric case requires A to be in symmetric-upper form. * * The result is returned in R, a pre-allocated sparse matrix of size nrow-by-1, * with R->nzmax >= nrow. R is assumed to be packed (Rnz [0] is not updated); * the number of entries in R is given by Rp [0]. * * FUTURE WORK: a very minor change to this routine could allow it to compute * the nonzero pattern of x for any system Lx=b. The SUBTREE macro would need * to change, to eliminate its dependence on k. * * workspace: Flag (nrow) */ int CHOLMOD(row_subtree) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,f)' */ size_t krow, /* row k of L */ Int *Parent, /* elimination tree */ /* ---- output --- */ cholmod_sparse *R, /* pattern of L(k,:), 1-by-n with R->nzmax >= n */ /* --------------- */ cholmod_common *Common ) { Int *Rp, *Stack, *Flag, *Ap, *Ai, *Anz, *Fp, *Fi, *Fnz ; Int p, pend, parent, t, stype, nrow, k, pf, pfend, Fpacked, packed, sorted, top, len, i, mark ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (R, FALSE) ; RETURN_IF_NULL (Parent, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (R, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; stype = A->stype ; if (stype == 0) { RETURN_IF_NULL (F, FALSE) ; RETURN_IF_XTYPE_INVALID (F, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; } if (krow >= A->nrow) { ERROR (CHOLMOD_INVALID, "subtree: k invalid") ; return (FALSE) ; } if (R->ncol != 1 || A->nrow != R->nrow || A->nrow > R->nzmax) { ERROR (CHOLMOD_INVALID, "subtree: R invalid") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ nrow = A->nrow ; CHOLMOD(allocate_work) (nrow, 0, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if (stype > 0) { /* symmetric upper case: F is not needed. It may be NULL */ Fp = NULL ; Fi = NULL ; Fnz = NULL ; Fpacked = TRUE ; } else if (stype == 0) { /* unsymmetric case: F is required. */ Fp = F->p ; Fi = F->i ; Fnz = F->nz ; Fpacked = F->packed ; } else { /* symmetric lower triangular form not supported */ ERROR (CHOLMOD_INVALID, "symmetric lower not supported") ; return (FALSE) ; } Ap = A->p ; Ai = A->i ; Anz = A->nz ; packed = A->packed ; sorted = A->sorted ; k = krow ; Stack = R->i ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Flag = Common->Flag ; /* size nrow, Flag [i] < mark must hold */ /* mark = CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; /* ---------------------------------------------------------------------- */ /* compute the pattern of L(k,:) */ /* ---------------------------------------------------------------------- */ top = nrow ; /* Stack is empty */ Flag [k] = mark ; /* do not include diagonal entry in Stack */ #define SCATTER /* do not scatter numerical values */ #define PARENT(i) Parent [i] /* use Parent for etree */ if (stype != 0) { /* scatter kth col of triu (A), get pattern L(k,:) */ p = Ap [k] ; pend = (packed) ? (Ap [k+1]) : (p + Anz [k]) ; SUBTREE ; } else { /* scatter kth col of triu (beta*I+AA'), get pattern L(k,:) */ pf = Fp [k] ; pfend = (Fpacked) ? (Fp [k+1]) : (pf + Fnz [k]) ; for ( ; pf < pfend ; pf++) { /* get nonzero entry F (t,k) */ t = Fi [pf] ; p = Ap [t] ; pend = (packed) ? (Ap [t+1]) : (p + Anz [t]) ; SUBTREE ; } } #undef SCATTER #undef PARENT /* shift the stack upwards, to the first part of R */ len = nrow - top ; for (i = 0 ; i < len ; i++) { Stack [i] = Stack [top + i] ; } Rp = R->p ; Rp [0] = 0 ; Rp [1] = len ; R->sorted = FALSE ; CHOLMOD(clear_flag) (Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_row_lsubtree ================================================= */ /* ========================================================================== */ /* Identical to cholmod_row_subtree, except that the elimination tree is * obtained from L itself, as the first off-diagonal entry in each column. * L must be simplicial, not supernodal */ int CHOLMOD(row_lsubtree) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ Int *Fi, size_t fnz, /* nonzero pattern of kth row of A', not required * for the symmetric case. Need not be sorted. */ size_t krow, /* row k of L */ cholmod_factor *L, /* the factor L from which parent(i) is derived */ /* ---- output --- */ cholmod_sparse *R, /* pattern of L(k,:), 1-by-n with R->nzmax >= n */ /* --------------- */ cholmod_common *Common ) { Int *Rp, *Stack, *Flag, *Ap, *Ai, *Anz, *Lp, *Li, *Lnz ; Int p, pend, parent, t, stype, nrow, k, pf, packed, sorted, top, len, i, mark ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (R, FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (R, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; stype = A->stype ; if (stype == 0) { RETURN_IF_NULL (Fi, FALSE) ; } if (krow >= A->nrow) { ERROR (CHOLMOD_INVALID, "lsubtree: k invalid") ; return (FALSE) ; } if (R->ncol != 1 || A->nrow != R->nrow || A->nrow > R->nzmax) { ERROR (CHOLMOD_INVALID, "lsubtree: R invalid") ; return (FALSE) ; } if (L->is_super) { ERROR (CHOLMOD_INVALID, "lsubtree: L invalid (cannot be supernodal)") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ nrow = A->nrow ; CHOLMOD(allocate_work) (nrow, 0, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if (stype < 0) { /* symmetric lower triangular form not supported */ ERROR (CHOLMOD_INVALID, "symmetric lower not supported") ; return (FALSE) ; } Ap = A->p ; Ai = A->i ; Anz = A->nz ; packed = A->packed ; sorted = A->sorted ; k = krow ; Stack = R->i ; Lp = L->p ; Li = L->i ; Lnz = L->nz ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Flag = Common->Flag ; /* size nrow, Flag [i] < mark must hold */ mark = CHOLMOD(clear_flag) (Common) ; /* ---------------------------------------------------------------------- */ /* compute the pattern of L(k,:) */ /* ---------------------------------------------------------------------- */ top = nrow ; /* Stack is empty */ Flag [k] = mark ; /* do not include diagonal entry in Stack */ #define SCATTER /* do not scatter numerical values */ #define PARENT(i) (Lnz [i] > 1) ? (Li [Lp [i] + 1]) : EMPTY if (stype != 0) { /* scatter kth col of triu (A), get pattern L(k,:) */ p = Ap [k] ; pend = (packed) ? (Ap [k+1]) : (p + Anz [k]) ; SUBTREE ; } else { /* scatter kth col of triu (beta*I+AA'), get pattern L(k,:) */ for (pf = 0 ; pf < (Int) fnz ; pf++) { /* get nonzero entry F (t,k) */ t = Fi [pf] ; p = Ap [t] ; pend = (packed) ? (Ap [t+1]) : (p + Anz [t]) ; SUBTREE ; } } #undef SCATTER #undef PARENT /* shift the stack upwards, to the first part of R */ len = nrow - top ; for (i = 0 ; i < len ; i++) { Stack [i] = Stack [top + i] ; } Rp = R->p ; Rp [0] = 0 ; Rp [1] = len ; R->sorted = FALSE ; CHOLMOD(clear_flag) (Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_rowfac ======================================================= */ /* ========================================================================== */ /* This is the incremental factorization for general purpose usage. */ int CHOLMOD(rowfac) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,f)' */ double beta [2], /* factorize beta*I+A or beta*I+AA' */ size_t kstart, /* first row to factorize */ size_t kend, /* last row to factorize is kend-1 */ /* ---- in/out --- */ cholmod_factor *L, /* --------------- */ cholmod_common *Common ) { return (CHOLMOD(rowfac_mask) (A, F, beta, kstart, kend, NULL, NULL, L, Common)) ; } /* ========================================================================== */ /* === cholmod_rowfac_mask ================================================== */ /* ========================================================================== */ /* This is meant for use in LPDASA only. */ int CHOLMOD(rowfac_mask) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,f)' */ double beta [2], /* factorize beta*I+A or beta*I+AA' */ size_t kstart, /* first row to factorize */ size_t kend, /* last row to factorize is kend-1 */ Int *mask, /* size A->nrow. if mask[i] >= 0 row i is set to zero */ Int *RLinkUp, /* size A->nrow. link list of rows to compute */ /* ---- in/out --- */ cholmod_factor *L, /* --------------- */ cholmod_common *Common ) { Int n ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; if (L->xtype != CHOLMOD_PATTERN && A->xtype != L->xtype) { ERROR (CHOLMOD_INVALID, "xtype of A and L do not match") ; return (FALSE) ; } if (L->is_super) { ERROR (CHOLMOD_INVALID, "can only do simplicial factorization"); return (FALSE) ; } if (A->stype == 0) { RETURN_IF_NULL (F, FALSE) ; if (A->xtype != F->xtype) { ERROR (CHOLMOD_INVALID, "xtype of A and F do not match") ; return (FALSE) ; } } if (A->stype < 0) { /* symmetric lower triangular form not supported */ ERROR (CHOLMOD_INVALID, "symmetric lower not supported") ; return (FALSE) ; } if (kend > L->n) { ERROR (CHOLMOD_INVALID, "kend invalid") ; return (FALSE) ; } if (A->nrow != L->n) { ERROR (CHOLMOD_INVALID, "dimensions of A and L do not match") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; Common->rowfacfl = 0 ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* Xwork is of size n for the real case, 2*n for complex/zomplex */ n = L->n ; /* s = ((A->xtype != CHOLMOD_REAL) ? 2:1)*n */ s = CHOLMOD(mult_size_t) (n, ((A->xtype != CHOLMOD_REAL) ? 2:1), &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (n, n, s, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, A->nrow, Common)) ; /* ---------------------------------------------------------------------- */ /* factorize the matrix, using template routine */ /* ---------------------------------------------------------------------- */ if (RLinkUp == NULL) { switch (A->xtype) { case CHOLMOD_REAL: ok = r_cholmod_rowfac (A, F, beta, kstart, kend, L, Common) ; break ; case CHOLMOD_COMPLEX: ok = c_cholmod_rowfac (A, F, beta, kstart, kend, L, Common) ; break ; case CHOLMOD_ZOMPLEX: ok = z_cholmod_rowfac (A, F, beta, kstart, kend, L, Common) ; break ; } } else { switch (A->xtype) { case CHOLMOD_REAL: ok = r_cholmod_rowfac_mask (A, F, beta, kstart, kend, mask, RLinkUp, L, Common) ; break ; case CHOLMOD_COMPLEX: ok = c_cholmod_rowfac_mask (A, F, beta, kstart, kend, mask, RLinkUp, L, Common) ; break ; case CHOLMOD_ZOMPLEX: ok = z_cholmod_rowfac_mask (A, F, beta, kstart, kend, mask, RLinkUp, L, Common) ; break ; } } return (ok) ; } #endif SuiteSparse/CHOLMOD/Cholesky/cholmod_rowcolcounts.c0000644001170100242450000004373110635770550021247 0ustar davisfac/* ========================================================================== */ /* === Cholesky/cholmod_rowcolcounts ======================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Compute the row and column counts of the Cholesky factor L of the matrix * A or A*A'. The etree and its postordering must already be computed (see * cholmod_etree and cholmod_postorder) and given as inputs to this routine. * * For the symmetric case (LL'=A), A is accessed by column. Only the lower * triangular part of A is used. Entries not in this part of the matrix are * ignored. This is the same as storing the upper triangular part of A by * rows, with entries in the lower triangular part being ignored. NOTE: this * representation is the TRANSPOSE of the input to cholmod_etree. * * For the unsymmetric case (LL'=AA'), A is accessed by column. Equivalently, * if A is viewed as a matrix in compressed-row form, this routine computes * the row and column counts for L where LL'=A'A. If the input vector f is * present, then F*F' is analyzed instead, where F = A(:,f). * * The set f is held in fset and fsize. * fset = NULL means ":" in MATLAB. fset is ignored. * fset != NULL means f = fset [0..fset-1]. * fset != NULL and fsize = 0 means f is the empty set. * Common->status is set to CHOLMOD_INVALID if fset is invalid. * * In both cases, the columns of A need not be sorted. * A can be packed or unpacked. * * References: * J. Gilbert, E. Ng, B. Peyton, "An efficient algorithm to compute row and * column counts for sparse Cholesky factorization", SIAM J. Matrix Analysis & * Applic., vol 15, 1994, pp. 1075-1091. * * J. Gilbert, X. Li, E. Ng, B. Peyton, "Computing row and column counts for * sparse QR and LU factorization", BIT, vol 41, 2001, pp. 693-710. * * workspace: * if symmetric: Flag (nrow), Iwork (2*nrow) * if unsymmetric: Flag (nrow), Iwork (2*nrow+ncol), Head (nrow+1) * * Supports any xtype (pattern, real, complex, or zomplex). */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "cholmod_cholesky.h" /* ========================================================================== */ /* === initialize_node ====================================================== */ /* ========================================================================== */ static int initialize_node /* initial work for kth node in postordered etree */ ( Int k, /* at the kth step of the algorithm (and kth node) */ Int Post [ ], /* Post [k] = i, the kth node in postordered etree */ Int Parent [ ], /* Parent [i] is the parent of i in the etree */ Int ColCount [ ], /* ColCount [c] is the current weight of node c */ Int PrevNbr [ ] /* PrevNbr [u] = k if u was last considered at step k */ ) { Int p, parent ; /* determine p, the kth node in the postordered etree */ p = Post [k] ; /* adjust the weight if p is not a root of the etree */ parent = Parent [p] ; if (parent != EMPTY) { ColCount [parent]-- ; } /* flag node p to exclude self edges (p,p) */ PrevNbr [p] = k ; return (p) ; } /* ========================================================================== */ /* === process_edge ========================================================= */ /* ========================================================================== */ /* edge (p,u) is being processed. p < u is a descendant of its ancestor u in * the etree. node p is the kth node in the postordered etree. */ static void process_edge ( Int p, /* process edge (p,u) of the matrix */ Int u, Int k, /* we are at the kth node in the postordered etree */ Int First [ ], /* First [i] = k if the postordering of first * descendent of node i is k */ Int PrevNbr [ ], /* u was last considered at step k = PrevNbr [u] */ Int ColCount [ ], /* ColCount [c] is the current weight of node c */ Int PrevLeaf [ ], /* s = PrevLeaf [u] means that s was the last leaf * seen in the subtree rooted at u. */ Int RowCount [ ], /* RowCount [i] is # of nonzeros in row i of L, * including the diagonal. Not computed if NULL. */ Int SetParent [ ], /* the FIND/UNION data structure, which forms a set * of trees. A root i has i = SetParent [i]. Following * a path from i to the root q of the subtree containing * i means that q is the SetParent representative of i. * All nodes in the tree could have their SetParent * equal to the root q; the tree representation is used * to save time. When a path is traced from i to its * root q, the path is re-traversed to set the SetParent * of the whole path to be the root q. */ Int Level [ ] /* Level [i] = length of path from node i to root */ ) { Int prevleaf, q, s, sparent ; if (First [p] > PrevNbr [u]) { /* p is a leaf of the subtree of u */ ColCount [p]++ ; prevleaf = PrevLeaf [u] ; if (prevleaf == EMPTY) { /* p is the first leaf of subtree of u; RowCount will be incremented * by the length of the path in the etree from p up to u. */ q = u ; } else { /* q = FIND (prevleaf): find the root q of the * SetParent tree containing prevleaf */ for (q = prevleaf ; q != SetParent [q] ; q = SetParent [q]) { ; } /* the root q has been found; re-traverse the path and * perform path compression */ s = prevleaf ; for (s = prevleaf ; s != q ; s = sparent) { sparent = SetParent [s] ; SetParent [s] = q ; } /* adjust the RowCount and ColCount; RowCount will be incremented by * the length of the path from p to the SetParent root q, and * decrement the ColCount of q by one. */ ColCount [q]-- ; } if (RowCount != NULL) { /* if RowCount is being computed, increment it by the length of * the path from p to q */ RowCount [u] += (Level [p] - Level [q]) ; } /* p is a leaf of the subtree of u, so mark PrevLeaf [u] to be p */ PrevLeaf [u] = p ; } /* flag u has having been processed at step k */ PrevNbr [u] = k ; } /* ========================================================================== */ /* === finalize_node ======================================================== */ /* ========================================================================== */ static void finalize_node /* compute UNION (p, Parent [p]) */ ( Int p, Int Parent [ ], /* Parent [p] is the parent of p in the etree */ Int SetParent [ ] /* see process_edge, above */ ) { /* all nodes in the SetParent tree rooted at p now have as their final * root the node Parent [p]. This computes UNION (p, Parent [p]) */ if (Parent [p] != EMPTY) { SetParent [p] = Parent [p] ; } } /* ========================================================================== */ /* === cholmod_rowcolcounts ================================================= */ /* ========================================================================== */ int CHOLMOD(rowcolcounts) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ Int *Parent, /* size nrow. Parent [i] = p if p is the parent of i */ Int *Post, /* size nrow. Post [k] = i if i is the kth node in * the postordered etree. */ /* ---- output --- */ Int *RowCount, /* size nrow. RowCount [i] = # entries in the ith row of * L, including the diagonal. */ Int *ColCount, /* size nrow. ColCount [i] = # entries in the ith * column of L, including the diagonal. */ Int *First, /* size nrow. First [i] = k is the least postordering * of any descendant of i. */ Int *Level, /* size nrow. Level [i] is the length of the path from * i to the root, with Level [root] = 0. */ /* --------------- */ cholmod_common *Common ) { double fl, ff ; Int *Ap, *Ai, *Anz, *PrevNbr, *SetParent, *Head, *PrevLeaf, *Anext, *Ipost, *Iwork ; Int i, j, r, k, len, s, p, pend, inew, stype, nf, anz, inode, parent, nrow, ncol, packed, use_fset, jj ; size_t w ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (Parent, FALSE) ; RETURN_IF_NULL (Post, FALSE) ; RETURN_IF_NULL (ColCount, FALSE) ; RETURN_IF_NULL (First, FALSE) ; RETURN_IF_NULL (Level, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; stype = A->stype ; if (stype > 0) { /* symmetric with upper triangular part not supported */ ERROR (CHOLMOD_INVALID, "symmetric upper not supported") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ nrow = A->nrow ; /* the number of rows of A */ ncol = A->ncol ; /* the number of columns of A */ /* w = 2*nrow + (stype ? 0 : ncol) */ w = CHOLMOD(mult_size_t) (nrow, 2, &ok) ; w = CHOLMOD(add_size_t) (w, (stype ? 0 : ncol), &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (nrow, w, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } ASSERT (CHOLMOD(dump_perm) (Post, nrow, nrow, "Post", Common)) ; ASSERT (CHOLMOD(dump_parent) (Parent, nrow, "Parent", Common)) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Ap = A->p ; /* size ncol+1, column pointers for A */ Ai = A->i ; /* the row indices of A, of size nz=Ap[ncol+1] */ Anz = A->nz ; packed = A->packed ; ASSERT (IMPLIES (!packed, Anz != NULL)) ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Iwork = Common->Iwork ; SetParent = Iwork ; /* size nrow (i/i/l) */ PrevNbr = Iwork + nrow ; /* size nrow (i/i/l) */ Anext = Iwork + 2*((size_t) nrow) ; /* size ncol (i/i/l) (unsym only) */ PrevLeaf = Common->Flag ; /* size nrow */ Head = Common->Head ; /* size nrow+1 (unsym only)*/ /* ---------------------------------------------------------------------- */ /* find the first descendant and level of each node in the tree */ /* ---------------------------------------------------------------------- */ /* First [i] = k if the postordering of first descendent of node i is k */ /* Level [i] = length of path from node i to the root (Level [root] = 0) */ for (i = 0 ; i < nrow ; i++) { First [i] = EMPTY ; } /* postorder traversal of the etree */ for (k = 0 ; k < nrow ; k++) { /* node i of the etree is the kth node in the postordered etree */ i = Post [k] ; /* i is a leaf if First [i] is still EMPTY */ /* ColCount [i] starts at 1 if i is a leaf, zero otherwise */ ColCount [i] = (First [i] == EMPTY) ? 1 : 0 ; /* traverse the path from node i to the root, stopping if we find a * node r whose First [r] is already defined. */ len = 0 ; for (r = i ; (r != EMPTY) && (First [r] == EMPTY) ; r = Parent [r]) { First [r] = k ; len++ ; } if (r == EMPTY) { /* we hit a root node, the level of which is zero */ len-- ; } else { /* we stopped at node r, where Level [r] is already defined */ len += Level [r] ; } /* re-traverse the path from node i to r; set the level of each node */ for (s = i ; s != r ; s = Parent [s]) { Level [s] = len-- ; } } /* ---------------------------------------------------------------------- */ /* AA' case: sort columns of A according to first postordered row index */ /* ---------------------------------------------------------------------- */ fl = 0.0 ; if (stype == 0) { /* [ use PrevNbr [0..nrow-1] as workspace for Ipost */ Ipost = PrevNbr ; /* Ipost [i] = k if i is the kth node in the postordered etree. */ for (k = 0 ; k < nrow ; k++) { Ipost [Post [k]] = k ; } use_fset = (fset != NULL) ; if (use_fset) { nf = fsize ; /* clear Anext to check fset */ for (j = 0 ; j < ncol ; j++) { Anext [j] = -2 ; } /* find the first postordered row in each column of A (post,f) * and place the column in the corresponding link list */ for (jj = 0 ; jj < nf ; jj++) { j = fset [jj] ; if (j < 0 || j > ncol || Anext [j] != -2) { /* out-of-range or duplicate entry in fset */ ERROR (CHOLMOD_INVALID, "fset invalid") ; return (FALSE) ; } /* flag column j as having been seen */ Anext [j] = EMPTY ; } /* fset is now valid */ ASSERT (CHOLMOD(dump_perm) (fset, nf, ncol, "fset", Common)) ; } else { nf = ncol ; } for (jj = 0 ; jj < nf ; jj++) { j = (use_fset) ? (fset [jj]) : jj ; /* column j is in the fset; find the smallest row (if any) */ p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; ff = (double) MAX (0, pend - p) ; fl += ff*ff + ff ; if (pend > p) { k = Ipost [Ai [p]] ; for ( ; p < pend ; p++) { inew = Ipost [Ai [p]] ; k = MIN (k, inew) ; } /* place column j in link list k */ ASSERT (k >= 0 && k < nrow) ; Anext [j] = Head [k] ; Head [k] = j ; } } /* Ipost no longer needed for inverse postordering ] * Head [k] contains a link list of all columns whose first * postordered row index is equal to k, for k = 0 to nrow-1. */ } /* ---------------------------------------------------------------------- */ /* compute the row counts and node weights */ /* ---------------------------------------------------------------------- */ if (RowCount != NULL) { for (i = 0 ; i < nrow ; i++) { RowCount [i] = 1 ; } } for (i = 0 ; i < nrow ; i++) { PrevLeaf [i] = EMPTY ; PrevNbr [i] = EMPTY ; SetParent [i] = i ; /* every node is in its own set, by itself */ } if (stype != 0) { /* ------------------------------------------------------------------ */ /* symmetric case: LL' = A */ /* ------------------------------------------------------------------ */ /* also determine the number of entries in triu(A) */ anz = nrow ; for (k = 0 ; k < nrow ; k++) { /* j is the kth node in the postordered etree */ j = initialize_node (k, Post, Parent, ColCount, PrevNbr) ; /* for all nonzeros A(i,j) below the diagonal, in column j of A */ p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i > j) { /* j is a descendant of i in etree(A) */ anz++ ; process_edge (j, i, k, First, PrevNbr, ColCount, PrevLeaf, RowCount, SetParent, Level) ; } } /* update SetParent: UNION (j, Parent [j]) */ finalize_node (j, Parent, SetParent) ; } Common->anz = anz ; } else { /* ------------------------------------------------------------------ */ /* unsymmetric case: LL' = AA' */ /* ------------------------------------------------------------------ */ for (k = 0 ; k < nrow ; k++) { /* inode is the kth node in the postordered etree */ inode = initialize_node (k, Post, Parent, ColCount, PrevNbr) ; /* for all cols j whose first postordered row is k: */ for (j = Head [k] ; j != EMPTY ; j = Anext [j]) { /* k is the first postordered row in column j of A */ /* for all rows i in column j: */ p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; /* has i already been considered at this step k */ if (PrevNbr [i] < k) { /* inode is a descendant of i in etree(AA') */ /* process edge (inode,i) and set PrevNbr[i] to k */ process_edge (inode, i, k, First, PrevNbr, ColCount, PrevLeaf, RowCount, SetParent, Level) ; } } } /* clear link list k */ Head [k] = EMPTY ; /* update SetParent: UNION (inode, Parent [inode]) */ finalize_node (inode, Parent, SetParent) ; } } /* ---------------------------------------------------------------------- */ /* finish computing the column counts */ /* ---------------------------------------------------------------------- */ for (j = 0 ; j < nrow ; j++) { parent = Parent [j] ; if (parent != EMPTY) { /* add the ColCount of j to its parent */ ColCount [parent] += ColCount [j] ; } } /* ---------------------------------------------------------------------- */ /* clear workspace */ /* ---------------------------------------------------------------------- */ Common->mark = EMPTY ; /* CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* flop count and nnz(L) for subsequent LL' numerical factorization */ /* ---------------------------------------------------------------------- */ /* use double to avoid integer overflow. lnz cannot be NaN. */ Common->aatfl = fl ; Common->lnz = 0. ; fl = 0 ; for (j = 0 ; j < nrow ; j++) { ff = (double) (ColCount [j]) ; Common->lnz += ff ; fl += ff*ff ; } Common->fl = fl ; PRINT1 (("rowcol fl %g lnz %g\n", Common->fl, Common->lnz)) ; return (TRUE) ; } #endif SuiteSparse/CHOLMOD/Cholesky/t_cholmod_solve.c0000644001170100242450000001120210537777374020161 0ustar davisfac/* ========================================================================== */ /* === Cholesky/t_cholmod_solve ============================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Template routine for cholmod_solve. Supports any numeric xtype (real, * complex, or zomplex). The xtypes of all matrices (L and Y) must match. */ #include "cholmod_template.h" /* ========================================================================== */ /* === simplicial template solvers ========================================== */ /* ========================================================================== */ /* LL': solve Lx=b with non-unit diagonal */ #define LL #include "t_cholmod_lsolve.c" /* LDL': solve LDx=b */ #define LD #include "t_cholmod_lsolve.c" /* LDL': solve Lx=b with unit diagonal */ #include "t_cholmod_lsolve.c" /* LL': solve L'x=b with non-unit diagonal */ #define LL #include "t_cholmod_ltsolve.c" /* LDL': solve DL'x=b */ #define LD #include "t_cholmod_ltsolve.c" /* LDL': solve L'x=b with unit diagonal */ #include "t_cholmod_ltsolve.c" /* ========================================================================== */ /* === t_ldl_dsolve ========================================================= */ /* ========================================================================== */ /* Solve Dx=b for an LDL' factorization, where Y holds b' on input and x' on * output. */ static void TEMPLATE (ldl_dsolve) ( cholmod_factor *L, cholmod_dense *Y /* nr-by-n with leading dimension nr */ ) { double d [1] ; double *Lx, *Yx, *Yz ; Int *Lp ; Int n, nrhs, k, p, k1, k2 ; ASSERT (L->xtype == Y->xtype) ; /* L and Y must have the same xtype */ ASSERT (L->n == Y->ncol) ; /* dimensions must match */ ASSERT (Y->nrow == Y->d) ; /* leading dimension of Y = # rows of Y */ ASSERT (L->xtype != CHOLMOD_PATTERN) ; /* L is not symbolic */ ASSERT (!(L->is_super) && !(L->is_ll)) ; /* L is simplicial LDL' */ nrhs = Y->nrow ; n = L->n ; Lp = L->p ; Lx = L->x ; Yx = Y->x ; Yz = Y->z ; for (k = 0 ; k < n ; k++) { k1 = k*nrhs ; k2 = (k+1)*nrhs ; ASSIGN_REAL (d,0, Lx,Lp[k]) ; for (p = k1 ; p < k2 ; p++) { DIV_REAL (Yx,Yz,p, Yx,Yz,p, d,0) ; } } } /* ========================================================================== */ /* === t_simplicial_solver ================================================== */ /* ========================================================================== */ /* Solve a linear system, where Y' contains the (array-transposed) right-hand * side on input, and the solution on output. No permutations are applied; * these must have already been applied to Y on input. */ static void TEMPLATE (simplicial_solver) ( int sys, /* system to solve */ cholmod_factor *L, /* factor to use, a simplicial LL' or LDL' */ cholmod_dense *Y /* right-hand-side on input, solution on output */ ) { if (L->is_ll) { /* The factorization is LL' */ if (sys == CHOLMOD_A || sys == CHOLMOD_LDLt) { /* Solve Ax=b or LL'x=b */ TEMPLATE (ll_lsolve_k) (L, Y) ; TEMPLATE (ll_ltsolve_k) (L, Y) ; } else if (sys == CHOLMOD_L || sys == CHOLMOD_LD) { /* Solve Lx=b */ TEMPLATE (ll_lsolve_k) (L, Y) ; } else if (sys == CHOLMOD_Lt || sys == CHOLMOD_DLt) { /* Solve L'x=b */ TEMPLATE (ll_ltsolve_k) (L, Y) ; } } else { /* The factorization is LDL' */ if (sys == CHOLMOD_A || sys == CHOLMOD_LDLt) { /* Solve Ax=b or LDL'x=b */ TEMPLATE (ldl_lsolve_k) (L, Y) ; TEMPLATE (ldl_dltsolve_k) (L, Y) ; } else if (sys == CHOLMOD_LD) { /* Solve LDx=b */ TEMPLATE (ldl_ldsolve_k) (L, Y) ; } else if (sys == CHOLMOD_L) { /* Solve Lx=b */ TEMPLATE (ldl_lsolve_k) (L, Y) ; } else if (sys == CHOLMOD_Lt) { /* Solve L'x=b */ TEMPLATE (ldl_ltsolve_k) (L, Y) ; } else if (sys == CHOLMOD_DLt) { /* Solve DL'x=b */ TEMPLATE (ldl_dltsolve_k) (L, Y) ; } else if (sys == CHOLMOD_D) { /* Solve Dx=b */ TEMPLATE (ldl_dsolve) (L, Y) ; } } } #undef PATTERN #undef REAL #undef COMPLEX #undef ZOMPLEX SuiteSparse/CHOLMOD/Cholesky/cholmod_factorize.c0000644001170100242450000003435410537777320020500 0ustar davisfac/* ========================================================================== */ /* === Cholesky/cholmod_factorize =========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Computes the numerical factorization of a symmetric matrix. The primary * inputs to this routine are a sparse matrix A and the symbolic factor L from * cholmod_analyze or a prior numerical factor L. If A is symmetric, this * routine factorizes A(p,p)+beta*I (beta can be zero), where p is the * fill-reducing permutation (L->Perm). If A is unsymmetric, either * A(p,:)*A(p,:)'+beta*I or A(p,f)*A(p,f)'+beta*I is factorized. The set f and * the nonzero pattern of the matrix A must be the same as the matrix passed to * cholmod_analyze for the supernodal case. For the simplicial case, it can * be different, but it should be the same for best performance. beta is real. * * A simplicial factorization or supernodal factorization is chosen, based on * the type of the factor L. If L->is_super is TRUE, a supernodal LL' * factorization is computed. Otherwise, a simplicial numeric factorization * is computed, either LL' or LDL', depending on Common->final_ll. * * Once the factorization is complete, it can be left as is or optionally * converted into any simplicial numeric type, depending on the * Common->final_* parameters. If converted from a supernodal to simplicial * type, and the Common->final_resymbol parameter is true, then numerically * zero entries in L due to relaxed supernodal amalgamation are removed from * the simplicial factor (they are always left in the supernodal form of L). * Entries that are numerically zero but present in the simplicial symbolic * pattern of L are left in place (that is, the graph of L remains chordal). * This is required for the update/downdate/rowadd/rowdel routines to work * properly. * * workspace: Flag (nrow), Head (nrow+1), * if symmetric: Iwork (2*nrow+2*nsuper) * if unsymmetric: Iwork (2*nrow+MAX(2*nsuper,ncol)) * where nsuper is 0 if simplicial, or the # of relaxed supernodes in * L otherwise (nsuper <= nrow). * if simplicial: W (nrow). * Allocates up to two temporary copies of its input matrix (including * both pattern and numerical values). * * If the matrix is not positive definite the routine returns TRUE, but * sets Common->status to CHOLMOD_NOT_POSDEF and L->minor is set to the * column at which the failure occurred. Columns L->minor to L->n-1 are * set to zero. * * Supports any xtype (pattern, real, complex, or zomplex), except that the * input matrix A cannot be pattern-only. If L is simplicial, its numeric * xtype matches A on output. If L is supernodal, its xtype is real if A is * real, or complex if A is complex or zomplex. */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "cholmod_cholesky.h" #ifndef NSUPERNODAL #include "cholmod_supernodal.h" #endif /* ========================================================================== */ /* === cholmod_factorize ==================================================== */ /* ========================================================================== */ /* Factorizes PAP' (or PAA'P' if A->stype is 0), using a factor obtained * from cholmod_analyze. The analysis can be re-used simply by calling this * routine a second time with another matrix. A must have the same nonzero * pattern as that passed to cholmod_analyze. */ int CHOLMOD(factorize) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ /* ---- in/out --- */ cholmod_factor *L, /* resulting factorization */ /* --------------- */ cholmod_common *Common ) { double zero [2] ; zero [0] = 0 ; zero [1] = 0 ; return (CHOLMOD(factorize_p) (A, zero, NULL, 0, L, Common)) ; } /* ========================================================================== */ /* === cholmod_factorize_p ================================================== */ /* ========================================================================== */ /* Same as cholmod_factorize, but with more options. */ int CHOLMOD(factorize_p) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ double beta [2], /* factorize beta*I+A or beta*I+A'*A */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- in/out --- */ cholmod_factor *L, /* resulting factorization */ /* --------------- */ cholmod_common *Common ) { cholmod_sparse *S, *F, *A1, *A2 ; Int nrow, ncol, stype, convert, n, nsuper, grow2, status ; size_t s, t, uncol ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; nrow = A->nrow ; ncol = A->ncol ; n = L->n ; stype = A->stype ; if (L->n != A->nrow) { ERROR (CHOLMOD_INVALID, "A and L dimensions do not match") ; return (FALSE) ; } if (stype != 0 && nrow != ncol) { ERROR (CHOLMOD_INVALID, "matrix invalid") ; return (FALSE) ; } DEBUG (CHOLMOD(dump_sparse) (A, "A for cholmod_factorize", Common)) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ nsuper = (L->is_super ? L->nsuper : 0) ; uncol = ((stype != 0) ? 0 : ncol) ; /* s = 2*nrow + MAX (uncol, 2*nsuper) */ s = CHOLMOD(mult_size_t) (nsuper, 2, &ok) ; s = MAX (uncol, s) ; t = CHOLMOD(mult_size_t) (nrow, 2, &ok) ; s = CHOLMOD(add_size_t) (s, t, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (nrow, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } S = NULL ; F = NULL ; A1 = NULL ; A2 = NULL ; /* convert to another form when done, if requested */ convert = !(Common->final_asis) ; /* ---------------------------------------------------------------------- */ /* perform supernodal LL' or simplicial LDL' factorization */ /* ---------------------------------------------------------------------- */ if (L->is_super) { #ifndef NSUPERNODAL /* ------------------------------------------------------------------ */ /* supernodal factorization */ /* ------------------------------------------------------------------ */ if (L->ordering == CHOLMOD_NATURAL) { /* -------------------------------------------------------------- */ /* natural ordering */ /* -------------------------------------------------------------- */ if (stype > 0) { /* S = tril (A'), F not needed */ /* workspace: Iwork (nrow) */ A1 = CHOLMOD(ptranspose) (A, 2, NULL, NULL, 0, Common) ; S = A1 ; } else if (stype < 0) { /* This is the fastest option for the natural ordering */ /* S = A; F not needed */ S = A ; } else { /* F = A(:,f)' */ /* workspace: Iwork (nrow) */ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/ A1 = CHOLMOD(ptranspose) (A, 2, NULL, fset, fsize, Common) ; F = A1 ; /* S = A */ S = A ; } } else { /* -------------------------------------------------------------- */ /* permute the input matrix before factorization */ /* -------------------------------------------------------------- */ if (stype > 0) { /* This is the fastest option for factoring a permuted matrix */ /* S = tril (PAP'); F not needed */ /* workspace: Iwork (2*nrow) */ A1 = CHOLMOD(ptranspose) (A, 2, L->Perm, NULL, 0, Common) ; S = A1 ; } else if (stype < 0) { /* A2 = triu (PAP') */ /* workspace: Iwork (2*nrow) */ A2 = CHOLMOD(ptranspose) (A, 2, L->Perm, NULL, 0, Common) ; /* S = tril (A2'); F not needed */ /* workspace: Iwork (nrow) */ A1 = CHOLMOD(ptranspose) (A2, 2, NULL, NULL, 0, Common) ; S = A1 ; CHOLMOD(free_sparse) (&A2, Common) ; ASSERT (A2 == NULL) ; } else { /* F = A(p,f)' */ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/ A1 = CHOLMOD(ptranspose) (A, 2, L->Perm, fset, fsize, Common) ; F = A1 ; /* S = F' */ /* workspace: Iwork (nrow) */ A2 = CHOLMOD(ptranspose) (F, 2, NULL, NULL, 0, Common) ; S = A2 ; } } /* ------------------------------------------------------------------ */ /* supernodal factorization */ /* ------------------------------------------------------------------ */ /* workspace: Flag (nrow), Head (nrow+1), Iwork (2*nrow+2*nsuper) */ if (Common->status == CHOLMOD_OK) { CHOLMOD(super_numeric) (S, F, beta, L, Common) ; } status = Common->status ; ASSERT (IMPLIES (status >= CHOLMOD_OK, L->xtype != CHOLMOD_PATTERN)) ; /* ------------------------------------------------------------------ */ /* convert to final form, if requested */ /* ------------------------------------------------------------------ */ if (Common->status >= CHOLMOD_OK && convert) { /* workspace: none */ ok = CHOLMOD(change_factor) (L->xtype, Common->final_ll, Common->final_super, Common->final_pack, Common->final_monotonic, L, Common) ; if (ok && Common->final_resymbol && !(L->is_super)) { /* workspace: Flag (nrow), Head (nrow+1), * if symmetric: Iwork (2*nrow) * if unsymmetric: Iwork (2*nrow+ncol) */ CHOLMOD(resymbol_noperm) (S, fset, fsize, Common->final_pack, L, Common) ; } } #else /* ------------------------------------------------------------------ */ /* CHOLMOD Supernodal module not installed */ /* ------------------------------------------------------------------ */ status = CHOLMOD_NOT_INSTALLED ; ERROR (CHOLMOD_NOT_INSTALLED,"Supernodal module not installed") ; #endif } else { /* ------------------------------------------------------------------ */ /* simplicial LDL' factorization */ /* ------------------------------------------------------------------ */ /* Permute the input matrix A if necessary. cholmod_rowfac requires * triu(A) in column form for the symmetric case, and A in column form * for the unsymmetric case (the matrix S). The unsymmetric case * requires A in row form, or equivalently A' in column form (the * matrix F). */ if (L->ordering == CHOLMOD_NATURAL) { /* -------------------------------------------------------------- */ /* natural ordering */ /* -------------------------------------------------------------- */ if (stype > 0) { /* F is not needed, S = A */ S = A ; } else if (stype < 0) { /* F is not needed, S = A' */ /* workspace: Iwork (nrow) */ A2 = CHOLMOD(ptranspose) (A, 2, NULL, NULL, 0, Common) ; S = A2 ; } else { /* F = A (:,f)' */ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/ A1 = CHOLMOD(ptranspose) (A, 2, NULL, fset, fsize, Common) ; F = A1 ; S = A ; } } else { /* -------------------------------------------------------------- */ /* permute the input matrix before factorization */ /* -------------------------------------------------------------- */ if (stype > 0) { /* F = tril (A (p,p)') */ /* workspace: Iwork (2*nrow) */ A1 = CHOLMOD(ptranspose) (A, 2, L->Perm, NULL, 0, Common) ; /* A2 = triu (F') */ /* workspace: Iwork (nrow) */ A2 = CHOLMOD(ptranspose) (A1, 2, NULL, NULL, 0, Common) ; /* the symmetric case does not need F, free it and set to NULL*/ CHOLMOD(free_sparse) (&A1, Common) ; } else if (stype < 0) { /* A2 = triu (A (p,p)'), F not needed. This is the fastest * way to factorize a matrix using the simplicial routine * (cholmod_rowfac). */ /* workspace: Iwork (2*nrow) */ A2 = CHOLMOD(ptranspose) (A, 2, L->Perm, NULL, 0, Common) ; } else { /* F = A (p,f)' */ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/ A1 = CHOLMOD(ptranspose) (A, 2, L->Perm, fset, fsize, Common) ; F = A1 ; /* A2 = F' */ /* workspace: Iwork (nrow) */ A2 = CHOLMOD(ptranspose) (F, 2, NULL, NULL, 0, Common) ; } S = A2 ; } /* ------------------------------------------------------------------ */ /* simplicial LDL' or LL' factorization */ /* ------------------------------------------------------------------ */ /* factorize beta*I+S (symmetric) or beta*I+F*F' (unsymmetric) */ /* workspace: Flag (nrow), W (nrow), Iwork (2*nrow) */ if (Common->status == CHOLMOD_OK) { grow2 = Common->grow2 ; L->is_ll = BOOLEAN (Common->final_ll) ; if (L->xtype == CHOLMOD_PATTERN && Common->final_pack) { /* allocate a factor with exactly the space required */ Common->grow2 = 0 ; } CHOLMOD(rowfac) (S, F, beta, 0, nrow, L, Common) ; Common->grow2 = grow2 ; } status = Common->status ; /* ------------------------------------------------------------------ */ /* convert to final form, if requested */ /* ------------------------------------------------------------------ */ if (Common->status >= CHOLMOD_OK && convert) { /* workspace: none */ CHOLMOD(change_factor) (L->xtype, L->is_ll, FALSE, Common->final_pack, Common->final_monotonic, L, Common) ; } } /* ---------------------------------------------------------------------- */ /* free A1 and A2 if they exist */ /* ---------------------------------------------------------------------- */ CHOLMOD(free_sparse) (&A1, Common) ; CHOLMOD(free_sparse) (&A2, Common) ; Common->status = MAX (Common->status, status) ; return (Common->status >= CHOLMOD_OK) ; } #endif SuiteSparse/CHOLMOD/Cholesky/t_cholmod_ltsolve.c0000644001170100242450000005375610537777364020544 0ustar davisfac/* ========================================================================== */ /* === Cholesky/t_cholmod_ltsolve =========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Template routine to solve L'x=b with unit or non-unit diagonal, or * solve DL'x=b. * * The numeric xtype of L and Y must match. Y contains b on input and x on * output, stored in row-form. Y is nrow-by-n, where nrow must equal 1 for the * complex or zomplex cases, and nrow <= 4 for the real case. * * This file is not compiled separately. It is included in t_cholmod_solve.c * instead. It contains no user-callable routines. * * workspace: none * * Supports real, complex, and zomplex factors. */ /* undefine all prior definitions */ #undef FORM_NAME #undef LSOLVE #undef DIAG /* -------------------------------------------------------------------------- */ /* define the method */ /* -------------------------------------------------------------------------- */ #ifdef LL /* LL': solve Lx=b with non-unit diagonal */ #define FORM_NAME(prefix,rank) prefix ## ll_ltsolve_ ## rank #define DIAG #elif defined (LD) /* LDL': solve LDx=b */ #define FORM_NAME(prefix,rank) prefix ## ldl_dltsolve_ ## rank #define DIAG #else /* LDL': solve Lx=b with unit diagonal */ #define FORM_NAME(prefix,rank) prefix ## ldl_ltsolve_ ## rank #endif /* LSOLVE(k) defines the name of a routine for an n-by-k right-hand-side. */ #define LSOLVE(prefix,rank) FORM_NAME(prefix,rank) #ifdef REAL /* ========================================================================== */ /* === LSOLVE (1) =========================================================== */ /* ========================================================================== */ /* Solve L'x=b, where b has 1 column */ static void LSOLVE (PREFIX,1) ( cholmod_factor *L, double X [ ] /* n-by-1 in row form */ ) { double *Lx = L->x ; Int *Li = L->i ; Int *Lp = L->p ; Int *Lnz = L->nz ; Int j, n = L->n ; for (j = n-1 ; j >= 0 ; ) { /* get the start, end, and length of column j */ Int p = Lp [j] ; Int lnz = Lnz [j] ; Int pend = p + lnz ; /* find a chain of supernodes (up to j, j-1, and j-2) */ if (j < 4 || lnz != Lnz [j-1] - 1 || Li [Lp [j-1]+1] != j) { /* -------------------------------------------------------------- */ /* solve with a single column of L */ /* -------------------------------------------------------------- */ double y = X [j] ; #ifdef DIAG double d = Lx [p] ; #endif #ifdef LD y /= d ; #endif for (p++ ; p < pend ; p++) { y -= Lx [p] * X [Li [p]] ; } #ifdef LL X [j] = y / d ; #else X [j] = y ; #endif j-- ; /* advance to the next column of L */ } else if (lnz != Lnz [j-2]-2 || Li [Lp [j-2]+2] != j) { /* -------------------------------------------------------------- */ /* solve with a supernode of two columns of L */ /* -------------------------------------------------------------- */ double y [2], t ; Int q = Lp [j-1] ; #ifdef DIAG double d [2] ; d [0] = Lx [p] ; d [1] = Lx [q] ; #endif t = Lx [q+1] ; #ifdef LD y [0] = X [j ] / d [0] ; y [1] = X [j-1] / d [1] ; #else y [0] = X [j ] ; y [1] = X [j-1] ; #endif for (p++, q += 2 ; p < pend ; p++, q++) { Int i = Li [p] ; y [0] -= Lx [p] * X [i] ; y [1] -= Lx [q] * X [i] ; } #ifdef LL y [0] /= d [0] ; y [1] = (y [1] - t * y [0]) / d [1] ; #else y [1] -= t * y [0] ; #endif X [j ] = y [0] ; X [j-1] = y [1] ; j -= 2 ; /* advance to the next column of L */ } else { /* -------------------------------------------------------------- */ /* solve with a supernode of three columns of L */ /* -------------------------------------------------------------- */ double y [3], t [3] ; Int q = Lp [j-1] ; Int r = Lp [j-2] ; #ifdef DIAG double d [3] ; d [0] = Lx [p] ; d [1] = Lx [q] ; d [2] = Lx [r] ; #endif t [0] = Lx [q+1] ; t [1] = Lx [r+1] ; t [2] = Lx [r+2] ; #ifdef LD y [0] = X [j] / d [0] ; y [1] = X [j-1] / d [1] ; y [2] = X [j-2] / d [2] ; #else y [0] = X [j] ; y [1] = X [j-1] ; y [2] = X [j-2] ; #endif for (p++, q += 2, r += 3 ; p < pend ; p++, q++, r++) { Int i = Li [p] ; y [0] -= Lx [p] * X [i] ; y [1] -= Lx [q] * X [i] ; y [2] -= Lx [r] * X [i] ; } #ifdef LL y [0] /= d [0] ; y [1] = (y [1] - t [0] * y [0]) / d [1] ; y [2] = (y [2] - t [2] * y [0] - t [1] * y [1]) / d [2] ; #else y [1] -= t [0] * y [0] ; y [2] -= t [2] * y [0] + t [1] * y [1] ; #endif X [j-2] = y [2] ; X [j-1] = y [1] ; X [j ] = y [0] ; j -= 3 ; /* advance to the next column of L */ } } } /* ========================================================================== */ /* === LSOLVE (2) =========================================================== */ /* ========================================================================== */ /* Solve L'x=b, where b has 2 columns */ static void LSOLVE (PREFIX,2) ( cholmod_factor *L, double X [ ][2] /* n-by-2 in row form */ ) { double *Lx = L->x ; Int *Li = L->i ; Int *Lp = L->p ; Int *Lnz = L->nz ; Int j, n = L->n ; for (j = n-1 ; j >= 0 ; ) { /* get the start, end, and length of column j */ Int p = Lp [j] ; Int lnz = Lnz [j] ; Int pend = p + lnz ; /* find a chain of supernodes (up to j, j-1, and j-2) */ if (j < 4 || lnz != Lnz [j-1] - 1 || Li [Lp [j-1]+1] != j) { /* -------------------------------------------------------------- */ /* solve with a single column of L */ /* -------------------------------------------------------------- */ double y [2] ; #ifdef DIAG double d = Lx [p] ; #endif #ifdef LD y [0] = X [j][0] / d ; y [1] = X [j][1] / d ; #else y [0] = X [j][0] ; y [1] = X [j][1] ; #endif for (p++ ; p < pend ; p++) { Int i = Li [p] ; y [0] -= Lx [p] * X [i][0] ; y [1] -= Lx [p] * X [i][1] ; } #ifdef LL X [j][0] = y [0] / d ; X [j][1] = y [1] / d ; #else X [j][0] = y [0] ; X [j][1] = y [1] ; #endif j-- ; /* advance to the next column of L */ } else if (lnz != Lnz [j-2]-2 || Li [Lp [j-2]+2] != j) { /* -------------------------------------------------------------- */ /* solve with a supernode of two columns of L */ /* -------------------------------------------------------------- */ double y [2][2], t ; Int q = Lp [j-1] ; #ifdef DIAG double d [2] ; d [0] = Lx [p] ; d [1] = Lx [q] ; #endif t = Lx [q+1] ; #ifdef LD y [0][0] = X [j ][0] / d [0] ; y [0][1] = X [j ][1] / d [0] ; y [1][0] = X [j-1][0] / d [1] ; y [1][1] = X [j-1][1] / d [1] ; #else y [0][0] = X [j ][0] ; y [0][1] = X [j ][1] ; y [1][0] = X [j-1][0] ; y [1][1] = X [j-1][1] ; #endif for (p++, q += 2 ; p < pend ; p++, q++) { Int i = Li [p] ; y [0][0] -= Lx [p] * X [i][0] ; y [0][1] -= Lx [p] * X [i][1] ; y [1][0] -= Lx [q] * X [i][0] ; y [1][1] -= Lx [q] * X [i][1] ; } #ifdef LL y [0][0] /= d [0] ; y [0][1] /= d [0] ; y [1][0] = (y [1][0] - t * y [0][0]) / d [1] ; y [1][1] = (y [1][1] - t * y [0][1]) / d [1] ; #else y [1][0] -= t * y [0][0] ; y [1][1] -= t * y [0][1] ; #endif X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j-1][0] = y [1][0] ; X [j-1][1] = y [1][1] ; j -= 2 ; /* advance to the next column of L */ } else { /* -------------------------------------------------------------- */ /* solve with a supernode of three columns of L */ /* -------------------------------------------------------------- */ double y [3][2], t [3] ; Int q = Lp [j-1] ; Int r = Lp [j-2] ; #ifdef DIAG double d [3] ; d [0] = Lx [p] ; d [1] = Lx [q] ; d [2] = Lx [r] ; #endif t [0] = Lx [q+1] ; t [1] = Lx [r+1] ; t [2] = Lx [r+2] ; #ifdef LD y [0][0] = X [j ][0] / d [0] ; y [0][1] = X [j ][1] / d [0] ; y [1][0] = X [j-1][0] / d [1] ; y [1][1] = X [j-1][1] / d [1] ; y [2][0] = X [j-2][0] / d [2] ; y [2][1] = X [j-2][1] / d [2] ; #else y [0][0] = X [j ][0] ; y [0][1] = X [j ][1] ; y [1][0] = X [j-1][0] ; y [1][1] = X [j-1][1] ; y [2][0] = X [j-2][0] ; y [2][1] = X [j-2][1] ; #endif for (p++, q += 2, r += 3 ; p < pend ; p++, q++, r++) { Int i = Li [p] ; y [0][0] -= Lx [p] * X [i][0] ; y [0][1] -= Lx [p] * X [i][1] ; y [1][0] -= Lx [q] * X [i][0] ; y [1][1] -= Lx [q] * X [i][1] ; y [2][0] -= Lx [r] * X [i][0] ; y [2][1] -= Lx [r] * X [i][1] ; } #ifdef LL y [0][0] /= d [0] ; y [0][1] /= d [0] ; y [1][0] = (y [1][0] - t [0] * y [0][0]) / d [1] ; y [1][1] = (y [1][1] - t [0] * y [0][1]) / d [1] ; y [2][0] = (y [2][0] - t [2] * y [0][0] - t [1] * y [1][0]) / d [2]; y [2][1] = (y [2][1] - t [2] * y [0][1] - t [1] * y [1][1]) / d [2]; #else y [1][0] -= t [0] * y [0][0] ; y [1][1] -= t [0] * y [0][1] ; y [2][0] -= t [2] * y [0][0] + t [1] * y [1][0] ; y [2][1] -= t [2] * y [0][1] + t [1] * y [1][1] ; #endif X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j-1][0] = y [1][0] ; X [j-1][1] = y [1][1] ; X [j-2][0] = y [2][0] ; X [j-2][1] = y [2][1] ; j -= 3 ; /* advance to the next column of L */ } } } /* ========================================================================== */ /* === LSOLVE (3) =========================================================== */ /* ========================================================================== */ /* Solve L'x=b, where b has 3 columns */ static void LSOLVE (PREFIX,3) ( cholmod_factor *L, double X [ ][3] /* n-by-3 in row form */ ) { double *Lx = L->x ; Int *Li = L->i ; Int *Lp = L->p ; Int *Lnz = L->nz ; Int j, n = L->n ; for (j = n-1 ; j >= 0 ; ) { /* get the start, end, and length of column j */ Int p = Lp [j] ; Int lnz = Lnz [j] ; Int pend = p + lnz ; /* find a chain of supernodes (up to j, j-1, and j-2) */ if (j < 4 || lnz != Lnz [j-1] - 1 || Li [Lp [j-1]+1] != j) { /* -------------------------------------------------------------- */ /* solve with a single column of L */ /* -------------------------------------------------------------- */ double y [3] ; #ifdef DIAG double d = Lx [p] ; #endif #ifdef LD y [0] = X [j][0] / d ; y [1] = X [j][1] / d ; y [2] = X [j][2] / d ; #else y [0] = X [j][0] ; y [1] = X [j][1] ; y [2] = X [j][2] ; #endif for (p++ ; p < pend ; p++) { Int i = Li [p] ; y [0] -= Lx [p] * X [i][0] ; y [1] -= Lx [p] * X [i][1] ; y [2] -= Lx [p] * X [i][2] ; } #ifdef LL X [j][0] = y [0] / d ; X [j][1] = y [1] / d ; X [j][2] = y [2] / d ; #else X [j][0] = y [0] ; X [j][1] = y [1] ; X [j][2] = y [2] ; #endif j-- ; /* advance to the next column of L */ } else if (lnz != Lnz [j-2]-2 || Li [Lp [j-2]+2] != j) { /* -------------------------------------------------------------- */ /* solve with a supernode of two columns of L */ /* -------------------------------------------------------------- */ double y [2][3], t ; Int q = Lp [j-1] ; #ifdef DIAG double d [2] ; d [0] = Lx [p] ; d [1] = Lx [q] ; #endif t = Lx [q+1] ; #ifdef LD y [0][0] = X [j ][0] / d [0] ; y [0][1] = X [j ][1] / d [0] ; y [0][2] = X [j ][2] / d [0] ; y [1][0] = X [j-1][0] / d [1] ; y [1][1] = X [j-1][1] / d [1] ; y [1][2] = X [j-1][2] / d [1] ; #else y [0][0] = X [j ][0] ; y [0][1] = X [j ][1] ; y [0][2] = X [j ][2] ; y [1][0] = X [j-1][0] ; y [1][1] = X [j-1][1] ; y [1][2] = X [j-1][2] ; #endif for (p++, q += 2 ; p < pend ; p++, q++) { Int i = Li [p] ; y [0][0] -= Lx [p] * X [i][0] ; y [0][1] -= Lx [p] * X [i][1] ; y [0][2] -= Lx [p] * X [i][2] ; y [1][0] -= Lx [q] * X [i][0] ; y [1][1] -= Lx [q] * X [i][1] ; y [1][2] -= Lx [q] * X [i][2] ; } #ifdef LL y [0][0] /= d [0] ; y [0][1] /= d [0] ; y [0][2] /= d [0] ; y [1][0] = (y [1][0] - t * y [0][0]) / d [1] ; y [1][1] = (y [1][1] - t * y [0][1]) / d [1] ; y [1][2] = (y [1][2] - t * y [0][2]) / d [1] ; #else y [1][0] -= t * y [0][0] ; y [1][1] -= t * y [0][1] ; y [1][2] -= t * y [0][2] ; #endif X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j ][2] = y [0][2] ; X [j-1][0] = y [1][0] ; X [j-1][1] = y [1][1] ; X [j-1][2] = y [1][2] ; j -= 2 ; /* advance to the next column of L */ } else { /* -------------------------------------------------------------- */ /* solve with a supernode of three columns of L */ /* -------------------------------------------------------------- */ double y [3][3], t [3] ; Int q = Lp [j-1] ; Int r = Lp [j-2] ; #ifdef DIAG double d [3] ; d [0] = Lx [p] ; d [1] = Lx [q] ; d [2] = Lx [r] ; #endif t [0] = Lx [q+1] ; t [1] = Lx [r+1] ; t [2] = Lx [r+2] ; #ifdef LD y [0][0] = X [j ][0] / d [0] ; y [0][1] = X [j ][1] / d [0] ; y [0][2] = X [j ][2] / d [0] ; y [1][0] = X [j-1][0] / d [1] ; y [1][1] = X [j-1][1] / d [1] ; y [1][2] = X [j-1][2] / d [1] ; y [2][0] = X [j-2][0] / d [2] ; y [2][1] = X [j-2][1] / d [2] ; y [2][2] = X [j-2][2] / d [2] ; #else y [0][0] = X [j ][0] ; y [0][1] = X [j ][1] ; y [0][2] = X [j ][2] ; y [1][0] = X [j-1][0] ; y [1][1] = X [j-1][1] ; y [1][2] = X [j-1][2] ; y [2][0] = X [j-2][0] ; y [2][1] = X [j-2][1] ; y [2][2] = X [j-2][2] ; #endif for (p++, q += 2, r += 3 ; p < pend ; p++, q++, r++) { Int i = Li [p] ; y [0][0] -= Lx [p] * X [i][0] ; y [0][1] -= Lx [p] * X [i][1] ; y [0][2] -= Lx [p] * X [i][2] ; y [1][0] -= Lx [q] * X [i][0] ; y [1][1] -= Lx [q] * X [i][1] ; y [1][2] -= Lx [q] * X [i][2] ; y [2][0] -= Lx [r] * X [i][0] ; y [2][1] -= Lx [r] * X [i][1] ; y [2][2] -= Lx [r] * X [i][2] ; } #ifdef LL y [0][0] /= d [0] ; y [0][1] /= d [0] ; y [0][2] /= d [0] ; y [1][0] = (y [1][0] - t [0] * y [0][0]) / d [1] ; y [1][1] = (y [1][1] - t [0] * y [0][1]) / d [1] ; y [1][2] = (y [1][2] - t [0] * y [0][2]) / d [1] ; y [2][0] = (y [2][0] - t [2] * y [0][0] - t [1] * y [1][0]) / d [2]; y [2][1] = (y [2][1] - t [2] * y [0][1] - t [1] * y [1][1]) / d [2]; y [2][2] = (y [2][2] - t [2] * y [0][2] - t [1] * y [1][2]) / d [2]; #else y [1][0] -= t [0] * y [0][0] ; y [1][1] -= t [0] * y [0][1] ; y [1][2] -= t [0] * y [0][2] ; y [2][0] -= t [2] * y [0][0] + t [1] * y [1][0] ; y [2][1] -= t [2] * y [0][1] + t [1] * y [1][1] ; y [2][2] -= t [2] * y [0][2] + t [1] * y [1][2] ; #endif X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j ][2] = y [0][2] ; X [j-1][0] = y [1][0] ; X [j-1][1] = y [1][1] ; X [j-1][2] = y [1][2] ; X [j-2][0] = y [2][0] ; X [j-2][1] = y [2][1] ; X [j-2][2] = y [2][2] ; j -= 3 ; /* advance to the next column of L */ } } } /* ========================================================================== */ /* === LSOLVE (4) =========================================================== */ /* ========================================================================== */ /* Solve L'x=b, where b has 4 columns */ static void LSOLVE (PREFIX,4) ( cholmod_factor *L, double X [ ][4] /* n-by-4 in row form */ ) { double *Lx = L->x ; Int *Li = L->i ; Int *Lp = L->p ; Int *Lnz = L->nz ; Int j, n = L->n ; for (j = n-1 ; j >= 0 ; ) { /* get the start, end, and length of column j */ Int p = Lp [j] ; Int lnz = Lnz [j] ; Int pend = p + lnz ; /* find a chain of supernodes (up to j, j-1, and j-2) */ if (j < 4 || lnz != Lnz [j-1] - 1 || Li [Lp [j-1]+1] != j) { /* -------------------------------------------------------------- */ /* solve with a single column of L */ /* -------------------------------------------------------------- */ double y [4] ; #ifdef DIAG double d = Lx [p] ; #endif #ifdef LD y [0] = X [j][0] / d ; y [1] = X [j][1] / d ; y [2] = X [j][2] / d ; y [3] = X [j][3] / d ; #else y [0] = X [j][0] ; y [1] = X [j][1] ; y [2] = X [j][2] ; y [3] = X [j][3] ; #endif for (p++ ; p < pend ; p++) { Int i = Li [p] ; y [0] -= Lx [p] * X [i][0] ; y [1] -= Lx [p] * X [i][1] ; y [2] -= Lx [p] * X [i][2] ; y [3] -= Lx [p] * X [i][3] ; } #ifdef LL X [j][0] = y [0] / d ; X [j][1] = y [1] / d ; X [j][2] = y [2] / d ; X [j][3] = y [3] / d ; #else X [j][0] = y [0] ; X [j][1] = y [1] ; X [j][2] = y [2] ; X [j][3] = y [3] ; #endif j-- ; /* advance to the next column of L */ } else /* if (j == 1 || lnz != Lnz [j-2]-2 || Li [Lp [j-2]+2] != j) */ { /* -------------------------------------------------------------- */ /* solve with a supernode of two columns of L */ /* -------------------------------------------------------------- */ double y [2][4], t ; Int q = Lp [j-1] ; #ifdef DIAG double d [2] ; d [0] = Lx [p] ; d [1] = Lx [q] ; #endif t = Lx [q+1] ; #ifdef LD y [0][0] = X [j ][0] / d [0] ; y [0][1] = X [j ][1] / d [0] ; y [0][2] = X [j ][2] / d [0] ; y [0][3] = X [j ][3] / d [0] ; y [1][0] = X [j-1][0] / d [1] ; y [1][1] = X [j-1][1] / d [1] ; y [1][2] = X [j-1][2] / d [1] ; y [1][3] = X [j-1][3] / d [1] ; #else y [0][0] = X [j ][0] ; y [0][1] = X [j ][1] ; y [0][2] = X [j ][2] ; y [0][3] = X [j ][3] ; y [1][0] = X [j-1][0] ; y [1][1] = X [j-1][1] ; y [1][2] = X [j-1][2] ; y [1][3] = X [j-1][3] ; #endif for (p++, q += 2 ; p < pend ; p++, q++) { Int i = Li [p] ; y [0][0] -= Lx [p] * X [i][0] ; y [0][1] -= Lx [p] * X [i][1] ; y [0][2] -= Lx [p] * X [i][2] ; y [0][3] -= Lx [p] * X [i][3] ; y [1][0] -= Lx [q] * X [i][0] ; y [1][1] -= Lx [q] * X [i][1] ; y [1][2] -= Lx [q] * X [i][2] ; y [1][3] -= Lx [q] * X [i][3] ; } #ifdef LL y [0][0] /= d [0] ; y [0][1] /= d [0] ; y [0][2] /= d [0] ; y [0][3] /= d [0] ; y [1][0] = (y [1][0] - t * y [0][0]) / d [1] ; y [1][1] = (y [1][1] - t * y [0][1]) / d [1] ; y [1][2] = (y [1][2] - t * y [0][2]) / d [1] ; y [1][3] = (y [1][3] - t * y [0][3]) / d [1] ; #else y [1][0] -= t * y [0][0] ; y [1][1] -= t * y [0][1] ; y [1][2] -= t * y [0][2] ; y [1][3] -= t * y [0][3] ; #endif X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j ][2] = y [0][2] ; X [j ][3] = y [0][3] ; X [j-1][0] = y [1][0] ; X [j-1][1] = y [1][1] ; X [j-1][2] = y [1][2] ; X [j-1][3] = y [1][3] ; j -= 2 ; /* advance to the next column of L */ } /* NOTE: with 4 right-hand-sides, it suffices to exploit dynamic * supernodes of just size 1 and 2. 3-column supernodes are not * needed. */ } } #endif /* ========================================================================== */ /* === LSOLVE (k) =========================================================== */ /* ========================================================================== */ static void LSOLVE (PREFIX,k) ( cholmod_factor *L, cholmod_dense *Y /* nr-by-n where nr is 1 to 4 */ ) { #ifndef REAL #ifdef DIAG double d [1] ; #endif double yx [2] ; #ifdef ZOMPLEX double yz [1] ; double *Lz = L->z ; double *Xz = Y->z ; #endif double *Lx = L->x ; double *Xx = Y->x ; Int *Li = L->i ; Int *Lp = L->p ; Int *Lnz = L->nz ; Int i, j, n = L->n ; #endif ASSERT (L->xtype == Y->xtype) ; /* L and Y must have the same xtype */ ASSERT (L->n == Y->ncol) ; /* dimensions must match */ ASSERT (Y->nrow == Y->d) ; /* leading dimension of Y = # rows of Y */ ASSERT (L->xtype != CHOLMOD_PATTERN) ; /* L is not symbolic */ ASSERT (!(L->is_super)) ; /* L is simplicial LL' or LDL' */ #ifdef REAL /* ---------------------------------------------------------------------- */ /* solve a real linear system, with 1 to 4 RHS's and dynamic supernodes */ /* ---------------------------------------------------------------------- */ ASSERT (Y->nrow <= 4) ; switch (Y->nrow) { case 1: LSOLVE (PREFIX,1) (L, Y->x) ; break ; case 2: LSOLVE (PREFIX,2) (L, Y->x) ; break ; case 3: LSOLVE (PREFIX,3) (L, Y->x) ; break ; case 4: LSOLVE (PREFIX,4) (L, Y->x) ; break ; } #else /* ---------------------------------------------------------------------- */ /* solve a complex linear system, with just one right-hand-side */ /* ---------------------------------------------------------------------- */ ASSERT (Y->nrow == 1) ; for (j = n-1 ; j >= 0 ; j--) { /* get the start, end, and length of column j */ Int p = Lp [j] ; Int lnz = Lnz [j] ; Int pend = p + lnz ; /* y = X [j] ; */ ASSIGN (yx,yz,0, Xx,Xz,j) ; #ifdef DIAG /* d = Lx [p] ; */ ASSIGN_REAL (d,0, Lx,p) ; #endif #ifdef LD /* y /= d ; */ DIV_REAL (yx,yz,0, yx,yz,0, d,0) ; #endif for (p++ ; p < pend ; p++) { /* y -= conj (Lx [p]) * X [Li [p]] ; */ i = Li [p] ; MULTSUBCONJ (yx,yz,0, Lx,Lz,p, Xx,Xz,i) ; } #ifdef LL /* X [j] = y / d ; */ DIV_REAL (Xx,Xz,j, yx,yz,0, d,0) ; #else /* X [j] = y ; */ ASSIGN (Xx,Xz,j, yx,yz,0) ; #endif } #endif } /* prepare for the next inclusion of this file in cholmod_solve.c */ #undef LL #undef LD SuiteSparse/CHOLMOD/Cholesky/cholmod_amd.c0000644001170100242450000001613510616661406017243 0ustar davisfac/* ========================================================================== */ /* === Cholesky/cholmod_amd ================================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* CHOLMOD interface to the AMD ordering routine. Orders A if the matrix is * symmetric. On output, Perm [k] = i if row/column i of A is the kth * row/column of P*A*P'. This corresponds to A(p,p) in MATLAB notation. * * If A is unsymmetric, cholmod_amd orders A*A'. On output, Perm [k] = i if * row/column i of A*A' is the kth row/column of P*A*A'*P'. This corresponds to * A(p,:)*A(p,:)' in MATLAB notation. If f is present, A(p,f)*A(p,f)' is * ordered. * * Computes the flop count for a subsequent LL' factorization, the number * of nonzeros in L, and the number of nonzeros in the matrix ordered (A, * A*A' or A(:,f)*A(:,f)'). * * workspace: Iwork (6*nrow). Head (nrow). * * Allocates a temporary copy of A+A' or A*A' (with * both upper and lower triangular parts) as input to AMD. * * Supports any xtype (pattern, real, complex, or zomplex) */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "amd.h" #include "cholmod_cholesky.h" #if (!defined (AMD_VERSION) || (AMD_VERSION < AMD_VERSION_CODE (2,0))) #error "AMD v2.0 or later is required" #endif /* ========================================================================== */ /* === cholmod_amd ========================================================== */ /* ========================================================================== */ int CHOLMOD(amd) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- output --- */ Int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) { double Info [AMD_INFO], Control2 [AMD_CONTROL], *Control ; Int *Cp, *Len, *Nv, *Head, *Elen, *Degree, *Wi, *Iwork, *Next ; cholmod_sparse *C ; Int j, n, cnz ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; n = A->nrow ; RETURN_IF_NULL (Perm, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; Common->status = CHOLMOD_OK ; if (n == 0) { /* nothing to do */ Common->fl = 0 ; Common->lnz = 0 ; Common->anz = 0 ; return (TRUE) ; } /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ /* Note: this is less than the space used in cholmod_analyze, so if * cholmod_amd is being called by that routine, no space will be * allocated. */ /* s = MAX (6*n, A->ncol) */ s = CHOLMOD(mult_size_t) (n, 6, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } s = MAX (s, A->ncol) ; CHOLMOD(allocate_work) (n, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } Iwork = Common->Iwork ; Degree = Iwork ; /* size n */ Wi = Iwork + n ; /* size n */ Len = Iwork + 2*((size_t) n) ; /* size n */ Nv = Iwork + 3*((size_t) n) ; /* size n */ Next = Iwork + 4*((size_t) n) ; /* size n */ Elen = Iwork + 5*((size_t) n) ; /* size n */ Head = Common->Head ; /* size n+1, but only n is used */ /* ---------------------------------------------------------------------- */ /* construct the input matrix for AMD */ /* ---------------------------------------------------------------------- */ if (A->stype == 0) { /* C = A*A' or A(:,f)*A(:,f)', add extra space of nnz(C)/2+n to C */ C = CHOLMOD(aat) (A, fset, fsize, -2, Common) ; } else { /* C = A+A', but use only the upper triangular part of A if A->stype = 1 * and only the lower part of A if A->stype = -1. Add extra space of * nnz(C)/2+n to C. */ C = CHOLMOD(copy) (A, 0, -2, Common) ; } if (Common->status < CHOLMOD_OK) { /* out of memory, fset invalid, or other error */ return (FALSE) ; } Cp = C->p ; for (j = 0 ; j < n ; j++) { Len [j] = Cp [j+1] - Cp [j] ; } /* C does not include the diagonal, and both upper and lower parts. * Common->anz includes the diagonal, and just the lower part of C */ cnz = Cp [n] ; Common->anz = cnz / 2 + n ; /* ---------------------------------------------------------------------- */ /* order C using AMD */ /* ---------------------------------------------------------------------- */ /* get parameters */ if (Common->current < 0 || Common->current >= CHOLMOD_MAXMETHODS) { /* use AMD defaults */ Control = NULL ; } else { Control = Control2 ; Control [AMD_DENSE] = Common->method [Common->current].prune_dense ; Control [AMD_AGGRESSIVE] = Common->method [Common->current].aggressive ; } /* AMD_2 does not use amd_malloc and amd_free, but set these pointers just * be safe. */ amd_malloc = Common->malloc_memory ; amd_free = Common->free_memory ; amd_calloc = Common->calloc_memory ; amd_realloc = Common->realloc_memory ; /* AMD_2 doesn't print anything either, but future versions might, * so set the amd_printf pointer too. */ amd_printf = Common->print_function ; #ifdef LONG amd_l2 (n, C->p, C->i, Len, C->nzmax, cnz, Nv, Next, Perm, Head, Elen, Degree, Wi, Control, Info) ; #else amd_2 (n, C->p, C->i, Len, C->nzmax, cnz, Nv, Next, Perm, Head, Elen, Degree, Wi, Control, Info) ; #endif /* LL' flop count. Need to subtract n for LL' flop count. Note that this * is a slight upper bound which is often exact (see AMD/Source/amd_2.c for * details). cholmod_analyze computes an exact flop count and fill-in. */ Common->fl = Info [AMD_NDIV] + 2 * Info [AMD_NMULTSUBS_LDL] + n ; /* Info [AMD_LNZ] excludes the diagonal */ Common->lnz = n + Info [AMD_LNZ] ; /* ---------------------------------------------------------------------- */ /* free the AMD workspace and clear the persistent workspace in Common */ /* ---------------------------------------------------------------------- */ ASSERT (IMPLIES (Common->status == CHOLMOD_OK, CHOLMOD(dump_perm) (Perm, n, n, "AMD2 perm", Common))) ; CHOLMOD(free_sparse) (&C, Common) ; for (j = 0 ; j <= n ; j++) { Head [j] = EMPTY ; } return (TRUE) ; } #endif SuiteSparse/CHOLMOD/Cholesky/License.txt0000644001170100242450000000206410540000262016727 0ustar davisfacCHOLMOD/Cholesky module, Copyright (C) 2005-2006, Timothy A. Davis CHOLMOD is also available under other licenses; contact authors for details. http://www.cise.ufl.edu/research/sparse Note that this license is for the CHOLMOD/Cholesky module only. All CHOLMOD modules are licensed separately. -------------------------------------------------------------------------------- This Module is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This Module is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA SuiteSparse/CHOLMOD/Cholesky/cholmod_rcond.c0000644001170100242450000001151510537777331017613 0ustar davisfac/* ========================================================================== */ /* === Cholesky/cholmod_rcond =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Return a rough estimate of the reciprocal of the condition number: * the minimum entry on the diagonal of L (or absolute entry of D for an LDL' * factorization) divided by the maximum entry (squared for LL'). L can be * real, complex, or zomplex. Returns -1 on error, 0 if the matrix is singular * or has a zero entry on the diagonal of L, 1 if the matrix is 0-by-0, or * min(diag(L))/max(diag(L)) otherwise. Never returns NaN; if L has a NaN on * the diagonal it returns zero instead. * * For an LL' factorization, (min(diag(L))/max(diag(L)))^2 is returned. * For an LDL' factorization, (min(diag(D))/max(diag(D))) is returned. */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "cholmod_cholesky.h" /* ========================================================================== */ /* === LMINMAX ============================================================== */ /* ========================================================================== */ /* Update lmin and lmax for one entry L(j,j) */ #define FIRST_LMINMAX(Ljj,lmin,lmax) \ { \ double ljj = Ljj ; \ if (IS_NAN (ljj)) \ { \ return (0) ; \ } \ lmin = ljj ; \ lmax = ljj ; \ } #define LMINMAX(Ljj,lmin,lmax) \ { \ double ljj = Ljj ; \ if (IS_NAN (ljj)) \ { \ return (0) ; \ } \ if (ljj < lmin) \ { \ lmin = ljj ; \ } \ else if (ljj > lmax) \ { \ lmax = ljj ; \ } \ } /* ========================================================================== */ /* === cholmod_rcond ======================================================== */ /* ========================================================================== */ double CHOLMOD(rcond) /* return min(diag(L)) / max(diag(L)) */ ( /* ---- input ---- */ cholmod_factor *L, /* --------------- */ cholmod_common *Common ) { double lmin, lmax, rcond ; double *Lx ; Int *Lpi, *Lpx, *Super, *Lp ; Int n, e, nsuper, s, k1, k2, psi, psend, psx, nsrow, nscol, jj, j ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (L, EMPTY) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, EMPTY) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ n = L->n ; if (n == 0) { return (1) ; } if (L->minor < L->n) { return (0) ; } e = (L->xtype == CHOLMOD_COMPLEX) ? 2 : 1 ; if (L->is_super) { /* L is supernodal */ nsuper = L->nsuper ; /* number of supernodes in L */ Lpi = L->pi ; /* column pointers for integer pattern */ Lpx = L->px ; /* column pointers for numeric values */ Super = L->super ; /* supernode sizes */ Lx = L->x ; /* numeric values */ FIRST_LMINMAX (Lx [0], lmin, lmax) ; /* first diagonal entry of L */ for (s = 0 ; s < nsuper ; s++) { k1 = Super [s] ; /* first column in supernode s */ k2 = Super [s+1] ; /* last column in supernode is k2-1 */ psi = Lpi [s] ; /* first row index is L->s [psi] */ psend = Lpi [s+1] ; /* last row index is L->s [psend-1] */ psx = Lpx [s] ; /* first numeric entry is Lx [psx] */ nsrow = psend - psi ; /* supernode is nsrow-by-nscol */ nscol = k2 - k1 ; for (jj = 0 ; jj < nscol ; jj++) { LMINMAX (Lx [e * (psx + jj + jj*nsrow)], lmin, lmax) ; } } } else { /* L is simplicial */ Lp = L->p ; Lx = L->x ; if (L->is_ll) { /* LL' factorization */ FIRST_LMINMAX (Lx [Lp [0]], lmin, lmax) ; for (j = 1 ; j < n ; j++) { LMINMAX (Lx [e * Lp [j]], lmin, lmax) ; } } else { /* LDL' factorization, the diagonal might be negative */ FIRST_LMINMAX (fabs (Lx [Lp [0]]), lmin, lmax) ; for (j = 1 ; j < n ; j++) { LMINMAX (fabs (Lx [e * Lp [j]]), lmin, lmax) ; } } } rcond = lmin / lmax ; if (L->is_ll) { rcond = rcond*rcond ; } return (rcond) ; } #endif SuiteSparse/CHOLMOD/Cholesky/cholmod_resymbol.c0000644001170100242450000004446710635770507020353 0ustar davisfac/* ========================================================================== */ /* === Cholesky/cholmod_resymbol ============================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Recompute the symbolic pattern of L. Entries not in the symbolic pattern * are dropped. L->Perm can be used (or not) to permute the input matrix A. * * These routines are used after a supernodal factorization is converted into * a simplicial one, to remove zero entries that were added due to relaxed * supernode amalgamation. They can also be used after a series of downdates * to remove entries that would no longer be present if the matrix were * factorized from scratch. A downdate (cholmod_updown) does not remove any * entries from L. * * workspace: Flag (nrow), Head (nrow+1), * if symmetric: Iwork (2*nrow) * if unsymmetric: Iwork (2*nrow+ncol). * Allocates up to 2 copies of its input matrix A (pattern only). */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "cholmod_cholesky.h" /* ========================================================================== */ /* === cholmod_resymbol ===================================================== */ /* ========================================================================== */ /* Remove entries from L that are not in the factorization of P*A*P', P*A*A'*P', * or P*F*F'*P' (depending on A->stype and whether fset is NULL or not). * * cholmod_resymbol is the same as cholmod_resymbol_noperm, except that it * first permutes A according to L->Perm. A can be upper/lower/unsymmetric, * in contrast to cholmod_resymbol_noperm (which can be lower or unsym). */ int CHOLMOD(resymbol) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int pack, /* if TRUE, pack the columns of L */ /* ---- in/out --- */ cholmod_factor *L, /* factorization, entries pruned on output */ /* --------------- */ cholmod_common *Common ) { cholmod_sparse *H, *F, *G ; Int stype, nrow, ncol ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; Common->status = CHOLMOD_OK ; if (L->is_super) { /* cannot operate on a supernodal factorization */ ERROR (CHOLMOD_INVALID, "cannot operate on supernodal L") ; return (FALSE) ; } if (L->n != A->nrow) { /* dimensions must agree */ ERROR (CHOLMOD_INVALID, "A and L dimensions do not match") ; return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ stype = A->stype ; nrow = A->nrow ; ncol = A->ncol ; /* s = 2*nrow + (stype ? 0 : ncol) */ s = CHOLMOD(mult_size_t) (nrow, 2, &ok) ; s = CHOLMOD(add_size_t) (s, (stype ? 0 : ncol), &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (nrow, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* permute the input matrix if necessary */ /* ---------------------------------------------------------------------- */ H = NULL ; G = NULL ; if (stype > 0) { if (L->ordering == CHOLMOD_NATURAL) { /* F = triu(A)' */ /* workspace: Iwork (nrow) */ G = CHOLMOD(ptranspose) (A, 0, NULL, NULL, 0, Common) ; } else { /* F = triu(A(p,p))' */ /* workspace: Iwork (2*nrow) */ G = CHOLMOD(ptranspose) (A, 0, L->Perm, NULL, 0, Common) ; } F = G ; } else if (stype < 0) { if (L->ordering == CHOLMOD_NATURAL) { F = A ; } else { /* G = triu(A(p,p))' */ /* workspace: Iwork (2*nrow) */ G = CHOLMOD(ptranspose) (A, 0, L->Perm, NULL, 0, Common) ; /* H = G' */ /* workspace: Iwork (nrow) */ H = CHOLMOD(ptranspose) (G, 0, NULL, NULL, 0, Common) ; F = H ; } } else { if (L->ordering == CHOLMOD_NATURAL) { F = A ; } else { /* G = A(p,f)' */ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/ G = CHOLMOD(ptranspose) (A, 0, L->Perm, fset, fsize, Common) ; /* H = G' */ /* workspace: Iwork (ncol) */ H = CHOLMOD(ptranspose) (G, 0, NULL, NULL, 0, Common) ; F = H ; } } /* No need to check for failure here. cholmod_resymbol_noperm will return * FALSE if F is NULL. */ /* ---------------------------------------------------------------------- */ /* resymbol */ /* ---------------------------------------------------------------------- */ ok = CHOLMOD(resymbol_noperm) (F, fset, fsize, pack, L, Common) ; /* ---------------------------------------------------------------------- */ /* free the temporary matrices, if they exist */ /* ---------------------------------------------------------------------- */ CHOLMOD(free_sparse) (&H, Common) ; CHOLMOD(free_sparse) (&G, Common) ; return (ok) ; } /* ========================================================================== */ /* === cholmod_resymbol_noperm ============================================== */ /* ========================================================================== */ /* Redo symbolic LDL' or LL' factorization of I + F*F' or I+A, where F=A(:,f). * * L already exists, but is a superset of the true dynamic pattern (simple * column downdates and row deletions haven't pruned anything). Just redo the * symbolic factorization and drop entries that are no longer there. The * diagonal is not modified. The number of nonzeros in column j of L * (L->nz[j]) can decrease. The column pointers (L->p[j]) remain unchanged if * pack is FALSE or if L is not monotonic. Otherwise, the columns of L are * packed in place. * * For the symmetric case, the columns of the lower triangular part of A * are accessed by column. NOTE that this the transpose of the general case. * * For the unsymmetric case, F=A(:,f) is accessed by column. * * A need not be sorted, and can be packed or unpacked. If L->Perm is not * identity, then A must already be permuted according to the permutation used * to factorize L. The advantage of using this routine is that it does not * need to create permuted copies of A first. * * This routine can be called if L is only partially factored via cholmod_rowfac * since all it does is prune. If an entry is in F*F' or A, but not in L, it * isn't added to L. * * L must be simplicial LDL' or LL'; it cannot be supernodal or symbolic. * * The set f is held in fset and fsize. * fset = NULL means ":" in MATLAB. fset is ignored. * fset != NULL means f = fset [0..fset-1]. * fset != NULL and fsize = 0 means f is the empty set. * There can be no duplicates in fset. * Common->status is set to CHOLMOD_INVALID if fset is invalid. * * workspace: Flag (nrow), Head (nrow+1), * if symmetric: Iwork (2*nrow) * if unsymmetric: Iwork (2*nrow+ncol). * Unlike cholmod_resymbol, this routine does not allocate any temporary * copies of its input matrix. */ int CHOLMOD(resymbol_noperm) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int pack, /* if TRUE, pack the columns of L */ /* ---- in/out --- */ cholmod_factor *L, /* factorization, entries pruned on output */ /* --------------- */ cholmod_common *Common ) { double *Lx, *Lz ; Int i, j, k, row, parent, p, pend, pdest, ncol, apacked, sorted, nrow, nf, use_fset, mark, jj, stype, xtype ; Int *Ap, *Ai, *Anz, *Li, *Lp, *Lnz, *Flag, *Head, *Link, *Anext, *Iwork ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (L, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; ncol = A->ncol ; nrow = A->nrow ; stype = A->stype ; ASSERT (IMPLIES (stype != 0, nrow == ncol)) ; if (stype > 0) { /* symmetric, with upper triangular part, not supported */ ERROR (CHOLMOD_INVALID, "symmetric upper not supported ") ; return (FALSE) ; } if (L->is_super) { /* cannot operate on a supernodal or symbolic factorization */ ERROR (CHOLMOD_INVALID, "cannot operate on supernodal L") ; return (FALSE) ; } if (L->n != A->nrow) { /* dimensions must agree */ ERROR (CHOLMOD_INVALID, "A and L dimensions do not match") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = 2*nrow + (stype ? 0 : ncol) */ s = CHOLMOD(mult_size_t) (nrow, 2, &ok) ; if (stype != 0) { s = CHOLMOD(add_size_t) (s, ncol, &ok) ; } if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (nrow, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; /* out of memory */ } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Ai = A->i ; Ap = A->p ; Anz = A->nz ; apacked = A->packed ; sorted = A->sorted ; Li = L->i ; Lx = L->x ; Lz = L->z ; Lp = L->p ; Lnz = L->nz ; xtype = L->xtype ; /* If L is monotonic on input, then it can be packed or * unpacked on output, depending on the pack input parameter. */ /* cannot pack a non-monotonic matrix */ if (!(L->is_monotonic)) { pack = FALSE ; } ASSERT (L->nzmax >= (size_t) (Lp [L->n])) ; pdest = 0 ; PRINT1 (("\n\n===================== Resymbol pack %d Apacked %d\n", pack, A->packed)) ; ASSERT (CHOLMOD(dump_sparse) (A, "ReSymbol A:", Common) >= 0) ; DEBUG (CHOLMOD(dump_factor) (L, "ReSymbol initial L (i, x):", Common)) ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Flag = Common->Flag ; /* size nrow */ Head = Common->Head ; /* size nrow+1 */ Iwork = Common->Iwork ; Link = Iwork ; /* size nrow (i/i/l) [ */ Lnz = Iwork + nrow ; /* size nrow (i/i/l), if L not packed */ Anext = Iwork + 2*((size_t) nrow) ; /* size ncol (i/i/l), unsym. only */ for (j = 0 ; j < nrow ; j++) { Link [j] = EMPTY ; } /* use Lnz in L itself */ Lnz = L->nz ; ASSERT (Lnz != NULL) ; /* ---------------------------------------------------------------------- */ /* for the unsymmetric case, queue each column of A (:,f) */ /* ---------------------------------------------------------------------- */ /* place each column of the basis set on the link list corresponding to */ /* the smallest row index in that column */ if (stype == 0) { use_fset = (fset != NULL) ; if (use_fset) { nf = fsize ; /* This is the only O(ncol) loop in cholmod_resymbol. * It is required only to check the fset. */ for (j = 0 ; j < ncol ; j++) { Anext [j] = -2 ; } for (jj = 0 ; jj < nf ; jj++) { j = fset [jj] ; if (j < 0 || j > ncol || Anext [j] != -2) { /* out-of-range or duplicate entry in fset */ ERROR (CHOLMOD_INVALID, "fset invalid") ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; return (FALSE) ; } /* flag column j as having been seen */ Anext [j] = EMPTY ; } /* the fset is now valid */ ASSERT (CHOLMOD(dump_perm) (fset, nf, ncol, "fset", Common)) ; } else { nf = ncol ; } for (jj = 0 ; jj < nf ; jj++) { j = (use_fset) ? (fset [jj]) : jj ; /* column j is the fset; find the smallest row (if any) */ p = Ap [j] ; pend = (apacked) ? (Ap [j+1]) : (p + Anz [j]) ; if (pend > p) { k = Ai [p] ; if (!sorted) { for ( ; p < pend ; p++) { k = MIN (k, Ai [p]) ; } } /* place column j on link list k */ ASSERT (k >= 0 && k < nrow) ; Anext [j] = Head [k] ; Head [k] = j ; } } } /* ---------------------------------------------------------------------- */ /* recompute symbolic LDL' factorization */ /* ---------------------------------------------------------------------- */ for (k = 0 ; k < nrow ; k++) { #ifndef NDEBUG PRINT1 (("\n\n================== Initial column k = "ID"\n", k)) ; for (p = Lp [k] ; p < Lp [k] + Lnz [k] ; p++) { PRINT1 ((" row: "ID" value: ", Li [p])) ; PRINT1 (("\n")) ; } PRINT1 (("Recomputing LDL, column k = "ID"\n", k)) ; #endif /* ------------------------------------------------------------------ */ /* compute column k of I+F*F' or I+A */ /* ------------------------------------------------------------------ */ /* flag the diagonal entry */ /* mark = CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; Flag [k] = mark ; PRINT1 ((" row: "ID" (diagonal)\n", k)) ; if (stype != 0) { /* merge column k of A into Flag (lower triangular part only) */ p = Ap [k] ; pend = (apacked) ? (Ap [k+1]) : (p + Anz [k]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i > k) { Flag [i] = mark ; } } } else { /* for each column j whos first row index is in row k */ for (j = Head [k] ; j != EMPTY ; j = Anext [j]) { /* merge column j of A into Flag */ PRINT1 ((" ---- A column "ID"\n", j)) ; p = Ap [j] ; pend = (apacked) ? (Ap [j+1]) : (p + Anz [j]) ; PRINT1 ((" length "ID" adding\n", pend-p)) ; for ( ; p < pend ; p++) { #ifndef NDEBUG ASSERT (Ai [p] >= k && Ai [p] < nrow) ; if (Flag [Ai [p]] < mark) PRINT1 ((" row "ID"\n", Ai [p])) ; #endif Flag [Ai [p]] = mark ; } } /* clear the kth link list */ Head [k] = EMPTY ; } /* ------------------------------------------------------------------ */ /* compute pruned pattern of kth column of L = union of children */ /* ------------------------------------------------------------------ */ /* for each column j of L whose parent is k */ for (j = Link [k] ; j != EMPTY ; j = Link [j]) { /* merge column j of L into Flag */ PRINT1 ((" ---- L column "ID"\n", k)) ; ASSERT (j < k) ; ASSERT (Lnz [j] > 0) ; p = Lp [j] ; pend = p + Lnz [j] ; ASSERT (Li [p] == j && Li [p+1] == k) ; p++ ; /* skip past the diagonal entry */ for ( ; p < pend ; p++) { /* add to pattern */ ASSERT (Li [p] >= k && Li [p] < nrow) ; Flag [Li [p]] = mark ; } } /* ------------------------------------------------------------------ */ /* prune the kth column of L */ /* ------------------------------------------------------------------ */ PRINT1 (("Final column of L:\n")) ; p = Lp [k] ; pend = p + Lnz [k] ; if (pack) { /* shift column k upwards */ Lp [k] = pdest ; } else { /* leave column k in place, just reduce Lnz [k] */ pdest = p ; } for ( ; p < pend ; p++) { ASSERT (pdest < pend) ; ASSERT (pdest <= p) ; row = Li [p] ; ASSERT (row >= k && row < nrow) ; if (Flag [row] == mark) { /* keep this entry */ Li [pdest] = row ; if (xtype == CHOLMOD_REAL) { Lx [pdest] = Lx [p] ; } else if (xtype == CHOLMOD_COMPLEX) { Lx [2*pdest ] = Lx [2*p ] ; Lx [2*pdest+1] = Lx [2*p+1] ; } else if (xtype == CHOLMOD_ZOMPLEX) { Lx [pdest] = Lx [p] ; Lz [pdest] = Lz [p] ; } pdest++ ; } } /* ------------------------------------------------------------------ */ /* prepare this column for its parent */ /* ------------------------------------------------------------------ */ Lnz [k] = pdest - Lp [k] ; PRINT1 ((" L("ID") length "ID"\n", k, Lnz [k])) ; ASSERT (Lnz [k] > 0) ; /* parent is the first entry in the column after the diagonal */ parent = (Lnz [k] > 1) ? (Li [Lp [k] + 1]) : EMPTY ; PRINT1 (("parent ("ID") = "ID"\n", k, parent)) ; ASSERT ((parent > k && parent < nrow) || (parent == EMPTY)) ; if (parent != EMPTY) { Link [k] = Link [parent] ; Link [parent] = k ; } } /* done using Iwork for Link, Lnz (if needed), and Anext ] */ /* ---------------------------------------------------------------------- */ /* convert L to packed, if requested */ /* ---------------------------------------------------------------------- */ if (pack) { /* finalize Lp */ Lp [nrow] = pdest ; /* Shrink L to be just large enough. It cannot fail. */ /* workspace: none */ ASSERT ((size_t) (Lp [nrow]) <= L->nzmax) ; CHOLMOD(reallocate_factor) (Lp [nrow], L, Common) ; ASSERT (Common->status >= CHOLMOD_OK) ; } /* ---------------------------------------------------------------------- */ /* clear workspace */ /* ---------------------------------------------------------------------- */ /* CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; DEBUG (CHOLMOD(dump_factor) (L, "ReSymbol final L (i, x):", Common)) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; return (TRUE) ; } #endif SuiteSparse/CHOLMOD/Cholesky/cholmod_analyze.c0000644001170100242450000007477710616661432020164 0ustar davisfac/* ========================================================================== */ /* === Cholesky/cholmod_analyze ============================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Order and analyze a matrix (either simplicial or supernodal), in prepartion * for numerical factorization via cholmod_factorize or via the "expert" * routines cholmod_rowfac and cholmod_super_numeric. * * symmetric case: A or A(p,p) * unsymmetric case: AA', A(p,:)*A(p,:)', A(:,f)*A(:,f)', or A(p,f)*A(p,f)' * * For the symmetric case, only the upper or lower triangular part of A is * accessed (depending on the type of A). LL'=A (or permuted A) is analzed. * For the unsymmetric case (LL'=AA' or permuted A). * * There can be no duplicate entries in p or f. p is of length m if A is * m-by-n. f can be length 0 to n. * * In both cases, the columns of A need not be sorted. A can be in packed * or unpacked form. * * Ordering options include: * * natural: A is not permuted to reduce fill-in * given: a permutation can be provided to this routine (UserPerm) * AMD: approximate minumum degree (AMD for the symmetric case, * COLAMD for the AA' case). * METIS: nested dissection with METIS_NodeND * NESDIS: nested dissection using METIS_NodeComputeSeparator, * typically followed by a constrained minimum degree * (CAMD for the symmetric case, CCOLAMD for the AA' case). * * Multiple ordering options can be tried (up to 9 of them), and the best one * is selected (the one that gives the smallest number of nonzeros in the * simplicial factor L). If one method fails, cholmod_analyze keeps going, and * picks the best among the methods that succeeded. This routine fails (and * returns NULL) if either initial memory allocation fails, all ordering methods * fail, or the supernodal analysis (if requested) fails. By default, the 9 * methods available are: * * 1) given permutation (skipped if UserPerm is NULL) * 2) AMD (symmetric case) or COLAMD (unsymmetric case) * 3) METIS with default parameters * 4) NESDIS with default parameters (stopping the partitioning when * the graph is of size nd_small = 200 or less, remove nodes with * more than max (16, prune_dense * sqrt (n)) nodes where * prune_dense = 10, and follow partitioning with CCOLAMD, a * constrained minimum degree ordering). * 5) natural * 6) NESDIS, nd_small = 20000, prune_dense = 10 * 7) NESDIS, nd_small = 4, prune_dense = 10, no min degree * 8) NESDIS, nd_small = 200, prune_dense = 0 * 9) COLAMD for A*A' or AMD for A * * By default, the first two are tried, and METIS is tried if AMD reports a high * flop count and fill-in. Let fl denote the flop count for the AMD, ordering, * nnz(L) the # of nonzeros in L, and nnz(tril(A)) (or A*A'). If * fl/nnz(L) >= 500 and nnz(L)/nnz(tril(A)) >= 5, then METIS is attempted. The * best ordering is used (UserPerm if given, AMD, and METIS if attempted). If * you do not have METIS, only the first two will be tried (user permutation, * if provided, and AMD/COLAMD). This default behavior is obtained when * Common->nmethods is zero. In this case, methods 0, 1, and 2 in * Common->method [..] are reset to User-provided, AMD, and METIS (or NESDIS * if Common->default_nesdis is set to the non-default value of TRUE), * respectively. * * You can modify these 9 methods and the number of methods tried by changing * parameters in the Common argument. If you know the best ordering for your * matrix, set Common->nmethods to 1 and set Common->method[0].ordering to the * requested ordering method. Parameters for each method can also be modified * (refer to cholmod.h for details). * * Note that it is possible for METIS to terminate your program if it runs out * of memory. This is not the case for any CHOLMOD or minimum degree ordering * routine (AMD, COLAMD, CAMD, CCOLAMD, or CSYMAMD). Since NESDIS relies on * METIS, it too can terminate your program. * * The factor L is returned as simplicial symbolic (L->is_super FALSE) if * Common->supernodal <= CHOLMOD_SIMPLICIAL (0) or as supernodal symbolic if * Common->supernodal >= CHOLMOD_SUPERNODAL (2). If Common->supernodal is * equal to CHOLMOD_AUTO (1), then L is simplicial if the flop count per * nonzero in L is less than Common->supernodal_switch (default: 40), and * is returned as a supernodal factor otherwise. * * In both cases, L->xtype is CHOLMOD_PATTERN. * A subsequent call to cholmod_factorize will perform a * simplicial or supernodal factorization, depending on the type of L. * * For the simplicial case, L contains the fill-reducing permutation (L->Perm) * and the counts of nonzeros in each column of L (L->ColCount). For the * supernodal case, L also contains the nonzero pattern of each supernode. * * workspace: Flag (nrow), Head (nrow+1) * if symmetric: Iwork (6*nrow) * if unsymmetric: Iwork (6*nrow+ncol). * calls various ordering routines, which typically allocate O(nnz(A)) * temporary workspace ((2 to 3)*nnz(A) * sizeof (Int) is typical, but it * can be much higher if A*A' must be explicitly formed for METIS). Also * allocates up to 2 temporary (permuted/transpose) copies of the nonzero * pattern of A, and up to 3*n*sizeof(Int) additional workspace. * * Supports any xtype (pattern, real, complex, or zomplex) */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "cholmod_cholesky.h" #ifndef NSUPERNODAL #include "cholmod_supernodal.h" #endif #ifndef NPARTITION #include "cholmod_partition.h" #endif /* ========================================================================== */ /* === cholmod_analyze ====================================================== */ /* ========================================================================== */ /* Orders and analyzes A, AA', PAP', or PAA'P' and returns a symbolic factor * that can later be passed to cholmod_factorize. */ cholmod_factor *CHOLMOD(analyze) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order and analyze */ /* --------------- */ cholmod_common *Common ) { return (CHOLMOD(analyze_p) (A, NULL, NULL, 0, Common)) ; } /* ========================================================================== */ /* === permute_matrices ===================================================== */ /* ========================================================================== */ /* Permute and transpose a matrix. Allocates the A1 and A2 matrices, if needed, * or returns them as NULL if not needed. */ static int permute_matrices ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to permute */ Int ordering, /* ordering method used */ Int *Perm, /* fill-reducing permutation */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ Int do_rowcolcounts,/* if TRUE, compute both S and F. If FALSE, only * S is needed for the symmetric case, and only F for * the unsymmetric case */ /* ---- output --- */ cholmod_sparse **A1_handle, /* see comments below for A1, A2, S, F */ cholmod_sparse **A2_handle, cholmod_sparse **S_handle, cholmod_sparse **F_handle, /* --------------- */ cholmod_common *Common ) { cholmod_sparse *A1, *A2, *S, *F ; *A1_handle = NULL ; *A2_handle = NULL ; *S_handle = NULL ; *F_handle = NULL ; A1 = NULL ; A2 = NULL ; if (ordering == CHOLMOD_NATURAL) { /* ------------------------------------------------------------------ */ /* natural ordering of A */ /* ------------------------------------------------------------------ */ if (A->stype < 0) { /* symmetric lower case: A already in lower form, so S=A' */ /* workspace: Iwork (nrow) */ A2 = CHOLMOD(ptranspose) (A, 0, NULL, NULL, 0, Common) ; F = A ; S = A2 ; } else if (A->stype > 0) { /* symmetric upper case: F = pattern of triu (A)', S = A */ /* workspace: Iwork (nrow) */ if (do_rowcolcounts) { /* F not needed for symmetric case if do_rowcolcounts FALSE */ A1 = CHOLMOD(ptranspose) (A, 0, NULL, fset, fsize, Common) ; } F = A1 ; S = A ; } else { /* unsymmetric case: F = pattern of A (:,f)', S = A */ /* workspace: Iwork (nrow if no fset, MAX(nrow,ncol) if fset) */ A1 = CHOLMOD(ptranspose) (A, 0, NULL, fset, fsize, Common) ; F = A1 ; S = A ; } } else { /* ------------------------------------------------------------------ */ /* A is permuted */ /* ------------------------------------------------------------------ */ if (A->stype < 0) { /* symmetric lower case: S = tril (A (p,p))' and F = S' */ /* workspace: Iwork (2*nrow) */ A2 = CHOLMOD(ptranspose) (A, 0, Perm, NULL, 0, Common) ; S = A2 ; /* workspace: Iwork (nrow) */ if (do_rowcolcounts) { /* F not needed for symmetric case if do_rowcolcounts FALSE */ A1 = CHOLMOD(ptranspose) (A2, 0, NULL, NULL, 0, Common) ; } F = A1 ; } else if (A->stype > 0) { /* symmetric upper case: F = triu (A (p,p))' and S = F' */ /* workspace: Iwork (2*nrow) */ A1 = CHOLMOD(ptranspose) (A, 0, Perm, NULL, 0, Common) ; F = A1 ; /* workspace: Iwork (nrow) */ A2 = CHOLMOD(ptranspose) (A1, 0, NULL, NULL, 0, Common) ; S = A2 ; } else { /* unsymmetric case: F = A (p,f)' and S = F' */ /* workspace: Iwork (nrow if no fset, MAX(nrow,ncol) if fset) */ A1 = CHOLMOD(ptranspose) (A, 0, Perm, fset, fsize, Common) ; F = A1 ; if (do_rowcolcounts) { /* S not needed for unsymmetric case if do_rowcolcounts FALSE */ /* workspace: Iwork (nrow) */ A2 = CHOLMOD(ptranspose) (A1, 0, NULL, NULL, 0, Common) ; } S = A2 ; } } /* If any cholmod_*transpose fails, one or more matrices will be NULL */ *A1_handle = A1 ; *A2_handle = A2 ; *S_handle = S ; *F_handle = F ; return (Common->status == CHOLMOD_OK) ; } /* ========================================================================== */ /* === cholmod_analyze_ordering ============================================= */ /* ========================================================================== */ /* Given a matrix A and its fill-reducing permutation, compute the elimination * tree, its (non-weighted) postordering, and the number of nonzeros in each * column of L. Also computes the flop count, the total nonzeros in L, and * the nonzeros in A (Common->fl, Common->lnz, and Common->anz). * * The column counts of L, flop count, and other statistics from * cholmod_rowcolcounts are not computed if ColCount is NULL. * * workspace: Iwork (2*nrow if symmetric, 2*nrow+ncol if unsymmetric), * Flag (nrow), Head (nrow+1) */ int CHOLMOD(analyze_ordering) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ int ordering, /* ordering method used */ Int *Perm, /* size n, fill-reducing permutation to analyze */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- output --- */ Int *Parent, /* size n, elimination tree */ Int *Post, /* size n, postordering of elimination tree */ Int *ColCount, /* size n, nnz in each column of L */ /* ---- workspace */ Int *First, /* size nworkspace for cholmod_postorder */ Int *Level, /* size n workspace for cholmod_postorder */ /* --------------- */ cholmod_common *Common ) { cholmod_sparse *A1, *A2, *S, *F ; Int n, ok, do_rowcolcounts ; /* check inputs */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; n = A->nrow ; do_rowcolcounts = (ColCount != NULL) ; /* permute A according to Perm and fset */ ok = permute_matrices (A, ordering, Perm, fset, fsize, do_rowcolcounts, &A1, &A2, &S, &F, Common) ; /* find etree of S (symmetric upper/lower case) or F (unsym case) */ /* workspace: symmmetric: Iwork (nrow), unsym: Iwork (nrow+ncol) */ ok = ok && CHOLMOD(etree) (A->stype ? S:F, Parent, Common) ; /* postorder the etree (required by cholmod_rowcolcounts) */ /* workspace: Iwork (2*nrow) */ ok = ok && (CHOLMOD(postorder) (Parent, n, NULL, Post, Common) == n) ; /* cholmod_postorder doesn't set Common->status if it returns < n */ Common->status = (!ok && Common->status == CHOLMOD_OK) ? CHOLMOD_INVALID : Common->status ; /* analyze LL'=S or SS' or S(:,f)*S(:,f)' */ /* workspace: * if symmetric: Flag (nrow), Iwork (2*nrow) * if unsymmetric: Flag (nrow), Iwork (2*nrow+ncol), Head (nrow+1) */ if (do_rowcolcounts) { ok = ok && CHOLMOD(rowcolcounts) (A->stype ? F:S, fset, fsize, Parent, Post, NULL, ColCount, First, Level, Common) ; } /* free temporary matrices and return result */ CHOLMOD(free_sparse) (&A1, Common) ; CHOLMOD(free_sparse) (&A2, Common) ; return (ok) ; } /* ========================================================================== */ /* === Free workspace and return L ========================================== */ /* ========================================================================== */ #define FREE_WORKSPACE_AND_RETURN \ { \ Common->no_workspace_reallocate = FALSE ; \ CHOLMOD(free) (n, sizeof (Int), Lparent, Common) ; \ CHOLMOD(free) (n, sizeof (Int), Perm, Common) ; \ CHOLMOD(free) (n, sizeof (Int), ColCount, Common) ; \ if (Common->status < CHOLMOD_OK) \ { \ CHOLMOD(free_factor) (&L, Common) ; \ } \ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; \ return (L) ; \ } /* ========================================================================== */ /* === cholmod_analyze_p ==================================================== */ /* ========================================================================== */ /* Orders and analyzes A, AA', PAP', PAA'P', FF', or PFF'P and returns a * symbolic factor that can later be passed to cholmod_factorize, where * F = A(:,fset) if fset is not NULL and A->stype is zero. * UserPerm is tried if non-NULL. */ cholmod_factor *CHOLMOD(analyze_p) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order and analyze */ Int *UserPerm, /* user-provided permutation, size A->nrow */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* --------------- */ cholmod_common *Common ) { double lnz_best ; Int *First, *Level, *Work4n, *Cmember, *CParent, *ColCount, *Lperm, *Parent, *Post, *Perm, *Lparent, *Lcolcount ; cholmod_factor *L ; Int k, n, ordering, method, nmethods, status, default_strategy, ncol, uncol, skip_analysis, skip_best ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ; Common->status = CHOLMOD_OK ; status = CHOLMOD_OK ; Common->selected = EMPTY ; Common->called_nd = FALSE ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ n = A->nrow ; ncol = A->ncol ; uncol = (A->stype == 0) ? (A->ncol) : 0 ; /* ---------------------------------------------------------------------- */ /* set the default strategy */ /* ---------------------------------------------------------------------- */ lnz_best = (double) EMPTY ; skip_best = FALSE ; nmethods = MIN (Common->nmethods, CHOLMOD_MAXMETHODS) ; nmethods = MAX (0, nmethods) ; PRINT1 (("nmethods "ID"\n", nmethods)) ; default_strategy = (nmethods == 0) ; if (default_strategy) { /* default strategy: try UserPerm, if given. Try AMD for A, or COLAMD * to order A*A'. Try METIS for the symmetric case only if AMD reports * a high degree of fill-in and flop count. Always try METIS for the * unsymmetric case. METIS is not tried if the Partition Module * isn't installed. If Common->default_nesdis is TRUE, then NESDIS * is used as the 3rd ordering instead. */ Common->method [0].ordering = CHOLMOD_GIVEN ;/* skip if UserPerm NULL */ Common->method [1].ordering = CHOLMOD_AMD ; Common->method [2].ordering = (Common->default_nesdis ? CHOLMOD_NESDIS : CHOLMOD_METIS) ; #ifndef NPARTITION nmethods = 3 ; #else nmethods = 2 ; #endif } #ifdef NSUPERNODAL /* CHOLMOD Supernodal module not installed, just do simplicial analysis */ Common->supernodal = CHOLMOD_SIMPLICIAL ; #endif /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* Note: enough space needs to be allocated here so that routines called by * cholmod_analyze do not reallocate the space. */ /* s = 6*n + uncol */ s = CHOLMOD(mult_size_t) (n, 6, &ok) ; s = CHOLMOD(add_size_t) (s, uncol, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (NULL) ; } CHOLMOD(allocate_work) (n, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; /* out of memory */ } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ensure that subsequent routines, called by cholmod_analyze, do not * reallocate any workspace. This is set back to FALSE in the * FREE_WORKSPACE_AND_RETURN macro, which is the only way this function * returns to its caller. */ Common->no_workspace_reallocate = TRUE ; /* Use the last 4*n Int's in Iwork for Parent, First, Level, and Post, since * other CHOLMOD routines will use the first 2n+uncol space. The ordering * routines (cholmod_amd, cholmod_colamd, cholmod_ccolamd, cholmod_metis) * are an exception. They can use all 6n + ncol space, since the contents * of Parent, First, Level, and Post are not needed across calls to those * routines. */ Work4n = Common->Iwork ; Work4n += 2*((size_t) n) + uncol ; Parent = Work4n ; First = Work4n + n ; Level = Work4n + 2*((size_t) n) ; Post = Work4n + 3*((size_t) n) ; /* note that this assignment means that cholmod_nested_dissection, * cholmod_ccolamd, and cholmod_camd can use only the first 4n+uncol * space in Common->Iwork */ Cmember = Post ; CParent = Level ; /* ---------------------------------------------------------------------- */ /* allocate more workspace, and an empty simplicial symbolic factor */ /* ---------------------------------------------------------------------- */ L = CHOLMOD(allocate_factor) (n, Common) ; Lparent = CHOLMOD(malloc) (n, sizeof (Int), Common) ; Perm = CHOLMOD(malloc) (n, sizeof (Int), Common) ; ColCount = CHOLMOD(malloc) (n, sizeof (Int), Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ FREE_WORKSPACE_AND_RETURN ; } Lperm = L->Perm ; Lcolcount = L->ColCount ; Common->anz = EMPTY ; /* ---------------------------------------------------------------------- */ /* try all the requested ordering options and backup to AMD if needed */ /* ---------------------------------------------------------------------- */ /* turn off error handling [ */ Common->try_catch = TRUE ; for (method = 0 ; method <= nmethods ; method++) { /* ------------------------------------------------------------------ */ /* determine the method to try */ /* ------------------------------------------------------------------ */ Common->fl = EMPTY ; Common->lnz = EMPTY ; skip_analysis = FALSE ; if (method == nmethods) { /* All methods failed: backup to AMD */ if (Common->selected == EMPTY && !default_strategy) { PRINT1 (("All methods requested failed: backup to AMD\n")) ; ordering = CHOLMOD_AMD ; } else { break ; } } else { ordering = Common->method [method].ordering ; } Common->current = method ; PRINT1 (("method "ID": Try method: "ID"\n", method, ordering)) ; /* ------------------------------------------------------------------ */ /* find the fill-reducing permutation */ /* ------------------------------------------------------------------ */ if (ordering == CHOLMOD_NATURAL) { /* -------------------------------------------------------------- */ /* natural ordering */ /* -------------------------------------------------------------- */ for (k = 0 ; k < n ; k++) { Perm [k] = k ; } } else if (ordering == CHOLMOD_GIVEN) { /* -------------------------------------------------------------- */ /* use given ordering of A, if provided */ /* -------------------------------------------------------------- */ if (UserPerm == NULL) { /* this is not an error condition */ PRINT1 (("skip, no user perm given\n")) ; continue ; } for (k = 0 ; k < n ; k++) { /* UserPerm is checked in cholmod_ptranspose */ Perm [k] = UserPerm [k] ; } } else if (ordering == CHOLMOD_AMD) { /* -------------------------------------------------------------- */ /* AMD ordering of A, A*A', or A(:,f)*A(:,f)' */ /* -------------------------------------------------------------- */ CHOLMOD(amd) (A, fset, fsize, Perm, Common) ; skip_analysis = TRUE ; } else if (ordering == CHOLMOD_COLAMD) { /* -------------------------------------------------------------- */ /* AMD for symmetric case, COLAMD for A*A' or A(:,f)*A(:,f)' */ /* -------------------------------------------------------------- */ if (A->stype) { CHOLMOD(amd) (A, fset, fsize, Perm, Common) ; skip_analysis = TRUE ; } else { /* Alternative: CHOLMOD(ccolamd) (A, fset, fsize, NULL, Perm, Common) ; */ /* do not postorder, it is done later, below */ /* workspace: Iwork (4*nrow+uncol), Flag (nrow), Head (nrow+1)*/ CHOLMOD(colamd) (A, fset, fsize, FALSE, Perm, Common) ; } } else if (ordering == CHOLMOD_METIS) { /* -------------------------------------------------------------- */ /* use METIS_NodeND directly (via a CHOLMOD wrapper) */ /* -------------------------------------------------------------- */ #ifndef NPARTITION /* postorder parameter is false, because it will be later, below */ /* workspace: Iwork (4*nrow+uncol), Flag (nrow), Head (nrow+1) */ Common->called_nd = TRUE ; CHOLMOD(metis) (A, fset, fsize, FALSE, Perm, Common) ; #else Common->status = CHOLMOD_NOT_INSTALLED ; #endif } else if (ordering == CHOLMOD_NESDIS) { /* -------------------------------------------------------------- */ /* use CHOLMOD's nested dissection */ /* -------------------------------------------------------------- */ /* this method is based on METIS' node bissection routine * (METIS_NodeComputeSeparator). In contrast to METIS_NodeND, * it calls CAMD or CCOLAMD on the whole graph, instead of MMD * on just the leaves. */ #ifndef NPARTITION /* workspace: Flag (nrow), Head (nrow+1), Iwork (2*nrow) */ Common->called_nd = TRUE ; CHOLMOD(nested_dissection) (A, fset, fsize, Perm, CParent, Cmember, Common) ; #else Common->status = CHOLMOD_NOT_INSTALLED ; #endif } else { /* -------------------------------------------------------------- */ /* invalid ordering method */ /* -------------------------------------------------------------- */ Common->status = CHOLMOD_INVALID ; PRINT1 (("No such ordering: "ID"\n", ordering)) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; if (Common->status < CHOLMOD_OK) { /* out of memory, or method failed */ status = MIN (status, Common->status) ; Common->status = CHOLMOD_OK ; continue ; } /* ------------------------------------------------------------------ */ /* analyze the ordering */ /* ------------------------------------------------------------------ */ if (!skip_analysis) { if (!CHOLMOD(analyze_ordering) (A, ordering, Perm, fset, fsize, Parent, Post, ColCount, First, Level, Common)) { /* ordering method failed; clear status and try next method */ status = MIN (status, Common->status) ; Common->status = CHOLMOD_OK ; continue ; } } ASSERT (Common->fl >= 0 && Common->lnz >= 0) ; Common->method [method].fl = Common->fl ; Common->method [method].lnz = Common->lnz ; PRINT1 (("lnz %g fl %g\n", Common->lnz, Common->fl)) ; /* ------------------------------------------------------------------ */ /* pick the best method */ /* ------------------------------------------------------------------ */ /* fl.pt. compare, but lnz can never be NaN */ if (Common->selected == EMPTY || Common->lnz < lnz_best) { Common->selected = method ; PRINT1 (("this is best so far, method "ID"\n", method)) ; L->ordering = ordering ; lnz_best = Common->lnz ; for (k = 0 ; k < n ; k++) { Lperm [k] = Perm [k] ; } /* save the results of cholmod_analyze_ordering, if it was called */ skip_best = skip_analysis ; if (!skip_analysis) { /* save the column count; becomes permanent part of L */ for (k = 0 ; k < n ; k++) { Lcolcount [k] = ColCount [k] ; } /* Parent is needed for weighted postordering and for supernodal * analysis. Does not become a permanent part of L */ for (k = 0 ; k < n ; k++) { Lparent [k] = Parent [k] ; } } } /* ------------------------------------------------------------------ */ /* determine if METIS is to be skipped */ /* ------------------------------------------------------------------ */ if (default_strategy && ordering == CHOLMOD_AMD) { if ((Common->fl < 500 * Common->lnz) || (Common->lnz < 5 * Common->anz)) { /* AMD found an ordering with less than 500 flops per nonzero in * L, or one with a fill-in ratio (nnz(L)/nnz(A)) of less than * 5. This is pretty good, and it's unlikely that METIS will do * better (this heuristic is based on tests on all symmetric * positive definite matrices in the UF sparse matrix * collection, and it works well across a wide range of * problems). METIS can take much more time and AMD. */ break ; } } } /* turn error printing back on ] */ Common->try_catch = FALSE ; /* ---------------------------------------------------------------------- */ /* return if no ordering method succeeded */ /* ---------------------------------------------------------------------- */ if (Common->selected == EMPTY) { /* All methods failed. * If two or more methods failed, they may have failed for different * reasons. Both would clear Common->status and skip to the next * method. Common->status needs to be restored here to the worst error * obtained in any of the methods. CHOLMOD_INVALID is worse * than CHOLMOD_OUT_OF_MEMORY, since the former implies something may * be wrong with the user's input. CHOLMOD_OUT_OF_MEMORY is simply an * indication of lack of resources. */ ASSERT (status < CHOLMOD_OK) ; ERROR (status, "all methods failed") ; FREE_WORKSPACE_AND_RETURN ; } /* ---------------------------------------------------------------------- */ /* do the analysis for AMD, if skipped */ /* ---------------------------------------------------------------------- */ Common->fl = Common->method [Common->selected].fl ; Common->lnz = Common->method [Common->selected].lnz ; ASSERT (Common->lnz >= 0) ; if (skip_best) { if (!CHOLMOD(analyze_ordering) (A, L->ordering, Lperm, fset, fsize, Lparent, Post, Lcolcount, First, Level, Common)) { /* out of memory, or method failed */ FREE_WORKSPACE_AND_RETURN ; } } /* ---------------------------------------------------------------------- */ /* postorder the etree, weighted by the column counts */ /* ---------------------------------------------------------------------- */ if (Common->postorder) { /* combine the fill-reducing ordering with the weighted postorder */ /* workspace: Iwork (2*nrow) */ if (CHOLMOD(postorder) (Lparent, n, Lcolcount, Post, Common) == n) { /* use First and Level as workspace [ */ Int *Wi = First, *InvPost = Level ; Int newchild, oldchild, newparent, oldparent ; for (k = 0 ; k < n ; k++) { Wi [k] = Lperm [Post [k]] ; } for (k = 0 ; k < n ; k++) { Lperm [k] = Wi [k] ; } for (k = 0 ; k < n ; k++) { Wi [k] = Lcolcount [Post [k]] ; } for (k = 0 ; k < n ; k++) { Lcolcount [k] = Wi [k] ; } for (k = 0 ; k < n ; k++) { InvPost [Post [k]] = k ; } /* updated Lparent needed only for supernodal case */ for (newchild = 0 ; newchild < n ; newchild++) { oldchild = Post [newchild] ; oldparent = Lparent [oldchild] ; newparent = (oldparent == EMPTY) ? EMPTY : InvPost [oldparent] ; Wi [newchild] = newparent ; } for (k = 0 ; k < n ; k++) { Lparent [k] = Wi [k] ; } /* done using Iwork as workspace ] */ /* L is now postordered, no longer in natural ordering */ if (L->ordering == CHOLMOD_NATURAL) { L->ordering = CHOLMOD_POSTORDERED ; } } } /* ---------------------------------------------------------------------- */ /* supernodal analysis, if requested or if selected automatically */ /* ---------------------------------------------------------------------- */ #ifndef NSUPERNODAL if (Common->supernodal > CHOLMOD_AUTO || (Common->supernodal == CHOLMOD_AUTO && Common->lnz > 0 && (Common->fl / Common->lnz) >= Common->supernodal_switch)) { cholmod_sparse *S, *F, *A2, *A1 ; permute_matrices (A, L->ordering, Lperm, fset, fsize, TRUE, &A1, &A2, &S, &F, Common) ; /* workspace: Flag (nrow), Head (nrow), Iwork (5*nrow) */ CHOLMOD(super_symbolic) (S, F, Lparent, L, Common) ; PRINT1 (("status %d\n", Common->status)) ; CHOLMOD(free_sparse) (&A1, Common) ; CHOLMOD(free_sparse) (&A2, Common) ; } #endif /* ---------------------------------------------------------------------- */ /* free temporary matrices and workspace, and return result L */ /* ---------------------------------------------------------------------- */ FREE_WORKSPACE_AND_RETURN ; } #endif SuiteSparse/CHOLMOD/Cholesky/cholmod_colamd.c0000644001170100242450000001566210537777310017751 0ustar davisfac/* ========================================================================== */ /* === Cholesky/cholmod_colamd ============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* CHOLMOD interface to the COLAMD ordering routine (version 2.4 or later). * Finds a permutation p such that the Cholesky factorization of PAA'P' is * sparser than AA' using colamd. If the postorder input parameter is TRUE, * the column etree is found and postordered, and the colamd ordering is then * combined with its postordering. A must be unsymmetric. * * There can be no duplicate entries in f. * f can be length 0 to n if A is m-by-n. * * workspace: Iwork (4*nrow+ncol), Head (nrow+1), Flag (nrow) * Allocates a copy of its input matrix, which * is then used as CCOLAMD's workspace. * * Supports any xtype (pattern, real, complex, or zomplex) */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "colamd.h" #include "cholmod_cholesky.h" #if (!defined (COLAMD_VERSION) || (COLAMD_VERSION < COLAMD_VERSION_CODE (2,5))) #error "COLAMD v2.5 or later is required" #endif /* ========================================================================== */ /* === cholmod_colamd ======================================================= */ /* ========================================================================== */ int CHOLMOD(colamd) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int postorder, /* if TRUE, follow with a coletree postorder */ /* ---- output --- */ Int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) { double knobs [COLAMD_KNOBS] ; cholmod_sparse *C ; Int *NewPerm, *Parent, *Post, *Work2n ; Int k, nrow, ncol ; size_t s, alen ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (Perm, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; if (A->stype != 0) { ERROR (CHOLMOD_INVALID, "matrix must be unsymmetric") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nrow = A->nrow ; ncol = A->ncol ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* Note: this is less than the space used in cholmod_analyze, so if * cholmod_colamd is being called by that routine, no space will be * allocated. */ /* s = 4*nrow + ncol */ s = CHOLMOD(mult_size_t) (nrow, 4, &ok) ; s = CHOLMOD(add_size_t) (s, ncol, &ok) ; #ifdef LONG alen = colamd_l_recommended (A->nzmax, ncol, nrow) ; colamd_l_set_defaults (knobs) ; #else alen = colamd_recommended (A->nzmax, ncol, nrow) ; colamd_set_defaults (knobs) ; #endif if (!ok || alen == 0) { ERROR (CHOLMOD_TOO_LARGE, "matrix invalid or too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (0, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* allocate COLAMD workspace */ /* ---------------------------------------------------------------------- */ /* colamd_printf is only available in colamd v2.4 or later */ colamd_printf = Common->print_function ; C = CHOLMOD(allocate_sparse) (ncol, nrow, alen, TRUE, TRUE, 0, CHOLMOD_PATTERN, Common) ; /* ---------------------------------------------------------------------- */ /* copy (and transpose) the input matrix A into the colamd workspace */ /* ---------------------------------------------------------------------- */ /* C = A (:,f)', which also packs A if needed. */ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset) */ ok = CHOLMOD(transpose_unsym) (A, 0, NULL, fset, fsize, C, Common) ; /* ---------------------------------------------------------------------- */ /* order the matrix (destroys the contents of C->i and C->p) */ /* ---------------------------------------------------------------------- */ /* get parameters */ if (Common->current < 0 || Common->current >= CHOLMOD_MAXMETHODS) { /* this is the CHOLMOD default, not the COLAMD default */ knobs [COLAMD_DENSE_ROW] = -1 ; } else { /* get the knobs from the Common parameters */ knobs [COLAMD_DENSE_COL] = Common->method[Common->current].prune_dense ; knobs [COLAMD_DENSE_ROW] = Common->method[Common->current].prune_dense2; knobs [COLAMD_AGGRESSIVE] = Common->method[Common->current].aggressive ; } if (ok) { Int *Cp ; Int stats [COLAMD_STATS] ; Cp = C->p ; #ifdef LONG colamd_l (ncol, nrow, alen, C->i, Cp, knobs, stats) ; #else colamd (ncol, nrow, alen, C->i, Cp, knobs, stats) ; #endif ok = stats [COLAMD_STATUS] ; ok = (ok == COLAMD_OK || ok == COLAMD_OK_BUT_JUMBLED) ; /* permutation returned in C->p, if the ordering succeeded */ for (k = 0 ; k < nrow ; k++) { Perm [k] = Cp [k] ; } } CHOLMOD(free_sparse) (&C, Common) ; /* ---------------------------------------------------------------------- */ /* column etree postordering */ /* ---------------------------------------------------------------------- */ if (postorder) { /* use the last 2*n space in Iwork for Parent and Post */ Work2n = Common->Iwork ; Work2n += 2*((size_t) nrow) + ncol ; Parent = Work2n ; /* size nrow (i/i/l) */ Post = Work2n + nrow ; /* size nrow (i/i/l) */ /* workspace: Iwork (2*nrow+ncol), Flag (nrow), Head (nrow+1) */ ok = ok && CHOLMOD(analyze_ordering) (A, CHOLMOD_COLAMD, Perm, fset, fsize, Parent, Post, NULL, NULL, NULL, Common) ; /* combine the colamd permutation with its postordering */ if (ok) { NewPerm = Common->Iwork ; /* size nrow (i/i/l) */ for (k = 0 ; k < nrow ; k++) { NewPerm [k] = Perm [Post [k]] ; } for (k = 0 ; k < nrow ; k++) { Perm [k] = NewPerm [k] ; } } } return (ok) ; } #endif SuiteSparse/CHOLMOD/Cholesky/t_cholmod_lsolve.c0000644001170100242450000006306110537777360020342 0ustar davisfac/* ========================================================================== */ /* === Cholesky/t_cholmod_lsolve ============================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Template routine to solve Lx=b with unit or non-unit diagonal, or * solve LDx=b. * * The numeric xtype of L and Y must match. Y contains b on input and x on * output, stored in row-form. Y is nrow-by-n, where nrow must equal 1 for the * complex or zomplex cases, and nrow <= 4 for the real case. * * This file is not compiled separately. It is included in t_cholmod_solve.c * instead. It contains no user-callable routines. * * workspace: none * * Supports real, complex, and zomplex factors. */ /* undefine all prior definitions */ #undef FORM_NAME #undef LSOLVE /* -------------------------------------------------------------------------- */ /* define the method */ /* -------------------------------------------------------------------------- */ #ifdef LL /* LL': solve Lx=b with non-unit diagonal */ #define FORM_NAME(prefix,rank) prefix ## ll_lsolve_ ## rank #elif defined (LD) /* LDL': solve LDx=b */ #define FORM_NAME(prefix,rank) prefix ## ldl_ldsolve_ ## rank #else /* LDL': solve Lx=b with unit diagonal */ #define FORM_NAME(prefix,rank) prefix ## ldl_lsolve_ ## rank #endif /* LSOLVE(k) defines the name of a routine for an n-by-k right-hand-side. */ #define LSOLVE(prefix,rank) FORM_NAME(prefix,rank) #ifdef REAL /* ========================================================================== */ /* === LSOLVE (1) =========================================================== */ /* ========================================================================== */ /* Solve Lx=b, where b has 1 column */ static void LSOLVE (PREFIX,1) ( cholmod_factor *L, double X [ ] /* n-by-1 in row form */ ) { double *Lx = L->x ; Int *Li = L->i ; Int *Lp = L->p ; Int *Lnz = L->nz ; Int j, n = L->n ; for (j = 0 ; j < n ; ) { /* get the start, end, and length of column j */ Int p = Lp [j] ; Int lnz = Lnz [j] ; Int pend = p + lnz ; /* find a chain of supernodes (up to j, j+1, and j+2) */ if (lnz < 4 || lnz != Lnz [j+1] + 1 || Li [p+1] != j+1) { /* -------------------------------------------------------------- */ /* solve with a single column of L */ /* -------------------------------------------------------------- */ double y = X [j] ; #ifdef LL y /= Lx [p] ; X [j] = y ; #elif defined (LD) X [j] = y / Lx [p] ; #endif for (p++ ; p < pend ; p++) { X [Li [p]] -= Lx [p] * y ; } j++ ; /* advance to next column of L */ } else if (lnz != Lnz [j+2] + 2 || Li [p+2] != j+2) { /* -------------------------------------------------------------- */ /* solve with a supernode of two columns of L */ /* -------------------------------------------------------------- */ double y [2] ; Int q = Lp [j+1] ; #ifdef LL y [0] = X [j] / Lx [p] ; y [1] = (X [j+1] - Lx [p+1] * y [0]) / Lx [q] ; X [j ] = y [0] ; X [j+1] = y [1] ; #elif defined (LD) y [0] = X [j] ; y [1] = X [j+1] - Lx [p+1] * y [0] ; X [j ] = y [0] / Lx [p] ; X [j+1] = y [1] / Lx [q] ; #else y [0] = X [j] ; y [1] = X [j+1] - Lx [p+1] * y [0] ; X [j+1] = y [1] ; #endif for (p += 2, q++ ; p < pend ; p++, q++) { X [Li [p]] -= Lx [p] * y [0] + Lx [q] * y [1] ; } j += 2 ; /* advance to next column of L */ } else { /* -------------------------------------------------------------- */ /* solve with a supernode of three columns of L */ /* -------------------------------------------------------------- */ double y [3] ; Int q = Lp [j+1] ; Int r = Lp [j+2] ; #ifdef LL y [0] = X [j] / Lx [p] ; y [1] = (X [j+1] - Lx [p+1] * y [0]) / Lx [q] ; y [2] = (X [j+2] - Lx [p+2] * y [0] - Lx [q+1] * y [1]) / Lx [r] ; X [j ] = y [0] ; X [j+1] = y [1] ; X [j+2] = y [2] ; #elif defined (LD) y [0] = X [j] ; y [1] = X [j+1] - Lx [p+1] * y [0] ; y [2] = X [j+2] - Lx [p+2] * y [0] - Lx [q+1] * y [1] ; X [j ] = y [0] / Lx [p] ; X [j+1] = y [1] / Lx [q] ; X [j+2] = y [2] / Lx [r] ; #else y [0] = X [j] ; y [1] = X [j+1] - Lx [p+1] * y [0] ; y [2] = X [j+2] - Lx [p+2] * y [0] - Lx [q+1] * y [1] ; X [j+1] = y [1] ; X [j+2] = y [2] ; #endif for (p += 3, q += 2, r++ ; p < pend ; p++, q++, r++) { X [Li [p]] -= Lx [p] * y [0] + Lx [q] * y [1] + Lx [r] * y [2] ; } j += 3 ; /* advance to next column of L */ } } } /* ========================================================================== */ /* === LSOLVE (2) =========================================================== */ /* ========================================================================== */ /* Solve Lx=b, where b has 2 columns */ static void LSOLVE (PREFIX,2) ( cholmod_factor *L, double X [ ][2] /* n-by-2 in row form */ ) { double *Lx = L->x ; Int *Li = L->i ; Int *Lp = L->p ; Int *Lnz = L->nz ; Int j, n = L->n ; for (j = 0 ; j < n ; ) { /* get the start, end, and length of column j */ Int p = Lp [j] ; Int lnz = Lnz [j] ; Int pend = p + lnz ; /* find a chain of supernodes (up to j, j+1, and j+2) */ if (lnz < 4 || lnz != Lnz [j+1] + 1 || Li [p+1] != j+1) { /* -------------------------------------------------------------- */ /* solve with a single column of L */ /* -------------------------------------------------------------- */ double y [2] ; y [0] = X [j][0] ; y [1] = X [j][1] ; #ifdef LL y [0] /= Lx [p] ; y [1] /= Lx [p] ; X [j][0] = y [0] ; X [j][1] = y [1] ; #elif defined (LD) X [j][0] = y [0] / Lx [p] ; X [j][1] = y [1] / Lx [p] ; #endif for (p++ ; p < pend ; p++) { Int i = Li [p] ; X [i][0] -= Lx [p] * y [0] ; X [i][1] -= Lx [p] * y [1] ; } j++ ; /* advance to next column of L */ } else if (lnz != Lnz [j+2] + 2 || Li [p+2] != j+2) { /* -------------------------------------------------------------- */ /* solve with a supernode of two columns of L */ /* -------------------------------------------------------------- */ double y [2][2] ; Int q = Lp [j+1] ; y [0][0] = X [j][0] ; y [0][1] = X [j][1] ; #ifdef LL y [0][0] /= Lx [p] ; y [0][1] /= Lx [p] ; y [1][0] = (X [j+1][0] - Lx [p+1] * y [0][0]) / Lx [q] ; y [1][1] = (X [j+1][1] - Lx [p+1] * y [0][1]) / Lx [q] ; X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; #elif defined (LD) y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; X [j ][0] = y [0][0] / Lx [p] ; X [j ][1] = y [0][1] / Lx [p] ; X [j+1][0] = y [1][0] / Lx [q] ; X [j+1][1] = y [1][1] / Lx [q] ; #else y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; #endif for (p += 2, q++ ; p < pend ; p++, q++) { Int i = Li [p] ; X [i][0] -= Lx [p] * y [0][0] + Lx [q] * y [1][0] ; X [i][1] -= Lx [p] * y [0][1] + Lx [q] * y [1][1] ; } j += 2 ; /* advance to next column of L */ } else { /* -------------------------------------------------------------- */ /* solve with a supernode of three columns of L */ /* -------------------------------------------------------------- */ double y [3][2] ; Int q = Lp [j+1] ; Int r = Lp [j+2] ; y [0][0] = X [j][0] ; y [0][1] = X [j][1] ; #ifdef LL y [0][0] /= Lx [p] ; y [0][1] /= Lx [p] ; y [1][0] = (X [j+1][0] - Lx[p+1] * y[0][0]) / Lx [q] ; y [1][1] = (X [j+1][1] - Lx[p+1] * y[0][1]) / Lx [q] ; y [2][0] = (X [j+2][0] - Lx[p+2] * y[0][0] - Lx[q+1]*y[1][0])/Lx[r]; y [2][1] = (X [j+2][1] - Lx[p+2] * y[0][1] - Lx[q+1]*y[1][1])/Lx[r]; X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; X [j+2][0] = y [2][0] ; X [j+2][1] = y [2][1] ; #elif defined (LD) y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ; y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ; X [j ][0] = y [0][0] / Lx [p] ; X [j ][1] = y [0][1] / Lx [p] ; X [j+1][0] = y [1][0] / Lx [q] ; X [j+1][1] = y [1][1] / Lx [q] ; X [j+2][0] = y [2][0] / Lx [r] ; X [j+2][1] = y [2][1] / Lx [r] ; #else y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ; y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; X [j+2][0] = y [2][0] ; X [j+2][1] = y [2][1] ; #endif for (p += 3, q += 2, r++ ; p < pend ; p++, q++, r++) { Int i = Li [p] ; X[i][0] -= Lx[p] * y[0][0] + Lx[q] * y[1][0] + Lx[r] * y[2][0] ; X[i][1] -= Lx[p] * y[0][1] + Lx[q] * y[1][1] + Lx[r] * y[2][1] ; } j += 3 ; /* advance to next column of L */ } } } /* ========================================================================== */ /* === LSOLVE (3) =========================================================== */ /* ========================================================================== */ /* Solve Lx=b, where b has 3 columns */ static void LSOLVE (PREFIX,3) ( cholmod_factor *L, double X [ ][3] /* n-by-3 in row form */ ) { double *Lx = L->x ; Int *Li = L->i ; Int *Lp = L->p ; Int *Lnz = L->nz ; Int j, n = L->n ; for (j = 0 ; j < n ; ) { /* get the start, end, and length of column j */ Int p = Lp [j] ; Int lnz = Lnz [j] ; Int pend = p + lnz ; /* find a chain of supernodes (up to j, j+1, and j+2) */ if (lnz < 4 || lnz != Lnz [j+1] + 1 || Li [p+1] != j+1) { /* -------------------------------------------------------------- */ /* solve with a single column of L */ /* -------------------------------------------------------------- */ double y [3] ; y [0] = X [j][0] ; y [1] = X [j][1] ; y [2] = X [j][2] ; #ifdef LL y [0] /= Lx [p] ; y [1] /= Lx [p] ; y [2] /= Lx [p] ; X [j][0] = y [0] ; X [j][1] = y [1] ; X [j][2] = y [2] ; #elif defined (LD) X [j][0] = y [0] / Lx [p] ; X [j][1] = y [1] / Lx [p] ; X [j][2] = y [2] / Lx [p] ; #endif for (p++ ; p < pend ; p++) { Int i = Li [p] ; double lx = Lx [p] ; X [i][0] -= lx * y [0] ; X [i][1] -= lx * y [1] ; X [i][2] -= lx * y [2] ; } j++ ; /* advance to next column of L */ } else if (lnz != Lnz [j+2] + 2 || Li [p+2] != j+2) { /* -------------------------------------------------------------- */ /* solve with a supernode of two columns of L */ /* -------------------------------------------------------------- */ double y [2][3] ; Int q = Lp [j+1] ; y [0][0] = X [j][0] ; y [0][1] = X [j][1] ; y [0][2] = X [j][2] ; #ifdef LL y [0][0] /= Lx [p] ; y [0][1] /= Lx [p] ; y [0][2] /= Lx [p] ; y [1][0] = (X [j+1][0] - Lx [p+1] * y [0][0]) / Lx [q] ; y [1][1] = (X [j+1][1] - Lx [p+1] * y [0][1]) / Lx [q] ; y [1][2] = (X [j+1][2] - Lx [p+1] * y [0][2]) / Lx [q] ; X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j ][2] = y [0][2] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; X [j+1][2] = y [1][2] ; #elif defined (LD) y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ; X [j ][0] = y [0][0] / Lx [p] ; X [j ][1] = y [0][1] / Lx [p] ; X [j ][2] = y [0][2] / Lx [p] ; X [j+1][0] = y [1][0] / Lx [q] ; X [j+1][1] = y [1][1] / Lx [q] ; X [j+1][2] = y [1][2] / Lx [q] ; #else y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; X [j+1][2] = y [1][2] ; #endif for (p += 2, q++ ; p < pend ; p++, q++) { Int i = Li [p] ; double lx [2] ; lx [0] = Lx [p] ; lx [1] = Lx [q] ; X [i][0] -= lx [0] * y [0][0] + lx [1] * y [1][0] ; X [i][1] -= lx [0] * y [0][1] + lx [1] * y [1][1] ; X [i][2] -= lx [0] * y [0][2] + lx [1] * y [1][2] ; } j += 2 ; /* advance to next column of L */ } else { /* -------------------------------------------------------------- */ /* solve with a supernode of three columns of L */ /* -------------------------------------------------------------- */ double y [3][3] ; Int q = Lp [j+1] ; Int r = Lp [j+2] ; y [0][0] = X [j][0] ; y [0][1] = X [j][1] ; y [0][2] = X [j][2] ; #ifdef LL y [0][0] /= Lx [p] ; y [0][1] /= Lx [p] ; y [0][2] /= Lx [p] ; y [1][0] = (X [j+1][0] - Lx[p+1] * y[0][0]) / Lx [q] ; y [1][1] = (X [j+1][1] - Lx[p+1] * y[0][1]) / Lx [q] ; y [1][2] = (X [j+1][2] - Lx[p+1] * y[0][2]) / Lx [q] ; y [2][0] = (X [j+2][0] - Lx[p+2] * y[0][0] - Lx[q+1]*y[1][0])/Lx[r]; y [2][1] = (X [j+2][1] - Lx[p+2] * y[0][1] - Lx[q+1]*y[1][1])/Lx[r]; y [2][2] = (X [j+2][2] - Lx[p+2] * y[0][2] - Lx[q+1]*y[1][2])/Lx[r]; X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j ][2] = y [0][2] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; X [j+1][2] = y [1][2] ; X [j+2][0] = y [2][0] ; X [j+2][1] = y [2][1] ; X [j+2][2] = y [2][2] ; #elif defined (LD) y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ; y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ; y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ; y [2][2] = X [j+2][2] - Lx [p+2] * y [0][2] - Lx [q+1] * y [1][2] ; X [j ][0] = y [0][0] / Lx [p] ; X [j ][1] = y [0][1] / Lx [p] ; X [j ][2] = y [0][2] / Lx [p] ; X [j+1][0] = y [1][0] / Lx [q] ; X [j+1][1] = y [1][1] / Lx [q] ; X [j+1][2] = y [1][2] / Lx [q] ; X [j+2][0] = y [2][0] / Lx [r] ; X [j+2][1] = y [2][1] / Lx [r] ; X [j+2][2] = y [2][2] / Lx [r] ; #else y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ; y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ; y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ; y [2][2] = X [j+2][2] - Lx [p+2] * y [0][2] - Lx [q+1] * y [1][2] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; X [j+1][2] = y [1][2] ; X [j+2][0] = y [2][0] ; X [j+2][1] = y [2][1] ; X [j+2][2] = y [2][2] ; #endif for (p += 3, q += 2, r++ ; p < pend ; p++, q++, r++) { Int i = Li [p] ; double lx [3] ; lx [0] = Lx [p] ; lx [1] = Lx [q] ; lx [2] = Lx [r] ; X [i][0] -= lx[0] * y[0][0] + lx[1] * y[1][0] + lx[2] * y[2][0]; X [i][1] -= lx[0] * y[0][1] + lx[1] * y[1][1] + lx[2] * y[2][1]; X [i][2] -= lx[0] * y[0][2] + lx[1] * y[1][2] + lx[2] * y[2][2]; } j += 3 ; /* advance to next column of L */ } } } /* ========================================================================== */ /* === LSOLVE (4) =========================================================== */ /* ========================================================================== */ /* Solve Lx=b, where b has 4 columns */ static void LSOLVE (PREFIX,4) ( cholmod_factor *L, double X [ ][4] /* n-by-4 in row form */ ) { double *Lx = L->x ; Int *Li = L->i ; Int *Lp = L->p ; Int *Lnz = L->nz ; Int j, n = L->n ; for (j = 0 ; j < n ; ) { /* get the start, end, and length of column j */ Int p = Lp [j] ; Int lnz = Lnz [j] ; Int pend = p + lnz ; /* find a chain of supernodes (up to j, j+1, and j+2) */ if (lnz < 4 || lnz != Lnz [j+1] + 1 || Li [p+1] != j+1) { /* -------------------------------------------------------------- */ /* solve with a single column of L */ /* -------------------------------------------------------------- */ double y [4] ; y [0] = X [j][0] ; y [1] = X [j][1] ; y [2] = X [j][2] ; y [3] = X [j][3] ; #ifdef LL y [0] /= Lx [p] ; y [1] /= Lx [p] ; y [2] /= Lx [p] ; y [3] /= Lx [p] ; X [j][0] = y [0] ; X [j][1] = y [1] ; X [j][2] = y [2] ; X [j][3] = y [3] ; #elif defined (LD) X [j][0] = y [0] / Lx [p] ; X [j][1] = y [1] / Lx [p] ; X [j][2] = y [2] / Lx [p] ; X [j][3] = y [3] / Lx [p] ; #endif for (p++ ; p < pend ; p++) { Int i = Li [p] ; double lx = Lx [p] ; X [i][0] -= lx * y [0] ; X [i][1] -= lx * y [1] ; X [i][2] -= lx * y [2] ; X [i][3] -= lx * y [3] ; } j++ ; /* advance to next column of L */ } else if (lnz != Lnz [j+2] + 2 || Li [p+2] != j+2) { /* -------------------------------------------------------------- */ /* solve with a supernode of two columns of L */ /* -------------------------------------------------------------- */ double y [2][4] ; Int q = Lp [j+1] ; y [0][0] = X [j][0] ; y [0][1] = X [j][1] ; y [0][2] = X [j][2] ; y [0][3] = X [j][3] ; #ifdef LL y [0][0] /= Lx [p] ; y [0][1] /= Lx [p] ; y [0][2] /= Lx [p] ; y [0][3] /= Lx [p] ; y [1][0] = (X [j+1][0] - Lx [p+1] * y [0][0]) / Lx [q] ; y [1][1] = (X [j+1][1] - Lx [p+1] * y [0][1]) / Lx [q] ; y [1][2] = (X [j+1][2] - Lx [p+1] * y [0][2]) / Lx [q] ; y [1][3] = (X [j+1][3] - Lx [p+1] * y [0][3]) / Lx [q] ; X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j ][2] = y [0][2] ; X [j ][3] = y [0][3] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; X [j+1][2] = y [1][2] ; X [j+1][3] = y [1][3] ; #elif defined (LD) y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ; y [1][3] = X [j+1][3] - Lx [p+1] * y [0][3] ; X [j ][0] = y [0][0] / Lx [p] ; X [j ][1] = y [0][1] / Lx [p] ; X [j ][2] = y [0][2] / Lx [p] ; X [j ][3] = y [0][3] / Lx [p] ; X [j+1][0] = y [1][0] / Lx [q] ; X [j+1][1] = y [1][1] / Lx [q] ; X [j+1][2] = y [1][2] / Lx [q] ; X [j+1][3] = y [1][3] / Lx [q] ; #else y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ; y [1][3] = X [j+1][3] - Lx [p+1] * y [0][3] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; X [j+1][2] = y [1][2] ; X [j+1][3] = y [1][3] ; #endif for (p += 2, q++ ; p < pend ; p++, q++) { Int i = Li [p] ; double lx [2] ; lx [0] = Lx [p] ; lx [1] = Lx [q] ; X [i][0] -= lx [0] * y [0][0] + lx [1] * y [1][0] ; X [i][1] -= lx [0] * y [0][1] + lx [1] * y [1][1] ; X [i][2] -= lx [0] * y [0][2] + lx [1] * y [1][2] ; X [i][3] -= lx [0] * y [0][3] + lx [1] * y [1][3] ; } j += 2 ; /* advance to next column of L */ } else { /* -------------------------------------------------------------- */ /* solve with a supernode of three columns of L */ /* -------------------------------------------------------------- */ double y [3][4] ; Int q = Lp [j+1] ; Int r = Lp [j+2] ; y [0][0] = X [j][0] ; y [0][1] = X [j][1] ; y [0][2] = X [j][2] ; y [0][3] = X [j][3] ; #ifdef LL y [0][0] /= Lx [p] ; y [0][1] /= Lx [p] ; y [0][2] /= Lx [p] ; y [0][3] /= Lx [p] ; y [1][0] = (X [j+1][0] - Lx[p+1] * y[0][0]) / Lx [q] ; y [1][1] = (X [j+1][1] - Lx[p+1] * y[0][1]) / Lx [q] ; y [1][2] = (X [j+1][2] - Lx[p+1] * y[0][2]) / Lx [q] ; y [1][3] = (X [j+1][3] - Lx[p+1] * y[0][3]) / Lx [q] ; y [2][0] = (X [j+2][0] - Lx[p+2] * y[0][0] - Lx[q+1]*y[1][0])/Lx[r]; y [2][1] = (X [j+2][1] - Lx[p+2] * y[0][1] - Lx[q+1]*y[1][1])/Lx[r]; y [2][2] = (X [j+2][2] - Lx[p+2] * y[0][2] - Lx[q+1]*y[1][2])/Lx[r]; y [2][3] = (X [j+2][3] - Lx[p+2] * y[0][3] - Lx[q+1]*y[1][3])/Lx[r]; X [j ][0] = y [0][0] ; X [j ][1] = y [0][1] ; X [j ][2] = y [0][2] ; X [j ][3] = y [0][3] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; X [j+1][2] = y [1][2] ; X [j+1][3] = y [1][3] ; X [j+2][0] = y [2][0] ; X [j+2][1] = y [2][1] ; X [j+2][2] = y [2][2] ; X [j+2][3] = y [2][3] ; #elif defined (LD) y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ; y [1][3] = X [j+1][3] - Lx [p+1] * y [0][3] ; y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ; y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ; y [2][2] = X [j+2][2] - Lx [p+2] * y [0][2] - Lx [q+1] * y [1][2] ; y [2][3] = X [j+2][3] - Lx [p+2] * y [0][3] - Lx [q+1] * y [1][3] ; X [j ][0] = y [0][0] / Lx [p] ; X [j ][1] = y [0][1] / Lx [p] ; X [j ][2] = y [0][2] / Lx [p] ; X [j ][3] = y [0][3] / Lx [p] ; X [j+1][0] = y [1][0] / Lx [q] ; X [j+1][1] = y [1][1] / Lx [q] ; X [j+1][2] = y [1][2] / Lx [q] ; X [j+1][3] = y [1][3] / Lx [q] ; X [j+2][0] = y [2][0] / Lx [r] ; X [j+2][1] = y [2][1] / Lx [r] ; X [j+2][2] = y [2][2] / Lx [r] ; X [j+2][3] = y [2][3] / Lx [r] ; #else y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ; y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ; y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ; y [1][3] = X [j+1][3] - Lx [p+1] * y [0][3] ; y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ; y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ; y [2][2] = X [j+2][2] - Lx [p+2] * y [0][2] - Lx [q+1] * y [1][2] ; y [2][3] = X [j+2][3] - Lx [p+2] * y [0][3] - Lx [q+1] * y [1][3] ; X [j+1][0] = y [1][0] ; X [j+1][1] = y [1][1] ; X [j+1][2] = y [1][2] ; X [j+1][3] = y [1][3] ; X [j+2][0] = y [2][0] ; X [j+2][1] = y [2][1] ; X [j+2][2] = y [2][2] ; X [j+2][3] = y [2][3] ; #endif for (p += 3, q += 2, r++ ; p < pend ; p++, q++, r++) { Int i = Li [p] ; double lx [3] ; lx [0] = Lx [p] ; lx [1] = Lx [q] ; lx [2] = Lx [r] ; X [i][0] -= lx[0] * y[0][0] + lx[1] * y[1][0] + lx[2] * y[2][0]; X [i][1] -= lx[0] * y[0][1] + lx[1] * y[1][1] + lx[2] * y[2][1]; X [i][2] -= lx[0] * y[0][2] + lx[1] * y[1][2] + lx[2] * y[2][2]; X [i][3] -= lx[0] * y[0][3] + lx[1] * y[1][3] + lx[2] * y[2][3]; } j += 3 ; /* advance to next column of L */ } } } #endif /* ========================================================================== */ /* === LSOLVE (k) =========================================================== */ /* ========================================================================== */ static void LSOLVE (PREFIX,k) ( cholmod_factor *L, cholmod_dense *Y /* nr-by-n where nr is 1 to 4 */ ) { #ifndef REAL double yx [2] ; #ifdef ZOMPLEX double yz [1] ; double *Lz = L->z ; double *Xz = Y->z ; #endif double *Lx = L->x ; double *Xx = Y->x ; Int *Li = L->i ; Int *Lp = L->p ; Int *Lnz = L->nz ; Int i, j, n = L->n ; #endif ASSERT (L->xtype == Y->xtype) ; /* L and Y must have the same xtype */ ASSERT (L->n == Y->ncol) ; /* dimensions must match */ ASSERT (Y->nrow == Y->d) ; /* leading dimension of Y = # rows of Y */ ASSERT (L->xtype != CHOLMOD_PATTERN) ; /* L is not symbolic */ ASSERT (!(L->is_super)) ; /* L is simplicial LL' or LDL' */ #ifdef REAL /* ---------------------------------------------------------------------- */ /* solve a real linear system, with 1 to 4 RHS's and dynamic supernodes */ /* ---------------------------------------------------------------------- */ ASSERT (Y->nrow <= 4) ; switch (Y->nrow) { case 1: LSOLVE (PREFIX,1) (L, Y->x) ; break ; case 2: LSOLVE (PREFIX,2) (L, Y->x) ; break ; case 3: LSOLVE (PREFIX,3) (L, Y->x) ; break ; case 4: LSOLVE (PREFIX,4) (L, Y->x) ; break ; } #else /* ---------------------------------------------------------------------- */ /* solve a complex linear system, with just one right-hand-side */ /* ---------------------------------------------------------------------- */ ASSERT (Y->nrow == 1) ; for (j = 0 ; j < n ; j++) { /* get the start, end, and length of column j */ Int p = Lp [j] ; Int lnz = Lnz [j] ; Int pend = p + lnz ; /* y = X [j] ; */ ASSIGN (yx,yz,0, Xx,Xz,j) ; #ifdef LL /* y /= Lx [p] ; */ /* X [j] = y ; */ DIV_REAL (yx,yz,0, yx,yz,0, Lx,p) ; ASSIGN (Xx,Xz,j, yx,yz,0) ; #elif defined (LD) /* X [j] = y / Lx [p] ; */ DIV_REAL (Xx,Xz,j, yx,yz,0, Lx,p) ; #endif for (p++ ; p < pend ; p++) { /* X [Li [p]] -= Lx [p] * y ; */ i = Li [p] ; MULTSUB (Xx,Xz,i, Lx,Lz,p, yx,yz,0) ; } } #endif } /* prepare for the next inclusion of this file in cholmod_solve.c */ #undef LL #undef LD SuiteSparse/CHOLMOD/Cholesky/cholmod_solve.c0000644001170100242450000007610610616607410017631 0ustar davisfac/* ========================================================================== */ /* === Cholesky/cholmod_solve =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Solve one of the following systems: * * Ax=b 0: CHOLMOD_A also applies the permutation L->Perm * LDL'x=b 1: CHOLMOD_LDLt does not apply L->Perm * LDx=b 2: CHOLMOD_LD * DL'x=b 3: CHOLMOD_DLt * Lx=b 4: CHOLMOD_L * L'x=b 5: CHOLMOD_Lt * Dx=b 6: CHOLMOD_D * x=Pb 7: CHOLMOD_P apply a permutation (P is L->Perm) * x=P'b 8: CHOLMOD_Pt apply an inverse permutation * * The factorization can be simplicial LDL', simplicial LL', or supernodal LL'. * For an LL' factorization, D is the identity matrix. Thus CHOLMOD_LD and * CHOLMOD_L solve the same system if an LL' factorization was performed, * for example. * * The supernodal solver uses BLAS routines dtrsv, dgemv, dtrsm, and dgemm, * or their complex counterparts ztrsv, zgemv, ztrsm, and zgemm. * * If both L and B are real, then X is returned real. If either is complex * or zomplex, X is returned as either complex or zomplex, depending on the * Common->prefer_zomplex parameter. * * Supports any numeric xtype (pattern-only matrices not supported). * * This routine does not check to see if the diagonal of L or D is zero, * because sometimes a partial solve can be done with indefinite or singular * matrix. If you wish to check in your own code, test L->minor. If * L->minor == L->n, then the matrix has no zero diagonal entries. * If k = L->minor < L->n, then L(k,k) is zero for an LL' factorization, or * D(k,k) is zero for an LDL' factorization. * * This routine returns X as NULL only if it runs out of memory. If L is * indefinite or singular, then X may contain Inf's or NaN's, but it will * exist on output. */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "cholmod_cholesky.h" #ifndef NSUPERNODAL #include "cholmod_supernodal.h" #endif /* ========================================================================== */ /* === TEMPLATE ============================================================= */ /* ========================================================================== */ #define REAL #include "t_cholmod_solve.c" #define COMPLEX #include "t_cholmod_solve.c" #define ZOMPLEX #include "t_cholmod_solve.c" /* ========================================================================== */ /* === Permutation macro ==================================================== */ /* ========================================================================== */ /* If Perm is NULL, it is interpretted as the identity permutation */ #define P(k) ((Perm == NULL) ? (k) : Perm [k]) /* ========================================================================== */ /* === perm ================================================================= */ /* ========================================================================== */ /* Y = B (P (1:nrow), k1 : min (k1+ncols,ncol)-1) where B is nrow-by-ncol. * * Creates a permuted copy of a contiguous set of columns of B. * Y is already allocated on input. Y must be of sufficient size. Let nk be * the number of columns accessed in B. Y->xtype determines the complexity of * the result. * * If B is real and Y is complex (or zomplex), only the real part of B is * copied into Y. The imaginary part of Y is set to zero. * * If B is complex (or zomplex) and Y is real, both the real and imaginary and * parts of B are returned in Y. Y is returned as nrow-by-2*nk. The even * columns of Y contain the real part of B and the odd columns contain the * imaginary part of B. Y->nzmax must be >= 2*nrow*nk. Otherise, Y is * returned as nrow-by-nk with leading dimension nrow. Y->nzmax must be >= * nrow*nk. * * The case where the input (B) is real and the output (Y) is zomplex is * not used. */ static void perm ( /* ---- input ---- */ cholmod_dense *B, /* input matrix B */ Int *Perm, /* optional input permutation (can be NULL) */ Int k1, /* first column of B to copy */ Int ncols, /* last column to copy is min(k1+ncols,B->ncol)-1 */ /* ---- in/out --- */ cholmod_dense *Y /* output matrix Y, already allocated */ ) { double *Yx, *Yz, *Bx, *Bz ; Int k2, nk, p, k, j, nrow, ncol, d, dual, dj, j2 ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ ncol = B->ncol ; nrow = B->nrow ; k2 = MIN (k1+ncols, ncol) ; nk = MAX (k2 - k1, 0) ; dual = (Y->xtype == CHOLMOD_REAL && B->xtype != CHOLMOD_REAL) ? 2 : 1 ; d = B->d ; Bx = B->x ; Bz = B->z ; Yx = Y->x ; Yz = Y->z ; Y->nrow = nrow ; Y->ncol = dual*nk ; Y->d = nrow ; ASSERT (((Int) Y->nzmax) >= nrow*nk*dual) ; /* ---------------------------------------------------------------------- */ /* Y = B (P (1:nrow), k1:k2-1) */ /* ---------------------------------------------------------------------- */ switch (Y->xtype) { case CHOLMOD_REAL: switch (B->xtype) { case CHOLMOD_REAL: /* Y real, B real */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [k + j2] = Bx [p] ; /* real */ } } break ; case CHOLMOD_COMPLEX: /* Y real, B complex. Y is nrow-by-2*nk */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * 2 * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [k + j2 ] = Bx [2*p ] ; /* real */ Yx [k + j2 + nrow] = Bx [2*p+1] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y real, B zomplex. Y is nrow-by-2*nk */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * 2 * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [k + j2 ] = Bx [p] ; /* real */ Yx [k + j2 + nrow] = Bz [p] ; /* imag */ } } break ; } break ; case CHOLMOD_COMPLEX: switch (B->xtype) { case CHOLMOD_REAL: /* Y complex, B real */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * 2 * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [2*k + j2] = Bx [p] ; /* real */ Yx [2*k+1 + j2] = 0 ; /* imag */ } } break ; case CHOLMOD_COMPLEX: /* Y complex, B complex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * 2 * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [2*k + j2] = Bx [2*p ] ; /* real */ Yx [2*k+1 + j2] = Bx [2*p+1] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y complex, B zomplex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * 2 * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [2*k + j2] = Bx [p] ; /* real */ Yx [2*k+1 + j2] = Bz [p] ; /* imag */ } } break ; } break ; case CHOLMOD_ZOMPLEX: switch (B->xtype) { #if 0 case CHOLMOD_REAL: /* this case is not used */ break ; #endif case CHOLMOD_COMPLEX: /* Y zomplex, B complex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [k + j2] = Bx [2*p ] ; /* real */ Yz [k + j2] = Bx [2*p+1] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y zomplex, B zomplex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [k + j2] = Bx [p] ; /* real */ Yz [k + j2] = Bz [p] ; /* imag */ } } break ; } break ; } } /* ========================================================================== */ /* === iperm ================================================================ */ /* ========================================================================== */ /* X (P (1:nrow), k1 : min (k1+ncols,ncol)-1) = Y where X is nrow-by-ncol. * * Copies and permutes Y into a contiguous set of columns of X. X is already * allocated on input. Y must be of sufficient size. Let nk be the number * of columns accessed in X. X->xtype determines the complexity of the result. * * If X is real and Y is complex (or zomplex), only the real part of B is * copied into X. The imaginary part of Y is ignored. * * If X is complex (or zomplex) and Y is real, both the real and imaginary and * parts of Y are returned in X. Y is nrow-by-2*nk. The even * columns of Y contain the real part of B and the odd columns contain the * imaginary part of B. Y->nzmax must be >= 2*nrow*nk. Otherise, Y is * nrow-by-nk with leading dimension nrow. Y->nzmax must be >= nrow*nk. * * The case where the input (Y) is complex and the output (X) is real, * and the case where the input (Y) is zomplex and the output (X) is real, * are not used. */ static void iperm ( /* ---- input ---- */ cholmod_dense *Y, /* input matrix Y */ Int *Perm, /* optional input permutation (can be NULL) */ Int k1, /* first column of B to copy */ Int ncols, /* last column to copy is min(k1+ncols,B->ncol)-1 */ /* ---- in/out --- */ cholmod_dense *X /* output matrix X, already allocated */ ) { double *Yx, *Yz, *Xx, *Xz ; Int k2, nk, p, k, j, nrow, ncol, d, dj, j2 ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ ncol = X->ncol ; nrow = X->nrow ; k2 = MIN (k1+ncols, ncol) ; nk = MAX (k2 - k1, 0) ; d = X->d ; Xx = X->x ; Xz = X->z ; Yx = Y->x ; Yz = Y->z ; ASSERT (((Int) Y->nzmax) >= nrow*nk* ((X->xtype != CHOLMOD_REAL && Y->xtype == CHOLMOD_REAL) ? 2:1)) ; /* ---------------------------------------------------------------------- */ /* X (P (1:nrow), k1:k2-1) = Y */ /* ---------------------------------------------------------------------- */ switch (Y->xtype) { case CHOLMOD_REAL: switch (X->xtype) { case CHOLMOD_REAL: /* Y real, X real */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [p] = Yx [k + j2] ; /* real */ } } break ; case CHOLMOD_COMPLEX: /* Y real, X complex. Y is nrow-by-2*nk */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * 2 * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [2*p ] = Yx [k + j2 ] ; /* real */ Xx [2*p+1] = Yx [k + j2 + nrow] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y real, X zomplex. Y is nrow-by-2*nk */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * 2 * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [p] = Yx [k + j2 ] ; /* real */ Xz [p] = Yx [k + j2 + nrow] ; /* imag */ } } break ; } break ; case CHOLMOD_COMPLEX: switch (X->xtype) { #if 0 case CHOLMOD_REAL: /* this case is not used */ break ; #endif case CHOLMOD_COMPLEX: /* Y complex, X complex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * 2 * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [2*p ] = Yx [2*k + j2] ; /* real */ Xx [2*p+1] = Yx [2*k+1 + j2] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y complex, X zomplex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * 2 * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [p] = Yx [2*k + j2] ; /* real */ Xz [p] = Yx [2*k+1 + j2] ; /* imag */ } } break ; } break ; case CHOLMOD_ZOMPLEX: switch (X->xtype) { #if 0 case CHOLMOD_REAL: /* this case is not used */ break ; #endif case CHOLMOD_COMPLEX: /* Y zomplex, X complex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [2*p ] = Yx [k + j2] ; /* real */ Xx [2*p+1] = Yz [k + j2] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y zomplex, X zomplex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = nrow * (j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [p] = Yx [k + j2] ; /* real */ Xz [p] = Yz [k + j2] ; /* imag */ } } break ; } break ; } } /* ========================================================================== */ /* === ptrans =============================================================== */ /* ========================================================================== */ /* Y = B (P (1:nrow), k1 : min (k1+ncols,ncol)-1)' where B is nrow-by-ncol. * * Creates a permuted and transposed copy of a contiguous set of columns of B. * Y is already allocated on input. Y must be of sufficient size. Let nk be * the number of columns accessed in B. Y->xtype determines the complexity of * the result. * * If B is real and Y is complex (or zomplex), only the real part of B is * copied into Y. The imaginary part of Y is set to zero. * * If B is complex (or zomplex) and Y is real, both the real and imaginary and * parts of B are returned in Y. Y is returned as 2*nk-by-nrow. The even * rows of Y contain the real part of B and the odd rows contain the * imaginary part of B. Y->nzmax must be >= 2*nrow*nk. Otherise, Y is * returned as nk-by-nrow with leading dimension nk. Y->nzmax must be >= * nrow*nk. * * The array transpose is performed, not the complex conjugate transpose. */ static void ptrans ( /* ---- input ---- */ cholmod_dense *B, /* input matrix B */ Int *Perm, /* optional input permutation (can be NULL) */ Int k1, /* first column of B to copy */ Int ncols, /* last column to copy is min(k1+ncols,B->ncol)-1 */ /* ---- in/out --- */ cholmod_dense *Y /* output matrix Y, already allocated */ ) { double *Yx, *Yz, *Bx, *Bz ; Int k2, nk, p, k, j, nrow, ncol, d, dual, dj, j2 ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ ncol = B->ncol ; nrow = B->nrow ; k2 = MIN (k1+ncols, ncol) ; nk = MAX (k2 - k1, 0) ; dual = (Y->xtype == CHOLMOD_REAL && B->xtype != CHOLMOD_REAL) ? 2 : 1 ; d = B->d ; Bx = B->x ; Bz = B->z ; Yx = Y->x ; Yz = Y->z ; Y->nrow = dual*nk ; Y->ncol = nrow ; Y->d = dual*nk ; ASSERT (((Int) Y->nzmax) >= nrow*nk*dual) ; /* ---------------------------------------------------------------------- */ /* Y = B (P (1:nrow), k1:k2-1)' */ /* ---------------------------------------------------------------------- */ switch (Y->xtype) { case CHOLMOD_REAL: switch (B->xtype) { case CHOLMOD_REAL: /* Y real, B real */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = j-k1 ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [j2 + k*nk] = Bx [p] ; /* real */ } } break ; case CHOLMOD_COMPLEX: /* Y real, B complex. Y is 2*nk-by-nrow */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = 2*(j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [j2 + k*2*nk] = Bx [2*p ] ; /* real */ Yx [j2+1 + k*2*nk] = Bx [2*p+1] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y real, B zomplex. Y is 2*nk-by-nrow */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = 2*(j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [j2 + k*2*nk] = Bx [p] ; /* real */ Yx [j2+1 + k*2*nk] = Bz [p] ; /* imag */ } } break ; } break ; case CHOLMOD_COMPLEX: switch (B->xtype) { case CHOLMOD_REAL: /* Y complex, B real */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = 2*(j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [j2 + k*2*nk] = Bx [p] ; /* real */ Yx [j2+1 + k*2*nk] = 0 ; /* imag */ } } break ; case CHOLMOD_COMPLEX: /* Y complex, B complex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = 2*(j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [j2 + k*2*nk] = Bx [2*p ] ; /* real */ Yx [j2+1 + k*2*nk] = Bx [2*p+1] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y complex, B zomplex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = 2*(j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [j2 + k*2*nk] = Bx [p] ; /* real */ Yx [j2+1 + k*2*nk] = Bz [p] ; /* imag */ } } break ; } break ; case CHOLMOD_ZOMPLEX: switch (B->xtype) { case CHOLMOD_REAL: /* Y zomplex, B real */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = j-k1 ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [j2 + k*nk] = Bx [p] ; /* real */ Yz [j2 + k*nk] = 0 ; /* imag */ } } break ; case CHOLMOD_COMPLEX: /* Y zomplex, B complex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = j-k1 ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [j2 + k*nk] = Bx [2*p ] ; /* real */ Yz [j2 + k*nk] = Bx [2*p+1] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y zomplex, B zomplex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = j-k1 ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Yx [j2 + k*nk] = Bx [p] ; /* real */ Yz [j2 + k*nk] = Bz [p] ; /* imag */ } } break ; } break ; } } /* ========================================================================== */ /* === iptrans ============================================================== */ /* ========================================================================== */ /* X (P (1:nrow), k1 : min (k1+ncols,ncol)-1) = Y' where X is nrow-by-ncol. * * Copies into a permuted and transposed contiguous set of columns of X. * X is already allocated on input. Y must be of sufficient size. Let nk be * the number of columns accessed in X. X->xtype determines the complexity of * the result. * * If X is real and Y is complex (or zomplex), only the real part of Y is * copied into X. The imaginary part of Y is ignored. * * If X is complex (or zomplex) and Y is real, both the real and imaginary and * parts of X are returned in Y. Y is 2*nk-by-nrow. The even * rows of Y contain the real part of X and the odd rows contain the * imaginary part of X. Y->nzmax must be >= 2*nrow*nk. Otherise, Y is * nk-by-nrow with leading dimension nk. Y->nzmax must be >= nrow*nk. * * The case where Y is complex or zomplex, and X is real, is not used. * * The array transpose is performed, not the complex conjugate transpose. */ static void iptrans ( /* ---- input ---- */ cholmod_dense *Y, /* input matrix Y */ Int *Perm, /* optional input permutation (can be NULL) */ Int k1, /* first column of X to copy into */ Int ncols, /* last column to copy is min(k1+ncols,X->ncol)-1 */ /* ---- in/out --- */ cholmod_dense *X /* output matrix X, already allocated */ ) { double *Yx, *Yz, *Xx, *Xz ; Int k2, nk, p, k, j, nrow, ncol, d, dj, j2 ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ ncol = X->ncol ; nrow = X->nrow ; k2 = MIN (k1+ncols, ncol) ; nk = MAX (k2 - k1, 0) ; d = X->d ; Xx = X->x ; Xz = X->z ; Yx = Y->x ; Yz = Y->z ; ASSERT (((Int) Y->nzmax) >= nrow*nk* ((X->xtype != CHOLMOD_REAL && Y->xtype == CHOLMOD_REAL) ? 2:1)) ; /* ---------------------------------------------------------------------- */ /* X (P (1:nrow), k1:k2-1) = Y' */ /* ---------------------------------------------------------------------- */ switch (Y->xtype) { case CHOLMOD_REAL: switch (X->xtype) { case CHOLMOD_REAL: /* Y real, X real */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = j-k1 ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [p] = Yx [j2 + k*nk] ; /* real */ } } break ; case CHOLMOD_COMPLEX: /* Y real, X complex. Y is 2*nk-by-nrow */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = 2*(j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [2*p ] = Yx [j2 + k*2*nk] ; /* real */ Xx [2*p+1] = Yx [j2+1 + k*2*nk] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y real, X zomplex. Y is 2*nk-by-nrow */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = 2*(j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [p] = Yx [j2 + k*2*nk] ; /* real */ Xz [p] = Yx [j2+1 + k*2*nk] ; /* imag */ } } break ; } break ; case CHOLMOD_COMPLEX: switch (X->xtype) { #if 0 case CHOLMOD_REAL: /* this case is not used */ break ; #endif case CHOLMOD_COMPLEX: /* Y complex, X complex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = 2*(j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [2*p ] = Yx [j2 + k*2*nk] ; /* real */ Xx [2*p+1] = Yx [j2+1 + k*2*nk] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y complex, X zomplex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = 2*(j-k1) ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [p] = Yx [j2 + k*2*nk] ; /* real */ Xz [p] = Yx [j2+1 + k*2*nk] ; /* imag */ } } break ; } break ; case CHOLMOD_ZOMPLEX: switch (X->xtype) { #if 0 case CHOLMOD_REAL: /* this case is not used */ break ; #endif case CHOLMOD_COMPLEX: /* Y zomplex, X complex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = j-k1 ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [2*p ] = Yx [j2 + k*nk] ; /* real */ Xx [2*p+1] = Yz [j2 + k*nk] ; /* imag */ } } break ; case CHOLMOD_ZOMPLEX: /* Y zomplex, X zomplex */ for (j = k1 ; j < k2 ; j++) { dj = d*j ; j2 = j-k1 ; for (k = 0 ; k < nrow ; k++) { p = P(k) + dj ; Xx [p] = Yx [j2 + k*nk] ; /* real */ Xz [p] = Yz [j2 + k*nk] ; /* imag */ } } break ; } break ; } } /* ========================================================================== */ /* === cholmod_solve ======================================================== */ /* ========================================================================== */ /* Solve a linear system. * * The factorization can be simplicial LDL', simplicial LL', or supernodal LL'. * The Dx=b solve returns silently for the LL' factorizations (it is implicitly * identity). */ cholmod_dense *CHOLMOD(solve) ( /* ---- input ---- */ int sys, /* system to solve */ cholmod_factor *L, /* factorization to use */ cholmod_dense *B, /* right-hand-side */ /* --------------- */ cholmod_common *Common ) { cholmod_dense *Y = NULL, *X = NULL ; Int *Perm ; Int n, nrhs, ncols, ctype, xtype, k1, nr, ytype ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (L, NULL) ; RETURN_IF_NULL (B, NULL) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ; RETURN_IF_XTYPE_INVALID (B, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ; if (sys < CHOLMOD_A || sys > CHOLMOD_Pt) { ERROR (CHOLMOD_INVALID, "invalid system") ; return (NULL) ; } if (B->d < L->n || B->nrow != L->n) { ERROR (CHOLMOD_INVALID, "dimensions of L and B do not match") ; return (NULL) ; } DEBUG (CHOLMOD(dump_factor) (L, "L", Common)) ; DEBUG (CHOLMOD(dump_dense) (B, "B", Common)) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ if ((sys == CHOLMOD_P || sys == CHOLMOD_Pt || sys == CHOLMOD_A) && L->ordering != CHOLMOD_NATURAL) { Perm = L->Perm ; } else { /* do not use L->Perm; use the identity permutation instead */ Perm = NULL ; } nrhs = B->ncol ; n = L->n ; /* ---------------------------------------------------------------------- */ /* allocate the result X */ /* ---------------------------------------------------------------------- */ ctype = (Common->prefer_zomplex) ? CHOLMOD_ZOMPLEX : CHOLMOD_COMPLEX ; if (sys == CHOLMOD_P || sys == CHOLMOD_Pt) { /* x=Pb and x=P'b return X real if B is real; X is the preferred * complex/zcomplex type if B is complex or zomplex */ xtype = (B->xtype == CHOLMOD_REAL) ? CHOLMOD_REAL : ctype ; } else if (L->xtype == CHOLMOD_REAL && B->xtype == CHOLMOD_REAL) { /* X is real if both L and B are real */ xtype = CHOLMOD_REAL ; } else { /* X is complex, use the preferred complex/zomplex type */ xtype = ctype ; } X = CHOLMOD(allocate_dense) (n, nrhs, n, xtype, Common) ; if (Common->status < CHOLMOD_OK) { return (NULL) ; } /* ---------------------------------------------------------------------- */ /* solve using L, D, L', P, or some combination */ /* ---------------------------------------------------------------------- */ if (sys == CHOLMOD_P) { /* ------------------------------------------------------------------ */ /* x = P*b */ /* ------------------------------------------------------------------ */ perm (B, Perm, 0, nrhs, X) ; } else if (sys == CHOLMOD_Pt) { /* ------------------------------------------------------------------ */ /* x = P'*b */ /* ------------------------------------------------------------------ */ iperm (B, Perm, 0, nrhs, X) ; } else if (L->is_super) { /* ------------------------------------------------------------------ */ /* solve using a supernodal LL' factorization */ /* ------------------------------------------------------------------ */ #ifndef NSUPERNODAL Int blas_ok = TRUE ; /* allocate workspace */ cholmod_dense *E ; Int dual ; dual = (L->xtype == CHOLMOD_REAL && B->xtype != CHOLMOD_REAL) ? 2 : 1 ; Y = CHOLMOD(allocate_dense) (n, dual*nrhs, n, L->xtype, Common) ; E = CHOLMOD(allocate_dense) (dual*nrhs, L->maxesize, dual*nrhs, L->xtype, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_dense) (&X, Common) ; CHOLMOD(free_dense) (&Y, Common) ; CHOLMOD(free_dense) (&E, Common) ; return (NULL) ; } perm (B, Perm, 0, nrhs, Y) ; /* Y = P*B */ if (sys == CHOLMOD_A || sys == CHOLMOD_LDLt) { blas_ok = CHOLMOD(super_lsolve) (L, Y, E, Common) ; /* Y = L\Y */ blas_ok = blas_ok && CHOLMOD(super_ltsolve) (L, Y, E, Common) ; /* Y = L'\Y*/ } else if (sys == CHOLMOD_L || sys == CHOLMOD_LD) { blas_ok = CHOLMOD(super_lsolve) (L, Y, E, Common) ; /* Y = L\Y */ } else if (sys == CHOLMOD_Lt || sys == CHOLMOD_DLt) { blas_ok = CHOLMOD(super_ltsolve) (L, Y, E, Common) ; /* Y = L'\Y*/ } CHOLMOD(free_dense) (&E, Common) ; iperm (Y, Perm, 0, nrhs, X) ; /* X = P'*Y */ if (CHECK_BLAS_INT && !blas_ok) { /* Integer overflow in the BLAS. This is probably impossible, * since the BLAS were used to create the supernodal factorization. * It might be possible for the calls to the BLAS to differ between * factorization and forward/backsolves, however. This statement * is untested; it does not appear in the compiled code if * CHECK_BLAS_INT is true (when the same integer is used in CHOLMOD * and the BLAS. */ CHOLMOD(free_dense) (&X, Common) ; } #else /* CHOLMOD Supernodal module not installed */ ERROR (CHOLMOD_NOT_INSTALLED,"Supernodal module not installed") ; #endif } else { /* ------------------------------------------------------------------ */ /* solve using a simplicial LL' or LDL' factorization */ /* ------------------------------------------------------------------ */ if (L->xtype == CHOLMOD_REAL && B->xtype == CHOLMOD_REAL) { /* L, B, and Y are all real */ /* solve with up to 4 columns of B at a time */ ncols = 4 ; nr = MAX (4, nrhs) ; ytype = CHOLMOD_REAL ; } else if (L->xtype == CHOLMOD_REAL) { /* solve with one column of B (real/imag), at a time */ ncols = 1 ; nr = 2 ; ytype = CHOLMOD_REAL ; } else { /* L is complex or zomplex, B is real/complex/zomplex, Y has the * same complexity as L. Solve with one column of B at a time. */ ncols = 1 ; nr = 1 ; ytype = L->xtype ; } Y = CHOLMOD(allocate_dense) (nr, n, nr, ytype, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_dense) (&X, Common) ; CHOLMOD(free_dense) (&Y, Common) ; return (NULL) ; } for (k1 = 0 ; k1 < nrhs ; k1 += ncols) { /* -------------------------------------------------------------- */ /* Y = B (P, k1:k1+ncols-1)' = (P * B (:,...))' */ /* -------------------------------------------------------------- */ ptrans (B, Perm, k1, ncols, Y) ; /* -------------------------------------------------------------- */ /* solve Y = (L' \ (L \ Y'))', or other system, with template */ /* -------------------------------------------------------------- */ switch (L->xtype) { case CHOLMOD_REAL: r_simplicial_solver (sys, L, Y) ; break ; case CHOLMOD_COMPLEX: c_simplicial_solver (sys, L, Y) ; break ; case CHOLMOD_ZOMPLEX: z_simplicial_solver (sys, L, Y) ; break ; } /* -------------------------------------------------------------- */ /* X (P, k1:k2+ncols-1) = Y' */ /* -------------------------------------------------------------- */ iptrans (Y, Perm, k1, ncols, X) ; } } CHOLMOD(free_dense) (&Y, Common) ; DEBUG (CHOLMOD(dump_dense) (X, "X result", Common)) ; return (X) ; } #endif SuiteSparse/CHOLMOD/Cholesky/cholmod_etree.c0000644001170100242450000001604310537777315017615 0ustar davisfac/* ========================================================================== */ /* === Cholesky/cholmod_etree =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Compute the elimination tree of A or A'*A * * In the symmetric case, the upper triangular part of A is used. Entries not * in this part of the matrix are ignored. Computing the etree of a symmetric * matrix from just its lower triangular entries is not supported. * * In the unsymmetric case, all of A is used, and the etree of A'*A is computed. * * References: * * J. Liu, "A compact row storage scheme for Cholesky factors", ACM Trans. * Math. Software, vol 12, 1986, pp. 127-148. * * J. Liu, "The role of elimination trees in sparse factorization", SIAM J. * Matrix Analysis & Applic., vol 11, 1990, pp. 134-172. * * J. Gilbert, X. Li, E. Ng, B. Peyton, "Computing row and column counts for * sparse QR and LU factorization", BIT, vol 41, 2001, pp. 693-710. * * workspace: symmetric: Iwork (nrow), unsymmetric: Iwork (nrow+ncol) * * Supports any xtype (pattern, real, complex, or zomplex) */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "cholmod_cholesky.h" /* ========================================================================== */ /* === update_etree ========================================================= */ /* ========================================================================== */ static void update_etree ( /* inputs, not modified */ Int k, /* process the edge (k,i) in the input graph */ Int i, /* inputs, modified on output */ Int Parent [ ], /* Parent [t] = p if p is the parent of t */ Int Ancestor [ ] /* Ancestor [t] is the ancestor of node t in the partially-constructed etree */ ) { Int a ; for ( ; ; ) /* traverse the path from k to the root of the tree */ { a = Ancestor [k] ; if (a == i) { /* final ancestor reached; no change to tree */ return ; } /* perform path compression */ Ancestor [k] = i ; if (a == EMPTY) { /* final ancestor undefined; this is a new edge in the tree */ Parent [k] = i ; return ; } /* traverse up to the ancestor of k */ k = a ; } } /* ========================================================================== */ /* === cholmod_etree ======================================================== */ /* ========================================================================== */ /* Find the elimination tree of A or A'*A */ int CHOLMOD(etree) ( /* ---- input ---- */ cholmod_sparse *A, /* ---- output --- */ Int *Parent, /* size ncol. Parent [j] = p if p is the parent of j */ /* --------------- */ cholmod_common *Common ) { Int *Ap, *Ai, *Anz, *Ancestor, *Prev, *Iwork ; Int i, j, jprev, p, pend, nrow, ncol, packed, stype ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (Parent, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ stype = A->stype ; /* s = A->nrow + (stype ? 0 : A->ncol) */ s = CHOLMOD(add_size_t) (A->nrow, (stype ? 0 : A->ncol), &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (0, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; /* out of memory */ } ASSERT (CHOLMOD(dump_sparse) (A, "etree", Common) >= 0) ; Iwork = Common->Iwork ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ ncol = A->ncol ; /* the number of columns of A */ nrow = A->nrow ; /* the number of rows of A */ Ap = A->p ; /* size ncol+1, column pointers for A */ Ai = A->i ; /* the row indices of A */ Anz = A->nz ; /* number of nonzeros in each column of A */ packed = A->packed ; Ancestor = Iwork ; /* size ncol (i/i/l) */ for (j = 0 ; j < ncol ; j++) { Parent [j] = EMPTY ; Ancestor [j] = EMPTY ; } /* ---------------------------------------------------------------------- */ /* compute the etree */ /* ---------------------------------------------------------------------- */ if (stype > 0) { /* ------------------------------------------------------------------ */ /* symmetric (upper) case: compute etree (A) */ /* ------------------------------------------------------------------ */ for (j = 0 ; j < ncol ; j++) { /* for each row i in column j of triu(A), excluding the diagonal */ p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i < j) { update_etree (i, j, Parent, Ancestor) ; } } } } else if (stype == 0) { /* ------------------------------------------------------------------ */ /* unsymmetric case: compute etree (A'*A) */ /* ------------------------------------------------------------------ */ Prev = Iwork + ncol ; /* size nrow (i/i/l) */ for (i = 0 ; i < nrow ; i++) { Prev [i] = EMPTY ; } for (j = 0 ; j < ncol ; j++) { /* for each row i in column j of A */ p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { /* a graph is constructed dynamically with one path per row * of A. If the ith row of A contains column indices * (j1,j2,j3,j4) then the new graph has edges (j1,j2), (j2,j3), * and (j3,j4). When at node i of this path-graph, all edges * (jprev,j) are considered, where jprev Copyright (C) This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Also add information on how to contact you by electronic and paper mail. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the library, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the library `Frob' (a library for tweaking knobs) written by James Random Hacker. , 1 April 1990 Ty Coon, President of Vice That's all there is to it! SuiteSparse/CHOLMOD/Cholesky/cholmod_spsolve.c0000644001170100242450000002371610634317702020175 0ustar davisfac/* ========================================================================== */ /* === Cholesky/cholmod_spsolve ============================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Given an LL' or LDL' factorization of A, solve one of the following systems: * * Ax=b 0: CHOLMOD_A also applies the permutation L->Perm * LDL'x=b 1: CHOLMOD_LDLt does not apply L->Perm * LDx=b 2: CHOLMOD_LD * DL'x=b 3: CHOLMOD_DLt * Lx=b 4: CHOLMOD_L * L'x=b 5: CHOLMOD_Lt * Dx=b 6: CHOLMOD_D * x=Pb 7: CHOLMOD_P apply a permutation (P is L->Perm) * x=P'b 8: CHOLMOD_Pt apply an inverse permutation * * where b and x are sparse. If L and b are real, then x is real. Otherwise, * x is complex or zomplex, depending on the Common->prefer_zomplex parameter. * All xtypes of x and b are supported (real, complex, and zomplex). */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "cholmod_cholesky.h" /* ========================================================================== */ /* === EXPAND_AS_NEEDED ===================================================== */ /* ========================================================================== */ /* Double the size of the sparse matrix X, if we have run out of space. */ #define EXPAND_AS_NEEDED \ if (xnz >= nzmax) \ { \ nzmax *= 2 ; \ CHOLMOD(reallocate_sparse) (nzmax, X, Common) ; \ if (Common->status < CHOLMOD_OK) \ { \ CHOLMOD(free_sparse) (&X, Common) ; \ CHOLMOD(free_dense) (&X4, Common) ; \ CHOLMOD(free_dense) (&B4, Common) ; \ return (NULL) ; \ } \ Xi = X->i ; \ Xx = X->x ; \ Xz = X->z ; \ } /* ========================================================================== */ /* === cholmod_spolve ======================================================= */ /* ========================================================================== */ cholmod_sparse *CHOLMOD(spsolve) /* returns the sparse solution X */ ( /* ---- input ---- */ int sys, /* system to solve */ cholmod_factor *L, /* factorization to use */ cholmod_sparse *B, /* right-hand-side */ /* --------------- */ cholmod_common *Common ) { double x, z ; cholmod_dense *X4, *B4 ; cholmod_sparse *X ; double *Bx, *Bz, *Xx, *Xz, *B4x, *B4z, *X4x, *X4z ; Int *Bi, *Bp, *Xp, *Xi, *Bnz ; Int n, nrhs, q, p, i, j, jfirst, jlast, packed, block, pend, j_n, xtype ; size_t xnz, nzmax ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (L, NULL) ; RETURN_IF_NULL (B, NULL) ; RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ; RETURN_IF_XTYPE_INVALID (B, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ; if (L->n != B->nrow) { ERROR (CHOLMOD_INVALID, "dimensions of L and B do not match") ; return (NULL) ; } if (B->stype) { ERROR (CHOLMOD_INVALID, "B cannot be stored in symmetric mode") ; return (NULL) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace B4 and initial result X */ /* ---------------------------------------------------------------------- */ n = L->n ; nrhs = B->ncol ; /* X is real if both L and B are real, complex/zomplex otherwise */ xtype = (L->xtype == CHOLMOD_REAL && B->xtype == CHOLMOD_REAL) ? CHOLMOD_REAL : (Common->prefer_zomplex ? CHOLMOD_ZOMPLEX : CHOLMOD_COMPLEX) ; /* solve up to 4 columns at a time */ block = MIN (nrhs, 4) ; /* initial size of X is at most 4*n */ nzmax = n*block ; X = CHOLMOD(spzeros) (n, nrhs, nzmax, xtype, Common) ; B4 = CHOLMOD(zeros) (n, block, B->xtype, Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_sparse) (&X, Common) ; CHOLMOD(free_dense) (&B4, Common) ; return (NULL) ; } Bp = B->p ; Bi = B->i ; Bx = B->x ; Bz = B->z ; Bnz = B->nz ; packed = B->packed ; Xp = X->p ; Xi = X->i ; Xx = X->x ; Xz = X->z ; xnz = 0 ; B4x = B4->x ; B4z = B4->z ; /* ---------------------------------------------------------------------- */ /* solve in chunks of 4 columns at a time */ /* ---------------------------------------------------------------------- */ for (jfirst = 0 ; jfirst < nrhs ; jfirst += block) { /* ------------------------------------------------------------------ */ /* adjust the number of columns of B4 */ /* ------------------------------------------------------------------ */ jlast = MIN (nrhs, jfirst + block) ; B4->ncol = jlast - jfirst ; /* ------------------------------------------------------------------ */ /* scatter B(jfirst:jlast-1) into B4 */ /* ------------------------------------------------------------------ */ for (j = jfirst ; j < jlast ; j++) { p = Bp [j] ; pend = (packed) ? (Bp [j+1]) : (p + Bnz [j]) ; j_n = (j-jfirst)*n ; switch (B->xtype) { case CHOLMOD_REAL: for ( ; p < pend ; p++) { B4x [Bi [p] + j_n] = Bx [p] ; } break ; case CHOLMOD_COMPLEX: for ( ; p < pend ; p++) { q = Bi [p] + j_n ; B4x [2*q ] = Bx [2*p ] ; B4x [2*q+1] = Bx [2*p+1] ; } break ; case CHOLMOD_ZOMPLEX: for ( ; p < pend ; p++) { q = Bi [p] + j_n ; B4x [q] = Bx [p] ; B4z [q] = Bz [p] ; } break ; } } /* ------------------------------------------------------------------ */ /* solve the system (X4 = A\B4 or other system) */ /* ------------------------------------------------------------------ */ X4 = CHOLMOD(solve) (sys, L, B4, Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free_sparse) (&X, Common) ; CHOLMOD(free_dense) (&B4, Common) ; CHOLMOD(free_dense) (&X4, Common) ; return (NULL) ; } ASSERT (X4->xtype == xtype) ; X4x = X4->x ; X4z = X4->z ; /* ------------------------------------------------------------------ */ /* append the solution onto X */ /* ------------------------------------------------------------------ */ for (j = jfirst ; j < jlast ; j++) { Xp [j] = xnz ; j_n = (j-jfirst)*n ; if ( xnz + n <= nzmax) { /* ---------------------------------------------------------- */ /* X is guaranteed to be large enough */ /* ---------------------------------------------------------- */ switch (xtype) { case CHOLMOD_REAL: for (i = 0 ; i < n ; i++) { x = X4x [i + j_n] ; if (IS_NONZERO (x)) { Xi [xnz] = i ; Xx [xnz] = x ; xnz++ ; } } break ; case CHOLMOD_COMPLEX: for (i = 0 ; i < n ; i++) { x = X4x [2*(i + j_n) ] ; z = X4x [2*(i + j_n)+1] ; if (IS_NONZERO (x) || IS_NONZERO (z)) { Xi [xnz] = i ; Xx [2*xnz ] = x ; Xx [2*xnz+1] = z ; xnz++ ; } } break ; case CHOLMOD_ZOMPLEX: for (i = 0 ; i < n ; i++) { x = X4x [i + j_n] ; z = X4z [i + j_n] ; if (IS_NONZERO (x) || IS_NONZERO (z)) { Xi [xnz] = i ; Xx [xnz] = x ; Xz [xnz] = z ; xnz++ ; } } break ; } } else { /* ---------------------------------------------------------- */ /* X may need to increase in size */ /* ---------------------------------------------------------- */ switch (xtype) { case CHOLMOD_REAL: for (i = 0 ; i < n ; i++) { x = X4x [i + j_n] ; if (IS_NONZERO (x)) { EXPAND_AS_NEEDED ; Xi [xnz] = i ; Xx [xnz] = x ; xnz++ ; } } break ; case CHOLMOD_COMPLEX: for (i = 0 ; i < n ; i++) { x = X4x [2*(i + j_n) ] ; z = X4x [2*(i + j_n)+1] ; if (IS_NONZERO (x) || IS_NONZERO (z)) { EXPAND_AS_NEEDED ; Xi [xnz] = i ; Xx [2*xnz ] = x ; Xx [2*xnz+1] = z ; xnz++ ; } } break ; case CHOLMOD_ZOMPLEX: for (i = 0 ; i < n ; i++) { x = X4x [i + j_n] ; z = X4z [i + j_n] ; if (IS_NONZERO (x) || IS_NONZERO (z)) { EXPAND_AS_NEEDED ; Xi [xnz] = i ; Xx [xnz] = x ; Xz [xnz] = z ; xnz++ ; } } break ; } } } CHOLMOD(free_dense) (&X4, Common) ; /* ------------------------------------------------------------------ */ /* clear B4 for next iteration */ /* ------------------------------------------------------------------ */ if (jlast < nrhs) { for (j = jfirst ; j < jlast ; j++) { p = Bp [j] ; pend = (packed) ? (Bp [j+1]) : (p + Bnz [j]) ; j_n = (j-jfirst)*n ; switch (B->xtype) { case CHOLMOD_REAL: for ( ; p < pend ; p++) { B4x [Bi [p] + j_n] = 0 ; } break ; case CHOLMOD_COMPLEX: for ( ; p < pend ; p++) { q = Bi [p] + j_n ; B4x [2*q ] = 0 ; B4x [2*q+1] = 0 ; } break ; case CHOLMOD_ZOMPLEX: for ( ; p < pend ; p++) { q = Bi [p] + j_n ; B4x [q] = 0 ; B4z [q] = 0 ; } break ; } } } } Xp [nrhs] = xnz ; /* ---------------------------------------------------------------------- */ /* reduce X in size, free workspace, and return result */ /* ---------------------------------------------------------------------- */ ASSERT (xnz <= X->nzmax) ; CHOLMOD(reallocate_sparse) (xnz, X, Common) ; ASSERT (Common->status == CHOLMOD_OK) ; CHOLMOD(free_dense) (&B4, Common) ; return (X) ; } #endif SuiteSparse/CHOLMOD/Cholesky/cholmod_postorder.c0000644001170100242450000002301210537777324020524 0ustar davisfac/* ========================================================================== */ /* === Cholesky/cholmod_postorder =========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Compute the postorder of a tree. */ #ifndef NCHOLESKY #include "cholmod_internal.h" #include "cholmod_cholesky.h" /* ========================================================================== */ /* === dfs ================================================================== */ /* ========================================================================== */ /* The code below includes both a recursive and non-recursive depth-first-search * of a tree. The recursive code is simpler, but can lead to stack overflow. * It is left here for reference, to understand what the non-recursive code * is computing. To try the recursive version, uncomment the following * #define, or compile the code with -DRECURSIVE. Be aware that stack * overflow may occur. #define RECURSIVE */ #ifdef RECURSIVE /* recursive version: a working code for reference only, not actual use */ static Int dfs /* return the new value of k */ ( Int p, /* start a DFS at node p */ Int k, /* start the node numbering at k */ Int Post [ ], /* Post ordering, modified on output */ Int Head [ ], /* Head [p] = youngest child of p; EMPTY on output */ Int Next [ ], /* Next [j] = sibling of j; unmodified */ Int Pstack [ ] /* unused */ ) { Int j ; /* start a DFS at each child of node p */ for (j = Head [p] ; j != EMPTY ; j = Next [j]) { /* start a DFS at child node j */ k = dfs (j, k, Post, Head, Next, Pstack) ; } Post [k++] = p ; /* order node p as the kth node */ Head [p] = EMPTY ; /* link list p no longer needed */ return (k) ; /* the next node will be numbered k */ } #else /* non-recursive version for actual use */ static Int dfs /* return the new value of k */ ( Int p, /* start the DFS at a root node p */ Int k, /* start the node numbering at k */ Int Post [ ], /* Post ordering, modified on output */ Int Head [ ], /* Head [p] = youngest child of p; EMPTY on output */ Int Next [ ], /* Next [j] = sibling of j; unmodified */ Int Pstack [ ] /* workspace of size n, undefined on input or output */ ) { Int j, phead ; /* put the root node on the stack */ Pstack [0] = p ; phead = 0 ; /* while the stack is not empty, do: */ while (phead >= 0) { /* grab the node p from top of the stack and get its youngest child j */ p = Pstack [phead] ; j = Head [p] ; if (j == EMPTY) { /* all children of p ordered. remove p from stack and order it */ phead-- ; Post [k++] = p ; /* order node p as the kth node */ } else { /* leave p on the stack. Start a DFS at child node j by putting * j on the stack and removing j from the list of children of p. */ Head [p] = Next [j] ; Pstack [++phead] = j ; } } return (k) ; /* the next node will be numbered k */ } #endif /* ========================================================================== */ /* === cholmod_postorder ==================================================== */ /* ========================================================================== */ /* Postorder a tree. The tree is either an elimination tree (the output from * from cholmod_etree) or a component tree (from cholmod_nested_dissection). * * An elimination tree is a complete tree of n nodes with Parent [j] > j or * Parent [j] = EMPTY if j is a root. On output Post [0..n-1] is a complete * permutation vector. * * A component tree is a subset of 0..n-1. Parent [j] = -2 if node j is not * in the component tree. Parent [j] = EMPTY if j is a root of the component * tree, and Parent [j] is in the range 0 to n-1 if j is in the component * tree but not a root. On output, Post [k] is defined only for nodes in * the component tree. Post [k] = j if node j is the kth node in the * postordered component tree, where k is in the range 0 to the number of * components minus 1. * * Node j is ignored and not included in the postorder if Parent [j] < EMPTY. * * As a result, check_parent (Parent, n,...) may fail on input, since * cholmod_check_parent assumes Parent is an elimination tree. Similarly, * cholmod_check_perm (Post, ...) may fail on output, since Post is a partial * permutation if Parent is a component tree. * * An optional node weight can be given. When starting a postorder at node j, * the children of j are ordered in decreasing order of their weight. * If no weights are given (Weight is NULL) then children are ordered in * decreasing order of their node number. The weight of a node must be in the * range 0 to n-1. Weights outside that range are silently converted to that * range (weights < 0 are treated as zero, and weights >= n are treated as n-1). * * * workspace: Head (n), Iwork (2*n) */ UF_long CHOLMOD(postorder) /* return # of nodes postordered */ ( /* ---- input ---- */ Int *Parent, /* size n. Parent [j] = p if p is the parent of j */ size_t n, Int *Weight, /* size n, optional. Weight [j] is weight of node j */ /* ---- output --- */ Int *Post, /* size n. Post [k] = j is kth in postordered tree */ /* --------------- */ cholmod_common *Common ) { Int *Head, *Next, *Pstack, *Iwork ; Int j, p, k, w, nextj ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (Parent, EMPTY) ; RETURN_IF_NULL (Post, EMPTY) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = 2*n */ s = CHOLMOD(mult_size_t) (n, 2, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (EMPTY) ; } CHOLMOD(allocate_work) (n, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (EMPTY) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Head = Common->Head ; /* size n+1, initially all EMPTY */ Iwork = Common->Iwork ; Next = Iwork ; /* size n (i/i/l) */ Pstack = Iwork + n ; /* size n (i/i/l) */ /* ---------------------------------------------------------------------- */ /* construct a link list of children for each node */ /* ---------------------------------------------------------------------- */ if (Weight == NULL) { /* in reverse order so children are in ascending order in each list */ for (j = n-1 ; j >= 0 ; j--) { p = Parent [j] ; if (p >= 0 && p < ((Int) n)) { /* add j to the list of children for node p */ Next [j] = Head [p] ; Head [p] = j ; } } /* Head [p] = j if j is the youngest (least-numbered) child of p */ /* Next [j1] = j2 if j2 is the next-oldest sibling of j1 */ } else { /* First, construct a set of link lists according to Weight. * * Whead [w] = j if node j is the first node in bucket w. * Next [j1] = j2 if node j2 follows j1 in a link list. */ Int *Whead = Pstack ; /* use Pstack as workspace for Whead [ */ for (w = 0 ; w < ((Int) n) ; w++) { Whead [w] = EMPTY ; } /* do in forward order, so nodes that ties are ordered by node index */ for (j = 0 ; j < ((Int) n) ; j++) { p = Parent [j] ; if (p >= 0 && p < ((Int) n)) { w = Weight [j] ; w = MAX (0, w) ; w = MIN (w, ((Int) n) - 1) ; /* place node j at the head of link list for weight w */ Next [j] = Whead [w] ; Whead [w] = j ; } } /* traverse weight buckets, placing each node in its parent's list */ for (w = n-1 ; w >= 0 ; w--) { for (j = Whead [w] ; j != EMPTY ; j = nextj) { nextj = Next [j] ; /* put node j in the link list of its parent */ p = Parent [j] ; ASSERT (p >= 0 && p < ((Int) n)) ; Next [j] = Head [p] ; Head [p] = j ; } } /* Whead no longer needed ] */ /* Head [p] = j if j is the lightest child of p */ /* Next [j1] = j2 if j2 is the next-heaviest sibling of j1 */ } /* ---------------------------------------------------------------------- */ /* start a DFS at each root node of the etree */ /* ---------------------------------------------------------------------- */ k = 0 ; for (j = 0 ; j < ((Int) n) ; j++) { if (Parent [j] == EMPTY) { /* j is the root of a tree; start a DFS here */ k = dfs (j, k, Post, Head, Next, Pstack) ; } } /* this would normally be EMPTY already, unless Parent is invalid */ for (j = 0 ; j < ((Int) n) ; j++) { Head [j] = EMPTY ; } PRINT1 (("postordered "ID" nodes\n", k)) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; return (k) ; } #endif SuiteSparse/CHOLMOD/Cholesky/t_cholmod_rowfac.c0000644001170100242450000003234310635770603020306 0ustar davisfac/* ========================================================================== */ /* === Cholesky/t_cholmod_rowfac ============================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Template routine for cholmod_rowfac. Supports any numeric xtype * (real, complex, or zomplex). * * workspace: Iwork (n), Flag (n), Xwork (n if real, 2*n if complex) */ #include "cholmod_template.h" #ifdef MASK static int TEMPLATE (cholmod_rowfac_mask) #else static int TEMPLATE (cholmod_rowfac) #endif ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,f)' */ double beta [2], /* factorize beta*I+A or beta*I+AA' (beta [0] only) */ size_t kstart, /* first row to factorize */ size_t kend, /* last row to factorize is kend-1 */ #ifdef MASK /* These inputs are used for cholmod_rowfac_mask only */ Int *mask, /* size A->nrow. if mask[i] then W(i) is set to zero */ Int *RLinkUp, /* size A->nrow. link list of rows to compute */ #endif /* ---- in/out --- */ cholmod_factor *L, /* --------------- */ cholmod_common *Common ) { double yx [2], lx [2], fx [2], dk [1], di [1], fl = 0 ; #ifdef ZOMPLEX double yz [1], lz [1], fz [1] ; #endif double *Ax, *Az, *Lx, *Lz, *Wx, *Wz, *Fx, *Fz ; Int *Ap, *Anz, *Ai, *Lp, *Lnz, *Li, *Lnext, *Flag, *Stack, *Fp, *Fi, *Fnz, *Iwork ; Int i, p, k, t, pf, pfend, top, s, mark, pend, n, lnz, is_ll, multadds, use_dbound, packed, stype, Fpacked, sorted, nzmax, len, parent ; #ifndef REAL Int dk_imaginary ; #endif /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ PRINT1 (("\nin cholmod_rowfac, kstart %d kend %d stype %d\n", kstart, kend, A->stype)) ; DEBUG (CHOLMOD(dump_factor) (L, "Initial L", Common)) ; n = A->nrow ; stype = A->stype ; if (stype > 0) { /* symmetric upper case: F is not needed. It may be NULL */ Fp = NULL ; Fi = NULL ; Fx = NULL ; Fz = NULL ; Fnz = NULL ; Fpacked = TRUE ; } else { /* unsymmetric case: F is required. */ Fp = F->p ; Fi = F->i ; Fx = F->x ; Fz = F->z ; Fnz = F->nz ; Fpacked = F->packed ; } Ap = A->p ; /* size A->ncol+1, column pointers of A */ Ai = A->i ; /* size nz = Ap [A->ncol], row indices of A */ Ax = A->x ; /* size nz, numeric values of A */ Az = A->z ; Anz = A->nz ; packed = A->packed ; sorted = A->sorted ; use_dbound = IS_GT_ZERO (Common->dbound) ; /* get the current factors L (and D for LDL'); allocate space if needed */ is_ll = L->is_ll ; if (L->xtype == CHOLMOD_PATTERN) { /* ------------------------------------------------------------------ */ /* L is symbolic only; allocate and initialize L (and D for LDL') */ /* ------------------------------------------------------------------ */ /* workspace: none */ CHOLMOD(change_factor) (A->xtype, is_ll, FALSE, FALSE, TRUE, L, Common); if (Common->status < CHOLMOD_OK) { /* out of memory */ return (FALSE) ; } ASSERT (L->minor == (size_t) n) ; } else if (kstart == 0 && kend == (size_t) n) { /* ------------------------------------------------------------------ */ /* refactorization; reset L->nz and L->minor to restart factorization */ /* ------------------------------------------------------------------ */ L->minor = n ; Lnz = L->nz ; for (k = 0 ; k < n ; k++) { Lnz [k] = 1 ; } } ASSERT (is_ll == L->is_ll) ; ASSERT (L->xtype != CHOLMOD_PATTERN) ; DEBUG (CHOLMOD(dump_factor) (L, "L ready", Common)) ; DEBUG (CHOLMOD(dump_sparse) (A, "A ready", Common)) ; DEBUG (if (stype == 0) CHOLMOD(dump_sparse) (F, "F ready", Common)) ; /* inputs, can be modified on output: */ Lp = L->p ; /* size n+1 */ ASSERT (Lp != NULL) ; /* outputs, contents defined on input for incremental case only: */ Lnz = L->nz ; /* size n */ Lnext = L->next ; /* size n+2 */ Li = L->i ; /* size L->nzmax, can change in size */ Lx = L->x ; /* size L->nzmax or 2*L->nzmax, can change in size */ Lz = L->z ; /* size L->nzmax for zomplex case, can change in size */ nzmax = L->nzmax ; ASSERT (Lnz != NULL && Li != NULL && Lx != NULL) ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Iwork = Common->Iwork ; Stack = Iwork ; /* size n (i/i/l) */ Flag = Common->Flag ; /* size n, Flag [i] < mark must hold */ Wx = Common->Xwork ; /* size n if real, 2*n if complex or * zomplex. Xwork [i] == 0 must hold. */ Wz = Wx + n ; /* size n for zomplex case only */ mark = Common->mark ; ASSERT ((Int) Common->xworksize >= (L->xtype == CHOLMOD_REAL ? 1:2)*n) ; /* ---------------------------------------------------------------------- */ /* compute LDL' or LL' factorization by rows */ /* ---------------------------------------------------------------------- */ #ifdef MASK #define NEXT(k) k = RLinkUp [k] #else #define NEXT(k) k++ #endif for (k = kstart ; k < ((Int) kend) ; NEXT(k)) { PRINT1 (("\n===============K "ID" Lnz [k] "ID"\n", k, Lnz [k])) ; /* ------------------------------------------------------------------ */ /* compute pattern of kth row of L and scatter kth input column */ /* ------------------------------------------------------------------ */ /* column k of L is currently empty */ ASSERT (Lnz [k] == 1) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 2*n, Common)) ; top = n ; /* Stack is empty */ Flag [k] = mark ; /* do not include diagonal entry in Stack */ /* use Li [Lp [i]+1] for etree */ #define PARENT(i) (Lnz [i] > 1) ? (Li [Lp [i] + 1]) : EMPTY if (stype > 0) { /* scatter kth col of triu (beta*I+AA'), get pattern L(k,:) */ p = Ap [k] ; pend = (packed) ? (Ap [k+1]) : (p + Anz [k]) ; /* W [i] = Ax [i] ; scatter column of A */ #define SCATTER ASSIGN(Wx,Wz,i, Ax,Az,p) SUBTREE ; #undef SCATTER } else { /* scatter kth col of triu (beta*I+AA'), get pattern L(k,:) */ pf = Fp [k] ; pfend = (Fpacked) ? (Fp [k+1]) : (pf + Fnz [k]) ; for ( ; pf < pfend ; pf++) { /* get nonzero entry F (t,k) */ t = Fi [pf] ; /* fk = Fx [pf] */ ASSIGN (fx, fz, 0, Fx, Fz, pf) ; p = Ap [t] ; pend = (packed) ? (Ap [t+1]) : (p + Anz [t]) ; multadds = 0 ; /* W [i] += Ax [p] * fx ; scatter column of A*A' */ #define SCATTER MULTADD (Wx,Wz,i, Ax,Az,p, fx,fz,0) ; multadds++ ; SUBTREE ; #undef SCATTER #ifdef REAL fl += 2 * ((double) multadds) ; #else fl += 8 * ((double) multadds) ; #endif } } #undef PARENT /* ------------------------------------------------------------------ */ /* if mask is present, set the corresponding entries in W to zero */ /* ------------------------------------------------------------------ */ #ifdef MASK /* remove the dead element of Wx */ if (mask != NULL) { #if 0 /* older version */ for (p = n; p > top;) { i = Stack [--p] ; if ( mask [i] >= 0 ) { CLEAR (Wx,Wz,i) ; /* set W(i) to zero */ } } #endif for (s = top ; s < n ; s++) { i = Stack [s] ; if (mask [i] >= 0) { CLEAR (Wx,Wz,i) ; /* set W(i) to zero */ } } } #endif /* nonzero pattern of kth row of L is now in Stack [top..n-1]. * Flag [Stack [top..n-1]] is equal to mark, but no longer needed */ /* mark = CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; /* ------------------------------------------------------------------ */ /* compute kth row of L and store in column form */ /* ------------------------------------------------------------------ */ /* Solve L (0:k-1, 0:k-1) * y (0:k-1) = b (0:k-1) where * b (0:k) = A (0:k,k) or A(0:k,:) * F(:,k) is in W and Stack. * * For LDL' factorization: * L (k, 0:k-1) = y (0:k-1) ./ D (0:k-1) * D (k) = b (k) - L (k, 0:k-1) * y (0:k-1) * * For LL' factorization: * L (k, 0:k-1) = y (0:k-1) * L (k,k) = sqrt (b (k) - L (k, 0:k-1) * L (0:k-1, k)) */ /* dk = W [k] + beta */ ADD_REAL (dk,0, Wx,k, beta,0) ; #ifndef REAL /* In the unsymmetric case, the imaginary part of W[k] must be real, * since F is assumed to be the complex conjugate transpose of A. In * the symmetric case, W[k] is the diagonal of A. If the imaginary part * of W[k] is nonzero, then the Cholesky factorization cannot be * computed; A is not positive definite */ dk_imaginary = (stype > 0) ? (IMAG_IS_NONZERO (Wx,Wz,k)) : FALSE ; #endif /* W [k] = 0.0 ; */ CLEAR (Wx,Wz,k) ; for (s = top ; s < n ; s++) { /* get i for each nonzero entry L(k,i) */ i = Stack [s] ; /* y = W [i] ; */ ASSIGN (yx,yz,0, Wx,Wz,i) ; /* W [i] = 0.0 ; */ CLEAR (Wx,Wz,i) ; lnz = Lnz [i] ; p = Lp [i] ; ASSERT (lnz > 0 && Li [p] == i) ; pend = p + lnz ; /* di = Lx [p] ; the diagonal entry L or D(i,i), which is real */ ASSIGN_REAL (di,0, Lx,p) ; if (i >= (Int) L->minor || IS_ZERO (di [0])) { /* For the LL' factorization, L(i,i) is zero. For the LDL', * D(i,i) is zero. Skip column i of L, and set L(k,i) = 0. */ CLEAR (lx,lz,0) ; p = pend ; } else if (is_ll) { #ifdef REAL fl += 2 * ((double) (pend - p - 1)) + 3 ; #else fl += 8 * ((double) (pend - p - 1)) + 6 ; #endif /* forward solve using L (i:(k-1),i) */ /* divide by L(i,i), which must be real and nonzero */ /* y /= di [0] */ DIV_REAL (yx,yz,0, yx,yz,0, di,0) ; for (p++ ; p < pend ; p++) { /* W [Li [p]] -= Lx [p] * y ; */ MULTSUB (Wx,Wz,Li[p], Lx,Lz,p, yx,yz,0) ; } /* do not scale L; compute dot product for L(k,k) */ /* L(k,i) = conj(y) ; */ ASSIGN_CONJ (lx,lz,0, yx,yz,0) ; /* d -= conj(y) * y ; */ LLDOT (dk,0, yx,yz,0) ; } else { #ifdef REAL fl += 2 * ((double) (pend - p - 1)) + 3 ; #else fl += 8 * ((double) (pend - p - 1)) + 6 ; #endif /* forward solve using D (i,i) and L ((i+1):(k-1),i) */ for (p++ ; p < pend ; p++) { /* W [Li [p]] -= Lx [p] * y ; */ MULTSUB (Wx,Wz,Li[p], Lx,Lz,p, yx,yz,0) ; } /* Scale L (k,0:k-1) for LDL' factorization, compute D (k,k)*/ #ifdef REAL /* L(k,i) = y/d */ lx [0] = yx [0] / di [0] ; /* d -= L(k,i) * y */ dk [0] -= lx [0] * yx [0] ; #else /* L(k,i) = conj(y) ; */ ASSIGN_CONJ (lx,lz,0, yx,yz,0) ; /* L(k,i) /= di ; */ DIV_REAL (lx,lz,0, lx,lz,0, di,0) ; /* d -= conj(y) * y / di */ LDLDOT (dk,0, yx,yz,0, di,0) ; #endif } /* determine if column i of L can hold the new L(k,i) entry */ if (p >= Lp [Lnext [i]]) { /* column i needs to grow */ PRINT1 (("Factor Colrealloc "ID", old Lnz "ID"\n", i, Lnz [i])); if (!CHOLMOD(reallocate_column) (i, lnz + 1, L, Common)) { /* out of memory, L is now simplicial symbolic */ for (i = 0 ; i < n ; i++) { /* W [i] = 0 ; */ CLEAR (Wx,Wz,i) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, n, Common)) ; return (FALSE) ; } Li = L->i ; /* L->i, L->x, L->z may have moved */ Lx = L->x ; Lz = L->z ; p = Lp [i] + lnz ; /* contents of L->p changed */ ASSERT (p < Lp [Lnext [i]]) ; } /* store L (k,i) in the column form matrix of L */ Li [p] = k ; /* Lx [p] = L(k,i) ; */ ASSIGN (Lx,Lz,p, lx,lz,0) ; Lnz [i]++ ; } /* ------------------------------------------------------------------ */ /* ensure abs (d) >= dbound if dbound is given, and store it in L */ /* ------------------------------------------------------------------ */ p = Lp [k] ; Li [p] = k ; if (k >= (Int) L->minor) { /* the matrix is already not positive definite */ dk [0] = 0 ; } else if (use_dbound) { /* modify the diagonal to force LL' or LDL' to exist */ dk [0] = CHOLMOD(dbound) (is_ll ? fabs (dk [0]) : dk [0], Common) ; } else if ((is_ll ? (IS_LE_ZERO (dk [0])) : (IS_ZERO (dk [0]))) #ifndef REAL || dk_imaginary #endif ) { /* the matrix has just been found to be not positive definite */ dk [0] = 0 ; L->minor = k ; ERROR (CHOLMOD_NOT_POSDEF, "not positive definite") ; } if (is_ll) { /* this is counted as one flop, below */ dk [0] = sqrt (dk [0]) ; } /* Lx [p] = D(k,k) = d ; real part only */ ASSIGN_REAL (Lx,p, dk,0) ; CLEAR_IMAG (Lx,Lz,p) ; } #undef NEXT if (is_ll) fl += MAX ((Int) kend - (Int) kstart, 0) ; /* count sqrt's */ Common->rowfacfl = fl ; DEBUG (CHOLMOD(dump_factor) (L, "final cholmod_rowfac", Common)) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, n, Common)) ; return (TRUE) ; } #undef PATTERN #undef REAL #undef COMPLEX #undef ZOMPLEX SuiteSparse/CHOLMOD/MatrixOps/0000755001170100242450000000000010677243320014766 5ustar davisfacSuiteSparse/CHOLMOD/MatrixOps/cholmod_ssmult.c0000644001170100242450000003401510660074474020175 0ustar davisfac/* ========================================================================== */ /* === MatrixOps/cholmod_ssmult ============================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* C = A*B. Multiply two sparse matrices. * * A and B can be packed or unpacked, sorted or unsorted, and of any stype. * If A or B are symmetric, an internal unsymmetric copy is made first, however. * C is computed as if A and B are unsymmetric, and then if the stype input * parameter requests a symmetric form (upper or lower) the matrix is converted * into that form. * * C is returned as packed, and either unsorted or sorted, depending on the * "sorted" input parameter. If C is returned sorted, then either C = (B'*A')' * or C = (A*B)'' is computed, depending on the number of nonzeros in A, B, and * C. * * workspace: * if C unsorted: Flag (A->nrow), W (A->nrow) if values * if C sorted: Flag (B->ncol), W (B->ncol) if values * Iwork (max (A->ncol, A->nrow, B->nrow, B->ncol)) * allocates temporary copies for A, B, and C, if required. * * Only pattern and real matrices are supported. Complex and zomplex matrices * are supported only when the numerical values are not computed ("values" * is FALSE). */ #ifndef NMATRIXOPS #include "cholmod_internal.h" #include "cholmod_matrixops.h" /* ========================================================================== */ /* === cholmod_ssmult ======================================================= */ /* ========================================================================== */ cholmod_sparse *CHOLMOD(ssmult) ( /* ---- input ---- */ cholmod_sparse *A, /* left matrix to multiply */ cholmod_sparse *B, /* right matrix to multiply */ int stype, /* requested stype of C */ int values, /* TRUE: do numerical values, FALSE: pattern only */ int sorted, /* if TRUE then return C with sorted columns */ /* --------------- */ cholmod_common *Common ) { double bjt ; double *Ax, *Bx, *Cx, *W ; Int *Ap, *Anz, *Ai, *Bp, *Bnz, *Bi, *Cp, *Ci, *Flag ; cholmod_sparse *C, *A2, *B2, *A3, *B3, *C2 ; Int apacked, bpacked, j, i, pa, paend, pb, pbend, ncol, mark, cnz, t, p, nrow, anz, bnz, do_swap_and_transpose, n1, n2 ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; RETURN_IF_NULL (B, NULL) ; values = values && (A->xtype != CHOLMOD_PATTERN) && (B->xtype != CHOLMOD_PATTERN) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; RETURN_IF_XTYPE_INVALID (B, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; if (A->ncol != B->nrow) { /* inner dimensions must agree */ ERROR (CHOLMOD_INVALID, "A and B inner dimensions must match") ; return (NULL) ; } /* A and B must have the same numerical type if values is TRUE (both must * be CHOLMOD_REAL, this is implicitly checked above) */ Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ if (A->nrow <= 1) { /* C will be implicitly sorted, so no need to sort it here */ sorted = FALSE ; } if (sorted) { n1 = MAX (A->nrow, B->ncol) ; } else { n1 = A->nrow ; } n2 = MAX4 (A->ncol, A->nrow, B->nrow, B->ncol) ; CHOLMOD(allocate_work) (n1, n2, values ? n1 : 0, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1 : 0, Common)) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ /* convert A to unsymmetric, if necessary */ A2 = NULL ; B2 = NULL ; if (A->stype) { /* workspace: Iwork (max (A->nrow,A->ncol)) */ A2 = CHOLMOD(copy) (A, 0, values, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)) ; return (NULL) ; } A = A2 ; } /* convert B to unsymmetric, if necessary */ if (B->stype) { /* workspace: Iwork (max (B->nrow,B->ncol)) */ B2 = CHOLMOD(copy) (B, 0, values, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&A2, Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)) ; return (NULL) ; } B = B2 ; } ASSERT (CHOLMOD(dump_sparse) (A, "A", Common) >= 0) ; ASSERT (CHOLMOD(dump_sparse) (B, "B", Common) >= 0) ; /* get the A matrix */ Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; apacked = A->packed ; /* get the B matrix */ Bp = B->p ; Bnz = B->nz ; Bi = B->i ; Bx = B->x ; bpacked = B->packed ; /* get the size of C */ nrow = A->nrow ; ncol = B->ncol ; /* get workspace */ W = Common->Xwork ; /* size nrow, unused if values is FALSE */ Flag = Common->Flag ; /* size nrow, Flag [0..nrow-1] < mark on input*/ /* ---------------------------------------------------------------------- */ /* count the number of entries in the result C */ /* ---------------------------------------------------------------------- */ cnz = 0 ; for (j = 0 ; j < ncol ; j++) { /* clear the Flag array */ /* mark = CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; /* for each nonzero B(t,j) in column j, do: */ pb = Bp [j] ; pbend = (bpacked) ? (Bp [j+1]) : (pb + Bnz [j]) ; for ( ; pb < pbend ; pb++) { /* B(t,j) is nonzero */ t = Bi [pb] ; /* add the nonzero pattern of A(:,t) to the pattern of C(:,j) */ pa = Ap [t] ; paend = (apacked) ? (Ap [t+1]) : (pa + Anz [t]) ; for ( ; pa < paend ; pa++) { i = Ai [pa] ; if (Flag [i] != mark) { Flag [i] = mark ; cnz++ ; } } } if (cnz < 0) { break ; /* integer overflow case */ } } /* mark = CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; /* ---------------------------------------------------------------------- */ /* check for integer overflow */ /* ---------------------------------------------------------------------- */ if (cnz < 0) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)) ; return (NULL) ; } /* ---------------------------------------------------------------------- */ /* Determine how to return C sorted (if requested) */ /* ---------------------------------------------------------------------- */ do_swap_and_transpose = FALSE ; if (sorted) { /* Determine the best way to return C with sorted columns. Computing * C = (B'*A')' takes cnz + anz + bnz time (ignoring O(n) terms). * Sorting C when done, C = (A*B)'', takes 2*cnz time. Pick the one * with the least amount of work. */ anz = CHOLMOD(nnz) (A, Common) ; bnz = CHOLMOD(nnz) (B, Common) ; do_swap_and_transpose = (anz + bnz < cnz) ; if (do_swap_and_transpose) { /* -------------------------------------------------------------- */ /* C = (B'*A')' */ /* -------------------------------------------------------------- */ /* workspace: Iwork (A->nrow) */ A3 = CHOLMOD(ptranspose) (A, values, NULL, NULL, 0, Common) ; CHOLMOD(free_sparse) (&A2, Common) ; A2 = A3 ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)); return (NULL) ; } /* workspace: Iwork (B->nrow) */ B3 = CHOLMOD(ptranspose) (B, values, NULL, NULL, 0, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; B2 = B3 ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)); return (NULL) ; } A = B2 ; B = A2 ; /* get the new A matrix */ Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; apacked = A->packed ; /* get the new B matrix */ Bp = B->p ; Bnz = B->nz ; Bi = B->i ; Bx = B->x ; bpacked = B->packed ; /* get the size of C' */ nrow = A->nrow ; ncol = B->ncol ; } } /* ---------------------------------------------------------------------- */ /* allocate C */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(allocate_sparse) (nrow, ncol, cnz, FALSE, TRUE, 0, values ? A->xtype : CHOLMOD_PATTERN, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)) ; return (NULL) ; } Cp = C->p ; Ci = C->i ; Cx = C->x ; /* ---------------------------------------------------------------------- */ /* C = A*B */ /* ---------------------------------------------------------------------- */ cnz = 0 ; if (values) { /* pattern and values */ for (j = 0 ; j < ncol ; j++) { /* clear the Flag array */ /* mark = CHOLMOD(clear_flag (Common)) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; /* start column j of C */ Cp [j] = cnz ; /* for each nonzero B(t,j) in column j, do: */ pb = Bp [j] ; pbend = (bpacked) ? (Bp [j+1]) : (pb + Bnz [j]) ; for ( ; pb < pbend ; pb++) { /* B(t,j) is nonzero */ t = Bi [pb] ; bjt = Bx [pb] ; /* add the nonzero pattern of A(:,t) to the pattern of C(:,j) * and scatter the values into W */ pa = Ap [t] ; paend = (apacked) ? (Ap [t+1]) : (pa + Anz [t]) ; for ( ; pa < paend ; pa++) { i = Ai [pa] ; if (Flag [i] != mark) { Flag [i] = mark ; Ci [cnz++] = i ; } W [i] += Ax [pa] * bjt ; } } /* gather the values into C(:,j) */ for (p = Cp [j] ; p < cnz ; p++) { i = Ci [p] ; Cx [p] = W [i] ; W [i] = 0 ; } } } else { /* pattern only */ for (j = 0 ; j < ncol ; j++) { /* clear the Flag array */ /* mark = CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; mark = Common->mark ; /* start column j of C */ Cp [j] = cnz ; /* for each nonzero B(t,j) in column j, do: */ pb = Bp [j] ; pbend = (bpacked) ? (Bp [j+1]) : (pb + Bnz [j]) ; for ( ; pb < pbend ; pb++) { /* B(t,j) is nonzero */ t = Bi [pb] ; /* add the nonzero pattern of A(:,t) to the pattern of C(:,j) */ pa = Ap [t] ; paend = (apacked) ? (Ap [t+1]) : (pa + Anz [t]) ; for ( ; pa < paend ; pa++) { i = Ai [pa] ; if (Flag [i] != mark) { Flag [i] = mark ; Ci [cnz++] = i ; } } } } } Cp [ncol] = cnz ; ASSERT (MAX (1,cnz) == C->nzmax) ; /* ---------------------------------------------------------------------- */ /* clear workspace and free temporary matrices */ /* ---------------------------------------------------------------------- */ CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; /* CHOLMOD(clear_flag) (Common) ; */ CHOLMOD_CLEAR_FLAG (Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)) ; /* ---------------------------------------------------------------------- */ /* convert C to a symmetric upper/lower matrix if requested */ /* ---------------------------------------------------------------------- */ /* convert C in place, which cannot fail since no memory is allocated */ if (stype > 0) { /* C = triu (C), in place */ (void) CHOLMOD(band_inplace) (0, ncol, values, C, Common) ; C->stype = 1 ; } else if (stype < 0) { /* C = tril (C), in place */ (void) CHOLMOD(band_inplace) (-nrow, 0, values, C, Common) ; C->stype = -1 ; } ASSERT (Common->status >= CHOLMOD_OK) ; /* ---------------------------------------------------------------------- */ /* sort C, if requested */ /* ---------------------------------------------------------------------- */ if (sorted) { if (do_swap_and_transpose) { /* workspace: Iwork (C->ncol), which is A->nrow since C=(B'*A') */ C2 = CHOLMOD(ptranspose) (C, values, NULL, NULL, 0, Common) ; CHOLMOD(free_sparse) (&C, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)); return (NULL) ; } C = C2 ; } else { /* workspace: Iwork (max (C->nrow,C->ncol)) */ if (!CHOLMOD(sort) (C, Common)) { /* out of memory */ CHOLMOD(free_sparse) (&C, Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)); return (NULL) ; } } } /* ---------------------------------------------------------------------- */ /* return result */ /* ---------------------------------------------------------------------- */ DEBUG (CHOLMOD(dump_sparse) (C, "ssmult", Common) >= 0) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)) ; return (C) ; } #endif SuiteSparse/CHOLMOD/MatrixOps/cholmod_drop.c0000644001170100242450000001207210537777671017625 0ustar davisfac/* ========================================================================== */ /* === MatrixOps/cholmod_drop =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Drop small entries from A, and entries in the ignored part of A if A * is symmetric. None of the matrix operations drop small numerical entries * from a matrix, except for this one. NaN's and Inf's are kept. * * workspace: none * * Supports pattern and real matrices, complex and zomplex not supported. */ #ifndef NMATRIXOPS #include "cholmod_internal.h" #include "cholmod_matrixops.h" /* ========================================================================== */ /* === cholmod_drop ========================================================= */ /* ========================================================================== */ int CHOLMOD(drop) ( /* ---- input ---- */ double tol, /* keep entries with absolute value > tol */ /* ---- in/out --- */ cholmod_sparse *A, /* matrix to drop entries from */ /* --------------- */ cholmod_common *Common ) { double aij ; double *Ax ; Int *Ap, *Ai, *Anz ; Int packed, i, j, nrow, ncol, p, pend, nz, values ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_REAL, FALSE) ; Common->status = CHOLMOD_OK ; ASSERT (CHOLMOD(dump_sparse) (A, "A predrop", Common) >= 0) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Ap = A->p ; Ai = A->i ; Ax = A->x ; Anz = A->nz ; packed = A->packed ; ncol = A->ncol ; nrow = A->nrow ; values = (A->xtype != CHOLMOD_PATTERN) ; nz = 0 ; if (values) { /* ------------------------------------------------------------------ */ /* drop small numerical entries from A, and entries in ignored part */ /* ------------------------------------------------------------------ */ if (A->stype > 0) { /* -------------------------------------------------------------- */ /* A is symmetric, with just upper triangular part stored */ /* -------------------------------------------------------------- */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; Ap [j] = nz ; for ( ; p < pend ; p++) { i = Ai [p] ; aij = Ax [p] ; if (i <= j && (fabs (aij) > tol || IS_NAN (aij))) { Ai [nz] = i ; Ax [nz] = aij ; nz++ ; } } } } else if (A->stype < 0) { /* -------------------------------------------------------------- */ /* A is symmetric, with just lower triangular part stored */ /* -------------------------------------------------------------- */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; Ap [j] = nz ; for ( ; p < pend ; p++) { i = Ai [p] ; aij = Ax [p] ; if (i >= j && (fabs (aij) > tol || IS_NAN (aij))) { Ai [nz] = i ; Ax [nz] = aij ; nz++ ; } } } } else { /* -------------------------------------------------------------- */ /* both parts of A present, just drop small entries */ /* -------------------------------------------------------------- */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; Ap [j] = nz ; for ( ; p < pend ; p++) { i = Ai [p] ; aij = Ax [p] ; if (fabs (aij) > tol || IS_NAN (aij)) { Ai [nz] = i ; Ax [nz] = aij ; nz++ ; } } } } Ap [ncol] = nz ; /* reduce A->i and A->x in size */ ASSERT (MAX (1,nz) <= A->nzmax) ; CHOLMOD(reallocate_sparse) (nz, A, Common) ; ASSERT (Common->status >= CHOLMOD_OK) ; } else { /* ------------------------------------------------------------------ */ /* consider only the pattern of A */ /* ------------------------------------------------------------------ */ /* Note that cholmod_band_inplace calls cholmod_reallocate_sparse */ if (A->stype > 0) { CHOLMOD(band_inplace) (0, ncol, 0, A, Common) ; } else if (A->stype < 0) { CHOLMOD(band_inplace) (-nrow, 0, 0, A, Common) ; } } ASSERT (CHOLMOD(dump_sparse) (A, "A dropped", Common) >= 0) ; return (TRUE) ; } #endif SuiteSparse/CHOLMOD/MatrixOps/License.txt0000644001170100242450000000204510540000276017100 0ustar davisfacCHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis CHOLMOD is also available under other licenses; contact authors for details. http://www.cise.ufl.edu/research/sparse Note that this license is for the CHOLMOD/MatrixOps module only. All CHOLMOD modules are licensed separately. -------------------------------------------------------------------------------- This Module is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This Module is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. SuiteSparse/CHOLMOD/MatrixOps/cholmod_norm.c0000644001170100242450000002641210537777677017645 0ustar davisfac/* ========================================================================== */ /* === MatrixOps/cholmod_norm =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* r = norm (A), compute the infinity-norm, 1-norm, or 2-norm of a sparse or * dense matrix. Can compute the 2-norm only for a dense column vector. * Returns -1 if an error occurs. * * Pattern, real, complex, and zomplex sparse matrices are supported. */ #ifndef NMATRIXOPS #include "cholmod_internal.h" #include "cholmod_matrixops.h" /* ========================================================================== */ /* === abs_value ============================================================ */ /* ========================================================================== */ /* Compute the absolute value of a real, complex, or zomplex value */ static double abs_value ( int xtype, double *Ax, double *Az, Int p, cholmod_common *Common ) { double s = 0 ; switch (xtype) { case CHOLMOD_PATTERN: s = 1 ; break ; case CHOLMOD_REAL: s = fabs (Ax [p]) ; break ; case CHOLMOD_COMPLEX: s = Common->hypotenuse (Ax [2*p], Ax [2*p+1]) ; break ; case CHOLMOD_ZOMPLEX: s = Common->hypotenuse (Ax [p], Az [p]) ; break ; } return (s) ; } /* ========================================================================== */ /* === cholmod_norm_dense =================================================== */ /* ========================================================================== */ double CHOLMOD(norm_dense) ( /* ---- input ---- */ cholmod_dense *X, /* matrix to compute the norm of */ int norm, /* type of norm: 0: inf. norm, 1: 1-norm, 2: 2-norm */ /* --------------- */ cholmod_common *Common ) { double xnorm, s, x, z ; double *Xx, *Xz, *W ; Int nrow, ncol, d, i, j, use_workspace, xtype ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (X, EMPTY) ; RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, EMPTY) ; Common->status = CHOLMOD_OK ; ncol = X->ncol ; if (norm < 0 || norm > 2 || (norm == 2 && ncol > 1)) { ERROR (CHOLMOD_INVALID, "invalid norm") ; return (EMPTY) ; } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nrow = X->nrow ; d = X->d ; Xx = X->x ; Xz = X->z ; xtype = X->xtype ; /* ---------------------------------------------------------------------- */ /* allocate workspace, if needed */ /* ---------------------------------------------------------------------- */ W = NULL ; use_workspace = (norm == 0 && ncol > 4) ; if (use_workspace) { CHOLMOD(allocate_work) (0, 0, nrow, Common) ; W = Common->Xwork ; if (Common->status < CHOLMOD_OK) { /* oops, no workspace */ use_workspace = FALSE ; } } /* ---------------------------------------------------------------------- */ /* compute the norm */ /* ---------------------------------------------------------------------- */ xnorm = 0 ; if (use_workspace) { /* ------------------------------------------------------------------ */ /* infinity-norm = max row sum, using stride-1 access of X */ /* ------------------------------------------------------------------ */ DEBUG (for (i = 0 ; i < nrow ; i++) ASSERT (W [i] == 0)) ; /* this is faster than stride-d, but requires O(nrow) workspace */ for (j = 0 ; j < ncol ; j++) { for (i = 0 ; i < nrow ; i++) { W [i] += abs_value (xtype, Xx, Xz, i+j*d, Common) ; } } for (i = 0 ; i < nrow ; i++) { s = W [i] ; if ((IS_NAN (s) || s > xnorm) && !IS_NAN (xnorm)) { xnorm = s ; } W [i] = 0 ; } } else if (norm == 0) { /* ------------------------------------------------------------------ */ /* infinity-norm = max row sum, using stride-d access of X */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < nrow ; i++) { s = 0 ; for (j = 0 ; j < ncol ; j++) { s += abs_value (xtype, Xx, Xz, i+j*d, Common) ; } if ((IS_NAN (s) || s > xnorm) && !IS_NAN (xnorm)) { xnorm = s ; } } } else if (norm == 1) { /* ------------------------------------------------------------------ */ /* 1-norm = max column sum */ /* ------------------------------------------------------------------ */ for (j = 0 ; j < ncol ; j++) { s = 0 ; for (i = 0 ; i < nrow ; i++) { s += abs_value (xtype, Xx, Xz, i+j*d, Common) ; } if ((IS_NAN (s) || s > xnorm) && !IS_NAN (xnorm)) { xnorm = s ; } } } else { /* ------------------------------------------------------------------ */ /* 2-norm = sqrt (sum (X.^2)) */ /* ------------------------------------------------------------------ */ switch (xtype) { case CHOLMOD_REAL: for (i = 0 ; i < nrow ; i++) { x = Xx [i] ; xnorm += x*x ; } break ; case CHOLMOD_COMPLEX: for (i = 0 ; i < nrow ; i++) { x = Xx [2*i ] ; z = Xx [2*i+1] ; xnorm += x*x + z*z ; } break ; case CHOLMOD_ZOMPLEX: for (i = 0 ; i < nrow ; i++) { x = Xx [i] ; z = Xz [i] ; xnorm += x*x + z*z ; } break ; } xnorm = sqrt (xnorm) ; } /* ---------------------------------------------------------------------- */ /* return result */ /* ---------------------------------------------------------------------- */ return (xnorm) ; } /* ========================================================================== */ /* === cholmod_norm_sparse ================================================== */ /* ========================================================================== */ double CHOLMOD(norm_sparse) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to compute the norm of */ int norm, /* type of norm: 0: inf. norm, 1: 1-norm */ /* --------------- */ cholmod_common *Common ) { double anorm, s ; double *Ax, *Az, *W ; Int *Ap, *Ai, *Anz ; Int i, j, p, pend, nrow, ncol, packed, xtype ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (A, EMPTY) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ; Common->status = CHOLMOD_OK ; ncol = A->ncol ; nrow = A->nrow ; if (norm < 0 || norm > 1) { ERROR (CHOLMOD_INVALID, "invalid norm") ; return (EMPTY) ; } if (A->stype && nrow != ncol) { ERROR (CHOLMOD_INVALID, "matrix invalid") ; return (EMPTY) ; } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Ap = A->p ; Ai = A->i ; Ax = A->x ; Az = A->z ; Anz = A->nz ; packed = A->packed ; xtype = A->xtype ; /* ---------------------------------------------------------------------- */ /* allocate workspace, if needed */ /* ---------------------------------------------------------------------- */ W = NULL ; if (A->stype || norm == 0) { CHOLMOD(allocate_work) (0, 0, nrow, Common) ; W = Common->Xwork ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (EMPTY) ; } DEBUG (for (i = 0 ; i < nrow ; i++) ASSERT (W [i] == 0)) ; } /* ---------------------------------------------------------------------- */ /* compute the norm */ /* ---------------------------------------------------------------------- */ anorm = 0 ; if (A->stype > 0) { /* ------------------------------------------------------------------ */ /* A is symmetric with upper triangular part stored */ /* ------------------------------------------------------------------ */ /* infinity-norm = 1-norm = max row/col sum */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; s = abs_value (xtype, Ax, Az, p, Common) ; if (i == j) { W [i] += s ; } else if (i < j) { W [i] += s ; W [j] += s ; } } } } else if (A->stype < 0) { /* ------------------------------------------------------------------ */ /* A is symmetric with lower triangular part stored */ /* ------------------------------------------------------------------ */ /* infinity-norm = 1-norm = max row/col sum */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; s = abs_value (xtype, Ax, Az, p, Common) ; if (i == j) { W [i] += s ; } else if (i > j) { W [i] += s ; W [j] += s ; } } } } else if (norm == 0) { /* ------------------------------------------------------------------ */ /* A is unsymmetric, compute the infinity-norm */ /* ------------------------------------------------------------------ */ /* infinity-norm = max row sum */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { W [Ai [p]] += abs_value (xtype, Ax, Az, p, Common) ; } } } else { /* ------------------------------------------------------------------ */ /* A is unsymmetric, compute the 1-norm */ /* ------------------------------------------------------------------ */ /* 1-norm = max column sum */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; if (xtype == CHOLMOD_PATTERN) { s = pend - p ; } else { s = 0 ; for ( ; p < pend ; p++) { s += abs_value (xtype, Ax, Az, p, Common) ; } } if ((IS_NAN (s) || s > anorm) && !IS_NAN (anorm)) { anorm = s ; } } } /* ---------------------------------------------------------------------- */ /* compute the max row sum */ /* ---------------------------------------------------------------------- */ if (A->stype || norm == 0) { for (i = 0 ; i < nrow ; i++) { s = W [i] ; if ((IS_NAN (s) || s > anorm) && !IS_NAN (anorm)) { anorm = s ; } W [i] = 0 ; } } /* ---------------------------------------------------------------------- */ /* return result */ /* ---------------------------------------------------------------------- */ return (anorm) ; } #endif SuiteSparse/CHOLMOD/MatrixOps/gpl.txt0000644001170100242450000004313310253404124016304 0ustar davisfac GNU GENERAL PUBLIC LICENSE Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. 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SuiteSparse/CHOLMOD/MatrixOps/cholmod_scale.c0000644001170100242450000001441210537777717017751 0ustar davisfac/* ========================================================================== */ /* === MatrixOps/cholmod_scale ============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* scale a matrix: A = diag(s)*A, A*diag(s), s*A, or diag(s)*A*diag(s) * * A can be of any type (packed/unpacked, upper/lower/unsymmetric). * The symmetry of A is ignored; all entries in the matrix are modified. * * If A is m-by-n unsymmetric but scaled symmtrically, the result is * A = diag (s (1:m)) * A * diag (s (1:n)). * * Note: diag(s) should be interpretted as spdiags(s,0,n,n) where n=length(s). * * Row or column scaling of a symmetric matrix still results in a symmetric * matrix, since entries are still ignored by other routines. * For example, when row-scaling a symmetric matrix where just the upper * triangular part is stored (and lower triangular entries ignored) * A = diag(s)*triu(A) is performed, where the result A is also * symmetric-upper. This has the effect of modifying the implicit lower * triangular part. In MATLAB notation: * * U = diag(s)*triu(A) ; * L = tril (U',-1) * A = L + U ; * * The scale parameter determines the kind of scaling to perform: * * CHOLMOD_SCALAR: s[0]*A * CHOLMOD_ROW: diag(s)*A * CHOLMOD_COL: A*diag(s) * CHOLMOD_SYM: diag(s)*A*diag(s) * * The size of S depends on the scale parameter: * * CHOLMOD_SCALAR: size 1 * CHOLMOD_ROW: size nrow-by-1 or 1-by-nrow * CHOLMOD_COL: size ncol-by-1 or 1-by-ncol * CHOLMOD_SYM: size max(nrow,ncol)-by-1, or 1-by-max(nrow,ncol) * * workspace: none * * Only real matrices are supported. */ #ifndef NMATRIXOPS #include "cholmod_internal.h" #include "cholmod_matrixops.h" /* ========================================================================== */ /* === cholmod_scale ======================================================== */ /* ========================================================================== */ int CHOLMOD(scale) ( /* ---- input ---- */ cholmod_dense *S, /* scale factors (scalar or vector) */ int scale, /* type of scaling to compute */ /* ---- in/out --- */ cholmod_sparse *A, /* matrix to scale */ /* --------------- */ cholmod_common *Common ) { double t ; double *Ax, *s ; Int *Ap, *Anz, *Ai ; Int packed, j, ncol, nrow, p, pend, sncol, snrow, nn, ok ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (S, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ; RETURN_IF_XTYPE_INVALID (S, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ; ncol = A->ncol ; nrow = A->nrow ; sncol = S->ncol ; snrow = S->nrow ; if (scale == CHOLMOD_SCALAR) { ok = (snrow == 1 && sncol == 1) ; } else if (scale == CHOLMOD_ROW) { ok = (snrow == nrow && sncol == 1) || (snrow == 1 && sncol == nrow) ; } else if (scale == CHOLMOD_COL) { ok = (snrow == ncol && sncol == 1) || (snrow == 1 && sncol == ncol) ; } else if (scale == CHOLMOD_SYM) { nn = MAX (nrow, ncol) ; ok = (snrow == nn && sncol == 1) || (snrow == 1 && sncol == nn) ; } else { /* scale invalid */ ERROR (CHOLMOD_INVALID, "invalid scaling option") ; return (FALSE) ; } if (!ok) { /* S is wrong size */ ERROR (CHOLMOD_INVALID, "invalid scale factors") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; packed = A->packed ; s = S->x ; /* ---------------------------------------------------------------------- */ /* scale the matrix */ /* ---------------------------------------------------------------------- */ if (scale == CHOLMOD_ROW) { /* ------------------------------------------------------------------ */ /* A = diag(s)*A, row scaling */ /* ------------------------------------------------------------------ */ for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { Ax [p] *= s [Ai [p]] ; } } } else if (scale == CHOLMOD_COL) { /* ------------------------------------------------------------------ */ /* A = A*diag(s), column scaling */ /* ------------------------------------------------------------------ */ for (j = 0 ; j < ncol ; j++) { t = s [j] ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { Ax [p] *= t ; } } } else if (scale == CHOLMOD_SYM) { /* ------------------------------------------------------------------ */ /* A = diag(s)*A*diag(s), symmetric scaling */ /* ------------------------------------------------------------------ */ for (j = 0 ; j < ncol ; j++) { t = s [j] ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { Ax [p] *= t * s [Ai [p]] ; } } } else if (scale == CHOLMOD_SCALAR) { /* ------------------------------------------------------------------ */ /* A = s[0] * A, scalar scaling */ /* ------------------------------------------------------------------ */ t = s [0] ; for (j = 0 ; j < ncol ; j++) { p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { Ax [p] *= t ; } } } ASSERT (CHOLMOD(dump_sparse) (A, "A scaled", Common) >= 0) ; return (TRUE) ; } #endif SuiteSparse/CHOLMOD/MatrixOps/cholmod_submatrix.c0000644001170100242450000003163710677243305020672 0ustar davisfac/* ========================================================================== */ /* === MatrixOps/cholmod_submatrix ========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* C = A (rset,cset), where C becomes length(rset)-by-length(cset) in dimension. * rset and cset can have duplicate entries. A and C must be unsymmetric. C * is packed. If the sorted flag is TRUE on input, or rset is sorted and A is * sorted, then C is sorted; otherwise C is unsorted. * * A NULL rset or cset means "[ ]" in MATLAB notation. * If the length of rset or cset is negative, it denotes ":" in MATLAB notation. * * For permuting a matrix, this routine is an alternative to cholmod_ptranspose * (which permutes and transposes a matrix and can work on symmetric matrices). * * The time taken by this routine is O(A->nrow) if the Common workspace needs * to be initialized, plus O(C->nrow + C->ncol + nnz (A (:,cset))). Thus, if C * is small and the workspace is not initialized, the time can be dominated by * the call to cholmod_allocate_work. However, once the workspace is * allocated, subsequent calls take less time. * * workspace: Iwork (max (A->nrow + length (rset), length (cset))). * allocates temporary copy of C if it is to be returned sorted. * * Future work: A common case occurs where A has sorted columns, and rset is in * the form lo:hi in MATLAB notation. This routine could exploit that case * to run even faster when the matrix is sorted, particularly when lo is small. * * Only pattern and real matrices are supported. Complex and zomplex matrices * are supported only when "values" is FALSE. */ #ifndef NMATRIXOPS #include "cholmod_internal.h" #include "cholmod_matrixops.h" /* ========================================================================== */ /* === check_subset ========================================================= */ /* ========================================================================== */ /* Check the rset or cset, and return TRUE if valid, FALSE if invalid */ static int check_subset (Int *set, Int len, Int n) { Int k ; if (set == NULL) { return (TRUE) ; } for (k = 0 ; k < len ; k++) { if (set [k] < 0 || set [k] >= n) { return (FALSE) ; } } return (TRUE) ; } /* ========================================================================== */ /* === cholmod_submatrix ==================================================== */ /* ========================================================================== */ cholmod_sparse *CHOLMOD(submatrix) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to subreference */ Int *rset, /* set of row indices, duplicates OK */ UF_long rsize, /* size of rset, or -1 for ":" */ Int *cset, /* set of column indices, duplicates OK */ UF_long csize, /* size of cset, or -1 for ":" */ int values, /* if TRUE compute the numerical values of C */ int sorted, /* if TRUE then return C with sorted columns */ /* --------------- */ cholmod_common *Common ) { double aij = 0 ; double *Ax, *Cx ; Int *Ap, *Ai, *Anz, *Ci, *Cp, *Head, *Rlen, *Rnext, *Iwork ; cholmod_sparse *C ; Int packed, ancol, anrow, cnrow, cncol, nnz, i, j, csorted, ilast, p, pend, pdest, ci, cj, head, nr, nc ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; values = (values && (A->xtype != CHOLMOD_PATTERN)) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; if (A->stype != 0) { /* A must be unsymmetric */ ERROR (CHOLMOD_INVALID, "symmetric upper or lower case not supported") ; return (NULL) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ ancol = A->ncol ; anrow = A->nrow ; nr = rsize ; nc = csize ; if (rset == NULL) { /* nr = 0 denotes rset = [ ], nr < 0 denotes rset = 0:anrow-1 */ nr = (nr < 0) ? (-1) : 0 ; } if (cset == NULL) { /* nr = 0 denotes cset = [ ], nr < 0 denotes cset = 0:ancol-1 */ nc = (nc < 0) ? (-1) : 0 ; } cnrow = (nr < 0) ? anrow : nr ; /* negative rset means rset = 0:anrow-1 */ cncol = (nc < 0) ? ancol : nc ; /* negative cset means cset = 0:ancol-1 */ if (nr < 0 && nc < 0) { /* ------------------------------------------------------------------ */ /* C = A (:,:), use cholmod_copy instead */ /* ------------------------------------------------------------------ */ /* workspace: Iwork (max (C->nrow,C->ncol)) */ PRINT1 (("submatrix C = A (:,:)\n")) ; C = CHOLMOD(copy) (A, 0, values, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } return (C) ; } PRINT1 (("submatrix nr "ID" nc "ID" Cnrow "ID" Cncol "ID"" " Anrow "ID" Ancol "ID"\n", nr, nc, cnrow, cncol, anrow, ancol)) ; /* s = MAX3 (anrow+MAX(0,nr), cncol, cnrow) ; */ s = CHOLMOD(add_size_t) (anrow, MAX (0,nr), &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (NULL) ; } s = MAX3 (s, ((size_t) cncol), ((size_t) cnrow)) ; CHOLMOD(allocate_work) (anrow, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; packed = A->packed ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Head = Common->Head ; /* size anrow */ Iwork = Common->Iwork ; Rlen = Iwork ; /* size anrow (i/i/l) */ Rnext = Iwork + anrow ; /* size nr (i/i/l), not used if nr < 0 */ /* ---------------------------------------------------------------------- */ /* construct inverse of rset and compute nnz (C) */ /* ---------------------------------------------------------------------- */ PRINT1 (("nr "ID" nc "ID"\n", nr, nc)) ; PRINT1 (("anrow "ID" ancol "ID"\n", anrow, ancol)) ; PRINT1 (("cnrow "ID" cncol "ID"\n", cnrow, cncol)) ; DEBUG (for (i = 0 ; i < nr ; i++) PRINT2 (("rset ["ID"] = "ID"\n", i, rset [i]))); DEBUG (for (i = 0 ; i < nc ; i++) PRINT2 (("cset ["ID"] = "ID"\n", i, cset [i]))); /* C is sorted if A and rset are sorted, or if C has one row or less */ csorted = A->sorted || (cnrow <= 1) ; if (!check_subset (rset, nr, anrow)) { ERROR (CHOLMOD_INVALID, "invalid rset") ; return (NULL) ; } if (!check_subset (cset, nc, ancol)) { ERROR (CHOLMOD_INVALID, "invalid cset") ; return (NULL) ; } nnz = 0 ; if (nr < 0) { /* C = A (:,cset) where cset = [ ] or cset is not empty */ ASSERT (IMPLIES (cncol > 0, cset != NULL)) ; for (cj = 0 ; cj < cncol ; cj++) { /* construct column cj of C, which is column j of A */ j = cset [cj] ; nnz += (packed) ? (Ap [j+1] - Ap [j]) : MAX (0, Anz [j]) ; } } else { /* C = A (rset,cset), where rset is not empty but cset might be empty */ /* create link lists in reverse order to preserve natural order */ ilast = anrow ; for (ci = nr-1 ; ci >= 0 ; ci--) { /* row i of A becomes row ci of C; add ci to ith link list */ i = rset [ci] ; head = Head [i] ; Rlen [i] = (head == EMPTY) ? 1 : (Rlen [i] + 1) ; Rnext [ci] = head ; Head [i] = ci ; if (i > ilast) { /* row indices in columns of C will not be sorted */ csorted = FALSE ; } ilast = i ; } #ifndef NDEBUG for (i = 0 ; i < anrow ; i++) { Int k = 0 ; Int rlen = (Head [i] != EMPTY) ? Rlen [i] : -1 ; PRINT1 (("Row "ID" Rlen "ID": ", i, rlen)) ; for (ci = Head [i] ; ci != EMPTY ; ci = Rnext [ci]) { k++ ; PRINT2 ((""ID" ", ci)) ; } PRINT1 (("\n")) ; ASSERT (IMPLIES (Head [i] != EMPTY, k == Rlen [i])) ; } #endif /* count nonzeros in C */ for (cj = 0 ; cj < cncol ; cj++) { /* count rows in column cj of C, which is column j of A */ j = (nc < 0) ? cj : (cset [cj]) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { /* row i of A becomes multiple rows (ci) of C */ i = Ai [p] ; ASSERT (i >= 0 && i < anrow) ; if (Head [i] != EMPTY) { nnz += Rlen [i] ; } } } } PRINT1 (("nnz (C) "ID"\n", nnz)) ; /* rset and cset are now valid */ DEBUG (CHOLMOD(dump_subset) (rset, rsize, anrow, "rset", Common)) ; DEBUG (CHOLMOD(dump_subset) (cset, csize, ancol, "cset", Common)) ; /* ---------------------------------------------------------------------- */ /* allocate C */ /* ---------------------------------------------------------------------- */ C = CHOLMOD(allocate_sparse) (cnrow, cncol, nnz, csorted, TRUE, 0, values ? A->xtype : CHOLMOD_PATTERN, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ for (i = 0 ; i < anrow ; i++) { Head [i] = EMPTY ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; return (NULL) ; } Cp = C->p ; Ci = C->i ; Cx = C->x ; /* ---------------------------------------------------------------------- */ /* C = A (rset,cset) */ /* ---------------------------------------------------------------------- */ pdest = 0 ; if (nnz == 0) { /* C has no nonzeros */ for (cj = 0 ; cj <= cncol ; cj++) { Cp [cj] = 0 ; } } else if (nr < 0) { /* C = A (:,cset), where cset is not empty */ for (cj = 0 ; cj < cncol ; cj++) { /* construct column cj of C, which is column j of A */ PRINT1 (("construct cj = j = "ID"\n", cj)) ; j = cset [cj] ; Cp [cj] = pdest ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { Ci [pdest] = Ai [p] ; if (values) { Cx [pdest] = Ax [p] ; } pdest++ ; ASSERT (pdest <= nnz) ; } } } else { /* C = A (rset,cset), where rset is not empty but cset might be empty */ for (cj = 0 ; cj < cncol ; cj++) { /* construct column cj of C, which is column j of A */ PRINT1 (("construct cj = "ID"\n", cj)) ; j = (nc < 0) ? cj : (cset [cj]) ; PRINT1 (("cj = "ID"\n", j)) ; Cp [cj] = pdest ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { /* row (Ai [p]) of A becomes multiple rows (ci) of C */ PRINT2 (("i: "ID" becomes: ", Ai [p])) ; if (values) { aij = Ax [p] ; } for (ci = Head [Ai [p]] ; ci != EMPTY ; ci = Rnext [ci]) { PRINT3 ((""ID" ", ci)) ; Ci [pdest] = ci ; if (values) { Cx [pdest] = aij ; } pdest++ ; ASSERT (pdest <= nnz) ; } PRINT2 (("\n")) ; } } } Cp [cncol] = pdest ; ASSERT (nnz == pdest) ; /* ---------------------------------------------------------------------- */ /* clear workspace */ /* ---------------------------------------------------------------------- */ for (ci = 0 ; ci < nr ; ci++) { Head [rset [ci]] = EMPTY ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* sort C, if requested */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_sparse) (C , "C before sort", Common) >= 0) ; if (sorted && !csorted) { /* workspace: Iwork (max (C->nrow,C->ncol)) */ if (!CHOLMOD(sort) (C, Common)) { /* out of memory */ CHOLMOD(free_sparse) (&C, Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; return (NULL) ; } } /* ---------------------------------------------------------------------- */ /* return result */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_sparse) (C , "Final C", Common) >= 0) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; return (C) ; } #endif SuiteSparse/CHOLMOD/MatrixOps/cholmod_symmetry.c0000644001170100242450000004004010660074506020526 0ustar davisfac/* ========================================================================== */ /* === MatrixOps/cholmod_symmetry =========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Determines if a sparse matrix is rectangular, unsymmetric, symmetric, * skew-symmetric, or Hermitian. It does so by looking at its numerical values * of both upper and lower triangular parts of a CHOLMOD "unsymmetric" * matrix, where A->stype == 0. The transpose of A is NOT constructed. * * If not unsymmetric, it also determines if the matrix has a diagonal whose * entries are all real and positive (and thus a candidate for sparse Cholesky * if A->stype is changed to a nonzero value). * * Note that a Matrix Market "general" matrix is either rectangular or * unsymmetric. * * The row indices in the column of each matrix MUST be sorted for this function * to work properly (A->sorted must be TRUE). This routine returns EMPTY if * A->stype is not zero, or if A->sorted is FALSE. The exception to this rule * is if A is rectangular. * * If option == 0, then this routine returns immediately when it finds a * non-positive diagonal entry (or one with nonzero imaginary part). If the * matrix is not a candidate for sparse Cholesky, it returns the value * CHOLMOD_MM_UNSYMMETRIC, even if the matrix might in fact be symmetric or * Hermitian. * * This routine is useful inside the MATLAB backslash, which must look at an * arbitrary matrix (A->stype == 0) and determine if it is a candidate for * sparse Cholesky. In that case, option should be 0. * * This routine is also useful when writing a MATLAB matrix to a file in * Rutherford/Boeing or Matrix Market format. Those formats require a * determination as to the symmetry of the matrix, and thus this routine should * not return upon encountering the first non-positive diagonal. In this case, * option should be 1. * * If option is 2, this function can be used to compute the numerical and * pattern symmetry, where 0 is a completely unsymmetric matrix, and 1 is a * perfectly symmetric matrix. This option is used when computing the following * statistics for the matrices in the UF Sparse Matrix Collection. * * numerical symmetry: number of matched offdiagonal nonzeros over * the total number of offdiagonal entries. A real entry A(i,j), i ~= j, * is matched if A (j,i) == A (i,j), but this is only counted if both * A(j,i) and A(i,j) are nonzero. This does not depend on Z. * (If A is complex, then the above test is modified; A (i,j) is matched * if conj (A (j,i)) == A (i,j)). * * Then numeric symmetry = xmatched / nzoffdiag, or 1 if nzoffdiag = 0. * * pattern symmetry: number of matched offdiagonal entries over the * total number of offdiagonal entries. An entry A(i,j), i ~= j, is * matched if A (j,i) is also an entry. * * Then pattern symmetry = pmatched / nzoffdiag, or 1 if nzoffdiag = 0. * * The symmetry of a matrix with no offdiagonal entries is equal to 1. * * A workspace of size ncol integers is allocated; EMPTY is returned if this * allocation fails. * * Summary of return values: * * EMPTY (-1) out of memory, stype not zero, A not sorted * CHOLMOD_MM_RECTANGULAR 1 A is rectangular * CHOLMOD_MM_UNSYMMETRIC 2 A is unsymmetric * CHOLMOD_MM_SYMMETRIC 3 A is symmetric, but with non-pos. diagonal * CHOLMOD_MM_HERMITIAN 4 A is Hermitian, but with non-pos. diagonal * CHOLMOD_MM_SKEW_SYMMETRIC 5 A is skew symmetric * CHOLMOD_MM_SYMMETRIC_POSDIAG 6 A is symmetric with positive diagonal * CHOLMOD_MM_HERMITIAN_POSDIAG 7 A is Hermitian with positive diagonal * * See also the spsym mexFunction, which is a MATLAB interface for this code. * * If the matrix is a candidate for sparse Cholesky, it will return a result * CHOLMOD_MM_SYMMETRIC_POSDIAG if real, or CHOLMOD_MM_HERMITIAN_POSDIAG if * complex. Otherwise, it will return a value less than this. This is true * regardless of the value of the option parameter. */ #ifndef NMATRIXOPS #include "cholmod_internal.h" #include "cholmod_matrixops.h" /* ========================================================================== */ /* === get_value ============================================================ */ /* ========================================================================== */ /* Get the pth value in the matrix. */ static void get_value ( double *Ax, /* real values, or real/imag. for CHOLMOD_COMPLEX type */ double *Az, /* imaginary values for CHOLMOD_ZOMPLEX type */ Int p, /* get the pth entry */ Int xtype, /* A->xtype: pattern, real, complex, or zomplex */ double *x, /* the real part */ double *z /* the imaginary part */ ) { switch (xtype) { case CHOLMOD_PATTERN: *x = 1 ; *z = 0 ; break ; case CHOLMOD_REAL: *x = Ax [p] ; *z = 0 ; break ; case CHOLMOD_COMPLEX: *x = Ax [2*p] ; *z = Ax [2*p+1] ; break ; case CHOLMOD_ZOMPLEX: *x = Ax [p] ; *z = Az [p] ; break ; } } /* ========================================================================== */ /* === cholmod_symmetry ===================================================== */ /* ========================================================================== */ /* Determine the symmetry of a matrix, and check its diagonal. * * option 0: Do not count # of matched pairs. Quick return if the * the matrix has a zero, negative, or imaginary diagonal entry. * * option 1: Do not count # of matched pairs. Do not return quickly if * the matrix has a zero, negative, or imaginary diagonal entry. * The result 1 to 7 is accurately computed: * * EMPTY (-1) out of memory, stype not zero, A not sorted * CHOLMOD_MM_RECTANGULAR 1 A is rectangular * CHOLMOD_MM_UNSYMMETRIC 2 A is unsymmetric * CHOLMOD_MM_SYMMETRIC 3 A is symmetric, with non-pos. diagonal * CHOLMOD_MM_HERMITIAN 4 A is Hermitian, with non-pos. diagonal * CHOLMOD_MM_SKEW_SYMMETRIC 5 A is skew symmetric * CHOLMOD_MM_SYMMETRIC_POSDIAG 6 is symmetric with positive diagonal * CHOLMOD_MM_HERMITIAN_POSDIAG 7 A is Hermitian with positive diagonal * * The routine returns as soon as the above is determined (that is, it * can return as soon as it determines the matrix is unsymmetric). * * option 2: All of the above, but also compute the number of matched off- * diagonal entries (of two types). xmatched is the number of * nonzero entries for which A(i,j) = conj(A(j,i)). pmatched is * the number of entries (i,j) for which A(i,j) and A(j,i) are both in * the pattern of A (the value doesn't matter). nzoffdiag is the total * number of off-diagonal entries in the pattern. nzdiag is the number of * diagonal entries in the pattern. * * With option 0 or 1, or if the matrix is rectangular, xmatched, pmatched, * nzoffdiag, and nzdiag are not computed. * * Note that a matched pair, A(i,j) and A(j,i) for i != j, is counted twice * (once per entry). */ int CHOLMOD(symmetry) ( /* ---- input ---- */ cholmod_sparse *A, int option, /* option 0, 1, or 2 (see above) */ /* ---- output --- */ /* outputs ignored if any are NULL */ Int *p_xmatched, /* # of matched numerical entries */ Int *p_pmatched, /* # of matched entries in pattern */ Int *p_nzoffdiag, /* # of off diagonal entries */ Int *p_nzdiag, /* # of diagonal entries */ /* --------------- */ cholmod_common *Common ) { double aij_real = 0, aij_imag = 0, aji_real = 0, aji_imag = 0 ; double *Ax, *Az ; Int *Ap, *Ai, *Anz, *munch ; Int packed, nrow, ncol, xtype, is_symmetric, is_skew, is_hermitian, posdiag, j, p, pend, i, piend, result, xmatched, pmatched, nzdiag, i2, found ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (A, EMPTY) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ; Common->status = CHOLMOD_OK ; ASSERT (CHOLMOD(dump_sparse) (A, "cholmod_symmetry", Common) >= 0) ; if (p_xmatched == NULL || p_pmatched == NULL || p_nzoffdiag == NULL || p_nzdiag == NULL) { /* option 2 is not performed if any output parameter is NULL */ option = MAX (option, 1) ; } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Ap = A->p ; Ai = A->i ; Ax = A->x ; Az = A->z ; Anz = A->nz ; packed = A->packed ; ncol = A->ncol ; nrow = A->nrow ; xtype = A->xtype ; /* ---------------------------------------------------------------------- */ /* check if rectangular, unsorted, or stype is not zero */ /* ---------------------------------------------------------------------- */ if (nrow != ncol) { /* matrix is rectangular */ return (CHOLMOD_MM_RECTANGULAR) ; } if (!(A->sorted) || A->stype != 0) { /* this function cannot determine the type or symmetry */ return (EMPTY) ; } /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* this function requires uninitialized Int workspace of size ncol */ CHOLMOD(allocate_work) (0, ncol, 0, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (EMPTY) ; } munch = Common->Iwork ; /* the munch array is size ncol */ /* ---------------------------------------------------------------------- */ /* determine symmetry of a square matrix */ /* ---------------------------------------------------------------------- */ /* a complex or zomplex matrix is Hermitian until proven otherwise */ is_hermitian = (xtype >= CHOLMOD_COMPLEX) ; /* any matrix is symmetric until proven otherwise */ is_symmetric = TRUE ; /* a non-pattern matrix is skew-symmetric until proven otherwise */ is_skew = (xtype != CHOLMOD_PATTERN) ; /* a matrix has positive diagonal entries until proven otherwise */ posdiag = TRUE ; /* munch pointers start at the top of each column */ for (j = 0 ; j < ncol ; j++) { munch [j] = Ap [j] ; } xmatched = 0 ; pmatched = 0 ; nzdiag = 0 ; for (j = 0 ; j < ncol ; j++) /* examine each column of A */ { /* ------------------------------------------------------------------ */ /* look at the entire munch column j */ /* ------------------------------------------------------------------ */ /* start at the munch point of column j, and go to end of the column */ p = munch [j] ; pend = (packed) ? (Ap [j+1]) : (Ap [j] + Anz [j]) ; for ( ; p < pend ; p++) { /* get the row index of A(i,j) */ i = Ai [p] ; if (i < j) { /* ---------------------------------------------------------- */ /* A(i,j) in triu(A), but matching A(j,i) not in tril(A) */ /* ---------------------------------------------------------- */ /* entry A(i,j) is unmatched; it appears in the upper triangular * part, but not the lower triangular part. The matrix is * unsymmetric. */ is_hermitian = FALSE ; is_symmetric = FALSE ; is_skew = FALSE ; } else if (i == j) { /* ---------------------------------------------------------- */ /* the diagonal A(j,j) is present; check its value */ /* ---------------------------------------------------------- */ get_value (Ax, Az, p, xtype, &aij_real, &aij_imag) ; if (aij_real != 0. || aij_imag != 0.) { /* diagonal is nonzero; matrix is not skew-symmetric */ nzdiag++ ; is_skew = FALSE ; } if (aij_real <= 0. || aij_imag != 0.) { /* diagonal negative or imaginary; not chol candidate */ posdiag = FALSE ; } if (aij_imag != 0.) { /* imaginary part is present; not Hermitian */ is_hermitian = FALSE ; } } else /* i > j */ { /* ---------------------------------------------------------- */ /* consider column i, up to and including row j */ /* ---------------------------------------------------------- */ /* munch the entry at top of column i up to and incl row j */ piend = (packed) ? (Ap [i+1]) : (Ap [i] + Anz [i]) ; found = FALSE ; for ( ; munch [i] < piend ; munch [i]++) { i2 = Ai [munch [i]] ; if (i2 < j) { /* -------------------------------------------------- */ /* A(i2,i) in triu(A) but A(i,i2) not in tril(A) */ /* -------------------------------------------------- */ /* The matrix is unsymmetric. */ is_hermitian = FALSE ; is_symmetric = FALSE ; is_skew = FALSE ; } else if (i2 == j) { /* -------------------------------------------------- */ /* both A(i,j) and A(j,i) exist in the matrix */ /* -------------------------------------------------- */ /* this is one more matching entry in the pattern */ pmatched += 2 ; found = TRUE ; /* get the value of A(i,j) */ get_value (Ax, Az, p, xtype, &aij_real, &aij_imag) ; /* get the value of A(j,i) */ get_value (Ax, Az, munch [i], xtype, &aji_real, &aji_imag) ; /* compare A(i,j) with A(j,i) */ if (aij_real != aji_real || aij_imag != aji_imag) { /* the matrix cannot be symmetric */ is_symmetric = FALSE ; } if (aij_real != -aji_real || aij_imag != aji_imag) { /* the matrix cannot be skew-symmetric */ is_skew = FALSE ; } if (aij_real != aji_real || aij_imag != -aji_imag) { /* the matrix cannot be Hermitian */ is_hermitian = FALSE ; } else { /* A(i,j) and A(j,i) are numerically matched */ xmatched += 2 ; } } else /* i2 > j */ { /* -------------------------------------------------- */ /* entry A(i2,i) is not munched; consider it later */ /* -------------------------------------------------- */ break ; } } if (!found) { /* A(i,j) in tril(A) but A(j,i) not in triu(A). * The matrix is unsymmetric. */ is_hermitian = FALSE ; is_symmetric = FALSE ; is_skew = FALSE ; } } if (option < 2 && !(is_symmetric || is_skew || is_hermitian)) { /* matrix is unsymmetric; terminate the test */ return (CHOLMOD_MM_UNSYMMETRIC) ; } } /* ------------------------------------------------------------------ */ /* quick return if not Cholesky candidate */ /* ------------------------------------------------------------------ */ if (option < 1 && (!posdiag || nzdiag < ncol)) { /* Diagonal entry not present, or present but negative or with * nonzero imaginary part. Quick return for option 0. */ return (CHOLMOD_MM_UNSYMMETRIC) ; } } /* ---------------------------------------------------------------------- */ /* return the results */ /* ---------------------------------------------------------------------- */ if (option >= 2) { *p_xmatched = xmatched ; *p_pmatched = pmatched ; *p_nzoffdiag = CHOLMOD(nnz) (A, Common) - nzdiag ; *p_nzdiag = nzdiag ; } result = CHOLMOD_MM_UNSYMMETRIC ; if (is_hermitian) { /* complex Hermitian matrix, with either pos. or non-pos. diagonal */ result = posdiag ? CHOLMOD_MM_HERMITIAN_POSDIAG : CHOLMOD_MM_HERMITIAN ; } else if (is_symmetric) { /* real or complex symmetric matrix, with pos. or non-pos. diagonal */ result = posdiag ? CHOLMOD_MM_SYMMETRIC_POSDIAG : CHOLMOD_MM_SYMMETRIC ; } else if (is_skew) { /* real or complex skew-symmetric matrix */ result = CHOLMOD_MM_SKEW_SYMMETRIC ; } return (result) ; } #endif SuiteSparse/CHOLMOD/MatrixOps/t_cholmod_sdmult.c0000644001170100242450000004460010537777741020514 0ustar davisfac/* ========================================================================== */ /* === MatrixOps/t_cholmod_sdmult =========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Template routine for cholmod_sdmult */ #include "cholmod_template.h" #undef ADVANCE #ifdef REAL #define ADVANCE(x,z,d) x += d #elif defined (COMPLEX) #define ADVANCE(x,z,d) x += 2*d #else #define ADVANCE(x,z,d) x += d ; z += d #endif /* ========================================================================== */ /* === t_cholmod_sdmult ===================================================== */ /* ========================================================================== */ static void TEMPLATE (cholmod_sdmult) ( /* ---- input ---- */ cholmod_sparse *A, /* sparse matrix to multiply */ int transpose, /* use A if 0, or A' otherwise */ double alpha [2], /* scale factor for A */ double beta [2], /* scale factor for Y */ cholmod_dense *X, /* dense matrix to multiply */ /* ---- in/out --- */ cholmod_dense *Y, /* resulting dense matrix */ /* -- workspace -- */ double *W /* size 4*nx if needed, twice that for c/zomplex case */ ) { double yx [8], xx [8], ax [2] ; #ifdef ZOMPLEX double yz [4], xz [4], az [1] ; double betaz [1], alphaz [1] ; #endif double *Ax, *Az, *Xx, *Xz, *Yx, *Yz, *w, *Wz ; Int *Ap, *Ai, *Anz ; size_t nx, ny, dx, dy ; Int packed, nrow, ncol, j, k, p, pend, kcol, i ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ #ifdef ZOMPLEX betaz [0] = beta [1] ; alphaz [0] = alpha [1] ; #endif ny = transpose ? A->ncol : A->nrow ; /* required length of Y */ nx = transpose ? A->nrow : A->ncol ; /* required length of X */ nrow = A->nrow ; ncol = A->ncol ; Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; Az = A->z ; packed = A->packed ; Xx = X->x ; Xz = X->z ; Yx = Y->x ; Yz = Y->z ; kcol = X->ncol ; dy = Y->d ; dx = X->d ; w = W ; Wz = W + 4*nx ; /* ---------------------------------------------------------------------- */ /* Y = beta * Y */ /* ---------------------------------------------------------------------- */ if (ENTRY_IS_ZERO (beta, betaz, 0)) { for (k = 0 ; k < kcol ; k++) { for (i = 0 ; i < ((Int) ny) ; i++) { /* y [i] = 0. ; */ CLEAR (Yx, Yz, i) ; } /* y += dy ; */ ADVANCE (Yx,Yz,dy) ; } } else if (!ENTRY_IS_ONE (beta, betaz, 0)) { for (k = 0 ; k < kcol ; k++) { for (i = 0 ; i < ((Int) ny) ; i++) { /* y [i] *= beta [0] ; */ MULT (Yx,Yz,i, Yx,Yz,i, beta,betaz, 0) ; } /* y += dy ; */ ADVANCE (Yx,Yz,dy) ; } } if (ENTRY_IS_ZERO (alpha, alphaz, 0)) { /* nothing else to do */ return ; } /* ---------------------------------------------------------------------- */ /* Y += alpha * op(A) * X, where op(A)=A or A' */ /* ---------------------------------------------------------------------- */ Yx = Y->x ; Yz = Y->z ; k = 0 ; if (A->stype == 0) { if (transpose) { /* -------------------------------------------------------------- */ /* Y += alpha * A' * x, unsymmetric case */ /* -------------------------------------------------------------- */ if (kcol % 4 == 1) { for (j = 0 ; j < ncol ; j++) { /* yj = 0. ; */ CLEAR (yx, yz, 0) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { /* yj += conj(Ax [p]) * x [Ai [p]] ; */ i = Ai [p] ; ASSIGN_CONJ (ax,az,0, Ax,Az,p) ; MULTADD (yx,yz,0, ax,az,0, Xx,Xz,i) ; } /* y [j] += alpha [0] * yj ; */ MULTADD (Yx,Yz,j, alpha,alphaz,0, yx,yz,0) ; } /* y += dy ; */ /* x += dx ; */ ADVANCE (Yx,Yz,dy) ; ADVANCE (Xx,Xz,dx) ; k++ ; } else if (kcol % 4 == 2) { for (j = 0 ; j < ncol ; j++) { /* yj0 = 0. ; */ /* yj1 = 0. ; */ CLEAR (yx,yz,0) ; CLEAR (yx,yz,1) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; /* aij = conj (Ax [p]) ; */ ASSIGN_CONJ (ax,az,0, Ax,Az,p) ; /* yj0 += aij * x [i ] ; */ /* yj1 += aij * x [i+dx] ; */ MULTADD (yx,yz,0, ax,az,0, Xx,Xz,i) ; MULTADD (yx,yz,1, ax,az,0, Xx,Xz,i+dx) ; } /* y [j ] += alpha [0] * yj0 ; */ /* y [j+dy] += alpha [0] * yj1 ; */ MULTADD (Yx,Yz,j, alpha,alphaz,0, yx,yz,0) ; MULTADD (Yx,Yz,j+dy, alpha,alphaz,0, yx,yz,1) ; } /* y += 2*dy ; */ /* x += 2*dx ; */ ADVANCE (Yx,Yz,2*dy) ; ADVANCE (Xx,Xz,2*dx) ; k += 2 ; } else if (kcol % 4 == 3) { for (j = 0 ; j < ncol ; j++) { /* yj0 = 0. ; */ /* yj1 = 0. ; */ /* yj2 = 0. ; */ CLEAR (yx,yz,0) ; CLEAR (yx,yz,1) ; CLEAR (yx,yz,2) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; /* aij = conj (Ax [p]) ; */ ASSIGN_CONJ (ax,az,0, Ax,Az,p) ; /* yj0 += aij * x [i ] ; */ /* yj1 += aij * x [i+ dx] ; */ /* yj2 += aij * x [i+2*dx] ; */ MULTADD (yx,yz,0, ax,az,0, Xx,Xz,i) ; MULTADD (yx,yz,1, ax,az,0, Xx,Xz,i+dx) ; MULTADD (yx,yz,2, ax,az,0, Xx,Xz,i+2*dx) ; } /* y [j ] += alpha [0] * yj0 ; */ /* y [j+ dy] += alpha [0] * yj1 ; */ /* y [j+2*dy] += alpha [0] * yj2 ; */ MULTADD (Yx,Yz,j, alpha,alphaz,0, yx,yz,0) ; MULTADD (Yx,Yz,j+dy, alpha,alphaz,0, yx,yz,1) ; MULTADD (Yx,Yz,j+2*dy, alpha,alphaz,0, yx,yz,2) ; } /* y += 3*dy ; */ /* x += 3*dx ; */ ADVANCE (Yx,Yz,3*dy) ; ADVANCE (Xx,Xz,3*dx) ; k += 3 ; } for ( ; k < kcol ; k += 4) { for (j = 0 ; j < ncol ; j++) { /* yj0 = 0. ; */ /* yj1 = 0. ; */ /* yj2 = 0. ; */ /* yj3 = 0. ; */ CLEAR (yx,yz,0) ; CLEAR (yx,yz,1) ; CLEAR (yx,yz,2) ; CLEAR (yx,yz,3) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; /* aij = conj(Ax [p]) ; */ ASSIGN_CONJ (ax,az,0, Ax,Az,p) ; /* yj0 += aij * x [i ] ; */ /* yj1 += aij * x [i+ dx] ; */ /* yj2 += aij * x [i+2*dx] ; */ /* yj3 += aij * x [i+3*dx] ; */ MULTADD (yx,yz,0, ax,az,0, Xx,Xz,i) ; MULTADD (yx,yz,1, ax,az,0, Xx,Xz,i+dx) ; MULTADD (yx,yz,2, ax,az,0, Xx,Xz,i+2*dx) ; MULTADD (yx,yz,3, ax,az,0, Xx,Xz,i+3*dx) ; } /* y [j ] += alpha [0] * yj0 ; */ /* y [j+ dy] += alpha [0] * yj1 ; */ /* y [j+2*dy] += alpha [0] * yj2 ; */ /* y [j+3*dy] += alpha [0] * yj3 ; */ MULTADD (Yx,Yz,j, alpha,alphaz,0, yx,yz,0) ; MULTADD (Yx,Yz,j+dy, alpha,alphaz,0, yx,yz,1) ; MULTADD (Yx,Yz,j+2*dy, alpha,alphaz,0, yx,yz,2) ; MULTADD (Yx,Yz,j+3*dy, alpha,alphaz,0, yx,yz,3) ; } /* y += 4*dy ; */ /* x += 4*dx ; */ ADVANCE (Yx,Yz,4*dy) ; ADVANCE (Xx,Xz,4*dx) ; } } else { /* -------------------------------------------------------------- */ /* Y += alpha * A * x, unsymmetric case */ /* -------------------------------------------------------------- */ if (kcol % 4 == 1) { for (j = 0 ; j < ncol ; j++) { /* xj = alpha [0] * x [j] ; */ MULT (xx,xz,0, alpha,alphaz,0, Xx,Xz,j) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { /* y [Ai [p]] += Ax [p] * xj ; */ i = Ai [p] ; MULTADD (Yx,Yz,i, Ax,Az,p, xx,xz,0) ; } } /* y += dy ; */ /* x += dx ; */ ADVANCE (Yx,Yz,dy) ; ADVANCE (Xx,Xz,dx) ; k++ ; } else if (kcol % 4 == 2) { for (j = 0 ; j < ncol ; j++) { /* xj0 = alpha [0] * x [j ] ; */ /* xj1 = alpha [0] * x [j+dx] ; */ MULT (xx,xz,0, alpha,alphaz,0, Xx,Xz,j) ; MULT (xx,xz,1, alpha,alphaz,0, Xx,Xz,j+dx) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; /* aij = Ax [p] ; */ ASSIGN (ax,az,0, Ax,Az,p) ; /* y [i ] += aij * xj0 ; */ /* y [i+dy] += aij * xj1 ; */ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ; MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ; } } /* y += 2*dy ; */ /* x += 2*dx ; */ ADVANCE (Yx,Yz,2*dy) ; ADVANCE (Xx,Xz,2*dx) ; k += 2 ; } else if (kcol % 4 == 3) { for (j = 0 ; j < ncol ; j++) { /* xj0 = alpha [0] * x [j ] ; */ /* xj1 = alpha [0] * x [j+ dx] ; */ /* xj2 = alpha [0] * x [j+2*dx] ; */ MULT (xx,xz,0, alpha,alphaz,0, Xx,Xz,j) ; MULT (xx,xz,1, alpha,alphaz,0, Xx,Xz,j+dx) ; MULT (xx,xz,2, alpha,alphaz,0, Xx,Xz,j+2*dx) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; /* aij = Ax [p] ; */ ASSIGN (ax,az,0, Ax,Az,p) ; /* y [i ] += aij * xj0 ; */ /* y [i+ dy] += aij * xj1 ; */ /* y [i+2*dy] += aij * xj2 ; */ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ; MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ; MULTADD (Yx,Yz,i+2*dy, ax,az,0, xx,xz,2) ; } } /* y += 3*dy ; */ /* x += 3*dx ; */ ADVANCE (Yx,Yz,3*dy) ; ADVANCE (Xx,Xz,3*dx) ; k += 3 ; } for ( ; k < kcol ; k += 4) { for (j = 0 ; j < ncol ; j++) { /* xj0 = alpha [0] * x [j ] ; */ /* xj1 = alpha [0] * x [j+ dx] ; */ /* xj2 = alpha [0] * x [j+2*dx] ; */ /* xj3 = alpha [0] * x [j+3*dx] ; */ MULT (xx,xz,0, alpha,alphaz,0, Xx,Xz,j) ; MULT (xx,xz,1, alpha,alphaz,0, Xx,Xz,j+dx) ; MULT (xx,xz,2, alpha,alphaz,0, Xx,Xz,j+2*dx) ; MULT (xx,xz,3, alpha,alphaz,0, Xx,Xz,j+3*dx) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; /* aij = Ax [p] ; */ ASSIGN (ax,az,0, Ax,Az,p) ; /* y [i ] += aij * xj0 ; */ /* y [i+ dy] += aij * xj1 ; */ /* y [i+2*dy] += aij * xj2 ; */ /* y [i+3*dy] += aij * xj3 ; */ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ; MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ; MULTADD (Yx,Yz,i+2*dy, ax,az,0, xx,xz,2) ; MULTADD (Yx,Yz,i+3*dy, ax,az,0, xx,xz,3) ; } } /* y += 4*dy ; */ /* x += 4*dx ; */ ADVANCE (Yx,Yz,4*dy) ; ADVANCE (Xx,Xz,4*dx) ; } } } else { /* ------------------------------------------------------------------ */ /* Y += alpha * (A or A') * x, symmetric case (upper/lower) */ /* ------------------------------------------------------------------ */ /* Only the upper/lower triangular part and the diagonal of A is used. * Since both x and y are written to in the innermost loop, this * code can experience cache bank conflicts if x is used directly. * Thus, a copy is made of x, four columns at a time, if x has * four or more columns. */ if (kcol % 4 == 1) { for (j = 0 ; j < ncol ; j++) { /* yj = 0. ; */ CLEAR (yx,yz,0) ; /* xj = alpha [0] * x [j] ; */ MULT (xx,xz,0, alpha,alphaz,0, Xx,Xz,j) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i == j) { /* y [i] += Ax [p] * xj ; */ MULTADD (Yx,Yz,i, Ax,Az,p, xx,xz,0) ; } else if ((A->stype > 0 && i < j) || (A->stype < 0 && i > j)) { /* aij = Ax [p] ; */ ASSIGN (ax,az,0, Ax,Az,p) ; /* y [i] += aij * xj ; */ /* yj += aij * x [i] ; */ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ; MULTADDCONJ (yx,yz,0, ax,az,0, Xx,Xz,i) ; } } /* y [j] += alpha [0] * yj ; */ MULTADD (Yx,Yz,j, alpha,alphaz,0, yx,yz,0) ; } /* y += dy ; */ /* x += dx ; */ ADVANCE (Yx,Yz,dy) ; ADVANCE (Xx,Xz,dx) ; k++ ; } else if (kcol % 4 == 2) { for (j = 0 ; j < ncol ; j++) { /* yj0 = 0. ; */ /* yj1 = 0. ; */ CLEAR (yx,yz,0) ; CLEAR (yx,yz,1) ; /* xj0 = alpha [0] * x [j ] ; */ /* xj1 = alpha [0] * x [j+dx] ; */ MULT (xx,xz,0, alpha,alphaz,0, Xx,Xz,j) ; MULT (xx,xz,1, alpha,alphaz,0, Xx,Xz,j+dx) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i == j) { /* aij = Ax [p] ; */ ASSIGN (ax,az,0, Ax,Az,p) ; /* y [i ] += aij * xj0 ; */ /* y [i+dy] += aij * xj1 ; */ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ; MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ; } else if ((A->stype > 0 && i < j) || (A->stype < 0 && i > j)) { /* aij = Ax [p] ; */ ASSIGN (ax,az,0, Ax,Az,p) ; /* y [i ] += aij * xj0 ; */ /* y [i+dy] += aij * xj1 ; */ /* yj0 += aij * x [i ] ; */ /* yj1 += aij * x [i+dx] ; */ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ; MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ; MULTADDCONJ (yx,yz,0, ax,az,0, Xx,Xz,i) ; MULTADDCONJ (yx,yz,1, ax,az,0, Xx,Xz,i+dx) ; } } /* y [j ] += alpha [0] * yj0 ; */ /* y [j+dy] += alpha [0] * yj1 ; */ MULTADD (Yx,Yz,j, alpha,alphaz,0, yx,yz,0) ; MULTADD (Yx,Yz,j+dy, alpha,alphaz,0, yx,yz,1) ; } /* y += 2*dy ; */ /* x += 2*dx ; */ ADVANCE (Yx,Yz,2*dy) ; ADVANCE (Xx,Xz,2*dx) ; k += 2 ; } else if (kcol % 4 == 3) { for (j = 0 ; j < ncol ; j++) { /* yj0 = 0. ; */ /* yj1 = 0. ; */ /* yj2 = 0. ; */ CLEAR (yx,yz,0) ; CLEAR (yx,yz,1) ; CLEAR (yx,yz,2) ; /* xj0 = alpha [0] * x [j ] ; */ /* xj1 = alpha [0] * x [j+ dx] ; */ /* xj2 = alpha [0] * x [j+2*dx] ; */ MULT (xx,xz,0, alpha,alphaz,0, Xx,Xz,j) ; MULT (xx,xz,1, alpha,alphaz,0, Xx,Xz,j+dx) ; MULT (xx,xz,2, alpha,alphaz,0, Xx,Xz,j+2*dx) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i == j) { /* aij = Ax [p] ; */ ASSIGN (ax,az,0, Ax,Az,p) ; /* y [i ] += aij * xj0 ; */ /* y [i+ dy] += aij * xj1 ; */ /* y [i+2*dy] += aij * xj2 ; */ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ; MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ; MULTADD (Yx,Yz,i+2*dy, ax,az,0, xx,xz,2) ; } else if ((A->stype > 0 && i < j) || (A->stype < 0 && i > j)) { /* aij = Ax [p] ; */ ASSIGN (ax,az,0, Ax,Az,p) ; /* y [i ] += aij * xj0 ; */ /* y [i+ dy] += aij * xj1 ; */ /* y [i+2*dy] += aij * xj2 ; */ /* yj0 += aij * x [i ] ; */ /* yj1 += aij * x [i+ dx] ; */ /* yj2 += aij * x [i+2*dx] ; */ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ; MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ; MULTADD (Yx,Yz,i+2*dy, ax,az,0, xx,xz,2) ; MULTADDCONJ (yx,yz,0, ax,az,0, Xx,Xz,i) ; MULTADDCONJ (yx,yz,1, ax,az,0, Xx,Xz,i+dx) ; MULTADDCONJ (yx,yz,2, ax,az,0, Xx,Xz,i+2*dx) ; } } /* y [j ] += alpha [0] * yj0 ; */ /* y [j+ dy] += alpha [0] * yj1 ; */ /* y [j+2*dy] += alpha [0] * yj2 ; */ MULTADD (Yx,Yz,j, alpha,alphaz,0, yx,yz,0) ; MULTADD (Yx,Yz,j+dy, alpha,alphaz,0, yx,yz,1) ; MULTADD (Yx,Yz,j+2*dy, alpha,alphaz,0, yx,yz,2) ; } /* y += 3*dy ; */ /* x += 3*dx ; */ ADVANCE (Yx,Yz,3*dy) ; ADVANCE (Xx,Xz,3*dx) ; k += 3 ; } /* copy four columns of X into W, and put in row form */ for ( ; k < kcol ; k += 4) { for (j = 0 ; j < ncol ; j++) { /* w [4*j ] = x [j ] ; */ /* w [4*j+1] = x [j+ dx] ; */ /* w [4*j+2] = x [j+2*dx] ; */ /* w [4*j+3] = x [j+3*dx] ; */ ASSIGN (w,Wz,4*j , Xx,Xz,j ) ; ASSIGN (w,Wz,4*j+1, Xx,Xz,j+dx ) ; ASSIGN (w,Wz,4*j+2, Xx,Xz,j+2*dx) ; ASSIGN (w,Wz,4*j+3, Xx,Xz,j+3*dx) ; } for (j = 0 ; j < ncol ; j++) { /* yj0 = 0. ; */ /* yj1 = 0. ; */ /* yj2 = 0. ; */ /* yj3 = 0. ; */ CLEAR (yx,yz,0) ; CLEAR (yx,yz,1) ; CLEAR (yx,yz,2) ; CLEAR (yx,yz,3) ; /* xj0 = alpha [0] * w [4*j ] ; */ /* xj1 = alpha [0] * w [4*j+1] ; */ /* xj2 = alpha [0] * w [4*j+2] ; */ /* xj3 = alpha [0] * w [4*j+3] ; */ MULT (xx,xz,0, alpha,alphaz,0, w,Wz,4*j) ; MULT (xx,xz,1, alpha,alphaz,0, w,Wz,4*j+1) ; MULT (xx,xz,2, alpha,alphaz,0, w,Wz,4*j+2) ; MULT (xx,xz,3, alpha,alphaz,0, w,Wz,4*j+3) ; p = Ap [j] ; pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ; for ( ; p < pend ; p++) { i = Ai [p] ; if (i == j) { /* aij = Ax [p] ; */ ASSIGN (ax,az,0, Ax,Az,p) ; /* y [i ] += aij * xj0 ; */ /* y [i+ dy] += aij * xj1 ; */ /* y [i+2*dy] += aij * xj2 ; */ /* y [i+3*dy] += aij * xj3 ; */ MULTADD (Yx,Yz,i , ax,az,0, xx,xz,0) ; MULTADD (Yx,Yz,i+dy , ax,az,0, xx,xz,1) ; MULTADD (Yx,Yz,i+2*dy, ax,az,0, xx,xz,2) ; MULTADD (Yx,Yz,i+3*dy, ax,az,0, xx,xz,3) ; } else if ((A->stype > 0 && i < j) || (A->stype < 0 && i > j)) { /* aij = Ax [p] ; */ ASSIGN (ax,az,0, Ax,Az,p) ; /* y [i ] += aij * xj0 ; */ /* y [i+ dy] += aij * xj1 ; */ /* y [i+2*dy] += aij * xj2 ; */ /* y [i+3*dy] += aij * xj3 ; */ /* yj0 += aij * w [4*i ] ; */ /* yj1 += aij * w [4*i+1] ; */ /* yj2 += aij * w [4*i+2] ; */ /* yj3 += aij * w [4*i+3] ; */ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ; MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ; MULTADD (Yx,Yz,i+2*dy, ax,az,0, xx,xz,2) ; MULTADD (Yx,Yz,i+3*dy, ax,az,0, xx,xz,3) ; MULTADDCONJ (yx,yz,0, ax,az,0, w,Wz,4*i) ; MULTADDCONJ (yx,yz,1, ax,az,0, w,Wz,4*i+1) ; MULTADDCONJ (yx,yz,2, ax,az,0, w,Wz,4*i+2) ; MULTADDCONJ (yx,yz,3, ax,az,0, w,Wz,4*i+3) ; } } /* y [j ] += alpha [0] * yj0 ; */ /* y [j+ dy] += alpha [0] * yj1 ; */ /* y [j+2*dy] += alpha [0] * yj2 ; */ /* y [j+3*dy] += alpha [0] * yj3 ; */ MULTADD (Yx,Yz,j , alpha,alphaz,0, yx,yz,0) ; MULTADD (Yx,Yz,j+dy , alpha,alphaz,0, yx,yz,1) ; MULTADD (Yx,Yz,j+2*dy, alpha,alphaz,0, yx,yz,2) ; MULTADD (Yx,Yz,j+3*dy, alpha,alphaz,0, yx,yz,3) ; } /* y += 4*dy ; */ /* x += 4*dx ; */ ADVANCE (Yx,Yz,4*dy) ; ADVANCE (Xx,Xz,4*dx) ; } } } #undef PATTERN #undef REAL #undef COMPLEX #undef ZOMPLEX SuiteSparse/CHOLMOD/MatrixOps/cholmod_sdmult.c0000644001170100242450000001241710537777723020172 0ustar davisfac/* ========================================================================== */ /* === MatrixOps/cholmod_sdmult ============================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Sparse matrix times dense matrix: * Y = alpha*(A*X) + beta*Y or Y = alpha*(A'*X) + beta*Y, * where A is sparse and X and Y are dense. * * when using A, X has A->ncol columns and Y has A->nrow rows * when using A', X has A->nrow columns and Y has A->ncol rows * * workspace: none in Common. Temporary workspace of size 4*(X->nrow) is used * if A is stored in symmetric form and X has four columns or more. If the * workspace is not available, a slower method is used instead that requires * no workspace. * * transpose = 0: use A * otherwise, use A' (complex conjugate transpose) * * transpose is ignored if the matrix is symmetric or Hermitian. * (the array transpose A.' is not supported). * * Supports real, complex, and zomplex matrices, but the xtypes of A, X, and Y * must all match. */ #ifndef NMATRIXOPS #include "cholmod_internal.h" #include "cholmod_matrixops.h" /* ========================================================================== */ /* === TEMPLATE ============================================================= */ /* ========================================================================== */ #define REAL #include "t_cholmod_sdmult.c" #define COMPLEX #include "t_cholmod_sdmult.c" #define ZOMPLEX #include "t_cholmod_sdmult.c" /* ========================================================================== */ /* === cholmod_sdmult ======================================================= */ /* ========================================================================== */ int CHOLMOD(sdmult) ( /* ---- input ---- */ cholmod_sparse *A, /* sparse matrix to multiply */ int transpose, /* use A if 0, otherwise use A' */ double alpha [2], /* scale factor for A */ double beta [2], /* scale factor for Y */ cholmod_dense *X, /* dense matrix to multiply */ /* ---- in/out --- */ cholmod_dense *Y, /* resulting dense matrix */ /* --------------- */ cholmod_common *Common ) { double *w ; size_t nx, ny ; Int e ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (X, FALSE) ; RETURN_IF_NULL (Y, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; RETURN_IF_XTYPE_INVALID (Y, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ; ny = transpose ? A->ncol : A->nrow ; /* required length of Y */ nx = transpose ? A->nrow : A->ncol ; /* required length of X */ if (X->nrow != nx || X->ncol != Y->ncol || Y->nrow != ny) { /* X and/or Y have the wrong dimension */ ERROR (CHOLMOD_INVALID, "X and/or Y have wrong dimensions") ; return (FALSE) ; } if (A->xtype != X->xtype || A->xtype != Y->xtype) { ERROR (CHOLMOD_INVALID, "A, X, and Y must have same xtype") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace, if required */ /* ---------------------------------------------------------------------- */ w = NULL ; e = (A->xtype == CHOLMOD_REAL ? 1:2) ; if (A->stype && X->ncol >= 4) { w = CHOLMOD(malloc) (nx, 4*e*sizeof (double), Common) ; } if (Common->status < CHOLMOD_OK) { return (FALSE) ; /* out of memory */ } /* ---------------------------------------------------------------------- */ /* Y = alpha*op(A)*X + beta*Y via template routine */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_sparse) (A, "A", Common) >= 0) ; DEBUG (CHOLMOD(dump_dense) (X, "X", Common)) ; DEBUG (if (IS_NONZERO (beta [0]) || (IS_NONZERO (beta [1]) && A->xtype != CHOLMOD_REAL)) CHOLMOD(dump_dense) (Y, "Y", Common)) ; switch (A->xtype) { case CHOLMOD_REAL: r_cholmod_sdmult (A, transpose, alpha, beta, X, Y, w) ; break ; case CHOLMOD_COMPLEX: c_cholmod_sdmult (A, transpose, alpha, beta, X, Y, w) ; break ; case CHOLMOD_ZOMPLEX: z_cholmod_sdmult (A, transpose, alpha, beta, X, Y, w) ; break ; } /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ CHOLMOD(free) (4*nx, e*sizeof (double), w, Common) ; DEBUG (CHOLMOD(dump_dense) (Y, "Y", Common)) ; return (TRUE) ; } #endif SuiteSparse/CHOLMOD/MatrixOps/cholmod_horzcat.c0000644001170100242450000001423710537777674020343 0ustar davisfac/* ========================================================================== */ /* === MatrixOps/cholmod_horzcat ============================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Horizontal concatenation, C = [A , B] in MATLAB notation. * * A and B can be up/lo/unsym; C is unsymmetric and packed. * A and B must have the same number of rows. * C is sorted if both A and B are sorted. * * workspace: Iwork (max (A->nrow, A->ncol, B->nrow, B->ncol)). * allocates temporary copies of A and B if they are symmetric. * * A and B must have the same numeric xtype, unless values is FALSE. * A and B cannot be complex or zomplex, unless values is FALSE. */ #ifndef NMATRIXOPS #include "cholmod_internal.h" #include "cholmod_matrixops.h" /* ========================================================================== */ /* === cholmod_horzcat ====================================================== */ /* ========================================================================== */ cholmod_sparse *CHOLMOD(horzcat) ( /* ---- input ---- */ cholmod_sparse *A, /* left matrix to concatenate */ cholmod_sparse *B, /* right matrix to concatenate */ int values, /* if TRUE compute the numerical values of C */ /* --------------- */ cholmod_common *Common ) { double *Ax, *Bx, *Cx ; Int *Ap, *Ai, *Anz, *Bp, *Bi, *Bnz, *Cp, *Ci ; cholmod_sparse *C, *A2, *B2 ; Int apacked, bpacked, ancol, bncol, ncol, nrow, anz, bnz, nz, j, p, pend, pdest ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; RETURN_IF_NULL (B, NULL) ; values = values && (A->xtype != CHOLMOD_PATTERN) && (B->xtype != CHOLMOD_PATTERN) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; RETURN_IF_XTYPE_INVALID (B, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; if (A->nrow != B->nrow) { /* A and B must have the same number of rows */ ERROR (CHOLMOD_INVALID, "A and B must have same # rows") ; return (NULL) ; } /* A and B must have the same numerical type if values is TRUE (both must * be CHOLMOD_REAL, this is implicitly checked above) */ Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ ancol = A->ncol ; bncol = B->ncol ; nrow = A->nrow ; CHOLMOD(allocate_work) (0, MAX3 (nrow, ancol, bncol), 0, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ /* convert A to unsymmetric, if necessary */ A2 = NULL ; if (A->stype != 0) { /* workspace: Iwork (max (A->nrow,A->ncol)) */ A2 = CHOLMOD(copy) (A, 0, values, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } A = A2 ; } /* convert B to unsymmetric, if necessary */ B2 = NULL ; if (B->stype != 0) { /* workspace: Iwork (max (B->nrow,B->ncol)) */ B2 = CHOLMOD(copy) (B, 0, values, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&A2, Common) ; return (NULL) ; } B = B2 ; } Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; apacked = A->packed ; Bp = B->p ; Bnz = B->nz ; Bi = B->i ; Bx = B->x ; bpacked = B->packed ; /* ---------------------------------------------------------------------- */ /* allocate C */ /* ---------------------------------------------------------------------- */ anz = CHOLMOD(nnz) (A, Common) ; bnz = CHOLMOD(nnz) (B, Common) ; ncol = ancol + bncol ; nz = anz + bnz ; C = CHOLMOD(allocate_sparse) (nrow, ncol, nz, A->sorted && B->sorted, TRUE, 0, values ? A->xtype : CHOLMOD_PATTERN, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; return (NULL) ; } Cp = C->p ; Ci = C->i ; Cx = C->x ; /* ---------------------------------------------------------------------- */ /* C = [A , B] */ /* ---------------------------------------------------------------------- */ pdest = 0 ; /* copy A as the first A->ncol columns of C */ for (j = 0 ; j < ancol ; j++) { /* A(:,j) is the jth column of C */ p = Ap [j] ; pend = (apacked) ? (Ap [j+1]) : (p + Anz [j]) ; Cp [j] = pdest ; for ( ; p < pend ; p++) { Ci [pdest] = Ai [p] ; if (values) Cx [pdest] = Ax [p] ; pdest++ ; } } /* copy B as the next B->ncol columns of C */ for (j = 0 ; j < bncol ; j++) { /* B(:,j) is the (ancol+j)th column of C */ p = Bp [j] ; pend = (bpacked) ? (Bp [j+1]) : (p + Bnz [j]) ; Cp [ancol + j] = pdest ; for ( ; p < pend ; p++) { Ci [pdest] = Bi [p] ; if (values) Cx [pdest] = Bx [p] ; pdest++ ; } } Cp [ncol] = pdest ; ASSERT (pdest == anz + bnz) ; /* ---------------------------------------------------------------------- */ /* free the unsymmetric copies of A and B, and return C */ /* ---------------------------------------------------------------------- */ CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; return (C) ; } #endif SuiteSparse/CHOLMOD/MatrixOps/cholmod_vertcat.c0000644001170100242450000001404010537777736020330 0ustar davisfac/* ========================================================================== */ /* === MatrixOps/cholmod_vertcat ============================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Vertical concatenation, C = [A ; B] in MATLAB notation. * * A and B can be up/lo/unsym; C is unsymmetric and packed. * A and B must have the same number of columns. * C is sorted if both A and B are sorted. * * workspace: Iwork (max (A->nrow, A->ncol, B->nrow, B->ncol)). * allocates temporary copies of A and B if they are symmetric. * * Only pattern and real matrices are supported. Complex and zomplex matrices * are supported only if "values" is FALSE. */ #ifndef NMATRIXOPS #include "cholmod_internal.h" #include "cholmod_matrixops.h" /* ========================================================================== */ /* === cholmod_vertcat ====================================================== */ /* ========================================================================== */ cholmod_sparse *CHOLMOD(vertcat) ( /* ---- input ---- */ cholmod_sparse *A, /* left matrix to concatenate */ cholmod_sparse *B, /* right matrix to concatenate */ int values, /* if TRUE compute the numerical values of C */ /* --------------- */ cholmod_common *Common ) { double *Ax, *Bx, *Cx ; Int *Ap, *Ai, *Anz, *Bp, *Bi, *Bnz, *Cp, *Ci ; cholmod_sparse *C, *A2, *B2 ; Int apacked, bpacked, anrow, bnrow, ncol, nrow, anz, bnz, nz, j, p, pend, pdest ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (NULL) ; RETURN_IF_NULL (A, NULL) ; RETURN_IF_NULL (B, NULL) ; values = values && (A->xtype != CHOLMOD_PATTERN) && (B->xtype != CHOLMOD_PATTERN) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; RETURN_IF_XTYPE_INVALID (B, CHOLMOD_PATTERN, values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ; if (A->ncol != B->ncol) { /* A and B must have the same number of columns */ ERROR (CHOLMOD_INVALID, "A and B must have same # of columns") ; return (NULL) ; } /* A and B must have the same numerical type if values is TRUE (both must * be CHOLMOD_REAL, this is implicitly checked above) */ Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ anrow = A->nrow ; bnrow = B->nrow ; ncol = A->ncol ; CHOLMOD(allocate_work) (0, MAX3 (anrow, bnrow, ncol), 0, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ /* convert A to unsymmetric, if necessary */ A2 = NULL ; if (A->stype != 0) { /* workspace: Iwork (max (A->nrow,A->ncol)) */ A2 = CHOLMOD(copy) (A, 0, values, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ return (NULL) ; } A = A2 ; } /* convert B to unsymmetric, if necessary */ B2 = NULL ; if (B->stype != 0) { /* workspace: Iwork (max (B->nrow,B->ncol)) */ B2 = CHOLMOD(copy) (B, 0, values, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&A2, Common) ; return (NULL) ; } B = B2 ; } Ap = A->p ; Anz = A->nz ; Ai = A->i ; Ax = A->x ; apacked = A->packed ; Bp = B->p ; Bnz = B->nz ; Bi = B->i ; Bx = B->x ; bpacked = B->packed ; /* ---------------------------------------------------------------------- */ /* allocate C */ /* ---------------------------------------------------------------------- */ anz = CHOLMOD(nnz) (A, Common) ; bnz = CHOLMOD(nnz) (B, Common) ; nrow = anrow + bnrow ; nz = anz + bnz ; C = CHOLMOD(allocate_sparse) (nrow, ncol, nz, A->sorted && B->sorted, TRUE, 0, values ? A->xtype : CHOLMOD_PATTERN, Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; return (NULL) ; } Cp = C->p ; Ci = C->i ; Cx = C->x ; /* ---------------------------------------------------------------------- */ /* C = [A ; B] */ /* ---------------------------------------------------------------------- */ pdest = 0 ; for (j = 0 ; j < ncol ; j++) { /* attach A(:,j) as the first part of C(:,j) */ p = Ap [j] ; pend = (apacked) ? (Ap [j+1]) : (p + Anz [j]) ; Cp [j] = pdest ; for ( ; p < pend ; p++) { Ci [pdest] = Ai [p] ; if (values) { Cx [pdest] = Ax [p] ; } pdest++ ; } /* attach B(:,j) as the second part of C(:,j) */ p = Bp [j] ; pend = (bpacked) ? (Bp [j+1]) : (p + Bnz [j]) ; for ( ; p < pend ; p++) { Ci [pdest] = Bi [p] + anrow ; if (values) { Cx [pdest] = Bx [p] ; } pdest++ ; } } Cp [ncol] = pdest ; ASSERT (pdest == nz) ; /* ---------------------------------------------------------------------- */ /* free the unsymmetric copies of A and B, and return C */ /* ---------------------------------------------------------------------- */ CHOLMOD(free_sparse) (&A2, Common) ; CHOLMOD(free_sparse) (&B2, Common) ; return (C) ; } #endif SuiteSparse/CHOLMOD/Include/0000755001170100242450000000000010711427613014421 5ustar davisfacSuiteSparse/CHOLMOD/Include/cholmod_cholesky.h0000644001170100242450000004561410537777516020152 0ustar davisfac/* ========================================================================== */ /* === Include/cholmod_cholesky.h =========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_cholesky.h. Copyright (C) 2005-2006, Timothy A. Davis * CHOLMOD/Include/cholmod_cholesky.h is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* CHOLMOD Cholesky module. * * Sparse Cholesky routines: analysis, factorization, and solve. * * The primary routines are all that a user requires to order, analyze, and * factorize a sparse symmetric positive definite matrix A (or A*A'), and * to solve Ax=b (or A*A'x=b). The primary routines rely on the secondary * routines, the CHOLMOD Core module, and the AMD and COLAMD packages. They * make optional use of the CHOLMOD Supernodal and Partition modules, the * METIS package, and the CCOLAMD package. * * Primary routines: * ----------------- * * cholmod_analyze order and analyze (simplicial or supernodal) * cholmod_factorize simplicial or supernodal Cholesky factorization * cholmod_solve solve a linear system (simplicial or supernodal) * cholmod_spsolve solve a linear system (sparse x and b) * * Secondary routines: * ------------------ * * cholmod_analyze_p analyze, with user-provided permutation or f set * cholmod_factorize_p factorize, with user-provided permutation or f * cholmod_analyze_ordering analyze a fill-reducing ordering * cholmod_etree find the elimination tree * cholmod_rowcolcounts compute the row/column counts of L * cholmod_amd order using AMD * cholmod_colamd order using COLAMD * cholmod_rowfac incremental simplicial factorization * cholmod_rowfac_mask rowfac, specific to LPDASA * cholmod_row_subtree find the nonzero pattern of a row of L * cholmod_resymbol recompute the symbolic pattern of L * cholmod_resymbol_noperm recompute the symbolic pattern of L, no L->Perm * cholmod_postorder postorder a tree * * Requires the Core module, and two packages: AMD and COLAMD. * Optionally uses the Supernodal and Partition modules. * Required by the Partition module. */ #ifndef CHOLMOD_CHOLESKY_H #define CHOLMOD_CHOLESKY_H #include "cholmod_config.h" #include "cholmod_core.h" #ifndef NPARTITION #include "cholmod_partition.h" #endif #ifndef NSUPERNODAL #include "cholmod_supernodal.h" #endif /* -------------------------------------------------------------------------- */ /* cholmod_analyze: order and analyze (simplicial or supernodal) */ /* -------------------------------------------------------------------------- */ /* Orders and analyzes A, AA', PAP', or PAA'P' and returns a symbolic factor * that can later be passed to cholmod_factorize. */ cholmod_factor *cholmod_analyze ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order and analyze */ /* --------------- */ cholmod_common *Common ) ; cholmod_factor *cholmod_l_analyze (cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_analyze_p: analyze, with user-provided permutation or f set */ /* -------------------------------------------------------------------------- */ /* Orders and analyzes A, AA', PAP', PAA'P', FF', or PFF'P and returns a * symbolic factor that can later be passed to cholmod_factorize, where * F = A(:,fset) if fset is not NULL and A->stype is zero. * UserPerm is tried if non-NULL. */ cholmod_factor *cholmod_analyze_p ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order and analyze */ int *UserPerm, /* user-provided permutation, size A->nrow */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* --------------- */ cholmod_common *Common ) ; cholmod_factor *cholmod_l_analyze_p (cholmod_sparse *, UF_long *, UF_long *, size_t, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_factorize: simplicial or supernodal Cholesky factorization */ /* -------------------------------------------------------------------------- */ /* Factorizes PAP' (or PAA'P' if A->stype is 0), using a factor obtained * from cholmod_analyze. The analysis can be re-used simply by calling this * routine a second time with another matrix. A must have the same nonzero * pattern as that passed to cholmod_analyze. */ int cholmod_factorize ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ /* ---- in/out --- */ cholmod_factor *L, /* resulting factorization */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_factorize (cholmod_sparse *, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_factorize_p: factorize, with user-provided permutation or fset */ /* -------------------------------------------------------------------------- */ /* Same as cholmod_factorize, but with more options. */ int cholmod_factorize_p ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ double beta [2], /* factorize beta*I+A or beta*I+A'*A */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- in/out --- */ cholmod_factor *L, /* resulting factorization */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_factorize_p (cholmod_sparse *, double *, UF_long *, size_t, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_solve: solve a linear system (simplicial or supernodal) */ /* -------------------------------------------------------------------------- */ /* Solves one of many linear systems with a dense right-hand-side, using the * factorization from cholmod_factorize (or as modified by any other CHOLMOD * routine). D is identity for LL' factorizations. */ #define CHOLMOD_A 0 /* solve Ax=b */ #define CHOLMOD_LDLt 1 /* solve LDL'x=b */ #define CHOLMOD_LD 2 /* solve LDx=b */ #define CHOLMOD_DLt 3 /* solve DL'x=b */ #define CHOLMOD_L 4 /* solve Lx=b */ #define CHOLMOD_Lt 5 /* solve L'x=b */ #define CHOLMOD_D 6 /* solve Dx=b */ #define CHOLMOD_P 7 /* permute x=Px */ #define CHOLMOD_Pt 8 /* permute x=P'x */ cholmod_dense *cholmod_solve /* returns the solution X */ ( /* ---- input ---- */ int sys, /* system to solve */ cholmod_factor *L, /* factorization to use */ cholmod_dense *B, /* right-hand-side */ /* --------------- */ cholmod_common *Common ) ; cholmod_dense *cholmod_l_solve (int, cholmod_factor *, cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_spsolve: solve a linear system with a sparse right-hand-side */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_spsolve ( /* ---- input ---- */ int sys, /* system to solve */ cholmod_factor *L, /* factorization to use */ cholmod_sparse *B, /* right-hand-side */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_spsolve (int, cholmod_factor *, cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_etree: find the elimination tree of A or A'*A */ /* -------------------------------------------------------------------------- */ int cholmod_etree ( /* ---- input ---- */ cholmod_sparse *A, /* ---- output --- */ int *Parent, /* size ncol. Parent [j] = p if p is the parent of j */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_etree (cholmod_sparse *, UF_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_rowcolcounts: compute the row/column counts of L */ /* -------------------------------------------------------------------------- */ int cholmod_rowcolcounts ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int *Parent, /* size nrow. Parent [i] = p if p is the parent of i */ int *Post, /* size nrow. Post [k] = i if i is the kth node in * the postordered etree. */ /* ---- output --- */ int *RowCount, /* size nrow. RowCount [i] = # entries in the ith row of * L, including the diagonal. */ int *ColCount, /* size nrow. ColCount [i] = # entries in the ith * column of L, including the diagonal. */ int *First, /* size nrow. First [i] = k is the least postordering * of any descendant of i. */ int *Level, /* size nrow. Level [i] is the length of the path from * i to the root, with Level [root] = 0. */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_rowcolcounts (cholmod_sparse *, UF_long *, size_t, UF_long *, UF_long *, UF_long *, UF_long *, UF_long *, UF_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_analyze_ordering: analyze a fill-reducing ordering */ /* -------------------------------------------------------------------------- */ int cholmod_analyze_ordering ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ int ordering, /* ordering method used */ int *Perm, /* size n, fill-reducing permutation to analyze */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- output --- */ int *Parent, /* size n, elimination tree */ int *Post, /* size n, postordering of elimination tree */ int *ColCount, /* size n, nnz in each column of L */ /* ---- workspace */ int *First, /* size nworkspace for cholmod_postorder */ int *Level, /* size n workspace for cholmod_postorder */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_analyze_ordering (cholmod_sparse *, int, UF_long *, UF_long *, size_t, UF_long *, UF_long *, UF_long *, UF_long *, UF_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_amd: order using AMD */ /* -------------------------------------------------------------------------- */ /* Finds a permutation P to reduce fill-in in the factorization of P*A*P' * or P*A*A'P' */ int cholmod_amd ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- output --- */ int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_amd (cholmod_sparse *, UF_long *, size_t, UF_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_colamd: order using COLAMD */ /* -------------------------------------------------------------------------- */ /* Finds a permutation P to reduce fill-in in the factorization of P*A*A'*P'. * Orders F*F' where F = A (:,fset) if fset is not NULL */ int cholmod_colamd ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int postorder, /* if TRUE, follow with a coletree postorder */ /* ---- output --- */ int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_colamd (cholmod_sparse *, UF_long *, size_t, int, UF_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_rowfac: incremental simplicial factorization */ /* -------------------------------------------------------------------------- */ /* Partial or complete simplicial factorization. Rows and columns kstart:kend-1 * of L and D must be initially equal to rows/columns kstart:kend-1 of the * identity matrix. Row k can only be factorized if all descendants of node * k in the elimination tree have been factorized. */ int cholmod_rowfac ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,fset)' */ double beta [2], /* factorize beta*I+A or beta*I+A'*A */ size_t kstart, /* first row to factorize */ size_t kend, /* last row to factorize is kend-1 */ /* ---- in/out --- */ cholmod_factor *L, /* --------------- */ cholmod_common *Common ) ; int cholmod_l_rowfac (cholmod_sparse *, cholmod_sparse *, double *, size_t, size_t, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_rowfac_mask: incremental simplicial factorization */ /* -------------------------------------------------------------------------- */ /* cholmod_rowfac_mask is a version of cholmod_rowfac that is specific to * LPDASA. It is unlikely to be needed by any other application. */ int cholmod_rowfac_mask ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,fset)' */ double beta [2], /* factorize beta*I+A or beta*I+A'*A */ size_t kstart, /* first row to factorize */ size_t kend, /* last row to factorize is kend-1 */ int *mask, /* if mask[i] >= 0, then set row i to zero */ int *RLinkUp, /* link list of rows to compute */ /* ---- in/out --- */ cholmod_factor *L, /* --------------- */ cholmod_common *Common ) ; int cholmod_l_rowfac_mask (cholmod_sparse *, cholmod_sparse *, double *, size_t, size_t, UF_long *, UF_long *, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_row_subtree: find the nonzero pattern of a row of L */ /* -------------------------------------------------------------------------- */ /* Find the nonzero pattern of x for the system Lx=b where L = (0:k-1,0:k-1) * and b = kth column of A or A*A' (rows 0 to k-1 only) */ int cholmod_row_subtree ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,fset)' */ size_t k, /* row k of L */ int *Parent, /* elimination tree */ /* ---- output --- */ cholmod_sparse *R, /* pattern of L(k,:), 1-by-n with R->nzmax >= n */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_row_subtree (cholmod_sparse *, cholmod_sparse *, size_t, UF_long *, cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_row_lsubtree: find the nonzero pattern of a row of L */ /* -------------------------------------------------------------------------- */ /* Identical to cholmod_row_subtree, except that it finds the elimination tree * from L itself. */ int cholmod_row_lsubtree ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ int *Fi, size_t fnz, /* nonzero pattern of kth row of A', not required * for the symmetric case. Need not be sorted. */ size_t k, /* row k of L */ cholmod_factor *L, /* the factor L from which parent(i) is derived */ /* ---- output --- */ cholmod_sparse *R, /* pattern of L(k,:), 1-by-n with R->nzmax >= n */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_row_lsubtree (cholmod_sparse *, UF_long *, size_t, size_t, cholmod_factor *, cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_resymbol: recompute the symbolic pattern of L */ /* -------------------------------------------------------------------------- */ /* Remove entries from L that are not in the factorization of P*A*P', P*A*A'*P', * or P*F*F'*P' (depending on A->stype and whether fset is NULL or not). * * cholmod_resymbol is the same as cholmod_resymbol_noperm, except that it * first permutes A according to L->Perm. A can be upper/lower/unsymmetric, * in contrast to cholmod_resymbol_noperm (which can be lower or unsym). */ int cholmod_resymbol ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int pack, /* if TRUE, pack the columns of L */ /* ---- in/out --- */ cholmod_factor *L, /* factorization, entries pruned on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_resymbol (cholmod_sparse *, UF_long *, size_t, int, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_resymbol_noperm: recompute the symbolic pattern of L, no L->Perm */ /* -------------------------------------------------------------------------- */ /* Remove entries from L that are not in the factorization of A, A*A', * or F*F' (depending on A->stype and whether fset is NULL or not). */ int cholmod_resymbol_noperm ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int pack, /* if TRUE, pack the columns of L */ /* ---- in/out --- */ cholmod_factor *L, /* factorization, entries pruned on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_resymbol_noperm (cholmod_sparse *, UF_long *, size_t, int, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_rcond: compute rough estimate of reciprocal of condition number */ /* -------------------------------------------------------------------------- */ double cholmod_rcond /* return min(diag(L)) / max(diag(L)) */ ( /* ---- input ---- */ cholmod_factor *L, /* --------------- */ cholmod_common *Common ) ; double cholmod_l_rcond (cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_postorder: Compute the postorder of a tree */ /* -------------------------------------------------------------------------- */ UF_long cholmod_postorder /* return # of nodes postordered */ ( /* ---- input ---- */ int *Parent, /* size n. Parent [j] = p if p is the parent of j */ size_t n, int *Weight_p, /* size n, optional. Weight [j] is weight of node j */ /* ---- output --- */ int *Post, /* size n. Post [k] = j is kth in postordered tree */ /* --------------- */ cholmod_common *Common ) ; UF_long cholmod_l_postorder (UF_long *, size_t, UF_long *, UF_long *, cholmod_common *) ; #endif SuiteSparse/CHOLMOD/Include/cholmod_matrixops.h0000644001170100242450000002063610614157460020336 0ustar davisfac/* ========================================================================== */ /* === Include/cholmod_matrixops.h ========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_matrixops.h. * Copyright (C) 2005-2006, Timothy A. Davis * CHOLMOD/Include/cholmod_matrixops.h is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* CHOLMOD MatrixOps module. * * Basic operations on sparse and dense matrices. * * cholmod_drop A = entries in A with abs. value >= tol * cholmod_norm_dense s = norm (X), 1-norm, inf-norm, or 2-norm * cholmod_norm_sparse s = norm (A), 1-norm or inf-norm * cholmod_horzcat C = [A,B] * cholmod_scale A = diag(s)*A, A*diag(s), s*A or diag(s)*A*diag(s) * cholmod_sdmult Y = alpha*(A*X) + beta*Y or alpha*(A'*X) + beta*Y * cholmod_ssmult C = A*B * cholmod_submatrix C = A (i,j), where i and j are arbitrary vectors * cholmod_vertcat C = [A ; B] * * A, B, C: sparse matrices (cholmod_sparse) * X, Y: dense matrices (cholmod_dense) * s: scalar or vector * * Requires the Core module. Not required by any other CHOLMOD module. */ #ifndef CHOLMOD_MATRIXOPS_H #define CHOLMOD_MATRIXOPS_H #include "cholmod_core.h" /* -------------------------------------------------------------------------- */ /* cholmod_drop: drop entries with small absolute value */ /* -------------------------------------------------------------------------- */ int cholmod_drop ( /* ---- input ---- */ double tol, /* keep entries with absolute value > tol */ /* ---- in/out --- */ cholmod_sparse *A, /* matrix to drop entries from */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_drop (double, cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_norm_dense: s = norm (X), 1-norm, inf-norm, or 2-norm */ /* -------------------------------------------------------------------------- */ double cholmod_norm_dense ( /* ---- input ---- */ cholmod_dense *X, /* matrix to compute the norm of */ int norm, /* type of norm: 0: inf. norm, 1: 1-norm, 2: 2-norm */ /* --------------- */ cholmod_common *Common ) ; double cholmod_l_norm_dense (cholmod_dense *, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_norm_sparse: s = norm (A), 1-norm or inf-norm */ /* -------------------------------------------------------------------------- */ double cholmod_norm_sparse ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to compute the norm of */ int norm, /* type of norm: 0: inf. norm, 1: 1-norm */ /* --------------- */ cholmod_common *Common ) ; double cholmod_l_norm_sparse (cholmod_sparse *, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_horzcat: C = [A,B] */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_horzcat ( /* ---- input ---- */ cholmod_sparse *A, /* left matrix to concatenate */ cholmod_sparse *B, /* right matrix to concatenate */ int values, /* if TRUE compute the numerical values of C */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_horzcat (cholmod_sparse *, cholmod_sparse *, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_scale: A = diag(s)*A, A*diag(s), s*A or diag(s)*A*diag(s) */ /* -------------------------------------------------------------------------- */ /* scaling modes, selected by the scale input parameter: */ #define CHOLMOD_SCALAR 0 /* A = s*A */ #define CHOLMOD_ROW 1 /* A = diag(s)*A */ #define CHOLMOD_COL 2 /* A = A*diag(s) */ #define CHOLMOD_SYM 3 /* A = diag(s)*A*diag(s) */ int cholmod_scale ( /* ---- input ---- */ cholmod_dense *S, /* scale factors (scalar or vector) */ int scale, /* type of scaling to compute */ /* ---- in/out --- */ cholmod_sparse *A, /* matrix to scale */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_scale (cholmod_dense *, int, cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_sdmult: Y = alpha*(A*X) + beta*Y or alpha*(A'*X) + beta*Y */ /* -------------------------------------------------------------------------- */ /* Sparse matrix times dense matrix */ int cholmod_sdmult ( /* ---- input ---- */ cholmod_sparse *A, /* sparse matrix to multiply */ int transpose, /* use A if 0, or A' otherwise */ double alpha [2], /* scale factor for A */ double beta [2], /* scale factor for Y */ cholmod_dense *X, /* dense matrix to multiply */ /* ---- in/out --- */ cholmod_dense *Y, /* resulting dense matrix */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_sdmult (cholmod_sparse *, int, double *, double *, cholmod_dense *, cholmod_dense *Y, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_ssmult: C = A*B */ /* -------------------------------------------------------------------------- */ /* Sparse matrix times sparse matrix */ cholmod_sparse *cholmod_ssmult ( /* ---- input ---- */ cholmod_sparse *A, /* left matrix to multiply */ cholmod_sparse *B, /* right matrix to multiply */ int stype, /* requested stype of C */ int values, /* TRUE: do numerical values, FALSE: pattern only */ int sorted, /* if TRUE then return C with sorted columns */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_ssmult (cholmod_sparse *, cholmod_sparse *, int, int, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_submatrix: C = A (r,c), where i and j are arbitrary vectors */ /* -------------------------------------------------------------------------- */ /* rsize < 0 denotes ":" in MATLAB notation, or more precisely 0:(A->nrow)-1. * In this case, r can be NULL. An rsize of zero, or r = NULL and rsize >= 0, * denotes "[ ]" in MATLAB notation (the empty set). * Similar rules hold for csize. */ cholmod_sparse *cholmod_submatrix ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to subreference */ int *rset, /* set of row indices, duplicates OK */ UF_long rsize, /* size of r; rsize < 0 denotes ":" */ int *cset, /* set of column indices, duplicates OK */ UF_long csize, /* size of c; csize < 0 denotes ":" */ int values, /* if TRUE compute the numerical values of C */ int sorted, /* if TRUE then return C with sorted columns */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_submatrix (cholmod_sparse *, UF_long *, UF_long, UF_long *, UF_long, int, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_vertcat: C = [A ; B] */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_vertcat ( /* ---- input ---- */ cholmod_sparse *A, /* left matrix to concatenate */ cholmod_sparse *B, /* right matrix to concatenate */ int values, /* if TRUE compute the numerical values of C */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_vertcat (cholmod_sparse *, cholmod_sparse *, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_symmetry: determine if a sparse matrix is symmetric */ /* -------------------------------------------------------------------------- */ int cholmod_symmetry ( /* ---- input ---- */ cholmod_sparse *A, int option, /* ---- output ---- */ int *xmatched, int *pmatched, int *nzoffdiag, int *nzdiag, /* --------------- */ cholmod_common *Common ) ; int cholmod_l_symmetry (cholmod_sparse *, int, UF_long *, UF_long *, UF_long *, UF_long *, cholmod_common *) ; #endif SuiteSparse/CHOLMOD/Include/cholmod_template.h0000644001170100242450000002200110301202262020067 0ustar davisfac/* ========================================================================== */ /* === Include/cholmod_template.h =========================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* undefine current xtype macros, and then define macros for current type */ /* -------------------------------------------------------------------------- */ #undef TEMPLATE #undef XTYPE #undef XTYPE2 #undef XTYPE_OK #undef ENTRY_IS_NONZERO #undef ENTRY_IS_ZERO #undef ENTRY_IS_ONE #undef IMAG_IS_NONZERO #undef ASSEMBLE #undef ASSIGN #undef ASSIGN_CONJ #undef ASSIGN2 #undef ASSIGN2_CONJ #undef ASSIGN_REAL #undef MULT #undef MULTADD #undef ADD #undef ADD_REAL #undef MULTSUB #undef MULTADDCONJ #undef MULTSUBCONJ #undef LLDOT #undef CLEAR #undef DIV #undef DIV_REAL #undef MULT_REAL #undef CLEAR_IMAG #undef LDLDOT #undef PREFIX #undef ENTRY_SIZE #undef XPRINT0 #undef XPRINT1 #undef XPRINT2 #undef XPRINT3 /* -------------------------------------------------------------------------- */ /* pattern */ /* -------------------------------------------------------------------------- */ #ifdef PATTERN #define PREFIX p_ #define TEMPLATE(name) P_TEMPLATE(name) #define XTYPE CHOLMOD_PATTERN #define XTYPE2 CHOLMOD_REAL #define XTYPE_OK(type) (TRUE) #define ENTRY_IS_NONZERO(ax,az,q) (TRUE) #define ENTRY_IS_ZERO(ax,az,q) (FALSE) #define ENTRY_IS_ONE(ax,az,q) (TRUE) #define IMAG_IS_NONZERO(ax,az,q) (FALSE) #define ENTRY_SIZE 0 #define ASSEMBLE(x,z,p,ax,az,q) #define ASSIGN(x,z,p,ax,az,q) #define ASSIGN_CONJ(x,z,p,ax,az,q) #define ASSIGN2(x,z,p,ax,az,q) P_ASSIGN2(x,z,p,ax,az,q) #define ASSIGN2_CONJ(x,z,p,ax,az,q) P_ASSIGN2(x,z,p,ax,az,q) #define ASSIGN_REAL(x,p,ax,q) #define MULT(x,z,p,ax,az,q,bx,bz,pb) #define MULTADD(x,z,p,ax,az,q,bx,bz,pb) #define ADD(x,z,p,ax,az,q,bx,bz,pb) #define ADD_REAL(x,p, ax,q, bx,r) #define MULTSUB(x,z,p,ax,az,q,bx,bz,pb) #define MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb) #define MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb) #define LLDOT(x,p,ax,az,q) #define CLEAR(x,z,p) #define CLEAR_IMAG(x,z,p) #define DIV(x,z,p,ax,az,q) #define DIV_REAL(x,z,p, ax,az,q, bx,r) #define MULT_REAL(x,z,p, ax,az,q, bx,r) #define LDLDOT(x,p, ax,az,q, bx,r) #define XPRINT0(x,z,p) P_PRINT(0,x,z,p) #define XPRINT1(x,z,p) P_PRINT(1,x,z,p) #define XPRINT2(x,z,p) P_PRINT(2,x,z,p) #define XPRINT3(x,z,p) P_PRINT(3,x,z,p) /* -------------------------------------------------------------------------- */ /* real */ /* -------------------------------------------------------------------------- */ #elif defined (REAL) #define PREFIX r_ #define TEMPLATE(name) R_TEMPLATE(name) #define XTYPE CHOLMOD_REAL #define XTYPE2 CHOLMOD_REAL #define XTYPE_OK(type) R_XTYPE_OK(type) #define ENTRY_IS_NONZERO(ax,az,q) R_IS_NONZERO(ax,az,q) #define ENTRY_IS_ZERO(ax,az,q) R_IS_ZERO(ax,az,q) #define ENTRY_IS_ONE(ax,az,q) R_IS_ONE(ax,az,q) #define IMAG_IS_NONZERO(ax,az,q) (FALSE) #define ENTRY_SIZE 1 #define ASSEMBLE(x,z,p,ax,az,q) R_ASSEMBLE(x,z,p,ax,az,q) #define ASSIGN(x,z,p,ax,az,q) R_ASSIGN(x,z,p,ax,az,q) #define ASSIGN_CONJ(x,z,p,ax,az,q) R_ASSIGN(x,z,p,ax,az,q) #define ASSIGN2(x,z,p,ax,az,q) R_ASSIGN(x,z,p,ax,az,q) #define ASSIGN2_CONJ(x,z,p,ax,az,q) R_ASSIGN(x,z,p,ax,az,q) #define ASSIGN_REAL(x,p,ax,q) R_ASSIGN_REAL(x,p,ax,q) #define MULT(x,z,p,ax,az,q,bx,bz,pb) R_MULT(x,z,p,ax,az,q,bx,bz,pb) #define MULTADD(x,z,p,ax,az,q,bx,bz,pb) R_MULTADD(x,z,p,ax,az,q,bx,bz,pb) #define ADD(x,z,p,ax,az,q,bx,bz,pb) R_ADD(x,z,p,ax,az,q,bx,bz,pb) #define ADD_REAL(x,p, ax,q, bx,r) R_ADD_REAL(x,p, ax,q, bx,r) #define MULTSUB(x,z,p,ax,az,q,bx,bz,pb) R_MULTSUB(x,z,p,ax,az,q,bx,bz,pb) #define MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb) \ R_MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb) #define MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb) \ R_MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb) #define LLDOT(x,p,ax,az,q) R_LLDOT(x,p,ax,az,q) #define CLEAR(x,z,p) R_CLEAR(x,z,p) #define CLEAR_IMAG(x,z,p) R_CLEAR_IMAG(x,z,p) #define DIV(x,z,p,ax,az,q) R_DIV(x,z,p,ax,az,q) #define DIV_REAL(x,z,p, ax,az,q, bx,r) R_DIV_REAL(x,z,p, ax,az,q, bx,r) #define MULT_REAL(x,z,p, ax,az,q, bx,r) R_MULT_REAL(x,z,p, ax,az,q, bx,r) #define LDLDOT(x,p, ax,az,q, bx,r) R_LDLDOT(x,p, ax,az,q, bx,r) #define XPRINT0(x,z,p) R_PRINT(0,x,z,p) #define XPRINT1(x,z,p) R_PRINT(1,x,z,p) #define XPRINT2(x,z,p) R_PRINT(2,x,z,p) #define XPRINT3(x,z,p) R_PRINT(3,x,z,p) /* -------------------------------------------------------------------------- */ /* complex */ /* -------------------------------------------------------------------------- */ #elif defined (COMPLEX) #define PREFIX c_ #ifdef NCONJUGATE #define TEMPLATE(name) CT_TEMPLATE(name) #else #define TEMPLATE(name) C_TEMPLATE(name) #endif #define ASSEMBLE(x,z,p,ax,az,q) C_ASSEMBLE(x,z,p,ax,az,q) #define ASSIGN(x,z,p,ax,az,q) C_ASSIGN(x,z,p,ax,az,q) #define ASSIGN_CONJ(x,z,p,ax,az,q) C_ASSIGN_CONJ(x,z,p,ax,az,q) #define ASSIGN2(x,z,p,ax,az,q) C_ASSIGN(x,z,p,ax,az,q) #define ASSIGN2_CONJ(x,z,p,ax,az,q) C_ASSIGN_CONJ(x,z,p,ax,az,q) #define ASSIGN_REAL(x,p,ax,q) C_ASSIGN_REAL(x,p,ax,q) #define XTYPE CHOLMOD_COMPLEX #define XTYPE2 CHOLMOD_COMPLEX #define XTYPE_OK(type) C_XTYPE_OK(type) #define ENTRY_IS_NONZERO(ax,az,q) C_IS_NONZERO(ax,az,q) #define ENTRY_IS_ZERO(ax,az,q) C_IS_ZERO(ax,az,q) #define ENTRY_IS_ONE(ax,az,q) C_IS_ONE(ax,az,q) #define IMAG_IS_NONZERO(ax,az,q) C_IMAG_IS_NONZERO(ax,az,q) #define ENTRY_SIZE 2 #define MULTADD(x,z,p,ax,az,q,bx,bz,pb) C_MULTADD(x,z,p,ax,az,q,bx,bz,pb) #define MULT(x,z,p,ax,az,q,bx,bz,pb) C_MULT(x,z,p,ax,az,q,bx,bz,pb) #define ADD(x,z,p,ax,az,q,bx,bz,pb) C_ADD(x,z,p,ax,az,q,bx,bz,pb) #define ADD_REAL(x,p, ax,q, bx,r) C_ADD_REAL(x,p, ax,q, bx,r) #define MULTSUB(x,z,p,ax,az,q,bx,bz,pb) C_MULTSUB(x,z,p,ax,az,q,bx,bz,pb) #define MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb) \ C_MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb) #define MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb) \ C_MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb) #define LLDOT(x,p,ax,az,q) C_LLDOT(x,p,ax,az,q) #define CLEAR(x,z,p) C_CLEAR(x,z,p) #define CLEAR_IMAG(x,z,p) C_CLEAR_IMAG(x,z,p) #define DIV(x,z,p,ax,az,q) C_DIV(x,z,p,ax,az,q) #define DIV_REAL(x,z,p, ax,az,q, bx,r) C_DIV_REAL(x,z,p, ax,az,q, bx,r) #define MULT_REAL(x,z,p, ax,az,q, bx,r) C_MULT_REAL(x,z,p, ax,az,q, bx,r) #define LDLDOT(x,p, ax,az,q, bx,r) C_LDLDOT(x,p, ax,az,q, bx,r) #define XPRINT0(x,z,p) C_PRINT(0,x,z,p) #define XPRINT1(x,z,p) C_PRINT(1,x,z,p) #define XPRINT2(x,z,p) C_PRINT(2,x,z,p) #define XPRINT3(x,z,p) C_PRINT(3,x,z,p) /* -------------------------------------------------------------------------- */ /* zomplex */ /* -------------------------------------------------------------------------- */ #elif defined (ZOMPLEX) #define PREFIX z_ #ifdef NCONJUGATE #define TEMPLATE(name) ZT_TEMPLATE(name) #else #define TEMPLATE(name) Z_TEMPLATE(name) #endif #define ASSEMBLE(x,z,p,ax,az,q) Z_ASSEMBLE(x,z,p,ax,az,q) #define ASSIGN(x,z,p,ax,az,q) Z_ASSIGN(x,z,p,ax,az,q) #define ASSIGN_CONJ(x,z,p,ax,az,q) Z_ASSIGN_CONJ(x,z,p,ax,az,q) #define ASSIGN2(x,z,p,ax,az,q) Z_ASSIGN(x,z,p,ax,az,q) #define ASSIGN2_CONJ(x,z,p,ax,az,q) Z_ASSIGN_CONJ(x,z,p,ax,az,q) #define ASSIGN_REAL(x,p,ax,q) Z_ASSIGN_REAL(x,p,ax,q) #define XTYPE CHOLMOD_ZOMPLEX #define XTYPE2 CHOLMOD_ZOMPLEX #define XTYPE_OK(type) Z_XTYPE_OK(type) #define ENTRY_IS_NONZERO(ax,az,q) Z_IS_NONZERO(ax,az,q) #define ENTRY_IS_ZERO(ax,az,q) Z_IS_ZERO(ax,az,q) #define ENTRY_IS_ONE(ax,az,q) Z_IS_ONE(ax,az,q) #define IMAG_IS_NONZERO(ax,az,q) Z_IMAG_IS_NONZERO(ax,az,q) #define ENTRY_SIZE 1 #define MULTADD(x,z,p,ax,az,q,bx,bz,pb) Z_MULTADD(x,z,p,ax,az,q,bx,bz,pb) #define MULT(x,z,p,ax,az,q,bx,bz,pb) Z_MULT(x,z,p,ax,az,q,bx,bz,pb) #define ADD(x,z,p,ax,az,q,bx,bz,pb) Z_ADD(x,z,p,ax,az,q,bx,bz,pb) #define ADD_REAL(x,p, ax,q, bx,r) Z_ADD_REAL(x,p, ax,q, bx,r) #define MULTSUB(x,z,p,ax,az,q,bx,bz,pb) Z_MULTSUB(x,z,p,ax,az,q,bx,bz,pb) #define MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb) \ Z_MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb) #define MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb) \ Z_MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb) #define LLDOT(x,p,ax,az,q) Z_LLDOT(x,p,ax,az,q) #define CLEAR(x,z,p) Z_CLEAR(x,z,p) #define CLEAR_IMAG(x,z,p) Z_CLEAR_IMAG(x,z,p) #define DIV(x,z,p,ax,az,q) Z_DIV(x,z,p,ax,az,q) #define DIV_REAL(x,z,p, ax,az,q, bx,r) Z_DIV_REAL(x,z,p, ax,az,q, bx,r) #define MULT_REAL(x,z,p, ax,az,q, bx,r) Z_MULT_REAL(x,z,p, ax,az,q, bx,r) #define LDLDOT(x,p, ax,az,q, bx,r) Z_LDLDOT(x,p, ax,az,q, bx,r) #define XPRINT0(x,z,p) Z_PRINT(0,x,z,p) #define XPRINT1(x,z,p) Z_PRINT(1,x,z,p) #define XPRINT2(x,z,p) Z_PRINT(2,x,z,p) #define XPRINT3(x,z,p) Z_PRINT(3,x,z,p) #endif SuiteSparse/CHOLMOD/Include/cholmod_partition.h0000644001170100242450000002122210537777552020327 0ustar davisfac/* ========================================================================== */ /* === Include/cholmod_partition.h ========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_partition.h. * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis * CHOLMOD/Include/cholmod_partition.h is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* CHOLMOD Partition module. * * Graph partitioning and graph-partition-based orderings. Includes an * interface to CCOLAMD and CSYMAMD, constrained minimum degree ordering * methods which order a matrix following constraints determined via nested * dissection. * * cholmod_nested_dissection CHOLMOD nested dissection ordering * cholmod_metis METIS nested dissection ordering (METIS_NodeND) * cholmod_ccolamd interface to CCOLAMD ordering * cholmod_csymamd interface to CSYMAMD ordering * cholmod_camd interface to CAMD ordering * cholmod_bisect graph partitioner (currently based on METIS) * cholmod_metis_bisector direct interface to METIS_NodeComputeSeparator * * Requires the Core and Cholesky modules, and three packages: METIS, CAMD, * and CCOLAMD. Optionally used by the Cholesky module. * * Note that METIS does not have a version that uses UF_long integers. If you * try to use cholmod_nested_dissection, cholmod_metis, cholmod_bisect, or * cholmod_metis_bisector on a matrix that is too large, an error code will be * returned. METIS does have an "idxtype", which could be redefined as UF_long, * if you wish to edit METIS or use compile-time flags to redefine idxtype. */ #ifndef CHOLMOD_PARTITION_H #define CHOLMOD_PARTITION_H #include "cholmod_core.h" /* -------------------------------------------------------------------------- */ /* cholmod_nested_dissection */ /* -------------------------------------------------------------------------- */ /* Order A, AA', or A(:,f)*A(:,f)' using CHOLMOD's nested dissection method * (METIS's node bisector applied recursively to compute the separator tree * and constraint sets, followed by CCOLAMD using the constraints). Usually * finds better orderings than METIS_NodeND, but takes longer. */ UF_long cholmod_nested_dissection /* returns # of components */ ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- output --- */ int *Perm, /* size A->nrow, output permutation */ int *CParent, /* size A->nrow. On output, CParent [c] is the parent * of component c, or EMPTY if c is a root, and where * c is in the range 0 to # of components minus 1 */ int *Cmember, /* size A->nrow. Cmember [j] = c if node j of A is * in component c */ /* --------------- */ cholmod_common *Common ) ; UF_long cholmod_l_nested_dissection (cholmod_sparse *, UF_long *, size_t, UF_long *, UF_long *, UF_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_metis */ /* -------------------------------------------------------------------------- */ /* Order A, AA', or A(:,f)*A(:,f)' using METIS_NodeND. */ int cholmod_metis ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int postorder, /* if TRUE, follow with etree or coletree postorder */ /* ---- output --- */ int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_metis (cholmod_sparse *, UF_long *, size_t, int, UF_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_ccolamd */ /* -------------------------------------------------------------------------- */ /* Order AA' or A(:,f)*A(:,f)' using CCOLAMD. */ int cholmod_ccolamd ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int *Cmember, /* size A->nrow. Cmember [i] = c if row i is in the * constraint set c. c must be >= 0. The # of * constraint sets is max (Cmember) + 1. If Cmember is * NULL, then it is interpretted as Cmember [i] = 0 for * all i */ /* ---- output --- */ int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_ccolamd (cholmod_sparse *, UF_long *, size_t, UF_long *, UF_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_csymamd */ /* -------------------------------------------------------------------------- */ /* Order A using CSYMAMD. */ int cholmod_csymamd ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ /* ---- output --- */ int *Cmember, /* size nrow. see cholmod_ccolamd above */ int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_csymamd (cholmod_sparse *, UF_long *, UF_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_camd */ /* -------------------------------------------------------------------------- */ /* Order A using CAMD. */ int cholmod_camd ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- output --- */ int *Cmember, /* size nrow. see cholmod_ccolamd above */ int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_camd (cholmod_sparse *, UF_long *, size_t, UF_long *, UF_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_bisect */ /* -------------------------------------------------------------------------- */ /* Finds a node bisector of A, A*A', A(:,f)*A(:,f)'. */ UF_long cholmod_bisect /* returns # of nodes in separator */ ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to bisect */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int compress, /* if TRUE, compress the graph first */ /* ---- output --- */ int *Partition, /* size A->nrow. Node i is in the left graph if * Partition [i] = 0, the right graph if 1, and in the * separator if 2. */ /* --------------- */ cholmod_common *Common ) ; UF_long cholmod_l_bisect (cholmod_sparse *, UF_long *, size_t, int, UF_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_metis_bisector */ /* -------------------------------------------------------------------------- */ /* Find a set of nodes that bisects the graph of A or AA' (direct interface * to METIS_NodeComputeSeparator). */ UF_long cholmod_metis_bisector /* returns separator size */ ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to bisect */ int *Anw, /* size A->nrow, node weights */ int *Aew, /* size nz, edge weights */ /* ---- output --- */ int *Partition, /* size A->nrow. see cholmod_bisect above. */ /* --------------- */ cholmod_common *Common ) ; UF_long cholmod_l_metis_bisector (cholmod_sparse *, UF_long *, UF_long *, UF_long *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_collapse_septree */ /* -------------------------------------------------------------------------- */ /* Collapse nodes in a separator tree. */ UF_long cholmod_collapse_septree ( /* ---- input ---- */ size_t n, /* # of nodes in the graph */ size_t ncomponents, /* # of nodes in the separator tree (must be <= n) */ double nd_oksep, /* collapse if #sep >= nd_oksep * #nodes in subtree */ size_t nd_small, /* collapse if #nodes in subtree < nd_small */ /* ---- in/out --- */ int *CParent, /* size ncomponents; from cholmod_nested_dissection */ int *Cmember, /* size n; from cholmod_nested_dissection */ /* --------------- */ cholmod_common *Common ) ; UF_long cholmod_l_collapse_septree (size_t, size_t, double, size_t, UF_long *, UF_long *, cholmod_common *) ; #endif SuiteSparse/CHOLMOD/Include/cholmod_internal.h0000644001170100242450000003426310677244150020127 0ustar davisfac/* ========================================================================== */ /* === Include/cholmod_internal.h =========================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_internal.h. * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis * CHOLMOD/Include/cholmod_internal.h is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* CHOLMOD internal include file. * * This file contains internal definitions for CHOLMOD, not meant to be included * in user code. They define macros that are not prefixed with CHOLMOD_. This * file can safely #include'd in user code if you want to make use of the * macros defined here, and don't mind the possible name conflicts with your * code, however. * * Required by all CHOLMOD routines. Not required by any user routine that * uses CHOLMOMD. Unless debugging is enabled, this file does not require any * CHOLMOD module (not even the Core module). * * If debugging is enabled, all CHOLMOD modules require the Check module. * Enabling debugging requires that this file be editted. Debugging cannot be * enabled with a compiler flag. This is because CHOLMOD is exceedingly slow * when debugging is enabled. Debugging is meant for development of CHOLMOD * itself, not by users of CHOLMOD. */ #ifndef CHOLMOD_INTERNAL_H #define CHOLMOD_INTERNAL_H /* ========================================================================== */ /* === large file I/O ======================================================= */ /* ========================================================================== */ /* Definitions for large file I/O must come before any other #includes. If * this causes problems (may not be portable to all platforms), then compile * CHOLMOD with -DNLARGEFILE. You must do this for MATLAB 6.5 and earlier, * for example. */ #include "cholmod_io64.h" /* ========================================================================== */ /* === debugging and basic includes ========================================= */ /* ========================================================================== */ /* turn off debugging */ #ifndef NDEBUG #define NDEBUG #endif /* Uncomment this line to enable debugging. CHOLMOD will be very slow. #undef NDEBUG */ #ifdef MATLAB_MEX_FILE #include "mex.h" #endif #if !defined(NPRINT) || !defined(NDEBUG) #include #endif #include #include #include #include #include /* ========================================================================== */ /* === basic definitions ==================================================== */ /* ========================================================================== */ /* Some non-conforming compilers insist on defining TRUE and FALSE. */ #undef TRUE #undef FALSE #define TRUE 1 #define FALSE 0 #define BOOLEAN(x) ((x) ? TRUE : FALSE) /* NULL should already be defined, but ensure it is here. */ #ifndef NULL #define NULL ((void *) 0) #endif /* FLIP is a "negation about -1", and is used to mark an integer i that is * normally non-negative. FLIP (EMPTY) is EMPTY. FLIP of a number > EMPTY * is negative, and FLIP of a number < EMTPY is positive. FLIP (FLIP (i)) = i * for all integers i. UNFLIP (i) is >= EMPTY. */ #define EMPTY (-1) #define FLIP(i) (-(i)-2) #define UNFLIP(i) (((i) < EMPTY) ? FLIP (i) : (i)) /* MAX and MIN are not safe to use for NaN's */ #define MAX(a,b) (((a) > (b)) ? (a) : (b)) #define MAX3(a,b,c) (((a) > (b)) ? (MAX (a,c)) : (MAX (b,c))) #define MAX4(a,b,c,d) (((a) > (b)) ? (MAX3 (a,c,d)) : (MAX3 (b,c,d))) #define MIN(a,b) (((a) < (b)) ? (a) : (b)) #define IMPLIES(p,q) (!(p) || (q)) /* find the sign: -1 if x < 0, 1 if x > 0, zero otherwise. * Not safe for NaN's */ #define SIGN(x) (((x) < 0) ? (-1) : (((x) > 0) ? 1 : 0)) /* round up an integer x to a multiple of s */ #define ROUNDUP(x,s) ((s) * (((x) + ((s) - 1)) / (s))) #define ERROR(status,msg) \ CHOLMOD(error) (status, __FILE__, __LINE__, msg, Common) /* Check a pointer and return if null. Set status to invalid, unless the * status is already "out of memory" */ #define RETURN_IF_NULL(A,result) \ { \ if ((A) == NULL) \ { \ if (Common->status != CHOLMOD_OUT_OF_MEMORY) \ { \ ERROR (CHOLMOD_INVALID, "argument missing") ; \ } \ return (result) ; \ } \ } /* Return if Common is NULL or invalid */ #define RETURN_IF_NULL_COMMON(result) \ { \ if (Common == NULL) \ { \ return (result) ; \ } \ if (Common->itype != ITYPE || Common->dtype != DTYPE) \ { \ Common->status = CHOLMOD_INVALID ; \ return (result) ; \ } \ } #define IS_NAN(x) CHOLMOD_IS_NAN(x) #define IS_ZERO(x) CHOLMOD_IS_ZERO(x) #define IS_NONZERO(x) CHOLMOD_IS_NONZERO(x) #define IS_LT_ZERO(x) CHOLMOD_IS_LT_ZERO(x) #define IS_GT_ZERO(x) CHOLMOD_IS_GT_ZERO(x) #define IS_LE_ZERO(x) CHOLMOD_IS_LE_ZERO(x) /* 1e308 is a huge number that doesn't take many characters to print in a * file, in CHOLMOD/Check/cholmod_read and _write. Numbers larger than this * are interpretted as Inf, since sscanf doesn't read in Inf's properly. * This assumes IEEE double precision arithmetic. DBL_MAX would be a little * better, except that it takes too many digits to print in a file. */ #define HUGE_DOUBLE 1e308 /* ========================================================================== */ /* === int/UF_long and double/float definitions ============================= */ /* ========================================================================== */ /* CHOLMOD is designed for 3 types of integer variables: * * (1) all integers are int * (2) most integers are int, some are UF_long * (3) all integers are UF_long * * and two kinds of floating-point values: * * (1) double * (2) float * * the complex types (ANSI-compatible complex, and MATLAB-compatable zomplex) * are based on the double or float type, and are not selected here. They * are typically selected via template routines. * * This gives 6 different modes in which CHOLMOD can be compiled (only the * first two are currently supported): * * DINT double, int prefix: cholmod_ * DLONG double, UF_long prefix: cholmod_l_ * DMIX double, mixed int/UF_long prefix: cholmod_m_ * SINT float, int prefix: cholmod_si_ * SLONG float, UF_long prefix: cholmod_sl_ * SMIX float, mixed int/log prefix: cholmod_sm_ * * These are selected with compile time flags (-DDLONG, for example). If no * flag is selected, the default is DINT. * * All six versions use the same include files. The user-visible include files * are completely independent of which int/UF_long/double/float version is being * used. The integer / real types in all data structures (sparse, triplet, * dense, common, and triplet) are defined at run-time, not compile-time, so * there is only one "cholmod_sparse" data type. Void pointers are used inside * that data structure to point to arrays of the proper type. Each data * structure has an itype and dtype field which determines the kind of basic * types used. These are defined in Include/cholmod_core.h. * * FUTURE WORK: support all six types (float, and mixed int/UF_long) * * UF_long is normally defined as long. However, for WIN64 it is __int64. * It can also be redefined for other platforms, by modifying UFconfig.h. */ #include "UFconfig.h" /* -------------------------------------------------------------------------- */ /* Size_max: the largest value of size_t */ /* -------------------------------------------------------------------------- */ #define Size_max ((size_t) (-1)) /* routines for doing arithmetic on size_t, and checking for overflow */ size_t cholmod_add_size_t (size_t a, size_t b, int *ok) ; size_t cholmod_mult_size_t (size_t a, size_t k, int *ok) ; size_t cholmod_l_add_size_t (size_t a, size_t b, int *ok) ; size_t cholmod_l_mult_size_t (size_t a, size_t k, int *ok) ; /* -------------------------------------------------------------------------- */ /* double (also complex double), UF_long */ /* -------------------------------------------------------------------------- */ #ifdef DLONG #define Real double #define Int UF_long #define Int_max UF_long_max #define CHOLMOD(name) cholmod_l_ ## name #define LONG #define DOUBLE #define ITYPE CHOLMOD_LONG #define DTYPE CHOLMOD_DOUBLE #define ID UF_long_id /* -------------------------------------------------------------------------- */ /* double, int/UF_long */ /* -------------------------------------------------------------------------- */ #elif defined (DMIX) #error "mixed int/UF_long not yet supported" /* -------------------------------------------------------------------------- */ /* single, int */ /* -------------------------------------------------------------------------- */ #elif defined (SINT) #error "single-precision not yet supported" /* -------------------------------------------------------------------------- */ /* single, UF_long */ /* -------------------------------------------------------------------------- */ #elif defined (SLONG) #error "single-precision not yet supported" /* -------------------------------------------------------------------------- */ /* single, int/UF_long */ /* -------------------------------------------------------------------------- */ #elif defined (SMIX) #error "single-precision not yet supported" /* -------------------------------------------------------------------------- */ /* double (also complex double), int: this is the default */ /* -------------------------------------------------------------------------- */ #else #ifndef DINT #define DINT #endif #define INT #define DOUBLE #define Real double #define Int int #define Int_max INT_MAX #define CHOLMOD(name) cholmod_ ## name #define ITYPE CHOLMOD_INT #define DTYPE CHOLMOD_DOUBLE #define ID "%d" #endif /* ========================================================================== */ /* === real/complex arithmetic ============================================== */ /* ========================================================================== */ #include "cholmod_complexity.h" /* ========================================================================== */ /* === Architecture and BLAS ================================================ */ /* ========================================================================== */ #include "cholmod_blas.h" /* ========================================================================== */ /* === debugging definitions ================================================ */ /* ========================================================================== */ #ifndef NDEBUG #include #include "cholmod.h" /* The cholmod_dump routines are in the Check module. No CHOLMOD routine * calls the cholmod_check_* or cholmod_print_* routines in the Check module, * since they use Common workspace that may already be in use. Instead, they * use the cholmod_dump_* routines defined there, which allocate their own * workspace if they need it. */ #ifndef EXTERN #define EXTERN extern #endif /* double, int */ EXTERN int cholmod_dump ; EXTERN int cholmod_dump_malloc ; UF_long cholmod_dump_sparse (cholmod_sparse *, char *, cholmod_common *) ; int cholmod_dump_factor (cholmod_factor *, char *, cholmod_common *) ; int cholmod_dump_triplet (cholmod_triplet *, char *, cholmod_common *) ; int cholmod_dump_dense (cholmod_dense *, char *, cholmod_common *) ; int cholmod_dump_subset (int *, size_t, size_t, char *, cholmod_common *) ; int cholmod_dump_perm (int *, size_t, size_t, char *, cholmod_common *) ; int cholmod_dump_parent (int *, size_t, char *, cholmod_common *) ; void cholmod_dump_init (char *, cholmod_common *) ; int cholmod_dump_mem (char *, UF_long, cholmod_common *) ; void cholmod_dump_real (char *, Real *, UF_long, UF_long, int, int, cholmod_common *) ; void cholmod_dump_super (UF_long, int *, int *, int *, int *, double *, int, cholmod_common *) ; int cholmod_dump_partition (UF_long, int *, int *, int *, int *, UF_long, cholmod_common *) ; int cholmod_dump_work(int, int, UF_long, cholmod_common *) ; /* double, UF_long */ EXTERN int cholmod_l_dump ; EXTERN int cholmod_l_dump_malloc ; UF_long cholmod_l_dump_sparse (cholmod_sparse *, char *, cholmod_common *) ; int cholmod_l_dump_factor (cholmod_factor *, char *, cholmod_common *) ; int cholmod_l_dump_triplet (cholmod_triplet *, char *, cholmod_common *) ; int cholmod_l_dump_dense (cholmod_dense *, char *, cholmod_common *) ; int cholmod_l_dump_subset (UF_long *, size_t, size_t, char *, cholmod_common *) ; int cholmod_l_dump_perm (UF_long *, size_t, size_t, char *, cholmod_common *) ; int cholmod_l_dump_parent (UF_long *, size_t, char *, cholmod_common *) ; void cholmod_l_dump_init (char *, cholmod_common *) ; int cholmod_l_dump_mem (char *, UF_long, cholmod_common *) ; void cholmod_l_dump_real (char *, Real *, UF_long, UF_long, int, int, cholmod_common *) ; void cholmod_l_dump_super (UF_long, UF_long *, UF_long *, UF_long *, UF_long *, double *, int, cholmod_common *) ; int cholmod_l_dump_partition (UF_long, UF_long *, UF_long *, UF_long *, UF_long *, UF_long, cholmod_common *) ; int cholmod_l_dump_work(int, int, UF_long, cholmod_common *) ; #define DEBUG_INIT(s,Common) { CHOLMOD(dump_init)(s, Common) ; } #define ASSERT(expression) (assert (expression)) #define PRK(k,params) \ { \ if (CHOLMOD(dump) >= (k) && Common->print_function != NULL) \ { \ (Common->print_function) params ; \ } \ } #define PRINT0(params) PRK (0, params) #define PRINT1(params) PRK (1, params) #define PRINT2(params) PRK (2, params) #define PRINT3(params) PRK (3, params) #define PRINTM(params) \ { \ if (CHOLMOD(dump_malloc) > 0) \ { \ printf params ; \ } \ } #define DEBUG(statement) statement #else /* Debugging disabled (the normal case) */ #define PRK(k,params) #define DEBUG_INIT(s,Common) #define PRINT0(params) #define PRINT1(params) #define PRINT2(params) #define PRINT3(params) #define PRINTM(params) #define ASSERT(expression) #define DEBUG(statement) #endif #endif SuiteSparse/CHOLMOD/Include/cholmod.h0000644001170100242450000000742210540000233016205 0ustar davisfac/* ========================================================================== */ /* === Include/cholmod.h ==================================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod.h. * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis * CHOLMOD/Include/cholmod.h is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * * Portions of CHOLMOD (the Core and Partition Modules) are copyrighted by the * University of Florida. The Modify Module is co-authored by William W. * Hager, Univ. of Florida. * * Acknowledgements: this work was supported in part by the National Science * Foundation (NFS CCR-0203270 and DMS-9803599), and a grant from Sandia * National Laboratories (Dept. of Energy) which supported the development of * CHOLMOD's Partition Module. * -------------------------------------------------------------------------- */ /* CHOLMOD include file, for inclusion user programs. * * The include files listed below include a short description of each user- * callable routine. Each routine in CHOLMOD has a consistent interface. * More details about the CHOLMOD data types is in the cholmod_core.h file. * * Naming convention: * ------------------ * * All routine names, data types, and CHOLMOD library files use the * cholmod_ prefix. All macros and other #define's use the CHOLMOD * prefix. * * Return value: * ------------- * * Most CHOLMOD routines return an int (TRUE (1) if successful, or FALSE * (0) otherwise. A UF_long or double return value is >= 0 if successful, * or -1 otherwise. A size_t return value is > 0 if successful, or 0 * otherwise. * * If a routine returns a pointer, it is a pointer to a newly allocated * object or NULL if a failure occured, with one exception. cholmod_free * always returns NULL. * * "Common" parameter: * ------------------ * * The last parameter in all CHOLMOD routines is a pointer to the CHOLMOD * "Common" object. This contains control parameters, statistics, and * workspace used between calls to CHOLMOD. It is always an input/output * parameter. * * Input, Output, and Input/Output parameters: * ------------------------------------------- * * Input parameters are listed first. They are not modified by CHOLMOD. * * Input/output are listed next. They must be defined on input, and * are modified on output. * * Output parameters are listed next. If they are pointers, they must * point to allocated space on input, but their contents are not defined * on input. * * Workspace parameters appear next. They are used in only two routines * in the Supernodal module. * * The cholmod_common *Common parameter always appears as the last * parameter. It is always an input/output parameter. */ #ifndef CHOLMOD_H #define CHOLMOD_H /* make it easy for C++ programs to include CHOLMOD */ #ifdef __cplusplus extern "C" { #endif /* assume large file support. If problems occur, compile with -DNLARGEFILE */ #include "cholmod_io64.h" /* define UF_long */ #include "UFconfig.h" #include "cholmod_config.h" /* CHOLMOD always includes the Core module. */ #include "cholmod_core.h" #ifndef NCHECK #include "cholmod_check.h" #endif #ifndef NCHOLESKY #include "cholmod_cholesky.h" #endif #ifndef NMATRIXOPS #include "cholmod_matrixops.h" #endif #ifndef NMODIFY #include "cholmod_modify.h" #endif #ifndef NPARTITION #include "cholmod_partition.h" #endif #ifndef NSUPERNODAL #include "cholmod_supernodal.h" #endif #ifdef __cplusplus } #endif #endif SuiteSparse/CHOLMOD/Include/cholmod_blas.h0000644001170100242450000003223710677545130017235 0ustar davisfac/* ========================================================================== */ /* === Include/cholmod_blas.h =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_blas.h. * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis * CHOLMOD/Include/cholmod_blas.h is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* This does not need to be included in the user's program. */ #ifndef CHOLMOD_BLAS_H #define CHOLMOD_BLAS_H /* ========================================================================== */ /* === Architecture ========================================================= */ /* ========================================================================== */ #if defined (__sun) || defined (MSOL2) || defined (ARCH_SOL2) #define CHOLMOD_SOL2 #define CHOLMOD_ARCHITECTURE "Sun Solaris" #elif defined (__sgi) || defined (MSGI) || defined (ARCH_SGI) #define CHOLMOD_SGI #define CHOLMOD_ARCHITECTURE "SGI Irix" #elif defined (__linux) || defined (MGLNX86) || defined (ARCH_GLNX86) #define CHOLMOD_LINUX #define CHOLMOD_ARCHITECTURE "Linux" #elif defined (_AIX) || defined (MIBM_RS) || defined (ARCH_IBM_RS) #define CHOLMOD_AIX #define CHOLMOD_ARCHITECTURE "IBM AIX" #define BLAS_NO_UNDERSCORE #elif defined (__alpha) || defined (MALPHA) || defined (ARCH_ALPHA) #define CHOLMOD_ALPHA #define CHOLMOD_ARCHITECTURE "Compaq Alpha" #elif defined (_WIN32) || defined (WIN32) || defined (_WIN64) || defined (WIN64) #if defined (__MINGW32__) || defined (__MINGW32__) #define CHOLMOD_MINGW #elif defined (__CYGWIN32__) || defined (__CYGWIN32__) #define CHOLMOD_CYGWIN #else #define CHOLMOD_WINDOWS #define BLAS_NO_UNDERSCORE #endif #define CHOLMOD_ARCHITECTURE "Microsoft Windows" #elif defined (__hppa) || defined (__hpux) || defined (MHPUX) || defined (ARCH_HPUX) #define CHOLMOD_HP #define CHOLMOD_ARCHITECTURE "HP Unix" #define BLAS_NO_UNDERSCORE #elif defined (__hp700) || defined (MHP700) || defined (ARCH_HP700) #define CHOLMOD_HP #define CHOLMOD_ARCHITECTURE "HP 700 Unix" #define BLAS_NO_UNDERSCORE #else /* If the architecture is unknown, and you call the BLAS, you may need to */ /* define BLAS_BY_VALUE, BLAS_NO_UNDERSCORE, and/or BLAS_CHAR_ARG yourself. */ #define CHOLMOD_ARCHITECTURE "unknown" #endif /* ========================================================================== */ /* === BLAS and LAPACK names ================================================ */ /* ========================================================================== */ /* Prototypes for the various versions of the BLAS. */ /* Determine if the 64-bit Sun Performance BLAS is to be used */ #if defined(CHOLMOD_SOL2) && !defined(NSUNPERF) && defined(LONG) && defined(LONGBLAS) #define SUN64 #endif #ifdef SUN64 #define BLAS_DTRSV dtrsv_64_ #define BLAS_DGEMV dgemv_64_ #define BLAS_DTRSM dtrsm_64_ #define BLAS_DGEMM dgemm_64_ #define BLAS_DSYRK dsyrk_64_ #define BLAS_DGER dger_64_ #define BLAS_DSCAL dscal_64_ #define LAPACK_DPOTRF dpotrf_64_ #define BLAS_ZTRSV ztrsv_64_ #define BLAS_ZGEMV zgemv_64_ #define BLAS_ZTRSM ztrsm_64_ #define BLAS_ZGEMM zgemm_64_ #define BLAS_ZHERK zherk_64_ #define BLAS_ZGER zgeru_64_ #define BLAS_ZSCAL zscal_64_ #define LAPACK_ZPOTRF zpotrf_64_ #elif defined (BLAS_NO_UNDERSCORE) #define BLAS_DTRSV dtrsv #define BLAS_DGEMV dgemv #define BLAS_DTRSM dtrsm #define BLAS_DGEMM dgemm #define BLAS_DSYRK dsyrk #define BLAS_DGER dger #define BLAS_DSCAL dscal #define LAPACK_DPOTRF dpotrf #define BLAS_ZTRSV ztrsv #define BLAS_ZGEMV zgemv #define BLAS_ZTRSM ztrsm #define BLAS_ZGEMM zgemm #define BLAS_ZHERK zherk #define BLAS_ZGER zgeru #define BLAS_ZSCAL zscal #define LAPACK_ZPOTRF zpotrf #else #define BLAS_DTRSV dtrsv_ #define BLAS_DGEMV dgemv_ #define BLAS_DTRSM dtrsm_ #define BLAS_DGEMM dgemm_ #define BLAS_DSYRK dsyrk_ #define BLAS_DGER dger_ #define BLAS_DSCAL dscal_ #define LAPACK_DPOTRF dpotrf_ #define BLAS_ZTRSV ztrsv_ #define BLAS_ZGEMV zgemv_ #define BLAS_ZTRSM ztrsm_ #define BLAS_ZGEMM zgemm_ #define BLAS_ZHERK zherk_ #define BLAS_ZGER zgeru_ #define BLAS_ZSCAL zscal_ #define LAPACK_ZPOTRF zpotrf_ #endif /* ========================================================================== */ /* === BLAS and LAPACK integer arguments ==================================== */ /* ========================================================================== */ /* CHOLMOD can be compiled with -D'LONGBLAS=long' for the Sun Performance * Library, or -D'LONGBLAS=long long' for SGI's SCSL BLAS. This defines the * integer used in the BLAS for the cholmod_l_* routines. * * The "int" version of CHOLMOD always uses the "int" version of the BLAS. */ #if defined (LONGBLAS) && defined (LONG) #define BLAS_INT LONGBLAS #else #define BLAS_INT int #endif /* If the BLAS integer is smaller than the basic CHOLMOD integer, then we need * to check for integer overflow when converting from one to the other. If * any integer overflows, the externally-defined blas_ok variable is set to * FALSE. blas_ok should be set to TRUE before calling any BLAS_* macro. */ #define CHECK_BLAS_INT (sizeof (BLAS_INT) < sizeof (Int)) #define EQ(K,k) (((BLAS_INT) K) == ((Int) k)) /* ========================================================================== */ /* === BLAS and LAPACK prototypes and macros ================================ */ /* ========================================================================== */ void BLAS_DGEMV (char *trans, BLAS_INT *m, BLAS_INT *n, double *alpha, double *A, BLAS_INT *lda, double *X, BLAS_INT *incx, double *beta, double *Y, BLAS_INT *incy) ; #define BLAS_dgemv(trans,m,n,alpha,A,lda,X,incx,beta,Y,incy) \ { \ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \ && EQ (INCY,incy) ; \ } \ if (blas_ok) \ { \ BLAS_DGEMV (trans, &M, &N, alpha, A, &LDA, X, &INCX, beta, Y, &INCY) ; \ } \ } void BLAS_ZGEMV (char *trans, BLAS_INT *m, BLAS_INT *n, double *alpha, double *A, BLAS_INT *lda, double *X, BLAS_INT *incx, double *beta, double *Y, BLAS_INT *incy) ; #define BLAS_zgemv(trans,m,n,alpha,A,lda,X,incx,beta,Y,incy) \ { \ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \ && EQ (INCY,incy) ; \ } \ if (blas_ok) \ { \ BLAS_ZGEMV (trans, &M, &N, alpha, A, &LDA, X, &INCX, beta, Y, &INCY) ; \ } \ } void BLAS_DTRSV (char *uplo, char *trans, char *diag, BLAS_INT *n, double *A, BLAS_INT *lda, double *X, BLAS_INT *incx) ; #define BLAS_dtrsv(uplo,trans,diag,n,A,lda,X,incx) \ { \ BLAS_INT N = n, LDA = lda, INCX = incx ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) ; \ } \ if (blas_ok) \ { \ BLAS_DTRSV (uplo, trans, diag, &N, A, &LDA, X, &INCX) ; \ } \ } void BLAS_ZTRSV (char *uplo, char *trans, char *diag, BLAS_INT *n, double *A, BLAS_INT *lda, double *X, BLAS_INT *incx) ; #define BLAS_ztrsv(uplo,trans,diag,n,A,lda,X,incx) \ { \ BLAS_INT N = n, LDA = lda, INCX = incx ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) ; \ } \ if (blas_ok) \ { \ BLAS_ZTRSV (uplo, trans, diag, &N, A, &LDA, X, &INCX) ; \ } \ } void BLAS_DTRSM (char *side, char *uplo, char *transa, char *diag, BLAS_INT *m, BLAS_INT *n, double *alpha, double *A, BLAS_INT *lda, double *B, BLAS_INT *ldb) ; #define BLAS_dtrsm(side,uplo,transa,diag,m,n,alpha,A,lda,B,ldb) \ { \ BLAS_INT M = m, N = n, LDA = lda, LDB = ldb ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (LDB,ldb) ; \ } \ if (blas_ok) \ { \ BLAS_DTRSM (side, uplo, transa, diag, &M, &N, alpha, A, &LDA, B, &LDB);\ } \ } void BLAS_ZTRSM (char *side, char *uplo, char *transa, char *diag, BLAS_INT *m, BLAS_INT *n, double *alpha, double *A, BLAS_INT *lda, double *B, BLAS_INT *ldb) ; #define BLAS_ztrsm(side,uplo,transa,diag,m,n,alpha,A,lda,B,ldb) \ { \ BLAS_INT M = m, N = n, LDA = lda, LDB = ldb ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (LDB,ldb) ; \ } \ if (blas_ok) \ { \ BLAS_ZTRSM (side, uplo, transa, diag, &M, &N, alpha, A, &LDA, B, &LDB);\ } \ } void BLAS_DGEMM (char *transa, char *transb, BLAS_INT *m, BLAS_INT *n, BLAS_INT *k, double *alpha, double *A, BLAS_INT *lda, double *B, BLAS_INT *ldb, double *beta, double *C, BLAS_INT *ldc) ; #define BLAS_dgemm(transa,transb,m,n,k,alpha,A,lda,B,ldb,beta,C,ldc) \ { \ BLAS_INT M = m, N = n, K = k, LDA = lda, LDB = ldb, LDC = ldc ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (K,k) && EQ (LDA,lda) \ && EQ (LDB,ldb) && EQ (LDC,ldc) ; \ } \ if (blas_ok) \ { \ BLAS_DGEMM (transa, transb, &M, &N, &K, alpha, A, &LDA, B, &LDB, beta, \ C, &LDC) ; \ } \ } void BLAS_ZGEMM (char *transa, char *transb, BLAS_INT *m, BLAS_INT *n, BLAS_INT *k, double *alpha, double *A, BLAS_INT *lda, double *B, BLAS_INT *ldb, double *beta, double *C, BLAS_INT *ldc) ; #define BLAS_zgemm(transa,transb,m,n,k,alpha,A,lda,B,ldb,beta,C,ldc) \ { \ BLAS_INT M = m, N = n, K = k, LDA = lda, LDB = ldb, LDC = ldc ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (K,k) && EQ (LDA,lda) \ && EQ (LDB,ldb) && EQ (LDC,ldc) ; \ } \ if (blas_ok) \ { \ BLAS_ZGEMM (transa, transb, &M, &N, &K, alpha, A, &LDA, B, &LDB, beta, \ C, &LDC) ; \ } \ } void BLAS_DSYRK (char *uplo, char *trans, BLAS_INT *n, BLAS_INT *k, double *alpha, double *A, BLAS_INT *lda, double *beta, double *C, BLAS_INT *ldc) ; #define BLAS_dsyrk(uplo,trans,n,k,alpha,A,lda,beta,C,ldc) \ { \ BLAS_INT N = n, K = k, LDA = lda, LDC = ldc ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (N,n) && EQ (K,k) && EQ (LDA,lda) && EQ (LDC,ldc) ; \ } \ if (blas_ok) \ { \ BLAS_DSYRK (uplo, trans, &N, &K, alpha, A, &LDA, beta, C, &LDC) ; \ } \ } \ void BLAS_ZHERK (char *uplo, char *trans, BLAS_INT *n, BLAS_INT *k, double *alpha, double *A, BLAS_INT *lda, double *beta, double *C, BLAS_INT *ldc) ; #define BLAS_zherk(uplo,trans,n,k,alpha,A,lda,beta,C,ldc) \ { \ BLAS_INT N = n, K = k, LDA = lda, LDC = ldc ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (N,n) && EQ (K,k) && EQ (LDA,lda) && EQ (LDC,ldc) ; \ } \ if (blas_ok) \ { \ BLAS_ZHERK (uplo, trans, &N, &K, alpha, A, &LDA, beta, C, &LDC) ; \ } \ } \ void LAPACK_DPOTRF (char *uplo, BLAS_INT *n, double *A, BLAS_INT *lda, BLAS_INT *info) ; #define LAPACK_dpotrf(uplo,n,A,lda,info) \ { \ BLAS_INT N = n, LDA = lda, INFO = 1 ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (N,n) && EQ (LDA,lda) ; \ } \ if (blas_ok) \ { \ LAPACK_DPOTRF (uplo, &N, A, &LDA, &INFO) ; \ } \ info = INFO ; \ } void LAPACK_ZPOTRF (char *uplo, BLAS_INT *n, double *A, BLAS_INT *lda, BLAS_INT *info) ; #define LAPACK_zpotrf(uplo,n,A,lda,info) \ { \ BLAS_INT N = n, LDA = lda, INFO = 1 ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (N,n) && EQ (LDA,lda) ; \ } \ if (blas_ok) \ { \ LAPACK_ZPOTRF (uplo, &N, A, &LDA, &INFO) ; \ } \ info = INFO ; \ } /* ========================================================================== */ void BLAS_DSCAL (BLAS_INT *n, double *alpha, double *Y, BLAS_INT *incy) ; #define BLAS_dscal(n,alpha,Y,incy) \ { \ BLAS_INT N = n, INCY = incy ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (N,n) && EQ (INCY,incy) ; \ } \ if (blas_ok) \ { \ BLAS_DSCAL (&N, alpha, Y, &INCY) ; \ } \ } void BLAS_ZSCAL (BLAS_INT *n, double *alpha, double *Y, BLAS_INT *incy) ; #define BLAS_zscal(n,alpha,Y,incy) \ { \ BLAS_INT N = n, INCY = incy ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (N,n) && EQ (INCY,incy) ; \ } \ if (blas_ok) \ { \ BLAS_ZSCAL (&N, alpha, Y, &INCY) ; \ } \ } void BLAS_DGER (BLAS_INT *m, BLAS_INT *n, double *alpha, double *X, BLAS_INT *incx, double *Y, BLAS_INT *incy, double *A, BLAS_INT *lda) ; #define BLAS_dger(m,n,alpha,X,incx,Y,incy,A,lda) \ { \ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \ && EQ (INCY,incy) ; \ } \ if (blas_ok) \ { \ BLAS_DGER (&M, &N, alpha, X, &INCX, Y, &INCY, A, &LDA) ; \ } \ } void BLAS_ZGER (BLAS_INT *m, BLAS_INT *n, double *alpha, double *X, BLAS_INT *incx, double *Y, BLAS_INT *incy, double *A, BLAS_INT *lda) ; #define BLAS_zgeru(m,n,alpha,X,incx,Y,incy,A,lda) \ { \ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \ if (CHECK_BLAS_INT) \ { \ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \ && EQ (INCY,incy) ; \ } \ if (blas_ok) \ { \ BLAS_ZGER (&M, &N, alpha, X, &INCX, Y, &INCY, A, &LDA) ; \ } \ } #endif SuiteSparse/CHOLMOD/Include/cholmod_core.h0000644001170100242450000027241410711425463017242 0ustar davisfac/* ========================================================================== */ /* === Include/cholmod_core.h =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_core.h. * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis * CHOLMOD/Include/cholmod_core.h is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* CHOLMOD Core module: basic CHOLMOD objects and routines. * Required by all CHOLMOD modules. Requires no other module or package. * * The CHOLMOD modules are: * * Core basic data structures and definitions * Check check/print the 5 CHOLMOD objects, & 3 types of integer vectors * Cholesky sparse Cholesky factorization * Modify sparse Cholesky update/downdate/row-add/row-delete * MatrixOps sparse matrix functions (add, multiply, norm, ...) * Supernodal supernodal sparse Cholesky factorization * Partition graph-partitioning based orderings * * The CHOLMOD objects: * -------------------- * * cholmod_common parameters, statistics, and workspace * cholmod_sparse a sparse matrix in compressed column form * cholmod_factor an LL' or LDL' factorization * cholmod_dense a dense matrix * cholmod_triplet a sparse matrix in "triplet" form * * The Core module described here defines the CHOLMOD data structures, and * basic operations on them. To create and solve a sparse linear system Ax=b, * the user must create A and b, populate them with values, and then pass them * to the routines in the CHOLMOD Cholesky module. There are two primary * methods for creating A: (1) allocate space for a column-oriented sparse * matrix and fill it with pattern and values, or (2) create a triplet form * matrix and convert it to a sparse matrix. The latter option is simpler. * * The matrices b and x are typically dense matrices, but can also be sparse. * You can allocate and free them as dense matrices with the * cholmod_allocate_dense and cholmod_free_dense routines. * * The cholmod_factor object contains the symbolic and numeric LL' or LDL' * factorization of sparse symmetric matrix. The matrix must be positive * definite for an LL' factorization. It need only be symmetric and have well- * conditioned leading submatrices for it to have an LDL' factorization * (CHOLMOD does not pivot for numerical stability). It is typically created * with the cholmod_factorize routine in the Cholesky module, but can also * be initialized to L=D=I in the Core module and then modified by the Modify * module. It must be freed with cholmod_free_factor, defined below. * * The Core routines for each object are described below. Each list is split * into two parts: the primary routines and secondary routines. * * ============================================================================ * === cholmod_common ========================================================= * ============================================================================ * * The Common object contains control parameters, statistics, and * You must call cholmod_start before calling any other CHOLMOD routine, and * must call cholmod_finish as your last call to CHOLMOD, with two exceptions: * you may call cholmod_print_common and cholmod_check_common in the Check * module after calling cholmod_finish. * * cholmod_start first call to CHOLMOD * cholmod_finish last call to CHOLMOD * ----------------------------- * cholmod_defaults restore default parameters * cholmod_maxrank maximum rank for update/downdate * cholmod_allocate_work allocate workspace in Common * cholmod_free_work free workspace in Common * cholmod_clear_flag clear Flag workspace in Common * cholmod_error called when CHOLMOD encounters an error * cholmod_dbound for internal use in CHOLMOD only * cholmod_hypot compute sqrt (x*x + y*y) accurately * cholmod_divcomplex complex division, c = a/b * * ============================================================================ * === cholmod_sparse ========================================================= * ============================================================================ * * A sparse matrix is held in compressed column form. In the basic type * ("packed", which corresponds to a MATLAB sparse matrix), an n-by-n matrix * with nz entries is held in three arrays: p of size n+1, i of size nz, and x * of size nz. Row indices of column j are held in i [p [j] ... p [j+1]-1] and * in the same locations in x. There may be no duplicate entries in a column. * Row indices in each column may be sorted or unsorted (CHOLMOD keeps track). * A->stype determines the storage mode: 0 if both upper/lower parts are stored, * -1 if A is symmetric and just tril(A) is stored, +1 if symmetric and triu(A) * is stored. * * cholmod_allocate_sparse allocate a sparse matrix * cholmod_free_sparse free a sparse matrix * ----------------------------- * cholmod_reallocate_sparse change the size (# entries) of sparse matrix * cholmod_nnz number of nonzeros in a sparse matrix * cholmod_speye sparse identity matrix * cholmod_spzeros sparse zero matrix * cholmod_transpose transpose a sparse matrix * cholmod_ptranspose transpose/permute a sparse matrix * cholmod_transpose_unsym transpose/permute an unsymmetric sparse matrix * cholmod_transpose_sym transpose/permute a symmetric sparse matrix * cholmod_sort sort row indices in each column of sparse matrix * cholmod_band C = tril (triu (A,k1), k2) * cholmod_band_inplace A = tril (triu (A,k1), k2) * cholmod_aat C = A*A' * cholmod_copy_sparse C = A, create an exact copy of a sparse matrix * cholmod_copy C = A, with possible change of stype * cholmod_add C = alpha*A + beta*B * cholmod_sparse_xtype change the xtype of a sparse matrix * * ============================================================================ * === cholmod_factor ========================================================= * ============================================================================ * * The data structure for an LL' or LDL' factorization is too complex to * describe in one sentence. This object can hold the symbolic analysis alone, * or in combination with a "simplicial" (similar to a sparse matrix) or * "supernodal" form of the numerical factorization. Only the routine to free * a factor is primary, since a factor object is created by the factorization * routine (cholmod_factorize). It must be freed with cholmod_free_factor. * * cholmod_free_factor free a factor * ----------------------------- * cholmod_allocate_factor allocate a factor (LL' or LDL') * cholmod_reallocate_factor change the # entries in a factor * cholmod_change_factor change the type of factor (e.g., LDL' to LL') * cholmod_pack_factor pack the columns of a factor * cholmod_reallocate_column resize a single column of a factor * cholmod_factor_to_sparse create a sparse matrix copy of a factor * cholmod_copy_factor create a copy of a factor * cholmod_factor_xtype change the xtype of a factor * * Note that there is no cholmod_sparse_to_factor routine to create a factor * as a copy of a sparse matrix. It could be done, after a fashion, but a * lower triangular sparse matrix would not necessarily have a chordal graph, * which would break the many CHOLMOD routines that rely on this property. * * ============================================================================ * === cholmod_dense ========================================================== * ============================================================================ * * The solve routines and some of the MatrixOps and Modify routines use dense * matrices as inputs. These are held in column-major order. With a leading * dimension of d, the entry in row i and column j is held in x [i+j*d]. * * cholmod_allocate_dense allocate a dense matrix * cholmod_free_dense free a dense matrix * ----------------------------- * cholmod_zeros allocate a dense matrix of all zeros * cholmod_ones allocate a dense matrix of all ones * cholmod_eye allocate a dense identity matrix * cholmod_sparse_to_dense create a dense matrix copy of a sparse matrix * cholmod_dense_to_sparse create a sparse matrix copy of a dense matrix * cholmod_copy_dense create a copy of a dense matrix * cholmod_copy_dense2 copy a dense matrix (pre-allocated) * cholmod_dense_xtype change the xtype of a dense matrix * * ============================================================================ * === cholmod_triplet ======================================================== * ============================================================================ * * A sparse matrix held in triplet form is the simplest one for a user to * create. It consists of a list of nz entries in arbitrary order, held in * three arrays: i, j, and x, each of length nk. The kth entry is in row i[k], * column j[k], with value x[k]. There may be duplicate values; if A(i,j) * appears more than once, its value is the sum of the entries with those row * and column indices. * * cholmod_allocate_triplet allocate a triplet matrix * cholmod_triplet_to_sparse create a sparse matrix copy of a triplet matrix * cholmod_free_triplet free a triplet matrix * ----------------------------- * cholmod_reallocate_triplet change the # of entries in a triplet matrix * cholmod_sparse_to_triplet create a triplet matrix copy of a sparse matrix * cholmod_copy_triplet create a copy of a triplet matrix * cholmod_triplet_xtype change the xtype of a triplet matrix * * ============================================================================ * === memory management ====================================================== * ============================================================================ * * cholmod_malloc malloc wrapper * cholmod_calloc calloc wrapper * cholmod_free free wrapper * cholmod_realloc realloc wrapper * cholmod_realloc_multiple realloc wrapper for multiple objects * * ============================================================================ * === Core CHOLMOD prototypes ================================================ * ============================================================================ * * All CHOLMOD routines (in all modules) use the following protocol for return * values, with one exception: * * int TRUE (1) if successful, or FALSE (0) otherwise. * (exception: cholmod_divcomplex) * UF_long a value >= 0 if successful, or -1 otherwise. * double a value >= 0 if successful, or -1 otherwise. * size_t a value > 0 if successful, or 0 otherwise. * void * a non-NULL pointer to newly allocated memory if * successful, or NULL otherwise. * cholmod_sparse * a non-NULL pointer to a newly allocated matrix * if successful, or NULL otherwise. * cholmod_factor * a non-NULL pointer to a newly allocated factor * if successful, or NULL otherwise. * cholmod_triplet * a non-NULL pointer to a newly allocated triplet * matrix if successful, or NULL otherwise. * cholmod_dense * a non-NULL pointer to a newly allocated triplet * matrix if successful, or NULL otherwise. * * The last parameter to all routines is always a pointer to the CHOLMOD * Common object. * * TRUE and FALSE are not defined here, since they may conflict with the user * program. A routine that described here returning TRUE or FALSE returns 1 * or 0, respectively. Any TRUE/FALSE parameter is true if nonzero, false if * zero. */ #ifndef CHOLMOD_CORE_H #define CHOLMOD_CORE_H /* ========================================================================== */ /* === CHOLMOD version ====================================================== */ /* ========================================================================== */ /* All versions of CHOLMOD will include the following definitions. * As an example, to test if the version you are using is 1.3 or later: * * if (CHOLMOD_VERSION >= CHOLMOD_VER_CODE (1,3)) ... * * This also works during compile-time: * * #if CHOLMOD_VERSION >= CHOLMOD_VER_CODE (1,3) * printf ("This is version 1.3 or later\n") ; * #else * printf ("This is version is earlier than 1.3\n") ; * #endif */ #define CHOLMOD_DATE "Nov 1, 2007" #define CHOLMOD_VER_CODE(main,sub) ((main) * 1000 + (sub)) #define CHOLMOD_MAIN_VERSION 1 #define CHOLMOD_SUB_VERSION 6 #define CHOLMOD_SUBSUB_VERSION 0 #define CHOLMOD_VERSION \ CHOLMOD_VER_CODE(CHOLMOD_MAIN_VERSION,CHOLMOD_SUB_VERSION) /* ========================================================================== */ /* === non-CHOLMOD include files ============================================ */ /* ========================================================================== */ /* This is the only non-CHOLMOD include file imposed on the user program. * It required for size_t definition used here. CHOLMOD itself includes other * ANSI C89 standard #include files, but does not expose them to the user. * * CHOLMOD assumes that your C compiler is ANSI C89 compliant. It does not make * use of ANSI C99 features. */ #include #include /* ========================================================================== */ /* === CHOLMOD objects ====================================================== */ /* ========================================================================== */ /* Each CHOLMOD object has its own type code. */ #define CHOLMOD_COMMON 0 #define CHOLMOD_SPARSE 1 #define CHOLMOD_FACTOR 2 #define CHOLMOD_DENSE 3 #define CHOLMOD_TRIPLET 4 /* ========================================================================== */ /* === CHOLMOD Common ======================================================= */ /* ========================================================================== */ /* itype defines the types of integer used: */ #define CHOLMOD_INT 0 /* all integer arrays are int */ #define CHOLMOD_INTLONG 1 /* most are int, some are UF_long */ #define CHOLMOD_LONG 2 /* all integer arrays are UF_long */ /* The itype of all parameters for all CHOLMOD routines must match. * FUTURE WORK: CHOLMOD_INTLONG is not yet supported. */ /* dtype defines what the numerical type is (double or float): */ #define CHOLMOD_DOUBLE 0 /* all numerical values are double */ #define CHOLMOD_SINGLE 1 /* all numerical values are float */ /* The dtype of all parameters for all CHOLMOD routines must match. * * Scalar floating-point values are always passed as double arrays of size 2 * (for the real and imaginary parts). They are typecast to float as needed. * FUTURE WORK: the float case is not supported yet. */ /* xtype defines the kind of numerical values used: */ #define CHOLMOD_PATTERN 0 /* pattern only, no numerical values */ #define CHOLMOD_REAL 1 /* a real matrix */ #define CHOLMOD_COMPLEX 2 /* a complex matrix (ANSI C99 compatible) */ #define CHOLMOD_ZOMPLEX 3 /* a complex matrix (MATLAB compatible) */ /* The xtype of all parameters for all CHOLMOD routines must match. * * CHOLMOD_PATTERN: x and z are ignored. * CHOLMOD_DOUBLE: x is non-null of size nzmax, z is ignored. * CHOLMOD_COMPLEX: x is non-null of size 2*nzmax doubles, z is ignored. * CHOLMOD_ZOMPLEX: x and z are non-null of size nzmax * * In the real case, z is ignored. The kth entry in the matrix is x [k]. * There are two methods for the complex case. In the ANSI C99-compatible * CHOLMOD_COMPLEX case, the real and imaginary parts of the kth entry * are in x [2*k] and x [2*k+1], respectively. z is ignored. In the * MATLAB-compatible CHOLMOD_ZOMPLEX case, the real and imaginary * parts of the kth entry are in x [k] and z [k]. * * Scalar floating-point values are always passed as double arrays of size 2 * (real and imaginary parts). The imaginary part of a scalar is ignored if * the routine operates on a real matrix. * * These Modules support complex and zomplex matrices, with a few exceptions: * * Check all routines * Cholesky all routines * Core all except cholmod_aat, add, band, copy * Demo all routines * Partition all routines * Supernodal all routines support any real, complex, or zomplex input. * There will never be a supernodal zomplex L; a complex * supernodal L is created if A is zomplex. * Tcov all routines * Valgrind all routines * * These Modules provide partial support for complex and zomplex matrices: * * MATLAB all routines support real and zomplex only, not complex, * with the exception of ldlupdate, which supports * real matrices only. This is a minor constraint since * MATLAB's matrices are all real or zomplex. * MatrixOps only norm_dense, norm_sparse, and sdmult support complex * and zomplex * * These Modules do not support complex and zomplex matrices at all: * * Modify all routines support real matrices only */ /* Definitions for cholmod_common: */ #define CHOLMOD_MAXMETHODS 9 /* maximum number of different methods that * cholmod_analyze can try. Must be >= 9. */ /* Common->status values. zero means success, negative means a fatal error, * positive is a warning. */ #define CHOLMOD_OK 0 /* success */ #define CHOLMOD_NOT_INSTALLED (-1) /* failure: method not installed */ #define CHOLMOD_OUT_OF_MEMORY (-2) /* failure: out of memory */ #define CHOLMOD_TOO_LARGE (-3) /* failure: integer overflow occured */ #define CHOLMOD_INVALID (-4) /* failure: invalid input */ #define CHOLMOD_NOT_POSDEF (1) /* warning: matrix not pos. def. */ #define CHOLMOD_DSMALL (2) /* warning: D for LDL' or diag(L) or * LL' has tiny absolute value */ /* ordering method (also used for L->ordering) */ #define CHOLMOD_NATURAL 0 /* use natural ordering */ #define CHOLMOD_GIVEN 1 /* use given permutation */ #define CHOLMOD_AMD 2 /* use minimum degree (AMD) */ #define CHOLMOD_METIS 3 /* use METIS' nested dissection */ #define CHOLMOD_NESDIS 4 /* use CHOLMOD's version of nested dissection: * node bisector applied recursively, followed * by constrained minimum degree (CSYMAMD or * CCOLAMD) */ #define CHOLMOD_COLAMD 5 /* use AMD for A, COLAMD for A*A' */ /* POSTORDERED is not a method, but a result of natural ordering followed by a * weighted postorder. It is used for L->ordering, not method [ ].ordering. */ #define CHOLMOD_POSTORDERED 6 /* natural ordering, postordered. */ /* supernodal strategy (for Common->supernodal) */ #define CHOLMOD_SIMPLICIAL 0 /* always do simplicial */ #define CHOLMOD_AUTO 1 /* select simpl/super depending on matrix */ #define CHOLMOD_SUPERNODAL 2 /* always do supernodal */ typedef struct cholmod_common_struct { /* ---------------------------------------------------------------------- */ /* parameters for symbolic/numeric factorization and update/downdate */ /* ---------------------------------------------------------------------- */ double dbound ; /* Smallest absolute value of diagonal entries of D * for LDL' factorization and update/downdate/rowadd/ * rowdel, or the diagonal of L for an LL' factorization. * Entries in the range 0 to dbound are replaced with dbound. * Entries in the range -dbound to 0 are replaced with -dbound. No * changes are made to the diagonal if dbound <= 0. Default: zero */ double grow0 ; /* For a simplicial factorization, L->i and L->x can * grow if necessary. grow0 is the factor by which * it grows. For the initial space, L is of size MAX (1,grow0) times * the required space. If L runs out of space, the new size of L is * MAX(1.2,grow0) times the new required space. If you do not plan on * modifying the LDL' factorization in the Modify module, set grow0 to * zero (or set grow2 to 0, see below). Default: 1.2 */ double grow1 ; size_t grow2 ; /* For a simplicial factorization, each column j of L * is initialized with space equal to * grow1*L->ColCount[j] + grow2. If grow0 < 1, grow1 < 1, or grow2 == 0, * then the space allocated is exactly equal to L->ColCount[j]. If the * column j runs out of space, it increases to grow1*need + grow2 in * size, where need is the total # of nonzeros in that column. If you do * not plan on modifying the factorization in the Modify module, set * grow2 to zero. Default: grow1 = 1.2, grow2 = 5. */ size_t maxrank ; /* rank of maximum update/downdate. Valid values: * 2, 4, or 8. A value < 2 is set to 2, and a * value > 8 is set to 8. It is then rounded up to the next highest * power of 2, if not already a power of 2. Workspace (Xwork, below) of * size nrow-by-maxrank double's is allocated for the update/downdate. * If an update/downdate of rank-k is requested, with k > maxrank, * it is done in steps of maxrank. Default: 8, which is fastest. * Memory usage can be reduced by setting maxrank to 2 or 4. */ double supernodal_switch ; /* supernodal vs simplicial factorization */ int supernodal ; /* If Common->supernodal <= CHOLMOD_SIMPLICIAL * (0) then cholmod_analyze performs a * simplicial analysis. If >= CHOLMOD_SUPERNODAL (2), then a supernodal * analysis is performed. If == CHOLMOD_AUTO (1) and * flop/nnz(L) < Common->supernodal_switch, then a simplicial analysis * is done. A supernodal analysis done otherwise. * Default: CHOLMOD_AUTO. Default supernodal_switch = 40 */ int final_asis ; /* If TRUE, then ignore the other final_* parameters * (except for final_pack). * The factor is left as-is when done. Default: TRUE.*/ int final_super ; /* If TRUE, leave a factor in supernodal form when * supernodal factorization is finished. If FALSE, * then convert to a simplicial factor when done. * Default: TRUE */ int final_ll ; /* If TRUE, leave factor in LL' form when done. * Otherwise, leave in LDL' form. Default: FALSE */ int final_pack ; /* If TRUE, pack the columns when done. If TRUE, and * cholmod_factorize is called with a symbolic L, L is * allocated with exactly the space required, using L->ColCount. If you * plan on modifying the factorization, set Common->final_pack to FALSE, * and each column will be given a little extra slack space for future * growth in fill-in due to updates. Default: TRUE */ int final_monotonic ; /* If TRUE, ensure columns are monotonic when done. * Default: TRUE */ int final_resymbol ;/* if cholmod_factorize performed a supernodal * factorization, final_resymbol is true, and * final_super is FALSE (convert a simplicial numeric factorization), * then numerically zero entries that resulted from relaxed supernodal * amalgamation are removed. This does not remove entries that are zero * due to exact numeric cancellation, since doing so would break the * update/downdate rowadd/rowdel routines. Default: FALSE. */ /* supernodal relaxed amalgamation parameters: */ double zrelax [3] ; size_t nrelax [3] ; /* Let ns be the total number of columns in two adjacent supernodes. * Let z be the fraction of zero entries in the two supernodes if they * are merged (z includes zero entries from prior amalgamations). The * two supernodes are merged if: * (ns <= nrelax [0]) || (no new zero entries added) || * (ns <= nrelax [1] && z < zrelax [0]) || * (ns <= nrelax [2] && z < zrelax [1]) || (z < zrelax [2]) * * Default parameters result in the following rule: * (ns <= 4) || (no new zero entries added) || * (ns <= 16 && z < 0.8) || (ns <= 48 && z < 0.1) || (z < 0.05) */ int prefer_zomplex ; /* X = cholmod_solve (sys, L, B, Common) computes * x=A\b or solves a related system. If L and B are * both real, then X is real. Otherwise, X is returned as * CHOLMOD_COMPLEX if Common->prefer_zomplex is FALSE, or * CHOLMOD_ZOMPLEX if Common->prefer_zomplex is TRUE. This parameter * is needed because there is no supernodal zomplex L. Suppose the * caller wants all complex matrices to be stored in zomplex form * (MATLAB, for example). A supernodal L is returned in complex form * if A is zomplex. B can be real, and thus X = cholmod_solve (L,B) * should return X as zomplex. This cannot be inferred from the input * arguments L and B. Default: FALSE, since all data types are * supported in CHOLMOD_COMPLEX form and since this is the native type * of LAPACK and the BLAS. Note that the MATLAB/cholmod.c mexFunction * sets this parameter to TRUE, since MATLAB matrices are in * CHOLMOD_ZOMPLEX form. */ int prefer_upper ; /* cholmod_analyze and cholmod_factorize work * fastest when a symmetric matrix is stored in * upper triangular form when a fill-reducing ordering is used. In * MATLAB, this corresponds to how x=A\b works. When the matrix is * ordered as-is, they work fastest when a symmetric matrix is in lower * triangular form. In MATLAB, R=chol(A) does the opposite. This * parameter affects only how cholmod_read returns a symmetric matrix. * If TRUE (the default case), a symmetric matrix is always returned in * upper-triangular form (A->stype = 1). */ int quick_return_if_not_posdef ; /* if TRUE, the supernodal numeric * factorization will return quickly if * the matrix is not positive definite. Default: FALSE. */ /* ---------------------------------------------------------------------- */ /* printing and error handling options */ /* ---------------------------------------------------------------------- */ int print ; /* print level. Default: 3 */ int precise ; /* if TRUE, print 16 digits. Otherwise print 5 */ int (*print_function) (const char *, ...) ; /* pointer to printf */ int try_catch ; /* if TRUE, then ignore errors; CHOLMOD is in the middle * of a try/catch block. No error message is printed * and the Common->error_handler function is not called. */ void (*error_handler) (int status, char *file, int line, char *message) ; /* Common->error_handler is the user's error handling routine. If not * NULL, this routine is called if an error occurs in CHOLMOD. status * can be CHOLMOD_OK (0), negative for a fatal error, and positive for * a warning. file is a string containing the name of the source code * file where the error occured, and line is the line number in that * file. message is a string describing the error in more detail. */ /* ---------------------------------------------------------------------- */ /* ordering options */ /* ---------------------------------------------------------------------- */ /* The cholmod_analyze routine can try many different orderings and select * the best one. It can also try one ordering method multiple times, with * different parameter settings. The default is to use three orderings, * the user's permutation (if provided), AMD which is the fastest ordering * and generally gives good fill-in, and METIS. CHOLMOD's nested dissection * (METIS with a constrained AMD) usually gives a better ordering than METIS * alone (by about 5% to 10%) but it takes more time. * * If you know the method that is best for your matrix, set Common->nmethods * to 1 and set Common->method [0] to the set of parameters for that method. * If you set it to 1 and do not provide a permutation, then only AMD will * be called. * * If METIS is not available, the default # of methods tried is 2 (the user * permutation, if any, and AMD). * * To try other methods, set Common->nmethods to the number of methods you * want to try. The suite of default methods and their parameters is * described in the cholmod_defaults routine, and summarized here: * * Common->method [i]: * i = 0: user-provided ordering (cholmod_analyze_p only) * i = 1: AMD (for both A and A*A') * i = 2: METIS * i = 3: CHOLMOD's nested dissection (NESDIS), default parameters * i = 4: natural * i = 5: NESDIS with nd_small = 20000 * i = 6: NESDIS with nd_small = 4, no constrained minimum degree * i = 7: NESDIS with no dense node removal * i = 8: AMD for A, COLAMD for A*A' * * You can modify the suite of methods you wish to try by modifying * Common.method [...] after calling cholmod_start or cholmod_defaults. * * For example, to use AMD, followed by a weighted postordering: * * Common->nmethods = 1 ; * Common->method [0].ordering = CHOLMOD_AMD ; * Common->postorder = TRUE ; * * To use the natural ordering (with no postordering): * * Common->nmethods = 1 ; * Common->method [0].ordering = CHOLMOD_NATURAL ; * Common->postorder = FALSE ; * * If you are going to factorize hundreds or more matrices with the same * nonzero pattern, you may wish to spend a great deal of time finding a * good permutation. In this case, try setting Common->nmethods to 9. * The time spent in cholmod_analysis will be very high, but you need to * call it only once. * * cholmod_analyze sets Common->current to a value between 0 and nmethods-1. * Each ordering method uses the set of options defined by this parameter. */ int nmethods ; /* The number of ordering methods to try. Default: 0. * nmethods = 0 is a special case. cholmod_analyze * will try the user-provided ordering (if given) and AMD. Let fl and * lnz be the flop count and nonzeros in L from AMD's ordering. Let * anz be the number of nonzeros in the upper or lower triangular part * of the symmetric matrix A. If fl/lnz < 500 or lnz/anz < 5, then this * is a good ordering, and METIS is not attempted. Otherwise, METIS is * tried. The best ordering found is used. If nmethods > 0, the * methods used are given in the method[ ] array, below. The first * three methods in the default suite of orderings is (1) use the given * permutation (if provided), (2) use AMD, and (3) use METIS. Maximum * allowed value is CHOLMOD_MAXMETHODS. */ int current ; /* The current method being tried. Default: 0. Valid * range is 0 to nmethods-1. */ int selected ; /* The best method found. */ /* The suite of ordering methods and parameters: */ struct cholmod_method_struct { /* statistics for this method */ double lnz ; /* nnz(L) excl. zeros from supernodal amalgamation, * for a "pure" L */ double fl ; /* flop count for a "pure", real simplicial LL' * factorization, with no extra work due to * amalgamation. Subtract n to get the LDL' flop count. Multiply * by about 4 if the matrix is complex or zomplex. */ /* ordering method parameters */ double prune_dense ;/* dense row/col control for AMD, SYMAMD, CSYMAMD, * and NESDIS (cholmod_nested_dissection). For a * symmetric n-by-n matrix, rows/columns with more than * MAX (16, prune_dense * sqrt (n)) entries are removed prior to * ordering. They appear at the end of the re-ordered matrix. * * If prune_dense < 0, only completely dense rows/cols are removed. * * This paramater is also the dense column control for COLAMD and * CCOLAMD. For an m-by-n matrix, columns with more than * MAX (16, prune_dense * sqrt (MIN (m,n))) entries are removed prior * to ordering. They appear at the end of the re-ordered matrix. * CHOLMOD factorizes A*A', so it calls COLAMD and CCOLAMD with A', * not A. Thus, this parameter affects the dense *row* control for * CHOLMOD's matrix, and the dense *column* control for COLAMD and * CCOLAMD. * * Removing dense rows and columns improves the run-time of the * ordering methods. It has some impact on ordering quality * (usually minimal, sometimes good, sometimes bad). * * Default: 10. */ double prune_dense2 ;/* dense row control for COLAMD and CCOLAMD. * Rows with more than MAX (16, dense2 * sqrt (n)) * for an m-by-n matrix are removed prior to ordering. CHOLMOD's * matrix is transposed before ordering it with COLAMD or CCOLAMD, * so this controls the dense *columns* of CHOLMOD's matrix, and * the dense *rows* of COLAMD's or CCOLAMD's matrix. * * If prune_dense2 < 0, only completely dense rows/cols are removed. * * Default: -1. Note that this is not the default for COLAMD and * CCOLAMD. -1 is best for Cholesky. 10 is best for LU. */ double nd_oksep ; /* in NESDIS, when a node separator is computed, it * discarded if nsep >= nd_oksep*n, where nsep is * the number of nodes in the separator, and n is the size of the * graph being cut. Valid range is 0 to 1. If 1 or greater, the * separator is discarded if it consists of the entire graph. * Default: 1 */ double other1 [4] ; /* future expansion */ size_t nd_small ; /* do not partition graphs with fewer nodes than * nd_small, in NESDIS. Default: 200 (same as * METIS) */ size_t other2 [4] ; /* future expansion */ int aggressive ; /* Aggresive absorption in AMD, COLAMD, SYMAMD, * CCOLAMD, and CSYMAMD. Default: TRUE */ int order_for_lu ; /* CCOLAMD can be optimized to produce an ordering * for LU or Cholesky factorization. CHOLMOD only * performs a Cholesky factorization. However, you may wish to use * CHOLMOD as an interface for CCOLAMD but use it for your own LU * factorization. In this case, order_for_lu should be set to FALSE. * When factorizing in CHOLMOD itself, you should *** NEVER *** set * this parameter FALSE. Default: TRUE. */ int nd_compress ; /* If TRUE, compress the graph and subgraphs before * partitioning them in NESDIS. Default: TRUE */ int nd_camd ; /* If 1, follow the nested dissection ordering * with a constrained minimum degree ordering that * respects the partitioning just found (using CAMD). If 2, use * CSYMAMD instead. If you set nd_small very small, you may not need * this ordering, and can save time by setting it to zero (no * constrained minimum degree ordering). Default: 1. */ int nd_components ; /* The nested dissection ordering finds a node * separator that splits the graph into two parts, * which may be unconnected. If nd_components is TRUE, each of * these connected components is split independently. If FALSE, * each part is split as a whole, even if it consists of more than * one connected component. Default: FALSE */ /* fill-reducing ordering to use */ int ordering ; size_t other3 [4] ; /* future expansion */ } method [CHOLMOD_MAXMETHODS + 1] ; int postorder ; /* If TRUE, cholmod_analyze follows the ordering with a * weighted postorder of the elimination tree. Improves * supernode amalgamation. Does not affect fundamental nnz(L) and * flop count. Default: TRUE. */ /* ---------------------------------------------------------------------- */ /* memory management routines */ /* ---------------------------------------------------------------------- */ void *(*malloc_memory) (size_t) ; /* pointer to malloc */ void *(*realloc_memory) (void *, size_t) ; /* pointer to realloc */ void (*free_memory) (void *) ; /* pointer to free */ void *(*calloc_memory) (size_t, size_t) ; /* pointer to calloc */ /* ---------------------------------------------------------------------- */ /* routines for complex arithmetic */ /* ---------------------------------------------------------------------- */ int (*complex_divide) (double ax, double az, double bx, double bz, double *cx, double *cz) ; /* flag = complex_divide (ax, az, bx, bz, &cx, &cz) computes the complex * division c = a/b, where ax and az hold the real and imaginary part * of a, and b and c are stored similarly. flag is returned as 1 if * a divide-by-zero occurs, or 0 otherwise. By default, the function * pointer Common->complex_divide is set equal to cholmod_divcomplex. */ double (*hypotenuse) (double x, double y) ; /* s = hypotenuse (x,y) computes s = sqrt (x*x + y*y), but does so more * accurately. By default, the function pointer Common->hypotenuse is * set equal to cholmod_hypot. See also the hypot function in the C99 * standard, which has an identical syntax and function. If you have * a C99-compliant compiler, you can set Common->hypotenuse = hypot. */ /* ---------------------------------------------------------------------- */ /* METIS workarounds */ /* ---------------------------------------------------------------------- */ double metis_memory ; /* This is a parameter for CHOLMOD's interface to * METIS, not a parameter to METIS itself. METIS * uses an amount of memory that is difficult to estimate precisely * beforehand. If it runs out of memory, it terminates your program. * All routines in CHOLMOD except for CHOLMOD's interface to METIS * return an error status and safely return to your program if they run * out of memory. To mitigate this problem, the CHOLMOD interface * can allocate a single block of memory equal in size to an empirical * upper bound of METIS's memory usage times the Common->metis_memory * parameter, and then immediately free it. It then calls METIS. If * this pre-allocation fails, it is possible that METIS will fail as * well, and so CHOLMOD returns with an out-of-memory condition without * calling METIS. * * METIS_NodeND (used in the CHOLMOD_METIS ordering option) with its * default parameter settings typically uses about (4*nz+40n+4096) * times sizeof(int) memory, where nz is equal to the number of entries * in A for the symmetric case or AA' if an unsymmetric matrix is * being ordered (where nz includes both the upper and lower parts * of A or AA'). The observed "upper bound" (with 2 exceptions), * measured in an instrumented copy of METIS 4.0.1 on thousands of * matrices, is (10*nz+50*n+4096) * sizeof(int). Two large matrices * exceeded this bound, one by almost a factor of 2 (Gupta/gupta2). * * If your program is terminated by METIS, try setting metis_memory to * 2.0, or even higher if needed. By default, CHOLMOD assumes that METIS * does not have this problem (so that CHOLMOD will work correctly when * this issue is fixed in METIS). Thus, the default value is zero. * This work-around is not guaranteed anyway. * * If a matrix exceeds this predicted memory usage, AMD is attempted * instead. It, too, may run out of memory, but if it does so it will * not terminate your program. */ double metis_dswitch ; /* METIS_NodeND in METIS 4.0.1 gives a seg */ size_t metis_nswitch ; /* fault with one matrix of order n = 3005 and * nz = 6,036,025. This is a very dense graph. * The workaround is to use AMD instead of METIS for matrices of dimension * greater than Common->metis_nswitch (default 3000) or more and with * density of Common->metis_dswitch (default 0.66) or more. * cholmod_nested_dissection has no problems with the same matrix, even * though it uses METIS_NodeComputeSeparator on this matrix. If this * seg fault does not affect you, set metis_nswitch to zero or less, * and CHOLMOD will not switch to AMD based just on the density of the * matrix (it will still switch to AMD if the metis_memory parameter * causes the switch). */ /* ---------------------------------------------------------------------- */ /* workspace */ /* ---------------------------------------------------------------------- */ /* CHOLMOD has several routines that take less time than the size of * workspace they require. Allocating and initializing the workspace would * dominate the run time, unless workspace is allocated and initialized * just once. CHOLMOD allocates this space when needed, and holds it here * between calls to CHOLMOD. cholmod_start sets these pointers to NULL * (which is why it must be the first routine called in CHOLMOD). * cholmod_finish frees the workspace (which is why it must be the last * call to CHOLMOD). */ size_t nrow ; /* size of Flag and Head */ UF_long mark ; /* mark value for Flag array */ size_t iworksize ; /* size of Iwork. Upper bound: 6*nrow+ncol */ size_t xworksize ; /* size of Xwork, in bytes. * maxrank*nrow*sizeof(double) for update/downdate. * 2*nrow*sizeof(double) otherwise */ /* initialized workspace: contents needed between calls to CHOLMOD */ void *Flag ; /* size nrow, an integer array. Kept cleared between * calls to cholmod rouines (Flag [i] < mark) */ void *Head ; /* size nrow+1, an integer array. Kept cleared between * calls to cholmod routines (Head [i] = EMPTY) */ void *Xwork ; /* a double array. Its size varies. It is nrow for * most routines (cholmod_rowfac, cholmod_add, * cholmod_aat, cholmod_norm, cholmod_ssmult) for the real case, twice * that when the input matrices are complex or zomplex. It is of size * 2*nrow for cholmod_rowadd and cholmod_rowdel. For cholmod_updown, * its size is maxrank*nrow where maxrank is 2, 4, or 8. Kept cleared * between calls to cholmod (set to zero). */ /* uninitialized workspace, contents not needed between calls to CHOLMOD */ void *Iwork ; /* size iworksize, 2*nrow+ncol for most routines, * up to 6*nrow+ncol for cholmod_analyze. */ int itype ; /* If CHOLMOD_LONG, Flag, Head, and Iwork are UF_long. * Otherwise all three arrays are int. */ int dtype ; /* double or float */ /* Common->itype and Common->dtype are used to define the types of all * sparse matrices, triplet matrices, dense matrices, and factors * created using this Common struct. The itypes and dtypes of all * parameters to all CHOLMOD routines must match. */ int no_workspace_reallocate ; /* this is an internal flag, used as a * precaution by cholmod_analyze. It is normally false. If true, * cholmod_allocate_work is not allowed to reallocate any workspace; * they must use the existing workspace in Common (Iwork, Flag, Head, * and Xwork). Added for CHOLMOD v1.1 */ /* ---------------------------------------------------------------------- */ /* statistics */ /* ---------------------------------------------------------------------- */ /* fl and lnz are set only in cholmod_analyze and cholmod_rowcolcounts, * in the Cholesky modudle. modfl is set only in the Modify module. */ int status ; /* error code */ double fl ; /* LL' flop count from most recent analysis */ double lnz ; /* fundamental nz in L */ double anz ; /* nonzeros in tril(A) if A is symmetric/lower, * triu(A) if symmetric/upper, or tril(A*A') if * unsymmetric, in last call to cholmod_analyze. */ double modfl ; /* flop count from most recent update/downdate/ * rowadd/rowdel (excluding flops to modify the * solution to Lx=b, if computed) */ size_t malloc_count ; /* # of objects malloc'ed minus the # free'd*/ size_t memory_usage ; /* peak memory usage in bytes */ size_t memory_inuse ; /* current memory usage in bytes */ double nrealloc_col ; /* # of column reallocations */ double nrealloc_factor ;/* # of factor reallocations due to col. reallocs */ double ndbounds_hit ; /* # of times diagonal modified by dbound */ double rowfacfl ; /* # of flops in last call to cholmod_rowfac */ double aatfl ; /* # of flops to compute A(:,f)*A(:,f)' */ /* ---------------------------------------------------------------------- */ /* future expansion */ /* ---------------------------------------------------------------------- */ /* To allow CHOLMOD to be updated without recompiling the user application, * additional space is set aside here for future statistics, parameters, * and workspace. Note: additional entries were added in v1.1 to the * method array, above, and thus v1.0 and v1.1 are not binary compatible. * * v1.1 to the current version are binary compatible. */ double other1 [16] ; UF_long other2 [16] ; int other3 [13] ; /* reduced from size 16 in v1.1. */ int prefer_binary ; /* cholmod_read_triplet converts a symmetric * pattern-only matrix into a real matrix. If * prefer_binary is FALSE, the diagonal entries are set to 1 + the degree * of the row/column, and off-diagonal entries are set to -1 (resulting * in a positive definite matrix if the diagonal is zero-free). Most * symmetric patterns are the pattern a positive definite matrix. If * this parameter is TRUE, then the matrix is returned with a 1 in each * entry, instead. Default: FALSE. Added in v1.3. */ /* control parameter (added for v1.2): */ int default_nesdis ; /* Default: FALSE. If FALSE, then the default * ordering strategy (when Common->nmethods == 0) * is to try the given ordering (if present), AMD, and then METIS if AMD * reports high fill-in. If Common->default_nesdis is TRUE then NESDIS * is used instead in the default strategy. */ /* statistic (added for v1.2): */ int called_nd ; /* TRUE if the last call to * cholmod_analyze called NESDIS or METIS. */ size_t other4 [16] ; void *other5 [16] ; } cholmod_common ; /* -------------------------------------------------------------------------- */ /* cholmod_start: first call to CHOLMOD */ /* -------------------------------------------------------------------------- */ int cholmod_start ( cholmod_common *Common ) ; int cholmod_l_start (cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_finish: last call to CHOLMOD */ /* -------------------------------------------------------------------------- */ int cholmod_finish ( cholmod_common *Common ) ; int cholmod_l_finish (cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_defaults: restore default parameters */ /* -------------------------------------------------------------------------- */ int cholmod_defaults ( cholmod_common *Common ) ; int cholmod_l_defaults (cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_maxrank: return valid maximum rank for update/downdate */ /* -------------------------------------------------------------------------- */ size_t cholmod_maxrank /* returns validated value of Common->maxrank */ ( /* ---- input ---- */ size_t n, /* A and L will have n rows */ /* --------------- */ cholmod_common *Common ) ; size_t cholmod_l_maxrank (size_t, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_allocate_work: allocate workspace in Common */ /* -------------------------------------------------------------------------- */ int cholmod_allocate_work ( /* ---- input ---- */ size_t nrow, /* size: Common->Flag (nrow), Common->Head (nrow+1) */ size_t iworksize, /* size of Common->Iwork */ size_t xworksize, /* size of Common->Xwork */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_allocate_work (size_t, size_t, size_t, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_free_work: free workspace in Common */ /* -------------------------------------------------------------------------- */ int cholmod_free_work ( cholmod_common *Common ) ; int cholmod_l_free_work (cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_clear_flag: clear Flag workspace in Common */ /* -------------------------------------------------------------------------- */ /* use a macro for speed */ #define CHOLMOD_CLEAR_FLAG(Common) \ { \ Common->mark++ ; \ if (Common->mark <= 0) \ { \ Common->mark = EMPTY ; \ CHOLMOD (clear_flag) (Common) ; \ } \ } UF_long cholmod_clear_flag ( cholmod_common *Common ) ; UF_long cholmod_l_clear_flag (cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_error: called when CHOLMOD encounters an error */ /* -------------------------------------------------------------------------- */ int cholmod_error ( /* ---- input ---- */ int status, /* error status */ char *file, /* name of source code file where error occured */ int line, /* line number in source code file where error occured*/ char *message, /* error message */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_error (int, char *, int, char *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_dbound: for internal use in CHOLMOD only */ /* -------------------------------------------------------------------------- */ double cholmod_dbound /* returns modified diagonal entry of D or L */ ( /* ---- input ---- */ double dj, /* diagonal entry of D for LDL' or L for LL' */ /* --------------- */ cholmod_common *Common ) ; double cholmod_l_dbound (double, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_hypot: compute sqrt (x*x + y*y) accurately */ /* -------------------------------------------------------------------------- */ double cholmod_hypot ( /* ---- input ---- */ double x, double y ) ; double cholmod_l_hypot (double, double) ; /* -------------------------------------------------------------------------- */ /* cholmod_divcomplex: complex division, c = a/b */ /* -------------------------------------------------------------------------- */ int cholmod_divcomplex /* return 1 if divide-by-zero, 0 otherise */ ( /* ---- input ---- */ double ar, double ai, /* real and imaginary parts of a */ double br, double bi, /* real and imaginary parts of b */ /* ---- output --- */ double *cr, double *ci /* real and imaginary parts of c */ ) ; int cholmod_l_divcomplex (double, double, double, double, double *, double *) ; /* ========================================================================== */ /* === Core/cholmod_sparse ================================================== */ /* ========================================================================== */ /* A sparse matrix stored in compressed-column form. */ typedef struct cholmod_sparse_struct { size_t nrow ; /* the matrix is nrow-by-ncol */ size_t ncol ; size_t nzmax ; /* maximum number of entries in the matrix */ /* pointers to int or UF_long: */ void *p ; /* p [0..ncol], the column pointers */ void *i ; /* i [0..nzmax-1], the row indices */ /* for unpacked matrices only: */ void *nz ; /* nz [0..ncol-1], the # of nonzeros in each col. In * packed form, the nonzero pattern of column j is in * A->i [A->p [j] ... A->p [j+1]-1]. In unpacked form, column j is in * A->i [A->p [j] ... A->p [j]+A->nz[j]-1] instead. In both cases, the * numerical values (if present) are in the corresponding locations in * the array x (or z if A->xtype is CHOLMOD_ZOMPLEX). */ /* pointers to double or float: */ void *x ; /* size nzmax or 2*nzmax, if present */ void *z ; /* size nzmax, if present */ int stype ; /* Describes what parts of the matrix are considered: * * 0: matrix is "unsymmetric": use both upper and lower triangular parts * (the matrix may actually be symmetric in pattern and value, but * both parts are explicitly stored and used). May be square or * rectangular. * >0: matrix is square and symmetric, use upper triangular part. * Entries in the lower triangular part are ignored. * <0: matrix is square and symmetric, use lower triangular part. * Entries in the upper triangular part are ignored. * * Note that stype>0 and stype<0 are different for cholmod_sparse and * cholmod_triplet. See the cholmod_triplet data structure for more * details. */ int itype ; /* CHOLMOD_INT: p, i, and nz are int. * CHOLMOD_INTLONG: p is UF_long, i and nz are int. * CHOLMOD_LONG: p, i, and nz are UF_long. */ int xtype ; /* pattern, real, complex, or zomplex */ int dtype ; /* x and z are double or float */ int sorted ; /* TRUE if columns are sorted, FALSE otherwise */ int packed ; /* TRUE if packed (nz ignored), FALSE if unpacked * (nz is required) */ } cholmod_sparse ; /* -------------------------------------------------------------------------- */ /* cholmod_allocate_sparse: allocate a sparse matrix */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_allocate_sparse ( /* ---- input ---- */ size_t nrow, /* # of rows of A */ size_t ncol, /* # of columns of A */ size_t nzmax, /* max # of nonzeros of A */ int sorted, /* TRUE if columns of A sorted, FALSE otherwise */ int packed, /* TRUE if A will be packed, FALSE otherwise */ int stype, /* stype of A */ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_allocate_sparse (size_t, size_t, size_t, int, int, int, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_free_sparse: free a sparse matrix */ /* -------------------------------------------------------------------------- */ int cholmod_free_sparse ( /* ---- in/out --- */ cholmod_sparse **A, /* matrix to deallocate, NULL on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_free_sparse (cholmod_sparse **, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_reallocate_sparse: change the size (# entries) of sparse matrix */ /* -------------------------------------------------------------------------- */ int cholmod_reallocate_sparse ( /* ---- input ---- */ size_t nznew, /* new # of entries in A */ /* ---- in/out --- */ cholmod_sparse *A, /* matrix to reallocate */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_reallocate_sparse ( size_t, cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_nnz: return number of nonzeros in a sparse matrix */ /* -------------------------------------------------------------------------- */ UF_long cholmod_nnz ( /* ---- input ---- */ cholmod_sparse *A, /* --------------- */ cholmod_common *Common ) ; UF_long cholmod_l_nnz (cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_speye: sparse identity matrix */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_speye ( /* ---- input ---- */ size_t nrow, /* # of rows of A */ size_t ncol, /* # of columns of A */ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_speye (size_t, size_t, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_spzeros: sparse zero matrix */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_spzeros ( /* ---- input ---- */ size_t nrow, /* # of rows of A */ size_t ncol, /* # of columns of A */ size_t nzmax, /* max # of nonzeros of A */ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_spzeros (size_t, size_t, size_t, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_transpose: transpose a sparse matrix */ /* -------------------------------------------------------------------------- */ /* Return A' or A.' The "values" parameter is 0, 1, or 2 to denote the pattern * transpose, the array transpose (A.'), and the complex conjugate transpose * (A'). */ cholmod_sparse *cholmod_transpose ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to transpose */ int values, /* 0: pattern, 1: array transpose, 2: conj. transpose */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_transpose (cholmod_sparse *, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_transpose_unsym: transpose an unsymmetric sparse matrix */ /* -------------------------------------------------------------------------- */ /* Compute F = A', A (:,f)', or A (p,f)', where A is unsymmetric and F is * already allocated. See cholmod_transpose for a simpler routine. */ int cholmod_transpose_unsym ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to transpose */ int values, /* 0: pattern, 1: array transpose, 2: conj. transpose */ int *Perm, /* size nrow, if present (can be NULL) */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- output --- */ cholmod_sparse *F, /* F = A', A(:,f)', or A(p,f)' */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_transpose_unsym (cholmod_sparse *, int, UF_long *, UF_long *, size_t, cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_transpose_sym: transpose a symmetric sparse matrix */ /* -------------------------------------------------------------------------- */ /* Compute F = A' or A (p,p)', where A is symmetric and F is already allocated. * See cholmod_transpose for a simpler routine. */ int cholmod_transpose_sym ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to transpose */ int values, /* 0: pattern, 1: array transpose, 2: conj. transpose */ int *Perm, /* size nrow, if present (can be NULL) */ /* ---- output --- */ cholmod_sparse *F, /* F = A' or A(p,p)' */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_transpose_sym (cholmod_sparse *, int, UF_long *, cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_ptranspose: transpose a sparse matrix */ /* -------------------------------------------------------------------------- */ /* Return A' or A(p,p)' if A is symmetric. Return A', A(:,f)', or A(p,f)' if * A is unsymmetric. */ cholmod_sparse *cholmod_ptranspose ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to transpose */ int values, /* 0: pattern, 1: array transpose, 2: conj. transpose */ int *Perm, /* if non-NULL, F = A(p,f) or A(p,p) */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_ptranspose (cholmod_sparse *, int, UF_long *, UF_long *, size_t, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_sort: sort row indices in each column of sparse matrix */ /* -------------------------------------------------------------------------- */ int cholmod_sort ( /* ---- in/out --- */ cholmod_sparse *A, /* matrix to sort */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_sort (cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_band: C = tril (triu (A,k1), k2) */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_band ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to extract band matrix from */ UF_long k1, /* ignore entries below the k1-st diagonal */ UF_long k2, /* ignore entries above the k2-nd diagonal */ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_band (cholmod_sparse *, UF_long, UF_long, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_band_inplace: A = tril (triu (A,k1), k2) */ /* -------------------------------------------------------------------------- */ int cholmod_band_inplace ( /* ---- input ---- */ UF_long k1, /* ignore entries below the k1-st diagonal */ UF_long k2, /* ignore entries above the k2-nd diagonal */ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */ /* ---- in/out --- */ cholmod_sparse *A, /* matrix from which entries not in band are removed */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_band_inplace (UF_long, UF_long, int, cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_aat: C = A*A' or A(:,f)*A(:,f)' */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_aat ( /* ---- input ---- */ cholmod_sparse *A, /* input matrix; C=A*A' is constructed */ int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag), * -2: pattern only, no diagonal, add 50%+n extra * space to C */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_aat (cholmod_sparse *, UF_long *, size_t, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_copy_sparse: C = A, create an exact copy of a sparse matrix */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_copy_sparse ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_copy_sparse (cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_copy: C = A, with possible change of stype */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_copy ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to copy */ int stype, /* requested stype of C */ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_copy (cholmod_sparse *, int, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_add: C = alpha*A + beta*B */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_add ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to add */ cholmod_sparse *B, /* matrix to add */ double alpha [2], /* scale factor for A */ double beta [2], /* scale factor for B */ int values, /* if TRUE compute the numerical values of C */ int sorted, /* if TRUE, sort columns of C */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_add (cholmod_sparse *, cholmod_sparse *, double *, double *, int, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_sparse_xtype: change the xtype of a sparse matrix */ /* -------------------------------------------------------------------------- */ int cholmod_sparse_xtype ( /* ---- input ---- */ int to_xtype, /* requested xtype (pattern, real, complex, zomplex) */ /* ---- in/out --- */ cholmod_sparse *A, /* sparse matrix to change */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_sparse_xtype (int, cholmod_sparse *, cholmod_common *) ; /* ========================================================================== */ /* === Core/cholmod_factor ================================================== */ /* ========================================================================== */ /* A symbolic and numeric factorization, either simplicial or supernodal. * In all cases, the row indices in the columns of L are kept sorted. */ typedef struct cholmod_factor_struct { /* ---------------------------------------------------------------------- */ /* for both simplicial and supernodal factorizations */ /* ---------------------------------------------------------------------- */ size_t n ; /* L is n-by-n */ size_t minor ; /* If the factorization failed, L->minor is the column * at which it failed (in the range 0 to n-1). A value * of n means the factorization was successful or * the matrix has not yet been factorized. */ /* ---------------------------------------------------------------------- */ /* symbolic ordering and analysis */ /* ---------------------------------------------------------------------- */ void *Perm ; /* size n, permutation used */ void *ColCount ; /* size n, column counts for simplicial L */ /* ---------------------------------------------------------------------- */ /* simplicial factorization */ /* ---------------------------------------------------------------------- */ size_t nzmax ; /* size of i and x */ void *p ; /* p [0..ncol], the column pointers */ void *i ; /* i [0..nzmax-1], the row indices */ void *x ; /* x [0..nzmax-1], the numerical values */ void *z ; void *nz ; /* nz [0..ncol-1], the # of nonzeros in each column. * i [p [j] ... p [j]+nz[j]-1] contains the row indices, * and the numerical values are in the same locatins * in x. The value of i [p [k]] is always k. */ void *next ; /* size ncol+2. next [j] is the next column in i/x */ void *prev ; /* size ncol+2. prev [j] is the prior column in i/x. * head of the list is ncol+1, and the tail is ncol. */ /* ---------------------------------------------------------------------- */ /* supernodal factorization */ /* ---------------------------------------------------------------------- */ /* Note that L->x is shared with the simplicial data structure. L->x has * size L->nzmax for a simplicial factor, and size L->xsize for a supernodal * factor. */ size_t nsuper ; /* number of supernodes */ size_t ssize ; /* size of s, integer part of supernodes */ size_t xsize ; /* size of x, real part of supernodes */ size_t maxcsize ; /* size of largest update matrix */ size_t maxesize ; /* max # of rows in supernodes, excl. triangular part */ void *super ; /* size nsuper+1, first col in each supernode */ void *pi ; /* size nsuper+1, pointers to integer patterns */ void *px ; /* size nsuper+1, pointers to real parts */ void *s ; /* size ssize, integer part of supernodes */ /* ---------------------------------------------------------------------- */ /* factorization type */ /* ---------------------------------------------------------------------- */ int ordering ; /* ordering method used */ int is_ll ; /* TRUE if LL', FALSE if LDL' */ int is_super ; /* TRUE if supernodal, FALSE if simplicial */ int is_monotonic ; /* TRUE if columns of L appear in order 0..n-1. * Only applicable to simplicial numeric types. */ /* There are 8 types of factor objects that cholmod_factor can represent * (only 6 are used): * * Numeric types (xtype is not CHOLMOD_PATTERN) * -------------------------------------------- * * simplicial LDL': (is_ll FALSE, is_super FALSE). Stored in compressed * column form, using the simplicial components above (nzmax, p, i, * x, z, nz, next, and prev). The unit diagonal of L is not stored, * and D is stored in its place. There are no supernodes. * * simplicial LL': (is_ll TRUE, is_super FALSE). Uses the same storage * scheme as the simplicial LDL', except that D does not appear. * The first entry of each column of L is the diagonal entry of * that column of L. * * supernodal LDL': (is_ll FALSE, is_super TRUE). Not used. * FUTURE WORK: add support for supernodal LDL' * * supernodal LL': (is_ll TRUE, is_super TRUE). A supernodal factor, * using the supernodal components described above (nsuper, ssize, * xsize, maxcsize, maxesize, super, pi, px, s, x, and z). * * * Symbolic types (xtype is CHOLMOD_PATTERN) * ----------------------------------------- * * simplicial LDL': (is_ll FALSE, is_super FALSE). Nothing is present * except Perm and ColCount. * * simplicial LL': (is_ll TRUE, is_super FALSE). Identical to the * simplicial LDL', except for the is_ll flag. * * supernodal LDL': (is_ll FALSE, is_super TRUE). Not used. * FUTURE WORK: add support for supernodal LDL' * * supernodal LL': (is_ll TRUE, is_super TRUE). A supernodal symbolic * factorization. The simplicial symbolic information is present * (Perm and ColCount), as is all of the supernodal factorization * except for the numerical values (x and z). */ int itype ; /* The integer arrays are Perm, ColCount, p, i, nz, * next, prev, super, pi, px, and s. If itype is * CHOLMOD_INT, all of these are int arrays. * CHOLMOD_INTLONG: p, pi, px are UF_long, others int. * CHOLMOD_LONG: all integer arrays are UF_long. */ int xtype ; /* pattern, real, complex, or zomplex */ int dtype ; /* x and z double or float */ } cholmod_factor ; /* -------------------------------------------------------------------------- */ /* cholmod_allocate_factor: allocate a factor (symbolic LL' or LDL') */ /* -------------------------------------------------------------------------- */ cholmod_factor *cholmod_allocate_factor ( /* ---- input ---- */ size_t n, /* L is n-by-n */ /* --------------- */ cholmod_common *Common ) ; cholmod_factor *cholmod_l_allocate_factor (size_t, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_free_factor: free a factor */ /* -------------------------------------------------------------------------- */ int cholmod_free_factor ( /* ---- in/out --- */ cholmod_factor **L, /* factor to free, NULL on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_free_factor (cholmod_factor **, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_reallocate_factor: change the # entries in a factor */ /* -------------------------------------------------------------------------- */ int cholmod_reallocate_factor ( /* ---- input ---- */ size_t nznew, /* new # of entries in L */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_reallocate_factor (size_t, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_change_factor: change the type of factor (e.g., LDL' to LL') */ /* -------------------------------------------------------------------------- */ int cholmod_change_factor ( /* ---- input ---- */ int to_xtype, /* to CHOLMOD_PATTERN, _REAL, _COMPLEX, _ZOMPLEX */ int to_ll, /* TRUE: convert to LL', FALSE: LDL' */ int to_super, /* TRUE: convert to supernodal, FALSE: simplicial */ int to_packed, /* TRUE: pack simplicial columns, FALSE: do not pack */ int to_monotonic, /* TRUE: put simplicial columns in order, FALSE: not */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_change_factor ( int, int, int, int, int, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_pack_factor: pack the columns of a factor */ /* -------------------------------------------------------------------------- */ /* Pack the columns of a simplicial factor. Unlike cholmod_change_factor, * it can pack the columns of a factor even if they are not stored in their * natural order (non-monotonic). */ int cholmod_pack_factor ( /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_pack_factor (cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_reallocate_column: resize a single column of a factor */ /* -------------------------------------------------------------------------- */ int cholmod_reallocate_column ( /* ---- input ---- */ size_t j, /* the column to reallocate */ size_t need, /* required size of column j */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_reallocate_column (size_t, size_t, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_factor_to_sparse: create a sparse matrix copy of a factor */ /* -------------------------------------------------------------------------- */ /* Only operates on numeric factors, not symbolic ones */ cholmod_sparse *cholmod_factor_to_sparse ( /* ---- in/out --- */ cholmod_factor *L, /* factor to copy, converted to symbolic on output */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_factor_to_sparse (cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_copy_factor: create a copy of a factor */ /* -------------------------------------------------------------------------- */ cholmod_factor *cholmod_copy_factor ( /* ---- input ---- */ cholmod_factor *L, /* factor to copy */ /* --------------- */ cholmod_common *Common ) ; cholmod_factor *cholmod_l_copy_factor (cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_factor_xtype: change the xtype of a factor */ /* -------------------------------------------------------------------------- */ int cholmod_factor_xtype ( /* ---- input ---- */ int to_xtype, /* requested xtype (real, complex, or zomplex) */ /* ---- in/out --- */ cholmod_factor *L, /* factor to change */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_factor_xtype (int, cholmod_factor *, cholmod_common *) ; /* ========================================================================== */ /* === Core/cholmod_dense =================================================== */ /* ========================================================================== */ /* A dense matrix in column-oriented form. It has no itype since it contains * no integers. Entry in row i and column j is located in x [i+j*d]. */ typedef struct cholmod_dense_struct { size_t nrow ; /* the matrix is nrow-by-ncol */ size_t ncol ; size_t nzmax ; /* maximum number of entries in the matrix */ size_t d ; /* leading dimension (d >= nrow must hold) */ void *x ; /* size nzmax or 2*nzmax, if present */ void *z ; /* size nzmax, if present */ int xtype ; /* pattern, real, complex, or zomplex */ int dtype ; /* x and z double or float */ } cholmod_dense ; /* -------------------------------------------------------------------------- */ /* cholmod_allocate_dense: allocate a dense matrix (contents uninitialized) */ /* -------------------------------------------------------------------------- */ cholmod_dense *cholmod_allocate_dense ( /* ---- input ---- */ size_t nrow, /* # of rows of matrix */ size_t ncol, /* # of columns of matrix */ size_t d, /* leading dimension */ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) ; cholmod_dense *cholmod_l_allocate_dense (size_t, size_t, size_t, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_zeros: allocate a dense matrix and set it to zero */ /* -------------------------------------------------------------------------- */ cholmod_dense *cholmod_zeros ( /* ---- input ---- */ size_t nrow, /* # of rows of matrix */ size_t ncol, /* # of columns of matrix */ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) ; cholmod_dense *cholmod_l_zeros (size_t, size_t, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_ones: allocate a dense matrix and set it to all ones */ /* -------------------------------------------------------------------------- */ cholmod_dense *cholmod_ones ( /* ---- input ---- */ size_t nrow, /* # of rows of matrix */ size_t ncol, /* # of columns of matrix */ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) ; cholmod_dense *cholmod_l_ones (size_t, size_t, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_eye: allocate a dense matrix and set it to the identity matrix */ /* -------------------------------------------------------------------------- */ cholmod_dense *cholmod_eye ( /* ---- input ---- */ size_t nrow, /* # of rows of matrix */ size_t ncol, /* # of columns of matrix */ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) ; cholmod_dense *cholmod_l_eye (size_t, size_t, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_free_dense: free a dense matrix */ /* -------------------------------------------------------------------------- */ int cholmod_free_dense ( /* ---- in/out --- */ cholmod_dense **X, /* dense matrix to deallocate, NULL on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_free_dense (cholmod_dense **, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_sparse_to_dense: create a dense matrix copy of a sparse matrix */ /* -------------------------------------------------------------------------- */ cholmod_dense *cholmod_sparse_to_dense ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) ; cholmod_dense *cholmod_l_sparse_to_dense (cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_dense_to_sparse: create a sparse matrix copy of a dense matrix */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_dense_to_sparse ( /* ---- input ---- */ cholmod_dense *X, /* matrix to copy */ int values, /* TRUE if values to be copied, FALSE otherwise */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_dense_to_sparse (cholmod_dense *, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_copy_dense: create a copy of a dense matrix */ /* -------------------------------------------------------------------------- */ cholmod_dense *cholmod_copy_dense ( /* ---- input ---- */ cholmod_dense *X, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) ; cholmod_dense *cholmod_l_copy_dense (cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_copy_dense2: copy a dense matrix (pre-allocated) */ /* -------------------------------------------------------------------------- */ int cholmod_copy_dense2 ( /* ---- input ---- */ cholmod_dense *X, /* matrix to copy */ /* ---- output --- */ cholmod_dense *Y, /* copy of matrix X */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_copy_dense2 (cholmod_dense *, cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_dense_xtype: change the xtype of a dense matrix */ /* -------------------------------------------------------------------------- */ int cholmod_dense_xtype ( /* ---- input ---- */ int to_xtype, /* requested xtype (real, complex,or zomplex) */ /* ---- in/out --- */ cholmod_dense *X, /* dense matrix to change */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_dense_xtype (int, cholmod_dense *, cholmod_common *) ; /* ========================================================================== */ /* === Core/cholmod_triplet ================================================= */ /* ========================================================================== */ /* A sparse matrix stored in triplet form. */ typedef struct cholmod_triplet_struct { size_t nrow ; /* the matrix is nrow-by-ncol */ size_t ncol ; size_t nzmax ; /* maximum number of entries in the matrix */ size_t nnz ; /* number of nonzeros in the matrix */ void *i ; /* i [0..nzmax-1], the row indices */ void *j ; /* j [0..nzmax-1], the column indices */ void *x ; /* size nzmax or 2*nzmax, if present */ void *z ; /* size nzmax, if present */ int stype ; /* Describes what parts of the matrix are considered: * * 0: matrix is "unsymmetric": use both upper and lower triangular parts * (the matrix may actually be symmetric in pattern and value, but * both parts are explicitly stored and used). May be square or * rectangular. * >0: matrix is square and symmetric. Entries in the lower triangular * part are transposed and added to the upper triangular part when * the matrix is converted to cholmod_sparse form. * <0: matrix is square and symmetric. Entries in the upper triangular * part are transposed and added to the lower triangular part when * the matrix is converted to cholmod_sparse form. * * Note that stype>0 and stype<0 are different for cholmod_sparse and * cholmod_triplet. The reason is simple. You can permute a symmetric * triplet matrix by simply replacing a row and column index with their * new row and column indices, via an inverse permutation. Suppose * P = L->Perm is your permutation, and Pinv is an array of size n. * Suppose a symmetric matrix A is represent by a triplet matrix T, with * entries only in the upper triangular part. Then the following code: * * Ti = T->i ; * Tj = T->j ; * for (k = 0 ; k < n ; k++) Pinv [P [k]] = k ; * for (k = 0 ; k < nz ; k++) Ti [k] = Pinv [Ti [k]] ; * for (k = 0 ; k < nz ; k++) Tj [k] = Pinv [Tj [k]] ; * * creates the triplet form of C=P*A*P'. However, if T initially * contains just the upper triangular entries (T->stype = 1), after * permutation it has entries in both the upper and lower triangular * parts. These entries should be transposed when constructing the * cholmod_sparse form of A, which is what cholmod_triplet_to_sparse * does. Thus: * * C = cholmod_triplet_to_sparse (T, 0, &Common) ; * * will return the matrix C = P*A*P'. * * Since the triplet matrix T is so simple to generate, it's quite easy * to remove entries that you do not want, prior to converting T to the * cholmod_sparse form. So if you include these entries in T, CHOLMOD * assumes that there must be a reason (such as the one above). Thus, * no entry in a triplet matrix is ever ignored. */ int itype ; /* CHOLMOD_LONG: i and j are UF_long. Otherwise int. */ int xtype ; /* pattern, real, complex, or zomplex */ int dtype ; /* x and z are double or float */ } cholmod_triplet ; /* -------------------------------------------------------------------------- */ /* cholmod_allocate_triplet: allocate a triplet matrix */ /* -------------------------------------------------------------------------- */ cholmod_triplet *cholmod_allocate_triplet ( /* ---- input ---- */ size_t nrow, /* # of rows of T */ size_t ncol, /* # of columns of T */ size_t nzmax, /* max # of nonzeros of T */ int stype, /* stype of T */ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */ /* --------------- */ cholmod_common *Common ) ; cholmod_triplet *cholmod_l_allocate_triplet (size_t, size_t, size_t, int, int, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_free_triplet: free a triplet matrix */ /* -------------------------------------------------------------------------- */ int cholmod_free_triplet ( /* ---- in/out --- */ cholmod_triplet **T, /* triplet matrix to deallocate, NULL on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_free_triplet (cholmod_triplet **, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_reallocate_triplet: change the # of entries in a triplet matrix */ /* -------------------------------------------------------------------------- */ int cholmod_reallocate_triplet ( /* ---- input ---- */ size_t nznew, /* new # of entries in T */ /* ---- in/out --- */ cholmod_triplet *T, /* triplet matrix to modify */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_reallocate_triplet (size_t, cholmod_triplet *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_sparse_to_triplet: create a triplet matrix copy of a sparse matrix*/ /* -------------------------------------------------------------------------- */ cholmod_triplet *cholmod_sparse_to_triplet ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) ; cholmod_triplet *cholmod_l_sparse_to_triplet (cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_triplet_to_sparse: create a sparse matrix copy of a triplet matrix*/ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_triplet_to_sparse ( /* ---- input ---- */ cholmod_triplet *T, /* matrix to copy */ size_t nzmax, /* allocate at least this much space in output matrix */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_triplet_to_sparse (cholmod_triplet *, size_t, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_copy_triplet: create a copy of a triplet matrix */ /* -------------------------------------------------------------------------- */ cholmod_triplet *cholmod_copy_triplet ( /* ---- input ---- */ cholmod_triplet *T, /* matrix to copy */ /* --------------- */ cholmod_common *Common ) ; cholmod_triplet *cholmod_l_copy_triplet (cholmod_triplet *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_triplet_xtype: change the xtype of a triplet matrix */ /* -------------------------------------------------------------------------- */ int cholmod_triplet_xtype ( /* ---- input ---- */ int to_xtype, /* requested xtype (pattern, real, complex,or zomplex)*/ /* ---- in/out --- */ cholmod_triplet *T, /* triplet matrix to change */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_triplet_xtype (int, cholmod_triplet *, cholmod_common *) ; /* ========================================================================== */ /* === Core/cholmod_memory ================================================== */ /* ========================================================================== */ /* The user may make use of these, just like malloc and free. You can even * malloc an object and safely free it with cholmod_free, and visa versa * (except that the memory usage statistics will be corrupted). These routines * do differ from malloc and free. If cholmod_free is given a NULL pointer, * for example, it does nothing (unlike the ANSI free). cholmod_realloc does * not return NULL if given a non-NULL pointer and a nonzero size, even if it * fails (it returns the original pointer and sets an error code in * Common->status instead). * * CHOLMOD keeps track of the amount of memory it has allocated, and so the * cholmod_free routine also takes the size of the object being freed. This * is only used for statistics. If you, the user of CHOLMOD, pass the wrong * size, the only consequence is that the memory usage statistics will be * corrupted. */ void *cholmod_malloc /* returns pointer to the newly malloc'd block */ ( /* ---- input ---- */ size_t n, /* number of items */ size_t size, /* size of each item */ /* --------------- */ cholmod_common *Common ) ; void *cholmod_l_malloc (size_t, size_t, cholmod_common *) ; void *cholmod_calloc /* returns pointer to the newly calloc'd block */ ( /* ---- input ---- */ size_t n, /* number of items */ size_t size, /* size of each item */ /* --------------- */ cholmod_common *Common ) ; void *cholmod_l_calloc (size_t, size_t, cholmod_common *) ; void *cholmod_free /* always returns NULL */ ( /* ---- input ---- */ size_t n, /* number of items */ size_t size, /* size of each item */ /* ---- in/out --- */ void *p, /* block of memory to free */ /* --------------- */ cholmod_common *Common ) ; void *cholmod_l_free (size_t, size_t, void *, cholmod_common *) ; void *cholmod_realloc /* returns pointer to reallocated block */ ( /* ---- input ---- */ size_t nnew, /* requested # of items in reallocated block */ size_t size, /* size of each item */ /* ---- in/out --- */ void *p, /* block of memory to realloc */ size_t *n, /* current size on input, nnew on output if successful*/ /* --------------- */ cholmod_common *Common ) ; void *cholmod_l_realloc (size_t, size_t, void *, size_t *, cholmod_common *) ; int cholmod_realloc_multiple ( /* ---- input ---- */ size_t nnew, /* requested # of items in reallocated blocks */ int nint, /* number of int/UF_long blocks */ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */ /* ---- in/out --- */ void **I, /* int or UF_long block */ void **J, /* int or UF_long block */ void **X, /* complex, double, or float block */ void **Z, /* zomplex case only: double or float block */ size_t *n, /* current size of the I,J,X,Z blocks on input, * nnew on output if successful */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_realloc_multiple (size_t, int, int, void **, void **, void **, void **, size_t *, cholmod_common *) ; /* ========================================================================== */ /* === symmetry types ======================================================= */ /* ========================================================================== */ #define CHOLMOD_MM_RECTANGULAR 1 #define CHOLMOD_MM_UNSYMMETRIC 2 #define CHOLMOD_MM_SYMMETRIC 3 #define CHOLMOD_MM_HERMITIAN 4 #define CHOLMOD_MM_SKEW_SYMMETRIC 5 #define CHOLMOD_MM_SYMMETRIC_POSDIAG 6 #define CHOLMOD_MM_HERMITIAN_POSDIAG 7 /* ========================================================================== */ /* === Numerical relop macros =============================================== */ /* ========================================================================== */ /* These macros correctly handle the NaN case. * * CHOLMOD_IS_NAN(x): * True if x is NaN. False otherwise. The commonly-existing isnan(x) * function could be used, but it's not in Kernighan & Ritchie 2nd edition * (ANSI C89). It may appear in , but I'm not certain about * portability. The expression x != x is true if and only if x is NaN, * according to the IEEE 754 floating-point standard. * * CHOLMOD_IS_ZERO(x): * True if x is zero. False if x is nonzero, NaN, or +/- Inf. * This is (x == 0) if the compiler is IEEE 754 compliant. * * CHOLMOD_IS_NONZERO(x): * True if x is nonzero, NaN, or +/- Inf. False if x zero. * This is (x != 0) if the compiler is IEEE 754 compliant. * * CHOLMOD_IS_LT_ZERO(x): * True if x is < zero or -Inf. False if x is >= 0, NaN, or +Inf. * This is (x < 0) if the compiler is IEEE 754 compliant. * * CHOLMOD_IS_GT_ZERO(x): * True if x is > zero or +Inf. False if x is <= 0, NaN, or -Inf. * This is (x > 0) if the compiler is IEEE 754 compliant. * * CHOLMOD_IS_LE_ZERO(x): * True if x is <= zero or -Inf. False if x is > 0, NaN, or +Inf. * This is (x <= 0) if the compiler is IEEE 754 compliant. */ #ifdef CHOLMOD_WINDOWS /* Yes, this is exceedingly ugly. Blame Microsoft, which hopelessly */ /* violates the IEEE 754 floating-point standard in a bizarre way. */ /* If you're using an IEEE 754-compliant compiler, then x != x is true */ /* iff x is NaN. For Microsoft, (x < x) is true iff x is NaN. */ /* So either way, this macro safely detects a NaN. */ #define CHOLMOD_IS_NAN(x) (((x) != (x)) || (((x) < (x)))) #define CHOLMOD_IS_ZERO(x) (((x) == 0.) && !CHOLMOD_IS_NAN(x)) #define CHOLMOD_IS_NONZERO(x) (((x) != 0.) || CHOLMOD_IS_NAN(x)) #define CHOLMOD_IS_LT_ZERO(x) (((x) < 0.) && !CHOLMOD_IS_NAN(x)) #define CHOLMOD_IS_GT_ZERO(x) (((x) > 0.) && !CHOLMOD_IS_NAN(x)) #define CHOLMOD_IS_LE_ZERO(x) (((x) <= 0.) && !CHOLMOD_IS_NAN(x)) #else /* These all work properly, according to the IEEE 754 standard ... except on */ /* a PC with windows. Works fine in Linux on the same PC... */ #define CHOLMOD_IS_NAN(x) ((x) != (x)) #define CHOLMOD_IS_ZERO(x) ((x) == 0.) #define CHOLMOD_IS_NONZERO(x) ((x) != 0.) #define CHOLMOD_IS_LT_ZERO(x) ((x) < 0.) #define CHOLMOD_IS_GT_ZERO(x) ((x) > 0.) #define CHOLMOD_IS_LE_ZERO(x) ((x) <= 0.) #endif #endif SuiteSparse/CHOLMOD/Include/cholmod_check.h0000644001170100242450000003435110537777506017401 0ustar davisfac/* ========================================================================== */ /* === Include/cholmod_check.h ============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_check.h. Copyright (C) 2005-2006, Timothy A. Davis * CHOLMOD/Include/cholmod_check.h is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* CHOLMOD Check module. * * Routines that check and print the 5 basic data types in CHOLMOD, and 3 kinds * of integer vectors (subset, perm, and parent), and read in matrices from a * file: * * cholmod_check_common check/print the Common object * cholmod_print_common * * cholmod_check_sparse check/print a sparse matrix in column-oriented form * cholmod_print_sparse * * cholmod_check_dense check/print a dense matrix * cholmod_print_dense * * cholmod_check_factor check/print a Cholesky factorization * cholmod_print_factor * * cholmod_check_triplet check/print a sparse matrix in triplet form * cholmod_print_triplet * * cholmod_check_subset check/print a subset (integer vector in given range) * cholmod_print_subset * * cholmod_check_perm check/print a permutation (an integer vector) * cholmod_print_perm * * cholmod_check_parent check/print an elimination tree (an integer vector) * cholmod_print_parent * * cholmod_read_triplet read a matrix in triplet form (any Matrix Market * "coordinate" format, or a generic triplet format). * * cholmod_read_sparse read a matrix in sparse form (same file format as * cholmod_read_triplet). * * cholmod_read_dense read a dense matrix (any Matrix Market "array" * format, or a generic dense format). * * cholmod_write_sparse write a sparse matrix to a Matrix Market file. * * cholmod_write_dense write a dense matrix to a Matrix Market file. * * cholmod_print_common and cholmod_check_common are the only two routines that * you may call after calling cholmod_finish. * * Requires the Core module. Not required by any CHOLMOD module, except when * debugging is enabled (in which case all modules require the Check module). * * See cholmod_read.c for a description of the file formats supported by the * cholmod_read_* routines. */ #ifndef CHOLMOD_CHECK_H #define CHOLMOD_CHECK_H #include "cholmod_core.h" #include /* -------------------------------------------------------------------------- */ /* cholmod_check_common: check the Common object */ /* -------------------------------------------------------------------------- */ int cholmod_check_common ( cholmod_common *Common ) ; int cholmod_l_check_common (cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_print_common: print the Common object */ /* -------------------------------------------------------------------------- */ int cholmod_print_common ( /* ---- input ---- */ char *name, /* printed name of Common object */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_print_common (char *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_check_sparse: check a sparse matrix */ /* -------------------------------------------------------------------------- */ int cholmod_check_sparse ( /* ---- input ---- */ cholmod_sparse *A, /* sparse matrix to check */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_check_sparse (cholmod_sparse *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_print_sparse */ /* -------------------------------------------------------------------------- */ int cholmod_print_sparse ( /* ---- input ---- */ cholmod_sparse *A, /* sparse matrix to print */ char *name, /* printed name of sparse matrix */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_print_sparse (cholmod_sparse *, char *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_check_dense: check a dense matrix */ /* -------------------------------------------------------------------------- */ int cholmod_check_dense ( /* ---- input ---- */ cholmod_dense *X, /* dense matrix to check */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_check_dense (cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_print_dense: print a dense matrix */ /* -------------------------------------------------------------------------- */ int cholmod_print_dense ( /* ---- input ---- */ cholmod_dense *X, /* dense matrix to print */ char *name, /* printed name of dense matrix */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_print_dense (cholmod_dense *, char *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_check_factor: check a factor */ /* -------------------------------------------------------------------------- */ int cholmod_check_factor ( /* ---- input ---- */ cholmod_factor *L, /* factor to check */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_check_factor (cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_print_factor: print a factor */ /* -------------------------------------------------------------------------- */ int cholmod_print_factor ( /* ---- input ---- */ cholmod_factor *L, /* factor to print */ char *name, /* printed name of factor */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_print_factor (cholmod_factor *, char *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_check_triplet: check a sparse matrix in triplet form */ /* -------------------------------------------------------------------------- */ int cholmod_check_triplet ( /* ---- input ---- */ cholmod_triplet *T, /* triplet matrix to check */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_check_triplet (cholmod_triplet *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_print_triplet: print a triplet matrix */ /* -------------------------------------------------------------------------- */ int cholmod_print_triplet ( /* ---- input ---- */ cholmod_triplet *T, /* triplet matrix to print */ char *name, /* printed name of triplet matrix */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_print_triplet (cholmod_triplet *, char *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_check_subset: check a subset */ /* -------------------------------------------------------------------------- */ int cholmod_check_subset ( /* ---- input ---- */ int *Set, /* Set [0:len-1] is a subset of 0:n-1. Duplicates OK */ UF_long len, /* size of Set (an integer array) */ size_t n, /* 0:n-1 is valid range */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_check_subset (UF_long *, UF_long, size_t, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_print_subset: print a subset */ /* -------------------------------------------------------------------------- */ int cholmod_print_subset ( /* ---- input ---- */ int *Set, /* Set [0:len-1] is a subset of 0:n-1. Duplicates OK */ UF_long len, /* size of Set (an integer array) */ size_t n, /* 0:n-1 is valid range */ char *name, /* printed name of Set */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_print_subset (UF_long *, UF_long, size_t, char *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_check_perm: check a permutation */ /* -------------------------------------------------------------------------- */ int cholmod_check_perm ( /* ---- input ---- */ int *Perm, /* Perm [0:len-1] is a permutation of subset of 0:n-1 */ size_t len, /* size of Perm (an integer array) */ size_t n, /* 0:n-1 is valid range */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_check_perm (UF_long *, size_t, size_t, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_print_perm: print a permutation vector */ /* -------------------------------------------------------------------------- */ int cholmod_print_perm ( /* ---- input ---- */ int *Perm, /* Perm [0:len-1] is a permutation of subset of 0:n-1 */ size_t len, /* size of Perm (an integer array) */ size_t n, /* 0:n-1 is valid range */ char *name, /* printed name of Perm */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_print_perm (UF_long *, size_t, size_t, char *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_check_parent: check an elimination tree */ /* -------------------------------------------------------------------------- */ int cholmod_check_parent ( /* ---- input ---- */ int *Parent, /* Parent [0:n-1] is an elimination tree */ size_t n, /* size of Parent */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_check_parent (UF_long *, size_t, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_print_parent */ /* -------------------------------------------------------------------------- */ int cholmod_print_parent ( /* ---- input ---- */ int *Parent, /* Parent [0:n-1] is an elimination tree */ size_t n, /* size of Parent */ char *name, /* printed name of Parent */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_print_parent (UF_long *, size_t, char *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_read_sparse: read a sparse matrix from a file */ /* -------------------------------------------------------------------------- */ cholmod_sparse *cholmod_read_sparse ( /* ---- input ---- */ FILE *f, /* file to read from, must already be open */ /* --------------- */ cholmod_common *Common ) ; cholmod_sparse *cholmod_l_read_sparse (FILE *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_read_triplet: read a triplet matrix from a file */ /* -------------------------------------------------------------------------- */ cholmod_triplet *cholmod_read_triplet ( /* ---- input ---- */ FILE *f, /* file to read from, must already be open */ /* --------------- */ cholmod_common *Common ) ; cholmod_triplet *cholmod_l_read_triplet (FILE *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_read_dense: read a dense matrix from a file */ /* -------------------------------------------------------------------------- */ cholmod_dense *cholmod_read_dense ( /* ---- input ---- */ FILE *f, /* file to read from, must already be open */ /* --------------- */ cholmod_common *Common ) ; cholmod_dense *cholmod_l_read_dense (FILE *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_read_matrix: read a sparse or dense matrix from a file */ /* -------------------------------------------------------------------------- */ void *cholmod_read_matrix ( /* ---- input ---- */ FILE *f, /* file to read from, must already be open */ int prefer, /* If 0, a sparse matrix is always return as a * cholmod_triplet form. It can have any stype * (symmetric-lower, unsymmetric, or * symmetric-upper). * If 1, a sparse matrix is returned as an unsymmetric * cholmod_sparse form (A->stype == 0), with both * upper and lower triangular parts present. * This is what the MATLAB mread mexFunction does, * since MATLAB does not have an stype. * If 2, a sparse matrix is returned with an stype of 0 * or 1 (unsymmetric, or symmetric with upper part * stored). * This argument has no effect for dense matrices. */ /* ---- output---- */ int *mtype, /* CHOLMOD_TRIPLET, CHOLMOD_SPARSE or CHOLMOD_DENSE */ /* --------------- */ cholmod_common *Common ) ; void *cholmod_l_read_matrix (FILE *, int, int *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_write_sparse: write a sparse matrix to a file */ /* -------------------------------------------------------------------------- */ int cholmod_write_sparse ( /* ---- input ---- */ FILE *f, /* file to write to, must already be open */ cholmod_sparse *A, /* matrix to print */ cholmod_sparse *Z, /* optional matrix with pattern of explicit zeros */ char *comments, /* optional filename of comments to include */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_write_sparse (FILE *, cholmod_sparse *, cholmod_sparse *, char *c, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_write_dense: write a dense matrix to a file */ /* -------------------------------------------------------------------------- */ int cholmod_write_dense ( /* ---- input ---- */ FILE *f, /* file to write to, must already be open */ cholmod_dense *X, /* matrix to print */ char *comments, /* optional filename of comments to include */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_write_dense (FILE *, cholmod_dense *, char *, cholmod_common *) ; #endif SuiteSparse/CHOLMOD/Include/cholmod_io64.h0000644001170100242450000000325610540000236017052 0ustar davisfac/* ========================================================================== */ /* === Include/cholmod_io64 ================================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_io64.h. * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis * CHOLMOD/Include/cholmod_io64.h is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Definitions required for large file I/O, which must come before any other * #includes. These are not used if -DNLARGEFILE is defined at compile time. * Large file support may not be portable across all platforms and compilers; * if you encounter an error here, compile your code with -DNLARGEFILE. In * particular, you must use -DNLARGEFILE for MATLAB 6.5 or earlier (which does * not have the io64.h include file). */ #ifndef CHOLMOD_IO_H #define CHOLMOD_IO_H /* skip all of this if NLARGEFILE is defined at the compiler command line */ #ifndef NLARGEFILE #if defined(MATLAB_MEX_FILE) || defined(MATHWORKS) /* CHOLMOD is being compiled as a MATLAB MEX file, or for use inside MATLAB */ #include "io64.h" #else /* CHOLMOD is being compiled in a stand-alone library */ #undef _LARGEFILE64_SOURCE #define _LARGEFILE64_SOURCE #undef _FILE_OFFSET_BITS #define _FILE_OFFSET_BITS 64 #endif #endif #endif SuiteSparse/CHOLMOD/Include/License.txt0000644001170100242450000000046210540000242016527 0ustar davisfacCHOLMOD/Include/* files. Copyright (C) 2005-2006, either Univ. of Florida or T. Davis, depending on the file. http://www.cise.ufl.edu/research/sparse Refer to each include file in this directory; each file is licensed separately, according to the Module for which it contains definitions and prototypes. SuiteSparse/CHOLMOD/Include/cholmod_supernodal.h0000644001170100242450000001253710537777554020505 0ustar davisfac/* ========================================================================== */ /* === Include/cholmod_supernodal.h ========================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_supernodal.h. * Copyright (C) 2005-2006, Timothy A. Davis * CHOLMOD/Include/cholmod_supernodal.h is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* CHOLMOD Supernodal module. * * Supernodal analysis, factorization, and solve. The simplest way to use * these routines is via the Cholesky module. It does not provide any * fill-reducing orderings, but does accept the orderings computed by the * Cholesky module. It does not require the Cholesky module itself, however. * * Primary routines: * ----------------- * cholmod_super_symbolic supernodal symbolic analysis * cholmod_super_numeric supernodal numeric factorization * cholmod_super_lsolve supernodal Lx=b solve * cholmod_super_ltsolve supernodal L'x=b solve * * Prototypes for the BLAS and LAPACK routines that CHOLMOD uses are listed * below, including how they are used in CHOLMOD. * * BLAS routines: * -------------- * dtrsv solve Lx=b or L'x=b, L non-unit diagonal, x and b stride-1 * dtrsm solve LX=B or L'X=b, L non-unit diagonal * dgemv y=y-A*x or y=y-A'*x (x and y stride-1) * dgemm C=A*B', C=C-A*B, or C=C-A'*B * dsyrk C=tril(A*A') * * LAPACK routines: * ---------------- * dpotrf LAPACK: A=chol(tril(A)) * * Requires the Core module, and two external packages: LAPACK and the BLAS. * Optionally used by the Cholesky module. */ #ifndef CHOLMOD_SUPERNODAL_H #define CHOLMOD_SUPERNODAL_H #include "cholmod_core.h" /* -------------------------------------------------------------------------- */ /* cholmod_super_symbolic */ /* -------------------------------------------------------------------------- */ /* Analyzes A, AA', or A(:,f)*A(:,f)' in preparation for a supernodal numeric * factorization. The user need not call this directly; cholmod_analyze is * a "simple" wrapper for this routine. */ int cholmod_super_symbolic ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to analyze */ cholmod_sparse *F, /* F = A' or A(:,f)' */ int *Parent, /* elimination tree */ /* ---- in/out --- */ cholmod_factor *L, /* simplicial symbolic on input, * supernodal symbolic on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_super_symbolic (cholmod_sparse *, cholmod_sparse *, UF_long *, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_super_numeric */ /* -------------------------------------------------------------------------- */ /* Computes the numeric LL' factorization of A, AA', or A(:,f)*A(:,f)' using * a BLAS-based supernodal method. The user need not call this directly; * cholmod_factorize is a "simple" wrapper for this routine. */ int cholmod_super_numeric ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to factorize */ cholmod_sparse *F, /* F = A' or A(:,f)' */ double beta [2], /* beta*I is added to diagonal of matrix to factorize */ /* ---- in/out --- */ cholmod_factor *L, /* factorization */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_super_numeric (cholmod_sparse *, cholmod_sparse *, double *, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_super_lsolve */ /* -------------------------------------------------------------------------- */ /* Solve Lx=b where L is from a supernodal numeric factorization. The user * need not call this routine directly. cholmod_solve is a "simple" wrapper * for this routine. */ int cholmod_super_lsolve ( /* ---- input ---- */ cholmod_factor *L, /* factor to use for the forward solve */ /* ---- output ---- */ cholmod_dense *X, /* b on input, solution to Lx=b on output */ /* ---- workspace */ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_super_lsolve (cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_super_ltsolve */ /* -------------------------------------------------------------------------- */ /* Solve L'x=b where L is from a supernodal numeric factorization. The user * need not call this routine directly. cholmod_solve is a "simple" wrapper * for this routine. */ int cholmod_super_ltsolve ( /* ---- input ---- */ cholmod_factor *L, /* factor to use for the backsolve */ /* ---- output ---- */ cholmod_dense *X, /* b on input, solution to L'x=b on output */ /* ---- workspace */ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_super_ltsolve (cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ; #endif SuiteSparse/CHOLMOD/Include/README.txt0000644001170100242450000000235110540000142016100 0ustar davisfacCHOLMOD: a sparse Cholesky factorization package. The Include/*.h files in this directory provide a basic documentation of all user-callable routines and user-visible data structures in the CHOLMOD package. Start with cholmod.h, which describes the general structure of the parameter lists of CHOLMOD routines. cholmod_core.h describes the data structures and basic operations on them (creating and deleting them). cholmod.h single include file for all user programs cholmod_config.h CHOLMOD compile-time configuration cholmod_core.h Core module: data structures and basic support routines cholmod_check.h Check module: check/print CHOLMOD data structures cholmod_cholesky.h Cholesky module: LL' and LDL' factorization cholmod_matrixops.h MatrixOps module: sparse matrix operators (add, mult,..) cholmod_modify.h Modify module: update/downdate/... cholmod_partition.h Partition module: nested dissection ordering cholmod_supernodal.h Supernodal module: supernodal Cholesky These include files are not used in user programs, but in CHOLMOD only: cholmod_blas.h BLAS definitions cholmod_complexity.h complex arithmetic cholmod_template.h complex arithmetic for template routines cholmod_internal.h internal definitions, not visible to user program SuiteSparse/CHOLMOD/Include/cholmod_modify.h0000644001170100242450000003125110537777547017614 0ustar davisfac/* ========================================================================== */ /* === Include/cholmod_modify.h ============================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_modify.h. * Copyright (C) 2005-2006, Timothy A. Davis and William W. Hager * CHOLMOD/Include/cholmod_modify.h is licensed under Version 2.0 of the GNU * General Public License. See gpl.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* CHOLMOD Modify module. * * Sparse Cholesky modification routines: update / downdate / rowadd / rowdel. * Can also modify a corresponding solution to Lx=b when L is modified. This * module is most useful when applied on a Cholesky factorization computed by * the Cholesky module, but it does not actually require the Cholesky module. * The Core module can create an identity Cholesky factorization (LDL' where * L=D=I) that can then by modified by these routines. * * Primary routines: * ----------------- * * cholmod_updown multiple rank update/downdate * cholmod_rowadd add a row to an LDL' factorization * cholmod_rowdel delete a row from an LDL' factorization * * Secondary routines: * ------------------- * * cholmod_updown_solve update/downdate, and modify solution to Lx=b * cholmod_updown_mark update/downdate, and modify solution to partial Lx=b * cholmod_updown_mask update/downdate for LPDASA * cholmod_rowadd_solve add a row, and update solution to Lx=b * cholmod_rowadd_mark add a row, and update solution to partial Lx=b * cholmod_rowdel_solve delete a row, and downdate Lx=b * cholmod_rowdel_mark delete a row, and downdate solution to partial Lx=b * * Requires the Core module. Not required by any other CHOLMOD module. */ #ifndef CHOLMOD_MODIFY_H #define CHOLMOD_MODIFY_H #include "cholmod_core.h" /* -------------------------------------------------------------------------- */ /* cholmod_updown: multiple rank update/downdate */ /* -------------------------------------------------------------------------- */ /* Compute the new LDL' factorization of LDL'+CC' (an update) or LDL'-CC' * (a downdate). The factor object L need not be an LDL' factorization; it * is converted to one if it isn't. */ int cholmod_updown ( /* ---- input ---- */ int update, /* TRUE for update, FALSE for downdate */ cholmod_sparse *C, /* the incoming sparse update */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_updown (int, cholmod_sparse *, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_updown_solve: update/downdate, and modify solution to Lx=b */ /* -------------------------------------------------------------------------- */ /* Does the same as cholmod_updown, except that it also updates/downdates the * solution to Lx=b+DeltaB. x and b must be n-by-1 dense matrices. b is not * need as input to this routine, but a sparse change to b is (DeltaB). Only * entries in DeltaB corresponding to columns modified in L are accessed; the * rest must be zero. */ int cholmod_updown_solve ( /* ---- input ---- */ int update, /* TRUE for update, FALSE for downdate */ cholmod_sparse *C, /* the incoming sparse update */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_updown_solve (int, cholmod_sparse *, cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_updown_mark: update/downdate, and modify solution to partial Lx=b */ /* -------------------------------------------------------------------------- */ /* Does the same as cholmod_updown_solve, except only part of L is used in * the update/downdate of the solution to Lx=b. This routine is an "expert" * routine. It is meant for use in LPDASA only. See cholmod_updown.c for * a description of colmark. */ int cholmod_updown_mark ( /* ---- input ---- */ int update, /* TRUE for update, FALSE for downdate */ cholmod_sparse *C, /* the incoming sparse update */ int *colmark, /* int array of size n. See cholmod_updown.c */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_updown_mark (int, cholmod_sparse *, UF_long *, cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_updown_mask: update/downdate, for LPDASA */ /* -------------------------------------------------------------------------- */ /* Does the same as cholmod_updown_mark, except has an additional "mask" * argument. This routine is an "expert" routine. It is meant for use in * LPDASA only. See cholmod_updown.c for a description of mask. */ int cholmod_updown_mask ( /* ---- input ---- */ int update, /* TRUE for update, FALSE for downdate */ cholmod_sparse *C, /* the incoming sparse update */ int *colmark, /* int array of size n. See cholmod_updown.c */ int *mask, /* size n */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_updown_mask (int, cholmod_sparse *, UF_long *, UF_long *, cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_rowadd: add a row to an LDL' factorization (a rank-2 update) */ /* -------------------------------------------------------------------------- */ /* cholmod_rowadd adds a row to the LDL' factorization. It computes the kth * row and kth column of L, and then updates the submatrix L (k+1:n,k+1:n) * accordingly. The kth row and column of L must originally be equal to the * kth row and column of the identity matrix. The kth row/column of L is * computed as the factorization of the kth row/column of the matrix to * factorize, which is provided as a single n-by-1 sparse matrix R. */ int cholmod_rowadd ( /* ---- input ---- */ size_t k, /* row/column index to add */ cholmod_sparse *R, /* row/column of matrix to factorize (n-by-1) */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_rowadd (size_t, cholmod_sparse *, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_rowadd_solve: add a row, and update solution to Lx=b */ /* -------------------------------------------------------------------------- */ /* Does the same as cholmod_rowadd, and also updates the solution to Lx=b * See cholmod_updown for a description of how Lx=b is updated. There is on * additional parameter: bk specifies the new kth entry of b. */ int cholmod_rowadd_solve ( /* ---- input ---- */ size_t k, /* row/column index to add */ cholmod_sparse *R, /* row/column of matrix to factorize (n-by-1) */ double bk [2], /* kth entry of the right-hand-side b */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_rowadd_solve (size_t, cholmod_sparse *, double *, cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_rowadd_mark: add a row, and update solution to partial Lx=b */ /* -------------------------------------------------------------------------- */ /* Does the same as cholmod_rowadd_solve, except only part of L is used in * the update/downdate of the solution to Lx=b. This routine is an "expert" * routine. It is meant for use in LPDASA only. */ int cholmod_rowadd_mark ( /* ---- input ---- */ size_t k, /* row/column index to add */ cholmod_sparse *R, /* row/column of matrix to factorize (n-by-1) */ double bk [2], /* kth entry of the right hand side, b */ int *colmark, /* int array of size n. See cholmod_updown.c */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_rowadd_mark (size_t, cholmod_sparse *, double *, UF_long *, cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_rowdel: delete a row from an LDL' factorization (a rank-2 update) */ /* -------------------------------------------------------------------------- */ /* Sets the kth row and column of L to be the kth row and column of the identity * matrix, and updates L(k+1:n,k+1:n) accordingly. To reduce the running time, * the caller can optionally provide the nonzero pattern (or an upper bound) of * kth row of L, as the sparse n-by-1 vector R. Provide R as NULL if you want * CHOLMOD to determine this itself, which is easier for the caller, but takes * a little more time. */ int cholmod_rowdel ( /* ---- input ---- */ size_t k, /* row/column index to delete */ cholmod_sparse *R, /* NULL, or the nonzero pattern of kth row of L */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_rowdel (size_t, cholmod_sparse *, cholmod_factor *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_rowdel_solve: delete a row, and downdate Lx=b */ /* -------------------------------------------------------------------------- */ /* Does the same as cholmod_rowdel, but also downdates the solution to Lx=b. * When row/column k of A is "deleted" from the system A*y=b, this can induce * a change to x, in addition to changes arising when L and b are modified. * If this is the case, the kth entry of y is required as input (yk) */ int cholmod_rowdel_solve ( /* ---- input ---- */ size_t k, /* row/column index to delete */ cholmod_sparse *R, /* NULL, or the nonzero pattern of kth row of L */ double yk [2], /* kth entry in the solution to A*y=b */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_rowdel_solve (size_t, cholmod_sparse *, double *, cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ; /* -------------------------------------------------------------------------- */ /* cholmod_rowdel_mark: delete a row, and downdate solution to partial Lx=b */ /* -------------------------------------------------------------------------- */ /* Does the same as cholmod_rowdel_solve, except only part of L is used in * the update/downdate of the solution to Lx=b. This routine is an "expert" * routine. It is meant for use in LPDASA only. */ int cholmod_rowdel_mark ( /* ---- input ---- */ size_t k, /* row/column index to delete */ cholmod_sparse *R, /* NULL, or the nonzero pattern of kth row of L */ double yk [2], /* kth entry in the solution to A*y=b */ int *colmark, /* int array of size n. See cholmod_updown.c */ /* ---- in/out --- */ cholmod_factor *L, /* factor to modify */ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */ cholmod_dense *DeltaB, /* change in b, zero on output */ /* --------------- */ cholmod_common *Common ) ; int cholmod_l_rowdel_mark (size_t, cholmod_sparse *, double *, UF_long *, cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ; #endif SuiteSparse/CHOLMOD/Include/cholmod_complexity.h0000644001170100242450000002224410301235304020465 0ustar davisfac/* ========================================================================== */ /* === Include/cholmod_complexity.h ========================================= */ /* ========================================================================== */ /* Define operations on pattern, real, complex, and zomplex objects. * * The xtype of an object defines it numerical type. A qttern object has no * numerical values (A->x and A->z are NULL). A real object has no imaginary * qrt (A->x is used, A->z is NULL). A complex object has an imaginary qrt * that is stored interleaved with its real qrt (A->x is of size 2*nz, A->z * is NULL). A zomplex object has both real and imaginary qrts, which are * stored seqrately, as in MATLAB (A->x and A->z are both used). * * XTYPE is CHOLMOD_PATTERN, _REAL, _COMPLEX or _ZOMPLEX, and is the xtype of * the template routine under construction. XTYPE2 is equal to XTYPE, except * if XTYPE is CHOLMOD_PATTERN, in which case XTYPE is CHOLMOD_REAL. * XTYPE and XTYPE2 are defined in cholmod_template.h. */ /* -------------------------------------------------------------------------- */ /* pattern */ /* -------------------------------------------------------------------------- */ #define P_TEMPLATE(name) p_ ## name #define P_ASSIGN2(x,z,p,ax,az,q) x [p] = 1 #define P_PRINT(k,x,z,p) PRK(k, ("1")) /* -------------------------------------------------------------------------- */ /* real */ /* -------------------------------------------------------------------------- */ #define R_TEMPLATE(name) r_ ## name #define R_ASSEMBLE(x,z,p,ax,az,q) x [p] += ax [q] #define R_ASSIGN(x,z,p,ax,az,q) x [p] = ax [q] #define R_ASSIGN_CONJ(x,z,p,ax,az,q) x [p] = ax [q] #define R_ASSIGN_REAL(x,p,ax,q) x [p] = ax [q] #define R_XTYPE_OK(type) ((type) == CHOLMOD_REAL) #define R_IS_NONZERO(ax,az,q) IS_NONZERO (ax [q]) #define R_IS_ZERO(ax,az,q) IS_ZERO (ax [q]) #define R_IS_ONE(ax,az,q) (ax [q] == 1) #define R_MULT(x,z,p, ax,az,q, bx,bz,r) x [p] = ax [q] * bx [r] #define R_MULTADD(x,z,p, ax,az,q, bx,bz,r) x [p] += ax [q] * bx [r] #define R_MULTSUB(x,z,p, ax,az,q, bx,bz,r) x [p] -= ax [q] * bx [r] #define R_MULTADDCONJ(x,z,p, ax,az,q, bx,bz,r) x [p] += ax [q] * bx [r] #define R_MULTSUBCONJ(x,z,p, ax,az,q, bx,bz,r) x [p] -= ax [q] * bx [r] #define R_ADD(x,z,p, ax,az,q, bx,bz,r) x [p] = ax [q] + bx [r] #define R_ADD_REAL(x,p, ax,q, bx,r) x [p] = ax [q] + bx [r] #define R_CLEAR(x,z,p) x [p] = 0 #define R_CLEAR_IMAG(x,z,p) #define R_DIV(x,z,p,ax,az,q) x [p] /= ax [q] #define R_LLDOT(x,p, ax,az,q) x [p] -= ax [q] * ax [q] #define R_PRINT(k,x,z,p) PRK(k, ("%24.16e", x [p])) #define R_DIV_REAL(x,z,p, ax,az,q, bx,r) x [p] = ax [q] / bx [r] #define R_MULT_REAL(x,z,p, ax,az,q, bx,r) x [p] = ax [q] * bx [r] #define R_LDLDOT(x,p, ax,az,q, bx,r) x [p] -=(ax[q] * ax[q])/ bx[r] /* -------------------------------------------------------------------------- */ /* complex */ /* -------------------------------------------------------------------------- */ #define C_TEMPLATE(name) c_ ## name #define CT_TEMPLATE(name) ct_ ## name #define C_ASSEMBLE(x,z,p,ax,az,q) \ x [2*(p) ] += ax [2*(q) ] ; \ x [2*(p)+1] += ax [2*(q)+1] #define C_ASSIGN(x,z,p,ax,az,q) \ x [2*(p) ] = ax [2*(q) ] ; \ x [2*(p)+1] = ax [2*(q)+1] #define C_ASSIGN_REAL(x,p,ax,q) x [2*(p)] = ax [2*(q)] #define C_ASSIGN_CONJ(x,z,p,ax,az,q) \ x [2*(p) ] = ax [2*(q) ] ; \ x [2*(p)+1] = -ax [2*(q)+1] #define C_XTYPE_OK(type) ((type) == CHOLMOD_COMPLEX) #define C_IS_NONZERO(ax,az,q) \ (IS_NONZERO (ax [2*(q)]) || IS_NONZERO (ax [2*(q)+1])) #define C_IS_ZERO(ax,az,q) \ (IS_ZERO (ax [2*(q)]) && IS_ZERO (ax [2*(q)+1])) #define C_IS_ONE(ax,az,q) \ ((ax [2*(q)] == 1) && IS_ZERO (ax [2*(q)+1])) #define C_IMAG_IS_NONZERO(ax,az,q) (IS_NONZERO (ax [2*(q)+1])) #define C_MULT(x,z,p, ax,az,q, bx,bz,r) \ x [2*(p) ] = ax [2*(q) ] * bx [2*(r)] - ax [2*(q)+1] * bx [2*(r)+1] ; \ x [2*(p)+1] = ax [2*(q)+1] * bx [2*(r)] + ax [2*(q) ] * bx [2*(r)+1] #define C_MULTADD(x,z,p, ax,az,q, bx,bz,r) \ x [2*(p) ] += ax [2*(q) ] * bx [2*(r)] - ax [2*(q)+1] * bx [2*(r)+1] ; \ x [2*(p)+1] += ax [2*(q)+1] * bx [2*(r)] + ax [2*(q) ] * bx [2*(r)+1] #define C_MULTSUB(x,z,p, ax,az,q, bx,bz,r) \ x [2*(p) ] -= ax [2*(q) ] * bx [2*(r)] - ax [2*(q)+1] * bx [2*(r)+1] ; \ x [2*(p)+1] -= ax [2*(q)+1] * bx [2*(r)] + ax [2*(q) ] * bx [2*(r)+1] /* s += conj(a)*b */ #define C_MULTADDCONJ(x,z,p, ax,az,q, bx,bz,r) \ x [2*(p) ] += ax [2*(q) ] * bx [2*(r)] + ax [2*(q)+1] * bx [2*(r)+1] ; \ x [2*(p)+1] += (-ax [2*(q)+1]) * bx [2*(r)] + ax [2*(q) ] * bx [2*(r)+1] /* s -= conj(a)*b */ #define C_MULTSUBCONJ(x,z,p, ax,az,q, bx,bz,r) \ x [2*(p) ] -= ax [2*(q) ] * bx [2*(r)] + ax [2*(q)+1] * bx [2*(r)+1] ; \ x [2*(p)+1] -= (-ax [2*(q)+1]) * bx [2*(r)] + ax [2*(q) ] * bx [2*(r)+1] #define C_ADD(x,z,p, ax,az,q, bx,bz,r) \ x [2*(p) ] = ax [2*(q) ] + bx [2*(r) ] ; \ x [2*(p)+1] = ax [2*(q)+1] + bx [2*(r)+1] #define C_ADD_REAL(x,p, ax,q, bx,r) \ x [2*(p)] = ax [2*(q)] + bx [2*(r)] #define C_CLEAR(x,z,p) \ x [2*(p) ] = 0 ; \ x [2*(p)+1] = 0 #define C_CLEAR_IMAG(x,z,p) \ x [2*(p)+1] = 0 /* s = s / a */ #define C_DIV(x,z,p,ax,az,q) \ Common->complex_divide ( \ x [2*(p)], x [2*(p)+1], \ ax [2*(q)], ax [2*(q)+1], \ &x [2*(p)], &x [2*(p)+1]) /* s -= conj(a)*a ; note that the result of conj(a)*a is real */ #define C_LLDOT(x,p, ax,az,q) \ x [2*(p)] -= ax [2*(q)] * ax [2*(q)] + ax [2*(q)+1] * ax [2*(q)+1] #define C_PRINT(k,x,z,p) PRK(k, ("(%24.16e,%24.16e)", x [2*(p)], x [2*(p)+1])) #define C_DIV_REAL(x,z,p, ax,az,q, bx,r) \ x [2*(p) ] = ax [2*(q) ] / bx [2*(r)] ; \ x [2*(p)+1] = ax [2*(q)+1] / bx [2*(r)] #define C_MULT_REAL(x,z,p, ax,az,q, bx,r) \ x [2*(p) ] = ax [2*(q) ] * bx [2*(r)] ; \ x [2*(p)+1] = ax [2*(q)+1] * bx [2*(r)] /* s -= conj(a)*a/t */ #define C_LDLDOT(x,p, ax,az,q, bx,r) \ x [2*(p)] -= (ax [2*(q)] * ax [2*(q)] + ax [2*(q)+1] * ax [2*(q)+1]) / bx[r] /* -------------------------------------------------------------------------- */ /* zomplex */ /* -------------------------------------------------------------------------- */ #define Z_TEMPLATE(name) z_ ## name #define ZT_TEMPLATE(name) zt_ ## name #define Z_ASSEMBLE(x,z,p,ax,az,q) \ x [p] += ax [q] ; \ z [p] += az [q] #define Z_ASSIGN(x,z,p,ax,az,q) \ x [p] = ax [q] ; \ z [p] = az [q] #define Z_ASSIGN_REAL(x,p,ax,q) x [p] = ax [q] #define Z_ASSIGN_CONJ(x,z,p,ax,az,q) \ x [p] = ax [q] ; \ z [p] = -az [q] #define Z_XTYPE_OK(type) ((type) == CHOLMOD_ZOMPLEX) #define Z_IS_NONZERO(ax,az,q) \ (IS_NONZERO (ax [q]) || IS_NONZERO (az [q])) #define Z_IS_ZERO(ax,az,q) \ (IS_ZERO (ax [q]) && IS_ZERO (az [q])) #define Z_IS_ONE(ax,az,q) \ ((ax [q] == 1) && IS_ZERO (az [q])) #define Z_IMAG_IS_NONZERO(ax,az,q) (IS_NONZERO (az [q])) #define Z_MULT(x,z,p, ax,az,q, bx,bz,r) \ x [p] = ax [q] * bx [r] - az [q] * bz [r] ; \ z [p] = az [q] * bx [r] + ax [q] * bz [r] #define Z_MULTADD(x,z,p, ax,az,q, bx,bz,r) \ x [p] += ax [q] * bx [r] - az [q] * bz [r] ; \ z [p] += az [q] * bx [r] + ax [q] * bz [r] #define Z_MULTSUB(x,z,p, ax,az,q, bx,bz,r) \ x [p] -= ax [q] * bx [r] - az [q] * bz [r] ; \ z [p] -= az [q] * bx [r] + ax [q] * bz [r] #define Z_MULTADDCONJ(x,z,p, ax,az,q, bx,bz,r) \ x [p] += ax [q] * bx [r] + az [q] * bz [r] ; \ z [p] += (-az [q]) * bx [r] + ax [q] * bz [r] #define Z_MULTSUBCONJ(x,z,p, ax,az,q, bx,bz,r) \ x [p] -= ax [q] * bx [r] + az [q] * bz [r] ; \ z [p] -= (-az [q]) * bx [r] + ax [q] * bz [r] #define Z_ADD(x,z,p, ax,az,q, bx,bz,r) \ x [p] = ax [q] + bx [r] ; \ z [p] = az [q] + bz [r] #define Z_ADD_REAL(x,p, ax,q, bx,r) \ x [p] = ax [q] + bx [r] #define Z_CLEAR(x,z,p) \ x [p] = 0 ; \ z [p] = 0 #define Z_CLEAR_IMAG(x,z,p) \ z [p] = 0 /* s = s/a */ #define Z_DIV(x,z,p,ax,az,q) \ Common->complex_divide (x [p], z [p], ax [q], az [q], &x [p], &z [p]) /* s -= conj(a)*a ; note that the result of conj(a)*a is real */ #define Z_LLDOT(x,p, ax,az,q) \ x [p] -= ax [q] * ax [q] + az [q] * az [q] #define Z_PRINT(k,x,z,p) PRK(k, ("(%24.16e,%24.16e)", x [p], z [p])) #define Z_DIV_REAL(x,z,p, ax,az,q, bx,r) \ x [p] = ax [q] / bx [r] ; \ z [p] = az [q] / bx [r] #define Z_MULT_REAL(x,z,p, ax,az,q, bx,r) \ x [p] = ax [q] * bx [r] ; \ z [p] = az [q] * bx [r] /* s -= conj(a)*a/t */ #define Z_LDLDOT(x,p, ax,az,q, bx,r) \ x [p] -= (ax [q] * ax [q] + az [q] * az [q]) / bx[r] /* -------------------------------------------------------------------------- */ /* all classes */ /* -------------------------------------------------------------------------- */ /* Check if A->xtype and the two arrays A->x and A->z are valid. Set status to * invalid, unless status is already "out of memory". A can be a sparse matrix, * dense matrix, factor, or triplet. */ #define RETURN_IF_XTYPE_INVALID(A,xtype1,xtype2,result) \ { \ if ((A)->xtype < (xtype1) || (A)->xtype > (xtype2) || \ ((A)->xtype != CHOLMOD_PATTERN && ((A)->x) == NULL) || \ ((A)->xtype == CHOLMOD_ZOMPLEX && ((A)->z) == NULL)) \ { \ if (Common->status != CHOLMOD_OUT_OF_MEMORY) \ { \ ERROR (CHOLMOD_INVALID, "invalid xtype") ; \ } \ return (result) ; \ } \ } SuiteSparse/CHOLMOD/Include/cholmod_config.h0000644001170100242450000000613210537777527017570 0ustar davisfac/* ========================================================================== */ /* === Include/cholmod_config.h ============================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Include/cholmod_config.h. * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis * CHOLMOD/Include/cholmod_config.h is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* CHOLMOD configuration file, for inclusion in user programs. * * You do not have to edit any CHOLMOD files to compile and install CHOLMOD. * However, if you do not use all of CHOLMOD's modules, you need to compile * with the appropriate flag, or edit this file to add the appropriate #define. * * If you wish to use CHOLMOD under the GNU LGPL license only, then you must * compile CHOLMOD with -DNMATRIXOPS -DNSUPERNODAL and -DNMODIFY. This can * be done using just -DNGPL. * * Compiler flags for CHOLMOD: * * -DNCHECK do not include the Check module. License: GNU LGPL * -DNCHOLESKY do not include the Cholesky module. License: GNU LGPL * -DNPARTITION do not include the Partition module. License: GNU LGPL * * -DNGPL do not include any GNU GPL Modules in the CHOLMOD library. * -DNMATRIXOPS do not include the MatrixOps module. License: GNU GPL * -DNMODIFY do not include the Modify module. License: GNU GPL * -DNSUPERNODAL do not include the Supernodal module. License: GNU GPL * * -DNPRINT do not print anything * * -D'LONGBLAS=long' or -DLONGBLAS='long long' defines the integers used by * LAPACK and the BLAS. Use LONGBLAS=long on Solaris to use * the 64-bit Sun Performance BLAS in cholmod_l_* routines. * You may need to use -D'LONGBLAS=long long' on the SGI * (this is not tested). * * -DNSUNPERF for Solaris only. If defined, do not use the Sun * Performance Library. The default is to use SunPerf. * You must compile CHOLMOD with -xlic_lib=sunperf. * * The Core Module (License GNU LGPL) is always included in the CHOLMOD library. */ #ifndef CHOLMOD_CONFIG_H #define CHOLMOD_CONFIG_H /* Use the compiler flag, or uncomment the definition(s), if you want to use * one or more non-default installation options: */ /* #define NCHECK #define NCHOLESKY #define NPARTITION #define NGPL #define NMATRIXOPS #define NMODIFY #define NSUPERNODAL #define NPRINT #define LONGBLAS long #define LONGBLAS long long #define NSUNPERF */ /* -------------------------------------------------------------------------- */ /* if NGPL is defined, disable all GNU GPL Modules */ /* -------------------------------------------------------------------------- */ #ifdef NGPL #define NMATRIXOPS #define NMODIFY #define NSUPERNODAL #endif #endif SuiteSparse/CHOLMOD/Valgrind/0000755001170100242450000000000010620203650014574 5ustar davisfacSuiteSparse/CHOLMOD/Valgrind/tmp/0000755001170100242450000000000010533706431015404 5ustar davisfacSuiteSparse/CHOLMOD/Valgrind/suppress0000644001170100242450000000007610301462236016411 0ustar davisfac{ complexity Memcheck:Value8 fun:change_complexity } SuiteSparse/CHOLMOD/Valgrind/Make.inc0000644001170100242450000000021110533351143016142 0ustar davisfac# valgrind options V = valgrind --suppressions=suppress --quiet # covall is not used COVER = # no test coverage needed CFLAGS = -O0 -g SuiteSparse/CHOLMOD/Valgrind/Makefile0000644001170100242450000000137310533351241016243 0ustar davisfac doall: links go links: touch links ln -s ../Tcov/amdtest.c ln -s ../Tcov/aug.c ln -s ../Tcov/camdtest.c ln -s ../Tcov/cctest.c ln -s ../Tcov/cm.c ln -s ../Tcov/cm.h ln -s ../Tcov/cmread.c ln -s ../Tcov/ctest.c ln -s ../Tcov/huge.c ln -s ../Tcov/leak.c ln -s ../Tcov/lpdemo.c ln -s ../Tcov/memory.c ln -s ../Tcov/null2.c ln -s ../Tcov/null.c ln -s ../Tcov/raw_factor.c ln -s ../Tcov/solve.c ln -s ../Tcov/test_ops.c ln -s ../Tcov/unpack.c ln -s ../Tcov/comments.txt ln -s ../Tcov/Matrix include ../Tcov/Makefile dopurge: distclean - $(RM) amdtest.c aug.c camdtest.c cctest.c cm.c cm.h cmread.c \ ctest.c huge.c leak.c lpdemo.c memory.c null2.c null.c \ raw_factor.c solve.c test_ops.c unpack.c comments.txt \ links Matrix SuiteSparse/CHOLMOD/Valgrind/License.txt0000644001170100242450000000204410540000314016710 0ustar davisfacCHOLMOD/Valgrind Module. Copyright (C) 2005-2006, Timothy A. Davis. CHOLMOD is also available under other licenses; contact authors for details. http://www.cise.ufl.edu/research/sparse Note that this license is for the CHOLMOD/Valgrind module only. All CHOLMOD modules are licensed separately. -------------------------------------------------------------------------------- This Module is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This Module is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. SuiteSparse/CHOLMOD/Valgrind/README.txt0000644001170100242450000000143110533346161016301 0ustar davisfacTorture test for CHOLMOD, using valgrind. Requires Linux. Type "make" to compile and run CHOLMOMD with valgrind. Every line of CHOLMOD will be exercised, and its results checked. The line "All tests passed" should appear in each output file (*.grind). Valgrind should report no errors, and no malloc'd blocks should be in use at exit. Note that many, many error messages will appear in the test output itself (tmp/*.out), because all of CHOLMOD's error handling is checked as well. These errors are expected. To remove all but the source files and output files from this directory, type "make clean". To remove all but the files in the original distribution and the symbolic links, type "make distclean". To remove all but the files in the original distribution, type "make dopurge". SuiteSparse/CHOLMOD/Valgrind/gpl.txt0000644001170100242450000004313310253411166016130 0ustar davisfac GNU GENERAL PUBLIC LICENSE Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users. This General Public License applies to most of the Free Software Foundation's software and to any other program whose authors commit to using it. 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If the program is interactive, make it output a short notice like this when it starts in an interactive mode: Gnomovision version 69, Copyright (C) year name of author Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the program `Gnomovision' (which makes passes at compilers) written by James Hacker. , 1 April 1989 Ty Coon, President of Vice This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Library General Public License instead of this License. SuiteSparse/CHOLMOD/README.txt0000644001170100242450000001024610711425410014530 0ustar davisfacCHOLMOD: a sparse CHOLesky MODification package Version 1.6, Nov 1, 2007. Copyright (c) 2005-2007. ----------------------------------------------- CHOLMOD is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or AA', updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system Lx=b, and many other sparse matrix functions for both symmetric and unsymmetric matrices. Its supernodal Cholesky factorization relies on LAPACK and the Level-3 BLAS, and obtains a substantial fraction of the peak performance of the BLAS. Both real and complex matrices are supported. CHOLMOD is written in ANSI/ISO C, with both C and MATLAB interfaces. This code works on Microsoft Windows and many versions of Unix and Linux. Some Modules of CHOLMOD are copyrighted by the University of Florida (the Core and Partition Modules). The rest are copyrighted by the authors: Timothy A. Davis (all of them), and William W. Hager (the Modify Module). CHOLMOD relies on several other packages: AMD, CAMD, COLAMD, CCOLAMD, UFconfig, METIS, the BLAS, and LAPACK. All but METIS, the BLAS, and LAPACK are part of SuiteSparse. AMD is authored by T. Davis, Iain Duff, and Patrick Amestoy. COLAMD is authored by T. Davis and Stefan Larimore, with algorithmic design in collaboration with John Gilbert and Esmond Ng. CCOLAMD is authored by T. Davis and Siva Rajamanickam. CAMD is authored by T. Davis and Y. Chen. LAPACK and the BLAS are authored by Jack Dongarra and many others. LAPACK is available at http://www.netlib.org/lapack METIS is authored by George Karypis, Univ. of Minnesota. Its use in CHOLMOD is optional. See http://www-users.cs.umn.edu/~karypis/metis. Place a copy of the metis-4.0 directory in the same directory that contains the CHOLMOD, AMD, COLAMD, and CCOLAMD directories prior to compiling with "make". If you do not wish to use METIS, you must edit UFconfig and change the line: CHOLMOD_CONFIG = to CHOLMOD_CONFIG = -DNPARTITION The CHOLMOD, AMD, COLAMD, CCOLAMD, and UFconfig directories must all reside in a common parent directory. To compile all these libraries, edit UFconfig/UFconfig.mk to reflect your environment (C compiler, location of the BLAS, and so on) and then type "make" in either the CHOLMOD directory or in the parent directory of CHOLMOD. See each package for more details on how to compile them. For use in MATLAB (on any system, including Windows): start MATLAB, cd to the CHOLMOD/MATLAB directory, and type cholmod_make in the MATLAB Command Window. This is the best way to compile CHOLMOD for MATLAB; it provides a workaround for a METIS design feature, in which METIS terminates your program (and thus MATLAB) if it runs out of memory. Using cholmod_make also ensures your mexFunctions are compiled with -fexceptions, so that exceptions are handled properly (when hitting control-C in the MATLAB command window, for example). If you have MATLAB 7.2 or earlier and use "make mex", you must first edit UFconfig/UFconfig.h to remove the "-largeArrayDims" option from the MEX command (or just use cholmod_make.m inside MATLAB). On the Pentium, do NOT use the Intel MKL BLAS prior to MKL Version 8.0 with CHOLMOD. Older versions (prior to 8.0) have a bug in dgemm when computing A*B'. The bug generates a NaN result, when the inputs are well-defined. Use the Goto BLAS or the MKL v8.0 BLAS instead. The Goto BLAS is faster and more reliable. See http://www.tacc.utexas.edu/~kgoto/ or http://www.cs.utexas.edu/users/flame/goto/. Sadly, the Intel MKL BLAS 7.x is the default for MATLAB 7.0.4. See http://www.mathworks.com/support/bugreports/details.html?rp=252103 for more details. To workaround this problem on Linux, set environment variable BLAS_VERSION to libmkl_p3.so:libguide.so. On Windows, set environment variable BLAS_VERSION to mkl_p3.dll. Better yet, get MATLAB 7sp3 (MATLAB 7.1) or later. Acknowledgements: this work was supported in part by the National Science Foundation (NFS CCR-0203270 and DMS-9803599), and a grant from Sandia National Laboratories (Dept. of Energy) which supported the development of CHOLMOD's Partition Module. SuiteSparse/CHOLMOD/Partition/0000755001170100242450000000000010677243363015020 5ustar davisfacSuiteSparse/CHOLMOD/Partition/cholmod_nesdis.c0000644001170100242450000020702110677243325020156 0ustar davisfac/* ========================================================================== */ /* === Partition/cholmod_nesdis ============================================= */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Partition Module. * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Partition Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* CHOLMOD nested dissection and graph partitioning. * * cholmod_bisect: * * Finds a set of nodes that partitions the graph into two parts. * Compresses the graph first. Requires METIS. * * cholmod_nested_dissection: * * Nested dissection, using its own compression and connected-commponents * algorithms, an external graph partitioner (METIS), and a constrained * minimum degree ordering algorithm (CCOLAMD or CSYMAMD). Typically * gives better orderings than METIS_NodeND (about 5% to 10% fewer * nonzeros in L). * * cholmod_collapse_septree: * * Prune the separator tree returned by cholmod_nested_dissection. * * This file contains several routines private to this file: * * partition compress and partition a graph * clear_flag clear Common->Flag, but do not modify negative entries * find_components find the connected components of a graph * * Supports any xtype (pattern, real, complex, or zomplex). */ #ifndef NPARTITION #include "cholmod_internal.h" #include "cholmod_partition.h" #include "cholmod_cholesky.h" /* ========================================================================== */ /* === partition ============================================================ */ /* ========================================================================== */ /* Find a set of nodes that partition a graph. The graph must be symmetric * with no diagonal entries. To compress the graph first, compress is TRUE * and on input Hash [j] holds the hash key for node j, which must be in the * range 0 to csize-1. The input graph (Cp, Ci) is destroyed. Cew is all 1's * on input and output. Cnw [j] > 0 is the initial weight of node j. On * output, Cnw [i] = 0 if node i is absorbed into j and the original weight * Cnw [i] is added to Cnw [j]. If compress is FALSE, the graph is not * compressed and Cnw and Hash are unmodified. The partition itself is held in * the output array Part of size n. Part [j] is 0, 1, or 2, depending on * whether node j is in the left part of the graph, the right part, or the * separator, respectively. Note that the input graph need not be connected, * and the output subgraphs (the three parts) may also be unconnected. * * Returns the size of the separator, in terms of the sum of the weights of * the nodes. It is guaranteed to be between 1 and the total weight of all * the nodes. If it is of size less than the total weight, then both the left * and right parts are guaranteed to be non-empty (this guarantee depends on * cholmod_metis_bisector). */ static UF_long partition /* size of separator or -1 if failure */ ( /* inputs, not modified on output */ #ifndef NDEBUG Int csize, /* upper bound on # of edges in the graph; * csize >= MAX (n, nnz(C)) must hold. */ #endif int compress, /* if TRUE the compress the graph first */ /* input/output */ Int Hash [ ], /* Hash [i] = hash >= 0 is the hash function for node * i on input. On output, Hash [i] = FLIP (j) if node * i is absorbed into j. Hash [i] >= 0 if i has not * been absorbed. */ /* input graph, compressed graph of cn nodes on output */ cholmod_sparse *C, /* input/output */ Int Cnw [ ], /* size n. Cnw [j] > 0 is the weight of node j on * input. On output, if node i is absorbed into * node j, then Cnw [i] = 0 and the original weight of * node i is added to Cnw [j]. The sum of Cnw [0..n-1] * is not modified. */ /* workspace */ Int Cew [ ], /* size csize, all 1's on input and output */ /* more workspace, undefined on input and output */ Int Cmap [ ], /* size n (i/i/l) */ /* output */ Int Part [ ], /* size n, Part [j] = 0, 1, or 2. */ cholmod_common *Common ) { Int n, hash, head, i, j, k, p, pend, ilen, ilast, pi, piend, jlen, ok, cn, csep, pdest, nodes_pruned, nz, total_weight, jscattered ; Int *Cp, *Ci, *Next, *Hhead ; #ifndef NDEBUG Int cnt, pruned ; double work = 0, goodwork = 0 ; #endif /* ---------------------------------------------------------------------- */ /* quick return for small or empty graphs */ /* ---------------------------------------------------------------------- */ n = C->nrow ; Cp = C->p ; Ci = C->i ; nz = Cp [n] ; PRINT2 (("Partition start, n "ID" nz "ID"\n", n, nz)) ; total_weight = 0 ; for (j = 0 ; j < n ; j++) { ASSERT (Cnw [j] > 0) ; total_weight += Cnw [j] ; } if (n <= 2) { /* very small graph */ for (j = 0 ; j < n ; j++) { Part [j] = 2 ; } return (total_weight) ; } else if (nz <= 0) { /* no edges, this is easy */ PRINT2 (("diagonal matrix\n")) ; k = n/2 ; for (j = 0 ; j < k ; j++) { Part [j] = 0 ; } for ( ; j < n ; j++) { Part [j] = 1 ; } /* ensure the separator is not empty (required by nested dissection) */ Part [n-1] = 2 ; return (Cnw [n-1]) ; } #ifndef NDEBUG ASSERT (n > 1 && nz > 0) ; PRINT2 (("original graph:\n")) ; for (j = 0 ; j < n ; j++) { PRINT2 ((""ID": ", j)) ; for (p = Cp [j] ; p < Cp [j+1] ; p++) { i = Ci [p] ; PRINT3 ((""ID" ", i)) ; ASSERT (i >= 0 && i < n && i != j) ; } PRINT2 (("hash: "ID"\n", Hash [j])) ; } DEBUG (for (p = 0 ; p < csize ; p++) ASSERT (Cew [p] == 1)) ; #endif nodes_pruned = 0 ; if (compress) { /* ------------------------------------------------------------------ */ /* get workspace */ /* ------------------------------------------------------------------ */ Next = Part ; /* use Part as workspace for Next [ */ Hhead = Cew ; /* use Cew as workspace for Hhead [ */ /* ------------------------------------------------------------------ */ /* create the hash buckets */ /* ------------------------------------------------------------------ */ for (j = 0 ; j < n ; j++) { /* get the hash key for node j */ hash = Hash [j] ; ASSERT (hash >= 0 && hash < csize) ; head = Hhead [hash] ; if (head > EMPTY) { /* hash bucket for this hash key is empty. */ head = EMPTY ; } else { /* hash bucket for this hash key is not empty. get old head */ head = FLIP (head) ; ASSERT (head >= 0 && head < n) ; } /* node j becomes the new head of the hash bucket. FLIP it so that * we can tell the difference between an empty or non-empty hash * bucket. */ Hhead [hash] = FLIP (j) ; Next [j] = head ; ASSERT (head >= EMPTY && head < n) ; } #ifndef NDEBUG for (cnt = 0, k = 0 ; k < n ; k++) { ASSERT (Hash [k] >= 0 && Hash [k] < csize) ; /* k is alive */ hash = Hash [k] ; ASSERT (hash >= 0 && hash < csize) ; head = Hhead [hash] ; ASSERT (head < EMPTY) ; /* hash bucket not empty */ j = FLIP (head) ; ASSERT (j >= 0 && j < n) ; if (j == k) { PRINT2 (("hash "ID": ", hash)) ; for ( ; j != EMPTY ; j = Next [j]) { PRINT3 ((" "ID"", j)) ; ASSERT (j >= 0 && j < n) ; ASSERT (Hash [j] == hash) ; cnt++ ; ASSERT (cnt <= n) ; } PRINT2 (("\n")) ; } } ASSERT (cnt == n) ; #endif /* ------------------------------------------------------------------ */ /* scan the non-empty hash buckets for indistinguishable nodes */ /* ------------------------------------------------------------------ */ /* If there are no hash collisions and no compression occurs, this takes * O(n) time. If no hash collisions, but some nodes are removed, this * takes time O(n+e) where e is the sum of the degress of the nodes * that are removed. Even with many hash collisions (a rare case), * this algorithm has never been observed to perform more than nnz(A) * useless work. * * Cmap is used as workspace to mark nodes of the graph, [ * for comparing the nonzero patterns of two nodes i and j. */ #define Cmap_MARK(i) Cmap [i] = j #define Cmap_MARKED(i) (Cmap [i] == j) for (i = 0 ; i < n ; i++) { Cmap [i] = EMPTY ; } for (k = 0 ; k < n ; k++) { hash = Hash [k] ; ASSERT (hash >= FLIP (n-1) && hash < csize) ; if (hash < 0) { /* node k has already been absorbed into some other node */ ASSERT (FLIP (Hash [k]) >= 0 && FLIP (Hash [k] < n)) ; continue ; } head = Hhead [hash] ; ASSERT (head < EMPTY || head == 1) ; if (head == 1) { /* hash bucket is already empty */ continue ; } PRINT2 (("\n--------------------hash "ID":\n", hash)) ; for (j = FLIP (head) ; j != EMPTY && Next[j] > EMPTY ; j = Next [j]) { /* compare j with all nodes i following it in hash bucket */ ASSERT (j >= 0 && j < n && Hash [j] == hash) ; p = Cp [j] ; pend = Cp [j+1] ; jlen = pend - p ; jscattered = FALSE ; DEBUG (for (i = 0 ; i < n ; i++) ASSERT (!Cmap_MARKED (i))) ; DEBUG (pruned = FALSE) ; ilast = j ; for (i = Next [j] ; i != EMPTY ; i = Next [i]) { ASSERT (i >= 0 && i < n && Hash [i] == hash && i != j) ; pi = Cp [i] ; piend = Cp [i+1] ; ilen = piend - pi ; DEBUG (work++) ; if (ilen != jlen) { /* i and j have different degrees */ ilast = i ; continue ; } /* scatter the pattern of node j, if not already */ if (!jscattered) { Cmap_MARK (j) ; for ( ; p < pend ; p++) { Cmap_MARK (Ci [p]) ; } jscattered = TRUE ; DEBUG (work += jlen) ; } for (ok = Cmap_MARKED (i) ; ok && pi < piend ; pi++) { ok = Cmap_MARKED (Ci [pi]) ; DEBUG (work++) ; } if (ok) { /* found it. kill node i and merge it into j */ PRINT2 (("found "ID" absorbed into "ID"\n", i, j)) ; Hash [i] = FLIP (j) ; Cnw [j] += Cnw [i] ; Cnw [i] = 0 ; ASSERT (ilast != i && ilast >= 0 && ilast < n) ; Next [ilast] = Next [i] ; /* delete i from bucket */ nodes_pruned++ ; DEBUG (goodwork += (ilen+1)) ; DEBUG (pruned = TRUE) ; } else { /* i and j are different */ ilast = i ; } } DEBUG (if (pruned) goodwork += jlen) ; } /* empty the hash bucket, restoring Cew */ Hhead [hash] = 1 ; } DEBUG (if (((work - goodwork) / (double) nz) > 0.20) PRINT0 (( "work %12g good %12g nz %12g (wasted work/nz: %6.2f )\n", work, goodwork, (double) nz, (work - goodwork) / ((double) nz)))) ; /* All hash buckets now empty. Cmap no longer needed as workspace. ] * Cew no longer needed as Hhead; Cew is now restored to all ones. ] * Part no longer needed as workspace for Next. ] */ } /* Edge weights are all one, node weights reflect node absorption */ DEBUG (for (p = 0 ; p < csize ; p++) ASSERT (Cew [p] == 1)) ; DEBUG (for (cnt = 0, j = 0 ; j < n ; j++) cnt += Cnw [j]) ; ASSERT (cnt == total_weight) ; /* ---------------------------------------------------------------------- */ /* compress and partition the graph */ /* ---------------------------------------------------------------------- */ if (nodes_pruned == 0) { /* ------------------------------------------------------------------ */ /* no pruning done at all. Do not create the compressed graph */ /* ------------------------------------------------------------------ */ /* FUTURE WORK: could call CHACO, SCOTCH, ... here too */ csep = CHOLMOD(metis_bisector) (C, Cnw, Cew, Part, Common) ; } else if (nodes_pruned == n-1) { /* ------------------------------------------------------------------ */ /* only one node left. This is a dense graph */ /* ------------------------------------------------------------------ */ PRINT2 (("completely dense graph\n")) ; csep = total_weight ; for (j = 0 ; j < n ; j++) { Part [j] = 2 ; } } else { /* ------------------------------------------------------------------ */ /* compress the graph and partition the compressed graph */ /* ------------------------------------------------------------------ */ /* ------------------------------------------------------------------ */ /* create the map from the uncompressed graph to the compressed graph */ /* ------------------------------------------------------------------ */ /* Cmap [j] = k if node j is alive and the kth node of compressed graph. * The mapping is done monotonically (that is, k <= j) to simplify the * uncompression later on. Cmap [j] = EMPTY if node j is dead. */ for (j = 0 ; j < n ; j++) { Cmap [j] = EMPTY ; } k = 0 ; for (j = 0 ; j < n ; j++) { if (Cnw [j] > 0) { ASSERT (k <= j) ; Cmap [j] = k++ ; } } cn = k ; /* # of nodes in compressed graph */ PRINT2 (("compressed graph from "ID" to "ID" nodes\n", n, cn)) ; ASSERT (cn > 1 && cn == n - nodes_pruned) ; /* ------------------------------------------------------------------ */ /* create the compressed graph */ /* ------------------------------------------------------------------ */ k = 0 ; pdest = 0 ; for (j = 0 ; j < n ; j++) { if (Cnw [j] > 0) { /* node j in the full graph is node k in the compressed graph */ ASSERT (k <= j && Cmap [j] == k) ; p = Cp [j] ; pend = Cp [j+1] ; Cp [k] = pdest ; Cnw [k] = Cnw [j] ; for ( ; p < pend ; p++) { /* prune dead nodes, and remap to new node numbering */ i = Ci [p] ; ASSERT (i >= 0 && i < n && i != j) ; i = Cmap [i] ; ASSERT (i >= EMPTY && i < cn && i != k) ; if (i > EMPTY) { ASSERT (pdest <= p) ; Ci [pdest++] = i ; } } k++ ; } } Cp [cn] = pdest ; C->nrow = cn ; C->ncol = cn ; /* affects mem stats unless restored when C free'd */ #ifndef NDEBUG PRINT2 (("pruned graph ("ID"/"ID") nodes, ("ID"/"ID") edges\n", cn, n, pdest, nz)) ; PRINT2 (("compressed graph:\n")) ; for (cnt = 0, j = 0 ; j < cn ; j++) { PRINT2 ((""ID": ", j)) ; for (p = Cp [j] ; p < Cp [j+1] ; p++) { i = Ci [p] ; PRINT3 ((""ID" ", i)) ; ASSERT (i >= 0 && i < cn && i != j) ; } PRINT2 (("weight: "ID"\n", Cnw [j])) ; ASSERT (Cnw [j] > 0) ; cnt += Cnw [j] ; } ASSERT (cnt == total_weight) ; for (j = 0 ; j < n ; j++) PRINT2 (("Cmap ["ID"] = "ID"\n", j, Cmap[j])); ASSERT (k == cn) ; #endif /* ------------------------------------------------------------------ */ /* find the separator of the compressed graph */ /* ------------------------------------------------------------------ */ /* FUTURE WORK: could call CHACO, SCOTCH, ... here too */ csep = CHOLMOD(metis_bisector) (C, Cnw, Cew, Part, Common) ; if (csep < 0) { /* failed */ return (-1) ; } PRINT2 (("Part: ")) ; DEBUG (for (j = 0 ; j < cn ; j++) PRINT2 ((""ID" ", Part [j]))) ; PRINT2 (("\n")) ; /* Cp and Ci no longer needed */ /* ------------------------------------------------------------------ */ /* find the separator of the uncompressed graph */ /* ------------------------------------------------------------------ */ /* expand the separator to live nodes in the uncompressed graph */ for (j = n-1 ; j >= 0 ; j--) { /* do this in reverse order so that Cnw can be expanded in place */ k = Cmap [j] ; ASSERT (k >= EMPTY && k < n) ; if (k > EMPTY) { /* node k in compressed graph and is node j in full graph */ ASSERT (k <= j) ; ASSERT (Hash [j] >= EMPTY) ; Part [j] = Part [k] ; Cnw [j] = Cnw [k] ; } else { /* node j is a dead node */ Cnw [j] = 0 ; DEBUG (Part [j] = EMPTY) ; ASSERT (Hash [j] < EMPTY) ; } } /* find the components for the dead nodes */ for (i = 0 ; i < n ; i++) { if (Hash [i] < EMPTY) { /* node i has been absorbed into node j */ j = FLIP (Hash [i]) ; ASSERT (Part [i] == EMPTY && j >= 0 && j < n && Cnw [i] == 0) ; Part [i] = Part [j] ; } ASSERT (Part [i] >= 0 && Part [i] <= 2) ; } #ifndef NDEBUG PRINT2 (("Part: ")) ; for (cnt = 0, j = 0 ; j < n ; j++) { ASSERT (Part [j] != EMPTY) ; PRINT2 ((""ID" ", Part [j])) ; if (Part [j] == 2) cnt += Cnw [j] ; } PRINT2 (("\n")) ; PRINT2 (("csep "ID" "ID"\n", cnt, csep)) ; ASSERT (cnt == csep) ; for (cnt = 0, j = 0 ; j < n ; j++) cnt += Cnw [j] ; ASSERT (cnt == total_weight) ; #endif } /* ---------------------------------------------------------------------- */ /* return the separator (or -1 if error) */ /* ---------------------------------------------------------------------- */ PRINT2 (("Partition done, n "ID" csep "ID"\n", n, csep)) ; return (csep) ; } /* ========================================================================== */ /* === clear_flag =========================================================== */ /* ========================================================================== */ /* A node j has been removed from the graph if Flag [j] < EMPTY. * If Flag [j] >= EMPTY && Flag [j] < mark, then node j is alive but unmarked. * Flag [j] == mark means that node j is alive and marked. Incrementing mark * means that all nodes are either (still) dead, or live but unmarked. * * If Map is NULL, then on output, Common->mark < Common->Flag [i] for all i * from 0 to Common->nrow. This is the same output condition as * cholmod_clear_flag, except that this routine maintains the Flag [i] < EMPTY * condition as well, if that condition was true on input. * * If Map is non-NULL, then on output, Common->mark < Common->Flag [i] for all * i in the set Map [0..cn-1]. * * workspace: Flag (nrow) */ static UF_long clear_flag (Int *Map, Int cn, cholmod_common *Common) { Int nrow, i ; Int *Flag ; PRINT2 (("old mark %ld\n", Common->mark)) ; Common->mark++ ; PRINT2 (("new mark %ld\n", Common->mark)) ; if (Common->mark <= 0) { nrow = Common->nrow ; Flag = Common->Flag ; if (Map != NULL) { for (i = 0 ; i < cn ; i++) { /* if Flag [Map [i]] < EMPTY, leave it alone */ if (Flag [Map [i]] >= EMPTY) { Flag [Map [i]] = EMPTY ; } } /* now Flag [Map [i]] <= EMPTY for all i */ } else { for (i = 0 ; i < nrow ; i++) { /* if Flag [i] < EMPTY, leave it alone */ if (Flag [i] >= EMPTY) { Flag [i] = EMPTY ; } } /* now Flag [i] <= EMPTY for all i */ } Common->mark = 0 ; } return (Common->mark) ; } /* ========================================================================== */ /* === find_components ====================================================== */ /* ========================================================================== */ /* Find all connected components of the current subgraph C. The subgraph C * consists of the nodes of B that appear in the set Map [0..cn-1]. If Map * is NULL, then it is assumed to be the identity mapping * (Map [0..cn-1] = 0..cn-1). * * A node j does not appear in B if it has been ordered (Flag [j] < EMPTY, * which means that j has been ordered and is "deleted" from B). * * If the size of a component is large, it is placed on the component stack, * Cstack. Otherwise, its nodes are ordered and it is not placed on the Cstack. * * A component S is defined by a "representative node" (repnode for short) * called the snode, which is one of the nodes in the subgraph. Likewise, the * subgraph C is defined by its repnode, called cnode. * * If Part is not NULL on input, then Part [i] determines how the components * are placed on the stack. Components containing nodes i with Part [i] == 0 * are placed first, followed by components with Part [i] == 1. * * The first node placed in each of the two parts is flipped when placed in * the Cstack. This allows the components of the two parts to be found simply * by traversing the Cstack. * * workspace: Flag (nrow) */ static void find_components ( /* inputs, not modified on output */ cholmod_sparse *B, Int Map [ ], /* size n, only Map [0..cn-1] used */ Int cn, /* # of nodes in C */ Int cnode, /* root node of component C, or EMPTY if C is the * entire graph B */ Int Part [ ], /* size cn, optional */ /* input/output */ Int Bnz [ ], /* size n. Bnz [j] = # nonzeros in column j of B. * Reduce since B is pruned of dead nodes. */ Int CParent [ ], /* CParent [i] = j if component with repnode j is * the parent of the component with repnode i. * CParent [i] = EMPTY if the component with * repnode i is a root of the separator tree. * CParent [i] is -2 if i is not a repnode. */ Int Cstack [ ], /* component stack for nested dissection */ Int *top, /* Cstack [0..top] contains root nodes of the * the components currently in the stack */ /* workspace, undefined on input and output: */ Int Queue [ ], /* size n, for breadth-first search */ cholmod_common *Common ) { Int n, mark, cj, j, sj, sn, p, i, snode, pstart, pdest, pend, nd_components, part, first, save_mark ; Int *Bp, *Bi, *Flag ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ PRINT2 (("find components: cn %d\n", cn)) ; Flag = Common->Flag ; /* size n */ /* force initialization of Flag [Map [0..cn-1]] */ save_mark = Common->mark ; /* save the current mark */ Common->mark = EMPTY ; /* clear Flag; preserve Flag [Map [i]] if Flag [Map [i]] already < EMPTY */ /* this takes O(cn) time */ mark = clear_flag (Map, cn, Common) ; Bp = B->p ; Bi = B->i ; n = B->nrow ; ASSERT (cnode >= EMPTY && cnode < n) ; ASSERT (IMPLIES (cnode >= 0, Flag [cnode] < EMPTY)) ; /* get ordering parameters */ nd_components = Common->method [Common->current].nd_components ; /* ---------------------------------------------------------------------- */ /* find the connected components of C via a breadth-first search */ /* ---------------------------------------------------------------------- */ part = (Part == NULL) ? 0 : 1 ; /* examine each part (part 1 and then part 0) */ for (part = (Part == NULL) ? 0 : 1 ; part >= 0 ; part--) { /* first is TRUE for the first connected component in each part */ first = TRUE ; /* find all connected components in the current part */ for (cj = 0 ; cj < cn ; cj++) { /* get node snode, which is node cj of C. It might already be in * the separator of C (and thus ordered, with Flag [snode] < EMPTY) */ snode = (Map == NULL) ? (cj) : (Map [cj]) ; ASSERT (snode >= 0 && snode < n) ; if (Flag [snode] >= EMPTY && Flag [snode] < mark && ((Part == NULL) || Part [cj] == part)) { /* ---------------------------------------------------------- */ /* find new connected component S */ /* ---------------------------------------------------------- */ /* node snode is the repnode of a connected component S, the * parent of which is cnode, the repnode of C. If cnode is * EMPTY then C is the original graph B. */ PRINT2 (("----------:::snode "ID" cnode "ID"\n", snode, cnode)); ASSERT (CParent [snode] == -2) ; if (first || nd_components) { /* If this is the first node in this part, then it becomes * the repnode of all components in this part, and all * components in this part form a single node in the * separator tree. If nd_components is TRUE, then all * connected components form their own node in the * separator tree. */ CParent [snode] = cnode ; } /* place j in the queue and mark it */ Queue [0] = snode ; Flag [snode] = mark ; sn = 1 ; /* breadth-first traversal, starting at node j */ for (sj = 0 ; sj < sn ; sj++) { /* get node j from head of Queue and traverse its edges */ j = Queue [sj] ; PRINT2 ((" j: "ID"\n", j)) ; ASSERT (j >= 0 && j < n) ; ASSERT (Flag [j] == mark) ; pstart = Bp [j] ; pdest = pstart ; pend = pstart + Bnz [j] ; for (p = pstart ; p < pend ; p++) { i = Bi [p] ; if (i != j && Flag [i] >= EMPTY) { /* node is still in the graph */ Bi [pdest++] = i ; if (Flag [i] < mark) { /* node i is in this component S, and unflagged * (first time node i has been seen in this BFS) * place node i in the queue and mark it */ Queue [sn++] = i ; Flag [i] = mark ; } } } /* edges to dead nodes have been removed */ Bnz [j] = pdest - pstart ; } /* ---------------------------------------------------------- */ /* order S if it is small; place it on Cstack otherwise */ /* ---------------------------------------------------------- */ PRINT2 (("sn "ID"\n", sn)) ; /* place the new component on the Cstack. Flip the node if * is the first connected component of the current part, * or if all components are treated as their own node in * the separator tree. */ Cstack [++(*top)] = (first || nd_components) ? FLIP (snode) : snode ; first = FALSE ; } } } /* restore the flag (normally taking O(1) time except for Int overflow) */ Common->mark = save_mark++ ; clear_flag (NULL, 0, Common) ; DEBUG (for (i = 0 ; i < n ; i++) ASSERT (Flag [i] < Common->mark)) ; } /* ========================================================================== */ /* === cholmod_bisect ======================================================= */ /* ========================================================================== */ /* Finds a node bisector of A, A*A', A(:,f)*A(:,f)'. * * workspace: Flag (nrow), * Iwork (nrow if symmetric, max (nrow,ncol) if unsymmetric). * Allocates a temporary matrix B=A*A' or B=A, * and O(nnz(A)) temporary memory space. */ UF_long CHOLMOD(bisect) /* returns # of nodes in separator */ ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to bisect */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int compress, /* if TRUE, compress the graph first */ /* ---- output --- */ Int *Partition, /* size A->nrow. Node i is in the left graph if * Partition [i] = 0, the right graph if 1, and in the * separator if 2. */ /* --------------- */ cholmod_common *Common ) { Int *Bp, *Bi, *Hash, *Cmap, *Bnw, *Bew, *Iwork ; cholmod_sparse *B ; unsigned Int hash ; Int j, n, bnz, sepsize, p, pend ; size_t csize, s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (A, EMPTY) ; RETURN_IF_NULL (Partition, EMPTY) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* quick return */ /* ---------------------------------------------------------------------- */ n = A->nrow ; if (n == 0) { return (0) ; } /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = n + MAX (n, A->ncol) */ s = CHOLMOD(add_size_t) (A->nrow, MAX (A->nrow, A->ncol), &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (EMPTY) ; } CHOLMOD(allocate_work) (n, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (EMPTY) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; Iwork = Common->Iwork ; Hash = Iwork ; /* size n, (i/l/l) */ Cmap = Iwork + n ; /* size n, (i/i/l) */ /* ---------------------------------------------------------------------- */ /* convert the matrix to adjacency list form */ /* ---------------------------------------------------------------------- */ /* The input graph to must be symmetric, with no diagonal entries * present. The columns need not be sorted. */ /* B = A, A*A', or A(:,f)*A(:,f)', upper and lower parts present */ if (A->stype) { /* Add the upper/lower part to a symmetric lower/upper matrix by * converting to unsymmetric mode */ /* workspace: Iwork (nrow) */ B = CHOLMOD(copy) (A, 0, -1, Common) ; } else { /* B = A*A' or A(:,f)*A(:,f)', no diagonal */ /* workspace: Flag (nrow), Iwork (max (nrow,ncol)) */ B = CHOLMOD(aat) (A, fset, fsize, -1, Common) ; } if (Common->status < CHOLMOD_OK) { return (EMPTY) ; } Bp = B->p ; Bi = B->i ; bnz = Bp [n] ; ASSERT ((Int) (B->nrow) == n && (Int) (B->ncol) == n) ; /* B does not include the diagonal, and both upper and lower parts. * Common->anz includes the diagonal, and just the lower part of B */ Common->anz = bnz / 2 + ((double) n) ; /* Bew should be at least size n for the hash function to work well */ /* this cannot cause overflow, because the matrix is already created */ csize = MAX (((size_t) n) + 1, (size_t) bnz) ; /* create the graph using Flag as workspace for node weights [ */ Bnw = Common->Flag ; /* size n workspace */ /* compute hash for each node if compression requested */ if (compress) { for (j = 0 ; j < n ; j++) { hash = j ; pend = Bp [j+1] ; for (p = Bp [j] ; p < pend ; p++) { hash += Bi [p] ; ASSERT (Bi [p] != j) ; } /* finalize the hash key for node j */ hash %= csize ; Hash [j] = (Int) hash ; ASSERT (Hash [j] >= 0 && Hash [j] < csize) ; } } /* allocate edge weights */ Bew = CHOLMOD(malloc) (csize, sizeof (Int), Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&B, Common) ; CHOLMOD(free) (csize, sizeof (Int), Bew, Common) ; return (EMPTY) ; } /* graph has unit node and edge weights */ for (j = 0 ; j < n ; j++) { Bnw [j] = 1 ; } for (s = 0 ; s < csize ; s++) { Bew [s] = 1 ; } /* ---------------------------------------------------------------------- */ /* compress and partition the graph */ /* ---------------------------------------------------------------------- */ sepsize = partition ( #ifndef NDEBUG csize, #endif compress, Hash, B, Bnw, Bew, Cmap, Partition, Common) ; /* contents of Bp, Bi, Bnw, and Bew no longer needed ] */ /* If partition fails, free the workspace below and return sepsize < 0 */ /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ B->ncol = n ; /* restore size for memory usage statistics */ CHOLMOD(free_sparse) (&B, Common) ; Common->mark = EMPTY ; CHOLMOD_CLEAR_FLAG (Common) ; CHOLMOD(free) (csize, sizeof (Int), Bew, Common) ; return (sepsize) ; } /* ========================================================================== */ /* === cholmod_nested_dissection ============================================ */ /* ========================================================================== */ /* This method uses a node bisector, applied recursively (but using a * non-recursive algorithm). Once the graph is partitioned, it calls a * constrained min degree code (CAMD or CSYMAMD for A+A', and CCOLAMD for A*A') * to order all the nodes in the graph - but obeying the constraints determined * by the separators. This routine is similar to METIS_NodeND, except for how * it treats the leaf nodes. METIS_NodeND orders the leaves of the separator * tree with MMD, ignoring the rest of the matrix when ordering a single leaf. * This routine orders the whole matrix with CSYMAMD or CCOLAMD, all at once, * when the graph partitioning is done. * * This function also returns a postorderd separator tree (CParent), and a * mapping of nodes in the graph to nodes in the separator tree (Cmember). * * workspace: Flag (nrow), Head (nrow+1), Iwork (4*nrow + (ncol if unsymmetric)) * Allocates a temporary matrix B=A*A' or B=A, * and O(nnz(A)) temporary memory space. * Allocates an additional 3*n*sizeof(Int) temporary workspace */ UF_long CHOLMOD(nested_dissection) /* returns # of components, or -1 if error */ ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ /* ---- output --- */ Int *Perm, /* size A->nrow, output permutation */ Int *CParent, /* size A->nrow. On output, CParent [c] is the parent * of component c, or EMPTY if c is a root, and where * c is in the range 0 to # of components minus 1 */ Int *Cmember, /* size A->nrow. Cmember [j] = c if node j of A is * in component c */ /* --------------- */ cholmod_common *Common ) { double prune_dense, nd_oksep ; Int *Bp, *Bi, *Bnz, *Cstack, *Imap, *Map, *Flag, *Head, *Next, *Bnw, *Iwork, *Ipost, *NewParent, *Hash, *Cmap, *Cp, *Ci, *Cew, *Cnw, *Part, *Post, *Work3n ; unsigned Int hash ; Int n, bnz, top, i, j, k, cnode, cdense, p, cj, cn, ci, cnz, mark, c, uncol, sepsize, parent, ncomponents, threshold, ndense, pstart, pdest, pend, nd_compress, nd_camd, csize, jnext, nd_small, total_weight, nchild, child = EMPTY ; cholmod_sparse *B, *C ; size_t s ; int ok = TRUE ; DEBUG (Int cnt) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (A, EMPTY) ; RETURN_IF_NULL (Perm, EMPTY) ; RETURN_IF_NULL (CParent, EMPTY) ; RETURN_IF_NULL (Cmember, EMPTY) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* quick return */ /* ---------------------------------------------------------------------- */ n = A->nrow ; if (n == 0) { return (1) ; } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ /* get ordering parameters */ prune_dense = Common->method [Common->current].prune_dense ; nd_compress = Common->method [Common->current].nd_compress ; nd_oksep = Common->method [Common->current].nd_oksep ; nd_oksep = MAX (0, nd_oksep) ; nd_oksep = MIN (1, nd_oksep) ; nd_camd = Common->method [Common->current].nd_camd ; nd_small = Common->method [Common->current].nd_small ; nd_small = MAX (4, nd_small) ; PRINT0 (("nd_components %d nd_small %d nd_oksep %g\n", Common->method [Common->current].nd_components, nd_small, nd_oksep)) ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = 4*n + uncol */ uncol = (A->stype == 0) ? A->ncol : 0 ; s = CHOLMOD(mult_size_t) (n, 4, &ok) ; s = CHOLMOD(add_size_t) (s, uncol, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (EMPTY) ; } CHOLMOD(allocate_work) (n, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (EMPTY) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ Flag = Common->Flag ; /* size n */ Head = Common->Head ; /* size n+1, all equal to -1 */ Iwork = Common->Iwork ; Imap = Iwork ; /* size n, same as Queue in find_components */ Map = Iwork + n ; /* size n */ Bnz = Iwork + 2*((size_t) n) ; /* size n */ Hash = Iwork + 3*((size_t) n) ; /* size n */ Work3n = CHOLMOD(malloc) (n, 3*sizeof (Int), Common) ; Part = Work3n ; /* size n */ Bnw = Part + n ; /* size n */ Cnw = Bnw + n ; /* size n */ Cstack = Perm ; /* size n, use Perm as workspace for Cstack [ */ Cmap = Cmember ; /* size n, use Cmember as workspace [ */ if (Common->status < CHOLMOD_OK) { return (EMPTY) ; } /* ---------------------------------------------------------------------- */ /* convert B to symmetric form with both upper/lower parts present */ /* ---------------------------------------------------------------------- */ /* B = A+A', A*A', or A(:,f)*A(:,f)', upper and lower parts present */ if (A->stype) { /* Add the upper/lower part to a symmetric lower/upper matrix by * converting to unsymmetric mode */ /* workspace: Iwork (nrow) */ B = CHOLMOD(copy) (A, 0, -1, Common) ; } else { /* B = A*A' or A(:,f)*A(:,f)', no diagonal */ /* workspace: Flag (nrow), Iwork (max (nrow,ncol)) */ B = CHOLMOD(aat) (A, fset, fsize, -1, Common) ; } if (Common->status < CHOLMOD_OK) { CHOLMOD(free) (3*n, sizeof (Int), Work3n, Common) ; return (EMPTY) ; } Bp = B->p ; Bi = B->i ; bnz = CHOLMOD(nnz) (B, Common) ; ASSERT ((Int) (B->nrow) == n && (Int) (B->ncol) == n) ; csize = MAX (n, bnz) ; ASSERT (CHOLMOD(dump_sparse) (B, "B for nd:", Common) >= 0) ; /* ---------------------------------------------------------------------- */ /* initializations */ /* ---------------------------------------------------------------------- */ /* all nodes start out unmarked and unordered (Type 4, see below) */ Common->mark = EMPTY ; CHOLMOD_CLEAR_FLAG (Common) ; ASSERT (Flag == Common->Flag) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; for (j = 0 ; j < n ; j++) { CParent [j] = -2 ; } /* prune dense nodes from B */ if (IS_NAN (prune_dense) || prune_dense < 0) { /* only remove completely dense nodes */ threshold = n-2 ; } else { /* remove nodes with degree more than threshold */ threshold = (Int) (MAX (16, prune_dense * sqrt ((double) (n)))) ; threshold = MIN (n, threshold) ; } ndense = 0 ; cnode = EMPTY ; cdense = EMPTY ; for (j = 0 ; j < n ; j++) { Bnz [j] = Bp [j+1] - Bp [j] ; if (Bnz [j] > threshold) { /* node j is dense, prune it from B */ PRINT2 (("j is dense %d\n", j)) ; ndense++ ; if (cnode == EMPTY) { /* first dense node found becomes root of this component, * which contains all of the dense nodes found here */ cdense = j ; cnode = j ; CParent [cnode] = EMPTY ; } Flag [j] = FLIP (cnode) ; } } B->packed = FALSE ; ASSERT (B->nz == NULL) ; if (ndense == n) { /* all nodes removed: Perm is identity, all nodes in component zero, * and the separator tree has just one node. */ PRINT2 (("all nodes are dense\n")) ; for (k = 0 ; k < n ; k++) { Perm [k] = k ; Cmember [k] = 0 ; } CParent [0] = EMPTY ; CHOLMOD(free_sparse) (&B, Common) ; CHOLMOD(free) (3*n, sizeof (Int), Work3n, Common) ; Common->mark = EMPTY ; CHOLMOD_CLEAR_FLAG (Common) ; return (1) ; } /* Cp and Ci are workspace to construct the subgraphs to partition */ C = CHOLMOD(allocate_sparse) (n, n, csize, FALSE, TRUE, 0, CHOLMOD_PATTERN, Common) ; Cew = CHOLMOD(malloc) (csize, sizeof (Int), Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&C, Common) ; CHOLMOD(free_sparse) (&B, Common) ; CHOLMOD(free) (csize, sizeof (Int), Cew, Common) ; CHOLMOD(free) (3*n, sizeof (Int), Work3n, Common) ; Common->mark = EMPTY ; CHOLMOD_CLEAR_FLAG (Common) ; PRINT2 (("out of memory for C, etc\n")) ; return (EMPTY) ; } Cp = C->p ; Ci = C->i ; /* create initial unit node and edge weights */ for (j = 0 ; j < n ; j++) { Bnw [j] = 1 ; } for (p = 0 ; p < csize ; p++) { Cew [p] = 1 ; } /* push the initial connnected components of B onto the Cstack */ top = EMPTY ; /* Cstack is empty */ /* workspace: Flag (nrow), Iwork (nrow); use Imap as workspace for Queue [*/ find_components (B, NULL, n, cnode, NULL, Bnz, CParent, Cstack, &top, Imap, Common) ; /* done using Imap as workspace for Queue ] */ /* Nodes can now be of Type 0, 1, 2, or 4 (see definition below) */ /* ---------------------------------------------------------------------- */ /* while Cstack is not empty, do: */ /* ---------------------------------------------------------------------- */ while (top >= 0) { /* clear the Flag array, but do not modify negative entries in Flag */ mark = clear_flag (NULL, 0, Common) ; DEBUG (for (i = 0 ; i < n ; i++) Imap [i] = EMPTY) ; /* ------------------------------------------------------------------ */ /* get node(s) from the top of the Cstack */ /* ------------------------------------------------------------------ */ /* i is the repnode of its (unordered) connected component. Get * all repnodes for all connected components of a single part. If * each connected component is to be ordered separately (nd_components * is TRUE), then this while loop iterates just once. */ cnode = EMPTY ; cn = 0 ; while (cnode == EMPTY) { i = Cstack [top--] ; if (i < 0) { /* this is the last node in this component */ i = FLIP (i) ; cnode = i ; } ASSERT (i >= 0 && i < n && Flag [i] >= EMPTY) ; /* place i in the queue and mark it */ Map [cn] = i ; Flag [i] = mark ; Imap [i] = cn ; cn++ ; } ASSERT (cnode != EMPTY) ; /* During ordering, there are five kinds of nodes in the graph of B, * based on Flag [j] and CParent [j] for nodes j = 0 to n-1: * * Type 0: If cnode is a repnode of an unordered component, then * CParent [cnode] is in the range EMPTY to n-1 and * Flag [cnode] >= EMPTY. This is a "live" node. * * Type 1: If cnode is a repnode of an ordered separator component, * then Flag [cnode] < EMPTY and FLAG [cnode] = FLIP (cnode). * CParent [cnode] is in the range EMPTY to n-1. cnode is a root of * the separator tree if CParent [cnode] == EMPTY. This node is dead. * * Type 2: If node j isn't a repnode, has not been absorbed via * graph compression into another node, but is in an ordered separator * component, then cnode = FLIP (Flag [j]) gives the repnode of the * component that contains j and CParent [j] is -2. This node is dead. * Note that Flag [j] < EMPTY. * * Type 3: If node i has been absorbed via graph compression into some * other node j = FLIP (Flag [i]) where j is not a repnode. * CParent [j] is -2. Node i may or may not be in an ordered * component. This node is dead. Note that Flag [j] < EMPTY. * * Type 4: If node j is "live" (not in an ordered component, and not * absorbed into any other node), then Flag [j] >= EMPTY. * * Only "live" nodes (of type 0 or 4) are placed in a subgraph to be * partitioned. Node j is alive if Flag [j] >= EMPTY, and dead if * Flag [j] < EMPTY. */ /* ------------------------------------------------------------------ */ /* create the subgraph for this connected component C */ /* ------------------------------------------------------------------ */ /* Do a breadth-first search of the graph starting at cnode. * use Map [0..cn-1] for nodes in the component C [ * use Cnw and Cew for node and edge weights of the resulting subgraph [ * use Cp and Ci for the resulting subgraph [ * use Imap [i] for all nodes i in B that are in the component C [ */ cnz = 0 ; total_weight = 0 ; for (cj = 0 ; cj < cn ; cj++) { /* get node j from the head of the queue; it is node cj of C */ j = Map [cj] ; ASSERT (Flag [j] == mark) ; Cp [cj] = cnz ; Cnw [cj] = Bnw [j] ; ASSERT (Cnw [cj] >= 0) ; total_weight += Cnw [cj] ; pstart = Bp [j] ; pdest = pstart ; pend = pstart + Bnz [j] ; hash = cj ; for (p = pstart ; p < pend ; p++) { i = Bi [p] ; /* prune diagonal entries and dead edges from B */ if (i != j && Flag [i] >= EMPTY) { /* live node i is in the current component */ Bi [pdest++] = i ; if (Flag [i] != mark) { /* First time node i has been seen, it is a new node * of C. place node i in the queue and mark it */ Map [cn] = i ; Flag [i] = mark ; Imap [i] = cn ; cn++ ; } /* place the edge (cj,ci) in the adjacency list of cj */ ci = Imap [i] ; ASSERT (ci >= 0 && ci < cn && ci != cj && cnz < csize) ; Ci [cnz++] = ci ; hash += ci ; } } /* edges to dead nodes have been removed */ Bnz [j] = pdest - pstart ; /* finalize the hash key for column j */ hash %= csize ; Hash [cj] = (Int) hash ; ASSERT (Hash [cj] >= 0 && Hash [cj] < csize) ; } Cp [cn] = cnz ; C->nrow = cn ; C->ncol = cn ; /* affects mem stats unless restored when C free'd */ /* contents of Imap no longer needed ] */ #ifndef NDEBUG for (cj = 0 ; cj < cn ; cj++) { j = Map [cj] ; PRINT2 (("----------------------------C column cj: "ID" j: "ID"\n", cj, j)) ; ASSERT (j >= 0 && j < n) ; ASSERT (Flag [j] >= EMPTY) ; for (p = Cp [cj] ; p < Cp [cj+1] ; p++) { ci = Ci [p] ; i = Map [ci] ; PRINT3 (("ci: "ID" i: "ID"\n", ci, i)) ; ASSERT (ci != cj && ci >= 0 && ci < cn) ; ASSERT (i != j && i >= 0 && i < n) ; ASSERT (Flag [i] >= EMPTY) ; } } #endif PRINT0 (("consider cn %d nd_small %d ", cn, nd_small)) ; if (cn < nd_small) /* could be 'total_weight < nd_small' instead */ { /* place all nodes in the separator */ PRINT0 ((" too small\n")) ; sepsize = total_weight ; } else { /* Cp and Ci now contain the component, with cn nodes and cnz * nonzeros. The mapping of a node cj into node j the main graph * B is given by Map [cj] = j */ PRINT0 ((" cut\n")) ; /* -------------------------------------------------------------- */ /* compress and partition the graph C */ /* -------------------------------------------------------------- */ /* The edge weights Cew [0..csize-1] are all 1's on input to and * output from the partition routine. */ sepsize = partition ( #ifndef NDEBUG csize, #endif nd_compress, Hash, C, Cnw, Cew, Cmap, Part, Common) ; /* contents of Cp and Ci no longer needed ] */ if (sepsize < 0) { /* failed */ C->ncol = n ; /* restore size for memory usage statistics */ CHOLMOD(free_sparse) (&C, Common) ; CHOLMOD(free_sparse) (&B, Common) ; CHOLMOD(free) (csize, sizeof (Int), Cew, Common) ; CHOLMOD(free) (3*n, sizeof (Int), Work3n, Common) ; Common->mark = EMPTY ; CHOLMOD_CLEAR_FLAG (Common) ; return (EMPTY) ; } /* -------------------------------------------------------------- */ /* compress B based on how C was compressed */ /* -------------------------------------------------------------- */ for (ci = 0 ; ci < cn ; ci++) { if (Hash [ci] < EMPTY) { /* ci is dead in C, having been absorbed into cj */ cj = FLIP (Hash [ci]) ; PRINT2 (("In C, "ID" absorbed into "ID" (wgt now "ID")\n", ci, cj, Cnw [cj])) ; /* i is dead in B, having been absorbed into j */ i = Map [ci] ; j = Map [cj] ; PRINT2 (("In B, "ID" (wgt "ID") => "ID" (wgt "ID")\n", i, Bnw [i], j, Bnw [j], Cnw [cj])) ; /* more than one node may be absorbed into j. This is * accounted for in Cnw [cj]. Assign it here rather * than += Bnw [i] */ Bnw [i] = 0 ; Bnw [j] = Cnw [cj] ; Flag [i] = FLIP (j) ; } } DEBUG (for (cnt = 0, j = 0 ; j < n ; j++) cnt += Bnw [j]) ; ASSERT (cnt == n) ; } /* contents of Cnw [0..cn-1] no longer needed ] */ /* ------------------------------------------------------------------ */ /* order the separator, and stack the components when C is split */ /* ------------------------------------------------------------------ */ /* one more component has been found: either the separator of C, * or all of C */ ASSERT (sepsize >= 0 && sepsize <= total_weight) ; PRINT0 (("sepsize %d tot %d : %8.4f ", sepsize, total_weight, ((double) sepsize) / ((double) total_weight))) ; if (sepsize == total_weight || sepsize == 0 || sepsize > nd_oksep * total_weight) { /* Order the nodes in the component. The separator is too large, * or empty. Note that the partition routine cannot return a * sepsize of zero, but it can return a separator consisting of the * whole graph. The "sepsize == 0" test is kept, above, in case the * partition routine changes. In either case, this component * remains unsplit, and becomes a leaf of the separator tree. */ PRINT2 (("cnode %d sepsize zero or all of graph: "ID"\n", cnode, sepsize)) ; for (cj = 0 ; cj < cn ; cj++) { j = Map [cj] ; Flag [j] = FLIP (cnode) ; PRINT2 ((" node cj: "ID" j: "ID" ordered\n", cj, j)) ; } ASSERT (Flag [cnode] == FLIP (cnode)) ; ASSERT (cnode != EMPTY && Flag [cnode] < EMPTY) ; PRINT0 (("discarded\n")) ; } else { /* Order the nodes in the separator of C and find a new repnode * cnode that is in the separator of C. This requires the separator * to be non-empty. */ PRINT0 (("sepsize not tiny: "ID"\n", sepsize)) ; parent = CParent [cnode] ; ASSERT (parent >= EMPTY && parent < n) ; CParent [cnode] = -2 ; cnode = EMPTY ; for (cj = 0 ; cj < cn ; cj++) { j = Map [cj] ; if (Part [cj] == 2) { /* All nodes in the separator become part of a component * whose repnode is cnode */ PRINT2 (("node cj: "ID" j: "ID" ordered\n", cj, j)) ; if (cnode == EMPTY) { PRINT2(("------------new cnode: cj "ID" j "ID"\n", cj, j)) ; cnode = j ; } Flag [j] = FLIP (cnode) ; } else { PRINT2 ((" node cj: "ID" j: "ID" not ordered\n", cj, j)) ; } } ASSERT (cnode != EMPTY && Flag [cnode] < EMPTY) ; ASSERT (CParent [cnode] == -2) ; CParent [cnode] = parent ; /* find the connected components when C is split, and push * them on the Cstack. Use Imap as workspace for Queue. [ */ /* workspace: Flag (nrow) */ find_components (B, Map, cn, cnode, Part, Bnz, CParent, Cstack, &top, Imap, Common) ; /* done using Imap as workspace for Queue ] */ } /* contents of Map [0..cn-1] no longer needed ] */ } /* done using Cmember as workspace for Cmap ] */ /* done using Perm as workspace for Cstack ] */ /* ---------------------------------------------------------------------- */ /* place nodes removed via compression into their proper component */ /* ---------------------------------------------------------------------- */ /* At this point, all nodes are of Type 1, 2, or 3, as defined above. */ for (i = 0 ; i < n ; i++) { /* find the repnode cnode that contains node i */ j = FLIP (Flag [i]) ; PRINT2 (("\nfind component for "ID", in: "ID"\n", i, j)) ; ASSERT (j >= 0 && j < n) ; DEBUG (cnt = 0) ; while (CParent [j] == -2) { j = FLIP (Flag [j]) ; PRINT2 ((" walk up to "ID" ", j)) ; ASSERT (j >= 0 && j < n) ; PRINT2 ((" CParent "ID"\n", CParent [j])) ; ASSERT (cnt < n) ; DEBUG (cnt++) ; } cnode = j ; ASSERT (cnode >= 0 && cnode < n) ; ASSERT (CParent [cnode] >= EMPTY && CParent [cnode] < n) ; PRINT2 (("i "ID" is in component with cnode "ID"\n", i, cnode)) ; ASSERT (Flag [cnode] == FLIP (cnode)) ; /* Mark all nodes along the path from i to cnode as being in the * component whos repnode is cnode. Perform path compression. */ j = FLIP (Flag [i]) ; Flag [i] = FLIP (cnode) ; DEBUG (cnt = 0) ; while (CParent [j] == -2) { ASSERT (j >= 0 && j < n) ; jnext = FLIP (Flag [j]) ; PRINT2 ((" "ID" walk "ID" set cnode to "ID"\n", i, j, cnode)) ; ASSERT (cnt < n) ; DEBUG (cnt++) ; Flag [j] = FLIP (cnode) ; j = jnext ; } } /* At this point, all nodes fall into Types 1 or 2, as defined above. */ #ifndef NDEBUG for (j = 0 ; j < n ; j++) { PRINT2 (("j %d CParent %d ", j, CParent [j])) ; if (CParent [j] >= EMPTY && CParent [j] < n) { /* case 1: j is a repnode of a component */ cnode = j ; PRINT2 ((" a repnode\n")) ; } else { /* case 2: j is not a repnode of a component */ cnode = FLIP (Flag [j]) ; PRINT2 ((" repnode is %d\n", cnode)) ; ASSERT (cnode >= 0 && cnode < n) ; ASSERT (CParent [cnode] >= EMPTY && CParent [cnode] < n) ; } ASSERT (Flag [cnode] == FLIP (cnode)) ; /* case 3 no longer holds */ } #endif /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ C->ncol = n ; /* restore size for memory usage statistics */ CHOLMOD(free_sparse) (&C, Common) ; CHOLMOD(free_sparse) (&B, Common) ; CHOLMOD(free) (csize, sizeof (Int), Cew, Common) ; CHOLMOD(free) (3*n, sizeof (Int), Work3n, Common) ; /* ---------------------------------------------------------------------- */ /* handle dense nodes */ /* ---------------------------------------------------------------------- */ /* The separator tree has nodes with either no children or two or more * children - with one exception. There may exist a single root node with * exactly one child, which holds the dense rows/columns of the matrix. * Delete this node if it exists. */ if (ndense > 0) { ASSERT (CParent [cdense] == EMPTY) ; /* cdense has no parent */ /* find the children of cdense */ nchild = 0 ; for (j = 0 ; j < n ; j++) { if (CParent [j] == cdense) { nchild++ ; child = j ; } } if (nchild == 1) { /* the cdense node has just one child; merge the two nodes */ PRINT1 (("root has one child\n")) ; CParent [cdense] = -2 ; /* cdense is deleted */ CParent [child] = EMPTY ; /* child becomes a root */ for (j = 0 ; j < n ; j++) { if (Flag [j] == FLIP (cdense)) { /* j is a dense node */ PRINT1 (("dense %d\n", j)) ; Flag [j] = FLIP (child) ; } } } } /* ---------------------------------------------------------------------- */ /* postorder the components */ /* ---------------------------------------------------------------------- */ DEBUG (for (cnt = 0, j = 0 ; j < n ; j++) if (CParent [j] != -2) cnt++) ; /* use Cmember as workspace for Post [ */ Post = Cmember ; /* cholmod_postorder uses Head and Iwork [0..2n]. It does not use Flag, * which here holds the mapping of nodes to repnodes. It ignores all nodes * for which CParent [j] < -1, so it operates just on the repnodes. */ /* workspace: Head (n), Iwork (2*n) */ ncomponents = CHOLMOD(postorder) (CParent, n, NULL, Post, Common) ; ASSERT (cnt == ncomponents) ; /* use Iwork [0..n-1] as workspace for Ipost ( */ Ipost = Iwork ; DEBUG (for (j = 0 ; j < n ; j++) Ipost [j] = EMPTY) ; /* compute inverse postorder */ for (c = 0 ; c < ncomponents ; c++) { cnode = Post [c] ; ASSERT (cnode >= 0 && cnode < n) ; Ipost [cnode] = c ; ASSERT (Head [c] == EMPTY) ; } /* adjust the parent array */ /* Iwork [n..2n-1] used for NewParent [ */ NewParent = Iwork + n ; for (c = 0 ; c < ncomponents ; c++) { parent = CParent [Post [c]] ; NewParent [c] = (parent == EMPTY) ? EMPTY : (Ipost [parent]) ; } for (c = 0 ; c < ncomponents ; c++) { CParent [c] = NewParent [c] ; } ASSERT (CHOLMOD(dump_parent) (CParent, ncomponents, "CParent", Common)) ; /* Iwork [n..2n-1] no longer needed for NewParent ] */ /* Cmember no longer needed for Post ] */ #ifndef NDEBUG /* count the number of children of each node */ for (c = 0 ; c < ncomponents ; c++) { Cmember [c] = 0 ; } for (c = 0 ; c < ncomponents ; c++) { if (CParent [c] != EMPTY) Cmember [CParent [c]]++ ; } for (c = 0 ; c < ncomponents ; c++) { /* a node is either a leaf, or has 2 or more children */ ASSERT (Cmember [c] == 0 || Cmember [c] >= 2) ; } #endif /* ---------------------------------------------------------------------- */ /* place each node in its component */ /* ---------------------------------------------------------------------- */ for (j = 0 ; j < n ; j++) { /* node j is in the cth component, whose repnode is cnode */ cnode = FLIP (Flag [j]) ; PRINT2 (("j "ID" flag "ID" cnode "ID"\n", j, Flag [j], FLIP (Flag [j]))) ; ASSERT (cnode >= 0 && cnode < n) ; c = Ipost [cnode] ; ASSERT (c >= 0 && c < ncomponents) ; Cmember [j] = c ; } /* Flag no longer needed for the node-to-component mapping */ /* done using Iwork [0..n-1] as workspace for Ipost ) */ /* ---------------------------------------------------------------------- */ /* clear the Flag array */ /* ---------------------------------------------------------------------- */ Common->mark = EMPTY ; CHOLMOD_CLEAR_FLAG (Common) ; ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* find the permutation */ /* ---------------------------------------------------------------------- */ PRINT1 (("nd_camd: %d A->stype %d\n", nd_camd, A->stype)) ; if (nd_camd) { /* ------------------------------------------------------------------ */ /* apply camd, csymamd, or ccolamd using the Cmember constraints */ /* ------------------------------------------------------------------ */ if (A->stype != 0) { /* ordering A+A', so fset and fsize are ignored. * Add the upper/lower part to a symmetric lower/upper matrix by * converting to unsymmetric mode * workspace: Iwork (nrow) */ B = CHOLMOD(copy) (A, 0, -1, Common) ; if (Common->status < CHOLMOD_OK) { PRINT0 (("make symmetric failed\n")) ; return (EMPTY) ; } ASSERT ((Int) (B->nrow) == n && (Int) (B->ncol) == n) ; PRINT2 (("nested dissection (2)\n")) ; B->stype = -1 ; if (nd_camd == 2) { /* workspace: Head (nrow+1), Iwork (nrow) if symmetric-upper */ ok = CHOLMOD(csymamd) (B, Cmember, Perm, Common) ; } else { /* workspace: Head (nrow), Iwork (4*nrow) */ ok = CHOLMOD(camd) (B, NULL, 0, Cmember, Perm, Common) ; } CHOLMOD(free_sparse) (&B, Common) ; if (!ok) { /* failed */ PRINT0 (("camd/csymamd failed\n")) ; return (EMPTY) ; } } else { /* ordering A*A' or A(:,f)*A(:,f)' */ /* workspace: Iwork (nrow if no fset; MAX(nrow,ncol) if fset) */ if (!CHOLMOD(ccolamd) (A, fset, fsize, Cmember, Perm, Common)) { /* ccolamd failed */ PRINT2 (("ccolamd failed\n")) ; return (EMPTY) ; } } } else { /* ------------------------------------------------------------------ */ /* natural ordering of each component */ /* ------------------------------------------------------------------ */ /* use Iwork [0..n-1] for Next [ */ Next = Iwork ; /* ------------------------------------------------------------------ */ /* place the nodes in link lists, one list per component */ /* ------------------------------------------------------------------ */ /* do so in reverse order, to preserve original ordering */ for (j = n-1 ; j >= 0 ; j--) { /* node j is in the cth component */ c = Cmember [j] ; ASSERT (c >= 0 && c < ncomponents) ; /* place node j in link list for component c */ Next [j] = Head [c] ; Head [c] = j ; } /* ------------------------------------------------------------------ */ /* order each node in each component */ /* ------------------------------------------------------------------ */ k = 0 ; for (c = 0 ; c < ncomponents ; c++) { for (j = Head [c] ; j != EMPTY ; j = Next [j]) { Perm [k++] = j ; } Head [c] = EMPTY ; } ASSERT (k == n) ; /* done using Iwork [0..n-1] for Next ] */ } /* ---------------------------------------------------------------------- */ /* clear workspace and return number of components */ /* ---------------------------------------------------------------------- */ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; return (ncomponents) ; } /* ========================================================================== */ /* === cholmod_collapse_septree ============================================= */ /* ========================================================================== */ /* cholmod_nested_dissection returns the separator tree that was used in the * constrained minimum degree algorithm. Parameter settings (nd_small, * nd_oksep, etc) that give a good fill-reducing ordering may give too fine of * a separator tree for other uses (parallelism, multi-level LPDASA, etc). This * function takes as input the separator tree computed by * cholmod_nested_dissection, and collapses selected subtrees into single * nodes. A subtree is collapsed if its root node (the separator) is large * compared to the total number of nodes in the subtree, or if the subtree is * small. Note that the separator tree may actually be a forest. * * nd_oksep and nd_small act just like the ordering parameters in Common. * Returns the new number of nodes in the separator tree. */ UF_long CHOLMOD(collapse_septree) ( /* ---- input ---- */ size_t n, /* # of nodes in the graph */ size_t ncomponents, /* # of nodes in the separator tree (must be <= n) */ double nd_oksep, /* collapse if #sep >= nd_oksep * #nodes in subtree */ size_t nd_small, /* collapse if #nodes in subtree < nd_small */ /* ---- in/out --- */ Int *CParent, /* size ncomponents; from cholmod_nested_dissection */ Int *Cmember, /* size n; from cholmod_nested_dissection */ /* --------------- */ cholmod_common *Common ) { Int *First, *Count, *Csubtree, *W, *Map ; Int c, j, k, nc, sepsize, total_weight, parent, nc_new, first ; int collapse = FALSE, ok = TRUE ; size_t s ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (CParent, EMPTY) ; RETURN_IF_NULL (Cmember, EMPTY) ; if (n < ncomponents) { ERROR (CHOLMOD_INVALID, "invalid separator tree") ; return (EMPTY) ; } Common->status = CHOLMOD_OK ; nc = ncomponents ; if (n <= 1 || ncomponents <= 1) { /* no change; tree is one node already */ return (nc) ; } nd_oksep = MAX (0, nd_oksep) ; nd_oksep = MIN (1, nd_oksep) ; nd_small = MAX (4, nd_small) ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = 3*ncomponents */ s = CHOLMOD(mult_size_t) (ncomponents, 3, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (EMPTY) ; } CHOLMOD(allocate_work) (0, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (EMPTY) ; } W = Common->Iwork ; Count = W ; W += ncomponents ; /* size ncomponents */ Csubtree = W ; W += ncomponents ; /* size ncomponents */ First = W ; W += ncomponents ; /* size ncomponents */ /* ---------------------------------------------------------------------- */ /* find the first descendant of each node of the separator tree */ /* ---------------------------------------------------------------------- */ for (c = 0 ; c < nc ; c++) { First [c] = EMPTY ; } for (k = 0 ; k < nc ; k++) { for (c = k ; c != EMPTY && First [c] == -1 ; c = CParent [c]) { ASSERT (c >= 0 && c < nc) ; First [c] = k ; } } /* ---------------------------------------------------------------------- */ /* find the number of nodes of the graph in each node of the tree */ /* ---------------------------------------------------------------------- */ for (c = 0 ; c < nc ; c++) { Count [c] = 0 ; } for (j = 0 ; j < (Int) n ; j++) { ASSERT (Cmember [j] >= 0 && Cmember [j] < nc) ; Count [Cmember [j]]++ ; } /* ---------------------------------------------------------------------- */ /* find the number of nodes in each subtree */ /* ---------------------------------------------------------------------- */ for (c = 0 ; c < nc ; c++) { /* each subtree includes its root */ Csubtree [c] = Count [c] ; PRINT1 ((ID" size "ID" parent "ID" first "ID"\n", c, Count [c], CParent [c], First [c])) ; } for (c = 0 ; c < nc ; c++) { /* add the subtree of the child, c, into the count of its parent */ parent = CParent [c] ; ASSERT (parent >= EMPTY && parent < nc) ; if (parent != EMPTY) { Csubtree [parent] += Csubtree [c] ; } } #ifndef NDEBUG /* the sum of the roots should be n */ j = 0 ; for (c = 0 ; c < nc ; c++) if (CParent [c] == EMPTY) j += Csubtree [c] ; ASSERT (j == (Int) n) ; #endif /* ---------------------------------------------------------------------- */ /* find subtrees to collapse */ /* ---------------------------------------------------------------------- */ /* consider all nodes in reverse post-order */ for (c = nc-1 ; c >= 0 ; c--) { /* consider the subtree rooted at node c */ sepsize = Count [c] ; total_weight = Csubtree [c] ; PRINT1 (("Node "ID" sepsize "ID" subtree "ID" ratio %g\n", c, sepsize, total_weight, ((double) sepsize)/((double) total_weight))) ; first = First [c] ; if (first < c && /* c must not be a leaf */ (sepsize > nd_oksep * total_weight || total_weight < (int) nd_small)) { /* this separator is too large, or the subtree is too small. * collapse the tree, by converting the entire subtree rooted at * c into a single node. The subtree consists of all nodes from * First[c] to the root c. Flag all nodes from First[c] to c-1 * as dead. */ collapse = TRUE ; for (k = first ; k < c ; k++) { CParent [k] = -2 ; PRINT1 ((" collapse node "ID"\n", k)) ; } /* continue at the next node, first-1 */ c = first ; } } PRINT1 (("collapse: %d\n", collapse)) ; /* ---------------------------------------------------------------------- */ /* compress the tree */ /* ---------------------------------------------------------------------- */ Map = Count ; /* Count no longer needed */ nc_new = nc ; if (collapse) { nc_new = 0 ; for (c = 0 ; c < nc ; c++) { Map [c] = nc_new ; if (CParent [c] >= EMPTY) { /* node c is alive, and becomes node Map[c] in the new tree. * Increment nc_new for the next node c. */ nc_new++ ; } } PRINT1 (("Collapse the tree from "ID" to "ID" nodes\n", nc, nc_new)) ; ASSERT (nc_new > 0) ; for (c = 0 ; c < nc ; c++) { parent = CParent [c] ; if (parent >= EMPTY) { /* node c is alive */ CParent [Map [c]] = (parent == EMPTY) ? EMPTY : Map [parent] ; } } for (j = 0 ; j < (Int) n ; j++) { PRINT1 (("j "ID" Cmember[j] "ID" Map[Cmember[j]] "ID"\n", j, Cmember [j], Map [Cmember [j]])) ; Cmember [j] = Map [Cmember [j]] ; } } /* ---------------------------------------------------------------------- */ /* return new size of separator tree */ /* ---------------------------------------------------------------------- */ return (nc_new) ; } #endif SuiteSparse/CHOLMOD/Partition/cholmod_ccolamd.c0000644001170100242450000001512510537777770020310 0ustar davisfac/* ========================================================================== */ /* === Partition/cholmod_ccolamd ============================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Partition Module. * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Partition Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* CHOLMOD interface to the CCOLAMD ordering routine. Finds a permutation * p such that the Cholesky factorization of PAA'P' is sparser than AA'. * The column etree is found and postordered, and the ccolamd ordering is then * combined with its postordering. A must be unsymmetric. * * workspace: Iwork (MAX (nrow,ncol)) * Allocates a copy of its input matrix, which is * then used as CCOLAMD's workspace. * * Supports any xtype (pattern, real, complex, or zomplex). */ #ifndef NPARTITION #include "cholmod_internal.h" #include "ccolamd.h" #include "cholmod_partition.h" #if (CCOLAMD_VERSION < CCOLAMD_VERSION_CODE (2,5)) #error "CCOLAMD v2.0 or later is required" #endif /* ========================================================================== */ /* === ccolamd_interface ==================================================== */ /* ========================================================================== */ /* Order with ccolamd */ static int ccolamd_interface ( cholmod_sparse *A, size_t alen, Int *Perm, Int *Cmember, Int *fset, Int fsize, cholmod_sparse *C, cholmod_common *Common ) { double knobs [CCOLAMD_KNOBS] ; Int *Cp = NULL ; Int ok, k, nrow, ncol, stats [CCOLAMD_STATS] ; nrow = A->nrow ; ncol = A->ncol ; /* ---------------------------------------------------------------------- */ /* copy (and transpose) the input matrix A into the ccolamd workspace */ /* ---------------------------------------------------------------------- */ /* C = A (:,f)', which also packs A if needed. */ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset non-NULL) */ ok = CHOLMOD(transpose_unsym) (A, 0, NULL, fset, fsize, C, Common) ; /* ---------------------------------------------------------------------- */ /* order the matrix (destroys the contents of C->i and C->p) */ /* ---------------------------------------------------------------------- */ /* get parameters */ #ifdef LONG ccolamd_l_set_defaults (knobs) ; #else ccolamd_set_defaults (knobs) ; #endif if (Common->current < 0 || Common->current >= CHOLMOD_MAXMETHODS) { /* this is the CHOLMOD default, not the CCOLAMD default */ knobs [CCOLAMD_DENSE_ROW] = -1 ; } else { /* get the knobs from the Common parameters */ knobs [CCOLAMD_DENSE_COL] =Common->method[Common->current].prune_dense ; knobs [CCOLAMD_DENSE_ROW] =Common->method[Common->current].prune_dense2; knobs [CCOLAMD_AGGRESSIVE]=Common->method[Common->current].aggressive ; knobs [CCOLAMD_LU] =Common->method[Common->current].order_for_lu; } if (ok) { #ifdef LONG ccolamd_l (ncol, nrow, alen, C->i, C->p, knobs, stats, Cmember) ; #else ccolamd (ncol, nrow, alen, C->i, C->p, knobs, stats, Cmember) ; #endif ok = stats [CCOLAMD_STATUS] ; ok = (ok == CCOLAMD_OK || ok == CCOLAMD_OK_BUT_JUMBLED) ; /* permutation returned in C->p, if the ordering succeeded */ Cp = C->p ; for (k = 0 ; k < nrow ; k++) { Perm [k] = Cp [k] ; } } return (ok) ; } /* ========================================================================== */ /* === cholmod_ccolamd ====================================================== */ /* ========================================================================== */ /* Order AA' or A(:,f)*A(:,f)' using CCOLAMD. */ int CHOLMOD(ccolamd) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ Int *Cmember, /* size A->nrow. Cmember [i] = c if row i is in the * constraint set c. c must be >= 0. The # of * constraint sets is max (Cmember) + 1. If Cmember is * NULL, then it is interpretted as Cmember [i] = 0 for * all i */ /* ---- output --- */ Int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) { cholmod_sparse *C ; Int ok, nrow, ncol ; size_t alen ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (Perm, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; if (A->stype != 0) { ERROR (CHOLMOD_INVALID, "matrix must be unsymmetric") ; return (FALSE) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nrow = A->nrow ; ncol = A->ncol ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ #ifdef LONG alen = ccolamd_l_recommended (A->nzmax, ncol, nrow) ; #else alen = ccolamd_recommended (A->nzmax, ncol, nrow) ; #endif if (alen == 0) { ERROR (CHOLMOD_TOO_LARGE, "matrix invalid or too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (0, MAX (nrow,ncol), 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } C = CHOLMOD(allocate_sparse) (ncol, nrow, alen, TRUE, TRUE, 0, CHOLMOD_PATTERN, Common) ; /* ---------------------------------------------------------------------- */ /* order with ccolamd */ /* ---------------------------------------------------------------------- */ ok = ccolamd_interface (A, alen, Perm, Cmember, fset, fsize, C, Common) ; /* ---------------------------------------------------------------------- */ /* free the workspace and return result */ /* ---------------------------------------------------------------------- */ CHOLMOD(free_sparse) (&C, Common) ; return (ok) ; } #endif SuiteSparse/CHOLMOD/Partition/cholmod_camd.c0000644001170100242450000001727510605210247017573 0ustar davisfac/* ========================================================================== */ /* === Partition/cholmod_camd =============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Partition Module. Copyright (C) 2005-2006, Timothy A. Davis * The CHOLMOD/Partition Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* CHOLMOD interface to the CAMD ordering routine. Orders A if the matrix is * symmetric. On output, Perm [k] = i if row/column i of A is the kth * row/column of P*A*P'. This corresponds to A(p,p) in MATLAB notation. * * If A is unsymmetric, cholmod_camd orders A*A'. On output, Perm [k] = i if * row/column i of A*A' is the kth row/column of P*A*A'*P'. This corresponds to * A(p,:)*A(p,:)' in MATLAB notation. If f is present, A(p,f)*A(p,f)' is * ordered. * * Computes the flop count for a subsequent LL' factorization, the number * of nonzeros in L, and the number of nonzeros in the matrix ordered (A, * A*A' or A(:,f)*A(:,f)'). * * workspace: Iwork (4*nrow). Head (nrow). * * Allocates a temporary copy of A+A' or A*A' (with * both upper and lower triangular parts) as input to CAMD. * Also allocates 3*(n+1) additional integer workspace (not in Common). * * Supports any xtype (pattern, real, complex, or zomplex) */ #ifndef NPARTITION #include "cholmod_internal.h" #include "camd.h" #include "cholmod_partition.h" #if (CAMD_VERSION < CAMD_VERSION_CODE (2,0)) #error "CAMD v2.0 or later is required" #endif /* ========================================================================== */ /* === cholmod_camd ========================================================= */ /* ========================================================================== */ int CHOLMOD(camd) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ Int *Cmember, /* size nrow. see cholmod_ccolamd.c for description.*/ /* ---- output ---- */ Int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) { double Info [CAMD_INFO], Control2 [CAMD_CONTROL], *Control ; Int *Cp, *Len, *Nv, *Head, *Elen, *Degree, *Wi, *Next, *BucketSet, *Work3n, *p ; cholmod_sparse *C ; Int j, n, cnz ; size_t s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; n = A->nrow ; /* s = 4*n */ s = CHOLMOD(mult_size_t) (n, 4, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } RETURN_IF_NULL (Perm, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; Common->status = CHOLMOD_OK ; if (n == 0) { /* nothing to do */ Common->fl = 0 ; Common->lnz = 0 ; Common->anz = 0 ; return (TRUE) ; } /* ---------------------------------------------------------------------- */ /* get workspace */ /* ---------------------------------------------------------------------- */ /* cholmod_analyze has allocated Cmember at Common->Iwork + 5*n+uncol, and * CParent at Common->Iwork + 4*n+uncol, where uncol is 0 if A is symmetric * or A->ncol otherwise. Thus, only the first 4n integers in Common->Iwork * can be used here. */ CHOLMOD(allocate_work) (n, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } p = Common->Iwork ; Degree = p ; p += n ; /* size n */ Elen = p ; p += n ; /* size n */ Len = p ; p += n ; /* size n */ Nv = p ; p += n ; /* size n */ Work3n = CHOLMOD(malloc) (n+1, 3*sizeof (Int), Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } p = Work3n ; Next = p ; p += n ; /* size n */ Wi = p ; p += (n+1) ; /* size n+1 */ BucketSet = p ; /* size n */ Head = Common->Head ; /* size n+1 */ /* ---------------------------------------------------------------------- */ /* construct the input matrix for CAMD */ /* ---------------------------------------------------------------------- */ if (A->stype == 0) { /* C = A*A' or A(:,f)*A(:,f)', add extra space of nnz(C)/2+n to C */ C = CHOLMOD(aat) (A, fset, fsize, -2, Common) ; } else { /* C = A+A', but use only the upper triangular part of A if A->stype = 1 * and only the lower part of A if A->stype = -1. Add extra space of * nnz(C)/2+n to C. */ C = CHOLMOD(copy) (A, 0, -2, Common) ; } if (Common->status < CHOLMOD_OK) { /* out of memory, fset invalid, or other error */ CHOLMOD(free) (n+1, 3*sizeof (Int), Work3n, Common) ; return (FALSE) ; } Cp = C->p ; for (j = 0 ; j < n ; j++) { Len [j] = Cp [j+1] - Cp [j] ; } /* C does not include the diagonal, and both upper and lower parts. * Common->anz includes the diagonal, and just the lower part of C */ cnz = Cp [n] ; Common->anz = cnz / 2 + n ; /* ---------------------------------------------------------------------- */ /* order C using CAMD */ /* ---------------------------------------------------------------------- */ /* get parameters */ if (Common->current < 0 || Common->current >= CHOLMOD_MAXMETHODS) { /* use CAMD defaults */ Control = NULL ; } else { Control = Control2 ; Control [CAMD_DENSE] = Common->method [Common->current].prune_dense ; Control [CAMD_AGGRESSIVE] = Common->method [Common->current].aggressive; } /* CAMD_2 does not use camd_malloc and camd_free, but set these pointers * just be safe. */ camd_malloc = Common->malloc_memory ; camd_free = Common->free_memory ; camd_calloc = Common->calloc_memory ; camd_realloc = Common->realloc_memory ; /* CAMD_2 doesn't print anything either, but future versions might, * so set the camd_printf pointer too. */ camd_printf = Common->print_function ; #ifdef LONG /* DEBUG (camd_l_debug_init ("cholmod_l_camd")) ; */ camd_l2 (n, C->p, C->i, Len, C->nzmax, cnz, Nv, Next, Perm, Head, Elen, Degree, Wi, Control, Info, Cmember, BucketSet) ; #else /* DEBUG (camd_debug_init ("cholmod_camd")) ; */ camd_2 (n, C->p, C->i, Len, C->nzmax, cnz, Nv, Next, Perm, Head, Elen, Degree, Wi, Control, Info, Cmember, BucketSet) ; #endif /* LL' flop count. Need to subtract n for LL' flop count. Note that this * is a slight upper bound which is often exact (see CAMD/Source/camd_2.c * for details). cholmod_analyze computes an exact flop count and * fill-in. */ Common->fl = Info [CAMD_NDIV] + 2 * Info [CAMD_NMULTSUBS_LDL] + n ; /* Info [CAMD_LNZ] excludes the diagonal */ Common->lnz = n + Info [CAMD_LNZ] ; /* ---------------------------------------------------------------------- */ /* free the CAMD workspace and clear the persistent workspace in Common */ /* ---------------------------------------------------------------------- */ ASSERT (IMPLIES (Common->status == CHOLMOD_OK, CHOLMOD(dump_perm) (Perm, n, n, "CAMD2 perm", Common))) ; CHOLMOD(free_sparse) (&C, Common) ; for (j = 0 ; j <= n ; j++) { Head [j] = EMPTY ; } CHOLMOD(free) (n+1, 3*sizeof (Int), Work3n, Common) ; return (TRUE) ; } #endif SuiteSparse/CHOLMOD/Partition/cholmod_csymamd.c0000644001170100242450000001123210537777772020340 0ustar davisfac/* ========================================================================== */ /* === Partition/cholmod_csymamd ============================================ */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Partition Module. * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Partition Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* CHOLMOD interface to the CSYMAMD ordering routine. Finds a permutation * p such that the Cholesky factorization of PAP' is sparser than A. * The column etree is found and postordered, and the CSYMAMD * ordering is then combined with its postordering. If A is unsymmetric, * A+A' is ordered (A must be square). * * workspace: Head (nrow+1) * * Supports any xtype (pattern, real, complex, or zomplex). */ #ifndef NPARTITION #include "cholmod_internal.h" #include "ccolamd.h" #include "cholmod_partition.h" #if (CCOLAMD_VERSION < CCOLAMD_VERSION_CODE (2,5)) #error "CCOLAMD v2.0 or later is required" #endif /* ========================================================================== */ /* === cholmod_csymamd ====================================================== */ /* ========================================================================== */ int CHOLMOD(csymamd) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ /* ---- output --- */ Int *Cmember, /* size nrow. see cholmod_ccolamd.c for description */ Int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) { double knobs [CCOLAMD_KNOBS] ; Int *perm, *Head ; Int ok, i, nrow, stats [CCOLAMD_STATS] ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (Perm, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; Common->status = CHOLMOD_OK ; if (A->nrow != A->ncol || !(A->packed)) { ERROR (CHOLMOD_INVALID, "matrix must be square and packed") ; return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ nrow = A->nrow ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ CHOLMOD(allocate_work) (nrow, 0, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } /* ---------------------------------------------------------------------- */ /* order the matrix (does not affect A->p or A->i) */ /* ---------------------------------------------------------------------- */ perm = Common->Head ; /* size nrow+1 (i/l/l) */ /* get parameters */ #ifdef LONG ccolamd_l_set_defaults (knobs) ; #else ccolamd_set_defaults (knobs) ; #endif if (Common->current >= 0 && Common->current < CHOLMOD_MAXMETHODS) { /* get the knobs from the Common parameters */ knobs [CCOLAMD_DENSE_ROW] =Common->method[Common->current].prune_dense ; knobs [CCOLAMD_AGGRESSIVE]=Common->method[Common->current].aggressive ; } { #ifdef LONG csymamd_l (nrow, A->i, A->p, perm, knobs, stats, Common->calloc_memory, Common->free_memory, Cmember, A->stype) ; #else csymamd (nrow, A->i, A->p, perm, knobs, stats, Common->calloc_memory, Common->free_memory, Cmember, A->stype) ; #endif ok = stats [CCOLAMD_STATUS] ; } if (ok == CCOLAMD_ERROR_out_of_memory) { ERROR (CHOLMOD_OUT_OF_MEMORY, "out of memory") ; } ok = (ok == CCOLAMD_OK || ok == CCOLAMD_OK_BUT_JUMBLED) ; /* ---------------------------------------------------------------------- */ /* free the workspace and return result */ /* ---------------------------------------------------------------------- */ /* permutation returned in perm [0..n-1] */ for (i = 0 ; i < nrow ; i++) { Perm [i] = perm [i] ; } /* clear Head workspace (used for perm, in csymamd): */ Head = Common->Head ; for (i = 0 ; i <= nrow ; i++) { Head [i] = EMPTY ; } return (ok) ; } #endif SuiteSparse/CHOLMOD/Partition/License.txt0000644001170100242450000000212110540000304017106 0ustar davisfacCHOLMOD/Partition Module. Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis CHOLMOD is also available under other licenses; contact authors for details. http://www.cise.ufl.edu/research/sparse Note that this license is for the CHOLMOD/Partition module only. All CHOLMOD modules are licensed separately. -------------------------------------------------------------------------------- This Module is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This Module is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA SuiteSparse/CHOLMOD/Partition/cholmod_metis.c0000644001170100242450000006377610616661625020033 0ustar davisfac/* ========================================================================== */ /* === Partition/cholmod_metis ============================================== */ /* ========================================================================== */ /* ----------------------------------------------------------------------------- * CHOLMOD/Partition Module. * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis * The CHOLMOD/Partition Module is licensed under Version 2.1 of the GNU * Lesser General Public License. See lesser.txt for a text of the license. * CHOLMOD is also available under other licenses; contact authors for details. * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* CHOLMOD interface to the METIS package (Version 4.0.1): * * cholmod_metis_bisector: * * Wrapper for METIS_NodeComputeSeparator. Finds a set of nodes that * partitions the graph into two parts. * * cholmod_metis: * * Wrapper for METIS_NodeND, METIS's own nested dissection algorithm. * Typically faster than cholmod_nested_dissection, mostly because it * uses minimum degree on just the leaves of the separator tree, rather * than the whole matrix. * * Note that METIS does not return an error if it runs out of memory. Instead, * it terminates the program. This interface attempts to avoid that problem * by preallocating space that should be large enough for any memory allocations * within METIS, and then freeing that space, just before the call to METIS. * While this is not guaranteed to work, it is very unlikely to fail. If you * encounter this problem, increase Common->metis_memory. If you don't mind * having your program terminated, set Common->metis_memory to zero (a value of * 2.0 is usually safe). Several other METIS workarounds are made in the * routines in this file. See the description of metis_memory_ok, just below, * for more details. * * FUTURE WORK: interfaces to other partitioners (CHACO, SCOTCH, JOSTLE, ... ) * * workspace: several size-nz and size-n temporary arrays. Uses no workspace * in Common. * * Supports any xtype (pattern, real, complex, or zomplex). */ #ifndef NPARTITION #include "cholmod_internal.h" #undef ASSERT #include "metis.h" /* METIS has its own ASSERT that it reveals to the user, so remove it here: */ #undef ASSERT /* and redefine it back again */ #ifndef NDEBUG #define ASSERT(expression) (assert (expression)) #else #define ASSERT(expression) #endif #include "cholmod_partition.h" #include "cholmod_cholesky.h" /* ========================================================================== */ /* === dumpgraph ============================================================ */ /* ========================================================================== */ /* For dumping the input graph to METIS_NodeND, to check with METIS's onmetis * and graphchk programs. For debugging only. To use, uncomment this #define: #define DUMP_GRAPH */ #ifdef DUMP_GRAPH #include /* After dumping the graph with this routine, run "onmetis metisgraph" */ static void dumpgraph (idxtype *Mp, idxtype *Mi, UF_long n, cholmod_common *Common) { UF_long i, j, p, nz ; FILE *f ; nz = Mp [n] ; printf ("Dumping METIS graph n %ld nz %ld\n", n, nz) ; /* DUMP_GRAPH */ f = fopen ("metisgraph", "w") ; if (f == NULL) { ERROR (-99, "cannot open metisgraph") ; return ; } fprintf (f, "%ld %ld\n", n, nz/2) ; /* DUMP_GRAPH */ for (j = 0 ; j < n ; j++) { for (p = Mp [j] ; p < Mp [j+1] ; p++) { i = Mi [p] ; fprintf (f, " %ld", i+1) ; /* DUMP_GRAPH */ } fprintf (f, "\n") ; /* DUMP_GRAPH */ } fclose (f) ; } #endif /* ========================================================================== */ /* === metis_memory_ok ====================================================== */ /* ========================================================================== */ /* METIS_NodeND and METIS_NodeComputeSeparator will terminate your program it * they run out of memory. In an attempt to workaround METIS' behavior, this * routine allocates a single block of memory of size equal to an observed * upper bound on METIS' memory usage. It then immediately deallocates the * block. If the allocation fails, METIS is not called. * * Median memory usage for a graph with n nodes and nz edges (counting each * edge twice, or both upper and lower triangular parts of a matrix) is * 4*nz + 40*n + 4096 integers. A "typical" upper bound is 10*nz + 50*n + 4096 * integers. Nearly all matrices tested fit within that upper bound, with the * exception two in the UF sparse matrix collection: Schenk_IBMNA/c-64 and * Gupta/gupta2. The latter exceeds the "upper bound" by a factor of just less * than 2. * * If you do not mind having your program terminated if it runs out of memory, * set Common->metis_memory to zero. Its default value is 2, which allows for * some memory fragmentation, and also accounts for the Gupta/gupta2 matrix. * * An alternative, if CHOLMOD is used in MATLAB, is to use a version of METIS * (4.0.2, perhaps) proposed to George Karypis. This version uses function * pointer for malloc and free. They can be set to mxMalloc and mxFree * (see sputil_config in MATLAB/sputil.c). On Linux, with gcc, you must also * compile CHOLMOD, METIS, AMD, COLAMD, and CCOLAMD with the -fexceptions * compiler flag. With this configuration, mxMalloc safely aborts the * mexFunction, frees all memory allocted by METIS, and safely returns to * MATLAB. You may then set Common->metis_memory = 0. */ #define GUESS(nz,n) (10 * (nz) + 50 * (n) + 4096) static int metis_memory_ok ( Int n, Int nz, cholmod_common *Common ) { double s ; void *p ; size_t metis_guard ; if (Common->metis_memory <= 0) { /* do not prevent METIS from running out of memory */ return (TRUE) ; } n = MAX (1, n) ; nz = MAX (0, nz) ; /* compute in double, to avoid integer overflow */ s = GUESS ((double) nz, (double) n) ; s *= Common->metis_memory ; if (s * sizeof (idxtype) >= ((double) Size_max)) { /* don't even attempt to malloc such a large block */ return (FALSE) ; } /* recompute in size_t */ metis_guard = GUESS ((size_t) nz, (size_t) n) ; metis_guard *= Common->metis_memory ; /* attempt to malloc the block */ p = CHOLMOD(malloc) (metis_guard, sizeof (idxtype), Common) ; if (p == NULL) { /* failure - return out-of-memory condition */ return (FALSE) ; } /* success - free the block */ CHOLMOD(free) (metis_guard, sizeof (idxtype), p, Common) ; return (TRUE) ; } /* ========================================================================== */ /* === cholmod_metis_bisector =============================================== */ /* ========================================================================== */ /* Finds a set of nodes that bisects the graph of A or AA' (direct interface * to METIS_NodeComputeSeparator). * * The input matrix A must be square, symmetric (with both upper and lower * parts present) and with no diagonal entries. These conditions are NOT * checked. */ UF_long CHOLMOD(metis_bisector) /* returns separator size */ ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to bisect */ Int *Anw, /* size A->nrow, node weights */ Int *Aew, /* size nz, edge weights */ /* ---- output --- */ Int *Partition, /* size A->nrow */ /* --------------- */ cholmod_common *Common ) { Int *Ap, *Ai ; idxtype *Mp, *Mi, *Mnw, *Mew, *Mpart ; Int n, nleft, nright, j, p, csep, total_weight, lightest, nz ; int Opt [8], nn, csp ; size_t n1 ; DEBUG (Int nsep) ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (EMPTY) ; RETURN_IF_NULL (A, EMPTY) ; RETURN_IF_NULL (Anw, EMPTY) ; RETURN_IF_NULL (Aew, EMPTY) ; RETURN_IF_NULL (Partition, EMPTY) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ; if (A->stype || A->nrow != A->ncol) { /* A must be square, with both upper and lower parts present */ ERROR (CHOLMOD_INVALID, "matrix must be square, symmetric," " and with both upper/lower parts present") ; return (EMPTY) ; } Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* quick return */ /* ---------------------------------------------------------------------- */ n = A->nrow ; if (n == 0) { return (0) ; } n1 = ((size_t) n) + 1 ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Ap = A->p ; Ai = A->i ; nz = Ap [n] ; /* ---------------------------------------------------------------------- */ /* METIS does not have a 64-bit integer version */ /* ---------------------------------------------------------------------- */ #ifdef LONG if (sizeof (Int) > sizeof (idxtype) && MAX (n,nz) > INT_MAX / sizeof (int)) { /* CHOLMOD's matrix is too large for METIS */ return (EMPTY) ; } #endif /* ---------------------------------------------------------------------- */ /* set default options */ /* ---------------------------------------------------------------------- */ Opt [0] = 0 ; /* use defaults */ Opt [1] = 3 ; /* matching type */ Opt [2] = 1 ; /* init. partitioning algo*/ Opt [3] = 2 ; /* refinement algorithm */ Opt [4] = 0 ; /* no debug */ Opt [5] = 0 ; /* unused */ Opt [6] = 0 ; /* unused */ Opt [7] = -1 ; /* random seed */ DEBUG (for (j = 0 ; j < n ; j++) ASSERT (Anw [j] > 0)) ; /* ---------------------------------------------------------------------- */ /* copy Int to METIS idxtype, if necessary */ /* ---------------------------------------------------------------------- */ DEBUG (for (j = 0 ; j < nz ; j++) ASSERT (Aew [j] > 0)) ; if (sizeof (Int) == sizeof (idxtype)) { /* this is the typical case */ Mi = (idxtype *) Ai ; Mew = (idxtype *) Aew ; Mp = (idxtype *) Ap ; Mnw = (idxtype *) Anw ; Mpart = (idxtype *) Partition ; } else { /* idxtype and Int differ; copy the graph into the METIS idxtype */ Mi = CHOLMOD(malloc) (nz, sizeof (idxtype), Common) ; Mew = CHOLMOD(malloc) (nz, sizeof (idxtype), Common) ; Mp = CHOLMOD(malloc) (n1, sizeof (idxtype), Common) ; Mnw = CHOLMOD(malloc) (n, sizeof (idxtype), Common) ; Mpart = CHOLMOD(malloc) (n, sizeof (idxtype), Common) ; if (Common->status < CHOLMOD_OK) { CHOLMOD(free) (nz, sizeof (idxtype), Mi, Common) ; CHOLMOD(free) (nz, sizeof (idxtype), Mew, Common) ; CHOLMOD(free) (n1, sizeof (idxtype), Mp, Common) ; CHOLMOD(free) (n, sizeof (idxtype), Mnw, Common) ; CHOLMOD(free) (n, sizeof (idxtype), Mpart, Common) ; return (EMPTY) ; } for (p = 0 ; p < nz ; p++) { Mi [p] = Ai [p] ; } for (p = 0 ; p < nz ; p++) { Mew [p] = Aew [p] ; } for (j = 0 ; j <= n ; j++) { Mp [j] = Ap [j] ; } for (j = 0 ; j < n ; j++) { Mnw [j] = Anw [j] ; } } /* ---------------------------------------------------------------------- */ /* METIS workaround: try to ensure METIS doesn't run out of memory */ /* ---------------------------------------------------------------------- */ if (!metis_memory_ok (n, nz, Common)) { /* METIS might ask for too much memory and thus terminate the program */ if (sizeof (Int) != sizeof (idxtype)) { CHOLMOD(free) (nz, sizeof (idxtype), Mi, Common) ; CHOLMOD(free) (nz, sizeof (idxtype), Mew, Common) ; CHOLMOD(free) (n1, sizeof (idxtype), Mp, Common) ; CHOLMOD(free) (n, sizeof (idxtype), Mnw, Common) ; CHOLMOD(free) (n, sizeof (idxtype), Mpart, Common) ; } return (EMPTY) ; } /* ---------------------------------------------------------------------- */ /* partition the graph */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG PRINT1 (("Metis graph, n = "ID"\n", n)) ; for (j = 0 ; j < n ; j++) { Int ppp ; PRINT2 (("M(:,"ID") node weight "ID"\n", j, (Int) Mnw [j])) ; ASSERT (Mnw [j] > 0) ; for (ppp = Mp [j] ; ppp < Mp [j+1] ; ppp++) { PRINT3 ((" "ID" : "ID"\n", (Int) Mi [ppp], (Int) Mew [ppp])) ; ASSERT (Mi [ppp] != j) ; ASSERT (Mew [ppp] > 0) ; } } #endif nn = n ; METIS_NodeComputeSeparator (&nn, Mp, Mi, Mnw, Mew, Opt, &csp, Mpart) ; n = nn ; csep = csp ; PRINT1 (("METIS csep "ID"\n", csep)) ; /* ---------------------------------------------------------------------- */ /* copy the results back from idxtype, if required */ /* ---------------------------------------------------------------------- */ if (sizeof (Int) != sizeof (idxtype)) { for (j = 0 ; j < n ; j++) { Partition [j] = Mpart [j] ; } CHOLMOD(free) (nz, sizeof (idxtype), Mi, Common) ; CHOLMOD(free) (nz, sizeof (idxtype), Mew, Common) ; CHOLMOD(free) (n1, sizeof (idxtype), Mp, Common) ; CHOLMOD(free) (n, sizeof (idxtype), Mnw, Common) ; CHOLMOD(free) (n, sizeof (idxtype), Mpart, Common) ; } /* ---------------------------------------------------------------------- */ /* ensure a reasonable separator */ /* ---------------------------------------------------------------------- */ /* METIS can return a valid separator with no nodes in (for example) the * left part. In this case, there really is no separator. CHOLMOD * prefers, in this case, for all nodes to be in the separator (and both * left and right parts to be empty). Also, if the graph is unconnected, * METIS can return a valid empty separator. CHOLMOD prefers at least one * node in the separator. Note that cholmod_nested_dissection only calls * this routine on connected components, but cholmod_bisect can call this * routine for any graph. */ if (csep == 0) { /* The separator is empty, select lightest node as separator. If * ties, select the highest numbered node. */ lightest = 0 ; for (j = 0 ; j < n ; j++) { if (Anw [j] <= Anw [lightest]) { lightest = j ; } } PRINT1 (("Force "ID" as sep\n", lightest)) ; Partition [lightest] = 2 ; csep = Anw [lightest] ; } /* determine the node weights in the left and right part of the graph */ nleft = 0 ; nright = 0 ; DEBUG (nsep = 0) ; for (j = 0 ; j < n ; j++) { PRINT1 (("Partition ["ID"] = "ID"\n", j, Partition [j])) ; if (Partition [j] == 0) { nleft += Anw [j] ; } else if (Partition [j] == 1) { nright += Anw [j] ; } #ifndef NDEBUG else { ASSERT (Partition [j] == 2) ; nsep += Anw [j] ; } #endif } ASSERT (csep == nsep) ; total_weight = nleft + nright + csep ; if (csep < total_weight) { /* The separator is less than the whole graph. Make sure the left and * right parts are either both empty or both non-empty. */ PRINT1 (("nleft "ID" nright "ID" csep "ID" tot "ID"\n", nleft, nright, csep, total_weight)) ; ASSERT (nleft + nright + csep == total_weight) ; ASSERT (nleft > 0 || nright > 0) ; if ((nleft == 0 && nright > 0) || (nleft > 0 && nright == 0)) { /* left or right is empty; put all nodes in the separator */ PRINT1 (("Force all in sep\n")) ; csep = total_weight ; for (j = 0 ; j < n ; j++) { Partition [j] = 2 ; } } } ASSERT (CHOLMOD(dump_partition) (n, Ap, Ai, Anw, Partition, csep, Common)) ; /* ---------------------------------------------------------------------- */ /* return the sum of the weights of nodes in the separator */ /* ---------------------------------------------------------------------- */ return (csep) ; } /* ========================================================================== */ /* === cholmod_metis ======================================================== */ /* ========================================================================== */ /* CHOLMOD wrapper for the METIS_NodeND ordering routine. Creates A+A', * A*A' or A(:,f)*A(:,f)' and then calls METIS_NodeND on the resulting graph. * This routine is comparable to cholmod_nested_dissection, except that it * calls METIS_NodeND directly, and it does not return the separator tree. * * workspace: Flag (nrow), Iwork (4*n+uncol) * Allocates a temporary matrix B=A*A' or B=A. */ int CHOLMOD(metis) ( /* ---- input ---- */ cholmod_sparse *A, /* matrix to order */ Int *fset, /* subset of 0:(A->ncol)-1 */ size_t fsize, /* size of fset */ int postorder, /* if TRUE, follow with etree or coletree postorder */ /* ---- output --- */ Int *Perm, /* size A->nrow, output permutation */ /* --------------- */ cholmod_common *Common ) { double d ; Int *Iperm, *Iwork, *Bp, *Bi ; idxtype *Mp, *Mi, *Mperm, *Miperm ; cholmod_sparse *B ; Int i, j, n, nz, p, identity, uncol ; int Opt [8], nn, zero = 0 ; size_t n1, s ; int ok = TRUE ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ RETURN_IF_NULL_COMMON (FALSE) ; RETURN_IF_NULL (A, FALSE) ; RETURN_IF_NULL (Perm, FALSE) ; RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ; Common->status = CHOLMOD_OK ; /* ---------------------------------------------------------------------- */ /* quick return */ /* ---------------------------------------------------------------------- */ n = A->nrow ; if (n == 0) { return (TRUE) ; } n1 = ((size_t) n) + 1 ; /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* s = 4*n + uncol */ uncol = (A->stype == 0) ? A->ncol : 0 ; s = CHOLMOD(mult_size_t) (n, 4, &ok) ; s = CHOLMOD(add_size_t) (s, uncol, &ok) ; if (!ok) { ERROR (CHOLMOD_TOO_LARGE, "problem too large") ; return (FALSE) ; } CHOLMOD(allocate_work) (n, s, 0, Common) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; /* ---------------------------------------------------------------------- */ /* convert the matrix to adjacency list form */ /* ---------------------------------------------------------------------- */ /* The input graph for METIS must be symmetric, with both upper and lower * parts present, and with no diagonal entries. The columns need not be * sorted. * B = A+A', A*A', or A(:,f)*A(:,f)', upper and lower parts present */ if (A->stype) { /* Add the upper/lower part to a symmetric lower/upper matrix by * converting to unsymmetric mode */ /* workspace: Iwork (nrow) */ B = CHOLMOD(copy) (A, 0, -1, Common) ; } else { /* B = A*A' or A(:,f)*A(:,f)', no diagonal */ /* workspace: Flag (nrow), Iwork (max (nrow,ncol)) */ B = CHOLMOD(aat) (A, fset, fsize, -1, Common) ; } ASSERT (CHOLMOD(dump_sparse) (B, "B for NodeND", Common) >= 0) ; if (Common->status < CHOLMOD_OK) { return (FALSE) ; } ASSERT (B->nrow == A->nrow) ; /* ---------------------------------------------------------------------- */ /* get inputs */ /* ---------------------------------------------------------------------- */ Iwork = Common->Iwork ; Iperm = Iwork ; /* size n (i/i/l) */ Bp = B->p ; Bi = B->i ; nz = Bp [n] ; /* ---------------------------------------------------------------------- */ /* METIS does not have a UF_long integer version */ /* ---------------------------------------------------------------------- */ #ifdef LONG if (sizeof (Int) > sizeof (idxtype) && MAX (n,nz) > INT_MAX / sizeof (int)) { /* CHOLMOD's matrix is too large for METIS */ CHOLMOD(free_sparse) (&B, Common) ; return (FALSE) ; } #endif /* B does not include the diagonal, and both upper and lower parts. * Common->anz includes the diagonal, and just the lower part of B */ Common->anz = nz / 2 + n ; /* ---------------------------------------------------------------------- */ /* set control parameters for METIS_NodeND */ /* ---------------------------------------------------------------------- */ Opt [0] = 0 ; /* use defaults */ Opt [1] = 3 ; /* matching type */ Opt [2] = 1 ; /* init. partitioning algo*/ Opt [3] = 2 ; /* refinement algorithm */ Opt [4] = 0 ; /* no debug */ Opt [5] = 1 ; /* initial compression */ Opt [6] = 0 ; /* no dense node removal */ Opt [7] = 1 ; /* number of separators @ each step */ /* ---------------------------------------------------------------------- */ /* allocate the METIS input arrays, if needed */ /* ---------------------------------------------------------------------- */ if (sizeof (Int) == sizeof (idxtype)) { /* This is the typical case. */ Miperm = (idxtype *) Iperm ; Mperm = (idxtype *) Perm ; Mp = (idxtype *) Bp ; Mi = (idxtype *) Bi ; } else { /* allocate graph for METIS only if Int and idxtype differ */ Miperm = CHOLMOD(malloc) (n, sizeof (idxtype), Common) ; Mperm = CHOLMOD(malloc) (n, sizeof (idxtype), Common) ; Mp = CHOLMOD(malloc) (n1, sizeof (idxtype), Common) ; Mi = CHOLMOD(malloc) (nz, sizeof (idxtype), Common) ; if (Common->status < CHOLMOD_OK) { /* out of memory */ CHOLMOD(free_sparse) (&B, Common) ; CHOLMOD(free) (n, sizeof (idxtype), Miperm, Common) ; CHOLMOD(free) (n, sizeof (idxtype), Mperm, Common) ; CHOLMOD(free) (n1, sizeof (idxtype), Mp, Common) ; CHOLMOD(free) (nz, sizeof (idxtype), Mi, Common) ; return (FALSE) ; } for (j = 0 ; j <= n ; j++) { Mp [j] = Bp [j] ; } for (p = 0 ; p < nz ; p++) { Mi [p] = Bi [p] ; } } /* ---------------------------------------------------------------------- */ /* METIS workarounds */ /* ---------------------------------------------------------------------- */ identity = FALSE ; if (nz == 0) { /* The matrix has no off-diagonal entries. METIS_NodeND fails in this * case, so avoid using it. The best permutation is identity anyway, * so this is an easy fix. */ identity = TRUE ; PRINT1 (("METIS:: no nz\n")) ; } else if (Common->metis_nswitch > 0) { /* METIS_NodeND in METIS 4.0.1 gives a seg fault with one matrix of * order n = 3005 and nz = 6,036,025, including the diagonal entries. * The workaround is to return the identity permutation instead of using * METIS for matrices of dimension 3000 or more and with density of 66% * or more - admittedly an uncertain fix, but such matrices are so dense * that any reasonable ordering will do, even identity (n^2 is only 50% * higher than nz in this case). CHOLMOD's nested dissection method * (cholmod_nested_dissection) has no problems with the same matrix, * even though it too uses METIS_NodeComputeSeparator. The matrix is * derived from LPnetlib/lpi_cplex1 in the UF sparse matrix collection. * If C is the lpi_cplex matrix (of order 3005-by-5224), A = (C*C')^2 * results in the seg fault. The seg fault also occurs in the stand- * alone onmetis program that comes with METIS. If a future version of * METIS fixes this problem, then set Common->metis_nswitch to zero. */ d = ((double) nz) / (((double) n) * ((double) n)) ; if (n > (Int) (Common->metis_nswitch) && d > Common->metis_dswitch) { identity = TRUE ; PRINT1 (("METIS:: nswitch/dswitch activated\n")) ; } } if (!identity && !metis_memory_ok (n, nz, Common)) { /* METIS might ask for too much memory and thus terminate the program */ identity = TRUE ; } /* ---------------------------------------------------------------------- */ /* find the permutation */ /* ---------------------------------------------------------------------- */ if (identity) { /* no need to do the postorder */ postorder = FALSE ; for (i = 0 ; i < n ; i++) { Mperm [i] = i ; } } else { #ifdef DUMP_GRAPH /* DUMP_GRAPH */ printf ("Calling METIS_NodeND n "ID" nz "ID"" "density %g\n", n, nz, ((double) nz) / (((double) n) * ((double) n))); dumpgraph (Mp, Mi, n, Common) ; #endif nn = n ; METIS_NodeND (&nn, Mp, Mi, &zero, Opt, Mperm, Miperm) ; n = nn ; PRINT0 (("METIS_NodeND done\n")) ; } /* ---------------------------------------------------------------------- */ /* free the METIS input arrays */ /* ---------------------------------------------------------------------- */ if (sizeof (Int) != sizeof (idxtype)) { for (i = 0 ; i < n ; i++) { Perm [i] = (Int) (Mperm [i]) ; } CHOLMOD(free) (n, sizeof (idxtype), Miperm, Common) ; CHOLMOD(free) (n, sizeof (idxtype), Mperm, Common) ; CHOLMOD(free) (n+1, sizeof (idxtype), Mp, Common) ; CHOLMOD(free) (nz, sizeof (idxtype), Mi, Common) ; } CHOLMOD(free_sparse) (&B, Common) ; /* ---------------------------------------------------------------------- */ /* etree or column-etree postordering, using the Cholesky Module */ /* ---------------------------------------------------------------------- */ if (postorder) { Int *Parent, *Post, *NewPerm ; Int k ; Parent = Iwork + 2*((size_t) n) + uncol ; /* size n = nrow */ Post = Parent + n ; /* size n */ /* workspace: Iwork (2*nrow+uncol), Flag (nrow), Head (nrow+1) */ CHOLMOD(analyze_ordering) (A, CHOLMOD_METIS, Perm, fset, fsize, Parent, Post, NULL, NULL, NULL, Common) ; if (Common->status == CHOLMOD_OK) { /* combine the METIS permutation with its postordering */ NewPerm = Parent ; /* use Parent as workspace */ for (k = 0 ; k < n ; k++) { NewPerm [k] = Perm [Post [k]] ; } for (k = 0 ; k < n ; k++) { Perm [k] = NewPerm [k] ; } } } ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; PRINT1 (("cholmod_metis done\n")) ; return (Common->status == CHOLMOD_OK) ; } #endif SuiteSparse/CHOLMOD/Partition/lesser.txt0000644001170100242450000006350010253404171017044 0ustar davisfac GNU LESSER GENERAL PUBLIC LICENSE Version 2.1, February 1999 Copyright (C) 1991, 1999 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. 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SuiteSparse/UFconfig/0000755001170100242450000000000010711722217013447 5ustar davisfacSuiteSparse/UFconfig/UFconfig.h0000644001170100242450000001014610712415671015326 0ustar davisfac/* ========================================================================== */ /* === UFconfig.h =========================================================== */ /* ========================================================================== */ /* Configuration file for SuiteSparse: a Suite of Sparse matrix packages * (AMD, COLAMD, CCOLAMD, CAMD, CHOLMOD, UMFPACK, CXSparse, and others). * * UFconfig.h provides the definition of the long integer. On most systems, * a C program can be compiled in LP64 mode, in which long's and pointers are * both 64-bits, and int's are 32-bits. Windows 64, however, uses the LLP64 * model, in which int's and long's are 32-bits, and long long's and pointers * are 64-bits. * * SuiteSparse packages that include long integer versions are * intended for the LP64 mode. However, as a workaround for Windows 64 * (and perhaps other systems), the long integer can be redefined. * * If _WIN64 is defined, then the __int64 type is used instead of long. * * The long integer can also be defined at compile time. For example, this * could be added to UFconfig.mk: * * CFLAGS = -O -D'UF_long=long long' -D'UF_long_max=9223372036854775801' \ * -D'UF_long_id="%lld"' * * This file defines UF_long as either long (on all but _WIN64) or * __int64 on Windows 64. The intent is that a UF_long is always a 64-bit * integer in a 64-bit code. ptrdiff_t might be a better choice than long; * it is always the same size as a pointer. * * This file also defines the SUITESPARSE_VERSION and related definitions. * * Copyright (c) 2007, University of Florida. No licensing restrictions * apply to this file or to the UFconfig directory. Author: Timothy A. Davis. */ #ifndef _UFCONFIG_H #define _UFCONFIG_H #ifdef __cplusplus extern "C" { #endif #include /* ========================================================================== */ /* === UF_long ============================================================== */ /* ========================================================================== */ #ifndef UF_long #ifdef _WIN64 #define UF_long __int64 #define UF_long_max _I64_MAX #define UF_long_id "%I64d" #else #define UF_long long #define UF_long_max LONG_MAX #define UF_long_id "%ld" #endif #endif /* ========================================================================== */ /* === SuiteSparse version ================================================== */ /* ========================================================================== */ /* SuiteSparse is not a package itself, but a collection of packages, some of * which must be used together (UMFPACK requires AMD, CHOLMOD requires AMD, * COLAMD, CAMD, and CCOLAMD, etc). A version number is provided here for the * collection itself. The versions of packages within each version of * SuiteSparse are meant to work together. Combining one packge from one * version of SuiteSparse, with another package from another version of * SuiteSparse, may or may not work. * * SuiteSparse Version 3.1.0 contains the following packages: * * AMD version 2.2.0 * CAMD version 2.2.0 * COLAMD version 2.7.1 * CCOLAMD version 2.7.1 * CHOLMOD version 1.6.0 * CSparse version 2.2.1 * CXSparse version 2.2.1 * KLU version 1.0.1 * BTF version 1.0.1 * LDL version 2.0.1 * UFconfig version number is the same as SuiteSparse * UMFPACK version 5.2.0 * RBio version 1.1.1 * UFcollection version 1.1.1 * LINFACTOR version 1.1.0 * MESHND version 1.1.0 * SSMULT version 1.1.0 * MATLAB_Tools no specific version number * * Other package dependencies: * BLAS required by CHOLMOD and UMFPACK * LAPACK required by CHOLMOD * METIS 4.0.1 required by CHOLMOD (optional) and KLU (optional) */ #define SUITESPARSE_DATE "Nov 1, 2007" #define SUITESPARSE_VER_CODE(main,sub) ((main) * 1000 + (sub)) #define SUITESPARSE_MAIN_VERSION 3 #define SUITESPARSE_SUB_VERSION 1 #define SUITESPARSE_SUBSUB_VERSION 0 #define SUITESPARSE_VERSION \ SUITESPARSE_VER_CODE(SUITESPARSE_MAIN_VERSION,SUITESPARSE_SUB_VERSION) #ifdef __cplusplus } #endif #endif SuiteSparse/UFconfig/README.txt0000644001170100242450000000307510711430676015157 0ustar davisfacUFconfig contains configuration settings for all many of the software packages that I develop or co-author. Note that older versions of some of these packages do not require UFconfig. Package Description ------- ----------- AMD approximate minimum degree ordering CAMD constrained AMD COLAMD column approximate minimum degree ordering CCOLAMD constrained approximate minimum degree ordering UMFPACK sparse LU factorization, with the BLAS CXSparse int/long/real/complex version of CSparse CHOLMOD sparse Cholesky factorization, update/downdate KLU sparse LU factorization, BLAS-free BTF permutation to block triangular form LDL concise sparse LDL' LPDASA LP Dual Active Set Algorithm UFconfig is not required by: CSparse a Concise Sparse matrix package RBio read/write files in Rutherford/Boeing format UFcollection tools for managing the UF Sparse Matrix Collection LINFACTOR simple m-file to show how to use LU and CHOL to solve Ax=b MESHND 2D and 3D mesh generation and nested dissection ordering MATLAB_Tools misc collection of m-files SSMULT sparse matrix times sparse matrix, for use in MATLAB In addition, the xerbla/ directory contains Fortan and C versions of the BLAS/LAPACK xerbla routine, which is called when an invalid input is passed to the BLAS or LAPACK. The xerbla provided here does not print any message, so the entire Fortran I/O library does not need to be linked into a C application. Most versions of the BLAS contain xerbla, but those from K. Goto do not. Use this if you need too. SuiteSparse/UFconfig/xerbla/0000755001170100242450000000000010711435720014724 5ustar davisfacSuiteSparse/UFconfig/xerbla/Makefile0000644001170100242450000000071610367441762016402 0ustar davisfac# Makefile for null-output xerbla default: ccode include ../UFconfig.mk ccode: libcerbla.a fortran: libxerbla.a all: libxerbla.a libcerbla.a # Fortran version: libxerbla.a: xerbla.f $(F77) $(F77FLAGS) -c xerbla.f $(AR) libxerbla.a xerbla.o - $(RM) xerbla.o # C version: libcerbla.a: xerbla.c xerbla.h $(CC) $(CFLAGS) -c xerbla.c $(AR) libcerbla.a xerbla.o - $(RM) xerbla.o distclean: purge purge: clean - $(RM) *.o *.a clean: - $(RM) $(CLEAN) SuiteSparse/UFconfig/xerbla/xerbla.c0000644001170100242450000000020710301441524016336 0ustar davisfac void xerbla_ (char *srname, int *info) { /* do nothing */ ; } void xerbla (char *srname, int *info) { /* do nothing */ ; } SuiteSparse/UFconfig/xerbla/xerbla.f0000644001170100242450000000236010130774511016350 0ustar davisfac SUBROUTINE XERBLA( SRNAME, INFO ) * * -- LAPACK auxiliary routine (version 3.0) -- * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., * Courant Institute, Argonne National Lab, and Rice University * September 30, 1994 * * .. Scalar Arguments .. CHARACTER*6 SRNAME INTEGER INFO * .. * * Purpose * ======= * * XERBLA is an error handler for the LAPACK routines. * It is called by an LAPACK routine if an input parameter has an * invalid value. A message is printed and execution stops. * * Installers may consider modifying the STOP statement in order to * call system-specific exception-handling facilities. * * Arguments * ========= * * SRNAME (input) CHARACTER*6 * The name of the routine which called XERBLA. * * INFO (input) INTEGER * The position of the invalid parameter in the parameter list * of the calling routine. * * ===================================================================== * * .. Executable Statements .. * ***** WRITE( *, FMT = 9999 )SRNAME, INFO * ***** STOP * ***** 9999 FORMAT( ' ** On entry to ', A6, ' parameter number ', I2, ' had ', ***** $ 'an illegal value' ) * * End of XERBLA * END SuiteSparse/UFconfig/xerbla/xerbla.h0000644001170100242450000000012210301441547016344 0ustar davisfacvoid xerbla_ (char *srname, int *info) ; void xerbla (char *srname, int *info) ; SuiteSparse/UFconfig/UFconfig.mk0000644001170100242450000002575510707647340015526 0ustar davisfac#=============================================================================== # UFconfig.mk: common configuration file for the SuiteSparse #=============================================================================== # This file contains all configuration settings for all packages authored or # co-authored by Tim Davis at the University of Florida: # # Package Version Description # ------- ------- ----------- # AMD 1.2 or later approximate minimum degree ordering # COLAMD 2.4 or later column approximate minimum degree ordering # CCOLAMD 1.0 or later constrained column approximate minimum degree ordering # CAMD any constrained approximate minimum degree ordering # UMFPACK 4.5 or later sparse LU factorization, with the BLAS # CHOLMOD any sparse Cholesky factorization, update/downdate # KLU 0.8 or later sparse LU factorization, BLAS-free # BTF 0.8 or later permutation to block triangular form # LDL 1.2 or later concise sparse LDL' # LPDASA any linear program solve (dual active set algorithm) # CXSparse any extended version of CSparse (int/long, real/complex) # # The UFconfig directory and the above packages should all appear in a single # directory, in order for the Makefile's within each package to find this file. # # To enable an option of the form "# OPTION = ...", edit this file and # delete the "#" in the first column of the option you wish to use. #------------------------------------------------------------------------------ # Generic configuration #------------------------------------------------------------------------------ # C compiler and compiler flags: These will normally not give you optimal # performance. You should select the optimization parameters that are best # for your system. On Linux, use "CFLAGS = -O3 -fexceptions" for example. CC = cc CFLAGS = -O # ranlib, and ar, for generating libraries RANLIB = ranlib AR = ar cr # delete and rename a file RM = rm -f MV = mv -f # Fortran compiler (not normally required) F77 = f77 F77FLAGS = -O F77LIB = # C and Fortran libraries LIB = -lm # For compiling MATLAB mexFunctions (MATLAB 7.5) MEX = mex -O -largeArrayDims -lmwlapack -lmwblas # For compiling MATLAB mexFunctions (MATLAB 7.3 and 7.4) # MEX = mex -O -largeArrayDims -lmwlapack # For MATLAB 7.2 or earlier, you must use one of these options: # MEX = mex -O -lmwlapack # MEX = mex -O # Which version of MAKE you are using (default is "make") # MAKE = make # MAKE = gmake #------------------------------------------------------------------------------ # BLAS and LAPACK configuration: #------------------------------------------------------------------------------ # UMFPACK and CHOLMOD both require the BLAS. CHOLMOD also requires LAPACK. # See Kazushige Goto's BLAS at http://www.cs.utexas.edu/users/flame/goto/ or # http://www.tacc.utexas.edu/~kgoto/ for the best BLAS to use with CHOLMOD. # LAPACK is at http://www.netlib.org/lapack/ . You can use the standard # Fortran LAPACK along with Goto's BLAS to obtain very good performance. # CHOLMOD gets a peak numeric factorization rate of 3.6 Gflops on a 3.2 GHz # Pentium 4 (512K cache, 4GB main memory) with the Goto BLAS, and 6 Gflops # on a 2.5Ghz dual-core AMD Opteron. # These settings will probably not work, since there is no fixed convention for # naming the BLAS and LAPACK library (*.a or *.so) files. # Using the Goto BLAS: # BLAS = -lgoto -lgfortran -lgfortranbegin # This is probably slow ... it might connect to the Standard Reference BLAS: BLAS = -lblas -lgfortran -lgfortranbegin LAPACK = -llapack # The BLAS might not contain xerbla, an error-handling routine for LAPACK and # the BLAS. Also, the standard xerbla requires the Fortran I/O library, and # stops the application program if an error occurs. A C version of xerbla # distributed with this software (UFconfig/xerbla/libcerbla.a) includes a # Fortran-callable xerbla routine that prints nothing and does not stop the # application program. This is optional. # XERBLA = ../../UFconfig/xerbla/libcerbla.a # If you wish to use the XERBLA in LAPACK and/or the BLAS instead, # use this option: XERBLA = # If you wish to use the Fortran UFconfig/xerbla/xerbla.f instead, use this: # XERBLA = ../../UFconfig/xerbla/libxerbla.a #------------------------------------------------------------------------------ # METIS, optionally used by CHOLMOD #------------------------------------------------------------------------------ # If you do not have METIS, or do not wish to use it in CHOLMOD, you must # compile CHOLMOD with the -DNPARTITION flag. You must also use the # "METIS =" option, below. # The path is relative to where it is used, in CHOLMOD/Lib, CHOLMOD/MATLAB, etc. # You may wish to use an absolute path. METIS is optional. Compile # CHOLMOD with -DNPARTITION if you do not wish to use METIS. METIS_PATH = ../../metis-4.0 METIS = ../../metis-4.0/libmetis.a # If you use CHOLMOD_CONFIG = -DNPARTITION then you must use the following # options: # METIS_PATH = # METIS = #------------------------------------------------------------------------------ # UMFPACK configuration: #------------------------------------------------------------------------------ # Configuration flags for UMFPACK. See UMFPACK/Source/umf_config.h for details. # # -DNBLAS do not use the BLAS. UMFPACK will be very slow. # -D'LONGBLAS=long' or -DLONGBLAS='long long' defines the integers used by # LAPACK and the BLAS (defaults to 'int') # -DNSUNPERF do not use the Sun Perf. Library (default is use it on Solaris) # -DNPOSIX do not use POSIX routines sysconf and times. # -DGETRUSAGE use getrusage # -DNO_TIMER do not use any timing routines # -DNRECIPROCAL do not multiply by the reciprocal # -DNO_DIVIDE_BY_ZERO do not divide by zero UMFPACK_CONFIG = #------------------------------------------------------------------------------ # CHOLMOD configuration #------------------------------------------------------------------------------ # CHOLMOD Library Modules, which appear in libcholmod.a: # Core requires: none # Check requires: Core # Cholesky requires: Core, AMD, COLAMD. optional: Partition, Supernodal # MatrixOps requires: Core # Modify requires: Core # Partition requires: Core, CCOLAMD, METIS. optional: Cholesky # Supernodal requires: Core, BLAS, LAPACK # # CHOLMOD test/demo Modules (all are GNU GPL, do not appear in libcholmod.a): # Tcov requires: Core, Check, Cholesky, MatrixOps, Modify, Supernodal # optional: Partition # Valgrind same as Tcov # Demo requires: Core, Check, Cholesky, MatrixOps, Supernodal # optional: Partition # # Configuration flags: # -DNCHECK do not include the Check module. License GNU LGPL # -DNCHOLESKY do not include the Cholesky module. License GNU LGPL # -DNPARTITION do not include the Partition module. License GNU LGPL # also do not include METIS. # -DNGPL do not include any GNU GPL Modules in the CHOLMOD library: # -DNMATRIXOPS do not include the MatrixOps module. License GNU GPL # -DNMODIFY do not include the Modify module. License GNU GPL # -DNSUPERNODAL do not include the Supernodal module. License GNU GPL # # -DNPRINT do not print anything. # -D'LONGBLAS=long' or -DLONGBLAS='long long' defines the integers used by # LAPACK and the BLAS (defaults to 'int') # -DNSUNPERF for Solaris only. If defined, do not use the Sun # Performance Library CHOLMOD_CONFIG = #------------------------------------------------------------------------------ # Linux #------------------------------------------------------------------------------ # Using default compilers: # CC = gcc CFLAGS = -O3 # alternatives: # CFLAGS = -g -fexceptions \ -Wall -W -Wshadow -Wmissing-prototypes -Wstrict-prototypes \ -Wredundant-decls -Wnested-externs -Wdisabled-optimization -ansi # CFLAGS = -O3 -fexceptions \ -Wall -W -Werror -Wshadow -Wmissing-prototypes -Wstrict-prototypes \ -Wredundant-decls -Wnested-externs -Wdisabled-optimization -ansi # CFLAGS = -O3 -fexceptions -D_FILE_OFFSET_BITS=64 -D_LARGEFILE64_SOURCE # CFLAGS = -O3 # consider: # -fforce-addr -fmove-all-movables -freduce-all-givs -ftsp-ordering # -frename-registers -ffast-math -funroll-loops # Using the Goto BLAS: # BLAS = -lgoto -lfrtbegin -lg2c $(XERBLA) -lpthread # Using Intel's icc and ifort compilers: # (does not work for mexFunctions unless you add a mexopts.sh file) # F77 = ifort # CC = icc # CFLAGS = -O3 -xN -vec_report=0 # CFLAGS = -g # old (broken): CFLAGS = -ansi -O3 -ip -tpp7 -xW -vec_report0 # 64bit: # F77FLAGS = -O -m64 # CFLAGS = -O3 -fexceptions -m64 # BLAS = -lgoto64 -lfrtbegin -lg2c -lpthread $(XERBLA) # LAPACK = -llapack64 # SUSE Linux 10.1, AMD Opteron, with GOTO Blas # F77 = gfortran # BLAS = -lgoto_opteron64 -lgfortran # SUSE Linux 10.1, Intel Pentium, with GOTO Blas # F77 = gfortran # BLAS = -lgoto -lgfortran #------------------------------------------------------------------------------ # Solaris #------------------------------------------------------------------------------ # 32-bit # CFLAGS = -KPIC -dalign -xc99=%none -Xc -xlibmieee -xO5 -xlibmil # 64-bit # CFLAGS = -KPIC -dalign -xc99=%none -Xc -xlibmieee -xO5 -xlibmil -xarch=v9 # BLAS = -xlic_lib=sunperf # LAPACK = #------------------------------------------------------------------------------ # Compaq Alpha #------------------------------------------------------------------------------ # 64-bit mode only # CFLAGS = -O2 -std1 # BLAS = -ldxml # LAPACK = #------------------------------------------------------------------------------ # Macintosh #------------------------------------------------------------------------------ # CC = gcc # CFLAGS = -O3 -fno-common -no-cpp-precomp -fexceptions # LIB = -lstdc++ # BLAS = -framework Accelerate # LAPACK = -framework Accelerate #------------------------------------------------------------------------------ # IBM RS 6000 #------------------------------------------------------------------------------ # BLAS = -lessl # LAPACK = # 32-bit mode: # CFLAGS = -O4 -qipa -qmaxmem=16384 -qproto # F77FLAGS = -O4 -qipa -qmaxmem=16384 # 64-bit mode: # CFLAGS = -O4 -qipa -qmaxmem=16384 -q64 -qproto # F77FLAGS = -O4 -qipa -qmaxmem=16384 -q64 # AR = ar -X64 #------------------------------------------------------------------------------ # SGI IRIX #------------------------------------------------------------------------------ # BLAS = -lscsl # LAPACK = # 32-bit mode # CFLAGS = -O # 64-bit mode (32 bit int's and 64-bit long's): # CFLAGS = -64 # F77FLAGS = -64 # SGI doesn't have ranlib # RANLIB = echo #------------------------------------------------------------------------------ # AMD Opteron (64 bit) #------------------------------------------------------------------------------ # BLAS = -lgoto_opteron64 -lg2c # LAPACK = -llapack_opteron64 # SUSE Linux 10.1, AMD Opteron # F77 = gfortran # BLAS = -lgoto_opteron64 -lgfortran # LAPACK = -llapack_opteron64 #------------------------------------------------------------------------------ # remove object files and profile output #------------------------------------------------------------------------------ CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.tcov *.gcov gmon.out *.bak *.d SuiteSparse/COLAMD/0000755001170100242450000000000010617111314012701 5ustar davisfacSuiteSparse/COLAMD/Doc/0000755001170100242450000000000010621174457013422 5ustar davisfacSuiteSparse/COLAMD/Doc/ChangeLog0000644001170100242450000001075110620614776015202 0ustar davisfacMay 31, 2007: version 2.7.0 * ported to 64-bit MATLAB * subdirectories added (Source/, Include/, Lib/, Doc/, MATLAB/, Demo/) Dec 12, 2006, version 2.5.2 * minor MATLAB cleanup. MATLAB functions renamed colamd2 and symamd2, so that they do not conflict with the built-in versions. Note that the MATLAB built-in functions colamd and symamd are identical to the colamd and symamd functions here. Aug 31, 2006: Version 2.5.1 * minor change to colamd.m and symamd.m, to use etree instead of sparsfun. Apr. 30, 2006: Version 2.5 * colamd_recommended modified, to do more careful integer overflow checking. It now returns size_t, not int. colamd_l_recommended also returns size_t. A zero is returned if an error occurs. A postive return value denotes success. In v2.4 and earlier, -1 was returned on error (an int or long). * long replaced with UF_long integer, which is long except on WIN64. Nov 15, 2005: * minor editting of comments; version number (2.4) unchanged. Changes from Version 2.3 to 2.4 (Aug 30, 2005) * Makefile now relies on ../UFconfig/UFconfig.mk * changed the dense row/col detection. The meaning of the knobs has thus changed. * added an option to turn off aggressive absorption. It was always on in versions 2.3 and earlier. * added a #define'd version number * added a function pointer (colamd_printf) for COLAMD's printing. * added a -DNPRINT option, to turn off printing at compile-time. * added a check for integer overflow in colamd_recommended * minor changes to allow for more simpler 100% test coverage * bug fix. If symamd v2.3 fails to allocate its copy of the input matrix, then it erroneously frees a calloc'd workspace twice. This bug has no effect on the MATLAB symamd mexFunction, since mxCalloc terminates the mexFunction if it fails to allocate memory. Similarly, UMFPACK is not affected because it does not use symamd. The bug has no effect on the colamd ordering routine in v2.3. Changes from Version 2.2 to 2.3 (Sept. 8, 2003) * removed the call to the MATLAB spparms ('spumoni') function. This can take a lot of time if you are ordering many small matrices. Only affects the MATLAB interface (colamdmex.c, symamdmex.c, colamdtestmex.c, and symamdtestmex.c). The usage of the optional 2nd argument to the colamd and symamd mexFunctions was changed accordingly. Changes from Version 2.1 to 2.2 (Sept. 23, 2002) * extensive testing routines added (colamd_test.m, colamdtestmex.c, and symamdtestmex.c), and the Makefile modified accordingly. * a few typos in the comments corrected * use of the MATLAB "flops" command removed from colamd_demo, and an m-file routine luflops.m added. * an explicit typecast from unsigned to int added, for COLAMD_C and COLAMD_R in colamd.h. * #include added to colamd_example.c Changes from Version 2.0 to 2.1 (May 4, 2001) * TRUE and FALSE are predefined on some systems, so they are defined here only if not already defined. * web site changed * UNIX Makefile modified, to handle the case if "." is not in your path. Changes from Version 1.0 to 2.0 (January 31, 2000) No bugs were found in version 1.1. These changes merely add new functionality. * added the COLAMD_RECOMMENDED (nnz, n_row, n_col) macro. * moved the output statistics, from A, to a separate output argument. The arguments changed for the C-callable routines. * added colamd_report and symamd_report. * added a C-callable symamd routine. Formerly, symamd was only available as a mexFunction from MATLAB. * added error-checking to symamd. Formerly, it assumed its input was error-free. * added the optional stats and knobs arguments to the symamd mexFunction * deleted colamd_help. A help message is still available from "help colamd" and "help symamd" in MATLAB. * deleted colamdtree.m and symamdtree.m. Now, colamd.m and symamd.m also do the elimination tree post-ordering. The Version 1.1 colamd and symamd mexFunctions, which do not do the post- ordering, are now visible as colamdmex and symamdmex from MATLAB. Essentialy, the post-ordering is now the default behavior of colamd.m and symamd.m, to match the behavior of colmmd and symmmd. The post-ordering is only available in the MATLAB interface, not the C-callable interface. * made a slight change to the dense row/column detection in symamd, to match the stated specifications. SuiteSparse/COLAMD/Doc/lesser.txt0000644001170100242450000006350010263213546015457 0ustar davisfac GNU LESSER GENERAL PUBLIC LICENSE Version 2.1, February 1999 Copyright (C) 1991, 1999 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. [This is the first released version of the Lesser GPL. It also counts as the successor of the GNU Library Public License, version 2, hence the version number 2.1.] Preamble The licenses for most software are designed to take away your freedom to share and change it. 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SuiteSparse/COLAMD/Lib/0000755001170100242450000000000010711435722013416 5ustar davisfacSuiteSparse/COLAMD/Lib/Makefile0000644001170100242450000000143710617104633015062 0ustar davisfac#------------------------------------------------------------------------------- # COLAMD Makefile #------------------------------------------------------------------------------- default: libcolamd.a include ../../UFconfig/UFconfig.mk I = -I../Include -I../../UFconfig INC = ../Include/colamd.h ../../UFconfig/UFconfig.h SRC = ../Source/colamd.c ../Source/colamd_global.c # creates libcolamd.a, a C-callable COLAMD library libcolamd.a: $(SRC) $(INC) $(CC) $(CFLAGS) $(I) -c ../Source/colamd_global.c $(CC) $(CFLAGS) $(I) -c ../Source/colamd.c $(CC) $(CFLAGS) $(I) -c ../Source/colamd.c -DDLONG -o colamd_l.o $(AR) libcolamd.a colamd.o colamd_l.o colamd_global.o ccode: libcolamd.a library: libcolamd.a clean: - $(RM) $(CLEAN) purge: distclean distclean: clean - $(RM) libcolamd.a SuiteSparse/COLAMD/Demo/0000755001170100242450000000000010711435722013574 5ustar davisfacSuiteSparse/COLAMD/Demo/colamd_l_example.c0000644001170100242450000001361110537764112017233 0ustar davisfac/* ========================================================================== */ /* === colamd and symamd example ============================================ */ /* ========================================================================== */ /* COLAMD / SYMAMD example colamd example of use, to order the columns of a 5-by-4 matrix with 11 nonzero entries in the following nonzero pattern, with default knobs. x 0 x 0 x 0 x x 0 x x 0 0 0 x x x x 0 0 symamd example of use, to order the rows and columns of a 5-by-5 matrix with 13 nonzero entries in the following nonzero pattern, with default knobs. x x 0 0 0 x x x x 0 0 x x 0 0 0 x 0 x x 0 0 0 x x (where x denotes a nonzero value). See http://www.cise.ufl.edu/research/sparse/colamd/ (the colamd.c file) for the routines this program calls, and for the License. */ /* ========================================================================== */ #include #include "colamd.h" #define A_NNZ 11 #define A_NROW 5 #define A_NCOL 4 #define ALEN 150 #define B_NNZ 4 #define B_N 5 /* define UF_long */ #include "UFconfig.h" int main (void) { /* ====================================================================== */ /* input matrix A definition */ /* ====================================================================== */ UF_long A [ALEN] = { 0, 1, 4, /* row indices of nonzeros in column 0 */ 2, 4, /* row indices of nonzeros in column 1 */ 0, 1, 2, 3, /* row indices of nonzeros in column 2 */ 1, 3} ; /* row indices of nonzeros in column 3 */ UF_long p [ ] = { 0, /* column 0 is in A [0..2] */ 3, /* column 1 is in A [3..4] */ 5, /* column 2 is in A [5..8] */ 9, /* column 3 is in A [9..10] */ A_NNZ} ; /* number of nonzeros in A */ /* ====================================================================== */ /* input matrix B definition */ /* ====================================================================== */ UF_long B [ ] = { /* Note: only strictly lower triangular part */ /* is included, since symamd ignores the */ /* diagonal and upper triangular part of B. */ 1, /* row indices of nonzeros in column 0 */ 2, 3, /* row indices of nonzeros in column 1 */ /* row indices of nonzeros in column 2 (none) */ 4 /* row indices of nonzeros in column 3 */ } ; /* row indices of nonzeros in column 4 (none) */ UF_long q [ ] = { 0, /* column 0 is in B [0] */ 1, /* column 1 is in B [1..2] */ 3, /* column 2 is empty */ 3, /* column 3 is in B [3] */ 4, /* column 4 is empty */ B_NNZ} ; /* number of nonzeros in strictly lower B */ /* ====================================================================== */ /* other variable definitions */ /* ====================================================================== */ UF_long perm [B_N+1] ; /* note the size is N+1 */ UF_long stats [COLAMD_STATS] ;/* for colamd and symamd output statistics */ UF_long row, col, pp, length, ok ; /* ====================================================================== */ /* dump the input matrix A */ /* ====================================================================== */ printf ("colamd %d-by-%d input matrix:\n", A_NROW, A_NCOL) ; for (col = 0 ; col < A_NCOL ; col++) { length = p [col+1] - p [col] ; printf ("Column %ld, with %ld entries:\n", col, length) ; for (pp = p [col] ; pp < p [col+1] ; pp++) { row = A [pp] ; printf (" row %ld\n", row) ; } } /* ====================================================================== */ /* order the matrix. Note that this destroys A and overwrites p */ /* ====================================================================== */ ok = colamd_l (A_NROW, A_NCOL, ALEN, A, p, (double *) NULL, stats) ; colamd_l_report (stats) ; if (!ok) { printf ("colamd error!\n") ; exit (1) ; } /* ====================================================================== */ /* print the column ordering */ /* ====================================================================== */ printf ("colamd_l column ordering:\n") ; printf ("1st column: %ld\n", p [0]) ; printf ("2nd column: %ld\n", p [1]) ; printf ("3rd column: %ld\n", p [2]) ; printf ("4th column: %ld\n", p [3]) ; /* ====================================================================== */ /* dump the strictly lower triangular part of symmetric input matrix B */ /* ====================================================================== */ printf ("\n\nsymamd_l %d-by-%d input matrix:\n", B_N, B_N) ; printf ("Entries in strictly lower triangular part:\n") ; for (col = 0 ; col < B_N ; col++) { length = q [col+1] - q [col] ; printf ("Column %ld, with %ld entries:\n", col, length) ; for (pp = q [col] ; pp < q [col+1] ; pp++) { row = B [pp] ; printf (" row %ld\n", row) ; } } /* ====================================================================== */ /* order the matrix B. Note that this does not modify B or q. */ /* ====================================================================== */ ok = symamd_l (B_N, B, q, perm, (double *) NULL, stats, &calloc, &free) ; symamd_l_report (stats) ; if (!ok) { printf ("symamd error!\n") ; exit (1) ; } /* ====================================================================== */ /* print the symmetric ordering */ /* ====================================================================== */ printf ("symamd_l column ordering:\n") ; printf ("1st row/column: %ld\n", perm [0]) ; printf ("2nd row/column: %ld\n", perm [1]) ; printf ("3rd row/column: %ld\n", perm [2]) ; printf ("4th row/column: %ld\n", perm [3]) ; printf ("5th row/column: %ld\n", perm [4]) ; exit (0) ; } SuiteSparse/COLAMD/Demo/Makefile0000644001170100242450000000253110617104724015235 0ustar davisfac#----------------------------------------------------------------------------- # compile the COLAMD demo #----------------------------------------------------------------------------- default: colamd_example colamd_l_example include ../../UFconfig/UFconfig.mk I = -I../Include -I../../UFconfig C = $(CC) $(CFLAGS) $(I) library: ( cd ../Lib ; $(MAKE) ) #------------------------------------------------------------------------------ # Create the demo program, run it, and compare the output #------------------------------------------------------------------------------ dist: colamd_example: colamd_example.c library $(C) -o colamd_example colamd_example.c ../Lib/libcolamd.a -lm - ./colamd_example > my_colamd_example.out - diff colamd_example.out my_colamd_example.out colamd_l_example: colamd_l_example.c library $(C) -o colamd_l_example colamd_l_example.c ../Lib/libcolamd.a -lm - ./colamd_l_example > my_colamd_l_example.out - diff colamd_example.out my_colamd_example.out #------------------------------------------------------------------------------ # Remove all but the files in the original distribution #------------------------------------------------------------------------------ clean: - $(RM) $(CLEAN) purge: distclean distclean: clean - $(RM) colamd_example colamd_l_example - $(RM) my_colamd_example.out my_colamd_l_example.out SuiteSparse/COLAMD/Demo/colamd_l_example.out0000644001170100242450000000213710711431226017610 0ustar davisfaccolamd 5-by-4 input matrix: Column 0, with 3 entries: row 0 row 1 row 4 Column 1, with 2 entries: row 2 row 4 Column 2, with 4 entries: row 0 row 1 row 2 row 3 Column 3, with 2 entries: row 1 row 3 colamd version 2.7, Nov 1, 2007: OK. colamd: number of dense or empty rows ignored: 0 colamd: number of dense or empty columns ignored: 0 colamd: number of garbage collections performed: 0 colamd_l column ordering: 1st column: 1 2nd column: 0 3rd column: 2 4th column: 3 symamd_l 5-by-5 input matrix: Entries in strictly lower triangular part: Column 0, with 1 entries: row 1 Column 1, with 2 entries: row 2 row 3 Column 2, with 0 entries: Column 3, with 1 entries: row 4 Column 4, with 0 entries: symamd version 2.7, Nov 1, 2007: OK. symamd: number of dense or empty rows ignored: 0 symamd: number of dense or empty columns ignored: 0 symamd: number of garbage collections performed: 0 symamd_l column ordering: 1st row/column: 0 2nd row/column: 2 3rd row/column: 1 4th row/column: 3 5th row/column: 4 SuiteSparse/COLAMD/Demo/colamd_example.out0000644001170100242450000000213110711431226017267 0ustar davisfaccolamd 5-by-4 input matrix: Column 0, with 3 entries: row 0 row 1 row 4 Column 1, with 2 entries: row 2 row 4 Column 2, with 4 entries: row 0 row 1 row 2 row 3 Column 3, with 2 entries: row 1 row 3 colamd version 2.7, Nov 1, 2007: OK. colamd: number of dense or empty rows ignored: 0 colamd: number of dense or empty columns ignored: 0 colamd: number of garbage collections performed: 0 colamd column ordering: 1st column: 1 2nd column: 0 3rd column: 2 4th column: 3 symamd 5-by-5 input matrix: Entries in strictly lower triangular part: Column 0, with 1 entries: row 1 Column 1, with 2 entries: row 2 row 3 Column 2, with 0 entries: Column 3, with 1 entries: row 4 Column 4, with 0 entries: symamd version 2.7, Nov 1, 2007: OK. symamd: number of dense or empty rows ignored: 0 symamd: number of dense or empty columns ignored: 0 symamd: number of garbage collections performed: 0 symamd column ordering: 1st row/column: 0 2nd row/column: 2 3rd row/column: 1 4th row/column: 3 5th row/column: 4 SuiteSparse/COLAMD/Demo/colamd_example.c0000644001170100242450000001344510537764057016735 0ustar davisfac/* ========================================================================== */ /* === colamd and symamd example ============================================ */ /* ========================================================================== */ /* COLAMD / SYMAMD example colamd example of use, to order the columns of a 5-by-4 matrix with 11 nonzero entries in the following nonzero pattern, with default knobs. x 0 x 0 x 0 x x 0 x x 0 0 0 x x x x 0 0 symamd example of use, to order the rows and columns of a 5-by-5 matrix with 13 nonzero entries in the following nonzero pattern, with default knobs. x x 0 0 0 x x x x 0 0 x x 0 0 0 x 0 x x 0 0 0 x x (where x denotes a nonzero value). See http://www.cise.ufl.edu/research/sparse/colamd/ (the colamd.c file) for the routines this program calls, and for the License. */ /* ========================================================================== */ #include #include "colamd.h" #define A_NNZ 11 #define A_NROW 5 #define A_NCOL 4 #define ALEN 150 #define B_NNZ 4 #define B_N 5 int main (void) { /* ====================================================================== */ /* input matrix A definition */ /* ====================================================================== */ int A [ALEN] = { 0, 1, 4, /* row indices of nonzeros in column 0 */ 2, 4, /* row indices of nonzeros in column 1 */ 0, 1, 2, 3, /* row indices of nonzeros in column 2 */ 1, 3} ; /* row indices of nonzeros in column 3 */ int p [ ] = { 0, /* column 0 is in A [0..2] */ 3, /* column 1 is in A [3..4] */ 5, /* column 2 is in A [5..8] */ 9, /* column 3 is in A [9..10] */ A_NNZ} ; /* number of nonzeros in A */ /* ====================================================================== */ /* input matrix B definition */ /* ====================================================================== */ int B [ ] = { /* Note: only strictly lower triangular part */ /* is included, since symamd ignores the */ /* diagonal and upper triangular part of B. */ 1, /* row indices of nonzeros in column 0 */ 2, 3, /* row indices of nonzeros in column 1 */ /* row indices of nonzeros in column 2 (none) */ 4 /* row indices of nonzeros in column 3 */ } ; /* row indices of nonzeros in column 4 (none) */ int q [ ] = { 0, /* column 0 is in B [0] */ 1, /* column 1 is in B [1..2] */ 3, /* column 2 is empty */ 3, /* column 3 is in B [3] */ 4, /* column 4 is empty */ B_NNZ} ; /* number of nonzeros in strictly lower B */ /* ====================================================================== */ /* other variable definitions */ /* ====================================================================== */ int perm [B_N+1] ; /* note the size is N+1 */ int stats [COLAMD_STATS] ; /* for colamd and symamd output statistics */ int row, col, pp, length, ok ; /* ====================================================================== */ /* dump the input matrix A */ /* ====================================================================== */ printf ("colamd %d-by-%d input matrix:\n", A_NROW, A_NCOL) ; for (col = 0 ; col < A_NCOL ; col++) { length = p [col+1] - p [col] ; printf ("Column %d, with %d entries:\n", col, length) ; for (pp = p [col] ; pp < p [col+1] ; pp++) { row = A [pp] ; printf (" row %d\n", row) ; } } /* ====================================================================== */ /* order the matrix. Note that this destroys A and overwrites p */ /* ====================================================================== */ ok = colamd (A_NROW, A_NCOL, ALEN, A, p, (double *) NULL, stats) ; colamd_report (stats) ; if (!ok) { printf ("colamd error!\n") ; exit (1) ; } /* ====================================================================== */ /* print the column ordering */ /* ====================================================================== */ printf ("colamd column ordering:\n") ; printf ("1st column: %d\n", p [0]) ; printf ("2nd column: %d\n", p [1]) ; printf ("3rd column: %d\n", p [2]) ; printf ("4th column: %d\n", p [3]) ; /* ====================================================================== */ /* dump the strictly lower triangular part of symmetric input matrix B */ /* ====================================================================== */ printf ("\n\nsymamd %d-by-%d input matrix:\n", B_N, B_N) ; printf ("Entries in strictly lower triangular part:\n") ; for (col = 0 ; col < B_N ; col++) { length = q [col+1] - q [col] ; printf ("Column %d, with %d entries:\n", col, length) ; for (pp = q [col] ; pp < q [col+1] ; pp++) { row = B [pp] ; printf (" row %d\n", row) ; } } /* ====================================================================== */ /* order the matrix B. Note that this does not modify B or q. */ /* ====================================================================== */ ok = symamd (B_N, B, q, perm, (double *) NULL, stats, &calloc, &free) ; symamd_report (stats) ; if (!ok) { printf ("symamd error!\n") ; exit (1) ; } /* ====================================================================== */ /* print the symmetric ordering */ /* ====================================================================== */ printf ("symamd column ordering:\n") ; printf ("1st row/column: %d\n", perm [0]) ; printf ("2nd row/column: %d\n", perm [1]) ; printf ("3rd row/column: %d\n", perm [2]) ; printf ("4th row/column: %d\n", perm [3]) ; printf ("5th row/column: %d\n", perm [4]) ; exit (0) ; } SuiteSparse/COLAMD/Makefile0000644001170100242450000000223110617104476014352 0ustar davisfac#------------------------------------------------------------------------------ # COLAMD Makefile #------------------------------------------------------------------------------ default: demo include ../UFconfig/UFconfig.mk # Compile all C code, including the C-callable routine and the mexFunctions. # Do not the MATLAB interface. demo: ( cd Lib ; $(MAKE) ) ( cd Demo ; $(MAKE) ) # Compile all C code, including the C-callable routine and the mexFunctions. all: ( cd Lib ; $(MAKE) ) ( cd Demo ; $(MAKE) ) ( cd MATLAB ; $(MAKE) ) # compile just the C-callable libraries (not mexFunctions or Demos) library: ( cd Lib ; $(MAKE) ) # remove object files, but keep the compiled programs and library archives clean: ( cd Lib ; $(MAKE) clean ) ( cd Demo ; $(MAKE) clean ) ( cd MATLAB ; $(MAKE) clean ) # clean, and then remove compiled programs and library archives purge: ( cd Lib ; $(MAKE) purge ) ( cd Demo ; $(MAKE) purge ) ( cd MATLAB ; $(MAKE) purge ) distclean: purge # get ready for distribution dist: purge ( cd Demo ; $(MAKE) dist ) ccode: library lib: library # compile the MATLAB mexFunction mex: ( cd MATLAB ; $(MAKE) ) SuiteSparse/COLAMD/MATLAB/0000755001170100242450000000000010711653376013657 5ustar davisfacSuiteSparse/COLAMD/MATLAB/symamdtestmex.c0000644001170100242450000003123510616374617016735 0ustar davisfac/* ========================================================================== */ /* === symamdtest mexFunction =============================================== */ /* ========================================================================== */ /* SYMAMD test function This MATLAB mexFunction is for testing only. It is not meant for production use. See symamdmex.c instead. Usage: [ P, stats ] = symamdtest (A, knobs) ; See symamd.m for a description. knobs is required. knobs (1) dense row control knobs (2) spumoni knobs (3) for testing only. Controls how the input matrix is jumbled prior to calling symamd, to test its error handling capability. Authors: The authors of the code itself are Stefan I. Larimore and Timothy A. Davis (davis at cise.ufl.edu), University of Florida. The algorithm was developed in collaboration with John Gilbert, Xerox PARC, and Esmond Ng, Oak Ridge National Laboratory. Acknowledgements: This work was supported by the National Science Foundation, under grants DMS-9504974 and DMS-9803599. Notice: Copyright (c) 1998-2007, Timothy A. Davis. All Rights Reserved. See http://www.cise.ufl.edu/research/sparse/colamd (the colamd.c file) for the License. Availability: The colamd/symamd library is available at http://www.cise.ufl.edu/research/sparse/colamd/ This is the http://www.cise.ufl.edu/research/sparse/colamd/symamdtestmex.c file. It requires the colamd.c and colamd.h files. */ /* ========================================================================== */ /* === Include files ======================================================== */ /* ========================================================================== */ #include "colamd.h" #include "mex.h" #include "matrix.h" #include #include #include "UFconfig.h" static void dump_matrix ( UF_long A [ ], UF_long p [ ], UF_long n_row, UF_long n_col, UF_long Alen, UF_long limit ) ; /* ========================================================================== */ /* === symamd mexFunction =================================================== */ /* ========================================================================== */ void mexFunction ( /* === Parameters ======================================================= */ int nlhs, /* number of left-hand sides */ mxArray *plhs [], /* left-hand side matrices */ int nrhs, /* number of right--hand sides */ const mxArray *prhs [] /* right-hand side matrices */ ) { /* === Local variables ================================================== */ UF_long *perm ; /* column ordering of M and ordering of A */ UF_long *A ; /* row indices of input matrix A */ UF_long *p ; /* column pointers of input matrix A */ UF_long n_col ; /* number of columns of A */ UF_long n_row ; /* number of rows of A */ UF_long full ; /* TRUE if input matrix full, FALSE if sparse */ double knobs [COLAMD_KNOBS] ; /* colamd user-controllable parameters */ double *out_perm ; /* output permutation vector */ double *out_stats ; /* output stats vector */ double *in_knobs ; /* input knobs vector */ UF_long i ; /* loop counter */ mxArray *Ainput ; /* input matrix handle */ UF_long spumoni ; /* verbosity variable */ UF_long stats2 [COLAMD_STATS] ; /* stats for symamd */ UF_long *cp, *cp_end, result, nnz, col, length ; UF_long *stats ; stats = stats2 ; colamd_printf = mexPrintf ; /* COLAMD printf routine */ /* === Check inputs ===================================================== */ if (nrhs < 1 || nrhs > 2 || nlhs < 0 || nlhs > 2) { mexErrMsgTxt ( "symamd: incorrect number of input and/or output arguments.") ; } if (nrhs != 2) { mexErrMsgTxt ("symamdtest: knobs are required") ; } /* for testing we require all 3 knobs */ if (mxGetNumberOfElements (prhs [1]) != 3) { mexErrMsgTxt ("symamdtest: must have all 3 knobs for testing") ; } /* === Get knobs ======================================================== */ colamd_l_set_defaults (knobs) ; spumoni = 0 ; /* check for user-passed knobs */ if (nrhs == 2) { in_knobs = mxGetPr (prhs [1]) ; i = mxGetNumberOfElements (prhs [1]) ; if (i > 0) knobs [COLAMD_DENSE_ROW] = in_knobs [0] ; if (i > 1) spumoni = (UF_long) in_knobs [1] ; } /* print knob settings if spumoni is set */ if (spumoni) { mexPrintf ("\nsymamd version %d.%d, %s:\n", COLAMD_MAIN_VERSION, COLAMD_SUB_VERSION, COLAMD_DATE) ; if (knobs [COLAMD_DENSE_ROW] >= 0) { mexPrintf ("knobs(1): %g, rows/cols with > " "max(16,%g*sqrt(size(A,2))) entries removed\n", in_knobs [0], knobs [COLAMD_DENSE_ROW]) ; } else { mexPrintf ("knobs(1): %g, no dense rows removed\n", in_knobs [0]) ; } mexPrintf ("knobs(2): %g, statistics and knobs printed\n", in_knobs [1]) ; mexPrintf ("Testing %d\n", in_knobs [2]) ; } /* === If A is full, convert to a sparse matrix ========================= */ Ainput = (mxArray *) prhs [0] ; if (mxGetNumberOfDimensions (Ainput) != 2) { mexErrMsgTxt ("symamd: input matrix must be 2-dimensional.") ; } full = !mxIsSparse (Ainput) ; if (full) { mexCallMATLAB (1, &Ainput, 1, (mxArray **) prhs, "sparse") ; } /* === Allocate workspace for symamd ==================================== */ /* get size of matrix */ n_row = mxGetM (Ainput) ; n_col = mxGetN (Ainput) ; if (n_col != n_row) { mexErrMsgTxt ("symamd: matrix must be square.") ; } /* p = mxGetJc (Ainput) ; */ p = (UF_long *) mxCalloc (n_col+1, sizeof (UF_long)) ; (void) memcpy (p, mxGetJc (Ainput), (n_col+1)*sizeof (UF_long)) ; nnz = p [n_col] ; if (spumoni > 0) { mexPrintf ("symamdtest: nnz %d\n", nnz) ; } /* A = mxGetIr (Ainput) ; */ A = (UF_long *) mxCalloc (nnz+1, sizeof (UF_long)) ; (void) memcpy (A, mxGetIr (Ainput), nnz*sizeof (UF_long)) ; perm = (UF_long *) mxCalloc (n_col+1, sizeof (UF_long)) ; /* === Jumble matrix ======================================================== */ /* knobs [2] FOR TESTING ONLY: Specifies how to jumble matrix 0 : No jumbling 1 : (no errors) 2 : Make first pointer non-zero 3 : Make column pointers not non-decreasing 4 : (no errors) 5 : Make row indices not strictly increasing 6 : Make a row index greater or equal to n_row 7 : Set A = NULL 8 : Set p = NULL 9 : Repeat row index 10: make row indices not sorted 11: jumble columns massively (note this changes the pattern of the matrix A.) 12: Set stats = NULL 13: Make n_col less than zero */ /* jumble appropriately */ switch ((UF_long) in_knobs [2]) { case 0 : if (spumoni > 0) { mexPrintf ("symamdtest: no errors expected\n") ; } result = 1 ; /* no errors */ break ; case 1 : if (spumoni > 0) { mexPrintf ("symamdtest: no errors expected (1)\n") ; } result = 1 ; break ; case 2 : if (spumoni > 0) { mexPrintf ("symamdtest: p [0] nonzero\n") ; } result = 0 ; /* p [0] must be zero */ p [0] = 1 ; break ; case 3 : if (spumoni > 0) { mexPrintf ("symamdtest: negative length last column\n") ; } result = (n_col == 0) ; /* p must be monotonically inc. */ p [n_col] = p [0] ; break ; case 4 : if (spumoni > 0) { mexPrintf ("symamdtest: no errors expected (4)\n") ; } result = 1 ; break ; case 5 : if (spumoni > 0) { mexPrintf ("symamdtest: row index out of range (-1)\n") ; } if (nnz > 0) /* row index out of range */ { result = 0 ; A [nnz-1] = -1 ; } else { if (spumoni > 0) { mexPrintf ("Note: no row indices to put out of range\n") ; } result = 1 ; } break ; case 6 : if (spumoni > 0) { mexPrintf ("symamdtest: row index out of range (ncol)\n") ; } if (nnz > 0) /* row index out of range */ { result = 0 ; A [nnz-1] = n_col ; } else { if (spumoni > 0) { mexPrintf ("Note: no row indices to put out of range\n") ; } result = 1 ; } break ; case 7 : if (spumoni > 0) { mexPrintf ("symamdtest: A not present\n") ; } result = 0 ; /* A not present */ A = (UF_long *) NULL ; break ; case 8 : if (spumoni > 0) { mexPrintf ("symamdtest: p not present\n") ; } result = 0 ; /* p not present */ p = (UF_long *) NULL ; break ; case 9 : if (spumoni > 0) { mexPrintf ("symamdtest: duplicate row index\n") ; } result = 1 ; /* duplicate row index */ for (col = 0 ; col < n_col ; col++) { length = p [col+1] - p [col] ; if (length > 1) { A [p [col+1]-2] = A [p [col+1] - 1] ; if (spumoni > 0) { mexPrintf ("Made duplicate row %d in col %d\n", A [p [col+1] - 1], col) ; } break ; } } if (spumoni > 1) { dump_matrix (A, p, n_row, n_col, nnz, col+2) ; } break ; case 10 : if (spumoni > 0) { mexPrintf ("symamdtest: unsorted column\n") ; } result = 1 ; /* jumbled columns */ for (col = 0 ; col < n_col ; col++) { length = p [col+1] - p [col] ; if (length > 1) { i = A[p [col]] ; A [p [col]] = A[p [col] + 1] ; A [p [col] + 1] = i ; if (spumoni > 0) { mexPrintf ("Unsorted column %d \n", col) ; } break ; } } if (spumoni > 1) { dump_matrix (A, p, n_row, n_col, nnz, col+2) ; } break ; case 11 : if (spumoni > 0) { mexPrintf ("symamdtest: massive jumbling\n") ; } result = 1 ; /* massive jumbling, but no errors */ srand (1) ; for (i = 0 ; i < n_col ; i++) { cp = &A [p [i]] ; cp_end = &A [p [i+1]] ; while (cp < cp_end) { *cp++ = rand() % n_row ; } } if (spumoni > 1) { dump_matrix (A, p, n_row, n_col, nnz, n_col) ; } break ; case 12 : if (spumoni > 0) { mexPrintf ("symamdtest: stats not present\n") ; } result = 0 ; /* stats not present */ stats = (UF_long *) NULL ; break ; case 13 : if (spumoni > 0) { mexPrintf ("symamdtest: ncol out of range\n") ; } result = 0 ; /* ncol out of range */ n_col = -1 ; break ; } /* === Order the rows and columns of A (does not destroy A) ============= */ if (!symamd_l (n_col, A, p, perm, knobs, stats, &mxCalloc, &mxFree)) { /* return p = -1 if colamd failed */ plhs [0] = mxCreateDoubleMatrix (1, 1, mxREAL) ; out_perm = mxGetPr (plhs [0]) ; out_perm [0] = -1 ; mxFree (p) ; mxFree (A) ; if (spumoni > 0 || result) { symamd_l_report (stats) ; } if (result) { mexErrMsgTxt ("symamd should have returned TRUE\n") ; } return ; /* mexErrMsgTxt ("symamd error!") ; */ } if (!result) { symamd_l_report (stats) ; mexErrMsgTxt ("symamd should have returned FALSE\n") ; } if (full) { mxDestroyArray (Ainput) ; } /* === Return the permutation vector ==================================== */ plhs [0] = mxCreateDoubleMatrix (1, n_col, mxREAL) ; out_perm = mxGetPr (plhs [0]) ; for (i = 0 ; i < n_col ; i++) { /* symamd is 0-based, but MATLAB expects this to be 1-based */ out_perm [i] = perm [i] + 1 ; } mxFree (perm) ; /* === Return the stats vector ========================================== */ /* print stats if spumoni > 0 */ if (spumoni > 0) { symamd_l_report (stats) ; } if (nlhs == 2) { plhs [1] = mxCreateDoubleMatrix (1, COLAMD_STATS, mxREAL) ; out_stats = mxGetPr (plhs [1]) ; for (i = 0 ; i < COLAMD_STATS ; i++) { out_stats [i] = stats [i] ; } /* fix stats (5) and (6), for 1-based information on jumbled matrix. */ /* note that this correction doesn't occur if symamd returns FALSE */ out_stats [COLAMD_INFO1] ++ ; out_stats [COLAMD_INFO2] ++ ; } } #ifdef MIN #undef MIN #endif #define MIN(a,b) (((a) < (b)) ? (a) : (b)) static void dump_matrix ( UF_long A [ ], UF_long p [ ], UF_long n_row, UF_long n_col, UF_long Alen, UF_long limit ) { UF_long col, k, row ; mexPrintf ("dump matrix: nrow %d ncol %d Alen %d\n", n_row, n_col, Alen) ; if (!A) { mexPrintf ("A not present\n") ; return ; } if (!p) { mexPrintf ("p not present\n") ; return ; } for (col = 0 ; col < MIN (n_col, limit) ; col++) { mexPrintf ("column %d, p[col] %d, p [col+1] %d, length %d\n", col, p [col], p [col+1], p [col+1] - p [col]) ; for (k = p [col] ; k < p [col+1] ; k++) { row = A [k] ; mexPrintf (" %d", row) ; } mexPrintf ("\n") ; } } SuiteSparse/COLAMD/MATLAB/colamd_test.m0000644001170100242450000002670310707726301016335 0ustar davisfacfunction colamd_test %COLAMD_TEST test colamd2 and symamd2 % Example: % colamd_test % % COLAMD and SYMAMD testing function. Here we try to give colamd2 and symamd2 % every possible type of matrix and erroneous input that they may encounter. % We want either a valid permutation returned or we want them to fail % gracefully. % % You are prompted as to whether or not the colamd2 and symand routines and % the test mexFunctions are to be compiled. % % See also colamd2, symamd2 % Copyright 1998-2007, Timothy A. Davis, and Stefan Larimore % Developed in collaboration with J. Gilbert and E. Ng. help colamd_test fprintf ('Compiling colamd2, symamd2, and test mexFunctions.\n') ; colamd_make ; d = '' ; if (~isempty (strfind (computer, '64'))) d = '-largeArrayDims' ; end cmd = sprintf ('mex -DDLONG -O %s -I../../UFconfig -I../Include ', d) ; src = '../Source/colamd.c ../Source/colamd_global.c' ; eval ([cmd 'colamdtestmex.c ' src]) ; eval ([cmd 'symamdtestmex.c ' src]) ; fprintf ('Done compiling.\n') ; fprintf ('\nThe following codes will be tested:\n') ; which colamd2 which symamd2 which colamd2mex which symamd2mex which colamdtestmex which symamdtestmex fprintf ('\nStarting the tests. Please be patient.\n') ; h = waitbar (0, 'COLAMD test') ; rand ('state', 0) ; randn ('state', 0) ; A = sprandn (500,500,0.4) ; p = colamd2 (A, [10 10 1]) ; check_perm (p, A) ; p = colamd2 (A, [2 7 1]) ; check_perm (p, A) ; p = symamd2 (A, [10 1]) ; check_perm (p, A) ; p = symamd2 (A, [7 1]) ; check_perm (p, A) ; p = symamd2 (A, [4 1]) ; check_perm (p, A) ; fprintf ('Null matrices') ; A = zeros (0,0) ; A = sparse (A) ; [p, stats] = colamd2 (A, [10 10 0]) ; %#ok check_perm (p, A) ; [p, stats] = symamd2 (A, [10 0]) ; %#ok check_perm (p, A) ; A = zeros (0, 100) ; A = sparse (A) ; [p, stats] = colamd2 (A, [10 10 0]) ; %#ok check_perm (p, A) ; A = zeros (100, 0) ; A = sparse (A) ; [p, stats] = colamd2 (A, [10 10 0]) ; check_perm (p, A) ; fprintf (' OK\n') ; fprintf ('Matrices with a few dense row/cols\n') ; for trial = 1:20 waitbar (trial/20, h, 'COLAMD: with dense rows/cols') ; % random square unsymmetric matrix A = rand_matrix (1000, 1000, 1, 10, 20) ; for tol = [0:.1:2 3:20 1e6] [p, stats] = colamd2 (A, [tol tol 0]) ; %#ok check_perm (p, A) ; B = A + A' ; [p, stats] = symamd2 (B, [tol 0]) ; %#ok check_perm (p, A) ; [p, stats] = colamd2 (A, [tol 1 0]) ; %#ok check_perm (p, A) ; [p, stats] = colamd2 (A, [1 tol 0]) ; %#ok check_perm (p, A) ; end end fprintf (' OK\n') ; fprintf ('General matrices\n') ; for trial = 1:400 waitbar (trial/400, h, 'COLAMD: general') ; % matrix of random mtype mtype = irand (3) ; A = rand_matrix (2000, 2000, mtype, 0, 0) ; p = colamd2 (A) ; check_perm (p, A) ; if (mtype == 3) p = symamd2 (A) ; check_perm (p, A) ; end end fprintf (' OK\n') ; fprintf ('Test error handling with invalid inputs\n') ; % Check different erroneous input. for trial = 1:30 waitbar (trial/30, h, 'COLAMD: error handling') ; A = rand_matrix (1000, 1000, 2, 0, 0) ; [m n] = size (A) ; for err = 1:13 p = Tcolamd (A, [n n 0 0 err]) ; if (p ~= -1) %#ok check_perm (p, A) ; end if (err == 1) % check different (valid) input args to colamd2 p = Acolamd (A) ; p2 = Acolamd (A, [10 10 0 0 0]) ; if (any (p ~= p2)) error ('colamd2: mismatch 1!') ; end [p2 stats] = Acolamd (A) ; %#ok if (any (p ~= p2)) error ('colamd2: mismatch 2!') ; end [p2 stats] = Acolamd (A, [10 10 0 0 0]) ; if (any (p ~= p2)) error ('colamd2: mismatch 3!') ; end end B = A'*A ; p = Tsymamd (B, [n 0 err]) ; if (p ~= -1) %#ok check_perm (p, A) ; end if (err == 1) % check different (valid) input args to symamd2 p = Asymamd (B) ; check_perm (p, A) ; p2 = Asymamd (B, [10 0 0]) ; if (any (p ~= p2)) error ('symamd2: mismatch 1!') ; end [p2 stats] = Asymamd (B) ; %#ok if (any (p ~= p2)) error ('symamd2: mismatch 2!') ; end [p2 stats] = Asymamd (B, [10 0 0]) ; %#ok if (any (p ~= p2)) error ('symamd2: mismatch 3!') ; end end end end fprintf (' OK\n') ; fprintf ('Matrices with a few empty columns\n') ; for trial = 1:400 % some are square, some are rectangular n = 0 ; while (n < 5) A = rand_matrix (1000, 1000, irand (2), 0, 0) ; [m n] = size (A) ; end % Add 5 null columns at random locations. null_col = randperm (n) ; null_col = sort (null_col (1:5)) ; A (:, null_col) = 0 ; % Order the matrix and make sure that the null columns are ordered last. [p, stats] = colamd2 (A, [1e6 1e6 0]) ; check_perm (p, A) ; % if (stats (2) ~= 5) % stats (2) % error ('colamd2: wrong number of null columns') ; % end % find all null columns in A null_col = find (sum (spones (A), 1) == 0) ; nnull = length (null_col) ; %#ok if (any (null_col ~= p ((n-4):n))) error ('colamd2: Null cols are not ordered last in natural order') ; end end fprintf (' OK\n') ; fprintf ('Matrices with a few empty rows and columns\n') ; for trial = 1:400 waitbar (trial/400, h, 'COLAMD: with empty rows/cols') ; % symmetric matrices n = 0 ; while (n < 5) A = rand_matrix (1000, 1000, 3, 0, 0) ; [m n] = size (A) ; end % Add 5 null columns and rows at random locations. null_col = randperm (n) ; null_col = sort (null_col (1:5)) ; A (:, null_col) = 0 ; A (null_col, :) = 0 ; % Order the matrix and make sure that the null rows/cols are ordered last. [p,stats] = symamd2 (A, [10 0]) ; check_perm (p, A) ; % find actual number of null rows and columns Alo = tril (A, -1) ; nnull = length (find (sum (Alo') == 0 & sum (Alo) == 0)) ; %#ok if (stats (2) ~= nnull | nnull < 5) %#ok error ('symamd2: wrong number of null columns') ; end if (any (null_col ~= p ((n-4):n))) error ('symamd2: Null cols are not ordered last in natural order') ; end end fprintf (' OK\n') ; fprintf ('Matrices with a few empty rows\n') ; % Test matrices with null rows inserted. for trial = 1:400 waitbar (trial/400, h, 'COLAMD: with null rows') ; m = 0 ; while (m < 5) A = rand_matrix (1000, 1000, 2, 0, 0) ; [m n] = size (A) ; %#ok end % Add 5 null rows at random locations. null_row = randperm (m) ; null_row = sort (null_row (1:5)) ; A (null_row, :) = 0 ; p = colamd2 (A, [10 10 0]) ; check_perm (p, A) ; if (stats (1) ~= 5) error ('colamd2: wrong number of null rows') ; end end fprintf (' OK\n') ; fprintf ('\ncolamd2 and symamd2: all tests passed\n\n') ; close (h) ; %------------------------------------------------------------------------------- function [p,stats] = Acolamd (S, knobs) % Acolamd: compare colamd2 and Tcolamd results if (nargin < 3) if (nargout == 1) [p] = colamd2 (S) ; [p1] = Tcolamd (S, [10 10 0 0 0]) ; else [p, stats] = colamd2 (S) ; [p1, stats1] = Tcolamd (S, [10 10 0 0 0]) ; %#ok end else if (nargout == 1) [p] = colamd2 (S, knobs (1:3)) ; [p1] = Tcolamd (S, knobs) ; else [p, stats] = colamd2 (S, knobs (1:3)) ; [p1, stats1] = Tcolamd (S, knobs) ; %#ok end end check_perm (p, S) ; check_perm (p1, S) ; if (any (p1 ~= p)) error ('Acolamd mismatch!') ; end %------------------------------------------------------------------------------- function [p,stats] = Asymamd (S, knobs) % Asymamd: compare symamd2 and Tsymamd results if (nargin < 3) if (nargout == 1) [p] = symamd2 (S) ; [p1] = Tsymamd (S, [10 0 0]) ; else [p, stats] = symamd2 (S) ; [p1, stats1] = Tsymamd (S, [10 0 0]) ; %#ok end else if (nargout == 1) [p] = symamd2 (S, knobs (1:2)) ; [p1] = Tsymamd (S, knobs) ; else [p, stats] = symamd2 (S, knobs (1:2)) ; [p1, stats1] = Tsymamd (S, knobs) ; %#ok end end if (any (p1 ~= p)) error ('Asymamd mismatch!') ; end %------------------------------------------------------------------------------- function check_perm (p, A) % check_perm: check for a valid permutation vector if (isempty (A) & isempty (p)) %#ok % empty permutation vectors of empty matrices are OK return end if (isempty (p)) error ('bad permutation: cannot be empty') ; end [m n] = size (A) ; [pm pn] = size (p) ; if (pn == 1) % force p to be a row vector p = p' ; [pm pn] = size (p) ; end if (n ~= pn) error ('bad permutation: wrong size') ; end if (pm ~= 1) ; % p must be a vector error ('bad permutation: not a vector') ; else if (any (sort (p) - (1:pn))) error ('bad permutation') ; end end %------------------------------------------------------------------------------- function i = irand (n) % irand: return a random integer between 1 and n i = min (n, 1 + floor (rand * n)) ; %------------------------------------------------------------------------------- function A = rand_matrix (nmax, mmax, mtype, drows, dcols) % rand_matrix: return a random sparse matrix % % A = rand_matrix (nmax, mmax, mtype, drows, dcols) % % A binary matrix of random size, at most nmax-by-mmax, with drows dense rows % and dcols dense columns. % % mtype 1: square unsymmetric (mmax is ignored) % mtype 2: rectangular % mtype 3: symmetric (mmax is ignored) n = irand (nmax) ; if (mtype ~= 2) % square m = n ; else m = irand (mmax) ; end A = sprand (m, n, 10 / max (m,n)) ; if (drows > 0) % add dense rows for k = 1:drows i = irand (m) ; nz = irand (n) ; p = randperm (n) ; p = p (1:nz) ; A (i,p) = 1 ; end end if (dcols > 0) % add dense cols for k = 1:dcols j = irand (n) ; nz = irand (m) ; p = randperm (m) ; p = p (1:nz) ; A (p,j) = 1 ; end end A = spones (A) ; % ensure that there are no empty columns d = find (full (sum (A)) == 0) ; %#ok A (m,d) = 1 ; %#ok % ensure that there are no empty rows d = find (full (sum (A,2)) == 0) ; %#ok A (d,n) = 1 ; %#ok if (mtype == 3) % symmetric A = A + A' + speye (n) ; end A = spones (A) ; %------------------------------------------------------------------------------- function [p,stats] = Tcolamd (S, knobs) % Tcolamd: run colamd2 in a testing mode if (nargout <= 1 & nargin == 1) %#ok p = colamdtestmex (S) ; elseif (nargout <= 1 & nargin == 2) %#ok p = colamdtestmex (S, knobs) ; elseif (nargout == 2 & nargin == 1) %#ok [p, stats] = colamdtestmex (S) ; elseif (nargout == 2 & nargin == 2) %#ok [p, stats] = colamdtestmex (S, knobs) ; else error ('colamd2: incorrect number of input and/or output arguments') ; end if (p (1) ~= -1) [ignore, q] = etree (S (:,p), 'col') ; p = p (q) ; check_perm (p, S) ; end %------------------------------------------------------------------------------- function [p, stats] = Tsymamd (S, knobs) % Tsymamd: run symamd2 in a testing mode if (nargout <= 1 & nargin == 1) %#ok p = symamdtestmex (S) ; elseif (nargout <= 1 & nargin == 2) %#ok p = symamdtestmex (S, knobs) ; elseif (nargout == 2 & nargin == 1) %#ok [p, stats] = symamdtestmex (S) ; elseif (nargout == 2 & nargin == 2) %#ok [p, stats] = symamdtestmex (S, knobs) ; else error ('symamd2: incorrect number of input and/or output arguments') ; end if (p (1) ~= -1) [ignore, q] = etree (S (p,p)) ; p = p (q) ; check_perm (p, S) ; end SuiteSparse/COLAMD/MATLAB/Makefile0000644001170100242450000000133210617240161015303 0ustar davisfac# COLAMD Makefile for MATLAB mexFunctions default: colamd2 symamd2 include ../../UFconfig/UFconfig.mk I = -I../../UFconfig -I../Include INC = ../Include/colamd.h ../../UFconfig/UFconfig.h SRC = ../Source/colamd.c ../Source/colamd_global.c MX = $(MEX) -DDLONG $(I) # Compiles the MATLAB-callable routines mex: colamd2 symamd2 symamd2: symamdmex.c $(INC) $(SRC) $(MX) -output symamd2mex symamdmex.c $(SRC) colamd2: colamdmex.c $(INC) $(SRC) $(MX) -output colamd2mex colamdmex.c $(SRC) # Compiles the extensive test code test: mex colamdtestmex.c symamdtestmex.c $(INC) $(SRC) $(MX) colamdtestmex.c $(SRC) $(MX) symamdtestmex.c $(SRC) clean: - $(RM) $(CLEAN) purge: distclean distclean: clean - $(RM) *.mex* *.dll SuiteSparse/COLAMD/MATLAB/colamdmex.c0000644001170100242450000001525310616370076015777 0ustar davisfac/* ========================================================================== */ /* === colamd mexFunction =================================================== */ /* ========================================================================== */ /* Usage: P = colamd2 (A) ; [ P, stats ] = colamd2 (A, knobs) ; see colamd.m for a description. Authors: The authors of the code itself are Stefan I. Larimore and Timothy A. Davis (davis at cise.ufl.edu), University of Florida. The algorithm was developed in collaboration with John Gilbert, Xerox PARC, and Esmond Ng, Oak Ridge National Laboratory. Acknowledgements: This work was supported by the National Science Foundation, under grants DMS-9504974 and DMS-9803599. Notice: Copyright (c) 1998-2007, Timothy A. Davis, All Rights Reserved. See http://www.cise.ufl.edu/research/sparse/colamd (the colamd.c file) for the License. Availability: The colamd/symamd library is available at http://www.cise.ufl.edu/research/sparse/colamd/ This is the http://www.cise.ufl.edu/research/sparse/colamd/colamdmex.c file. It requires the colamd.c and colamd.h files. */ /* ========================================================================== */ /* === Include files ======================================================== */ /* ========================================================================== */ #include "colamd.h" #include "mex.h" #include "matrix.h" #include #include #include "UFconfig.h" /* ========================================================================== */ /* === colamd mexFunction =================================================== */ /* ========================================================================== */ void mexFunction ( /* === Parameters ======================================================= */ int nlhs, /* number of left-hand sides */ mxArray *plhs [], /* left-hand side matrices */ int nrhs, /* number of right--hand sides */ const mxArray *prhs [] /* right-hand side matrices */ ) { /* === Local variables ================================================== */ UF_long *A ; /* colamd's copy of the matrix, and workspace */ UF_long *p ; /* colamd's copy of the column pointers */ UF_long Alen ; /* size of A */ UF_long n_col ; /* number of columns of A */ UF_long n_row ; /* number of rows of A */ UF_long nnz ; /* number of entries in A */ UF_long full ; /* TRUE if input matrix full, FALSE if sparse */ double knobs [COLAMD_KNOBS] ; /* colamd user-controllable parameters */ double *out_perm ; /* output permutation vector */ double *out_stats ; /* output stats vector */ double *in_knobs ; /* input knobs vector */ UF_long i ; /* loop counter */ mxArray *Ainput ; /* input matrix handle */ UF_long spumoni ; /* verbosity variable */ UF_long stats [COLAMD_STATS] ; /* stats for colamd */ colamd_printf = mexPrintf ; /* COLAMD printf routine */ /* === Check inputs ===================================================== */ if (nrhs < 1 || nrhs > 2 || nlhs < 0 || nlhs > 2) { mexErrMsgTxt ( "colamd: incorrect number of input and/or output arguments") ; } /* === Get knobs ======================================================== */ colamd_l_set_defaults (knobs) ; spumoni = 0 ; /* check for user-passed knobs */ if (nrhs == 2) { in_knobs = mxGetPr (prhs [1]) ; i = mxGetNumberOfElements (prhs [1]) ; if (i > 0) knobs [COLAMD_DENSE_ROW] = in_knobs [0] ; if (i > 1) knobs [COLAMD_DENSE_COL] = in_knobs [1] ; if (i > 2) spumoni = (UF_long) (in_knobs [2] != 0) ; } /* print knob settings if spumoni is set */ if (spumoni) { mexPrintf ("\ncolamd version %d.%d, %s:\n", COLAMD_MAIN_VERSION, COLAMD_SUB_VERSION, COLAMD_DATE) ; if (knobs [COLAMD_DENSE_ROW] >= 0) { mexPrintf ("knobs(1): %g, rows with > max(16,%g*sqrt(size(A,2)))" " entries removed\n", in_knobs [0], knobs [COLAMD_DENSE_ROW]) ; } else { mexPrintf ("knobs(1): %g, only completely dense rows removed\n", in_knobs [0]) ; } if (knobs [COLAMD_DENSE_COL] >= 0) { mexPrintf ("knobs(2): %g, cols with > max(16,%g*sqrt(min(size(A)))" " entries removed\n", in_knobs [1], knobs [COLAMD_DENSE_COL]) ; } else { mexPrintf ("knobs(2): %g, only completely dense columns removed\n", in_knobs [1]) ; } mexPrintf ("knobs(3): %g, statistics and knobs printed\n", in_knobs [2]) ; } /* === If A is full, convert to a sparse matrix ========================= */ Ainput = (mxArray *) prhs [0] ; if (mxGetNumberOfDimensions (Ainput) != 2) { mexErrMsgTxt ("colamd: input matrix must be 2-dimensional") ; } full = !mxIsSparse (Ainput) ; if (full) { mexCallMATLAB (1, &Ainput, 1, (mxArray **) prhs, "sparse") ; } /* === Allocate workspace for colamd ==================================== */ /* get size of matrix */ n_row = mxGetM (Ainput) ; n_col = mxGetN (Ainput) ; /* get column pointer vector so we can find nnz */ p = (UF_long *) mxCalloc (n_col+1, sizeof (UF_long)) ; (void) memcpy (p, mxGetJc (Ainput), (n_col+1)*sizeof (UF_long)) ; nnz = p [n_col] ; Alen = (UF_long) colamd_l_recommended (nnz, n_row, n_col) ; if (Alen == 0) { mexErrMsgTxt ("colamd: problem too large") ; } /* === Copy input matrix into workspace ================================= */ A = (UF_long *) mxCalloc (Alen, sizeof (UF_long)) ; (void) memcpy (A, mxGetIr (Ainput), nnz*sizeof (UF_long)) ; if (full) { mxDestroyArray (Ainput) ; } /* === Order the columns (destroys A) =================================== */ if (!colamd_l (n_row, n_col, Alen, A, p, knobs, stats)) { colamd_l_report (stats) ; mexErrMsgTxt ("colamd error!") ; } mxFree (A) ; /* === Return the permutation vector ==================================== */ plhs [0] = mxCreateDoubleMatrix (1, n_col, mxREAL) ; out_perm = mxGetPr (plhs [0]) ; for (i = 0 ; i < n_col ; i++) { /* colamd is 0-based, but MATLAB expects this to be 1-based */ out_perm [i] = p [i] + 1 ; } mxFree (p) ; /* === Return the stats vector ========================================== */ /* print stats if spumoni is set */ if (spumoni) { colamd_l_report (stats) ; } if (nlhs == 2) { plhs [1] = mxCreateDoubleMatrix (1, COLAMD_STATS, mxREAL) ; out_stats = mxGetPr (plhs [1]) ; for (i = 0 ; i < COLAMD_STATS ; i++) { out_stats [i] = stats [i] ; } /* fix stats (5) and (6), for 1-based information on jumbled matrix. */ /* note that this correction doesn't occur if symamd returns FALSE */ out_stats [COLAMD_INFO1] ++ ; out_stats [COLAMD_INFO2] ++ ; } } SuiteSparse/COLAMD/MATLAB/colamdtestmex.c0000644001170100242450000003370410616374454016704 0ustar davisfac/* ========================================================================== */ /* === colamdtest mexFunction =============================================== */ /* ========================================================================== */ /* COLAMD test function This MATLAB mexFunction is for testing only. It is not meant for production use. See colamdmex.c instead. Usage: [ P, stats ] = colamdtest (A, knobs) ; See colamd.m for a description. knobs is required. knobs (1) dense row control knobs (2) dense column control knobs (3) spumoni knobs (4) for testing only. Controls the workspace used by colamd. knobs (5) for testing only. Controls how the input matrix is jumbled prior to calling colamd, to test its error handling capability. Authors: The authors of the code itself are Stefan I. Larimore and Timothy A. Davis (davis at cise.ufl.edu), University of Florida. The algorithm was developed in collaboration with John Gilbert, Xerox PARC, and Esmond Ng, Oak Ridge National Laboratory. Acknowledgements: This work was supported by the National Science Foundation, under grants DMS-9504974 and DMS-9803599. Notice: Copyright (c) 1998-2007, Timothy A. Davis, All Rights Reserved. See http://www.cise.ufl.edu/research/sparse/colamd (the colamd.c file) for the License. Availability: The colamd/symamd library is available at http://www.cise.ufl.edu/research/sparse/colamd/ This is the http://www.cise.ufl.edu/research/sparse/colamd/colamdtestmex.c file. It requires the colamd.c and colamd.h files. */ /* ========================================================================== */ /* === Include files ======================================================== */ /* ========================================================================== */ #include "colamd.h" #include "mex.h" #include "matrix.h" #include #include #include "UFconfig.h" static void dump_matrix ( UF_long A [ ], UF_long p [ ], UF_long n_row, UF_long n_col, UF_long Alen, UF_long limit ) ; /* ========================================================================== */ /* === colamd mexFunction =================================================== */ /* ========================================================================== */ void mexFunction ( /* === Parameters ======================================================= */ int nlhs, /* number of left-hand sides */ mxArray *plhs [], /* left-hand side matrices */ int nrhs, /* number of right--hand sides */ const mxArray *prhs [] /* right-hand side matrices */ ) { /* === Local variables ================================================== */ UF_long *A ; /* colamd's copy of the matrix, and workspace */ UF_long *p ; /* colamd's copy of the column pointers */ UF_long Alen ; /* size of A */ UF_long n_col ; /* number of columns of A */ UF_long n_row ; /* number of rows of A */ UF_long nnz ; /* number of entries in A */ UF_long full ; /* TRUE if input matrix full, FALSE if sparse */ double knobs [COLAMD_KNOBS] ; /* colamd user-controllable parameters */ double *out_perm ; /* output permutation vector */ double *out_stats ; /* output stats vector */ double *in_knobs ; /* input knobs vector */ UF_long i ; /* loop counter */ mxArray *Ainput ; /* input matrix handle */ UF_long spumoni ; /* verbosity variable */ UF_long stats2 [COLAMD_STATS] ; /* stats for colamd */ UF_long *cp, *cp_end, result, col, length ; UF_long *stats ; stats = stats2 ; colamd_printf = mexPrintf ; /* COLAMD printf routine */ /* === Check inputs ===================================================== */ if (nrhs < 1 || nrhs > 2 || nlhs < 0 || nlhs > 2) { mexErrMsgTxt ( "colamd: incorrect number of input and/or output arguments") ; } if (nrhs != 2) { mexErrMsgTxt ("colamdtest: knobs are required") ; } /* for testing we require all 5 knobs */ if (mxGetNumberOfElements (prhs [1]) != 5) { mexErrMsgTxt ("colamd: must have all 5 knobs for testing") ; } /* === Get knobs ======================================================== */ colamd_l_set_defaults (knobs) ; spumoni = 0 ; /* check for user-passed knobs */ if (nrhs == 2) { in_knobs = mxGetPr (prhs [1]) ; i = mxGetNumberOfElements (prhs [1]) ; if (i > 0) knobs [COLAMD_DENSE_ROW] = in_knobs [0] ; if (i > 1) knobs [COLAMD_DENSE_COL] = in_knobs [1] ; if (i > 2) spumoni = (UF_long) in_knobs [2] ; } /* print knob settings if spumoni is set */ if (spumoni) { mexPrintf ("\ncolamd version %d.%d, %s:\n", COLAMD_MAIN_VERSION, COLAMD_SUB_VERSION, COLAMD_DATE) ; if (knobs [COLAMD_DENSE_ROW] >= 0) { mexPrintf ("knobs(1): %g, rows with > max(16,%g*sqrt(size(A,2)))" " entries removed\n", in_knobs [0], knobs [COLAMD_DENSE_ROW]) ; } else { mexPrintf ("knobs(1): %g, only completely dense rows removed\n", in_knobs [0]) ; } if (knobs [COLAMD_DENSE_COL] >= 0) { mexPrintf ("knobs(2): %g, cols with > max(16,%g*sqrt(min(size(A)))" " entries removed\n", in_knobs [1], knobs [COLAMD_DENSE_COL]) ; } else { mexPrintf ("knobs(2): %g, only completely dense columns removed\n", in_knobs [1]) ; } mexPrintf ("knobs(3): %g, statistics and knobs printed\n", in_knobs [2]) ; } /* === If A is full, convert to a sparse matrix ========================= */ Ainput = (mxArray *) prhs [0] ; if (mxGetNumberOfDimensions (Ainput) != 2) { mexErrMsgTxt ("colamd: input matrix must be 2-dimensional") ; } full = !mxIsSparse (Ainput) ; if (full) { mexCallMATLAB (1, &Ainput, 1, (mxArray **) prhs, "sparse") ; } /* === Allocate workspace for colamd ==================================== */ /* get size of matrix */ n_row = mxGetM (Ainput) ; n_col = mxGetN (Ainput) ; /* get column pointer vector so we can find nnz */ p = (UF_long *) mxCalloc (n_col+1, sizeof (UF_long)) ; (void) memcpy (p, mxGetJc (Ainput), (n_col+1)*sizeof (UF_long)) ; nnz = p [n_col] ; Alen = (UF_long) colamd_l_recommended (nnz, n_row, n_col) ; if (Alen == 0) { mexErrMsgTxt ("colamd: problem too large") ; } /* === Modify size of Alen if testing ======================================= */ /* knobs [3] amount of workspace given to colamd. < 0 : TIGHT memory > 0 : MIN + knob [3] - 1 == 0 : RECOMMENDED memory */ /* Here only for testing */ /* size of the Col and Row structures */ #define COLAMD_C(n_col) (((n_col) + 1) * 24 / sizeof (UF_long)) #define COLAMD_R(n_row) (((n_row) + 1) * 16 / sizeof (UF_long)) #ifdef MIN #undef MIN #endif #define MIN(a,b) (((a) < (b)) ? (a) : (b)) #define COLAMD_MIN_MEMORY(nnz,n_row,n_col) \ (2 * (nnz) + COLAMD_C (n_col) + COLAMD_R (n_row)) /* get knob [3], if negative */ if (in_knobs [3] < 0) { Alen = COLAMD_MIN_MEMORY (nnz, n_row, n_col) + n_col ; } else if (in_knobs [3] > 0) { Alen = COLAMD_MIN_MEMORY (nnz, n_row, n_col) + in_knobs [3] - 1 ; } /* otherwise, we use the recommended amount set above */ /* === Copy input matrix into workspace ================================= */ A = (UF_long *) mxCalloc (Alen, sizeof (UF_long)) ; (void) memcpy (A, mxGetIr (Ainput), nnz*sizeof (UF_long)) ; if (full) { mxDestroyArray (Ainput) ; } /* === Jumble matrix ======================================================== */ /* knobs [4] FOR TESTING ONLY: Specifies how to jumble matrix 0 : No jumbling 1 : Make n_row less than zero 2 : Make first pointer non-zero 3 : Make column pointers not non-decreasing 4 : Make a column pointer greater or equal to Alen 5 : Make row indices not strictly increasing 6 : Make a row index greater or equal to n_row 7 : Set A = NULL 8 : Set p = NULL 9 : Repeat row index 10: make row indices not sorted 11: jumble columns massively (note this changes the pattern of the matrix A.) 12: Set stats = NULL 13: Make n_col less than zero */ /* jumble appropriately */ switch ((UF_long) in_knobs [4]) { case 0 : if (spumoni > 0) { mexPrintf ("colamdtest: no errors expected\n") ; } result = 1 ; /* no errors */ break ; case 1 : if (spumoni > 0) { mexPrintf ("colamdtest: nrow out of range\n") ; } result = 0 ; /* nrow out of range */ n_row = -1 ; break ; case 2 : if (spumoni > 0) { mexPrintf ("colamdtest: p [0] nonzero\n") ; } result = 0 ; /* p [0] must be zero */ p [0] = 1 ; break ; case 3 : if (spumoni > 0) { mexPrintf ("colamdtest: negative length last column\n") ; } result = (n_col == 0) ; /* p must be monotonically inc. */ p [n_col] = p [0] ; break ; case 4 : if (spumoni > 0) { mexPrintf ("colamdtest: Alen too small\n") ; } result = 0 ; /* out of memory */ p [n_col] = Alen ; break ; case 5 : if (spumoni > 0) { mexPrintf ("colamdtest: row index out of range (-1)\n") ; } if (nnz > 0) /* row index out of range */ { result = 0 ; A [nnz-1] = -1 ; } else { if (spumoni > 0) { mexPrintf ("Note: no row indices to put out of range\n") ; } result = 1 ; } break ; case 6 : if (spumoni > 0) { mexPrintf ("colamdtest: row index out of range (n_row)\n") ; } if (nnz > 0) /* row index out of range */ { if (spumoni > 0) { mexPrintf ("Changing A[nnz-1] from %d to %d\n", A [nnz-1], n_row) ; } result = 0 ; A [nnz-1] = n_row ; } else { if (spumoni > 0) { mexPrintf ("Note: no row indices to put out of range\n") ; } result = 1 ; } break ; case 7 : if (spumoni > 0) { mexPrintf ("colamdtest: A not present\n") ; } result = 0 ; /* A not present */ A = (UF_long *) NULL ; break ; case 8 : if (spumoni > 0) { mexPrintf ("colamdtest: p not present\n") ; } result = 0 ; /* p not present */ p = (UF_long *) NULL ; break ; case 9 : if (spumoni > 0) { mexPrintf ("colamdtest: duplicate row index\n") ; } result = 1 ; /* duplicate row index */ for (col = 0 ; col < n_col ; col++) { length = p [col+1] - p [col] ; if (length > 1) { A [p [col]] = A [p [col] + 1] ; if (spumoni > 0) { mexPrintf ("Made duplicate row %d in col %d\n", A [p [col] + 1], col) ; } break ; } } if (spumoni > 1) { dump_matrix (A, p, n_row, n_col, Alen, col+2) ; } break ; case 10 : if (spumoni > 0) { mexPrintf ("colamdtest: unsorted column\n") ; } result = 1 ; /* jumbled columns */ for (col = 0 ; col < n_col ; col++) { length = p [col+1] - p [col] ; if (length > 1) { i = A[p [col]] ; A [p [col]] = A[p [col] + 1] ; A [p [col] + 1] = i ; if (spumoni > 0) { mexPrintf ("Unsorted column %d \n", col) ; } break ; } } if (spumoni > 1) { dump_matrix (A, p, n_row, n_col, Alen, col+2) ; } break ; case 11 : if (spumoni > 0) { mexPrintf ("colamdtest: massive jumbling\n") ; } result = 1 ; /* massive jumbling, but no errors */ srand (1) ; for (i = 0 ; i < n_col ; i++) { cp = &A [p [i]] ; cp_end = &A [p [i+1]] ; while (cp < cp_end) { *cp++ = rand() % n_row ; } } if (spumoni > 1) { dump_matrix (A, p, n_row, n_col, Alen, n_col) ; } break ; case 12 : if (spumoni > 0) { mexPrintf ("colamdtest: stats not present\n") ; } result = 0 ; /* stats not present */ stats = (UF_long *) NULL ; break ; case 13 : if (spumoni > 0) { mexPrintf ("colamdtest: ncol out of range\n") ; } result = 0 ; /* ncol out of range */ n_col = -1 ; break ; } /* === Order the columns (destroys A) =================================== */ if (!colamd_l (n_row, n_col, Alen, A, p, knobs, stats)) { /* return p = -1 if colamd failed */ plhs [0] = mxCreateDoubleMatrix (1, 1, mxREAL) ; out_perm = mxGetPr (plhs [0]) ; out_perm [0] = -1 ; mxFree (p) ; mxFree (A) ; if (spumoni > 0 || result) { colamd_l_report (stats) ; } if (result) { mexErrMsgTxt ("colamd should have returned TRUE\n") ; } return ; /* mexErrMsgTxt ("colamd error!") ; */ } if (!result) { colamd_l_report (stats) ; mexErrMsgTxt ("colamd should have returned FALSE\n") ; } mxFree (A) ; /* === Return the permutation vector ==================================== */ plhs [0] = mxCreateDoubleMatrix (1, n_col, mxREAL) ; out_perm = mxGetPr (plhs [0]) ; for (i = 0 ; i < n_col ; i++) { /* colamd is 0-based, but MATLAB expects this to be 1-based */ out_perm [i] = p [i] + 1 ; } mxFree (p) ; /* === Return the stats vector ========================================== */ /* print stats if spumoni > 0 */ if (spumoni > 0) { colamd_l_report (stats) ; } if (nlhs == 2) { plhs [1] = mxCreateDoubleMatrix (1, COLAMD_STATS, mxREAL) ; out_stats = mxGetPr (plhs [1]) ; for (i = 0 ; i < COLAMD_STATS ; i++) { out_stats [i] = stats [i] ; } /* fix stats (5) and (6), for 1-based information on jumbled matrix. */ /* note that this correction doesn't occur if symamd returns FALSE */ out_stats [COLAMD_INFO1] ++ ; out_stats [COLAMD_INFO2] ++ ; } } static void dump_matrix ( UF_long A [ ], UF_long p [ ], UF_long n_row, UF_long n_col, UF_long Alen, UF_long limit ) { UF_long col, k, row ; mexPrintf ("dump matrix: nrow %d ncol %d Alen %d\n", n_row, n_col, Alen) ; for (col = 0 ; col < MIN (n_col, limit) ; col++) { mexPrintf ("column %d, p[col] %d, p [col+1] %d, length %d\n", col, p [col], p [col+1], p [col+1] - p [col]) ; for (k = p [col] ; k < p [col+1] ; k++) { row = A [k] ; mexPrintf (" %d", row) ; } mexPrintf ("\n") ; } } SuiteSparse/COLAMD/MATLAB/symamd2.m0000644001170100242450000001052610620670500015400 0ustar davisfacfunction [p, stats] = symamd2 (S, knobs) %SYMAMD Symmetric approximate minimum degree permutation. % P = SYMAMD2(S) for a symmetric positive definite matrix S, returns the % permutation vector p such that S(p,p) tends to have a sparser Cholesky % factor than S. Sometimes SYMAMD works well for symmetric indefinite % matrices too. The matrix S is assumed to be symmetric; only the % strictly lower triangular part is referenced. S must be square. % Note that p = amd(S) is much faster and generates comparable orderings. % The ordering is followed by an elimination tree post-ordering. % % Note that this function is source code for the built-in MATLAB symamd % function. It has been renamed here to symamd2 to avoid a filename clash. % symamd and symamd2 are identical. % % See also SYMAMD, AMD, COLAMD, COLAMD2. % % Example: % P = symamd2 (S) % [P, stats] = symamd2 (S, knobs) % % knobs is an optional one- to two-element input vector. If S is n-by-n, % then rows and columns with more than max(16,knobs(1)*sqrt(n)) entries are % removed prior to ordering, and ordered last in the output permutation P. % No rows/columns are removed if knobs(1)<0. If knobs(2) is nonzero, stats % and knobs are printed. The default is knobs = [10 0]. Note that knobs % differs from earlier versions of symamd. % Copyright 1998-2007, Timothy A. Davis, and Stefan Larimore % Developed in collaboration with J. Gilbert and E. Ng. % Acknowledgements: This work was supported by the National Science % Foundation, under grants DMS-9504974 and DMS-9803599. %------------------------------------------------------------------------------- % perform the symamd ordering: %------------------------------------------------------------------------------- if (nargout <= 1 & nargin == 1) %#ok p = symamd2mex (S) ; elseif (nargout <= 1 & nargin == 2) %#ok p = symamd2mex (S, knobs) ; elseif (nargout == 2 & nargin == 1) %#ok [p, stats] = symamd2mex (S) ; elseif (nargout == 2 & nargin == 2) %#ok [p, stats] = symamd2mex (S, knobs) ; else error('symamd: incorrect number of input and/or output arguments.') ; end %------------------------------------------------------------------------------- % symmetric elimination tree post-ordering: %------------------------------------------------------------------------------- [ignore, q] = etree (S (p,p)) ; p = p (q) ; % stats is an optional 20-element output vector that provides data about the % ordering and the validity of the input matrix S. Ordering statistics are % in stats (1:3). stats (1) = stats (2) is the number of dense or empty % rows and columns ignored by SYMAMD and stats (3) is the number of % garbage collections performed on the internal data structure used by % SYMAMD (roughly of size 8.4*nnz(tril(S,-1)) + 9*n integers). % % MATLAB built-in functions are intended to generate valid sparse matrices, % with no duplicate entries, with ascending row indices of the nonzeros % in each column, with a non-negative number of entries in each column (!) % and so on. If a matrix is invalid, then SYMAMD may or may not be able % to continue. If there are duplicate entries (a row index appears two or % more times in the same column) or if the row indices in a column are out % of order, then SYMAMD can correct these errors by ignoring the duplicate % entries and sorting each column of its internal copy of the matrix S (the % input matrix S is not repaired, however). If a matrix is invalid in other % ways then SYMAMD cannot continue, an error message is printed, and no % output arguments (P or stats) are returned. SYMAMD is thus a simple way % to check a sparse matrix to see if it's valid. % % stats (4:7) provide information if SYMAMD was able to continue. The % matrix is OK if stats (4) is zero, or 1 if invalid. stats (5) is the % rightmost column index that is unsorted or contains duplicate entries, % or zero if no such column exists. stats (6) is the last seen duplicate % or out-of-order row index in the column index given by stats (5), or zero % if no such row index exists. stats (7) is the number of duplicate or % out-of-order row indices. % % stats (8:20) is always zero in the current version of SYMAMD (reserved % for future use). SuiteSparse/COLAMD/MATLAB/Contents.m0000644001170100242450000000132010620367666015631 0ustar davisfac% COLAMD, column approximate minimum degree ordering % % Primary: % colamd2 - Column approximate minimum degree permutation. % symamd2 - SYMAMD Symmetric approximate minimum degree permutation. % % helper and test functions: % colamd_demo - demo for colamd, column approx minimum degree ordering algorithm % colamd_make - compiles COLAMD2 and SYMAMD2 for MATLAB % colamd_make - compiles and installs COLAMD2 and SYMAMD2 for MATLAB % colamd_test - test colamd2 and symamd2 % luflops - compute the flop count for sparse LU factorization % % Example: % p = colamd2 (A) % % Copyright 1998-2007, Timothy A. Davis, and Stefan Larimore % Developed in collaboration with J. Gilbert and E. Ng. SuiteSparse/COLAMD/MATLAB/colamd_install.m0000644001170100242450000000106610620367611017016 0ustar davisfacfunction colamd_install %COLAMD_MAKE to compile and install the colamd2 and symamd2 mexFunction. % Your current directory must be COLAMD/MATLAB for this function to work. % % Example: % colamd_install % % See also colamd2, symamd2. % Copyright 1998-2007, Timothy A. Davis, and Stefan Larimore % Developed in collaboration with J. Gilbert and E. Ng. colamd_make addpath (pwd) fprintf ('\nThe following path has been added. You may wish to add it\n') ; fprintf ('permanently, using the MATLAB pathtool command.\n') ; fprintf ('%s\n\n', pwd) ; colamd_demo SuiteSparse/COLAMD/MATLAB/colamd_demo.m0000644001170100242450000001514210620367601016273 0ustar davisfac%COLAMD_DEMO demo for colamd, column approx minimum degree ordering algorithm % % Example: % colamd_demo % % The following m-files and mexFunctions provide alternative sparse matrix % ordering methods for MATLAB. They are typically faster (sometimes much % faster) and typically provide better orderings than their MATLAB counterparts: % % colamd a replacement for colmmd. % % Typical usage: p = colamd (A) ; % % symamd a replacement for symmmd. Based on colamd. % % Typical usage: p = symamd (A) ; % % For a description of the methods used, see the colamd.c file. % % http://www.cise.ufl.edu/research/sparse/colamd/ % % See also colamd, symamd % Minor changes: in MATLAB 7, symmmd and colmmd are flagged as "obsolete". % This demo checks if they exist, so it should still work when they are removed. % Copyright 1998-2007, Timothy A. Davis, and Stefan Larimore % Developed in collaboration with J. Gilbert and E. Ng. %------------------------------------------------------------------------------- % Print the introduction, the help info, and compile the mexFunctions %------------------------------------------------------------------------------- fprintf (1, '\n-----------------------------------------------------------\n') ; fprintf (1, 'Colamd2/symamd2 demo.') ; fprintf (1, '\n-----------------------------------------------------------\n') ; help colamd_demo ; fprintf (1, '\n-----------------------------------------------------------\n') ; fprintf (1, 'Colamd help information:') ; fprintf (1, '\n-----------------------------------------------------------\n') ; help colamd2 ; fprintf (1, '\n-----------------------------------------------------------\n') ; fprintf (1, 'Symamd help information:') ; fprintf (1, '\n-----------------------------------------------------------\n') ; help symamd2 ; %------------------------------------------------------------------------------- % Solving Ax=b %------------------------------------------------------------------------------- n = 100 ; fprintf (1, '\n-----------------------------------------------------------\n') ; fprintf (1, 'Solving Ax=b for a small %d-by-%d random matrix:', n, n) ; fprintf (1, '\n-----------------------------------------------------------\n') ; fprintf (1, '\nNote: Random sparse matrices are AWFUL test cases.\n') ; fprintf (1, 'They''re just easy to generate in a demo.\n') ; % set up the system rand ('state', 0) ; randn ('state', 0) ; spparms ('default') ; A = sprandn (n, n, 5/n) + speye (n) ; b = (1:n)' ; fprintf (1, '\n\nSolving via lu (PAQ = LU), where Q is from colamd2:\n') ; q = colamd2 (A) ; I = speye (n) ; Q = I (:, q) ; [L,U,P] = lu (A*Q) ; fl = luflops (L, U) ; x = Q * (U \ (L \ (P * b))) ; fprintf (1, '\nFlop count for [L,U,P] = lu (A*Q): %d\n', fl) ; fprintf (1, 'residual: %e\n', norm (A*x-b)); try fprintf (1, '\n\nSolving via lu (PAQ = LU), where Q is from colmmd:\n') ; q = colmmd (A) ; I = speye (n) ; Q = I (:, q) ; [L,U,P] = lu (A*Q) ; fl = luflops (L, U) ; x = Q * (U \ (L \ (P * b))) ; fprintf (1, '\nFlop count for [L,U,P] = lu (A*Q): %d\n', fl) ; fprintf (1, 'residual: %e\n', ... norm (A*x-b)) ; catch fprintf (1, 'colmmd is obsolete; test skipped\n') ; end fprintf (1, '\n\nSolving via lu (PA = LU), without regard for sparsity:\n') ; [L,U,P] = lu (A) ; fl = luflops (L, U) ; x = U \ (L \ (P * b)) ; fprintf (1, '\nFlop count for [L,U,P] = lu (A*Q): %d\n', fl) ; fprintf (1, 'residual: %e\n', norm (A*x-b)); %------------------------------------------------------------------------------- % Large demo for colamd2 %------------------------------------------------------------------------------- fprintf (1, '\n-----------------------------------------------------------\n') ; fprintf (1, 'Large demo for colamd2 (symbolic analysis only):') ; fprintf (1, '\n-----------------------------------------------------------\n') ; rand ('state', 0) ; randn ('state', 0) ; spparms ('default') ; n = 1000 ; fprintf (1, 'Generating a random %d-by-%d sparse matrix.\n', n, n) ; A = sprandn (n, n, 5/n) + speye (n) ; fprintf (1, '\n\nUnordered matrix:\n') ; lnz = symbfact (A, 'col') ; fprintf (1, 'nz in Cholesky factors of A''A: %d\n', sum (lnz)) ; fprintf (1, 'flop count for Cholesky of A''A: %d\n', sum (lnz.^2)) ; tic ; p = colamd2 (A) ; t = toc ; lnz = symbfact (A (:,p), 'col') ; fprintf (1, '\n\nColamd run time: %f\n', t) ; fprintf (1, 'colamd2 ordering quality: \n') ; fprintf (1, 'nz in Cholesky factors of A(:,p)''A(:,p): %d\n', sum (lnz)) ; fprintf (1, 'flop count for Cholesky of A(:,p)''A(:,p): %d\n', sum (lnz.^2)) ; try tic ; p = colmmd (A) ; t = toc ; lnz = symbfact (A (:,p), 'col') ; fprintf (1, '\n\nColmmd run time: %f\n', t) ; fprintf (1, 'colmmd ordering quality: \n') ; fprintf (1, 'nz in Cholesky factors of A(:,p)''A(:,p): %d\n', sum (lnz)) ; fprintf (1, 'flop count for Cholesky of A(:,p)''A(:,p): %d\n', ... sum (lnz.^2)) ; catch fprintf (1, 'colmmd is obsolete; test skipped\n') ; end %------------------------------------------------------------------------------- % Large demo for symamd2 %------------------------------------------------------------------------------- fprintf (1, '\n-----------------------------------------------------------\n') ; fprintf (1, 'Large demo for symamd2 (symbolic analysis only):') ; fprintf (1, '\n-----------------------------------------------------------\n') ; fprintf (1, 'Generating a random symmetric %d-by-%d sparse matrix.\n', n, n) ; A = A+A' ; fprintf (1, '\n\nUnordered matrix:\n') ; lnz = symbfact (A, 'sym') ; fprintf (1, 'nz in Cholesky factors of A: %d\n', sum (lnz)) ; fprintf (1, 'flop count for Cholesky of A: %d\n', sum (lnz.^2)) ; tic ; p = symamd2 (A) ; t = toc ; lnz = symbfact (A (p,p), 'sym') ; fprintf (1, '\n\nSymamd run time: %f\n', t) ; fprintf (1, 'symamd2 ordering quality: \n') ; fprintf (1, 'nz in Cholesky factors of A(p,p): %d\n', sum (lnz)) ; fprintf (1, 'flop count for Cholesky of A(p,p): %d\n', sum (lnz.^2)) ; try tic ; p = symmmd (A) ; t = toc ; lnz = symbfact (A (p,p), 'sym') ; fprintf (1, '\n\nSymmmd run time: %f\n', t) ; fprintf (1, 'symmmd ordering quality: \n') ; fprintf (1, 'nz in Cholesky factors of A(p,p): %d\n', sum (lnz)) ; fprintf (1, 'flop count for Cholesky of A(p,p): %d\n', sum (lnz.^2)) ; catch fprintf (1, 'symmmd is obsolete\n') ; end SuiteSparse/COLAMD/MATLAB/colamd2.m0000644001170100242450000001052410620670472015353 0ustar davisfacfunction [p,stats] = colamd2 (S, knobs) %COLAMD2 Column approximate minimum degree permutation. % P = COLAMD2(S) returns the column approximate minimum degree permutation % vector for the sparse matrix S. For a non-symmetric matrix S, S(:,P) % tends to have sparser LU factors than S. The Cholesky factorization of % S(:,P)'*S(:,P) also tends to be sparser than that of S'*S. The ordering % is followed by a column elimination tree post-ordering. % % Note that this function is the source code for the built-in MATLAB colamd % function. It has been renamed here to colamd2 to avoid a filename clash. % colamd and colamd2 are identical. % % See also COLAMD, AMD, SYMAMD, SYMAMD2. % % Example: % P = colamd2 (S) % [P, stats] = colamd2 (S, knobs) % % knobs is an optional one- to three-element input vector. If S is m-by-n, % then rows with more than max(16,knobs(1)*sqrt(n)) entries are ignored. % Columns with more than max(16,knobs(2)*sqrt(min(m,n))) entries are % removed prior to ordering, and ordered last in the output permutation P. % Only completely dense rows or columns are removed if knobs(1) and knobs(2) % are < 0, respectively. If knobs(3) is nonzero, stats and knobs are % printed. The default is knobs = [10 10 0]. Note that knobs differs from % earlier versions of colamd. % Copyright 1998-2007, Timothy A. Davis, and Stefan Larimore % Developed in collaboration with J. Gilbert and E. Ng. % % Acknowledgements: This work was supported by the National Science % Foundation, under grants DMS-9504974 and DMS-9803599. %------------------------------------------------------------------------------- % Perform the colamd ordering: %------------------------------------------------------------------------------- if (nargout <= 1 & nargin == 1) %#ok p = colamd2mex (S) ; elseif (nargout <= 1 & nargin == 2) %#ok p = colamd2mex (S, knobs) ; elseif (nargout == 2 & nargin == 1) %#ok [p, stats] = colamd2mex (S) ; elseif (nargout == 2 & nargin == 2) %#ok [p, stats] = colamd2mex (S, knobs) ; else error ('colamd: incorrect number of input and/or output arguments') ; end %------------------------------------------------------------------------------- % column elimination tree post-ordering: %------------------------------------------------------------------------------- [ignore, q] = etree (S (:,p), 'col') ; p = p (q) ; % stats is an optional 20-element output vector that provides data about the % ordering and the validity of the input matrix S. Ordering statistics are % in stats (1:3). stats (1) and stats (2) are the number of dense or empty % rows and columns ignored by COLAMD and stats (3) is the number of % garbage collections performed on the internal data structure used by % COLAMD (roughly of size 2.2*nnz(S) + 4*m + 7*n integers). % % MATLAB built-in functions are intended to generate valid sparse matrices, % with no duplicate entries, with ascending row indices of the nonzeros % in each column, with a non-negative number of entries in each column (!) % and so on. If a matrix is invalid, then COLAMD may or may not be able % to continue. If there are duplicate entries (a row index appears two or % more times in the same column) or if the row indices in a column are out % of order, then COLAMD can correct these errors by ignoring the duplicate % entries and sorting each column of its internal copy of the matrix S (the % input matrix S is not repaired, however). If a matrix is invalid in other % ways then COLAMD cannot continue, an error message is printed, and no % output arguments (P or stats) are returned. COLAMD is thus a simple way % to check a sparse matrix to see if it's valid. % % stats (4:7) provide information if COLAMD was able to continue. The % matrix is OK if stats (4) is zero, or 1 if invalid. stats (5) is the % rightmost column index that is unsorted or contains duplicate entries, % or zero if no such column exists. stats (6) is the last seen duplicate % or out-of-order row index in the column index given by stats (5), or zero % if no such row index exists. stats (7) is the number of duplicate or % out-of-order row indices. % % stats (8:20) is always zero in the current version of COLAMD (reserved % for future use). SuiteSparse/COLAMD/MATLAB/symamdmex.c0000644001170100242450000001376110616374605016036 0ustar davisfac/* ========================================================================== */ /* === symamd mexFunction =================================================== */ /* ========================================================================== */ /* SYMAMD mexFunction Usage: P = symamd2 (A) ; [ P, stats ] = symamd2 (A, knobs) ; See symamd.m for a description. Authors: The authors of the code itself are Stefan I. Larimore and Timothy A. Davis (davis at cise.ufl.edu), University of Florida. The algorithm was developed in collaboration with John Gilbert, Xerox PARC, and Esmond Ng, Oak Ridge National Laboratory. Acknowledgements: This work was supported by the National Science Foundation, under grants DMS-9504974 and DMS-9803599. Notice: Copyright (c) 1998-2007, Timothy A. Davis. All Rights Reserved. See http://www.cise.ufl.edu/research/sparse/colamd (the colamd.c file) for the License. Availability: The colamd/symamd library is available at http://www.cise.ufl.edu/research/sparse/colamd/ This is the http://www.cise.ufl.edu/research/sparse/colamd/symamdmex.c file. It requires the colamd.c and colamd.h files. */ /* ========================================================================== */ /* === Include files ======================================================== */ /* ========================================================================== */ #include "colamd.h" #include "mex.h" #include "matrix.h" #include #include "UFconfig.h" /* ========================================================================== */ /* === symamd mexFunction =================================================== */ /* ========================================================================== */ void mexFunction ( /* === Parameters ======================================================= */ int nlhs, /* number of left-hand sides */ mxArray *plhs [], /* left-hand side matrices */ int nrhs, /* number of right--hand sides */ const mxArray *prhs [] /* right-hand side matrices */ ) { /* === Local variables ================================================== */ UF_long *perm ; /* column ordering of M and ordering of A */ UF_long *A ; /* row indices of input matrix A */ UF_long *p ; /* column pointers of input matrix A */ UF_long n_col ; /* number of columns of A */ UF_long n_row ; /* number of rows of A */ UF_long full ; /* TRUE if input matrix full, FALSE if sparse */ double knobs [COLAMD_KNOBS] ; /* colamd user-controllable parameters */ double *out_perm ; /* output permutation vector */ double *out_stats ; /* output stats vector */ double *in_knobs ; /* input knobs vector */ UF_long i ; /* loop counter */ mxArray *Ainput ; /* input matrix handle */ UF_long spumoni ; /* verbosity variable */ UF_long stats [COLAMD_STATS] ; /* stats for symamd */ colamd_printf = mexPrintf ; /* COLAMD printf routine */ /* === Check inputs ===================================================== */ if (nrhs < 1 || nrhs > 2 || nlhs < 0 || nlhs > 2) { mexErrMsgTxt ( "symamd: incorrect number of input and/or output arguments.") ; } /* === Get knobs ======================================================== */ colamd_l_set_defaults (knobs) ; spumoni = 0 ; /* check for user-passed knobs */ if (nrhs == 2) { in_knobs = mxGetPr (prhs [1]) ; i = mxGetNumberOfElements (prhs [1]) ; if (i > 0) knobs [COLAMD_DENSE_ROW] = in_knobs [0] ; if (i > 1) spumoni = (UF_long) (in_knobs [1] != 0) ; } /* print knob settings if spumoni is set */ if (spumoni) { mexPrintf ("\nsymamd version %d.%d, %s:\n", COLAMD_MAIN_VERSION, COLAMD_SUB_VERSION, COLAMD_DATE) ; if (knobs [COLAMD_DENSE_ROW] >= 0) { mexPrintf ("knobs(1): %g, rows/cols with > " "max(16,%g*sqrt(size(A,2))) entries removed\n", in_knobs [0], knobs [COLAMD_DENSE_ROW]) ; } else { mexPrintf ("knobs(1): %g, no dense rows removed\n", in_knobs [0]) ; } mexPrintf ("knobs(2): %g, statistics and knobs printed\n", in_knobs [1]) ; } /* === If A is full, convert to a sparse matrix ========================= */ Ainput = (mxArray *) prhs [0] ; if (mxGetNumberOfDimensions (Ainput) != 2) { mexErrMsgTxt ("symamd: input matrix must be 2-dimensional.") ; } full = !mxIsSparse (Ainput) ; if (full) { mexCallMATLAB (1, &Ainput, 1, (mxArray **) prhs, "sparse") ; } /* === Allocate workspace for symamd ==================================== */ /* get size of matrix */ n_row = mxGetM (Ainput) ; n_col = mxGetN (Ainput) ; if (n_col != n_row) { mexErrMsgTxt ("symamd: matrix must be square.") ; } A = (UF_long *) mxGetIr (Ainput) ; p = (UF_long *) mxGetJc (Ainput) ; perm = (UF_long *) mxCalloc (n_col+1, sizeof (UF_long)) ; /* === Order the rows and columns of A (does not destroy A) ============= */ if (!symamd_l (n_col, A, p, perm, knobs, stats, &mxCalloc, &mxFree)) { symamd_l_report (stats) ; mexErrMsgTxt ("symamd error!") ; } if (full) { mxDestroyArray (Ainput) ; } /* === Return the permutation vector ==================================== */ plhs [0] = mxCreateDoubleMatrix (1, n_col, mxREAL) ; out_perm = mxGetPr (plhs [0]) ; for (i = 0 ; i < n_col ; i++) { /* symamd is 0-based, but MATLAB expects this to be 1-based */ out_perm [i] = perm [i] + 1 ; } mxFree (perm) ; /* === Return the stats vector ========================================== */ /* print stats if spumoni is set */ if (spumoni) { symamd_l_report (stats) ; } if (nlhs == 2) { plhs [1] = mxCreateDoubleMatrix (1, COLAMD_STATS, mxREAL) ; out_stats = mxGetPr (plhs [1]) ; for (i = 0 ; i < COLAMD_STATS ; i++) { out_stats [i] = stats [i] ; } /* fix stats (5) and (6), for 1-based information on jumbled matrix. */ /* note that this correction doesn't occur if symamd returns FALSE */ out_stats [COLAMD_INFO1] ++ ; out_stats [COLAMD_INFO2] ++ ; } } SuiteSparse/COLAMD/MATLAB/luflops.m0000644001170100242450000000272410620367702015520 0ustar davisfacfunction fl = luflops (L, U) %LUFLOPS compute the flop count for sparse LU factorization % % Example: % fl = luflops (L,U) % % Given a sparse LU factorization (L and U), return the flop count required % by a conventional LU factorization algorithm to compute it. L and U can % be either sparse or full matrices. L must be lower triangular and U must % be upper triangular. Do not attempt to use this on the permuted L from % [L,U] = lu (A). Instead, use [L,U,P] = lu (A) or [L,U,P,Q] = lu (A). % % Note that there is a subtle undercount in this estimate. Suppose A is % completely dense, but during LU factorization exact cancellation occurs, % causing some of the entries in L and U to become identically zero. The % flop count returned by this routine is an undercount. There is a simple % way to fix this (L = spones (L) + spones (tril (A))), but the fix is partial. % It can also occur that some entry in L is a "symbolic" fill-in (zero in % A, but a fill-in entry and thus must be computed), but numerically % zero. The only way to get a reliable LU factorization would be to do a % purely symbolic factorization of A. This cannot be done with % symbfact (A, 'col'). % % See NA Digest, Vol 00, #50, Tuesday, Dec. 5, 2000 % % See also symbfact % Copyright 1998-2007, Timothy A. Davis Lnz = full (sum (spones (L))) - 1 ; % off diagonal nz in cols of L Unz = full (sum (spones (U')))' - 1 ; % off diagonal nz in rows of U fl = 2*Lnz*Unz + sum (Lnz) ; SuiteSparse/COLAMD/MATLAB/colamd_make.m0000644001170100242450000000142710620367650016271 0ustar davisfacfunction colamd_make %COLAMD_MAKE compiles COLAMD2 and SYMAMD2 for MATLAB % % Example: % colamd_make % % See also colamd, symamd % Copyright 1998-2007, Timothy A. Davis, and Stefan Larimore % Developed in collaboration with J. Gilbert and E. Ng. details = 0 ; % 1 if details of each command are to be printed d = '' ; if (~isempty (strfind (computer, '64'))) d = '-largeArrayDims' ; end src = '../Source/colamd.c ../Source/colamd_global.c' ; cmd = sprintf ('mex -DDLONG -O %s -I../../UFconfig -I../Include -output ', d) ; s = [cmd 'colamd2mex colamdmex.c ' src] ; if (details) fprintf ('%s\n', s) ; end eval (s) ; s = [cmd 'symamd2mex symamdmex.c ' src] ; if (details) fprintf ('%s\n', s) ; end eval (s) ; fprintf ('COLAMD2 and SYMAMD2 successfully compiled.\n') ; SuiteSparse/COLAMD/Include/0000755001170100242450000000000010617102731014267 5ustar davisfacSuiteSparse/COLAMD/Include/colamd.h0000644001170100242450000002073110711427105015702 0ustar davisfac/* ========================================================================== */ /* === colamd/symamd prototypes and definitions ============================= */ /* ========================================================================== */ /* COLAMD / SYMAMD include file You must include this file (colamd.h) in any routine that uses colamd, symamd, or the related macros and definitions. Authors: The authors of the code itself are Stefan I. Larimore and Timothy A. Davis (davis at cise.ufl.edu), University of Florida. The algorithm was developed in collaboration with John Gilbert, Xerox PARC, and Esmond Ng, Oak Ridge National Laboratory. Acknowledgements: This work was supported by the National Science Foundation, under grants DMS-9504974 and DMS-9803599. Notice: Copyright (c) 1998-2007, Timothy A. Davis, All Rights Reserved. THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. Permission is hereby granted to use, copy, modify, and/or distribute this program, provided that the Copyright, this License, and the Availability of the original version is retained on all copies and made accessible to the end-user of any code or package that includes COLAMD or any modified version of COLAMD. Availability: The colamd/symamd library is available at http://www.cise.ufl.edu/research/sparse/colamd/ This is the http://www.cise.ufl.edu/research/sparse/colamd/colamd.h file. It is required by the colamd.c, colamdmex.c, and symamdmex.c files, and by any C code that calls the routines whose prototypes are listed below, or that uses the colamd/symamd definitions listed below. */ #ifndef COLAMD_H #define COLAMD_H /* make it easy for C++ programs to include COLAMD */ #ifdef __cplusplus extern "C" { #endif /* ========================================================================== */ /* === Include files ======================================================== */ /* ========================================================================== */ #include /* ========================================================================== */ /* === COLAMD version ======================================================= */ /* ========================================================================== */ /* COLAMD Version 2.4 and later will include the following definitions. * As an example, to test if the version you are using is 2.4 or later: * * #ifdef COLAMD_VERSION * if (COLAMD_VERSION >= COLAMD_VERSION_CODE (2,4)) ... * #endif * * This also works during compile-time: * * #if defined(COLAMD_VERSION) && (COLAMD_VERSION >= COLAMD_VERSION_CODE (2,4)) * printf ("This is version 2.4 or later\n") ; * #else * printf ("This is an early version\n") ; * #endif * * Versions 2.3 and earlier of COLAMD do not include a #define'd version number. */ #define COLAMD_DATE "Nov 1, 2007" #define COLAMD_VERSION_CODE(main,sub) ((main) * 1000 + (sub)) #define COLAMD_MAIN_VERSION 2 #define COLAMD_SUB_VERSION 7 #define COLAMD_SUBSUB_VERSION 1 #define COLAMD_VERSION \ COLAMD_VERSION_CODE(COLAMD_MAIN_VERSION,COLAMD_SUB_VERSION) /* ========================================================================== */ /* === Knob and statistics definitions ====================================== */ /* ========================================================================== */ /* size of the knobs [ ] array. Only knobs [0..1] are currently used. */ #define COLAMD_KNOBS 20 /* number of output statistics. Only stats [0..6] are currently used. */ #define COLAMD_STATS 20 /* knobs [0] and stats [0]: dense row knob and output statistic. */ #define COLAMD_DENSE_ROW 0 /* knobs [1] and stats [1]: dense column knob and output statistic. */ #define COLAMD_DENSE_COL 1 /* knobs [2]: aggressive absorption */ #define COLAMD_AGGRESSIVE 2 /* stats [2]: memory defragmentation count output statistic */ #define COLAMD_DEFRAG_COUNT 2 /* stats [3]: colamd status: zero OK, > 0 warning or notice, < 0 error */ #define COLAMD_STATUS 3 /* stats [4..6]: error info, or info on jumbled columns */ #define COLAMD_INFO1 4 #define COLAMD_INFO2 5 #define COLAMD_INFO3 6 /* error codes returned in stats [3]: */ #define COLAMD_OK (0) #define COLAMD_OK_BUT_JUMBLED (1) #define COLAMD_ERROR_A_not_present (-1) #define COLAMD_ERROR_p_not_present (-2) #define COLAMD_ERROR_nrow_negative (-3) #define COLAMD_ERROR_ncol_negative (-4) #define COLAMD_ERROR_nnz_negative (-5) #define COLAMD_ERROR_p0_nonzero (-6) #define COLAMD_ERROR_A_too_small (-7) #define COLAMD_ERROR_col_length_negative (-8) #define COLAMD_ERROR_row_index_out_of_bounds (-9) #define COLAMD_ERROR_out_of_memory (-10) #define COLAMD_ERROR_internal_error (-999) /* ========================================================================== */ /* === Prototypes of user-callable routines ================================= */ /* ========================================================================== */ /* define UF_long */ #include "UFconfig.h" size_t colamd_recommended /* returns recommended value of Alen, */ /* or 0 if input arguments are erroneous */ ( int nnz, /* nonzeros in A */ int n_row, /* number of rows in A */ int n_col /* number of columns in A */ ) ; size_t colamd_l_recommended /* returns recommended value of Alen, */ /* or 0 if input arguments are erroneous */ ( UF_long nnz, /* nonzeros in A */ UF_long n_row, /* number of rows in A */ UF_long n_col /* number of columns in A */ ) ; void colamd_set_defaults /* sets default parameters */ ( /* knobs argument is modified on output */ double knobs [COLAMD_KNOBS] /* parameter settings for colamd */ ) ; void colamd_l_set_defaults /* sets default parameters */ ( /* knobs argument is modified on output */ double knobs [COLAMD_KNOBS] /* parameter settings for colamd */ ) ; int colamd /* returns (1) if successful, (0) otherwise*/ ( /* A and p arguments are modified on output */ int n_row, /* number of rows in A */ int n_col, /* number of columns in A */ int Alen, /* size of the array A */ int A [], /* row indices of A, of size Alen */ int p [], /* column pointers of A, of size n_col+1 */ double knobs [COLAMD_KNOBS],/* parameter settings for colamd */ int stats [COLAMD_STATS] /* colamd output statistics and error codes */ ) ; UF_long colamd_l /* returns (1) if successful, (0) otherwise*/ ( /* A and p arguments are modified on output */ UF_long n_row, /* number of rows in A */ UF_long n_col, /* number of columns in A */ UF_long Alen, /* size of the array A */ UF_long A [], /* row indices of A, of size Alen */ UF_long p [], /* column pointers of A, of size n_col+1 */ double knobs [COLAMD_KNOBS],/* parameter settings for colamd */ UF_long stats [COLAMD_STATS]/* colamd output statistics and error codes */ ) ; int symamd /* return (1) if OK, (0) otherwise */ ( int n, /* number of rows and columns of A */ int A [], /* row indices of A */ int p [], /* column pointers of A */ int perm [], /* output permutation, size n_col+1 */ double knobs [COLAMD_KNOBS], /* parameters (uses defaults if NULL) */ int stats [COLAMD_STATS], /* output statistics and error codes */ void * (*allocate) (size_t, size_t), /* pointer to calloc (ANSI C) or */ /* mxCalloc (for MATLAB mexFunction) */ void (*release) (void *) /* pointer to free (ANSI C) or */ /* mxFree (for MATLAB mexFunction) */ ) ; UF_long symamd_l /* return (1) if OK, (0) otherwise */ ( UF_long n, /* number of rows and columns of A */ UF_long A [], /* row indices of A */ UF_long p [], /* column pointers of A */ UF_long perm [], /* output permutation, size n_col+1 */ double knobs [COLAMD_KNOBS], /* parameters (uses defaults if NULL) */ UF_long stats [COLAMD_STATS], /* output statistics and error codes */ void * (*allocate) (size_t, size_t), /* pointer to calloc (ANSI C) or */ /* mxCalloc (for MATLAB mexFunction) */ void (*release) (void *) /* pointer to free (ANSI C) or */ /* mxFree (for MATLAB mexFunction) */ ) ; void colamd_report ( int stats [COLAMD_STATS] ) ; void colamd_l_report ( UF_long stats [COLAMD_STATS] ) ; void symamd_report ( int stats [COLAMD_STATS] ) ; void symamd_l_report ( UF_long stats [COLAMD_STATS] ) ; #ifndef EXTERN #define EXTERN extern #endif EXTERN int (*colamd_printf) (const char *, ...) ; #ifdef __cplusplus } #endif #endif /* COLAMD_H */ SuiteSparse/COLAMD/Source/0000755001170100242450000000000010617104442014145 5ustar davisfacSuiteSparse/COLAMD/Source/colamd_global.c0000644001170100242450000000155710616374354017112 0ustar davisfac/* ========================================================================== */ /* === colamd_global.c ====================================================== */ /* ========================================================================== */ /* ---------------------------------------------------------------------------- * COLAMD, Copyright (C) 2007, Timothy A. Davis. * See License.txt for the Version 2.1 of the GNU Lesser General Public License * http://www.cise.ufl.edu/research/sparse * -------------------------------------------------------------------------- */ /* Global variables for COLAMD */ #ifndef NPRINT #ifdef MATLAB_MEX_FILE #include "mex.h" int (*colamd_printf) (const char *, ...) = mexPrintf ; #else #include int (*colamd_printf) (const char *, ...) = printf ; #endif #else int (*colamd_printf) (const char *, ...) = ((void *) 0) ; #endif SuiteSparse/COLAMD/Source/colamd.c0000644001170100242450000032304610616374311015563 0ustar davisfac/* ========================================================================== */ /* === colamd/symamd - a sparse matrix column ordering algorithm ============ */ /* ========================================================================== */ /* COLAMD / SYMAMD colamd: an approximate minimum degree column ordering algorithm, for LU factorization of symmetric or unsymmetric matrices, QR factorization, least squares, interior point methods for linear programming problems, and other related problems. symamd: an approximate minimum degree ordering algorithm for Cholesky factorization of symmetric matrices. Purpose: Colamd computes a permutation Q such that the Cholesky factorization of (AQ)'(AQ) has less fill-in and requires fewer floating point operations than A'A. This also provides a good ordering for sparse partial pivoting methods, P(AQ) = LU, where Q is computed prior to numerical factorization, and P is computed during numerical factorization via conventional partial pivoting with row interchanges. Colamd is the column ordering method used in SuperLU, part of the ScaLAPACK library. It is also available as built-in function in MATLAB Version 6, available from MathWorks, Inc. (http://www.mathworks.com). This routine can be used in place of colmmd in MATLAB. Symamd computes a permutation P of a symmetric matrix A such that the Cholesky factorization of PAP' has less fill-in and requires fewer floating point operations than A. Symamd constructs a matrix M such that M'M has the same nonzero pattern of A, and then orders the columns of M using colmmd. The column ordering of M is then returned as the row and column ordering P of A. Authors: The authors of the code itself are Stefan I. Larimore and Timothy A. Davis (davis at cise.ufl.edu), University of Florida. The algorithm was developed in collaboration with John Gilbert, Xerox PARC, and Esmond Ng, Oak Ridge National Laboratory. Acknowledgements: This work was supported by the National Science Foundation, under grants DMS-9504974 and DMS-9803599. Copyright and License: Copyright (c) 1998-2007, Timothy A. Davis, All Rights Reserved. COLAMD is also available under alternate licenses, contact T. Davis for details. This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Permission is hereby granted to use or copy this program under the terms of the GNU LGPL, provided that the Copyright, this License, and the Availability of the original version is retained on all copies. User documentation of any code that uses this code or any modified version of this code must cite the Copyright, this License, the Availability note, and "Used by permission." Permission to modify the code and to distribute modified code is granted, provided the Copyright, this License, and the Availability note are retained, and a notice that the code was modified is included. Availability: The colamd/symamd library is available at http://www.cise.ufl.edu/research/sparse/colamd/ This is the http://www.cise.ufl.edu/research/sparse/colamd/colamd.c file. It requires the colamd.h file. It is required by the colamdmex.c and symamdmex.c files, for the MATLAB interface to colamd and symamd. Appears as ACM Algorithm 836. See the ChangeLog file for changes since Version 1.0. References: T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, An approximate column minimum degree ordering algorithm, ACM Transactions on Mathematical Software, vol. 30, no. 3., pp. 353-376, 2004. T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, Algorithm 836: COLAMD, an approximate column minimum degree ordering algorithm, ACM Transactions on Mathematical Software, vol. 30, no. 3., pp. 377-380, 2004. */ /* ========================================================================== */ /* === Description of user-callable routines ================================ */ /* ========================================================================== */ /* COLAMD includes both int and UF_long versions of all its routines. The * description below is for the int version. For UF_long, all int arguments * become UF_long. UF_long is normally defined as long, except for WIN64. ---------------------------------------------------------------------------- colamd_recommended: ---------------------------------------------------------------------------- C syntax: #include "colamd.h" size_t colamd_recommended (int nnz, int n_row, int n_col) ; size_t colamd_l_recommended (UF_long nnz, UF_long n_row, UF_long n_col) ; Purpose: Returns recommended value of Alen for use by colamd. Returns 0 if any input argument is negative. The use of this routine is optional. Not needed for symamd, which dynamically allocates its own memory. Note that in v2.4 and earlier, these routines returned int or long. They now return a value of type size_t. Arguments (all input arguments): int nnz ; Number of nonzeros in the matrix A. This must be the same value as p [n_col] in the call to colamd - otherwise you will get a wrong value of the recommended memory to use. int n_row ; Number of rows in the matrix A. int n_col ; Number of columns in the matrix A. ---------------------------------------------------------------------------- colamd_set_defaults: ---------------------------------------------------------------------------- C syntax: #include "colamd.h" colamd_set_defaults (double knobs [COLAMD_KNOBS]) ; colamd_l_set_defaults (double knobs [COLAMD_KNOBS]) ; Purpose: Sets the default parameters. The use of this routine is optional. Arguments: double knobs [COLAMD_KNOBS] ; Output only. NOTE: the meaning of the dense row/col knobs has changed in v2.4 knobs [0] and knobs [1] control dense row and col detection: Colamd: rows with more than max (16, knobs [COLAMD_DENSE_ROW] * sqrt (n_col)) entries are removed prior to ordering. Columns with more than max (16, knobs [COLAMD_DENSE_COL] * sqrt (MIN (n_row,n_col))) entries are removed prior to ordering, and placed last in the output column ordering. Symamd: uses only knobs [COLAMD_DENSE_ROW], which is knobs [0]. Rows and columns with more than max (16, knobs [COLAMD_DENSE_ROW] * sqrt (n)) entries are removed prior to ordering, and placed last in the output ordering. COLAMD_DENSE_ROW and COLAMD_DENSE_COL are defined as 0 and 1, respectively, in colamd.h. Default values of these two knobs are both 10. Currently, only knobs [0] and knobs [1] are used, but future versions may use more knobs. If so, they will be properly set to their defaults by the future version of colamd_set_defaults, so that the code that calls colamd will not need to change, assuming that you either use colamd_set_defaults, or pass a (double *) NULL pointer as the knobs array to colamd or symamd. knobs [2]: aggressive absorption knobs [COLAMD_AGGRESSIVE] controls whether or not to do aggressive absorption during the ordering. Default is TRUE. ---------------------------------------------------------------------------- colamd: ---------------------------------------------------------------------------- C syntax: #include "colamd.h" int colamd (int n_row, int n_col, int Alen, int *A, int *p, double knobs [COLAMD_KNOBS], int stats [COLAMD_STATS]) ; UF_long colamd_l (UF_long n_row, UF_long n_col, UF_long Alen, UF_long *A, UF_long *p, double knobs [COLAMD_KNOBS], UF_long stats [COLAMD_STATS]) ; Purpose: Computes a column ordering (Q) of A such that P(AQ)=LU or (AQ)'AQ=LL' have less fill-in and require fewer floating point operations than factorizing the unpermuted matrix A or A'A, respectively. Returns: TRUE (1) if successful, FALSE (0) otherwise. Arguments: int n_row ; Input argument. Number of rows in the matrix A. Restriction: n_row >= 0. Colamd returns FALSE if n_row is negative. int n_col ; Input argument. Number of columns in the matrix A. Restriction: n_col >= 0. Colamd returns FALSE if n_col is negative. int Alen ; Input argument. Restriction (see note): Alen >= 2*nnz + 6*(n_col+1) + 4*(n_row+1) + n_col Colamd returns FALSE if these conditions are not met. Note: this restriction makes an modest assumption regarding the size of the two typedef's structures in colamd.h. We do, however, guarantee that Alen >= colamd_recommended (nnz, n_row, n_col) will be sufficient. Note: the macro version does not check for integer overflow, and thus is not recommended. Use the colamd_recommended routine instead. int A [Alen] ; Input argument, undefined on output. A is an integer array of size Alen. Alen must be at least as large as the bare minimum value given above, but this is very low, and can result in excessive run time. For best performance, we recommend that Alen be greater than or equal to colamd_recommended (nnz, n_row, n_col), which adds nnz/5 to the bare minimum value given above. On input, the row indices of the entries in column c of the matrix are held in A [(p [c]) ... (p [c+1]-1)]. The row indices in a given column c need not be in ascending order, and duplicate row indices may be be present. However, colamd will work a little faster if both of these conditions are met (Colamd puts the matrix into this format, if it finds that the the conditions are not met). The matrix is 0-based. That is, rows are in the range 0 to n_row-1, and columns are in the range 0 to n_col-1. Colamd returns FALSE if any row index is out of range. The contents of A are modified during ordering, and are undefined on output. int p [n_col+1] ; Both input and output argument. p is an integer array of size n_col+1. On input, it holds the "pointers" for the column form of the matrix A. Column c of the matrix A is held in A [(p [c]) ... (p [c+1]-1)]. The first entry, p [0], must be zero, and p [c] <= p [c+1] must hold for all c in the range 0 to n_col-1. The value p [n_col] is thus the total number of entries in the pattern of the matrix A. Colamd returns FALSE if these conditions are not met. On output, if colamd returns TRUE, the array p holds the column permutation (Q, for P(AQ)=LU or (AQ)'(AQ)=LL'), where p [0] is the first column index in the new ordering, and p [n_col-1] is the last. That is, p [k] = j means that column j of A is the kth pivot column, in AQ, where k is in the range 0 to n_col-1 (p [0] = j means that column j of A is the first column in AQ). If colamd returns FALSE, then no permutation is returned, and p is undefined on output. double knobs [COLAMD_KNOBS] ; Input argument. See colamd_set_defaults for a description. int stats [COLAMD_STATS] ; Output argument. Statistics on the ordering, and error status. See colamd.h for related definitions. Colamd returns FALSE if stats is not present. stats [0]: number of dense or empty rows ignored. stats [1]: number of dense or empty columns ignored (and ordered last in the output permutation p) Note that a row can become "empty" if it contains only "dense" and/or "empty" columns, and similarly a column can become "empty" if it only contains "dense" and/or "empty" rows. stats [2]: number of garbage collections performed. This can be excessively high if Alen is close to the minimum required value. stats [3]: status code. < 0 is an error code. > 1 is a warning or notice. 0 OK. Each column of the input matrix contained row indices in increasing order, with no duplicates. 1 OK, but columns of input matrix were jumbled (unsorted columns or duplicate entries). Colamd had to do some extra work to sort the matrix first and remove duplicate entries, but it still was able to return a valid permutation (return value of colamd was TRUE). stats [4]: highest numbered column that is unsorted or has duplicate entries. stats [5]: last seen duplicate or unsorted row index. stats [6]: number of duplicate or unsorted row indices. -1 A is a null pointer -2 p is a null pointer -3 n_row is negative stats [4]: n_row -4 n_col is negative stats [4]: n_col -5 number of nonzeros in matrix is negative stats [4]: number of nonzeros, p [n_col] -6 p [0] is nonzero stats [4]: p [0] -7 A is too small stats [4]: required size stats [5]: actual size (Alen) -8 a column has a negative number of entries stats [4]: column with < 0 entries stats [5]: number of entries in col -9 a row index is out of bounds stats [4]: column with bad row index stats [5]: bad row index stats [6]: n_row, # of rows of matrx -10 (unused; see symamd.c) -999 (unused; see symamd.c) Future versions may return more statistics in the stats array. Example: See http://www.cise.ufl.edu/research/sparse/colamd/example.c for a complete example. To order the columns of a 5-by-4 matrix with 11 nonzero entries in the following nonzero pattern x 0 x 0 x 0 x x 0 x x 0 0 0 x x x x 0 0 with default knobs and no output statistics, do the following: #include "colamd.h" #define ALEN 100 int A [ALEN] = {0, 1, 4, 2, 4, 0, 1, 2, 3, 1, 3} ; int p [ ] = {0, 3, 5, 9, 11} ; int stats [COLAMD_STATS] ; colamd (5, 4, ALEN, A, p, (double *) NULL, stats) ; The permutation is returned in the array p, and A is destroyed. ---------------------------------------------------------------------------- symamd: ---------------------------------------------------------------------------- C syntax: #include "colamd.h" int symamd (int n, int *A, int *p, int *perm, double knobs [COLAMD_KNOBS], int stats [COLAMD_STATS], void (*allocate) (size_t, size_t), void (*release) (void *)) ; UF_long symamd_l (UF_long n, UF_long *A, UF_long *p, UF_long *perm, double knobs [COLAMD_KNOBS], UF_long stats [COLAMD_STATS], void (*allocate) (size_t, size_t), void (*release) (void *)) ; Purpose: The symamd routine computes an ordering P of a symmetric sparse matrix A such that the Cholesky factorization PAP' = LL' remains sparse. It is based on a column ordering of a matrix M constructed so that the nonzero pattern of M'M is the same as A. The matrix A is assumed to be symmetric; only the strictly lower triangular part is accessed. You must pass your selected memory allocator (usually calloc/free or mxCalloc/mxFree) to symamd, for it to allocate memory for the temporary matrix M. Returns: TRUE (1) if successful, FALSE (0) otherwise. Arguments: int n ; Input argument. Number of rows and columns in the symmetrix matrix A. Restriction: n >= 0. Symamd returns FALSE if n is negative. int A [nnz] ; Input argument. A is an integer array of size nnz, where nnz = p [n]. The row indices of the entries in column c of the matrix are held in A [(p [c]) ... (p [c+1]-1)]. The row indices in a given column c need not be in ascending order, and duplicate row indices may be present. However, symamd will run faster if the columns are in sorted order with no duplicate entries. The matrix is 0-based. That is, rows are in the range 0 to n-1, and columns are in the range 0 to n-1. Symamd returns FALSE if any row index is out of range. The contents of A are not modified. int p [n+1] ; Input argument. p is an integer array of size n+1. On input, it holds the "pointers" for the column form of the matrix A. Column c of the matrix A is held in A [(p [c]) ... (p [c+1]-1)]. The first entry, p [0], must be zero, and p [c] <= p [c+1] must hold for all c in the range 0 to n-1. The value p [n] is thus the total number of entries in the pattern of the matrix A. Symamd returns FALSE if these conditions are not met. The contents of p are not modified. int perm [n+1] ; Output argument. On output, if symamd returns TRUE, the array perm holds the permutation P, where perm [0] is the first index in the new ordering, and perm [n-1] is the last. That is, perm [k] = j means that row and column j of A is the kth column in PAP', where k is in the range 0 to n-1 (perm [0] = j means that row and column j of A are the first row and column in PAP'). The array is used as a workspace during the ordering, which is why it must be of length n+1, not just n. double knobs [COLAMD_KNOBS] ; Input argument. See colamd_set_defaults for a description. int stats [COLAMD_STATS] ; Output argument. Statistics on the ordering, and error status. See colamd.h for related definitions. Symamd returns FALSE if stats is not present. stats [0]: number of dense or empty row and columns ignored (and ordered last in the output permutation perm). Note that a row/column can become "empty" if it contains only "dense" and/or "empty" columns/rows. stats [1]: (same as stats [0]) stats [2]: number of garbage collections performed. stats [3]: status code. < 0 is an error code. > 1 is a warning or notice. 0 OK. Each column of the input matrix contained row indices in increasing order, with no duplicates. 1 OK, but columns of input matrix were jumbled (unsorted columns or duplicate entries). Symamd had to do some extra work to sort the matrix first and remove duplicate entries, but it still was able to return a valid permutation (return value of symamd was TRUE). stats [4]: highest numbered column that is unsorted or has duplicate entries. stats [5]: last seen duplicate or unsorted row index. stats [6]: number of duplicate or unsorted row indices. -1 A is a null pointer -2 p is a null pointer -3 (unused, see colamd.c) -4 n is negative stats [4]: n -5 number of nonzeros in matrix is negative stats [4]: # of nonzeros (p [n]). -6 p [0] is nonzero stats [4]: p [0] -7 (unused) -8 a column has a negative number of entries stats [4]: column with < 0 entries stats [5]: number of entries in col -9 a row index is out of bounds stats [4]: column with bad row index stats [5]: bad row index stats [6]: n_row, # of rows of matrx -10 out of memory (unable to allocate temporary workspace for M or count arrays using the "allocate" routine passed into symamd). Future versions may return more statistics in the stats array. void * (*allocate) (size_t, size_t) A pointer to a function providing memory allocation. The allocated memory must be returned initialized to zero. For a C application, this argument should normally be a pointer to calloc. For a MATLAB mexFunction, the routine mxCalloc is passed instead. void (*release) (size_t, size_t) A pointer to a function that frees memory allocated by the memory allocation routine above. For a C application, this argument should normally be a pointer to free. For a MATLAB mexFunction, the routine mxFree is passed instead. ---------------------------------------------------------------------------- colamd_report: ---------------------------------------------------------------------------- C syntax: #include "colamd.h" colamd_report (int stats [COLAMD_STATS]) ; colamd_l_report (UF_long stats [COLAMD_STATS]) ; Purpose: Prints the error status and statistics recorded in the stats array on the standard error output (for a standard C routine) or on the MATLAB output (for a mexFunction). Arguments: int stats [COLAMD_STATS] ; Input only. Statistics from colamd. ---------------------------------------------------------------------------- symamd_report: ---------------------------------------------------------------------------- C syntax: #include "colamd.h" symamd_report (int stats [COLAMD_STATS]) ; symamd_l_report (UF_long stats [COLAMD_STATS]) ; Purpose: Prints the error status and statistics recorded in the stats array on the standard error output (for a standard C routine) or on the MATLAB output (for a mexFunction). Arguments: int stats [COLAMD_STATS] ; Input only. Statistics from symamd. */ /* ========================================================================== */ /* === Scaffolding code definitions ======================================== */ /* ========================================================================== */ /* Ensure that debugging is turned off: */ #ifndef NDEBUG #define NDEBUG #endif /* turn on debugging by uncommenting the following line #undef NDEBUG */ /* Our "scaffolding code" philosophy: In our opinion, well-written library code should keep its "debugging" code, and just normally have it turned off by the compiler so as not to interfere with performance. This serves several purposes: (1) assertions act as comments to the reader, telling you what the code expects at that point. All assertions will always be true (unless there really is a bug, of course). (2) leaving in the scaffolding code assists anyone who would like to modify the code, or understand the algorithm (by reading the debugging output, one can get a glimpse into what the code is doing). (3) (gasp!) for actually finding bugs. This code has been heavily tested and "should" be fully functional and bug-free ... but you never know... The code will become outrageously slow when debugging is enabled. To control the level of debugging output, set an environment variable D to 0 (little), 1 (some), 2, 3, or 4 (lots). When debugging, you should see the following message on the standard output: colamd: debug version, D = 1 (THIS WILL BE SLOW!) or a similar message for symamd. If you don't, then debugging has not been enabled. */ /* ========================================================================== */ /* === Include files ======================================================== */ /* ========================================================================== */ #include "colamd.h" #include #include #ifdef MATLAB_MEX_FILE #include "mex.h" #include "matrix.h" #endif /* MATLAB_MEX_FILE */ #if !defined (NPRINT) || !defined (NDEBUG) #include #endif #ifndef NULL #define NULL ((void *) 0) #endif /* ========================================================================== */ /* === int or UF_long ======================================================= */ /* ========================================================================== */ /* define UF_long */ #include "UFconfig.h" #ifdef DLONG #define Int UF_long #define ID UF_long_id #define Int_MAX UF_long_max #define COLAMD_recommended colamd_l_recommended #define COLAMD_set_defaults colamd_l_set_defaults #define COLAMD_MAIN colamd_l #define SYMAMD_MAIN symamd_l #define COLAMD_report colamd_l_report #define SYMAMD_report symamd_l_report #else #define Int int #define ID "%d" #define Int_MAX INT_MAX #define COLAMD_recommended colamd_recommended #define COLAMD_set_defaults colamd_set_defaults #define COLAMD_MAIN colamd #define SYMAMD_MAIN symamd #define COLAMD_report colamd_report #define SYMAMD_report symamd_report #endif /* ========================================================================== */ /* === Row and Column structures ============================================ */ /* ========================================================================== */ /* User code that makes use of the colamd/symamd routines need not directly */ /* reference these structures. They are used only for colamd_recommended. */ typedef struct Colamd_Col_struct { Int start ; /* index for A of first row in this column, or DEAD */ /* if column is dead */ Int length ; /* number of rows in this column */ union { Int thickness ; /* number of original columns represented by this */ /* col, if the column is alive */ Int parent ; /* parent in parent tree super-column structure, if */ /* the column is dead */ } shared1 ; union { Int score ; /* the score used to maintain heap, if col is alive */ Int order ; /* pivot ordering of this column, if col is dead */ } shared2 ; union { Int headhash ; /* head of a hash bucket, if col is at the head of */ /* a degree list */ Int hash ; /* hash value, if col is not in a degree list */ Int prev ; /* previous column in degree list, if col is in a */ /* degree list (but not at the head of a degree list) */ } shared3 ; union { Int degree_next ; /* next column, if col is in a degree list */ Int hash_next ; /* next column, if col is in a hash list */ } shared4 ; } Colamd_Col ; typedef struct Colamd_Row_struct { Int start ; /* index for A of first col in this row */ Int length ; /* number of principal columns in this row */ union { Int degree ; /* number of principal & non-principal columns in row */ Int p ; /* used as a row pointer in init_rows_cols () */ } shared1 ; union { Int mark ; /* for computing set differences and marking dead rows*/ Int first_column ;/* first column in row (used in garbage collection) */ } shared2 ; } Colamd_Row ; /* ========================================================================== */ /* === Definitions ========================================================== */ /* ========================================================================== */ /* Routines are either PUBLIC (user-callable) or PRIVATE (not user-callable) */ #define PUBLIC #define PRIVATE static #define DENSE_DEGREE(alpha,n) \ ((Int) MAX (16.0, (alpha) * sqrt ((double) (n)))) #define MAX(a,b) (((a) > (b)) ? (a) : (b)) #define MIN(a,b) (((a) < (b)) ? (a) : (b)) #define ONES_COMPLEMENT(r) (-(r)-1) /* -------------------------------------------------------------------------- */ /* Change for version 2.1: define TRUE and FALSE only if not yet defined */ /* -------------------------------------------------------------------------- */ #ifndef TRUE #define TRUE (1) #endif #ifndef FALSE #define FALSE (0) #endif /* -------------------------------------------------------------------------- */ #define EMPTY (-1) /* Row and column status */ #define ALIVE (0) #define DEAD (-1) /* Column status */ #define DEAD_PRINCIPAL (-1) #define DEAD_NON_PRINCIPAL (-2) /* Macros for row and column status update and checking. */ #define ROW_IS_DEAD(r) ROW_IS_MARKED_DEAD (Row[r].shared2.mark) #define ROW_IS_MARKED_DEAD(row_mark) (row_mark < ALIVE) #define ROW_IS_ALIVE(r) (Row [r].shared2.mark >= ALIVE) #define COL_IS_DEAD(c) (Col [c].start < ALIVE) #define COL_IS_ALIVE(c) (Col [c].start >= ALIVE) #define COL_IS_DEAD_PRINCIPAL(c) (Col [c].start == DEAD_PRINCIPAL) #define KILL_ROW(r) { Row [r].shared2.mark = DEAD ; } #define KILL_PRINCIPAL_COL(c) { Col [c].start = DEAD_PRINCIPAL ; } #define KILL_NON_PRINCIPAL_COL(c) { Col [c].start = DEAD_NON_PRINCIPAL ; } /* ========================================================================== */ /* === Colamd reporting mechanism =========================================== */ /* ========================================================================== */ #if defined (MATLAB_MEX_FILE) || defined (MATHWORKS) /* In MATLAB, matrices are 1-based to the user, but 0-based internally */ #define INDEX(i) ((i)+1) #else /* In C, matrices are 0-based and indices are reported as such in *_report */ #define INDEX(i) (i) #endif /* All output goes through the PRINTF macro. */ #define PRINTF(params) { if (colamd_printf != NULL) (void) colamd_printf params ; } /* ========================================================================== */ /* === Prototypes of PRIVATE routines ======================================= */ /* ========================================================================== */ PRIVATE Int init_rows_cols ( Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int A [], Int p [], Int stats [COLAMD_STATS] ) ; PRIVATE void init_scoring ( Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int A [], Int head [], double knobs [COLAMD_KNOBS], Int *p_n_row2, Int *p_n_col2, Int *p_max_deg ) ; PRIVATE Int find_ordering ( Int n_row, Int n_col, Int Alen, Colamd_Row Row [], Colamd_Col Col [], Int A [], Int head [], Int n_col2, Int max_deg, Int pfree, Int aggressive ) ; PRIVATE void order_children ( Int n_col, Colamd_Col Col [], Int p [] ) ; PRIVATE void detect_super_cols ( #ifndef NDEBUG Int n_col, Colamd_Row Row [], #endif /* NDEBUG */ Colamd_Col Col [], Int A [], Int head [], Int row_start, Int row_length ) ; PRIVATE Int garbage_collection ( Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int A [], Int *pfree ) ; PRIVATE Int clear_mark ( Int tag_mark, Int max_mark, Int n_row, Colamd_Row Row [] ) ; PRIVATE void print_report ( char *method, Int stats [COLAMD_STATS] ) ; /* ========================================================================== */ /* === Debugging prototypes and definitions ================================= */ /* ========================================================================== */ #ifndef NDEBUG #include /* colamd_debug is the *ONLY* global variable, and is only */ /* present when debugging */ PRIVATE Int colamd_debug = 0 ; /* debug print level */ #define DEBUG0(params) { PRINTF (params) ; } #define DEBUG1(params) { if (colamd_debug >= 1) PRINTF (params) ; } #define DEBUG2(params) { if (colamd_debug >= 2) PRINTF (params) ; } #define DEBUG3(params) { if (colamd_debug >= 3) PRINTF (params) ; } #define DEBUG4(params) { if (colamd_debug >= 4) PRINTF (params) ; } #ifdef MATLAB_MEX_FILE #define ASSERT(expression) (mxAssert ((expression), "")) #else #define ASSERT(expression) (assert (expression)) #endif /* MATLAB_MEX_FILE */ PRIVATE void colamd_get_debug /* gets the debug print level from getenv */ ( char *method ) ; PRIVATE void debug_deg_lists ( Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int head [], Int min_score, Int should, Int max_deg ) ; PRIVATE void debug_mark ( Int n_row, Colamd_Row Row [], Int tag_mark, Int max_mark ) ; PRIVATE void debug_matrix ( Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int A [] ) ; PRIVATE void debug_structures ( Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int A [], Int n_col2 ) ; #else /* NDEBUG */ /* === No debugging ========================================================= */ #define DEBUG0(params) ; #define DEBUG1(params) ; #define DEBUG2(params) ; #define DEBUG3(params) ; #define DEBUG4(params) ; #define ASSERT(expression) #endif /* NDEBUG */ /* ========================================================================== */ /* === USER-CALLABLE ROUTINES: ============================================== */ /* ========================================================================== */ /* ========================================================================== */ /* === colamd_recommended =================================================== */ /* ========================================================================== */ /* The colamd_recommended routine returns the suggested size for Alen. This value has been determined to provide good balance between the number of garbage collections and the memory requirements for colamd. If any argument is negative, or if integer overflow occurs, a 0 is returned as an error condition. 2*nnz space is required for the row and column indices of the matrix. COLAMD_C (n_col) + COLAMD_R (n_row) space is required for the Col and Row arrays, respectively, which are internal to colamd (roughly 6*n_col + 4*n_row). An additional n_col space is the minimal amount of "elbow room", and nnz/5 more space is recommended for run time efficiency. Alen is approximately 2.2*nnz + 7*n_col + 4*n_row + 10. This function is not needed when using symamd. */ /* add two values of type size_t, and check for integer overflow */ static size_t t_add (size_t a, size_t b, int *ok) { (*ok) = (*ok) && ((a + b) >= MAX (a,b)) ; return ((*ok) ? (a + b) : 0) ; } /* compute a*k where k is a small integer, and check for integer overflow */ static size_t t_mult (size_t a, size_t k, int *ok) { size_t i, s = 0 ; for (i = 0 ; i < k ; i++) { s = t_add (s, a, ok) ; } return (s) ; } /* size of the Col and Row structures */ #define COLAMD_C(n_col,ok) \ ((t_mult (t_add (n_col, 1, ok), sizeof (Colamd_Col), ok) / sizeof (Int))) #define COLAMD_R(n_row,ok) \ ((t_mult (t_add (n_row, 1, ok), sizeof (Colamd_Row), ok) / sizeof (Int))) PUBLIC size_t COLAMD_recommended /* returns recommended value of Alen. */ ( /* === Parameters ======================================================= */ Int nnz, /* number of nonzeros in A */ Int n_row, /* number of rows in A */ Int n_col /* number of columns in A */ ) { size_t s, c, r ; int ok = TRUE ; if (nnz < 0 || n_row < 0 || n_col < 0) { return (0) ; } s = t_mult (nnz, 2, &ok) ; /* 2*nnz */ c = COLAMD_C (n_col, &ok) ; /* size of column structures */ r = COLAMD_R (n_row, &ok) ; /* size of row structures */ s = t_add (s, c, &ok) ; s = t_add (s, r, &ok) ; s = t_add (s, n_col, &ok) ; /* elbow room */ s = t_add (s, nnz/5, &ok) ; /* elbow room */ ok = ok && (s < Int_MAX) ; return (ok ? s : 0) ; } /* ========================================================================== */ /* === colamd_set_defaults ================================================== */ /* ========================================================================== */ /* The colamd_set_defaults routine sets the default values of the user- controllable parameters for colamd and symamd: Colamd: rows with more than max (16, knobs [0] * sqrt (n_col)) entries are removed prior to ordering. Columns with more than max (16, knobs [1] * sqrt (MIN (n_row,n_col))) entries are removed prior to ordering, and placed last in the output column ordering. Symamd: Rows and columns with more than max (16, knobs [0] * sqrt (n)) entries are removed prior to ordering, and placed last in the output ordering. knobs [0] dense row control knobs [1] dense column control knobs [2] if nonzero, do aggresive absorption knobs [3..19] unused, but future versions might use this */ PUBLIC void COLAMD_set_defaults ( /* === Parameters ======================================================= */ double knobs [COLAMD_KNOBS] /* knob array */ ) { /* === Local variables ================================================== */ Int i ; if (!knobs) { return ; /* no knobs to initialize */ } for (i = 0 ; i < COLAMD_KNOBS ; i++) { knobs [i] = 0 ; } knobs [COLAMD_DENSE_ROW] = 10 ; knobs [COLAMD_DENSE_COL] = 10 ; knobs [COLAMD_AGGRESSIVE] = TRUE ; /* default: do aggressive absorption*/ } /* ========================================================================== */ /* === symamd =============================================================== */ /* ========================================================================== */ PUBLIC Int SYMAMD_MAIN /* return TRUE if OK, FALSE otherwise */ ( /* === Parameters ======================================================= */ Int n, /* number of rows and columns of A */ Int A [], /* row indices of A */ Int p [], /* column pointers of A */ Int perm [], /* output permutation, size n+1 */ double knobs [COLAMD_KNOBS], /* parameters (uses defaults if NULL) */ Int stats [COLAMD_STATS], /* output statistics and error codes */ void * (*allocate) (size_t, size_t), /* pointer to calloc (ANSI C) or */ /* mxCalloc (for MATLAB mexFunction) */ void (*release) (void *) /* pointer to free (ANSI C) or */ /* mxFree (for MATLAB mexFunction) */ ) { /* === Local variables ================================================== */ Int *count ; /* length of each column of M, and col pointer*/ Int *mark ; /* mark array for finding duplicate entries */ Int *M ; /* row indices of matrix M */ size_t Mlen ; /* length of M */ Int n_row ; /* number of rows in M */ Int nnz ; /* number of entries in A */ Int i ; /* row index of A */ Int j ; /* column index of A */ Int k ; /* row index of M */ Int mnz ; /* number of nonzeros in M */ Int pp ; /* index into a column of A */ Int last_row ; /* last row seen in the current column */ Int length ; /* number of nonzeros in a column */ double cknobs [COLAMD_KNOBS] ; /* knobs for colamd */ double default_knobs [COLAMD_KNOBS] ; /* default knobs for colamd */ #ifndef NDEBUG colamd_get_debug ("symamd") ; #endif /* NDEBUG */ /* === Check the input arguments ======================================== */ if (!stats) { DEBUG0 (("symamd: stats not present\n")) ; return (FALSE) ; } for (i = 0 ; i < COLAMD_STATS ; i++) { stats [i] = 0 ; } stats [COLAMD_STATUS] = COLAMD_OK ; stats [COLAMD_INFO1] = -1 ; stats [COLAMD_INFO2] = -1 ; if (!A) { stats [COLAMD_STATUS] = COLAMD_ERROR_A_not_present ; DEBUG0 (("symamd: A not present\n")) ; return (FALSE) ; } if (!p) /* p is not present */ { stats [COLAMD_STATUS] = COLAMD_ERROR_p_not_present ; DEBUG0 (("symamd: p not present\n")) ; return (FALSE) ; } if (n < 0) /* n must be >= 0 */ { stats [COLAMD_STATUS] = COLAMD_ERROR_ncol_negative ; stats [COLAMD_INFO1] = n ; DEBUG0 (("symamd: n negative %d\n", n)) ; return (FALSE) ; } nnz = p [n] ; if (nnz < 0) /* nnz must be >= 0 */ { stats [COLAMD_STATUS] = COLAMD_ERROR_nnz_negative ; stats [COLAMD_INFO1] = nnz ; DEBUG0 (("symamd: number of entries negative %d\n", nnz)) ; return (FALSE) ; } if (p [0] != 0) { stats [COLAMD_STATUS] = COLAMD_ERROR_p0_nonzero ; stats [COLAMD_INFO1] = p [0] ; DEBUG0 (("symamd: p[0] not zero %d\n", p [0])) ; return (FALSE) ; } /* === If no knobs, set default knobs =================================== */ if (!knobs) { COLAMD_set_defaults (default_knobs) ; knobs = default_knobs ; } /* === Allocate count and mark ========================================== */ count = (Int *) ((*allocate) (n+1, sizeof (Int))) ; if (!count) { stats [COLAMD_STATUS] = COLAMD_ERROR_out_of_memory ; DEBUG0 (("symamd: allocate count (size %d) failed\n", n+1)) ; return (FALSE) ; } mark = (Int *) ((*allocate) (n+1, sizeof (Int))) ; if (!mark) { stats [COLAMD_STATUS] = COLAMD_ERROR_out_of_memory ; (*release) ((void *) count) ; DEBUG0 (("symamd: allocate mark (size %d) failed\n", n+1)) ; return (FALSE) ; } /* === Compute column counts of M, check if A is valid ================== */ stats [COLAMD_INFO3] = 0 ; /* number of duplicate or unsorted row indices*/ for (i = 0 ; i < n ; i++) { mark [i] = -1 ; } for (j = 0 ; j < n ; j++) { last_row = -1 ; length = p [j+1] - p [j] ; if (length < 0) { /* column pointers must be non-decreasing */ stats [COLAMD_STATUS] = COLAMD_ERROR_col_length_negative ; stats [COLAMD_INFO1] = j ; stats [COLAMD_INFO2] = length ; (*release) ((void *) count) ; (*release) ((void *) mark) ; DEBUG0 (("symamd: col %d negative length %d\n", j, length)) ; return (FALSE) ; } for (pp = p [j] ; pp < p [j+1] ; pp++) { i = A [pp] ; if (i < 0 || i >= n) { /* row index i, in column j, is out of bounds */ stats [COLAMD_STATUS] = COLAMD_ERROR_row_index_out_of_bounds ; stats [COLAMD_INFO1] = j ; stats [COLAMD_INFO2] = i ; stats [COLAMD_INFO3] = n ; (*release) ((void *) count) ; (*release) ((void *) mark) ; DEBUG0 (("symamd: row %d col %d out of bounds\n", i, j)) ; return (FALSE) ; } if (i <= last_row || mark [i] == j) { /* row index is unsorted or repeated (or both), thus col */ /* is jumbled. This is a notice, not an error condition. */ stats [COLAMD_STATUS] = COLAMD_OK_BUT_JUMBLED ; stats [COLAMD_INFO1] = j ; stats [COLAMD_INFO2] = i ; (stats [COLAMD_INFO3]) ++ ; DEBUG1 (("symamd: row %d col %d unsorted/duplicate\n", i, j)) ; } if (i > j && mark [i] != j) { /* row k of M will contain column indices i and j */ count [i]++ ; count [j]++ ; } /* mark the row as having been seen in this column */ mark [i] = j ; last_row = i ; } } /* v2.4: removed free(mark) */ /* === Compute column pointers of M ===================================== */ /* use output permutation, perm, for column pointers of M */ perm [0] = 0 ; for (j = 1 ; j <= n ; j++) { perm [j] = perm [j-1] + count [j-1] ; } for (j = 0 ; j < n ; j++) { count [j] = perm [j] ; } /* === Construct M ====================================================== */ mnz = perm [n] ; n_row = mnz / 2 ; Mlen = COLAMD_recommended (mnz, n_row, n) ; M = (Int *) ((*allocate) (Mlen, sizeof (Int))) ; DEBUG0 (("symamd: M is %d-by-%d with %d entries, Mlen = %g\n", n_row, n, mnz, (double) Mlen)) ; if (!M) { stats [COLAMD_STATUS] = COLAMD_ERROR_out_of_memory ; (*release) ((void *) count) ; (*release) ((void *) mark) ; DEBUG0 (("symamd: allocate M (size %g) failed\n", (double) Mlen)) ; return (FALSE) ; } k = 0 ; if (stats [COLAMD_STATUS] == COLAMD_OK) { /* Matrix is OK */ for (j = 0 ; j < n ; j++) { ASSERT (p [j+1] - p [j] >= 0) ; for (pp = p [j] ; pp < p [j+1] ; pp++) { i = A [pp] ; ASSERT (i >= 0 && i < n) ; if (i > j) { /* row k of M contains column indices i and j */ M [count [i]++] = k ; M [count [j]++] = k ; k++ ; } } } } else { /* Matrix is jumbled. Do not add duplicates to M. Unsorted cols OK. */ DEBUG0 (("symamd: Duplicates in A.\n")) ; for (i = 0 ; i < n ; i++) { mark [i] = -1 ; } for (j = 0 ; j < n ; j++) { ASSERT (p [j+1] - p [j] >= 0) ; for (pp = p [j] ; pp < p [j+1] ; pp++) { i = A [pp] ; ASSERT (i >= 0 && i < n) ; if (i > j && mark [i] != j) { /* row k of M contains column indices i and j */ M [count [i]++] = k ; M [count [j]++] = k ; k++ ; mark [i] = j ; } } } /* v2.4: free(mark) moved below */ } /* count and mark no longer needed */ (*release) ((void *) count) ; (*release) ((void *) mark) ; /* v2.4: free (mark) moved here */ ASSERT (k == n_row) ; /* === Adjust the knobs for M =========================================== */ for (i = 0 ; i < COLAMD_KNOBS ; i++) { cknobs [i] = knobs [i] ; } /* there are no dense rows in M */ cknobs [COLAMD_DENSE_ROW] = -1 ; cknobs [COLAMD_DENSE_COL] = knobs [COLAMD_DENSE_ROW] ; /* === Order the columns of M =========================================== */ /* v2.4: colamd cannot fail here, so the error check is removed */ (void) COLAMD_MAIN (n_row, n, (Int) Mlen, M, perm, cknobs, stats) ; /* Note that the output permutation is now in perm */ /* === get the statistics for symamd from colamd ======================== */ /* a dense column in colamd means a dense row and col in symamd */ stats [COLAMD_DENSE_ROW] = stats [COLAMD_DENSE_COL] ; /* === Free M =========================================================== */ (*release) ((void *) M) ; DEBUG0 (("symamd: done.\n")) ; return (TRUE) ; } /* ========================================================================== */ /* === colamd =============================================================== */ /* ========================================================================== */ /* The colamd routine computes a column ordering Q of a sparse matrix A such that the LU factorization P(AQ) = LU remains sparse, where P is selected via partial pivoting. The routine can also be viewed as providing a permutation Q such that the Cholesky factorization (AQ)'(AQ) = LL' remains sparse. */ PUBLIC Int COLAMD_MAIN /* returns TRUE if successful, FALSE otherwise*/ ( /* === Parameters ======================================================= */ Int n_row, /* number of rows in A */ Int n_col, /* number of columns in A */ Int Alen, /* length of A */ Int A [], /* row indices of A */ Int p [], /* pointers to columns in A */ double knobs [COLAMD_KNOBS],/* parameters (uses defaults if NULL) */ Int stats [COLAMD_STATS] /* output statistics and error codes */ ) { /* === Local variables ================================================== */ Int i ; /* loop index */ Int nnz ; /* nonzeros in A */ size_t Row_size ; /* size of Row [], in integers */ size_t Col_size ; /* size of Col [], in integers */ size_t need ; /* minimum required length of A */ Colamd_Row *Row ; /* pointer into A of Row [0..n_row] array */ Colamd_Col *Col ; /* pointer into A of Col [0..n_col] array */ Int n_col2 ; /* number of non-dense, non-empty columns */ Int n_row2 ; /* number of non-dense, non-empty rows */ Int ngarbage ; /* number of garbage collections performed */ Int max_deg ; /* maximum row degree */ double default_knobs [COLAMD_KNOBS] ; /* default knobs array */ Int aggressive ; /* do aggressive absorption */ int ok ; #ifndef NDEBUG colamd_get_debug ("colamd") ; #endif /* NDEBUG */ /* === Check the input arguments ======================================== */ if (!stats) { DEBUG0 (("colamd: stats not present\n")) ; return (FALSE) ; } for (i = 0 ; i < COLAMD_STATS ; i++) { stats [i] = 0 ; } stats [COLAMD_STATUS] = COLAMD_OK ; stats [COLAMD_INFO1] = -1 ; stats [COLAMD_INFO2] = -1 ; if (!A) /* A is not present */ { stats [COLAMD_STATUS] = COLAMD_ERROR_A_not_present ; DEBUG0 (("colamd: A not present\n")) ; return (FALSE) ; } if (!p) /* p is not present */ { stats [COLAMD_STATUS] = COLAMD_ERROR_p_not_present ; DEBUG0 (("colamd: p not present\n")) ; return (FALSE) ; } if (n_row < 0) /* n_row must be >= 0 */ { stats [COLAMD_STATUS] = COLAMD_ERROR_nrow_negative ; stats [COLAMD_INFO1] = n_row ; DEBUG0 (("colamd: nrow negative %d\n", n_row)) ; return (FALSE) ; } if (n_col < 0) /* n_col must be >= 0 */ { stats [COLAMD_STATUS] = COLAMD_ERROR_ncol_negative ; stats [COLAMD_INFO1] = n_col ; DEBUG0 (("colamd: ncol negative %d\n", n_col)) ; return (FALSE) ; } nnz = p [n_col] ; if (nnz < 0) /* nnz must be >= 0 */ { stats [COLAMD_STATUS] = COLAMD_ERROR_nnz_negative ; stats [COLAMD_INFO1] = nnz ; DEBUG0 (("colamd: number of entries negative %d\n", nnz)) ; return (FALSE) ; } if (p [0] != 0) { stats [COLAMD_STATUS] = COLAMD_ERROR_p0_nonzero ; stats [COLAMD_INFO1] = p [0] ; DEBUG0 (("colamd: p[0] not zero %d\n", p [0])) ; return (FALSE) ; } /* === If no knobs, set default knobs =================================== */ if (!knobs) { COLAMD_set_defaults (default_knobs) ; knobs = default_knobs ; } aggressive = (knobs [COLAMD_AGGRESSIVE] != FALSE) ; /* === Allocate the Row and Col arrays from array A ===================== */ ok = TRUE ; Col_size = COLAMD_C (n_col, &ok) ; /* size of Col array of structs */ Row_size = COLAMD_R (n_row, &ok) ; /* size of Row array of structs */ /* need = 2*nnz + n_col + Col_size + Row_size ; */ need = t_mult (nnz, 2, &ok) ; need = t_add (need, n_col, &ok) ; need = t_add (need, Col_size, &ok) ; need = t_add (need, Row_size, &ok) ; if (!ok || need > (size_t) Alen || need > Int_MAX) { /* not enough space in array A to perform the ordering */ stats [COLAMD_STATUS] = COLAMD_ERROR_A_too_small ; stats [COLAMD_INFO1] = need ; stats [COLAMD_INFO2] = Alen ; DEBUG0 (("colamd: Need Alen >= %d, given only Alen = %d\n", need,Alen)); return (FALSE) ; } Alen -= Col_size + Row_size ; Col = (Colamd_Col *) &A [Alen] ; Row = (Colamd_Row *) &A [Alen + Col_size] ; /* === Construct the row and column data structures ===================== */ if (!init_rows_cols (n_row, n_col, Row, Col, A, p, stats)) { /* input matrix is invalid */ DEBUG0 (("colamd: Matrix invalid\n")) ; return (FALSE) ; } /* === Initialize scores, kill dense rows/columns ======================= */ init_scoring (n_row, n_col, Row, Col, A, p, knobs, &n_row2, &n_col2, &max_deg) ; /* === Order the supercolumns =========================================== */ ngarbage = find_ordering (n_row, n_col, Alen, Row, Col, A, p, n_col2, max_deg, 2*nnz, aggressive) ; /* === Order the non-principal columns ================================== */ order_children (n_col, Col, p) ; /* === Return statistics in stats ======================================= */ stats [COLAMD_DENSE_ROW] = n_row - n_row2 ; stats [COLAMD_DENSE_COL] = n_col - n_col2 ; stats [COLAMD_DEFRAG_COUNT] = ngarbage ; DEBUG0 (("colamd: done.\n")) ; return (TRUE) ; } /* ========================================================================== */ /* === colamd_report ======================================================== */ /* ========================================================================== */ PUBLIC void COLAMD_report ( Int stats [COLAMD_STATS] ) { print_report ("colamd", stats) ; } /* ========================================================================== */ /* === symamd_report ======================================================== */ /* ========================================================================== */ PUBLIC void SYMAMD_report ( Int stats [COLAMD_STATS] ) { print_report ("symamd", stats) ; } /* ========================================================================== */ /* === NON-USER-CALLABLE ROUTINES: ========================================== */ /* ========================================================================== */ /* There are no user-callable routines beyond this point in the file */ /* ========================================================================== */ /* === init_rows_cols ======================================================= */ /* ========================================================================== */ /* Takes the column form of the matrix in A and creates the row form of the matrix. Also, row and column attributes are stored in the Col and Row structs. If the columns are un-sorted or contain duplicate row indices, this routine will also sort and remove duplicate row indices from the column form of the matrix. Returns FALSE if the matrix is invalid, TRUE otherwise. Not user-callable. */ PRIVATE Int init_rows_cols /* returns TRUE if OK, or FALSE otherwise */ ( /* === Parameters ======================================================= */ Int n_row, /* number of rows of A */ Int n_col, /* number of columns of A */ Colamd_Row Row [], /* of size n_row+1 */ Colamd_Col Col [], /* of size n_col+1 */ Int A [], /* row indices of A, of size Alen */ Int p [], /* pointers to columns in A, of size n_col+1 */ Int stats [COLAMD_STATS] /* colamd statistics */ ) { /* === Local variables ================================================== */ Int col ; /* a column index */ Int row ; /* a row index */ Int *cp ; /* a column pointer */ Int *cp_end ; /* a pointer to the end of a column */ Int *rp ; /* a row pointer */ Int *rp_end ; /* a pointer to the end of a row */ Int last_row ; /* previous row */ /* === Initialize columns, and check column pointers ==================== */ for (col = 0 ; col < n_col ; col++) { Col [col].start = p [col] ; Col [col].length = p [col+1] - p [col] ; if (Col [col].length < 0) { /* column pointers must be non-decreasing */ stats [COLAMD_STATUS] = COLAMD_ERROR_col_length_negative ; stats [COLAMD_INFO1] = col ; stats [COLAMD_INFO2] = Col [col].length ; DEBUG0 (("colamd: col %d length %d < 0\n", col, Col [col].length)) ; return (FALSE) ; } Col [col].shared1.thickness = 1 ; Col [col].shared2.score = 0 ; Col [col].shared3.prev = EMPTY ; Col [col].shared4.degree_next = EMPTY ; } /* p [0..n_col] no longer needed, used as "head" in subsequent routines */ /* === Scan columns, compute row degrees, and check row indices ========= */ stats [COLAMD_INFO3] = 0 ; /* number of duplicate or unsorted row indices*/ for (row = 0 ; row < n_row ; row++) { Row [row].length = 0 ; Row [row].shared2.mark = -1 ; } for (col = 0 ; col < n_col ; col++) { last_row = -1 ; cp = &A [p [col]] ; cp_end = &A [p [col+1]] ; while (cp < cp_end) { row = *cp++ ; /* make sure row indices within range */ if (row < 0 || row >= n_row) { stats [COLAMD_STATUS] = COLAMD_ERROR_row_index_out_of_bounds ; stats [COLAMD_INFO1] = col ; stats [COLAMD_INFO2] = row ; stats [COLAMD_INFO3] = n_row ; DEBUG0 (("colamd: row %d col %d out of bounds\n", row, col)) ; return (FALSE) ; } if (row <= last_row || Row [row].shared2.mark == col) { /* row index are unsorted or repeated (or both), thus col */ /* is jumbled. This is a notice, not an error condition. */ stats [COLAMD_STATUS] = COLAMD_OK_BUT_JUMBLED ; stats [COLAMD_INFO1] = col ; stats [COLAMD_INFO2] = row ; (stats [COLAMD_INFO3]) ++ ; DEBUG1 (("colamd: row %d col %d unsorted/duplicate\n",row,col)); } if (Row [row].shared2.mark != col) { Row [row].length++ ; } else { /* this is a repeated entry in the column, */ /* it will be removed */ Col [col].length-- ; } /* mark the row as having been seen in this column */ Row [row].shared2.mark = col ; last_row = row ; } } /* === Compute row pointers ============================================= */ /* row form of the matrix starts directly after the column */ /* form of matrix in A */ Row [0].start = p [n_col] ; Row [0].shared1.p = Row [0].start ; Row [0].shared2.mark = -1 ; for (row = 1 ; row < n_row ; row++) { Row [row].start = Row [row-1].start + Row [row-1].length ; Row [row].shared1.p = Row [row].start ; Row [row].shared2.mark = -1 ; } /* === Create row form ================================================== */ if (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED) { /* if cols jumbled, watch for repeated row indices */ for (col = 0 ; col < n_col ; col++) { cp = &A [p [col]] ; cp_end = &A [p [col+1]] ; while (cp < cp_end) { row = *cp++ ; if (Row [row].shared2.mark != col) { A [(Row [row].shared1.p)++] = col ; Row [row].shared2.mark = col ; } } } } else { /* if cols not jumbled, we don't need the mark (this is faster) */ for (col = 0 ; col < n_col ; col++) { cp = &A [p [col]] ; cp_end = &A [p [col+1]] ; while (cp < cp_end) { A [(Row [*cp++].shared1.p)++] = col ; } } } /* === Clear the row marks and set row degrees ========================== */ for (row = 0 ; row < n_row ; row++) { Row [row].shared2.mark = 0 ; Row [row].shared1.degree = Row [row].length ; } /* === See if we need to re-create columns ============================== */ if (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED) { DEBUG0 (("colamd: reconstructing column form, matrix jumbled\n")) ; #ifndef NDEBUG /* make sure column lengths are correct */ for (col = 0 ; col < n_col ; col++) { p [col] = Col [col].length ; } for (row = 0 ; row < n_row ; row++) { rp = &A [Row [row].start] ; rp_end = rp + Row [row].length ; while (rp < rp_end) { p [*rp++]-- ; } } for (col = 0 ; col < n_col ; col++) { ASSERT (p [col] == 0) ; } /* now p is all zero (different than when debugging is turned off) */ #endif /* NDEBUG */ /* === Compute col pointers ========================================= */ /* col form of the matrix starts at A [0]. */ /* Note, we may have a gap between the col form and the row */ /* form if there were duplicate entries, if so, it will be */ /* removed upon the first garbage collection */ Col [0].start = 0 ; p [0] = Col [0].start ; for (col = 1 ; col < n_col ; col++) { /* note that the lengths here are for pruned columns, i.e. */ /* no duplicate row indices will exist for these columns */ Col [col].start = Col [col-1].start + Col [col-1].length ; p [col] = Col [col].start ; } /* === Re-create col form =========================================== */ for (row = 0 ; row < n_row ; row++) { rp = &A [Row [row].start] ; rp_end = rp + Row [row].length ; while (rp < rp_end) { A [(p [*rp++])++] = row ; } } } /* === Done. Matrix is not (or no longer) jumbled ====================== */ return (TRUE) ; } /* ========================================================================== */ /* === init_scoring ========================================================= */ /* ========================================================================== */ /* Kills dense or empty columns and rows, calculates an initial score for each column, and places all columns in the degree lists. Not user-callable. */ PRIVATE void init_scoring ( /* === Parameters ======================================================= */ Int n_row, /* number of rows of A */ Int n_col, /* number of columns of A */ Colamd_Row Row [], /* of size n_row+1 */ Colamd_Col Col [], /* of size n_col+1 */ Int A [], /* column form and row form of A */ Int head [], /* of size n_col+1 */ double knobs [COLAMD_KNOBS],/* parameters */ Int *p_n_row2, /* number of non-dense, non-empty rows */ Int *p_n_col2, /* number of non-dense, non-empty columns */ Int *p_max_deg /* maximum row degree */ ) { /* === Local variables ================================================== */ Int c ; /* a column index */ Int r, row ; /* a row index */ Int *cp ; /* a column pointer */ Int deg ; /* degree of a row or column */ Int *cp_end ; /* a pointer to the end of a column */ Int *new_cp ; /* new column pointer */ Int col_length ; /* length of pruned column */ Int score ; /* current column score */ Int n_col2 ; /* number of non-dense, non-empty columns */ Int n_row2 ; /* number of non-dense, non-empty rows */ Int dense_row_count ; /* remove rows with more entries than this */ Int dense_col_count ; /* remove cols with more entries than this */ Int min_score ; /* smallest column score */ Int max_deg ; /* maximum row degree */ Int next_col ; /* Used to add to degree list.*/ #ifndef NDEBUG Int debug_count ; /* debug only. */ #endif /* NDEBUG */ /* === Extract knobs ==================================================== */ /* Note: if knobs contains a NaN, this is undefined: */ if (knobs [COLAMD_DENSE_ROW] < 0) { /* only remove completely dense rows */ dense_row_count = n_col-1 ; } else { dense_row_count = DENSE_DEGREE (knobs [COLAMD_DENSE_ROW], n_col) ; } if (knobs [COLAMD_DENSE_COL] < 0) { /* only remove completely dense columns */ dense_col_count = n_row-1 ; } else { dense_col_count = DENSE_DEGREE (knobs [COLAMD_DENSE_COL], MIN (n_row, n_col)) ; } DEBUG1 (("colamd: densecount: %d %d\n", dense_row_count, dense_col_count)) ; max_deg = 0 ; n_col2 = n_col ; n_row2 = n_row ; /* === Kill empty columns =============================================== */ /* Put the empty columns at the end in their natural order, so that LU */ /* factorization can proceed as far as possible. */ for (c = n_col-1 ; c >= 0 ; c--) { deg = Col [c].length ; if (deg == 0) { /* this is a empty column, kill and order it last */ Col [c].shared2.order = --n_col2 ; KILL_PRINCIPAL_COL (c) ; } } DEBUG1 (("colamd: null columns killed: %d\n", n_col - n_col2)) ; /* === Kill dense columns =============================================== */ /* Put the dense columns at the end, in their natural order */ for (c = n_col-1 ; c >= 0 ; c--) { /* skip any dead columns */ if (COL_IS_DEAD (c)) { continue ; } deg = Col [c].length ; if (deg > dense_col_count) { /* this is a dense column, kill and order it last */ Col [c].shared2.order = --n_col2 ; /* decrement the row degrees */ cp = &A [Col [c].start] ; cp_end = cp + Col [c].length ; while (cp < cp_end) { Row [*cp++].shared1.degree-- ; } KILL_PRINCIPAL_COL (c) ; } } DEBUG1 (("colamd: Dense and null columns killed: %d\n", n_col - n_col2)) ; /* === Kill dense and empty rows ======================================== */ for (r = 0 ; r < n_row ; r++) { deg = Row [r].shared1.degree ; ASSERT (deg >= 0 && deg <= n_col) ; if (deg > dense_row_count || deg == 0) { /* kill a dense or empty row */ KILL_ROW (r) ; --n_row2 ; } else { /* keep track of max degree of remaining rows */ max_deg = MAX (max_deg, deg) ; } } DEBUG1 (("colamd: Dense and null rows killed: %d\n", n_row - n_row2)) ; /* === Compute initial column scores ==================================== */ /* At this point the row degrees are accurate. They reflect the number */ /* of "live" (non-dense) columns in each row. No empty rows exist. */ /* Some "live" columns may contain only dead rows, however. These are */ /* pruned in the code below. */ /* now find the initial matlab score for each column */ for (c = n_col-1 ; c >= 0 ; c--) { /* skip dead column */ if (COL_IS_DEAD (c)) { continue ; } score = 0 ; cp = &A [Col [c].start] ; new_cp = cp ; cp_end = cp + Col [c].length ; while (cp < cp_end) { /* get a row */ row = *cp++ ; /* skip if dead */ if (ROW_IS_DEAD (row)) { continue ; } /* compact the column */ *new_cp++ = row ; /* add row's external degree */ score += Row [row].shared1.degree - 1 ; /* guard against integer overflow */ score = MIN (score, n_col) ; } /* determine pruned column length */ col_length = (Int) (new_cp - &A [Col [c].start]) ; if (col_length == 0) { /* a newly-made null column (all rows in this col are "dense" */ /* and have already been killed) */ DEBUG2 (("Newly null killed: %d\n", c)) ; Col [c].shared2.order = --n_col2 ; KILL_PRINCIPAL_COL (c) ; } else { /* set column length and set score */ ASSERT (score >= 0) ; ASSERT (score <= n_col) ; Col [c].length = col_length ; Col [c].shared2.score = score ; } } DEBUG1 (("colamd: Dense, null, and newly-null columns killed: %d\n", n_col-n_col2)) ; /* At this point, all empty rows and columns are dead. All live columns */ /* are "clean" (containing no dead rows) and simplicial (no supercolumns */ /* yet). Rows may contain dead columns, but all live rows contain at */ /* least one live column. */ #ifndef NDEBUG debug_structures (n_row, n_col, Row, Col, A, n_col2) ; #endif /* NDEBUG */ /* === Initialize degree lists ========================================== */ #ifndef NDEBUG debug_count = 0 ; #endif /* NDEBUG */ /* clear the hash buckets */ for (c = 0 ; c <= n_col ; c++) { head [c] = EMPTY ; } min_score = n_col ; /* place in reverse order, so low column indices are at the front */ /* of the lists. This is to encourage natural tie-breaking */ for (c = n_col-1 ; c >= 0 ; c--) { /* only add principal columns to degree lists */ if (COL_IS_ALIVE (c)) { DEBUG4 (("place %d score %d minscore %d ncol %d\n", c, Col [c].shared2.score, min_score, n_col)) ; /* === Add columns score to DList =============================== */ score = Col [c].shared2.score ; ASSERT (min_score >= 0) ; ASSERT (min_score <= n_col) ; ASSERT (score >= 0) ; ASSERT (score <= n_col) ; ASSERT (head [score] >= EMPTY) ; /* now add this column to dList at proper score location */ next_col = head [score] ; Col [c].shared3.prev = EMPTY ; Col [c].shared4.degree_next = next_col ; /* if there already was a column with the same score, set its */ /* previous pointer to this new column */ if (next_col != EMPTY) { Col [next_col].shared3.prev = c ; } head [score] = c ; /* see if this score is less than current min */ min_score = MIN (min_score, score) ; #ifndef NDEBUG debug_count++ ; #endif /* NDEBUG */ } } #ifndef NDEBUG DEBUG1 (("colamd: Live cols %d out of %d, non-princ: %d\n", debug_count, n_col, n_col-debug_count)) ; ASSERT (debug_count == n_col2) ; debug_deg_lists (n_row, n_col, Row, Col, head, min_score, n_col2, max_deg) ; #endif /* NDEBUG */ /* === Return number of remaining columns, and max row degree =========== */ *p_n_col2 = n_col2 ; *p_n_row2 = n_row2 ; *p_max_deg = max_deg ; } /* ========================================================================== */ /* === find_ordering ======================================================== */ /* ========================================================================== */ /* Order the principal columns of the supercolumn form of the matrix (no supercolumns on input). Uses a minimum approximate column minimum degree ordering method. Not user-callable. */ PRIVATE Int find_ordering /* return the number of garbage collections */ ( /* === Parameters ======================================================= */ Int n_row, /* number of rows of A */ Int n_col, /* number of columns of A */ Int Alen, /* size of A, 2*nnz + n_col or larger */ Colamd_Row Row [], /* of size n_row+1 */ Colamd_Col Col [], /* of size n_col+1 */ Int A [], /* column form and row form of A */ Int head [], /* of size n_col+1 */ Int n_col2, /* Remaining columns to order */ Int max_deg, /* Maximum row degree */ Int pfree, /* index of first free slot (2*nnz on entry) */ Int aggressive ) { /* === Local variables ================================================== */ Int k ; /* current pivot ordering step */ Int pivot_col ; /* current pivot column */ Int *cp ; /* a column pointer */ Int *rp ; /* a row pointer */ Int pivot_row ; /* current pivot row */ Int *new_cp ; /* modified column pointer */ Int *new_rp ; /* modified row pointer */ Int pivot_row_start ; /* pointer to start of pivot row */ Int pivot_row_degree ; /* number of columns in pivot row */ Int pivot_row_length ; /* number of supercolumns in pivot row */ Int pivot_col_score ; /* score of pivot column */ Int needed_memory ; /* free space needed for pivot row */ Int *cp_end ; /* pointer to the end of a column */ Int *rp_end ; /* pointer to the end of a row */ Int row ; /* a row index */ Int col ; /* a column index */ Int max_score ; /* maximum possible score */ Int cur_score ; /* score of current column */ unsigned Int hash ; /* hash value for supernode detection */ Int head_column ; /* head of hash bucket */ Int first_col ; /* first column in hash bucket */ Int tag_mark ; /* marker value for mark array */ Int row_mark ; /* Row [row].shared2.mark */ Int set_difference ; /* set difference size of row with pivot row */ Int min_score ; /* smallest column score */ Int col_thickness ; /* "thickness" (no. of columns in a supercol) */ Int max_mark ; /* maximum value of tag_mark */ Int pivot_col_thickness ; /* number of columns represented by pivot col */ Int prev_col ; /* Used by Dlist operations. */ Int next_col ; /* Used by Dlist operations. */ Int ngarbage ; /* number of garbage collections performed */ #ifndef NDEBUG Int debug_d ; /* debug loop counter */ Int debug_step = 0 ; /* debug loop counter */ #endif /* NDEBUG */ /* === Initialization and clear mark ==================================== */ max_mark = INT_MAX - n_col ; /* INT_MAX defined in */ tag_mark = clear_mark (0, max_mark, n_row, Row) ; min_score = 0 ; ngarbage = 0 ; DEBUG1 (("colamd: Ordering, n_col2=%d\n", n_col2)) ; /* === Order the columns ================================================ */ for (k = 0 ; k < n_col2 ; /* 'k' is incremented below */) { #ifndef NDEBUG if (debug_step % 100 == 0) { DEBUG2 (("\n... Step k: %d out of n_col2: %d\n", k, n_col2)) ; } else { DEBUG3 (("\n----------Step k: %d out of n_col2: %d\n", k, n_col2)) ; } debug_step++ ; debug_deg_lists (n_row, n_col, Row, Col, head, min_score, n_col2-k, max_deg) ; debug_matrix (n_row, n_col, Row, Col, A) ; #endif /* NDEBUG */ /* === Select pivot column, and order it ============================ */ /* make sure degree list isn't empty */ ASSERT (min_score >= 0) ; ASSERT (min_score <= n_col) ; ASSERT (head [min_score] >= EMPTY) ; #ifndef NDEBUG for (debug_d = 0 ; debug_d < min_score ; debug_d++) { ASSERT (head [debug_d] == EMPTY) ; } #endif /* NDEBUG */ /* get pivot column from head of minimum degree list */ while (head [min_score] == EMPTY && min_score < n_col) { min_score++ ; } pivot_col = head [min_score] ; ASSERT (pivot_col >= 0 && pivot_col <= n_col) ; next_col = Col [pivot_col].shared4.degree_next ; head [min_score] = next_col ; if (next_col != EMPTY) { Col [next_col].shared3.prev = EMPTY ; } ASSERT (COL_IS_ALIVE (pivot_col)) ; /* remember score for defrag check */ pivot_col_score = Col [pivot_col].shared2.score ; /* the pivot column is the kth column in the pivot order */ Col [pivot_col].shared2.order = k ; /* increment order count by column thickness */ pivot_col_thickness = Col [pivot_col].shared1.thickness ; k += pivot_col_thickness ; ASSERT (pivot_col_thickness > 0) ; DEBUG3 (("Pivot col: %d thick %d\n", pivot_col, pivot_col_thickness)) ; /* === Garbage_collection, if necessary ============================= */ needed_memory = MIN (pivot_col_score, n_col - k) ; if (pfree + needed_memory >= Alen) { pfree = garbage_collection (n_row, n_col, Row, Col, A, &A [pfree]) ; ngarbage++ ; /* after garbage collection we will have enough */ ASSERT (pfree + needed_memory < Alen) ; /* garbage collection has wiped out the Row[].shared2.mark array */ tag_mark = clear_mark (0, max_mark, n_row, Row) ; #ifndef NDEBUG debug_matrix (n_row, n_col, Row, Col, A) ; #endif /* NDEBUG */ } /* === Compute pivot row pattern ==================================== */ /* get starting location for this new merged row */ pivot_row_start = pfree ; /* initialize new row counts to zero */ pivot_row_degree = 0 ; /* tag pivot column as having been visited so it isn't included */ /* in merged pivot row */ Col [pivot_col].shared1.thickness = -pivot_col_thickness ; /* pivot row is the union of all rows in the pivot column pattern */ cp = &A [Col [pivot_col].start] ; cp_end = cp + Col [pivot_col].length ; while (cp < cp_end) { /* get a row */ row = *cp++ ; DEBUG4 (("Pivot col pattern %d %d\n", ROW_IS_ALIVE (row), row)) ; /* skip if row is dead */ if (ROW_IS_ALIVE (row)) { rp = &A [Row [row].start] ; rp_end = rp + Row [row].length ; while (rp < rp_end) { /* get a column */ col = *rp++ ; /* add the column, if alive and untagged */ col_thickness = Col [col].shared1.thickness ; if (col_thickness > 0 && COL_IS_ALIVE (col)) { /* tag column in pivot row */ Col [col].shared1.thickness = -col_thickness ; ASSERT (pfree < Alen) ; /* place column in pivot row */ A [pfree++] = col ; pivot_row_degree += col_thickness ; } } } } /* clear tag on pivot column */ Col [pivot_col].shared1.thickness = pivot_col_thickness ; max_deg = MAX (max_deg, pivot_row_degree) ; #ifndef NDEBUG DEBUG3 (("check2\n")) ; debug_mark (n_row, Row, tag_mark, max_mark) ; #endif /* NDEBUG */ /* === Kill all rows used to construct pivot row ==================== */ /* also kill pivot row, temporarily */ cp = &A [Col [pivot_col].start] ; cp_end = cp + Col [pivot_col].length ; while (cp < cp_end) { /* may be killing an already dead row */ row = *cp++ ; DEBUG3 (("Kill row in pivot col: %d\n", row)) ; KILL_ROW (row) ; } /* === Select a row index to use as the new pivot row =============== */ pivot_row_length = pfree - pivot_row_start ; if (pivot_row_length > 0) { /* pick the "pivot" row arbitrarily (first row in col) */ pivot_row = A [Col [pivot_col].start] ; DEBUG3 (("Pivotal row is %d\n", pivot_row)) ; } else { /* there is no pivot row, since it is of zero length */ pivot_row = EMPTY ; ASSERT (pivot_row_length == 0) ; } ASSERT (Col [pivot_col].length > 0 || pivot_row_length == 0) ; /* === Approximate degree computation =============================== */ /* Here begins the computation of the approximate degree. The column */ /* score is the sum of the pivot row "length", plus the size of the */ /* set differences of each row in the column minus the pattern of the */ /* pivot row itself. The column ("thickness") itself is also */ /* excluded from the column score (we thus use an approximate */ /* external degree). */ /* The time taken by the following code (compute set differences, and */ /* add them up) is proportional to the size of the data structure */ /* being scanned - that is, the sum of the sizes of each column in */ /* the pivot row. Thus, the amortized time to compute a column score */ /* is proportional to the size of that column (where size, in this */ /* context, is the column "length", or the number of row indices */ /* in that column). The number of row indices in a column is */ /* monotonically non-decreasing, from the length of the original */ /* column on input to colamd. */ /* === Compute set differences ====================================== */ DEBUG3 (("** Computing set differences phase. **\n")) ; /* pivot row is currently dead - it will be revived later. */ DEBUG3 (("Pivot row: ")) ; /* for each column in pivot row */ rp = &A [pivot_row_start] ; rp_end = rp + pivot_row_length ; while (rp < rp_end) { col = *rp++ ; ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ; DEBUG3 (("Col: %d\n", col)) ; /* clear tags used to construct pivot row pattern */ col_thickness = -Col [col].shared1.thickness ; ASSERT (col_thickness > 0) ; Col [col].shared1.thickness = col_thickness ; /* === Remove column from degree list =========================== */ cur_score = Col [col].shared2.score ; prev_col = Col [col].shared3.prev ; next_col = Col [col].shared4.degree_next ; ASSERT (cur_score >= 0) ; ASSERT (cur_score <= n_col) ; ASSERT (cur_score >= EMPTY) ; if (prev_col == EMPTY) { head [cur_score] = next_col ; } else { Col [prev_col].shared4.degree_next = next_col ; } if (next_col != EMPTY) { Col [next_col].shared3.prev = prev_col ; } /* === Scan the column ========================================== */ cp = &A [Col [col].start] ; cp_end = cp + Col [col].length ; while (cp < cp_end) { /* get a row */ row = *cp++ ; row_mark = Row [row].shared2.mark ; /* skip if dead */ if (ROW_IS_MARKED_DEAD (row_mark)) { continue ; } ASSERT (row != pivot_row) ; set_difference = row_mark - tag_mark ; /* check if the row has been seen yet */ if (set_difference < 0) { ASSERT (Row [row].shared1.degree <= max_deg) ; set_difference = Row [row].shared1.degree ; } /* subtract column thickness from this row's set difference */ set_difference -= col_thickness ; ASSERT (set_difference >= 0) ; /* absorb this row if the set difference becomes zero */ if (set_difference == 0 && aggressive) { DEBUG3 (("aggressive absorption. Row: %d\n", row)) ; KILL_ROW (row) ; } else { /* save the new mark */ Row [row].shared2.mark = set_difference + tag_mark ; } } } #ifndef NDEBUG debug_deg_lists (n_row, n_col, Row, Col, head, min_score, n_col2-k-pivot_row_degree, max_deg) ; #endif /* NDEBUG */ /* === Add up set differences for each column ======================= */ DEBUG3 (("** Adding set differences phase. **\n")) ; /* for each column in pivot row */ rp = &A [pivot_row_start] ; rp_end = rp + pivot_row_length ; while (rp < rp_end) { /* get a column */ col = *rp++ ; ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ; hash = 0 ; cur_score = 0 ; cp = &A [Col [col].start] ; /* compact the column */ new_cp = cp ; cp_end = cp + Col [col].length ; DEBUG4 (("Adding set diffs for Col: %d.\n", col)) ; while (cp < cp_end) { /* get a row */ row = *cp++ ; ASSERT(row >= 0 && row < n_row) ; row_mark = Row [row].shared2.mark ; /* skip if dead */ if (ROW_IS_MARKED_DEAD (row_mark)) { DEBUG4 ((" Row %d, dead\n", row)) ; continue ; } DEBUG4 ((" Row %d, set diff %d\n", row, row_mark-tag_mark)); ASSERT (row_mark >= tag_mark) ; /* compact the column */ *new_cp++ = row ; /* compute hash function */ hash += row ; /* add set difference */ cur_score += row_mark - tag_mark ; /* integer overflow... */ cur_score = MIN (cur_score, n_col) ; } /* recompute the column's length */ Col [col].length = (Int) (new_cp - &A [Col [col].start]) ; /* === Further mass elimination ================================= */ if (Col [col].length == 0) { DEBUG4 (("further mass elimination. Col: %d\n", col)) ; /* nothing left but the pivot row in this column */ KILL_PRINCIPAL_COL (col) ; pivot_row_degree -= Col [col].shared1.thickness ; ASSERT (pivot_row_degree >= 0) ; /* order it */ Col [col].shared2.order = k ; /* increment order count by column thickness */ k += Col [col].shared1.thickness ; } else { /* === Prepare for supercolumn detection ==================== */ DEBUG4 (("Preparing supercol detection for Col: %d.\n", col)) ; /* save score so far */ Col [col].shared2.score = cur_score ; /* add column to hash table, for supercolumn detection */ hash %= n_col + 1 ; DEBUG4 ((" Hash = %d, n_col = %d.\n", hash, n_col)) ; ASSERT (((Int) hash) <= n_col) ; head_column = head [hash] ; if (head_column > EMPTY) { /* degree list "hash" is non-empty, use prev (shared3) of */ /* first column in degree list as head of hash bucket */ first_col = Col [head_column].shared3.headhash ; Col [head_column].shared3.headhash = col ; } else { /* degree list "hash" is empty, use head as hash bucket */ first_col = - (head_column + 2) ; head [hash] = - (col + 2) ; } Col [col].shared4.hash_next = first_col ; /* save hash function in Col [col].shared3.hash */ Col [col].shared3.hash = (Int) hash ; ASSERT (COL_IS_ALIVE (col)) ; } } /* The approximate external column degree is now computed. */ /* === Supercolumn detection ======================================== */ DEBUG3 (("** Supercolumn detection phase. **\n")) ; detect_super_cols ( #ifndef NDEBUG n_col, Row, #endif /* NDEBUG */ Col, A, head, pivot_row_start, pivot_row_length) ; /* === Kill the pivotal column ====================================== */ KILL_PRINCIPAL_COL (pivot_col) ; /* === Clear mark =================================================== */ tag_mark = clear_mark (tag_mark+max_deg+1, max_mark, n_row, Row) ; #ifndef NDEBUG DEBUG3 (("check3\n")) ; debug_mark (n_row, Row, tag_mark, max_mark) ; #endif /* NDEBUG */ /* === Finalize the new pivot row, and column scores ================ */ DEBUG3 (("** Finalize scores phase. **\n")) ; /* for each column in pivot row */ rp = &A [pivot_row_start] ; /* compact the pivot row */ new_rp = rp ; rp_end = rp + pivot_row_length ; while (rp < rp_end) { col = *rp++ ; /* skip dead columns */ if (COL_IS_DEAD (col)) { continue ; } *new_rp++ = col ; /* add new pivot row to column */ A [Col [col].start + (Col [col].length++)] = pivot_row ; /* retrieve score so far and add on pivot row's degree. */ /* (we wait until here for this in case the pivot */ /* row's degree was reduced due to mass elimination). */ cur_score = Col [col].shared2.score + pivot_row_degree ; /* calculate the max possible score as the number of */ /* external columns minus the 'k' value minus the */ /* columns thickness */ max_score = n_col - k - Col [col].shared1.thickness ; /* make the score the external degree of the union-of-rows */ cur_score -= Col [col].shared1.thickness ; /* make sure score is less or equal than the max score */ cur_score = MIN (cur_score, max_score) ; ASSERT (cur_score >= 0) ; /* store updated score */ Col [col].shared2.score = cur_score ; /* === Place column back in degree list ========================= */ ASSERT (min_score >= 0) ; ASSERT (min_score <= n_col) ; ASSERT (cur_score >= 0) ; ASSERT (cur_score <= n_col) ; ASSERT (head [cur_score] >= EMPTY) ; next_col = head [cur_score] ; Col [col].shared4.degree_next = next_col ; Col [col].shared3.prev = EMPTY ; if (next_col != EMPTY) { Col [next_col].shared3.prev = col ; } head [cur_score] = col ; /* see if this score is less than current min */ min_score = MIN (min_score, cur_score) ; } #ifndef NDEBUG debug_deg_lists (n_row, n_col, Row, Col, head, min_score, n_col2-k, max_deg) ; #endif /* NDEBUG */ /* === Resurrect the new pivot row ================================== */ if (pivot_row_degree > 0) { /* update pivot row length to reflect any cols that were killed */ /* during super-col detection and mass elimination */ Row [pivot_row].start = pivot_row_start ; Row [pivot_row].length = (Int) (new_rp - &A[pivot_row_start]) ; ASSERT (Row [pivot_row].length > 0) ; Row [pivot_row].shared1.degree = pivot_row_degree ; Row [pivot_row].shared2.mark = 0 ; /* pivot row is no longer dead */ DEBUG1 (("Resurrect Pivot_row %d deg: %d\n", pivot_row, pivot_row_degree)) ; } } /* === All principal columns have now been ordered ====================== */ return (ngarbage) ; } /* ========================================================================== */ /* === order_children ======================================================= */ /* ========================================================================== */ /* The find_ordering routine has ordered all of the principal columns (the representatives of the supercolumns). The non-principal columns have not yet been ordered. This routine orders those columns by walking up the parent tree (a column is a child of the column which absorbed it). The final permutation vector is then placed in p [0 ... n_col-1], with p [0] being the first column, and p [n_col-1] being the last. It doesn't look like it at first glance, but be assured that this routine takes time linear in the number of columns. Although not immediately obvious, the time taken by this routine is O (n_col), that is, linear in the number of columns. Not user-callable. */ PRIVATE void order_children ( /* === Parameters ======================================================= */ Int n_col, /* number of columns of A */ Colamd_Col Col [], /* of size n_col+1 */ Int p [] /* p [0 ... n_col-1] is the column permutation*/ ) { /* === Local variables ================================================== */ Int i ; /* loop counter for all columns */ Int c ; /* column index */ Int parent ; /* index of column's parent */ Int order ; /* column's order */ /* === Order each non-principal column ================================== */ for (i = 0 ; i < n_col ; i++) { /* find an un-ordered non-principal column */ ASSERT (COL_IS_DEAD (i)) ; if (!COL_IS_DEAD_PRINCIPAL (i) && Col [i].shared2.order == EMPTY) { parent = i ; /* once found, find its principal parent */ do { parent = Col [parent].shared1.parent ; } while (!COL_IS_DEAD_PRINCIPAL (parent)) ; /* now, order all un-ordered non-principal columns along path */ /* to this parent. collapse tree at the same time */ c = i ; /* get order of parent */ order = Col [parent].shared2.order ; do { ASSERT (Col [c].shared2.order == EMPTY) ; /* order this column */ Col [c].shared2.order = order++ ; /* collaps tree */ Col [c].shared1.parent = parent ; /* get immediate parent of this column */ c = Col [c].shared1.parent ; /* continue until we hit an ordered column. There are */ /* guarranteed not to be anymore unordered columns */ /* above an ordered column */ } while (Col [c].shared2.order == EMPTY) ; /* re-order the super_col parent to largest order for this group */ Col [parent].shared2.order = order ; } } /* === Generate the permutation ========================================= */ for (c = 0 ; c < n_col ; c++) { p [Col [c].shared2.order] = c ; } } /* ========================================================================== */ /* === detect_super_cols ==================================================== */ /* ========================================================================== */ /* Detects supercolumns by finding matches between columns in the hash buckets. Check amongst columns in the set A [row_start ... row_start + row_length-1]. The columns under consideration are currently *not* in the degree lists, and have already been placed in the hash buckets. The hash bucket for columns whose hash function is equal to h is stored as follows: if head [h] is >= 0, then head [h] contains a degree list, so: head [h] is the first column in degree bucket h. Col [head [h]].headhash gives the first column in hash bucket h. otherwise, the degree list is empty, and: -(head [h] + 2) is the first column in hash bucket h. For a column c in a hash bucket, Col [c].shared3.prev is NOT a "previous column" pointer. Col [c].shared3.hash is used instead as the hash number for that column. The value of Col [c].shared4.hash_next is the next column in the same hash bucket. Assuming no, or "few" hash collisions, the time taken by this routine is linear in the sum of the sizes (lengths) of each column whose score has just been computed in the approximate degree computation. Not user-callable. */ PRIVATE void detect_super_cols ( /* === Parameters ======================================================= */ #ifndef NDEBUG /* these two parameters are only needed when debugging is enabled: */ Int n_col, /* number of columns of A */ Colamd_Row Row [], /* of size n_row+1 */ #endif /* NDEBUG */ Colamd_Col Col [], /* of size n_col+1 */ Int A [], /* row indices of A */ Int head [], /* head of degree lists and hash buckets */ Int row_start, /* pointer to set of columns to check */ Int row_length /* number of columns to check */ ) { /* === Local variables ================================================== */ Int hash ; /* hash value for a column */ Int *rp ; /* pointer to a row */ Int c ; /* a column index */ Int super_c ; /* column index of the column to absorb into */ Int *cp1 ; /* column pointer for column super_c */ Int *cp2 ; /* column pointer for column c */ Int length ; /* length of column super_c */ Int prev_c ; /* column preceding c in hash bucket */ Int i ; /* loop counter */ Int *rp_end ; /* pointer to the end of the row */ Int col ; /* a column index in the row to check */ Int head_column ; /* first column in hash bucket or degree list */ Int first_col ; /* first column in hash bucket */ /* === Consider each column in the row ================================== */ rp = &A [row_start] ; rp_end = rp + row_length ; while (rp < rp_end) { col = *rp++ ; if (COL_IS_DEAD (col)) { continue ; } /* get hash number for this column */ hash = Col [col].shared3.hash ; ASSERT (hash <= n_col) ; /* === Get the first column in this hash bucket ===================== */ head_column = head [hash] ; if (head_column > EMPTY) { first_col = Col [head_column].shared3.headhash ; } else { first_col = - (head_column + 2) ; } /* === Consider each column in the hash bucket ====================== */ for (super_c = first_col ; super_c != EMPTY ; super_c = Col [super_c].shared4.hash_next) { ASSERT (COL_IS_ALIVE (super_c)) ; ASSERT (Col [super_c].shared3.hash == hash) ; length = Col [super_c].length ; /* prev_c is the column preceding column c in the hash bucket */ prev_c = super_c ; /* === Compare super_c with all columns after it ================ */ for (c = Col [super_c].shared4.hash_next ; c != EMPTY ; c = Col [c].shared4.hash_next) { ASSERT (c != super_c) ; ASSERT (COL_IS_ALIVE (c)) ; ASSERT (Col [c].shared3.hash == hash) ; /* not identical if lengths or scores are different */ if (Col [c].length != length || Col [c].shared2.score != Col [super_c].shared2.score) { prev_c = c ; continue ; } /* compare the two columns */ cp1 = &A [Col [super_c].start] ; cp2 = &A [Col [c].start] ; for (i = 0 ; i < length ; i++) { /* the columns are "clean" (no dead rows) */ ASSERT (ROW_IS_ALIVE (*cp1)) ; ASSERT (ROW_IS_ALIVE (*cp2)) ; /* row indices will same order for both supercols, */ /* no gather scatter nessasary */ if (*cp1++ != *cp2++) { break ; } } /* the two columns are different if the for-loop "broke" */ if (i != length) { prev_c = c ; continue ; } /* === Got it! two columns are identical =================== */ ASSERT (Col [c].shared2.score == Col [super_c].shared2.score) ; Col [super_c].shared1.thickness += Col [c].shared1.thickness ; Col [c].shared1.parent = super_c ; KILL_NON_PRINCIPAL_COL (c) ; /* order c later, in order_children() */ Col [c].shared2.order = EMPTY ; /* remove c from hash bucket */ Col [prev_c].shared4.hash_next = Col [c].shared4.hash_next ; } } /* === Empty this hash bucket ======================================= */ if (head_column > EMPTY) { /* corresponding degree list "hash" is not empty */ Col [head_column].shared3.headhash = EMPTY ; } else { /* corresponding degree list "hash" is empty */ head [hash] = EMPTY ; } } } /* ========================================================================== */ /* === garbage_collection =================================================== */ /* ========================================================================== */ /* Defragments and compacts columns and rows in the workspace A. Used when all avaliable memory has been used while performing row merging. Returns the index of the first free position in A, after garbage collection. The time taken by this routine is linear is the size of the array A, which is itself linear in the number of nonzeros in the input matrix. Not user-callable. */ PRIVATE Int garbage_collection /* returns the new value of pfree */ ( /* === Parameters ======================================================= */ Int n_row, /* number of rows */ Int n_col, /* number of columns */ Colamd_Row Row [], /* row info */ Colamd_Col Col [], /* column info */ Int A [], /* A [0 ... Alen-1] holds the matrix */ Int *pfree /* &A [0] ... pfree is in use */ ) { /* === Local variables ================================================== */ Int *psrc ; /* source pointer */ Int *pdest ; /* destination pointer */ Int j ; /* counter */ Int r ; /* a row index */ Int c ; /* a column index */ Int length ; /* length of a row or column */ #ifndef NDEBUG Int debug_rows ; DEBUG2 (("Defrag..\n")) ; for (psrc = &A[0] ; psrc < pfree ; psrc++) ASSERT (*psrc >= 0) ; debug_rows = 0 ; #endif /* NDEBUG */ /* === Defragment the columns =========================================== */ pdest = &A[0] ; for (c = 0 ; c < n_col ; c++) { if (COL_IS_ALIVE (c)) { psrc = &A [Col [c].start] ; /* move and compact the column */ ASSERT (pdest <= psrc) ; Col [c].start = (Int) (pdest - &A [0]) ; length = Col [c].length ; for (j = 0 ; j < length ; j++) { r = *psrc++ ; if (ROW_IS_ALIVE (r)) { *pdest++ = r ; } } Col [c].length = (Int) (pdest - &A [Col [c].start]) ; } } /* === Prepare to defragment the rows =================================== */ for (r = 0 ; r < n_row ; r++) { if (ROW_IS_DEAD (r) || (Row [r].length == 0)) { /* This row is already dead, or is of zero length. Cannot compact * a row of zero length, so kill it. NOTE: in the current version, * there are no zero-length live rows. Kill the row (for the first * time, or again) just to be safe. */ KILL_ROW (r) ; } else { /* save first column index in Row [r].shared2.first_column */ psrc = &A [Row [r].start] ; Row [r].shared2.first_column = *psrc ; ASSERT (ROW_IS_ALIVE (r)) ; /* flag the start of the row with the one's complement of row */ *psrc = ONES_COMPLEMENT (r) ; #ifndef NDEBUG debug_rows++ ; #endif /* NDEBUG */ } } /* === Defragment the rows ============================================== */ psrc = pdest ; while (psrc < pfree) { /* find a negative number ... the start of a row */ if (*psrc++ < 0) { psrc-- ; /* get the row index */ r = ONES_COMPLEMENT (*psrc) ; ASSERT (r >= 0 && r < n_row) ; /* restore first column index */ *psrc = Row [r].shared2.first_column ; ASSERT (ROW_IS_ALIVE (r)) ; ASSERT (Row [r].length > 0) ; /* move and compact the row */ ASSERT (pdest <= psrc) ; Row [r].start = (Int) (pdest - &A [0]) ; length = Row [r].length ; for (j = 0 ; j < length ; j++) { c = *psrc++ ; if (COL_IS_ALIVE (c)) { *pdest++ = c ; } } Row [r].length = (Int) (pdest - &A [Row [r].start]) ; ASSERT (Row [r].length > 0) ; #ifndef NDEBUG debug_rows-- ; #endif /* NDEBUG */ } } /* ensure we found all the rows */ ASSERT (debug_rows == 0) ; /* === Return the new value of pfree ==================================== */ return ((Int) (pdest - &A [0])) ; } /* ========================================================================== */ /* === clear_mark =========================================================== */ /* ========================================================================== */ /* Clears the Row [].shared2.mark array, and returns the new tag_mark. Return value is the new tag_mark. Not user-callable. */ PRIVATE Int clear_mark /* return the new value for tag_mark */ ( /* === Parameters ======================================================= */ Int tag_mark, /* new value of tag_mark */ Int max_mark, /* max allowed value of tag_mark */ Int n_row, /* number of rows in A */ Colamd_Row Row [] /* Row [0 ... n_row-1].shared2.mark is set to zero */ ) { /* === Local variables ================================================== */ Int r ; if (tag_mark <= 0 || tag_mark >= max_mark) { for (r = 0 ; r < n_row ; r++) { if (ROW_IS_ALIVE (r)) { Row [r].shared2.mark = 0 ; } } tag_mark = 1 ; } return (tag_mark) ; } /* ========================================================================== */ /* === print_report ========================================================= */ /* ========================================================================== */ PRIVATE void print_report ( char *method, Int stats [COLAMD_STATS] ) { Int i1, i2, i3 ; PRINTF (("\n%s version %d.%d, %s: ", method, COLAMD_MAIN_VERSION, COLAMD_SUB_VERSION, COLAMD_DATE)) ; if (!stats) { PRINTF (("No statistics available.\n")) ; return ; } i1 = stats [COLAMD_INFO1] ; i2 = stats [COLAMD_INFO2] ; i3 = stats [COLAMD_INFO3] ; if (stats [COLAMD_STATUS] >= 0) { PRINTF (("OK. ")) ; } else { PRINTF (("ERROR. ")) ; } switch (stats [COLAMD_STATUS]) { case COLAMD_OK_BUT_JUMBLED: PRINTF(("Matrix has unsorted or duplicate row indices.\n")) ; PRINTF(("%s: number of duplicate or out-of-order row indices: %d\n", method, i3)) ; PRINTF(("%s: last seen duplicate or out-of-order row index: %d\n", method, INDEX (i2))) ; PRINTF(("%s: last seen in column: %d", method, INDEX (i1))) ; /* no break - fall through to next case instead */ case COLAMD_OK: PRINTF(("\n")) ; PRINTF(("%s: number of dense or empty rows ignored: %d\n", method, stats [COLAMD_DENSE_ROW])) ; PRINTF(("%s: number of dense or empty columns ignored: %d\n", method, stats [COLAMD_DENSE_COL])) ; PRINTF(("%s: number of garbage collections performed: %d\n", method, stats [COLAMD_DEFRAG_COUNT])) ; break ; case COLAMD_ERROR_A_not_present: PRINTF(("Array A (row indices of matrix) not present.\n")) ; break ; case COLAMD_ERROR_p_not_present: PRINTF(("Array p (column pointers for matrix) not present.\n")) ; break ; case COLAMD_ERROR_nrow_negative: PRINTF(("Invalid number of rows (%d).\n", i1)) ; break ; case COLAMD_ERROR_ncol_negative: PRINTF(("Invalid number of columns (%d).\n", i1)) ; break ; case COLAMD_ERROR_nnz_negative: PRINTF(("Invalid number of nonzero entries (%d).\n", i1)) ; break ; case COLAMD_ERROR_p0_nonzero: PRINTF(("Invalid column pointer, p [0] = %d, must be zero.\n", i1)); break ; case COLAMD_ERROR_A_too_small: PRINTF(("Array A too small.\n")) ; PRINTF((" Need Alen >= %d, but given only Alen = %d.\n", i1, i2)) ; break ; case COLAMD_ERROR_col_length_negative: PRINTF (("Column %d has a negative number of nonzero entries (%d).\n", INDEX (i1), i2)) ; break ; case COLAMD_ERROR_row_index_out_of_bounds: PRINTF (("Row index (row %d) out of bounds (%d to %d) in column %d.\n", INDEX (i2), INDEX (0), INDEX (i3-1), INDEX (i1))) ; break ; case COLAMD_ERROR_out_of_memory: PRINTF(("Out of memory.\n")) ; break ; /* v2.4: internal-error case deleted */ } } /* ========================================================================== */ /* === colamd debugging routines ============================================ */ /* ========================================================================== */ /* When debugging is disabled, the remainder of this file is ignored. */ #ifndef NDEBUG /* ========================================================================== */ /* === debug_structures ===================================================== */ /* ========================================================================== */ /* At this point, all empty rows and columns are dead. All live columns are "clean" (containing no dead rows) and simplicial (no supercolumns yet). Rows may contain dead columns, but all live rows contain at least one live column. */ PRIVATE void debug_structures ( /* === Parameters ======================================================= */ Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int A [], Int n_col2 ) { /* === Local variables ================================================== */ Int i ; Int c ; Int *cp ; Int *cp_end ; Int len ; Int score ; Int r ; Int *rp ; Int *rp_end ; Int deg ; /* === Check A, Row, and Col ============================================ */ for (c = 0 ; c < n_col ; c++) { if (COL_IS_ALIVE (c)) { len = Col [c].length ; score = Col [c].shared2.score ; DEBUG4 (("initial live col %5d %5d %5d\n", c, len, score)) ; ASSERT (len > 0) ; ASSERT (score >= 0) ; ASSERT (Col [c].shared1.thickness == 1) ; cp = &A [Col [c].start] ; cp_end = cp + len ; while (cp < cp_end) { r = *cp++ ; ASSERT (ROW_IS_ALIVE (r)) ; } } else { i = Col [c].shared2.order ; ASSERT (i >= n_col2 && i < n_col) ; } } for (r = 0 ; r < n_row ; r++) { if (ROW_IS_ALIVE (r)) { i = 0 ; len = Row [r].length ; deg = Row [r].shared1.degree ; ASSERT (len > 0) ; ASSERT (deg > 0) ; rp = &A [Row [r].start] ; rp_end = rp + len ; while (rp < rp_end) { c = *rp++ ; if (COL_IS_ALIVE (c)) { i++ ; } } ASSERT (i > 0) ; } } } /* ========================================================================== */ /* === debug_deg_lists ====================================================== */ /* ========================================================================== */ /* Prints the contents of the degree lists. Counts the number of columns in the degree list and compares it to the total it should have. Also checks the row degrees. */ PRIVATE void debug_deg_lists ( /* === Parameters ======================================================= */ Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int head [], Int min_score, Int should, Int max_deg ) { /* === Local variables ================================================== */ Int deg ; Int col ; Int have ; Int row ; /* === Check the degree lists =========================================== */ if (n_col > 10000 && colamd_debug <= 0) { return ; } have = 0 ; DEBUG4 (("Degree lists: %d\n", min_score)) ; for (deg = 0 ; deg <= n_col ; deg++) { col = head [deg] ; if (col == EMPTY) { continue ; } DEBUG4 (("%d:", deg)) ; while (col != EMPTY) { DEBUG4 ((" %d", col)) ; have += Col [col].shared1.thickness ; ASSERT (COL_IS_ALIVE (col)) ; col = Col [col].shared4.degree_next ; } DEBUG4 (("\n")) ; } DEBUG4 (("should %d have %d\n", should, have)) ; ASSERT (should == have) ; /* === Check the row degrees ============================================ */ if (n_row > 10000 && colamd_debug <= 0) { return ; } for (row = 0 ; row < n_row ; row++) { if (ROW_IS_ALIVE (row)) { ASSERT (Row [row].shared1.degree <= max_deg) ; } } } /* ========================================================================== */ /* === debug_mark =========================================================== */ /* ========================================================================== */ /* Ensures that the tag_mark is less that the maximum and also ensures that each entry in the mark array is less than the tag mark. */ PRIVATE void debug_mark ( /* === Parameters ======================================================= */ Int n_row, Colamd_Row Row [], Int tag_mark, Int max_mark ) { /* === Local variables ================================================== */ Int r ; /* === Check the Row marks ============================================== */ ASSERT (tag_mark > 0 && tag_mark <= max_mark) ; if (n_row > 10000 && colamd_debug <= 0) { return ; } for (r = 0 ; r < n_row ; r++) { ASSERT (Row [r].shared2.mark < tag_mark) ; } } /* ========================================================================== */ /* === debug_matrix ========================================================= */ /* ========================================================================== */ /* Prints out the contents of the columns and the rows. */ PRIVATE void debug_matrix ( /* === Parameters ======================================================= */ Int n_row, Int n_col, Colamd_Row Row [], Colamd_Col Col [], Int A [] ) { /* === Local variables ================================================== */ Int r ; Int c ; Int *rp ; Int *rp_end ; Int *cp ; Int *cp_end ; /* === Dump the rows and columns of the matrix ========================== */ if (colamd_debug < 3) { return ; } DEBUG3 (("DUMP MATRIX:\n")) ; for (r = 0 ; r < n_row ; r++) { DEBUG3 (("Row %d alive? %d\n", r, ROW_IS_ALIVE (r))) ; if (ROW_IS_DEAD (r)) { continue ; } DEBUG3 (("start %d length %d degree %d\n", Row [r].start, Row [r].length, Row [r].shared1.degree)) ; rp = &A [Row [r].start] ; rp_end = rp + Row [r].length ; while (rp < rp_end) { c = *rp++ ; DEBUG4 ((" %d col %d\n", COL_IS_ALIVE (c), c)) ; } } for (c = 0 ; c < n_col ; c++) { DEBUG3 (("Col %d alive? %d\n", c, COL_IS_ALIVE (c))) ; if (COL_IS_DEAD (c)) { continue ; } DEBUG3 (("start %d length %d shared1 %d shared2 %d\n", Col [c].start, Col [c].length, Col [c].shared1.thickness, Col [c].shared2.score)) ; cp = &A [Col [c].start] ; cp_end = cp + Col [c].length ; while (cp < cp_end) { r = *cp++ ; DEBUG4 ((" %d row %d\n", ROW_IS_ALIVE (r), r)) ; } } } PRIVATE void colamd_get_debug ( char *method ) { FILE *f ; colamd_debug = 0 ; /* no debug printing */ f = fopen ("debug", "r") ; if (f == (FILE *) NULL) { colamd_debug = 0 ; } else { fscanf (f, "%d", &colamd_debug) ; fclose (f) ; } DEBUG0 (("%s: debug version, D = %d (THIS WILL BE SLOW!)\n", method, colamd_debug)) ; } #endif /* NDEBUG */ SuiteSparse/COLAMD/README.txt0000644001170100242450000001236510617111160014405 0ustar davisfacThe COLAMD ordering method - Version 2.7 ------------------------------------------------------------------------------- The COLAMD column approximate minimum degree ordering algorithm computes a permutation vector P such that the LU factorization of A (:,P) tends to be sparser than that of A. The Cholesky factorization of (A (:,P))'*(A (:,P)) will also tend to be sparser than that of A'*A. SYMAMD is a symmetric minimum degree ordering method based on COLAMD, available as a MATLAB-callable function. It constructs a matrix M such that M'*M has the same pattern as A, and then uses COLAMD to compute a column ordering of M. Colamd and symamd tend to be faster and generate better orderings than their MATLAB counterparts, colmmd and symmmd. To compile and test the colamd m-files and mexFunctions, just unpack the COLAMD/ directory from the COLAMD.tar.gz file, and run MATLAB from within that directory. Next, type colamd_test to compile and test colamd and symamd. This will work on any computer with MATLAB (Unix, PC, or Mac). Alternatively, type "make" (in Unix) to compile and run a simple example C code, without using MATLAB. To compile and install the colamd m-files and mexFunctions, just cd to COLAMD/MATLAB and type colamd_install in the MATLAB command window. A short demo will run. Optionally, type colamd_test to run an extensive tests. Type "make" in Unix in the COLAMD directory to compile the C-callable library and to run a short demo. If you have MATLAB 7.2 or earlier, you must first edit UFconfig/UFconfig.h to remove the "-largeArrayDims" option from the MEX command (or just use colamd_make.m inside MATLAB). Colamd is a built-in routine in MATLAB, available from The Mathworks, Inc. Under most cases, the compiled COLAMD from Versions 2.0 to the current version do not differ. Colamd Versions 2.2 and 2.3 differ only in their mexFunction interaces to MATLAB. v2.4 fixes a bug in the symamd routine in v2.3. The bug (in v2.3 and earlier) has no effect on the MATLAB symamd mexFunction. v2.5 adds additional checks for integer overflow, so that the "int" version can be safely used with 64-bit pointers. Refer to the ChangeLog for more details. To use colamd and symamd within an application written in C, all you need are colamd.c, colamd_global.c, and colamd.h, which are the C-callable colamd/symamd codes. See colamd.c for more information on how to call colamd from a C program. Requires UFconfig, in the ../UFconfig directory relative to this directory. Copyright (c) 1998-2007, Timothy A. Davis, All Rights Reserved. See http://www.cise.ufl.edu/research/sparse/colamd (the colamd.c file) for the License. Related papers: T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, An approximate column minimum degree ordering algorithm, ACM Transactions on Mathematical Software, vol. 30, no. 3., pp. 353-376, 2004. T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, Algorithm 836: COLAMD, an approximate column minimum degree ordering algorithm, ACM Transactions on Mathematical Software, vol. 30, no. 3., pp. 377-380, 2004. "An approximate minimum degree column ordering algorithm", S. I. Larimore, MS Thesis, Dept. of Computer and Information Science and Engineering, University of Florida, Gainesville, FL, 1998. CISE Tech Report TR-98-016. Available at ftp://ftp.cise.ufl.edu/cis/tech-reports/tr98/tr98-016.ps via anonymous ftp. Approximate Deficiency for Ordering the Columns of a Matrix, J. L. Kern, Senior Thesis, Dept. of Computer and Information Science and Engineering, University of Florida, Gainesville, FL, 1999. Available at http://www.cise.ufl.edu/~davis/Kern/kern.ps Authors: Stefan I. Larimore and Timothy A. Davis, University of Florida, in collaboration with John Gilbert, Xerox PARC (now at UC Santa Barbara), and Esmong Ng, Lawrence Berkeley National Laboratory (much of this work he did while at Oak Ridge National Laboratory). COLAMD files: Demo simple demo Doc additional documentation (see colamd.c for more) Include include file Lib compiled C-callable library Makefile primary Unix Makefile MATLAB MATLAB functions README.txt this file Source C source code ./Demo: colamd_example.c simple example colamd_example.out output of colamd_example.c colamd_l_example.c simple example, long integers colamd_l_example.out output of colamd_l_example.c Makefile Makefile for C demos ./Doc: ChangeLog change log lesser.txt license ./Include: colamd.h include file ./Lib: Makefile Makefile for C-callable library ./MATLAB: colamd2.m MATLAB interface for colamd2 colamd_demo.m simple demo colamd_install.m compile and install colamd2 and symamd2 colamd_make.m compile colamd2 and symamd2 colamdmex.ca MATLAB mexFunction for colamd2 colamd_test.m extensive test colamdtestmex.c test function for colamd Contents.m contents of the MATLAB directory luflops.m test code Makefile Makefile for MATLAB functions symamd2.m MATLAB interface for symamd2 symamdmex.c MATLAB mexFunction for symamd2 symamdtestmex.c test function for symamd ./Source: colamd.c primary source code colamd_global.c globally defined function pointers (malloc, free, ...) SuiteSparse/LINFACTOR/0000755001170100242450000000000010711445626013276 5ustar davisfacSuiteSparse/LINFACTOR/lintests.m0000644001170100242450000000274610710677546015341 0ustar davisfacfunction lintests %LINTESTS test linfactor with many different kinds of systems. % Compares x=A\b, linfactor and (ack!) inv(A)*b. You should never, ever use % inv(A) to solve a linear system. % % Example % lintests % % See also lintest, linfactor, mldivide. % Copyright 2007, Timothy A. Davis rand ('state', 0) ; help linfactor for n = [100 1000 2000] fprintf ('\nn: %d (with all nonzero matrix A)\n', n) ; % dense LU A = rand (n) ; b = rand (n,1) ; lintest (A,b) ; % sparse LU A = sparse (A) ; lintest (A,b) ; % dense Cholesky A = A*A' + 10*eye(n) ; lintest (A,b) ; % sparse Cholesky A = sparse (A) ; lintest (A,b) ; end for n = [1000 2000 1e5] % note that UMFPACK is not particularly fast for tridiagonal matrices % (see "doc mldivide", which uses a specialized tridiagonal solver) fprintf ('\nn: %d (sparse tridiagonal matrix)\n', n) ; % sparse LU e = rand (n, 1) ; b = rand (n, 1) ; A = spdiags ([e 4*e e], -1:1, n, n) ; lintest (A,b) ; % sparse Cholesky e = ones (n, 1) ; A = spdiags ([e 4*e e], -1:1, n, n) ; lintest (A,b) ; end % sparse LU again fprintf ('\nwest0479:\n') ; load west0479 ; n = size (west0479, 1) ; b = rand (n, 1) ; lintest (west0479, b) ; % completely break inv(A) with a simple 2-by-2 matrix ... fprintf ('\nbreak inv(A) with a trivial 2-by-2 matrix:\n') ; s = warning ('off', 'MATLAB:singularMatrix') ; lintest (rand(2) * realmin/2, ones(2,1)) ; warning (s) ; SuiteSparse/LINFACTOR/Contents.m0000644001170100242450000000200010627014733015236 0ustar davisfac% LINFACTOR % % This simple MATLAB function shows you how to use LU or CHOL to factor a matrix % and then solve a linear system A*x=b. % % Files % linfactor - factorize a matrix, or use the factors to solve Ax=b. % lintests - test linfactor with many different kinds of systems. % lintest - test A*x=b, using linfactor, x=A\b, and (ack!) the explicit inv(A). % % Example: % F = linfactor (A) ; % factor A, returning an object F % x = linfactor (F,b) ; % solve Ax=b using F (the factorization of A) % lintests ; % test linfactor with various kinds of systems % Copyright 2007, Timothy A. Davis, University of Florida. % % License: this software is free for any use. No warranty included or implied. % You must agree to only one condition to use this software: you must be aware % that you have been told that using inv(A) is a horrible, awful, and absoluty % abysmal method for solving a linear system of equations. If you do not % agree to this condition, you must delete this software. SuiteSparse/LINFACTOR/linfactor.m0000644001170100242450000001450310711445626015440 0ustar davisfacfunction [result, t] = linfactor (arg1, arg2) %LINFACTOR factorize a matrix, or use the factors to solve Ax=b. % Uses LU or CHOL to factorize A, or uses a previously computed factorization to % solve a linear system. This function automatically selects an LU or Cholesky % factorization, depending on the matrix. A better method would be for you to % select it yourself. Note that mldivide uses a faster method for detecting % whether or not A is a candidate for sparse Cholesky factorization (see spsym % in the CHOLMOD package, for example). % % Example: % F = linfactor (A) ; % factorizes A into the object F % x = linfactor (F,b) ; % uses F to solve Ax=b % norm (A*x-b) % % A second output is the time taken by the method, ignoring the overhead of % determining which method to use. This makes for a fairer comparison between % methods, since normally the user will know if the matrix is supposed to be % symmetric positive definite or not, and whether or not the matrix is sparse. % Also, the overhead here is much higher than mldivide or spsym. % % This function has its limitations: % % (1) determining whether or not the matrix is symmetric via nnz(A-A') is slow. % mldivide (and spsym in CHOLMOD) do it much faster. % % (2) MATLAB really needs a sparse linsolve. See cs_lsolve, cs_ltsolve, and % cs_usolve in CSparse, for example. % % (3) this function really needs to be written as a mexFunction. % % (4) the full power of mldivide is not brought to bear. For example, UMFPACK % is not very fast for sparse tridiagonal matrices. It's about a factor of % four slower than a specialized tridiagonal solver as used in mldivide. % % (5) permuting a sparse vector or matrix is slower in MATLAB than it should be; % a built-in linfactor would reduce this overhead. % % (6) mldivide when using UMFPACK uses relaxed partial pivoting and then % iterative refinement. This leads to sparser LU factors, and typically % accurate results. linfactor uses sparse LU without iterative refinement. % % The primary purpose of this function is to answer The Perennially Asked % Question (or The PAQ for short (*)): "Why not use x=inv(A)*b to solve Ax=b? % How do I use LU or CHOL to solve Ax=b?" The full answer is below. The short % answer to The PAQ (*) is "PAQ=LU ... ;-) ... never EVER use inv(A) to solve % Ax=b." % % The secondary purpose of this function is to provide a prototype for some of % the functionality of a true MATLAB built-in linfactor function. % % Finally, the third purpose of this function is that you might find it actually % useful for production use, since its syntax is simpler than factorizing the % matrix yourself and then using the factors to solve the system. % % See also lu, chol, mldivide, linsolve, umfpack, cholmod. % % Oh, did I tell you never to use inv(A) to solve Ax=b? % % Requires MATLAB 7.3 (R2006b) or later. % Copyright 2007, Timothy A. Davis, University of Florida % VERSION 1.1.0, Nov 1, 2007 if (nargin < 1 | nargin > 2 | nargout > 2) %#ok error ('Usage: F=linfactor(A) or x=linfactor(F,b)') ; end if (nargin == 1) %--------------------------------------------------------------------------- % F = linfactor (A) ; %--------------------------------------------------------------------------- A = arg1 ; [m n] = size (A) ; if (m ~= n) error ('linfactor: A must be square') ; end if (issparse (A)) % try sparse Cholesky (CHOLMOD): L*L' = P*A*P' if (nnz (A-A') == 0 & all (diag (A) > 0)) %#ok try tic ; [L, g, PT] = chol (A, 'lower') ; t = toc ; if (g == 0) result.L = L ; result.LT = L' ; % takes more memory, but solve is faster result.P = PT' ; % ditto. Need a sparse linsolve here... result.PT = PT ; result.kind = 'sparse Cholesky: L*L'' = P*A*P''' ; result.code = 0 ; return end catch % matrix is symmetric, but not positive definite % (or we ran out of memory) end end % try sparse LU (UMFPACK, with row scaling): L*U = P*(R\A)*Q tic ; [L, U, P, Q, R] = lu (A) ; t = toc ; result.L = L ; result.U = U ; result.P = P ; result.Q = Q ; result.R = R ; result.kind = 'sparse LU: L*U = P*(R\A)*Q where R is diagonal' ; result.code = 1 ; else % try dense Cholesky (LAPACK): L*L' = A if (nnz (A-A') == 0 & all (diag (A) > 0)) %#ok try tic ; L = chol (A, 'lower') ; t = toc ; result.L = L ; result.kind = 'dense Cholesky: L*L'' = A' ; result.code = 2 ; return catch % matrix is symmetric, but not positive definite % (or we ran out of memory) end end % try dense LU (LAPACK): L*U = A(p,:) tic ; [L, U, p] = lu (A, 'vector') ; t = toc ; result.L = L ; result.U = U ; result.p = p ; result.kind = 'dense LU: L*U = A(p,:)' ; result.code = 3 ; end else %--------------------------------------------------------------------------- % x = linfactor (F,b) %--------------------------------------------------------------------------- F = arg1 ; b = arg2 ; if (F.code == 0) % sparse Cholesky: MATLAB could use a sparse linsolve here ... tic ; result = F.PT * (F.LT \ (F.L \ (F.P * b))) ; t = toc ; elseif (F.code == 1) % sparse LU: MATLAB could use a sparse linsolve here too ... tic ; result = F.Q * (F.U \ (F.L \ (F.P * (F.R \ b)))) ; t = toc ; elseif (F.code == 2) % dense Cholesky: result = F.L' \ (F.L \ b) ; lower.LT = true ; upper.LT = true ; upper.TRANSA = true ; tic ; result = linsolve (F.L, linsolve (F.L, b, lower), upper) ; t = toc ; elseif (F.code == 3) % dense LU: result = F.U \ (F.L \ b (F.p,:)) ; lower.LT = true ; upper.UT = true ; tic ; result = linsolve (F.U, linsolve (F.L, b (F.p,:), lower), upper) ; t = toc ; end end SuiteSparse/LINFACTOR/README.txt0000644001170100242450000000520210627050234014764 0ustar davisfacLINFACTOR factorize a matrix, or use the factors to solve Ax=b. Uses LU or CHOL to factorize A, or uses a previously computed factorization to solve a linear system. This function automatically selects an LU or Cholesky factorization, depending on the matrix. A better method would be for you to select it yourself. Note that mldivide uses a faster method for detecting whether or not A is a candidate for sparse Cholesky factorization (see spsym in the CHOLMOD package, for example). Example: F = linfactor (A) ; % factorizes A into the object F x = linfactor (F,b) ; % uses F to solve Ax=b norm (A*x-b) A second output is the time taken by the method, ignoring the overhead of determining which method to use. This makes for a fairer comparison between methods, since normally the user will know if the matrix is supposed to be symmetric positive definite or not, and whether or not the matrix is sparse. Also, the overhead here is much higher than mldivide or spsym. This function has its limitations: (1) determining whether or not the matrix is symmetric via nnz(A-A') is slow. mldivide (and spsym in CHOLMOD) do it much faster. (2) MATLAB really needs a sparse linsolve. See cs_lsolve, cs_ltsolve, and cs_usolve in CSparse, for example. (3) this function really needs to be written as a mexFunction. (4) the full power of mldivide is not brought to bear. For example, UMFPACK is not very fast for sparse tridiagonal matrices. It's about a factor of four slower than a specialized tridiagonal solver as used in mldivide. (5) permuting a sparse vector or matrix is slower in MATLAB than it should be; a built-in linfactor would reduce this overhead. (6) mldivide when using UMFPACK uses relaxed partial pivoting and then iterative refinement. This leads to sparser LU factors, and typically accurate results. linfactor uses sparse LU without iterative refinement. The primary purpose of this function is to answer The Perennially Asked Question (or The PAQ for short (*)): "Why not use x=inv(A)*b to solve Ax=b? How do I use LU or CHOL to solve Ax=b?" The full answer is below. The short answer to The PAQ (*) is "PAQ=LU ... ;-) ... never EVER use inv(A) to solve Ax=b." The secondary purpose of this function is to provide a prototype for some of the functionality of a true MATLAB built-in linfactor function. Finally, the third purpose of this function is that you might find it actually useful for production use, since its syntax is simpler than factorizing the matrix yourself and then using the factors to solve the system. See also lu, chol, mldivide, linsolve, umfpack, cholmod. Oh, did I tell you never to use inv(A) to solve Ax=b? SuiteSparse/LINFACTOR/lintest.m0000644001170100242450000001226110710136023015123 0ustar davisfacfunction lintest (A,b) %LINTEST test A*x=b, using linfactor, x=A\b, and (ack!) the explicit inv(A). % The results printed include the breakeven point, which is the number of % systems Ax=b that must be solved with the same A but different b for the % inv(A) method to be faster than linfactor. Using inv(A) is always % numerically dubious, and typically slower. However because of MATLAB's % interpretive overhead, linfactor can be slightly slower in its % forward/backsolves. A true linfactor mexFunction would probably be just as % fast as inv(A)*b when A is full. You should never ever use inv(A) to solve % a linear system. % % Example: % load west0479 % b = rand (size (west0479,1), 1) ; % lintest (west0479, b) ; % % See also linfactor, lintests, mldivide % Copyright 2007, Timothy A. Davis %------------------------------------------------------------------------------- % warmup, to make sure functions are loaded, for accurate timings %------------------------------------------------------------------------------- F = linfactor (1) ; x = linfactor (F, 1) ; %#ok F = linfactor (sparse (1)) ; x = linfactor (F, 1) ; %#ok F = linfactor (sparse (-1)) ; x = linfactor (F, 1) ; %#ok S = inv (1) ; x = S*1 ; %#ok S = inv (sparse (1)) ; x = S*1 ; %#ok S = inv (sparse (-1)) ; x = S*1 ; %#ok x = rand (2) \ rand (2,1) ; %#ok x = sparse (rand (2)) \ rand (2,1) ; %#ok clear x F S %------------------------------------------------------------------------------- % linfactor %------------------------------------------------------------------------------- % do this several times for accurate timings t1 = 0 ; trials = 0 ; while (t1 < 1) [F, t] = linfactor (A) ; % factorize A t1 = t1 + t ; trials = trials + 1 ; end t1 = t1 / trials ; % do this several times for accurate timings t2 = 0 ; trials = 0 ; while (t2 < 1) [x, t] = linfactor (F, b) ; % use the factors to solve Ax=b t2 = t2 + t ; trials = trials + 1 ; end t2 = t2 / trials ; resid = norm (A*x-b,1) / (norm (A,1) * norm (x,1) + norm (b,1)) ; fprintf ('%-16s factor time: %10.6f solve time: %10.6f resid: %8.2e\n', ... F.kind (1:(find(F.kind == ':', 1, 'first'))), t1, t2, resid) ; %------------------------------------------------------------------------------- % inv %------------------------------------------------------------------------------- % Try again using inv(A)*b. This is a really horrible way to solve Ax=b. I'm % doing it here precisely to show that it is typically slower, except when there % are a huge number of right-hand-sides to solve and A is small. inv(A) also % tends to be less accurate, but random matrices do not trigger that problem. % It fails hopelessly when A is large, sparse, and where max(diff(r)) is large % where [p,q,r,s] = dmperm(A). Never, ever use inv(A) to solve a linear system. % Oh, did I tell you never to use inv(A) to solve Ax=b? try % do this several times for accurate timings t3 = 0 ; trials = 0 ; while (t3 < 1) tic ; S = inv (A) ; %#ok t = toc ; t3 = t3 + t ; trials = trials + 1 ; end t3 = t3 / trials ; % do this several times for accurate timings t4 = 0 ; trials = 0 ; while (t4 < 1) tic ; x = S*b ; t = toc ; t4 = t4 + t ; trials = trials + 1 ; end t4 = t4 / trials ; resid = norm (A*x-b,1) / (norm (A,1) * norm (x,1) + norm (b,1)) ; fprintf ('%-16s factor time: %10.6f solve time: %10.6f resid: %8.2e\n', ... 'inv(A)', t3, t4, resid) ; % determine the breakeven point where using inv(A) is faster nrhs = max (1, ceil ((t3 - t1) / (t2 - t4))) ; if (t1 < t3 & t2 < t4) %#ok fprintf ('inv(A) breakeven: never\n') ; elseif (t3 < t1 & t4 < t2) %#ok fprintf ('inv(A) breakeven: > 0\n') ; elseif (t1 < t3 & t4 < t2) %#ok fprintf ('inv(A) breakeven: > %d\n', nrhs) ; else fprintf ('inv(A) breakeven: < %d\n', nrhs) ; end catch % inv(A) probably ran out of memory fprintf ('inv(A) failed\n') ; fprintf ('inv(A) breakeven: never\n') ; end %------------------------------------------------------------------------------- % backslash %------------------------------------------------------------------------------- % do this several times for accurate timings t0 = 0 ; trials = 0 ; while (t0 < 1) tic ; x = A\b ; % solve Ax=b t = toc ; t0 = t0 + t ; trials = trials + 1 ; end t0 = t0 / trials ; resid = norm (A*x-b,1) / (norm (A,1) * norm (x,1) + norm (b,1)) ; fprintf ('%-16s total time: %10.6f resid: %8.2e\n', ... 'x = A\b', t0, resid) ; fprintf ('\n') ; SuiteSparse/CXSparse_newfiles.tar.gz0000644001170100242450000214364610712165166016507 0ustar davisfact(G]s6_Ϳ5Y$۳ɦJL\M*I5b #[_ A-;]HnF6oYqv~zvzEog`yogxE !/uԛ/LB: ^q/ˀ⭱R!Tz5TJ5UE(@4PA!˂4KYi<> p$!JaIoA)-ݖϿafgIx'E*7/\j? 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Davis, Chapman Hall / CRC Press, 7th edition. % Controls the parameters a, b, c, n, azimuth, and elevation, using % sliders. To the whole range of each parameter, click on the button to % the right of each slider. % % Example: % shellgui % % See also GUIDE, SEASHELL % Copyright 2006 Timothy A. Davis % Last Modified by GUIDE v2.5 29-Jul-2006 11:33:37 % Begin initialization code - DO NOT EDIT gui_Singleton = 1; gui_State = struct('gui_Name', mfilename, ... 'gui_Singleton', gui_Singleton, ... 'gui_OpeningFcn', @shellgui_OpeningFcn, ... 'gui_OutputFcn', @shellgui_OutputFcn, ... 'gui_LayoutFcn', [] , ... 'gui_Callback', []); if nargin && ischar(varargin{1}) gui_State.gui_Callback = str2func(varargin{1}); end if nargout [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:}); else gui_mainfcn(gui_State, varargin{:}); end % End initialization code - DO NOT EDIT % --- Executes just before shellgui is made visible. function shellgui_OpeningFcn(hObject, eventdata, handles, varargin) %#ok % This function has no output args, see OutputFcn. % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % varargin command line arguments to shellgui (see VARARGIN) % Choose default command line output for shellgui handles.output = hObject; % Update handles structure guidata(hObject, handles); % UIWAIT makes shellgui wait for user response (see UIRESUME) % uiwait(handles.figure1); % --- Outputs from this function are returned to the command line. function varargout = shellgui_OutputFcn(hObject, eventdata, handles) %#ok % varargout cell array for returning output args (see VARARGOUT); % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Get default command line output from handles structure varargout{1} = handles.output; % --- Executes on slider movement. function slider1_Callback(hObject, eventdata, handles) %#ok % hObject handle to slider1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'Value') returns position of slider % get(hObject,'Min') and get(hObject,'Max') to determine range of slider global a b c n azimuth elevation a = get (hObject, 'Value') ; seashell (a, b, c, n, azimuth, elevation) ; % --- Executes during object creation, after setting all properties. function slider1_CreateFcn(hObject, eventdata, handles) %#ok % hObject handle to slider1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: slider controls usually have a light gray background. if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor',[.9 .9 .9]); end % --- Executes on slider movement. function slider2_Callback(hObject, eventdata, handles) %#ok % hObject handle to slider2 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'Value') returns position of slider % get(hObject,'Min') and get(hObject,'Max') to determine range of slider global a b c n azimuth elevation b = get (hObject, 'Value') ; seashell (a, b, c, n, azimuth, elevation) ; % --- Executes during object creation, after setting all properties. function slider2_CreateFcn(hObject, eventdata, handles) %#ok % hObject handle to slider2 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: slider controls usually have a light gray background. if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor',[.9 .9 .9]); end global a b c n azimuth elevation a = -0.2 ; b = 0.5 ; c = 0.1 ; n = 2 ; azimuth = -150 ; elevation = 10 ; seashell ; % --- Executes on slider movement. function slider3_Callback(hObject, eventdata, handles) %#ok % hObject handle to slider3 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'Value') returns position of slider % get(hObject,'Min') and get(hObject,'Max') to determine range of slider global a b c n azimuth elevation c = get (hObject, 'Value') ; seashell (a, b, c, n, azimuth, elevation) ; % --- Executes during object creation, after setting all properties. function slider3_CreateFcn(hObject, eventdata, handles) %#ok % hObject handle to slider3 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: slider controls usually have a light gray background. if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor',[.9 .9 .9]); end % --- Executes on slider movement. function slider4_Callback(hObject, eventdata, handles) %#ok % hObject handle to slider2 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'Value') returns position of slider % get(hObject,'Min') and get(hObject,'Max') to determine range of slider global a b c n azimuth elevation n = get (hObject, 'Value') ; seashell (a, b, c, n, azimuth, elevation) ; % --- Executes during object creation, after setting all properties. function slider4_CreateFcn(hObject, eventdata, handles) %#ok % hObject handle to slider2 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: slider controls usually have a light gray background. if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor',[.9 .9 .9]); end % --- Executes on slider movement. function slider8_Callback(hObject, eventdata, handles) %#ok % hObject handle to slider8 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'Value') returns position of slider % get(hObject,'Min') and get(hObject,'Max') to determine range of slider global a b c n azimuth elevation azimuth = get (hObject, 'Value') ; seashell (a, b, c, n, azimuth, elevation) ; % --- Executes during object creation, after setting all properties. function slider8_CreateFcn(hObject, eventdata, handles) %#ok % hObject handle to slider8 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: slider controls usually have a light gray background. if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor',[.9 .9 .9]); end % --- Executes on slider movement. function slider9_Callback(hObject, eventdata, handles) %#ok % hObject handle to slider9 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'Value') returns position of slider % get(hObject,'Min') and get(hObject,'Max') to determine range of slider global a b c n azimuth elevation elevation = get (hObject, 'Value') ; seashell (a, b, c, n, azimuth, elevation) ; % --- Executes during object creation, after setting all properties. function slider9_CreateFcn(hObject, eventdata, handles) %#ok % hObject handle to slider9 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: slider controls usually have a light gray background. if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor',[.9 .9 .9]); end % --- Executes on button press in pushbutton3. function pushbutton3_Callback(hObject, eventdata, handles) %#ok % hObject handle to pushbutton3 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) global a b c n azimuth elevation seashell (a, b, c, n, Inf, elevation) ; seashell (a, b, c, n, azimuth, elevation) ; % --- Executes on button press in pushbutton4. function pushbutton4_Callback(hObject, eventdata, handles) %#ok % hObject handle to pushbutton4 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) global a b c n azimuth elevation for a2 = -1:.1:1 seashell (a2, b, c, n, azimuth, elevation) ; drawnow end seashell (a, b, c, n, azimuth, elevation) ; % --- Executes on button press in pushbutton5. function pushbutton5_Callback(hObject, eventdata, handles) %#ok % hObject handle to pushbutton5 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) global a b c n azimuth elevation for b2 = -1:.1:1 seashell (a, b2, c, n, azimuth, elevation) ; drawnow end seashell (a, b, c, n, azimuth, elevation) ; % --- Executes on button press in pushbutton6. function pushbutton6_Callback(hObject, eventdata, handles) %#ok % hObject handle to pushbutton6 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) global a b c n azimuth elevation for c2 = -1:.1:1 seashell (a, b, c2, n, azimuth, elevation) ; drawnow end seashell (a, b, c, n, azimuth, elevation) ; % --- Executes on button press in pushbutton7. function pushbutton7_Callback(hObject, eventdata, handles) %#ok % hObject handle to pushbutton7 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) global a b c n azimuth elevation for n2 = 0:.5:8 seashell (a, b, c, n2, azimuth, elevation) ; drawnow end seashell (a, b, c, n, azimuth, elevation) ; % --- Executes on button press in pushbutton8. function pushbutton8_Callback(hObject, eventdata, handles) %#ok % hObject handle to pushbutton8 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) global a b c n azimuth elevation for el = -80:10:80 seashell (a, b, c, n, azimuth, el) ; drawnow end seashell (a, b, c, n, azimuth, elevation) ; % --- Executes on button press in pushbutton9. function pushbutton9_Callback(hObject, eventdata, handles) %#ok % hObject handle to pushbutton9 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) web ('http://www.cise.ufl.edu/research/sparse/MATLAB') ; SuiteSparse/MATLAB_Tools/shellgui/Contents.m0000644001170100242450000000026110707670102017655 0ustar davisfac% SHELLGUI % % Files % shellgui - GUI interface for seashell function % seashell - draws a pretty Florida seashell, using a 3D parametric surface. % % Example % shellgui SuiteSparse/MATLAB_Tools/shellgui/shellgui.fig0000644001170100242450000172534710505224666020237 0ustar davisfacMATLAB 5.0 MAT-file, Platform: GLNX86, Created on: Sat Sep 23 08:33:58 2006 IM_xKd"Uf MEmb7132x* +.誫H V<'MRYHg|Ǘy"оV^quKס8qįC_n$4ͨiO,O⁴7n'{ Iԝp}Z_z>4<'Y~mA(Liʿz7sY;~kc+Jw%h+^lF/۱ޙGYOwqohؕ8;yiEoI{gqOY8l odNI#'ېS83ʣmiMѴw?$}noFYlpus}ŕϛި=OB}ц 6lr%P9G0`0>80` a[CB Dz- Ї?0?,` :8pCCoS@VTCB }M?X}K΁G_PϩQ>VP,? }D=>:X~@=8zzXG=t|z(p4ۜ7 < ^% %/< '<,e Y?IO~e֏~^ËAxyx aM4DM4DM#4Y3ߞ73_4z1o_6::z@'T_PzD/gTߨQzH%OT_T9TϩS'F>tF?T}zSU}~U=V=zZm1z\3]{bP?B 7㇄/QDg1xƿI~?(4~G'97ƏR3Uj-a?S?0~sR' _#՟SN1~hhROO־nkƿ9E:070G#tHXa"@V@ 1`0`(`€^Jd:TzUNw e|w=#|O-)3W/_4d~l~gk_ws7m,8{Yw|tv:ٙL8}bSLg}v/3}iWٙt>o3k;lΩ=pcqa=glGra<FXx|yIj\9s+V0G|'n,(_6yTn\#F7"G^WG<.W.̑3  '6=Ī‰M23M2~pbLz̮)@3( '}&fU>+-fW>,1fY>-5f[>.9f]>/=f_YOX7˳f=cyڬ,O7>G0..7o|ɍ@!tCĉFBBB2@ }5=0C]Jեv(!<#<]qചNOOϨϪϩϫ///Y}y53]ӿtM }o3ѿOycf|= G#čO̳}jyfYؾ0<3+,l_gxcy37̦xϞ#g ;\?n8h?{gǁ '8l?{ώ3Ư3qba~93|f.?g9rfe?;\ĉs̰TjZVſub░p#{lX'&n2v0pv_ٲaqLL2rqeaٳeneq}9g`/Y]lUZE&MD ?bM)"-1tvwvwdvf33< FL0QSc`4vPU. 2@<3߹瞙s)R%R½m.`xg > 41)X,b|6`0 ,;0 ,@@`;oQ|`805@>x |`X| X(@zð;~ 0`O`@!@{߅;߆7p2EgO#>v4c*;Li`< V)5-Dž/-iS,'ɝ ) g8qBDM$xA*ՍPk ȃ7֔go3;i&3_ww0n:s`͙vqOݱ{V)gĘ$cyq7;zV>g}i&c}|[#ɕ) V{ٱA syBRSJ/8aWK KK|ѵ62m#-Yީ!.YWlSg2KC*-<\ᢆr?+ȅn_dǑ\D<׭Rf. 7[oEq6\7oq\]\T6:u]q/u]xCXk^{R=upmTsmy@ep(9.UN!-jBj5;r)][Y/%ᅳoŒx!]+9\REc2Hr{v΍_3#=.z\u_?gA\6J-\LfڧؿoHo{lZX?FKmuԼ>|١¡jisF^U묡V{AR^F/ HFSrq؋SxNcHE>kK[wߥ7jqRg8z`Qֻ}QY 4U}חJHT(C'DL<3%SkޫnދDTB2d i}yo}{}緇u\-I֦\8:;8Z8XPYؚ;[S.f6KaU Q4sl ?VΦRb.nΖfm_{;bO6a%h{?1k>EQՔ/lne`/eK`-] u+kW{t(!u5uVttwRpt13uqf%G[Skvy7g3W ÿk(]CFIY俞UԌ֮l06.%XZb5p9mDнK0Q}=0}pd~ lBj'3o`Ϊ̯pgLW?Z]u n`+wI:|Vt߀MH'|}L]&3m%E2~sӏ&£yM/st%BUp+Z9 {ux %S/u۽X]u9Y|x# Cb{T?ڹ߈M<ߌmhdA$tk4 EEy<3 #FZddW1H'#洼=2rg _޸yP D$CLiF3igp_sֻՈ>hJ첓 ǙRfғJ$ MO=Rv TGd"k]vZ qW$d _9#0?I3*V%?]ȆcBb< y0/gͳve hs 6|)3x0NX"1}.۵&[ ks0o Om=v_oDz}`:Gh7)0klDI}aixf&Oy'^=|s o~LbBVݿ_ ',JASܧ2n bG*;x0)R)Pø˷jJp3kA3a8GXPv2ط[.0O}*W҅Tx2lMq<9/𦅀s؆~&:u׎ly^hћGQD5} .p]j\;: |c&ur[{YzƇfF(qL{kmqꇞεs}J~,4H.Y^ʅx/+ʼSduE%30sw‰vʻnol7CUp[[.KY4_x}n+>kԔ}: ;(Igo0WEf [-v4"32ʏ[GßH Ev됑+2"WߖUl ~ 2*GsohjwoFnF[Hb򙪺+Wub+S05.3Fʻ9 j*7; 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The first four control the coefficients of % the parametric surface (u and v are the surface parameters): % % x = (a*(1-v/(2*pi)).*(1+cos(u)) + c) .* cos(n*v) ; % y = (a*(1-v/(2*pi)).*(1+cos(u)) + c) .* sin(n*v) ; % z = b*v/(2*pi) + a*(1-v/(2*pi)) .* sin(u) ; % % a,b: these determine how pointy or flat the shell is (informally...) % c: determines how much the shell overlaps with itself % n: the number of spirals in the shell % % azimuth, elevation: determines the viewing angle (see the 'view' function) % res: the mesh size (res-by-res). A larger number gives a smoother surface. % % If the azimuth is Inf, then the seashell view is spun dynamically. % Also try seashell ('spin') ; % % References: % T. Davis & K. Sigmon, MATLAB Primer, 7th edition, CRC Press, 2005, pp. 80. % von Seggern, CRC Standard Curves and Surfaces, 2nd edition, CRC Press, % 1993, pp. 306-307. % % Example: % seashell ; % draws the front cover of the MATLAB Primer % seashell (-0.5) ; % draws the back cover % seashell (a,b,c,n,az,el,res) ; % all options, defaults: % % a=-0.2, b=0.5, c=0.1, n=2, az=-150, el=10, res=128 % % for a = -1:.1:1 % seashell (a) ; % drawnow ; % end % for b = -1:.1:1 % seashell (-.2, b) ; % drawnow % end % % See also SHELLGUI, SURF, VIEW, LINSPACE, MESHGRID, SHADING, LIGHTING, % LIGHTANGLE, COLORMAP, AXIS, MATERIAL, SIN, COS, PI. % Copyright 2006, Tim Davis, University of Florida % use default input parameters, if not present if (nargin == 1 && ischar (a)) in = -1 ; else in = nargin ; end if (in < 1) a = -0.2 ; end if (in < 2) b = 0.5 ; end if (in < 3) c = 0.1 ; end if (in < 4) n = 2 ; end if (in < 5) azimuth = -150 ; end if (in < 6) elevation = 10 ; end if (in < 7) res = 128 ; end if (in == -1) azimuth = Inf ; end % sanity checks if (a == 0) a = 0.01 ; end if (n <= 0) n = 0.1 ; end % construct the res-by-res mesh t = linspace(0, 2*pi, res) ; [u,v] = meshgrid(t) ; % define the surface x = (a*(1-v/(2*pi)).*(1+cos(u)) + c) .* cos(n*v) ; y = (a*(1-v/(2*pi)).*(1+cos(u)) + c) .* sin(n*v) ; z = b*v/(2*pi) + a*(1-v/(2*pi)) .* sin(u) ; % plot the surface surf(x,y,z,y) shading interp axis off axis equal colormap(hsv(1024)) material shiny lighting gouraud lightangle(80, -40) lightangle(-90, 60) % fix the view, or spin the seashell if (isfinite (azimuth)) view([azimuth elevation]) else for az = -180:10:180 view ([az elevation]) drawnow end end SuiteSparse/MATLAB_Tools/gipper.m0000644001170100242450000001642410707667626015563 0ustar davisfacfunction files_out = gipper (directory, include, exclude, exclude_hidden) %GIPPER zip selected files and subdirectories (gipper = grep + zip) % % files = gipper (directory, include, exclude, exclude_hidden) ; % % Creates a zip file of all files and subdirectories in a directory. A file in % the directory or any of its subdirectories whose name matches any expression % in 'include' via regexp is added to the zip file. A file that matches any % expression in 'exclude' is not added. A subdirectory whose name or full % pathname matches any expression in 'exclude' is not searched. The name of % the zip file is the name of the directory, with '.zip' appended. % % 'include' and 'exclude' are either cells of strings, or just single strings. % % With no outputs, a list of files is printed and the user is prompted before % proceeding. Otherwise, the gipper proceeds without prompting and returns a % list of files that were added to the zip file. % % By default, all files and subdirectories of the directory are included, except % that hidden files and directories (those whose names start with a dot, '.') % are excluded. % % If any parameter is empty or not present, the defaults are used: % directory: defaults to the current directory % include: defaults to include all files and directories % exclude: defaults to exclude nothing, as modified by 'exclude_hidden' % exclude_hidden: 1 (exclude hidden files and directories) % % Empty directories or subdirectories are never included. % % Example: % % suppose 'X' is the name of the current directory. % % % include all files in X (except hidden files) in the zip file ../X.zip % gipper % % % create mytoolbox.zip archive of the 'X/mytoolbox' directory % gipper mytoolbox % % % only include *.m files in ../X.zip % gipper '' '\.m$' % % % create ../X.zip, but exclude compiled object and MEX files % gipper ('', '', { '\.o$' '\.obj$', ['\.' mexext '$'] }) % % % include everything, including hidden files, in ../X.zip % gipper ('', '', '', 0) % % % zip mytoolbox, except hidden files and the mytoolbox/old directory % gipper mytoolbox '' old % % % these are the same, except gipper also traverses subdirectories % gipper ('', { '\.m$', '\.*mat$' }) % zip ('../X', { '*.m', '*.mat' }) % % See also zip, regexp, unzip. % NOTE: if the directory name is empty or not present, and you hit control-C % while the gipper is running, your current directory will now be the parent. % You must install the gipper first, by placing it in your MATLAB path. % Copyright 2007, Timothy A. Davis, Univ. of Florida. Win one for the gipper. % Created May 2007, using MATLAB 7.4 (R2007a). Requires MATLAB 6.5 or later. % exclude hidden files and directories by default if (nargin < 4) exclude_hidden = 1 ; end % exclude nothing by default (as modified by exclude_hidden) if (nargin < 3) exclude = { } ; end exclude = cleanup (exclude) ; % append the hidden file and directory rule, if requested if (exclude_hidden) exclude = union (exclude, { '^\.', [ '\' filesep '\.' ] }) ; end % always exclude '.' and '..' files exclude = union (exclude, { '^\.$', '^\.\.$' }) ; % include all files by default if (nargin < 2 || isempty (include)) include = { '.' } ; end include = cleanup (include) ; % operate on the current directory, if not specified if (nargin < 1 || isempty (directory)) here = pwd ; directory = here ((find (here == filesep, 1, 'last') + 1) : end) ; % use try-catch so that if a failure occurs, we go back to current % directory. Unfortunately, this mechanism does not catch a control-C. gipper_found = 0 ; try % run the gipper in the parent cd ('..') ; % if gipper.m is not in the path, it will no longer exist gipper_found = ~isempty (which ('gipper')) ; if (gipper_found) if (nargout == 0) fprintf ('Note that if you terminate gipper with control-C, ') ; fprintf ('your\ndirectory be changed to the parent') ; fprintf (' (as in "cd ..").\n') ; gipper (directory, include, exclude, exclude_hidden) ; else files_out = gipper (directory, include, exclude,exclude_hidden); end end catch cd (here) ; rethrow (lasterror) ; end % go back to where we started cd (here) ; if (~gipper_found) fprintf ('To install the gipper, type "pathtool" and add\n') ; fprintf ('the directory in which it resides:\n') ; fprintf ('%s\n', which (mfilename)) ; error ('You must install the gipper first.') ; end return else if (nargout == 0) fprintf ('\ngipper: creating %s%s%s.zip\n', pwd, filesep, directory) ; end end % get the list of files to zip n = 0 ; files = { } ; for file = dir (directory)' [files, n] = finder (files, n, directory, file.name, include, exclude) ; end files = files (1:n)' ; % cannot create an empty zip file if (isempty (files)) warning ('gipper:nothing', 'nothing to zip; no zip file created') ; if (nargout > 0) files_out = files ; end return end % return the list of files, or confirm if (nargout == 0) % print the list of files and ask for confirmation first fprintf ('Creating a zip archive containing these files:\n\n') ; for k = 1:length(files) fprintf (' %s\n', files {k}) ; end fprintf ('\nCreating the zip archive: %s', directory) ; if (isempty (regexp (directory, '\.zip$', 'once'))) fprintf ('.zip') ; end fprintf ('\n') ; reply = input ('Proceed? (yes or no, default is yes): ', 's') ; if (~isempty (reply) && lower (reply (1)) == 'n') fprintf ('zip file not created\n') ; return end else % zip the files without asking files_out = files ; end % zip the files zip (directory, files) ; %------------------------------------------------------------------------------- function [files, n] = finder (files, n, prefix, name, include, exclude) % finder: return a list of files to zip % fullname includes the entire path to the file or directory fullname = [prefix filesep name] ; if (isdir (fullname)) % always traverse a subdirectory to look for files to include, unless the % directory name or fullname itself is explicitly excluded. if (~(grep (name, exclude) || grep (fullname, exclude))) % the directory is selected, recursively traverse it for file = dir (fullname)' [files, n] = finder (files, n, fullname, file.name, ... include, exclude) ; end end else % this is a file, apply the include/exclude rules to just the file name % itself not the fullname. if (grep (name, include) && ~grep (name, exclude)) % the file is selected for the archive. Use a dynamic-table approach % to speed up the dynamic growth of the table. n = n + 1 ; files {n} = fullname ; if (n == length (files)) files {2*n} = [ ] ; end end end %------------------------------------------------------------------------------- function match = grep (string, list) % grep: determine if a string matches an expression in a list match = 0 ; for expression = list if (~isempty (regexp (string, expression {1}, 'once'))) match = 1 ; return ; end end %------------------------------------------------------------------------------- function s = cleanup (s) % cleanup: ensure the input list is in the proper format s = s (:)' ; % make sure it is a row vector if (ischar (s)) s = { s } ; % if it is a string, convert it into a cell with one string end SuiteSparse/MATLAB_Tools/pagerankdemo.m0000644001170100242450000001423510707715111016707 0ustar davisfacfunction pagerankdemo (steps) % PAGERANKDEMO draw a 6-node web and compute its pagerank % % PAGERANKDEMO draws the 6-node "tiny web" in Section 2.11 of "Numerical % Computing with MATLAB", by Cleve Moler, SIAM, 2004. It then simulates the % computation of Google's PageRank algorithm, by randomly selecting links to % traverse. If a link is traversed, the edge and the target node are displayed % in red. If the "random surfer" jumps to an arbitrary page, the target node % is displayed in blue. The number of hits at each node, and the page rank % (in %) are displayed % on each node. Note that after a large number of % steps, the PageRanks (in percentages) converge to the values given in Section % 2.11 of Moler (alpha: .321, sigma: .2007, beta: .1705, delta: .1368, % gamma: .1066, rho: .0643). See http://www.mathworks.com/moler for more % details (the pagerank M-file, in particular). % % Note that this method is NOT how the PageRank is actually computed. Instead % the eigenvalue problem A*x=x is solved for x, where A is the Markov % transition matrix, A = p*G*D + e*z', where G is the binary matrix used here. % The method here is a simplistic random-hopping demonstration of the Markov % process, to motivate the A*x=x formulation of the problem. In this example, % A does control how the transitions are made, but the matrix A is not formed % explicitly. % % This demo only operates on a single graph. It is meant as a simple demo % only, suitable for in-class use. To compute the PageRanks for an arbitrary % graph, use pagerank.m, or the power method (repeat x=A*x until convergence, % where A is the Markov transition matrix of the web). % % Example: % pagerankdemo % pagerankdemo (1000) % run 1000 steps with no user input, then quit % % See also pagerank % % I suggest single-stepping a dozen times or so to see the link traversal in % process, and then type "1000". Hit control-C to quit. % % Copyright 2007, Tim Davis, University of Florida % Initial graph Graph = graphinit ; rand ('state', 0) ; n = size (Graph.G, 1) ; help pagerankdemo % initialize the page counts hits = zeros (1,n) ; oldwhere = 1 ; where = 1 ; hits (where) = 1 ; set (Graph.node (where), 'FaceColor', [0 0 1]) ; p = 0.85 ; % probability a link will be followed c = sum (Graph.G) ; % outgoing degree links = cell (1,n) ; for k = 1:n links {k} = find (Graph.G (:,k)) ; end follow_link = 0 ; if (nargin < 1) input ('hit enter to start at node alpha: ') ; end % write the stats to the figure set (Graph.nodelabel (where), 'string', ... sprintf ('%s %d (%3.1f%%)', Graph.nodes {where}, hits (where), ... 100 * hits (where) / sum (hits))) ; if (nargin < 1) input ('hit enter to take one step: ') ; steps = 1 ; end % repeat while (1) % clear the old color and old arrow set (Graph.node (where), 'FaceColor', [0 1 0]) ; if (follow_link) set (Graph.arrows (where,oldwhere), 'LineWidth', 2) ; set (Graph.arrows (where,oldwhere), 'Color', [0 0 0]) ; end % determine where to go to next oldwhere = where ; if (c (where) == 0 || rand > p) % no outgoing links, or ignore the links follow_link = 0 ; where = floor (n * rand + 1) ; set (Graph.node (where), 'FaceColor', [0 0 1]) ; else % move along the link follow_link = 1 ; where = links{where}(floor (c (where) * rand + 1)) ; set (Graph.node (where), 'FaceColor', [1 0 0]) ; set (Graph.arrows (where,oldwhere), 'LineWidth', 5) ; set (Graph.arrows (where,oldwhere), 'Color', [1 0 0]) ; end % increment the hit count hits (where) = hits (where) + 1 ; % write the stats to the figure for k = 1:n set (Graph.nodelabel (k), 'string', ... sprintf ('%s %d (%3.1f%%)', Graph.nodes {k}, hits (k), ... 100 * hits (k) / sum (hits))) ; end drawnow % go the next step steps = steps - 1 ; if (steps <= 0) if (nargin > 0) break ; end steps = input ... ('number of steps to make (default 1, control-C to quit): ') ; if (steps == 0) break ; end if (isempty (steps)) steps = 1 ; end end end %------------------------------------------------------------------------------- function Graph = graphinit % GRAPHINIT create the tiny-web example in Moler, section 2.11, and draw it. % Example % G = graphinit ; figure (1) clf nodes = { 'alpha', 'beta', 'gamma', 'delta', 'rho', 'sigma' } ; xy = [ 0 4 1 3 1 2 2 4 2 0 0 0 ] ; x = xy (:,1) ; y = xy (:,2) ; % scale x and y to be in the range 0.1 to 0.9 x = 0.8 * x / 2 + .1 ; y = 0.8 * y / 4 + .1 ; xy = [x y] ; xy_delta = [ .08 .04 0 -.03 -.02 -1 .04 0 0 -.05 .04 -1 -.03 0 -1 .03 0 0 ] ; xd = xy_delta (:,1) ; yd = xy_delta (:,2) ; tjust = xy_delta (:,3) ; G = [ 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 ] ; clf n = size (G,1) ; axes ('Position', [0 0 1 1], 'Visible', 'off') ; node = zeros (n,1) ; nodelabel = zeros (n,1) ; for k = 1:n node (k) = annotation ('ellipse', [x(k)-.025 y(k)-.025 .05 .05]) ; set (node (k), 'LineWidth', 2) ; set (node (k), 'FaceColor', [0 1 0]) ; nodelabel (k) = text (x (k) + xd (k), y (k) + yd (k), nodes {k}, ... 'Units', 'normalized', 'FontSize', 16) ; if (tjust (k) < 0) set (nodelabel (k), 'HorizontalAlignment', 'right') ; end end axis off % Yes, I realize that this is overkill; arrows should be sparse. % This example is not meant for large graphs. arrows = zeros (n,n) ; [i j] = find (G) ; for k = 1:length (i) % get the center of the two nodes figx = [x(j(k)) x(i(k))] ; figy = [y(j(k)) y(i(k))] ; % [figx figy] = dsxy2figxy (gca, axx, axy); % shorten the arrows by s units at each end s = 0.03 ; len = sqrt (diff (figx)^2 + diff (figy)^2) ; fy (1) = diff (figy) * (s/len) + figy(1) ; fy (2) = diff (figy) * (1-s/len) + figy(1) ; fx (1) = diff (figx) * (s/len) + figx(1) ; fx (2) = diff (figx) * (1-s/len) + figx(1) ; arrows (i(k),j(k)) = annotation ('arrow', fx, fy) ; set (arrows (i(k),j(k)), 'LineWidth', 2) ; set (arrows (i(k),j(k)), 'HeadLength', 20) ; set (arrows (i(k),j(k)), 'HeadWidth', 20) ; end Graph.G = G ; Graph.nodes = nodes ; Graph.node = node ; Graph.xy = xy ; Graph.xy_delta = xy_delta ; Graph.nodelabel = nodelabel ; Graph.arrows = arrows ; SuiteSparse/MATLAB_Tools/Contents.m0000644001170100242450000000141410707671462016054 0ustar davisfac% MATLAB_TOOLS: a collection of small tools for use in MATLAB % % Files % gipper - zip selected files and subdirectories (gipper = grep + zip) % hprintf - fprintf with hypertext links not highlighted in the command window. % pagerankdemo - draw a 6-node web and compute its pagerank % % Directories: % shellgui draw a pretty seashell % waitmex use a waitbar in a C mexFunction % % Examples: % gipper % add all files in current directory X to X.zip % hprintf (format, arg1, ...) % fprint with links not highlighted % pagerankdemo % run the pagerank demo % shellgui % draw a pretty seashell % waitmex % example mexFunction that creates a waitbar % % Copyright 2007, Tim Davis, University of Florida SuiteSparse/MATLAB_Tools/hprintf.m0000644001170100242450000000656110707666462015745 0ustar davisfacfunction count = hprintf (varargin) %HPRINTF fprintf with hypertext links not highlighted in the command window. % hprintf does this by replacing the string "href=" with "HREF=". If the file % descriptor is not present, the output defaults to the command window, just % like fprintf. Note that all browsers accept either href= or HREF=, so your % hypertext links will not be affected except within the MATLAB Command Window. % General usage is identical to fprintf: % % hprintf (format, arg1, arg2, ...) % hprintf (fid, format, arg1, arg2, ...) % count = hprintf ( ... same as above ... ) % % Example: % fprintf ('MathWorks\n') ; % fprintf ('%d\n', 42) ; % hprintf ('MathWorks\n') ; % hprintf ('%d\n', 42) ; % % For a discussion, see Kristin's blog and the comments there at % http://blogs.mathworks.com/desktop/2007/07/09 % (Kristin's blog). % % NOTE: the examples above are modified by "help hprintf" so that you cannot % see the HREF= text. To see the examples properly (without hypertext % highlighting) use: % % edit hprintf % % To try the examples above, use hprintf with no inputs (note that this usage % of hprintf also flags an error, to exactly mimic the fprintf behavior): % % hprintf % % Here is a slightly more complex example that has the advantage of being % printed properly by "help hprintf": % % % a string template with hypertext contents: % str = 'MathWorks\n' ; % % made into an active hypertext, which will be underlined when % % displayed in the command window: % hstr = strrep (str, 'AREF', 'href') ; % fprintf (hstr) ; % % displays: 'MathWorks' % hprintf (hstr) ; % % displays: 'MathWorks' % % See also fprintf, strrep, sprintf. % Copyright 2007, T. Davis, with thanks to 'us' (us at neurol dot unizh dot ch) % for suggestions. % Aug 25, 2007 if (nargin < 1) % try hprintf help hprintf fprintf ('\nhypertext highlighting with fprintf:\n\n') ; fprintf ('MathWorks\n') ; fprintf ('%d\n', 42) ; fprintf ('\nhypertext highlighting turned off with hprintf:\n\n') ; hprintf ('MathWorks\n') ; hprintf ('%d\n\n', 42) ; % flag an error, to mimic fprintf behavior error ('Not enough input arguments') ; elseif (nargout > 1) % mimic fprintf error ('Too many output arguments') ; else if (ischar (varargin {1})) % mimic fprintf ('hello world %d\n', 42), with no file ID cnt = fprintf (strrep (sprintf (varargin {:}), 'href=', 'HREF=')) ; else % mimic fprintf (fid, 'hello world %d\n', 42), with file ID given cnt = fprintf (varargin {1}, ... strrep (sprintf (varargin {2:end}), 'href=', 'HREF=')) ; end if (nargout > 0) % return the fprintf output count = cnt ; end end SuiteSparse/MATLAB_Tools/waitmex/0000755001170100242450000000000010711226761015550 5ustar davisfacSuiteSparse/MATLAB_Tools/waitmex/waitex.m0000644001170100242450000000202710711100134017211 0ustar davisfacfunction result = waitex %WAITEX same as the waitexample mexFunction, just in M instead of C. % The only purpose of this function is to serve as a precise description of % what the waitexample mexFunction does. % % Example: % waitex % draw a waitbar, make progress, and then close the waitbar % h = waitex ; % same as above, except leave the waitbar on the screen % % and return the handle h to the waitbar. % % See also waitbar, waitexample. % Copyright 2007, T. Davis x = 0 ; h = waitbar (0, 'Please wait...') ; for i = 0:100 if (i == 50) waitbar (i/100, h, 'over half way there') ; else waitbar (i/100, h) ; end % do some useless work for j = 0:1e5 x = useless (x) ; end end if (nargout > 0) % h is return to the caller, leave the waitbar on the screen result = h ; else % close the waitbar, and do not return the handle h close (h) ; end function x = useless (x) %USELESS do some useless work (x = useless (x) just increments x) x = x + 1 ; SuiteSparse/MATLAB_Tools/waitmex/README.txt0000644001170100242450000000177610707667027017272 0ustar davisfacWAITMEX provides a simple way of using a waitbar from within a C mexFunction. Files: README.txt this file waitexample.c a C mexFunction that uses the waitmex.c functions waitexample.m help for waitexample waitex.m a MATLAB m-file equivalent of waitexample.m waitmex.c four functions for accessing a waitbar in a mexFunction waitmex.h include file required for using waitmex.c waitmex.m compiles the waitexample mexFunction For more help, and to compile, install, and test the waitmex functions, type: waitmex in the MATLAB Command Window. For details on how to call the waitmex functions, see waitmex.c, and see the examples given in waitexample.c. These functions should be easily adaptable to any of the many replacements for waitbar posted on the MATLAB Central File Exchange, particularly if they use the same input and output arguments as the MATLAB waitbar. Copyright 2007, Tim Davis, University of Florida. http://www.cise.ufl.edu/~davis Aug 27, 2007 SuiteSparse/MATLAB_Tools/waitmex/waitexample.c0000644001170100242450000000224510707667101020241 0ustar davisfac#include "waitmex.h" /* The MATLAB equivalent of this function is give in waitex.m. Compile with: mex waitexample.c waitmex.c */ void useless (double *x) ; void useless (double *x) { (*x)++ ; } void mexFunction (int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ]) { int i, j ; double x = 0 ; waitbar *h ; /* just like h = waitbar (0, 'Please wait...') in MATLAB */ h = waitbar_create (0, "Please wait...") ; for (i = 0 ; i <= 100 ; i++) { if (i == 50) { /* just like waitbar (i/100, h, 'over half way there') in MATLAB */ waitbar_update (((double) i) / 100., h, "over half way there") ; } else { /* just like waitbar (i/100, h) in MATLAB */ waitbar_update (((double) i) / 100., h, NULL) ; } /* do some useless work */ for (j = 0 ; j <= 10000000 ; j++) useless (&x) ; } if (nargout > 0) { /* return the handle to the waitbar, if requested */ pargout [0] = waitbar_return (h) ; } else { /* just like close (h) in MATLAB */ waitbar_destroy (h) ; } } SuiteSparse/MATLAB_Tools/waitmex/waitexample.m0000644001170100242450000000071210663345160020247 0ustar davisfacfunction waitexample %WAITEXAMPLE a C mexFunction that serves as an example for waitmex. % % Example: % waitexample % draw a waitbar, make progress, and then close the waitbar % h = waitexample; % same as above, except leave the waitbar on the screen % % and return the handle h to the waitbar. % % See also waitbar, waitex. % Copyright 2007, T. Davis error ('waitexample mexFunction not found ... it must be compiled first') ; SuiteSparse/MATLAB_Tools/waitmex/waitmex.c0000644001170100242450000001176110663345770017410 0ustar davisfac/* -------------------------------------------------------------------------- */ /* waitmex functions */ /* -------------------------------------------------------------------------- */ /* This file includes the following functions for handling waitbars in MATLAB: waitbar_create: create a waitbar waitbar_update: update a waitbar waitbar_destroy: destroy a waitbar waitbar_return: return a waitbar in C MATLAB equivalent ---- ----------------- h = waitbar_create (x,msg) h = waitbar (x,msg) waitbar_update (x,h,NULL) waitbar (x,h) waitbar_update (x,h,msg) waitbar (x,h,msg) waitbar_destroy (h) close (h) waitbar_return (h) for returning h from a mexFunction Tim Davis, 2007, University of Florida. */ #include "waitmex.h" /* -------------------------------------------------------------------------- */ /* waitbar_create: create a waitbar */ /* -------------------------------------------------------------------------- */ /* Create a waitbar and return a point to the new waitbar. Example: * h = waitbar_create (x, "Please wait...") in C is just like * h = waitbar (x, 'Please wait') in MATLAB, where x is a fraction between * 0 and 1. */ waitbar *waitbar_create /* return a pointer to the new waitbar */ ( double fraction, /* fraction from 0 to 1 */ char *message /* message to display */ ) { int error ; waitbar *h ; h = mxMalloc (sizeof (waitbar)) ; h->fraction = mxCreateDoubleScalar (fraction) ; h->message = mxCreateString (message) ; /* h = waitbar (fraction, message) ; */ h->inputs [0] = h->fraction ; h->inputs [1] = h->message ; error = mexCallMATLAB (1, h->outputs, 2, h->inputs, "waitbar") ; if (error) { mexErrMsgTxt ("unable to create waitbar") ; } /* save the MATLAB handle h in the waitbar struct */ h->handle = h->outputs [0] ; return (h) ; } /* -------------------------------------------------------------------------- */ /* waitbar_update: update a waitbar */ /* -------------------------------------------------------------------------- */ /* Update the length of the bar in an existing waitbar. Example: * waitbar_update (x, h, NULL) in C is just like waitbar (x,h) in MATLAB, * where h is the handle to the existing waitbar. The message is not changed. * To change the message, use waitbar_update (x, h, "new message"), which is * just like waitbar (x, h, 'new message') in MATLAB. */ void waitbar_update ( double fraction, waitbar *h, char *message ) { int error ; if (h == NULL) return ; /* nothing to do */ (* mxGetPr (h->fraction)) = fraction ; /* update the fraction */ h->inputs [0] = h->fraction ; /* define the inputs x and h */ h->inputs [1] = h->handle ; if (message == NULL) { /* use the existing message; waitbar (x,h) in MATLAB */ error = mexCallMATLAB (0, h->outputs, 2, h->inputs, "waitbar") ; } else { /* define a new message; waitbar (x,h,message) in MATLAB */ mxDestroyArray (h->message) ; h->message = mxCreateString (message) ; h->inputs [2] = h->message ; error = mexCallMATLAB (0, h->outputs, 3, h->inputs, "waitbar") ; } if (error) { mexErrMsgTxt ("unable to update waitbar") ; } } /* -------------------------------------------------------------------------- */ /* waitbar_destroy: destroy a waitbar */ /* -------------------------------------------------------------------------- */ /* Destroys a waitbar; same as close(h) in MATLAB */ void waitbar_destroy ( waitbar *h ) { int error ; if (h == NULL) return ; /* nothing to do */ h->inputs [0] = h->handle ; mxDestroyArray (h->fraction) ; /* free the internal mxArrays */ mxDestroyArray (h->message) ; error = mexCallMATLAB (0, h->outputs, 1, h->inputs, "close") ; mxDestroyArray (h->handle) ; mxFree (h) ; if (error) { mexErrMsgTxt ("error closing waitbar") ; } } /* -------------------------------------------------------------------------- */ /* waitbar_return: return a waitbar handle to the caller */ /* -------------------------------------------------------------------------- */ /* This function frees the space used internally in a mexFunction for managing * the waitbar, and returns the mxArray handle to the caller. The waitbar still * exists in MATLAB. Example: pargout [0] = waitbar_return (h) to return the * MATLAB handle to the caller of your mexFunction. */ mxArray *waitbar_return ( waitbar *h ) { mxArray *handle ; if (h == NULL) return (NULL) ; /* nothing to do */ handle = h->handle ; /* get the MATLAB handle */ mxDestroyArray (h->fraction) ; /* free the internal mxArrays */ mxDestroyArray (h->message) ; mxFree (h) ; return (handle) ; /* return the MATLAB handle */ } SuiteSparse/MATLAB_Tools/waitmex/waitmex.h0000644001170100242450000000136210663345312017401 0ustar davisfac/* -------------------------------------------------------------------------- */ /* waitmex include file */ /* -------------------------------------------------------------------------- */ #ifndef _WAITMEX_H #define _WAITMEX_H #include "mex.h" typedef struct waitbar_struct { mxArray *inputs [3] ; /* waitbar inputs */ mxArray *outputs [2] ; /* waitbar outputs */ mxArray *handle ; /* handle from waitbar */ mxArray *fraction ; /* fraction from 0 to 1 (a scalar) */ mxArray *message ; /* waitbar message */ } waitbar ; waitbar *waitbar_create (double, char *) ; void waitbar_update (double, waitbar *, char *) ; void waitbar_destroy (waitbar *) ; mxArray *waitbar_return (waitbar *) ; #endif SuiteSparse/MATLAB_Tools/waitmex/waitmex.m0000644001170100242450000000206210663346112017403 0ustar davisfacfunction waitmex %WAITMEX a small library for using a waitbar within a C mexFunction. % This waitmex function compiles an example mexFunction, adds the current % directory to your MATLAB path, and runs two examples (one in C, one in M). % % in C MATLAB M-file equivalent % ---- ------------------------ % h = waitbar_create (x,msg) ; h = waitbar (x,msg) % waitbar_update (x,h,NULL) ; waitbar (x,h) % waitbar_update (x,h,msg) ; waitbar (x,h,msg) % waitbar_destroy (h) ; close (h) % waitbar_return (h) ; for returning h from a mexFunction % % Example: % waitmex % % % See also waitex, waitexample, waitbar, pathtool. % Copyright 2007, T. Davis help waitmex fprintf ('\ncompiling an example:\n') ; fprintf ('mex waitexample.c waitmex.c\n') ; mex waitexample.c waitmex.c addpath (pwd) ; fprintf ('\ntrying the example mexFunction:\n') ; fprintf ('waitexample\n') ; waitexample fprintf ('\ntrying the m-file equivalent of waitexample:\n') ; fprintf ('waitex\n') ; waitex SuiteSparse/MATLAB_Tools/getversion.m0000644001170100242450000000345710712357223016445 0ustar davisfacfunction v = getversion %GETVERSION return MATLAB version number as a double. % GETVERSION determines the MATLAB version, and returns it as a double. This % allows simple inequality comparisons to select code variants based on ranges % of MATLAB versions. % % As of MATLAB 7.5, the version numbers are listed below: % % MATLAB version getversion return value % ------------------------------- ----------------------- % 7.5.0.342 (R2007b) 7.5 % 7.4.0.287 (R2007a) 7.4 % 7.3.0.267 (R2006b) 7.3 % 7.2.0.232 (R2006a) 7.2 % 7.1.0.246 (R14) Service Pack 3 7.1 % 7.0.4.365 (R14) Service Pack 2 7.04 % 7.0.1.24704 (R14) Service Pack 1 7.01 % 6.5.2.202935 (R13) Service Pack 2 6.52 % 6.1.0.4865 (R12.1) 6.1 % ... % 5.3.1.something (R11.1) 5.31 % 3.2 whatever 3.2 % % Example: % % v = getversion ; % if (v >= 7.0) % this code is for MATLAB 7.x and later % elseif (v == 6.52) % this code is for MATLAB 6.5.2 % else % this code is for MATLAB versions prior to 6.5.2 % end % % This getversion function has been tested on versions 6.1 through 7.5, but it % should work in any MATLAB that has the functions version, sscanf, and length. % % See also version, ver, verLessThan. % Copyright 2007, Timothy A. Davis, Univ. of Florida % This function does not use ver, in the interest of speed and portability. % "version" is a built-in that is about 100 times faster than the ver m-file. % ver returns a struct, and structs do not exist in old versions of MATLAB. % All 3 functions used here (version, sscanf, and length) are built-in. v = sscanf (version, '%d.%d.%d') ; v = 10.^(0:-1:-(length(v)-1)) * v ; SuiteSparse/UFcollection/0000755001170100242450000000000010711673461014343 5ustar davisfacSuiteSparse/UFcollection/Doc/0000755001170100242450000000000010711430334015036 5ustar davisfacSuiteSparse/UFcollection/Doc/License.txt0000644001170100242450000000170110532557175017176 0ustar davisfacUFcollection toolbox. Version 1.0. Copyright (C) 2006, Timothy A. Davis UFcollection is also available under other licenses; contact authors for details. http://www.cise.ufl.edu/research/sparse -------------------------------------------------------------------------------- UFcollection is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. UFcollection is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. SuiteSparse/UFcollection/Doc/gpl.txt0000644001170100242450000004313310532556673016405 0ustar davisfac GNU GENERAL PUBLIC LICENSE Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users. This General Public License applies to most of the Free Software Foundation's software and to any other program whose authors commit to using it. (Some other Free Software Foundation software is covered by the GNU Library General Public License instead.) You can apply it to your programs, too. When we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for this service if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free programs; and that you know you can do these things. To protect your rights, we need to make restrictions that forbid anyone to deny you these rights or to ask you to surrender the rights. These restrictions translate to certain responsibilities for you if you distribute copies of the software, or if you modify it. For example, if you distribute copies of such a program, whether gratis or for a fee, you must give the recipients all the rights that you have. You must make sure that they, too, receive or can get the source code. And you must show them these terms so they know their rights. We protect your rights with two steps: (1) copyright the software, and (2) offer you this license which gives you legal permission to copy, distribute and/or modify the software. Also, for each author's protection and ours, we want to make certain that everyone understands that there is no warranty for this free software. If the software is modified by someone else and passed on, we want its recipients to know that what they have is not the original, so that any problems introduced by others will not reflect on the original authors' reputations. Finally, any free program is threatened constantly by software patents. We wish to avoid the danger that redistributors of a free program will individually obtain patent licenses, in effect making the program proprietary. To prevent this, we have made it clear that any patent must be licensed for everyone's free use or not licensed at all. The precise terms and conditions for copying, distribution and modification follow. GNU GENERAL PUBLIC LICENSE TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION 0. This License applies to any program or other work which contains a notice placed by the copyright holder saying it may be distributed under the terms of this General Public License. The "Program", below, refers to any such program or work, and a "work based on the Program" means either the Program or any derivative work under copyright law: that is to say, a work containing the Program or a portion of it, either verbatim or with modifications and/or translated into another language. (Hereinafter, translation is included without limitation in the term "modification".) Each licensee is addressed as "you". Activities other than copying, distribution and modification are not covered by this License; they are outside its scope. 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It is safest to attach them to the start of each source file to most effectively convey the exclusion of warranty; and each file should have at least the "copyright" line and a pointer to where the full notice is found. Copyright (C) This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Also add information on how to contact you by electronic and paper mail. If the program is interactive, make it output a short notice like this when it starts in an interactive mode: Gnomovision version 69, Copyright (C) year name of author Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the program `Gnomovision' (which makes passes at compilers) written by James Hacker. , 1 April 1989 Ty Coon, President of Vice This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Library General Public License instead of this License. SuiteSparse/UFcollection/Doc/ChangeLog0000644001170100242450000000071510711430332016611 0ustar davisfacNov 1, 2007, version 1.1.1 * added isND field to the index * minor change to web page creation May 31, 2007, version 1.1.0 * port to 64-bit MATLAB Dec 12, 2006, version 1.0.1 * very minor MATLAB cleanup Dec 2, 2006, version 1.0. * UFcollection Version 1.0 released. Used for substantial changes to the UF Sparse Matrix Collection. See the Change Log for that collection at http://www.cise.ufl.edu/research/sparse/mat/ChangeLog. SuiteSparse/UFcollection/UFlist.m0000644001170100242450000002316210677241002015724 0ustar davisfacfunction UFlist (what, group) %UFLIST create a web page index for the UF Sparse Matrix Collection % % Usage: UFlist (what) % % what: % 'group' sort by group, then filename % 'name' sort by name % 'dimension' sort by max row or col dimension % 'id' sort by id (default, if "what" is not present) % 'number of nonzeros' sort by number of nonzeros % 'type' sort by type, then dimension % 'symmetry' sort by symmetry. Rectangular matrices first, sorted by % min(nrow,ncol)-max(nrow,ncol), then numerical symmetry % 0 to just less than one. Then numerical symmetry = 1 % but not spd (sorted by dimension). Then spd sorted % by dimension. % % If two arguments are present, only that group is created. % In this case, "what" must be "group". % % Example: % % UFlist ('id') % UFlist ('group', 'HB') % % See also UFget, UFint. % Copyright 2006-2007, Timothy A. Davis index = UFget ; if (nargin < 1) what = 'id' ; end by_group = (nargin > 1) ; % create the primary directory [url topdir] = UFlocation ; matrices = [topdir 'matrices'] ; if (~exist (matrices, 'dir')) mkdir (matrices) ; end if (by_group) fprintf ('group: %s\n', group) ; loc = '../' ; if (~exist ([matrices filesep group], 'dir')) mkdir ([matrices filesep group]) ; end f = fopen ([matrices filesep group filesep 'index.html'], 'w') ; else fprintf ('list: %s\n', what) ; f = fopen ([matrices filesep 'list_by_' what '.html'], 'w') ; loc = '' ; end if (f < 0) error ('unable to create html file\n') ; end nmat = length (index.nrows) ; % add the header fprintf (f, ... '\n') ; fprintf (f, '\n') ; fprintf (f, '') ; if (by_group) fprintf (f, 'UF Sparse Matrix Collection - %s group', group) ; else fprintf (f, '<title>UF Sparse Matrix Collection - sorted by ') ; if (strcmp (what, 'nnz')) fprintf (f, 'number of nonzeros') ; else fprintf (f, '%s', what) ; end end fprintf (f, '\n') ; fprintf (f, '\n') ; fprintf (f, ... '

  • UF Sparse Matrix Collection
    \n', loc) ; if (by_group) fprintf (f, '

    UF Sparse Matrix Collection: %s group.

    \n', group) ; else fprintf (f, '

    UF Sparse Matrix Collection, sorted by %s.\n', what) ; fprintf (f, ' Click on a column header to sort by that column.

    \n') ; end % add link to mat//README.txt if (by_group) fprintf (f, '

  • ', group) ; fprintf (f, 'Click here for a description of the %s group.\n', group) ; end fprintf (f, '
  • ', loc) ; fprintf (f, 'Click here for a list of all matrix groups.\n') ; fprintf (f, '
  • ', loc) ; fprintf (f, 'Click here for a list of all matrices.\n') ; fprintf (f, '

    \n') ; % sort by filename [ignore, iname] = sort (lower (index.Name)) ; if (by_group) list = [ ] ; for i = 1:nmat if (strcmp (group, index.Group {i})) list = [list i] ; %#ok end end [ignore i] = sort (lower (index.Name (list))) ; list = list (i) ; if (isempty (list)) error ('empty group!') ; end elseif (strcmp (what, 'group')) % sort by filename, then stable sort by group [ignore, i] = sort (lower (index.Group (iname))) ; list = iname (i) ; elseif (strcmp (what, 'name')) % sort by filename only list = iname' ; elseif (strcmp (what, 'dimension')) % sort by filename, then stable sort by max dimension [ignore, i] = sort (max (index.nrows (iname), index.ncols (iname))) ; list = iname (i) ; elseif (strcmp (what, 'id')) list = 1:nmat ; elseif (strcmp (what, 'nnz')) % sort by filename, then stable sort by nnz [ignore, i] = sort (index.nnz (iname)) ; list = iname (i) ; elseif (strcmp (what, 'symmetry')) % 'symmetry' sort by symmetry. Rectangular matrices first, sorted by % min(nrow,ncol)-max(nrow,ncol), then numerical symmetry % 0 to just less than one. Then numerical symmetry = 1 % but not spd (sorted by dimension). Then spd sorted % by dimension. s1 = min (index.nrows, index.ncols) - max (index.nrows, index.ncols) ; s2 = index.numerical_symmetry ; s2 (find (s2) == -1) = 1 ; s3 = index.posdef ; s3 (find (s3) == -1) = 2 ; s4 = max (index.nrows, index.ncols) ; [ignore list] = sortrows ([s1' s2' s3' s4'], [1 2 3 4]) ; elseif (strcmp (what, 'type')) [ignore i1] = sort (max (index.nrows, index.ncols)) ; s = index.RBtype (i1,:) ; [ignore i2] = sortrows (s) ; list = i1 (i2) ; else error ('unknown list') ; end % ensure list is a row vector list = list (:)' ; % print the header fprintf (f, '\n') ; if (by_group) fprintf (f, '\n') ; fprintf (f, '\n') ; fprintf (f, '\n') ; fprintf (f, '\n') ; fprintf (f, '\n') ; fprintf (f, '\n') ; fprintf (f, '\n') ; fprintf (f, '\n') ; fprintf (f, '\n') ; fprintf (f, '\n') ; else fprintf (f, '\n') ; fprintf (f, '\n', loc) ; fprintf (f, '\n', loc) ; fprintf (f, '\n') ; fprintf (f, '\n', loc) ; fprintf (f, '\n', loc) ; fprintf (f, '\n', loc) ; fprintf (f, '\n', loc) ; fprintf (f, '\n', loc) ; fprintf (f, '\n', loc) ; end for id = list group = index.Group {id} ; name = index.Name {id} ; nrows = index.nrows (id) ; ncols = index.ncols (id) ; nz = index.nnz (id) ; sym = index.numerical_symmetry (id) ; mtype = index.RBtype (id,:) ; s = index.posdef (id) ; if (s == 0) ss = '-' ; elseif (s == 1) ss = 'yes' ; else ss = '?' ; end fprintf (f, '\n') ; % thumbnail link to the matrix page fprintf (f, '\n') ; % group if (by_group) fprintf (f, '\n', name, name) ; else fprintf (f, '%s\n', group, name, name) ; end % id fprintf (f, '\n', id) ; % download links fprintf (f, '\n') ; % nrow fprintf (f, '\n', UFint (nrows)) ; % ncols fprintf (f, '\n', UFint (ncols)) ; % nz fprintf (f, '\n', UFint (nz)) ; % print the Rutherford/Boeing type mattype = '' ; if (mtype (1) == 'r') mattype = 'real' ; elseif (mtype (1) == 'c') mattype = 'complex' ; elseif (mtype (1) == 'i') mattype = 'integer' ; elseif (mtype (1) == 'p') mattype = 'binary' ; end if (mtype (2) == 'r') mattype = [mattype ' rectangular'] ; %#ok elseif (mtype (2) == 'u') mattype = [mattype ' unsymmetric'] ; %#ok elseif (mtype (2) == 's') mattype = [mattype ' symmetric'] ; %#ok elseif (mtype (2) == 'h') mattype = [mattype ' Hermitian'] ; %#ok elseif (mtype (2) == 'z') mattype = [mattype ' skew-symmetric'] ; %#ok end fprintf (f, '\n', mattype) ; % numerical symmetry (as a percentage) if (sym == -1) fprintf (f, '\n') ; elseif (sym == 1) fprintf (f, '\n') ; elseif (nrows ~= ncols) fprintf (f, '\n') ; else if (sym > 0 && sym < 0.01) fprintf (f, '\n', sym * 100) ; else fprintf (f, '\n', sym * 100) ; end end % positive definite? fprintf (f, '\n', ss) ; fprintf (f, '\n\n') ; end fprintf (f, '
    thumbnailGroup\n') ; fprintf (f, 'and Nameiddownload# rows# colsnonzerostypesymspd?thumbnailGroup\n', loc) ; fprintf (f, 'and Nameiddownload# rows# colsnonzerostypesymspd?
    \n') ; w = 'width="96" height="72"' ; if (by_group) fprintf (f, '%s/%s\n', name) ; else fprintf (f, '%s/%s\n', group, name) ; end fprintf (f, '%s/', group) ; else fprintf (f, '%s/', group, group); end % name if (by_group) fprintf (f, '%s%d\n') ; fprintf (f, 'MAT', loc, group, name) ; fprintf (f, ', MM', loc, group, name) ; fprintf (f, ', RB', loc, group, name) ; fprintf (f, '%s%s%s%s?yes-%5.2f%%%5.0f%%%s
    \n\n') ; fprintf (f, '

    Maintained by '); fprintf (f, 'Tim Davis, last updated %s.', date) ; fprintf (f, '
    Matrix pictures by cspy, a MATLAB', ... url) ; fprintf (f, ' function in the CSparse package.\n', ... url) ; fprintf (f, '
    See UFget to download directly', ... url) ; fprintf (f, ' into MATLAB.') ; fprintf (f, '\n') ; fprintf (f, '\n') ; fclose (f) ; SuiteSparse/UFcollection/UFpage.m0000644001170100242450000004255710620400343015667 0ustar davisfacfunction UFpage (matrix, index, figures) %UFPAGE create web page for a matrix in UF Sparse Matrix Collection % % Usage: % UFpage (matrix, index, figures) % % matrix: id or name of matrix to create the web page for. % index: the UF index, from UFget. % figures: 1 if the figures are to be created, 0 otherwise % % Example: % % UFpage (267) % UFpage ('HB/west0479') % % See also UFget, cspy, UFgplot, UFint. % This function assumes that the mat/, MM/, and RB/ directories all reside in % the same parent directory, given by the download directory specified by % UFget_defaults. % Copyright 2006-2007, Timothy A. Davis %------------------------------------------------------------------------------- % get inputs %------------------------------------------------------------------------------- if (nargin < 2) index = UFget ; end if (nargin < 3) figures = 1 ; end %------------------------------------------------------------------------------- % get the Problem and its contents %------------------------------------------------------------------------------- Problem = UFget (matrix,index) ; disp (Problem) ; fullname = Problem.name ; s = strfind (fullname, '/') ; grp = fullname (1:s-1) ; name = fullname (s+1:end) ; id = Problem.id ; % create the primary directory [url topdir] = UFlocation ; matrices = [topdir 'matrices'] ; if (~exist (matrices, 'dir')) mkdir (matrices) ; end % create the group directory if (~exist ([matrices filesep grp], 'dir')) mkdir ([matrices filesep grp]) ; end % determine the full path of the problem fullpath = regexprep ([matrices filesep fullname], '[\/\\]', filesep) ; ptitle = Problem.title ; z = 0 ; if (isfield (Problem, 'Zeros')) z = nnz (Problem.Zeros) ; Problem = rmfield (Problem, 'Zeros') ; end nblocks = index.nblocks (id) ; ncc = index.ncc (id) ; has_b = isfield (Problem, 'b') ; has_x = isfield (Problem, 'x') ; has_aux = isfield (Problem, 'aux') ; if (has_b) b = Problem.b ; Problem = rmfield (Problem, 'b') ; if (iscell (b)) b = sprintf ('cell %d-by-%d\n', size (b)) ; elseif (issparse (b)) b = sprintf ('sparse %d-by-%d\n', size (b)) ; else b = sprintf ('full %d-by-%d\n', size (b)) ; end end if (has_x) x = Problem.x ; Problem = rmfield (Problem, 'x') ; if (iscell (x)) x = sprintf ('cell %d-by-%d\n', size (x)) ; elseif (issparse (x)) x = sprintf ('sparse %d-by-%d\n', size (x)) ; else x = sprintf ('full %d-by-%d\n', size (x)) ; end end nodename = [ ] ; if (has_aux) aux = Problem.aux ; Problem = rmfield (Problem, 'aux') ; auxfields = fields (aux) ; has_coord = isfield (aux, 'coord') ; has_nodename = isfield (aux, 'nodename') ; auxs = cell (1, length (auxfields)) ; for k = 1:length(auxfields) siz = size (aux.(auxfields{k})) ; if (iscell (aux.(auxfields{k}))) auxs {k} = sprintf ('cell %d-by-%d\n', siz) ; elseif (issparse (aux.(auxfields{k}))) auxs {k} = sprintf ('sparse %d-by-%d\n', siz) ; else auxs {k} = sprintf ('full %d-by-%d\n', siz) ; end end if (has_coord) xyz = aux.coord ; end if (has_nodename) nodename = aux.nodename ; end clear aux else has_coord = 0 ; end kind = Problem.kind ; if (isfield (Problem, 'notes')) notes = Problem.notes ; else notes = '' ; end au = Problem.author ; ed = Problem.ed ; da = Problem.date ; m = index.nrows (id) ; n = index.ncols (id) ; nz = index.nnz (id) ; nnzdiag = index.nnzdiag (id) ; if (strfind (kind, 'graph')) bipartite = ~isempty (strfind (kind, 'bipartite')) ; directed = ~isempty (regexp (kind, '\ 1) & (isempty (strfind (kind, 'graph'))) ; if (do_dmspy) try cs_dmspy (A, 128) ; title ('Dulmage-Mendelsohn permutation') ; catch fprintf ('dmspy failed\n') ; delete ([fullpath '_dmperm.png']) ; do_dmspy = 0 ; end print (gcf, '-dpng', '-r64', [fullpath '_dmperm.png']) ; end %--------------------------------------------------------------------------- % create the ccspy figure %--------------------------------------------------------------------------- do_scc = (ncc > 1) ; if (do_dmspy && m == n && nnzdiag == n) % don't do scc for a square matrix with zero-free diagonal do_scc = 0 ; end if (do_scc) try ccspy (A, bipartite, 128) ; if (bipartite) title ('connected components of the bipartite graph') ; else title ('strongly connected components of the graph') ; end print (gcf, '-dpng', '-r64', [fullpath '_scc.png']) ; catch fprintf ('ccspy failed\n') ; delete ([fullpath '_cc.png']) ; do_scc = 0 ; end end else %--------------------------------------------------------------------------- % the plots already exist - check the files %--------------------------------------------------------------------------- do_scc = exist ([fullpath '_scc.png'], 'file') ; do_dmspy = exist ([fullpath '_dmperm.png'], 'file') ; do_gplot = exist ([fullpath '_gplot.png'], 'file') ; end clear Problem %------------------------------------------------------------------------------- % create the web page for the matrix %------------------------------------------------------------------------------- f = fopen ([fullpath '.html'], 'w') ; if (f < 0) error ('unable to create matrix web page') ; end % add the header fprintf (f,'\n'); fprintf (f, '\n') ; fprintf (f, '%s sparse matrix\n', fullname) ; fprintf (f, '\n') ; % link to UF collection fprintf (f, '

  • UF Sparse Matrix Collection\n') ; % link to group fprintf (f, '
  • Matrix group: %s\n', grp) ; % add link to mat//README.txt fprintf (f, '
  • ', grp) ; fprintf (f, 'Click here for a description of the %s group.\n', grp) ; % link to all matrices fprintf (f, '
  • ') ; fprintf (f, 'Click here for a list of all matrices\n') ; % link to all groups fprintf (f, '
  • ') ; fprintf (f, 'Click here for a list of all matrix groups\n') ; % matrix name and description fprintf (f, '

  • Matrix: %s\n', fullname) ; fprintf (f, '
  • Description: %s\n', ptitle) ; % download link for MATLAB format fprintf (f, ... '
  • download as a MATLAB mat-file',... fullname) ; fsize (f, [topdir 'mat/' fullname '.mat']) ; fprintf (f, 'Use UFget(%d)', url, id) ; fprintf (f, ' or UFget(''%s'') in MATLAB.\n', fullname) ; % download link for Matrix Market format fprintf (f, ... '
  • download in Matrix Market format',... fullname) ; fsize (f, [topdir 'MM/' fullname '.tar.gz']) ; % download link for Rutherford/Boeing format fprintf (f, ... '
  • download in Rutherford/Boeing format',... fullname) ; fsize (f, [topdir 'RB/' fullname '.tar.gz']) ; %------------------------------------------------------------------------------- % link to images %------------------------------------------------------------------------------- fprintf (f, '

    %s\n', fullname, name) ; % dmspy, if it exists if (do_dmspy) fprintf (f, '

    dmperm of %s\n', ... fullname, name) ; end % ccspy, if it exists if (do_scc) fprintf (f, '

    scc of %s\n', ... fullname, name) ; end % gplot, if it exists if (do_gplot) fprintf (f, '

    ') ; fprintf (f, ... '%s graph\n', ... name, fullname, name) ; end %------------------------------------------------------------------------------- % table of matrix properties %------------------------------------------------------------------------------- fprintf (f, '

    \n') ; stat (f, 'Matrix properties', '%s', ' ') ; stat (f, 'number of rows', '%s', UFint (m)) ; stat (f, 'number of columns', '%s', UFint (n)) ; stat (f, 'nonzeros', '%s', UFint (nz)) ; srank = index.sprank (id) ; if (srank == min (m,n)) stat (f, 'structural full rank?', '%s', 'yes') ; else stat (f, 'structural full rank?', '%s', 'no') ; end stat (f, 'structural rank', '%s', UFint (srank)) ; stat (f, '# of blocks from dmperm', '%s', UFint (nblocks)) ; stat (f, '# strongly connected comp.', '%s', UFint (ncc)) ; if (srank == min (m,n)) stat (f, 'entries not in dmperm blocks', '%s', ... UFint (index.nzoff (id))) ; end stat (f, 'explicit zero entries', '%s', UFint (z)) ; s = index.pattern_symmetry (id) ; if (s == 1) stat (f, 'nonzero pattern symmetry', '%s', 'symmetric') ; else stat (f, 'nonzero pattern symmetry', '%8.0f%%', s*100) ; end s = index.numerical_symmetry (id) ; if (s == -1) stat (f, 'numeric value symmetry', '%s', 'unknown') ; elseif (s == 1) stat (f, 'numeric value symmetry', '%s', 'symmetric') ; else stat (f, 'numeric value symmetry', '%8.0f%%', s*100) ; end % print the Rutherford/Boeing type mtype = index.RBtype (id,:) ; ss = '-' ; if (mtype (1) == 'r') ss = 'real' ; elseif (mtype (1) == 'c') ss = 'complex' ; elseif (mtype (1) == 'i') ss = 'integer' ; elseif (mtype (1) == 'p') ss = 'binary' ; end stat (f, 'type', '%s', ss) ; ss = '-' ; if (mtype (2) == 'r') ss = 'rectangular' ; elseif (mtype (2) == 'u') ss = 'unsymmetric' ; elseif (mtype (2) == 's') ss = 'symmetric' ; elseif (mtype (2) == 'h') ss = 'Hermitian' ; elseif (mtype (2) == 'z') ss = 'skew-symmetric' ; end stat (f, 'structure', '%s', ss) ; if (index.cholcand (id) == 1) ss = 'yes' ; elseif (index.cholcand (id) == 0) ss = 'no' ; else ss = '?' ; end stat (f, 'Cholesky candidate?', '%s', ss) ; s = index.posdef (id) ; if (s == 0) ss = 'no' ; elseif (s == 1) ss = 'yes' ; else ss = 'unknown' ; end stat (f, 'positive definite?', '%s', ss) ; fprintf (f, '

    \n') ; %------------------------------------------------------------------------------- % problem author, ed, kind %------------------------------------------------------------------------------- fprintf (f, '

    \n') ; fprintf (f, '\n', au) ; fprintf (f, '\n', ed) ; fprintf (f, '\n', da) ; fprintf (f, '\n', kind); s = index.isND (id) ; if (s == 0) ss = 'no' ; else ss = 'yes' ; end fprintf (f, '\n', ss) ; fprintf (f, '
    author%s
    editor%s
    date%s
    kind%s
    2D/3D problem?%s

    \n') ; %------------------------------------------------------------------------------- % fields %------------------------------------------------------------------------------- if (has_b || has_x || has_aux) fprintf (f, '

    \n') ; stat (f, 'Additional fields', '%s', 'size and type') ; if (has_b) stat (f, 'b', '%s', b) ; end if (has_x) stat (f, 'x', '%s', x) ; end if (has_aux) for k = 1:length(auxfields) stat (f, auxfields{k}, '%s', char (auxs{k})) ; end end fprintf (f, '

    \n') ; end %------------------------------------------------------------------------------- % Notes %------------------------------------------------------------------------------- if (~isempty (notes)) fprintf (f, '

    Notes:

    \n') ;
    for k = 1:size(notes,1)
	fprintf (f, '%s\n', notes (k,:)) ;
    end
    fprintf (f, '
    \n') ; end %------------------------------------------------------------------------------- % ordering statistics %------------------------------------------------------------------------------- fprintf (f, '

    \n') ; if (nblocks == 1 || index.nzoff (id) == -2) stat (f, ... 'Ordering statistics:', ... '%s', 'AMD', 'METIS') ; if (index.amd_lnz (id) > -2) stat (f, 'nnz(chol(P*(A+A''+s*I)*P''))', '%s', ... UFint (index.amd_lnz (id)), ... UFint (index.metis_lnz (id))) ; stat (f, 'Cholesky flop count', '%7.1e', ... index.amd_flops (id), ... index.metis_flops (id)) ; stat (f, 'nnz(L+U), no partial pivoting', '%s', ... UFint (2*index.amd_lnz (id) - min(m,n)), ... UFint (2*index.metis_lnz (id) - min(m,n))) ; end stat (f, 'nnz(V) for QR, upper bound nnz(L) for LU', '%s', ... UFint (index.amd_vnz (id)), ... UFint (index.metis_vnz (id))) ; stat (f, 'nnz(R) for QR, upper bound nnz(U) for LU', '%s', ... UFint (index.amd_rnz (id)), ... UFint (index.metis_rnz (id))) ; else stat (f, ... 'Ordering statistics:', ... '%s', 'AMD', 'METIS', 'DMPERM+') ; if (index.amd_lnz (id) > -2) stat (f, 'nnz(chol(P*(A+A''+s*I)*P''))', '%s', ... UFint (index.amd_lnz (id)), ... UFint (index.metis_lnz (id)), ... UFint (index.dmperm_lnz (id))) ; stat (f, 'Cholesky flop count', '%7.1e', ... index.amd_flops (id), ... index.metis_flops (id), ... index.dmperm_flops (id)) ; stat (f, 'nnz(L+U), no partial pivoting', '%s', ... UFint (2*index.amd_lnz (id) - min(m,n)), ... UFint (2*index.metis_lnz (id) - min(m,n)), ... UFint (index.dmperm_lnz (id) + index.dmperm_unz (id)-min(m,n))) ; end stat (f, 'nnz(V) for QR, upper bound nnz(L) for LU', '%s', ... UFint (index.amd_vnz (id)), ... UFint (index.metis_vnz (id)), ... UFint (index.dmperm_vnz (id))) ; stat (f, 'nnz(R) for QR, upper bound nnz(U) for LU', '%s', ... UFint (index.amd_rnz (id)), ... UFint (index.metis_rnz (id)), ... UFint (index.dmperm_rnz (id))) ; end fprintf (f, '

    \n') ; %------------------------------------------------------------------------------- % note regarding orderings %------------------------------------------------------------------------------- if (z > 0) fprintf (f, '

    Note that all matrix statistics (except nonzero'); fprintf (f, ' pattern symmetry) exclude the %d explicit zero entries.\n',z); fprintf (f, '\n') ; end %------------------------------------------------------------------------------- % etc ... %------------------------------------------------------------------------------- fprintf (f, '

    Maintained by '); fprintf (f, 'Tim Davis, last updated %s.', date) ; fprintf (f, '
    Matrix pictures by cspy, a ', url) ; fprintf (f, 'MATLAB function in the CSparse', url) ; fprintf (f, ' package.\n\n\n') ; fclose (f) ; %------------------------------------------------------------------------------- function fsize (f, filename) % fsize: print the filesize d = dir (regexprep (filename, '[\/\\]', filesep)) ; if (isempty (d)) fprintf ('\n') ; elseif (d.bytes < 1024) fprintf (f, ', file size: %4d bytes.\n', d.bytes) ; elseif (d.bytes > 2^20) fprintf (f, ', file size: %8.0f MB.\n', d.bytes / 2^20) ; else fprintf (f, ', file size: %8.0f KB.\n', d.bytes / 2^10) ; end %------------------------------------------------------------------------------- function stat (f, what, format, value1, value2, value3) % stat: print one row of a table s = val (format, value1) ; fprintf (f, '%s%s\n', what, s) ; if (nargin > 4) fprintf (f, '%s\n', val (format, value2)) ; end if (nargin > 5) fprintf (f, '%s\n', val (format, value3)) ; end fprintf (f, '\n') ; %------------------------------------------------------------------------------- function s = val (format, value) % val: print a value in a table if (~ischar (value) && value < 0) s = '-' ; else s = sprintf (format, value) ; end SuiteSparse/UFcollection/UFread.m0000644001170100242450000003243210711673330015666 0ustar davisfacfunction Problem = UFread (directory, tmp) %UFREAD read a Problem in Matrix Market or Rutherford/Boeing format % containing a set of files created by UFwrite, in either Matrix Market or % Rutherford/Boeing format. See UFwrite for a description of the Problem struct. % % Usage: Problem = UFread (directory) % % Example: % % load west0479 % clear Problem % Problem.name = 'HB/west0479' ; % Problem.title = '8 STAGE COLUMN SECTION, ALL SECTIONS RIGOROUS (CHEM.ENG.)'; % Problem.A = west0479 ; % Problem.id = 267 ; % the id number of west0479 in the UF collection % Problem.date = '1983' ; % Problem.author = 'A. Westerberg' ; % Problem.ed = 'I. Duff, R. Grimes, J. Lewis' % Problem.kind = 'chemical process simulation problem' ; % UFwrite (Problem, 'RB/', '') ; % Prob3 = UFread ('RB/HB/west0479') % isequal (Problem, Prob3) % % This part of the example requires CHOLMOD, for the mread function: % % UFwrite (Problem, 'MM/') ; % Prob2 = UFread ('MM/HB/west0479') % isequal (Problem, Prob2) % % You can also compare this Problem with the version in the UF Sparse Matrix % Collection, with UFget(267) or UFget('HB/west0479'). Note that this includes % the 22 explicit zero entries present in the west0479 Harwell/Boeing matrix, % but not included in the MATLAB west0479.mat demo matrix. Those entries are % present in the UF Sparse Matrix Collection. This example assumes your current % directory is the RBio directory, containing the west0479 problem in the % RBio/Test directory: % % Prob5 = UFget ('HB/west0479') % Prob6 = UFread ('Test/west0479') % isequal (Prob5, Prob6) % % The directory can be a compressed tar file of the form "name.tar.gz", in % which case the tarfile is uncompressed into a temporary directory, and % the temporary directory is deleted when done. The '.tar.gz' should not be % part of the directory argument. In this case, a 2nd input argument can be % provided: Problem = UFread (directory, tmp). The problem is extracted into % the tmp directory. If tmp is not present, the output of the tempdir function % is used instead. % % Note that UFget is much faster than UFread. UFread is useful if you are % short on disk space, and want to have just one copy of the collection that % can be read by MATLAB (via UFread) and a non-MATLAB program (the MM or RB % versions of the collection). % % See also UFwrite, mread, mwrite, RBread, RBread, UFget, untar, tempdir. % Optionally uses the CHOLMOD mread mexFunction, for reading Problems in % Matrix Market format. % Copyright 2006-2007, Timothy A. Davis, Univ. of Florida %------------------------------------------------------------------------------- % determine the Problem name from the directory name %------------------------------------------------------------------------------- directory = regexprep (directory, '[\/\\]', filesep) ; t = find (directory == filesep) ; if (isempty (t)) name = directory ; else name = directory (t(end)+1:end) ; end %------------------------------------------------------------------------------- % open the directory, or untar the tar.gz file %------------------------------------------------------------------------------- d = dir (directory) ; is_tar = 0 ; if (isempty (d)) % look for a .tar.gz file if (nargin < 2) tmpdir = [tempname '_UFread_' name] ; else tmpdir = [tmp filesep name] ; end try % try untaring the problem untar ([directory '.tar.gz'], tmpdir) ; catch % untar failed, make sure tmpdir is deleted try rmdir (tmpdir, 's') ; catch end error (['unable to read problem: ' directory]) ; end directory = [tmpdir filesep name] ; d = dir (directory) ; is_tar = 1 ; end %------------------------------------------------------------------------------- % read the problem %------------------------------------------------------------------------------- try %--------------------------------------------------------------------------- % get name, title, id, kind, date, author, editor, notes from master file %--------------------------------------------------------------------------- masterfile = [directory filesep name] ; [Problem notes RB] = get_header (masterfile) ; %--------------------------------------------------------------------------- % get the A and Zero matrices from the master file and add to the Problem %--------------------------------------------------------------------------- if (RB) % read in the primary Rutherford/Boeing file [Problem.A Zeros] = RBread ([masterfile '.rb']) ; else % read in the primary Matrix Market file. Get patterns as binary. [Problem.A Zeros] = mread ([masterfile '.mtx'], 1) ; end if (nnz (Zeros) > 0) Problem.Zeros = Zeros ; end % add the notes after A and Zeros if (~isempty (notes)) Problem.notes = notes ; end namelen = length (name) ; %--------------------------------------------------------------------------- % read b, x, aux (incl. any aux.cell sequences), stored as separate files %--------------------------------------------------------------------------- for k = 1:length(d) % get the next filename in the directory file = d(k).name ; fullfilename = [directory filesep file] ; if (length (file) < length (name) + 1) % unrecognized file; skip it continue elseif (strcmp (file, [name '.mtx'])) % skip the master file; already read in continue elseif (strcmp (file, [name '_b.mtx'])) % read in b as a Matrix Market file Problem.b = mtx_read (fullfilename, RB) ; elseif (strcmp (file, [name '_x.mtx'])) % read in x as a Matrix Market file Problem.x = mtx_read (fullfilename, RB) ; elseif (strcmp (file, [name '_b.rb'])) % read in b as a Rutherford/Boeing file Problem.b = RBread (fullfilename) ; elseif (strcmp (file, [name '_x.rb'])) % read in x as a Rutherford/Boeing file Problem.x = RBread (fullfilename) ; elseif (strcmp (file (1:length(name)+1), [name '_'])) % read in an aux component, in the form name_whatever.mtx thedot = find (file == '.', 1, 'last') ; ext = file (thedot:end) ; if (strcmp (ext, '.txt')) % get a txt file % first, determine the longest line in the file f = fopen (fullfilename) ; if (f < 0) error (['cannot open ' fullfilename]) ; end len = 0 ; nline = 0 ; while (1) s = fgetl (f) ; if (~ischar (s)) break end len = max (len, length (s)) ; nline = nline + 1 ; end fclose (f) ; % next, read in the file as a char array C = repmat (' ', nline, len) ; f = fopen (fullfilename) ; if (f < 0) error (['cannot open ' fullfilename]) ; end i = 0 ; while (1) s = fgetl (f) ; if (~ischar (s)) break end i = i + 1 ; len = length (s) ; if (len > 0) C (i, 1:len) = s ; end end fclose (f) ; elseif (strcmp (ext, '.mtx')) % read a full or sparse auxiliary matrix in the Matrix Market % form, or a full auxiliary matrix in the Rutherford/Boeing form. C = mtx_read (fullfilename, RB) ; elseif (strcmp (ext, '.rb')) % read in a sparse matrix, for a Rutherford/Boeing collection C = RBread (fullfilename) ; else % this file is not recognized - skip it. C = [ ] ; end % determine the name of the component and place it in the Problem if (~isempty (C)) % Determine if this is part of an aux.whatever cell sequence. % These filenames have the form name_whatever_#.mtx, where name % is the name of the Problem, and # is a number (1 or more % digts) greater than zero. If # = i, this becomes the % aux.whatever{i} matrix. suffix = file (namelen+2:thedot-1) ; t = find (suffix == '_', 1, 'last') ; what = suffix (1:t-1) ; i = str2num (suffix (t+1:end)) ; %#ok if (~isempty (i) && i > 0 && ~isempty (what)) % this is part of aux.whatever{i} cell array Problem.aux.(what) {i,1} = C ; elseif (~isempty (suffix)) % this is not a cell, simply an aux.whatever matrix Problem.aux.(suffix) = C ; end end end end %--------------------------------------------------------------------------- % delete the uncompressed version of the tar file %--------------------------------------------------------------------------- if (is_tar) rmdir (tmpdir, 's') ; end catch %--------------------------------------------------------------------------- % catch the error, delete the temp directory, and rethrow the error %--------------------------------------------------------------------------- try if (is_tar) rmdir (tmpdir, 's') ; end catch end rethrow (lasterror) ; end %------------------------------------------------------------------------------- % get_header: get the header of the master file (Group/name/name.txt or .mtx) %------------------------------------------------------------------------------- function [Problem, notes, RB] = get_header (masterfile) % Get the name, title, id, kind, date, author, editor and notes from the master % file. The name, title, and id are required. They appear as structured % comments in the Matrix Market file (masterfile.mtx) or in the text file for % a problem in Rutherford/Boeing format (masterfile.txt). RB is returned as % 1 if the problem is in Rutherford/Boeing format, 0 otherwise. % first assume it's in Matrix Market format f = fopen ([masterfile '.mtx'], 'r') ; if (f < 0) % oops, that failed. This must be a problem in Rutherford/Boeing format RB = 1 ; f = fopen ([masterfile '.txt'], 'r') ; if (f < 0) % oops again, this is not a valid problem in the UF Sparse collection error (['invalid problem: ' masterfile]) ; end else % we found the Matrix Market file RB = 0 ; end Problem = [ ] ; notes = [ ] ; while (1) % get the next line s = fgetl (f) ; if (~ischar (s) || length (s) < 3 || s (1) ~= '%') % end of file or end of leading comments ... no notes found fclose (f) ; [Problem notes] = valid_problem (Problem, [ ]) ; return ; end % remove the leading '% ' and get the first token s = s (3:end) ; [t r] = strtok (s) ; % parse the line if (strcmp (t, 'name:')) % get the Problem.name. It must be of the form Group/Name. Problem.name = strtrim (r) ; if (length (find (Problem.name == '/')) ~= 1) fclose (f) ; error (['invalid problem name ' Problem.name]) ; end elseif (s (1) == '[') % get the Problem.title k = find (s == ']', 1, 'last') ; if (isempty (k)) fclose (f) ; error ('invalid problem title') ; end Problem.title = s (2:k-1) ; elseif (strcmp (t, 'id:')) % get the Problem.id Problem.id = str2num (r) ; %#ok if (isempty (Problem.id) || Problem.id < 0) fclose (f) ; error ('invalid problem id') ; end elseif (strcmp (t, 'kind:')) % get the Problem.kind Problem.kind = strtrim (r) ; elseif (strcmp (t, 'date:')) % get the Problem.date Problem.date = strtrim (r) ; elseif (strcmp (t, 'author:')) % get the Problem.author Problem.author = strtrim (r) ; elseif (strcmp (t, 'ed:')) % get the Problem.ed Problem.ed = strtrim (r) ; elseif (strcmp (t, 'notes:')) % get the notes, which always appear last k = 0 ; notes = [ ] ; while (1) % get the next line s = fgetl (f) ; if (~ischar (s) || length (s) < 2 || ~strcmp (s (1:2), '% ')) % end of file or end of notes ... convert notes to char array fclose (f) ; [Problem notes] = valid_problem (Problem, notes) ; return ; end % add the line to the notes k = k + 1 ; notes {k} = s ; %#ok end end end %------------------------------------------------------------------------------- % valid_problem: determine if a problem is valid, and finalizes the notes %------------------------------------------------------------------------------- function [Problem, notes] = valid_problem (Problem, notes) % make sure the required fields (name, title, id, date, author, ed) are present. % Convert notes to char, and strip off the leading '% ', inserted when the notes % were printed in the Matrix Market file. if (~isfield (Problem, 'name') || ~isfield (Problem, 'title') || ... ~isfield (Problem, 'id') || ~isfield (Problem, 'date') || ... ~isfield (Problem, 'author') || ~isfield (Problem, 'ed') || ... ~isfield (Problem, 'kind')) error ('invalid Problem mfile') ; end if (~isempty (notes)) notes = char (notes) ; notes = notes (:, 3:end) ; end %------------------------------------------------------------------------------- % mtx_read: read a *.mtx file %------------------------------------------------------------------------------- % In the Rutherford/Boeing form, a *.mtx file is used only for full matrices, % using a tiny subset of the Matrix Market format. In the Matrix Market form, % the *.mtx is used for all b, x, and aux matrices (both full and sparse). function C = mtx_read (file, RB) if (~RB) % Get a Matrix Market file, using full Matrix Market features. C = mread (file, 1) ; else % mread is not installed. The RB format uses a tiny subset of the Matrix % Market format for full matrices: just the one header line, and no comment % or blank lines permitted. Allowable header lines are: % %%MatrixMarket matrix array real general % %%MatrixMarket matrix array complex general % This tiny subset can be read by UFfull_read. C = UFfull_read (file) ; end SuiteSparse/UFcollection/UFfull_write.c0000644001170100242450000001106410617476236017126 0ustar davisfac/* ========================================================================== */ /* === UFcollection/UFfull ================================================== */ /* ========================================================================== */ /* UFcollection: a MATLAB toolbox for managing the UF Sparse Matrix Collection. * Copyright (c) 2007, Timothy A. Davis, Univ. Florida. */ /* ========================================================================== */ /* UFfull_write (filename, X): write a full matrix to a file. A small subset of * the Matrix Market format is used. The first line is one of: * * %%MatrixMarket matrix real complex general * %%MatrixMarket matrix array complex general * * The 2nd line contains two numbers: m and n, where X is m-by-n. The next * m*n lines contain the numerical values (one per line if real, two per line * if complex, containing the real and imaginary parts). The values are * listed in column-major order. The resulting file can be read by any * Matrix Market reader, or by UFfull_read. No comments or blank lines are * used. */ #ifndef NLARGEFILE #include "io64.h" #endif #include "UFconfig.h" #include "mex.h" #include #define MAXLINE 1030 #define BIG 1e308 /* -------------------------------------------------------------------------- */ /* print_value */ /* -------------------------------------------------------------------------- */ static void print_value (FILE *f, double x, char *s) { double y ; int k, width ; /* change -inf to -BIG, and change +inf and nan to +BIG */ if (x != x || x >= BIG) { x = BIG ; } else if (x <= -BIG) { x = -BIG ; } /* convert to int and back again */ k = (int) x ; y = (double) k ; if (y == x) { /* x is a small integer */ fprintf (f, "%d", k) ; } else { /* x is not an integer, use the smallest width possible */ for (width = 6 ; width < 20 ; width++) { /* write the value to a string, read it back in, and check */ sprintf (s, "%.*g", width, x) ; sscanf (s, "%lg", &y) ; if (x == y) break ; } fprintf (f, "%s", s) ; } } /* -------------------------------------------------------------------------- */ /* UFfull */ /* -------------------------------------------------------------------------- */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { int iscomplex ; size_t nrow, ncol, i, j ; double *Ax, *Az ; char filename [MAXLINE], s [MAXLINE] ; FILE *f ; /* ---------------------------------------------------------------------- */ /* check inputs */ /* ---------------------------------------------------------------------- */ if (nargout > 0 || nargin != 2) { mexErrMsgTxt ("usage: UFfull (filename,A)") ; } if (mxIsSparse (pargin [1]) || !mxIsClass (pargin [1], "double")) { mexErrMsgTxt ("A must be full and double") ; } /* ---------------------------------------------------------------------- */ /* get filename and open the file */ /* ---------------------------------------------------------------------- */ if (!mxIsChar (pargin [0])) { mexErrMsgTxt ("first parameter must be a filename") ; } mxGetString (pargin [0], filename, MAXLINE) ; f = fopen (filename, "w") ; if (f == NULL) { mexErrMsgTxt ("error openning file") ; } /* ---------------------------------------------------------------------- */ /* get the matrix */ /* ---------------------------------------------------------------------- */ iscomplex = mxIsComplex (pargin [1]) ; nrow = mxGetM (pargin [1]) ; ncol = mxGetN (pargin [1]) ; Ax = mxGetPr (pargin [1]) ; Az = mxGetPi (pargin [1]) ; /* ---------------------------------------------------------------------- */ /* write the matrix */ /* ---------------------------------------------------------------------- */ if (iscomplex) { fprintf (f, "%%%%MatrixMarket matrix array complex general\n") ; } else { fprintf (f, "%%%%MatrixMarket matrix array real general\n") ; } fprintf (f, "%d %d\n", nrow, ncol) ; for (j = 0 ; j < ncol ; j++) { for (i = 0 ; i < nrow ; i++) { print_value (f, Ax [i + j*nrow], s) ; if (iscomplex) { fprintf (f, " ") ; print_value (f, Az [i + j*nrow], s) ; } fprintf (f, "\n") ; } } /* ---------------------------------------------------------------------- */ /* close the file */ /* ---------------------------------------------------------------------- */ fclose (f) ; } SuiteSparse/UFcollection/UFfull_write.m0000644001170100242450000000171010620400402017105 0ustar davisfacfunction UFfull_write (filename, A) %#ok %UFFULL_WRITE write a full matrix using a subset of Matrix Market format % Usage: % % UFfull_write (filename, A) % % A small subset of the Matrix Market format is used. The first line is one of: % % %%MatrixMarket matrix real complex general % %%MatrixMarket matrix array complex general % % The second line contains two numbers: m and n, where A is m-by-n. The next % m*n lines contain the numerical values (one per line if real, two per line % if complex, containing the real and imaginary parts). The values are listed % in column-major order. The resulting file can be read by any Matrix Market % reader, or by UFfull_read. No comments or blank lines are used. % % Example: % x = rand (8) % UFfull_write ('xfile', x) % y = UFfull_read ('xfile') % norm (x-y) % % See also mread, mwrite, RBwrite, RBread. % Copyright 2006-2007, Timothy A. Davis error ('UFfull_write mexFunction not found') ; SuiteSparse/UFcollection/dsxy2figxy.m0000644001170100242450000000443010620400104016617 0ustar davisfacfunction varargout = dsxy2figxy(varargin) %DSXY2FIGXY Transform point or position from axis to figure coords % Transforms [axx axy] or [xypos] from axes hAx (data) coords into coords % wrt GCF for placing annotation objects that use figure coords into data % space. The annotation objects this can be used for are % arrow, doublearrow, textarrow % ellipses (coordinates must be transformed to [x, y, width, height]) % Note that line, text, and rectangle anno objects already are placed % on a plot using axes coordinates and must be located within an axes. % Example to compute a position and apply to an annotation: % Example: % [axx axy] = ginput(2); % [figx figy] = getaxannopos(gca, axx, axy); % har = annotation('textarrow',figx,figy); % set(har,'String',['(' num2str(axx(2)) ',' num2str(axy(2)) ')']) % % See also annotation, plot, ginput. % Copyright 2006-2007, The MathWorks, Inc. Used by permission (see % http://www.mathworks.com/access/helpdesk/help/techdoc/creating_plots/ % bquk5ia-4.html). %% Obtain arguments (only limited argument checking is performed). % Determine if axes handle is specified if length(varargin{1})== 1 && ishandle(varargin{1}) && ... strcmp(get(varargin{1},'type'),'axes') hAx = varargin{1}; varargin = varargin(2:end); else hAx = gca; end; % Parse either a position vector or two 2-D point tuples if length(varargin)==1 % Must be a 4-element POS vector pos = varargin{1}; else [x,y] = deal(varargin{:}); % Two tuples (start & end points) end %% Get limits axun = get(hAx,'Units'); set(hAx,'Units','normalized'); % Need normaized units to do the xform axpos = get(hAx,'Position'); axlim = axis(hAx); % Get the axis limits [xlim ylim (zlim)] axwidth = diff(axlim(1:2)); axheight = diff(axlim(3:4)); %% Transform data from figure space to data space if exist('x','var') % Transform a and return pair of points varargout{1} = (x-axlim(1))*axpos(3)/axwidth + axpos(1); varargout{2} = (y-axlim(3))*axpos(4)/axheight + axpos(2); else % Transform and return a position rectangle pos(1) = (pos(1)-axlim(1))/axwidth*axpos(3) + axpos(1); pos(2) = (pos(2)-axlim(3))/axheight*axpos(4) + axpos(2); pos(3) = pos(3)*axpos(3)/axwidth; pos(4) = pos(4)*axpos(4)/axheight; varargout{1} = pos; end %% Restore axes units set(hAx,'Units',axun) SuiteSparse/UFcollection/UFlists.m0000644001170100242450000000630310677241026016113 0ustar davisfacfunction UFlists %UFLISTS create the web pages for each matrix list (group, name, etc.) % Places the web pages in the matrices/ subdirectory of the current directory. % % Example: % UFlists % % See also UFget, UFlist % Copyright 2006-2007, Timothy A. Davis % create all the web pages for the lists UFlist ('group') ; UFlist ('name') ; UFlist ('id') ; UFlist ('dimension') ; UFlist ('nnz') ; UFlist ('symmetry') ; UFlist ('type') ; % do all the group pages, and the list of groups index = UFget ; nmat = length (index.nrows) ; [ignore, i] = sort (index.Group) ; g = index.Group (i) ; % create the primary directory [url topdir] = UFlocation ; matrices = [topdir 'matrices'] ; if (~exist (matrices, 'dir')) mkdir (matrices) ; end % create the groups.html file f = fopen ([matrices filesep 'groups.html'], 'w') ; if (f < 0) error ('unable to create groups.html file\n') ; end % add the header fprintf (f, ... '\n') ; fprintf (f, '\n') ; fprintf (f, 'UF Sparse Matrix Collection: group list') ; fprintf (f, '\n') ; fprintf (f, '\n') ; fprintf (f, '

  • UF Sparse Matrix Collection\n') ; fprintf (f, '

    List of matrix groups in the UF Sparse Matrix Collection:\n') ; fprintf (f, '

    \n') ; fprintf (f, '\n') ; fprintf (f, '\n') ; fprintf (f, '\n') ; fprintf (f, '\n') ; % find all the groups group = '' ; ngroup = 0 ; for i = 1:nmat if (strcmp (group, g {i})) continue end group = g {i} ; ngroup = ngroup + 1 ; groups {ngroup} = group ; %#ok end nmat = 0 ; for i = 1:ngroup group = groups {i} ; UFlist ('group', group) ; fprintf (f, '\n') ; % link to group fprintf (f, '\n', group, group) ; % number of matrices d = dir ([topdir 'mat' filesep group filesep '*.mat']) ; nmat_group = size (d,1) ; fprintf (f, '\n', nmat_group) ; nmat = nmat + nmat_group ; % link to README.txt file ("details") f2 = fopen ([topdir filesep 'mat' filesep group filesep 'README.txt'], 'r'); if (f2 < 0) error (['no README file for group: ' group]) ; else s = fgets (f2) ; fprintf (f, ... '\n', group) ; end % one-line description (first line of README.txt) fprintf (f, '\n', s) ; fclose (f2); fprintf (f, '\n') ; end fprintf (f, '
    Group# matricesdetailsdescription
    %s%ddetails%s
    \n') ; fprintf (f, '

    Total number of matrices in UF Sparse Matrix Collection:') ; fprintf (f, ' %d\n', nmat) ; fprintf (f, '

    Maintained by '); fprintf (f, 'Tim Davis, last updated %s.', date) ; fprintf (f, '
    Matrix pictures by cspy, a MATLAB', ... url) ; fprintf (f, ' function in the CSparse package.\n', ... url) ; fprintf (f, '\n') ; fprintf (f, '\n') ; fclose (f) ; SuiteSparse/UFcollection/UFcollection_install.m0000644001170100242450000000122610623063453020632 0ustar davisfacfunction UFcollection_install (nlargefile) %UFCOLLECTION_INSTALL install the UFcollection toolbox % % Example: % UFcollection_install % % See also UFget. % Copyright 2006-2007, Timothy A. Davis if (nargin < 1) % try with large-file I/O nlargefile = 0 ; end if (nlargefile) fprintf ('Trying to compile without large file support...\n') ; mex -I../UFconfig -DNLARGEFILE UFfull_write.c else try mex -I../UFconfig UFfull_write.c catch fprintf ('Trying to compile without large file support...\n') ; mex -I../UFconfig -DNLARGEFILE UFfull_write.c end end addpath (pwd) ; fprintf ('UFcollection toolbox successfully compiled.\n') ; SuiteSparse/UFcollection/Contents.m0000644001170100242450000000333010620400407016300 0ustar davisfac% UFcollection: software for managing the UF Sparse Matrix Collection % % To create the index: % % UFindex - create the index for the UF Sparse Matrix Collection % UFstats - compute matrix statistics for the UF Sparse Matrix Collection % % To create the web pages: % % UFallpages - create all web pages for the UF Sparse Matrix Collection % UFgplot - draw a plot of the graph of a sparse matrix % UFint - print an integer to a string, adding commas every 3 digits % UFlist - create a web page index for the UF Sparse Matrix Collection % UFlists - create the web pages for each matrix list (group, name, etc.) % UFlocation - URL and top-level directory of the UF Sparse Matrix Collection % UFpage - create web page for a matrix in UF Sparse Matrix Collection % UFpages - create web page for each matrix in UF Sparse Matrix Collection % dsxy2figxy - Transform point or position from axis to figure coords % % To create the Matrix Market and Rutherford/Boeing versions of the collection: % % UFexport - export to Matrix Market and Rutherford/Boeing formats % UFread - read a Problem in Matrix Market or Rutherford/Boeing format % UFwrite - write a Problem in Matrix Market or Rutherford/Boeing format % UFfull_read - read a full matrix using a subset of Matrix Market format % UFfull_write - write a full matrix using a subset of Matrix Market format % % Other: % % UFcollection_install - install the UFcollection toolbox % % Example: % UFindex % create index (UF_Index.mat) for use by UFget % UFallpages % create all web pages for the UF Sparse Matrix Collection % % Requires UFget, CSparse, CHOLMOD, AMD, COLAMD, METIS. % Copyright 2006-2007, Timothy A. Davis SuiteSparse/UFcollection/UFallpages.m0000644001170100242450000000067210620400326016534 0ustar davisfacfunction UFallpages (figures) %UFALLPAGES create all web pages for the UF Sparse Matrix Collection % with the exception of the top-level index.html file (which is created % manually). % % Example: % % UFallpages % UFallpages(0) % does not create figures (assumes they already exist) % % See also UFget, UFlists, UFpages. % Copyright 2006-2007, Timothy A. Davis if (nargin < 1) figures = 1 ; end UFlists ; UFpages (figures) ; SuiteSparse/UFcollection/UFstats.m0000644001170100242450000003725010623341426016114 0ustar davisfacfunction stats = UFstats (A, kind, nometis, Z) %UFSTATS compute matrix statistics for the UF Sparse Matrix Collection % Example: % stats = UFstats (A,kind,nometis,Z) % % A: a sparse matrix % kind: a string with the Problem.kind % nometis: if nonzero then metis(A,'col') is not used, nor is metis used in the % dmperm+ ordering. % Z: empty, or a sparse matrix the same size as A. Only used for psym and % nzero statistics, described below. % % Requires amd, cholmod, metis, RBio, and CSparse. Computes the following % statistics, returning them as fields in the stats struct: % % nrows number of rows % ncols number of columns % nnz number of entries in A % RBtype Rutherford/Boeing type % isBinary 1 if binary, 0 otherwise % isReal 1 if real, 0 if complex % cholcand 1 if a candidate for sparse Cholesky, 0 otherwise % nsym numeric symmetry (0 to 1, where 1=symmetric) % psym pattern symmetry (0 to 1, where 1=symmetric) % nnzdiag nnz (diag (A)) if A is square, 0 otherwise % nzero nnz (Z) % amd_lnz nnz(L) for chol(C(p,p)) where, C=A+A', p=amd(C) % amd_flops flop count for chol(C(p,p)) where, C=A+A', p=amd(C) % amd_vnz nnz in Householder vectors for qr(A(:,colamd(A))) % amd_rnz nnz in R for qr(A(:,colamd(A))) % metis_lnz nnz(L) for chol(C(p,p)) where, C=A+A', p=metis(C) % metis_flops flop count for chol(C(p,p)) where, C=A+A', p=metis(C) % metis_vnz nnz in Householder vectors for qr(A(:,metis(A,'col'))) % metis_rnz nnz in R for qr(A(:,metis(A,'col'))) % nblocks # of blocks from dmperm % sprank sprank(A) % nzoff # of entries not in diagonal blocks from dmperm % ncc # of strongly connected components % dmperm_lnz nnz(L), using dmperm plus amd or metis % dmperm_unz nnz(U), using dmperm plus amd or metis % dmperm_flops flop count with dperm plus % dmperm_vnz nnz in Householder vectors for dmperm plus % dmperm_rnz nnz in R for dmperm plus % posdef 1 if positive definite, 0 otherwise % isND 1 if a 2D/3D problem, 0 otherwise % % The *_lnz, *_unz, and *_flops statistics are not computed for rectangular % or structurally singular matrices. nzoff and the dmperm_* stats are not % computed for structurally singular matrices. If a statistic is not computed, % it is set to -2. If an attempt to compute the statistic was made but failed, % it is set to -1. % % See also UFget, UFindex, amd, metis, RBtype, cs_scc, cs_sqr, dmperm. % Copyright 2006-2007, Timothy A. Davis % Requires the SuiteSparse set of packages: CHOLMOD, AMD, COLAMD, RBio, CSparse; % and METIS. if (nargin < 3) nometis = 0 ; end %------------------------------------------------------------------------------- % ensure the matrix is sparse %------------------------------------------------------------------------------- if (~issparse (A)) A = sparse (A) ; end %------------------------------------------------------------------------------- % basic stats %------------------------------------------------------------------------------- tic ; [m n] = size (A) ; stats.nrows = m ; stats.ncols = n ; stats.nnz = nnz (A) ; stats.RBtype = RBtype (A) ; % Rutherford/Boeing type stats.isBinary = (stats.RBtype (1) == 'p') ; stats.isReal = (stats.RBtype (1) ~= 'c') ; fprintf ('RBtype: %s time: %g\n', stats.RBtype, toc) ; %------------------------------------------------------------------------------- % symmetry and Cholesky candidacy %------------------------------------------------------------------------------- % get the symmetry tic ; [s xmatched pmatched nzoffdiag nnzdiag] = spsym (A) ; stats.cholcand = (s >= 6) ; % check if Cholesky candidate if (m ~= n) stats.nsym = 0 ; stats.psym = 0 ; elseif (nzoffdiag > 0) stats.nsym = xmatched / nzoffdiag ; stats.psym = pmatched / nzoffdiag ; else stats.nsym = 1 ; stats.psym = 1 ; end fprintf ('cholcand: %d\n', stats.cholcand) ; fprintf ('nsym: %g psym: %g time: %g\n', stats.nsym, stats.psym, toc) ; tic ; stats.nnzdiag = nnzdiag ; if (nargin > 3) stats.nzero = nnz (Z) ; % recompute the pattern symmetry with Z included if (m == n) try AZ = A+Z ; if (nnz (AZ) ~= nnz (A) + nnz (Z)) error ('A and Z overlap!') end [s xmatched pmatched nzoffdiag] = spsym (AZ) ; clear AZ if (nzoffdiag > 0) stats.psym = pmatched / nzoffdiag ; else stats.psym = 1 ; end catch fprintf ('failed to compute symmetry of pattern of A+Z\n') ; end end else stats.nzero = 0 ; end fprintf ('nsym: %g psym: %g time: %g\n', stats.nsym, stats.psym, toc) ; tic ; %------------------------------------------------------------------------------- % intialize ordering statistics %------------------------------------------------------------------------------- % if square, Cholesky of C(p,p) where C=A+A', p = amd(C) stats.amd_lnz = -1 ; % nnz (chol (C)) stats.amd_flops = -1 ; % flop counts for chol (C) % if square or rectangular stats.amd_vnz = -1 ; % nnz (V), upper bound on L, for A(:,colamd(A)) stats.amd_rnz = -1 ; % nnz (R), upper bound on U, for A(:,colamd(A)) % if square, Cholesky of C(p,p) where C=A+A', p = metis(C) stats.metis_lnz = -1 ; % nnz (chol (C)) stats.metis_flops = -1 ; % flop counts for chol (C) % if square or rectangular stats.metis_vnz = -1 ; % nnz (V), upper bound on L, for A(:,metis(A)) stats.metis_rnz = -1 ; % nnz (R), upper bound on U, for A(:,metis(A)) % dmperm analysis stats.nblocks = -1 ; % # of blocks in block-triangular form stats.sprank = -1 ; % structural rank stats.nzoff = -1 ; % # of entries of A in off-diagonal blocks % cs_scc2 stats.ncc = -1 ; % # of strongly connected components % dmperm: best of amd/metis on each square block, best of colamd/metis % on rectangular blocks stats.dmperm_lnz = -1 ; % nnz (L), for square struct full rank matrices stats.dmperm_unz = -1 ; % nnz (U) + nzoff, for square struct full rank mat stats.dmperm_flops = -1 ; % Cholesky flop count of each square block stats.dmperm_vnz = -1 ; % nnz (V), upper bound on L stats.dmperm_rnz = -1 ; % nnz (R), upper bound on U stats.isND = -1 ; % 1 if 2D/3D problem, 0 otherwise d = max (m,n) ; % if the matrix has a symmetric nonzero pattern, nzoff will always be zero if (stats.psym == 1) stats.nzoff = 0 ; end %------------------------------------------------------------------------------- % determine if positive definite %------------------------------------------------------------------------------- if (~stats.cholcand) % not a candidate for Cholesky, so it cannot be positive definite stats.posdef = 0 ; else % try chol try [x, cstats] = cholmod2 (A, ones (stats.ncols,1)) ; rcond = cstats (1) ; fprintf ('rcond: %g\n', rcond) ; stats.posdef = (rcond > 0) ; catch % chol failed disp (lasterr) ; fprintf ('sparse Cholesky failed\n') ; stats.posdef = -1 ; end clear x cstats end fprintf ('posdef: %d time: %g\n', stats.posdef, toc) ; tic ; %------------------------------------------------------------------------------- % transpose A if m < n, for ordering methods %------------------------------------------------------------------------------- if (m < n) try A = A' ; % A is now tall and thin, or square catch disp (lasterr) ; fprintf ('transpose failed...\n') ; return ; end [m n] = size (A) ; end if (~isreal (A)) try A = spones (A) ; catch disp (lasterr) ; fprintf ('conversion from complex failed...\n') ; return ; end end fprintf ('computed A transpose if needed, time: %g\n', toc) ; tic ; %------------------------------------------------------------------------------- % order entire matrix with AMD and METIS, if square %------------------------------------------------------------------------------- if (m == n) tic ; try if (stats.RBtype (2) == 'u') C = A|A' ; else C = A ; end catch disp (lasterr) ; fprintf ('A+A'' failed\n') ; end fprintf ('computed A+A'', time: %g\n', toc) ; % order the whole matrix with AMD tic ; try p = amd (C) ; c = symbfact (C (p,p)) ; stats.amd_lnz = sum (c) ; stats.amd_flops = sum (c.^2) ; catch disp (lasterr) ; fprintf ('amd failed\n') ; end clear p c fprintf ('AMD lnz %d flops %g time: %g\n', ... stats.amd_lnz, stats.amd_flops, toc) ; % order the whole matrix with METIS tic ; try p = metis (C) ; c = symbfact (C (p,p)) ; stats.metis_lnz = sum (c) ; stats.metis_flops = sum (c.^2) ; catch disp (lasterr) ; fprintf ('metis failed\n') ; end clear p c C fprintf ('METIS lnz %d flops %g time: %g\n', ... stats.metis_lnz, stats.metis_flops, toc) ; else % not computed if rectangular stats.amd_lnz = -2 ; stats.amd_flops = -2 ; stats.metis_lnz = -2 ; stats.metis_flops = -2 ; end %------------------------------------------------------------------------------- % order entire matrix with COLAMD, for LU bounds %------------------------------------------------------------------------------- tic ; try % do not ignore any rows, and do not do etree postordering q = colamd2mex (A, [d 10]) ; [vnz,rnz] = cs_sqr (A (:,q)) ; stats.amd_rnz = rnz ; stats.amd_vnz = vnz ; catch disp (lasterr) ; fprintf ('colamd2 and cs_sqr failed\n') ; end clear q fprintf ('COLAMD rnz %d vnz %d time: %g\n', stats.amd_rnz, stats.amd_vnz, toc) ; tic ; %------------------------------------------------------------------------------- % order entire matrix with METIS, for LU bounds %------------------------------------------------------------------------------- if (~nometis) try q = metis (A, 'col') ; [vnz,rnz] = cs_sqr (A (:,q)) ; stats.metis_rnz = rnz ; stats.metis_vnz = vnz ; catch disp (lasterr) ; fprintf ('metis(A''*A) and cs_sqr failed\n') ; end end clear q fprintf ('METIS rnz %d vnz %d time: %g\n', ... stats.metis_rnz, stats.metis_vnz, toc) ; tic ; %------------------------------------------------------------------------------- % strongly connected components %------------------------------------------------------------------------------- try % find the # of strongly connected components of the graph of a square A, % or # of connected components of the bipartite graph of a rectangular A. % [p,q,r,s] = cs_scc2 (A) ; if (m == n) [p r] = cs_scc (A) ; else [p r] = cs_scc (spaugment (A)) ; end stats.ncc = length (r) - 1 ; clear p r catch disp (lasterr) ; fprintf ('cs_scc failed\n') ; end fprintf ('scc %d, time: %g\n', stats.ncc, toc) ; tic ; %------------------------------------------------------------------------------- % isND %------------------------------------------------------------------------------- s = 0 ; if (strfind (kind, 'structural')) s = 1 ; elseif (strfind (kind, 'fluid')) s = 1 ; elseif (strfind (kind, '2D')) s = 1 ; elseif (strfind (kind, 'reduction')) s = 1 ; elseif (strfind (kind, 'electromagnetics')) s = 1 ; elseif (strfind (kind, 'semiconductor')) s = 1 ; elseif (strfind (kind, 'thermal')) s = 1 ; elseif (strfind (kind, 'materials')) s = 1 ; elseif (strfind (kind, 'acoustics')) s = 1 ; elseif (strfind (kind, 'vision')) s = 1 ; elseif (strfind (kind, 'robotics')) s = 1 ; end stats.isND = s ; fprintf ('isND %d\n', stats.isND) ; %------------------------------------------------------------------------------- % Dulmage-Mendelsohn permutation, and order each block %------------------------------------------------------------------------------- try % find the Dulmage-Mendelsohn decomposition [p,q,r,s,cc,rr] = cs_dmperm (A) ; nblocks = length (r) - 1 ; stats.nblocks = nblocks ; stats.sprank = rr(4)-1 ; catch disp (lasterr) ; fprintf ('cs_dmperm failed\n') ; end fprintf ('sprank %d, time: %g\n', stats.sprank, toc) ; fprintf ('nblocks %d\n', stats.nblocks) ; tic ok_square = 1 ; ok_vnz = 1 ; try mm = diff (r) ; nn = diff (s) ; square = all (mm == nn) ; if (~square) % not computed if the matrix is rectangular stats.dmperm_lnz = -2 ; stats.dmperm_unz = -2 ; stats.dmperm_flops = -2 ; end if (stats.sprank < min (m,n)) % do not report DMPERM results for structurally singular matrices stats.nzoff = -2 ; stats.dmperm_lnz = -2 ; stats.dmperm_unz = -2 ; stats.dmperm_flops = -2 ; stats.dmperm_vnz = -2 ; stats.dmperm_rnz = -2 ; elseif (nblocks == n && m == n) % square triangular or diagonal C = A (p,q) ; clear p q r s stats.nzoff = nnz (triu (C, 1)) ; stats.dmperm_lnz = n ; stats.dmperm_unz = n + stats.nzoff ; stats.dmperm_flops = n ; stats.dmperm_vnz = n ; stats.dmperm_rnz = nnz (C) ; elseif (nblocks == 1 && m == n) % only one block of structural full rank, so don't redo analysis clear p q r s stats.nzoff = 0 ; if (stats.metis_lnz < 0 || stats.amd_lnz < stats.metis_lnz) stats.dmperm_lnz = stats.amd_lnz ; stats.dmperm_unz = stats.amd_lnz ; stats.dmperm_flops = stats.amd_flops ; else stats.dmperm_lnz = stats.metis_lnz ; stats.dmperm_unz = stats.metis_lnz ; stats.dmperm_flops = stats.metis_flops ; end if (stats.metis_vnz < 0 || stats.amd_rnz < stats.metis_rnz) stats.dmperm_vnz = stats.amd_vnz ; stats.dmperm_rnz = stats.amd_rnz ; else stats.dmperm_vnz = stats.metis_vnz ; stats.dmperm_rnz = stats.metis_rnz ; end else % analyze each block of the permuted matrix C = A (p,q) ; clear p q nzoff = nnz (C) ; lnz = 0 ; unz = 0 ; flops = 0 ; vnz = 0 ; rnz = 0 ; for k = 1:nblocks i1 = r (k) ; i2 = r (k+1) - 1 ; j1 = s (k) ; j2 = s (k+1) - 1 ; if (i2-i1 == 1 && j2-j1 == 1) % singleton case nzoff = nzoff - 1 ; unz = unz + 1 ; lnz = lnz + 1 ; flops = flops + 1 ; rnz = rnz + 1 ; vnz = vnz + 1 ; continue ; end % get the kth block S = C (i1:i2, j1:j2) ; [ms ns] = size (S) ; nzoff = nzoff - nnz (S) ; if (ok_square) try if (square) % all blocks are square, analyze a square block % best of amd and metis if (nometis) [pblock c] = analyze (S|S', 'sym', 1) ; else [pblock c] = analyze (S|S', 'sym', 3) ; end lnzblock = sum (c) ; unz = unz + lnzblock ; lnz = lnz + lnzblock ; flops = flops + sum (c.^2) ; clear c pblock end catch % ordering failed, but keep going to compute nzoff ok_square = 0 ; end end if (ok_vnz) try % analyze a rectangular block, or LU bounds for square block if (ms < ns) S = S' ; end % best of amd and metis try if (nometis) pblock = analyze (S, 'col', 1) ; else pblock = analyze (S, 'col', 3) ; end catch pblock = colamd2mex (S, [d 10]) ; end [vnz2,rnz2] = cs_sqr (S (:, pblock)) ; rnz = rnz + rnz2 ; vnz = vnz + vnz2 ; catch % ordering failed, but keep going to compute nzoff ok_vnz = 0 ; end end clear S pblock end stats.nzoff = nzoff ; if (ok_square) if (~square) stats.dmperm_unz = -2 ; stats.dmperm_lnz = -2 ; stats.dmperm_flops = -2 ; else stats.dmperm_lnz = lnz ; stats.dmperm_unz = unz + nzoff ; stats.dmperm_flops = flops ; end end if (ok_vnz) stats.dmperm_vnz = vnz ; stats.dmperm_rnz = rnz + nzoff ; end clear C r s end if (~ok_square) disp (lasterr) ; fprintf ('cs_dmperm (square: lnz, unz, flops) ordering failed\n') ; end if (~ok_vnz) disp (lasterr) ; fprintf ('cs_dmperm (LU bounds: vnz, rnz) ordering failed\n') ; end catch disp (lasterr) ; fprintf ('cs_dmperm ordering and nzoff failed\n') ; end fprintf ('dmperm stats done, time %g\n', toc) ; fprintf ('UFstats done\n') ; SuiteSparse/UFcollection/UFint.m0000644001170100242450000000170610620400333015533 0ustar davisfacfunction s = UFint (x) %UFINT print an integer to a string, adding commas every 3 digits % If negative, the result is the single character '-'. % % Example: % UFint (-2) % UFint (2^30) % % See also sprintf. % Copyright 2006-2007, Timothy A. Davis if (x < 0) s = '-' ; return end t = sprintf ('%d', fix (x)) ; len = length (t) ; if (len <= 3 || len > 12 || ~isempty (strfind (t, 'e'))) s = t ; elseif (len == 4) s = [ t(1) ',' t(2:4) ] ; elseif (len == 5) s = [ t(1:2) ',' t(3:5) ] ; elseif (len == 6) s = [ t(1:3) ',' t(4:6) ] ; elseif (len == 7) s = [ t(1) ',' t(2:4) ',' t(5:7) ] ; elseif (len == 8) s = [ t(1:2) ',' t(3:5) ',' t(6:8) ] ; elseif (len == 9) s = [ t(1:3) ',' t(4:6) ',' t(7:9) ] ; elseif (len == 10) s = [ t(1) ',' t(2:4) ',' t(5:7) ',' t(8:10) ] ; elseif (len == 11) s = [ t(1:2) ',' t(3:5) ',' t(6:8) ',' t(9:11) ] ; elseif (len == 12) s = [ t(1:3) ',' t(4:6) ',' t(7:9) ',' t(10:12) ] ; end SuiteSparse/UFcollection/UFlocation.m0000644001170100242450000000062710620400342016552 0ustar davisfacfunction [url, topdir] = UFlocation %UFLOCATION URL and top-level directory of the UF Sparse Matrix Collection % % Example: % [url, topdir] = UFlocation % % See also UFget. % Copyright 2006-2007, Timothy A. Davis params = UFget_defaults ; t = find (params.dir == filesep) ; topdir = regexprep (params.dir (1:t(end-1)), '[\/\\]', filesep) ; t = find (params.url == '/') ; url = params.url (1:t(end)) ; SuiteSparse/UFcollection/UFgplot.m0000644001170100242450000000640610620400331016066 0ustar davisfacfunction UFgplot (A, xyz, directed, nodename) %UFGPLOT draw a plot of the graph of a sparse matrix % Usage: % UFgplot (A, xyz, directed, nodename) % % A: a square sparse matrix of size n-by-n. % xyz: an n-by-2 or n-by-3 array of the XY or XYZ coordinates of each node. % directed: 1 if A is directed, 0 otherwise. 0 if not present. % nodename: a char array with n rows, or empty, containing the name of each % node. Not used if not present. % % Example: % % Problem = UFget ('Pajek/football') ; % UFgplot (Problem.A, Problem.aux.coord, 1, Problem.aux.nodename) ; % % See also gplot, UFget. % Copyright 2006-2007, Timothy A. Davis %------------------------------------------------------------------------------- % check inputs %------------------------------------------------------------------------------- [m n] = size (A) ; if (m ~= n) error ('A must be square') ; end if (nargin < 4) nodename = [ ] ; end if (nargin < 3) directed = 0 ; end %------------------------------------------------------------------------------- % determine if 2D or 3D %------------------------------------------------------------------------------- if (size (xyz, 2) == 2) %--------------------------------------------------------------------------- % no Z coordinates, draw a 2D graph %--------------------------------------------------------------------------- xy = xyz ; if (directed) ti = '2D directed graph' ; else ti = '2D undirected graph' ; end else %--------------------------------------------------------------------------- % a 3D graph; rotate for better viewing %--------------------------------------------------------------------------- dx = -45 ; dy = 45 ; dz = 45 ; a = dx * (2*pi/360) ; xrotation = [ 1 0 0 0 cos(a) sin(a) 0 -sin(a) cos(a) ] ; b = dy * (2*pi/360) ; yrotation = [ cos(b) 0 -sin(b) 0 1 0 sin(b) 0 cos(b) ] ; c = dz * (2*pi/360) ; zrotation = [ cos(c) sin(c) 0 -sin(c) cos(c) 0 0 0 1 ] ; r = xrotation * yrotation * zrotation ; xy = xyz * r ; xy = xy (:,1:2) ; if (directed) ti = '3D directed graph' ; else ti = '3D undirected graph' ; end end %------------------------------------------------------------------------------- % draw the graph %------------------------------------------------------------------------------- [X,Y] = gplot (A, xy) ; if (n < 100) msize = 12 ; else msize = 6 ; end if (n < 200) if (directed) plot (X, Y, 'mo', 'MarkerEdgeColor', 'k', ... 'MarkerFaceColor', [.49 1 .63], 'MarkerSize', msize) ; hold on axis equal axis off for k = 0:(length(X) / 3)-1 [x1 y1] = dsxy2figxy (gca, X (3*k+1), Y (3*k+1)) ; [x2 y2] = dsxy2figxy (gca, X (3*k+2), Y (3*k+2)) ; annotation ('arrow', [x1 x2], [y1 y2], 'Color', [1 0 1], ... 'HeadWidth', 4, 'HeadLength', 8) ; end else plot (X, Y, '-mo', 'MarkerEdgeColor', 'k', ... 'MarkerFaceColor', [.49 1 .63], 'MarkerSize', msize) ; hold on axis equal axis off end if (~isempty (nodename) && n < 100) for k = 1:n text (xy (k,1), xy (k,2), [' ' nodename(k,:)], ... 'Interpreter', 'none') ; end end else plot (X, Y, '-m.', 'MarkerEdgeColor', 'k') ; axis equal axis off end title (ti) ; hold off SuiteSparse/UFcollection/README.txt0000644001170100242450000001627510711427467016057 0ustar davisfacUFcollection, Version 1.1.1, Nov 1, 2007. UFcollection is a MATLAB toolbox for managing the UF Sparse Matrix Collection. If you are a MATLAB user of the collection, you would not normally need to use this toolbox. It contains code for creating the index for the collection (the UF_Index.mat file in the UFget package), for creating the web pages for the collection, and creating the Matrix Market and Rutherford/Boeing versions of the matrices. This code is posted here primarily so that users of the collection can see how the matrices and their statistics were generated. This software (UFread, specifically) also allows the user to keep a single copy of the collection for use both inside MATLAB and outside MATLAB. The MM/ and RB/ versions of the collection can be read into MATLAB via UFread, even without explicitly extracting the tar files. They can also be read by non-MATLAB programs. Since the whole collection is about 8GB in size (compressed, as of Dec 2006), this can save some space. UFread is much slower than UFget, however. -------------------------------------------------------------------------------- MATLAB help for the UFcollection toolbox: -------------------------------------------------------------------------------- UFcollection: software for managing the UF Sparse Matrix Collection To create the index: UFindex - create the index for the UF Sparse Matrix Collection UFstats - compute matrix statistics for the UF Sparse Matrix Collection To create the web pages: UFallpages - create all web pages for the UF Sparse Matrix Collection UFgplot - draw a plot of the graph of a sparse matrix UFint - print an integer to a string, adding commas every 3 digits UFlist - create a web page index for the UF Sparse Matrix Collection UFlists - create the web pages for each matrix list (group, name, etc.) UFlocation - URL and top-level directory of the UF Sparse Matrix Collection UFpage - create web page for a matrix in UF Sparse Matrix Collection UFpages - create web page for each matrix in UF Sparse Matrix Collection dsxy2figxy - Transform point or position from axis to figure coords To create the Matrix Market and Rutherford/Boeing versions of the collection: UFexport - export to Matrix Market and Rutherford/Boeing formats UFread - read a Problem in Matrix Market or Rutherford/Boeing format UFwrite - write a Problem in Matrix Market or Rutherford/Boeing format UFfull_read - read a full matrix using a subset of Matrix Market format UFfull_write - write a full matrix using a subset of Matrix Market format Example: UFindex % create index (UF_Index.mat) for use by UFget UFallpages % create all web pages for the UF Sparse Matrix Collection Requires UFget, CSparse, CHOLMOD, AMD, COLAMD, RBio, and METIS. Copyright 2007, Timothy A. Davis -------------------------------------------------------------------------------- Files: -------------------------------------------------------------------------------- Contents.m MATLAB help dsxy2figxy.m convert XY points for plot annotations Makefile Unix/Linux installation, or use UFcollection_install README.txt this file UFallpages.m create all web pages UFexport.m export to MM and RB UFcollection_install.m installation UFfull_read.m read a full matrix UFfull_write.c write a full matrix UFfull_write.m MATLAB help for UFfull_write UFgplot.m plot a graph UFindex.m create UF_Index.mat UFint.m print an integer UFlist.m create a web page index UFlists.m create all web page indices UFlocation.m URL and directory for the collection UFpage.m create a web page for a matrix UFpages.m create web pages for all matrices UFread.m read a Problem UFstats.m compute statistics about a matrix UFwrite.m write a Problem ./Doc: gpl.txt GNU GPL license License.txt -------------------------------------------------------------------------------- To add a matrix to the collection: -------------------------------------------------------------------------------- These instructions are for the maintainer of the collection (that is, just notes to myself), but they also indicate how the above software is used. Requires most of SuiteSparse (UFget, CHOLMOD, AMD, COLAMD, CSparse, RBio, and UFcollection), and METIS 4.0.1. 1) Get the matrix into MATLAB (method depending on how the matrix was submitted). Use load and sparse2, RBread, mread, or specialized code written just for that matrix. 2) Add the matrix to the end of UF_Listing.txt (a line in the form Group/Name). 3) Create a new directory /cise/research/sparse/public_html/mat/Group, where Group is the new matrix group. Add a README.txt file to this directory, the first line of which is a one-line summary that will appear in the top-level web page for the collection. Skip this step if adding a matrix to an existing group. 4) Create the Problem struct; type "help UFwrite" for details. Required fields: Problem.name full name of the matrix (Group/Name) Problem.title short descriptive title Problem.A the sparse matrix Problem.id integer corresponding to the line number in UF_Listing.txt Problem.date date the matrix was created, or added to the collection Problem.author matrix author Problem.ed matrix editor/collector Problem.kind a string. For a description, see: http://www.cise.ufl.edu/research/sparse/matrices/kind.html optional fields: Problem.Zeros binary pattern of explicit zero entries Problem.b right-hand-side Problem.x solution Problem.notes a char array Problem.aux auxiliary matrices (contents are problem dependent) Save to a MATLAB mat-file. In the mat directory, do: save (Problem.name, 'Problem', '-v7') ; 5) Compute matrix statistics and extend the UF_Index: UFindex (ids) where ids is a list of the new matrix id's. If updating UF_Index.mat, a copy must exist in the current directory for UFindex to find it. (At UF, do so in the 2sparse/Matrix directory, and copy the current UF_Index.mat there first). Copy the new UF_Index.mat file into /cise/research/sparse/public_html/mat. 6) Update the web pages: In the /cise/research/sparse/public_html directory, do: UFlists UFpages (1, ids) 7) Export the matrix in Matrix Market and Rutherford/Boeing formats. UFexport (ids) or UFexport (ids, 'check') then tar and compress the resulting MM/Group/Name and RB/Group/Name directories, one per Problem (if UFexport has not already done so). Copy the MM and RB matrices from the 2sparse/MM and /RB directories into the sparse/public_html directory. 8) Make the collection world-readable. In /cise/research/sparse/public_html do: chmod -R og+rX mat matrices MM RB 9) Optional: if a new group was added, manually edit the /cise/research/sparse/public_html/matrices/index.html file, adding a new thumbnail image to the Sample Gallery. If a new Problem.kind was introduced, describe it in the matrices/kind.html file. SuiteSparse/UFcollection/UFpages.m0000644001170100242450000000142610620400345016042 0ustar davisfacfunction UFpages (figures, list) %UFPAGES create web page for each matrix in UF Sparse Matrix Collection % Usage: UFpages (figures, list) % % figures: 1 if figures are to be created, 0 otherwise % list: list of matrix id's to process. All matrices in the collection are % processed if not present. % % Example: % % UFpages % create all the pages % UFpages (0) % create all the pages, but not the figures % UFpages (1,1:10) % create pages for just matrices 1 to 10 % UFpages (0,1:10) % ditto, but do not create the figures % % See also UFpage, UFget. % Copyright 2006-2007, Timothy A. Davis if (nargin < 1) figures = 1 ; end index = UFget ; if (nargin < 2) list = 1:length (index.nrows) ; end for i = list UFpage (i, index, figures) ; end SuiteSparse/UFcollection/UFexport.m0000644001170100242450000000437210621142302016264 0ustar davisfacfunction UFexport (list, check, tmp) %UFEXPORT export to Matrix Market and Rutherford/Boeing formats % % Example: % UFexport ; % export the entire collection % UFexport (list) ; % just export matrices whose id's are given in the list % UFexport (list, 'check') ; % also read them back in, to check % % If the list is empty, all matrices in the collection are exported. % A 3rd argument tmp changes the tmp directory for UFread. % % See also UFget, UFwrite, RBio, mwrite. % Copyright 2006-2007, Timothy A. Davis %------------------------------------------------------------------------------- % get the input arguments %------------------------------------------------------------------------------- index = UFget ; nmat = length (index.nrows) ; if (nargin < 1 || isempty (list)) list = 1:nmat ; end check = ((nargin > 1) && strcmp (check, 'check')) ; if (nargin < 3) tmp = '' ; end %------------------------------------------------------------------------------- % determine the top-level directory to use %------------------------------------------------------------------------------- [url topdir] = UFlocation ; %------------------------------------------------------------------------------- % export the matrices %------------------------------------------------------------------------------- for id = list % get the MATLAB version Problem = UFget (id, index) ; disp (Problem) ; % create the MM and RB versions UFwrite (Problem, [topdir 'MM'], 'MM', 'tar') ; UFwrite (Problem, [topdir 'RB'], 'RB', 'tar') ; % check the new MM and RB versions if (check) for format = { 'MM' , 'RB' } try if (isempty (tmp)) P2 = UFread ([topdir format{1} filesep Problem.name]) ; else P2 = UFread ([topdir format{1} filesep Problem.name], tmp) ; end catch % The Problem may be too large for two copies to be in the % MATLAB workspace at the same time. This is not an error, % but it means that the Problem cannot be checked. P2 = [ ] ; fprintf ('Unable to read %s/%s\n', format {1}, Problem.name) ; fprintf ('%s\n', lasterr) ; end if (~isempty (P2) && ~isequal (Problem, P2)) error ('%s version mismatch: %s\n', format {1}, Problem.name) ; end clear P2 end end end SuiteSparse/UFcollection/UFindex.m0000644001170100242450000003242110623341712016056 0ustar davisfacfunction UF_Index = UFindex (matrixlist) %UFINDEX create the index for the UF Sparse Matrix Collection % % UF_Index = UFindex (matrixlist) % % matrixlist: an integer list, in the range of 1 to the length of the % UF_Listing.txt file, containing a list of matrices for which to modify % the UF_Index entries. If matrixlist is not present, then the UF_Index % is created from scratch. % % UF_Index: a struct containing the index information, with the % following fields, assuming that there are n matrices in the collection: % % LastRevisionDate: a string with the date and time the index was updated. % DowloadTimeStamp: date and time the index was last downloaded. % % Group: an n-by-1 cell array. Group {i} is the group for matrix i. % Name: n-by-1 cell array. Name {i} is the name of matrix i. % % The following fields are n-by-1 vectors unless otherwise specified. % nrows(id) gives the number of rows of the matrix with id = Problem.id, % for example. % % nrows number of rows % ncols number of columns % nnz number of entries in A % RBtype Rutherford/Boeing type, an n-by-3 char array % isBinary 1 if binary, 0 otherwise % isReal 1 if real, 0 if complex % cholcand 1 if a candidate for sparse Cholesky, 0 otherwise % numerical_symmetry numeric symmetry (0 to 1, where 1=symmetric) % pattern_symmetry pattern symmetry (0 to 1, where 1=symmetric) % nnzdiag nnz (diag (A)) if A is square, 0 otherwise % nzero nnz (Problem.Zeros) % amd_lnz nnz(L) for chol(C(p,p)) where, C=A+A', p=amd(C) % amd_flops flop count for chol(C(p,p)) where, C=A+A', p=amd(C) % amd_vnz nnz in Householder vectors for qr(A(:,colamd(A))) % amd_rnz nnz in R for qr(A(:,colamd(A))) % metis_lnz nnz(L) for chol(C(p,p)) where, C=A+A', p=metis(C) % metis_flops flop count for chol(C(p,p)) where, C=A+A', p=metis(C) % metis_vnz nnz in Householder vectors for qr(A(:,metis(A,'col'))) % metis_rnz nnz in R for qr(A(:,metis(A,'col'))) % nblocks # of blocks from dmperm % sprank sprank(A) % nzoff # of entries not in diagonal blocks from dmperm % ncc # of strongly connected components % dmperm_lnz nnz(L), using dmperm plus amd or metis % dmperm_unz nnz(U), using dmperm plus amd or metis % dmperm_flops flop count with dperm plus % dmperm_vnz nnz in Householder vectors for dmperm plus % dmperm_rnz nnz in R for dmperm plus % posdef 1 if positive definite, 0 otherwise % isND 1 if a 2D/3D problem, 0 otherwise % % If the statistic is not computed, it is set to -2. Some statistics are not % computed for rectangular or structurally singular matrices, for example. % If an attempt to compute the statistic was made, but failed, it is set to -1. % % Example: % UFindex % UFindex (267:300) % % See also UFstats, amd, metis, RBtype, cs_scc, cs_sqr, cs_dmperm. % Copyright 2006-2007, Timothy A. Davis % Requires the SuiteSparse set of packages: CHOLMOD, AMD, COLAMD, RBio, CSparse; % and METIS. % 10/13/2001: Created by Erich Mirabal % 12/6/2001, 1/17/2003, 11/16/2006: modified by Tim Davis %------------------------------------------------------------------------------- % initialize an empty index %------------------------------------------------------------------------------- % load the filenames [url topdir] = UFlocation ; files = textread ([topdir 'mat' filesep 'UF_Listing.txt'], '%s') ; % if no input, assume we have to do the whole file list create_new = 0 ; if (nargin < 1) matrixlist = 1:length(files) ; create_new = 1 ; else % validate the input : range is limited by the files variable if (min (matrixlist) < 1) || (max (matrixlist) > length (files)) error ('%s: %s', mfilename, 'Invalid input parameter.') ; end end if (~create_new) % load the index from file fprintf ('Loading existing UF_Index.mat file\n') ; UF_Index = load ('UF_Index.mat') ; UF_Index = UF_Index.UF_Index ; end % revision tracking device UF_Index.LastRevisionDate = datestr (now) ; % the index structure needs a download date for version tracking UF_Index.DownloadTimeStamp = now ; % start the index from scratch if (create_new) fprintf ('Creating new UF_Index.mat file\n') ; nothing = -ones (1, length (files)) ; UF_Index.Group = cell (size (files)) ; UF_Index.Name = cell (size (files)) ; UF_Index.nrows = nothing ; UF_Index.ncols = nothing ; UF_Index.nnz = nothing ; UF_Index.nzero = nothing ; UF_Index.pattern_symmetry = nothing ; UF_Index.numerical_symmetry = nothing ; UF_Index.isBinary = nothing ; UF_Index.isReal = nothing ; % removed has_b, has_guess, has_x, has_Zeros, is_lp, has_coord, zdiag UF_Index.nnzdiag = nothing ; UF_Index.posdef = nothing ; UF_Index.amd_lnz = nothing ; UF_Index.amd_flops = nothing ; UF_Index.amd_vnz = nothing ; UF_Index.amd_rnz = nothing ; UF_Index.metis_lnz = nothing ; UF_Index.metis_flops = nothing ; UF_Index.metis_vnz = nothing ; UF_Index.metis_rnz = nothing ; UF_Index.nblocks = nothing ; UF_Index.sprank = nothing ; UF_Index.nzoff = nothing ; UF_Index.dmperm_lnz = nothing ; UF_Index.dmperm_unz = nothing ; UF_Index.dmperm_flops = nothing ; UF_Index.dmperm_vnz = nothing ; UF_Index.dmperm_rnz = nothing ; % added RBtype, cholcand, ncc UF_Index.RBtype = char (' '*ones (length (files),3)) ; UF_Index.cholcand = nothing ; UF_Index.ncc = nothing ; % added isND UF_Index.isND = nothing ; else % make sure we have the right length for the arrays if length (UF_Index.nrows) < max (matrixlist) len = max (matrixlist) - length (UF_Index.nrows) ; nothing = -ones (1, len) ; if (len > 0) % don't worry about the cell arrays, only append to numeric arrays UF_Index.nrows = [UF_Index.nrows nothing] ; UF_Index.ncols = [UF_Index.ncols nothing] ; UF_Index.nnz = [UF_Index.nnz nothing] ; UF_Index.nzero = [UF_Index.nzero nothing] ; UF_Index.pattern_symmetry = [UF_Index.pattern_symmetry nothing] ; UF_Index.numerical_symmetry = [UF_Index.numerical_symmetry nothing]; UF_Index.isBinary = [UF_Index.isBinary nothing] ; UF_Index.isReal = [UF_Index.isReal nothing] ; UF_Index.nnzdiag = [UF_Index.nnzdiag nothing] ; UF_Index.posdef = [UF_Index.posdef nothing] ; UF_Index.amd_lnz = [UF_Index.amd_lnz nothing] ; UF_Index.amd_flops = [UF_Index.amd_flops nothing] ; UF_Index.amd_vnz = [UF_Index.amd_vnz nothing] ; UF_Index.amd_rnz = [UF_Index.amd_rnz nothing] ; UF_Index.metis_lnz = [UF_Index.metis_lnz nothing] ; UF_Index.metis_flops= [UF_Index.metis_flops nothing] ; UF_Index.metis_vnz = [UF_Index.metis_vnz nothing] ; UF_Index.metis_rnz = [UF_Index.metis_rnz nothing] ; UF_Index.nblocks = [UF_Index.nblocks nothing] ; UF_Index.sprank = [UF_Index.sprank nothing] ; UF_Index.nzoff = [UF_Index.nzoff nothing] ; UF_Index.dmperm_lnz = [UF_Index.dmperm_lnz nothing] ; UF_Index.dmperm_unz = [UF_Index.dmperm_unz nothing] ; UF_Index.dmperm_flops= [UF_Index.dmperm_flops nothing] ; UF_Index.dmperm_vnz = [UF_Index.dmperm_vnz nothing] ; UF_Index.dmperm_rnz = [UF_Index.dmperm_rnz nothing] ; UF_Index.RBtype = [UF_Index.RBtype ; char (' '*ones (len,3))] ; UF_Index.cholcand = [UF_Index.cholcand nothing] ; UF_Index.ncc = [UF_Index.ncc nothing] ; UF_Index.isND = [UF_Index.isND nothing] ; end end end fprintf ('Will process %d files\n', length (matrixlist)) ; nmat = length (UF_Index.nrows) ; filesize = zeros (nmat,1) ; %------------------------------------------------------------------------------- % look through the directory listing, and sort matrixlist by size %------------------------------------------------------------------------------- for i = matrixlist % note that the matrix is not loaded in this for loop ffile = deblank (files {i}) ; % group is the first part of the string up to the character before % the last file separator gi = find (ffile == filesep) ; gi = gi (end) ; groupN = char (ffile (1:gi-1)) ; % name is the last section of the string after the last file separator matrixN = char (ffile (gi+1:end)) ; % get the directory info of the .mat file fileInfo = dir ([topdir 'mat' filesep ffile '.mat']) ; % set the file's data into the data arrays UF_Index.Name {i} = matrixN ; UF_Index.Group {i} = groupN ; if (length (fileInfo) > 0) %#ok filesize (i) = fileInfo.bytes ; else filesize (i) = 9999999999 ; end % fprintf ('%s / %s filesize %d\n', groupN, matrixN, fileInfo.bytes) ; end fprintf ('\n======================================================\n') ; fprintf ('Matrices will processed in the following order:\n') ; for i = matrixlist ffile = deblank (files {i}) ; fprintf ('Matrix %d: %s filesize %d\n', i, ffile, filesize (i)) ; if (filesize (i) == 9999999999) fprintf ('skip this file\n') ; continue ; end end %------------------------------------------------------------------------------- % load the matrices %------------------------------------------------------------------------------- % metis (A,'col') fails with a seg fault for these matrices: skip_metis = [850 858 1257 1258] ; % these matrices are known to be positive definite, and indefinite, % respectively, but sparse Cholesky fails (on a 4GB Penitum 4) on some of them: known_posdef = [ 939 1252 1267 1268 1423 1453 1455 ] ; known_indef = [ 1348:1368 1586 1411 ] ; % these matrices are known to be irreducible, but dmperm fails known_irreducible = 916 ; for k = 1:length (matrixlist) %--------------------------------------------------------------------------- % get the matrix %--------------------------------------------------------------------------- id = matrixlist (k) ; ffile = deblank (files {id}) ; fprintf ('\n============================== Matrix %d: %s\n', id, ffile) ; if (filesize (id) == 9999999999) fprintf ('skip this file\n') ; continue ; end load ([topdir 'mat' filesep ffile]) ; % display the Problem struct disp (Problem) ; %--------------------------------------------------------------------------- % get all stats %--------------------------------------------------------------------------- nometis = any (id == skip_metis) ; if (nometis) fprintf ('skip metis - will fail\n') ; end fprintf ('%s/%s\n', UF_Index.Group {id}, UF_Index.Name {id}) ; if (isfield (Problem, 'Zeros')) stats = UFstats (Problem.A, Problem.kind, nometis, Problem.Zeros) ; else stats = UFstats (Problem.A, Problem.kind, nometis) ; end %--------------------------------------------------------------------------- % fix special cases %--------------------------------------------------------------------------- if (stats.posdef == -1) if (any (id == known_posdef)) fprintf ('known posdef\n') ; stats.posdef = 1 ; elseif (any (id == known_indef)) fprintf ('known indef\n') ; stats.posdef = 0 ; end end if (any (id == known_irreducible) && stats.sprank < 0) % full sprank, and not reducible to block triangular form, % but the matrix is to big for dmperm fprintf ('known irreducible\n') ; stats.sprank = stats.nrows ; stats.nzoff = 0 ; stats.nblocks = 1 ; stats.ncc = 1 ; end % display the stats disp (stats) ; %--------------------------------------------------------------------------- % save the stats in the index %--------------------------------------------------------------------------- UF_Index.nrows (id) = stats.nrows ; UF_Index.ncols (id) = stats.ncols ; UF_Index.nnz (id) = stats.nnz ; UF_Index.nzero (id) = stats.nzero ; UF_Index.pattern_symmetry (id) = stats.psym ; UF_Index.numerical_symmetry (id) = stats.nsym ; UF_Index.isBinary (id) = stats.isBinary ; UF_Index.isReal (id) = stats.isReal ; UF_Index.nnzdiag (id) = stats.nnzdiag ; UF_Index.posdef (id) = stats.posdef ; UF_Index.amd_lnz (id) = stats.amd_lnz ; UF_Index.amd_flops (id) = stats.amd_flops ; UF_Index.amd_vnz (id) = stats.amd_vnz ; UF_Index.amd_rnz (id) = stats.amd_rnz ; UF_Index.metis_lnz (id) = stats.metis_lnz ; UF_Index.metis_flops (id) = stats.metis_flops ; UF_Index.metis_vnz (id) = stats.metis_vnz ; UF_Index.metis_rnz (id) = stats.metis_rnz ; UF_Index.nblocks (id) = stats.nblocks ; UF_Index.sprank (id) = stats.sprank ; UF_Index.nzoff (id) = stats.nzoff ; UF_Index.dmperm_lnz (id) = stats.dmperm_lnz ; UF_Index.dmperm_unz (id) = stats.dmperm_unz ; UF_Index.dmperm_flops (id) = stats.dmperm_flops ; UF_Index.dmperm_vnz (id) = stats.dmperm_vnz ; UF_Index.dmperm_rnz (id) = stats.dmperm_rnz ; UF_Index.RBtype (id,:) = stats.RBtype ; UF_Index.cholcand (id) = stats.cholcand ; UF_Index.ncc (id) = stats.ncc ; UF_Index.isND (id) = stats.isND ; %--------------------------------------------------------------------------- % clear the problem and save the index %--------------------------------------------------------------------------- clear Problem save UF_Index UF_Index % flush the diary if (strcmp (get (0, 'Diary'), 'on')) diary off diary on end end SuiteSparse/UFcollection/UFfull_read.m0000644001170100242450000000410210620400372016672 0ustar davisfacfunction A = UFfull_read (file) %UFFULL_READ read a full matrix using a subset of Matrix Market format % This function reads in a file generated by UFfull_write. It cannot read % arbitrary Matrix Market formatted files. See UFfull_write for a description % of the file format. % % Example: % x = rand (8) % UFfull_write ('xfile', x) % y = UFfull_read ('xfile') % norm (x-y) % % See also mread, mwrite, RBwrite, RBread. % Copyright 2006-2007, Timothy A. Davis % open the file f = fopen (file, 'r') ; if (f < 0) error (['cannot open: ' file]) ; end % ignore the header line - determine real/complex from # of entries in each row s = fgetl (f) ; %#ok % read in the # of rows and columns [siz count] = fscanf (f, '%d %d', 2) ; if (count ~= 2) error (['invalid file: ' file]) ; end m = siz (1) ; n = siz (2) ; % read in the rest of the matrix A = fscanf (f, '%g') ; % This is an unfortunate workaround. fscanf in C and MATLAB, and the read % statement in Fortran, cannot interpret the character strings 'Inf', '-Inf', % or 'NaN' as the appropriate value. Thus, a special huge value (1e308) is % used to represent these values (Inf and NaN both become 1e308). A sparse % matrix typically won't included any Inf's or NaN's, but auxiliary arrays can, % for some problems. For example, the bounds of an LP can be +Inf or -Inf; % lo(i) = -Inf means that there is no lower bound on the ith variable. % % The identical workaround is used in UFfull_write, mread, mwrite, RBread, and % RBwrite. 1e308 was chosen because it's close to the largest IEEE double % precision number of 1.7977e308, and because the string '1e308' is short, % leading to more compact files. Note that NaN's are treated as +Inf. A (A == 1e308) = Inf ; A (A == -1e308) = -Inf ; % reshape the matrix into its final form if (length (A) == m*n) % this is a real matrix A = reshape (A, m, n) ; elseif (length (A) == 2*m*n) % this is a complex matrix A = reshape (A (1:2:end), m, n) + reshape (A (2:2:end), m, n) * 1i ; else error (['invalid file: ' file]) ; end % close the file fclose (f) ; SuiteSparse/UFcollection/UFwrite.m0000644001170100242450000004253510620400365016105 0ustar davisfacfunction UFwrite (Problem, Master, arg3, arg4) %UFWRITE write a Problem in Matrix Market or Rutherford/Boeing format % containing a set of text files in either Matrix Market or Rutherford/Boeing % format. The Problem can be read from the files back into MATLAB via UFread. % See http://www.cise.ufl.edu/research/sparse/matrices for the UF Sparse % Matrix Collection home page. The Problem directory is optionally compressed % via tar and gzip. Arguments 3 and 4, below, are optional and can appear in % any order. % % UFwrite (Problem) % Matrix Market format, no tar, use current dir. % % The following usages write the Problem into the Master/Group/Name directory, % where Problem.name = 'Group/Name' is given in the Problem. % % UFwrite (Problem, Master) % Matrix Market, no tar % UFwrite (Problem, Master, 'MM') % ditto % UFwrite (Problem, Master, 'RB') % Rutherford/Boeing, no tar % UFwrite (Problem, Master, 'tar') % Matrix Market, with tar % UFwrite (Problem, Master, 'MM', 'tar') % ditto % UFwrite (Problem, Master, 'RB', 'tar') % Rutherford/Boeing, with tar % % Problem is a struct, in the UF Sparse Matrix format (see below). Master is % the top-level directory in which directory containing the problem will be % placed. Master defaults to the current working directory if not present (an % empty string also means the current directory will be used). % % The following fields are always present in a UF Sparse Matrix Problem: % % name the group directory and problem name (i.e. 'HB/arc130') % % title short descriptive title % % A an m-by-n sparse matrix, real or complex % % id an integer in the range of 1 to the # of problems in the % collection. Identical to the line number of % http://www.cise.ufl.edu/research/sparse/mat/UF_Listing.txt % containing the Problem.name. New matrices are always added at % the end of this list. % % date a string containing the date the matrix was created, or added % to the collection if the creating date is unknown (but is likely % close to the creation date); empty string otherwise. % % author a string containing the name of the author; the computational % scientist who created the matrix from his or her application. % Empty string, or "author unknown" if unknown. % % ed a string containing the name of the editor/collector; the person % who acquired the matrix from the author, for inclusion in this % (or other) sparse matrix / graph collections. % % kind a string (i.e. 'directed graph') describing the type of problem; % a list of words from a well-defined set (see the UF Sparse % Matrix Collection home page for a description, or % http://www.cise.ufl.edu/research/sparse/matrices/kind.html). % % A Problem struct may also have the following optional fields. % % Zeros pattern of explicit zero entries in A as a binary m-by-n matrix. % These entries are provided by the matrix submittor with zero % numerical value. MATLAB drops explicit zero entries from any % sparse matrix. These entries can be important to the problem, % if (for example) the matrix is first in a series of matrices % arising in a nonlinear solver (those entries will become nonzero % later). These entries are thus kept in the binary matrix Zeros. % % b right-hand-side, any size, real or complex, full or sparse % % x supposed solution to A*x=b, any size, real or complex, full or % sparse % % notes a character array with notes about the problem. % % aux a struct, containing auxiliary information. The contents of % this struct are problem dependent, but its fields must not % end with '_[0-9]*' where [0-9]* means zero or more digits, nor % can there be an aux.b or aux.x matrix (there can be aux.b % and aux.x cells). The aux struct must not include any structs, % just matrices and cell arrays of matrices. The matrices in aux % can be full or sparse, and real, complex, or char. % % ------------------------------------------------- % for Problems written in Rutherford/Boeing format: % ------------------------------------------------- % % The Problem.name (including the full 'Group/Name'), date, author, and editor % define the Rutherford/Boeing title (first line of the file), followed by a % '|' in the 72nd column, and then up to 8 characters of the key. If the key % is an empty string, the Problem.id is used as the key. The A and Zeros % matrices are merged and written to this file. The full name, title, id, % kind, date, author, editor, and notes are written to a file of the same name % as the primary file, but with a .txt extension. % % Additional Rutherford/Boeing files are created for b, x, and each sparse % matrix in aux. Full arrays are written using a tiny subset of the Matrix % Market format. The first line of the file is the header, either of: % % %%MatrixMarket array real general % %%MatrixMarket array complex general % % The 2nd row contains the # of rows and columns, and subsequent lines contain % one matrix entry each (two values if complex) listed in column-major order. % No comments or blank lines are permitted. The header is ignored when the % matrix is read back in by UFread; the real/complex case is determined by how % many entries appear on each line. You can of course read these files with % mread, the Matrix Market reader. The header is added only to make it easier % for functions *other* than UFread to read and understand the data (the file % can be read in by mread, for example, but mread is not required). Thus, a % complete Rutherord/Boeing directory can be read/written via UFread/UFwrite, % without requiring the installation of mread/mwrite (in CHOLMOD), or % mmread/mmread (M-file functions from NIST that read/write a Matrix Market % file). % % --------------------------------------------- % for Problems written in Matrix Market format: % --------------------------------------------- % % The name, title, A, id, Zeros, kind, date, author, editor, and notes fields of % the Problem are written to the primary Matrix Market file, with a .mtx % extension. Additional Matrix Market files are created for b (as name_b), % x (as name_x), and each sparse or full matrix in aux. % % ----------------- % for both formats: % ----------------- % % A matrix Problem.aux.whatever is written out as name_whatever.xxx, without % the 'aux' part. If Problem.aux.whatever is a char array, it is written as % the file name_whatever.txt, with one line per row of the char array (trailing % spaces in each line are not printed). If aux.whatever is a cell array, each % entry aux.whatever{i} is written as the file name_whatever_.xxx % (name_whatever_1.mtx, name_whatever_2.mtx, etc). All files are placed in the % single directory, given by the Problem.name (Group/Name, or 'HB/arc130' for % example). Each directory can only hold one MATLAB Problem struct of the UF % Sparse Matrix Collection. % % Example: % % Problem = UFget ('HB/arc130') % get the HB/arc130 MATLAB Problem % UFwrite (Problem) ; % write a MM version in current directory % UFwrite (Problem, 'MM') ; % write a MM version in MM/HB/arc130 % UFwrite (Problem, '', 'RB') ; % write a RB version in current directory % % See also mwrite, mread, RBwrite, RBread, UFread, UFget, tar % Optionally uses the CHOLMOD mwrite mexFunction, for writing Problems in % Matrix Market format. % Copyright 2006-2007, Timothy A. Davis, University of Florida. %------------------------------------------------------------------------------- % check inputs %------------------------------------------------------------------------------- if (nargin < 2) % place the result in the current directory Master = '' ; end if (nargin < 3) arg3 = '' ; end if (nargin < 4) arg4 = '' ; end arg3 = lower (arg3) ; arg4 = lower (arg4) ; do_tar = (strcmp (arg3, 'tar') | strcmp (arg4, 'tar')) ; RB = (strcmp (arg3, 'rb') | strcmp (arg4, 'rb')) ; Master = regexprep (Master, '[\/\\]', filesep) ; if (~isempty (Master) && Master (end) ~= filesep) Master = [Master filesep] ; end %------------------------------------------------------------------------------- % create the problem directory. Do not report any errors %------------------------------------------------------------------------------- t = find (Problem.name == '/') ; group = Problem.name (1:t-1) ; name = Problem.name (t+1:end) ; groupdir = [Master group] ; probdir = [groupdir filesep name] ; probname = [probdir filesep name] ; s = warning ('query', 'MATLAB:MKDIR:DirectoryExists') ; % get current state warning ('off', 'MATLAB:MKDIR:DirectoryExists') ; mkdir (groupdir) ; mkdir (probdir) ; warning (s) ; % restore state %------------------------------------------------------------------------------- % write the name, title, id, kind, date, author, ed, list of fields, and notes %------------------------------------------------------------------------------- cfile = [probname '.txt'] ; if (RB) prefix = '%' ; else prefix = '' ; end cf = fopen (cfile, 'w') ; print_header (cf, prefix, Problem.name) ; fprintf (cf, '%s [%s]\n', prefix, Problem.title) ; fprintf (cf, '%s id: %d\n', prefix, Problem.id) ; fprintf (cf, '%s date: %s\n', prefix, Problem.date) ; fprintf (cf, '%s author: %s\n', prefix, Problem.author) ; fprintf (cf, '%s ed: %s\n', prefix, Problem.ed) ; fprintf (cf, '%s fields:', prefix) ; s = fields (Problem) ; for k = 1:length(s) fprintf (cf, ' %s', s {k}) ; end fprintf (cf, '\n') ; if (isfield (Problem, 'aux')) aux = Problem.aux ; fprintf (cf, '%s aux:', prefix) ; auxfields = fields (aux) ; for k = 1:length(auxfields) fprintf (cf, ' %s', auxfields {k}) ; end fprintf (cf, '\n') ; else auxfields = { } ; end fprintf (cf, '%s kind: %s\n', prefix, Problem.kind) ; print_separator (cf, prefix) ; if (isfield (Problem, 'notes')) fprintf (cf, '%s notes:\n', prefix) ; for k = 1:size (Problem.notes,1) fprintf (cf, '%s %s\n', prefix, Problem.notes (k,:)) ; end print_separator (cf, prefix) ; end fclose(cf) ; %------------------------------------------------------------------------------- % write out the A and Z matrices to the RB or MM primary file %------------------------------------------------------------------------------- A = Problem.A ; [m n] = size (A) ; if (~issparse (A) || m == 0 || n == 0) error ('A must be sparse and non-empty') ; end if (isfield (Problem, 'Zeros')) Z = Problem.Zeros ; if (any (size (A) ~= size (Z)) || ~isreal (Z) || ~issparse (Z)) error ('Zeros must have same size as A, and be sparse and real') ; end else Z = [ ] ; end % use the Problem.id number as the RB key key = sprintf ('%d', Problem.id) ; if (RB) % write the files in Rutherford/Boeing form ptitle = [Problem.name '; ' Problem.date '; ' etal(Problem.author)] ; ptitle = [ptitle '; ed: ' etal(Problem.ed)] ; % note that b, g, and x are NOT written to the RB file RBwrite ([probname '.rb'], A, Z, ptitle, key) ; else % write the files in Matrix Market form mwrite ([probname '.mtx'], A, Z, cfile) ; delete (cfile) ; % the comments file has been included in the .mtx file. end %------------------------------------------------------------------------------- % write out the b and x matrices as separate files %------------------------------------------------------------------------------- if (isfield (Problem, 'b')) write_component (probname, Problem.name, 'b', Problem.b, cfile, ... prefix, RB, [key 'b']) ; end if (isfield (Problem, 'x')) write_component (probname, Problem.name, 'x', Problem.x, cfile, ... prefix, RB, [key 'x']) ; end %------------------------------------------------------------------------------- % write out each component of aux, each in a separate file %------------------------------------------------------------------------------- for k = 1:length(auxfields) what = auxfields {k} ; X = aux.(what) ; if (~iscell (X) && (strcmp (what, 'b') || strcmp (what, 'x'))) % aux.b or aux.x would get written out with the same filename as the % Problem.b and Problem.x matrices, and read back in by UFread as % Problem.b and Problem.x instead of aux.b and aux.x. error (['invalid aux component: ' what]) ; end if (regexp (what, '_[0-9]*\>')) % aux.whatever_42 would be written as the file name_whatever_42, which % would be intrepretted as aux.whatever{42} when read back in by UFread. error (['invalid aux component: ' what]) ; end if (iscell (X)) len = length (X) ; for i = 1:len % this problem includes a sequence of matrices in the new % format (kind = 'sequence', and Problem.id > 1377). write_component (probname, Problem.name, ... sprintf (fmt (i, len), what, i) , X{i}, cfile, ... prefix, RB, [key what(1) sprintf('%d', i)]) ; end else % This is a non-cell component of aux. For an LP problem, this might % be c, lo, or hi. For an Oberwolfach model reduction problem, this % might be M, C, or E. For a graph in the Pajek collection, it could % be a vector 'year', with the publication of each article in the graph. % The possibilities are endless, and problem dependent. Adding new % components to aux can be done without modifying UFread or UFwrite. write_component (probname, Problem.name, what, X, cfile, ... prefix, RB, [key what]) ; end end %------------------------------------------------------------------------------- % tar up the result, if requested %------------------------------------------------------------------------------- if (do_tar) try tar ([probdir '.tar.gz'], probdir) ; rmdir (probdir, 's') ; catch warning ('SuiteSparse:UFwrite', ... 'unable to create tar file; directly left uncompressed') ; end end %------------------------------------------------------------------------------- % fmt %------------------------------------------------------------------------------- function s = fmt (i, len) % fmt: determine the format to use for the name of component in a aux.cell array if (len < 10) s = '%s_%d' ; % x1 through x9 elseif (len < 100) if (i < 10) s = '%s_0%d' ; % x01 through x09 else s = '%s_%d' ; % x10 through x99 end else if (i < 10) s = '%s_00%d' ; % x001 through x009 elseif (i < 100) s = '%s_0%d' ; % x010 through x099 else s = '%s_%d' ; % x100 through x999 end end %------------------------------------------------------------------------------- % write_component %------------------------------------------------------------------------------- function write_component (probname, name, what, X, cfile, prefix, RB, key) % write_component: write out a single component of the Problem to a file if (isempty (X)) % empty matrices (one or more zero dimensions) are not supported error (['invalid component: ' what ' (cannot be empty)']) ; elseif (ischar (X)) % Write out a char array as a text file. Remove trailing spaces from the % strings. Keep the leading spaces; they might be significant. ff = fopen ([probname '_' what '.txt'], 'w') ; for i = 1:size (X,1) fprintf (ff, '%s\n', deblank (X (i,:))) ; end fclose (ff) ; elseif (RB) % write out a full or sparse matrix in Rutherford/Boeing format if (issparse (X)) % write out the component as a Rutherford/Boeing sparse matrix RBwrite ([probname '_' what '.rb'], X, [ ], [name '_' what], key) ; else % Write out a full matrix in column oriented form, % using a tiny subset of the Matrix Market format for full matrices. UFfull_write ([probname '_' what '.mtx'], X) ; end else % write out the component in Matrix Market format (full or sparse) cf = fopen (cfile, 'w') ; print_header (cf, prefix, name, what) ; print_separator (cf, prefix) ; fclose(cf) ; mwrite ([probname '_' what '.mtx'], X, cfile) ; delete (cfile) ; end %------------------------------------------------------------------------------- % print_separator %------------------------------------------------------------------------------- function print_separator (cf, prefix) % print_separator: print a separator line in the comment file fprintf (cf, '%s---------------------------------------', prefix) ; fprintf (cf, '----------------------------------------\n') ; %------------------------------------------------------------------------------- % print_header %------------------------------------------------------------------------------- function print_header (cf, prefix, name, what) % print_header: print the header to the comment file print_separator (cf, prefix) ; fprintf (cf, '%s UF Sparse Matrix Collection, Tim Davis\n', prefix) ; fprintf (cf, '%s http://www.cise.ufl.edu/research/sparse/matrices/%s\n', ... prefix, name) ; fprintf (cf, '%s name: %s', prefix, name) ; if (nargin > 3) fprintf (cf, ' : %s matrix', what) ; end fprintf (cf, '\n') ; %------------------------------------------------------------------------------- % etal %------------------------------------------------------------------------------- function s = etal(name) % etal: change a long list of authors to first author 'et al.' t = find (name == ',') ; if (length (t) > 1) s = [name(1:t(1)-1) ' et al.'] ; else s = name ; end